Subgroups — C₂₃×#33581 #19181207

Order 5888.

706 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#510	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3147	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×Q₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2211	C₂	1	4	yes	maximal, complemented
5	C₂₃×#2209	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2207	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2150	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2139	C₂	1	2	yes	maximal, complemented
9	C₂×C₂₃×#135	—	2	1	no	—
10	C₂×C₂₃×#135	C₂²	1	2	yes	—
11	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
12	C₂₃×#532	—	2	1	no	—
13	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
14	C₂₃×#510	—	2	8	no	—
15	C₂×C₂₃×Q₃₂	C₂²	1	4	yes	—
16	C₂×C₂₃×SD₃₂	C₂²	1	4	yes	—
17	C₂×C₂₃×M₃₂	C₂²	1	2	yes	—
18	C₂₃×#495	—	2	1	no	—
19	C₂₃×#495	C₂²	1	2	yes	—
20	C₂₃×#494	C₂²	1	1	yes	characteristic
21	C₂₃×#493	C₂²	1	1	yes	characteristic
22	C₂₃×#492	—	2	1	no	—
23	C₄×Q₁₆×C₂₃	—	2	1	no	—
24	C₄×Q₁₆×C₂₃	—	2	1	no	—
25	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
26	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
27	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#103	—	2	1	no	—
29	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
30	C₂₃×C₄⋊C₁₆	C₂²	1	2	yes	—
31	C₂₃×C₄⋊C₁₆	C₂²	1	2	yes	—
32	C₂₃×#358	C₂²	1	4	yes	—
33	C₂₃×#357	C₂²	1	4	yes	—
34	C₂×#41×C₂₃	—	2	2	no	—
35	C₂²×Q₈×C₂₃	—	2	1	no	—
36	C₂₃×#135	—	2	4	no	—
37	C₂₃×#135	—	2	4	no	—
38	C₂₃×#135	—	4	4	no	—
39	C₂×Q₁₆×C₂₃	—	2	1	no	—
40	C₂×Q₁₆×C₂₃	—	2	1	no	—
41	C₂×Q₁₆×C₂₃	—	2	2	no	—
42	C₂×Q₁₆×C₂₃	D₄	1	4	yes	complemented
43	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
44	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
45	C₂×SD₁₆×C₂₃	—	2	2	no	—
46	C₂×SD₁₆×C₂₃	—	2	2	no	—
47	C₂×D₈×C₂₃	—	2	1	no	—
48	C₂×D₈×C₂₃	C₂³	1	2	yes	—
49	C₂²×C₈×C₂₃	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
51	C₂₃×C₄⋊Q₈	—	2	1	no	—
52	C₂₃×#127	—	2	1	no	—
53	C₂₃×#124	—	2	2	no	—
54	C₂₃×#121	—	4	1	no	—
55	C₂₃×#121	—	4	1	no	—
56	C₄×Q₈×C₂₃	—	2	2	no	—
57	C₄×Q₈×C₂₃	—	2	2	no	—
58	C₄×Q₈×C₂₃	—	4	1	no	—
59	C₄×Q₈×C₂₃	—	4	1	no	—
60	C₄×D₄×C₂₃	—	4	1	no	—
61	C₄×D₄×C₂₃	—	4	1	no	—
62	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
63	C₂×C₄⋊C₄×C₂₃	—	4	1	no	—
64	C₂×C₄²×C₂₃	—	4	1	no	—
65	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
66	C₂₃×Q₃₂	—	2	8	no	—
67	C₂₃×SD₃₂	—	2	8	no	—
68	C₂₃×M₃₂	—	2	4	no	—
69	C₂×C₁₆×C₂₃	C₂³	1	4	yes	—
70	C₂₃×#107	—	2	1	no	—
71	C₂₃×#107	C₂³	1	2	yes	—
72	C₂₃×#103	—	2	2	no	—
73	C₂₃×#103	—	2	2	no	—
74	C₄×C₈×C₂₃	D₄	1	1	yes	characteristic
75	C₄×C₈×C₂₃	D₄	1	1	yes	characteristic
76	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
77	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
78	#41×C₂₃	—	4	4	no	—
79	#41×C₂₃	—	4	4	no	—
80	C₂×Q₈×C₂₃	—	2	4	no	—
81	C₂×Q₈×C₂₃	—	2	2	no	—
82	C₂×Q₈×C₂₃	—	2	2	no	—
83	C₂×Q₈×C₂₃	—	4	1	no	—
84	C₂×Q₈×C₂₃	—	4	2	no	—
85	C₂×D₄×C₂₃	—	2	2	no	—
86	C₂×D₄×C₂₃	—	4	2	no	—
87	C₂×D₄×C₂₃	—	4	1	no	—
88	C₂×D₄×C₂₃	—	4	1	no	—
89	C₂²×C₄×C₂₃	—	4	1	no	—
90	C₂²×C₄×C₂₃	—	4	1	no	—
91	C₂²×C₄×C₂₃	—	4	2	no	—
92	C₂²×C₄×C₂₃	D₈	1	1	yes	characteristic
93	C₂²×C₄×C₂₃	D₈	1	1	yes	characteristic
94	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
95	Q₁₆×C₂₃	—	2	4	no	—
96	Q₁₆×C₂₃	—	2	2	no	—
97	Q₁₆×C₂₃	—	2	2	no	—
98	Q₁₆×C₂₃	—	2	2	no	—
99	Q₁₆×C₂₃	—	4	2	no	—
100	Q₁₆×C₂₃	C₂×D₄	1	4	yes	—
101	SD₁₆×C₂₃	—	4	4	no	—
102	SD₁₆×C₂₃	—	4	4	no	—
103	D₈×C₂₃	—	2	2	no	—
104	D₈×C₂₃	—	2	2	no	—
105	D₈×C₂₃	—	4	2	no	—
106	C₂×C₈×C₂₃	—	2	2	no	—
107	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
108	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
109	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
110	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
111	C₂×C₈×C₂₃	#41	1	2	yes	—
112	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
113	C₄⋊C₄×C₂₃	—	2	2	no	—
114	C₄⋊C₄×C₂₃	—	4	1	no	—
115	C₄⋊C₄×C₂₃	—	4	2	no	—
116	C₄⋊C₄×C₂₃	—	4	2	no	—
117	C₄⋊C₄×C₂₃	—	4	1	no	—
118	C₄⋊C₄×C₂₃	—	4	1	no	—
119	C₂²⋊C₄×C₂₃	—	4	2	no	—
120	C₂²⋊C₄×C₂₃	—	4	2	no	—
121	C₄²×C₂₃	—	4	2	no	—
122	C₄²×C₂₃	—	4	2	no	—
123	C₄²×C₂₃	D₈	1	1	yes	characteristic
124	C₄²×C₂₃	D₈	1	1	yes	characteristic
125	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
127	C₁₆×C₂₃	—	2	4	no	—
128	#33581	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂³×C₂₃	—	4	2	no	—
130	C₂³×C₂₃	C₂×D₈	1	1	yes	characteristic
131	Q₈×C₂₃	—	2	4	no	—
132	Q₈×C₂₃	—	4	2	no	—
133	Q₈×C₂₃	—	4	4	no	—
134	Q₈×C₂₃	—	4	2	no	—
135	Q₈×C₂₃	—	4	2	no	—
136	D₄×C₂₃	—	4	2	no	—
137	D₄×C₂₃	—	4	2	no	—
138	D₄×C₂₃	—	8	2	no	—
139	D₄×C₂₃	—	8	4	no	—
140	D₄×C₂₃	—	8	2	no	—
141	C₂×C₄×C₂₃	—	2	2	no	—
142	C₂×C₄×C₂₃	—	4	1	no	—
143	C₂×C₄×C₂₃	—	4	2	no	—
144	C₂×C₄×C₂₃	—	4	4	no	—
145	C₂×C₄×C₂₃	—	4	2	no	—
146	C₂×C₄×C₂₃	—	4	2	no	—
147	C₂×C₄×C₂₃	—	8	2	no	—
148	C₂×C₄×C₂₃	—	8	4	no	—
149	C₂×C₄×C₂₃	#121	1	2	yes	—
150	C₂×C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
151	C₂×C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
152	C₂×C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
153	C₂×C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
154	C₂×C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
155	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
156	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
157	C₈×C₂₃	—	2	1	no	—
158	C₈×C₂₃	—	2	1	no	—
159	C₈×C₂₃	#121	1	2	yes	—
160	C₈×C₂₃	C₂²×D₄	1	1	yes	characteristic
161	C₈×C₂₃	C₂×#41	1	1	yes	characteristic
162	C₂×#510	C₂×C₂₃	1	2	yes	complemented
163	#3147	C₂×C₂₃	1	1	yes	characteristic
164	C₂×C₄×Q₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
165	#2211	C₂×C₂₃	1	4	yes	complemented
166	#2209	C₂×C₂₃	1	2	yes	complemented
167	#2207	C₂×C₂₃	1	2	yes	complemented
168	#2150	C₂×C₂₃	1	1	yes	characteristic, complemented
169	#2139	C₂×C₂₃	1	2	yes	complemented
170	C₂²×C₂₃	—	2	1	no	—
171	C₂²×C₂₃	—	2	1	no	—
172	C₂²×C₂₃	—	8	2	no	—
173	C₂²×C₂₃	—	8	2	no	—
174	C₂²×C₂₃	—	8	2	no	—
175	C₂²×C₂₃	#459	1	2	yes	—
176	C₂²×C₂₃	C₂²×D₈	1	1	yes	characteristic
177	C₄×C₂₃	—	2	1	no	—
178	C₄×C₂₃	—	2	1	no	—
179	C₄×C₂₃	—	2	1	no	—
180	C₄×C₂₃	—	4	4	no	—
181	C₄×C₂₃	—	8	2	no	—
182	C₄×C₂₃	—	8	2	no	—
183	C₄×C₂₃	#459	1	2	yes	—
184	C₄×C₂₃	#510	1	2	yes	complemented
185	C₄×C₂₃	C₂×#121	1	1	yes	characteristic
186	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₂×#135	—	2	1	no	—
188	C₂×#135	C₂²×C₂₃	1	2	yes	—
189	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
190	#532	—	2	1	no	—
191	C₂×C₄×Q₈	—	2	1	no	—
192	#510	—	2	8	no	—
193	C₂×Q₃₂	C₂²×C₂₃	1	4	yes	—
194	C₂×SD₃₂	C₂²×C₂₃	1	4	yes	—
195	C₂×M₃₂	C₂²×C₂₃	1	2	yes	—
196	#495	—	2	1	no	—
197	#495	C₂²×C₂₃	1	2	yes	—
198	#494	C₂²×C₂₃	1	1	yes	characteristic
199	#493	C₂²×C₂₃	1	1	yes	characteristic
200	#492	—	2	1	no	—
201	C₄×Q₁₆	—	2	1	no	—
202	C₄×Q₁₆	—	2	1	no	—
203	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
204	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
205	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
206	C₂×#103	—	2	1	no	—
207	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
208	C₄⋊C₁₆	C₂²×C₂₃	1	2	yes	—
209	C₄⋊C₁₆	C₂²×C₂₃	1	2	yes	—
210	#358	C₂²×C₂₃	1	4	yes	—
211	#357	C₂²×C₂₃	1	4	yes	—
212	C₂×C₂₃	—	2	2	no	—
213	C₂×C₂₃	—	16	2	no	—
214	C₂×C₂₃	C₂×#459	1	1	yes	characteristic
215	C₂×C₂₃	C₂×#510	1	1	yes	characteristic
216	C₂×C₂₃	#3414	1	1	yes	characteristic
217	C₂×#41	—	2	2	no	—
218	C₂²×Q₈	—	2	1	no	—
219	#135	—	2	4	no	—
220	#135	—	2	4	no	—
221	#135	—	4	4	no	—
222	C₂×Q₁₆	—	2	1	no	—
223	C₂×Q₁₆	—	2	1	no	—
224	C₂×Q₁₆	—	2	2	no	—
225	C₂×Q₁₆	D₄×C₂₃	1	4	yes	complemented
226	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
227	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
228	C₂×SD₁₆	—	2	2	no	—
229	C₂×SD₁₆	—	2	2	no	—
230	C₂×D₈	—	2	1	no	—
231	C₂×D₈	C₂³×C₂₃	1	2	yes	—
232	C₂²×C₈	D₄×C₂₃	1	1	yes	characteristic
233	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
234	C₄⋊Q₈	—	2	1	no	—
235	#127	—	2	1	no	—
236	#124	—	2	2	no	—
237	#121	—	4	1	no	—
238	#121	—	4	1	no	—
239	C₄×Q₈	—	2	2	no	—
240	C₄×Q₈	—	2	2	no	—
241	C₄×Q₈	—	4	1	no	—
242	C₄×Q₈	—	4	1	no	—
243	C₄×D₄	—	4	1	no	—
244	C₄×D₄	—	4	1	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	4	1	no	—
247	C₂×C₄²	—	4	1	no	—
248	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
249	Q₃₂	—	2	8	no	—
250	SD₃₂	—	2	8	no	—
251	M₃₂	—	2	4	no	—
252	C₂×C₁₆	C₂³×C₂₃	1	4	yes	—
253	#107	—	2	1	no	—
254	#107	C₂³×C₂₃	1	2	yes	—
255	#103	—	2	2	no	—
256	#103	—	2	2	no	—
257	C₄×C₈	D₄×C₂₃	1	1	yes	characteristic
258	C₄×C₈	D₄×C₂₃	1	1	yes	characteristic
259	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
260	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
261	C₂₃	#33581	1	1	yes	characteristic, direct product factor, Sylow
262	#41	—	4	4	no	—
263	#41	—	4	4	no	—
264	C₂×Q₈	—	2	4	no	—
265	C₂×Q₈	—	2	2	no	—
266	C₂×Q₈	—	2	2	no	—
267	C₂×Q₈	—	4	1	no	—
268	C₂×Q₈	—	4	2	no	—
269	C₂×D₄	—	2	2	no	—
270	C₂×D₄	—	4	2	no	—
271	C₂×D₄	—	4	1	no	—
272	C₂×D₄	—	4	1	no	—
273	C₂²×C₄	—	4	1	no	—
274	C₂²×C₄	—	4	1	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	D₈×C₂₃	1	1	yes	characteristic
277	C₂²×C₄	D₈×C₂₃	1	1	yes	characteristic
278	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
279	Q₁₆	—	2	4	no	—
280	Q₁₆	—	2	2	no	—
281	Q₁₆	—	2	2	no	—
282	Q₁₆	—	2	2	no	—
283	Q₁₆	—	4	2	no	—
284	Q₁₆	C₂×D₄×C₂₃	1	4	yes	—
285	SD₁₆	—	4	4	no	—
286	SD₁₆	—	4	4	no	—
287	D₈	—	2	2	no	—
288	D₈	—	2	2	no	—
289	D₈	—	4	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
292	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
293	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
294	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
295	C₂×C₈	#41×C₂₃	1	2	yes	—
296	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	4	1	no	—
299	C₄⋊C₄	—	4	2	no	—
300	C₄⋊C₄	—	4	2	no	—
301	C₄⋊C₄	—	4	1	no	—
302	C₄⋊C₄	—	4	1	no	—
303	C₂²⋊C₄	—	4	2	no	—
304	C₂²⋊C₄	—	4	2	no	—
305	C₄²	—	4	2	no	—
306	C₄²	—	4	2	no	—
307	C₄²	D₈×C₂₃	1	1	yes	characteristic
308	C₄²	D₈×C₂₃	1	1	yes	characteristic
309	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
310	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
311	C₁₆	—	2	4	no	—
312	C₂³	—	4	2	no	—
313	C₂³	C₂×D₈×C₂₃	1	1	yes	characteristic
314	Q₈	—	2	4	no	—
315	Q₈	—	4	2	no	—
316	Q₈	—	4	4	no	—
317	Q₈	—	4	2	no	—
318	Q₈	—	4	2	no	—
319	D₄	—	4	2	no	—
320	D₄	—	4	2	no	—
321	D₄	—	8	2	no	—
322	D₄	—	8	4	no	—
323	D₄	—	8	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	8	2	no	—
331	C₂×C₄	—	8	4	no	—
332	C₂×C₄	C₂₃×#121	1	2	yes	—
333	C₂×C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
334	C₂×C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
335	C₂×C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
336	C₂×C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
337	C₂×C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
338	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
339	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
340	C₈	—	2	1	no	—
341	C₈	—	2	1	no	—
342	C₈	C₂₃×#121	1	2	yes	—
343	C₈	C₂²×D₄×C₂₃	1	1	yes	characteristic
344	C₈	C₂×#41×C₂₃	1	1	yes	characteristic
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	8	2	no	—
348	C₂²	—	8	2	no	—
349	C₂²	—	8	2	no	—
350	C₂²	C₂₃×#459	1	2	yes	—
351	C₂²	C₂²×D₈×C₂₃	1	1	yes	characteristic
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	4	4	no	—
356	C₄	—	8	2	no	—
357	C₄	—	8	2	no	—
358	C₄	C₂₃×#459	1	2	yes	—
359	C₄	C₂₃×#510	1	2	yes	complemented
360	C₄	C₂×C₂₃×#121	1	1	yes	characteristic
361	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
362	C₂	—	2	2	no	—
363	C₂	—	16	2	no	—
364	C₂	C₂×C₂₃×#459	1	1	yes	characteristic
365	C₂	C₂×C₂₃×#510	1	1	yes	characteristic
366	C₂	C₂₃×#3414	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₂₃
prime radical	C₂₃×#3147	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ C₂×C₄×C₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#510	C₂	semidirect
3. C₂×C₄×Q₁₆×C₂₃	C₂	semidirect
4. C₂₃×#2211	C₂	semidirect
5. C₂₃×#2209	C₂	semidirect
6. C₂₃×#2207	C₂	semidirect
7. C₂₃×#2150	C₂	semidirect
8. C₂₃×#2139	C₂	semidirect
42. C₂×Q₁₆×C₂₃	D₄	semidirect
128. #33581	C₂₃	direct (N × H)
162. C₂×#510	C₂×C₂₃	semidirect
164. C₂×C₄×Q₁₆	C₂×C₂₃	semidirect
165. #2211	C₂×C₂₃	semidirect
166. #2209	C₂×C₂₃	semidirect
167. #2207	C₂×C₂₃	semidirect
168. #2150	C₂×C₂₃	semidirect
169. #2139	C₂×C₂₃	semidirect
184. C₄×C₂₃	#510	semidirect
225. C₂×Q₁₆	D₄×C₂₃	semidirect
261. C₂₃	#33581	direct (N × H)
359. C₄	C₂₃×#510	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#510	2
C₂₃×#3147	2
C₂×C₄×Q₁₆×C₂₃	2
C₂₃×#2211	2
C₂₃×#2209	2
C₂₃×#2207	2
C₂₃×#2150	2
C₂₃×#2139	2
#33581	23

Subgroups — C23×#33581 #19181207

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#33581 #19181207