Finite Group Databasebeta

← #29651413

Subgroups — #29651413

Order 15616.

566 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455854C211yesmaximal, characteristic
2#21454921C211yesmaximal, characteristic
3#21454909C211yesmaximal, characteristic
4#21444725C211yesmaximal, characteristic, complemented
5#21444713C211yesmaximal, characteristic, complemented
6#21444693C211yesmaximal, characteristic, complemented
7#21444687C211yesmaximal, characteristic, complemented
8#21444672C211yesmaximal, characteristic, complemented
9#21444666C211yesmaximal, characteristic, complemented
10#21444635C211yesmaximal, characteristic, complemented
11#21444623C211yesmaximal, characteristic, complemented
12#21444600C211yesmaximal, characteristic
13#21444215C211yesmaximal, characteristic
14#21444119C211yesmaximal, characteristic
15C61×#1497C211yesmaximal, characteristic
16C2×C4×Dic122C2211yescharacteristic
17#16840095C411yescharacteristic
18#16840095C411yescharacteristic
19#16840054C411yescharacteristic
20#16840054C411yescharacteristic
21#16839969C411yescharacteristic
22#16839969C411yescharacteristic
23#16839917C411yescharacteristic
24#16839917C411yescharacteristic
25#16839893—21no—
26#16839893C2211yescharacteristic
27#16839893C2211yescharacteristic
28#16839890—21no—
29#16839890—21no—
30#16839889C2211yescharacteristic
31#16839889C2211yescharacteristic
32Q8×#92418—21no—
33Q8×#92418C2211yescharacteristic
34Q8×#92418C2211yescharacteristic
35#16839886C2211yescharacteristic
36#16839886C2211yescharacteristic
37C4×#11758202C2211yescharacteristic
38C4×#11758202C2211yescharacteristic
39C4×#11758202C2211yescharacteristic
40C4×#11758202C2211yescharacteristic
41#16839823—21no—
42#16839823—21no—
43#16839816—21no—
44#16839815C2211yescharacteristic
45#16839815C2211yescharacteristic
46#16839815C2211yescharacteristic
47#16839812—21no—
48#16839514C2211yescharacteristic
49#16839514C2211yescharacteristic
50#16839512C2211yescharacteristic
51#16839512C2211yescharacteristic
52#16839494C2211yescharacteristic
53#16839494C2211yescharacteristic
54#16839494C2211yescharacteristic
55#16839494C2211yescharacteristic
56#16839484C2211yescharacteristic
57#16839484C2211yescharacteristic
58#16839483C2211yescharacteristic
59C8×#92418C2211yescharacteristic
60C61×#533C2211yescharacteristic
61C61×#432C2211yescharacteristic
62C61×#431C2211yescharacteristic
63C61×Q8⋊C8C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×Q8⋊C8C2211yescharacteristic
66C61×Q8⋊C8C2211yescharacteristic
67C22×Dic122C2×C411yescharacteristic
68C2×#11758202C2×C411yescharacteristic
69C2×#11758202C2×C411yescharacteristic
70C2×#11758202C2×C411yescharacteristic
71C2×#11758202C2×C411yescharacteristic
72C4×Dic122—21no—
73C4×Dic122—21no—
74C4×Dic122C2×C411yescharacteristic
75C4×Dic122C2×C411yescharacteristic
76C4×Dic122C2311yescharacteristic
77C4×Dic122C2311yescharacteristic
78C2×C4⋊Dic61C2×C411yescharacteristic
79C2×#11758196—21no—
80C2×C4×Dic61—21no—
81#14519710C2×C411yescharacteristic
82#14519710C2×C411yescharacteristic
83#14519710C2×C411yescharacteristic
84#14519710C2×C411yescharacteristic
85C4⋊#92418—21no—
86C4⋊#92418—21no—
87C4⋊#92418—21no—
88C4⋊#92418—21no—
89C4⋊#92418C2×C411yescharacteristic
90C4⋊#92418C2×C411yescharacteristic
91C4⋊#92418D411yescharacteristic
92C4⋊#92418D411yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95#14519706—21no—
96#14519706—21no—
97#14519706—21no—
98#14519706—21no—
99#14519701C2×C411yescharacteristic
100#14519701C2×C411yescharacteristic
101#14519701C2×C411yescharacteristic
102#14519701C2×C411yescharacteristic
103#14519700C2×C411yescharacteristic
104#14519700C2×C411yescharacteristic
105#14519700C2×C411yescharacteristic
106#14519700C2×C411yescharacteristic
107C22⋊#92418—21no—
108C22⋊#92418C2×C411yescharacteristic
109C22⋊#92418C2×C411yescharacteristic
110C22⋊#92418D411yescharacteristic
111C22⋊#92418D411yescharacteristic
112#14519688—21no—
113#14519688—21no—
114#14519687—21no—
115#14519687—21no—
116C4×#92418—21no—
117C4×#92418—21no—
118C4×#92418—21no—
119C4×#92418C2311yescharacteristic
120C4×#92418C2311yescharacteristic
121C4×#92418C2311yescharacteristic
122C4×#92418C2311yescharacteristic
123C8×Dic61—21no—
124C8×Dic61—21no—
125C4⋊Q8×C61C2×C411yescharacteristic
126C4⋊Q8×C61C2×C411yescharacteristic
127#125×C61—21no—
128C22⋊Q8×C61—21no—
129C22⋊Q8×C61C2×C411yescharacteristic
130C22⋊Q8×C61C2×C411yescharacteristic
131C4×Q8×C61—21no—
132C4×Q8×C61C2311yescharacteristic
133C4×Q8×C61C2311yescharacteristic
134#117×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
144C2×Q8×C61—21no—
145C2×Q8×C61C22×C411yescharacteristic
146C2×Q8×C61C22×C411yescharacteristic
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61#4111yescharacteristic
150C22×Dic61—21no—
151C22×Dic61—21no—
152C2×Dic122—22no—
153C2×Dic122—21no—
154C2×Dic122—41no—
155C2×Dic122C22×C411yescharacteristic
156C2×Dic122C22×C411yescharacteristic
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61C22×C411yescharacteristic
169C4⋊C4×C61C22×C411yescharacteristic
170C22⋊C4×C61—21no—
171C22⋊C4×C61—21no—
172C42×C61—21no—
173C42×C61—21no—
174C42×C61C22×C411yescharacteristic
175C42×C61C2×D411yescharacteristic
176C42×C61#4111yescharacteristic
177C42×C61C2411yescharacteristic
178#11758202—22no—
179#11758202—22no—
180#11758202—41no—
181#11758202—41no—
182C4⋊Dic61—21no—
183C4⋊Dic61C22×C411yescharacteristic
184C4⋊Dic61C22×C411yescharacteristic
185#11758196—21no—
186#11758196—21no—
187#11758196—21no—
188#11758196—21no—
189C4×Dic61—21no—
190C4×Dic61—21no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C2×#92418—21no—
194C2×#92418—21no—
195C2×#92418C22×C411yescharacteristic
196C2×#92418C22×C411yescharacteristic
197C2×#92418C22×C411yescharacteristic
198C2×#92418C22×C411yescharacteristic
199C2×#92418C2×D411yescharacteristic
200C2×#92418C2×D411yescharacteristic
201C2×#92418C2×D411yescharacteristic
202C2×#92418C2×D411yescharacteristic
203C23×C61C4×D411yescharacteristic
204Q8×C61—21no—
205Q8×C61—21no—
206Q8×C61—21no—
207Q8×C61—21no—
208Q8×C61—42no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—41no—
218C2×C4×C61C4×D411yescharacteristic
219C2×C4×C61C4×D411yescharacteristic
220C2×C4×C61C4×D411yescharacteristic
221C2×C4×C61C23×C411yescharacteristic
222C2×C4×C61C22×D411yescharacteristic
223C2×C4×C61C2×#4111yescharacteristic
224C2×Dic61—21no—
225C2×Dic61—21no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—42no—
229C2×Dic61—42no—
230Dic122—21no—
231Dic122—21no—
232Dic122—21no—
233Dic122—42no—
234Dic122#13112yes—
235C8×C61—41no—
236C8×C61—41no—
237C8×C61—41no—
238C8×C61—41no—
239#92418—21no—
240#92418—21no—
241#92418—21no—
242#92418—21no—
243#92418—21no—
244#92418—21no—
245#92418—21no—
246#92418—21no—
247#92418—41no—
248#92418—41no—
249#18032—611nomaximal, Sylow
250C22×C61—21no—
251C22×C61—21no—
252C22×C61—21no—
253C22×C61C2×C4×D411yescharacteristic
254C4×C61—21no—
255C4×C61—21no—
256C4×C61—21no—
257C4×C61—21no—
258C4×C61—41no—
259C4×C61—41no—
260C4×C61—41no—
261C4×C61—41no—
262C4×C61C2×#13111yescharacteristic
263C4×C61#56811yescharacteristic
264C4×C61#57811yescharacteristic
265C4×C61#57811yescharacteristic
266Dic61—22no—
267Dic61—41no—
268Dic61—41no—
269Dic61—41no—
270#3104—611no—
271#2986—611no—
272#2984—611no—
273#1593—611no—
274#1591—611no—
275#1587—611no—
276#1587—611no—
277#1584—611no—
278#1584—611no—
279#1579—611no—
280C8×Q16—611no—
281#1572—611no—
282#1497D6111yescharacteristic
283#1479—611no—
284#1454—611no—
285C2×C61—41no—
286C2×C61#293311yescharacteristic
287C2×C61#295011yescharacteristic
288C2×C61#295511yescharacteristic
289#533C2×D6111yescharacteristic
290C2×C4×Q8—611no—
291#484—611no—
292#484—611no—
293#477—611no—
294#477—611no—
295#462—611no—
296#462—611no—
297#451—611no—
298#451—611no—
299#446—611no—
300#446—611no—
301#446—611no—
302#446—611no—
303#446—1221no—
304#446—1221no—
305#446—1221no—
306C8×Q8—611no—
307C8×Q8—611no—
308C8×Q8—611no—
309C8×Q8—611no—
310C8×Q8—1221no—
311C4×Q16—611no—
312C4×Q16—611no—
313C4×Q16—611no—
314C4×Q16—611no—
315#433—1221no—
316#433—1221no—
317#432—1221no—
318#432C2×D6111yescharacteristic
319#431—611no—
320#431—611no—
321#431—611no—
322#431—1221no—
323#431C2×D6111yescharacteristic
324#335—611no—
325#335—611no—
326#334—611no—
327#334—611no—
328Q8⋊C8—611no—
329Q8⋊C8—611no—
330Q8⋊C8—611no—
331Q8⋊C8—611no—
332Q8⋊C8C2×D6111yescharacteristic
333Q8⋊C8C2×D6111yescharacteristic
334Q8⋊C8C2×D6111yescharacteristic
335Q8⋊C8C2×D6111yescharacteristic
336#322—611no—
337#322—611no—
338#322—611no—
339C82—611no—
340C61#1803211yescharacteristic, complemented, Sylow
341C22×Q8—611no—
342C2×Q16—611no—
343C2×Q16—611no—
344C2×Q16—611no—
345C2×Q16—611no—
346C4⋊Q8C4×D6111yescharacteristic
347C4⋊Q8C4×D6111yescharacteristic
348#125—21no—
349C22⋊Q8—21no—
350C22⋊Q8C4×D6111yescharacteristic
351C22⋊Q8C4×D6111yescharacteristic
352C4×Q8—21no—
353C4×Q8—611no—
354C4×Q8—611no—
355C4×Q8—611no—
356C4×Q8—611no—
357C4×Q8—1221no—
358C4×Q8—1221no—
359C4×Q8C22×D6111yescharacteristic
360C4×Q8C22×D6111yescharacteristic
361#117—21no—
362C2×C4⋊C4—611no—
363C2×C4⋊C4—1221no—
364C2×C42—1221no—
365C2×C42C22×D6111yescharacteristic
366#107—611no—
367#107—611no—
368#107—611no—
369#107—611no—
370C4⋊C8—21no—
371C4⋊C8—611no—
372C4⋊C8—611no—
373C4⋊C8—611no—
374C4⋊C8—611no—
375C4⋊C8—611no—
376C4⋊C8—611no—
377C4⋊C8—1221no—
378C4⋊C8—1221no—
379C4⋊C8—1221no—
380C4⋊C8—1221no—
381C4⋊C8—1221no—
382C4⋊C8—1221no—
383C4⋊C8—1221no—
384C4⋊C8—1221no—
385C4⋊C8C22×D6111yescharacteristic
386C4⋊C8C22×D6111yescharacteristic
387#103—611no—
388#103—611no—
389#103—611no—
390#103—611no—
391#103—611no—
392#103—611no—
393#103—611no—
394#103—611no—
395C22⋊C8—21no—
396C22⋊C8—21no—
397C22⋊C8—611no—
398C22⋊C8—611no—
399C22⋊C8—611no—
400C22⋊C8—611no—
401C22⋊C8—1221no—
402#97—21no—
403#97—1221no—
404#97—1221no—
405#97—1221no—
406#97—1221no—
407C4×C8—611no—
408C4×C8—611no—
409C4×C8—611no—
410C4×C8—611no—
411C4×C8—1221no—
412C4×C8—1221no—
413C4×C8—1221no—
414C4×C8—1221no—
415C4×C8—1221no—
416C4×C8C22×D6111yescharacteristic
417C4×C8C22×D6111yescharacteristic
418C2×Q8—21no—
419C2×Q8—611no—
420C2×Q8—611no—
421C2×Q8—1222no—
422C2×Q8—1221no—
423C2×Q8—2441no—
424C2×Q8C2×C4×D6111yescharacteristic
425C2×Q8C2×C4×D6111yescharacteristic
426C22×C4—1221no—
427C22×C4—1221no—
428C22×C4C2×C4×D6111yescharacteristic
429C22×C4D4×D6111yescharacteristic
430C22×C4#1175822411yescharacteristic
431Q16—1222no—
432Q16—1222no—
433Q16—2441no—
434Q16—2441no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—611no—
440C2×C8—611no—
441C2×C8—611no—
442C2×C8—611no—
443C2×C8—611no—
444C2×C8—611no—
445C2×C8—611no—
446C2×C8—611no—
447C2×C8—1221no—
448C2×C8—1221no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—611no—
457C4⋊C4—611no—
458C4⋊C4—1221no—
459C4⋊C4—1221no—
460C4⋊C4—1221no—
461C4⋊C4—1221no—
462C4⋊C4—1221no—
463C4⋊C4C2×C4×D6111yescharacteristic
464C4⋊C4C2×C4×D6111yescharacteristic
465C22⋊C4—21no—
466C22⋊C4—21no—
467C42—21no—
468C42—21no—
469C42—1221no—
470C42—1221no—
471C42—1221no—
472C42—1221no—
473C42C2×C4×D6111yescharacteristic
474C42D4×D6111yescharacteristic
475C42#1175822411yescharacteristic
476C42C23×D6111yescharacteristic
477C23#1451973711yescharacteristic
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—42no—
483Q8—612no—
484Q8—1221no—
485Q8—1221no—
486Q8—1221no—
487Q8—2442no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—41no—
497C2×C4—1221no—
498C2×C4—1221no—
499C2×C4—1221no—
500C2×C4—1221no—
501C2×C4—2442no—
502C2×C4—2442no—
503C2×C4#1451973711yescharacteristic
504C2×C4#1451973711yescharacteristic
505C2×C4#1451973711yescharacteristic
506C2×C4C22×C4×D6111yescharacteristic
507C2×C4C2×D4×D6111yescharacteristic
508C2×C4C2×#1175822411yescharacteristic
509C8—41no—
510C8—41no—
511C8—41no—
512C8—41no—
513C8—1221no—
514C8—1221no—
515C8—1221no—
516C8—1221no—
517C8—1221no—
518C8—1221no—
519C8—1221no—
520C8—1221no—
521C8—2441no—
522C8—2441no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22C2×#1451973711yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—1222no—
536C4—2441no—
537C4—2441no—
538C4—2441no—
539C4#131×D6111yescharacteristic
540C4#1684052711yescharacteristic
541C4#1684057811yescharacteristic
542C4#1684057811yescharacteristic
543C2—41no—
544C2#2145454911yescharacteristic
545C2#2145468311yescharacteristic
546C2#2145471811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1497C2
socleC22×C61C2×C4×D4
prime radicalC23×C61C4×D4
cosocleC42×C61C24
hypercenter#1497D61
hypocenterC61#18032
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1497

Complements

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

NH ≅ G/Ntype
4. #21444725C2semidirect
5. #21444713C2semidirect
6. #21444693C2semidirect
7. #21444687C2semidirect
8. #21444672C2semidirect
9. #21444666C2semidirect
10. #21444635C2semidirect
11. #21444623C2semidirect
340. C61#18032semidirect

Maximal subgroups

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

subgroupindex
#214558542
#214549212
#214549092
#214447252
#214447132
#214446932
#214446872
#214446722
#214446662
#214446352
#214446232
#214446002
#214442152
#214441192
C61×#14972
#1803261