Finite Group Databasebeta

← #29650124

Subgroups — #29650124

Order 15616.

598 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455884C211yesmaximal, characteristic
2#21454928C211yesmaximal, characteristic
3#21454914C211yesmaximal, characteristic, complemented
4#21444693C211yesmaximal, characteristic, complemented
5#21444679C211yesmaximal, characteristic, complemented
6#21444672C211yesmaximal, characteristic, complemented
7#21444658C211yesmaximal, characteristic, complemented
8#21444635C211yesmaximal, characteristic, complemented
9#21444634C211yesmaximal, characteristic, complemented
10#21444623C211yesmaximal, characteristic, complemented
11#21444616C211yesmaximal, characteristic, complemented
12#21444602C211yesmaximal, characteristic, complemented
13#21444254C211yesmaximal, characteristic
14#21444119C211yesmaximal, characteristic, complemented
15C61×#1481C211yesmaximal, characteristic, complemented
16C4×#11758222C2211yescharacteristic
17#16840100C411yescharacteristic
18#16840100C411yescharacteristic
19#16840044C411yescharacteristic
20#16840039C411yescharacteristic
21#16839969C411yescharacteristic
22#16839964C411yescharacteristic
23#16839922C411yescharacteristic
24#16839922C411yescharacteristic
25#16839893—21no—
26#16839893—21no—
27#16839893C2211yescharacteristic
28#16839893C2211yescharacteristic
29Q8×#92418C2211yescharacteristic
30Q8×#92418C2211yescharacteristic
31#16839886C2211yescharacteristic
32#16839886C2211yescharacteristic
33C4×#11758202C2211yescharacteristic
34C4×#11758202C2211yescharacteristic
35C4×#11758201C2211yescharacteristic
36C4×#11758201C2211yescharacteristic
37#16839827C2211yescharacteristic
38#16839827C2211yescharacteristic
39C8×C22⋊D61—21no—
40C8×C22⋊D61—21no—
41#16839823—21no—
42#16839823—21no—
43#16839819C2211yescharacteristic
44#16839815C2211yescharacteristic
45#16839815C2211yescharacteristic
46#16839814—21no—
47C4⋊C8×D61—21no—
48#16839514C2211yescharacteristic
49#16839514C2211yescharacteristic
50#16839512C2211yescharacteristic
51#16839512C2211yescharacteristic
52#16839494C2211yescharacteristic
53#16839494C2211yescharacteristic
54#16839491C2211yescharacteristic
55#16839491C2211yescharacteristic
56#16839484C2211yescharacteristic
57#16839484C2211yescharacteristic
58#16839483C2211yescharacteristic
59C8×#92418C2211yescharacteristic
60C61×#533C2211yescharacteristic
61C61×#431C2211yescharacteristic
62C2×C4⋊C8×C61C2211yescharacteristic
63C61×Q8⋊C8C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×Q8⋊C8C2211yescharacteristic
66C61×Q8⋊C8C2211yescharacteristic
67C2×#11758222C2×C411yescharacteristic
68C2×#11758202C2×C411yescharacteristic
69C2×#11758202C2×C411yescharacteristic
70C2×#11758201C2×C411yescharacteristic
71C2×#11758201C2×C411yescharacteristic
72C2×C8×D61—21no—
73C2×C8×D61—21no—
74C4×Dic122C2×C411yescharacteristic
75C4×Dic122C2311yescharacteristic
76C4×D244C2×C411yescharacteristic
77C4×D244C2311yescharacteristic
78C4×C22⋊D61—21no—
79C4×C22⋊D61—21no—
80#14519736C2×C411yescharacteristic
81#14519734—21no—
82C42×D61—21no—
83#14519710C2×C411yescharacteristic
84#14519710C2×C411yescharacteristic
85#14519708C2×C411yescharacteristic
86#14519708C2×C411yescharacteristic
87C4⋊#92418—21no—
88C4⋊#92418—21no—
89C4⋊#92418—21no—
90C4⋊#92418—21no—
91C4⋊#92418C2×C411yescharacteristic
92C4⋊#92418C2×C411yescharacteristic
93C4⋊#92418D411yescharacteristic
94C4⋊#92418D411yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
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#14519697C2×C411yescharacteristic
106#14519697C2×C411yescharacteristic
107C22⋊#92418—21no—
108C22⋊#92418C2×C411yescharacteristic
109C22⋊#92418C2×C411yescharacteristic
110C22⋊#92418D411yescharacteristic
111C22⋊#92418D411yescharacteristic
112#14519689—21no—
113#14519689—21no—
114#14519688—21no—
115#14519688—21no—
116#14519688—21no—
117C4×#92418—21no—
118C4×#92418—21no—
119C4×#92418C2311yescharacteristic
120C4×#92418C2311yescharacteristic
121C4×#92418C2311yescharacteristic
122C4×#92418C2311yescharacteristic
123C8×Dic61—21no—
124C8×Dic61—21no—
125C22×C8×C61—21no—
126C4⋊Q8×C61C2×C411yescharacteristic
127C4⋊Q8×C61C2×C411yescharacteristic
128#125×C61—21no—
129C22⋊Q8×C61—21no—
130C22⋊Q8×C61C2×C411yescharacteristic
131C22⋊Q8×C61C2×C411yescharacteristic
132C4×Q8×C61—21no—
133C4×Q8×C61C2311yescharacteristic
134C4×Q8×C61C2311yescharacteristic
135#117×C61—21no—
136C2×C42×C61C2311yescharacteristic
137C4⋊C8×C61—21no—
138C4⋊C8×C61—21no—
139C4⋊C8×C61C2311yescharacteristic
140C4⋊C8×C61C2311yescharacteristic
141C22⋊C8×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
150C2×C22⋊D61—21no—
151#11758222—22no—
152#11758222—22no—
153C2×D244C22×C411yescharacteristic
154C2×C4×D61—21no—
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×Dic122C22×C411yescharacteristic
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—81no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61C22×C411yescharacteristic
171C4⋊C4×C61C22×C411yescharacteristic
172C22⋊C4×C61—21no—
173C22⋊C4×C61—21no—
174C42×C61—21no—
175C42×C61—21no—
176C42×C61C22×C411yescharacteristic
177C42×C61C2×D411yescharacteristic
178C42×C61#4111yescharacteristic
179C42×C61C2411yescharacteristic
180C22⋊Dic61—21no—
181#11758202—22no—
182#11758202—22no—
183#11758201—22no—
184#11758201—22no—
185#11758198—21no—
186#11758198—21no—
187C4⋊Dic61C22×C411yescharacteristic
188C4⋊Dic61C22×C411yescharacteristic
189#11758196—21no—
190#11758196—21no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418C22×C411yescharacteristic
197C2×#92418C22×C411yescharacteristic
198C2×#92418C22×C411yescharacteristic
199C2×#92418C22×C411yescharacteristic
200C2×#92418C2×D411yescharacteristic
201C2×#92418C2×D411yescharacteristic
202C2×#92418C2×D411yescharacteristic
203C2×#92418C2×D411yescharacteristic
204C8×D61—81no—
205C8×D61—81no—
206C23×C61C4×D411yescharacteristic
207C22×D61—21no—
208Q8×C61—21no—
209Q8×C61—21no—
210Q8×C61—21no—
211Q8×C61—21no—
212Q8×C61—81no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—41no—
222C2×C4×C61C4×D411yescharacteristic
223C2×C4×C61C4×D411yescharacteristic
224C2×C4×C61C4×D411yescharacteristic
225C2×C4×C61C23×C411yescharacteristic
226C2×C4×C61C22×D411yescharacteristic
227C2×C4×C61C2×#4111yescharacteristic
228C22⋊D61—24no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232D244—21no—
233D244#13112yes—
234C4×D61—24no—
235C4×D61—41no—
236C4×D61—41no—
237C4×D61—81no—
238Dic122—21no—
239Dic122#13112yes—
240C8×C61—41no—
241C8×C61—41no—
242C8×C61—41no—
243C8×C61—41no—
244#92418—21no—
245#92418—21no—
246#92418—21no—
247#92418—21no—
248#92418—21no—
249#92418—21no—
250#92418—21no—
251#92418—21no—
252#92418—41no—
253#92418—41no—
254#17921—611nomaximal, Sylow
255C22×C61—21no—
256C22×C61—21no—
257C22×C61—21no—
258C22×C61C2×C4×D411yescharacteristic
259C2×D61—22no—
260C2×D61—41no—
261C2×D61—41no—
262C4×C61—21no—
263C4×C61—21no—
264C4×C61—21no—
265C4×C61—21no—
266C4×C61—41no—
267C4×C61—41no—
268C4×C61—41no—
269C4×C61—41no—
270C4×C61C2×#13111yescharacteristic
271C4×C61C2×#13111yescharacteristic
272C4×C61#57711yescharacteristic
273C4×C61#57811yescharacteristic
274Dic61—22no—
275Dic61—41no—
276Dic61—41no—
277#3107—611no—
278#2988—611no—
279#2985—611no—
280#1587—611no—
281#1585—611no—
282#1584—611no—
283#1582—611no—
284#1579—611no—
285SD16⋊C8—611no—
286C8×Q16—611no—
287C8×SD16—611no—
288#1573—611no—
289#1488—611no—
290#1481D6111yescharacteristic, complemented
291#1454—611no—
292C2×C61—41no—
293C2×C61#292911yescharacteristic
294C2×C61#294711yescharacteristic
295C2×C61#295711yescharacteristic
296D61—42no—
297#533C2×D6111yescharacteristic
298C4×#41—611no—
299#485—611no—
300#485—611no—
301#475—611no—
302#474—611no—
303#462—611no—
304#461—611no—
305#452—611no—
306#452—611no—
307#446—611no—
308#446—611no—
309#446—1221no—
310#446—1221no—
311C8×Q8—611no—
312C8×Q8—611no—
313C8×Q8—611no—
314C8×Q8—611no—
315C4×Q16—611no—
316C4×Q16—611no—
317C4×SD16—611no—
318C4×SD16—611no—
319C8×D4—611no—
320C8×D4—611no—
321C8×D4—1221no—
322C8×D4—1221no—
323#433—1221no—
324#433—1221no—
325#432—611no—
326#431—611no—
327#431—611no—
328#431—1221no—
329#431C2×D6111yescharacteristic
330C2×C4⋊C8—1221no—
331C2×C4⋊C8C2×D6111yescharacteristic
332#335—611no—
333#335—611no—
334#334—611no—
335#334—611no—
336Q8⋊C8—611no—
337Q8⋊C8—611no—
338Q8⋊C8C2×D6111yescharacteristic
339Q8⋊C8C2×D6111yescharacteristic
340Q8⋊C8C2×D6111yescharacteristic
341Q8⋊C8C2×D6111yescharacteristic
342D4⋊C8—611no—
343D4⋊C8—611no—
344#322—611no—
345#322—611no—
346#322—611no—
347C82—611no—
348C61#1792111yescharacteristic, complemented, Sylow
349C2×#41—611no—
350C2×Q16—611no—
351C2×Q16—611no—
352C2×SD16—611no—
353C2×SD16—611no—
354C22×C8—21no—
355C22×C8—1221no—
356C22×C8—1221no—
357C4⋊Q8C4×D6111yescharacteristic
358C4⋊Q8C4×D6111yescharacteristic
359#125—21no—
360C22⋊Q8—21no—
361C22⋊Q8C4×D6111yescharacteristic
362C22⋊Q8C4×D6111yescharacteristic
363C4×Q8—21no—
364C4×Q8—611no—
365C4×Q8—611no—
366C4×Q8C22×D6111yescharacteristic
367C4×Q8C22×D6111yescharacteristic
368C4×D4—611no—
369C4×D4—611no—
370C4×D4—1221no—
371C4×D4—1221no—
372#117—21no—
373#117—611no—
374#117—1221no—
375C2×C42—1221no—
376C2×C42C22×D6111yescharacteristic
377#107—611no—
378#107—611no—
379#106—611no—
380#106—611no—
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—611no—
384C4⋊C8—611no—
385C4⋊C8—611no—
386C4⋊C8—611no—
387C4⋊C8—611no—
388C4⋊C8—611no—
389C4⋊C8—1221no—
390C4⋊C8—1221no—
391C4⋊C8—1221no—
392C4⋊C8—1221no—
393C4⋊C8—1221no—
394C4⋊C8—1221no—
395C4⋊C8C22×D6111yescharacteristic
396C4⋊C8C22×D6111yescharacteristic
397#103—611no—
398#103—611no—
399#103—611no—
400#103—611no—
401#103—611no—
402#103—611no—
403#102—611no—
404#102—611no—
405C22⋊C8—21no—
406C22⋊C8—611no—
407C22⋊C8—611no—
408C22⋊C8—611no—
409C22⋊C8—611no—
410C22⋊C8—1221no—
411C22⋊C8—1221no—
412C22⋊C8—1221no—
413#97—1221no—
414#97—1221no—
415#97—1221no—
416C4×C8—611no—
417C4×C8—611no—
418C4×C8—611no—
419C4×C8—611no—
420C4×C8—1221no—
421C4×C8—1221no—
422C4×C8—1221no—
423C4×C8—1221no—
424C4×C8C22×D6111yescharacteristic
425C4×C8C22×D6111yescharacteristic
426#41—1222no—
427#41—1222no—
428C2×Q8—21no—
429C2×Q8—611no—
430C2×Q8C2×C4×D6111yescharacteristic
431C2×Q8C2×C4×D6111yescharacteristic
432C2×D4—611no—
433C2×D4—1221no—
434C22×C4—1221no—
435C22×C4—1221no—
436C22×C4—1221no—
437C22×C4C2×C4×D6111yescharacteristic
438C22×C4D4×D6111yescharacteristic
439C22×C4#1175822411yescharacteristic
440Q16—1222no—
441Q16—1222no—
442SD16—1222no—
443SD16—1222no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—81no—
449C2×C8—611no—
450C2×C8—611no—
451C2×C8—611no—
452C2×C8—611no—
453C2×C8—611no—
454C2×C8—611no—
455C2×C8—611no—
456C2×C8—611no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8—4881no—
460C2×C8—4881no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—611no—
469C4⋊C4—611no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4C2×C4×D6111yescharacteristic
473C4⋊C4C2×C4×D6111yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—1221no—
477C22⋊C4—1221no—
478C22⋊C4—1221no—
479C42—21no—
480C42—21no—
481C42—1221no—
482C42—1221no—
483C42—1221no—
484C42C2×C4×D6111yescharacteristic
485C42D4×D6111yescharacteristic
486C42#1175822411yescharacteristic
487C42C23×D6111yescharacteristic
488C23—1221no—
489C23#1451973711yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—81no—
495Q8—612no—
496Q8—1221no—
497D4—612no—
498D4—1224no—
499D4—1221no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—1224no—
510C2×C4—1221no—
511C2×C4—1221no—
512C2×C4—1221no—
513C2×C4—4881no—
514C2×C4—2441no—
515C2×C4—2441no—
516C2×C4#1451973711yescharacteristic
517C2×C4#1451973711yescharacteristic
518C2×C4#1451973711yescharacteristic
519C2×C4C22×C4×D6111yescharacteristic
520C2×C4C2×D4×D6111yescharacteristic
521C2×C4C2×#1175822411yescharacteristic
522C8—41no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—1221no—
527C8—1221no—
528C8—1221no—
529C8—1221no—
530C8—1221no—
531C8—1221no—
532C8—1221no—
533C8—1221no—
534C8—2441no—
535C8—2441no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—1222no—
540C22—2441no—
541C22—2441no—
542C22C2×#1451973711yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—1222no—
552C4—2441no—
553C4—2441no—
554C4#131×D6111yescharacteristic
555C4#131×D6111yescharacteristic
556C4#1684056811yescharacteristic
557C4#1684057511yescharacteristic
558C2—41no—
559C2—2442no—
560C2#2145451611yescharacteristic
561C2#2145465611yescharacteristic
562C2#2145473211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1481C2
socleC22×C61C2×C4×D4
prime radicalC2×#11758222C2×C4
cosocleC42×C61C24
hypercenter#1481D61
hypocenterC61#17921
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
3. #21454914C2semidirect
4. #21444693C2semidirect
5. #21444679C2semidirect
6. #21444672C2semidirect
7. #21444658C2semidirect
8. #21444635C2semidirect
9. #21444634C2semidirect
10. #21444623C2semidirect
11. #21444616C2semidirect
12. #21444602C2semidirect
14. #21444119C2semidirect
15. C61×#1481C2semidirect
290. #1481D61semidirect
348. C61#17921semidirect

Maximal subgroups

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

subgroupindex
#214558842
#214549282
#214549142
#214446932
#214446792
#214446722
#214446582
#214446352
#214446342
#214446232
#214446162
#214446022
#214442542
#214441192
C61×#14812
#1792161