Subgroups — C₂₃×#61848 #19209474

Order 5888.

1660 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3501	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3388	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3386	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3381	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3372	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3372	C₂	1	4	yes	maximal, complemented
8	C₂₃×#3359	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3242	C₂	1	4	yes	maximal, complemented
10	C₂₃×#3237	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3231	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3123	C₂	1	4	yes	maximal
13	C₂₃×#3110	C₂	1	1	yes	maximal, characteristic
14	C₂₃×#3101	C₂	1	1	yes	maximal, characteristic
15	C₂₃×#2985	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#564	—	2	2	no	—
17	C₂₃×#557	—	2	1	no	—
18	C₂₃×#557	—	2	1	no	—
19	C₂₃×#557	C₂²	1	2	yes	complemented
20	C₂₃×#557	C₂²	1	2	yes	complemented
21	C₂₃×#557	C₂²	1	2	yes	complemented
22	C₂₃×#557	C₂²	1	2	yes	complemented
23	C₂₃×#554	—	2	1	no	—
24	C₂₃×#554	—	2	2	no	—
25	C₂₃×#554	C₂²	1	2	yes	—
26	C₂₃×#554	C₂²	1	4	yes	—
27	D₄×Q₈×C₂₃	—	2	1	no	—
28	D₄×Q₈×C₂₃	C₂²	1	2	yes	—
29	C₂₃×#544	C₂²	1	2	yes	—
30	C₂₃×#543	—	2	2	no	—
31	C₂₃×#541	—	2	2	no	—
32	C₂₃×#541	—	2	2	no	—
33	C₂₃×#541	C₂²	1	4	yes	—
34	C₂₃×#533	C₂²	1	1	yes	characteristic
35	C₂₃×#533	C₂²	1	1	yes	characteristic
36	C₂₃×#533	C₂²	1	1	yes	characteristic
37	C₂₃×#533	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×C₂²⋊Q₈	—	2	2	no	—
39	C₂₃×#518	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
41	C₂₃×#501	C₂²	1	2	yes	complemented
42	C₂₃×#501	C₂²	1	4	yes	complemented
43	C₂₃×#500	C₂²	1	1	yes	characteristic, complemented
44	C₂₃×#499	C₂²	1	4	yes	complemented
45	C₂₃×#498	C₂²	1	1	yes	characteristic, complemented
46	C₂₃×#491	C₂²	1	2	yes	complemented
47	C₂₃×#491	C₂²	1	4	yes	complemented
48	C₂₃×#487	C₂²	1	1	yes	characteristic, complemented
49	C₂₃×#487	C₂²	1	1	yes	characteristic, complemented
50	C₂₃×#487	C₂²	1	4	yes	complemented
51	C₂₃×#485	C₂²	1	4	yes	—
52	C₂₃×#485	C₂²	1	4	yes	—
53	C₂₃×#484	C₂²	1	2	yes	—
54	C₂₃×#483	C₂²	1	2	yes	—
55	C₂₃×#479	C₂²	1	4	yes	complemented
56	C₂₃×#479	C₂²	1	4	yes	complemented
57	C₂₃×#479	C₂²	1	4	yes	complemented
58	C₂₃×#478	C₂²	1	4	yes	—
59	C₂₃×#478	C₂²	1	4	yes	—
60	C₂₃×#477	C₂²	1	2	yes	complemented
61	C₂₃×#477	C₂²	1	4	yes	complemented
62	C₂₃×#476	C₂²	1	2	yes	—
63	C₂₃×#475	C₂²	1	2	yes	complemented
64	C₂₃×#475	C₂²	1	4	yes	complemented
65	C₂₃×#474	C₂²	1	2	yes	—
66	C₂₃×#461	C₂²	1	2	yes	—
67	C₂₃×#461	C₂²	1	2	yes	—
68	C₂₃×#461	C₂²	1	4	yes	—
69	C₂₃×#461	C₂²	1	4	yes	—
70	C₂₃×#450	C₂²	1	2	yes	—
71	C₂₃×#450	C₂²	1	2	yes	—
72	C₂₃×#446	C₂²	1	2	yes	complemented
73	C₂₃×#446	C₂²	1	4	yes	complemented
74	C₈×Q₈×C₂₃	C₂²	1	2	yes	complemented
75	C₂₃×#440	C₂²	1	4	yes	—
76	C₂₃×#440	C₂²	1	4	yes	—
77	C₂₃×#440	C₂²	1	4	yes	—
78	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
79	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
80	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	—
81	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	—
82	C₂₃×#433	C₂²	1	4	yes	—
83	C₂₃×#432	C₂²	1	1	yes	characteristic
84	C₂₃×#431	C₂²	1	1	yes	characteristic
85	C₂²×Q₈×C₂₃	—	2	2	no	—
86	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₂₃	—	2	1	no	—
88	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
89	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
90	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
91	C₂₃×C₄⋊Q₈	—	2	2	no	—
92	C₂₃×C₄⋊Q₈	—	2	2	no	—
93	C₂₃×C₄⋊Q₈	—	2	2	no	—
94	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
95	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
96	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
97	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
98	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
99	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
100	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
101	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
102	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
103	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
104	C₂₃×#126	—	2	4	no	—
105	C₂₃×#126	—	2	4	no	—
106	C₂₃×#125	—	2	2	no	—
107	C₂₃×#125	—	2	2	no	—
108	C₂₃×#125	—	2	2	no	—
109	C₂₃×#125	—	2	4	no	—
110	C₂₃×#125	—	2	4	no	—
111	C₂₃×#125	—	2	4	no	—
112	C₂₃×#125	—	2	4	no	—
113	C₂₃×#125	—	2	4	no	—
114	C₂₃×#125	—	2	4	no	—
115	C₂₃×#125	—	2	1	no	—
116	C₂₃×#125	—	2	1	no	—
117	C₂₃×#125	D₄	1	2	yes	—
118	C₂₃×#125	C₂³	1	4	yes	—
119	C₂₃×#125	C₂³	1	2	yes	—
120	C₂₃×#125	C₂³	1	4	yes	—
121	C₂₃×C₂²⋊Q₈	—	2	2	no	—
122	C₂₃×C₂²⋊Q₈	—	2	4	no	—
123	C₂₃×C₂²⋊Q₈	—	2	1	no	—
124	C₂₃×C₂²⋊Q₈	—	2	1	no	—
125	C₂₃×C₂²⋊Q₈	—	2	1	no	—
126	C₂₃×C₂²⋊Q₈	—	2	1	no	—
127	C₂₃×C₂²⋊Q₈	—	2	4	no	—
128	C₂₃×C₂²⋊Q₈	—	2	2	no	—
129	C₂₃×C₂²⋊Q₈	—	2	4	no	—
130	C₂₃×C₂²⋊Q₈	—	2	4	no	—
131	C₂₃×C₂²⋊Q₈	—	2	4	no	—
132	C₂₃×C₂²⋊Q₈	—	2	4	no	—
133	C₂₃×C₂²⋊Q₈	D₄	1	2	yes	—
134	C₂₃×C₂²⋊Q₈	D₄	1	2	yes	—
135	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
136	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
137	C₄×Q₈×C₂₃	—	2	2	no	—
138	C₄×Q₈×C₂₃	—	2	2	no	—
139	C₄×Q₈×C₂₃	—	2	2	no	—
140	C₄×Q₈×C₂₃	—	2	2	no	—
141	C₄×Q₈×C₂₃	—	2	1	no	—
142	C₄×Q₈×C₂₃	—	2	1	no	—
143	C₄×Q₈×C₂₃	—	2	1	no	—
144	C₄×Q₈×C₂₃	—	2	1	no	—
145	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
146	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
147	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
148	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
149	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
150	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
151	C₄×D₄×C₂₃	—	2	2	no	—
152	C₄×D₄×C₂₃	—	2	2	no	—
153	C₄×D₄×C₂₃	—	2	1	no	—
154	C₄×D₄×C₂₃	—	2	1	no	—
155	C₄×D₄×C₂₃	C₂³	1	2	yes	—
156	C₄×D₄×C₂₃	C₂³	1	4	yes	—
157	C₄×D₄×C₂₃	C₂³	1	4	yes	—
158	C₄×D₄×C₂₃	C₂³	1	2	yes	—
159	C₂₃×#117	—	2	1	no	—
160	C₂₃×#117	—	2	1	no	—
161	C₂₃×#117	C₂³	1	2	yes	—
162	C₂₃×#117	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
164	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
165	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
166	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
167	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
168	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
169	C₂₃×#107	C₂³	1	4	yes	—
170	C₂₃×#107	C₂³	1	4	yes	—
171	C₂₃×#107	C₂³	1	4	yes	—
172	C₂₃×#106	C₂³	1	2	yes	—
173	C₂₃×#106	C₂³	1	4	yes	—
174	C₂₃×#106	C₂³	1	2	yes	—
175	C₂₃×#106	C₂³	1	4	yes	—
176	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
177	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
178	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
179	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
180	C₂₃×#103	C₂³	1	4	yes	—
181	C₂₃×#103	C₂³	1	2	yes	—
182	C₂₃×#103	C₂³	1	4	yes	—
183	C₂₃×#103	C₂³	1	2	yes	—
184	C₂₃×#103	C₂³	1	4	yes	—
185	C₂₃×#103	C₂³	1	4	yes	—
186	C₂₃×#103	C₂³	1	4	yes	—
187	C₂₃×#102	C₂³	1	2	yes	—
188	C₂₃×#102	C₂³	1	4	yes	—
189	C₂₃×#102	C₂³	1	2	yes	—
190	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
191	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
192	C₂₃×#97	C₂³	1	2	yes	—
193	C₂₃×#97	C₂³	1	4	yes	—
194	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₂₃	C₂³	1	4	yes	—
197	C₂⁴×C₂₃	—	2	1	no	—
198	C₂×Q₈×C₂₃	—	2	1	no	—
199	C₂×Q₈×C₂₃	—	2	1	no	—
200	C₂×Q₈×C₂₃	—	2	1	no	—
201	C₂×Q₈×C₂₃	—	2	1	no	—
202	C₂×Q₈×C₂₃	—	2	4	no	—
203	C₂×Q₈×C₂₃	—	8	4	no	—
204	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
205	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
206	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
207	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
208	C₂×D₄×C₂₃	—	2	4	no	—
209	C₂×D₄×C₂₃	—	2	1	no	—
210	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₂₃	—	2	1	no	—
212	C₂²×C₄×C₂₃	—	2	2	no	—
213	C₂²×C₄×C₂₃	—	2	4	no	—
214	C₂²×C₄×C₂₃	—	2	4	no	—
215	C₂²×C₄×C₂₃	—	2	2	no	—
216	C₂²×C₄×C₂₃	—	8	2	no	—
217	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
220	SD₁₆×C₂₃	—	2	4	no	—
221	SD₁₆×C₂₃	—	2	4	no	—
222	SD₁₆×C₂₃	—	2	8	no	—
223	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
224	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
225	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
226	C₄⋊C₄×C₂₃	—	2	2	no	—
227	C₄⋊C₄×C₂₃	—	2	1	no	—
228	C₄⋊C₄×C₂₃	—	2	4	no	—
229	C₄⋊C₄×C₂₃	—	2	4	no	—
230	C₄⋊C₄×C₂₃	—	2	4	no	—
231	C₄⋊C₄×C₂₃	—	2	1	no	—
232	C₄⋊C₄×C₂₃	—	2	1	no	—
233	C₄⋊C₄×C₂₃	—	2	1	no	—
234	C₄⋊C₄×C₂₃	—	2	1	no	—
235	C₄⋊C₄×C₂₃	—	2	1	no	—
236	C₄⋊C₄×C₂₃	—	2	1	no	—
237	C₄⋊C₄×C₂₃	—	2	1	no	—
238	C₄⋊C₄×C₂₃	—	2	2	no	—
239	C₄⋊C₄×C₂₃	—	2	1	no	—
240	C₄⋊C₄×C₂₃	—	2	2	no	—
241	C₄⋊C₄×C₂₃	—	2	2	no	—
242	C₄⋊C₄×C₂₃	—	2	4	no	—
243	C₄⋊C₄×C₂₃	—	2	4	no	—
244	C₄⋊C₄×C₂₃	—	2	4	no	—
245	C₄⋊C₄×C₂₃	—	2	4	no	—
246	C₄⋊C₄×C₂₃	—	2	2	no	—
247	C₄⋊C₄×C₂₃	—	2	2	no	—
248	C₄⋊C₄×C₂₃	—	2	4	no	—
249	C₄⋊C₄×C₂₃	—	2	4	no	—
250	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
251	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
252	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
253	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
254	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
255	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
256	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
257	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
258	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
259	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
260	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
261	C₂²⋊C₄×C₂₃	—	2	2	no	—
262	C₂²⋊C₄×C₂₃	—	2	2	no	—
263	C₂²⋊C₄×C₂₃	—	2	2	no	—
264	C₂²⋊C₄×C₂₃	—	2	4	no	—
265	C₂²⋊C₄×C₂₃	—	2	4	no	—
266	C₂²⋊C₄×C₂₃	—	2	2	no	—
267	C₂²⋊C₄×C₂₃	—	2	2	no	—
268	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
269	C₄²×C₂₃	—	2	2	no	—
270	C₄²×C₂₃	—	2	2	no	—
271	C₄²×C₂₃	—	2	2	no	—
272	C₄²×C₂₃	—	2	4	no	—
273	C₄²×C₂₃	—	2	4	no	—
274	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
275	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
276	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
277	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
278	C₄²×C₂₃	C₂⁴	1	4	yes	—
279	#61848	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
280	C₂³×C₂₃	—	2	4	no	—
281	C₂³×C₂₃	—	2	2	no	—
282	C₂³×C₂₃	—	8	1	no	—
283	C₂³×C₂₃	—	8	1	no	—
284	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
285	Q₈×C₂₃	—	2	4	no	—
286	Q₈×C₂₃	—	2	2	no	—
287	Q₈×C₂₃	—	2	4	no	—
288	Q₈×C₂₃	—	2	2	no	—
289	Q₈×C₂₃	—	4	2	no	—
290	Q₈×C₂₃	—	4	2	no	—
291	Q₈×C₂₃	—	4	2	no	—
292	Q₈×C₂₃	—	4	2	no	—
293	Q₈×C₂₃	—	8	1	no	—
294	Q₈×C₂₃	—	8	4	no	—
295	D₄×C₂₃	—	2	4	no	—
296	D₄×C₂₃	—	2	2	no	—
297	D₄×C₂₃	2₋¹⁺⁴	1	4	yes	—
298	C₂×C₄×C₂₃	—	2	2	no	—
299	C₂×C₄×C₂₃	—	2	2	no	—
300	C₂×C₄×C₂₃	—	2	2	no	—
301	C₂×C₄×C₂₃	—	2	2	no	—
302	C₂×C₄×C₂₃	—	2	2	no	—
303	C₂×C₄×C₂₃	—	2	2	no	—
304	C₂×C₄×C₂₃	—	2	2	no	—
305	C₂×C₄×C₂₃	—	2	2	no	—
306	C₂×C₄×C₂₃	—	2	2	no	—
307	C₂×C₄×C₂₃	—	4	1	no	—
308	C₂×C₄×C₂₃	—	4	4	no	—
309	C₂×C₄×C₂₃	—	8	4	no	—
310	C₂×C₄×C₂₃	—	8	2	no	—
311	C₂×C₄×C₂₃	—	8	4	no	—
312	C₂×C₄×C₂₃	—	8	1	no	—
313	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
314	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
315	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
316	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
317	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
318	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
321	C₈×C₂₃	—	2	2	no	—
322	C₈×C₂₃	—	2	4	no	—
323	C₈×C₂₃	—	2	2	no	—
324	#3556	C₂×C₂₃	1	1	yes	characteristic, complemented
325	#3501	C₂×C₂₃	1	1	yes	characteristic
326	#3388	C₂×C₂₃	1	4	yes	complemented
327	#3386	C₂×C₂₃	1	2	yes	complemented
328	#3381	C₂×C₂₃	1	2	yes	complemented
329	#3372	C₂×C₂₃	1	2	yes	complemented
330	#3372	C₂×C₂₃	1	4	yes	complemented
331	#3359	C₂×C₂₃	1	2	yes	complemented
332	#3242	C₂×C₂₃	1	4	yes	complemented
333	#3237	C₂×C₂₃	1	1	yes	characteristic, complemented
334	#3231	C₂×C₂₃	1	1	yes	characteristic, complemented
335	#3123	C₂×C₂₃	1	4	yes	—
336	#3110	C₂×C₂₃	1	1	yes	characteristic
337	#3101	C₂×C₂₃	1	1	yes	characteristic
338	#2985	C₂×C₂₃	1	1	yes	characteristic, complemented
339	C₂²×C₂₃	—	2	1	no	—
340	C₂²×C₂₃	—	2	1	no	—
341	C₂²×C₂₃	—	2	4	no	—
342	C₂²×C₂₃	—	2	1	no	—
343	C₂²×C₂₃	—	4	2	no	—
344	C₂²×C₂₃	—	4	2	no	—
345	C₂²×C₂₃	—	8	4	no	—
346	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
347	C₄×C₂₃	—	2	1	no	—
348	C₄×C₂₃	—	2	1	no	—
349	C₄×C₂₃	—	2	4	no	—
350	C₄×C₂₃	—	2	1	no	—
351	C₄×C₂₃	—	2	1	no	—
352	C₄×C₂₃	—	2	4	no	—
353	C₄×C₂₃	—	4	2	no	—
354	C₄×C₂₃	—	4	2	no	—
355	C₄×C₂₃	—	4	2	no	—
356	C₄×C₂₃	—	4	2	no	—
357	C₄×C₂₃	—	4	2	no	—
358	C₄×C₂₃	—	4	2	no	—
359	C₄×C₂₃	—	4	2	no	—
360	C₄×C₂₃	#577	1	2	yes	—
361	C₄×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
362	#564	—	2	2	no	—
363	#557	—	2	1	no	—
364	#557	—	2	1	no	—
365	#557	C₂²×C₂₃	1	2	yes	complemented
366	#557	C₂²×C₂₃	1	2	yes	complemented
367	#557	C₂²×C₂₃	1	2	yes	complemented
368	#557	C₂²×C₂₃	1	2	yes	complemented
369	#554	—	2	1	no	—
370	#554	—	2	2	no	—
371	#554	C₂²×C₂₃	1	2	yes	—
372	#554	C₂²×C₂₃	1	4	yes	—
373	D₄×Q₈	—	2	1	no	—
374	D₄×Q₈	C₂²×C₂₃	1	2	yes	—
375	#544	C₂²×C₂₃	1	2	yes	—
376	#543	—	2	2	no	—
377	#541	—	2	2	no	—
378	#541	—	2	2	no	—
379	#541	C₂²×C₂₃	1	4	yes	—
380	#533	C₂²×C₂₃	1	1	yes	characteristic
381	#533	C₂²×C₂₃	1	1	yes	characteristic
382	#533	C₂²×C₂₃	1	1	yes	characteristic
383	#533	C₂²×C₂₃	1	1	yes	characteristic
384	C₂×C₂²⋊Q₈	—	2	2	no	—
385	#518	C₂²×C₂₃	1	2	yes	—
386	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
387	#501	C₂²×C₂₃	1	4	yes	complemented
388	#501	C₂²×C₂₃	1	2	yes	complemented
389	#500	C₂²×C₂₃	1	1	yes	characteristic, complemented
390	#499	C₂²×C₂₃	1	4	yes	complemented
391	#498	C₂²×C₂₃	1	1	yes	characteristic, complemented
392	#491	C₂²×C₂₃	1	2	yes	complemented
393	#491	C₂²×C₂₃	1	4	yes	complemented
394	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
395	#487	C₂²×C₂₃	1	4	yes	complemented
396	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
397	#485	C₂²×C₂₃	1	4	yes	—
398	#485	C₂²×C₂₃	1	4	yes	—
399	#484	C₂²×C₂₃	1	2	yes	—
400	#483	C₂²×C₂₃	1	2	yes	—
401	#479	C₂²×C₂₃	1	4	yes	complemented
402	#479	C₂²×C₂₃	1	4	yes	complemented
403	#479	C₂²×C₂₃	1	4	yes	complemented
404	#478	C₂²×C₂₃	1	4	yes	—
405	#478	C₂²×C₂₃	1	4	yes	—
406	#477	C₂²×C₂₃	1	2	yes	complemented
407	#477	C₂²×C₂₃	1	4	yes	complemented
408	#476	C₂²×C₂₃	1	2	yes	—
409	#475	C₂²×C₂₃	1	2	yes	complemented
410	#475	C₂²×C₂₃	1	4	yes	complemented
411	#474	C₂²×C₂₃	1	2	yes	—
412	#461	C₂²×C₂₃	1	2	yes	—
413	#461	C₂²×C₂₃	1	2	yes	—
414	#461	C₂²×C₂₃	1	4	yes	—
415	#461	C₂²×C₂₃	1	4	yes	—
416	#450	C₂²×C₂₃	1	2	yes	—
417	#450	C₂²×C₂₃	1	2	yes	—
418	#446	C₂²×C₂₃	1	2	yes	complemented
419	#446	C₂²×C₂₃	1	4	yes	complemented
420	C₈×Q₈	C₂²×C₂₃	1	2	yes	complemented
421	#440	C₂²×C₂₃	1	4	yes	—
422	#440	C₂²×C₂₃	1	4	yes	—
423	#440	C₂²×C₂₃	1	4	yes	—
424	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
425	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
426	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	—
427	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	—
428	#433	C₂²×C₂₃	1	4	yes	—
429	#432	C₂²×C₂₃	1	1	yes	characteristic
430	#431	C₂²×C₂₃	1	1	yes	characteristic
431	C₂×C₂₃	—	4	1	no	—
432	C₂×C₂₃	—	4	4	no	—
433	C₂×C₂₃	#3486	1	1	yes	characteristic
434	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
435	C₂×C₂₃	#3586	1	1	yes	characteristic
436	C₂²×Q₈	—	2	2	no	—
437	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
438	C₂³×C₄	—	2	1	no	—
439	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
440	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
441	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
442	C₄⋊Q₈	—	2	2	no	—
443	C₄⋊Q₈	—	2	2	no	—
444	C₄⋊Q₈	—	2	2	no	—
445	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
446	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
447	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
448	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
449	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
450	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
451	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
452	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
453	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
454	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
455	#126	—	2	4	no	—
456	#126	—	2	4	no	—
457	#125	—	2	2	no	—
458	#125	—	2	2	no	—
459	#125	—	2	4	no	—
460	#125	—	2	4	no	—
461	#125	—	2	4	no	—
462	#125	—	2	4	no	—
463	#125	—	2	4	no	—
464	#125	—	2	4	no	—
465	#125	—	2	2	no	—
466	#125	—	2	1	no	—
467	#125	—	2	1	no	—
468	#125	D₄×C₂₃	1	2	yes	—
469	#125	C₂³×C₂₃	1	2	yes	—
470	#125	C₂³×C₂₃	1	4	yes	—
471	#125	C₂³×C₂₃	1	4	yes	—
472	C₂²⋊Q₈	—	2	2	no	—
473	C₂²⋊Q₈	—	2	4	no	—
474	C₂²⋊Q₈	—	2	1	no	—
475	C₂²⋊Q₈	—	2	1	no	—
476	C₂²⋊Q₈	—	2	1	no	—
477	C₂²⋊Q₈	—	2	1	no	—
478	C₂²⋊Q₈	—	2	2	no	—
479	C₂²⋊Q₈	—	2	4	no	—
480	C₂²⋊Q₈	—	2	4	no	—
481	C₂²⋊Q₈	—	2	4	no	—
482	C₂²⋊Q₈	—	2	4	no	—
483	C₂²⋊Q₈	—	2	4	no	—
484	C₂²⋊Q₈	D₄×C₂₃	1	2	yes	—
485	C₂²⋊Q₈	D₄×C₂₃	1	2	yes	—
486	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
487	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
488	C₄×Q₈	—	2	2	no	—
489	C₄×Q₈	—	2	2	no	—
490	C₄×Q₈	—	2	2	no	—
491	C₄×Q₈	—	2	2	no	—
492	C₄×Q₈	—	2	1	no	—
493	C₄×Q₈	—	2	1	no	—
494	C₄×Q₈	—	2	1	no	—
495	C₄×Q₈	—	2	1	no	—
496	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
497	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
498	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
499	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
500	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
501	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
502	C₄×D₄	—	2	2	no	—
503	C₄×D₄	—	2	2	no	—
504	C₄×D₄	—	2	1	no	—
505	C₄×D₄	—	2	1	no	—
506	C₄×D₄	C₂³×C₂₃	1	2	yes	—
507	C₄×D₄	C₂³×C₂₃	1	2	yes	—
508	C₄×D₄	C₂³×C₂₃	1	4	yes	—
509	C₄×D₄	C₂³×C₂₃	1	4	yes	—
510	#117	—	2	1	no	—
511	#117	—	2	1	no	—
512	#117	C₂³×C₂₃	1	2	yes	—
513	#117	C₂³×C₂₃	1	2	yes	—
514	C₂×C₄⋊C₄	—	2	4	no	—
515	C₂×C₄⋊C₄	—	2	2	no	—
516	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
517	C₂×C₂²⋊C₄	—	2	1	no	—
518	C₂×C₂²⋊C₄	—	2	4	no	—
519	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
520	#107	C₂³×C₂₃	1	4	yes	—
521	#107	C₂³×C₂₃	1	4	yes	—
522	#107	C₂³×C₂₃	1	4	yes	—
523	#106	C₂³×C₂₃	1	2	yes	—
524	#106	C₂³×C₂₃	1	4	yes	—
525	#106	C₂³×C₂₃	1	2	yes	—
526	#106	C₂³×C₂₃	1	4	yes	—
527	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
528	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
529	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
530	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
531	#103	C₂³×C₂₃	1	4	yes	—
532	#103	C₂³×C₂₃	1	2	yes	—
533	#103	C₂³×C₂₃	1	4	yes	—
534	#103	C₂³×C₂₃	1	2	yes	—
535	#103	C₂³×C₂₃	1	4	yes	—
536	#103	C₂³×C₂₃	1	4	yes	—
537	#103	C₂³×C₂₃	1	4	yes	—
538	#102	C₂³×C₂₃	1	2	yes	—
539	#102	C₂³×C₂₃	1	4	yes	—
540	#102	C₂³×C₂₃	1	2	yes	—
541	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
542	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
543	#97	C₂³×C₂₃	1	2	yes	—
544	#97	C₂³×C₂₃	1	4	yes	—
545	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
546	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
547	C₄×C₈	C₂³×C₂₃	1	4	yes	—
548	C₂₃	#61848	1	1	yes	characteristic, direct product factor, Sylow
549	C₂⁴	—	2	1	no	—
550	C₂×Q₈	—	2	1	no	—
551	C₂×Q₈	—	2	1	no	—
552	C₂×Q₈	—	2	1	no	—
553	C₂×Q₈	—	2	1	no	—
554	C₂×Q₈	—	2	4	no	—
555	C₂×Q₈	—	8	4	no	—
556	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
557	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
558	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
559	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
560	C₂×D₄	—	2	4	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	2	no	—
565	C₂²×C₄	—	2	4	no	—
566	C₂²×C₄	—	2	4	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	8	2	no	—
569	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
570	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
571	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
572	SD₁₆	—	2	4	no	—
573	SD₁₆	—	2	4	no	—
574	SD₁₆	—	2	8	no	—
575	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
576	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
577	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
578	C₄⋊C₄	—	2	2	no	—
579	C₄⋊C₄	—	2	1	no	—
580	C₄⋊C₄	—	2	4	no	—
581	C₄⋊C₄	—	2	4	no	—
582	C₄⋊C₄	—	2	4	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	2	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	2	no	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	—	2	4	no	—
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
603	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
604	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
605	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
606	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
607	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
608	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
609	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
610	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
611	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
612	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
613	C₂²⋊C₄	—	2	2	no	—
614	C₂²⋊C₄	—	2	2	no	—
615	C₂²⋊C₄	—	2	2	no	—
616	C₂²⋊C₄	—	2	4	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	2	no	—
619	C₂²⋊C₄	—	2	2	no	—
620	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
621	C₄²	—	2	2	no	—
622	C₄²	—	2	2	no	—
623	C₄²	—	2	2	no	—
624	C₄²	—	2	4	no	—
625	C₄²	—	2	4	no	—
626	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
627	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
628	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
629	C₄²	C₂⁴×C₂₃	1	4	yes	—
630	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
631	C₂³	—	2	4	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	8	1	no	—
634	C₂³	—	8	1	no	—
635	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
636	Q₈	—	2	4	no	—
637	Q₈	—	2	2	no	—
638	Q₈	—	2	4	no	—
639	Q₈	—	2	2	no	—
640	Q₈	—	4	2	no	—
641	Q₈	—	4	2	no	—
642	Q₈	—	4	2	no	—
643	Q₈	—	4	2	no	—
644	Q₈	—	8	4	no	—
645	Q₈	—	8	1	no	—
646	D₄	—	2	4	no	—
647	D₄	—	2	2	no	—
648	D₄	C₂₃×2₋¹⁺⁴	1	4	yes	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	4	no	—
660	C₂×C₄	—	8	2	no	—
661	C₂×C₄	—	8	4	no	—
662	C₂×C₄	—	8	4	no	—
663	C₂×C₄	—	8	1	no	—
664	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
665	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
666	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
667	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
668	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
669	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
670	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
671	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
672	C₈	—	2	2	no	—
673	C₈	—	2	2	no	—
674	C₈	—	2	4	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	4	no	—
677	C₂²	—	2	1	no	—
678	C₂²	—	2	1	no	—
679	C₂²	—	4	2	no	—
680	C₂²	—	4	2	no	—
681	C₂²	—	8	4	no	—
682	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	2	4	no	—
686	C₄	—	2	1	no	—
687	C₄	—	2	1	no	—
688	C₄	—	2	4	no	—
689	C₄	—	4	2	no	—
690	C₄	—	4	2	no	—
691	C₄	—	4	2	no	—
692	C₄	—	4	2	no	—
693	C₄	—	4	2	no	—
694	C₄	—	4	2	no	—
695	C₄	—	4	2	no	—
696	C₄	C₂₃×#577	1	2	yes	—
697	C₄	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
698	C₂	—	4	1	no	—
699	C₂	—	4	4	no	—
700	C₂	C₂₃×#3486	1	1	yes	characteristic
701	C₂	C₂×C₂₃×#577	1	1	yes	characteristic
702	C₂	C₂₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂²×D₄×C₂₃	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3556	C₂	semidirect
3. C₂₃×#3388	C₂	semidirect
4. C₂₃×#3386	C₂	semidirect
5. C₂₃×#3381	C₂	semidirect
6. C₂₃×#3372	C₂	semidirect
7. C₂₃×#3372	C₂	semidirect
8. C₂₃×#3359	C₂	semidirect
9. C₂₃×#3242	C₂	semidirect
10. C₂₃×#3237	C₂	semidirect
11. C₂₃×#3231	C₂	semidirect
15. C₂₃×#2985	C₂	semidirect
19. C₂₃×#557	C₂²	semidirect
20. C₂₃×#557	C₂²	semidirect
21. C₂₃×#557	C₂²	semidirect
22. C₂₃×#557	C₂²	semidirect
41. C₂₃×#501	C₂²	semidirect
42. C₂₃×#501	C₂²	semidirect
43. C₂₃×#500	C₂²	semidirect
44. C₂₃×#499	C₂²	semidirect
45. C₂₃×#498	C₂²	semidirect
46. C₂₃×#491	C₂²	semidirect
47. C₂₃×#491	C₂²	semidirect
48. C₂₃×#487	C₂²	semidirect
49. C₂₃×#487	C₂²	semidirect
50. C₂₃×#487	C₂²	semidirect
55. C₂₃×#479	C₂²	semidirect
56. C₂₃×#479	C₂²	semidirect
57. C₂₃×#479	C₂²	semidirect
60. C₂₃×#477	C₂²	semidirect
61. C₂₃×#477	C₂²	semidirect
63. C₂₃×#475	C₂²	semidirect
64. C₂₃×#475	C₂²	semidirect
72. C₂₃×#446	C₂²	semidirect
73. C₂₃×#446	C₂²	semidirect
74. C₈×Q₈×C₂₃	C₂²	semidirect
279. #61848	C₂₃	direct (N × H)
324. #3556	C₂×C₂₃	semidirect
326. #3388	C₂×C₂₃	semidirect
327. #3386	C₂×C₂₃	semidirect
328. #3381	C₂×C₂₃	semidirect
329. #3372	C₂×C₂₃	semidirect
330. #3372	C₂×C₂₃	semidirect
331. #3359	C₂×C₂₃	semidirect
332. #3242	C₂×C₂₃	semidirect
333. #3237	C₂×C₂₃	semidirect
334. #3231	C₂×C₂₃	semidirect
338. #2985	C₂×C₂₃	semidirect
365. #557	C₂²×C₂₃	semidirect
366. #557	C₂²×C₂₃	semidirect
367. #557	C₂²×C₂₃	semidirect
368. #557	C₂²×C₂₃	semidirect
387. #501	C₂²×C₂₃	semidirect
388. #501	C₂²×C₂₃	semidirect
389. #500	C₂²×C₂₃	semidirect
390. #499	C₂²×C₂₃	semidirect
391. #498	C₂²×C₂₃	semidirect
392. #491	C₂²×C₂₃	semidirect
393. #491	C₂²×C₂₃	semidirect
394. #487	C₂²×C₂₃	semidirect
395. #487	C₂²×C₂₃	semidirect
396. #487	C₂²×C₂₃	semidirect
401. #479	C₂²×C₂₃	semidirect
402. #479	C₂²×C₂₃	semidirect
403. #479	C₂²×C₂₃	semidirect
406. #477	C₂²×C₂₃	semidirect
407. #477	C₂²×C₂₃	semidirect
409. #475	C₂²×C₂₃	semidirect
410. #475	C₂²×C₂₃	semidirect
418. #446	C₂²×C₂₃	semidirect
419. #446	C₂²×C₂₃	semidirect
420. C₈×Q₈	C₂²×C₂₃	semidirect
548. C₂₃	#61848	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#3556	2
C₂₃×#3501	2
C₂₃×#3388	2
C₂₃×#3386	2
C₂₃×#3381	2
C₂₃×#3372	2
C₂₃×#3359	2
C₂₃×#3242	2
C₂₃×#3237	2
C₂₃×#3231	2
C₂₃×#3123	2
C₂₃×#3110	2
C₂₃×#3101	2
C₂₃×#2985	2
#61848	23

Subgroups — C23×#61848 #19209474

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61848 #19209474