Group #22610896 — subgroups

Subgroups — #22610896

Order 9344.

252 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 109 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×#14556583	C₂	1	1	yes	maximal, characteristic
2	#17988453	C₂	1	1	yes	maximal, characteristic
3	#17988350	C₂	1	4	yes	maximal
4	C₂×C₄×C₈×C₇₃	C₂	1	1	yes	maximal, characteristic
5	#14556583	—	2	2	no	—
6	#14556583	C₄	1	4	yes	complemented
7	C₂×C₄⋊Dic₇₃	C₂²	1	2	yes	—
8	C₂×C₄⋊Dic₇₃	C₂²	1	2	yes	—
9	C₂×#11924007	—	2	2	no	—
10	#14556498	—	2	2	no	—
11	C₂²×C₈×C₇₃	C₂²	1	2	yes	—
12	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₇₃	—	2	2	no	—
14	C₂²×Dic₇₃	—	2	2	no	—
15	C₂²×Dic₇₃	—	2	2	no	—
16	C₄⋊Dic₇₃	—	2	2	no	—
17	C₄⋊Dic₇₃	—	2	4	no	—
18	C₄⋊Dic₇₃	C₂×C₄	1	4	yes	—
19	#11924007	—	2	8	no	—
20	C₂²×C₄×C₇₃	D₄	1	2	yes	—
21	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
22	C₂×C₈×C₇₃	—	2	2	no	—
23	C₂×C₈×C₇₃	—	2	2	no	—
24	C₂×C₈×C₇₃	Q₈	1	4	yes	—
25	C₄²×C₇₃	C₂×C₄	1	2	yes	—
26	C₄²×C₇₃	D₄	1	2	yes	—
27	C₂³×C₇₃	C₂×D₄	1	1	yes	characteristic
28	C₂×C₄×C₇₃	—	2	4	no	—
29	C₂×C₄×C₇₃	C₂²⋊C₄	1	4	yes	—
30	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₇₃	C₂×Q₈	1	2	yes	—
33	C₂×C₄×C₇₃	#41	1	2	yes	—
34	C₂×Dic₇₃	—	2	4	no	—
35	C₂×Dic₇₃	—	4	4	no	—
36	C₂×Dic₇₃	—	4	2	no	—
37	C₂×Dic₇₃	—	4	4	no	—
38	C₈×C₇₃	—	2	4	no	—
39	C₂²×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
40	C₂²×C₇₃	#124	1	1	yes	characteristic
41	C₂²×C₇₃	C₄⋊Q₈	1	1	yes	characteristic
42	C₂²×C₇₃	#135	1	4	yes	—
43	C₄×C₇₃	—	2	4	no	—
44	C₄×C₇₃	C₄×Q₈	1	2	yes	—
45	C₄×C₇₃	C₂²⋊Q₈	1	2	yes	—
46	Dic₇₃	—	4	4	no	—
47	Dic₇₃	—	8	2	no	—
48	C₂×C₇₃	#391	1	1	yes	characteristic
49	C₂×C₇₃	#416	1	2	yes	—
50	C₂×C₇₃	#488	1	2	yes	—
51	C₂×C₇₃	#499	1	2	yes	—
52	#1991	—	73	1	no	maximal, Sylow
53	C₇₃	#1991	1	1	yes	characteristic, complemented, Sylow
54	C₂×#125	—	73	1	no	—
55	C₂×C₄×C₈	D₇₃	1	1	yes	characteristic
56	#382	—	73	1	no	—
57	#340	—	73	4	no	—
58	C₂²×C₈	C₂×D₇₃	1	2	yes	—
59	#125	—	73	4	no	—
60	#125	—	146	2	no	—
61	C₂×C₄⋊C₄	—	73	2	no	—
62	C₂×C₄⋊C₄	—	73	2	no	—
63	C₂×C₄⋊C₄	—	146	2	no	—
64	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
65	C₄×C₈	—	2	2	no	—
66	#95	—	146	2	no	—
67	C₂²×C₄	—	146	2	no	—
68	C₂²×C₄	—	146	2	no	—
69	C₂²×C₄	D₂₉₂	1	2	yes	—
70	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
71	C₂×C₈	—	2	2	no	—
72	C₂×C₈	—	2	2	no	—
73	C₂×C₈	Dic₁₄₆	1	4	yes	—
74	C₄⋊C₄	—	73	4	no	—
75	C₄⋊C₄	—	146	4	no	—
76	C₄⋊C₄	—	146	8	no	—
77	C₄⋊C₄	—	146	2	no	—
78	C₄²	C₄×D₇₃	1	2	yes	—
79	C₄²	C₂²⋊D₇₃	1	2	yes	—
80	C₂³	C₂×D₂₉₂	1	1	yes	characteristic
81	C₂×C₄	—	2	4	no	—
82	C₂×C₄	—	292	4	no	—
83	C₂×C₄	—	292	2	no	—
84	C₂×C₄	—	292	4	no	—
85	C₂×C₄	—	146	4	no	—
86	C₂×C₄	#11924005	1	4	yes	—
87	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
88	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
89	C₂×C₄	C₂×Dic₁₄₆	1	2	yes	—
90	C₂×C₄	#11924028	1	2	yes	—
91	C₈	—	2	4	no	—
92	C₂²	C₂×#11924005	1	1	yes	characteristic
93	C₂²	#14556579	1	1	yes	characteristic
94	C₂²	#14556591	1	1	yes	characteristic
95	C₂²	#14556613	1	4	yes	—
96	C₄	—	2	4	no	—
97	C₄	—	292	4	no	—
98	C₄	—	584	2	no	—
99	C₄	C₄×Dic₁₄₆	1	2	yes	—
100	C₄	#14556570	1	2	yes	—
101	C₂	#17988493	1	1	yes	characteristic
102	C₂	#17988584	1	2	yes	—
103	C₂	#17988942	1	2	yes	—
104	C₂	#17988989	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556583

C₂

yes

maximal, characteristic

#17988453

C₂

yes

maximal, characteristic

#17988350

C₂

yes

maximal

C₂×C₄×C₈×C₇₃

C₂

yes

maximal, characteristic

#14556583

—

#14556583

C₄

yes

complemented

C₂×C₄⋊Dic₇₃

C₂²

yes

—

C₂×C₄⋊Dic₇₃

C₂²

yes

—

C₂×#11924007

—

#14556498

—

C₂²×C₈×C₇₃

C₂²

yes

—

C₂×C₄²×C₇₃

C₂²

yes

characteristic

C₄×C₈×C₇₃

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

C₂×C₄

yes

—

#11924007

—

C₂²×C₄×C₇₃

D₄

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

Q₈

yes

—

C₄²×C₇₃

C₂×C₄

yes

—

C₄²×C₇₃

D₄

yes

—

C₂³×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×Q₈

yes

—

C₂×C₄×C₇₃

#41

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₈×C₇₃

—

C₂²×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₇₃

#124

yes

characteristic

C₂²×C₇₃

C₄⋊Q₈

yes

characteristic

C₂²×C₇₃

#135

yes

—

C₄×C₇₃

—

C₄×C₇₃

C₄×Q₈

yes

—

C₄×C₇₃

C₂²⋊Q₈

yes

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

#391

yes

characteristic

C₂×C₇₃

#416

yes

—

C₂×C₇₃

#488

yes

—

C₂×C₇₃

#499

yes

—

#1991

—

maximal, Sylow

C₇₃

#1991

yes

characteristic, complemented, Sylow

C₂×#125

—

C₂×C₄×C₈

D₇₃

yes

characteristic

#382

—

#340

—

C₂²×C₈

C₂×D₇₃

yes

—

#125

—

#125

—

146

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

146

—

C₂×C₄²

C₂×D₇₃

yes

characteristic

C₄×C₈

—

#95

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

D₂₉₂

yes

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₁₄₆

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄²

C₄×D₇₃

yes

—

C₄²

C₂²⋊D₇₃

yes

—

C₂³

C₂×D₂₉₂

yes

characteristic

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

146

—

C₂×C₄

#11924005

yes

—

C₂×C₄

C₂×C₄×D₇₃

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

C₂×C₄

C₂×Dic₁₄₆

yes

—

C₂×C₄

#11924028

yes

—

C₈

—

C₂²

yes

C₂²

yes

C₂²

yes

C₂²

yes

—

C₄

—

C₄

—

292

—

C₄

—

584

—

C₄

C₄×Dic₁₄₆

yes

—

100

C₄

#14556570

yes

—

101

C₂

#17988493

yes

characteristic

102

C₂

#17988584

yes

—

103

C₂

#17988942

yes

—

104

C₂

#17988989

yes

—

	subgroup	G/H
center	C₂³	C₂×D₂₉₂
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	C₂×C₄×C₈×C₇₃	C₂
socle	C₂³×C₇₃	C₂×D₄
hypercenter	C₂×C₄×C₈	D₇₃
hypocenter	C₇₃	#1991
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂³

C₂×D₂₉₂

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

C₂×C₄×C₈×C₇₃

C₂

socle

C₂³×C₇₃

C₂×D₄

hypercenter

C₂×C₄×C₈

D₇₃

hypocenter

C₇₃

#1991

LCS

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
6. #14556583	C₄	semidirect
53. C₇₃	#1991	semidirect

H ≅ G/N

type

6. #14556583

C₄

semidirect

53. C₇₃

#1991

semidirect

Subgroups — #22610896

Conjugacy classes of subgroups

Complements