Group #11740690 — subgroups

Subgroups — #11740690

Order 896.

416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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×C₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#6433	C₂	1	1	yes	maximal, characteristic
3	#90002	C₂	1	4	yes	maximal
4	#89754	C₂	1	8	yes	maximal
5	#89704	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₇×Q₈	C₂²	1	2	yes	—
7	C₇×C₄⋊Q₈	—	2	4	no	—
8	C₂×C₇×C₄⋊C₄	C₂²	1	4	yes	—
9	C₂×C₄²×C₇	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₇	C₂²	1	2	yes	—
11	C₂×Dic₇⋊C₄	C₂²	1	4	yes	—
12	C₂×C₄×Dic₇	C₂²	1	2	yes	—
13	#6433	—	2	4	no	—
14	C₇⋊#95	C₂²	1	4	yes	—
15	C₇⋊#95	C₂²	1	16	yes	—
16	#2642	—	7	1	no	maximal, Sylow
17	C₂×C₇×Q₈	—	2	4	no	—
18	C₂×C₇×Q₈	—	2	8	no	—
19	C₂²×C₄×C₇	C₂³	1	4	yes	—
20	C₂²×C₄×C₇	C₂³	1	2	yes	—
21	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
22	C₂²×Dic₇	C₂³	1	4	yes	—
23	C₂²×Dic₇	C₂³	1	4	yes	—
24	C₇×C₄⋊C₄	—	2	8	no	—
25	C₄²×C₇	D₄	1	4	yes	—
26	C₄⋊Dic₇	—	2	4	no	—
27	Dic₇⋊C₄	—	2	8	no	—
28	C₄×Dic₇	—	2	4	no	—
29	C₂×C₄⋊Q₈	D₇	1	1	yes	characteristic
30	C₂×#125	—	7	1	no	—
31	#400	—	7	8	no	—
32	#391	—	7	4	no	—
33	#376	—	7	1	no	—
34	C₂³×C₇	C₂⁴	1	1	yes	characteristic
35	C₇×Q₈	—	4	8	no	—
36	C₂×C₄×C₇	—	2	4	no	—
37	C₂×C₄×C₇	—	2	4	no	—
38	C₂×C₄×C₇	—	2	8	no	—
39	C₂×C₄×C₇	C₂×D₄	1	4	yes	—
40	C₂×C₄×C₇	C₂×D₄	1	2	yes	—
41	C₂×C₄×C₇	#41	1	4	yes	—
42	C₂×Dic₇	—	2	4	no	—
43	C₂×Dic₇	—	2	4	no	—
44	C₂×Dic₇	—	2	8	no	—
45	C₂×Dic₇	—	2	8	no	—
46	C₂²×Q₈	C₂×D₇	1	2	yes	—
47	C₄⋊Q₈	—	2	4	no	—
48	#125	—	14	4	no	—
49	C₂×C₄⋊C₄	—	7	4	no	—
50	C₂×C₄⋊C₄	—	7	2	no	—
51	C₂×C₄⋊C₄	C₂×D₇	1	4	yes	—
52	C₂×C₄²	—	7	2	no	—
53	C₂×C₄²	C₂×D₇	1	1	yes	characteristic
54	#95	—	7	4	no	—
55	#95	—	7	16	no	—
56	C₂²×C₇	C₂²×D₄	1	1	yes	characteristic
57	C₂²×C₇	C₂×#41	1	2	yes	—
58	C₂²×C₇	2₋¹⁺⁴	1	4	yes	—
59	C₄×C₇	—	2	4	no	—
60	C₄×C₇	—	4	4	no	—
61	C₄×C₇	#124	1	4	yes	—
62	Dic₇	—	4	4	no	—
63	Dic₇	—	4	4	no	—
64	C₂×Q₈	—	2	8	no	—
65	C₂×Q₈	—	2	4	no	—
66	C₂²×C₄	—	7	4	no	—
67	C₂²×C₄	—	7	4	no	—
68	C₂²×C₄	C₂²×D₇	1	4	yes	—
69	C₂²×C₄	C₂²×D₇	1	2	yes	—
70	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
71	C₄⋊C₄	—	2	8	no	—
72	C₄⋊C₄	—	14	8	no	—
73	C₄⋊C₄	—	14	4	no	—
74	C₄²	—	14	4	no	—
75	C₄²	C₂²⋊D₇	1	4	yes	—
76	C₂×C₇	C₂×#124	1	1	yes	characteristic
77	C₂×C₇	#536	1	2	yes	—
78	C₂×C₇	#541	1	4	yes	—
79	C₂³	C₂³×D₇	1	1	yes	characteristic
80	Q₈	—	4	8	no	—
81	C₂×C₄	—	2	4	no	—
82	C₂×C₄	—	2	8	no	—
83	C₂×C₄	—	2	4	no	—
84	C₂×C₄	—	14	4	no	—
85	C₂×C₄	—	14	8	no	—
86	C₂×C₄	—	14	8	no	—
87	C₂×C₄	—	14	4	no	—
88	C₂×C₄	#1159	1	4	yes	—
89	C₂×C₄	C₂×C₂²⋊D₇	1	4	yes	—
90	C₂×C₄	C₂×C₂²⋊D₇	1	2	yes	—
91	C₇	#2642	1	1	yes	characteristic, complemented, Sylow
92	C₂²	C₂×#1159	1	2	yes	—
93	C₂²	#6551	1	4	yes	—
94	C₂²	C₂²×C₂²⋊D₇	1	1	yes	characteristic
95	C₄	—	2	4	no	—
96	C₄	—	4	4	no	—
97	C₄	—	28	4	no	—
98	C₄	—	28	4	no	—
99	C₄	#6499	1	4	yes	—
100	C₂	#90422	1	4	yes	—
101	C₂	C₂×#6499	1	1	yes	characteristic
102	C₂	#90507	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₇×C₄⋊Q₈

C₂

yes

maximal, characteristic

C₂×#6433

C₂

yes

maximal, characteristic

#90002

C₂

yes

maximal

#89754

C₂

yes

maximal

#89704

C₂

yes

maximal, characteristic

C₂²×C₇×Q₈

C₂²

yes

—

C₇×C₄⋊Q₈

—

C₂×C₇×C₄⋊C₄

C₂²

yes

—

C₂×C₄²×C₇

C₂²

yes

characteristic

C₂×C₄⋊Dic₇

C₂²

yes

—

C₂×Dic₇⋊C₄

C₂²

yes

—

C₂×C₄×Dic₇

C₂²

yes

—

#6433

—

C₇⋊#95

C₂²

yes

—

C₇⋊#95

C₂²

yes

—

#2642

—

maximal, Sylow

C₂×C₇×Q₈

—

C₂×C₇×Q₈

—

C₂²×C₄×C₇

C₂³

yes

—

C₂²×C₄×C₇

C₂³

yes

—

C₂²×C₄×C₇

C₂³

yes

characteristic

C₂²×Dic₇

C₂³

yes

—

C₂²×Dic₇

C₂³

yes

—

C₇×C₄⋊C₄

—

C₄²×C₇

D₄

yes

—

C₄⋊Dic₇

—

Dic₇⋊C₄

—

C₄×Dic₇

—

C₂×C₄⋊Q₈

D₇

yes

—

—

—

—

C₂³×C₇

C₂⁴

yes

characteristic

C₇×Q₈

—

C₂×C₄×C₇

—

C₂×C₄×C₇

—

C₂×C₄×C₇

—

C₂×C₄×C₇

C₂×D₄

yes

—

C₂×C₄×C₇

C₂×D₄

yes

—

C₂×C₄×C₇

#41

yes

—

C₂×Dic₇

—

C₂×Dic₇

—

C₂×Dic₇

—

C₂×Dic₇

—

C₂²×Q₈

C₂×D₇

yes

—

C₄⋊Q₈

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₇

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×D₇

yes

characteristic

#95

—

#95

—

C₂²×C₇

C₂²×D₄

yes

characteristic

C₂²×C₇

C₂×#41

yes

—

C₂²×C₇

2₋¹⁺⁴

yes

—

C₄×C₇

—

C₄×C₇

—

C₄×C₇

#124

yes

—

Dic₇

—

Dic₇

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₇

yes

—

C₂²×C₄

C₂²×D₇

yes

—

C₂²×C₄

C₂²×D₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂²⋊D₇

yes

—

C₂×C₇

C₂×#124

yes

characteristic

C₂×C₇

#536

yes

—

C₂×C₇

#541

yes

—

C₂³

C₂³×D₇

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#1159

yes

—

C₂×C₄

C₂×C₂²⋊D₇

yes

—

C₂×C₄

C₂×C₂²⋊D₇

yes

—

C₇

#2642

yes

characteristic, complemented, Sylow

C₂²

C₂×#1159

yes

—

C₂²

#6551

yes

—

C₂²

C₂²×C₂²⋊D₇

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

#6499

yes

—

100

C₂

#90422

yes

—

101

C₂

C₂×#6499

yes

characteristic

102

C₂

#90507

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇
commutator, socle, prime radical, cosocle	C₂³×C₇	C₂⁴
Fitting	C₂×C₇×C₄⋊Q₈	C₂
hypercenter	C₂×C₄⋊Q₈	D₇
hypocenter	C₇	#2642
LCS	G ▷ C₂³×C₇ ▷ C₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

subgroup

G/H

center, Frattini

C₂³

C₂³×D₇

commutator, socle, prime radical, cosocle

C₂³×C₇

C₂⁴

Fitting

C₂×C₇×C₄⋊Q₈

C₂

hypercenter

C₂×C₄⋊Q₈

D₇

C₇

G ▷ C₂³×C₇ ▷ C₇

C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

N	H ≅ G/N	type
91. C₇	#2642	semidirect

H ≅ G/N

type

91. C₇

#2642

semidirect

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

subgroup	index
C₂×C₇×C₄⋊Q₈	2
C₂×#6433	2
#90002	2
#89754	2
#89704	2
#2642	7

subgroup

index

C₂×C₇×C₄⋊Q₈

Subgroups — #11740690

Conjugacy classes of subgroups

Complements

Maximal subgroups