Subgroups — C₂₃×#61485 #19209111

Order 5888.

1862 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3522	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3396	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×Q₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3375	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3338	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#3334	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3333	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3308	C₂	1	4	yes	maximal, complemented
9	C₂₃×#3287	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3285	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3175	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3124	C₂	1	4	yes	maximal, complemented
14	C₂₃×#3112	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2951	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×Q₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₂₃×#135	C₂²	1	2	yes	—
19	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
20	C₂₃×#559	—	2	2	no	—
21	C₂₃×#559	C₂²	1	2	yes	—
22	Q₈²×C₂₃	C₂²	1	2	yes	—
23	C₂₃×#554	—	2	2	no	—
24	C₂₃×#554	C₂²	1	2	yes	—
25	C₂₃×#550	C₂²	1	2	yes	—
26	C₂₃×#548	C₂²	1	4	yes	—
27	C₂₃×#547	—	2	4	no	—
28	C₂₃×#547	C₂²	1	4	yes	—
29	C₂₃×#542	—	2	4	no	—
30	C₂₃×#542	C₂²	1	4	yes	—
31	C₂₃×#532	—	2	2	no	—
32	C₂₃×#532	C₂²	1	2	yes	—
33	C₂₃×#529	—	2	2	no	—
34	C₂₃×#529	C₂²	1	1	yes	characteristic
35	C₂₃×#520	C₂²	1	4	yes	—
36	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
37	C₂₃×#500	C₂²	1	1	yes	characteristic
38	C₂₃×#500	C₂²	1	2	yes	—
39	C₂₃×#495	C₂²	1	2	yes	—
40	C₂₃×#493	C₂²	1	1	yes	characteristic
41	C₂₃×#489	C₂²	1	4	yes	—
42	C₂₃×#486	C₂²	1	2	yes	—
43	C₂₃×#484	C₂²	1	4	yes	—
44	C₂₃×#480	C₂²	1	4	yes	—
45	C₂₃×#480	C₂²	1	4	yes	—
46	C₂₃×#477	C₂²	1	4	yes	—
47	C₂₃×#477	C₂²	1	2	yes	—
48	C₂₃×#477	C₂²	1	2	yes	—
49	C₂₃×#474	C₂²	1	4	yes	—
50	C₂₃×#468	C₂²	1	4	yes	—
51	C₂₃×#467	C₂²	1	2	yes	—
52	C₂₃×#466	C₂²	1	2	yes	—
53	C₂₃×#466	C₂²	1	2	yes	—
54	C₂₃×#466	C₂²	1	2	yes	—
55	C₂₃×#464	C₂²	1	4	yes	—
56	C₂₃×#463	C₂²	1	4	yes	—
57	C₂₃×#460	C₂²	1	2	yes	—
58	C₂₃×#460	C₂²	1	2	yes	—
59	C₂₃×#452	C₂²	1	4	yes	—
60	C₂₃×#449	C₂²	1	4	yes	—
61	C₂₃×#448	C₂²	1	4	yes	—
62	C₂₃×#446	C₂²	1	1	yes	characteristic
63	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic
64	C₂₃×#440	C₂²	1	4	yes	—
65	C₂₃×#440	C₂²	1	4	yes	—
66	C₂₃×#440	C₂²	1	4	yes	—
67	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
68	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
69	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
70	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
71	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
72	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
73	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
74	C₄×D₈×C₂₃	C₂²	1	2	yes	—
75	C₄×D₈×C₂₃	C₂²	1	2	yes	—
76	C₄×D₈×C₂₃	C₂²	1	2	yes	—
77	C₂₃×#436	C₂²	1	1	yes	characteristic
78	C₂₃×#435	C₂²	1	2	yes	—
79	C₈×D₄×C₂₃	C₂²	1	2	yes	—
80	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
81	C₂₃×#433	C₂²	1	2	yes	—
82	C₂₃×#432	C₂²	1	1	yes	characteristic
83	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
84	C₂×C₂₃×#107	C₂²	1	2	yes	—
85	C₂₃×#417	C₂²	1	4	yes	—
86	C₂×C₂₃×#103	C₂²	1	2	yes	—
87	C₂₃×#405	C₂²	1	2	yes	—
88	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
89	C₂×#41×C₂₃	—	2	4	no	—
90	C₂×#41×C₂₃	—	2	2	no	—
91	C₂×#41×C₂₃	C₂³	1	4	yes	—
92	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
93	C₂₃×#135	—	2	8	no	—
94	C₂×Q₁₆×C₂₃	—	2	4	no	—
95	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
96	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
97	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
98	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
99	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
100	C₂×D₈×C₂₃	C₂³	1	2	yes	—
101	C₂×D₈×C₂₃	C₂³	1	2	yes	—
102	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
103	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
105	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
106	C₂₃×C₄⋊Q₈	—	2	4	no	—
107	C₂₃×C₄⋊Q₈	—	2	2	no	—
108	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
109	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
110	C₂₃×#127	—	2	2	no	—
111	C₂₃×#127	C₂³	1	2	yes	—
112	C₂₃×#126	—	2	4	no	—
113	C₂₃×#126	D₄	1	2	yes	—
114	C₂₃×#125	—	2	2	no	—
115	C₂₃×#125	D₄	1	1	yes	characteristic
116	C₂₃×#124	—	2	2	no	—
117	C₂₃×#124	—	2	4	no	—
118	C₂₃×#124	—	2	4	no	—
119	C₂₃×#124	—	2	2	no	—
120	C₂₃×#124	D₄	1	1	yes	characteristic
121	C₂₃×#124	C₂³	1	4	yes	—
122	C₂₃×#123	—	2	4	no	—
123	C₂₃×#123	—	2	4	no	—
124	C₂₃×#123	—	2	4	no	—
125	C₂₃×#123	—	2	4	no	—
126	C₂₃×#123	D₄	1	2	yes	—
127	C₂₃×C₂²⋊Q₈	—	2	4	no	—
128	C₂₃×C₂²⋊Q₈	—	2	4	no	—
129	C₂₃×C₂²⋊Q₈	—	2	4	no	—
130	C₂₃×C₂²⋊Q₈	—	2	4	no	—
131	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
132	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
133	C₂₃×#121	—	2	4	no	—
134	C₂₃×#121	—	2	2	no	—
135	C₂₃×#121	—	2	4	no	—
136	C₂₃×#121	D₄	1	1	yes	characteristic
137	C₂₃×#121	C₂³	1	4	yes	—
138	C₂₃×#121	C₂³	1	4	yes	—
139	C₄×Q₈×C₂₃	—	2	2	no	—
140	C₄×Q₈×C₂₃	—	2	2	no	—
141	C₄×Q₈×C₂₃	—	2	2	no	—
142	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
143	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
144	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
145	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
146	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
147	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
148	C₄×D₄×C₂₃	—	2	2	no	—
149	C₄×D₄×C₂₃	—	2	2	no	—
150	C₄×D₄×C₂₃	—	2	2	no	—
151	C₄×D₄×C₂₃	—	2	4	no	—
152	C₄×D₄×C₂₃	—	2	4	no	—
153	C₄×D₄×C₂₃	—	2	4	no	—
154	C₄×D₄×C₂₃	—	2	2	no	—
155	C₄×D₄×C₂₃	C₂³	1	4	yes	—
156	C₄×D₄×C₂₃	C₂³	1	4	yes	—
157	C₄×D₄×C₂₃	C₂³	1	2	yes	—
158	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
159	C₂₃×#117	—	2	4	no	—
160	C₂₃×#117	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
162	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
163	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
165	C₂×C₄²×C₂₃	—	2	2	no	—
166	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
167	C₂₃×#107	C₂³	1	1	yes	characteristic
168	C₂₃×#107	C₂³	1	2	yes	—
169	C₂₃×#107	C₂³	1	1	yes	characteristic
170	C₂₃×#107	C₂³	1	2	yes	—
171	C₂₃×#107	C₂³	1	4	yes	—
172	C₂₃×#107	C₂³	1	2	yes	—
173	C₂₃×#107	C₂³	1	4	yes	—
174	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
175	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
176	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
177	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
178	C₂₃×#103	C₂³	1	2	yes	—
179	C₂₃×#103	C₂³	1	2	yes	—
180	C₂₃×#103	C₂³	1	2	yes	—
181	C₂₃×#103	C₂³	1	2	yes	—
182	C₂₃×#103	C₂³	1	4	yes	—
183	C₂₃×#103	C₂³	1	4	yes	—
184	C₂₃×#102	C₂³	1	4	yes	—
185	C₂₃×#102	C₂³	1	4	yes	—
186	C₂₃×#102	C₂³	1	4	yes	—
187	C₂₃×#102	C₂³	1	4	yes	—
188	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
189	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
190	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
191	C₂₃×#97	C₂³	1	2	yes	—
192	C₂₃×#97	C₂³	1	2	yes	—
193	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
194	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₂₃	C₂³	1	2	yes	—
198	#41×C₂₃	—	2	8	no	—
199	#41×C₂₃	—	4	4	no	—
200	#41×C₂₃	—	8	4	no	—
201	#41×C₂₃	—	8	8	no	—
202	C₂×Q₈×C₂₃	—	2	2	no	—
203	C₂×Q₈×C₂₃	—	2	4	no	—
204	C₂×Q₈×C₂₃	—	2	2	no	—
205	C₂×Q₈×C₂₃	—	2	4	no	—
206	C₂×Q₈×C₂₃	—	4	2	no	—
207	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
208	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
209	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
210	C₂×D₄×C₂₃	—	2	4	no	—
211	C₂×D₄×C₂₃	—	2	4	no	—
212	C₂×D₄×C₂₃	—	2	4	no	—
213	C₂×D₄×C₂₃	—	2	2	no	—
214	C₂×D₄×C₂₃	—	2	2	no	—
215	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
216	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
217	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
218	C₂²×C₄×C₂₃	—	2	2	no	—
219	C₂²×C₄×C₂₃	—	2	2	no	—
220	C₂²×C₄×C₂₃	—	2	4	no	—
221	C₂²×C₄×C₂₃	—	2	4	no	—
222	C₂²×C₄×C₂₃	—	2	4	no	—
223	C₂²×C₄×C₂₃	—	2	4	no	—
224	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
228	Q₁₆×C₂₃	—	2	4	no	—
229	Q₁₆×C₂₃	—	2	2	no	—
230	Q₁₆×C₂₃	#41	1	4	yes	complemented
231	SD₁₆×C₂₃	—	2	8	no	—
232	SD₁₆×C₂₃	—	4	4	no	—
233	D₈×C₂₃	—	2	4	no	—
234	D₈×C₂₃	—	4	2	no	—
235	M₁₆×C₂₃	—	4	2	no	—
236	C₂×C₈×C₂₃	—	2	2	no	—
237	C₂×C₈×C₂₃	—	2	4	no	—
238	C₂×C₈×C₂₃	—	4	1	no	—
239	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
240	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
241	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
242	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
243	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
244	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
245	C₄⋊C₄×C₂₃	—	2	2	no	—
246	C₄⋊C₄×C₂₃	—	2	4	no	—
247	C₄⋊C₄×C₂₃	—	2	4	no	—
248	C₄⋊C₄×C₂₃	—	2	2	no	—
249	C₄⋊C₄×C₂₃	—	2	2	no	—
250	C₄⋊C₄×C₂₃	—	2	2	no	—
251	C₄⋊C₄×C₂₃	—	2	2	no	—
252	C₄⋊C₄×C₂₃	—	2	2	no	—
253	C₄⋊C₄×C₂₃	—	2	4	no	—
254	C₄⋊C₄×C₂₃	—	2	4	no	—
255	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
256	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
257	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
258	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
259	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
260	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
261	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
263	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
264	C₂²⋊C₄×C₂₃	—	2	4	no	—
265	C₂²⋊C₄×C₂₃	—	2	4	no	—
266	C₂²⋊C₄×C₂₃	—	2	4	no	—
267	C₂²⋊C₄×C₂₃	—	2	4	no	—
268	C₂²⋊C₄×C₂₃	—	2	4	no	—
269	C₂²⋊C₄×C₂₃	—	2	4	no	—
270	C₂²⋊C₄×C₂₃	—	2	4	no	—
271	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
272	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
273	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
274	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
275	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
276	C₄²×C₂₃	—	2	2	no	—
277	C₄²×C₂₃	—	2	2	no	—
278	C₄²×C₂₃	—	2	2	no	—
279	C₄²×C₂₃	—	2	2	no	—
280	C₄²×C₂₃	—	2	4	no	—
281	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
282	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
284	C₄²×C₂₃	C₂⁴	1	2	yes	—
285	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
286	#61485	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
287	C₂³×C₂₃	—	2	4	no	—
288	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
289	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
290	Q₈×C₂₃	—	2	2	no	—
291	Q₈×C₂₃	—	2	2	no	—
292	Q₈×C₂₃	—	2	2	no	—
293	Q₈×C₂₃	—	2	2	no	—
294	Q₈×C₂₃	—	4	4	no	—
295	Q₈×C₂₃	—	8	2	no	—
296	Q₈×C₂₃	—	8	4	no	—
297	Q₈×C₂₃	C₂×#41	1	4	yes	—
298	D₄×C₂₃	—	2	4	no	—
299	D₄×C₂₃	—	2	2	no	—
300	D₄×C₂₃	—	2	4	no	—
301	D₄×C₂₃	—	2	4	no	—
302	D₄×C₂₃	—	4	8	no	—
303	D₄×C₂₃	—	4	8	no	—
304	D₄×C₂₃	—	4	4	no	—
305	D₄×C₂₃	—	8	2	no	—
306	D₄×C₂₃	—	8	4	no	—
307	C₂×C₄×C₂₃	—	2	2	no	—
308	C₂×C₄×C₂₃	—	2	2	no	—
309	C₂×C₄×C₂₃	—	2	2	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	2	no	—
314	C₂×C₄×C₂₃	—	2	2	no	—
315	C₂×C₄×C₂₃	—	2	2	no	—
316	C₂×C₄×C₂₃	—	2	2	no	—
317	C₂×C₄×C₂₃	—	2	4	no	—
318	C₂×C₄×C₂₃	—	4	8	no	—
319	C₂×C₄×C₂₃	—	4	4	no	—
320	C₂×C₄×C₂₃	—	4	4	no	—
321	C₂×C₄×C₂₃	—	8	4	no	—
322	C₂×C₄×C₂₃	—	8	4	no	—
323	C₂×C₄×C₂₃	—	8	4	no	—
324	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
326	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
330	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
331	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
333	C₈×C₂₃	—	2	2	no	—
334	C₈×C₂₃	—	2	1	no	—
335	C₈×C₂₃	—	2	1	no	—
336	C₈×C₂₃	—	2	1	no	—
337	C₈×C₂₃	—	2	2	no	—
338	C₈×C₂₃	C₂×#41	1	2	yes	—
339	#3522	C₂×C₂₃	1	2	yes	complemented
340	#3396	C₂×C₂₃	1	1	yes	characteristic, complemented
341	Q₈×Q₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
342	#3375	C₂×C₂₃	1	2	yes	complemented
343	#3338	C₂×C₂₃	1	1	yes	characteristic, complemented
344	#3334	C₂×C₂₃	1	2	yes	complemented
345	#3333	C₂×C₂₃	1	2	yes	complemented
346	#3308	C₂×C₂₃	1	4	yes	complemented
347	#3287	C₂×C₂₃	1	1	yes	characteristic, complemented
348	#3285	C₂×C₂₃	1	2	yes	complemented
349	#3175	C₂×C₂₃	1	2	yes	complemented
350	#3169	C₂×C₂₃	1	1	yes	characteristic, complemented
351	#3124	C₂×C₂₃	1	4	yes	complemented
352	#3112	C₂×C₂₃	1	2	yes	complemented
353	#2966	C₂×C₂₃	1	1	yes	characteristic, complemented
354	#2951	C₂×C₂₃	1	2	yes	complemented
355	C₂×C₄×Q₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
356	C₂²×C₂₃	—	2	1	no	—
357	C₂²×C₂₃	—	2	1	no	—
358	C₂²×C₂₃	—	2	2	no	—
359	C₂²×C₂₃	—	2	2	no	—
360	C₂²×C₂₃	—	2	2	no	—
361	C₂²×C₂₃	—	4	4	no	—
362	C₂²×C₂₃	—	4	4	no	—
363	C₂²×C₂₃	—	4	4	no	—
364	C₂²×C₂₃	#576	1	2	yes	—
365	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
366	C₄×C₂₃	—	2	2	no	—
367	C₄×C₂₃	—	2	1	no	—
368	C₄×C₂₃	—	2	4	no	—
369	C₄×C₂₃	—	2	1	no	—
370	C₄×C₂₃	—	2	1	no	—
371	C₄×C₂₃	—	2	2	no	—
372	C₄×C₂₃	—	2	1	no	—
373	C₄×C₂₃	—	2	2	no	—
374	C₄×C₂₃	—	4	2	no	—
375	C₄×C₂₃	—	4	2	no	—
376	C₄×C₂₃	—	4	2	no	—
377	C₄×C₂₃	—	4	4	no	—
378	C₄×C₂₃	#578	1	2	yes	—
379	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
380	C₄×C₂₃	#585	1	1	yes	characteristic
381	C₂×#135	C₂²×C₂₃	1	2	yes	—
382	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
383	#559	—	2	2	no	—
384	#559	C₂²×C₂₃	1	2	yes	—
385	Q₈²	C₂²×C₂₃	1	2	yes	—
386	#554	—	2	2	no	—
387	#554	C₂²×C₂₃	1	2	yes	—
388	#550	C₂²×C₂₃	1	2	yes	—
389	#548	C₂²×C₂₃	1	4	yes	—
390	#547	—	2	4	no	—
391	#547	C₂²×C₂₃	1	4	yes	—
392	#542	—	2	4	no	—
393	#542	C₂²×C₂₃	1	4	yes	—
394	#532	—	2	2	no	—
395	#532	C₂²×C₂₃	1	2	yes	—
396	#529	—	2	2	no	—
397	#529	C₂²×C₂₃	1	1	yes	characteristic
398	#520	C₂²×C₂₃	1	4	yes	—
399	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
400	#500	C₂²×C₂₃	1	2	yes	—
401	#500	C₂²×C₂₃	1	1	yes	characteristic
402	#495	C₂²×C₂₃	1	2	yes	—
403	#493	C₂²×C₂₃	1	1	yes	characteristic
404	#489	C₂²×C₂₃	1	4	yes	—
405	#486	C₂²×C₂₃	1	2	yes	—
406	#484	C₂²×C₂₃	1	4	yes	—
407	#480	C₂²×C₂₃	1	4	yes	—
408	#480	C₂²×C₂₃	1	4	yes	—
409	#477	C₂²×C₂₃	1	2	yes	—
410	#477	C₂²×C₂₃	1	2	yes	—
411	#477	C₂²×C₂₃	1	4	yes	—
412	#474	C₂²×C₂₃	1	4	yes	—
413	#468	C₂²×C₂₃	1	4	yes	—
414	#467	C₂²×C₂₃	1	2	yes	—
415	#466	C₂²×C₂₃	1	2	yes	—
416	#466	C₂²×C₂₃	1	2	yes	—
417	#466	C₂²×C₂₃	1	2	yes	—
418	#464	C₂²×C₂₃	1	4	yes	—
419	#463	C₂²×C₂₃	1	4	yes	—
420	#460	C₂²×C₂₃	1	2	yes	—
421	#460	C₂²×C₂₃	1	2	yes	—
422	#452	C₂²×C₂₃	1	4	yes	—
423	#449	C₂²×C₂₃	1	4	yes	—
424	#448	C₂²×C₂₃	1	4	yes	—
425	#446	C₂²×C₂₃	1	1	yes	characteristic
426	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic
427	#440	C₂²×C₂₃	1	4	yes	—
428	#440	C₂²×C₂₃	1	4	yes	—
429	#440	C₂²×C₂₃	1	4	yes	—
430	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
431	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
432	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
433	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
434	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
435	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
436	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
437	C₄×D₈	C₂²×C₂₃	1	2	yes	—
438	C₄×D₈	C₂²×C₂₃	1	2	yes	—
439	C₄×D₈	C₂²×C₂₃	1	2	yes	—
440	#436	C₂²×C₂₃	1	1	yes	characteristic
441	#435	C₂²×C₂₃	1	2	yes	—
442	C₈×D₄	C₂²×C₂₃	1	2	yes	—
443	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
444	#433	C₂²×C₂₃	1	2	yes	—
445	#432	C₂²×C₂₃	1	1	yes	characteristic
446	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
447	C₂×#107	C₂²×C₂₃	1	2	yes	—
448	#417	C₂²×C₂₃	1	4	yes	—
449	C₂×#103	C₂²×C₂₃	1	2	yes	—
450	#405	C₂²×C₂₃	1	2	yes	—
451	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
452	C₂×C₂₃	—	2	2	no	—
453	C₂×C₂₃	—	4	2	no	—
454	C₂×C₂₃	—	8	4	no	—
455	C₂×C₂₃	D₄×#41	1	1	yes	characteristic
456	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
457	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
458	C₂×#41	—	2	4	no	—
459	C₂×#41	—	2	2	no	—
460	C₂×#41	C₂³×C₂₃	1	4	yes	—
461	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
462	#135	—	2	8	no	—
463	C₂×Q₁₆	—	2	4	no	—
464	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
465	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
466	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
467	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
468	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
469	C₂×D₈	C₂³×C₂₃	1	2	yes	—
470	C₂×D₈	C₂³×C₂₃	1	2	yes	—
471	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
472	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
473	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
474	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
475	C₄⋊Q₈	—	2	2	no	—
476	C₄⋊Q₈	—	2	4	no	—
477	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
478	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
479	#127	—	2	2	no	—
480	#127	C₂³×C₂₃	1	2	yes	—
481	#126	—	2	4	no	—
482	#126	D₄×C₂₃	1	2	yes	—
483	#125	—	2	2	no	—
484	#125	D₄×C₂₃	1	1	yes	characteristic
485	#124	—	2	2	no	—
486	#124	—	2	4	no	—
487	#124	—	2	4	no	—
488	#124	—	2	2	no	—
489	#124	D₄×C₂₃	1	1	yes	characteristic
490	#124	C₂³×C₂₃	1	4	yes	—
491	#123	—	2	4	no	—
492	#123	—	2	4	no	—
493	#123	—	2	4	no	—
494	#123	—	2	4	no	—
495	#123	D₄×C₂₃	1	2	yes	—
496	C₂²⋊Q₈	—	2	4	no	—
497	C₂²⋊Q₈	—	2	4	no	—
498	C₂²⋊Q₈	—	2	4	no	—
499	C₂²⋊Q₈	—	2	4	no	—
500	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
501	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
502	#121	—	2	4	no	—
503	#121	—	2	2	no	—
504	#121	—	2	4	no	—
505	#121	D₄×C₂₃	1	1	yes	characteristic
506	#121	C₂³×C₂₃	1	4	yes	—
507	#121	C₂³×C₂₃	1	4	yes	—
508	C₄×Q₈	—	2	2	no	—
509	C₄×Q₈	—	2	2	no	—
510	C₄×Q₈	—	2	2	no	—
511	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
512	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
513	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
514	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
515	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
516	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
517	C₄×D₄	—	2	2	no	—
518	C₄×D₄	—	2	2	no	—
519	C₄×D₄	—	2	2	no	—
520	C₄×D₄	—	2	4	no	—
521	C₄×D₄	—	2	4	no	—
522	C₄×D₄	—	2	4	no	—
523	C₄×D₄	—	2	2	no	—
524	C₄×D₄	C₂³×C₂₃	1	4	yes	—
525	C₄×D₄	C₂³×C₂₃	1	4	yes	—
526	C₄×D₄	C₂³×C₂₃	1	2	yes	—
527	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
528	#117	—	2	4	no	—
529	#117	C₂³×C₂₃	1	2	yes	—
530	C₂×C₄⋊C₄	—	2	2	no	—
531	C₂×C₄⋊C₄	—	2	4	no	—
532	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
534	C₂×C₄²	—	2	2	no	—
535	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
536	#107	C₂³×C₂₃	1	1	yes	characteristic
537	#107	C₂³×C₂₃	1	2	yes	—
538	#107	C₂³×C₂₃	1	1	yes	characteristic
539	#107	C₂³×C₂₃	1	2	yes	—
540	#107	C₂³×C₂₃	1	4	yes	—
541	#107	C₂³×C₂₃	1	2	yes	—
542	#107	C₂³×C₂₃	1	4	yes	—
543	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
544	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
545	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
546	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
547	#103	C₂³×C₂₃	1	2	yes	—
548	#103	C₂³×C₂₃	1	2	yes	—
549	#103	C₂³×C₂₃	1	2	yes	—
550	#103	C₂³×C₂₃	1	2	yes	—
551	#103	C₂³×C₂₃	1	4	yes	—
552	#103	C₂³×C₂₃	1	4	yes	—
553	#102	C₂³×C₂₃	1	4	yes	—
554	#102	C₂³×C₂₃	1	4	yes	—
555	#102	C₂³×C₂₃	1	4	yes	—
556	#102	C₂³×C₂₃	1	4	yes	—
557	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
558	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
559	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
560	#97	C₂³×C₂₃	1	2	yes	—
561	#97	C₂³×C₂₃	1	2	yes	—
562	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
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	2	yes	—
567	C₂₃	#61485	1	1	yes	characteristic, direct product factor, Sylow
568	#41	—	2	8	no	—
569	#41	—	4	4	no	—
570	#41	—	8	4	no	—
571	#41	—	8	8	no	—
572	C₂×Q₈	—	2	2	no	—
573	C₂×Q₈	—	2	4	no	—
574	C₂×Q₈	—	2	2	no	—
575	C₂×Q₈	—	2	4	no	—
576	C₂×Q₈	—	4	2	no	—
577	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
578	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
579	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
580	C₂×D₄	—	2	4	no	—
581	C₂×D₄	—	2	4	no	—
582	C₂×D₄	—	2	4	no	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
586	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
587	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
588	C₂²×C₄	—	2	2	no	—
589	C₂²×C₄	—	2	2	no	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	—	2	4	no	—
592	C₂²×C₄	—	2	4	no	—
593	C₂²×C₄	—	2	4	no	—
594	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
595	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
598	Q₁₆	—	2	4	no	—
599	Q₁₆	—	2	2	no	—
600	Q₁₆	#41×C₂₃	1	4	yes	complemented
601	SD₁₆	—	2	8	no	—
602	SD₁₆	—	4	4	no	—
603	D₈	—	2	4	no	—
604	D₈	—	4	2	no	—
605	M₁₆	—	4	2	no	—
606	C₂×C₈	—	2	2	no	—
607	C₂×C₈	—	2	4	no	—
608	C₂×C₈	—	4	1	no	—
609	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
610	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
611	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
612	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
613	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
614	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
626	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
627	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
628	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
629	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
630	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
631	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
632	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
633	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
642	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
643	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
644	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
645	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
646	C₄²	—	2	2	no	—
647	C₄²	—	2	2	no	—
648	C₄²	—	2	2	no	—
649	C₄²	—	2	2	no	—
650	C₄²	—	2	4	no	—
651	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
652	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
653	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
654	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
655	C₄²	C₂⁴×C₂₃	1	2	yes	—
656	C₂³	—	2	4	no	—
657	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
658	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
659	Q₈	—	2	2	no	—
660	Q₈	—	2	2	no	—
661	Q₈	—	2	2	no	—
662	Q₈	—	2	2	no	—
663	Q₈	—	4	4	no	—
664	Q₈	—	8	2	no	—
665	Q₈	—	8	4	no	—
666	Q₈	C₂×#41×C₂₃	1	4	yes	—
667	D₄	—	2	4	no	—
668	D₄	—	2	2	no	—
669	D₄	—	2	4	no	—
670	D₄	—	2	4	no	—
671	D₄	—	4	8	no	—
672	D₄	—	4	8	no	—
673	D₄	—	4	4	no	—
674	D₄	—	8	2	no	—
675	D₄	—	8	4	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	4	no	—
687	C₂×C₄	—	4	8	no	—
688	C₂×C₄	—	4	4	no	—
689	C₂×C₄	—	4	4	no	—
690	C₂×C₄	—	8	4	no	—
691	C₂×C₄	—	8	4	no	—
692	C₂×C₄	—	8	4	no	—
693	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
694	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
695	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
696	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
697	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
698	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
699	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
700	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
701	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
702	C₈	—	2	2	no	—
703	C₈	—	2	1	no	—
704	C₈	—	2	1	no	—
705	C₈	—	2	1	no	—
706	C₈	—	2	2	no	—
707	C₈	C₂×#41×C₂₃	1	2	yes	—
708	C₂²	—	2	1	no	—
709	C₂²	—	2	1	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	2	2	no	—
713	C₂²	—	4	4	no	—
714	C₂²	—	4	4	no	—
715	C₂²	—	4	4	no	—
716	C₂²	C₂₃×#576	1	2	yes	—
717	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
718	C₄	—	2	2	no	—
719	C₄	—	2	1	no	—
720	C₄	—	2	4	no	—
721	C₄	—	2	1	no	—
722	C₄	—	2	1	no	—
723	C₄	—	2	2	no	—
724	C₄	—	2	1	no	—
725	C₄	—	2	2	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	2	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	4	no	—
730	C₄	C₂₃×#578	1	2	yes	—
731	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
732	C₄	C₂₃×#585	1	1	yes	characteristic
733	C₂	—	2	2	no	—
734	C₂	—	4	2	no	—
735	C₂	—	8	4	no	—
736	C₂	D₄×#41×C₂₃	1	1	yes	characteristic
737	C₂	C₂×C₂₃×#576	1	1	yes	characteristic
738	C₂	C₂×C₂₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3522	C₂	semidirect
2. C₂₃×#3396	C₂	semidirect
3. Q₈×Q₁₆×C₂₃	C₂	semidirect
4. C₂₃×#3375	C₂	semidirect
5. C₂₃×#3338	C₂	semidirect
6. C₂₃×#3334	C₂	semidirect
7. C₂₃×#3333	C₂	semidirect
8. C₂₃×#3308	C₂	semidirect
9. C₂₃×#3287	C₂	semidirect
10. C₂₃×#3285	C₂	semidirect
11. C₂₃×#3175	C₂	semidirect
12. C₂₃×#3169	C₂	semidirect
13. C₂₃×#3124	C₂	semidirect
14. C₂₃×#3112	C₂	semidirect
15. C₂₃×#2966	C₂	semidirect
16. C₂₃×#2951	C₂	semidirect
17. C₂×C₄×Q₁₆×C₂₃	C₂	semidirect
230. Q₁₆×C₂₃	#41	semidirect
286. #61485	C₂₃	direct (N × H)
339. #3522	C₂×C₂₃	semidirect
340. #3396	C₂×C₂₃	semidirect
341. Q₈×Q₁₆	C₂×C₂₃	semidirect
342. #3375	C₂×C₂₃	semidirect
343. #3338	C₂×C₂₃	semidirect
344. #3334	C₂×C₂₃	semidirect
345. #3333	C₂×C₂₃	semidirect
346. #3308	C₂×C₂₃	semidirect
347. #3287	C₂×C₂₃	semidirect
348. #3285	C₂×C₂₃	semidirect
349. #3175	C₂×C₂₃	semidirect
350. #3169	C₂×C₂₃	semidirect
351. #3124	C₂×C₂₃	semidirect
352. #3112	C₂×C₂₃	semidirect
353. #2966	C₂×C₂₃	semidirect
354. #2951	C₂×C₂₃	semidirect
355. C₂×C₄×Q₁₆	C₂×C₂₃	semidirect
567. C₂₃	#61485	direct (N × H)
600. Q₁₆	#41×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#3522	2
C₂₃×#3396	2
Q₈×Q₁₆×C₂₃	2
C₂₃×#3375	2
C₂₃×#3338	2
C₂₃×#3334	2
C₂₃×#3333	2
C₂₃×#3308	2
C₂₃×#3287	2
C₂₃×#3285	2
C₂₃×#3175	2
C₂₃×#3169	2
C₂₃×#3124	2
C₂₃×#3112	2
C₂₃×#2966	2
C₂₃×#2951	2
C₂×C₄×Q₁₆×C₂₃	2
#61485	23

Subgroups — C23×#61485 #19209111

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61485 #19209111