Group #19157978 — subgroups

Subgroups — C₂₃×#10352 #19157978

Order 5888.

416 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 138 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	C₂₃×#2571	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#1987	C₂	1	2	yes	maximal
3	C₂₃×#1956	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1296	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#1279	C₂	1	2	yes	maximal
6	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
7	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
8	C₂×C₂₃×#103	—	2	2	no	—
9	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
10	C₂₃×#400	—	2	2	no	—
11	C₂₃×#389	—	2	2	no	—
12	C₂₃×#384	C₂²	1	1	yes	characteristic
13	C₂₃×#382	—	2	2	no	—
14	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
15	C₂₃×#340	—	2	2	no	—
16	C₂₃×#340	—	2	2	no	—
17	C₂²×Q₈×C₂₃	—	2	1	no	—
18	C₂²×C₈×C₂₃	—	2	1	no	—
19	C₂²×C₈×C₂₃	—	2	2	no	—
20	C₂₃×C₄⋊Q₈	—	2	2	no	—
21	C₂₃×C₄⋊Q₈	—	2	1	no	—
22	C₂₃×C₄⋊Q₈	Q₈	1	2	yes	—
23	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
24	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
25	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
26	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
27	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
28	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
29	C₂×C₄²×C₂₃	—	2	2	no	—
30	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
31	C₂₃×C₄⋊C₈	—	2	2	no	—
32	C₂₃×C₄⋊C₈	—	2	2	no	—
33	C₂₃×#103	—	4	4	no	—
34	C₄×C₈×C₂₃	—	2	2	no	—
35	C₂₃×#95	—	2	2	no	—
36	C₂₃×#95	—	2	4	no	—
37	C₂₃×#95	—	2	2	no	—
38	C₂×Q₈×C₂₃	—	2	2	no	—
39	C₂×Q₈×C₂₃	—	4	2	no	—
40	C₂×Q₈×C₂₃	—	4	2	no	—
41	C₂×Q₈×C₂₃	—	4	1	no	—
42	C₂²×C₄×C₂₃	—	2	2	no	—
43	C₂²×C₄×C₂₃	—	2	2	no	—
44	C₂²×C₄×C₂₃	—	2	2	no	—
45	C₂²×C₄×C₂₃	—	4	1	no	—
46	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
47	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
48	C₂×C₈×C₂₃	—	2	2	no	—
49	C₂×C₈×C₂₃	—	4	1	no	—
50	C₂×C₈×C₂₃	—	4	1	no	—
51	C₂×C₈×C₂₃	—	4	2	no	—
52	C₂×C₈×C₂₃	—	4	2	no	—
53	C₂×C₈×C₂₃	—	4	2	no	—
54	C₄⋊C₄×C₂₃	—	2	4	no	—
55	C₄⋊C₄×C₂₃	—	2	2	no	—
56	C₄⋊C₄×C₂₃	—	2	2	no	—
57	C₄⋊C₄×C₂₃	—	2	2	no	—
58	C₄⋊C₄×C₂₃	—	2	2	no	—
59	C₄⋊C₄×C₂₃	—	4	2	no	—
60	C₄⋊C₄×C₂₃	—	4	2	no	—
61	C₄⋊C₄×C₂₃	—	4	2	no	—
62	C₄⋊C₄×C₂₃	—	4	2	no	—
63	C₄⋊C₄×C₂₃	—	8	2	no	—
64	C₄²×C₂₃	—	4	2	no	—
65	C₄²×C₂₃	—	4	2	no	—
66	C₄²×C₂₃	C₂×Q₈	1	1	yes	characteristic
67	C₄²×C₂₃	#41	1	1	yes	characteristic
68	C₄²×C₂₃	#41	1	2	yes	—
69	#10352	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
70	C₂³×C₂₃	#120	1	1	yes	characteristic
71	Q₈×C₂₃	—	4	4	no	—
72	Q₈×C₂₃	—	8	2	no	—
73	C₂×C₄×C₂₃	—	2	1	no	—
74	C₂×C₄×C₂₃	—	2	1	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	—	4	2	no	—
79	C₂×C₄×C₂₃	—	4	2	no	—
80	C₂×C₄×C₂₃	—	4	4	no	—
81	C₂×C₄×C₂₃	—	4	2	no	—
82	C₂×C₄×C₂₃	—	4	2	no	—
83	C₂×C₄×C₂₃	—	4	2	no	—
84	C₂×C₄×C₂₃	—	8	1	no	—
85	C₂×C₄×C₂₃	—	8	1	no	—
86	C₂×C₄×C₂₃	C₂²⋊Q₈	1	1	yes	characteristic
87	C₂×C₄×C₂₃	C₂²⋊Q₈	1	2	yes	—
88	C₂×C₄×C₂₃	#124	1	1	yes	characteristic
89	C₂×C₄×C₂₃	#124	1	2	yes	—
90	C₂×C₄×C₂₃	#135	1	2	yes	—
91	C₂×C₄×C₂₃	#135	1	2	yes	—
92	C₂×C₄×C₂₃	#137	1	2	yes	—
93	C₂×C₄×C₂₃	#137	1	2	yes	—
94	C₈×C₂₃	—	4	2	no	—
95	C₈×C₂₃	—	8	2	no	—
96	#2571	C₂×C₂₃	1	1	yes	characteristic
97	#1987	C₂×C₂₃	1	2	yes	—
98	#1956	C₂×C₂₃	1	1	yes	characteristic
99	#1296	C₂×C₂₃	1	1	yes	characteristic
100	#1279	C₂×C₂₃	1	2	yes	—
101	C₂²×C₂₃	#393	1	1	yes	characteristic
102	C₂²×C₂₃	#452	1	2	yes	—
103	C₂²×C₂₃	#452	1	2	yes	—
104	C₂²×C₂₃	#453	1	1	yes	characteristic
105	C₂²×C₂₃	#454	1	1	yes	characteristic
106	C₄×C₂₃	—	2	1	no	—
107	C₄×C₂₃	—	2	1	no	—
108	C₄×C₂₃	—	8	2	no	—
109	C₄×C₂₃	—	8	2	no	—
110	C₄×C₂₃	—	8	2	no	—
111	C₄×C₂₃	—	8	2	no	—
112	C₄×C₂₃	#479	1	2	yes	—
113	C₄×C₂₃	#479	1	2	yes	—
114	C₄×C₂₃	#488	1	2	yes	—
115	C₄×C₂₃	#491	1	2	yes	—
116	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
117	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
118	C₂×#103	—	2	2	no	—
119	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
120	#400	—	2	2	no	—
121	#389	—	2	2	no	—
122	#384	C₂²×C₂₃	1	1	yes	characteristic
123	#382	—	2	2	no	—
124	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
125	#340	—	2	2	no	—
126	#340	—	2	2	no	—
127	C₂×C₂₃	#1630	1	1	yes	characteristic
128	C₂×C₂₃	#1634	1	1	yes	characteristic
129	C₂×C₂₃	#1638	1	2	yes	—
130	C₂×C₂₃	#2026	1	2	yes	—
131	C₂×C₂₃	#2027	1	1	yes	characteristic
132	C₂²×Q₈	—	2	1	no	—
133	C₂²×C₈	—	2	1	no	—
134	C₂²×C₈	—	2	2	no	—
135	C₄⋊Q₈	—	2	2	no	—
136	C₄⋊Q₈	—	2	1	no	—
137	C₄⋊Q₈	Q₈×C₂₃	1	2	yes	—
138	C₂×C₄⋊C₄	—	2	2	no	—
139	C₂×C₄⋊C₄	—	2	2	no	—
140	C₂×C₄⋊C₄	—	2	2	no	—
141	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
142	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
143	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
144	C₂×C₄²	—	2	2	no	—
145	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
146	C₄⋊C₈	—	2	2	no	—
147	C₄⋊C₈	—	2	2	no	—
148	#103	—	4	4	no	—
149	C₄×C₈	—	2	2	no	—
150	#95	—	2	2	no	—
151	#95	—	2	4	no	—
152	#95	—	2	2	no	—
153	C₂₃	#10352	1	1	yes	characteristic, direct product factor, Sylow
154	C₂×Q₈	—	2	2	no	—
155	C₂×Q₈	—	4	2	no	—
156	C₂×Q₈	—	4	2	no	—
157	C₂×Q₈	—	4	1	no	—
158	C₂²×C₄	—	2	2	no	—
159	C₂²×C₄	—	2	2	no	—
160	C₂²×C₄	—	2	2	no	—
161	C₂²×C₄	—	4	1	no	—
162	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
163	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
164	C₂×C₈	—	2	2	no	—
165	C₂×C₈	—	4	1	no	—
166	C₂×C₈	—	4	1	no	—
167	C₂×C₈	—	4	2	no	—
168	C₂×C₈	—	4	2	no	—
169	C₂×C₈	—	4	2	no	—
170	C₄⋊C₄	—	2	4	no	—
171	C₄⋊C₄	—	2	2	no	—
172	C₄⋊C₄	—	2	2	no	—
173	C₄⋊C₄	—	2	2	no	—
174	C₄⋊C₄	—	2	2	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	—	8	2	no	—
180	C₄²	—	4	2	no	—
181	C₄²	—	4	2	no	—
182	C₄²	C₂×Q₈×C₂₃	1	1	yes	characteristic
183	C₄²	#41×C₂₃	1	2	yes	—
184	C₄²	#41×C₂₃	1	1	yes	characteristic
185	C₂³	C₂₃×#120	1	1	yes	characteristic
186	Q₈	—	4	4	no	—
187	Q₈	—	8	2	no	—
188	C₂×C₄	—	2	1	no	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	4	2	no	—
191	C₂×C₄	—	4	2	no	—
192	C₂×C₄	—	4	2	no	—
193	C₂×C₄	—	4	2	no	—
194	C₂×C₄	—	4	2	no	—
195	C₂×C₄	—	4	4	no	—
196	C₂×C₄	—	4	2	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	—	8	1	no	—
200	C₂×C₄	—	8	1	no	—
201	C₂×C₄	C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
202	C₂×C₄	C₂₃×C₂²⋊Q₈	1	2	yes	—
203	C₂×C₄	C₂₃×#124	1	1	yes	characteristic
204	C₂×C₄	C₂₃×#124	1	2	yes	—
205	C₂×C₄	C₂₃×#135	1	2	yes	—
206	C₂×C₄	C₂₃×#135	1	2	yes	—
207	C₂×C₄	C₂₃×#137	1	2	yes	—
208	C₂×C₄	C₂₃×#137	1	2	yes	—
209	C₈	—	4	2	no	—
210	C₈	—	8	2	no	—
211	C₂²	C₂₃×#393	1	1	yes	characteristic
212	C₂²	C₂₃×#452	1	2	yes	—
213	C₂²	C₂₃×#452	1	2	yes	—
214	C₂²	C₂₃×#453	1	1	yes	characteristic
215	C₂²	C₂₃×#454	1	1	yes	characteristic
216	C₄	—	2	1	no	—
217	C₄	—	2	1	no	—
218	C₄	—	8	2	no	—
219	C₄	—	8	2	no	—
220	C₄	—	8	2	no	—
221	C₄	—	8	2	no	—
222	C₄	C₂₃×#479	1	2	yes	—
223	C₄	C₂₃×#479	1	2	yes	—
224	C₄	C₂₃×#488	1	2	yes	—
225	C₄	C₂₃×#491	1	2	yes	—
226	C₂	C₂₃×#1630	1	1	yes	characteristic
227	C₂	C₂₃×#1634	1	1	yes	characteristic
228	C₂	C₂₃×#1638	1	2	yes	—
229	C₂	C₂₃×#2026	1	2	yes	—
230	C₂	C₂₃×#2027	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂₃×#2571

C₂

yes

maximal, characteristic

C₂₃×#1987

C₂

yes

maximal

C₂₃×#1956

C₂

yes

maximal, characteristic

C₂₃×#1296

C₂

yes

maximal, characteristic

C₂₃×#1279

C₂

yes

maximal

C₂×C₂₃×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₂₃×C₄⋊C₈

C₂²

yes

—

C₂×C₂₃×#103

—

C₂×C₄×C₈×C₂₃

C₂²

yes

characteristic

C₂₃×#400

—

C₂₃×#389

—

C₂₃×#384

C₂²

yes

characteristic

C₂₃×#382

—

C₄×C₄⋊C₄×C₂₃

C₂²

yes

—

C₂₃×#340

—

C₂₃×#340

—

C₂²×Q₈×C₂₃

—

C₂²×C₈×C₂₃

—

C₂²×C₈×C₂₃

—

C₂₃×C₄⋊Q₈

—

C₂₃×C₄⋊Q₈

—

C₂₃×C₄⋊Q₈

Q₈

yes

—

C₂×C₄⋊C₄×C₂₃

—

C₂×C₄⋊C₄×C₂₃

—

C₂×C₄⋊C₄×C₂₃

—

C₂×C₄⋊C₄×C₂₃

D₄

yes

—

C₂×C₄⋊C₄×C₂₃

D₄

yes

—

C₂×C₄⋊C₄×C₂₃

D₄

yes

—

C₂×C₄²×C₂₃

—

C₂×C₄²×C₂₃

C₂³

yes

characteristic

C₂₃×C₄⋊C₈

—

C₂₃×C₄⋊C₈

—

C₂₃×#103

—

C₄×C₈×C₂₃

—

C₂₃×#95

—

C₂₃×#95

—

C₂₃×#95

—

C₂×Q₈×C₂₃

—

C₂×Q₈×C₂₃

—

C₂×Q₈×C₂₃

—

C₂×Q₈×C₂₃

—

C₂²×C₄×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

—

C₄⋊C₄×C₂₃

—

C₄⋊C₄×C₂₃

—

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

—

C₄²×C₂₃

—

C₄²×C₂₃

C₂×Q₈

yes

C₄²×C₂₃

yes

C₄²×C₂₃

yes

—

#10352

C₂₃

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₂₃

#120

yes

characteristic

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

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₂₃

C₂²⋊Q₈

yes

—

C₂×C₄×C₂₃

#124

yes

characteristic

C₂×C₄×C₂₃

#124

yes

—

C₂×C₄×C₂₃

#135

yes

—

C₂×C₄×C₂₃

#135

yes

—

C₂×C₄×C₂₃

#137

yes

—

C₂×C₄×C₂₃

#137

yes

—

C₈×C₂₃

—

C₈×C₂₃

—

#2571

C₂×C₂₃

yes

characteristic

#1987

C₂×C₂₃

yes

—

#1956

C₂×C₂₃

yes

characteristic

#1296

C₂×C₂₃

yes

characteristic

100

#1279

C₂×C₂₃

yes

—

101

C₂²×C₂₃

#393

yes

characteristic

102

C₂²×C₂₃

#452

yes

—

103

C₂²×C₂₃

#452

yes

—

104

C₂²×C₂₃

#453

yes

characteristic

105

C₂²×C₂₃

#454

yes

characteristic

106

C₄×C₂₃

—

107

C₄×C₂₃

—

108

C₄×C₂₃

—

109

C₄×C₂₃

—

110

C₄×C₂₃

—

111

C₄×C₂₃

—

112

C₄×C₂₃

#479

yes

—

113

C₄×C₂₃

#479

yes

—

114

C₄×C₂₃

#488

yes

—

115

C₄×C₂₃

#491

yes

—

116

C₂×C₄⋊Q₈

C₂²×C₂₃

yes

characteristic

117

C₂×C₄⋊C₈

C₂²×C₂₃

yes

—

118

C₂×#103

—

119

C₂×C₄×C₈

C₂²×C₂₃

yes

characteristic

120

#400

—

121

#389

—

122

#384

C₂²×C₂₃

yes

characteristic

123

#382

—

124

C₄×C₄⋊C₄

C₂²×C₂₃

yes

—

125

#340

—

126

#340

—

127

C₂×C₂₃

#1630

yes

characteristic

128

C₂×C₂₃

#1634

yes

characteristic

129

C₂×C₂₃

#1638

yes

—

130

C₂×C₂₃

#2026

yes

—

131

C₂×C₂₃

#2027

yes

characteristic

132

C₂²×Q₈

—

133

C₂²×C₈

—

134

C₂²×C₈

—

135

C₄⋊Q₈

—

136

C₄⋊Q₈

—

137

C₄⋊Q₈

Q₈×C₂₃

yes

—

138

C₂×C₄⋊C₄

—

139

C₂×C₄⋊C₄

—

140

C₂×C₄⋊C₄

—

141

C₂×C₄⋊C₄

D₄×C₂₃

yes

—

142

C₂×C₄⋊C₄

D₄×C₂₃

yes

—

143

C₂×C₄⋊C₄

D₄×C₂₃

yes

—

144

C₂×C₄²

—

145

C₂×C₄²

C₂³×C₂₃

yes

characteristic

146

C₄⋊C₈

—

147

C₄⋊C₈

—

148

#103

—

149

C₄×C₈

—

150

#95

—

151

#95

—

152

#95

—

153

C₂₃

#10352

yes

characteristic, direct product factor, Sylow

154

C₂×Q₈

—

155

C₂×Q₈

—

156

C₂×Q₈

—

157

C₂×Q₈

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

C₂×D₄×C₂₃

yes

characteristic

163

C₂²×C₄

C₂×D₄×C₂₃

yes

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

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

—

181

C₄²

—

182

C₄²

C₂×Q₈×C₂₃

yes

characteristic

183

C₄²

#41×C₂₃

yes

—

184

C₄²

#41×C₂₃

yes

characteristic

185

C₂³

C₂₃×#120

yes

characteristic

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

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

C₂₃×C₂²⋊Q₈

yes

characteristic

202

C₂×C₄

C₂₃×C₂²⋊Q₈

yes

—

203

C₂×C₄

C₂₃×#124

yes

characteristic

204

C₂×C₄

C₂₃×#124

yes

—

205

C₂×C₄

C₂₃×#135

yes

—

206

C₂×C₄

C₂₃×#135

yes

—

207

C₂×C₄

C₂₃×#137

yes

—

208

C₂×C₄

C₂₃×#137

yes

—

209

C₈

—

210

C₈

—

211

C₂²

C₂₃×#393

yes

characteristic

212

C₂²

C₂₃×#452

yes

—

213

C₂²

C₂₃×#452

yes

—

214

C₂²

C₂₃×#453

yes

characteristic

215

C₂²

C₂₃×#454

yes

characteristic

216

C₄

—

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

C₂₃×#479

yes

—

223

C₄

C₂₃×#479

yes

—

224

C₄

C₂₃×#488

yes

—

225

C₄

C₂₃×#491

yes

—

226

C₂

C₂₃×#1630

yes

characteristic

227

C₂

C₂₃×#1634

yes

characteristic

228

C₂

C₂₃×#1638

yes

—

229

C₂

C₂₃×#2026

yes

—

230

C₂

C₂₃×#2027

yes

characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₃	#120
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

#120

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
69. #10352	C₂₃	direct (N × H)
153. C₂₃	#10352	direct (N × H)

H ≅ G/N

type

69. #10352

C₂₃

direct (N × H)

153. C₂₃

#10352

direct (N × H)

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

subgroup	index
C₂₃×#2571	2
C₂₃×#1987	2
C₂₃×#1956	2
C₂₃×#1296	2
C₂₃×#1279	2
#10352	23

subgroup

index

C₂₃×#2571

C₂₃×#1987

C₂₃×#1956

C₂₃×#1296

C₂₃×#1279

#10352

Subgroups — C₂₃×#10352 #19157978

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C23×#10352 #19157978

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#10352 #19157978