Subgroups — #15686691

Order 2944.

1212 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	#13092973	C₂	1	1	yes	maximal, characteristic, complemented
2	#13092971	C₂	1	1	yes	maximal, characteristic, complemented
3	#13092969	C₂	1	1	yes	maximal, characteristic, complemented
4	#13092966	C₂	1	1	yes	maximal, characteristic, complemented
5	#13092964	C₂	1	1	yes	maximal, characteristic, complemented
6	#13092962	C₂	1	1	yes	maximal, characteristic, complemented
7	#13092952	C₂	1	1	yes	maximal, characteristic, complemented
8	#13092951	C₂	1	1	yes	maximal, characteristic, complemented
9	#13092950	C₂	1	2	yes	maximal, complemented
10	#13092950	C₂	1	2	yes	maximal, complemented
11	#13092946	C₂	1	1	yes	maximal, characteristic, complemented
12	#13092945	C₂	1	2	yes	maximal, complemented
13	#13092944	C₂	1	2	yes	maximal, complemented
14	#13092930	C₂	1	1	yes	maximal, characteristic, complemented
15	#13092927	C₂	1	1	yes	maximal, characteristic, complemented
16	#13092926	C₂	1	2	yes	maximal, complemented
17	#13092925	C₂	1	2	yes	maximal, complemented
18	C₄×#67292	C₂	1	1	yes	maximal, characteristic, complemented
19	#13092885	C₂	1	2	yes	maximal, complemented
20	C₄×#67290	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#67290	C₂	1	2	yes	maximal, complemented
22	C₂×C₄²×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#67292	C₂²	1	1	yes	characteristic
25	C₂×#67290	C₂²	1	2	yes	—
26	C₂×#67290	C₂²	1	1	yes	characteristic
27	C₂×#67288	C₂²	1	2	yes	—
28	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
30	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
31	C₂₃×#126	C₂²	1	2	yes	complemented
32	C₂₃×#125	C₂²	1	1	yes	characteristic, complemented
33	C₂₃×#124	C₂²	1	1	yes	characteristic, complemented
34	C₂₃×#123	C₂²	1	2	yes	—
35	C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₂₃×#121	C₂²	1	1	yes	characteristic
37	C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
38	C₄×D₄×C₂₃	C₂²	1	2	yes	—
39	C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
40	C₂₃×#117	C₂²	1	2	yes	complemented
41	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
42	#10625117	C₂²	1	1	yes	characteristic
43	Q₈×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
44	#10625115	C₂²	1	1	yes	characteristic, complemented
45	#10625111	C₂²	1	1	yes	characteristic, complemented
46	#10625110	C₂²	1	2	yes	—
47	#10625109	C₂²	1	1	yes	characteristic
48	#10625108	C₂²	1	2	yes	—
49	D₄×Dic₂₃	C₂²	1	2	yes	—
50	D₄×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
51	#10625101	C₂²	1	1	yes	characteristic
52	#10625100	C₂²	1	2	yes	—
53	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	—
54	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	—
55	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
56	#10625095	C₂²	1	1	yes	characteristic
57	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic
58	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic
59	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic
60	C₂×C₄×Dic₂₃	C₂²	1	2	yes	complemented
61	#10625069	C₂²	1	2	yes	complemented
62	#10625068	C₂²	1	1	yes	characteristic
63	#10625067	C₂²	1	2	yes	—
64	#10625067	C₂²	1	2	yes	—
65	#10625067	C₂²	1	2	yes	—
66	#10625066	C₂²	1	1	yes	characteristic
67	#10625065	C₂²	1	2	yes	—
68	#10625065	C₂²	1	2	yes	—
69	#10625064	C₂²	1	2	yes	—
70	#10625064	C₂²	1	2	yes	—
71	#10625064	C₂²	1	2	yes	—
72	#10625064	C₂²	1	1	yes	characteristic, complemented
73	#10625063	C₂²	1	1	yes	characteristic
74	#10625063	C₂²	1	1	yes	characteristic
75	#10625063	C₂²	1	2	yes	complemented
76	#10625063	C₂²	1	2	yes	complemented
77	#10625060	C₂²	1	2	yes	complemented
78	#10625060	C₂²	1	2	yes	complemented
79	#10625059	C₂²	1	1	yes	characteristic, complemented
80	#10625059	C₂²	1	1	yes	characteristic, complemented
81	#10625058	C₂²	1	2	yes	complemented
82	#10625058	C₂²	1	1	yes	characteristic, complemented
83	#10625058	C₂²	1	2	yes	complemented
84	#10625058	C₂²	1	2	yes	complemented
85	#10625056	C₂²	1	2	yes	complemented
86	#10625056	C₂²	1	2	yes	complemented
87	#10625055	C₂²	1	2	yes	—
88	#10625055	C₂²	1	2	yes	—
89	#10625055	C₂²	1	2	yes	—
90	#10625054	C₂²	1	2	yes	—
91	#10625054	C₂²	1	2	yes	—
92	#10625053	C₂²	1	2	yes	—
93	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	—
94	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	—
95	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	—
96	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	—
97	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	complemented
98	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	complemented
99	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	complemented
100	#10625050	C₂²	1	2	yes	complemented
101	#10625049	C₂²	1	2	yes	—
102	#10625048	C₂²	1	2	yes	—
103	#10625048	C₂²	1	2	yes	complemented
104	#10625048	C₂²	1	2	yes	complemented
105	#10625047	C₂²	1	2	yes	complemented
106	#10625046	C₂²	1	1	yes	characteristic, complemented
107	C₄×D₉₂	C₂²	1	2	yes	—
108	C₄×D₉₂	C₂²	1	1	yes	characteristic, complemented
109	#10625043	C₂²	1	2	yes	—
110	#10625043	C₂²	1	2	yes	complemented
111	C₄²×D₂₃	C₂²	1	1	yes	characteristic
112	C₄²×D₂₃	C₂²	1	1	yes	characteristic
113	C₄²×D₂₃	C₂²	1	1	yes	characteristic
114	C₄²×D₂₃	C₂²	1	1	yes	characteristic
115	C₄²×D₂₃	C₂²	1	1	yes	characteristic
116	C₄²×D₂₃	C₂²	1	1	yes	characteristic
117	C₄²×D₂₃	C₂²	1	1	yes	characteristic
118	C₄²×D₂₃	C₂²	1	1	yes	characteristic
119	C₄²×D₂₃	C₂²	1	2	yes	complemented
120	#10625041	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₄₆	C₂²	1	2	yes	complemented
122	C₄×Dic₄₆	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₂₃	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₂₃	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₂₃	C₂³	1	2	yes	—
126	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
136	C₂²×Dic₂₃	C₂³	1	2	yes	—
137	C₂²×Dic₂₃	C₂³	1	2	yes	—
138	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
139	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
140	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
141	#67292	—	2	4	no	—
142	#67290	—	2	8	no	—
143	#67290	—	2	4	no	—
144	#67288	—	2	8	no	—
145	C₂×D₉₂	C₂³	1	2	yes	—
146	C₂×D₉₂	C₂³	1	1	yes	characteristic
147	C₂×D₉₂	C₂³	1	2	yes	—
148	C₂×C₄×D₂₃	—	2	4	no	—
149	C₂×C₄×D₂₃	—	2	4	no	—
150	C₂×C₄×D₂₃	—	2	4	no	—
151	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₂₃	C₂³	1	2	yes	—
162	C₂×C₄×D₂₃	C₂³	1	2	yes	—
163	C₂×C₄×D₂₃	C₂³	1	2	yes	—
164	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
165	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
166	C₂×Dic₄₆	C₂³	1	1	yes	characteristic
167	C₂×Dic₄₆	C₂³	1	2	yes	—
168	C₂×Dic₄₆	C₂³	1	2	yes	—
169	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
170	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
171	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
172	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
173	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
174	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
175	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
176	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
177	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
178	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
179	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
180	C₄²×C₂₃	C₂³	1	1	yes	characteristic
181	C₄²×C₂₃	C₂³	1	2	yes	—
182	C₄²×C₂₃	C₂³	1	1	yes	characteristic
183	C₄²×C₂₃	C₂³	1	1	yes	characteristic
184	C₄²×C₂₃	C₂³	1	1	yes	characteristic
185	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
186	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
187	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
188	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
198	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₂₃	C₂³	1	2	yes	—
200	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₂₃	C₂³	1	2	yes	—
202	Dic₂₃⋊C₄	C₂³	1	2	yes	—
203	Dic₂₃⋊C₄	C₂³	1	2	yes	—
204	Dic₂₃⋊C₄	C₂³	1	2	yes	—
205	Dic₂₃⋊C₄	C₂³	1	2	yes	—
206	Dic₂₃⋊C₄	C₂³	1	2	yes	—
207	Dic₂₃⋊C₄	C₂³	1	2	yes	—
208	Dic₂₃⋊C₄	C₂³	1	2	yes	—
209	Dic₂₃⋊C₄	C₂³	1	2	yes	—
210	Dic₂₃⋊C₄	C₂³	1	2	yes	—
211	Dic₂₃⋊C₄	C₂³	1	2	yes	—
212	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
213	C₄×Dic₂₃	C₂³	1	2	yes	—
214	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
215	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
216	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
217	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
218	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
219	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
220	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
221	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
222	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
223	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
224	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
225	C₄×Dic₂₃	C₂³	1	2	yes	—
226	C₄×Dic₂₃	C₂³	1	2	yes	—
227	C₄×Dic₂₃	C₂³	1	2	yes	—
228	C₄×Dic₂₃	C₂³	1	2	yes	—
229	C₂³×C₂₃	C₂⁴	1	2	yes	—
230	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
231	C₂²×D₂₃	—	2	2	no	—
232	C₂²×D₂₃	—	2	2	no	—
233	C₂²×D₂₃	—	2	2	no	—
234	C₂²×D₂₃	C₂⁴	1	2	yes	—
235	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
236	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
237	Q₈×C₂₃	—	2	2	no	—
238	D₄×C₂₃	—	2	4	no	—
239	D₄×C₂₃	—	2	2	no	—
240	C₂×C₄×C₂₃	—	2	2	no	—
241	C₂×C₄×C₂₃	—	2	2	no	—
242	C₂×C₄×C₂₃	—	2	2	no	—
243	C₂×C₄×C₂₃	—	2	4	no	—
244	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
249	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
250	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
251	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
253	C₂²⋊D₂₃	—	2	4	no	—
254	C₂²⋊D₂₃	—	2	4	no	—
255	C₂²⋊D₂₃	—	2	4	no	—
256	C₂²⋊D₂₃	—	2	4	no	—
257	C₂²⋊D₂₃	—	2	4	no	—
258	C₂×Dic₂₃	—	2	2	no	—
259	C₂×Dic₂₃	—	2	2	no	—
260	C₂×Dic₂₃	—	2	4	no	—
261	C₂×Dic₂₃	—	2	4	no	—
262	C₂×Dic₂₃	#41	1	4	yes	complemented
263	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₂₃	C₂⁴	1	2	yes	—
266	C₂×Dic₂₃	C₂⁴	1	2	yes	—
267	C₂×Dic₂₃	C₂⁴	1	2	yes	—
268	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
272	D₉₂	—	2	4	no	—
273	D₉₂	—	2	4	no	—
274	D₉₂	—	2	2	no	—
275	C₄×D₂₃	—	2	2	no	—
276	C₄×D₂₃	—	2	2	no	—
277	C₄×D₂₃	—	2	2	no	—
278	C₄×D₂₃	—	2	2	no	—
279	C₄×D₂₃	—	2	4	no	—
280	C₄×D₂₃	—	2	2	no	—
281	C₄×D₂₃	—	2	2	no	—
282	C₄×D₂₃	—	2	2	no	—
283	C₄×D₂₃	—	2	2	no	—
284	C₄×D₂₃	—	2	2	no	—
285	C₄×D₂₃	—	2	2	no	—
286	C₄×D₂₃	—	2	4	no	—
287	C₄×D₂₃	—	2	4	no	—
288	C₄×D₂₃	#41	1	4	yes	complemented
289	C₄×D₂₃	#41	1	4	yes	complemented
290	Dic₄₆	—	2	2	no	—
291	Dic₄₆	—	2	4	no	—
292	Dic₄₆	—	2	4	no	—
293	#3444	—	23	1	no	maximal, Sylow
294	C₂²×C₂₃	—	2	1	no	—
295	C₂²×C₂₃	—	2	1	no	—
296	C₂²×C₂₃	—	2	2	no	—
297	C₂²×C₂₃	—	2	2	no	—
298	C₂²×C₂₃	—	2	2	no	—
299	C₂²×C₂₃	C₂×#41	1	2	yes	—
300	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
301	C₂×D₂₃	—	2	8	no	—
302	C₂×D₂₃	—	2	1	no	—
303	C₂×D₂₃	—	2	1	no	—
304	C₂×D₂₃	—	2	1	no	—
305	C₂×D₂₃	—	2	1	no	—
306	C₂×D₂₃	—	2	2	no	—
307	C₂×D₂₃	—	2	2	no	—
308	C₂×D₂₃	—	2	2	no	—
309	C₂×D₂₃	C₂×#41	1	2	yes	—
310	C₂×D₂₃	C₂×#41	1	2	yes	—
311	C₄×C₂₃	—	2	2	no	—
312	C₄×C₂₃	—	2	2	no	—
313	C₄×C₂₃	—	2	1	no	—
314	C₄×C₂₃	—	2	1	no	—
315	C₄×C₂₃	—	2	1	no	—
316	C₄×C₂₃	—	2	1	no	—
317	C₄×C₂₃	—	2	2	no	—
318	C₄×C₂₃	C₂×#41	1	2	yes	—
319	C₄×C₂₃	C₂×#41	1	2	yes	—
320	Dic₂₃	—	2	2	no	—
321	Dic₂₃	—	2	2	no	—
322	Dic₂₃	—	2	2	no	—
323	Dic₂₃	—	2	1	no	—
324	Dic₂₃	—	2	1	no	—
325	Dic₂₃	C₂×#41	1	2	yes	—
326	Dic₂₃	C₂×#41	1	2	yes	—
327	Dic₂₃	C₂×#41	1	2	yes	—
328	Dic₂₃	C₂×#41	1	2	yes	—
329	#533	—	23	1	no	—
330	#533	—	23	1	no	—
331	#533	—	23	1	no	—
332	#532	—	23	1	no	—
333	#532	—	23	1	no	—
334	#532	—	23	1	no	—
335	#529	—	23	2	no	—
336	#529	—	23	2	no	—
337	#529	—	23	1	no	—
338	#529	—	23	1	no	—
339	#529	—	23	2	no	—
340	#529	—	23	2	no	—
341	#529	—	23	1	no	—
342	#529	D₂₃	1	1	yes	characteristic, complemented
343	#525	—	23	2	no	—
344	#525	—	23	1	no	—
345	#525	—	23	1	no	—
346	#525	—	23	2	no	—
347	C₄×#41	—	23	1	no	—
348	C₄×#41	—	23	2	no	—
349	C₄×#41	—	23	1	no	—
350	C₄×#41	—	23	2	no	—
351	C₂²×C₄²	—	23	1	no	—
352	C₂×C₂₃	—	2	2	no	—
353	C₂×C₂₃	—	4	2	no	—
354	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
355	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
356	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
357	D₂₃	—	2	2	no	—
358	D₂₃	—	2	2	no	—
359	D₂₃	—	4	2	no	—
360	C₂×#41	—	23	1	no	—
361	C₂×#41	—	23	2	no	—
362	C₂×#41	—	23	1	no	—
363	C₂×#41	—	23	2	no	—
364	C₂³×C₄	—	23	1	no	—
365	C₂³×C₄	—	23	1	no	—
366	C₂³×C₄	—	23	1	no	—
367	C₄⋊Q₈	—	23	1	no	—
368	C₄⋊Q₈	—	23	1	no	—
369	C₄⋊Q₈	—	23	1	no	—
370	#127	—	23	1	no	—
371	#126	—	23	2	no	—
372	#126	—	23	2	no	—
373	#126	—	23	2	no	—
374	#126	C₂×D₂₃	1	2	yes	complemented
375	#125	—	23	2	no	—
376	#125	—	23	2	no	—
377	#125	—	23	1	no	—
378	#125	C₂×D₂₃	1	1	yes	characteristic, complemented
379	#124	—	23	2	no	—
380	#124	—	23	2	no	—
381	#124	—	23	1	no	—
382	#124	C₂×D₂₃	1	1	yes	characteristic, complemented
383	#123	—	23	2	no	—
384	#123	—	23	2	no	—
385	#123	—	23	2	no	—
386	#123	—	23	2	no	—
387	#123	—	23	2	no	—
388	#123	C₂×D₂₃	1	2	yes	—
389	C₂²⋊Q₈	—	23	1	no	—
390	C₂²⋊Q₈	—	23	1	no	—
391	C₂²⋊Q₈	—	23	2	no	—
392	C₂²⋊Q₈	—	23	2	no	—
393	C₂²⋊Q₈	—	23	2	no	—
394	C₂²⋊Q₈	—	23	1	no	—
395	C₂²⋊Q₈	—	23	2	no	—
396	C₂²⋊Q₈	C₂×D₂₃	1	1	yes	characteristic
397	#121	—	23	1	no	—
398	#121	—	23	2	no	—
399	#121	—	23	1	no	—
400	#121	—	23	1	no	—
401	#121	—	23	2	no	—
402	#121	—	23	2	no	—
403	#121	—	23	2	no	—
404	#121	C₂×D₂₃	1	1	yes	characteristic
405	#120	—	23	2	no	—
406	#120	—	23	2	no	—
407	C₄×Q₈	—	23	1	no	—
408	C₄×Q₈	—	23	2	no	—
409	C₄×Q₈	—	23	2	no	—
410	C₄×Q₈	—	23	2	no	—
411	C₄×Q₈	—	23	1	no	—
412	C₄×Q₈	—	23	2	no	—
413	C₄×Q₈	—	23	1	no	—
414	C₄×Q₈	C₂×D₂₃	1	1	yes	characteristic, complemented
415	C₄×D₄	—	23	2	no	—
416	C₄×D₄	—	23	1	no	—
417	C₄×D₄	—	23	2	no	—
418	C₄×D₄	—	23	2	no	—
419	C₄×D₄	—	23	2	no	—
420	C₄×D₄	—	23	2	no	—
421	C₄×D₄	—	23	2	no	—
422	C₄×D₄	—	23	2	no	—
423	C₄×D₄	—	23	1	no	—
424	C₄×D₄	—	23	2	no	—
425	C₄×D₄	—	23	2	no	—
426	C₄×D₄	—	23	2	no	—
427	C₄×D₄	—	23	2	no	—
428	C₄×D₄	—	23	2	no	—
429	C₄×D₄	—	23	2	no	—
430	C₄×D₄	—	23	2	no	—
431	C₄×D₄	—	23	2	no	—
432	C₄×D₄	—	23	1	no	—
433	C₄×D₄	C₂×D₂₃	1	2	yes	—
434	C₄×D₄	C₂×D₂₃	1	1	yes	characteristic, complemented
435	#117	—	23	1	no	—
436	#117	—	23	1	no	—
437	#117	—	23	2	no	—
438	#117	—	23	2	no	—
439	#117	—	23	2	no	—
440	#117	—	23	2	no	—
441	#117	—	23	2	no	—
442	#117	—	23	2	no	—
443	#117	—	23	2	no	—
444	#117	C₂×D₂₃	1	2	yes	complemented
445	C₂×C₄²	—	23	2	no	—
446	C₂×C₄²	—	23	1	no	—
447	C₂×C₄²	—	23	1	no	—
448	C₂×C₄²	—	23	1	no	—
449	C₂×C₄²	—	23	2	no	—
450	C₂×C₄²	—	23	1	no	—
451	C₂×C₄²	—	23	1	no	—
452	C₂×C₄²	—	23	1	no	—
453	C₂×C₄²	—	23	1	no	—
454	C₂×C₄²	—	23	1	no	—
455	C₂×C₄²	—	23	1	no	—
456	C₂×C₄²	—	23	1	no	—
457	C₂×C₄²	—	23	1	no	—
458	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
459	C₂₃	#3444	1	1	yes	characteristic, complemented, Sylow
460	C₂⁴	—	23	1	no	—
461	#41	—	46	8	no	—
462	#41	—	46	8	no	—
463	#41	—	46	4	no	—
464	#41	—	46	4	no	—
465	C₂×Q₈	—	23	2	no	—
466	C₂×Q₈	—	23	2	no	—
467	C₂×Q₈	—	23	1	no	—
468	C₂×Q₈	C₂²×D₂₃	1	1	yes	characteristic
469	C₂×D₄	—	23	2	no	—
470	C₂×D₄	—	23	2	no	—
471	C₂×D₄	—	23	2	no	—
472	C₂×D₄	—	23	2	no	—
473	C₂×D₄	—	23	2	no	—
474	C₂×D₄	—	23	2	no	—
475	C₂×D₄	—	23	2	no	—
476	C₂×D₄	—	23	1	no	—
477	C₂×D₄	C₂²×D₂₃	1	2	yes	—
478	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
479	C₂²×C₄	—	23	1	no	—
480	C₂²×C₄	—	23	1	no	—
481	C₂²×C₄	—	23	1	no	—
482	C₂²×C₄	—	23	1	no	—
483	C₂²×C₄	—	23	1	no	—
484	C₂²×C₄	—	23	2	no	—
485	C₂²×C₄	—	23	2	no	—
486	C₂²×C₄	—	23	1	no	—
487	C₂²×C₄	—	23	1	no	—
488	C₂²×C₄	—	23	1	no	—
489	C₂²×C₄	—	23	1	no	—
490	C₂²×C₄	—	23	1	no	—
491	C₂²×C₄	—	23	1	no	—
492	C₂²×C₄	—	23	1	no	—
493	C₂²×C₄	—	23	1	no	—
494	C₂²×C₄	—	23	1	no	—
495	C₂²×C₄	—	23	2	no	—
496	C₂²×C₄	—	23	2	no	—
497	C₂²×C₄	—	23	1	no	—
498	C₂²×C₄	—	23	2	no	—
499	C₂²×C₄	—	46	4	no	—
500	C₂²×C₄	—	46	4	no	—
501	C₂²×C₄	—	46	4	no	—
502	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
503	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
504	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
505	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
506	C₄⋊C₄	—	23	2	no	—
507	C₄⋊C₄	—	23	2	no	—
508	C₄⋊C₄	—	23	2	no	—
509	C₄⋊C₄	—	23	2	no	—
510	C₄⋊C₄	—	23	1	no	—
511	C₄⋊C₄	—	23	1	no	—
512	C₄⋊C₄	—	23	2	no	—
513	C₄⋊C₄	—	23	2	no	—
514	C₄⋊C₄	—	23	2	no	—
515	C₄⋊C₄	—	23	2	no	—
516	C₄⋊C₄	—	23	2	no	—
517	C₄⋊C₄	—	23	2	no	—
518	C₄⋊C₄	—	23	2	no	—
519	C₄⋊C₄	—	23	2	no	—
520	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
521	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
522	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
523	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
525	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
526	C₂²⋊C₄	—	23	2	no	—
527	C₂²⋊C₄	—	23	2	no	—
528	C₂²⋊C₄	—	23	2	no	—
529	C₂²⋊C₄	—	23	2	no	—
530	C₂²⋊C₄	—	23	2	no	—
531	C₂²⋊C₄	—	23	2	no	—
532	C₂²⋊C₄	—	23	2	no	—
533	C₂²⋊C₄	—	23	2	no	—
534	C₂²⋊C₄	—	23	2	no	—
535	C₂²⋊C₄	—	23	2	no	—
536	C₂²⋊C₄	—	23	2	no	—
537	C₂²⋊C₄	—	23	2	no	—
538	C₂²⋊C₄	—	23	2	no	—
539	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
540	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
541	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
542	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
543	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
544	C₄²	—	23	1	no	—
545	C₄²	—	23	1	no	—
546	C₄²	—	23	1	no	—
547	C₄²	—	23	1	no	—
548	C₄²	—	23	1	no	—
549	C₄²	—	23	1	no	—
550	C₄²	—	23	1	no	—
551	C₄²	—	23	1	no	—
552	C₄²	—	23	1	no	—
553	C₄²	—	23	1	no	—
554	C₄²	—	23	2	no	—
555	C₄²	—	23	2	no	—
556	C₄²	—	23	2	no	—
557	C₄²	—	23	2	no	—
558	C₄²	—	23	1	no	—
559	C₄²	—	23	1	no	—
560	C₄²	—	23	2	no	—
561	C₄²	C₂²×D₂₃	1	1	yes	characteristic
562	C₄²	C₂²×D₂₃	1	1	yes	characteristic
563	C₄²	C₂²×D₂₃	1	1	yes	characteristic
564	C₄²	C₂²×D₂₃	1	1	yes	characteristic
565	C₄²	C₂²×D₂₃	1	2	yes	—
566	C₂³	—	23	1	no	—
567	C₂³	—	23	1	no	—
568	C₂³	—	23	2	no	—
569	C₂³	—	46	2	no	—
570	C₂³	—	46	2	no	—
571	C₂³	—	46	2	no	—
572	C₂³	C₂³×D₂₃	1	2	yes	—
573	C₂³	C₂³×D₂₃	1	1	yes	characteristic
574	Q₈	—	2	2	no	—
575	Q₈	—	46	4	no	—
576	Q₈	—	46	4	no	—
577	Q₈	—	46	2	no	—
578	D₄	—	2	4	no	—
579	D₄	—	2	2	no	—
580	D₄	—	46	4	no	—
581	D₄	—	46	4	no	—
582	D₄	—	46	4	no	—
583	D₄	—	46	4	no	—
584	D₄	—	46	4	no	—
585	D₄	—	46	4	no	—
586	D₄	—	46	4	no	—
587	D₄	—	46	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	23	4	no	—
593	C₂×C₄	—	23	1	no	—
594	C₂×C₄	—	23	1	no	—
595	C₂×C₄	—	23	1	no	—
596	C₂×C₄	—	23	1	no	—
597	C₂×C₄	—	23	4	no	—
598	C₂×C₄	—	23	4	no	—
599	C₂×C₄	—	23	1	no	—
600	C₂×C₄	—	23	1	no	—
601	C₂×C₄	—	23	2	no	—
602	C₂×C₄	—	23	2	no	—
603	C₂×C₄	—	23	2	no	—
604	C₂×C₄	—	46	2	no	—
605	C₂×C₄	—	46	2	no	—
606	C₂×C₄	—	46	2	no	—
607	C₂×C₄	—	46	2	no	—
608	C₂×C₄	—	46	2	no	—
609	C₂×C₄	—	46	2	no	—
610	C₂×C₄	—	46	4	no	—
611	C₂×C₄	—	46	4	no	—
612	C₂×C₄	—	46	2	no	—
613	C₂×C₄	—	46	2	no	—
614	C₂×C₄	—	46	2	no	—
615	C₂×C₄	—	46	2	no	—
616	C₂×C₄	—	46	4	no	—
617	C₂×C₄	—	46	4	no	—
618	C₂×C₄	—	46	2	no	—
619	C₂×C₄	—	46	2	no	—
620	C₂×C₄	—	46	4	no	—
621	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
622	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₂₃	1	2	yes	—
626	C₂×C₄	C₂³×D₂₃	1	2	yes	—
627	C₂×C₄	C₂³×D₂₃	1	2	yes	—
628	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
629	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
630	C₂²	—	2	1	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	23	2	no	—
636	C₂²	—	23	2	no	—
637	C₂²	—	46	8	no	—
638	C₂²	—	46	1	no	—
639	C₂²	—	46	1	no	—
640	C₂²	—	46	1	no	—
641	C₂²	—	46	1	no	—
642	C₂²	—	46	2	no	—
643	C₂²	—	46	2	no	—
644	C₂²	—	46	2	no	—
645	C₂²	#41×D₂₃	1	2	yes	—
646	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	1	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	2	no	—
654	C₄	—	23	2	no	—
655	C₄	—	23	2	no	—
656	C₄	—	23	2	no	—
657	C₄	—	23	2	no	—
658	C₄	—	46	1	no	—
659	C₄	—	46	1	no	—
660	C₄	—	46	2	no	—
661	C₄	—	46	2	no	—
662	C₄	—	46	2	no	—
663	C₄	#41×D₂₃	1	2	yes	—
664	C₄	#41×D₂₃	1	2	yes	—
665	C₂	—	2	2	no	—
666	C₂	—	4	2	no	—
667	C₂	—	46	2	no	—
668	C₂	—	46	2	no	—
669	C₂	—	92	2	no	—
670	C₂	C₂×#41×D₂₃	1	1	yes	characteristic
671	C₂	C₂×#41×D₂₃	1	1	yes	characteristic
672	C₂	C₂×#41×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₂₃
commutator, socle, cosocle	C₂²×C₂₃	C₂⁵
Frattini	C₂²	C₂⁴×D₂₃
Fitting	C₂₃×#529	C₂
hypercenter	#529	D₂₃
hypocenter	C₂₃	#3444
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ #529

Complements

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

N	H ≅ G/N	type
1. #13092973	C₂	semidirect
2. #13092971	C₂	semidirect
3. #13092969	C₂	semidirect
4. #13092966	C₂	semidirect
5. #13092964	C₂	semidirect
6. #13092962	C₂	semidirect
7. #13092952	C₂	semidirect
8. #13092951	C₂	semidirect
9. #13092950	C₂	semidirect
10. #13092950	C₂	semidirect
11. #13092946	C₂	semidirect
12. #13092945	C₂	semidirect
13. #13092944	C₂	semidirect
14. #13092930	C₂	semidirect
15. #13092927	C₂	semidirect
16. #13092926	C₂	semidirect
17. #13092925	C₂	semidirect
18. C₄×#67292	C₂	semidirect
19. #13092885	C₂	semidirect
20. C₄×#67290	C₂	semidirect
21. C₄×#67290	C₂	semidirect
22. C₂×C₄²×D₂₃	C₂	semidirect
23. C₂₃×#529	C₂	semidirect
31. C₂₃×#126	C₂²	semidirect
32. C₂₃×#125	C₂²	semidirect
33. C₂₃×#124	C₂²	semidirect
37. C₄×Q₈×C₂₃	C₂²	semidirect
39. C₄×D₄×C₂₃	C₂²	semidirect
40. C₂₃×#117	C₂²	semidirect
43. Q₈×Dic₂₃	C₂²	semidirect
44. #10625115	C₂²	semidirect
45. #10625111	C₂²	semidirect
50. D₄×Dic₂₃	C₂²	semidirect
55. C₄×C₂²⋊D₂₃	C₂²	semidirect
60. C₂×C₄×Dic₂₃	C₂²	semidirect
61. #10625069	C₂²	semidirect
72. #10625064	C₂²	semidirect
75. #10625063	C₂²	semidirect
76. #10625063	C₂²	semidirect
77. #10625060	C₂²	semidirect
78. #10625060	C₂²	semidirect
79. #10625059	C₂²	semidirect
80. #10625059	C₂²	semidirect
81. #10625058	C₂²	semidirect
82. #10625058	C₂²	semidirect
83. #10625058	C₂²	semidirect
84. #10625058	C₂²	semidirect
85. #10625056	C₂²	semidirect
86. #10625056	C₂²	semidirect
97. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
98. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
99. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
100. #10625050	C₂²	semidirect
103. #10625048	C₂²	semidirect
104. #10625048	C₂²	semidirect
105. #10625047	C₂²	semidirect
106. #10625046	C₂²	semidirect
108. C₄×D₉₂	C₂²	semidirect
110. #10625043	C₂²	semidirect
119. C₄²×D₂₃	C₂²	semidirect
120. #10625041	C₂²	semidirect
121. C₄×Dic₄₆	C₂²	semidirect
122. C₄×Dic₄₆	C₂²	semidirect
262. C₂×Dic₂₃	#41	semidirect
288. C₄×D₂₃	#41	semidirect
289. C₄×D₂₃	#41	semidirect
342. #529	D₂₃	semidirect
374. #126	C₂×D₂₃	semidirect
378. #125	C₂×D₂₃	semidirect
382. #124	C₂×D₂₃	semidirect
414. C₄×Q₈	C₂×D₂₃	semidirect
434. C₄×D₄	C₂×D₂₃	semidirect
444. #117	C₂×D₂₃	semidirect
459. C₂₃	#3444	semidirect

Maximal subgroups

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

subgroup	index
#13092973	2
#13092971	2
#13092969	2
#13092966	2
#13092964	2
#13092962	2
#13092952	2
#13092951	2
#13092950	2
#13092946	2
#13092945	2
#13092944	2
#13092930	2
#13092927	2
#13092926	2
#13092925	2
C₄×#67292	2
#13092885	2
C₄×#67290	2
C₂×C₄²×D₂₃	2
C₂₃×#529	2
#3444	23