Subgroups — C₂₃×#22511 #19170137

Order 5888.

1036 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#446	C₂	1	2	yes	maximal, complemented
3	C₂₃×#1985	C₂	1	2	yes	maximal, complemented
4	C₂₃×#1985	C₂	1	2	yes	maximal, complemented
5	C₂₃×#1984	C₂	1	2	yes	maximal, complemented
6	C₂₃×#1798	C₂	1	2	yes	maximal
7	C₂₃×#1797	C₂	1	1	yes	maximal, characteristic
8	C₂₃×#1750	C₂	1	2	yes	maximal
9	C₂₃×#1749	C₂	1	1	yes	maximal, characteristic
10	C₂₃×#533	—	2	8	no	—
11	C₂×C₂₃×C₄⋊Q₈	C₄	1	1	yes	characteristic
12	C₂×C₂₃×C₄⋊Q₈	C₄	1	1	yes	characteristic
13	C₂×C₂₃×#125	C₄	1	2	yes	—
14	C₂×C₂₃×C₂²⋊Q₈	C₄	1	1	yes	characteristic
15	C₂×C₂₃×C₂²⋊Q₈	C₄	1	1	yes	characteristic
16	C₂×C₂₃×C₂²⋊Q₈	C₄	1	2	yes	—
17	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
18	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
20	C₂×C₂₃×#117	C₂²	1	2	yes	—
21	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
22	C₂₃×#446	—	2	8	no	—
23	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
24	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
25	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
26	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#97	C₂²	1	2	yes	—
30	C₂×C₂₃×#97	C₂²	1	2	yes	—
31	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
32	C₂₃×#336	C₂²	1	1	yes	characteristic
33	C₂₃×#336	C₂²	1	2	yes	—
34	C₂₃×#336	C₂²	1	2	yes	—
35	C₂₃×#336	C₂²	1	2	yes	—
36	C₂₃×#336	C₂²	1	2	yes	—
37	C₂₃×#336	C₂²	1	1	yes	characteristic
38	C₂₃×#336	C₂²	1	2	yes	—
39	C₂²×Q₈×C₂₃	C₂×C₄	1	2	yes	—
40	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
41	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
46	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
47	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
48	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
49	C₂₃×C₄⋊Q₈	—	2	4	no	—
50	C₂₃×C₄⋊Q₈	—	2	4	no	—
51	C₂₃×#125	—	2	8	no	—
52	C₂₃×C₂²⋊Q₈	—	2	4	no	—
53	C₂₃×C₂²⋊Q₈	—	2	4	no	—
54	C₂₃×C₂²⋊Q₈	—	2	8	no	—
55	C₄×Q₈×C₂₃	—	2	4	no	—
56	C₄×Q₈×C₂₃	—	2	4	no	—
57	C₄×Q₈×C₂₃	—	2	4	no	—
58	C₄×Q₈×C₂₃	D₄	1	8	yes	—
59	C₂₃×#117	—	2	4	no	—
60	C₂₃×#117	—	2	4	no	—
61	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
62	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
63	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
64	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
65	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
68	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
69	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
71	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
72	C₂×C₄²×C₂₃	—	2	4	no	—
73	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
77	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
78	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
79	C₂₃×C₄⋊C₈	—	2	4	no	—
80	C₂₃×C₄⋊C₈	—	2	4	no	—
81	C₂₃×C₄⋊C₈	—	2	4	no	—
82	C₂₃×C₂²⋊C₈	—	2	2	no	—
83	C₂₃×C₂²⋊C₈	—	2	4	no	—
84	C₂₃×C₂²⋊C₈	Q₈	1	4	yes	complemented
85	C₂₃×#97	—	2	4	no	—
86	C₂₃×#97	—	2	4	no	—
87	C₄×C₈×C₂₃	—	2	4	no	—
88	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
89	C₂×Q₈×C₂₃	—	2	4	no	—
90	C₂×Q₈×C₂₃	—	2	2	no	—
91	C₂×Q₈×C₂₃	—	2	4	no	—
92	C₂×Q₈×C₂₃	—	4	1	no	—
93	C₂×Q₈×C₂₃	—	4	1	no	—
94	C₂×Q₈×C₂₃	—	4	2	no	—
95	C₂×Q₈×C₂₃	—	4	1	no	—
96	C₂×Q₈×C₂₃	—	4	1	no	—
97	C₂×Q₈×C₂₃	C₂²⋊C₄	1	4	yes	—
98	C₂²×C₄×C₂₃	—	2	2	no	—
99	C₂²×C₄×C₂₃	—	2	2	no	—
100	C₂²×C₄×C₂₃	—	2	2	no	—
101	C₂²×C₄×C₂₃	—	2	2	no	—
102	C₂²×C₄×C₂₃	—	2	2	no	—
103	C₂²×C₄×C₂₃	—	4	1	no	—
104	C₂²×C₄×C₂₃	—	4	1	no	—
105	C₂²×C₄×C₂₃	—	4	1	no	—
106	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₂₃	C₂×Q₈	1	2	yes	—
116	C₂²×C₄×C₂₃	#41	1	2	yes	—
117	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
123	C₂×C₈×C₂₃	—	2	2	no	—
124	C₂×C₈×C₂₃	—	2	2	no	—
125	C₂×C₈×C₂₃	—	2	2	no	—
126	C₂×C₈×C₂₃	—	2	2	no	—
127	C₂×C₈×C₂₃	—	2	2	no	—
128	C₂×C₈×C₂₃	—	2	2	no	—
129	C₂×C₈×C₂₃	C₂×Q₈	1	4	yes	—
130	C₄⋊C₄×C₂₃	—	2	4	no	—
131	C₄⋊C₄×C₂₃	—	2	4	no	—
132	C₄⋊C₄×C₂₃	—	2	4	no	—
133	C₄⋊C₄×C₂₃	—	2	4	no	—
134	C₄⋊C₄×C₂₃	—	2	4	no	—
135	C₄⋊C₄×C₂₃	—	2	4	no	—
136	C₄⋊C₄×C₂₃	—	2	2	no	—
137	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	8	yes	—
138	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	4	yes	—
139	C₂²⋊C₄×C₂₃	—	2	4	no	—
140	C₂²⋊C₄×C₂₃	—	2	4	no	—
141	C₄²×C₂₃	—	2	2	no	—
142	C₄²×C₂₃	—	2	2	no	—
143	C₄²×C₂₃	—	2	2	no	—
144	C₄²×C₂₃	—	2	2	no	—
145	C₄²×C₂₃	—	2	2	no	—
146	C₄²×C₂₃	C₂×D₄	1	4	yes	—
147	C₄²×C₂₃	C₂×D₄	1	4	yes	—
148	C₄²×C₂₃	C₂×D₄	1	4	yes	—
149	#22511	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₂³×C₂₃	—	2	1	no	—
151	C₂³×C₂₃	—	2	1	no	—
152	C₂³×C₂₃	—	2	1	no	—
153	C₂³×C₂₃	—	2	1	no	—
154	C₂³×C₂₃	—	2	1	no	—
155	C₂³×C₂₃	—	2	1	no	—
156	C₂³×C₂₃	C₄×Q₈	1	2	yes	—
157	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
158	Q₈×C₂₃	—	4	4	no	—
159	Q₈×C₂₃	—	4	8	no	—
160	Q₈×C₂₃	—	4	4	no	—
161	C₂×C₄×C₂₃	—	2	1	no	—
162	C₂×C₄×C₂₃	—	2	1	no	—
163	C₂×C₄×C₂₃	—	2	1	no	—
164	C₂×C₄×C₂₃	—	2	1	no	—
165	C₂×C₄×C₂₃	—	2	2	no	—
166	C₂×C₄×C₂₃	—	2	1	no	—
167	C₂×C₄×C₂₃	—	2	1	no	—
168	C₂×C₄×C₂₃	—	2	1	no	—
169	C₂×C₄×C₂₃	—	2	1	no	—
170	C₂×C₄×C₂₃	—	2	2	no	—
171	C₂×C₄×C₂₃	—	2	2	no	—
172	C₂×C₄×C₂₃	—	2	2	no	—
173	C₂×C₄×C₂₃	—	2	4	no	—
174	C₂×C₄×C₂₃	—	2	4	no	—
175	C₂×C₄×C₂₃	—	2	1	no	—
176	C₂×C₄×C₂₃	—	2	2	no	—
177	C₂×C₄×C₂₃	—	2	2	no	—
178	C₂×C₄×C₂₃	—	2	2	no	—
179	C₂×C₄×C₂₃	—	2	1	no	—
180	C₂×C₄×C₂₃	—	2	1	no	—
181	C₂×C₄×C₂₃	—	2	2	no	—
182	C₂×C₄×C₂₃	—	2	2	no	—
183	C₂×C₄×C₂₃	—	2	2	no	—
184	C₂×C₄×C₂₃	—	4	4	no	—
185	C₂×C₄×C₂₃	—	4	4	no	—
186	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
187	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
188	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	4	yes	—
189	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	4	yes	—
190	C₂×C₄×C₂₃	C₄×Q₈	1	2	yes	—
191	C₂×C₄×C₂₃	#131	1	2	yes	—
192	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
193	C₂×C₄×C₂₃	C₂²×Q₈	1	1	yes	characteristic
194	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
196	C₈×C₂₃	—	2	4	no	—
197	C₈×C₂₃	—	4	2	no	—
198	C₈×C₂₃	—	4	2	no	—
199	C₈×C₂₃	—	4	2	no	—
200	C₂×#533	C₂×C₂₃	1	1	yes	characteristic
201	C₂×#446	C₂×C₂₃	1	2	yes	complemented
202	#1985	C₂×C₂₃	1	2	yes	complemented
203	#1985	C₂×C₂₃	1	2	yes	complemented
204	#1984	C₂×C₂₃	1	2	yes	complemented
205	#1798	C₂×C₂₃	1	2	yes	—
206	#1797	C₂×C₂₃	1	1	yes	characteristic
207	#1750	C₂×C₂₃	1	2	yes	—
208	#1749	C₂×C₂₃	1	1	yes	characteristic
209	C₂²×C₂₃	—	2	2	no	—
210	C₂²×C₂₃	—	2	2	no	—
211	C₂²×C₂₃	—	2	2	no	—
212	C₂²×C₂₃	—	4	1	no	—
213	C₂²×C₂₃	—	4	1	no	—
214	C₂²×C₂₃	—	4	1	no	—
215	C₂²×C₂₃	—	4	1	no	—
216	C₂²×C₂₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
217	C₂²×C₂₃	C₂×C₄×Q₈	1	1	yes	characteristic
218	C₂²×C₂₃	#519	1	1	yes	characteristic
219	C₂²×C₂₃	C₂×#131	1	1	yes	characteristic
220	C₂²×C₂₃	#568	1	1	yes	characteristic
221	C₂²×C₂₃	#568	1	1	yes	characteristic
222	C₂²×C₂₃	#568	1	1	yes	characteristic
223	C₄×C₂₃	—	2	2	no	—
224	C₄×C₂₃	—	2	2	no	—
225	C₄×C₂₃	—	2	4	no	—
226	C₄×C₂₃	—	2	2	no	—
227	C₄×C₂₃	—	2	2	no	—
228	C₄×C₂₃	—	2	4	no	—
229	C₄×C₂₃	—	4	1	no	—
230	C₄×C₂₃	—	4	2	no	—
231	C₄×C₂₃	—	4	2	no	—
232	C₄×C₂₃	#548	1	2	yes	—
233	C₄×C₂₃	D₄×Q₈	1	2	yes	—
234	#533	—	2	8	no	—
235	C₂×C₄⋊Q₈	C₄×C₂₃	1	1	yes	characteristic
236	C₂×C₄⋊Q₈	C₄×C₂₃	1	1	yes	characteristic
237	C₂×#125	C₄×C₂₃	1	2	yes	—
238	C₂×C₂²⋊Q₈	C₄×C₂₃	1	1	yes	characteristic
239	C₂×C₂²⋊Q₈	C₄×C₂₃	1	1	yes	characteristic
240	C₂×C₂²⋊Q₈	C₄×C₂₃	1	2	yes	—
241	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
242	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
243	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
244	C₂×#117	C₂²×C₂₃	1	2	yes	—
245	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
246	#446	—	2	8	no	—
247	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
248	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
249	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
250	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
251	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
252	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
253	C₂×#97	C₂²×C₂₃	1	2	yes	—
254	C₂×#97	C₂²×C₂₃	1	2	yes	—
255	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
256	#336	C₂²×C₂₃	1	1	yes	characteristic
257	#336	C₂²×C₂₃	1	1	yes	characteristic
258	#336	C₂²×C₂₃	1	2	yes	—
259	#336	C₂²×C₂₃	1	2	yes	—
260	#336	C₂²×C₂₃	1	2	yes	—
261	#336	C₂²×C₂₃	1	2	yes	—
262	#336	C₂²×C₂₃	1	2	yes	—
263	C₂×C₂₃	—	4	2	no	—
264	C₂×C₂₃	Q₈×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₂₃	#2879	1	1	yes	characteristic
266	C₂×C₂₃	#2880	1	1	yes	characteristic
267	C₂×C₂₃	#2961	1	1	yes	characteristic
268	C₂×C₂₃	#2962	1	1	yes	characteristic
269	C₂×C₂₃	#2985	1	1	yes	characteristic
270	C₂×C₂₃	#2987	1	1	yes	characteristic
271	C₂²×Q₈	C₂×C₄×C₂₃	1	2	yes	—
272	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
273	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
274	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
275	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
276	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
277	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
278	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
279	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
280	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
281	C₄⋊Q₈	—	2	4	no	—
282	C₄⋊Q₈	—	2	4	no	—
283	#125	—	2	8	no	—
284	C₂²⋊Q₈	—	2	4	no	—
285	C₂²⋊Q₈	—	2	4	no	—
286	C₂²⋊Q₈	—	2	8	no	—
287	C₄×Q₈	—	2	4	no	—
288	C₄×Q₈	—	2	4	no	—
289	C₄×Q₈	—	2	4	no	—
290	C₄×Q₈	D₄×C₂₃	1	8	yes	—
291	#117	—	2	4	no	—
292	#117	—	2	4	no	—
293	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
294	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
295	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
296	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
297	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
298	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
300	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
301	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
302	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
303	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
304	C₂×C₄²	—	2	4	no	—
305	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
306	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
307	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
308	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
309	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
310	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
311	C₄⋊C₈	—	2	4	no	—
312	C₄⋊C₈	—	2	4	no	—
313	C₄⋊C₈	—	2	4	no	—
314	C₂²⋊C₈	—	2	4	no	—
315	C₂²⋊C₈	—	2	2	no	—
316	C₂²⋊C₈	Q₈×C₂₃	1	4	yes	complemented
317	#97	—	2	4	no	—
318	#97	—	2	4	no	—
319	C₄×C₈	—	2	4	no	—
320	C₂₃	#22511	1	1	yes	characteristic, direct product factor, Sylow
321	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
322	C₂×Q₈	—	2	4	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	4	no	—
325	C₂×Q₈	—	4	1	no	—
326	C₂×Q₈	—	4	1	no	—
327	C₂×Q₈	—	4	2	no	—
328	C₂×Q₈	—	4	1	no	—
329	C₂×Q₈	—	4	1	no	—
330	C₂×Q₈	C₂²⋊C₄×C₂₃	1	4	yes	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	4	1	no	—
337	C₂²×C₄	—	4	1	no	—
338	C₂²×C₄	—	4	1	no	—
339	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
340	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
341	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
342	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
343	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
344	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
345	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
346	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
347	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
348	C₂²×C₄	C₂×Q₈×C₂₃	1	2	yes	—
349	C₂²×C₄	#41×C₂₃	1	2	yes	—
350	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	C₂×Q₈×C₂₃	1	4	yes	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	8	yes	—
371	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	4	yes	—
372	C₂²⋊C₄	—	2	4	no	—
373	C₂²⋊C₄	—	2	4	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	2	no	—
379	C₄²	C₂×D₄×C₂₃	1	4	yes	—
380	C₄²	C₂×D₄×C₂₃	1	4	yes	—
381	C₄²	C₂×D₄×C₂₃	1	4	yes	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	1	no	—
388	C₂³	C₄×Q₈×C₂₃	1	2	yes	—
389	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
390	Q₈	—	4	4	no	—
391	Q₈	—	4	8	no	—
392	Q₈	—	4	4	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
419	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
420	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	4	yes	—
421	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	4	yes	—
422	C₂×C₄	C₄×Q₈×C₂₃	1	2	yes	—
423	C₂×C₄	C₂₃×#131	1	2	yes	—
424	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
425	C₂×C₄	C₂²×Q₈×C₂₃	1	1	yes	characteristic
426	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
427	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
428	C₈	—	2	4	no	—
429	C₈	—	4	2	no	—
430	C₈	—	4	2	no	—
431	C₈	—	4	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	1	no	—
439	C₂²	C₂²×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
440	C₂²	C₂×C₄×Q₈×C₂₃	1	1	yes	characteristic
441	C₂²	C₂₃×#519	1	1	yes	characteristic
442	C₂²	C₂×C₂₃×#131	1	1	yes	characteristic
443	C₂²	C₂₃×#568	1	1	yes	characteristic
444	C₂²	C₂₃×#568	1	1	yes	characteristic
445	C₂²	C₂₃×#568	1	1	yes	characteristic
446	C₄	—	2	2	no	—
447	C₄	—	2	2	no	—
448	C₄	—	2	4	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	4	no	—
452	C₄	—	4	1	no	—
453	C₄	—	4	2	no	—
454	C₄	—	4	2	no	—
455	C₄	C₂₃×#548	1	2	yes	—
456	C₄	D₄×Q₈×C₂₃	1	2	yes	—
457	C₂	—	4	2	no	—
458	C₂	Q₈×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
459	C₂	C₂₃×#2879	1	1	yes	characteristic
460	C₂	C₂₃×#2880	1	1	yes	characteristic
461	C₂	C₂₃×#2961	1	1	yes	characteristic
462	C₂	C₂₃×#2962	1	1	yes	characteristic
463	C₂	C₂₃×#2985	1	1	yes	characteristic
464	C₂	C₂₃×#2987	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#446	C₂	semidirect
3. C₂₃×#1985	C₂	semidirect
4. C₂₃×#1985	C₂	semidirect
5. C₂₃×#1984	C₂	semidirect
84. C₂₃×C₂²⋊C₈	Q₈	semidirect
149. #22511	C₂₃	direct (N × H)
201. C₂×#446	C₂×C₂₃	semidirect
202. #1985	C₂×C₂₃	semidirect
203. #1985	C₂×C₂₃	semidirect
204. #1984	C₂×C₂₃	semidirect
316. C₂²⋊C₈	Q₈×C₂₃	semidirect
320. C₂₃	#22511	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×#533	2
C₂×C₂₃×#446	2
C₂₃×#1985	2
C₂₃×#1984	2
C₂₃×#1798	2
C₂₃×#1797	2
C₂₃×#1750	2
C₂₃×#1749	2
#22511	23

Subgroups — C23×#22511 #19170137

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#22511 #19170137