Subgroups — C₂₃×#18806 #19166432

Order 5888.

1180 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#41×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#3228	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3110	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1654	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1651	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1649	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1647	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×#1553	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1488	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1478	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₂₃	—	2	1	no	—
17	C₂₃×#550	C₂²	1	1	yes	characteristic
18	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
19	C₂₃×#548	—	2	1	no	—
20	C₂₃×#547	—	2	1	no	—
21	C₂₃×#547	C₂²	1	1	yes	characteristic
22	C₂₃×#546	—	2	2	no	—
23	C₂₃×#546	—	2	1	no	—
24	D₄²×C₂₃	—	2	1	no	—
25	D₄²×C₂₃	C₂²	1	1	yes	characteristic
26	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
27	C₂₃×#532	—	2	1	no	—
28	C₂₃×#532	C₂²	1	1	yes	characteristic
29	C₂₃×#525	—	2	2	no	—
30	C₂₃×#525	—	2	1	no	—
31	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₂₃	—	2	1	no	—
33	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
34	C₂₃×#500	C₂²	1	1	yes	characteristic, complemented
35	C₂₃×#498	C₂²	1	1	yes	characteristic, complemented
36	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
37	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
38	C₂₃×#485	—	2	1	no	—
39	C₂₃×#484	—	2	1	no	—
40	C₂₃×#482	—	2	2	no	—
41	C₂₃×#478	—	2	2	no	—
42	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
43	C₂₃×#474	C₂²	1	1	yes	characteristic
44	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
45	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
46	C₂₃×#462	C₂²	1	1	yes	characteristic, complemented
47	C₂₃×#461	C₂²	1	1	yes	characteristic
48	C₂₃×#461	C₂²	1	1	yes	characteristic, complemented
49	C₂₃×#461	C₂²	1	1	yes	characteristic, complemented
50	C₂₃×#452	—	2	1	no	—
51	C₂₃×#450	—	2	1	no	—
52	C₂₃×#440	—	2	1	no	—
53	C₂₃×#440	—	2	1	no	—
54	C₄×Q₁₆×C₂₃	—	2	1	no	—
55	C₄×SD₁₆×C₂₃	—	2	1	no	—
56	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
57	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
58	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
59	C₂₃×#332	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#332	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	2	no	—
72	C₂×#41×C₂₃	—	2	2	no	—
73	C₂×#41×C₂₃	—	2	1	no	—
74	C₂×#41×C₂₃	—	2	1	no	—
75	C₂×#41×C₂₃	—	2	1	no	—
76	C₂×#41×C₂₃	—	4	4	no	—
77	C₂×#41×C₂₃	—	4	4	no	—
78	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
79	C₂²×Q₈×C₂₃	—	2	1	no	—
80	C₂²×D₄×C₂₃	—	2	2	no	—
81	C₂²×D₄×C₂₃	—	2	1	no	—
82	C₂²×D₄×C₂₃	—	2	1	no	—
83	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
84	C₂³×C₄×C₂₃	—	2	2	no	—
85	C₂³×C₄×C₂₃	—	2	1	no	—
86	C₂×Q₁₆×C₂₃	—	2	1	no	—
87	C₂×SD₁₆×C₂₃	—	2	1	no	—
88	C₂×SD₁₆×C₂₃	—	2	1	no	—
89	C₂×SD₁₆×C₂₃	—	2	1	no	—
90	C₂₃×C₄⋊Q₈	—	2	1	no	—
91	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
92	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
93	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
94	C₂₃×#127	—	2	1	no	—
95	C₂₃×#127	C₂³	1	1	yes	characteristic
96	C₂₃×#125	—	2	1	no	—
97	C₂₃×#124	—	2	2	no	—
98	C₂₃×#124	—	2	1	no	—
99	C₂₃×#123	—	2	2	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	1	no	—
104	C₂₃×C₂²⋊Q₈	—	2	1	no	—
105	C₂₃×C₂²⋊Q₈	—	2	2	no	—
106	C₂₃×C₂²⋊Q₈	—	2	1	no	—
107	C₂₃×C₂²⋊Q₈	—	2	1	no	—
108	C₂₃×#121	—	2	2	no	—
109	C₂₃×#121	—	2	2	no	—
110	C₂₃×#121	—	2	1	no	—
111	C₂₃×#121	—	2	2	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	D₄	1	2	yes	—
117	C₂₃×#120	—	2	2	no	—
118	C₂₃×#120	—	2	2	no	—
119	C₂₃×#120	—	2	2	no	—
120	C₄×Q₈×C₂₃	—	2	1	no	—
121	C₄×Q₈×C₂₃	—	2	1	no	—
122	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
123	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
124	C₄×D₄×C₂₃	—	2	2	no	—
125	C₄×D₄×C₂₃	—	2	2	no	—
126	C₄×D₄×C₂₃	—	2	2	no	—
127	C₄×D₄×C₂₃	—	2	1	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	D₄	1	1	yes	characteristic
135	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
136	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
137	C₄×D₄×C₂₃	D₄	1	2	yes	—
138	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
139	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
140	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
141	C₂₃×#117	—	2	1	no	—
142	C₂₃×#117	—	2	1	no	—
143	C₂₃×#117	D₄	1	1	yes	characteristic
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	1	no	—
148	C₂×C₄²×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×#107	—	2	2	no	—
154	C₂₃×#106	—	2	1	no	—
155	C₂₃×#106	—	2	2	no	—
156	C₂₃×C₄⋊C₈	—	2	1	no	—
157	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
158	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
159	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
160	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
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	1	no	—
167	C₂₃×#102	—	2	1	no	—
168	C₂₃×#102	—	2	1	no	—
169	C₂₃×#102	—	2	2	no	—
170	C₂₃×#102	—	2	2	no	—
171	C₂₃×C₂²⋊C₈	—	2	1	no	—
172	C₂₃×C₂²⋊C₈	—	2	1	no	—
173	C₂₃×C₂²⋊C₈	—	2	1	no	—
174	C₂₃×#97	—	2	1	no	—
175	C₄×C₈×C₂₃	—	2	1	no	—
176	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
177	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
178	C₂⁴×C₂₃	—	2	2	no	—
179	C₂⁴×C₂₃	—	2	1	no	—
180	#41×C₂₃	—	2	2	no	—
181	#41×C₂₃	—	2	2	no	—
182	#41×C₂₃	—	4	8	no	—
183	#41×C₂₃	—	4	2	no	—
184	#41×C₂₃	—	4	2	no	—
185	#41×C₂₃	—	4	8	no	—
186	#41×C₂₃	—	4	2	no	—
187	#41×C₂₃	—	4	2	no	—
188	#41×C₂₃	—	4	2	no	—
189	#41×C₂₃	—	4	2	no	—
190	C₂×Q₈×C₂₃	—	2	2	no	—
191	C₂×Q₈×C₂₃	—	2	1	no	—
192	C₂×Q₈×C₂₃	—	2	1	no	—
193	C₂×Q₈×C₂₃	—	2	1	no	—
194	C₂×Q₈×C₂₃	—	4	2	no	—
195	C₂×Q₈×C₂₃	—	4	2	no	—
196	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
197	C₂×D₄×C₂₃	—	2	1	no	—
198	C₂×D₄×C₂₃	—	2	2	no	—
199	C₂×D₄×C₂₃	—	2	2	no	—
200	C₂×D₄×C₂₃	—	2	2	no	—
201	C₂×D₄×C₂₃	—	2	2	no	—
202	C₂×D₄×C₂₃	—	2	2	no	—
203	C₂×D₄×C₂₃	—	2	2	no	—
204	C₂×D₄×C₂₃	—	2	2	no	—
205	C₂×D₄×C₂₃	—	2	1	no	—
206	C₂×D₄×C₂₃	—	2	1	no	—
207	C₂×D₄×C₂₃	—	2	1	no	—
208	C₂×D₄×C₂₃	—	4	1	no	—
209	C₂×D₄×C₂₃	—	4	2	no	—
210	C₂×D₄×C₂₃	—	4	8	no	—
211	C₂×D₄×C₂₃	—	4	2	no	—
212	C₂×D₄×C₂₃	—	4	2	no	—
213	C₂×D₄×C₂₃	—	4	2	no	—
214	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
215	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
216	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
217	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
218	C₂²×C₄×C₂₃	—	2	1	no	—
219	C₂²×C₄×C₂₃	—	2	2	no	—
220	C₂²×C₄×C₂₃	—	2	2	no	—
221	C₂²×C₄×C₂₃	—	2	2	no	—
222	C₂²×C₄×C₂₃	—	2	1	no	—
223	C₂²×C₄×C₂₃	—	2	1	no	—
224	C₂²×C₄×C₂₃	—	2	2	no	—
225	C₂²×C₄×C₂₃	—	2	1	no	—
226	C₂²×C₄×C₂₃	—	2	1	no	—
227	C₂²×C₄×C₂₃	—	2	1	no	—
228	C₂²×C₄×C₂₃	—	2	1	no	—
229	C₂²×C₄×C₂₃	—	2	1	no	—
230	C₂²×C₄×C₂₃	—	4	8	no	—
231	C₂²×C₄×C₂₃	—	4	2	no	—
232	C₂²×C₄×C₂₃	—	4	2	no	—
233	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
236	Q₁₆×C₂₃	—	4	2	no	—
237	SD₁₆×C₂₃	—	4	2	no	—
238	SD₁₆×C₂₃	—	4	2	no	—
239	SD₁₆×C₂₃	—	4	2	no	—
240	C₂×C₈×C₂₃	—	2	1	no	—
241	C₂×C₈×C₂₃	—	2	1	no	—
242	C₂×C₈×C₂₃	—	2	1	no	—
243	C₂×C₈×C₂₃	—	2	1	no	—
244	C₂×C₈×C₂₃	—	2	1	no	—
245	C₂×C₈×C₂₃	—	2	1	no	—
246	C₄⋊C₄×C₂₃	—	2	2	no	—
247	C₄⋊C₄×C₂₃	—	2	2	no	—
248	C₄⋊C₄×C₂₃	—	2	1	no	—
249	C₄⋊C₄×C₂₃	—	2	1	no	—
250	C₄⋊C₄×C₂₃	—	2	1	no	—
251	C₄⋊C₄×C₂₃	—	2	1	no	—
252	C₄⋊C₄×C₂₃	—	2	1	no	—
253	C₄⋊C₄×C₂₃	—	2	1	no	—
254	C₄⋊C₄×C₂₃	—	2	1	no	—
255	C₄⋊C₄×C₂₃	—	2	1	no	—
256	C₄⋊C₄×C₂₃	—	4	1	no	—
257	C₄⋊C₄×C₂₃	—	4	1	no	—
258	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
259	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
260	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
261	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
262	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
263	C₂²⋊C₄×C₂₃	—	2	2	no	—
264	C₂²⋊C₄×C₂₃	—	2	2	no	—
265	C₂²⋊C₄×C₂₃	—	2	2	no	—
266	C₂²⋊C₄×C₂₃	—	2	2	no	—
267	C₂²⋊C₄×C₂₃	—	2	1	no	—
268	C₂²⋊C₄×C₂₃	—	2	1	no	—
269	C₂²⋊C₄×C₂₃	—	2	2	no	—
270	C₂²⋊C₄×C₂₃	—	2	1	no	—
271	C₂²⋊C₄×C₂₃	—	2	1	no	—
272	C₂²⋊C₄×C₂₃	—	2	2	no	—
273	C₂²⋊C₄×C₂₃	—	2	1	no	—
274	C₂²⋊C₄×C₂₃	—	2	1	no	—
275	C₂²⋊C₄×C₂₃	—	2	1	no	—
276	C₂²⋊C₄×C₂₃	—	4	1	no	—
277	C₄²×C₂₃	—	2	1	no	—
278	C₄²×C₂₃	—	2	1	no	—
279	C₄²×C₂₃	—	2	1	no	—
280	C₄²×C₂₃	—	4	1	no	—
281	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
282	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
284	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
285	#18806	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
286	C₂³×C₂₃	—	2	1	no	—
287	C₂³×C₂₃	—	2	1	no	—
288	C₂³×C₂₃	—	2	1	no	—
289	C₂³×C₂₃	—	2	2	no	—
290	C₂³×C₂₃	—	4	2	no	—
291	C₂³×C₂₃	—	4	2	no	—
292	C₂³×C₂₃	—	4	4	no	—
293	C₂³×C₂₃	—	4	4	no	—
294	C₂³×C₂₃	—	8	1	no	—
295	C₂³×C₂₃	—	8	2	no	—
296	C₂³×C₂₃	#120	1	1	yes	characteristic
297	Q₈×C₂₃	—	2	1	no	—
298	Q₈×C₂₃	—	4	4	no	—
299	Q₈×C₂₃	—	4	1	no	—
300	Q₈×C₂₃	—	4	1	no	—
301	Q₈×C₂₃	—	4	1	no	—
302	Q₈×C₂₃	—	4	1	no	—
303	Q₈×C₂₃	—	4	1	no	—
304	Q₈×C₂₃	—	4	1	no	—
305	Q₈×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
306	D₄×C₂₃	—	2	4	no	—
307	D₄×C₂₃	—	2	1	no	—
308	D₄×C₂₃	—	2	1	no	—
309	D₄×C₂₃	—	2	1	no	—
310	D₄×C₂₃	—	2	1	no	—
311	D₄×C₂₃	—	4	2	no	—
312	D₄×C₂₃	—	4	2	no	—
313	D₄×C₂₃	—	4	4	no	—
314	D₄×C₂₃	—	4	4	no	—
315	D₄×C₂₃	—	4	4	no	—
316	D₄×C₂₃	—	4	4	no	—
317	D₄×C₂₃	—	4	4	no	—
318	D₄×C₂₃	—	4	1	no	—
319	D₄×C₂₃	—	4	1	no	—
320	D₄×C₂₃	—	4	1	no	—
321	D₄×C₂₃	—	4	1	no	—
322	D₄×C₂₃	—	8	2	no	—
323	D₄×C₂₃	#135	1	2	yes	—
324	D₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
325	C₂×C₄×C₂₃	—	2	4	no	—
326	C₂×C₄×C₂₃	—	2	1	no	—
327	C₂×C₄×C₂₃	—	2	1	no	—
328	C₂×C₄×C₂₃	—	2	1	no	—
329	C₂×C₄×C₂₃	—	2	1	no	—
330	C₂×C₄×C₂₃	—	2	1	no	—
331	C₂×C₄×C₂₃	—	2	1	no	—
332	C₂×C₄×C₂₃	—	2	1	no	—
333	C₂×C₄×C₂₃	—	2	1	no	—
334	C₂×C₄×C₂₃	—	2	2	no	—
335	C₂×C₄×C₂₃	—	2	1	no	—
336	C₂×C₄×C₂₃	—	4	1	no	—
337	C₂×C₄×C₂₃	—	4	2	no	—
338	C₂×C₄×C₂₃	—	4	4	no	—
339	C₂×C₄×C₂₃	—	4	4	no	—
340	C₂×C₄×C₂₃	—	4	2	no	—
341	C₂×C₄×C₂₃	—	4	4	no	—
342	C₂×C₄×C₂₃	—	4	2	no	—
343	C₂×C₄×C₂₃	—	4	4	no	—
344	C₂×C₄×C₂₃	—	4	1	no	—
345	C₂×C₄×C₂₃	—	4	1	no	—
346	C₂×C₄×C₂₃	—	4	1	no	—
347	C₂×C₄×C₂₃	—	4	1	no	—
348	C₂×C₄×C₂₃	—	4	1	no	—
349	C₂×C₄×C₂₃	—	4	1	no	—
350	C₂×C₄×C₂₃	—	4	1	no	—
351	C₂×C₄×C₂₃	—	4	1	no	—
352	C₂×C₄×C₂₃	—	8	1	no	—
353	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
354	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
355	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
356	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
359	C₈×C₂₃	—	4	1	no	—
360	C₈×C₂₃	—	4	1	no	—
361	C₈×C₂₃	—	4	1	no	—
362	C₈×C₂₃	—	4	1	no	—
363	C₈×C₂₃	—	4	1	no	—
364	C₈×C₂₃	—	4	1	no	—
365	D₄×#41	C₂×C₂₃	1	1	yes	characteristic
366	#3228	C₂×C₂₃	1	1	yes	characteristic, complemented
367	#3110	C₂×C₂₃	1	1	yes	characteristic, complemented
368	#3107	C₂×C₂₃	1	1	yes	characteristic, complemented
369	#1654	C₂×C₂₃	1	1	yes	characteristic, complemented
370	#1651	C₂×C₂₃	1	1	yes	characteristic, complemented
371	#1649	C₂×C₂₃	1	1	yes	characteristic, complemented
372	#1647	C₂×C₂₃	1	1	yes	characteristic, complemented
373	#1642	C₂×C₂₃	1	1	yes	characteristic, complemented
374	#1641	C₂×C₂₃	1	1	yes	characteristic, complemented
375	#1639	C₂×C₂₃	1	1	yes	characteristic, complemented
376	#1639	C₂×C₂₃	1	1	yes	characteristic, complemented
377	#1553	C₂×C₂₃	1	1	yes	characteristic, complemented
378	#1488	C₂×C₂₃	1	1	yes	characteristic, complemented
379	#1478	C₂×C₂₃	1	1	yes	characteristic, complemented
380	C₂²×C₂₃	—	2	1	no	—
381	C₂²×C₂₃	—	2	2	no	—
382	C₂²×C₂₃	—	2	1	no	—
383	C₂²×C₂₃	—	2	2	no	—
384	C₂²×C₂₃	—	2	1	no	—
385	C₂²×C₂₃	—	4	1	no	—
386	C₂²×C₂₃	—	4	1	no	—
387	C₂²×C₂₃	—	4	1	no	—
388	C₂²×C₂₃	—	4	1	no	—
389	C₂²×C₂₃	—	4	1	no	—
390	C₂²×C₂₃	—	4	2	no	—
391	C₂²×C₂₃	—	4	2	no	—
392	C₂²×C₂₃	—	4	1	no	—
393	C₂²×C₂₃	—	4	2	no	—
394	C₂²×C₂₃	—	4	1	no	—
395	C₂²×C₂₃	—	8	4	no	—
396	C₂²×C₂₃	—	8	8	no	—
397	C₂²×C₂₃	C₂×#120	1	1	yes	characteristic
398	C₄×C₂₃	—	2	1	no	—
399	C₄×C₂₃	—	2	1	no	—
400	C₄×C₂₃	—	2	2	no	—
401	C₄×C₂₃	—	2	1	no	—
402	C₄×C₂₃	—	2	1	no	—
403	C₄×C₂₃	—	4	1	no	—
404	C₄×C₂₃	—	4	1	no	—
405	C₄×C₂₃	—	4	2	no	—
406	C₄×C₂₃	—	4	1	no	—
407	C₄×C₂₃	—	4	1	no	—
408	C₄×C₂₃	—	8	1	no	—
409	C₄×C₂₃	—	8	1	no	—
410	C₄×C₂₃	C₂×#135	1	1	yes	characteristic
411	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
412	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
413	C₄×C₂₃	#575	1	1	yes	characteristic
414	C₂²×#41	—	2	1	no	—
415	#550	C₂²×C₂₃	1	1	yes	characteristic
416	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
417	#548	—	2	1	no	—
418	#547	—	2	1	no	—
419	#547	C₂²×C₂₃	1	1	yes	characteristic
420	#546	—	2	2	no	—
421	#546	—	2	1	no	—
422	D₄²	—	2	1	no	—
423	D₄²	C₂²×C₂₃	1	1	yes	characteristic
424	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
425	#532	—	2	1	no	—
426	#532	C₂²×C₂₃	1	1	yes	characteristic
427	#525	—	2	2	no	—
428	#525	—	2	1	no	—
429	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
430	C₂×C₄×D₄	—	2	1	no	—
431	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
432	#500	C₂²×C₂₃	1	1	yes	characteristic, complemented
433	#498	C₂²×C₂₃	1	1	yes	characteristic, complemented
434	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
435	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
436	#485	—	2	1	no	—
437	#484	—	2	1	no	—
438	#482	—	2	2	no	—
439	#478	—	2	2	no	—
440	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
441	#474	C₂²×C₂₃	1	1	yes	characteristic
442	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
443	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
444	#462	C₂²×C₂₃	1	1	yes	characteristic, complemented
445	#461	C₂²×C₂₃	1	1	yes	characteristic
446	#461	C₂²×C₂₃	1	1	yes	characteristic, complemented
447	#461	C₂²×C₂₃	1	1	yes	characteristic, complemented
448	#452	—	2	1	no	—
449	#450	—	2	1	no	—
450	#440	—	2	1	no	—
451	#440	—	2	1	no	—
452	C₄×Q₁₆	—	2	1	no	—
453	C₄×SD₁₆	—	2	1	no	—
454	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
455	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
456	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
457	#332	C₂²×C₂₃	1	1	yes	characteristic, complemented
458	#332	C₂²×C₂₃	1	1	yes	characteristic, complemented
459	#331	C₂²×C₂₃	1	1	yes	characteristic, complemented
460	#331	C₂²×C₂₃	1	1	yes	characteristic, complemented
461	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
462	Q₈⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
463	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
464	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
465	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
466	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
467	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
468	D₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
469	C₂×C₂₃	—	4	1	no	—
470	C₂×C₂₃	—	4	2	no	—
471	C₂×C₂₃	—	4	2	no	—
472	C₂×C₂₃	—	8	1	no	—
473	C₂×C₂₃	—	8	2	no	—
474	C₂×C₂₃	#3002	1	1	yes	characteristic
475	C₂×C₂₃	#3003	1	1	yes	characteristic
476	C₂×C₂₃	#3022	1	1	yes	characteristic
477	C₂×#41	—	2	2	no	—
478	C₂×#41	—	2	2	no	—
479	C₂×#41	—	2	1	no	—
480	C₂×#41	—	2	1	no	—
481	C₂×#41	—	2	1	no	—
482	C₂×#41	—	4	4	no	—
483	C₂×#41	—	4	4	no	—
484	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
485	C₂²×Q₈	—	2	1	no	—
486	C₂²×D₄	—	2	2	no	—
487	C₂²×D₄	—	2	1	no	—
488	C₂²×D₄	—	2	1	no	—
489	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
490	C₂³×C₄	—	2	2	no	—
491	C₂³×C₄	—	2	1	no	—
492	C₂×Q₁₆	—	2	1	no	—
493	C₂×SD₁₆	—	2	1	no	—
494	C₂×SD₁₆	—	2	1	no	—
495	C₂×SD₁₆	—	2	1	no	—
496	C₄⋊Q₈	—	2	1	no	—
497	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
498	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
499	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
500	#127	—	2	1	no	—
501	#127	C₂³×C₂₃	1	1	yes	characteristic
502	#125	—	2	1	no	—
503	#124	—	2	2	no	—
504	#124	—	2	1	no	—
505	#123	—	2	2	no	—
506	#123	—	2	2	no	—
507	#123	—	2	2	no	—
508	C₂²⋊Q₈	—	2	2	no	—
509	C₂²⋊Q₈	—	2	1	no	—
510	C₂²⋊Q₈	—	2	2	no	—
511	C₂²⋊Q₈	—	2	1	no	—
512	C₂²⋊Q₈	—	2	1	no	—
513	C₂²⋊Q₈	—	2	1	no	—
514	#121	—	2	2	no	—
515	#121	—	2	2	no	—
516	#121	—	2	2	no	—
517	#121	—	2	1	no	—
518	#121	—	2	1	no	—
519	#121	—	2	1	no	—
520	#121	—	2	1	no	—
521	#121	—	2	1	no	—
522	#121	D₄×C₂₃	1	2	yes	—
523	#120	—	2	2	no	—
524	#120	—	2	2	no	—
525	#120	—	2	2	no	—
526	C₄×Q₈	—	2	1	no	—
527	C₄×Q₈	—	2	1	no	—
528	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
529	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
530	C₄×D₄	—	2	2	no	—
531	C₄×D₄	—	2	2	no	—
532	C₄×D₄	—	2	2	no	—
533	C₄×D₄	—	2	1	no	—
534	C₄×D₄	—	2	1	no	—
535	C₄×D₄	—	2	1	no	—
536	C₄×D₄	—	2	1	no	—
537	C₄×D₄	—	2	1	no	—
538	C₄×D₄	—	2	1	no	—
539	C₄×D₄	—	2	1	no	—
540	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
541	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
542	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
543	C₄×D₄	D₄×C₂₃	1	2	yes	—
544	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
545	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
546	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
547	#117	—	2	1	no	—
548	#117	—	2	1	no	—
549	#117	D₄×C₂₃	1	1	yes	characteristic
550	C₂×C₄⋊C₄	—	2	1	no	—
551	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
552	C₂×C₂²⋊C₄	—	2	2	no	—
553	C₂×C₂²⋊C₄	—	2	1	no	—
554	C₂×C₄²	—	2	1	no	—
555	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
556	#107	—	2	1	no	—
557	#107	—	2	1	no	—
558	#107	—	2	1	no	—
559	#107	—	2	2	no	—
560	#106	—	2	1	no	—
561	#106	—	2	2	no	—
562	C₄⋊C₈	—	2	1	no	—
563	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
564	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
565	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
566	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
567	#103	—	2	1	no	—
568	#103	—	2	1	no	—
569	#103	—	2	1	no	—
570	#103	—	2	1	no	—
571	#103	—	2	1	no	—
572	#102	—	2	1	no	—
573	#102	—	2	1	no	—
574	#102	—	2	1	no	—
575	#102	—	2	2	no	—
576	#102	—	2	2	no	—
577	C₂²⋊C₈	—	2	1	no	—
578	C₂²⋊C₈	—	2	1	no	—
579	C₂²⋊C₈	—	2	1	no	—
580	#97	—	2	1	no	—
581	C₄×C₈	—	2	1	no	—
582	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
583	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
584	C₂₃	#18806	1	1	yes	characteristic, direct product factor, Sylow
585	C₂⁴	—	2	2	no	—
586	C₂⁴	—	2	1	no	—
587	#41	—	2	2	no	—
588	#41	—	2	2	no	—
589	#41	—	4	8	no	—
590	#41	—	4	2	no	—
591	#41	—	4	2	no	—
592	#41	—	4	8	no	—
593	#41	—	4	2	no	—
594	#41	—	4	2	no	—
595	#41	—	4	2	no	—
596	#41	—	4	2	no	—
597	C₂×Q₈	—	2	2	no	—
598	C₂×Q₈	—	2	1	no	—
599	C₂×Q₈	—	2	1	no	—
600	C₂×Q₈	—	2	1	no	—
601	C₂×Q₈	—	4	2	no	—
602	C₂×Q₈	—	4	2	no	—
603	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
604	C₂×D₄	—	2	1	no	—
605	C₂×D₄	—	2	2	no	—
606	C₂×D₄	—	2	2	no	—
607	C₂×D₄	—	2	2	no	—
608	C₂×D₄	—	2	2	no	—
609	C₂×D₄	—	2	2	no	—
610	C₂×D₄	—	2	2	no	—
611	C₂×D₄	—	2	2	no	—
612	C₂×D₄	—	2	1	no	—
613	C₂×D₄	—	2	1	no	—
614	C₂×D₄	—	2	1	no	—
615	C₂×D₄	—	4	1	no	—
616	C₂×D₄	—	4	8	no	—
617	C₂×D₄	—	4	2	no	—
618	C₂×D₄	—	4	2	no	—
619	C₂×D₄	—	4	2	no	—
620	C₂×D₄	—	4	2	no	—
621	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
622	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
623	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
624	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	2	2	no	—
627	C₂²×C₄	—	2	2	no	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	2	1	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	4	8	no	—
638	C₂²×C₄	—	4	2	no	—
639	C₂²×C₄	—	4	2	no	—
640	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
641	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
642	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
643	Q₁₆	—	4	2	no	—
644	SD₁₆	—	4	2	no	—
645	SD₁₆	—	4	2	no	—
646	SD₁₆	—	4	2	no	—
647	C₂×C₈	—	2	1	no	—
648	C₂×C₈	—	2	1	no	—
649	C₂×C₈	—	2	1	no	—
650	C₂×C₈	—	2	1	no	—
651	C₂×C₈	—	2	1	no	—
652	C₂×C₈	—	2	1	no	—
653	C₄⋊C₄	—	2	2	no	—
654	C₄⋊C₄	—	2	2	no	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	—	2	1	no	—
659	C₄⋊C₄	—	2	1	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	—	4	1	no	—
664	C₄⋊C₄	—	4	1	no	—
665	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
666	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
667	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
668	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
669	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
670	C₂²⋊C₄	—	2	2	no	—
671	C₂²⋊C₄	—	2	2	no	—
672	C₂²⋊C₄	—	2	2	no	—
673	C₂²⋊C₄	—	2	2	no	—
674	C₂²⋊C₄	—	2	1	no	—
675	C₂²⋊C₄	—	2	1	no	—
676	C₂²⋊C₄	—	2	2	no	—
677	C₂²⋊C₄	—	2	1	no	—
678	C₂²⋊C₄	—	2	1	no	—
679	C₂²⋊C₄	—	2	2	no	—
680	C₂²⋊C₄	—	2	1	no	—
681	C₂²⋊C₄	—	2	1	no	—
682	C₂²⋊C₄	—	2	1	no	—
683	C₂²⋊C₄	—	4	1	no	—
684	C₄²	—	2	1	no	—
685	C₄²	—	2	1	no	—
686	C₄²	—	2	1	no	—
687	C₄²	—	4	1	no	—
688	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
689	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
690	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
691	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
692	C₂³	—	2	1	no	—
693	C₂³	—	2	1	no	—
694	C₂³	—	2	1	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	4	2	no	—
697	C₂³	—	4	2	no	—
698	C₂³	—	4	4	no	—
699	C₂³	—	4	4	no	—
700	C₂³	—	8	1	no	—
701	C₂³	—	8	2	no	—
702	C₂³	C₂₃×#120	1	1	yes	characteristic
703	Q₈	—	2	1	no	—
704	Q₈	—	4	4	no	—
705	Q₈	—	4	1	no	—
706	Q₈	—	4	1	no	—
707	Q₈	—	4	1	no	—
708	Q₈	—	4	1	no	—
709	Q₈	—	4	1	no	—
710	Q₈	—	4	1	no	—
711	Q₈	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
712	D₄	—	2	4	no	—
713	D₄	—	2	1	no	—
714	D₄	—	2	1	no	—
715	D₄	—	2	1	no	—
716	D₄	—	2	1	no	—
717	D₄	—	4	2	no	—
718	D₄	—	4	2	no	—
719	D₄	—	4	4	no	—
720	D₄	—	4	4	no	—
721	D₄	—	4	4	no	—
722	D₄	—	4	4	no	—
723	D₄	—	4	4	no	—
724	D₄	—	4	1	no	—
725	D₄	—	4	1	no	—
726	D₄	—	4	1	no	—
727	D₄	—	4	1	no	—
728	D₄	—	8	2	no	—
729	D₄	C₂₃×#135	1	2	yes	—
730	D₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
731	C₂×C₄	—	2	4	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	4	1	no	—
743	C₂×C₄	—	4	2	no	—
744	C₂×C₄	—	4	4	no	—
745	C₂×C₄	—	4	4	no	—
746	C₂×C₄	—	4	2	no	—
747	C₂×C₄	—	4	4	no	—
748	C₂×C₄	—	4	2	no	—
749	C₂×C₄	—	4	4	no	—
750	C₂×C₄	—	4	1	no	—
751	C₂×C₄	—	4	1	no	—
752	C₂×C₄	—	4	1	no	—
753	C₂×C₄	—	4	1	no	—
754	C₂×C₄	—	4	1	no	—
755	C₂×C₄	—	4	1	no	—
756	C₂×C₄	—	4	1	no	—
757	C₂×C₄	—	4	1	no	—
758	C₂×C₄	—	8	1	no	—
759	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
760	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
761	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
762	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
763	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
764	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
765	C₈	—	4	1	no	—
766	C₈	—	4	1	no	—
767	C₈	—	4	1	no	—
768	C₈	—	4	1	no	—
769	C₈	—	4	1	no	—
770	C₈	—	4	1	no	—
771	C₂²	—	2	1	no	—
772	C₂²	—	2	2	no	—
773	C₂²	—	2	1	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	2	1	no	—
776	C₂²	—	4	1	no	—
777	C₂²	—	4	1	no	—
778	C₂²	—	4	1	no	—
779	C₂²	—	4	1	no	—
780	C₂²	—	4	1	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	4	1	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	4	1	no	—
786	C₂²	—	8	4	no	—
787	C₂²	—	8	8	no	—
788	C₂²	C₂×C₂₃×#120	1	1	yes	characteristic
789	C₄	—	2	1	no	—
790	C₄	—	2	1	no	—
791	C₄	—	2	2	no	—
792	C₄	—	2	1	no	—
793	C₄	—	2	1	no	—
794	C₄	—	4	1	no	—
795	C₄	—	4	1	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	1	no	—
798	C₄	—	4	1	no	—
799	C₄	—	8	1	no	—
800	C₄	—	8	1	no	—
801	C₄	C₂×C₂₃×#135	1	1	yes	characteristic
802	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
803	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
804	C₄	C₂₃×#575	1	1	yes	characteristic
805	C₂	—	4	1	no	—
806	C₂	—	4	2	no	—
807	C₂	—	4	2	no	—
808	C₂	—	8	1	no	—
809	C₂	—	8	2	no	—
810	C₂	C₂₃×#3002	1	1	yes	characteristic
811	C₂	C₂₃×#3003	1	1	yes	characteristic
812	C₂	C₂₃×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₃
prime radical	D₄×#41×C₂₃	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×#3228	C₂	semidirect
3. C₂₃×#3110	C₂	semidirect
4. C₂₃×#3107	C₂	semidirect
5. C₂₃×#1654	C₂	semidirect
6. C₂₃×#1651	C₂	semidirect
7. C₂₃×#1649	C₂	semidirect
8. C₂₃×#1647	C₂	semidirect
9. C₂₃×#1642	C₂	semidirect
10. C₂₃×#1641	C₂	semidirect
11. C₂₃×#1639	C₂	semidirect
12. C₂₃×#1639	C₂	semidirect
13. C₂₃×#1553	C₂	semidirect
14. C₂₃×#1488	C₂	semidirect
15. C₂₃×#1478	C₂	semidirect
26. C₂₃×#533	C₂²	semidirect
34. C₂₃×#500	C₂²	semidirect
35. C₂₃×#498	C₂²	semidirect
36. C₂₃×#486	C₂²	semidirect
37. C₂₃×#486	C₂²	semidirect
42. C₂₃×#475	C₂²	semidirect
44. C₂₃×#474	C₂²	semidirect
45. C₂₃×#474	C₂²	semidirect
46. C₂₃×#462	C₂²	semidirect
48. C₂₃×#461	C₂²	semidirect
49. C₂₃×#461	C₂²	semidirect
56. C₂₃×#432	C₂²	semidirect
57. C₂₃×#431	C₂²	semidirect
58. C₂₃×#431	C₂²	semidirect
59. C₂₃×#332	C₂²	semidirect
60. C₂₃×#332	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
285. #18806	C₂₃	direct (N × H)
366. #3228	C₂×C₂₃	semidirect
367. #3110	C₂×C₂₃	semidirect
368. #3107	C₂×C₂₃	semidirect
369. #1654	C₂×C₂₃	semidirect
370. #1651	C₂×C₂₃	semidirect
371. #1649	C₂×C₂₃	semidirect
372. #1647	C₂×C₂₃	semidirect
373. #1642	C₂×C₂₃	semidirect
374. #1641	C₂×C₂₃	semidirect
375. #1639	C₂×C₂₃	semidirect
376. #1639	C₂×C₂₃	semidirect
377. #1553	C₂×C₂₃	semidirect
378. #1488	C₂×C₂₃	semidirect
379. #1478	C₂×C₂₃	semidirect
424. #533	C₂²×C₂₃	semidirect
432. #500	C₂²×C₂₃	semidirect
433. #498	C₂²×C₂₃	semidirect
434. #486	C₂²×C₂₃	semidirect
435. #486	C₂²×C₂₃	semidirect
440. #475	C₂²×C₂₃	semidirect
442. #474	C₂²×C₂₃	semidirect
443. #474	C₂²×C₂₃	semidirect
444. #462	C₂²×C₂₃	semidirect
446. #461	C₂²×C₂₃	semidirect
447. #461	C₂²×C₂₃	semidirect
454. #432	C₂²×C₂₃	semidirect
455. #431	C₂²×C₂₃	semidirect
456. #431	C₂²×C₂₃	semidirect
457. #332	C₂²×C₂₃	semidirect
458. #332	C₂²×C₂₃	semidirect
459. #331	C₂²×C₂₃	semidirect
460. #331	C₂²×C₂₃	semidirect
461. Q₈⋊C₈	C₂²×C₂₃	semidirect
462. Q₈⋊C₈	C₂²×C₂₃	semidirect
465. D₄⋊C₈	C₂²×C₂₃	semidirect
466. D₄⋊C₈	C₂²×C₂₃	semidirect
467. D₄⋊C₈	C₂²×C₂₃	semidirect
468. D₄⋊C₈	C₂²×C₂₃	semidirect
584. C₂₃	#18806	direct (N × H)

Maximal subgroups

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

subgroup	index
D₄×#41×C₂₃	2
C₂₃×#3228	2
C₂₃×#3110	2
C₂₃×#3107	2
C₂₃×#1654	2
C₂₃×#1651	2
C₂₃×#1649	2
C₂₃×#1647	2
C₂₃×#1642	2
C₂₃×#1641	2
C₂₃×#1639	2
C₂₃×#1553	2
C₂₃×#1488	2
C₂₃×#1478	2
#18806	23

Subgroups — C23×#18806 #19166432

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#18806 #19166432