Subgroups — D₂₃×#547 #15686850

Order 2944.

1632 conjugacy classes of subgroups.

The subgroup lattice has 510 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	#13093072	C₂	1	1	yes	maximal, characteristic, complemented
3	#13093071	C₂	1	1	yes	maximal, characteristic, complemented
4	#13093070	C₂	1	1	yes	maximal, characteristic, complemented
5	#13093069	C₂	1	2	yes	maximal, complemented
6	#13093068	C₂	1	2	yes	maximal, complemented
7	#13093067	C₂	1	2	yes	maximal, complemented
8	#13093066	C₂	1	2	yes	maximal, complemented
9	#13093065	C₂	1	4	yes	maximal, complemented
10	C₄⋊Q₈×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#123×D₂₃	C₂	1	4	yes	maximal, complemented
12	C₂²⋊Q₈×D₂₃	C₂	1	2	yes	maximal, complemented
13	#121×D₂₃	C₂	1	2	yes	maximal, complemented
14	C₄×D₄×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×D₄×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄⋊C₄×D₂₃	C₂	1	2	yes	maximal, complemented
17	C₂₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#41×C₂₃	C₂²	1	2	yes	complemented
19	#41×D₂₃	—	2	16	no	—
20	C₂×#67292	C₂²	1	2	yes	complemented
21	C₂×Q₈×D₂₃	C₂²	1	2	yes	—
22	C₂×#67290	C₂²	1	4	yes	complemented
23	C₂×#67290	C₂²	1	2	yes	complemented
24	C₂×D₄×D₂₃	C₂²	1	1	yes	characteristic
25	C₂×D₄×D₂₃	C₂²	1	4	yes	—
26	C₂×D₄×D₂₃	C₂²	1	1	yes	characteristic
27	C₂×#67288	C₂²	1	4	yes	complemented
28	C₂×#67288	C₂²	1	2	yes	complemented
29	C₂²×C₄×D₂₃	C₂²	1	2	yes	—
30	C₂²×C₄×D₂₃	C₂²	1	4	yes	—
31	C₂²×C₄×D₂₃	C₂²	1	2	yes	—
32	C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₂₃×#123	C₂²	1	4	yes	complemented
34	C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
35	C₂₃×#121	C₂²	1	2	yes	complemented
36	C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
37	C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
39	#10625117	C₂²	1	2	yes	complemented
40	#10625115	C₂²	1	2	yes	complemented
41	#10625110	C₂²	1	4	yes	complemented
42	#10625109	C₂²	1	2	yes	complemented
43	#10625106	C₂²	1	4	yes	complemented
44	D₄×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
45	D₄×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
46	#10625101	C₂²	1	2	yes	complemented
47	#10625100	C₂²	1	4	yes	complemented
48	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
49	C₄×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
50	C₂×C₄⋊Dic₂₃	C₂²	1	2	yes	complemented
51	#10625095	C₂²	1	2	yes	complemented
52	C₂×Dic₂₃⋊C₄	C₂²	1	4	yes	complemented
53	#10625068	C₂²	1	2	yes	complemented
54	#10625067	C₂²	1	4	yes	complemented
55	#10625066	C₂²	1	2	yes	complemented
56	#10625065	C₂²	1	4	yes	complemented
57	#10625065	C₂²	1	4	yes	complemented
58	#10625064	C₂²	1	1	yes	characteristic, complemented
59	#10625064	C₂²	1	1	yes	characteristic, complemented
60	C₄⋊C₄×D₂₃	C₂²	1	1	yes	characteristic
61	C₄⋊C₄×D₂₃	C₂²	1	2	yes	—
62	C₄⋊C₄×D₂₃	C₂²	1	4	yes	—
63	C₄⋊C₄×D₂₃	C₂²	1	1	yes	characteristic
64	C₄⋊C₄×D₂₃	C₂²	1	2	yes	—
65	C₄⋊C₄×D₂₃	C₂²	1	4	yes	complemented
66	C₄⋊C₄×D₂₃	C₂²	1	2	yes	complemented
67	C₄⋊C₄×D₂₃	C₂²	1	2	yes	complemented
68	#10625059	C₂²	1	2	yes	complemented
69	#10625059	C₂²	1	2	yes	complemented
70	#10625057	C₂²	1	4	yes	complemented
71	#10625055	C₂²	1	4	yes	complemented
72	#10625054	C₂²	1	4	yes	complemented
73	#10625054	C₂²	1	4	yes	complemented
74	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	complemented
75	(C₂²⋊D₂₃)⋊C₄	C₂²	1	2	yes	complemented
76	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	—
77	C₂²⋊C₄×D₂₃	C₂²	1	2	yes	—
78	C₂²⋊C₄×D₂₃	C₂²	1	4	yes	—
79	#10625049	C₂²	1	4	yes	complemented
80	C₄×D₉₂	C₂²	1	1	yes	characteristic, complemented
81	C₄×D₉₂	C₂²	1	1	yes	characteristic, complemented
82	C₄²×D₂₃	C₂²	1	1	yes	characteristic
83	#10625040	C₂²	1	1	yes	characteristic, complemented
84	C₂³×D₂₃	C₂³	1	2	yes	—
85	C₂³×D₂₃	C₂³	1	2	yes	—
86	#41×C₂₃	—	2	8	no	—
87	C₂×Q₈×C₂₃	C₂³	1	2	yes	—
88	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
89	C₂×D₄×C₂₃	C₂³	1	4	yes	—
90	C₂×D₄×C₂₃	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₂₃	C₂³	1	4	yes	—
92	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
93	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
94	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
95	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
96	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
97	C₂×C₂²⋊D₂₃	C₂³	1	2	yes	—
98	C₂²×Dic₂₃	C₂³	1	2	yes	—
99	C₂²×Dic₂₃	C₂³	1	2	yes	—
100	C₂²×Dic₂₃	C₂³	1	4	yes	—
101	#67292	—	2	8	no	—
102	Q₈×D₂₃	—	2	8	no	—
103	#67290	—	2	8	no	—
104	#67290	—	2	16	no	—
105	D₄×D₂₃	—	2	16	no	—
106	D₄×D₂₃	—	2	4	no	—
107	D₄×D₂₃	D₄	1	8	yes	complemented
108	#67288	—	2	16	no	—
109	#67288	—	2	8	no	—
110	C₂×D₉₂	C₂³	1	1	yes	characteristic
111	C₂×D₉₂	C₂³	1	4	yes	—
112	C₂×D₉₂	C₂³	1	1	yes	characteristic
113	C₂×C₄×D₂₃	—	2	16	no	—
114	C₂×C₄×D₂₃	—	2	8	no	—
115	C₂×C₄×D₂₃	—	2	8	no	—
116	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
117	C₂×C₄×D₂₃	C₂³	1	2	yes	—
118	C₂×C₄×D₂₃	C₂³	1	2	yes	—
119	C₂×C₄×D₂₃	C₂³	1	2	yes	—
120	C₂×C₄×D₂₃	C₂³	1	2	yes	—
121	C₂×C₄×D₂₃	C₂³	1	4	yes	—
122	C₂×C₄×D₂₃	C₂³	1	2	yes	—
123	C₂×C₄×D₂₃	C₂³	1	2	yes	—
124	C₂×C₄×D₂₃	C₂³	1	4	yes	—
125	C₂×C₄×D₂₃	C₂³	1	4	yes	—
126	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
127	C₂×C₄×D₂₃	C₂³	1	1	yes	characteristic
128	C₂×Dic₄₆	C₂³	1	2	yes	—
129	C₂×Dic₄₆	C₂³	1	4	yes	—
130	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
131	C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
132	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
133	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
134	C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
135	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
136	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
137	C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
138	C₄²×C₂₃	C₂³	1	1	yes	characteristic
139	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
140	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
141	C₂²⋊Dic₂₃	C₂³	1	2	yes	—
142	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
143	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
144	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
145	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
146	(C₂×D₂₃)⋊C₄	C₂³	1	2	yes	—
147	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
148	C₄⋊Dic₂₃	C₂³	1	2	yes	—
149	C₄⋊Dic₂₃	C₂³	1	2	yes	—
150	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
151	C₄⋊Dic₂₃	C₂³	1	1	yes	characteristic
152	C₄⋊Dic₂₃	C₂³	1	4	yes	—
153	Dic₂₃⋊C₄	C₂³	1	2	yes	—
154	Dic₂₃⋊C₄	C₂³	1	4	yes	—
155	Dic₂₃⋊C₄	C₂³	1	2	yes	—
156	Dic₂₃⋊C₄	C₂³	1	4	yes	—
157	Dic₂₃⋊C₄	C₂³	1	4	yes	—
158	Dic₂₃⋊C₄	C₂³	1	4	yes	—
159	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
160	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
161	C₄×Dic₂₃	C₂³	1	1	yes	characteristic
162	C₂³×C₂₃	C₂⁴	1	2	yes	—
163	C₂³×C₂₃	C₂⁴	1	2	yes	—
164	C₂²×D₂₃	—	2	4	no	—
165	C₂²×D₂₃	—	2	4	no	—
166	C₂²×D₂₃	—	2	4	no	—
167	C₂²×D₂₃	—	2	4	no	—
168	C₂²×D₂₃	—	2	4	no	—
169	C₂²×D₂₃	C₂×D₄	1	8	yes	—
170	C₂²×D₂₃	C₂⁴	1	2	yes	—
171	C₂²×D₂₃	C₂⁴	1	2	yes	—
172	C₂²×D₂₃	C₂⁴	1	1	yes	characteristic
173	Q₈×C₂₃	—	2	4	no	—
174	D₄×C₂₃	—	2	8	no	—
175	D₄×C₂₃	—	2	2	no	—
176	D₄×C₂₃	C₂×D₄	1	4	yes	complemented
177	C₂×C₄×C₂₃	—	2	8	no	—
178	C₂×C₄×C₂₃	—	2	4	no	—
179	C₂×C₄×C₂₃	—	2	4	no	—
180	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
181	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
182	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
183	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
184	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
185	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
186	C₂²⋊D₂₃	—	2	8	no	—
187	C₂²⋊D₂₃	—	2	8	no	—
188	C₂²⋊D₂₃	—	2	4	no	—
189	C₂²⋊D₂₃	C₂×D₄	1	8	yes	complemented
190	C₂×Dic₂₃	—	2	8	no	—
191	C₂×Dic₂₃	—	2	4	no	—
192	C₂×Dic₂₃	—	2	4	no	—
193	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
194	C₂×Dic₂₃	C₂⁴	1	2	yes	—
195	C₂×Dic₂₃	C₂⁴	1	4	yes	—
196	C₂×Dic₂₃	C₂⁴	1	2	yes	—
197	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
198	C₂×Dic₂₃	C₂⁴	1	1	yes	characteristic
199	D₉₂	—	2	8	no	—
200	D₉₂	—	2	2	no	—
201	D₉₂	C₂×D₄	1	4	yes	complemented
202	C₄×D₂₃	—	2	4	no	—
203	C₄×D₂₃	—	2	8	no	—
204	C₄×D₂₃	—	2	8	no	—
205	C₄×D₂₃	—	2	8	no	—
206	C₄×D₂₃	—	2	4	no	—
207	C₄×D₂₃	—	2	2	no	—
208	C₄×D₂₃	—	2	4	no	—
209	C₄×D₂₃	—	2	4	no	—
210	C₄×D₂₃	—	2	4	no	—
211	C₄×D₂₃	—	2	4	no	—
212	C₄×D₂₃	C₂×D₄	1	4	yes	—
213	C₄×D₂₃	#41	1	4	yes	complemented
214	Dic₄₆	—	2	4	no	—
215	Dic₄₆	—	2	8	no	—
216	C₂×#547	—	23	1	no	maximal, Sylow
217	C₂²×C₂₃	—	2	2	no	—
218	C₂²×C₂₃	—	2	2	no	—
219	C₂²×C₂₃	—	2	2	no	—
220	C₂²×C₂₃	—	2	2	no	—
221	C₂²×C₂₃	—	2	2	no	—
222	C₂²×C₂₃	C₂²×D₄	1	4	yes	—
223	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
224	C₂×D₂₃	—	2	2	no	—
225	C₂×D₂₃	—	2	2	no	—
226	C₂×D₂₃	—	2	16	no	—
227	C₂×D₂₃	—	2	2	no	—
228	C₂×D₂₃	—	2	2	no	—
229	C₂×D₂₃	—	2	2	no	—
230	C₂×D₂₃	—	4	8	no	—
231	C₂×D₂₃	C₂²×D₄	1	4	yes	—
232	C₂×D₂₃	C₂²×D₄	1	2	yes	—
233	C₂×D₂₃	C₂×#41	1	2	yes	—
234	C₂×D₂₃	2₋¹⁺⁴	1	2	yes	—
235	C₄×C₂₃	—	2	4	no	—
236	C₄×C₂₃	—	2	2	no	—
237	C₄×C₂₃	—	2	2	no	—
238	C₄×C₂₃	—	2	1	no	—
239	C₄×C₂₃	C₂²×D₄	1	2	yes	—
240	C₄×C₂₃	C₂×#41	1	2	yes	complemented
241	Dic₂₃	—	2	4	no	—
242	Dic₂₃	—	2	2	no	—
243	Dic₂₃	—	2	2	no	—
244	Dic₂₃	—	2	1	no	—
245	Dic₂₃	C₂²×D₄	1	2	yes	—
246	Dic₂₃	C₂×#41	1	2	yes	complemented
247	C₂²×#41	—	23	2	no	—
248	#547	—	23	2	no	—
249	#547	—	23	1	no	—
250	#547	—	23	4	no	—
251	#547	—	23	2	no	—
252	#547	—	23	2	no	—
253	#547	—	23	1	no	—
254	#547	—	23	1	no	—
255	#547	—	23	2	no	—
256	#547	D₂₃	1	1	yes	characteristic, direct product factor
257	C₂×C₄⋊Q₈	—	23	1	no	—
258	C₂×#123	—	23	4	no	—
259	C₂×C₂²⋊Q₈	—	23	2	no	—
260	C₂×#121	—	23	2	no	—
261	C₂×C₄×D₄	—	23	1	no	—
262	C₂×C₄×D₄	—	23	1	no	—
263	C₂²×C₄⋊C₄	—	23	2	no	—
264	C₂×C₂₃	—	2	4	no	—
265	C₂×C₂₃	—	4	2	no	—
266	C₂×C₂₃	C₂³×D₄	1	1	yes	characteristic
267	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
268	C₂×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
269	D₂₃	—	2	4	no	—
270	D₂₃	—	4	2	no	—
271	D₂₃	#547	1	4	yes	direct product factor
272	C₂×#41	—	23	2	no	—
273	C₂×#41	—	23	2	no	—
274	C₂×#41	—	23	4	no	—
275	C₂×#41	—	23	2	no	—
276	C₂×#41	—	23	4	no	—
277	C₂×#41	—	46	16	no	—
278	C₂×#41	C₂×D₂₃	1	2	yes	complemented
279	C₂²×Q₈	—	23	2	no	—
280	C₂²×D₄	—	23	1	no	—
281	C₂²×D₄	—	23	1	no	—
282	C₂²×D₄	—	23	4	no	—
283	C₂³×C₄	—	23	2	no	—
284	C₂³×C₄	—	23	4	no	—
285	C₂³×C₄	—	23	2	no	—
286	C₄⋊Q₈	—	23	2	no	—
287	C₄⋊Q₈	—	23	2	no	—
288	C₄⋊Q₈	—	23	2	no	—
289	C₄⋊Q₈	—	23	1	no	—
290	C₄⋊Q₈	C₂×D₂₃	1	1	yes	characteristic, complemented
291	#123	—	23	4	no	—
292	#123	—	23	4	no	—
293	#123	—	23	4	no	—
294	#123	—	23	4	no	—
295	#123	—	23	4	no	—
296	#123	—	23	4	no	—
297	#123	—	23	4	no	—
298	#123	C₂×D₂₃	1	4	yes	complemented
299	C₂²⋊Q₈	—	23	2	no	—
300	C₂²⋊Q₈	—	23	2	no	—
301	C₂²⋊Q₈	—	23	4	no	—
302	C₂²⋊Q₈	—	23	2	no	—
303	C₂²⋊Q₈	—	23	4	no	—
304	C₂²⋊Q₈	C₂×D₂₃	1	2	yes	complemented
305	#121	—	23	2	no	—
306	#121	—	23	4	no	—
307	#121	—	23	2	no	—
308	#121	—	23	2	no	—
309	#121	—	23	4	no	—
310	#121	C₂×D₂₃	1	2	yes	complemented
311	C₄×D₄	—	23	1	no	—
312	C₄×D₄	—	23	1	no	—
313	C₄×D₄	—	23	2	no	—
314	C₄×D₄	—	23	2	no	—
315	C₄×D₄	—	23	1	no	—
316	C₄×D₄	—	23	1	no	—
317	C₄×D₄	—	23	2	no	—
318	C₄×D₄	—	23	2	no	—
319	C₄×D₄	—	23	1	no	—
320	C₄×D₄	—	23	1	no	—
321	C₄×D₄	C₂×D₂₃	1	1	yes	characteristic, complemented
322	C₄×D₄	C₂×D₂₃	1	1	yes	characteristic, complemented
323	C₂×C₄⋊C₄	—	23	4	no	—
324	C₂×C₄⋊C₄	—	23	2	no	—
325	C₂×C₄⋊C₄	—	23	1	no	—
326	C₂×C₄⋊C₄	—	23	2	no	—
327	C₂×C₄⋊C₄	—	23	4	no	—
328	C₂×C₄⋊C₄	—	23	4	no	—
329	C₂×C₄⋊C₄	—	23	2	no	—
330	C₂×C₄⋊C₄	—	23	2	no	—
331	C₂×C₄⋊C₄	—	23	1	no	—
332	C₂×C₄⋊C₄	—	23	2	no	—
333	C₂×C₄⋊C₄	C₂×D₂₃	1	2	yes	complemented
334	C₂×C₂²⋊C₄	—	23	2	no	—
335	C₂×C₂²⋊C₄	—	23	2	no	—
336	C₂×C₂²⋊C₄	—	23	4	no	—
337	C₂×C₄²	—	23	1	no	—
338	C₂₃	C₂×#547	1	1	yes	characteristic, complemented, Sylow
339	C₂⁴	—	23	2	no	—
340	C₂⁴	—	23	2	no	—
341	#41	—	2	8	no	—
342	#41	—	46	16	no	—
343	#41	—	46	8	no	—
344	#41	—	46	16	no	—
345	#41	—	46	8	no	—
346	#41	—	46	8	no	—
347	C₂×Q₈	—	23	4	no	—
348	C₂×Q₈	—	23	2	no	—
349	C₂×Q₈	—	46	8	no	—
350	C₂×Q₈	C₂²×D₂₃	1	2	yes	—
351	C₂×D₄	—	23	2	no	—
352	C₂×D₄	—	23	8	no	—
353	C₂×D₄	—	23	2	no	—
354	C₂×D₄	—	23	4	no	—
355	C₂×D₄	—	23	4	no	—
356	C₂×D₄	—	23	1	no	—
357	C₂×D₄	—	23	1	no	—
358	C₂×D₄	—	23	4	no	—
359	C₂×D₄	—	46	4	no	—
360	C₂×D₄	—	46	16	no	—
361	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
362	C₂×D₄	C₂²×D₂₃	1	4	yes	—
363	C₂×D₄	C₂²×D₂₃	1	1	yes	characteristic
364	C₂²×C₄	—	23	1	no	—
365	C₂²×C₄	—	23	1	no	—
366	C₂²×C₄	—	23	2	no	—
367	C₂²×C₄	—	23	4	no	—
368	C₂²×C₄	—	23	2	no	—
369	C₂²×C₄	—	23	1	no	—
370	C₂²×C₄	—	23	2	no	—
371	C₂²×C₄	—	23	2	no	—
372	C₂²×C₄	—	23	4	no	—
373	C₂²×C₄	—	23	2	no	—
374	C₂²×C₄	—	23	2	no	—
375	C₂²×C₄	—	23	4	no	—
376	C₂²×C₄	—	23	4	no	—
377	C₂²×C₄	—	23	2	no	—
378	C₂²×C₄	—	23	2	no	—
379	C₂²×C₄	—	46	8	no	—
380	C₂²×C₄	—	46	8	no	—
381	C₂²×C₄	—	46	16	no	—
382	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
383	C₂²×C₄	C₂²×D₂₃	1	4	yes	—
384	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
385	C₄⋊C₄	—	23	2	no	—
386	C₄⋊C₄	—	23	1	no	—
387	C₄⋊C₄	—	23	4	no	—
388	C₄⋊C₄	—	23	2	no	—
389	C₄⋊C₄	—	23	4	no	—
390	C₄⋊C₄	—	23	4	no	—
391	C₄⋊C₄	—	23	4	no	—
392	C₄⋊C₄	—	23	2	no	—
393	C₄⋊C₄	—	23	1	no	—
394	C₄⋊C₄	—	23	4	no	—
395	C₄⋊C₄	—	23	2	no	—
396	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
397	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
398	C₄⋊C₄	C₂²×D₂₃	1	4	yes	—
399	C₄⋊C₄	C₂²×D₂₃	1	1	yes	characteristic
400	C₄⋊C₄	C₂²×D₂₃	1	2	yes	—
401	C₂²⋊C₄	—	23	2	no	—
402	C₂²⋊C₄	—	23	2	no	—
403	C₂²⋊C₄	—	23	4	no	—
404	C₂²⋊C₄	—	23	2	no	—
405	C₂²⋊C₄	—	23	2	no	—
406	C₂²⋊C₄	—	23	2	no	—
407	C₂²⋊C₄	—	23	2	no	—
408	C₂²⋊C₄	—	23	4	no	—
409	C₂²⋊C₄	—	23	4	no	—
410	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
411	C₂²⋊C₄	C₂²×D₂₃	1	2	yes	—
412	C₂²⋊C₄	C₂²×D₂₃	1	4	yes	—
413	C₄²	—	23	1	no	—
414	C₄²	—	23	1	no	—
415	C₄²	—	23	1	no	—
416	C₄²	C₂²×D₂₃	1	1	yes	characteristic
417	C₂³	—	23	1	no	—
418	C₂³	—	23	8	no	—
419	C₂³	—	23	2	no	—
420	C₂³	—	23	2	no	—
421	C₂³	—	46	4	no	—
422	C₂³	—	46	4	no	—
423	C₂³	—	46	4	no	—
424	C₂³	—	46	4	no	—
425	C₂³	—	46	4	no	—
426	C₂³	C₂³×D₂₃	1	2	yes	—
427	C₂³	C₂³×D₂₃	1	2	yes	—
428	Q₈	—	2	4	no	—
429	Q₈	—	46	8	no	—
430	Q₈	—	46	4	no	—
431	D₄	—	2	8	no	—
432	D₄	—	2	2	no	—
433	D₄	—	23	8	no	—
434	D₄	—	23	4	no	—
435	D₄	—	46	8	no	—
436	D₄	—	46	4	no	—
437	D₄	—	46	8	no	—
438	D₄	—	46	8	no	—
439	D₄	—	46	2	no	—
440	D₄	D₄×D₂₃	1	4	yes	complemented
441	C₂×C₄	—	2	8	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	23	1	no	—
445	C₂×C₄	—	23	1	no	—
446	C₂×C₄	—	23	4	no	—
447	C₂×C₄	—	23	4	no	—
448	C₂×C₄	—	23	1	no	—
449	C₂×C₄	—	23	2	no	—
450	C₂×C₄	—	23	2	no	—
451	C₂×C₄	—	23	4	no	—
452	C₂×C₄	—	46	4	no	—
453	C₂×C₄	—	46	4	no	—
454	C₂×C₄	—	46	4	no	—
455	C₂×C₄	—	46	8	no	—
456	C₂×C₄	—	46	8	no	—
457	C₂×C₄	—	46	8	no	—
458	C₂×C₄	—	46	4	no	—
459	C₂×C₄	—	46	2	no	—
460	C₂×C₄	—	46	4	no	—
461	C₂×C₄	—	46	4	no	—
462	C₂×C₄	—	46	8	no	—
463	C₂×C₄	—	46	4	no	—
464	C₂×C₄	—	46	4	no	—
465	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
466	C₂×C₄	C₂³×D₂₃	1	2	yes	—
467	C₂×C₄	C₂³×D₂₃	1	2	yes	—
468	C₂×C₄	C₂³×D₂₃	1	4	yes	—
469	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
470	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
471	C₂²	—	2	2	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	23	2	no	—
477	C₂²	—	23	2	no	—
478	C₂²	—	23	2	no	—
479	C₂²	—	23	4	no	—
480	C₂²	—	46	16	no	—
481	C₂²	—	46	2	no	—
482	C₂²	—	46	2	no	—
483	C₂²	—	46	2	no	—
484	C₂²	—	46	2	no	—
485	C₂²	—	46	2	no	—
486	C₂²	—	92	8	no	—
487	C₂²	C₂×D₄×D₂₃	1	4	yes	—
488	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
489	C₄	—	2	2	no	—
490	C₄	—	2	4	no	—
491	C₄	—	2	2	no	—
492	C₄	—	2	1	no	—
493	C₄	—	23	2	no	—
494	C₄	—	23	2	no	—
495	C₄	—	46	2	no	—
496	C₄	—	46	4	no	—
497	C₄	—	46	2	no	—
498	C₄	—	46	1	no	—
499	C₄	C₂×D₄×D₂₃	1	2	yes	—
500	C₄	#41×D₂₃	1	2	yes	complemented
501	C₂	—	2	4	no	—
502	C₂	—	4	2	no	—
503	C₂	—	23	4	no	—
504	C₂	—	46	4	no	—
505	C₂	—	92	2	no	—
506	C₂	C₂²×D₄×D₂₃	1	1	yes	characteristic
507	C₂	C₂×#41×D₂₃	1	1	yes	characteristic
508	C₂	2₋¹⁺⁴×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₃
commutator, socle, cosocle	C₂²×C₂₃	C₂⁵
Fitting	C₂₃×#547	C₂
hypercenter	#547	D₂₃
hypocenter	C₂₃	C₂×#547
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ #547

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₂₃	C₂	semidirect
2. #13093072	C₂	semidirect
3. #13093071	C₂	semidirect
4. #13093070	C₂	semidirect
5. #13093069	C₂	semidirect
6. #13093068	C₂	semidirect
7. #13093067	C₂	semidirect
8. #13093066	C₂	semidirect
9. #13093065	C₂	semidirect
10. C₄⋊Q₈×D₂₃	C₂	semidirect
11. #123×D₂₃	C₂	semidirect
12. C₂²⋊Q₈×D₂₃	C₂	semidirect
13. #121×D₂₃	C₂	semidirect
14. C₄×D₄×D₂₃	C₂	semidirect
15. C₄×D₄×D₂₃	C₂	semidirect
16. C₂×C₄⋊C₄×D₂₃	C₂	semidirect
17. C₂₃×#547	C₂	semidirect
18. C₂×#41×C₂₃	C₂²	semidirect
20. C₂×#67292	C₂²	semidirect
22. C₂×#67290	C₂²	semidirect
23. C₂×#67290	C₂²	semidirect
27. C₂×#67288	C₂²	semidirect
28. C₂×#67288	C₂²	semidirect
32. C₂₃×C₄⋊Q₈	C₂²	semidirect
33. C₂₃×#123	C₂²	semidirect
34. C₂₃×C₂²⋊Q₈	C₂²	semidirect
35. C₂₃×#121	C₂²	semidirect
36. C₄×D₄×C₂₃	C₂²	semidirect
37. C₄×D₄×C₂₃	C₂²	semidirect
38. C₂×C₄⋊C₄×C₂₃	C₂²	semidirect
39. #10625117	C₂²	semidirect
40. #10625115	C₂²	semidirect
41. #10625110	C₂²	semidirect
42. #10625109	C₂²	semidirect
43. #10625106	C₂²	semidirect
44. D₄×Dic₂₃	C₂²	semidirect
45. D₄×Dic₂₃	C₂²	semidirect
46. #10625101	C₂²	semidirect
47. #10625100	C₂²	semidirect
48. C₄×C₂²⋊D₂₃	C₂²	semidirect
49. C₄×C₂²⋊D₂₃	C₂²	semidirect
50. C₂×C₄⋊Dic₂₃	C₂²	semidirect
51. #10625095	C₂²	semidirect
52. C₂×Dic₂₃⋊C₄	C₂²	semidirect
53. #10625068	C₂²	semidirect
54. #10625067	C₂²	semidirect
55. #10625066	C₂²	semidirect
56. #10625065	C₂²	semidirect
57. #10625065	C₂²	semidirect
58. #10625064	C₂²	semidirect
59. #10625064	C₂²	semidirect
65. C₄⋊C₄×D₂₃	C₂²	semidirect
66. C₄⋊C₄×D₂₃	C₂²	semidirect
67. C₄⋊C₄×D₂₃	C₂²	semidirect
68. #10625059	C₂²	semidirect
69. #10625059	C₂²	semidirect
70. #10625057	C₂²	semidirect
71. #10625055	C₂²	semidirect
72. #10625054	C₂²	semidirect
73. #10625054	C₂²	semidirect
74. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
75. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
79. #10625049	C₂²	semidirect
80. C₄×D₉₂	C₂²	semidirect
81. C₄×D₉₂	C₂²	semidirect
83. #10625040	C₂²	semidirect
107. D₄×D₂₃	D₄	semidirect
176. D₄×C₂₃	C₂×D₄	semidirect
189. C₂²⋊D₂₃	C₂×D₄	semidirect
201. D₉₂	C₂×D₄	semidirect
213. C₄×D₂₃	#41	semidirect
240. C₄×C₂₃	C₂×#41	semidirect
246. Dic₂₃	C₂×#41	semidirect
256. #547	D₂₃	direct (N × H)
271. D₂₃	#547	direct (N × H)
278. C₂×#41	C₂×D₂₃	semidirect
290. C₄⋊Q₈	C₂×D₂₃	semidirect
298. #123	C₂×D₂₃	semidirect
304. C₂²⋊Q₈	C₂×D₂₃	semidirect
310. #121	C₂×D₂₃	semidirect
321. C₄×D₄	C₂×D₂₃	semidirect
322. C₄×D₄	C₂×D₂₃	semidirect
333. C₂×C₄⋊C₄	C₂×D₂₃	semidirect
338. C₂₃	C₂×#547	semidirect
440. D₄	D₄×D₂₃	semidirect
500. 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
#13093072	2
#13093071	2
#13093070	2
#13093069	2
#13093068	2
#13093067	2
#13093066	2
#13093065	2
C₄⋊Q₈×D₂₃	2
#123×D₂₃	2
C₂²⋊Q₈×D₂₃	2
#121×D₂₃	2
C₄×D₄×D₂₃	2
C₂×C₄⋊C₄×D₂₃	2
C₂₃×#547	2
C₂×#547	23

Subgroups — D23×#547 #15686850

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₃×#547 #15686850