Group #22613224 — subgroups

Subgroups — #22613224

Order 9344.

504 conjugacy classes of subgroups; only the 189 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 189 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×C₄×Dic₁₄₆	C₂	1	2	yes	maximal
2	#17988519	C₂	1	4	yes	maximal
3	#17988508	C₂	1	4	yes	maximal
4	C₄×C₄⋊Dic₇₃	C₂	1	4	yes	maximal
5	#376×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₄₆	C₂²	1	2	yes	—
7	C₄×Dic₁₄₆	—	2	8	no	—
8	C₂×C₄⋊Dic₇₃	C₂²	1	8	yes	—
9	C₂×C₄⋊Dic₇₃	C₂²	1	2	yes	—
10	C₂×#11924007	C₂²	1	4	yes	—
11	C₂×C₄×Dic₇₃	C₂²	1	4	yes	—
12	#14556498	C₂²	1	4	yes	—
13	#14556498	C₂²	1	4	yes	—
14	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×C₄²×C₇₃	C₂²	1	2	yes	—
16	#95×C₇₃	C₂²	1	4	yes	—
17	C₂×Dic₁₄₆	—	2	4	no	—
18	C₂×Dic₁₄₆	—	2	8	no	—
19	C₂²×Dic₇₃	C₂³	1	4	yes	—
20	C₂²×Dic₇₃	C₂³	1	4	yes	—
21	C₄⋊Dic₇₃	—	2	4	no	—
22	C₄⋊Dic₇₃	—	2	16	no	—
23	#11924007	—	2	8	no	—
24	C₄×Dic₇₃	—	2	8	no	—
25	C₂²×C₄×C₇₃	C₂³	1	2	yes	—
26	C₂²×C₄×C₇₃	C₂³	1	4	yes	—
27	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
28	C₄²×C₇₃	D₄	1	4	yes	—
29	C₄²×C₇₃	Q₈	1	8	yes	complemented
30	C₂³×C₇₃	C₂⁴	1	1	yes	characteristic
31	C₂×C₄×C₇₃	—	2	8	no	—
32	C₂×C₄×C₇₃	—	2	4	no	—
33	C₂×C₄×C₇₃	C₂×D₄	1	4	yes	—
34	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
35	C₂×C₄×C₇₃	C₂×Q₈	1	8	yes	—
36	C₂×C₄×C₇₃	C₂×Q₈	1	4	yes	—
37	C₂×Dic₇₃	—	2	4	no	—
38	C₂×Dic₇₃	—	2	4	no	—
39	C₂×Dic₇₃	—	2	4	no	—
40	C₂×Dic₇₃	—	2	8	no	—
41	C₂×Dic₇₃	#41	1	8	yes	—
42	Dic₁₄₆	—	2	16	no	—
43	C₂²×C₇₃	C₂²×D₄	1	1	yes	characteristic
44	C₂²×C₇₃	C₂²×Q₈	1	2	yes	—
45	C₂²×C₇₃	C₂×#41	1	4	yes	—
46	C₄×C₇₃	—	2	4	no	—
47	C₄×C₇₃	—	2	8	no	—
48	C₄×C₇₃	C₄⋊Q₈	1	4	yes	—
49	Dic₇₃	—	2	8	no	—
50	Dic₇₃	—	4	4	no	—
51	C₂×C₇₃	#525	1	2	yes	—
52	C₂×C₇₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
53	C₂×C₇₃	#533	1	4	yes	—
54	#2399	—	73	1	no	maximal, Sylow
55	C₇₃	#2399	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₄×Q₈	—	73	2	no	—
57	#398	—	73	4	no	—
58	#395	—	73	4	no	—
59	C₄×C₄⋊C₄	—	73	4	no	—
60	#376	D₇₃	1	1	yes	characteristic
61	C₂²×Q₈	—	73	2	no	—
62	C₄×Q₈	—	146	8	no	—
63	C₂×C₄⋊C₄	—	73	4	no	—
64	C₂×C₄⋊C₄	—	73	2	no	—
65	C₂×C₄⋊C₄	—	73	8	no	—
66	C₂×C₄²	—	73	4	no	—
67	C₂×C₄²	C₂×D₇₃	1	2	yes	—
68	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
69	#95	—	73	4	no	—
70	#95	—	73	4	no	—
71	#95	C₂×D₇₃	1	4	yes	—
72	C₂×Q₈	—	146	8	no	—
73	C₂×Q₈	—	146	4	no	—
74	C₂²×C₄	—	73	4	no	—
75	C₂²×C₄	—	73	4	no	—
76	C₂²×C₄	C₂²×D₇₃	1	2	yes	—
77	C₂²×C₄	C₂²×D₇₃	1	4	yes	—
78	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
79	C₄⋊C₄	—	146	16	no	—
80	C₄⋊C₄	—	146	8	no	—
81	C₄⋊C₄	—	146	4	no	—
82	C₄²	—	146	8	no	—
83	C₄²	Dic₁₄₆	1	8	yes	complemented
84	C₄²	D₂₉₂	1	4	yes	—
85	C₂³	C₂³×D₇₃	1	1	yes	characteristic
86	Q₈	—	146	16	no	—
87	C₂×C₄	—	2	8	no	—
88	C₂×C₄	—	2	4	no	—
89	C₂×C₄	—	73	8	no	—
90	C₂×C₄	—	146	4	no	—
91	C₂×C₄	—	146	8	no	—
92	C₂×C₄	—	146	4	no	—
93	C₂×C₄	—	146	4	no	—
94	C₂×C₄	C₂×D₂₉₂	1	4	yes	—
95	C₂×C₄	C₂×D₂₉₂	1	2	yes	—
96	C₂×C₄	C₂×Dic₁₄₆	1	8	yes	—
97	C₂×C₄	C₂×Dic₁₄₆	1	4	yes	—
98	C₂²	C₂²×D₂₉₂	1	1	yes	characteristic
99	C₂²	C₂²×Dic₁₄₆	1	2	yes	—
100	C₂²	#41×D₇₃	1	4	yes	—
101	C₄	—	2	8	no	—
102	C₄	—	2	4	no	—
103	C₄	—	292	4	no	—
104	C₄	—	146	8	no	—
105	C₄	#14556591	1	4	yes	—
106	C₂	#17989099	1	2	yes	—
107	C₂	C₂×#14556591	1	1	yes	characteristic
108	C₂	#17989140	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×Dic₁₄₆

C₂

yes

maximal

#17988519

C₂

yes

maximal

#17988508

C₂

yes

maximal

C₄×C₄⋊Dic₇₃

C₂

yes

maximal

#376×C₇₃

C₂

yes

maximal, characteristic

C₂²×Dic₁₄₆

C₂²

yes

—

C₄×Dic₁₄₆

—

C₂×C₄⋊Dic₇₃

C₂²

yes

—

C₂×C₄⋊Dic₇₃

C₂²

yes

—

C₂×#11924007

C₂²

yes

—

C₂×C₄×Dic₇₃

C₂²

yes

—

#14556498

C₂²

yes

—

#14556498

C₂²

yes

—

C₂×C₄²×C₇₃

C₂²

yes

characteristic

C₂×C₄²×C₇₃

C₂²

yes

—

#95×C₇₃

C₂²

yes

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂²×Dic₇₃

C₂³

yes

—

C₂²×Dic₇₃

C₂³

yes

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

#11924007

—

C₄×Dic₇₃

—

C₂²×C₄×C₇₃

C₂³

yes

—

C₂²×C₄×C₇₃

C₂³

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₄²×C₇₃

D₄

yes

—

C₄²×C₇₃

Q₈

yes

complemented

C₂³×C₇₃

C₂⁴

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

C₂×Q₈

yes

—

C₂×C₄×C₇₃

C₂×Q₈

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

#41

yes

—

Dic₁₄₆

—

C₂²×C₇₃

C₂²×D₄

yes

characteristic

C₂²×C₇₃

C₂²×Q₈

yes

—

C₂²×C₇₃

C₂×#41

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₄⋊Q₈

yes

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

#525

yes

—

C₂×C₇₃

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₇₃

#533

yes

—

#2399

—

maximal, Sylow

C₇₃

#2399

yes

characteristic, complemented, Sylow

C₂×C₄×Q₈

—

#398

—

#395

—

C₄×C₄⋊C₄

—

#376

D₇₃

yes

characteristic

C₂²×Q₈

—

C₄×Q₈

—

146

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₇₃

yes

—

C₂×C₄²

C₂×D₇₃

yes

—

—

C₂×D₇₃

yes

—

C₂×Q₈

—

146

—

C₂×Q₈

—

146

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₃

yes

—

C₂²×C₄

C₂²×D₇₃

yes

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄²

—

146

—

C₄²

Dic₁₄₆

yes

complemented

C₄²

D₂₉₂

yes

—

C₂³

C₂³×D₇₃

yes

characteristic

Q₈

—

146

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

C₂×D₂₉₂

yes

—

C₂×C₄

C₂×D₂₉₂

yes

—

C₂×C₄

C₂×Dic₁₄₆

yes

—

C₂×C₄

C₂×Dic₁₄₆

yes

—

C₂²

C₂²×D₂₉₂

yes

characteristic

C₂²

C₂²×Dic₁₄₆

yes

—

100

C₂²

#41×D₇₃

yes

—

101

C₄

—

102

C₄

—

103

C₄

—

292

—

104

C₄

—

146

—

105

C₄

#14556591

yes

—

106

C₂

#17989099

yes

—

107

C₂

C₂×#14556591

yes

characteristic

108

C₂

#17989140

yes

—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₇₃
commutator, socle	C₂³×C₇₃	C₂⁴
Frattini	C₂³	C₂³×D₇₃
Fitting	#376×C₇₃	C₂
hypercenter	#376	D₇₃
hypocenter	C₇₃	#2399
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ #376

subgroup

G/H

center

C₂²×C₄

C₂²×D₇₃

commutator, socle

C₂³×C₇₃

C₂⁴

Frattini

C₂³

C₂³×D₇₃

Fitting

#376×C₇₃

C₂

D₇₃

C₇₃

G ▷ C₂³×C₇₃ ▷ C₇₃

C₁ ◁ C₂²×C₄ ◁ #376

N	H ≅ G/N	type
29. C₄²×C₇₃	Q₈	semidirect
55. C₇₃	#2399	semidirect
83. C₄²	Dic₁₄₆	semidirect

H ≅ G/N

type

29. C₄²×C₇₃

Q₈

semidirect

55. C₇₃

#2399

semidirect

83. C₄²

Dic₁₄₆

semidirect

Subgroups — #22613224

Conjugacy classes of subgroups

Complements