Subgroups — C₂₃×#10855 #19158481

Order 5888.

802 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#423	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2285	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂₃×#344	C₂	1	4	yes	maximal
5	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	—
6	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	—
7	C₂×C₂₃×#117	C₂²	1	2	yes	—
8	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
9	C₂₃×#423	—	2	1	no	—
10	C₂₃×#423	—	2	1	no	—
11	C₂₃×#423	—	2	2	no	—
12	C₂×C₂₃×C₄⋊C₈	C₄	1	4	yes	complemented
13	C₄×M₁₆×C₂₃	—	2	1	no	—
14	C₄×M₁₆×C₂₃	—	2	1	no	—
15	C₄×M₁₆×C₂₃	C₄	1	2	yes	complemented
16	C₄×M₁₆×C₂₃	C₄	1	2	yes	complemented
17	C₂×C₂₃×#97	—	2	1	no	—
18	C₂×C₄×C₈×C₂₃	—	2	1	no	—
19	C₂₃×#384	—	2	1	no	—
20	C₂₃×#382	—	2	1	no	—
21	C₂₃×#380	C₄	1	4	yes	—
22	C₄×C₄⋊C₄×C₂₃	—	2	2	no	—
23	C₂₃×#344	—	2	8	no	—
24	C₂³×C₄×C₂₃	C₂×C₄	1	2	yes	—
25	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
26	C₂×M₁₆×C₂₃	—	2	2	no	—
27	C₂×M₁₆×C₂₃	—	2	2	no	—
28	C₂×M₁₆×C₂₃	—	2	2	no	—
29	C₂×M₁₆×C₂₃	—	2	4	no	—
30	C₂×M₁₆×C₂₃	—	2	2	no	—
31	C₂×M₁₆×C₂₃	—	2	2	no	—
32	C₂×M₁₆×C₂₃	—	2	4	no	—
33	C₂×M₁₆×C₂₃	C₂×C₄	1	4	yes	—
34	C₂×M₁₆×C₂₃	D₄	1	4	yes	—
35	C₂×M₁₆×C₂₃	Q₈	1	4	yes	—
36	C₂²×C₈×C₂₃	—	2	2	no	—
37	C₂²×C₈×C₂₃	C₂×C₄	1	4	yes	—
38	C₂₃×#117	—	2	4	no	—
39	C₂₃×#117	—	2	4	no	—
40	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
41	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
42	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	4	yes	—
43	C₂×C₄²×C₂₃	—	2	2	no	—
44	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₂₃	D₄	1	2	yes	—
50	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₂₃	Q₈	1	2	yes	—
53	C₂₃×C₄⋊C₈	—	2	4	no	—
54	C₂₃×C₄⋊C₈	—	2	4	no	—
55	C₂₃×#97	—	2	2	no	—
56	C₂₃×#97	—	2	2	no	—
57	C₄×C₈×C₂₃	—	2	2	no	—
58	C₄×C₈×C₂₃	—	2	2	no	—
59	C₂₃×#95	—	2	4	no	—
60	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
61	C₂²×C₄×C₂₃	—	2	4	no	—
62	C₂²×C₄×C₂₃	—	4	4	no	—
63	C₂²×C₄×C₂₃	C₄²	1	2	yes	—
64	C₂²×C₄×C₂₃	C₄²	1	2	yes	—
65	C₂²×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
66	C₂²×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
67	C₂²×C₄×C₂₃	C₄⋊C₄	1	2	yes	—
68	C₂²×C₄×C₂₃	C₄⋊C₄	1	2	yes	—
69	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
75	C₂²×C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
76	C₂²×C₄×C₂₃	C₂×Q₈	1	2	yes	—
77	C₂²×C₄×C₂₃	#41	1	2	yes	—
78	C₂²×C₄×C₂₃	#41	1	2	yes	—
79	M₁₆×C₂₃	—	2	4	no	—
80	M₁₆×C₂₃	—	2	4	no	—
81	M₁₆×C₂₃	—	2	4	no	—
82	M₁₆×C₂₃	—	4	4	no	—
83	M₁₆×C₂₃	—	4	2	no	—
84	M₁₆×C₂₃	—	4	2	no	—
85	M₁₆×C₂₃	C₄⋊C₄	1	8	yes	complemented
86	C₂×C₈×C₂₃	—	2	4	no	—
87	C₂×C₈×C₂₃	—	2	4	no	—
88	C₂×C₈×C₂₃	—	2	4	no	—
89	C₂×C₈×C₂₃	—	2	4	no	—
90	C₂×C₈×C₂₃	—	2	8	no	—
91	C₄⋊C₄×C₂₃	—	4	8	no	—
92	C₄⋊C₄×C₂₃	—	4	4	no	—
93	C₂²⋊C₄×C₂₃	—	2	8	no	—
94	C₄²×C₂₃	—	4	2	no	—
95	C₄²×C₂₃	—	4	2	no	—
96	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
97	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
98	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
99	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
100	C₄²×C₂₃	C₂²⋊C₄	1	2	yes	—
101	C₄²×C₂₃	C₂²⋊C₄	1	2	yes	—
102	C₄²×C₂₃	C₄⋊C₄	1	2	yes	—
103	C₄²×C₂₃	C₄⋊C₄	1	2	yes	—
104	C₄²×C₂₃	C₄⋊C₄	1	2	yes	—
105	C₄²×C₂₃	C₄⋊C₄	1	2	yes	—
106	#10855	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
107	C₂³×C₂₃	—	4	2	no	—
108	C₂³×C₂₃	C₂×C₄²	1	1	yes	characteristic
109	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
110	C₂³×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
111	C₂³×C₂₃	C₄×D₄	1	2	yes	—
112	C₂³×C₂₃	C₄×Q₈	1	2	yes	—
113	C₂×C₄×C₂₃	—	2	4	no	—
114	C₂×C₄×C₂₃	—	2	4	no	—
115	C₂×C₄×C₂₃	—	2	4	no	—
116	C₂×C₄×C₂₃	—	4	2	no	—
117	C₂×C₄×C₂₃	—	4	2	no	—
118	C₂×C₄×C₂₃	—	4	2	no	—
119	C₂×C₄×C₂₃	—	4	8	no	—
120	C₂×C₄×C₂₃	—	4	4	no	—
121	C₂×C₄×C₂₃	#95	1	2	yes	—
122	C₂×C₄×C₂₃	#95	1	2	yes	—
123	C₂×C₄×C₂₃	#95	1	2	yes	—
124	C₂×C₄×C₂₃	#95	1	2	yes	—
125	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
126	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
127	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	2	yes	—
128	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
129	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₂₃	#117	1	2	yes	—
131	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
132	C₂×C₄×C₂₃	C₄×Q₈	1	2	yes	—
133	C₂×C₄×C₂₃	#121	1	2	yes	—
134	C₂×C₄×C₂₃	#121	1	2	yes	—
135	C₂×C₄×C₂₃	C₂²⋊Q₈	1	2	yes	—
136	C₂×C₄×C₂₃	C₂²⋊Q₈	1	2	yes	—
137	C₂×C₄×C₂₃	#124	1	1	yes	characteristic
138	C₂×C₄×C₂₃	#124	1	1	yes	characteristic
139	C₂×C₄×C₂₃	#125	1	2	yes	—
140	C₂×C₄×C₂₃	#127	1	1	yes	characteristic
141	C₂×C₄×C₂₃	C₄⋊Q₈	1	2	yes	—
142	C₂×C₄×C₂₃	C₄⋊Q₈	1	1	yes	characteristic
143	C₈×C₂₃	—	2	8	no	—
144	C₈×C₂₃	—	4	4	no	—
145	C₂×#423	C₂×C₂₃	1	1	yes	characteristic
146	C₂×C₄×M₁₆	C₂×C₂₃	1	1	yes	characteristic
147	#2285	C₂×C₂₃	1	1	yes	characteristic
148	C₂×#344	C₂×C₂₃	1	4	yes	—
149	C₂²×C₂₃	—	2	2	no	—
150	C₂²×C₂₃	—	2	2	no	—
151	C₂²×C₂₃	—	2	2	no	—
152	C₂²×C₂₃	—	4	2	no	—
153	C₂²×C₂₃	—	4	2	no	—
154	C₂²×C₂₃	C₂×#95	1	1	yes	characteristic
155	C₂²×C₂₃	C₄×C₄⋊C₄	1	2	yes	—
156	C₂²×C₂₃	#389	1	2	yes	—
157	C₂²×C₂₃	#390	1	1	yes	characteristic
158	C₂²×C₂₃	#391	1	1	yes	characteristic
159	C₄×C₂₃	—	2	2	no	—
160	C₄×C₂₃	—	2	2	no	—
161	C₄×C₂₃	—	2	2	no	—
162	C₄×C₂₃	—	8	4	no	—
163	C₄×C₂₃	#344	1	4	yes	complemented
164	C₄×C₂₃	#380	1	2	yes	—
165	C₄×C₂₃	#382	1	1	yes	characteristic
166	C₄×C₂₃	#384	1	1	yes	characteristic
167	C₄×C₂₃	#389	1	2	yes	—
168	C₄×C₂₃	#390	1	1	yes	characteristic
169	C₄×C₂₃	#391	1	1	yes	characteristic
170	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	—
171	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	—
172	C₂×#117	C₂²×C₂₃	1	2	yes	—
173	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
174	#423	—	2	1	no	—
175	#423	—	2	1	no	—
176	#423	—	2	2	no	—
177	C₂×C₄⋊C₈	C₄×C₂₃	1	4	yes	complemented
178	C₄×M₁₆	—	2	1	no	—
179	C₄×M₁₆	—	2	1	no	—
180	C₄×M₁₆	C₄×C₂₃	1	2	yes	complemented
181	C₄×M₁₆	C₄×C₂₃	1	2	yes	complemented
182	C₂×#97	—	2	1	no	—
183	C₂×C₄×C₈	—	2	1	no	—
184	#384	—	2	1	no	—
185	#382	—	2	1	no	—
186	#380	C₄×C₂₃	1	4	yes	—
187	C₄×C₄⋊C₄	—	2	2	no	—
188	#344	—	2	8	no	—
189	C₂×C₂₃	—	2	1	no	—
190	C₂×C₂₃	—	2	2	no	—
191	C₂×C₂₃	—	2	2	no	—
192	C₂×C₂₃	—	2	1	no	—
193	C₂×C₂₃	C₄⋊#95	1	1	yes	characteristic
194	C₂×C₂₃	C₂×#344	1	2	yes	—
195	C₂³×C₄	C₂×C₄×C₂₃	1	2	yes	—
196	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
197	C₂×M₁₆	—	2	2	no	—
198	C₂×M₁₆	—	2	2	no	—
199	C₂×M₁₆	—	2	2	no	—
200	C₂×M₁₆	—	2	4	no	—
201	C₂×M₁₆	—	2	2	no	—
202	C₂×M₁₆	—	2	2	no	—
203	C₂×M₁₆	—	2	4	no	—
204	C₂×M₁₆	C₂×C₄×C₂₃	1	4	yes	—
205	C₂×M₁₆	D₄×C₂₃	1	4	yes	—
206	C₂×M₁₆	Q₈×C₂₃	1	4	yes	—
207	C₂²×C₈	—	2	2	no	—
208	C₂²×C₈	C₂×C₄×C₂₃	1	4	yes	—
209	#117	—	2	4	no	—
210	#117	—	2	4	no	—
211	C₂×C₄⋊C₄	—	2	4	no	—
212	C₂×C₄⋊C₄	—	2	2	no	—
213	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	4	yes	—
214	C₂×C₄²	—	2	2	no	—
215	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
216	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
217	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
218	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
219	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
220	C₂×C₄²	D₄×C₂₃	1	2	yes	—
221	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
222	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
223	C₂×C₄²	Q₈×C₂₃	1	2	yes	—
224	C₄⋊C₈	—	2	4	no	—
225	C₄⋊C₈	—	2	4	no	—
226	#97	—	2	2	no	—
227	#97	—	2	2	no	—
228	C₄×C₈	—	2	2	no	—
229	C₄×C₈	—	2	2	no	—
230	#95	—	2	4	no	—
231	C₂₃	#10855	1	1	yes	characteristic, direct product factor, Sylow
232	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
233	C₂²×C₄	—	2	4	no	—
234	C₂²×C₄	—	4	4	no	—
235	C₂²×C₄	C₄²×C₂₃	1	2	yes	—
236	C₂²×C₄	C₄²×C₂₃	1	2	yes	—
237	C₂²×C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
238	C₂²×C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
239	C₂²×C₄	C₄⋊C₄×C₂₃	1	2	yes	—
240	C₂²×C₄	C₄⋊C₄×C₂₃	1	2	yes	—
241	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
242	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
243	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
244	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
245	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
246	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
247	C₂²×C₄	C₂×Q₈×C₂₃	1	1	yes	characteristic
248	C₂²×C₄	C₂×Q₈×C₂₃	1	2	yes	—
249	C₂²×C₄	#41×C₂₃	1	2	yes	—
250	C₂²×C₄	#41×C₂₃	1	2	yes	—
251	M₁₆	—	2	4	no	—
252	M₁₆	—	2	4	no	—
253	M₁₆	—	2	4	no	—
254	M₁₆	—	4	4	no	—
255	M₁₆	—	4	2	no	—
256	M₁₆	—	4	2	no	—
257	M₁₆	C₄⋊C₄×C₂₃	1	8	yes	complemented
258	C₂×C₈	—	2	4	no	—
259	C₂×C₈	—	2	4	no	—
260	C₂×C₈	—	2	4	no	—
261	C₂×C₈	—	2	4	no	—
262	C₂×C₈	—	2	8	no	—
263	C₄⋊C₄	—	4	8	no	—
264	C₄⋊C₄	—	4	4	no	—
265	C₂²⋊C₄	—	2	8	no	—
266	C₄²	—	4	2	no	—
267	C₄²	—	4	2	no	—
268	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
269	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
270	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
271	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
272	C₄²	C₂²⋊C₄×C₂₃	1	2	yes	—
273	C₄²	C₂²⋊C₄×C₂₃	1	2	yes	—
274	C₄²	C₄⋊C₄×C₂₃	1	2	yes	—
275	C₄²	C₄⋊C₄×C₂₃	1	2	yes	—
276	C₄²	C₄⋊C₄×C₂₃	1	2	yes	—
277	C₄²	C₄⋊C₄×C₂₃	1	2	yes	—
278	C₂³	—	4	2	no	—
279	C₂³	C₂×C₄²×C₂₃	1	1	yes	characteristic
280	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
281	C₂³	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
282	C₂³	C₄×D₄×C₂₃	1	2	yes	—
283	C₂³	C₄×Q₈×C₂₃	1	2	yes	—
284	C₂×C₄	—	2	4	no	—
285	C₂×C₄	—	2	4	no	—
286	C₂×C₄	—	2	4	no	—
287	C₂×C₄	—	4	2	no	—
288	C₂×C₄	—	4	2	no	—
289	C₂×C₄	—	4	2	no	—
290	C₂×C₄	—	4	8	no	—
291	C₂×C₄	—	4	4	no	—
292	C₂×C₄	C₂₃×#95	1	2	yes	—
293	C₂×C₄	C₂₃×#95	1	2	yes	—
294	C₂×C₄	C₂₃×#95	1	2	yes	—
295	C₂×C₄	C₂₃×#95	1	2	yes	—
296	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
297	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
298	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	2	yes	—
299	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
300	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
301	C₂×C₄	C₂₃×#117	1	2	yes	—
302	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
303	C₂×C₄	C₄×Q₈×C₂₃	1	2	yes	—
304	C₂×C₄	C₂₃×#121	1	2	yes	—
305	C₂×C₄	C₂₃×#121	1	2	yes	—
306	C₂×C₄	C₂₃×C₂²⋊Q₈	1	2	yes	—
307	C₂×C₄	C₂₃×C₂²⋊Q₈	1	2	yes	—
308	C₂×C₄	C₂₃×#124	1	1	yes	characteristic
309	C₂×C₄	C₂₃×#124	1	1	yes	characteristic
310	C₂×C₄	C₂₃×#125	1	2	yes	—
311	C₂×C₄	C₂₃×#127	1	1	yes	characteristic
312	C₂×C₄	C₂₃×C₄⋊Q₈	1	2	yes	—
313	C₂×C₄	C₂₃×C₄⋊Q₈	1	1	yes	characteristic
314	C₈	—	2	8	no	—
315	C₈	—	4	4	no	—
316	C₂²	—	2	2	no	—
317	C₂²	—	2	2	no	—
318	C₂²	—	2	2	no	—
319	C₂²	—	4	2	no	—
320	C₂²	—	4	2	no	—
321	C₂²	C₂×C₂₃×#95	1	1	yes	characteristic
322	C₂²	C₄×C₄⋊C₄×C₂₃	1	2	yes	—
323	C₂²	C₂₃×#389	1	2	yes	—
324	C₂²	C₂₃×#390	1	1	yes	characteristic
325	C₂²	C₂₃×#391	1	1	yes	characteristic
326	C₄	—	2	2	no	—
327	C₄	—	2	2	no	—
328	C₄	—	2	2	no	—
329	C₄	—	8	4	no	—
330	C₄	C₂₃×#344	1	4	yes	complemented
331	C₄	C₂₃×#380	1	2	yes	—
332	C₄	C₂₃×#382	1	1	yes	characteristic
333	C₄	C₂₃×#384	1	1	yes	characteristic
334	C₄	C₂₃×#389	1	2	yes	—
335	C₄	C₂₃×#390	1	1	yes	characteristic
336	C₄	C₂₃×#391	1	1	yes	characteristic
337	C₂	—	2	1	no	—
338	C₂	—	2	2	no	—
339	C₂	—	2	2	no	—
340	C₂	—	2	1	no	—
341	C₂	C₂₃×C₄⋊#95	1	1	yes	characteristic
342	C₂	C₂×C₂₃×#344	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂×C₂²⋊C₄
commutator	C₂³	C₂×C₄²×C₂₃
Frattini, cosocle	C₂³×C₄	C₂³×C₂₃
socle	C₂²×C₂₃	C₂×#95
prime radical	C₂⁴×C₂₃	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
12. C₂×C₂₃×C₄⋊C₈	C₄	semidirect
15. C₄×M₁₆×C₂₃	C₄	semidirect
16. C₄×M₁₆×C₂₃	C₄	semidirect
85. M₁₆×C₂₃	C₄⋊C₄	semidirect
106. #10855	C₂₃	direct (N × H)
163. C₄×C₂₃	#344	semidirect
177. C₂×C₄⋊C₈	C₄×C₂₃	semidirect
180. C₄×M₁₆	C₄×C₂₃	semidirect
181. C₄×M₁₆	C₄×C₂₃	semidirect
231. C₂₃	#10855	direct (N × H)
257. M₁₆	C₄⋊C₄×C₂₃	semidirect
330. C₄	C₂₃×#344	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#423	2
C₂×C₄×M₁₆×C₂₃	2
C₂₃×#2285	2
C₂×C₂₃×#344	2
#10855	23

Subgroups — C23×#10855 #19158481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#10855 #19158481