Finite Group Databasebeta

← #29667586

Subgroups — #29667586

Order 15616.

550 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#21457186C211yesmaximal, characteristic
2#21457000C211yesmaximal, characteristic
3#21456978C211yesmaximal, characteristic, complemented
4#21454975C211yesmaximal, characteristic
5#21445397C211yesmaximal, characteristic, complemented
6#21445376C211yesmaximal, characteristic, complemented
7#21445346C211yesmaximal, characteristic, complemented
8#21445317C211yesmaximal, characteristic, complemented
9#21445280C211yesmaximal, characteristic, complemented
10#21445245C211yesmaximal, characteristic, complemented
11#21445217C211yesmaximal, characteristic, complemented
12#21445200C211yesmaximal, characteristic, complemented
13#21444607C211yesmaximal, characteristic, complemented
14#21444507C211yesmaximal, characteristic, complemented
15C61×#1542C211yesmaximal, characteristic, complemented
16#16840319C2211yescharacteristic
17#16840296C2211yescharacteristic
18#16840165C2211yescharacteristic
19#16840164—21no—
20#16840158C2211yescharacteristic
21#16840117—21no—
22#16840114C2211yescharacteristic
23#16840114C2211yescharacteristic
24#16840104—21no—
25#16840103—21no—
26#16840103—21no—
27#16840087—21no—
28#16840069—21no—
29#16840066—21no—
30#16840066—21no—
31#16840058C2211yescharacteristic
32#16840054C2211yescharacteristic
33#16840053C2211yescharacteristic
34#16840049C2211yescharacteristic
35#16840048C2211yescharacteristic
36#16840043C2211yescharacteristic
37#16840018—21no—
38#16840010—21no—
39#16839984—21no—
40#16839969C2211yescharacteristic
41#16839964C2211yescharacteristic
42#16839889C2211yescharacteristic
43#16839886C2211yescharacteristic
44#16839839C2211yescharacteristic
45#16839833—21no—
46#16839827C2211yescharacteristic
47C8×C22⋊D61—21no—
48#16839822—21no—
49#16839815C2211yescharacteristic
50#16839787—21no—
51#16839786C2211yescharacteristic
52#16839514C2211yescharacteristic
53#16839514C2211yescharacteristic
54#16839512C2211yescharacteristic
55#16839512C2211yescharacteristic
56#16839510C2211yescharacteristic
57#16839510C2211yescharacteristic
58#16839509C2211yescharacteristic
59#16839509C2211yescharacteristic
60C61×#533C2211yescharacteristic
61C61×#431C2211yescharacteristic
62C2×C4⋊C8×C61C2211yescharacteristic
63C61×#333C2211yescharacteristic
64C61×#333C2211yescharacteristic
65C61×#332C2211yescharacteristic
66C61×#332C2211yescharacteristic
67C2×#11758202—21no—
68C2×#11758201—21no—
69C2×#11758194—21no—
70C2×#11758189—21no—
71C2×C8×D61—21no—
72#14519777C2311yescharacteristic
73#14519777C2311yescharacteristic
74#14519771—21no—
75#14519769—21no—
76#14519769D411yescharacteristic
77#14519765D411yescharacteristic
78#14519760—21no—
79#14519756—21no—
80#14519756—21no—
81#14519756D411yescharacteristic
82#14519751D411yescharacteristic
83C4×Dic122—21no—
84C4×Dic122—21no—
85C4×Dic122C2311yescharacteristic
86C4×D244C2311yescharacteristic
87C4×C22⋊D61—21no—
88#14519736—21no—
89#14519734—21no—
90#14519711—21no—
91#14519711—21no—
92#14519710—21no—
93#14519710—21no—
94#14519710—21no—
95#14519709—21no—
96#14519709—21no—
97#14519708—21no—
98#14519708—21no—
99#14519708—21no—
100C4⋊#92418—21no—
101C4⋊#92418D411yescharacteristic
102C4⋊#92418D411yescharacteristic
103C4⋊#92418C2311yescharacteristic
104C4⋊#92418C2311yescharacteristic
105#14519706—21no—
106#14519706—21no—
107#14519702—21no—
108#14519702—21no—
109#14519701—21no—
110#14519701—21no—
111#14519700—21no—
112#14519700—21no—
113#14519700—21no—
114#14519700—21no—
115#14519700—21no—
116#14519699—21no—
117#14519699—21no—
118#14519697—21no—
119C22⋊#92418D411yescharacteristic
120C22⋊#92418D411yescharacteristic
121#14519689—21no—
122#14519689—21no—
123#14519687—21no—
124C4×#92418C2311yescharacteristic
125C4×#92418C2311yescharacteristic
126C8×Dic61—21no—
127C22×C8×C61—21no—
128C4⋊Q8×C61C2311yescharacteristic
129C4⋊Q8×C61C2311yescharacteristic
130#125×C61—21no—
131C22⋊Q8×C61—21no—
132C22⋊Q8×C61—21no—
133C4×Q8×C61—21no—
134C4×Q8×C61—21no—
135#117×C61—21no—
136C2×C42×C61C2311yescharacteristic
137C4⋊C8×C61—21no—
138C4⋊C8×C61C2311yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140C4⋊C8×C61C2311yescharacteristic
141C4⋊C8×C61C2311yescharacteristic
142C22⋊C8×C61—21no—
143C4×C8×C61—21no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61#4111yescharacteristic
149C2×C22⋊D61—21no—
150C2×D244C2×D411yescharacteristic
151C2×C4×D61—21no—
152C2×Dic122—21no—
153C2×Dic122—21no—
154C2×Dic122C2×D411yescharacteristic
155C2×C8×C61—21no—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—81no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—41no—
165C4⋊C4×C61—41no—
166C22⋊C4×C61—41no—
167C42×C61—41no—
168C42×C61C2×D411yescharacteristic
169C42×C61C2×D411yescharacteristic
170C42×C61#4111yescharacteristic
171C42×C61C2411yescharacteristic
172C22⋊Dic61—21no—
173C22⋊Dic61—41no—
174#11758202—81no—
175#11758201—81no—
176#11758198—21no—
177#11758198—21no—
178#11758198—21no—
179#11758198—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61C2×D411yescharacteristic
185C4⋊Dic61C2×D411yescharacteristic
186#11758196—21no—
187#11758196—21no—
188#11758196—21no—
189#11758196—21no—
190#11758196—41no—
191#11758196—41no—
192C4×Dic61—21no—
193C4×Dic61—41no—
194#11758194—81no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418C2×D411yescharacteristic
198C2×#92418C2×D411yescharacteristic
199C2×#92418C2×D411yescharacteristic
200C2×#92418C2×D411yescharacteristic
201#11758189—81no—
202C8×D61—81no—
203C23×C61#12111yescharacteristic
204C22×D61—21no—
205Q8×C61—41no—
206Q8×C61—41no—
207Q8×C61—81no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—41no—
213C2×C4×C61—41no—
214C2×C4×C61—41no—
215C2×C4×C61#12111yescharacteristic
216C2×C4×C61#12111yescharacteristic
217C2×C4×C61#12111yescharacteristic
218C2×C4×C61C22×D411yescharacteristic
219C2×C4×C61C22×D411yescharacteristic
220C2×C4×C61C2×#4111yescharacteristic
221C22⋊D61—42no—
222C2×Dic61—21no—
223C2×Dic61—21no—
224C2×Dic61—21no—
225C2×Dic61—41no—
226C2×Dic61—41no—
227D244—21no—
228D244—21no—
229C4×D61—41no—
230C4×D61—41no—
231Dic122—21no—
232Dic122—21no—
233Dic122—41no—
234Dic122—41no—
235Dic122—81no—
236C8×C61—41no—
237C8×C61—41no—
238C8×C61—41no—
239C8×C61—41no—
240#92418—21no—
241#92418—21no—
242#92418—21no—
243#92418—21no—
244#92418—41no—
245#92418—41no—
246#19587—611nomaximal, Sylow
247C22×C61—21no—
248C22×C61—21no—
249C22×C61—21no—
250C22×C61C2×#12111yescharacteristic
251C2×D61—41no—
252C2×D61—41no—
253C2×D61—41no—
254C4×C61—21no—
255C4×C61—21no—
256C4×C61—21no—
257C4×C61—21no—
258C4×C61—81no—
259C4×C61—81no—
260C4×C61#57711yescharacteristic
261C4×C61#57711yescharacteristic
262C4×C61#57811yescharacteristic
263C4×C61#57811yescharacteristic
264Dic61—41no—
265Dic61—41no—
266Dic61—41no—
267Dic61—81no—
268Dic61—81no—
269#3252—611no—
270#3233—611no—
271#3231—611no—
272#2994—611no—
273#1703—611no—
274#1700—611no—
275#1696—611no—
276#1691—611no—
277#1684—611no—
278#1679—611no—
279#1675—611no—
280#1672—611no—
281#1574—611no—
282#1550—611no—
283#1542D6111yescharacteristic, complemented
284C2×C61—41no—
285C2×C61#304611yescharacteristic
286C2×C61#306311yescharacteristic
287C2×C61#306711yescharacteristic
288D61—81no—
289#533—611no—
290#533C2×D6111yescharacteristic
291#529—611no—
292#500—611no—
293#499—1221no—
294#498—611no—
295#488—1221no—
296#487—611no—
297#487—611no—
298#485—1221no—
299#485—1221no—
300#485—1221no—
301#482—1221no—
302#479—1221no—
303#479—1221no—
304#479—1221no—
305#477—611no—
306#477—611no—
307#476—611no—
308#476—611no—
309#475—611no—
310#474—611no—
311#470—1221no—
312#468—1221no—
313#464—1221no—
314#462—611no—
315#461—611no—
316#446—611no—
317C8×Q8—611no—
318#436—611no—
319#435—1221no—
320C8×D4—611no—
321C8×D4—1221no—
322#433—1221no—
323#431—611no—
324#431C2×D6111yescharacteristic
325#424—1221no—
326#423—611no—
327C2×C4⋊C8C2×D6111yescharacteristic
328#335—611no—
329#335—611no—
330#334—611no—
331#334—611no—
332#333—611no—
333#333—611no—
334#333C2×D6111yescharacteristic
335#333C2×D6111yescharacteristic
336#332—611no—
337#332—611no—
338#332C2×D6111yescharacteristic
339#332C2×D6111yescharacteristic
340C61#1958711yescharacteristic, complemented, Sylow
341C2×Q16—1221no—
342C2×SD16—1221no—
343C2×M16—1221no—
344C2×M16—1221no—
345C22×C8—21no—
346C22×C8—1221no—
347C4⋊Q8—611no—
348C4⋊Q8—611no—
349C4⋊Q8C22×D6111yescharacteristic
350C4⋊Q8C22×D6111yescharacteristic
351#126—1221no—
352#125—21no—
353#125—611no—
354#125—1221no—
355#124—611no—
356#123—1221no—
357C22⋊Q8—21no—
358C22⋊Q8—21no—
359C22⋊Q8—611no—
360C22⋊Q8—1221no—
361C22⋊Q8—1221no—
362#121—611no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—611no—
366C4×Q8—1221no—
367C4×Q8—1221no—
368C4×D4—611no—
369C4×D4—1221no—
370#117—21no—
371#117—1221no—
372#117—1221no—
373C2×C42C22×D6111yescharacteristic
374#107—1221no—
375#107—1221no—
376#107—1221no—
377#107—1221no—
378#107—1221no—
379#106—1221no—
380#106—1221no—
381#106—1221no—
382#106—1221no—
383#106—1221no—
384C4⋊C8—21no—
385C4⋊C8—611no—
386C4⋊C8—611no—
387C4⋊C8—611no—
388C4⋊C8—611no—
389C4⋊C8—1221no—
390C4⋊C8—1221no—
391C4⋊C8—1221no—
392C4⋊C8C22×D6111yescharacteristic
393C4⋊C8C22×D6111yescharacteristic
394C4⋊C8C22×D6111yescharacteristic
395C4⋊C8C22×D6111yescharacteristic
396#103—1221no—
397#103—1221no—
398#103—1221no—
399#103—1221no—
400#103—1221no—
401#103—1221no—
402#103—1221no—
403#103—1221no—
404#103—1221no—
405#102—1221no—
406#102—1221no—
407#102—1221no—
408C22⋊C8—21no—
409C22⋊C8—611no—
410C22⋊C8—611no—
411C22⋊C8—1221no—
412C22⋊C8—1221no—
413#97—1221no—
414C4×C8—21no—
415C4×C8—611no—
416C4×C8—611no—
417C4×C8—1221no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—611no—
421C2×Q8—1221no—
422C2×Q8—1221no—
423C2×D4—611no—
424C2×D4—1221no—
425C22×C4—1221no—
426C22×C4#1175822211yescharacteristic
427C22×C4D4×D6111yescharacteristic
428C22×C4D4×D6111yescharacteristic
429Q16—4881no—
430SD16—4881no—
431M16—4881no—
432M16—4881no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—81no—
438C2×C8—611no—
439C2×C8—611no—
440C2×C8—611no—
441C2×C8—611no—
442C2×C8—1221no—
443C2×C8—1221no—
444C2×C8—4881no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—41no—
450C4⋊C4—41no—
451C4⋊C4—611no—
452C4⋊C4—611no—
453C4⋊C4—1221no—
454C4⋊C4—1221no—
455C4⋊C4—1221no—
456C4⋊C4—1221no—
457C4⋊C4—1221no—
458C4⋊C4—1221no—
459C4⋊C4—1221no—
460C4⋊C4—1221no—
461C4⋊C4—2441no—
462C4⋊C4—2441no—
463C22⋊C4—41no—
464C22⋊C4—1221no—
465C22⋊C4—1221no—
466C22⋊C4—1221no—
467C22⋊C4—1221no—
468C22⋊C4—1221no—
469C22⋊C4—2441no—
470C42—41no—
471C42—1221no—
472C42—2441no—
473C42#1175822211yescharacteristic
474C42D4×D6111yescharacteristic
475C42D4×D6111yescharacteristic
476C42C23×D6111yescharacteristic
477C23—1221no—
478C23#1451975011yescharacteristic
479Q8—41no—
480Q8—41no—
481Q8—81no—
482Q8—1221no—
483Q8—1221no—
484Q8—4881no—
485Q8—2441no—
486Q8—2441no—
487D4—1221no—
488D4—1221no—
489D4—2442no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—1221no—
498C2×C4—1221no—
499C2×C4—1221no—
500C2×C4—2441no—
501C2×C4—2441no—
502C2×C4—2441no—
503C2×C4—2441no—
504C2×C4#1451975011yescharacteristic
505C2×C4#1451975011yescharacteristic
506C2×C4#1451975011yescharacteristic
507C2×C4C2×D4×D6111yescharacteristic
508C2×C4C2×D4×D6111yescharacteristic
509C2×C4C2×#1175822211yescharacteristic
510C8—41no—
511C8—41no—
512C8—41no—
513C8—41no—
514C8—1221no—
515C8—1221no—
516C8—1221no—
517C8—1221no—
518C8—2441no—
519C8—2441no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—2441no—
524C22—2441no—
525C22—2441no—
526C22C2×#1451975011yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—81no—
532C4—81no—
533C4—4881no—
534C4—4881no—
535C4—2441no—
536C4—2441no—
537C4—2441no—
538C4#1684056811yescharacteristic
539C4#1684056911yescharacteristic
540C4#1684057511yescharacteristic
541C4#1684057611yescharacteristic
542C2—41no—
543C2—4881no—
544C2#2145537411yescharacteristic
545C2#2145551311yescharacteristic
546C2#2145553811yescharacteristic
subgroupG/H
centerC22C2×#14519750
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1542C2
socleC22×C61C2×#121
prime radical#14519751D4
hypercenter#1542D61
hypocenterC61#19587
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1542

Complements

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

NH ≅ G/Ntype
3. #21456978C2semidirect
5. #21445397C2semidirect
6. #21445376C2semidirect
7. #21445346C2semidirect
8. #21445317C2semidirect
9. #21445280C2semidirect
10. #21445245C2semidirect
11. #21445217C2semidirect
12. #21445200C2semidirect
13. #21444607C2semidirect
14. #21444507C2semidirect
15. C61×#1542C2semidirect
283. #1542D61semidirect
340. C61#19587semidirect

Maximal subgroups

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

subgroupindex
#214571862
#214570002
#214569782
#214549752
#214453972
#214453762
#214453462
#214453172
#214452802
#214452452
#214452172
#214452002
#214446072
#214445072
C61×#15422
#1958761