Subgroups — C₂₃×#34224 #19181850

Order 5888.

2330 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#529	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2373	C₂	1	4	yes	maximal, complemented
3	C₂₃×#2370	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2367	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2357	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2356	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2351	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2349	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2347	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2343	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2322	C₂	1	4	yes	maximal, complemented
12	C₂₃×#2318	C₂	1	2	yes	maximal, complemented
13	C₄×C₂₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
14	C₄×C₂₃×#121	C₂	1	2	yes	maximal
15	C₂₃×#2283	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2275	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×C₄⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#529	C₄	1	16	yes	complemented
19	C₂×C₂₃×#126	C₂²	1	2	yes	—
20	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#123	C₂²	1	2	yes	—
23	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	—
28	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#117	C₂²	1	2	yes	—
32	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
33	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
34	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
35	C₂₃×#391	C₂²	1	2	yes	—
36	C₂₃×#390	C₂²	1	2	yes	—
37	C₂₃×#389	C₂²	1	2	yes	—
38	C₂₃×#389	C₂²	1	2	yes	—
39	C₂₃×#389	C₂²	1	4	yes	—
40	C₂₃×#389	C₂²	1	4	yes	—
41	C₂₃×#388	C₂²	1	4	yes	—
42	C₂₃×#388	C₂²	1	4	yes	—
43	C₂₃×#388	C₂²	1	4	yes	—
44	C₂₃×#388	C₂²	1	4	yes	—
45	C₂₃×#387	C₂²	1	4	yes	—
46	C₂₃×#387	C₂²	1	4	yes	—
47	C₂₃×#387	C₂²	1	4	yes	—
48	C₂₃×#387	C₂²	1	4	yes	—
49	C₂₃×#386	C₂²	1	4	yes	—
50	C₂₃×#385	C₂²	1	4	yes	—
51	C₂₃×#385	C₂²	1	4	yes	—
52	C₂₃×#385	C₂²	1	4	yes	—
53	C₂₃×#383	C₂²	1	2	yes	—
54	C₂₃×#383	C₂²	1	2	yes	—
55	C₂₃×#382	C₂²	1	1	yes	characteristic
56	C₂₃×#382	C₂²	1	1	yes	characteristic
57	C₂₃×#382	C₂²	1	2	yes	—
58	C₂₃×#381	C₂²	1	2	yes	—
59	C₂₃×#381	C₂²	1	2	yes	—
60	C₂₃×#380	C₂²	1	2	yes	—
61	C₂₃×#380	C₂²	1	2	yes	—
62	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
63	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
64	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
65	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
66	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
67	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
68	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
69	C₄×C₄⋊C₄×C₂₃	C₂²	1	4	yes	—
70	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
71	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
72	C₄×C₄⋊C₄×C₂₃	C₂²	1	4	yes	—
73	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
74	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
75	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
76	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
77	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
78	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
79	C₂₃×#376	C₂²	1	2	yes	—
80	C₂₃×#376	C₂²	1	2	yes	—
81	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
82	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
83	C₂×C₂₃×#95	C₂²	1	2	yes	—
84	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
86	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
90	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
91	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
93	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
94	C₂₃×#126	C₂×C₄	1	16	yes	complemented
95	C₂₃×#125	C₂×C₄	1	8	yes	complemented
96	C₂₃×#124	C₂×C₄	1	8	yes	complemented
97	C₂₃×#123	C₂×C₄	1	16	yes	complemented
98	C₂₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
99	C₂₃×#121	C₂×C₄	1	8	yes	—
100	C₄×Q₈×C₂₃	—	4	4	no	—
101	C₄×Q₈×C₂₃	C₂×C₄	1	8	yes	complemented
102	C₄×D₄×C₂₃	—	2	16	no	—
103	C₄×D₄×C₂₃	—	4	4	no	—
104	C₄×D₄×C₂₃	C₂×C₄	1	8	yes	complemented
105	C₄×D₄×C₂₃	C₂×C₄	1	16	yes	complemented
106	C₂₃×#117	C₂×C₄	1	16	yes	complemented
107	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
108	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
126	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
131	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
132	C₂×C₄²×C₂₃	—	4	4	no	—
133	C₂×C₄²×C₂₃	C₂×C₄	1	8	yes	complemented
134	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
135	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
136	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
137	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
138	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
139	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
140	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
141	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
142	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
144	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
147	C₂₃×#95	C₂³	1	1	yes	characteristic
148	C₂₃×#95	C₂³	1	2	yes	—
149	C₂₃×#95	C₂³	1	1	yes	characteristic
150	C₂₃×#95	C₂³	1	2	yes	—
151	C₂₃×#95	C₂³	1	4	yes	—
152	C₂₃×#95	C₂³	1	1	yes	characteristic
153	C₂₃×#95	C₂³	1	1	yes	characteristic
154	C₂₃×#95	C₂³	1	2	yes	—
155	C₂₃×#95	C₂³	1	2	yes	—
156	C₂₃×#95	C₂³	1	4	yes	—
157	C₂₃×#95	C₂³	1	4	yes	—
158	C₂₃×#95	C₂³	1	2	yes	—
159	C₂₃×#95	C₂³	1	2	yes	—
160	C₂₃×#95	C₂³	1	4	yes	—
161	C₂₃×#95	C₂³	1	4	yes	—
162	C₂₃×#95	C₂³	1	4	yes	—
163	C₂₃×#95	C₂³	1	4	yes	—
164	C₂₃×#95	C₂³	1	4	yes	—
165	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
166	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
167	C₂×Q₈×C₂₃	—	2	2	no	—
168	C₂×Q₈×C₂₃	—	2	2	no	—
169	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
170	C₂×D₄×C₂₃	—	2	8	no	—
171	C₂×D₄×C₂₃	—	2	2	no	—
172	C₂×D₄×C₂₃	—	2	2	no	—
173	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
174	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
175	C₂²×C₄×C₂₃	—	2	4	no	—
176	C₂²×C₄×C₂₃	—	2	2	no	—
177	C₂²×C₄×C₂₃	—	2	2	no	—
178	C₂²×C₄×C₂₃	—	2	4	no	—
179	C₂²×C₄×C₂₃	—	2	8	no	—
180	C₂²×C₄×C₂₃	—	4	2	no	—
181	C₂²×C₄×C₂₃	—	4	2	no	—
182	C₂²×C₄×C₂₃	—	4	2	no	—
183	C₂²×C₄×C₂₃	—	4	2	no	—
184	C₂²×C₄×C₂₃	—	4	4	no	—
185	C₂²×C₄×C₂₃	—	4	2	no	—
186	C₂²×C₄×C₂₃	—	4	4	no	—
187	C₂²×C₄×C₂₃	—	4	4	no	—
188	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
189	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
190	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
191	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	—
192	C₂²×C₄×C₂₃	#41	1	8	yes	—
193	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
194	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
195	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
199	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
200	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
208	C₄⋊C₄×C₂₃	—	2	4	no	—
209	C₄⋊C₄×C₂₃	—	2	4	no	—
210	C₄⋊C₄×C₂₃	—	2	4	no	—
211	C₄⋊C₄×C₂₃	—	2	4	no	—
212	C₄⋊C₄×C₂₃	—	2	8	no	—
213	C₄⋊C₄×C₂₃	—	2	4	no	—
214	C₄⋊C₄×C₂₃	—	2	4	no	—
215	C₄⋊C₄×C₂₃	—	4	4	no	—
216	C₄⋊C₄×C₂₃	—	4	4	no	—
217	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
218	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
219	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
220	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
221	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
222	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
223	C₂²⋊C₄×C₂₃	—	2	8	no	—
224	C₂²⋊C₄×C₂₃	—	2	8	no	—
225	C₂²⋊C₄×C₂₃	—	4	4	no	—
226	C₂²⋊C₄×C₂₃	—	4	4	no	—
227	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
228	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
229	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
230	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
231	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
232	C₄²×C₂₃	—	2	8	no	—
233	C₄²×C₂₃	—	2	4	no	—
234	C₄²×C₂₃	—	2	4	no	—
235	C₄²×C₂₃	—	4	2	no	—
236	C₄²×C₂₃	—	4	2	no	—
237	C₄²×C₂₃	—	4	4	no	—
238	C₄²×C₂₃	—	4	4	no	—
239	C₄²×C₂₃	—	4	4	no	—
240	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
241	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
242	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
243	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
244	C₄²×C₂₃	C₂²×C₄	1	8	yes	—
245	#34224	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
246	C₂³×C₂₃	—	2	1	no	—
247	C₂³×C₂₃	—	2	1	no	—
248	C₂³×C₂₃	—	2	2	no	—
249	C₂³×C₂₃	—	2	4	no	—
250	C₂³×C₂₃	—	2	2	no	—
251	C₂³×C₂₃	—	2	2	no	—
252	C₂³×C₂₃	—	2	4	no	—
253	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
254	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
255	C₂³×C₂₃	C₂×#41	1	4	yes	—
256	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
257	Q₈×C₂₃	—	2	8	no	—
258	D₄×C₂₃	—	2	16	no	—
259	D₄×C₂₃	—	2	8	no	—
260	C₂×C₄×C₂₃	—	2	8	no	—
261	C₂×C₄×C₂₃	—	2	4	no	—
262	C₂×C₄×C₂₃	—	2	2	no	—
263	C₂×C₄×C₂₃	—	2	2	no	—
264	C₂×C₄×C₂₃	—	2	2	no	—
265	C₂×C₄×C₂₃	—	2	2	no	—
266	C₂×C₄×C₂₃	—	2	1	no	—
267	C₂×C₄×C₂₃	—	2	2	no	—
268	C₂×C₄×C₂₃	—	2	1	no	—
269	C₂×C₄×C₂₃	—	2	2	no	—
270	C₂×C₄×C₂₃	—	2	2	no	—
271	C₂×C₄×C₂₃	—	2	2	no	—
272	C₂×C₄×C₂₃	—	2	4	no	—
273	C₂×C₄×C₂₃	—	2	2	no	—
274	C₂×C₄×C₂₃	—	2	2	no	—
275	C₂×C₄×C₂₃	—	2	8	no	—
276	C₂×C₄×C₂₃	—	2	4	no	—
277	C₂×C₄×C₂₃	—	2	4	no	—
278	C₂×C₄×C₂₃	—	2	2	no	—
279	C₂×C₄×C₂₃	—	2	2	no	—
280	C₂×C₄×C₂₃	—	2	2	no	—
281	C₂×C₄×C₂₃	—	2	2	no	—
282	C₂×C₄×C₂₃	—	2	4	no	—
283	C₂×C₄×C₂₃	—	2	4	no	—
284	C₂×C₄×C₂₃	—	2	4	no	—
285	C₂×C₄×C₂₃	—	2	4	no	—
286	C₂×C₄×C₂₃	—	2	2	no	—
287	C₂×C₄×C₂₃	—	2	2	no	—
288	C₂×C₄×C₂₃	—	4	4	no	—
289	C₂×C₄×C₂₃	—	4	8	no	—
290	C₂×C₄×C₂₃	—	4	8	no	—
291	C₂×C₄×C₂₃	—	4	8	no	—
292	C₂×C₄×C₂₃	—	8	8	no	—
293	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
294	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
295	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
296	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
297	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
298	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
299	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
300	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
301	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
302	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
303	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
304	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
305	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
306	C₂×#529	C₂×C₂₃	1	1	yes	characteristic
307	#2373	C₂×C₂₃	1	4	yes	complemented
308	#2370	C₂×C₂₃	1	2	yes	complemented
309	#2367	C₂×C₂₃	1	2	yes	complemented
310	#2357	C₂×C₂₃	1	1	yes	characteristic, complemented
311	#2356	C₂×C₂₃	1	1	yes	characteristic, complemented
312	#2351	C₂×C₂₃	1	1	yes	characteristic, complemented
313	#2349	C₂×C₂₃	1	1	yes	characteristic, complemented
314	#2347	C₂×C₂₃	1	2	yes	complemented
315	#2343	C₂×C₂₃	1	2	yes	complemented
316	#2322	C₂×C₂₃	1	4	yes	complemented
317	#2318	C₂×C₂₃	1	2	yes	complemented
318	C₄×C₂²⋊Q₈	C₂×C₂₃	1	2	yes	complemented
319	C₄×#121	C₂×C₂₃	1	2	yes	—
320	#2283	C₂×C₂₃	1	1	yes	characteristic, complemented
321	#2275	C₂×C₂₃	1	2	yes	complemented
322	C₂×C₄×C₄⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
323	C₂²×C₂₃	—	2	2	no	—
324	C₂²×C₂₃	—	2	2	no	—
325	C₂²×C₂₃	—	2	4	no	—
326	C₂²×C₂₃	—	2	4	no	—
327	C₂²×C₂₃	—	2	4	no	—
328	C₂²×C₂₃	—	2	4	no	—
329	C₂²×C₂₃	—	2	4	no	—
330	C₂²×C₂₃	—	4	4	no	—
331	C₂²×C₂₃	—	4	4	no	—
332	C₂²×C₂₃	C₄×#41	1	4	yes	—
333	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
334	C₂²×C₂₃	C₂²×#41	1	2	yes	—
335	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
336	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
337	C₂²×C₂₃	#585	1	2	yes	—
338	C₄×C₂₃	—	2	2	no	—
339	C₄×C₂₃	—	2	2	no	—
340	C₄×C₂₃	—	2	4	no	—
341	C₄×C₂₃	—	2	2	no	—
342	C₄×C₂₃	—	2	4	no	—
343	C₄×C₂₃	—	2	2	no	—
344	C₄×C₂₃	—	2	2	no	—
345	C₄×C₂₃	—	2	4	no	—
346	C₄×C₂₃	—	2	4	no	—
347	C₄×C₂₃	—	2	4	no	—
348	C₄×C₂₃	—	4	2	no	—
349	C₄×C₂₃	—	4	2	no	—
350	C₄×C₂₃	—	4	4	no	—
351	C₄×C₂₃	—	4	4	no	—
352	C₄×C₂₃	#520	1	4	yes	—
353	#529	C₄×C₂₃	1	16	yes	complemented
354	C₂×#126	C₂²×C₂₃	1	2	yes	—
355	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
356	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
357	C₂×#123	C₂²×C₂₃	1	2	yes	—
358	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
359	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
360	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
361	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
362	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	—
363	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
364	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
365	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
366	C₂×#117	C₂²×C₂₃	1	2	yes	—
367	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
368	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
369	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
370	#391	C₂²×C₂₃	1	2	yes	—
371	#390	C₂²×C₂₃	1	2	yes	—
372	#389	C₂²×C₂₃	1	4	yes	—
373	#389	C₂²×C₂₃	1	4	yes	—
374	#389	C₂²×C₂₃	1	2	yes	—
375	#389	C₂²×C₂₃	1	2	yes	—
376	#388	C₂²×C₂₃	1	4	yes	—
377	#388	C₂²×C₂₃	1	4	yes	—
378	#388	C₂²×C₂₃	1	4	yes	—
379	#388	C₂²×C₂₃	1	4	yes	—
380	#387	C₂²×C₂₃	1	4	yes	—
381	#387	C₂²×C₂₃	1	4	yes	—
382	#387	C₂²×C₂₃	1	4	yes	—
383	#387	C₂²×C₂₃	1	4	yes	—
384	#386	C₂²×C₂₃	1	4	yes	—
385	#385	C₂²×C₂₃	1	4	yes	—
386	#385	C₂²×C₂₃	1	4	yes	—
387	#385	C₂²×C₂₃	1	4	yes	—
388	#383	C₂²×C₂₃	1	2	yes	—
389	#383	C₂²×C₂₃	1	2	yes	—
390	#382	C₂²×C₂₃	1	2	yes	—
391	#382	C₂²×C₂₃	1	1	yes	characteristic
392	#382	C₂²×C₂₃	1	1	yes	characteristic
393	#381	C₂²×C₂₃	1	2	yes	—
394	#381	C₂²×C₂₃	1	2	yes	—
395	#380	C₂²×C₂₃	1	2	yes	—
396	#380	C₂²×C₂₃	1	2	yes	—
397	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
398	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
399	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
400	C₄×C₄⋊C₄	C₂²×C₂₃	1	4	yes	—
401	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
402	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
403	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
404	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
405	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
406	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
407	C₄×C₄⋊C₄	C₂²×C₂₃	1	4	yes	—
408	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
409	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
410	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
411	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
412	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
413	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
414	#376	C₂²×C₂₃	1	2	yes	—
415	#376	C₂²×C₂₃	1	2	yes	—
416	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
417	C₂×#95	C₂²×C₂₃	1	2	yes	—
418	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
419	C₂×C₂₃	—	2	4	no	—
420	C₂×C₂₃	—	4	4	no	—
421	C₂×C₂₃	C₂×C₄×#41	1	1	yes	characteristic
422	C₂×C₂₃	C₂×#520	1	1	yes	characteristic
423	C₂×C₂₃	#3428	1	1	yes	characteristic
424	C₂×C₂₃	#3505	1	2	yes	—
425	C₂×C₂₃	#3507	1	2	yes	—
426	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
427	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
428	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
429	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
430	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
431	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
432	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
433	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
434	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
435	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
436	#126	C₂×C₄×C₂₃	1	16	yes	complemented
437	#125	C₂×C₄×C₂₃	1	8	yes	complemented
438	#124	C₂×C₄×C₂₃	1	8	yes	complemented
439	#123	C₂×C₄×C₂₃	1	16	yes	complemented
440	C₂²⋊Q₈	C₂×C₄×C₂₃	1	8	yes	complemented
441	#121	C₂×C₄×C₂₃	1	8	yes	—
442	C₄×Q₈	—	4	4	no	—
443	C₄×Q₈	C₂×C₄×C₂₃	1	8	yes	complemented
444	C₄×D₄	—	2	16	no	—
445	C₄×D₄	—	4	4	no	—
446	C₄×D₄	C₂×C₄×C₂₃	1	8	yes	complemented
447	C₄×D₄	C₂×C₄×C₂₃	1	16	yes	complemented
448	#117	C₂×C₄×C₂₃	1	16	yes	complemented
449	C₂×C₄⋊C₄	—	2	8	no	—
450	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
451	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
452	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
453	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
454	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
455	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
456	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
457	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
458	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
459	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
460	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
461	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
463	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
464	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
465	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
466	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
467	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
468	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
474	C₂×C₄²	—	4	4	no	—
475	C₂×C₄²	C₂×C₄×C₂₃	1	8	yes	complemented
476	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
477	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
478	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
479	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
480	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
481	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
482	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
483	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
484	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
485	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
486	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
487	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
488	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
489	#95	C₂³×C₂₃	1	1	yes	characteristic
490	#95	C₂³×C₂₃	1	1	yes	characteristic
491	#95	C₂³×C₂₃	1	2	yes	—
492	#95	C₂³×C₂₃	1	2	yes	—
493	#95	C₂³×C₂₃	1	4	yes	—
494	#95	C₂³×C₂₃	1	1	yes	characteristic
495	#95	C₂³×C₂₃	1	1	yes	characteristic
496	#95	C₂³×C₂₃	1	2	yes	—
497	#95	C₂³×C₂₃	1	2	yes	—
498	#95	C₂³×C₂₃	1	4	yes	—
499	#95	C₂³×C₂₃	1	4	yes	—
500	#95	C₂³×C₂₃	1	2	yes	—
501	#95	C₂³×C₂₃	1	2	yes	—
502	#95	C₂³×C₂₃	1	4	yes	—
503	#95	C₂³×C₂₃	1	4	yes	—
504	#95	C₂³×C₂₃	1	4	yes	—
505	#95	C₂³×C₂₃	1	4	yes	—
506	#95	C₂³×C₂₃	1	4	yes	—
507	C₂₃	#34224	1	1	yes	characteristic, direct product factor, Sylow
508	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
509	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
510	C₂×Q₈	—	2	2	no	—
511	C₂×Q₈	—	2	2	no	—
512	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
513	C₂×D₄	—	2	8	no	—
514	C₂×D₄	—	2	2	no	—
515	C₂×D₄	—	2	2	no	—
516	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
517	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
518	C₂²×C₄	—	2	4	no	—
519	C₂²×C₄	—	2	2	no	—
520	C₂²×C₄	—	2	2	no	—
521	C₂²×C₄	—	2	4	no	—
522	C₂²×C₄	—	2	8	no	—
523	C₂²×C₄	—	4	2	no	—
524	C₂²×C₄	—	4	2	no	—
525	C₂²×C₄	—	4	2	no	—
526	C₂²×C₄	—	4	2	no	—
527	C₂²×C₄	—	4	4	no	—
528	C₂²×C₄	—	4	2	no	—
529	C₂²×C₄	—	4	4	no	—
530	C₂²×C₄	—	4	4	no	—
531	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
532	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
533	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
534	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	—
535	C₂²×C₄	#41×C₂₃	1	8	yes	—
536	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
537	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
538	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
539	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
540	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
541	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
542	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
543	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
544	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
545	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
546	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
547	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
548	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
550	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
551	C₄⋊C₄	—	2	4	no	—
552	C₄⋊C₄	—	2	4	no	—
553	C₄⋊C₄	—	2	4	no	—
554	C₄⋊C₄	—	2	4	no	—
555	C₄⋊C₄	—	2	8	no	—
556	C₄⋊C₄	—	2	4	no	—
557	C₄⋊C₄	—	2	4	no	—
558	C₄⋊C₄	—	4	4	no	—
559	C₄⋊C₄	—	4	4	no	—
560	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
561	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
562	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
563	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
564	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
565	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
566	C₂²⋊C₄	—	2	8	no	—
567	C₂²⋊C₄	—	2	8	no	—
568	C₂²⋊C₄	—	4	4	no	—
569	C₂²⋊C₄	—	4	4	no	—
570	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
571	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
572	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
573	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
574	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
575	C₄²	—	2	8	no	—
576	C₄²	—	2	4	no	—
577	C₄²	—	2	4	no	—
578	C₄²	—	4	2	no	—
579	C₄²	—	4	2	no	—
580	C₄²	—	4	4	no	—
581	C₄²	—	4	4	no	—
582	C₄²	—	4	4	no	—
583	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
584	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
585	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
586	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
587	C₄²	C₂²×C₄×C₂₃	1	8	yes	—
588	C₂³	—	2	1	no	—
589	C₂³	—	2	1	no	—
590	C₂³	—	2	2	no	—
591	C₂³	—	2	4	no	—
592	C₂³	—	2	2	no	—
593	C₂³	—	2	2	no	—
594	C₂³	—	2	4	no	—
595	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
596	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
597	C₂³	C₂×#41×C₂₃	1	4	yes	—
598	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
599	Q₈	—	2	8	no	—
600	D₄	—	2	16	no	—
601	D₄	—	2	8	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	8	no	—
617	C₂×C₄	—	2	8	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	4	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	4	no	—
626	C₂×C₄	—	2	4	no	—
627	C₂×C₄	—	2	4	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	4	4	no	—
631	C₂×C₄	—	4	8	no	—
632	C₂×C₄	—	4	8	no	—
633	C₂×C₄	—	4	8	no	—
634	C₂×C₄	—	8	8	no	—
635	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
636	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
637	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
638	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
639	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
640	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
641	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
642	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
643	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
644	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
645	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
646	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
647	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
648	C₂²	—	2	2	no	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	4	no	—
651	C₂²	—	2	4	no	—
652	C₂²	—	2	4	no	—
653	C₂²	—	2	4	no	—
654	C₂²	—	2	4	no	—
655	C₂²	—	4	4	no	—
656	C₂²	—	4	4	no	—
657	C₂²	C₄×#41×C₂₃	1	4	yes	—
658	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
659	C₂²	C₂²×#41×C₂₃	1	2	yes	—
660	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
661	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
662	C₂²	C₂₃×#585	1	2	yes	—
663	C₄	—	2	2	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	4	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	4	no	—
668	C₄	—	2	2	no	—
669	C₄	—	2	2	no	—
670	C₄	—	2	4	no	—
671	C₄	—	2	4	no	—
672	C₄	—	2	4	no	—
673	C₄	—	4	2	no	—
674	C₄	—	4	2	no	—
675	C₄	—	4	4	no	—
676	C₄	—	4	4	no	—
677	C₄	C₂₃×#520	1	4	yes	—
678	C₂	—	2	4	no	—
679	C₂	—	4	4	no	—
680	C₂	C₂×C₄×#41×C₂₃	1	1	yes	characteristic
681	C₂	C₂×C₂₃×#520	1	1	yes	characteristic
682	C₂	C₂₃×#3428	1	1	yes	characteristic
683	C₂	C₂₃×#3505	1	2	yes	—
684	C₂	C₂₃×#3507	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂×C₂₃×#121	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2373	C₂	semidirect
3. C₂₃×#2370	C₂	semidirect
4. C₂₃×#2367	C₂	semidirect
5. C₂₃×#2357	C₂	semidirect
6. C₂₃×#2356	C₂	semidirect
7. C₂₃×#2351	C₂	semidirect
8. C₂₃×#2349	C₂	semidirect
9. C₂₃×#2347	C₂	semidirect
10. C₂₃×#2343	C₂	semidirect
11. C₂₃×#2322	C₂	semidirect
12. C₂₃×#2318	C₂	semidirect
13. C₄×C₂₃×C₂²⋊Q₈	C₂	semidirect
15. C₂₃×#2283	C₂	semidirect
16. C₂₃×#2275	C₂	semidirect
17. C₂×C₄×C₄⋊C₄×C₂₃	C₂	semidirect
18. C₂₃×#529	C₄	semidirect
94. C₂₃×#126	C₂×C₄	semidirect
95. C₂₃×#125	C₂×C₄	semidirect
96. C₂₃×#124	C₂×C₄	semidirect
97. C₂₃×#123	C₂×C₄	semidirect
98. C₂₃×C₂²⋊Q₈	C₂×C₄	semidirect
101. C₄×Q₈×C₂₃	C₂×C₄	semidirect
104. C₄×D₄×C₂₃	C₂×C₄	semidirect
105. C₄×D₄×C₂₃	C₂×C₄	semidirect
106. C₂₃×#117	C₂×C₄	semidirect
133. C₂×C₄²×C₂₃	C₂×C₄	semidirect
245. #34224	C₂₃	direct (N × H)
307. #2373	C₂×C₂₃	semidirect
308. #2370	C₂×C₂₃	semidirect
309. #2367	C₂×C₂₃	semidirect
310. #2357	C₂×C₂₃	semidirect
311. #2356	C₂×C₂₃	semidirect
312. #2351	C₂×C₂₃	semidirect
313. #2349	C₂×C₂₃	semidirect
314. #2347	C₂×C₂₃	semidirect
315. #2343	C₂×C₂₃	semidirect
316. #2322	C₂×C₂₃	semidirect
317. #2318	C₂×C₂₃	semidirect
318. C₄×C₂²⋊Q₈	C₂×C₂₃	semidirect
320. #2283	C₂×C₂₃	semidirect
321. #2275	C₂×C₂₃	semidirect
322. C₂×C₄×C₄⋊C₄	C₂×C₂₃	semidirect
353. #529	C₄×C₂₃	semidirect
436. #126	C₂×C₄×C₂₃	semidirect
437. #125	C₂×C₄×C₂₃	semidirect
438. #124	C₂×C₄×C₂₃	semidirect
439. #123	C₂×C₄×C₂₃	semidirect
440. C₂²⋊Q₈	C₂×C₄×C₂₃	semidirect
443. C₄×Q₈	C₂×C₄×C₂₃	semidirect
446. C₄×D₄	C₂×C₄×C₂₃	semidirect
447. C₄×D₄	C₂×C₄×C₂₃	semidirect
448. #117	C₂×C₄×C₂₃	semidirect
475. C₂×C₄²	C₂×C₄×C₂₃	semidirect
507. C₂₃	#34224	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#529	2
C₂₃×#2373	2
C₂₃×#2370	2
C₂₃×#2367	2
C₂₃×#2357	2
C₂₃×#2356	2
C₂₃×#2351	2
C₂₃×#2349	2
C₂₃×#2347	2
C₂₃×#2343	2
C₂₃×#2322	2
C₂₃×#2318	2
C₄×C₂₃×C₂²⋊Q₈	2
C₄×C₂₃×#121	2
C₂₃×#2283	2
C₂₃×#2275	2
C₂×C₄×C₄⋊C₄×C₂₃	2
#34224	23

Subgroups — C23×#34224 #19181850

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#34224 #19181850