Subgroups — #15686957

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	#13093138	C₂	1	1	yes	maximal, characteristic, complemented
2	#13093131	C₂	1	1	yes	maximal, characteristic, complemented
3	#13093125	C₂	1	1	yes	maximal, characteristic, complemented
4	#13093119	C₂	1	1	yes	maximal, characteristic, complemented
5	#13093114	C₂	1	1	yes	maximal, characteristic, complemented
6	#13093109	C₂	1	1	yes	maximal, characteristic, complemented
7	#13093104	C₂	1	2	yes	maximal, complemented
8	#13093101	C₂	1	1	yes	maximal, characteristic, complemented
9	#13093098	C₂	1	2	yes	maximal, complemented
10	#13093090	C₂	1	2	yes	maximal, complemented
11	#13093067	C₂	1	1	yes	maximal, characteristic, complemented
12	#13093054	C₂	1	2	yes	maximal, complemented
13	#13092970	C₂	1	1	yes	maximal, characteristic, complemented
14	#13092949	C₂	1	2	yes	maximal, complemented
15	#13092947	C₂	1	2	yes	maximal, complemented
16	#13092947	C₂	1	2	yes	maximal, complemented
17	#13092924	C₂	1	1	yes	maximal, characteristic, complemented
18	#41×Dic₂₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#67290	C₂	1	2	yes	maximal, complemented
20	C₂×C₄×C₂²⋊D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#10625097	C₂	1	1	yes	maximal, characteristic, complemented
22	#117×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#41×C₂₃	C₂²	1	1	yes	characteristic
25	C₂³×C₄×C₂₃	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
27	C₂×#67290	C₂²	1	2	yes	—
28	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
29	C₂₃×#123	C₂²	1	2	yes	—
30	C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₂₃×#121	C₂²	1	1	yes	characteristic, complemented
33	C₂₃×#121	C₂²	1	1	yes	characteristic, complemented
34	C₂₃×#120	C₂²	1	2	yes	—
35	C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
36	C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
37	C₂₃×#117	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊Dic₂₃	C₂²	1	2	yes	—
39	C₂×C₂²⋊Dic₂₃	C₂²	1	1	yes	characteristic
40	#10625117	C₂²	1	1	yes	characteristic, complemented
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	#10625110	C₂²	1	2	yes	—
45	#10625110	C₂²	1	2	yes	—
46	#10625109	C₂²	1	2	yes	—
47	#10625109	C₂²	1	1	yes	characteristic, complemented
48	#10625109	C₂²	1	1	yes	characteristic, complemented
49	#10625108	C₂²	1	2	yes	—
50	#10625107	C₂²	1	2	yes	complemented
51	#10625106	C₂²	1	2	yes	—
52	#10625106	C₂²	1	2	yes	complemented
53	#10625106	C₂²	1	2	yes	complemented
54	D₄×Dic₂₃	C₂²	1	2	yes	—
55	D₄×Dic₂₃	C₂²	1	2	yes	—
56	D₄×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
57	D₄×Dic₂₃	C₂²	1	2	yes	complemented
58	D₄×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
59	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
60	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
61	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
62	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
63	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
64	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
65	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
66	C₄×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
67	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
68	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
69	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic
70	#10625097	C₂²	1	1	yes	characteristic
71	#10625097	C₂²	1	1	yes	characteristic
72	#10625097	C₂²	1	2	yes	—
73	#10625097	C₂²	1	1	yes	characteristic, complemented
74	#10625097	C₂²	1	1	yes	characteristic, complemented
75	#10625097	C₂²	1	2	yes	complemented
76	#10625097	C₂²	1	2	yes	complemented
77	C₂×C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic, complemented
78	C₂×C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic, complemented
79	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
80	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic
81	C₂×C₄×Dic₂₃	C₂²	1	2	yes	complemented
82	C₂×C₄×Dic₂₃	C₂²	1	2	yes	complemented
83	#10625069	C₂²	1	2	yes	complemented
84	#10625069	C₂²	1	2	yes	complemented
85	#10625068	C₂²	1	2	yes	complemented
86	#10625063	C₂²	1	1	yes	characteristic, complemented
87	#10625063	C₂²	1	1	yes	characteristic, complemented
88	#10625063	C₂²	1	2	yes	complemented
89	C₄⋊C₄×D₂₃	C₂²	1	1	yes	characteristic, complemented
90	C₄⋊C₄×D₂₃	C₂²	1	1	yes	characteristic, complemented
91	#10625061	C₂²	1	2	yes	complemented
92	#10625061	C₂²	1	1	yes	characteristic, complemented
93	#10625061	C₂²	1	1	yes	characteristic, complemented
94	#10625060	C₂²	1	2	yes	complemented
95	#10625060	C₂²	1	2	yes	complemented
96	#10625059	C₂²	1	1	yes	characteristic, complemented
97	#10625059	C₂²	1	1	yes	characteristic, complemented
98	#10625058	C₂²	1	2	yes	complemented
99	#10625057	C₂²	1	2	yes	—
100	#10625057	C₂²	1	2	yes	complemented
101	#10625056	C₂²	1	2	yes	—
102	#10625056	C₂²	1	2	yes	complemented
103	#10625054	C₂²	1	2	yes	—
104	#10625054	C₂²	1	2	yes	complemented
105	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	—
106	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	complemented
107	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	—
108	#10625050	C₂²	1	2	yes	complemented
109	#10625050	C₂²	1	2	yes	complemented
110	#10625050	C₂²	1	2	yes	complemented
111	#10625050	C₂²	1	2	yes	complemented
112	#10625049	C₂²	1	2	yes	—
113	#10625049	C₂²	1	2	yes	—
114	#10625049	C₂²	1	2	yes	complemented
115	#10625049	C₂²	1	2	yes	complemented
116	#10625048	C₂²	1	2	yes	—
117	#10625048	C₂²	1	2	yes	complemented
118	#10625048	C₂²	1	2	yes	complemented
119	#10625043	C₂²	1	2	yes	complemented
120	C₄²×D₂₃	C₂²	1	2	yes	complemented
121	C₄×Dic₄₆	C₂²	1	2	yes	complemented
122	C₄×Dic₄₆	C₂²	1	2	yes	complemented
123	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
124	C₂³×D₂₃	C₂³	1	1	yes	characteristic
125	#41×C₂₃	—	2	4	no	—
126	C₂×Q₈×C₂₃	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₂₃	C₂³	1	2	yes	—
128	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₂₃	C₂³	1	2	yes	—
130	C₂×D₄×C₂₃	C₂³	1	2	yes	—
131	C₂²×C₄×C₂₃	—	2	4	no	—
132	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
134	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₂₃	—	2	4	no	—
140	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₂₃	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₂₃	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₂₃	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₂₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
151	C₂²×Dic₂₃	C₂³	1	2	yes	—
152	C₂²×Dic₂₃	C₂³	1	2	yes	—
153	#67290	—	2	8	no	—
154	C₂×C₄×D₂₃	—	2	4	no	—
155	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₂₃	C₂³	1	2	yes	—
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	2	yes	—
161	C₂×Dic₄₆	C₂³	1	2	yes	—
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	1	yes	characteristic
166	C₄⋊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	2	yes	—
170	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
171	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
172	C₄²×C₂₃	C₂³	1	2	yes	—
173	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
174	C₂²⋊Dic₂₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
181	C₂²⋊Dic₂₃	C₂³	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
191	(C₂×D₂₃)⋊C₄	C₂³	1	1	yes	characteristic
192	(C₂×D₂₃)⋊C₄	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	C₄⋊Dic₂₃	C₂³	1	2	yes	—
198	C₄⋊Dic₂₃	C₂³	1	2	yes	—
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	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	1	yes	characteristic
212	Dic₂₃⋊C₄	C₂³	1	2	yes	—
213	Dic₂₃⋊C₄	C₂³	1	1	yes	characteristic
214	Dic₂₃⋊C₄	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	2	yes	—
218	C₄×Dic₂₃	C₂³	1	2	yes	—
219	C₄×Dic₂₃	C₂³	1	2	yes	—
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	2	yes	—
225	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
226	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
227	C₂³×C₂₃	—	2	2	no	—
228	C₂³×C₂₃	—	2	2	no	—
229	C₂³×C₂₃	—	4	1	no	—
230	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
231	C₂³×C₂₃	C₂⁴	1	2	yes	—
232	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
233	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
234	C₂²×D₂₃	—	2	2	no	—
235	C₂²×D₂₃	—	2	2	no	—
236	C₂²×D₂₃	—	4	1	no	—
237	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
238	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
239	Q₈×C₂₃	—	2	2	no	—
240	D₄×C₂₃	—	2	4	no	—
241	D₄×C₂₃	—	2	4	no	—
242	D₄×C₂₃	—	2	2	no	—
243	D₄×C₂₃	—	4	2	no	—
244	C₂×C₄×C₂₃	—	2	2	no	—
245	C₂×C₄×C₂₃	—	2	2	no	—
246	C₂×C₄×C₂₃	—	2	2	no	—
247	C₂×C₄×C₂₃	—	2	2	no	—
248	C₂×C₄×C₂₃	—	2	2	no	—
249	C₂×C₄×C₂₃	—	2	4	no	—
250	C₂×C₄×C₂₃	#41	1	4	yes	complemented
251	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
253	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
254	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
255	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
258	C₂²⋊D₂₃	—	2	2	no	—
259	C₂²⋊D₂₃	—	2	4	no	—
260	C₂²⋊D₂₃	—	2	2	no	—
261	C₂²⋊D₂₃	—	2	2	no	—
262	C₂²⋊D₂₃	—	4	2	no	—
263	C₂²⋊D₂₃	#41	1	4	yes	complemented
264	C₂×Dic₂₃	—	2	2	no	—
265	C₂×Dic₂₃	—	2	4	no	—
266	C₂×Dic₂₃	—	2	4	no	—
267	C₂×Dic₂₃	—	2	2	no	—
268	C₂×Dic₂₃	—	4	1	no	—
269	C₂×Dic₂₃	—	4	2	no	—
270	C₂×Dic₂₃	—	4	2	no	—
271	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
273	C₂×Dic₂₃	C₂⁴	1	2	yes	—
274	C₂×Dic₂₃	C₂⁴	1	2	yes	—
275	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₂₃	C₂⁴	1	2	yes	—
277	C₂×Dic₂₃	C₂⁴	1	2	yes	—
278	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
281	C₄×D₂₃	—	2	4	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	—	4	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	1	no	—
293	C₂²×C₂₃	—	2	1	no	—
294	C₂²×C₂₃	—	2	2	no	—
295	C₂²×C₂₃	—	2	1	no	—
296	C₂²×C₂₃	—	2	1	no	—
297	C₂²×C₂₃	—	2	2	no	—
298	C₂²×C₂₃	—	2	2	no	—
299	C₂²×C₂₃	—	2	1	no	—
300	C₂²×C₂₃	—	4	4	no	—
301	C₂²×C₂₃	C₂×#41	1	2	yes	—
302	C₂²×C₂₃	C₂×#41	1	2	yes	—
303	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
304	C₂×D₂₃	—	2	1	no	—
305	C₂×D₂₃	—	2	1	no	—
306	C₂×D₂₃	—	2	1	no	—
307	C₂×D₂₃	—	2	1	no	—
308	C₂×D₂₃	—	2	1	no	—
309	C₂×D₂₃	—	4	4	no	—
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	2	no	—
315	C₄×C₂₃	—	2	2	no	—
316	C₄×C₂₃	C₂×#41	1	2	yes	—
317	C₄×C₂₃	C₂×#41	1	2	yes	—
318	Dic₂₃	—	2	2	no	—
319	Dic₂₃	—	2	1	no	—
320	Dic₂₃	—	2	1	no	—
321	Dic₂₃	—	2	2	no	—
322	Dic₂₃	—	2	1	no	—
323	Dic₂₃	—	2	1	no	—
324	Dic₂₃	—	2	2	no	—
325	Dic₂₃	—	2	2	no	—
326	Dic₂₃	—	2	1	no	—
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	—	23	1	no	—
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	D₂₃	1	1	yes	characteristic, complemented
346	C₄×#41	—	23	1	no	—
347	C₄×#41	—	23	2	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	—	2	2	no	—
353	C₂×C₂₃	—	4	2	no	—
354	C₂×C₂₃	—	4	1	no	—
355	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
356	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
357	C₂×C₂₃	#585	1	1	yes	characteristic
358	D₂₃	—	2	2	no	—
359	D₂₃	—	4	1	no	—
360	C₂×#41	—	23	2	no	—
361	C₂×#41	C₂×D₂₃	1	1	yes	characteristic
362	C₂²×D₄	—	23	1	no	—
363	C₂³×C₄	—	23	1	no	—
364	C₂³×C₄	C₂×D₂₃	1	1	yes	characteristic
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	—	23	2	no	—
373	#125	—	23	2	no	—
374	#125	—	23	2	no	—
375	#125	—	23	2	no	—
376	#125	—	23	1	no	—
377	#125	—	23	1	no	—
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	—
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	2	no	—
395	C₂²⋊Q₈	—	23	2	no	—
396	C₂²⋊Q₈	C₂×D₂₃	1	1	yes	characteristic, complemented
397	C₂²⋊Q₈	C₂×D₂₃	1	1	yes	characteristic, complemented
398	#121	—	23	1	no	—
399	#121	—	23	1	no	—
400	#121	—	23	2	no	—
401	#121	—	23	2	no	—
402	#121	—	23	2	no	—
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	C₂×D₂₃	1	2	yes	—
407	C₄×Q₈	—	23	1	no	—
408	C₄×Q₈	—	23	1	no	—
409	C₄×Q₈	—	23	2	no	—
410	C₄×Q₈	—	23	2	no	—
411	C₄×Q₈	—	23	2	no	—
412	C₄×D₄	—	23	2	no	—
413	C₄×D₄	—	23	1	no	—
414	C₄×D₄	—	23	2	no	—
415	C₄×D₄	—	23	2	no	—
416	C₄×D₄	—	23	1	no	—
417	C₄×D₄	—	23	1	no	—
418	C₄×D₄	—	23	1	no	—
419	C₄×D₄	—	23	1	no	—
420	C₄×D₄	—	23	1	no	—
421	C₄×D₄	—	23	1	no	—
422	C₄×D₄	—	23	1	no	—
423	C₄×D₄	—	23	1	no	—
424	C₄×D₄	—	23	1	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	C₂×D₂₃	1	2	yes	complemented
430	C₄×D₄	C₂×D₂₃	1	2	yes	complemented
431	#117	—	23	1	no	—
432	#117	—	23	1	no	—
433	#117	—	23	2	no	—
434	#117	—	23	2	no	—
435	#117	—	23	1	no	—
436	#117	—	23	1	no	—
437	#117	—	23	2	no	—
438	#117	—	23	1	no	—
439	#117	—	23	1	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
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	—	23	1	no	—
451	C₂×C₂²⋊C₄	—	23	2	no	—
452	C₂×C₂²⋊C₄	—	23	1	no	—
453	C₂×C₂²⋊C₄	—	23	1	no	—
454	C₂×C₂²⋊C₄	—	23	2	no	—
455	C₂×C₄²	—	23	2	no	—
456	C₂×C₄²	—	23	1	no	—
457	C₂×C₄²	—	23	2	no	—
458	C₂×C₄²	—	23	2	no	—
459	C₂₃	#3475	1	1	yes	characteristic, complemented, Sylow
460	C₂⁴	—	23	1	no	—
461	C₂⁴	C₂²×D₂₃	1	1	yes	characteristic
462	#41	—	2	4	no	—
463	#41	—	46	8	no	—
464	C₂×Q₈	—	23	2	no	—
465	C₂×Q₈	—	23	2	no	—
466	C₂×Q₈	C₂²×D₂₃	1	1	yes	characteristic
467	C₂×D₄	—	23	1	no	—
468	C₂×D₄	—	23	2	no	—
469	C₂×D₄	—	23	1	no	—
470	C₂×D₄	—	23	1	no	—
471	C₂×D₄	—	23	1	no	—
472	C₂×D₄	—	23	2	no	—
473	C₂×D₄	—	46	4	no	—
474	C₂×D₄	C₂²×D₂₃	1	2	yes	—
475	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
476	C₂×D₄	C₂²×D₂₃	1	2	yes	—
477	C₂×D₄	C₂²×D₂₃	1	2	yes	—
478	C₂²×C₄	—	2	4	no	—
479	C₂²×C₄	—	23	2	no	—
480	C₂²×C₄	—	23	1	no	—
481	C₂²×C₄	—	23	2	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	2	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	2	no	—
492	C₂²×C₄	—	46	4	no	—
493	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
494	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
495	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
496	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
497	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
498	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
499	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
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	1	no	—
505	C₄⋊C₄	—	23	2	no	—
506	C₄⋊C₄	—	23	2	no	—
507	C₄⋊C₄	—	23	2	no	—
508	C₄⋊C₄	—	23	2	no	—
509	C₄⋊C₄	—	23	1	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	—	23	2	no	—
521	C₄⋊C₄	—	23	2	no	—
522	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
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	1	no	—
528	C₂²⋊C₄	—	23	2	no	—
529	C₂²⋊C₄	—	23	2	no	—
530	C₂²⋊C₄	—	23	2	no	—
531	C₂²⋊C₄	—	23	1	no	—
532	C₂²⋊C₄	—	23	1	no	—
533	C₂²⋊C₄	—	23	1	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	1	no	—
539	C₂²⋊C₄	—	23	2	no	—
540	C₂²⋊C₄	—	23	2	no	—
541	C₂²⋊C₄	—	23	1	no	—
542	C₂²⋊C₄	—	23	1	no	—
543	C₂²⋊C₄	—	23	1	no	—
544	C₂²⋊C₄	—	23	2	no	—
545	C₂²⋊C₄	—	23	2	no	—
546	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
547	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
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	2	no	—
553	C₄²	—	23	2	no	—
554	C₄²	—	23	2	no	—
555	C₄²	—	23	2	no	—
556	C₄²	—	23	1	no	—
557	C₄²	—	23	1	no	—
558	C₄²	—	23	2	no	—
559	C₄²	—	23	2	no	—
560	C₄²	—	23	1	no	—
561	C₄²	—	23	1	no	—
562	C₄²	—	23	2	no	—
563	C₄²	C₂²×D₂₃	1	2	yes	—
564	C₂³	—	2	2	no	—
565	C₂³	—	2	2	no	—
566	C₂³	—	4	1	no	—
567	C₂³	—	23	1	no	—
568	C₂³	—	23	1	no	—
569	C₂³	—	46	2	no	—
570	C₂³	—	46	2	no	—
571	C₂³	—	92	1	no	—
572	C₂³	C₂³×D₂₃	1	1	yes	characteristic
573	C₂³	C₂³×D₂₃	1	2	yes	—
574	C₂³	C₂³×D₂₃	1	1	yes	characteristic
575	C₂³	C₂³×D₂₃	1	1	yes	characteristic
576	Q₈	—	2	2	no	—
577	Q₈	—	46	4	no	—
578	Q₈	—	92	2	no	—
579	D₄	—	2	4	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	2	no	—
588	D₄	—	92	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	4	no	—
595	C₂×C₄	—	23	1	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	1	no	—
601	C₂×C₄	—	23	2	no	—
602	C₂×C₄	—	23	2	no	—
603	C₂×C₄	—	23	1	no	—
604	C₂×C₄	—	23	1	no	—
605	C₂×C₄	—	46	4	no	—
606	C₂×C₄	—	46	2	no	—
607	C₂×C₄	—	46	4	no	—
608	C₂×C₄	—	46	2	no	—
609	C₂×C₄	—	46	4	no	—
610	C₂×C₄	—	46	2	no	—
611	C₂×C₄	—	46	2	no	—
612	C₂×C₄	—	46	2	no	—
613	C₂×C₄	—	46	2	no	—
614	C₂×C₄	—	92	2	no	—
615	C₂×C₄	—	92	2	no	—
616	C₂×C₄	—	92	2	no	—
617	C₂×C₄	—	92	1	no	—
618	C₂×C₄	#67290	1	4	yes	complemented
619	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
620	C₂×C₄	C₂³×D₂₃	1	2	yes	—
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	1	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	4	4	no	—
637	C₂²	—	23	2	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	C₂×#67290	1	2	yes	—
645	C₂²	#41×D₂₃	1	2	yes	—
646	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
647	C₄	—	2	2	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	23	2	no	—
653	C₄	—	46	2	no	—
654	C₄	—	46	1	no	—
655	C₄	—	46	2	no	—
656	C₄	—	46	1	no	—
657	C₄	—	46	1	no	—
658	C₄	—	46	2	no	—
659	C₄	—	46	1	no	—
660	C₄	—	46	2	no	—
661	C₄	—	46	1	no	—
662	C₄	C₂×#67290	1	2	yes	—
663	C₄	C₂×#67290	1	2	yes	—
664	C₂	—	2	2	no	—
665	C₂	—	2	2	no	—
666	C₂	—	4	1	no	—
667	C₂	—	4	2	no	—
668	C₂	—	46	2	no	—
669	C₂	—	92	1	no	—
670	C₂	C₂×#41×D₂₃	1	1	yes	characteristic
671	C₂	C₂²×#67290	1	1	yes	characteristic
672	C₂	#13093253	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₂₃
commutator, socle, cosocle	C₂²×C₂₃	C₂⁵
Frattini	C₂²	C₂⁴×D₂₃
Fitting	C₂₃×#525	C₂
hypercenter	#525	D₂₃
hypocenter	C₂₃	#3475
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ #525

Complements

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

N	H ≅ G/N	type
1. #13093138	C₂	semidirect
2. #13093131	C₂	semidirect
3. #13093125	C₂	semidirect
4. #13093119	C₂	semidirect
5. #13093114	C₂	semidirect
6. #13093109	C₂	semidirect
7. #13093104	C₂	semidirect
8. #13093101	C₂	semidirect
9. #13093098	C₂	semidirect
10. #13093090	C₂	semidirect
11. #13093067	C₂	semidirect
12. #13093054	C₂	semidirect
13. #13092970	C₂	semidirect
14. #13092949	C₂	semidirect
15. #13092947	C₂	semidirect
16. #13092947	C₂	semidirect
17. #13092924	C₂	semidirect
18. #41×Dic₂₃	C₂	semidirect
19. C₄×#67290	C₂	semidirect
20. C₂×C₄×C₂²⋊D₂₃	C₂	semidirect
21. C₂×#10625097	C₂	semidirect
22. #117×D₂₃	C₂	semidirect
23. C₂₃×#525	C₂	semidirect
30. C₂₃×C₂²⋊Q₈	C₂²	semidirect
31. C₂₃×C₂²⋊Q₈	C₂²	semidirect
32. C₂₃×#121	C₂²	semidirect
33. C₂₃×#121	C₂²	semidirect
35. C₄×D₄×C₂₃	C₂²	semidirect
36. C₄×D₄×C₂₃	C₂²	semidirect
40. #10625117	C₂²	semidirect
41. #10625117	C₂²	semidirect
42. Q₈×Dic₂₃	C₂²	semidirect
43. Q₈×Dic₂₃	C₂²	semidirect
47. #10625109	C₂²	semidirect
48. #10625109	C₂²	semidirect
50. #10625107	C₂²	semidirect
52. #10625106	C₂²	semidirect
53. #10625106	C₂²	semidirect
56. D₄×Dic₂₃	C₂²	semidirect
57. D₄×Dic₂₃	C₂²	semidirect
58. D₄×Dic₂₃	C₂²	semidirect
67. C₄×C₂²⋊D₂₃	C₂²	semidirect
68. C₄×C₂²⋊D₂₃	C₂²	semidirect
73. #10625097	C₂²	semidirect
74. #10625097	C₂²	semidirect
75. #10625097	C₂²	semidirect
76. #10625097	C₂²	semidirect
77. C₂×C₄⋊Dic₂₃	C₂²	semidirect
78. C₂×C₄⋊Dic₂₃	C₂²	semidirect
81. C₂×C₄×Dic₂₃	C₂²	semidirect
82. C₂×C₄×Dic₂₃	C₂²	semidirect
83. #10625069	C₂²	semidirect
84. #10625069	C₂²	semidirect
85. #10625068	C₂²	semidirect
86. #10625063	C₂²	semidirect
87. #10625063	C₂²	semidirect
88. #10625063	C₂²	semidirect
89. C₄⋊C₄×D₂₃	C₂²	semidirect
90. C₄⋊C₄×D₂₃	C₂²	semidirect
91. #10625061	C₂²	semidirect
92. #10625061	C₂²	semidirect
93. #10625061	C₂²	semidirect
94. #10625060	C₂²	semidirect
95. #10625060	C₂²	semidirect
96. #10625059	C₂²	semidirect
97. #10625059	C₂²	semidirect
98. #10625058	C₂²	semidirect
100. #10625057	C₂²	semidirect
102. #10625056	C₂²	semidirect
104. #10625054	C₂²	semidirect
106. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
108. #10625050	C₂²	semidirect
109. #10625050	C₂²	semidirect
110. #10625050	C₂²	semidirect
111. #10625050	C₂²	semidirect
114. #10625049	C₂²	semidirect
115. #10625049	C₂²	semidirect
117. #10625048	C₂²	semidirect
118. #10625048	C₂²	semidirect
119. #10625043	C₂²	semidirect
120. C₄²×D₂₃	C₂²	semidirect
121. C₄×Dic₄₆	C₂²	semidirect
122. C₄×Dic₄₆	C₂²	semidirect
250. C₂×C₄×C₂₃	#41	semidirect
263. C₂²⋊D₂₃	#41	semidirect
345. #525	D₂₃	semidirect
396. C₂²⋊Q₈	C₂×D₂₃	semidirect
397. C₂²⋊Q₈	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
459. C₂₃	#3475	semidirect
618. C₂×C₄	#67290	semidirect

Maximal subgroups

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

subgroup	index
#13093138	2
#13093131	2
#13093125	2
#13093119	2
#13093114	2
#13093109	2
#13093104	2
#13093101	2
#13093098	2
#13093090	2
#13093067	2
#13093054	2
#13092970	2
#13092949	2
#13092947	2
#13092924	2
#41×Dic₂₃	2
C₄×#67290	2
C₂×C₄×C₂²⋊D₂₃	2
C₂×#10625097	2
#117×D₂₃	2
C₂₃×#525	2
#3475	23