Finite Group Databasebeta

← #17056403

Subgroups — #17056403

Order 4352.

708 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14538568C211yesmaximal, characteristic
2#14537728C211yesmaximal, characteristic, complemented
3#14537350C211yesmaximal, characteristic
4#14529759C211yesmaximal, characteristic, complemented
5#14529558C211yesmaximal, characteristic, complemented
6#14529537C211yesmaximal, characteristic, complemented
7#14529536C211yesmaximal, characteristic, complemented
8#14529383C211yesmaximal, characteristic, complemented
9#14529382C211yesmaximal, characteristic, complemented
10#14529061C211yesmaximal, characteristic
11#14529059C211yesmaximal, characteristic
12#14528638C211yesmaximal, characteristic, complemented
13#14528629C211yesmaximal, characteristic
14#104×Dic17C211yesmaximal, characteristic
15C17×#1765C211yesmaximal, characteristic
16C2×#10587634C2211yescharacteristic
17#11763362C2211yescharacteristic
18#41×Dic17C2211yescharacteristic
19#11763118C411yescharacteristic, complemented
20#11763114C411yescharacteristic, complemented
21#11763111C411yescharacteristic, complemented
22#11763107C411yescharacteristic, complemented
23#11763102C411yescharacteristic, complemented
24#11763097C411yescharacteristic, complemented
25#11763092C411yescharacteristic, complemented
26#11763087C411yescharacteristic, complemented
27#11762939—21no—
28#11762937—21no—
29#11762937—21no—
30C8×Dic34—21no—
31C2×#10587490C2211yescharacteristic
32C2×#10587493C2211yescharacteristic
33#11762847C2211yescharacteristic
34#11762845C2211yescharacteristic
35#11762837—21no—
36#11762837C2211yescharacteristic
37#11762836C2211yescharacteristic
38#11762835—21no—
39#11762835C2211yescharacteristic
40#11762835C2211yescharacteristic
41#11762832—21no—
42#11762832C2211yescharacteristic
43C2×#10587485—21no—
44C2×#10587485C2211yescharacteristic
45C2×#10587485C2211yescharacteristic
46C2×#10587508C2211yescharacteristic
47#11762805C2211yescharacteristic
48#11762767C2211yescharacteristic
49M16×Dic17C2211yescharacteristic
50C2×#10587474C2211yescharacteristic
51C42×Dic17C2211yescharacteristic
52#11762573C2211yescharacteristic
53#11762570C2211yescharacteristic
54#11762570C2211yescharacteristic
55#11762569C2211yescharacteristic
56#11762569C2211yescharacteristic
57#11762568C2211yescharacteristic
58#11762563C2211yescharacteristic
59#11762563C2211yescharacteristic
60C2×C17×#131C2211yescharacteristic
61C2×C17×#104C2211yescharacteristic
62C17×#416C2211yescharacteristic
63C17×#405C2211yescharacteristic
64C2×C17×#97C2211yescharacteristic
65C17×#341C2211yescharacteristic
66C17×#339C2211yescharacteristic
67C2×#41×C17C2311yescharacteristic
68C17×#131—22no—
69C17×#131—41no—
70C2×M16×C17—21no—
71C2×M16×C17C2311yescharacteristic
72C2×M16×C17C2311yescharacteristic
73C22×C8×C17—21no—
74C22×C8×C17C2311yescharacteristic
75C22×C8×C17C2311yescharacteristic
76C17×#117C2311yescharacteristic
77C2×C42×C17C2311yescharacteristic
78#10587634—22no—
79#10587634—41no—
80Q8×Dic17C2×C411yescharacteristic
81Q8×Dic17C2×C411yescharacteristic
82D4×Dic17—21no—
83D4×Dic17—21no—
84D4×Dic17C2×C411yescharacteristic
85D4×Dic17C2×C411yescharacteristic
86#10587612—21no—
87#10587612C2311yescharacteristic
88#10587612C2311yescharacteristic
89C2×C4×Dic17—21no—
90C2×C4×Dic17—21no—
91C2×C4×Dic17—21no—
92C2×C4×Dic17C2311yescharacteristic
93C2×C4×Dic17C2311yescharacteristic
94C2×#63223—21no—
95C2×#63223C2311yescharacteristic
96C2×#63223C2311yescharacteristic
97C22×#3622—21no—
98C22×#3622C2311yescharacteristic
99C22×#3622C2311yescharacteristic
100#10587576C2×C411yescharacteristic
101#10587576C2×C411yescharacteristic
102#10587574C2×C411yescharacteristic
103#10587574C2×C411yescharacteristic
104#10587564—21no—
105#10587564—21no—
106C4×Dic34—21no—
107C4×Dic34—21no—
108C17×#104Q814yescomplemented
109C17×#103C2×C411yescharacteristic
110C17×#103C2×C411yescharacteristic
111C17×#102C2×C411yescharacteristic
112C17×#102C2×C411yescharacteristic
113C17×#97—21no—
114C17×#97—41no—
115C4×C8×C17—21no—
116#10587508—22no—
117#10587506C2×C411yescharacteristic
118#10587506C2×C411yescharacteristic
119#10587503C2×C411yescharacteristic
120#10587503C2×C411yescharacteristic
121#10587493—41no—
122#10587490—41no—
123#10587489C2×C411yescharacteristic
124#10587489C2×C411yescharacteristic
125#10587488C2×C411yescharacteristic
126#10587488C2×C411yescharacteristic
127#10587486—21no—
128#10587486—21no—
129#10587485—21no—
130#10587485—21no—
131#10587485—21no—
132#10587485—21no—
133#10587485—21no—
134#10587485—21no—
135#10587485—21no—
136#10587485—21no—
137#10587485C2×C411yescharacteristic
138#10587485C2×C411yescharacteristic
139#10587485C2×C411yescharacteristic
140#10587485C2×C411yescharacteristic
141#10587485D411yescharacteristic
142#10587485D411yescharacteristic
143#10587485D411yescharacteristic
144#10587485D411yescharacteristic
145C8×Dic17—21no—
146C8×Dic17—21no—
147#10587479C2×C411yescharacteristic
148#10587479C2×C411yescharacteristic
149#10587478C2×C411yescharacteristic
150#10587478C2×C411yescharacteristic
151C4⋊#3622—21no—
152C4⋊#3622—21no—
153#10587474—41no—
154#41×C17—21no—
155#41×C17—21no—
156#41×C17C2×Q812yes—
157#41×C17#4112yes—
158C2×Q8×C17C22×C411yescharacteristic
159C2×D4×C17—21no—
160C2×D4×C17C22×C411yescharacteristic
161C22×C4×C17—21no—
162C22×C4×C17—21no—
163C22×C4×C17C2411yescharacteristic
164C22×Dic17—21no—
165C22×Dic17—21no—
166C22×Dic17—21no—
167C22×Dic17#4111yescharacteristic
168C22×Dic17#4111yescharacteristic
169C2×Dic34—21no—
170C2×Dic34—21no—
171M16×C17—21no—
172M16×C17—21no—
173M16×C17—21no—
174M16×C17—42no—
175M16×C17C2×Q812yes—
176C2×C8×C17—21no—
177C2×C8×C17—21no—
178C2×C8×C17—21no—
179C2×C8×C17—21no—
180C2×C8×C17—21no—
181C2×C8×C17—21no—
182C2×C8×C17—42no—
183C2×C8×C17C22×C411yescharacteristic
184C2×C8×C17C22×C411yescharacteristic
185C2×C8×C17C2×D411yescharacteristic
186C2×C8×C17C2×D411yescharacteristic
187C4⋊C4×C17C22×C411yescharacteristic
188C4⋊C4×C17C22×C411yescharacteristic
189C22⋊C4×C17—21no—
190C42×C17—21no—
191C42×C17—21no—
192C42×C17C2×Q812yes—
193C22⋊Dic17—21no—
194C22⋊Dic17—21no—
195C22⋊Dic17—21no—
196C22⋊Dic17—21no—
197C4⋊Dic17—21no—
198C4⋊Dic17—21no—
199C4⋊Dic17—21no—
200C4⋊Dic17—21no—
201C4⋊Dic17C22×C411yescharacteristic
202C4⋊Dic17C22×C411yescharacteristic
203C4⋊Dic17C22×C411yescharacteristic
204C4⋊Dic17C22×C411yescharacteristic
205#63225—21no—
206#63225—21no—
207#63225—21no—
208#63225—21no—
209C4×Dic17—21no—
210C4×Dic17—21no—
211C4×Dic17—21no—
212C4×Dic17—21no—
213C4×Dic17—21no—
214C4×Dic17—21no—
215C4×Dic17—42no—
216C4×Dic17—42no—
217C4×Dic17C22×C411yescharacteristic
218C4×Dic17C22×C411yescharacteristic
219C4×Dic17C2×D411yescharacteristic
220C4×Dic17C2×D411yescharacteristic
221#63223—21no—
222#63223—21no—
223#63223—21no—
224#63223—21no—
225#63223—42no—
226C2×#3622—21no—
227C2×#3622—21no—
228C2×#3622—21no—
229C2×#3622—21no—
230C2×#3622—21no—
231C2×#3622—21no—
232C2×#3622—42no—
233C2×#3622C22×C411yescharacteristic
234C2×#3622C22×C411yescharacteristic
235C2×#3622C2×D411yescharacteristic
236C2×#3622C2×D411yescharacteristic
237#22983—171nomaximal, Sylow
238C23×C17—21no—
239C23×C17C2×#4111yescharacteristic
240Q8×C17—21no—
241Q8×C17C4×Q812yes—
242D4×C17—22no—
243D4×C17—22no—
244D4×C17—21no—
245D4×C17C4×Q812yes—
246C2×C4×C17—21no—
247C2×C4×C17—22no—
248C2×C4×C17—22no—
249C2×C4×C17—21no—
250C2×C4×C17—21no—
251C2×C4×C17—22no—
252C2×C4×C17—41no—
253C2×C4×C17—41no—
254C2×C4×C17C23×C411yescharacteristic
255C2×C4×C17C22×D411yescharacteristic
256C2×C4×C17C22×Q811yescharacteristic
257C2×C4×C17C2×#4111yescharacteristic
258C2×C4×C17H(5,𝔽2)11yescharacteristic
259C2×C4×C172−1+411yescharacteristic
260C2×Dic17—22no—
261C2×Dic17—22no—
262C2×Dic17—21no—
263C2×Dic17—21no—
264C2×Dic17—21no—
265C2×Dic17—21no—
266C2×Dic17—41no—
267C2×Dic17—41no—
268C2×Dic17—41no—
269C2×Dic17—42no—
270C2×Dic17—81no—
271C2×Dic17C4×D411yescharacteristic
272C2×Dic17C4×D411yescharacteristic
273C2×Dic17C4×D411yescharacteristic
274C2×Dic17C4×D411yescharacteristic
275Dic34—42no—
276Dic34—81no—
277C8×C17—21no—
278C8×C17—21no—
279C8×C17—21no—
280C8×C17—21no—
281C8×C17—22no—
282C8×C17—41no—
283#3622—21no—
284#3622—21no—
285#3622—21no—
286#3622—21no—
287#3622—41no—
288#3622—41no—
289#3076—171no—
290#2962—171no—
291#2906—171no—
292#1994—171no—
293#1950—171no—
294#1946—171no—
295#1946—171no—
296#1922—171no—
297#1922—171no—
298#1866—171no—
299#1866—171no—
300#1767—171no—
301#1765—171no—
302#1765D1711yescharacteristic
303C4×#104—171no—
304C22×C17—21no—
305C22×C17—21no—
306C22×C17—22no—
307C22×C17—41no—
308C22×C17—41no—
309C22×C17C2×C4×D411yescharacteristic
310C22×C17#55211yescharacteristic
311C22×C17#55411yescharacteristic
312C4×C17—22no—
313C4×C17—42no—
314C4×C17—41no—
315C4×C17—41no—
316C4×C17C2×C4×Q811yescharacteristic
317C4×C17#52011yescharacteristic
318C4×C17#54611yescharacteristic
319C4×C17D4×Q811yescharacteristic
320Dic17—21no—
321Dic17—21no—
322Dic17—21no—
323Dic17—42no—
324Dic17—41no—
325Dic17—41no—
326Dic17—41no—
327Dic17—41no—
328Dic17#44412yes—
329C2×#131—171no—
330C2×#131C2×D1711yescharacteristic
331#533—171no—
332C4×#41—171no—
333#479—171no—
334#479—171no—
335#478—171no—
336#478—171no—
337#477—171no—
338#476—171no—
339#475—171no—
340#474—171no—
341#446—341no—
342#446—341no—
343#446—341no—
344C8×Q8—341no—
345C2×#108—171no—
346C2×#108—171no—
347#427—171no—
348#427—171no—
349#424—171no—
350#424—171no—
351#424—171no—
352#424—171no—
353#424—341no—
354#424—341no—
355#423—171no—
356#423—341no—
357C2×C4⋊C8—171no—
358C2×C4⋊C8—171no—
359C2×C4⋊C8—341no—
360C2×#104—171no—
361C2×#104C2×D1711yescharacteristic
362#416—171no—
363#416C2×D1711yescharacteristic
364#405—171no—
365#405C2×D1711yescharacteristic
366C4×M16—171no—
367C2×#97—171no—
368C2×#97C2×D1711yescharacteristic
369C43—171no—
370#341—171no—
371#341C2×D1711yescharacteristic
372#339—171no—
373#339—171no—
374#339—171no—
375#339—171no—
376#339—171no—
377#339C2×D1711yescharacteristic
378#336—171no—
379#336—171no—
380C2×C17—21no—
381C2×C17—21no—
382C2×C17—42no—
383C2×C17#236011yescharacteristic
384C2×C17C2×#44411yescharacteristic
385C2×C17#295611yescharacteristic
386C2×#41C22×D1711yescharacteristic
387#131—22no—
388#131—41no—
389#131—342no—
390#131—681no—
391C2×M16—21no—
392C2×M16—171no—
393C2×M16—171no—
394C2×M16—341no—
395C2×M16C22×D1711yescharacteristic
396C2×M16C22×D1711yescharacteristic
397C22×C8—21no—
398C22×C8—171no—
399C22×C8—171no—
400C22×C8—341no—
401C22×C8C22×D1711yescharacteristic
402C22×C8C22×D1711yescharacteristic
403C4⋊Q8—171no—
404C4⋊Q8—171no—
405#125—171no—
406#125—171no—
407C22⋊Q8—341no—
408C22⋊Q8—341no—
409C4×Q8—171no—
410C4×Q8—171no—
411C4×Q8—341no—
412C4×Q8—341no—
413C4×D4—171no—
414C4×D4—171no—
415C4×D4—341no—
416C4×D4—341no—
417#117—171no—
418#117—171no—
419#117—341no—
420#117C22×D1711yescharacteristic
421C2×C42—171no—
422C2×C42—171no—
423C2×C42—341no—
424C2×C42—341no—
425C2×C42—341no—
426C2×C42C22×D1711yescharacteristic
427#108—681no—
428#108—681no—
429#107—171no—
430#107—171no—
431#107—171no—
432#107—171no—
433#106—171no—
434#106—171no—
435#106—171no—
436#106—171no—
437C4⋊C8—171no—
438C4⋊C8—171no—
439C4⋊C8—171no—
440C4⋊C8—171no—
441C4⋊C8—171no—
442C4⋊C8—171no—
443C4⋊C8—171no—
444C4⋊C8—171no—
445C4⋊C8—341no—
446C4⋊C8—341no—
447C4⋊C8—341no—
448C4⋊C8—341no—
449C4⋊C8—341no—
450C4⋊C8—341no—
451C4⋊C8—341no—
452C4⋊C8—341no—
453C4⋊C8—341no—
454C4⋊C8—341no—
455#104—342no—
456#104Dic3414yescomplemented
457#103—171no—
458#103—171no—
459#103C4×D1711yescharacteristic
460#103C4×D1711yescharacteristic
461#102—171no—
462#102—171no—
463#102C4×D1711yescharacteristic
464#102C4×D1711yescharacteristic
465#97—21no—
466#97—41no—
467#97—341no—
468#97—341no—
469#97—681no—
470C4×C8—21no—
471C4×C8—341no—
472C4×C8—341no—
473C17#2298311yescharacteristic, complemented, Sylow
474#41—21no—
475#41—21no—
476#41C2×Dic3412yes—
477#41#6325212yes—
478C2×Q8—341no—
479C2×Q8—341no—
480C2×Q8C2×C4×D1711yescharacteristic
481C2×D4—21no—
482C2×D4C2×C4×D1711yescharacteristic
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—171no—
486C22×C4—171no—
487C22×C4—341no—
488C22×C4—341no—
489C22×C4—341no—
490C22×C4C23×D1711yescharacteristic
491M16—21no—
492M16—21no—
493M16—21no—
494M16—42no—
495M16—341no—
496M16—341no—
497M16—341no—
498M16—341no—
499M16—682no—
500M16C2×Dic3412yes—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—42no—
508C2×C8—171no—
509C2×C8—171no—
510C2×C8—171no—
511C2×C8—171no—
512C2×C8—341no—
513C2×C8—341no—
514C2×C8—341no—
515C2×C8—341no—
516C2×C8—341no—
517C2×C8—341no—
518C2×C8—682no—
519C2×C8C2×C4×D1711yescharacteristic
520C2×C8C2×C4×D1711yescharacteristic
521C2×C8D4×D1711yescharacteristic
522C2×C8D4×D1711yescharacteristic
523C4⋊C4—171no—
524C4⋊C4—171no—
525C4⋊C4—171no—
526C4⋊C4—171no—
527C4⋊C4—341no—
528C4⋊C4—341no—
529C4⋊C4—341no—
530C4⋊C4—341no—
531C4⋊C4—341no—
532C4⋊C4—341no—
533C4⋊C4—341no—
534C4⋊C4—341no—
535C4⋊C4C2×C4×D1711yescharacteristic
536C4⋊C4C2×C4×D1711yescharacteristic
537C22⋊C4—21no—
538C22⋊C4—341no—
539C22⋊C4—341no—
540C22⋊C4—341no—
541C22⋊C4—341no—
542C42—21no—
543C42—21no—
544C42—171no—
545C42—171no—
546C42—171no—
547C42—171no—
548C42—341no—
549C42—341no—
550C42—341no—
551C42—341no—
552C42—341no—
553C42—341no—
554C42—682no—
555C42—682no—
556C42C2×Dic3412yes—
557C23—21no—
558C23#41×D1711yescharacteristic
559Q8—21no—
560Q8—682no—
561Q8—1361no—
562Q8C4×Dic3412yes—
563D4—22no—
564D4—22no—
565D4—21no—
566D4C4×Dic3412yes—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—171no—
576C2×C4—171no—
577C2×C4—171no—
578C2×C4—171no—
579C2×C4—342no—
580C2×C4—342no—
581C2×C4—341no—
582C2×C4—341no—
583C2×C4—341no—
584C2×C4—341no—
585C2×C4—682no—
586C2×C4—681no—
587C2×C4—681no—
588C2×C4—681no—
589C2×C4—1361no—
590C2×C4C22×Dic3411yescharacteristic
591C2×C4C22×C4×D1711yescharacteristic
592C2×C4C2×#6325211yescharacteristic
593C2×C4C2×D4×D1711yescharacteristic
594C2×C4#1058769111yescharacteristic
595C2×C4#1058769711yescharacteristic
596C8—22no—
597C8—21no—
598C8—21no—
599C8—21no—
600C8—21no—
601C8—41no—
602C8—341no—
603C8—341no—
604C8—341no—
605C8—341no—
606C8—681no—
607C8—681no—
608C22—21no—
609C22—21no—
610C22—22no—
611C22—41no—
612C22—41no—
613C22C4×D4×D1711yescharacteristic
614C22#1176349211yescharacteristic
615C22#1176351811yescharacteristic
616C4—22no—
617C4—42no—
618C4—41no—
619C4—41no—
620C4—172no—
621C4—341no—
622C4—341no—
623C4—341no—
624C4—682no—
625C4—681no—
626C4—681no—
627C4—681no—
628C4—681no—
629C4C2×C4×Dic3411yescharacteristic
630C4#1176328811yescharacteristic
631C4#1176344911yescharacteristic
632C4D4×Dic3411yescharacteristic
633C2—21no—
634C2—21no—
635C2—42no—
636C2#1453179011yescharacteristic
637C2D17×#44411yescharacteristic
638C2#1453769211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1765C2
socleC22×C17C2×C4×D4
prime radicalC2×#41×C17C23
cosocleC22×C4×C17C24
hypercenter#1765D17
hypocenterC17#22983
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1765

Complements

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

NH ≅ G/Ntype
2. #14537728C2semidirect
4. #14529759C2semidirect
5. #14529558C2semidirect
6. #14529537C2semidirect
7. #14529536C2semidirect
8. #14529383C2semidirect
9. #14529382C2semidirect
12. #14528638C2semidirect
19. #11763118C4semidirect
20. #11763114C4semidirect
21. #11763111C4semidirect
22. #11763107C4semidirect
23. #11763102C4semidirect
24. #11763097C4semidirect
25. #11763092C4semidirect
26. #11763087C4semidirect
108. C17×#104Q8semidirect
456. #104Dic34semidirect
473. C17#22983semidirect

Maximal subgroups

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

subgroupindex
#145385682
#145377282
#145373502
#145297592
#145295582
#145295372
#145295362
#145293832
#145293822
#145290612
#145290592
#145286382
#145286292
#104×Dic172
C17×#17652
#2298317