Group #22626296 — subgroups

Subgroups — #22626296

Order 9344.

138 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 70 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	C₄⋊#11924031	C₂	1	2	yes	maximal, complemented
2	C₂²⋊#11924031	C₂	1	2	yes	maximal
3	#17989475	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#11924031	C₂	1	1	yes	maximal, characteristic, complemented
5	#17988543	C₂	1	1	yes	maximal, characteristic
6	C₂×#11924031	C₂²	1	2	yes	—
7	C₂×#11924031	C₂²	1	2	yes	—
8	C₂×#11924012	C₄	1	1	yes	characteristic
9	C₂²×#10596831	C₂²	1	1	yes	characteristic
10	#14556502	C₄	1	1	yes	characteristic
11	#14556502	C₄	1	1	yes	characteristic
12	C₄×#10596831	C₂²	1	1	yes	characteristic
13	C₄×#10596831	C₂²	1	1	yes	characteristic
14	#117×C₇₃	C₄	1	1	yes	characteristic
15	#11924031	—	2	2	no	—
16	#11924031	—	2	2	no	—
17	#11924012	—	2	2	no	—
18	C₂×#10596831	—	2	2	no	—
19	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
20	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
21	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
22	C₂×#10596831	C₂³	1	1	yes	characteristic
23	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
24	C₄⋊C₄×C₇₃	C₈	1	2	yes	—
25	C₂²⋊C₄×C₇₃	C₈	1	2	yes	—
26	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
27	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₇₃	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₇₃	—	2	1	no	—
30	C₂×C₄×C₇₃	—	2	1	no	—
31	C₂×C₄×C₇₃	C₂×C₈	1	2	yes	—
32	C₂×C₄×C₇₃	C₂×C₈	1	2	yes	—
33	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
34	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
35	#10596831	—	2	1	no	—
36	#10596831	—	2	1	no	—
37	#10596831	M₁₆	1	2	yes	—
38	#10596831	#41	1	2	yes	—
39	C₂²×C₇₃	—	2	1	no	—
40	C₂²×C₇₃	—	2	2	no	—
41	C₂²×C₇₃	C₂²×C₈	1	1	yes	characteristic
42	C₄×C₇₃	—	2	1	no	—
43	C₄×C₇₃	—	2	2	no	—
44	C₄×C₇₃	—	2	2	no	—
45	C₄×C₇₃	#117	1	1	yes	characteristic
46	C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
47	C₂×C₇₃	—	4	1	no	—
48	C₂×C₇₃	#431	1	1	yes	characteristic
49	C₂×C₇₃	#504	1	2	yes	—
50	#2164	—	73	1	no	maximal, Sylow
51	C₇₃	#2164	1	1	yes	characteristic, complemented, Sylow
52	#405	—	73	1	no	—
53	C₄⋊C₁₆	—	73	2	no	—
54	C₂²⋊C₁₆	—	73	2	no	—
55	#346	—	73	1	no	—
56	C₄×C₁₆	—	73	1	no	—
57	C₂×M₁₆	—	73	1	no	—
58	C₂²×C₈	—	73	1	no	—
59	#117	#64408	1	1	yes	characteristic
60	C₂×C₁₆	—	73	2	no	—
61	C₂×C₁₆	—	73	2	no	—
62	#97	—	73	1	no	—
63	#97	—	73	1	no	—
64	C₄×C₈	—	73	1	no	—
65	C₄×C₈	—	73	1	no	—
66	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
67	M₁₆	—	146	2	no	—
68	C₂×C₈	—	73	1	no	—
69	C₂×C₈	—	73	1	no	—
70	C₂×C₈	—	73	1	no	—
71	C₂×C₈	—	73	1	no	—
72	C₂×C₈	—	146	2	no	—
73	C₄⋊C₄	#10596833	1	2	yes	—
74	C₂²⋊C₄	#10596833	1	2	yes	—
75	C₄²	C₂×#64408	1	1	yes	characteristic
76	C₄²	C₂×#64408	1	1	yes	characteristic
77	C₁₆	—	146	2	no	—
78	C₁₆	—	146	2	no	—
79	C₂³	C₂×#10596833	1	1	yes	characteristic
80	C₂×C₄	—	2	1	no	—
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	C₂×#10596833	1	2	yes	—
83	C₂×C₄	C₂×#10596833	1	2	yes	—
84	C₂×C₄	C₂×#10596833	1	1	yes	characteristic
85	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
86	C₈	—	73	2	no	—
87	C₈	—	73	2	no	—
88	C₈	—	146	1	no	—
89	C₈	—	146	1	no	—
90	C₂²	—	2	2	no	—
91	C₂²	—	2	1	no	—
92	C₂²	C₂²×#10596833	1	1	yes	characteristic
93	C₄	—	2	2	no	—
94	C₄	—	2	2	no	—
95	C₄	—	2	1	no	—
96	C₄	#14556670	1	1	yes	characteristic
97	C₄	D₇₃⋊M₁₆	1	1	yes	characteristic
98	C₂	—	4	1	no	—
99	C₂	#17989603	1	1	yes	characteristic
100	C₂	#17989645	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊#11924031

C₂

yes

maximal, complemented

C₂²⋊#11924031

C₂

yes

maximal

#17989475

C₂

yes

maximal, characteristic, complemented

C₄×#11924031

C₂

yes

maximal, characteristic, complemented

#17988543

C₂

yes

maximal, characteristic

C₂×#11924031

C₂²

yes

—

C₂×#11924031

C₂²

yes

—

C₂×#11924012

C₄

yes

characteristic

C₂²×#10596831

C₂²

yes

characteristic

#14556502

C₄

yes

characteristic

#14556502

C₄

yes

characteristic

C₄×#10596831

C₂²

yes

characteristic

C₄×#10596831

C₂²

yes

characteristic

#117×C₇₃

C₄

yes

—

—

—

—

C₂×C₄

yes

characteristic

C₂×#10596831

C₂×C₄

yes

characteristic

C₂×#10596831

C₂×C₄

yes

characteristic

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

characteristic

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₂³×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₈

yes

—

C₂×C₄×C₇₃

C₂×C₈

yes

—

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

—

—

M₁₆

yes

—

#10596831

#41

yes

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂²×C₈

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#117

yes

characteristic

C₄×C₇₃

C₂×M₁₆

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

#431

yes

characteristic

C₂×C₇₃

#504

yes

—

#2164

—

maximal, Sylow

C₇₃

#2164

yes

characteristic, complemented, Sylow

#405

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

#346

—

C₄×C₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

#117

#64408

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

C₂×#64408

yes

characteristic

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₄⋊C₄

#10596833

yes

—

C₂²⋊C₄

#10596833

yes

—

C₄²

yes

C₄²

yes

C₁₆

—

146

—

C₁₆

—

146

—

C₂³

C₂×#10596833

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×#10596833

yes

—

C₂×C₄

C₂×#10596833

yes

—

C₂×C₄

C₂×#10596833

yes

characteristic

C₂×C₄

C₂²×#64408

yes

characteristic

C₈

—

C₈

—

C₈

—

146

—

C₈

—

146

—

C₂²

—

C₂²

—

C₂²

C₂²×#10596833

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

#14556670

yes

characteristic

C₄

D₇₃⋊M₁₆

yes

characteristic

C₂

—

C₂

#17989603

yes

characteristic

100

C₂

#17989645

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#64408
commutator, socle	C₂²×C₇₃	C₂²×C₈
Fitting	#117×C₇₃	C₄
hypercenter	#117	#64408
hypocenter	C₇₃	#2164
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ #117

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#64408

commutator, socle

C₂²×C₇₃

C₂²×C₈

Fitting

#117×C₇₃

C₄

C₇₃

G ▷ C₂²×C₇₃ ▷ C₇₃

C₁ ◁ C₂×C₄ ◁ #117

N	H ≅ G/N	type
1. C₄⋊#11924031	C₂	semidirect
3. #17989475	C₂	semidirect
4. C₄×#11924031	C₂	semidirect
51. C₇₃	#2164	semidirect

H ≅ G/N

type

1. C₄⋊#11924031

C₂

semidirect

3. #17989475

C₂

semidirect

4. C₄×#11924031

C₂

semidirect

51. C₇₃

#2164

semidirect

Subgroups — #22626296

Conjugacy classes of subgroups

Complements