Subgroups — C₂²⋊#20263706 #38762302

Order 25408.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20263706	C₂	1	2	yes	maximal, complemented
2	C₂²×C₈×C₃₉₇	C₂	1	1	yes	maximal, characteristic
3	#20263706	—	2	2	no	—
4	C₂²×C₄×C₃₉₇	C₄	1	1	yes	characteristic
5	C₂×C₈×C₃₉₇	—	2	2	no	—
6	C₂×C₈×C₃₉₇	C₄	1	1	yes	characteristic
7	C₂×C₈×C₃₉₇	C₂²	1	1	yes	characteristic
8	C₂³×C₃₉₇	C₈	1	1	yes	characteristic
9	C₂×C₄×C₃₉₇	—	2	1	no	—
10	C₂×C₄×C₃₉₇	—	2	1	no	—
11	C₂×C₄×C₃₉₇	C₈	1	1	yes	characteristic
12	C₂×C₄×C₃₉₇	C₂×C₄	1	1	yes	characteristic
13	C₈×C₃₉₇	—	2	1	no	—
14	C₈×C₃₉₇	D₄	1	2	yes	—
15	C₂²×C₃₉₇	—	2	1	no	—
16	C₂²×C₃₉₇	—	2	1	no	—
17	C₂²×C₃₉₇	C₁₆	1	2	yes	complemented
18	C₂²×C₃₉₇	C₂×C₈	1	1	yes	characteristic
19	C₄×C₃₉₇	—	2	1	no	—
20	C₄×C₃₉₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₃₉₇	M₁₆	1	1	yes	characteristic
22	C₂×C₃₉₇	—	2	2	no	—
23	C₂×C₃₉₇	C₂²⋊C₈	1	1	yes	characteristic
24	C₂×C₃₉₇	C₂×C₁₆	1	1	yes	characteristic
25	C₂×C₃₉₇	M₃₂	1	1	yes	characteristic
26	C₃₉₇	C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
27	C₂²⋊C₁₆	—	397	1	no	maximal, Sylow
28	C₂²×C₈	D₃₉₇	1	1	yes	characteristic
29	C₂×C₁₆	—	397	2	no	—
30	C₂²×C₄	Dic₃₉₇	1	1	yes	characteristic
31	C₂×C₈	—	2	2	no	—
32	C₂×C₈	Dic₃₉₇	1	1	yes	characteristic
33	C₂×C₈	C₂×D₃₉₇	1	1	yes	characteristic
34	C₁₆	—	794	2	no	—
35	C₂³	#15691787	1	1	yes	characteristic
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	2	1	no	—
38	C₂×C₄	#15691787	1	1	yes	characteristic
39	C₂×C₄	C₂×Dic₃₉₇	1	1	yes	characteristic
40	C₈	—	2	1	no	—
41	C₈	C₂²⋊D₃₉₇	1	2	yes	—
42	C₂²	—	2	1	no	—
43	C₂²	—	2	1	no	—
44	C₂²	#20263706	1	2	yes	complemented
45	C₂²	C₂×#15691787	1	1	yes	characteristic
46	C₄	—	2	1	no	—
47	C₄	C₂²⋊Dic₃₉₇	1	1	yes	characteristic
48	C₄	#20263715	1	1	yes	characteristic
49	C₂	—	2	2	no	—
50	C₂	C₂²⋊#15691787	1	1	yes	characteristic
51	C₂	C₂×#20263706	1	1	yes	characteristic
52	C₂	#27163036	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×D₃₉₇
commutator	C₂×C₃₉₇	C₂×C₁₆
Fitting	C₂²×C₈×C₃₉₇	C₂
socle	C₂²×C₃₉₇	C₂×C₈
prime radical	C₂³×C₃₉₇	C₈
cosocle	C₂×C₈×C₃₉₇	C₂²
hypercenter	C₂²×C₈	D₃₉₇
hypocenter	C₃₉₇	C₂²⋊C₁₆
LCS	G ▷ C₂×C₃₉₇ ▷ C₃₉₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#20263706	C₂	semidirect
17. C₂²×C₃₉₇	C₁₆	semidirect
26. C₃₉₇	C₂²⋊C₁₆	semidirect
44. C₂²	#20263706	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20263706	2
C₂²×C₈×C₃₉₇	2
C₂²⋊C₁₆	397

Subgroups — C22⋊#20263706 #38762302

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊#20263706 #38762302