Subgroups — #15683881

Order 2944.

596 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10625085	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10625082	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10625087	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₈×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#13092985	C₂	1	1	yes	maximal, characteristic, complemented
6	#13092980	C₂	1	1	yes	maximal, characteristic, complemented
7	#13092806	C₂	1	1	yes	maximal, characteristic, complemented
8	#13092805	C₂	1	1	yes	maximal, characteristic, complemented
9	#13092803	C₂	1	1	yes	maximal, characteristic, complemented
10	#13092799	C₂	1	1	yes	maximal, characteristic, complemented
11	#13092798	C₂	1	1	yes	maximal, characteristic, complemented
12	#13092793	C₂	1	1	yes	maximal, characteristic, complemented
13	#13092792	C₂	1	1	yes	maximal, characteristic, complemented
14	#13092374	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#496	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#67292	C₂²	1	1	yes	characteristic
17	C₂×#67290	C₂²	1	1	yes	characteristic
18	C₂×D₄×D₂₃	C₂²	1	1	yes	characteristic
19	C₂×D₄×D₂₃	C₂²	1	1	yes	characteristic
20	C₂×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
21	C₂×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
22	C₂×D₈×C₂₃	C₂²	1	1	yes	characteristic
23	C₂×D₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
24	C₂₃×#127	C₂²	1	1	yes	characteristic, complemented
25	C₂₃×#124	C₂²	1	1	yes	characteristic, complemented
26	#10625118	C₂²	1	1	yes	characteristic, complemented
27	C₂×#67275	C₂²	1	1	yes	characteristic, complemented
28	C₂×#67274	C₂²	1	1	yes	characteristic, complemented
29	#10625111	C₂²	1	1	yes	characteristic, complemented
30	#10625111	C₂²	1	1	yes	characteristic, complemented
31	#10625110	—	2	2	no	—
32	#10625108	—	2	2	no	—
33	#10625107	C₂²	1	1	yes	characteristic, complemented
34	C₂×#67273	C₂²	1	1	yes	characteristic, complemented
35	C₂×#67272	C₂²	1	1	yes	characteristic
36	C₂×#67272	C₂²	1	1	yes	characteristic
37	C₂×#67272	C₂²	1	1	yes	characteristic, complemented
38	C₂×#67272	C₂²	1	1	yes	characteristic, complemented
39	C₂×#67272	C₂²	1	1	yes	characteristic, complemented
40	#10625087	—	2	4	no	—
41	#10625085	—	2	4	no	—
42	#10625082	—	2	4	no	—
43	D₈×D₂₃	—	2	4	no	—
44	C₂×D₁₈₄	C₂²	1	1	yes	characteristic
45	C₂×D₁₈₄	C₂²	1	1	yes	characteristic, complemented
46	C₂×#67263	C₂²	1	1	yes	characteristic, complemented
47	C₂×#67263	C₂²	1	1	yes	characteristic, complemented
48	C₂×#67262	C₂²	1	1	yes	characteristic
49	C₂×C₈×D₂₃	C₂²	1	1	yes	characteristic
50	#10625055	—	2	2	no	—
51	#10625053	—	2	2	no	—
52	#10625046	C₂²	1	1	yes	characteristic, complemented
53	#10625045	C₂²	1	1	yes	characteristic, complemented
54	#10625043	C₂²	1	1	yes	characteristic
55	C₂₃×#97	C₂²	1	1	yes	characteristic, complemented
56	#10624997	C₂²	1	1	yes	characteristic, complemented
57	C₈×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
58	C₄×C₂₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
59	C₂³×D₂₃	—	2	1	no	—
60	C₂³×D₂₃	—	2	1	no	—
61	C₂×Q₈×C₂₃	C₂³	1	1	yes	characteristic
62	C₂×D₄×C₂₃	—	2	2	no	—
63	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
64	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
65	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊D₂₃	—	2	1	no	—
67	C₂×C₂²⋊D₂₃	—	2	1	no	—
68	C₂×C₂²⋊D₂₃	—	2	1	no	—
69	C₂×C₂²⋊D₂₃	—	2	2	no	—
70	C₂×C₂²⋊D₂₃	—	2	2	no	—
71	C₂²×Dic₂₃	—	2	1	no	—
72	#67292	—	2	2	no	—
73	#67292	—	2	2	no	—
74	#67290	—	2	2	no	—
75	#67290	—	2	2	no	—
76	D₄×D₂₃	—	2	2	no	—
77	D₄×D₂₃	—	2	2	no	—
78	D₄×D₂₃	—	2	2	no	—
79	D₄×D₂₃	—	2	2	no	—
80	C₂×D₉₂	—	2	1	no	—
81	C₂×D₉₂	—	2	2	no	—
82	C₂×D₉₂	C₂³	1	1	yes	characteristic
83	C₂×D₉₂	C₂³	1	1	yes	characteristic
84	C₂×D₉₂	C₂³	1	1	yes	characteristic
85	C₂×C₄×D₂₃	—	2	1	no	—
86	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
87	C₂×Dic₄₆	C₂³	1	1	yes	characteristic
88	SD₁₆×C₂₃	—	2	2	no	—
89	SD₁₆×C₂₃	—	2	2	no	—
90	D₈×C₂₃	—	2	2	no	—
91	D₈×C₂₃	—	2	2	no	—
92	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
93	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
94	C₂²⋊C₄×C₂₃	—	2	2	no	—
95	C₄²×C₂₃	C₂³	1	1	yes	characteristic
96	C₂²⋊Dic₂₃	—	2	2	no	—
97	#67275	—	2	2	no	—
98	#67274	—	2	2	no	—
99	#67273	—	2	2	no	—
100	#67272	—	2	2	no	—
101	#67272	—	2	2	no	—
102	#67272	—	2	2	no	—
103	#67272	—	2	2	no	—
104	#67272	—	2	2	no	—
105	(C₂×D₂₃)⋊C₄	—	2	2	no	—
106	(C₂×D₂₃)⋊C₄	—	2	2	no	—
107	(C₂×D₂₃)⋊C₄	D₄	1	2	yes	—
108	Dic₂₃⋊C₄	D₄	1	2	yes	—
109	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
110	C₂×C₂₃⋊C₈	C₂³	1	1	yes	characteristic
111	C₂×C₂₃⋊C₈	C₂³	1	1	yes	characteristic
112	D₁₈₄	—	2	2	no	—
113	D₁₈₄	—	2	2	no	—
114	#67263	—	2	2	no	—
115	#67263	—	2	2	no	—
116	#67262	D₄	1	4	yes	complemented
117	C₈×D₂₃	D₄	1	4	yes	complemented
118	C₂³×C₂₃	—	2	1	no	—
119	C₂³×C₂₃	—	2	1	no	—
120	C₂³×C₂₃	—	2	1	no	—
121	C₂²×D₂₃	—	2	1	no	—
122	C₂²×D₂₃	—	2	1	no	—
123	C₂²×D₂₃	—	2	1	no	—
124	C₂²×D₂₃	—	4	2	no	—
125	C₂²×D₂₃	—	4	2	no	—
126	C₂²×D₂₃	—	8	2	no	—
127	C₂²×D₂₃	—	8	2	no	—
128	C₂²×D₂₃	C₂×D₄	1	1	yes	characteristic
129	Q₈×C₂₃	—	2	1	no	—
130	Q₈×C₂₃	—	2	1	no	—
131	D₄×C₂₃	—	2	1	no	—
132	D₄×C₂₃	—	2	1	no	—
133	D₄×C₂₃	—	2	1	no	—
134	D₄×C₂₃	—	2	1	no	—
135	D₄×C₂₃	—	2	1	no	—
136	D₄×C₂₃	—	2	1	no	—
137	D₄×C₂₃	—	8	2	no	—
138	C₂×C₄×C₂₃	—	2	1	no	—
139	C₂×C₄×C₂₃	C₂×D₄	1	2	yes	—
140	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
141	C₂²⋊D₂₃	—	4	2	no	—
142	C₂²⋊D₂₃	—	4	2	no	—
143	C₂²⋊D₂₃	—	4	2	no	—
144	C₂²⋊D₂₃	—	8	2	no	—
145	C₂²⋊D₂₃	—	8	2	no	—
146	C₂×Dic₂₃	—	2	1	no	—
147	C₂×Dic₂₃	—	4	2	no	—
148	C₂×Dic₂₃	C₂×D₄	1	2	yes	—
149	C₂×Dic₂₃	C₂×D₄	1	1	yes	characteristic
150	D₉₂	—	2	1	no	—
151	D₉₂	—	2	1	no	—
152	D₉₂	—	2	1	no	—
153	D₉₂	—	2	1	no	—
154	D₉₂	—	2	1	no	—
155	D₉₂	—	2	1	no	—
156	D₉₂	—	4	2	no	—
157	D₉₂	—	8	2	no	—
158	C₄×D₂₃	—	4	2	no	—
159	C₄×D₂₃	C₂×D₄	1	2	yes	—
160	C₄×D₂₃	C₂×D₄	1	2	yes	—
161	Dic₄₆	—	2	1	no	—
162	Dic₄₆	—	2	1	no	—
163	C₈×C₂₃	C₂×D₄	1	2	yes	—
164	C₈×C₂₃	C₂×D₄	1	2	yes	—
165	C₂₃⋊C₈	C₂×D₄	1	2	yes	—
166	C₂₃⋊C₈	C₂×D₄	1	2	yes	—
167	#3155	—	23	1	no	maximal, Sylow
168	C₂²×C₂₃	—	4	1	no	—
169	C₂²×C₂₃	—	4	1	no	—
170	C₂²×C₂₃	—	4	1	no	—
171	C₂²×C₂₃	—	4	2	no	—
172	C₂²×C₂₃	—	4	2	no	—
173	C₂²×C₂₃	—	4	2	no	—
174	C₂²×C₂₃	C₂²×D₄	1	1	yes	characteristic
175	C₂×D₂₃	—	2	2	no	—
176	C₂×D₂₃	—	4	1	no	—
177	C₂×D₂₃	—	4	1	no	—
178	C₂×D₂₃	—	4	1	no	—
179	C₂×D₂₃	—	4	2	no	—
180	C₂×D₂₃	—	4	2	no	—
181	C₂×D₂₃	—	4	2	no	—
182	C₂×D₂₃	—	8	4	no	—
183	C₂×D₂₃	—	8	4	no	—
184	C₂×D₂₃	#127	1	2	yes	—
185	C₄×C₂₃	—	2	2	no	—
186	C₄×C₂₃	—	4	1	no	—
187	C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
188	C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
189	Dic₂₃	—	2	2	no	—
190	Dic₂₃	—	4	1	no	—
191	Dic₂₃	#127	1	2	yes	—
192	C₂×AGL(1,ℤ/8)	—	23	1	no	—
193	C₂×AGL(1,ℤ/8)	—	23	1	no	—
194	C₂×#135	—	23	1	no	—
195	C₂²×D₈	—	23	1	no	—
196	#535	—	23	1	no	—
197	#535	—	23	1	no	—
198	#496	—	23	1	no	—
199	#496	—	23	1	no	—
200	#496	—	23	1	no	—
201	#496	D₂₃	1	1	yes	characteristic, complemented
202	#495	—	23	1	no	—
203	#495	—	23	1	no	—
204	#493	—	23	1	no	—
205	#493	—	23	1	no	—
206	#405	—	23	1	no	—
207	C₂×C₂₃	—	8	1	no	—
208	C₂×C₂₃	—	8	1	no	—
209	C₂×C₂₃	—	8	1	no	—
210	C₂×C₂₃	C₂×#127	1	1	yes	characteristic
211	C₂×C₂₃	#576	1	2	yes	—
212	D₂₃	—	2	2	no	—
213	D₂₃	—	8	1	no	—
214	D₂₃	—	8	1	no	—
215	D₂₃	—	8	1	no	—
216	C₂×#41	—	23	1	no	—
217	C₂×#41	—	23	1	no	—
218	C₂²×D₄	—	23	1	no	—
219	C₂²×D₄	—	23	1	no	—
220	AGL(1,ℤ/8)	—	46	4	no	—
221	AGL(1,ℤ/8)	—	46	4	no	—
222	#135	—	46	4	no	—
223	C₂×Q₁₆	—	23	1	no	—
224	C₂×SD₁₆	—	23	1	no	—
225	C₂×SD₁₆	—	23	1	no	—
226	C₂×SD₁₆	—	23	1	no	—
227	C₂×SD₁₆	—	23	1	no	—
228	C₂×SD₁₆	C₂×D₂₃	1	1	yes	characteristic, complemented
229	C₂×SD₁₆	C₂×D₂₃	1	1	yes	characteristic, complemented
230	C₂×D₈	—	23	1	no	—
231	C₂×D₈	—	23	1	no	—
232	C₂×D₈	—	23	1	no	—
233	C₂×D₈	—	23	1	no	—
234	C₂×D₈	—	23	1	no	—
235	C₂×D₈	—	23	1	no	—
236	C₂×D₈	—	23	1	no	—
237	C₂×D₈	—	46	4	no	—
238	C₂×D₈	C₂×D₂₃	1	1	yes	characteristic
239	C₂×D₈	C₂×D₂₃	1	1	yes	characteristic, complemented
240	C₂×M₁₆	—	23	1	no	—
241	C₂²×C₈	—	23	1	no	—
242	#127	—	23	1	no	—
243	#127	—	23	1	no	—
244	#127	—	23	1	no	—
245	#127	C₂×D₂₃	1	1	yes	characteristic, complemented
246	#124	—	23	1	no	—
247	#124	—	23	1	no	—
248	#124	—	23	1	no	—
249	#124	C₂×D₂₃	1	1	yes	characteristic, complemented
250	#121	—	46	2	no	—
251	#121	—	46	2	no	—
252	#120	—	46	2	no	—
253	#120	—	46	2	no	—
254	#117	—	23	1	no	—
255	#97	—	23	1	no	—
256	#97	C₂×D₂₃	1	1	yes	characteristic, complemented
257	C₄×C₈	—	23	1	no	—
258	C₄×C₈	—	23	1	no	—
259	C₂₃	#3155	1	1	yes	characteristic, complemented, Sylow
260	C₂⁴	—	46	1	no	—
261	C₂⁴	—	46	1	no	—
262	#41	—	46	2	no	—
263	#41	—	46	2	no	—
264	#41	—	46	2	no	—
265	#41	—	46	2	no	—
266	C₂×Q₈	—	23	1	no	—
267	C₂×Q₈	C₂²×D₂₃	1	1	yes	characteristic
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	23	1	no	—
270	C₂×D₄	—	23	1	no	—
271	C₂×D₄	—	23	1	no	—
272	C₂×D₄	—	46	1	no	—
273	C₂×D₄	—	46	2	no	—
274	C₂×D₄	—	46	2	no	—
275	C₂×D₄	—	46	2	no	—
276	C₂×D₄	—	46	2	no	—
277	C₂×D₄	—	46	1	no	—
278	C₂×D₄	—	46	1	no	—
279	C₂×D₄	—	46	2	no	—
280	C₂×D₄	—	46	2	no	—
281	C₂×D₄	—	46	1	no	—
282	C₂×D₄	—	46	2	no	—
283	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
284	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
285	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
286	C₂²×C₄	—	23	1	no	—
287	C₂²×C₄	—	46	1	no	—
288	C₂²×C₄	—	46	1	no	—
289	Q₁₆	—	46	2	no	—
290	SD₁₆	—	2	2	no	—
291	SD₁₆	—	2	2	no	—
292	SD₁₆	—	46	2	no	—
293	SD₁₆	—	46	2	no	—
294	SD₁₆	—	46	2	no	—
295	SD₁₆	—	46	2	no	—
296	D₈	—	2	2	no	—
297	D₈	—	2	2	no	—
298	D₈	—	46	2	no	—
299	D₈	—	46	2	no	—
300	D₈	—	46	2	no	—
301	D₈	—	46	2	no	—
302	D₈	—	46	2	no	—
303	D₈	—	46	2	no	—
304	D₈	—	46	2	no	—
305	M₁₆	—	23	4	no	—
306	C₂×C₈	—	23	1	no	—
307	C₂×C₈	—	23	1	no	—
308	C₂×C₈	—	23	4	no	—
309	C₂×C₈	C₂²×D₂₃	1	1	yes	characteristic
310	C₂×C₈	C₂²×D₂₃	1	1	yes	characteristic
311	C₄⋊C₄	—	23	2	no	—
312	C₂²⋊C₄	—	2	2	no	—
313	C₂²⋊C₄	—	23	2	no	—
314	C₂²⋊C₄	—	46	2	no	—
315	C₂²⋊C₄	—	46	2	no	—
316	C₂²⋊C₄	—	46	2	no	—
317	C₄²	—	23	1	no	—
318	C₄²	C₂²×D₂₃	1	1	yes	characteristic
319	C₂³	—	2	1	no	—
320	C₂³	—	2	1	no	—
321	C₂³	—	2	1	no	—
322	C₂³	—	23	1	no	—
323	C₂³	—	46	1	no	—
324	C₂³	—	46	1	no	—
325	C₂³	—	46	1	no	—
326	C₂³	—	92	2	no	—
327	C₂³	—	92	2	no	—
328	C₂³	—	184	2	no	—
329	C₂³	—	184	2	no	—
330	Q₈	—	2	1	no	—
331	Q₈	—	2	1	no	—
332	Q₈	—	46	1	no	—
333	Q₈	—	46	1	no	—
334	D₄	—	2	1	no	—
335	D₄	—	2	1	no	—
336	D₄	—	2	1	no	—
337	D₄	—	2	1	no	—
338	D₄	—	2	1	no	—
339	D₄	—	2	1	no	—
340	D₄	—	8	2	no	—
341	D₄	—	46	1	no	—
342	D₄	—	46	1	no	—
343	D₄	—	46	1	no	—
344	D₄	—	46	1	no	—
345	D₄	—	46	1	no	—
346	D₄	—	46	1	no	—
347	D₄	—	92	2	no	—
348	D₄	—	92	2	no	—
349	D₄	—	92	2	no	—
350	D₄	—	92	2	no	—
351	D₄	—	184	2	no	—
352	D₄	—	184	2	no	—
353	D₄	—	184	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	23	1	no	—
356	C₂×C₄	—	23	2	no	—
357	C₂×C₄	—	23	2	no	—
358	C₂×C₄	—	23	2	no	—
359	C₂×C₄	—	46	1	no	—
360	C₂×C₄	—	92	2	no	—
361	C₂×C₄	—	92	2	no	—
362	C₂×C₄	D₄×D₂₃	1	2	yes	—
363	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
364	C₈	—	23	2	no	—
365	C₈	—	23	2	no	—
366	C₈	D₄×D₂₃	1	2	yes	—
367	C₈	D₄×D₂₃	1	2	yes	—
368	C₂²	—	4	1	no	—
369	C₂²	—	4	1	no	—
370	C₂²	—	4	1	no	—
371	C₂²	—	4	2	no	—
372	C₂²	—	4	2	no	—
373	C₂²	—	4	2	no	—
374	C₂²	—	23	2	no	—
375	C₂²	—	46	2	no	—
376	C₂²	—	92	1	no	—
377	C₂²	—	92	1	no	—
378	C₂²	—	92	1	no	—
379	C₂²	—	92	2	no	—
380	C₂²	—	92	2	no	—
381	C₂²	—	92	2	no	—
382	C₂²	—	184	4	no	—
383	C₂²	—	184	4	no	—
384	C₂²	C₂×D₄×D₂₃	1	1	yes	characteristic
385	C₄	—	2	2	no	—
386	C₄	—	4	1	no	—
387	C₄	—	23	2	no	—
388	C₄	—	46	2	no	—
389	C₄	—	92	1	no	—
390	C₄	C₂×D₄×D₂₃	1	1	yes	characteristic
391	C₄	C₂×D₄×D₂₃	1	1	yes	characteristic
392	C₂	—	8	1	no	—
393	C₂	—	8	1	no	—
394	C₂	—	8	1	no	—
395	C₂	—	46	2	no	—
396	C₂	—	184	1	no	—
397	C₂	—	184	1	no	—
398	C₂	—	184	1	no	—
399	C₂	#127×D₂₃	1	1	yes	characteristic
400	C₂	#13093221	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₄×D₂₃
commutator, cosocle	C₂×C₄×C₂₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₂₃
Fitting	C₂₃×#496	C₂
socle	C₂²×C₂₃	C₂²×D₄
hypercenter	#496	D₂₃
hypocenter	C₂₃	#3155
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #496

Complements

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

N	H ≅ G/N	type
1. C₂×#10625085	C₂	semidirect
2. C₂×#10625082	C₂	semidirect
3. C₂×#10625087	C₂	semidirect
4. C₂×D₈×D₂₃	C₂	semidirect
5. #13092985	C₂	semidirect
6. #13092980	C₂	semidirect
7. #13092806	C₂	semidirect
8. #13092805	C₂	semidirect
9. #13092803	C₂	semidirect
10. #13092799	C₂	semidirect
11. #13092798	C₂	semidirect
12. #13092793	C₂	semidirect
13. #13092792	C₂	semidirect
14. #13092374	C₂	semidirect
15. C₂₃×#496	C₂	semidirect
20. C₂×SD₁₆×C₂₃	C₂²	semidirect
21. C₂×SD₁₆×C₂₃	C₂²	semidirect
23. C₂×D₈×C₂₃	C₂²	semidirect
24. C₂₃×#127	C₂²	semidirect
25. C₂₃×#124	C₂²	semidirect
26. #10625118	C₂²	semidirect
27. C₂×#67275	C₂²	semidirect
28. C₂×#67274	C₂²	semidirect
29. #10625111	C₂²	semidirect
30. #10625111	C₂²	semidirect
33. #10625107	C₂²	semidirect
34. C₂×#67273	C₂²	semidirect
37. C₂×#67272	C₂²	semidirect
38. C₂×#67272	C₂²	semidirect
39. C₂×#67272	C₂²	semidirect
45. C₂×D₁₈₄	C₂²	semidirect
46. C₂×#67263	C₂²	semidirect
47. C₂×#67263	C₂²	semidirect
52. #10625046	C₂²	semidirect
53. #10625045	C₂²	semidirect
55. C₂₃×#97	C₂²	semidirect
56. #10624997	C₂²	semidirect
57. C₈×Dic₂₃	C₂²	semidirect
58. C₄×C₂₃⋊C₈	C₂²	semidirect
116. #67262	D₄	semidirect
117. C₈×D₂₃	D₄	semidirect
201. #496	D₂₃	semidirect
228. C₂×SD₁₆	C₂×D₂₃	semidirect
229. C₂×SD₁₆	C₂×D₂₃	semidirect
239. C₂×D₈	C₂×D₂₃	semidirect
245. #127	C₂×D₂₃	semidirect
249. #124	C₂×D₂₃	semidirect
256. #97	C₂×D₂₃	semidirect
259. C₂₃	#3155	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10625085	2
C₂×#10625082	2
C₂×#10625087	2
C₂×D₈×D₂₃	2
#13092985	2
#13092980	2
#13092806	2
#13092805	2
#13092803	2
#13092799	2
#13092798	2
#13092793	2
#13092792	2
#13092374	2
C₂₃×#496	2
#3155	23