Group #22608751 — subgroups

Subgroups — #22608751

Order 9344.

160 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 73 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	C₈×Dic₁₄₆	C₂	1	2	yes	maximal
2	C₄×Dic₂₉₂	C₂	1	1	yes	maximal, characteristic
3	#17988338	C₂	1	1	yes	maximal, characteristic
4	#17988319	C₂	1	2	yes	maximal
5	#322×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₂₉₂	C₄	1	1	yes	characteristic
7	C₄×Dic₁₄₆	C₂²	1	2	yes	—
8	#14556525	C₄	1	1	yes	characteristic
9	C₄⋊#10596831	C₂²	1	2	yes	—
10	#14556520	—	2	2	no	—
11	#14556516	C₄	1	2	yes	—
12	C₈×Dic₇₃	—	2	2	no	—
13	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×Dic₁₄₆	C₂×C₄	1	2	yes	—
17	Dic₂₉₂	C₈	1	4	yes	complemented
18	C₂×#10596831	—	2	2	no	—
19	C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
20	#11924007	—	2	2	no	—
21	C₄×Dic₇₃	—	2	2	no	—
22	C₂×C₈×C₇₃	—	2	1	no	—
23	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₇₃	D₄	1	2	yes	—
26	C₄²×C₇₃	C₂³	1	1	yes	characteristic
27	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
30	C₂×Dic₇₃	—	2	2	no	—
31	C₂×Dic₇₃	—	2	2	no	—
32	Dic₁₄₆	—	2	2	no	—
33	Dic₁₄₆	C₂×C₈	1	4	yes	—
34	C₈×C₇₃	—	2	1	no	—
35	C₈×C₇₃	—	2	2	no	—
36	C₈×C₇₃	—	4	1	no	—
37	C₈×C₇₃	C₂×C₈	1	2	yes	—
38	#10596831	—	4	2	no	—
39	C₂²×C₇₃	C₄×D₄	1	1	yes	characteristic
40	C₄×C₇₃	—	2	1	no	—
41	C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
42	C₄×C₇₃	#131	1	1	yes	characteristic
43	C₄×C₇₃	#137	1	2	yes	—
44	Dic₇₃	—	2	4	no	—
45	Dic₇₃	—	4	2	no	—
46	C₂×C₇₃	C₈×D₄	1	1	yes	characteristic
47	C₂×C₇₃	#441	1	1	yes	characteristic
48	C₂×C₇₃	#444	1	1	yes	characteristic
49	#1579	—	73	1	no	maximal, Sylow
50	C₇₃	#1579	1	1	yes	characteristic, complemented, Sylow
51	C₈×Q₈	—	73	2	no	—
52	C₄×Q₁₆	—	73	1	no	—
53	#334	—	73	1	no	—
54	Q₈⋊C₈	—	73	2	no	—
55	#322	D₇₃	1	1	yes	characteristic
56	C₂×Q₁₆	—	73	1	no	—
57	C₄×Q₈	—	73	2	no	—
58	#107	—	73	1	no	—
59	C₄⋊C₈	—	73	2	no	—
60	C₄⋊C₈	—	146	2	no	—
61	#103	—	73	2	no	—
62	C₄×C₈	—	146	2	no	—
63	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
64	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
65	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
66	C₂×Q₈	—	73	2	no	—
67	Q₁₆	—	73	4	no	—
68	C₂×C₈	—	2	1	no	—
69	C₂×C₈	—	146	2	no	—
70	C₂×C₈	C₄×D₇₃	1	1	yes	characteristic
71	C₂×C₈	C₄×D₇₃	1	1	yes	characteristic
72	C₂×C₈	D₂₉₂	1	2	yes	—
73	C₄⋊C₄	—	73	2	no	—
74	C₄⋊C₄	—	146	2	no	—
75	C₄²	—	146	2	no	—
76	C₄²	C₂²×D₇₃	1	1	yes	characteristic
77	Q₈	—	73	4	no	—
78	Q₈	—	146	2	no	—
79	C₂×C₄	—	146	2	no	—
80	C₂×C₄	—	146	2	no	—
81	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
82	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
83	C₂×C₄	#11924028	1	1	yes	characteristic
84	C₈	—	2	1	no	—
85	C₈	—	2	2	no	—
86	C₈	—	4	1	no	—
87	C₈	—	292	2	no	—
88	C₈	C₈×D₇₃	1	2	yes	—
89	C₂²	C₄×D₂₉₂	1	1	yes	characteristic
90	C₄	—	2	1	no	—
91	C₄	—	292	2	no	—
92	C₄	—	146	4	no	—
93	C₄	C₂×C₈×D₇₃	1	1	yes	characteristic
94	C₄	#14556597	1	1	yes	characteristic
95	C₄	#14556624	1	2	yes	—
96	C₂	C₈×D₂₉₂	1	1	yes	characteristic
97	C₂	#17988695	1	1	yes	characteristic
98	C₂	#17988710	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₈×Dic₁₄₆

C₂

yes

maximal

C₄×Dic₂₉₂

C₂

yes

maximal, characteristic

#17988338

C₂

yes

maximal, characteristic

#17988319

C₂

yes

maximal

#322×C₇₃

C₂

yes

maximal, characteristic

C₂×Dic₂₉₂

C₄

yes

characteristic

C₄×Dic₁₄₆

C₂²

yes

—

#14556525

C₄

yes

characteristic

C₄⋊#10596831

C₂²

yes

—

#14556520

—

#14556516

C₄

yes

—

C₈×Dic₇₃

—

C₄×C₈×C₇₃

C₂²

yes

characteristic

C₄×C₈×C₇₃

C₂²

yes

characteristic

C₄×C₈×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

C₂×C₄

yes

—

Dic₂₉₂

C₈

yes

complemented

C₂×#10596831

—

C₄⋊Dic₇₃

C₂×C₄

yes

—

#11924007

—

C₄×Dic₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

D₄

yes

—

C₄²×C₇₃

C₂³

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

#41

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

C₂×C₈

yes

—

C₈×C₇₃

—

C₈×C₇₃

—

C₈×C₇₃

—

C₈×C₇₃

C₂×C₈

yes

—

#10596831

—

C₂²×C₇₃

C₄×D₄

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

C₂²×C₈

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

C₈×D₄

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₈×Q₈

—

C₄×Q₁₆

—

#334

—

Q₈⋊C₈

—

#322

D₇₃

yes

characteristic

C₂×Q₁₆

—

C₄×Q₈

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

146

—

#103

—

C₄×C₈

—

146

—

C₄×C₈

C₂×D₇₃

yes

characteristic

C₄×C₈

C₂×D₇₃

yes

characteristic

C₄×C₈

C₂×D₇₃

yes

characteristic

C₂×Q₈

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

C₄×D₇₃

yes

characteristic

C₂×C₈

C₄×D₇₃

yes

characteristic

C₂×C₈

D₂₉₂

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

146

—

C₄²

—

146

—

C₄²

C₂²×D₇₃

yes

characteristic

Q₈

—

Q₈

—

146

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

C₂×C₄×D₇₃

yes

characteristic

C₂×C₄

C₂×D₂₉₂

yes

characteristic

C₂×C₄

#11924028

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

292

—

C₈

C₈×D₇₃

yes

—

C₂²

C₄×D₂₉₂

yes

characteristic

C₄

—

C₄

—

292

—

C₄

—

146

—

C₄

C₂×C₈×D₇₃

yes

C₄

yes

C₄

yes

—

C₂

C₈×D₂₉₂

yes

C₂

yes

C₂

yes

	subgroup	G/H
center	C₂×C₄	C₂×D₂₉₂
commutator	C₄×C₇₃	C₂²×C₈
Frattini	C₄²	C₂²×D₇₃
Fitting	#322×C₇₃	C₂
socle	C₂²×C₇₃	C₄×D₄
hypercenter	#322	D₇₃
hypocenter	C₇₃	#1579
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #322

subgroup

G/H

center

C₂×C₄

C₂×D₂₉₂

commutator

C₄×C₇₃

C₂²×C₈

Frattini

C₄²

C₂²×D₇₃

Fitting

#322×C₇₃

C₂

socle

C₂²×C₇₃

C₄×D₄

D₇₃

C₇₃

G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #322

N	H ≅ G/N	type
17. Dic₂₉₂	C₈	semidirect
50. C₇₃	#1579	semidirect

H ≅ G/N

type

17. Dic₂₉₂

C₈

semidirect

50. C₇₃

#1579

semidirect

Subgroups — #22608751

Conjugacy classes of subgroups

Complements