Finite Group Databasebeta

← #29667589

Subgroups — #29667589

Order 15616.

568 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457150C211yesmaximal, characteristic
2#21457040C211yesmaximal, characteristic
3#21454981C211yesmaximal, characteristic
4#21445398C211yesmaximal, characteristic, complemented
5#21445391C211yesmaximal, characteristic, complemented
6#21445322C211yesmaximal, characteristic, complemented
7#21445315C211yesmaximal, characteristic, complemented
8#21445274C211yesmaximal, characteristic, complemented
9#21445267C211yesmaximal, characteristic, complemented
10#21445198C211yesmaximal, characteristic, complemented
11#21445191C211yesmaximal, characteristic, complemented
12#21444604C211yesmaximal, characteristic, complemented
13#21444519C211yesmaximal, characteristic, complemented
14C2×#16839511C211yesmaximal, characteristic, complemented
15C61×#3229C211yesmaximal, characteristic, complemented
16#16840296C2211yescharacteristic
17#16840168—21no—
18#16840124—21no—
19#16840092—21no—
20#16840075—21no—
21#16840069—21no—
22#16840054C2211yescharacteristic
23#16840054C2211yescharacteristic
24#16840049C2211yescharacteristic
25#16840049C2211yescharacteristic
26#16840044C2211yescharacteristic
27#16840039C2211yescharacteristic
28#16840001—21no—
29#16839993—21no—
30#16839984—21no—
31#16839969C2211yescharacteristic
32#16839964C2211yescharacteristic
33#16839892C2211yescharacteristic
34C8×Dic122C2211yescharacteristic
35#16839841C2211yescharacteristic
36#16839830—21no—
37C8×D244C2211yescharacteristic
38#16839825—21no—
39#16839822—21no—
40#16839819C2211yescharacteristic
41#16839787—21no—
42C2×C4⋊#92418C2211yescharacteristic
43C2×C4⋊#92418C2211yescharacteristic
44#16839515C2211yescharacteristic
45#16839515C2211yescharacteristic
46#16839513C2211yescharacteristic
47#16839513C2211yescharacteristic
48#16839511C2211yescharacteristic
49#16839511C2211yescharacteristic
50#16839511C2211yescharacteristic
51#16839511C2211yescharacteristic
52#16839508C2211yescharacteristic
53#16839508C2211yescharacteristic
54#16839508C2211yescharacteristic
55#16839508C2211yescharacteristic
56C61×#533C2211yescharacteristic
57C2×C4⋊Q8×C61C2211yescharacteristic
58C61×#498C2211yescharacteristic
59C61×#498C2211yescharacteristic
60C61×#487C2211yescharacteristic
61C61×#487C2211yescharacteristic
62C61×#483—21no—
63C61×#483—21no—
64C61×#475—21no—
65C61×#475—21no—
66C61×#431C2211yescharacteristic
67C2×#11758202—21no—
68C2×#11758201—21no—
69C2×#11758189—21no—
70C22×#92418—21no—
71C22×#92418—21no—
72C2×C8×D61—21no—
73#14519771—21no—
74#14519769D411yescharacteristic
75#14519765D411yescharacteristic
76#14519760—21no—
77#14519756D411yescharacteristic
78#14519751D411yescharacteristic
79C4×Dic122C2311yescharacteristic
80C4×D244C2311yescharacteristic
81C4×C22⋊D61—21no—
82#14519734—21no—
83#14519710—21no—
84#14519710—21no—
85#14519710—21no—
86#14519708—21no—
87#14519708—21no—
88#14519708—21no—
89C4⋊#92418—21no—
90C4⋊#92418—21no—
91C4⋊#92418C2311yescharacteristic
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519706—21no—
98#14519706—21no—
99#14519701—21no—
100#14519701—21no—
101#14519700—21no—
102#14519700—21no—
103#14519700—21no—
104#14519697—21no—
105#14519697—21no—
106#14519697—21no—
107C22⋊#92418—21no—
108#14519689—21no—
109#14519689—21no—
110#14519688—21no—
111#14519687—21no—
112C8×Dic61—21no—
113C22×Q8×C61—21no—
114C4⋊Q8×C61—21no—
115C4⋊Q8×C61—21no—
116C4⋊Q8×C61—21no—
117C4⋊Q8×C61C2311yescharacteristic
118C4⋊Q8×C61C2311yescharacteristic
119C4⋊Q8×C61C2311yescharacteristic
120C4⋊Q8×C61C2311yescharacteristic
121#125×C61—21no—
122C22⋊Q8×C61—21no—
123C22⋊Q8×C61—21no—
124C4×Q8×C61—21no—
125C4×Q8×C61—21no—
126#117×C61—21no—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61—21no—
129C2×C42×C61C2311yescharacteristic
130#106×C61—21no—
131#106×C61—21no—
132#106×C61—21no—
133#106×C61—21no—
134C4⋊C8×C61D411yescharacteristic
135C4⋊C8×C61D411yescharacteristic
136#103×C61—21no—
137#103×C61—21no—
138#103×C61—21no—
139#103×C61—21no—
140C22⋊C8×C61D411yescharacteristic
141C22⋊C8×C61D411yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—41no—
149C2×Q8×C61—82no—
150C22×C4×C61—41no—
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61#4111yescharacteristic
154C2×C22⋊D61—21no—
155C2×D244C2×D411yescharacteristic
156C2×C4×D61—21no—
157C2×Dic122C2×D411yescharacteristic
158C2×C8×C61C2×D411yescharacteristic
159C2×C8×C61C2×D411yescharacteristic
160C2×C8×C61C2×D411yescharacteristic
161C2×C8×C61C2×D411yescharacteristic
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×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—41no—
171C4⋊C4×C61—41no—
172C4⋊C4×C61—41no—
173C4⋊C4×C61—41no—
174C22⋊C4×C61—41no—
175C42×C61—41no—
176C42×C61C2×D411yescharacteristic
177C42×C61C2×D411yescharacteristic
178C42×C61#4111yescharacteristic
179C42×C61C2411yescharacteristic
180C22⋊Dic61—21no—
181#11758202—81no—
182#11758201—81no—
183#11758198—21no—
184#11758198—21no—
185#11758198—21no—
186#11758198—21no—
187C4⋊Dic61C2×D411yescharacteristic
188C4⋊Dic61C2×D411yescharacteristic
189#11758196—21no—
190#11758196—21no—
191#11758196—21no—
192#11758196—21no—
193C4×Dic61—21no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—81no—
201C2×#92418—81no—
202#11758189—81no—
203C8×D61—81no—
204C23×C61#12111yescharacteristic
205C22×D61—21no—
206Q8×C61—41no—
207Q8×C61—41no—
208Q8×C61—41no—
209Q8×C61—41no—
210Q8×C61—82no—
211Q8×C61—81no—
212Q8×C61—81no—
213C2×C4×C61—22no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—82no—
223C2×C4×C61#12111yescharacteristic
224C2×C4×C61#12111yescharacteristic
225C2×C4×C61#12111yescharacteristic
226C2×C4×C61C22×D411yescharacteristic
227C2×C4×C61C22×D411yescharacteristic
228C2×C4×C61C2×#4111yescharacteristic
229C22⋊D61—42no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233D244—21no—
234D244—21no—
235C4×D61—41no—
236C4×D61—41no—
237Dic122—21no—
238Dic122—21no—
239C8×C61—21no—
240C8×C61—21no—
241C8×C61—21no—
242C8×C61—21no—
243#92418—41no—
244#92418—41no—
245#92418—41no—
246#92418—41no—
247#92418—41no—
248#92418—41no—
249#19588—611nomaximal, Sylow
250C22×C61—21no—
251C22×C61—21no—
252C22×C61#47112yes—
253C22×C61C2×#12111yescharacteristic
254C2×D61—41no—
255C2×D61—41no—
256C2×D61—41no—
257C4×C61—21no—
258C4×C61—21no—
259C4×C61—21no—
260C4×C61—21no—
261C4×C61—81no—
262C4×C61—81no—
263C4×C61—81no—
264C4×C61—81no—
265C4×C61#57711yescharacteristic
266C4×C61#57711yescharacteristic
267C4×C61#57811yescharacteristic
268C4×C61#57811yescharacteristic
269Dic61—41no—
270Dic61—41no—
271Dic61—41no—
272#3248—611no—
273#3238—611no—
274#3229D6111yescharacteristic, complemented
275#2994—611no—
276#1704—611no—
277#1703—611no—
278#1692—611no—
279#1691—611no—
280#1684—611no—
281#1683—611no—
282#1672—611no—
283#1671—611no—
284#1573—611no—
285#1552—611no—
286C2×#333—611no—
287C2×C61—22no—
288C2×C61#304611yescharacteristic
289C2×C61#306311yescharacteristic
290C2×C61C2×#47111yescharacteristic
291D61—81no—
292#533C2×D6111yescharacteristic
293C2×C4⋊Q8C2×D6111yescharacteristic
294#529—611no—
295#501—1221no—
296#498C2×D6111yescharacteristic
297#498C2×D6111yescharacteristic
298#489—1221no—
299#487C2×D6111yescharacteristic
300#487C2×D6111yescharacteristic
301#483—21no—
302#483—21no—
303#483—1221no—
304#480—1221no—
305#479—1221no—
306#477—611no—
307#477—611no—
308#476—611no—
309#476—611no—
310#475—21no—
311#475—21no—
312#475—611no—
313#474—611no—
314#467—1221no—
315#465—1221no—
316#464—1221no—
317#462—611no—
318#461—611no—
319#446—611no—
320C8×Q8—611no—
321#436—611no—
322#435—1221no—
323C8×D4—611no—
324C8×D4—1221no—
325#433—1221no—
326#432—611no—
327#431C2×D6111yescharacteristic
328#424—1221no—
329C2×C4⋊C8—611no—
330C2×C4⋊C8—611no—
331#335—611no—
332#335—611no—
333#334—611no—
334#334—611no—
335#333—611no—
336#333—611no—
337#333—611no—
338#333—611no—
339#332—611no—
340#332—611no—
341#332—611no—
342#332—611no—
343C61#1958811yescharacteristic, complemented, Sylow
344C22×Q8—21no—
345C2×Q16—1221no—
346C2×SD16—1221no—
347C2×M16—1221no—
348C22×C8—1221no—
349C22×C8—1221no—
350C22×C8—1221no—
351C4⋊Q8—21no—
352C4⋊Q8—21no—
353C4⋊Q8—21no—
354C4⋊Q8C22×D6111yescharacteristic
355C4⋊Q8C22×D6111yescharacteristic
356C4⋊Q8C22×D6111yescharacteristic
357C4⋊Q8C22×D6111yescharacteristic
358#126—1221no—
359#125—21no—
360#125—611no—
361#124—611no—
362#123—1221no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—611no—
366#121—611no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8—611no—
370C4×D4—611no—
371C4×D4—1221no—
372#117—21no—
373#117—1221no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C42C22×D6111yescharacteristic
377#107—1221no—
378#107—1221no—
379#107—1221no—
380#106—21no—
381#106—21no—
382#106—21no—
383#106—21no—
384#106—1221no—
385#106—1221no—
386#106—1221no—
387C4⋊C8—611no—
388C4⋊C8—611no—
389C4⋊C8—611no—
390C4⋊C8—611no—
391C4⋊C8—611no—
392C4⋊C8—611no—
393C4⋊C8—1221no—
394C4⋊C8—1221no—
395C4⋊C8—1221no—
396C4⋊C8—1221no—
397C4⋊C8C22⋊D6111yescharacteristic
398C4⋊C8C22⋊D6111yescharacteristic
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—1221no—
404#103—1221no—
405#103—1221no—
406#103—1221no—
407#103—1221no—
408#102—1221no—
409#102—1221no—
410#102—1221no—
411C22⋊C8—1221no—
412C22⋊C8—1221no—
413C22⋊C8—1221no—
414C22⋊C8C22⋊D6111yescharacteristic
415C22⋊C8C22⋊D6111yescharacteristic
416#97—1221no—
417#97—1221no—
418C4×C8—1221no—
419C4×C8C22×D6111yescharacteristic
420C4×C8C22×D6111yescharacteristic
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—41no—
426C2×Q8—82no—
427C2×Q8—611no—
428C2×D4—611no—
429C2×D4—1221no—
430C22×C4—41no—
431C22×C4—1221no—
432C22×C4D4×D6111yescharacteristic
433C22×C4#1175822411yescharacteristic
434C22×C4C2×C22⋊D6111yescharacteristic
435Q16—4881no—
436SD16—4881no—
437M16—4881no—
438C2×C8—1221no—
439C2×C8—1221no—
440C2×C8—1221no—
441C2×C8—1221no—
442C2×C8—1221no—
443C2×C8—1221no—
444C2×C8—4881no—
445C2×C8—4881no—
446C2×C8—4881no—
447C2×C8C2×C22⋊D6111yescharacteristic
448C2×C8C2×C22⋊D6111yescharacteristic
449C2×C8C2×C22⋊D6111yescharacteristic
450C2×C8C2×C22⋊D6111yescharacteristic
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—611no—
464C4⋊C4—611no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C22⋊C4—41no—
470C22⋊C4—1221no—
471C22⋊C4—1221no—
472C22⋊C4—1221no—
473C22⋊C4—1221no—
474C22⋊C4—1221no—
475C42—41no—
476C42—1221no—
477C42D4×D6111yescharacteristic
478C42#1175822411yescharacteristic
479C42C2×C22⋊D6111yescharacteristic
480C42C23×D6111yescharacteristic
481C23—1221no—
482C23#1451974811yescharacteristic
483Q8—41no—
484Q8—41no—
485Q8—41no—
486Q8—41no—
487Q8—81no—
488Q8—81no—
489Q8—82no—
490Q8—1221no—
491Q8—1221no—
492D4—1221no—
493D4—1221no—
494D4—2442no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—82no—
505C2×C4—1221no—
506C2×C4—1221no—
507C2×C4—1221no—
508C2×C4—2441no—
509C2×C4—2441no—
510C2×C4#1451974811yescharacteristic
511C2×C4#1451974811yescharacteristic
512C2×C4#1451974811yescharacteristic
513C2×C4C2×D4×D6111yescharacteristic
514C2×C4C22×C22⋊D6111yescharacteristic
515C2×C4C2×#1175822411yescharacteristic
516C8—21no—
517C8—21no—
518C8—21no—
519C8—21no—
520C8—2441no—
521C8—2441no—
522C8—2441no—
523C8—2441no—
524C8—2441no—
525C8—2441no—
526C22—21no—
527C22—21no—
528C22—2441no—
529C22—2441no—
530C22—2441no—
531C22#1684002212yes—
532C22C2×#1451974811yescharacteristic
533C4—21no—
534C4—21no—
535C4—21no—
536C4—21no—
537C4—81no—
538C4—81no—
539C4—81no—
540C4—81no—
541C4—2441no—
542C4—2441no—
543C4—2441no—
544C4#1684057011yescharacteristic
545C4#1684057111yescharacteristic
546C4#1684057711yescharacteristic
547C4#1684057811yescharacteristic
548C2—22no—
549C2—4881no—
550C2#2145536511yescharacteristic
551C2#2145550411yescharacteristic
552C2C2×#1684002211yescharacteristic
subgroupG/H
centerC22C2×#14519748
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3229C2
socleC22×C61C2×#121
prime radical#14519751D4
hypercenter#3229D61
hypocenterC61#19588
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3229

Complements

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

NH ≅ G/Ntype
4. #21445398C2semidirect
5. #21445391C2semidirect
6. #21445322C2semidirect
7. #21445315C2semidirect
8. #21445274C2semidirect
9. #21445267C2semidirect
10. #21445198C2semidirect
11. #21445191C2semidirect
12. #21444604C2semidirect
13. #21444519C2semidirect
14. C2×#16839511C2semidirect
15. C61×#3229C2semidirect
274. #3229D61semidirect
343. C61#19588semidirect

Maximal subgroups

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

subgroupindex
#214571502
#214570402
#214549812
#214453982
#214453912
#214453222
#214453152
#214452742
#214452672
#214451982
#214451912
#214446042
#214445192
C2×#168395112
C61×#32292
#1958861