Subgroups — C₂₃×#61478 #19209104

Order 5888.

1768 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3518	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3393	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×Q₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3369	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3342	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3341	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#3329	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3313	C₂	1	4	yes	maximal, complemented
9	D₄×Q₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3285	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3175	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3170	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3121	C₂	1	4	yes	maximal, complemented
14	C₂₃×#3116	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2950	C₂	1	2	yes	maximal, complemented
17	C₄×C₂₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
19	C₂²×Q₁₆×C₂₃	C₂²	1	2	yes	—
20	Q₈²×C₂₃	C₂²	1	2	yes	—
21	C₂₃×#556	—	2	4	no	—
22	C₂₃×#556	—	2	2	no	—
23	C₂₃×#556	C₂²	1	2	yes	—
24	C₂₃×#556	C₂²	1	4	yes	—
25	C₂₃×#555	—	2	2	no	—
26	C₂₃×#555	C₂²	1	2	yes	—
27	D₄×Q₈×C₂₃	C₂²	1	2	yes	—
28	C₂₃×#548	C₂²	1	4	yes	—
29	C₂₃×#542	—	2	4	no	—
30	C₂₃×#542	C₂²	1	4	yes	—
31	C₂₃×#533	—	2	2	no	—
32	C₂₃×#533	C₂²	1	2	yes	—
33	C₂₃×#529	—	2	2	no	—
34	C₂₃×#529	C₂²	1	1	yes	characteristic
35	C₂₃×#519	C₂²	1	4	yes	—
36	C₄×#41×C₂₃	C₂²	1	2	yes	—
37	C₂₃×#500	C₂²	1	1	yes	characteristic
38	C₂₃×#500	C₂²	1	2	yes	—
39	C₂₃×#495	C₂²	1	2	yes	—
40	C₂₃×#494	C₂²	1	1	yes	characteristic
41	C₂₃×#489	C₂²	1	4	yes	—
42	C₂₃×#487	C₂²	1	2	yes	—
43	C₂₃×#485	C₂²	1	4	yes	—
44	C₂₃×#485	C₂²	1	4	yes	—
45	C₂₃×#482	C₂²	1	4	yes	—
46	C₂₃×#477	C₂²	1	4	yes	—
47	C₂₃×#477	C₂²	1	2	yes	—
48	C₂₃×#476	C₂²	1	2	yes	—
49	C₂₃×#475	C₂²	1	4	yes	—
50	C₂₃×#468	C₂²	1	4	yes	—
51	C₂₃×#467	C₂²	1	2	yes	—
52	C₂₃×#467	C₂²	1	2	yes	—
53	C₂₃×#467	C₂²	1	2	yes	—
54	C₂₃×#466	C₂²	1	2	yes	—
55	C₂₃×#464	C₂²	1	4	yes	—
56	C₂₃×#464	C₂²	1	4	yes	—
57	C₂₃×#462	C₂²	1	2	yes	—
58	C₂₃×#461	C₂²	1	2	yes	—
59	C₂₃×#452	C₂²	1	4	yes	—
60	C₂₃×#451	C₂²	1	4	yes	—
61	C₂₃×#448	C₂²	1	4	yes	—
62	C₂₃×#446	C₂²	1	1	yes	characteristic
63	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic
64	C₂₃×#441	C₂²	1	4	yes	—
65	C₂₃×#441	C₂²	1	4	yes	—
66	C₂₃×#440	C₂²	1	4	yes	—
67	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
68	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
69	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
70	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
71	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
72	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
73	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
74	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
75	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
76	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
77	C₂₃×#436	C₂²	1	1	yes	characteristic
78	C₂₃×#435	C₂²	1	2	yes	—
79	C₈×D₄×C₂₃	C₂²	1	2	yes	—
80	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
81	C₂₃×#433	C₂²	1	2	yes	—
82	C₂₃×#432	C₂²	1	1	yes	characteristic
83	C₂₃×#427	C₂²	1	1	yes	characteristic
84	C₂₃×#427	C₂²	1	2	yes	—
85	C₂₃×#419	C₂²	1	4	yes	—
86	C₂₃×#416	C₂²	1	2	yes	—
87	C₂₃×#405	C₂²	1	2	yes	—
88	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
89	C₂×#41×C₂₃	C₂³	1	2	yes	—
90	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
91	C₂₃×#135	—	2	4	no	—
92	C₂×Q₁₆×C₂₃	—	2	8	no	—
93	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
94	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
95	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
96	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
97	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
98	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
99	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
100	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
101	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
102	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
104	C₂₃×C₄⋊Q₈	—	2	2	no	—
105	C₂₃×C₄⋊Q₈	—	2	2	no	—
106	C₂₃×C₄⋊Q₈	—	2	4	no	—
107	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
108	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
109	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
110	C₂₃×#126	—	2	4	no	—
111	C₂₃×#126	—	2	4	no	—
112	C₂₃×#126	—	2	4	no	—
113	C₂₃×#126	—	2	4	no	—
114	C₂₃×#126	D₄	1	2	yes	—
115	C₂₃×#125	—	2	2	no	—
116	C₂₃×#125	D₄	1	1	yes	characteristic
117	C₂₃×#124	—	2	4	no	—
118	C₂₃×#124	—	2	4	no	—
119	C₂₃×#124	—	2	4	no	—
120	C₂₃×#124	—	2	4	no	—
121	C₂₃×#124	D₄	1	1	yes	characteristic
122	C₂₃×#124	C₂³	1	4	yes	—
123	C₂₃×#123	—	2	4	no	—
124	C₂₃×#123	D₄	1	2	yes	—
125	C₂₃×C₂²⋊Q₈	—	2	2	no	—
126	C₂₃×C₂²⋊Q₈	—	2	2	no	—
127	C₂₃×C₂²⋊Q₈	—	2	4	no	—
128	C₂₃×C₂²⋊Q₈	—	2	4	no	—
129	C₂₃×C₂²⋊Q₈	—	2	4	no	—
130	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
131	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
132	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
133	C₂₃×#121	—	2	4	no	—
134	C₂₃×#121	—	2	2	no	—
135	C₂₃×#121	D₄	1	1	yes	characteristic
136	C₂₃×#121	C₂³	1	4	yes	—
137	C₄×Q₈×C₂₃	—	2	2	no	—
138	C₄×Q₈×C₂₃	—	2	4	no	—
139	C₄×Q₈×C₂₃	—	2	4	no	—
140	C₄×Q₈×C₂₃	—	2	4	no	—
141	C₄×Q₈×C₂₃	—	2	2	no	—
142	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
143	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
144	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
145	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
146	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
147	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
148	C₄×D₄×C₂₃	—	2	2	no	—
149	C₄×D₄×C₂₃	—	2	2	no	—
150	C₄×D₄×C₂₃	—	2	2	no	—
151	C₄×D₄×C₂₃	—	2	4	no	—
152	C₄×D₄×C₂₃	C₂³	1	2	yes	—
153	C₄×D₄×C₂₃	C₂³	1	2	yes	—
154	C₄×D₄×C₂₃	C₂³	1	2	yes	—
155	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
156	C₂₃×#117	—	2	2	no	—
157	C₂₃×#117	—	2	2	no	—
158	C₂₃×#117	—	2	2	no	—
159	C₂₃×#117	—	2	4	no	—
160	C₂₃×#117	—	2	4	no	—
161	C₂₃×#117	—	2	2	no	—
162	C₂₃×#117	C₂³	1	4	yes	—
163	C₂₃×#117	C₂³	1	2	yes	—
164	C₂₃×#117	C₂³	1	2	yes	—
165	C₂×C₄²×C₂₃	—	2	2	no	—
166	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
167	C₂₃×#107	C₂³	1	1	yes	characteristic
168	C₂₃×#107	C₂³	1	1	yes	characteristic
169	C₂₃×#107	C₂³	1	2	yes	—
170	C₂₃×#107	C₂³	1	2	yes	—
171	C₂₃×#107	C₂³	1	4	yes	—
172	C₂₃×#106	C₂³	1	2	yes	—
173	C₂₃×#106	C₂³	1	4	yes	—
174	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
175	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
176	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
177	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
178	C₂₃×#103	C₂³	1	2	yes	—
179	C₂₃×#103	C₂³	1	2	yes	—
180	C₂₃×#103	C₂³	1	4	yes	—
181	C₂₃×#103	C₂³	1	4	yes	—
182	C₂₃×#103	C₂³	1	4	yes	—
183	C₂₃×#103	C₂³	1	4	yes	—
184	C₂₃×#103	C₂³	1	4	yes	—
185	C₂₃×#102	C₂³	1	2	yes	—
186	C₂₃×#102	C₂³	1	2	yes	—
187	C₂₃×#102	C₂³	1	4	yes	—
188	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
189	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
190	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
191	C₂₃×#97	C₂³	1	2	yes	—
192	C₂₃×#97	C₂³	1	2	yes	—
193	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
194	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₂₃	C₂³	1	2	yes	—
198	#41×C₂₃	—	2	4	no	—
199	#41×C₂₃	—	4	2	no	—
200	C₂×Q₈×C₂₃	—	2	4	no	—
201	C₂×Q₈×C₂₃	—	2	2	no	—
202	C₂×Q₈×C₂₃	—	2	4	no	—
203	C₂×Q₈×C₂₃	—	2	8	no	—
204	C₂×Q₈×C₂₃	—	4	4	no	—
205	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
206	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
207	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
208	C₂×D₄×C₂₃	—	2	2	no	—
209	C₂×D₄×C₂₃	—	2	4	no	—
210	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
211	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
212	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₂₃	—	2	4	no	—
214	C₂²×C₄×C₂₃	—	2	2	no	—
215	C₂²×C₄×C₂₃	—	2	2	no	—
216	C₂²×C₄×C₂₃	—	2	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	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
221	Q₁₆×C₂₃	—	2	8	no	—
222	Q₁₆×C₂₃	—	2	4	no	—
223	Q₁₆×C₂₃	—	4	2	no	—
224	Q₁₆×C₂₃	#41	1	4	yes	—
225	SD₁₆×C₂₃	—	2	4	no	—
226	SD₁₆×C₂₃	—	4	4	no	—
227	D₈×C₂₃	—	2	2	no	—
228	M₁₆×C₂₃	—	4	2	no	—
229	C₂×C₈×C₂₃	—	2	4	no	—
230	C₂×C₈×C₂₃	—	2	2	no	—
231	C₂×C₈×C₂₃	—	4	1	no	—
232	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
233	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
234	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
235	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
236	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
237	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
238	C₄⋊C₄×C₂₃	—	2	2	no	—
239	C₄⋊C₄×C₂₃	—	2	2	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	4	no	—
248	C₄⋊C₄×C₂₃	—	2	4	no	—
249	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
250	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
251	C₄⋊C₄×C₂₃	C₂×D₄	1	2	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	C₂⁴	1	2	yes	—
256	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
257	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
258	C₂²⋊C₄×C₂₃	—	2	4	no	—
259	C₂²⋊C₄×C₂₃	—	2	4	no	—
260	C₂²⋊C₄×C₂₃	—	2	2	no	—
261	C₂²⋊C₄×C₂₃	—	2	4	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	4	no	—
267	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
268	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
269	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
270	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
271	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
272	C₄²×C₂₃	—	2	2	no	—
273	C₄²×C₂₃	—	2	2	no	—
274	C₄²×C₂₃	—	2	2	no	—
275	C₄²×C₂₃	—	2	4	no	—
276	C₄²×C₂₃	—	2	4	no	—
277	C₄²×C₂₃	—	2	4	no	—
278	C₄²×C₂₃	—	2	4	no	—
279	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
280	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
281	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
282	C₄²×C₂₃	C₂⁴	1	2	yes	—
283	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
284	#61478	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
285	C₂³×C₂₃	—	2	2	no	—
286	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
287	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
288	Q₈×C₂₃	—	2	2	no	—
289	Q₈×C₂₃	—	2	2	no	—
290	Q₈×C₂₃	—	2	4	no	—
291	Q₈×C₂₃	—	2	4	no	—
292	Q₈×C₂₃	—	4	8	no	—
293	Q₈×C₂₃	—	8	2	no	—
294	Q₈×C₂₃	—	8	4	no	—
295	Q₈×C₂₃	C₂×#41	1	4	yes	—
296	D₄×C₂₃	—	2	2	no	—
297	D₄×C₂₃	—	2	2	no	—
298	D₄×C₂₃	—	2	2	no	—
299	D₄×C₂₃	—	4	2	no	—
300	D₄×C₂₃	—	4	4	no	—
301	D₄×C₂₃	—	8	4	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	1	no	—
306	C₂×C₄×C₂₃	—	2	1	no	—
307	C₂×C₄×C₂₃	—	2	2	no	—
308	C₂×C₄×C₂₃	—	2	2	no	—
309	C₂×C₄×C₂₃	—	2	4	no	—
310	C₂×C₄×C₂₃	—	2	4	no	—
311	C₂×C₄×C₂₃	—	2	2	no	—
312	C₂×C₄×C₂₃	—	4	1	no	—
313	C₂×C₄×C₂₃	—	4	4	no	—
314	C₂×C₄×C₂₃	—	4	8	no	—
315	C₂×C₄×C₂₃	—	4	4	no	—
316	C₂×C₄×C₂₃	—	8	2	no	—
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	C₂²×D₄	1	2	yes	—
321	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
322	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
323	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
324	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
326	C₈×C₂₃	—	2	1	no	—
327	C₈×C₂₃	—	2	2	no	—
328	C₈×C₂₃	—	2	1	no	—
329	C₈×C₂₃	—	2	1	no	—
330	C₈×C₂₃	—	2	2	no	—
331	C₈×C₂₃	C₂×#41	1	2	yes	—
332	#3518	C₂×C₂₃	1	2	yes	complemented
333	#3393	C₂×C₂₃	1	1	yes	characteristic, complemented
334	Q₈×Q₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
335	#3369	C₂×C₂₃	1	2	yes	complemented
336	#3342	C₂×C₂₃	1	2	yes	complemented
337	#3341	C₂×C₂₃	1	1	yes	characteristic, complemented
338	#3329	C₂×C₂₃	1	2	yes	complemented
339	#3313	C₂×C₂₃	1	4	yes	complemented
340	D₄×Q₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
341	#3285	C₂×C₂₃	1	2	yes	complemented
342	#3175	C₂×C₂₃	1	2	yes	complemented
343	#3170	C₂×C₂₃	1	1	yes	characteristic, complemented
344	#3121	C₂×C₂₃	1	4	yes	complemented
345	#3116	C₂×C₂₃	1	2	yes	complemented
346	#2966	C₂×C₂₃	1	1	yes	characteristic, complemented
347	#2950	C₂×C₂₃	1	2	yes	complemented
348	C₄×#135	C₂×C₂₃	1	1	yes	characteristic, complemented
349	C₂²×C₂₃	—	2	1	no	—
350	C₂²×C₂₃	—	2	2	no	—
351	C₂²×C₂₃	—	2	2	no	—
352	C₂²×C₂₃	—	2	1	no	—
353	C₂²×C₂₃	—	2	1	no	—
354	C₂²×C₂₃	—	2	2	no	—
355	C₂²×C₂₃	—	4	2	no	—
356	C₂²×C₂₃	—	4	2	no	—
357	C₂²×C₂₃	—	4	2	no	—
358	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
359	C₄×C₂₃	—	2	1	no	—
360	C₄×C₂₃	—	2	1	no	—
361	C₄×C₂₃	—	2	2	no	—
362	C₄×C₂₃	—	2	1	no	—
363	C₄×C₂₃	—	2	2	no	—
364	C₄×C₂₃	—	2	4	no	—
365	C₄×C₂₃	—	2	1	no	—
366	C₄×C₂₃	—	2	2	no	—
367	C₄×C₂₃	—	4	2	no	—
368	C₄×C₂₃	—	4	4	no	—
369	C₄×C₂₃	—	4	4	no	—
370	C₄×C₂₃	—	4	2	no	—
371	C₄×C₂₃	#578	1	2	yes	—
372	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
373	C₄×C₂₃	#585	1	1	yes	characteristic
374	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
375	C₂²×Q₁₆	C₂²×C₂₃	1	2	yes	—
376	Q₈²	C₂²×C₂₃	1	2	yes	—
377	#556	—	2	4	no	—
378	#556	—	2	2	no	—
379	#556	C₂²×C₂₃	1	2	yes	—
380	#556	C₂²×C₂₃	1	4	yes	—
381	#555	—	2	2	no	—
382	#555	C₂²×C₂₃	1	2	yes	—
383	D₄×Q₈	C₂²×C₂₃	1	2	yes	—
384	#548	C₂²×C₂₃	1	4	yes	—
385	#542	—	2	4	no	—
386	#542	C₂²×C₂₃	1	4	yes	—
387	#533	—	2	2	no	—
388	#533	C₂²×C₂₃	1	2	yes	—
389	#529	—	2	2	no	—
390	#529	C₂²×C₂₃	1	1	yes	characteristic
391	#519	C₂²×C₂₃	1	4	yes	—
392	C₄×#41	C₂²×C₂₃	1	2	yes	—
393	#500	C₂²×C₂₃	1	1	yes	characteristic
394	#500	C₂²×C₂₃	1	2	yes	—
395	#495	C₂²×C₂₃	1	2	yes	—
396	#494	C₂²×C₂₃	1	1	yes	characteristic
397	#489	C₂²×C₂₃	1	4	yes	—
398	#487	C₂²×C₂₃	1	2	yes	—
399	#485	C₂²×C₂₃	1	4	yes	—
400	#485	C₂²×C₂₃	1	4	yes	—
401	#482	C₂²×C₂₃	1	4	yes	—
402	#477	C₂²×C₂₃	1	2	yes	—
403	#477	C₂²×C₂₃	1	4	yes	—
404	#476	C₂²×C₂₃	1	2	yes	—
405	#475	C₂²×C₂₃	1	4	yes	—
406	#468	C₂²×C₂₃	1	4	yes	—
407	#467	C₂²×C₂₃	1	2	yes	—
408	#467	C₂²×C₂₃	1	2	yes	—
409	#467	C₂²×C₂₃	1	2	yes	—
410	#466	C₂²×C₂₃	1	2	yes	—
411	#464	C₂²×C₂₃	1	4	yes	—
412	#464	C₂²×C₂₃	1	4	yes	—
413	#462	C₂²×C₂₃	1	2	yes	—
414	#461	C₂²×C₂₃	1	2	yes	—
415	#452	C₂²×C₂₃	1	4	yes	—
416	#451	C₂²×C₂₃	1	4	yes	—
417	#448	C₂²×C₂₃	1	4	yes	—
418	#446	C₂²×C₂₃	1	1	yes	characteristic
419	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic
420	#441	C₂²×C₂₃	1	4	yes	—
421	#441	C₂²×C₂₃	1	4	yes	—
422	#440	C₂²×C₂₃	1	4	yes	—
423	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
424	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
425	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
426	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
427	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
428	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
429	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
430	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
431	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
432	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
433	#436	C₂²×C₂₃	1	1	yes	characteristic
434	#435	C₂²×C₂₃	1	2	yes	—
435	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
436	C₈×D₄	C₂²×C₂₃	1	2	yes	—
437	#433	C₂²×C₂₃	1	2	yes	—
438	#432	C₂²×C₂₃	1	1	yes	characteristic
439	#427	C₂²×C₂₃	1	2	yes	—
440	#427	C₂²×C₂₃	1	1	yes	characteristic
441	#419	C₂²×C₂₃	1	4	yes	—
442	#416	C₂²×C₂₃	1	2	yes	—
443	#405	C₂²×C₂₃	1	2	yes	—
444	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
445	C₂×C₂₃	—	4	1	no	—
446	C₂×C₂₃	—	4	2	no	—
447	C₂×C₂₃	—	8	2	no	—
448	C₂×C₂₃	D₄×#41	1	1	yes	characteristic
449	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
450	C₂×C₂₃	#3584	1	1	yes	characteristic
451	C₂×#41	C₂³×C₂₃	1	2	yes	—
452	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
453	#135	—	2	4	no	—
454	C₂×Q₁₆	—	2	8	no	—
455	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
456	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
457	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
458	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
459	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
460	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
461	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
462	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
463	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
464	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
465	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
466	C₄⋊Q₈	—	2	2	no	—
467	C₄⋊Q₈	—	2	2	no	—
468	C₄⋊Q₈	—	2	4	no	—
469	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
470	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
471	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
472	#126	—	2	4	no	—
473	#126	—	2	4	no	—
474	#126	—	2	4	no	—
475	#126	—	2	4	no	—
476	#126	D₄×C₂₃	1	2	yes	—
477	#125	—	2	2	no	—
478	#125	D₄×C₂₃	1	1	yes	characteristic
479	#124	—	2	4	no	—
480	#124	—	2	4	no	—
481	#124	—	2	4	no	—
482	#124	—	2	4	no	—
483	#124	D₄×C₂₃	1	1	yes	characteristic
484	#124	C₂³×C₂₃	1	4	yes	—
485	#123	—	2	4	no	—
486	#123	D₄×C₂₃	1	2	yes	—
487	C₂²⋊Q₈	—	2	2	no	—
488	C₂²⋊Q₈	—	2	2	no	—
489	C₂²⋊Q₈	—	2	4	no	—
490	C₂²⋊Q₈	—	2	4	no	—
491	C₂²⋊Q₈	—	2	4	no	—
492	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
493	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
494	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
495	#121	—	2	2	no	—
496	#121	—	2	4	no	—
497	#121	D₄×C₂₃	1	1	yes	characteristic
498	#121	C₂³×C₂₃	1	4	yes	—
499	C₄×Q₈	—	2	2	no	—
500	C₄×Q₈	—	2	4	no	—
501	C₄×Q₈	—	2	4	no	—
502	C₄×Q₈	—	2	4	no	—
503	C₄×Q₈	—	2	2	no	—
504	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
505	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
506	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
507	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
508	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
509	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	—	2	2	no	—
513	C₄×D₄	—	2	4	no	—
514	C₄×D₄	C₂³×C₂₃	1	2	yes	—
515	C₄×D₄	C₂³×C₂₃	1	2	yes	—
516	C₄×D₄	C₂³×C₂₃	1	2	yes	—
517	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
518	#117	—	2	2	no	—
519	#117	—	2	2	no	—
520	#117	—	2	2	no	—
521	#117	—	2	4	no	—
522	#117	—	2	4	no	—
523	#117	—	2	2	no	—
524	#117	C₂³×C₂₃	1	2	yes	—
525	#117	C₂³×C₂₃	1	4	yes	—
526	#117	C₂³×C₂₃	1	2	yes	—
527	C₂×C₄²	—	2	2	no	—
528	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
529	#107	C₂³×C₂₃	1	1	yes	characteristic
530	#107	C₂³×C₂₃	1	1	yes	characteristic
531	#107	C₂³×C₂₃	1	2	yes	—
532	#107	C₂³×C₂₃	1	2	yes	—
533	#107	C₂³×C₂₃	1	4	yes	—
534	#106	C₂³×C₂₃	1	2	yes	—
535	#106	C₂³×C₂₃	1	4	yes	—
536	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
537	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
538	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
539	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
540	#103	C₂³×C₂₃	1	2	yes	—
541	#103	C₂³×C₂₃	1	2	yes	—
542	#103	C₂³×C₂₃	1	4	yes	—
543	#103	C₂³×C₂₃	1	4	yes	—
544	#103	C₂³×C₂₃	1	4	yes	—
545	#103	C₂³×C₂₃	1	4	yes	—
546	#103	C₂³×C₂₃	1	4	yes	—
547	#102	C₂³×C₂₃	1	2	yes	—
548	#102	C₂³×C₂₃	1	2	yes	—
549	#102	C₂³×C₂₃	1	4	yes	—
550	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
551	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
552	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
553	#97	C₂³×C₂₃	1	2	yes	—
554	#97	C₂³×C₂₃	1	2	yes	—
555	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
556	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
557	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
558	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
559	C₄×C₈	C₂³×C₂₃	1	2	yes	—
560	C₂₃	#61478	1	1	yes	characteristic, direct product factor, Sylow
561	#41	—	2	4	no	—
562	#41	—	4	2	no	—
563	C₂×Q₈	—	2	4	no	—
564	C₂×Q₈	—	2	2	no	—
565	C₂×Q₈	—	2	4	no	—
566	C₂×Q₈	—	2	8	no	—
567	C₂×Q₈	—	4	4	no	—
568	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
569	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
570	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
571	C₂×D₄	—	2	2	no	—
572	C₂×D₄	—	2	4	no	—
573	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
574	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
575	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
576	C₂²×C₄	—	2	4	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
581	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
582	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
583	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
584	Q₁₆	—	2	8	no	—
585	Q₁₆	—	2	4	no	—
586	Q₁₆	—	4	2	no	—
587	Q₁₆	#41×C₂₃	1	4	yes	—
588	SD₁₆	—	2	4	no	—
589	SD₁₆	—	4	4	no	—
590	D₈	—	2	2	no	—
591	M₁₆	—	4	2	no	—
592	C₂×C₈	—	2	4	no	—
593	C₂×C₈	—	2	2	no	—
594	C₂×C₈	—	4	1	no	—
595	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
596	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
597	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
598	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
599	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
600	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	2	2	no	—
603	C₄⋊C₄	—	2	2	no	—
604	C₄⋊C₄	—	2	2	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	2	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
613	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
614	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
615	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
616	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
617	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
618	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
619	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
620	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₂²⋊C₄	—	2	4	no	—
623	C₂²⋊C₄	—	2	2	no	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	2	2	no	—
626	C₂²⋊C₄	—	2	2	no	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
631	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
632	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
633	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
634	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
635	C₄²	—	2	2	no	—
636	C₄²	—	2	2	no	—
637	C₄²	—	2	2	no	—
638	C₄²	—	2	4	no	—
639	C₄²	—	2	4	no	—
640	C₄²	—	2	4	no	—
641	C₄²	—	2	4	no	—
642	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
643	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
644	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
645	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
646	C₄²	C₂⁴×C₂₃	1	2	yes	—
647	C₂³	—	2	2	no	—
648	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
649	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
650	Q₈	—	2	2	no	—
651	Q₈	—	2	2	no	—
652	Q₈	—	2	4	no	—
653	Q₈	—	2	4	no	—
654	Q₈	—	4	8	no	—
655	Q₈	—	8	2	no	—
656	Q₈	—	8	4	no	—
657	Q₈	C₂×#41×C₂₃	1	4	yes	—
658	D₄	—	2	2	no	—
659	D₄	—	2	2	no	—
660	D₄	—	2	2	no	—
661	D₄	—	4	2	no	—
662	D₄	—	4	4	no	—
663	D₄	—	8	4	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	4	no	—
672	C₂×C₄	—	2	4	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	4	no	—
676	C₂×C₄	—	4	8	no	—
677	C₂×C₄	—	4	4	no	—
678	C₂×C₄	—	8	2	no	—
679	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
680	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
681	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
682	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
683	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
684	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
685	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
686	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
687	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
688	C₈	—	2	1	no	—
689	C₈	—	2	2	no	—
690	C₈	—	2	1	no	—
691	C₈	—	2	1	no	—
692	C₈	—	2	2	no	—
693	C₈	C₂×#41×C₂₃	1	2	yes	—
694	C₂²	—	2	2	no	—
695	C₂²	—	2	1	no	—
696	C₂²	—	2	1	no	—
697	C₂²	—	2	2	no	—
698	C₂²	—	2	1	no	—
699	C₂²	—	2	2	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	2	no	—
703	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
704	C₄	—	2	1	no	—
705	C₄	—	2	2	no	—
706	C₄	—	2	4	no	—
707	C₄	—	2	1	no	—
708	C₄	—	2	2	no	—
709	C₄	—	2	1	no	—
710	C₄	—	2	1	no	—
711	C₄	—	2	2	no	—
712	C₄	—	4	4	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	2	no	—
715	C₄	—	4	4	no	—
716	C₄	C₂₃×#578	1	2	yes	—
717	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
718	C₄	C₂₃×#585	1	1	yes	characteristic
719	C₂	—	4	2	no	—
720	C₂	—	4	1	no	—
721	C₂	—	8	2	no	—
722	C₂	D₄×#41×C₂₃	1	1	yes	characteristic
723	C₂	C₂×C₂₃×#578	1	1	yes	characteristic
724	C₂	C₂₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3518	C₂	semidirect
2. C₂₃×#3393	C₂	semidirect
3. Q₈×Q₁₆×C₂₃	C₂	semidirect
4. C₂₃×#3369	C₂	semidirect
5. C₂₃×#3342	C₂	semidirect
6. C₂₃×#3341	C₂	semidirect
7. C₂₃×#3329	C₂	semidirect
8. C₂₃×#3313	C₂	semidirect
9. D₄×Q₁₆×C₂₃	C₂	semidirect
10. C₂₃×#3285	C₂	semidirect
11. C₂₃×#3175	C₂	semidirect
12. C₂₃×#3170	C₂	semidirect
13. C₂₃×#3121	C₂	semidirect
14. C₂₃×#3116	C₂	semidirect
15. C₂₃×#2966	C₂	semidirect
16. C₂₃×#2950	C₂	semidirect
17. C₄×C₂₃×#135	C₂	semidirect
284. #61478	C₂₃	direct (N × H)
332. #3518	C₂×C₂₃	semidirect
333. #3393	C₂×C₂₃	semidirect
334. Q₈×Q₁₆	C₂×C₂₃	semidirect
335. #3369	C₂×C₂₃	semidirect
336. #3342	C₂×C₂₃	semidirect
337. #3341	C₂×C₂₃	semidirect
338. #3329	C₂×C₂₃	semidirect
339. #3313	C₂×C₂₃	semidirect
340. D₄×Q₁₆	C₂×C₂₃	semidirect
341. #3285	C₂×C₂₃	semidirect
342. #3175	C₂×C₂₃	semidirect
343. #3170	C₂×C₂₃	semidirect
344. #3121	C₂×C₂₃	semidirect
345. #3116	C₂×C₂₃	semidirect
346. #2966	C₂×C₂₃	semidirect
347. #2950	C₂×C₂₃	semidirect
348. C₄×#135	C₂×C₂₃	semidirect
560. C₂₃	#61478	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×#3518	2
C₂₃×#3393	2
Q₈×Q₁₆×C₂₃	2
C₂₃×#3369	2
C₂₃×#3342	2
C₂₃×#3341	2
C₂₃×#3329	2
C₂₃×#3313	2
D₄×Q₁₆×C₂₃	2
C₂₃×#3285	2
C₂₃×#3175	2
C₂₃×#3170	2
C₂₃×#3121	2
C₂₃×#3116	2
C₂₃×#2966	2
C₂₃×#2950	2
C₄×C₂₃×#135	2
#61478	23

Subgroups — C23×#61478 #19209104

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61478 #19209104