Subgroups — D₂₃×#551 #15686890

Order 2944.

1328 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093098	C₂	1	1	yes	maximal, characteristic, complemented
2	#13093097	C₂	1	1	yes	maximal, characteristic, complemented
3	#13093096	C₂	1	2	yes	maximal, complemented
4	#13093095	C₂	1	1	yes	maximal, characteristic, complemented
5	#13093094	C₂	1	2	yes	maximal, complemented
6	#13093093	C₂	1	2	yes	maximal, complemented
7	#13093092	C₂	1	2	yes	maximal, complemented
8	#13093091	C₂	1	2	yes	maximal, complemented
9	#13093090	C₂	1	2	yes	maximal, complemented
10	#126×D₂₃	C₂	1	2	yes	maximal, complemented
11	#124×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#123×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
13	#123×D₂₃	C₂	1	2	yes	maximal, complemented
14	C₂²⋊Q₈×D₂₃	C₂	1	2	yes	maximal, complemented
15	#120×D₂₃	C₂	1	1	yes	maximal, characteristic
16	C₄×D₄×D₂₃	C₂	1	2	yes	maximal, complemented
17	#117×D₂₃	C₂	1	2	yes	maximal, complemented
18	C₂×C₂²⋊C₄×D₂₃	C₂	1	2	yes	maximal, complemented
19	C₂₃×#551	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×D₂₃	C₂²	1	1	yes	characteristic
21	C₂×Q₈×D₂₃	C₂²	1	1	yes	characteristic, complemented
22	C₂×D₄×D₂₃	C₂²	1	2	yes	—
23	C₂×D₄×D₂₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄×D₂₃	C₂²	1	2	yes	—
25	C₂²×C₄×D₂₃	C₂²	1	2	yes	—
26	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic, complemented
27	C₂₃×#126	C₂²	1	2	yes	complemented
28	C₂₃×#124	C₂²	1	1	yes	characteristic, complemented
29	C₂₃×#123	C₂²	1	1	yes	characteristic, complemented
30	C₂₃×#123	C₂²	1	2	yes	complemented
31	C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
32	C₂₃×#120	C₂²	1	1	yes	characteristic
33	C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
34	C₂₃×#117	C₂²	1	2	yes	complemented
35	C₂×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
36	#10625124	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊Dic₂₃	C₂²	1	2	yes	complemented
38	#10625118	C₂²	1	1	yes	characteristic, complemented
39	#10625117	C₂²	1	2	yes	complemented
40	#10625108	C₂²	1	2	yes	—
41	#10625108	C₂²	1	1	yes	characteristic
42	#10625107	C₂²	1	1	yes	characteristic, complemented
43	#10625106	C₂²	1	1	yes	characteristic, complemented
44	#10625106	C₂²	1	2	yes	complemented
45	D₄×Dic₂₃	C₂²	1	2	yes	complemented
46	#10625100	C₂²	1	1	yes	characteristic, complemented
47	#10625100	C₂²	1	2	yes	complemented
48	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
49	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
50	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	2	yes	complemented
51	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	2	yes	complemented
52	#10625097	C₂²	1	2	yes	complemented
53	#10625095	C₂²	1	2	yes	complemented
54	#10625069	C₂²	1	2	yes	complemented
55	#10625069	C₂²	1	2	yes	complemented
56	#10625069	C₂²	1	2	yes	complemented
57	#10625068	C₂²	1	2	yes	complemented
58	#10625067	C₂²	1	2	yes	complemented
59	#10625067	C₂²	1	2	yes	complemented
60	#10625065	C₂²	1	2	yes	complemented
61	#10625065	C₂²	1	2	yes	complemented
62	#10625065	C₂²	1	2	yes	complemented
63	#10625064	C₂²	1	2	yes	complemented
64	#10625063	C₂²	1	2	yes	complemented
65	#10625063	C₂²	1	2	yes	complemented
66	C₄⋊C₄×D₂₃	C₂²	1	2	yes	complemented
67	C₄⋊C₄×D₂₃	C₂²	1	2	yes	complemented
68	C₄⋊C₄×D₂₃	C₂²	1	2	yes	complemented
69	C₄⋊C₄×D₂₃	C₂²	1	2	yes	complemented
70	#10625057	C₂²	1	1	yes	characteristic, complemented
71	#10625057	C₂²	1	2	yes	complemented
72	#10625056	C₂²	1	2	yes	complemented
73	#10625056	C₂²	1	2	yes	complemented
74	#10625054	C₂²	1	2	yes	complemented
75	#10625054	C₂²	1	2	yes	complemented
76	#10625054	C₂²	1	2	yes	complemented
77	#10625053	C₂²	1	2	yes	—
78	#10625053	C₂²	1	1	yes	characteristic
79	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	complemented
80	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	complemented
81	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	—
82	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	—
83	C₂²⋊C₄×D₂₃	C₂²	1	1	yes	characteristic
84	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	—
85	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	—
86	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	—
87	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	complemented
88	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	complemented
89	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	complemented
90	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	complemented
91	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	complemented
92	C₂²⋊C₄×D₂₃	C₂²	1	1	yes	characteristic, complemented
93	#10625050	C₂²	1	2	yes	complemented
94	#10625050	C₂²	1	2	yes	complemented
95	#10625050	C₂²	1	2	yes	complemented
96	#10625049	C₂²	1	2	yes	complemented
97	#10625049	C₂²	1	2	yes	complemented
98	#10625048	C₂²	1	2	yes	complemented
99	#10625048	C₂²	1	2	yes	complemented
100	#10625047	C₂²	1	2	yes	complemented
101	#10625046	C₂²	1	1	yes	characteristic, complemented
102	C₄×D₉₂	C₂²	1	2	yes	complemented
103	#10625043	C₂²	1	2	yes	complemented
104	#10625043	C₂²	1	2	yes	complemented
105	C₄²×D₂₃	C₂²	1	1	yes	characteristic, complemented
106	C₄²×D₂₃	C₂²	1	2	yes	complemented
107	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
108	C₂³×D₂₃	—	2	8	no	—
109	C₂³×D₂₃	—	4	2	no	—
110	C₂³×D₂₃	C₂³	1	1	yes	characteristic
111	C₂³×D₂₃	C₂³	1	1	yes	characteristic
112	C₂³×D₂₃	C₂³	1	1	yes	characteristic
113	C₂³×D₂₃	C₂³	1	2	yes	—
114	C₂³×D₂₃	C₂³	1	2	yes	—
115	C₂×Q₈×C₂₃	C₂³	1	1	yes	characteristic, complemented
116	C₂×D₄×C₂₃	C₂³	1	2	yes	—
117	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
118	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
119	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
120	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic, complemented
121	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
122	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
123	C₂×C₂²⋊D₂₃	C₂³	1	1	yes	characteristic
124	C₂×C₂²⋊D₂₃	C₂³	1	1	yes	characteristic
125	C₂²×Dic₂₃	C₂³	1	2	yes	—
126	C₂²×Dic₂₃	C₂³	1	2	yes	—
127	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic, complemented
128	Q₈×D₂₃	—	4	2	no	—
129	D₄×D₂₃	—	2	8	no	—
130	D₄×D₂₃	—	4	2	no	—
131	C₂×D₉₂	C₂³	1	2	yes	—
132	C₂×D₉₂	C₂³	1	1	yes	characteristic
133	C₂×C₄×D₂₃	—	2	8	no	—
134	C₂×C₄×D₂₃	—	4	4	no	—
135	C₂×C₄×D₂₃	—	4	2	no	—
136	C₂×C₄×D₂₃	C₂³	1	2	yes	—
137	C₂×C₄×D₂₃	C₂³	1	2	yes	—
138	C₂×C₄×D₂₃	C₂³	1	2	yes	—
139	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₂₃	C₂³	1	2	yes	—
141	C₂×C₄×D₂₃	C₂³	1	2	yes	—
142	C₂×C₄×D₂₃	C₂³	1	2	yes	—
143	C₂×C₄×D₂₃	C₂³	1	2	yes	—
144	C₂×C₄×D₂₃	C₂³	1	2	yes	—
145	C₂×C₄×D₂₃	C₂³	1	2	yes	—
146	C₂×C₄×D₂₃	C₂³	1	2	yes	complemented
147	C₂×Dic₄₆	C₂³	1	1	yes	characteristic, complemented
148	C₂×Dic₄₆	C₂³	1	2	yes	complemented
149	C₄⋊C₄×C₂₃	C₂³	1	2	yes	complemented
150	C₄⋊C₄×C₂₃	C₂³	1	2	yes	complemented
151	C₄⋊C₄×C₂₃	C₂³	1	2	yes	complemented
152	C₄⋊C₄×C₂₃	C₂³	1	2	yes	complemented
153	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
154	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
155	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
156	C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
157	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
158	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
159	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	complemented
160	C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic, complemented
161	C₄²×C₂₃	C₂³	1	1	yes	characteristic, complemented
162	C₄²×C₂₃	C₂³	1	2	yes	complemented
163	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
164	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
165	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
166	C₂²⋊Dic₂₃	C₂³	1	1	yes	characteristic
167	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
168	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
169	C₂²⋊Dic₂₃	C₂³	1	1	yes	characteristic, complemented
170	C₂²⋊Dic₂₃	C₂³	1	2	yes	complemented
171	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
172	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
173	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
174	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
175	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
176	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
177	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
178	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
179	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
180	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
181	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	complemented
183	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	complemented
184	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	complemented
185	C₄⋊Dic₂₃	C₂³	1	2	yes	complemented
186	C₄⋊Dic₂₃	C₂³	1	2	yes	complemented
187	C₄⋊Dic₂₃	C₂³	1	2	yes	complemented
188	C₄⋊Dic₂₃	C₂³	1	2	yes	complemented
189	Dic₂₃⋊C₄	C₂³	1	2	yes	complemented
190	Dic₂₃⋊C₄	C₂³	1	2	yes	complemented
191	Dic₂₃⋊C₄	C₂³	1	2	yes	complemented
192	Dic₂₃⋊C₄	C₂³	1	2	yes	complemented
193	Dic₂₃⋊C₄	C₂³	1	2	yes	complemented
194	Dic₂₃⋊C₄	C₂³	1	2	yes	complemented
195	Dic₂₃⋊C₄	C₂³	1	2	yes	complemented
196	Dic₂₃⋊C₄	C₂³	1	2	yes	complemented
197	C₄×Dic₂₃	C₂³	1	2	yes	complemented
198	C₄×Dic₂₃	C₂³	1	2	yes	complemented
199	C₄×Dic₂₃	C₂³	1	1	yes	characteristic, complemented
200	C₄×Dic₂₃	C₂³	1	2	yes	complemented
201	C₄×Dic₂₃	C₂³	1	2	yes	complemented
202	C₂³×C₂₃	—	2	4	no	—
203	C₂³×C₂₃	—	4	1	no	—
204	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
205	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
206	C₂³×C₂₃	C₂⁴	1	2	yes	—
207	C₂²×D₂₃	—	2	4	no	—
208	C₂²×D₂₃	—	2	4	no	—
209	C₂²×D₂₃	—	2	4	no	—
210	C₂²×D₂₃	—	2	4	no	—
211	C₂²×D₂₃	—	2	4	no	—
212	C₂²×D₂₃	—	2	4	no	—
213	C₂²×D₂₃	—	2	4	no	—
214	C₂²×D₂₃	—	2	2	no	—
215	C₂²×D₂₃	—	2	2	no	—
216	C₂²×D₂₃	—	4	1	no	—
217	C₂²×D₂₃	—	4	2	no	—
218	C₂²×D₂₃	—	4	16	no	—
219	C₂²×D₂₃	#41	1	8	yes	—
220	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
221	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
222	C₂²×D₂₃	C₂⁴	1	2	yes	—
223	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
224	Q₈×C₂₃	—	4	1	no	—
225	D₄×C₂₃	—	2	4	no	—
226	D₄×C₂₃	—	4	1	no	—
227	C₂×C₄×C₂₃	—	2	4	no	—
228	C₂×C₄×C₂₃	—	4	2	no	—
229	C₂×C₄×C₂₃	—	4	1	no	—
230	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
231	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
232	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
233	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
234	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
235	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
236	C₂²⋊D₂₃	—	2	4	no	—
237	C₂²⋊D₂₃	—	2	4	no	—
238	C₂²⋊D₂₃	—	4	1	no	—
239	C₂²⋊D₂₃	—	4	1	no	—
240	C₂×Dic₂₃	—	2	4	no	—
241	C₂×Dic₂₃	—	4	2	no	—
242	C₂×Dic₂₃	—	4	1	no	—
243	C₂×Dic₂₃	C₂⁴	1	2	yes	—
244	C₂×Dic₂₃	C₂⁴	1	2	yes	—
245	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
246	C₂×Dic₂₃	C₂⁴	1	2	yes	—
247	C₂×Dic₂₃	C₂⁴	1	2	yes	—
248	C₂×Dic₂₃	C₂⁴	1	2	yes	—
249	D₉₂	—	2	4	no	—
250	D₉₂	—	4	1	no	—
251	C₄×D₂₃	—	2	4	no	—
252	C₄×D₂₃	—	2	4	no	—
253	C₄×D₂₃	—	2	4	no	—
254	C₄×D₂₃	—	2	4	no	—
255	C₄×D₂₃	—	2	4	no	—
256	C₄×D₂₃	—	2	4	no	—
257	C₄×D₂₃	—	2	4	no	—
258	C₄×D₂₃	—	2	2	no	—
259	C₄×D₂₃	—	4	2	no	—
260	C₄×D₂₃	—	4	2	no	—
261	C₄×D₂₃	—	4	2	no	—
262	Dic₄₆	—	4	1	no	—
263	Dic₄₆	—	4	2	no	—
264	C₂×#551	—	23	1	no	maximal, Sylow
265	C₂²×C₂₃	—	2	2	no	—
266	C₂²×C₂₃	—	2	2	no	—
267	C₂²×C₂₃	—	2	2	no	—
268	C₂²×C₂₃	—	2	2	no	—
269	C₂²×C₂₃	—	2	1	no	—
270	C₂²×C₂₃	—	2	1	no	—
271	C₂²×C₂₃	—	4	4	no	—
272	C₂²×C₂₃	C₂×#41	1	4	yes	—
273	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
274	C₂×D₂₃	—	2	2	no	—
275	C₂×D₂₃	—	2	2	no	—
276	C₂×D₂₃	—	2	16	no	—
277	C₂×D₂₃	—	2	2	no	—
278	C₂×D₂₃	—	2	2	no	—
279	C₂×D₂₃	—	2	1	no	—
280	C₂×D₂₃	—	2	1	no	—
281	C₂×D₂₃	—	4	4	no	—
282	C₂×D₂₃	—	4	8	no	—
283	C₂×D₂₃	—	4	4	no	—
284	C₂×D₂₃	—	4	4	no	—
285	C₂×D₂₃	C₂×#41	1	4	yes	—
286	C₂×D₂₃	C₂×#41	1	4	yes	—
287	C₂×D₂₃	H(5,𝔽₂)	1	2	yes	—
288	C₄×C₂₃	—	2	2	no	—
289	C₄×C₂₃	—	2	2	no	—
290	C₄×C₂₃	—	2	2	no	—
291	C₄×C₂₃	—	2	2	no	—
292	C₄×C₂₃	—	2	1	no	—
293	C₄×C₂₃	—	2	2	no	—
294	Dic₂₃	—	2	2	no	—
295	Dic₂₃	—	2	2	no	—
296	Dic₂₃	—	2	2	no	—
297	Dic₂₃	—	2	2	no	—
298	Dic₂₃	—	2	1	no	—
299	Dic₂₃	—	2	2	no	—
300	#551	—	23	2	no	—
301	#551	—	23	1	no	—
302	#551	—	23	2	no	—
303	#551	—	23	1	no	—
304	#551	—	23	2	no	—
305	#551	—	23	1	no	—
306	#551	—	23	2	no	—
307	#551	—	23	2	no	—
308	#551	—	23	2	no	—
309	#551	D₂₃	1	1	yes	characteristic, direct product factor
310	C₂×#126	—	23	2	no	—
311	C₂×#124	—	23	1	no	—
312	C₂×#123	—	23	2	no	—
313	C₂×#123	—	23	1	no	—
314	C₂×C₂²⋊Q₈	—	23	2	no	—
315	C₂×#120	—	23	1	no	—
316	C₂×C₄×D₄	—	23	2	no	—
317	C₂×#117	—	23	2	no	—
318	C₂²×C₂²⋊C₄	—	23	2	no	—
319	C₂×C₂₃	—	2	4	no	—
320	C₂×C₂₃	—	4	1	no	—
321	C₂×C₂₃	—	4	1	no	—
322	C₂×C₂₃	C₂²×#41	1	2	yes	—
323	C₂×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
324	D₂₃	—	2	4	no	—
325	D₂₃	—	4	1	no	—
326	D₂₃	—	4	1	no	—
327	D₂₃	#551	1	4	yes	direct product factor
328	C₂⁵	—	23	1	no	—
329	C₂²×Q₈	—	23	1	no	—
330	C₂²×D₄	—	23	2	no	—
331	C₂²×D₄	—	23	1	no	—
332	C₂³×C₄	—	23	2	no	—
333	C₂³×C₄	—	23	2	no	—
334	C₂³×C₄	—	23	1	no	—
335	#126	—	23	2	no	—
336	#126	—	23	2	no	—
337	#126	—	23	2	no	—
338	#126	—	23	2	no	—
339	#126	—	23	2	no	—
340	#126	—	23	2	no	—
341	#126	—	23	2	no	—
342	#126	C₂×D₂₃	1	2	yes	complemented
343	#124	—	23	1	no	—
344	#124	—	23	1	no	—
345	#124	—	23	2	no	—
346	#124	—	23	2	no	—
347	#124	—	23	1	no	—
348	#124	C₂×D₂₃	1	1	yes	characteristic, complemented
349	#123	—	23	2	no	—
350	#123	—	23	1	no	—
351	#123	—	23	2	no	—
352	#123	—	23	1	no	—
353	#123	—	23	2	no	—
354	#123	—	23	2	no	—
355	#123	—	23	2	no	—
356	#123	—	23	2	no	—
357	#123	—	23	2	no	—
358	#123	—	23	2	no	—
359	#123	—	23	2	no	—
360	#123	—	23	1	no	—
361	#123	C₂×D₂₃	1	1	yes	characteristic, complemented
362	#123	C₂×D₂₃	1	2	yes	complemented
363	C₂²⋊Q₈	—	23	2	no	—
364	C₂²⋊Q₈	—	23	2	no	—
365	C₂²⋊Q₈	—	23	2	no	—
366	C₂²⋊Q₈	—	23	2	no	—
367	C₂²⋊Q₈	—	23	2	no	—
368	C₂²⋊Q₈	—	23	2	no	—
369	C₂²⋊Q₈	—	23	2	no	—
370	C₂²⋊Q₈	C₂×D₂₃	1	2	yes	complemented
371	#120	—	23	1	no	—
372	#120	—	23	2	no	—
373	#120	—	23	1	no	—
374	#120	—	23	1	no	—
375	#120	—	23	2	no	—
376	#120	C₂×D₂₃	1	1	yes	characteristic
377	C₄×D₄	—	23	2	no	—
378	C₄×D₄	—	23	2	no	—
379	C₄×D₄	—	23	2	no	—
380	C₄×D₄	—	23	2	no	—
381	C₄×D₄	—	23	2	no	—
382	C₄×D₄	—	23	2	no	—
383	C₄×D₄	—	23	2	no	—
384	C₄×D₄	C₂×D₂₃	1	2	yes	complemented
385	#117	—	23	2	no	—
386	#117	—	23	2	no	—
387	#117	—	23	2	no	—
388	#117	—	23	2	no	—
389	#117	—	23	2	no	—
390	#117	—	23	2	no	—
391	#117	—	23	2	no	—
392	#117	C₂×D₂₃	1	2	yes	complemented
393	C₂×C₄⋊C₄	—	23	2	no	—
394	C₂×C₄⋊C₄	—	23	2	no	—
395	C₂×C₄⋊C₄	—	23	2	no	—
396	C₂×C₄⋊C₄	—	23	2	no	—
397	C₂×C₂²⋊C₄	—	23	2	no	—
398	C₂×C₂²⋊C₄	—	23	2	no	—
399	C₂×C₂²⋊C₄	—	23	2	no	—
400	C₂×C₂²⋊C₄	—	23	2	no	—
401	C₂×C₂²⋊C₄	—	23	2	no	—
402	C₂×C₂²⋊C₄	—	23	2	no	—
403	C₂×C₂²⋊C₄	—	23	2	no	—
404	C₂×C₂²⋊C₄	—	23	2	no	—
405	C₂×C₂²⋊C₄	—	23	2	no	—
406	C₂×C₂²⋊C₄	—	23	2	no	—
407	C₂×C₂²⋊C₄	—	23	2	no	—
408	C₂×C₂²⋊C₄	—	23	2	no	—
409	C₂×C₂²⋊C₄	—	23	1	no	—
410	C₂×C₂²⋊C₄	—	23	2	no	—
411	C₂×C₂²⋊C₄	—	23	1	no	—
412	C₂×C₂²⋊C₄	C₂×D₂₃	1	2	yes	complemented
413	C₂×C₄²	—	23	1	no	—
414	C₂×C₄²	—	23	2	no	—
415	C₂₃	C₂×#551	1	1	yes	characteristic, complemented, Sylow
416	C₂⁴	—	23	2	no	—
417	C₂⁴	—	23	1	no	—
418	C₂⁴	—	23	1	no	—
419	C₂⁴	—	23	1	no	—
420	C₂⁴	—	23	2	no	—
421	C₂⁴	—	46	8	no	—
422	C₂⁴	—	92	2	no	—
423	C₂⁴	C₂²×D₂₃	1	1	yes	characteristic
424	C₂×Q₈	—	23	2	no	—
425	C₂×Q₈	—	23	1	no	—
426	C₂×Q₈	—	92	2	no	—
427	C₂×Q₈	C₂²×D₂₃	1	1	yes	characteristic, complemented
428	C₂×D₄	—	23	2	no	—
429	C₂×D₄	—	23	2	no	—
430	C₂×D₄	—	23	1	no	—
431	C₂×D₄	—	23	1	no	—
432	C₂×D₄	—	23	2	no	—
433	C₂×D₄	—	23	1	no	—
434	C₂×D₄	—	46	8	no	—
435	C₂×D₄	—	92	2	no	—
436	C₂×D₄	C₂²×D₂₃	1	2	yes	—
437	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
438	C₂²×C₄	—	23	2	no	—
439	C₂²×C₄	—	23	2	no	—
440	C₂²×C₄	—	23	1	no	—
441	C₂²×C₄	—	23	2	no	—
442	C₂²×C₄	—	23	2	no	—
443	C₂²×C₄	—	23	2	no	—
444	C₂²×C₄	—	23	1	no	—
445	C₂²×C₄	—	23	2	no	—
446	C₂²×C₄	—	23	2	no	—
447	C₂²×C₄	—	23	2	no	—
448	C₂²×C₄	—	23	2	no	—
449	C₂²×C₄	—	23	2	no	—
450	C₂²×C₄	—	23	2	no	—
451	C₂²×C₄	—	23	2	no	—
452	C₂²×C₄	—	46	8	no	—
453	C₂²×C₄	—	92	4	no	—
454	C₂²×C₄	—	92	2	no	—
455	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
456	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
457	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic, complemented
458	C₄⋊C₄	—	23	2	no	—
459	C₄⋊C₄	—	23	2	no	—
460	C₄⋊C₄	—	23	2	no	—
461	C₄⋊C₄	—	23	2	no	—
462	C₄⋊C₄	—	23	2	no	—
463	C₄⋊C₄	—	23	2	no	—
464	C₄⋊C₄	—	23	2	no	—
465	C₄⋊C₄	—	23	2	no	—
466	C₄⋊C₄	—	23	2	no	—
467	C₄⋊C₄	—	23	2	no	—
468	C₄⋊C₄	—	23	2	no	—
469	C₄⋊C₄	—	23	2	no	—
470	C₄⋊C₄	C₂²×D₂₃	1	2	yes	complemented
471	C₄⋊C₄	C₂²×D₂₃	1	2	yes	complemented
472	C₄⋊C₄	C₂²×D₂₃	1	2	yes	complemented
473	C₄⋊C₄	C₂²×D₂₃	1	2	yes	complemented
474	C₂²⋊C₄	—	23	2	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	2	no	—
480	C₂²⋊C₄	—	23	1	no	—
481	C₂²⋊C₄	—	23	1	no	—
482	C₂²⋊C₄	—	23	2	no	—
483	C₂²⋊C₄	—	23	2	no	—
484	C₂²⋊C₄	—	23	2	no	—
485	C₂²⋊C₄	—	23	2	no	—
486	C₂²⋊C₄	—	23	2	no	—
487	C₂²⋊C₄	—	23	2	no	—
488	C₂²⋊C₄	—	23	2	no	—
489	C₂²⋊C₄	—	23	2	no	—
490	C₂²⋊C₄	—	23	2	no	—
491	C₂²⋊C₄	—	23	2	no	—
492	C₂²⋊C₄	—	23	2	no	—
493	C₂²⋊C₄	—	23	2	no	—
494	C₂²⋊C₄	—	23	2	no	—
495	C₂²⋊C₄	—	23	2	no	—
496	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
497	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
498	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
499	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
500	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
501	C₂²⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
502	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	complemented
503	C₂²⋊C₄	C₂²×D₂₃	1	1	yes	characteristic, complemented
504	C₄²	—	23	1	no	—
505	C₄²	—	23	2	no	—
506	C₄²	—	23	2	no	—
507	C₄²	—	23	2	no	—
508	C₄²	—	23	2	no	—
509	C₄²	C₂²×D₂₃	1	1	yes	characteristic, complemented
510	C₄²	C₂²×D₂₃	1	2	yes	complemented
511	C₂³	—	2	4	no	—
512	C₂³	—	4	1	no	—
513	C₂³	—	23	1	no	—
514	C₂³	—	23	8	no	—
515	C₂³	—	23	2	no	—
516	C₂³	—	23	1	no	—
517	C₂³	—	23	1	no	—
518	C₂³	—	46	4	no	—
519	C₂³	—	46	4	no	—
520	C₂³	—	46	2	no	—
521	C₂³	—	46	4	no	—
522	C₂³	—	46	2	no	—
523	C₂³	—	46	4	no	—
524	C₂³	—	46	4	no	—
525	C₂³	—	46	4	no	—
526	C₂³	—	46	4	no	—
527	C₂³	—	92	2	no	—
528	C₂³	—	92	1	no	—
529	C₂³	—	92	16	no	—
530	C₂³	C₂³×D₂₃	1	1	yes	characteristic
531	C₂³	C₂³×D₂₃	1	1	yes	characteristic
532	C₂³	C₂³×D₂₃	1	2	yes	—
533	Q₈	—	4	1	no	—
534	Q₈	—	92	2	no	—
535	Q₈	—	92	1	no	—
536	D₄	—	2	4	no	—
537	D₄	—	4	1	no	—
538	D₄	—	46	4	no	—
539	D₄	—	46	4	no	—
540	D₄	—	46	4	no	—
541	D₄	—	92	1	no	—
542	D₄	—	92	1	no	—
543	D₄	—	92	1	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	23	2	no	—
548	C₂×C₄	—	23	2	no	—
549	C₂×C₄	—	23	2	no	—
550	C₂×C₄	—	23	1	no	—
551	C₂×C₄	—	23	2	no	—
552	C₂×C₄	—	23	2	no	—
553	C₂×C₄	—	46	4	no	—
554	C₂×C₄	—	46	4	no	—
555	C₂×C₄	—	46	4	no	—
556	C₂×C₄	—	46	4	no	—
557	C₂×C₄	—	46	4	no	—
558	C₂×C₄	—	46	4	no	—
559	C₂×C₄	—	46	4	no	—
560	C₂×C₄	—	46	2	no	—
561	C₂×C₄	—	46	4	no	—
562	C₂×C₄	—	92	2	no	—
563	C₂×C₄	—	92	2	no	—
564	C₂×C₄	—	92	2	no	—
565	C₂×C₄	—	92	1	no	—
566	C₂×C₄	—	92	2	no	—
567	C₂×C₄	C₂³×D₂₃	1	2	yes	—
568	C₂×C₄	C₂³×D₂₃	1	2	yes	—
569	C₂×C₄	C₂³×D₂₃	1	2	yes	—
570	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
571	C₂×C₄	C₂³×D₂₃	1	2	yes	—
572	C₂×C₄	C₂³×D₂₃	1	2	yes	—
573	C₂²	—	2	2	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	4	4	no	—
580	C₂²	—	23	4	no	—
581	C₂²	—	23	2	no	—
582	C₂²	—	23	4	no	—
583	C₂²	—	46	16	no	—
584	C₂²	—	46	2	no	—
585	C₂²	—	46	2	no	—
586	C₂²	—	46	2	no	—
587	C₂²	—	46	2	no	—
588	C₂²	—	46	1	no	—
589	C₂²	—	46	1	no	—
590	C₂²	—	92	8	no	—
591	C₂²	—	92	4	no	—
592	C₂²	—	92	4	no	—
593	C₂²	—	92	4	no	—
594	C₂²	#41×D₂₃	1	4	yes	—
595	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
596	C₄	—	2	2	no	—
597	C₄	—	2	2	no	—
598	C₄	—	2	2	no	—
599	C₄	—	2	2	no	—
600	C₄	—	2	2	no	—
601	C₄	—	2	1	no	—
602	C₄	—	46	2	no	—
603	C₄	—	46	2	no	—
604	C₄	—	46	2	no	—
605	C₄	—	46	2	no	—
606	C₄	—	46	2	no	—
607	C₄	—	46	1	no	—
608	C₂	—	2	4	no	—
609	C₂	—	4	1	no	—
610	C₂	—	4	1	no	—
611	C₂	—	23	4	no	—
612	C₂	—	46	4	no	—
613	C₂	—	92	1	no	—
614	C₂	—	92	1	no	—
615	C₂	C₂×#41×D₂₃	1	2	yes	—
616	C₂	H(5,𝔽₂)×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₃
commutator, socle, cosocle	C₂²×C₂₃	C₂⁵
Fitting	C₂₃×#551	C₂
prime radical	#120×D₂₃	C₂
hypercenter	#551	D₂₃
hypocenter	C₂₃	C₂×#551
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ #551

Complements

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

N	H ≅ G/N	type
1. #13093098	C₂	semidirect
2. #13093097	C₂	semidirect
3. #13093096	C₂	semidirect
4. #13093095	C₂	semidirect
5. #13093094	C₂	semidirect
6. #13093093	C₂	semidirect
7. #13093092	C₂	semidirect
8. #13093091	C₂	semidirect
9. #13093090	C₂	semidirect
10. #126×D₂₃	C₂	semidirect
11. #124×D₂₃	C₂	semidirect
12. #123×D₂₃	C₂	semidirect
13. #123×D₂₃	C₂	semidirect
14. C₂²⋊Q₈×D₂₃	C₂	semidirect
16. C₄×D₄×D₂₃	C₂	semidirect
17. #117×D₂₃	C₂	semidirect
18. C₂×C₂²⋊C₄×D₂₃	C₂	semidirect
19. C₂₃×#551	C₂	semidirect
21. C₂×Q₈×D₂₃	C₂²	semidirect
26. C₂²×C₄×D₂₃	C₂²	semidirect
27. C₂₃×#126	C₂²	semidirect
28. C₂₃×#124	C₂²	semidirect
29. C₂₃×#123	C₂²	semidirect
30. C₂₃×#123	C₂²	semidirect
31. C₂₃×C₂²⋊Q₈	C₂²	semidirect
33. C₄×D₄×C₂₃	C₂²	semidirect
34. C₂₃×#117	C₂²	semidirect
35. C₂×C₂²⋊C₄×C₂₃	C₂²	semidirect
37. C₂×C₂²⋊Dic₂₃	C₂²	semidirect
38. #10625118	C₂²	semidirect
39. #10625117	C₂²	semidirect
42. #10625107	C₂²	semidirect
43. #10625106	C₂²	semidirect
44. #10625106	C₂²	semidirect
45. D₄×Dic₂₃	C₂²	semidirect
46. #10625100	C₂²	semidirect
47. #10625100	C₂²	semidirect
48. C₄×C₂²⋊D₂₃	C₂²	semidirect
49. C₄×C₂²⋊D₂₃	C₂²	semidirect
50. C₂×(C₂×D₂₃)⋊C₄	C₂²	semidirect
51. C₂×(C₂×D₂₃)⋊C₄	C₂²	semidirect
52. #10625097	C₂²	semidirect
53. #10625095	C₂²	semidirect
54. #10625069	C₂²	semidirect
55. #10625069	C₂²	semidirect
56. #10625069	C₂²	semidirect
57. #10625068	C₂²	semidirect
58. #10625067	C₂²	semidirect
59. #10625067	C₂²	semidirect
60. #10625065	C₂²	semidirect
61. #10625065	C₂²	semidirect
62. #10625065	C₂²	semidirect
63. #10625064	C₂²	semidirect
64. #10625063	C₂²	semidirect
65. #10625063	C₂²	semidirect
66. C₄⋊C₄×D₂₃	C₂²	semidirect
67. C₄⋊C₄×D₂₃	C₂²	semidirect
68. C₄⋊C₄×D₂₃	C₂²	semidirect
69. C₄⋊C₄×D₂₃	C₂²	semidirect
70. #10625057	C₂²	semidirect
71. #10625057	C₂²	semidirect
72. #10625056	C₂²	semidirect
73. #10625056	C₂²	semidirect
74. #10625054	C₂²	semidirect
75. #10625054	C₂²	semidirect
76. #10625054	C₂²	semidirect
79. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
80. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
87. C₂²⋊C₄×D₂₃	C₂²	semidirect
88. C₂²⋊C₄×D₂₃	C₂²	semidirect
89. C₂²⋊C₄×D₂₃	C₂²	semidirect
90. C₂²⋊C₄×D₂₃	C₂²	semidirect
91. C₂²⋊C₄×D₂₃	C₂²	semidirect
92. C₂²⋊C₄×D₂₃	C₂²	semidirect
93. #10625050	C₂²	semidirect
94. #10625050	C₂²	semidirect
95. #10625050	C₂²	semidirect
96. #10625049	C₂²	semidirect
97. #10625049	C₂²	semidirect
98. #10625048	C₂²	semidirect
99. #10625048	C₂²	semidirect
100. #10625047	C₂²	semidirect
101. #10625046	C₂²	semidirect
102. C₄×D₉₂	C₂²	semidirect
103. #10625043	C₂²	semidirect
104. #10625043	C₂²	semidirect
105. C₄²×D₂₃	C₂²	semidirect
106. C₄²×D₂₃	C₂²	semidirect
115. C₂×Q₈×C₂₃	C₂³	semidirect
120. C₂²×C₄×C₂₃	C₂³	semidirect
127. C₂²×Dic₂₃	C₂³	semidirect
146. C₂×C₄×D₂₃	C₂³	semidirect
147. C₂×Dic₄₆	C₂³	semidirect
148. C₂×Dic₄₆	C₂³	semidirect
149. C₄⋊C₄×C₂₃	C₂³	semidirect
150. C₄⋊C₄×C₂₃	C₂³	semidirect
151. C₄⋊C₄×C₂₃	C₂³	semidirect
152. C₄⋊C₄×C₂₃	C₂³	semidirect
159. C₂²⋊C₄×C₂₃	C₂³	semidirect
160. C₂²⋊C₄×C₂₃	C₂³	semidirect
161. C₄²×C₂₃	C₂³	semidirect
162. C₄²×C₂₃	C₂³	semidirect
169. C₂²⋊Dic₂₃	C₂³	semidirect
170. C₂²⋊Dic₂₃	C₂³	semidirect
182. (C₂×D₂₃)⋊C₄	C₂³	semidirect
183. (C₂×D₂₃)⋊C₄	C₂³	semidirect
184. (C₂×D₂₃)⋊C₄	C₂³	semidirect
185. C₄⋊Dic₂₃	C₂³	semidirect
186. C₄⋊Dic₂₃	C₂³	semidirect
187. C₄⋊Dic₂₃	C₂³	semidirect
188. C₄⋊Dic₂₃	C₂³	semidirect
189. Dic₂₃⋊C₄	C₂³	semidirect
190. Dic₂₃⋊C₄	C₂³	semidirect
191. Dic₂₃⋊C₄	C₂³	semidirect
192. Dic₂₃⋊C₄	C₂³	semidirect
193. Dic₂₃⋊C₄	C₂³	semidirect
194. Dic₂₃⋊C₄	C₂³	semidirect
195. Dic₂₃⋊C₄	C₂³	semidirect
196. Dic₂₃⋊C₄	C₂³	semidirect
197. C₄×Dic₂₃	C₂³	semidirect
198. C₄×Dic₂₃	C₂³	semidirect
199. C₄×Dic₂₃	C₂³	semidirect
200. C₄×Dic₂₃	C₂³	semidirect
201. C₄×Dic₂₃	C₂³	semidirect
309. #551	D₂₃	direct (N × H)
327. D₂₃	#551	direct (N × H)
342. #126	C₂×D₂₃	semidirect
348. #124	C₂×D₂₃	semidirect
361. #123	C₂×D₂₃	semidirect
362. #123	C₂×D₂₃	semidirect
370. C₂²⋊Q₈	C₂×D₂₃	semidirect
384. C₄×D₄	C₂×D₂₃	semidirect
392. #117	C₂×D₂₃	semidirect
412. C₂×C₂²⋊C₄	C₂×D₂₃	semidirect
415. C₂₃	C₂×#551	semidirect
427. C₂×Q₈	C₂²×D₂₃	semidirect
457. C₂²×C₄	C₂²×D₂₃	semidirect
470. C₄⋊C₄	C₂²×D₂₃	semidirect
471. C₄⋊C₄	C₂²×D₂₃	semidirect
472. C₄⋊C₄	C₂²×D₂₃	semidirect
473. C₄⋊C₄	C₂²×D₂₃	semidirect
502. C₂²⋊C₄	C₂²×D₂₃	semidirect
503. C₂²⋊C₄	C₂²×D₂₃	semidirect
509. C₄²	C₂²×D₂₃	semidirect
510. C₄²	C₂²×D₂₃	semidirect

Maximal subgroups

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

subgroup	index
#13093098	2
#13093097	2
#13093096	2
#13093095	2
#13093094	2
#13093093	2
#13093092	2
#13093091	2
#13093090	2
#126×D₂₃	2
#124×D₂₃	2
#123×D₂₃	2
C₂²⋊Q₈×D₂₃	2
#120×D₂₃	2
C₄×D₄×D₂₃	2
#117×D₂₃	2
C₂×C₂²⋊C₄×D₂₃	2
C₂₃×#551	2
C₂×#551	23

Subgroups — D23×#551 #15686890

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₃×#551 #15686890