Group #33007766 — subgroups

Subgroups — #33007766

Order 18688.

1774 conjugacy classes of subgroups; only the 667 normal subgroups are shown.

normal subgroups only

This group has 1774 conjugacy classes of subgroups — too many to draw. Only its 667 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×C₄×C₄⋊Dic₇₃	C₂	1	6	yes	maximal
2	#22608196	C₂	1	8	yes	maximal
3	C₂×#376×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄⋊Dic₇₃	C₂²	1	12	yes	—
5	C₂²×C₄×Dic₇₃	C₂²	1	4	yes	—
6	C₄×C₄⋊Dic₇₃	—	2	24	no	—
7	C₂×#14556498	C₂²	1	12	yes	—
8	C₂²×C₄²×C₇₃	C₂²	1	3	yes	—
9	#376×C₇₃	C₄	1	8	yes	complemented
10	C₂×#95×C₇₃	C₂²	1	4	yes	—
11	C₂³×Dic₇₃	C₂³	1	8	yes	—
12	C₂×C₄⋊Dic₇₃	—	2	48	no	—
13	C₂×C₄⋊Dic₇₃	—	2	24	no	—
14	C₂×C₄×Dic₇₃	—	2	24	no	—
15	#14556498	—	2	24	no	—
16	C₂³×C₄×C₇₃	C₂³	1	6	yes	—
17	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
18	C₂×C₄²×C₇₃	C₂×C₄	1	12	yes	—
19	C₂×C₄²×C₇₃	D₄	1	12	yes	—
20	C₂×C₄²×C₇₃	Q₈	1	12	yes	—
21	#95×C₇₃	C₂×C₄	1	16	yes	—
22	C₂²×Dic₇₃	—	2	24	no	—
23	C₂²×Dic₇₃	—	2	24	no	—
24	C₂²×Dic₇₃	#41	1	16	yes	—
25	C₄⋊Dic₇₃	—	2	96	no	—
26	C₄×Dic₇₃	—	4	16	no	—
27	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
28	C₂²×C₄×C₇₃	—	2	24	no	—
29	C₂²×C₄×C₇₃	C₂²×C₄	1	12	yes	—
30	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
31	C₂²×C₄×C₇₃	C₂×D₄	1	12	yes	—
32	C₂²×C₄×C₇₃	C₂×D₄	1	6	yes	—
33	C₂²×C₄×C₇₃	C₂×Q₈	1	12	yes	—
34	C₂²×C₄×C₇₃	C₂×Q₈	1	6	yes	—
35	C₄²×C₇₃	C₄⋊C₄	1	48	yes	complemented
36	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
37	C₂³×C₇₃	C₂²×D₄	1	3	yes	—
38	C₂³×C₇₃	C₂²×Q₈	1	3	yes	—
39	C₂³×C₇₃	C₂×#41	1	8	yes	—
40	C₂×C₄×C₇₃	—	2	24	no	—
41	C₂×C₄×C₇₃	—	2	24	no	—
42	C₂×C₄×C₇₃	—	2	24	no	—
43	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	24	yes	—
44	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	12	yes	—
45	C₂×C₄×C₇₃	#127	1	4	yes	—
46	C₂×C₄×C₇₃	C₄⋊Q₈	1	12	yes	—
47	C₂×Dic₇₃	—	2	48	no	—
48	C₂×Dic₇₃	—	4	24	no	—
49	C₂×Dic₇₃	—	4	8	no	—
50	C₂²×C₇₃	C₂²×C₄⋊C₄	1	3	yes	—
51	C₂²×C₇₃	C₄×#41	1	4	yes	—
52	C₂²×C₇₃	#525	1	12	yes	—
53	C₂²×C₇₃	C₂×#127	1	1	yes	characteristic
54	C₂²×C₇₃	C₂×C₄⋊Q₈	1	3	yes	—
55	C₂²×C₇₃	#533	1	12	yes	—
56	C₄×C₇₃	—	2	24	no	—
57	C₄×C₇₃	#384	1	8	yes	—
58	Dic₇₃	—	4	16	no	—
59	#13856	—	73	1	no	maximal, Sylow
60	C₂×C₇₃	C₂×#384	1	1	yes	characteristic
61	C₂×C₇₃	#2296	1	6	yes	—
62	C₂×C₇₃	#2397	1	2	yes	—
63	C₂×C₇₃	#2399	1	6	yes	—
64	C₂×C₄×C₄⋊C₄	—	73	6	no	—
65	C₂×#376	D₇₃	1	1	yes	characteristic
66	#1444	—	73	8	no	—
67	C₇₃	#13856	1	1	yes	characteristic, complemented, Sylow
68	C₂²×C₄⋊C₄	—	73	12	no	—
69	C₂²×C₄²	—	73	4	no	—
70	C₂²×C₄²	C₂×D₇₃	1	3	yes	—
71	C₄×C₄⋊C₄	—	146	24	no	—
72	#376	Dic₇₃	1	8	yes	complemented
73	C₂×#95	—	73	12	no	—
74	C₂×#95	C₂×D₇₃	1	4	yes	—
75	C₂³×C₄	—	73	8	no	—
76	C₂³×C₄	C₂²×D₇₃	1	6	yes	—
77	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
78	C₂×C₄⋊C₄	—	146	48	no	—
79	C₂×C₄⋊C₄	—	146	24	no	—
80	C₂×C₄²	—	146	24	no	—
81	C₂×C₄²	Dic₁₄₆	1	12	yes	—
82	C₂×C₄²	D₂₉₂	1	12	yes	—
83	C₂×C₄²	C₂×Dic₇₃	1	12	yes	—
84	#95	—	146	24	no	—
85	#95	C₂×Dic₇₃	1	16	yes	—
86	C₂⁴	C₂³×D₇₃	1	1	yes	characteristic
87	C₂²×C₄	—	2	24	no	—
88	C₂²×C₄	—	73	16	no	—
89	C₂²×C₄	—	146	24	no	—
90	C₂²×C₄	—	146	24	no	—
91	C₂²×C₄	C₂²×Dic₇₃	1	12	yes	—
92	C₂²×C₄	C₂²×Dic₇₃	1	2	yes	—
93	C₂²×C₄	C₂×D₂₉₂	1	12	yes	—
94	C₂²×C₄	C₂×D₂₉₂	1	6	yes	—
95	C₂²×C₄	C₂×Dic₁₄₆	1	12	yes	—
96	C₂²×C₄	C₂×Dic₁₄₆	1	6	yes	—
97	C₄⋊C₄	—	146	96	no	—
98	C₄²	—	292	16	no	—
99	C₄²	C₄⋊Dic₇₃	1	48	yes	complemented
100	C₂³	C₂³×Dic₇₃	1	1	yes	characteristic
101	C₂³	C₂²×D₂₉₂	1	3	yes	—
102	C₂³	C₂²×Dic₁₄₆	1	3	yes	—
103	C₂³	#41×D₇₃	1	8	yes	—
104	C₂×C₄	—	2	24	no	—
105	C₂×C₄	—	2	24	no	—
106	C₂×C₄	—	2	24	no	—
107	C₂×C₄	—	292	8	no	—
108	C₂×C₄	—	292	24	no	—
109	C₂×C₄	—	146	48	no	—
110	C₂×C₄	C₂×C₄⋊Dic₇₃	1	24	yes	—
111	C₂×C₄	C₂×C₄⋊Dic₇₃	1	12	yes	—
112	C₂×C₄	#14556588	1	4	yes	—
113	C₂×C₄	#14556591	1	12	yes	—
114	C₂²	C₂²×C₄⋊Dic₇₃	1	3	yes	—
115	C₂²	#41×Dic₇₃	1	4	yes	—
116	C₂²	#17989099	1	12	yes	—
117	C₂²	C₂×#14556588	1	1	yes	characteristic
118	C₂²	C₂×#14556591	1	3	yes	—
119	C₂²	#17989140	1	12	yes	—
120	C₄	—	2	24	no	—
121	C₄	—	292	16	no	—
122	C₄	#17988457	1	8	yes	—
123	C₂	C₂×#17988457	1	1	yes	characteristic
124	C₂	#22612415	1	6	yes	—
125	C₂	#22613212	1	2	yes	—
126	C₂	#22613224	1	6	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×C₄⋊Dic₇₃

C₂

yes

maximal

#22608196

C₂

yes

maximal

C₂×#376×C₇₃

C₂

yes

maximal, characteristic

C₂²×C₄⋊Dic₇₃

C₂²

yes

—

C₂²×C₄×Dic₇₃

C₂²

yes

—

C₄×C₄⋊Dic₇₃

—

C₂×#14556498

C₂²

yes

—

C₂²×C₄²×C₇₃

C₂²

yes

—

#376×C₇₃

C₄

yes

complemented

C₂×#95×C₇₃

C₂²

yes

—

C₂³×Dic₇₃

C₂³

yes

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄×Dic₇₃

—

#14556498

—

C₂³×C₄×C₇₃

C₂³

yes

—

C₂³×C₄×C₇₃

C₂³

yes

characteristic

C₂×C₄²×C₇₃

C₂×C₄

yes

—

C₂×C₄²×C₇₃

D₄

yes

—

C₂×C₄²×C₇₃

Q₈

yes

—

#95×C₇₃

C₂×C₄

yes

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

#41

yes

—

C₄⋊Dic₇₃

—

C₄×Dic₇₃

—

C₂⁴×C₇₃

C₂⁴

yes

characteristic

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

—

C₂²×C₄×C₇₃

C₂×D₄

yes

—

C₂²×C₄×C₇₃

C₂×D₄

yes

—

C₂²×C₄×C₇₃

C₂×Q₈

yes

—

C₂²×C₄×C₇₃

C₂×Q₈

yes

—

C₄²×C₇₃

C₄⋊C₄

yes

complemented

C₂³×C₇₃

C₂³×C₄

yes

characteristic

C₂³×C₇₃

C₂²×D₄

yes

—

C₂³×C₇₃

C₂²×Q₈

yes

—

C₂³×C₇₃

C₂×#41

yes

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₇₃

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₇₃

#127

yes

—

C₂×C₄×C₇₃

C₄⋊Q₈

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂²×C₇₃

C₂²×C₄⋊C₄

yes

—

C₂²×C₇₃

C₄×#41

yes

—

C₂²×C₇₃

#525

yes

—

C₂²×C₇₃

C₂×#127

yes

characteristic

C₂²×C₇₃

C₂×C₄⋊Q₈

yes

—

C₂²×C₇₃

#533

yes

—

C₄×C₇₃

—

C₄×C₇₃

#384

yes

—

Dic₇₃

—

—

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₂×C₇₃

#2397

yes

—

C₂×C₇₃

#2399

yes

—

C₂×C₄×C₄⋊C₄

—

C₂×#376

D₇₃

yes

characteristic

#1444

—

C₇₃

#13856

yes

characteristic, complemented, Sylow

C₂²×C₄⋊C₄

—

C₂²×C₄²

—

C₂²×C₄²

C₂×D₇₃

yes

—

C₄×C₄⋊C₄

—

146

—

#376

Dic₇₃

yes

complemented

C₂×#95

—

C₂×#95

C₂×D₇₃

yes

—

C₂³×C₄

—

C₂³×C₄

C₂²×D₇₃

yes

—

C₂³×C₄

C₂²×D₇₃

yes

characteristic

C₂×C₄⋊C₄

—

146

—

C₂×C₄⋊C₄

—

146

—

C₂×C₄²

—

146

—

C₂×C₄²

Dic₁₄₆

yes

—

C₂×C₄²

D₂₉₂

yes

—

C₂×C₄²

C₂×Dic₇₃

yes

—

#95

—

146

—

#95

C₂×Dic₇₃

yes

—

C₂⁴

C₂³×D₇₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

146

—

C₂²×C₄

—

146

—

C₂²×C₄

C₂²×Dic₇₃

yes

—

C₂²×C₄

C₂²×Dic₇₃

yes

—

C₂²×C₄

C₂×D₂₉₂

yes

—

C₂²×C₄

C₂×D₂₉₂

yes

—

C₂²×C₄

C₂×Dic₁₄₆

yes

—

C₂²×C₄

C₂×Dic₁₄₆

yes

—

C₄⋊C₄

—

146

—

C₄²

—

292

—

C₄²

C₄⋊Dic₇₃

yes

complemented

100

C₂³

C₂³×Dic₇₃

yes

characteristic

101

C₂³

C₂²×D₂₉₂

yes

—

102

C₂³

C₂²×Dic₁₄₆

yes

—

103

C₂³

#41×D₇₃

yes

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

292

—

108

C₂×C₄

—

292

—

109

C₂×C₄

—

146

—

110

C₂×C₄

C₂×C₄⋊Dic₇₃

yes

—

111

C₂×C₄

C₂×C₄⋊Dic₇₃

yes

—

112

C₂×C₄

#14556588

yes

—

113

C₂×C₄

#14556591

yes

—

114

C₂²

C₂²×C₄⋊Dic₇₃

yes

—

115

C₂²

#41×Dic₇₃

yes

—

116

C₂²

#17989099

yes

—

117

C₂²

C₂×#14556588

yes

characteristic

118

C₂²

C₂×#14556591

yes

—

119

C₂²

#17989140

yes

—

120

C₄

—

121

C₄

—

292

—

122

C₄

#17988457

yes

—

123

C₂

C₂×#17988457

yes

characteristic

124

C₂

#22612415

yes

—

125

C₂

#22613212

yes

—

126

C₂

#22613224

yes

—

	subgroup	G/H
center	C₂³×C₄	C₂²×D₇₃
commutator	C₂³×C₇₃	C₂³×C₄
Frattini	C₂⁴	C₂³×D₇₃
Fitting	C₂×#376×C₇₃	C₂
socle, prime radical, cosocle	C₂⁴×C₇₃	C₂⁴
hypercenter	C₂×#376	D₇₃
hypocenter	C₇₃	#13856
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×#376

subgroup

G/H

center

C₂³×C₄

C₂²×D₇₃

commutator

C₂³×C₇₃

C₂³×C₄

Frattini

C₂⁴

C₂³×D₇₃

Fitting

C₂×#376×C₇₃

C₂

socle, prime radical, cosocle

C₂⁴×C₇₃

C₂⁴

D₇₃

C₇₃

G ▷ C₂³×C₇₃ ▷ C₇₃

C₁ ◁ C₂³×C₄ ◁ C₂×#376

N	H ≅ G/N	type
9. #376×C₇₃	C₄	semidirect
35. C₄²×C₇₃	C₄⋊C₄	semidirect
67. C₇₃	#13856	semidirect
72. #376	Dic₇₃	semidirect
99. C₄²	C₄⋊Dic₇₃	semidirect

H ≅ G/N

type

9. #376×C₇₃

C₄

semidirect

35. C₄²×C₇₃

C₄⋊C₄

semidirect

67. C₇₃

#13856

semidirect

72. #376

Dic₇₃

semidirect

99. C₄²

C₄⋊Dic₇₃

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₄×C₄⋊Dic₇₃	2
#22608196	2
C₂×#376×C₇₃	2
#13856	73

subgroup

index

C₂×C₄×C₄⋊Dic₇₃

#22608196

C₂×#376×C₇₃

#13856

Subgroups — #33007766

Conjugacy classes of subgroups

Complements

Maximal subgroups