Subgroups — C₂₃×#2450 #15670069

Order 2944.

584 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#398	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#396	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#393	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#391	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#387	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#386	C₂	1	1	yes	maximal, characteristic
10	C₂₃×#386	C₂	1	1	yes	maximal, characteristic
11	C₂₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₃×#95	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₈×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×D₄×C₂₃	C₂²	1	1	yes	characteristic
18	C₂³×C₄×C₂₃	C₂²	1	1	yes	characteristic
19	C₂³×C₄×C₂₃	C₂²	1	1	yes	characteristic
20	C₂³×C₄×C₂₃	C₂²	1	1	yes	characteristic
21	C₂³×C₄×C₂₃	C₂²	1	1	yes	characteristic
22	C₂₃×C₂²⋊Q₈	—	2	4	no	—
23	C₄×D₄×C₂₃	—	2	4	no	—
24	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
40	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
41	C₂₃×#95	C₂²	1	1	yes	characteristic
42	C₂₃×#95	C₂²	1	1	yes	characteristic
43	C₂₃×#95	C₂²	1	1	yes	characteristic
44	C₂₃×#95	C₂²	1	1	yes	characteristic
45	C₂₃×#95	C₂²	1	1	yes	characteristic
46	C₂₃×#95	C₂²	1	1	yes	characteristic
47	C₂₃×#95	C₂²	1	1	yes	characteristic
48	C₂₃×#95	C₂²	1	1	yes	characteristic
49	C₂₃×#95	C₂²	1	1	yes	characteristic
50	C₂₃×#95	C₂²	1	1	yes	characteristic
51	C₂₃×#95	C₂²	1	1	yes	characteristic
52	C₂₃×#95	C₂²	1	1	yes	characteristic
53	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
54	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
55	C₂×Q₈×C₂₃	—	2	2	no	—
56	C₂×Q₈×C₂₃	—	2	2	no	—
57	C₂×Q₈×C₂₃	—	4	1	no	—
58	C₂×D₄×C₂₃	—	2	2	no	—
59	C₂×D₄×C₂₃	—	2	2	no	—
60	C₂×D₄×C₂₃	Q₈	1	4	yes	complemented
61	C₂²×C₄×C₂₃	—	2	2	no	—
62	C₂²×C₄×C₂₃	—	2	2	no	—
63	C₂²×C₄×C₂₃	—	2	2	no	—
64	C₂²×C₄×C₂₃	—	2	2	no	—
65	C₂²×C₄×C₂₃	—	2	2	no	—
66	C₂²×C₄×C₂₃	—	2	2	no	—
67	C₂²×C₄×C₂₃	—	2	2	no	—
68	C₂²×C₄×C₂₃	—	4	1	no	—
69	C₂²×C₄×C₂₃	—	4	1	no	—
70	C₂²×C₄×C₂₃	—	4	1	no	—
71	C₂²×C₄×C₂₃	—	4	1	no	—
72	C₂²×C₄×C₂₃	—	4	1	no	—
73	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
75	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
76	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
77	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
78	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
80	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
82	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
83	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
84	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
85	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
86	C₄⋊C₄×C₂₃	—	2	2	no	—
87	C₄⋊C₄×C₂₃	—	2	2	no	—
88	C₄⋊C₄×C₂₃	—	2	2	no	—
89	C₄⋊C₄×C₂₃	—	2	2	no	—
90	C₄⋊C₄×C₂₃	—	2	2	no	—
91	C₄⋊C₄×C₂₃	—	4	1	no	—
92	C₄⋊C₄×C₂₃	—	4	1	no	—
93	C₄⋊C₄×C₂₃	—	4	1	no	—
94	C₂²⋊C₄×C₂₃	—	2	2	no	—
95	C₂²⋊C₄×C₂₃	—	2	2	no	—
96	C₂²⋊C₄×C₂₃	—	2	2	no	—
97	C₂²⋊C₄×C₂₃	—	2	2	no	—
98	C₂²⋊C₄×C₂₃	—	4	1	no	—
99	C₂²⋊C₄×C₂₃	—	4	1	no	—
100	C₂²⋊C₄×C₂₃	—	4	1	no	—
101	C₂²⋊C₄×C₂₃	D₄	1	4	yes	—
102	C₄²×C₂₃	—	2	2	no	—
103	C₂³×C₂₃	—	2	1	no	—
104	C₂³×C₂₃	—	2	1	no	—
105	C₂³×C₂₃	—	2	1	no	—
106	C₂³×C₂₃	—	2	1	no	—
107	C₂³×C₂₃	—	2	1	no	—
108	C₂³×C₂₃	—	2	1	no	—
109	C₂³×C₂₃	—	2	1	no	—
110	C₂³×C₂₃	—	2	1	no	—
111	C₂³×C₂₃	—	2	1	no	—
112	C₂³×C₂₃	—	2	1	no	—
113	C₂³×C₂₃	C₂×D₄	1	2	yes	—
114	C₂³×C₂₃	C₂×Q₈	1	2	yes	—
115	C₂³×C₂₃	C₂×Q₈	1	2	yes	—
116	C₂³×C₂₃	#41	1	2	yes	—
117	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
118	Q₈×C₂₃	—	4	4	no	—
119	D₄×C₂₃	—	2	8	no	—
120	C₂×C₄×C₂₃	—	2	1	no	—
121	C₂×C₄×C₂₃	—	2	1	no	—
122	C₂×C₄×C₂₃	—	2	1	no	—
123	C₂×C₄×C₂₃	—	2	1	no	—
124	C₂×C₄×C₂₃	—	2	1	no	—
125	C₂×C₄×C₂₃	—	2	1	no	—
126	C₂×C₄×C₂₃	—	2	1	no	—
127	C₂×C₄×C₂₃	—	2	1	no	—
128	C₂×C₄×C₂₃	—	2	1	no	—
129	C₂×C₄×C₂₃	—	2	1	no	—
130	C₂×C₄×C₂₃	—	2	1	no	—
131	C₂×C₄×C₂₃	—	2	1	no	—
132	C₂×C₄×C₂₃	—	2	1	no	—
133	C₂×C₄×C₂₃	—	2	1	no	—
134	C₂×C₄×C₂₃	—	2	1	no	—
135	C₂×C₄×C₂₃	—	2	1	no	—
136	C₂×C₄×C₂₃	—	2	1	no	—
137	C₂×C₄×C₂₃	—	2	1	no	—
138	C₂×C₄×C₂₃	—	2	1	no	—
139	C₂×C₄×C₂₃	—	2	1	no	—
140	C₂×C₄×C₂₃	—	2	1	no	—
141	C₂×C₄×C₂₃	—	2	1	no	—
142	C₂×C₄×C₂₃	—	2	1	no	—
143	C₂×C₄×C₂₃	—	2	1	no	—
144	C₂×C₄×C₂₃	—	2	1	no	—
145	C₂×C₄×C₂₃	—	2	1	no	—
146	C₂×C₄×C₂₃	—	2	1	no	—
147	C₂×C₄×C₂₃	—	2	1	no	—
148	C₂×C₄×C₂₃	—	2	1	no	—
149	C₂×C₄×C₂₃	—	2	1	no	—
150	C₂×C₄×C₂₃	—	2	1	no	—
151	C₂×C₄×C₂₃	—	2	1	no	—
152	C₂×C₄×C₂₃	—	2	1	no	—
153	C₂×C₄×C₂₃	—	2	1	no	—
154	C₂×C₄×C₂₃	—	4	4	no	—
155	C₂×C₄×C₂₃	—	4	4	no	—
156	C₂×C₄×C₂₃	—	4	4	no	—
157	C₂×C₄×C₂₃	—	4	4	no	—
158	C₂×C₄×C₂₃	C₂×D₄	1	2	yes	—
159	C₂×C₄×C₂₃	C₂×D₄	1	2	yes	—
160	C₂×C₄×C₂₃	C₂×Q₈	1	2	yes	—
161	C₂×C₄×C₂₃	#41	1	2	yes	—
162	C₂×C₄×C₂₃	#41	1	2	yes	—
163	#2450	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂²×C₂₃	—	2	2	no	—
165	C₂²×C₂₃	—	2	2	no	—
166	C₂²×C₂₃	—	2	2	no	—
167	C₂²×C₂₃	—	2	2	no	—
168	C₂²×C₂₃	—	2	2	no	—
169	C₂²×C₂₃	—	2	2	no	—
170	C₂²×C₂₃	—	2	2	no	—
171	C₂²×C₂₃	—	2	2	no	—
172	C₂²×C₂₃	—	2	2	no	—
173	C₂²×C₂₃	—	4	1	no	—
174	C₂²×C₂₃	—	4	1	no	—
175	C₂²×C₂₃	—	4	1	no	—
176	C₂²×C₂₃	—	4	1	no	—
177	C₂²×C₂₃	C₂²⋊Q₈	1	4	yes	—
178	C₂²×C₂₃	C₂²×D₄	1	1	yes	characteristic
179	C₂²×C₂₃	C₂²×Q₈	1	1	yes	characteristic
180	C₂²×C₂₃	C₂×#41	1	1	yes	characteristic
181	C₂²×C₂₃	C₂×#41	1	1	yes	characteristic
182	C₂²×C₂₃	C₂×#41	1	1	yes	characteristic
183	C₂²×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
184	C₂²×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
185	C₄×C₂₃	—	2	2	no	—
186	C₄×C₂₃	—	2	2	no	—
187	C₄×C₂₃	—	2	2	no	—
188	C₄×C₂₃	—	2	2	no	—
189	C₄×C₂₃	—	2	2	no	—
190	C₄×C₂₃	—	4	1	no	—
191	C₄×C₂₃	—	4	1	no	—
192	C₄×C₂₃	—	4	1	no	—
193	C₄×C₂₃	—	4	1	no	—
194	C₄×C₂₃	—	4	1	no	—
195	C₄×C₂₃	—	4	1	no	—
196	C₄×C₂₃	—	4	1	no	—
197	C₄×C₂₃	—	4	1	no	—
198	C₂×C₂²⋊Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
199	C₂×C₄×D₄	C₂×C₂₃	1	1	yes	characteristic
200	#400	C₂×C₂₃	1	1	yes	characteristic, complemented
201	#398	C₂×C₂₃	1	1	yes	characteristic, complemented
202	#396	C₂×C₂₃	1	1	yes	characteristic, complemented
203	#393	C₂×C₂₃	1	1	yes	characteristic, complemented
204	#391	C₂×C₂₃	1	1	yes	characteristic, complemented
205	#387	C₂×C₂₃	1	1	yes	characteristic, complemented
206	#386	C₂×C₂₃	1	1	yes	characteristic
207	#386	C₂×C₂₃	1	1	yes	characteristic
208	#385	C₂×C₂₃	1	1	yes	characteristic, complemented
209	#385	C₂×C₂₃	1	1	yes	characteristic, complemented
210	#385	C₂×C₂₃	1	1	yes	characteristic, complemented
211	#380	C₂×C₂₃	1	1	yes	characteristic, complemented
212	C₂×#95	C₂×C₂₃	1	1	yes	characteristic, complemented
213	C₂×C₂₃	—	2	4	no	—
214	C₂×C₂₃	—	4	2	no	—
215	C₂×C₂₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
216	C₂×C₂₃	#529	1	1	yes	characteristic
217	C₂×C₂₃	#538	1	1	yes	characteristic
218	C₂×C₂₃	#546	1	1	yes	characteristic
219	C₂×C₂₃	#546	1	1	yes	characteristic
220	C₂×C₂₃	#554	1	1	yes	characteristic
221	C₂×C₂₃	#554	1	1	yes	characteristic
222	C₂²×Q₈	C₂²×C₂₃	1	1	yes	characteristic
223	C₂²×D₄	C₂²×C₂₃	1	1	yes	characteristic
224	C₂³×C₄	C₂²×C₂₃	1	1	yes	characteristic
225	C₂³×C₄	C₂²×C₂₃	1	1	yes	characteristic
226	C₂³×C₄	C₂²×C₂₃	1	1	yes	characteristic
227	C₂³×C₄	C₂²×C₂₃	1	1	yes	characteristic
228	C₂²⋊Q₈	—	2	4	no	—
229	C₄×D₄	—	2	4	no	—
230	C₂×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
231	C₂×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
232	C₂×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
233	C₂×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
234	C₂×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
235	C₂×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
236	C₂×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
237	C₂×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
238	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
239	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
240	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
241	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
242	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
243	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
244	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
245	C₂×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
246	C₂×C₄²	C₂²×C₂₃	1	1	yes	characteristic
247	#95	C₂²×C₂₃	1	1	yes	characteristic
248	#95	C₂²×C₂₃	1	1	yes	characteristic
249	#95	C₂²×C₂₃	1	1	yes	characteristic
250	#95	C₂²×C₂₃	1	1	yes	characteristic
251	#95	C₂²×C₂₃	1	1	yes	characteristic
252	#95	C₂²×C₂₃	1	1	yes	characteristic
253	#95	C₂²×C₂₃	1	1	yes	characteristic
254	#95	C₂²×C₂₃	1	1	yes	characteristic
255	#95	C₂²×C₂₃	1	1	yes	characteristic
256	#95	C₂²×C₂₃	1	1	yes	characteristic
257	#95	C₂²×C₂₃	1	1	yes	characteristic
258	#95	C₂²×C₂₃	1	1	yes	characteristic
259	C₂₃	#2450	1	1	yes	characteristic, direct product factor, Sylow
260	C₂⁴	C₂³×C₂₃	1	1	yes	characteristic
261	C₂⁴	C₂³×C₂₃	1	1	yes	characteristic
262	C₂×Q₈	—	2	2	no	—
263	C₂×Q₈	—	2	2	no	—
264	C₂×Q₈	—	4	1	no	—
265	C₂×D₄	—	2	2	no	—
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	Q₈×C₂₃	1	4	yes	complemented
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	4	1	no	—
276	C₂²×C₄	—	4	1	no	—
277	C₂²×C₄	—	4	1	no	—
278	C₂²×C₄	—	4	1	no	—
279	C₂²×C₄	—	4	1	no	—
280	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
281	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
282	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
283	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
284	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
285	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
286	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
287	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
288	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
289	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
290	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
291	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
292	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	4	1	no	—
299	C₄⋊C₄	—	4	1	no	—
300	C₄⋊C₄	—	4	1	no	—
301	C₂²⋊C₄	—	2	2	no	—
302	C₂²⋊C₄	—	2	2	no	—
303	C₂²⋊C₄	—	2	2	no	—
304	C₂²⋊C₄	—	2	2	no	—
305	C₂²⋊C₄	—	4	1	no	—
306	C₂²⋊C₄	—	4	1	no	—
307	C₂²⋊C₄	—	4	1	no	—
308	C₂²⋊C₄	D₄×C₂₃	1	4	yes	—
309	C₄²	—	2	2	no	—
310	C₂³	—	2	1	no	—
311	C₂³	—	2	1	no	—
312	C₂³	—	2	1	no	—
313	C₂³	—	2	1	no	—
314	C₂³	—	2	1	no	—
315	C₂³	—	2	1	no	—
316	C₂³	—	2	1	no	—
317	C₂³	—	2	1	no	—
318	C₂³	—	2	1	no	—
319	C₂³	—	2	1	no	—
320	C₂³	C₂×D₄×C₂₃	1	2	yes	—
321	C₂³	C₂×Q₈×C₂₃	1	2	yes	—
322	C₂³	C₂×Q₈×C₂₃	1	2	yes	—
323	C₂³	#41×C₂₃	1	2	yes	—
324	C₂³	C₂⁴×C₂₃	1	1	yes	characteristic
325	Q₈	—	4	4	no	—
326	D₄	—	2	8	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	C₂×D₄×C₂₃	1	2	yes	—
366	C₂×C₄	C₂×D₄×C₂₃	1	2	yes	—
367	C₂×C₄	C₂×Q₈×C₂₃	1	2	yes	—
368	C₂×C₄	#41×C₂₃	1	2	yes	—
369	C₂×C₄	#41×C₂₃	1	2	yes	—
370	C₂²	—	2	2	no	—
371	C₂²	—	2	2	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	4	1	no	—
380	C₂²	—	4	1	no	—
381	C₂²	—	4	1	no	—
382	C₂²	—	4	1	no	—
383	C₂²	C₂₃×C₂²⋊Q₈	1	4	yes	—
384	C₂²	C₂²×D₄×C₂₃	1	1	yes	characteristic
385	C₂²	C₂²×Q₈×C₂₃	1	1	yes	characteristic
386	C₂²	C₂×#41×C₂₃	1	1	yes	characteristic
387	C₂²	C₂×#41×C₂₃	1	1	yes	characteristic
388	C₂²	C₂×#41×C₂₃	1	1	yes	characteristic
389	C₂²	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
390	C₂²	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
391	C₄	—	2	2	no	—
392	C₄	—	2	2	no	—
393	C₄	—	2	2	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	2	no	—
396	C₄	—	4	1	no	—
397	C₄	—	4	1	no	—
398	C₄	—	4	1	no	—
399	C₄	—	4	1	no	—
400	C₄	—	4	1	no	—
401	C₄	—	4	1	no	—
402	C₄	—	4	1	no	—
403	C₄	—	4	1	no	—
404	C₂	—	2	4	no	—
405	C₂	—	4	2	no	—
406	C₂	C₂×C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
407	C₂	C₂₃×#529	1	1	yes	characteristic
408	C₂	C₂₃×#538	1	1	yes	characteristic
409	C₂	C₂₃×#546	1	1	yes	characteristic
410	C₂	C₂₃×#546	1	1	yes	characteristic
411	C₂	C₂₃×#554	1	1	yes	characteristic
412	C₂	C₂₃×#554	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×C₂²⋊Q₈	C₂	semidirect
3. C₂₃×#400	C₂	semidirect
4. C₂₃×#398	C₂	semidirect
5. C₂₃×#396	C₂	semidirect
6. C₂₃×#393	C₂	semidirect
7. C₂₃×#391	C₂	semidirect
8. C₂₃×#387	C₂	semidirect
11. C₂₃×#385	C₂	semidirect
12. C₂₃×#385	C₂	semidirect
13. C₂₃×#385	C₂	semidirect
14. C₂₃×#380	C₂	semidirect
15. C₂×C₂₃×#95	C₂	semidirect
60. C₂×D₄×C₂₃	Q₈	semidirect
163. #2450	C₂₃	direct (N × H)
198. C₂×C₂²⋊Q₈	C₂×C₂₃	semidirect
200. #400	C₂×C₂₃	semidirect
201. #398	C₂×C₂₃	semidirect
202. #396	C₂×C₂₃	semidirect
203. #393	C₂×C₂₃	semidirect
204. #391	C₂×C₂₃	semidirect
205. #387	C₂×C₂₃	semidirect
208. #385	C₂×C₂₃	semidirect
209. #385	C₂×C₂₃	semidirect
210. #385	C₂×C₂₃	semidirect
211. #380	C₂×C₂₃	semidirect
212. C₂×#95	C₂×C₂₃	semidirect
259. C₂₃	#2450	direct (N × H)
267. C₂×D₄	Q₈×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×C₂²⋊Q₈	2
C₂×C₄×D₄×C₂₃	2
C₂₃×#400	2
C₂₃×#398	2
C₂₃×#396	2
C₂₃×#393	2
C₂₃×#391	2
C₂₃×#387	2
C₂₃×#386	2
C₂₃×#385	2
C₂₃×#380	2
C₂×C₂₃×#95	2
#2450	23

Subgroups — C23×#2450 #15670069

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#2450 #15670069