Group #19157026 — subgroups

Subgroups — C₂₃×#9400 #19157026

Order 5888.

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

normal subgroups only

This group has 466 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×#2983	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2567	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#1801	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1548	C₂	1	2	yes	maximal
5	C₂₃×#1303	C₂	1	2	yes	maximal
6	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
7	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
8	C₂₃×#446	—	2	4	no	—
9	C₂₃×#432	—	2	2	no	—
10	C₂₃×#431	C₂²	1	2	yes	—
11	C₂₃×#423	C₂²	1	2	yes	—
12	C₂×C₂₃×#101	—	2	1	no	—
13	C₂₃×#395	C₄	1	4	yes	—
14	C₂₃×#391	—	2	1	no	—
15	C₂₃×#389	—	2	2	no	—
16	C₂₃×#384	—	2	1	no	—
17	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
18	C₂₃×#343	—	2	1	no	—
19	C₂₃×#333	—	2	4	no	—
20	C₂²×Q₈×C₂₃	C₂×C₄	1	2	yes	—
21	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
22	C₂×M₁₆×C₂₃	—	2	2	no	—
23	C₂₃×C₄⋊Q₈	—	2	2	no	—
24	C₂₃×C₄⋊Q₈	—	2	2	no	—
25	C₄×Q₈×C₂₃	—	2	2	no	—
26	C₄×Q₈×C₂₃	—	2	2	no	—
27	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
28	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
29	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
30	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
31	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
32	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
33	C₂×C₄²×C₂₃	—	2	1	no	—
34	C₂×C₄²×C₂₃	D₄	1	2	yes	—
35	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
36	C₂₃×C₄⋊C₈	—	2	4	no	—
37	C₂₃×C₄⋊C₈	—	2	2	no	—
38	C₂₃×C₄⋊C₈	—	2	2	no	—
39	C₂₃×C₄⋊C₈	D₄	1	4	yes	—
40	C₂₃×#101	—	4	2	no	—
41	C₂₃×C₂²⋊C₈	—	2	2	no	—
42	C₂₃×#97	—	2	4	no	—
43	C₄×C₈×C₂₃	—	2	2	no	—
44	C₂₃×#95	—	2	4	no	—
45	C₂₃×#95	C₂×C₄	1	2	yes	—
46	C₂×Q₈×C₂₃	—	2	2	no	—
47	C₂×Q₈×C₂₃	—	2	1	no	—
48	C₂×Q₈×C₂₃	—	2	1	no	—
49	C₂×Q₈×C₂₃	—	2	2	no	—
50	C₂×Q₈×C₂₃	—	2	4	no	—
51	C₂×Q₈×C₂₃	—	8	2	no	—
52	C₂²×C₄×C₂₃	—	2	2	no	—
53	C₂²×C₄×C₂₃	—	2	2	no	—
54	C₂²×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
55	C₂²×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
56	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
57	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
59	M₁₆×C₂₃	—	4	2	no	—
60	M₁₆×C₂₃	—	4	2	no	—
61	C₂×C₈×C₂₃	—	2	4	no	—
62	C₂×C₈×C₂₃	—	4	2	no	—
63	C₄⋊C₄×C₂₃	—	2	4	no	—
64	C₄⋊C₄×C₂₃	—	2	4	no	—
65	C₄⋊C₄×C₂₃	—	2	2	no	—
66	C₄⋊C₄×C₂₃	—	4	1	no	—
67	C₄⋊C₄×C₂₃	—	4	2	no	—
68	C₄⋊C₄×C₂₃	—	4	1	no	—
69	C₄⋊C₄×C₂₃	—	8	4	no	—
70	C₄²×C₂₃	—	2	2	no	—
71	C₄²×C₂₃	—	2	2	no	—
72	C₄²×C₂₃	—	4	1	no	—
73	C₄²×C₂₃	—	4	1	no	—
74	C₄²×C₂₃	C₂×D₄	1	2	yes	—
75	C₄²×C₂₃	#41	1	2	yes	—
76	#9400	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
78	Q₈×C₂₃	—	4	2	no	—
79	Q₈×C₂₃	—	4	2	no	—
80	Q₈×C₂₃	—	8	4	no	—
81	C₂×C₄×C₂₃	—	2	2	no	—
82	C₂×C₄×C₂₃	—	2	4	no	—
83	C₂×C₄×C₂₃	—	2	2	no	—
84	C₂×C₄×C₂₃	—	2	2	no	—
85	C₂×C₄×C₂₃	—	2	2	no	—
86	C₂×C₄×C₂₃	—	2	2	no	—
87	C₂×C₄×C₂₃	—	4	1	no	—
88	C₂×C₄×C₂₃	—	4	2	no	—
89	C₂×C₄×C₂₃	—	4	2	no	—
90	C₂×C₄×C₂₃	—	4	2	no	—
91	C₂×C₄×C₂₃	—	4	4	no	—
92	C₂×C₄×C₂₃	—	4	2	no	—
93	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
94	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
95	C₂×C₄×C₂₃	#121	1	2	yes	—
96	C₂×C₄×C₂₃	#123	1	1	yes	characteristic
97	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	1	yes	characteristic
98	C₂×C₄×C₂₃	#137	1	2	yes	—
99	C₂×C₄×C₂₃	#137	1	1	yes	characteristic
100	C₈×C₂₃	—	4	4	no	—
101	C₈×C₂₃	—	8	2	no	—
102	#2983	C₂×C₂₃	1	1	yes	characteristic
103	#2567	C₂×C₂₃	1	1	yes	characteristic
104	#1801	C₂×C₂₃	1	1	yes	characteristic
105	#1548	C₂×C₂₃	1	2	yes	—
106	#1303	C₂×C₂₃	1	2	yes	—
107	C₂²×C₂₃	—	2	1	no	—
108	C₂²×C₂₃	—	2	1	no	—
109	C₂²×C₂₃	#386	1	1	yes	characteristic
110	C₂²×C₂₃	#417	1	1	yes	characteristic
111	C₂²×C₂₃	#419	1	1	yes	characteristic
112	C₄×C₂₃	—	2	1	no	—
113	C₄×C₂₃	—	2	2	no	—
114	C₄×C₂₃	—	4	4	no	—
115	C₄×C₂₃	—	4	2	no	—
116	C₄×C₂₃	—	4	2	no	—
117	C₄×C₂₃	—	8	2	no	—
118	C₄×C₂₃	#456	1	2	yes	—
119	C₄×C₂₃	#468	1	2	yes	—
120	C₄×C₂₃	#470	1	2	yes	—
121	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
122	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
123	#446	—	2	4	no	—
124	#432	—	2	2	no	—
125	#431	C₂²×C₂₃	1	2	yes	—
126	#423	C₂²×C₂₃	1	2	yes	—
127	C₂×#101	—	2	1	no	—
128	#395	C₄×C₂₃	1	4	yes	—
129	#391	—	2	1	no	—
130	#389	—	2	2	no	—
131	#384	—	2	1	no	—
132	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
133	#343	—	2	1	no	—
134	#333	—	2	4	no	—
135	C₂×C₂₃	—	2	1	no	—
136	C₂×C₂₃	—	2	1	no	—
137	C₂×C₂₃	#1886	1	1	yes	characteristic
138	C₂×C₂₃	#1894	1	1	yes	characteristic
139	C₂×C₂₃	#1914	1	1	yes	characteristic
140	C₂²×Q₈	C₂×C₄×C₂₃	1	2	yes	—
141	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
142	C₂×M₁₆	—	2	2	no	—
143	C₄⋊Q₈	—	2	2	no	—
144	C₄⋊Q₈	—	2	2	no	—
145	C₄×Q₈	—	2	2	no	—
146	C₄×Q₈	—	2	2	no	—
147	C₂×C₄⋊C₄	—	2	1	no	—
148	C₂×C₄⋊C₄	—	2	1	no	—
149	C₂×C₄⋊C₄	—	2	1	no	—
150	C₂×C₄⋊C₄	—	2	4	no	—
151	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
152	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
153	C₂×C₄²	—	2	1	no	—
154	C₂×C₄²	D₄×C₂₃	1	2	yes	—
155	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
156	C₄⋊C₈	—	2	4	no	—
157	C₄⋊C₈	—	2	2	no	—
158	C₄⋊C₈	—	2	2	no	—
159	C₄⋊C₈	D₄×C₂₃	1	4	yes	—
160	#101	—	4	2	no	—
161	C₂²⋊C₈	—	2	2	no	—
162	#97	—	2	4	no	—
163	C₄×C₈	—	2	2	no	—
164	#95	—	2	4	no	—
165	#95	C₂×C₄×C₂₃	1	2	yes	—
166	C₂₃	#9400	1	1	yes	characteristic, direct product factor, Sylow
167	C₂×Q₈	—	2	2	no	—
168	C₂×Q₈	—	2	1	no	—
169	C₂×Q₈	—	2	1	no	—
170	C₂×Q₈	—	2	2	no	—
171	C₂×Q₈	—	2	4	no	—
172	C₂×Q₈	—	8	2	no	—
173	C₂²×C₄	—	2	2	no	—
174	C₂²×C₄	—	2	2	no	—
175	C₂²×C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
176	C₂²×C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
177	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
178	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
179	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
180	M₁₆	—	4	2	no	—
181	M₁₆	—	4	2	no	—
182	C₂×C₈	—	2	4	no	—
183	C₂×C₈	—	4	2	no	—
184	C₄⋊C₄	—	2	4	no	—
185	C₄⋊C₄	—	2	4	no	—
186	C₄⋊C₄	—	2	2	no	—
187	C₄⋊C₄	—	4	1	no	—
188	C₄⋊C₄	—	4	2	no	—
189	C₄⋊C₄	—	4	1	no	—
190	C₄⋊C₄	—	8	4	no	—
191	C₄²	—	2	2	no	—
192	C₄²	—	2	2	no	—
193	C₄²	—	4	1	no	—
194	C₄²	—	4	1	no	—
195	C₄²	C₂×D₄×C₂₃	1	2	yes	—
196	C₄²	#41×C₂₃	1	2	yes	—
197	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
198	Q₈	—	4	2	no	—
199	Q₈	—	4	2	no	—
200	Q₈	—	8	4	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	4	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	4	1	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	4	2	no	—
210	C₂×C₄	—	4	2	no	—
211	C₂×C₄	—	4	4	no	—
212	C₂×C₄	—	4	2	no	—
213	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
214	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
215	C₂×C₄	C₂₃×#121	1	2	yes	—
216	C₂×C₄	C₂₃×#123	1	1	yes	characteristic
217	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
218	C₂×C₄	C₂₃×#137	1	2	yes	—
219	C₂×C₄	C₂₃×#137	1	1	yes	characteristic
220	C₈	—	4	4	no	—
221	C₈	—	8	2	no	—
222	C₂²	—	2	1	no	—
223	C₂²	—	2	1	no	—
224	C₂²	C₂₃×#386	1	1	yes	characteristic
225	C₂²	C₂₃×#417	1	1	yes	characteristic
226	C₂²	C₂₃×#419	1	1	yes	characteristic
227	C₄	—	2	1	no	—
228	C₄	—	2	2	no	—
229	C₄	—	4	4	no	—
230	C₄	—	4	2	no	—
231	C₄	—	4	2	no	—
232	C₄	—	8	2	no	—
233	C₄	C₂₃×#456	1	2	yes	—
234	C₄	C₂₃×#468	1	2	yes	—
235	C₄	C₂₃×#470	1	2	yes	—
236	C₂	—	2	1	no	—
237	C₂	—	2	1	no	—
238	C₂	C₂₃×#1886	1	1	yes	characteristic
239	C₂	C₂₃×#1894	1	1	yes	characteristic
240	C₂	C₂₃×#1914	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂₃×#2983

C₂

yes

maximal, characteristic

C₂₃×#2567

C₂

yes

maximal, characteristic

C₂₃×#1801

C₂

yes

maximal, characteristic

C₂₃×#1548

C₂

yes

maximal

C₂₃×#1303

C₂

yes

maximal

C₂×C₂₃×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₄×Q₈×C₂₃

C₂²

yes

characteristic

C₂₃×#446

—

C₂₃×#432

—

C₂₃×#431

C₂²

yes

—

C₂₃×#423

C₂²

yes

—

C₂×C₂₃×#101

—

C₂₃×#395

C₄

yes

—

C₂₃×#391

—

C₂₃×#389

—

C₂₃×#384

—

C₄×C₄⋊C₄×C₂₃

C₂²

yes

characteristic

C₂₃×#343

—

C₂₃×#333

—

C₂²×Q₈×C₂₃

C₂×C₄

yes

—

C₂²×Q₈×C₂₃

D₄

yes

characteristic

C₂×M₁₆×C₂₃

—

C₂₃×C₄⋊Q₈

—

C₂₃×C₄⋊Q₈

—

C₄×Q₈×C₂₃

—

C₄×Q₈×C₂₃

—

C₂×C₄⋊C₄×C₂₃

—

C₂×C₄⋊C₄×C₂₃

—

C₂×C₄⋊C₄×C₂₃

—

C₂×C₄⋊C₄×C₂₃

—

C₂×C₄⋊C₄×C₂₃

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₂₃

D₄

yes

characteristic

C₂×C₄²×C₂₃

—

C₂×C₄²×C₂₃

D₄

yes

—

C₂×C₄²×C₂₃

C₂³

yes

characteristic

C₂₃×C₄⋊C₈

—

C₂₃×C₄⋊C₈

—

C₂₃×C₄⋊C₈

—

C₂₃×C₄⋊C₈

D₄

yes

—

C₂₃×#101

—

C₂₃×C₂²⋊C₈

—

C₂₃×#97

—

C₄×C₈×C₂₃

—

C₂₃×#95

—

C₂₃×#95

C₂×C₄

yes

—

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

yes

—

C₂²×C₄×C₂₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₂₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₂₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₂₃

C₂×D₄

yes

characteristic

M₁₆×C₂₃

—

M₁₆×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

—

C₄²×C₂₃

—

C₄²×C₂₃

—

C₄²×C₂₃

—

C₄²×C₂₃

—

C₄²×C₂₃

C₂×D₄

yes

—

C₄²×C₂₃

#41

yes

—

#9400

C₂₃

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₂₃

C₂×C₂²⋊C₄

yes

characteristic

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

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

C₄×D₄

yes

—

C₂×C₄×C₂₃

#120

yes

characteristic

C₂×C₄×C₂₃

#121

yes

—

C₂×C₄×C₂₃

yes

C₂×C₄×C₂₃

yes

C₂×C₄×C₂₃

yes

—

C₂×C₄×C₂₃

#137

yes

characteristic

100

C₈×C₂₃

—

101

C₈×C₂₃

—

102

#2983

C₂×C₂₃

yes

characteristic

103

#2567

C₂×C₂₃

yes

characteristic

104

#1801

C₂×C₂₃

yes

characteristic

105

#1548

C₂×C₂₃

yes

—

106

#1303

C₂×C₂₃

yes

—

107

C₂²×C₂₃

—

108

C₂²×C₂₃

—

109

C₂²×C₂₃

#386

yes

characteristic

110

C₂²×C₂₃

#417

yes

characteristic

111

C₂²×C₂₃

#419

yes

characteristic

112

C₄×C₂₃

—

113

C₄×C₂₃

—

114

C₄×C₂₃

—

115

C₄×C₂₃

—

116

C₄×C₂₃

—

117

C₄×C₂₃

—

118

C₄×C₂₃

#456

yes

—

119

C₄×C₂₃

#468

yes

—

120

C₄×C₂₃

#470

yes

—

121

C₂×C₄⋊Q₈

C₂²×C₂₃

yes

characteristic

122

C₂×C₄×Q₈

C₂²×C₂₃

yes

characteristic

123

#446

—

124

#432

—

125

#431

C₂²×C₂₃

yes

—

126

#423

C₂²×C₂₃

yes

—

127

C₂×#101

—

128

#395

C₄×C₂₃

yes

—

129

#391

—

130

#389

—

131

#384

—

132

C₄×C₄⋊C₄

C₂²×C₂₃

yes

characteristic

133

#343

—

134

#333

—

135

C₂×C₂₃

—

136

C₂×C₂₃

—

137

C₂×C₂₃

#1886

yes

characteristic

138

C₂×C₂₃

#1894

yes

characteristic

139

C₂×C₂₃

#1914

yes

characteristic

140

C₂²×Q₈

C₂×C₄×C₂₃

yes

—

141

C₂²×Q₈

D₄×C₂₃

yes

characteristic

142

C₂×M₁₆

—

143

C₄⋊Q₈

—

144

C₄⋊Q₈

—

145

C₄×Q₈

—

146

C₄×Q₈

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

C₂×C₄×C₂₃

yes

—

152

C₂×C₄⋊C₄

D₄×C₂₃

yes

characteristic

153

C₂×C₄²

—

154

C₂×C₄²

D₄×C₂₃

yes

—

155

C₂×C₄²

C₂³×C₂₃

yes

characteristic

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

D₄×C₂₃

yes

—

160

#101

—

161

C₂²⋊C₈

—

162

#97

—

163

C₄×C₈

—

164

#95

—

165

#95

C₂×C₄×C₂₃

yes

—

166

C₂₃

#9400

yes

characteristic, direct product factor, Sylow

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂×Q₈

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

C₂²⋊C₄×C₂₃

yes

—

176

C₂²×C₄

C₂²⋊C₄×C₂₃

yes

—

177

C₂²×C₄

C₂²×C₄×C₂₃

yes

characteristic

178

C₂²×C₄

C₂×D₄×C₂₃

yes

characteristic

179

C₂²×C₄

C₂×D₄×C₂₃

yes

characteristic

180

M₁₆

—

181

M₁₆

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄²

—

192

C₄²

—

193

C₄²

—

194

C₄²

—

195

C₄²

C₂×D₄×C₂₃

yes

—

196

C₄²

#41×C₂₃

yes

—

197

C₂³

C₂×C₂²⋊C₄×C₂₃

yes

characteristic

198

Q₈

—

199

Q₈

—

200

Q₈

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

C₄×D₄×C₂₃

yes

—

214

C₂×C₄

C₂₃×#120

yes

characteristic

215

C₂×C₄

C₂₃×#121

yes

—

216

C₂×C₄

C₂₃×#123

yes

characteristic

217

C₂×C₄

C₂₃×AGL(1,ℤ/8)

yes

characteristic

218

C₂×C₄

C₂₃×#137

yes

—

219

C₂×C₄

C₂₃×#137

yes

characteristic

220

C₈

—

221

C₈

—

222

C₂²

—

223

C₂²

—

224

C₂²

C₂₃×#386

yes

characteristic

225

C₂²

C₂₃×#417

yes

characteristic

226

C₂²

C₂₃×#419

yes

characteristic

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

C₂₃×#456

yes

—

234

C₄

C₂₃×#468

yes

—

235

C₄

C₂₃×#470

yes

—

236

C₂

—

237

C₂

—

238

C₂

C₂₃×#1886

yes

characteristic

239

C₂

C₂₃×#1894

yes

characteristic

240

C₂

C₂₃×#1914

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	#386
commutator	C₂²×C₄	C₂²×C₄×C₂₃
Frattini, cosocle	C₂×C₄²	C₂³×C₂₃
prime radical	C₂³×C₂₃	C₂×C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

subgroup

G/H

center, socle

C₂²×C₂₃

#386

commutator

C₂²×C₄

C₂²×C₄×C₂₃

Frattini, cosocle

C₂×C₄²

C₂³×C₂₃

prime radical

C₂³×C₂₃

C₂×C₂²⋊C₄

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

N	H ≅ G/N	type
76. #9400	C₂₃	direct (N × H)
166. C₂₃	#9400	direct (N × H)

H ≅ G/N

type

76. #9400

C₂₃

direct (N × H)

166. C₂₃

#9400

direct (N × H)

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

subgroup	index
C₂₃×#2983	2
C₂₃×#2567	2
C₂₃×#1801	2
C₂₃×#1548	2
C₂₃×#1303	2
#9400	23

subgroup

index

C₂₃×#2983

C₂₃×#2567

C₂₃×#1801

C₂₃×#1548

C₂₃×#1303

#9400

Subgroups — C₂₃×#9400 #19157026

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C23×#9400 #19157026

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#9400 #19157026