Subgroups — #361×C₃₉₇ #38762015

Order 25408.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈×C₃₉₇	C₂	1	1	yes	maximal, characteristic
2	M₃₂×C₃₉₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#108×C₃₉₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄×C₃₉₇	—	2	1	no	—
5	D₈×C₃₉₇	—	2	1	no	—
6	D₈×C₃₉₇	C₄	1	2	yes	—
7	M₁₆×C₃₉₇	—	2	1	no	—
8	C₂×C₈×C₃₉₇	C₂²	1	1	yes	characteristic
9	C₁₆×C₃₉₇	—	2	1	no	—
10	C₂³×C₃₉₇	—	4	1	no	—
11	D₄×C₃₉₇	—	2	2	no	—
12	D₄×C₃₉₇	—	4	1	no	—
13	C₂×C₄×C₃₉₇	D₄	1	1	yes	characteristic
14	C₈×C₃₉₇	—	4	1	no	—
15	C₈×C₃₉₇	C₂×C₄	1	1	yes	characteristic
16	C₈×C₃₉₇	D₄	1	1	yes	characteristic
17	C₂²×C₃₉₇	—	4	2	no	—
18	C₂²×C₃₉₇	—	8	2	no	—
19	C₂²×C₃₉₇	SD₁₆	1	1	yes	characteristic
20	C₄×C₃₉₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₃₉₇	D₈	1	1	yes	characteristic
22	C₂×C₃₉₇	—	2	1	no	—
23	C₂×C₃₉₇	—	8	2	no	—
24	C₂×C₃₉₇	#102	1	1	yes	characteristic
25	C₃₉₇	#361	1	1	yes	characteristic, direct product factor, Sylow
26	#361	C₃₉₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
27	C₂×D₈	C₂×C₃₉₇	1	1	yes	characteristic
28	M₃₂	C₂×C₃₉₇	1	1	yes	characteristic, complemented
29	#108	C₂×C₃₉₇	1	1	yes	characteristic, complemented
30	C₂×D₄	—	2	1	no	—
31	D₈	—	2	1	no	—
32	D₈	C₄×C₃₉₇	1	2	yes	—
33	M₁₆	—	2	1	no	—
34	C₂×C₈	C₂²×C₃₉₇	1	1	yes	characteristic
35	C₁₆	—	2	1	no	—
36	C₂³	—	4	1	no	—
37	D₄	—	2	2	no	—
38	D₄	—	4	1	no	—
39	C₂×C₄	D₄×C₃₉₇	1	1	yes	characteristic
40	C₈	—	4	1	no	—
41	C₈	C₂×C₄×C₃₉₇	1	1	yes	characteristic
42	C₈	D₄×C₃₉₇	1	1	yes	characteristic
43	C₂²	—	4	2	no	—
44	C₂²	—	8	2	no	—
45	C₂²	SD₁₆×C₃₉₇	1	1	yes	characteristic
46	C₄	C₂²⋊C₄×C₃₉₇	1	1	yes	characteristic
47	C₄	D₈×C₃₉₇	1	1	yes	characteristic
48	C₂	—	2	1	no	—
49	C₂	—	8	2	no	—
50	C₂	#102×C₃₉₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃₉₇	#102
commutator	C₈	C₂×C₄×C₃₉₇
Frattini, cosocle	C₂×C₈	C₂²×C₃₉₇
prime radical	C₂×D₈×C₃₉₇	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃₉₇ ◁ C₂×C₄×C₃₉₇ ◁ C₂×C₈×C₃₉₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. M₃₂×C₃₉₇	C₂	semidirect
3. #108×C₃₉₇	C₂	semidirect
25. C₃₉₇	#361	direct (N × H)
26. #361	C₃₉₇	direct (N × H)
28. M₃₂	C₂×C₃₉₇	semidirect
29. #108	C₂×C₃₉₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₈×C₃₉₇	2
M₃₂×C₃₉₇	2
#108×C₃₉₇	2
#361	397

Subgroups — #361×C397 #38762015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #361×C₃₉₇ #38762015