Subgroups — #38768756

Order 25472.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20263891	C₂	1	2	yes	maximal
2	C₄×#15691870	C₂	1	2	yes	maximal
3	#27163783	C₂	1	2	yes	maximal
4	C₂×#97×C₁₉₉	C₂	1	1	yes	maximal, characteristic
5	C₂×#15691870	C₂²	1	4	yes	—
6	#20263891	C₄	1	8	yes	complemented
7	#20263866	—	2	2	no	—
8	C₄×C₁₉₉⋊C₈	—	2	2	no	—
9	C₂²×C₈×C₁₉₉	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₁₉₉	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₁₉₉	C₂²	1	1	yes	characteristic
12	#97×C₁₉₉	C₄	1	4	yes	—
13	#15691870	—	2	4	no	—
14	#15691870	C₂×C₄	1	8	yes	—
15	C₂×C₁₉₉⋊C₈	—	2	4	no	—
16	C₂²×C₄×C₁₉₉	Q₈	1	2	yes	—
17	C₂²×C₄×C₁₉₉	C₂³	1	1	yes	characteristic
18	C₂×C₈×C₁₉₉	—	2	2	no	—
19	C₂×C₈×C₁₉₉	C₂×C₄	1	4	yes	—
20	C₂×C₈×C₁₉₉	C₂×C₄	1	2	yes	—
21	C₂×C₈×C₁₉₉	C₂×C₄	1	2	yes	—
22	C₄²×C₁₉₉	C₂×C₄	1	2	yes	—
23	C₄²×C₁₉₉	D₄	1	2	yes	—
24	C₁₉₉⋊C₈	—	2	8	no	—
25	C₂³×C₁₉₉	C₂×Q₈	1	1	yes	characteristic
26	C₂×C₄×C₁₉₉	—	4	2	no	—
27	C₂×C₄×C₁₉₉	C₄⋊C₄	1	4	yes	—
28	C₂×C₄×C₁₉₉	C₂²×C₄	1	2	yes	—
29	C₂×C₄×C₁₉₉	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₄×C₁₉₉	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₁₉₉	#41	1	2	yes	—
32	C₈×C₁₉₉	—	2	2	no	—
33	C₈×C₁₉₉	C₄²	1	4	yes	—
34	C₂²×C₁₉₉	—	2	2	no	—
35	C₂²×C₁₉₉	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₂²×C₁₉₉	C₄×Q₈	1	2	yes	—
37	C₄×C₁₉₉	—	2	4	no	—
38	C₄×C₁₉₉	C₂×C₄²	1	1	yes	characteristic
39	C₄×C₁₉₉	#117	1	1	yes	characteristic
40	C₄×C₁₉₉	C₄×D₄	1	2	yes	—
41	C₂×C₁₉₉	—	2	2	no	—
42	C₂×C₁₉₉	C₄×C₄⋊C₄	1	1	yes	characteristic
43	C₂×C₁₉₉	#430	1	2	yes	—
44	C₁₉₉	#1778	1	1	yes	characteristic, complemented, Sylow
45	#1778	—	199	1	no	maximal, Sylow
46	C₂×#108	—	199	2	no	—
47	C₄×M₁₆	—	199	2	no	—
48	C₂×#97	D₁₉₉	1	1	yes	characteristic
49	#341	—	199	2	no	—
50	C₂×M₁₆	—	199	4	no	—
51	C₂²×C₈	C₂×D₁₉₉	1	1	yes	characteristic
52	C₂²×C₈	C₂×D₁₉₉	1	1	yes	characteristic
53	C₂×C₄²	C₂×D₁₉₉	1	1	yes	characteristic
54	#108	—	199	8	no	—
55	#97	—	398	2	no	—
56	#97	Dic₁₉₉	1	4	yes	—
57	C₄×C₈	—	398	2	no	—
58	C₂²×C₄	Dic₃₉₈	1	2	yes	—
59	C₂²×C₄	C₂²×D₁₉₉	1	1	yes	characteristic
60	M₁₆	—	398	4	no	—
61	M₁₆	—	199	8	no	—
62	C₂×C₈	—	2	2	no	—
63	C₂×C₈	—	398	4	no	—
64	C₂×C₈	C₄×D₁₉₉	1	4	yes	—
65	C₂×C₈	C₂×Dic₁₉₉	1	2	yes	—
66	C₂×C₈	C₂×Dic₁₉₉	1	2	yes	—
67	C₄²	C₂×Dic₁₉₉	1	2	yes	—
68	C₄²	D₇₉₆	1	2	yes	—
69	C₂³	C₂×Dic₃₉₈	1	1	yes	characteristic
70	C₂×C₄	—	4	2	no	—
71	C₂×C₄	C₄⋊Dic₁₉₉	1	4	yes	—
72	C₂×C₄	C₂×C₄×D₁₉₉	1	2	yes	—
73	C₂×C₄	C₂²×Dic₁₉₉	1	1	yes	characteristic
74	C₂×C₄	C₂×D₇₉₆	1	1	yes	characteristic
75	C₂×C₄	#15691886	1	2	yes	—
76	C₈	—	2	2	no	—
77	C₈	—	398	8	no	—
78	C₈	C₄×Dic₁₉₉	1	4	yes	—
79	C₂²	—	2	2	no	—
80	C₂²	C₂×C₄⋊Dic₁₉₉	1	1	yes	characteristic
81	C₂²	C₄×Dic₃₉₈	1	2	yes	—
82	C₄	—	2	4	no	—
83	C₄	C₂×C₄×Dic₁₉₉	1	1	yes	characteristic
84	C₄	#20263914	1	1	yes	characteristic
85	C₄	C₄×D₇₉₆	1	2	yes	—
86	C₂	—	2	2	no	—
87	C₂	C₄×C₄⋊Dic₁₉₉	1	1	yes	characteristic
88	C₂	#27164067	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₇₉₆
commutator	C₄×C₁₉₉	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₁₉₉
Fitting	C₂×#97×C₁₉₉	C₂
socle	C₂²×C₁₉₉	C₂×C₄⋊C₄
prime radical	C₂³×C₁₉₉	C₂×Q₈
cosocle	C₂²×C₄×C₁₉₉	C₂³
hypercenter	C₂×#97	D₁₉₉
hypocenter	C₁₉₉	#1778
LCS	G ▷ C₄×C₁₉₉ ▷ C₂×C₁₉₉ ▷ C₁₉₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
6. #20263891	C₄	semidirect
44. C₁₉₉	#1778	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20263891	2
C₄×#15691870	2
#27163783	2
C₂×#97×C₁₉₉	2
#1778	199