Group #44449062 — subgroups

Subgroups — C₂×#461×C₂₃₃ #44449062

Order 29824.

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

normal subgroups only

This group has 544 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	C₂²×SD₁₆×C₂₃₃	C₂	1	2	yes	maximal
2	C₂×C₄⋊Q₈×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×D₄×C₂₃₃	C₂	1	1	yes	maximal, characteristic
4	#461×C₂₃₃	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₄⋊C₈×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#103×C₂₃₃	C₂	1	2	yes	maximal, complemented
7	C₂²×Q₈×C₂₃₃	C₂²	1	2	yes	—
8	C₂²×D₄×C₂₃₃	C₂²	1	1	yes	characteristic
9	C₂³×C₄×C₂₃₃	—	2	1	no	—
10	C₂×SD₁₆×C₂₃₃	—	2	8	no	—
11	C₂×SD₁₆×C₂₃₃	C₂²	1	8	yes	—
12	C₂²×C₈×C₂₃₃	C₂²	1	2	yes	—
13	C₄⋊Q₈×C₂₃₃	—	2	2	no	—
14	C₄⋊Q₈×C₂₃₃	C₂²	1	4	yes	complemented
15	C₄×D₄×C₂₃₃	—	2	2	no	—
16	C₄×D₄×C₂₃₃	C₂²	1	4	yes	—
17	C₂×C₄⋊C₄×C₂₃₃	—	2	1	no	—
18	C₂×C₄⋊C₄×C₂₃₃	—	2	1	no	—
19	C₂×C₄⋊C₄×C₂₃₃	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊C₄×C₂₃₃	—	2	1	no	—
21	C₂×C₄²×C₂₃₃	C₂²	1	1	yes	characteristic
22	C₄⋊C₈×C₂₃₃	C₂²	1	4	yes	complemented
23	#103×C₂₃₃	C₂²	1	8	yes	complemented
24	C₂⁴×C₂₃₃	—	2	1	no	—
25	C₂×Q₈×C₂₃₃	—	2	2	no	—
26	C₂×Q₈×C₂₃₃	—	2	4	no	—
27	C₂×Q₈×C₂₃₃	—	2	4	no	—
28	C₂×Q₈×C₂₃₃	C₂³	1	4	yes	—
29	C₂×D₄×C₂₃₃	—	2	1	no	—
30	C₂×D₄×C₂₃₃	—	2	2	no	—
31	C₂×D₄×C₂₃₃	D₄	1	4	yes	—
32	C₂×D₄×C₂₃₃	C₂³	1	2	yes	—
33	C₂²×C₄×C₂₃₃	—	2	1	no	—
34	C₂²×C₄×C₂₃₃	—	2	2	no	—
35	C₂²×C₄×C₂₃₃	—	2	4	no	—
36	C₂²×C₄×C₂₃₃	—	4	4	no	—
37	C₂²×C₄×C₂₃₃	D₄	1	1	yes	characteristic
38	C₂²×C₄×C₂₃₃	D₄	1	1	yes	characteristic
39	C₂²×C₄×C₂₃₃	C₂³	1	1	yes	characteristic
40	SD₁₆×C₂₃₃	—	2	16	no	—
41	C₂×C₈×C₂₃₃	—	2	4	no	—
42	C₂×C₈×C₂₃₃	C₂³	1	4	yes	—
43	C₄⋊C₄×C₂₃₃	—	2	4	no	—
44	C₄⋊C₄×C₂₃₃	—	2	4	no	—
45	C₄⋊C₄×C₂₃₃	—	2	1	no	—
46	C₄⋊C₄×C₂₃₃	C₂³	1	2	yes	—
47	C₂²⋊C₄×C₂₃₃	—	2	4	no	—
48	C₄²×C₂₃₃	D₄	1	2	yes	—
49	C₄²×C₂₃₃	C₂³	1	2	yes	—
50	C₂³×C₂₃₃	—	2	4	no	—
51	C₂³×C₂₃₃	—	2	2	no	—
52	C₂³×C₂₃₃	—	4	2	no	—
53	C₂³×C₂₃₃	—	4	2	no	—
54	C₂³×C₂₃₃	C₂×D₄	1	1	yes	characteristic
55	Q₈×C₂₃₃	—	2	4	no	—
56	Q₈×C₂₃₃	—	2	4	no	—
57	Q₈×C₂₃₃	—	4	4	no	—
58	D₄×C₂₃₃	—	2	4	no	—
59	D₄×C₂₃₃	—	2	2	no	—
60	D₄×C₂₃₃	C₂×D₄	1	4	yes	—
61	C₂×C₄×C₂₃₃	—	2	2	no	—
62	C₂×C₄×C₂₃₃	—	2	2	no	—
63	C₂×C₄×C₂₃₃	—	2	4	no	—
64	C₂×C₄×C₂₃₃	—	4	4	no	—
65	C₂×C₄×C₂₃₃	—	4	2	no	—
66	C₂×C₄×C₂₃₃	—	4	8	no	—
67	C₂×C₄×C₂₃₃	SD₁₆	1	4	yes	complemented
68	C₂×C₄×C₂₃₃	C₂×D₄	1	2	yes	—
69	C₂×C₄×C₂₃₃	C₂×D₄	1	1	yes	characteristic
70	C₂×C₄×C₂₃₃	C₂×D₄	1	2	yes	—
71	C₂×C₄×C₂₃₃	C₂×D₄	1	2	yes	—
72	C₂×C₄×C₂₃₃	#41	1	2	yes	—
73	C₂×C₄×C₂₃₃	C₂⁴	1	1	yes	characteristic
74	C₈×C₂₃₃	—	2	4	no	—
75	C₂²×C₂₃₃	—	2	4	no	—
76	C₂²×C₂₃₃	—	4	2	no	—
77	C₂²×C₂₃₃	—	4	2	no	—
78	C₂²×C₂₃₃	—	4	8	no	—
79	C₂²×C₂₃₃	#121	1	2	yes	—
80	C₂²×C₂₃₃	C₂×SD₁₆	1	2	yes	—
81	C₂²×C₂₃₃	#137	1	2	yes	—
82	C₂²×C₂₃₃	C₂²×D₄	1	1	yes	characteristic
83	C₄×C₂₃₃	—	2	2	no	—
84	C₄×C₂₃₃	—	4	4	no	—
85	C₄×C₂₃₃	—	4	2	no	—
86	C₄×C₂₃₃	#121	1	2	yes	—
87	C₄×C₂₃₃	C₂×SD₁₆	1	4	yes	complemented
88	C₄×C₂₃₃	C₂²×D₄	1	1	yes	characteristic
89	C₄×C₂₃₃	C₂×#41	1	1	yes	characteristic
90	C₂×C₂₃₃	—	4	4	no	—
91	C₂×C₂₃₃	#461	1	4	yes	direct product factor
92	C₂×C₂₃₃	C₂×#121	1	1	yes	characteristic
93	C₂×C₂₃₃	C₂²×SD₁₆	1	1	yes	characteristic
94	C₂×C₂₃₃	C₂×#137	1	1	yes	characteristic
95	C₂₃₃	C₂×#461	1	1	yes	characteristic, direct product factor, Sylow
96	C₂×#461	C₂₃₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
97	C₂²×SD₁₆	C₂×C₂₃₃	1	2	yes	—
98	C₂×C₄⋊Q₈	C₂×C₂₃₃	1	1	yes	characteristic, complemented
99	C₂×C₄×D₄	C₂×C₂₃₃	1	1	yes	characteristic
100	#461	C₂×C₂₃₃	1	8	yes	direct product factor
101	C₂×C₄⋊C₈	C₂×C₂₃₃	1	1	yes	characteristic, complemented
102	C₂×#103	C₂×C₂₃₃	1	2	yes	complemented
103	C₂²×Q₈	C₂²×C₂₃₃	1	2	yes	—
104	C₂²×D₄	C₂²×C₂₃₃	1	1	yes	characteristic
105	C₂³×C₄	—	2	1	no	—
106	C₂×SD₁₆	—	2	8	no	—
107	C₂×SD₁₆	C₂²×C₂₃₃	1	8	yes	—
108	C₂²×C₈	C₂²×C₂₃₃	1	2	yes	—
109	C₄⋊Q₈	—	2	2	no	—
110	C₄⋊Q₈	C₂²×C₂₃₃	1	4	yes	complemented
111	C₄×D₄	—	2	2	no	—
112	C₄×D₄	C₂²×C₂₃₃	1	4	yes	—
113	C₂×C₄⋊C₄	—	2	1	no	—
114	C₂×C₄⋊C₄	—	2	1	no	—
115	C₂×C₄⋊C₄	C₂²×C₂₃₃	1	1	yes	characteristic
116	C₂×C₂²⋊C₄	—	2	1	no	—
117	C₂×C₄²	C₂²×C₂₃₃	1	1	yes	characteristic
118	C₄⋊C₈	C₂²×C₂₃₃	1	4	yes	complemented
119	#103	C₂²×C₂₃₃	1	8	yes	complemented
120	C₂⁴	—	2	1	no	—
121	C₂×Q₈	—	2	2	no	—
122	C₂×Q₈	—	2	4	no	—
123	C₂×Q₈	—	2	4	no	—
124	C₂×Q₈	C₂³×C₂₃₃	1	4	yes	—
125	C₂×D₄	—	2	1	no	—
126	C₂×D₄	—	2	2	no	—
127	C₂×D₄	D₄×C₂₃₃	1	4	yes	—
128	C₂×D₄	C₂³×C₂₃₃	1	2	yes	—
129	C₂²×C₄	—	2	1	no	—
130	C₂²×C₄	—	2	2	no	—
131	C₂²×C₄	—	2	4	no	—
132	C₂²×C₄	—	4	4	no	—
133	C₂²×C₄	D₄×C₂₃₃	1	1	yes	characteristic
134	C₂²×C₄	D₄×C₂₃₃	1	1	yes	characteristic
135	C₂²×C₄	C₂³×C₂₃₃	1	1	yes	characteristic
136	SD₁₆	—	2	16	no	—
137	C₂×C₈	—	2	4	no	—
138	C₂×C₈	C₂³×C₂₃₃	1	4	yes	—
139	C₄⋊C₄	—	2	4	no	—
140	C₄⋊C₄	—	2	4	no	—
141	C₄⋊C₄	—	2	1	no	—
142	C₄⋊C₄	C₂³×C₂₃₃	1	2	yes	—
143	C₂²⋊C₄	—	2	4	no	—
144	C₄²	D₄×C₂₃₃	1	2	yes	—
145	C₄²	C₂³×C₂₃₃	1	2	yes	—
146	C₂³	—	2	4	no	—
147	C₂³	—	2	2	no	—
148	C₂³	—	4	2	no	—
149	C₂³	—	4	2	no	—
150	C₂³	C₂×D₄×C₂₃₃	1	1	yes	characteristic
151	Q₈	—	2	4	no	—
152	Q₈	—	2	4	no	—
153	Q₈	—	4	4	no	—
154	D₄	—	2	4	no	—
155	D₄	—	2	2	no	—
156	D₄	C₂×D₄×C₂₃₃	1	4	yes	—
157	C₂×C₄	—	2	2	no	—
158	C₂×C₄	—	2	2	no	—
159	C₂×C₄	—	2	4	no	—
160	C₂×C₄	—	4	4	no	—
161	C₂×C₄	—	4	2	no	—
162	C₂×C₄	—	4	8	no	—
163	C₂×C₄	SD₁₆×C₂₃₃	1	4	yes	complemented
164	C₂×C₄	C₂×D₄×C₂₃₃	1	2	yes	—
165	C₂×C₄	C₂×D₄×C₂₃₃	1	1	yes	characteristic
166	C₂×C₄	C₂×D₄×C₂₃₃	1	2	yes	—
167	C₂×C₄	C₂×D₄×C₂₃₃	1	2	yes	—
168	C₂×C₄	#41×C₂₃₃	1	2	yes	—
169	C₂×C₄	C₂⁴×C₂₃₃	1	1	yes	characteristic
170	C₈	—	2	4	no	—
171	C₂²	—	2	4	no	—
172	C₂²	—	4	8	no	—
173	C₂²	—	4	2	no	—
174	C₂²	—	4	2	no	—
175	C₂²	#121×C₂₃₃	1	2	yes	—
176	C₂²	C₂×SD₁₆×C₂₃₃	1	2	yes	—
177	C₂²	#137×C₂₃₃	1	2	yes	—
178	C₂²	C₂²×D₄×C₂₃₃	1	1	yes	characteristic
179	C₄	—	2	2	no	—
180	C₄	—	4	4	no	—
181	C₄	—	4	2	no	—
182	C₄	#121×C₂₃₃	1	2	yes	—
183	C₄	C₂×SD₁₆×C₂₃₃	1	4	yes	complemented
184	C₄	C₂²×D₄×C₂₃₃	1	1	yes	characteristic
185	C₄	C₂×#41×C₂₃₃	1	1	yes	characteristic
186	C₂	—	4	4	no	—
187	C₂	#461×C₂₃₃	1	4	yes	direct product factor
188	C₂	C₂×#121×C₂₃₃	1	1	yes	characteristic
189	C₂	C₂²×SD₁₆×C₂₃₃	1	1	yes	characteristic
190	C₂	C₂×#137×C₂₃₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×SD₁₆×C₂₃₃

C₂

yes

maximal

C₂×C₄⋊Q₈×C₂₃₃

C₂

yes

maximal, characteristic, complemented

C₂×C₄×D₄×C₂₃₃

C₂

yes

maximal, characteristic

#461×C₂₃₃

C₂

yes

maximal, direct product factor

C₂×C₄⋊C₈×C₂₃₃

C₂

yes

maximal, characteristic, complemented

C₂×#103×C₂₃₃

C₂

yes

maximal, complemented

C₂²×Q₈×C₂₃₃

C₂²

yes

—

C₂²×D₄×C₂₃₃

C₂²

yes

characteristic

C₂³×C₄×C₂₃₃

—

C₂×SD₁₆×C₂₃₃

—

C₂×SD₁₆×C₂₃₃

C₂²

yes

—

C₂²×C₈×C₂₃₃

C₂²

yes

—

C₄⋊Q₈×C₂₃₃

—

C₄⋊Q₈×C₂₃₃

C₂²

yes

complemented

C₄×D₄×C₂₃₃

—

C₄×D₄×C₂₃₃

C₂²

yes

—

C₂×C₄⋊C₄×C₂₃₃

—

C₂×C₄⋊C₄×C₂₃₃

—

C₂×C₄⋊C₄×C₂₃₃

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₂₃₃

—

C₂×C₄²×C₂₃₃

C₂²

yes

characteristic

C₄⋊C₈×C₂₃₃

C₂²

yes

complemented

#103×C₂₃₃

C₂²

yes

complemented

C₂⁴×C₂₃₃

—

C₂×Q₈×C₂₃₃

—

C₂×Q₈×C₂₃₃

—

C₂×Q₈×C₂₃₃

—

C₂×Q₈×C₂₃₃

C₂³

yes

—

C₂×D₄×C₂₃₃

—

C₂×D₄×C₂₃₃

—

C₂×D₄×C₂₃₃

D₄

yes

—

C₂×D₄×C₂₃₃

C₂³

yes

—

C₂²×C₄×C₂₃₃

—

C₂²×C₄×C₂₃₃

—

C₂²×C₄×C₂₃₃

—

C₂²×C₄×C₂₃₃

—

C₂²×C₄×C₂₃₃

D₄

yes

characteristic

C₂²×C₄×C₂₃₃

D₄

yes

characteristic

C₂²×C₄×C₂₃₃

C₂³

yes

characteristic

SD₁₆×C₂₃₃

—

C₂×C₈×C₂₃₃

—

C₂×C₈×C₂₃₃

C₂³

yes

—

C₄⋊C₄×C₂₃₃

—

C₄⋊C₄×C₂₃₃

—

C₄⋊C₄×C₂₃₃

—

C₄⋊C₄×C₂₃₃

C₂³

yes

—

C₂²⋊C₄×C₂₃₃

—

C₄²×C₂₃₃

D₄

yes

—

C₄²×C₂₃₃

C₂³

yes

—

C₂³×C₂₃₃

—

C₂³×C₂₃₃

—

C₂³×C₂₃₃

—

C₂³×C₂₃₃

—

C₂³×C₂₃₃

C₂×D₄

yes

characteristic

Q₈×C₂₃₃

—

Q₈×C₂₃₃

—

Q₈×C₂₃₃

—

D₄×C₂₃₃

—

D₄×C₂₃₃

—

D₄×C₂₃₃

C₂×D₄

yes

—

C₂×C₄×C₂₃₃

—

C₂×C₄×C₂₃₃

—

C₂×C₄×C₂₃₃

—

C₂×C₄×C₂₃₃

—

C₂×C₄×C₂₃₃

—

C₂×C₄×C₂₃₃

—

C₂×C₄×C₂₃₃

SD₁₆

yes

complemented

C₂×C₄×C₂₃₃

C₂×D₄

yes

—

C₂×C₄×C₂₃₃

C₂×D₄

yes

characteristic

C₂×C₄×C₂₃₃

C₂×D₄

yes

—

C₂×C₄×C₂₃₃

C₂×D₄

yes

—

C₂×C₄×C₂₃₃

#41

yes

—

C₂×C₄×C₂₃₃

C₂⁴

yes

characteristic

C₈×C₂₃₃

—

C₂²×C₂₃₃

—

C₂²×C₂₃₃

—

C₂²×C₂₃₃

—

C₂²×C₂₃₃

—

C₂²×C₂₃₃

#121

yes

—

C₂²×C₂₃₃

C₂×SD₁₆

yes

—

C₂²×C₂₃₃

#137

yes

—

C₂²×C₂₃₃

C₂²×D₄

yes

characteristic

C₄×C₂₃₃

—

C₄×C₂₃₃

—

C₄×C₂₃₃

—

C₄×C₂₃₃

#121

yes

—

C₄×C₂₃₃

C₂×SD₁₆

yes

complemented

C₄×C₂₃₃

C₂²×D₄

yes

characteristic

C₄×C₂₃₃

C₂×#41

yes

characteristic

C₂×C₂₃₃

—

C₂×C₂₃₃

#461

yes

direct product factor

C₂×C₂₃₃

C₂×#121

yes

characteristic

C₂×C₂₃₃

C₂²×SD₁₆

yes

C₂×C₂₃₃

yes

C₂₃₃

yes

characteristic, direct product factor, Sylow

C₂×#461

C₂₃₃

yes

maximal, characteristic, direct product factor, Sylow

C₂²×SD₁₆

C₂×C₂₃₃

yes

—

C₂×C₄⋊Q₈

C₂×C₂₃₃

yes

characteristic, complemented

C₂×C₄×D₄

C₂×C₂₃₃

yes

characteristic

100

#461

C₂×C₂₃₃

yes

direct product factor

101

C₂×C₄⋊C₈

C₂×C₂₃₃

yes

characteristic, complemented

102

C₂×#103

C₂×C₂₃₃

yes

complemented

103

C₂²×Q₈

C₂²×C₂₃₃

yes

—

104

C₂²×D₄

C₂²×C₂₃₃

yes

characteristic

105

C₂³×C₄

—

106

C₂×SD₁₆

—

107

C₂×SD₁₆

C₂²×C₂₃₃

yes

—

108

C₂²×C₈

C₂²×C₂₃₃

yes

—

109

C₄⋊Q₈

—

110

C₄⋊Q₈

C₂²×C₂₃₃

yes

complemented

111

C₄×D₄

—

112

C₄×D₄

C₂²×C₂₃₃

yes

—

113

C₂×C₄⋊C₄

—

114

C₂×C₄⋊C₄

—

115

C₂×C₄⋊C₄

C₂²×C₂₃₃

yes

characteristic

116

C₂×C₂²⋊C₄

—

117

C₂×C₄²

C₂²×C₂₃₃

yes

characteristic

118

C₄⋊C₈

C₂²×C₂₃₃

yes

complemented

119

#103

C₂²×C₂₃₃

yes

complemented

120

C₂⁴

—

121

C₂×Q₈

—

122

C₂×Q₈

—

123

C₂×Q₈

—

124

C₂×Q₈

C₂³×C₂₃₃

yes

—

125

C₂×D₄

—

126

C₂×D₄

—

127

C₂×D₄

D₄×C₂₃₃

yes

—

128

C₂×D₄

C₂³×C₂₃₃

yes

—

129

C₂²×C₄

—

130

C₂²×C₄

—

131

C₂²×C₄

—

132

C₂²×C₄

—

133

C₂²×C₄

D₄×C₂₃₃

yes

characteristic

134

C₂²×C₄

D₄×C₂₃₃

yes

characteristic

135

C₂²×C₄

C₂³×C₂₃₃

yes

characteristic

136

SD₁₆

—

137

C₂×C₈

—

138

C₂×C₈

C₂³×C₂₃₃

yes

—

139

C₄⋊C₄

—

140

C₄⋊C₄

—

141

C₄⋊C₄

—

142

C₄⋊C₄

C₂³×C₂₃₃

yes

—

143

C₂²⋊C₄

—

144

C₄²

D₄×C₂₃₃

yes

—

145

C₄²

C₂³×C₂₃₃

yes

—

146

C₂³

—

147

C₂³

—

148

C₂³

—

149

C₂³

—

150

C₂³

C₂×D₄×C₂₃₃

yes

characteristic

151

Q₈

—

152

Q₈

—

153

Q₈

—

154

D₄

—

155

D₄

—

156

D₄

C₂×D₄×C₂₃₃

yes

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

SD₁₆×C₂₃₃

yes

complemented

164

C₂×C₄

C₂×D₄×C₂₃₃

yes

—

165

C₂×C₄

C₂×D₄×C₂₃₃

yes

characteristic

166

C₂×C₄

C₂×D₄×C₂₃₃

yes

—

167

C₂×C₄

C₂×D₄×C₂₃₃

yes

—

168

C₂×C₄

#41×C₂₃₃

yes

—

169

C₂×C₄

C₂⁴×C₂₃₃

yes

characteristic

170

C₈

—

171

C₂²

—

172

C₂²

—

173

C₂²

—

174

C₂²

—

175

C₂²

#121×C₂₃₃

yes

—

176

C₂²

C₂×SD₁₆×C₂₃₃

yes

—

177

C₂²

#137×C₂₃₃

yes

—

178

C₂²

C₂²×D₄×C₂₃₃

yes

characteristic

179

C₄

—

180

C₄

—

181

C₄

—

182

C₄

#121×C₂₃₃

yes

—

183

C₄

C₂×SD₁₆×C₂₃₃

yes

complemented

184

C₄

C₂²×D₄×C₂₃₃

yes

characteristic

185

C₄

C₂×#41×C₂₃₃

yes

characteristic

186

C₂

—

187

C₂

#461×C₂₃₃

yes

direct product factor

188

C₂

C₂×#121×C₂₃₃

yes

characteristic

189

C₂

C₂²×SD₁₆×C₂₃₃

yes

characteristic

190

C₂

C₂×#137×C₂₃₃

yes

characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃₃
prime radical	C₂²×D₄×C₂₃₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃₃ ◁ C₂×C₄²×C₂₃₃ ◁ G

subgroup

G/H

center, socle

C₂³×C₂₃₃

C₂×D₄

commutator, Frattini, cosocle

C₂×C₄

C₂⁴×C₂₃₃

prime radical

C₂²×D₄×C₂₃₃

C₂²

LCS

G ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₂₃₃ ◁ C₂×C₄²×C₂₃₃ ◁ G

N	H ≅ G/N	type
2. C₂×C₄⋊Q₈×C₂₃₃	C₂	semidirect
4. #461×C₂₃₃	C₂	direct (N × H)
5. C₂×C₄⋊C₈×C₂₃₃	C₂	semidirect
6. C₂×#103×C₂₃₃	C₂	semidirect
14. C₄⋊Q₈×C₂₃₃	C₂²	semidirect
22. C₄⋊C₈×C₂₃₃	C₂²	semidirect
23. #103×C₂₃₃	C₂²	semidirect
67. C₂×C₄×C₂₃₃	SD₁₆	semidirect
87. C₄×C₂₃₃	C₂×SD₁₆	semidirect
91. C₂×C₂₃₃	#461	direct (N × H)
95. C₂₃₃	C₂×#461	direct (N × H)
96. C₂×#461	C₂₃₃	direct (N × H)
98. C₂×C₄⋊Q₈	C₂×C₂₃₃	semidirect
100. #461	C₂×C₂₃₃	direct (N × H)
101. C₂×C₄⋊C₈	C₂×C₂₃₃	semidirect
102. C₂×#103	C₂×C₂₃₃	semidirect
110. C₄⋊Q₈	C₂²×C₂₃₃	semidirect
118. C₄⋊C₈	C₂²×C₂₃₃	semidirect
119. #103	C₂²×C₂₃₃	semidirect
163. C₂×C₄	SD₁₆×C₂₃₃	semidirect
183. C₄	C₂×SD₁₆×C₂₃₃	semidirect
187. C₂	#461×C₂₃₃	direct (N × H)

H ≅ G/N

type

2. C₂×C₄⋊Q₈×C₂₃₃

C₂

semidirect

4. #461×C₂₃₃

C₂

direct (N × H)

5. C₂×C₄⋊C₈×C₂₃₃

C₂

semidirect

6. C₂×#103×C₂₃₃

C₂

semidirect

14. C₄⋊Q₈×C₂₃₃

C₂²

semidirect

22. C₄⋊C₈×C₂₃₃

C₂²

semidirect

23. #103×C₂₃₃

C₂²

semidirect

67. C₂×C₄×C₂₃₃

SD₁₆

semidirect

87. C₄×C₂₃₃

C₂×SD₁₆

semidirect

91. C₂×C₂₃₃

#461

direct (N × H)

95. C₂₃₃

C₂×#461

direct (N × H)

96. C₂×#461

C₂₃₃

direct (N × H)

98. C₂×C₄⋊Q₈

C₂×C₂₃₃

semidirect

100. #461

C₂×C₂₃₃

direct (N × H)

101. C₂×C₄⋊C₈

C₂×C₂₃₃

semidirect

102. C₂×#103

C₂×C₂₃₃

semidirect

110. C₄⋊Q₈

C₂²×C₂₃₃

semidirect

118. C₄⋊C₈

C₂²×C₂₃₃

semidirect

119. #103

C₂²×C₂₃₃

semidirect

163. C₂×C₄

SD₁₆×C₂₃₃

semidirect

183. C₄

C₂×SD₁₆×C₂₃₃

semidirect

187. C₂

#461×C₂₃₃

direct (N × H)

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

subgroup	index
C₂²×SD₁₆×C₂₃₃	2
C₂×C₄⋊Q₈×C₂₃₃	2
C₂×C₄×D₄×C₂₃₃	2
#461×C₂₃₃	2
C₂×C₄⋊C₈×C₂₃₃	2
C₂×#103×C₂₃₃	2
C₂×#461	233

subgroup

index

C₂²×SD₁₆×C₂₃₃

C₂×C₄⋊Q₈×C₂₃₃

C₂×C₄×D₄×C₂₃₃

#461×C₂₃₃

C₂×C₄⋊C₈×C₂₃₃

C₂×#103×C₂₃₃

C₂×#461

233

Subgroups — C₂×#461×C₂₃₃ #44449062

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#461×C233 #44449062

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#461×C₂₃₃ #44449062