Group #22611713 — subgroups

Subgroups — #22611713

Order 9344.

152 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 85 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	C₂²×#11924003	C₂	1	1	yes	maximal, characteristic
2	#17988625	C₂	1	1	yes	maximal, characteristic
3	#17988414	C₂	1	2	yes	maximal, complemented
4	#17988412	C₂	1	2	yes	maximal, complemented
5	#427×C₇₃	C₂	1	1	yes	maximal, characteristic
6	#14556550	—	2	1	no	—
7	C₂×#11924003	C₄	1	4	yes	complemented
8	C₂×#11924003	C₂²	1	1	yes	characteristic
9	C₂×#11924003	C₂²	1	1	yes	characteristic
10	#14556525	C₂²	1	2	yes	—
11	#14556523	—	2	1	no	—
12	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
13	#117×C₇₃	—	2	1	no	—
14	#107×C₇₃	C₂²	1	2	yes	—
15	#106×C₇₃	—	2	1	no	—
16	C₄⋊Dic₇₃	—	2	2	no	—
17	C₂²⋊Dic₇₃	—	4	1	no	—
18	C₄×Dic₇₃	—	4	1	no	—
19	#11924003	C₂×C₄	1	2	yes	—
20	#11924003	C₂×C₄	1	2	yes	—
21	C₂²×C₄×C₇₃	D₄	1	1	yes	characteristic
22	C₂×C₈×C₇₃	C₂×C₄	1	2	yes	—
23	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
24	C₂×C₈×C₇₃	Q₈	1	2	yes	—
25	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
26	C₄⋊C₄×C₇₃	—	2	2	no	—
27	C₂²⋊C₄×C₇₃	—	4	1	no	—
28	C₄²×C₇₃	—	4	1	no	—
29	C₂³×C₇₃	D₈	1	1	yes	characteristic
30	C₂×C₄×C₇₃	—	4	2	no	—
31	C₂×C₄×C₇₃	C₄⋊C₄	1	2	yes	—
32	C₂×C₄×C₇₃	D₈	1	1	yes	characteristic
33	C₂×C₄×C₇₃	Q₁₆	1	2	yes	—
34	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
35	C₂×Dic₇₃	—	4	2	no	—
36	C₈×C₇₃	C₄⋊C₄	1	2	yes	—
37	C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
38	C₈×C₇₃	C₂×Q₈	1	1	yes	characteristic
39	C₂²×C₇₃	—	2	2	no	—
40	C₂²×C₇₃	#107	1	2	yes	—
41	C₂²×C₇₃	C₂×D₈	1	1	yes	characteristic
42	C₄×C₇₃	—	8	2	no	—
43	C₄×C₇₃	#107	1	2	yes	—
44	C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
45	C₄×C₇₃	C₂×Q₁₆	1	1	yes	characteristic
46	Dic₇₃	—	8	2	no	—
47	C₂×C₇₃	—	2	2	no	—
48	C₂×C₇₃	C₂×#107	1	1	yes	characteristic
49	C₂×C₇₃	#508	1	2	yes	—
50	#2158	—	73	1	no	maximal, Sylow
51	C₇₃	#2158	1	1	yes	characteristic, complemented, Sylow
52	C₂²×C₁₆	—	73	1	no	—
53	#427	—	73	1	no	—
54	#427	D₇₃	1	1	yes	characteristic
55	#367	—	73	2	no	—
56	#366	—	73	2	no	—
57	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
58	#117	—	2	1	no	—
59	#117	—	146	1	no	—
60	C₂×C₁₆	—	73	4	no	—
61	C₂×C₁₆	—	73	1	no	—
62	C₂×C₁₆	—	73	1	no	—
63	#107	—	73	2	no	—
64	#107	C₂×D₇₃	1	2	yes	—
65	#106	—	2	1	no	—
66	#106	—	146	1	no	—
67	C₂²×C₄	C₂²⋊D₇₃	1	1	yes	characteristic
68	C₂×C₈	Dic₁₄₆	1	2	yes	—
69	C₂×C₈	C₄×D₇₃	1	2	yes	—
70	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
71	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
72	C₄⋊C₄	—	2	2	no	—
73	C₄⋊C₄	—	146	2	no	—
74	C₂²⋊C₄	—	4	1	no	—
75	C₂²⋊C₄	—	292	1	no	—
76	C₄²	—	4	1	no	—
77	C₄²	—	292	1	no	—
78	C₁₆	—	73	2	no	—
79	C₁₆	—	73	2	no	—
80	C₂³	#11924013	1	1	yes	characteristic
81	C₂×C₄	—	4	2	no	—
82	C₂×C₄	—	292	2	no	—
83	C₂×C₄	#11924007	1	2	yes	—
84	C₂×C₄	#11924013	1	1	yes	characteristic
85	C₂×C₄	#11924018	1	2	yes	—
86	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
87	C₈	#11924007	1	2	yes	—
88	C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
89	C₈	C₂×Dic₁₄₆	1	1	yes	characteristic
90	C₂²	—	2	2	no	—
91	C₂²	#14556524	1	2	yes	—
92	C₂²	C₂×#11924013	1	1	yes	characteristic
93	C₄	—	8	2	no	—
94	C₄	—	584	2	no	—
95	C₄	#14556524	1	2	yes	—
96	C₄	C₂×#11924007	1	1	yes	characteristic
97	C₄	C₂×#11924018	1	1	yes	characteristic
98	C₂	—	2	2	no	—
99	C₂	C₂×#14556524	1	1	yes	characteristic
100	C₂	#17989017	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#11924003

C₂

yes

maximal, characteristic

#17988625

C₂

yes

maximal, characteristic

#17988414

C₂

yes

maximal, complemented

#17988412

C₂

yes

maximal, complemented

#427×C₇₃

C₂

yes

maximal, characteristic

#14556550

—

C₂×#11924003

C₄

yes

complemented

C₂×#11924003

C₂²

yes

characteristic

C₂×#11924003

C₂²

yes

characteristic

#14556525

C₂²

yes

—

#14556523

—

C₂²×C₈×C₇₃

C₂²

yes

characteristic

#117×C₇₃

—

#107×C₇₃

C₂²

yes

—

#106×C₇₃

—

C₄⋊Dic₇₃

—

C₂²⋊Dic₇₃

—

C₄×Dic₇₃

—

#11924003

C₂×C₄

yes

—

#11924003

C₂×C₄

yes

—

C₂²×C₄×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

—

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

Q₈

yes

—

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₄⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₂³×C₇₃

D₈

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₄⋊C₄

yes

—

C₂×C₄×C₇₃

D₈

yes

characteristic

C₂×C₄×C₇₃

Q₁₆

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

—

C₈×C₇₃

C₄⋊C₄

yes

—

C₈×C₇₃

C₂²×C₄

yes

characteristic

C₈×C₇₃

C₂×Q₈

yes

characteristic

C₂²×C₇₃

—

C₂²×C₇₃

#107

yes

—

C₂²×C₇₃

C₂×D₈

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

#107

yes

—

C₄×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₇₃

C₂×Q₁₆

yes

characteristic

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

C₂×#107

yes

characteristic

C₂×C₇₃

#508

yes

—

#2158

—

maximal, Sylow

C₇₃

#2158

yes

characteristic, complemented, Sylow

C₂²×C₁₆

—

#427

—

#427

D₇₃

yes

characteristic

#367

—

#366

—

C₂²×C₈

C₂×D₇₃

yes

characteristic

#117

—

#117

—

146

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

#107

—

#107

C₂×D₇₃

yes

—

#106

—

#106

—

146

—

C₂²×C₄

C₂²⋊D₇₃

yes

characteristic

C₂×C₈

Dic₁₄₆

yes

—

C₂×C₈

C₄×D₇₃

yes

—

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

C₂×C₈

C₂²×D₇₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

146

—

C₂²⋊C₄

—

C₂²⋊C₄

—

292

—

C₄²

—

C₄²

—

292

—

C₁₆

—

C₁₆

—

C₂³

#11924013

yes

characteristic

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

#11924007

yes

—

C₂×C₄

#11924013

yes

characteristic

C₂×C₄

#11924018

yes

—

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

C₈

#11924007

yes

—

C₈

C₂×C₄×D₇₃

yes

characteristic

C₈

C₂×Dic₁₄₆

yes

characteristic

C₂²

—

C₂²

#14556524

yes

—

C₂²

C₂×#11924013

yes

characteristic

C₄

—

C₄

—

584

—

C₄

#14556524

yes

—

C₄

yes

C₄

yes

C₂

—

C₂

C₂×#14556524

yes

characteristic

100

C₂

#17989017

yes

—

	subgroup	G/H
center	C₂×C₄	#11924013
commutator	C₈×C₇₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	#427×C₇₃	C₂
socle	C₂²×C₇₃	C₂×D₈
hypercenter	#427	D₇₃
hypocenter	C₇₃	#2158
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #427

subgroup

G/H

center

C₂×C₄

#11924013

commutator

C₈×C₇₃

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₇₃

Fitting

#427×C₇₃

C₂

socle

C₂²×C₇₃

C₂×D₈

D₇₃

C₇₃

G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #427

N	H ≅ G/N	type
3. #17988414	C₂	semidirect
4. #17988412	C₂	semidirect
7. C₂×#11924003	C₄	semidirect
51. C₇₃	#2158	semidirect

H ≅ G/N

type

3. #17988414

C₂

semidirect

4. #17988412

C₂

semidirect

7. C₂×#11924003

C₄

semidirect

51. C₇₃

#2158

semidirect

Subgroups — #22611713

Conjugacy classes of subgroups

Complements