Finite Group Databasebeta

← #17241857

Subgroups — #17241857

Order 4352.

2184 conjugacy classes of subgroups.

The subgroup lattice has 1636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763423C211yesmaximal, characteristic, complemented
2C2×#11763394C211yesmaximal, characteristic, complemented
3#14537114C211yesmaximal, characteristic, complemented
4#14537080C211yesmaximal, characteristic, complemented
5#14535700C211yesmaximal, characteristic, complemented
6#14535603C211yesmaximal, characteristic, complemented
7#14535599C211yesmaximal, characteristic, complemented
8#14535557C211yesmaximal, characteristic, complemented
9#14535376C211yesmaximal, characteristic, complemented
10#14535356C211yesmaximal, characteristic, complemented
11#14535333C211yesmaximal, characteristic, complemented
12#14535266C211yesmaximal, characteristic, complemented
13#14535226C211yesmaximal, characteristic, complemented
14#14535192C211yesmaximal, characteristic, complemented
15#14535171C211yesmaximal, characteristic, complemented
16#14535164C211yesmaximal, characteristic, complemented
17#14535090C211yesmaximal, characteristic, complemented
18#14535059C211yesmaximal, characteristic, complemented
19#14534988C211yesmaximal, characteristic, complemented
20#14534940C211yesmaximal, characteristic, complemented
21#14534915C211yesmaximal, characteristic, complemented
22#14534464C211yesmaximal, characteristic, complemented
23#14534419C211yesmaximal, characteristic, complemented
24#14534389C211yesmaximal, characteristic, complemented
25#14534374C211yesmaximal, characteristic, complemented
26#14534269C211yesmaximal, characteristic, complemented
27#14533939C211yesmaximal, characteristic, complemented
28#14532206C211yesmaximal, characteristic, complemented
29#14532165C211yesmaximal, characteristic, complemented
30#14531226C211yesmaximal, characteristic, complemented
31C17×#2670C211yesmaximal, characteristic, complemented
32#11763423—28no—
33#11763394—28no—
34C2×#10587630C2211yescharacteristic, complemented
35C2×#10587562C2211yescharacteristic, complemented
36C2×#10587565C2211yescharacteristic
37C2×#10587565C2211yescharacteristic
38C2×#10587565C2211yescharacteristic
39C2×#10587622C2211yescharacteristic
40C2×#10587571C2211yescharacteristic
41C2×#10587571C2211yescharacteristic
42C2×#10587571C2211yescharacteristic, complemented
43C2×#10587569C2211yescharacteristic
44C2×#10587569C2211yescharacteristic, complemented
45C2×#10587621C2211yescharacteristic
46C2×#10587621C2211yescharacteristic
47C2×#10587564C2211yescharacteristic
48C2×#10587564C2211yescharacteristic
49C2×#10587564C2211yescharacteristic, complemented
50C2×#10587564C2211yescharacteristic, complemented
51C2×#10587632C2211yescharacteristic, complemented
52C2×#10587625C2211yescharacteristic
53C2×#10587625C2211yescharacteristic
54C2×#10587625C2211yescharacteristic
55C2×#10587624C2211yescharacteristic
56C2×#10587624C2211yescharacteristic
57C2×#10587639C2211yescharacteristic
58C2×C4×Dic34C2211yescharacteristic, complemented
59C2×D4×Dic17C2211yescharacteristic
60C2×#10587567C2211yescharacteristic
61C2×#10587563C2211yescharacteristic
62C2×#10587563C2211yescharacteristic, complemented
63C22×C22⋊Dic17C2211yescharacteristic
64C2×C42×D17C2211yescharacteristic, complemented
65#11762750C2211yescharacteristic, complemented
66#11762749C2211yescharacteristic, complemented
67#11762745C2211yescharacteristic
68#11762745C2211yescharacteristic
69#11762741C2211yescharacteristic, complemented
70#11762739C2211yescharacteristic, complemented
71#11762738C2211yescharacteristic, complemented
72#11762738C2211yescharacteristic, complemented
73#11762737C2211yescharacteristic
74#11762737C2211yescharacteristic
75#11762737C2211yescharacteristic
76#11762737C2211yescharacteristic
77#11762737C2211yescharacteristic, complemented
78#11762734C2211yescharacteristic
79#11762734C2211yescharacteristic
80#11762734C2211yescharacteristic, complemented
81#11762732C2211yescharacteristic
82#11762732C2211yescharacteristic
83#11762732C2211yescharacteristic
84#11762732C2211yescharacteristic, complemented
85#11762730C2211yescharacteristic, complemented
86#11762729C2211yescharacteristic, complemented
87#11762728C2211yescharacteristic, complemented
88#11762725C2211yescharacteristic
89#11762725C2211yescharacteristic, complemented
90#11762724C2211yescharacteristic
91#11762724C2211yescharacteristic
92#11762723C2211yescharacteristic
93#11762723C2211yescharacteristic
94#11762723C2211yescharacteristic
95#11762723C2211yescharacteristic
96#11762723C2211yescharacteristic
97#11762723C2211yescharacteristic
98#11762723C2211yescharacteristic
99#11762721C2211yescharacteristic
100#11762721C2211yescharacteristic
101#11762721C2211yescharacteristic
102#11762721C2211yescharacteristic
103#11762721C2211yescharacteristic, complemented
104#11762721C2211yescharacteristic, complemented
105#11762717C2211yescharacteristic
106#11762717C2211yescharacteristic, complemented
107#11762716C2211yescharacteristic, complemented
108#11762715C2211yescharacteristic, complemented
109#11762714C2211yescharacteristic, complemented
110#11762713C2211yescharacteristic, complemented
111#11762712C2211yescharacteristic
112#11762712C2211yescharacteristic
113#11762712C2211yescharacteristic
114#11762712C2211yescharacteristic
115#11762712C2211yescharacteristic, complemented
116#11762708C2211yescharacteristic, complemented
117#11762707C2211yescharacteristic, complemented
118#11762706C2211yescharacteristic, complemented
119#11762706C2211yescharacteristic, complemented
120#11762704C2211yescharacteristic, complemented
121#11762703C2211yescharacteristic
122#11762703C2211yescharacteristic
123#11762703C2211yescharacteristic, complemented
124#11762703C2211yescharacteristic, complemented
125#11762702C2211yescharacteristic
126#11762702C2211yescharacteristic
127#11762702C2211yescharacteristic
128#11762702C2211yescharacteristic
129#11762702C2211yescharacteristic, complemented
130#11762702C2211yescharacteristic, complemented
131#11762702C2211yescharacteristic, complemented
132#11762697C2211yescharacteristic
133#11762697C2211yescharacteristic
134#11762697C2211yescharacteristic
135#11762697C2211yescharacteristic
136#11762697C2211yescharacteristic
137#11762697C2211yescharacteristic, complemented
138#11762697C2211yescharacteristic, complemented
139#11762694C2211yescharacteristic, complemented
140#11762693C2211yescharacteristic, complemented
141#11762693C2211yescharacteristic, complemented
142#11762692C2211yescharacteristic, complemented
143#11762692C2211yescharacteristic, complemented
144#11762691C2211yescharacteristic, complemented
145#11762689C2211yescharacteristic
146#11762689C2211yescharacteristic
147#11762689C2211yescharacteristic
148#11762689C2211yescharacteristic, complemented
149#11762689C2211yescharacteristic, complemented
150#11762685C2211yescharacteristic
151#11762685C2211yescharacteristic
152#11762685C2211yescharacteristic
153#11762685C2211yescharacteristic
154#11762685C2211yescharacteristic
155#11762685C2211yescharacteristic, complemented
156#11762685C2211yescharacteristic, complemented
157#11762685C2211yescharacteristic, complemented
158#11762684C2211yescharacteristic
159#11762683C2211yescharacteristic, complemented
160#11762681C2211yescharacteristic, complemented
161#11762681C2211yescharacteristic, complemented
162#11762680C2211yescharacteristic, complemented
163#11762675C2211yescharacteristic, complemented
164#11762670C2211yescharacteristic
165#11762670C2211yescharacteristic
166#11762667C2211yescharacteristic, complemented
167#11762666C2211yescharacteristic, complemented
168#11762665C2211yescharacteristic
169#11762665C2211yescharacteristic
170C4⋊C4×Dic17C2211yescharacteristic, complemented
171C22⋊C4×Dic17C2211yescharacteristic
172#11762656C2211yescharacteristic, complemented
173#11762654C2211yescharacteristic, complemented
174C2×C17×#124C2211yescharacteristic
175C2×C17×#124C2211yescharacteristic
176C2×C17×#120C2211yescharacteristic
177C2×C17×#120C2211yescharacteristic
178C17×#394C2211yescharacteristic
179C17×#394C2211yescharacteristic
180C17×#393C2211yescharacteristic
181C17×#392C2211yescharacteristic
182C17×#392C2211yescharacteristic
183C17×#392C2211yescharacteristic
184C17×#390C2211yescharacteristic
185C17×#390C2211yescharacteristic
186C17×#388C2211yescharacteristic
187C17×#388C2211yescharacteristic
188C17×#379C2211yescharacteristic
189C25×C17C2311yescharacteristic
190C22×Q8×C17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C22×D4×C17C2311yescharacteristic
193C22×D4×C17C2311yescharacteristic
194C22×D4×C17C2311yescharacteristic
195C22×D4×C17C2311yescharacteristic
196C22×D4×C17C2311yescharacteristic
197C22×D4×C17C2311yescharacteristic
198C22×C22⋊D17C2311yescharacteristic
199C22×C22⋊D17C2311yescharacteristic
200C22×C22⋊D17C2311yescharacteristic
201C22×C22⋊D17C2311yescharacteristic
202C22×C22⋊D17C2311yescharacteristic
203C23×Dic17C2311yescharacteristic
204C23×Dic17C2311yescharacteristic
205C23×Dic17C2311yescharacteristic
206C23×Dic17C2311yescharacteristic
207C22×C4×D17C2311yescharacteristic
208C22×C4×D17C2311yescharacteristic
209C22×C4×D17C2311yescharacteristic
210C22×Dic34C2311yescharacteristic
211C22×Dic34C2311yescharacteristic
212C22×Dic34C2311yescharacteristic
213C17×#124—24no—
214C17×#124—42no—
215C17×#120—24no—
216C17×#120—42no—
217C2×C4⋊C4×C17C2311yescharacteristic
218C2×C4⋊C4×C17C2311yescharacteristic
219C2×C22⋊C4×C17C2311yescharacteristic
220C2×C22⋊C4×C17C2311yescharacteristic
221C2×C22⋊C4×C17C2311yescharacteristic
222C2×C22⋊C4×C17C2311yescharacteristic
223C2×C22⋊C4×C17C2311yescharacteristic
224C2×C22⋊C4×C17C2311yescharacteristic
225C2×C22⋊C4×C17C2311yescharacteristic
226C2×C22⋊C4×C17C2311yescharacteristic
227C2×C22⋊C4×C17C2311yescharacteristic
228C2×C22⋊C4×C17C2311yescharacteristic
229C2×C22⋊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×C42×C17C2311yescharacteristic
238C2×C42×C17C2311yescharacteristic
239#10587639—24no—
240C2×C22⋊Dic17—24no—
241C2×C22⋊Dic17C2311yescharacteristic
242C2×C22⋊Dic17C2311yescharacteristic
243C2×C22⋊Dic17C2311yescharacteristic
244C2×C22⋊Dic17C2311yescharacteristic
245C2×C22⋊Dic17C2311yescharacteristic
246C2×C22⋊Dic17C2311yescharacteristic
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
272#10587632—24no—
273#10587630—24no—
274#10587625—24no—
275#10587625—24no—
276#10587625—24no—
277#10587624—24no—
278#10587624—42no—
279#10587622—24no—
280#10587621—24no—
281#10587621—24no—
282D4×Dic17—24no—
283C2×#63227C2311yescharacteristic
284C2×#63227C2311yescharacteristic
285C2×#63227C2311yescharacteristic
286C2×#63227C2311yescharacteristic
287C2×#63227C2311yescharacteristic
288C2×#63227C2311yescharacteristic
289C2×#63227C2311yescharacteristic
290C2×C4⋊Dic17C2311yescharacteristic
291C2×C4⋊Dic17C2311yescharacteristic
292C2×C4⋊Dic17C2311yescharacteristic
293C2×C4⋊Dic17C2311yescharacteristic
294C2×C4⋊Dic17C2311yescharacteristic
295C2×C4⋊Dic17C2311yescharacteristic
296C2×C4⋊Dic17C2311yescharacteristic
297C2×C4⋊Dic17C2311yescharacteristic
298C2×C4⋊Dic17C2311yescharacteristic
299C2×#63225C2311yescharacteristic
300C2×#63225C2311yescharacteristic
301C2×#63225C2311yescharacteristic
302C2×#63225C2311yescharacteristic
303C2×#63225C2311yescharacteristic
304C2×#63225C2311yescharacteristic
305C2×#63225C2311yescharacteristic
306C2×#63225C2311yescharacteristic
307C2×#63225C2311yescharacteristic
308C2×#63225C2311yescharacteristic
309C2×#63225C2311yescharacteristic
310C2×#63225C2311yescharacteristic
311C2×#63225C2311yescharacteristic
312C2×#63225C2311yescharacteristic
313C2×#63225C2311yescharacteristic
314C2×#63225C2311yescharacteristic
315C2×#63225C2311yescharacteristic
316C2×C4×Dic17C2311yescharacteristic
317C2×C4×Dic17C2311yescharacteristic
318C2×C4×Dic17C2311yescharacteristic
319C2×C4×Dic17C2311yescharacteristic
320C2×C4×Dic17C2311yescharacteristic
321C2×C4×Dic17C2311yescharacteristic
322C2×C4×Dic17C2311yescharacteristic
323C2×C4×Dic17C2311yescharacteristic
324C2×C4×Dic17C2311yescharacteristic
325#10587571—24no—
326#10587571—24no—
327#10587571—24no—
328#10587569—24no—
329#10587569—24no—
330#10587567D418yescomplemented
331#10587565—24no—
332#10587565—24no—
333#10587565—24no—
334#10587564—24no—
335#10587564—24no—
336#10587564—24no—
337#10587564—42no—
338#10587563—24no—
339#10587563—42no—
340#10587562—24no—
341C42×D17—42no—
342C4×Dic34—24no—
343C17×#95C2311yescharacteristic
344C17×#95C2311yescharacteristic
345C17×#95C2311yescharacteristic
346C17×#95C2311yescharacteristic
347#10587502C2311yescharacteristic
348#10587502C2311yescharacteristic
349#10587502C2311yescharacteristic
350#10587502C2311yescharacteristic
351#10587502C2311yescharacteristic
352#10587502C2311yescharacteristic
353#10587502C2311yescharacteristic
354#10587502C2311yescharacteristic
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
379C24×C17—22no—
380C24×C17—41no—
381C24×C17—41no—
382C24×C17—41no—
383C24×C17—41no—
384C24×C17—41no—
385C24×C17—41no—
386C24×C17C2411yescharacteristic
387C24×C17C2411yescharacteristic
388C24×C17C2411yescharacteristic
389C24×C17C2411yescharacteristic
390C24×C17C2411yescharacteristic
391C23×D17C2411yescharacteristic
392C2×Q8×C17—22no—
393C2×Q8×C17—41no—
394C2×Q8×C17—41no—
395C2×D4×C17—22no—
396C2×D4×C17—22no—
397C2×D4×C17—22no—
398C2×D4×C17—22no—
399C2×D4×C17—22no—
400C2×D4×C17—41no—
401C2×D4×C17—41no—
402C2×D4×C17—41no—
403C2×D4×C17—41no—
404C2×D4×C17—41no—
405C2×D4×C17—41no—
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—
416C22×C4×C17C2411yescharacteristic
417C22×C4×C17C2411yescharacteristic
418C22×C4×C17C2411yescharacteristic
419C22×C4×C17C2411yescharacteristic
420C22×C4×C17C2411yescharacteristic
421C22×C4×C17C2411yescharacteristic
422C22×C4×C17C2411yescharacteristic
423C22×C4×C17C2411yescharacteristic
424C22×C4×C17C2411yescharacteristic
425C22×C4×C17C2411yescharacteristic
426C2×C22⋊D17—22no—
427C2×C22⋊D17—22no—
428C2×C22⋊D17—22no—
429C2×C22⋊D17—22no—
430C2×C22⋊D17—41no—
431C2×C22⋊D17—41no—
432C2×C22⋊D17—41no—
433C2×C22⋊D17—41no—
434C2×C22⋊D17—41no—
435C2×C22⋊D17—41no—
436C2×C22⋊D17—41no—
437C2×C22⋊D17—41no—
438C2×C22⋊D17—41no—
439C2×C22⋊D17—41no—
440C2×C22⋊D17C2×D414yes—
441C22×Dic17—22no—
442C22×Dic17—22no—
443C22×Dic17—22no—
444C22×Dic17—41no—
445C22×Dic17—41no—
446C22×Dic17—41no—
447C22×Dic17—41no—
448C22×Dic17—41no—
449C22×Dic17—41no—
450C22×Dic17—41no—
451C22×Dic17—41no—
452C22×Dic17C2×D414yes—
453C22×Dic17C2411yescharacteristic
454C22×Dic17C2411yescharacteristic
455C22×Dic17C2411yescharacteristic
456C22×Dic17C2411yescharacteristic
457C22×Dic17C2411yescharacteristic
458C22×Dic17C2411yescharacteristic
459C22×Dic17C2411yescharacteristic
460C22×Dic17C2411yescharacteristic
461C22×Dic17C2411yescharacteristic
462C22×Dic17C2411yescharacteristic
463C22×Dic17C2411yescharacteristic
464C22×Dic17C2411yescharacteristic
465C22×Dic17C2411yescharacteristic
466C22×Dic17C2411yescharacteristic
467C22×Dic17C2411yescharacteristic
468C2×C4×D17—22no—
469C2×C4×D17—41no—
470C2×C4×D17—41no—
471C2×C4×D17—41no—
472C2×C4×D17—41no—
473C2×C4×D17—41no—
474C2×C4×D17—41no—
475C2×C4×D17—41no—
476C2×C4×D17C2×D414yes—
477C2×Dic34—22no—
478C2×Dic34—22no—
479C2×Dic34—22no—
480C2×Dic34—41no—
481C2×Dic34—41no—
482C2×Dic34—41no—
483C2×Dic34—41no—
484C2×Dic34—41no—
485C2×Dic34—41no—
486C4⋊C4×C17—41no—
487C4⋊C4×C17—41no—
488C22⋊C4×C17—22no—
489C22⋊C4×C17—22no—
490C22⋊C4×C17—22no—
491C22⋊C4×C17—22no—
492C22⋊C4×C17—22no—
493C22⋊C4×C17—22no—
494C22⋊C4×C17—22no—
495C22⋊C4×C17—22no—
496C22⋊C4×C17—41no—
497C22⋊C4×C17—41no—
498C22⋊C4×C17—41no—
499C22⋊C4×C17—41no—
500C22⋊C4×C17—41no—
501C22⋊C4×C17—41no—
502C22⋊C4×C17—41no—
503C22⋊C4×C17—41no—
504C22⋊C4×C17—41no—
505C22⋊C4×C17C2×D414yes—
506C42×C17—22no—
507C42×C17—22no—
508C22⋊Dic17—22no—
509C22⋊Dic17—22no—
510C22⋊Dic17—22no—
511C22⋊Dic17—22no—
512C22⋊Dic17—22no—
513C22⋊Dic17—22no—
514C22⋊Dic17—22no—
515C22⋊Dic17—22no—
516C22⋊Dic17—22no—
517C22⋊Dic17—22no—
518C22⋊Dic17—22no—
519C22⋊Dic17—22no—
520C22⋊Dic17—22no—
521C22⋊Dic17—41no—
522C22⋊Dic17—41no—
523C22⋊Dic17—41no—
524C22⋊Dic17—41no—
525C22⋊Dic17—41no—
526C22⋊Dic17—41no—
527C22⋊Dic17—41no—
528C22⋊Dic17—41no—
529C22⋊Dic17—41no—
530C22⋊Dic17—41no—
531C22⋊Dic17—41no—
532C22⋊Dic17—41no—
533C22⋊Dic17—41no—
534C22⋊Dic17—41no—
535C22⋊Dic17—41no—
536C22⋊Dic17—41no—
537C22⋊Dic17—41no—
538C22⋊Dic17—41no—
539#63227—22no—
540#63227—22no—
541#63227—22no—
542#63227—22no—
543#63227—41no—
544#63227—41no—
545#63227C2×D414yes—
546C4⋊Dic17—22no—
547C4⋊Dic17—22no—
548C4⋊Dic17—22no—
549C4⋊Dic17—22no—
550C4⋊Dic17—22no—
551C4⋊Dic17—41no—
552C4⋊Dic17—41no—
553C4⋊Dic17—41no—
554C4⋊Dic17—41no—
555#63225—22no—
556#63225—22no—
557#63225—22no—
558#63225—22no—
559#63225—22no—
560#63225—22no—
561#63225—22no—
562#63225—22no—
563#63225—22no—
564#63225—22no—
565#63225—22no—
566#63225—41no—
567#63225—41no—
568#63225—41no—
569#63225—41no—
570#63225—41no—
571#63225C2×D414yes—
572C4×Dic17—22no—
573C4×Dic17—22no—
574C4×Dic17—22no—
575C4×Dic17—22no—
576C4×Dic17—41no—
577C4×Dic17—41no—
578C4×Dic17—41no—
579C4×Dic17—41no—
580C4×Dic17C2×D414yes—
581#36745—171nomaximal, Sylow
582C23×C17—21no—
583C23×C17—21no—
584C23×C17—21no—
585C23×C17—21no—
586C23×C17—21no—
587C23×C17—21no—
588C23×C17—21no—
589C23×C17—21no—
590C23×C17—21no—
591C23×C17—21no—
592C23×C17—21no—
593C23×C17—21no—
594C23×C17—21no—
595C23×C17—21no—
596C23×C17—21no—
597C23×C17—21no—
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—44no—
617C23×C17—82no—
618C23×C17—82no—
619C23×C17—82no—
620C23×C17—82no—
621C23×C17—82no—
622C23×C17—82no—
623C23×C17C22×D412yes—
624C23×C17C2511yescharacteristic
625C22×D17—21no—
626C22×D17—21no—
627C22×D17—21no—
628C22×D17—21no—
629C22×D17—21no—
630C22×D17—21no—
631C22×D17C22×D412yes—
632Q8×C17—82no—
633D4×C17—44no—
634D4×C17—82no—
635D4×C17—82no—
636D4×C17—82no—
637D4×C17—82no—
638D4×C17—82no—
639D4×C17—82no—
640C2×C4×C17—21no—
641C2×C4×C17—21no—
642C2×C4×C17—21no—
643C2×C4×C17—21no—
644C2×C4×C17—21no—
645C2×C4×C17—21no—
646C2×C4×C17—21no—
647C2×C4×C17—21no—
648C2×C4×C17—21no—
649C2×C4×C17—21no—
650C2×C4×C17—21no—
651C2×C4×C17—21no—
652C2×C4×C17—21no—
653C2×C4×C17—21no—
654C2×C4×C17—21no—
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×C17C22×D412yes—
668C2×C4×C17C22×D412yes—
669C2×C4×C17H(5,𝔽2)12yes—
670C22⋊D17—44no—
671C22⋊D17—82no—
672C22⋊D17—82no—
673C22⋊D17—82no—
674C22⋊D17—82no—
675C2×Dic17—21no—
676C2×Dic17—21no—
677C2×Dic17—21no—
678C2×Dic17—21no—
679C2×Dic17—21no—
680C2×Dic17—21no—
681C2×Dic17—21no—
682C2×Dic17—21no—
683C2×Dic17—21no—
684C2×Dic17—21no—
685C2×Dic17—21no—
686C2×Dic17—21no—
687C2×Dic17—21no—
688C2×Dic17—21no—
689C2×Dic17—21no—
690C2×Dic17—21no—
691C2×Dic17—21no—
692C2×Dic17—21no—
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—44no—
718C2×Dic17—44no—
719C2×Dic17—82no—
720C2×Dic17—82no—
721C2×Dic17C22×D412yes—
722C2×Dic17C22×D412yes—
723C2×Dic17C22×D412yes—
724C4×D17—44no—
725C4×D17—44no—
726C4×D17—44no—
727Dic34—44no—
728Dic34—82no—
729Dic34—82no—
730C2×#542—171no—
731C2×#538—171no—
732#2854—171no—
733#2850—171no—
734#2723—171no—
735#2716—171no—
736#2715—171no—
737#2712—171no—
738#2700—171no—
739#2698—171no—
740#2696—171no—
741#2691—171no—
742#2688—171no—
743#2686—171no—
744#2685—171no—
745#2684—171no—
746#2676—171no—
747#2674—171no—
748#2670D1711yescharacteristic, complemented
749#2668—171no—
750#2663—171no—
751#2661—171no—
752#2610—171no—
753#2604—171no—
754#2602—171no—
755#2601—171no—
756#2592—171no—
757#2561—171no—
758#2415—171no—
759#2411—171no—
760#2290—171no—
761C22×C17—22no—
762C22×C17—22no—
763C22×C17—22no—
764C22×C17—41no—
765C22×C17—41no—
766C22×C17—41no—
767C22×C17—41no—
768C22×C17—41no—
769C22×C17—41no—
770C22×C17—41no—
771C22×C17—41no—
772C22×C17—41no—
773C22×C17—41no—
774C22×C17—41no—
775C22×C17—41no—
776C22×C17—41no—
777C22×C17—41no—
778C22×C17—41no—
779C22×C17—41no—
780C22×C17—41no—
781C22×C17—41no—
782C22×C17—41no—
783C22×C17—41no—
784C22×C17—41no—
785C22×C17—41no—
786C22×C17—41no—
787C22×C17—41no—
788C22×C17—41no—
789C22×C17—41no—
790C22×C17—41no—
791C22×C17—41no—
792C22×C17—41no—
793C22×C17—41no—
794C22×C17—41no—
795C22×C17—41no—
796C22×C17—88no—
797C22×C17C23×D411yescharacteristic
798C22×C17C2×H(5,𝔽2)11yescharacteristic
799C22×C17#58511yescharacteristic
800C22×C17#58511yescharacteristic
801C22×C17#58511yescharacteristic
802C22×C17#58511yescharacteristic
803C22×C17#58511yescharacteristic
804C2×D17—22no—
805C2×D17—22no—
806C2×D17—22no—
807C2×D17—41no—
808C2×D17—41no—
809C2×D17—41no—
810C2×D17—41no—
811C4×C17—22no—
812C4×C17—22no—
813C4×C17—22no—
814C4×C17—41no—
815C4×C17—41no—
816C4×C17—41no—
817C4×C17—41no—
818C4×C17—41no—
819C4×C17—41no—
820C4×C17—41no—
821Dic17—22no—
822Dic17—22no—
823Dic17—22no—
824Dic17—41no—
825Dic17—41no—
826Dic17—41no—
827Dic17—41no—
828Dic17—41no—
829Dic17—41no—
830Dic17—41no—
831Dic17—41no—
832Dic17—41no—
833Dic17—41no—
834Dic17—41no—
835Dic17—41no—
836#542—348no—
837#538—348no—
838C2×C4⋊Q8—171no—
839C2×#126—171no—
840C2×#126—171no—
841C2×#126—171no—
842C2×#126—171no—
843C2×#124—171no—
844C2×#124—171no—
845C2×#124—171no—
846C2×#124—171no—
847C2×#124C2×D1711yescharacteristic
848C2×#124C2×D1711yescharacteristic
849C2×#123—171no—
850C2×#123—171no—
851C2×#123—171no—
852C2×#123—171no—
853C2×C22⋊Q8—171no—
854C2×C22⋊Q8—171no—
855C2×C22⋊Q8—171no—
856C2×C22⋊Q8—171no—
857C2×C22⋊Q8—171no—
858C2×#121—171no—
859C2×#121—171no—
860C2×#121—171no—
861C2×#121—171no—
862C2×#121—171no—
863C2×#120—171no—
864C2×#120C2×D1711yescharacteristic
865C2×#120C2×D1711yescharacteristic
866C2×C4×Q8—171no—
867C2×C4×D4—171no—
868C2×C4×D4—171no—
869C2×#117—171no—
870C2×#117—171no—
871C22×C22⋊C4—171no—
872C22×C42—171no—
873#400—171no—
874#400—171no—
875#399—171no—
876#399—171no—
877#398—171no—
878#398—171no—
879#397—171no—
880#397—171no—
881#397—171no—
882#397—171no—
883#397—171no—
884#397—171no—
885#397—171no—
886#397—171no—
887#397—171no—
888#397—171no—
889#396—171no—
890#396—171no—
891#396—171no—
892#396—171no—
893#395—171no—
894#395—171no—
895#395—171no—
896#394—171no—
897#394—171no—
898#394—171no—
899#394—171no—
900#394—171no—
901#394—171no—
902#394—171no—
903#394—171no—
904#394—171no—
905#394—171no—
906#394—171no—
907#394C2×D1711yescharacteristic
908#394C2×D1711yescharacteristic
909#393—171no—
910#393—171no—
911#393—171no—
912#393—171no—
913#393—171no—
914#393—171no—
915#393C2×D1711yescharacteristic
916#392—171no—
917#392—171no—
918#392C2×D1711yescharacteristic
919#392C2×D1711yescharacteristic
920#392C2×D1711yescharacteristic
921#391—171no—
922#391—171no—
923#391—171no—
924#391—171no—
925#390—171no—
926#390—171no—
927#390—171no—
928#390—171no—
929#390—171no—
930#390C2×D1711yescharacteristic
931#390C2×D1711yescharacteristic
932#389—171no—
933#389—171no—
934#389—171no—
935#389—171no—
936#389—171no—
937#388—171no—
938#388—171no—
939#388—171no—
940#388—171no—
941#388—171no—
942#388—171no—
943#388—171no—
944#388—171no—
945#388—171no—
946#388—171no—
947#388—171no—
948#388—171no—
949#388—171no—
950#388—171no—
951#388—171no—
952#388—171no—
953#388—171no—
954#388—171no—
955#388C2×D1711yescharacteristic
956#388C2×D1711yescharacteristic
957#387—171no—
958#387—171no—
959#387—171no—
960#387—171no—
961#387—171no—
962#387—171no—
963#386—171no—
964#386—171no—
965#386—171no—
966#386—171no—
967#386—171no—
968#386—171no—
969#386—171no—
970#386—171no—
971#386—171no—
972#386—171no—
973#386—171no—
974#386—171no—
975#386—171no—
976#385—171no—
977#385—171no—
978#385—171no—
979#385—171no—
980#385—171no—
981#382—171no—
982#381—171no—
983#381—171no—
984#380—171no—
985#380—171no—
986#379—171no—
987#379—171no—
988#379C2×D1711yescharacteristic
989C4×C4⋊C4—171no—
990C4×C22⋊C4—171no—
991C4×C22⋊C4—171no—
992#376—171no—
993C2×C17—42no—
994C2×C17—81no—
995C2×C17—81no—
996C2×C17—81no—
997C2×C17—81no—
998C2×C17#344911yescharacteristic
999C2×C17#349611yescharacteristic
1000C2×C17#350011yescharacteristic
1001C2×C17#353311yescharacteristic
1002C2×C17#354011yescharacteristic
1003C2×C17#356611yescharacteristic
1004C2×C17#356811yescharacteristic
1005D17—42no—
1006C25C22×D1711yescharacteristic
1007C22×Q8—171no—
1008C22×Q8—171no—
1009C22×Q8—171no—
1010C22×Q8C22×D1711yescharacteristic
1011C22×D4—171no—
1012C22×D4—171no—
1013C22×D4—171no—
1014C22×D4—171no—
1015C22×D4—171no—
1016C22×D4C22×D1711yescharacteristic
1017C22×D4C22×D1711yescharacteristic
1018C22×D4C22×D1711yescharacteristic
1019C22×D4C22×D1711yescharacteristic
1020C22×D4C22×D1711yescharacteristic
1021C22×D4C22×D1711yescharacteristic
1022C22×D4C22×D1711yescharacteristic
1023C23×C4—171no—
1024C23×C4—171no—
1025C23×C4—171no—
1026C23×C4—171no—
1027C23×C4—171no—
1028C23×C4—171no—
1029C23×C4—171no—
1030C4⋊Q8—344no—
1031#126—344no—
1032#126—344no—
1033#126—344no—
1034#126—344no—
1035#124—24no—
1036#124—42no—
1037#124—344no—
1038#124—344no—
1039#124—344no—
1040#124—344no—
1041#123—344no—
1042#123—344no—
1043#123—344no—
1044#123—344no—
1045C22⋊Q8—344no—
1046C22⋊Q8—344no—
1047C22⋊Q8—344no—
1048C22⋊Q8—344no—
1049C22⋊Q8—682no—
1050#121—344no—
1051#121—344no—
1052#121—344no—
1053#121—344no—
1054#121—682no—
1055#120—24no—
1056#120—42no—
1057#120—344no—
1058C4×Q8—344no—
1059C4×D4—178no—
1060C4×D4—344no—
1061#117—344no—
1062#117—682no—
1063C2×C4⋊C4—171no—
1064C2×C4⋊C4—171no—
1065C2×C4⋊C4—171no—
1066C2×C4⋊C4—171no—
1067C2×C4⋊C4—171no—
1068C2×C4⋊C4—171no—
1069C2×C4⋊C4—171no—
1070C2×C4⋊C4—171no—
1071C2×C4⋊C4—171no—
1072C2×C4⋊C4—171no—
1073C2×C4⋊C4—171no—
1074C2×C4⋊C4—171no—
1075C2×C4⋊C4—171no—
1076C2×C4⋊C4—171no—
1077C2×C4⋊C4—171no—
1078C2×C4⋊C4—171no—
1079C2×C4⋊C4—171no—
1080C2×C4⋊C4—171no—
1081C2×C4⋊C4—171no—
1082C2×C4⋊C4—171no—
1083C2×C4⋊C4—171no—
1084C2×C4⋊C4—171no—
1085C2×C4⋊C4—171no—
1086C2×C4⋊C4—171no—
1087C2×C4⋊C4—171no—
1088C2×C4⋊C4—171no—
1089C2×C4⋊C4C22×D1711yescharacteristic
1090C2×C4⋊C4C22×D1711yescharacteristic
1091C2×C22⋊C4—171no—
1092C2×C22⋊C4—171no—
1093C2×C22⋊C4—171no—
1094C2×C22⋊C4—171no—
1095C2×C22⋊C4—171no—
1096C2×C22⋊C4—171no—
1097C2×C22⋊C4—171no—
1098C2×C22⋊C4—171no—
1099C2×C22⋊C4—171no—
1100C2×C22⋊C4—171no—
1101C2×C22⋊C4—171no—
1102C2×C22⋊C4—171no—
1103C2×C22⋊C4—171no—
1104C2×C22⋊C4—171no—
1105C2×C22⋊C4—171no—
1106C2×C22⋊C4—171no—
1107C2×C22⋊C4—171no—
1108C2×C22⋊C4—171no—
1109C2×C22⋊C4—171no—
1110C2×C22⋊C4—171no—
1111C2×C22⋊C4—171no—
1112C2×C22⋊C4—171no—
1113C2×C22⋊C4—171no—
1114C2×C22⋊C4—171no—
1115C2×C22⋊C4—171no—
1116C2×C22⋊C4—171no—
1117C2×C22⋊C4—171no—
1118C2×C22⋊C4—171no—
1119C2×C22⋊C4—171no—
1120C2×C22⋊C4—171no—
1121C2×C22⋊C4—171no—
1122C2×C22⋊C4—171no—
1123C2×C22⋊C4—171no—
1124C2×C22⋊C4—171no—
1125C2×C22⋊C4—171no—
1126C2×C22⋊C4—171no—
1127C2×C22⋊C4—171no—
1128C2×C22⋊C4—171no—
1129C2×C22⋊C4—344no—
1130C2×C22⋊C4C22×D1711yescharacteristic
1131C2×C22⋊C4C22×D1711yescharacteristic
1132C2×C22⋊C4C22×D1711yescharacteristic
1133C2×C22⋊C4C22×D1711yescharacteristic
1134C2×C22⋊C4C22×D1711yescharacteristic
1135C2×C22⋊C4C22×D1711yescharacteristic
1136C2×C22⋊C4C22×D1711yescharacteristic
1137C2×C22⋊C4C22×D1711yescharacteristic
1138C2×C22⋊C4C22×D1711yescharacteristic
1139C2×C22⋊C4C22×D1711yescharacteristic
1140C2×C22⋊C4C22×D1711yescharacteristic
1141C2×C22⋊C4C22×D1711yescharacteristic
1142C2×C22⋊C4C22×D1711yescharacteristic
1143C2×C22⋊C4C22×D1711yescharacteristic
1144C2×C22⋊C4C22×D1711yescharacteristic
1145C2×C22⋊C4C22×D1711yescharacteristic
1146C2×C22⋊C4C22×D1711yescharacteristic
1147C2×C22⋊C4C22×D1711yescharacteristic
1148C2×C42—171no—
1149C2×C42—171no—
1150C2×C42—171no—
1151C2×C42—171no—
1152C2×C42—171no—
1153C2×C42—171no—
1154C2×C42—171no—
1155C2×C42—171no—
1156C2×C42—171no—
1157C2×C42—682no—
1158C2×C42C22×D1711yescharacteristic
1159C2×C42C22×D1711yescharacteristic
1160#95—171no—
1161#95—171no—
1162#95—171no—
1163#95—171no—
1164#95—171no—
1165#95—171no—
1166#95—171no—
1167#95—171no—
1168#95—171no—
1169#95—171no—
1170#95—171no—
1171#95—171no—
1172#95—171no—
1173#95—171no—
1174#95—171no—
1175#95—171no—
1176#95—171no—
1177#95—171no—
1178#95—171no—
1179#95—171no—
1180#95—171no—
1181#95—171no—
1182#95—171no—
1183#95—171no—
1184#95—171no—
1185#95—171no—
1186#95—171no—
1187#95—171no—
1188#95—171no—
1189#95—171no—
1190#95—171no—
1191#95—171no—
1192#95C22×D1711yescharacteristic
1193#95C22×D1711yescharacteristic
1194#95C22×D1711yescharacteristic
1195#95C22×D1711yescharacteristic
1196C17#3674511yescharacteristic, complemented, Sylow
1197C24—22no—
1198C24—41no—
1199C24—41no—
1200C24—41no—
1201C24—41no—
1202C24—41no—
1203C24—41no—
1204C24—171no—
1205C24C23×D1711yescharacteristic
1206C24C23×D1711yescharacteristic
1207C24C23×D1711yescharacteristic
1208C24C23×D1711yescharacteristic
1209C24C23×D1711yescharacteristic
1210C2×Q8—22no—
1211C2×Q8—41no—
1212C2×Q8—41no—
1213C2×Q8—342no—
1214C2×Q8—342no—
1215C2×Q8—342no—
1216C2×Q8—681no—
1217C2×Q8—681no—
1218C2×Q8—681no—
1219C2×Q8—681no—
1220C2×Q8—681no—
1221C2×Q8—681no—
1222C2×D4—22no—
1223C2×D4—22no—
1224C2×D4—22no—
1225C2×D4—22no—
1226C2×D4—22no—
1227C2×D4—41no—
1228C2×D4—41no—
1229C2×D4—41no—
1230C2×D4—41no—
1231C2×D4—41no—
1232C2×D4—41no—
1233C2×D4—41no—
1234C2×D4—41no—
1235C2×D4—41no—
1236C2×D4—41no—
1237C2×D4—41no—
1238C2×D4—41no—
1239C2×D4—41no—
1240C2×D4—41no—
1241C2×D4—41no—
1242C2×D4—41no—
1243C2×D4—174no—
1244C2×D4—342no—
1245C2×D4—342no—
1246C2×D4—342no—
1247C2×D4—342no—
1248C2×D4—681no—
1249C2×D4—681no—
1250C2×D4—681no—
1251C2×D4—681no—
1252C2×D4—681no—
1253C2×D4—681no—
1254C2×D4—681no—
1255C2×D4—681no—
1256C2×D4—681no—
1257C2×D4—681no—
1258C22×C4—171no—
1259C22×C4—171no—
1260C22×C4—171no—
1261C22×C4—174no—
1262C22×C4—174no—
1263C22×C4—171no—
1264C22×C4—171no—
1265C22×C4—171no—
1266C22×C4—171no—
1267C22×C4—171no—
1268C22×C4—171no—
1269C22×C4—171no—
1270C22×C4—171no—
1271C22×C4—171no—
1272C22×C4—171no—
1273C22×C4—171no—
1274C22×C4—171no—
1275C22×C4—342no—
1276C22×C4—342no—
1277C22×C4—342no—
1278C22×C4—342no—
1279C22×C4—681no—
1280C22×C4—681no—
1281C22×C4—681no—
1282C22×C4—681no—
1283C22×C4—681no—
1284C22×C4—681no—
1285C22×C4—681no—
1286C22×C4—681no—
1287C22×C4—681no—
1288C22×C4—681no—
1289C22×C4—681no—
1290C22×C4—681no—
1291C22×C4—681no—
1292C22×C4—681no—
1293C22×C4—681no—
1294C22×C4C23×D1711yescharacteristic
1295C22×C4C23×D1711yescharacteristic
1296C22×C4C23×D1711yescharacteristic
1297C22×C4C23×D1711yescharacteristic
1298C22×C4C23×D1711yescharacteristic
1299C22×C4C23×D1711yescharacteristic
1300C22×C4C23×D1711yescharacteristic
1301C22×C4C23×D1711yescharacteristic
1302C22×C4C23×D1711yescharacteristic
1303C22×C4C23×D1711yescharacteristic
1304C4⋊C4—41no—
1305C4⋊C4—41no—
1306C4⋊C4—174no—
1307C4⋊C4—342no—
1308C4⋊C4—342no—
1309C4⋊C4—342no—
1310C4⋊C4—342no—
1311C4⋊C4—342no—
1312C4⋊C4—342no—
1313C4⋊C4—342no—
1314C4⋊C4—342no—
1315C4⋊C4—342no—
1316C4⋊C4—342no—
1317C4⋊C4—342no—
1318C4⋊C4—342no—
1319C4⋊C4—342no—
1320C4⋊C4—342no—
1321C4⋊C4—342no—
1322C4⋊C4—342no—
1323C4⋊C4—681no—
1324C4⋊C4—681no—
1325C4⋊C4—681no—
1326C4⋊C4—681no—
1327C4⋊C4—681no—
1328C4⋊C4—681no—
1329C4⋊C4—681no—
1330C4⋊C4—681no—
1331C4⋊C4—681no—
1332C22⋊C4—22no—
1333C22⋊C4—22no—
1334C22⋊C4—22no—
1335C22⋊C4—22no—
1336C22⋊C4—22no—
1337C22⋊C4—22no—
1338C22⋊C4—22no—
1339C22⋊C4—22no—
1340C22⋊C4—41no—
1341C22⋊C4—41no—
1342C22⋊C4—41no—
1343C22⋊C4—41no—
1344C22⋊C4—41no—
1345C22⋊C4—41no—
1346C22⋊C4—41no—
1347C22⋊C4—41no—
1348C22⋊C4—41no—
1349C22⋊C4—174no—
1350C22⋊C4—342no—
1351C22⋊C4—342no—
1352C22⋊C4—342no—
1353C22⋊C4—342no—
1354C22⋊C4—342no—
1355C22⋊C4—342no—
1356C22⋊C4—342no—
1357C22⋊C4—342no—
1358C22⋊C4—342no—
1359C22⋊C4—342no—
1360C22⋊C4—342no—
1361C22⋊C4—342no—
1362C22⋊C4—342no—
1363C22⋊C4—342no—
1364C22⋊C4—342no—
1365C22⋊C4—342no—
1366C22⋊C4—342no—
1367C22⋊C4—681no—
1368C22⋊C4—681no—
1369C22⋊C4—681no—
1370C22⋊C4—681no—
1371C22⋊C4—681no—
1372C22⋊C4—681no—
1373C22⋊C4—681no—
1374C22⋊C4—681no—
1375C22⋊C4—681no—
1376C22⋊C4—681no—
1377C22⋊C4—681no—
1378C22⋊C4—681no—
1379C22⋊C4—681no—
1380C22⋊C4—681no—
1381C22⋊C4—681no—
1382C22⋊C4—681no—
1383C22⋊C4—681no—
1384C22⋊C4—681no—
1385C22⋊C4—681no—
1386C22⋊C4—681no—
1387C22⋊C4D4×D1714yes—
1388C42—22no—
1389C42—22no—
1390C42—174no—
1391C42—342no—
1392C42—342no—
1393C42—342no—
1394C42—342no—
1395C42—681no—
1396C42—681no—
1397C42—681no—
1398C42—681no—
1399C23—21no—
1400C23—21no—
1401C23—21no—
1402C23—21no—
1403C23—21no—
1404C23—21no—
1405C23—21no—
1406C23—21no—
1407C23—21no—
1408C23—21no—
1409C23—21no—
1410C23—21no—
1411C23—21no—
1412C23—21no—
1413C23—21no—
1414C23—21no—
1415C23—21no—
1416C23—21no—
1417C23—21no—
1418C23—21no—
1419C23—21no—
1420C23—21no—
1421C23—21no—
1422C23—21no—
1423C23—21no—
1424C23—21no—
1425C23—21no—
1426C23—21no—
1427C23—21no—
1428C23—21no—
1429C23—21no—
1430C23—21no—
1431C23—21no—
1432C23—21no—
1433C23—44no—
1434C23—82no—
1435C23—82no—
1436C23—82no—
1437C23—82no—
1438C23—82no—
1439C23—82no—
1440C23—172no—
1441C23—341no—
1442C23—341no—
1443C23—341no—
1444C23—341no—
1445C23—341no—
1446C23—341no—
1447C23C2×D4×D1712yes—
1448C23C24×D1711yescharacteristic
1449Q8—82no—
1450Q8—684no—
1451Q8—1362no—
1452Q8—1362no—
1453D4—44no—
1454D4—82no—
1455D4—82no—
1456D4—82no—
1457D4—82no—
1458D4—82no—
1459D4—82no—
1460D4—684no—
1461D4—1362no—
1462D4—1362no—
1463D4—1362no—
1464D4—1362no—
1465C2×C4—21no—
1466C2×C4—21no—
1467C2×C4—21no—
1468C2×C4—21no—
1469C2×C4—21no—
1470C2×C4—21no—
1471C2×C4—21no—
1472C2×C4—21no—
1473C2×C4—21no—
1474C2×C4—21no—
1475C2×C4—21no—
1476C2×C4—21no—
1477C2×C4—21no—
1478C2×C4—21no—
1479C2×C4—21no—
1480C2×C4—21no—
1481C2×C4—21no—
1482C2×C4—21no—
1483C2×C4—21no—
1484C2×C4—21no—
1485C2×C4—21no—
1486C2×C4—21no—
1487C2×C4—21no—
1488C2×C4—21no—
1489C2×C4—21no—
1490C2×C4—21no—
1491C2×C4—21no—
1492C2×C4—172no—
1493C2×C4—172no—
1494C2×C4—172no—
1495C2×C4—341no—
1496C2×C4—341no—
1497C2×C4—341no—
1498C2×C4—341no—
1499C2×C4—341no—
1500C2×C4—341no—
1501C2×C4—341no—
1502C2×C4—341no—
1503C2×C4—341no—
1504C2×C4—341no—
1505C2×C4—341no—
1506C2×C4—341no—
1507C2×C4—341no—
1508C2×C4—341no—
1509C2×C4—341no—
1510C2×C4—341no—
1511C2×C4—341no—
1512C2×C4—341no—
1513C2×C4—341no—
1514C2×C4—341no—
1515C2×C4—341no—
1516C2×C4—341no—
1517C2×C4—341no—
1518C2×C4—341no—
1519C2×C4—341no—
1520C2×C4—341no—
1521C2×C4—341no—
1522C2×C4—341no—
1523C2×C4—341no—
1524C2×C4—341no—
1525C2×C4—341no—
1526C2×C4—341no—
1527C2×C4—341no—
1528C2×C4—341no—
1529C2×C4—341no—
1530C2×C4—341no—
1531C2×C4—341no—
1532C2×C4—341no—
1533C2×C4—341no—
1534C2×C4—341no—
1535C2×C4—341no—
1536C2×C4—341no—
1537C2×C4—684no—
1538C2×C4—684no—
1539C2×C4—684no—
1540C2×C4—684no—
1541C2×C4—684no—
1542C2×C4—1362no—
1543C2×C4—1362no—
1544C2×C4C2×D4×D1712yes—
1545C2×C4C2×D4×D1712yes—
1546C2×C4#1058769112yes—
1547C22—22no—
1548C22—22no—
1549C22—22no—
1550C22—41no—
1551C22—41no—
1552C22—41no—
1553C22—41no—
1554C22—41no—
1555C22—41no—
1556C22—41no—
1557C22—41no—
1558C22—41no—
1559C22—41no—
1560C22—41no—
1561C22—41no—
1562C22—41no—
1563C22—41no—
1564C22—41no—
1565C22—41no—
1566C22—41no—
1567C22—41no—
1568C22—41no—
1569C22—41no—
1570C22—41no—
1571C22—41no—
1572C22—41no—
1573C22—41no—
1574C22—41no—
1575C22—41no—
1576C22—41no—
1577C22—41no—
1578C22—41no—
1579C22—41no—
1580C22—41no—
1581C22—41no—
1582C22—88no—
1583C22—342no—
1584C22—342no—
1585C22—342no—
1586C22—681no—
1587C22—681no—
1588C22—681no—
1589C22—681no—
1590C22C22×D4×D1711yescharacteristic
1591C22C2×#1058769111yescharacteristic
1592C22#1176364411yescharacteristic
1593C22#1176364411yescharacteristic
1594C22#1176364411yescharacteristic
1595C22#1176364411yescharacteristic
1596C22#1176364511yescharacteristic
1597C4—22no—
1598C4—22no—
1599C4—22no—
1600C4—41no—
1601C4—41no—
1602C4—41no—
1603C4—41no—
1604C4—41no—
1605C4—41no—
1606C4—41no—
1607C4—342no—
1608C4—342no—
1609C4—342no—
1610C4—681no—
1611C4—681no—
1612C4—681no—
1613C4—681no—
1614C4—681no—
1615C4—681no—
1616C4—681no—
1617C4—681no—
1618C4—681no—
1619C4—681no—
1620C4—681no—
1621C4—681no—
1622C2—42no—
1623C2—81no—
1624C2—81no—
1625C2—81no—
1626C2—81no—
1627C2—682no—
1628C2#1454211511yescharacteristic
1629C2#1454254011yescharacteristic
1630C2#1454257011yescharacteristic
1631C2#1454294311yescharacteristic
1632C2#1454305011yescharacteristic
1633C2#1454345111yescharacteristic
1634C2#1454347811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2670C2
hypercenter#2670D17
hypocenterC17#36745
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2670

Complements

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

NH ≅ G/Ntype
1. C2×#11763423C2semidirect
2. C2×#11763394C2semidirect
3. #14537114C2semidirect
4. #14537080C2semidirect
5. #14535700C2semidirect
6. #14535603C2semidirect
7. #14535599C2semidirect
8. #14535557C2semidirect
9. #14535376C2semidirect
10. #14535356C2semidirect
11. #14535333C2semidirect
12. #14535266C2semidirect
13. #14535226C2semidirect
14. #14535192C2semidirect
15. #14535171C2semidirect
16. #14535164C2semidirect
17. #14535090C2semidirect
18. #14535059C2semidirect
19. #14534988C2semidirect
20. #14534940C2semidirect
21. #14534915C2semidirect
22. #14534464C2semidirect
23. #14534419C2semidirect
24. #14534389C2semidirect
25. #14534374C2semidirect
26. #14534269C2semidirect
27. #14533939C2semidirect
28. #14532206C2semidirect
29. #14532165C2semidirect
30. #14531226C2semidirect
31. C17×#2670C2semidirect
34. C2×#10587630C22semidirect
35. C2×#10587562C22semidirect
42. C2×#10587571C22semidirect
44. C2×#10587569C22semidirect
49. C2×#10587564C22semidirect
50. C2×#10587564C22semidirect
51. C2×#10587632C22semidirect
58. C2×C4×Dic34C22semidirect
62. C2×#10587563C22semidirect
64. C2×C42×D17C22semidirect
65. #11762750C22semidirect
66. #11762749C22semidirect
69. #11762741C22semidirect
70. #11762739C22semidirect
71. #11762738C22semidirect
72. #11762738C22semidirect
77. #11762737C22semidirect
80. #11762734C22semidirect
84. #11762732C22semidirect
85. #11762730C22semidirect
86. #11762729C22semidirect
87. #11762728C22semidirect
89. #11762725C22semidirect
103. #11762721C22semidirect
104. #11762721C22semidirect
106. #11762717C22semidirect
107. #11762716C22semidirect
108. #11762715C22semidirect
109. #11762714C22semidirect
110. #11762713C22semidirect
115. #11762712C22semidirect
116. #11762708C22semidirect
117. #11762707C22semidirect
118. #11762706C22semidirect
119. #11762706C22semidirect
120. #11762704C22semidirect
123. #11762703C22semidirect
124. #11762703C22semidirect
129. #11762702C22semidirect
130. #11762702C22semidirect
131. #11762702C22semidirect
137. #11762697C22semidirect
138. #11762697C22semidirect
139. #11762694C22semidirect
140. #11762693C22semidirect
141. #11762693C22semidirect
142. #11762692C22semidirect
143. #11762692C22semidirect
144. #11762691C22semidirect
148. #11762689C22semidirect
149. #11762689C22semidirect
155. #11762685C22semidirect
156. #11762685C22semidirect
157. #11762685C22semidirect
159. #11762683C22semidirect
160. #11762681C22semidirect
161. #11762681C22semidirect
162. #11762680C22semidirect
163. #11762675C22semidirect
166. #11762667C22semidirect
167. #11762666C22semidirect
170. C4⋊C4×Dic17C22semidirect
172. #11762656C22semidirect
173. #11762654C22semidirect
330. #10587567D4semidirect
748. #2670D17semidirect
1196. C17#36745semidirect

Maximal subgroups

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

subgroupindex
C2×#117634232
C2×#117633942
#145371142
#145370802
#145357002
#145356032
#145355992
#145355572
#145353762
#145353562
#145353332
#145352662
#145352262
#145351922
#145351712
#145351642
#145350902
#145350592
#145349882
#145349402
#145349152
#145344642
#145344192
#145343892
#145343742
#145342692
#145339392
#145322062
#145321652
#145312262
C17×#26702
#3674517