Finite Group Databasebeta

← #17043457

Subgroups — #17043457

Order 4352.

1486 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763320C211yesmaximal, characteristic
2#14531167C211yesmaximal, characteristic, complemented
3#14529230C214yesmaximal, complemented
4#14529086C214yesmaximal, complemented
5#14528881C212yesmaximal, complemented
6#14528727C212yesmaximal, complemented
7C2×C17×#407C211yesmaximal, characteristic, complemented
8C22×#63252C2211yescharacteristic
9#11763320—21no—
10#11763320—21no—
11#11763320—21no—
12#11763320—21no—
13#11763320C412yescomplemented
14#11763320C412yescomplemented
15#11763320C2212yes—
16#11763320C2212yes—
17C2×#10587615—21no—
18C2×#10587610C411yescharacteristic, complemented
19C2×#10587610C411yescharacteristic, complemented
20C2×#10587616C411yescharacteristic, complemented
21C2×#10587616C411yescharacteristic, complemented
22C2×#10587639—21no—
23C2×C4×C22⋊D17—21no—
24C2×C4×C22⋊D17—21no—
25C2×#10587612C2211yescharacteristic
26C2×#10587612C2212yescomplemented
27C2×#10587496C2218yescomplemented
28#11762672—21no—
29#11762669—21no—
30#11762669—21no—
31#11762665—21no—
32C4×C22⋊Dic17C2212yes—
33C4×C22⋊Dic17C2212yescomplemented
34#11762570C2218yescomplemented
35C24×C4×C17C2211yescharacteristic
36C22×M16×C17C2212yescomplemented
37C17×#407—21no—
38C17×#407—21no—
39C17×#407C2212yes—
40C17×#407C2212yescomplemented
41C2×C17×C22⋊C8—21no—
42C2×C17×C22⋊C8—21no—
43C25×C17D411yescharacteristic
44C23×C4×C17—44no—
45C23×C4×C17C2×C411yescharacteristic
46C23×C4×C17C2×C411yescharacteristic
47C23×C4×C17C2×C411yescharacteristic
48C23×C4×C17C2×C411yescharacteristic
49C23×C4×C17D411yescharacteristic
50C23×C4×C17D411yescharacteristic
51C23×C4×C17D411yescharacteristic
52C23×C4×C17D411yescharacteristic
53C23×C4×C17D411yescharacteristic
54C23×C4×C17D411yescharacteristic
55C23×C4×C17D411yescharacteristic
56C23×C4×C17C2311yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C22×C22⋊D17—21no—
60C22×C22⋊D17—21no—
61C22×C22⋊D17—21no—
62C2×#63252—21no—
63C2×#63252—21no—
64C2×#63252—44no—
65C2×#63252C2×C412yes—
66C2×#63252C2312yes—
67C22×D68C2×C411yescharacteristic
68C22×C4×D17—21no—
69C22×Dic34C2×C411yescharacteristic
70C2×M16×C17—22no—
71C2×M16×C17—44no—
72C2×M16×C17C2314yes—
73C22×C8×C17—22no—
74#10587639—22no—
75#10587639—22no—
76#10587639—22no—
77#10587639—22no—
78C2×C22⋊Dic17—21no—
79C2×C22⋊Dic17—21no—
80C2×C22⋊Dic17—21no—
81C2×C22⋊Dic17—22no—
82C2×C22⋊Dic17—22no—
83C2×C22⋊Dic17—22no—
84#10587616—21no—
85#10587616—21no—
86#10587616—21no—
87#10587616—21no—
88#10587616C2×C412yes—
89#10587616C2×C412yes—
90#10587616C2×C412yes—
91#10587616C2×C412yes—
92#10587615—22no—
93#10587615—22no—
94#10587615—22no—
95#10587615—22no—
96C4×C22⋊D17—22no—
97C4×C22⋊D17—22no—
98C4×C22⋊D17—22no—
99C4×C22⋊D17—22no—
100C4×C22⋊D17—22no—
101C4×C22⋊D17—22no—
102C4×C22⋊D17—22no—
103C4×C22⋊D17—22no—
104C2×#63227—21no—
105C2×#63227—21no—
106#10587612—21no—
107#10587612—21no—
108#10587612—44no—
109#10587612C2×C412yes—
110#10587612C2312yes—
111C2×C4⋊Dic17—22no—
112C2×C4⋊Dic17C2×C411yescharacteristic
113C2×C4⋊Dic17C2×C411yescharacteristic
114#10587610—21no—
115#10587610—21no—
116#10587610—21no—
117#10587610—21no—
118#10587610C2×C412yes—
119#10587610C2×C412yes—
120#10587610C2×C412yes—
121#10587610C2×C412yes—
122C2×#63225—21no—
123C2×#63225—21no—
124C2×C4×Dic17—21no—
125C2×C4×Dic17C2314yes—
126C17×C22⋊C8—22no—
127C17×C22⋊C8—22no—
128C17×C22⋊C8—22no—
129C17×C22⋊C8—22no—
130#10587502—22no—
131#10587502—22no—
132#10587496—48no—
133C24×C17—42no—
134C24×C17—42no—
135C24×C17—42no—
136C24×C17C22⋊C411yescharacteristic
137C24×C17C22⋊C411yescharacteristic
138C24×C17C22⋊C411yescharacteristic
139C24×C17C22⋊C411yescharacteristic
140C24×C17C2×D411yescharacteristic
141C24×C17C2×D411yescharacteristic
142C24×C17C2×D411yescharacteristic
143C23×D17—21no—
144C22×C4×C17—24no—
145C22×C4×C17—24no—
146C22×C4×C17—24no—
147C22×C4×C17—42no—
148C22×C4×C17—42no—
149C22×C4×C17—42no—
150C22×C4×C17—42no—
151C22×C4×C17—42no—
152C22×C4×C17—42no—
153C22×C4×C17—42no—
154C22×C4×C17—42no—
155C22×C4×C17—42no—
156C22×C4×C17—42no—
157C22×C4×C17—42no—
158C22×C4×C17C22⋊C411yescharacteristic
159C22×C4×C17C22⋊C411yescharacteristic
160C22×C4×C17C22⋊C411yescharacteristic
161C22×C4×C17C22⋊C411yescharacteristic
162C22×C4×C17C22⋊C411yescharacteristic
163C22×C4×C17C22⋊C411yescharacteristic
164C22×C4×C17C22⋊C411yescharacteristic
165C22×C4×C17C22⋊C411yescharacteristic
166C22×C4×C17C22⋊C411yescharacteristic
167C22×C4×C17C22⋊C411yescharacteristic
168C22×C4×C17C22⋊C411yescharacteristic
169C22×C4×C17C22⋊C411yescharacteristic
170C22×C4×C17C22×C411yescharacteristic
171C22×C4×C17C22×C411yescharacteristic
172C22×C4×C17C22×C411yescharacteristic
173C22×C4×C17C22×C411yescharacteristic
174C22×C4×C17C22×C411yescharacteristic
175C22×C4×C17C22×C411yescharacteristic
176C22×C4×C17C2×D411yescharacteristic
177C22×C4×C17C2×D411yescharacteristic
178C22×C4×C17C2×D411yescharacteristic
179C22×C4×C17C2×D411yescharacteristic
180C22×C4×C17C2×D411yescharacteristic
181C22×C4×C17C2×D411yescharacteristic
182C22×C4×C17C2×D411yescharacteristic
183C22×C4×C17C2×D411yescharacteristic
184C22×C4×C17C2×D411yescharacteristic
185C22×C4×C17C2411yescharacteristic
186C2×C22⋊D17—22no—
187C2×C22⋊D17—22no—
188C2×C22⋊D17—22no—
189C2×C22⋊D17—22no—
190C2×C22⋊D17—22no—
191C2×C22⋊D17—22no—
192C2×C22⋊D17—44no—
193C2×C22⋊D17—44no—
194C2×C22⋊D17—44no—
195C22×Dic17—21no—
196C22×Dic17—21no—
197C22×Dic17—21no—
198C22×Dic17—24no—
199#63252—28no—
200#63252—44no—
201#63252—44no—
202#63252—44no—
203C2×D68—21no—
204C2×D68—42no—
205C2×D68C22×C412yes—
206C2×C4×D17—22no—
207C2×C4×D17—22no—
208C2×C4×D17—44no—
209C2×Dic34—21no—
210C2×Dic34—42no—
211C2×Dic34C22×C412yes—
212M16×C17—28no—
213M16×C17—44no—
214C2×C8×C17—24no—
215C2×C8×C17—44no—
216C22⋊Dic17—22no—
217C22⋊Dic17—22no—
218C22⋊Dic17—22no—
219C22⋊Dic17—22no—
220C22⋊Dic17—22no—
221C22⋊Dic17—22no—
222C22⋊Dic17—44no—
223C22⋊Dic17—44no—
224C22⋊Dic17—44no—
225#63227—22no—
226#63227—22no—
227#63227—22no—
228#63227—22no—
229C4⋊Dic17—21no—
230C4⋊Dic17—21no—
231C4⋊Dic17—44no—
232C4⋊Dic17C22×C412yes—
233C4⋊Dic17C22×C412yes—
234#63225—22no—
235#63225—22no—
236#63225—22no—
237#63225—22no—
238C4×Dic17—22no—
239C4×Dic17—22no—
240C4×Dic17—28no—
241#21774—171nomaximal, Sylow
242C23×C17—22no—
243C23×C17—22no—
244C23×C17—22no—
245C23×C17—22no—
246C23×C17—22no—
247C23×C17—22no—
248C23×C17—22no—
249C23×C17—22no—
250C23×C17—22no—
251C23×C17—41no—
252C23×C17—41no—
253C23×C17—41no—
254C23×C17—41no—
255C23×C17—41no—
256C23×C17—41no—
257C23×C17—41no—
258C23×C17—41no—
259C23×C17—41no—
260C23×C17—41no—
261C23×C17—41no—
262C23×C17—41no—
263C23×C17—416no—
264C23×C17C2×C22⋊C411yescharacteristic
265C23×C17C2×C22⋊C411yescharacteristic
266C23×C17C2×C22⋊C411yescharacteristic
267C23×C17C2×C22⋊C411yescharacteristic
268C23×C17C2×C22⋊C411yescharacteristic
269C23×C17C2×C22⋊C411yescharacteristic
270C23×C17C22×D411yescharacteristic
271C22×D17—22no—
272C22×D17—42no—
273C22×D17—42no—
274C22×D17—42no—
275C2×C4×C17—22no—
276C2×C4×C17—22no—
277C2×C4×C17—22no—
278C2×C4×C17—22no—
279C2×C4×C17—22no—
280C2×C4×C17—22no—
281C2×C4×C17—22no—
282C2×C4×C17—22no—
283C2×C4×C17—22no—
284C2×C4×C17—22no—
285C2×C4×C17—22no—
286C2×C4×C17—22no—
287C2×C4×C17—22no—
288C2×C4×C17—22no—
289C2×C4×C17—22no—
290C2×C4×C17—41no—
291C2×C4×C17—41no—
292C2×C4×C17—41no—
293C2×C4×C17—41no—
294C2×C4×C17—41no—
295C2×C4×C17—41no—
296C2×C4×C17—41no—
297C2×C4×C17—41no—
298C2×C4×C17—41no—
299C2×C4×C17—41no—
300C2×C4×C17—41no—
301C2×C4×C17—41no—
302C2×C4×C17C2×C22⋊C411yescharacteristic
303C2×C4×C17C2×C22⋊C411yescharacteristic
304C2×C4×C17C2×C22⋊C411yescharacteristic
305C2×C4×C17C2×C22⋊C411yescharacteristic
306C2×C4×C17C2×C22⋊C411yescharacteristic
307C2×C4×C17C2×C22⋊C411yescharacteristic
308C2×C4×C17C23×C411yescharacteristic
309C2×C4×C17C22×D411yescharacteristic
310C2×C4×C17H(5,𝔽2)14yes—
311C22⋊D17—44no—
312C22⋊D17—44no—
313C22⋊D17—44no—
314C22⋊D17—44no—
315C22⋊D17—44no—
316C22⋊D17—44no—
317C2×Dic17—22no—
318C2×Dic17—22no—
319C2×Dic17—22no—
320C2×Dic17—42no—
321C2×Dic17—42no—
322C2×Dic17—42no—
323C2×Dic17—44no—
324C2×Dic17—44no—
325C2×Dic17—44no—
326D68—24no—
327D68—42no—
328C4×D17—44no—
329C4×D17—44no—
330Dic34—24no—
331Dic34—42no—
332C8×C17—44no—
333C2×#525—171no—
334C2×#407D1711yescharacteristic, complemented
335#2280—171no—
336#1897—174no—
337#1871—174no—
338#1826—172no—
339#1789—172no—
340C22×C17—21no—
341C22×C17—21no—
342C22×C17—21no—
343C22×C17—21no—
344C22×C17—21no—
345C22×C17—21no—
346C22×C17—21no—
347C22×C17—21no—
348C22×C17—21no—
349C22×C17—21no—
350C22×C17—21no—
351C22×C17—21no—
352C22×C17—21no—
353C22×C17—21no—
354C22×C17—21no—
355C22×C17—21no—
356C22×C17—21no—
357C22×C17—21no—
358C22×C17—44no—
359C22×C17—44no—
360C22×C17—44no—
361C22×C17—44no—
362C22×C17—44no—
363C22×C17—44no—
364C22×C17—44no—
365C22×C17#42112yes—
366C22×C17#42112yes—
367C22×C17C22×C22⋊C411yescharacteristic
368C22×C17#53412yes—
369C2×D17—42no—
370C2×D17—42no—
371C2×D17—42no—
372C2×D17—84no—
373C4×C17—21no—
374C4×C17—21no—
375C4×C17—21no—
376C4×C17—21no—
377C4×C17—21no—
378C4×C17—21no—
379C4×C17#51812yes—
380C4×C17#53412yes—
381Dic17—42no—
382Dic17—42no—
383Dic17—42no—
384Dic17—84no—
385C22×#41—171no—
386C24×C4C2×D1711yescharacteristic
387C22×M16C2×D1712yescomplemented
388#525—172no—
389#525—172no—
390#525—172no—
391#525—172no—
392#525—341no—
393#525—341no—
394#525—341no—
395#525—341no—
396C2×#123—341no—
397C2×C22⋊Q8—171no—
398C2×C22⋊Q8—171no—
399C2×#121—171no—
400C2×#121—171no—
401C2×#120—341no—
402C2×C4×D4—341no—
403C2×C4×D4—341no—
404C2×#117—172no—
405C2×#117—171no—
406C2×#104—178no—
407#407—21no—
408#407—21no—
409#407C2×D1712yes—
410#407C2×D1712yescomplemented
411C2×C22⋊C8—21no—
412C2×C22⋊C8—21no—
413#381—341no—
414#380—341no—
415#380—341no—
416#379—341no—
417C4×C22⋊C4—172no—
418C4×C22⋊C4—172no—
419#339—178no—
420C2×C17—22no—
421C2×C17—22no—
422C2×C17—22no—
423C2×C17—41no—
424C2×C17—41no—
425C2×C17—41no—
426C2×C17—41no—
427C2×C17#230811yescharacteristic
428C2×C17C2×#42111yescharacteristic
429C2×C17C2×#42111yescharacteristic
430D17—82no—
431C25D6811yescharacteristic
432C2×#41—172no—
433C2×#41—172no—
434C2×#41—341no—
435C2×#41—341no—
436C2×#41—684no—
437C22×Q8—171no—
438C22×D4—171no—
439C22×D4—341no—
440C22×D4—341no—
441C22×D4—341no—
442C23×C4—44no—
443C23×C4—341no—
444C23×C4C4×D1711yescharacteristic
445C23×C4C4×D1711yescharacteristic
446C23×C4C4×D1711yescharacteristic
447C23×C4C4×D1711yescharacteristic
448C23×C4D6811yescharacteristic
449C23×C4D6811yescharacteristic
450C23×C4D6811yescharacteristic
451C23×C4C22⋊D1711yescharacteristic
452C23×C4C22⋊D1711yescharacteristic
453C23×C4C22⋊D1711yescharacteristic
454C23×C4C22⋊D1711yescharacteristic
455C23×C4C22×D1711yescharacteristic
456C23×C4C22×D1711yescharacteristic
457C23×C4C22×D1711yescharacteristic
458C2×M16—22no—
459C2×M16—44no—
460C2×M16C22×D1714yes—
461C22×C8—22no—
462#123—342no—
463#123—342no—
464#123—342no—
465#123—342no—
466C22⋊Q8—172no—
467C22⋊Q8—172no—
468C22⋊Q8—172no—
469C22⋊Q8—172no—
470C22⋊Q8—341no—
471C22⋊Q8—341no—
472C22⋊Q8—341no—
473C22⋊Q8—341no—
474#121—172no—
475#121—172no—
476#121—172no—
477#121—172no—
478#121—341no—
479#121—341no—
480#121—341no—
481#121—341no—
482#120—342no—
483#120—342no—
484#120—342no—
485#120—342no—
486C4×D4—342no—
487C4×D4—342no—
488C4×D4—342no—
489C4×D4—342no—
490C4×D4—342no—
491C4×D4—342no—
492C4×D4—342no—
493C4×D4—342no—
494#117—172no—
495#117—172no—
496#117—341no—
497#117—341no—
498#117—684no—
499C2×C4⋊C4—171no—
500C2×C4⋊C4—171no—
501C2×C4⋊C4—341no—
502C2×C4⋊C4—341no—
503C2×C4⋊C4—342no—
504C2×C22⋊C4—341no—
505C2×C22⋊C4—341no—
506C2×C22⋊C4—341no—
507C2×C22⋊C4—341no—
508C2×C22⋊C4—341no—
509C2×C22⋊C4—342no—
510C2×C22⋊C4—342no—
511C2×C22⋊C4—342no—
512C2×C42—174no—
513C2×C42—341no—
514#104—688no—
515C22⋊C8—22no—
516C22⋊C8—22no—
517C22⋊C8—22no—
518C22⋊C8—22no—
519#95—342no—
520#95—342no—
521C17#2177411yescharacteristic, complemented, Sylow
522C24—42no—
523C24—42no—
524C24—42no—
525C24—341no—
526C24#6322711yescharacteristic
527C24#6322711yescharacteristic
528C24#6322711yescharacteristic
529C24#6322711yescharacteristic
530C24C2×D6811yescharacteristic
531C24C2×D6811yescharacteristic
532C24C2×D6811yescharacteristic
533#41—348no—
534#41—684no—
535#41—684no—
536#41—684no—
537C2×Q8—172no—
538C2×Q8—341no—
539C2×Q8—682no—
540C2×D4—172no—
541C2×D4—342no—
542C2×D4—342no—
543C2×D4—342no—
544C2×D4—342no—
545C2×D4—342no—
546C2×D4—342no—
547C2×D4—341no—
548C2×D4—682no—
549C2×D4—684no—
550C2×D4—684no—
551C2×D4—684no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—341no—
567C22×C4—341no—
568C22×C4—341no—
569C22×C4—342no—
570C22×C4—342no—
571C22×C4—344no—
572C22×C4—684no—
573C22×C4#6322711yescharacteristic
574C22×C4#6322711yescharacteristic
575C22×C4#6322711yescharacteristic
576C22×C4#6322711yescharacteristic
577C22×C4#6322711yescharacteristic
578C22×C4#6322711yescharacteristic
579C22×C4#6322711yescharacteristic
580C22×C4#6322711yescharacteristic
581C22×C4#6322711yescharacteristic
582C22×C4#6322711yescharacteristic
583C22×C4#6322711yescharacteristic
584C22×C4#6322711yescharacteristic
585C22×C4C2×C4×D1711yescharacteristic
586C22×C4C2×C4×D1711yescharacteristic
587C22×C4C2×C4×D1711yescharacteristic
588C22×C4C2×C4×D1711yescharacteristic
589C22×C4C2×C4×D1711yescharacteristic
590C22×C4C2×C4×D1711yescharacteristic
591C22×C4C2×D6811yescharacteristic
592C22×C4C2×D6811yescharacteristic
593C22×C4C2×D6811yescharacteristic
594C22×C4C2×C22⋊D1711yescharacteristic
595C22×C4C2×C22⋊D1711yescharacteristic
596C22×C4C2×C22⋊D1711yescharacteristic
597C22×C4C2×C22⋊D1711yescharacteristic
598C22×C4C2×C22⋊D1711yescharacteristic
599C22×C4C2×C22⋊D1711yescharacteristic
600C22×C4C23×D1711yescharacteristic
601M16—28no—
602M16—44no—
603C2×C8—24no—
604C2×C8—44no—
605C4⋊C4—172no—
606C4⋊C4—172no—
607C4⋊C4—341no—
608C4⋊C4—341no—
609C4⋊C4—342no—
610C4⋊C4—342no—
611C4⋊C4—342no—
612C4⋊C4—342no—
613C4⋊C4—684no—
614C22⋊C4—342no—
615C22⋊C4—342no—
616C22⋊C4—342no—
617C22⋊C4—342no—
618C22⋊C4—342no—
619C22⋊C4—342no—
620C22⋊C4—342no—
621C22⋊C4—342no—
622C22⋊C4—342no—
623C22⋊C4—342no—
624C22⋊C4—684no—
625C22⋊C4—684no—
626C22⋊C4—684no—
627C42—342no—
628C42—342no—
629C42—348no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—416no—
652C23—342no—
653C23—682no—
654C23—682no—
655C23—682no—
656C23C2×#6322711yescharacteristic
657C23C2×#6322711yescharacteristic
658C23C2×#6322711yescharacteristic
659C23C2×#6322711yescharacteristic
660C23C2×#6322711yescharacteristic
661C23C2×#6322711yescharacteristic
662C23C22×D6811yescharacteristic
663Q8—344no—
664Q8—682no—
665D4—344no—
666D4—682no—
667D4—684no—
668D4—684no—
669D4—684no—
670D4—684no—
671D4—684no—
672D4—684no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—342no—
701C2×C4—342no—
702C2×C4—342no—
703C2×C4—684no—
704C2×C4—682no—
705C2×C4—682no—
706C2×C4—682no—
707C2×C4—684no—
708C2×C4—684no—
709C2×C4—684no—
710C2×C4—684no—
711C2×C4C2×#6322711yescharacteristic
712C2×C4C2×#6322711yescharacteristic
713C2×C4C2×#6322711yescharacteristic
714C2×C4C2×#6322711yescharacteristic
715C2×C4C2×#6322711yescharacteristic
716C2×C4C2×#6322711yescharacteristic
717C2×C4C22×C4×D1711yescharacteristic
718C2×C4#1058769114yes—
719C2×C4C22×C22⋊D1711yescharacteristic
720C8—44no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—682no—
747C22—682no—
748C22—682no—
749C22—1364no—
750C22#1176282512yes—
751C22#1176282512yes—
752C22C22×#6322711yescharacteristic
753C22#1176337112yes—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—21no—
760C4—682no—
761C4—682no—
762C4—682no—
763C4—1364no—
764C4#1176328212yes—
765C4#1176336812yes—
766C2—22no—
767C2—22no—
768C2—22no—
769C2—41no—
770C2—41no—
771C2—41no—
772C2—41no—
773C2—1362no—
774C2#1453135911yescharacteristic
775C2C2×#1176282511yescharacteristic
776C2C2×#1176282511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C17×#407C2
socleC22×C17C22×C22⋊C4
prime radicalC2×#11763320C2
cosocleC22×C4×C17C24
hypercenterC2×#407D17
hypocenterC17#21774
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. #14531167C2semidirect
3. #14529230C2semidirect
4. #14529086C2semidirect
5. #14528881C2semidirect
6. #14528727C2semidirect
7. C2×C17×#407C2semidirect
13. #11763320C4semidirect
14. #11763320C4semidirect
18. C2×#10587610C4semidirect
19. C2×#10587610C4semidirect
20. C2×#10587616C4semidirect
21. C2×#10587616C4semidirect
26. C2×#10587612C22semidirect
27. C2×#10587496C22semidirect
33. C4×C22⋊Dic17C22semidirect
34. #11762570C22semidirect
36. C22×M16×C17C22semidirect
40. C17×#407C22semidirect
334. C2×#407D17semidirect
387. C22×M16C2×D17semidirect
410. #407C2×D17semidirect
521. C17#21774semidirect

Maximal subgroups

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

subgroupindex
C2×#117633202
#145311672
#145292302
#145290862
#145288812
#145287272
C2×C17×#4072
#2177417