Subgroups — #15682129

Order 2944.

544 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#67267	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×M₁₆×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₂²⋊D₂₃	C₂	1	1	yes	maximal, characteristic
4	#13092492	C₂	1	2	yes	maximal, complemented
5	#13092491	C₂	1	2	yes	maximal, complemented
6	#13092485	C₂	1	2	yes	maximal, complemented
7	(C₂²⋊D₂₃)⋊C₈	C₂	1	2	yes	maximal, complemented
8	#13092440	C₂	1	1	yes	maximal, characteristic, complemented
9	#13092380	C₂	1	1	yes	maximal, characteristic, complemented
10	M₁₆×Dic₂₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#407	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₄×C₂₃	C₂²	1	1	yes	characteristic
13	C₂²×C₂²⋊D₂₃	C₄	1	1	yes	characteristic
14	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
15	C₂×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
16	C₂×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊Dic₂₃	C₄	1	1	yes	characteristic
18	C₄×C₂²⋊D₂₃	C₄	1	1	yes	characteristic
19	C₄×C₂²⋊D₂₃	C₄	1	1	yes	characteristic
20	C₄×C₂²⋊D₂₃	C₄	1	1	yes	characteristic
21	C₄×C₂²⋊D₂₃	C₄	1	1	yes	characteristic
22	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
23	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
25	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
26	C₂×(C₂×D₂₃)⋊C₄	C₄	1	1	yes	characteristic
27	C₂×Dic₂₃⋊C₄	C₄	1	1	yes	characteristic
28	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic
29	C₂×#67267	—	2	4	no	—
30	C₂×#67267	C₂²	1	1	yes	characteristic
31	C₂×#67267	C₂²	1	1	yes	characteristic
32	C₂×#67267	C₂²	1	2	yes	complemented
33	C₂²×C₂₃⋊C₈	C₂²	1	2	yes	complemented
34	M₁₆×D₂₃	—	2	4	no	—
35	C₂×#67262	C₂²	1	2	yes	complemented
36	C₂×C₈×D₂₃	C₂²	1	2	yes	complemented
37	C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
38	C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
39	(C₂×D₂₃)⋊C₈	C₂²	1	2	yes	complemented
40	(C₂×D₂₃)⋊C₈	C₂²	1	2	yes	complemented
41	#10624997	C₂²	1	2	yes	complemented
42	Dic₂₃⋊C₈	C₂²	1	2	yes	complemented
43	Dic₂₃⋊C₈	C₂²	1	2	yes	complemented
44	C₈×Dic₂₃	C₂²	1	2	yes	complemented
45	C₂⁴×C₂₃	C₂×C₄	1	1	yes	characteristic
46	C₂³×D₂₃	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₄×C₂₃	—	2	2	no	—
48	C₂²×C₄×C₂₃	—	2	2	no	—
49	C₂²×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
53	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
54	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
55	C₂×C₂²⋊D₂₃	—	2	4	no	—
56	C₂×C₂²⋊D₂₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₂²⋊D₂₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₂²⋊D₂₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₂²⋊D₂₃	C₂×C₄	1	1	yes	characteristic
60	C₂²×Dic₂₃	C₂×C₄	1	1	yes	characteristic
61	C₂²×Dic₂₃	C₂×C₄	1	1	yes	characteristic
62	C₂²×Dic₂₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×D₂₃	—	2	2	no	—
64	C₂×C₄×D₂₃	—	2	2	no	—
65	C₂×C₄×D₂₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄×D₂₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
68	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
69	M₁₆×C₂₃	—	2	2	no	—
70	M₁₆×C₂₃	—	2	2	no	—
71	C₂×C₈×C₂₃	C₂³	1	2	yes	—
72	C₂×C₈×C₂₃	C₂³	1	2	yes	—
73	C₂²⋊Dic₂₃	C₂×C₄	1	1	yes	characteristic
74	C₂²⋊Dic₂₃	C₂×C₄	1	1	yes	characteristic
75	C₂²⋊Dic₂₃	C₂×C₄	1	1	yes	characteristic
76	C₂²⋊Dic₂₃	C₂×C₄	1	1	yes	characteristic
77	(C₂×D₂₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
78	(C₂×D₂₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
79	(C₂×D₂₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
80	(C₂×D₂₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
81	Dic₂₃⋊C₄	C₂×C₄	1	1	yes	characteristic
82	Dic₂₃⋊C₄	C₂×C₄	1	1	yes	characteristic
83	Dic₂₃⋊C₄	C₂×C₄	1	1	yes	characteristic
84	Dic₂₃⋊C₄	C₂×C₄	1	1	yes	characteristic
85	C₄×Dic₂₃	C₂×C₄	1	1	yes	characteristic
86	C₄×Dic₂₃	C₂×C₄	1	1	yes	characteristic
87	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
88	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
89	#67267	—	2	2	no	—
90	#67267	—	2	4	no	—
91	#67267	D₄	1	4	yes	complemented
92	C₂×C₂₃⋊C₈	—	2	4	no	—
93	C₂×C₂₃⋊C₈	C₂³	1	2	yes	—
94	C₂×C₂₃⋊C₈	C₂³	1	2	yes	—
95	#67262	—	2	4	no	—
96	C₈×D₂₃	—	2	4	no	—
97	C₂³×C₂₃	—	2	2	no	—
98	C₂³×C₂₃	—	2	2	no	—
99	C₂³×C₂₃	—	4	1	no	—
100	C₂³×C₂₃	C₂²×C₄	1	1	yes	characteristic
101	C₂³×C₂₃	C₂²×C₄	1	1	yes	characteristic
102	C₂³×C₂₃	C₂²×C₄	1	1	yes	characteristic
103	C₂²×D₂₃	—	2	2	no	—
104	C₂²×D₂₃	—	2	2	no	—
105	C₂²×D₂₃	—	4	1	no	—
106	C₂²×D₂₃	C₂²×C₄	1	1	yes	characteristic
107	C₂²×D₂₃	C₂²×C₄	1	1	yes	characteristic
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	1	no	—
112	C₂×C₄×C₂₃	—	2	1	no	—
113	C₂×C₄×C₂₃	—	2	1	no	—
114	C₂×C₄×C₂₃	—	2	1	no	—
115	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×C₂₃	C₂×D₄	1	2	yes	—
119	C₂×C₄×C₂₃	#41	1	2	yes	—
120	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
121	C₂²⋊D₂₃	—	2	2	no	—
122	C₂²⋊D₂₃	—	2	2	no	—
123	C₂²⋊D₂₃	—	2	2	no	—
124	C₂²⋊D₂₃	M₁₆	1	4	yes	complemented
125	C₂×Dic₂₃	—	2	2	no	—
126	C₂×Dic₂₃	—	2	2	no	—
127	C₂×Dic₂₃	—	4	1	no	—
128	C₂×Dic₂₃	C₂²×C₄	1	1	yes	characteristic
129	C₂×Dic₂₃	C₂²×C₄	1	1	yes	characteristic
130	C₂×Dic₂₃	C₂²×C₄	1	1	yes	characteristic
131	C₂×Dic₂₃	C₂²×C₄	1	1	yes	characteristic
132	C₂×Dic₂₃	C₂²×C₄	1	1	yes	characteristic
133	C₂×Dic₂₃	C₂²×C₄	1	1	yes	characteristic
134	C₄×D₂₃	—	2	2	no	—
135	C₄×D₂₃	—	2	2	no	—
136	C₄×D₂₃	—	2	1	no	—
137	C₄×D₂₃	—	2	1	no	—
138	C₄×D₂₃	—	2	1	no	—
139	C₄×D₂₃	—	2	1	no	—
140	C₈×C₂₃	—	2	2	no	—
141	C₈×C₂₃	—	2	2	no	—
142	C₂₃⋊C₈	—	2	2	no	—
143	C₂₃⋊C₈	C₂×D₄	1	4	yes	complemented
144	D₄×M₁₆	—	23	1	no	maximal, Sylow
145	C₂²×C₂₃	—	2	1	no	—
146	C₂²×C₂₃	—	2	1	no	—
147	C₂²×C₂₃	—	2	1	no	—
148	C₂²×C₂₃	—	2	1	no	—
149	C₂²×C₂₃	—	2	1	no	—
150	C₂²×C₂₃	—	2	1	no	—
151	C₂²×C₂₃	—	2	1	no	—
152	C₂²×C₂₃	—	4	4	no	—
153	C₂²×C₂₃	C₄×D₄	1	2	yes	—
154	C₂²×C₂₃	C₂×M₁₆	1	2	yes	complemented
155	C₂²×C₂₃	C₂³×C₄	1	1	yes	characteristic
156	C₂×D₂₃	—	2	1	no	—
157	C₂×D₂₃	—	2	1	no	—
158	C₂×D₂₃	—	2	1	no	—
159	C₂×D₂₃	—	2	1	no	—
160	C₂×D₂₃	—	2	1	no	—
161	C₂×D₂₃	—	4	4	no	—
162	C₂×D₂₃	C₂×M₁₆	1	2	yes	complemented
163	C₄×C₂₃	—	2	1	no	—
164	C₄×C₂₃	—	2	1	no	—
165	C₄×C₂₃	C₄×D₄	1	2	yes	—
166	C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
167	C₄×C₂₃	C₂×#41	1	1	yes	characteristic
168	Dic₂₃	—	2	1	no	—
169	Dic₂₃	—	2	1	no	—
170	Dic₂₃	—	2	1	no	—
171	Dic₂₃	—	2	1	no	—
172	Dic₂₃	—	2	1	no	—
173	Dic₂₃	C₂×M₁₆	1	2	yes	complemented
174	C₂²×M₁₆	—	23	1	no	—
175	C₂²×M₁₆	—	23	1	no	—
176	C₂×C₄×D₄	—	23	1	no	—
177	#436	—	23	2	no	—
178	#435	—	23	2	no	—
179	#435	—	23	2	no	—
180	C₈×D₄	—	23	2	no	—
181	#423	—	23	1	no	—
182	#407	—	23	1	no	—
183	#407	D₂₃	1	1	yes	characteristic, complemented
184	C₄×M₁₆	—	23	1	no	—
185	C₂×C₂₃	—	2	2	no	—
186	C₂×C₂₃	—	2	2	no	—
187	C₂×C₂₃	—	4	1	no	—
188	C₂×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
189	C₂×C₂₃	C₂²×M₁₆	1	1	yes	characteristic
190	C₂×C₂₃	#568	1	1	yes	characteristic
191	D₂₃	—	2	2	no	—
192	D₂₃	—	4	1	no	—
193	C₂²×D₄	—	23	1	no	—
194	C₂³×C₄	—	23	1	no	—
195	C₂³×C₄	C₂×D₂₃	1	1	yes	characteristic
196	C₂×M₁₆	—	23	1	no	—
197	C₂×M₁₆	—	23	1	no	—
198	C₂×M₁₆	—	23	2	no	—
199	C₂×M₁₆	—	23	2	no	—
200	C₂×M₁₆	—	46	4	no	—
201	C₂×M₁₆	—	46	4	no	—
202	C₂×M₁₆	C₂×D₂₃	1	1	yes	characteristic
203	C₂×M₁₆	C₂×D₂₃	1	1	yes	characteristic
204	C₂²×C₈	—	23	2	no	—
205	C₂²×C₈	—	23	2	no	—
206	C₄×D₄	—	23	1	no	—
207	C₄×D₄	—	23	1	no	—
208	C₄×D₄	—	23	1	no	—
209	C₄×D₄	—	23	1	no	—
210	C₄×D₄	—	23	1	no	—
211	C₄×D₄	—	23	1	no	—
212	C₄×D₄	—	23	1	no	—
213	C₄×D₄	—	23	1	no	—
214	C₂×C₄⋊C₄	—	23	1	no	—
215	C₂×C₂²⋊C₄	—	23	1	no	—
216	C₂×C₂²⋊C₄	—	23	1	no	—
217	C₂×C₄²	—	23	1	no	—
218	C₄⋊C₈	—	23	2	no	—
219	C₄⋊C₈	—	23	2	no	—
220	C₂²⋊C₈	—	23	2	no	—
221	C₂²⋊C₈	—	23	2	no	—
222	C₂²⋊C₈	C₂×D₂₃	1	2	yes	complemented
223	C₂²⋊C₈	C₂×D₂₃	1	2	yes	complemented
224	#97	—	23	2	no	—
225	C₄×C₈	—	23	2	no	—
226	C₂₃	D₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
227	C₂⁴	—	23	1	no	—
228	C₂⁴	C₄×D₂₃	1	1	yes	characteristic
229	C₂×D₄	—	23	1	no	—
230	C₂×D₄	—	23	1	no	—
231	C₂×D₄	—	23	1	no	—
232	C₂×D₄	—	23	1	no	—
233	C₂×D₄	—	46	4	no	—
234	C₂²×C₄	—	2	2	no	—
235	C₂²×C₄	—	2	2	no	—
236	C₂²×C₄	—	23	1	no	—
237	C₂²×C₄	—	23	1	no	—
238	C₂²×C₄	—	23	1	no	—
239	C₂²×C₄	—	23	1	no	—
240	C₂²×C₄	—	23	1	no	—
241	C₂²×C₄	—	23	1	no	—
242	C₂²×C₄	—	23	1	no	—
243	C₂²×C₄	—	46	2	no	—
244	C₂²×C₄	—	46	2	no	—
245	C₂²×C₄	C₄×D₂₃	1	1	yes	characteristic
246	C₂²×C₄	C₄×D₂₃	1	1	yes	characteristic
247	C₂²×C₄	C₄×D₂₃	1	1	yes	characteristic
248	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
249	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
250	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
251	M₁₆	—	2	2	no	—
252	M₁₆	—	2	2	no	—
253	M₁₆	—	23	4	no	—
254	M₁₆	—	46	4	no	—
255	M₁₆	—	46	4	no	—
256	M₁₆	—	46	2	no	—
257	C₂×C₈	—	23	2	no	—
258	C₂×C₈	—	23	2	no	—
259	C₂×C₈	—	46	4	no	—
260	C₂×C₈	—	46	4	no	—
261	C₂×C₈	C₂²×D₂₃	1	2	yes	—
262	C₂×C₈	C₂²×D₂₃	1	2	yes	—
263	C₄⋊C₄	—	23	1	no	—
264	C₄⋊C₄	—	23	1	no	—
265	C₄⋊C₄	—	23	1	no	—
266	C₄⋊C₄	—	23	1	no	—
267	C₂²⋊C₄	—	23	1	no	—
268	C₂²⋊C₄	—	23	1	no	—
269	C₂²⋊C₄	—	23	1	no	—
270	C₂²⋊C₄	—	23	1	no	—
271	C₂²⋊C₄	—	23	1	no	—
272	C₂²⋊C₄	—	23	1	no	—
273	C₂²⋊C₄	—	23	1	no	—
274	C₂²⋊C₄	—	23	1	no	—
275	C₄²	—	23	1	no	—
276	C₄²	—	23	1	no	—
277	C₄²	—	23	1	no	—
278	C₄²	—	23	1	no	—
279	C₂³	—	2	2	no	—
280	C₂³	—	2	2	no	—
281	C₂³	—	4	1	no	—
282	C₂³	—	23	1	no	—
283	C₂³	—	23	1	no	—
284	C₂³	—	46	2	no	—
285	C₂³	—	46	2	no	—
286	C₂³	—	92	1	no	—
287	C₂³	C₂×C₄×D₂₃	1	1	yes	characteristic
288	C₂³	C₂×C₄×D₂₃	1	1	yes	characteristic
289	C₂³	C₂×C₄×D₂₃	1	1	yes	characteristic
290	D₄	—	23	4	no	—
291	D₄	—	46	2	no	—
292	D₄	—	46	2	no	—
293	D₄	—	46	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	23	1	no	—
302	C₂×C₄	—	23	1	no	—
303	C₂×C₄	—	23	1	no	—
304	C₂×C₄	—	23	1	no	—
305	C₂×C₄	—	23	1	no	—
306	C₂×C₄	—	23	1	no	—
307	C₂×C₄	—	46	2	no	—
308	C₂×C₄	—	46	2	no	—
309	C₂×C₄	—	46	2	no	—
310	C₂×C₄	—	46	2	no	—
311	C₂×C₄	—	46	1	no	—
312	C₂×C₄	—	46	1	no	—
313	C₂×C₄	—	46	1	no	—
314	C₂×C₄	—	46	1	no	—
315	C₂×C₄	—	92	1	no	—
316	C₂×C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
317	C₂×C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
318	C₂×C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
319	C₂×C₄	D₄×D₂₃	1	2	yes	—
320	C₂×C₄	#67290	1	2	yes	—
321	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
322	C₈	—	2	2	no	—
323	C₈	—	2	2	no	—
324	C₈	—	23	4	no	—
325	C₈	—	46	2	no	—
326	C₂²	—	2	1	no	—
327	C₂²	—	2	1	no	—
328	C₂²	—	2	1	no	—
329	C₂²	—	2	1	no	—
330	C₂²	—	2	1	no	—
331	C₂²	—	2	1	no	—
332	C₂²	—	2	1	no	—
333	C₂²	—	4	4	no	—
334	C₂²	—	23	2	no	—
335	C₂²	—	46	1	no	—
336	C₂²	—	46	1	no	—
337	C₂²	—	46	1	no	—
338	C₂²	—	46	1	no	—
339	C₂²	—	46	1	no	—
340	C₂²	—	92	4	no	—
341	C₂²	(C₂²⋊D₂₃)⋊C₄	1	2	yes	—
342	C₂²	M₁₆×D₂₃	1	2	yes	complemented
343	C₂²	C₂²×C₄×D₂₃	1	1	yes	characteristic
344	C₄	—	2	1	no	—
345	C₄	—	2	1	no	—
346	C₄	—	23	2	no	—
347	C₄	—	46	1	no	—
348	C₄	—	46	1	no	—
349	C₄	—	46	1	no	—
350	C₄	—	46	1	no	—
351	C₄	—	46	1	no	—
352	C₄	(C₂²⋊D₂₃)⋊C₄	1	2	yes	—
353	C₄	C₂×D₄×D₂₃	1	1	yes	characteristic
354	C₄	C₂×#67290	1	1	yes	characteristic
355	C₂	—	2	2	no	—
356	C₂	—	2	2	no	—
357	C₂	—	4	1	no	—
358	C₂	—	46	2	no	—
359	C₂	—	92	1	no	—
360	C₂	C₂×(C₂²⋊D₂₃)⋊C₄	1	1	yes	characteristic
361	C₂	C₂×M₁₆×D₂₃	1	1	yes	characteristic
362	C₂	#13093183	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₂₃
commutator, socle	C₂²×C₂₃	C₂³×C₄
Fitting	C₂₃×#407	C₂
prime radical	C₂²×C₂²⋊D₂₃	C₄
cosocle	C₂×C₄×C₂₃	C₂⁴
hypercenter	#407	D₂₃
hypocenter	C₂₃	D₄×M₁₆
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ #407

Complements

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

N	H ≅ G/N	type
1. C₂²×#67267	C₂	semidirect
2. C₂×M₁₆×D₂₃	C₂	semidirect
4. #13092492	C₂	semidirect
5. #13092491	C₂	semidirect
6. #13092485	C₂	semidirect
7. (C₂²⋊D₂₃)⋊C₈	C₂	semidirect
8. #13092440	C₂	semidirect
9. #13092380	C₂	semidirect
10. M₁₆×Dic₂₃	C₂	semidirect
11. C₂₃×#407	C₂	semidirect
32. C₂×#67267	C₂²	semidirect
33. C₂²×C₂₃⋊C₈	C₂²	semidirect
35. C₂×#67262	C₂²	semidirect
36. C₂×C₈×D₂₃	C₂²	semidirect
37. C₂₃×C₂²⋊C₈	C₂²	semidirect
38. C₂₃×C₂²⋊C₈	C₂²	semidirect
39. (C₂×D₂₃)⋊C₈	C₂²	semidirect
40. (C₂×D₂₃)⋊C₈	C₂²	semidirect
41. #10624997	C₂²	semidirect
42. Dic₂₃⋊C₈	C₂²	semidirect
43. Dic₂₃⋊C₈	C₂²	semidirect
44. C₈×Dic₂₃	C₂²	semidirect
91. #67267	D₄	semidirect
124. C₂²⋊D₂₃	M₁₆	semidirect
143. C₂₃⋊C₈	C₂×D₄	semidirect
154. C₂²×C₂₃	C₂×M₁₆	semidirect
162. C₂×D₂₃	C₂×M₁₆	semidirect
173. Dic₂₃	C₂×M₁₆	semidirect
183. #407	D₂₃	semidirect
222. C₂²⋊C₈	C₂×D₂₃	semidirect
223. C₂²⋊C₈	C₂×D₂₃	semidirect
226. C₂₃	D₄×M₁₆	semidirect
342. C₂²	M₁₆×D₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#67267	2
C₂×M₁₆×D₂₃	2
C₂×C₄×C₂²⋊D₂₃	2
#13092492	2
#13092491	2
#13092485	2
(C₂²⋊D₂₃)⋊C₈	2
#13092440	2
#13092380	2
M₁₆×Dic₂₃	2
C₂₃×#407	2
D₄×M₁₆	23