Subgroups — #38745005

Order 25216.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27161495	C₂	1	1	yes	maximal, characteristic
2	#27160913	C₂	1	1	yes	maximal, characteristic, complemented
3	#27160912	C₂	1	2	yes	maximal, complemented
4	C₃₂×D₁₉₇	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₂×C₁₉₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#20263332	C₄	1	1	yes	characteristic
7	#20263266	C₄	1	1	yes	characteristic
8	#20263265	C₄	1	2	yes	—
9	C₁₆×D₁₉₇	C₂²	1	2	yes	—
10	#20263232	C₂²	1	2	yes	—
11	C₂×C₁₆×C₁₉₇	C₂²	1	1	yes	characteristic
12	C₃₂×C₁₉₇	C₂²	1	1	yes	characteristic
13	C₃₂×C₁₉₇	C₂²	1	1	yes	characteristic
14	#15691358	C₈	1	1	yes	characteristic
15	#15691342	C₈	1	1	yes	characteristic
16	#15691341	C₈	1	2	yes	—
17	C₈×D₁₉₇	C₂×C₄	1	2	yes	—
18	#15691333	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₁₉₇	C₂×C₄	1	1	yes	characteristic
20	C₁₆×C₁₉₇	C₂×C₄	1	1	yes	characteristic
21	C₁₆×C₁₉₇	C₂³	1	1	yes	characteristic
22	Dic₃₉₄	C₁₆	1	1	yes	characteristic
23	D₇₈₈	C₁₆	1	1	yes	characteristic
24	C₂²⋊D₁₉₇	C₁₆	1	2	yes	—
25	C₄×D₁₉₇	C₂×C₈	1	2	yes	—
26	#13096802	C₂×C₈	1	2	yes	—
27	C₂×C₄×C₁₉₇	C₂×C₈	1	1	yes	characteristic
28	C₈×C₁₉₇	C₂×C₈	1	1	yes	characteristic
29	C₈×C₁₉₇	C₂²×C₄	1	1	yes	characteristic
30	C₂²×C₁₉₇	C₂×C₁₆	1	1	yes	characteristic
31	C₂×D₁₉₇	C₂×C₁₆	1	2	yes	—
32	C₄×C₁₉₇	C₂×C₁₆	1	1	yes	characteristic
33	C₄×C₁₉₇	C₂²×C₈	1	1	yes	characteristic
34	Dic₁₉₇	C₂×C₁₆	1	2	yes	—
35	C₂×C₁₉₇	—	2	1	no	—
36	C₂×C₁₉₇	C₂²×C₁₆	1	1	yes	characteristic
37	D₁₉₇	—	2	2	no	—
38	C₁₉₇	#2258	1	1	yes	characteristic, complemented, Sylow
39	#2258	—	197	1	no	maximal, Sylow
40	#504	—	197	1	no	—
41	M₆₄	—	197	1	no	—
42	M₆₄	—	197	2	no	—
43	C₂×C₃₂	—	197	2	no	—
44	C₂×C₃₂	D₁₉₇	1	1	yes	characteristic, complemented
45	#131	—	197	1	no	—
46	M₃₂	—	197	1	no	—
47	M₃₂	—	197	2	no	—
48	C₂×C₁₆	—	197	2	no	—
49	C₂×C₁₆	C₂×D₁₉₇	1	1	yes	characteristic
50	C₃₂	—	197	2	no	—
51	C₃₂	C₂×D₁₉₇	1	1	yes	characteristic
52	C₃₂	C₂×D₁₉₇	1	1	yes	characteristic
53	#41	—	197	1	no	—
54	M₁₆	—	197	1	no	—
55	M₁₆	—	197	2	no	—
56	C₂×C₈	—	197	2	no	—
57	C₂×C₈	C₄×D₁₉₇	1	1	yes	characteristic
58	C₁₆	—	197	2	no	—
59	C₁₆	C₄×D₁₉₇	1	1	yes	characteristic
60	C₁₆	C₂²×D₁₉₇	1	1	yes	characteristic
61	Q₈	—	197	1	no	—
62	D₄	—	197	2	no	—
63	D₄	—	197	1	no	—
64	C₂×C₄	—	197	2	no	—
65	C₂×C₄	C₈×D₁₉₇	1	1	yes	characteristic
66	C₈	—	197	2	no	—
67	C₈	C₈×D₁₉₇	1	1	yes	characteristic
68	C₈	C₂×C₄×D₁₉₇	1	1	yes	characteristic
69	C₂²	—	197	2	no	—
70	C₂²	C₁₆×D₁₉₇	1	1	yes	characteristic
71	C₄	—	197	2	no	—
72	C₄	C₁₆×D₁₉₇	1	1	yes	characteristic
73	C₄	C₂×C₈×D₁₉₇	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	394	2	no	—
76	C₂	C₂×C₁₆×D₁₉₇	1	1	yes	characteristic

	subgroup	G/H
center	C₃₂	C₂×D₁₉₇
commutator, socle	C₂×C₁₉₇	C₂²×C₁₆
Frattini	C₁₆	C₂²×D₁₉₇
Fitting	C₂×C₃₂×C₁₉₇	C₂
prime radical	#15691358	C₈
cosocle	C₁₆×C₁₉₇	C₂³
hypercenter	C₂×C₃₂	D₁₉₇
hypocenter	C₁₉₇	#2258
LCS	G ▷ C₂×C₁₉₇ ▷ C₁₉₇
UCS	C₁ ◁ C₃₂ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. #27160913	C₂	semidirect
3. #27160912	C₂	semidirect
4. C₃₂×D₁₉₇	C₂	semidirect
5. C₂×C₃₂×C₁₉₇	C₂	semidirect
38. C₁₉₇	#2258	semidirect
44. C₂×C₃₂	D₁₉₇	semidirect

Maximal subgroups

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

subgroup	index
#27161495	2
#27160913	2
#27160912	2
C₃₂×D₁₉₇	2
C₂×C₃₂×C₁₉₇	2
#2258	197