Finite Group Databasebeta

← #29649913

Subgroups — #29649913

Order 15616.

634 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455837C211yesmaximal, characteristic
2#21454788C211yesmaximal, characteristic, complemented
3#41×#92418C211yesmaximal, characteristic, complemented
4#21444666C211yesmaximal, characteristic, complemented
5#21444659C211yesmaximal, characteristic, complemented
6#21444652C211yesmaximal, characteristic, complemented
7#21444645C211yesmaximal, characteristic, complemented
8#21444623C211yesmaximal, characteristic, complemented
9#21444622C211yesmaximal, characteristic, complemented
10#21444616C211yesmaximal, characteristic, complemented
11#21444611C211yesmaximal, characteristic, complemented
12#21444600C211yesmaximal, characteristic, complemented
13#21444228C211yesmaximal, characteristic, complemented
14#21444103C211yesmaximal, characteristic, complemented
15C61×#1488C211yesmaximal, characteristic, complemented
16#16840296C2211yescharacteristic
17#16840103C411yescharacteristic
18#16840086C411yescharacteristic
19#16840069C411yescharacteristic
20#16840062C411yescharacteristic
21#16839984C411yescharacteristic
22#16839977C411yescharacteristic
23#16839924C411yescharacteristic
24#16839907C411yescharacteristic
25#16839889C2211yescharacteristic
26Q8×#92418C2211yescharacteristic
27Q8×#92418C2211yescharacteristic
28#16839886C2211yescharacteristic
29C4×#11758202C2211yescharacteristic
30C4×#11758201C2211yescharacteristic
31C4×#11758200C2211yescharacteristic
32C4×#11758199C2211yescharacteristic
33#16839839C2211yescharacteristic
34#16839830—21no—
35D4×#92418—21no—
36D4×#92418—21no—
37D4×#92418C2211yescharacteristic
38D4×#92418C2211yescharacteristic
39#16839827C2211yescharacteristic
40#16839825—21no—
41#16839824—21no—
42#16839815—21no—
43#16839815C2211yescharacteristic
44#16839815C2211yescharacteristic
45#16839719—21no—
46C2×C4×#92418—21no—
47C2×C4×#92418C2211yescharacteristic
48#16839514C2211yescharacteristic
49#16839514C2211yescharacteristic
50#16839512C2211yescharacteristic
51#16839512C2211yescharacteristic
52#16839494C2211yescharacteristic
53#16839494C2211yescharacteristic
54#16839491C2211yescharacteristic
55#16839491C2211yescharacteristic
56#16839484C2211yescharacteristic
57#16839484C2211yescharacteristic
58C8×#92418C2211yescharacteristic
59C8×#92418C2211yescharacteristic
60C4×#41×C61C2211yescharacteristic
61C61×#432C2211yescharacteristic
62C61×#431C2211yescharacteristic
63C61×Q8⋊C8C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C61×D4⋊C8C2211yescharacteristic
67C2×#11758202C2×C411yescharacteristic
68C2×#11758200C2×C411yescharacteristic
69C2×#11758201C2×C411yescharacteristic
70C2×#11758199C2×C411yescharacteristic
71C2×#11758189—21no—
72C22×#92418—21no—
73C22×#92418—21no—
74C22×#92418D411yescharacteristic
75C22×#92418D411yescharacteristic
76C2×C8×D61—21no—
77#14519771—21no—
78#14519769C2×C411yescharacteristic
79#14519765C2×C411yescharacteristic
80#14519760—21no—
81#14519756C2×C411yescharacteristic
82#14519751C2×C411yescharacteristic
83C4×Dic122C2311yescharacteristic
84C4×D244C2311yescharacteristic
85C4×C22⋊D61—21no—
86#14519734—21no—
87#14519710C2×C411yescharacteristic
88#14519710C2×C411yescharacteristic
89#14519708C2×C411yescharacteristic
90#14519708C2×C411yescharacteristic
91C4⋊#92418—21no—
92C4⋊#92418—21no—
93C4⋊#92418C2×C411yescharacteristic
94C4⋊#92418C2×C411yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519706—21no—
98#14519706—21no—
99#14519701C2×C411yescharacteristic
100#14519701C2×C411yescharacteristic
101#14519700C2×C411yescharacteristic
102#14519700C2×C411yescharacteristic
103#14519698C2×C411yescharacteristic
104#14519698C2×C411yescharacteristic
105#14519697C2×C411yescharacteristic
106#14519697C2×C411yescharacteristic
107C22⋊#92418—21no—
108C22⋊#92418—21no—
109C22⋊#92418—21no—
110C22⋊#92418C2×C411yescharacteristic
111C22⋊#92418C2×C411yescharacteristic
112#14519689—21no—
113#14519689—21no—
114#14519687—21no—
115C4×#92418—21no—
116C4×#92418—21no—
117C4×#92418—21no—
118C4×#92418D411yescharacteristic
119C4×#92418D411yescharacteristic
120C4×#92418C2311yescharacteristic
121C4×#92418C2311yescharacteristic
122C4×#92418C2311yescharacteristic
123C4×#92418C2311yescharacteristic
124C8×Dic61—21no—
125C2×#41×C61C2×C411yescharacteristic
126C4×Q8×C61C2×C411yescharacteristic
127C4×Q8×C61C2311yescharacteristic
128C4×D4×C61—21no—
129C4×D4×C61—21no—
130C4×D4×C61C2×C411yescharacteristic
131C4×D4×C61C2311yescharacteristic
132#117×C61—21no—
133#117×C61C2×C411yescharacteristic
134C2×C42×C61—21no—
135C2×C42×C61C2311yescharacteristic
136C4⋊C8×C61—21no—
137C4⋊C8×C61C2311yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139C22⋊C8×C61—21no—
140C22⋊C8×C61—21no—
141#97×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144#41×C61—22no—
145#41×C61—22no—
146C2×Q8×C61C22×C411yescharacteristic
147C2×D4×C61—21no—
148C2×D4×C61C22×C411yescharacteristic
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61#4111yescharacteristic
155C2×C22⋊D61—21no—
156C2×D244C22×C411yescharacteristic
157C2×C4×D61—21no—
158C2×Dic122C22×C411yescharacteristic
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61C22×C411yescharacteristic
166C4⋊C4×C61C22×C411yescharacteristic
167C22⋊C4×C61—21no—
168C22⋊C4×C61—21no—
169C22⋊C4×C61—21no—
170C42×C61—21no—
171C42×C61—21no—
172C42×C61—21no—
173C42×C61C22×C411yescharacteristic
174C42×C61C2×D411yescharacteristic
175C42×C61#4111yescharacteristic
176C42×C61C2411yescharacteristic
177C22⋊Dic61—21no—
178#11758202—22no—
179#11758201—22no—
180#11758200—22no—
181#11758199—22no—
182#11758198—21no—
183#11758198—21no—
184#11758198—21no—
185#11758198—21no—
186C4⋊Dic61C22×C411yescharacteristic
187C4⋊Dic61C22×C411yescharacteristic
188#11758196—21no—
189#11758196—21no—
190#11758196—21no—
191#11758196—21no—
192C4×Dic61—21no—
193C2×#92418—22no—
194C2×#92418—22no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—42no—
198C2×#92418—42no—
199C2×#92418C22×C411yescharacteristic
200C2×#92418C22×C411yescharacteristic
201C2×#92418C22×C411yescharacteristic
202C2×#92418C22×C411yescharacteristic
203C2×#92418C2×D411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206C2×#92418C2×D411yescharacteristic
207#11758189—42no—
208C8×D61—42no—
209C23×C61—21no—
210C23×C61C4×D411yescharacteristic
211C22×D61—21no—
212Q8×C61—21no—
213Q8×C61#13112yes—
214D4×C61—24no—
215D4×C61—21no—
216D4×C61#13112yes—
217C2×C4×C61—24no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—41no—
226C2×C4×C61—42no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61C4×D411yescharacteristic
230C2×C4×C61C4×D411yescharacteristic
231C2×C4×C61C4×D411yescharacteristic
232C2×C4×C61C23×C411yescharacteristic
233C2×C4×C61C22×D411yescharacteristic
234C2×C4×C61C2×#4111yescharacteristic
235C22⋊D61—42no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239D244—21no—
240D244—21no—
241C4×D61—41no—
242C4×D61—41no—
243Dic122—21no—
244Dic122—21no—
245C8×C61—41no—
246C8×C61—41no—
247C8×C61—41no—
248C8×C61—41no—
249#92418—21no—
250#92418—21no—
251#92418—21no—
252#92418—21no—
253#92418—21no—
254#92418—21no—
255#92418—41no—
256#92418—41no—
257#92418#13512yes—
258#92418#13512yes—
259#17904—611nomaximal, Sylow
260C22×C61—21no—
261C22×C61—22no—
262C22×C61—21no—
263C22×C61—21no—
264C22×C61—41no—
265C22×C61—41no—
266C22×C61C2×C4×D411yescharacteristic
267C2×D61—41no—
268C2×D61—41no—
269C2×D61—41no—
270C4×C61—21no—
271C4×C61—22no—
272C4×C61—21no—
273C4×C61—21no—
274C4×C61—21no—
275C4×C61—41no—
276C4×C61—41no—
277C4×C61C2×#13111yescharacteristic
278C4×C61C2×#13111yescharacteristic
279C4×C61C2×#13511yescharacteristic
280C4×C61C2×#13511yescharacteristic
281Dic61—41no—
282Dic61—41no—
283Dic61—41no—
284#3102—611no—
285#2966—611no—
286C8×#41—611no—
287#1584—611no—
288#1583—611no—
289#1582—611no—
290#1581—611no—
291C8×Q16—611no—
292C8×SD16—611no—
293C8×SD16—611no—
294C8×D8—611no—
295#1572—611no—
296#1488D6111yescharacteristic, complemented
297#1482—611no—
298#1450—611no—
299C2×C61—41no—
300C2×C61—42no—
301C2×C61#292911yescharacteristic
302C2×C61C4×#13511yescharacteristic
303C2×C61#295511yescharacteristic
304D61—81no—
305#529—611no—
306C4×#41C2×D6111yescharacteristic
307#485—611no—
308#482—611no—
309#479—611no—
310#478—611no—
311#464—611no—
312#463—611no—
313#452—611no—
314#449—611no—
315#446—611no—
316C8×Q8—611no—
317C8×Q8—611no—
318C8×Q8—611no—
319C4×Q16—611no—
320C4×SD16—611no—
321C4×SD16—611no—
322C4×D8—611no—
323#436—611no—
324#435—1221no—
325C8×D4—611no—
326C8×D4—611no—
327C8×D4—611no—
328C8×D4—1221no—
329C8×D4—1221no—
330C8×D4—1221no—
331#433—1221no—
332#432C2×D6111yescharacteristic
333#431—611no—
334#431—611no—
335#431—1221no—
336#431C2×D6111yescharacteristic
337#405—1221no—
338C2×C4×C8—611no—
339C2×C4×C8—1221no—
340#335—611no—
341#335—611no—
342#334—611no—
343#334—611no—
344Q8⋊C8—611no—
345Q8⋊C8—611no—
346Q8⋊C8C2×D6111yescharacteristic
347Q8⋊C8C2×D6111yescharacteristic
348D4⋊C8—611no—
349D4⋊C8—611no—
350D4⋊C8C2×D6111yescharacteristic
351D4⋊C8C2×D6111yescharacteristic
352#322—611no—
353#322—611no—
354C82—611no—
355C82—611no—
356C61#1790411yescharacteristic, complemented, Sylow
357C2×#41C4×D6111yescharacteristic
358C2×Q16—611no—
359C2×SD16—611no—
360C2×SD16—611no—
361C2×D8—611no—
362C2×M16—1221no—
363C22×C8—611no—
364C22×C8—611no—
365C22×C8—1221no—
366C22×C8—1221no—
367C22×C8—1221no—
368#126—1221no—
369#125—611no—
370#124—611no—
371#123—1221no—
372C22⋊Q8—611no—
373#121—611no—
374C4×Q8—611no—
375C4×Q8C4×D6111yescharacteristic
376C4×Q8C22×D6111yescharacteristic
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—611no—
380C4×D4—1221no—
381C4×D4C4×D6111yescharacteristic
382C4×D4C22×D6111yescharacteristic
383#117—21no—
384#117—1221no—
385#117C4×D6111yescharacteristic
386C2×C42—21no—
387C2×C42C22×D6111yescharacteristic
388#107—611no—
389#107—611no—
390#106—611no—
391#106—611no—
392C4⋊C8—21no—
393C4⋊C8—611no—
394C4⋊C8—611no—
395C4⋊C8—611no—
396C4⋊C8—611no—
397C4⋊C8—1221no—
398C4⋊C8—1221no—
399C4⋊C8—1221no—
400C4⋊C8—1221no—
401C4⋊C8C22×D6111yescharacteristic
402C4⋊C8C22×D6111yescharacteristic
403#103—611no—
404#103—611no—
405#103—611no—
406#103—611no—
407#102—611no—
408#102—611no—
409#102—611no—
410#102—611no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413C22⋊C8—611no—
414C22⋊C8—611no—
415C22⋊C8—1221no—
416C22⋊C8—1221no—
417C22⋊C8—1221no—
418C22⋊C8—1221no—
419C22⋊C8—1221no—
420#97—21no—
421#97—1221no—
422C4×C8—611no—
423C4×C8—611no—
424C4×C8—611no—
425C4×C8—611no—
426C4×C8—611no—
427C4×C8—611no—
428C4×C8—1221no—
429C4×C8—1221no—
430C4×C8—1221no—
431C4×C8—1221no—
432C4×C8C22×D6111yescharacteristic
433C4×C8C22×D6111yescharacteristic
434#41—22no—
435#41—22no—
436C2×Q8—611no—
437C2×Q8C2×C4×D6111yescharacteristic
438C2×D4—21no—
439C2×D4—611no—
440C2×D4—1221no—
441C2×D4C2×C4×D6111yescharacteristic
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—1221no—
446C22×C4C2×C4×D6111yescharacteristic
447C22×C4D4×D6111yescharacteristic
448C22×C4#1175822411yescharacteristic
449Q16—1222no—
450SD16—1222no—
451SD16—1222no—
452D8—1222no—
453M16—2442no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—611no—
459C2×C8—611no—
460C2×C8—611no—
461C2×C8—611no—
462C2×C8—611no—
463C2×C8—611no—
464C2×C8—611no—
465C2×C8—611no—
466C2×C8—1222no—
467C2×C8—1222no—
468C2×C8—1221no—
469C2×C8—1221no—
470C2×C8—2442no—
471C2×C8—2442no—
472C2×C8—2442no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—611no—
476C4⋊C4—611no—
477C4⋊C4—1221no—
478C4⋊C4—1221no—
479C4⋊C4—1221no—
480C4⋊C4—1221no—
481C4⋊C4C2×C4×D6111yescharacteristic
482C4⋊C4C2×C4×D6111yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—1221no—
487C22⋊C4—1221no—
488C22⋊C4—1221no—
489C22⋊C4—1221no—
490C22⋊C4—1221no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—1221no—
495C42C2×C4×D6111yescharacteristic
496C42D4×D6111yescharacteristic
497C42#1175822411yescharacteristic
498C42C23×D6111yescharacteristic
499C23—21no—
500C23—1221no—
501C23#1451973711yescharacteristic
502Q8—21no—
503Q8—1221no—
504Q8—1221no—
505Q8#1451978512yes—
506D4—24no—
507D4—21no—
508D4—1221no—
509D4—1221no—
510D4—2442no—
511D4#1451978512yes—
512C2×C4—24no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—1221no—
525C2×C4—1221no—
526C2×C4—1221no—
527C2×C4—2441no—
528C2×C4—2441no—
529C2×C4#1451973711yescharacteristic
530C2×C4#1451973711yescharacteristic
531C2×C4#1451973711yescharacteristic
532C2×C4C22×C4×D6111yescharacteristic
533C2×C4C2×D4×D6111yescharacteristic
534C2×C4C2×#1175822411yescharacteristic
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—612no—
540C8—612no—
541C8—1221no—
542C8—1221no—
543C8—1221no—
544C8—1221no—
545C8—1221no—
546C8—1221no—
547C8—2441no—
548C8—2441no—
549C22—21no—
550C22—21no—
551C22—22no—
552C22—21no—
553C22—41no—
554C22—41no—
555C22—2441no—
556C22—2441no—
557C22—2441no—
558C22C2×#1451973711yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—22no—
563C4—21no—
564C4—41no—
565C4—41no—
566C4—2441no—
567C4—2441no—
568C4—2441no—
569C4C2×#1451978511yescharacteristic
570C4C2×#1451978511yescharacteristic
571C4#135×D6111yescharacteristic
572C4#135×D6111yescharacteristic
573C2—41no—
574C2—42no—
575C2—4881no—
576C2#2145450911yescharacteristic
577C2#2145458711yescharacteristic
578C2#2145471811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1488C2
socleC22×C61C2×C4×D4
prime radical#16839907C4
cosocleC42×C61C24
hypercenter#1488D61
hypocenterC61#17904
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1488

Complements

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

NH ≅ G/Ntype
2. #21454788C2semidirect
3. #41×#92418C2semidirect
4. #21444666C2semidirect
5. #21444659C2semidirect
6. #21444652C2semidirect
7. #21444645C2semidirect
8. #21444623C2semidirect
9. #21444622C2semidirect
10. #21444616C2semidirect
11. #21444611C2semidirect
12. #21444600C2semidirect
13. #21444228C2semidirect
14. #21444103C2semidirect
15. C61×#1488C2semidirect
296. #1488D61semidirect
356. C61#17904semidirect

Maximal subgroups

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

subgroupindex
#214558372
#214547882
#41×#924182
#214446662
#214446592
#214446522
#214446452
#214446232
#214446222
#214446162
#214446112
#214446002
#214442282
#214441032
C61×#14882
#1790461