Group #22624944 — subgroups

Subgroups — #22624944

Order 9344.

102 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 102 conjugacy classes of subgroups — too many to draw. Only its 32 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	#17989508	C₂	1	1	yes	maximal, characteristic, complemented
2	#17989449	C₂	1	1	yes	maximal, characteristic, complemented
3	#17988972	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924031	—	2	1	no	—
5	C₄⋊#10596833	—	2	1	no	—
6	C₂×#11924015	—	2	1	no	—
7	C₂×D₅₈₄	C₄	1	1	yes	characteristic
8	#14556580	—	2	1	no	—
9	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
10	C₂×Q₁₆×C₇₃	C₄	1	1	yes	characteristic
11	C₂×#10596833	—	4	1	no	—
12	#11924031	—	4	1	no	—
13	C₂×D₂₉₂	—	2	1	no	—
14	#11924015	—	4	1	no	—
15	#11924015	—	4	1	no	—
16	D₅₈₄	—	4	1	no	—
17	C₂×#10596831	D₄	1	1	yes	characteristic
18	#11924005	—	4	1	no	—
19	#11924005	—	4	1	no	—
20	C₄×Dic₇₃	D₄	1	1	yes	characteristic
21	C₂×Q₈×C₇₃	—	2	1	no	—
22	Q₁₆×C₇₃	—	4	1	no	—
23	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
24	C₂²×D₇₃	—	4	1	no	—
25	Q₈×C₇₃	—	4	1	no	—
26	Q₈×C₇₃	—	4	1	no	—
27	C₂×C₄×C₇₃	—	4	1	no	—
28	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×Dic₇₃	D₈	1	1	yes	characteristic
30	C₂×Dic₇₃	SD₁₆	1	1	yes	characteristic
31	D₂₉₂	—	4	1	no	—
32	D₂₉₂	—	4	1	no	—
33	#10596833	—	8	1	no	—
34	C₈×C₇₃	—	2	1	no	—
35	#10596831	D₈	1	1	yes	characteristic
36	#10596831	SD₁₆	1	1	yes	characteristic
37	C₂²×C₇₃	#102	1	1	yes	characteristic
38	C₂×D₇₃	—	8	1	no	—
39	C₂×D₇₃	—	8	1	no	—
40	C₂×D₇₃	—	8	1	no	—
41	C₄×C₇₃	—	8	1	no	—
42	C₄×C₇₃	#100	1	1	yes	characteristic
43	C₄×C₇₃	#102	1	1	yes	characteristic
44	Dic₇₃	—	2	1	no	—
45	Dic₇₃	—	2	1	no	—
46	C₂×C₇₃	#331	1	1	yes	characteristic
47	C₂×C₇₃	#359	1	1	yes	characteristic
48	C₂×C₇₃	#360	1	1	yes	characteristic
49	D₇₃	—	16	1	no	—
50	#1360	—	73	1	no	maximal, Sylow
51	C₇₃	#1360	1	1	yes	characteristic, complemented, Sylow
52	#495	—	73	1	no	—
53	C₄⋊C₁₆	—	73	1	no	—
54	#334	—	73	1	no	—
55	C₂×Q₁₆	#64408	1	1	yes	characteristic
56	C₂×SD₁₆	—	146	1	no	—
57	C₂×D₈	—	73	1	no	—
58	#124	—	146	1	no	—
59	C₂×C₁₆	—	146	1	no	—
60	C₄⋊C₈	—	146	1	no	—
61	C₄×C₈	—	73	1	no	—
62	C₂×Q₈	—	2	1	no	—
63	C₂×D₄	—	146	1	no	—
64	Q₁₆	—	4	1	no	—
65	SD₁₆	—	292	1	no	—
66	SD₁₆	—	292	1	no	—
67	D₈	—	292	1	no	—
68	C₂×C₈	—	292	1	no	—
69	C₂×C₈	—	73	1	no	—
70	C₂×C₈	C₂×#64408	1	1	yes	characteristic
71	C₂²⋊C₄	—	292	1	no	—
72	C₂²⋊C₄	—	292	1	no	—
73	C₄²	—	73	1	no	—
74	C₁₆	—	292	1	no	—
75	C₂³	—	292	1	no	—
76	Q₈	—	4	1	no	—
77	Q₈	—	4	1	no	—
78	D₄	—	292	1	no	—
79	D₄	—	292	1	no	—
80	C₂×C₄	—	4	1	no	—
81	C₂×C₄	—	73	1	no	—
82	C₂×C₄	—	73	1	no	—
83	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
84	C₈	—	2	1	no	—
85	C₈	—	584	1	no	—
86	C₈	—	73	1	no	—
87	C₈	—	73	1	no	—
88	C₂²	—	584	1	no	—
89	C₂²	—	584	1	no	—
90	C₂²	—	584	1	no	—
91	C₂²	#14556653	1	1	yes	characteristic
92	C₄	—	8	1	no	—
93	C₄	—	146	1	no	—
94	C₄	—	146	1	no	—
95	C₄	#14556651	1	1	yes	characteristic
96	C₄	#14556653	1	1	yes	characteristic
97	C₂	—	1168	1	no	—
98	C₂	#17989445	1	1	yes	characteristic
99	C₂	#17989502	1	1	yes	characteristic
100	C₂	#17989504	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989508

C₂

yes

maximal, characteristic, complemented

#17989449

C₂

yes

maximal, characteristic, complemented

#17988972

C₂

yes

maximal, characteristic

C₂×#11924031

—

C₄⋊#10596833

—

C₂×#11924015

—

C₂×D₅₈₄

C₄

yes

characteristic

#14556580

—

C₈×Dic₇₃

C₂²

yes

characteristic

C₂×Q₁₆×C₇₃

C₄

yes

characteristic

C₂×#10596833

—

#11924031

—

C₂×D₂₉₂

—

#11924015

—

#11924015

—

D₅₈₄

—

C₂×#10596831

D₄

yes

characteristic

#11924005

—

#11924005

—

C₄×Dic₇₃

D₄

yes

characteristic

C₂×Q₈×C₇₃

—

Q₁₆×C₇₃

—

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂²×D₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₇₃

D₈

yes

characteristic

C₂×Dic₇₃

SD₁₆

yes

characteristic

D₂₉₂

—

D₂₉₂

—

#10596833

—

C₈×C₇₃

—

#10596831

D₈

yes

characteristic

#10596831

SD₁₆

yes

characteristic

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

—

#1360

—

maximal, Sylow

C₇₃

#1360

yes

characteristic, complemented, Sylow

#495

—

C₄⋊C₁₆

—

#334

—

C₂×Q₁₆

#64408

yes

characteristic

C₂×SD₁₆

—

146

—

C₂×D₈

—

#124

—

146

—

C₂×C₁₆

—

146

—

C₄⋊C₈

—

146

—

C₄×C₈

—

C₂×Q₈

—

C₂×D₄

—

146

—

Q₁₆

—

SD₁₆

—

292

—

SD₁₆

—

292

—

D₈

—

292

—

C₂×C₈

—

292

—

C₂×C₈

—

C₂×C₈

C₂×#64408

yes

characteristic

C₂²⋊C₄

—

292

—

C₂²⋊C₄

—

292

—

C₄²

—

C₁₆

—

292

—

C₂³

—

292

—

Q₈

—

Q₈

—

D₄

—

292

—

D₄

—

292

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊#64408

yes

characteristic

C₈

—

C₈

—

584

—

C₈

—

C₈

—

C₂²

—

584

—

C₂²

—

584

—

C₂²

—

584

—

C₂²

#14556653

yes

characteristic

C₄

—

C₄

—

146

—

C₄

—

146

—

C₄

yes

C₄

yes

C₂

—

1168

—

C₂

yes

C₂

yes

100

C₂

#17989504

yes

characteristic

	subgroup	G/H
center	C₂²	#14556653
commutator	C₂×C₈×C₇₃	C₂×C₄
Frattini	C₂×C₈	C₂×#64408
Fitting	C₂×Q₁₆×C₇₃	C₄
socle	C₂²×C₇₃	#102
hypercenter	C₂×Q₁₆	#64408
hypocenter	C₇₃	#1360
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

subgroup

G/H

center

C₂²

#14556653

commutator

C₂×C₈×C₇₃

C₂×C₄

Frattini

C₂×C₈

C₂×#64408

Fitting

C₂×Q₁₆×C₇₃

C₄

C₂²×C₇₃

C₂×Q₁₆

C₇₃

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

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

N	H ≅ G/N	type
1. #17989508	C₂	semidirect
2. #17989449	C₂	semidirect
51. C₇₃	#1360	semidirect

H ≅ G/N

type

1. #17989508

C₂

semidirect

2. #17989449

C₂

semidirect

51. C₇₃

#1360

semidirect

Subgroups — #22624944

Conjugacy classes of subgroups

Complements