Subgroups — C₂₃×#21604 #19169230

Order 5888.

834 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×#446	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#405	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2396	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1985	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1940	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1916	C₂	1	2	yes	maximal, complemented
7	C₂₃×#1850	C₂	1	2	yes	maximal
8	C₂₃×#1798	C₂	1	1	yes	maximal, characteristic
9	C₂₃×#1770	C₂	1	2	yes	maximal, complemented
10	C₈×C₄⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1753	C₂	1	2	yes	maximal
12	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
15	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
16	C₂₃×#446	—	2	4	no	—
17	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂₃×#405	—	2	4	no	—
23	C₂×C₂₃×#97	C₂²	1	2	yes	—
24	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
29	C₂₃×#400	C₄	1	1	yes	characteristic
30	C₂₃×#399	C₄	1	1	yes	characteristic
31	C₂₃×#398	C₄	1	2	yes	—
32	C₂₃×#396	C₄	1	2	yes	—
33	C₂₃×#395	C₄	1	1	yes	characteristic
34	C₂₃×#393	C₄	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
36	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
37	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
38	C₂₃×#336	C₂²	1	2	yes	—
39	C₂₃×#336	C₂²	1	2	yes	—
40	C₂₃×#336	C₂²	1	2	yes	—
41	C₂₃×#336	C₂²	1	2	yes	—
42	C₂₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
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	Q₈	1	4	yes	complemented
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	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
57	C₄×Q₈×C₂₃	—	2	2	no	—
58	C₄×Q₈×C₂₃	—	2	2	no	—
59	C₂₃×#117	—	2	2	no	—
60	C₂₃×#117	—	2	2	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	1	yes	characteristic
64	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
65	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
68	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
69	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
72	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
73	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
74	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
76	C₂₃×C₄⋊C₈	—	2	4	no	—
77	C₂₃×C₄⋊C₈	—	2	4	no	—
78	C₂₃×C₄⋊C₈	—	2	2	no	—
79	C₂₃×C₄⋊C₈	—	2	2	no	—
80	C₂₃×C₂²⋊C₈	—	2	4	no	—
81	C₂₃×#97	—	2	2	no	—
82	C₂₃×#97	—	2	4	no	—
83	C₂₃×#97	—	2	2	no	—
84	C₄×C₈×C₂₃	—	2	2	no	—
85	C₄×C₈×C₂₃	—	2	4	no	—
86	C₄×C₈×C₂₃	D₄	1	4	yes	—
87	C₂₃×#95	C₂×C₄	1	2	yes	—
88	C₂₃×#95	C₂×C₄	1	2	yes	—
89	C₂₃×#95	C₂×C₄	1	2	yes	—
90	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
91	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
92	C₂₃×#95	C₂×C₄	1	2	yes	—
93	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
94	C₂×Q₈×C₂₃	—	2	2	no	—
95	C₂×Q₈×C₂₃	—	4	2	no	—
96	C₂²×C₄×C₂₃	—	2	1	no	—
97	C₂²×C₄×C₂₃	—	2	1	no	—
98	C₂²×C₄×C₂₃	—	2	1	no	—
99	C₂²×C₄×C₂₃	—	2	1	no	—
100	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₂₃	C₂×Q₈	1	2	yes	—
110	C₂²×C₄×C₂₃	#41	1	2	yes	—
111	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
112	M₁₆×C₂₃	—	2	8	no	—
113	C₂×C₈×C₂₃	—	2	8	no	—
114	C₂×C₈×C₂₃	—	2	1	no	—
115	C₂×C₈×C₂₃	—	2	1	no	—
116	C₂×C₈×C₂₃	—	2	1	no	—
117	C₂×C₈×C₂₃	—	2	1	no	—
118	C₂×C₈×C₂₃	—	2	1	no	—
119	C₂×C₈×C₂₃	—	2	1	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	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₂₃	C₂×Q₈	1	2	yes	—
129	C₂×C₈×C₂₃	C₂×Q₈	1	2	yes	—
130	C₂×C₈×C₂₃	#41	1	2	yes	—
131	C₂×C₈×C₂₃	#41	1	2	yes	—
132	C₄⋊C₄×C₂₃	—	2	2	no	—
133	C₄⋊C₄×C₂₃	—	2	2	no	—
134	C₄⋊C₄×C₂₃	—	2	2	no	—
135	C₄⋊C₄×C₂₃	—	2	4	no	—
136	C₄⋊C₄×C₂₃	—	2	4	no	—
137	C₄⋊C₄×C₂₃	—	2	4	no	—
138	C₄⋊C₄×C₂₃	—	4	2	no	—
139	C₂²⋊C₄×C₂₃	—	2	2	no	—
140	C₂²⋊C₄×C₂₃	—	2	2	no	—
141	C₂²⋊C₄×C₂₃	—	2	4	no	—
142	C₂²⋊C₄×C₂₃	—	4	2	no	—
143	C₄²×C₂₃	—	2	2	no	—
144	C₄²×C₂₃	—	2	1	no	—
145	C₄²×C₂₃	—	2	2	no	—
146	C₄²×C₂₃	—	2	1	no	—
147	C₄²×C₂₃	—	2	2	no	—
148	C₄²×C₂₃	—	2	2	no	—
149	C₄²×C₂₃	C₂×D₄	1	2	yes	—
150	C₄²×C₂₃	#41	1	2	yes	—
151	#21604	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₂³×C₂₃	—	2	1	no	—
153	C₂³×C₂₃	—	2	1	no	—
154	C₂³×C₂₃	—	2	2	no	—
155	C₂³×C₂₃	—	2	2	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	C₂×C₄×C₂₃	—	2	1	no	—
160	C₂×C₄×C₂₃	—	2	2	no	—
161	C₂×C₄×C₂₃	—	2	1	no	—
162	C₂×C₄×C₂₃	—	2	2	no	—
163	C₂×C₄×C₂₃	—	2	2	no	—
164	C₂×C₄×C₂₃	—	2	2	no	—
165	C₂×C₄×C₂₃	—	2	2	no	—
166	C₂×C₄×C₂₃	—	2	2	no	—
167	C₂×C₄×C₂₃	—	2	2	no	—
168	C₂×C₄×C₂₃	—	2	2	no	—
169	C₂×C₄×C₂₃	—	2	1	no	—
170	C₂×C₄×C₂₃	—	2	1	no	—
171	C₂×C₄×C₂₃	—	2	2	no	—
172	C₂×C₄×C₂₃	—	2	2	no	—
173	C₂×C₄×C₂₃	—	2	2	no	—
174	C₂×C₄×C₂₃	—	2	2	no	—
175	C₂×C₄×C₂₃	—	2	2	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	2	no	—
180	C₂×C₄×C₂₃	—	2	2	no	—
181	C₂×C₄×C₂₃	—	2	2	no	—
182	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
183	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
184	C₂×C₄×C₂₃	C₄×Q₈	1	2	yes	—
185	C₂×C₄×C₂₃	#131	1	4	yes	—
186	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₂₃	C₂²×Q₈	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	2	no	—
193	C₈×C₂₃	—	2	2	no	—
194	C₈×C₂₃	—	2	2	no	—
195	C₈×C₂₃	—	4	2	no	—
196	C₈×C₂₃	—	4	2	no	—
197	C₈×C₂₃	C₂²⋊Q₈	1	4	yes	—
198	C₂×#446	C₂×C₂₃	1	1	yes	characteristic, complemented
199	C₂×#405	C₂×C₂₃	1	1	yes	characteristic
200	#2396	C₂×C₂₃	1	1	yes	characteristic
201	#1985	C₂×C₂₃	1	1	yes	characteristic, complemented
202	#1940	C₂×C₂₃	1	1	yes	characteristic, complemented
203	#1916	C₂×C₂₃	1	2	yes	complemented
204	#1850	C₂×C₂₃	1	2	yes	—
205	#1798	C₂×C₂₃	1	1	yes	characteristic
206	#1770	C₂×C₂₃	1	2	yes	complemented
207	C₈×C₄⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
208	#1753	C₂×C₂₃	1	2	yes	—
209	C₂²×C₂₃	—	2	4	no	—
210	C₂²×C₂₃	—	2	2	no	—
211	C₂²×C₂₃	—	4	1	no	—
212	C₂²×C₂₃	—	4	1	no	—
213	C₂²×C₂₃	—	4	2	no	—
214	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
215	C₂²×C₂₃	C₂×C₄×Q₈	1	1	yes	characteristic
216	C₂²×C₂₃	C₄×#41	1	1	yes	characteristic
217	C₂²×C₂₃	C₂×#131	1	2	yes	—
218	C₂²×C₂₃	#568	1	2	yes	—
219	C₄×C₂₃	—	2	2	no	—
220	C₄×C₂₃	—	2	2	no	—
221	C₄×C₂₃	—	2	4	no	—
222	C₄×C₂₃	—	2	2	no	—
223	C₄×C₂₃	—	4	1	no	—
224	C₄×C₂₃	—	4	2	no	—
225	C₄×C₂₃	—	4	1	no	—
226	C₄×C₂₃	—	4	2	no	—
227	C₄×C₂₃	—	4	2	no	—
228	C₄×C₂₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
229	C₄×C₂₃	#525	1	1	yes	characteristic
230	C₄×C₂₃	#529	1	1	yes	characteristic
231	C₄×C₂₃	#533	1	1	yes	characteristic
232	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
233	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
234	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
235	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
236	#446	—	2	4	no	—
237	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
238	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
239	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
240	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
241	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
242	#405	—	2	4	no	—
243	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
244	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
245	C₂×#97	C₂²×C₂₃	1	2	yes	—
246	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
247	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
248	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
249	#400	C₄×C₂₃	1	1	yes	characteristic
250	#399	C₄×C₂₃	1	1	yes	characteristic
251	#398	C₄×C₂₃	1	2	yes	—
252	#396	C₄×C₂₃	1	2	yes	—
253	#395	C₄×C₂₃	1	1	yes	characteristic
254	#393	C₄×C₂₃	1	1	yes	characteristic
255	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
256	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
257	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
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	C₄×C₂²⋊Q₈	1	1	yes	characteristic
265	C₂×C₂₃	#2930	1	1	yes	characteristic
266	C₂×C₂₃	#2931	1	1	yes	characteristic
267	C₂×C₂₃	#2962	1	2	yes	—
268	C₂×C₂₃	#2968	1	2	yes	—
269	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
270	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
271	C₂×M₁₆	—	2	2	no	—
272	C₂×M₁₆	—	2	2	no	—
273	C₂×M₁₆	Q₈×C₂₃	1	4	yes	complemented
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	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
280	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
281	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
282	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
283	C₄×Q₈	—	2	2	no	—
284	C₄×Q₈	—	2	2	no	—
285	#117	—	2	2	no	—
286	#117	—	2	2	no	—
287	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
290	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
292	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
293	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
294	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
295	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
296	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
297	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
298	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
299	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
300	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
301	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
302	C₄⋊C₈	—	2	4	no	—
303	C₄⋊C₈	—	2	4	no	—
304	C₄⋊C₈	—	2	2	no	—
305	C₄⋊C₈	—	2	2	no	—
306	C₂²⋊C₈	—	2	4	no	—
307	#97	—	2	2	no	—
308	#97	—	2	4	no	—
309	#97	—	2	2	no	—
310	C₄×C₈	—	2	2	no	—
311	C₄×C₈	—	2	4	no	—
312	C₄×C₈	D₄×C₂₃	1	4	yes	—
313	#95	C₂×C₄×C₂₃	1	2	yes	—
314	#95	C₂×C₄×C₂₃	1	2	yes	—
315	#95	C₂×C₄×C₂₃	1	2	yes	—
316	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
317	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
318	#95	C₂×C₄×C₂₃	1	2	yes	—
319	C₂₃	#21604	1	1	yes	characteristic, direct product factor, Sylow
320	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	4	2	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
328	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
329	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
330	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
331	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
332	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
333	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
334	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
335	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
336	C₂²×C₄	C₂×Q₈×C₂₃	1	2	yes	—
337	C₂²×C₄	#41×C₂₃	1	2	yes	—
338	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
339	M₁₆	—	2	8	no	—
340	C₂×C₈	—	2	8	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
354	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
355	C₂×C₈	C₂×Q₈×C₂₃	1	2	yes	—
356	C₂×C₈	C₂×Q₈×C₂₃	1	2	yes	—
357	C₂×C₈	#41×C₂₃	1	2	yes	—
358	C₂×C₈	#41×C₂₃	1	2	yes	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	4	no	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	—	4	2	no	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	2	2	no	—
368	C₂²⋊C₄	—	2	4	no	—
369	C₂²⋊C₄	—	4	2	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	2	no	—
376	C₄²	C₂×D₄×C₂₃	1	2	yes	—
377	C₄²	#41×C₂₃	1	2	yes	—
378	C₂³	—	2	2	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	1	no	—
381	C₂³	—	2	1	no	—
382	C₂³	C₄×Q₈×C₂₃	1	2	yes	—
383	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
384	Q₈	—	4	4	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
409	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
410	C₂×C₄	C₄×Q₈×C₂₃	1	2	yes	—
411	C₂×C₄	C₂₃×#131	1	4	yes	—
412	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
413	C₂×C₄	C₂²×Q₈×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	2	no	—
419	C₈	—	2	2	no	—
420	C₈	—	2	2	no	—
421	C₈	—	4	2	no	—
422	C₈	—	4	2	no	—
423	C₈	C₂₃×C₂²⋊Q₈	1	4	yes	—
424	C₂²	—	2	4	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	4	1	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	4	2	no	—
429	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
430	C₂²	C₂×C₄×Q₈×C₂₃	1	1	yes	characteristic
431	C₂²	C₄×#41×C₂₃	1	1	yes	characteristic
432	C₂²	C₂×C₂₃×#131	1	2	yes	—
433	C₂²	C₂₃×#568	1	2	yes	—
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	2	4	no	—
437	C₄	—	2	2	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	1	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	1	no	—
442	C₄	—	4	2	no	—
443	C₄	C₂×C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
444	C₄	C₂₃×#525	1	1	yes	characteristic
445	C₄	C₂₃×#529	1	1	yes	characteristic
446	C₄	C₂₃×#533	1	1	yes	characteristic
447	C₂	—	4	2	no	—
448	C₂	C₄×C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
449	C₂	C₂₃×#2930	1	1	yes	characteristic
450	C₂	C₂₃×#2931	1	1	yes	characteristic
451	C₂	C₂₃×#2962	1	2	yes	—
452	C₂	C₂₃×#2968	1	2	yes	—

	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
1. C₂×C₂₃×#446	C₂	semidirect
4. C₂₃×#1985	C₂	semidirect
5. C₂₃×#1940	C₂	semidirect
6. C₂₃×#1916	C₂	semidirect
9. C₂₃×#1770	C₂	semidirect
10. C₈×C₄⋊C₄×C₂₃	C₂	semidirect
47. C₂×M₁₆×C₂₃	Q₈	semidirect
151. #21604	C₂₃	direct (N × H)
198. C₂×#446	C₂×C₂₃	semidirect
201. #1985	C₂×C₂₃	semidirect
202. #1940	C₂×C₂₃	semidirect
203. #1916	C₂×C₂₃	semidirect
206. #1770	C₂×C₂₃	semidirect
207. C₈×C₄⋊C₄	C₂×C₂₃	semidirect
273. C₂×M₁₆	Q₈×C₂₃	semidirect
319. C₂₃	#21604	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×#446	2
C₂×C₂₃×#405	2
C₂₃×#2396	2
C₂₃×#1985	2
C₂₃×#1940	2
C₂₃×#1916	2
C₂₃×#1850	2
C₂₃×#1798	2
C₂₃×#1770	2
C₈×C₄⋊C₄×C₂₃	2
C₂₃×#1753	2
#21604	23

Subgroups — C23×#21604 #19169230

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#21604 #19169230