Group #22624969 — subgroups

Subgroups — #22624969

Order 9344.

160 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 90 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	C₂²×#11924031	C₂	1	2	yes	maximal
2	C₂×C₄×#10596831	C₂	1	1	yes	maximal, characteristic
3	C₂×#11924031	—	2	2	no	—
4	C₂×#11924031	—	2	2	no	—
5	C₂×#11924031	C₄	1	4	yes	complemented
6	C₂²×#10596831	C₄	1	1	yes	characteristic
7	C₂²×#10596831	C₂²	1	1	yes	characteristic
8	C₄×#10596831	—	2	2	no	—
9	C₂×C₄²×C₇₃	C₄	1	1	yes	characteristic
10	#11924031	—	2	4	no	—
11	C₂×#10596831	—	2	1	no	—
12	C₂×#10596831	—	2	1	no	—
13	C₂×#10596831	C₈	1	2	yes	—
14	C₂×#10596831	C₂×C₄	1	2	yes	—
15	C₂×#10596831	D₄	1	1	yes	characteristic
16	C₂×#10596831	D₄	1	2	yes	—
17	C₂×#10596831	Q₈	1	1	yes	characteristic
18	C₂²×C₄×C₇₃	C₈	1	2	yes	—
19	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₇₃	—	2	1	no	—
21	C₄²×C₇₃	—	2	1	no	—
22	C₂³×C₇₃	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₇₃	—	2	2	no	—
24	C₂×C₄×C₇₃	—	2	2	no	—
25	C₂×C₄×C₇₃	C₁₆	1	4	yes	complemented
26	C₂×C₄×C₇₃	C₄²	1	1	yes	characteristic
27	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₇₃	M₁₆	1	1	yes	characteristic
31	C₂×C₄×C₇₃	M₁₆	1	1	yes	characteristic
32	#10596831	—	2	2	no	—
33	#10596831	C₂²⋊C₄	1	2	yes	—
34	#10596831	C₄⋊C₄	1	2	yes	—
35	C₂²×C₇₃	C₄×C₈	1	1	yes	characteristic
36	C₂²×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
37	C₂²×C₇₃	C₄⋊C₈	1	1	yes	characteristic
38	C₂²×C₇₃	C₂×C₁₆	1	2	yes	—
39	C₂²×C₇₃	M₃₂	1	2	yes	—
40	C₄×C₇₃	—	2	4	no	—
41	C₄×C₇₃	#95	1	1	yes	characteristic
42	C₄×C₇₃	#97	1	1	yes	characteristic
43	C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
44	C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
45	C₂×C₇₃	#336	1	1	yes	characteristic
46	C₂×C₇₃	C₄×C₁₆	1	1	yes	characteristic
47	C₂×C₇₃	#346	1	1	yes	characteristic
48	C₂×C₇₃	C₂²⋊C₁₆	1	2	yes	—
49	C₂×C₇₃	C₄⋊C₁₆	1	2	yes	—
50	#1374	—	73	1	no	maximal, Sylow
51	C₇₃	#1374	1	1	yes	characteristic, complemented, Sylow
52	C₂²×C₁₆	—	73	2	no	—
53	C₂×C₄×C₈	—	73	1	no	—
54	C₂²×C₈	—	73	1	no	—
55	C₂²×C₈	—	73	1	no	—
56	C₂×C₄²	#64408	1	1	yes	characteristic
57	C₂×C₁₆	—	73	4	no	—
58	C₂×C₁₆	—	146	2	no	—
59	C₂×C₁₆	—	146	2	no	—
60	C₄×C₈	—	146	2	no	—
61	C₂²×C₄	#10596833	1	2	yes	—
62	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
63	C₂×C₈	—	73	2	no	—
64	C₂×C₈	—	73	2	no	—
65	C₂×C₈	—	73	1	no	—
66	C₂×C₈	—	73	1	no	—
67	C₂×C₈	—	73	2	no	—
68	C₂×C₈	—	146	1	no	—
69	C₂×C₈	—	146	1	no	—
70	C₄²	—	2	1	no	—
71	C₄²	—	2	1	no	—
72	C₁₆	—	146	4	no	—
73	C₂³	C₂×#10596833	1	1	yes	characteristic
74	C₂×C₄	—	2	2	no	—
75	C₂×C₄	—	2	2	no	—
76	C₂×C₄	#11924031	1	4	yes	complemented
77	C₂×C₄	C₄×#64408	1	1	yes	characteristic
78	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
79	C₂×C₄	C₄⋊#64408	1	1	yes	characteristic
80	C₂×C₄	#11924036	1	1	yes	characteristic
81	C₂×C₄	#11924037	1	1	yes	characteristic
82	C₂×C₄	#11924038	1	1	yes	characteristic
83	C₈	—	73	2	no	—
84	C₈	—	73	2	no	—
85	C₈	—	146	2	no	—
86	C₂²	C₄×#10596833	1	1	yes	characteristic
87	C₂²	C₂²⋊#10596833	1	1	yes	characteristic
88	C₂²	C₄⋊#10596833	1	1	yes	characteristic
89	C₂²	C₂×#11924031	1	2	yes	—
90	C₂²	#14556665	1	2	yes	—
91	C₄	—	2	4	no	—
92	C₄	(C₂×#64408)⋊C₄	1	1	yes	characteristic
93	C₄	#14556646	1	1	yes	characteristic
94	C₄	#14556648	1	1	yes	characteristic
95	C₄	#14556658	1	1	yes	characteristic
96	C₂	#17989453	1	1	yes	characteristic
97	C₂	C₄×#11924031	1	1	yes	characteristic
98	C₂	#17989475	1	1	yes	characteristic
99	C₂	C₂²⋊#11924031	1	2	yes	—
100	C₂	C₄⋊#11924031	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#11924031

C₂

yes

maximal

C₂×C₄×#10596831

C₂

yes

maximal, characteristic

C₂×#11924031

—

C₂×#11924031

—

C₂×#11924031

C₄

yes

complemented

C₂²×#10596831

C₄

yes

characteristic

C₂²×#10596831

C₂²

yes

characteristic

C₄×#10596831

—

C₂×C₄²×C₇₃

C₄

yes

—

—

—

C₈

yes

—

C₂×#10596831

C₂×C₄

yes

—

C₂×#10596831

D₄

yes

characteristic

C₂×#10596831

D₄

yes

—

C₂×#10596831

Q₈

yes

characteristic

C₂²×C₄×C₇₃

C₈

yes

—

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₄²×C₇₃

—

C₄²×C₇₃

—

C₂³×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₁₆

yes

complemented

C₂×C₄×C₇₃

C₄²

yes

characteristic

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

M₁₆

yes

characteristic

C₂×C₄×C₇₃

M₁₆

yes

characteristic

#10596831

—

#10596831

C₂²⋊C₄

yes

—

#10596831

C₄⋊C₄

yes

—

C₂²×C₇₃

C₄×C₈

yes

characteristic

C₂²×C₇₃

C₂²⋊C₈

yes

characteristic

C₂²×C₇₃

C₄⋊C₈

yes

characteristic

C₂²×C₇₃

C₂×C₁₆

yes

—

C₂²×C₇₃

M₃₂

yes

—

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

C₂²⋊C₈

yes

characteristic

C₄×C₇₃

C₄⋊C₈

yes

characteristic

C₂×C₇₃

#336

yes

characteristic

C₂×C₇₃

C₄×C₁₆

yes

characteristic

C₂×C₇₃

#346

yes

characteristic

C₂×C₇₃

C₂²⋊C₁₆

yes

—

C₂×C₇₃

C₄⋊C₁₆

yes

—

#1374

—

maximal, Sylow

C₇₃

#1374

yes

characteristic, complemented, Sylow

C₂²×C₁₆

—

C₂×C₄×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

#64408

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

146

—

C₂×C₁₆

—

146

—

C₄×C₈

—

146

—

C₂²×C₄

#10596833

yes

—

C₂²×C₄

C₂×#64408

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₄²

—

C₄²

—

C₁₆

—

146

—

C₂³

C₂×#10596833

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

C₈

—

C₈

—

146

—

C₂²

yes

C₂²

yes

C₂²

yes

C₂²

yes

—

C₂²

#14556665

yes

—

C₄

—

C₄

yes

C₄

yes

C₄

yes

C₄

yes

C₂

yes

C₂

yes

C₂

yes

C₂

yes

—

100

C₂

C₄⋊#11924031

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂×#64408
commutator	C₂×C₇₃	C₄×C₁₆
Fitting	C₂×C₄²×C₇₃	C₄
socle	C₂³×C₇₃	C₂×C₈
hypercenter	C₂×C₄²	#64408
hypocenter	C₇₃	#1374
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

subgroup

G/H

center, Frattini

C₂²×C₄

C₂×#64408

commutator

C₂×C₇₃

C₄×C₁₆

Fitting

C₂×C₄²×C₇₃

C₄

socle

C₂³×C₇₃

C₂×C₈

C₂×C₄²

C₇₃

G ▷ C₂×C₇₃ ▷ C₇₃

C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

N	H ≅ G/N	type
5. C₂×#11924031	C₄	semidirect
25. C₂×C₄×C₇₃	C₁₆	semidirect
51. C₇₃	#1374	semidirect
76. C₂×C₄	#11924031	semidirect

H ≅ G/N

type

5. C₂×#11924031

C₄

semidirect

25. C₂×C₄×C₇₃

C₁₆

semidirect

51. C₇₃

#1374

semidirect

76. C₂×C₄

#11924031

semidirect

Subgroups — #22624969

Conjugacy classes of subgroups

Complements