Group #19128337 — subgroups

Subgroups — D₄×D₃₃₂ #19128337

Order 5312.

428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 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×D₃₃₂	C₂	1	2	yes	maximal, complemented
2	C₂×D₄×D₈₃	C₂	1	2	yes	maximal, complemented
3	#14581789	C₂	1	1	yes	maximal, characteristic, complemented
4	#14581767	C₂	1	2	yes	maximal, complemented
5	#14581766	C₂	1	2	yes	maximal, complemented
6	#14581762	C₂	1	4	yes	maximal, complemented
7	C₄×D₃₃₂	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×D₄×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₈₃	C₂²	1	4	yes	complemented
10	C₂×D₃₃₂	—	2	8	no	—
11	C₂×D₃₃₂	C₂²	1	1	yes	characteristic
12	C₂×D₃₃₂	C₂²	1	4	yes	complemented
13	C₂×D₃₃₂	C₂²	1	2	yes	complemented
14	C₂×D₃₃₂	C₂²	1	2	yes	complemented
15	C₂×D₃₃₂	C₂²	1	2	yes	complemented
16	C₂×C₂²⋊D₈₃	C₂²	1	4	yes	complemented
17	D₄×D₈₃	—	2	8	no	—
18	C₂×C₄×D₈₃	C₂²	1	2	yes	complemented
19	C₄⋊Dic₈₃	C₂²	1	1	yes	characteristic, complemented
20	(C₂×D₈₃)⋊C₄	C₂²	1	2	yes	complemented
21	(C₂×D₈₃)⋊C₄	C₂²	1	4	yes	complemented
22	C₂×D₄×C₈₃	C₂²	1	1	yes	characteristic
23	C₂²×C₄×C₈₃	C₂²	1	2	yes	complemented
24	C₄⋊C₄×C₈₃	C₂²	1	1	yes	characteristic, complemented
25	C₂²⋊C₄×C₈₃	C₂²	1	2	yes	complemented
26	C₄²×C₈₃	C₂²	1	1	yes	characteristic, complemented
27	C₂³×C₈₃	C₂³	1	2	yes	—
28	C₂²×D₈₃	—	2	8	no	—
29	C₂²×D₈₃	—	2	8	no	—
30	C₂²×D₈₃	—	4	4	no	—
31	C₂²×D₈₃	C₂³	1	4	yes	—
32	C₂²×D₈₃	C₂³	1	2	yes	—
33	D₄×C₈₃	D₄	1	4	yes	complemented
34	C₂×C₄×C₈₃	—	2	4	no	—
35	C₂×C₄×C₈₃	C₂³	1	1	yes	characteristic
36	C₂×C₄×C₈₃	C₂³	1	2	yes	—
37	C₂×C₄×C₈₃	C₂³	1	1	yes	characteristic
38	C₂×C₄×C₈₃	C₂³	1	1	yes	characteristic
39	C₂²⋊D₈₃	—	2	8	no	—
40	C₂×Dic₈₃	C₂³	1	2	yes	—
41	D₃₃₂	—	2	8	no	—
42	D₃₃₂	—	2	4	no	—
43	D₃₃₂	—	2	4	no	—
44	D₃₃₂	—	4	2	no	—
45	D₃₃₂	D₄	1	4	yes	direct product factor
46	C₄×D₈₃	—	2	4	no	—
47	C₂²×C₈₃	—	2	2	no	—
48	C₂²×C₈₃	—	2	2	no	—
49	C₂²×C₈₃	C₂×D₄	1	4	yes	complemented
50	C₂²×C₈₃	C₂⁴	1	1	yes	characteristic
51	C₂×D₈₃	—	2	2	no	—
52	C₂×D₈₃	—	2	2	no	—
53	C₂×D₈₃	—	2	4	no	—
54	C₂×D₈₃	—	2	4	no	—
55	C₂×D₈₃	—	2	4	no	—
56	C₂×D₈₃	—	4	16	no	—
57	C₂×D₈₃	C₂×D₄	1	4	yes	complemented
58	C₄×C₈₃	—	2	2	no	—
59	C₄×C₈₃	—	2	1	no	—
60	C₄×C₈₃	C₂×D₄	1	2	yes	complemented
61	C₄×C₈₃	C₂×D₄	1	2	yes	complemented
62	Dic₈₃	—	2	2	no	—
63	C₂×C₈₃	—	2	4	no	—
64	C₂×C₈₃	C₂²×D₄	1	1	yes	characteristic
65	C₂×C₈₃	C₂²×D₄	1	1	yes	characteristic
66	C₂×C₈₃	H(5,𝔽₂)	1	1	yes	characteristic
67	D₈₃	—	2	4	no	—
68	D₈₃	—	4	4	no	—
69	C₈₃	D₄²	1	1	yes	characteristic, complemented, Sylow
70	D₄²	—	83	1	no	maximal, Sylow
71	C₂²×D₄	—	83	2	no	—
72	C₂²×D₄	—	83	2	no	—
73	#127	—	83	1	no	—
74	#121	—	83	2	no	—
75	#121	—	83	2	no	—
76	#120	—	83	4	no	—
77	C₄×D₄	—	83	1	no	—
78	C₄×D₄	D₈₃	1	1	yes	characteristic, complemented
79	C₂⁴	—	83	4	no	—
80	C₂×D₄	—	83	4	no	—
81	C₂×D₄	—	83	2	no	—
82	C₂×D₄	—	83	1	no	—
83	C₂×D₄	—	83	4	no	—
84	C₂×D₄	—	83	2	no	—
85	C₂×D₄	—	83	2	no	—
86	C₂×D₄	—	166	8	no	—
87	C₂×D₄	—	166	8	no	—
88	C₂×D₄	C₂×D₈₃	1	1	yes	characteristic
89	C₂²×C₄	—	83	2	no	—
90	C₂²×C₄	C₂×D₈₃	1	2	yes	complemented
91	C₄⋊C₄	—	83	1	no	—
92	C₄⋊C₄	C₂×D₈₃	1	1	yes	characteristic, complemented
93	C₂²⋊C₄	—	83	2	no	—
94	C₂²⋊C₄	—	83	4	no	—
95	C₂²⋊C₄	C₂×D₈₃	1	2	yes	complemented
96	C₄²	C₂×D₈₃	1	1	yes	characteristic, complemented
97	C₂³	—	332	4	no	—
98	C₂³	—	83	2	no	—
99	C₂³	—	83	4	no	—
100	C₂³	—	166	8	no	—
101	C₂³	—	166	8	no	—
102	C₂³	C₂²×D₈₃	1	2	yes	—
103	D₄	—	332	2	no	—
104	D₄	—	83	4	no	—
105	D₄	—	166	8	no	—
106	D₄	—	166	8	no	—
107	D₄	—	166	4	no	—
108	D₄	—	166	4	no	—
109	D₄	D₃₃₂	1	4	yes	direct product factor
110	C₂×C₄	—	2	4	no	—
111	C₂×C₄	—	83	2	no	—
112	C₂×C₄	—	166	4	no	—
113	C₂×C₄	C₂²×D₈₃	1	1	yes	characteristic
114	C₂×C₄	C₂²×D₈₃	1	2	yes	—
115	C₂×C₄	C₂²×D₈₃	1	1	yes	characteristic
116	C₂×C₄	C₂²×D₈₃	1	1	yes	characteristic
117	C₂²	—	2	2	no	—
118	C₂²	—	2	2	no	—
119	C₂²	—	332	16	no	—
120	C₂²	—	83	4	no	—
121	C₂²	—	166	4	no	—
122	C₂²	—	166	4	no	—
123	C₂²	—	166	4	no	—
124	C₂²	—	166	2	no	—
125	C₂²	—	166	2	no	—
126	C₂²	C₂×D₃₃₂	1	4	yes	complemented
127	C₂²	C₂³×D₈₃	1	1	yes	characteristic
128	C₄	—	2	2	no	—
129	C₄	—	2	1	no	—
130	C₄	—	166	2	no	—
131	C₄	D₄×D₈₃	1	2	yes	complemented
132	C₄	C₂×D₃₃₂	1	2	yes	complemented
133	C₂	—	2	4	no	—
134	C₂	—	332	4	no	—
135	C₂	—	166	4	no	—
136	C₂	C₂×D₄×D₈₃	1	1	yes	characteristic
137	C₂	C₂²×D₃₃₂	1	1	yes	characteristic
138	C₂	#14581838	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×D₃₃₂

C₂

yes

maximal, complemented

C₂×D₄×D₈₃

C₂

yes

maximal, complemented

#14581789

C₂

yes

maximal, characteristic, complemented

#14581767

C₂

yes

maximal, complemented

#14581766

C₂

yes

maximal, complemented

#14581762

C₂

yes

maximal, complemented

C₄×D₃₃₂

C₂

yes

maximal, characteristic, complemented

C₄×D₄×C₈₃

C₂

yes

maximal, characteristic, complemented

C₂³×D₈₃

C₂²

yes

complemented

C₂×D₃₃₂

—

C₂×D₃₃₂

C₂²

yes

characteristic

C₂×D₃₃₂

C₂²

yes

complemented

C₂×D₃₃₂

C₂²

yes

complemented

C₂×D₃₃₂

C₂²

yes

complemented

C₂×D₃₃₂

C₂²

yes

complemented

C₂×C₂²⋊D₈₃

C₂²

yes

complemented

D₄×D₈₃

—

C₂×C₄×D₈₃

C₂²

yes

complemented

C₄⋊Dic₈₃

C₂²

yes

characteristic, complemented

(C₂×D₈₃)⋊C₄

C₂²

yes

complemented

(C₂×D₈₃)⋊C₄

C₂²

yes

complemented

C₂×D₄×C₈₃

C₂²

yes

characteristic

C₂²×C₄×C₈₃

C₂²

yes

complemented

C₄⋊C₄×C₈₃

C₂²

yes

characteristic, complemented

C₂²⋊C₄×C₈₃

C₂²

yes

complemented

C₄²×C₈₃

C₂²

yes

characteristic, complemented

C₂³×C₈₃

C₂³

yes

—

C₂²×D₈₃

—

C₂²×D₈₃

—

C₂²×D₈₃

—

C₂²×D₈₃

C₂³

yes

—

C₂²×D₈₃

C₂³

yes

—

D₄×C₈₃

D₄

yes

complemented

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

C₂³

yes

characteristic

C₂×C₄×C₈₃

C₂³

yes

—

C₂×C₄×C₈₃

C₂³

yes

characteristic

C₂×C₄×C₈₃

C₂³

yes

characteristic

C₂²⋊D₈₃

—

C₂×Dic₈₃

C₂³

yes

—

D₃₃₂

—

D₃₃₂

—

D₃₃₂

—

D₃₃₂

—

D₃₃₂

D₄

yes

direct product factor

C₄×D₈₃

—

C₂²×C₈₃

—

C₂²×C₈₃

—

C₂²×C₈₃

C₂×D₄

yes

complemented

C₂²×C₈₃

C₂⁴

yes

characteristic

C₂×D₈₃

—

C₂×D₈₃

—

C₂×D₈₃

—

C₂×D₈₃

—

C₂×D₈₃

—

C₂×D₈₃

—

C₂×D₈₃

C₂×D₄

yes

complemented

C₄×C₈₃

—

C₄×C₈₃

—

C₄×C₈₃

C₂×D₄

yes

complemented

C₄×C₈₃

C₂×D₄

yes

complemented

Dic₈₃

—

C₂×C₈₃

—

C₂×C₈₃

C₂²×D₄

yes

characteristic

C₂×C₈₃

C₂²×D₄

yes

characteristic

C₂×C₈₃

H(5,𝔽₂)

yes

characteristic

D₈₃

—

D₈₃

—

C₈₃

D₄²

yes

characteristic, complemented, Sylow

D₄²

—

maximal, Sylow

C₂²×D₄

—

C₂²×D₄

—

—

—

—

—

C₄×D₄

—

C₄×D₄

D₈₃

yes

characteristic, complemented

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

166

—

C₂×D₄

—

166

—

C₂×D₄

C₂×D₈₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₂×D₈₃

yes

complemented

C₄⋊C₄

—

C₄⋊C₄

C₂×D₈₃

yes

characteristic, complemented

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

C₂×D₈₃

yes

complemented

C₄²

C₂×D₈₃

yes

characteristic, complemented

C₂³

—

332

—

C₂³

—

C₂³

—

100

C₂³

—

166

—

101

C₂³

—

166

—

102

C₂³

C₂²×D₈₃

yes

—

103

D₄

—

332

—

104

D₄

—

105

D₄

—

166

—

106

D₄

—

166

—

107

D₄

—

166

—

108

D₄

—

166

—

109

D₄

D₃₃₂

yes

direct product factor

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

166

—

113

C₂×C₄

C₂²×D₈₃

yes

characteristic

114

C₂×C₄

C₂²×D₈₃

yes

—

115

C₂×C₄

C₂²×D₈₃

yes

characteristic

116

C₂×C₄

C₂²×D₈₃

yes

characteristic

117

C₂²

—

118

C₂²

—

119

C₂²

—

332

—

120

C₂²

—

121

C₂²

—

166

—

122

C₂²

—

166

—

123

C₂²

—

166

—

124

C₂²

—

166

—

125

C₂²

—

166

—

126

C₂²

C₂×D₃₃₂

yes

complemented

127

C₂²

C₂³×D₈₃

yes

characteristic

128

C₄

—

129

C₄

—

130

C₄

—

166

—

131

C₄

D₄×D₈₃

yes

complemented

132

C₄

C₂×D₃₃₂

yes

complemented

133

C₂

—

134

C₂

—

332

—

135

C₂

—

166

—

136

C₂

C₂×D₄×D₈₃

yes

characteristic

137

C₂

C₂²×D₃₃₂

yes

characteristic

138

C₂

#14581838

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₈₃
commutator, socle	C₂²×C₈₃	C₂⁴
Fitting	C₄×D₄×C₈₃	C₂
hypercenter	C₄×D₄	D₈₃
hypocenter	C₈₃	D₄²
LCS	G ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₄×D₄

subgroup

G/H

center, Frattini

C₂²

C₂³×D₈₃

commutator, socle

C₂²×C₈₃

C₂⁴

Fitting

C₄×D₄×C₈₃

C₂

hypercenter

C₄×D₄

D₈₃

hypocenter

C₈₃

D₄²

LCS

G ▷ C₂²×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂² ◁ C₄×D₄

N	H ≅ G/N	type
1. C₂²×D₃₃₂	C₂	semidirect
2. C₂×D₄×D₈₃	C₂	semidirect
3. #14581789	C₂	semidirect
4. #14581767	C₂	semidirect
5. #14581766	C₂	semidirect
6. #14581762	C₂	semidirect
7. C₄×D₃₃₂	C₂	semidirect
8. C₄×D₄×C₈₃	C₂	semidirect
9. C₂³×D₈₃	C₂²	semidirect
12. C₂×D₃₃₂	C₂²	semidirect
13. C₂×D₃₃₂	C₂²	semidirect
14. C₂×D₃₃₂	C₂²	semidirect
15. C₂×D₃₃₂	C₂²	semidirect
16. C₂×C₂²⋊D₈₃	C₂²	semidirect
18. C₂×C₄×D₈₃	C₂²	semidirect
19. C₄⋊Dic₈₃	C₂²	semidirect
20. (C₂×D₈₃)⋊C₄	C₂²	semidirect
21. (C₂×D₈₃)⋊C₄	C₂²	semidirect
23. C₂²×C₄×C₈₃	C₂²	semidirect
24. C₄⋊C₄×C₈₃	C₂²	semidirect
25. C₂²⋊C₄×C₈₃	C₂²	semidirect
26. C₄²×C₈₃	C₂²	semidirect
33. D₄×C₈₃	D₄	semidirect
45. D₃₃₂	D₄	direct (N × H)
49. C₂²×C₈₃	C₂×D₄	semidirect
57. C₂×D₈₃	C₂×D₄	semidirect
60. C₄×C₈₃	C₂×D₄	semidirect
61. C₄×C₈₃	C₂×D₄	semidirect
69. C₈₃	D₄²	semidirect
78. C₄×D₄	D₈₃	semidirect
90. C₂²×C₄	C₂×D₈₃	semidirect
92. C₄⋊C₄	C₂×D₈₃	semidirect
95. C₂²⋊C₄	C₂×D₈₃	semidirect
96. C₄²	C₂×D₈₃	semidirect
109. D₄	D₃₃₂	direct (N × H)
126. C₂²	C₂×D₃₃₂	semidirect
131. C₄	D₄×D₈₃	semidirect
132. C₄	C₂×D₃₃₂	semidirect

H ≅ G/N

type

1. C₂²×D₃₃₂

C₂

semidirect

2. C₂×D₄×D₈₃

C₂

semidirect

3. #14581789

C₂

semidirect

4. #14581767

C₂

semidirect

5. #14581766

C₂

semidirect

6. #14581762

C₂

semidirect

7. C₄×D₃₃₂

C₂

semidirect

8. C₄×D₄×C₈₃

C₂

semidirect

9. C₂³×D₈₃

C₂²

semidirect

12. C₂×D₃₃₂

C₂²

semidirect

13. C₂×D₃₃₂

C₂²

semidirect

14. C₂×D₃₃₂

C₂²

semidirect

15. C₂×D₃₃₂

C₂²

semidirect

16. C₂×C₂²⋊D₈₃

C₂²

semidirect

18. C₂×C₄×D₈₃

C₂²

semidirect

19. C₄⋊Dic₈₃

C₂²

semidirect

20. (C₂×D₈₃)⋊C₄

C₂²

semidirect

21. (C₂×D₈₃)⋊C₄

C₂²

semidirect

23. C₂²×C₄×C₈₃

C₂²

semidirect

24. C₄⋊C₄×C₈₃

C₂²

semidirect

25. C₂²⋊C₄×C₈₃

C₂²

semidirect

26. C₄²×C₈₃

C₂²

semidirect

33. D₄×C₈₃

D₄

semidirect

45. D₃₃₂

D₄

direct (N × H)

49. C₂²×C₈₃

C₂×D₄

semidirect

57. C₂×D₈₃

C₂×D₄

semidirect

60. C₄×C₈₃

C₂×D₄

semidirect

61. C₄×C₈₃

C₂×D₄

semidirect

69. C₈₃

D₄²

semidirect

78. C₄×D₄

D₈₃

semidirect

90. C₂²×C₄

C₂×D₈₃

semidirect

92. C₄⋊C₄

C₂×D₈₃

semidirect

95. C₂²⋊C₄

C₂×D₈₃

semidirect

96. C₄²

C₂×D₈₃

semidirect

109. D₄

D₃₃₂

direct (N × H)

126. C₂²

C₂×D₃₃₂

semidirect

131. C₄

D₄×D₈₃

semidirect

132. C₄

C₂×D₃₃₂

semidirect

Subgroups — D₄×D₃₃₂ #19128337

Conjugacy classes of subgroups

Complements

Subgroups — D4×D332 #19128337

Conjugacy classes of subgroups

Complements

Subgroups — D₄×D₃₃₂ #19128337