Subgroups — #38745006

Order 25216.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27160913	C₂	1	3	yes	maximal, complemented
2	C₂×#20263232	C₂	1	3	yes	maximal, complemented
3	#504×C₁₉₇	C₂	1	1	yes	maximal, characteristic
4	#20263232	C₂²	1	1	yes	characteristic
5	#20263232	C₂²	1	3	yes	—
6	#131×C₁₉₇	C₄	1	1	yes	characteristic
7	M₃₂×C₁₉₇	C₄	1	3	yes	—
8	C₂×C₁₆×C₁₉₇	C₂²	1	3	yes	—
9	#41×C₁₉₇	C₈	1	1	yes	characteristic
10	M₁₆×C₁₉₇	C₈	1	3	yes	—
11	C₂×C₈×C₁₉₇	C₂×C₄	1	3	yes	—
12	C₁₆×C₁₉₇	C₂×C₄	1	3	yes	—
13	C₁₆×C₁₉₇	C₂³	1	1	yes	characteristic
14	Q₈×C₁₉₇	C₁₆	1	1	yes	characteristic
15	D₄×C₁₉₇	C₁₆	1	3	yes	—
16	C₂×C₄×C₁₉₇	C₂×C₈	1	3	yes	—
17	C₈×C₁₉₇	C₂×C₈	1	3	yes	—
18	C₈×C₁₉₇	C₂²×C₄	1	1	yes	characteristic
19	C₂²×C₁₉₇	C₂×C₁₆	1	3	yes	—
20	C₄×C₁₉₇	C₂×C₁₆	1	3	yes	—
21	C₄×C₁₉₇	C₂²×C₈	1	1	yes	characteristic
22	C₂×C₁₉₇	—	2	3	no	—
23	C₂×C₁₉₇	C₂²×C₁₆	1	1	yes	characteristic
24	C₁₉₇	#2258	1	1	yes	characteristic, complemented, Sylow
25	#2258	—	197	1	no	maximal, Sylow
26	#504	D₁₉₇	1	1	yes	characteristic
27	M₆₄	—	197	3	no	—
28	C₂×C₃₂	—	197	3	no	—
29	#131	Dic₁₉₇	1	1	yes	characteristic
30	M₃₂	Dic₁₉₇	1	3	yes	—
31	C₂×C₁₆	C₂×D₁₉₇	1	3	yes	—
32	C₃₂	—	197	1	no	—
33	C₃₂	—	197	3	no	—
34	#41	#13096802	1	1	yes	characteristic
35	M₁₆	#13096802	1	3	yes	—
36	C₂×C₈	C₂×Dic₁₉₇	1	3	yes	—
37	C₁₆	C₂×Dic₁₉₇	1	3	yes	—
38	C₁₆	C₂²×D₁₉₇	1	1	yes	characteristic
39	Q₈	#15691333	1	1	yes	characteristic
40	D₄	#15691333	1	3	yes	—
41	C₂×C₄	C₂×#13096802	1	3	yes	—
42	C₈	C₂×#13096802	1	3	yes	—
43	C₈	C₂²×Dic₁₉₇	1	1	yes	characteristic
44	C₂²	C₂×#15691333	1	3	yes	—
45	C₄	C₂×#15691333	1	3	yes	—
46	C₄	C₂²×#13096802	1	1	yes	characteristic
47	C₂	—	2	3	no	—
48	C₂	C₂²×#15691333	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₁₆	C₂²×D₁₉₇
commutator, socle	C₂×C₁₉₇	C₂²×C₁₆
Fitting	#504×C₁₉₇	C₂
prime radical	#41×C₁₉₇	C₈
cosocle	C₁₆×C₁₉₇	C₂³
hypercenter	#504	D₁₉₇
hypocenter	C₁₉₇	#2258
LCS	G ▷ C₂×C₁₉₇ ▷ C₁₉₇
UCS	C₁ ◁ C₁₆ ◁ #504

Complements

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

N	H ≅ G/N	type
1. #27160913	C₂	semidirect
2. C₂×#20263232	C₂	semidirect
24. C₁₉₇	#2258	semidirect

Maximal subgroups

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

subgroup	index
#27160913	2
C₂×#20263232	2
#504×C₁₉₇	2
#2258	197