Group #22617923 — subgroups

Subgroups — #22617923

Order 9344.

432 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 149 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	#17988507	C₂	1	3	yes	maximal
2	#17988506	C₂	1	2	yes	maximal
3	#17988492	C₂	1	3	yes	maximal
4	#17988491	C₂	1	6	yes	maximal
5	#395×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₄₆	C₂²	1	1	yes	characteristic
7	C₂²×Dic₁₄₆	C₂²	1	3	yes	—
8	C₂×#11924007	C₂²	1	6	yes	—
9	C₂×C₄×Dic₇₃	C₂²	1	3	yes	—
10	#14556498	C₂²	1	6	yes	—
11	#14556498	C₂²	1	6	yes	—
12	#14556498	C₂²	1	3	yes	—
13	C₂²×Q₈×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₄×C₇₃	C₂²	1	3	yes	—
15	#95×C₇₃	C₂²	1	3	yes	—
16	C₂×Dic₁₄₆	—	4	3	no	—
17	C₂×Dic₁₄₆	—	4	3	no	—
18	C₂×Dic₁₄₆	—	4	3	no	—
19	C₂×Dic₁₄₆	Q₈	1	12	yes	complemented
20	C₂²×Dic₇₃	C₂³	1	2	yes	—
21	C₂²×Dic₇₃	C₂³	1	6	yes	—
22	#11924007	—	4	6	no	—
23	C₄×Dic₇₃	—	4	3	no	—
24	C₂×Q₈×C₇₃	—	4	3	no	—
25	C₂²×C₄×C₇₃	C₂³	1	3	yes	—
26	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
27	C₂²×C₄×C₇₃	C₂³	1	3	yes	—
28	C₄⋊C₄×C₇₃	—	4	3	no	—
29	C₂³×C₇₃	C₂⁴	1	1	yes	characteristic
30	Q₈×C₇₃	—	4	4	no	—
31	C₂×C₄×C₇₃	—	2	3	no	—
32	C₂×C₄×C₇₃	—	2	3	no	—
33	C₂×C₄×C₇₃	—	2	3	no	—
34	C₂×C₄×C₇₃	—	2	3	no	—
35	C₂×C₄×C₇₃	—	2	6	no	—
36	C₂×C₄×C₇₃	C₂×Q₈	1	6	yes	—
37	C₂×Dic₇₃	—	2	6	no	—
38	C₂×Dic₇₃	—	2	6	no	—
39	C₂×Dic₇₃	—	2	6	no	—
40	C₂×Dic₇₃	C₂×Q₈	1	12	yes	—
41	Dic₁₄₆	—	4	12	no	—
42	Dic₁₄₆	—	4	4	no	—
43	C₂²×C₇₃	C₂²×Q₈	1	3	yes	—
44	C₂²×C₇₃	H(5,𝔽₂)	1	3	yes	—
45	C₂²×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
46	C₄×C₇₃	—	2	6	no	—
47	C₄×C₇₃	—	4	1	no	—
48	C₄×C₇₃	—	4	3	no	—
49	Dic₇₃	—	2	12	no	—
50	Dic₇₃	—	4	2	no	—
51	C₂×C₇₃	#543	1	3	yes	—
52	C₂×C₇₃	Q₈²	1	3	yes	—
53	C₂×C₇₃	H(3,𝔽₄)	1	1	yes	characteristic
54	#2811	—	73	1	no	maximal, Sylow
55	C₇₃	#2811	1	1	yes	characteristic, complemented, Sylow
56	#395	—	73	2	no	—
57	#395	—	73	3	no	—
58	#395	D₇₃	1	1	yes	characteristic
59	#391	—	73	3	no	—
60	#391	—	73	6	no	—
61	C₂²×Q₈	—	73	1	no	—
62	C₂²×Q₈	—	73	3	no	—
63	C₂²×Q₈	C₂×D₇₃	1	1	yes	characteristic
64	C₂×C₄⋊C₄	—	73	6	no	—
65	C₂×C₄⋊C₄	C₂×D₇₃	1	3	yes	—
66	C₂×C₄²	—	73	3	no	—
67	#95	—	73	3	no	—
68	#95	—	73	6	no	—
69	#95	—	73	6	no	—
70	#95	C₂×D₇₃	1	3	yes	—
71	C₂×Q₈	—	4	3	no	—
72	C₂×Q₈	—	292	3	no	—
73	C₂×Q₈	—	292	3	no	—
74	C₂×Q₈	—	292	3	no	—
75	C₂×Q₈	—	73	12	no	—
76	C₂²×C₄	—	73	6	no	—
77	C₂²×C₄	—	73	2	no	—
78	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
79	C₂²×C₄	C₂²×D₇₃	1	3	yes	—
80	C₂²×C₄	C₂²×D₇₃	1	3	yes	—
81	C₄⋊C₄	—	4	3	no	—
82	C₄⋊C₄	—	292	6	no	—
83	C₄²	—	292	3	no	—
84	C₂³	C₂³×D₇₃	1	1	yes	characteristic
85	Q₈	—	4	4	no	—
86	Q₈	—	292	12	no	—
87	Q₈	—	292	4	no	—
88	C₂×C₄	—	2	3	no	—
89	C₂×C₄	—	2	3	no	—
90	C₂×C₄	—	2	3	no	—
91	C₂×C₄	—	2	3	no	—
92	C₂×C₄	—	2	6	no	—
93	C₂×C₄	—	73	12	no	—
94	C₂×C₄	—	146	6	no	—
95	C₂×C₄	—	146	6	no	—
96	C₂×C₄	—	146	6	no	—
97	C₂×C₄	Q₈×D₇₃	1	6	yes	—
98	C₂²	C₂×Q₈×D₇₃	1	3	yes	—
99	C₂²	#14556636	1	3	yes	—
100	C₂²	#14556637	1	1	yes	characteristic
101	C₄	—	2	6	no	—
102	C₄	—	4	3	no	—
103	C₄	—	4	1	no	—
104	C₄	—	292	2	no	—
105	C₄	—	146	12	no	—
106	C₂	#17989212	1	3	yes	—
107	C₂	#17989317	1	3	yes	—
108	C₂	#17989330	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988507

C₂

yes

maximal

#17988506

C₂

yes

maximal

#17988492

C₂

yes

maximal

#17988491

C₂

yes

maximal

#395×C₇₃

C₂

yes

maximal, characteristic

C₂²×Dic₁₄₆

C₂²

yes

characteristic

C₂²×Dic₁₄₆

C₂²

yes

—

C₂×#11924007

C₂²

yes

—

C₂×C₄×Dic₇₃

C₂²

yes

—

#14556498

C₂²

yes

—

#14556498

C₂²

yes

—

#14556498

C₂²

yes

—

C₂²×Q₈×C₇₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₇₃

C₂²

yes

—

#95×C₇₃

C₂²

yes

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

Q₈

yes

complemented

C₂²×Dic₇₃

C₂³

yes

—

C₂²×Dic₇₃

C₂³

yes

—

#11924007

—

C₄×Dic₇₃

—

C₂×Q₈×C₇₃

—

C₂²×C₄×C₇₃

C₂³

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₂²×C₄×C₇₃

C₂³

yes

—

C₄⋊C₄×C₇₃

—

C₂³×C₇₃

C₂⁴

yes

characteristic

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×Q₈

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂×Q₈

yes

—

Dic₁₄₆

—

Dic₁₄₆

—

C₂²×C₇₃

C₂²×Q₈

yes

—

C₂²×C₇₃

H(5,𝔽₂)

yes

—

C₂²×C₇₃

H(5,𝔽₂)

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

#543

yes

—

C₂×C₇₃

Q₈²

yes

—

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#395

—

#395

—

#395

D₇₃

yes

characteristic

#391

—

#391

—

C₂²×Q₈

—

C₂²×Q₈

—

C₂²×Q₈

C₂×D₇₃

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₇₃

yes

—

C₂×C₄²

—

—

—

—

C₂×D₇₃

yes

—

C₂×Q₈

—

C₂×Q₈

—

292

—

C₂×Q₈

—

292

—

C₂×Q₈

—

292

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

C₂²×C₄

C₂²×D₇₃

yes

—

C₂²×C₄

C₂²×D₇₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

292

—

C₄²

—

292

—

C₂³

C₂³×D₇₃

yes

characteristic

Q₈

—

Q₈

—

292

—

Q₈

—

292

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

Q₈×D₇₃

yes

—

C₂²

C₂×Q₈×D₇₃

yes

—

C₂²

#14556636

yes

—

100

C₂²

#14556637

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

—

104

C₄

—

292

—

105

C₄

—

146

—

106

C₂

#17989212

yes

—

107

C₂

#17989317

yes

—

108

C₂

#17989330

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇₃
commutator, socle	C₂³×C₇₃	C₂⁴
Fitting	#395×C₇₃	C₂
hypercenter	#395	D₇₃
hypocenter	C₇₃	#2811
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ #395

subgroup

G/H

center, Frattini

C₂³

C₂³×D₇₃

commutator, socle

C₂³×C₇₃

C₂⁴

Fitting

#395×C₇₃

C₂

D₇₃

C₇₃

G ▷ C₂³×C₇₃ ▷ C₇₃

C₁ ◁ C₂³ ◁ #395

N	H ≅ G/N	type
19. C₂×Dic₁₄₆	Q₈	semidirect
55. C₇₃	#2811	semidirect

H ≅ G/N

type

19. C₂×Dic₁₄₆

Q₈

semidirect

55. C₇₃

#2811

semidirect

Subgroups — #22617923

Conjugacy classes of subgroups

Complements