Group #33740 — subgroups

Subgroups — #33740

Order 256.

266 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 103 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	#3176	C₂	1	2	yes	maximal, complemented
2	#2253	C₂	1	1	yes	maximal, characteristic, complemented
3	#2246	C₂	1	1	yes	maximal, characteristic, complemented
4	#2244	C₂	1	2	yes	maximal, complemented
5	#2218	C₂	1	2	yes	maximal, complemented
6	#2215	C₂	1	2	yes	maximal, complemented
7	#2177	C₂	1	2	yes	maximal, complemented
8	C₄×D₁₆	C₂	1	2	yes	maximal, complemented
9	#2108	C₂	1	1	yes	maximal, characteristic, complemented
10	#540	—	2	2	no	—
11	C₂×D₁₆	C₂²	1	2	yes	—
12	C₂×D₁₆	C₂²	1	2	yes	—
13	C₂×M₃₂	C₂²	1	1	yes	characteristic
14	C₂²×C₁₆	C₂²	1	1	yes	characteristic
15	#499	C₂²	1	2	yes	—
16	#493	C₂²	1	2	yes	—
17	#490	—	2	2	no	—
18	#469	—	2	2	no	—
19	#466	C₂²	1	4	yes	—
20	#442	—	2	2	no	—
21	C₄×D₈	C₂²	1	4	yes	—
22	#405	C₂²	1	1	yes	characteristic
23	#367	C₂²	1	2	yes	—
24	#366	C₂²	1	2	yes	—
25	#357	C₂²	1	4	yes	—
26	#357	C₂²	1	4	yes	—
27	#346	C₂²	1	1	yes	characteristic
28	#346	C₂²	1	1	yes	characteristic
29	C₄×C₁₆	C₂²	1	1	yes	characteristic
30	C₄×C₁₆	C₂²	1	1	yes	characteristic
31	C₂×D₈	—	2	2	no	—
32	C₂×D₈	C₂³	1	4	yes	—
33	C₂×M₁₆	D₄	1	1	yes	characteristic
34	C₂²×C₈	C₂³	1	1	yes	characteristic
35	#127	—	2	2	no	—
36	#125	—	2	2	no	—
37	#123	—	4	4	no	—
38	#121	—	2	4	no	—
39	#121	—	4	4	no	—
40	C₄×D₄	—	2	4	no	—
41	#117	D₄	1	1	yes	characteristic
42	D₁₆	—	2	4	no	—
43	D₁₆	—	2	4	no	—
44	M₃₂	—	2	2	no	—
45	C₂×C₁₆	—	2	2	no	—
46	C₂×C₁₆	C₂³	1	1	yes	characteristic
47	C₂×C₁₆	C₂³	1	1	yes	characteristic
48	C₂×C₁₆	C₂³	1	1	yes	characteristic
49	C₂×C₁₆	C₂³	1	1	yes	characteristic
50	#107	C₂³	1	4	yes	—
51	#106	—	2	2	no	—
52	#102	—	2	4	no	—
53	#102	—	2	4	no	—
54	#97	D₄	1	1	yes	characteristic
55	#97	D₄	1	1	yes	characteristic
56	C₄×C₈	C₂³	1	1	yes	characteristic
57	C₄×C₈	C₂³	1	1	yes	characteristic
58	C₂×D₄	—	2	4	no	—
59	C₂×D₄	—	4	4	no	—
60	C₂×D₄	—	4	4	no	—
61	C₂²×C₄	—	4	4	no	—
62	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
63	D₈	—	2	4	no	—
64	D₈	—	2	4	no	—
65	D₈	—	4	4	no	—
66	M₁₆	—	2	2	no	—
67	C₂×C₈	—	2	1	no	—
68	C₂×C₈	—	2	1	no	—
69	C₂×C₈	C₂×D₄	1	1	yes	characteristic
70	C₂×C₈	C₂×D₄	1	1	yes	characteristic
71	C₂×C₈	C₂×D₄	1	1	yes	characteristic
72	C₂×C₈	C₂⁴	1	1	yes	characteristic
73	C₄⋊C₄	—	2	4	no	—
74	C₄⋊C₄	—	4	4	no	—
75	C₄⋊C₄	D₈	1	2	yes	—
76	C₂²⋊C₄	—	4	4	no	—
77	C₂²⋊C₄	—	4	4	no	—
78	C₂²⋊C₄	D₈	1	2	yes	—
79	C₄²	C₂×D₄	1	1	yes	characteristic
80	C₄²	C₂×D₄	1	1	yes	characteristic
81	C₁₆	—	2	1	no	—
82	C₁₆	—	2	1	no	—
83	C₁₆	#41	1	2	yes	—
84	C₁₆	#41	1	2	yes	—
85	C₂³	—	4	4	no	—
86	C₂³	C₂×D₈	1	1	yes	characteristic
87	D₄	—	4	4	no	—
88	D₄	—	4	4	no	—
89	D₄	—	16	4	no	—
90	D₄	—	16	4	no	—
91	C₂×C₄	—	2	1	no	—
92	C₂×C₄	—	2	1	no	—
93	C₂×C₄	—	4	4	no	—
94	C₂×C₄	—	16	4	no	—
95	C₂×C₄	C₂×D₈	1	2	yes	—
96	C₂×C₄	C₂×D₈	1	2	yes	—
97	C₂×C₄	C₂×D₈	1	1	yes	characteristic
98	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
99	C₈	—	2	1	no	—
100	C₈	—	2	1	no	—
101	C₈	#135	1	2	yes	—
102	C₈	C₂×#41	1	1	yes	characteristic
103	C₈	C₂×#41	1	1	yes	characteristic
104	C₂²	—	2	2	no	—
105	C₂²	—	2	1	no	—
106	C₂²	—	8	4	no	—
107	C₂²	—	8	4	no	—
108	C₂²	—	8	4	no	—
109	C₂²	C₂²×D₈	1	1	yes	characteristic
110	C₄	—	2	2	no	—
111	C₄	—	2	2	no	—
112	C₄	—	2	1	no	—
113	C₄	—	8	4	no	—
114	C₄	#532	1	1	yes	characteristic
115	C₄	C₂×#135	1	1	yes	characteristic
116	C₂	—	4	1	no	—
117	C₂	—	16	4	no	—
118	C₂	#3169	1	1	yes	characteristic
119	C₂	#3415	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#3176

C₂

yes

maximal, complemented

#2253

C₂

yes

maximal, characteristic, complemented

#2246

C₂

yes

maximal, characteristic, complemented

#2244

C₂

yes

maximal, complemented

#2218

C₂

yes

maximal, complemented

#2215

C₂

yes

maximal, complemented

#2177

C₂

yes

maximal, complemented

C₄×D₁₆

C₂

yes

maximal, complemented

#2108

C₂

yes

maximal, characteristic, complemented

#540

—

C₂×D₁₆

C₂²

yes

—

C₂×D₁₆

C₂²

yes

—

C₂×M₃₂

C₂²

yes

characteristic

C₂²×C₁₆

C₂²

yes

characteristic

#499

C₂²

yes

—

#493

C₂²

yes

—

#490

—

#469

—

#466

C₂²

yes

—

#442

—

C₄×D₈

C₂²

yes

—

#405

C₂²

yes

characteristic

#367

C₂²

yes

—

#366

C₂²

yes

—

#357

C₂²

yes

—

#357

C₂²

yes

—

#346

C₂²

yes

characteristic

#346

C₂²

yes

characteristic

C₄×C₁₆

C₂²

yes

characteristic

C₄×C₁₆

C₂²

yes

characteristic

C₂×D₈

—

C₂×D₈

C₂³

yes

—

C₂×M₁₆

D₄

yes

characteristic

C₂²×C₈

C₂³

yes

—

—

—

—

—

C₄×D₄

—

#117

D₄

yes

characteristic

D₁₆

—

D₁₆

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂³

yes

characteristic

C₂×C₁₆

C₂³

yes

characteristic

C₂×C₁₆

C₂³

yes

characteristic

C₂×C₁₆

C₂³

yes

characteristic

#107

C₂³

yes

—

—

—

—

D₄

yes

characteristic

#97

D₄

yes

characteristic

C₄×C₈

C₂³

yes

characteristic

C₄×C₈

C₂³

yes

characteristic

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₄

yes

characteristic

D₈

—

D₈

—

D₈

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×D₄

yes

characteristic

C₂×C₈

C₂×D₄

yes

characteristic

C₂×C₈

C₂×D₄

yes

characteristic

C₂×C₈

C₂⁴

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

D₈

yes

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

D₈

yes

—

C₄²

C₂×D₄

yes

characteristic

C₄²

C₂×D₄

yes

characteristic

C₁₆

—

C₁₆

—

C₁₆

#41

yes

—

C₁₆

#41

yes

—

C₂³

—

C₂³

C₂×D₈

yes

characteristic

D₄

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₈

yes

—

C₂×C₄

C₂×D₈

yes

—

C₂×C₄

C₂×D₈

yes

characteristic

C₂×C₄

C₂²×D₄

yes

characteristic

C₈

—

100

C₈

—

101

C₈

#135

yes

—

102

C₈

C₂×#41

yes

characteristic

103

C₈

C₂×#41

yes

characteristic

104

C₂²

—

105

C₂²

—

106

C₂²

—

107

C₂²

—

108

C₂²

—

109

C₂²

C₂²×D₈

yes

characteristic

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

#532

yes

characteristic

115

C₄

C₂×#135

yes

characteristic

116

C₂

—

117

C₂

—

118

C₂

#3169

yes

characteristic

119

C₂

#3415

yes

—

	subgroup	G/H
center, socle	C₂²	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ #117 ◁ #405 ◁ G
LECS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

subgroup

G/H

center, socle

C₂²

C₂²×D₈

commutator, Frattini, cosocle

C₂×C₈

C₂⁴

LCS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂² ◁ #117 ◁ #405 ◁ G

LECS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

N	H ≅ G/N	type
1. #3176	C₂	semidirect
2. #2253	C₂	semidirect
3. #2246	C₂	semidirect
4. #2244	C₂	semidirect
5. #2218	C₂	semidirect
6. #2215	C₂	semidirect
7. #2177	C₂	semidirect
8. C₄×D₁₆	C₂	semidirect
9. #2108	C₂	semidirect

H ≅ G/N

type

1. #3176

C₂

semidirect

2. #2253

C₂

semidirect

3. #2246

C₂

semidirect

4. #2244

C₂

semidirect

5. #2218

C₂

semidirect

6. #2215

C₂

semidirect

7. #2177

C₂

semidirect

8. C₄×D₁₆

C₂

semidirect

9. #2108

C₂

semidirect

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

subgroup	index
#3176	2
#2253	2
#2246	2
#2244	2
#2218	2
#2215	2
#2177	2
C₄×D₁₆	2
#2108	2

subgroup

index

C₄×D₁₆

Subgroups — #33740

Conjugacy classes of subgroups

Complements

Maximal subgroups