Subgroups — #15682202

Order 2944.

548 conjugacy classes of subgroups.

The subgroup lattice has 384 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
2	C₄×#67292	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#13092530	C₂	1	1	yes	maximal, characteristic, complemented
5	#13092527	C₂	1	1	yes	maximal, characteristic, complemented
6	#13092515	C₂	1	1	yes	maximal, characteristic, complemented
7	SD₁₆×Dic₂₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#13092502	C₂	1	1	yes	maximal, characteristic, complemented
9	#13092499	C₂	1	1	yes	maximal, characteristic, complemented
10	#13092497	C₂	1	1	yes	maximal, characteristic, complemented
11	#13092458	C₂	1	1	yes	maximal, characteristic, complemented
12	#13092420	C₂	1	1	yes	maximal, characteristic, complemented
13	#13092417	C₂	1	1	yes	maximal, characteristic, complemented
14	#13092369	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#440	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#67292	C₂²	1	1	yes	characteristic
17	C₂×D₄×D₂₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₂₃	—	2	1	no	—
19	C₂×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
20	C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
21	C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
22	Q₈×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
23	C₂×#67274	C₂²	1	1	yes	characteristic
24	D₄×Dic₂₃	C₂²	1	1	yes	characteristic
25	C₂×#67272	C₂²	1	1	yes	characteristic
26	C₄×C₂²⋊D₂₃	—	2	1	no	—
27	#10625085	C₄	1	8	yes	complemented
28	C₂×D₁₈₄	C₂²	1	1	yes	characteristic
29	C₂×#67262	C₂²	1	1	yes	characteristic
30	C₂×#67262	C₂²	1	1	yes	characteristic
31	#10625064	—	2	1	no	—
32	#10625064	C₂²	1	1	yes	characteristic
33	#10625064	C₂²	1	1	yes	characteristic, complemented
34	#10625063	—	2	1	no	—
35	#10625063	C₂²	1	1	yes	characteristic
36	C₄⋊C₄×D₂₃	C₂²	1	1	yes	characteristic
37	(C₂²⋊D₂₃)⋊C₄	—	2	1	no	—
38	C₂²⋊C₄×D₂₃	—	2	1	no	—
39	C₄×D₉₂	—	2	1	no	—
40	C₄×D₉₂	C₂²	1	1	yes	characteristic
41	C₄×D₉₂	C₂²	1	1	yes	characteristic, complemented
42	C₄²×D₂₃	—	2	1	no	—
43	C₄²×D₂₃	C₂²	1	1	yes	characteristic
44	C₂₃×#107	C₂²	1	1	yes	characteristic, complemented
45	C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
46	C₂₃×#102	C₂²	1	1	yes	characteristic
47	C₂₃×#97	C₂²	1	1	yes	characteristic, complemented
48	#10625017	C₂²	1	1	yes	characteristic, complemented
49	#10625014	C₂²	1	1	yes	characteristic
50	#10625003	C₂²	1	1	yes	characteristic
51	#10625003	C₂²	1	1	yes	characteristic, complemented
52	#10624999	C₂²	1	1	yes	characteristic, complemented
53	C₈×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
54	C₈×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
55	#10624991	C₂²	1	1	yes	characteristic
56	#10624991	C₂²	1	1	yes	characteristic, complemented
57	#10624990	C₂²	1	1	yes	characteristic, complemented
58	#10624989	C₂²	1	1	yes	characteristic, complemented
59	#10624985	C₂²	1	1	yes	characteristic, complemented
60	C₂³×D₂₃	—	2	1	no	—
61	C₂×Q₈×C₂₃	C₂³	1	1	yes	characteristic
62	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₂₃	—	2	1	no	—
64	C₂×C₂²⋊D₂₃	—	2	1	no	—
65	C₂²×Dic₂₃	—	2	1	no	—
66	#67292	—	2	2	no	—
67	#67292	C₂×C₄	1	4	yes	complemented
68	D₄×D₂₃	—	2	2	no	—
69	D₄×D₂₃	C₂×C₄	1	4	yes	complemented
70	C₂×D₉₂	—	2	1	no	—
71	C₂×D₉₂	C₂³	1	1	yes	characteristic
72	C₂×D₉₂	C₂³	1	1	yes	characteristic
73	C₂×C₄×D₂₃	—	2	1	no	—
74	C₂×C₄×D₂₃	—	2	1	no	—
75	C₂×C₄×D₂₃	—	2	1	no	—
76	C₂×C₄×D₂₃	—	2	1	no	—
77	C₂×C₄×D₂₃	—	2	1	no	—
78	C₂×C₄×D₂₃	—	2	1	no	—
79	C₂×C₄×D₂₃	—	4	4	no	—
80	C₂×C₄×D₂₃	D₄	1	1	yes	characteristic
81	C₂×C₄×D₂₃	D₄	1	1	yes	characteristic
82	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
83	SD₁₆×C₂₃	C₂×C₄	1	4	yes	complemented
84	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
85	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
86	C₄⋊C₄×C₂₃	—	2	1	no	—
87	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
88	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
89	C₂²⋊C₄×C₂₃	—	2	1	no	—
90	C₄²×C₂₃	—	2	1	no	—
91	C₄²×C₂₃	C₂³	1	1	yes	characteristic
92	C₂²⋊Dic₂₃	—	2	1	no	—
93	#67274	C₂×C₄	1	4	yes	complemented
94	#67272	C₂×C₄	1	4	yes	complemented
95	(C₂×D₂₃)⋊C₄	—	2	1	no	—
96	(C₂×D₂₃)⋊C₄	—	2	1	no	—
97	(C₂×D₂₃)⋊C₄	—	2	1	no	—
98	(C₂×D₂₃)⋊C₄	—	2	1	no	—
99	(C₂×D₂₃)⋊C₄	—	2	1	no	—
100	C₄⋊Dic₂₃	—	2	1	no	—
101	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
102	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
103	Dic₂₃⋊C₄	—	2	1	no	—
104	C₄×Dic₂₃	—	2	1	no	—
105	C₄×Dic₂₃	—	2	1	no	—
106	C₄×Dic₂₃	D₄	1	1	yes	characteristic
107	C₄×Dic₂₃	D₄	1	1	yes	characteristic
108	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
109	C₂×C₂₃⋊C₈	C₂³	1	1	yes	characteristic
110	C₂×C₂₃⋊C₈	C₂³	1	1	yes	characteristic
111	D₁₈₄	C₂×C₄	1	4	yes	complemented
112	#67262	—	2	2	no	—
113	#67262	C₂×C₄	1	4	yes	complemented
114	C₂³×C₂₃	—	2	1	no	—
115	C₂²×D₂₃	—	2	1	no	—
116	C₂²×D₂₃	—	2	1	no	—
117	C₂²×D₂₃	—	2	4	no	—
118	C₂²×D₂₃	—	4	2	no	—
119	C₂²×D₂₃	—	4	2	no	—
120	C₂²×D₂₃	C₂×D₄	1	1	yes	characteristic
121	Q₈×C₂₃	—	2	1	no	—
122	Q₈×C₂₃	C₂²×C₄	1	2	yes	complemented
123	D₄×C₂₃	—	2	1	no	—
124	D₄×C₂₃	C₂²×C₄	1	2	yes	—
125	C₂×C₄×C₂₃	—	2	1	no	—
126	C₂×C₄×C₂₃	—	2	1	no	—
127	C₂×C₄×C₂₃	—	2	1	no	—
128	C₂×C₄×C₂₃	—	4	2	no	—
129	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
130	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
131	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
132	C₂²⋊D₂₃	—	2	4	no	—
133	C₂×Dic₂₃	—	2	1	no	—
134	C₂×Dic₂₃	—	2	1	no	—
135	C₂×Dic₂₃	—	4	2	no	—
136	C₂×Dic₂₃	C₂×D₄	1	1	yes	characteristic
137	C₂×Dic₂₃	C₂×D₄	1	1	yes	characteristic
138	C₂×Dic₂₃	C₂×D₄	1	1	yes	characteristic
139	D₉₂	—	2	4	no	—
140	D₉₂	—	2	1	no	—
141	D₉₂	—	2	1	no	—
142	D₉₂	C₂²×C₄	1	2	yes	—
143	D₉₂	C₂²×C₄	1	2	yes	complemented
144	C₄×D₂₃	—	2	4	no	—
145	C₄×D₂₃	—	2	2	no	—
146	C₄×D₂₃	—	4	1	no	—
147	C₄×D₂₃	—	4	2	no	—
148	C₄×D₂₃	—	4	2	no	—
149	C₄×D₂₃	—	4	2	no	—
150	C₄×D₂₃	—	4	2	no	—
151	C₄×D₂₃	—	4	2	no	—
152	C₄×D₂₃	C₂²×C₄	1	2	yes	—
153	C₄×D₂₃	#41	1	2	yes	—
154	C₈×C₂₃	—	2	1	no	—
155	C₈×C₂₃	C₂²×C₄	1	2	yes	complemented
156	C₂₃⋊C₈	—	2	1	no	—
157	C₂₃⋊C₈	C₂²×C₄	1	2	yes	complemented
158	C₄×AGL(1,ℤ/8)	—	23	1	no	maximal, Sylow
159	C₂²×C₂₃	—	2	2	no	—
160	C₂²×C₂₃	—	4	1	no	—
161	C₂²×C₂₃	—	4	1	no	—
162	C₂²×C₂₃	C₂²×D₄	1	1	yes	characteristic
163	C₂×D₂₃	—	2	1	no	—
164	C₂×D₂₃	—	2	1	no	—
165	C₂×D₂₃	—	2	2	no	—
166	C₂×D₂₃	—	2	2	no	—
167	C₂×D₂₃	—	4	8	no	—
168	C₂×D₂₃	—	4	1	no	—
169	C₂×D₂₃	—	4	1	no	—
170	C₂×D₂₃	—	4	1	no	—
171	C₂×D₂₃	—	4	1	no	—
172	C₂×D₂₃	C₄×D₄	1	2	yes	—
173	C₄×C₂₃	—	2	2	no	—
174	C₄×C₂₃	—	2	1	no	—
175	C₄×C₂₃	—	2	1	no	—
176	C₄×C₂₃	—	4	1	no	—
177	C₄×C₂₃	—	4	1	no	—
178	C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
179	C₄×C₂₃	C₂×#41	1	1	yes	characteristic
180	Dic₂₃	—	2	1	no	—
181	Dic₂₃	—	4	1	no	—
182	Dic₂₃	—	4	1	no	—
183	Dic₂₃	C₄×D₄	1	2	yes	—
184	Dic₂₃	AGL(1,ℤ/8)	1	2	yes	complemented
185	C₂×AGL(1,ℤ/8)	—	23	1	no	—
186	C₄×#41	—	23	1	no	—
187	C₂×C₄×D₄	—	23	1	no	—
188	#442	—	23	1	no	—
189	#442	—	23	1	no	—
190	#440	—	23	1	no	—
191	#440	D₂₃	1	1	yes	characteristic, complemented
192	C₄×SD₁₆	—	23	1	no	—
193	C₄×SD₁₆	—	23	1	no	—
194	C₄×D₈	—	23	1	no	—
195	C₄×D₈	—	23	1	no	—
196	#428	—	23	1	no	—
197	#418	—	23	1	no	—
198	#417	—	23	1	no	—
199	C₄×M₁₆	—	23	1	no	—
200	C₂×C₂₃	—	4	2	no	—
201	C₂×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
202	C₂×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
203	C₂×C₂₃	#575	1	1	yes	characteristic
204	D₂₃	—	2	2	no	—
205	D₂₃	—	4	2	no	—
206	D₂₃	—	4	2	no	—
207	C₂×#41	—	23	1	no	—
208	C₂²×D₄	—	23	1	no	—
209	C₂³×C₄	—	46	1	no	—
210	AGL(1,ℤ/8)	—	23	8	no	—
211	C₂×SD₁₆	—	23	1	no	—
212	C₂×SD₁₆	C₂×D₂₃	1	1	yes	characteristic
213	C₂×D₈	—	23	1	no	—
214	C₂×D₈	—	23	1	no	—
215	C₂×M₁₆	—	23	1	no	—
216	C₂×M₁₆	—	23	1	no	—
217	C₄×Q₈	—	23	1	no	—
218	C₄×Q₈	C₂×D₂₃	1	1	yes	characteristic, complemented
219	C₄×D₄	—	23	1	no	—
220	C₄×D₄	—	23	1	no	—
221	C₄×D₄	—	23	1	no	—
222	C₄×D₄	—	23	1	no	—
223	C₄×D₄	—	23	1	no	—
224	C₄×D₄	—	46	1	no	—
225	C₄×D₄	—	46	1	no	—
226	C₄×D₄	—	46	1	no	—
227	C₄×D₄	—	46	1	no	—
228	C₄×D₄	C₂×D₂₃	1	1	yes	characteristic
229	#117	—	23	1	no	—
230	#117	—	46	1	no	—
231	C₂×C₄⋊C₄	—	23	1	no	—
232	C₂×C₂²⋊C₄	—	46	1	no	—
233	C₂×C₄²	—	23	1	no	—
234	C₂×C₄²	—	46	1	no	—
235	#107	—	23	1	no	—
236	#107	C₂×D₂₃	1	1	yes	characteristic, complemented
237	#106	—	23	1	no	—
238	#106	—	23	1	no	—
239	#103	—	23	1	no	—
240	#103	C₂×D₂₃	1	1	yes	characteristic, complemented
241	#102	—	23	1	no	—
242	#102	—	23	1	no	—
243	#102	—	23	1	no	—
244	#102	—	23	1	no	—
245	#102	—	23	1	no	—
246	#102	C₂×D₂₃	1	1	yes	characteristic
247	#97	—	23	1	no	—
248	#97	C₂×D₂₃	1	1	yes	characteristic, complemented
249	C₄×C₈	—	23	1	no	—
250	C₄×C₈	—	23	1	no	—
251	C₂₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
252	C₂⁴	—	46	1	no	—
253	#41	—	23	4	no	—
254	#41	—	46	2	no	—
255	C₂×Q₈	C₂²×D₂₃	1	1	yes	characteristic
256	C₂×D₄	—	23	4	no	—
257	C₂×D₄	—	23	1	no	—
258	C₂×D₄	—	23	1	no	—
259	C₂×D₄	—	46	1	no	—
260	C₂×D₄	—	46	2	no	—
261	C₂×D₄	—	46	1	no	—
262	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	23	1	no	—
265	C₂²×C₄	—	23	1	no	—
266	C₂²×C₄	—	23	1	no	—
267	C₂²×C₄	—	46	1	no	—
268	C₂²×C₄	—	46	1	no	—
269	C₂²×C₄	—	46	1	no	—
270	C₂²×C₄	—	46	1	no	—
271	C₂²×C₄	—	46	1	no	—
272	C₂²×C₄	—	46	1	no	—
273	C₂²×C₄	—	46	1	no	—
274	C₂²×C₄	—	92	4	no	—
275	SD₁₆	—	23	4	no	—
276	SD₁₆	C₄×D₂₃	1	4	yes	complemented
277	D₈	—	23	4	no	—
278	D₈	—	23	4	no	—
279	M₁₆	—	23	4	no	—
280	M₁₆	—	46	2	no	—
281	C₂×C₈	—	23	1	no	—
282	C₂×C₈	—	23	1	no	—
283	C₂×C₈	C₂²×D₂₃	1	1	yes	characteristic
284	C₂×C₈	C₂²×D₂₃	1	1	yes	characteristic
285	C₄⋊C₄	—	2	1	no	—
286	C₄⋊C₄	—	23	1	no	—
287	C₄⋊C₄	—	23	1	no	—
288	C₄⋊C₄	—	46	1	no	—
289	C₄⋊C₄	—	46	1	no	—
290	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
291	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
292	C₂²⋊C₄	—	2	1	no	—
293	C₂²⋊C₄	—	46	1	no	—
294	C₂²⋊C₄	—	46	1	no	—
295	C₂²⋊C₄	—	46	1	no	—
296	C₂²⋊C₄	—	46	1	no	—
297	C₂²⋊C₄	—	46	1	no	—
298	C₂²⋊C₄	—	46	1	no	—
299	C₄²	—	2	1	no	—
300	C₄²	—	23	1	no	—
301	C₄²	—	23	1	no	—
302	C₄²	—	23	1	no	—
303	C₄²	—	46	1	no	—
304	C₄²	—	46	1	no	—
305	C₄²	C₂²×D₂₃	1	1	yes	characteristic
306	C₂³	—	2	1	no	—
307	C₂³	—	23	1	no	—
308	C₂³	—	46	4	no	—
309	C₂³	—	46	1	no	—
310	C₂³	—	46	1	no	—
311	C₂³	—	92	2	no	—
312	C₂³	—	92	2	no	—
313	Q₈	—	2	1	no	—
314	Q₈	C₂×C₄×D₂₃	1	2	yes	complemented
315	D₄	—	2	1	no	—
316	D₄	—	23	2	no	—
317	D₄	—	23	2	no	—
318	D₄	—	46	4	no	—
319	D₄	—	46	4	no	—
320	D₄	—	46	1	no	—
321	D₄	—	46	1	no	—
322	D₄	C₂×C₄×D₂₃	1	2	yes	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	23	1	no	—
328	C₂×C₄	—	23	1	no	—
329	C₂×C₄	—	23	2	no	—
330	C₂×C₄	—	23	2	no	—
331	C₂×C₄	—	23	1	no	—
332	C₂×C₄	—	46	2	no	—
333	C₂×C₄	—	46	4	no	—
334	C₂×C₄	—	46	1	no	—
335	C₂×C₄	—	46	1	no	—
336	C₂×C₄	—	92	1	no	—
337	C₂×C₄	—	92	2	no	—
338	C₂×C₄	—	92	2	no	—
339	C₂×C₄	—	92	2	no	—
340	C₂×C₄	—	92	2	no	—
341	C₂×C₄	—	92	2	no	—
342	C₂×C₄	—	92	2	no	—
343	C₂×C₄	D₄×D₂₃	1	1	yes	characteristic
344	C₂×C₄	D₄×D₂₃	1	1	yes	characteristic
345	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
346	C₈	—	2	1	no	—
347	C₈	—	23	2	no	—
348	C₈	—	46	1	no	—
349	C₈	C₂×C₄×D₂₃	1	2	yes	complemented
350	C₂²	—	2	2	no	—
351	C₂²	—	4	1	no	—
352	C₂²	—	4	1	no	—
353	C₂²	—	23	2	no	—
354	C₂²	—	46	1	no	—
355	C₂²	—	46	1	no	—
356	C₂²	—	46	2	no	—
357	C₂²	—	46	2	no	—
358	C₂²	—	92	8	no	—
359	C₂²	—	92	1	no	—
360	C₂²	—	92	1	no	—
361	C₂²	—	92	1	no	—
362	C₂²	—	92	1	no	—
363	C₂²	C₂×D₄×D₂₃	1	1	yes	characteristic
364	C₄	—	2	2	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	4	1	no	—
368	C₄	—	4	1	no	—
369	C₄	—	23	2	no	—
370	C₄	—	23	2	no	—
371	C₄	—	46	1	no	—
372	C₄	—	92	1	no	—
373	C₄	—	92	1	no	—
374	C₄	C₂²×C₄×D₂₃	1	1	yes	characteristic
375	C₄	#41×D₂₃	1	1	yes	characteristic
376	C₂	—	4	2	no	—
377	C₂	—	46	2	no	—
378	C₂	—	92	2	no	—
379	C₂	—	92	2	no	—
380	C₂	C₄×D₄×D₂₃	1	1	yes	characteristic
381	C₂	AGL(1,ℤ/8)×D₂₃	1	1	yes	characteristic
382	C₂	#13093216	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₂₃
commutator	C₄×C₂₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₂₃
Fitting	C₂₃×#440	C₂
socle	C₂²×C₂₃	C₂²×D₄
prime radical	C₂×#10625085	C₂
cosocle	C₂×C₄×C₂₃	C₂⁴
hypercenter	#440	D₂₃
hypocenter	C₂₃	C₄×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #440

Complements

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

N	H ≅ G/N	type
2. C₄×#67292	C₂	semidirect
3. C₄×D₄×D₂₃	C₂	semidirect
4. #13092530	C₂	semidirect
5. #13092527	C₂	semidirect
6. #13092515	C₂	semidirect
7. SD₁₆×Dic₂₃	C₂	semidirect
8. #13092502	C₂	semidirect
9. #13092499	C₂	semidirect
10. #13092497	C₂	semidirect
11. #13092458	C₂	semidirect
12. #13092420	C₂	semidirect
13. #13092417	C₂	semidirect
14. #13092369	C₂	semidirect
15. C₂₃×#440	C₂	semidirect
20. C₄×Q₈×C₂₃	C₂²	semidirect
22. Q₈×Dic₂₃	C₂²	semidirect
27. #10625085	C₄	semidirect
33. #10625064	C₂²	semidirect
41. C₄×D₉₂	C₂²	semidirect
44. C₂₃×#107	C₂²	semidirect
45. C₂₃×#103	C₂²	semidirect
47. C₂₃×#97	C₂²	semidirect
48. #10625017	C₂²	semidirect
51. #10625003	C₂²	semidirect
52. #10624999	C₂²	semidirect
53. C₈×Dic₂₃	C₂²	semidirect
54. C₈×Dic₂₃	C₂²	semidirect
56. #10624991	C₂²	semidirect
57. #10624990	C₂²	semidirect
58. #10624989	C₂²	semidirect
59. #10624985	C₂²	semidirect
67. #67292	C₂×C₄	semidirect
69. D₄×D₂₃	C₂×C₄	semidirect
83. SD₁₆×C₂₃	C₂×C₄	semidirect
93. #67274	C₂×C₄	semidirect
94. #67272	C₂×C₄	semidirect
111. D₁₈₄	C₂×C₄	semidirect
113. #67262	C₂×C₄	semidirect
122. Q₈×C₂₃	C₂²×C₄	semidirect
143. D₉₂	C₂²×C₄	semidirect
155. C₈×C₂₃	C₂²×C₄	semidirect
157. C₂₃⋊C₈	C₂²×C₄	semidirect
184. Dic₂₃	AGL(1,ℤ/8)	semidirect
191. #440	D₂₃	semidirect
218. C₄×Q₈	C₂×D₂₃	semidirect
236. #107	C₂×D₂₃	semidirect
240. #103	C₂×D₂₃	semidirect
248. #97	C₂×D₂₃	semidirect
251. C₂₃	C₄×AGL(1,ℤ/8)	semidirect
276. SD₁₆	C₄×D₂₃	semidirect
314. Q₈	C₂×C₄×D₂₃	semidirect
349. C₈	C₂×C₄×D₂₃	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
C₄×#67292	2
C₄×D₄×D₂₃	2
#13092530	2
#13092527	2
#13092515	2
SD₁₆×Dic₂₃	2
#13092502	2
#13092499	2
#13092497	2
#13092458	2
#13092420	2
#13092417	2
#13092369	2
C₂₃×#440	2
C₄×AGL(1,ℤ/8)	23