Group #22624981 — subgroups

Subgroups — #22624981

Order 9344.

132 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 62 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×#14556665	C₂	1	1	yes	maximal, characteristic
2	C₂×#14556665	C₂	1	1	yes	maximal, characteristic
3	#17988543	C₂	1	1	yes	maximal, characteristic
4	#14556665	—	2	1	no	—
5	#14556665	—	2	1	no	—
6	#14556665	—	2	1	no	—
7	#14556665	C₄	1	2	yes	complemented
8	C₂×#11924031	—	2	1	no	—
9	C₂×#11924031	C₄	1	2	yes	complemented
10	C₂×#11924012	C₄	1	1	yes	characteristic
11	C₂²×#10596831	C₂²	1	1	yes	characteristic
12	#14556502	—	2	1	no	—
13	C₄×#10596831	—	2	1	no	—
14	#117×C₇₃	C₄	1	1	yes	characteristic
15	#11924031	—	2	2	no	—
16	#11924031	—	2	2	no	—
17	#11924012	—	2	1	no	—
18	#11924012	C₈	1	2	yes	—
19	C₂×#10596831	—	2	1	no	—
20	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
21	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
22	C₂×#10596831	D₄	1	1	yes	characteristic
23	C₂×#10596831	D₄	1	1	yes	characteristic
24	C₂×#10596831	D₄	1	1	yes	characteristic
25	C₂×#10596831	Q₈	1	1	yes	characteristic
26	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
27	C₄⋊C₄×C₇₃	—	2	1	no	—
28	C₂²⋊C₄×C₇₃	C₈	1	2	yes	—
29	C₄²×C₇₃	—	2	1	no	—
30	C₂³×C₇₃	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₇₃	—	2	2	no	—
32	C₂×C₄×C₇₃	C₄²	1	1	yes	characteristic
33	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
36	C₂×C₄×C₇₃	M₁₆	1	1	yes	characteristic
37	C₂×C₄×C₇₃	M₁₆	1	1	yes	characteristic
38	#10596831	—	2	2	no	—
39	#10596831	C₂²⋊C₄	1	1	yes	characteristic
40	#10596831	C₂²⋊C₄	1	1	yes	characteristic
41	#10596831	C₄⋊C₄	1	1	yes	characteristic
42	#10596831	C₄⋊C₄	1	1	yes	characteristic
43	C₂²×C₇₃	—	4	1	no	—
44	C₂²×C₇₃	C₄×C₈	1	1	yes	characteristic
45	C₂²×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
46	C₂²×C₇₃	C₄⋊C₈	1	1	yes	characteristic
47	C₄×C₇₃	—	4	2	no	—
48	C₄×C₇₃	#95	1	1	yes	characteristic
49	C₄×C₇₃	#97	1	1	yes	characteristic
50	C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
51	C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
52	C₂×C₇₃	—	2	1	no	—
53	C₂×C₇₃	—	2	1	no	—
54	C₂×C₇₃	—	2	1	no	—
55	C₂×C₇₃	#336	1	1	yes	characteristic
56	#1378	—	73	1	no	maximal, Sylow
57	C₇₃	#1378	1	1	yes	characteristic, complemented, Sylow
58	C₂×M₃₂	—	73	1	no	—
59	C₂×M₃₂	—	73	1	no	—
60	#405	—	73	1	no	—
61	C₂×M₁₆	—	73	1	no	—
62	C₂²×C₈	—	73	1	no	—
63	#117	#64408	1	1	yes	characteristic
64	M₃₂	—	73	2	no	—
65	M₃₂	—	146	1	no	—
66	M₃₂	—	146	1	no	—
67	M₃₂	—	146	1	no	—
68	C₂×C₁₆	—	73	2	no	—
69	C₂×C₁₆	—	146	1	no	—
70	#97	—	146	1	no	—
71	C₄×C₈	—	146	1	no	—
72	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
73	M₁₆	—	73	2	no	—
74	M₁₆	—	146	1	no	—
75	C₂×C₈	—	73	1	no	—
76	C₂×C₈	—	73	1	no	—
77	C₂×C₈	—	73	1	no	—
78	C₂×C₈	—	73	1	no	—
79	C₂×C₈	—	73	1	no	—
80	C₂×C₈	—	73	1	no	—
81	C₂×C₈	—	146	1	no	—
82	C₄⋊C₄	—	2	1	no	—
83	C₂²⋊C₄	#10596833	1	2	yes	—
84	C₄²	—	2	1	no	—
85	C₁₆	—	146	2	no	—
86	C₁₆	—	146	2	no	—
87	C₂³	C₂×#10596833	1	1	yes	characteristic
88	C₂×C₄	—	2	2	no	—
89	C₂×C₄	C₄×#64408	1	1	yes	characteristic
90	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
91	C₂×C₄	C₄⋊#64408	1	1	yes	characteristic
92	C₂×C₄	#11924036	1	1	yes	characteristic
93	C₂×C₄	#11924037	1	1	yes	characteristic
94	C₂×C₄	#11924038	1	1	yes	characteristic
95	C₈	—	73	1	no	—
96	C₈	—	73	1	no	—
97	C₈	—	73	1	no	—
98	C₈	—	73	1	no	—
99	C₈	—	146	2	no	—
100	C₂²	—	4	1	no	—
101	C₂²	C₄×#10596833	1	1	yes	characteristic
102	C₂²	C₂²⋊#10596833	1	1	yes	characteristic
103	C₂²	C₄⋊#10596833	1	1	yes	characteristic
104	C₄	—	4	2	no	—
105	C₄	(C₂×#64408)⋊C₄	1	1	yes	characteristic
106	C₄	#14556646	1	1	yes	characteristic
107	C₄	#14556648	1	1	yes	characteristic
108	C₄	#14556658	1	1	yes	characteristic
109	C₂	—	2	1	no	—
110	C₂	—	2	1	no	—
111	C₂	—	2	1	no	—
112	C₂	#17989453	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556665

C₂

yes

maximal, characteristic

C₂×#14556665

C₂

yes

maximal, characteristic

#17988543

C₂

yes

maximal, characteristic

—

—

—

C₄

yes

complemented

C₂×#11924031

—

C₂×#11924031

C₄

yes

complemented

C₂×#11924012

C₄

yes

characteristic

C₂²×#10596831

C₂²

yes

characteristic

#14556502

—

C₄×#10596831

—

#117×C₇₃

C₄

yes

—

—

—

C₈

yes

—

C₂×#10596831

—

C₂×#10596831

C₂×C₄

yes

characteristic

C₂×#10596831

C₂×C₄

yes

characteristic

C₂×#10596831

D₄

yes

characteristic

C₂×#10596831

D₄

yes

characteristic

C₂×#10596831

D₄

yes

characteristic

C₂×#10596831

Q₈

yes

characteristic

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₄⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

C₈

yes

—

C₄²×C₇₃

—

C₂³×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₄²

yes

characteristic

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

M₁₆

yes

characteristic

C₂×C₄×C₇₃

M₁₆

yes

characteristic

#10596831

—

#10596831

C₂²⋊C₄

yes

characteristic

#10596831

C₂²⋊C₄

yes

characteristic

#10596831

C₄⋊C₄

yes

characteristic

#10596831

C₄⋊C₄

yes

characteristic

C₂²×C₇₃

—

C₂²×C₇₃

C₄×C₈

yes

characteristic

C₂²×C₇₃

C₂²⋊C₈

yes

characteristic

C₂²×C₇₃

C₄⋊C₈

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

C₂²⋊C₈

yes

characteristic

C₄×C₇₃

C₄⋊C₈

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂×M₃₂

—

#405

—

C₂×M₁₆

—

C₂²×C₈

—

#117

#64408

yes

characteristic

M₃₂

—

M₃₂

—

146

—

M₃₂

—

146

—

M₃₂

—

146

—

C₂×C₁₆

—

C₂×C₁₆

—

146

—

#97

—

146

—

C₄×C₈

—

146

—

C₂²×C₄

C₂×#64408

yes

characteristic

M₁₆

—

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₄⋊C₄

—

C₂²⋊C₄

#10596833

yes

—

C₄²

—

C₁₆

—

146

—

C₁₆

—

146

—

C₂³

C₂×#10596833

yes

characteristic

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

—

146

—

100

C₂²

—

101

C₂²

C₄×#10596833

yes

characteristic

102

C₂²

C₂²⋊#10596833

yes

characteristic

103

C₂²

C₄⋊#10596833

yes

characteristic

104

C₄

—

105

C₄

(C₂×#64408)⋊C₄

yes

characteristic

106

C₄

#14556646

yes

characteristic

107

C₄

#14556648

yes

characteristic

108

C₄

#14556658

yes

characteristic

109

C₂

—

110

C₂

—

111

C₂

—

112

C₂

#17989453

yes

characteristic

	subgroup	G/H
center	C₄	(C₂×#64408)⋊C₄
commutator	C₂²×C₇₃	C₄×C₈
Frattini	C₂²×C₄	C₂×#64408
Fitting	#117×C₇₃	C₄
socle	C₂×C₇₃	#336
hypercenter	#117	#64408
hypocenter	C₇₃	#1378
LCS	G ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #117

subgroup

G/H

center

C₄

(C₂×#64408)⋊C₄

commutator

C₂²×C₇₃

C₄×C₈

Frattini

C₂²×C₄

C₂×#64408

Fitting

#117×C₇₃

C₄

C₂×C₇₃

C₇₃

G ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #117

N	H ≅ G/N	type
7. #14556665	C₄	semidirect
9. C₂×#11924031	C₄	semidirect
57. C₇₃	#1378	semidirect

H ≅ G/N

type

7. #14556665

C₄

semidirect

9. C₂×#11924031

C₄

semidirect

57. C₇₃

#1378

semidirect

Subgroups — #22624981

Conjugacy classes of subgroups

Complements