Group #22626140 — subgroups

Subgroups — #22626140

Order 9344.

184 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 114 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	C₂²×#11924031	C₂	1	1	yes	maximal, characteristic
3	#17989475	C₂	1	2	yes	maximal, complemented
4	C₄×#11924031	C₂	1	2	yes	maximal, complemented
5	#17988543	C₂	1	1	yes	maximal, characteristic
6	#14556665	C₄	1	4	yes	complemented
7	C₂×#11924031	C₄	1	4	yes	complemented
8	C₂×#11924031	C₂²	1	1	yes	characteristic
9	C₂×#11924031	C₂²	1	1	yes	characteristic
10	C₂×#11924031	C₂²	1	2	yes	—
11	C₂×#11924012	C₄	1	1	yes	characteristic
12	C₂²×#10596831	C₂²	1	1	yes	characteristic
13	#14556502	C₄	1	2	yes	—
14	C₄×#10596831	C₂²	1	2	yes	—
15	#117×C₇₃	C₄	1	1	yes	characteristic
16	#11924031	C₂×C₄	1	2	yes	—
17	#11924031	C₂×C₄	1	2	yes	—
18	#11924031	C₂×C₄	1	4	yes	—
19	#11924012	C₈	1	4	yes	—
20	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
21	C₂×#10596831	C₂×C₄	1	2	yes	—
22	C₂×#10596831	C₂×C₄	1	2	yes	—
23	C₂×#10596831	C₂×C₄	1	2	yes	—
24	C₂×#10596831	C₂³	1	1	yes	characteristic
25	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
26	C₄⋊C₄×C₇₃	C₈	1	2	yes	—
27	C₂²⋊C₄×C₇₃	C₈	1	2	yes	—
28	C₄²×C₇₃	C₂×C₄	1	2	yes	—
29	C₂³×C₇₃	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₇₃	C₄²	1	2	yes	—
31	C₂×C₄×C₇₃	C₂×C₈	1	4	yes	—
32	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
33	C₂×C₄×C₇₃	C₂×C₈	1	2	yes	—
34	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
35	#10596831	C₄²	1	2	yes	—
36	#10596831	C₂×C₈	1	4	yes	—
37	#10596831	C₂²×C₄	1	1	yes	characteristic
38	#10596831	C₂²×C₄	1	1	yes	characteristic
39	C₂²×C₇₃	—	2	2	no	—
40	C₂²×C₇₃	C₄×C₈	1	2	yes	—
41	C₂²×C₇₃	C₂²×C₈	1	1	yes	characteristic
42	C₄×C₇₃	—	2	4	no	—
43	C₄×C₇₃	C₄×C₈	1	2	yes	—
44	C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
45	C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
46	C₂×C₇₃	—	2	2	no	—
47	C₂×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
48	C₂×C₇₃	#504	1	2	yes	—
49	#2108	—	73	1	no	maximal, Sylow
50	C₇₃	#2108	1	1	yes	characteristic, complemented, Sylow
51	C₂×M₃₂	—	73	1	no	—
52	C₂²×C₁₆	—	73	1	no	—
53	#405	—	73	1	no	—
54	#346	—	73	2	no	—
55	C₄×C₁₆	—	73	2	no	—
56	C₂×M₁₆	—	73	1	no	—
57	C₂²×C₈	—	73	1	no	—
58	#117	#64408	1	1	yes	characteristic
59	M₃₂	—	73	4	no	—
60	C₂×C₁₆	—	73	1	no	—
61	C₂×C₁₆	—	73	2	no	—
62	C₂×C₁₆	—	73	1	no	—
63	C₂×C₁₆	—	73	4	no	—
64	#97	—	73	2	no	—
65	C₄×C₈	—	73	2	no	—
66	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
67	M₁₆	—	73	4	no	—
68	C₂×C₈	—	73	2	no	—
69	C₂×C₈	—	73	2	no	—
70	C₂×C₈	—	73	2	no	—
71	C₂×C₈	—	73	1	no	—
72	C₂×C₈	—	73	1	no	—
73	C₄⋊C₄	#10596833	1	2	yes	—
74	C₂²⋊C₄	#10596833	1	2	yes	—
75	C₄²	C₂×#64408	1	2	yes	—
76	C₁₆	—	73	2	no	—
77	C₁₆	—	73	2	no	—
78	C₁₆	—	73	4	no	—
79	C₂³	C₂×#10596833	1	1	yes	characteristic
80	C₂×C₄	C₄×#64408	1	2	yes	—
81	C₂×C₄	C₂×#10596833	1	4	yes	—
82	C₂×C₄	C₂×#10596833	1	1	yes	characteristic
83	C₂×C₄	#11924036	1	2	yes	—
84	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
85	C₈	—	73	4	no	—
86	C₈	—	73	1	no	—
87	C₈	—	73	1	no	—
88	C₈	—	73	2	no	—
89	C₂²	—	2	2	no	—
90	C₂²	C₄×#10596833	1	2	yes	—
91	C₂²	C₂²×#10596833	1	1	yes	characteristic
92	C₄	—	2	4	no	—
93	C₄	C₄×#10596833	1	2	yes	—
94	C₄	C₂×C₄×#64408	1	1	yes	characteristic
95	C₄	C₂×#11924036	1	1	yes	characteristic
96	C₂	—	2	2	no	—
97	C₂	C₂×C₄×#10596833	1	1	yes	characteristic
98	C₂	#17989645	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556665

C₂

yes

maximal, characteristic

C₂²×#11924031

C₂

yes

maximal, characteristic

#17989475

C₂

yes

maximal, complemented

C₄×#11924031

C₂

yes

maximal, complemented

#17988543

C₂

yes

maximal, characteristic

#14556665

C₄

yes

complemented

C₂×#11924031

C₄

yes

complemented

C₂×#11924031

C₂²

yes

characteristic

C₂×#11924031

C₂²

yes

characteristic

C₂×#11924031

C₂²

yes

—

C₂×#11924012

C₄

yes

characteristic

C₂²×#10596831

C₂²

yes

characteristic

#14556502

C₄

yes

—

C₄×#10596831

C₂²

yes

—

#117×C₇₃

C₄

yes

characteristic

#11924031

C₂×C₄

yes

—

#11924031

C₂×C₄

yes

—

#11924031

C₂×C₄

yes

—

#11924012

C₈

yes

—

C₂×#10596831

C₂×C₄

yes

characteristic

C₂×#10596831

C₂×C₄

yes

—

C₂×#10596831

C₂×C₄

yes

—

C₂×#10596831

C₂×C₄

yes

—

C₂×#10596831

C₂³

yes

characteristic

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₄⋊C₄×C₇₃

C₈

yes

—

C₂²⋊C₄×C₇₃

C₈

yes

—

C₄²×C₇₃

C₂×C₄

yes

—

C₂³×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

C₄²

yes

—

C₂×C₄×C₇₃

C₂×C₈

yes

—

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

C₂×C₈

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

#10596831

C₄²

yes

—

#10596831

C₂×C₈

yes

—

#10596831

C₂²×C₄

yes

characteristic

#10596831

C₂²×C₄

yes

characteristic

C₂²×C₇₃

—

C₂²×C₇₃

C₄×C₈

yes

—

C₂²×C₇₃

C₂²×C₈

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

C₄×C₈

yes

—

C₄×C₇₃

C₂×C₄²

yes

characteristic

C₄×C₇₃

C₂²×C₈

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

C₂×C₄×C₈

yes

characteristic

C₂×C₇₃

#504

yes

—

#2108

—

maximal, Sylow

C₇₃

#2108

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂²×C₁₆

—

#405

—

#346

—

C₄×C₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

#117

#64408

yes

characteristic

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

#97

—

C₄×C₈

—

C₂²×C₄

C₂×#64408

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

#10596833

yes

—

C₂²⋊C₄

#10596833

yes

—

C₄²

C₂×#64408

yes

—

C₁₆

—

C₁₆

—

C₁₆

—

C₂³

C₂×#10596833

yes

characteristic

C₂×C₄

C₄×#64408

yes

—

C₂×C₄

C₂×#10596833

yes

—

C₂×C₄

C₂×#10596833

yes

characteristic

C₂×C₄

#11924036

yes

—

C₂×C₄

C₂²×#64408

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

C₄×#10596833

yes

—

C₂²

C₂²×#10596833

yes

characteristic

C₄

—

C₄

C₄×#10596833

yes

—

C₄

C₂×C₄×#64408

yes

characteristic

C₄

C₂×#11924036

yes

characteristic

C₂

—

C₂

C₂×C₄×#10596833

yes

characteristic

C₂

#17989645

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#64408
commutator	C₂×C₇₃	C₂×C₄×C₈
Fitting	#117×C₇₃	C₄
socle	C₂²×C₇₃	C₂²×C₈
hypercenter	#117	#64408
hypocenter	C₇₃	#2108
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ #117

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#64408

commutator

C₂×C₇₃

C₂×C₄×C₈

Fitting

#117×C₇₃

C₄

socle

C₂²×C₇₃

C₂²×C₈

C₇₃

G ▷ C₂×C₇₃ ▷ C₇₃

C₁ ◁ C₂×C₄ ◁ #117

N	H ≅ G/N	type
3. #17989475	C₂	semidirect
4. C₄×#11924031	C₂	semidirect
6. #14556665	C₄	semidirect
7. C₂×#11924031	C₄	semidirect
50. C₇₃	#2108	semidirect

H ≅ G/N

type

3. #17989475

C₂

semidirect

4. C₄×#11924031

C₂

semidirect

6. #14556665

C₄

semidirect

7. C₂×#11924031

C₄

semidirect

50. C₇₃

#2108

semidirect

Subgroups — #22626140

Conjugacy classes of subgroups

Complements