Group #22615879 — subgroups

Subgroups — #22615879

Order 9344.

416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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	C₂×#14556591	C₂	1	1	yes	maximal, characteristic
2	C₂×#14556583	C₂	1	1	yes	maximal, characteristic
3	#17988527	C₂	1	8	yes	maximal
4	#17988493	C₂	1	4	yes	maximal
5	#376×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₄₆	C₂²	1	2	yes	—
7	#14556591	—	2	4	no	—
8	#14556583	—	2	4	no	—
9	C₂×C₄⋊Dic₇₃	C₂²	1	4	yes	—
10	C₂×C₄⋊Dic₇₃	C₂²	1	2	yes	—
11	C₂×#11924007	C₂²	1	4	yes	—
12	#14556498	C₂²	1	16	yes	—
13	C₂×C₄²×C₇₃	C₂²	1	2	yes	—
14	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
15	#95×C₇₃	C₂²	1	4	yes	—
16	C₂×Dic₁₄₆	—	2	4	no	—
17	C₂×Dic₁₄₆	—	2	8	no	—
18	C₂²×Dic₇₃	C₂³	1	4	yes	—
19	C₂²×Dic₇₃	C₂³	1	4	yes	—
20	C₄⋊Dic₇₃	—	2	4	no	—
21	C₄⋊Dic₇₃	—	2	8	no	—
22	#11924007	—	2	8	no	—
23	C₂²×C₄×C₇₃	C₂³	1	4	yes	—
24	C₂²×C₄×C₇₃	C₂³	1	2	yes	—
25	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
26	C₄²×C₇₃	—	2	4	no	—
27	C₄²×C₇₃	D₄	1	4	yes	—
28	C₂³×C₇₃	C₂⁴	1	1	yes	characteristic
29	C₂×C₄×C₇₃	—	2	4	no	—
30	C₂×C₄×C₇₃	—	2	4	no	—
31	C₂×C₄×C₇₃	—	2	8	no	—
32	C₂×C₄×C₇₃	C₂×D₄	1	4	yes	—
33	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
34	C₂×C₄×C₇₃	#41	1	4	yes	—
35	C₂×Dic₇₃	—	2	4	no	—
36	C₂×Dic₇₃	—	2	4	no	—
37	C₂×Dic₇₃	—	2	8	no	—
38	C₂×Dic₇₃	—	2	8	no	—
39	Dic₁₄₆	—	4	8	no	—
40	C₂²×C₇₃	C₂²×D₄	1	1	yes	characteristic
41	C₂²×C₇₃	C₂×#41	1	2	yes	—
42	C₂²×C₇₃	2₋¹⁺⁴	1	4	yes	—
43	C₄×C₇₃	—	2	4	no	—
44	C₄×C₇₃	—	4	4	no	—
45	C₄×C₇₃	#124	1	4	yes	—
46	Dic₇₃	—	4	4	no	—
47	Dic₇₃	—	4	4	no	—
48	C₂×C₇₃	C₂×#124	1	1	yes	characteristic
49	C₂×C₇₃	#536	1	2	yes	—
50	C₂×C₇₃	#541	1	4	yes	—
51	#2642	—	73	1	no	maximal, Sylow
52	C₇₃	#2642	1	1	yes	characteristic, complemented, Sylow
53	C₂×C₄⋊Q₈	—	73	1	no	—
54	C₂×#125	—	73	1	no	—
55	#400	—	73	8	no	—
56	#391	—	73	4	no	—
57	#376	D₇₃	1	1	yes	characteristic
58	C₂²×Q₈	—	73	2	no	—
59	C₄⋊Q₈	—	146	4	no	—
60	#125	—	146	4	no	—
61	C₂×C₄⋊C₄	—	73	4	no	—
62	C₂×C₄⋊C₄	—	73	2	no	—
63	C₂×C₄⋊C₄	—	73	4	no	—
64	C₂×C₄²	C₂×D₇₃	1	2	yes	—
65	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
66	#95	—	73	16	no	—
67	#95	C₂×D₇₃	1	4	yes	—
68	C₂×Q₈	—	146	4	no	—
69	C₂×Q₈	—	146	8	no	—
70	C₂²×C₄	—	73	4	no	—
71	C₂²×C₄	—	73	4	no	—
72	C₂²×C₄	C₂²×D₇₃	1	4	yes	—
73	C₂²×C₄	C₂²×D₇₃	1	2	yes	—
74	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
75	C₄⋊C₄	—	146	8	no	—
76	C₄⋊C₄	—	146	4	no	—
77	C₄⋊C₄	—	146	8	no	—
78	C₄²	—	2	4	no	—
79	C₄²	D₂₉₂	1	4	yes	—
80	C₂³	C₂³×D₇₃	1	1	yes	characteristic
81	Q₈	—	292	8	no	—
82	C₂×C₄	—	2	4	no	—
83	C₂×C₄	—	2	4	no	—
84	C₂×C₄	—	2	8	no	—
85	C₂×C₄	—	146	4	no	—
86	C₂×C₄	—	146	4	no	—
87	C₂×C₄	—	146	8	no	—
88	C₂×C₄	—	146	8	no	—
89	C₂×C₄	C₂×D₂₉₂	1	4	yes	—
90	C₂×C₄	C₂×D₂₉₂	1	2	yes	—
91	C₂×C₄	#11924028	1	4	yes	—
92	C₂²	C₂²×D₂₉₂	1	1	yes	characteristic
93	C₂²	C₂×#11924028	1	2	yes	—
94	C₂²	#14556638	1	4	yes	—
95	C₄	—	2	4	no	—
96	C₄	—	4	4	no	—
97	C₄	—	292	4	no	—
98	C₄	—	292	4	no	—
99	C₄	#14556579	1	4	yes	—
100	C₂	C₂×#14556579	1	1	yes	characteristic
101	C₂	#17989163	1	2	yes	—
102	C₂	#17989199	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556591

C₂

yes

maximal, characteristic

C₂×#14556583

C₂

yes

maximal, characteristic

#17988527

C₂

yes

maximal

#17988493

C₂

yes

maximal

#376×C₇₃

C₂

yes

maximal, characteristic

C₂²×Dic₁₄₆

C₂²

yes

—

#14556591

—

#14556583

—

C₂×C₄⋊Dic₇₃

C₂²

yes

—

C₂×C₄⋊Dic₇₃

C₂²

yes

—

C₂×#11924007

C₂²

yes

—

#14556498

C₂²

yes

—

C₂×C₄²×C₇₃

C₂²

yes

—

C₂×C₄²×C₇₃

C₂²

yes

characteristic

#95×C₇₃

C₂²

yes

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂²×Dic₇₃

C₂³

yes

—

C₂²×Dic₇₃

C₂³

yes

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

#11924007

—

C₂²×C₄×C₇₃

C₂³

yes

—

C₂²×C₄×C₇₃

C₂³

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₄²×C₇₃

—

C₄²×C₇₃

D₄

yes

—

C₂³×C₇₃

C₂⁴

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

#41

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

C₂²×C₇₃

C₂²×D₄

yes

characteristic

C₂²×C₇₃

C₂×#41

yes

—

C₂²×C₇₃

2₋¹⁺⁴

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#124

yes

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

C₂×#124

yes

characteristic

C₂×C₇₃

#536

yes

—

C₂×C₇₃

#541

yes

—

#2642

—

maximal, Sylow

C₇₃

#2642

yes

characteristic, complemented, Sylow

C₂×C₄⋊Q₈

—

—

—

—

D₇₃

yes

characteristic

C₂²×Q₈

—

C₄⋊Q₈

—

146

—

#125

—

146

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₇₃

yes

—

C₂×C₄²

C₂×D₇₃

yes

characteristic

#95

—

#95

C₂×D₇₃

yes

—

C₂×Q₈

—

146

—

C₂×Q₈

—

146

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₃

yes

—

C₂²×C₄

C₂²×D₇₃

yes

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄²

—

C₄²

D₂₉₂

yes

—

C₂³

C₂³×D₇₃

yes

characteristic

Q₈

—

292

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

C₂×D₂₉₂

yes

—

C₂×C₄

C₂×D₂₉₂

yes

—

C₂×C₄

#11924028

yes

—

C₂²

C₂²×D₂₉₂

yes

characteristic

C₂²

C₂×#11924028

yes

—

C₂²

#14556638

yes

—

C₄

—

C₄

—

C₄

—

292

—

C₄

—

292

—

C₄

#14556579

yes

—

100

C₂

C₂×#14556579

yes

characteristic

101

C₂

#17989163

yes

—

102

C₂

#17989199

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇₃
commutator, socle	C₂³×C₇₃	C₂⁴
Fitting	#376×C₇₃	C₂
hypercenter	#376	D₇₃
hypocenter	C₇₃	#2642
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ #376

subgroup

G/H

center, Frattini

C₂³

C₂³×D₇₃

commutator, socle

C₂³×C₇₃

C₂⁴

Fitting

#376×C₇₃

C₂

D₇₃

C₇₃

G ▷ C₂³×C₇₃ ▷ C₇₃

C₁ ◁ C₂³ ◁ #376

N	H ≅ G/N	type
52. C₇₃	#2642	semidirect

H ≅ G/N

type

52. C₇₃

#2642

semidirect

Subgroups — #22615879

Conjugacy classes of subgroups

Complements