Group #38770338 — subgroups

Subgroups — #38770338

Order 25472.

224 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20263889	C₂	1	1	yes	maximal, characteristic
2	#27163916	C₂	1	2	yes	maximal
3	#27163781	C₂	1	2	yes	maximal
4	#27163781	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊C₈×C₁₉₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Dic₁₉₉	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₁₉₉	C₂²	1	2	yes	—
8	C₂×Dic₁₉₉⋊C₄	—	2	2	no	—
9	#20263889	—	2	2	no	—
10	C₁₉₉⋊#95	—	2	2	no	—
11	C₂²×C₈×C₁₉₉	C₂²	1	1	yes	characteristic
12	C₂²×C₈×C₁₉₉	C₂²	1	1	yes	characteristic
13	C₂×C₄²×C₁₉₉	C₂²	1	1	yes	characteristic
14	C₄⋊C₈×C₁₉₉	—	2	2	no	—
15	C₂²×Dic₁₉₉	—	2	2	no	—
16	C₂²×Dic₁₉₉	—	2	2	no	—
17	C₄⋊Dic₁₉₉	—	2	2	no	—
18	C₄⋊Dic₁₉₉	—	2	2	no	—
19	C₄⋊Dic₁₉₉	—	2	2	no	—
20	C₄⋊Dic₁₉₉	Q₈	1	4	yes	—
21	Dic₁₉₉⋊C₄	—	4	4	no	—
22	C₂²×C₄×C₁₉₉	D₄	1	1	yes	characteristic
23	C₂²×C₄×C₁₉₉	D₄	1	1	yes	characteristic
24	C₂²×C₄×C₁₉₉	C₂³	1	1	yes	characteristic
25	C₂×C₈×C₁₉₉	—	2	2	no	—
26	C₂×C₈×C₁₉₉	—	2	1	no	—
27	C₂×C₈×C₁₉₉	—	2	2	no	—
28	C₂×C₈×C₁₉₉	D₄	1	2	yes	—
29	C₄²×C₁₉₉	—	2	1	no	—
30	C₄²×C₁₉₉	—	2	1	no	—
31	C₂×Dic₁₉₉	—	2	4	no	—
32	C₂×Dic₁₉₉	—	4	2	no	—
33	C₂×Dic₁₉₉	—	4	2	no	—
34	C₂×Dic₁₉₉	—	4	2	no	—
35	C₂×Dic₁₉₉	—	4	2	no	—
36	C₂×Dic₁₉₉	—	4	2	no	—
37	C₂³×C₁₉₉	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₁₉₉	—	2	1	no	—
39	C₂×C₄×C₁₉₉	—	2	1	no	—
40	C₂×C₄×C₁₉₉	—	2	1	no	—
41	C₂×C₄×C₁₉₉	—	2	2	no	—
42	C₂×C₄×C₁₉₉	D₈	1	2	yes	—
43	C₂×C₄×C₁₉₉	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₁₉₉	C₂×Q₈	1	2	yes	—
45	C₂×C₄×C₁₉₉	#41	1	2	yes	—
46	C₂×C₄×C₁₉₉	#41	1	1	yes	characteristic
47	C₈×C₁₉₉	—	2	2	no	—
48	C₈×C₁₉₉	—	4	1	no	—
49	C₂²×C₁₉₉	#121	1	1	yes	characteristic
50	C₂²×C₁₉₉	C₂²⋊Q₈	1	2	yes	—
51	C₂²×C₁₉₉	C₂×D₈	1	1	yes	characteristic
52	C₂²×C₁₉₉	#135	1	1	yes	characteristic
53	C₂²×C₁₉₉	#137	1	2	yes	—
54	C₄×C₁₉₉	—	2	2	no	—
55	C₄×C₁₉₉	—	4	1	no	—
56	C₄×C₁₉₉	#123	1	1	yes	characteristic
57	C₄×C₁₉₉	#125	1	2	yes	—
58	C₄×C₁₉₉	C₄⋊Q₈	1	1	yes	characteristic
59	Dic₁₉₉	—	4	4	no	—
60	Dic₁₉₉	—	8	2	no	—
61	C₂×C₁₉₉	#398	1	1	yes	characteristic
62	C₂×C₁₉₉	#466	1	1	yes	characteristic
63	C₂×C₁₉₉	#470	1	1	yes	characteristic
64	C₂×C₁₉₉	#474	1	2	yes	—
65	C₂×C₁₉₉	#479	1	2	yes	—
66	C₁₉₉	#2086	1	1	yes	characteristic, complemented, Sylow
67	#2086	—	199	1	no	maximal, Sylow
68	C₂×#107	—	199	1	no	—
69	C₂×C₄⋊C₈	D₁₉₉	1	1	yes	characteristic
70	#389	—	199	2	no	—
71	#340	—	199	2	no	—
72	#340	—	199	1	no	—
73	C₂²×C₈	C₂×D₁₉₉	1	1	yes	characteristic
74	C₂²×C₈	C₂×D₁₉₉	1	1	yes	characteristic
75	C₂×C₄⋊C₄	—	398	2	no	—
76	C₂×C₄⋊C₄	—	199	2	no	—
77	C₂×C₄⋊C₄	—	199	2	no	—
78	C₂×C₄²	C₂×D₁₉₉	1	1	yes	characteristic
79	#107	—	398	2	no	—
80	C₄⋊C₈	—	2	2	no	—
81	#95	—	398	2	no	—
82	C₂²×C₄	—	398	2	no	—
83	C₂²×C₄	—	398	2	no	—
84	C₂²×C₄	D₇₉₆	1	1	yes	characteristic
85	C₂²×C₄	D₇₉₆	1	1	yes	characteristic
86	C₂²×C₄	C₂²×D₁₉₉	1	1	yes	characteristic
87	C₂×C₈	—	2	2	no	—
88	C₂×C₈	—	2	1	no	—
89	C₂×C₈	—	2	2	no	—
90	C₂×C₈	C₂²⋊D₁₉₉	1	2	yes	—
91	C₄⋊C₄	—	796	4	no	—
92	C₄⋊C₄	—	398	2	no	—
93	C₄⋊C₄	—	398	2	no	—
94	C₄⋊C₄	—	398	2	no	—
95	C₄⋊C₄	—	199	4	no	—
96	C₄²	—	2	1	no	—
97	C₄²	—	2	1	no	—
98	C₂³	C₂×D₇₉₆	1	1	yes	characteristic
99	C₂×C₄	—	2	1	no	—
100	C₂×C₄	—	2	1	no	—
101	C₂×C₄	—	2	2	no	—
102	C₂×C₄	—	2	1	no	—
103	C₂×C₄	—	796	2	no	—
104	C₂×C₄	—	796	2	no	—
105	C₂×C₄	—	796	2	no	—
106	C₂×C₄	—	796	2	no	—
107	C₂×C₄	—	796	2	no	—
108	C₂×C₄	—	398	4	no	—
109	C₂×C₄	D₁₅₉₂	1	2	yes	—
110	C₂×C₄	C₂×C₂²⋊D₁₉₉	1	1	yes	characteristic
111	C₂×C₄	Q₈×D₁₉₉	1	2	yes	—
112	C₂×C₄	#15691885	1	2	yes	—
113	C₂×C₄	#15691886	1	1	yes	characteristic
114	C₈	—	2	2	no	—
115	C₈	—	4	1	no	—
116	C₂²	#20263929	1	1	yes	characteristic
117	C₂²	#20263935	1	2	yes	—
118	C₂²	C₂×D₁₅₉₂	1	1	yes	characteristic
119	C₂²	#20263977	1	1	yes	characteristic
120	C₂²	#20263988	1	2	yes	—
121	C₄	—	2	2	no	—
122	C₄	—	4	1	no	—
123	C₄	—	796	4	no	—
124	C₄	—	1592	2	no	—
125	C₄	#20263936	1	1	yes	characteristic
126	C₄	#20263945	1	2	yes	—
127	C₄	#20263953	1	1	yes	characteristic
128	C₂	#27163948	1	1	yes	characteristic
129	C₂	#27164254	1	1	yes	characteristic
130	C₂	#27164276	1	1	yes	characteristic
131	C₂	#27164299	1	2	yes	—
132	C₂	#27164326	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#20263889

C₂

yes

maximal, characteristic

#27163916

C₂

yes

maximal

#27163781

C₂

yes

maximal

#27163781

C₂

yes

maximal, characteristic

C₂×C₄⋊C₈×C₁₉₉

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₁₉₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉₉

C₂²

yes

—

C₂×Dic₁₉₉⋊C₄

—

#20263889

—

C₁₉₉⋊#95

—

C₂²×C₈×C₁₉₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉₉

C₂²

yes

characteristic

C₄⋊C₈×C₁₉₉

—

C₂²×Dic₁₉₉

—

C₂²×Dic₁₉₉

—

C₄⋊Dic₁₉₉

—

C₄⋊Dic₁₉₉

—

C₄⋊Dic₁₉₉

—

C₄⋊Dic₁₉₉

Q₈

yes

—

Dic₁₉₉⋊C₄

—

C₂²×C₄×C₁₉₉

D₄

yes

characteristic

C₂²×C₄×C₁₉₉

D₄

yes

characteristic

C₂²×C₄×C₁₉₉

C₂³

yes

characteristic

C₂×C₈×C₁₉₉

—

C₂×C₈×C₁₉₉

—

C₂×C₈×C₁₉₉

—

C₂×C₈×C₁₉₉

D₄

yes

—

C₄²×C₁₉₉

—

C₄²×C₁₉₉

—

C₂×Dic₁₉₉

—

C₂×Dic₁₉₉

—

C₂×Dic₁₉₉

—

C₂×Dic₁₉₉

—

C₂×Dic₁₉₉

—

C₂×Dic₁₉₉

—

C₂³×C₁₉₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉₉

—

C₂×C₄×C₁₉₉

—

C₂×C₄×C₁₉₉

—

C₂×C₄×C₁₉₉

—

C₂×C₄×C₁₉₉

D₈

yes

—

C₂×C₄×C₁₉₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉₉

#41

yes

—

C₂×C₄×C₁₉₉

#41

yes

characteristic

C₈×C₁₉₉

—

C₈×C₁₉₉

—

C₂²×C₁₉₉

#121

yes

characteristic

C₂²×C₁₉₉

C₂²⋊Q₈

yes

—

C₂²×C₁₉₉

C₂×D₈

yes

C₂²×C₁₉₉

yes

C₂²×C₁₉₉

yes

—

C₄×C₁₉₉

—

C₄×C₁₉₉

—

C₄×C₁₉₉

#123

yes

characteristic

C₄×C₁₉₉

#125

yes

—

C₄×C₁₉₉

C₄⋊Q₈

yes

characteristic

Dic₁₉₉

—

Dic₁₉₉

—

C₂×C₁₉₉

yes

C₂×C₁₉₉

yes

C₂×C₁₉₉

yes

C₂×C₁₉₉

yes

—

C₂×C₁₉₉

#479

yes

—

C₁₉₉

#2086

yes

characteristic, complemented, Sylow

#2086

—

199

maximal, Sylow

C₂×#107

—

199

—

C₂×C₄⋊C₈

D₁₉₉

yes

characteristic

#389

—

199

—

#340

—

199

—

#340

—

199

—

C₂²×C₈

C₂×D₁₉₉

yes

characteristic

C₂²×C₈

C₂×D₁₉₉

yes

characteristic

C₂×C₄⋊C₄

—

398

—

C₂×C₄⋊C₄

—

199

—

C₂×C₄⋊C₄

—

199

—

C₂×C₄²

C₂×D₁₉₉

yes

characteristic

#107

—

398

—

C₄⋊C₈

—

#95

—

398

—

C₂²×C₄

—

398

—

C₂²×C₄

—

398

—

C₂²×C₄

D₇₉₆

yes

characteristic

C₂²×C₄

D₇₉₆

yes

characteristic

C₂²×C₄

C₂²×D₁₉₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₁₉₉

yes

—

C₄⋊C₄

—

796

—

C₄⋊C₄

—

398

—

C₄⋊C₄

—

398

—

C₄⋊C₄

—

398

—

C₄⋊C₄

—

199

—

C₄²

—

C₄²

—

C₂³

C₂×D₇₉₆

yes

characteristic

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

796

—

104

C₂×C₄

—

796

—

105

C₂×C₄

—

796

—

106

C₂×C₄

—

796

—

107

C₂×C₄

—

796

—

108

C₂×C₄

—

398

—

109

C₂×C₄

D₁₅₉₂

yes

—

110

C₂×C₄

C₂×C₂²⋊D₁₉₉

yes

characteristic

111

C₂×C₄

Q₈×D₁₉₉

yes

—

112

C₂×C₄

#15691885

yes

—

113

C₂×C₄

#15691886

yes

characteristic

114

C₈

—

115

C₈

—

116

C₂²

#20263929

yes

characteristic

117

C₂²

#20263935

yes

—

118

C₂²

C₂×D₁₅₉₂

yes

characteristic

119

C₂²

#20263977

yes

characteristic

120

C₂²

#20263988

yes

—

121

C₄

—

122

C₄

—

123

C₄

—

796

—

124

C₄

—

1592

—

125

C₄

#20263936

yes

characteristic

126

C₄

#20263945

yes

—

127

C₄

#20263953

yes

characteristic

128

C₂

#27163948

yes

characteristic

129

C₂

#27164254

yes

characteristic

130

C₂

#27164276

yes

characteristic

131

C₂

#27164299

yes

—

132

C₂

#27164326

yes

—

	subgroup	G/H
center	C₂³	C₂×D₇₉₆
commutator, cosocle	C₂²×C₄×C₁₉₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉₉
Fitting	C₂×C₄⋊C₈×C₁₉₉	C₂
socle, prime radical	C₂³×C₁₉₉	C₂×D₄
hypercenter	C₂×C₄⋊C₈	D₁₉₉
hypocenter	C₁₉₉	#2086
LCS	G ▷ C₂²×C₄×C₁₉₉ ▷ C₂×C₁₉₉ ▷ C₁₉₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

subgroup

G/H

center

C₂³

C₂×D₇₉₆

commutator, cosocle

C₂²×C₄×C₁₉₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉₉

Fitting

C₂×C₄⋊C₈×C₁₉₉

C₂

socle, prime radical

C₂³×C₁₉₉

C₂×D₄

hypercenter

C₂×C₄⋊C₈

D₁₉₉

hypocenter

C₁₉₉

#2086

LCS

G ▷ C₂²×C₄×C₁₉₉ ▷ C₂×C₁₉₉ ▷ C₁₉₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
66. C₁₉₉	#2086	semidirect

H ≅ G/N

type

66. C₁₉₉

#2086

semidirect

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

subgroup	index
C₂×#20263889	2
#27163916	2
#27163781	2
C₂×C₄⋊C₈×C₁₉₉	2
#2086	199

subgroup

index

C₂×C₄⋊C₈×C₁₉₉

199

Subgroups — #38770338

Conjugacy classes of subgroups

Complements

Maximal subgroups