Finite Group Databasebeta

← #30612953

Subgroups — #30612953

Order 15616.

594 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462632C211yesmaximal, characteristic
2#21462607C211yesmaximal, characteristic, complemented
3#21461465C211yesmaximal, characteristic, complemented
4#21461464C211yesmaximal, characteristic, complemented
5#21461462C211yesmaximal, characteristic, complemented
6#21461460C211yesmaximal, characteristic, complemented
7#21461407C211yesmaximal, characteristic, complemented
8#21461406C211yesmaximal, characteristic, complemented
9#21461402C211yesmaximal, characteristic, complemented
10SD16×#92420C211yesmaximal, characteristic, complemented
11#21461383C211yesmaximal, characteristic, complemented
12#21461181C211yesmaximal, characteristic, complemented
13#21461174C211yesmaximal, characteristic
14M16×#92420C211yesmaximal, characteristic, complemented
15#21456418C211yesmaximal, characteristic
16#16840814—21no—
17#16840813C2211yescharacteristic
18#16840812C2211yescharacteristic
19#16840812C2211yescharacteristic
20#16840811—21no—
21#16840811C2211yescharacteristic
22#16840811C2211yescharacteristic
23Q8×#92420C2211yescharacteristic
24#16840797C2211yescharacteristic
25#16840793—21no—
26D4×#92420—21no—
27D4×#92420C2211yescharacteristic
28#16840786—21no—
29#16840783C2211yescharacteristic
30#16840778C2211yescharacteristic
31#16840768—21no—
32#16840765C2211yescharacteristic
33#16840726—21no—
34#16840726—21no—
35C2×C4×#92420C2211yescharacteristic
36#16840626C2211yescharacteristic
37#16840625C2211yescharacteristic
38#16840624C2211yescharacteristic
39#16840623C2211yescharacteristic
40#16840612C2211yescharacteristic
41#16840612C2211yescharacteristic
42#16840612C2211yescharacteristic
43#16840612C2211yescharacteristic
44Q8⋊#92420C2211yescharacteristic
45Q8⋊#92420C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48#16840603C2211yescharacteristic
49#16840603C2211yescharacteristic
50C8×#92420C2211yescharacteristic
51C8×#92420C2211yescharacteristic
52#16840314C2211yescharacteristic
53#16840293C2211yescharacteristic
54#16840170C411yescharacteristic
55#16840153C411yescharacteristic
56#16840129C411yescharacteristic
57#16840120C411yescharacteristic
58#16840020C411yescharacteristic
59#16840018C411yescharacteristic
60#16840006C411yescharacteristic
61#16839856C2211yescharacteristic
62#16839854C2211yescharacteristic
63#16839853C2211yescharacteristic
64SD16×Dic61C2211yescharacteristic
65M16×Dic61C2211yescharacteristic
66C61×#468C411yescharacteristic
67C2×#11758217—21no—
68C2×#11758217—21no—
69C22×#92420—21no—
70C22×#92420D411yescharacteristic
71C22×#92420D411yescharacteristic
72#14519844—21no—
73#14519844—21no—
74#14519844—21no—
75#14519844—21no—
76C4⋊#92420—21no—
77C4⋊#92420—21no—
78C4⋊#92420—21no—
79C4⋊#92420—21no—
80C4⋊#92420C2311yescharacteristic
81C4⋊#92420C2311yescharacteristic
82C4⋊#92420C2311yescharacteristic
83C4⋊#92420C2311yescharacteristic
84C22⋊#92420—21no—
85C22⋊#92420—21no—
86C22⋊#92420—21no—
87C22⋊#92420—21no—
88#14519832—21no—
89#14519832—21no—
90#14519832—21no—
91#14519832—21no—
92C4×#92420—21no—
93C4×#92420—21no—
94C4×#92420—21no—
95C4×#92420D411yescharacteristic
96C4×#92420D411yescharacteristic
97C4×#92420C2311yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C2×Dic244C2×C411yescharacteristic
102C2×#11758202C2×C411yescharacteristic
103C2×#11758200C2×C411yescharacteristic
104C2×#11758194C2×C411yescharacteristic
105#14519776C2×C411yescharacteristic
106#14519775C2×C411yescharacteristic
107#14519770—21no—
108#14519768C2×C411yescharacteristic
109#14519767—21no—
110#14519764C2×C411yescharacteristic
111#14519758—21no—
112#14519756C2×C411yescharacteristic
113#14519756C2×C411yescharacteristic
114#14519754—21no—
115Q8×Dic61C2311yescharacteristic
116#14519742—21no—
117#14519742C2311yescharacteristic
118#14519742C2311yescharacteristic
119D4×Dic61—21no—
120D4×Dic61C2311yescharacteristic
121#14519733—21no—
122#14519733—21no—
123C2×C4×Dic61C2311yescharacteristic
124#14519710C2×C411yescharacteristic
125#14519709C2×C411yescharacteristic
126#14519708C2×C411yescharacteristic
127#14519702C2×C411yescharacteristic
128#14519702C2×C411yescharacteristic
129#14519701C2×C411yescharacteristic
130#14519700C2×C411yescharacteristic
131#14519700C2×C411yescharacteristic
132#14519698C2×C411yescharacteristic
133#14519687C2×C411yescharacteristic
134#14519687C2×C411yescharacteristic
135C8×Dic61C2311yescharacteristic
136C8×Dic61C2311yescharacteristic
137C2×SD16×C61C2×C411yescharacteristic
138C2×M16×C61C2×C411yescharacteristic
139C22⋊Q8×C61C2×C411yescharacteristic
140#121×C61C2×C411yescharacteristic
141#107×C61C2×C411yescharacteristic
142#103×C61C2×C411yescharacteristic
143#102×C61C2×C411yescharacteristic
144C2×Q8×C61C22×C411yescharacteristic
145C2×D4×C61—21no—
146C2×D4×C61C22×C411yescharacteristic
147C22×C4×C61C22×C411yescharacteristic
148C22×Dic61—21no—
149C22×Dic61C2×D411yescharacteristic
150C22×Dic61#4111yescharacteristic
151C2×Dic122—21no—
152C2×Dic122C22×C411yescharacteristic
153C2×Dic122C22×C411yescharacteristic
154#11758217—42no—
155#11758217—42no—
156C2×#92420—22no—
157C2×#92420—21no—
158C2×#92420—21no—
159C2×#92420—21no—
160C2×#92420—21no—
161C2×#92420—21no—
162C2×#92420—21no—
163C2×#92420—41no—
164C2×#92420—42no—
165C2×#92420C2×D411yescharacteristic
166C2×#92420C2×D411yescharacteristic
167C2×#92420C2×D411yescharacteristic
168C2×#92420C2×D411yescharacteristic
169SD16×C61—22no—
170M16×C61—22no—
171C2×C8×C61C22×C411yescharacteristic
172C2×C8×C61C22×C411yescharacteristic
173C4⋊C4×C61—21no—
174C4⋊C4×C61C22×C411yescharacteristic
175C4⋊C4×C61C22×C411yescharacteristic
176C22⋊C4×C61—21no—
177C22⋊C4×C61—21no—
178C22⋊Dic61—21no—
179C22⋊Dic61—21no—
180C22⋊Dic61—21no—
181C22⋊Dic61—21no—
182C22⋊Dic61—21no—
183#11758202—22no—
184#11758200—22no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61C22×C411yescharacteristic
188C4⋊Dic61C22×C411yescharacteristic
189#11758196—21no—
190#11758196—21no—
191#11758196—21no—
192#11758196—21no—
193#11758196—21no—
194#11758196—21no—
195#11758196—21no—
196#11758196—21no—
197C4×Dic61—21no—
198C4×Dic61—21no—
199C4×Dic61—21no—
200C4×Dic61C22×C411yescharacteristic
201C4×Dic61C2×D411yescharacteristic
202C4×Dic61#4111yescharacteristic
203C4×Dic61C2411yescharacteristic
204#11758194—22no—
205C2×#92418C22×C411yescharacteristic
206C2×#92418C22×C411yescharacteristic
207Dic244—22no—
208C23×C61—21no—
209C23×C61C4×D411yescharacteristic
210Q8×C61—21no—
211Q8×C61—21no—
212D4×C61—21no—
213D4×C61—21no—
214D4×C61—42no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61C4×D411yescharacteristic
221C2×C4×C61C23×C411yescharacteristic
222C2×Dic61—21no—
223C2×Dic61—21no—
224C2×Dic61—21no—
225C2×Dic61—21no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—41no—
229C2×Dic61—41no—
230C2×Dic61—41no—
231C2×Dic61C4×D411yescharacteristic
232C2×Dic61C4×D411yescharacteristic
233C2×Dic61C22×D411yescharacteristic
234C2×Dic61C2×#4111yescharacteristic
235Dic122—21no—
236Dic122—21no—
237Dic122—21no—
238Dic122—21no—
239Dic122—42no—
240#92420—21no—
241#92420—21no—
242#92420—21no—
243#92420—41no—
244#92420—41no—
245#92420—41no—
246#92420—41no—
247#92420—41no—
248#92420—41no—
249#92420#13712yes—
250C8×C61—21no—
251C8×C61#13112yes—
252#92418—21no—
253#92418#13112yes—
254#17965—611nomaximal, Sylow
255C22×C61—21no—
256C22×C61—21no—
257C22×C61—21no—
258C22×C61—41no—
259C22×C61—41no—
260C22×C61—41no—
261C22×C61C2×C4×D411yescharacteristic
262C4×C61—21no—
263C4×C61—41no—
264C4×C61—41no—
265C4×C61—41no—
266C4×C61C2×#13111yescharacteristic
267C4×C61C2×#13111yescharacteristic
268Dic61—21no—
269Dic61—21no—
270Dic61—21no—
271Dic61—41no—
272Dic61—41no—
273Dic61—41no—
274Dic61—41no—
275Dic61C2×#13711yescharacteristic
276Dic61#57511yescharacteristic
277#3172—611no—
278#2966—611no—
279#2960—611no—
280#1593—611no—
281#1593—611no—
282#1592—611no—
283#1592—611no—
284C8×Q16—611no—
285C8×Q16—611no—
286C8×SD16—611no—
287C8×SD16—611no—
288#1569—611no—
289#1497—611no—
290#1495—611no—
291C8×M16—611no—
292C2×C61—41no—
293C2×C61—81no—
294C2×C61#293111yescharacteristic
295C2×C61C4×#13711yescharacteristic
296C2×C61#295511yescharacteristic
297#533—611no—
298#529—611no—
299#501—611no—
300#497—611no—
301#491—611no—
302#489—611no—
303#470—611no—
304#470—611no—
305#468—611no—
306#468#692311yescharacteristic
307#446—611no—
308#446—611no—
309#446—611no—
310#446—1221no—
311C8×Q8—611no—
312C8×Q8—611no—
313C8×Q8—611no—
314C8×Q8—1221no—
315C4×Q16—611no—
316C4×Q16—611no—
317C4×SD16—611no—
318C4×SD16—611no—
319#436—611no—
320#435—1221no—
321C8×D4—611no—
322C8×D4—1221no—
323#433—1221no—
324#432—611no—
325#431—611no—
326#424—1221no—
327#423—611no—
328#405—1221no—
329#405—1221no—
330C4×M16—611no—
331C2×C4×C8—611no—
332#335—611no—
333#335—611no—
334#334—611no—
335#334—611no—
336Q8⋊C8—611no—
337Q8⋊C8—611no—
338Q8⋊C8—611no—
339Q8⋊C8—611no—
340Q8⋊C8—611no—
341Q8⋊C8—611no—
342D4⋊C8—611no—
343D4⋊C8—611no—
344#322—611no—
345#322—611no—
346C82—611no—
347C82—611no—
348C61#1796511yescharacteristic, complemented, Sylow
349C2×Q16—611no—
350C2×Q16—611no—
351C2×SD16—611no—
352C2×SD16C2×#692311yescharacteristic
353C2×M16—611no—
354C2×M16—1221no—
355C2×M16—1221no—
356C2×M16C2×#692311yescharacteristic
357C22×C8—611no—
358C22×C8—611no—
359C22×C8—1221no—
360C4⋊Q8—611no—
361C4⋊Q8—611no—
362#126—1221no—
363#125—611no—
364#125—1221no—
365#124—611no—
366#123—1221no—
367C22⋊Q8—611no—
368C22⋊Q8—611no—
369C22⋊Q8—1221no—
370C22⋊Q8C2×#692311yescharacteristic
371#121C2×#692311yescharacteristic
372C4×Q8—611no—
373C4×Q8—611no—
374C4×Q8—611no—
375C4×Q8—1221no—
376C4×D4—611no—
377C4×D4—1221no—
378#117—1221no—
379#117—1221no—
380C2×C42—611no—
381#107—611no—
382#107C2×#692311yescharacteristic
383#106—611no—
384#106—611no—
385C4⋊C8—611no—
386C4⋊C8—611no—
387C4⋊C8—611no—
388C4⋊C8—611no—
389C4⋊C8—1221no—
390C4⋊C8—1221no—
391C4⋊C8—1221no—
392C4⋊C8—1221no—
393C4⋊C8—1221no—
394C4⋊C8—1221no—
395C4⋊C8—1221no—
396C4⋊C8—1221no—
397#103—611no—
398#103—611no—
399#103—611no—
400#103—611no—
401#103—611no—
402#103C2×#692311yescharacteristic
403#102—611no—
404#102C2×#692311yescharacteristic
405C22⋊C8—1221no—
406C22⋊C8—1221no—
407C22⋊C8—1221no—
408C22⋊C8—1221no—
409#97—611no—
410#97—611no—
411#97—1221no—
412#97—1221no—
413#97—1221no—
414#97—1221no—
415C4×C8—611no—
416C4×C8—611no—
417C4×C8—611no—
418C4×C8—611no—
419C4×C8—611no—
420C4×C8—611no—
421C4×C8—611no—
422C4×C8—611no—
423C4×C8—1221no—
424C4×C8—1221no—
425C4×C8—1221no—
426C2×Q8—611no—
427C2×Q8—611no—
428C2×Q8—1221no—
429C2×Q8C22×#692311yescharacteristic
430C2×D4—21no—
431C2×D4C22×#692311yescharacteristic
432C22×C4—611no—
433C22×C4—611no—
434C22×C4—1221no—
435C22×C4C22×#692311yescharacteristic
436Q16—1222no—
437Q16—1222no—
438SD16—22no—
439SD16—1222no—
440M16—22no—
441M16—1222no—
442M16—2442no—
443M16—2442no—
444C2×C8—611no—
445C2×C8—611no—
446C2×C8—611no—
447C2×C8—611no—
448C2×C8—611no—
449C2×C8—611no—
450C2×C8—1222no—
451C2×C8—1221no—
452C2×C8—1221no—
453C2×C8—1221no—
454C2×C8—1221no—
455C2×C8—1221no—
456C2×C8—1221no—
457C2×C8—2442no—
458C2×C8—2441no—
459C2×C8C22×#692311yescharacteristic
460C2×C8C22×#692311yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—611no—
463C4⋊C4—611no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4C22×#692311yescharacteristic
475C4⋊C4C22×#692311yescharacteristic
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—1221no—
479C22⋊C4—1221no—
480C22⋊C4—1221no—
481C22⋊C4—1221no—
482C22⋊C4—1221no—
483C42—611no—
484C42—611no—
485C42—611no—
486C42—611no—
487C42—1221no—
488C42—1221no—
489C42—1221no—
490C23—21no—
491C23D4×#692311yescharacteristic
492Q8—21no—
493Q8—21no—
494Q8—1221no—
495Q8—1221no—
496Q8—1221no—
497Q8—1221no—
498Q8—2442no—
499D4—21no—
500D4—21no—
501D4—42no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—611no—
508C2×C4—611no—
509C2×C4—611no—
510C2×C4—611no—
511C2×C4—1221no—
512C2×C4—1221no—
513C2×C4—1221no—
514C2×C4—1221no—
515C2×C4—1221no—
516C2×C4—1221no—
517C2×C4—2441no—
518C2×C4—2441no—
519C2×C4—2441no—
520C2×C4D4×#692311yescharacteristic
521C2×C4C23×#692311yescharacteristic
522C8—21no—
523C8—612no—
524C8—612no—
525C8—1221no—
526C8—1221no—
527C8—1221no—
528C8—1221no—
529C8—2441no—
530C8—2441no—
531C8—2441no—
532C8—2441no—
533C8—2441no—
534C8—2441no—
535C8#1451986412yes—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22C2×D4×#692311yescharacteristic
543C4—21no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—611no—
548C4—611no—
549C4—1221no—
550C4—1221no—
551C4—1221no—
552C4—2441no—
553C4—2441no—
554C4—2441no—
555C4—2441no—
556C4C2×#1451986411yescharacteristic
557C4D61⋊#13111yescharacteristic
558C2—41no—
559C2—81no—
560C2#2146254211yescharacteristic
561C2#137×#692311yescharacteristic
562C2#2146259111yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#468C4
socleC22×C61C2×C4×D4
prime radical#121×C61C2×C4
cosocleC4×Dic61C24
hypercenter#468#6923
hypocenterC61#17965
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
2. #21462607C2semidirect
3. #21461465C2semidirect
4. #21461464C2semidirect
5. #21461462C2semidirect
6. #21461460C2semidirect
7. #21461407C2semidirect
8. #21461406C2semidirect
9. #21461402C2semidirect
10. SD16×#92420C2semidirect
11. #21461383C2semidirect
12. #21461181C2semidirect
14. M16×#92420C2semidirect
348. C61#17965semidirect

Maximal subgroups

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

subgroupindex
#214626322
#214626072
#214614652
#214614642
#214614622
#214614602
#214614072
#214614062
#214614022
SD16×#924202
#214613832
#214611812
#214611742
M16×#924202
#214564182
#1796561