Finite Group Databasebeta

← #30622104

Subgroups — #30622104

Order 15616.

708 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462617C211yesmaximal, characteristic, complemented
2#21462467C211yesmaximal, characteristic
3#21462005C211yesmaximal, characteristic, complemented
4#21461935C211yesmaximal, characteristic, complemented
5#21461929C211yesmaximal, characteristic, complemented
6#21461928C211yesmaximal, characteristic, complemented
7#21461887C211yesmaximal, characteristic, complemented
8#21461886C211yesmaximal, characteristic, complemented
9#21461789C211yesmaximal, characteristic
10#21461787C211yesmaximal, characteristic
11#21461606C211yesmaximal, characteristic, complemented
12#21461600C211yesmaximal, characteristic
13#21461600C211yesmaximal, characteristic
14C4×#14519842C211yesmaximal, characteristic
15#21455606C211yesmaximal, characteristic
16C2×#14519865C2211yescharacteristic
17C2×#14519865C2211yescharacteristic
18#16840814—21no—
19#16840814—21no—
20#16840812—21no—
21#16840811—21no—
22C2×#14519848C2211yescharacteristic
23C2×#14519847C2211yescharacteristic
24#16840769—21no—
25#16840769—21no—
26#16840769C2211yescharacteristic
27#16840769C2211yescharacteristic
28#16840769C2211yescharacteristic
29#16840769C2211yescharacteristic
30#16840767—21no—
31#16840767C2211yescharacteristic
32D61⋊(C4⋊C8)—21no—
33D61⋊(C4⋊C8)C2211yescharacteristic
34C2×#14519842C2211yescharacteristic
35C2×#14519842C2211yescharacteristic
36#16840727C2211yescharacteristic
37#16840727C2211yescharacteristic
38C4×#11758213C2211yescharacteristic
39C2×#14519831C2211yescharacteristic
40C2×#14519831C2211yescharacteristic
41C42×#6923C2211yescharacteristic
42#16840638C2211yescharacteristic
43#16840638C2211yescharacteristic
44#16840632C2211yescharacteristic
45#16840632C2211yescharacteristic
46#16840632C2211yescharacteristic
47#16840632C2211yescharacteristic
48#16840632C2211yescharacteristic
49#16840632C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52#16840318C2211yescharacteristic
53C4×#11758226C2211yescharacteristic
54#16840069C411yescharacteristic, complemented
55#16840063C411yescharacteristic, complemented
56#16840059C411yescharacteristic, complemented
57#16840055C411yescharacteristic, complemented
58#16840051C411yescharacteristic, complemented
59#16840045C411yescharacteristic, complemented
60#16840041C411yescharacteristic, complemented
61#16839799C2211yescharacteristic
62#16839797C2211yescharacteristic
63C4⋊C8×D61C2211yescharacteristic
64#16839757C2211yescharacteristic
65#16839757C2211yescharacteristic
66C61×#479C411yescharacteristic, complemented
67#14519865—22no—
68#14519865—22no—
69#14519865—41no—
70#14519865—41no—
71C2×#11758213—21no—
72C2×#11758213—21no—
73C2×#11758213C2311yescharacteristic
74C2×#11758213C2311yescharacteristic
75C2×#11758213C2311yescharacteristic
76C2×#11758213C2311yescharacteristic
77C2×D61⋊C8—21no—
78C2×D61⋊C8—21no—
79C2×D61⋊C8C2311yescharacteristic
80C2×D61⋊C8C2311yescharacteristic
81C2×C4×#6923—21no—
82C2×C4×#6923—21no—
83C2×C4×#6923C2311yescharacteristic
84C2×C4×#6923C2311yescharacteristic
85#14519848—41no—
86#14519847—41no—
87#14519844—21no—
88#14519844—21no—
89#14519844—21no—
90#14519844—21no—
91#14519844—21no—
92#14519844—21no—
93#14519844D411yescharacteristic
94#14519844D411yescharacteristic
95C4⋊#92420—21no—
96C4⋊#92420—21no—
97C4⋊#92420—21no—
98C4⋊#92420—21no—
99C4⋊#92420D411yescharacteristic
100C4⋊#92420D411yescharacteristic
101#14519842—22no—
102#14519842Q814yescomplemented
103#14519832—21no—
104#14519832—21no—
105#14519832—21no—
106#14519831—41no—
107#14519831—41no—
108C4×#92420—21no—
109C4×#92420—21no—
110C4×#92420—21no—
111C2×#11758226C2311yescharacteristic
112C2×C8×D61C2311yescharacteristic
113C2×C8×D61C2311yescharacteristic
114#14519776C2×C411yescharacteristic
115#14519776C2×C411yescharacteristic
116#14519769C2×C411yescharacteristic
117#14519755—21no—
118#14519755—21no—
119Q8×Dic61C2×C411yescharacteristic
120#14519742—21no—
121#14519742—21no—
122C4×D244—21no—
123C4×D244C2×C411yescharacteristic
124#14519739—21no—
125#14519739C2×C411yescharacteristic
126#14519735—21no—
127#14519735C2311yescharacteristic
128#14519735C2311yescharacteristic
129#14519735C2311yescharacteristic
130C42×D61—21no—
131C42×D61C2311yescharacteristic
132#14519711C2×C411yescharacteristic
133#14519710C2×C411yescharacteristic
134#14519710C2×C411yescharacteristic
135#14519709C2×C411yescharacteristic
136#14519708C2×C411yescharacteristic
137#14519708C2×C411yescharacteristic
138C4⋊#92418C2×C411yescharacteristic
139#14519706C2×C411yescharacteristic
140#14519706C2×C411yescharacteristic
141#14519701C2×C411yescharacteristic
142#14519701C2×C411yescharacteristic
143#14519699C2×C411yescharacteristic
144#14519699C2×C411yescharacteristic
145#14519697C2×C411yescharacteristic
146#14519697C2×C411yescharacteristic
147#125×C61C2×C411yescharacteristic
148C4×Q8×C61C2×C411yescharacteristic
149#107×C61C2×C411yescharacteristic
150#106×C61C2×C411yescharacteristic
151C4⋊C8×C61C2×C411yescharacteristic
152#103×C61C2×C411yescharacteristic
153#103×C61C2×C411yescharacteristic
154C22×#6923—21no—
155C22×#6923—21no—
156C2×Q8×C61C22×C411yescharacteristic
157#11758226—21no—
158#11758226—21no—
159#11758226C2×Q812yes—
160#11758226#4112yes—
161C2×D244—21no—
162C2×D244C22×C411yescharacteristic
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×C4×D61—21no—
166C2×C4×D61#4111yescharacteristic
167C2×C4×D61#4111yescharacteristic
168C2×C4×D61C2411yescharacteristic
169C2×Dic122—21no—
170C2×Dic122—21no—
171C2×#92420—21no—
172C2×#92420—21no—
173C2×#92420—21no—
174C2×#92420—21no—
175C2×#92420C2×D411yescharacteristic
176C2×#92420C2×D411yescharacteristic
177C2×#92420C2×D411yescharacteristic
178C2×#92420C2×D411yescharacteristic
179C4×#6923—21no—
180C4×#6923—21no—
181C4×#6923—21no—
182C4×#6923—42no—
183C4×#6923—42no—
184C4×#6923C2×Q812yes—
185#11758213—21no—
186#11758213—21no—
187#11758213—21no—
188#11758213—21no—
189#11758213—21no—
190#11758213—21no—
191#11758213—21no—
192#11758213—42no—
193#11758213—42no—
194#11758213C2×Q812yes—
195D61⋊C8—21no—
196D61⋊C8—21no—
197D61⋊C8—21no—
198D61⋊C8—21no—
199D61⋊C8—42no—
200D61⋊C8—42no—
201C2×C8×C61C22×C411yescharacteristic
202C2×C8×C61C22×C411yescharacteristic
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61C22×C411yescharacteristic
207C4⋊C4×C61C22×C411yescharacteristic
208C4⋊C4×C61C22×C411yescharacteristic
209C42×C61—21no—
210C42×C61C22×C411yescharacteristic
211#11758198—21no—
212#11758198—21no—
213#11758198—21no—
214#11758198—21no—
215#11758198—21no—
216C4⋊Dic61—21no—
217C4⋊Dic61C22×C411yescharacteristic
218C4⋊Dic61C22×C411yescharacteristic
219C4⋊Dic61C22×C411yescharacteristic
220#11758196—21no—
221#11758196—21no—
222#11758196—21no—
223#11758196—21no—
224C4×Dic61—21no—
225C4×Dic61—21no—
226C4×Dic61—21no—
227C4×Dic61—21no—
228C4×Dic61C22×C411yescharacteristic
229C4×Dic61C2×D411yescharacteristic
230C4×Dic61C2×D411yescharacteristic
231C2×#92418C22×C411yescharacteristic
232C2×#92418C22×C411yescharacteristic
233C8×D61—21no—
234C8×D61—21no—
235C8×D61—21no—
236C8×D61—21no—
237C22×D61—21no—
238C22×D61C2×#4111yescharacteristic
239C2×#6923—22no—
240C2×#6923—22no—
241C2×#6923—41no—
242C2×#6923—41no—
243C2×#6923—41no—
244C2×#6923—41no—
245Q8×C61—21no—
246Q8×C61C4×Q812yes—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61C4×D411yescharacteristic
252C2×C4×C61C4×D411yescharacteristic
253C2×C4×C61C23×C411yescharacteristic
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61C4×D411yescharacteristic
258C2×Dic61C4×D411yescharacteristic
259C2×Dic61C22×D411yescharacteristic
260D244—22no—
261D244—22no—
262D244—21no—
263D244C4×Q812yes—
264C4×D61—22no—
265C4×D61—22no—
266C4×D61—22no—
267C4×D61—41no—
268C4×D61—42no—
269C4×D61—81no—
270C4×D61C22×Q811yescharacteristic
271C4×D61C2×#4111yescharacteristic
272C4×D61H(5,𝔽2)11yescharacteristic
273C4×D612−1+411yescharacteristic
274Dic122—42no—
275Dic122—81no—
276#92420—21no—
277#92420—21no—
278#92420—21no—
279#92420—21no—
280#92420—22no—
281#92420—41no—
282#92420—41no—
283#92420—41no—
284C8×C61—21no—
285C8×C61—21no—
286#92418—21no—
287#92418—21no—
288#22983—611nomaximal, Sylow
289C22×C61C2×C4×D411yescharacteristic
290C2×D61—21no—
291C2×D61—21no—
292C2×D61—22no—
293C2×D61—41no—
294C2×D61—41no—
295C2×D61#55211yescharacteristic
296C2×D61#55411yescharacteristic
297#6923—42no—
298#6923—42no—
299C4×C61—22no—
300C4×C61—21no—
301C4×C61—21no—
302C4×C61—41no—
303C4×C61—41no—
304C4×C61—41no—
305C4×C61C2×C4×Q811yescharacteristic
306C4×C61#52011yescharacteristic
307Dic61—21no—
308Dic61—41no—
309Dic61—41no—
310Dic61—41no—
311Dic61#44412yes—
312Dic61#54611yescharacteristic
313Dic61D4×Q811yescharacteristic
314#3076—611no—
315#2962—611no—
316#2906—611no—
317#1994—611no—
318#1950—611no—
319#1946—611no—
320#1946—611no—
321#1922—611no—
322#1922—611no—
323#1866—611no—
324#1866—611no—
325#1767—611no—
326#1765—611no—
327#1765—611no—
328C4×#104—611no—
329C2×C61#236011yescharacteristic
330C2×C61C2×#44411yescharacteristic
331C2×C61#295611yescharacteristic
332D61—21no—
333D61—21no—
334D61—42no—
335C2×#131—611no—
336C2×#131—611no—
337#533—611no—
338C4×#41—611no—
339#479—611no—
340#479#692311yescharacteristic, complemented
341#478—611no—
342#478—611no—
343#477—611no—
344#476—611no—
345#475—611no—
346#474—611no—
347#446—1221no—
348#446—1221no—
349#446—1221no—
350C8×Q8—1221no—
351C2×#108—611no—
352C2×#108—611no—
353#427—611no—
354#427—611no—
355#424—611no—
356#424—611no—
357#424—611no—
358#424—611no—
359#424—1221no—
360#424—1221no—
361#423—611no—
362#423—1221no—
363C2×C4⋊C8—611no—
364C2×C4⋊C8—611no—
365C2×C4⋊C8—1221no—
366C2×#104—611no—
367C2×#104—611no—
368#416—611no—
369#416—611no—
370#405—611no—
371#405—611no—
372C4×M16—611no—
373C2×#97—611no—
374C2×#97—611no—
375C43—611no—
376#341—611no—
377#341—611no—
378#339—611no—
379#339—611no—
380#339—611no—
381#339—611no—
382#339—611no—
383#339—611no—
384#336—611no—
385#336—611no—
386C61#2298311yescharacteristic, complemented, Sylow
387C2×#41—611no—
388#131—1222no—
389#131—1222no—
390#131—2441no—
391#131—2441no—
392C2×M16—611no—
393C2×M16—611no—
394C2×M16—611no—
395C2×M16—611no—
396C2×M16—1221no—
397C2×M16—1221no—
398C22×C8—611no—
399C22×C8—611no—
400C22×C8—611no—
401C22×C8—611no—
402C22×C8—1221no—
403C22×C8—1221no—
404C4⋊Q8—611no—
405C4⋊Q8—611no—
406#125—611no—
407#125C2×#692311yescharacteristic
408C22⋊Q8—1221no—
409C22⋊Q8—1221no—
410C4×Q8—611no—
411C4×Q8—1221no—
412C4×Q8—1221no—
413C4×Q8C2×#692311yescharacteristic
414C4×D4—611no—
415C4×D4—611no—
416C4×D4—1221no—
417C4×D4—1221no—
418#117—611no—
419#117—611no—
420#117—611no—
421#117—1221no—
422C2×C42—611no—
423C2×C42—611no—
424C2×C42—611no—
425C2×C42—1221no—
426C2×C42—1221no—
427C2×C42—1221no—
428#108—2441no—
429#108—2441no—
430#107—611no—
431#107—611no—
432#107—611no—
433#107C2×#692311yescharacteristic
434#106—611no—
435#106—611no—
436#106—611no—
437#106C2×#692311yescharacteristic
438C4⋊C8—611no—
439C4⋊C8—611no—
440C4⋊C8—611no—
441C4⋊C8—611no—
442C4⋊C8—611no—
443C4⋊C8—611no—
444C4⋊C8—611no—
445C4⋊C8—1221no—
446C4⋊C8—1221no—
447C4⋊C8—1221no—
448C4⋊C8—1221no—
449C4⋊C8—1221no—
450C4⋊C8—1221no—
451C4⋊C8—1221no—
452C4⋊C8—1221no—
453C4⋊C8—1221no—
454C4⋊C8—1221no—
455C4⋊C8C2×#692311yescharacteristic
456#104—614no—
457#104—1222no—
458#103—611no—
459#103—611no—
460#103C2×#692311yescharacteristic
461#103C2×#692311yescharacteristic
462#102—611no—
463#102—611no—
464#102—611no—
465#102—611no—
466#97—1221no—
467#97—1221no—
468#97—1221no—
469#97—2441no—
470#97—2441no—
471C4×C8—1221no—
472C4×C8—1221no—
473C4×C8—1221no—
474#41—612no—
475#41—612no—
476#41—1221no—
477#41—1221no—
478C2×Q8—1221no—
479C2×Q8—1221no—
480C2×Q8C22×#692311yescharacteristic
481C2×D4—611no—
482C2×D4—1221no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—1221no—
487C22×C4—1221no—
488C22×C4—1221no—
489C22×C4—1221no—
490C22×C4—1221no—
491M16—612no—
492M16—1221no—
493M16—1221no—
494M16—1221no—
495M16—1221no—
496M16—1221no—
497M16—1221no—
498M16—1221no—
499M16—2442no—
500M16—2442no—
501C2×C8—611no—
502C2×C8—611no—
503C2×C8—611no—
504C2×C8—611no—
505C2×C8—611no—
506C2×C8—611no—
507C2×C8—1221no—
508C2×C8—1221no—
509C2×C8—1221no—
510C2×C8—1221no—
511C2×C8—1221no—
512C2×C8—1221no—
513C2×C8—1221no—
514C2×C8—1221no—
515C2×C8—1221no—
516C2×C8—1221no—
517C2×C8—1221no—
518C2×C8—1221no—
519C2×C8—2442no—
520C2×C8—2442no—
521C2×C8C22×#692311yescharacteristic
522C2×C8C22×#692311yescharacteristic
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—611no—
527C4⋊C4—611no—
528C4⋊C4—611no—
529C4⋊C4—1221no—
530C4⋊C4—1221no—
531C4⋊C4—1221no—
532C4⋊C4—1221no—
533C4⋊C4—1221no—
534C4⋊C4C22×#692311yescharacteristic
535C4⋊C4C22×#692311yescharacteristic
536C4⋊C4C22×#692311yescharacteristic
537C22⋊C4—1221no—
538C22⋊C4—1221no—
539C22⋊C4—1221no—
540C22⋊C4—1221no—
541C22⋊C4—1221no—
542C42—21no—
543C42—611no—
544C42—611no—
545C42—611no—
546C42—612no—
547C42—1221no—
548C42—1221no—
549C42—1221no—
550C42—1221no—
551C42—1221no—
552C42—1221no—
553C42—1221no—
554C42—2442no—
555C42—2442no—
556C42C22×#692311yescharacteristic
557C23—611no—
558C23—1221no—
559Q8—21no—
560Q8—4881no—
561Q8—2442no—
562Q8Q8×#692312yes—
563D4—612no—
564D4—1222no—
565D4—1222no—
566D4—1221no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—611no—
572C2×C4—611no—
573C2×C4—611no—
574C2×C4—611no—
575C2×C4—611no—
576C2×C4—611no—
577C2×C4—611no—
578C2×C4—1222no—
579C2×C4—1222no—
580C2×C4—1222no—
581C2×C4—1222no—
582C2×C4—1222no—
583C2×C4—1221no—
584C2×C4—1221no—
585C2×C4—1221no—
586C2×C4—4881no—
587C2×C4—2441no—
588C2×C4—2442no—
589C2×C4—2441no—
590C2×C4—2441no—
591C2×C4—2441no—
592C2×C4—2441no—
593C2×C4D4×#692311yescharacteristic
594C2×C4D4×#692311yescharacteristic
595C2×C4C23×#692311yescharacteristic
596C8—21no—
597C8—21no—
598C8—1221no—
599C8—1221no—
600C8—1221no—
601C8—1221no—
602C8—1222no—
603C8—1221no—
604C8—1221no—
605C8—2441no—
606C8—2441no—
607C8—2441no—
608C22—611no—
609C22—611no—
610C22—1221no—
611C22—1221no—
612C22—1222no—
613C22—2441no—
614C22—2441no—
615C22C2×D4×#692311yescharacteristic
616C4—21no—
617C4—21no—
618C4—22no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—612no—
623C4—611no—
624C4—611no—
625C4—1221no—
626C4—2442no—
627C4—2442no—
628C4—2441no—
629C4—2441no—
630C4—2441no—
631C4C2×Q8×#692311yescharacteristic
632C4#1684083111yescharacteristic
633C2—1221no—
634C2—1221no—
635C2—2442no—
636C2#2146234311yescharacteristic
637C2D61⋊#44411yescharacteristic
638C2#2146259411yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#479C4
socleC22×C61C2×C4×D4
prime radicalC2×#11758226C23
cosocleC2×C4×D61C24
hypercenter#479#6923
hypocenterC61#22983
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #21462617C2semidirect
3. #21462005C2semidirect
4. #21461935C2semidirect
5. #21461929C2semidirect
6. #21461928C2semidirect
7. #21461887C2semidirect
8. #21461886C2semidirect
11. #21461606C2semidirect
54. #16840069C4semidirect
55. #16840063C4semidirect
56. #16840059C4semidirect
57. #16840055C4semidirect
58. #16840051C4semidirect
59. #16840045C4semidirect
60. #16840041C4semidirect
66. C61×#479C4semidirect
102. #14519842Q8semidirect
340. #479#6923semidirect
386. C61#22983semidirect

Maximal subgroups

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

subgroupindex
#214626172
#214624672
#214620052
#214619352
#214619292
#214619282
#214618872
#214618862
#214617892
#214617872
#214616062
#214616002
C4×#145198422
#214556062
#2298361