Subgroups — #358×C₃₉₇ #38762012

Order 25408.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×C₃₉₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₆×C₃₉₇	C₂	1	1	yes	maximal, characteristic
3	#107×C₃₉₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈×C₃₉₇	—	2	1	no	—
5	Q₁₆×C₃₉₇	—	2	1	no	—
6	Q₁₆×C₃₉₇	C₄	1	2	yes	complemented
7	C₂×C₈×C₃₉₇	C₂²	1	1	yes	characteristic
8	C₄⋊C₄×C₃₉₇	—	2	1	no	—
9	C₁₆×C₃₉₇	—	2	1	no	—
10	Q₈×C₃₉₇	—	2	2	no	—
11	Q₈×C₃₉₇	—	4	1	no	—
12	C₂×C₄×C₃₉₇	—	4	1	no	—
13	C₂×C₄×C₃₉₇	—	4	1	no	—
14	C₂×C₄×C₃₉₇	D₄	1	1	yes	characteristic
15	C₈×C₃₉₇	C₂×C₄	1	1	yes	characteristic
16	C₈×C₃₉₇	D₄	1	1	yes	characteristic
17	C₂²×C₃₉₇	D₈	1	1	yes	characteristic
18	C₄×C₃₉₇	—	4	2	no	—
19	C₄×C₃₉₇	—	8	1	no	—
20	C₄×C₃₉₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₃₉₇	SD₁₆	1	1	yes	characteristic
22	C₂×C₃₉₇	#102	1	1	yes	characteristic
23	C₂×C₃₉₇	SD₃₂	1	1	yes	characteristic
24	C₂×C₃₉₇	Q₃₂	1	1	yes	characteristic
25	C₃₉₇	#358	1	1	yes	characteristic, direct product factor, Sylow
26	#358	C₃₉₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
27	C₂×Q₁₆	C₂×C₃₉₇	1	1	yes	characteristic
28	C₂×C₁₆	C₂×C₃₉₇	1	1	yes	characteristic
29	#107	C₂×C₃₉₇	1	1	yes	characteristic
30	C₂×Q₈	—	2	1	no	—
31	Q₁₆	—	2	1	no	—
32	Q₁₆	C₄×C₃₉₇	1	2	yes	complemented
33	C₂×C₈	C₂²×C₃₉₇	1	1	yes	characteristic
34	C₄⋊C₄	—	2	1	no	—
35	C₁₆	—	2	1	no	—
36	Q₈	—	2	2	no	—
37	Q₈	—	4	1	no	—
38	C₂×C₄	—	4	1	no	—
39	C₂×C₄	—	4	1	no	—
40	C₂×C₄	D₄×C₃₉₇	1	1	yes	characteristic
41	C₈	C₂×C₄×C₃₉₇	1	1	yes	characteristic
42	C₈	D₄×C₃₉₇	1	1	yes	characteristic
43	C₂²	D₈×C₃₉₇	1	1	yes	characteristic
44	C₄	—	4	2	no	—
45	C₄	—	8	1	no	—
46	C₄	C₂²⋊C₄×C₃₉₇	1	1	yes	characteristic
47	C₄	SD₁₆×C₃₉₇	1	1	yes	characteristic
48	C₂	#102×C₃₉₇	1	1	yes	characteristic
49	C₂	SD₃₂×C₃₉₇	1	1	yes	characteristic
50	C₂	Q₃₂×C₃₉₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
6. Q₁₆×C₃₉₇	C₄	semidirect
25. C₃₉₇	#358	direct (N × H)
26. #358	C₃₉₇	direct (N × H)
32. Q₁₆	C₄×C₃₉₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₁₆×C₃₉₇	2
C₂×C₁₆×C₃₉₇	2
#107×C₃₉₇	2
#358	397

Subgroups — #358×C397 #38762012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #358×C₃₉₇ #38762012