Subgroups — C₂₃×#21063 #19168689

Order 5888.

1238 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#428	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#418	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₂₃×#102	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#2309	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#2274	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1926	C₂	1	4	yes	maximal, complemented
7	C₂₃×#1925	C₂	1	4	yes	maximal, complemented
8	C₂₃×#1735	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1729	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
13	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
14	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
15	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
17	C₂₃×#428	—	2	4	no	—
18	C₂×C₂₃×#107	C₂²	1	2	yes	complemented
19	C₂×C₂₃×#106	C₂²	1	2	yes	complemented
20	C₂₃×#418	C₄	1	8	yes	complemented
21	C₂×C₂₃×#102	—	2	4	no	—
22	C₂×C₂₃×#102	C₂²	1	4	yes	—
23	C₂×C₂₃×#102	C₂²	1	4	yes	—
24	C₂₃×#390	—	2	2	no	—
25	C₂₃×#390	C₂²	1	2	yes	—
26	C₂₃×#390	C₂²	1	2	yes	—
27	C₂₃×#379	—	2	2	no	—
28	C₄×C₄⋊C₄×C₂₃	—	2	2	no	—
29	C₄×C₄⋊C₄×C₂₃	C₂²	1	4	yes	complemented
30	C₄×C₂²⋊C₄×C₂₃	—	2	2	no	—
31	C₂₃×#340	C₂²	1	2	yes	complemented
32	C₂₃×#340	C₂²	1	2	yes	complemented
33	C₂₃×#336	C₂²	1	4	yes	complemented
34	C₂⁵×C₂₃	—	2	1	no	—
35	C₂²×D₄×C₂₃	—	2	2	no	—
36	C₂²×D₄×C₂₃	—	2	1	no	—
37	C₂²×D₄×C₂₃	—	2	2	no	—
38	C₂²×D₄×C₂₃	—	2	2	no	—
39	C₂²×D₄×C₂₃	—	2	2	no	—
40	C₂²×D₄×C₂₃	—	2	2	no	—
41	C₂²×D₄×C₂₃	C₂×C₄	1	4	yes	—
42	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
43	C₂³×C₄×C₂₃	—	2	1	no	—
44	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
45	C₂×M₁₆×C₂₃	—	2	2	no	—
46	C₂×M₁₆×C₂₃	—	2	2	no	—
47	C₂×M₁₆×C₂₃	C₂×C₄	1	4	yes	—
48	C₂²×C₈×C₂₃	—	2	2	no	—
49	C₂²×C₈×C₂₃	—	2	2	no	—
50	C₂²×C₈×C₂₃	—	2	2	no	—
51	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
52	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
53	C₂₃×#117	—	2	2	no	—
54	C₂₃×#117	—	2	2	no	—
55	C₂₃×#117	—	2	2	no	—
56	C₂₃×#117	—	2	2	no	—
57	C₂₃×#117	—	2	2	no	—
58	C₂₃×#117	C₂×C₄	1	4	yes	—
59	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
60	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
61	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
62	C₂×C₄⋊C₄×C₂₃	D₄	1	4	yes	—
63	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
67	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
70	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
71	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
72	C₂×C₄²×C₂₃	—	2	1	no	—
73	C₂×C₄²×C₂₃	—	2	1	no	—
74	C₂×C₄²×C₂₃	—	2	4	no	—
75	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
76	C₂₃×#107	—	2	4	no	—
77	C₂₃×#106	—	2	4	no	—
78	C₂₃×#102	—	2	8	no	—
79	C₂₃×#102	C₂×C₄	1	16	yes	complemented
80	C₂₃×#95	—	2	4	no	—
81	C₂⁴×C₂₃	—	2	2	no	—
82	C₂⁴×C₂₃	—	2	4	no	—
83	C₂⁴×C₂₃	—	4	2	no	—
84	C₂⁴×C₂₃	—	4	2	no	—
85	C₂⁴×C₂₃	—	8	2	no	—
86	C₂⁴×C₂₃	—	8	2	no	—
87	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
88	C₂×D₄×C₂₃	—	2	8	no	—
89	C₂×D₄×C₂₃	—	2	8	no	—
90	C₂×D₄×C₂₃	—	2	4	no	—
91	C₂×D₄×C₂₃	—	2	2	no	—
92	C₂×D₄×C₂₃	—	2	2	no	—
93	C₂×D₄×C₂₃	—	2	2	no	—
94	C₂×D₄×C₂₃	—	2	2	no	—
95	C₂×D₄×C₂₃	—	2	2	no	—
96	C₂×D₄×C₂₃	—	4	2	no	—
97	C₂×D₄×C₂₃	—	4	2	no	—
98	C₂×D₄×C₂₃	—	4	4	no	—
99	C₂×D₄×C₂₃	—	4	4	no	—
100	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
101	C₂²×C₄×C₂₃	—	2	2	no	—
102	C₂²×C₄×C₂₃	—	2	2	no	—
103	C₂²×C₄×C₂₃	—	2	4	no	—
104	C₂²×C₄×C₂₃	—	2	1	no	—
105	C₂²×C₄×C₂₃	—	2	1	no	—
106	C₂²×C₄×C₂₃	—	8	2	no	—
107	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
109	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₂₃	#41	1	2	yes	—
112	C₂²×C₄×C₂₃	#41	1	2	yes	—
113	C₂²×C₄×C₂₃	#41	1	2	yes	—
114	C₂²×C₄×C₂₃	#41	1	2	yes	—
115	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
116	M₁₆×C₂₃	—	2	8	no	—
117	C₂×C₈×C₂₃	—	2	2	no	—
118	C₂×C₈×C₂₃	—	2	2	no	—
119	C₂×C₈×C₂₃	—	2	2	no	—
120	C₂×C₈×C₂₃	—	2	2	no	—
121	C₂×C₈×C₂₃	—	2	2	no	—
122	C₂×C₈×C₂₃	—	4	4	no	—
123	C₂×C₈×C₂₃	C₂²×C₄	1	4	yes	—
124	C₄⋊C₄×C₂₃	—	2	4	no	—
125	C₄⋊C₄×C₂₃	—	2	4	no	—
126	C₄⋊C₄×C₂₃	—	2	2	no	—
127	C₄⋊C₄×C₂₃	—	2	2	no	—
128	C₄⋊C₄×C₂₃	—	2	1	no	—
129	C₄⋊C₄×C₂₃	—	2	1	no	—
130	C₄⋊C₄×C₂₃	—	2	1	no	—
131	C₄⋊C₄×C₂₃	—	2	1	no	—
132	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
133	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
134	C₂²⋊C₄×C₂₃	—	2	4	no	—
135	C₂²⋊C₄×C₂₃	—	2	4	no	—
136	C₂²⋊C₄×C₂₃	—	4	2	no	—
137	C₂²⋊C₄×C₂₃	—	8	4	no	—
138	C₂²⋊C₄×C₂₃	—	8	4	no	—
139	C₄²×C₂₃	—	2	4	no	—
140	C₄²×C₂₃	—	2	2	no	—
141	C₄²×C₂₃	—	2	2	no	—
142	C₄²×C₂₃	—	4	2	no	—
143	C₄²×C₂₃	—	8	4	no	—
144	#21063	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂³×C₂₃	—	2	2	no	—
146	C₂³×C₂₃	—	2	2	no	—
147	C₂³×C₂₃	—	2	4	no	—
148	C₂³×C₂₃	—	4	2	no	—
149	C₂³×C₂₃	—	4	2	no	—
150	C₂³×C₂₃	—	4	4	no	—
151	C₂³×C₂₃	—	4	4	no	—
152	C₂³×C₂₃	—	4	8	no	—
153	C₂³×C₂₃	—	8	8	no	—
154	C₂³×C₂₃	—	8	8	no	—
155	C₂³×C₂₃	—	8	4	no	—
156	C₂³×C₂₃	—	8	4	no	—
157	C₂³×C₂₃	C₄×D₄	1	2	yes	—
158	C₂³×C₂₃	#121	1	2	yes	—
159	C₂³×C₂₃	#123	1	2	yes	—
160	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
161	D₄×C₂₃	—	2	4	no	—
162	D₄×C₂₃	—	2	4	no	—
163	D₄×C₂₃	—	4	2	no	—
164	D₄×C₂₃	—	4	2	no	—
165	D₄×C₂₃	—	4	8	no	—
166	C₂×C₄×C₂₃	—	2	4	no	—
167	C₂×C₄×C₂₃	—	2	4	no	—
168	C₂×C₄×C₂₃	—	2	4	no	—
169	C₂×C₄×C₂₃	—	2	4	no	—
170	C₂×C₄×C₂₃	—	2	4	no	—
171	C₂×C₄×C₂₃	—	4	2	no	—
172	C₂×C₄×C₂₃	—	4	4	no	—
173	C₂×C₄×C₂₃	—	4	2	no	—
174	C₂×C₄×C₂₃	—	4	1	no	—
175	C₂×C₄×C₂₃	—	4	1	no	—
176	C₂×C₄×C₂₃	—	4	2	no	—
177	C₂×C₄×C₂₃	—	4	2	no	—
178	C₂×C₄×C₂₃	—	8	4	no	—
179	C₂×C₄×C₂₃	#117	1	4	yes	—
180	C₂×C₄×C₂₃	C₄×D₄	1	4	yes	—
181	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
182	C₂×C₄×C₂₃	#121	1	2	yes	—
183	C₂×C₄×C₂₃	#123	1	2	yes	—
184	C₂×C₄×C₂₃	#124	1	4	yes	—
185	C₂×C₄×C₂₃	#126	1	4	yes	—
186	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
191	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
192	C₈×C₂₃	—	2	4	no	—
193	C₈×C₂₃	—	4	2	no	—
194	C₂×#428	C₂×C₂₃	1	1	yes	characteristic, complemented
195	C₂×#418	C₂×C₂₃	1	1	yes	characteristic
196	C₂²×#102	C₂×C₂₃	1	1	yes	characteristic
197	#2309	C₂×C₂₃	1	1	yes	characteristic
198	#2274	C₂×C₂₃	1	1	yes	characteristic, complemented
199	#1926	C₂×C₂₃	1	4	yes	complemented
200	#1925	C₂×C₂₃	1	4	yes	complemented
201	#1735	C₂×C₂₃	1	1	yes	characteristic, complemented
202	#1729	C₂×C₂₃	1	1	yes	characteristic, complemented
203	C₂²×C₂₃	—	2	4	no	—
204	C₂²×C₂₃	—	2	4	no	—
205	C₂²×C₂₃	—	2	2	no	—
206	C₂²×C₂₃	—	2	2	no	—
207	C₂²×C₂₃	—	4	8	no	—
208	C₂²×C₂₃	—	4	4	no	—
209	C₂²×C₂₃	—	8	16	no	—
210	C₂²×C₂₃	—	8	4	no	—
211	C₂²×C₂₃	—	8	2	no	—
212	C₂²×C₂₃	—	8	2	no	—
213	C₂²×C₂₃	#388	1	4	yes	—
214	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
215	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
216	C₂²×C₂₃	C₂×#123	1	1	yes	characteristic
217	C₂²×C₂₃	#576	1	2	yes	—
218	C₂²×C₂₃	#577	1	2	yes	—
219	C₄×C₂₃	—	4	4	no	—
220	C₄×C₂₃	—	4	4	no	—
221	C₄×C₂₃	—	4	4	no	—
222	C₄×C₂₃	—	8	1	no	—
223	C₄×C₂₃	—	8	1	no	—
224	C₄×C₂₃	#388	1	4	yes	—
225	C₄×C₂₃	C₂×#117	1	1	yes	characteristic
226	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
227	C₄×C₂₃	C₂×#124	1	1	yes	characteristic
228	C₄×C₂₃	C₂×#126	1	1	yes	characteristic
229	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
230	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
231	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
232	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
233	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
234	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
235	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
236	#428	—	2	4	no	—
237	C₂×#107	C₂²×C₂₃	1	2	yes	complemented
238	C₂×#106	C₂²×C₂₃	1	2	yes	complemented
239	#418	C₄×C₂₃	1	8	yes	complemented
240	C₂×#102	—	2	4	no	—
241	C₂×#102	C₂²×C₂₃	1	4	yes	—
242	C₂×#102	C₂²×C₂₃	1	4	yes	—
243	#390	—	2	2	no	—
244	#390	C₂²×C₂₃	1	2	yes	—
245	#390	C₂²×C₂₃	1	2	yes	—
246	#379	—	2	2	no	—
247	C₄×C₄⋊C₄	—	2	2	no	—
248	C₄×C₄⋊C₄	C₂²×C₂₃	1	4	yes	complemented
249	C₄×C₂²⋊C₄	—	2	2	no	—
250	#340	C₂²×C₂₃	1	2	yes	complemented
251	#340	C₂²×C₂₃	1	2	yes	complemented
252	#336	C₂²×C₂₃	1	4	yes	complemented
253	C₂×C₂₃	—	2	4	no	—
254	C₂×C₂₃	—	8	4	no	—
255	C₂×C₂₃	C₂×#388	1	1	yes	characteristic
256	C₂×C₂₃	#2946	1	2	yes	—
257	C₂×C₂₃	#3041	1	1	yes	characteristic
258	C₂×C₂₃	#3043	1	1	yes	characteristic
259	C₂×C₂₃	#3096	1	2	yes	—
260	C₂⁵	—	2	1	no	—
261	C₂²×D₄	—	2	2	no	—
262	C₂²×D₄	—	2	1	no	—
263	C₂²×D₄	—	2	2	no	—
264	C₂²×D₄	—	2	2	no	—
265	C₂²×D₄	—	2	2	no	—
266	C₂²×D₄	—	2	2	no	—
267	C₂²×D₄	C₂×C₄×C₂₃	1	4	yes	—
268	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
269	C₂³×C₄	—	2	1	no	—
270	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
271	C₂×M₁₆	—	2	2	no	—
272	C₂×M₁₆	—	2	2	no	—
273	C₂×M₁₆	C₂×C₄×C₂₃	1	4	yes	—
274	C₂²×C₈	—	2	2	no	—
275	C₂²×C₈	—	2	2	no	—
276	C₂²×C₈	—	2	2	no	—
277	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
278	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
279	#117	—	2	2	no	—
280	#117	—	2	2	no	—
281	#117	—	2	2	no	—
282	#117	—	2	2	no	—
283	#117	—	2	2	no	—
284	#117	C₂×C₄×C₂₃	1	4	yes	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
288	C₂×C₄⋊C₄	D₄×C₂₃	1	4	yes	—
289	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₂²⋊C₄	—	2	4	no	—
296	C₂×C₂²⋊C₄	—	2	4	no	—
297	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	—	2	4	no	—
301	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
302	#107	—	2	4	no	—
303	#106	—	2	4	no	—
304	#102	—	2	8	no	—
305	#102	C₂×C₄×C₂₃	1	16	yes	complemented
306	#95	—	2	4	no	—
307	C₂₃	#21063	1	1	yes	characteristic, direct product factor, Sylow
308	C₂⁴	—	2	2	no	—
309	C₂⁴	—	2	4	no	—
310	C₂⁴	—	4	2	no	—
311	C₂⁴	—	4	2	no	—
312	C₂⁴	—	8	2	no	—
313	C₂⁴	—	8	2	no	—
314	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
315	C₂×D₄	—	2	8	no	—
316	C₂×D₄	—	2	8	no	—
317	C₂×D₄	—	2	4	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	4	2	no	—
324	C₂×D₄	—	4	2	no	—
325	C₂×D₄	—	4	4	no	—
326	C₂×D₄	—	4	4	no	—
327	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	8	2	no	—
334	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
336	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
338	C₂²×C₄	#41×C₂₃	1	2	yes	—
339	C₂²×C₄	#41×C₂₃	1	2	yes	—
340	C₂²×C₄	#41×C₂₃	1	2	yes	—
341	C₂²×C₄	#41×C₂₃	1	2	yes	—
342	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
343	M₁₆	—	2	8	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	4	4	no	—
350	C₂×C₈	C₂²×C₄×C₂₃	1	4	yes	—
351	C₄⋊C₄	—	2	4	no	—
352	C₄⋊C₄	—	2	4	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
360	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
361	C₂²⋊C₄	—	2	4	no	—
362	C₂²⋊C₄	—	2	4	no	—
363	C₂²⋊C₄	—	4	2	no	—
364	C₂²⋊C₄	—	8	4	no	—
365	C₂²⋊C₄	—	8	4	no	—
366	C₄²	—	2	4	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	4	2	no	—
370	C₄²	—	8	4	no	—
371	C₂³	—	2	2	no	—
372	C₂³	—	2	2	no	—
373	C₂³	—	2	4	no	—
374	C₂³	—	4	4	no	—
375	C₂³	—	4	4	no	—
376	C₂³	—	4	8	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	8	8	no	—
380	C₂³	—	8	4	no	—
381	C₂³	—	8	4	no	—
382	C₂³	—	8	8	no	—
383	C₂³	C₄×D₄×C₂₃	1	2	yes	—
384	C₂³	C₂₃×#121	1	2	yes	—
385	C₂³	C₂₃×#123	1	2	yes	—
386	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
387	D₄	—	2	4	no	—
388	D₄	—	2	4	no	—
389	D₄	—	4	8	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	4	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	8	4	no	—
405	C₂×C₄	C₂₃×#117	1	4	yes	—
406	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
407	C₂×C₄	C₄×D₄×C₂₃	1	4	yes	—
408	C₂×C₄	C₂₃×#121	1	2	yes	—
409	C₂×C₄	C₂₃×#123	1	2	yes	—
410	C₂×C₄	C₂₃×#124	1	4	yes	—
411	C₂×C₄	C₂₃×#126	1	4	yes	—
412	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
413	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
414	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
415	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
416	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
417	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
418	C₈	—	2	4	no	—
419	C₈	—	4	2	no	—
420	C₂²	—	2	4	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	2	4	no	—
424	C₂²	—	4	8	no	—
425	C₂²	—	4	4	no	—
426	C₂²	—	8	16	no	—
427	C₂²	—	8	2	no	—
428	C₂²	—	8	2	no	—
429	C₂²	—	8	4	no	—
430	C₂²	C₂₃×#388	1	4	yes	—
431	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
432	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
433	C₂²	C₂×C₂₃×#123	1	1	yes	characteristic
434	C₂²	C₂₃×#576	1	2	yes	—
435	C₂²	C₂₃×#577	1	2	yes	—
436	C₄	—	4	4	no	—
437	C₄	—	4	4	no	—
438	C₄	—	4	4	no	—
439	C₄	—	8	1	no	—
440	C₄	—	8	1	no	—
441	C₄	C₂₃×#388	1	4	yes	—
442	C₄	C₂×C₂₃×#117	1	1	yes	characteristic
443	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
444	C₄	C₂×C₂₃×#124	1	1	yes	characteristic
445	C₄	C₂×C₂₃×#126	1	1	yes	characteristic
446	C₂	—	2	4	no	—
447	C₂	—	8	4	no	—
448	C₂	C₂×C₂₃×#388	1	1	yes	characteristic
449	C₂	C₂₃×#2946	1	2	yes	—
450	C₂	C₂₃×#3041	1	1	yes	characteristic
451	C₂	C₂₃×#3043	1	1	yes	characteristic
452	C₂	C₂₃×#3096	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂³×D₄×C₂₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₂₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#428	C₂	semidirect
5. C₂₃×#2274	C₂	semidirect
6. C₂₃×#1926	C₂	semidirect
7. C₂₃×#1925	C₂	semidirect
8. C₂₃×#1735	C₂	semidirect
9. C₂₃×#1729	C₂	semidirect
18. C₂×C₂₃×#107	C₂²	semidirect
19. C₂×C₂₃×#106	C₂²	semidirect
20. C₂₃×#418	C₄	semidirect
29. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
31. C₂₃×#340	C₂²	semidirect
32. C₂₃×#340	C₂²	semidirect
33. C₂₃×#336	C₂²	semidirect
79. C₂₃×#102	C₂×C₄	semidirect
144. #21063	C₂₃	direct (N × H)
194. C₂×#428	C₂×C₂₃	semidirect
198. #2274	C₂×C₂₃	semidirect
199. #1926	C₂×C₂₃	semidirect
200. #1925	C₂×C₂₃	semidirect
201. #1735	C₂×C₂₃	semidirect
202. #1729	C₂×C₂₃	semidirect
237. C₂×#107	C₂²×C₂₃	semidirect
238. C₂×#106	C₂²×C₂₃	semidirect
239. #418	C₄×C₂₃	semidirect
248. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
250. #340	C₂²×C₂₃	semidirect
251. #340	C₂²×C₂₃	semidirect
252. #336	C₂²×C₂₃	semidirect
305. #102	C₂×C₄×C₂₃	semidirect
307. C₂₃	#21063	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#428	2
C₂×C₂₃×#418	2
C₂²×C₂₃×#102	2
C₂₃×#2309	2
C₂₃×#2274	2
C₂₃×#1926	2
C₂₃×#1925	2
C₂₃×#1735	2
C₂₃×#1729	2
#21063	23

Subgroups — C23×#21063 #19168689

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#21063 #19168689