Subgroups — #38766886

Order 25472.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27164395	C₂	1	1	yes	maximal, characteristic
2	#27163839	C₂	1	1	yes	maximal, characteristic, complemented
3	#364×C₁₉₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₅₉₂	—	2	1	no	—
5	C₂×D₁₅₉₂	—	2	1	no	—
6	#20263952	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×D₇₉₆	—	2	2	no	—
11	C₂×D₇₉₆	—	4	2	no	—
12	D₁₅₉₂	—	4	1	no	—
13	D₁₅₉₂	—	4	1	no	—
14	D₁₅₉₂	—	4	1	no	—
15	D₁₅₉₂	—	4	1	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	C₂²×D₁₉₉	—	4	2	no	—
22	D₇₉₆	—	4	2	no	—
23	D₇₉₆	—	4	2	no	—
24	D₇₉₆	—	8	4	no	—
25	C₂×C₄×C₁₉₉	—	2	1	no	—
26	C₂×C₄×C₁₉₉	C₂²⋊C₄	1	1	yes	characteristic
27	C₈×C₁₉₉	D₈	1	1	yes	characteristic
28	C₈×C₁₉₉	D₈	1	1	yes	characteristic
29	C₈×C₁₉₉	SD₁₆	1	1	yes	characteristic
30	C₈×C₁₉₉	SD₁₆	1	1	yes	characteristic
31	C₂²×C₁₉₉	#100	1	1	yes	characteristic
32	C₂×D₁₉₉	—	8	4	no	—
33	C₂×D₁₉₉	—	8	2	no	—
34	C₄×C₁₉₉	—	2	2	no	—
35	C₄×C₁₉₉	#102	1	1	yes	characteristic
36	C₄×C₁₉₉	#102	1	1	yes	characteristic
37	C₂×C₁₉₉	—	2	1	no	—
38	C₂×C₁₉₉	#331	1	1	yes	characteristic
39	D₁₉₉	—	16	2	no	—
40	C₁₉₉	#1357	1	1	yes	characteristic, complemented, Sylow
41	#1357	—	199	1	no	maximal, Sylow
42	#493	—	199	1	no	—
43	#364	—	199	1	no	—
44	#364	D₁₉₉	1	1	yes	characteristic, complemented
45	C₂×D₈	—	398	1	no	—
46	C₂×D₈	—	398	1	no	—
47	#127	—	199	2	no	—
48	M₃₂	—	2	1	no	—
49	M₃₂	—	398	1	no	—
50	C₄×C₈	C₂×D₁₉₉	1	1	yes	characteristic
51	C₂×D₄	—	796	2	no	—
52	C₂×D₄	—	398	2	no	—
53	D₈	—	796	1	no	—
54	D₈	—	796	1	no	—
55	D₈	—	796	1	no	—
56	D₈	—	796	1	no	—
57	C₂×C₈	C₂²⋊D₁₉₉	1	1	yes	characteristic
58	C₂×C₈	D₇₉₆	1	1	yes	characteristic
59	C₄²	C₄×D₁₉₉	1	1	yes	characteristic
60	C₁₆	—	4	1	no	—
61	C₁₆	—	796	1	no	—
62	C₂³	—	796	2	no	—
63	D₄	—	796	2	no	—
64	D₄	—	796	2	no	—
65	D₄	—	1592	4	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	(C₂×D₁₉₉)⋊C₄	1	1	yes	characteristic
68	C₈	#15691871	1	1	yes	characteristic
69	C₈	D₁₅₉₂	1	1	yes	characteristic
70	C₈	#15691873	1	1	yes	characteristic
71	C₈	#15691875	1	1	yes	characteristic
72	C₂²	—	1592	4	no	—
73	C₂²	—	1592	2	no	—
74	C₂²	#20263871	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	#20263875	1	1	yes	characteristic
77	C₄	#20263877	1	1	yes	characteristic
78	C₂	—	2	1	no	—
79	C₂	—	3184	2	no	—
80	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	#27164395	C₂
cosocle	C₄×C₈×C₁₉₉	C₂²
hypercenter	#364	D₁₉₉
hypocenter	C₁₉₉	#1357
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
2. #27163839	C₂	semidirect
3. #364×C₁₉₉	C₂	semidirect
40. C₁₉₉	#1357	semidirect
44. #364	D₁₉₉	semidirect

Maximal subgroups

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

subgroup	index
#27164395	2
#27163839	2
#364×C₁₉₉	2
#1357	199