Finite Group Databasebeta

← #17241180

Subgroups — #17241180

Order 4352.

2440 conjugacy classes of subgroups.

The subgroup lattice has 1676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763426C211yesmaximal, characteristic, complemented
2C2×#11763315C211yesmaximal, characteristic, complemented
3#14537074C211yesmaximal, characteristic, complemented
4#14537069C211yesmaximal, characteristic, complemented
5#14535337C211yesmaximal, characteristic, complemented
6#14535318C211yesmaximal, characteristic, complemented
7#14535281C211yesmaximal, characteristic, complemented
8#14535262C211yesmaximal, characteristic, complemented
9#14535241C211yesmaximal, characteristic, complemented
10#14535188C211yesmaximal, characteristic, complemented
11#14535179C211yesmaximal, characteristic, complemented
12#14535162C211yesmaximal, characteristic, complemented
13#14535100C211yesmaximal, characteristic, complemented
14#14535078C211yesmaximal, characteristic, complemented
15#14535071C211yesmaximal, characteristic, complemented
16#14535067C211yesmaximal, characteristic, complemented
17#14535029C211yesmaximal, characteristic, complemented
18#14535014C211yesmaximal, characteristic, complemented
19#14535006C211yesmaximal, characteristic, complemented
20#14534703C211yesmaximal, characteristic, complemented
21#14534624C211yesmaximal, characteristic, complemented
22#14534458C211yesmaximal, characteristic, complemented
23#14534389C211yesmaximal, characteristic, complemented
24#14534362C211yesmaximal, characteristic, complemented
25#14534346C211yesmaximal, characteristic, complemented
26#14534139C211yesmaximal, characteristic, complemented
27#14533968C211yesmaximal, characteristic, complemented
28#14532407C211yesmaximal, characteristic, complemented
29#14532390C211yesmaximal, characteristic, complemented
30#14531410C211yesmaximal, characteristic, complemented
31C17×#2668C211yesmaximal, characteristic, complemented
32C22×#63254C2211yescharacteristic
33C24×Dic17C2211yescharacteristic
34#11763426—28no—
35C2×#10587574C2211yescharacteristic, complemented
36C2×#10587574C2211yescharacteristic, complemented
37C2×#10587565C2211yescharacteristic
38C2×#10587565C2211yescharacteristic, complemented
39C2×#10587622C2211yescharacteristic
40C2×#10587622C2211yescharacteristic
41C2×#10587622C2211yescharacteristic, complemented
42C2×#10587571C2211yescharacteristic
43#11763315—28no—
44C2×#10587572C2211yescharacteristic
45C2×#10587621C2211yescharacteristic
46C2×#10587621C2211yescharacteristic
47C2×#10587621C2211yescharacteristic
48C2×#10587621C2211yescharacteristic, complemented
49C2×#10587610C2211yescharacteristic, complemented
50C2×#10587564C2211yescharacteristic
51C2×#10587564C2211yescharacteristic
52C2×#10587564C2211yescharacteristic
53C2×#10587564C2211yescharacteristic
54C2×#10587564C2211yescharacteristic
55C2×#10587564C2211yescharacteristic, complemented
56C2×#10587625C2211yescharacteristic
57C2×#10587625C2211yescharacteristic
58C2×#10587625C2211yescharacteristic, complemented
59C2×#10587639C2211yescharacteristic
60C2×#10587573C2211yescharacteristic, complemented
61C2×D4×Dic17C2211yescharacteristic
62C2×D4×Dic17C2211yescharacteristic
63C2×#10587567C2211yescharacteristic
64C2×#10587567C2211yescharacteristic
65C2×#10587612C2211yescharacteristic, complemented
66C2×#10587563C2211yescharacteristic
67#11762751C2211yescharacteristic, complemented
68#11762751C2211yescharacteristic, complemented
69#11762745C2211yescharacteristic
70#11762745C2211yescharacteristic, complemented
71#11762744C2211yescharacteristic, complemented
72#11762743C2211yescharacteristic, complemented
73#11762743C2211yescharacteristic, complemented
74#11762740C2211yescharacteristic, complemented
75#11762740C2211yescharacteristic, complemented
76#11762738C2211yescharacteristic, complemented
77#11762737C2211yescharacteristic
78#11762737C2211yescharacteristic
79#11762734C2211yescharacteristic, complemented
80#11762733C2211yescharacteristic, complemented
81#11762732C2211yescharacteristic
82#11762732C2211yescharacteristic, complemented
83#11762732C2211yescharacteristic, complemented
84#11762730C2211yescharacteristic, complemented
85#11762730C2211yescharacteristic, complemented
86#11762729C2211yescharacteristic, complemented
87#11762729C2211yescharacteristic, complemented
88#11762725C2211yescharacteristic
89#11762725C2211yescharacteristic
90#11762725C2211yescharacteristic
91#11762725C2211yescharacteristic, complemented
92#11762724C2211yescharacteristic
93#11762724C2211yescharacteristic
94#11762724C2211yescharacteristic, complemented
95#11762724C2211yescharacteristic, complemented
96#11762723C2211yescharacteristic
97#11762723C2211yescharacteristic
98#11762723C2211yescharacteristic
99#11762723C2211yescharacteristic, complemented
100#11762722C2211yescharacteristic, complemented
101#11762722C2211yescharacteristic, complemented
102#11762721C2211yescharacteristic
103#11762721C2211yescharacteristic
104#11762721C2211yescharacteristic
105#11762721C2211yescharacteristic, complemented
106#11762717C2211yescharacteristic
107#11762717C2211yescharacteristic
108#11762717C2211yescharacteristic
109#11762713C2211yescharacteristic, complemented
110#11762712C2211yescharacteristic
111#11762709C2211yescharacteristic
112#11762709C2211yescharacteristic
113#11762709C2211yescharacteristic
114#11762706C2211yescharacteristic, complemented
115#11762704C2211yescharacteristic, complemented
116#11762704C2211yescharacteristic, complemented
117#11762703C2211yescharacteristic
118#11762703C2211yescharacteristic, complemented
119#11762702C2211yescharacteristic
120#11762702C2211yescharacteristic
121#11762702C2211yescharacteristic, complemented
122#11762701C2211yescharacteristic, complemented
123#11762697C2211yescharacteristic
124#11762697C2211yescharacteristic
125#11762697C2211yescharacteristic
126#11762697C2211yescharacteristic
127#11762696C2211yescharacteristic, complemented
128#11762694C2211yescharacteristic, complemented
129#11762694C2211yescharacteristic, complemented
130#11762692C2211yescharacteristic, complemented
131#11762692C2211yescharacteristic, complemented
132#11762692C2211yescharacteristic, complemented
133#11762691C2211yescharacteristic, complemented
134#11762691C2211yescharacteristic, complemented
135#11762689C2211yescharacteristic
136#11762689C2211yescharacteristic
137#11762689C2211yescharacteristic
138#11762689C2211yescharacteristic
139#11762689C2211yescharacteristic
140#11762689C2211yescharacteristic
141#11762689C2211yescharacteristic
142#11762688C2211yescharacteristic, complemented
143#11762688C2211yescharacteristic, complemented
144#11762685C2211yescharacteristic, complemented
145#11762684C2211yescharacteristic
146#11762684C2211yescharacteristic
147#11762684C2211yescharacteristic
148#11762683C2211yescharacteristic, complemented
149#11762682C2211yescharacteristic, complemented
150#11762682C2211yescharacteristic, complemented
151#11762681C2211yescharacteristic
152#11762681C2211yescharacteristic
153#11762681C2211yescharacteristic
154#11762681C2211yescharacteristic
155#11762681C2211yescharacteristic
156#11762681C2211yescharacteristic
157#11762681C2211yescharacteristic
158#11762681C2211yescharacteristic, complemented
159#11762680C2211yescharacteristic, complemented
160#11762680C2211yescharacteristic, complemented
161#11762676C2211yescharacteristic, complemented
162#11762673C2211yescharacteristic, complemented
163#11762670C2211yescharacteristic
164#11762670C2211yescharacteristic
165#11762669C2211yescharacteristic, complemented
166#11762667C2211yescharacteristic
167#11762667C2211yescharacteristic
168#11762667C2211yescharacteristic
169#11762667C2211yescharacteristic, complemented
170#11762665C2211yescharacteristic
171#11762665C2211yescharacteristic
172C22⋊C4×Dic17C2211yescharacteristic, complemented
173C2×#10587502C2211yescharacteristic, complemented
174C2×C17×#121C2211yescharacteristic
175C2×C17×#121C2211yescharacteristic
176C2×C17×#120C2211yescharacteristic
177C2×C17×#120C2211yescharacteristic
178C17×#399C2211yescharacteristic
179C17×#397C2211yescharacteristic
180C17×#397C2211yescharacteristic
181C17×#394C2211yescharacteristic
182C17×#394C2211yescharacteristic
183C17×#392C2211yescharacteristic
184C17×#386C2211yescharacteristic
185C17×#386C2211yescharacteristic
186C17×#386C2211yescharacteristic
187C17×#386C2211yescharacteristic
188C17×#379C2211yescharacteristic
189C25×C17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C22×D4×C17C2311yescharacteristic
193C22×D4×C17C2311yescharacteristic
194C22×D4×C17C2311yescharacteristic
195C22×D4×C17C2311yescharacteristic
196C22×D4×C17C2311yescharacteristic
197C23×C4×C17C2311yescharacteristic
198C23×C4×C17C2311yescharacteristic
199C22×C22⋊D17C2311yescharacteristic
200C22×C22⋊D17C2311yescharacteristic
201C22×C22⋊D17C2311yescharacteristic
202C22×C22⋊D17C2311yescharacteristic
203C22×C22⋊D17C2311yescharacteristic
204C23×Dic17—24no—
205C23×Dic17—42no—
206C23×Dic17—42no—
207C23×Dic17C2311yescharacteristic
208C23×Dic17C2311yescharacteristic
209C23×Dic17C2311yescharacteristic
210C23×Dic17C2311yescharacteristic
211C23×Dic17C2311yescharacteristic
212C23×Dic17C2311yescharacteristic
213C23×Dic17C2311yescharacteristic
214C23×Dic17C2311yescharacteristic
215C2×#63254—24no—
216C2×#63254—42no—
217C2×#63254—42no—
218C22×C4×D17C2311yescharacteristic
219C22×Dic34C2311yescharacteristic
220C22×Dic34C2311yescharacteristic
221C22×Dic34C2311yescharacteristic
222C22×Dic34C2311yescharacteristic
223C17×#121—24no—
224C17×#121—42no—
225C17×#120—24no—
226C17×#120—42no—
227C2×C4⋊C4×C17C2311yescharacteristic
228C2×C4⋊C4×C17C2311yescharacteristic
229C2×C4⋊C4×C17C2311yescharacteristic
230C2×C22⋊C4×C17C2311yescharacteristic
231C2×C22⋊C4×C17C2311yescharacteristic
232C2×C22⋊C4×C17C2311yescharacteristic
233C2×C22⋊C4×C17C2311yescharacteristic
234C2×C22⋊C4×C17C2311yescharacteristic
235C2×C22⋊C4×C17C2311yescharacteristic
236C2×C22⋊C4×C17C2311yescharacteristic
237C2×C22⋊C4×C17C2311yescharacteristic
238C2×C22⋊C4×C17C2311yescharacteristic
239C2×C22⋊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
246#10587639—24no—
247C2×C22⋊Dic17C2311yescharacteristic
248C2×C22⋊Dic17C2311yescharacteristic
249C2×C22⋊Dic17C2311yescharacteristic
250C2×C22⋊Dic17C2311yescharacteristic
251C2×C22⋊Dic17C2311yescharacteristic
252C2×C22⋊Dic17C2311yescharacteristic
253C2×C22⋊Dic17C2311yescharacteristic
254C2×C22⋊Dic17C2311yescharacteristic
255C2×C22⋊Dic17C2311yescharacteristic
256C2×C22⋊Dic17C2311yescharacteristic
257C2×C22⋊Dic17C2311yescharacteristic
258C2×C22⋊Dic17C2311yescharacteristic
259C2×C22⋊Dic17C2311yescharacteristic
260C2×C22⋊Dic17C2311yescharacteristic
261C2×C22⋊Dic17C2311yescharacteristic
262C2×C22⋊Dic17C2311yescharacteristic
263C2×C22⋊Dic17C2311yescharacteristic
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
274#10587625—24no—
275#10587625—24no—
276#10587625—42no—
277#10587622—24no—
278#10587622—24no—
279#10587622—24no—
280#10587621—24no—
281#10587621—24no—
282#10587621—24no—
283#10587621—42no—
284D4×Dic17—24no—
285D4×Dic17D418yescomplemented
286C2×#63227C2311yescharacteristic
287C2×#63227C2311yescharacteristic
288C2×#63227C2311yescharacteristic
289C2×#63227C2311yescharacteristic
290C2×#63227C2311yescharacteristic
291C2×#63227C2311yescharacteristic
292C2×#63227C2311yescharacteristic
293C2×#63227C2311yescharacteristic
294C2×#63227C2311yescharacteristic
295#10587612—24no—
296C2×C4⋊Dic17C2311yescharacteristic
297C2×C4⋊Dic17C2311yescharacteristic
298C2×C4⋊Dic17C2311yescharacteristic
299C2×C4⋊Dic17C2311yescharacteristic
300C2×C4⋊Dic17C2311yescharacteristic
301C2×C4⋊Dic17C2311yescharacteristic
302C2×C4⋊Dic17C2311yescharacteristic
303C2×C4⋊Dic17C2311yescharacteristic
304#10587610—24no—
305C2×#63225C2311yescharacteristic
306C2×#63225C2311yescharacteristic
307C2×#63225C2311yescharacteristic
308C2×#63225C2311yescharacteristic
309C2×#63225C2311yescharacteristic
310C2×#63225C2311yescharacteristic
311C2×#63225C2311yescharacteristic
312C2×#63225C2311yescharacteristic
313C2×#63225C2311yescharacteristic
314C2×#63225C2311yescharacteristic
315C2×#63225C2311yescharacteristic
316C2×#63225C2311yescharacteristic
317C2×#63225C2311yescharacteristic
318C2×#63225C2311yescharacteristic
319C2×#63225C2311yescharacteristic
320C2×#63225C2311yescharacteristic
321C2×#63225C2311yescharacteristic
322C2×#63225C2311yescharacteristic
323C2×#63225C2311yescharacteristic
324C2×#63225C2311yescharacteristic
325C2×#63225C2311yescharacteristic
326C2×C4×Dic17C2311yescharacteristic
327C2×C4×Dic17C2311yescharacteristic
328C2×C4×Dic17C2311yescharacteristic
329C2×C4×Dic17C2311yescharacteristic
330C2×C4×Dic17C2311yescharacteristic
331C2×C4×Dic17C2311yescharacteristic
332C2×C4×Dic17C2311yescharacteristic
333#10587574—24no—
334#10587574—42no—
335#10587573—24no—
336#10587572—24no—
337#10587571—42no—
338#10587567—24no—
339#10587567—24no—
340#10587565—24no—
341#10587565—24no—
342#10587564—24no—
343#10587564—24no—
344#10587564—24no—
345#10587564—24no—
346#10587564—42no—
347#10587564—42no—
348#10587563—24no—
349C17×#95C2311yescharacteristic
350C17×#95C2311yescharacteristic
351C17×#95C2311yescharacteristic
352C17×#95C2311yescharacteristic
353C17×#95C2311yescharacteristic
354C17×#95C2311yescharacteristic
355#10587502C2311yescharacteristic
356#10587502C2311yescharacteristic
357#10587502C2311yescharacteristic
358#10587502C2311yescharacteristic
359#10587502C2311yescharacteristic
360#10587502C2311yescharacteristic
361#10587502C2311yescharacteristic
362#10587502C2311yescharacteristic
363#10587502C2311yescharacteristic
364#10587502C2311yescharacteristic
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
385C24×C17—22no—
386C24×C17—22no—
387C24×C17—22no—
388C24×C17—41no—
389C24×C17—41no—
390C24×C17—41no—
391C24×C17—41no—
392C24×C17C2411yescharacteristic
393C24×C17C2411yescharacteristic
394C24×C17C2411yescharacteristic
395C24×C17C2411yescharacteristic
396C24×C17C2411yescharacteristic
397C23×D17C2411yescharacteristic
398C2×D4×C17—22no—
399C2×D4×C17—22no—
400C2×D4×C17—22no—
401C2×D4×C17—22no—
402C2×D4×C17—22no—
403C2×D4×C17—22no—
404C2×D4×C17—22no—
405C2×D4×C17—22no—
406C2×D4×C17—41no—
407C2×D4×C17—41no—
408C2×D4×C17—41no—
409C2×D4×C17—41no—
410C2×D4×C17—41no—
411C2×D4×C17—41no—
412C2×D4×C17—41no—
413C2×D4×C17—41no—
414C2×D4×C17—41no—
415C2×D4×C17—41no—
416C2×D4×C17—41no—
417C2×D4×C17—41no—
418C2×D4×C17C2×D414yes—
419C22×C4×C17—22no—
420C22×C4×C17—41no—
421C22×C4×C17—41no—
422C22×C4×C17—41no—
423C22×C4×C17—41no—
424C22×C4×C17—41no—
425C22×C4×C17C2411yescharacteristic
426C22×C4×C17C2411yescharacteristic
427C22×C4×C17C2411yescharacteristic
428C22×C4×C17C2411yescharacteristic
429C22×C4×C17C2411yescharacteristic
430C22×C4×C17C2411yescharacteristic
431C22×C4×C17C2411yescharacteristic
432C22×C4×C17C2411yescharacteristic
433C22×C4×C17C2411yescharacteristic
434C22×C4×C17C2411yescharacteristic
435C2×C22⋊D17—22no—
436C2×C22⋊D17—22no—
437C2×C22⋊D17—22no—
438C2×C22⋊D17—22no—
439C2×C22⋊D17—22no—
440C2×C22⋊D17—22no—
441C2×C22⋊D17—22no—
442C2×C22⋊D17—41no—
443C2×C22⋊D17—41no—
444C2×C22⋊D17—41no—
445C2×C22⋊D17—41no—
446C2×C22⋊D17—41no—
447C2×C22⋊D17—41no—
448C2×C22⋊D17—41no—
449C2×C22⋊D17—41no—
450C22×Dic17—22no—
451C22×Dic17—22no—
452C22×Dic17—22no—
453C22×Dic17—22no—
454C22×Dic17—22no—
455C22×Dic17—22no—
456C22×Dic17—22no—
457C22×Dic17—22no—
458C22×Dic17—22no—
459C22×Dic17—22no—
460C22×Dic17—41no—
461C22×Dic17—41no—
462C22×Dic17—41no—
463C22×Dic17—41no—
464C22×Dic17—41no—
465C22×Dic17—41no—
466C22×Dic17—41no—
467C22×Dic17—41no—
468C22×Dic17—41no—
469C22×Dic17—41no—
470C22×Dic17—41no—
471C22×Dic17—41no—
472C22×Dic17—416no—
473C22×Dic17C2×D414yes—
474C22×Dic17C2×D414yes—
475C22×Dic17C2411yescharacteristic
476C22×Dic17C2411yescharacteristic
477C22×Dic17C2411yescharacteristic
478C22×Dic17C2411yescharacteristic
479C22×Dic17C2411yescharacteristic
480C22×Dic17C2411yescharacteristic
481C22×Dic17C2411yescharacteristic
482C22×Dic17C2411yescharacteristic
483C22×Dic17C2411yescharacteristic
484C22×Dic17C2411yescharacteristic
485C22×Dic17C2411yescharacteristic
486C22×Dic17C2411yescharacteristic
487C22×Dic17C2411yescharacteristic
488C22×Dic17C2411yescharacteristic
489C22×Dic17C2411yescharacteristic
490#63254—416no—
491C2×C4×D17—22no—
492C2×C4×D17—41no—
493C2×C4×D17—41no—
494C2×Dic34—22no—
495C2×Dic34—22no—
496C2×Dic34—22no—
497C2×Dic34—22no—
498C2×Dic34—22no—
499C2×Dic34—41no—
500C2×Dic34—41no—
501C2×Dic34—41no—
502C2×Dic34—41no—
503C2×Dic34—41no—
504C2×Dic34—41no—
505C2×Dic34—41no—
506C4⋊C4×C17—22no—
507C4⋊C4×C17—41no—
508C4⋊C4×C17—41no—
509C22⋊C4×C17—22no—
510C22⋊C4×C17—22no—
511C22⋊C4×C17—22no—
512C22⋊C4×C17—22no—
513C22⋊C4×C17—22no—
514C22⋊C4×C17—22no—
515C22⋊C4×C17—22no—
516C22⋊C4×C17—41no—
517C22⋊C4×C17—41no—
518C22⋊C4×C17—41no—
519C22⋊C4×C17—41no—
520C22⋊C4×C17—41no—
521C22⋊C4×C17—41no—
522C22⋊C4×C17—41no—
523C22⋊C4×C17—41no—
524C22⋊C4×C17—41no—
525C22⋊Dic17—22no—
526C22⋊Dic17—22no—
527C22⋊Dic17—22no—
528C22⋊Dic17—22no—
529C22⋊Dic17—22no—
530C22⋊Dic17—22no—
531C22⋊Dic17—22no—
532C22⋊Dic17—22no—
533C22⋊Dic17—22no—
534C22⋊Dic17—22no—
535C22⋊Dic17—22no—
536C22⋊Dic17—22no—
537C22⋊Dic17—22no—
538C22⋊Dic17—22no—
539C22⋊Dic17—41no—
540C22⋊Dic17—41no—
541C22⋊Dic17—41no—
542C22⋊Dic17—41no—
543C22⋊Dic17—41no—
544C22⋊Dic17—41no—
545C22⋊Dic17—41no—
546C22⋊Dic17—41no—
547C22⋊Dic17—41no—
548C22⋊Dic17—41no—
549C22⋊Dic17—41no—
550C22⋊Dic17C2×D414yes—
551C22⋊Dic17C2×D414yes—
552#63227—22no—
553#63227—22no—
554#63227—41no—
555#63227—41no—
556#63227—41no—
557#63227—41no—
558#63227—41no—
559#63227—41no—
560#63227—41no—
561C4⋊Dic17—22no—
562C4⋊Dic17—22no—
563C4⋊Dic17—22no—
564C4⋊Dic17—22no—
565C4⋊Dic17—41no—
566C4⋊Dic17—41no—
567C4⋊Dic17—41no—
568C4⋊Dic17C2×D414yes—
569#63225—22no—
570#63225—22no—
571#63225—22no—
572#63225—22no—
573#63225—22no—
574#63225—22no—
575#63225—22no—
576#63225—22no—
577#63225—22no—
578#63225—22no—
579#63225—22no—
580#63225—22no—
581#63225—41no—
582#63225—41no—
583#63225—41no—
584#63225—41no—
585#63225—41no—
586#63225—41no—
587#63225—41no—
588#63225—41no—
589#63225—41no—
590C4×Dic17—22no—
591C4×Dic17—22no—
592C4×Dic17—22no—
593C4×Dic17—22no—
594C4×Dic17—41no—
595C4×Dic17—41no—
596C4×Dic17C2×D414yes—
597#36712—171nomaximal, Sylow
598C23×C17—21no—
599C23×C17—21no—
600C23×C17—21no—
601C23×C17—21no—
602C23×C17—21no—
603C23×C17—21no—
604C23×C17—21no—
605C23×C17—21no—
606C23×C17—21no—
607C23×C17—21no—
608C23×C17—21no—
609C23×C17—21no—
610C23×C17—21no—
611C23×C17—21no—
612C23×C17—21no—
613C23×C17—21no—
614C23×C17—21no—
615C23×C17—21no—
616C23×C17—21no—
617C23×C17—21no—
618C23×C17—21no—
619C23×C17—21no—
620C23×C17—21no—
621C23×C17—21no—
622C23×C17—21no—
623C23×C17—21no—
624C23×C17—21no—
625C23×C17—21no—
626C23×C17—21no—
627C23×C17—21no—
628C23×C17—21no—
629C23×C17—44no—
630C23×C17—44no—
631C23×C17—44no—
632C23×C17—44no—
633C23×C17—44no—
634C23×C17—44no—
635C23×C17—44no—
636C23×C17C22×D412yes—
637C23×C17C22×D412yes—
638C23×C17H(5,𝔽2)12yes—
639C23×C172−1+412yes—
640C23×C17C2511yescharacteristic
641C22×D17—21no—
642C22×D17—21no—
643C22×D17—21no—
644C22×D17—21no—
645C22×D17—21no—
646C22×D17—21no—
647C22×D17—21no—
648D4×C17—44no—
649D4×C17—44no—
650D4×C17—44no—
651D4×C17—82no—
652D4×C17—82no—
653D4×C17—82no—
654D4×C17—82no—
655C2×C4×C17—21no—
656C2×C4×C17—21no—
657C2×C4×C17—21no—
658C2×C4×C17—21no—
659C2×C4×C17—21no—
660C2×C4×C17—21no—
661C2×C4×C17—21no—
662C2×C4×C17—21no—
663C2×C4×C17—21no—
664C2×C4×C17—21no—
665C2×C4×C17—21no—
666C2×C4×C17—21no—
667C2×C4×C17—21no—
668C2×C4×C17—21no—
669C2×C4×C17—21no—
670C2×C4×C17—21no—
671C2×C4×C17—21no—
672C2×C4×C17—21no—
673C2×C4×C17—21no—
674C2×C4×C17—21no—
675C2×C4×C17—21no—
676C2×C4×C17—21no—
677C2×C4×C17—21no—
678C2×C4×C17—21no—
679C2×C4×C17—21no—
680C2×C4×C17—21no—
681C2×C4×C17—21no—
682C2×C4×C17—21no—
683C2×C4×C17—21no—
684C2×C4×C17—44no—
685C2×C4×C17—82no—
686C2×C4×C17C22×D412yes—
687C22⋊D17—44no—
688C22⋊D17—44no—
689C22⋊D17—44no—
690C22⋊D17—44no—
691C22⋊D17—82no—
692C2×Dic17—28no—
693C2×Dic17—21no—
694C2×Dic17—21no—
695C2×Dic17—21no—
696C2×Dic17—21no—
697C2×Dic17—21no—
698C2×Dic17—21no—
699C2×Dic17—21no—
700C2×Dic17—21no—
701C2×Dic17—21no—
702C2×Dic17—21no—
703C2×Dic17—21no—
704C2×Dic17—21no—
705C2×Dic17—21no—
706C2×Dic17—21no—
707C2×Dic17—21no—
708C2×Dic17—21no—
709C2×Dic17—21no—
710C2×Dic17—21no—
711C2×Dic17—21no—
712C2×Dic17—21no—
713C2×Dic17—21no—
714C2×Dic17—21no—
715C2×Dic17—21no—
716C2×Dic17—21no—
717C2×Dic17—21no—
718C2×Dic17—21no—
719C2×Dic17—21no—
720C2×Dic17—21no—
721C2×Dic17—21no—
722C2×Dic17—21no—
723C2×Dic17—21no—
724C2×Dic17—21no—
725C2×Dic17—21no—
726C2×Dic17—21no—
727C2×Dic17—21no—
728C2×Dic17—21no—
729C2×Dic17—21no—
730C2×Dic17—21no—
731C2×Dic17—21no—
732C2×Dic17—21no—
733C2×Dic17—44no—
734C2×Dic17—44no—
735C2×Dic17—44no—
736C2×Dic17—44no—
737C2×Dic17—44no—
738C2×Dic17—44no—
739C2×Dic17—82no—
740C2×Dic17C22×D412yes—
741C2×Dic17C22×D412yes—
742C2×Dic17C22×D412yes—
743C2×Dic17C22×D412yes—
744C2×Dic17H(5,𝔽2)12yes—
745C4×D17—44no—
746Dic34—44no—
747Dic34—44no—
748Dic34—82no—
749Dic34—82no—
750C2×#542—171no—
751C2×#525—171no—
752#2849—171no—
753#2848—171no—
754#2696—171no—
755#2695—171no—
756#2692—171no—
757#2691—171no—
758#2689—171no—
759#2686—171no—
760#2685—171no—
761#2684—171no—
762#2677—171no—
763#2676—171no—
764#2674—171no—
765#2674—171no—
766#2672—171no—
767#2671—171no—
768#2670—171no—
769#2668D1711yescharacteristic, complemented
770#2638—171no—
771#2630—171no—
772#2609—171no—
773#2602—171no—
774#2599—171no—
775#2598—171no—
776#2580—171no—
777#2564—171no—
778#2432—171no—
779#2430—171no—
780#2318—171no—
781C22×C17—22no—
782C22×C17—22no—
783C22×C17—22no—
784C22×C17—22no—
785C22×C17—22no—
786C22×C17—22no—
787C22×C17—22no—
788C22×C17—22no—
789C22×C17—22no—
790C22×C17—22no—
791C22×C17—22no—
792C22×C17—22no—
793C22×C17—416no—
794C22×C17—41no—
795C22×C17—41no—
796C22×C17—41no—
797C22×C17—41no—
798C22×C17—41no—
799C22×C17—41no—
800C22×C17—41no—
801C22×C17—41no—
802C22×C17—41no—
803C22×C17—41no—
804C22×C17—41no—
805C22×C17—41no—
806C22×C17—41no—
807C22×C17—41no—
808C22×C17—41no—
809C22×C17—41no—
810C22×C17—41no—
811C22×C17—41no—
812C22×C17—41no—
813C22×C17—41no—
814C22×C17—41no—
815C22×C17—41no—
816C22×C17—41no—
817C22×C17C23×D411yescharacteristic
818C22×C17C2×H(5,𝔽2)11yescharacteristic
819C22×C17C2×H(5,𝔽2)11yescharacteristic
820C22×C17C2×2−1+411yescharacteristic
821C22×C17#58511yescharacteristic
822C22×C17#58511yescharacteristic
823C22×C17#58511yescharacteristic
824C2×D17—41no—
825C2×D17—41no—
826C2×D17—41no—
827C2×D17—41no—
828C2×D17—41no—
829C2×D17—41no—
830C2×D17—41no—
831C4×C17—22no—
832C4×C17—41no—
833C4×C17—41no—
834C4×C17—41no—
835C4×C17—41no—
836C4×C17—41no—
837C4×C17—41no—
838C4×C17—41no—
839C4×C17—41no—
840C4×C17—41no—
841Dic17—22no—
842Dic17—22no—
843Dic17—22no—
844Dic17—22no—
845Dic17—22no—
846Dic17—41no—
847Dic17—41no—
848Dic17—41no—
849Dic17—41no—
850Dic17—41no—
851Dic17—41no—
852Dic17—41no—
853Dic17—41no—
854Dic17—41no—
855Dic17—41no—
856C22×#41—171no—
857C24×C4—171no—
858#542—348no—
859C2×C4⋊Q8—171no—
860C2×C4⋊Q8—171no—
861C2×#126—171no—
862C2×#126—171no—
863C2×#124—171no—
864C2×#124—171no—
865C2×#124—171no—
866C2×#124—171no—
867#525—348no—
868C2×#123—171no—
869C2×#123—171no—
870C2×#123—171no—
871C2×#123—171no—
872C2×#123—171no—
873C2×C22⋊Q8—171no—
874C2×C22⋊Q8—171no—
875C2×C22⋊Q8—171no—
876C2×C22⋊Q8—171no—
877C2×C22⋊Q8—171no—
878C2×C22⋊Q8—171no—
879C2×C22⋊Q8—171no—
880C2×#121—171no—
881C2×#121—171no—
882C2×#121—171no—
883C2×#121C2×D1711yescharacteristic
884C2×#121C2×D1711yescharacteristic
885C2×#120—171no—
886C2×#120C2×D1711yescharacteristic
887C2×#120C2×D1711yescharacteristic
888C2×C4×Q8—171no—
889C2×C4×D4—171no—
890C2×C4×D4—171no—
891C2×C4×D4—171no—
892C2×C4×D4—171no—
893C2×#117—171no—
894C2×#117—171no—
895#400—171no—
896#400—171no—
897#399—171no—
898#399—171no—
899#399—171no—
900#399C2×D1711yescharacteristic
901#398—171no—
902#398—171no—
903#398—171no—
904#398—171no—
905#397—171no—
906#397—171no—
907#397—171no—
908#397—171no—
909#397C2×D1711yescharacteristic
910#397C2×D1711yescharacteristic
911#396—171no—
912#396—171no—
913#396—171no—
914#396—171no—
915#395—171no—
916#395—171no—
917#395—171no—
918#395—171no—
919#394—171no—
920#394—171no—
921#394—171no—
922#394—171no—
923#394—171no—
924#394—171no—
925#394—171no—
926#394—171no—
927#394—171no—
928#394—171no—
929#394—171no—
930#394—171no—
931#394C2×D1711yescharacteristic
932#394C2×D1711yescharacteristic
933#393—171no—
934#393—171no—
935#393—171no—
936#393—171no—
937#393—171no—
938#393—171no—
939#392—171no—
940#392—171no—
941#392—171no—
942#392C2×D1711yescharacteristic
943#391—171no—
944#390—171no—
945#390—171no—
946#390—171no—
947#390—171no—
948#389—171no—
949#389—171no—
950#389—171no—
951#388—171no—
952#388—171no—
953#388—171no—
954#388—171no—
955#388—171no—
956#388—171no—
957#388—171no—
958#388—171no—
959#388—171no—
960#388—171no—
961#387—171no—
962#387—171no—
963#387—171no—
964#387—171no—
965#387—171no—
966#387—171no—
967#387—171no—
968#387—171no—
969#386—171no—
970#386—171no—
971#386—171no—
972#386—171no—
973#386—171no—
974#386—171no—
975#386—171no—
976#386—171no—
977#386—171no—
978#386—171no—
979#386C2×D1711yescharacteristic
980#386C2×D1711yescharacteristic
981#386C2×D1711yescharacteristic
982#386C2×D1711yescharacteristic
983#385—171no—
984#385—171no—
985#385—171no—
986#385—171no—
987#385—171no—
988#385—171no—
989#385—171no—
990#385—171no—
991#385—171no—
992#385—171no—
993#385—171no—
994#385—171no—
995#385—171no—
996#385—171no—
997#385—171no—
998#385—171no—
999#383—171no—
1000#382—171no—
1001#381—171no—
1002#381—171no—
1003#380—171no—
1004#380—171no—
1005#380—171no—
1006#380—171no—
1007#380—171no—
1008#379—171no—
1009#379—171no—
1010#379C2×D1711yescharacteristic
1011C4×C22⋊C4—171no—
1012C2×#95—171no—
1013C2×C17—42no—
1014C2×C17—42no—
1015C2×C17—42no—
1016C2×C17—42no—
1017C2×C17—81no—
1018C2×C17#344911yescharacteristic
1019C2×C17#348411yescharacteristic
1020C2×C17#348911yescharacteristic
1021C2×C17#353311yescharacteristic
1022C2×C17#353511yescharacteristic
1023C2×C17#354011yescharacteristic
1024C2×C17#354111yescharacteristic
1025D17—81no—
1026C25C22×D1711yescharacteristic
1027C2×#41—344no—
1028C2×#41—682no—
1029C2×#41—682no—
1030C22×Q8—171no—
1031C22×Q8—171no—
1032C22×Q8—171no—
1033C22×Q8—171no—
1034C22×D4—171no—
1035C22×D4—171no—
1036C22×D4—171no—
1037C22×D4—171no—
1038C22×D4—171no—
1039C22×D4C22×D1711yescharacteristic
1040C22×D4C22×D1711yescharacteristic
1041C22×D4C22×D1711yescharacteristic
1042C22×D4C22×D1711yescharacteristic
1043C22×D4C22×D1711yescharacteristic
1044C22×D4C22×D1711yescharacteristic
1045C22×D4C22×D1711yescharacteristic
1046C23×C4—171no—
1047C23×C4—171no—
1048C23×C4—171no—
1049C23×C4—171no—
1050C23×C4—171no—
1051C23×C4—171no—
1052C23×C4—171no—
1053C23×C4—171no—
1054C23×C4—171no—
1055C23×C4—344no—
1056C23×C4—682no—
1057C23×C4—682no—
1058C23×C4C22×D1711yescharacteristic
1059C23×C4C22×D1711yescharacteristic
1060C4⋊Q8—344no—
1061C4⋊Q8—682no—
1062#126—344no—
1063#126—344no—
1064#124—344no—
1065#124—344no—
1066#124—344no—
1067#124—682no—
1068#123—344no—
1069#123—344no—
1070#123—344no—
1071#123—344no—
1072#123—682no—
1073C22⋊Q8—344no—
1074C22⋊Q8—344no—
1075C22⋊Q8—344no—
1076C22⋊Q8—344no—
1077C22⋊Q8—344no—
1078C22⋊Q8—682no—
1079C22⋊Q8—682no—
1080#121—24no—
1081#121—42no—
1082#121—344no—
1083#121—344no—
1084#121—682no—
1085#120—24no—
1086#120—42no—
1087#120—344no—
1088C4×Q8—344no—
1089C4×D4—178no—
1090C4×D4—344no—
1091C4×D4—344no—
1092C4×D4—344no—
1093#117—344no—
1094#117—344no—
1095C2×C4⋊C4—171no—
1096C2×C4⋊C4—171no—
1097C2×C4⋊C4—171no—
1098C2×C4⋊C4—171no—
1099C2×C4⋊C4—171no—
1100C2×C4⋊C4—171no—
1101C2×C4⋊C4—171no—
1102C2×C4⋊C4—171no—
1103C2×C4⋊C4—171no—
1104C2×C4⋊C4—171no—
1105C2×C4⋊C4—171no—
1106C2×C4⋊C4—171no—
1107C2×C4⋊C4—171no—
1108C2×C4⋊C4—171no—
1109C2×C4⋊C4—171no—
1110C2×C4⋊C4—171no—
1111C2×C4⋊C4—171no—
1112C2×C4⋊C4—171no—
1113C2×C4⋊C4—171no—
1114C2×C4⋊C4—171no—
1115C2×C4⋊C4—171no—
1116C2×C4⋊C4—171no—
1117C2×C4⋊C4—171no—
1118C2×C4⋊C4—171no—
1119C2×C4⋊C4—171no—
1120C2×C4⋊C4—171no—
1121C2×C4⋊C4—171no—
1122C2×C4⋊C4—171no—
1123C2×C4⋊C4—171no—
1124C2×C4⋊C4C22×D1711yescharacteristic
1125C2×C4⋊C4C22×D1711yescharacteristic
1126C2×C4⋊C4C22×D1711yescharacteristic
1127C2×C22⋊C4—171no—
1128C2×C22⋊C4—171no—
1129C2×C22⋊C4—171no—
1130C2×C22⋊C4—171no—
1131C2×C22⋊C4—171no—
1132C2×C22⋊C4—171no—
1133C2×C22⋊C4—171no—
1134C2×C22⋊C4—171no—
1135C2×C22⋊C4—171no—
1136C2×C22⋊C4—171no—
1137C2×C22⋊C4—171no—
1138C2×C22⋊C4—171no—
1139C2×C22⋊C4—171no—
1140C2×C22⋊C4—171no—
1141C2×C22⋊C4—171no—
1142C2×C22⋊C4—171no—
1143C2×C22⋊C4—171no—
1144C2×C22⋊C4—171no—
1145C2×C22⋊C4—171no—
1146C2×C22⋊C4—171no—
1147C2×C22⋊C4—171no—
1148C2×C22⋊C4—171no—
1149C2×C22⋊C4—171no—
1150C2×C22⋊C4—171no—
1151C2×C22⋊C4—171no—
1152C2×C22⋊C4—171no—
1153C2×C22⋊C4—171no—
1154C2×C22⋊C4—171no—
1155C2×C22⋊C4—171no—
1156C2×C22⋊C4—171no—
1157C2×C22⋊C4—171no—
1158C2×C22⋊C4—171no—
1159C2×C22⋊C4—171no—
1160C2×C22⋊C4—171no—
1161C2×C22⋊C4—171no—
1162C2×C22⋊C4—171no—
1163C2×C22⋊C4C22×D1711yescharacteristic
1164C2×C22⋊C4C22×D1711yescharacteristic
1165C2×C22⋊C4C22×D1711yescharacteristic
1166C2×C22⋊C4C22×D1711yescharacteristic
1167C2×C22⋊C4C22×D1711yescharacteristic
1168C2×C22⋊C4C22×D1711yescharacteristic
1169C2×C22⋊C4C22×D1711yescharacteristic
1170C2×C22⋊C4C22×D1711yescharacteristic
1171C2×C22⋊C4C22×D1711yescharacteristic
1172C2×C22⋊C4C22×D1711yescharacteristic
1173C2×C22⋊C4C22×D1711yescharacteristic
1174C2×C22⋊C4C22×D1711yescharacteristic
1175C2×C22⋊C4C22×D1711yescharacteristic
1176C2×C22⋊C4C22×D1711yescharacteristic
1177C2×C22⋊C4C22×D1711yescharacteristic
1178C2×C22⋊C4C22×D1711yescharacteristic
1179C2×C42—171no—
1180C2×C42—171no—
1181C2×C42—171no—
1182C2×C42—171no—
1183C2×C42—171no—
1184C2×C42—171no—
1185C2×C42—171no—
1186#95—171no—
1187#95—171no—
1188#95—171no—
1189#95—171no—
1190#95—171no—
1191#95—171no—
1192#95—171no—
1193#95—171no—
1194#95—171no—
1195#95—171no—
1196#95—171no—
1197#95—171no—
1198#95—171no—
1199#95—171no—
1200#95—171no—
1201#95—171no—
1202#95—171no—
1203#95—171no—
1204#95—171no—
1205#95—171no—
1206#95—171no—
1207#95—171no—
1208#95—171no—
1209#95—171no—
1210#95—171no—
1211#95—171no—
1212#95—171no—
1213#95—171no—
1214#95—171no—
1215#95—171no—
1216#95C22×D1711yescharacteristic
1217#95C22×D1711yescharacteristic
1218#95C22×D1711yescharacteristic
1219#95C22×D1711yescharacteristic
1220#95C22×D1711yescharacteristic
1221#95C22×D1711yescharacteristic
1222C17#3671211yescharacteristic, complemented, Sylow
1223C24—22no—
1224C24—22no—
1225C24—22no—
1226C24—41no—
1227C24—41no—
1228C24—41no—
1229C24—41no—
1230C24—171no—
1231C24C23×D1711yescharacteristic
1232C24C23×D1711yescharacteristic
1233C24C23×D1711yescharacteristic
1234C24C23×D1711yescharacteristic
1235C24C23×D1711yescharacteristic
1236#41—6816no—
1237C2×Q8—342no—
1238C2×Q8—342no—
1239C2×Q8—342no—
1240C2×Q8—342no—
1241C2×Q8—342no—
1242C2×Q8—681no—
1243C2×Q8—681no—
1244C2×Q8—681no—
1245C2×Q8—681no—
1246C2×Q8—681no—
1247C2×Q8—681no—
1248C2×Q8—681no—
1249C2×D4—22no—
1250C2×D4—22no—
1251C2×D4—22no—
1252C2×D4—22no—
1253C2×D4—22no—
1254C2×D4—22no—
1255C2×D4—22no—
1256C2×D4—22no—
1257C2×D4—41no—
1258C2×D4—41no—
1259C2×D4—41no—
1260C2×D4—41no—
1261C2×D4—41no—
1262C2×D4—41no—
1263C2×D4—41no—
1264C2×D4—41no—
1265C2×D4—41no—
1266C2×D4—41no—
1267C2×D4—41no—
1268C2×D4—41no—
1269C2×D4—342no—
1270C2×D4—342no—
1271C2×D4—342no—
1272C2×D4—342no—
1273C2×D4—342no—
1274C2×D4—342no—
1275C2×D4—342no—
1276C2×D4—681no—
1277C2×D4—681no—
1278C2×D4—681no—
1279C2×D4—681no—
1280C2×D4—681no—
1281C2×D4—681no—
1282C2×D4—681no—
1283C2×D4—681no—
1284C2×D4D4×D1714yes—
1285C22×C4—22no—
1286C22×C4—41no—
1287C22×C4—41no—
1288C22×C4—41no—
1289C22×C4—41no—
1290C22×C4—41no—
1291C22×C4—171no—
1292C22×C4—171no—
1293C22×C4—171no—
1294C22×C4—171no—
1295C22×C4—171no—
1296C22×C4—174no—
1297C22×C4—174no—
1298C22×C4—171no—
1299C22×C4—171no—
1300C22×C4—171no—
1301C22×C4—171no—
1302C22×C4—171no—
1303C22×C4—171no—
1304C22×C4—171no—
1305C22×C4—171no—
1306C22×C4—171no—
1307C22×C4—171no—
1308C22×C4—342no—
1309C22×C4—342no—
1310C22×C4—342no—
1311C22×C4—342no—
1312C22×C4—342no—
1313C22×C4—342no—
1314C22×C4—342no—
1315C22×C4—342no—
1316C22×C4—342no—
1317C22×C4—342no—
1318C22×C4—342no—
1319C22×C4—681no—
1320C22×C4—681no—
1321C22×C4—681no—
1322C22×C4—681no—
1323C22×C4—681no—
1324C22×C4—681no—
1325C22×C4—681no—
1326C22×C4—681no—
1327C22×C4—681no—
1328C22×C4—681no—
1329C22×C4—681no—
1330C22×C4—681no—
1331C22×C4—681no—
1332C22×C4—681no—
1333C22×C4—6816no—
1334C22×C4C23×D1711yescharacteristic
1335C22×C4C23×D1711yescharacteristic
1336C22×C4C23×D1711yescharacteristic
1337C22×C4C23×D1711yescharacteristic
1338C22×C4C23×D1711yescharacteristic
1339C22×C4C23×D1711yescharacteristic
1340C22×C4C23×D1711yescharacteristic
1341C22×C4C23×D1711yescharacteristic
1342C22×C4C23×D1711yescharacteristic
1343C22×C4C23×D1711yescharacteristic
1344C4⋊C4—22no—
1345C4⋊C4—41no—
1346C4⋊C4—41no—
1347C4⋊C4—174no—
1348C4⋊C4—342no—
1349C4⋊C4—342no—
1350C4⋊C4—342no—
1351C4⋊C4—342no—
1352C4⋊C4—342no—
1353C4⋊C4—342no—
1354C4⋊C4—342no—
1355C4⋊C4—342no—
1356C4⋊C4—342no—
1357C4⋊C4—342no—
1358C4⋊C4—342no—
1359C4⋊C4—342no—
1360C4⋊C4—342no—
1361C4⋊C4—342no—
1362C4⋊C4—342no—
1363C4⋊C4—342no—
1364C4⋊C4—681no—
1365C4⋊C4—681no—
1366C4⋊C4—681no—
1367C4⋊C4—681no—
1368C4⋊C4—681no—
1369C4⋊C4—681no—
1370C4⋊C4—681no—
1371C4⋊C4—681no—
1372C4⋊C4—681no—
1373C4⋊C4—681no—
1374C4⋊C4—681no—
1375C4⋊C4—681no—
1376C22⋊C4—22no—
1377C22⋊C4—22no—
1378C22⋊C4—22no—
1379C22⋊C4—22no—
1380C22⋊C4—22no—
1381C22⋊C4—22no—
1382C22⋊C4—22no—
1383C22⋊C4—41no—
1384C22⋊C4—41no—
1385C22⋊C4—41no—
1386C22⋊C4—41no—
1387C22⋊C4—41no—
1388C22⋊C4—41no—
1389C22⋊C4—41no—
1390C22⋊C4—41no—
1391C22⋊C4—41no—
1392C22⋊C4—174no—
1393C22⋊C4—174no—
1394C22⋊C4—342no—
1395C22⋊C4—342no—
1396C22⋊C4—342no—
1397C22⋊C4—342no—
1398C22⋊C4—342no—
1399C22⋊C4—342no—
1400C22⋊C4—342no—
1401C22⋊C4—342no—
1402C22⋊C4—342no—
1403C22⋊C4—342no—
1404C22⋊C4—342no—
1405C22⋊C4—342no—
1406C22⋊C4—342no—
1407C22⋊C4—342no—
1408C22⋊C4—342no—
1409C22⋊C4—342no—
1410C22⋊C4—681no—
1411C22⋊C4—681no—
1412C22⋊C4—681no—
1413C22⋊C4—681no—
1414C22⋊C4—681no—
1415C22⋊C4—681no—
1416C22⋊C4—681no—
1417C22⋊C4—681no—
1418C22⋊C4—681no—
1419C22⋊C4—681no—
1420C22⋊C4—681no—
1421C22⋊C4—681no—
1422C22⋊C4—681no—
1423C22⋊C4—681no—
1424C22⋊C4—681no—
1425C22⋊C4—681no—
1426C22⋊C4—681no—
1427C22⋊C4—681no—
1428C42—174no—
1429C42—342no—
1430C42—342no—
1431C42—342no—
1432C42—342no—
1433C42—681no—
1434C42—681no—
1435C23—21no—
1436C23—21no—
1437C23—21no—
1438C23—21no—
1439C23—21no—
1440C23—21no—
1441C23—21no—
1442C23—21no—
1443C23—21no—
1444C23—21no—
1445C23—21no—
1446C23—21no—
1447C23—21no—
1448C23—21no—
1449C23—21no—
1450C23—21no—
1451C23—21no—
1452C23—21no—
1453C23—21no—
1454C23—21no—
1455C23—21no—
1456C23—21no—
1457C23—21no—
1458C23—21no—
1459C23—21no—
1460C23—21no—
1461C23—21no—
1462C23—21no—
1463C23—21no—
1464C23—21no—
1465C23—21no—
1466C23—44no—
1467C23—44no—
1468C23—44no—
1469C23—44no—
1470C23—44no—
1471C23—44no—
1472C23—44no—
1473C23—341no—
1474C23—341no—
1475C23—341no—
1476C23—341no—
1477C23—341no—
1478C23—341no—
1479C23—341no—
1480C23C2×D4×D1712yes—
1481C23C2×D4×D1712yes—
1482C23#1058769112yes—
1483C23#1058769712yes—
1484C23C24×D1711yescharacteristic
1485Q8—684no—
1486Q8—684no—
1487Q8—1362no—
1488Q8—1362no—
1489D4—44no—
1490D4—44no—
1491D4—44no—
1492D4—82no—
1493D4—82no—
1494D4—82no—
1495D4—82no—
1496D4—684no—
1497D4—684no—
1498D4—684no—
1499D4—684no—
1500D4—1362no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—21no—
1508C2×C4—21no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—21no—
1514C2×C4—21no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—21no—
1522C2×C4—21no—
1523C2×C4—21no—
1524C2×C4—21no—
1525C2×C4—21no—
1526C2×C4—21no—
1527C2×C4—21no—
1528C2×C4—21no—
1529C2×C4—21no—
1530C2×C4—44no—
1531C2×C4—82no—
1532C2×C4—172no—
1533C2×C4—172no—
1534C2×C4—172no—
1535C2×C4—172no—
1536C2×C4—172no—
1537C2×C4—348no—
1538C2×C4—341no—
1539C2×C4—341no—
1540C2×C4—341no—
1541C2×C4—341no—
1542C2×C4—341no—
1543C2×C4—341no—
1544C2×C4—341no—
1545C2×C4—341no—
1546C2×C4—341no—
1547C2×C4—341no—
1548C2×C4—341no—
1549C2×C4—341no—
1550C2×C4—341no—
1551C2×C4—341no—
1552C2×C4—341no—
1553C2×C4—341no—
1554C2×C4—341no—
1555C2×C4—341no—
1556C2×C4—341no—
1557C2×C4—341no—
1558C2×C4—341no—
1559C2×C4—341no—
1560C2×C4—341no—
1561C2×C4—341no—
1562C2×C4—341no—
1563C2×C4—341no—
1564C2×C4—341no—
1565C2×C4—341no—
1566C2×C4—341no—
1567C2×C4—341no—
1568C2×C4—341no—
1569C2×C4—341no—
1570C2×C4—341no—
1571C2×C4—341no—
1572C2×C4—341no—
1573C2×C4—341no—
1574C2×C4—341no—
1575C2×C4—341no—
1576C2×C4—341no—
1577C2×C4—341no—
1578C2×C4—684no—
1579C2×C4—684no—
1580C2×C4—684no—
1581C2×C4—684no—
1582C2×C4—684no—
1583C2×C4—684no—
1584C2×C4—684no—
1585C2×C4—1362no—
1586C2×C4C2×D4×D1712yes—
1587C22—22no—
1588C22—22no—
1589C22—22no—
1590C22—22no—
1591C22—22no—
1592C22—22no—
1593C22—22no—
1594C22—22no—
1595C22—22no—
1596C22—22no—
1597C22—22no—
1598C22—22no—
1599C22—416no—
1600C22—41no—
1601C22—41no—
1602C22—41no—
1603C22—41no—
1604C22—41no—
1605C22—41no—
1606C22—41no—
1607C22—41no—
1608C22—41no—
1609C22—41no—
1610C22—41no—
1611C22—41no—
1612C22—41no—
1613C22—41no—
1614C22—41no—
1615C22—41no—
1616C22—41no—
1617C22—41no—
1618C22—41no—
1619C22—41no—
1620C22—41no—
1621C22—41no—
1622C22—41no—
1623C22—681no—
1624C22—681no—
1625C22—681no—
1626C22—681no—
1627C22—681no—
1628C22—681no—
1629C22—681no—
1630C22C22×D4×D1711yescharacteristic
1631C22H(5,𝔽2)×D1711yescharacteristic
1632C22C2×#1058769111yescharacteristic
1633C22C2×#1058769711yescharacteristic
1634C22#1176364411yescharacteristic
1635C22#1176364411yescharacteristic
1636C22#1176364411yescharacteristic
1637C4—22no—
1638C4—41no—
1639C4—41no—
1640C4—41no—
1641C4—41no—
1642C4—41no—
1643C4—41no—
1644C4—41no—
1645C4—41no—
1646C4—41no—
1647C4—342no—
1648C4—342no—
1649C4—342no—
1650C4—342no—
1651C4—342no—
1652C4—681no—
1653C4—681no—
1654C4—681no—
1655C4—681no—
1656C4—681no—
1657C4—681no—
1658C4—681no—
1659C4—681no—
1660C4—681no—
1661C4—681no—
1662C2—42no—
1663C2—42no—
1664C2—42no—
1665C2—42no—
1666C2—81no—
1667C2—1361no—
1668C2#1454211011yescharacteristic
1669C2#1454241211yescharacteristic
1670C2#1454245511yescharacteristic
1671C2#1454294511yescharacteristic
1672C2#1454298111yescharacteristic
1673C2#1454305111yescharacteristic
1674C2#1454306411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2668C2
hypercenter#2668D17
hypocenterC17#36712
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2668

Complements

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

NH ≅ G/Ntype
1. C2×#11763426C2semidirect
2. C2×#11763315C2semidirect
3. #14537074C2semidirect
4. #14537069C2semidirect
5. #14535337C2semidirect
6. #14535318C2semidirect
7. #14535281C2semidirect
8. #14535262C2semidirect
9. #14535241C2semidirect
10. #14535188C2semidirect
11. #14535179C2semidirect
12. #14535162C2semidirect
13. #14535100C2semidirect
14. #14535078C2semidirect
15. #14535071C2semidirect
16. #14535067C2semidirect
17. #14535029C2semidirect
18. #14535014C2semidirect
19. #14535006C2semidirect
20. #14534703C2semidirect
21. #14534624C2semidirect
22. #14534458C2semidirect
23. #14534389C2semidirect
24. #14534362C2semidirect
25. #14534346C2semidirect
26. #14534139C2semidirect
27. #14533968C2semidirect
28. #14532407C2semidirect
29. #14532390C2semidirect
30. #14531410C2semidirect
31. C17×#2668C2semidirect
35. C2×#10587574C22semidirect
36. C2×#10587574C22semidirect
38. C2×#10587565C22semidirect
41. C2×#10587622C22semidirect
48. C2×#10587621C22semidirect
49. C2×#10587610C22semidirect
55. C2×#10587564C22semidirect
58. C2×#10587625C22semidirect
60. C2×#10587573C22semidirect
65. C2×#10587612C22semidirect
67. #11762751C22semidirect
68. #11762751C22semidirect
70. #11762745C22semidirect
71. #11762744C22semidirect
72. #11762743C22semidirect
73. #11762743C22semidirect
74. #11762740C22semidirect
75. #11762740C22semidirect
76. #11762738C22semidirect
79. #11762734C22semidirect
80. #11762733C22semidirect
82. #11762732C22semidirect
83. #11762732C22semidirect
84. #11762730C22semidirect
85. #11762730C22semidirect
86. #11762729C22semidirect
87. #11762729C22semidirect
91. #11762725C22semidirect
94. #11762724C22semidirect
95. #11762724C22semidirect
99. #11762723C22semidirect
100. #11762722C22semidirect
101. #11762722C22semidirect
105. #11762721C22semidirect
109. #11762713C22semidirect
114. #11762706C22semidirect
115. #11762704C22semidirect
116. #11762704C22semidirect
118. #11762703C22semidirect
121. #11762702C22semidirect
122. #11762701C22semidirect
127. #11762696C22semidirect
128. #11762694C22semidirect
129. #11762694C22semidirect
130. #11762692C22semidirect
131. #11762692C22semidirect
132. #11762692C22semidirect
133. #11762691C22semidirect
134. #11762691C22semidirect
142. #11762688C22semidirect
143. #11762688C22semidirect
144. #11762685C22semidirect
148. #11762683C22semidirect
149. #11762682C22semidirect
150. #11762682C22semidirect
158. #11762681C22semidirect
159. #11762680C22semidirect
160. #11762680C22semidirect
161. #11762676C22semidirect
162. #11762673C22semidirect
165. #11762669C22semidirect
169. #11762667C22semidirect
172. C22⋊C4×Dic17C22semidirect
173. C2×#10587502C22semidirect
285. D4×Dic17D4semidirect
769. #2668D17semidirect
1222. C17#36712semidirect

Maximal subgroups

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

subgroupindex
C2×#117634262
C2×#117633152
#145370742
#145370692
#145353372
#145353182
#145352812
#145352622
#145352412
#145351882
#145351792
#145351622
#145351002
#145350782
#145350712
#145350672
#145350292
#145350142
#145350062
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