Group #19157943 — subgroups

Subgroups — C₂₃×#10317 #19157943

Order 5888.

554 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 170 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×C₂₃×#498	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#487	C₂	1	2	yes	maximal
3	C₂₃×#1990	C₂	1	2	yes	maximal
4	C₂₃×#1956	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#1273	C₂	1	1	yes	maximal, characteristic
6	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
7	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
8	C₂₃×#498	—	2	4	no	—
9	C₂₃×#487	—	2	4	no	—
10	C₂₃×#487	—	2	4	no	—
11	C₂×C₂₃×#106	—	2	2	no	—
12	C₂×C₂₃×#103	—	2	4	no	—
13	C₂×C₂₃×#103	—	2	2	no	—
14	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
16	C₂₃×#384	C₂²	1	1	yes	characteristic
17	C₂₃×#340	—	2	4	no	—
18	C₂²×Q₈×C₂₃	—	2	1	no	—
19	C₂²×Q₈×C₂₃	—	2	2	no	—
20	C₂²×C₈×C₂₃	D₄	1	4	yes	—
21	C₂²×C₈×C₂₃	D₄	1	2	yes	—
22	C₂₃×C₄⋊Q₈	—	2	2	no	—
23	C₂₃×C₄⋊Q₈	—	2	2	no	—
24	C₂₃×C₄⋊Q₈	—	2	2	no	—
25	C₂₃×C₄⋊Q₈	—	2	2	no	—
26	C₂₃×C₄⋊Q₈	—	2	1	no	—
27	C₂₃×C₄⋊Q₈	D₄	1	2	yes	—
28	C₂₃×C₄⋊Q₈	D₄	1	4	yes	—
29	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
30	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
31	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
32	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
33	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
34	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
35	C₂₃×#106	—	2	8	no	—
36	C₂₃×#103	—	2	16	no	—
37	C₂₃×#103	—	4	4	no	—
38	C₄×C₈×C₂₃	—	2	2	no	—
39	C₄×C₈×C₂₃	—	2	2	no	—
40	C₄×C₈×C₂₃	—	2	2	no	—
41	C₂×Q₈×C₂₃	—	2	4	no	—
42	C₂×Q₈×C₂₃	—	2	2	no	—
43	C₂×Q₈×C₂₃	—	4	1	no	—
44	C₂×Q₈×C₂₃	—	4	2	no	—
45	C₂×Q₈×C₂₃	—	4	2	no	—
46	C₂×Q₈×C₂₃	—	4	4	no	—
47	C₂×Q₈×C₂₃	—	4	2	no	—
48	C₂×Q₈×C₂₃	—	4	4	no	—
49	C₂²×C₄×C₂₃	—	4	1	no	—
50	C₂²×C₄×C₂₃	—	4	2	no	—
51	C₂²×C₄×C₂₃	—	4	1	no	—
52	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
54	C₂×C₈×C₂₃	—	2	2	no	—
55	C₂×C₈×C₂₃	—	2	2	no	—
56	C₂×C₈×C₂₃	—	2	4	no	—
57	C₂×C₈×C₂₃	—	2	4	no	—
58	C₂×C₈×C₂₃	—	2	4	no	—
59	C₂×C₈×C₂₃	SD₁₆	1	4	yes	—
60	C₄⋊C₄×C₂₃	—	2	4	no	—
61	C₄⋊C₄×C₂₃	—	2	4	no	—
62	C₄⋊C₄×C₂₃	—	2	4	no	—
63	C₄⋊C₄×C₂₃	—	4	2	no	—
64	C₄⋊C₄×C₂₃	—	4	2	no	—
65	C₄⋊C₄×C₂₃	—	4	2	no	—
66	C₄⋊C₄×C₂₃	—	4	2	no	—
67	C₄⋊C₄×C₂₃	—	4	4	no	—
68	C₄²×C₂₃	C₂×D₄	1	2	yes	—
69	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
70	C₄²×C₂₃	#41	1	1	yes	characteristic
71	#10317	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
72	C₂³×C₂₃	#127	1	1	yes	characteristic
73	Q₈×C₂₃	—	4	8	no	—
74	Q₈×C₂₃	—	4	4	no	—
75	Q₈×C₂₃	—	8	2	no	—
76	Q₈×C₂₃	—	8	4	no	—
77	C₂×C₄×C₂₃	—	4	2	no	—
78	C₂×C₄×C₂₃	—	4	4	no	—
79	C₂×C₄×C₂₃	—	8	1	no	—
80	C₂×C₄×C₂₃	—	8	2	no	—
81	C₂×C₄×C₂₃	—	8	1	no	—
82	C₂×C₄×C₂₃	—	8	2	no	—
83	C₂×C₄×C₂₃	—	8	1	no	—
84	C₂×C₄×C₂₃	—	8	2	no	—
85	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
86	C₂×C₄×C₂₃	#120	1	2	yes	—
87	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
88	C₂×C₄×C₂₃	#121	1	2	yes	—
89	C₂×C₄×C₂₃	C₂×SD₁₆	1	2	yes	—
90	C₂×C₄×C₂₃	#135	1	4	yes	—
91	C₂×C₄×C₂₃	#137	1	2	yes	—
92	C₂×C₄×C₂₃	#137	1	4	yes	—
93	C₈×C₂₃	—	2	4	no	—
94	C₈×C₂₃	—	4	4	no	—
95	C₂×#498	C₂×C₂₃	1	1	yes	characteristic
96	C₂×#487	C₂×C₂₃	1	2	yes	—
97	#1990	C₂×C₂₃	1	2	yes	—
98	#1956	C₂×C₂₃	1	1	yes	characteristic
99	#1273	C₂×C₂₃	1	1	yes	characteristic
100	C₂²×C₂₃	#392	1	1	yes	characteristic
101	C₂²×C₂₃	#492	1	1	yes	characteristic
102	C₂²×C₂₃	#495	1	2	yes	—
103	C₂²×C₂₃	#497	1	2	yes	—
104	C₂²×C₂₃	#497	1	1	yes	characteristic
105	C₄×C₂₃	—	8	2	no	—
106	C₄×C₂₃	—	8	4	no	—
107	C₄×C₂₃	—	16	1	no	—
108	C₄×C₂₃	#448	1	2	yes	—
109	C₄×C₂₃	#452	1	4	yes	—
110	C₄×C₂₃	#461	1	2	yes	—
111	C₄×C₂₃	#464	1	4	yes	—
112	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
113	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
114	#498	—	2	4	no	—
115	#487	—	2	4	no	—
116	#487	—	2	4	no	—
117	C₂×#106	—	2	2	no	—
118	C₂×#103	—	2	4	no	—
119	C₂×#103	—	2	2	no	—
120	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
121	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
122	#384	C₂²×C₂₃	1	1	yes	characteristic
123	#340	—	2	4	no	—
124	C₂×C₂₃	#1708	1	1	yes	characteristic
125	C₂×C₂₃	#1716	1	1	yes	characteristic
126	C₂×C₂₃	#1718	1	2	yes	—
127	C₂×C₂₃	#2013	1	1	yes	characteristic
128	C₂×C₂₃	#2015	1	2	yes	—
129	C₂²×Q₈	—	2	1	no	—
130	C₂²×Q₈	—	2	2	no	—
131	C₂²×C₈	D₄×C₂₃	1	4	yes	—
132	C₂²×C₈	D₄×C₂₃	1	2	yes	—
133	C₄⋊Q₈	—	2	2	no	—
134	C₄⋊Q₈	—	2	2	no	—
135	C₄⋊Q₈	—	2	2	no	—
136	C₄⋊Q₈	—	2	2	no	—
137	C₄⋊Q₈	—	2	1	no	—
138	C₄⋊Q₈	D₄×C₂₃	1	2	yes	—
139	C₄⋊Q₈	D₄×C₂₃	1	4	yes	—
140	C₂×C₄⋊C₄	—	2	2	no	—
141	C₂×C₄⋊C₄	—	2	2	no	—
142	C₂×C₄⋊C₄	—	2	2	no	—
143	C₂×C₄⋊C₄	—	2	2	no	—
144	C₂×C₄⋊C₄	—	2	1	no	—
145	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
146	#106	—	2	8	no	—
147	#103	—	2	16	no	—
148	#103	—	4	4	no	—
149	C₄×C₈	—	2	2	no	—
150	C₄×C₈	—	2	2	no	—
151	C₄×C₈	—	2	2	no	—
152	C₂₃	#10317	1	1	yes	characteristic, direct product factor, Sylow
153	C₂×Q₈	—	2	4	no	—
154	C₂×Q₈	—	2	2	no	—
155	C₂×Q₈	—	4	1	no	—
156	C₂×Q₈	—	4	2	no	—
157	C₂×Q₈	—	4	2	no	—
158	C₂×Q₈	—	4	4	no	—
159	C₂×Q₈	—	4	2	no	—
160	C₂×Q₈	—	4	4	no	—
161	C₂²×C₄	—	4	1	no	—
162	C₂²×C₄	—	4	2	no	—
163	C₂²×C₄	—	4	1	no	—
164	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
165	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
166	C₂×C₈	—	2	2	no	—
167	C₂×C₈	—	2	2	no	—
168	C₂×C₈	—	2	4	no	—
169	C₂×C₈	—	2	4	no	—
170	C₂×C₈	—	2	4	no	—
171	C₂×C₈	SD₁₆×C₂₃	1	4	yes	—
172	C₄⋊C₄	—	2	4	no	—
173	C₄⋊C₄	—	2	4	no	—
174	C₄⋊C₄	—	2	4	no	—
175	C₄⋊C₄	—	4	2	no	—
176	C₄⋊C₄	—	4	2	no	—
177	C₄⋊C₄	—	4	2	no	—
178	C₄⋊C₄	—	4	2	no	—
179	C₄⋊C₄	—	4	4	no	—
180	C₄²	C₂×D₄×C₂₃	1	2	yes	—
181	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
182	C₄²	#41×C₂₃	1	1	yes	characteristic
183	C₂³	C₂₃×#127	1	1	yes	characteristic
184	Q₈	—	4	8	no	—
185	Q₈	—	4	4	no	—
186	Q₈	—	8	2	no	—
187	Q₈	—	8	4	no	—
188	C₂×C₄	—	4	2	no	—
189	C₂×C₄	—	4	4	no	—
190	C₂×C₄	—	8	1	no	—
191	C₂×C₄	—	8	2	no	—
192	C₂×C₄	—	8	1	no	—
193	C₂×C₄	—	8	2	no	—
194	C₂×C₄	—	8	1	no	—
195	C₂×C₄	—	8	2	no	—
196	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
197	C₂×C₄	C₂₃×#120	1	2	yes	—
198	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
199	C₂×C₄	C₂₃×#121	1	2	yes	—
200	C₂×C₄	C₂×SD₁₆×C₂₃	1	2	yes	—
201	C₂×C₄	C₂₃×#135	1	4	yes	—
202	C₂×C₄	C₂₃×#137	1	2	yes	—
203	C₂×C₄	C₂₃×#137	1	4	yes	—
204	C₈	—	2	4	no	—
205	C₈	—	4	4	no	—
206	C₂²	C₂₃×#392	1	1	yes	characteristic
207	C₂²	C₂₃×#492	1	1	yes	characteristic
208	C₂²	C₂₃×#495	1	2	yes	—
209	C₂²	C₂₃×#497	1	2	yes	—
210	C₂²	C₂₃×#497	1	1	yes	characteristic
211	C₄	—	8	2	no	—
212	C₄	—	8	4	no	—
213	C₄	—	16	1	no	—
214	C₄	C₂₃×#448	1	2	yes	—
215	C₄	C₂₃×#452	1	4	yes	—
216	C₄	C₂₃×#461	1	2	yes	—
217	C₄	C₂₃×#464	1	4	yes	—
218	C₂	C₂₃×#1708	1	1	yes	characteristic
219	C₂	C₂₃×#1716	1	1	yes	characteristic
220	C₂	C₂₃×#1718	1	2	yes	—
221	C₂	C₂₃×#2013	1	1	yes	characteristic
222	C₂	C₂₃×#2015	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₂₃×#498

C₂

yes

maximal, characteristic

C₂×C₂₃×#487

C₂

yes

maximal

C₂₃×#1990

C₂

yes

maximal

C₂₃×#1956

C₂

yes

maximal, characteristic

C₂₃×#1273

C₂

yes

maximal, characteristic

C₂×C₂₃×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₂₃×C₄⋊Q₈

C₂²

yes

—

C₂₃×#498

—

C₂₃×#487

—

C₂₃×#487

—

C₂×C₂₃×#106

—

C₂×C₂₃×#103

—

C₂×C₂₃×#103

—

C₂×C₄×C₈×C₂₃

C₂²

yes

characteristic

C₂×C₄×C₈×C₂₃

C₂²

yes

—

C₂₃×#384

C₂²

yes

characteristic

C₂₃×#340

—

C₂²×Q₈×C₂₃

—

C₂²×Q₈×C₂₃

—

C₂²×C₈×C₂₃

D₄

yes

—

C₂²×C₈×C₂₃

D₄

yes

—

C₂₃×C₄⋊Q₈

—

C₂₃×C₄⋊Q₈

—

C₂₃×C₄⋊Q₈

—

C₂₃×C₄⋊Q₈

—

C₂₃×C₄⋊Q₈

—

C₂₃×C₄⋊Q₈

D₄

yes

—

C₂₃×C₄⋊Q₈

D₄

yes

—

C₂×C₄⋊C₄×C₂₃

—

C₂×C₄⋊C₄×C₂₃

—

C₂×C₄⋊C₄×C₂₃

—

C₂×C₄⋊C₄×C₂₃

—

C₂×C₄⋊C₄×C₂₃

—

C₂×C₄²×C₂₃

C₂³

yes

characteristic

C₂₃×#106

—

C₂₃×#103

—

C₂₃×#103

—

C₄×C₈×C₂₃

—

C₄×C₈×C₂₃

—

C₄×C₈×C₂₃

—

C₂×Q₈×C₂₃

—

C₂×Q₈×C₂₃

—

C₂×Q₈×C₂₃

—

C₂×Q₈×C₂₃

—

C₂×Q₈×C₂₃

—

C₂×Q₈×C₂₃

—

C₂×Q₈×C₂₃

—

C₂×Q₈×C₂₃

—

C₂²×C₄×C₂₃

—

C₂²×C₄×C₂₃

—

C₂²×C₄×C₂₃

—

C₂²×C₄×C₂₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₂₃

C₂×D₄

yes

—

C₂×C₈×C₂₃

—

C₂×C₈×C₂₃

—

C₂×C₈×C₂₃

—

C₂×C₈×C₂₃

—

C₂×C₈×C₂₃

—

C₂×C₈×C₂₃

SD₁₆

yes

—

C₄⋊C₄×C₂₃

—

C₄⋊C₄×C₂₃

—

C₄⋊C₄×C₂₃

—

C₄⋊C₄×C₂₃

—

C₄⋊C₄×C₂₃

—

C₄⋊C₄×C₂₃

—

C₄⋊C₄×C₂₃

—

C₄⋊C₄×C₂₃

—

C₄²×C₂₃

C₂×D₄

yes

—

C₄²×C₂₃

C₂×D₄

yes

C₄²×C₂₃

yes

C₂₃

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₂₃

#127

yes

characteristic

Q₈×C₂₃

—

Q₈×C₂₃

—

Q₈×C₂₃

—

Q₈×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

#120

yes

characteristic

C₂×C₄×C₂₃

#120

yes

—

C₂×C₄×C₂₃

#121

yes

characteristic

C₂×C₄×C₂₃

#121

yes

—

C₂×C₄×C₂₃

C₂×SD₁₆

yes

—

C₂×C₄×C₂₃

#135

yes

—

C₂×C₄×C₂₃

#137

yes

—

C₂×C₄×C₂₃

#137

yes

—

C₈×C₂₃

—

C₈×C₂₃

—

C₂×#498

C₂×C₂₃

yes

characteristic

C₂×#487

C₂×C₂₃

yes

—

#1990

C₂×C₂₃

yes

—

#1956

C₂×C₂₃

yes

characteristic

#1273

C₂×C₂₃

yes

characteristic

100

C₂²×C₂₃

#392

yes

characteristic

101

C₂²×C₂₃

#492

yes

characteristic

102

C₂²×C₂₃

#495

yes

—

103

C₂²×C₂₃

#497

yes

—

104

C₂²×C₂₃

#497

yes

characteristic

105

C₄×C₂₃

—

106

C₄×C₂₃

—

107

C₄×C₂₃

—

108

C₄×C₂₃

#448

yes

—

109

C₄×C₂₃

#452

yes

—

110

C₄×C₂₃

#461

yes

—

111

C₄×C₂₃

#464

yes

—

112

C₂×C₄⋊Q₈

C₂²×C₂₃

yes

characteristic

113

C₂×C₄⋊Q₈

C₂²×C₂₃

yes

—

114

#498

—

115

#487

—

116

#487

—

117

C₂×#106

—

118

C₂×#103

—

119

C₂×#103

—

120

C₂×C₄×C₈

C₂²×C₂₃

yes

—

121

C₂×C₄×C₈

C₂²×C₂₃

yes

characteristic

122

#384

C₂²×C₂₃

yes

characteristic

123

#340

—

124

C₂×C₂₃

#1708

yes

characteristic

125

C₂×C₂₃

#1716

yes

characteristic

126

C₂×C₂₃

#1718

yes

—

127

C₂×C₂₃

#2013

yes

characteristic

128

C₂×C₂₃

#2015

yes

—

129

C₂²×Q₈

—

130

C₂²×Q₈

—

131

C₂²×C₈

D₄×C₂₃

yes

—

132

C₂²×C₈

D₄×C₂₃

yes

—

133

C₄⋊Q₈

—

134

C₄⋊Q₈

—

135

C₄⋊Q₈

—

136

C₄⋊Q₈

—

137

C₄⋊Q₈

—

138

C₄⋊Q₈

D₄×C₂₃

yes

—

139

C₄⋊Q₈

D₄×C₂₃

yes

—

140

C₂×C₄⋊C₄

—

141

C₂×C₄⋊C₄

—

142

C₂×C₄⋊C₄

—

143

C₂×C₄⋊C₄

—

144

C₂×C₄⋊C₄

—

145

C₂×C₄²

C₂³×C₂₃

yes

characteristic

146

#106

—

147

#103

—

148

#103

—

149

C₄×C₈

—

150

C₄×C₈

—

151

C₄×C₈

—

152

C₂₃

#10317

yes

characteristic, direct product factor, Sylow

153

C₂×Q₈

—

154

C₂×Q₈

—

155

C₂×Q₈

—

156

C₂×Q₈

—

157

C₂×Q₈

—

158

C₂×Q₈

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

—

164

C₂²×C₄

C₂×D₄×C₂₃

yes

characteristic

165

C₂²×C₄

C₂×D₄×C₂₃

yes

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

SD₁₆×C₂₃

yes

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄²

C₂×D₄×C₂₃

yes

—

181

C₄²

C₂×D₄×C₂₃

yes

characteristic

182

C₄²

#41×C₂₃

yes

characteristic

183

C₂³

C₂₃×#127

yes

characteristic

184

Q₈

—

185

Q₈

—

186

Q₈

—

187

Q₈

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

C₂₃×#120

yes

characteristic

197

C₂×C₄

C₂₃×#120

yes

—

198

C₂×C₄

C₂₃×#121

yes

characteristic

199

C₂×C₄

C₂₃×#121

yes

—

200

C₂×C₄

C₂×SD₁₆×C₂₃

yes

—

201

C₂×C₄

C₂₃×#135

yes

—

202

C₂×C₄

C₂₃×#137

yes

—

203

C₂×C₄

C₂₃×#137

yes

—

204

C₈

—

205

C₈

—

206

C₂²

C₂₃×#392

yes

characteristic

207

C₂²

C₂₃×#492

yes

characteristic

208

C₂²

C₂₃×#495

yes

—

209

C₂²

C₂₃×#497

yes

—

210

C₂²

C₂₃×#497

yes

characteristic

211

C₄

—

212

C₄

—

213

C₄

—

214

C₄

C₂₃×#448

yes

—

215

C₄

C₂₃×#452

yes

—

216

C₄

C₂₃×#461

yes

—

217

C₄

C₂₃×#464

yes

—

218

C₂

C₂₃×#1708

yes

characteristic

219

C₂

C₂₃×#1716

yes

characteristic

220

C₂

C₂₃×#1718

yes

—

221

C₂

C₂₃×#2013

yes

characteristic

222

C₂

C₂₃×#2015

yes

—

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₃	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₂₃
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₂₃

#127

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₂₃

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

N	H ≅ G/N	type
71. #10317	C₂₃	direct (N × H)
152. C₂₃	#10317	direct (N × H)

H ≅ G/N

type

71. #10317

C₂₃

direct (N × H)

152. C₂₃

#10317

direct (N × H)

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

subgroup	index
C₂×C₂₃×#498	2
C₂×C₂₃×#487	2
C₂₃×#1990	2
C₂₃×#1956	2
C₂₃×#1273	2
#10317	23

subgroup

index

C₂×C₂₃×#498

C₂×C₂₃×#487

C₂₃×#1990

C₂₃×#1956

C₂₃×#1273

#10317

Subgroups — C₂₃×#10317 #19157943

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C23×#10317 #19157943

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#10317 #19157943