Subgroups — C₂₃×#18628 #19166254

Order 5888.

998 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3519	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#3248	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3131	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3110	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1646	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1646	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1644	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1643	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1642	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1641	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1639	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1639	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1551	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1494	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#555	C₂²	1	1	yes	characteristic
17	C₂₃×#554	C₂²	1	1	yes	characteristic
18	C₂₃×#553	—	2	1	no	—
19	C₂₃×#553	—	2	1	no	—
20	C₂₃×#550	C₂²	1	1	yes	characteristic
21	C₂₃×#546	—	2	2	no	—
22	C₂₃×#546	—	2	1	no	—
23	D₄²×C₂₃	—	2	1	no	—
24	D₄²×C₂₃	C₂²	1	1	yes	characteristic
25	C₂₃×#540	—	2	1	no	—
26	C₂₃×#538	—	2	2	no	—
27	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
28	C₂₃×#532	C₂²	1	1	yes	characteristic
29	C₂₃×#529	C₂²	1	1	yes	characteristic
30	C₂₃×#525	—	2	1	no	—
31	C₂×C₂₃×#121	—	2	1	no	—
32	C₂₃×#518	—	2	1	no	—
33	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
34	C₂₃×#488	—	2	2	no	—
35	C₂₃×#487	C₂²	1	1	yes	characteristic, complemented
36	C₂₃×#487	C₂²	1	1	yes	characteristic, complemented
37	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
38	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
39	C₂₃×#484	—	2	1	no	—
40	C₂₃×#479	—	2	1	no	—
41	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
42	C₂₃×#474	C₂²	1	1	yes	characteristic
43	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
44	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
45	C₂₃×#467	—	2	1	no	—
46	C₂₃×#465	—	2	1	no	—
47	C₂₃×#464	—	2	1	no	—
48	C₂₃×#462	C₂²	1	1	yes	characteristic, complemented
49	C₂₃×#461	C₂²	1	1	yes	characteristic
50	C₂₃×#461	C₂²	1	1	yes	characteristic, complemented
51	C₂₃×#461	C₂²	1	1	yes	characteristic, complemented
52	C₂₃×#450	—	2	1	no	—
53	C₂₃×#440	—	2	1	no	—
54	C₂₃×#440	—	2	1	no	—
55	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
57	C₂₃×#416	—	2	2	no	—
58	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
59	C₂₃×#333	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#333	C₂²	1	1	yes	characteristic, complemented
61	C₂₃×#331	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#331	C₂²	1	1	yes	characteristic, complemented
63	C₂₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
64	C₂₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
65	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
67	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
68	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
69	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
70	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
71	C₂×#41×C₂₃	—	2	1	no	—
72	C₂×#41×C₂₃	D₄	1	2	yes	—
73	C₂²×D₄×C₂₃	—	2	2	no	—
74	C₂²×D₄×C₂₃	—	2	1	no	—
75	C₂²×D₄×C₂₃	—	2	1	no	—
76	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
77	C₂³×C₄×C₂₃	—	2	1	no	—
78	C₂×Q₁₆×C₂₃	—	2	1	no	—
79	C₂×SD₁₆×C₂₃	—	2	1	no	—
80	C₂×SD₁₆×C₂₃	—	2	1	no	—
81	C₂×SD₁₆×C₂₃	—	2	1	no	—
82	C₂²×C₈×C₂₃	—	2	1	no	—
83	C₂²×C₈×C₂₃	—	2	1	no	—
84	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
87	C₂₃×#127	—	2	1	no	—
88	C₂₃×#127	C₂³	1	1	yes	characteristic
89	C₂₃×#126	—	2	2	no	—
90	C₂₃×#126	—	2	1	no	—
91	C₂₃×#125	—	2	1	no	—
92	C₂₃×#125	—	2	1	no	—
93	C₂₃×#125	D₄	1	1	yes	characteristic
94	C₂₃×#124	—	2	2	no	—
95	C₂₃×#124	D₄	1	1	yes	characteristic
96	C₂₃×#124	D₄	1	2	yes	—
97	C₂₃×#123	—	2	2	no	—
98	C₂₃×#123	—	2	2	no	—
99	C₂₃×#123	—	2	2	no	—
100	C₂₃×#123	—	2	1	no	—
101	C₂₃×C₂²⋊Q₈	—	2	1	no	—
102	C₂₃×C₂²⋊Q₈	—	2	2	no	—
103	C₂₃×C₂²⋊Q₈	—	2	1	no	—
104	C₂₃×C₂²⋊Q₈	—	2	1	no	—
105	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
106	C₂₃×#121	—	2	2	no	—
107	C₂₃×#121	—	2	2	no	—
108	C₂₃×#121	—	2	2	no	—
109	C₂₃×#121	—	2	2	no	—
110	C₂₃×#121	—	2	2	no	—
111	C₂₃×#121	—	2	1	no	—
112	C₂₃×#121	—	2	1	no	—
113	C₂₃×#121	—	2	1	no	—
114	C₂₃×#121	—	2	1	no	—
115	C₂₃×#121	—	2	1	no	—
116	C₂₃×#121	—	2	1	no	—
117	C₂₃×#121	—	2	1	no	—
118	C₂₃×#121	D₄	1	1	yes	characteristic
119	C₂₃×#120	—	2	2	no	—
120	C₂₃×#120	—	2	2	no	—
121	C₂₃×#120	—	2	2	no	—
122	C₄×Q₈×C₂₃	—	2	1	no	—
123	C₄×Q₈×C₂₃	—	2	1	no	—
124	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
125	C₄×D₄×C₂₃	—	2	2	no	—
126	C₄×D₄×C₂₃	—	2	2	no	—
127	C₄×D₄×C₂₃	—	2	2	no	—
128	C₄×D₄×C₂₃	—	2	1	no	—
129	C₄×D₄×C₂₃	—	2	1	no	—
130	C₄×D₄×C₂₃	—	2	1	no	—
131	C₄×D₄×C₂₃	—	2	1	no	—
132	C₄×D₄×C₂₃	—	2	1	no	—
133	C₄×D₄×C₂₃	—	2	1	no	—
134	C₄×D₄×C₂₃	—	2	1	no	—
135	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
136	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
137	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
138	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
139	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
140	C₂₃×#117	—	2	1	no	—
141	C₂₃×#117	—	2	1	no	—
142	C₂₃×#117	—	2	1	no	—
143	C₂₃×#117	—	2	1	no	—
144	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
145	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
146	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
147	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
148	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
149	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
150	C₂₃×#107	—	2	1	no	—
151	C₂₃×#107	—	2	1	no	—
152	C₂₃×#107	—	2	1	no	—
153	C₂₃×#106	—	2	1	no	—
154	C₂₃×C₄⋊C₈	—	2	1	no	—
155	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
156	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
157	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
158	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
159	C₂₃×#103	—	2	2	no	—
160	C₂₃×#103	—	2	2	no	—
161	C₂₃×#103	—	2	1	no	—
162	C₂₃×#103	—	2	1	no	—
163	C₂₃×#103	—	2	1	no	—
164	C₂₃×#103	—	2	1	no	—
165	C₂₃×#103	—	2	1	no	—
166	C₂₃×#102	—	2	2	no	—
167	C₂₃×#102	—	2	2	no	—
168	C₂₃×#102	—	2	1	no	—
169	C₂₃×#102	—	2	1	no	—
170	C₂₃×#102	—	2	1	no	—
171	C₂₃×C₂²⋊C₈	—	2	1	no	—
172	C₂₃×#97	—	2	1	no	—
173	C₄×C₈×C₂₃	—	2	1	no	—
174	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
175	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
176	C₂⁴×C₂₃	—	2	2	no	—
177	C₂⁴×C₂₃	—	2	1	no	—
178	#41×C₂₃	—	4	4	no	—
179	#41×C₂₃	—	8	1	no	—
180	#41×C₂₃	—	8	1	no	—
181	C₂×Q₈×C₂₃	—	2	1	no	—
182	C₂×Q₈×C₂₃	—	2	1	no	—
183	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
184	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
185	C₂×D₄×C₂₃	—	2	2	no	—
186	C₂×D₄×C₂₃	—	2	2	no	—
187	C₂×D₄×C₂₃	—	2	2	no	—
188	C₂×D₄×C₂₃	—	2	1	no	—
189	C₂×D₄×C₂₃	—	2	2	no	—
190	C₂×D₄×C₂₃	—	2	2	no	—
191	C₂×D₄×C₂₃	—	2	2	no	—
192	C₂×D₄×C₂₃	—	2	2	no	—
193	C₂×D₄×C₂₃	—	2	1	no	—
194	C₂×D₄×C₂₃	—	2	1	no	—
195	C₂×D₄×C₂₃	—	2	1	no	—
196	C₂×D₄×C₂₃	—	4	1	no	—
197	C₂×D₄×C₂₃	—	4	2	no	—
198	C₂×D₄×C₂₃	—	4	2	no	—
199	C₂×D₄×C₂₃	—	8	1	no	—
200	C₂×D₄×C₂₃	—	8	1	no	—
201	C₂×D₄×C₂₃	—	8	4	no	—
202	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
203	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
204	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
205	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
206	C₂²×C₄×C₂₃	—	2	2	no	—
207	C₂²×C₄×C₂₃	—	2	2	no	—
208	C₂²×C₄×C₂₃	—	2	1	no	—
209	C₂²×C₄×C₂₃	—	2	1	no	—
210	C₂²×C₄×C₂₃	—	2	1	no	—
211	C₂²×C₄×C₂₃	—	2	1	no	—
212	C₂²×C₄×C₂₃	—	2	1	no	—
213	C₂²×C₄×C₂₃	—	2	2	no	—
214	C₂²×C₄×C₂₃	—	2	1	no	—
215	C₂²×C₄×C₂₃	—	8	1	no	—
216	C₂²×C₄×C₂₃	—	8	1	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	C₂×D₄	1	1	yes	characteristic
220	Q₁₆×C₂₃	—	8	1	no	—
221	SD₁₆×C₂₃	—	4	2	no	—
222	SD₁₆×C₂₃	—	4	2	no	—
223	SD₁₆×C₂₃	—	8	1	no	—
224	C₂×C₈×C₂₃	—	2	1	no	—
225	C₂×C₈×C₂₃	—	2	1	no	—
226	C₂×C₈×C₂₃	—	2	1	no	—
227	C₂×C₈×C₂₃	—	2	1	no	—
228	C₂×C₈×C₂₃	—	2	1	no	—
229	C₂×C₈×C₂₃	—	2	1	no	—
230	C₂×C₈×C₂₃	—	4	2	no	—
231	C₂×C₈×C₂₃	—	8	1	no	—
232	C₄⋊C₄×C₂₃	—	2	2	no	—
233	C₄⋊C₄×C₂₃	—	2	2	no	—
234	C₄⋊C₄×C₂₃	—	2	1	no	—
235	C₄⋊C₄×C₂₃	—	2	1	no	—
236	C₄⋊C₄×C₂₃	—	2	1	no	—
237	C₄⋊C₄×C₂₃	—	2	1	no	—
238	C₄⋊C₄×C₂₃	—	2	1	no	—
239	C₄⋊C₄×C₂₃	—	2	1	no	—
240	C₄⋊C₄×C₂₃	—	2	1	no	—
241	C₄⋊C₄×C₂₃	—	2	1	no	—
242	C₄⋊C₄×C₂₃	—	2	1	no	—
243	C₄⋊C₄×C₂₃	—	2	1	no	—
244	C₄⋊C₄×C₂₃	—	2	1	no	—
245	C₄⋊C₄×C₂₃	—	4	1	no	—
246	C₄⋊C₄×C₂₃	—	4	1	no	—
247	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
248	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
249	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
250	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
251	C₂²⋊C₄×C₂₃	—	2	2	no	—
252	C₂²⋊C₄×C₂₃	—	2	2	no	—
253	C₂²⋊C₄×C₂₃	—	2	2	no	—
254	C₂²⋊C₄×C₂₃	—	2	2	no	—
255	C₂²⋊C₄×C₂₃	—	2	2	no	—
256	C₂²⋊C₄×C₂₃	—	2	1	no	—
257	C₂²⋊C₄×C₂₃	—	2	1	no	—
258	C₂²⋊C₄×C₂₃	—	2	1	no	—
259	C₂²⋊C₄×C₂₃	—	2	1	no	—
260	C₂²⋊C₄×C₂₃	—	2	2	no	—
261	C₂²⋊C₄×C₂₃	—	2	1	no	—
262	C₂²⋊C₄×C₂₃	—	2	1	no	—
263	C₂²⋊C₄×C₂₃	—	2	2	no	—
264	C₂²⋊C₄×C₂₃	—	2	1	no	—
265	C₂²⋊C₄×C₂₃	—	2	1	no	—
266	C₂²⋊C₄×C₂₃	—	2	1	no	—
267	C₂²⋊C₄×C₂₃	—	4	1	no	—
268	C₄²×C₂₃	—	2	2	no	—
269	C₄²×C₂₃	—	2	1	no	—
270	C₄²×C₂₃	—	4	1	no	—
271	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
272	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
273	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
274	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
275	#18628	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
276	C₂³×C₂₃	—	2	1	no	—
277	C₂³×C₂₃	—	2	1	no	—
278	C₂³×C₂₃	—	2	1	no	—
279	C₂³×C₂₃	—	2	2	no	—
280	C₂³×C₂₃	—	4	2	no	—
281	C₂³×C₂₃	—	4	4	no	—
282	C₂³×C₂₃	—	4	2	no	—
283	C₂³×C₂₃	—	8	1	no	—
284	C₂³×C₂₃	—	8	2	no	—
285	C₂³×C₂₃	—	8	2	no	—
286	C₂³×C₂₃	#120	1	1	yes	characteristic
287	Q₈×C₂₃	—	2	1	no	—
288	Q₈×C₂₃	—	2	1	no	—
289	Q₈×C₂₃	—	4	2	no	—
290	Q₈×C₂₃	—	4	1	no	—
291	Q₈×C₂₃	—	4	1	no	—
292	Q₈×C₂₃	—	4	1	no	—
293	Q₈×C₂₃	—	4	1	no	—
294	D₄×C₂₃	—	2	1	no	—
295	D₄×C₂₃	—	2	1	no	—
296	D₄×C₂₃	—	2	1	no	—
297	D₄×C₂₃	—	2	1	no	—
298	D₄×C₂₃	—	2	1	no	—
299	D₄×C₂₃	—	4	2	no	—
300	D₄×C₂₃	—	4	2	no	—
301	D₄×C₂₃	—	4	4	no	—
302	D₄×C₂₃	—	4	2	no	—
303	D₄×C₂₃	—	4	4	no	—
304	D₄×C₂₃	—	4	1	no	—
305	D₄×C₂₃	—	4	1	no	—
306	D₄×C₂₃	—	4	1	no	—
307	D₄×C₂₃	—	4	1	no	—
308	D₄×C₂₃	—	8	2	no	—
309	D₄×C₂₃	—	8	2	no	—
310	D₄×C₂₃	—	8	2	no	—
311	D₄×C₂₃	—	8	2	no	—
312	D₄×C₂₃	#135	1	2	yes	—
313	C₂×C₄×C₂₃	—	2	2	no	—
314	C₂×C₄×C₂₃	—	2	1	no	—
315	C₂×C₄×C₂₃	—	2	1	no	—
316	C₂×C₄×C₂₃	—	2	1	no	—
317	C₂×C₄×C₂₃	—	2	1	no	—
318	C₂×C₄×C₂₃	—	2	1	no	—
319	C₂×C₄×C₂₃	—	2	1	no	—
320	C₂×C₄×C₂₃	—	2	1	no	—
321	C₂×C₄×C₂₃	—	2	2	no	—
322	C₂×C₄×C₂₃	—	2	1	no	—
323	C₂×C₄×C₂₃	—	2	1	no	—
324	C₂×C₄×C₂₃	—	4	1	no	—
325	C₂×C₄×C₂₃	—	4	1	no	—
326	C₂×C₄×C₂₃	—	4	1	no	—
327	C₂×C₄×C₂₃	—	4	1	no	—
328	C₂×C₄×C₂₃	—	4	1	no	—
329	C₂×C₄×C₂₃	—	4	1	no	—
330	C₂×C₄×C₂₃	—	4	1	no	—
331	C₂×C₄×C₂₃	—	4	1	no	—
332	C₂×C₄×C₂₃	—	8	1	no	—
333	C₂×C₄×C₂₃	—	8	1	no	—
334	C₂×C₄×C₂₃	—	8	2	no	—
335	C₂×C₄×C₂₃	—	8	1	no	—
336	C₂×C₄×C₂₃	—	8	2	no	—
337	C₂×C₄×C₂₃	—	8	2	no	—
338	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
339	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
340	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
341	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
344	C₈×C₂₃	—	4	1	no	—
345	C₈×C₂₃	—	4	1	no	—
346	C₈×C₂₃	—	4	1	no	—
347	C₈×C₂₃	—	4	1	no	—
348	C₈×C₂₃	—	4	1	no	—
349	C₈×C₂₃	—	4	1	no	—
350	#3519	C₂×C₂₃	1	1	yes	characteristic
351	#3248	C₂×C₂₃	1	1	yes	characteristic, complemented
352	#3131	C₂×C₂₃	1	1	yes	characteristic, complemented
353	#3110	C₂×C₂₃	1	1	yes	characteristic, complemented
354	#1646	C₂×C₂₃	1	1	yes	characteristic, complemented
355	#1646	C₂×C₂₃	1	1	yes	characteristic, complemented
356	#1644	C₂×C₂₃	1	1	yes	characteristic, complemented
357	#1643	C₂×C₂₃	1	1	yes	characteristic, complemented
358	#1642	C₂×C₂₃	1	1	yes	characteristic, complemented
359	#1641	C₂×C₂₃	1	1	yes	characteristic, complemented
360	#1639	C₂×C₂₃	1	1	yes	characteristic, complemented
361	#1639	C₂×C₂₃	1	1	yes	characteristic, complemented
362	#1551	C₂×C₂₃	1	1	yes	characteristic, complemented
363	#1494	C₂×C₂₃	1	1	yes	characteristic, complemented
364	C₂×D₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
365	C₂²×C₂₃	—	2	1	no	—
366	C₂²×C₂₃	—	2	1	no	—
367	C₂²×C₂₃	—	2	2	no	—
368	C₂²×C₂₃	—	4	1	no	—
369	C₂²×C₂₃	—	4	1	no	—
370	C₂²×C₂₃	—	4	1	no	—
371	C₂²×C₂₃	—	4	1	no	—
372	C₂²×C₂₃	—	4	2	no	—
373	C₂²×C₂₃	—	4	1	no	—
374	C₂²×C₂₃	—	4	2	no	—
375	C₂²×C₂₃	—	4	1	no	—
376	C₂²×C₂₃	—	4	2	no	—
377	C₂²×C₂₃	—	4	1	no	—
378	C₂²×C₂₃	—	4	1	no	—
379	C₂²×C₂₃	—	8	4	no	—
380	C₂²×C₂₃	—	16	4	no	—
381	C₂²×C₂₃	#455	1	2	yes	—
382	C₂²×C₂₃	C₂×#120	1	1	yes	characteristic
383	C₄×C₂₃	—	2	1	no	—
384	C₄×C₂₃	—	2	1	no	—
385	C₄×C₂₃	—	2	1	no	—
386	C₄×C₂₃	—	2	1	no	—
387	C₄×C₂₃	—	4	1	no	—
388	C₄×C₂₃	—	4	1	no	—
389	C₄×C₂₃	—	4	1	no	—
390	C₄×C₂₃	—	4	1	no	—
391	C₄×C₂₃	—	4	1	no	—
392	C₄×C₂₃	—	4	2	no	—
393	C₄×C₂₃	—	8	1	no	—
394	C₄×C₂₃	—	8	1	no	—
395	C₄×C₂₃	C₂×#135	1	1	yes	characteristic
396	C₄×C₂₃	#575	1	1	yes	characteristic
397	C₄×C₂₃	#576	1	1	yes	characteristic
398	C₄×C₂₃	#577	1	1	yes	characteristic
399	#555	C₂²×C₂₃	1	1	yes	characteristic
400	#554	C₂²×C₂₃	1	1	yes	characteristic
401	#553	—	2	1	no	—
402	#553	—	2	1	no	—
403	#550	C₂²×C₂₃	1	1	yes	characteristic
404	#546	—	2	2	no	—
405	#546	—	2	1	no	—
406	D₄²	—	2	1	no	—
407	D₄²	C₂²×C₂₃	1	1	yes	characteristic
408	#540	—	2	1	no	—
409	#538	—	2	2	no	—
410	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
411	#532	C₂²×C₂₃	1	1	yes	characteristic
412	#529	C₂²×C₂₃	1	1	yes	characteristic
413	#525	—	2	1	no	—
414	C₂×#121	—	2	1	no	—
415	#518	—	2	1	no	—
416	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
417	#488	—	2	2	no	—
418	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
419	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
420	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
421	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
422	#484	—	2	1	no	—
423	#479	—	2	1	no	—
424	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
425	#474	C₂²×C₂₃	1	1	yes	characteristic
426	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
427	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
428	#467	—	2	1	no	—
429	#465	—	2	1	no	—
430	#464	—	2	1	no	—
431	#462	C₂²×C₂₃	1	1	yes	characteristic, complemented
432	#461	C₂²×C₂₃	1	1	yes	characteristic
433	#461	C₂²×C₂₃	1	1	yes	characteristic, complemented
434	#461	C₂²×C₂₃	1	1	yes	characteristic, complemented
435	#450	—	2	1	no	—
436	#440	—	2	1	no	—
437	#440	—	2	1	no	—
438	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
439	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
440	#416	—	2	2	no	—
441	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
442	#333	C₂²×C₂₃	1	1	yes	characteristic, complemented
443	#333	C₂²×C₂₃	1	1	yes	characteristic, complemented
444	#331	C₂²×C₂₃	1	1	yes	characteristic, complemented
445	#331	C₂²×C₂₃	1	1	yes	characteristic, complemented
446	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
447	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
448	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
449	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
450	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
451	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
452	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
453	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
454	C₂×C₂₃	—	2	2	no	—
455	C₂×C₂₃	—	4	2	no	—
456	C₂×C₂₃	—	8	1	no	—
457	C₂×C₂₃	—	8	2	no	—
458	C₂×C₂₃	—	8	1	no	—
459	C₂×C₂₃	#3002	1	1	yes	characteristic
460	C₂×C₂₃	#3012	1	1	yes	characteristic
461	C₂×C₂₃	C₂×#455	1	1	yes	characteristic
462	C₂×#41	—	2	1	no	—
463	C₂×#41	D₄×C₂₃	1	2	yes	—
464	C₂²×D₄	—	2	2	no	—
465	C₂²×D₄	—	2	1	no	—
466	C₂²×D₄	—	2	1	no	—
467	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
468	C₂³×C₄	—	2	1	no	—
469	C₂×Q₁₆	—	2	1	no	—
470	C₂×SD₁₆	—	2	1	no	—
471	C₂×SD₁₆	—	2	1	no	—
472	C₂×SD₁₆	—	2	1	no	—
473	C₂²×C₈	—	2	1	no	—
474	C₂²×C₈	—	2	1	no	—
475	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
476	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
477	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
478	#127	—	2	1	no	—
479	#127	C₂³×C₂₃	1	1	yes	characteristic
480	#126	—	2	2	no	—
481	#126	—	2	1	no	—
482	#125	—	2	1	no	—
483	#125	—	2	1	no	—
484	#125	D₄×C₂₃	1	1	yes	characteristic
485	#124	—	2	2	no	—
486	#124	D₄×C₂₃	1	1	yes	characteristic
487	#124	D₄×C₂₃	1	2	yes	—
488	#123	—	2	2	no	—
489	#123	—	2	2	no	—
490	#123	—	2	2	no	—
491	#123	—	2	1	no	—
492	C₂²⋊Q₈	—	2	1	no	—
493	C₂²⋊Q₈	—	2	2	no	—
494	C₂²⋊Q₈	—	2	1	no	—
495	C₂²⋊Q₈	—	2	1	no	—
496	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
497	#121	—	2	2	no	—
498	#121	—	2	2	no	—
499	#121	—	2	2	no	—
500	#121	—	2	2	no	—
501	#121	—	2	1	no	—
502	#121	—	2	2	no	—
503	#121	—	2	1	no	—
504	#121	—	2	1	no	—
505	#121	—	2	1	no	—
506	#121	—	2	1	no	—
507	#121	—	2	1	no	—
508	#121	—	2	1	no	—
509	#121	D₄×C₂₃	1	1	yes	characteristic
510	#120	—	2	2	no	—
511	#120	—	2	2	no	—
512	#120	—	2	2	no	—
513	C₄×Q₈	—	2	1	no	—
514	C₄×Q₈	—	2	1	no	—
515	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
516	C₄×D₄	—	2	2	no	—
517	C₄×D₄	—	2	2	no	—
518	C₄×D₄	—	2	2	no	—
519	C₄×D₄	—	2	1	no	—
520	C₄×D₄	—	2	1	no	—
521	C₄×D₄	—	2	1	no	—
522	C₄×D₄	—	2	1	no	—
523	C₄×D₄	—	2	1	no	—
524	C₄×D₄	—	2	1	no	—
525	C₄×D₄	—	2	1	no	—
526	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
527	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
528	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
529	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
530	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
531	#117	—	2	1	no	—
532	#117	—	2	1	no	—
533	#117	—	2	1	no	—
534	#117	—	2	1	no	—
535	C₂×C₄⋊C₄	—	2	1	no	—
536	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
537	C₂×C₂²⋊C₄	—	2	2	no	—
538	C₂×C₂²⋊C₄	—	2	2	no	—
539	C₂×C₂²⋊C₄	—	2	1	no	—
540	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
541	#107	—	2	1	no	—
542	#107	—	2	1	no	—
543	#107	—	2	1	no	—
544	#106	—	2	1	no	—
545	C₄⋊C₈	—	2	1	no	—
546	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
547	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
548	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
549	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
550	#103	—	2	2	no	—
551	#103	—	2	2	no	—
552	#103	—	2	1	no	—
553	#103	—	2	1	no	—
554	#103	—	2	1	no	—
555	#103	—	2	1	no	—
556	#103	—	2	1	no	—
557	#102	—	2	2	no	—
558	#102	—	2	2	no	—
559	#102	—	2	1	no	—
560	#102	—	2	1	no	—
561	#102	—	2	1	no	—
562	C₂²⋊C₈	—	2	1	no	—
563	#97	—	2	1	no	—
564	C₄×C₈	—	2	1	no	—
565	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
566	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
567	C₂₃	#18628	1	1	yes	characteristic, direct product factor, Sylow
568	C₂⁴	—	2	2	no	—
569	C₂⁴	—	2	1	no	—
570	#41	—	4	4	no	—
571	#41	—	8	1	no	—
572	#41	—	8	1	no	—
573	C₂×Q₈	—	2	1	no	—
574	C₂×Q₈	—	2	1	no	—
575	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
576	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
577	C₂×D₄	—	2	2	no	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	2	2	no	—
580	C₂×D₄	—	2	1	no	—
581	C₂×D₄	—	2	2	no	—
582	C₂×D₄	—	2	2	no	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	2	1	no	—
586	C₂×D₄	—	2	1	no	—
587	C₂×D₄	—	2	1	no	—
588	C₂×D₄	—	4	1	no	—
589	C₂×D₄	—	4	2	no	—
590	C₂×D₄	—	4	2	no	—
591	C₂×D₄	—	8	1	no	—
592	C₂×D₄	—	8	1	no	—
593	C₂×D₄	—	8	4	no	—
594	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
595	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
596	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
597	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	8	1	no	—
608	C₂²×C₄	—	8	1	no	—
609	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
610	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
611	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
612	Q₁₆	—	8	1	no	—
613	SD₁₆	—	4	2	no	—
614	SD₁₆	—	4	2	no	—
615	SD₁₆	—	8	1	no	—
616	C₂×C₈	—	2	1	no	—
617	C₂×C₈	—	2	1	no	—
618	C₂×C₈	—	2	1	no	—
619	C₂×C₈	—	2	1	no	—
620	C₂×C₈	—	2	1	no	—
621	C₂×C₈	—	2	1	no	—
622	C₂×C₈	—	4	2	no	—
623	C₂×C₈	—	8	1	no	—
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	2	2	no	—
626	C₄⋊C₄	—	2	1	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	—	2	1	no	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	—	2	1	no	—
637	C₄⋊C₄	—	4	1	no	—
638	C₄⋊C₄	—	4	1	no	—
639	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
640	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
641	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
642	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	2	no	—
647	C₂²⋊C₄	—	2	2	no	—
648	C₂²⋊C₄	—	2	1	no	—
649	C₂²⋊C₄	—	2	1	no	—
650	C₂²⋊C₄	—	2	1	no	—
651	C₂²⋊C₄	—	2	1	no	—
652	C₂²⋊C₄	—	2	2	no	—
653	C₂²⋊C₄	—	2	1	no	—
654	C₂²⋊C₄	—	2	1	no	—
655	C₂²⋊C₄	—	2	2	no	—
656	C₂²⋊C₄	—	2	1	no	—
657	C₂²⋊C₄	—	2	1	no	—
658	C₂²⋊C₄	—	2	1	no	—
659	C₂²⋊C₄	—	4	1	no	—
660	C₄²	—	2	2	no	—
661	C₄²	—	2	1	no	—
662	C₄²	—	4	1	no	—
663	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
664	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
665	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
666	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
667	C₂³	—	2	1	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	4	2	no	—
672	C₂³	—	4	4	no	—
673	C₂³	—	4	2	no	—
674	C₂³	—	8	1	no	—
675	C₂³	—	8	2	no	—
676	C₂³	—	8	2	no	—
677	C₂³	C₂₃×#120	1	1	yes	characteristic
678	Q₈	—	2	1	no	—
679	Q₈	—	2	1	no	—
680	Q₈	—	4	2	no	—
681	Q₈	—	4	1	no	—
682	Q₈	—	4	1	no	—
683	Q₈	—	4	1	no	—
684	Q₈	—	4	1	no	—
685	D₄	—	2	1	no	—
686	D₄	—	2	1	no	—
687	D₄	—	2	1	no	—
688	D₄	—	2	1	no	—
689	D₄	—	2	1	no	—
690	D₄	—	4	2	no	—
691	D₄	—	4	2	no	—
692	D₄	—	4	4	no	—
693	D₄	—	4	2	no	—
694	D₄	—	4	4	no	—
695	D₄	—	4	1	no	—
696	D₄	—	4	1	no	—
697	D₄	—	4	1	no	—
698	D₄	—	4	1	no	—
699	D₄	—	8	2	no	—
700	D₄	—	8	2	no	—
701	D₄	—	8	2	no	—
702	D₄	—	8	2	no	—
703	D₄	C₂₃×#135	1	2	yes	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	8	1	no	—
724	C₂×C₄	—	8	1	no	—
725	C₂×C₄	—	8	2	no	—
726	C₂×C₄	—	8	1	no	—
727	C₂×C₄	—	8	2	no	—
728	C₂×C₄	—	8	2	no	—
729	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
730	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
731	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
732	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
733	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
734	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
735	C₈	—	4	1	no	—
736	C₈	—	4	1	no	—
737	C₈	—	4	1	no	—
738	C₈	—	4	1	no	—
739	C₈	—	4	1	no	—
740	C₈	—	4	1	no	—
741	C₂²	—	2	1	no	—
742	C₂²	—	2	1	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	4	1	no	—
745	C₂²	—	4	1	no	—
746	C₂²	—	4	1	no	—
747	C₂²	—	4	1	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	1	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	1	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	4	1	no	—
754	C₂²	—	4	1	no	—
755	C₂²	—	8	4	no	—
756	C₂²	—	16	4	no	—
757	C₂²	C₂₃×#455	1	2	yes	—
758	C₂²	C₂×C₂₃×#120	1	1	yes	characteristic
759	C₄	—	2	1	no	—
760	C₄	—	2	1	no	—
761	C₄	—	2	1	no	—
762	C₄	—	2	1	no	—
763	C₄	—	4	1	no	—
764	C₄	—	4	1	no	—
765	C₄	—	4	1	no	—
766	C₄	—	4	1	no	—
767	C₄	—	4	1	no	—
768	C₄	—	4	2	no	—
769	C₄	—	8	1	no	—
770	C₄	—	8	1	no	—
771	C₄	C₂×C₂₃×#135	1	1	yes	characteristic
772	C₄	C₂₃×#575	1	1	yes	characteristic
773	C₄	C₂₃×#576	1	1	yes	characteristic
774	C₄	C₂₃×#577	1	1	yes	characteristic
775	C₂	—	2	2	no	—
776	C₂	—	4	2	no	—
777	C₂	—	8	1	no	—
778	C₂	—	8	1	no	—
779	C₂	—	8	2	no	—
780	C₂	C₂₃×#3002	1	1	yes	characteristic
781	C₂	C₂₃×#3012	1	1	yes	characteristic
782	C₂	C₂×C₂₃×#455	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₃
prime radical	C₂₃×#3519	C₂
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
2. C₂₃×#3248	C₂	semidirect
3. C₂₃×#3131	C₂	semidirect
4. C₂₃×#3110	C₂	semidirect
5. C₂₃×#1646	C₂	semidirect
6. C₂₃×#1646	C₂	semidirect
7. C₂₃×#1644	C₂	semidirect
8. C₂₃×#1643	C₂	semidirect
9. C₂₃×#1642	C₂	semidirect
10. C₂₃×#1641	C₂	semidirect
11. C₂₃×#1639	C₂	semidirect
12. C₂₃×#1639	C₂	semidirect
13. C₂₃×#1551	C₂	semidirect
14. C₂₃×#1494	C₂	semidirect
15. C₂×C₂₃×D₄⋊C₈	C₂	semidirect
27. C₂₃×#533	C₂²	semidirect
35. C₂₃×#487	C₂²	semidirect
36. C₂₃×#487	C₂²	semidirect
37. C₂₃×#486	C₂²	semidirect
38. C₂₃×#486	C₂²	semidirect
41. C₂₃×#475	C₂²	semidirect
43. C₂₃×#474	C₂²	semidirect
44. C₂₃×#474	C₂²	semidirect
48. C₂₃×#462	C₂²	semidirect
50. C₂₃×#461	C₂²	semidirect
51. C₂₃×#461	C₂²	semidirect
55. C₂₃×#432	C₂²	semidirect
56. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
58. C₂×C₄×C₈×C₂₃	C₂²	semidirect
59. C₂₃×#333	C₂²	semidirect
60. C₂₃×#333	C₂²	semidirect
61. C₂₃×#331	C₂²	semidirect
62. C₂₃×#331	C₂²	semidirect
63. C₂₃×Q₈⋊C₈	C₂²	semidirect
64. C₂₃×Q₈⋊C₈	C₂²	semidirect
67. C₂₃×D₄⋊C₈	C₂²	semidirect
68. C₂₃×D₄⋊C₈	C₂²	semidirect
69. C₂₃×D₄⋊C₈	C₂²	semidirect
70. C₂₃×D₄⋊C₈	C₂²	semidirect
275. #18628	C₂₃	direct (N × H)
351. #3248	C₂×C₂₃	semidirect
352. #3131	C₂×C₂₃	semidirect
353. #3110	C₂×C₂₃	semidirect
354. #1646	C₂×C₂₃	semidirect
355. #1646	C₂×C₂₃	semidirect
356. #1644	C₂×C₂₃	semidirect
357. #1643	C₂×C₂₃	semidirect
358. #1642	C₂×C₂₃	semidirect
359. #1641	C₂×C₂₃	semidirect
360. #1639	C₂×C₂₃	semidirect
361. #1639	C₂×C₂₃	semidirect
362. #1551	C₂×C₂₃	semidirect
363. #1494	C₂×C₂₃	semidirect
364. C₂×D₄⋊C₈	C₂×C₂₃	semidirect
410. #533	C₂²×C₂₃	semidirect
418. #487	C₂²×C₂₃	semidirect
419. #487	C₂²×C₂₃	semidirect
420. #486	C₂²×C₂₃	semidirect
421. #486	C₂²×C₂₃	semidirect
424. #475	C₂²×C₂₃	semidirect
426. #474	C₂²×C₂₃	semidirect
427. #474	C₂²×C₂₃	semidirect
431. #462	C₂²×C₂₃	semidirect
433. #461	C₂²×C₂₃	semidirect
434. #461	C₂²×C₂₃	semidirect
438. #432	C₂²×C₂₃	semidirect
439. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
441. C₂×C₄×C₈	C₂²×C₂₃	semidirect
442. #333	C₂²×C₂₃	semidirect
443. #333	C₂²×C₂₃	semidirect
444. #331	C₂²×C₂₃	semidirect
445. #331	C₂²×C₂₃	semidirect
446. Q₈⋊C₈	C₂²×C₂₃	semidirect
447. Q₈⋊C₈	C₂²×C₂₃	semidirect
450. D₄⋊C₈	C₂²×C₂₃	semidirect
451. D₄⋊C₈	C₂²×C₂₃	semidirect
452. D₄⋊C₈	C₂²×C₂₃	semidirect
453. D₄⋊C₈	C₂²×C₂₃	semidirect
567. C₂₃	#18628	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×#3519	2
C₂₃×#3248	2
C₂₃×#3131	2
C₂₃×#3110	2
C₂₃×#1646	2
C₂₃×#1644	2
C₂₃×#1643	2
C₂₃×#1642	2
C₂₃×#1641	2
C₂₃×#1639	2
C₂₃×#1551	2
C₂₃×#1494	2
C₂×C₂₃×D₄⋊C₈	2
#18628	23

Subgroups — C23×#18628 #19166254

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#18628 #19166254