Subgroups — C₂₃×#19389 #19167015

Order 5888.

684 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3207	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3109	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3100	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2972	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1683	C₂	1	2	yes	maximal, complemented
6	C₂₃×#1677	C₂	1	2	yes	maximal, complemented
7	C₂₃×#1667	C₂	1	2	yes	maximal, complemented
8	C₂₃×#1665	C₂	1	2	yes	maximal, complemented
9	C₂₃×#1572	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1553	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1543	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#532	C₂²	1	1	yes	characteristic
13	C₂₃×#532	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
15	C₂₃×#493	C₂²	1	1	yes	characteristic, complemented
16	C₂₃×#492	C₂²	1	1	yes	characteristic, complemented
17	C₂₃×#487	C₂²	1	1	yes	characteristic, complemented
18	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
19	C₂₃×#481	—	2	1	no	—
20	C₂₃×#480	—	2	1	no	—
21	C₂₃×#476	C₂²	1	2	yes	—
22	C₂₃×#474	C₂²	1	2	yes	—
23	C₂₃×#463	—	2	2	no	—
24	C₂₃×#459	C₂²	1	2	yes	—
25	C₂₃×#459	C₂²	1	2	yes	—
26	C₂₃×#449	—	2	2	no	—
27	C₂₃×#447	—	2	1	no	—
28	C₂₃×#447	—	2	1	no	—
29	C₂₃×#442	—	2	2	no	—
30	C₄×D₈×C₂₃	—	2	2	no	—
31	C₈×D₄×C₂₃	—	2	2	no	—
32	C₈×D₄×C₂₃	C₂²	1	2	yes	—
33	C₈×D₄×C₂₃	C₂²	1	2	yes	—
34	C₂₃×#432	C₂²	1	1	yes	characteristic
35	C₂₃×#431	C₂²	1	1	yes	characteristic
36	C₂₃×#431	C₂²	1	1	yes	characteristic
37	C₂₃×#431	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×C₂²⋊C₈	—	2	2	no	—
39	C₂₃×#335	C₂²	1	2	yes	complemented
40	C₂₃×#334	C₂²	1	2	yes	complemented
41	C₂₃×#333	C₂²	1	2	yes	complemented
42	C₂₃×#332	C₂²	1	2	yes	complemented
43	C₂₃×#331	C₂²	1	2	yes	complemented
44	C₂₃×#331	C₂²	1	2	yes	complemented
45	C₂×#41×C₂₃	—	2	1	no	—
46	C₂×#41×C₂₃	—	2	1	no	—
47	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₂₃	—	2	1	no	—
49	C₂×SD₁₆×C₂₃	—	2	2	no	—
50	C₂×D₈×C₂₃	—	2	2	no	—
51	C₂×D₈×C₂₃	—	2	2	no	—
52	C₂×D₈×C₂₃	—	2	2	no	—
53	C₂²×C₈×C₂₃	—	2	2	no	—
54	C₂²×C₈×C₂₃	—	2	2	no	—
55	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
56	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
57	C₂₃×#127	C₂³	1	1	yes	characteristic
58	C₂₃×#127	C₂³	1	1	yes	characteristic
59	C₂₃×#124	—	2	1	no	—
60	C₂₃×#124	—	2	1	no	—
61	C₂₃×#121	—	2	1	no	—
62	C₂₃×#121	—	2	1	no	—
63	C₂₃×#121	—	2	1	no	—
64	C₂₃×#121	—	2	1	no	—
65	C₄×D₄×C₂₃	—	2	1	no	—
66	C₄×D₄×C₂₃	—	2	1	no	—
67	C₄×D₄×C₂₃	—	2	1	no	—
68	C₄×D₄×C₂₃	—	2	1	no	—
69	C₄×D₄×C₂₃	—	2	1	no	—
70	C₄×D₄×C₂₃	—	2	1	no	—
71	C₄×D₄×C₂₃	D₄	1	2	yes	—
72	C₄×D₄×C₂₃	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
75	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
76	C₂₃×#107	—	2	2	no	—
77	C₂₃×#106	—	2	2	no	—
78	C₂₃×C₄⋊C₈	D₄	1	2	yes	—
79	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
80	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
81	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
82	C₂₃×#103	—	2	2	no	—
83	C₂₃×#102	—	2	2	no	—
84	C₂₃×#102	—	2	2	no	—
85	C₂₃×#102	—	2	2	no	—
86	C₂₃×#102	—	2	2	no	—
87	C₂₃×#102	—	2	2	no	—
88	C₂₃×C₂²⋊C₈	—	2	1	no	—
89	C₂₃×C₂²⋊C₈	—	2	1	no	—
90	C₂₃×C₂²⋊C₈	—	2	1	no	—
91	C₂₃×C₂²⋊C₈	—	2	2	no	—
92	C₂₃×C₂²⋊C₈	—	2	2	no	—
93	C₂₃×C₂²⋊C₈	D₄	1	2	yes	—
94	C₂₃×#97	—	2	1	no	—
95	C₄×C₈×C₂₃	—	2	1	no	—
96	C₄×C₈×C₂₃	—	2	1	no	—
97	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
99	C₂⁴×C₂₃	—	2	1	no	—
100	#41×C₂₃	—	8	2	no	—
101	#41×C₂₃	—	8	2	no	—
102	C₂×Q₈×C₂₃	—	2	1	no	—
103	C₂×Q₈×C₂₃	—	2	1	no	—
104	C₂×D₄×C₂₃	—	2	4	no	—
105	C₂×D₄×C₂₃	—	2	1	no	—
106	C₂×D₄×C₂₃	—	2	1	no	—
107	C₂×D₄×C₂₃	—	2	1	no	—
108	C₂×D₄×C₂₃	—	2	1	no	—
109	C₂×D₄×C₂₃	—	2	1	no	—
110	C₂×D₄×C₂₃	—	2	1	no	—
111	C₂×D₄×C₂₃	—	2	1	no	—
112	C₂×D₄×C₂₃	—	4	1	no	—
113	C₂×D₄×C₂₃	—	4	1	no	—
114	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₂₃	—	2	1	no	—
116	C₂²×C₄×C₂₃	—	2	2	no	—
117	C₂²×C₄×C₂₃	—	2	2	no	—
118	C₂²×C₄×C₂₃	—	4	1	no	—
119	C₂²×C₄×C₂₃	—	4	1	no	—
120	C₂²×C₄×C₂₃	—	8	2	no	—
121	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
124	SD₁₆×C₂₃	—	8	2	no	—
125	D₈×C₂₃	—	4	4	no	—
126	D₈×C₂₃	—	4	4	no	—
127	D₈×C₂₃	—	8	2	no	—
128	C₂×C₈×C₂₃	—	2	2	no	—
129	C₂×C₈×C₂₃	—	2	2	no	—
130	C₂×C₈×C₂₃	—	2	2	no	—
131	C₂×C₈×C₂₃	—	8	2	no	—
132	C₂×C₈×C₂₃	—	8	2	no	—
133	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
135	C₄⋊C₄×C₂₃	—	2	1	no	—
136	C₄⋊C₄×C₂₃	—	2	1	no	—
137	C₄⋊C₄×C₂₃	—	2	1	no	—
138	C₄⋊C₄×C₂₃	—	2	1	no	—
139	C₄⋊C₄×C₂₃	—	2	1	no	—
140	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
141	C₂²⋊C₄×C₂₃	—	2	2	no	—
142	C₂²⋊C₄×C₂₃	—	2	2	no	—
143	C₂²⋊C₄×C₂₃	—	4	1	no	—
144	C₂²⋊C₄×C₂₃	—	4	1	no	—
145	C₂²⋊C₄×C₂₃	—	4	1	no	—
146	C₂²⋊C₄×C₂₃	—	4	1	no	—
147	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₂₃	#41	1	1	yes	characteristic
150	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
151	#19389	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₂³×C₂₃	—	2	4	no	—
153	C₂³×C₂₃	—	2	2	no	—
154	C₂³×C₂₃	—	4	1	no	—
155	C₂³×C₂₃	—	4	1	no	—
156	C₂³×C₂₃	—	8	1	no	—
157	C₂³×C₂₃	—	8	1	no	—
158	C₂³×C₂₃	#121	1	1	yes	characteristic
159	Q₈×C₂₃	—	4	2	no	—
160	Q₈×C₂₃	—	8	1	no	—
161	D₄×C₂₃	—	2	4	no	—
162	D₄×C₂₃	—	2	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	1	no	—
168	D₄×C₂₃	—	8	1	no	—
169	D₄×C₂₃	—	8	2	no	—
170	D₄×C₂₃	—	8	2	no	—
171	D₄×C₂₃	#135	1	4	yes	—
172	C₂×C₄×C₂₃	—	2	2	no	—
173	C₂×C₄×C₂₃	—	2	2	no	—
174	C₂×C₄×C₂₃	—	2	2	no	—
175	C₂×C₄×C₂₃	—	4	1	no	—
176	C₂×C₄×C₂₃	—	4	2	no	—
177	C₂×C₄×C₂₃	—	4	2	no	—
178	C₂×C₄×C₂₃	—	4	1	no	—
179	C₂×C₄×C₂₃	—	4	1	no	—
180	C₂×C₄×C₂₃	—	8	2	no	—
181	C₂×C₄×C₂₃	—	8	2	no	—
182	C₂×C₄×C₂₃	—	8	2	no	—
183	C₂×C₄×C₂₃	—	8	1	no	—
184	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
185	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
186	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
187	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
190	C₈×C₂₃	—	2	2	no	—
191	C₈×C₂₃	—	2	2	no	—
192	C₈×C₂₃	—	4	2	no	—
193	C₈×C₂₃	—	4	2	no	—
194	C₈×C₂₃	—	4	2	no	—
195	#3207	C₂×C₂₃	1	1	yes	characteristic, complemented
196	#3109	C₂×C₂₃	1	1	yes	characteristic, complemented
197	#3100	C₂×C₂₃	1	1	yes	characteristic, complemented
198	#2972	C₂×C₂₃	1	1	yes	characteristic, complemented
199	#1683	C₂×C₂₃	1	2	yes	complemented
200	#1677	C₂×C₂₃	1	2	yes	complemented
201	#1667	C₂×C₂₃	1	2	yes	complemented
202	#1665	C₂×C₂₃	1	2	yes	complemented
203	#1572	C₂×C₂₃	1	1	yes	characteristic, complemented
204	#1553	C₂×C₂₃	1	1	yes	characteristic, complemented
205	#1543	C₂×C₂₃	1	1	yes	characteristic, complemented
206	C₂²×C₂₃	—	2	1	no	—
207	C₂²×C₂₃	—	2	1	no	—
208	C₂²×C₂₃	—	2	4	no	—
209	C₂²×C₂₃	—	2	1	no	—
210	C₂²×C₂₃	—	4	2	no	—
211	C₂²×C₂₃	—	4	2	no	—
212	C₂²×C₂₃	—	8	4	no	—
213	C₂²×C₂₃	—	8	1	no	—
214	C₂²×C₂₃	—	8	1	no	—
215	C₂²×C₂₃	—	8	1	no	—
216	C₂²×C₂₃	—	8	1	no	—
217	C₂²×C₂₃	—	8	1	no	—
218	C₂²×C₂₃	—	8	1	no	—
219	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
220	C₄×C₂₃	—	2	1	no	—
221	C₄×C₂₃	—	2	1	no	—
222	C₄×C₂₃	—	2	1	no	—
223	C₄×C₂₃	—	2	1	no	—
224	C₄×C₂₃	—	4	2	no	—
225	C₄×C₂₃	—	8	1	no	—
226	C₄×C₂₃	—	8	1	no	—
227	C₄×C₂₃	C₂×#135	1	2	yes	—
228	C₄×C₂₃	#576	1	2	yes	—
229	#532	C₂²×C₂₃	1	1	yes	characteristic
230	#532	C₂²×C₂₃	1	1	yes	characteristic
231	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
232	#493	C₂²×C₂₃	1	1	yes	characteristic, complemented
233	#492	C₂²×C₂₃	1	1	yes	characteristic, complemented
234	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
235	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
236	#481	—	2	1	no	—
237	#480	—	2	1	no	—
238	#476	C₂²×C₂₃	1	2	yes	—
239	#474	C₂²×C₂₃	1	2	yes	—
240	#463	—	2	2	no	—
241	#459	C₂²×C₂₃	1	2	yes	—
242	#459	C₂²×C₂₃	1	2	yes	—
243	#449	—	2	2	no	—
244	#447	—	2	1	no	—
245	#447	—	2	1	no	—
246	#442	—	2	2	no	—
247	C₄×D₈	—	2	2	no	—
248	C₈×D₄	—	2	2	no	—
249	C₈×D₄	C₂²×C₂₃	1	2	yes	—
250	C₈×D₄	C₂²×C₂₃	1	2	yes	—
251	#432	C₂²×C₂₃	1	1	yes	characteristic
252	#431	C₂²×C₂₃	1	1	yes	characteristic
253	#431	C₂²×C₂₃	1	1	yes	characteristic
254	#431	C₂²×C₂₃	1	1	yes	characteristic
255	C₂×C₂²⋊C₈	—	2	2	no	—
256	#335	C₂²×C₂₃	1	2	yes	complemented
257	#334	C₂²×C₂₃	1	2	yes	complemented
258	#333	C₂²×C₂₃	1	2	yes	complemented
259	#332	C₂²×C₂₃	1	2	yes	complemented
260	#331	C₂²×C₂₃	1	2	yes	complemented
261	#331	C₂²×C₂₃	1	2	yes	complemented
262	C₂×C₂₃	—	4	1	no	—
263	C₂×C₂₃	—	4	4	no	—
264	C₂×C₂₃	—	16	1	no	—
265	C₂×C₂₃	—	16	1	no	—
266	C₂×C₂₃	#3041	1	1	yes	characteristic
267	C₂×C₂₃	#3050	1	1	yes	characteristic
268	C₂×C₂₃	#3068	1	1	yes	characteristic
269	C₂×#41	—	2	1	no	—
270	C₂×#41	—	2	1	no	—
271	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
272	C₂³×C₄	—	2	1	no	—
273	C₂×SD₁₆	—	2	2	no	—
274	C₂×D₈	—	2	2	no	—
275	C₂×D₈	—	2	2	no	—
276	C₂×D₈	—	2	2	no	—
277	C₂²×C₈	—	2	2	no	—
278	C₂²×C₈	—	2	2	no	—
279	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
280	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
281	#127	C₂³×C₂₃	1	1	yes	characteristic
282	#127	C₂³×C₂₃	1	1	yes	characteristic
283	#124	—	2	1	no	—
284	#124	—	2	1	no	—
285	#121	—	2	1	no	—
286	#121	—	2	1	no	—
287	#121	—	2	1	no	—
288	#121	—	2	1	no	—
289	C₄×D₄	—	2	1	no	—
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	—	2	1	no	—
293	C₄×D₄	—	2	1	no	—
294	C₄×D₄	—	2	1	no	—
295	C₄×D₄	D₄×C₂₃	1	2	yes	—
296	C₄×D₄	C₂³×C₂₃	1	2	yes	—
297	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
298	C₂×C₂²⋊C₄	—	2	1	no	—
299	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
300	#107	—	2	2	no	—
301	#106	—	2	2	no	—
302	C₄⋊C₈	D₄×C₂₃	1	2	yes	—
303	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
304	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
305	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
306	#103	—	2	2	no	—
307	#102	—	2	2	no	—
308	#102	—	2	2	no	—
309	#102	—	2	2	no	—
310	#102	—	2	2	no	—
311	#102	—	2	2	no	—
312	C₂²⋊C₈	—	2	1	no	—
313	C₂²⋊C₈	—	2	1	no	—
314	C₂²⋊C₈	—	2	1	no	—
315	C₂²⋊C₈	—	2	2	no	—
316	C₂²⋊C₈	—	2	2	no	—
317	C₂²⋊C₈	D₄×C₂₃	1	2	yes	—
318	#97	—	2	1	no	—
319	C₄×C₈	—	2	1	no	—
320	C₄×C₈	—	2	1	no	—
321	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
322	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
323	C₂₃	#19389	1	1	yes	characteristic, direct product factor, Sylow
324	C₂⁴	—	2	1	no	—
325	#41	—	8	2	no	—
326	#41	—	8	2	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×D₄	—	2	4	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	4	1	no	—
338	C₂×D₄	—	4	1	no	—
339	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	4	1	no	—
344	C₂²×C₄	—	4	1	no	—
345	C₂²×C₄	—	8	2	no	—
346	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
348	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
349	SD₁₆	—	8	2	no	—
350	D₈	—	4	4	no	—
351	D₈	—	4	4	no	—
352	D₈	—	8	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	8	2	no	—
357	C₂×C₈	—	8	2	no	—
358	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
359	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	2	2	no	—
368	C₂²⋊C₄	—	4	1	no	—
369	C₂²⋊C₄	—	4	1	no	—
370	C₂²⋊C₄	—	4	1	no	—
371	C₂²⋊C₄	—	4	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	4	no	—
377	C₂³	—	2	2	no	—
378	C₂³	—	4	1	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	8	1	no	—
381	C₂³	—	8	1	no	—
382	C₂³	C₂₃×#121	1	1	yes	characteristic
383	Q₈	—	4	2	no	—
384	Q₈	—	8	1	no	—
385	D₄	—	2	4	no	—
386	D₄	—	2	2	no	—
387	D₄	—	4	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	8	1	no	—
392	D₄	—	8	1	no	—
393	D₄	—	8	2	no	—
394	D₄	—	8	2	no	—
395	D₄	C₂₃×#135	1	4	yes	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	8	2	no	—
405	C₂×C₄	—	8	2	no	—
406	C₂×C₄	—	8	2	no	—
407	C₂×C₄	—	8	1	no	—
408	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
409	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
410	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
411	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
412	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
413	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
414	C₈	—	2	2	no	—
415	C₈	—	2	2	no	—
416	C₈	—	4	2	no	—
417	C₈	—	4	2	no	—
418	C₈	—	4	2	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	4	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	8	4	no	—
426	C₂²	—	8	1	no	—
427	C₂²	—	8	1	no	—
428	C₂²	—	8	1	no	—
429	C₂²	—	8	1	no	—
430	C₂²	—	8	1	no	—
431	C₂²	—	8	1	no	—
432	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	4	2	no	—
438	C₄	—	8	1	no	—
439	C₄	—	8	1	no	—
440	C₄	C₂×C₂₃×#135	1	2	yes	—
441	C₄	C₂₃×#576	1	2	yes	—
442	C₂	—	4	1	no	—
443	C₂	—	4	4	no	—
444	C₂	—	16	1	no	—
445	C₂	—	16	1	no	—
446	C₂	C₂₃×#3041	1	1	yes	characteristic
447	C₂	C₂₃×#3050	1	1	yes	characteristic
448	C₂	C₂₃×#3068	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×#3207	C₂	semidirect
2. C₂₃×#3109	C₂	semidirect
3. C₂₃×#3100	C₂	semidirect
4. C₂₃×#2972	C₂	semidirect
5. C₂₃×#1683	C₂	semidirect
6. C₂₃×#1677	C₂	semidirect
7. C₂₃×#1667	C₂	semidirect
8. C₂₃×#1665	C₂	semidirect
9. C₂₃×#1572	C₂	semidirect
10. C₂₃×#1553	C₂	semidirect
11. C₂₃×#1543	C₂	semidirect
15. C₂₃×#493	C₂²	semidirect
16. C₂₃×#492	C₂²	semidirect
17. C₂₃×#487	C₂²	semidirect
18. C₂₃×#486	C₂²	semidirect
39. C₂₃×#335	C₂²	semidirect
40. C₂₃×#334	C₂²	semidirect
41. C₂₃×#333	C₂²	semidirect
42. C₂₃×#332	C₂²	semidirect
43. C₂₃×#331	C₂²	semidirect
44. C₂₃×#331	C₂²	semidirect
151. #19389	C₂₃	direct (N × H)
195. #3207	C₂×C₂₃	semidirect
196. #3109	C₂×C₂₃	semidirect
197. #3100	C₂×C₂₃	semidirect
198. #2972	C₂×C₂₃	semidirect
199. #1683	C₂×C₂₃	semidirect
200. #1677	C₂×C₂₃	semidirect
201. #1667	C₂×C₂₃	semidirect
202. #1665	C₂×C₂₃	semidirect
203. #1572	C₂×C₂₃	semidirect
204. #1553	C₂×C₂₃	semidirect
205. #1543	C₂×C₂₃	semidirect
232. #493	C₂²×C₂₃	semidirect
233. #492	C₂²×C₂₃	semidirect
234. #487	C₂²×C₂₃	semidirect
235. #486	C₂²×C₂₃	semidirect
256. #335	C₂²×C₂₃	semidirect
257. #334	C₂²×C₂₃	semidirect
258. #333	C₂²×C₂₃	semidirect
259. #332	C₂²×C₂₃	semidirect
260. #331	C₂²×C₂₃	semidirect
261. #331	C₂²×C₂₃	semidirect
323. C₂₃	#19389	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×#3207	2
C₂₃×#3109	2
C₂₃×#3100	2
C₂₃×#2972	2
C₂₃×#1683	2
C₂₃×#1677	2
C₂₃×#1667	2
C₂₃×#1665	2
C₂₃×#1572	2
C₂₃×#1553	2
C₂₃×#1543	2
#19389	23

Subgroups — C23×#19389 #19167015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#19389 #19167015