Subgroups — C₂×C₂₃×#1487 #19165067

Order 5888.

1282 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×Q₈×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#431	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃×#423	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1487	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₂₃×Q₈⋊C₈	C₂	1	4	yes	maximal, complemented
6	C₂³×Q₈×C₂₃	C₄	1	1	yes	characteristic
7	C₂²×M₁₆×C₂₃	—	2	1	no	—
8	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
9	C₂×C₄×Q₈×C₂₃	—	2	2	no	—
10	C₂×C₄×Q₈×C₂₃	—	2	2	no	—
11	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
12	C₂×C₄×Q₈×C₂₃	C₄	1	4	yes	—
13	C₂×C₄×Q₈×C₂₃	C₄	1	2	yes	—
14	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₂₃	C₂²	1	4	yes	—
16	C₂²×C₄⋊C₄×C₂₃	—	2	1	no	—
17	C₂²×C₄⋊C₄×C₂₃	C₄	1	1	yes	characteristic
18	C₂²×C₄²×C₂₃	—	2	1	no	—
19	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
20	C₂₃×#431	—	2	2	no	—
21	C₂₃×#431	C₂²	1	4	yes	—
22	C₂₃×#423	—	2	2	no	—
23	C₂₃×#423	C₂²	1	4	yes	—
24	C₂×C₂₃×C₄⋊C₈	—	2	1	no	—
25	C₂×C₂₃×C₄⋊C₈	—	2	1	no	—
26	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
27	C₂×C₂₃×C₂²⋊C₈	—	2	1	no	—
28	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
29	C₂₃×Q₈⋊C₈	C₂²	1	16	yes	complemented
30	C₂²×Q₈×C₂₃	—	2	8	no	—
31	C₂²×Q₈×C₂₃	—	2	2	no	—
32	C₂²×Q₈×C₂₃	—	2	1	no	—
33	C₂²×Q₈×C₂₃	C₂×C₄	1	4	yes	—
34	C₂²×Q₈×C₂₃	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₂₃	—	2	1	no	—
36	C₂³×C₄×C₂₃	—	2	1	no	—
37	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
40	C₂×M₁₆×C₂₃	—	2	4	no	—
41	C₂×M₁₆×C₂₃	—	4	4	no	—
42	C₂²×C₈×C₂₃	—	2	2	no	—
43	C₂²×C₈×C₂₃	—	2	2	no	—
44	C₄×Q₈×C₂₃	—	2	4	no	—
45	C₄×Q₈×C₂₃	—	2	4	no	—
46	C₄×Q₈×C₂₃	—	2	4	no	—
47	C₄×Q₈×C₂₃	—	2	4	no	—
48	C₄×Q₈×C₂₃	—	2	2	no	—
49	C₄×Q₈×C₂₃	—	2	2	no	—
50	C₄×Q₈×C₂₃	—	2	4	no	—
51	C₄×Q₈×C₂₃	C₂×C₄	1	4	yes	—
52	C₄×Q₈×C₂₃	C₂×C₄	1	8	yes	—
53	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
54	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
55	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
56	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
57	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
58	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
59	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
60	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	4	yes	—
61	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
62	C₂×C₄²×C₂₃	—	2	2	no	—
63	C₂×C₄²×C₂₃	—	2	4	no	—
64	C₂×C₄²×C₂₃	—	2	4	no	—
65	C₂×C₄²×C₂₃	—	2	2	no	—
66	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
68	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₂₃	D₄	1	2	yes	—
70	C₂×C₄²×C₂₃	D₄	1	2	yes	—
71	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
73	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
74	C₂₃×C₄⋊C₈	—	2	4	no	—
75	C₂₃×C₄⋊C₈	—	2	4	no	—
76	C₂₃×C₄⋊C₈	—	2	2	no	—
77	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
78	C₂₃×C₂²⋊C₈	—	2	4	no	—
79	C₄×C₈×C₂₃	—	2	2	no	—
80	C₄×C₈×C₂₃	C₂³	1	4	yes	—
81	C₂⁴×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
82	C₂×Q₈×C₂₃	—	2	16	no	—
83	C₂×Q₈×C₂₃	—	2	8	no	—
84	C₂×Q₈×C₂₃	—	2	16	no	—
85	C₂×Q₈×C₂₃	—	2	4	no	—
86	C₂×Q₈×C₂₃	—	2	2	no	—
87	C₂×Q₈×C₂₃	—	2	4	no	—
88	C₂×Q₈×C₂₃	M₁₆	1	8	yes	complemented
89	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
90	C₂²×C₄×C₂₃	—	2	8	no	—
91	C₂²×C₄×C₂₃	—	2	4	no	—
92	C₂²×C₄×C₂₃	—	2	2	no	—
93	C₂²×C₄×C₂₃	—	2	4	no	—
94	C₂²×C₄×C₂₃	—	2	4	no	—
95	C₂²×C₄×C₂₃	—	2	2	no	—
96	C₂²×C₄×C₂₃	—	4	2	no	—
97	C₂²×C₄×C₂₃	—	4	4	no	—
98	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
99	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
100	C₂²×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
101	C₂²×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
102	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
103	C₂²×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
104	C₂²×C₄×C₂₃	SD₁₆	1	4	yes	—
105	C₂²×C₄×C₂₃	Q₁₆	1	4	yes	—
106	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
112	M₁₆×C₂₃	—	4	8	no	—
113	C₂×C₈×C₂₃	—	2	4	no	—
114	C₂×C₈×C₂₃	—	2	4	no	—
115	C₂×C₈×C₂₃	—	4	4	no	—
116	C₂×C₈×C₂₃	—	4	4	no	—
117	C₄⋊C₄×C₂₃	—	2	8	no	—
118	C₄⋊C₄×C₂₃	—	2	4	no	—
119	C₄⋊C₄×C₂₃	—	2	4	no	—
120	C₄⋊C₄×C₂₃	—	2	2	no	—
121	C₄⋊C₄×C₂₃	—	2	4	no	—
122	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
123	C₄²×C₂₃	—	2	8	no	—
124	C₄²×C₂₃	—	2	4	no	—
125	C₄²×C₂₃	—	2	4	no	—
126	C₄²×C₂₃	C₂²⋊C₄	1	2	yes	—
127	C₄²×C₂₃	C₂²⋊C₄	1	2	yes	—
128	C₄²×C₂₃	C₂²⋊C₄	1	2	yes	—
129	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
130	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₂₃	C₂×D₄	1	2	yes	—
132	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₂₃	C₂×D₄	1	2	yes	—
134	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
136	C₂×#1487	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂³×C₂₃	—	2	2	no	—
138	C₂³×C₂₃	—	2	2	no	—
139	C₂³×C₂₃	#103	1	4	yes	—
140	C₂³×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
141	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
142	Q₈×C₂₃	—	2	16	no	—
143	Q₈×C₂₃	—	2	4	no	—
144	Q₈×C₂₃	—	2	8	no	—
145	Q₈×C₂₃	C₂×M₁₆	1	8	yes	complemented
146	C₂×C₄×C₂₃	—	2	16	no	—
147	C₂×C₄×C₂₃	—	2	4	no	—
148	C₂×C₄×C₂₃	—	2	8	no	—
149	C₂×C₄×C₂₃	—	2	2	no	—
150	C₂×C₄×C₂₃	—	2	2	no	—
151	C₂×C₄×C₂₃	—	2	2	no	—
152	C₂×C₄×C₂₃	—	2	4	no	—
153	C₂×C₄×C₂₃	—	2	4	no	—
154	C₂×C₄×C₂₃	—	2	4	no	—
155	C₂×C₄×C₂₃	—	4	2	no	—
156	C₂×C₄×C₂₃	—	4	2	no	—
157	C₂×C₄×C₂₃	—	4	8	no	—
158	C₂×C₄×C₂₃	—	4	4	no	—
159	C₂×C₄×C₂₃	#103	1	8	yes	—
160	C₂×C₄×C₂₃	#103	1	4	yes	—
161	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
162	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
164	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₂₃	C₂×M₁₆	1	4	yes	—
168	C₂×C₄×C₂₃	C₂×SD₁₆	1	2	yes	—
169	C₂×C₄×C₂₃	C₂×SD₁₆	1	4	yes	—
170	C₂×C₄×C₂₃	C₂×Q₁₆	1	4	yes	—
171	C₂×C₄×C₂₃	C₂×Q₁₆	1	2	yes	—
172	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
175	C₈×C₂₃	—	4	4	no	—
176	C₈×C₂₃	—	4	4	no	—
177	C₂²×C₄×Q₈	C₂×C₂₃	1	1	yes	characteristic
178	C₂×#431	C₂×C₂₃	1	1	yes	characteristic
179	C₂×#423	C₂×C₂₃	1	1	yes	characteristic
180	#1487	C₂×C₂₃	1	8	yes	direct product factor
181	C₂×Q₈⋊C₈	C₂×C₂₃	1	4	yes	complemented
182	C₂²×C₂₃	—	2	2	no	—
183	C₂²×C₂₃	—	2	2	no	—
184	C₂²×C₂₃	—	2	8	no	—
185	C₂²×C₂₃	#407	1	2	yes	—
186	C₂²×C₂₃	C₂×#103	1	4	yes	—
187	C₂²×C₂₃	C₂×#103	1	2	yes	—
188	C₂²×C₂₃	#421	1	2	yes	—
189	C₂²×C₂₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
190	C₄×C₂₃	—	2	8	no	—
191	C₄×C₂₃	—	2	2	no	—
192	C₄×C₂₃	—	2	1	no	—
193	C₄×C₂₃	—	2	1	no	—
194	C₄×C₂₃	—	2	2	no	—
195	C₄×C₂₃	—	4	4	no	—
196	C₄×C₂₃	#407	1	2	yes	—
197	C₄×C₂₃	C₂×#103	1	4	yes	—
198	C₄×C₂₃	C₂×#103	1	2	yes	—
199	C₄×C₂₃	C₂²×M₁₆	1	2	yes	—
200	C₄×C₂₃	C₂²×SD₁₆	1	1	yes	characteristic
201	C₄×C₂₃	C₂²×Q₁₆	1	1	yes	characteristic
202	C₂³×Q₈	C₄×C₂₃	1	1	yes	characteristic
203	C₂²×M₁₆	—	2	1	no	—
204	C₂×C₄×Q₈	—	2	1	no	—
205	C₂×C₄×Q₈	—	2	2	no	—
206	C₂×C₄×Q₈	—	2	1	no	—
207	C₂×C₄×Q₈	—	2	2	no	—
208	C₂×C₄×Q₈	C₄×C₂₃	1	4	yes	—
209	C₂×C₄×Q₈	C₄×C₂₃	1	2	yes	—
210	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
211	C₂×C₄×Q₈	C₂²×C₂₃	1	4	yes	—
212	C₂²×C₄⋊C₄	—	2	1	no	—
213	C₂²×C₄⋊C₄	C₄×C₂₃	1	1	yes	characteristic
214	C₂²×C₄²	—	2	1	no	—
215	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
216	#431	—	2	2	no	—
217	#431	C₂²×C₂₃	1	4	yes	—
218	#423	—	2	2	no	—
219	#423	C₂²×C₂₃	1	4	yes	—
220	C₂×C₄⋊C₈	—	2	1	no	—
221	C₂×C₄⋊C₈	—	2	1	no	—
222	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
223	C₂×C₂²⋊C₈	—	2	1	no	—
224	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
225	Q₈⋊C₈	C₂²×C₂₃	1	16	yes	complemented
226	C₂×C₂₃	—	2	4	no	—
227	C₂×C₂₃	#1487	1	4	yes	direct product factor
228	C₂×C₂₃	C₂×#407	1	1	yes	characteristic
229	C₂×C₂₃	C₂²×#103	1	1	yes	characteristic
230	C₂×C₂₃	C₂×#421	1	1	yes	characteristic
231	C₂²×Q₈	—	2	8	no	—
232	C₂²×Q₈	—	2	2	no	—
233	C₂²×Q₈	—	2	1	no	—
234	C₂²×Q₈	C₂×C₄×C₂₃	1	4	yes	—
235	C₂²×Q₈	C₂×C₄×C₂₃	1	2	yes	—
236	C₂³×C₄	—	2	1	no	—
237	C₂³×C₄	—	2	1	no	—
238	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
239	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
240	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
241	C₂×M₁₆	—	2	4	no	—
242	C₂×M₁₆	—	4	4	no	—
243	C₂²×C₈	—	2	2	no	—
244	C₂²×C₈	—	2	2	no	—
245	C₄×Q₈	—	2	4	no	—
246	C₄×Q₈	—	2	4	no	—
247	C₄×Q₈	—	2	4	no	—
248	C₄×Q₈	—	2	2	no	—
249	C₄×Q₈	—	2	4	no	—
250	C₄×Q₈	—	2	2	no	—
251	C₄×Q₈	—	2	4	no	—
252	C₄×Q₈	C₂×C₄×C₂₃	1	4	yes	—
253	C₄×Q₈	C₂×C₄×C₂₃	1	8	yes	—
254	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	4	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	4	no	—
261	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	4	yes	—
262	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
263	C₂×C₄²	—	2	4	no	—
264	C₂×C₄²	—	2	2	no	—
265	C₂×C₄²	—	2	2	no	—
266	C₂×C₄²	—	2	4	no	—
267	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
268	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
269	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
270	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
271	C₂×C₄²	D₄×C₂₃	1	2	yes	—
272	C₂×C₄²	D₄×C₂₃	1	2	yes	—
273	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
274	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
275	C₄⋊C₈	—	2	4	no	—
276	C₄⋊C₈	—	2	4	no	—
277	C₄⋊C₈	—	2	2	no	—
278	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
279	C₂²⋊C₈	—	2	4	no	—
280	C₄×C₈	—	2	2	no	—
281	C₄×C₈	C₂³×C₂₃	1	4	yes	—
282	C₂₃	C₂×#1487	1	1	yes	characteristic, direct product factor, Sylow
283	C₂⁴	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
284	C₂×Q₈	—	2	16	no	—
285	C₂×Q₈	—	2	8	no	—
286	C₂×Q₈	—	2	16	no	—
287	C₂×Q₈	—	2	4	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	2	4	no	—
290	C₂×Q₈	M₁₆×C₂₃	1	8	yes	complemented
291	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
292	C₂²×C₄	—	2	8	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	—	4	4	no	—
300	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
301	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
302	C₂²×C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
303	C₂²×C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
304	C₂²×C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
305	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
306	C₂²×C₄	SD₁₆×C₂₃	1	4	yes	—
307	C₂²×C₄	Q₁₆×C₂₃	1	4	yes	—
308	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
309	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
310	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
312	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
314	M₁₆	—	4	8	no	—
315	C₂×C₈	—	2	4	no	—
316	C₂×C₈	—	2	4	no	—
317	C₂×C₈	—	4	4	no	—
318	C₂×C₈	—	4	4	no	—
319	C₄⋊C₄	—	2	8	no	—
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
325	C₄²	—	2	4	no	—
326	C₄²	—	2	8	no	—
327	C₄²	—	2	4	no	—
328	C₄²	C₂²⋊C₄×C₂₃	1	2	yes	—
329	C₄²	C₂²⋊C₄×C₂₃	1	2	yes	—
330	C₄²	C₂²⋊C₄×C₂₃	1	2	yes	—
331	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
332	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
333	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
334	C₄²	C₂×D₄×C₂₃	1	2	yes	—
335	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
336	C₄²	C₂×D₄×C₂₃	1	2	yes	—
337	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
338	C₂³	—	2	2	no	—
339	C₂³	—	2	2	no	—
340	C₂³	C₂₃×#103	1	4	yes	—
341	C₂³	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
342	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
343	Q₈	—	2	16	no	—
344	Q₈	—	2	4	no	—
345	Q₈	—	2	8	no	—
346	Q₈	C₂×M₁₆×C₂₃	1	8	yes	complemented
347	C₂×C₄	—	2	16	no	—
348	C₂×C₄	—	2	8	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	8	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	C₂₃×#103	1	8	yes	—
361	C₂×C₄	C₂₃×#103	1	4	yes	—
362	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
363	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
364	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
365	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
366	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
367	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
368	C₂×C₄	C₂×M₁₆×C₂₃	1	4	yes	—
369	C₂×C₄	C₂×SD₁₆×C₂₃	1	2	yes	—
370	C₂×C₄	C₂×SD₁₆×C₂₃	1	4	yes	—
371	C₂×C₄	C₂×Q₁₆×C₂₃	1	4	yes	—
372	C₂×C₄	C₂×Q₁₆×C₂₃	1	2	yes	—
373	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
374	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
375	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
376	C₈	—	4	4	no	—
377	C₈	—	4	4	no	—
378	C₂²	—	2	8	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	C₂₃×#407	1	2	yes	—
382	C₂²	C₂×C₂₃×#103	1	4	yes	—
383	C₂²	C₂×C₂₃×#103	1	2	yes	—
384	C₂²	C₂₃×#421	1	2	yes	—
385	C₂²	C₂²×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
386	C₄	—	2	8	no	—
387	C₄	—	2	2	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	2	no	—
391	C₄	—	4	4	no	—
392	C₄	C₂₃×#407	1	2	yes	—
393	C₄	C₂×C₂₃×#103	1	2	yes	—
394	C₄	C₂×C₂₃×#103	1	4	yes	—
395	C₄	C₂²×M₁₆×C₂₃	1	2	yes	—
396	C₄	C₂²×SD₁₆×C₂₃	1	1	yes	characteristic
397	C₄	C₂²×Q₁₆×C₂₃	1	1	yes	characteristic
398	C₂	—	2	4	no	—
399	C₂	C₂₃×#1487	1	4	yes	direct product factor
400	C₂	C₂×C₂₃×#407	1	1	yes	characteristic
401	C₂	C₂²×C₂₃×#103	1	1	yes	characteristic
402	C₂	C₂×C₂₃×#421	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₂₃×#1487	C₂	direct (N × H)
5. C₂×C₂₃×Q₈⋊C₈	C₂	semidirect
29. C₂₃×Q₈⋊C₈	C₂²	semidirect
88. C₂×Q₈×C₂₃	M₁₆	semidirect
136. C₂×#1487	C₂₃	direct (N × H)
145. Q₈×C₂₃	C₂×M₁₆	semidirect
180. #1487	C₂×C₂₃	direct (N × H)
181. C₂×Q₈⋊C₈	C₂×C₂₃	semidirect
225. Q₈⋊C₈	C₂²×C₂₃	semidirect
227. C₂×C₂₃	#1487	direct (N × H)
282. C₂₃	C₂×#1487	direct (N × H)
290. C₂×Q₈	M₁₆×C₂₃	semidirect
346. Q₈	C₂×M₁₆×C₂₃	semidirect
399. C₂	C₂₃×#1487	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×Q₈×C₂₃	2
C₂×C₂₃×#431	2
C₂×C₂₃×#423	2
C₂₃×#1487	2
C₂×C₂₃×Q₈⋊C₈	2
C₂×#1487	23

Subgroups — C2×C23×#1487 #19165067

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#1487 #19165067