Finite Group Databasebeta

← #30613690

Subgroups — #30613690

Order 15616.

656 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462651C211yesmaximal, characteristic, complemented
2#21462562C211yesmaximal, characteristic, complemented
3#21461469C211yesmaximal, characteristic, complemented
4#21461455C211yesmaximal, characteristic, complemented
5#21461448C211yesmaximal, characteristic, complemented
6#21461440C211yesmaximal, characteristic, complemented
7#21461424C211yesmaximal, characteristic, complemented
8#21461420C211yesmaximal, characteristic, complemented
9SD16⋊#92420C211yesmaximal, characteristic, complemented
10D8×#92420C211yesmaximal, characteristic, complemented
11#21461371C211yesmaximal, characteristic, complemented
12#21461139C211yesmaximal, characteristic, complemented
13#21461135C211yesmaximal, characteristic, complemented
14#21461043C211yesmaximal, characteristic, complemented
15#21456411C211yesmaximal, characteristic
16C2×#14519864—21no—
17#16840813C2211yescharacteristic
18Q8×#92420C2211yescharacteristic
19#16840797C2211yescharacteristic
20#16840797C2211yescharacteristic
21#16840797C2211yescharacteristic
22#16840795—21no—
23#16840793—21no—
24#16840793—21no—
25#16840791—21no—
26D4×#92420C2211yescharacteristic
27D4×#92420C2211yescharacteristic
28D4×#92420C2211yescharacteristic
29#16840786—21no—
30#16840781C2211yescharacteristic
31D61⋊(C4⋊C8)C2211yescharacteristic
32#16840736—21no—
33#16840726—21no—
34C4×#11758213C2211yescharacteristic
35C4×#11758213C2211yescharacteristic
36#16840626C2211yescharacteristic
37#16840625C2211yescharacteristic
38#16840624C2211yescharacteristic
39#16840623C2211yescharacteristic
40Q8⋊#92420C2211yescharacteristic
41Q8⋊#92420C2211yescharacteristic
42D4⋊#92420C2211yescharacteristic
43D4⋊#92420C2211yescharacteristic
44D4⋊#92420C2211yescharacteristic
45D4⋊#92420C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48#92420⋊C8C2211yescharacteristic
49#92420⋊C8C2211yescharacteristic
50#16840603C2211yescharacteristic
51C8×#92420C2211yescharacteristic
52#16840310C2211yescharacteristic
53#16840291C2211yescharacteristic
54#16840171C411yescharacteristic
55#16840126C411yescharacteristic
56#16840121C411yescharacteristic
57#16840012C411yescharacteristic
58#16840012C411yescharacteristic
59#16840005C411yescharacteristic
60#16840005C411yescharacteristic
61SD16×Dic61C2211yescharacteristic
62SD16×Dic61C2211yescharacteristic
63D8×Dic61C2211yescharacteristic
64D8×Dic61C2211yescharacteristic
65#16839714C2211yescharacteristic
66C61×#496C411yescharacteristic
67#14519864—44no—
68C2×#11758213—21no—
69C2×#11758213D411yescharacteristic
70C2×#11758213D411yescharacteristic
71C2×#11758217—21no—
72C2×#11758217—21no—
73C2×#11758217—21no—
74C2×D61⋊C8—21no—
75C22×#92420—21no—
76C22×#92420—21no—
77C22×#92420—21no—
78#14519844—21no—
79#14519844—21no—
80C4⋊#92420—21no—
81C4⋊#92420C2311yescharacteristic
82C4⋊#92420C2311yescharacteristic
83C4⋊#92420C2311yescharacteristic
84C4⋊#92420C2311yescharacteristic
85#14519834—21no—
86C22⋊#92420—21no—
87C22⋊#92420—21no—
88C22⋊#92420—21no—
89C22⋊#92420—21no—
90C22⋊#92420—21no—
91C22⋊#92420—21no—
92#14519832—21no—
93#14519832—21no—
94#14519832D411yescharacteristic
95#14519832D411yescharacteristic
96C4×#92420—21no—
97C4×#92420—21no—
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C4×#92420C2311yescharacteristic
102C2×#11758224—21no—
103C2×#11758189C2×C411yescharacteristic
104C2×#11758189C2×C411yescharacteristic
105#14519777C2×C411yescharacteristic
106#14519770—21no—
107#14519769C2×C411yescharacteristic
108#14519764—21no—
109#14519759—21no—
110#14519753C2×C411yescharacteristic
111#14519748—21no—
112#14519748C2×C411yescharacteristic
113#14519748C2×C411yescharacteristic
114#14519748C2×C411yescharacteristic
115Q8×Dic61C2311yescharacteristic
116D4×Dic61—21no—
117D4×Dic61C2311yescharacteristic
118D4×Dic61C2311yescharacteristic
119D4×Dic61C2311yescharacteristic
120#14519737—21no—
121#14519733—21no—
122C42×D61C2311yescharacteristic
123#14519711C2×C411yescharacteristic
124#14519711C2×C411yescharacteristic
125#14519709C2×C411yescharacteristic
126#14519709C2×C411yescharacteristic
127#14519701C2×C411yescharacteristic
128#14519701C2×C411yescharacteristic
129#14519698C2×C411yescharacteristic
130#14519698C2×C411yescharacteristic
131#14519698C2×C411yescharacteristic
132#14519698C2×C411yescharacteristic
133#14519698C2×C411yescharacteristic
134#14519698C2×C411yescharacteristic
135#14519688C2×C411yescharacteristic
136C8×Dic61C2311yescharacteristic
137C8×Dic61C2311yescharacteristic
138C2×SD16×C61C2×C411yescharacteristic
139C2×SD16×C61C2×C411yescharacteristic
140C2×D8×C61C2×C411yescharacteristic
141C2×D8×C61C2×C411yescharacteristic
142#127×C61C2×C411yescharacteristic
143#124×C61C2×C411yescharacteristic
144#97×C61C2×C411yescharacteristic
145C2×Q8×C61C22×C411yescharacteristic
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61C22×C411yescharacteristic
149C2×D4×C61C22×C411yescharacteristic
150C2×D4×C61C22×C411yescharacteristic
151C2×C22⋊D61—21no—
152C2×C22⋊D61—21no—
153C2×C22⋊D61—21no—
154C22×Dic61—21no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157#11758224—42no—
158#11758224—42no—
159C2×C4×D61C22×C411yescharacteristic
160C2×C4×D61C2×D411yescharacteristic
161C2×C4×D61#4111yescharacteristic
162C2×Dic122—21no—
163#11758217—42no—
164#11758217—42no—
165#11758217—42no—
166C2×#92420—21no—
167C2×#92420—21no—
168C2×#92420—21no—
169C2×#92420—21no—
170C2×#92420—21no—
171C2×#92420—21no—
172C2×#92420—42no—
173C2×#92420—42no—
174C2×#92420—42no—
175C2×#92420C2×D411yescharacteristic
176C2×#92420C2×D411yescharacteristic
177C2×#92420C2×D411yescharacteristic
178C2×#92420C2×D411yescharacteristic
179#11758213—22no—
180#11758213—41no—
181#11758213—42no—
182D61⋊C8—42no—
183SD16×C61—22no—
184SD16×C61—41no—
185D8×C61—22no—
186D8×C61—41no—
187C2×C8×C61C22×C411yescharacteristic
188C2×C8×C61C22×C411yescharacteristic
189C22⋊C4×C61—21no—
190C22⋊C4×C61—21no—
191C42×C61C22×C411yescharacteristic
192C22⋊Dic61—21no—
193C22⋊Dic61—21no—
194C22⋊Dic61—21no—
195C22⋊Dic61—21no—
196C22⋊Dic61—21no—
197C22⋊Dic61—21no—
198#11758198—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61C22×C411yescharacteristic
202C4⋊Dic61C22×C411yescharacteristic
203C4⋊Dic61C22×C411yescharacteristic
204C4⋊Dic61C22×C411yescharacteristic
205#11758196—21no—
206#11758196—21no—
207#11758196—21no—
208C4×Dic61—21no—
209C4×Dic61C2×D411yescharacteristic
210C4×Dic61#4111yescharacteristic
211C4×Dic61C2411yescharacteristic
212C2×#92418C22×C411yescharacteristic
213C2×#92418C22×C411yescharacteristic
214#11758189—22no—
215#11758189—41no—
216C23×C61—21no—
217C23×C61—21no—
218C23×C61—21no—
219C22×D61C4×D411yescharacteristic
220Q8×C61—21no—
221Q8×C61—21no—
222D4×C61—21no—
223D4×C61—21no—
224D4×C61—21no—
225D4×C61—21no—
226D4×C61—21no—
227D4×C61—21no—
228D4×C61—42no—
229D4×C61—81no—
230C2×C4×C61—21no—
231C2×C4×C61C4×D411yescharacteristic
232C2×C4×C61C4×D411yescharacteristic
233C2×C4×C61C23×C411yescharacteristic
234C22⋊D61—42no—
235C22⋊D61—42no—
236C22⋊D61—81no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61C4×D411yescharacteristic
248C2×Dic61C22×D411yescharacteristic
249C2×Dic61C2×#4111yescharacteristic
250C4×D61—21no—
251C4×D61—21no—
252C4×D61—21no—
253C4×D61—21no—
254C4×D61—41no—
255Dic122—42no—
256#92420—22no—
257#92420—21no—
258#92420—21no—
259#92420—21no—
260#92420—41no—
261#92420—41no—
262#92420—41no—
263#92420—41no—
264#92420—41no—
265#92420AGL(1,ℤ/8)12yes—
266C8×C61—21no—
267C8×C61#13112yescomplemented
268#92418—21no—
269#92418—21no—
270#18076—611nomaximal, Sylow
271C22×C61—41no—
272C22×C61—41no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61—41no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61C2×C4×D411yescharacteristic
281C2×D61—21no—
282C2×D61—21no—
283C2×D61—21no—
284C4×C61—21no—
285C4×C61—21no—
286C4×C61—41no—
287C4×C61C2×#13111yescharacteristic
288C4×C61#56811yescharacteristic
289Dic61—21no—
290Dic61—21no—
291Dic61—41no—
292Dic61—41no—
293Dic61—41no—
294Dic61—41no—
295Dic61C2×AGL(1,ℤ/8)11yescharacteristic
296Dic61#57511yescharacteristic
297#3171—611no—
298#2969—611no—
299#2935—611no—
300#1594—611no—
301#1590—611no—
302#1588—611no—
303#1586—611no—
304#1582—611no—
305#1581—611no—
306SD16⋊C8—611no—
307C8×D8—611no—
308#1565—611no—
309#1484—611no—
310#1483—611no—
311#1455—611no—
312C2×C61—81no—
313C2×C61—81no—
314C2×C61—81no—
315C2×C61#293511yescharacteristic
316C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
317C2×C61#295611yescharacteristic
318D61—41no—
319C2×#131—1221no—
320#532—611no—
321#529—611no—
322#501—611no—
323#496#692311yescharacteristic
324#490—611no—
325#489—611no—
326#469—611no—
327#469—611no—
328#468—611no—
329#468—611no—
330#446—611no—
331C8×Q8—611no—
332C4×SD16—611no—
333C4×SD16—611no—
334C4×D8—611no—
335C4×D8—611no—
336#436—611no—
337#436—611no—
338#436—611no—
339#436—1221no—
340#435—1221no—
341#435—1221no—
342#435—1221no—
343C8×D4—611no—
344C8×D4—611no—
345C8×D4—611no—
346#433—1221no—
347#431—611no—
348C2×C4⋊C8—611no—
349#408—1221no—
350#405—1221no—
351C4×M16—611no—
352C4×M16—611no—
353C4×M16—611no—
354#335—611no—
355#335—611no—
356#334—611no—
357#334—611no—
358Q8⋊C8—611no—
359Q8⋊C8—611no—
360D4⋊C8—611no—
361D4⋊C8—611no—
362D4⋊C8—611no—
363D4⋊C8—611no—
364D4⋊C8—611no—
365D4⋊C8—611no—
366#322—611no—
367#322—611no—
368#322—611no—
369C82—611no—
370C61#1807611yescharacteristic, complemented, Sylow
371C2×#41—1221no—
372C2×SD16C2×#692311yescharacteristic
373C2×SD16C2×#692311yescharacteristic
374C2×D8C2×#692311yescharacteristic
375C2×D8C2×#692311yescharacteristic
376#131—2444no—
377C2×M16—611no—
378C2×M16—611no—
379C2×M16—611no—
380C2×M16—611no—
381C2×M16—1221no—
382C2×M16—1221no—
383C2×M16—1221no—
384C2×M16—1221no—
385C22×C8—1221no—
386C22×C8—1221no—
387C22×C8—1221no—
388C22×C8—1221no—
389C4⋊Q8—611no—
390#127C2×#692311yescharacteristic
391#126—1221no—
392#125—611no—
393#124—1221no—
394#124C2×#692311yescharacteristic
395#123—1221no—
396C22⋊Q8—611no—
397#121—611no—
398#121—611no—
399#121—611no—
400#121—1221no—
401C4×Q8—611no—
402C4×D4—611no—
403C4×D4—611no—
404C4×D4—611no—
405C4×D4—1221no—
406C4×D4—1221no—
407#117—1221no—
408C2×C42—611no—
409#107—611no—
410#107—611no—
411#106—611no—
412#106—611no—
413C4⋊C8—611no—
414C4⋊C8—611no—
415C4⋊C8—611no—
416C4⋊C8—611no—
417C4⋊C8—1221no—
418C4⋊C8—1221no—
419C4⋊C8—1221no—
420#103—611no—
421#103—611no—
422#102—611no—
423#102—611no—
424#102—611no—
425#102—611no—
426#102—611no—
427#102—611no—
428C22⋊C8—1221no—
429C22⋊C8—1221no—
430C22⋊C8—1221no—
431C22⋊C8—1221no—
432C22⋊C8—1221no—
433C22⋊C8—1221no—
434C22⋊C8—1221no—
435#97—611no—
436#97—611no—
437#97—611no—
438#97—1221no—
439#97—1221no—
440#97C2×#692311yescharacteristic
441C4×C8—611no—
442C4×C8—611no—
443C4×C8—611no—
444C4×C8—611no—
445C4×C8—611no—
446C4×C8—611no—
447C4×C8—1221no—
448C4×C8—1221no—
449#41—2442no—
450#41—2442no—
451C2×Q8—1221no—
452C2×Q8C22×#692311yescharacteristic
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—1221no—
456C2×D4—1221no—
457C2×D4—1221no—
458C2×D4C22×#692311yescharacteristic
459C2×D4C22×#692311yescharacteristic
460C2×D4C22×#692311yescharacteristic
461C22×C4—611no—
462C22×C4—611no—
463C22×C4—611no—
464C22×C4—1221no—
465C22×C4—1221no—
466C22×C4—1221no—
467SD16—22no—
468SD16—41no—
469D8—22no—
470D8—41no—
471M16—1222no—
472M16—1222no—
473M16—2441no—
474M16—2442no—
475M16—2441no—
476M16—2442no—
477M16—2442no—
478M16—2442no—
479C2×C8—611no—
480C2×C8—611no—
481C2×C8—611no—
482C2×C8—611no—
483C2×C8—611no—
484C2×C8—611no—
485C2×C8—1221no—
486C2×C8—1221no—
487C2×C8—1221no—
488C2×C8—1221no—
489C2×C8—1221no—
490C2×C8—1221no—
491C2×C8—2442no—
492C2×C8—2442no—
493C2×C8—2442no—
494C2×C8—2442no—
495C2×C8C22×#692311yescharacteristic
496C2×C8C22×#692311yescharacteristic
497C4⋊C4—611no—
498C4⋊C4—611no—
499C4⋊C4—611no—
500C4⋊C4—611no—
501C4⋊C4—1221no—
502C4⋊C4—1221no—
503C4⋊C4—1221no—
504C4⋊C4—1221no—
505C4⋊C4—1221no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—1221no—
509C22⋊C4—1221no—
510C22⋊C4—1221no—
511C22⋊C4—1221no—
512C22⋊C4—1221no—
513C22⋊C4—1221no—
514C22⋊C4—1221no—
515C42—611no—
516C42—611no—
517C42—611no—
518C42—1221no—
519C42C22×#692311yescharacteristic
520C23—21no—
521C23—21no—
522C23—21no—
523C23—611no—
524Q8—21no—
525Q8—21no—
526Q8—2442no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—21no—
532D4—21no—
533D4—42no—
534D4—81no—
535D4—4881no—
536D4—2442no—
537D4—2442no—
538C2×C4—21no—
539C2×C4—611no—
540C2×C4—611no—
541C2×C4—611no—
542C2×C4—1221no—
543C2×C4—1221no—
544C2×C4—1221no—
545C2×C4—1221no—
546C2×C4—1221no—
547C2×C4—1221no—
548C2×C4—1221no—
549C2×C4—1221no—
550C2×C4—2441no—
551C2×C4—2441no—
552C2×C4—2441no—
553C2×C4—2441no—
554C2×C4—2441no—
555C2×C4—2441no—
556C2×C4—2441no—
557C2×C4D4×#692311yescharacteristic
558C2×C4D4×#692311yescharacteristic
559C2×C4C23×#692311yescharacteristic
560C8—21no—
561C8—612no—
562C8—1221no—
563C8—1221no—
564C8—1221no—
565C8—1222no—
566C8—1221no—
567C8—1221no—
568C8—2441no—
569C8—2441no—
570C8—2441no—
571C8—2441no—
572C8—2441no—
573C8#1451986412yescomplemented
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—1221no—
584C22—1221no—
585C22—1221no—
586C22C2×D4×#692311yescharacteristic
587C4—21no—
588C4—21no—
589C4—41no—
590C4—611no—
591C4—611no—
592C4—1221no—
593C4—1221no—
594C4—2441no—
595C4—2441no—
596C4—2441no—
597C4—2441no—
598C4C2×#1451986411yescharacteristic
599C4#1684084011yescharacteristic
600C2—81no—
601C2—81no—
602C2—81no—
603C2—2441no—
604C2#2146256211yescharacteristic
605C2AGL(1,ℤ/8)×#692311yescharacteristic
606C2#2146259311yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#496C4
socleC22×C61C2×C4×D4
prime radical#21456411C2
cosocleC4×Dic61C24
hypercenter#496#6923
hypocenterC61#18076
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #21462651C2semidirect
2. #21462562C2semidirect
3. #21461469C2semidirect
4. #21461455C2semidirect
5. #21461448C2semidirect
6. #21461440C2semidirect
7. #21461424C2semidirect
8. #21461420C2semidirect
9. SD16⋊#92420C2semidirect
10. D8×#92420C2semidirect
11. #21461371C2semidirect
12. #21461139C2semidirect
13. #21461135C2semidirect
14. #21461043C2semidirect
267. C8×C61#131semidirect
370. C61#18076semidirect
573. C8#14519864semidirect

Maximal subgroups

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

subgroupindex
#214626512
#214625622
#214614692
#214614552
#214614482
#214614402
#214614242
#214614202
SD16⋊#924202
D8×#924202
#214613712
#214611392
#214611352
#214610432
#214564112
#1807661