Subgroups — C₂₃×#62788 #19210414

Order 5888.

7094 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3523	C₂	1	4	yes	maximal, complemented
2	C₂₃×#3522	C₂	1	4	yes	maximal, complemented
3	C₂₃×#3516	C₂	1	8	yes	maximal, complemented
4	C₂₃×#3507	C₂	1	6	yes	maximal, complemented
5	C₂₃×#3502	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#3497	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#3492	C₂	1	6	yes	maximal, complemented
8	C₂₃×#3486	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3482	C₂	1	8	yes	maximal, complemented
10	C₂₃×#3480	C₂	1	4	yes	maximal, complemented
11	Q₈×#41×C₂₃	C₂	1	4	yes	maximal, complemented
12	C₂₃×#3461	C₂	1	6	yes	maximal, complemented
13	C₂₃×#3444	C₂	1	6	yes	maximal, complemented
14	C₄×C₂₃×2₋¹⁺⁴	C₂	1	2	yes	maximal, complemented
15	C₂²×C₄×Q₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	2	yes	—
17	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic
18	C₂₃×#559	C₂²	1	12	yes	complemented
19	Q₈²×C₂₃	C₂²	1	4	yes	complemented
20	C₂₃×#557	C₂²	1	12	yes	complemented
21	C₂₃×#557	C₂²	1	4	yes	complemented
22	C₂₃×#557	C₂²	1	8	yes	complemented
23	C₂₃×#556	C₂²	1	12	yes	complemented
24	C₂₃×#556	C₂²	1	24	yes	complemented
25	C₂₃×#554	C₂²	1	24	yes	—
26	C₂₃×#554	C₂²	1	12	yes	complemented
27	C₂₃×#553	C₂²	1	24	yes	—
28	C₂₃×#552	C₂²	1	24	yes	—
29	C₂₃×#552	C₂²	1	24	yes	complemented
30	C₂₃×#550	C₂²	1	4	yes	complemented
31	D₄×Q₈×C₂₃	C₂²	1	8	yes	—
32	D₄×Q₈×C₂₃	C₂²	1	8	yes	—
33	D₄×Q₈×C₂₃	C₂²	1	4	yes	complemented
34	C₂₃×#548	C₂²	1	8	yes	—
35	C₂₃×#548	C₂²	1	8	yes	—
36	C₂₃×#548	C₂²	1	8	yes	complemented
37	C₂₃×#547	C₂²	1	24	yes	—
38	C₂₃×#544	C₂²	1	6	yes	—
39	C₂₃×#542	C₂²	1	24	yes	complemented
40	C₂₃×#541	C₂²	1	24	yes	complemented
41	C₂₃×#539	C₂²	1	24	yes	—
42	C₂₃×#537	C₂²	1	6	yes	—
43	C₂₃×#536	C₂²	1	12	yes	—
44	C₂₃×#533	C₂²	1	6	yes	—
45	C₂₃×#533	C₂²	1	6	yes	—
46	C₂₃×#533	C₂²	1	6	yes	—
47	C₂₃×#533	C₂²	1	24	yes	complemented
48	C₂₃×#532	C₂²	1	6	yes	—
49	C₂₃×#532	C₂²	1	6	yes	—
50	C₂₃×#532	C₂²	1	6	yes	—
51	C₂₃×#529	C₂²	1	12	yes	—
52	C₂₃×#529	C₂²	1	12	yes	—
53	C₂₃×#529	C₂²	1	12	yes	—
54	C₂₃×#529	C₂²	1	12	yes	—
55	C₂₃×#529	C₂²	1	12	yes	—
56	C₂₃×#529	C₂²	1	12	yes	—
57	C₂₃×#529	C₂²	1	24	yes	complemented
58	C₂₃×#525	C₂²	1	4	yes	—
59	C₂₃×#525	C₂²	1	12	yes	—
60	C₂₃×#525	C₂²	1	12	yes	—
61	C₂₃×#520	C₂²	1	12	yes	—
62	C₂₃×#520	C₂²	1	8	yes	complemented
63	C₂₃×#519	C₂²	1	2	yes	—
64	C₂₃×#519	C₂²	1	8	yes	complemented
65	C₄×#41×C₂₃	C₂²	1	12	yes	—
66	C₄×#41×C₂₃	C₂²	1	12	yes	—
67	C₄×#41×C₂₃	C₂²	1	12	yes	—
68	C₄×#41×C₂₃	C₂²	1	8	yes	complemented
69	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
70	C₂×C₄×Q₈×C₂₃	C₂²	1	3	yes	—
71	C₂×C₄×Q₈×C₂₃	C₂²	1	4	yes	—
72	C₂×C₄×Q₈×C₂₃	C₂²	1	4	yes	—
73	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
74	C₂×C₄×Q₈×C₂₃	C₂²	1	3	yes	—
75	C₂×C₄×Q₈×C₂₃	C₂²	1	4	yes	—
76	C₂×C₄×Q₈×C₂₃	C₂²	1	4	yes	—
77	C₂×C₄×Q₈×C₂₃	C₂²	1	8	yes	complemented
78	C₂²×C₄⋊C₄×C₂₃	C₂²	1	3	yes	—
79	C₂²×C₄²×C₂₃	C₂²	1	3	yes	—
80	C₂₃×2₋¹⁺⁴	—	2	16	no	—
81	C₂×#41×C₂₃	C₂³	1	8	yes	—
82	C₂×#41×C₂₃	C₂³	1	12	yes	—
83	C₂×#41×C₂₃	C₂³	1	4	yes	—
84	C₂×#41×C₂₃	C₂³	1	12	yes	—
85	C₂²×Q₈×C₂₃	—	2	8	no	—
86	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
87	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
88	C₂²×Q₈×C₂₃	C₂³	1	8	yes	—
89	C₂²×Q₈×C₂₃	C₂³	1	3	yes	—
90	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₂₃	C₂³	1	3	yes	—
92	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₂₃	C₂³	1	3	yes	—
94	C₂₃×C₄⋊Q₈	C₂³	1	24	yes	—
95	C₂₃×C₄⋊Q₈	C₂³	1	24	yes	—
96	C₂₃×C₄⋊Q₈	C₂³	1	6	yes	—
97	C₂₃×C₄⋊Q₈	C₂³	1	6	yes	—
98	C₂₃×C₄⋊Q₈	C₂³	1	6	yes	—
99	C₂₃×#127	C₂³	1	6	yes	—
100	C₂₃×#126	C₂³	1	48	yes	—
101	C₂₃×#126	C₂³	1	24	yes	—
102	C₂₃×#126	C₂³	1	24	yes	—
103	C₂₃×#125	C₂³	1	48	yes	—
104	C₂₃×#125	C₂³	1	24	yes	—
105	C₂₃×#125	C₂³	1	12	yes	—
106	C₂₃×#125	C₂³	1	12	yes	—
107	C₂₃×#125	C₂³	1	12	yes	—
108	C₂₃×#124	C₂³	1	24	yes	—
109	C₂₃×#124	C₂³	1	12	yes	—
110	C₂₃×#124	C₂³	1	12	yes	—
111	C₂₃×#124	C₂³	1	12	yes	—
112	C₂₃×#123	C₂³	1	24	yes	—
113	C₂₃×#123	C₂³	1	48	yes	—
114	C₂₃×#123	C₂³	1	8	yes	—
115	C₂₃×#123	C₂³	1	24	yes	—
116	C₂₃×C₂²⋊Q₈	C₂³	1	48	yes	—
117	C₂₃×C₂²⋊Q₈	C₂³	1	24	yes	—
118	C₂₃×C₂²⋊Q₈	C₂³	1	24	yes	—
119	C₂₃×C₂²⋊Q₈	C₂³	1	24	yes	—
120	C₂₃×C₂²⋊Q₈	C₂³	1	12	yes	—
121	C₂₃×C₂²⋊Q₈	C₂³	1	12	yes	—
122	C₂₃×C₂²⋊Q₈	C₂³	1	12	yes	—
123	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
124	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
125	C₂₃×C₂²⋊Q₈	C₂³	1	12	yes	—
126	C₂₃×#121	C₂³	1	12	yes	—
127	C₂₃×#121	C₂³	1	24	yes	—
128	C₂₃×#121	C₂³	1	12	yes	—
129	C₂₃×#121	C₂³	1	12	yes	—
130	C₂₃×#121	C₂³	1	4	yes	—
131	C₂₃×#121	C₂³	1	4	yes	—
132	C₂₃×#121	C₂³	1	12	yes	—
133	C₂₃×#120	C₂³	1	8	yes	—
134	C₄×Q₈×C₂₃	C₂³	1	8	yes	—
135	C₄×Q₈×C₂₃	C₂³	1	8	yes	—
136	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
137	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
138	C₄×Q₈×C₂₃	C₂³	1	24	yes	—
139	C₄×Q₈×C₂₃	C₂³	1	12	yes	—
140	C₄×Q₈×C₂₃	C₂³	1	12	yes	—
141	C₄×Q₈×C₂₃	C₂³	1	12	yes	—
142	C₄×Q₈×C₂₃	C₂³	1	12	yes	—
143	C₄×Q₈×C₂₃	C₂³	1	12	yes	—
144	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
145	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
146	C₄×Q₈×C₂₃	C₂³	1	12	yes	—
147	C₄×Q₈×C₂₃	C₂³	1	12	yes	—
148	C₄×Q₈×C₂₃	C₂³	1	12	yes	—
149	C₄×Q₈×C₂₃	C₂³	1	12	yes	—
150	C₄×Q₈×C₂₃	C₂³	1	12	yes	—
151	C₄×D₄×C₂₃	C₂³	1	24	yes	—
152	C₄×D₄×C₂₃	C₂³	1	24	yes	—
153	C₄×D₄×C₂₃	C₂³	1	24	yes	—
154	C₄×D₄×C₂₃	C₂³	1	12	yes	—
155	C₄×D₄×C₂₃	C₂³	1	12	yes	—
156	C₄×D₄×C₂₃	C₂³	1	24	yes	—
157	C₄×D₄×C₂₃	C₂³	1	12	yes	—
158	C₄×D₄×C₂₃	C₂³	1	8	yes	—
159	C₄×D₄×C₂₃	C₂³	1	8	yes	—
160	C₄×D₄×C₂₃	C₂³	1	12	yes	—
161	C₄×D₄×C₂₃	C₂³	1	24	yes	—
162	C₄×D₄×C₂₃	C₂³	1	12	yes	—
163	C₄×D₄×C₂₃	C₂³	1	12	yes	—
164	C₂₃×#117	C₂³	1	12	yes	—
165	C₂₃×#117	C₂³	1	24	yes	—
166	C₂₃×#117	C₂³	1	24	yes	—
167	C₂₃×#117	C₂³	1	4	yes	—
168	C₂₃×#117	C₂³	1	12	yes	—
169	C₂₃×#117	C₂³	1	24	yes	—
170	C₂₃×#117	C₂³	1	24	yes	—
171	C₂×C₄⋊C₄×C₂₃	C₂³	1	12	yes	—
172	C₂×C₄⋊C₄×C₂₃	C₂³	1	24	yes	—
173	C₂×C₄⋊C₄×C₂₃	C₂³	1	12	yes	—
174	C₂×C₄⋊C₄×C₂₃	C₂³	1	3	yes	—
175	C₂×C₄⋊C₄×C₂₃	C₂³	1	3	yes	—
176	C₂×C₄⋊C₄×C₂₃	C₂³	1	6	yes	—
177	C₂×C₄²×C₂₃	C₂³	1	3	yes	—
178	C₂×C₄²×C₂₃	C₂³	1	6	yes	—
179	C₂×C₄²×C₂₃	C₂³	1	6	yes	—
180	C₂×C₄²×C₂₃	C₂³	1	6	yes	—
181	C₂×C₄²×C₂₃	C₂³	1	3	yes	—
182	C₂×C₄²×C₂₃	C₂³	1	3	yes	—
183	C₂×C₄²×C₂₃	C₂³	1	6	yes	—
184	C₂×C₄²×C₂₃	C₂³	1	3	yes	—
185	C₂×C₄²×C₂₃	C₂³	1	24	yes	—
186	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
187	#41×C₂₃	—	2	32	no	—
188	#41×C₂₃	—	2	48	no	—
189	#41×C₂₃	—	2	16	no	—
190	#41×C₂₃	—	4	24	no	—
191	C₂×Q₈×C₂₃	—	2	16	no	—
192	C₂×Q₈×C₂₃	—	2	16	no	—
193	C₂×Q₈×C₂₃	—	2	32	no	—
194	C₂×Q₈×C₂₃	—	2	12	no	—
195	C₂×Q₈×C₂₃	#41	1	8	yes	complemented
196	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
197	C₂×Q₈×C₂₃	C₂⁴	1	12	yes	—
198	C₂×Q₈×C₂₃	C₂⁴	1	12	yes	—
199	C₂×Q₈×C₂₃	C₂⁴	1	12	yes	—
200	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
201	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
202	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
203	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
204	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
205	C₂×D₄×C₂₃	C₂⁴	1	12	yes	—
206	C₂×D₄×C₂₃	C₂⁴	1	12	yes	—
207	C₂²×C₄×C₂₃	—	2	12	no	—
208	C₂²×C₄×C₂₃	—	2	4	no	—
209	C₂²×C₄×C₂₃	—	4	6	no	—
210	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₂₃	C₂⁴	1	6	yes	—
214	C₂²×C₄×C₂₃	C₂⁴	1	6	yes	—
215	C₂²×C₄×C₂₃	C₂⁴	1	6	yes	—
216	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
217	C₂²×C₄×C₂₃	C₂⁴	1	24	yes	—
218	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
221	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
222	C₂²×C₄×C₂₃	C₂⁴	1	6	yes	—
223	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
224	C₂²×C₄×C₂₃	C₂⁴	1	24	yes	—
225	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
226	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
227	C₄⋊C₄×C₂₃	C₂⁴	1	12	yes	—
228	C₄⋊C₄×C₂₃	C₂⁴	1	12	yes	—
229	C₄⋊C₄×C₂₃	C₂⁴	1	24	yes	—
230	C₄⋊C₄×C₂₃	C₂⁴	1	12	yes	—
231	C₄⋊C₄×C₂₃	C₂⁴	1	24	yes	—
232	C₄⋊C₄×C₂₃	C₂⁴	1	12	yes	—
233	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
234	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
235	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
236	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
237	C₄⋊C₄×C₂₃	C₂⁴	1	12	yes	—
238	C₄⋊C₄×C₂₃	C₂⁴	1	12	yes	—
239	C₄⋊C₄×C₂₃	C₂⁴	1	24	yes	—
240	C₄⋊C₄×C₂₃	C₂⁴	1	24	yes	—
241	C₄⋊C₄×C₂₃	C₂⁴	1	24	yes	—
242	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
243	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
244	C₂²⋊C₄×C₂₃	C₂⁴	1	24	yes	—
245	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
246	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
247	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
248	C₂²⋊C₄×C₂₃	C₂⁴	1	24	yes	—
249	C₂²⋊C₄×C₂₃	C₂⁴	1	24	yes	—
250	C₂²⋊C₄×C₂₃	C₂⁴	1	24	yes	—
251	C₄²×C₂₃	C₂⁴	1	6	yes	—
252	C₄²×C₂₃	C₂⁴	1	6	yes	—
253	C₄²×C₂₃	C₂⁴	1	6	yes	—
254	C₄²×C₂₃	C₂⁴	1	6	yes	—
255	C₄²×C₂₃	C₂⁴	1	6	yes	—
256	C₄²×C₂₃	C₂⁴	1	6	yes	—
257	C₄²×C₂₃	C₂⁴	1	24	yes	—
258	C₄²×C₂₃	C₂⁴	1	24	yes	—
259	C₄²×C₂₃	C₂⁴	1	6	yes	—
260	C₄²×C₂₃	C₂⁴	1	6	yes	—
261	C₄²×C₂₃	C₂⁴	1	8	yes	—
262	#62788	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
263	C₂³×C₂₃	—	2	2	no	—
264	C₂³×C₂₃	—	2	2	no	—
265	C₂³×C₂₃	—	2	2	no	—
266	C₂³×C₂₃	C₂⁵	1	8	yes	—
267	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
268	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
269	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
270	Q₈×C₂₃	—	2	24	no	—
271	Q₈×C₂₃	—	2	24	no	—
272	Q₈×C₂₃	—	2	8	no	—
273	Q₈×C₂₃	—	4	12	no	—
274	Q₈×C₂₃	C₂×#41	1	16	yes	—
275	D₄×C₂₃	—	2	16	no	—
276	D₄×C₂₃	—	2	16	no	—
277	D₄×C₂₃	—	2	16	no	—
278	D₄×C₂₃	—	2	24	no	—
279	D₄×C₂₃	—	2	8	no	—
280	D₄×C₂₃	—	4	12	no	—
281	C₂×C₄×C₂₃	—	2	6	no	—
282	C₂×C₄×C₂₃	—	2	2	no	—
283	C₂×C₄×C₂₃	—	2	12	no	—
284	C₂×C₄×C₂₃	—	2	12	no	—
285	C₂×C₄×C₂₃	—	2	12	no	—
286	C₂×C₄×C₂₃	—	2	48	no	—
287	C₂×C₄×C₂₃	—	2	2	no	—
288	C₂×C₄×C₂₃	—	2	2	no	—
289	C₂×C₄×C₂₃	—	2	2	no	—
290	C₂×C₄×C₂₃	—	2	2	no	—
291	C₂×C₄×C₂₃	—	2	16	no	—
292	C₂×C₄×C₂₃	—	4	3	no	—
293	C₂×C₄×C₂₃	—	4	6	no	—
294	C₂×C₄×C₂₃	—	4	3	no	—
295	C₂×C₄×C₂₃	—	4	24	no	—
296	C₂×C₄×C₂₃	C₂×#41	1	12	yes	—
297	C₂×C₄×C₂₃	2₋¹⁺⁴	1	4	yes	complemented
298	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
299	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
300	C₂×C₄×C₂₃	C₂⁵	1	6	yes	—
301	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
302	C₂×C₄×C₂₃	C₂⁵	1	6	yes	—
303	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
304	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
305	C₂×C₄×C₂₃	C₂⁵	1	6	yes	—
306	C₂×C₄×C₂₃	C₂⁵	1	6	yes	—
307	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
308	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
309	#3523	C₂×C₂₃	1	4	yes	complemented
310	#3522	C₂×C₂₃	1	4	yes	complemented
311	#3516	C₂×C₂₃	1	8	yes	complemented
312	#3507	C₂×C₂₃	1	6	yes	complemented
313	#3502	C₂×C₂₃	1	1	yes	characteristic, complemented
314	#3497	C₂×C₂₃	1	1	yes	characteristic, complemented
315	#3492	C₂×C₂₃	1	6	yes	complemented
316	#3486	C₂×C₂₃	1	2	yes	complemented
317	#3482	C₂×C₂₃	1	8	yes	complemented
318	#3480	C₂×C₂₃	1	4	yes	complemented
319	Q₈×#41	C₂×C₂₃	1	4	yes	complemented
320	#3461	C₂×C₂₃	1	6	yes	complemented
321	#3444	C₂×C₂₃	1	6	yes	complemented
322	C₄×2₋¹⁺⁴	C₂×C₂₃	1	2	yes	complemented
323	C₂²×C₄×Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
324	C₂²×C₂₃	—	2	8	no	—
325	C₂²×C₂₃	—	2	1	no	—
326	C₂²×C₂₃	—	2	1	no	—
327	C₂²×C₂₃	—	2	1	no	—
328	C₂²×C₂₃	—	2	1	no	—
329	C₂²×C₂₃	—	2	1	no	—
330	C₂²×C₂₃	—	2	1	no	—
331	C₂²×C₂₃	—	2	8	no	—
332	C₂²×C₂₃	—	2	8	no	—
333	C₂²×C₂₃	—	2	8	no	—
334	C₂²×C₂₃	C₂²×#41	1	2	yes	—
335	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
336	C₂²×C₂₃	#585	1	2	yes	—
337	C₂²×C₂₃	C₂⁶	1	1	yes	characteristic
338	C₄×C₂₃	—	2	8	no	—
339	C₄×C₂₃	—	2	6	no	—
340	C₄×C₂₃	—	2	1	no	—
341	C₄×C₂₃	—	2	1	no	—
342	C₄×C₂₃	—	2	8	no	—
343	C₄×C₂₃	—	2	6	no	—
344	C₄×C₂₃	—	2	6	no	—
345	C₄×C₂₃	—	2	8	no	—
346	C₄×C₂₃	C₂²×#41	1	12	yes	—
347	C₄×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
348	C₄×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
349	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	2	yes	—
350	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
351	#559	C₂²×C₂₃	1	12	yes	complemented
352	Q₈²	C₂²×C₂₃	1	4	yes	complemented
353	#557	C₂²×C₂₃	1	12	yes	complemented
354	#557	C₂²×C₂₃	1	4	yes	complemented
355	#557	C₂²×C₂₃	1	8	yes	complemented
356	#556	C₂²×C₂₃	1	12	yes	complemented
357	#556	C₂²×C₂₃	1	24	yes	complemented
358	#554	C₂²×C₂₃	1	24	yes	—
359	#554	C₂²×C₂₃	1	12	yes	complemented
360	#553	C₂²×C₂₃	1	24	yes	—
361	#552	C₂²×C₂₃	1	24	yes	—
362	#552	C₂²×C₂₃	1	24	yes	complemented
363	#550	C₂²×C₂₃	1	4	yes	complemented
364	D₄×Q₈	C₂²×C₂₃	1	8	yes	—
365	D₄×Q₈	C₂²×C₂₃	1	8	yes	—
366	D₄×Q₈	C₂²×C₂₃	1	4	yes	complemented
367	#548	C₂²×C₂₃	1	8	yes	—
368	#548	C₂²×C₂₃	1	8	yes	—
369	#548	C₂²×C₂₃	1	8	yes	complemented
370	#547	C₂²×C₂₃	1	24	yes	—
371	#544	C₂²×C₂₃	1	6	yes	—
372	#542	C₂²×C₂₃	1	24	yes	complemented
373	#541	C₂²×C₂₃	1	24	yes	complemented
374	#539	C₂²×C₂₃	1	24	yes	—
375	#537	C₂²×C₂₃	1	6	yes	—
376	#536	C₂²×C₂₃	1	12	yes	—
377	#533	C₂²×C₂₃	1	6	yes	—
378	#533	C₂²×C₂₃	1	6	yes	—
379	#533	C₂²×C₂₃	1	6	yes	—
380	#533	C₂²×C₂₃	1	24	yes	complemented
381	#532	C₂²×C₂₃	1	6	yes	—
382	#532	C₂²×C₂₃	1	6	yes	—
383	#532	C₂²×C₂₃	1	6	yes	—
384	#529	C₂²×C₂₃	1	12	yes	—
385	#529	C₂²×C₂₃	1	12	yes	—
386	#529	C₂²×C₂₃	1	12	yes	—
387	#529	C₂²×C₂₃	1	12	yes	—
388	#529	C₂²×C₂₃	1	12	yes	—
389	#529	C₂²×C₂₃	1	12	yes	—
390	#529	C₂²×C₂₃	1	24	yes	complemented
391	#525	C₂²×C₂₃	1	4	yes	—
392	#525	C₂²×C₂₃	1	12	yes	—
393	#525	C₂²×C₂₃	1	12	yes	—
394	#520	C₂²×C₂₃	1	12	yes	—
395	#520	C₂²×C₂₃	1	8	yes	complemented
396	#519	C₂²×C₂₃	1	2	yes	—
397	#519	C₂²×C₂₃	1	8	yes	complemented
398	C₄×#41	C₂²×C₂₃	1	12	yes	—
399	C₄×#41	C₂²×C₂₃	1	12	yes	—
400	C₄×#41	C₂²×C₂₃	1	12	yes	—
401	C₄×#41	C₂²×C₂₃	1	8	yes	complemented
402	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
403	C₂×C₄×Q₈	C₂²×C₂₃	1	3	yes	—
404	C₂×C₄×Q₈	C₂²×C₂₃	1	4	yes	—
405	C₂×C₄×Q₈	C₂²×C₂₃	1	4	yes	—
406	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
407	C₂×C₄×Q₈	C₂²×C₂₃	1	3	yes	—
408	C₂×C₄×Q₈	C₂²×C₂₃	1	4	yes	—
409	C₂×C₄×Q₈	C₂²×C₂₃	1	4	yes	—
410	C₂×C₄×Q₈	C₂²×C₂₃	1	8	yes	complemented
411	C₂²×C₄⋊C₄	C₂²×C₂₃	1	3	yes	—
412	C₂²×C₄²	C₂²×C₂₃	1	3	yes	—
413	C₂×C₂₃	—	2	2	no	—
414	C₂×C₂₃	—	2	2	no	—
415	C₂×C₂₃	—	2	2	no	—
416	C₂×C₂₃	—	4	8	no	—
417	C₂×C₂₃	C₂³×#41	1	1	yes	characteristic
418	C₂×C₂₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
419	C₂×C₂₃	C₂×#585	1	1	yes	characteristic
420	2₋¹⁺⁴	—	2	16	no	—
421	C₂×#41	C₂³×C₂₃	1	4	yes	—
422	C₂×#41	C₂³×C₂₃	1	12	yes	—
423	C₂×#41	C₂³×C₂₃	1	8	yes	—
424	C₂×#41	C₂³×C₂₃	1	12	yes	—
425	C₂²×Q₈	—	2	8	no	—
426	C₂²×Q₈	C₂³×C₂₃	1	3	yes	—
427	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
428	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
429	C₂²×Q₈	C₂³×C₂₃	1	8	yes	—
430	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
431	C₂³×C₄	C₂³×C₂₃	1	3	yes	—
432	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
433	C₂³×C₄	C₂³×C₂₃	1	3	yes	—
434	C₄⋊Q₈	C₂³×C₂₃	1	6	yes	—
435	C₄⋊Q₈	C₂³×C₂₃	1	6	yes	—
436	C₄⋊Q₈	C₂³×C₂₃	1	6	yes	—
437	C₄⋊Q₈	C₂³×C₂₃	1	24	yes	—
438	C₄⋊Q₈	C₂³×C₂₃	1	24	yes	—
439	#127	C₂³×C₂₃	1	6	yes	—
440	#126	C₂³×C₂₃	1	24	yes	—
441	#126	C₂³×C₂₃	1	24	yes	—
442	#126	C₂³×C₂₃	1	48	yes	—
443	#125	C₂³×C₂₃	1	12	yes	—
444	#125	C₂³×C₂₃	1	12	yes	—
445	#125	C₂³×C₂₃	1	12	yes	—
446	#125	C₂³×C₂₃	1	24	yes	—
447	#125	C₂³×C₂₃	1	48	yes	—
448	#124	C₂³×C₂₃	1	12	yes	—
449	#124	C₂³×C₂₃	1	12	yes	—
450	#124	C₂³×C₂₃	1	12	yes	—
451	#124	C₂³×C₂₃	1	24	yes	—
452	#123	C₂³×C₂₃	1	8	yes	—
453	#123	C₂³×C₂₃	1	24	yes	—
454	#123	C₂³×C₂₃	1	24	yes	—
455	#123	C₂³×C₂₃	1	48	yes	—
456	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
457	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
458	C₂²⋊Q₈	C₂³×C₂₃	1	12	yes	—
459	C₂²⋊Q₈	C₂³×C₂₃	1	12	yes	—
460	C₂²⋊Q₈	C₂³×C₂₃	1	12	yes	—
461	C₂²⋊Q₈	C₂³×C₂₃	1	12	yes	—
462	C₂²⋊Q₈	C₂³×C₂₃	1	24	yes	—
463	C₂²⋊Q₈	C₂³×C₂₃	1	24	yes	—
464	C₂²⋊Q₈	C₂³×C₂₃	1	24	yes	—
465	C₂²⋊Q₈	C₂³×C₂₃	1	48	yes	—
466	#121	C₂³×C₂₃	1	4	yes	—
467	#121	C₂³×C₂₃	1	4	yes	—
468	#121	C₂³×C₂₃	1	12	yes	—
469	#121	C₂³×C₂₃	1	12	yes	—
470	#121	C₂³×C₂₃	1	12	yes	—
471	#121	C₂³×C₂₃	1	12	yes	—
472	#121	C₂³×C₂₃	1	24	yes	—
473	#120	C₂³×C₂₃	1	8	yes	—
474	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
475	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
476	C₄×Q₈	C₂³×C₂₃	1	12	yes	—
477	C₄×Q₈	C₂³×C₂₃	1	12	yes	—
478	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
479	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
480	C₄×Q₈	C₂³×C₂₃	1	12	yes	—
481	C₄×Q₈	C₂³×C₂₃	1	12	yes	—
482	C₄×Q₈	C₂³×C₂₃	1	12	yes	—
483	C₄×Q₈	C₂³×C₂₃	1	8	yes	—
484	C₄×Q₈	C₂³×C₂₃	1	24	yes	—
485	C₄×Q₈	C₂³×C₂₃	1	12	yes	—
486	C₄×Q₈	C₂³×C₂₃	1	12	yes	—
487	C₄×Q₈	C₂³×C₂₃	1	12	yes	—
488	C₄×Q₈	C₂³×C₂₃	1	12	yes	—
489	C₄×Q₈	C₂³×C₂₃	1	12	yes	—
490	C₄×Q₈	C₂³×C₂₃	1	8	yes	—
491	C₄×D₄	C₂³×C₂₃	1	8	yes	—
492	C₄×D₄	C₂³×C₂₃	1	8	yes	—
493	C₄×D₄	C₂³×C₂₃	1	12	yes	—
494	C₄×D₄	C₂³×C₂₃	1	24	yes	—
495	C₄×D₄	C₂³×C₂₃	1	12	yes	—
496	C₄×D₄	C₂³×C₂₃	1	24	yes	—
497	C₄×D₄	C₂³×C₂₃	1	24	yes	—
498	C₄×D₄	C₂³×C₂₃	1	24	yes	—
499	C₄×D₄	C₂³×C₂₃	1	12	yes	—
500	C₄×D₄	C₂³×C₂₃	1	12	yes	—
501	C₄×D₄	C₂³×C₂₃	1	12	yes	—
502	C₄×D₄	C₂³×C₂₃	1	12	yes	—
503	C₄×D₄	C₂³×C₂₃	1	24	yes	—
504	#117	C₂³×C₂₃	1	4	yes	—
505	#117	C₂³×C₂₃	1	12	yes	—
506	#117	C₂³×C₂₃	1	24	yes	—
507	#117	C₂³×C₂₃	1	12	yes	—
508	#117	C₂³×C₂₃	1	24	yes	—
509	#117	C₂³×C₂₃	1	24	yes	—
510	#117	C₂³×C₂₃	1	24	yes	—
511	C₂×C₄⋊C₄	C₂³×C₂₃	1	3	yes	—
512	C₂×C₄⋊C₄	C₂³×C₂₃	1	3	yes	—
513	C₂×C₄⋊C₄	C₂³×C₂₃	1	6	yes	—
514	C₂×C₄⋊C₄	C₂³×C₂₃	1	12	yes	—
515	C₂×C₄⋊C₄	C₂³×C₂₃	1	12	yes	—
516	C₂×C₄⋊C₄	C₂³×C₂₃	1	24	yes	—
517	C₂×C₄²	C₂³×C₂₃	1	3	yes	—
518	C₂×C₄²	C₂³×C₂₃	1	6	yes	—
519	C₂×C₄²	C₂³×C₂₃	1	6	yes	—
520	C₂×C₄²	C₂³×C₂₃	1	3	yes	—
521	C₂×C₄²	C₂³×C₂₃	1	6	yes	—
522	C₂×C₄²	C₂³×C₂₃	1	3	yes	—
523	C₂×C₄²	C₂³×C₂₃	1	6	yes	—
524	C₂×C₄²	C₂³×C₂₃	1	3	yes	—
525	C₂×C₄²	C₂³×C₂₃	1	24	yes	—
526	C₂₃	#62788	1	1	yes	characteristic, direct product factor, Sylow
527	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
528	#41	—	2	32	no	—
529	#41	—	2	48	no	—
530	#41	—	2	16	no	—
531	#41	—	4	24	no	—
532	C₂×Q₈	—	2	16	no	—
533	C₂×Q₈	—	2	16	no	—
534	C₂×Q₈	—	2	32	no	—
535	C₂×Q₈	—	2	12	no	—
536	C₂×Q₈	#41×C₂₃	1	8	yes	complemented
537	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
538	C₂×Q₈	C₂⁴×C₂₃	1	12	yes	—
539	C₂×Q₈	C₂⁴×C₂₃	1	12	yes	—
540	C₂×Q₈	C₂⁴×C₂₃	1	12	yes	—
541	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
542	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
543	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
544	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
545	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
546	C₂×D₄	C₂⁴×C₂₃	1	12	yes	—
547	C₂×D₄	C₂⁴×C₂₃	1	12	yes	—
548	C₂²×C₄	—	2	12	no	—
549	C₂²×C₄	—	2	4	no	—
550	C₂²×C₄	—	4	6	no	—
551	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
552	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
553	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
554	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
555	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
556	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
557	C₂²×C₄	C₂⁴×C₂₃	1	6	yes	—
558	C₂²×C₄	C₂⁴×C₂₃	1	6	yes	—
559	C₂²×C₄	C₂⁴×C₂₃	1	6	yes	—
560	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
561	C₂²×C₄	C₂⁴×C₂₃	1	24	yes	—
562	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
563	C₂²×C₄	C₂⁴×C₂₃	1	6	yes	—
564	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
565	C₂²×C₄	C₂⁴×C₂₃	1	24	yes	—
566	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
567	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
568	C₄⋊C₄	C₂⁴×C₂₃	1	12	yes	—
569	C₄⋊C₄	C₂⁴×C₂₃	1	12	yes	—
570	C₄⋊C₄	C₂⁴×C₂₃	1	24	yes	—
571	C₄⋊C₄	C₂⁴×C₂₃	1	12	yes	—
572	C₄⋊C₄	C₂⁴×C₂₃	1	24	yes	—
573	C₄⋊C₄	C₂⁴×C₂₃	1	12	yes	—
574	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
575	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
576	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
577	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
578	C₄⋊C₄	C₂⁴×C₂₃	1	12	yes	—
579	C₄⋊C₄	C₂⁴×C₂₃	1	12	yes	—
580	C₄⋊C₄	C₂⁴×C₂₃	1	24	yes	—
581	C₄⋊C₄	C₂⁴×C₂₃	1	24	yes	—
582	C₄⋊C₄	C₂⁴×C₂₃	1	24	yes	—
583	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
584	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
585	C₂²⋊C₄	C₂⁴×C₂₃	1	24	yes	—
586	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
587	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
588	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
589	C₂²⋊C₄	C₂⁴×C₂₃	1	24	yes	—
590	C₂²⋊C₄	C₂⁴×C₂₃	1	24	yes	—
591	C₂²⋊C₄	C₂⁴×C₂₃	1	24	yes	—
592	C₄²	C₂⁴×C₂₃	1	6	yes	—
593	C₄²	C₂⁴×C₂₃	1	6	yes	—
594	C₄²	C₂⁴×C₂₃	1	6	yes	—
595	C₄²	C₂⁴×C₂₃	1	8	yes	—
596	C₄²	C₂⁴×C₂₃	1	6	yes	—
597	C₄²	C₂⁴×C₂₃	1	6	yes	—
598	C₄²	C₂⁴×C₂₃	1	6	yes	—
599	C₄²	C₂⁴×C₂₃	1	6	yes	—
600	C₄²	C₂⁴×C₂₃	1	6	yes	—
601	C₄²	C₂⁴×C₂₃	1	24	yes	—
602	C₄²	C₂⁴×C₂₃	1	24	yes	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	2	no	—
605	C₂³	—	2	2	no	—
606	C₂³	C₂⁵×C₂₃	1	8	yes	—
607	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
608	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
609	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
610	Q₈	—	2	24	no	—
611	Q₈	—	2	24	no	—
612	Q₈	—	2	8	no	—
613	Q₈	—	4	12	no	—
614	Q₈	C₂×#41×C₂₃	1	16	yes	—
615	D₄	—	2	16	no	—
616	D₄	—	2	16	no	—
617	D₄	—	2	16	no	—
618	D₄	—	2	24	no	—
619	D₄	—	2	8	no	—
620	D₄	—	4	12	no	—
621	C₂×C₄	—	2	6	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	12	no	—
624	C₂×C₄	—	2	12	no	—
625	C₂×C₄	—	2	12	no	—
626	C₂×C₄	—	2	48	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	16	no	—
632	C₂×C₄	—	4	3	no	—
633	C₂×C₄	—	4	6	no	—
634	C₂×C₄	—	4	3	no	—
635	C₂×C₄	—	4	24	no	—
636	C₂×C₄	C₂×#41×C₂₃	1	12	yes	—
637	C₂×C₄	C₂₃×2₋¹⁺⁴	1	4	yes	complemented
638	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
639	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
640	C₂×C₄	C₂⁵×C₂₃	1	6	yes	—
641	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
642	C₂×C₄	C₂⁵×C₂₃	1	6	yes	—
643	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
644	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
645	C₂×C₄	C₂⁵×C₂₃	1	6	yes	—
646	C₂×C₄	C₂⁵×C₂₃	1	6	yes	—
647	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
648	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
649	C₂²	—	2	8	no	—
650	C₂²	—	2	1	no	—
651	C₂²	—	2	1	no	—
652	C₂²	—	2	1	no	—
653	C₂²	—	2	1	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	8	no	—
657	C₂²	—	2	8	no	—
658	C₂²	—	2	8	no	—
659	C₂²	C₂²×#41×C₂₃	1	2	yes	—
660	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
661	C₂²	C₂₃×#585	1	2	yes	—
662	C₂²	C₂⁶×C₂₃	1	1	yes	characteristic
663	C₄	—	2	8	no	—
664	C₄	—	2	6	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	8	no	—
668	C₄	—	2	6	no	—
669	C₄	—	2	6	no	—
670	C₄	—	2	8	no	—
671	C₄	C₂²×#41×C₂₃	1	12	yes	—
672	C₄	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
673	C₄	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
674	C₂	—	2	2	no	—
675	C₂	—	2	2	no	—
676	C₂	—	2	2	no	—
677	C₂	—	4	8	no	—
678	C₂	C₂³×#41×C₂₃	1	1	yes	characteristic
679	C₂	C₂²×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
680	C₂	C₂×C₂₃×#585	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₂₃
socle	C₂²×C₂₃	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3523	C₂	semidirect
2. C₂₃×#3522	C₂	semidirect
3. C₂₃×#3516	C₂	semidirect
4. C₂₃×#3507	C₂	semidirect
5. C₂₃×#3502	C₂	semidirect
6. C₂₃×#3497	C₂	semidirect
7. C₂₃×#3492	C₂	semidirect
8. C₂₃×#3486	C₂	semidirect
9. C₂₃×#3482	C₂	semidirect
10. C₂₃×#3480	C₂	semidirect
11. Q₈×#41×C₂₃	C₂	semidirect
12. C₂₃×#3461	C₂	semidirect
13. C₂₃×#3444	C₂	semidirect
14. C₄×C₂₃×2₋¹⁺⁴	C₂	semidirect
15. C₂²×C₄×Q₈×C₂₃	C₂	semidirect
18. C₂₃×#559	C₂²	semidirect
19. Q₈²×C₂₃	C₂²	semidirect
20. C₂₃×#557	C₂²	semidirect
21. C₂₃×#557	C₂²	semidirect
22. C₂₃×#557	C₂²	semidirect
23. C₂₃×#556	C₂²	semidirect
24. C₂₃×#556	C₂²	semidirect
26. C₂₃×#554	C₂²	semidirect
29. C₂₃×#552	C₂²	semidirect
30. C₂₃×#550	C₂²	semidirect
33. D₄×Q₈×C₂₃	C₂²	semidirect
36. C₂₃×#548	C₂²	semidirect
39. C₂₃×#542	C₂²	semidirect
40. C₂₃×#541	C₂²	semidirect
47. C₂₃×#533	C₂²	semidirect
57. C₂₃×#529	C₂²	semidirect
62. C₂₃×#520	C₂²	semidirect
64. C₂₃×#519	C₂²	semidirect
68. C₄×#41×C₂₃	C₂²	semidirect
77. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
195. C₂×Q₈×C₂₃	#41	semidirect
262. #62788	C₂₃	direct (N × H)
297. C₂×C₄×C₂₃	2₋¹⁺⁴	semidirect
309. #3523	C₂×C₂₃	semidirect
310. #3522	C₂×C₂₃	semidirect
311. #3516	C₂×C₂₃	semidirect
312. #3507	C₂×C₂₃	semidirect
313. #3502	C₂×C₂₃	semidirect
314. #3497	C₂×C₂₃	semidirect
315. #3492	C₂×C₂₃	semidirect
316. #3486	C₂×C₂₃	semidirect
317. #3482	C₂×C₂₃	semidirect
318. #3480	C₂×C₂₃	semidirect
319. Q₈×#41	C₂×C₂₃	semidirect
320. #3461	C₂×C₂₃	semidirect
321. #3444	C₂×C₂₃	semidirect
322. C₄×2₋¹⁺⁴	C₂×C₂₃	semidirect
323. C₂²×C₄×Q₈	C₂×C₂₃	semidirect
351. #559	C₂²×C₂₃	semidirect
352. Q₈²	C₂²×C₂₃	semidirect
353. #557	C₂²×C₂₃	semidirect
354. #557	C₂²×C₂₃	semidirect
355. #557	C₂²×C₂₃	semidirect
356. #556	C₂²×C₂₃	semidirect
357. #556	C₂²×C₂₃	semidirect
359. #554	C₂²×C₂₃	semidirect
362. #552	C₂²×C₂₃	semidirect
363. #550	C₂²×C₂₃	semidirect
366. D₄×Q₈	C₂²×C₂₃	semidirect
369. #548	C₂²×C₂₃	semidirect
372. #542	C₂²×C₂₃	semidirect
373. #541	C₂²×C₂₃	semidirect
380. #533	C₂²×C₂₃	semidirect
390. #529	C₂²×C₂₃	semidirect
395. #520	C₂²×C₂₃	semidirect
397. #519	C₂²×C₂₃	semidirect
401. C₄×#41	C₂²×C₂₃	semidirect
410. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
526. C₂₃	#62788	direct (N × H)
536. C₂×Q₈	#41×C₂₃	semidirect
637. C₂×C₄	C₂₃×2₋¹⁺⁴	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#3523	2
C₂₃×#3522	2
C₂₃×#3516	2
C₂₃×#3507	2
C₂₃×#3502	2
C₂₃×#3497	2
C₂₃×#3492	2
C₂₃×#3486	2
C₂₃×#3482	2
C₂₃×#3480	2
Q₈×#41×C₂₃	2
C₂₃×#3461	2
C₂₃×#3444	2
C₄×C₂₃×2₋¹⁺⁴	2
C₂²×C₄×Q₈×C₂₃	2
#62788	23

Subgroups — C23×#62788 #19210414

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#62788 #19210414