Subgroups — #15682097

Order 2944.

492 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10625078	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×M₁₆×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#13092926	C₂	1	1	yes	maximal, characteristic
4	#13092496	C₂	1	1	yes	maximal, characteristic, complemented
5	#13092493	C₂	1	1	yes	maximal, characteristic, complemented
6	#13092493	C₂	1	1	yes	maximal, characteristic, complemented
7	#13092491	C₂	1	1	yes	maximal, characteristic, complemented
8	#13092489	C₂	1	1	yes	maximal, characteristic, complemented
9	#13092487	C₂	1	1	yes	maximal, characteristic, complemented
10	#13092485	C₂	1	1	yes	maximal, characteristic, complemented
11	#13092442	C₂	1	1	yes	maximal, characteristic, complemented
12	#13092382	C₂	1	1	yes	maximal, characteristic, complemented
13	#13092379	C₂	1	1	yes	maximal, characteristic, complemented
14	#13092371	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#436	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#67288	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
18	C₂×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₂×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
20	C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
21	#10625110	C₄	1	1	yes	characteristic
22	#10625108	C₄	1	1	yes	characteristic
23	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
25	C₂×#67267	C₂²	1	1	yes	characteristic
26	C₂²×C₂₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
27	#10625078	—	2	4	no	—
28	M₁₆×D₂₃	—	2	4	no	—
29	C₂×#67262	C₂²	1	1	yes	characteristic
30	C₂×#67262	C₂²	1	1	yes	characteristic
31	C₂×#67262	C₂²	1	1	yes	characteristic
32	C₂×#67262	C₂²	1	1	yes	characteristic
33	C₂×#67262	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₈×D₂₃	C₂²	1	1	yes	characteristic
35	C₂×C₈×D₂₃	C₂²	1	1	yes	characteristic
36	C₂×C₈×D₂₃	C₂²	1	1	yes	characteristic, complemented
37	#10625067	C₄	1	1	yes	characteristic
38	#10625065	C₄	1	1	yes	characteristic
39	#10625055	C₄	1	1	yes	characteristic
40	#10625054	C₄	1	1	yes	characteristic
41	#10625053	C₄	1	1	yes	characteristic
42	#10625049	C₄	1	1	yes	characteristic
43	C₄×D₉₂	C₂²	1	1	yes	characteristic
44	#10625043	C₂²	1	1	yes	characteristic
45	C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
46	C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
47	C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
48	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
49	C₂²⋊(C₂₃⋊C₈)	C₂²	1	1	yes	characteristic
50	C₂²⋊(C₂₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
51	(C₂×D₂₃)⋊C₈	C₂²	1	1	yes	characteristic
52	(C₂×D₂₃)⋊C₈	C₂²	1	1	yes	characteristic
53	(C₂×D₂₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
54	(C₂×D₂₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
55	#10624997	C₂²	1	1	yes	characteristic, complemented
56	Dic₂₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
57	Dic₂₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
58	C₈×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
59	C₄⋊(C₂₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
60	#10624985	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₂₃	C₂×C₄	1	1	yes	characteristic
62	C₂×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
65	C₂×C₂²⋊D₂₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₂²⋊D₂₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₂²⋊D₂₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₂²⋊D₂₃	C₂×C₄	1	1	yes	characteristic
69	C₂²×Dic₂₃	C₂×C₄	1	1	yes	characteristic
70	#67288	—	2	2	no	—
71	#67288	—	2	2	no	—
72	C₂×D₉₂	C₂×C₄	1	1	yes	characteristic
73	C₂×D₉₂	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄×D₂₃	—	2	2	no	—
75	C₂×C₄×D₂₃	—	2	2	no	—
76	C₂×C₄×D₂₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×D₂₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
79	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
80	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
81	C₂×Dic₄₆	C₂×C₄	1	1	yes	characteristic
82	M₁₆×C₂₃	—	2	2	no	—
83	M₁₆×C₂₃	—	2	2	no	—
84	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
85	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
86	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
87	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
88	C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
89	C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
90	C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
91	C₄²×C₂₃	C₂³	1	1	yes	characteristic
92	C₂²⋊Dic₂₃	C₂×C₄	1	1	yes	characteristic
93	C₂²⋊Dic₂₃	C₂×C₄	1	1	yes	characteristic
94	(C₂×D₂₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
95	(C₂×D₂₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
96	(C₂×D₂₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
97	(C₂×D₂₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
98	(C₂×D₂₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
99	(C₂×D₂₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
100	C₄⋊Dic₂₃	C₂×C₄	1	1	yes	characteristic
101	Dic₂₃⋊C₄	C₂×C₄	1	1	yes	characteristic
102	Dic₂₃⋊C₄	C₂×C₄	1	1	yes	characteristic
103	Dic₂₃⋊C₄	C₂×C₄	1	1	yes	characteristic
104	Dic₂₃⋊C₄	C₂×C₄	1	1	yes	characteristic
105	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
106	#67267	—	2	2	no	—
107	C₂×C₂₃⋊C₈	—	2	2	no	—
108	C₂×C₂₃⋊C₈	C₂³	1	1	yes	characteristic
109	C₂×C₂₃⋊C₈	C₂³	1	1	yes	characteristic
110	C₂×C₂₃⋊C₈	C₂³	1	1	yes	characteristic
111	C₂×C₂₃⋊C₈	C₂³	1	1	yes	characteristic
112	#67262	—	2	2	no	—
113	#67262	—	2	2	no	—
114	#67262	—	2	2	no	—
115	#67262	—	2	2	no	—
116	#67262	—	2	2	no	—
117	C₈×D₂₃	—	2	2	no	—
118	C₈×D₂₃	—	2	2	no	—
119	C₈×D₂₃	D₄	1	4	yes	complemented
120	C₂³×C₂₃	C₂²×C₄	1	1	yes	characteristic
121	C₂³×C₂₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×D₂₃	—	2	2	no	—
123	C₂²×D₂₃	—	4	1	no	—
124	C₂²×D₂₃	—	4	1	no	—
125	C₂²×D₂₃	C₂²×C₄	1	1	yes	characteristic
126	C₂²×D₂₃	C₂²×C₄	1	1	yes	characteristic
127	C₂²×D₂₃	C₂²×C₄	1	1	yes	characteristic
128	D₄×C₂₃	—	4	1	no	—
129	C₂×C₄×C₂₃	—	2	1	no	—
130	C₂×C₄×C₂₃	—	2	1	no	—
131	C₂×C₄×C₂₃	—	2	1	no	—
132	C₂×C₄×C₂₃	—	2	1	no	—
133	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
138	C₂²⋊D₂₃	—	2	2	no	—
139	C₂²⋊D₂₃	—	2	2	no	—
140	C₂²⋊D₂₃	—	4	1	no	—
141	C₂²⋊D₂₃	—	4	1	no	—
142	C₂×Dic₂₃	—	2	2	no	—
143	C₂×Dic₂₃	C₂²×C₄	1	1	yes	characteristic
144	C₂×Dic₂₃	C₂²×C₄	1	1	yes	characteristic
145	C₂×Dic₂₃	C₂²×C₄	1	1	yes	characteristic
146	C₂×Dic₂₃	C₂²×C₄	1	1	yes	characteristic
147	C₂×Dic₂₃	C₂²×C₄	1	1	yes	characteristic
148	D₉₂	—	2	2	no	—
149	D₉₂	—	4	1	no	—
150	C₄×D₂₃	—	2	2	no	—
151	C₄×D₂₃	—	2	1	no	—
152	C₄×D₂₃	—	2	1	no	—
153	C₄×D₂₃	—	2	1	no	—
154	C₄×D₂₃	—	2	1	no	—
155	C₄×D₂₃	—	2	2	no	—
156	C₄×D₂₃	C₂×D₄	1	2	yes	—
157	C₄×D₂₃	#41	1	2	yes	—
158	Dic₄₆	—	2	2	no	—
159	C₈×C₂₃	—	2	1	no	—
160	C₈×C₂₃	—	2	1	no	—
161	C₈×C₂₃	—	2	1	no	—
162	C₈×C₂₃	C₂×D₄	1	2	yes	—
163	C₂₃⋊C₈	—	2	1	no	—
164	C₂₃⋊C₈	—	2	1	no	—
165	C₂₃⋊C₈	—	2	1	no	—
166	C₂₃⋊C₈	C₂×D₄	1	2	yes	—
167	#2930	—	23	1	no	maximal, Sylow
168	C₂²×C₂₃	—	2	1	no	—
169	C₂²×C₂₃	—	2	1	no	—
170	C₂²×C₂₃	—	2	1	no	—
171	C₂²×C₂₃	—	2	1	no	—
172	C₂²×C₂₃	—	2	1	no	—
173	C₂²×C₂₃	—	2	1	no	—
174	C₂²×C₂₃	C₂³×C₄	1	1	yes	characteristic
175	C₂×D₂₃	—	2	1	no	—
176	C₂×D₂₃	—	2	1	no	—
177	C₂×D₂₃	—	2	1	no	—
178	C₂×D₂₃	—	2	1	no	—
179	C₂×D₂₃	—	2	1	no	—
180	C₂×D₂₃	—	2	1	no	—
181	C₂×D₂₃	—	2	1	no	—
182	C₂×D₂₃	—	2	1	no	—
183	C₂×D₂₃	—	4	4	no	—
184	C₂×D₂₃	C₄×D₄	1	2	yes	—
185	C₄×C₂₃	—	2	1	no	—
186	C₄×C₂₃	—	2	1	no	—
187	C₄×C₂₃	—	2	1	no	—
188	C₄×C₂₃	—	2	1	no	—
189	C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
190	C₄×C₂₃	C₂×#41	1	1	yes	characteristic
191	Dic₂₃	—	2	1	no	—
192	Dic₂₃	—	2	1	no	—
193	Dic₂₃	—	2	1	no	—
194	Dic₂₃	—	2	1	no	—
195	Dic₂₃	C₄×D₄	1	2	yes	—
196	C₂×#131	—	23	1	no	—
197	C₂²×M₁₆	—	23	1	no	—
198	#525	—	23	1	no	—
199	#436	—	23	1	no	—
200	#436	—	23	1	no	—
201	#436	—	23	1	no	—
202	#436	D₂₃	1	1	yes	characteristic, complemented
203	#435	—	23	1	no	—
204	#435	—	23	1	no	—
205	#435	—	23	1	no	—
206	#435	—	23	1	no	—
207	#424	—	23	1	no	—
208	#408	—	23	1	no	—
209	#407	—	23	1	no	—
210	#405	—	23	1	no	—
211	C₂×C₂₃	—	4	1	no	—
212	C₂×C₂₃	—	4	1	no	—
213	C₂×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
214	C₂×C₂₃	#568	1	1	yes	characteristic
215	C₂×C₂₃	#568	1	1	yes	characteristic
216	D₂₃	—	2	2	no	—
217	D₂₃	—	4	1	no	—
218	D₂₃	—	4	1	no	—
219	C₂×#41	—	23	1	no	—
220	C₂³×C₄	—	23	1	no	—
221	#131	—	46	4	no	—
222	C₂×M₁₆	—	23	1	no	—
223	C₂×M₁₆	—	23	1	no	—
224	C₂×M₁₆	—	23	1	no	—
225	C₂×M₁₆	—	23	1	no	—
226	C₂×M₁₆	—	23	1	no	—
227	C₂×M₁₆	—	23	1	no	—
228	C₂×M₁₆	—	46	4	no	—
229	C₂×M₁₆	C₂×D₂₃	1	1	yes	characteristic
230	C₂×M₁₆	C₂×D₂₃	1	1	yes	characteristic, complemented
231	C₂²×C₈	—	23	1	no	—
232	C₂²×C₈	—	23	1	no	—
233	C₂²×C₈	—	23	1	no	—
234	C₂²×C₈	—	23	1	no	—
235	#123	—	23	1	no	—
236	#123	—	23	1	no	—
237	C₂²⋊Q₈	—	23	1	no	—
238	C₂²⋊Q₈	—	23	1	no	—
239	#121	—	23	1	no	—
240	#121	—	23	1	no	—
241	#120	—	23	1	no	—
242	#120	—	23	1	no	—
243	C₄×D₄	—	23	1	no	—
244	C₄×D₄	—	23	1	no	—
245	C₄×D₄	—	23	1	no	—
246	C₄×D₄	C₂×D₂₃	1	1	yes	characteristic
247	#117	—	23	1	no	—
248	C₄⋊C₈	—	23	1	no	—
249	C₄⋊C₈	—	23	1	no	—
250	C₄⋊C₈	—	23	1	no	—
251	C₄⋊C₈	C₂×D₂₃	1	1	yes	characteristic, complemented
252	C₂²⋊C₈	—	23	1	no	—
253	C₂²⋊C₈	—	23	1	no	—
254	C₂²⋊C₈	—	23	1	no	—
255	C₂²⋊C₈	—	23	1	no	—
256	C₂²⋊C₈	—	23	1	no	—
257	C₂²⋊C₈	—	23	1	no	—
258	C₂²⋊C₈	C₂×D₂₃	1	1	yes	characteristic
259	C₂²⋊C₈	C₂×D₂₃	1	1	yes	characteristic, complemented
260	#97	—	23	1	no	—
261	#97	—	23	1	no	—
262	C₄×C₈	—	23	1	no	—
263	C₄×C₈	C₂×D₂₃	1	1	yes	characteristic, complemented
264	C₂₃	#2930	1	1	yes	characteristic, complemented, Sylow
265	C₂⁴	—	23	1	no	—
266	#41	—	46	2	no	—
267	#41	—	46	2	no	—
268	C₂×Q₈	—	23	1	no	—
269	C₂×D₄	—	23	1	no	—
270	C₂×D₄	—	23	1	no	—
271	C₂×D₄	—	23	1	no	—
272	C₂×D₄	—	23	1	no	—
273	C₂×D₄	—	23	1	no	—
274	C₂×D₄	—	23	1	no	—
275	C₂×D₄	C₄×D₂₃	1	1	yes	characteristic
276	C₂²×C₄	—	23	1	no	—
277	C₂²×C₄	—	23	1	no	—
278	C₂²×C₄	—	23	1	no	—
279	C₂²×C₄	—	23	1	no	—
280	C₂²×C₄	—	23	1	no	—
281	C₂²×C₄	—	23	1	no	—
282	C₂²×C₄	—	46	2	no	—
283	C₂²×C₄	—	46	2	no	—
284	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
285	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
286	M₁₆	—	2	2	no	—
287	M₁₆	—	2	2	no	—
288	M₁₆	—	46	2	no	—
289	M₁₆	—	46	2	no	—
290	M₁₆	—	46	2	no	—
291	M₁₆	—	46	2	no	—
292	M₁₆	—	46	2	no	—
293	M₁₆	—	46	2	no	—
294	C₂×C₈	—	23	1	no	—
295	C₂×C₈	—	23	4	no	—
296	C₂×C₈	—	23	1	no	—
297	C₂×C₈	—	23	1	no	—
298	C₂×C₈	—	23	1	no	—
299	C₂×C₈	—	46	2	no	—
300	C₂×C₈	—	46	2	no	—
301	C₂×C₈	—	46	2	no	—
302	C₂×C₈	C₂²×D₂₃	1	1	yes	characteristic
303	C₂×C₈	C₂²×D₂₃	1	1	yes	characteristic
304	C₂×C₈	C₂²×D₂₃	1	1	yes	characteristic
305	C₂×C₈	C₂²×D₂₃	1	1	yes	characteristic
306	C₄⋊C₄	—	23	1	no	—
307	C₄⋊C₄	—	23	1	no	—
308	C₄⋊C₄	—	23	1	no	—
309	C₄⋊C₄	—	23	1	no	—
310	C₄⋊C₄	—	23	1	no	—
311	C₄⋊C₄	C₄×D₂₃	1	1	yes	characteristic
312	C₂²⋊C₄	—	23	1	no	—
313	C₂²⋊C₄	—	23	1	no	—
314	C₂²⋊C₄	—	23	1	no	—
315	C₂²⋊C₄	—	23	1	no	—
316	C₂²⋊C₄	—	23	1	no	—
317	C₂²⋊C₄	—	23	1	no	—
318	C₂²⋊C₄	—	23	1	no	—
319	C₂²⋊C₄	—	23	1	no	—
320	C₂²⋊C₄	C₄×D₂₃	1	1	yes	characteristic
321	C₂²⋊C₄	C₄×D₂₃	1	1	yes	characteristic
322	C₄²	—	23	1	no	—
323	C₄²	C₂²×D₂₃	1	1	yes	characteristic
324	C₂³	—	23	1	no	—
325	C₂³	—	23	1	no	—
326	C₂³	—	23	1	no	—
327	C₂³	—	46	2	no	—
328	C₂³	—	92	1	no	—
329	C₂³	—	92	1	no	—
330	C₂³	C₂×C₄×D₂₃	1	1	yes	characteristic
331	C₂³	C₂×C₄×D₂₃	1	1	yes	characteristic
332	Q₈	—	46	2	no	—
333	D₄	—	4	1	no	—
334	D₄	—	46	2	no	—
335	D₄	—	46	2	no	—
336	D₄	—	46	2	no	—
337	D₄	—	92	1	no	—
338	D₄	—	92	1	no	—
339	D₄	—	92	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	23	1	no	—
345	C₂×C₄	—	23	2	no	—
346	C₂×C₄	—	23	2	no	—
347	C₂×C₄	—	23	1	no	—
348	C₂×C₄	—	23	1	no	—
349	C₂×C₄	—	23	1	no	—
350	C₂×C₄	—	23	1	no	—
351	C₂×C₄	—	46	2	no	—
352	C₂×C₄	—	46	2	no	—
353	C₂×C₄	—	46	2	no	—
354	C₂×C₄	—	46	1	no	—
355	C₂×C₄	—	46	1	no	—
356	C₂×C₄	—	46	1	no	—
357	C₂×C₄	—	46	1	no	—
358	C₂×C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
359	C₂×C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
360	C₂×C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
361	C₂×C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
362	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	—	2	1	no	—
366	C₈	—	23	2	no	—
367	C₈	—	46	1	no	—
368	C₈	—	46	1	no	—
369	C₈	—	46	1	no	—
370	C₈	D₄×D₂₃	1	2	yes	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	23	2	no	—
378	C₂²	—	46	1	no	—
379	C₂²	—	46	1	no	—
380	C₂²	—	46	1	no	—
381	C₂²	—	46	1	no	—
382	C₂²	—	46	1	no	—
383	C₂²	—	46	1	no	—
384	C₂²	—	46	1	no	—
385	C₂²	—	46	1	no	—
386	C₂²	—	92	4	no	—
387	C₂²	C₂²×C₄×D₂₃	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	23	2	no	—
393	C₄	—	46	1	no	—
394	C₄	—	46	1	no	—
395	C₄	—	46	1	no	—
396	C₄	—	46	1	no	—
397	C₄	C₂×D₄×D₂₃	1	1	yes	characteristic
398	C₄	#41×D₂₃	1	1	yes	characteristic
399	C₂	—	4	1	no	—
400	C₂	—	4	1	no	—
401	C₂	—	46	2	no	—
402	C₂	—	92	1	no	—
403	C₂	—	92	1	no	—
404	C₂	C₄×D₄×D₂₃	1	1	yes	characteristic
405	C₂	#13093182	1	1	yes	characteristic
406	C₂	#13093183	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₂₃
commutator, socle	C₂²×C₂₃	C₂³×C₄
Fitting	C₂₃×#436	C₂
prime radical	#13092926	C₂
cosocle	C₂×C₄×C₂₃	C₂⁴
hypercenter	#436	D₂₃
hypocenter	C₂₃	#2930
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ #436

Complements

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

N	H ≅ G/N	type
1. C₂×#10625078	C₂	semidirect
2. C₂×M₁₆×D₂₃	C₂	semidirect
4. #13092496	C₂	semidirect
5. #13092493	C₂	semidirect
6. #13092493	C₂	semidirect
7. #13092491	C₂	semidirect
8. #13092489	C₂	semidirect
9. #13092487	C₂	semidirect
10. #13092485	C₂	semidirect
11. #13092442	C₂	semidirect
12. #13092382	C₂	semidirect
13. #13092379	C₂	semidirect
14. #13092371	C₂	semidirect
15. C₂₃×#436	C₂	semidirect
19. C₂×M₁₆×C₂₃	C₂²	semidirect
26. C₂²×C₂₃⋊C₈	C₂²	semidirect
33. C₂×#67262	C₂²	semidirect
36. C₂×C₈×D₂₃	C₂²	semidirect
45. C₂₃×C₄⋊C₈	C₂²	semidirect
47. C₂₃×C₂²⋊C₈	C₂²	semidirect
48. C₄×C₈×C₂₃	C₂²	semidirect
50. C₂²⋊(C₂₃⋊C₈)	C₂²	semidirect
53. (C₂×D₂₃)⋊C₈	C₂²	semidirect
54. (C₂×D₂₃)⋊C₈	C₂²	semidirect
55. #10624997	C₂²	semidirect
56. Dic₂₃⋊C₈	C₂²	semidirect
57. Dic₂₃⋊C₈	C₂²	semidirect
58. C₈×Dic₂₃	C₂²	semidirect
59. C₄⋊(C₂₃⋊C₈)	C₂²	semidirect
60. #10624985	C₂²	semidirect
119. C₈×D₂₃	D₄	semidirect
202. #436	D₂₃	semidirect
230. C₂×M₁₆	C₂×D₂₃	semidirect
251. C₄⋊C₈	C₂×D₂₃	semidirect
259. C₂²⋊C₈	C₂×D₂₃	semidirect
263. C₄×C₈	C₂×D₂₃	semidirect
264. C₂₃	#2930	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10625078	2
C₂×M₁₆×D₂₃	2
#13092926	2
#13092496	2
#13092493	2
#13092491	2
#13092489	2
#13092487	2
#13092485	2
#13092442	2
#13092382	2
#13092379	2
#13092371	2
C₂₃×#436	2
#2930	23