Subgroups — C₂₃×#36635 #19184261

Order 5888.

2006 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2864	C₂	1	2	yes	maximal, complemented
2	C₂₃×#2863	C₂	1	4	yes	maximal, complemented
3	C₂₃×#2862	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2859	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2857	C₂	1	2	yes	maximal
6	C₂₃×#2855	C₂	1	4	yes	maximal
7	C₂₃×#2851	C₂	1	2	yes	maximal
8	C₄×C₂₃×C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
9	C₄×C₂₃×#125	C₂	1	2	yes	maximal, complemented
10	C₄×C₂₃×C₂²⋊Q₈	C₂	1	4	yes	maximal
11	C₂₃×#2295	C₂	1	4	yes	maximal, complemented
12	C₂₃×#2283	C₂	1	2	yes	maximal
13	C₂×C₄³×C₂₃	C₂	1	1	yes	maximal, characteristic
14	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₂₃×#125	C₂²	1	2	yes	—
16	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	—
17	C₂×C₄×Q₈×C₂₃	C₂²	1	4	yes	—
18	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
19	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
21	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
23	C₂₃×#391	C₂²	1	4	yes	—
24	C₂₃×#391	C₂²	1	4	yes	—
25	C₂₃×#391	C₂²	1	4	yes	—
26	C₂₃×#391	C₂²	1	4	yes	—
27	C₂₃×#389	C₂²	1	4	yes	—
28	C₂₃×#389	C₂²	1	4	yes	—
29	C₂₃×#389	C₂²	1	4	yes	—
30	C₂₃×#389	C₂²	1	4	yes	—
31	C₂₃×#389	C₂²	1	4	yes	—
32	C₂₃×#389	C₂²	1	4	yes	—
33	C₂₃×#387	C₂²	1	8	yes	—
34	C₂₃×#387	C₂²	1	8	yes	—
35	C₂₃×#387	C₂²	1	8	yes	—
36	C₂₃×#387	C₂²	1	8	yes	—
37	C₂₃×#385	C₂²	1	8	yes	—
38	C₂₃×#384	C₂²	1	2	yes	—
39	C₂₃×#383	C₂²	1	4	yes	—
40	C₂₃×#382	C₂²	1	2	yes	—
41	C₂₃×#382	C₂²	1	2	yes	—
42	C₂₃×#382	C₂²	1	2	yes	—
43	C₂₃×#381	C₂²	1	4	yes	—
44	C₂₃×#380	C₂²	1	4	yes	—
45	C₂₃×#380	C₂²	1	4	yes	—
46	C₄×C₄⋊C₄×C₂₃	C₂²	1	4	yes	—
47	C₄×C₄⋊C₄×C₂₃	C₂²	1	8	yes	—
48	C₄×C₄⋊C₄×C₂₃	C₂²	1	4	yes	—
49	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
50	C₂₃×#376	C₂²	1	4	yes	—
51	C₄³×C₂₃	C₂²	1	2	yes	—
52	C₄³×C₂₃	C₂²	1	1	yes	characteristic
53	C₄³×C₂₃	C₂²	1	1	yes	characteristic
54	C₄³×C₂₃	C₂²	1	1	yes	characteristic
55	C₄³×C₂₃	C₂²	1	2	yes	—
56	C₄³×C₂₃	C₂²	1	1	yes	characteristic
57	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
58	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
59	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
63	C₂₃×C₄⋊Q₈	—	2	8	no	—
64	C₂₃×#125	—	2	8	no	—
65	C₂₃×C₂²⋊Q₈	—	2	16	no	—
66	C₄×Q₈×C₂₃	—	2	16	no	—
67	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
68	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
69	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
70	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
71	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
72	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
73	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
74	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
75	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
76	C₂×C₄²×C₂₃	—	2	8	no	—
77	C₂×C₄²×C₂₃	—	2	8	no	—
78	C₂×C₄²×C₂₃	—	2	4	no	—
79	C₂×C₄²×C₂₃	—	2	4	no	—
80	C₂×C₄²×C₂₃	Q₈	1	8	yes	complemented
81	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
82	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
83	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
84	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
85	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
88	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
89	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
90	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
91	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
92	C₂×C₄²×C₂₃	C₂³	1	8	yes	—
93	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
100	C₂₃×#95	C₂³	1	8	yes	—
101	C₂₃×#95	C₂³	1	4	yes	—
102	C₂₃×#95	C₂³	1	4	yes	—
103	C₂₃×#95	C₂³	1	4	yes	—
104	C₂₃×#95	C₂³	1	4	yes	—
105	C₂₃×#95	C₂³	1	8	yes	—
106	C₂₃×#95	C₂³	1	8	yes	—
107	C₂₃×#95	C₂³	1	8	yes	—
108	C₂₃×#95	C₂³	1	8	yes	—
109	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
110	C₂×Q₈×C₂₃	—	2	8	no	—
111	C₂×Q₈×C₂₃	—	2	8	no	—
112	C₂×Q₈×C₂₃	—	2	8	no	—
113	C₂²×C₄×C₂₃	—	2	4	no	—
114	C₂²×C₄×C₂₃	—	2	4	no	—
115	C₂²×C₄×C₂₃	—	2	4	no	—
116	C₂²×C₄×C₂₃	—	2	4	no	—
117	C₂²×C₄×C₂₃	—	2	4	no	—
118	C₂²×C₄×C₂₃	—	2	4	no	—
119	C₂²×C₄×C₂₃	—	2	4	no	—
120	C₂²×C₄×C₂₃	—	2	2	no	—
121	C₂²×C₄×C₂₃	—	2	2	no	—
122	C₂²×C₄×C₂₃	C₂×Q₈	1	4	yes	—
123	C₂²×C₄×C₂₃	C₂×Q₈	1	4	yes	—
124	C₂²×C₄×C₂₃	C₂×Q₈	1	4	yes	—
125	C₂²×C₄×C₂₃	#41	1	8	yes	—
126	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
127	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
128	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
129	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
130	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
131	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
132	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
133	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
134	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
135	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
136	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
137	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
138	C₄⋊C₄×C₂₃	—	2	8	no	—
139	C₄⋊C₄×C₂₃	—	2	16	no	—
140	C₄⋊C₄×C₂₃	—	2	8	no	—
141	C₄⋊C₄×C₂₃	—	2	16	no	—
142	C₄⋊C₄×C₂₃	—	2	16	no	—
143	C₄⋊C₄×C₂₃	—	2	8	no	—
144	C₄⋊C₄×C₂₃	—	2	8	no	—
145	C₄⋊C₄×C₂₃	—	2	8	no	—
146	C₂²⋊C₄×C₂₃	—	2	16	no	—
147	C₄²×C₂₃	—	2	4	no	—
148	C₄²×C₂₃	—	2	4	no	—
149	C₄²×C₂₃	—	2	4	no	—
150	C₄²×C₂₃	—	2	4	no	—
151	C₄²×C₂₃	—	2	4	no	—
152	C₄²×C₂₃	—	2	4	no	—
153	C₄²×C₂₃	—	2	4	no	—
154	C₄²×C₂₃	—	2	4	no	—
155	C₄²×C₂₃	—	2	4	no	—
156	C₄²×C₂₃	—	2	2	no	—
157	C₄²×C₂₃	—	2	2	no	—
158	C₄²×C₂₃	—	2	16	no	—
159	C₄²×C₂₃	C₂×Q₈	1	4	yes	—
160	C₄²×C₂₃	C₂×Q₈	1	4	yes	—
161	C₄²×C₂₃	C₂×Q₈	1	4	yes	—
162	C₄²×C₂₃	C₂×Q₈	1	4	yes	—
163	C₄²×C₂₃	#41	1	8	yes	—
164	C₄²×C₂₃	#41	1	4	yes	—
165	C₄²×C₂₃	#41	1	4	yes	—
166	#36635	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂³×C₂₃	—	2	1	no	—
168	C₂³×C₂₃	—	2	2	no	—
169	C₂³×C₂₃	—	2	1	no	—
170	C₂³×C₂₃	C₂²×Q₈	1	2	yes	—
171	C₂³×C₂₃	C₂×#41	1	4	yes	—
172	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
173	Q₈×C₂₃	—	4	16	no	—
174	C₂×C₄×C₂₃	—	2	16	no	—
175	C₂×C₄×C₂₃	—	2	8	no	—
176	C₂×C₄×C₂₃	—	2	2	no	—
177	C₂×C₄×C₂₃	—	2	2	no	—
178	C₂×C₄×C₂₃	—	2	1	no	—
179	C₂×C₄×C₂₃	—	2	2	no	—
180	C₂×C₄×C₂₃	—	2	2	no	—
181	C₂×C₄×C₂₃	—	2	2	no	—
182	C₂×C₄×C₂₃	—	2	1	no	—
183	C₂×C₄×C₂₃	—	2	2	no	—
184	C₂×C₄×C₂₃	—	2	2	no	—
185	C₂×C₄×C₂₃	—	2	2	no	—
186	C₂×C₄×C₂₃	—	2	2	no	—
187	C₂×C₄×C₂₃	—	2	16	no	—
188	C₂×C₄×C₂₃	—	2	8	no	—
189	C₂×C₄×C₂₃	—	2	8	no	—
190	C₂×C₄×C₂₃	—	2	8	no	—
191	C₂×C₄×C₂₃	—	2	8	no	—
192	C₂×C₄×C₂₃	—	2	8	no	—
193	C₂×C₄×C₂₃	—	2	8	no	—
194	C₂×C₄×C₂₃	—	2	8	no	—
195	C₂×C₄×C₂₃	—	2	8	no	—
196	C₂×C₄×C₂₃	C₂²×Q₈	1	2	yes	—
197	C₂×C₄×C₂₃	C₂²×Q₈	1	2	yes	—
198	C₂×C₄×C₂₃	C₂²×Q₈	1	2	yes	—
199	C₂×C₄×C₂₃	C₂²×Q₈	1	2	yes	—
200	C₂×C₄×C₂₃	C₂²×Q₈	1	2	yes	—
201	C₂×C₄×C₂₃	C₂²×Q₈	1	2	yes	—
202	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
203	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
204	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
205	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
206	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
207	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
208	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
209	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
210	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
211	#2864	C₂×C₂₃	1	2	yes	complemented
212	#2863	C₂×C₂₃	1	4	yes	complemented
213	#2862	C₂×C₂₃	1	1	yes	characteristic, complemented
214	#2859	C₂×C₂₃	1	1	yes	characteristic, complemented
215	#2857	C₂×C₂₃	1	2	yes	—
216	#2855	C₂×C₂₃	1	4	yes	—
217	#2851	C₂×C₂₃	1	2	yes	—
218	C₄×C₄⋊Q₈	C₂×C₂₃	1	2	yes	complemented
219	C₄×#125	C₂×C₂₃	1	2	yes	complemented
220	C₄×C₂²⋊Q₈	C₂×C₂₃	1	4	yes	—
221	#2295	C₂×C₂₃	1	4	yes	complemented
222	#2283	C₂×C₂₃	1	2	yes	—
223	C₂×C₄³	C₂×C₂₃	1	1	yes	characteristic
224	C₂²×C₂₃	—	2	4	no	—
225	C₂²×C₂₃	—	2	2	no	—
226	C₂²×C₂₃	—	2	2	no	—
227	C₂²×C₂₃	—	2	4	no	—
228	C₂²×C₂₃	#533	1	4	yes	—
229	C₂²×C₂₃	C₂³×Q₈	1	1	yes	characteristic
230	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
231	C₂²×C₂₃	C₂²×#41	1	2	yes	—
232	C₂²×C₂₃	C₂²×#41	1	2	yes	—
233	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
234	C₄×C₂₃	—	2	4	no	—
235	C₄×C₂₃	—	2	2	no	—
236	C₄×C₂₃	—	2	2	no	—
237	C₄×C₂₃	—	2	2	no	—
238	C₄×C₂₃	—	2	2	no	—
239	C₄×C₂₃	—	2	4	no	—
240	C₄×C₂₃	—	2	4	no	—
241	C₄×C₂₃	—	4	8	no	—
242	C₄×C₂₃	—	4	8	no	—
243	C₄×C₂₃	#529	1	8	yes	—
244	C₄×C₂₃	#533	1	4	yes	—
245	C₄×C₂₃	#533	1	4	yes	—
246	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
247	C₂×#125	C₂²×C₂₃	1	2	yes	—
248	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	—
249	C₂×C₄×Q₈	C₂²×C₂₃	1	4	yes	—
250	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
251	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
252	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
253	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
254	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
255	#391	C₂²×C₂₃	1	4	yes	—
256	#391	C₂²×C₂₃	1	4	yes	—
257	#391	C₂²×C₂₃	1	4	yes	—
258	#391	C₂²×C₂₃	1	4	yes	—
259	#389	C₂²×C₂₃	1	4	yes	—
260	#389	C₂²×C₂₃	1	4	yes	—
261	#389	C₂²×C₂₃	1	4	yes	—
262	#389	C₂²×C₂₃	1	4	yes	—
263	#389	C₂²×C₂₃	1	4	yes	—
264	#389	C₂²×C₂₃	1	4	yes	—
265	#387	C₂²×C₂₃	1	8	yes	—
266	#387	C₂²×C₂₃	1	8	yes	—
267	#387	C₂²×C₂₃	1	8	yes	—
268	#387	C₂²×C₂₃	1	8	yes	—
269	#385	C₂²×C₂₃	1	8	yes	—
270	#384	C₂²×C₂₃	1	2	yes	—
271	#383	C₂²×C₂₃	1	4	yes	—
272	#382	C₂²×C₂₃	1	2	yes	—
273	#382	C₂²×C₂₃	1	2	yes	—
274	#382	C₂²×C₂₃	1	2	yes	—
275	#381	C₂²×C₂₃	1	4	yes	—
276	#380	C₂²×C₂₃	1	4	yes	—
277	#380	C₂²×C₂₃	1	4	yes	—
278	C₄×C₄⋊C₄	C₂²×C₂₃	1	4	yes	—
279	C₄×C₄⋊C₄	C₂²×C₂₃	1	8	yes	—
280	C₄×C₄⋊C₄	C₂²×C₂₃	1	4	yes	—
281	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
282	#376	C₂²×C₂₃	1	4	yes	—
283	C₄³	C₂²×C₂₃	1	1	yes	characteristic
284	C₄³	C₂²×C₂₃	1	1	yes	characteristic
285	C₄³	C₂²×C₂₃	1	1	yes	characteristic
286	C₄³	C₂²×C₂₃	1	2	yes	—
287	C₄³	C₂²×C₂₃	1	1	yes	characteristic
288	C₄³	C₂²×C₂₃	1	2	yes	—
289	C₂×C₂₃	—	2	4	no	—
290	C₂×C₂₃	C₂×#529	1	2	yes	—
291	C₂×C₂₃	C₂×#533	1	1	yes	characteristic
292	C₂×C₂₃	C₂×#533	1	1	yes	characteristic
293	C₂×C₂₃	C₂×#533	1	1	yes	characteristic
294	C₂×C₂₃	#3444	1	2	yes	—
295	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
296	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
297	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
298	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
299	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
300	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
301	C₄⋊Q₈	—	2	8	no	—
302	#125	—	2	8	no	—
303	C₂²⋊Q₈	—	2	16	no	—
304	C₄×Q₈	—	2	16	no	—
305	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
306	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
307	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
308	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
309	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
310	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
311	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
312	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
313	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
314	C₂×C₄²	—	2	8	no	—
315	C₂×C₄²	—	2	8	no	—
316	C₂×C₄²	—	2	4	no	—
317	C₂×C₄²	—	2	4	no	—
318	C₂×C₄²	Q₈×C₂₃	1	8	yes	complemented
319	C₂×C₄²	C₂³×C₂₃	1	8	yes	—
320	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
321	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
322	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
323	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
324	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
325	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
326	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
327	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
328	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
329	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
330	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
331	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
332	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
333	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
334	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
335	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
336	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
337	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
338	#95	C₂³×C₂₃	1	8	yes	—
339	#95	C₂³×C₂₃	1	4	yes	—
340	#95	C₂³×C₂₃	1	4	yes	—
341	#95	C₂³×C₂₃	1	4	yes	—
342	#95	C₂³×C₂₃	1	4	yes	—
343	#95	C₂³×C₂₃	1	8	yes	—
344	#95	C₂³×C₂₃	1	8	yes	—
345	#95	C₂³×C₂₃	1	8	yes	—
346	#95	C₂³×C₂₃	1	8	yes	—
347	C₂₃	#36635	1	1	yes	characteristic, direct product factor, Sylow
348	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
349	C₂×Q₈	—	2	8	no	—
350	C₂×Q₈	—	2	8	no	—
351	C₂×Q₈	—	2	8	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	C₂×Q₈×C₂₃	1	4	yes	—
362	C₂²×C₄	C₂×Q₈×C₂₃	1	4	yes	—
363	C₂²×C₄	C₂×Q₈×C₂₃	1	4	yes	—
364	C₂²×C₄	#41×C₂₃	1	8	yes	—
365	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
366	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
367	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
368	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
369	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
370	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
371	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
372	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
373	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
374	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
375	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
376	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
377	C₄⋊C₄	—	2	8	no	—
378	C₄⋊C₄	—	2	16	no	—
379	C₄⋊C₄	—	2	8	no	—
380	C₄⋊C₄	—	2	16	no	—
381	C₄⋊C₄	—	2	16	no	—
382	C₄⋊C₄	—	2	8	no	—
383	C₄⋊C₄	—	2	8	no	—
384	C₄⋊C₄	—	2	8	no	—
385	C₂²⋊C₄	—	2	16	no	—
386	C₄²	—	2	4	no	—
387	C₄²	—	2	4	no	—
388	C₄²	—	2	4	no	—
389	C₄²	—	2	4	no	—
390	C₄²	—	2	4	no	—
391	C₄²	—	2	4	no	—
392	C₄²	—	2	4	no	—
393	C₄²	—	2	4	no	—
394	C₄²	—	2	4	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	16	no	—
398	C₄²	C₂×Q₈×C₂₃	1	4	yes	—
399	C₄²	C₂×Q₈×C₂₃	1	4	yes	—
400	C₄²	C₂×Q₈×C₂₃	1	4	yes	—
401	C₄²	C₂×Q₈×C₂₃	1	4	yes	—
402	C₄²	#41×C₂₃	1	8	yes	—
403	C₄²	#41×C₂₃	1	4	yes	—
404	C₄²	#41×C₂₃	1	4	yes	—
405	C₂³	—	2	1	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	1	no	—
408	C₂³	C₂²×Q₈×C₂₃	1	2	yes	—
409	C₂³	C₂×#41×C₂₃	1	4	yes	—
410	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
411	Q₈	—	4	16	no	—
412	C₂×C₄	—	2	16	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	8	no	—
425	C₂×C₄	—	2	16	no	—
426	C₂×C₄	—	2	8	no	—
427	C₂×C₄	—	2	8	no	—
428	C₂×C₄	—	2	8	no	—
429	C₂×C₄	—	2	8	no	—
430	C₂×C₄	—	2	8	no	—
431	C₂×C₄	—	2	8	no	—
432	C₂×C₄	—	2	8	no	—
433	C₂×C₄	—	2	8	no	—
434	C₂×C₄	C₂²×Q₈×C₂₃	1	2	yes	—
435	C₂×C₄	C₂²×Q₈×C₂₃	1	2	yes	—
436	C₂×C₄	C₂²×Q₈×C₂₃	1	2	yes	—
437	C₂×C₄	C₂²×Q₈×C₂₃	1	2	yes	—
438	C₂×C₄	C₂²×Q₈×C₂₃	1	2	yes	—
439	C₂×C₄	C₂²×Q₈×C₂₃	1	2	yes	—
440	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
441	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
442	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
443	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
444	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
445	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
446	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
447	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
448	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
449	C₂²	—	2	4	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	4	no	—
453	C₂²	C₂₃×#533	1	4	yes	—
454	C₂²	C₂³×Q₈×C₂₃	1	1	yes	characteristic
455	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
456	C₂²	C₂²×#41×C₂₃	1	2	yes	—
457	C₂²	C₂²×#41×C₂₃	1	2	yes	—
458	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
459	C₄	—	2	4	no	—
460	C₄	—	2	2	no	—
461	C₄	—	2	2	no	—
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	2	4	no	—
465	C₄	—	2	4	no	—
466	C₄	—	4	8	no	—
467	C₄	—	4	8	no	—
468	C₄	C₂₃×#529	1	8	yes	—
469	C₄	C₂₃×#533	1	4	yes	—
470	C₄	C₂₃×#533	1	4	yes	—
471	C₂	—	2	4	no	—
472	C₂	C₂×C₂₃×#529	1	2	yes	—
473	C₂	C₂×C₂₃×#533	1	1	yes	characteristic
474	C₂	C₂×C₂₃×#533	1	1	yes	characteristic
475	C₂	C₂×C₂₃×#533	1	1	yes	characteristic
476	C₂	C₂₃×#3444	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂₃×#2864	C₂	semidirect
2. C₂₃×#2863	C₂	semidirect
3. C₂₃×#2862	C₂	semidirect
4. C₂₃×#2859	C₂	semidirect
8. C₄×C₂₃×C₄⋊Q₈	C₂	semidirect
9. C₄×C₂₃×#125	C₂	semidirect
11. C₂₃×#2295	C₂	semidirect
80. C₂×C₄²×C₂₃	Q₈	semidirect
166. #36635	C₂₃	direct (N × H)
211. #2864	C₂×C₂₃	semidirect
212. #2863	C₂×C₂₃	semidirect
213. #2862	C₂×C₂₃	semidirect
214. #2859	C₂×C₂₃	semidirect
218. C₄×C₄⋊Q₈	C₂×C₂₃	semidirect
219. C₄×#125	C₂×C₂₃	semidirect
221. #2295	C₂×C₂₃	semidirect
318. C₂×C₄²	Q₈×C₂₃	semidirect
347. C₂₃	#36635	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#2864	2
C₂₃×#2863	2
C₂₃×#2862	2
C₂₃×#2859	2
C₂₃×#2857	2
C₂₃×#2855	2
C₂₃×#2851	2
C₄×C₂₃×C₄⋊Q₈	2
C₄×C₂₃×#125	2
C₄×C₂₃×C₂²⋊Q₈	2
C₂₃×#2295	2
C₂₃×#2283	2
C₂×C₄³×C₂₃	2
#36635	23

Subgroups — C23×#36635 #19184261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#36635 #19184261