Subgroups — Q₆₄×D₁₉₇ #38745015

Order 25216.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₃₂×D₁₉₇	C₂	1	2	yes	maximal
2	Dic₃₁₅₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#27160919	C₂	1	2	yes	maximal, complemented
4	C₃₂×D₁₉₇	C₂	1	1	yes	maximal, characteristic
5	Q₆₄×C₁₉₇	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₁₆×D₁₉₇	—	2	2	no	—
7	Dic₁₅₇₆	C₂²	1	2	yes	—
8	#20263272	—	2	2	no	—
9	C₁₆×D₁₉₇	C₂²	1	1	yes	characteristic
10	#20263232	C₂²	1	1	yes	characteristic
11	Q₃₂×C₁₉₇	C₂²	1	2	yes	—
12	C₃₂×C₁₉₇	C₂²	1	1	yes	characteristic
13	Q₈×D₁₉₇	—	4	2	no	—
14	Dic₇₈₈	—	2	2	no	—
15	#15691348	—	4	2	no	—
16	C₈×D₁₉₇	D₄	1	1	yes	characteristic
17	#15691333	D₄	1	1	yes	characteristic
18	Q₁₆×C₁₉₇	—	2	2	no	—
19	C₁₆×C₁₉₇	C₂³	1	1	yes	characteristic
20	Dic₃₉₄	—	4	2	no	—
21	Dic₃₉₄	—	8	2	no	—
22	C₄×D₁₉₇	—	8	2	no	—
23	C₄×D₁₉₇	D₈	1	1	yes	characteristic
24	#13096802	D₈	1	1	yes	characteristic
25	Q₈×C₁₉₇	—	4	2	no	—
26	C₈×C₁₉₇	C₂×D₄	1	1	yes	characteristic
27	C₂×D₁₉₇	D₁₆	1	1	yes	characteristic
28	C₄×C₁₉₇	—	8	2	no	—
29	C₄×C₁₉₇	C₂×D₈	1	1	yes	characteristic
30	Dic₁₉₇	—	8	2	no	—
31	Dic₁₉₇	D₁₆	1	1	yes	characteristic
32	C₂×C₁₉₇	C₂×D₁₆	1	1	yes	characteristic
33	D₁₉₇	Q₆₄	1	2	yes	direct product factor
34	C₁₉₇	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
35	C₂×Q₆₄	—	197	1	no	maximal, Sylow
36	C₂×Q₃₂	—	197	2	no	—
37	Q₆₄	—	197	2	no	—
38	Q₆₄	—	197	1	no	—
39	Q₆₄	D₁₉₇	1	1	yes	characteristic, direct product factor
40	C₂×C₃₂	—	197	1	no	—
41	C₂×Q₁₆	—	394	2	no	—
42	Q₃₂	—	394	2	no	—
43	Q₃₂	—	197	2	no	—
44	Q₃₂	C₂×D₁₉₇	1	2	yes	—
45	C₂×C₁₆	—	197	1	no	—
46	C₃₂	—	197	1	no	—
47	C₃₂	C₂×D₁₉₇	1	1	yes	characteristic
48	C₂×Q₈	—	788	2	no	—
49	Q₁₆	—	2	2	no	—
50	Q₁₆	—	788	2	no	—
51	Q₁₆	—	394	2	no	—
52	C₂×C₈	—	197	1	no	—
53	C₁₆	—	197	1	no	—
54	C₁₆	C₂²×D₁₉₇	1	1	yes	characteristic
55	Q₈	—	4	2	no	—
56	Q₈	—	788	2	no	—
57	Q₈	—	1576	2	no	—
58	C₂×C₄	—	1576	2	no	—
59	C₂×C₄	—	197	1	no	—
60	C₈	—	197	1	no	—
61	C₈	D₄×D₁₉₇	1	1	yes	characteristic
62	C₂²	—	197	1	no	—
63	C₄	—	8	2	no	—
64	C₄	—	1576	2	no	—
65	C₄	—	197	1	no	—
66	C₄	D₈×D₁₉₇	1	1	yes	characteristic
67	C₂	—	197	2	no	—
68	C₂	D₁₆×D₁₉₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₆×D₁₉₇
commutator, cosocle	C₁₆×C₁₉₇	C₂³
Frattini	C₁₆	C₂²×D₁₉₇
Fitting	Q₆₄×C₁₉₇	C₂
socle	C₂×C₁₉₇	C₂×D₁₆
prime radical	C₂×D₁₉₇	D₁₆
hypercenter	Q₆₄	D₁₉₇
hypocenter	C₁₉₇	C₂×Q₆₄
LCS	G ▷ C₁₆×C₁₉₇ ▷ C₈×C₁₉₇ ▷ C₄×C₁₉₇ ▷ C₂×C₁₉₇ ▷ C₁₉₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₆₄

Complements

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

N	H ≅ G/N	type
2. Dic₃₁₅₂	C₂	semidirect
3. #27160919	C₂	semidirect
5. Q₆₄×C₁₉₇	C₂	semidirect
33. D₁₉₇	Q₆₄	direct (N × H)
34. C₁₉₇	C₂×Q₆₄	semidirect
39. Q₆₄	D₁₉₇	direct (N × H)

Maximal subgroups

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

subgroup	index
Q₃₂×D₁₉₇	2
Dic₃₁₅₂	2
#27160919	2
C₃₂×D₁₉₇	2
Q₆₄×C₁₉₇	2
C₂×Q₆₄	197

Subgroups — Q64×D197 #38745015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₆₄×D₁₉₇ #38745015