Group #22624924 — subgroups

Subgroups — #22624924

Order 9344.

104 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 30 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	#17989482	C₂	1	1	yes	maximal, characteristic
2	#17989463	C₂	1	1	yes	maximal, characteristic
3	#17988829	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924038	—	2	1	no	—
5	C₂×#11924031	—	2	1	no	—
6	C₂×Dic₂₉₂	C₄	1	1	yes	characteristic
7	C₂×C₈×D₇₃	C₂²	1	1	yes	characteristic
8	#14556571	—	2	1	no	—
9	#14556514	—	2	1	no	—
10	#107×C₇₃	C₄	1	1	yes	characteristic
11	#11924038	—	2	2	no	—
12	#11924038	—	4	1	no	—
13	C₂×#10596833	—	4	1	no	—
14	#11924031	—	4	1	no	—
15	C₂×Dic₁₄₆	—	2	1	no	—
16	C₂×C₄×D₇₃	D₄	1	1	yes	characteristic
17	Dic₂₉₂	—	4	1	no	—
18	C₂×#10596831	D₄	1	1	yes	characteristic
19	C₈×D₇₃	—	4	1	no	—
20	C₄⋊Dic₇₃	—	4	1	no	—
21	#11924005	—	4	1	no	—
22	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
23	C₄⋊C₄×C₇₃	—	2	1	no	—
24	C₂²×D₇₃	SD₁₆	1	1	yes	characteristic
25	C₂×C₄×C₇₃	—	4	1	no	—
26	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×Dic₇₃	—	4	1	no	—
28	C₂×Dic₇₃	D₈	1	1	yes	characteristic
29	C₄×D₇₃	—	2	1	no	—
30	C₄×D₇₃	—	2	1	no	—
31	Dic₁₄₆	—	4	1	no	—
32	Dic₁₄₆	—	4	1	no	—
33	#10596833	—	4	2	no	—
34	C₈×C₇₃	—	2	1	no	—
35	#10596831	—	2	1	no	—
36	C₂²×C₇₃	#102	1	1	yes	characteristic
37	C₂×D₇₃	—	2	1	no	—
38	C₂×D₇₃	—	2	1	no	—
39	C₂×D₇₃	—	2	1	no	—
40	C₄×C₇₃	—	8	1	no	—
41	C₄×C₇₃	#99	1	1	yes	characteristic
42	C₄×C₇₃	#104	1	1	yes	characteristic
43	Dic₇₃	—	2	1	no	—
44	Dic₇₃	—	8	1	no	—
45	C₂×C₇₃	#327	1	1	yes	characteristic
46	C₂×C₇₃	#359	1	1	yes	characteristic
47	C₂×C₇₃	#362	1	1	yes	characteristic
48	D₇₃	—	4	1	no	—
49	#1350	—	73	1	no	maximal, Sylow
50	C₇₃	#1350	1	1	yes	characteristic, complemented, Sylow
51	#467	—	73	1	no	—
52	C₂²⋊C₁₆	—	73	1	no	—
53	#341	—	73	1	no	—
54	C₂×Q₁₆	—	73	1	no	—
55	C₂×M₁₆	—	146	1	no	—
56	C₂²×C₈	—	73	1	no	—
57	C₂²⋊Q₈	—	146	1	no	—
58	C₂×C₁₆	—	146	1	no	—
59	#107	#64408	1	1	yes	characteristic
60	#103	—	146	1	no	—
61	C₂×Q₈	—	146	1	no	—
62	C₂²×C₄	—	73	1	no	—
63	Q₁₆	—	292	1	no	—
64	M₁₆	—	292	1	no	—
65	M₁₆	—	146	2	no	—
66	C₂×C₈	—	292	1	no	—
67	C₂×C₈	—	292	1	no	—
68	C₂×C₈	—	73	1	no	—
69	C₂×C₈	C₂×#64408	1	1	yes	characteristic
70	C₄⋊C₄	—	2	1	no	—
71	C₄⋊C₄	—	292	1	no	—
72	C₂²⋊C₄	—	292	1	no	—
73	C₁₆	—	292	1	no	—
74	C₂³	—	73	1	no	—
75	Q₈	—	292	1	no	—
76	Q₈	—	292	1	no	—
77	C₂×C₄	—	4	1	no	—
78	C₂×C₄	—	292	1	no	—
79	C₂×C₄	—	73	1	no	—
80	C₂×C₄	—	146	1	no	—
81	C₂×C₄	—	146	1	no	—
82	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	292	2	no	—
85	C₈	—	146	1	no	—
86	C₂²	—	146	1	no	—
87	C₂²	—	146	1	no	—
88	C₂²	—	146	1	no	—
89	C₂²	#14556653	1	1	yes	characteristic
90	C₄	—	8	1	no	—
91	C₄	—	584	1	no	—
92	C₄	—	146	1	no	—
93	C₄	#14556650	1	1	yes	characteristic
94	C₄	#14556656	1	1	yes	characteristic
95	C₂	—	292	1	no	—
96	C₂	#17989439	1	1	yes	characteristic
97	C₂	#17989501	1	1	yes	characteristic
98	C₂	#17989506	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989482

C₂

yes

maximal, characteristic

#17989463

C₂

yes

maximal, characteristic

#17988829

C₂

yes

maximal, characteristic

C₂×#11924038

—

C₂×#11924031

—

C₂×Dic₂₉₂

C₄

yes

characteristic

C₂×C₈×D₇₃

C₂²

yes

characteristic

#14556571

—

#14556514

—

#107×C₇₃

C₄

yes

—

—

—

—

C₂×Dic₁₄₆

—

C₂×C₄×D₇₃

D₄

yes

characteristic

Dic₂₉₂

—

C₂×#10596831

D₄

yes

characteristic

C₈×D₇₃

—

C₄⋊Dic₇₃

—

#11924005

—

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₄⋊C₄×C₇₃

—

C₂²×D₇₃

SD₁₆

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

D₈

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

#10596833

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

#102

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

D₇₃

—

#1350

—

maximal, Sylow

C₇₃

#1350

yes

characteristic, complemented, Sylow

#467

—

C₂²⋊C₁₆

—

#341

—

C₂×Q₁₆

—

C₂×M₁₆

—

146

—

C₂²×C₈

—

C₂²⋊Q₈

—

146

—

C₂×C₁₆

—

146

—

yes

—

146

—

C₂×Q₈

—

146

—

C₂²×C₄

—

Q₁₆

—

292

—

M₁₆

—

292

—

M₁₆

—

146

—

C₂×C₈

—

292

—

C₂×C₈

—

292

—

C₂×C₈

—

C₂×C₈

C₂×#64408

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

292

—

C₂²⋊C₄

—

292

—

C₁₆

—

292

—

C₂³

—

Q₈

—

292

—

Q₈

—

292

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

C₂²⋊#64408

yes

characteristic

C₈

—

C₈

—

292

—

C₈

—

146

—

C₂²

—

146

—

C₂²

—

146

—

C₂²

—

146

—

C₂²

#14556653

yes

characteristic

C₄

—

C₄

—

584

—

C₄

—

146

—

C₄

yes

C₄

yes

C₂

—

292

—

C₂

yes

C₂

yes

C₂

yes

	subgroup	G/H
center	C₂²	#14556653
commutator	C₂×C₈×C₇₃	C₂×C₄
Frattini	C₂×C₈	C₂×#64408
Fitting	#107×C₇₃	C₄
socle	C₂²×C₇₃	#102
hypercenter	#107	#64408
hypocenter	C₇₃	#1350
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

subgroup

G/H

center

C₂²

#14556653

commutator

C₂×C₈×C₇₃

C₂×C₄

Frattini

C₂×C₈

C₂×#64408

Fitting

#107×C₇₃

C₄

C₂²×C₇₃

C₇₃

G ▷ C₂×C₈×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

N	H ≅ G/N	type
50. C₇₃	#1350	semidirect

H ≅ G/N

type

50. C₇₃

#1350

semidirect

Subgroups — #22624924

Conjugacy classes of subgroups

Complements