Group #22625649 — subgroups

Subgroups — #22625649

Order 9344.

240 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 90 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	#17989546	C₂	1	1	yes	maximal, characteristic
2	#17989523	C₂	1	1	yes	maximal, characteristic
3	#17989452	C₂	1	4	yes	maximal
4	C₄×C₈×D₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#11924036	C₂²	1	2	yes	—
6	C₂×C₄×#64408	C₂²	1	2	yes	—
7	#14556646	C₄	1	4	yes	complemented
8	(C₂×#64408)⋊C₄	C₄	1	4	yes	—
9	C₂×C₈×D₇₃	C₂²	1	2	yes	—
10	C₄²×D₇₃	C₂²	1	1	yes	characteristic
11	C₄×#10596831	C₄	1	1	yes	characteristic, complemented
12	C₈×Dic₇₃	C₄	1	2	yes	complemented
13	C₄×C₈×C₇₃	C₄	1	1	yes	characteristic, complemented
14	C₂²×#64408	C₂×C₄	1	4	yes	—
15	#11924036	—	2	4	no	—
16	C₂×#10596833	C₂×C₄	1	4	yes	—
17	C₄×#64408	—	2	4	no	—
18	C₂×C₄×D₇₃	C₂×C₄	1	2	yes	—
19	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
20	C₂×#10596831	C₂×C₄	1	2	yes	—
21	C₈×D₇₃	—	2	4	no	—
22	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
23	C₄×Dic₇₃	C₂×C₄	1	2	yes	—
24	C₂×C₈×C₇₃	C₂×C₄	1	2	yes	—
25	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
26	C₂²×D₇₃	C₂²×C₄	1	1	yes	characteristic
27	C₂×#64408	—	2	4	no	—
28	C₂×#64408	—	2	8	no	—
29	C₂×C₄×C₇₃	C₄²	1	2	yes	—
30	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₇₃	C₄²	1	2	yes	—
32	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
33	C₄×D₇₃	—	2	4	no	—
34	C₄×D₇₃	#41	1	4	yes	—
35	#10596833	—	2	4	no	—
36	C₈×C₇₃	—	2	2	no	—
37	#10596831	—	2	2	no	—
38	C₂²×C₇₃	C₂×C₄²	1	1	yes	characteristic
39	C₂×D₇₃	#117	1	2	yes	—
40	C₂×D₇₃	#131	1	4	yes	—
41	#64408	—	4	4	no	—
42	C₄×C₇₃	—	2	2	no	—
43	C₄×C₇₃	#117	1	2	yes	—
44	Dic₇₃	—	2	2	no	—
45	Dic₇₃	#117	1	2	yes	—
46	C₂×C₇₃	#376	1	1	yes	characteristic
47	C₂×C₇₃	#405	1	2	yes	—
48	D₇₃	#433	1	4	yes	—
49	#1746	—	73	1	no	maximal, Sylow
50	C₇₃	#1746	1	1	yes	characteristic, complemented, Sylow
51	C₂×#97	—	73	1	no	—
52	C₂×C₄×C₈	—	73	1	no	—
53	#376	—	73	1	no	—
54	#336	—	73	4	no	—
55	C₂²×C₈	—	73	2	no	—
56	C₂²×C₈	—	73	2	no	—
57	C₂×C₄²	—	73	1	no	—
58	C₂×C₄²	—	73	2	no	—
59	#97	—	73	4	no	—
60	C₄×C₈	—	73	2	no	—
61	C₄×C₈	—	73	1	no	—
62	C₄×C₈	#64408	1	1	yes	characteristic, complemented
63	#95	—	73	4	no	—
64	C₂²×C₄	—	73	1	no	—
65	C₂²×C₄	—	73	2	no	—
66	C₂²×C₄	—	73	4	no	—
67	C₂×C₈	—	73	4	no	—
68	C₂×C₈	—	73	2	no	—
69	C₂×C₈	—	146	4	no	—
70	C₂×C₈	—	146	4	no	—
71	C₂×C₈	C₂×#64408	1	2	yes	—
72	C₄²	—	73	2	no	—
73	C₄²	—	73	1	no	—
74	C₄²	—	146	4	no	—
75	C₄²	C₂×#64408	1	1	yes	characteristic
76	C₂³	—	73	1	no	—
77	C₂×C₄	—	73	1	no	—
78	C₂×C₄	—	73	4	no	—
79	C₂×C₄	—	73	2	no	—
80	C₂×C₄	—	146	4	no	—
81	C₂×C₄	—	146	4	no	—
82	C₂×C₄	—	146	8	no	—
83	C₂×C₄	C₄×#64408	1	2	yes	—
84	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
85	C₈	—	2	2	no	—
86	C₈	—	146	4	no	—
87	C₈	—	146	2	no	—
88	C₂²	—	73	2	no	—
89	C₂²	—	73	4	no	—
90	C₂²	C₂×C₄×#64408	1	1	yes	characteristic
91	C₄	—	2	2	no	—
92	C₄	—	292	4	no	—
93	C₄	—	73	2	no	—
94	C₄	—	146	2	no	—
95	C₄	#14556670	1	2	yes	—
96	C₂	—	73	4	no	—
97	C₂	#17989523	1	1	yes	characteristic
98	C₂	#17989550	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#17989546

C₂

yes

maximal, characteristic

#17989523

C₂

yes

maximal, characteristic

#17989452

C₂

yes

maximal

C₄×C₈×D₇₃

C₂

yes

maximal, characteristic

C₂×#11924036

C₂²

yes

—

C₂×C₄×#64408

C₂²

yes

—

#14556646

C₄

yes

complemented

(C₂×#64408)⋊C₄

C₄

yes

—

C₂×C₈×D₇₃

C₂²

yes

—

C₄²×D₇₃

C₂²

yes

characteristic

C₄×#10596831

C₄

yes

characteristic, complemented

C₈×Dic₇₃

C₄

yes

complemented

C₄×C₈×C₇₃

C₄

yes

characteristic, complemented

C₂²×#64408

C₂×C₄

yes

—

#11924036

—

C₂×#10596833

C₂×C₄

yes

—

C₄×#64408

—

C₂×C₄×D₇₃

C₂×C₄

yes

—

C₂×C₄×D₇₃

C₂³

yes

characteristic

C₂×#10596831

C₂×C₄

yes

—

C₈×D₇₃

—

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

C₂×C₄

yes

—

C₂×C₈×C₇₃

C₂×C₄

yes

—

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₂²×D₇₃

C₂²×C₄

yes

characteristic

C₂×#64408

—

C₂×#64408

—

C₂×C₄×C₇₃

C₄²

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

C₄²

yes

—

C₂×Dic₇₃

C₂²×C₄

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

#41

yes

—

#10596833

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

C₂×C₄²

yes

characteristic

C₂×D₇₃

#117

yes

—

C₂×D₇₃

#131

yes

—

#64408

—

C₄×C₇₃

—

C₄×C₇₃

#117

yes

—

Dic₇₃

—

Dic₇₃

#117

yes

—

C₂×C₇₃

#376

yes

characteristic

C₂×C₇₃

#405

yes

—

D₇₃

#433

yes

—

#1746

—

maximal, Sylow

C₇₃

#1746

yes

characteristic, complemented, Sylow

C₂×#97

—

C₂×C₄×C₈

—

#376

—

#336

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#64408

yes

characteristic, complemented

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

C₂×#64408

yes

—

C₄²

—

C₄²

—

C₄²

—

146

—

C₄²

C₂×#64408

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

C₄×#64408

yes

—

C₂×C₄

C₂²×#64408

yes

characteristic

C₈

—

C₈

—

146

—

C₈

—

146

—

C₂²

—

C₂²

—

C₂²

C₂×C₄×#64408

yes

characteristic

C₄

—

C₄

—

292

—

C₄

—

C₄

—

146

—

C₄

#14556670

yes

—

C₂

—

C₂

#17989523

yes

characteristic

C₂

#17989550

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#64408
commutator, socle	C₂²×C₇₃	C₂×C₄²
Fitting	C₄×C₈×C₇₃	C₄
hypercenter	C₄×C₈	#64408
hypocenter	C₇₃	#1746
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#64408

commutator, socle

C₂²×C₇₃

C₂×C₄²

Fitting

C₄×C₈×C₇₃

C₄

C₄×C₈

C₇₃

G ▷ C₂²×C₇₃ ▷ C₇₃

C₁ ◁ C₂×C₄ ◁ C₄×C₈

N	H ≅ G/N	type
7. #14556646	C₄	semidirect
11. C₄×#10596831	C₄	semidirect
12. C₈×Dic₇₃	C₄	semidirect
13. C₄×C₈×C₇₃	C₄	semidirect
50. C₇₃	#1746	semidirect
62. C₄×C₈	#64408	semidirect

H ≅ G/N

type

7. #14556646

C₄

semidirect

11. C₄×#10596831

C₄

semidirect

12. C₈×Dic₇₃

C₄

semidirect

13. C₄×C₈×C₇₃

C₄

semidirect

50. C₇₃

#1746

semidirect

62. C₄×C₈

#64408

semidirect

Subgroups — #22625649

Conjugacy classes of subgroups

Complements