Subgroups — #38740751

Order 25216.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27160900	C₂	1	2	yes	maximal
2	#494×C₁₉₇	C₂	1	1	yes	maximal, characteristic
3	#20263266	—	2	2	no	—
4	C₂×Q₁₆×C₁₉₇	—	2	2	no	—
5	C₄⋊Q₈×C₁₉₇	C₄	1	2	yes	—
6	C₄×C₈×C₁₉₇	C₂²	1	1	yes	characteristic
7	#15691333	—	4	2	no	—
8	C₂×Q₈×C₁₉₇	—	2	2	no	—
9	Q₁₆×C₁₉₇	—	4	2	no	—
10	Q₁₆×C₁₉₇	—	4	2	no	—
11	C₂×C₈×C₁₉₇	D₄	1	2	yes	—
12	C₄⋊C₄×C₁₉₇	—	4	2	no	—
13	C₄²×C₁₉₇	C₂×C₄	1	1	yes	characteristic
14	Q₈×C₁₉₇	—	4	4	no	—
15	C₂×C₄×C₁₉₇	—	2	1	no	—
16	C₂×C₄×C₁₉₇	—	4	2	no	—
17	C₂×C₄×C₁₉₇	C₂²⋊C₄	1	1	yes	characteristic
18	C₈×C₁₉₇	D₈	1	2	yes	—
19	C₈×C₁₉₇	SD₁₆	1	2	yes	—
20	C₂²×C₁₉₇	#100	1	1	yes	characteristic
21	C₄×C₁₉₇	—	2	2	no	—
22	C₄×C₁₉₇	—	8	2	no	—
23	C₄×C₁₉₇	#102	1	2	yes	—
24	C₂×C₁₉₇	—	2	1	no	—
25	C₂×C₁₉₇	#331	1	1	yes	characteristic
26	C₁₉₇	#1358	1	1	yes	characteristic, complemented, Sylow
27	#1358	—	197	1	no	maximal, Sylow
28	#494	D₁₉₇	1	1	yes	characteristic
29	#364	—	197	2	no	—
30	C₂×Q₁₆	—	2	2	no	—
31	C₄⋊Q₈	Dic₁₉₇	1	2	yes	—
32	M₃₂	—	394	2	no	—
33	C₄×C₈	C₂×D₁₉₇	1	1	yes	characteristic
34	C₂×Q₈	—	2	2	no	—
35	Q₁₆	—	4	2	no	—
36	Q₁₆	—	4	2	no	—
37	C₂×C₈	C₂²⋊D₁₉₇	1	2	yes	—
38	C₄⋊C₄	—	4	2	no	—
39	C₄²	C₂×Dic₁₉₇	1	1	yes	characteristic
40	C₁₆	—	788	2	no	—
41	Q₈	—	4	4	no	—
42	C₂×C₄	—	2	1	no	—
43	C₂×C₄	—	4	2	no	—
44	C₂×C₄	C₂²⋊Dic₁₉₇	1	1	yes	characteristic
45	C₈	#15691343	1	2	yes	—
46	C₈	#15691346	1	2	yes	—
47	C₂²	#20263243	1	1	yes	characteristic
48	C₄	—	2	2	no	—
49	C₄	—	8	2	no	—
50	C₄	#20263247	1	2	yes	—
51	C₂	—	2	1	no	—
52	C₂	#27160823	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#27160823
commutator	C₄²×C₁₉₇	C₂×C₄
Frattini	C₄×C₈	C₂×D₁₉₇
Fitting	#494×C₁₉₇	C₂
socle	C₂×C₁₉₇	#331
prime radical	C₂²×C₁₉₇	#100
cosocle	C₄×C₈×C₁₉₇	C₂²
hypercenter	#494	D₁₉₇
hypocenter	C₁₉₇	#1358
LCS	G ▷ C₄²×C₁₉₇ ▷ C₂×C₄×C₁₉₇ ▷ C₂×C₁₉₇ ▷ C₁₉₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #494

Complements

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

N	H ≅ G/N	type
26. C₁₉₇	#1358	semidirect

Maximal subgroups

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

subgroup	index
#27160900	2
#494×C₁₉₇	2
#1358	197