Finite Group Databasebeta

← #29670269

Subgroups — #29670269

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#21458692C211yesmaximal, characteristic
2#21458497C211yesmaximal, characteristic, complemented
3#21458207C211yesmaximal, characteristic
4#21445497C211yesmaximal, characteristic, complemented
5#21445325C211yesmaximal, characteristic, complemented
6#21445272C211yesmaximal, characteristic
7#21445221C211yesmaximal, characteristic, complemented
8#21445220C211yesmaximal, characteristic, complemented
9#21445033C211yesmaximal, characteristic
10#21444976C211yesmaximal, characteristic, complemented
11#21444959C211yesmaximal, characteristic, complemented
12#21444951C211yesmaximal, characteristic
13#21444667C211yesmaximal, characteristic, complemented
14SD16⋊#92418C211yesmaximal, characteristic
15C61×#3385C211yesmaximal, characteristic
16#16840491C2211yescharacteristic
17#16840469C2211yescharacteristic
18#16840165C2211yescharacteristic
19#16840162—21no—
20#16840160C2211yescharacteristic
21#16840141C2211yescharacteristic
22#16840114—21no—
23#16840114C2211yescharacteristic
24#16840112C2211yescharacteristic
25#16840097—21no—
26#16840095—21no—
27#16840067—21no—
28#16840064—21no—
29#16840057C2211yescharacteristic
30#16840057C2211yescharacteristic
31#16840054—21no—
32#16840054C2211yescharacteristic
33#16840054C2211yescharacteristic
34#16840042C2211yescharacteristic
35#16840001—21no—
36#16839972—21no—
37#16839972C2211yescharacteristic
38Q8×#92418C2211yescharacteristic
39C8×Dic122C2211yescharacteristic
40C4×#11758202—21no—
41C4×#11758202C2211yescharacteristic
42SD16×Dic61—21no—
43D4×#92418C2211yescharacteristic
44C2×#14519710—21no—
45#16839515C2211yescharacteristic
46#16839514C2211yescharacteristic
47#16839511C2211yescharacteristic
48#16839511C2211yescharacteristic
49#16839510C2211yescharacteristic
50#16839507C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53#16839492C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55#16839483C2211yescharacteristic
56Q82×C61C2211yescharacteristic
57C61×#554C2211yescharacteristic
58C61×#501—21no—
59C61×#500C2211yescharacteristic
60C61×#479—21no—
61C61×#477C2211yescharacteristic
62C61×#476C2211yescharacteristic
63C61×#474—21no—
64C61×#446C2211yescharacteristic
65C61×#440—21no—
66C4×SD16×C61C2211yescharacteristic
67C2×#11758202—21no—
68C2×#11758202—41no—
69C2×#11758202D411yescharacteristic
70C22×#92418—21no—
71#14519777—21no—
72#14519777C2311yescharacteristic
73#14519777C2311yescharacteristic
74#14519768—21no—
75#14519768—21no—
76#14519768—41no—
77#14519756—21no—
78#14519754—41no—
79Q8×Dic61—21no—
80C4×Dic122—21no—
81C4×Dic122C2311yescharacteristic
82D4×Dic61—21no—
83C2×C4⋊Dic61—21no—
84#14519710—21no—
85#14519710—21no—
86#14519710—21no—
87#14519710—21no—
88#14519710—21no—
89#14519710—21no—
90#14519710—21no—
91#14519710D411yescharacteristic
92#14519709—21no—
93#14519709—21no—
94C4⋊#92418—21no—
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98#14519706—21no—
99#14519701—21no—
100#14519701—21no—
101#14519701—41no—
102#14519701D411yescharacteristic
103#14519700—21no—
104#14519700—21no—
105#14519700—21no—
106#14519700—21no—
107#14519700—21no—
108#14519700D411yescharacteristic
109#14519698—21no—
110C22⋊#92418—21no—
111C4×#92418—21no—
112C4×#92418C2311yescharacteristic
113C4×#92418C2311yescharacteristic
114C8×Dic61—21no—
115C2×SD16×C61D411yescharacteristic
116C4⋊Q8×C61—21no—
117C4⋊Q8×C61—21no—
118C4⋊Q8×C61—41no—
119C4⋊Q8×C61C2311yescharacteristic
120C4⋊Q8×C61C2311yescharacteristic
121#125×C61—21no—
122C22⋊Q8×C61—21no—
123C22⋊Q8×C61—41no—
124C4×Q8×C61—21no—
125C4×Q8×C61—21no—
126C4×Q8×C61C2311yescharacteristic
127C4×Q8×C61C2311yescharacteristic
128C4×D4×C61—21no—
129C4×D4×C61C2311yescharacteristic
130C2×C4⋊C4×C61—21no—
131#107×C61—21no—
132#107×C61—21no—
133#107×C61—21no—
134#106×C61—21no—
135#106×C61D411yescharacteristic
136C4⋊C8×C61—21no—
137C4⋊C8×C61C2311yescharacteristic
138#103×C61—21no—
139#103×C61D411yescharacteristic
140#102×C61—21no—
141#102×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×D4×C61C2×D411yescharacteristic
150C22×C4×C61—21no—
151C22×C4×C61—41no—
152C22×Dic61—41no—
153C2×Dic122—21no—
154C2×Dic122—21no—
155C2×Dic122C2×D411yescharacteristic
156SD16×C61Q1614yescomplemented
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—41no—
167C4⋊C4×C61—41no—
168C4⋊C4×C61—41no—
169C4⋊C4×C61—41no—
170C4⋊C4×C61C2×D411yescharacteristic
171C4⋊C4×C61C2×D411yescharacteristic
172C4⋊C4×C61C2×D411yescharacteristic
173C22⋊C4×C61—21no—
174C22⋊C4×C61—41no—
175C42×C61—21no—
176C42×C61—21no—
177C42×C61—41no—
178C42×C61C2411yescharacteristic
179C22⋊Dic61—41no—
180#11758202—41no—
181#11758202—42no—
182#11758202—82no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—41no—
188C4⋊Dic61—41no—
189C4⋊Dic61—41no—
190C4⋊Dic61C2×D411yescharacteristic
191#11758196—21no—
192#11758196—41no—
193#11758196—41no—
194C4×Dic61—21no—
195C4×Dic61—41no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—42no—
201C2×#92418C2×D411yescharacteristic
202C2×#92418C2×D411yescharacteristic
203C23×C61—21no—
204Q8×C61—21no—
205Q8×C61—21no—
206Q8×C61—21no—
207Q8×C61—81no—
208Q8×C61—81no—
209Q8×C61—161no—
210Q8×C61C2×Q1612yes—
211D4×C61—21no—
212D4×C61C2×Q1612yes—
213C2×C4×C61—21no—
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—161no—
223C2×C4×C61C22×D411yescharacteristic
224C2×C4×C61C22×D411yescharacteristic
225C2×C4×C61H(5,𝔽2)11yescharacteristic
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—41no—
229C2×Dic61—41no—
230C2×Dic61—161no—
231Dic122—21no—
232Dic122—21no—
233Dic122—41no—
234Dic122—41no—
235Dic122—81no—
236C8×C61—21no—
237C8×C61—41no—
238C8×C61C2×Q1612yes—
239#92418—21no—
240#92418—21no—
241#92418—41no—
242#92418—41no—
243#92418—41no—
244#92418—41no—
245#19816—611nomaximal, Sylow
246C22×C61—22no—
247C22×C61—41no—
248C22×C61—41no—
249C22×C61D4211yescharacteristic
250C4×C61—22no—
251C4×C61—21no—
252C4×C61—41no—
253C4×C61—41no—
254C4×C61—41no—
255C4×C61—41no—
256C4×C61—81no—
257C4×C61—81no—
258C4×C61C22×Q1611yescharacteristic
259C4×C61#57511yescharacteristic
260C4×C61#57811yescharacteristic
261C4×C61#57811yescharacteristic
262Dic61—41no—
263Dic61—41no—
264Dic61—81no—
265Dic61—81no—
266#3385D6111yescharacteristic
267#3381—611no—
268#3363—611no—
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—42no—
282C2×C61#326911yescharacteristic
283C2×C61D4×Q1611yescharacteristic
284C2×C61#328811yescharacteristic
285Q82C2×D6111yescharacteristic
286#557—611no—
287#554—611no—
288#554C2×D6111yescharacteristic
289#501—21no—
290#500—611no—
291#500C2×D6111yescharacteristic
292#499—1221no—
293#498—611no—
294#494—611no—
295#487—611no—
296#487—611no—
297#487—1221no—
298#484—1221no—
299#484—1221no—
300#479—21no—
301#479—1221no—
302#478—1221no—
303#477—611no—
304#477—611no—
305#477—611no—
306#477—611no—
307#477—1221no—
308#477C2×D6111yescharacteristic
309#476C2×D6111yescharacteristic
310#474—21no—
311#474—611no—
312#467—1221no—
313#462—611no—
314#462—1221no—
315#446C2×D6111yescharacteristic
316C8×Q8—611no—
317C8×Q8—611no—
318#440—21no—
319C4×Q16—611no—
320C4×Q16—1221no—
321C4×SD16—1221no—
322C4×SD16C2×D6111yescharacteristic
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—611no—
338C2×Q16—1221no—
339C2×Q16—2441no—
340C2×SD16C22⋊D6111yescharacteristic
341C22×C8—1221no—
342C4⋊Q8—21no—
343C4⋊Q8—21no—
344C4⋊Q8—41no—
345C4⋊Q8—611no—
346C4⋊Q8—611no—
347C4⋊Q8—1221no—
348C4⋊Q8C22×D6111yescharacteristic
349C4⋊Q8C22×D6111yescharacteristic
350#125—21no—
351#125—1221no—
352#125—1221no—
353#125—2441no—
354C22⋊Q8—21no—
355C22⋊Q8—41no—
356C22⋊Q8—1221no—
357C22⋊Q8—2441no—
358C4×Q8—21no—
359C4×Q8—21no—
360C4×Q8—611no—
361C4×Q8—1221no—
362C4×Q8—1221no—
363C4×Q8C22×D6111yescharacteristic
364C4×Q8C22×D6111yescharacteristic
365C4×D4—21no—
366C4×D4—1221no—
367C4×D4C22×D6111yescharacteristic
368C2×C4⋊C4—21no—
369C2×C4⋊C4—1221no—
370#107—21no—
371#107—21no—
372#107—21no—
373#107—611no—
374#107—1221no—
375#107—1221no—
376#107—1221no—
377#107—1221no—
378#107—1221no—
379#107—1221no—
380#107—1221no—
381#106—21no—
382#106—1221no—
383#106—1221no—
384#106C22⋊D6111yescharacteristic
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—611no—
394#103—611no—
395#103—1221no—
396#103—1221no—
397#103—1221no—
398#103—1221no—
399#103—1221no—
400#103—1221no—
401#103—1221no—
402#103—2441no—
403#103C22⋊D6111yescharacteristic
404#102—21no—
405#102—1221no—
406#102C22⋊D6111yescharacteristic
407C22⋊C8—1221no—
408#97—21no—
409C4×C8—611no—
410C4×C8—611no—
411C4×C8—1221no—
412C4×C8—1221no—
413C4×C8C22×D6111yescharacteristic
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—41no—
417C2×Q8—611no—
418C2×Q8—1221no—
419C2×Q8—1221no—
420C2×Q8D4×D6111yescharacteristic
421C2×Q8C2×C22⋊D6111yescharacteristic
422C2×D4C2×C22⋊D6111yescharacteristic
423C22×C4—21no—
424C22×C4—41no—
425C22×C4—2441no—
426Q16—4882no—
427Q16—2441no—
428Q16—2442no—
429SD16#1175820214yescomplemented
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—41no—
447C4⋊C4—41no—
448C4⋊C4—41no—
449C4⋊C4—41no—
450C4⋊C4—611no—
451C4⋊C4—1221no—
452C4⋊C4—1221no—
453C4⋊C4—1221no—
454C4⋊C4—1221no—
455C4⋊C4—1221no—
456C4⋊C4—2441no—
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—21no—
465C22⋊C4—41no—
466C22⋊C4—2441no—
467C42—21no—
468C42—21no—
469C42—41no—
470C42—1221no—
471C42—2441no—
472C42C23×D6111yescharacteristic
473C23—21no—
474Q8—21no—
475Q8—21no—
476Q8—21no—
477Q8—81no—
478Q8—81no—
479Q8—161no—
480Q8—1221no—
481Q8—1221no—
482Q8—4881no—
483Q8—2441no—
484Q8—2441no—
485Q8C2×#1175820212yes—
486D4—21no—
487D4C2×#1175820212yes—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—161no—
498C2×C4—1221no—
499C2×C4—1221no—
500C2×C4—9761no—
501C2×C4—2441no—
502C2×C4—2441no—
503C2×C4C2×D4×D6111yescharacteristic
504C2×C4C22×C22⋊D6111yescharacteristic
505C2×C4#1451982211yescharacteristic
506C8—21no—
507C8—41no—
508C8—1221no—
509C8—1221no—
510C8—2441no—
511C8—2441no—
512C8—2441no—
513C8—2441no—
514C8C2×#1175820212yes—
515C22—22no—
516C22—41no—
517C22—41no—
518C22D4×C22⋊D6111yescharacteristic
519C4—22no—
520C4—21no—
521C4—41no—
522C4—41no—
523C4—41no—
524C4—41no—
525C4—81no—
526C4—81no—
527C4—4881no—
528C4—4881no—
529C4—2441no—
530C4—2441no—
531C4C22×#1175820211yescharacteristic
532C4#1684056111yescharacteristic
533C4#1684057711yescharacteristic
534C4#1684057811yescharacteristic
535C2—42no—
536C2#2145736811yescharacteristic
537C2D4×#1175820211yescharacteristic
538C2#2145758311yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3385C2
socleC22×C61D42
prime radicalC2×D4×C61C2×D4
hypercenter#3385D61
hypocenterC61#19816
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3385

Complements

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

NH ≅ G/Ntype
2. #21458497C2semidirect
4. #21445497C2semidirect
5. #21445325C2semidirect
7. #21445221C2semidirect
8. #21445220C2semidirect
10. #21444976C2semidirect
11. #21444959C2semidirect
13. #21444667C2semidirect
156. SD16×C61Q16semidirect
336. C61#19816semidirect
429. SD16#11758202semidirect

Maximal subgroups

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

subgroupindex
#214586922
#214584972
#214582072
#214454972
#214453252
#214452722
#214452212
#214452202
#214450332
#214449762
#214449592
#214449512
#214446672
SD16⋊#924182
C61×#33852
#1981661