Finite Group Databasebeta

← #30622684

Subgroups — #30622684

Order 15616.

626 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462617C211yesmaximal, characteristic
2#21462615C211yesmaximal, characteristic
3#21461996C211yesmaximal, characteristic
4#21461995C211yesmaximal, characteristic
5#21461929C211yesmaximal, characteristic
6#21461927C211yesmaximal, characteristic
7#21461887C211yesmaximal, characteristic
8#21461886C211yesmaximal, characteristic
9#21461886C211yesmaximal, characteristic
10#21461884C211yesmaximal, characteristic
11#21461639C211yesmaximal, characteristic
12#21461626C211yesmaximal, characteristic
13#21461622C211yesmaximal, characteristic
14#21461617C211yesmaximal, characteristic
15#21456340C211yesmaximal, characteristic
16#16840814—21no—
17#16840814—21no—
18#16840813—21no—
19#16840813—21no—
20#16840812—21no—
21#16840812—21no—
22#16840811—21no—
23#16840811—21no—
24C2×#14519848C2211yescharacteristic
25C2×#14519847C2211yescharacteristic
26#16840769C2211yescharacteristic
27#16840769C2211yescharacteristic
28#16840769C2211yescharacteristic
29#16840769C2211yescharacteristic
30D61⋊(C4⋊C8)C2211yescharacteristic
31#16840727C2211yescharacteristic
32#16840727C2211yescharacteristic
33#16840727C2211yescharacteristic
34#16840727C2211yescharacteristic
35C4×#11758213C2211yescharacteristic
36C4×#11758213C2211yescharacteristic
37C2×#14519831C2211yescharacteristic
38C2×C8×#6923C2211yescharacteristic
39C4×C4⋊#6923C2211yescharacteristic
40#16840638C2211yescharacteristic
41#16840638C2211yescharacteristic
42#16840632C2211yescharacteristic
43#16840632C2211yescharacteristic
44#16840632C2211yescharacteristic
45#16840632C2211yescharacteristic
46#16840632C2211yescharacteristic
47#16840632C2211yescharacteristic
48#16840632C2211yescharacteristic
49#16840632C2211yescharacteristic
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×#6923C2311yescharacteristic
75C2×C4×#6923C2311yescharacteristic
76#14519848—22no—
77#14519847Q814yescomplemented
78#14519844—21no—
79#14519844—21no—
80#14519844—21no—
81#14519844—21no—
82#14519844D411yescharacteristic
83#14519844D411yescharacteristic
84C4⋊#92420—21no—
85C4⋊#92420—21no—
86C4⋊#92420—21no—
87C4⋊#92420—21no—
88C4⋊#92420D411yescharacteristic
89C4⋊#92420D411yescharacteristic
90#14519832—21no—
91#14519832—21no—
92#14519832—21no—
93#14519832—21no—
94#14519832—21no—
95#14519832—21no—
96#14519831—22no—
97C4×#92420—21no—
98C4×#92420—21no—
99C4×#92420—21no—
100C4×#92420—21no—
101C4×#92420—21no—
102C4×#92420—21no—
103C8×#6923—22no—
104(C2×#6923)⋊C4—21no—
105C2×C8×D61C2311yescharacteristic
106C2×C8×D61C2311yescharacteristic
107#14519777C2×C411yescharacteristic
108#14519776C2×C411yescharacteristic
109#14519776C2×C411yescharacteristic
110#14519769C2×C411yescharacteristic
111#14519768C2×C411yescharacteristic
112#14519768C2×C411yescharacteristic
113#14519757—21no—
114#14519755—21no—
115#14519755—21no—
116#14519753—21no—
117Q8×Dic61—21no—
118#14519742—21no—
119#14519742—21no—
120#14519742—21no—
121#14519735C2311yescharacteristic
122#14519735C2311yescharacteristic
123#14519735C2311yescharacteristic
124#14519735C2311yescharacteristic
125C42×D61C2311yescharacteristic
126#14519711C2×C411yescharacteristic
127#14519711C2×C411yescharacteristic
128#14519710C2×C411yescharacteristic
129#14519710C2×C411yescharacteristic
130#14519710C2×C411yescharacteristic
131#14519710C2×C411yescharacteristic
132#14519709C2×C411yescharacteristic
133#14519709C2×C411yescharacteristic
134#14519708C2×C411yescharacteristic
135#14519708C2×C411yescharacteristic
136#14519708C2×C411yescharacteristic
137#14519708C2×C411yescharacteristic
138#14519688C2×C411yescharacteristic
139#14519687C2×C411yescharacteristic
140#14519687C2×C411yescharacteristic
141C4⋊Q8×C61C2×C411yescharacteristic
142#125×C61C2×C411yescharacteristic
143#107×C61C2×C411yescharacteristic
144#107×C61C2×C411yescharacteristic
145#106×C61C2×C411yescharacteristic
146#106×C61C2×C411yescharacteristic
147#97×C61C2×C411yescharacteristic
148C22×#6923—21no—
149C22×#6923—21no—
150C2×Q8×C61—21no—
151C2×C4×D61#4111yescharacteristic
152C2×C4×D61#4111yescharacteristic
153C2×C4×D61C2411yescharacteristic
154C2×Dic122—21no—
155C2×Dic122—21no—
156C2×Dic122—21no—
157C2×#92420—21no—
158C2×#92420—21no—
159C2×#92420—21no—
160C2×#92420—21no—
161C2×#92420C2×D411yescharacteristic
162C2×#92420C2×D411yescharacteristic
163C2×#92420C2×D411yescharacteristic
164C2×#92420C2×D411yescharacteristic
165C4⋊#6923—42no—
166C4×#6923—21no—
167C4×#6923—21no—
168C4×#6923—21no—
169C4×#6923—21no—
170#11758213—21no—
171#11758213—21no—
172#11758213—21no—
173#11758213—21no—
174#11758213—21no—
175#11758213—21no—
176#11758213C2×Q812yes—
177#11758213C2×Q812yes—
178D61⋊C8—21no—
179D61⋊C8—21no—
180D61⋊C8—21no—
181D61⋊C8—21no—
182C2×C8×C61C22×C411yescharacteristic
183C2×C8×C61C22×C411yescharacteristic
184C4⋊C4×C61—21no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61—21no—
187C4⋊C4×C61C22×C411yescharacteristic
188C4⋊C4×C61C22×C411yescharacteristic
189C4⋊C4×C61C22×C411yescharacteristic
190C4⋊C4×C61C22×C411yescharacteristic
191C42×C61C22×C411yescharacteristic
192#11758198—21no—
193#11758198—21no—
194#11758198—21no—
195#11758198—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61C22×C411yescharacteristic
200C4⋊Dic61C22×C411yescharacteristic
201C4⋊Dic61C22×C411yescharacteristic
202C4⋊Dic61C22×C411yescharacteristic
203#11758196—21no—
204#11758196—21no—
205#11758196—21no—
206#11758196—21no—
207#11758196—21no—
208#11758196—21no—
209C4×Dic61—21no—
210C4×Dic61—21no—
211C4×Dic61—21no—
212C4×Dic61—21no—
213C4×Dic61C22×C411yescharacteristic
214C4×Dic61C2×D411yescharacteristic
215C4×Dic61C2×D411yescharacteristic
216C2×#92418C22×C411yescharacteristic
217C2×#92418C22×C411yescharacteristic
218C8×D61—21no—
219C8×D61—21no—
220C8×D61C2×Q812yes—
221C8×D61#4112yes—
222C22×D61C2×#4111yescharacteristic
223C2×#6923—22no—
224C2×#6923—41no—
225C2×#6923—41no—
226C2×#6923—41no—
227C2×#6923—41no—
228C2×#6923—41no—
229Q8×C61—81no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61C4×D411yescharacteristic
235C2×C4×C61C4×D411yescharacteristic
236C2×C4×C61C23×C411yescharacteristic
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61C4×D411yescharacteristic
242C2×Dic61C4×D411yescharacteristic
243C2×Dic61C22×D411yescharacteristic
244C4×D61—41no—
245C4×D61—41no—
246C4×D61C22×Q811yescharacteristic
247C4×D61C2×#4111yescharacteristic
248C4×D612−1+411yescharacteristic
249C4×D612−1+411yescharacteristic
250Dic122—42no—
251Dic122—42no—
252Dic122—81no—
253#92420—21no—
254#92420—21no—
255#92420—21no—
256#92420—21no—
257#92420—22no—
258#92420—22no—
259#92420—41no—
260#92420—41no—
261C8×C61—21no—
262C8×C61C4×Q812yes—
263#92418—21no—
264#92418C4×Q812yes—
265#23172—611nomaximal, Sylow
266C22×C61C2×C4×D411yescharacteristic
267C2×D61—21no—
268C2×D61—21no—
269C2×D61#55611yescharacteristic
270C2×D61#55711yescharacteristic
271#6923—42no—
272#6923—81no—
273C4×C61—21no—
274C4×C61—21no—
275C4×C61—41no—
276C4×C61—41no—
277C4×C61—41no—
278C4×C61—41no—
279C4×C61C2×C4×Q811yescharacteristic
280C4×C61#51911yescharacteristic
281Dic61—21no—
282Dic61—21no—
283Dic61—41no—
284Dic61—41no—
285Dic61—41no—
286Dic61—41no—
287Dic61#54711yescharacteristic
288Dic61D4×Q811yescharacteristic
289#3162—611no—
290#2962—611no—
291#2962—611no—
292#1986—611no—
293#1986—611no—
294#1946—611no—
295#1945—611no—
296#1922—611no—
297#1922—611no—
298#1922—611no—
299#1922—611no—
300#1778—611no—
301#1773—611no—
302#1772—611no—
303#1771—611no—
304C2×C61#236511yescharacteristic
305C2×C61#295511yescharacteristic
306C2×C61#295611yescharacteristic
307D61—21no—
308D61—21no—
309#533—611no—
310#533—611no—
311#501—611no—
312#501—611no—
313#501—611no—
314#501—611no—
315#501—611no—
316#501—611no—
317#501—611no—
318#501#692311yescharacteristic, complemented
319#446—1221no—
320#446—1221no—
321#446—1221no—
322#446—1221no—
323#446—1221no—
324#446—1221no—
325C8×Q8—1221no—
326C8×Q8—1221no—
327C2×#108—611no—
328C2×#108—611no—
329#427—611no—
330#427—611no—
331#427—611no—
332#427—611no—
333#424—611no—
334#424—611no—
335#424—611no—
336#424—611no—
337C2×C4⋊C8—611no—
338#405—611no—
339#405—611no—
340#405—611no—
341#405—611no—
342C4×M16—611no—
343C4×M16—611no—
344C2×#97—611no—
345C2×#97—611no—
346C2×C4×C8—611no—
347C4×C4⋊C4—611no—
348#341—611no—
349#341—611no—
350#339—611no—
351#339—611no—
352#339—611no—
353#339—611no—
354#339—611no—
355#339—611no—
356#339—611no—
357#339—611no—
358#336—611no—
359#336—611no—
360C61#2317211yescharacteristic, complemented, Sylow
361C2×M16—611no—
362C2×M16—611no—
363C2×M16—611no—
364C2×M16—611no—
365C22×C8—611no—
366C22×C8—611no—
367C22×C8—611no—
368C22×C8—611no—
369C4⋊Q8—611no—
370C4⋊Q8—611no—
371C4⋊Q8—611no—
372C4⋊Q8C2×#692311yescharacteristic
373#125—611no—
374#125—611no—
375#125—611no—
376#125C2×#692311yescharacteristic
377C22⋊Q8—1221no—
378C22⋊Q8—1221no—
379C22⋊Q8—1221no—
380C22⋊Q8—1221no—
381C4×Q8—1221no—
382C4×Q8—1221no—
383C4×Q8—1221no—
384C4×Q8—1221no—
385#117—611no—
386#117—611no—
387#117—611no—
388#117—611no—
389C2×C4⋊C4—1221no—
390C2×C42—611no—
391C2×C42—611no—
392C2×C42—611no—
393#108—614no—
394#108—1222no—
395#107—611no—
396#107—611no—
397#107—611no—
398#107—611no—
399#107—611no—
400#107—611no—
401#107C2×#692311yescharacteristic
402#107C2×#692311yescharacteristic
403#106—611no—
404#106—611no—
405#106—611no—
406#106—611no—
407#106—611no—
408#106—611no—
409#106C2×#692311yescharacteristic
410#106C2×#692311yescharacteristic
411C4⋊C8—611no—
412C4⋊C8—611no—
413C4⋊C8—611no—
414C4⋊C8—611no—
415C4⋊C8—1221no—
416C4⋊C8—1221no—
417C4⋊C8—1221no—
418C4⋊C8—1221no—
419C4⋊C8—1221no—
420C4⋊C8—1221no—
421C4⋊C8—1221no—
422C4⋊C8—1221no—
423#97—611no—
424#97—611no—
425#97—611no—
426#97—1221no—
427#97—1221no—
428#97—1222no—
429#97—1221no—
430#97—1221no—
431#97—1221no—
432#97—1221no—
433#97C2×#692311yescharacteristic
434C4×C8—1221no—
435C4×C8—1221no—
436C4×C8—1222no—
437C4×C8—1221no—
438C4×C8—1221no—
439C4×C8—1221no—
440C4×C8—1221no—
441#95—1221no—
442C2×Q8—21no—
443C2×Q8—1221no—
444C2×Q8—1221no—
445C2×Q8—1221no—
446C22×C4—611no—
447C22×C4—611no—
448C22×C4—611no—
449C22×C4—1221no—
450C22×C4—1221no—
451M16—612no—
452M16—612no—
453M16—1221no—
454M16—1221no—
455M16—1221no—
456M16—1221no—
457M16—1221no—
458M16—1221no—
459C2×C8—611no—
460C2×C8—612no—
461C2×C8—612no—
462C2×C8—611no—
463C2×C8—611no—
464C2×C8—611no—
465C2×C8—611no—
466C2×C8—611no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—1221no—
470C2×C8—1221no—
471C2×C8—1221no—
472C2×C8—1221no—
473C2×C8—1221no—
474C2×C8—1221no—
475C2×C8—1221no—
476C2×C8—1221no—
477C2×C8C22×#692311yescharacteristic
478C2×C8C22×#692311yescharacteristic
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—611no—
483C4⋊C4—611no—
484C4⋊C4—611no—
485C4⋊C4—611no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—1221no—
490C4⋊C4—1221no—
491C4⋊C4—1221no—
492C4⋊C4—1221no—
493C4⋊C4—1221no—
494C4⋊C4—1221no—
495C4⋊C4—2442no—
496C4⋊C4C22×#692311yescharacteristic
497C4⋊C4C22×#692311yescharacteristic
498C4⋊C4C22×#692311yescharacteristic
499C4⋊C4C22×#692311yescharacteristic
500C22⋊C4—1221no—
501C22⋊C4—1221no—
502C22⋊C4—1221no—
503C22⋊C4—1221no—
504C42—611no—
505C42—611no—
506C42—611no—
507C42—1221no—
508C42—1221no—
509C42—1221no—
510C42—1221no—
511C42—1221no—
512C42—1221no—
513C42—1221no—
514C42—1221no—
515C42C22×#692311yescharacteristic
516C23—611no—
517Q8—81no—
518Q8—4881no—
519Q8—2442no—
520Q8—2442no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—611no—
526C2×C4—611no—
527C2×C4—611no—
528C2×C4—611no—
529C2×C4—611no—
530C2×C4—611no—
531C2×C4—611no—
532C2×C4—1222no—
533C2×C4—1221no—
534C2×C4—1221no—
535C2×C4—1221no—
536C2×C4—1221no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4—2441no—
544C2×C4D4×#692311yescharacteristic
545C2×C4D4×#692311yescharacteristic
546C2×C4C23×#692311yescharacteristic
547C8—21no—
548C8—612no—
549C8—1221no—
550C8—1221no—
551C8—1221no—
552C8—1221no—
553C8—1222no—
554C8—1222no—
555C8—1221no—
556C8—2441no—
557C8—2441no—
558C8Q8×#692312yes—
559C22—611no—
560C22—611no—
561C22—1221no—
562C22—1221no—
563C22C2×D4×#692311yescharacteristic
564C4—21no—
565C4—21no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—611no—
571C4—611no—
572C4—1221no—
573C4—1221no—
574C4—4881no—
575C4—2442no—
576C4—2441no—
577C4—2441no—
578C4—2441no—
579C4—2441no—
580C4C2×Q8×#692311yescharacteristic
581C4#1684083011yescharacteristic
582C2—1221no—
583C2—1221no—
584C2#2146234811yescharacteristic
585C2#2146259211yescharacteristic
586C2#2146259311yescharacteristic
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#23172
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
77. #14519847Q8semidirect
318. #501#6923semidirect
360. C61#23172semidirect

Maximal subgroups

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

subgroupindex
#214626172
#214626152
#214619962
#214619952
#214619292
#214619272
#214618872
#214618862
#214618842
#214616392
#214616262
#214616222
#214616172
#214563402
#2317261