Subgroups — #38763386

Order 25408.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#15691794	C₂	1	2	yes	maximal
2	C₈×Dic₃₉₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#15691794	—	2	2	no	—
4	C₂×#15691787	C₄	1	1	yes	characteristic
5	C₄×Dic₃₉₇	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₃₉₇	C₄	1	1	yes	characteristic
7	#15691794	—	4	2	no	—
8	C₂×Dic₃₉₇	D₄	1	1	yes	characteristic
9	C₂×Dic₃₉₇	Q₈	1	1	yes	characteristic
10	#15691787	C₈	1	2	yes	complemented
11	C₂×C₄×C₃₉₇	C₂×C₄	1	1	yes	characteristic
12	C₈×C₃₉₇	—	2	1	no	—
13	C₂²×C₃₉₇	C₄⋊C₄	1	1	yes	characteristic
14	C₄×C₃₉₇	C₂×C₈	1	1	yes	characteristic
15	C₄×C₃₉₇	M₁₆	1	1	yes	characteristic
16	Dic₃₉₇	—	2	1	no	—
17	Dic₃₉₇	D₈	1	1	yes	characteristic
18	Dic₃₉₇	Q₁₆	1	1	yes	characteristic
19	C₂×C₃₉₇	C₄⋊C₈	1	1	yes	characteristic
20	C₂×C₃₉₇	#107	1	1	yes	characteristic
21	C₂×C₃₉₇	#108	1	1	yes	characteristic
22	C₃₉₇	#335	1	1	yes	characteristic, complemented, Sylow
23	#335	—	397	1	no	maximal, Sylow
24	C₄⋊C₈	—	397	2	no	—
25	C₄×C₈	—	397	1	no	—
26	C₂×C₈	—	794	2	no	—
27	C₂×C₈	—	397	1	no	—
28	C₂×C₈	#13097544	1	1	yes	characteristic
29	C₄²	—	397	1	no	—
30	C₂×C₄	—	397	1	no	—
31	C₂×C₄	—	397	1	no	—
32	C₂×C₄	C₂×#13097544	1	1	yes	characteristic
33	C₈	—	2	1	no	—
34	C₈	—	1588	2	no	—
35	C₈	—	397	2	no	—
36	C₂²	C₄⋊#13097544	1	1	yes	characteristic
37	C₄	—	794	1	no	—
38	C₄	—	397	1	no	—
39	C₄	—	397	1	no	—
40	C₄	D₃₉₇⋊C₈	1	1	yes	characteristic
41	C₄	#20263740	1	1	yes	characteristic
42	C₂	#27163163	1	1	yes	characteristic
43	C₂	#27163165	1	1	yes	characteristic
44	C₂	#27163166	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊#13097544
commutator	C₄×C₃₉₇	C₂×C₈
Frattini	C₂×C₄	C₂×#13097544
Fitting	C₂×C₈×C₃₉₇	C₄
socle, prime radical	C₂²×C₃₉₇	C₄⋊C₄
cosocle	C₄×Dic₃₉₇	C₂²
hypercenter	C₂×C₈	#13097544
hypocenter	C₃₉₇	#335
LCS	G ▷ C₄×C₃₉₇ ▷ C₂×C₃₉₇ ▷ C₃₉₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
10. #15691787	C₈	semidirect
22. C₃₉₇	#335	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#15691794	2
C₈×Dic₃₉₇	2
#335	397