Subgroups — C₂₃×#61293 #19208919

Order 5888.

1874 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3506	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3347	C₂	1	8	yes	maximal, complemented
3	C₂₃×#3345	C₂	1	8	yes	maximal, complemented
4	C₂₃×#3162	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3096	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3077	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3058	C₂	1	2	yes	maximal, complemented
8	C₂×C₂₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2932	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2912	C₂	1	2	yes	maximal, complemented
11	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
12	C₂×C₂₃×#131	C₂²	1	2	yes	—
13	C₂₃×#559	—	2	4	no	—
14	C₂₃×#556	—	2	2	no	—
15	C₂₃×#555	C₂²	1	4	yes	complemented
16	C₂₃×#553	C₂²	1	8	yes	complemented
17	C₂₃×#550	—	2	2	no	—
18	C₂₃×#547	C₂²	1	4	yes	complemented
19	C₂₃×#538	—	2	4	no	—
20	C₂₃×#535	C₂²	1	4	yes	—
21	C₂₃×#533	C₂²	1	2	yes	—
22	C₂₃×#532	C₂²	1	1	yes	characteristic
23	C₂₃×#525	—	2	4	no	—
24	C₂₃×#520	C₂²	1	4	yes	—
25	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
26	C₂₃×#501	C₂²	1	4	yes	complemented
27	C₂₃×#501	C₂²	1	4	yes	complemented
28	C₂₃×#482	C₂²	1	8	yes	complemented
29	C₂₃×#482	C₂²	1	8	yes	complemented
30	C₂₃×#481	C₂²	1	8	yes	complemented
31	C₂₃×#480	C₂²	1	8	yes	complemented
32	C₂₃×#478	C₂²	1	8	yes	complemented
33	C₂₃×#476	C₂²	1	4	yes	complemented
34	C₂₃×#474	C₂²	1	4	yes	complemented
35	C₂₃×#469	C₂²	1	4	yes	—
36	C₂₃×#469	C₂²	1	4	yes	—
37	C₂₃×#466	C₂²	1	8	yes	—
38	C₂₃×#442	C₂²	1	8	yes	—
39	C₂₃×#435	C₂²	1	8	yes	complemented
40	C₂₃×#428	C₂²	1	4	yes	—
41	C₂₃×#428	C₂²	1	8	yes	complemented
42	C₂₃×#427	C₂²	1	2	yes	—
43	C₂₃×#427	C₂²	1	2	yes	—
44	C₂₃×#427	C₂²	1	4	yes	complemented
45	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
46	C₂×C₂₃×#106	C₂²	1	4	yes	complemented
47	C₂₃×#423	C₂²	1	1	yes	characteristic
48	C₂₃×#418	C₂²	1	4	yes	—
49	C₂×C₂₃×#102	C₂²	1	2	yes	—
50	C₂₃×#408	C₂²	1	2	yes	—
51	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
52	C₂×#41×C₂₃	—	2	4	no	—
53	C₂×#41×C₂₃	C₂³	1	2	yes	—
54	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
55	C₂³×C₄×C₂₃	—	2	2	no	—
56	C₂×D₈×C₂₃	—	2	4	no	—
57	C₂×D₈×C₂₃	C₂³	1	4	yes	—
58	C₂₃×#131	—	2	8	no	—
59	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
60	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
61	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
62	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
64	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
65	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
66	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
67	C₂₃×#127	—	2	4	no	—
68	C₂₃×#127	D₄	1	1	yes	characteristic
69	C₂₃×#126	—	2	8	no	—
70	C₂₃×#125	C₂³	1	4	yes	—
71	C₂₃×#124	—	2	4	no	—
72	C₂₃×#124	—	2	8	no	—
73	C₂₃×#124	D₄	1	2	yes	—
74	C₂₃×#123	—	2	8	no	—
75	C₂₃×#123	—	2	8	no	—
76	C₂₃×C₂²⋊Q₈	—	2	2	no	—
77	C₂₃×C₂²⋊Q₈	—	2	2	no	—
78	C₂₃×C₂²⋊Q₈	—	2	4	no	—
79	C₂₃×#121	—	2	8	no	—
80	C₂₃×#121	—	2	4	no	—
81	C₂₃×#121	D₄	1	4	yes	—
82	C₂₃×#121	C₂³	1	8	yes	—
83	C₂₃×#121	C₂³	1	8	yes	—
84	C₂₃×#120	—	2	8	no	—
85	C₄×Q₈×C₂₃	—	2	4	no	—
86	C₄×Q₈×C₂₃	—	2	2	no	—
87	C₄×Q₈×C₂₃	—	2	2	no	—
88	C₄×D₄×C₂₃	—	2	4	no	—
89	C₄×D₄×C₂₃	—	2	8	no	—
90	C₄×D₄×C₂₃	—	2	8	no	—
91	C₄×D₄×C₂₃	—	2	2	no	—
92	C₄×D₄×C₂₃	—	2	2	no	—
93	C₄×D₄×C₂₃	C₂³	1	4	yes	—
94	C₄×D₄×C₂₃	C₂³	1	4	yes	—
95	C₄×D₄×C₂₃	C₂³	1	4	yes	—
96	C₂₃×#117	—	2	4	no	—
97	C₂₃×#117	C₂³	1	8	yes	—
98	C₂₃×#117	C₂³	1	4	yes	—
99	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
100	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
101	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
102	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
103	C₂₃×#107	C₂³	1	4	yes	—
104	C₂₃×#107	C₂³	1	4	yes	—
105	C₂₃×#107	C₂³	1	8	yes	—
106	C₂₃×#106	C₂³	1	4	yes	—
107	C₂₃×#106	C₂³	1	2	yes	—
108	C₂₃×#106	C₂³	1	8	yes	—
109	C₂₃×#106	C₂³	1	2	yes	—
110	C₂₃×#106	C₂³	1	2	yes	—
111	C₂₃×#106	C₂³	1	2	yes	—
112	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
113	C₂₃×#102	C₂³	1	8	yes	—
114	C₂₃×#102	C₂³	1	8	yes	—
115	C₂₃×#102	C₂³	1	8	yes	—
116	C₂₃×C₂²⋊C₈	C₂³	1	8	yes	—
117	C₂₃×#97	C₂³	1	4	yes	—
118	C₂⁴×C₂₃	—	2	2	no	—
119	#41×C₂₃	—	2	4	no	—
120	#41×C₂₃	—	2	4	no	—
121	#41×C₂₃	—	8	8	no	—
122	C₂×Q₈×C₂₃	—	2	2	no	—
123	C₂×Q₈×C₂₃	—	2	2	no	—
124	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
125	C₂×D₄×C₂₃	—	2	8	no	—
126	C₂×D₄×C₂₃	—	2	8	no	—
127	C₂×D₄×C₂₃	—	2	2	no	—
128	C₂×D₄×C₂₃	—	2	4	no	—
129	C₂×D₄×C₂₃	—	2	4	no	—
130	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
131	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
132	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
133	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
134	C₂²×C₄×C₂₃	—	2	2	no	—
135	C₂²×C₄×C₂₃	—	2	8	no	—
136	C₂²×C₄×C₂₃	—	2	4	no	—
137	C₂²×C₄×C₂₃	—	2	4	no	—
138	C₂²×C₄×C₂₃	—	8	4	no	—
139	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
141	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
142	D₈×C₂₃	—	2	8	no	—
143	M₁₆×C₂₃	—	2	4	no	—
144	M₁₆×C₂₃	—	2	8	no	—
145	C₂×C₈×C₂₃	—	2	2	no	—
146	C₂×C₈×C₂₃	—	2	8	no	—
147	C₂×C₈×C₂₃	#41	1	4	yes	complemented
148	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
149	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
150	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
151	C₄⋊C₄×C₂₃	—	2	2	no	—
152	C₄⋊C₄×C₂₃	—	2	8	no	—
153	C₄⋊C₄×C₂₃	—	2	2	no	—
154	C₄⋊C₄×C₂₃	—	2	4	no	—
155	C₄⋊C₄×C₂₃	—	2	4	no	—
156	C₄⋊C₄×C₂₃	—	2	2	no	—
157	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
158	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
159	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
160	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
161	C₂²⋊C₄×C₂₃	—	2	4	no	—
162	C₂²⋊C₄×C₂₃	—	2	8	no	—
163	C₂²⋊C₄×C₂₃	—	2	4	no	—
164	C₂²⋊C₄×C₂₃	—	2	4	no	—
165	C₂²⋊C₄×C₂₃	—	2	8	no	—
166	C₂²⋊C₄×C₂₃	—	2	8	no	—
167	C₂²⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
168	C₄²×C₂₃	—	2	8	no	—
169	C₄²×C₂₃	—	2	4	no	—
170	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₂₃	C₂⁴	1	2	yes	—
173	#61293	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂³×C₂₃	—	2	4	no	—
175	C₂³×C₂₃	—	4	4	no	—
176	C₂³×C₂₃	—	8	2	no	—
177	C₂³×C₂₃	—	8	2	no	—
178	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
179	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
180	Q₈×C₂₃	—	2	4	no	—
181	Q₈×C₂₃	—	4	4	no	—
182	Q₈×C₂₃	—	8	2	no	—
183	D₄×C₂₃	—	2	8	no	—
184	D₄×C₂₃	—	2	4	no	—
185	D₄×C₂₃	—	2	4	no	—
186	D₄×C₂₃	—	2	4	no	—
187	D₄×C₂₃	—	4	4	no	—
188	D₄×C₂₃	—	4	4	no	—
189	D₄×C₂₃	—	8	8	no	—
190	D₄×C₂₃	—	8	8	no	—
191	C₂×C₄×C₂₃	—	2	4	no	—
192	C₂×C₄×C₂₃	—	2	4	no	—
193	C₂×C₄×C₂₃	—	2	4	no	—
194	C₂×C₄×C₂₃	—	2	4	no	—
195	C₂×C₄×C₂₃	—	2	4	no	—
196	C₂×C₄×C₂₃	—	4	2	no	—
197	C₂×C₄×C₂₃	—	4	8	no	—
198	C₂×C₄×C₂₃	—	8	4	no	—
199	C₂×C₄×C₂₃	—	8	2	no	—
200	C₂×C₄×C₂₃	—	8	8	no	—
201	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
202	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
203	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
204	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
206	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
207	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
208	C₈×C₂₃	—	2	4	no	—
209	C₈×C₂₃	—	2	2	no	—
210	C₈×C₂₃	C₂×#41	1	4	yes	—
211	#3506	C₂×C₂₃	1	2	yes	complemented
212	#3347	C₂×C₂₃	1	8	yes	complemented
213	#3345	C₂×C₂₃	1	8	yes	complemented
214	#3162	C₂×C₂₃	1	1	yes	characteristic, complemented
215	#3096	C₂×C₂₃	1	4	yes	complemented
216	#3077	C₂×C₂₃	1	2	yes	complemented
217	#3058	C₂×C₂₃	1	2	yes	complemented
218	C₂×#442	C₂×C₂₃	1	1	yes	characteristic, complemented
219	#2932	C₂×C₂₃	1	1	yes	characteristic, complemented
220	#2912	C₂×C₂₃	1	2	yes	complemented
221	C₂²×C₂₃	—	2	2	no	—
222	C₂²×C₂₃	—	2	8	no	—
223	C₂²×C₂₃	—	2	4	no	—
224	C₂²×C₂₃	—	4	4	no	—
225	C₂²×C₂₃	—	4	4	no	—
226	C₂²×C₂₃	—	4	4	no	—
227	C₂²×C₂₃	—	8	8	no	—
228	C₂²×C₂₃	#547	1	2	yes	—
229	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
230	C₄×C₂₃	—	2	2	no	—
231	C₄×C₂₃	—	2	2	no	—
232	C₄×C₂₃	—	2	4	no	—
233	C₄×C₂₃	—	4	4	no	—
234	C₄×C₂₃	—	4	4	no	—
235	C₄×C₂₃	—	4	4	no	—
236	C₄×C₂₃	#547	1	2	yes	—
237	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
238	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
239	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
240	C₂×#131	C₂²×C₂₃	1	2	yes	—
241	#559	—	2	4	no	—
242	#556	—	2	2	no	—
243	#555	C₂²×C₂₃	1	4	yes	complemented
244	#553	C₂²×C₂₃	1	8	yes	complemented
245	#550	—	2	2	no	—
246	#547	C₂²×C₂₃	1	4	yes	complemented
247	#538	—	2	4	no	—
248	#535	C₂²×C₂₃	1	4	yes	—
249	#533	C₂²×C₂₃	1	2	yes	—
250	#532	C₂²×C₂₃	1	1	yes	characteristic
251	#525	—	2	4	no	—
252	#520	C₂²×C₂₃	1	4	yes	—
253	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
254	#501	C₂²×C₂₃	1	4	yes	complemented
255	#501	C₂²×C₂₃	1	4	yes	complemented
256	#482	C₂²×C₂₃	1	8	yes	complemented
257	#482	C₂²×C₂₃	1	8	yes	complemented
258	#481	C₂²×C₂₃	1	8	yes	complemented
259	#480	C₂²×C₂₃	1	8	yes	complemented
260	#478	C₂²×C₂₃	1	8	yes	complemented
261	#476	C₂²×C₂₃	1	4	yes	complemented
262	#474	C₂²×C₂₃	1	4	yes	complemented
263	#469	C₂²×C₂₃	1	4	yes	—
264	#469	C₂²×C₂₃	1	4	yes	—
265	#466	C₂²×C₂₃	1	8	yes	—
266	#442	C₂²×C₂₃	1	8	yes	—
267	#435	C₂²×C₂₃	1	8	yes	complemented
268	#428	C₂²×C₂₃	1	4	yes	—
269	#428	C₂²×C₂₃	1	8	yes	complemented
270	#427	C₂²×C₂₃	1	2	yes	—
271	#427	C₂²×C₂₃	1	2	yes	—
272	#427	C₂²×C₂₃	1	4	yes	complemented
273	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
274	C₂×#106	C₂²×C₂₃	1	4	yes	complemented
275	#423	C₂²×C₂₃	1	1	yes	characteristic
276	#418	C₂²×C₂₃	1	4	yes	—
277	C₂×#102	C₂²×C₂₃	1	2	yes	—
278	#408	C₂²×C₂₃	1	2	yes	—
279	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
280	C₂×C₂₃	—	2	2	no	—
281	C₂×C₂₃	—	4	4	no	—
282	C₂×C₂₃	—	8	4	no	—
283	C₂×C₂₃	C₂×#547	1	1	yes	characteristic
284	C₂×C₂₃	#3585	1	2	yes	—
285	C₂×#41	—	2	4	no	—
286	C₂×#41	C₂³×C₂₃	1	2	yes	—
287	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
288	C₂³×C₄	—	2	2	no	—
289	C₂×D₈	—	2	4	no	—
290	C₂×D₈	C₂³×C₂₃	1	4	yes	—
291	#131	—	2	8	no	—
292	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
293	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
294	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
295	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
296	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
297	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
298	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
299	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
300	#127	—	2	4	no	—
301	#127	D₄×C₂₃	1	1	yes	characteristic
302	#126	—	2	8	no	—
303	#125	C₂³×C₂₃	1	4	yes	—
304	#124	—	2	4	no	—
305	#124	—	2	8	no	—
306	#124	D₄×C₂₃	1	2	yes	—
307	#123	—	2	8	no	—
308	#123	—	2	8	no	—
309	C₂²⋊Q₈	—	2	2	no	—
310	C₂²⋊Q₈	—	2	2	no	—
311	C₂²⋊Q₈	—	2	4	no	—
312	#121	—	2	4	no	—
313	#121	—	2	8	no	—
314	#121	D₄×C₂₃	1	4	yes	—
315	#121	C₂³×C₂₃	1	8	yes	—
316	#121	C₂³×C₂₃	1	8	yes	—
317	#120	—	2	8	no	—
318	C₄×Q₈	—	2	4	no	—
319	C₄×Q₈	—	2	2	no	—
320	C₄×Q₈	—	2	2	no	—
321	C₄×D₄	—	2	8	no	—
322	C₄×D₄	—	2	4	no	—
323	C₄×D₄	—	2	8	no	—
324	C₄×D₄	—	2	2	no	—
325	C₄×D₄	—	2	2	no	—
326	C₄×D₄	C₂³×C₂₃	1	4	yes	—
327	C₄×D₄	C₂³×C₂₃	1	4	yes	—
328	C₄×D₄	C₂³×C₂₃	1	4	yes	—
329	#117	—	2	4	no	—
330	#117	C₂³×C₂₃	1	4	yes	—
331	#117	C₂³×C₂₃	1	8	yes	—
332	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
333	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
336	#107	C₂³×C₂₃	1	4	yes	—
337	#107	C₂³×C₂₃	1	4	yes	—
338	#107	C₂³×C₂₃	1	8	yes	—
339	#106	C₂³×C₂₃	1	4	yes	—
340	#106	C₂³×C₂₃	1	2	yes	—
341	#106	C₂³×C₂₃	1	8	yes	—
342	#106	C₂³×C₂₃	1	2	yes	—
343	#106	C₂³×C₂₃	1	2	yes	—
344	#106	C₂³×C₂₃	1	2	yes	—
345	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
346	#102	C₂³×C₂₃	1	8	yes	—
347	#102	C₂³×C₂₃	1	8	yes	—
348	#102	C₂³×C₂₃	1	8	yes	—
349	C₂²⋊C₈	C₂³×C₂₃	1	8	yes	—
350	#97	C₂³×C₂₃	1	4	yes	—
351	C₂₃	#61293	1	1	yes	characteristic, direct product factor, Sylow
352	C₂⁴	—	2	2	no	—
353	#41	—	2	4	no	—
354	#41	—	2	4	no	—
355	#41	—	8	8	no	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
359	C₂×D₄	—	2	8	no	—
360	C₂×D₄	—	2	8	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	4	no	—
363	C₂×D₄	—	2	4	no	—
364	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
365	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
366	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
367	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	8	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	8	4	no	—
373	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
374	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
375	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
376	D₈	—	2	8	no	—
377	M₁₆	—	2	4	no	—
378	M₁₆	—	2	8	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	8	no	—
381	C₂×C₈	#41×C₂₃	1	4	yes	complemented
382	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
383	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
384	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	8	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	4	no	—
389	C₄⋊C₄	—	2	4	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
392	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
393	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
394	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
395	C₂²⋊C₄	—	2	4	no	—
396	C₂²⋊C₄	—	2	8	no	—
397	C₂²⋊C₄	—	2	4	no	—
398	C₂²⋊C₄	—	2	4	no	—
399	C₂²⋊C₄	—	2	8	no	—
400	C₂²⋊C₄	—	2	8	no	—
401	C₂²⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
402	C₄²	—	2	8	no	—
403	C₄²	—	2	4	no	—
404	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
405	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
406	C₄²	C₂⁴×C₂₃	1	2	yes	—
407	C₂³	—	2	4	no	—
408	C₂³	—	4	4	no	—
409	C₂³	—	8	2	no	—
410	C₂³	—	8	2	no	—
411	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
412	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
413	Q₈	—	2	4	no	—
414	Q₈	—	4	4	no	—
415	Q₈	—	8	2	no	—
416	D₄	—	2	8	no	—
417	D₄	—	2	4	no	—
418	D₄	—	2	4	no	—
419	D₄	—	2	4	no	—
420	D₄	—	4	4	no	—
421	D₄	—	4	4	no	—
422	D₄	—	8	8	no	—
423	D₄	—	8	8	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	8	no	—
431	C₂×C₄	—	8	4	no	—
432	C₂×C₄	—	8	2	no	—
433	C₂×C₄	—	8	8	no	—
434	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
435	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
436	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
437	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
438	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
439	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
440	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
441	C₈	—	2	4	no	—
442	C₈	—	2	2	no	—
443	C₈	C₂×#41×C₂₃	1	4	yes	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	2	8	no	—
447	C₂²	—	4	4	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	4	4	no	—
450	C₂²	—	8	8	no	—
451	C₂²	C₂₃×#547	1	2	yes	—
452	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
453	C₄	—	2	4	no	—
454	C₄	—	2	2	no	—
455	C₄	—	2	2	no	—
456	C₄	—	4	4	no	—
457	C₄	—	4	4	no	—
458	C₄	—	4	4	no	—
459	C₄	C₂₃×#547	1	2	yes	—
460	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
461	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
462	C₂	—	2	2	no	—
463	C₂	—	4	4	no	—
464	C₂	—	8	4	no	—
465	C₂	C₂×C₂₃×#547	1	1	yes	characteristic
466	C₂	C₂₃×#3585	1	2	yes	—

	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3506	C₂	semidirect
2. C₂₃×#3347	C₂	semidirect
3. C₂₃×#3345	C₂	semidirect
4. C₂₃×#3162	C₂	semidirect
5. C₂₃×#3096	C₂	semidirect
6. C₂₃×#3077	C₂	semidirect
7. C₂₃×#3058	C₂	semidirect
8. C₂×C₂₃×#442	C₂	semidirect
9. C₂₃×#2932	C₂	semidirect
10. C₂₃×#2912	C₂	semidirect
15. C₂₃×#555	C₂²	semidirect
16. C₂₃×#553	C₂²	semidirect
18. C₂₃×#547	C₂²	semidirect
26. C₂₃×#501	C₂²	semidirect
27. C₂₃×#501	C₂²	semidirect
28. C₂₃×#482	C₂²	semidirect
29. C₂₃×#482	C₂²	semidirect
30. C₂₃×#481	C₂²	semidirect
31. C₂₃×#480	C₂²	semidirect
32. C₂₃×#478	C₂²	semidirect
33. C₂₃×#476	C₂²	semidirect
34. C₂₃×#474	C₂²	semidirect
39. C₂₃×#435	C₂²	semidirect
41. C₂₃×#428	C₂²	semidirect
44. C₂₃×#427	C₂²	semidirect
46. C₂×C₂₃×#106	C₂²	semidirect
147. C₂×C₈×C₂₃	#41	semidirect
173. #61293	C₂₃	direct (N × H)
211. #3506	C₂×C₂₃	semidirect
212. #3347	C₂×C₂₃	semidirect
213. #3345	C₂×C₂₃	semidirect
214. #3162	C₂×C₂₃	semidirect
215. #3096	C₂×C₂₃	semidirect
216. #3077	C₂×C₂₃	semidirect
217. #3058	C₂×C₂₃	semidirect
218. C₂×#442	C₂×C₂₃	semidirect
219. #2932	C₂×C₂₃	semidirect
220. #2912	C₂×C₂₃	semidirect
243. #555	C₂²×C₂₃	semidirect
244. #553	C₂²×C₂₃	semidirect
246. #547	C₂²×C₂₃	semidirect
254. #501	C₂²×C₂₃	semidirect
255. #501	C₂²×C₂₃	semidirect
256. #482	C₂²×C₂₃	semidirect
257. #482	C₂²×C₂₃	semidirect
258. #481	C₂²×C₂₃	semidirect
259. #480	C₂²×C₂₃	semidirect
260. #478	C₂²×C₂₃	semidirect
261. #476	C₂²×C₂₃	semidirect
262. #474	C₂²×C₂₃	semidirect
267. #435	C₂²×C₂₃	semidirect
269. #428	C₂²×C₂₃	semidirect
272. #427	C₂²×C₂₃	semidirect
274. C₂×#106	C₂²×C₂₃	semidirect
351. C₂₃	#61293	direct (N × H)
381. C₂×C₈	#41×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#3506	2
C₂₃×#3347	2
C₂₃×#3345	2
C₂₃×#3162	2
C₂₃×#3096	2
C₂₃×#3077	2
C₂₃×#3058	2
C₂×C₂₃×#442	2
C₂₃×#2932	2
C₂₃×#2912	2
#61293	23

Subgroups — C23×#61293 #19208919

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61293 #19208919