Subgroups — #38766888

Order 25472.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27164398	C₂	1	1	yes	maximal, characteristic
2	#27163839	C₂	1	1	yes	maximal, characteristic
3	#364×C₁₉₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₇₉₆	—	2	1	no	—
5	C₂×Dic₇₉₆	—	2	1	no	—
6	#20263955	C₄	1	2	yes	—
7	#20263895	—	2	1	no	—
8	M₃₂×C₁₉₉	—	2	1	no	—
9	C₄×C₈×C₁₉₉	C₂²	1	1	yes	characteristic
10	C₂×Dic₃₉₈	—	2	2	no	—
11	Dic₇₉₆	—	4	1	no	—
12	Dic₇₉₆	—	4	1	no	—
13	Dic₇₉₆	—	4	1	no	—
14	Dic₇₉₆	—	4	1	no	—
15	C₄⋊Dic₁₉₉	—	4	2	no	—
16	C₁₉₉⋊C₁₆	—	4	1	no	—
17	C₂×C₈×C₁₉₉	D₄	1	1	yes	characteristic
18	C₂×C₈×C₁₉₉	D₄	1	1	yes	characteristic
19	C₄²×C₁₉₉	C₂×C₄	1	1	yes	characteristic
20	C₁₆×C₁₉₉	—	4	1	no	—
21	Dic₃₉₈	—	4	2	no	—
22	Dic₃₉₈	—	4	2	no	—
23	C₂×Dic₁₉₉	—	4	2	no	—
24	C₂×C₄×C₁₉₉	—	2	1	no	—
25	C₂×C₄×C₁₉₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₁₉₉	D₈	1	1	yes	characteristic
27	C₈×C₁₉₉	D₈	1	1	yes	characteristic
28	C₈×C₁₉₉	SD₁₆	1	1	yes	characteristic
29	C₈×C₁₉₉	SD₁₆	1	1	yes	characteristic
30	C₂²×C₁₉₉	#100	1	1	yes	characteristic
31	C₄×C₁₉₉	—	2	2	no	—
32	C₄×C₁₉₉	#102	1	1	yes	characteristic
33	C₄×C₁₉₉	#102	1	1	yes	characteristic
34	Dic₁₉₉	—	8	2	no	—
35	C₂×C₁₉₉	—	2	1	no	—
36	C₂×C₁₉₉	#331	1	1	yes	characteristic
37	C₁₉₉	#1358	1	1	yes	characteristic, complemented, Sylow
38	#1358	—	199	1	no	maximal, Sylow
39	#494	—	199	1	no	—
40	#364	—	199	1	no	—
41	#364	D₁₉₉	1	1	yes	characteristic
42	C₂×Q₁₆	—	398	1	no	—
43	C₂×Q₁₆	—	398	1	no	—
44	C₄⋊Q₈	—	199	2	no	—
45	M₃₂	—	2	1	no	—
46	M₃₂	—	398	1	no	—
47	C₄×C₈	C₂×D₁₉₉	1	1	yes	characteristic
48	C₂×Q₈	—	398	2	no	—
49	Q₁₆	—	796	1	no	—
50	Q₁₆	—	796	1	no	—
51	Q₁₆	—	796	1	no	—
52	Q₁₆	—	796	1	no	—
53	C₂×C₈	C₂²⋊D₁₉₉	1	1	yes	characteristic
54	C₂×C₈	D₇₉₆	1	1	yes	characteristic
55	C₄⋊C₄	—	796	2	no	—
56	C₄²	C₄×D₁₉₉	1	1	yes	characteristic
57	C₁₆	—	4	1	no	—
58	C₁₆	—	796	1	no	—
59	Q₈	—	796	2	no	—
60	Q₈	—	796	2	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	796	2	no	—
63	C₂×C₄	(C₂×D₁₉₉)⋊C₄	1	1	yes	characteristic
64	C₈	#15691871	1	1	yes	characteristic
65	C₈	D₁₅₉₂	1	1	yes	characteristic
66	C₈	#15691873	1	1	yes	characteristic
67	C₈	#15691875	1	1	yes	characteristic
68	C₂²	#20263871	1	1	yes	characteristic
69	C₄	—	2	2	no	—
70	C₄	—	1592	2	no	—
71	C₄	#20263875	1	1	yes	characteristic
72	C₄	#20263877	1	1	yes	characteristic
73	C₂	—	2	1	no	—
74	C₂	#27163761	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#27163761
commutator	C₄²×C₁₉₉	C₂×C₄
Frattini	C₄×C₈	C₂×D₁₉₉
Fitting	#364×C₁₉₉	C₂
socle	C₂×C₁₉₉	#331
prime radical	C₂²×C₁₉₉	#100
cosocle	C₄×C₈×C₁₉₉	C₂²
hypercenter	#364	D₁₉₉
hypocenter	C₁₉₉	#1358
LCS	G ▷ C₄²×C₁₉₉ ▷ C₂×C₄×C₁₉₉ ▷ C₂×C₁₉₉ ▷ C₁₉₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
37. C₁₉₉	#1358	semidirect

Maximal subgroups

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

subgroup	index
#27164398	2
#27163839	2
#364×C₁₉₉	2
#1358	199