Group #22625465 — subgroups

Subgroups — #22625465

Order 9344.

228 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 60 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	#17989610	C₂	1	2	yes	maximal
2	#17989447	C₂	1	4	yes	maximal, complemented
3	C₄⋊Q₈×D₇₃	C₂	1	1	yes	maximal, characteristic
4	#14556658	C₂²	1	4	yes	—
5	#14556648	—	2	2	no	—
6	#14556646	—	2	2	no	—
7	C₂×Q₈×D₇₃	C₄	1	2	yes	—
8	#14556591	C₄	1	1	yes	characteristic
9	#14556590	—	2	2	no	—
10	#14556589	C₂²	1	2	yes	—
11	C₄⋊C₄×D₇₃	—	2	2	no	—
12	C₄²×D₇₃	C₂²	1	1	yes	characteristic
13	C₄⋊Q₈×C₇₃	C₄	1	1	yes	characteristic
14	C₂×#10596833	—	2	4	no	—
15	C₂×Dic₁₄₆	—	2	2	no	—
16	C₂×Dic₁₄₆	C₂×C₄	1	2	yes	—
17	Q₈×D₇₃	—	4	4	no	—
18	C₂×C₄×D₇₃	—	2	2	no	—
19	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×D₇₃	D₄	1	2	yes	—
21	C₄⋊Dic₇₃	—	2	2	no	—
22	#11924007	—	2	4	no	—
23	C₄×Dic₇₃	D₄	1	2	yes	—
24	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
25	C₂×Q₈×C₇₃	C₂×C₄	1	2	yes	—
26	C₄⋊C₄×C₇₃	—	2	2	no	—
27	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
29	Q₈×C₇₃	—	4	2	no	—
30	C₂×C₄×C₇₃	—	2	2	no	—
31	C₂×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
32	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
33	C₂×Dic₇₃	—	2	2	no	—
34	C₂×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×Dic₇₃	C₂×D₄	1	2	yes	—
36	C₄×D₇₃	—	2	2	no	—
37	C₄×D₇₃	—	2	4	no	—
38	C₄×D₇₃	—	4	4	no	—
39	Dic₁₄₆	—	4	4	no	—
40	Dic₁₄₆	—	4	2	no	—
41	#10596833	—	4	4	no	—
42	C₂²×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
43	C₂×D₇₃	—	2	2	no	—
44	C₂×D₇₃	#100	1	2	yes	—
45	C₄×C₇₃	—	2	1	no	—
46	C₄×C₇₃	—	2	2	no	—
47	C₄×C₇₃	—	4	2	no	—
48	Dic₇₃	—	2	1	no	—
49	Dic₇₃	—	4	2	no	—
50	Dic₇₃	#137	1	4	yes	—
51	C₂×C₇₃	C₂×#100	1	1	yes	characteristic
52	C₂×C₇₃	#419	1	2	yes	—
53	D₇₃	—	2	2	no	—
54	#1558	—	73	1	no	maximal, Sylow
55	C₇₃	#1558	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₄⋊Q₈	—	73	1	no	—
57	#432	—	73	2	no	—
58	#333	—	73	4	no	—
59	C₂²×Q₈	—	73	2	no	—
60	C₄⋊Q₈	—	73	2	no	—
61	C₄⋊Q₈	—	73	1	no	—
62	C₄⋊Q₈	—	146	2	no	—
63	C₄⋊Q₈	#64408	1	1	yes	characteristic
64	C₂×C₄⋊C₄	—	146	2	no	—
65	C₂×C₄²	—	73	1	no	—
66	C₄⋊C₈	—	73	4	no	—
67	C₂²⋊C₈	—	146	2	no	—
68	#97	—	146	2	no	—
69	C₂×Q₈	—	292	4	no	—
70	C₂×Q₈	—	73	2	no	—
71	C₂×Q₈	—	146	2	no	—
72	C₂×Q₈	C₂×#64408	1	2	yes	—
73	C₂²×C₄	—	73	2	no	—
74	C₂²×C₄	—	73	1	no	—
75	C₂²×C₄	—	146	2	no	—
76	C₂×C₈	—	146	4	no	—
77	C₄⋊C₄	—	2	2	no	—
78	C₄⋊C₄	—	146	4	no	—
79	C₄⋊C₄	—	146	2	no	—
80	C₄²	—	73	2	no	—
81	C₄²	—	73	1	no	—
82	C₄²	C₂×#64408	1	1	yes	characteristic
83	C₂³	—	73	1	no	—
84	Q₈	—	4	2	no	—
85	Q₈	—	292	2	no	—
86	Q₈	—	292	4	no	—
87	C₂×C₄	—	2	2	no	—
88	C₂×C₄	—	292	4	no	—
89	C₂×C₄	—	73	2	no	—
90	C₂×C₄	—	73	1	no	—
91	C₂×C₄	—	146	4	no	—
92	C₂×C₄	—	146	2	no	—
93	C₂×C₄	—	146	2	no	—
94	C₂×C₄	C₂²⋊#64408	1	2	yes	—
95	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
96	C₈	—	292	4	no	—
97	C₂²	—	73	2	no	—
98	C₂²	—	146	2	no	—
99	C₂²	C₂×C₂²⋊#64408	1	1	yes	characteristic
100	C₄	—	2	1	no	—
101	C₄	—	2	2	no	—
102	C₄	—	4	2	no	—
103	C₄	—	292	2	no	—
104	C₄	—	73	4	no	—
105	C₄	—	146	1	no	—
106	C₂	—	146	2	no	—
107	C₂	D₇₃⋊#100	1	1	yes	characteristic
108	C₂	#17989580	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#17989610

C₂

yes

maximal

#17989447

C₂

yes

maximal, complemented

C₄⋊Q₈×D₇₃

C₂

yes

maximal, characteristic

#14556658

C₂²

yes

—

#14556648

—

#14556646

—

C₂×Q₈×D₇₃

C₄

yes

—

#14556591

C₄

yes

characteristic

#14556590

—

#14556589

C₂²

yes

—

C₄⋊C₄×D₇₃

—

C₄²×D₇₃

C₂²

yes

characteristic

C₄⋊Q₈×C₇₃

C₄

yes

characteristic

C₂×#10596833

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

C₂×C₄

yes

—

Q₈×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₂×C₄×D₇₃

D₄

yes

—

C₄⋊Dic₇₃

—

#11924007

—

C₄×Dic₇₃

D₄

yes

—

C₄×Dic₇₃

C₂³

yes

characteristic

C₂×Q₈×C₇₃

C₂×C₄

yes

—

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₂²×D₇₃

C₂²⋊C₄

yes

characteristic

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₇₃

C₂×D₄

yes

—

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

#10596833

—

C₂²×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

#100

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

#137

yes

—

C₂×C₇₃

C₂×#100

yes

characteristic

C₂×C₇₃

#419

yes

—

D₇₃

—

#1558

—

maximal, Sylow

C₇₃

#1558

yes

characteristic, complemented, Sylow

C₂×C₄⋊Q₈

—

#432

—

#333

—

C₂²×Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

146

—

C₄⋊Q₈

#64408

yes

characteristic

C₂×C₄⋊C₄

—

146

—

C₂×C₄²

—

C₄⋊C₈

—

C₂²⋊C₈

—

146

—

#97

—

146

—

C₂×Q₈

—

292

—

C₂×Q₈

—

C₂×Q₈

—

146

—

C₂×Q₈

C₂×#64408

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

146

—

C₂×C₈

—

146

—

C₄⋊C₄

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄²

—

C₄²

—

C₄²

C₂×#64408

yes

characteristic

C₂³

—

Q₈

—

Q₈

—

292

—

Q₈

—

292

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

C₂²⋊#64408

yes

—

C₂×C₄

C₂²×#64408

yes

characteristic

C₈

—

292

—

C₂²

—

C₂²

—

146

—

C₂²

C₂×C₂²⋊#64408

yes

characteristic

100

C₄

—

101

C₄

—

102

C₄

—

103

C₄

—

292

—

104

C₄

—

105

C₄

—

146

—

106

C₂

—

146

—

107

C₂

D₇₃⋊#100

yes

characteristic

108

C₂

#17989580

yes

—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊#64408
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#64408
Fitting	C₄⋊Q₈×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₂²⋊C₄
hypercenter	C₄⋊Q₈	#64408
hypocenter	C₇₃	#1558
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

subgroup

G/H

center

C₂²

C₂×C₂²⋊#64408

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#64408

Fitting

C₄⋊Q₈×C₇₃

C₄

socle

C₂²×C₇₃

C₂×C₂²⋊C₄

C₄⋊Q₈

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

N	H ≅ G/N	type
2. #17989447	C₂	semidirect
55. C₇₃	#1558	semidirect

H ≅ G/N

type

2. #17989447

C₂

semidirect

55. C₇₃

#1558

semidirect

Subgroups — #22625465

Conjugacy classes of subgroups

Complements