Subgroups — C₂₃×#19222 #19166848

Order 5888.

628 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3247	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#1698	C₂	1	2	yes	maximal, complemented
5	C₂₃×#1697	C₂	1	2	yes	maximal, complemented
6	C₂₃×#1676	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1675	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1668	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1667	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₂₃×#335	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1551	C₂	1	2	yes	maximal, complemented
12	C₂₃×#532	C₂²	1	2	yes	—
13	C₂₃×#529	C₂²	1	1	yes	characteristic
14	C₂₃×#500	C₂²	1	1	yes	characteristic
15	C₂₃×#493	C₂²	1	1	yes	characteristic
16	C₂₃×#486	C₂²	1	2	yes	—
17	C₂₃×#478	—	2	2	no	—
18	C₂₃×#477	C₂²	1	2	yes	—
19	C₂₃×#476	C₂²	1	2	yes	—
20	C₂₃×#466	—	2	1	no	—
21	C₂₃×#466	—	2	1	no	—
22	C₂₃×#466	—	2	2	no	—
23	C₂₃×#465	—	2	2	no	—
24	C₂₃×#463	—	2	2	no	—
25	C₂₃×#460	C₂²	1	2	yes	—
26	C₂₃×#459	C₂²	1	2	yes	—
27	C₂₃×#446	C₂²	1	1	yes	characteristic
28	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic
29	C₄×D₈×C₂₃	—	2	1	no	—
30	C₄×D₈×C₂₃	—	2	1	no	—
31	C₂₃×#436	C₂²	1	1	yes	characteristic
32	C₂₃×#435	—	2	1	no	—
33	C₈×D₄×C₂₃	—	2	1	no	—
34	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
35	C₂₃×#433	—	2	1	no	—
36	C₂₃×#432	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
38	C₂₃×#405	—	2	1	no	—
39	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
40	C₂₃×#335	C₂²	1	1	yes	characteristic
41	C₂₃×#335	C₂²	1	1	yes	characteristic
42	C₂₃×#335	C₂²	1	2	yes	—
43	C₂₃×#333	C₂²	1	2	yes	—
44	C₂₃×#333	C₂²	1	2	yes	—
45	C₂₃×#331	C₂²	1	2	yes	—
46	C₂₃×#331	C₂²	1	2	yes	—
47	C₂×#41×C₂₃	—	2	2	no	—
48	C₂×SD₁₆×C₂₃	—	2	2	no	—
49	C₂×D₈×C₂₃	—	2	2	no	—
50	C₂×D₈×C₂₃	—	2	1	no	—
51	C₂×D₈×C₂₃	—	2	1	no	—
52	C₂×M₁₆×C₂₃	—	2	1	no	—
53	C₂²×C₈×C₂₃	—	2	2	no	—
54	C₂²×C₈×C₂₃	—	2	1	no	—
55	C₂²×C₈×C₂₃	D₄	1	1	yes	characteristic
56	C₂²×C₈×C₂₃	D₄	1	1	yes	characteristic
57	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
58	C₂₃×#127	C₂³	1	2	yes	—
59	C₂₃×#126	—	2	1	no	—
60	C₂₃×#125	D₄	1	1	yes	characteristic
61	C₂₃×#124	—	2	2	no	—
62	C₂₃×#124	D₄	1	1	yes	characteristic
63	C₂₃×#123	—	2	1	no	—
64	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
65	C₂₃×#121	—	2	2	no	—
66	C₂₃×#121	—	2	2	no	—
67	C₂₃×#121	D₄	1	1	yes	characteristic
68	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
69	C₄×D₄×C₂₃	—	2	1	no	—
70	C₄×D₄×C₂₃	—	2	2	no	—
71	C₄×D₄×C₂₃	—	2	2	no	—
72	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
73	C₂₃×#117	—	2	1	no	—
74	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
75	C₂₃×#107	—	2	1	no	—
76	C₂₃×#107	—	2	1	no	—
77	C₂₃×#107	—	2	2	no	—
78	C₂₃×#106	—	2	2	no	—
79	C₂₃×C₄⋊C₈	—	2	1	no	—
80	C₂₃×C₄⋊C₈	—	2	1	no	—
81	C₂₃×C₄⋊C₈	—	2	2	no	—
82	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
83	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
84	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
85	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
86	C₂₃×#103	—	2	2	no	—
87	C₂₃×#102	—	2	2	no	—
88	C₂₃×#102	—	2	2	no	—
89	C₂₃×#102	—	2	2	no	—
90	C₂₃×#102	—	2	2	no	—
91	C₂₃×#102	—	2	2	no	—
92	C₂₃×C₂²⋊C₈	—	2	1	no	—
93	C₂₃×C₂²⋊C₈	—	2	1	no	—
94	C₂₃×C₂²⋊C₈	—	2	1	no	—
95	C₂₃×#97	—	2	1	no	—
96	C₂₃×#97	—	2	1	no	—
97	C₄×C₈×C₂₃	—	2	1	no	—
98	C₄×C₈×C₂₃	D₄	1	1	yes	characteristic
99	C₄×C₈×C₂₃	D₄	1	1	yes	characteristic
100	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
102	#41×C₂₃	—	8	4	no	—
103	C₂×Q₈×C₂₃	—	2	2	no	—
104	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
105	C₂×D₄×C₂₃	—	2	1	no	—
106	C₂×D₄×C₂₃	—	2	2	no	—
107	C₂×D₄×C₂₃	—	2	2	no	—
108	C₂×D₄×C₂₃	—	2	2	no	—
109	C₂×D₄×C₂₃	—	4	2	no	—
110	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₂₃	—	2	1	no	—
112	C₂²×C₄×C₂₃	—	4	2	no	—
113	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
116	SD₁₆×C₂₃	—	8	2	no	—
117	D₈×C₂₃	—	4	2	no	—
118	D₈×C₂₃	—	4	2	no	—
119	D₈×C₂₃	—	8	2	no	—
120	M₁₆×C₂₃	—	4	2	no	—
121	C₂×C₈×C₂₃	—	2	2	no	—
122	C₂×C₈×C₂₃	—	2	2	no	—
123	C₂×C₈×C₂₃	—	2	2	no	—
124	C₂×C₈×C₂₃	—	2	1	no	—
125	C₂×C₈×C₂₃	—	2	1	no	—
126	C₂×C₈×C₂₃	—	4	1	no	—
127	C₂×C₈×C₂₃	—	4	2	no	—
128	C₂×C₈×C₂₃	—	8	2	no	—
129	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
133	C₄⋊C₄×C₂₃	—	2	1	no	—
134	C₄⋊C₄×C₂₃	—	2	1	no	—
135	C₄⋊C₄×C₂₃	—	2	1	no	—
136	C₄⋊C₄×C₂₃	—	2	1	no	—
137	C₄⋊C₄×C₂₃	—	2	2	no	—
138	C₄⋊C₄×C₂₃	—	2	2	no	—
139	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
140	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
141	C₂²⋊C₄×C₂₃	—	2	1	no	—
142	C₂²⋊C₄×C₂₃	—	2	1	no	—
143	C₂²⋊C₄×C₂₃	—	2	1	no	—
144	C₂²⋊C₄×C₂₃	—	2	1	no	—
145	C₂²⋊C₄×C₂₃	—	2	1	no	—
146	C₂²⋊C₄×C₂₃	—	4	2	no	—
147	C₂²⋊C₄×C₂₃	—	4	2	no	—
148	C₄²×C₂₃	—	2	1	no	—
149	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₂₃	#41	1	1	yes	characteristic
152	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
153	#19222	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₂³×C₂₃	—	2	1	no	—
155	C₂³×C₂₃	—	4	2	no	—
156	C₂³×C₂₃	#121	1	1	yes	characteristic
157	Q₈×C₂₃	—	2	1	no	—
158	Q₈×C₂₃	—	2	1	no	—
159	Q₈×C₂₃	—	8	2	no	—
160	D₄×C₂₃	—	2	1	no	—
161	D₄×C₂₃	—	2	1	no	—
162	D₄×C₂₃	—	4	2	no	—
163	D₄×C₂₃	—	4	2	no	—
164	D₄×C₂₃	—	4	2	no	—
165	D₄×C₂₃	—	4	2	no	—
166	D₄×C₂₃	—	4	2	no	—
167	D₄×C₂₃	—	8	2	no	—
168	D₄×C₂₃	—	8	4	no	—
169	C₂×C₄×C₂₃	—	2	2	no	—
170	C₂×C₄×C₂₃	—	2	1	no	—
171	C₂×C₄×C₂₃	—	2	1	no	—
172	C₂×C₄×C₂₃	—	2	1	no	—
173	C₂×C₄×C₂₃	—	2	1	no	—
174	C₂×C₄×C₂₃	—	2	1	no	—
175	C₂×C₄×C₂₃	—	2	1	no	—
176	C₂×C₄×C₂₃	—	2	1	no	—
177	C₂×C₄×C₂₃	—	4	1	no	—
178	C₂×C₄×C₂₃	—	4	1	no	—
179	C₂×C₄×C₂₃	—	4	2	no	—
180	C₂×C₄×C₂₃	—	8	4	no	—
181	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
182	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
183	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
184	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
187	C₈×C₂₃	—	2	1	no	—
188	C₈×C₂₃	—	2	1	no	—
189	C₈×C₂₃	—	2	1	no	—
190	C₈×C₂₃	—	4	1	no	—
191	C₈×C₂₃	—	4	1	no	—
192	C₈×C₂₃	—	4	2	no	—
193	C₈×C₂₃	—	4	2	no	—
194	C₈×C₂₃	#135	1	2	yes	—
195	#3247	C₂×C₂₃	1	2	yes	complemented
196	#3169	C₂×C₂₃	1	1	yes	characteristic, complemented
197	#2966	C₂×C₂₃	1	1	yes	characteristic, complemented
198	#1698	C₂×C₂₃	1	2	yes	complemented
199	#1697	C₂×C₂₃	1	2	yes	complemented
200	#1676	C₂×C₂₃	1	1	yes	characteristic, complemented
201	#1675	C₂×C₂₃	1	1	yes	characteristic, complemented
202	#1668	C₂×C₂₃	1	1	yes	characteristic, complemented
203	#1667	C₂×C₂₃	1	1	yes	characteristic, complemented
204	C₂×#335	C₂×C₂₃	1	1	yes	characteristic, complemented
205	#1551	C₂×C₂₃	1	2	yes	complemented
206	C₂²×C₂₃	—	2	1	no	—
207	C₂²×C₂₃	—	2	1	no	—
208	C₂²×C₂₃	—	4	1	no	—
209	C₂²×C₂₃	—	4	1	no	—
210	C₂²×C₂₃	—	4	1	no	—
211	C₂²×C₂₃	—	8	2	no	—
212	C₂²×C₂₃	—	8	2	no	—
213	C₂²×C₂₃	—	8	2	no	—
214	C₂²×C₂₃	#472	1	2	yes	—
215	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
216	C₄×C₂₃	—	2	1	no	—
217	C₄×C₂₃	—	2	1	no	—
218	C₄×C₂₃	—	2	1	no	—
219	C₄×C₂₃	—	2	1	no	—
220	C₄×C₂₃	—	4	1	no	—
221	C₄×C₂₃	—	4	1	no	—
222	C₄×C₂₃	—	4	1	no	—
223	C₄×C₂₃	—	8	2	no	—
224	C₄×C₂₃	C₂×#135	1	1	yes	characteristic
225	C₄×C₂₃	#575	1	1	yes	characteristic
226	C₄×C₂₃	#576	1	1	yes	characteristic
227	C₄×C₂₃	#578	1	1	yes	characteristic
228	#532	C₂²×C₂₃	1	2	yes	—
229	#529	C₂²×C₂₃	1	1	yes	characteristic
230	#500	C₂²×C₂₃	1	1	yes	characteristic
231	#493	C₂²×C₂₃	1	1	yes	characteristic
232	#486	C₂²×C₂₃	1	2	yes	—
233	#478	—	2	2	no	—
234	#477	C₂²×C₂₃	1	2	yes	—
235	#476	C₂²×C₂₃	1	2	yes	—
236	#466	—	2	1	no	—
237	#466	—	2	1	no	—
238	#466	—	2	2	no	—
239	#465	—	2	2	no	—
240	#463	—	2	2	no	—
241	#460	C₂²×C₂₃	1	2	yes	—
242	#459	C₂²×C₂₃	1	2	yes	—
243	#446	C₂²×C₂₃	1	1	yes	characteristic
244	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic
245	C₄×D₈	—	2	1	no	—
246	C₄×D₈	—	2	1	no	—
247	#436	C₂²×C₂₃	1	1	yes	characteristic
248	#435	—	2	1	no	—
249	C₈×D₄	—	2	1	no	—
250	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
251	#433	—	2	1	no	—
252	#432	C₂²×C₂₃	1	1	yes	characteristic
253	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
254	#405	—	2	1	no	—
255	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
256	#335	C₂²×C₂₃	1	1	yes	characteristic
257	#335	C₂²×C₂₃	1	1	yes	characteristic
258	#335	C₂²×C₂₃	1	2	yes	—
259	#333	C₂²×C₂₃	1	2	yes	—
260	#333	C₂²×C₂₃	1	2	yes	—
261	#331	C₂²×C₂₃	1	2	yes	—
262	#331	C₂²×C₂₃	1	2	yes	—
263	C₂×C₂₃	—	2	2	no	—
264	C₂×C₂₃	—	8	1	no	—
265	C₂×C₂₃	—	16	2	no	—
266	C₂×C₂₃	#3035	1	1	yes	characteristic
267	C₂×C₂₃	#3061	1	1	yes	characteristic
268	C₂×C₂₃	C₂×#472	1	1	yes	characteristic
269	C₂×#41	—	2	2	no	—
270	C₂×SD₁₆	—	2	2	no	—
271	C₂×D₈	—	2	2	no	—
272	C₂×D₈	—	2	1	no	—
273	C₂×D₈	—	2	1	no	—
274	C₂×M₁₆	—	2	1	no	—
275	C₂²×C₈	—	2	2	no	—
276	C₂²×C₈	—	2	1	no	—
277	C₂²×C₈	D₄×C₂₃	1	1	yes	characteristic
278	C₂²×C₈	D₄×C₂₃	1	1	yes	characteristic
279	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
280	#127	C₂³×C₂₃	1	2	yes	—
281	#126	—	2	1	no	—
282	#125	D₄×C₂₃	1	1	yes	characteristic
283	#124	—	2	2	no	—
284	#124	D₄×C₂₃	1	1	yes	characteristic
285	#123	—	2	1	no	—
286	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
287	#121	—	2	2	no	—
288	#121	—	2	2	no	—
289	#121	D₄×C₂₃	1	1	yes	characteristic
290	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	—	2	2	no	—
293	C₄×D₄	—	2	2	no	—
294	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
295	#117	—	2	1	no	—
296	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
297	#107	—	2	1	no	—
298	#107	—	2	1	no	—
299	#107	—	2	2	no	—
300	#106	—	2	2	no	—
301	C₄⋊C₈	—	2	1	no	—
302	C₄⋊C₈	—	2	1	no	—
303	C₄⋊C₈	—	2	2	no	—
304	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
305	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
306	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
307	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
308	#103	—	2	2	no	—
309	#102	—	2	2	no	—
310	#102	—	2	2	no	—
311	#102	—	2	2	no	—
312	#102	—	2	2	no	—
313	#102	—	2	2	no	—
314	C₂²⋊C₈	—	2	1	no	—
315	C₂²⋊C₈	—	2	1	no	—
316	C₂²⋊C₈	—	2	1	no	—
317	#97	—	2	1	no	—
318	#97	—	2	1	no	—
319	C₄×C₈	—	2	1	no	—
320	C₄×C₈	D₄×C₂₃	1	1	yes	characteristic
321	C₄×C₈	D₄×C₂₃	1	1	yes	characteristic
322	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
323	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
324	C₂₃	#19222	1	1	yes	characteristic, direct product factor, Sylow
325	#41	—	8	4	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	4	2	no	—
333	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
338	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
339	SD₁₆	—	8	2	no	—
340	D₈	—	4	2	no	—
341	D₈	—	4	2	no	—
342	D₈	—	8	2	no	—
343	M₁₆	—	4	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	4	1	no	—
350	C₂×C₈	—	4	2	no	—
351	C₂×C₈	—	8	2	no	—
352	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
353	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
354	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
355	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
363	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
364	C₂²⋊C₄	—	2	1	no	—
365	C₂²⋊C₄	—	2	1	no	—
366	C₂²⋊C₄	—	2	1	no	—
367	C₂²⋊C₄	—	2	1	no	—
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	4	2	no	—
370	C₂²⋊C₄	—	4	2	no	—
371	C₄²	—	2	1	no	—
372	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
373	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
374	C₄²	#41×C₂₃	1	1	yes	characteristic
375	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
376	C₂³	—	2	1	no	—
377	C₂³	—	4	2	no	—
378	C₂³	C₂₃×#121	1	1	yes	characteristic
379	Q₈	—	2	1	no	—
380	Q₈	—	2	1	no	—
381	Q₈	—	8	2	no	—
382	D₄	—	2	1	no	—
383	D₄	—	2	1	no	—
384	D₄	—	4	2	no	—
385	D₄	—	4	2	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	8	2	no	—
390	D₄	—	8	4	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	8	4	no	—
403	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
404	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
405	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
406	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
407	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
408	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
409	C₈	—	2	1	no	—
410	C₈	—	2	1	no	—
411	C₈	—	2	1	no	—
412	C₈	—	4	1	no	—
413	C₈	—	4	1	no	—
414	C₈	—	4	2	no	—
415	C₈	—	4	2	no	—
416	C₈	C₂₃×#135	1	2	yes	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	4	1	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	8	2	no	—
423	C₂²	—	8	2	no	—
424	C₂²	—	8	2	no	—
425	C₂²	C₂₃×#472	1	2	yes	—
426	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	4	1	no	—
432	C₄	—	4	1	no	—
433	C₄	—	4	1	no	—
434	C₄	—	8	2	no	—
435	C₄	C₂×C₂₃×#135	1	1	yes	characteristic
436	C₄	C₂₃×#575	1	1	yes	characteristic
437	C₄	C₂₃×#576	1	1	yes	characteristic
438	C₄	C₂₃×#578	1	1	yes	characteristic
439	C₂	—	2	2	no	—
440	C₂	—	8	1	no	—
441	C₂	—	16	2	no	—
442	C₂	C₂₃×#3035	1	1	yes	characteristic
443	C₂	C₂₃×#3061	1	1	yes	characteristic
444	C₂	C₂×C₂₃×#472	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3247	C₂	semidirect
2. C₂₃×#3169	C₂	semidirect
3. C₂₃×#2966	C₂	semidirect
4. C₂₃×#1698	C₂	semidirect
5. C₂₃×#1697	C₂	semidirect
6. C₂₃×#1676	C₂	semidirect
7. C₂₃×#1675	C₂	semidirect
8. C₂₃×#1668	C₂	semidirect
9. C₂₃×#1667	C₂	semidirect
10. C₂×C₂₃×#335	C₂	semidirect
11. C₂₃×#1551	C₂	semidirect
153. #19222	C₂₃	direct (N × H)
195. #3247	C₂×C₂₃	semidirect
196. #3169	C₂×C₂₃	semidirect
197. #2966	C₂×C₂₃	semidirect
198. #1698	C₂×C₂₃	semidirect
199. #1697	C₂×C₂₃	semidirect
200. #1676	C₂×C₂₃	semidirect
201. #1675	C₂×C₂₃	semidirect
202. #1668	C₂×C₂₃	semidirect
203. #1667	C₂×C₂₃	semidirect
204. C₂×#335	C₂×C₂₃	semidirect
205. #1551	C₂×C₂₃	semidirect
324. C₂₃	#19222	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×#3247	2
C₂₃×#3169	2
C₂₃×#2966	2
C₂₃×#1698	2
C₂₃×#1697	2
C₂₃×#1676	2
C₂₃×#1675	2
C₂₃×#1668	2
C₂₃×#1667	2
C₂×C₂₃×#335	2
C₂₃×#1551	2
#19222	23

Subgroups — C23×#19222 #19166848

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#19222 #19166848