Finite Group Databasebeta

← #30619283

Subgroups — #30619283

Order 15616.

594 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462612C211yesmaximal, characteristic
2#21462611C211yesmaximal, characteristic
3#21462005C211yesmaximal, characteristic
4#21462004C211yesmaximal, characteristic
5#21461887C211yesmaximal, characteristic
6#21461887C211yesmaximal, characteristic
7#21461886C211yesmaximal, characteristic
8#21461886C211yesmaximal, characteristic
9#21461885C211yesmaximal, characteristic
10#21461885C211yesmaximal, characteristic
11#21461884C211yesmaximal, characteristic
12#21461884C211yesmaximal, characteristic
13#21461745C211yesmaximal, characteristic
14#21461535C211yesmaximal, characteristic
15#21456340C211yesmaximal, characteristic
16#16840814—21no—
17#16840814—21no—
18#16840814—21no—
19#16840814—21no—
20#16840813—21no—
21#16840813—21no—
22#16840812—21no—
23#16840812—21no—
24#16840769C2211yescharacteristic
25#16840769C2211yescharacteristic
26#16840769C2211yescharacteristic
27#16840769C2211yescharacteristic
28#16840767C2211yescharacteristic
29#16840766C2211yescharacteristic
30#16840727C2211yescharacteristic
31#16840727C2211yescharacteristic
32#16840727C2211yescharacteristic
33#16840727C2211yescharacteristic
34#16840721C2211yescharacteristic
35C42×#6923C2211yescharacteristic
36#16840638C2211yescharacteristic
37#16840638C2211yescharacteristic
38#16840638C2211yescharacteristic
39#16840638C2211yescharacteristic
40#16840632C2211yescharacteristic
41#16840632C2211yescharacteristic
42#16840632C2211yescharacteristic
43#16840632C2211yescharacteristic
44#16840632C2211yescharacteristic
45#16840632C2211yescharacteristic
46#16840632C2211yescharacteristic
47#16840632C2211yescharacteristic
48(C2×#6923)⋊C8C2211yescharacteristic
49(C2×#6923)⋊C8C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52#16840318C2211yescharacteristic
53#16840317C2211yescharacteristic
54#16840172C411yescharacteristic, complemented
55#16840171C411yescharacteristic, complemented
56#16840170C411yescharacteristic, complemented
57#16840170C411yescharacteristic, complemented
58#16840169C411yescharacteristic, complemented
59#16840169C411yescharacteristic, complemented
60#16840168C411yescharacteristic, complemented
61#16839799C2211yescharacteristic
62#16839799C2211yescharacteristic
63#16839797C2211yescharacteristic
64#16839797C2211yescharacteristic
65#97×D61C2211yescharacteristic
66C61×#501C411yescharacteristic, complemented
67C2×#11758213C2311yescharacteristic
68C2×#11758213C2311yescharacteristic
69C2×#11758213C2311yescharacteristic
70C2×#11758213C2311yescharacteristic
71C2×D61⋊C8C2311yescharacteristic
72C2×D61⋊C8C2311yescharacteristic
73C2×C4×#6923—21no—
74C2×C4×#6923—21no—
75C2×C4×#6923C2311yescharacteristic
76C2×C4×#6923C2311yescharacteristic
77#14519844—21no—
78#14519844—21no—
79#14519844—21no—
80#14519844—21no—
81#14519844—21no—
82#14519844—21no—
83C4⋊#92420—21no—
84C4⋊#92420—21no—
85C4⋊#92420—21no—
86C4⋊#92420—21no—
87C4⋊#92420—21no—
88C4⋊#92420—21no—
89#14519832—21no—
90#14519832—21no—
91#14519832—21no—
92#14519832—21no—
93#14519832D411yescharacteristic
94#14519832D411yescharacteristic
95#14519832D411yescharacteristic
96#14519832D411yescharacteristic
97C4×#92420—21no—
98C4×#92420—21no—
99C4×#92420—21no—
100C4×#92420—21no—
101C2×C8×D61C2311yescharacteristic
102C2×C8×D61C2311yescharacteristic
103#14519777C2×C411yescharacteristic
104#14519776C2×C411yescharacteristic
105#14519776C2×C411yescharacteristic
106#14519769C2×C411yescharacteristic
107#14519768C2×C411yescharacteristic
108#14519768C2×C411yescharacteristic
109#14519757—21no—
110#14519755—21no—
111#14519755—21no—
112#14519753—21no—
113Q8×Dic61—21no—
114#14519742—21no—
115#14519742—21no—
116#14519742—21no—
117#14519735C2311yescharacteristic
118#14519735C2311yescharacteristic
119#14519735C2311yescharacteristic
120#14519735C2311yescharacteristic
121C42×D61C2311yescharacteristic
122#14519711C2×C411yescharacteristic
123#14519711C2×C411yescharacteristic
124#14519710C2×C411yescharacteristic
125#14519710C2×C411yescharacteristic
126#14519710C2×C411yescharacteristic
127#14519710C2×C411yescharacteristic
128#14519709C2×C411yescharacteristic
129#14519709C2×C411yescharacteristic
130#14519708C2×C411yescharacteristic
131#14519708C2×C411yescharacteristic
132#14519708C2×C411yescharacteristic
133#14519708C2×C411yescharacteristic
134#14519688C2×C411yescharacteristic
135#14519687C2×C411yescharacteristic
136#14519687C2×C411yescharacteristic
137C4⋊Q8×C61C2×C411yescharacteristic
138#125×C61C2×C411yescharacteristic
139#107×C61C2×C411yescharacteristic
140#107×C61C2×C411yescharacteristic
141#106×C61C2×C411yescharacteristic
142#106×C61C2×C411yescharacteristic
143#97×C61C2×C411yescharacteristic
144C22×#6923—21no—
145C22×#6923—21no—
146C2×Q8×C61—21no—
147C2×C4×D61#4111yescharacteristic
148C2×C4×D61#4111yescharacteristic
149C2×C4×D61C2411yescharacteristic
150C2×Dic122—21no—
151C2×Dic122—21no—
152C2×Dic122—21no—
153C2×#92420—21no—
154C2×#92420—21no—
155C2×#92420—21no—
156C2×#92420—21no—
157C2×#92420C2×D411yescharacteristic
158C2×#92420C2×D411yescharacteristic
159C2×#92420C2×D411yescharacteristic
160C2×#92420C2×D411yescharacteristic
161C4×#6923—21no—
162C4×#6923—21no—
163C4×#6923—21no—
164C4×#6923—21no—
165C4×#6923—42no—
166C4×#6923—42no—
167#11758213—21no—
168#11758213—21no—
169#11758213—21no—
170#11758213—21no—
171#11758213—21no—
172#11758213—21no—
173#11758213—21no—
174#11758213—21no—
175D61⋊C8—21no—
176D61⋊C8—21no—
177D61⋊C8—21no—
178D61⋊C8—21no—
179C2×C8×C61C22×C411yescharacteristic
180C2×C8×C61C22×C411yescharacteristic
181C4⋊C4×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61C22×C411yescharacteristic
185C4⋊C4×C61C22×C411yescharacteristic
186C4⋊C4×C61C22×C411yescharacteristic
187C4⋊C4×C61C22×C411yescharacteristic
188C42×C61C22×C411yescharacteristic
189#11758198—21no—
190#11758198—21no—
191#11758198—21no—
192#11758198—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61C22×C411yescharacteristic
197C4⋊Dic61C22×C411yescharacteristic
198C4⋊Dic61C22×C411yescharacteristic
199C4⋊Dic61C22×C411yescharacteristic
200#11758196—21no—
201#11758196—21no—
202#11758196—21no—
203#11758196—21no—
204#11758196—21no—
205#11758196—21no—
206C4×Dic61—21no—
207C4×Dic61—21no—
208C4×Dic61—21no—
209C4×Dic61—21no—
210C4×Dic61C22×C411yescharacteristic
211C4×Dic61C2×D411yescharacteristic
212C4×Dic61C2×D411yescharacteristic
213C2×#92418C22×C411yescharacteristic
214C2×#92418C22×C411yescharacteristic
215C8×D61—21no—
216C8×D61—21no—
217C8×D61—21no—
218C8×D61—21no—
219C22×D61C2×#4111yescharacteristic
220C2×#6923—22no—
221C2×#6923—22no—
222C2×#6923—41no—
223C2×#6923—41no—
224C2×#6923—41no—
225C2×#6923—41no—
226Q8×C61—81no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61C4×D411yescharacteristic
232C2×C4×C61C4×D411yescharacteristic
233C2×C4×C61C23×C411yescharacteristic
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61C4×D411yescharacteristic
239C2×Dic61C4×D411yescharacteristic
240C2×Dic61C22×D411yescharacteristic
241C4×D61—41no—
242C4×D61—41no—
243C4×D612−1+411yescharacteristic
244C4×D612−1+411yescharacteristic
245C4×D612−1+411yescharacteristic
246C4×D612−1+411yescharacteristic
247Dic122—81no—
248Dic122—81no—
249Dic122—81no—
250#92420—21no—
251#92420—21no—
252#92420—21no—
253#92420—21no—
254#92420—41no—
255#92420—41no—
256#92420—41no—
257#92420—41no—
258C8×C61—21no—
259C8×C61—21no—
260#92418—21no—
261#92418—21no—
262#22259—611nomaximal, Sylow
263C22×C61C2×C4×D411yescharacteristic
264C2×D61—21no—
265C2×D61—21no—
266C2×D61#54111yescharacteristic
267C2×D61#54111yescharacteristic
268#6923—42no—
269#6923—42no—
270C4×C61—21no—
271C4×C61—21no—
272C4×C61—41no—
273C4×C61—41no—
274C4×C61—41no—
275C4×C61—41no—
276C4×C61#51911yescharacteristic
277C4×C61#51911yescharacteristic
278Dic61—21no—
279Dic61—21no—
280Dic61—41no—
281Dic61—41no—
282Dic61—41no—
283Dic61—41no—
284Dic61#53611yescharacteristic
285Dic61#53611yescharacteristic
286#3162—611no—
287#2961—611no—
288#2961—611no—
289#1994—611no—
290#1994—611no—
291#1922—611no—
292#1922—611no—
293#1922—611no—
294#1922—611no—
295#1922—611no—
296#1922—611no—
297#1922—611no—
298#1922—611no—
299#1838—611no—
300#1745—611no—
301C2×C61#232711yescharacteristic
302C2×C61#295611yescharacteristic
303C2×C61#295611yescharacteristic
304D61—21no—
305D61—21no—
306#533—611no—
307#533—611no—
308#501—611no—
309#501—611no—
310#501—611no—
311#501—611no—
312#501—611no—
313#501—611no—
314#501—611no—
315#501#692311yescharacteristic, complemented
316#446—1221no—
317#446—1221no—
318#446—1221no—
319#446—1221no—
320#446—1221no—
321#446—1221no—
322#446—1221no—
323#446—1221no—
324#427—611no—
325#427—611no—
326#427—611no—
327#427—611no—
328#424—611no—
329#424—611no—
330#424—611no—
331#424—611no—
332#423—611no—
333#423—611no—
334#405—611no—
335#405—611no—
336#405—611no—
337#405—611no—
338C2×#97—611no—
339C2×#97—611no—
340C43—611no—
341#341—611no—
342#341—611no—
343#341—611no—
344#341—611no—
345#339—611no—
346#339—611no—
347#339—611no—
348#339—611no—
349#339—611no—
350#339—611no—
351#339—611no—
352#339—611no—
353#336—611no—
354#336—611no—
355#336—611no—
356#336—611no—
357C61#2225911yescharacteristic, complemented, Sylow
358C2×M16—611no—
359C2×M16—611no—
360C2×M16—611no—
361C2×M16—611no—
362C22×C8—611no—
363C22×C8—611no—
364C22×C8—611no—
365C22×C8—611no—
366C4⋊Q8—611no—
367C4⋊Q8—611no—
368C4⋊Q8—611no—
369C4⋊Q8C2×#692311yescharacteristic
370#125—611no—
371#125—611no—
372#125—611no—
373#125C2×#692311yescharacteristic
374C22⋊Q8—1221no—
375C22⋊Q8—1221no—
376C22⋊Q8—1221no—
377C22⋊Q8—1221no—
378C4×Q8—1221no—
379C4×Q8—1221no—
380C4×Q8—1221no—
381C4×Q8—1221no—
382#117—611no—
383#117—611no—
384#117—611no—
385#117—611no—
386C2×C42—611no—
387C2×C42—611no—
388C2×C42—611no—
389C2×C42—1221no—
390C2×C42—1221no—
391#107—611no—
392#107—611no—
393#107—611no—
394#107—611no—
395#107—611no—
396#107—611no—
397#107C2×#692311yescharacteristic
398#107C2×#692311yescharacteristic
399#106—611no—
400#106—611no—
401#106—611no—
402#106—611no—
403#106—611no—
404#106—611no—
405#106C2×#692311yescharacteristic
406#106C2×#692311yescharacteristic
407C4⋊C8—1221no—
408C4⋊C8—1221no—
409C4⋊C8—1221no—
410C4⋊C8—1221no—
411C4⋊C8—1221no—
412C4⋊C8—1221no—
413C4⋊C8—1221no—
414C4⋊C8—1221no—
415C4⋊C8—1221no—
416C4⋊C8—1221no—
417C4⋊C8—1221no—
418C4⋊C8—1221no—
419#97—611no—
420#97—611no—
421#97—611no—
422#97—611no—
423#97—611no—
424#97—611no—
425#97—611no—
426#97—1221no—
427#97—1221no—
428#97—1221no—
429#97—1221no—
430#97C2×#692311yescharacteristic
431C4×C8—1221no—
432C4×C8—1221no—
433C4×C8—1221no—
434C4×C8—1221no—
435C2×Q8—21no—
436C2×Q8—1221no—
437C2×Q8—1221no—
438C2×Q8—1221no—
439C22×C4—611no—
440C22×C4—611no—
441C22×C4—611no—
442C22×C4—1221no—
443C22×C4—1221no—
444M16—1221no—
445M16—1221no—
446M16—1221no—
447M16—1221no—
448M16—1221no—
449M16—1221no—
450M16—1221no—
451M16—1221no—
452C2×C8—611no—
453C2×C8—611no—
454C2×C8—611no—
455C2×C8—611no—
456C2×C8—611no—
457C2×C8—611no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—1221no—
463C2×C8—1221no—
464C2×C8—1221no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—1221no—
470C2×C8C22×#692311yescharacteristic
471C2×C8C22×#692311yescharacteristic
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—611no—
476C4⋊C4—611no—
477C4⋊C4—611no—
478C4⋊C4—611no—
479C4⋊C4—1221no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C4⋊C4—1221no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4C22×#692311yescharacteristic
489C4⋊C4C22×#692311yescharacteristic
490C4⋊C4C22×#692311yescharacteristic
491C4⋊C4C22×#692311yescharacteristic
492C22⋊C4—1221no—
493C22⋊C4—1221no—
494C22⋊C4—1221no—
495C22⋊C4—1221no—
496C42—611no—
497C42—611no—
498C42—611no—
499C42—1221no—
500C42—1221no—
501C42—1221no—
502C42—1221no—
503C42—1221no—
504C42—1221no—
505C42—1221no—
506C42—1221no—
507C42—2442no—
508C42—2442no—
509C42C22×#692311yescharacteristic
510C23—611no—
511Q8—81no—
512Q8—4881no—
513Q8—4881no—
514Q8—4881no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—611no—
520C2×C4—611no—
521C2×C4—611no—
522C2×C4—611no—
523C2×C4—611no—
524C2×C4—611no—
525C2×C4—611no—
526C2×C4—1222no—
527C2×C4—1222no—
528C2×C4—1221no—
529C2×C4—1221no—
530C2×C4—1221no—
531C2×C4—1221no—
532C2×C4—2441no—
533C2×C4—2441no—
534C2×C4—2441no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4—2441no—
538C2×C4D4×#692311yescharacteristic
539C2×C4D4×#692311yescharacteristic
540C2×C4C23×#692311yescharacteristic
541C8—21no—
542C8—21no—
543C8—1221no—
544C8—1221no—
545C8—1221no—
546C8—1221no—
547C8—1221no—
548C8—1221no—
549C8—2441no—
550C8—2441no—
551C8—2441no—
552C8—2441no—
553C22—611no—
554C22—611no—
555C22—1221no—
556C22—1221no—
557C22C2×D4×#692311yescharacteristic
558C4—21no—
559C4—21no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—611no—
565C4—611no—
566C4—1221no—
567C4—1221no—
568C4—2442no—
569C4—2442no—
570C4—2441no—
571C4—2441no—
572C4—2441no—
573C4—2441no—
574C4#1684083011yescharacteristic
575C4#1684083011yescharacteristic
576C2—1221no—
577C2—1221no—
578C2#2146231011yescharacteristic
579C2#2146259311yescharacteristic
580C2#2146259411yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#501C4
socleC22×C61C2×C4×D4
prime radicalC22×D61C2×#41
cosocleC2×C4×D61C24
hypercenter#501#6923
hypocenterC61#22259
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
54. #16840172C4semidirect
55. #16840171C4semidirect
56. #16840170C4semidirect
57. #16840170C4semidirect
58. #16840169C4semidirect
59. #16840169C4semidirect
60. #16840168C4semidirect
66. C61×#501C4semidirect
315. #501#6923semidirect
357. C61#22259semidirect

Maximal subgroups

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

subgroupindex
#214626122
#214626112
#214620052
#214620042
#214618872
#214618862
#214618852
#214618842
#214617452
#214615352
#214563402
#2225961