Group #22625422 — subgroups

Subgroups — #22625422

Order 9344.

194 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 58 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	#17989608	C₂	1	2	yes	maximal
2	#17989444	C₂	1	4	yes	maximal, complemented
3	#17989140	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#10596833	—	2	2	no	—
5	C₂²⋊#10596833	—	2	2	no	—
6	#14556646	C₂²	1	4	yes	—
7	#14556590	C₄	1	2	yes	—
8	#14556582	C₂²	1	2	yes	—
9	#14556568	—	2	2	no	—
10	C₄×Dic₁₄₆	—	2	2	no	—
11	#14556550	C₄	1	1	yes	characteristic
12	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
13	#117×C₇₃	C₄	1	1	yes	characteristic
14	C₂×#10596833	—	2	4	no	—
15	C₂×Dic₁₄₆	—	2	2	no	—
16	C₂²×Dic₇₃	D₄	1	2	yes	—
17	C₄⋊Dic₇₃	—	2	2	no	—
18	C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
19	#11924007	—	2	2	no	—
20	#11924007	—	2	2	no	—
21	C₂²⋊Dic₇₃	—	2	1	no	—
22	C₄×Dic₇₃	—	2	1	no	—
23	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
24	C₄×Dic₇₃	D₄	1	2	yes	—
25	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
26	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
27	C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
28	C₂²⋊C₄×C₇₃	—	2	1	no	—
29	C₄²×C₇₃	—	2	1	no	—
30	C₂³×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₇₃	—	2	2	no	—
32	C₂×C₄×C₇₃	—	2	2	no	—
33	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
35	C₂×Dic₇₃	—	2	2	no	—
36	C₂×Dic₇₃	—	4	2	no	—
37	C₂×Dic₇₃	C₂²⋊C₄	1	2	yes	—
38	C₂×Dic₇₃	C₂×D₄	1	2	yes	—
39	Dic₁₄₆	—	4	4	no	—
40	#10596833	—	4	4	no	—
41	C₂²×C₇₃	—	2	1	no	—
42	C₂²×C₇₃	—	2	2	no	—
43	C₂²×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
44	C₄×C₇₃	—	2	1	no	—
45	C₄×C₇₃	—	4	2	no	—
46	C₄×C₇₃	#101	1	2	yes	—
47	Dic₇₃	—	2	2	no	—
48	Dic₇₃	—	2	2	no	—
49	Dic₇₃	—	4	2	no	—
50	C₂×C₇₃	—	4	1	no	—
51	C₂×C₇₃	C₂×#101	1	1	yes	characteristic
52	C₂×C₇₃	#421	1	2	yes	—
53	#1537	—	73	1	no	maximal, Sylow
54	C₇₃	#1537	1	1	yes	characteristic, complemented, Sylow
55	#533	—	73	1	no	—
56	#432	—	73	2	no	—
57	#330	—	73	4	no	—
58	C₄⋊Q₈	—	73	2	no	—
59	#125	—	73	2	no	—
60	C₂²⋊Q₈	—	146	2	no	—
61	C₄×Q₈	—	146	2	no	—
62	#117	—	73	1	no	—
63	#117	#64408	1	1	yes	characteristic
64	C₂×C₄²	—	73	1	no	—
65	C₄⋊C₈	—	146	2	no	—
66	C₂²⋊C₈	—	146	2	no	—
67	#97	—	73	4	no	—
68	C₂×Q₈	—	146	2	no	—
69	C₂²×C₄	—	73	2	no	—
70	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
71	C₂×C₈	—	146	4	no	—
72	C₄⋊C₄	—	73	2	no	—
73	C₄⋊C₄	—	146	2	no	—
74	C₄⋊C₄	—	146	2	no	—
75	C₄⋊C₄	—	146	2	no	—
76	C₄⋊C₄	C₂×#64408	1	2	yes	—
77	C₂²⋊C₄	—	2	1	no	—
78	C₂²⋊C₄	—	146	1	no	—
79	C₄²	—	2	1	no	—
80	C₄²	—	73	2	no	—
81	C₄²	—	73	1	no	—
82	C₄²	—	73	1	no	—
83	C₄²	—	146	1	no	—
84	C₂³	C₂²⋊#64408	1	1	yes	characteristic
85	Q₈	—	292	4	no	—
86	C₂×C₄	—	2	2	no	—
87	C₂×C₄	—	2	2	no	—
88	C₂×C₄	—	292	2	no	—
89	C₂×C₄	—	73	2	no	—
90	C₂×C₄	—	73	2	no	—
91	C₂×C₄	—	146	2	no	—
92	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
93	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
94	C₈	—	292	4	no	—
95	C₂²	—	2	1	no	—
96	C₂²	—	2	2	no	—
97	C₂²	C₂×C₂²⋊#64408	1	1	yes	characteristic
98	C₄	—	2	1	no	—
99	C₄	—	4	2	no	—
100	C₄	—	292	2	no	—
101	C₄	—	146	2	no	—
102	C₄	—	146	2	no	—
103	C₄	#14556652	1	2	yes	—
104	C₂	—	4	1	no	—
105	C₂	C₂×#14556652	1	1	yes	characteristic
106	C₂	#17989584	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#17989608

C₂

yes

maximal

#17989444

C₂

yes

maximal, complemented

#17989140

C₂

yes

maximal, characteristic

C₄⋊#10596833

—

C₂²⋊#10596833

—

#14556646

C₂²

yes

—

#14556590

C₄

yes

—

#14556582

C₂²

yes

—

#14556568

—

C₄×Dic₁₄₆

—

#14556550

C₄

yes

characteristic

C₂×C₄×Dic₇₃

C₂²

yes

characteristic

#117×C₇₃

C₄

yes

characteristic

C₂×#10596833

—

C₂×Dic₁₄₆

—

C₂²×Dic₇₃

D₄

yes

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

C₂×C₄

yes

—

#11924007

—

#11924007

—

C₂²⋊Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

D₄

yes

—

C₄×Dic₇₃

C₂³

yes

characteristic

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₄⋊C₄×C₇₃

C₂×C₄

yes

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₂³×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂²⋊C₄

yes

—

C₂×Dic₇₃

C₂×D₄

yes

—

Dic₁₄₆

—

#10596833

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#101

yes

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

C₂×#101

yes

characteristic

C₂×C₇₃

#421

yes

—

#1537

—

maximal, Sylow

C₇₃

#1537

yes

characteristic, complemented, Sylow

#533

—

#432

—

#330

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

146

—

C₄×Q₈

—

146

—

—

yes

C₂×C₄²

—

C₄⋊C₈

—

146

—

C₂²⋊C₈

—

146

—

#97

—

C₂×Q₈

—

146

—

C₂²×C₄

—

C₂²×C₄

C₂×#64408

yes

characteristic

C₂×C₈

—

146

—

C₄⋊C₄

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

C₂×#64408

yes

—

C₂²⋊C₄

—

C₂²⋊C₄

—

146

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

146

—

C₂³

C₂²⋊#64408

yes

characteristic

Q₈

—

292

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

C₂²⋊#64408

yes

characteristic

C₂×C₄

C₂²×#64408

yes

characteristic

C₈

—

292

—

C₂²

—

C₂²

—

C₂²

C₂×C₂²⋊#64408

yes

characteristic

C₄

—

C₄

—

100

C₄

—

292

—

101

C₄

—

146

—

102

C₄

—

146

—

103

C₄

#14556652

yes

—

104

C₂

—

105

C₂

C₂×#14556652

yes

characteristic

106

C₂

#17989584

yes

—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊#64408
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#64408
Fitting	#117×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₂²⋊C₄
hypercenter	#117	#64408
hypocenter	C₇₃	#1537
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #117

subgroup

G/H

center

C₂²

C₂×C₂²⋊#64408

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#64408

Fitting

#117×C₇₃

C₄

socle

C₂²×C₇₃

C₂×C₂²⋊C₄

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #117

N	H ≅ G/N	type
2. #17989444	C₂	semidirect
54. C₇₃	#1537	semidirect

H ≅ G/N

type

2. #17989444

C₂

semidirect

54. C₇₃

#1537

semidirect

Subgroups — #22625422

Conjugacy classes of subgroups

Complements