Subgroups — #15686948

Order 2944.

1132 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093136	C₂	1	1	yes	maximal, characteristic, complemented
2	#13093131	C₂	1	1	yes	maximal, characteristic, complemented
3	#13093126	C₂	1	1	yes	maximal, characteristic, complemented
4	#13093110	C₂	1	2	yes	maximal, complemented
5	#13093109	C₂	1	1	yes	maximal, characteristic, complemented
6	#13093107	C₂	1	1	yes	maximal, characteristic, complemented
7	#13093104	C₂	1	2	yes	maximal, complemented
8	#13093098	C₂	1	2	yes	maximal, complemented
9	#13093093	C₂	1	2	yes	maximal, complemented
10	#13093066	C₂	1	1	yes	maximal, characteristic, complemented
11	#13093061	C₂	1	1	yes	maximal, characteristic, complemented
12	#13092969	C₂	1	1	yes	maximal, characteristic, complemented
13	#13092948	C₂	1	2	yes	maximal, complemented
14	#13092948	C₂	1	1	yes	maximal, characteristic, complemented
15	#13092946	C₂	1	1	yes	maximal, characteristic, complemented
16	#13092944	C₂	1	2	yes	maximal, complemented
17	#13092923	C₂	1	2	yes	maximal, complemented
18	#41×Dic₂₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#67290	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#67290	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×D₄×Dic₂₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#10625048	C₂	1	2	yes	maximal, complemented
23	C₂₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#41×C₂₃	C₂²	1	1	yes	characteristic
25	C₂²×D₄×C₂₃	C₂²	1	1	yes	characteristic
26	C₂³×Dic₂₃	C₂²	1	2	yes	—
27	C₂×#67290	C₂²	1	1	yes	characteristic
28	C₂×#67290	C₂²	1	1	yes	characteristic
29	C₂₃×#124	C₂²	1	1	yes	characteristic
30	C₂₃×#123	C₂²	1	2	yes	—
31	C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂₃×#121	C₂²	1	1	yes	characteristic
33	C₂₃×#121	C₂²	1	2	yes	—
34	C₂₃×#120	C₂²	1	2	yes	—
35	C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
36	C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
38	#10625124	C₂²	1	2	yes	—
39	C₂×C₂²⋊Dic₂₃	C₂²	1	2	yes	—
40	C₂×C₂²⋊Dic₂₃	C₂²	1	2	yes	—
41	#10625117	C₂²	1	1	yes	characteristic, complemented
42	Q₈×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
43	Q₈×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
44	#10625115	C₂²	1	1	yes	characteristic, complemented
45	#10625110	C₂²	1	2	yes	—
46	#10625110	C₂²	1	2	yes	complemented
47	#10625110	C₂²	1	2	yes	complemented
48	#10625109	C₂²	1	1	yes	characteristic
49	#10625107	C₂²	1	1	yes	characteristic
50	#10625107	C₂²	1	2	yes	complemented
51	#10625106	C₂²	1	2	yes	—
52	#10625106	C₂²	1	2	yes	—
53	#10625106	C₂²	1	2	yes	complemented
54	#10625106	C₂²	1	2	yes	complemented
55	D₄×Dic₂₃	C₂²	1	1	yes	characteristic
56	D₄×Dic₂₃	C₂²	1	1	yes	characteristic
57	D₄×Dic₂₃	C₂²	1	1	yes	characteristic
58	D₄×Dic₂₃	C₂²	1	1	yes	characteristic
59	D₄×Dic₂₃	C₂²	1	2	yes	—
60	D₄×Dic₂₃	C₂²	1	1	yes	characteristic
61	D₄×Dic₂₃	C₂²	1	2	yes	—
62	D₄×Dic₂₃	C₂²	1	1	yes	characteristic
63	D₄×Dic₂₃	C₂²	1	2	yes	complemented
64	D₄×Dic₂₃	C₂²	1	2	yes	complemented
65	D₄×Dic₂₃	C₂²	1	2	yes	complemented
66	#10625100	C₂²	1	2	yes	complemented
67	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
68	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic, complemented
69	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
70	#10625097	C₂²	1	1	yes	characteristic, complemented
71	#10625097	C₂²	1	2	yes	complemented
72	C₂×C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic
73	#10625095	C₂²	1	1	yes	characteristic
74	#10625095	C₂²	1	2	yes	complemented
75	#10625095	C₂²	1	1	yes	characteristic, complemented
76	C₂×Dic₂₃⋊C₄	C₂²	1	2	yes	complemented
77	C₂×Dic₂₃⋊C₄	C₂²	1	2	yes	complemented
78	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic
79	C₂×C₄×Dic₂₃	C₂²	1	2	yes	complemented
80	C₂×C₄×Dic₂₃	C₂²	1	2	yes	complemented
81	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
82	#10625069	C₂²	1	2	yes	complemented
83	#10625063	C₂²	1	1	yes	characteristic, complemented
84	#10625063	C₂²	1	1	yes	characteristic, complemented
85	#10625061	C₂²	1	1	yes	characteristic, complemented
86	#10625061	C₂²	1	2	yes	complemented
87	#10625060	C₂²	1	2	yes	complemented
88	#10625060	C₂²	1	2	yes	complemented
89	#10625059	C₂²	1	1	yes	characteristic, complemented
90	#10625058	C₂²	1	1	yes	characteristic, complemented
91	#10625058	C₂²	1	1	yes	characteristic, complemented
92	#10625058	C₂²	1	2	yes	complemented
93	#10625057	C₂²	1	2	yes	—
94	#10625056	C₂²	1	2	yes	complemented
95	#10625054	C₂²	1	2	yes	complemented
96	(C₂²⋊D₂₃)⋊C₄	C₂²	1	1	yes	characteristic
97	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	complemented
98	(C₂²⋊D₂₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
99	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	complemented
100	#10625050	C₂²	1	2	yes	complemented
101	#10625050	C₂²	1	2	yes	complemented
102	#10625050	C₂²	1	2	yes	complemented
103	#10625050	C₂²	1	2	yes	complemented
104	#10625050	C₂²	1	2	yes	complemented
105	#10625049	C₂²	1	2	yes	—
106	#10625049	C₂²	1	2	yes	complemented
107	#10625049	C₂²	1	2	yes	complemented
108	#10625049	C₂²	1	2	yes	complemented
109	#10625048	C₂²	1	1	yes	characteristic
110	#10625048	C₂²	1	2	yes	—
111	#10625048	C₂²	1	2	yes	—
112	#10625048	C₂²	1	2	yes	—
113	#10625048	C₂²	1	2	yes	complemented
114	#10625048	C₂²	1	2	yes	complemented
115	#10625048	C₂²	1	2	yes	complemented
116	#10625048	C₂²	1	2	yes	complemented
117	#10625048	C₂²	1	1	yes	characteristic, complemented
118	#10625048	C₂²	1	2	yes	complemented
119	C₄²×D₂₃	C₂²	1	1	yes	characteristic, complemented
120	#10625041	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₄₆	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₄₆	C₂²	1	1	yes	characteristic, complemented
123	C₂⁴×C₂₃	C₂³	1	2	yes	—
124	#41×C₂₃	—	2	4	no	—
125	C₂×Q₈×C₂₃	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₂₃	—	2	4	no	—
127	C₂×D₄×C₂₃	C₂³	1	2	yes	—
128	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₂₃	C₂³	1	2	yes	—
131	C₂×D₄×C₂₃	C₂³	1	2	yes	—
132	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
135	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₂₃	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₂₃	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
141	C₂²×Dic₂₃	—	2	8	no	—
142	C₂²×Dic₂₃	C₂³	1	2	yes	—
143	C₂²×Dic₂₃	C₂³	1	2	yes	—
144	C₂²×Dic₂₃	C₂³	1	2	yes	—
145	C₂²×Dic₂₃	C₂³	1	2	yes	—
146	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
147	C₂²×Dic₂₃	C₂³	1	2	yes	—
148	C₂²×Dic₂₃	C₂³	1	2	yes	—
149	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
150	C₂²×Dic₂₃	C₂³	1	2	yes	—
151	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
152	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
153	#67290	—	2	4	no	—
154	#67290	—	2	4	no	—
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×Dic₄₆	C₂³	1	1	yes	characteristic
159	C₂×Dic₄₆	C₂³	1	1	yes	characteristic
160	C₂×Dic₄₆	C₂³	1	2	yes	—
161	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
162	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
163	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
164	C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
165	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
166	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
167	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
168	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
169	C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
170	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
171	C₄²×C₂₃	C₂³	1	1	yes	characteristic
172	C₂²⋊Dic₂₃	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
174	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
175	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
176	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
177	C₂²⋊Dic₂₃	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
179	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
180	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
181	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
182	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
183	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
184	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
185	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
186	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
189	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
190	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
191	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
192	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
193	C₄⋊Dic₂₃	C₂³	1	2	yes	—
194	C₄⋊Dic₂₃	C₂³	1	2	yes	—
195	C₄⋊Dic₂₃	C₂³	1	2	yes	—
196	C₄⋊Dic₂₃	C₂³	1	2	yes	—
197	Dic₂₃⋊C₄	C₂³	1	1	yes	characteristic
198	Dic₂₃⋊C₄	C₂³	1	2	yes	—
199	Dic₂₃⋊C₄	C₂³	1	1	yes	characteristic
200	Dic₂₃⋊C₄	C₂³	1	2	yes	—
201	Dic₂₃⋊C₄	C₂³	1	2	yes	—
202	Dic₂₃⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
210	Dic₂₃⋊C₄	C₂³	1	2	yes	—
211	Dic₂₃⋊C₄	C₂³	1	2	yes	—
212	C₄×Dic₂₃	C₂³	1	2	yes	—
213	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
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	2	yes	—
219	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
220	C₄×Dic₂₃	C₂³	1	2	yes	—
221	C₄×Dic₂₃	C₂³	1	2	yes	—
222	C₄×Dic₂₃	C₂³	1	2	yes	—
223	C₄×Dic₂₃	C₂³	1	2	yes	—
224	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
225	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
226	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
227	C₂³×C₂₃	—	2	4	no	—
228	C₂³×C₂₃	—	2	4	no	—
229	C₂³×C₂₃	—	4	2	no	—
230	C₂³×C₂₃	C₂⁴	1	2	yes	—
231	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
232	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
233	C₂³×C₂₃	C₂⁴	1	2	yes	—
234	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
235	Q₈×C₂₃	—	2	2	no	—
236	D₄×C₂₃	—	2	2	no	—
237	D₄×C₂₃	—	2	4	no	—
238	D₄×C₂₃	—	2	4	no	—
239	D₄×C₂₃	—	2	2	no	—
240	D₄×C₂₃	—	4	2	no	—
241	D₄×C₂₃	#41	1	4	yes	complemented
242	C₂×C₄×C₂₃	—	2	4	no	—
243	C₂×C₄×C₂₃	—	2	2	no	—
244	C₂×C₄×C₂₃	—	2	2	no	—
245	C₂×C₄×C₂₃	—	4	2	no	—
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	1	yes	characteristic
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	2	no	—
255	C₂²⋊D₂₃	—	2	2	no	—
256	C₂²⋊D₂₃	—	4	2	no	—
257	C₂×Dic₂₃	—	2	4	no	—
258	C₂×Dic₂₃	—	2	4	no	—
259	C₂×Dic₂₃	—	2	2	no	—
260	C₂×Dic₂₃	—	2	4	no	—
261	C₂×Dic₂₃	—	2	4	no	—
262	C₂×Dic₂₃	—	2	4	no	—
263	C₂×Dic₂₃	—	2	4	no	—
264	C₂×Dic₂₃	—	4	1	no	—
265	C₂×Dic₂₃	—	4	2	no	—
266	C₂×Dic₂₃	—	4	1	no	—
267	C₂×Dic₂₃	#41	1	4	yes	complemented
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	2	yes	—
272	C₂×Dic₂₃	C₂⁴	1	2	yes	—
273	C₂×Dic₂₃	C₂⁴	1	2	yes	—
274	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₂₃	C₂⁴	1	2	yes	—
277	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
278	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
279	C₄×D₂₃	—	2	2	no	—
280	C₄×D₂₃	—	2	2	no	—
281	C₄×D₂₃	—	4	1	no	—
282	Dic₄₆	—	2	2	no	—
283	Dic₄₆	—	2	2	no	—
284	Dic₄₆	—	4	2	no	—
285	#3475	—	23	1	no	maximal, Sylow
286	C₂²×C₂₃	—	2	2	no	—
287	C₂²×C₂₃	—	2	1	no	—
288	C₂²×C₂₃	—	2	2	no	—
289	C₂²×C₂₃	—	2	1	no	—
290	C₂²×C₂₃	—	2	2	no	—
291	C₂²×C₂₃	—	2	1	no	—
292	C₂²×C₂₃	—	2	1	no	—
293	C₂²×C₂₃	—	2	2	no	—
294	C₂²×C₂₃	—	2	1	no	—
295	C₂²×C₂₃	—	2	2	no	—
296	C₂²×C₂₃	—	4	8	no	—
297	C₂²×C₂₃	C₂×#41	1	4	yes	—
298	C₂²×C₂₃	C₂×#41	1	2	yes	—
299	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
300	C₂×D₂₃	—	2	1	no	—
301	C₂×D₂₃	—	2	1	no	—
302	C₂×D₂₃	—	2	1	no	—
303	C₄×C₂₃	—	2	1	no	—
304	C₄×C₂₃	—	2	1	no	—
305	C₄×C₂₃	—	2	1	no	—
306	C₄×C₂₃	—	2	2	no	—
307	C₄×C₂₃	—	2	2	no	—
308	C₄×C₂₃	—	2	1	no	—
309	C₄×C₂₃	C₂×#41	1	2	yes	—
310	Dic₂₃	—	2	1	no	—
311	Dic₂₃	—	2	2	no	—
312	Dic₂₃	—	2	1	no	—
313	Dic₂₃	—	2	2	no	—
314	Dic₂₃	—	2	2	no	—
315	Dic₂₃	—	2	1	no	—
316	Dic₂₃	—	2	2	no	—
317	Dic₂₃	—	2	1	no	—
318	Dic₂₃	—	2	1	no	—
319	Dic₂₃	C₂×#41	1	2	yes	—
320	Dic₂₃	C₂×#41	1	2	yes	—
321	#556	—	23	1	no	—
322	#555	—	23	1	no	—
323	#554	—	23	1	no	—
324	#553	—	23	2	no	—
325	#552	—	23	2	no	—
326	#552	—	23	1	no	—
327	#552	—	23	1	no	—
328	#551	—	23	2	no	—
329	#551	—	23	2	no	—
330	#547	—	23	1	no	—
331	#546	—	23	1	no	—
332	#546	D₂₃	1	1	yes	characteristic, complemented
333	#533	—	23	1	no	—
334	#529	—	23	1	no	—
335	#529	—	23	2	no	—
336	#529	—	23	2	no	—
337	#529	—	23	1	no	—
338	#525	—	23	2	no	—
339	C₄×#41	—	23	1	no	—
340	C₄×#41	—	23	1	no	—
341	C₄×#41	—	23	1	no	—
342	C₂×C₄×D₄	—	23	1	no	—
343	C₂×#117	—	23	2	no	—
344	C₂×C₂₃	—	2	2	no	—
345	C₂×C₂₃	—	2	4	no	—
346	C₂×C₂₃	—	4	1	no	—
347	C₂×C₂₃	—	4	2	no	—
348	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
349	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
350	C₂×C₂₃	#585	1	1	yes	characteristic
351	D₂₃	—	4	1	no	—
352	C₂×#41	—	23	1	no	—
353	C₂×#41	—	23	1	no	—
354	C₂×#41	C₂×D₂₃	1	1	yes	characteristic
355	C₂²×D₄	C₂×D₂₃	1	1	yes	characteristic
356	C₂³×C₄	—	23	2	no	—
357	C₄⋊Q₈	—	23	1	no	—
358	C₄⋊Q₈	—	23	1	no	—
359	#126	—	23	2	no	—
360	#126	—	23	2	no	—
361	#126	—	23	2	no	—
362	#126	—	23	2	no	—
363	#126	—	23	2	no	—
364	#126	—	23	2	no	—
365	#125	—	23	2	no	—
366	#125	—	23	2	no	—
367	#125	—	23	1	no	—
368	#125	—	23	2	no	—
369	#125	—	23	1	no	—
370	#124	—	23	1	no	—
371	#124	—	23	2	no	—
372	#124	—	23	2	no	—
373	#124	C₂×D₂₃	1	1	yes	characteristic
374	#123	—	23	2	no	—
375	#123	—	23	2	no	—
376	#123	—	23	2	no	—
377	#123	—	23	2	no	—
378	#123	—	23	2	no	—
379	#123	—	23	2	no	—
380	#123	—	23	2	no	—
381	#123	C₂×D₂₃	1	2	yes	—
382	C₂²⋊Q₈	—	23	1	no	—
383	C₂²⋊Q₈	—	23	1	no	—
384	C₂²⋊Q₈	—	23	2	no	—
385	C₂²⋊Q₈	—	23	1	no	—
386	C₂²⋊Q₈	—	23	2	no	—
387	C₂²⋊Q₈	—	23	2	no	—
388	C₂²⋊Q₈	—	23	2	no	—
389	C₂²⋊Q₈	—	23	2	no	—
390	C₂²⋊Q₈	C₂×D₂₃	1	1	yes	characteristic
391	#121	—	23	2	no	—
392	#121	—	23	2	no	—
393	#121	—	23	2	no	—
394	#121	—	23	1	no	—
395	#121	C₂×D₂₃	1	2	yes	—
396	#121	C₂×D₂₃	1	1	yes	characteristic
397	#120	—	23	2	no	—
398	#120	C₂×D₂₃	1	2	yes	—
399	C₄×Q₈	—	23	1	no	—
400	C₄×Q₈	—	23	1	no	—
401	C₄×Q₈	—	23	1	no	—
402	C₄×Q₈	—	23	1	no	—
403	C₄×Q₈	—	23	2	no	—
404	C₄×Q₈	—	23	1	no	—
405	C₄×Q₈	—	23	1	no	—
406	C₄×D₄	—	23	1	no	—
407	C₄×D₄	—	23	1	no	—
408	C₄×D₄	—	23	2	no	—
409	C₄×D₄	—	23	1	no	—
410	C₄×D₄	—	23	2	no	—
411	C₄×D₄	—	23	1	no	—
412	C₄×D₄	—	23	2	no	—
413	C₄×D₄	—	23	1	no	—
414	C₄×D₄	—	23	1	no	—
415	C₄×D₄	—	23	2	no	—
416	C₄×D₄	—	23	2	no	—
417	C₄×D₄	—	23	1	no	—
418	C₄×D₄	—	23	1	no	—
419	C₄×D₄	—	23	2	no	—
420	C₄×D₄	—	23	2	no	—
421	C₄×D₄	—	23	1	no	—
422	C₄×D₄	—	23	1	no	—
423	C₄×D₄	—	23	2	no	—
424	C₄×D₄	C₂×D₂₃	1	1	yes	characteristic
425	C₄×D₄	C₂×D₂₃	1	1	yes	characteristic
426	#117	—	23	2	no	—
427	#117	—	23	1	no	—
428	#117	—	23	1	no	—
429	#117	—	23	1	no	—
430	#117	—	23	1	no	—
431	#117	—	23	2	no	—
432	#117	—	23	2	no	—
433	#117	—	23	2	no	—
434	#117	—	23	2	no	—
435	#117	—	23	2	no	—
436	#117	—	23	2	no	—
437	#117	—	23	2	no	—
438	#117	—	23	1	no	—
439	#117	—	23	2	no	—
440	C₂×C₄⋊C₄	—	23	2	no	—
441	C₂×C₄⋊C₄	—	23	2	no	—
442	C₂×C₄⋊C₄	—	23	1	no	—
443	C₂×C₂²⋊C₄	—	23	2	no	—
444	C₂×C₂²⋊C₄	—	23	2	no	—
445	C₂×C₂²⋊C₄	C₂×D₂₃	1	2	yes	—
446	C₂×C₄²	—	23	2	no	—
447	C₂×C₄²	—	23	2	no	—
448	C₂×C₄²	—	23	1	no	—
449	C₂×C₄²	—	23	1	no	—
450	C₂×C₄²	—	23	1	no	—
451	C₂₃	#3475	1	1	yes	characteristic, complemented, Sylow
452	C₂⁴	C₂²×D₂₃	1	2	yes	—
453	#41	—	2	4	no	—
454	#41	—	46	4	no	—
455	#41	—	46	4	no	—
456	C₂×Q₈	—	23	1	no	—
457	C₂×Q₈	—	23	1	no	—
458	C₂×Q₈	—	23	2	no	—
459	C₂×Q₈	C₂²×D₂₃	1	1	yes	characteristic
460	C₂×D₄	—	2	4	no	—
461	C₂×D₄	—	23	1	no	—
462	C₂×D₄	—	23	2	no	—
463	C₂×D₄	—	23	1	no	—
464	C₂×D₄	—	23	2	no	—
465	C₂×D₄	C₂²×D₂₃	1	2	yes	—
466	C₂×D₄	C₂²×D₂₃	1	2	yes	—
467	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
468	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
469	C₂×D₄	C₂²×D₂₃	1	2	yes	—
470	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
471	C₂²×C₄	—	23	1	no	—
472	C₂²×C₄	—	23	2	no	—
473	C₂²×C₄	—	23	2	no	—
474	C₂²×C₄	—	23	1	no	—
475	C₂²×C₄	—	23	2	no	—
476	C₂²×C₄	—	23	2	no	—
477	C₂²×C₄	—	23	2	no	—
478	C₂²×C₄	—	23	2	no	—
479	C₂²×C₄	—	23	1	no	—
480	C₂²×C₄	—	23	2	no	—
481	C₂²×C₄	—	23	1	no	—
482	C₂²×C₄	—	23	1	no	—
483	C₂²×C₄	—	23	1	no	—
484	C₂²×C₄	—	23	1	no	—
485	C₂²×C₄	—	46	8	no	—
486	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
487	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
488	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
489	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
490	C₄⋊C₄	—	23	1	no	—
491	C₄⋊C₄	—	23	1	no	—
492	C₄⋊C₄	—	23	1	no	—
493	C₄⋊C₄	—	23	2	no	—
494	C₄⋊C₄	—	23	2	no	—
495	C₄⋊C₄	—	23	2	no	—
496	C₄⋊C₄	—	23	2	no	—
497	C₄⋊C₄	—	23	2	no	—
498	C₄⋊C₄	—	23	2	no	—
499	C₄⋊C₄	—	23	1	no	—
500	C₄⋊C₄	—	23	2	no	—
501	C₄⋊C₄	—	23	1	no	—
502	C₄⋊C₄	—	23	1	no	—
503	C₄⋊C₄	—	23	1	no	—
504	C₄⋊C₄	—	23	2	no	—
505	C₄⋊C₄	—	23	2	no	—
506	C₄⋊C₄	—	23	2	no	—
507	C₄⋊C₄	—	23	2	no	—
508	C₄⋊C₄	—	23	1	no	—
509	C₄⋊C₄	—	23	2	no	—
510	C₄⋊C₄	—	23	2	no	—
511	C₄⋊C₄	—	23	2	no	—
512	C₄⋊C₄	—	23	2	no	—
513	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
514	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
515	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
516	C₂²⋊C₄	—	23	1	no	—
517	C₂²⋊C₄	—	23	2	no	—
518	C₂²⋊C₄	—	23	2	no	—
519	C₂²⋊C₄	—	23	2	no	—
520	C₂²⋊C₄	—	23	2	no	—
521	C₂²⋊C₄	—	23	2	no	—
522	C₂²⋊C₄	—	23	2	no	—
523	C₂²⋊C₄	—	23	2	no	—
524	C₂²⋊C₄	—	23	2	no	—
525	C₂²⋊C₄	—	23	2	no	—
526	C₂²⋊C₄	—	23	1	no	—
527	C₂²⋊C₄	—	23	2	no	—
528	C₂²⋊C₄	—	23	2	no	—
529	C₂²⋊C₄	—	23	1	no	—
530	C₂²⋊C₄	—	23	2	no	—
531	C₂²⋊C₄	—	23	1	no	—
532	C₂²⋊C₄	—	23	2	no	—
533	C₂²⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
534	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
535	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
536	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
537	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
538	C₂²⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
539	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
540	C₄²	—	23	1	no	—
541	C₄²	—	23	1	no	—
542	C₄²	—	23	1	no	—
543	C₄²	—	23	2	no	—
544	C₄²	—	23	2	no	—
545	C₄²	—	23	1	no	—
546	C₄²	—	23	2	no	—
547	C₄²	—	23	2	no	—
548	C₄²	—	23	2	no	—
549	C₄²	—	23	1	no	—
550	C₄²	—	23	1	no	—
551	C₄²	—	23	2	no	—
552	C₄²	—	23	1	no	—
553	C₄²	—	23	1	no	—
554	C₄²	—	23	1	no	—
555	C₄²	C₂²×D₂₃	1	1	yes	characteristic
556	C₂³	—	2	4	no	—
557	C₂³	—	2	4	no	—
558	C₂³	—	4	2	no	—
559	C₂³	—	23	1	no	—
560	C₂³	C₂³×D₂₃	1	2	yes	—
561	C₂³	C₂³×D₂₃	1	1	yes	characteristic
562	C₂³	C₂³×D₂₃	1	2	yes	—
563	C₂³	C₂³×D₂₃	1	1	yes	characteristic
564	Q₈	—	2	2	no	—
565	Q₈	—	46	2	no	—
566	Q₈	—	46	2	no	—
567	Q₈	—	92	2	no	—
568	D₄	—	2	4	no	—
569	D₄	—	2	4	no	—
570	D₄	—	2	2	no	—
571	D₄	—	2	2	no	—
572	D₄	—	4	2	no	—
573	D₄	—	46	2	no	—
574	D₄	—	46	4	no	—
575	D₄	—	46	2	no	—
576	D₄	—	92	2	no	—
577	D₄	#67290	1	4	yes	complemented
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	23	4	no	—
583	C₂×C₄	—	23	1	no	—
584	C₂×C₄	—	23	1	no	—
585	C₂×C₄	—	23	2	no	—
586	C₂×C₄	—	23	1	no	—
587	C₂×C₄	—	23	1	no	—
588	C₂×C₄	—	23	1	no	—
589	C₂×C₄	—	23	1	no	—
590	C₂×C₄	—	23	1	no	—
591	C₂×C₄	—	23	2	no	—
592	C₂×C₄	—	23	2	no	—
593	C₂×C₄	—	23	2	no	—
594	C₂×C₄	—	46	2	no	—
595	C₂×C₄	—	46	4	no	—
596	C₂×C₄	—	46	4	no	—
597	C₂×C₄	—	46	4	no	—
598	C₂×C₄	—	46	4	no	—
599	C₂×C₄	—	46	2	no	—
600	C₂×C₄	—	46	4	no	—
601	C₂×C₄	—	46	4	no	—
602	C₂×C₄	—	46	2	no	—
603	C₂×C₄	—	92	1	no	—
604	C₂×C₄	—	92	1	no	—
605	C₂×C₄	—	92	2	no	—
606	C₂×C₄	—	92	1	no	—
607	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
608	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
609	C₂×C₄	C₂³×D₂₃	1	2	yes	—
610	C₂×C₄	C₂³×D₂₃	1	2	yes	—
611	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
613	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
614	C₂²	—	2	2	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	2	1	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	4	8	no	—
625	C₂²	—	46	1	no	—
626	C₂²	—	46	1	no	—
627	C₂²	—	46	1	no	—
628	C₂²	C₂×#67290	1	4	yes	—
629	C₂²	#41×D₂₃	1	2	yes	—
630	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
631	C₄	—	2	1	no	—
632	C₄	—	2	1	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	2	no	—
637	C₄	—	23	2	no	—
638	C₄	—	23	2	no	—
639	C₄	—	46	2	no	—
640	C₄	—	46	2	no	—
641	C₄	—	46	1	no	—
642	C₄	—	46	1	no	—
643	C₄	—	46	2	no	—
644	C₄	—	46	1	no	—
645	C₄	—	46	1	no	—
646	C₄	—	46	2	no	—
647	C₄	—	46	1	no	—
648	C₄	C₂×#67290	1	2	yes	—
649	C₂	—	2	2	no	—
650	C₂	—	2	4	no	—
651	C₂	—	4	2	no	—
652	C₂	—	4	1	no	—
653	C₂	—	92	1	no	—
654	C₂	C₂×#41×D₂₃	1	1	yes	characteristic
655	C₂	C₂²×#67290	1	1	yes	characteristic
656	C₂	#13093252	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₃
commutator, socle, cosocle	C₂²×C₂₃	C₂⁵
Fitting	C₂₃×#546	C₂
hypercenter	#546	D₂₃
hypocenter	C₂₃	#3475
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. #13093136	C₂	semidirect
2. #13093131	C₂	semidirect
3. #13093126	C₂	semidirect
4. #13093110	C₂	semidirect
5. #13093109	C₂	semidirect
6. #13093107	C₂	semidirect
7. #13093104	C₂	semidirect
8. #13093098	C₂	semidirect
9. #13093093	C₂	semidirect
10. #13093066	C₂	semidirect
11. #13093061	C₂	semidirect
12. #13092969	C₂	semidirect
13. #13092948	C₂	semidirect
14. #13092948	C₂	semidirect
15. #13092946	C₂	semidirect
16. #13092944	C₂	semidirect
17. #13092923	C₂	semidirect
18. #41×Dic₂₃	C₂	semidirect
19. C₄×#67290	C₂	semidirect
20. C₄×#67290	C₂	semidirect
21. C₂×D₄×Dic₂₃	C₂	semidirect
22. C₂×#10625048	C₂	semidirect
23. C₂₃×#546	C₂	semidirect
41. #10625117	C₂²	semidirect
42. Q₈×Dic₂₃	C₂²	semidirect
43. Q₈×Dic₂₃	C₂²	semidirect
44. #10625115	C₂²	semidirect
46. #10625110	C₂²	semidirect
47. #10625110	C₂²	semidirect
50. #10625107	C₂²	semidirect
53. #10625106	C₂²	semidirect
54. #10625106	C₂²	semidirect
63. D₄×Dic₂₃	C₂²	semidirect
64. D₄×Dic₂₃	C₂²	semidirect
65. D₄×Dic₂₃	C₂²	semidirect
66. #10625100	C₂²	semidirect
68. C₄×C₂²⋊D₂₃	C₂²	semidirect
69. C₄×C₂²⋊D₂₃	C₂²	semidirect
70. #10625097	C₂²	semidirect
71. #10625097	C₂²	semidirect
74. #10625095	C₂²	semidirect
75. #10625095	C₂²	semidirect
76. C₂×Dic₂₃⋊C₄	C₂²	semidirect
77. C₂×Dic₂₃⋊C₄	C₂²	semidirect
79. C₂×C₄×Dic₂₃	C₂²	semidirect
80. C₂×C₄×Dic₂₃	C₂²	semidirect
81. C₂×C₄×Dic₂₃	C₂²	semidirect
82. #10625069	C₂²	semidirect
83. #10625063	C₂²	semidirect
84. #10625063	C₂²	semidirect
85. #10625061	C₂²	semidirect
86. #10625061	C₂²	semidirect
87. #10625060	C₂²	semidirect
88. #10625060	C₂²	semidirect
89. #10625059	C₂²	semidirect
90. #10625058	C₂²	semidirect
91. #10625058	C₂²	semidirect
92. #10625058	C₂²	semidirect
94. #10625056	C₂²	semidirect
95. #10625054	C₂²	semidirect
97. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
98. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
99. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
100. #10625050	C₂²	semidirect
101. #10625050	C₂²	semidirect
102. #10625050	C₂²	semidirect
103. #10625050	C₂²	semidirect
104. #10625050	C₂²	semidirect
106. #10625049	C₂²	semidirect
107. #10625049	C₂²	semidirect
108. #10625049	C₂²	semidirect
113. #10625048	C₂²	semidirect
114. #10625048	C₂²	semidirect
115. #10625048	C₂²	semidirect
116. #10625048	C₂²	semidirect
117. #10625048	C₂²	semidirect
118. #10625048	C₂²	semidirect
119. C₄²×D₂₃	C₂²	semidirect
120. #10625041	C₂²	semidirect
121. C₄×Dic₄₆	C₂²	semidirect
122. C₄×Dic₄₆	C₂²	semidirect
241. D₄×C₂₃	#41	semidirect
267. C₂×Dic₂₃	#41	semidirect
332. #546	D₂₃	semidirect
451. C₂₃	#3475	semidirect
577. D₄	#67290	semidirect

Maximal subgroups

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

subgroup	index
#13093136	2
#13093131	2
#13093126	2
#13093110	2
#13093109	2
#13093107	2
#13093104	2
#13093098	2
#13093093	2
#13093066	2
#13093061	2
#13092969	2
#13092948	2
#13092946	2
#13092944	2
#13092923	2
#41×Dic₂₃	2
C₄×#67290	2
C₂×D₄×Dic₂₃	2
C₂×#10625048	2
C₂₃×#546	2
#3475	23