Subgroups — D₂₃×#532 #15686674

Order 2944.

1728 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₂₃	C₂	1	2	yes	maximal, complemented
2	#13092968	C₂	1	1	yes	maximal, characteristic, complemented
3	#13092967	C₂	1	1	yes	maximal, characteristic, complemented
4	#13092966	C₂	1	2	yes	maximal, complemented
5	#13092965	C₂	1	1	yes	maximal, characteristic, complemented
6	#13092964	C₂	1	4	yes	maximal, complemented
7	#13092963	C₂	1	2	yes	maximal, complemented
8	#13092962	C₂	1	4	yes	maximal, complemented
9	C₄⋊Q₈×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#127×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#124×D₂₃	C₂	1	2	yes	maximal, complemented
12	#121×D₂₃	C₂	1	4	yes	maximal, complemented
13	C₄×D₄×D₂₃	C₂	1	4	yes	maximal, complemented
14	C₂×C₄²×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×C₂₃	C₂²	1	2	yes	complemented
17	#41×D₂₃	—	2	16	no	—
18	C₂×#67292	C₂²	1	2	yes	complemented
19	C₂×Q₈×D₂₃	C₂²	1	2	yes	—
20	C₂×#67290	C₂²	1	4	yes	complemented
21	C₂×#67290	C₂²	1	2	yes	complemented
22	C₂×D₄×D₂₃	C₂²	1	4	yes	—
23	C₂×D₄×D₂₃	C₂²	1	4	yes	—
24	C₂×D₄×D₂₃	C₂²	1	2	yes	—
25	C₂×#67288	C₂²	1	2	yes	complemented
26	C₂×#67288	C₂²	1	4	yes	complemented
27	C₂²×C₄×D₂₃	C₂²	1	4	yes	—
28	C₂²×C₄×D₂₃	C₂²	1	2	yes	—
29	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
30	C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₂₃×#127	C₂²	1	1	yes	characteristic, complemented
32	C₂₃×#124	C₂²	1	2	yes	complemented
33	C₂₃×#121	C₂²	1	4	yes	complemented
34	C₄×D₄×C₂₃	C₂²	1	4	yes	complemented
35	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic, complemented
36	#10625118	C₂²	1	2	yes	complemented
37	#10625115	C₂²	1	2	yes	complemented
38	#10625111	C₂²	1	4	yes	complemented
39	#10625111	C₂²	1	2	yes	complemented
40	#10625110	C₂²	1	8	yes	complemented
41	#10625109	C₂²	1	4	yes	complemented
42	#10625107	C₂²	1	2	yes	complemented
43	D₄×Dic₂₃	C₂²	1	4	yes	complemented
44	#10625101	C₂²	1	4	yes	complemented
45	C₄×C₂²⋊D₂₃	C₂²	1	8	yes	complemented
46	C₂×C₄×Dic₂₃	C₂²	1	2	yes	complemented
47	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
48	#10625066	C₂²	1	4	yes	complemented
49	#10625064	C₂²	1	4	yes	complemented
50	C₄⋊C₄×D₂₃	C₂²	1	4	yes	—
51	#10625059	C₂²	1	4	yes	complemented
52	#10625056	C₂²	1	8	yes	complemented
53	#10625055	C₂²	1	8	yes	complemented
54	(C₂²⋊D₂₃)⋊C₄	C₂²	1	8	yes	complemented
55	C₂²⋊C₄×D₂₃	C₂²	1	8	yes	—
56	#10625046	C₂²	1	2	yes	complemented
57	#10625045	C₂²	1	1	yes	characteristic, complemented
58	C₄×D₉₂	C₂²	1	4	yes	complemented
59	C₄²×D₂₃	C₂²	1	2	yes	—
60	C₄²×D₂₃	C₂²	1	1	yes	characteristic
61	C₄²×D₂₃	C₂²	1	1	yes	characteristic
62	C₄²×D₂₃	C₂²	1	2	yes	complemented
63	C₄²×D₂₃	C₂²	1	1	yes	characteristic, complemented
64	C₄²×D₂₃	C₂²	1	1	yes	characteristic, complemented
65	#10625040	C₂²	1	1	yes	characteristic, complemented
66	C₂³×D₂₃	C₂³	1	4	yes	—
67	C₂³×D₂₃	C₂³	1	1	yes	characteristic
68	#41×C₂₃	—	2	8	no	—
69	C₂×Q₈×C₂₃	C₂³	1	2	yes	—
70	C₂×D₄×C₂₃	C₂³	1	4	yes	—
71	C₂×D₄×C₂₃	C₂³	1	2	yes	—
72	C₂×D₄×C₂₃	C₂³	1	4	yes	—
73	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
74	C₂²×C₄×C₂₃	C₂³	1	4	yes	—
75	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
76	C₂×C₂²⋊D₂₃	C₂³	1	8	yes	—
77	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
78	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
79	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
80	C₂²×Dic₂₃	C₂³	1	4	yes	—
81	C₂²×Dic₂₃	C₂³	1	2	yes	—
82	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
83	#67292	—	2	8	no	—
84	Q₈×D₂₃	—	2	8	no	—
85	#67290	—	2	16	no	—
86	#67290	—	2	8	no	—
87	D₄×D₂₃	—	2	16	no	—
88	D₄×D₂₃	—	2	8	no	—
89	D₄×D₂₃	—	2	16	no	—
90	#67288	—	2	8	no	—
91	#67288	—	2	16	no	—
92	C₂×D₉₂	C₂³	1	4	yes	—
93	C₂×D₉₂	C₂³	1	2	yes	—
94	C₂×D₉₂	C₂³	1	4	yes	—
95	C₂×C₄×D₂₃	—	2	16	no	—
96	C₂×C₄×D₂₃	—	2	8	no	—
97	C₂×C₄×D₂₃	D₄	1	8	yes	complemented
98	C₂×C₄×D₂₃	C₂³	1	2	yes	—
99	C₂×C₄×D₂₃	C₂³	1	2	yes	—
100	C₂×C₄×D₂₃	C₂³	1	2	yes	—
101	C₂×C₄×D₂₃	C₂³	1	4	yes	—
102	C₂×C₄×D₂₃	C₂³	1	4	yes	—
103	C₂×C₄×D₂₃	C₂³	1	4	yes	—
104	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
105	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
106	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
107	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
108	C₂×C₄×D₂₃	C₂³	1	2	yes	—
109	C₂×Dic₄₆	C₂³	1	2	yes	—
110	C₂×Dic₄₆	C₂³	1	4	yes	—
111	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
112	C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
113	C₄²×C₂₃	C₂³	1	1	yes	characteristic
114	C₄²×C₂₃	C₂³	1	2	yes	—
115	C₄²×C₂₃	C₂³	1	1	yes	characteristic
116	C₂²⋊Dic₂₃	C₂³	1	8	yes	—
117	(C₂×D₂₃)⋊C₄	C₂³	1	8	yes	—
118	(C₂×D₂₃)⋊C₄	C₂³	1	8	yes	—
119	C₄⋊Dic₂₃	C₂³	1	4	yes	—
120	Dic₂₃⋊C₄	C₂³	1	8	yes	—
121	C₄×Dic₂₃	C₂³	1	2	yes	—
122	C₄×Dic₂₃	C₂³	1	2	yes	—
123	C₄×Dic₂₃	C₂³	1	2	yes	—
124	C₄×Dic₂₃	C₂³	1	2	yes	—
125	C₄×Dic₂₃	C₂³	1	2	yes	—
126	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
127	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
128	C₂³×C₂₃	C₂⁴	1	4	yes	—
129	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
130	C₂²×D₂₃	—	2	4	no	—
131	C₂²×D₂₃	—	2	8	no	—
132	C₂²×D₂₃	—	2	16	no	—
133	C₂²×D₂₃	C₂×D₄	1	4	yes	—
134	C₂²×D₂₃	C₂⁴	1	4	yes	—
135	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
136	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
137	Q₈×C₂₃	—	2	4	no	—
138	D₄×C₂₃	—	2	8	no	—
139	D₄×C₂₃	—	2	4	no	—
140	D₄×C₂₃	—	2	8	no	—
141	C₂×C₄×C₂₃	—	2	8	no	—
142	C₂×C₄×C₂₃	—	2	4	no	—
143	C₂×C₄×C₂₃	C₂×D₄	1	4	yes	complemented
144	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
145	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
146	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
147	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
148	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
149	C₂²⋊D₂₃	—	2	8	no	—
150	C₂²⋊D₂₃	—	2	8	no	—
151	C₂²⋊D₂₃	—	2	8	no	—
152	C₂²⋊D₂₃	—	2	16	no	—
153	C₂×Dic₂₃	—	2	8	no	—
154	C₂×Dic₂₃	—	2	4	no	—
155	C₂×Dic₂₃	C₂×D₄	1	4	yes	complemented
156	C₂×Dic₂₃	C₂⁴	1	2	yes	—
157	C₂×Dic₂₃	C₂⁴	1	4	yes	—
158	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
159	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
160	C₂×Dic₂₃	C₂⁴	1	2	yes	—
161	D₉₂	—	2	8	no	—
162	D₉₂	—	2	4	no	—
163	D₉₂	—	2	8	no	—
164	C₄×D₂₃	—	2	8	no	—
165	C₄×D₂₃	—	2	4	no	—
166	C₄×D₂₃	—	2	8	no	—
167	C₄×D₂₃	—	2	4	no	—
168	C₄×D₂₃	—	2	8	no	—
169	C₄×D₂₃	—	2	4	no	—
170	C₄×D₂₃	C₂×D₄	1	4	yes	—
171	C₄×D₂₃	C₂×D₄	1	4	yes	—
172	C₄×D₂₃	C₂×D₄	1	4	yes	complemented
173	C₄×D₂₃	C₂×D₄	1	4	yes	complemented
174	C₄×D₂₃	#41	1	8	yes	complemented
175	Dic₄₆	—	2	4	no	—
176	Dic₄₆	—	2	8	no	—
177	C₂×#532	—	23	1	no	maximal, Sylow
178	C₂²×C₂₃	—	2	2	no	—
179	C₂²×C₂₃	—	2	4	no	—
180	C₂²×C₂₃	—	2	8	no	—
181	C₂²×C₂₃	C₂²×D₄	1	2	yes	—
182	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
183	C₂×D₂₃	—	2	2	no	—
184	C₂×D₂₃	—	2	8	no	—
185	C₂×D₂₃	—	2	4	no	—
186	C₂×D₂₃	—	2	8	no	—
187	C₂×D₂₃	—	4	16	no	—
188	C₂×D₂₃	C₂²×D₄	1	2	yes	—
189	C₂×D₂₃	C₂²×D₄	1	2	yes	—
190	C₂×D₂₃	C₂×#41	1	4	yes	—
191	C₄×C₂₃	—	2	4	no	—
192	C₄×C₂₃	—	2	2	no	—
193	C₄×C₂₃	C₂²×D₄	1	2	yes	—
194	C₄×C₂₃	C₂²×D₄	1	2	yes	—
195	C₄×C₂₃	C₂×#41	1	4	yes	complemented
196	Dic₂₃	—	2	4	no	—
197	Dic₂₃	—	2	2	no	—
198	Dic₂₃	C₂²×D₄	1	2	yes	—
199	Dic₂₃	C₂²×D₄	1	2	yes	—
200	Dic₂₃	C₂×#41	1	4	yes	complemented
201	C₂²×#41	—	23	2	no	—
202	#532	—	23	2	no	—
203	#532	—	23	1	no	—
204	#532	—	23	1	no	—
205	#532	—	23	2	no	—
206	#532	—	23	4	no	—
207	#532	—	23	4	no	—
208	#532	—	23	1	no	—
209	#532	D₂₃	1	1	yes	characteristic, direct product factor
210	C₂×C₄⋊Q₈	—	23	1	no	—
211	C₂×#127	—	23	1	no	—
212	C₂×#124	—	23	2	no	—
213	C₂×#121	—	23	4	no	—
214	C₂×C₄×D₄	—	23	4	no	—
215	C₂²×C₄²	—	23	1	no	—
216	C₂×C₂₃	—	2	2	no	—
217	C₂×C₂₃	—	4	4	no	—
218	C₂×C₂₃	C₂³×D₄	1	1	yes	characteristic
219	C₂×C₂₃	C₂²×#41	1	2	yes	—
220	D₂₃	—	2	2	no	—
221	D₂₃	—	4	4	no	—
222	D₂₃	#532	1	4	yes	direct product factor
223	C₂×#41	—	23	2	no	—
224	C₂×#41	—	23	4	no	—
225	C₂×#41	—	23	2	no	—
226	C₂×#41	—	23	4	no	—
227	C₂×#41	—	23	2	no	—
228	C₂×#41	—	46	16	no	—
229	C₂×#41	C₂×D₂₃	1	2	yes	complemented
230	C₂²×Q₈	—	23	2	no	—
231	C₂²×D₄	—	23	4	no	—
232	C₂²×D₄	—	23	4	no	—
233	C₂²×D₄	—	23	2	no	—
234	C₂³×C₄	—	23	1	no	—
235	C₂³×C₄	—	23	4	no	—
236	C₂³×C₄	—	23	2	no	—
237	C₄⋊Q₈	—	23	2	no	—
238	C₄⋊Q₈	—	23	4	no	—
239	C₄⋊Q₈	—	23	1	no	—
240	C₄⋊Q₈	C₂×D₂₃	1	1	yes	characteristic, complemented
241	#127	—	23	2	no	—
242	#127	—	23	4	no	—
243	#127	—	23	1	no	—
244	#127	C₂×D₂₃	1	1	yes	characteristic, complemented
245	#124	—	23	2	no	—
246	#124	—	23	2	no	—
247	#124	—	23	8	no	—
248	#124	—	23	2	no	—
249	#124	C₂×D₂₃	1	2	yes	complemented
250	#121	—	23	4	no	—
251	#121	—	23	8	no	—
252	#121	—	23	4	no	—
253	#121	—	23	4	no	—
254	#121	—	23	8	no	—
255	#121	C₂×D₂₃	1	4	yes	complemented
256	C₄×D₄	—	23	4	no	—
257	C₄×D₄	—	23	8	no	—
258	C₄×D₄	—	23	4	no	—
259	C₄×D₄	—	23	8	no	—
260	C₄×D₄	—	23	4	no	—
261	C₄×D₄	C₂×D₂₃	1	4	yes	complemented
262	C₂×C₄⋊C₄	—	23	4	no	—
263	C₂×C₂²⋊C₄	—	23	8	no	—
264	C₂×C₄²	—	23	2	no	—
265	C₂×C₄²	—	23	1	no	—
266	C₂×C₄²	—	23	2	no	—
267	C₂×C₄²	—	23	1	no	—
268	C₂×C₄²	—	23	1	no	—
269	C₂×C₄²	—	23	1	no	—
270	C₂×C₄²	—	23	1	no	—
271	C₂×C₄²	—	23	2	no	—
272	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic, complemented
273	C₂₃	C₂×#532	1	1	yes	characteristic, complemented, Sylow
274	C₂⁴	—	23	1	no	—
275	C₂⁴	—	23	4	no	—
276	#41	—	2	8	no	—
277	#41	—	46	16	no	—
278	#41	—	46	16	no	—
279	#41	—	46	8	no	—
280	#41	—	46	8	no	—
281	#41	—	46	8	no	—
282	C₂×Q₈	—	23	4	no	—
283	C₂×Q₈	—	23	2	no	—
284	C₂×Q₈	—	46	8	no	—
285	C₂×Q₈	C₂²×D₂₃	1	2	yes	—
286	C₂×D₄	—	23	8	no	—
287	C₂×D₄	—	23	4	no	—
288	C₂×D₄	—	23	4	no	—
289	C₂×D₄	—	23	4	no	—
290	C₂×D₄	—	23	4	no	—
291	C₂×D₄	—	23	4	no	—
292	C₂×D₄	—	23	2	no	—
293	C₂×D₄	—	46	8	no	—
294	C₂×D₄	—	46	16	no	—
295	C₂×D₄	—	46	16	no	—
296	C₂×D₄	C₂²×D₂₃	1	4	yes	—
297	C₂×D₄	C₂²×D₂₃	1	4	yes	—
298	C₂×D₄	C₂²×D₂₃	1	2	yes	—
299	C₂²×C₄	—	23	1	no	—
300	C₂²×C₄	—	23	8	no	—
301	C₂²×C₄	—	23	2	no	—
302	C₂²×C₄	—	23	1	no	—
303	C₂²×C₄	—	23	1	no	—
304	C₂²×C₄	—	23	1	no	—
305	C₂²×C₄	—	23	1	no	—
306	C₂²×C₄	—	23	2	no	—
307	C₂²×C₄	—	23	4	no	—
308	C₂²×C₄	—	23	2	no	—
309	C₂²×C₄	—	23	2	no	—
310	C₂²×C₄	—	23	2	no	—
311	C₂²×C₄	—	23	4	no	—
312	C₂²×C₄	—	23	4	no	—
313	C₂²×C₄	—	23	4	no	—
314	C₂²×C₄	—	46	16	no	—
315	C₂²×C₄	—	46	8	no	—
316	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
317	C₂²×C₄	C₂²×D₂₃	1	4	yes	—
318	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
319	C₄⋊C₄	—	23	8	no	—
320	C₄⋊C₄	—	23	4	no	—
321	C₄⋊C₄	C₂²×D₂₃	1	4	yes	—
322	C₂²⋊C₄	—	23	8	no	—
323	C₂²⋊C₄	—	23	8	no	—
324	C₂²⋊C₄	—	23	8	no	—
325	C₂²⋊C₄	C₂²×D₂₃	1	8	yes	—
326	C₄²	—	23	2	no	—
327	C₄²	—	23	2	no	—
328	C₄²	—	23	2	no	—
329	C₄²	—	23	1	no	—
330	C₄²	—	23	1	no	—
331	C₄²	—	23	2	no	—
332	C₄²	—	23	2	no	—
333	C₄²	C₂²×D₂₃	1	1	yes	characteristic
334	C₄²	C₂²×D₂₃	1	1	yes	characteristic
335	C₄²	C₂²×D₂₃	1	2	yes	—
336	C₂³	—	23	1	no	—
337	C₂³	—	23	4	no	—
338	C₂³	—	23	1	no	—
339	C₂³	—	23	4	no	—
340	C₂³	—	46	4	no	—
341	C₂³	—	46	8	no	—
342	C₂³	—	46	16	no	—
343	C₂³	C₂³×D₂₃	1	4	yes	—
344	C₂³	C₂³×D₂₃	1	1	yes	characteristic
345	Q₈	—	2	4	no	—
346	Q₈	—	46	8	no	—
347	Q₈	—	46	4	no	—
348	D₄	—	2	8	no	—
349	D₄	—	2	4	no	—
350	D₄	—	2	8	no	—
351	D₄	—	46	8	no	—
352	D₄	—	46	8	no	—
353	D₄	—	46	16	no	—
354	D₄	—	46	8	no	—
355	D₄	—	46	8	no	—
356	D₄	—	46	4	no	—
357	D₄	—	46	8	no	—
358	C₂×C₄	—	2	8	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	23	4	no	—
361	C₂×C₄	—	23	2	no	—
362	C₂×C₄	—	23	1	no	—
363	C₂×C₄	—	23	1	no	—
364	C₂×C₄	—	23	4	no	—
365	C₂×C₄	—	23	4	no	—
366	C₂×C₄	—	23	4	no	—
367	C₂×C₄	—	23	4	no	—
368	C₂×C₄	—	23	8	no	—
369	C₂×C₄	—	23	2	no	—
370	C₂×C₄	—	23	4	no	—
371	C₂×C₄	—	46	8	no	—
372	C₂×C₄	—	46	4	no	—
373	C₂×C₄	—	46	8	no	—
374	C₂×C₄	—	46	4	no	—
375	C₂×C₄	—	46	8	no	—
376	C₂×C₄	—	46	4	no	—
377	C₂×C₄	—	46	8	no	—
378	C₂×C₄	—	46	4	no	—
379	C₂×C₄	D₄×D₂₃	1	4	yes	complemented
380	C₂×C₄	C₂³×D₂₃	1	2	yes	—
381	C₂×C₄	C₂³×D₂₃	1	4	yes	—
382	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
383	C₂×C₄	C₂³×D₂₃	1	2	yes	—
384	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
385	C₂²	—	2	2	no	—
386	C₂²	—	2	4	no	—
387	C₂²	—	2	8	no	—
388	C₂²	—	23	2	no	—
389	C₂²	—	23	4	no	—
390	C₂²	—	23	2	no	—
391	C₂²	—	46	8	no	—
392	C₂²	—	46	2	no	—
393	C₂²	—	46	4	no	—
394	C₂²	—	46	8	no	—
395	C₂²	—	92	16	no	—
396	C₂²	C₂×D₄×D₂₃	1	2	yes	—
397	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
398	C₄	—	2	4	no	—
399	C₄	—	2	2	no	—
400	C₄	—	23	2	no	—
401	C₄	—	23	2	no	—
402	C₄	—	23	4	no	—
403	C₄	—	46	4	no	—
404	C₄	—	46	2	no	—
405	C₄	C₂×D₄×D₂₃	1	2	yes	—
406	C₄	C₂×D₄×D₂₃	1	2	yes	—
407	C₄	#41×D₂₃	1	4	yes	complemented
408	C₂	—	2	2	no	—
409	C₂	—	4	4	no	—
410	C₂	—	23	4	no	—
411	C₂	—	46	2	no	—
412	C₂	—	92	4	no	—
413	C₂	C₂²×D₄×D₂₃	1	1	yes	characteristic
414	C₂	C₂×#41×D₂₃	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂³×D₂₃
commutator, socle, cosocle	C₂²×C₂₃	C₂⁵
Frattini	C₂²	C₂⁴×D₂₃
Fitting	C₂₃×#532	C₂
hypercenter	#532	D₂₃
hypocenter	C₂₃	C₂×#532
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ #532

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₂₃	C₂	semidirect
2. #13092968	C₂	semidirect
3. #13092967	C₂	semidirect
4. #13092966	C₂	semidirect
5. #13092965	C₂	semidirect
6. #13092964	C₂	semidirect
7. #13092963	C₂	semidirect
8. #13092962	C₂	semidirect
9. C₄⋊Q₈×D₂₃	C₂	semidirect
10. #127×D₂₃	C₂	semidirect
11. #124×D₂₃	C₂	semidirect
12. #121×D₂₃	C₂	semidirect
13. C₄×D₄×D₂₃	C₂	semidirect
14. C₂×C₄²×D₂₃	C₂	semidirect
15. C₂₃×#532	C₂	semidirect
16. C₂×#41×C₂₃	C₂²	semidirect
18. C₂×#67292	C₂²	semidirect
20. C₂×#67290	C₂²	semidirect
21. C₂×#67290	C₂²	semidirect
25. C₂×#67288	C₂²	semidirect
26. C₂×#67288	C₂²	semidirect
30. C₂₃×C₄⋊Q₈	C₂²	semidirect
31. C₂₃×#127	C₂²	semidirect
32. C₂₃×#124	C₂²	semidirect
33. C₂₃×#121	C₂²	semidirect
34. C₄×D₄×C₂₃	C₂²	semidirect
35. C₂×C₄²×C₂₃	C₂²	semidirect
36. #10625118	C₂²	semidirect
37. #10625115	C₂²	semidirect
38. #10625111	C₂²	semidirect
39. #10625111	C₂²	semidirect
40. #10625110	C₂²	semidirect
41. #10625109	C₂²	semidirect
42. #10625107	C₂²	semidirect
43. D₄×Dic₂₃	C₂²	semidirect
44. #10625101	C₂²	semidirect
45. C₄×C₂²⋊D₂₃	C₂²	semidirect
46. C₂×C₄×Dic₂₃	C₂²	semidirect
47. C₂×C₄×Dic₂₃	C₂²	semidirect
48. #10625066	C₂²	semidirect
49. #10625064	C₂²	semidirect
51. #10625059	C₂²	semidirect
52. #10625056	C₂²	semidirect
53. #10625055	C₂²	semidirect
54. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
56. #10625046	C₂²	semidirect
57. #10625045	C₂²	semidirect
58. C₄×D₉₂	C₂²	semidirect
62. C₄²×D₂₃	C₂²	semidirect
63. C₄²×D₂₃	C₂²	semidirect
64. C₄²×D₂₃	C₂²	semidirect
65. #10625040	C₂²	semidirect
97. C₂×C₄×D₂₃	D₄	semidirect
143. C₂×C₄×C₂₃	C₂×D₄	semidirect
155. C₂×Dic₂₃	C₂×D₄	semidirect
172. C₄×D₂₃	C₂×D₄	semidirect
173. C₄×D₂₃	C₂×D₄	semidirect
174. C₄×D₂₃	#41	semidirect
195. C₄×C₂₃	C₂×#41	semidirect
200. Dic₂₃	C₂×#41	semidirect
209. #532	D₂₃	direct (N × H)
222. D₂₃	#532	direct (N × H)
229. C₂×#41	C₂×D₂₃	semidirect
240. C₄⋊Q₈	C₂×D₂₃	semidirect
244. #127	C₂×D₂₃	semidirect
249. #124	C₂×D₂₃	semidirect
255. #121	C₂×D₂₃	semidirect
261. C₄×D₄	C₂×D₂₃	semidirect
272. C₂×C₄²	C₂×D₂₃	semidirect
273. C₂₃	C₂×#532	semidirect
379. C₂×C₄	D₄×D₂₃	semidirect
407. C₄	#41×D₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×D₂₃	2
#13092968	2
#13092967	2
#13092966	2
#13092965	2
#13092964	2
#13092963	2
#13092962	2
C₄⋊Q₈×D₂₃	2
#127×D₂₃	2
#124×D₂₃	2
#121×D₂₃	2
C₄×D₄×D₂₃	2
C₂×C₄²×D₂₃	2
C₂₃×#532	2
C₂×#532	23

Subgroups — D23×#532 #15686674

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₃×#532 #15686674