Subgroups — #362×C₃₉₇ #38762016

Order 25408.

54 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	M₃₂×C₃₉₇	C₂	1	1	yes	maximal, characteristic
3	#108×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	—
7	M₁₆×C₃₉₇	—	2	1	no	—
8	C₂×C₈×C₃₉₇	C₂²	1	1	yes	characteristic
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	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	SD₁₆	1	1	yes	characteristic
18	C₄×C₃₉₇	—	4	2	no	—
19	C₄×C₃₉₇	C₂²⋊C₄	1	1	yes	characteristic
20	C₄×C₃₉₇	D₈	1	1	yes	characteristic
21	C₂×C₃₉₇	—	2	1	no	—
22	C₂×C₃₉₇	#102	1	1	yes	characteristic
23	C₃₉₇	#362	1	1	yes	characteristic, direct product factor, Sylow
24	#362	C₃₉₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂×Q₁₆	C₂×C₃₉₇	1	1	yes	characteristic
26	M₃₂	C₂×C₃₉₇	1	1	yes	characteristic
27	#108	C₂×C₃₉₇	1	1	yes	characteristic
28	C₂×Q₈	—	2	1	no	—
29	Q₁₆	—	2	1	no	—
30	Q₁₆	C₄×C₃₉₇	1	2	yes	—
31	M₁₆	—	2	1	no	—
32	C₂×C₈	C₂²×C₃₉₇	1	1	yes	characteristic
33	C₁₆	—	2	1	no	—
34	Q₈	—	2	2	no	—
35	Q₈	—	4	1	no	—
36	C₂×C₄	—	4	1	no	—
37	C₂×C₄	D₄×C₃₉₇	1	1	yes	characteristic
38	C₈	—	4	1	no	—
39	C₈	C₂×C₄×C₃₉₇	1	1	yes	characteristic
40	C₈	D₄×C₃₉₇	1	1	yes	characteristic
41	C₂²	SD₁₆×C₃₉₇	1	1	yes	characteristic
42	C₄	—	4	2	no	—
43	C₄	C₂²⋊C₄×C₃₉₇	1	1	yes	characteristic
44	C₄	D₈×C₃₉₇	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	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	C₂²×C₃₉₇	SD₁₆
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
23. C₃₉₇	#362	direct (N × H)
24. #362	C₃₉₇	direct (N × H)

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
M₃₂×C₃₉₇	2
#108×C₃₉₇	2
#362	397

Subgroups — #362×C397 #38762016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #362×C₃₉₇ #38762016