Finite Group Databasebeta

← #17049813

Subgroups — #17049813

Order 4352.

1478 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763464C211yesmaximal, characteristic
2C2×#11762881C211yesmaximal, characteristic, complemented
3C2×#11762808C211yesmaximal, characteristic, complemented
4C2×#11762803C211yesmaximal, characteristic, complemented
5#14529707C211yesmaximal, characteristic, complemented
6#14529603C211yesmaximal, characteristic, complemented
7#14529215C211yesmaximal, characteristic, complemented
8#14529205C211yesmaximal, characteristic, complemented
9#14529096C211yesmaximal, characteristic, complemented
10#14529091C211yesmaximal, characteristic, complemented
11#14528791C211yesmaximal, characteristic, complemented
12#14528722C211yesmaximal, characteristic, complemented
13#14528722C211yesmaximal, characteristic, complemented
14#14528612C211yesmaximal, characteristic, complemented
15C17×#2352C211yesmaximal, characteristic, complemented
16C22×#63252C2211yescharacteristic
17C22×#63252C2211yescharacteristic
18C22×#63223C2211yescharacteristic
19C23×#3622C2211yescharacteristic
20#11763464—24no—
21#11763464C418yescomplemented
22C2×#10587555C2211yescharacteristic
23C2×#10587569—21no—
24C2×#10587569—21no—
25C2×#10587610C2211yescharacteristic
26C2×#10587610C2211yescharacteristic
27C2×#10587624—21no—
28C2×C4×D68C2211yescharacteristic
29C2×C4⋊C4×D17—21no—
30#11762881—24no—
31C2×C4⋊#3622C2211yescharacteristic
32#11762808—24no—
33#11762803—24no—
34C2×#10587481C2211yescharacteristic
35C2×#10587481C2211yescharacteristic
36C2×#10587481C2211yescharacteristic
37C2×#10587481C2211yescharacteristic
38C2×#10587481C2211yescharacteristic
39C2×#10587481C2211yescharacteristic
40C2×#10587481C2211yescharacteristic
41C2×#10587481C2211yescharacteristic
42C2×#10587480C2211yescharacteristic
43C2×#10587480C2211yescharacteristic
44C2×#10587480C2211yescharacteristic
45C2×#10587480C2211yescharacteristic
46C2×C22⋊#3622C2211yescharacteristic
47C2×C22⋊#3622C2211yescharacteristic
48C2×#10587474C2211yescharacteristic
49#11762571C2211yescharacteristic
50#11762571C2211yescharacteristic
51#11762571C2211yescharacteristic
52#11762571C2211yescharacteristic
53C2×C4×D4×C17C2211yescharacteristic
54C2×C17×#117C2211yescharacteristic
55C22×C4⋊C4×C17C2211yescharacteristic
56C17×#388—21no—
57C17×#387—21no—
58C17×#386—21no—
59C17×#382C2211yescharacteristic
60C17×#380C2211yescharacteristic
61C17×#380C2211yescharacteristic
62C4×C4⋊C4×C17C2211yescharacteristic
63C4×C22⋊C4×C17—21no—
64C22×D4×C17D411yescharacteristic
65C23×C4×C17—21no—
66C23×C4×C17C2311yescharacteristic
67C23×C4×C17C2311yescharacteristic
68C22×C22⋊D17—21no—
69C22×C22⋊D17—21no—
70C2×#63252—22no—
71C2×#63252—22no—
72C2×#63252—22no—
73C2×#63252—22no—
74C2×#63252—22no—
75C2×#63252—22no—
76C2×#63252—41no—
77C2×#63252—41no—
78C2×#63252—41no—
79C2×#63252—41no—
80C2×#63252C2×C414yes—
81C2×#63252C2×C414yescomplemented
82C22×D68C2311yescharacteristic
83C22×C4×D17—21no—
84C22×C4×D17—21no—
85C22×C4×D17—21no—
86C22×Dic34C2311yescharacteristic
87C22×Dic34C2311yescharacteristic
88C4×D4×C17C2×C414yes—
89C4×D4×C17D414yes—
90C17×#117—22no—
91C17×#117—41no—
92C2×C4⋊C4×C17—22no—
93C2×C4⋊C4×C17—21no—
94C2×C4⋊C4×C17—41no—
95C2×C4⋊C4×C17D411yescharacteristic
96C2×C4⋊C4×C17C2311yescharacteristic
97C2×C4⋊C4×C17C2311yescharacteristic
98C2×C4⋊C4×C17C2311yescharacteristic
99C2×C4⋊C4×C17C2311yescharacteristic
100C2×C22⋊C4×C17—21no—
101C2×C22⋊C4×C17—21no—
102C2×C22⋊C4×C17—21no—
103C2×C22⋊C4×C17D411yescharacteristic
104C2×C22⋊C4×C17D411yescharacteristic
105C2×C42×C17—21no—
106C2×C42×C17—21no—
107C2×C42×C17C2311yescharacteristic
108C2×C22⋊Dic17—21no—
109C2×C22⋊Dic17—21no—
110#10587624—28no—
111C2×#63227—21no—
112C2×C4⋊Dic17—21no—
113C2×C4⋊Dic17—21no—
114C2×C4⋊Dic17C2311yescharacteristic
115#10587610—22no—
116#10587610—22no—
117#10587610C2×C414yes—
118#10587610C2×C414yescomplemented
119C2×#63225—21no—
120C2×#63225—21no—
121C2×#63223—22no—
122C2×#63223—22no—
123C2×#63223—41no—
124C22×#3622—22no—
125C22×#3622—22no—
126C22×#3622—41no—
127C22×#3622C2311yescharacteristic
128C22×#3622C2311yescharacteristic
129C22×#3622C2311yescharacteristic
130C22×#3622C2311yescharacteristic
131C4⋊C4×D17—28no—
132#10587569—28no—
133#10587569—28no—
134C4×D68—22no—
135C4×D68C2×C414yescomplemented
136#10587555—22no—
137#10587555C2×C414yescomplemented
138C17×#95—21no—
139C17×#95—21no—
140C17×#95—21no—
141C17×#95—21no—
142C17×#95—21no—
143C22⋊#3622—22no—
144C22⋊#3622—22no—
145#10587481—22no—
146#10587481—22no—
147#10587481—22no—
148#10587481—22no—
149#10587481—41no—
150#10587481—41no—
151#10587481—41no—
152#10587481—41no—
153#10587480—22no—
154#10587480—22no—
155#10587480—22no—
156#10587480D414yescomplemented
157C4⋊#3622—22no—
158#10587474—22no—
159C24×C17C2×D411yescharacteristic
160C24×C17C2×D411yescharacteristic
161C23×D17—21no—
162C2×D4×C17—41no—
163C2×D4×C17—41no—
164C2×D4×C17C22⋊C414yes—
165C22×C4×C17—21no—
166C22×C4×C17—21no—
167C22×C4×C17—21no—
168C22×C4×C17—21no—
169C22×C4×C17—21no—
170C22×C4×C17—21no—
171C22×C4×C17—21no—
172C22×C4×C17—21no—
173C22×C4×C17—21no—
174C22×C4×C17—21no—
175C22×C4×C17—21no—
176C22×C4×C17—21no—
177C22×C4×C17—42no—
178C22×C4×C17—42no—
179C22×C4×C17—81no—
180C22×C4×C17C22×C412yes—
181C22×C4×C17C22×C412yes—
182C22×C4×C17C2×D412yes—
183C22×C4×C17C2×D412yes—
184C22×C4×C17C2×D411yescharacteristic
185C22×C4×C17C2×D411yescharacteristic
186C22×C4×C17C2×D411yescharacteristic
187C22×C4×C17C2×D411yescharacteristic
188C22×C4×C17C2411yescharacteristic
189C2×C22⋊D17—24no—
190C2×C22⋊D17—24no—
191C2×C22⋊D17—42no—
192C2×C22⋊D17—42no—
193C2×C22⋊D17—42no—
194C2×C22⋊D17—42no—
195C22×Dic17—21no—
196C22×Dic17—21no—
197C22×Dic17—21no—
198#63252—28no—
199#63252—28no—
200#63252—44no—
201#63252—44no—
202#63252—44no—
203#63252—44no—
204#63252—44no—
205#63252—44no—
206C2×D68—21no—
207C2×D68—21no—
208C2×D68—21no—
209C2×D68C22×C412yes—
210C2×D68C2×D412yes—
211C2×D68#4112yes—
212C2×C4×D17—24no—
213C2×C4×D17—24no—
214C2×C4×D17—24no—
215C2×C4×D17—42no—
216C2×C4×D17—42no—
217C2×C4×D17—42no—
218C2×C4×D17—42no—
219C2×C4×D17—42no—
220C2×C4×D17—42no—
221C2×Dic34—21no—
222C2×Dic34—21no—
223C2×Dic34—21no—
224C2×Dic34—21no—
225C2×Dic34—21no—
226C2×Dic34—21no—
227C2×Dic34—21no—
228C2×Dic34—21no—
229C2×Dic34—21no—
230C2×Dic34—21no—
231C2×Dic34C22×C412yes—
232C2×Dic34C22×C412yes—
233C4⋊C4×C17—21no—
234C4⋊C4×C17—21no—
235C4⋊C4×C17—21no—
236C4⋊C4×C17—21no—
237C4⋊C4×C17—21no—
238C4⋊C4×C17—21no—
239C4⋊C4×C17—21no—
240C4⋊C4×C17—42no—
241C4⋊C4×C17C22⋊C414yes—
242C4⋊C4×C17C2×D412yes—
243C22⋊C4×C17—42no—
244C22⋊C4×C17—42no—
245C22⋊C4×C17—81no—
246C22⋊C4×C17C22⋊C414yes—
247C22⋊C4×C17C22⋊C414yes—
248C42×C17—42no—
249C42×C17—81no—
250C42×C17C22×C412yes—
251C42×C17C2×D412yes—
252C22⋊Dic17—24no—
253C22⋊Dic17—24no—
254#63227—24no—
255C4⋊Dic17—24no—
256C4⋊Dic17—24no—
257C4⋊Dic17—21no—
258C4⋊Dic17C22×C412yes—
259#63225—24no—
260#63225—24no—
261#63223—44no—
262C2×#3622—21no—
263C2×#3622—21no—
264C2×#3622—21no—
265C2×#3622—21no—
266C2×#3622—21no—
267C2×#3622—21no—
268C2×#3622—21no—
269C2×#3622—21no—
270C2×#3622—21no—
271C2×#3622—21no—
272C2×#3622—21no—
273C2×#3622—44no—
274C2×#3622C2×D412yes—
275#22420—171nomaximal, Sylow
276C23×C17—21no—
277C23×C17—21no—
278C23×C17—21no—
279C23×C17—21no—
280C23×C17—21no—
281C23×C17—21no—
282C23×C17—21no—
283C23×C17—21no—
284C23×C17—21no—
285C23×C17—21no—
286C23×C17—21no—
287C23×C17—21no—
288C23×C17C2×C22⋊C412yes—
289C23×C17C2×C22⋊C412yes—
290C23×C17C22×D411yescharacteristic
291C22×D17—22no—
292C22×D17—22no—
293C22×D17—22no—
294C22×D17—41no—
295C22×D17—41no—
296C22×D17—41no—
297C22×D17—41no—
298D4×C17—44no—
299C2×C4×C17—21no—
300C2×C4×C17—21no—
301C2×C4×C17—21no—
302C2×C4×C17—21no—
303C2×C4×C17—21no—
304C2×C4×C17—21no—
305C2×C4×C17—21no—
306C2×C4×C17—21no—
307C2×C4×C17—22no—
308C2×C4×C17—22no—
309C2×C4×C17—22no—
310C2×C4×C17—22no—
311C2×C4×C17—22no—
312C2×C4×C17—22no—
313C2×C4×C17—22no—
314C2×C4×C17—22no—
315C2×C4×C17—22no—
316C2×C4×C17—41no—
317C2×C4×C17—41no—
318C2×C4×C17—41no—
319C2×C4×C17—41no—
320C2×C4×C17—41no—
321C2×C4×C17—41no—
322C2×C4×C17—41no—
323C2×C4×C17—41no—
324C2×C4×C17—41no—
325C2×C4×C17—41no—
326C2×C4×C17—41no—
327C2×C4×C17—84no—
328C2×C4×C17C2×C22⋊C412yes—
329C2×C4×C17C2×C22⋊C412yes—
330C2×C4×C17C2×C22⋊C412yes—
331C2×C4×C17C2×C22⋊C412yes—
332C2×C4×C17C23×C411yescharacteristic
333C2×C4×C17C22×D411yescharacteristic
334C2×C4×C17C22×D411yescharacteristic
335C2×C4×C17C2×#4111yescharacteristic
336C2×C4×C17H(5,𝔽2)11yescharacteristic
337C2×C4×C17H(5,𝔽2)11yescharacteristic
338C22⋊D17—48no—
339C22⋊D17—48no—
340C2×Dic17—22no—
341C2×Dic17—22no—
342C2×Dic17—22no—
343C2×Dic17—41no—
344C2×Dic17—41no—
345C2×Dic17—41no—
346C2×Dic17—41no—
347C2×Dic17—41no—
348C2×Dic17—41no—
349D68—22no—
350D68—22no—
351D68—22no—
352D68C4×D414yes—
353C4×D17—48no—
354C4×D17—48no—
355C4×D17—48no—
356Dic34—22no—
357Dic34—22no—
358Dic34—22no—
359Dic34—22no—
360Dic34—41no—
361Dic34—41no—
362Dic34—41no—
363Dic34—41no—
364#3622—22no—
365#3622—41no—
366#3622—41no—
367#3622—41no—
368C2×#547—171no—
369C2×#435—171no—
370C2×#417—171no—
371C2×#416—171no—
372#2352D1711yescharacteristic, complemented
373#1981—171no—
374#1960—171no—
375#1894—171no—
376#1892—171no—
377#1873—171no—
378#1872—171no—
379#1804—171no—
380#1788—171no—
381#1788—171no—
382#1762—171no—
383C22×C17—22no—
384C22×C17—22no—
385C22×C17—22no—
386C22×C17—22no—
387C22×C17—22no—
388C22×C17—22no—
389C22×C17—41no—
390C22×C17—41no—
391C22×C17—41no—
392C22×C17—41no—
393C22×C17—41no—
394C22×C17—41no—
395C22×C17—41no—
396C22×C17—41no—
397C22×C17C22×C22⋊C411yescharacteristic
398C22×C17D4211yescharacteristic
399C22×C17#54611yescharacteristic
400C22×C17#57511yescharacteristic
401C22×C17#57511yescharacteristic
402C22×C17#57711yescharacteristic
403C22×C17#57811yescharacteristic
404C2×D17—24no—
405C2×D17—42no—
406C2×D17—42no—
407C2×D17—42no—
408C2×D17—42no—
409C2×D17—42no—
410C2×D17—42no—
411C4×C17—22no—
412C4×C17—22no—
413C4×C17—22no—
414C4×C17—22no—
415C4×C17—42no—
416C4×C17—81no—
417C4×C17—81no—
418C4×C17—81no—
419C4×C17C2×C4×D411yescharacteristic
420C4×C17#51811yescharacteristic
421C4×C17D4211yescharacteristic
422C4×C17#54611yescharacteristic
423Dic17—42no—
424Dic17—42no—
425Dic17—42no—
426C22×#41—171no—
427C22×#41—171no—
428C22×M16—171no—
429C23×C8—171no—
430#547—178no—
431#547—344no—
432C2×C4⋊Q8—171no—
433C2×#123—341no—
434C2×#123—341no—
435C2×C22⋊Q8—171no—
436C2×C22⋊Q8—171no—
437C2×#121—341no—
438C2×C4×D4—171no—
439C2×C4×D4C2×D1711yescharacteristic
440C2×#117C2×D1711yescharacteristic
441C22×C4⋊C4—341no—
442C22×C4⋊C4C2×D1711yescharacteristic
443#435—344no—
444C2×C4⋊C8—171no—
445#417—344no—
446#416—344no—
447C2×#103—171no—
448C2×#103—171no—
449C2×#103—171no—
450C2×#103—171no—
451C2×#103—171no—
452C2×#103—171no—
453C2×#103—171no—
454C2×#103—171no—
455C2×#102—171no—
456C2×#102—171no—
457C2×#102—171no—
458C2×#102—171no—
459C2×C22⋊C8—171no—
460C2×C22⋊C8—171no—
461C2×#97—171no—
462#388—21no—
463#387—21no—
464#386—21no—
465#382C2×D1711yescharacteristic
466#380C2×D1711yescharacteristic
467#380C2×D1711yescharacteristic
468C4×C4⋊C4C2×D1711yescharacteristic
469C4×C22⋊C4—21no—
470#340—171no—
471#340—171no—
472#340—171no—
473#340—171no—
474C2×C17—42no—
475C2×C17—42no—
476C2×C17D4×C22⋊C411yescharacteristic
477C2×C17#289611yescharacteristic
478C2×C17#289811yescharacteristic
479C2×C17#326711yescharacteristic
480C2×C17#326911yescharacteristic
481C2×C17#330711yescharacteristic
482C2×C17#331511yescharacteristic
483D17—44no—
484C2×#41—174no—
485C2×#41—174no—
486C2×#41—342no—
487C2×#41—342no—
488C2×#41—342no—
489C2×#41—342no—
490C2×#41—342no—
491C2×#41—342no—
492C2×#41—681no—
493C2×#41—681no—
494C2×#41—681no—
495C2×#41—681no—
496C22×Q8—171no—
497C22×Q8—171no—
498C22×D4—171no—
499C22×D4—341no—
500C22×D4—341no—
501C22×D4C22⋊D1711yescharacteristic
502C23×C4—21no—
503C23×C4—341no—
504C23×C4—341no—
505C23×C4—341no—
506C23×C4C22×D1711yescharacteristic
507C23×C4C22×D1711yescharacteristic
508C2×M16—342no—
509C2×M16—342no—
510C2×M16—681no—
511C22×C8—171no—
512C22×C8—171no—
513C22×C8—171no—
514C22×C8—171no—
515C22×C8—342no—
516C22×C8—342no—
517C22×C8—681no—
518C4⋊Q8—174no—
519C4⋊Q8—342no—
520#123—348no—
521#123—348no—
522C22⋊Q8—174no—
523C22⋊Q8—174no—
524C22⋊Q8—342no—
525C22⋊Q8—342no—
526#121—348no—
527C4×D4—174no—
528C4×D4—342no—
529C4×D4C4×D1714yes—
530C4×D4D6814yes—
531#117—22no—
532#117—41no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—41no—
536C2×C4⋊C4—171no—
537C2×C4⋊C4—341no—
538C2×C4⋊C4—341no—
539C2×C4⋊C4—341no—
540C2×C4⋊C4—341no—
541C2×C4⋊C4—348no—
542C2×C4⋊C4C22⋊D1711yescharacteristic
543C2×C4⋊C4C22×D1711yescharacteristic
544C2×C4⋊C4C22×D1711yescharacteristic
545C2×C4⋊C4C22×D1711yescharacteristic
546C2×C4⋊C4C22×D1711yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—341no—
551C2×C22⋊C4—341no—
552C2×C22⋊C4—341no—
553C2×C22⋊C4C22⋊D1711yescharacteristic
554C2×C22⋊C4C22⋊D1711yescharacteristic
555C2×C42—21no—
556C2×C42—21no—
557C2×C42C22×D1711yescharacteristic
558C4⋊C8—342no—
559#103—342no—
560#103—342no—
561#103—342no—
562#103—342no—
563#103—681no—
564#103—681no—
565#103—681no—
566#103—681no—
567#102—174no—
568#102—342no—
569#102—342no—
570#102—342no—
571C22⋊C8—342no—
572C22⋊C8—342no—
573#97—342no—
574#95—21no—
575#95—21no—
576#95—21no—
577#95—21no—
578#95—21no—
579C17#2242011yescharacteristic, complemented, Sylow
580C24—341no—
581C24C2×C22⋊D1711yescharacteristic
582C24C2×C22⋊D1711yescharacteristic
583#41—348no—
584#41—348no—
585#41—684no—
586#41—684no—
587#41—684no—
588#41—684no—
589#41—684no—
590#41—684no—
591C2×Q8—172no—
592C2×Q8—172no—
593C2×Q8—341no—
594C2×Q8—341no—
595C2×Q8—341no—
596C2×Q8—341no—
597C2×Q8—341no—
598C2×Q8—341no—
599C2×Q8—341no—
600C2×Q8—341no—
601C2×Q8—341no—
602C2×Q8—341no—
603C2×D4—41no—
604C2×D4—41no—
605C2×D4—172no—
606C2×D4—172no—
607C2×D4—172no—
608C2×D4—344no—
609C2×D4—344no—
610C2×D4—341no—
611C2×D4—341no—
612C2×D4—341no—
613C2×D4—682no—
614C2×D4—682no—
615C2×D4—682no—
616C2×D4—682no—
617C2×D4#6322714yes—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—81no—
633C22×C4—341no—
634C22×C4—341no—
635C22×C4—341no—
636C22×C4—344no—
637C22×C4—344no—
638C22×C4—344no—
639C22×C4—682no—
640C22×C4—682no—
641C22×C4—682no—
642C22×C4—682no—
643C22×C4—682no—
644C22×C4—682no—
645C22×C4C2×C4×D1712yes—
646C22×C4C2×C4×D1712yes—
647C22×C4C2×D6812yes—
648C22×C4C2×D6812yes—
649C22×C4C2×C22⋊D1711yescharacteristic
650C22×C4C2×C22⋊D1711yescharacteristic
651C22×C4C2×C22⋊D1711yescharacteristic
652C22×C4C2×C22⋊D1711yescharacteristic
653C22×C4C23×D1711yescharacteristic
654M16—684no—
655C2×C8—172no—
656C2×C8—341no—
657C2×C8—341no—
658C2×C8—341no—
659C2×C8—341no—
660C2×C8—341no—
661C2×C8—341no—
662C2×C8—341no—
663C2×C8—341no—
664C2×C8—341no—
665C2×C8—341no—
666C2×C8—341no—
667C2×C8—684no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—42no—
676C4⋊C4—172no—
677C4⋊C4—341no—
678C4⋊C4—344no—
679C4⋊C4—344no—
680C4⋊C4—344no—
681C4⋊C4—344no—
682C4⋊C4#6322714yes—
683C4⋊C4D4×D1712yes—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—81no—
687C22⋊C4—344no—
688C22⋊C4—344no—
689C22⋊C4—344no—
690C22⋊C4#6322714yes—
691C22⋊C4#6322714yes—
692C42—42no—
693C42—81no—
694C42C2×C4×D1712yes—
695C42C2×D6812yes—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—342no—
709C23—342no—
710C23—342no—
711C23—681no—
712C23—681no—
713C23—681no—
714C23—681no—
715C23C2×#6322712yes—
716C23C2×#6322712yes—
717C23C22×C22⋊D1711yescharacteristic
718Q8—342no—
719Q8—342no—
720Q8—342no—
721Q8—342no—
722Q8—681no—
723Q8—681no—
724Q8—681no—
725Q8—681no—
726D4—44no—
727D4—174no—
728D4—342no—
729D4—342no—
730D4—342no—
731D4—688no—
732D4—688no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—84no—
762C2×C4—342no—
763C2×C4—342no—
764C2×C4—342no—
765C2×C4—688no—
766C2×C4—688no—
767C2×C4—688no—
768C2×C4—681no—
769C2×C4—681no—
770C2×C4—681no—
771C2×C4—681no—
772C2×C4—681no—
773C2×C4—681no—
774C2×C4C2×#6322712yes—
775C2×C4C2×#6322712yes—
776C2×C4C2×#6322712yes—
777C2×C4C2×#6322712yes—
778C2×C4C22×C4×D1711yescharacteristic
779C2×C4C22×D6811yescharacteristic
780C2×C4C2×D4×D1711yescharacteristic
781C2×C4#1058769111yescharacteristic
782C2×C4#41×D1711yescharacteristic
783C2×C4#1058769611yescharacteristic
784C8—342no—
785C8—681no—
786C8—681no—
787C8—681no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—344no—
803C22—682no—
804C22—682no—
805C22—682no—
806C22—682no—
807C22—682no—
808C22—682no—
809C22C22×#6322711yescharacteristic
810C22D4×C22⋊D1711yescharacteristic
811C22#1176344711yescharacteristic
812C22#1176360711yescharacteristic
813C22#1176360711yescharacteristic
814C22#1176362011yescharacteristic
815C22#1176362411yescharacteristic
816C4—22no—
817C4—22no—
818C4—22no—
819C4—22no—
820C4—42no—
821C4—81no—
822C4—81no—
823C4—81no—
824C4—682no—
825C4—682no—
826C4—682no—
827C4C4×D4×D1711yescharacteristic
828C4#1176328111yescharacteristic
829C4D4×D6811yescharacteristic
830C4#1176345411yescharacteristic
831C2—42no—
832C2—42no—
833C2—684no—
834C2D4×#6322711yescharacteristic
835C2#1453730111yescharacteristic
836C2#1453731411yescharacteristic
837C2#1454030511yescharacteristic
838C2#1454034011yescharacteristic
839C2#1454075411yescharacteristic
840C2#1454087411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#2352C2
socleC23×C17C22×D4
prime radicalC2×#11763464C2
cosocleC22×C4×C17C24
hypercenter#2352D17
hypocenterC17#22420
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. C2×#11762881C2semidirect
3. C2×#11762808C2semidirect
4. C2×#11762803C2semidirect
5. #14529707C2semidirect
6. #14529603C2semidirect
7. #14529215C2semidirect
8. #14529205C2semidirect
9. #14529096C2semidirect
10. #14529091C2semidirect
11. #14528791C2semidirect
12. #14528722C2semidirect
13. #14528722C2semidirect
14. #14528612C2semidirect
15. C17×#2352C2semidirect
21. #11763464C4semidirect
81. C2×#63252C2×C4semidirect
118. #10587610C2×C4semidirect
135. C4×D68C2×C4semidirect
137. #10587555C2×C4semidirect
156. #10587480D4semidirect
372. #2352D17semidirect
579. C17#22420semidirect

Maximal subgroups

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

subgroupindex
C2×#117634642
C2×#117628812
C2×#117628082
C2×#117628032
#145297072
#145296032
#145292152
#145292052
#145290962
#145290912
#145287912
#145287222
#145286122
C17×#23522
#2242017