Group #22612193 — subgroups

Subgroups — #22612193

Order 9344.

184 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 53 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×#14556534	C₂	1	2	yes	maximal, complemented
2	C₂×D₁₁₆₈	C₂	1	1	yes	maximal, characteristic
3	#17988972	C₂	1	2	yes	maximal, complemented
4	C₁₆×Dic₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₃₂×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11924015	—	2	2	no	—
7	C₂×D₅₈₄	C₂²	1	2	yes	—
8	#14556580	—	2	2	no	—
9	#14556534	—	2	4	no	—
10	D₁₁₆₈	—	2	2	no	—
11	C₂×#11924003	C₂²	1	1	yes	characteristic
12	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
13	C₂×Q₁₆×C₇₃	C₂²	1	2	yes	—
14	Q₃₂×C₇₃	—	2	2	no	—
15	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×D₂₉₂	—	2	2	no	—
17	#11924015	—	4	4	no	—
18	D₅₈₄	—	2	2	no	—
19	D₅₈₄	—	2	2	no	—
20	C₂×#10596831	D₄	1	1	yes	characteristic
21	#11924005	—	4	4	no	—
22	C₄×Dic₇₃	D₄	1	1	yes	characteristic
23	#11924003	D₄	1	2	yes	—
24	C₂×Q₈×C₇₃	—	2	2	no	—
25	Q₁₆×C₇₃	—	2	2	no	—
26	Q₁₆×C₇₃	—	2	2	no	—
27	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
28	C₁₆×C₇₃	D₄	1	2	yes	—
29	C₂²×D₇₃	—	4	2	no	—
30	Q₈×C₇₃	—	4	2	no	—
31	Q₈×C₇₃	—	4	2	no	—
32	C₂×C₄×C₇₃	—	4	2	no	—
33	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
34	C₂×Dic₇₃	D₈	1	2	yes	—
35	D₂₉₂	—	4	2	no	—
36	D₂₉₂	—	4	2	no	—
37	C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
38	C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
39	#10596831	D₈	1	2	yes	—
40	C₂²×C₇₃	C₂×D₈	1	1	yes	characteristic
41	C₂×D₇₃	—	8	2	no	—
42	C₂×D₇₃	—	8	4	no	—
43	C₄×C₇₃	—	8	2	no	—
44	C₄×C₇₃	#127	1	1	yes	characteristic
45	C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
46	Dic₇₃	—	2	2	no	—
47	C₂×C₇₃	#493	1	1	yes	characteristic
48	C₂×C₇₃	#508	1	2	yes	—
49	D₇₃	—	16	2	no	—
50	#2249	—	73	1	no	maximal, Sylow
51	C₇₃	#2249	1	1	yes	characteristic, complemented, Sylow
52	C₂×Q₃₂	D₇₃	1	1	yes	characteristic, complemented
53	C₂×SD₃₂	—	73	2	no	—
54	C₂×D₁₆	—	73	1	no	—
55	#495	—	73	2	no	—
56	C₄×C₁₆	—	73	1	no	—
57	C₂×Q₁₆	C₂×D₇₃	1	2	yes	—
58	C₂×SD₁₆	—	146	2	no	—
59	C₂×D₈	—	73	2	no	—
60	#124	—	146	2	no	—
61	Q₃₂	—	2	2	no	—
62	SD₃₂	—	146	4	no	—
63	D₁₆	—	146	2	no	—
64	C₂×C₁₆	—	73	1	no	—
65	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
66	C₄×C₈	—	73	1	no	—
67	C₂×Q₈	—	2	2	no	—
68	C₂×D₄	—	146	2	no	—
69	Q₁₆	—	2	2	no	—
70	Q₁₆	—	2	2	no	—
71	SD₁₆	—	292	4	no	—
72	D₈	—	146	2	no	—
73	D₈	—	146	2	no	—
74	C₂×C₈	—	73	1	no	—
75	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
76	C₂²⋊C₄	—	292	4	no	—
77	C₄²	—	73	1	no	—
78	C₁₆	—	73	2	no	—
79	C₁₆	C₂²⋊D₇₃	1	2	yes	—
80	C₂³	—	292	2	no	—
81	Q₈	—	4	2	no	—
82	Q₈	—	4	2	no	—
83	D₄	—	292	2	no	—
84	D₄	—	292	2	no	—
85	C₂×C₄	—	4	2	no	—
86	C₂×C₄	—	73	2	no	—
87	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
88	C₈	—	73	2	no	—
89	C₈	D₄×D₇₃	1	1	yes	characteristic
90	C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
91	C₂²	—	584	2	no	—
92	C₂²	—	584	4	no	—
93	C₂²	D₈×D₇₃	1	1	yes	characteristic
94	C₄	—	8	2	no	—
95	C₄	—	146	2	no	—
96	C₄	#14556587	1	1	yes	characteristic
97	C₄	D₈×D₇₃	1	1	yes	characteristic
98	C₂	—	1168	2	no	—
99	C₂	#17988962	1	1	yes	characteristic
100	C₂	#17989020	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556534

C₂

yes

maximal, complemented

C₂×D₁₁₆₈

C₂

yes

maximal, characteristic

#17988972

C₂

yes

maximal, complemented

C₁₆×Dic₇₃

C₂

yes

maximal, characteristic, complemented

C₂×Q₃₂×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂×#11924015

—

C₂×D₅₈₄

C₂²

yes

—

#14556580

—

#14556534

—

D₁₁₆₈

—

C₂×#11924003

C₂²

yes

characteristic

C₈×Dic₇₃

C₂²

yes

characteristic

C₂×Q₁₆×C₇₃

C₂²

yes

—

Q₃₂×C₇₃

—

C₂×C₁₆×C₇₃

C₂²

yes

characteristic

C₂×D₂₉₂

—

#11924015

—

D₅₈₄

—

D₅₈₄

—

C₂×#10596831

D₄

yes

characteristic

#11924005

—

C₄×Dic₇₃

D₄

yes

characteristic

#11924003

D₄

yes

—

C₂×Q₈×C₇₃

—

Q₁₆×C₇₃

—

Q₁₆×C₇₃

—

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₁₆×C₇₃

D₄

yes

—

C₂²×D₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

D₈

yes

—

D₂₉₂

—

D₂₉₂

—

C₈×C₇₃

C₂×D₄

yes

characteristic

C₈×C₇₃

C₂×D₄

yes

characteristic

#10596831

D₈

yes

—

C₂²×C₇₃

C₂×D₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#127

yes

characteristic

C₄×C₇₃

C₂×D₈

yes

characteristic

Dic₇₃

—

C₂×C₇₃

#493

yes

characteristic

C₂×C₇₃

#508

yes

—

D₇₃

—

#2249

—

maximal, Sylow

C₇₃

#2249

yes

characteristic, complemented, Sylow

C₂×Q₃₂

D₇₃

yes

characteristic, complemented

C₂×SD₃₂

—

C₂×D₁₆

—

#495

—

C₄×C₁₆

—

C₂×Q₁₆

C₂×D₇₃

yes

—

C₂×SD₁₆

—

146

—

C₂×D₈

—

#124

—

146

—

Q₃₂

—

SD₃₂

—

146

—

D₁₆

—

146

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₃

yes

characteristic

C₄×C₈

—

C₂×Q₈

—

C₂×D₄

—

146

—

Q₁₆

—

Q₁₆

—

SD₁₆

—

292

—

D₈

—

146

—

D₈

—

146

—

C₂×C₈

—

C₂×C₈

C₂²×D₇₃

yes

characteristic

C₂²⋊C₄

—

292

—

C₄²

—

C₁₆

—

C₁₆

C₂²⋊D₇₃

yes

—

C₂³

—

292

—

Q₈

—

Q₈

—

D₄

—

292

—

D₄

—

292

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₄×D₇₃

yes

characteristic

C₈

—

C₈

D₄×D₇₃

yes

characteristic

C₈

C₂×C₂²⋊D₇₃

yes

characteristic

C₂²

—

584

—

C₂²

—

584

—

C₂²

D₈×D₇₃

yes

characteristic

C₄

—

C₄

—

146

—

C₄

#14556587

yes

characteristic

C₄

D₈×D₇₃

yes

characteristic

C₂

—

1168

—

C₂

#17988962

yes

characteristic

100

C₂

#17989020

yes

—

	subgroup	G/H
center	C₂²	D₈×D₇₃
commutator	C₂×C₈×C₇₃	C₂³
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	C₂×Q₃₂×C₇₃	C₂
socle	C₂²×C₇₃	C₂×D₈
hypercenter	C₂×Q₃₂	D₇₃
hypocenter	C₇₃	#2249
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₃₂

subgroup

G/H

center

C₂²

D₈×D₇₃

commutator

C₂×C₈×C₇₃

C₂³

Frattini

C₂×C₈

C₂²×D₇₃

Fitting

C₂×Q₃₂×C₇₃

C₂

socle

C₂²×C₇₃

C₂×D₈

hypercenter

C₂×Q₃₂

D₇₃

hypocenter

C₇₃

#2249

LCS

G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₃₂

N	H ≅ G/N	type
1. C₂×#14556534	C₂	semidirect
3. #17988972	C₂	semidirect
4. C₁₆×Dic₇₃	C₂	semidirect
5. C₂×Q₃₂×C₇₃	C₂	semidirect
51. C₇₃	#2249	semidirect
52. C₂×Q₃₂	D₇₃	semidirect

H ≅ G/N

type

1. C₂×#14556534

C₂

semidirect

3. #17988972

C₂

semidirect

4. C₁₆×Dic₇₃

C₂

semidirect

5. C₂×Q₃₂×C₇₃

C₂

semidirect

51. C₇₃

#2249

semidirect

52. C₂×Q₃₂

D₇₃

semidirect

Subgroups — #22612193

Conjugacy classes of subgroups

Complements