Group #22625028 — subgroups

Subgroups — #22625028

Order 9344.

172 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 44 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	C₂×#14556652	C₂	1	2	yes	maximal
2	#17988493	C₂	1	1	yes	maximal, characteristic
3	C₂×#11924037	—	2	2	no	—
4	#14556652	—	2	2	no	—
5	#14556652	C₄	1	4	yes	complemented
6	C₂²×Dic₁₄₆	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₇₃	C₄	1	1	yes	characteristic
8	#14556498	—	2	2	no	—
9	C₂×C₄²×C₇₃	C₄	1	1	yes	characteristic
10	#11924037	—	2	4	no	—
11	#11924037	—	4	2	no	—
12	C₂×#10596833	—	4	2	no	—
13	C₂×Dic₁₄₆	—	4	1	no	—
14	C₂×Dic₁₄₆	—	4	1	no	—
15	C₂×Dic₁₄₆	C₂×C₄	1	2	yes	—
16	C₂×Dic₁₄₆	D₄	1	1	yes	characteristic
17	C₂×Dic₁₄₆	Q₈	1	1	yes	characteristic
18	C₂²×Dic₇₃	—	2	1	no	—
19	C₂²×Dic₇₃	D₄	1	2	yes	—
20	C₄⋊Dic₇₃	—	4	1	no	—
21	C₂²×C₄×C₇₃	—	2	1	no	—
22	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
23	C₄²×C₇₃	—	4	1	no	—
24	C₂³×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₇₃	—	2	1	no	—
26	C₂×C₄×C₇₃	—	2	1	no	—
27	C₂×C₄×C₇₃	—	2	2	no	—
28	C₂×C₄×C₇₃	—	4	1	no	—
29	C₂×C₄×C₇₃	—	4	1	no	—
30	C₂×C₄×C₇₃	C₄²	1	1	yes	characteristic
31	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
32	C₂×Dic₇₃	—	2	2	no	—
33	C₂×Dic₇₃	—	2	2	no	—
34	C₂×Dic₇₃	—	4	2	no	—
35	C₂×Dic₇₃	—	4	1	no	—
36	C₂×Dic₇₃	C₂²⋊C₄	1	2	yes	—
37	C₂×Dic₇₃	C₄⋊C₄	1	2	yes	—
38	Dic₁₄₆	—	4	2	no	—
39	Dic₁₄₆	—	4	1	no	—
40	Dic₁₄₆	—	4	1	no	—
41	#10596833	—	4	4	no	—
42	C₂²×C₇₃	—	2	1	no	—
43	C₂²×C₇₃	—	2	1	no	—
44	C₂²×C₇₃	#95	1	1	yes	characteristic
45	C₂²×C₇₃	#99	1	1	yes	characteristic
46	C₂²×C₇₃	#99	1	1	yes	characteristic
47	C₄×C₇₃	—	2	1	no	—
48	C₄×C₇₃	—	2	1	no	—
49	C₄×C₇₃	—	4	2	no	—
50	Dic₇₃	—	2	2	no	—
51	Dic₇₃	—	2	2	no	—
52	Dic₇₃	—	8	1	no	—
53	C₂×C₇₃	—	2	1	no	—
54	C₂×C₇₃	—	2	1	no	—
55	C₂×C₇₃	#342	1	1	yes	characteristic
56	C₂×C₇₃	#355	1	1	yes	characteristic
57	C₂×C₇₃	#356	1	1	yes	characteristic
58	#1394	—	73	1	no	maximal, Sylow
59	C₇₃	#1394	1	1	yes	characteristic, complemented, Sylow
60	C₂×#101	—	73	2	no	—
61	#391	—	73	1	no	—
62	C₂²×Q₈	—	73	1	no	—
63	C₂×M₁₆	—	146	2	no	—
64	C₂×C₄⋊C₄	—	73	1	no	—
65	C₂×C₄²	#64408	1	1	yes	characteristic
66	#101	—	73	4	no	—
67	#101	—	146	2	no	—
68	#95	—	146	2	no	—
69	C₂×Q₈	—	292	1	no	—
70	C₂×Q₈	—	292	1	no	—
71	C₂×Q₈	—	73	2	no	—
72	C₂×Q₈	—	73	1	no	—
73	C₂×Q₈	—	73	1	no	—
74	C₂²×C₄	—	2	1	no	—
75	C₂²×C₄	—	73	2	no	—
76	C₂²×C₄	—	146	1	no	—
77	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
78	M₁₆	—	292	2	no	—
79	M₁₆	—	146	4	no	—
80	C₂×C₈	—	292	2	no	—
81	C₄⋊C₄	—	292	1	no	—
82	C₄²	—	4	1	no	—
83	C₂³	C₂²⋊#64408	1	1	yes	characteristic
84	Q₈	—	292	2	no	—
85	Q₈	—	292	1	no	—
86	Q₈	—	292	1	no	—
87	C₂×C₄	—	2	1	no	—
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	2	2	no	—
90	C₂×C₄	—	4	1	no	—
91	C₂×C₄	—	4	1	no	—
92	C₂×C₄	—	292	2	no	—
93	C₂×C₄	—	292	1	no	—
94	C₂×C₄	—	73	2	no	—
95	C₂×C₄	—	73	2	no	—
96	C₂×C₄	—	146	2	no	—
97	C₂×C₄	—	146	2	no	—
98	C₂×C₄	C₄×#64408	1	1	yes	characteristic
99	C₂×C₄	C₄⋊#64408	1	1	yes	characteristic
100	C₈	—	292	4	no	—
101	C₂²	—	2	1	no	—
102	C₂²	—	2	1	no	—
103	C₂²	(C₂×#64408)⋊C₄	1	1	yes	characteristic
104	C₂²	#14556649	1	1	yes	characteristic
105	C₂²	#14556650	1	1	yes	characteristic
106	C₄	—	2	1	no	—
107	C₄	—	2	1	no	—
108	C₄	—	4	2	no	—
109	C₄	—	584	1	no	—
110	C₄	—	146	2	no	—
111	C₄	—	146	2	no	—
112	C₂	—	2	1	no	—
113	C₂	—	2	1	no	—
114	C₂	#17989465	1	1	yes	characteristic
115	C₂	#17989496	1	1	yes	characteristic
116	C₂	#17989498	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556652

C₂

yes

maximal

#17988493

C₂

yes

maximal, characteristic

C₂×#11924037

—

#14556652

—

#14556652

C₄

yes

complemented

C₂²×Dic₁₄₆

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₃

C₄

yes

characteristic

#14556498

—

C₂×C₄²×C₇₃

C₄

yes

—

—

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

C₂×C₄

yes

—

C₂×Dic₁₄₆

D₄

yes

characteristic

C₂×Dic₁₄₆

Q₈

yes

characteristic

C₂²×Dic₇₃

—

C₂²×Dic₇₃

D₄

yes

—

C₄⋊Dic₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₄²×C₇₃

—

C₂³×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₄²

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂²⋊C₄

yes

—

C₂×Dic₇₃

C₄⋊C₄

yes

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

#10596833

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂×#101

—

#391

—

C₂²×Q₈

—

C₂×M₁₆

—

146

—

C₂×C₄⋊C₄

—

C₂×C₄²

yes

—

—

146

—

#95

—

146

—

C₂×Q₈

—

292

—

C₂×Q₈

—

292

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

146

—

C₂²×C₄

C₂×#64408

yes

characteristic

M₁₆

—

292

—

M₁₆

—

146

—

C₂×C₈

—

292

—

C₄⋊C₄

—

292

—

C₄²

—

C₂³

C₂²⋊#64408

yes

characteristic

Q₈

—

292

—

Q₈

—

292

—

Q₈

—

292

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

yes

C₂×C₄

yes

100

C₈

—

292

—

101

C₂²

—

102

C₂²

—

103

C₂²

(C₂×#64408)⋊C₄

yes

characteristic

104

C₂²

#14556649

yes

characteristic

105

C₂²

#14556650

yes

characteristic

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

584

—

110

C₄

—

146

—

111

C₄

—

146

—

112

C₂

—

113

C₂

—

114

C₂

#17989465

yes

characteristic

115

C₂

#17989496

yes

characteristic

116

C₂

#17989498

yes

characteristic

	subgroup	G/H
center	C₂²	#14556650
commutator	C₂×C₄×C₇₃	C₄²
Frattini	C₂²×C₄	C₂×#64408
Fitting	C₂×C₄²×C₇₃	C₄
socle	C₂²×C₇₃	#99
hypercenter	C₂×C₄²	#64408
hypocenter	C₇₃	#1394
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄²

subgroup

G/H

center

C₂²

#14556650

commutator

C₂×C₄×C₇₃

C₄²

Frattini

C₂²×C₄

C₂×#64408

Fitting

C₂×C₄²×C₇₃

C₄

C₂²×C₇₃

C₂×C₄²

C₇₃

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

UCS

C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄²

N	H ≅ G/N	type
5. #14556652	C₄	semidirect
59. C₇₃	#1394	semidirect

H ≅ G/N

type

5. #14556652

C₄

semidirect

59. C₇₃

#1394

semidirect

Subgroups — #22625028

Conjugacy classes of subgroups

Complements