Subgroups — #349×C₃₉₇ #38762003

Order 25408.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×C₃₉₇	C₂	1	1	yes	maximal, characteristic
2	M₃₂×C₃₉₇	C₂	1	2	yes	maximal, complemented
3	C₂²×C₄×C₃₉₇	C₄	1	1	yes	characteristic
4	M₁₆×C₃₉₇	—	2	2	no	—
5	C₂×C₈×C₃₉₇	C₄	1	1	yes	characteristic
6	C₂×C₈×C₃₉₇	C₂²	1	1	yes	characteristic
7	C₁₆×C₃₉₇	—	2	2	no	—
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	—	4	1	no	—
17	C₂²×C₃₉₇	C₂×C₈	1	1	yes	characteristic
18	C₄×C₃₉₇	—	2	1	no	—
19	C₄×C₃₉₇	C₂²⋊C₄	1	1	yes	characteristic
20	C₄×C₃₉₇	M₁₆	1	1	yes	characteristic
21	C₂×C₃₉₇	—	2	1	no	—
22	C₂×C₃₉₇	—	4	1	no	—
23	C₂×C₃₉₇	C₂²⋊C₈	1	1	yes	characteristic
24	C₃₉₇	#349	1	1	yes	characteristic, direct product factor, Sylow
25	#349	C₃₉₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
26	C₂×M₁₆	C₂×C₃₉₇	1	1	yes	characteristic
27	M₃₂	C₂×C₃₉₇	1	2	yes	complemented
28	C₂²×C₄	C₄×C₃₉₇	1	1	yes	characteristic
29	M₁₆	—	2	2	no	—
30	C₂×C₈	C₄×C₃₉₇	1	1	yes	characteristic
31	C₂×C₈	C₂²×C₃₉₇	1	1	yes	characteristic
32	C₁₆	—	2	2	no	—
33	C₂³	C₈×C₃₉₇	1	1	yes	characteristic
34	C₂×C₄	—	2	1	no	—
35	C₂×C₄	—	2	1	no	—
36	C₂×C₄	C₈×C₃₉₇	1	1	yes	characteristic
37	C₂×C₄	C₂×C₄×C₃₉₇	1	1	yes	characteristic
38	C₈	—	2	1	no	—
39	C₈	D₄×C₃₉₇	1	2	yes	—
40	C₂²	—	2	1	no	—
41	C₂²	—	4	1	no	—
42	C₂²	C₂×C₈×C₃₉₇	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	C₂²⋊C₄×C₃₉₇	1	1	yes	characteristic
45	C₄	M₁₆×C₃₉₇	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	4	1	no	—
48	C₂	C₂²⋊C₈×C₃₉₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₃₉₇	C₂²⋊C₄
commutator	C₂²	C₂×C₈×C₃₉₇
Frattini, cosocle	C₂×C₈	C₂²×C₃₉₇
socle	C₂×C₃₉₇	C₂²⋊C₈
prime radical	C₂³×C₃₉₇	C₈
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ 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
24. C₃₉₇	#349	direct (N × H)
25. #349	C₃₉₇	direct (N × H)
27. M₃₂	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×M₁₆×C₃₉₇	2
M₃₂×C₃₉₇	2
#349	397

Subgroups — #349×C397 #38762003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #349×C₃₉₇ #38762003