Subgroups — #38740908

Order 25216.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20263232	C₂	1	2	yes	maximal
2	C₄×C₁₆×C₁₉₇	C₂	1	1	yes	maximal, characteristic
3	#20263232	—	2	2	no	—
4	C₂×C₁₆×C₁₉₇	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₁₉₇	C₂²	1	1	yes	characteristic
6	C₄×C₈×C₁₉₇	C₄	1	1	yes	characteristic
7	C₂×C₈×C₁₉₇	C₈	1	1	yes	characteristic
8	C₂×C₈×C₁₉₇	C₂×C₄	1	1	yes	characteristic
9	C₄²×C₁₉₇	C₈	1	1	yes	characteristic
10	C₁₆×C₁₉₇	—	2	1	no	—
11	C₁₆×C₁₉₇	D₄	1	1	yes	characteristic
12	C₁₆×C₁₉₇	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₁₉₇	C₁₆	1	1	yes	characteristic
14	C₂×C₄×C₁₉₇	C₁₆	1	1	yes	characteristic
15	C₂×C₄×C₁₉₇	C₂×C₈	1	1	yes	characteristic
16	C₈×C₁₉₇	—	2	1	no	—
17	C₈×C₁₉₇	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₁₉₇	M₁₆	1	1	yes	characteristic
19	C₂²×C₁₉₇	C₂×C₁₆	1	1	yes	characteristic
20	C₄×C₁₉₇	—	2	1	no	—
21	C₄×C₁₉₇	C₃₂	1	2	yes	complemented
22	C₄×C₁₉₇	C₄⋊C₈	1	1	yes	characteristic
23	C₄×C₁₉₇	M₃₂	1	1	yes	characteristic
24	C₂×C₁₉₇	C₄⋊C₁₆	1	1	yes	characteristic
25	C₂×C₁₉₇	C₂×C₃₂	1	1	yes	characteristic
26	C₂×C₁₉₇	M₆₄	1	1	yes	characteristic
27	C₁₉₇	C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
28	C₄⋊C₃₂	—	197	1	no	maximal, Sylow
29	C₂×C₃₂	—	197	2	no	—
30	C₄×C₁₆	D₁₉₇	1	1	yes	characteristic
31	C₂×C₁₆	Dic₁₉₇	1	1	yes	characteristic
32	C₂×C₁₆	C₂×D₁₉₇	1	1	yes	characteristic
33	C₄×C₈	Dic₁₉₇	1	1	yes	characteristic
34	C₃₂	—	394	2	no	—
35	C₂×C₈	#13096802	1	1	yes	characteristic
36	C₂×C₈	C₂×Dic₁₉₇	1	1	yes	characteristic
37	C₄²	#13096802	1	1	yes	characteristic
38	C₁₆	—	2	1	no	—
39	C₁₆	D₇₈₈	1	1	yes	characteristic
40	C₁₆	Dic₃₉₄	1	1	yes	characteristic
41	C₂×C₄	#15691333	1	1	yes	characteristic
42	C₂×C₄	#15691333	1	1	yes	characteristic
43	C₂×C₄	C₂×#13096802	1	1	yes	characteristic
44	C₈	—	2	1	no	—
45	C₈	C₄⋊Dic₁₉₇	1	1	yes	characteristic
46	C₈	#15691342	1	1	yes	characteristic
47	C₂²	C₂×#15691333	1	1	yes	characteristic
48	C₄	—	2	1	no	—
49	C₄	#20263232	1	2	yes	complemented
50	C₄	C₄⋊#13096802	1	1	yes	characteristic
51	C₄	#20263266	1	1	yes	characteristic
52	C₂	C₄⋊#15691333	1	1	yes	characteristic
53	C₂	C₂×#20263232	1	1	yes	characteristic
54	C₂	#27160913	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂×D₁₉₇
commutator	C₂×C₁₉₇	C₂×C₃₂
Fitting	C₄×C₁₆×C₁₉₇	C₂
socle, prime radical	C₂²×C₁₉₇	C₂×C₁₆
cosocle	C₂×C₁₆×C₁₉₇	C₂²
hypercenter	C₄×C₁₆	D₁₉₇
hypocenter	C₁₉₇	C₄⋊C₃₂
LCS	G ▷ C₂×C₁₉₇ ▷ C₁₉₇
UCS	C₁ ◁ C₂×C₁₆ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
21. C₄×C₁₉₇	C₃₂	semidirect
27. C₁₉₇	C₄⋊C₃₂	semidirect
49. C₄	#20263232	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20263232	2
C₄×C₁₆×C₁₉₇	2
C₄⋊C₃₂	197