Subgroups — #15686956

Order 2944.

1132 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	#13093135	C₂	1	1	yes	maximal, characteristic, complemented
2	#13093131	C₂	1	1	yes	maximal, characteristic, complemented
3	#13093122	C₂	1	1	yes	maximal, characteristic, complemented
4	#13093117	C₂	1	1	yes	maximal, characteristic, complemented
5	#13093107	C₂	1	1	yes	maximal, characteristic, complemented
6	#13093105	C₂	1	1	yes	maximal, characteristic, complemented
7	#13093103	C₂	1	2	yes	maximal, complemented
8	#13093096	C₂	1	2	yes	maximal, complemented
9	#13093095	C₂	1	2	yes	maximal, complemented
10	#13093067	C₂	1	1	yes	maximal, characteristic, complemented
11	#13093056	C₂	1	2	yes	maximal, complemented
12	#13092973	C₂	1	1	yes	maximal, characteristic, complemented
13	#13092950	C₂	1	2	yes	maximal, complemented
14	#13092948	C₂	1	2	yes	maximal, complemented
15	#13092944	C₂	1	2	yes	maximal, complemented
16	#13092927	C₂	1	1	yes	maximal, characteristic, complemented
17	#13092927	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#67290	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#67290	C₂	1	2	yes	maximal, complemented
20	C₄×D₄×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#10625063	C₂	1	1	yes	maximal, characteristic, complemented
22	#117×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#67290	C₂²	1	1	yes	characteristic
25	C₂×#67290	C₂²	1	2	yes	—
26	C₂×D₄×D₂₃	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
29	C₂₃×#126	C₂²	1	2	yes	complemented
30	C₂₃×#125	C₂²	1	1	yes	characteristic, complemented
31	C₂₃×#123	C₂²	1	2	yes	complemented
32	C₂₃×#121	C₂²	1	2	yes	—
33	C₂₃×#121	C₂²	1	1	yes	characteristic, complemented
34	C₂₃×#121	C₂²	1	1	yes	characteristic, complemented
35	C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
36	C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
37	C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
38	C₂₃×#117	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
40	#10625110	C₂²	1	2	yes	—
41	#10625109	C₂²	1	1	yes	characteristic, complemented
42	#10625109	C₂²	1	1	yes	characteristic, complemented
43	#10625108	C₂²	1	2	yes	—
44	#10625108	C₂²	1	2	yes	—
45	#10625107	C₂²	1	2	yes	complemented
46	#10625106	C₂²	1	2	yes	—
47	#10625106	C₂²	1	2	yes	complemented
48	D₄×Dic₂₃	C₂²	1	1	yes	characteristic
49	D₄×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
50	D₄×Dic₂₃	C₂²	1	2	yes	complemented
51	D₄×Dic₂₃	C₂²	1	2	yes	complemented
52	#10625100	C₂²	1	2	yes	complemented
53	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	—
55	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	—
57	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
58	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	2	yes	—
59	#10625097	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic, complemented
61	#10625095	C₂²	1	1	yes	characteristic, complemented
62	#10625095	C₂²	1	2	yes	complemented
63	#10625095	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₄×Dic₂₃	C₂²	1	2	yes	complemented
65	C₂×C₄×Dic₂₃	C₂²	1	2	yes	complemented
66	#10625069	C₂²	1	2	yes	complemented
67	#10625068	C₂²	1	1	yes	characteristic, complemented
68	#10625068	C₂²	1	1	yes	characteristic, complemented
69	#10625067	C₂²	1	2	yes	—
70	#10625067	C₂²	1	2	yes	—
71	#10625067	C₂²	1	2	yes	complemented
72	#10625065	C₂²	1	2	yes	—
73	#10625064	C₂²	1	1	yes	characteristic
74	#10625063	C₂²	1	1	yes	characteristic
75	#10625063	C₂²	1	1	yes	characteristic
76	#10625063	C₂²	1	1	yes	characteristic
77	#10625063	C₂²	1	2	yes	—
78	#10625063	C₂²	1	1	yes	characteristic, complemented
79	#10625063	C₂²	1	1	yes	characteristic, complemented
80	#10625063	C₂²	1	2	yes	complemented
81	#10625063	C₂²	1	2	yes	complemented
82	C₄⋊C₄×D₂₃	C₂²	1	1	yes	characteristic
83	C₄⋊C₄×D₂₃	C₂²	1	1	yes	characteristic, complemented
84	C₄⋊C₄×D₂₃	C₂²	1	1	yes	characteristic, complemented
85	#10625061	C₂²	1	2	yes	complemented
86	#10625060	C₂²	1	2	yes	complemented
87	#10625060	C₂²	1	2	yes	complemented
88	#10625059	C₂²	1	1	yes	characteristic, complemented
89	#10625059	C₂²	1	1	yes	characteristic, complemented
90	#10625058	C₂²	1	1	yes	characteristic, complemented
91	#10625058	C₂²	1	2	yes	complemented
92	#10625058	C₂²	1	2	yes	complemented
93	#10625056	C₂²	1	2	yes	—
94	#10625056	C₂²	1	2	yes	complemented
95	#10625055	C₂²	1	2	yes	—
96	#10625054	C₂²	1	2	yes	—
97	#10625054	C₂²	1	2	yes	—
98	#10625054	C₂²	1	2	yes	complemented
99	(C₂²⋊D₂₃)⋊C₄	C₂²	1	1	yes	characteristic
100	(C₂²⋊D₂₃)⋊C₄	C₂²	1	1	yes	characteristic
101	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	—
102	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	complemented
103	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	complemented
104	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	—
105	C₂²⋊C₄×D₂₃	C₂²	1	1	yes	characteristic
106	C₂²⋊C₄×D₂₃	C₂²	1	1	yes	characteristic
107	#10625050	C₂²	1	2	yes	complemented
108	#10625050	C₂²	1	2	yes	complemented
109	#10625050	C₂²	1	2	yes	complemented
110	#10625049	C₂²	1	2	yes	complemented
111	#10625048	C₂²	1	2	yes	complemented
112	#10625048	C₂²	1	2	yes	complemented
113	#10625048	C₂²	1	2	yes	complemented
114	#10625048	C₂²	1	2	yes	complemented
115	#10625047	C₂²	1	2	yes	complemented
116	C₄×D₉₂	C₂²	1	1	yes	characteristic
117	#10625043	C₂²	1	2	yes	—
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	C₂³×D₂₃	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₂₃	C₂³	1	2	yes	—
127	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₂₃	C₂³	1	2	yes	—
129	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
132	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₂₃	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₂₃	C₂³	1	1	yes	characteristic
138	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
139	C₂²×Dic₂₃	C₂³	1	2	yes	—
140	C₂²×Dic₂₃	C₂³	1	2	yes	—
141	C₂²×Dic₂₃	C₂³	1	2	yes	—
142	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
143	#67290	—	2	8	no	—
144	#67290	—	2	4	no	—
145	D₄×D₂₃	—	2	4	no	—
146	C₂×D₉₂	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₂₃	—	2	4	no	—
148	C₂×C₄×D₂₃	—	2	4	no	—
149	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₂₃	C₂³	1	2	yes	—
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	2	yes	—
159	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
160	C₂×Dic₄₆	C₂³	1	2	yes	—
161	C₂×Dic₄₆	C₂³	1	1	yes	characteristic
162	C₂×Dic₄₆	C₂³	1	2	yes	—
163	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
164	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
165	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
166	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
167	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
168	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
169	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
170	C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
171	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
172	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
173	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
174	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
175	C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
176	C₄²×C₂₃	C₂³	1	1	yes	characteristic
177	C₄²×C₂₃	C₂³	1	2	yes	—
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	1	yes	characteristic
184	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
185	C₂²⋊Dic₂₃	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	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
190	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
191	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
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	C₄⋊Dic₂₃	C₂³	1	2	yes	—
198	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
200	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₂₃	C₂³	1	2	yes	—
203	C₄⋊Dic₂₃	C₂³	1	2	yes	—
204	Dic₂₃⋊C₄	C₂³	1	1	yes	characteristic
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	Dic₂₃⋊C₄	C₂³	1	2	yes	—
213	Dic₂₃⋊C₄	C₂³	1	2	yes	—
214	Dic₂₃⋊C₄	C₂³	1	1	yes	characteristic
215	Dic₂₃⋊C₄	C₂³	1	2	yes	—
216	C₄×Dic₂₃	C₂³	1	2	yes	—
217	C₄×Dic₂₃	C₂³	1	2	yes	—
218	C₄×Dic₂₃	C₂³	1	2	yes	—
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	2	yes	—
223	C₄×Dic₂₃	C₂³	1	2	yes	—
224	C₄×Dic₂₃	C₂³	1	2	yes	—
225	C₄×Dic₂₃	C₂³	1	2	yes	—
226	C₄×Dic₂₃	C₂³	1	2	yes	—
227	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
228	C₂³×C₂₃	C₂⁴	1	2	yes	—
229	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
230	C₂²×D₂₃	—	2	2	no	—
231	C₂²×D₂₃	—	2	2	no	—
232	C₂²×D₂₃	—	2	2	no	—
233	C₂²×D₂₃	—	2	2	no	—
234	C₂²×D₂₃	—	4	1	no	—
235	C₂²×D₂₃	—	4	1	no	—
236	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
237	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
238	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
239	D₄×C₂₃	—	2	2	no	—
240	D₄×C₂₃	—	2	4	no	—
241	D₄×C₂₃	—	2	2	no	—
242	D₄×C₂₃	—	4	2	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	—	4	2	no	—
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	2	yes	—
253	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
255	C₂²⋊D₂₃	—	2	4	no	—
256	C₂²⋊D₂₃	—	2	4	no	—
257	C₂²⋊D₂₃	—	2	2	no	—
258	C₂²⋊D₂₃	—	4	2	no	—
259	C₂²⋊D₂₃	#41	1	4	yes	complemented
260	C₂×Dic₂₃	—	2	4	no	—
261	C₂×Dic₂₃	—	2	2	no	—
262	C₂×Dic₂₃	—	2	2	no	—
263	C₂×Dic₂₃	—	2	4	no	—
264	C₂×Dic₂₃	—	2	4	no	—
265	C₂×Dic₂₃	C₂⁴	1	2	yes	—
266	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₂₃	C₂⁴	1	2	yes	—
268	C₂×Dic₂₃	C₂⁴	1	2	yes	—
269	C₂×Dic₂₃	C₂⁴	1	2	yes	—
270	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
273	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
274	D₉₂	—	2	2	no	—
275	C₄×D₂₃	—	2	2	no	—
276	C₄×D₂₃	—	2	2	no	—
277	C₄×D₂₃	—	2	4	no	—
278	C₄×D₂₃	—	2	2	no	—
279	C₄×D₂₃	—	2	2	no	—
280	C₄×D₂₃	—	2	2	no	—
281	C₄×D₂₃	—	2	2	no	—
282	C₄×D₂₃	—	2	2	no	—
283	C₄×D₂₃	—	4	1	no	—
284	C₄×D₂₃	—	4	2	no	—
285	C₄×D₂₃	#41	1	4	yes	complemented
286	Dic₄₆	—	2	2	no	—
287	Dic₄₆	—	2	4	no	—
288	Dic₄₆	—	4	2	no	—
289	#3475	—	23	1	no	maximal, Sylow
290	C₂²×C₂₃	—	2	1	no	—
291	C₂²×C₂₃	—	2	1	no	—
292	C₂²×C₂₃	—	2	2	no	—
293	C₂²×C₂₃	—	2	2	no	—
294	C₂²×C₂₃	—	2	1	no	—
295	C₂²×C₂₃	—	2	1	no	—
296	C₂²×C₂₃	—	2	2	no	—
297	C₂²×C₂₃	—	2	1	no	—
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	C₂×D₂₃	—	2	1	no	—
304	C₂×D₂₃	—	2	1	no	—
305	C₂×D₂₃	—	2	1	no	—
306	C₂×D₂₃	—	2	1	no	—
307	C₂×D₂₃	—	4	4	no	—
308	C₂×D₂₃	—	4	4	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	1	no	—
313	C₄×C₂₃	—	2	1	no	—
314	C₄×C₂₃	—	2	1	no	—
315	C₄×C₂₃	—	2	2	no	—
316	C₄×C₂₃	—	2	1	no	—
317	C₄×C₂₃	—	2	2	no	—
318	C₄×C₂₃	C₂×#41	1	2	yes	—
319	Dic₂₃	—	2	2	no	—
320	Dic₂₃	—	2	2	no	—
321	Dic₂₃	—	2	1	no	—
322	Dic₂₃	—	2	1	no	—
323	Dic₂₃	—	2	2	no	—
324	Dic₂₃	—	2	1	no	—
325	Dic₂₃	—	2	2	no	—
326	Dic₂₃	C₂×#41	1	2	yes	—
327	Dic₂₃	C₂×#41	1	2	yes	—
328	#556	—	23	1	no	—
329	#555	—	23	1	no	—
330	#554	—	23	1	no	—
331	#553	—	23	1	no	—
332	#553	D₂₃	1	1	yes	characteristic, complemented
333	#552	—	23	2	no	—
334	#552	—	23	1	no	—
335	#552	—	23	1	no	—
336	#551	—	23	2	no	—
337	#551	—	23	2	no	—
338	#547	—	23	1	no	—
339	#546	—	23	2	no	—
340	#533	—	23	1	no	—
341	#529	—	23	2	no	—
342	#529	—	23	2	no	—
343	#529	—	23	2	no	—
344	#525	—	23	1	no	—
345	#525	—	23	1	no	—
346	C₄×#41	—	23	2	no	—
347	C₄×#41	—	23	1	no	—
348	C₂×C₄×D₄	—	23	1	no	—
349	C₂×#117	—	23	1	no	—
350	C₂×#117	—	23	1	no	—
351	C₂×C₂₃	—	2	2	no	—
352	C₂×C₂₃	—	4	1	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	#585	1	1	yes	characteristic
357	D₂₃	—	2	2	no	—
358	D₂₃	—	2	2	no	—
359	D₂₃	—	4	1	no	—
360	C₂×#41	—	23	1	no	—
361	C₂×#41	—	23	2	no	—
362	C₂²×D₄	—	23	1	no	—
363	C₂³×C₄	—	23	1	no	—
364	C₂³×C₄	—	23	1	no	—
365	C₄⋊Q₈	—	23	1	no	—
366	C₄⋊Q₈	—	23	1	no	—
367	#126	—	23	2	no	—
368	#126	—	23	2	no	—
369	#126	—	23	2	no	—
370	#126	—	23	2	no	—
371	#126	—	23	2	no	—
372	#126	C₂×D₂₃	1	2	yes	complemented
373	#125	—	23	2	no	—
374	#125	—	23	2	no	—
375	#125	—	23	2	no	—
376	#125	—	23	1	no	—
377	#125	C₂×D₂₃	1	1	yes	characteristic, complemented
378	#124	—	23	2	no	—
379	#124	—	23	2	no	—
380	#124	—	23	2	no	—
381	#123	—	23	2	no	—
382	#123	—	23	2	no	—
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	complemented
389	C₂²⋊Q₈	—	23	1	no	—
390	C₂²⋊Q₈	—	23	1	no	—
391	C₂²⋊Q₈	—	23	2	no	—
392	C₂²⋊Q₈	—	23	1	no	—
393	C₂²⋊Q₈	—	23	1	no	—
394	C₂²⋊Q₈	—	23	2	no	—
395	C₂²⋊Q₈	—	23	2	no	—
396	C₂²⋊Q₈	—	23	2	no	—
397	C₂²⋊Q₈	—	23	2	no	—
398	#121	—	23	1	no	—
399	#121	—	23	1	no	—
400	#121	—	23	2	no	—
401	#121	—	23	2	no	—
402	#121	C₂×D₂₃	1	2	yes	—
403	#121	C₂×D₂₃	1	1	yes	characteristic, complemented
404	#121	C₂×D₂₃	1	1	yes	characteristic, complemented
405	#120	—	23	2	no	—
406	#120	—	23	2	no	—
407	C₄×Q₈	—	23	2	no	—
408	C₄×Q₈	—	23	1	no	—
409	C₄×Q₈	—	23	2	no	—
410	C₄×Q₈	—	23	1	no	—
411	C₄×Q₈	—	23	2	no	—
412	C₄×D₄	—	23	1	no	—
413	C₄×D₄	—	23	2	no	—
414	C₄×D₄	—	23	1	no	—
415	C₄×D₄	—	23	2	no	—
416	C₄×D₄	—	23	1	no	—
417	C₄×D₄	—	23	1	no	—
418	C₄×D₄	—	23	2	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	1	no	—
424	C₄×D₄	—	23	2	no	—
425	C₄×D₄	—	23	2	no	—
426	C₄×D₄	—	23	2	no	—
427	C₄×D₄	—	23	1	no	—
428	C₄×D₄	C₂×D₂₃	1	1	yes	characteristic
429	C₄×D₄	C₂×D₂₃	1	2	yes	complemented
430	C₄×D₄	C₂×D₂₃	1	1	yes	characteristic, complemented
431	#117	—	23	1	no	—
432	#117	—	23	1	no	—
433	#117	—	23	1	no	—
434	#117	—	23	1	no	—
435	#117	—	23	2	no	—
436	#117	—	23	2	no	—
437	#117	—	23	1	no	—
438	#117	—	23	1	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	—	23	2	no	—
445	#117	C₂×D₂₃	1	1	yes	characteristic, complemented
446	C₂×C₄⋊C₄	—	23	1	no	—
447	C₂×C₄⋊C₄	—	23	1	no	—
448	C₂×C₄⋊C₄	—	23	1	no	—
449	C₂×C₄⋊C₄	—	23	1	no	—
450	C₂×C₄⋊C₄	C₂×D₂₃	1	1	yes	characteristic, complemented
451	C₂×C₂²⋊C₄	—	23	2	no	—
452	C₂×C₂²⋊C₄	—	23	2	no	—
453	C₂×C₂²⋊C₄	—	23	1	no	—
454	C₂×C₂²⋊C₄	—	23	1	no	—
455	C₂×C₄²	—	23	2	no	—
456	C₂×C₄²	—	23	2	no	—
457	C₂×C₄²	—	23	2	no	—
458	C₂×C₄²	—	23	1	no	—
459	C₂₃	#3475	1	1	yes	characteristic, complemented, Sylow
460	C₂⁴	—	23	1	no	—
461	C₂⁴	—	23	1	no	—
462	#41	—	46	4	no	—
463	#41	—	46	8	no	—
464	C₂×Q₈	—	23	1	no	—
465	C₂×Q₈	—	23	2	no	—
466	C₂×Q₈	—	23	2	no	—
467	C₂×D₄	—	23	1	no	—
468	C₂×D₄	—	23	2	no	—
469	C₂×D₄	—	23	2	no	—
470	C₂×D₄	—	23	1	no	—
471	C₂×D₄	—	23	2	no	—
472	C₂×D₄	—	23	1	no	—
473	C₂×D₄	—	46	4	no	—
474	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
475	C₂×D₄	C₂²×D₂₃	1	2	yes	—
476	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
477	C₂×D₄	C₂²×D₂₃	1	2	yes	—
478	C₂²×C₄	—	23	1	no	—
479	C₂²×C₄	—	23	1	no	—
480	C₂²×C₄	—	23	2	no	—
481	C₂²×C₄	—	23	2	no	—
482	C₂²×C₄	—	23	2	no	—
483	C₂²×C₄	—	23	1	no	—
484	C₂²×C₄	—	23	1	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	2	no	—
494	C₂²×C₄	—	46	4	no	—
495	C₂²×C₄	—	46	4	no	—
496	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
497	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
498	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
499	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
500	C₄⋊C₄	—	23	1	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	1	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	—	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	C₂²×D₂₃	1	1	yes	characteristic
520	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
521	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
522	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
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	1	no	—
528	C₂²⋊C₄	—	23	1	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	1	no	—
536	C₂²⋊C₄	—	23	2	no	—
537	C₂²⋊C₄	—	23	2	no	—
538	C₂²⋊C₄	—	23	2	no	—
539	C₂²⋊C₄	—	23	2	no	—
540	C₂²⋊C₄	—	23	1	no	—
541	C₂²⋊C₄	—	23	1	no	—
542	C₂²⋊C₄	—	23	1	no	—
543	C₂²⋊C₄	—	23	2	no	—
544	C₂²⋊C₄	—	23	2	no	—
545	C₂²⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
546	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
547	C₂²⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
548	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
549	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
550	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
551	C₄²	—	23	2	no	—
552	C₄²	—	23	1	no	—
553	C₄²	—	23	2	no	—
554	C₄²	—	23	2	no	—
555	C₄²	—	23	1	no	—
556	C₄²	—	23	2	no	—
557	C₄²	—	23	2	no	—
558	C₄²	—	23	2	no	—
559	C₄²	—	23	2	no	—
560	C₄²	—	23	1	no	—
561	C₄²	—	23	2	no	—
562	C₄²	C₂²×D₂₃	1	2	yes	—
563	C₄²	C₂²×D₂₃	1	1	yes	characteristic
564	C₂³	—	23	1	no	—
565	C₂³	—	23	1	no	—
566	C₂³	—	23	1	no	—
567	C₂³	—	46	2	no	—
568	C₂³	—	46	2	no	—
569	C₂³	—	46	2	no	—
570	C₂³	—	46	2	no	—
571	C₂³	—	92	1	no	—
572	C₂³	—	92	1	no	—
573	C₂³	C₂³×D₂₃	1	1	yes	characteristic
574	C₂³	C₂³×D₂₃	1	2	yes	—
575	C₂³	C₂³×D₂₃	1	1	yes	characteristic
576	Q₈	—	46	4	no	—
577	Q₈	—	46	2	no	—
578	Q₈	—	92	2	no	—
579	D₄	—	2	2	no	—
580	D₄	—	2	4	no	—
581	D₄	—	2	2	no	—
582	D₄	—	4	2	no	—
583	D₄	—	23	4	no	—
584	D₄	—	46	2	no	—
585	D₄	—	46	2	no	—
586	D₄	—	46	4	no	—
587	D₄	—	46	4	no	—
588	D₄	—	92	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	4	2	no	—
592	C₂×C₄	—	4	2	no	—
593	C₂×C₄	—	23	1	no	—
594	C₂×C₄	—	23	1	no	—
595	C₂×C₄	—	23	4	no	—
596	C₂×C₄	—	23	2	no	—
597	C₂×C₄	—	23	1	no	—
598	C₂×C₄	—	23	1	no	—
599	C₂×C₄	—	23	2	no	—
600	C₂×C₄	—	23	2	no	—
601	C₂×C₄	—	23	2	no	—
602	C₂×C₄	—	23	1	no	—
603	C₂×C₄	—	46	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	4	no	—
609	C₂×C₄	—	46	2	no	—
610	C₂×C₄	—	46	2	no	—
611	C₂×C₄	—	46	4	no	—
612	C₂×C₄	—	46	4	no	—
613	C₂×C₄	—	46	4	no	—
614	C₂×C₄	—	46	2	no	—
615	C₂×C₄	—	46	2	no	—
616	C₂×C₄	—	92	2	no	—
617	C₂×C₄	—	92	1	no	—
618	C₂×C₄	C₂³×D₂₃	1	2	yes	—
619	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
620	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₂₃	1	2	yes	—
622	C₂×C₄	C₂³×D₂₃	1	2	yes	—
623	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
626	C₂²	—	2	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	23	2	no	—
635	C₂²	—	23	2	no	—
636	C₂²	—	46	1	no	—
637	C₂²	—	46	1	no	—
638	C₂²	—	46	1	no	—
639	C₂²	—	46	1	no	—
640	C₂²	—	46	1	no	—
641	C₂²	—	46	1	no	—
642	C₂²	—	46	1	no	—
643	C₂²	—	92	4	no	—
644	C₂²	—	92	4	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	2	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	2	no	—
654	C₄	—	23	2	no	—
655	C₄	—	23	2	no	—
656	C₄	—	46	2	no	—
657	C₄	—	46	1	no	—
658	C₄	—	46	1	no	—
659	C₄	—	46	2	no	—
660	C₄	—	46	2	no	—
661	C₄	—	46	2	no	—
662	C₄	—	46	1	no	—
663	C₄	#41×D₂₃	1	2	yes	—
664	C₂	—	2	2	no	—
665	C₂	—	4	1	no	—
666	C₂	—	4	2	no	—
667	C₂	—	46	2	no	—
668	C₂	—	46	2	no	—
669	C₂	—	92	1	no	—
670	C₂	C₂×#41×D₂₃	1	1	yes	characteristic
671	C₂	C₂×#41×D₂₃	1	1	yes	characteristic
672	C₂	#13093252	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₃
commutator, socle, cosocle	C₂²×C₂₃	C₂⁵
Fitting	C₂₃×#553	C₂
hypercenter	#553	D₂₃
hypocenter	C₂₃	#3475
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. #13093135	C₂	semidirect
2. #13093131	C₂	semidirect
3. #13093122	C₂	semidirect
4. #13093117	C₂	semidirect
5. #13093107	C₂	semidirect
6. #13093105	C₂	semidirect
7. #13093103	C₂	semidirect
8. #13093096	C₂	semidirect
9. #13093095	C₂	semidirect
10. #13093067	C₂	semidirect
11. #13093056	C₂	semidirect
12. #13092973	C₂	semidirect
13. #13092950	C₂	semidirect
14. #13092948	C₂	semidirect
15. #13092944	C₂	semidirect
16. #13092927	C₂	semidirect
17. #13092927	C₂	semidirect
18. C₄×#67290	C₂	semidirect
19. C₄×#67290	C₂	semidirect
20. C₄×D₄×D₂₃	C₂	semidirect
21. C₂×#10625063	C₂	semidirect
22. #117×D₂₃	C₂	semidirect
23. C₂₃×#553	C₂	semidirect
29. C₂₃×#126	C₂²	semidirect
30. C₂₃×#125	C₂²	semidirect
31. C₂₃×#123	C₂²	semidirect
33. C₂₃×#121	C₂²	semidirect
34. C₂₃×#121	C₂²	semidirect
36. C₄×D₄×C₂₃	C₂²	semidirect
37. C₄×D₄×C₂₃	C₂²	semidirect
38. C₂₃×#117	C₂²	semidirect
39. C₂×C₄⋊C₄×C₂₃	C₂²	semidirect
41. #10625109	C₂²	semidirect
42. #10625109	C₂²	semidirect
45. #10625107	C₂²	semidirect
47. #10625106	C₂²	semidirect
49. D₄×Dic₂₃	C₂²	semidirect
50. D₄×Dic₂₃	C₂²	semidirect
51. D₄×Dic₂₃	C₂²	semidirect
52. #10625100	C₂²	semidirect
57. C₄×C₂²⋊D₂₃	C₂²	semidirect
59. #10625097	C₂²	semidirect
60. C₂×C₄⋊Dic₂₃	C₂²	semidirect
61. #10625095	C₂²	semidirect
62. #10625095	C₂²	semidirect
63. #10625095	C₂²	semidirect
64. C₂×C₄×Dic₂₃	C₂²	semidirect
65. C₂×C₄×Dic₂₃	C₂²	semidirect
66. #10625069	C₂²	semidirect
67. #10625068	C₂²	semidirect
68. #10625068	C₂²	semidirect
71. #10625067	C₂²	semidirect
78. #10625063	C₂²	semidirect
79. #10625063	C₂²	semidirect
80. #10625063	C₂²	semidirect
81. #10625063	C₂²	semidirect
83. C₄⋊C₄×D₂₃	C₂²	semidirect
84. C₄⋊C₄×D₂₃	C₂²	semidirect
85. #10625061	C₂²	semidirect
86. #10625060	C₂²	semidirect
87. #10625060	C₂²	semidirect
88. #10625059	C₂²	semidirect
89. #10625059	C₂²	semidirect
90. #10625058	C₂²	semidirect
91. #10625058	C₂²	semidirect
92. #10625058	C₂²	semidirect
94. #10625056	C₂²	semidirect
98. #10625054	C₂²	semidirect
102. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
103. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
107. #10625050	C₂²	semidirect
108. #10625050	C₂²	semidirect
109. #10625050	C₂²	semidirect
110. #10625049	C₂²	semidirect
111. #10625048	C₂²	semidirect
112. #10625048	C₂²	semidirect
113. #10625048	C₂²	semidirect
114. #10625048	C₂²	semidirect
115. #10625047	C₂²	semidirect
119. C₄²×D₂₃	C₂²	semidirect
120. #10625041	C₂²	semidirect
121. C₄×Dic₄₆	C₂²	semidirect
122. C₄×Dic₄₆	C₂²	semidirect
259. C₂²⋊D₂₃	#41	semidirect
285. C₄×D₂₃	#41	semidirect
332. #553	D₂₃	semidirect
372. #126	C₂×D₂₃	semidirect
377. #125	C₂×D₂₃	semidirect
388. #123	C₂×D₂₃	semidirect
403. #121	C₂×D₂₃	semidirect
404. #121	C₂×D₂₃	semidirect
429. C₄×D₄	C₂×D₂₃	semidirect
430. C₄×D₄	C₂×D₂₃	semidirect
445. #117	C₂×D₂₃	semidirect
450. C₂×C₄⋊C₄	C₂×D₂₃	semidirect
459. C₂₃	#3475	semidirect

Maximal subgroups

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

subgroup	index
#13093135	2
#13093131	2
#13093122	2
#13093117	2
#13093107	2
#13093105	2
#13093103	2
#13093096	2
#13093095	2
#13093067	2
#13093056	2
#13092973	2
#13092950	2
#13092948	2
#13092944	2
#13092927	2
C₄×#67290	2
C₄×D₄×D₂₃	2
C₂×#10625063	2
#117×D₂₃	2
C₂₃×#553	2
#3475	23