Subgroups — C₂₃×#34396 #19182022

Order 5888.

2486 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#525	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2378	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2377	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2359	C₂	1	4	yes	maximal, complemented
5	C₂₃×#2357	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2353	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2343	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2339	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2333	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2332	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2321	C₂	1	4	yes	maximal, complemented
12	C₂₃×#2319	C₂	1	2	yes	maximal, complemented
13	C₂₃×#2318	C₂	1	2	yes	maximal, complemented
14	C₂₃×#2280	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₃×#381	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
18	C₂₃×#525	C₄	1	16	yes	complemented
19	C₂×C₂₃×#123	C₂²	1	2	yes	—
20	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#120	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	—
26	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
28	C₂×C₂₃×#117	C₂²	1	2	yes	—
29	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
31	C₂₃×#391	C₂²	1	4	yes	complemented
32	C₂₃×#390	C₂²	1	4	yes	—
33	C₂₃×#390	C₂²	1	4	yes	—
34	C₂₃×#389	C₂²	1	4	yes	complemented
35	C₂₃×#388	C₂²	1	4	yes	—
36	C₂₃×#388	C₂²	1	4	yes	—
37	C₂₃×#388	C₂²	1	4	yes	—
38	C₂₃×#388	C₂²	1	4	yes	—
39	C₂₃×#388	C₂²	1	4	yes	complemented
40	C₂₃×#388	C₂²	1	4	yes	complemented
41	C₂₃×#387	C₂²	1	4	yes	complemented
42	C₂₃×#387	C₂²	1	4	yes	complemented
43	C₂₃×#387	C₂²	1	4	yes	complemented
44	C₂₃×#387	C₂²	1	4	yes	complemented
45	C₂₃×#386	C₂²	1	4	yes	—
46	C₂₃×#386	C₂²	1	4	yes	—
47	C₂₃×#386	C₂²	1	4	yes	—
48	C₂₃×#386	C₂²	1	4	yes	complemented
49	C₂₃×#385	C₂²	1	4	yes	—
50	C₂₃×#385	C₂²	1	4	yes	complemented
51	C₂₃×#383	C₂²	1	2	yes	complemented
52	C₂₃×#382	C₂²	1	2	yes	complemented
53	C₂₃×#381	C₂²	1	1	yes	characteristic
54	C₂₃×#381	C₂²	1	1	yes	characteristic
55	C₂₃×#381	C₂²	1	2	yes	—
56	C₂₃×#381	C₂²	1	2	yes	—
57	C₂₃×#381	C₂²	1	2	yes	—
58	C₂₃×#381	C₂²	1	2	yes	—
59	C₂₃×#381	C₂²	1	2	yes	complemented
60	C₂₃×#380	C₂²	1	2	yes	—
61	C₂₃×#380	C₂²	1	2	yes	—
62	C₂₃×#380	C₂²	1	2	yes	complemented
63	C₂₃×#379	C₂²	1	2	yes	—
64	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
65	C₄×C₄⋊C₄×C₂₃	C₂²	1	4	yes	complemented
66	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
67	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
68	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
69	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
70	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
71	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	complemented
72	C₂₃×#376	C₂²	1	2	yes	complemented
73	C₂×C₂₃×#95	C₂²	1	2	yes	—
74	C₂×C₂₃×#95	C₂²	1	2	yes	—
75	C₂×C₂₃×#95	C₂²	1	2	yes	complemented
76	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
77	C₂×#41×C₂₃	—	4	4	no	—
78	C₂×#41×C₂₃	C₂×C₄	1	8	yes	—
79	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
81	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
83	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
84	C₂³×C₄×C₂₃	—	4	4	no	—
85	C₂³×C₄×C₂₃	C₂×C₄	1	8	yes	complemented
86	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
89	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
90	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
95	C₂₃×#123	C₂×C₄	1	16	yes	complemented
96	C₂₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
97	C₂₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
98	C₂₃×#121	C₂×C₄	1	8	yes	complemented
99	C₂₃×#121	C₂×C₄	1	8	yes	complemented
100	C₂₃×#120	C₂×C₄	1	16	yes	complemented
101	C₄×D₄×C₂₃	—	4	8	no	—
102	C₄×D₄×C₂₃	C₂×C₄	1	16	yes	complemented
103	C₄×D₄×C₂₃	C₂×C₄	1	16	yes	complemented
104	C₂₃×#117	—	4	4	no	—
105	C₂₃×#117	C₂×C₄	1	8	yes	complemented
106	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
107	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
108	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
110	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
114	C₂×C₂²⋊C₄×C₂₃	—	4	4	no	—
115	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
116	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
117	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
118	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
119	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
121	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
122	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	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×C₄²×C₂₃	C₂³	1	4	yes	—
131	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
132	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
133	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
134	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
135	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
136	C₂₃×#95	C₂³	1	2	yes	—
137	C₂₃×#95	C₂³	1	2	yes	—
138	C₂₃×#95	C₂³	1	4	yes	—
139	C₂₃×#95	C₂³	1	2	yes	—
140	C₂₃×#95	C₂³	1	4	yes	—
141	C₂₃×#95	C₂³	1	2	yes	—
142	C₂₃×#95	C₂³	1	2	yes	—
143	C₂₃×#95	C₂³	1	4	yes	—
144	C₂₃×#95	C₂³	1	4	yes	—
145	C₂₃×#95	C₂³	1	2	yes	—
146	C₂₃×#95	C₂³	1	4	yes	—
147	C₂₃×#95	C₂³	1	4	yes	—
148	C₂₃×#95	C₂³	1	4	yes	—
149	C₂₃×#95	C₂³	1	4	yes	—
150	C₂₃×#95	C₂³	1	4	yes	—
151	C₂⁴×C₂₃	—	2	4	no	—
152	C₂⁴×C₂₃	—	4	2	no	—
153	C₂⁴×C₂₃	—	4	2	no	—
154	C₂⁴×C₂₃	C₂²×C₄	1	4	yes	—
155	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
156	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
157	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
158	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
159	#41×C₂₃	—	4	16	no	—
160	C₂×Q₈×C₂₃	—	4	2	no	—
161	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
162	C₂×D₄×C₂₃	—	2	8	no	—
163	C₂×D₄×C₂₃	—	4	2	no	—
164	C₂×D₄×C₂₃	—	4	4	no	—
165	C₂×D₄×C₂₃	—	4	2	no	—
166	C₂×D₄×C₂₃	—	4	2	no	—
167	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
168	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
169	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
170	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
171	C₂²×C₄×C₂₃	—	2	4	no	—
172	C₂²×C₄×C₂₃	—	2	4	no	—
173	C₂²×C₄×C₂₃	—	2	8	no	—
174	C₂²×C₄×C₂₃	—	4	16	no	—
175	C₂²×C₄×C₂₃	—	4	2	no	—
176	C₂²×C₄×C₂₃	—	4	2	no	—
177	C₂²×C₄×C₂₃	—	4	2	no	—
178	C₂²×C₄×C₂₃	—	4	2	no	—
179	C₂²×C₄×C₂₃	—	4	4	no	—
180	C₂²×C₄×C₂₃	—	4	4	no	—
181	C₂²×C₄×C₂₃	—	4	4	no	—
182	C₂²×C₄×C₂₃	—	4	4	no	—
183	C₂²×C₄×C₂₃	—	4	4	no	—
184	C₂²×C₄×C₂₃	—	4	4	no	—
185	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
186	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
187	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
188	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
189	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	—
190	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
191	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
192	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
193	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
194	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
195	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
196	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
201	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
203	C₄⋊C₄×C₂₃	—	4	4	no	—
204	C₄⋊C₄×C₂₃	—	4	4	no	—
205	C₄⋊C₄×C₂₃	—	4	4	no	—
206	C₄⋊C₄×C₂₃	—	4	4	no	—
207	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
208	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
209	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
210	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
211	C₂²⋊C₄×C₂₃	—	2	8	no	—
212	C₂²⋊C₄×C₂₃	—	4	2	no	—
213	C₂²⋊C₄×C₂₃	—	4	4	no	—
214	C₂²⋊C₄×C₂₃	—	4	2	no	—
215	C₂²⋊C₄×C₂₃	—	4	4	no	—
216	C₂²⋊C₄×C₂₃	—	4	2	no	—
217	C₂²⋊C₄×C₂₃	—	4	4	no	—
218	C₂²⋊C₄×C₂₃	—	4	2	no	—
219	C₂²⋊C₄×C₂₃	—	4	4	no	—
220	C₂²⋊C₄×C₂₃	—	4	4	no	—
221	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
222	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
223	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
224	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
225	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
226	C₄²×C₂₃	—	4	4	no	—
227	C₄²×C₂₃	—	4	4	no	—
228	C₄²×C₂₃	—	4	2	no	—
229	C₄²×C₂₃	—	4	2	no	—
230	C₄²×C₂₃	—	4	4	no	—
231	C₄²×C₂₃	C₂²×C₄	1	8	yes	—
232	#34396	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
233	C₂³×C₂₃	—	2	2	no	—
234	C₂³×C₂₃	—	2	2	no	—
235	C₂³×C₂₃	—	2	8	no	—
236	C₂³×C₂₃	—	2	2	no	—
237	C₂³×C₂₃	—	2	2	no	—
238	C₂³×C₂₃	—	2	4	no	—
239	C₂³×C₂₃	—	2	2	no	—
240	C₂³×C₂₃	—	2	2	no	—
241	C₂³×C₂₃	—	2	2	no	—
242	C₂³×C₂₃	—	2	4	no	—
243	C₂³×C₂₃	—	2	2	no	—
244	C₂³×C₂₃	—	2	2	no	—
245	C₂³×C₂₃	—	2	2	no	—
246	C₂³×C₂₃	—	4	4	no	—
247	C₂³×C₂₃	—	4	4	no	—
248	C₂³×C₂₃	—	4	16	no	—
249	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
250	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
251	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
252	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
253	C₂³×C₂₃	H(5,𝔽₂)	1	4	yes	—
254	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
255	Q₈×C₂₃	—	4	4	no	—
256	D₄×C₂₃	—	2	16	no	—
257	D₄×C₂₃	—	4	8	no	—
258	D₄×C₂₃	—	4	8	no	—
259	D₄×C₂₃	—	4	4	no	—
260	C₂×C₄×C₂₃	—	2	8	no	—
261	C₂×C₄×C₂₃	—	2	8	no	—
262	C₂×C₄×C₂₃	—	2	2	no	—
263	C₂×C₄×C₂₃	—	2	4	no	—
264	C₂×C₄×C₂₃	—	2	2	no	—
265	C₂×C₄×C₂₃	—	2	2	no	—
266	C₂×C₄×C₂₃	—	2	2	no	—
267	C₂×C₄×C₂₃	—	2	2	no	—
268	C₂×C₄×C₂₃	—	2	4	no	—
269	C₂×C₄×C₂₃	—	2	2	no	—
270	C₂×C₄×C₂₃	—	2	4	no	—
271	C₂×C₄×C₂₃	—	2	4	no	—
272	C₂×C₄×C₂₃	—	2	4	no	—
273	C₂×C₄×C₂₃	—	2	4	no	—
274	C₂×C₄×C₂₃	—	2	4	no	—
275	C₂×C₄×C₂₃	—	2	4	no	—
276	C₂×C₄×C₂₃	—	2	4	no	—
277	C₂×C₄×C₂₃	—	2	4	no	—
278	C₂×C₄×C₂₃	—	2	4	no	—
279	C₂×C₄×C₂₃	—	2	4	no	—
280	C₂×C₄×C₂₃	—	2	4	no	—
281	C₂×C₄×C₂₃	—	2	4	no	—
282	C₂×C₄×C₂₃	—	4	4	no	—
283	C₂×C₄×C₂₃	—	4	4	no	—
284	C₂×C₄×C₂₃	—	4	4	no	—
285	C₂×C₄×C₂₃	—	4	4	no	—
286	C₂×C₄×C₂₃	—	4	8	no	—
287	C₂×C₄×C₂₃	—	8	8	no	—
288	C₂×C₄×C₂₃	—	8	8	no	—
289	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
290	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
291	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
292	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
293	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
294	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
295	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
296	C₂×#525	C₂×C₂₃	1	1	yes	characteristic
297	#2378	C₂×C₂₃	1	2	yes	complemented
298	#2377	C₂×C₂₃	1	2	yes	complemented
299	#2359	C₂×C₂₃	1	4	yes	complemented
300	#2357	C₂×C₂₃	1	2	yes	complemented
301	#2353	C₂×C₂₃	1	2	yes	complemented
302	#2343	C₂×C₂₃	1	2	yes	complemented
303	#2339	C₂×C₂₃	1	2	yes	complemented
304	#2333	C₂×C₂₃	1	2	yes	complemented
305	#2332	C₂×C₂₃	1	2	yes	complemented
306	#2321	C₂×C₂₃	1	4	yes	complemented
307	#2319	C₂×C₂₃	1	2	yes	complemented
308	#2318	C₂×C₂₃	1	2	yes	complemented
309	#2280	C₂×C₂₃	1	1	yes	characteristic, complemented
310	C₂×#381	C₂×C₂₃	1	1	yes	characteristic, complemented
311	C₂²×C₂₃	—	2	2	no	—
312	C₂²×C₂₃	—	2	2	no	—
313	C₂²×C₂₃	—	2	8	no	—
314	C₂²×C₂₃	—	2	2	no	—
315	C₂²×C₂₃	—	2	2	no	—
316	C₂²×C₂₃	—	2	4	no	—
317	C₂²×C₂₃	—	2	2	no	—
318	C₂²×C₂₃	—	2	2	no	—
319	C₂²×C₂₃	—	2	4	no	—
320	C₂²×C₂₃	—	2	4	no	—
321	C₂²×C₂₃	—	2	2	no	—
322	C₂²×C₂₃	—	2	2	no	—
323	C₂²×C₂₃	—	4	16	no	—
324	C₂²×C₂₃	—	4	4	no	—
325	C₂²×C₂₃	—	4	4	no	—
326	C₂²×C₂₃	—	4	4	no	—
327	C₂²×C₂₃	—	4	4	no	—
328	C₂²×C₂₃	#518	1	4	yes	—
329	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
330	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
331	C₂²×C₂₃	#585	1	2	yes	—
332	C₂²×C₂₃	#585	1	2	yes	—
333	C₄×C₂₃	—	2	2	no	—
334	C₄×C₂₃	—	2	2	no	—
335	C₄×C₂₃	—	2	2	no	—
336	C₄×C₂₃	—	2	2	no	—
337	C₄×C₂₃	—	2	4	no	—
338	C₄×C₂₃	—	2	4	no	—
339	C₄×C₂₃	—	2	4	no	—
340	C₄×C₂₃	—	4	4	no	—
341	C₄×C₂₃	—	4	4	no	—
342	C₄×C₂₃	—	4	4	no	—
343	C₄×C₂₃	—	4	4	no	—
344	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
345	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
346	#525	C₄×C₂₃	1	16	yes	complemented
347	C₂×#123	C₂²×C₂₃	1	2	yes	—
348	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
349	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
350	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
351	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
352	C₂×#120	C₂²×C₂₃	1	2	yes	—
353	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	—
354	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
355	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
356	C₂×#117	C₂²×C₂₃	1	2	yes	—
357	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
358	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
359	#391	C₂²×C₂₃	1	4	yes	complemented
360	#390	C₂²×C₂₃	1	4	yes	—
361	#390	C₂²×C₂₃	1	4	yes	—
362	#389	C₂²×C₂₃	1	4	yes	complemented
363	#388	C₂²×C₂₃	1	4	yes	—
364	#388	C₂²×C₂₃	1	4	yes	—
365	#388	C₂²×C₂₃	1	4	yes	—
366	#388	C₂²×C₂₃	1	4	yes	—
367	#388	C₂²×C₂₃	1	4	yes	complemented
368	#388	C₂²×C₂₃	1	4	yes	complemented
369	#387	C₂²×C₂₃	1	4	yes	complemented
370	#387	C₂²×C₂₃	1	4	yes	complemented
371	#387	C₂²×C₂₃	1	4	yes	complemented
372	#387	C₂²×C₂₃	1	4	yes	complemented
373	#386	C₂²×C₂₃	1	4	yes	—
374	#386	C₂²×C₂₃	1	4	yes	—
375	#386	C₂²×C₂₃	1	4	yes	—
376	#386	C₂²×C₂₃	1	4	yes	complemented
377	#385	C₂²×C₂₃	1	4	yes	—
378	#385	C₂²×C₂₃	1	4	yes	complemented
379	#383	C₂²×C₂₃	1	2	yes	complemented
380	#382	C₂²×C₂₃	1	2	yes	complemented
381	#381	C₂²×C₂₃	1	1	yes	characteristic
382	#381	C₂²×C₂₃	1	1	yes	characteristic
383	#381	C₂²×C₂₃	1	2	yes	—
384	#381	C₂²×C₂₃	1	2	yes	—
385	#381	C₂²×C₂₃	1	2	yes	—
386	#381	C₂²×C₂₃	1	2	yes	—
387	#381	C₂²×C₂₃	1	2	yes	complemented
388	#380	C₂²×C₂₃	1	2	yes	—
389	#380	C₂²×C₂₃	1	2	yes	—
390	#380	C₂²×C₂₃	1	2	yes	complemented
391	#379	C₂²×C₂₃	1	2	yes	—
392	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
393	C₄×C₄⋊C₄	C₂²×C₂₃	1	4	yes	complemented
394	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
395	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
396	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
397	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
398	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
399	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	complemented
400	#376	C₂²×C₂₃	1	2	yes	complemented
401	C₂×#95	C₂²×C₂₃	1	2	yes	—
402	C₂×#95	C₂²×C₂₃	1	2	yes	—
403	C₂×#95	C₂²×C₂₃	1	2	yes	complemented
404	C₂×C₂₃	—	2	4	no	—
405	C₂×C₂₃	—	4	4	no	—
406	C₂×C₂₃	—	4	2	no	—
407	C₂×C₂₃	—	4	2	no	—
408	C₂×C₂₃	C₂×#518	1	1	yes	characteristic
409	C₂×C₂₃	#3428	1	1	yes	characteristic
410	C₂×C₂₃	#3428	1	1	yes	characteristic
411	C₂×C₂₃	#3533	1	4	yes	—
412	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
413	C₂×#41	—	4	4	no	—
414	C₂×#41	C₂×C₄×C₂₃	1	8	yes	—
415	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
416	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
417	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
418	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
419	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
420	C₂³×C₄	—	4	4	no	—
421	C₂³×C₄	C₂×C₄×C₂₃	1	8	yes	complemented
422	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
423	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
424	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
425	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
426	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
427	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
428	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
429	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
430	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
431	#123	C₂×C₄×C₂₃	1	16	yes	complemented
432	C₂²⋊Q₈	C₂×C₄×C₂₃	1	8	yes	complemented
433	C₂²⋊Q₈	C₂×C₄×C₂₃	1	8	yes	complemented
434	#121	C₂×C₄×C₂₃	1	8	yes	complemented
435	#121	C₂×C₄×C₂₃	1	8	yes	complemented
436	#120	C₂×C₄×C₂₃	1	16	yes	complemented
437	C₄×D₄	—	4	8	no	—
438	C₄×D₄	C₂×C₄×C₂₃	1	16	yes	complemented
439	C₄×D₄	C₂×C₄×C₂₃	1	16	yes	complemented
440	#117	—	4	4	no	—
441	#117	C₂×C₄×C₂₃	1	8	yes	complemented
442	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
443	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
444	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
445	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
446	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
449	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
450	C₂×C₂²⋊C₄	—	4	4	no	—
451	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
462	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
463	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
464	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
465	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
466	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
467	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
468	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
469	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
470	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
471	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
472	#95	C₂³×C₂₃	1	2	yes	—
473	#95	C₂³×C₂₃	1	2	yes	—
474	#95	C₂³×C₂₃	1	4	yes	—
475	#95	C₂³×C₂₃	1	2	yes	—
476	#95	C₂³×C₂₃	1	4	yes	—
477	#95	C₂³×C₂₃	1	2	yes	—
478	#95	C₂³×C₂₃	1	2	yes	—
479	#95	C₂³×C₂₃	1	4	yes	—
480	#95	C₂³×C₂₃	1	4	yes	—
481	#95	C₂³×C₂₃	1	2	yes	—
482	#95	C₂³×C₂₃	1	4	yes	—
483	#95	C₂³×C₂₃	1	4	yes	—
484	#95	C₂³×C₂₃	1	4	yes	—
485	#95	C₂³×C₂₃	1	4	yes	—
486	#95	C₂³×C₂₃	1	4	yes	—
487	C₂₃	#34396	1	1	yes	characteristic, direct product factor, Sylow
488	C₂⁴	—	2	4	no	—
489	C₂⁴	—	4	2	no	—
490	C₂⁴	—	4	2	no	—
491	C₂⁴	C₂²×C₄×C₂₃	1	4	yes	—
492	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
493	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
494	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
495	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
496	#41	—	4	16	no	—
497	C₂×Q₈	—	4	2	no	—
498	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
499	C₂×D₄	—	2	8	no	—
500	C₂×D₄	—	4	2	no	—
501	C₂×D₄	—	4	2	no	—
502	C₂×D₄	—	4	4	no	—
503	C₂×D₄	—	4	2	no	—
504	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
505	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
506	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
507	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
508	C₂²×C₄	—	2	4	no	—
509	C₂²×C₄	—	2	4	no	—
510	C₂²×C₄	—	2	8	no	—
511	C₂²×C₄	—	4	16	no	—
512	C₂²×C₄	—	4	2	no	—
513	C₂²×C₄	—	4	2	no	—
514	C₂²×C₄	—	4	2	no	—
515	C₂²×C₄	—	4	2	no	—
516	C₂²×C₄	—	4	4	no	—
517	C₂²×C₄	—	4	4	no	—
518	C₂²×C₄	—	4	4	no	—
519	C₂²×C₄	—	4	4	no	—
520	C₂²×C₄	—	4	4	no	—
521	C₂²×C₄	—	4	4	no	—
522	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
523	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
524	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
525	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
526	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	—
527	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
528	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
529	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
530	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
531	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
532	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
533	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
534	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
535	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
536	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
537	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
538	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
539	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
540	C₄⋊C₄	—	4	4	no	—
541	C₄⋊C₄	—	4	4	no	—
542	C₄⋊C₄	—	4	4	no	—
543	C₄⋊C₄	—	4	4	no	—
544	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
545	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
546	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
547	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
548	C₂²⋊C₄	—	2	8	no	—
549	C₂²⋊C₄	—	4	2	no	—
550	C₂²⋊C₄	—	4	4	no	—
551	C₂²⋊C₄	—	4	2	no	—
552	C₂²⋊C₄	—	4	4	no	—
553	C₂²⋊C₄	—	4	4	no	—
554	C₂²⋊C₄	—	4	2	no	—
555	C₂²⋊C₄	—	4	4	no	—
556	C₂²⋊C₄	—	4	2	no	—
557	C₂²⋊C₄	—	4	4	no	—
558	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
559	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
560	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
561	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
562	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
563	C₄²	—	4	2	no	—
564	C₄²	—	4	2	no	—
565	C₄²	—	4	4	no	—
566	C₄²	—	4	4	no	—
567	C₄²	—	4	4	no	—
568	C₄²	C₂²×C₄×C₂₃	1	8	yes	—
569	C₂³	—	2	2	no	—
570	C₂³	—	2	2	no	—
571	C₂³	—	2	2	no	—
572	C₂³	—	2	2	no	—
573	C₂³	—	2	4	no	—
574	C₂³	—	2	2	no	—
575	C₂³	—	2	2	no	—
576	C₂³	—	2	2	no	—
577	C₂³	—	2	4	no	—
578	C₂³	—	2	2	no	—
579	C₂³	—	2	2	no	—
580	C₂³	—	2	2	no	—
581	C₂³	—	2	8	no	—
582	C₂³	—	4	4	no	—
583	C₂³	—	4	4	no	—
584	C₂³	—	4	16	no	—
585	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
586	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
587	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
588	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
589	C₂³	C₂₃×H(5,𝔽₂)	1	4	yes	—
590	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
591	Q₈	—	4	4	no	—
592	D₄	—	2	16	no	—
593	D₄	—	4	4	no	—
594	D₄	—	4	8	no	—
595	D₄	—	4	8	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	8	no	—
605	C₂×C₄	—	2	8	no	—
606	C₂×C₄	—	2	4	no	—
607	C₂×C₄	—	2	4	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	2	4	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	4	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	4	4	no	—
619	C₂×C₄	—	4	4	no	—
620	C₂×C₄	—	4	4	no	—
621	C₂×C₄	—	4	4	no	—
622	C₂×C₄	—	4	8	no	—
623	C₂×C₄	—	8	8	no	—
624	C₂×C₄	—	8	8	no	—
625	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
626	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
627	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
628	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
629	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
630	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
631	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	8	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	4	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	2	4	no	—
641	C₂²	—	2	4	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	4	16	no	—
645	C₂²	—	4	4	no	—
646	C₂²	—	4	4	no	—
647	C₂²	—	4	4	no	—
648	C₂²	—	4	4	no	—
649	C₂²	C₂₃×#518	1	4	yes	—
650	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
651	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
652	C₂²	C₂₃×#585	1	2	yes	—
653	C₂²	C₂₃×#585	1	2	yes	—
654	C₄	—	2	2	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	4	no	—
659	C₄	—	2	4	no	—
660	C₄	—	2	4	no	—
661	C₄	—	4	4	no	—
662	C₄	—	4	4	no	—
663	C₄	—	4	4	no	—
664	C₄	—	4	4	no	—
665	C₂	—	2	4	no	—
666	C₂	—	4	2	no	—
667	C₂	—	4	2	no	—
668	C₂	—	4	4	no	—
669	C₂	C₂×C₂₃×#518	1	1	yes	characteristic
670	C₂	C₂₃×#3428	1	1	yes	characteristic
671	C₂	C₂₃×#3428	1	1	yes	characteristic
672	C₂	C₂₃×#3533	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂×C₂₃×#525	C₂
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×#2378	C₂	semidirect
3. C₂₃×#2377	C₂	semidirect
4. C₂₃×#2359	C₂	semidirect
5. C₂₃×#2357	C₂	semidirect
6. C₂₃×#2353	C₂	semidirect
7. C₂₃×#2343	C₂	semidirect
8. C₂₃×#2339	C₂	semidirect
9. C₂₃×#2333	C₂	semidirect
10. C₂₃×#2332	C₂	semidirect
11. C₂₃×#2321	C₂	semidirect
12. C₂₃×#2319	C₂	semidirect
13. C₂₃×#2318	C₂	semidirect
14. C₂₃×#2280	C₂	semidirect
15. C₂×C₂₃×#381	C₂	semidirect
18. C₂₃×#525	C₄	semidirect
31. C₂₃×#391	C₂²	semidirect
34. C₂₃×#389	C₂²	semidirect
39. C₂₃×#388	C₂²	semidirect
40. C₂₃×#388	C₂²	semidirect
41. C₂₃×#387	C₂²	semidirect
42. C₂₃×#387	C₂²	semidirect
43. C₂₃×#387	C₂²	semidirect
44. C₂₃×#387	C₂²	semidirect
48. C₂₃×#386	C₂²	semidirect
50. C₂₃×#385	C₂²	semidirect
51. C₂₃×#383	C₂²	semidirect
52. C₂₃×#382	C₂²	semidirect
59. C₂₃×#381	C₂²	semidirect
62. C₂₃×#380	C₂²	semidirect
64. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
65. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
70. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
71. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
72. C₂₃×#376	C₂²	semidirect
75. C₂×C₂₃×#95	C₂²	semidirect
85. C₂³×C₄×C₂₃	C₂×C₄	semidirect
95. C₂₃×#123	C₂×C₄	semidirect
96. C₂₃×C₂²⋊Q₈	C₂×C₄	semidirect
97. C₂₃×C₂²⋊Q₈	C₂×C₄	semidirect
98. C₂₃×#121	C₂×C₄	semidirect
99. C₂₃×#121	C₂×C₄	semidirect
100. C₂₃×#120	C₂×C₄	semidirect
102. C₄×D₄×C₂₃	C₂×C₄	semidirect
103. C₄×D₄×C₂₃	C₂×C₄	semidirect
105. C₂₃×#117	C₂×C₄	semidirect
232. #34396	C₂₃	direct (N × H)
297. #2378	C₂×C₂₃	semidirect
298. #2377	C₂×C₂₃	semidirect
299. #2359	C₂×C₂₃	semidirect
300. #2357	C₂×C₂₃	semidirect
301. #2353	C₂×C₂₃	semidirect
302. #2343	C₂×C₂₃	semidirect
303. #2339	C₂×C₂₃	semidirect
304. #2333	C₂×C₂₃	semidirect
305. #2332	C₂×C₂₃	semidirect
306. #2321	C₂×C₂₃	semidirect
307. #2319	C₂×C₂₃	semidirect
308. #2318	C₂×C₂₃	semidirect
309. #2280	C₂×C₂₃	semidirect
310. C₂×#381	C₂×C₂₃	semidirect
346. #525	C₄×C₂₃	semidirect
359. #391	C₂²×C₂₃	semidirect
362. #389	C₂²×C₂₃	semidirect
367. #388	C₂²×C₂₃	semidirect
368. #388	C₂²×C₂₃	semidirect
369. #387	C₂²×C₂₃	semidirect
370. #387	C₂²×C₂₃	semidirect
371. #387	C₂²×C₂₃	semidirect
372. #387	C₂²×C₂₃	semidirect
376. #386	C₂²×C₂₃	semidirect
378. #385	C₂²×C₂₃	semidirect
379. #383	C₂²×C₂₃	semidirect
380. #382	C₂²×C₂₃	semidirect
387. #381	C₂²×C₂₃	semidirect
390. #380	C₂²×C₂₃	semidirect
392. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
393. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
398. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
399. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
400. #376	C₂²×C₂₃	semidirect
403. C₂×#95	C₂²×C₂₃	semidirect
421. C₂³×C₄	C₂×C₄×C₂₃	semidirect
431. #123	C₂×C₄×C₂₃	semidirect
432. C₂²⋊Q₈	C₂×C₄×C₂₃	semidirect
433. C₂²⋊Q₈	C₂×C₄×C₂₃	semidirect
434. #121	C₂×C₄×C₂₃	semidirect
435. #121	C₂×C₄×C₂₃	semidirect
436. #120	C₂×C₄×C₂₃	semidirect
438. C₄×D₄	C₂×C₄×C₂₃	semidirect
439. C₄×D₄	C₂×C₄×C₂₃	semidirect
441. #117	C₂×C₄×C₂₃	semidirect
487. C₂₃	#34396	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×#525	2
C₂₃×#2378	2
C₂₃×#2377	2
C₂₃×#2359	2
C₂₃×#2357	2
C₂₃×#2353	2
C₂₃×#2343	2
C₂₃×#2339	2
C₂₃×#2333	2
C₂₃×#2332	2
C₂₃×#2321	2
C₂₃×#2319	2
C₂₃×#2318	2
C₂₃×#2280	2
C₂×C₂₃×#381	2
#34396	23

Subgroups — C23×#34396 #19182022

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#34396 #19182022