Group #22625414 — subgroups

Subgroups — #22625414

Order 9344.

196 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 56 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	#17989609	C₂	1	2	yes	maximal
2	#17989444	C₂	1	4	yes	maximal, complemented
3	#125×D₇₃	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#10596833	—	2	2	no	—
5	#14556648	—	2	2	no	—
6	#14556646	C₂²	1	4	yes	—
7	#14556583	C₄	1	1	yes	characteristic
8	#14556582	C₂²	1	2	yes	—
9	#14556581	—	2	2	no	—
10	C₄⋊C₄×D₇₃	—	2	2	no	—
11	C₄⋊C₄×D₇₃	C₄	1	2	yes	—
12	C₄²×D₇₃	C₂²	1	1	yes	characteristic
13	#125×C₇₃	C₄	1	1	yes	characteristic
14	C₂×#10596833	—	2	4	no	—
15	C₂×C₄×D₇₃	—	2	2	no	—
16	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×D₇₃	D₄	1	2	yes	—
18	C₄⋊Dic₇₃	—	2	2	no	—
19	C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
20	#11924007	—	2	2	no	—
21	#11924007	—	2	2	no	—
22	#11924007	—	2	2	no	—
23	C₄×Dic₇₃	D₄	1	2	yes	—
24	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
25	C₄⋊C₄×C₇₃	—	2	2	no	—
26	C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
27	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₇₃	—	2	2	no	—
30	C₂×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
31	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
32	C₂×Dic₇₃	—	2	2	no	—
33	C₂×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×Dic₇₃	C₂×D₄	1	2	yes	—
35	C₄×D₇₃	—	2	2	no	—
36	C₄×D₇₃	—	4	2	no	—
37	C₄×D₇₃	—	4	4	no	—
38	#10596833	—	4	4	no	—
39	C₂²×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
40	C₂×D₇₃	—	2	2	no	—
41	C₂×D₇₃	#101	1	2	yes	—
42	C₄×C₇₃	—	2	1	no	—
43	C₄×C₇₃	—	2	2	no	—
44	C₄×C₇₃	—	4	2	no	—
45	Dic₇₃	—	2	1	no	—
46	Dic₇₃	—	2	2	no	—
47	Dic₇₃	—	4	2	no	—
48	C₂×C₇₃	C₂×#101	1	1	yes	characteristic
49	C₂×C₇₃	#421	1	2	yes	—
50	D₇₃	—	2	2	no	—
51	#1534	—	73	1	no	maximal, Sylow
52	C₇₃	#1534	1	1	yes	characteristic, complemented, Sylow
53	C₂×#125	—	73	1	no	—
54	#432	—	73	2	no	—
55	#330	—	73	4	no	—
56	#125	—	73	2	no	—
57	#125	—	73	1	no	—
58	#125	—	146	2	no	—
59	#125	#64408	1	1	yes	characteristic
60	C₂×C₄⋊C₄	—	73	2	no	—
61	C₂×C₄⋊C₄	—	146	2	no	—
62	C₂×C₄²	—	73	1	no	—
63	C₄⋊C₈	—	146	2	no	—
64	C₂²⋊C₈	—	146	2	no	—
65	#97	—	73	4	no	—
66	C₂²×C₄	—	73	2	no	—
67	C₂²×C₄	—	73	1	no	—
68	C₂²×C₄	—	146	2	no	—
69	C₂×C₈	—	146	4	no	—
70	C₄⋊C₄	—	2	2	no	—
71	C₄⋊C₄	—	73	2	no	—
72	C₄⋊C₄	—	146	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	C₄²	—	73	2	no	—
78	C₄²	—	73	1	no	—
79	C₄²	C₂×#64408	1	1	yes	characteristic
80	C₂³	—	73	1	no	—
81	C₂×C₄	—	2	2	no	—
82	C₂×C₄	—	292	2	no	—
83	C₂×C₄	—	292	4	no	—
84	C₂×C₄	—	73	2	no	—
85	C₂×C₄	—	73	1	no	—
86	C₂×C₄	—	146	2	no	—
87	C₂×C₄	—	146	2	no	—
88	C₂×C₄	C₂²⋊#64408	1	2	yes	—
89	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
90	C₈	—	292	4	no	—
91	C₂²	—	73	2	no	—
92	C₂²	—	146	2	no	—
93	C₂²	C₂×C₂²⋊#64408	1	1	yes	characteristic
94	C₄	—	2	1	no	—
95	C₄	—	2	2	no	—
96	C₄	—	4	2	no	—
97	C₄	—	292	2	no	—
98	C₄	—	146	1	no	—
99	C₄	—	146	2	no	—
100	C₂	—	146	2	no	—
101	C₂	D₇₃⋊#101	1	1	yes	characteristic
102	C₂	#17989584	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#17989609

C₂

yes

maximal

#17989444

C₂

yes

maximal, complemented

#125×D₇₃

C₂

yes

maximal, characteristic

C₄⋊#10596833

—

#14556648

—

#14556646

C₂²

yes

—

#14556583

C₄

yes

characteristic

#14556582

C₂²

yes

—

#14556581

—

C₄⋊C₄×D₇₃

—

C₄⋊C₄×D₇₃

C₄

yes

—

C₄²×D₇₃

C₂²

yes

characteristic

#125×C₇₃

C₄

yes

characteristic

C₂×#10596833

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₂×C₄×D₇₃

D₄

yes

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

C₂×C₄

yes

—

#11924007

—

#11924007

—

#11924007

—

C₄×Dic₇₃

D₄

yes

—

C₄×Dic₇₃

C₂³

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

C₂×C₄

yes

—

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₂²×D₇₃

C₂²⋊C₄

yes

characteristic

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

—

#10596833

—

C₂²×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

#101

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

C₂×#101

yes

characteristic

C₂×C₇₃

#421

yes

—

D₇₃

—

#1534

—

maximal, Sylow

C₇₃

#1534

yes

characteristic, complemented, Sylow

—

—

—

—

—

—

146

—

#125

#64408

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

146

—

C₂×C₄²

—

C₄⋊C₈

—

146

—

C₂²⋊C₈

—

146

—

#97

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

146

—

C₂×C₈

—

146

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

C₂×#64408

yes

—

C₄²

—

C₄²

—

C₄²

C₂×#64408

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

C₂×C₄

—

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

C₄

—

C₄

—

C₄

—

C₄

—

292

—

C₄

—

146

—

C₄

—

146

—

100

C₂

—

146

—

101

C₂

D₇₃⋊#101

yes

characteristic

102

C₂

#17989584

yes

—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊#64408
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#64408
Fitting	#125×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₂²⋊C₄
hypercenter	#125	#64408
hypocenter	C₇₃	#1534
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #125

subgroup

G/H

center

C₂²

C₂×C₂²⋊#64408

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#64408

Fitting

#125×C₇₃

C₄

socle

C₂²×C₇₃

C₂×C₂²⋊C₄

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #125

N	H ≅ G/N	type
2. #17989444	C₂	semidirect
52. C₇₃	#1534	semidirect

H ≅ G/N

type

2. #17989444

C₂

semidirect

52. C₇₃

#1534

semidirect

Subgroups — #22625414

Conjugacy classes of subgroups

Complements