Finite Group Databasebeta

← #29677281

Subgroups — #29677281

Order 15616.

560 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458870C211yesmaximal, characteristic
2#21458633C211yesmaximal, characteristic
3#21458618C211yesmaximal, characteristic, complemented
4#21445421C211yesmaximal, characteristic
5#21445371C211yesmaximal, characteristic, complemented
6#21445361C211yesmaximal, characteristic
7#21445322C211yesmaximal, characteristic, complemented
8#21445291C211yesmaximal, characteristic
9#21445040C211yesmaximal, characteristic, complemented
10#21445004C211yesmaximal, characteristic
11#21444975C211yesmaximal, characteristic, complemented
12#21444915C211yesmaximal, characteristic
13#21444716C211yesmaximal, characteristic, complemented
14#21444714C211yesmaximal, characteristic, complemented
15C61×#3387C211yesmaximal, characteristic, complemented
16#16840497C2211yescharacteristic
17#16840490C2211yescharacteristic
18#16840155—21no—
19#16840135C2211yescharacteristic
20#16840130—21no—
21#16840124—21no—
22#16840112C2211yescharacteristic
23#16840112C2211yescharacteristic
24#16840110C2211yescharacteristic
25#16840110C2211yescharacteristic
26#16840069—21no—
27#16840054C2211yescharacteristic
28#16840047C2211yescharacteristic
29#16840039—21no—
30#16839987—21no—
31#16839984—21no—
32#16839972C2211yescharacteristic
33#16839969—21no—
34#16839969C2211yescharacteristic
35#16839966—21no—
36#16839962C2211yescharacteristic
37#16839962C2211yescharacteristic
38#16839893C2211yescharacteristic
39#16839893C2211yescharacteristic
40#16839892C2211yescharacteristic
41#16839867—21no—
42#16839861—21no—
43#16839860—21no—
44C4×#11758202C2211yescharacteristic
45#16839515C2211yescharacteristic
46#16839514C2211yescharacteristic
47#16839511C2211yescharacteristic
48#16839509C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839505C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53Q8⋊#92418C2211yescharacteristic
54#16839492C2211yescharacteristic
55C8×#92418C2211yescharacteristic
56Q82×C61C2211yescharacteristic
57C61×#557C2211yescharacteristic
58C61×#501—21no—
59C61×#498C2211yescharacteristic
60C61×#479—21no—
61C61×#477C2211yescharacteristic
62C61×#475—21no—
63C61×#475C2211yescharacteristic
64C61×#446C2211yescharacteristic
65C61×#441—21no—
66C4×Q16×C61C2211yescharacteristic
67C2×#11758202—21no—
68C2×#11758202—21no—
69C2×#11758202D411yescharacteristic
70C2×#11758190—21no—
71C2×#11758190—21no—
72C2×#11758201—21no—
73C2×#11758201—21no—
74#14519777C2311yescharacteristic
75#14519775—21no—
76#14519774C2311yescharacteristic
77#14519769—21no—
78#14519767—41no—
79#14519766—21no—
80#14519765—21no—
81#14519762—41no—
82C4×Dic122—21no—
83C4×Dic122C2311yescharacteristic
84#14519742—21no—
85C4×D244—21no—
86#14519739—21no—
87#14519710—21no—
88#14519710D411yescharacteristic
89#14519708—21no—
90C4⋊#92418—21no—
91C4⋊#92418—21no—
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95#14519706—21no—
96#14519701—21no—
97#14519701—21no—
98#14519701—21no—
99#14519701—21no—
100#14519701—41no—
101#14519701D411yescharacteristic
102#14519700—21no—
103#14519700—21no—
104#14519700D411yescharacteristic
105#14519697—21no—
106#14519697—21no—
107#14519697—21no—
108#14519697—21no—
109#14519697—41no—
110#14519688—21no—
111#14519688—21no—
112#14519687—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C2×Q16×C61D411yescharacteristic
116C4⋊Q8×C61—21no—
117C4⋊Q8×C61—21no—
118C4⋊Q8×C61—21no—
119C4⋊Q8×C61—41no—
120C4⋊Q8×C61C2311yescharacteristic
121C4⋊Q8×C61C2311yescharacteristic
122#125×C61—21no—
123#125×C61—41no—
124C4×Q8×C61—21no—
125C4×Q8×C61—21no—
126C4×Q8×C61—21no—
127C4×Q8×C61—21no—
128C4×Q8×C61C2311yescharacteristic
129C4×Q8×C61C2311yescharacteristic
130C4×Q8×C61C2311yescharacteristic
131#107×C61—21no—
132#107×C61D411yescharacteristic
133#106×C61—21no—
134#106×C61—21no—
135#106×C61—21no—
136C4⋊C8×C61—21no—
137C4⋊C8×C61C2311yescharacteristic
138#103×C61—21no—
139#103×C61—21no—
140#103×C61D411yescharacteristic
141#103×C61D411yescharacteristic
142#97×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—41no—
147C2×Q8×C61C2×D411yescharacteristic
148C2×Q8×C61C2×D411yescharacteristic
149C2×Q8×C61C2×D411yescharacteristic
150C2×D244—21no—
151C2×D244—21no—
152C2×D244—21no—
153C2×C4×D61—41no—
154C2×Dic122—21no—
155C2×Dic122C2×D411yescharacteristic
156Q16×C61—22no—
157C2×C8×C61—21no—
158C2×C8×C61C2×D411yescharacteristic
159C2×C8×C61C2×D411yescharacteristic
160C4⋊C4×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—41no—
168C4⋊C4×C61—41no—
169C4⋊C4×C61—41no—
170C4⋊C4×C61—41no—
171C4⋊C4×C61—41no—
172C4⋊C4×C61C2×D411yescharacteristic
173C4⋊C4×C61C2×D411yescharacteristic
174C4⋊C4×C61C2×D411yescharacteristic
175C42×C61—21no—
176C42×C61—21no—
177C42×C61—21no—
178C42×C61—41no—
179C42×C61—41no—
180C42×C61C2411yescharacteristic
181#11758202—41no—
182#11758202—42no—
183#11758202—81no—
184#11758201—42no—
185#11758201—81no—
186#11758198—41no—
187#11758198—41no—
188#11758198—41no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61C2×D411yescharacteristic
192#11758196—21no—
193#11758196—41no—
194#11758196—41no—
195#11758196—41no—
196C4×Dic61—21no—
197C4×Dic61—41no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418C2×D411yescharacteristic
203C2×#92418C2×D411yescharacteristic
204#11758190—42no—
205#11758190—81no—
206C22×D61—41no—
207Q8×C61—21no—
208Q8×C61—21no—
209Q8×C61—21no—
210Q8×C61—21no—
211Q8×C61—21no—
212Q8×C61—21no—
213Q8×C61—41no—
214Q8×C61—41no—
215Q8×C61—81no—
216Q8×C61—161no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61C22×D411yescharacteristic
226C2×C4×C61C22×D411yescharacteristic
227C2×C4×C61H(5,𝔽2)11yescharacteristic
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—41no—
231D244—41no—
232D244—41no—
233D244—41no—
234D244—41no—
235D244—81no—
236C4×D61—161no—
237Dic122—21no—
238Dic122—21no—
239Dic122—41no—
240Dic122—41no—
241C8×C61—21no—
242C8×C61—41no—
243C8×C61#13712yes—
244#92418—21no—
245#92418—21no—
246#92418—41no—
247#92418—41no—
248#92418—41no—
249#92418—41no—
250#20320—611nomaximal, Sylow
251C22×C61D4211yescharacteristic
252C2×D61—81no—
253C2×D61—81no—
254C2×D61—81no—
255C4×C61—21no—
256C4×C61—41no—
257C4×C61—41no—
258C4×C61—41no—
259C4×C61—41no—
260C4×C61—41no—
261C4×C61—41no—
262C4×C61—81no—
263C4×C61—81no—
264C4×C61C2×#13711yescharacteristic
265C4×C61#57511yescharacteristic
266C4×C61#57711yescharacteristic
267C4×C61#57811yescharacteristic
268Dic61—41no—
269Dic61—41no—
270Dic61—81no—
271#3400—611no—
272#3387D6111yescharacteristic, complemented
273#3375—611no—
274#3374—611no—
275#1708—611no—
276#1700—611no—
277#1698—611no—
278#1692—611no—
279#1686—611no—
280#1645—611no—
281#1640—611no—
282#1636—611no—
283#1626—611no—
284#1591—611no—
285#1591—611no—
286C2×C61#327711yescharacteristic
287C2×C61#327811yescharacteristic
288C2×C61#329011yescharacteristic
289D61—161no—
290#559—611no—
291Q82C2×D6111yescharacteristic
292#557—611no—
293#557C2×D6111yescharacteristic
294#501—21no—
295#498C2×D6111yescharacteristic
296#497—1221no—
297#492—611no—
298#491—1221no—
299#489—1221no—
300#487—611no—
301#487—611no—
302#486—611no—
303#486—611no—
304#479—21no—
305#479—1221no—
306#477—611no—
307#477C2×D6111yescharacteristic
308#475—21no—
309#475—611no—
310#475C2×D6111yescharacteristic
311#474—1221no—
312#464—1221no—
313#464—1221no—
314#462—611no—
315#462—611no—
316#462—1221no—
317#461—1221no—
318#460—611no—
319#460—611no—
320#446—611no—
321#446—611no—
322#446—611no—
323#446C2×D6111yescharacteristic
324#441—21no—
325#441—1221no—
326#440—1221no—
327#440—1221no—
328C4×Q16—611no—
329C4×Q16C2×D6111yescharacteristic
330#335—611no—
331#335—611no—
332#333—611no—
333#332—611no—
334#332—611no—
335#331—611no—
336Q8⋊C8—611no—
337Q8⋊C8—611no—
338Q8⋊C8—611no—
339Q8⋊C8—611no—
340C82—611no—
341C61#2032011yescharacteristic, complemented, Sylow
342C2×Q16—611no—
343C2×Q16—1221no—
344C2×Q16—1221no—
345C2×Q16C22⋊D6111yescharacteristic
346C2×SD16—1221no—
347C2×SD16—1221no—
348C2×SD16—1221no—
349C2×SD16—1221no—
350C4⋊Q8—21no—
351C4⋊Q8—21no—
352C4⋊Q8—21no—
353C4⋊Q8—41no—
354C4⋊Q8—611no—
355C4⋊Q8—1221no—
356C4⋊Q8C22×D6111yescharacteristic
357C4⋊Q8C22×D6111yescharacteristic
358#127—611no—
359#125—21no—
360#125—41no—
361#125—1221no—
362#125—2441no—
363#124—1221no—
364#124—1221no—
365#123—2441no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8—21no—
370C4×Q8—611no—
371C4×Q8—1221no—
372C4×Q8—1221no—
373C4×Q8C22×D6111yescharacteristic
374C4×Q8C22×D6111yescharacteristic
375C4×Q8C22×D6111yescharacteristic
376C4×D4—1221no—
377C4×D4—1221no—
378#107—21no—
379#107—611no—
380#107—1221no—
381#107C22⋊D6111yescharacteristic
382#106—21no—
383#106—21no—
384#106—21no—
385#106—1221no—
386C4⋊C8—21no—
387C4⋊C8—611no—
388C4⋊C8—611no—
389C4⋊C8—611no—
390C4⋊C8—1221no—
391C4⋊C8—1221no—
392C4⋊C8—1221no—
393C4⋊C8C22×D6111yescharacteristic
394#103—21no—
395#103—21no—
396#103—611no—
397#103—611no—
398#103—1221no—
399#103—1221no—
400#103—1221no—
401#103—1221no—
402#103—1221no—
403#103—1221no—
404#103—2441no—
405#103C22⋊D6111yescharacteristic
406#103C22⋊D6111yescharacteristic
407#102—1221no—
408#102—1221no—
409#102—1221no—
410#102—1221no—
411#102—2441no—
412#97—21no—
413#97—1221no—
414#97—1221no—
415#97—1221no—
416C4×C8—611no—
417C4×C8—611no—
418C4×C8C22×D6111yescharacteristic
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—41no—
422C2×Q8—611no—
423C2×Q8—1221no—
424C2×Q8D4×D6111yescharacteristic
425C2×Q8C2×C22⋊D6111yescharacteristic
426C2×Q8C2×C22⋊D6111yescharacteristic
427C2×D4—1221no—
428C2×D4—1221no—
429C2×D4—1221no—
430C22×C4—2441no—
431Q16—22no—
432Q16—4881no—
433Q16—2441no—
434Q16—2442no—
435SD16—4881no—
436SD16—4881no—
437SD16—2442no—
438SD16—2442no—
439C2×C8—21no—
440C2×C8—611no—
441C2×C8—611no—
442C2×C8—1221no—
443C2×C8—1221no—
444C2×C8—1221no—
445C2×C8—1221no—
446C2×C8C2×C22⋊D6111yescharacteristic
447C2×C8C2×C22⋊D6111yescharacteristic
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—611no—
461C4⋊C4—1221no—
462C4⋊C4—1221no—
463C4⋊C4—1221no—
464C4⋊C4—2441no—
465C4⋊C4—2441no—
466C4⋊C4—2441no—
467C4⋊C4D4×D6111yescharacteristic
468C4⋊C4C2×C22⋊D6111yescharacteristic
469C4⋊C4C2×C22⋊D6111yescharacteristic
470C22⋊C4—2441no—
471C22⋊C4—2441no—
472C22⋊C4—2441no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—41no—
477C42—41no—
478C42—1221no—
479C42—2441no—
480C42C23×D6111yescharacteristic
481C23—2441no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—21no—
486Q8—21no—
487Q8—21no—
488Q8—41no—
489Q8—41no—
490Q8—81no—
491Q8—161no—
492Q8—1221no—
493Q8—1221no—
494Q8—2441no—
495Q8—2441no—
496D4—4881no—
497D4—2441no—
498D4—2441no—
499D4—2441no—
500D4—2441no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—1221no—
510C2×C4—1221no—
511C2×C4—9761no—
512C2×C4—2441no—
513C2×C4C2×D4×D6111yescharacteristic
514C2×C4C22×C22⋊D6111yescharacteristic
515C2×C4#1451982211yescharacteristic
516C8—21no—
517C8—41no—
518C8—1221no—
519C8—1221no—
520C8—2441no—
521C8—2441no—
522C8—2441no—
523C8—2441no—
524C8#1451980812yes—
525C22—4881no—
526C22—4881no—
527C22—4881no—
528C22D4×C22⋊D6111yescharacteristic
529C4—21no—
530C4—41no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—81no—
537C4—81no—
538C4—4881no—
539C4—2441no—
540C4—2441no—
541C4C2×#1451980811yescharacteristic
542C4#1684056111yescharacteristic
543C4#1684057011yescharacteristic
544C4#1684057811yescharacteristic
545C2—9761no—
546C2#2145747011yescharacteristic
547C2#2145748111yescharacteristic
548C2#2145759911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3387C2
socleC22×C61D42
prime radical#14519774C23
hypercenter#3387D61
hypocenterC61#20320
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3387

Complements

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

NH ≅ G/Ntype
3. #21458618C2semidirect
5. #21445371C2semidirect
7. #21445322C2semidirect
9. #21445040C2semidirect
11. #21444975C2semidirect
13. #21444716C2semidirect
14. #21444714C2semidirect
15. C61×#3387C2semidirect
272. #3387D61semidirect
341. C61#20320semidirect

Maximal subgroups

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

subgroupindex
#214588702
#214586332
#214586182
#214454212
#214453712
#214453612
#214453222
#214452912
#214450402
#214450042
#214449752
#214449152
#214447162
#214447142
C61×#33872
#2032061