Group #93621 — subgroups

Subgroups — #93621

Order 512.

161 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 161 conjugacy classes of subgroups — too many to draw. Only its 50 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	#12658	C₂	1	1	yes	maximal, characteristic
2	#12595	C₂	1	1	yes	maximal, characteristic
3	#8800	C₂	1	1	yes	maximal, characteristic
4	#2150	—	2	1	no	—
5	C₂×#347	—	2	1	no	—
6	C₂×#347	C₄	1	2	yes	—
7	C₄×#97	C₂²	1	1	yes	characteristic
8	#1377	C₄	1	2	yes	—
9	#1376	—	2	1	no	—
10	#1375	—	2	1	no	—
11	#1281	—	2	1	no	—
12	#1276	C₄	1	2	yes	—
13	#1275	—	2	1	no	—
14	C₂×M₃₂	—	2	2	no	—
15	C₂×M₃₂	—	2	2	no	—
16	#431	—	2	2	no	—
17	C₂×#97	C₂×C₄	1	1	yes	characteristic
18	C₂×#97	C₂×C₄	1	1	yes	characteristic
19	C₂×#97	D₄	1	1	yes	characteristic
20	C₂×#97	D₄	1	1	yes	characteristic
21	C₂×C₄×C₈	D₄	1	1	yes	characteristic
22	C₂×C₄×C₈	Q₈	1	1	yes	characteristic
23	C₄³	C₂×C₄	1	1	yes	characteristic
24	C₄⋊C₁₆	—	2	4	no	—
25	#347	—	2	4	no	—
26	#347	—	4	2	no	—
27	C₂²×C₈	C₂²⋊C₄	1	1	yes	characteristic
28	C₂²×C₈	C₂²⋊C₄	1	1	yes	characteristic
29	C₂²×C₈	C₄⋊C₄	1	1	yes	characteristic
30	C₂²×C₈	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₄²	—	4	1	no	—
32	C₂×C₄²	C₄²	1	1	yes	characteristic
33	C₂×C₄²	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₄²	C₄⋊C₄	1	1	yes	characteristic
35	M₃₂	—	2	4	no	—
36	M₃₂	—	4	2	no	—
37	M₃₂	—	4	2	no	—
38	M₃₂	—	4	2	no	—
39	C₂×C₁₆	—	2	4	no	—
40	C₂×C₁₆	—	4	2	no	—
41	C₄⋊C₈	—	4	2	no	—
42	C₂²⋊C₈	—	4	2	no	—
43	#97	—	2	1	no	—
44	#97	—	2	1	no	—
45	#97	—	2	2	no	—
46	#97	—	4	1	no	—
47	#97	—	4	1	no	—
48	C₄×C₈	—	2	2	no	—
49	C₄×C₈	—	2	1	no	—
50	C₄×C₈	—	2	1	no	—
51	C₄×C₈	—	4	2	no	—
52	C₂²×C₄	—	2	1	no	—
53	C₂²×C₄	—	2	1	no	—
54	C₂²×C₄	—	2	1	no	—
55	C₂²×C₄	#95	1	1	yes	characteristic
56	C₂×C₈	—	2	1	no	—
57	C₂×C₈	—	2	1	no	—
58	C₂×C₈	—	2	1	no	—
59	C₂×C₈	—	2	1	no	—
60	C₂×C₈	—	2	1	no	—
61	C₂×C₈	—	2	1	no	—
62	C₂×C₈	—	2	1	no	—
63	C₂×C₈	—	2	1	no	—
64	C₂×C₈	—	2	1	no	—
65	C₂×C₈	—	2	1	no	—
66	C₂×C₈	—	8	2	no	—
67	C₂×C₈	#100	1	1	yes	characteristic
68	C₂×C₈	#101	1	1	yes	characteristic
69	C₂×C₈	#104	1	2	yes	—
70	C₄²	—	2	1	no	—
71	C₄²	—	2	1	no	—
72	C₄²	—	2	1	no	—
73	C₄²	—	2	1	no	—
74	C₄²	—	8	2	no	—
75	C₄²	#104	1	2	yes	—
76	C₄²	#108	1	1	yes	characteristic
77	C₄²	#108	1	1	yes	characteristic
78	C₁₆	—	4	4	no	—
79	C₁₆	—	4	4	no	—
80	C₂³	#344	1	1	yes	characteristic
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	4	2	no	—
85	C₂×C₄	—	4	1	no	—
86	C₂×C₄	—	8	1	no	—
87	C₂×C₄	—	8	1	no	—
88	C₂×C₄	H(3,ℤ/4)	1	1	yes	characteristic
89	C₂×C₄	#339	1	1	yes	characteristic
90	C₂×C₄	#339	1	1	yes	characteristic
91	C₂×C₄	#341	1	1	yes	characteristic
92	C₂×C₄	#343	1	1	yes	characteristic
93	C₂×C₄	#344	1	1	yes	characteristic
94	C₈	—	2	1	no	—
95	C₈	—	2	1	no	—
96	C₈	—	2	2	no	—
97	C₈	—	4	1	no	—
98	C₈	—	4	1	no	—
99	C₈	—	16	2	no	—
100	C₂²	—	4	1	no	—
101	C₂²	#1288	1	1	yes	characteristic
102	C₂²	#1302	1	1	yes	characteristic
103	C₂²	#1307	1	1	yes	characteristic
104	C₄	—	2	2	no	—
105	C₄	—	4	2	no	—
106	C₄	—	4	1	no	—
107	C₄	—	8	1	no	—
108	C₄	#1285	1	1	yes	characteristic
109	C₄	#1287	1	1	yes	characteristic
110	C₄	#1299	1	1	yes	characteristic
111	C₄	#1300	1	1	yes	characteristic
112	C₂	—	2	1	no	—
113	C₂	—	2	1	no	—
114	C₂	—	2	1	no	—
115	C₂	#7043	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#12658

C₂

yes

maximal, characteristic

#12595

C₂

yes

maximal, characteristic

#8800

C₂

yes

maximal, characteristic

#2150

—

C₂×#347

—

C₂×#347

C₄

yes

—

C₄×#97

C₂²

yes

characteristic

#1377

C₄

yes

—

—

—

—

C₄

yes

—

#1275

—

C₂×M₃₂

—

C₂×M₃₂

—

#431

—

C₂×#97

C₂×C₄

yes

characteristic

C₂×#97

C₂×C₄

yes

characteristic

C₂×#97

D₄

yes

characteristic

C₂×#97

D₄

yes

characteristic

C₂×C₄×C₈

D₄

yes

characteristic

C₂×C₄×C₈

Q₈

yes

characteristic

C₄³

C₂×C₄

yes

characteristic

C₄⋊C₁₆

—

#347

—

#347

—

C₂²×C₈

C₂²⋊C₄

yes

characteristic

C₂²×C₈

C₂²⋊C₄

yes

characteristic

C₂²×C₈

C₄⋊C₄

yes

characteristic

C₂²×C₈

C₄⋊C₄

yes

characteristic

C₂×C₄²

—

C₂×C₄²

C₄²

yes

characteristic

C₂×C₄²

C₂²⋊C₄

yes

characteristic

C₂×C₄²

C₄⋊C₄

yes

characteristic

M₃₂

—

M₃₂

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₄⋊C₈

—

C₂²⋊C₈

—

—

—

—

—

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

#95

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₂×C₈

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

#104

yes

—

C₄²

yes

C₄²

yes

C₁₆

—

C₁₆

—

C₂³

#344

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

C₈

—

C₈

—

C₈

—

C₈

—

C₈

—

100

C₂²

—

101

C₂²

#1288

yes

characteristic

102

C₂²

#1302

yes

characteristic

103

C₂²

#1307

yes

characteristic

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

#1285

yes

characteristic

109

C₄

#1287

yes

characteristic

110

C₄

#1299

yes

characteristic

111

C₄

#1300

yes

characteristic

112

C₂

—

113

C₂

—

114

C₂

—

115

C₂

#7043

yes

characteristic

	subgroup	G/H
center	C₄	#1300
commutator	C₂×C₄²	C₄²
Frattini, cosocle	C₄×#97	C₂²
socle	C₂	#7043
prime radical	C₂³	#344
LCS	G ▷ C₂×C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄² ◁ C₄×#97 ◁ G
LECS	G ▷ C₄×#97 ▷ C₂²×C₄ ▷ C₂ ▷ C₁

subgroup

G/H

center

C₄

#1300

commutator

C₂×C₄²

C₄²

Frattini, cosocle

C₄×#97

C₂²

C₂

C₂³

G ▷ C₂×C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₄ ◁ C₂×C₄² ◁ C₄×#97 ◁ G

LECS

G ▷ C₄×#97 ▷ C₂²×C₄ ▷ C₂ ▷ C₁

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

subgroup	index
#12658	2
#12595	2
#8800	2

subgroup

index

#12658

#12595

#8800

Subgroups — #93621

Conjugacy classes of subgroups

Maximal subgroups