Finite Group Databasebeta

← #29670276

Subgroups — #29670276

Order 15616.

564 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458725C211yesmaximal, characteristic
2#21458690C211yesmaximal, characteristic
3#21458213C211yesmaximal, characteristic
4#21445499C211yesmaximal, characteristic, complemented
5#21445323C211yesmaximal, characteristic, complemented
6#21445267C211yesmaximal, characteristic
7#21445223C211yesmaximal, characteristic, complemented
8#21445221C211yesmaximal, characteristic, complemented
9#21445031C211yesmaximal, characteristic
10#21444977C211yesmaximal, characteristic, complemented
11#21444959C211yesmaximal, characteristic, complemented
12#21444952C211yesmaximal, characteristic
13#21444670C211yesmaximal, characteristic, complemented
14#21444629C211yesmaximal, characteristic
15C61×#3363C211yesmaximal, characteristic, complemented
16#16840472C2211yescharacteristic
17#16840472C2211yescharacteristic
18#16840168—21no—
19#16840167C2211yescharacteristic
20#16840165C2211yescharacteristic
21#16840161—21no—
22#16840158C2211yescharacteristic
23#16840141C2211yescharacteristic
24#16840114C2211yescharacteristic
25#16840096—21no—
26#16840096—21no—
27#16840069—21no—
28#16840069—21no—
29#16840059—21no—
30#16840057C2211yescharacteristic
31#16840057C2211yescharacteristic
32#16840057C2211yescharacteristic
33#16840057C2211yescharacteristic
34#16840049C2211yescharacteristic
35#16840039—21no—
36#16840039C2211yescharacteristic
37#16840000—21no—
38#16839893C2211yescharacteristic
39Q8×#92418C2211yescharacteristic
40#16839860—21no—
41C4×#11758201—21no—
42C4×#11758201C2211yescharacteristic
43C8×D244C2211yescharacteristic
44#107×D61—21no—
45#16839515C2211yescharacteristic
46#16839514C2211yescharacteristic
47#16839511C2211yescharacteristic
48#16839510C2211yescharacteristic
49#16839510C2211yescharacteristic
50#16839508C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53Q8⋊#92418C2211yescharacteristic
54#16839489C2211yescharacteristic
55#16839484C2211yescharacteristic
56Q82×C61C2211yescharacteristic
57C61×#557C2211yescharacteristic
58C61×#487—21no—
59C61×#487C2211yescharacteristic
60C61×#477—21no—
61C61×#477C2211yescharacteristic
62C61×#462—21no—
63C61×#462C2211yescharacteristic
64C8×Q8×C61C2211yescharacteristic
65C4×Q16×C61—21no—
66C4×Q16×C61C2211yescharacteristic
67C2×#11758202—41no—
68C2×#11758201D411yescharacteristic
69C2×C8×D61—21no—
70#14519777C2311yescharacteristic
71#14519777C2311yescharacteristic
72#14519769—21no—
73#14519769—21no—
74#14519755—41no—
75#14519755—41no—
76#14519753—21no—
77#14519753—21no—
78C4×D244—21no—
79C4×D244—21no—
80C4×D244C2311yescharacteristic
81C4⋊C4×D61—21no—
82C4⋊C4×D61—21no—
83#14519711—21no—
84#14519711—21no—
85#14519710—21no—
86#14519710—21no—
87#14519710—21no—
88#14519710—21no—
89#14519710—21no—
90#14519710—21no—
91#14519710—21no—
92#14519708—21no—
93#14519708—21no—
94#14519708—21no—
95#14519708D411yescharacteristic
96C4⋊#92418—21no—
97C4⋊#92418—21no—
98C4⋊#92418C2311yescharacteristic
99C4⋊#92418C2311yescharacteristic
100C4⋊#92418C2311yescharacteristic
101#14519701—21no—
102#14519701—21no—
103#14519701—21no—
104#14519701—21no—
105#14519701D411yescharacteristic
106#14519700—41no—
107#14519697—21no—
108#14519697—21no—
109#14519697D411yescharacteristic
110#14519689—21no—
111#14519688—21no—
112C4×#92418—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C2×Q16×C61—21no—
116C2×Q16×C61D411yescharacteristic
117C4⋊Q8×C61—21no—
118C4⋊Q8×C61—21no—
119C4⋊Q8×C61—21no—
120C4⋊Q8×C61—41no—
121C4⋊Q8×C61C2311yescharacteristic
122C4⋊Q8×C61C2311yescharacteristic
123#125×C61—21no—
124#125×C61—41no—
125C4×Q8×C61—21no—
126C4×Q8×C61—21no—
127C4×Q8×C61—21no—
128C4×Q8×C61—21no—
129C4×Q8×C61C2311yescharacteristic
130C4×Q8×C61C2311yescharacteristic
131C4×Q8×C61C2311yescharacteristic
132#107×C61—21no—
133#107×C61D411yescharacteristic
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136#103×C61—21no—
137#103×C61—21no—
138#103×C61—21no—
139#103×C61—21no—
140#103×C61D411yescharacteristic
141#103×C61D411yescharacteristic
142C4×C8×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×D244C2×D411yescharacteristic
151C2×C4×D61—21no—
152C2×C4×D61—41no—
153C2×C4×D61—41no—
154C2×Dic122—21no—
155C2×Dic122—21no—
156Q16×C61—41no—
157Q16×C61—42no—
158C2×C8×C61—21no—
159C2×C8×C61C2×D411yescharacteristic
160C2×C8×C61C2×D411yescharacteristic
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×C61—41no—
169C4⋊C4×C61—41no—
170C4⋊C4×C61—41no—
171C4⋊C4×C61—41no—
172C4⋊C4×C61—41no—
173C4⋊C4×C61C2×D411yescharacteristic
174C4⋊C4×C61C2×D411yescharacteristic
175C4⋊C4×C61C2×D411yescharacteristic
176C42×C61—21no—
177C42×C61—21no—
178C42×C61—21no—
179C42×C61—41no—
180C42×C61—41no—
181C42×C61C2411yescharacteristic
182#11758202—82no—
183#11758201Q1614yescomplemented
184#11758198—21no—
185#11758198—41no—
186#11758198—41no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61C2×D411yescharacteristic
192#11758196—41no—
193#11758196—41no—
194#11758196—41no—
195#11758196—41no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418C2×D411yescharacteristic
201C2×#92418C2×D411yescharacteristic
202C8×D61—42no—
203C22×D61—21no—
204Q8×C61—21no—
205Q8×C61—21no—
206Q8×C61—21no—
207Q8×C61—21no—
208Q8×C61—21no—
209Q8×C61—41no—
210Q8×C61—41no—
211Q8×C61—81no—
212Q8×C61—161no—
213Q8×C61C2×Q1612yes—
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—41no—
221C2×C4×C61—41no—
222C2×C4×C61C22×D411yescharacteristic
223C2×C4×C61C22×D411yescharacteristic
224C2×C4×C61H(5,𝔽2)11yescharacteristic
225C2×Dic61—21no—
226C2×Dic61—41no—
227C2×Dic61—41no—
228D244—21no—
229D244C2×Q1612yes—
230C4×D61—41no—
231C4×D61—41no—
232C4×D61—161no—
233C4×D61—161no—
234Dic122—81no—
235Dic122—81no—
236C8×C61—21no—
237C8×C61—21no—
238C8×C61—41no—
239#92418—21no—
240#92418—41no—
241#92418—41no—
242#92418—41no—
243#92418—41no—
244#92418C2×Q1612yes—
245#19816—611nomaximal, Sylow
246C22×C61D4211yescharacteristic
247C2×D61—22no—
248C2×D61—41no—
249C2×D61—41no—
250C4×C61—22no—
251C4×C61—21no—
252C4×C61—41no—
253C4×C61—41no—
254C4×C61—41no—
255C4×C61—41no—
256C4×C61—41no—
257C4×C61—81no—
258C4×C61—81no—
259C4×C61C22×Q1611yescharacteristic
260C4×C61#57511yescharacteristic
261C4×C61#57811yescharacteristic
262C4×C61#57811yescharacteristic
263Dic61—41no—
264Dic61—81no—
265Dic61—81no—
266#3385—611no—
267#3381—611no—
268#3363D6111yescharacteristic, complemented
269#3338—611no—
270#1723—611no—
271#1692—611no—
272#1683—611no—
273#1676—611no—
274#1676—611no—
275#1644—611no—
276#1636—611no—
277#1633—611no—
278#1632—611no—
279#1584—611no—
280SD16⋊C8—611no—
281C2×C61#326911yescharacteristic
282C2×C61D4×Q1611yescharacteristic
283C2×C61#328811yescharacteristic
284D61—42no—
285Q82C2×D6111yescharacteristic
286#557C2×D6111yescharacteristic
287#554—611no—
288#554—611no—
289#501—1221no—
290#500—611no—
291#500—611no—
292#499—1221no—
293#498—611no—
294#494—611no—
295#487—21no—
296#487—611no—
297#487C2×D6111yescharacteristic
298#484—1221no—
299#484—1221no—
300#479—1221no—
301#479—1221no—
302#478—1221no—
303#477—21no—
304#477—611no—
305#477—611no—
306#477—611no—
307#477—611no—
308#477C2×D6111yescharacteristic
309#476—611no—
310#474—611no—
311#474—1221no—
312#467—1221no—
313#462—21no—
314#462C2×D6111yescharacteristic
315#446—611no—
316C8×Q8—611no—
317C8×Q8C2×D6111yescharacteristic
318#440—1221no—
319C4×Q16—21no—
320C4×Q16C2×D6111yescharacteristic
321C4×SD16—611no—
322C4×SD16—1221no—
323C8×D4—611no—
324C2×#107—1221no—
325#335—611no—
326#335—611no—
327#333—611no—
328#333—611no—
329#333—611no—
330#332—611no—
331Q8⋊C8—611no—
332Q8⋊C8—611no—
333Q8⋊C8—611no—
334D4⋊C8—611no—
335#322—611no—
336C61#1981611yescharacteristic, complemented, Sylow
337C2×Q16—21no—
338C2×Q16—2441no—
339C2×Q16C22⋊D6111yescharacteristic
340C2×SD16—611no—
341C22×C8—1221no—
342C4⋊Q8—21no—
343C4⋊Q8—21no—
344C4⋊Q8—21no—
345C4⋊Q8—41no—
346C4⋊Q8—611no—
347C4⋊Q8—611no—
348C4⋊Q8C22×D6111yescharacteristic
349C4⋊Q8C22×D6111yescharacteristic
350#125—21no—
351#125—41no—
352#125—1221no—
353#125—1221no—
354C22⋊Q8—1221no—
355C22⋊Q8—1221no—
356C22⋊Q8—2441no—
357C22⋊Q8—2441no—
358C4×Q8—21no—
359C4×Q8—21no—
360C4×Q8—21no—
361C4×Q8—21no—
362C4×Q8C22×D6111yescharacteristic
363C4×Q8C22×D6111yescharacteristic
364C4×Q8C22×D6111yescharacteristic
365C4×D4—611no—
366C4×D4—1221no—
367C4×D4—1221no—
368C2×C4⋊C4—1221no—
369C2×C4⋊C4—1221no—
370#107—21no—
371#107—1221no—
372#107—1221no—
373#107—1221no—
374#107—1221no—
375#107—1221no—
376#107—1221no—
377#107—1221no—
378#107—1221no—
379#107—1221no—
380#107C22⋊D6111yescharacteristic
381#106—611no—
382#106—1221no—
383#106—1221no—
384#106—1221no—
385C4⋊C8—21no—
386C4⋊C8—611no—
387C4⋊C8—611no—
388C4⋊C8—611no—
389C4⋊C8—1221no—
390C4⋊C8—1221no—
391C4⋊C8C22×D6111yescharacteristic
392#103—21no—
393#103—21no—
394#103—21no—
395#103—21no—
396#103—611no—
397#103—1221no—
398#103—1221no—
399#103—1221no—
400#103—1221no—
401#103—2441no—
402#103C22⋊D6111yescharacteristic
403#103C22⋊D6111yescharacteristic
404#102—611no—
405#102—1221no—
406#102—1221no—
407C22⋊C8—1221no—
408#97—1221no—
409C4×C8—21no—
410C4×C8—611no—
411C4×C8—611no—
412C4×C8—1221no—
413C4×C8C22×D6111yescharacteristic
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—41no—
417C2×Q8—1221no—
418C2×Q8—1221no—
419C2×Q8D4×D6111yescharacteristic
420C2×Q8C2×C22⋊D6111yescharacteristic
421C2×Q8C2×C22⋊D6111yescharacteristic
422C2×D4—611no—
423C22×C4—1221no—
424C22×C4—2441no—
425C22×C4—2441no—
426Q16—41no—
427Q16—42no—
428Q16—4882no—
429SD16—614no—
430C2×C8—21no—
431C2×C8—611no—
432C2×C8—611no—
433C2×C8—1221no—
434C2×C8—1221no—
435C2×C8—1221no—
436C2×C8—1221no—
437C2×C8—2442no—
438C2×C8C2×C22⋊D6111yescharacteristic
439C2×C8C2×C22⋊D6111yescharacteristic
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—41no—
448C4⋊C4—41no—
449C4⋊C4—41no—
450C4⋊C4—41no—
451C4⋊C4—41no—
452C4⋊C4—611no—
453C4⋊C4—1221no—
454C4⋊C4—1221no—
455C4⋊C4—1221no—
456C4⋊C4—1221no—
457C4⋊C4—2441no—
458C4⋊C4—2441no—
459C4⋊C4—2441no—
460C4⋊C4—2441no—
461C4⋊C4D4×D6111yescharacteristic
462C4⋊C4C2×C22⋊D6111yescharacteristic
463C4⋊C4C2×C22⋊D6111yescharacteristic
464C22⋊C4—1221no—
465C22⋊C4—2441no—
466C22⋊C4—2441no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—41no—
471C42—41no—
472C42C23×D6111yescharacteristic
473C23—1221no—
474Q8—21no—
475Q8—21no—
476Q8—21no—
477Q8—21no—
478Q8—21no—
479Q8—41no—
480Q8—41no—
481Q8—81no—
482Q8—161no—
483Q8—4881no—
484Q8—4881no—
485Q8Q16×D6112yes—
486D4—612no—
487D4—1221no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—1221no—
497C2×C4—9761no—
498C2×C4—9761no—
499C2×C4—2441no—
500C2×C4—2441no—
501C2×C4—2441no—
502C2×C4—2441no—
503C2×C4C2×D4×D6111yescharacteristic
504C2×C4C22×C22⋊D6111yescharacteristic
505C2×C4#1451982211yescharacteristic
506C8—21no—
507C8—21no—
508C8—41no—
509C8—612no—
510C8—1221no—
511C8—2441no—
512C8—2441no—
513C8—2441no—
514C8—2441no—
515C22—1222no—
516C22—2441no—
517C22—2441no—
518C22D4×C22⋊D6111yescharacteristic
519C4—22no—
520C4—21no—
521C4—41no—
522C4—41no—
523C4—41no—
524C4—41no—
525C4—41no—
526C4—81no—
527C4—81no—
528C4—4881no—
529C4—4881no—
530C4—2441no—
531C4C2×Q16×D6111yescharacteristic
532C4#1684056011yescharacteristic
533C4#1684057511yescharacteristic
534C4#1684057711yescharacteristic
535C2—2442no—
536C2#2145737511yescharacteristic
537C2Q16×C22⋊D6111yescharacteristic
538C2#2145758111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3363C2
socleC22×C61D42
prime radicalC2×D244C2×D4
hypercenter#3363D61
hypocenterC61#19816
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3363

Complements

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

NH ≅ G/Ntype
4. #21445499C2semidirect
5. #21445323C2semidirect
7. #21445223C2semidirect
8. #21445221C2semidirect
10. #21444977C2semidirect
11. #21444959C2semidirect
13. #21444670C2semidirect
15. C61×#3363C2semidirect
183. #11758201Q16semidirect
268. #3363D61semidirect
336. C61#19816semidirect

Maximal subgroups

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

subgroupindex
#214587252
#214586902
#214582132
#214454992
#214453232
#214452672
#214452232
#214452212
#214450312
#214449772
#214449592
#214449522
#214446702
#214446292
C61×#33632
#1981661