Subgroups — #38768961

Order 25472.

272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20263872	C₂	1	2	yes	maximal
2	#27163788	C₂	1	4	yes	maximal, complemented
3	#518×C₁₉₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#15691870	C₂²	1	4	yes	—
5	#20263872	—	2	4	no	—
6	C₂²×D₄×C₁₉₉	C₂²	1	1	yes	characteristic
7	C₄×D₄×C₁₉₉	—	2	4	no	—
8	#117×C₁₉₉	C₂²	1	2	yes	—
9	C₂×C₂²⋊C₄×C₁₉₉	C₄	1	4	yes	—
10	#15691870	—	2	4	no	—
11	#15691870	—	2	4	no	—
12	C₂×C₁₉₉⋊C₈	—	2	4	no	—
13	C₂⁴×C₁₉₉	C₂×C₄	1	2	yes	—
14	C₂×D₄×C₁₉₉	—	2	4	no	—
15	C₂×D₄×C₁₉₉	D₄	1	4	yes	—
16	C₂²×C₄×C₁₉₉	—	2	4	no	—
17	C₂²×C₄×C₁₉₉	C₂³	1	1	yes	characteristic
18	C₄⋊C₄×C₁₉₉	—	2	2	no	—
19	C₂²⋊C₄×C₁₉₉	—	2	4	no	—
20	C₂²⋊C₄×C₁₉₉	C₂×C₄	1	4	yes	—
21	C₄²×C₁₉₉	—	2	2	no	—
22	C₁₉₉⋊C₈	—	4	4	no	—
23	C₂³×C₁₉₉	—	2	4	no	—
24	C₂³×C₁₉₉	—	8	2	no	—
25	C₂³×C₁₉₉	C₂²⋊C₄	1	4	yes	—
26	C₂³×C₁₉₉	C₂²×C₄	1	1	yes	characteristic
27	D₄×C₁₉₉	—	2	8	no	—
28	C₂×C₄×C₁₉₉	—	2	4	no	—
29	C₂×C₄×C₁₉₉	—	8	4	no	—
30	C₂×C₄×C₁₉₉	C₂×D₄	1	2	yes	—
31	C₂×C₄×C₁₉₉	#41	1	4	yes	—
32	C₂²×C₁₉₉	—	2	4	no	—
33	C₂²×C₁₉₉	—	4	1	no	—
34	C₂²×C₁₉₉	—	4	4	no	—
35	C₂²×C₁₉₉	—	8	4	no	—
36	C₂²×C₁₉₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
37	C₂²×C₁₉₉	#117	1	2	yes	—
38	C₄×C₁₉₉	—	4	4	no	—
39	C₄×C₁₉₉	#123	1	4	yes	—
40	C₂×C₁₉₉	—	2	1	no	—
41	C₂×C₁₉₉	—	2	2	no	—
42	C₂×C₁₉₉	—	4	4	no	—
43	C₂×C₁₉₉	#381	1	1	yes	characteristic
44	C₁₉₉	#1829	1	1	yes	characteristic, complemented, Sylow
45	#1829	—	199	1	no	maximal, Sylow
46	#518	D₁₉₉	1	1	yes	characteristic
47	C₂×#100	—	199	2	no	—
48	#344	—	199	4	no	—
49	C₂²×D₄	C₂×D₁₉₉	1	1	yes	characteristic
50	C₂×M₁₆	—	199	4	no	—
51	C₄×D₄	—	2	4	no	—
52	#117	C₂×D₁₉₉	1	2	yes	—
53	C₂×C₂²⋊C₄	Dic₁₉₉	1	4	yes	—
54	#100	—	398	4	no	—
55	C₂⁴	C₂×Dic₁₉₉	1	2	yes	—
56	C₂×D₄	—	2	4	no	—
57	C₂×D₄	C₂²⋊D₁₉₉	1	4	yes	—
58	C₂²×C₄	—	2	4	no	—
59	C₂²×C₄	C₂²×D₁₉₉	1	1	yes	characteristic
60	M₁₆	—	398	4	no	—
61	M₁₆	—	398	4	no	—
62	C₂×C₈	—	398	4	no	—
63	C₄⋊C₄	—	2	2	no	—
64	C₂²⋊C₄	—	2	4	no	—
65	C₂²⋊C₄	C₂×Dic₁₉₉	1	4	yes	—
66	C₄²	—	2	2	no	—
67	C₂³	—	2	4	no	—
68	C₂³	—	8	2	no	—
69	C₂³	C₂²⋊Dic₁₉₉	1	4	yes	—
70	C₂³	C₂²×Dic₁₉₉	1	1	yes	characteristic
71	D₄	—	2	8	no	—
72	C₂×C₄	—	2	4	no	—
73	C₂×C₄	—	8	4	no	—
74	C₂×C₄	C₂×C₂²⋊D₁₉₉	1	2	yes	—
75	C₂×C₄	#15691886	1	4	yes	—
76	C₈	—	796	4	no	—
77	C₂²	—	2	4	no	—
78	C₂²	—	4	1	no	—
79	C₂²	—	4	4	no	—
80	C₂²	—	8	4	no	—
81	C₂²	C₂×C₂²⋊Dic₁₉₉	1	1	yes	characteristic
82	C₂²	#20263914	1	2	yes	—
83	C₄	—	4	4	no	—
84	C₄	#20263938	1	4	yes	—
85	C₂	—	2	1	no	—
86	C₂	—	2	2	no	—
87	C₂	—	4	4	no	—
88	C₂	#27163881	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#27163881
commutator	C₂³×C₁₉₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉₉
Fitting	#518×C₁₉₉	C₂
socle	C₂×C₁₉₉	#381
prime radical	C₂²×D₄×C₁₉₉	C₂²
cosocle	C₂²×C₄×C₁₉₉	C₂³
hypercenter	#518	D₁₉₉
hypocenter	C₁₉₉	#1829
LCS	G ▷ C₂³×C₁₉₉ ▷ C₂×C₁₉₉ ▷ C₁₉₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #518

Complements

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

N	H ≅ G/N	type
2. #27163788	C₂	semidirect
44. C₁₉₉	#1829	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20263872	2
#27163788	2
#518×C₁₉₉	2
#1829	199