Group #19156248 — subgroups

Subgroups — C₂₃×#8622 #19156248

Order 5888.

450 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 142 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×C₈×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#1568	C₂	1	2	yes	maximal, complemented
3	C₂₃×#1466	C₂	1	2	yes	maximal
4	C₂₃×#1290	C₂	1	2	yes	maximal, complemented
5	C₂³×C₈×C₂₃	C₄	1	2	yes	—
6	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
7	C₈×D₄×C₂₃	—	2	2	no	—
8	C₈×D₄×C₂₃	—	2	2	no	—
9	C₂₃×#432	C₂²	1	4	yes	—
10	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₂₃×C₂²⋊C₈	C₄	1	2	yes	—
12	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
13	C₂₃×#335	—	2	2	no	—
14	C₂₃×#334	—	2	2	no	—
15	C₂₃×#323	—	2	4	no	—
16	C₂²×D₄×C₂₃	Q₈	1	1	yes	characteristic
17	C₂³×C₄×C₂₃	C₂×C₄	1	2	yes	—
18	C₂²×C₈×C₂₃	—	2	2	no	—
19	C₂²×C₈×C₂₃	—	2	2	no	—
20	C₂²×C₈×C₂₃	—	4	4	no	—
21	C₂²×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₈×C₂₃	C₂×C₄	1	2	yes	—
23	C₂²×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
24	C₄×D₄×C₂₃	—	2	2	no	—
25	C₄×D₄×C₂₃	—	2	2	no	—
26	C₂×C₄⋊C₄×C₂₃	Q₈	1	1	yes	characteristic
27	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
28	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
29	C₂₃×C₄⋊C₈	—	2	2	no	—
30	C₂₃×C₄⋊C₈	—	2	4	no	—
31	C₂₃×C₂²⋊C₈	—	2	4	no	—
32	C₂₃×C₂²⋊C₈	—	2	4	no	—
33	C₂₃×#97	—	2	4	no	—
34	C₄×C₈×C₂₃	D₄	1	2	yes	—
35	C₄×C₈×C₂₃	D₄	1	2	yes	—
36	C₂⁴×C₂₃	C₄⋊C₄	1	2	yes	—
37	C₂×D₄×C₂₃	—	2	4	no	—
38	C₂×D₄×C₂₃	—	2	2	no	—
39	C₂²×C₄×C₂₃	—	2	2	no	—
40	C₂²×C₄×C₂₃	—	2	2	no	—
41	C₂²×C₄×C₂₃	—	4	2	no	—
42	C₂²×C₄×C₂₃	—	4	2	no	—
43	C₂²×C₄×C₂₃	C₄⋊C₄	1	2	yes	—
44	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
45	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
47	C₂×C₈×C₂₃	—	2	2	no	—
48	C₂×C₈×C₂₃	—	2	2	no	—
49	C₂×C₈×C₂₃	—	4	1	no	—
50	C₂×C₈×C₂₃	—	4	4	no	—
51	C₂×C₈×C₂₃	—	4	4	no	—
52	C₂×C₈×C₂₃	—	4	2	no	—
53	C₂×C₈×C₂₃	—	4	4	no	—
54	C₂×C₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
55	C₂×C₈×C₂₃	C₂²⋊C₄	1	2	yes	—
56	C₂×C₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
57	C₄⋊C₄×C₂₃	—	2	2	no	—
58	C₂²⋊C₄×C₂₃	—	2	4	no	—
59	C₄²×C₂₃	C₂×D₄	1	2	yes	—
60	C₄²×C₂₃	#41	1	2	yes	—
61	#8622	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂³×C₂₃	—	2	2	no	—
63	C₂³×C₂₃	—	2	2	no	—
64	C₂³×C₂₃	—	4	2	no	—
65	C₂³×C₂₃	—	4	2	no	—
66	C₂³×C₂₃	#108	1	4	yes	—
67	C₂³×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
68	D₄×C₂₃	—	2	8	no	—
69	C₂×C₄×C₂₃	—	2	2	no	—
70	C₂×C₄×C₂₃	—	2	1	no	—
71	C₂×C₄×C₂₃	—	2	1	no	—
72	C₂×C₄×C₂₃	—	2	2	no	—
73	C₂×C₄×C₂₃	—	4	1	no	—
74	C₂×C₄×C₂₃	—	4	4	no	—
75	C₂×C₄×C₂₃	—	4	2	no	—
76	C₂×C₄×C₂₃	—	4	2	no	—
77	C₂×C₄×C₂₃	—	4	2	no	—
78	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
79	C₂×C₄×C₂₃	#117	1	1	yes	characteristic
80	C₂×C₄×C₂₃	#121	1	2	yes	—
81	C₂×C₄×C₂₃	C₂²⋊Q₈	1	2	yes	—
82	C₈×C₂₃	—	2	1	no	—
83	C₈×C₂₃	—	2	2	no	—
84	C₈×C₂₃	—	4	2	no	—
85	C₈×C₂₃	—	8	4	no	—
86	C₈×C₂₃	#100	1	2	yes	—
87	C₂×C₈×D₄	C₂×C₂₃	1	1	yes	characteristic
88	#1568	C₂×C₂₃	1	2	yes	complemented
89	#1466	C₂×C₂₃	1	2	yes	—
90	#1290	C₂×C₂₃	1	2	yes	complemented
91	C₂²×C₂₃	—	2	1	no	—
92	C₂²×C₂₃	—	2	1	no	—
93	C₂²×C₂₃	—	2	4	no	—
94	C₂²×C₂₃	—	4	4	no	—
95	C₂²×C₂₃	—	4	4	no	—
96	C₂²×C₂₃	—	4	2	no	—
97	C₂²×C₂₃	—	4	2	no	—
98	C₂²×C₂₃	#380	1	1	yes	characteristic
99	C₂²×C₂₃	C₂×#108	1	2	yes	—
100	C₄×C₂₃	—	2	1	no	—
101	C₄×C₂₃	—	2	2	no	—
102	C₄×C₂₃	—	2	2	no	—
103	C₄×C₂₃	—	4	2	no	—
104	C₄×C₂₃	C₂×#100	1	1	yes	characteristic
105	C₄×C₂₃	#413	1	1	yes	characteristic
106	C₂³×C₈	C₄×C₂₃	1	2	yes	—
107	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
108	C₈×D₄	—	2	2	no	—
109	C₈×D₄	—	2	2	no	—
110	#432	C₂²×C₂₃	1	4	yes	—
111	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
112	C₂×C₂²⋊C₈	C₄×C₂₃	1	2	yes	—
113	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
114	#335	—	2	2	no	—
115	#334	—	2	2	no	—
116	#323	—	2	4	no	—
117	C₂×C₂₃	—	2	2	no	—
118	C₂×C₂₃	—	4	4	no	—
119	C₂×C₂₃	#1800	1	1	yes	characteristic
120	C₂×C₂₃	#1810	1	1	yes	characteristic
121	C₂×C₂₃	#1812	1	1	yes	characteristic
122	C₂²×D₄	Q₈×C₂₃	1	1	yes	characteristic
123	C₂³×C₄	C₂×C₄×C₂₃	1	2	yes	—
124	C₂²×C₈	—	2	2	no	—
125	C₂²×C₈	—	2	2	no	—
126	C₂²×C₈	—	4	4	no	—
127	C₂²×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
128	C₂²×C₈	C₂×C₄×C₂₃	1	2	yes	—
129	C₂²×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
130	C₄×D₄	—	2	2	no	—
131	C₄×D₄	—	2	2	no	—
132	C₂×C₄⋊C₄	Q₈×C₂₃	1	1	yes	characteristic
133	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
134	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
135	C₄⋊C₈	—	2	2	no	—
136	C₄⋊C₈	—	2	4	no	—
137	C₂²⋊C₈	—	2	4	no	—
138	C₂²⋊C₈	—	2	4	no	—
139	#97	—	2	4	no	—
140	C₄×C₈	D₄×C₂₃	1	2	yes	—
141	C₄×C₈	D₄×C₂₃	1	2	yes	—
142	C₂₃	#8622	1	1	yes	characteristic, direct product factor, Sylow
143	C₂⁴	C₄⋊C₄×C₂₃	1	2	yes	—
144	C₂×D₄	—	2	4	no	—
145	C₂×D₄	—	2	2	no	—
146	C₂²×C₄	—	2	2	no	—
147	C₂²×C₄	—	2	2	no	—
148	C₂²×C₄	—	4	2	no	—
149	C₂²×C₄	—	4	2	no	—
150	C₂²×C₄	C₄⋊C₄×C₂₃	1	2	yes	—
151	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
152	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
153	C₂²×C₄	C₂×Q₈×C₂₃	1	1	yes	characteristic
154	C₂×C₈	—	2	2	no	—
155	C₂×C₈	—	2	2	no	—
156	C₂×C₈	—	4	1	no	—
157	C₂×C₈	—	4	4	no	—
158	C₂×C₈	—	4	4	no	—
159	C₂×C₈	—	4	2	no	—
160	C₂×C₈	—	4	4	no	—
161	C₂×C₈	C₂²⋊C₄×C₂₃	1	2	yes	—
162	C₂×C₈	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
163	C₂×C₈	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
164	C₄⋊C₄	—	2	2	no	—
165	C₂²⋊C₄	—	2	4	no	—
166	C₄²	C₂×D₄×C₂₃	1	2	yes	—
167	C₄²	#41×C₂₃	1	2	yes	—
168	C₂³	—	2	2	no	—
169	C₂³	—	2	2	no	—
170	C₂³	—	4	2	no	—
171	C₂³	—	4	2	no	—
172	C₂³	C₂₃×#108	1	4	yes	—
173	C₂³	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
174	D₄	—	2	8	no	—
175	C₂×C₄	—	2	2	no	—
176	C₂×C₄	—	2	1	no	—
177	C₂×C₄	—	2	1	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	4	1	no	—
180	C₂×C₄	—	4	4	no	—
181	C₂×C₄	—	4	2	no	—
182	C₂×C₄	—	4	2	no	—
183	C₂×C₄	—	4	2	no	—
184	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
185	C₂×C₄	C₂₃×#117	1	1	yes	characteristic
186	C₂×C₄	C₂₃×#121	1	2	yes	—
187	C₂×C₄	C₂₃×C₂²⋊Q₈	1	2	yes	—
188	C₈	—	2	1	no	—
189	C₈	—	2	2	no	—
190	C₈	—	4	2	no	—
191	C₈	—	8	4	no	—
192	C₈	C₂₃×#100	1	2	yes	—
193	C₂²	—	2	1	no	—
194	C₂²	—	2	1	no	—
195	C₂²	—	2	4	no	—
196	C₂²	—	4	4	no	—
197	C₂²	—	4	4	no	—
198	C₂²	—	4	2	no	—
199	C₂²	—	4	2	no	—
200	C₂²	C₂₃×#380	1	1	yes	characteristic
201	C₂²	C₂×C₂₃×#108	1	2	yes	—
202	C₄	—	2	1	no	—
203	C₄	—	2	2	no	—
204	C₄	—	2	2	no	—
205	C₄	—	4	2	no	—
206	C₄	C₂×C₂₃×#100	1	1	yes	characteristic
207	C₄	C₂₃×#413	1	1	yes	characteristic
208	C₂	—	2	2	no	—
209	C₂	—	4	4	no	—
210	C₂	C₂₃×#1800	1	1	yes	characteristic
211	C₂	C₂₃×#1810	1	1	yes	characteristic
212	C₂	C₂₃×#1812	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₈×D₄×C₂₃

C₂

yes

maximal, characteristic

C₂₃×#1568

C₂

yes

maximal, complemented

C₂₃×#1466

C₂

yes

maximal

C₂₃×#1290

C₂

yes

maximal, complemented

C₂³×C₈×C₂₃

C₄

yes

—

C₂×C₄×D₄×C₂₃

C₂²

yes

characteristic

C₈×D₄×C₂₃

—

C₈×D₄×C₂₃

—

C₂₃×#432

C₂²

yes

—

C₂×C₂₃×C₄⋊C₈

C₂²

yes

characteristic

C₂×C₂₃×C₂²⋊C₈

C₄

yes

—

C₂×C₄×C₈×C₂₃

C₂²

yes

characteristic

C₂₃×#335

—

C₂₃×#334

—

C₂₃×#323

—

C₂²×D₄×C₂₃

Q₈

yes

characteristic

C₂³×C₄×C₂₃

C₂×C₄

yes

—

C₂²×C₈×C₂₃

—

C₂²×C₈×C₂₃

—

C₂²×C₈×C₂₃

—

C₂²×C₈×C₂₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₂₃

C₂×C₄

yes

—

C₂²×C₈×C₂₃

C₂×C₄

yes

characteristic

C₄×D₄×C₂₃

—

C₄×D₄×C₂₃

—

C₂×C₄⋊C₄×C₂₃

Q₈

yes

characteristic

C₂×C₂²⋊C₄×C₂₃

D₄

yes

—

C₂×C₄²×C₂₃

C₂³

yes

characteristic

C₂₃×C₄⋊C₈

—

C₂₃×C₄⋊C₈

—

C₂₃×C₂²⋊C₈

—

C₂₃×C₂²⋊C₈

—

C₂₃×#97

—

C₄×C₈×C₂₃

D₄

yes

—

C₄×C₈×C₂₃

D₄

yes

—

C₂⁴×C₂₃

C₄⋊C₄

yes

—

C₂×D₄×C₂₃

—

C₂×D₄×C₂₃

—

C₂²×C₄×C₂₃

—

C₂²×C₄×C₂₃

—

C₂²×C₄×C₂₃

—

C₂²×C₄×C₂₃

—

C₂²×C₄×C₂₃

C₄⋊C₄

yes

—

C₂²×C₄×C₂₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₂₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₂₃

C₂×Q₈

yes

characteristic

C₂×C₈×C₂₃

—

C₂×C₈×C₂₃

—

C₂×C₈×C₂₃

—

C₂×C₈×C₂₃

—

C₂×C₈×C₂₃

—

C₂×C₈×C₂₃

—

C₂×C₈×C₂₃

—

C₂×C₈×C₂₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₂₃

C₂²⋊C₄

yes

—

C₂×C₈×C₂₃

C₂²⋊C₄

yes

characteristic

C₄⋊C₄×C₂₃

—

C₂²⋊C₄×C₂₃

—

C₄²×C₂₃

C₂×D₄

yes

—

C₄²×C₂₃

#41

yes

—

#8622

C₂₃

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₂₃

—

C₂³×C₂₃

—

C₂³×C₂₃

—

C₂³×C₂₃

—

C₂³×C₂₃

#108

yes

—

C₂³×C₂₃

C₂×C₄⋊C₄

yes

characteristic

D₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

C₂×C₂²⋊C₄

yes

C₂×C₄×C₂₃

yes

C₂×C₄×C₂₃

yes

—

C₂×C₄×C₂₃

C₂²⋊Q₈

yes

—

C₈×C₂₃

—

C₈×C₂₃

—

C₈×C₂₃

—

C₈×C₂₃

—

C₈×C₂₃

#100

yes

—

C₂×C₈×D₄

C₂×C₂₃

yes

characteristic

#1568

C₂×C₂₃

yes

complemented

#1466

C₂×C₂₃

yes

—

#1290

C₂×C₂₃

yes

complemented

C₂²×C₂₃

—

C₂²×C₂₃

—

C₂²×C₂₃

—

C₂²×C₂₃

—

C₂²×C₂₃

—

C₂²×C₂₃

—

C₂²×C₂₃

—

C₂²×C₂₃

#380

yes

characteristic

C₂²×C₂₃

C₂×#108

yes

—

100

C₄×C₂₃

—

101

C₄×C₂₃

—

102

C₄×C₂₃

—

103

C₄×C₂₃

—

104

C₄×C₂₃

C₂×#100

yes

characteristic

105

C₄×C₂₃

#413

yes

characteristic

106

C₂³×C₈

C₄×C₂₃

yes

—

107

C₂×C₄×D₄

C₂²×C₂₃

yes

characteristic

108

C₈×D₄

—

109

C₈×D₄

—

110

#432

C₂²×C₂₃

yes

—

111

C₂×C₄⋊C₈

C₂²×C₂₃

yes

characteristic

112

C₂×C₂²⋊C₈

C₄×C₂₃

yes

—

113

C₂×C₄×C₈

C₂²×C₂₃

yes

characteristic

114

#335

—

115

#334

—

116

#323

—

117

C₂×C₂₃

—

118

C₂×C₂₃

—

119

C₂×C₂₃

#1800

yes

characteristic

120

C₂×C₂₃

#1810

yes

characteristic

121

C₂×C₂₃

#1812

yes

characteristic

122

C₂²×D₄

Q₈×C₂₃

yes

characteristic

123

C₂³×C₄

C₂×C₄×C₂₃

yes

—

124

C₂²×C₈

—

125

C₂²×C₈

—

126

C₂²×C₈

—

127

C₂²×C₈

C₂×C₄×C₂₃

yes

characteristic

128

C₂²×C₈

C₂×C₄×C₂₃

yes

—

129

C₂²×C₈

C₂×C₄×C₂₃

yes

characteristic

130

C₄×D₄

—

131

C₄×D₄

—

132

C₂×C₄⋊C₄

Q₈×C₂₃

yes

characteristic

133

C₂×C₂²⋊C₄

D₄×C₂₃

yes

—

134

C₂×C₄²

C₂³×C₂₃

yes

characteristic

135

C₄⋊C₈

—

136

C₄⋊C₈

—

137

C₂²⋊C₈

—

138

C₂²⋊C₈

—

139

#97

—

140

C₄×C₈

D₄×C₂₃

yes

—

141

C₄×C₈

D₄×C₂₃

yes

—

142

C₂₃

#8622

yes

characteristic, direct product factor, Sylow

143

C₂⁴

C₄⋊C₄×C₂₃

yes

—

144

C₂×D₄

—

145

C₂×D₄

—

146

C₂²×C₄

—

147

C₂²×C₄

—

148

C₂²×C₄

—

149

C₂²×C₄

—

150

C₂²×C₄

C₄⋊C₄×C₂₃

yes

—

151

C₂²×C₄

C₂²×C₄×C₂₃

yes

characteristic

152

C₂²×C₄

C₂×D₄×C₂₃

yes

characteristic

153

C₂²×C₄

C₂×Q₈×C₂₃

yes

characteristic

154

C₂×C₈

—

155

C₂×C₈

—

156

C₂×C₈

—

157

C₂×C₈

—

158

C₂×C₈

—

159

C₂×C₈

—

160

C₂×C₈

—

161

C₂×C₈

C₂²⋊C₄×C₂₃

yes

—

162

C₂×C₈

C₂²⋊C₄×C₂₃

yes

characteristic

163

C₂×C₈

C₂²⋊C₄×C₂₃

yes

characteristic

164

C₄⋊C₄

—

165

C₂²⋊C₄

—

166

C₄²

C₂×D₄×C₂₃

yes

—

167

C₄²

#41×C₂₃

yes

—

168

C₂³

—

169

C₂³

—

170

C₂³

—

171

C₂³

—

172

C₂³

C₂₃×#108

yes

—

173

C₂³

C₂×C₄⋊C₄×C₂₃

yes

characteristic

174

D₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

C₂×C₂²⋊C₄×C₂₃

yes

characteristic

185

C₂×C₄

C₂₃×#117

yes

characteristic

186

C₂×C₄

C₂₃×#121

yes

—

187

C₂×C₄

C₂₃×C₂²⋊Q₈

yes

—

188

C₈

—

189

C₈

—

190

C₈

—

191

C₈

—

192

C₈

C₂₃×#100

yes

—

193

C₂²

—

194

C₂²

—

195

C₂²

—

196

C₂²

—

197

C₂²

—

198

C₂²

—

199

C₂²

—

200

C₂²

C₂₃×#380

yes

characteristic

201

C₂²

C₂×C₂₃×#108

yes

—

202

C₄

—

203

C₄

—

204

C₄

—

205

C₄

—

206

C₄

C₂×C₂₃×#100

yes

characteristic

207

C₄

C₂₃×#413

yes

characteristic

208

C₂

—

209

C₂

—

210

C₂

C₂₃×#1800

yes

characteristic

211

C₂

C₂₃×#1810

yes

characteristic

212

C₂

C₂₃×#1812

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	#380
commutator	C₂²×C₄	C₂²×C₄×C₂₃
Frattini, cosocle	C₂×C₄²	C₂³×C₂₃
prime radical	C₂²×D₄×C₂₃	Q₈
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

subgroup

G/H

center, socle

C₂²×C₂₃

#380

commutator

C₂²×C₄

C₂²×C₄×C₂₃

Frattini, cosocle

C₂×C₄²

C₂³×C₂₃

prime radical

C₂²×D₄×C₂₃

Q₈

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

N	H ≅ G/N	type
2. C₂₃×#1568	C₂	semidirect
4. C₂₃×#1290	C₂	semidirect
61. #8622	C₂₃	direct (N × H)
88. #1568	C₂×C₂₃	semidirect
90. #1290	C₂×C₂₃	semidirect
142. C₂₃	#8622	direct (N × H)

H ≅ G/N

type

2. C₂₃×#1568

C₂

semidirect

4. C₂₃×#1290

C₂

semidirect

61. #8622

C₂₃

direct (N × H)

88. #1568

C₂×C₂₃

semidirect

90. #1290

C₂×C₂₃

semidirect

142. C₂₃

#8622

direct (N × H)

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

subgroup	index
C₂×C₈×D₄×C₂₃	2
C₂₃×#1568	2
C₂₃×#1466	2
C₂₃×#1290	2
#8622	23

subgroup

index

C₂×C₈×D₄×C₂₃

C₂₃×#1568

C₂₃×#1466

C₂₃×#1290

#8622

Subgroups — C₂₃×#8622 #19156248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C23×#8622 #19156248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#8622 #19156248