Subgroups — #38740630

Order 25216.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#15691333	C₂	1	2	yes	maximal
2	C₈²×C₁₉₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#15691333	C₄	1	4	yes	—
4	C₄×C₈×C₁₉₇	C₄	1	1	yes	characteristic
5	C₄×C₈×C₁₉₇	C₄	1	1	yes	characteristic
6	C₄×C₈×C₁₉₇	C₂²	1	1	yes	characteristic
7	#15691333	—	2	4	no	—
8	C₂×C₈×C₁₉₇	C₈	1	2	yes	—
9	C₂×C₈×C₁₉₇	C₈	1	2	yes	—
10	C₂×C₈×C₁₉₇	C₂×C₄	1	2	yes	—
11	C₄²×C₁₉₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₁₉₇	C₄²	1	1	yes	characteristic
13	C₂×C₄×C₁₉₇	C₂×C₈	1	1	yes	characteristic
14	C₂×C₄×C₁₉₇	C₂×C₈	1	1	yes	characteristic
15	C₈×C₁₉₇	—	2	2	no	—
16	C₈×C₁₉₇	C₁₆	1	4	yes	complemented
17	C₈×C₁₉₇	M₁₆	1	4	yes	—
18	C₂²×C₁₉₇	C₄×C₈	1	1	yes	characteristic
19	C₄×C₁₉₇	#97	1	2	yes	—
20	C₄×C₁₉₇	C₂×C₁₆	1	2	yes	—
21	C₄×C₁₉₇	M₃₂	1	2	yes	—
22	C₂×C₁₉₇	#322	1	1	yes	characteristic
23	C₂×C₁₉₇	C₄×C₁₆	1	1	yes	characteristic
24	C₂×C₁₉₇	#346	1	1	yes	characteristic
25	C₁₉₇	#1312	1	1	yes	characteristic, complemented, Sylow
26	#1312	—	197	1	no	maximal, Sylow
27	C₄×C₁₆	—	197	2	no	—
28	C₈²	D₁₉₇	1	1	yes	characteristic
29	C₂×C₁₆	—	197	4	no	—
30	C₄×C₈	Dic₁₉₇	1	1	yes	characteristic
31	C₄×C₈	Dic₁₉₇	1	1	yes	characteristic
32	C₄×C₈	C₂×D₁₉₇	1	1	yes	characteristic
33	C₂×C₈	#13096802	1	2	yes	—
34	C₂×C₈	#13096802	1	2	yes	—
35	C₂×C₈	C₄×D₁₉₇	1	2	yes	—
36	C₄²	C₂×Dic₁₉₇	1	1	yes	characteristic
37	C₁₆	—	394	4	no	—
38	C₂×C₄	C₄×Dic₁₉₇	1	1	yes	characteristic
39	C₂×C₄	C₂×#13096802	1	1	yes	characteristic
40	C₂×C₄	C₂×#13096802	1	1	yes	characteristic
41	C₈	—	2	2	no	—
42	C₈	#15691333	1	4	yes	complemented
43	C₈	#15691341	1	4	yes	—
44	C₂²	C₄×#13096802	1	1	yes	characteristic
45	C₄	#20263236	1	2	yes	—
46	C₄	C₂×#15691333	1	2	yes	—
47	C₄	#20263266	1	2	yes	—
48	C₂	#27160800	1	1	yes	characteristic
49	C₂	C₄×#15691333	1	1	yes	characteristic
50	C₂	#27160855	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄×C₈	C₂×D₁₉₇
commutator	C₂×C₁₉₇	C₄×C₁₆
Fitting	C₈²×C₁₉₇	C₂
socle, prime radical	C₂²×C₁₉₇	C₄×C₈
cosocle	C₄×C₈×C₁₉₇	C₂²
hypercenter	C₈²	D₁₉₇
hypocenter	C₁₉₇	#1312
LCS	G ▷ C₂×C₁₉₇ ▷ C₁₉₇
UCS	C₁ ◁ C₄×C₈ ◁ C₈²

Complements

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

N	H ≅ G/N	type
16. C₈×C₁₉₇	C₁₆	semidirect
25. C₁₉₇	#1312	semidirect
42. C₈	#15691333	semidirect

Maximal subgroups

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

subgroup	index
C₄×#15691333	2
C₈²×C₁₉₇	2
#1312	197