Group #19157018 — subgroups

Subgroups — C₂₃×#9392 #19157018

Order 5888.

486 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 154 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×#2982	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	C₈×Q₈×C₂₃	—	2	4	no	—
9	C₂₃×#431	—	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	C₄×C₈×C₂₃	—	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	2	no	—
48	C₂×Q₈×C₂₃	—	2	4	no	—
49	C₂×Q₈×C₂₃	—	8	2	no	—
50	C₂×Q₈×C₂₃	SD₁₆	1	2	yes	—
51	C₂×Q₈×C₂₃	Q₁₆	1	2	yes	—
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	2	no	—
73	C₄²×C₂₃	C₂×D₄	1	2	yes	—
74	C₄²×C₂₃	#41	1	2	yes	—
75	#9392	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
77	Q₈×C₂₃	—	2	4	no	—
78	Q₈×C₂₃	—	2	4	no	—
79	Q₈×C₂₃	—	8	4	no	—
80	C₂×C₄×C₂₃	—	2	2	no	—
81	C₂×C₄×C₂₃	—	2	2	no	—
82	C₂×C₄×C₂₃	—	2	2	no	—
83	C₂×C₄×C₂₃	—	2	4	no	—
84	C₂×C₄×C₂₃	—	2	2	no	—
85	C₂×C₄×C₂₃	—	4	1	no	—
86	C₂×C₄×C₂₃	—	4	2	no	—
87	C₂×C₄×C₂₃	—	4	2	no	—
88	C₂×C₄×C₂₃	—	4	2	no	—
89	C₂×C₄×C₂₃	—	4	4	no	—
90	C₂×C₄×C₂₃	—	4	2	no	—
91	C₂×C₄×C₂₃	#103	1	4	yes	—
92	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
93	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
94	C₂×C₄×C₂₃	#121	1	2	yes	—
95	C₂×C₄×C₂₃	#123	1	1	yes	characteristic
96	C₂×C₄×C₂₃	C₂×SD₁₆	1	1	yes	characteristic
97	C₂×C₄×C₂₃	C₂×Q₁₆	1	1	yes	characteristic
98	C₂×C₄×C₂₃	#135	1	2	yes	—
99	C₈×C₂₃	—	4	4	no	—
100	C₈×C₂₃	—	8	2	no	—
101	#2982	C₂×C₂₃	1	1	yes	characteristic
102	#2567	C₂×C₂₃	1	1	yes	characteristic
103	#1801	C₂×C₂₃	1	1	yes	characteristic
104	#1548	C₂×C₂₃	1	2	yes	—
105	#1303	C₂×C₂₃	1	2	yes	—
106	C₂²×C₂₃	—	2	1	no	—
107	C₂²×C₂₃	—	2	1	no	—
108	C₂²×C₂₃	#386	1	1	yes	characteristic
109	C₂²×C₂₃	C₂×#103	1	1	yes	characteristic
110	C₂²×C₂₃	#416	1	1	yes	characteristic
111	C₄×C₂₃	—	2	1	no	—
112	C₄×C₂₃	—	2	4	no	—
113	C₄×C₂₃	—	2	2	no	—
114	C₄×C₂₃	—	4	4	no	—
115	C₄×C₂₃	—	4	2	no	—
116	C₄×C₂₃	—	8	2	no	—
117	C₄×C₂₃	#456	1	2	yes	—
118	C₄×C₂₃	#465	1	2	yes	—
119	C₄×C₂₃	#467	1	2	yes	—
120	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
121	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
122	C₈×Q₈	—	2	4	no	—
123	#431	—	2	2	no	—
124	#431	C₂²×C₂₃	1	2	yes	—
125	#423	C₂²×C₂₃	1	2	yes	—
126	C₂×#101	—	2	1	no	—
127	#395	C₄×C₂₃	1	4	yes	—
128	#391	—	2	1	no	—
129	#389	—	2	2	no	—
130	#384	—	2	1	no	—
131	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
132	#343	—	2	1	no	—
133	#333	—	2	4	no	—
134	C₂×C₂₃	—	2	1	no	—
135	C₂×C₂₃	—	2	1	no	—
136	C₂×C₂₃	#1886	1	1	yes	characteristic
137	C₂×C₂₃	#1892	1	1	yes	characteristic
138	C₂×C₂₃	#1914	1	1	yes	characteristic
139	C₂²×Q₈	C₂×C₄×C₂₃	1	2	yes	—
140	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
141	C₂×M₁₆	—	2	2	no	—
142	C₄⋊Q₈	—	2	2	no	—
143	C₄⋊Q₈	—	2	2	no	—
144	C₄×Q₈	—	2	2	no	—
145	C₄×Q₈	—	2	2	no	—
146	C₂×C₄⋊C₄	—	2	1	no	—
147	C₂×C₄⋊C₄	—	2	1	no	—
148	C₂×C₄⋊C₄	—	2	1	no	—
149	C₂×C₄⋊C₄	—	2	4	no	—
150	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
151	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
152	C₂×C₄²	—	2	1	no	—
153	C₂×C₄²	D₄×C₂₃	1	2	yes	—
154	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
155	C₄⋊C₈	—	2	4	no	—
156	C₄⋊C₈	—	2	2	no	—
157	C₄⋊C₈	—	2	2	no	—
158	C₄⋊C₈	D₄×C₂₃	1	4	yes	—
159	#101	—	4	2	no	—
160	C₂²⋊C₈	—	2	2	no	—
161	C₄×C₈	—	2	4	no	—
162	C₄×C₈	—	2	2	no	—
163	#95	—	2	4	no	—
164	#95	C₂×C₄×C₂₃	1	2	yes	—
165	C₂₃	#9392	1	1	yes	characteristic, direct product factor, Sylow
166	C₂×Q₈	—	2	2	no	—
167	C₂×Q₈	—	2	2	no	—
168	C₂×Q₈	—	2	4	no	—
169	C₂×Q₈	—	8	2	no	—
170	C₂×Q₈	SD₁₆×C₂₃	1	2	yes	—
171	C₂×Q₈	Q₁₆×C₂₃	1	2	yes	—
172	C₂²×C₄	—	2	2	no	—
173	C₂²×C₄	—	2	2	no	—
174	C₂²×C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
175	C₂²×C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
176	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
177	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
178	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
179	M₁₆	—	4	2	no	—
180	M₁₆	—	4	2	no	—
181	C₂×C₈	—	2	4	no	—
182	C₂×C₈	—	4	2	no	—
183	C₄⋊C₄	—	2	4	no	—
184	C₄⋊C₄	—	2	4	no	—
185	C₄⋊C₄	—	2	2	no	—
186	C₄⋊C₄	—	4	1	no	—
187	C₄⋊C₄	—	4	2	no	—
188	C₄⋊C₄	—	4	1	no	—
189	C₄⋊C₄	—	8	4	no	—
190	C₄²	—	2	2	no	—
191	C₄²	—	2	2	no	—
192	C₄²	—	4	2	no	—
193	C₄²	C₂×D₄×C₂₃	1	2	yes	—
194	C₄²	#41×C₂₃	1	2	yes	—
195	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
196	Q₈	—	2	4	no	—
197	Q₈	—	2	4	no	—
198	Q₈	—	8	4	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	4	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	4	1	no	—
205	C₂×C₄	—	4	2	no	—
206	C₂×C₄	—	4	2	no	—
207	C₂×C₄	—	4	2	no	—
208	C₂×C₄	—	4	4	no	—
209	C₂×C₄	—	4	2	no	—
210	C₂×C₄	C₂₃×#103	1	4	yes	—
211	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
212	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
213	C₂×C₄	C₂₃×#121	1	2	yes	—
214	C₂×C₄	C₂₃×#123	1	1	yes	characteristic
215	C₂×C₄	C₂×SD₁₆×C₂₃	1	1	yes	characteristic
216	C₂×C₄	C₂×Q₁₆×C₂₃	1	1	yes	characteristic
217	C₂×C₄	C₂₃×#135	1	2	yes	—
218	C₈	—	4	4	no	—
219	C₈	—	8	2	no	—
220	C₂²	—	2	1	no	—
221	C₂²	—	2	1	no	—
222	C₂²	C₂₃×#386	1	1	yes	characteristic
223	C₂²	C₂×C₂₃×#103	1	1	yes	characteristic
224	C₂²	C₂₃×#416	1	1	yes	characteristic
225	C₄	—	2	1	no	—
226	C₄	—	2	4	no	—
227	C₄	—	2	2	no	—
228	C₄	—	4	4	no	—
229	C₄	—	4	2	no	—
230	C₄	—	8	2	no	—
231	C₄	C₂₃×#456	1	2	yes	—
232	C₄	C₂₃×#465	1	2	yes	—
233	C₄	C₂₃×#467	1	2	yes	—
234	C₂	—	2	1	no	—
235	C₂	—	2	1	no	—
236	C₂	C₂₃×#1886	1	1	yes	characteristic
237	C₂	C₂₃×#1892	1	1	yes	characteristic
238	C₂	C₂₃×#1914	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂₃×#2982

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

C₈×Q₈×C₂₃

—

C₂₃×#431

—

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

—

C₄×C₈×C₂₃

—

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

SD₁₆

yes

—

C₂×Q₈×C₂₃

Q₁₆

yes

—

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

C₂×D₄

yes

—

C₄²×C₂₃

#41

yes

—

#9392

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

#103

yes

—

C₂×C₄×C₂₃

C₄×D₄

yes

—

C₂×C₄×C₂₃

#120

yes

characteristic

C₂×C₄×C₂₃

#121

yes

—

C₂×C₄×C₂₃

#123

yes

characteristic

C₂×C₄×C₂₃

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₂₃

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₂₃

#135

yes

—

C₈×C₂₃

—

100

C₈×C₂₃

—

101

#2982

C₂×C₂₃

yes

characteristic

102

#2567

C₂×C₂₃

yes

characteristic

103

#1801

C₂×C₂₃

yes

characteristic

104

#1548

C₂×C₂₃

yes

—

105

#1303

C₂×C₂₃

yes

—

106

C₂²×C₂₃

—

107

C₂²×C₂₃

—

108

C₂²×C₂₃

#386

yes

characteristic

109

C₂²×C₂₃

C₂×#103

yes

characteristic

110

C₂²×C₂₃

#416

yes

characteristic

111

C₄×C₂₃

—

112

C₄×C₂₃

—

113

C₄×C₂₃

—

114

C₄×C₂₃

—

115

C₄×C₂₃

—

116

C₄×C₂₃

—

117

C₄×C₂₃

#456

yes

—

118

C₄×C₂₃

#465

yes

—

119

C₄×C₂₃

#467

yes

—

120

C₂×C₄⋊Q₈

C₂²×C₂₃

yes

characteristic

121

C₂×C₄×Q₈

C₂²×C₂₃

yes

characteristic

122

C₈×Q₈

—

123

#431

—

124

#431

C₂²×C₂₃

yes

—

125

#423

C₂²×C₂₃

yes

—

126

C₂×#101

—

127

#395

C₄×C₂₃

yes

—

128

#391

—

129

#389

—

130

#384

—

131

C₄×C₄⋊C₄

C₂²×C₂₃

yes

characteristic

132

#343

—

133

#333

—

134

C₂×C₂₃

—

135

C₂×C₂₃

—

136

C₂×C₂₃

#1886

yes

characteristic

137

C₂×C₂₃

#1892

yes

characteristic

138

C₂×C₂₃

#1914

yes

characteristic

139

C₂²×Q₈

C₂×C₄×C₂₃

yes

—

140

C₂²×Q₈

D₄×C₂₃

yes

characteristic

141

C₂×M₁₆

—

142

C₄⋊Q₈

—

143

C₄⋊Q₈

—

144

C₄×Q₈

—

145

C₄×Q₈

—

146

C₂×C₄⋊C₄

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

C₂×C₄×C₂₃

yes

—

151

C₂×C₄⋊C₄

D₄×C₂₃

yes

characteristic

152

C₂×C₄²

—

153

C₂×C₄²

D₄×C₂₃

yes

—

154

C₂×C₄²

C₂³×C₂₃

yes

characteristic

155

C₄⋊C₈

—

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄⋊C₈

D₄×C₂₃

yes

—

159

#101

—

160

C₂²⋊C₈

—

161

C₄×C₈

—

162

C₄×C₈

—

163

#95

—

164

#95

C₂×C₄×C₂₃

yes

—

165

C₂₃

#9392

yes

characteristic, direct product factor, Sylow

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

SD₁₆×C₂₃

yes

—

171

C₂×Q₈

Q₁₆×C₂₃

yes

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

C₂²⋊C₄×C₂₃

yes

—

175

C₂²×C₄

C₂²⋊C₄×C₂₃

yes

—

176

C₂²×C₄

C₂²×C₄×C₂₃

yes

characteristic

177

C₂²×C₄

C₂×D₄×C₂₃

yes

characteristic

178

C₂²×C₄

C₂×D₄×C₂₃

yes

characteristic

179

M₁₆

—

180

M₁₆

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄²

—

191

C₄²

—

192

C₄²

—

193

C₄²

C₂×D₄×C₂₃

yes

—

194

C₄²

#41×C₂₃

yes

—

195

C₂³

C₂×C₂²⋊C₄×C₂₃

yes

characteristic

196

Q₈

—

197

Q₈

—

198

Q₈

—

199

C₂×C₄

—

200

C₂×C₄

—

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

C₂₃×#103

yes

—

211

C₂×C₄

C₄×D₄×C₂₃

yes

—

212

C₂×C₄

C₂₃×#120

yes

characteristic

213

C₂×C₄

C₂₃×#121

yes

—

214

C₂×C₄

C₂₃×#123

yes

characteristic

215

C₂×C₄

C₂×SD₁₆×C₂₃

yes

characteristic

216

C₂×C₄

C₂×Q₁₆×C₂₃

yes

characteristic

217

C₂×C₄

C₂₃×#135

yes

—

218

C₈

—

219

C₈

—

220

C₂²

—

221

C₂²

—

222

C₂²

C₂₃×#386

yes

characteristic

223

C₂²

C₂×C₂₃×#103

yes

characteristic

224

C₂²

C₂₃×#416

yes

characteristic

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

C₂₃×#456

yes

—

232

C₄

C₂₃×#465

yes

—

233

C₄

C₂₃×#467

yes

—

234

C₂

—

235

C₂

—

236

C₂

C₂₃×#1886

yes

characteristic

237

C₂

C₂₃×#1892

yes

characteristic

238

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
75. #9392	C₂₃	direct (N × H)
165. C₂₃	#9392	direct (N × H)

H ≅ G/N

type

75. #9392

C₂₃

direct (N × H)

165. C₂₃

#9392

direct (N × H)

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

subgroup	index
C₂₃×#2982	2
C₂₃×#2567	2
C₂₃×#1801	2
C₂₃×#1548	2
C₂₃×#1303	2
#9392	23

subgroup

index

C₂₃×#2982

C₂₃×#2567

C₂₃×#1801

C₂₃×#1548

C₂₃×#1303

#9392

Subgroups — C₂₃×#9392 #19157018

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C23×#9392 #19157018

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#9392 #19157018