Finite Group Databasebeta

← #17241388

Subgroups — #17241388

Order 4352.

2644 conjugacy classes of subgroups.

The subgroup lattice has 1818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763394C211yesmaximal, characteristic, complemented
2C2×#11763315C211yesmaximal, characteristic, complemented
3#14537074C211yesmaximal, characteristic, complemented
4#14537064C211yesmaximal, characteristic, complemented
5#14535452C211yesmaximal, characteristic, complemented
6#14535405C211yesmaximal, characteristic, complemented
7#14535388C211yesmaximal, characteristic, complemented
8#14535369C211yesmaximal, characteristic, complemented
9#14535211C211yesmaximal, characteristic, complemented
10#14535152C211yesmaximal, characteristic, complemented
11#14535138C211yesmaximal, characteristic, complemented
12#14535133C211yesmaximal, characteristic, complemented
13#14535109C211yesmaximal, characteristic, complemented
14#14535109C211yesmaximal, characteristic, complemented
15#14535109C211yesmaximal, characteristic, complemented
16#14535037C211yesmaximal, characteristic, complemented
17#14535006C211yesmaximal, characteristic, complemented
18#14535001C211yesmaximal, characteristic, complemented
19#14534998C211yesmaximal, characteristic, complemented
20#14534670C211yesmaximal, characteristic, complemented
21#14534624C211yesmaximal, characteristic, complemented
22#14534468C211yesmaximal, characteristic, complemented
23#14534407C211yesmaximal, characteristic, complemented
24#14534374C211yesmaximal, characteristic, complemented
25#14534367C211yesmaximal, characteristic, complemented
26#14533750C211yesmaximal, characteristic, complemented
27#14533671C211yesmaximal, characteristic, complemented
28#14532124C211yesmaximal, characteristic, complemented
29#14532100C211yesmaximal, characteristic, complemented
30#14531421C211yesmaximal, characteristic, complemented
31C17×#2679C211yesmaximal, characteristic, complemented
32C22×#63254C2211yescharacteristic
33C24×Dic17C2211yescharacteristic, complemented
34#11763394—28no—
35C2×#10587626C2211yescharacteristic
36C2×#10587565C2211yescharacteristic, complemented
37C2×#10587565C2211yescharacteristic, complemented
38C2×#10587622C2211yescharacteristic
39C2×#10587571C2211yescharacteristic, complemented
40C2×#10587571C2211yescharacteristic, complemented
41#11763315—28no—
42C2×#10587572C2211yescharacteristic, complemented
43C2×#10587569C2211yescharacteristic, complemented
44C2×#10587621C2211yescharacteristic
45C2×#10587621C2211yescharacteristic
46C2×#10587621C2211yescharacteristic
47C2×#10587621C2211yescharacteristic
48C2×#10587582C2211yescharacteristic, complemented
49C2×#10587564C2211yescharacteristic, complemented
50C2×#10587564C2211yescharacteristic, complemented
51C2×#10587564C2211yescharacteristic, complemented
52C2×#10587570C2211yescharacteristic, complemented
53C2×#10587625C2211yescharacteristic
54C2×#10587625C2211yescharacteristic
55C2×#10587625C2211yescharacteristic
56C2×#10587625C2211yescharacteristic
57C2×#10587625C2211yescharacteristic
58C2×#10587625C2211yescharacteristic
59C2×#10587624C2211yescharacteristic
60C2×#10587639C2211yescharacteristic, complemented
61C2×#10587639C2211yescharacteristic, complemented
62C2×#10587639C2211yescharacteristic, complemented
63C2×#10587639C2211yescharacteristic, complemented
64C2×D4×Dic17C2211yescharacteristic
65C2×D4×Dic17C2211yescharacteristic
66C2×#10587567C2211yescharacteristic, complemented
67C2×#10587567C2211yescharacteristic, complemented
68C2×#10587567C2211yescharacteristic, complemented
69C2×#10587563C2211yescharacteristic, complemented
70C22×C22⋊Dic17C2211yescharacteristic, complemented
71#11762750C2211yescharacteristic, complemented
72#11762744C2211yescharacteristic, complemented
73#11762742C2211yescharacteristic, complemented
74#11762740C2211yescharacteristic, complemented
75#11762739C2211yescharacteristic, complemented
76#11762737C2211yescharacteristic, complemented
77#11762737C2211yescharacteristic, complemented
78#11762737C2211yescharacteristic, complemented
79#11762733C2211yescharacteristic, complemented
80#11762732C2211yescharacteristic, complemented
81#11762732C2211yescharacteristic, complemented
82#11762732C2211yescharacteristic, complemented
83#11762732C2211yescharacteristic, complemented
84#11762732C2211yescharacteristic, complemented
85#11762729C2211yescharacteristic, complemented
86#11762726C2211yescharacteristic, complemented
87#11762725C2211yescharacteristic, complemented
88#11762725C2211yescharacteristic, complemented
89#11762725C2211yescharacteristic, complemented
90#11762725C2211yescharacteristic, complemented
91#11762725C2211yescharacteristic, complemented
92#11762724C2211yescharacteristic, complemented
93#11762724C2211yescharacteristic, complemented
94#11762724C2211yescharacteristic, complemented
95#11762724C2211yescharacteristic, complemented
96#11762724C2211yescharacteristic, complemented
97#11762723C2211yescharacteristic
98#11762723C2211yescharacteristic
99#11762721C2211yescharacteristic, complemented
100#11762721C2211yescharacteristic, complemented
101#11762721C2211yescharacteristic, complemented
102#11762718C2211yescharacteristic, complemented
103#11762718C2211yescharacteristic, complemented
104#11762718C2211yescharacteristic, complemented
105#11762717C2211yescharacteristic
106#11762717C2211yescharacteristic
107#11762717C2211yescharacteristic
108#11762717C2211yescharacteristic
109#11762717C2211yescharacteristic
110#11762717C2211yescharacteristic
111#11762717C2211yescharacteristic
112#11762717C2211yescharacteristic
113#11762713C2211yescharacteristic, complemented
114#11762713C2211yescharacteristic, complemented
115#11762712C2211yescharacteristic
116#11762712C2211yescharacteristic
117#11762709C2211yescharacteristic, complemented
118#11762709C2211yescharacteristic, complemented
119#11762709C2211yescharacteristic, complemented
120#11762709C2211yescharacteristic, complemented
121#11762707C2211yescharacteristic, complemented
122#11762706C2211yescharacteristic, complemented
123#11762705C2211yescharacteristic, complemented
124#11762703C2211yescharacteristic, complemented
125#11762703C2211yescharacteristic, complemented
126#11762703C2211yescharacteristic, complemented
127#11762703C2211yescharacteristic, complemented
128#11762703C2211yescharacteristic, complemented
129#11762703C2211yescharacteristic, complemented
130#11762702C2211yescharacteristic, complemented
131#11762702C2211yescharacteristic, complemented
132#11762700C2211yescharacteristic, complemented
133#11762700C2211yescharacteristic, complemented
134#11762699C2211yescharacteristic, complemented
135#11762697C2211yescharacteristic, complemented
136#11762697C2211yescharacteristic, complemented
137#11762697C2211yescharacteristic, complemented
138#11762695C2211yescharacteristic, complemented
139#11762692C2211yescharacteristic, complemented
140#11762689C2211yescharacteristic
141#11762689C2211yescharacteristic
142#11762689C2211yescharacteristic
143#11762689C2211yescharacteristic
144#11762689C2211yescharacteristic
145#11762689C2211yescharacteristic
146#11762689C2211yescharacteristic
147#11762689C2211yescharacteristic
148#11762687C2211yescharacteristic, complemented
149#11762686C2211yescharacteristic, complemented
150#11762686C2211yescharacteristic, complemented
151#11762686C2211yescharacteristic, complemented
152#11762686C2211yescharacteristic, complemented
153#11762685C2211yescharacteristic, complemented
154#11762685C2211yescharacteristic, complemented
155#11762685C2211yescharacteristic, complemented
156#11762683C2211yescharacteristic, complemented
157#11762681C2211yescharacteristic, complemented
158#11762681C2211yescharacteristic, complemented
159#11762681C2211yescharacteristic, complemented
160#11762681C2211yescharacteristic, complemented
161#11762680C2211yescharacteristic, complemented
162#11762670C2211yescharacteristic, complemented
163#11762670C2211yescharacteristic, complemented
164#11762670C2211yescharacteristic, complemented
165#11762670C2211yescharacteristic, complemented
166#11762667C2211yescharacteristic, complemented
167#11762667C2211yescharacteristic, complemented
168#11762667C2211yescharacteristic, complemented
169#11762667C2211yescharacteristic, complemented
170#11762665C2211yescharacteristic, complemented
171#11762665C2211yescharacteristic, complemented
172C4⋊C4×Dic17C2211yescharacteristic, complemented
173#11762655C2211yescharacteristic, complemented
174C2×C17×#120C2211yescharacteristic
175C2×C17×#120C2211yescharacteristic
176C2×C17×#120C2211yescharacteristic
177C2×C17×#120C2211yescharacteristic
178C2×C17×#120C2211yescharacteristic
179C2×C17×#120C2211yescharacteristic
180C17×#394C2211yescharacteristic
181C17×#394C2211yescharacteristic
182C17×#394C2211yescharacteristic
183C17×#394C2211yescharacteristic
184C17×#394C2211yescharacteristic
185C17×#394C2211yescharacteristic
186C17×#390C2211yescharacteristic
187C17×#390C2211yescharacteristic
188C17×#390C2211yescharacteristic
189C25×C17C2311yescharacteristic
190C25×C17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C22×D4×C17C2311yescharacteristic
193C22×D4×C17C2311yescharacteristic
194C22×D4×C17C2311yescharacteristic
195C22×D4×C17C2311yescharacteristic
196C22×D4×C17C2311yescharacteristic
197C22×D4×C17C2311yescharacteristic
198C22×D4×C17C2311yescharacteristic
199C22×D4×C17C2311yescharacteristic
200C22×C22⋊D17C2311yescharacteristic
201C22×C22⋊D17C2311yescharacteristic
202C22×C22⋊D17C2311yescharacteristic
203C22×C22⋊D17C2311yescharacteristic
204C22×C22⋊D17C2311yescharacteristic
205C22×C22⋊D17C2311yescharacteristic
206C22×C22⋊D17C2311yescharacteristic
207C22×C22⋊D17C2311yescharacteristic
208C22×C22⋊D17C2311yescharacteristic
209C22×C22⋊D17C2311yescharacteristic
210C22×C22⋊D17C2311yescharacteristic
211C22×C22⋊D17C2311yescharacteristic
212C23×Dic17—24no—
213C23×Dic17—42no—
214C23×Dic17—42no—
215C23×Dic17C2311yescharacteristic
216C23×Dic17C2311yescharacteristic
217C23×Dic17C2311yescharacteristic
218C23×Dic17C2311yescharacteristic
219C23×Dic17C2311yescharacteristic
220C23×Dic17C2311yescharacteristic
221C23×Dic17C2311yescharacteristic
222C23×Dic17C2311yescharacteristic
223C2×#63254—24no—
224C2×#63254—42no—
225C2×#63254—42no—
226C22×D68C2311yescharacteristic
227C22×C4×D17C2311yescharacteristic
228C22×C4×D17C2311yescharacteristic
229C22×Dic34C2311yescharacteristic
230C22×Dic34C2311yescharacteristic
231C17×#120—24no—
232C17×#120—24no—
233C17×#120—42no—
234C17×#120—42no—
235C17×#120—42no—
236C17×#120—42no—
237C2×C4⋊C4×C17C2311yescharacteristic
238C2×C4⋊C4×C17C2311yescharacteristic
239C2×C4⋊C4×C17C2311yescharacteristic
240C2×C22⋊C4×C17C2311yescharacteristic
241C2×C22⋊C4×C17C2311yescharacteristic
242C2×C22⋊C4×C17C2311yescharacteristic
243C2×C22⋊C4×C17C2311yescharacteristic
244C2×C22⋊C4×C17C2311yescharacteristic
245C2×C22⋊C4×C17C2311yescharacteristic
246C2×C22⋊C4×C17C2311yescharacteristic
247C2×C22⋊C4×C17C2311yescharacteristic
248C2×C22⋊C4×C17C2311yescharacteristic
249C2×C22⋊C4×C17C2311yescharacteristic
250C2×C22⋊C4×C17C2311yescharacteristic
251C2×C22⋊C4×C17C2311yescharacteristic
252C2×C22⋊C4×C17C2311yescharacteristic
253C2×C22⋊C4×C17C2311yescharacteristic
254C2×C22⋊C4×C17C2311yescharacteristic
255C2×C22⋊C4×C17C2311yescharacteristic
256C2×C22⋊C4×C17C2311yescharacteristic
257C2×C22⋊C4×C17C2311yescharacteristic
258C2×C42×C17C2311yescharacteristic
259#10587639—24no—
260#10587639—24no—
261#10587639—42no—
262#10587639—42no—
263C2×C22⋊Dic17—24no—
264C2×C22⋊Dic17C2311yescharacteristic
265C2×C22⋊Dic17C2311yescharacteristic
266C2×C22⋊Dic17C2311yescharacteristic
267C2×C22⋊Dic17C2311yescharacteristic
268C2×C22⋊Dic17C2311yescharacteristic
269C2×C22⋊Dic17C2311yescharacteristic
270C2×C22⋊Dic17C2311yescharacteristic
271C2×C22⋊Dic17C2311yescharacteristic
272C2×C22⋊Dic17C2311yescharacteristic
273C2×C22⋊Dic17C2311yescharacteristic
274C2×C22⋊Dic17C2311yescharacteristic
275C2×C22⋊Dic17C2311yescharacteristic
276C2×C22⋊Dic17C2311yescharacteristic
277C2×C22⋊Dic17C2311yescharacteristic
278C2×C22⋊Dic17C2311yescharacteristic
279C2×C22⋊Dic17C2311yescharacteristic
280C2×C22⋊Dic17C2311yescharacteristic
281C2×C22⋊Dic17C2311yescharacteristic
282C2×C22⋊Dic17C2311yescharacteristic
283C2×C22⋊Dic17C2311yescharacteristic
284C2×C22⋊Dic17C2311yescharacteristic
285C2×C22⋊Dic17C2311yescharacteristic
286C2×C22⋊Dic17C2311yescharacteristic
287C2×C22⋊Dic17C2311yescharacteristic
288C2×C22⋊Dic17C2311yescharacteristic
289C2×C22⋊Dic17C2311yescharacteristic
290C2×C22⋊Dic17C2311yescharacteristic
291C2×C22⋊Dic17C2311yescharacteristic
292#10587626—42no—
293#10587625—24no—
294#10587625—24no—
295#10587625—24no—
296#10587625—24no—
297#10587625—42no—
298#10587625—42no—
299#10587624—24no—
300#10587622—24no—
301#10587621—24no—
302#10587621—24no—
303#10587621—42no—
304#10587621—42no—
305D4×Dic17—24no—
306D4×Dic17D418yescomplemented
307C2×#63227C2311yescharacteristic
308C2×#63227C2311yescharacteristic
309C2×#63227C2311yescharacteristic
310C2×#63227C2311yescharacteristic
311C2×#63227C2311yescharacteristic
312C2×#63227C2311yescharacteristic
313C2×#63227C2311yescharacteristic
314C2×#63227C2311yescharacteristic
315C2×#63227C2311yescharacteristic
316C2×#63227C2311yescharacteristic
317C2×#63227C2311yescharacteristic
318C2×#63227C2311yescharacteristic
319C2×#63227C2311yescharacteristic
320C2×#63227C2311yescharacteristic
321C2×C4⋊Dic17C2311yescharacteristic
322C2×C4⋊Dic17C2311yescharacteristic
323C2×C4⋊Dic17C2311yescharacteristic
324C2×C4⋊Dic17C2311yescharacteristic
325C2×C4⋊Dic17C2311yescharacteristic
326C2×#63225C2311yescharacteristic
327C2×#63225C2311yescharacteristic
328C2×#63225C2311yescharacteristic
329C2×#63225C2311yescharacteristic
330C2×#63225C2311yescharacteristic
331C2×#63225C2311yescharacteristic
332C2×#63225C2311yescharacteristic
333C2×#63225C2311yescharacteristic
334C2×#63225C2311yescharacteristic
335C2×#63225C2311yescharacteristic
336C2×#63225C2311yescharacteristic
337C2×#63225C2311yescharacteristic
338C2×#63225C2311yescharacteristic
339C2×#63225C2311yescharacteristic
340C2×#63225C2311yescharacteristic
341C2×#63225C2311yescharacteristic
342C2×C4×Dic17C2311yescharacteristic
343C2×C4×Dic17C2311yescharacteristic
344C2×C4×Dic17C2311yescharacteristic
345C2×C4×Dic17C2311yescharacteristic
346C2×C4×Dic17C2311yescharacteristic
347C2×C4×Dic17C2311yescharacteristic
348#10587582—42no—
349#10587572—24no—
350#10587571—24no—
351#10587571—42no—
352#10587570—42no—
353#10587569—24no—
354#10587567—24no—
355#10587567—24no—
356#10587567—24no—
357#10587565—24no—
358#10587565—24no—
359#10587564—24no—
360#10587564—24no—
361#10587564—24no—
362#10587563—24no—
363C17×#95C2311yescharacteristic
364C17×#95C2311yescharacteristic
365#10587502C2311yescharacteristic
366#10587502C2311yescharacteristic
367#10587502C2311yescharacteristic
368#10587502C2311yescharacteristic
369#10587502C2311yescharacteristic
370#10587502C2311yescharacteristic
371#10587502C2311yescharacteristic
372#10587502C2311yescharacteristic
373#10587502C2311yescharacteristic
374#10587502C2311yescharacteristic
375#10587502C2311yescharacteristic
376#10587502C2311yescharacteristic
377#10587502C2311yescharacteristic
378#10587502C2311yescharacteristic
379#10587502C2311yescharacteristic
380#10587502C2311yescharacteristic
381#10587502C2311yescharacteristic
382#10587502C2311yescharacteristic
383#10587502C2311yescharacteristic
384#10587502C2311yescharacteristic
385#10587502C2311yescharacteristic
386#10587502C2311yescharacteristic
387#10587502C2311yescharacteristic
388#10587502C2311yescharacteristic
389#10587502C2311yescharacteristic
390#10587502C2311yescharacteristic
391C24×C17—22no—
392C24×C17—22no—
393C24×C17—22no—
394C24×C17—22no—
395C24×C17—41no—
396C24×C17—41no—
397C24×C17—41no—
398C24×C17—41no—
399C24×C17—41no—
400C24×C17—41no—
401C24×C17—41no—
402C24×C17—41no—
403C24×C17—41no—
404C24×C17—41no—
405C24×C17C2411yescharacteristic
406C24×C17C2411yescharacteristic
407C24×C17C2411yescharacteristic
408C24×C17C2411yescharacteristic
409C24×C17C2411yescharacteristic
410C24×C17C2411yescharacteristic
411C23×D17C2411yescharacteristic
412C23×D17C2411yescharacteristic
413C2×D4×C17—22no—
414C2×D4×C17—22no—
415C2×D4×C17—22no—
416C2×D4×C17—22no—
417C2×D4×C17—22no—
418C2×D4×C17—22no—
419C2×D4×C17—22no—
420C2×D4×C17—22no—
421C2×D4×C17—22no—
422C2×D4×C17—22no—
423C2×D4×C17—41no—
424C2×D4×C17—41no—
425C2×D4×C17—41no—
426C2×D4×C17—41no—
427C2×D4×C17—41no—
428C2×D4×C17—41no—
429C2×D4×C17—41no—
430C2×D4×C17—41no—
431C2×D4×C17—41no—
432C2×D4×C17—41no—
433C2×D4×C17—41no—
434C2×D4×C17—41no—
435C2×D4×C17—41no—
436C2×D4×C17—41no—
437C2×D4×C17—41no—
438C2×D4×C17—41no—
439C2×D4×C17C2×D414yes—
440C22×C4×C17C2411yescharacteristic
441C22×C4×C17C2411yescharacteristic
442C22×C4×C17C2411yescharacteristic
443C22×C4×C17C2411yescharacteristic
444C22×C4×C17C2411yescharacteristic
445C22×C4×C17C2411yescharacteristic
446C22×C4×C17C2411yescharacteristic
447C22×C4×C17C2411yescharacteristic
448C22×C4×C17C2411yescharacteristic
449C2×C22⋊D17—22no—
450C2×C22⋊D17—22no—
451C2×C22⋊D17—22no—
452C2×C22⋊D17—22no—
453C2×C22⋊D17—22no—
454C2×C22⋊D17—22no—
455C2×C22⋊D17—22no—
456C2×C22⋊D17—22no—
457C2×C22⋊D17—22no—
458C2×C22⋊D17—22no—
459C2×C22⋊D17—22no—
460C2×C22⋊D17—22no—
461C2×C22⋊D17—22no—
462C2×C22⋊D17—41no—
463C2×C22⋊D17—41no—
464C2×C22⋊D17—41no—
465C2×C22⋊D17—41no—
466C2×C22⋊D17—41no—
467C2×C22⋊D17—41no—
468C2×C22⋊D17—41no—
469C2×C22⋊D17—41no—
470C2×C22⋊D17—41no—
471C2×C22⋊D17—41no—
472C2×C22⋊D17—41no—
473C2×C22⋊D17—41no—
474C2×C22⋊D17—41no—
475C2×C22⋊D17—41no—
476C2×C22⋊D17—41no—
477C2×C22⋊D17—41no—
478C2×C22⋊D17—41no—
479C2×C22⋊D17—41no—
480C2×C22⋊D17—41no—
481C2×C22⋊D17—41no—
482C2×C22⋊D17—41no—
483C2×C22⋊D17—41no—
484C2×C22⋊D17—41no—
485C22×Dic17—22no—
486C22×Dic17—22no—
487C22×Dic17—22no—
488C22×Dic17—22no—
489C22×Dic17—22no—
490C22×Dic17—22no—
491C22×Dic17—22no—
492C22×Dic17—22no—
493C22×Dic17—22no—
494C22×Dic17—22no—
495C22×Dic17—22no—
496C22×Dic17—41no—
497C22×Dic17—41no—
498C22×Dic17—41no—
499C22×Dic17—41no—
500C22×Dic17—41no—
501C22×Dic17—41no—
502C22×Dic17—41no—
503C22×Dic17—41no—
504C22×Dic17—41no—
505C22×Dic17—41no—
506C22×Dic17—41no—
507C22×Dic17—416no—
508C22×Dic17C2×D414yes—
509C22×Dic17C2×D414yes—
510C22×Dic17C2411yescharacteristic
511C22×Dic17C2411yescharacteristic
512C22×Dic17C2411yescharacteristic
513C22×Dic17C2411yescharacteristic
514C22×Dic17C2411yescharacteristic
515C22×Dic17C2411yescharacteristic
516C22×Dic17C2411yescharacteristic
517C22×Dic17C2411yescharacteristic
518C22×Dic17C2411yescharacteristic
519C22×Dic17C2411yescharacteristic
520C22×Dic17C2411yescharacteristic
521C22×Dic17C2411yescharacteristic
522C22×Dic17C2411yescharacteristic
523C22×Dic17C2411yescharacteristic
524#63254—416no—
525C2×D68—41no—
526C2×D68—41no—
527C2×D68—41no—
528C2×C4×D17—22no—
529C2×C4×D17—22no—
530C2×C4×D17—41no—
531C2×C4×D17—41no—
532C2×C4×D17—41no—
533C2×C4×D17—41no—
534C2×Dic34—22no—
535C2×Dic34—22no—
536C2×Dic34—22no—
537C2×Dic34—41no—
538C2×Dic34—41no—
539C2×Dic34—41no—
540C4⋊C4×C17—41no—
541C4⋊C4×C17—41no—
542C4⋊C4×C17—41no—
543C22⋊C4×C17—22no—
544C22⋊C4×C17—22no—
545C22⋊C4×C17—22no—
546C22⋊C4×C17—22no—
547C22⋊C4×C17—22no—
548C22⋊C4×C17—22no—
549C22⋊C4×C17—22no—
550C22⋊C4×C17—22no—
551C22⋊C4×C17—41no—
552C22⋊C4×C17—41no—
553C22⋊C4×C17—41no—
554C22⋊C4×C17—41no—
555C22⋊C4×C17—41no—
556C22⋊C4×C17—41no—
557C22⋊C4×C17—41no—
558C22⋊C4×C17—41no—
559C22⋊C4×C17—41no—
560C22⋊C4×C17—41no—
561C42×C17—41no—
562C22⋊Dic17—22no—
563C22⋊Dic17—22no—
564C22⋊Dic17—22no—
565C22⋊Dic17—22no—
566C22⋊Dic17—22no—
567C22⋊Dic17—22no—
568C22⋊Dic17—22no—
569C22⋊Dic17—22no—
570C22⋊Dic17—22no—
571C22⋊Dic17—22no—
572C22⋊Dic17—22no—
573C22⋊Dic17—22no—
574C22⋊Dic17—22no—
575C22⋊Dic17—22no—
576C22⋊Dic17—41no—
577C22⋊Dic17—41no—
578C22⋊Dic17—41no—
579C22⋊Dic17—41no—
580C22⋊Dic17—41no—
581C22⋊Dic17—41no—
582C22⋊Dic17—41no—
583C22⋊Dic17—41no—
584C22⋊Dic17—41no—
585C22⋊Dic17—41no—
586C22⋊Dic17—41no—
587C22⋊Dic17—41no—
588C22⋊Dic17C2×D414yes—
589C22⋊Dic17C2×D414yes—
590#63227—22no—
591#63227—22no—
592#63227—22no—
593#63227—22no—
594#63227—22no—
595#63227—41no—
596#63227—41no—
597#63227—41no—
598#63227—41no—
599#63227—41no—
600#63227—41no—
601#63227—41no—
602#63227—41no—
603#63227—41no—
604C4⋊Dic17—22no—
605C4⋊Dic17—22no—
606C4⋊Dic17—41no—
607C4⋊Dic17—41no—
608C4⋊Dic17C2×D414yes—
609#63225—22no—
610#63225—22no—
611#63225—22no—
612#63225—22no—
613#63225—22no—
614#63225—22no—
615#63225—22no—
616#63225—22no—
617#63225—22no—
618#63225—41no—
619#63225—41no—
620#63225—41no—
621#63225—41no—
622#63225—41no—
623#63225—41no—
624#63225—41no—
625C4×Dic17—22no—
626C4×Dic17—22no—
627C4×Dic17—41no—
628C4×Dic17—41no—
629C4×Dic17—41no—
630C4×Dic17C2×D414yes—
631#36724—171nomaximal, Sylow
632C23×C17—21no—
633C23×C17—21no—
634C23×C17—21no—
635C23×C17—21no—
636C23×C17—21no—
637C23×C17—21no—
638C23×C17—21no—
639C23×C17—21no—
640C23×C17—21no—
641C23×C17—21no—
642C23×C17—21no—
643C23×C17—21no—
644C23×C17—21no—
645C23×C17—21no—
646C23×C17—21no—
647C23×C17—21no—
648C23×C17—21no—
649C23×C17—21no—
650C23×C17—21no—
651C23×C17—21no—
652C23×C17—21no—
653C23×C17—21no—
654C23×C17—21no—
655C23×C17—21no—
656C23×C17—21no—
657C23×C17—21no—
658C23×C17—21no—
659C23×C17—21no—
660C23×C17—21no—
661C23×C17—21no—
662C23×C17—21no—
663C23×C17—21no—
664C23×C17—21no—
665C23×C17—21no—
666C23×C17—21no—
667C23×C17—21no—
668C23×C17—21no—
669C23×C17—21no—
670C23×C17—44no—
671C23×C17—44no—
672C23×C17—44no—
673C23×C17—44no—
674C23×C17—44no—
675C23×C17—44no—
676C23×C17—44no—
677C23×C17—44no—
678C23×C17—82no—
679C23×C17—82no—
680C23×C17—82no—
681C23×C17—82no—
682C23×C17—82no—
683C23×C17—82no—
684C23×C17C22×D412yes—
685C23×C17C22×D412yes—
686C23×C17H(5,𝔽2)12yes—
687C23×C17H(5,𝔽2)12yes—
688C23×C17C2511yescharacteristic
689C22×D17—21no—
690C22×D17—21no—
691C22×D17—21no—
692C22×D17—21no—
693C22×D17—21no—
694C22×D17—21no—
695C22×D17—21no—
696C22×D17—21no—
697C22×D17—21no—
698C22×D17—21no—
699C22×D17—21no—
700C22×D17—21no—
701C22×D17—21no—
702C22×D17—21no—
703D4×C17—44no—
704D4×C17—44no—
705D4×C17—44no—
706D4×C17—82no—
707D4×C17—82no—
708D4×C17—82no—
709D4×C17—82no—
710D4×C17—82no—
711D4×C17—82no—
712C2×C4×C17—21no—
713C2×C4×C17—21no—
714C2×C4×C17—21no—
715C2×C4×C17—21no—
716C2×C4×C17—21no—
717C2×C4×C17—21no—
718C2×C4×C17—21no—
719C2×C4×C17—21no—
720C2×C4×C17—21no—
721C2×C4×C17—21no—
722C2×C4×C17—21no—
723C2×C4×C17—21no—
724C2×C4×C17—21no—
725C2×C4×C17—21no—
726C2×C4×C17—21no—
727C2×C4×C17—21no—
728C2×C4×C17—21no—
729C2×C4×C17—21no—
730C2×C4×C17—21no—
731C2×C4×C17—21no—
732C2×C4×C17—21no—
733C2×C4×C17—21no—
734C2×C4×C17—21no—
735C2×C4×C17—21no—
736C2×C4×C17—21no—
737C2×C4×C17—21no—
738C2×C4×C17C22×D412yes—
739C22⋊D17—44no—
740C22⋊D17—44no—
741C22⋊D17—44no—
742C22⋊D17—44no—
743C22⋊D17—44no—
744C22⋊D17—82no—
745C22⋊D17—82no—
746C22⋊D17—82no—
747C22⋊D17—82no—
748C22⋊D17—82no—
749C22⋊D17—82no—
750C22⋊D17—82no—
751C2×Dic17—28no—
752C2×Dic17—21no—
753C2×Dic17—21no—
754C2×Dic17—21no—
755C2×Dic17—21no—
756C2×Dic17—21no—
757C2×Dic17—21no—
758C2×Dic17—21no—
759C2×Dic17—21no—
760C2×Dic17—21no—
761C2×Dic17—21no—
762C2×Dic17—21no—
763C2×Dic17—21no—
764C2×Dic17—21no—
765C2×Dic17—21no—
766C2×Dic17—21no—
767C2×Dic17—21no—
768C2×Dic17—21no—
769C2×Dic17—21no—
770C2×Dic17—21no—
771C2×Dic17—21no—
772C2×Dic17—21no—
773C2×Dic17—21no—
774C2×Dic17—21no—
775C2×Dic17—21no—
776C2×Dic17—21no—
777C2×Dic17—21no—
778C2×Dic17—21no—
779C2×Dic17—21no—
780C2×Dic17—21no—
781C2×Dic17—21no—
782C2×Dic17—21no—
783C2×Dic17—21no—
784C2×Dic17—21no—
785C2×Dic17—21no—
786C2×Dic17—21no—
787C2×Dic17—21no—
788C2×Dic17—21no—
789C2×Dic17—44no—
790C2×Dic17—44no—
791C2×Dic17—44no—
792C2×Dic17—44no—
793C2×Dic17—44no—
794C2×Dic17—44no—
795C2×Dic17—82no—
796C2×Dic17C22×D412yes—
797C2×Dic17C22×D412yes—
798C2×Dic17C22×D412yes—
799C2×Dic17C22×D412yes—
800C2×Dic17H(5,𝔽2)12yes—
801D68—82no—
802C4×D17—44no—
803C4×D17—82no—
804Dic34—44no—
805Dic34—82no—
806C2×#538—171no—
807C2×#525—171no—
808#2849—171no—
809#2847—171no—
810#2705—171no—
811#2702—171no—
812#2700—171no—
813#2699—171no—
814#2687—171no—
815#2682—171no—
816#2681—171no—
817#2681—171no—
818#2679D1711yescharacteristic, complemented
819#2678—171no—
820#2678—171no—
821#2678—171no—
822#2672—171no—
823#2670—171no—
824#2669—171no—
825#2669—171no—
826#2635—171no—
827#2630—171no—
828#2610—171no—
829#2603—171no—
830#2601—171no—
831#2600—171no—
832#2544—171no—
833#2534—171no—
834#2407—171no—
835#2404—171no—
836#2319—171no—
837C22×C17—22no—
838C22×C17—22no—
839C22×C17—22no—
840C22×C17—22no—
841C22×C17—22no—
842C22×C17—22no—
843C22×C17—22no—
844C22×C17—22no—
845C22×C17—22no—
846C22×C17—22no—
847C22×C17—22no—
848C22×C17—22no—
849C22×C17—416no—
850C22×C17—41no—
851C22×C17—41no—
852C22×C17—41no—
853C22×C17—41no—
854C22×C17—41no—
855C22×C17—41no—
856C22×C17—41no—
857C22×C17—41no—
858C22×C17—41no—
859C22×C17—41no—
860C22×C17—41no—
861C22×C17—41no—
862C22×C17—41no—
863C22×C17—41no—
864C22×C17—41no—
865C22×C17—41no—
866C22×C17—41no—
867C22×C17—41no—
868C22×C17—41no—
869C22×C17—41no—
870C22×C17—41no—
871C22×C17—41no—
872C22×C17—41no—
873C22×C17—41no—
874C22×C17—41no—
875C22×C17—41no—
876C22×C17—41no—
877C22×C17—41no—
878C22×C17—41no—
879C22×C17—41no—
880C22×C17—88no—
881C22×C17C23×D411yescharacteristic
882C22×C17C2×H(5,𝔽2)11yescharacteristic
883C22×C17C2×H(5,𝔽2)11yescharacteristic
884C22×C17C2×H(5,𝔽2)11yescharacteristic
885C22×C17#58511yescharacteristic
886C22×C17#58511yescharacteristic
887C22×C17#58511yescharacteristic
888C2×D17—41no—
889C2×D17—41no—
890C2×D17—41no—
891C2×D17—41no—
892C2×D17—41no—
893C2×D17—41no—
894C2×D17—41no—
895C2×D17—41no—
896C2×D17—41no—
897C2×D17—41no—
898C2×D17—41no—
899C2×D17—41no—
900C2×D17—41no—
901C2×D17—41no—
902C4×C17—22no—
903C4×C17—41no—
904C4×C17—41no—
905C4×C17—41no—
906C4×C17—41no—
907C4×C17—41no—
908C4×C17—41no—
909C4×C17—41no—
910C4×C17—41no—
911Dic17—22no—
912Dic17—22no—
913Dic17—22no—
914Dic17—22no—
915Dic17—22no—
916Dic17—41no—
917Dic17—41no—
918Dic17—41no—
919Dic17—41no—
920Dic17—41no—
921Dic17—41no—
922Dic17—41no—
923Dic17—41no—
924Dic17—41no—
925C22×#41—171no—
926C24×C4—171no—
927#538—348no—
928C2×#127—171no—
929C2×#126—171no—
930C2×#126—171no—
931C2×#124—171no—
932C2×#124—171no—
933C2×#124—171no—
934#525—348no—
935C2×#123—171no—
936C2×#123—171no—
937C2×#123—171no—
938C2×#123—171no—
939C2×#123—171no—
940C2×#123—171no—
941C2×C22⋊Q8—171no—
942C2×C22⋊Q8—171no—
943C2×C22⋊Q8—171no—
944C2×C22⋊Q8—171no—
945C2×#121—171no—
946C2×#121—171no—
947C2×#121—171no—
948C2×#121—171no—
949C2×#121—171no—
950C2×#121—171no—
951C2×#121—171no—
952C2×#121—171no—
953C2×#120—171no—
954C2×#120—171no—
955C2×#120—171no—
956C2×#120—171no—
957C2×#120C2×D1711yescharacteristic
958C2×#120C2×D1711yescharacteristic
959C2×#120C2×D1711yescharacteristic
960C2×#120C2×D1711yescharacteristic
961C2×#120C2×D1711yescharacteristic
962C2×#120C2×D1711yescharacteristic
963C2×C4×D4—171no—
964C2×C4×D4—171no—
965C2×C4×D4—171no—
966C2×C4×D4—171no—
967C2×C4×D4—171no—
968C2×#117—171no—
969C22×C22⋊C4—171no—
970#400—171no—
971#399—171no—
972#398—171no—
973#398—171no—
974#398—171no—
975#397—171no—
976#397—171no—
977#397—171no—
978#396—171no—
979#396—171no—
980#396—171no—
981#396—171no—
982#396—171no—
983#396—171no—
984#395—171no—
985#394—171no—
986#394—171no—
987#394—171no—
988#394—171no—
989#394—171no—
990#394—171no—
991#394—171no—
992#394—171no—
993#394—171no—
994#394—171no—
995#394—171no—
996#394—171no—
997#394—171no—
998#394C2×D1711yescharacteristic
999#394C2×D1711yescharacteristic
1000#394C2×D1711yescharacteristic
1001#394C2×D1711yescharacteristic
1002#394C2×D1711yescharacteristic
1003#394C2×D1711yescharacteristic
1004#393—171no—
1005#393—171no—
1006#393—171no—
1007#392—171no—
1008#392—171no—
1009#392—171no—
1010#392—171no—
1011#392—171no—
1012#392—171no—
1013#392—171no—
1014#392—171no—
1015#392—171no—
1016#392—171no—
1017#392—171no—
1018#391—171no—
1019#391—171no—
1020#390—171no—
1021#390—171no—
1022#390—171no—
1023#390—171no—
1024#390—171no—
1025#390—171no—
1026#390C2×D1711yescharacteristic
1027#390C2×D1711yescharacteristic
1028#390C2×D1711yescharacteristic
1029#389—171no—
1030#389—171no—
1031#389—171no—
1032#388—171no—
1033#388—171no—
1034#388—171no—
1035#388—171no—
1036#388—171no—
1037#388—171no—
1038#388—171no—
1039#388—171no—
1040#388—171no—
1041#388—171no—
1042#388—171no—
1043#388—171no—
1044#388—171no—
1045#388—171no—
1046#387—171no—
1047#387—171no—
1048#386—171no—
1049#386—171no—
1050#386—171no—
1051#386—171no—
1052#386—171no—
1053#386—171no—
1054#386—171no—
1055#386—171no—
1056#386—171no—
1057#386—171no—
1058#386—171no—
1059#386—171no—
1060#386—171no—
1061#386—171no—
1062#386—171no—
1063#386—171no—
1064#385—171no—
1065#385—171no—
1066#385—171no—
1067#385—171no—
1068#385—171no—
1069#385—171no—
1070#381—171no—
1071#381—171no—
1072#381—171no—
1073#381—171no—
1074#380—171no—
1075#380—171no—
1076#380—171no—
1077#380—171no—
1078#379—171no—
1079#379—171no—
1080C4×C4⋊C4—171no—
1081#376—171no—
1082C2×C17—42no—
1083C2×C17—42no—
1084C2×C17—42no—
1085C2×C17—42no—
1086C2×C17—81no—
1087C2×C17—81no—
1088C2×C17#344911yescharacteristic
1089C2×C17#348411yescharacteristic
1090C2×C17#348811yescharacteristic
1091C2×C17#353311yescharacteristic
1092C2×C17#353411yescharacteristic
1093C2×C17#354011yescharacteristic
1094C2×C17#354211yescharacteristic
1095D17—81no—
1096D17—81no—
1097C25C22×D1711yescharacteristic
1098C25C22×D1711yescharacteristic
1099C2×#41—344no—
1100C2×#41—682no—
1101C2×#41—682no—
1102C22×Q8—171no—
1103C22×Q8—171no—
1104C22×D4—171no—
1105C22×D4—171no—
1106C22×D4—171no—
1107C22×D4—171no—
1108C22×D4—171no—
1109C22×D4—171no—
1110C22×D4—171no—
1111C22×D4—171no—
1112C22×D4—171no—
1113C22×D4—171no—
1114C22×D4—171no—
1115C22×D4—171no—
1116C22×D4—171no—
1117C22×D4C22×D1711yescharacteristic
1118C22×D4C22×D1711yescharacteristic
1119C22×D4C22×D1711yescharacteristic
1120C22×D4C22×D1711yescharacteristic
1121C22×D4C22×D1711yescharacteristic
1122C22×D4C22×D1711yescharacteristic
1123C22×D4C22×D1711yescharacteristic
1124C22×D4C22×D1711yescharacteristic
1125C22×D4C22×D1711yescharacteristic
1126C23×C4—171no—
1127C23×C4—171no—
1128C23×C4—171no—
1129C23×C4—171no—
1130C23×C4—171no—
1131C23×C4—171no—
1132C23×C4—171no—
1133C23×C4—171no—
1134C23×C4—171no—
1135C23×C4—171no—
1136C23×C4—344no—
1137C23×C4—682no—
1138C23×C4—682no—
1139#127—682no—
1140#126—344no—
1141#126—344no—
1142#124—344no—
1143#124—344no—
1144#124—682no—
1145#123—344no—
1146#123—344no—
1147#123—344no—
1148#123—344no—
1149#123—682no—
1150#123—682no—
1151C22⋊Q8—344no—
1152C22⋊Q8—344no—
1153C22⋊Q8—344no—
1154C22⋊Q8—682no—
1155#121—344no—
1156#121—344no—
1157#121—344no—
1158#121—344no—
1159#121—344no—
1160#121—682no—
1161#121—682no—
1162#121—682no—
1163#120—24no—
1164#120—24no—
1165#120—42no—
1166#120—42no—
1167#120—42no—
1168#120—42no—
1169#120—344no—
1170#120—344no—
1171#120—682no—
1172#120—682no—
1173C4×D4—178no—
1174C4×D4—344no—
1175C4×D4—344no—
1176C4×D4—344no—
1177C4×D4—344no—
1178#117—344no—
1179C2×C4⋊C4—171no—
1180C2×C4⋊C4—171no—
1181C2×C4⋊C4—171no—
1182C2×C4⋊C4—171no—
1183C2×C4⋊C4—171no—
1184C2×C4⋊C4—171no—
1185C2×C4⋊C4—171no—
1186C2×C4⋊C4—171no—
1187C2×C4⋊C4—171no—
1188C2×C4⋊C4—171no—
1189C2×C4⋊C4—171no—
1190C2×C4⋊C4—171no—
1191C2×C4⋊C4—171no—
1192C2×C4⋊C4—171no—
1193C2×C4⋊C4—171no—
1194C2×C4⋊C4—171no—
1195C2×C4⋊C4—171no—
1196C2×C4⋊C4—171no—
1197C2×C4⋊C4—171no—
1198C2×C4⋊C4—171no—
1199C2×C4⋊C4—171no—
1200C2×C4⋊C4C22×D1711yescharacteristic
1201C2×C4⋊C4C22×D1711yescharacteristic
1202C2×C4⋊C4C22×D1711yescharacteristic
1203C2×C22⋊C4—171no—
1204C2×C22⋊C4—171no—
1205C2×C22⋊C4—171no—
1206C2×C22⋊C4—171no—
1207C2×C22⋊C4—171no—
1208C2×C22⋊C4—171no—
1209C2×C22⋊C4—171no—
1210C2×C22⋊C4—171no—
1211C2×C22⋊C4—171no—
1212C2×C22⋊C4—171no—
1213C2×C22⋊C4—171no—
1214C2×C22⋊C4—171no—
1215C2×C22⋊C4—171no—
1216C2×C22⋊C4—171no—
1217C2×C22⋊C4—171no—
1218C2×C22⋊C4—171no—
1219C2×C22⋊C4—171no—
1220C2×C22⋊C4—171no—
1221C2×C22⋊C4—171no—
1222C2×C22⋊C4—171no—
1223C2×C22⋊C4—171no—
1224C2×C22⋊C4—171no—
1225C2×C22⋊C4—171no—
1226C2×C22⋊C4—171no—
1227C2×C22⋊C4—171no—
1228C2×C22⋊C4—171no—
1229C2×C22⋊C4—171no—
1230C2×C22⋊C4—171no—
1231C2×C22⋊C4—171no—
1232C2×C22⋊C4—171no—
1233C2×C22⋊C4—171no—
1234C2×C22⋊C4—171no—
1235C2×C22⋊C4—171no—
1236C2×C22⋊C4—171no—
1237C2×C22⋊C4—171no—
1238C2×C22⋊C4—171no—
1239C2×C22⋊C4—171no—
1240C2×C22⋊C4—171no—
1241C2×C22⋊C4—171no—
1242C2×C22⋊C4—171no—
1243C2×C22⋊C4—171no—
1244C2×C22⋊C4—171no—
1245C2×C22⋊C4—344no—
1246C2×C22⋊C4C22×D1711yescharacteristic
1247C2×C22⋊C4C22×D1711yescharacteristic
1248C2×C22⋊C4C22×D1711yescharacteristic
1249C2×C22⋊C4C22×D1711yescharacteristic
1250C2×C22⋊C4C22×D1711yescharacteristic
1251C2×C22⋊C4C22×D1711yescharacteristic
1252C2×C22⋊C4C22×D1711yescharacteristic
1253C2×C22⋊C4C22×D1711yescharacteristic
1254C2×C22⋊C4C22×D1711yescharacteristic
1255C2×C22⋊C4C22×D1711yescharacteristic
1256C2×C22⋊C4C22×D1711yescharacteristic
1257C2×C22⋊C4C22×D1711yescharacteristic
1258C2×C22⋊C4C22×D1711yescharacteristic
1259C2×C22⋊C4C22×D1711yescharacteristic
1260C2×C22⋊C4C22×D1711yescharacteristic
1261C2×C22⋊C4C22×D1711yescharacteristic
1262C2×C22⋊C4C22×D1711yescharacteristic
1263C2×C22⋊C4C22×D1711yescharacteristic
1264C2×C42—171no—
1265C2×C42—171no—
1266C2×C42—171no—
1267C2×C42—171no—
1268C2×C42—171no—
1269C2×C42—171no—
1270C2×C42C22×D1711yescharacteristic
1271#95—171no—
1272#95—171no—
1273#95—171no—
1274#95—171no—
1275#95—171no—
1276#95—171no—
1277#95—171no—
1278#95—171no—
1279#95—171no—
1280#95—171no—
1281#95—171no—
1282#95—171no—
1283#95—171no—
1284#95—171no—
1285#95—171no—
1286#95—171no—
1287#95—171no—
1288#95—171no—
1289#95—171no—
1290#95—171no—
1291#95—171no—
1292#95—171no—
1293#95—171no—
1294#95—171no—
1295#95—171no—
1296#95—171no—
1297#95C22×D1711yescharacteristic
1298#95C22×D1711yescharacteristic
1299C17#3672411yescharacteristic, complemented, Sylow
1300C24—22no—
1301C24—22no—
1302C24—22no—
1303C24—22no—
1304C24—41no—
1305C24—41no—
1306C24—41no—
1307C24—41no—
1308C24—41no—
1309C24—41no—
1310C24—41no—
1311C24—41no—
1312C24—41no—
1313C24—41no—
1314C24—171no—
1315C24—171no—
1316C24C23×D1711yescharacteristic
1317C24C23×D1711yescharacteristic
1318C24C23×D1711yescharacteristic
1319C24C23×D1711yescharacteristic
1320C24C23×D1711yescharacteristic
1321C24C23×D1711yescharacteristic
1322#41—6816no—
1323C2×Q8—342no—
1324C2×Q8—342no—
1325C2×Q8—342no—
1326C2×Q8—681no—
1327C2×Q8—681no—
1328C2×Q8—681no—
1329C2×D4—22no—
1330C2×D4—22no—
1331C2×D4—22no—
1332C2×D4—22no—
1333C2×D4—22no—
1334C2×D4—22no—
1335C2×D4—22no—
1336C2×D4—22no—
1337C2×D4—22no—
1338C2×D4—22no—
1339C2×D4—41no—
1340C2×D4—41no—
1341C2×D4—41no—
1342C2×D4—41no—
1343C2×D4—41no—
1344C2×D4—41no—
1345C2×D4—41no—
1346C2×D4—41no—
1347C2×D4—41no—
1348C2×D4—41no—
1349C2×D4—41no—
1350C2×D4—41no—
1351C2×D4—41no—
1352C2×D4—41no—
1353C2×D4—41no—
1354C2×D4—41no—
1355C2×D4—342no—
1356C2×D4—342no—
1357C2×D4—342no—
1358C2×D4—342no—
1359C2×D4—342no—
1360C2×D4—342no—
1361C2×D4—342no—
1362C2×D4—342no—
1363C2×D4—342no—
1364C2×D4—342no—
1365C2×D4—342no—
1366C2×D4—342no—
1367C2×D4—342no—
1368C2×D4—681no—
1369C2×D4—681no—
1370C2×D4—681no—
1371C2×D4—681no—
1372C2×D4—681no—
1373C2×D4—681no—
1374C2×D4—681no—
1375C2×D4—681no—
1376C2×D4—681no—
1377C2×D4—681no—
1378C2×D4—681no—
1379C2×D4—681no—
1380C2×D4—681no—
1381C2×D4—681no—
1382C2×D4—681no—
1383C2×D4—681no—
1384C2×D4—681no—
1385C2×D4—681no—
1386C2×D4—681no—
1387C2×D4—681no—
1388C2×D4—681no—
1389C2×D4—681no—
1390C2×D4—681no—
1391C2×D4—681no—
1392C2×D4—681no—
1393C2×D4—681no—
1394C2×D4D4×D1714yes—
1395C22×C4—171no—
1396C22×C4—171no—
1397C22×C4—171no—
1398C22×C4—171no—
1399C22×C4—171no—
1400C22×C4—174no—
1401C22×C4—174no—
1402C22×C4—171no—
1403C22×C4—171no—
1404C22×C4—171no—
1405C22×C4—171no—
1406C22×C4—171no—
1407C22×C4—171no—
1408C22×C4—171no—
1409C22×C4—171no—
1410C22×C4—171no—
1411C22×C4—342no—
1412C22×C4—342no—
1413C22×C4—342no—
1414C22×C4—342no—
1415C22×C4—342no—
1416C22×C4—342no—
1417C22×C4—342no—
1418C22×C4—342no—
1419C22×C4—342no—
1420C22×C4—342no—
1421C22×C4—342no—
1422C22×C4—342no—
1423C22×C4—342no—
1424C22×C4—681no—
1425C22×C4—681no—
1426C22×C4—681no—
1427C22×C4—681no—
1428C22×C4—681no—
1429C22×C4—681no—
1430C22×C4—681no—
1431C22×C4—681no—
1432C22×C4—681no—
1433C22×C4—681no—
1434C22×C4—681no—
1435C22×C4—681no—
1436C22×C4—681no—
1437C22×C4—681no—
1438C22×C4—681no—
1439C22×C4—6816no—
1440C22×C4C23×D1711yescharacteristic
1441C22×C4C23×D1711yescharacteristic
1442C22×C4C23×D1711yescharacteristic
1443C22×C4C23×D1711yescharacteristic
1444C22×C4C23×D1711yescharacteristic
1445C22×C4C23×D1711yescharacteristic
1446C22×C4C23×D1711yescharacteristic
1447C22×C4C23×D1711yescharacteristic
1448C22×C4C23×D1711yescharacteristic
1449C4⋊C4—41no—
1450C4⋊C4—41no—
1451C4⋊C4—41no—
1452C4⋊C4—174no—
1453C4⋊C4—342no—
1454C4⋊C4—342no—
1455C4⋊C4—342no—
1456C4⋊C4—342no—
1457C4⋊C4—342no—
1458C4⋊C4—342no—
1459C4⋊C4—342no—
1460C4⋊C4—342no—
1461C4⋊C4—342no—
1462C4⋊C4—342no—
1463C4⋊C4—342no—
1464C4⋊C4—681no—
1465C4⋊C4—681no—
1466C4⋊C4—681no—
1467C4⋊C4—681no—
1468C4⋊C4—681no—
1469C4⋊C4—681no—
1470C4⋊C4—681no—
1471C4⋊C4—681no—
1472C4⋊C4—681no—
1473C22⋊C4—22no—
1474C22⋊C4—22no—
1475C22⋊C4—22no—
1476C22⋊C4—22no—
1477C22⋊C4—22no—
1478C22⋊C4—22no—
1479C22⋊C4—22no—
1480C22⋊C4—22no—
1481C22⋊C4—41no—
1482C22⋊C4—41no—
1483C22⋊C4—41no—
1484C22⋊C4—41no—
1485C22⋊C4—41no—
1486C22⋊C4—41no—
1487C22⋊C4—41no—
1488C22⋊C4—41no—
1489C22⋊C4—41no—
1490C22⋊C4—41no—
1491C22⋊C4—174no—
1492C22⋊C4—174no—
1493C22⋊C4—342no—
1494C22⋊C4—342no—
1495C22⋊C4—342no—
1496C22⋊C4—342no—
1497C22⋊C4—342no—
1498C22⋊C4—342no—
1499C22⋊C4—342no—
1500C22⋊C4—342no—
1501C22⋊C4—342no—
1502C22⋊C4—342no—
1503C22⋊C4—342no—
1504C22⋊C4—342no—
1505C22⋊C4—342no—
1506C22⋊C4—342no—
1507C22⋊C4—342no—
1508C22⋊C4—342no—
1509C22⋊C4—342no—
1510C22⋊C4—342no—
1511C22⋊C4—342no—
1512C22⋊C4—681no—
1513C22⋊C4—681no—
1514C22⋊C4—681no—
1515C22⋊C4—681no—
1516C22⋊C4—681no—
1517C22⋊C4—681no—
1518C22⋊C4—681no—
1519C22⋊C4—681no—
1520C22⋊C4—681no—
1521C22⋊C4—681no—
1522C22⋊C4—681no—
1523C22⋊C4—681no—
1524C22⋊C4—681no—
1525C22⋊C4—681no—
1526C22⋊C4—681no—
1527C22⋊C4—681no—
1528C22⋊C4—681no—
1529C22⋊C4—681no—
1530C22⋊C4—681no—
1531C22⋊C4—681no—
1532C22⋊C4—681no—
1533C42—41no—
1534C42—174no—
1535C42—342no—
1536C42—342no—
1537C42—681no—
1538C42—681no—
1539C42—681no—
1540C23—21no—
1541C23—21no—
1542C23—21no—
1543C23—21no—
1544C23—21no—
1545C23—21no—
1546C23—21no—
1547C23—21no—
1548C23—21no—
1549C23—21no—
1550C23—21no—
1551C23—21no—
1552C23—21no—
1553C23—21no—
1554C23—21no—
1555C23—21no—
1556C23—21no—
1557C23—21no—
1558C23—21no—
1559C23—21no—
1560C23—21no—
1561C23—21no—
1562C23—21no—
1563C23—21no—
1564C23—21no—
1565C23—21no—
1566C23—21no—
1567C23—21no—
1568C23—21no—
1569C23—21no—
1570C23—21no—
1571C23—21no—
1572C23—21no—
1573C23—21no—
1574C23—21no—
1575C23—21no—
1576C23—21no—
1577C23—21no—
1578C23—44no—
1579C23—44no—
1580C23—44no—
1581C23—44no—
1582C23—44no—
1583C23—44no—
1584C23—44no—
1585C23—44no—
1586C23—82no—
1587C23—82no—
1588C23—82no—
1589C23—82no—
1590C23—82no—
1591C23—82no—
1592C23—341no—
1593C23—341no—
1594C23—341no—
1595C23—341no—
1596C23—341no—
1597C23—341no—
1598C23—341no—
1599C23—341no—
1600C23—341no—
1601C23—341no—
1602C23—341no—
1603C23—341no—
1604C23—341no—
1605C23—341no—
1606C23C2×D4×D1712yes—
1607C23C2×D4×D1712yes—
1608C23#1058769112yes—
1609C23#1058769112yes—
1610C23C24×D1711yescharacteristic
1611Q8—684no—
1612Q8—1362no—
1613D4—44no—
1614D4—44no—
1615D4—44no—
1616D4—82no—
1617D4—82no—
1618D4—82no—
1619D4—82no—
1620D4—82no—
1621D4—82no—
1622D4—684no—
1623D4—684no—
1624D4—684no—
1625D4—684no—
1626D4—684no—
1627D4—1362no—
1628D4—1362no—
1629D4—1362no—
1630D4—1362no—
1631D4—1362no—
1632D4—1362no—
1633D4—1362no—
1634D4—1362no—
1635C2×C4—21no—
1636C2×C4—21no—
1637C2×C4—21no—
1638C2×C4—21no—
1639C2×C4—21no—
1640C2×C4—21no—
1641C2×C4—21no—
1642C2×C4—21no—
1643C2×C4—21no—
1644C2×C4—21no—
1645C2×C4—21no—
1646C2×C4—21no—
1647C2×C4—21no—
1648C2×C4—21no—
1649C2×C4—21no—
1650C2×C4—21no—
1651C2×C4—21no—
1652C2×C4—21no—
1653C2×C4—21no—
1654C2×C4—21no—
1655C2×C4—21no—
1656C2×C4—21no—
1657C2×C4—21no—
1658C2×C4—21no—
1659C2×C4—21no—
1660C2×C4—21no—
1661C2×C4—172no—
1662C2×C4—172no—
1663C2×C4—172no—
1664C2×C4—172no—
1665C2×C4—172no—
1666C2×C4—348no—
1667C2×C4—341no—
1668C2×C4—341no—
1669C2×C4—341no—
1670C2×C4—341no—
1671C2×C4—341no—
1672C2×C4—341no—
1673C2×C4—341no—
1674C2×C4—341no—
1675C2×C4—341no—
1676C2×C4—341no—
1677C2×C4—341no—
1678C2×C4—341no—
1679C2×C4—341no—
1680C2×C4—341no—
1681C2×C4—341no—
1682C2×C4—341no—
1683C2×C4—341no—
1684C2×C4—341no—
1685C2×C4—341no—
1686C2×C4—341no—
1687C2×C4—341no—
1688C2×C4—341no—
1689C2×C4—341no—
1690C2×C4—341no—
1691C2×C4—341no—
1692C2×C4—341no—
1693C2×C4—341no—
1694C2×C4—341no—
1695C2×C4—341no—
1696C2×C4—341no—
1697C2×C4—341no—
1698C2×C4—341no—
1699C2×C4—341no—
1700C2×C4—341no—
1701C2×C4—341no—
1702C2×C4—341no—
1703C2×C4—341no—
1704C2×C4—684no—
1705C2×C4—684no—
1706C2×C4—684no—
1707C2×C4—684no—
1708C2×C4—684no—
1709C2×C4—684no—
1710C2×C4—684no—
1711C2×C4—1362no—
1712C2×C4—1362no—
1713C2×C4C2×D4×D1712yes—
1714C22—22no—
1715C22—22no—
1716C22—22no—
1717C22—22no—
1718C22—22no—
1719C22—22no—
1720C22—22no—
1721C22—22no—
1722C22—22no—
1723C22—22no—
1724C22—22no—
1725C22—22no—
1726C22—416no—
1727C22—41no—
1728C22—41no—
1729C22—41no—
1730C22—41no—
1731C22—41no—
1732C22—41no—
1733C22—41no—
1734C22—41no—
1735C22—41no—
1736C22—41no—
1737C22—41no—
1738C22—41no—
1739C22—41no—
1740C22—41no—
1741C22—41no—
1742C22—41no—
1743C22—41no—
1744C22—41no—
1745C22—41no—
1746C22—41no—
1747C22—41no—
1748C22—41no—
1749C22—41no—
1750C22—41no—
1751C22—41no—
1752C22—41no—
1753C22—41no—
1754C22—41no—
1755C22—41no—
1756C22—41no—
1757C22—88no—
1758C22—681no—
1759C22—681no—
1760C22—681no—
1761C22—681no—
1762C22—681no—
1763C22—681no—
1764C22—681no—
1765C22—681no—
1766C22—681no—
1767C22—681no—
1768C22—681no—
1769C22—681no—
1770C22—681no—
1771C22—681no—
1772C22C22×D4×D1711yescharacteristic
1773C22H(5,𝔽2)×D1711yescharacteristic
1774C22C2×#1058769111yescharacteristic
1775C22C2×#1058769111yescharacteristic
1776C22#1176364411yescharacteristic
1777C22#1176364411yescharacteristic
1778C22#1176364411yescharacteristic
1779C4—22no—
1780C4—41no—
1781C4—41no—
1782C4—41no—
1783C4—41no—
1784C4—41no—
1785C4—41no—
1786C4—41no—
1787C4—41no—
1788C4—342no—
1789C4—342no—
1790C4—342no—
1791C4—342no—
1792C4—342no—
1793C4—681no—
1794C4—681no—
1795C4—681no—
1796C4—681no—
1797C4—681no—
1798C4—681no—
1799C4—681no—
1800C4—681no—
1801C4—681no—
1802C2—42no—
1803C2—42no—
1804C2—42no—
1805C2—42no—
1806C2—81no—
1807C2—81no—
1808C2—1361no—
1809C2—1361no—
1810C2#1454211011yescharacteristic
1811C2#1454241211yescharacteristic
1812C2#1454244411yescharacteristic
1813C2#1454294511yescharacteristic
1814C2#1454296211yescharacteristic
1815C2#1454305711yescharacteristic
1816C2#1454309511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2679C2
hypercenter#2679D17
hypocenterC17#36724
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2679

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#11763394C2semidirect
2. C2×#11763315C2semidirect
3. #14537074C2semidirect
4. #14537064C2semidirect
5. #14535452C2semidirect
6. #14535405C2semidirect
7. #14535388C2semidirect
8. #14535369C2semidirect
9. #14535211C2semidirect
10. #14535152C2semidirect
11. #14535138C2semidirect
12. #14535133C2semidirect
13. #14535109C2semidirect
14. #14535109C2semidirect
15. #14535109C2semidirect
16. #14535037C2semidirect
17. #14535006C2semidirect
18. #14535001C2semidirect
19. #14534998C2semidirect
20. #14534670C2semidirect
21. #14534624C2semidirect
22. #14534468C2semidirect
23. #14534407C2semidirect
24. #14534374C2semidirect
25. #14534367C2semidirect
26. #14533750C2semidirect
27. #14533671C2semidirect
28. #14532124C2semidirect
29. #14532100C2semidirect
30. #14531421C2semidirect
31. C17×#2679C2semidirect
33. C24×Dic17C22semidirect
36. C2×#10587565C22semidirect
37. C2×#10587565C22semidirect
39. C2×#10587571C22semidirect
40. C2×#10587571C22semidirect
42. C2×#10587572C22semidirect
43. C2×#10587569C22semidirect
48. C2×#10587582C22semidirect
49. C2×#10587564C22semidirect
50. C2×#10587564C22semidirect
51. C2×#10587564C22semidirect
52. C2×#10587570C22semidirect
60. C2×#10587639C22semidirect
61. C2×#10587639C22semidirect
62. C2×#10587639C22semidirect
63. C2×#10587639C22semidirect
66. C2×#10587567C22semidirect
67. C2×#10587567C22semidirect
68. C2×#10587567C22semidirect
69. C2×#10587563C22semidirect
70. C22×C22⋊Dic17C22semidirect
71. #11762750C22semidirect
72. #11762744C22semidirect
73. #11762742C22semidirect
74. #11762740C22semidirect
75. #11762739C22semidirect
76. #11762737C22semidirect
77. #11762737C22semidirect
78. #11762737C22semidirect
79. #11762733C22semidirect
80. #11762732C22semidirect
81. #11762732C22semidirect
82. #11762732C22semidirect
83. #11762732C22semidirect
84. #11762732C22semidirect
85. #11762729C22semidirect
86. #11762726C22semidirect
87. #11762725C22semidirect
88. #11762725C22semidirect
89. #11762725C22semidirect
90. #11762725C22semidirect
91. #11762725C22semidirect
92. #11762724C22semidirect
93. #11762724C22semidirect
94. #11762724C22semidirect
95. #11762724C22semidirect
96. #11762724C22semidirect
99. #11762721C22semidirect
100. #11762721C22semidirect
101. #11762721C22semidirect
102. #11762718C22semidirect
103. #11762718C22semidirect
104. #11762718C22semidirect
113. #11762713C22semidirect
114. #11762713C22semidirect
117. #11762709C22semidirect
118. #11762709C22semidirect
119. #11762709C22semidirect
120. #11762709C22semidirect
121. #11762707C22semidirect
122. #11762706C22semidirect
123. #11762705C22semidirect
124. #11762703C22semidirect
125. #11762703C22semidirect
126. #11762703C22semidirect
127. #11762703C22semidirect
128. #11762703C22semidirect
129. #11762703C22semidirect
130. #11762702C22semidirect
131. #11762702C22semidirect
132. #11762700C22semidirect
133. #11762700C22semidirect
134. #11762699C22semidirect
135. #11762697C22semidirect
136. #11762697C22semidirect
137. #11762697C22semidirect
138. #11762695C22semidirect
139. #11762692C22semidirect
148. #11762687C22semidirect
149. #11762686C22semidirect
150. #11762686C22semidirect
151. #11762686C22semidirect
152. #11762686C22semidirect
153. #11762685C22semidirect
154. #11762685C22semidirect
155. #11762685C22semidirect
156. #11762683C22semidirect
157. #11762681C22semidirect
158. #11762681C22semidirect
159. #11762681C22semidirect
160. #11762681C22semidirect
161. #11762680C22semidirect
162. #11762670C22semidirect
163. #11762670C22semidirect
164. #11762670C22semidirect
165. #11762670C22semidirect
166. #11762667C22semidirect
167. #11762667C22semidirect
168. #11762667C22semidirect
169. #11762667C22semidirect
170. #11762665C22semidirect
171. #11762665C22semidirect
172. C4⋊C4×Dic17C22semidirect
173. #11762655C22semidirect
306. D4×Dic17D4semidirect
818. #2679D17semidirect
1299. C17#36724semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117633942
C2×#117633152
#145370742
#145370642
#145354522
#145354052
#145353882
#145353692
#145352112
#145351522
#145351382
#145351332
#145351092
#145350372
#145350062
#145350012
#145349982
#145346702
#145346242
#145344682
#145344072
#145343742
#145343672
#145337502
#145336712
#145321242
#145321002
#145314212
C17×#26792
#3672417