Subgroups — #38740783

Order 25216.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#15691333	C₂	1	1	yes	maximal, characteristic
2	#27160832	C₂	1	1	yes	maximal, characteristic
3	#335×C₁₉₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#15691333	C₄	1	1	yes	characteristic
5	C₂×#15691333	C₄	1	1	yes	characteristic
6	C₄⋊#13096802	—	2	1	no	—
7	C₄⋊C₈×C₁₉₇	—	2	1	no	—
8	C₄×C₈×C₁₉₇	C₂²	1	1	yes	characteristic
9	C₂×#13096802	—	4	1	no	—
10	#15691333	—	2	1	no	—
11	#15691333	C₈	1	2	yes	complemented
12	C₂×C₈×C₁₉₇	—	4	1	no	—
13	C₂×C₈×C₁₉₇	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₁₉₇	Q₈	1	1	yes	characteristic
15	C₄²×C₁₉₇	D₄	1	1	yes	characteristic
16	#13096802	—	8	1	no	—
17	C₂×C₄×C₁₉₇	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₄×C₁₉₇	D₈	1	1	yes	characteristic
19	C₂×C₄×C₁₉₇	Q₁₆	1	1	yes	characteristic
20	C₈×C₁₉₇	—	2	1	no	—
21	C₈×C₁₉₇	—	8	1	no	—
22	C₈×C₁₉₇	C₂×C₈	1	1	yes	characteristic
23	C₈×C₁₉₇	M₁₆	1	1	yes	characteristic
24	C₂²×C₁₉₇	#107	1	1	yes	characteristic
25	C₄×C₁₉₇	—	2	1	no	—
26	C₄×C₁₉₇	C₄⋊C₈	1	1	yes	characteristic
27	C₄×C₁₉₇	#108	1	1	yes	characteristic
28	C₄×C₁₉₇	D₁₆	1	1	yes	characteristic
29	C₄×C₁₉₇	Q₃₂	1	1	yes	characteristic
30	C₂×C₁₉₇	#335	1	1	yes	characteristic
31	C₂×C₁₉₇	#366	1	1	yes	characteristic
32	C₂×C₁₉₇	#368	1	1	yes	characteristic
33	C₁₉₇	#1371	1	1	yes	characteristic, complemented, Sylow
34	#1371	—	197	1	no	maximal, Sylow
35	C₄×C₁₆	—	197	1	no	—
36	#335	—	197	1	no	—
37	#335	D₁₉₇	1	1	yes	characteristic
38	C₂×C₁₆	—	197	1	no	—
39	C₂×C₁₆	—	197	1	no	—
40	C₄⋊C₈	—	2	1	no	—
41	C₄⋊C₈	—	394	1	no	—
42	C₄×C₈	C₂×D₁₉₇	1	1	yes	characteristic
43	C₂×C₈	—	4	1	no	—
44	C₂×C₈	—	788	1	no	—
45	C₂×C₈	C₄×D₁₉₇	1	1	yes	characteristic
46	C₂×C₈	Dic₃₉₄	1	1	yes	characteristic
47	C₄²	C₂²⋊D₁₉₇	1	1	yes	characteristic
48	C₁₆	—	394	1	no	—
49	C₁₆	—	197	2	no	—
50	C₂×C₄	#15691337	1	1	yes	characteristic
51	C₂×C₄	#15691343	1	1	yes	characteristic
52	C₂×C₄	#15691348	1	1	yes	characteristic
53	C₈	—	2	1	no	—
54	C₈	—	8	1	no	—
55	C₈	—	1576	1	no	—
56	C₈	C₈×D₁₉₇	1	1	yes	characteristic
57	C₈	#15691341	1	1	yes	characteristic
58	C₂²	#20263259	1	1	yes	characteristic
59	C₄	—	2	1	no	—
60	C₄	#20263255	1	1	yes	characteristic
61	C₄	#20263261	1	1	yes	characteristic
62	C₄	#20263267	1	1	yes	characteristic
63	C₄	#20263272	1	1	yes	characteristic
64	C₂	#27160831	1	1	yes	characteristic
65	C₂	#27160904	1	1	yes	characteristic
66	C₂	#27160908	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#15691343
commutator	C₈×C₁₉₇	C₂×C₈
Frattini	C₄×C₈	C₂×D₁₉₇
Fitting	#335×C₁₉₇	C₂
socle, prime radical	C₂²×C₁₉₇	#107
cosocle	C₄×C₈×C₁₉₇	C₂²
hypercenter	#335	D₁₉₇
hypocenter	C₁₉₇	#1371
LCS	G ▷ C₈×C₁₉₇ ▷ C₄×C₁₉₇ ▷ C₂×C₁₉₇ ▷ C₁₉₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ #335

Complements

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

N	H ≅ G/N	type
11. #15691333	C₈	semidirect
33. C₁₉₇	#1371	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
#27160832	2
#335×C₁₉₇	2
#1371	197