Group #22626968 — subgroups

Subgroups — #22626968

Order 9344.

134 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 27 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	#17989673	C₂	1	2	yes	maximal
2	#17989533	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊#10596842	—	2	2	no	—
4	C₂×C₄⋊#64408	—	2	2	no	—
5	C₂×C₄⋊#64408	C₄	1	1	yes	characteristic
6	C₂×C₄⋊#64408	C₂²	1	1	yes	characteristic
7	C₄²×D₇₃	C₄	1	1	yes	characteristic
8	C₂×#10596842	—	4	2	no	—
9	C₂²×#64408	—	2	1	no	—
10	C₂²×#64408	D₄	1	2	yes	—
11	C₄⋊#64408	—	4	1	no	—
12	C₄⋊#64408	—	4	1	no	—
13	C₄⋊#64408	—	4	4	no	—
14	C₂×C₄×D₇₃	—	2	1	no	—
15	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
16	C₄×Dic₇₃	—	2	1	no	—
17	C₄×Dic₇₃	C₈	1	1	yes	characteristic, complemented
18	C₄²×C₇₃	C₈	1	1	yes	characteristic, complemented
19	C₂²×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
20	C₂×#64408	—	2	2	no	—
21	C₂×#64408	—	4	2	no	—
22	C₂×#64408	—	4	2	no	—
23	C₂×#64408	—	4	1	no	—
24	#10596842	—	8	2	no	—
25	C₂×C₄×C₇₃	—	2	1	no	—
26	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
27	C₂×Dic₇₃	—	2	1	no	—
28	C₂×Dic₇₃	M₁₆	1	1	yes	characteristic
29	C₄×D₇₃	—	2	2	no	—
30	C₄×D₇₃	—	2	2	no	—
31	C₄×D₇₃	—	2	1	no	—
32	C₄×D₇₃	—	2	1	no	—
33	C₂²×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
34	C₂×D₇₃	—	2	1	no	—
35	C₂×D₇₃	—	2	1	no	—
36	C₂×D₇₃	#99	1	1	yes	characteristic
37	C₂×D₇₃	#101	1	1	yes	characteristic
38	#64408	—	4	2	no	—
39	#64408	—	8	1	no	—
40	C₄×C₇₃	—	2	2	no	—
41	C₄×C₇₃	—	2	1	no	—
42	Dic₇₃	—	2	2	no	—
43	Dic₇₃	—	2	1	no	—
44	C₂×C₇₃	—	2	1	no	—
45	C₂×C₇₃	#324	1	1	yes	characteristic
46	D₇₃	—	2	1	no	—
47	D₇₃	#353	1	1	yes	characteristic
48	D₇₃	#356	1	1	yes	characteristic
49	#1325	—	73	1	no	maximal, Sylow
50	C₇₃	#1325	1	1	yes	characteristic, complemented, Sylow
51	#384	—	73	1	no	—
52	#324	—	73	2	no	—
53	C₂×C₄⋊C₄	—	73	1	no	—
54	C₂×C₄⋊C₄	—	73	1	no	—
55	C₂×C₄⋊C₄	—	146	2	no	—
56	C₂×C₄²	—	73	1	no	—
57	C₂²⋊C₈	—	146	2	no	—
58	C₂²×C₄	—	73	2	no	—
59	C₂²×C₄	—	73	1	no	—
60	C₂²×C₄	—	146	1	no	—
61	C₂²×C₄	—	146	1	no	—
62	C₂×C₈	—	292	2	no	—
63	C₄⋊C₄	—	292	4	no	—
64	C₄⋊C₄	—	292	1	no	—
65	C₄⋊C₄	—	292	1	no	—
66	C₄²	—	73	1	no	—
67	C₄²	—	146	1	no	—
68	C₄²	#10596842	1	1	yes	characteristic, complemented
69	C₂³	—	73	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	292	2	no	—
72	C₂×C₄	—	292	1	no	—
73	C₂×C₄	—	292	2	no	—
74	C₂×C₄	—	73	1	no	—
75	C₂×C₄	—	146	1	no	—
76	C₂×C₄	—	146	1	no	—
77	C₂×C₄	—	146	2	no	—
78	C₂×C₄	—	146	2	no	—
79	C₂×C₄	—	146	2	no	—
80	C₂×C₄	—	146	1	no	—
81	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
82	C₈	—	584	2	no	—
83	C₂²	—	73	1	no	—
84	C₂²	—	73	1	no	—
85	C₂²	—	146	1	no	—
86	C₂²	—	146	1	no	—
87	C₂²	C₂²⋊#10596842	1	1	yes	characteristic
88	C₄	—	2	2	no	—
89	C₄	—	2	1	no	—
90	C₄	—	292	2	no	—
91	C₄	—	584	1	no	—
92	C₄	—	146	2	no	—
93	C₄	—	146	1	no	—
94	C₂	—	2	1	no	—
95	C₂	—	73	1	no	—
96	C₂	—	73	1	no	—
97	C₂	—	146	1	no	—
98	C₂	#17989673	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989673

C₂

yes

maximal

#17989533

C₂

yes

maximal, characteristic

C₂²⋊#10596842

—

C₂×C₄⋊#64408

—

C₂×C₄⋊#64408

C₄

yes

characteristic

C₂×C₄⋊#64408

C₂²

yes

characteristic

C₄²×D₇₃

C₄

yes

characteristic

C₂×#10596842

—

C₂²×#64408

—

C₂²×#64408

D₄

yes

—

C₄⋊#64408

—

C₄⋊#64408

—

C₄⋊#64408

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

—

C₄×Dic₇₃

C₈

yes

characteristic, complemented

C₄²×C₇₃

C₈

yes

characteristic, complemented

C₂²×D₇₃

C₂²⋊C₄

yes

—

—

—

—

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

M₁₆

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

C₂²×C₇₃

C₂²⋊C₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

yes

C₂×D₇₃

yes

—

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#324

yes

characteristic

D₇₃

—

D₇₃

yes

D₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#384

—

#324

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

146

—

C₂×C₄²

—

C₂²⋊C₈

—

146

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

146

—

C₂²×C₄

—

146

—

C₂×C₈

—

292

—

C₄⋊C₄

—

292

—

C₄⋊C₄

—

292

—

C₄⋊C₄

—

292

—

C₄²

—

C₄²

—

146

—

C₄²

#10596842

yes

characteristic, complemented

C₂³

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

C₂×#10596842

yes

characteristic

C₈

—

584

—

C₂²

—

C₂²

—

C₂²

—

146

—

C₂²

—

146

—

C₂²

C₂²⋊#10596842

yes

characteristic

C₄

—

C₄

—

C₄

—

292

—

C₄

—

584

—

C₄

—

146

—

C₄

—

146

—

C₂

—

C₂

—

C₂

—

C₂

—

146

—

C₂

#17989673

yes

characteristic

	subgroup	G/H
center	C₂	#17989673
commutator	C₂×C₄×C₇₃	C₂×C₈
Frattini	C₂×C₄	C₂×#10596842
Fitting	C₄²×C₇₃	C₈
socle	C₂×C₇₃	#324
hypercenter	C₄²	#10596842
hypocenter	C₇₃	#1325
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄²

subgroup

G/H

center

C₂

#17989673

commutator

C₂×C₄×C₇₃

C₂×C₈

Frattini

C₂×C₄

C₂×#10596842

Fitting

C₄²×C₇₃

C₈

C₂×C₇₃

C₄²

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄²

N	H ≅ G/N	type
17. C₄×Dic₇₃	C₈	semidirect
18. C₄²×C₇₃	C₈	semidirect
50. C₇₃	#1325	semidirect
68. C₄²	#10596842	semidirect

H ≅ G/N

type

17. C₄×Dic₇₃

C₈

semidirect

18. C₄²×C₇₃

C₈

semidirect

50. C₇₃

#1325

semidirect

68. C₄²

#10596842

semidirect

Subgroups — #22626968

Conjugacy classes of subgroups

Complements