Group #34041983 — subgroups

Subgroups — C₂×#474×C₁₄₉ #34041983

Order 19072.

480 conjugacy classes of subgroups; only the 232 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 232 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⋊Q₈×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×D₄×C₁₄₉	C₂	1	1	yes	maximal, characteristic
3	#474×C₁₄₉	C₂	1	8	yes	maximal, direct product factor
4	C₂×#107×C₁₄₉	C₂	1	2	yes	maximal, complemented
5	C₂×C₄⋊C₈×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#102×C₁₄₉	C₂	1	2	yes	maximal
7	C₂²×Q₈×C₁₄₉	—	2	1	no	—
8	C₂²×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
9	C₂³×C₄×C₁₄₉	—	2	1	no	—
10	C₂²×C₈×C₁₄₉	C₂²	1	2	yes	—
11	C₄⋊Q₈×C₁₄₉	—	2	2	no	—
12	C₄⋊Q₈×C₁₄₉	C₂²	1	4	yes	complemented
13	C₄×D₄×C₁₄₉	—	2	2	no	—
14	C₄×D₄×C₁₄₉	C₂²	1	4	yes	—
15	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
16	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	2	yes	—
17	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊C₄×C₁₄₉	—	2	1	no	—
19	C₂×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
20	#107×C₁₄₉	C₂²	1	8	yes	complemented
21	C₄⋊C₈×C₁₄₉	C₂²	1	4	yes	complemented
22	#102×C₁₄₉	C₂²	1	8	yes	—
23	C₂⁴×C₁₄₉	—	2	1	no	—
24	C₂×Q₈×C₁₄₉	—	2	4	no	—
25	C₂×Q₈×C₁₄₉	—	4	4	no	—
26	C₂×D₄×C₁₄₉	—	2	1	no	—
27	C₂×D₄×C₁₄₉	—	2	2	no	—
28	C₂×D₄×C₁₄₉	Q₈	1	4	yes	complemented
29	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
30	C₂²×C₄×C₁₄₉	—	2	1	no	—
31	C₂²×C₄×C₁₄₉	—	2	2	no	—
32	C₂²×C₄×C₁₄₉	—	2	4	no	—
33	C₂²×C₄×C₁₄₉	—	4	4	no	—
34	C₂²×C₄×C₁₄₉	D₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₄₉	D₄	1	1	yes	characteristic
36	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
37	C₂×C₈×C₁₄₉	—	2	4	no	—
38	C₂×C₈×C₁₄₉	C₂³	1	4	yes	—
39	C₄⋊C₄×C₁₄₉	—	2	4	no	—
40	C₄⋊C₄×C₁₄₉	—	2	1	no	—
41	C₄⋊C₄×C₁₄₉	—	2	2	no	—
42	C₄⋊C₄×C₁₄₉	C₂³	1	4	yes	—
43	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
44	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
45	C₄²×C₁₄₉	D₄	1	2	yes	—
46	C₄²×C₁₄₉	C₂³	1	2	yes	—
47	C₂³×C₁₄₉	—	2	4	no	—
48	C₂³×C₁₄₉	—	2	2	no	—
49	C₂³×C₁₄₉	—	4	2	no	—
50	C₂³×C₁₄₉	—	4	2	no	—
51	C₂³×C₁₄₉	C₂×D₄	1	1	yes	characteristic
52	Q₈×C₁₄₉	—	4	8	no	—
53	D₄×C₁₄₉	—	2	4	no	—
54	D₄×C₁₄₉	—	2	2	no	—
55	D₄×C₁₄₉	C₂×Q₈	1	4	yes	complemented
56	C₂×C₄×C₁₄₉	—	2	2	no	—
57	C₂×C₄×C₁₄₉	—	2	2	no	—
58	C₂×C₄×C₁₄₉	—	2	4	no	—
59	C₂×C₄×C₁₄₉	—	4	2	no	—
60	C₂×C₄×C₁₄₉	—	4	4	no	—
61	C₂×C₄×C₁₄₉	—	4	8	no	—
62	C₂×C₄×C₁₄₉	D₈	1	4	yes	—
63	C₂×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
64	C₂×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
65	C₂×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
66	C₂×C₄×C₁₄₉	C₂×Q₈	1	2	yes	—
67	C₂×C₄×C₁₄₉	#41	1	2	yes	—
68	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
69	C₈×C₁₄₉	—	2	4	no	—
70	C₂²×C₁₄₉	—	2	4	no	—
71	C₂²×C₁₄₉	—	4	2	no	—
72	C₂²×C₁₄₉	—	4	2	no	—
73	C₂²×C₁₄₉	—	4	8	no	—
74	C₂²×C₁₄₉	C₂²⋊Q₈	1	2	yes	—
75	C₂²×C₁₄₉	C₂×D₈	1	2	yes	—
76	C₂²×C₁₄₉	#137	1	2	yes	—
77	C₂²×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
78	C₄×C₁₄₉	—	2	2	no	—
79	C₄×C₁₄₉	—	4	2	no	—
80	C₄×C₁₄₉	—	4	4	no	—
81	C₄×C₁₄₉	C₂²⋊Q₈	1	2	yes	—
82	C₄×C₁₄₉	C₂×D₈	1	4	yes	—
83	C₄×C₁₄₉	C₂²×Q₈	1	1	yes	characteristic
84	C₄×C₁₄₉	C₂×#41	1	1	yes	characteristic
85	C₂×C₁₄₉	—	4	4	no	—
86	C₂×C₁₄₉	#474	1	4	yes	direct product factor
87	C₂×C₁₄₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
88	C₂×C₁₄₉	C₂²×D₈	1	1	yes	characteristic
89	C₂×C₁₄₉	C₂×#137	1	1	yes	characteristic
90	C₁₄₉	C₂×#474	1	1	yes	characteristic, direct product factor, Sylow
91	C₂×#474	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
92	C₂×C₄⋊Q₈	C₂×C₁₄₉	1	1	yes	characteristic, complemented
93	C₂×C₄×D₄	C₂×C₁₄₉	1	1	yes	characteristic
94	#474	C₂×C₁₄₉	1	8	yes	direct product factor
95	C₂×#107	C₂×C₁₄₉	1	2	yes	complemented
96	C₂×C₄⋊C₈	C₂×C₁₄₉	1	1	yes	characteristic, complemented
97	C₂×#102	C₂×C₁₄₉	1	2	yes	—
98	C₂²×Q₈	—	2	1	no	—
99	C₂²×D₄	C₂²×C₁₄₉	1	1	yes	characteristic
100	C₂³×C₄	—	2	1	no	—
101	C₂²×C₈	C₂²×C₁₄₉	1	2	yes	—
102	C₄⋊Q₈	—	2	2	no	—
103	C₄⋊Q₈	C₂²×C₁₄₉	1	4	yes	complemented
104	C₄×D₄	—	2	2	no	—
105	C₄×D₄	C₂²×C₁₄₉	1	4	yes	—
106	C₂×C₄⋊C₄	—	2	1	no	—
107	C₂×C₄⋊C₄	C₂²×C₁₄₉	1	1	yes	characteristic
108	C₂×C₄⋊C₄	C₂²×C₁₄₉	1	2	yes	—
109	C₂×C₂²⋊C₄	—	2	1	no	—
110	C₂×C₄²	C₂²×C₁₄₉	1	1	yes	characteristic
111	#107	C₂²×C₁₄₉	1	8	yes	complemented
112	C₄⋊C₈	C₂²×C₁₄₉	1	4	yes	complemented
113	#102	C₂²×C₁₄₉	1	8	yes	—
114	C₂⁴	—	2	1	no	—
115	C₂×Q₈	—	2	4	no	—
116	C₂×Q₈	—	4	4	no	—
117	C₂×D₄	—	2	1	no	—
118	C₂×D₄	—	2	2	no	—
119	C₂×D₄	Q₈×C₁₄₉	1	4	yes	complemented
120	C₂×D₄	C₂³×C₁₄₉	1	2	yes	—
121	C₂²×C₄	—	2	1	no	—
122	C₂²×C₄	—	2	2	no	—
123	C₂²×C₄	—	2	4	no	—
124	C₂²×C₄	—	4	4	no	—
125	C₂²×C₄	D₄×C₁₄₉	1	1	yes	characteristic
126	C₂²×C₄	D₄×C₁₄₉	1	1	yes	characteristic
127	C₂²×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
128	C₂×C₈	—	2	4	no	—
129	C₂×C₈	C₂³×C₁₄₉	1	4	yes	—
130	C₄⋊C₄	—	2	4	no	—
131	C₄⋊C₄	—	2	1	no	—
132	C₄⋊C₄	—	2	2	no	—
133	C₄⋊C₄	C₂³×C₁₄₉	1	4	yes	—
134	C₄⋊C₄	C₂³×C₁₄₉	1	2	yes	—
135	C₂²⋊C₄	—	2	4	no	—
136	C₄²	D₄×C₁₄₉	1	2	yes	—
137	C₄²	C₂³×C₁₄₉	1	2	yes	—
138	C₂³	—	2	4	no	—
139	C₂³	—	2	2	no	—
140	C₂³	—	4	2	no	—
141	C₂³	—	4	2	no	—
142	C₂³	C₂×D₄×C₁₄₉	1	1	yes	characteristic
143	Q₈	—	4	8	no	—
144	D₄	—	2	4	no	—
145	D₄	—	2	2	no	—
146	D₄	C₂×Q₈×C₁₄₉	1	4	yes	complemented
147	C₂×C₄	—	2	2	no	—
148	C₂×C₄	—	2	2	no	—
149	C₂×C₄	—	2	4	no	—
150	C₂×C₄	—	4	2	no	—
151	C₂×C₄	—	4	4	no	—
152	C₂×C₄	—	4	8	no	—
153	C₂×C₄	D₈×C₁₄₉	1	4	yes	—
154	C₂×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
155	C₂×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
156	C₂×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
157	C₂×C₄	C₂×Q₈×C₁₄₉	1	2	yes	—
158	C₂×C₄	#41×C₁₄₉	1	2	yes	—
159	C₂×C₄	C₂⁴×C₁₄₉	1	1	yes	characteristic
160	C₈	—	2	4	no	—
161	C₂²	—	2	4	no	—
162	C₂²	—	4	8	no	—
163	C₂²	—	4	2	no	—
164	C₂²	—	4	2	no	—
165	C₂²	C₂²⋊Q₈×C₁₄₉	1	2	yes	—
166	C₂²	C₂×D₈×C₁₄₉	1	2	yes	—
167	C₂²	#137×C₁₄₉	1	2	yes	—
168	C₂²	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
169	C₄	—	2	2	no	—
170	C₄	—	4	2	no	—
171	C₄	—	4	4	no	—
172	C₄	C₂²⋊Q₈×C₁₄₉	1	2	yes	—
173	C₄	C₂×D₈×C₁₄₉	1	4	yes	—
174	C₄	C₂²×Q₈×C₁₄₉	1	1	yes	characteristic
175	C₄	C₂×#41×C₁₄₉	1	1	yes	characteristic
176	C₂	—	4	4	no	—
177	C₂	#474×C₁₄₉	1	4	yes	direct product factor
178	C₂	C₂×C₂²⋊Q₈×C₁₄₉	1	1	yes	characteristic
179	C₂	C₂²×D₈×C₁₄₉	1	1	yes	characteristic
180	C₂	C₂×#137×C₁₄₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊Q₈×C₁₄₉

C₂

yes

maximal, characteristic, complemented

C₂×C₄×D₄×C₁₄₉

C₂

yes

maximal, characteristic

#474×C₁₄₉

C₂

yes

maximal, direct product factor

C₂×#107×C₁₄₉

C₂

yes

maximal, complemented

C₂×C₄⋊C₈×C₁₄₉

C₂

yes

maximal, characteristic, complemented

C₂×#102×C₁₄₉

C₂

yes

maximal

C₂²×Q₈×C₁₄₉

—

C₂²×D₄×C₁₄₉

C₂²

yes

characteristic

C₂³×C₄×C₁₄₉

—

C₂²×C₈×C₁₄₉

C₂²

yes

—

C₄⋊Q₈×C₁₄₉

—

C₄⋊Q₈×C₁₄₉

C₂²

yes

complemented

C₄×D₄×C₁₄₉

—

C₄×D₄×C₁₄₉

C₂²

yes

—

C₂×C₄⋊C₄×C₁₄₉

—

C₂×C₄⋊C₄×C₁₄₉

C₂²

yes

—

C₂×C₄⋊C₄×C₁₄₉

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₁₄₉

—

C₂×C₄²×C₁₄₉

C₂²

yes

characteristic

#107×C₁₄₉

C₂²

yes

complemented

C₄⋊C₈×C₁₄₉

C₂²

yes

complemented

#102×C₁₄₉

C₂²

yes

—

C₂⁴×C₁₄₉

—

C₂×Q₈×C₁₄₉

—

C₂×Q₈×C₁₄₉

—

C₂×D₄×C₁₄₉

—

C₂×D₄×C₁₄₉

—

C₂×D₄×C₁₄₉

Q₈

yes

complemented

C₂×D₄×C₁₄₉

C₂³

yes

—

C₂²×C₄×C₁₄₉

—

C₂²×C₄×C₁₄₉

—

C₂²×C₄×C₁₄₉

—

C₂²×C₄×C₁₄₉

—

C₂²×C₄×C₁₄₉

D₄

yes

characteristic

C₂²×C₄×C₁₄₉

D₄

yes

characteristic

C₂²×C₄×C₁₄₉

C₂³

yes

characteristic

C₂×C₈×C₁₄₉

—

C₂×C₈×C₁₄₉

C₂³

yes

—

C₄⋊C₄×C₁₄₉

—

C₄⋊C₄×C₁₄₉

—

C₄⋊C₄×C₁₄₉

—

C₄⋊C₄×C₁₄₉

C₂³

yes

—

C₄⋊C₄×C₁₄₉

C₂³

yes

—

C₂²⋊C₄×C₁₄₉

—

C₄²×C₁₄₉

D₄

yes

—

C₄²×C₁₄₉

C₂³

yes

—

C₂³×C₁₄₉

—

C₂³×C₁₄₉

—

C₂³×C₁₄₉

—

C₂³×C₁₄₉

—

C₂³×C₁₄₉

C₂×D₄

yes

characteristic

Q₈×C₁₄₉

—

D₄×C₁₄₉

—

D₄×C₁₄₉

—

D₄×C₁₄₉

C₂×Q₈

yes

complemented

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

D₈

yes

—

C₂×C₄×C₁₄₉

C₂×D₄

yes

—

C₂×C₄×C₁₄₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₄₉

C₂×D₄

yes

—

C₂×C₄×C₁₄₉

C₂×Q₈

yes

—

C₂×C₄×C₁₄₉

#41

yes

—

C₂×C₄×C₁₄₉

C₂⁴

yes

characteristic

C₈×C₁₄₉

—

C₂²×C₁₄₉

—

C₂²×C₁₄₉

—

C₂²×C₁₄₉

—

C₂²×C₁₄₉

—

C₂²×C₁₄₉

C₂²⋊Q₈

yes

—

C₂²×C₁₄₉

C₂×D₈

yes

—

C₂²×C₁₄₉

#137

yes

—

C₂²×C₁₄₉

C₂²×D₄

yes

characteristic

C₄×C₁₄₉

—

C₄×C₁₄₉

—

C₄×C₁₄₉

—

C₄×C₁₄₉

C₂²⋊Q₈

yes

—

C₄×C₁₄₉

C₂×D₈

yes

—

C₄×C₁₄₉

C₂²×Q₈

yes

characteristic

C₄×C₁₄₉

C₂×#41

yes

characteristic

C₂×C₁₄₉

—

C₂×C₁₄₉

#474

yes

direct product factor

C₂×C₁₄₉

C₂×C₂²⋊Q₈

yes

characteristic

C₂×C₁₄₉

C₂²×D₈

yes

C₂×C₁₄₉

yes

C₁₄₉

yes

characteristic, direct product factor, Sylow

C₂×#474

C₁₄₉

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₄⋊Q₈

C₂×C₁₄₉

yes

characteristic, complemented

C₂×C₄×D₄

C₂×C₁₄₉

yes

characteristic

#474

C₂×C₁₄₉

yes

direct product factor

C₂×#107

C₂×C₁₄₉

yes

complemented

C₂×C₄⋊C₈

C₂×C₁₄₉

yes

characteristic, complemented

C₂×#102

C₂×C₁₄₉

yes

—

C₂²×Q₈

—

C₂²×D₄

C₂²×C₁₄₉

yes

characteristic

100

C₂³×C₄

—

101

C₂²×C₈

C₂²×C₁₄₉

yes

—

102

C₄⋊Q₈

—

103

C₄⋊Q₈

C₂²×C₁₄₉

yes

complemented

104

C₄×D₄

—

105

C₄×D₄

C₂²×C₁₄₉

yes

—

106

C₂×C₄⋊C₄

—

107

C₂×C₄⋊C₄

C₂²×C₁₄₉

yes

characteristic

108

C₂×C₄⋊C₄

C₂²×C₁₄₉

yes

—

109

C₂×C₂²⋊C₄

—

110

C₂×C₄²

C₂²×C₁₄₉

yes

characteristic

111

#107

C₂²×C₁₄₉

yes

complemented

112

C₄⋊C₈

C₂²×C₁₄₉

yes

complemented

113

#102

C₂²×C₁₄₉

yes

—

114

C₂⁴

—

115

C₂×Q₈

—

116

C₂×Q₈

—

117

C₂×D₄

—

118

C₂×D₄

—

119

C₂×D₄

Q₈×C₁₄₉

yes

complemented

120

C₂×D₄

C₂³×C₁₄₉

yes

—

121

C₂²×C₄

—

122

C₂²×C₄

—

123

C₂²×C₄

—

124

C₂²×C₄

—

125

C₂²×C₄

D₄×C₁₄₉

yes

characteristic

126

C₂²×C₄

D₄×C₁₄₉

yes

characteristic

127

C₂²×C₄

C₂³×C₁₄₉

yes

characteristic

128

C₂×C₈

—

129

C₂×C₈

C₂³×C₁₄₉

yes

—

130

C₄⋊C₄

—

131

C₄⋊C₄

—

132

C₄⋊C₄

—

133

C₄⋊C₄

C₂³×C₁₄₉

yes

—

134

C₄⋊C₄

C₂³×C₁₄₉

yes

—

135

C₂²⋊C₄

—

136

C₄²

D₄×C₁₄₉

yes

—

137

C₄²

C₂³×C₁₄₉

yes

—

138

C₂³

—

139

C₂³

—

140

C₂³

—

141

C₂³

—

142

C₂³

C₂×D₄×C₁₄₉

yes

characteristic

143

Q₈

—

144

D₄

—

145

D₄

—

146

D₄

C₂×Q₈×C₁₄₉

yes

complemented

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

D₈×C₁₄₉

yes

—

154

C₂×C₄

C₂×D₄×C₁₄₉

yes

—

155

C₂×C₄

C₂×D₄×C₁₄₉

yes

characteristic

156

C₂×C₄

C₂×D₄×C₁₄₉

yes

—

157

C₂×C₄

C₂×Q₈×C₁₄₉

yes

—

158

C₂×C₄

#41×C₁₄₉

yes

—

159

C₂×C₄

C₂⁴×C₁₄₉

yes

characteristic

160

C₈

—

161

C₂²

—

162

C₂²

—

163

C₂²

—

164

C₂²

—

165

C₂²

C₂²⋊Q₈×C₁₄₉

yes

—

166

C₂²

C₂×D₈×C₁₄₉

yes

—

167

C₂²

#137×C₁₄₉

yes

—

168

C₂²

C₂²×D₄×C₁₄₉

yes

characteristic

169

C₄

—

170

C₄

—

171

C₄

—

172

C₄

C₂²⋊Q₈×C₁₄₉

yes

—

173

C₄

C₂×D₈×C₁₄₉

yes

—

174

C₄

C₂²×Q₈×C₁₄₉

yes

characteristic

175

C₄

C₂×#41×C₁₄₉

yes

characteristic

176

C₂

—

177

C₂

#474×C₁₄₉

yes

direct product factor

178

C₂

C₂×C₂²⋊Q₈×C₁₄₉

yes

characteristic

179

C₂

C₂²×D₈×C₁₄₉

yes

characteristic

180

C₂

C₂×#137×C₁₄₉

yes

characteristic

	subgroup	G/H
center, socle	C₂³×C₁₄₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₄₉
prime radical	C₂²×D₄×C₁₄₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₄₉ ◁ C₂×C₄²×C₁₄₉ ◁ G

subgroup

G/H

center, socle

C₂³×C₁₄₉

C₂×D₄

commutator, Frattini, cosocle

C₂×C₄

C₂⁴×C₁₄₉

prime radical

C₂²×D₄×C₁₄₉

C₂²

LCS

G ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₁₄₉ ◁ C₂×C₄²×C₁₄₉ ◁ G

N	H ≅ G/N	type
1. C₂×C₄⋊Q₈×C₁₄₉	C₂	semidirect
3. #474×C₁₄₉	C₂	direct (N × H)
4. C₂×#107×C₁₄₉	C₂	semidirect
5. C₂×C₄⋊C₈×C₁₄₉	C₂	semidirect
12. C₄⋊Q₈×C₁₄₉	C₂²	semidirect
20. #107×C₁₄₉	C₂²	semidirect
21. C₄⋊C₈×C₁₄₉	C₂²	semidirect
28. C₂×D₄×C₁₄₉	Q₈	semidirect
55. D₄×C₁₄₉	C₂×Q₈	semidirect
86. C₂×C₁₄₉	#474	direct (N × H)
90. C₁₄₉	C₂×#474	direct (N × H)
91. C₂×#474	C₁₄₉	direct (N × H)
92. C₂×C₄⋊Q₈	C₂×C₁₄₉	semidirect
94. #474	C₂×C₁₄₉	direct (N × H)
95. C₂×#107	C₂×C₁₄₉	semidirect
96. C₂×C₄⋊C₈	C₂×C₁₄₉	semidirect
103. C₄⋊Q₈	C₂²×C₁₄₉	semidirect
111. #107	C₂²×C₁₄₉	semidirect
112. C₄⋊C₈	C₂²×C₁₄₉	semidirect
119. C₂×D₄	Q₈×C₁₄₉	semidirect
146. D₄	C₂×Q₈×C₁₄₉	semidirect
177. C₂	#474×C₁₄₉	direct (N × H)

H ≅ G/N

type

1. C₂×C₄⋊Q₈×C₁₄₉

C₂

semidirect

3. #474×C₁₄₉

C₂

direct (N × H)

4. C₂×#107×C₁₄₉

C₂

semidirect

5. C₂×C₄⋊C₈×C₁₄₉

C₂

semidirect

12. C₄⋊Q₈×C₁₄₉

C₂²

semidirect

20. #107×C₁₄₉

C₂²

semidirect

21. C₄⋊C₈×C₁₄₉

C₂²

semidirect

28. C₂×D₄×C₁₄₉

Q₈

semidirect

55. D₄×C₁₄₉

C₂×Q₈

semidirect

86. C₂×C₁₄₉

#474

direct (N × H)

90. C₁₄₉

C₂×#474

direct (N × H)

91. C₂×#474

C₁₄₉

direct (N × H)

92. C₂×C₄⋊Q₈

C₂×C₁₄₉

semidirect

94. #474

C₂×C₁₄₉

direct (N × H)

95. C₂×#107

C₂×C₁₄₉

semidirect

96. C₂×C₄⋊C₈

C₂×C₁₄₉

semidirect

103. C₄⋊Q₈

C₂²×C₁₄₉

semidirect

111. #107

C₂²×C₁₄₉

semidirect

112. C₄⋊C₈

C₂²×C₁₄₉

semidirect

119. C₂×D₄

Q₈×C₁₄₉

semidirect

146. D₄

C₂×Q₈×C₁₄₉

semidirect

177. C₂

#474×C₁₄₉

direct (N × H)

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

subgroup	index
C₂×C₄⋊Q₈×C₁₄₉	2
C₂×C₄×D₄×C₁₄₉	2
#474×C₁₄₉	2
C₂×#107×C₁₄₉	2
C₂×C₄⋊C₈×C₁₄₉	2
C₂×#102×C₁₄₉	2
C₂×#474	149

subgroup

index

C₂×C₄⋊Q₈×C₁₄₉

C₂×C₄×D₄×C₁₄₉

#474×C₁₄₉

C₂×#107×C₁₄₉

C₂×C₄⋊C₈×C₁₄₉

C₂×#102×C₁₄₉

C₂×#474

149

Subgroups — C₂×#474×C₁₄₉ #34041983

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#474×C149 #34041983

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#474×C₁₄₉ #34041983