Subgroups — C₂₃×#18648 #19166274

Order 5888.

934 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3520	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#3248	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3160	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3110	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1654	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1654	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1652	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1651	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1650	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1649	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1647	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1647	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1552	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×#556	C₂²	1	1	yes	characteristic
17	C₂₃×#554	—	2	1	no	—
18	C₂₃×#552	—	2	1	no	—
19	C₂₃×#551	—	2	2	no	—
20	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
21	C₂₃×#548	—	2	1	no	—
22	C₂₃×#547	C₂²	1	1	yes	characteristic
23	C₂₃×#547	C₂²	1	1	yes	characteristic
24	C₂₃×#546	—	2	1	no	—
25	C₂₃×#542	—	2	1	no	—
26	C₂₃×#539	—	2	2	no	—
27	C₂₃×#533	C₂²	1	1	yes	characteristic
28	C₂₃×#533	C₂²	1	1	yes	characteristic
29	C₂₃×#529	C₂²	1	1	yes	characteristic
30	C₂₃×#525	—	2	1	no	—
31	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
32	C₂₃×#520	—	2	1	no	—
33	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
34	C₂₃×#500	C₂²	1	1	yes	characteristic, complemented
35	C₂₃×#500	C₂²	1	1	yes	characteristic, complemented
36	C₂₃×#499	—	2	2	no	—
37	C₂₃×#498	C₂²	1	1	yes	characteristic, complemented
38	C₂₃×#498	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
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
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
56	C₂₃×#427	—	2	2	no	—
57	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
58	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
59	C₂₃×#332	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#332	C₂²	1	1	yes	characteristic, complemented
61	C₂₃×#332	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#332	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
68	C₂₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
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	—	2	1	no	—
73	C₂²×Q₈×C₂₃	—	2	1	no	—
74	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
75	C₂³×C₄×C₂₃	—	2	1	no	—
76	C₂×Q₁₆×C₂₃	—	2	1	no	—
77	C₂×SD₁₆×C₂₃	—	2	1	no	—
78	C₂×SD₁₆×C₂₃	—	2	1	no	—
79	C₂×SD₁₆×C₂₃	—	2	1	no	—
80	C₂²×C₈×C₂₃	—	2	1	no	—
81	C₂²×C₈×C₂₃	—	2	1	no	—
82	C₂₃×C₄⋊Q₈	—	2	1	no	—
83	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
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×#126	—	2	2	no	—
88	C₂₃×#126	—	2	2	no	—
89	C₂₃×#126	—	2	1	no	—
90	C₂₃×#125	—	2	2	no	—
91	C₂₃×#125	—	2	1	no	—
92	C₂₃×#125	D₄	1	1	yes	characteristic
93	C₂₃×#125	D₄	1	2	yes	—
94	C₂₃×#124	—	2	2	no	—
95	C₂₃×#124	—	2	1	no	—
96	C₂₃×#124	D₄	1	1	yes	characteristic
97	C₂₃×#123	—	2	2	no	—
98	C₂₃×#123	—	2	2	no	—
99	C₂₃×#123	—	2	1	no	—
100	C₂₃×#123	—	2	2	no	—
101	C₂₃×#123	—	2	2	no	—
102	C₂₃×C₂²⋊Q₈	—	2	2	no	—
103	C₂₃×C₂²⋊Q₈	—	2	2	no	—
104	C₂₃×C₂²⋊Q₈	—	2	2	no	—
105	C₂₃×C₂²⋊Q₈	—	2	1	no	—
106	C₂₃×C₂²⋊Q₈	—	2	1	no	—
107	C₂₃×C₂²⋊Q₈	—	2	1	no	—
108	C₂₃×C₂²⋊Q₈	—	2	1	no	—
109	C₂₃×C₂²⋊Q₈	—	2	1	no	—
110	C₂₃×C₂²⋊Q₈	—	2	2	no	—
111	C₂₃×C₂²⋊Q₈	—	2	1	no	—
112	C₂₃×C₂²⋊Q₈	—	2	1	no	—
113	C₂₃×C₂²⋊Q₈	—	2	1	no	—
114	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
115	C₂₃×#121	—	2	2	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	C₄×Q₈×C₂₃	—	2	1	no	—
121	C₄×Q₈×C₂₃	—	2	1	no	—
122	C₄×Q₈×C₂₃	—	2	1	no	—
123	C₄×Q₈×C₂₃	—	2	1	no	—
124	C₄×Q₈×C₂₃	—	2	1	no	—
125	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
126	C₄×D₄×C₂₃	—	2	2	no	—
127	C₄×D₄×C₂₃	—	2	2	no	—
128	C₄×D₄×C₂₃	—	2	2	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	D₄	1	1	yes	characteristic
134	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
135	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
136	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
137	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
138	C₂₃×#117	—	2	2	no	—
139	C₂₃×#117	—	2	1	no	—
140	C₂₃×#117	—	2	1	no	—
141	C₂₃×#117	—	2	1	no	—
142	C₂₃×#117	D₄	1	2	yes	—
143	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
144	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
145	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
146	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
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	2	no	—
151	C₂₃×#107	—	2	2	no	—
152	C₂₃×#107	—	2	1	no	—
153	C₂₃×#107	—	2	1	no	—
154	C₂₃×#107	—	2	1	no	—
155	C₂₃×#106	—	2	2	no	—
156	C₂₃×#106	—	2	2	no	—
157	C₂₃×#106	—	2	1	no	—
158	C₂₃×C₄⋊C₈	—	2	1	no	—
159	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
160	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
161	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
162	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
163	C₂₃×#103	—	2	1	no	—
164	C₂₃×#103	—	2	1	no	—
165	C₂₃×#103	—	2	1	no	—
166	C₂₃×#103	—	2	1	no	—
167	C₂₃×#103	—	2	1	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	1	no	—
177	#41×C₂₃	—	4	2	no	—
178	#41×C₂₃	—	4	2	no	—
179	#41×C₂₃	—	8	1	no	—
180	#41×C₂₃	—	8	1	no	—
181	C₂×Q₈×C₂₃	—	2	2	no	—
182	C₂×Q₈×C₂₃	—	2	1	no	—
183	C₂×Q₈×C₂₃	—	2	1	no	—
184	C₂×Q₈×C₂₃	—	2	1	no	—
185	C₂×Q₈×C₂₃	—	2	1	no	—
186	C₂×Q₈×C₂₃	—	8	1	no	—
187	C₂×Q₈×C₂₃	—	8	1	no	—
188	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
189	C₂×D₄×C₂₃	—	2	2	no	—
190	C₂×D₄×C₂₃	—	2	2	no	—
191	C₂×D₄×C₂₃	—	2	1	no	—
192	C₂×D₄×C₂₃	—	2	2	no	—
193	C₂×D₄×C₂₃	—	2	1	no	—
194	C₂×D₄×C₂₃	—	4	1	no	—
195	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
196	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
197	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₂₃	—	2	2	no	—
199	C₂²×C₄×C₂₃	—	2	2	no	—
200	C₂²×C₄×C₂₃	—	2	2	no	—
201	C₂²×C₄×C₂₃	—	2	1	no	—
202	C₂²×C₄×C₂₃	—	2	1	no	—
203	C₂²×C₄×C₂₃	—	2	1	no	—
204	C₂²×C₄×C₂₃	—	2	1	no	—
205	C₂²×C₄×C₂₃	—	2	1	no	—
206	C₂²×C₄×C₂₃	—	2	1	no	—
207	C₂²×C₄×C₂₃	—	8	1	no	—
208	C₂²×C₄×C₂₃	—	8	1	no	—
209	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
212	Q₁₆×C₂₃	—	8	1	no	—
213	SD₁₆×C₂₃	—	4	2	no	—
214	SD₁₆×C₂₃	—	4	2	no	—
215	SD₁₆×C₂₃	—	8	1	no	—
216	C₂×C₈×C₂₃	—	2	4	no	—
217	C₂×C₈×C₂₃	—	2	1	no	—
218	C₂×C₈×C₂₃	—	2	1	no	—
219	C₂×C₈×C₂₃	—	2	1	no	—
220	C₂×C₈×C₂₃	—	2	1	no	—
221	C₂×C₈×C₂₃	—	2	1	no	—
222	C₂×C₈×C₂₃	—	2	1	no	—
223	C₂×C₈×C₂₃	—	8	1	no	—
224	C₄⋊C₄×C₂₃	—	2	2	no	—
225	C₄⋊C₄×C₂₃	—	2	2	no	—
226	C₄⋊C₄×C₂₃	—	2	2	no	—
227	C₄⋊C₄×C₂₃	—	2	2	no	—
228	C₄⋊C₄×C₂₃	—	2	1	no	—
229	C₄⋊C₄×C₂₃	—	2	2	no	—
230	C₄⋊C₄×C₂₃	—	2	1	no	—
231	C₄⋊C₄×C₂₃	—	2	1	no	—
232	C₄⋊C₄×C₂₃	—	2	1	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	—	4	1	no	—
242	C₄⋊C₄×C₂₃	—	4	1	no	—
243	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
244	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
245	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
246	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
247	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
248	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
249	C₂²⋊C₄×C₂₃	—	2	2	no	—
250	C₂²⋊C₄×C₂₃	—	2	2	no	—
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	1	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	1	no	—
261	C₂²⋊C₄×C₂₃	—	2	1	no	—
262	C₂²⋊C₄×C₂₃	—	2	1	no	—
263	C₂²⋊C₄×C₂₃	—	2	1	no	—
264	C₂²⋊C₄×C₂₃	—	4	1	no	—
265	C₄²×C₂₃	—	2	2	no	—
266	C₄²×C₂₃	—	2	2	no	—
267	C₄²×C₂₃	—	2	1	no	—
268	C₄²×C₂₃	—	4	1	no	—
269	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
270	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
271	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
272	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
273	#18648	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
274	C₂³×C₂₃	—	2	1	no	—
275	C₂³×C₂₃	—	2	1	no	—
276	C₂³×C₂₃	—	2	1	no	—
277	C₂³×C₂₃	—	4	2	no	—
278	C₂³×C₂₃	—	4	2	no	—
279	C₂³×C₂₃	—	8	1	no	—
280	C₂³×C₂₃	#120	1	1	yes	characteristic
281	Q₈×C₂₃	—	2	1	no	—
282	Q₈×C₂₃	—	2	1	no	—
283	Q₈×C₂₃	—	4	1	no	—
284	Q₈×C₂₃	—	4	1	no	—
285	Q₈×C₂₃	—	4	1	no	—
286	Q₈×C₂₃	—	4	1	no	—
287	Q₈×C₂₃	—	4	1	no	—
288	Q₈×C₂₃	—	4	1	no	—
289	Q₈×C₂₃	—	4	1	no	—
290	Q₈×C₂₃	—	4	1	no	—
291	Q₈×C₂₃	—	8	2	no	—
292	D₄×C₂₃	—	2	1	no	—
293	D₄×C₂₃	—	2	1	no	—
294	D₄×C₂₃	—	2	1	no	—
295	D₄×C₂₃	—	2	1	no	—
296	D₄×C₂₃	—	2	1	no	—
297	D₄×C₂₃	—	4	2	no	—
298	D₄×C₂₃	—	4	4	no	—
299	D₄×C₂₃	—	4	2	no	—
300	D₄×C₂₃	—	8	2	no	—
301	D₄×C₂₃	#135	1	2	yes	—
302	C₂×C₄×C₂₃	—	2	2	no	—
303	C₂×C₄×C₂₃	—	2	1	no	—
304	C₂×C₄×C₂₃	—	2	1	no	—
305	C₂×C₄×C₂₃	—	2	1	no	—
306	C₂×C₄×C₂₃	—	2	1	no	—
307	C₂×C₄×C₂₃	—	2	1	no	—
308	C₂×C₄×C₂₃	—	2	2	no	—
309	C₂×C₄×C₂₃	—	2	1	no	—
310	C₂×C₄×C₂₃	—	2	1	no	—
311	C₂×C₄×C₂₃	—	2	2	no	—
312	C₂×C₄×C₂₃	—	2	1	no	—
313	C₂×C₄×C₂₃	—	2	1	no	—
314	C₂×C₄×C₂₃	—	4	4	no	—
315	C₂×C₄×C₂₃	—	4	1	no	—
316	C₂×C₄×C₂₃	—	4	1	no	—
317	C₂×C₄×C₂₃	—	4	1	no	—
318	C₂×C₄×C₂₃	—	4	1	no	—
319	C₂×C₄×C₂₃	—	4	1	no	—
320	C₂×C₄×C₂₃	—	4	1	no	—
321	C₂×C₄×C₂₃	—	4	1	no	—
322	C₂×C₄×C₂₃	—	4	1	no	—
323	C₂×C₄×C₂₃	—	8	1	no	—
324	C₂×C₄×C₂₃	—	8	1	no	—
325	C₂×C₄×C₂₃	—	8	1	no	—
326	C₂×C₄×C₂₃	—	8	2	no	—
327	C₂×C₄×C₂₃	—	8	2	no	—
328	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
329	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
330	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
331	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
334	C₈×C₂₃	—	2	2	no	—
335	C₈×C₂₃	—	2	2	no	—
336	C₈×C₂₃	—	4	1	no	—
337	C₈×C₂₃	—	4	1	no	—
338	C₈×C₂₃	—	4	1	no	—
339	C₈×C₂₃	—	4	1	no	—
340	#3520	C₂×C₂₃	1	1	yes	characteristic
341	#3248	C₂×C₂₃	1	1	yes	characteristic, complemented
342	#3160	C₂×C₂₃	1	1	yes	characteristic, complemented
343	#3110	C₂×C₂₃	1	1	yes	characteristic, complemented
344	#1654	C₂×C₂₃	1	1	yes	characteristic, complemented
345	#1654	C₂×C₂₃	1	1	yes	characteristic, complemented
346	#1652	C₂×C₂₃	1	1	yes	characteristic, complemented
347	#1651	C₂×C₂₃	1	1	yes	characteristic, complemented
348	#1650	C₂×C₂₃	1	1	yes	characteristic, complemented
349	#1649	C₂×C₂₃	1	1	yes	characteristic, complemented
350	#1647	C₂×C₂₃	1	1	yes	characteristic, complemented
351	#1647	C₂×C₂₃	1	1	yes	characteristic, complemented
352	#1552	C₂×C₂₃	1	1	yes	characteristic, complemented
353	#1494	C₂×C₂₃	1	1	yes	characteristic, complemented
354	C₂×D₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
355	C₂²×C₂₃	—	2	1	no	—
356	C₂²×C₂₃	—	2	1	no	—
357	C₂²×C₂₃	—	2	2	no	—
358	C₂²×C₂₃	—	4	1	no	—
359	C₂²×C₂₃	—	4	1	no	—
360	C₂²×C₂₃	—	4	1	no	—
361	C₂²×C₂₃	—	4	1	no	—
362	C₂²×C₂₃	—	4	1	no	—
363	C₂²×C₂₃	—	4	1	no	—
364	C₂²×C₂₃	—	4	1	no	—
365	C₂²×C₂₃	—	4	1	no	—
366	C₂²×C₂₃	—	8	4	no	—
367	C₂²×C₂₃	#456	1	2	yes	—
368	C₂²×C₂₃	C₂×#120	1	1	yes	characteristic
369	C₄×C₂₃	—	2	1	no	—
370	C₄×C₂₃	—	2	1	no	—
371	C₄×C₂₃	—	2	1	no	—
372	C₄×C₂₃	—	2	1	no	—
373	C₄×C₂₃	—	4	1	no	—
374	C₄×C₂₃	—	4	2	no	—
375	C₄×C₂₃	—	4	1	no	—
376	C₄×C₂₃	—	4	1	no	—
377	C₄×C₂₃	—	4	2	no	—
378	C₄×C₂₃	—	4	1	no	—
379	C₄×C₂₃	—	4	1	no	—
380	C₄×C₂₃	—	8	1	no	—
381	C₄×C₂₃	—	8	1	no	—
382	C₄×C₂₃	C₂×#135	1	1	yes	characteristic
383	C₄×C₂₃	#575	1	1	yes	characteristic
384	C₄×C₂₃	#576	1	1	yes	characteristic
385	C₄×C₂₃	#577	1	1	yes	characteristic
386	#556	C₂²×C₂₃	1	1	yes	characteristic
387	#554	—	2	1	no	—
388	#552	—	2	1	no	—
389	#551	—	2	2	no	—
390	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
391	#548	—	2	1	no	—
392	#547	C₂²×C₂₃	1	1	yes	characteristic
393	#547	C₂²×C₂₃	1	1	yes	characteristic
394	#546	—	2	1	no	—
395	#542	—	2	1	no	—
396	#539	—	2	2	no	—
397	#533	C₂²×C₂₃	1	1	yes	characteristic
398	#533	C₂²×C₂₃	1	1	yes	characteristic
399	#529	C₂²×C₂₃	1	1	yes	characteristic
400	#525	—	2	1	no	—
401	C₂×C₂²⋊Q₈	—	2	1	no	—
402	#520	—	2	1	no	—
403	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
404	#500	C₂²×C₂₃	1	1	yes	characteristic, complemented
405	#500	C₂²×C₂₃	1	1	yes	characteristic, complemented
406	#499	—	2	2	no	—
407	#498	C₂²×C₂₃	1	1	yes	characteristic, complemented
408	#498	C₂²×C₂₃	1	1	yes	characteristic, complemented
409	#484	—	2	1	no	—
410	#479	—	2	1	no	—
411	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
412	#474	C₂²×C₂₃	1	1	yes	characteristic
413	#474	C₂²×C₂₃	1	1	yes	characteristic
414	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
415	#467	—	2	1	no	—
416	#465	—	2	1	no	—
417	#464	—	2	1	no	—
418	#462	C₂²×C₂₃	1	1	yes	characteristic, complemented
419	#461	C₂²×C₂₃	1	1	yes	characteristic
420	#461	C₂²×C₂₃	1	1	yes	characteristic
421	#461	C₂²×C₂₃	1	1	yes	characteristic, complemented
422	#450	—	2	1	no	—
423	#440	—	2	1	no	—
424	#440	—	2	1	no	—
425	#432	C₂²×C₂₃	1	1	yes	characteristic
426	#427	—	2	2	no	—
427	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
428	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
429	#332	C₂²×C₂₃	1	1	yes	characteristic, complemented
430	#332	C₂²×C₂₃	1	1	yes	characteristic, complemented
431	#332	C₂²×C₂₃	1	1	yes	characteristic, complemented
432	#332	C₂²×C₂₃	1	1	yes	characteristic, complemented
433	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
434	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
435	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
436	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
437	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
438	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
439	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
440	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
441	C₂×C₂₃	—	2	2	no	—
442	C₂×C₂₃	—	4	2	no	—
443	C₂×C₂₃	—	8	1	no	—
444	C₂×C₂₃	—	8	1	no	—
445	C₂×C₂₃	#3002	1	1	yes	characteristic
446	C₂×C₂₃	#3012	1	1	yes	characteristic
447	C₂×C₂₃	C₂×#456	1	1	yes	characteristic
448	C₂×#41	—	2	1	no	—
449	C₂×#41	—	2	1	no	—
450	C₂²×Q₈	—	2	1	no	—
451	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
452	C₂³×C₄	—	2	1	no	—
453	C₂×Q₁₆	—	2	1	no	—
454	C₂×SD₁₆	—	2	1	no	—
455	C₂×SD₁₆	—	2	1	no	—
456	C₂×SD₁₆	—	2	1	no	—
457	C₂²×C₈	—	2	1	no	—
458	C₂²×C₈	—	2	1	no	—
459	C₄⋊Q₈	—	2	1	no	—
460	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
461	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
462	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
463	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
464	#126	—	2	2	no	—
465	#126	—	2	2	no	—
466	#126	—	2	1	no	—
467	#125	—	2	2	no	—
468	#125	—	2	1	no	—
469	#125	D₄×C₂₃	1	1	yes	characteristic
470	#125	D₄×C₂₃	1	2	yes	—
471	#124	—	2	2	no	—
472	#124	—	2	1	no	—
473	#124	D₄×C₂₃	1	1	yes	characteristic
474	#123	—	2	2	no	—
475	#123	—	2	2	no	—
476	#123	—	2	1	no	—
477	#123	—	2	2	no	—
478	#123	—	2	2	no	—
479	C₂²⋊Q₈	—	2	2	no	—
480	C₂²⋊Q₈	—	2	2	no	—
481	C₂²⋊Q₈	—	2	2	no	—
482	C₂²⋊Q₈	—	2	1	no	—
483	C₂²⋊Q₈	—	2	1	no	—
484	C₂²⋊Q₈	—	2	1	no	—
485	C₂²⋊Q₈	—	2	1	no	—
486	C₂²⋊Q₈	—	2	1	no	—
487	C₂²⋊Q₈	—	2	2	no	—
488	C₂²⋊Q₈	—	2	1	no	—
489	C₂²⋊Q₈	—	2	1	no	—
490	C₂²⋊Q₈	—	2	1	no	—
491	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
492	#121	—	2	2	no	—
493	#121	—	2	1	no	—
494	#121	—	2	1	no	—
495	#121	D₄×C₂₃	1	1	yes	characteristic
496	#120	—	2	2	no	—
497	C₄×Q₈	—	2	1	no	—
498	C₄×Q₈	—	2	1	no	—
499	C₄×Q₈	—	2	1	no	—
500	C₄×Q₈	—	2	1	no	—
501	C₄×Q₈	—	2	1	no	—
502	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
503	C₄×D₄	—	2	2	no	—
504	C₄×D₄	—	2	2	no	—
505	C₄×D₄	—	2	2	no	—
506	C₄×D₄	—	2	1	no	—
507	C₄×D₄	—	2	1	no	—
508	C₄×D₄	—	2	1	no	—
509	C₄×D₄	—	2	1	no	—
510	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
511	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
512	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
513	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
514	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
515	#117	—	2	2	no	—
516	#117	—	2	1	no	—
517	#117	—	2	1	no	—
518	#117	—	2	1	no	—
519	#117	D₄×C₂₃	1	2	yes	—
520	C₂×C₄⋊C₄	—	2	2	no	—
521	C₂×C₄⋊C₄	—	2	1	no	—
522	C₂×C₄⋊C₄	—	2	1	no	—
523	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
524	C₂×C₂²⋊C₄	—	2	2	no	—
525	C₂×C₂²⋊C₄	—	2	1	no	—
526	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
527	#107	—	2	2	no	—
528	#107	—	2	2	no	—
529	#107	—	2	1	no	—
530	#107	—	2	1	no	—
531	#107	—	2	1	no	—
532	#106	—	2	2	no	—
533	#106	—	2	2	no	—
534	#106	—	2	1	no	—
535	C₄⋊C₈	—	2	1	no	—
536	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
537	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
538	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
539	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
540	#103	—	2	1	no	—
541	#103	—	2	1	no	—
542	#103	—	2	1	no	—
543	#103	—	2	1	no	—
544	#103	—	2	1	no	—
545	#102	—	2	1	no	—
546	#102	—	2	1	no	—
547	#102	—	2	1	no	—
548	C₂²⋊C₈	—	2	1	no	—
549	#97	—	2	1	no	—
550	C₄×C₈	—	2	1	no	—
551	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
552	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
553	C₂₃	#18648	1	1	yes	characteristic, direct product factor, Sylow
554	C₂⁴	—	2	1	no	—
555	#41	—	4	2	no	—
556	#41	—	4	2	no	—
557	#41	—	8	1	no	—
558	#41	—	8	1	no	—
559	C₂×Q₈	—	2	2	no	—
560	C₂×Q₈	—	2	1	no	—
561	C₂×Q₈	—	2	1	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	—	8	1	no	—
565	C₂×Q₈	—	8	1	no	—
566	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
567	C₂×D₄	—	2	2	no	—
568	C₂×D₄	—	2	2	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	2	2	no	—
571	C₂×D₄	—	2	1	no	—
572	C₂×D₄	—	4	1	no	—
573	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
574	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
575	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	8	1	no	—
586	C₂²×C₄	—	8	1	no	—
587	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
588	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
589	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
590	Q₁₆	—	8	1	no	—
591	SD₁₆	—	4	2	no	—
592	SD₁₆	—	4	2	no	—
593	SD₁₆	—	8	1	no	—
594	C₂×C₈	—	2	4	no	—
595	C₂×C₈	—	2	1	no	—
596	C₂×C₈	—	2	1	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	2	1	no	—
599	C₂×C₈	—	2	1	no	—
600	C₂×C₈	—	2	1	no	—
601	C₂×C₈	—	8	1	no	—
602	C₄⋊C₄	—	2	2	no	—
603	C₄⋊C₄	—	2	2	no	—
604	C₄⋊C₄	—	2	2	no	—
605	C₄⋊C₄	—	2	2	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	2	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	2	1	no	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	—	4	1	no	—
620	C₄⋊C₄	—	4	1	no	—
621	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
622	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
623	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
624	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
625	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
626	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
627	C₂²⋊C₄	—	2	2	no	—
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	—	2	2	no	—
630	C₂²⋊C₄	—	2	2	no	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	2	1	no	—
633	C₂²⋊C₄	—	2	2	no	—
634	C₂²⋊C₄	—	2	1	no	—
635	C₂²⋊C₄	—	2	1	no	—
636	C₂²⋊C₄	—	2	1	no	—
637	C₂²⋊C₄	—	2	1	no	—
638	C₂²⋊C₄	—	2	1	no	—
639	C₂²⋊C₄	—	2	1	no	—
640	C₂²⋊C₄	—	2	1	no	—
641	C₂²⋊C₄	—	2	1	no	—
642	C₂²⋊C₄	—	4	1	no	—
643	C₄²	—	2	2	no	—
644	C₄²	—	2	2	no	—
645	C₄²	—	2	1	no	—
646	C₄²	—	4	1	no	—
647	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
648	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
649	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
650	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
651	C₂³	—	2	1	no	—
652	C₂³	—	2	1	no	—
653	C₂³	—	2	1	no	—
654	C₂³	—	4	2	no	—
655	C₂³	—	4	2	no	—
656	C₂³	—	8	1	no	—
657	C₂³	C₂₃×#120	1	1	yes	characteristic
658	Q₈	—	2	1	no	—
659	Q₈	—	2	1	no	—
660	Q₈	—	4	1	no	—
661	Q₈	—	4	1	no	—
662	Q₈	—	4	1	no	—
663	Q₈	—	4	1	no	—
664	Q₈	—	4	1	no	—
665	Q₈	—	4	1	no	—
666	Q₈	—	4	1	no	—
667	Q₈	—	4	1	no	—
668	Q₈	—	8	2	no	—
669	D₄	—	2	1	no	—
670	D₄	—	2	1	no	—
671	D₄	—	2	1	no	—
672	D₄	—	2	1	no	—
673	D₄	—	2	1	no	—
674	D₄	—	4	2	no	—
675	D₄	—	4	4	no	—
676	D₄	—	4	2	no	—
677	D₄	—	8	2	no	—
678	D₄	C₂₃×#135	1	2	yes	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	4	4	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	8	1	no	—
701	C₂×C₄	—	8	1	no	—
702	C₂×C₄	—	8	1	no	—
703	C₂×C₄	—	8	2	no	—
704	C₂×C₄	—	8	2	no	—
705	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
706	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
707	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
708	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
709	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
710	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
711	C₈	—	2	2	no	—
712	C₈	—	2	2	no	—
713	C₈	—	4	1	no	—
714	C₈	—	4	1	no	—
715	C₈	—	4	1	no	—
716	C₈	—	4	1	no	—
717	C₂²	—	2	1	no	—
718	C₂²	—	2	1	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	4	1	no	—
721	C₂²	—	4	1	no	—
722	C₂²	—	4	1	no	—
723	C₂²	—	4	1	no	—
724	C₂²	—	4	1	no	—
725	C₂²	—	4	1	no	—
726	C₂²	—	4	1	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	8	4	no	—
729	C₂²	C₂₃×#456	1	2	yes	—
730	C₂²	C₂×C₂₃×#120	1	1	yes	characteristic
731	C₄	—	2	1	no	—
732	C₄	—	2	1	no	—
733	C₄	—	2	1	no	—
734	C₄	—	2	1	no	—
735	C₄	—	4	1	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	1	no	—
738	C₄	—	4	1	no	—
739	C₄	—	4	2	no	—
740	C₄	—	4	1	no	—
741	C₄	—	4	1	no	—
742	C₄	—	8	1	no	—
743	C₄	—	8	1	no	—
744	C₄	C₂×C₂₃×#135	1	1	yes	characteristic
745	C₄	C₂₃×#575	1	1	yes	characteristic
746	C₄	C₂₃×#576	1	1	yes	characteristic
747	C₄	C₂₃×#577	1	1	yes	characteristic
748	C₂	—	2	2	no	—
749	C₂	—	4	2	no	—
750	C₂	—	8	1	no	—
751	C₂	—	8	1	no	—
752	C₂	C₂₃×#3002	1	1	yes	characteristic
753	C₂	C₂₃×#3012	1	1	yes	characteristic
754	C₂	C₂×C₂₃×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₃
prime radical	C₂₃×#3520	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×#3160	C₂	semidirect
4. C₂₃×#3110	C₂	semidirect
5. C₂₃×#1654	C₂	semidirect
6. C₂₃×#1654	C₂	semidirect
7. C₂₃×#1652	C₂	semidirect
8. C₂₃×#1651	C₂	semidirect
9. C₂₃×#1650	C₂	semidirect
10. C₂₃×#1649	C₂	semidirect
11. C₂₃×#1647	C₂	semidirect
12. C₂₃×#1647	C₂	semidirect
13. C₂₃×#1552	C₂	semidirect
14. C₂₃×#1494	C₂	semidirect
15. C₂×C₂₃×D₄⋊C₈	C₂	semidirect
34. C₂₃×#500	C₂²	semidirect
35. C₂₃×#500	C₂²	semidirect
37. C₂₃×#498	C₂²	semidirect
38. C₂₃×#498	C₂²	semidirect
41. C₂₃×#475	C₂²	semidirect
44. C₂₃×#474	C₂²	semidirect
48. C₂₃×#462	C₂²	semidirect
51. C₂₃×#461	C₂²	semidirect
59. C₂₃×#332	C₂²	semidirect
60. C₂₃×#332	C₂²	semidirect
61. C₂₃×#332	C₂²	semidirect
62. C₂₃×#332	C₂²	semidirect
63. C₂₃×Q₈⋊C₈	C₂²	semidirect
64. C₂₃×Q₈⋊C₈	C₂²	semidirect
69. C₂₃×D₄⋊C₈	C₂²	semidirect
70. C₂₃×D₄⋊C₈	C₂²	semidirect
273. #18648	C₂₃	direct (N × H)
341. #3248	C₂×C₂₃	semidirect
342. #3160	C₂×C₂₃	semidirect
343. #3110	C₂×C₂₃	semidirect
344. #1654	C₂×C₂₃	semidirect
345. #1654	C₂×C₂₃	semidirect
346. #1652	C₂×C₂₃	semidirect
347. #1651	C₂×C₂₃	semidirect
348. #1650	C₂×C₂₃	semidirect
349. #1649	C₂×C₂₃	semidirect
350. #1647	C₂×C₂₃	semidirect
351. #1647	C₂×C₂₃	semidirect
352. #1552	C₂×C₂₃	semidirect
353. #1494	C₂×C₂₃	semidirect
354. C₂×D₄⋊C₈	C₂×C₂₃	semidirect
404. #500	C₂²×C₂₃	semidirect
405. #500	C₂²×C₂₃	semidirect
407. #498	C₂²×C₂₃	semidirect
408. #498	C₂²×C₂₃	semidirect
411. #475	C₂²×C₂₃	semidirect
414. #474	C₂²×C₂₃	semidirect
418. #462	C₂²×C₂₃	semidirect
421. #461	C₂²×C₂₃	semidirect
429. #332	C₂²×C₂₃	semidirect
430. #332	C₂²×C₂₃	semidirect
431. #332	C₂²×C₂₃	semidirect
432. #332	C₂²×C₂₃	semidirect
433. Q₈⋊C₈	C₂²×C₂₃	semidirect
434. Q₈⋊C₈	C₂²×C₂₃	semidirect
439. D₄⋊C₈	C₂²×C₂₃	semidirect
440. D₄⋊C₈	C₂²×C₂₃	semidirect
553. C₂₃	#18648	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×#3520	2
C₂₃×#3248	2
C₂₃×#3160	2
C₂₃×#3110	2
C₂₃×#1654	2
C₂₃×#1652	2
C₂₃×#1651	2
C₂₃×#1650	2
C₂₃×#1649	2
C₂₃×#1647	2
C₂₃×#1552	2
C₂₃×#1494	2
C₂×C₂₃×D₄⋊C₈	2
#18648	23

Subgroups — C23×#18648 #19166274

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#18648 #19166274