Subgroups — C₂₃×#2342 #15669961

Order 2944.

792 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂²⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₂²⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#388	C₂	1	2	yes	maximal, complemented
5	C₂₃×#388	C₂	1	2	yes	maximal, complemented
6	C₂₃×#385	C₂	1	2	yes	maximal, complemented
7	C₂₃×#381	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#379	C₂	1	1	yes	maximal, characteristic
10	C₄×C₂²⋊C₄×C₂₃	C₂	1	2	yes	maximal, complemented
11	C₄×C₂²⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁵×C₂₃	C₂²	1	1	yes	characteristic
13	C₂³×C₄×C₂₃	C₂²	1	2	yes	—
14	C₂³×C₄×C₂₃	C₂²	1	1	yes	characteristic
15	C₂³×C₄×C₂₃	C₂²	1	1	yes	characteristic
16	C₂₃×#117	—	2	4	no	—
17	C₂×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
18	C₂×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
19	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
20	C₂×C₂²⋊C₄×C₂₃	C₄	1	8	yes	complemented
21	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
23	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
32	C₂×C₄²×C₂₃	C₂²	1	2	yes	complemented
33	C₂×C₄²×C₂₃	C₂²	1	2	yes	complemented
34	C₂₃×#95	C₂²	1	2	yes	complemented
35	C₂₃×#95	C₂²	1	2	yes	complemented
36	C₂₃×#95	C₂²	1	2	yes	complemented
37	C₂₃×#95	C₂²	1	2	yes	complemented
38	C₂⁴×C₂₃	—	2	2	no	—
39	C₂⁴×C₂₃	—	2	4	no	—
40	C₂⁴×C₂₃	—	2	2	no	—
41	C₂⁴×C₂₃	—	4	2	no	—
42	C₂⁴×C₂₃	C₂×C₄	1	4	yes	—
43	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
44	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
45	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
46	C₂²×C₄×C₂₃	—	2	2	no	—
47	C₂²×C₄×C₂₃	—	2	2	no	—
48	C₂²×C₄×C₂₃	—	2	4	no	—
49	C₂²×C₄×C₂₃	—	2	4	no	—
50	C₂²×C₄×C₂₃	—	4	2	no	—
51	C₂²×C₄×C₂₃	—	4	2	no	—
52	C₂²×C₄×C₂₃	C₂×C₄	1	4	yes	complemented
53	C₂²×C₄×C₂₃	C₂×C₄	1	4	yes	complemented
54	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
55	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
56	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
57	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
58	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
59	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
60	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
62	C₄⋊C₄×C₂₃	—	2	4	no	—
63	C₄⋊C₄×C₂₃	—	4	2	no	—
64	C₂²⋊C₄×C₂₃	—	2	2	no	—
65	C₂²⋊C₄×C₂₃	—	2	2	no	—
66	C₂²⋊C₄×C₂₃	—	2	4	no	—
67	C₂²⋊C₄×C₂₃	—	2	2	no	—
68	C₂²⋊C₄×C₂₃	—	2	4	no	—
69	C₂²⋊C₄×C₂₃	—	4	2	no	—
70	C₂²⋊C₄×C₂₃	C₂×C₄	1	4	yes	—
71	C₂²⋊C₄×C₂₃	C₂×C₄	1	4	yes	—
72	C₂²⋊C₄×C₂₃	C₂×C₄	1	4	yes	complemented
73	C₂²⋊C₄×C₂₃	C₂×C₄	1	4	yes	complemented
74	C₂²⋊C₄×C₂₃	D₄	1	4	yes	—
75	C₄²×C₂₃	—	2	4	no	—
76	C₄²×C₂₃	—	4	2	no	—
77	C₂³×C₂₃	—	2	1	no	—
78	C₂³×C₂₃	—	2	2	no	—
79	C₂³×C₂₃	—	2	1	no	—
80	C₂³×C₂₃	—	2	2	no	—
81	C₂³×C₂₃	—	2	2	no	—
82	C₂³×C₂₃	—	2	8	no	—
83	C₂³×C₂₃	—	2	8	no	—
84	C₂³×C₂₃	—	2	1	no	—
85	C₂³×C₂₃	—	2	2	no	—
86	C₂³×C₂₃	—	2	1	no	—
87	C₂³×C₂₃	—	2	2	no	—
88	C₂³×C₂₃	—	4	4	no	—
89	C₂³×C₂₃	—	4	8	no	—
90	C₂³×C₂₃	—	4	8	no	—
91	C₂³×C₂₃	C₂²×C₄	1	2	yes	—
92	C₂³×C₂₃	C₂²×C₄	1	2	yes	—
93	C₂³×C₂₃	C₂²×C₄	1	2	yes	—
94	C₂³×C₂₃	C₂×D₄	1	2	yes	—
95	C₂³×C₂₃	#41	1	4	yes	—
96	C₂³×C₂₃	#41	1	2	yes	—
97	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
98	C₂×C₄×C₂₃	—	2	8	no	—
99	C₂×C₄×C₂₃	—	2	1	no	—
100	C₂×C₄×C₂₃	—	2	1	no	—
101	C₂×C₄×C₂₃	—	2	1	no	—
102	C₂×C₄×C₂₃	—	2	1	no	—
103	C₂×C₄×C₂₃	—	2	2	no	—
104	C₂×C₄×C₂₃	—	2	2	no	—
105	C₂×C₄×C₂₃	—	2	2	no	—
106	C₂×C₄×C₂₃	—	2	2	no	—
107	C₂×C₄×C₂₃	—	2	2	no	—
108	C₂×C₄×C₂₃	—	2	2	no	—
109	C₂×C₄×C₂₃	—	2	2	no	—
110	C₂×C₄×C₂₃	—	2	2	no	—
111	C₂×C₄×C₂₃	—	2	2	no	—
112	C₂×C₄×C₂₃	—	2	2	no	—
113	C₂×C₄×C₂₃	—	2	2	no	—
114	C₂×C₄×C₂₃	—	2	2	no	—
115	C₂×C₄×C₂₃	—	2	2	no	—
116	C₂×C₄×C₂₃	—	4	4	no	—
117	C₂×C₄×C₂₃	—	4	8	no	—
118	C₂×C₄×C₂₃	C₂²×C₄	1	2	yes	—
119	C₂×C₄×C₂₃	C₂²×C₄	1	2	yes	—
120	C₂×C₄×C₂₃	C₂²×C₄	1	2	yes	—
121	C₂×C₄×C₂₃	C₂²×C₄	1	2	yes	—
122	C₂×C₄×C₂₃	C₂×D₄	1	4	yes	—
123	#2342	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂²×C₂₃	—	2	2	no	—
125	C₂²×C₂₃	—	2	2	no	—
126	C₂²×C₂₃	—	2	2	no	—
127	C₂²×C₂₃	—	2	2	no	—
128	C₂²×C₂₃	—	2	4	no	—
129	C₂²×C₂₃	—	2	4	no	—
130	C₂²×C₂₃	—	2	4	no	—
131	C₂²×C₂₃	—	2	4	no	—
132	C₂²×C₂₃	—	2	2	no	—
133	C₂²×C₂₃	—	2	2	no	—
134	C₂²×C₂₃	—	2	2	no	—
135	C₂²×C₂₃	—	4	16	no	—
136	C₂²×C₂₃	—	4	2	no	—
137	C₂²×C₂₃	—	4	2	no	—
138	C₂²×C₂₃	#117	1	4	yes	complemented
139	C₂²×C₂₃	C₄×D₄	1	4	yes	—
140	C₂²×C₂₃	C₂³×C₄	1	1	yes	characteristic
141	C₂²×C₂₃	C₂²×D₄	1	1	yes	characteristic
142	C₂²×C₂₃	C₂×#41	1	2	yes	—
143	C₂²×C₂₃	C₂×#41	1	1	yes	characteristic
144	C₂²×C₂₃	H(5,𝔽₂)	1	2	yes	—
145	C₄×C₂₃	—	2	2	no	—
146	C₄×C₂₃	—	2	2	no	—
147	C₄×C₂₃	—	2	2	no	—
148	C₄×C₂₃	—	2	2	no	—
149	C₄×C₂₃	—	2	4	no	—
150	C₄×C₂₃	—	4	2	no	—
151	C₄×C₂₃	—	4	2	no	—
152	C₄×C₂₃	—	4	2	no	—
153	C₂×#117	C₂×C₂₃	1	1	yes	characteristic, complemented
154	C₂²×C₂²⋊C₄	C₂×C₂₃	1	1	yes	characteristic
155	C₂²×C₂²⋊C₄	C₂×C₂₃	1	1	yes	characteristic
156	#388	C₂×C₂₃	1	2	yes	complemented
157	#388	C₂×C₂₃	1	2	yes	complemented
158	#385	C₂×C₂₃	1	2	yes	complemented
159	#381	C₂×C₂₃	1	1	yes	characteristic, complemented
160	#380	C₂×C₂₃	1	1	yes	characteristic, complemented
161	#379	C₂×C₂₃	1	1	yes	characteristic
162	C₄×C₂²⋊C₄	C₂×C₂₃	1	2	yes	complemented
163	C₄×C₂²⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
164	C₂×C₂₃	—	2	4	no	—
165	C₂×C₂₃	—	2	4	no	—
166	C₂×C₂₃	—	4	2	no	—
167	C₂×C₂₃	C₂×#117	1	1	yes	characteristic
168	C₂×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
169	C₂×C₂₃	#518	1	1	yes	characteristic
170	C₂×C₂₃	#546	1	2	yes	—
171	C₂×C₂₃	#551	1	2	yes	—
172	C₂⁵	C₂²×C₂₃	1	1	yes	characteristic
173	C₂³×C₄	C₂²×C₂₃	1	2	yes	—
174	C₂³×C₄	C₂²×C₂₃	1	1	yes	characteristic
175	C₂³×C₄	C₂²×C₂₃	1	1	yes	characteristic
176	#117	—	2	4	no	—
177	C₂×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
178	C₂×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
179	C₂×C₂²⋊C₄	—	2	4	no	—
180	C₂×C₂²⋊C₄	C₄×C₂₃	1	8	yes	complemented
181	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
182	C₂×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
183	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
184	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
185	C₂×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
186	C₂×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
187	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
188	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
189	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
190	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
191	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
192	C₂×C₄²	C₂²×C₂₃	1	2	yes	complemented
193	C₂×C₄²	C₂²×C₂₃	1	2	yes	complemented
194	#95	C₂²×C₂₃	1	2	yes	complemented
195	#95	C₂²×C₂₃	1	2	yes	complemented
196	#95	C₂²×C₂₃	1	2	yes	complemented
197	#95	C₂²×C₂₃	1	2	yes	complemented
198	C₂₃	#2342	1	1	yes	characteristic, direct product factor, Sylow
199	C₂⁴	—	2	2	no	—
200	C₂⁴	—	2	4	no	—
201	C₂⁴	—	2	2	no	—
202	C₂⁴	—	4	2	no	—
203	C₂⁴	C₂×C₄×C₂₃	1	4	yes	—
204	C₂⁴	C₂³×C₂₃	1	1	yes	characteristic
205	C₂⁴	C₂³×C₂₃	1	1	yes	characteristic
206	C₂⁴	C₂³×C₂₃	1	1	yes	characteristic
207	C₂²×C₄	—	2	2	no	—
208	C₂²×C₄	—	2	2	no	—
209	C₂²×C₄	—	2	4	no	—
210	C₂²×C₄	—	2	4	no	—
211	C₂²×C₄	—	4	2	no	—
212	C₂²×C₄	—	4	2	no	—
213	C₂²×C₄	C₂×C₄×C₂₃	1	4	yes	complemented
214	C₂²×C₄	C₂×C₄×C₂₃	1	4	yes	complemented
215	C₂²×C₄	C₂³×C₂₃	1	2	yes	—
216	C₂²×C₄	C₂³×C₂₃	1	2	yes	—
217	C₂²×C₄	C₂³×C₂₃	1	2	yes	—
218	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
219	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
220	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
221	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
222	C₂²×C₄	C₂³×C₂₃	1	2	yes	—
223	C₄⋊C₄	—	2	4	no	—
224	C₄⋊C₄	—	4	2	no	—
225	C₂²⋊C₄	—	2	2	no	—
226	C₂²⋊C₄	—	2	2	no	—
227	C₂²⋊C₄	—	2	4	no	—
228	C₂²⋊C₄	—	2	2	no	—
229	C₂²⋊C₄	—	2	4	no	—
230	C₂²⋊C₄	—	4	2	no	—
231	C₂²⋊C₄	C₂×C₄×C₂₃	1	4	yes	—
232	C₂²⋊C₄	C₂×C₄×C₂₃	1	4	yes	—
233	C₂²⋊C₄	C₂×C₄×C₂₃	1	4	yes	complemented
234	C₂²⋊C₄	C₂×C₄×C₂₃	1	4	yes	complemented
235	C₂²⋊C₄	D₄×C₂₃	1	4	yes	—
236	C₄²	—	2	4	no	—
237	C₄²	—	4	2	no	—
238	C₂³	—	2	1	no	—
239	C₂³	—	2	1	no	—
240	C₂³	—	2	2	no	—
241	C₂³	—	2	2	no	—
242	C₂³	—	2	2	no	—
243	C₂³	—	2	8	no	—
244	C₂³	—	2	8	no	—
245	C₂³	—	2	1	no	—
246	C₂³	—	2	2	no	—
247	C₂³	—	2	1	no	—
248	C₂³	—	2	2	no	—
249	C₂³	—	4	4	no	—
250	C₂³	—	4	8	no	—
251	C₂³	—	4	8	no	—
252	C₂³	C₂²×C₄×C₂₃	1	2	yes	—
253	C₂³	C₂²×C₄×C₂₃	1	2	yes	—
254	C₂³	C₂²×C₄×C₂₃	1	2	yes	—
255	C₂³	C₂×D₄×C₂₃	1	2	yes	—
256	C₂³	#41×C₂₃	1	4	yes	—
257	C₂³	#41×C₂₃	1	2	yes	—
258	C₂³	C₂⁴×C₂₃	1	1	yes	characteristic
259	C₂×C₄	—	2	8	no	—
260	C₂×C₄	—	2	1	no	—
261	C₂×C₄	—	2	1	no	—
262	C₂×C₄	—	2	1	no	—
263	C₂×C₄	—	2	1	no	—
264	C₂×C₄	—	2	2	no	—
265	C₂×C₄	—	2	2	no	—
266	C₂×C₄	—	2	2	no	—
267	C₂×C₄	—	2	2	no	—
268	C₂×C₄	—	2	2	no	—
269	C₂×C₄	—	2	2	no	—
270	C₂×C₄	—	2	2	no	—
271	C₂×C₄	—	2	2	no	—
272	C₂×C₄	—	2	2	no	—
273	C₂×C₄	—	2	2	no	—
274	C₂×C₄	—	2	2	no	—
275	C₂×C₄	—	2	2	no	—
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	4	4	no	—
278	C₂×C₄	—	4	8	no	—
279	C₂×C₄	C₂²×C₄×C₂₃	1	2	yes	—
280	C₂×C₄	C₂²×C₄×C₂₃	1	2	yes	—
281	C₂×C₄	C₂²×C₄×C₂₃	1	2	yes	—
282	C₂×C₄	C₂²×C₄×C₂₃	1	2	yes	—
283	C₂×C₄	C₂×D₄×C₂₃	1	4	yes	—
284	C₂²	—	2	4	no	—
285	C₂²	—	2	4	no	—
286	C₂²	—	2	2	no	—
287	C₂²	—	2	2	no	—
288	C₂²	—	2	2	no	—
289	C₂²	—	2	2	no	—
290	C₂²	—	2	4	no	—
291	C₂²	—	2	4	no	—
292	C₂²	—	2	2	no	—
293	C₂²	—	2	2	no	—
294	C₂²	—	2	2	no	—
295	C₂²	—	4	16	no	—
296	C₂²	—	4	2	no	—
297	C₂²	—	4	2	no	—
298	C₂²	C₂₃×#117	1	4	yes	complemented
299	C₂²	C₄×D₄×C₂₃	1	4	yes	—
300	C₂²	C₂³×C₄×C₂₃	1	1	yes	characteristic
301	C₂²	C₂²×D₄×C₂₃	1	1	yes	characteristic
302	C₂²	C₂×#41×C₂₃	1	1	yes	characteristic
303	C₂²	C₂×#41×C₂₃	1	2	yes	—
304	C₂²	C₂₃×H(5,𝔽₂)	1	2	yes	—
305	C₄	—	2	2	no	—
306	C₄	—	2	2	no	—
307	C₄	—	2	2	no	—
308	C₄	—	2	2	no	—
309	C₄	—	2	4	no	—
310	C₄	—	4	2	no	—
311	C₄	—	4	2	no	—
312	C₄	—	4	2	no	—
313	C₂	—	2	4	no	—
314	C₂	—	2	4	no	—
315	C₂	—	4	2	no	—
316	C₂	C₂×C₂₃×#117	1	1	yes	characteristic
317	C₂	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
318	C₂	C₂₃×#518	1	1	yes	characteristic
319	C₂	C₂₃×#546	1	2	yes	—
320	C₂	C₂₃×#551	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁴
commutator	C₂²	C₂³×C₄×C₂₃
Frattini, cosocle	C₂³	C₂⁴×C₂₃
prime radical	C₂⁵×C₂₃	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₂₃×#117	C₂	semidirect
4. C₂₃×#388	C₂	semidirect
5. C₂₃×#388	C₂	semidirect
6. C₂₃×#385	C₂	semidirect
7. C₂₃×#381	C₂	semidirect
8. C₂₃×#380	C₂	semidirect
10. C₄×C₂²⋊C₄×C₂₃	C₂	semidirect
11. C₄×C₂²⋊C₄×C₂₃	C₂	semidirect
17. C₂×C₄⋊C₄×C₂₃	C₂²	semidirect
18. C₂×C₄⋊C₄×C₂₃	C₂²	semidirect
20. C₂×C₂²⋊C₄×C₂₃	C₄	semidirect
32. C₂×C₄²×C₂₃	C₂²	semidirect
33. C₂×C₄²×C₂₃	C₂²	semidirect
34. C₂₃×#95	C₂²	semidirect
35. C₂₃×#95	C₂²	semidirect
36. C₂₃×#95	C₂²	semidirect
37. C₂₃×#95	C₂²	semidirect
52. C₂²×C₄×C₂₃	C₂×C₄	semidirect
53. C₂²×C₄×C₂₃	C₂×C₄	semidirect
72. C₂²⋊C₄×C₂₃	C₂×C₄	semidirect
73. C₂²⋊C₄×C₂₃	C₂×C₄	semidirect
123. #2342	C₂₃	direct (N × H)
138. C₂²×C₂₃	#117	semidirect
153. C₂×#117	C₂×C₂₃	semidirect
156. #388	C₂×C₂₃	semidirect
157. #388	C₂×C₂₃	semidirect
158. #385	C₂×C₂₃	semidirect
159. #381	C₂×C₂₃	semidirect
160. #380	C₂×C₂₃	semidirect
162. C₄×C₂²⋊C₄	C₂×C₂₃	semidirect
163. C₄×C₂²⋊C₄	C₂×C₂₃	semidirect
177. C₂×C₄⋊C₄	C₂²×C₂₃	semidirect
178. C₂×C₄⋊C₄	C₂²×C₂₃	semidirect
180. C₂×C₂²⋊C₄	C₄×C₂₃	semidirect
192. C₂×C₄²	C₂²×C₂₃	semidirect
193. C₂×C₄²	C₂²×C₂₃	semidirect
194. #95	C₂²×C₂₃	semidirect
195. #95	C₂²×C₂₃	semidirect
196. #95	C₂²×C₂₃	semidirect
197. #95	C₂²×C₂₃	semidirect
198. C₂₃	#2342	direct (N × H)
213. C₂²×C₄	C₂×C₄×C₂₃	semidirect
214. C₂²×C₄	C₂×C₄×C₂₃	semidirect
233. C₂²⋊C₄	C₂×C₄×C₂₃	semidirect
234. C₂²⋊C₄	C₂×C₄×C₂₃	semidirect
298. C₂²	C₂₃×#117	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#117	2
C₂²×C₂²⋊C₄×C₂₃	2
C₂₃×#388	2
C₂₃×#385	2
C₂₃×#381	2
C₂₃×#380	2
C₂₃×#379	2
C₄×C₂²⋊C₄×C₂₃	2
#2342	23

Subgroups — C23×#2342 #15669961

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#2342 #15669961