Group #22624919 — subgroups

Subgroups — #22624919

Order 9344.

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

normal subgroups only

This group has 116 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	#17989482	C₂	1	1	yes	maximal, characteristic
2	#17989461	C₂	1	1	yes	maximal, characteristic
3	#17988825	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊#64408	—	2	1	no	—
5	C₂×#11924031	—	2	1	no	—
6	C₂×C₈×D₇₃	C₂²	1	1	yes	characteristic
7	#14556567	—	2	1	no	—
8	#14556525	C₄	1	1	yes	characteristic, complemented
9	#14556515	—	2	1	no	—
10	C₂×Q₁₆×C₇₃	C₄	1	1	yes	characteristic, complemented
11	C₂²×#64408	—	4	1	no	—
12	C₄⋊#64408	—	2	2	no	—
13	C₄⋊#64408	—	4	1	no	—
14	#11924031	—	4	1	no	—
15	C₂×C₄×D₇₃	D₄	1	1	yes	characteristic
16	C₂×#10596831	D₄	1	1	yes	characteristic
17	C₈×D₇₃	—	4	1	no	—
18	C₄⋊Dic₇₃	—	2	1	no	—
19	#11924007	—	4	1	no	—
20	#11924005	—	4	1	no	—
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	D₈	1	1	yes	characteristic
25	C₂×#64408	—	4	2	no	—
26	C₂×#64408	—	8	1	no	—
27	C₂×#64408	—	8	1	no	—
28	Q₈×C₇₃	—	4	1	no	—
29	Q₈×C₇₃	—	4	1	no	—
30	C₂×C₄×C₇₃	—	4	1	no	—
31	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×Dic₇₃	—	4	1	no	—
33	C₂×Dic₇₃	SD₁₆	1	1	yes	characteristic
34	C₄×D₇₃	—	2	1	no	—
35	C₄×D₇₃	—	2	1	no	—
36	C₈×C₇₃	—	2	1	no	—
37	#10596831	—	2	1	no	—
38	C₂²×C₇₃	#102	1	1	yes	characteristic
39	C₂×D₇₃	—	2	1	no	—
40	C₂×D₇₃	—	2	1	no	—
41	C₂×D₇₃	SD₃₂	1	1	yes	characteristic
42	C₂×D₇₃	Q₃₂	1	1	yes	characteristic
43	#64408	—	8	2	no	—
44	C₄×C₇₃	—	8	1	no	—
45	C₄×C₇₃	#99	1	1	yes	characteristic
46	C₄×C₇₃	#104	1	1	yes	characteristic
47	Dic₇₃	—	2	1	no	—
48	Dic₇₃	—	8	1	no	—
49	C₂×C₇₃	#327	1	1	yes	characteristic
50	C₂×C₇₃	#358	1	1	yes	characteristic
51	C₂×C₇₃	#360	1	1	yes	characteristic
52	D₇₃	—	2	1	no	—
53	D₇₃	—	2	1	no	—
54	#1348	—	73	1	no	maximal, Sylow
55	C₇₃	#1348	1	1	yes	characteristic, complemented, Sylow
56	#467	—	73	1	no	—
57	C₂²⋊C₁₆	—	73	1	no	—
58	#340	—	73	1	no	—
59	C₂×Q₁₆	#64408	1	1	yes	characteristic, complemented
60	C₂²×C₈	—	73	1	no	—
61	C₂²⋊Q₈	—	146	1	no	—
62	C₂×C₄⋊C₄	—	146	1	no	—
63	C₂×C₁₆	—	146	1	no	—
64	#107	—	73	1	no	—
65	#103	—	146	1	no	—
66	C₂×Q₈	—	2	1	no	—
67	C₂²×C₄	—	292	1	no	—
68	C₂²×C₄	—	73	1	no	—
69	Q₁₆	—	4	1	no	—
70	C₂×C₈	—	292	1	no	—
71	C₂×C₈	—	73	1	no	—
72	C₂×C₈	C₂×#64408	1	1	yes	characteristic
73	C₄⋊C₄	—	292	1	no	—
74	C₄⋊C₄	—	292	1	no	—
75	C₄⋊C₄	—	146	2	no	—
76	C₄⋊C₄	—	146	1	no	—
77	C₂²⋊C₄	—	292	1	no	—
78	C₁₆	—	292	1	no	—
79	C₂³	—	73	1	no	—
80	Q₈	—	4	1	no	—
81	Q₈	—	4	1	no	—
82	C₂×C₄	—	4	1	no	—
83	C₂×C₄	—	292	2	no	—
84	C₂×C₄	—	292	1	no	—
85	C₂×C₄	—	584	1	no	—
86	C₂×C₄	—	584	1	no	—
87	C₂×C₄	—	73	1	no	—
88	C₂×C₄	—	146	1	no	—
89	C₂×C₄	—	146	1	no	—
90	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
91	C₈	—	2	1	no	—
92	C₈	—	146	1	no	—
93	C₂²	—	73	1	no	—
94	C₂²	—	73	1	no	—
95	C₂²	—	146	1	no	—
96	C₂²	—	146	1	no	—
97	C₂²	#14556653	1	1	yes	characteristic
98	C₄	—	8	1	no	—
99	C₄	—	584	2	no	—
100	C₄	—	584	1	no	—
101	C₄	—	146	1	no	—
102	C₄	#14556649	1	1	yes	characteristic
103	C₄	#14556655	1	1	yes	characteristic
104	C₂	—	146	1	no	—
105	C₂	—	146	1	no	—
106	C₂	#17989438	1	1	yes	characteristic
107	C₂	#17989500	1	1	yes	characteristic
108	C₂	#17989504	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989482

C₂

yes

maximal, characteristic

#17989461

C₂

yes

maximal, characteristic

#17988825

C₂

yes

maximal, characteristic

C₂×C₄⋊#64408

—

C₂×#11924031

—

C₂×C₈×D₇₃

C₂²

yes

characteristic

#14556567

—

#14556525

C₄

yes

characteristic, complemented

#14556515

—

C₂×Q₁₆×C₇₃

C₄

yes

characteristic, complemented

C₂²×#64408

—

C₄⋊#64408

—

C₄⋊#64408

—

#11924031

—

C₂×C₄×D₇₃

D₄

yes

characteristic

C₂×#10596831

D₄

yes

characteristic

C₈×D₇₃

—

C₄⋊Dic₇₃

—

#11924007

—

#11924005

—

C₂×Q₈×C₇₃

—

Q₁₆×C₇₃

—

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂²×D₇₃

D₈

yes

—

—

—

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

SD₁₆

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

#102

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

SD₃₂

yes

characteristic

C₂×D₇₃

Q₃₂

yes

characteristic

#64408

—

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

D₇₃

—

D₇₃

—

#1348

—

maximal, Sylow

C₇₃

#1348

yes

characteristic, complemented, Sylow

#467

—

C₂²⋊C₁₆

—

#340

—

C₂×Q₁₆

#64408

yes

characteristic, complemented

C₂²×C₈

—

C₂²⋊Q₈

—

146

—

C₂×C₄⋊C₄

—

146

—

C₂×C₁₆

—

146

—

#107

—

#103

—

146

—

C₂×Q₈

—

C₂²×C₄

—

292

—

C₂²×C₄

—

Q₁₆

—

C₂×C₈

—

292

—

C₂×C₈

—

C₂×C₈

C₂×#64408

yes

characteristic

C₄⋊C₄

—

292

—

C₄⋊C₄

—

292

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₂²⋊C₄

—

292

—

C₁₆

—

292

—

C₂³

—

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

584

—

C₂×C₄

—

584

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

C₂²⋊#64408

yes

characteristic

C₈

—

C₈

—

146

—

C₂²

—

C₂²

—

C₂²

—

146

—

C₂²

—

146

—

C₂²

#14556653

yes

characteristic

C₄

—

C₄

—

584

—

100

C₄

—

584

—

101

C₄

—

146

—

102

C₄

#14556649

yes

characteristic

103

C₄

#14556655

yes

characteristic

104

C₂

—

146

—

105

C₂

—

146

—

106

C₂

#17989438

yes

characteristic

107

C₂

#17989500

yes

characteristic

108

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	#1348
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
8. #14556525	C₄	semidirect
10. C₂×Q₁₆×C₇₃	C₄	semidirect
55. C₇₃	#1348	semidirect
59. C₂×Q₁₆	#64408	semidirect

H ≅ G/N

type

8. #14556525

C₄

semidirect

10. C₂×Q₁₆×C₇₃

C₄

semidirect

55. C₇₃

#1348

semidirect

59. C₂×Q₁₆

#64408

semidirect

Subgroups — #22624919

Conjugacy classes of subgroups

Complements