Subgroups — C₂₃×#23705 #19171331

Order 5888.

820 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Q₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#433	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2323	C₂	1	2	yes	maximal
4	C₂₃×#2086	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2075	C₂	1	1	yes	maximal, characteristic
6	C₂₃×#2068	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2056	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2036	C₂	1	2	yes	maximal
9	C₂₃×#2001	C₂	1	1	yes	maximal, characteristic
10	C₄×C₂₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1763	C₂	1	2	yes	maximal, complemented
12	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
13	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
15	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
16	C₄×Q₁₆×C₂₃	—	2	4	no	—
17	C₂₃×#433	—	2	4	no	—
18	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×#107	C₂²	1	2	yes	—
20	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#103	C₂²	1	2	yes	—
23	C₂×C₂₃×#103	C₂²	1	2	yes	—
24	C₂×C₂₃×#103	C₂²	1	2	yes	—
25	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
29	C₂₃×#391	C₂²	1	2	yes	—
30	C₂₃×#389	—	2	2	no	—
31	C₂₃×#389	C₂²	1	2	yes	—
32	C₂₃×#388	—	2	2	no	—
33	C₂₃×#388	—	2	2	no	—
34	C₂₃×#387	—	2	2	no	—
35	C₂₃×#380	C₂²	1	2	yes	—
36	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
37	C₂₃×#340	C₂²	1	1	yes	characteristic
38	C₂₃×#340	C₂²	1	2	yes	—
39	C₂₃×#340	C₂²	1	2	yes	—
40	C₂₃×#340	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
42	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
43	C₂×Q₁₆×C₂₃	—	2	4	no	—
44	C₂×Q₁₆×C₂₃	—	2	2	no	—
45	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
49	C₂₃×C₂²⋊Q₈	—	2	4	no	—
50	C₂₃×C₂²⋊Q₈	—	2	4	no	—
51	C₄×Q₈×C₂₃	—	2	4	no	—
52	C₄×Q₈×C₂₃	—	2	4	no	—
53	C₂₃×#117	—	2	2	no	—
54	C₂₃×#117	—	2	2	no	—
55	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
56	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
57	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
58	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
63	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₂₃	—	2	2	no	—
68	C₂×C₄²×C₂₃	—	2	2	no	—
69	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
71	C₂₃×#107	—	2	2	no	—
72	C₂₃×#107	—	2	4	no	—
73	C₂₃×C₄⋊C₈	—	2	2	no	—
74	C₂₃×C₄⋊C₈	—	2	2	no	—
75	C₂₃×#103	—	2	4	no	—
76	C₂₃×#103	—	2	4	no	—
77	C₂₃×#103	—	2	4	no	—
78	C₂₃×C₂²⋊C₈	—	2	2	no	—
79	C₂₃×C₂²⋊C₈	—	2	2	no	—
80	C₂₃×#97	—	2	2	no	—
81	C₄×C₈×C₂₃	D₄	1	4	yes	—
82	C₂₃×#95	—	2	2	no	—
83	C₂₃×#95	—	2	2	no	—
84	C₂₃×#95	—	2	2	no	—
85	C₂₃×#95	—	2	2	no	—
86	C₂₃×#95	—	2	2	no	—
87	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
88	C₂×Q₈×C₂₃	—	2	2	no	—
89	C₂×Q₈×C₂₃	—	2	2	no	—
90	C₂×Q₈×C₂₃	—	2	2	no	—
91	C₂×Q₈×C₂₃	—	2	2	no	—
92	C₂×Q₈×C₂₃	—	2	2	no	—
93	C₂×Q₈×C₂₃	#41	1	4	yes	—
94	C₂²×C₄×C₂₃	—	2	2	no	—
95	C₂²×C₄×C₂₃	—	2	2	no	—
96	C₂²×C₄×C₂₃	—	2	1	no	—
97	C₂²×C₄×C₂₃	—	2	1	no	—
98	C₂²×C₄×C₂₃	—	2	2	no	—
99	C₂²×C₄×C₂₃	—	2	2	no	—
100	C₂²×C₄×C₂₃	—	2	2	no	—
101	C₂²×C₄×C₂₃	—	2	2	no	—
102	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
108	Q₁₆×C₂₃	—	2	8	no	—
109	C₂×C₈×C₂₃	—	2	2	no	—
110	C₂×C₈×C₂₃	—	2	2	no	—
111	C₂×C₈×C₂₃	—	2	1	no	—
112	C₂×C₈×C₂₃	—	2	1	no	—
113	C₂×C₈×C₂₃	—	2	2	no	—
114	C₂×C₈×C₂₃	—	2	2	no	—
115	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
116	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
117	C₄⋊C₄×C₂₃	—	2	8	no	—
118	C₄⋊C₄×C₂₃	—	2	2	no	—
119	C₄⋊C₄×C₂₃	—	2	2	no	—
120	C₄⋊C₄×C₂₃	—	2	2	no	—
121	C₄⋊C₄×C₂₃	—	2	2	no	—
122	C₄⋊C₄×C₂₃	—	2	2	no	—
123	C₄⋊C₄×C₂₃	—	2	2	no	—
124	C₄⋊C₄×C₂₃	—	2	2	no	—
125	C₄⋊C₄×C₂₃	—	4	4	no	—
126	C₄⋊C₄×C₂₃	—	8	2	no	—
127	C₄⋊C₄×C₂₃	#41	1	4	yes	—
128	C₂²⋊C₄×C₂₃	—	2	8	no	—
129	C₂²⋊C₄×C₂₃	—	2	2	no	—
130	C₂²⋊C₄×C₂₃	—	2	2	no	—
131	C₂²⋊C₄×C₂₃	—	8	2	no	—
132	C₄²×C₂₃	—	2	1	no	—
133	C₄²×C₂₃	—	2	1	no	—
134	C₄²×C₂₃	—	4	4	no	—
135	C₄²×C₂₃	—	8	2	no	—
136	C₄²×C₂₃	C₂×D₄	1	2	yes	—
137	C₄²×C₂₃	#41	1	2	yes	—
138	#23705	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂³×C₂₃	—	2	1	no	—
140	C₂³×C₂₃	—	2	2	no	—
141	C₂³×C₂₃	—	2	1	no	—
142	C₂³×C₂₃	—	2	2	no	—
143	C₂³×C₂₃	—	2	1	no	—
144	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
145	Q₈×C₂₃	—	2	4	no	—
146	Q₈×C₂₃	—	2	4	no	—
147	Q₈×C₂₃	—	4	2	no	—
148	Q₈×C₂₃	—	4	2	no	—
149	C₂×C₄×C₂₃	—	2	1	no	—
150	C₂×C₄×C₂₃	—	2	2	no	—
151	C₂×C₄×C₂₃	—	2	1	no	—
152	C₂×C₄×C₂₃	—	2	1	no	—
153	C₂×C₄×C₂₃	—	2	1	no	—
154	C₂×C₄×C₂₃	—	2	1	no	—
155	C₂×C₄×C₂₃	—	2	4	no	—
156	C₂×C₄×C₂₃	—	2	4	no	—
157	C₂×C₄×C₂₃	—	2	2	no	—
158	C₂×C₄×C₂₃	—	2	1	no	—
159	C₂×C₄×C₂₃	—	2	2	no	—
160	C₂×C₄×C₂₃	—	2	1	no	—
161	C₂×C₄×C₂₃	—	4	2	no	—
162	C₂×C₄×C₂₃	—	4	2	no	—
163	C₂×C₄×C₂₃	—	4	2	no	—
164	C₂×C₄×C₂₃	—	4	2	no	—
165	C₂×C₄×C₂₃	—	4	1	no	—
166	C₂×C₄×C₂₃	—	4	2	no	—
167	C₂×C₄×C₂₃	—	4	1	no	—
168	C₂×C₄×C₂₃	—	4	2	no	—
169	C₂×C₄×C₂₃	—	4	2	no	—
170	C₂×C₄×C₂₃	—	4	2	no	—
171	C₂×C₄×C₂₃	—	4	2	no	—
172	C₂×C₄×C₂₃	—	4	2	no	—
173	C₂×C₄×C₂₃	—	4	2	no	—
174	C₂×C₄×C₂₃	#121	1	2	yes	—
175	C₂×C₄×C₂₃	#121	1	2	yes	—
176	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
178	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
179	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
180	C₈×C₂₃	—	2	2	no	—
181	C₈×C₂₃	—	2	2	no	—
182	C₈×C₂₃	—	4	1	no	—
183	C₈×C₂₃	—	4	1	no	—
184	C₂×C₄×Q₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
185	C₂×#433	C₂×C₂₃	1	1	yes	characteristic
186	#2323	C₂×C₂₃	1	2	yes	—
187	#2086	C₂×C₂₃	1	1	yes	characteristic, complemented
188	#2075	C₂×C₂₃	1	1	yes	characteristic
189	#2068	C₂×C₂₃	1	2	yes	complemented
190	#2056	C₂×C₂₃	1	1	yes	characteristic, complemented
191	#2036	C₂×C₂₃	1	2	yes	—
192	#2001	C₂×C₂₃	1	1	yes	characteristic
193	C₄×#107	C₂×C₂₃	1	1	yes	characteristic, complemented
194	#1763	C₂×C₂₃	1	2	yes	complemented
195	C₂²×C₂₃	—	4	2	no	—
196	C₂²×C₂₃	—	4	2	no	—
197	C₂²×C₂₃	—	4	1	no	—
198	C₂²×C₂₃	—	4	1	no	—
199	C₂²×C₂₃	—	4	1	no	—
200	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
201	C₂²×C₂₃	#525	1	2	yes	—
202	C₂²×C₂₃	#576	1	1	yes	characteristic
203	C₂²×C₂₃	#578	1	2	yes	—
204	C₂²×C₂₃	#578	1	1	yes	characteristic
205	C₄×C₂₃	—	2	2	no	—
206	C₄×C₂₃	—	2	2	no	—
207	C₄×C₂₃	—	4	4	no	—
208	C₄×C₂₃	—	4	1	no	—
209	C₄×C₂₃	—	4	4	no	—
210	C₄×C₂₃	—	4	1	no	—
211	C₄×C₂₃	—	4	1	no	—
212	C₄×C₂₃	—	8	2	no	—
213	C₄×C₂₃	—	8	2	no	—
214	C₄×C₂₃	#525	1	1	yes	characteristic
215	C₄×C₂₃	#529	1	2	yes	—
216	C₄×C₂₃	#532	1	1	yes	characteristic
217	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
218	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
219	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
220	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
221	C₄×Q₁₆	—	2	4	no	—
222	#433	—	2	4	no	—
223	C₂×#107	C₂²×C₂₃	1	2	yes	—
224	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
225	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
226	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
227	C₂×#103	C₂²×C₂₃	1	2	yes	—
228	C₂×#103	C₂²×C₂₃	1	2	yes	—
229	C₂×#103	C₂²×C₂₃	1	2	yes	—
230	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
231	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
232	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
233	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
234	#391	C₂²×C₂₃	1	2	yes	—
235	#389	—	2	2	no	—
236	#389	C₂²×C₂₃	1	2	yes	—
237	#388	—	2	2	no	—
238	#388	—	2	2	no	—
239	#387	—	2	2	no	—
240	#380	C₂²×C₂₃	1	2	yes	—
241	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
242	#340	C₂²×C₂₃	1	1	yes	characteristic
243	#340	C₂²×C₂₃	1	2	yes	—
244	#340	C₂²×C₂₃	1	1	yes	characteristic
245	#340	C₂²×C₂₃	1	2	yes	—
246	C₂×C₂₃	—	8	1	no	—
247	C₂×C₂₃	#2392	1	1	yes	characteristic
248	C₂×C₂₃	#3059	1	1	yes	characteristic
249	C₂×C₂₃	#3061	1	1	yes	characteristic
250	C₂×C₂₃	#3124	1	2	yes	—
251	C₂×C₂₃	#3127	1	2	yes	—
252	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
253	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
254	C₂×Q₁₆	—	2	4	no	—
255	C₂×Q₁₆	—	2	2	no	—
256	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
257	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
258	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
260	C₂²⋊Q₈	—	2	4	no	—
261	C₂²⋊Q₈	—	2	4	no	—
262	C₄×Q₈	—	2	4	no	—
263	C₄×Q₈	—	2	4	no	—
264	#117	—	2	2	no	—
265	#117	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
270	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
272	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
273	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
277	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
278	C₂×C₄²	—	2	2	no	—
279	C₂×C₄²	—	2	2	no	—
280	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
281	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
282	#107	—	2	2	no	—
283	#107	—	2	4	no	—
284	C₄⋊C₈	—	2	2	no	—
285	C₄⋊C₈	—	2	2	no	—
286	#103	—	2	4	no	—
287	#103	—	2	4	no	—
288	#103	—	2	4	no	—
289	C₂²⋊C₈	—	2	2	no	—
290	C₂²⋊C₈	—	2	2	no	—
291	#97	—	2	2	no	—
292	C₄×C₈	D₄×C₂₃	1	4	yes	—
293	#95	—	2	2	no	—
294	#95	—	2	2	no	—
295	#95	—	2	2	no	—
296	#95	—	2	2	no	—
297	#95	—	2	2	no	—
298	C₂₃	#23705	1	1	yes	characteristic, direct product factor, Sylow
299	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	#41×C₂₃	1	4	yes	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
319	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
320	Q₁₆	—	2	8	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
328	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
329	C₄⋊C₄	—	2	8	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	4	4	no	—
338	C₄⋊C₄	—	8	2	no	—
339	C₄⋊C₄	#41×C₂₃	1	4	yes	—
340	C₂²⋊C₄	—	2	8	no	—
341	C₂²⋊C₄	—	2	2	no	—
342	C₂²⋊C₄	—	2	2	no	—
343	C₂²⋊C₄	—	8	2	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	4	4	no	—
347	C₄²	—	8	2	no	—
348	C₄²	C₂×D₄×C₂₃	1	2	yes	—
349	C₄²	#41×C₂₃	1	2	yes	—
350	C₂³	—	2	1	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	2	1	no	—
353	C₂³	—	2	1	no	—
354	C₂³	—	2	2	no	—
355	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
356	Q₈	—	2	4	no	—
357	Q₈	—	2	4	no	—
358	Q₈	—	4	2	no	—
359	Q₈	—	4	2	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	C₂₃×#121	1	2	yes	—
386	C₂×C₄	C₂₃×#121	1	2	yes	—
387	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
388	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
389	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
390	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
391	C₈	—	2	2	no	—
392	C₈	—	2	2	no	—
393	C₈	—	4	1	no	—
394	C₈	—	4	1	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	1	no	—
400	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
401	C₂²	C₂₃×#525	1	2	yes	—
402	C₂²	C₂₃×#576	1	1	yes	characteristic
403	C₂²	C₂₃×#578	1	2	yes	—
404	C₂²	C₂₃×#578	1	1	yes	characteristic
405	C₄	—	2	2	no	—
406	C₄	—	2	2	no	—
407	C₄	—	4	1	no	—
408	C₄	—	4	1	no	—
409	C₄	—	4	4	no	—
410	C₄	—	4	1	no	—
411	C₄	—	4	4	no	—
412	C₄	—	8	2	no	—
413	C₄	—	8	2	no	—
414	C₄	C₂₃×#525	1	1	yes	characteristic
415	C₄	C₂₃×#529	1	2	yes	—
416	C₄	C₂₃×#532	1	1	yes	characteristic
417	C₂	—	8	1	no	—
418	C₂	C₂₃×#2392	1	1	yes	characteristic
419	C₂	C₂₃×#3059	1	1	yes	characteristic
420	C₂	C₂₃×#3061	1	1	yes	characteristic
421	C₂	C₂₃×#3124	1	2	yes	—
422	C₂	C₂₃×#3127	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂⁴×C₂₃	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₂₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×Q₁₆×C₂₃	C₂	semidirect
4. C₂₃×#2086	C₂	semidirect
6. C₂₃×#2068	C₂	semidirect
7. C₂₃×#2056	C₂	semidirect
10. C₄×C₂₃×#107	C₂	semidirect
11. C₂₃×#1763	C₂	semidirect
138. #23705	C₂₃	direct (N × H)
184. C₂×C₄×Q₁₆	C₂×C₂₃	semidirect
187. #2086	C₂×C₂₃	semidirect
189. #2068	C₂×C₂₃	semidirect
190. #2056	C₂×C₂₃	semidirect
193. C₄×#107	C₂×C₂₃	semidirect
194. #1763	C₂×C₂₃	semidirect
298. C₂₃	#23705	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×Q₁₆×C₂₃	2
C₂×C₂₃×#433	2
C₂₃×#2323	2
C₂₃×#2086	2
C₂₃×#2075	2
C₂₃×#2068	2
C₂₃×#2056	2
C₂₃×#2036	2
C₂₃×#2001	2
C₄×C₂₃×#107	2
C₂₃×#1763	2
#23705	23

Subgroups — C23×#23705 #19171331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#23705 #19171331