Subgroups — Q₈⋊C₁₆×C₁₉₇ #38738271

Order 25216.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×Q₈×C₁₉₇	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₁₆×C₁₉₇	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₆×C₁₉₇	C₂	1	1	yes	maximal, characteristic
4	C₄×Q₈×C₁₉₇	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₁₉₇	—	2	1	no	—
6	C₂×C₁₆×C₁₉₇	—	2	1	no	—
7	C₄⋊C₈×C₁₉₇	—	2	1	no	—
8	C₄⋊C₈×C₁₉₇	C₄	1	1	yes	characteristic
9	C₄×C₈×C₁₉₇	—	2	1	no	—
10	C₄×C₈×C₁₉₇	C₂²	1	1	yes	characteristic
11	C₂×Q₈×C₁₉₇	C₈	1	1	yes	characteristic
12	C₂×C₈×C₁₉₇	—	2	1	no	—
13	C₂×C₈×C₁₉₇	D₄	1	1	yes	characteristic
14	C₂×C₈×C₁₉₇	D₄	1	1	yes	characteristic
15	C₄⋊C₄×C₁₉₇	—	2	1	no	—
16	C₄⋊C₄×C₁₉₇	C₈	1	1	yes	characteristic
17	C₄²×C₁₉₇	—	2	1	no	—
18	C₄²×C₁₉₇	C₂×C₄	1	1	yes	characteristic
19	C₁₆×C₁₉₇	—	2	2	no	—
20	C₁₆×C₁₉₇	—	4	1	no	—
21	Q₈×C₁₉₇	—	2	1	no	—
22	Q₈×C₁₉₇	C₁₆	1	2	yes	complemented
23	C₂×C₄×C₁₉₇	—	2	1	no	—
24	C₂×C₄×C₁₉₇	—	2	1	no	—
25	C₂×C₄×C₁₉₇	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₁₉₇	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₁₉₇	M₁₆	1	1	yes	characteristic
28	C₈×C₁₉₇	—	2	1	no	—
29	C₈×C₁₉₇	—	4	1	no	—
30	C₈×C₁₉₇	SD₁₆	1	1	yes	characteristic
31	C₈×C₁₉₇	Q₁₆	1	1	yes	characteristic
32	C₂²×C₁₉₇	C₂²⋊C₈	1	1	yes	characteristic
33	C₄×C₁₉₇	—	2	2	no	—
34	C₄×C₁₉₇	—	2	1	no	—
35	C₄×C₁₉₇	—	4	1	no	—
36	C₄×C₁₉₇	#103	1	1	yes	characteristic
37	C₄×C₁₉₇	#104	1	1	yes	characteristic
38	C₄×C₁₉₇	C₂×C₁₆	1	1	yes	characteristic
39	C₄×C₁₉₇	M₃₂	1	1	yes	characteristic
40	C₂×C₁₉₇	Q₈⋊C₈	1	1	yes	characteristic
41	C₂×C₁₉₇	C₂²⋊C₁₆	1	1	yes	characteristic
42	C₂×C₁₉₇	#350	1	1	yes	characteristic
43	C₁₉₇	Q₈⋊C₁₆	1	1	yes	characteristic, direct product factor, Sylow
44	Q₈⋊C₁₆	C₁₉₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₈×Q₈	C₂×C₁₉₇	1	1	yes	characteristic
46	C₄⋊C₁₆	C₂×C₁₉₇	1	1	yes	characteristic
47	C₄×C₁₆	C₂×C₁₉₇	1	1	yes	characteristic
48	C₄×Q₈	C₄×C₁₉₇	1	1	yes	characteristic
49	C₂×C₁₆	—	2	1	no	—
50	C₂×C₁₆	—	2	1	no	—
51	C₄⋊C₈	—	2	1	no	—
52	C₄⋊C₈	C₄×C₁₉₇	1	1	yes	characteristic
53	C₄×C₈	—	2	1	no	—
54	C₄×C₈	C₂²×C₁₉₇	1	1	yes	characteristic
55	C₂×Q₈	C₈×C₁₉₇	1	1	yes	characteristic
56	C₂×C₈	—	2	1	no	—
57	C₂×C₈	D₄×C₁₉₇	1	1	yes	characteristic
58	C₂×C₈	D₄×C₁₉₇	1	1	yes	characteristic
59	C₄⋊C₄	—	2	1	no	—
60	C₄⋊C₄	C₈×C₁₉₇	1	1	yes	characteristic
61	C₄²	—	2	1	no	—
62	C₄²	C₂×C₄×C₁₉₇	1	1	yes	characteristic
63	C₁₆	—	2	2	no	—
64	C₁₆	—	4	1	no	—
65	Q₈	—	2	1	no	—
66	Q₈	C₁₆×C₁₉₇	1	2	yes	complemented
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	C₂²⋊C₄×C₁₉₇	1	1	yes	characteristic
70	C₂×C₄	C₂×C₈×C₁₉₇	1	1	yes	characteristic
71	C₂×C₄	M₁₆×C₁₉₇	1	1	yes	characteristic
72	C₈	—	2	1	no	—
73	C₈	—	4	1	no	—
74	C₈	SD₁₆×C₁₉₇	1	1	yes	characteristic
75	C₈	Q₁₆×C₁₉₇	1	1	yes	characteristic
76	C₂²	C₂²⋊C₈×C₁₉₇	1	1	yes	characteristic
77	C₄	—	2	2	no	—
78	C₄	—	2	1	no	—
79	C₄	—	4	1	no	—
80	C₄	#103×C₁₉₇	1	1	yes	characteristic
81	C₄	#104×C₁₉₇	1	1	yes	characteristic
82	C₄	C₂×C₁₆×C₁₉₇	1	1	yes	characteristic
83	C₄	M₃₂×C₁₉₇	1	1	yes	characteristic
84	C₂	Q₈⋊C₈×C₁₉₇	1	1	yes	characteristic
85	C₂	C₂²⋊C₁₆×C₁₉₇	1	1	yes	characteristic
86	C₂	#350×C₁₉₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₉₇	D₄
commutator	C₄	C₂×C₁₆×C₁₉₇
Frattini, cosocle	C₄×C₈	C₂²×C₁₉₇
socle, prime radical	C₂²×C₁₉₇	C₂²⋊C₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₉₇ ◁ C₄×C₈×C₁₉₇ ◁ G

Complements

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

N	H ≅ G/N	type
22. Q₈×C₁₉₇	C₁₆	semidirect
43. C₁₉₇	Q₈⋊C₁₆	direct (N × H)
44. Q₈⋊C₁₆	C₁₉₇	direct (N × H)
66. Q₈	C₁₆×C₁₉₇	semidirect

Maximal subgroups

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

subgroup	index
C₈×Q₈×C₁₉₇	2
C₄⋊C₁₆×C₁₉₇	2
C₄×C₁₆×C₁₉₇	2
Q₈⋊C₁₆	197

Subgroups — Q8⋊C16×C197 #38738271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈⋊C₁₆×C₁₉₇ #38738271