Subgroups — #38767026

Order 25472.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27164372	C₂	1	1	yes	maximal, characteristic
2	#27163813	C₂	1	1	yes	maximal, characteristic
3	#355×C₁₉₉	C₂	1	1	yes	maximal, characteristic
4	#20263947	C₄	1	1	yes	characteristic, complemented
5	#20263879	—	2	1	no	—
6	#20263876	—	2	1	no	—
7	#20263870	—	2	1	no	—
8	C₄×C₁₉₉⋊C₈	C₄	1	1	yes	characteristic, complemented
9	#124×C₁₉₉	C₂²	1	1	yes	characteristic
10	#101×C₁₉₉	—	2	1	no	—
11	C₂×C₁₉₉⋊C₈	—	2	1	no	—
12	C₄⋊Dic₁₉₉	—	2	1	no	—
13	Dic₁₉₉⋊C₄	—	4	1	no	—
14	C₂²⋊Dic₁₉₉	—	4	1	no	—
15	C₂×Q₈×C₁₉₉	D₄	1	1	yes	characteristic
16	C₂×D₄×C₁₉₉	D₄	1	1	yes	characteristic
17	M₁₆×C₁₉₉	—	4	1	no	—
18	C₂²⋊C₄×C₁₉₉	—	4	1	no	—
19	C₄²×C₁₉₉	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₁₉₉	—	4	1	no	—
21	C₂×Dic₁₉₉	—	8	1	no	—
22	C₁₉₉⋊C₈	—	4	1	no	—
23	C₂³×C₁₉₉	—	2	1	no	—
24	Q₈×C₁₉₉	—	4	1	no	—
25	D₄×C₁₉₉	—	4	1	no	—
26	C₂×C₄×C₁₉₉	—	2	1	no	—
27	C₂×C₄×C₁₉₉	—	2	1	no	—
28	C₂×C₄×C₁₉₉	C₂²⋊C₄	1	1	yes	characteristic
29	C₈×C₁₉₉	—	8	1	no	—
30	C₂²×C₁₉₉	—	4	1	no	—
31	C₂²×C₁₉₉	—	8	1	no	—
32	C₂²×C₁₉₉	#99	1	1	yes	characteristic
33	C₄×C₁₉₉	—	2	1	no	—
34	C₄×C₁₉₉	—	4	1	no	—
35	C₄×C₁₉₉	—	4	1	no	—
36	Dic₁₉₉	—	8	1	no	—
37	Dic₁₉₉	—	16	1	no	—
38	C₂×C₁₉₉	—	2	1	no	—
39	C₂×C₁₉₉	—	8	1	no	—
40	C₂×C₁₉₉	#354	1	1	yes	characteristic
41	C₁₉₉	#1414	1	1	yes	characteristic, complemented, Sylow
42	#1414	—	199	1	no	maximal, Sylow
43	#488	—	199	1	no	—
44	#355	D₁₉₉	1	1	yes	characteristic
45	#354	—	199	1	no	—
46	#125	—	199	1	no	—
47	#124	C₂×D₁₉₉	1	1	yes	characteristic
48	#103	—	398	1	no	—
49	#102	—	398	1	no	—
50	#101	—	2	1	no	—
51	#99	—	398	1	no	—
52	C₄×C₈	—	199	1	no	—
53	C₂×Q₈	C₂²⋊D₁₉₉	1	1	yes	characteristic
54	C₂×D₄	D₇₉₆	1	1	yes	characteristic
55	M₁₆	—	4	1	no	—
56	C₂×C₈	—	398	1	no	—
57	C₄⋊C₄	—	796	1	no	—
58	C₄⋊C₄	—	398	1	no	—
59	C₂²⋊C₄	—	4	1	no	—
60	C₂²⋊C₄	—	796	1	no	—
61	C₄²	C₄×D₁₉₉	1	1	yes	characteristic
62	C₂³	—	2	1	no	—
63	Q₈	—	4	1	no	—
64	D₄	—	4	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	796	1	no	—
68	C₂×C₄	—	1592	1	no	—
69	C₂×C₄	(C₂×D₁₉₉)⋊C₄	1	1	yes	characteristic
70	C₈	—	8	1	no	—
71	C₈	—	796	1	no	—
72	C₂²	—	4	1	no	—
73	C₂²	—	8	1	no	—
74	C₂²	#20263869	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	4	1	no	—
78	C₄	—	1592	1	no	—
79	C₄	—	3184	1	no	—
80	C₂	—	2	1	no	—
81	C₂	—	8	1	no	—
82	C₂	#27163812	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#27163812
commutator	C₄²×C₁₉₉	C₂×C₄
Frattini	#124	C₂×D₁₉₉
Fitting	#355×C₁₉₉	C₂
socle	C₂×C₁₉₉	#354
prime radical	C₂×D₄×C₁₉₉	D₄
cosocle	#124×C₁₉₉	C₂²
hypercenter	#355	D₁₉₉
hypocenter	C₁₉₉	#1414
LCS	G ▷ C₄²×C₁₉₉ ▷ C₂×C₄×C₁₉₉ ▷ C₂²×C₁₉₉ ▷ C₂×C₁₉₉ ▷ C₁₉₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #355

Complements

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

N	H ≅ G/N	type
4. #20263947	C₄	semidirect
8. C₄×C₁₉₉⋊C₈	C₄	semidirect
41. C₁₉₉	#1414	semidirect

Maximal subgroups

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

subgroup	index
#27164372	2
#27163813	2
#355×C₁₉₉	2
#1414	199