Subgroups — M₁₆×D₈×C₂₃ #19165660

Order 5888.

794 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₈×C₂₃	C₂	1	1	yes	maximal, characteristic
2	D₄×M₁₆×C₂₃	C₂	1	2	yes	maximal, complemented
3	C₂₃×#1589	C₂	1	2	yes	maximal, complemented
4	C₂₃×#1581	C₂	1	4	yes	maximal, complemented
5	C₈×D₈×C₂₃	C₂	1	2	yes	maximal, complemented
6	C₂₃×#1567	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1486	C₂	1	2	yes	maximal, complemented
8	C₈×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₈×C₂₃	C₄	1	1	yes	characteristic
10	C₂²×M₁₆×C₂₃	—	2	2	no	—
11	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
12	C₄×D₈×C₂₃	C₄	1	1	yes	characteristic
13	C₄×D₈×C₂₃	C₄	1	2	yes	—
14	C₄×D₈×C₂₃	C₄	1	1	yes	characteristic
15	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
16	C₄×D₈×C₂₃	C₂²	1	2	yes	—
17	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
18	C₂₃×#436	C₂²	1	4	yes	complemented
19	C₂₃×#435	—	2	4	no	—
20	C₈×D₄×C₂₃	C₂²	1	4	yes	complemented
21	C₂₃×#431	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#107	C₄	1	1	yes	characteristic
23	C₂₃×#423	C₂²	1	2	yes	—
24	C₂×C₂₃×#102	C₄	1	2	yes	—
25	C₂₃×#407	—	2	2	no	—
26	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
28	C₂₃×#335	C₂²	1	2	yes	complemented
29	C₂₃×#335	C₂²	1	2	yes	complemented
30	C₂₃×D₄⋊C₈	C₂²	1	4	yes	complemented
31	C₂₃×D₄⋊C₈	C₂²	1	4	yes	complemented
32	C₂₃×#322	C₂²	1	2	yes	complemented
33	C₈²×C₂₃	C₂²	1	2	yes	complemented
34	C₂²×D₄×C₂₃	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₂₃	—	2	2	no	—
36	C₂×D₈×C₂₃	—	2	4	no	—
37	C₂×D₈×C₂₃	C₂×C₄	1	2	yes	—
38	C₂×D₈×C₂₃	C₂×C₄	1	1	yes	characteristic
39	C₂×D₈×C₂₃	C₂×C₄	1	1	yes	characteristic
40	C₂×M₁₆×C₂₃	—	2	2	no	—
41	C₂×M₁₆×C₂₃	—	2	4	no	—
42	C₂×M₁₆×C₂₃	—	4	8	no	—
43	C₂×M₁₆×C₂₃	D₄	1	1	yes	characteristic
44	C₂×M₁₆×C₂₃	D₄	1	1	yes	characteristic
45	C₂²×C₈×C₂₃	—	2	4	no	—
46	C₂²×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
48	C₄×D₄×C₂₃	—	2	2	no	—
49	C₄×D₄×C₂₃	—	2	2	no	—
50	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
51	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
52	C₄×D₄×C₂₃	C₂³	1	2	yes	—
53	C₄×D₄×C₂₃	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
55	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
56	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
57	C₂₃×#107	C₂×C₄	1	2	yes	—
58	C₂₃×#107	C₂×C₄	1	1	yes	characteristic
59	C₂₃×#107	C₂×C₄	1	1	yes	characteristic
60	C₂₃×C₄⋊C₈	—	2	2	no	—
61	C₂₃×C₄⋊C₈	—	2	1	no	—
62	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
63	C₂₃×#102	C₂×C₄	1	2	yes	—
64	C₂₃×#102	C₂×C₄	1	2	yes	—
65	C₂₃×#102	C₂×C₄	1	2	yes	—
66	C₂₃×#102	C₂×C₄	1	2	yes	—
67	C₂₃×C₂²⋊C₈	—	2	1	no	—
68	C₂₃×C₂²⋊C₈	—	2	4	no	—
69	C₂₃×C₂²⋊C₈	—	2	4	no	—
70	C₂₃×#97	D₄	1	2	yes	—
71	C₄×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
72	C₄×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
73	C₄×C₈×C₂₃	C₂³	1	2	yes	—
74	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
75	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
76	C₄×C₈×C₂₃	C₂³	1	2	yes	—
77	C₂⁴×C₂₃	—	2	2	no	—
78	C₂×D₄×C₂₃	—	2	4	no	—
79	C₂×D₄×C₂₃	—	2	2	no	—
80	C₂×D₄×C₂₃	—	4	2	no	—
81	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
82	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₂₃	—	2	2	no	—
84	C₂²×C₄×C₂₃	—	2	2	no	—
85	C₂²×C₄×C₂₃	—	2	2	no	—
86	C₂²×C₄×C₂₃	—	2	2	no	—
87	C₂²×C₄×C₂₃	—	2	2	no	—
88	C₂²×C₄×C₂₃	—	4	4	no	—
89	C₂²×C₄×C₂₃	—	4	4	no	—
90	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
93	D₈×C₂₃	—	2	4	no	—
94	D₈×C₂₃	—	2	2	no	—
95	D₈×C₂₃	M₁₆	1	4	yes	direct product factor
96	M₁₆×C₂₃	—	2	2	no	—
97	M₁₆×C₂₃	—	4	4	no	—
98	M₁₆×C₂₃	—	4	8	no	—
99	M₁₆×C₂₃	D₈	1	4	yes	direct product factor
100	C₂×C₈×C₂₃	—	2	2	no	—
101	C₂×C₈×C₂₃	—	2	4	no	—
102	C₂×C₈×C₂₃	—	2	2	no	—
103	C₂×C₈×C₂₃	—	4	1	no	—
104	C₂×C₈×C₂₃	—	4	8	no	—
105	C₂×C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
110	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
111	C₄⋊C₄×C₂₃	—	2	2	no	—
112	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
113	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
114	C₂²⋊C₄×C₂₃	—	2	2	no	—
115	C₂²⋊C₄×C₂₃	—	2	2	no	—
116	C₂²⋊C₄×C₂₃	—	2	2	no	—
117	C₂²⋊C₄×C₂₃	—	2	2	no	—
118	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₂₃	#41	1	1	yes	characteristic
121	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
122	M₁₆×D₈	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
123	C₂³×C₂₃	—	2	2	no	—
124	C₂³×C₂₃	—	2	2	no	—
125	C₂³×C₂₃	—	4	4	no	—
126	C₂³×C₂₃	—	4	4	no	—
127	C₂³×C₂₃	—	8	2	no	—
128	C₂³×C₂₃	C₄×D₄	1	1	yes	characteristic
129	D₄×C₂₃	—	2	2	no	—
130	D₄×C₂₃	—	2	2	no	—
131	D₄×C₂₃	—	2	2	no	—
132	D₄×C₂₃	—	4	4	no	—
133	D₄×C₂₃	C₂×M₁₆	1	4	yes	complemented
134	C₂×C₄×C₂₃	—	2	1	no	—
135	C₂×C₄×C₂₃	—	2	1	no	—
136	C₂×C₄×C₂₃	—	2	2	no	—
137	C₂×C₄×C₂₃	—	2	2	no	—
138	C₂×C₄×C₂₃	—	4	1	no	—
139	C₂×C₄×C₂₃	—	4	4	no	—
140	C₂×C₄×C₂₃	—	4	2	no	—
141	C₂×C₄×C₂₃	—	4	2	no	—
142	C₂×C₄×C₂₃	—	4	2	no	—
143	C₂×C₄×C₂₃	—	4	2	no	—
144	C₂×C₄×C₂₃	—	4	4	no	—
145	C₂×C₄×C₂₃	—	4	4	no	—
146	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₂₃	C₂×D₈	1	2	yes	—
150	C₂×C₄×C₂₃	#135	1	2	yes	—
151	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
152	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
154	C₈×C₂₃	—	2	1	no	—
155	C₈×C₂₃	—	2	1	no	—
156	C₈×C₂₃	—	2	1	no	—
157	C₈×C₂₃	—	2	2	no	—
158	C₈×C₂₃	—	4	2	no	—
159	C₈×C₂₃	—	4	4	no	—
160	C₈×C₂₃	C₂×M₁₆	1	2	yes	complemented
161	C₈×C₂₃	C₂×D₈	1	4	yes	complemented
162	C₂×C₄×D₈	C₂×C₂₃	1	1	yes	characteristic
163	D₄×M₁₆	C₂×C₂₃	1	2	yes	complemented
164	#1589	C₂×C₂₃	1	2	yes	complemented
165	#1581	C₂×C₂₃	1	4	yes	complemented
166	C₈×D₈	C₂×C₂₃	1	2	yes	complemented
167	#1567	C₂×C₂₃	1	1	yes	characteristic, complemented
168	#1486	C₂×C₂₃	1	2	yes	complemented
169	C₈×M₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
170	C₂²×C₂₃	—	2	1	no	—
171	C₂²×C₂₃	—	2	1	no	—
172	C₂²×C₂₃	—	2	4	no	—
173	C₂²×C₂₃	—	4	2	no	—
174	C₂²×C₂₃	—	4	2	no	—
175	C₂²×C₂₃	—	4	2	no	—
176	C₂²×C₂₃	—	4	2	no	—
177	C₂²×C₂₃	—	4	2	no	—
178	C₂²×C₂₃	—	8	8	no	—
179	C₂²×C₂₃	C₄×D₈	1	2	yes	—
180	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
181	C₄×C₂₃	—	2	1	no	—
182	C₄×C₂₃	—	2	1	no	—
183	C₄×C₂₃	—	2	1	no	—
184	C₄×C₂₃	—	4	2	no	—
185	C₄×C₂₃	—	4	2	no	—
186	C₄×C₂₃	C₄×D₈	1	2	yes	—
187	C₄×C₂₃	C₂²×M₁₆	1	1	yes	characteristic
188	C₄×C₂₃	#568	1	1	yes	characteristic
189	C₄×C₂₃	C₂²×D₈	1	1	yes	characteristic
190	C₄×C₂₃	C₂×#135	1	1	yes	characteristic
191	C₂²×D₈	C₄×C₂₃	1	1	yes	characteristic
192	C₂²×M₁₆	—	2	2	no	—
193	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
194	C₄×D₈	C₄×C₂₃	1	2	yes	—
195	C₄×D₈	C₄×C₂₃	1	1	yes	characteristic
196	C₄×D₈	C₄×C₂₃	1	1	yes	characteristic
197	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
198	C₄×D₈	C₂²×C₂₃	1	2	yes	—
199	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
200	#436	C₂²×C₂₃	1	4	yes	complemented
201	#435	—	2	4	no	—
202	C₈×D₄	C₂²×C₂₃	1	4	yes	complemented
203	#431	C₂²×C₂₃	1	1	yes	characteristic
204	C₂×#107	C₄×C₂₃	1	1	yes	characteristic
205	#423	C₂²×C₂₃	1	2	yes	—
206	C₂×#102	C₄×C₂₃	1	2	yes	—
207	#407	—	2	2	no	—
208	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
209	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
210	#335	C₂²×C₂₃	1	2	yes	complemented
211	#335	C₂²×C₂₃	1	2	yes	complemented
212	D₄⋊C₈	C₂²×C₂₃	1	4	yes	complemented
213	D₄⋊C₈	C₂²×C₂₃	1	4	yes	complemented
214	#322	C₂²×C₂₃	1	2	yes	complemented
215	C₈²	C₂²×C₂₃	1	2	yes	complemented
216	C₂×C₂₃	—	2	2	no	—
217	C₂×C₂₃	—	4	4	no	—
218	C₂×C₂₃	—	8	2	no	—
219	C₂×C₂₃	D₄×M₁₆	1	1	yes	characteristic
220	C₂×C₂₃	C₂×C₄×D₈	1	1	yes	characteristic
221	C₂×C₂₃	#2957	1	1	yes	characteristic
222	C₂²×D₄	C₂×C₄×C₂₃	1	2	yes	—
223	C₂³×C₄	—	2	2	no	—
224	C₂×D₈	—	2	4	no	—
225	C₂×D₈	C₂×C₄×C₂₃	1	2	yes	—
226	C₂×D₈	C₂×C₄×C₂₃	1	1	yes	characteristic
227	C₂×D₈	C₂×C₄×C₂₃	1	1	yes	characteristic
228	C₂×M₁₆	—	2	2	no	—
229	C₂×M₁₆	—	2	4	no	—
230	C₂×M₁₆	—	4	8	no	—
231	C₂×M₁₆	D₄×C₂₃	1	1	yes	characteristic
232	C₂×M₁₆	D₄×C₂₃	1	1	yes	characteristic
233	C₂²×C₈	—	2	4	no	—
234	C₂²×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
235	C₂²×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
236	C₄×D₄	—	2	2	no	—
237	C₄×D₄	—	2	2	no	—
238	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
239	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
240	C₄×D₄	C₂³×C₂₃	1	2	yes	—
241	C₄×D₄	C₂³×C₂₃	1	2	yes	—
242	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
243	C₂×C₂²⋊C₄	—	2	2	no	—
244	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
245	#107	C₂×C₄×C₂₃	1	2	yes	—
246	#107	C₂×C₄×C₂₃	1	1	yes	characteristic
247	#107	C₂×C₄×C₂₃	1	1	yes	characteristic
248	C₄⋊C₈	—	2	2	no	—
249	C₄⋊C₈	—	2	1	no	—
250	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
251	#102	C₂×C₄×C₂₃	1	2	yes	—
252	#102	C₂×C₄×C₂₃	1	2	yes	—
253	#102	C₂×C₄×C₂₃	1	2	yes	—
254	#102	C₂×C₄×C₂₃	1	2	yes	—
255	C₂²⋊C₈	—	2	1	no	—
256	C₂²⋊C₈	—	2	4	no	—
257	C₂²⋊C₈	—	2	4	no	—
258	#97	D₄×C₂₃	1	2	yes	—
259	C₄×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
260	C₄×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
261	C₄×C₈	C₂³×C₂₃	1	2	yes	—
262	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
263	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
264	C₄×C₈	C₂³×C₂₃	1	2	yes	—
265	C₂₃	M₁₆×D₈	1	1	yes	characteristic, direct product factor, Sylow
266	C₂⁴	—	2	2	no	—
267	C₂×D₄	—	2	4	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	4	2	no	—
270	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
271	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	4	4	no	—
278	C₂²×C₄	—	4	4	no	—
279	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
280	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
281	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
282	D₈	—	2	4	no	—
283	D₈	—	2	2	no	—
284	D₈	M₁₆×C₂₃	1	4	yes	direct product factor
285	M₁₆	—	2	2	no	—
286	M₁₆	—	4	4	no	—
287	M₁₆	—	4	8	no	—
288	M₁₆	D₈×C₂₃	1	4	yes	direct product factor
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	4	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	4	1	no	—
293	C₂×C₈	—	4	8	no	—
294	C₂×C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
295	C₂×C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
296	C₂×C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
297	C₂×C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
298	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
299	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
302	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
303	C₂²⋊C₄	—	2	2	no	—
304	C₂²⋊C₄	—	2	2	no	—
305	C₂²⋊C₄	—	2	2	no	—
306	C₂²⋊C₄	—	2	2	no	—
307	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
308	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
309	C₄²	#41×C₂₃	1	1	yes	characteristic
310	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
311	C₂³	—	2	2	no	—
312	C₂³	—	2	2	no	—
313	C₂³	—	4	4	no	—
314	C₂³	—	4	4	no	—
315	C₂³	—	8	2	no	—
316	C₂³	C₄×D₄×C₂₃	1	1	yes	characteristic
317	D₄	—	2	2	no	—
318	D₄	—	2	2	no	—
319	D₄	—	2	2	no	—
320	D₄	—	4	4	no	—
321	D₄	C₂×M₁₆×C₂₃	1	4	yes	complemented
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
335	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
336	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
337	C₂×C₄	C₂×D₈×C₂₃	1	2	yes	—
338	C₂×C₄	C₂₃×#135	1	2	yes	—
339	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
340	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
341	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
342	C₈	—	2	1	no	—
343	C₈	—	2	1	no	—
344	C₈	—	2	1	no	—
345	C₈	—	2	2	no	—
346	C₈	—	4	2	no	—
347	C₈	—	4	4	no	—
348	C₈	C₂×M₁₆×C₂₃	1	2	yes	complemented
349	C₈	C₂×D₈×C₂₃	1	4	yes	complemented
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	4	no	—
353	C₂²	—	4	2	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	4	2	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	8	8	no	—
359	C₂²	C₄×D₈×C₂₃	1	2	yes	—
360	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	4	2	no	—
365	C₄	—	4	2	no	—
366	C₄	C₄×D₈×C₂₃	1	2	yes	—
367	C₄	C₂²×M₁₆×C₂₃	1	1	yes	characteristic
368	C₄	C₂₃×#568	1	1	yes	characteristic
369	C₄	C₂²×D₈×C₂₃	1	1	yes	characteristic
370	C₄	C₂×C₂₃×#135	1	1	yes	characteristic
371	C₂	—	2	2	no	—
372	C₂	—	4	4	no	—
373	C₂	—	8	2	no	—
374	C₂	D₄×M₁₆×C₂₃	1	1	yes	characteristic
375	C₂	C₂×C₄×D₈×C₂₃	1	1	yes	characteristic
376	C₂	C₂₃×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₄²	C₂⁴×C₂₃
socle	C₂²×C₂₃	C₂×C₄×D₄
prime radical	C₂²×D₈×C₂₃	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₄×M₁₆×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. D₄×M₁₆×C₂₃	C₂	semidirect
3. C₂₃×#1589	C₂	semidirect
4. C₂₃×#1581	C₂	semidirect
5. C₈×D₈×C₂₃	C₂	semidirect
6. C₂₃×#1567	C₂	semidirect
7. C₂₃×#1486	C₂	semidirect
8. C₈×M₁₆×C₂₃	C₂	semidirect
18. C₂₃×#436	C₂²	semidirect
20. C₈×D₄×C₂₃	C₂²	semidirect
28. C₂₃×#335	C₂²	semidirect
29. C₂₃×#335	C₂²	semidirect
30. C₂₃×D₄⋊C₈	C₂²	semidirect
31. C₂₃×D₄⋊C₈	C₂²	semidirect
32. C₂₃×#322	C₂²	semidirect
33. C₈²×C₂₃	C₂²	semidirect
95. D₈×C₂₃	M₁₆	direct (N × H)
99. M₁₆×C₂₃	D₈	direct (N × H)
122. M₁₆×D₈	C₂₃	direct (N × H)
133. D₄×C₂₃	C₂×M₁₆	semidirect
160. C₈×C₂₃	C₂×M₁₆	semidirect
161. C₈×C₂₃	C₂×D₈	semidirect
163. D₄×M₁₆	C₂×C₂₃	semidirect
164. #1589	C₂×C₂₃	semidirect
165. #1581	C₂×C₂₃	semidirect
166. C₈×D₈	C₂×C₂₃	semidirect
167. #1567	C₂×C₂₃	semidirect
168. #1486	C₂×C₂₃	semidirect
169. C₈×M₁₆	C₂×C₂₃	semidirect
200. #436	C₂²×C₂₃	semidirect
202. C₈×D₄	C₂²×C₂₃	semidirect
210. #335	C₂²×C₂₃	semidirect
211. #335	C₂²×C₂₃	semidirect
212. D₄⋊C₈	C₂²×C₂₃	semidirect
213. D₄⋊C₈	C₂²×C₂₃	semidirect
214. #322	C₂²×C₂₃	semidirect
215. C₈²	C₂²×C₂₃	semidirect
265. C₂₃	M₁₆×D₈	direct (N × H)
284. D₈	M₁₆×C₂₃	direct (N × H)
288. M₁₆	D₈×C₂₃	direct (N × H)
321. D₄	C₂×M₁₆×C₂₃	semidirect
348. C₈	C₂×M₁₆×C₂₃	semidirect
349. C₈	C₂×D₈×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₈×C₂₃	2
D₄×M₁₆×C₂₃	2
C₂₃×#1589	2
C₂₃×#1581	2
C₈×D₈×C₂₃	2
C₂₃×#1567	2
C₂₃×#1486	2
C₈×M₁₆×C₂₃	2
M₁₆×D₈	23

Subgroups — M16×D8×C23 #19165660

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — M₁₆×D₈×C₂₃ #19165660