Subgroups — C₂×C₂₃×#1627 #19166114

Order 5888.

1290 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#486	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#459	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#1627	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₂₃×#332	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×Q₈×C₂₃	—	2	1	no	—
10	C₂²×SD₁₆×C₂₃	—	2	1	no	—
11	C₂²×D₈×C₂₃	—	2	1	no	—
12	D₄×Q₈×C₂₃	—	2	2	no	—
13	D₄×Q₈×C₂₃	—	2	2	no	—
14	D₄×Q₈×C₂₃	—	2	2	no	—
15	D₄×Q₈×C₂₃	C₂²	1	4	yes	complemented
16	C₂×C₂₃×C₄⋊Q₈	—	2	1	no	—
17	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
20	C₂×C₂₃×C₂²⋊Q₈	—	2	2	no	—
21	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₂₃	—	2	1	no	—
23	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
24	C₂₃×#486	—	2	2	no	—
25	C₂₃×#486	C₂²	1	4	yes	complemented
26	C₂₃×#460	—	2	2	no	—
27	C₂₃×#460	C₂²	1	4	yes	complemented
28	C₂₃×#459	—	2	2	no	—
29	C₂₃×#459	C₂²	1	4	yes	—
30	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×#102	—	2	1	no	—
33	C₂×C₂₃×#102	—	2	1	no	—
34	C₂×C₂₃×#102	—	2	2	no	—
35	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
36	C₂₃×#332	C₂²	1	4	yes	complemented
37	C₂₃×Q₈⋊C₈	C₂²	1	4	yes	complemented
38	C₂₃×D₄⋊C₈	C₂²	1	4	yes	complemented
39	C₂²×Q₈×C₂₃	—	2	4	no	—
40	C₂²×Q₈×C₂₃	—	2	2	no	—
41	C₂²×Q₈×C₂₃	—	2	4	no	—
42	C₂²×Q₈×C₂₃	—	2	1	no	—
43	C₂²×Q₈×C₂₃	—	4	4	no	—
44	C₂²×Q₈×C₂₃	—	4	4	no	—
45	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
46	C₂²×D₄×C₂₃	—	2	1	no	—
47	C₂²×D₄×C₂₃	—	2	1	no	—
48	C₂²×D₄×C₂₃	—	2	1	no	—
49	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₂₃	—	2	2	no	—
51	C₂³×C₄×C₂₃	—	2	1	no	—
52	C₂×SD₁₆×C₂₃	—	2	4	no	—
53	C₂×SD₁₆×C₂₃	—	4	4	no	—
54	C₂×D₈×C₂₃	—	2	4	no	—
55	C₂×D₈×C₂₃	—	4	4	no	—
56	C₂²×C₈×C₂₃	—	2	1	no	—
57	C₂²×C₈×C₂₃	—	2	1	no	—
58	C₂²×C₈×C₂₃	—	2	1	no	—
59	C₂₃×C₄⋊Q₈	—	2	4	no	—
60	C₂₃×C₄⋊Q₈	—	2	4	no	—
61	C₂₃×C₄⋊Q₈	—	2	1	no	—
62	C₂₃×C₄⋊Q₈	—	2	1	no	—
63	C₂₃×C₄⋊Q₈	D₄	1	2	yes	—
64	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
65	C₂₃×#127	—	2	1	no	—
66	C₂₃×#127	—	2	1	no	—
67	C₂₃×#127	—	2	1	no	—
68	C₂₃×#127	C₂³	1	2	yes	—
69	C₂₃×C₂²⋊Q₈	—	2	4	no	—
70	C₂₃×C₂²⋊Q₈	—	2	8	no	—
71	C₂₃×C₂²⋊Q₈	—	2	4	no	—
72	C₂₃×C₂²⋊Q₈	—	2	8	no	—
73	C₄×Q₈×C₂₃	—	2	1	no	—
74	C₄×Q₈×C₂₃	—	2	1	no	—
75	C₄×Q₈×C₂₃	D₄	1	2	yes	—
76	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
77	C₄×D₄×C₂₃	—	2	4	no	—
78	C₄×D₄×C₂₃	—	2	4	no	—
79	C₄×D₄×C₂₃	—	2	1	no	—
80	C₄×D₄×C₂₃	—	2	1	no	—
81	C₄×D₄×C₂₃	D₄	1	2	yes	—
82	C₄×D₄×C₂₃	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
84	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
85	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
86	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
89	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
91	C₂×C₄²×C₂₃	—	2	1	no	—
92	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
93	C₂₃×C₄⋊C₈	—	2	1	no	—
94	C₂₃×C₄⋊C₈	—	2	1	no	—
95	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
96	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
97	C₂₃×#102	—	2	4	no	—
98	C₂₃×#102	—	2	4	no	—
99	C₂₃×#102	—	2	8	no	—
100	C₄×C₈×C₂₃	—	2	1	no	—
101	C₄×C₈×C₂₃	C₂³	1	2	yes	—
102	C₂⁴×C₂₃	—	2	1	no	—
103	C₂⁴×C₂₃	—	4	1	no	—
104	C₂×Q₈×C₂₃	—	2	8	no	—
105	C₂×Q₈×C₂₃	—	2	1	no	—
106	C₂×Q₈×C₂₃	—	2	2	no	—
107	C₂×Q₈×C₂₃	—	2	2	no	—
108	C₂×Q₈×C₂₃	—	2	2	no	—
109	C₂×Q₈×C₂₃	—	4	8	no	—
110	C₂×Q₈×C₂₃	—	4	8	no	—
111	C₂×Q₈×C₂₃	—	4	16	no	—
112	C₂×Q₈×C₂₃	—	4	8	no	—
113	C₂×Q₈×C₂₃	—	4	2	no	—
114	C₂×Q₈×C₂₃	—	4	2	no	—
115	C₂×Q₈×C₂₃	D₈	1	4	yes	complemented
116	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
117	C₂×D₄×C₂₃	—	2	1	no	—
118	C₂×D₄×C₂₃	—	2	2	no	—
119	C₂×D₄×C₂₃	—	2	2	no	—
120	C₂×D₄×C₂₃	—	2	2	no	—
121	C₂×D₄×C₂₃	—	2	2	no	—
122	C₂×D₄×C₂₃	—	4	4	no	—
123	C₂×D₄×C₂₃	—	4	1	no	—
124	C₂×D₄×C₂₃	—	4	1	no	—
125	C₂×D₄×C₂₃	—	4	1	no	—
126	C₂×D₄×C₂₃	—	4	2	no	—
127	C₂×D₄×C₂₃	—	4	2	no	—
128	C₂×D₄×C₂₃	—	4	2	no	—
129	C₂×D₄×C₂₃	—	4	2	no	—
130	C₂×D₄×C₂₃	SD₁₆	1	4	yes	complemented
131	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₂₃	—	2	1	no	—
133	C₂²×C₄×C₂₃	—	2	8	no	—
134	C₂²×C₄×C₂₃	—	2	1	no	—
135	C₂²×C₄×C₂₃	—	2	2	no	—
136	C₂²×C₄×C₂₃	—	2	1	no	—
137	C₂²×C₄×C₂₃	—	2	2	no	—
138	C₂²×C₄×C₂₃	—	2	2	no	—
139	C₂²×C₄×C₂₃	—	4	8	no	—
140	C₂²×C₄×C₂₃	—	4	2	no	—
141	C₂²×C₄×C₂₃	—	4	2	no	—
142	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
145	SD₁₆×C₂₃	—	4	8	no	—
146	D₈×C₂₃	—	4	8	no	—
147	C₂×C₈×C₂₃	—	2	2	no	—
148	C₂×C₈×C₂₃	—	2	2	no	—
149	C₂×C₈×C₂₃	—	2	2	no	—
150	C₂×C₈×C₂₃	—	4	2	no	—
151	C₂×C₈×C₂₃	—	4	2	no	—
152	C₂×C₈×C₂₃	—	4	2	no	—
153	C₄⋊C₄×C₂₃	—	2	8	no	—
154	C₄⋊C₄×C₂₃	—	2	2	no	—
155	C₄⋊C₄×C₂₃	—	2	2	no	—
156	C₄⋊C₄×C₂₃	—	2	1	no	—
157	C₄⋊C₄×C₂₃	—	2	1	no	—
158	C₄⋊C₄×C₂₃	—	2	2	no	—
159	C₄⋊C₄×C₂₃	—	2	2	no	—
160	C₄⋊C₄×C₂₃	—	2	2	no	—
161	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
162	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
163	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
164	C₂²⋊C₄×C₂₃	—	2	8	no	—
165	C₂²⋊C₄×C₂₃	—	2	2	no	—
166	C₂²⋊C₄×C₂₃	—	2	2	no	—
167	C₄²×C₂₃	—	2	2	no	—
168	C₄²×C₂₃	—	2	2	no	—
169	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
173	C₂×#1627	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂³×C₂₃	—	2	2	no	—
175	C₂³×C₂₃	—	2	4	no	—
176	C₂³×C₂₃	—	4	2	no	—
177	C₂³×C₂₃	—	4	2	no	—
178	C₂³×C₂₃	—	4	2	no	—
179	C₂³×C₂₃	—	8	2	no	—
180	C₂³×C₂₃	—	8	2	no	—
181	C₂³×C₂₃	—	8	2	no	—
182	C₂³×C₂₃	#120	1	1	yes	characteristic
183	Q₈×C₂₃	—	2	2	no	—
184	Q₈×C₂₃	—	2	4	no	—
185	Q₈×C₂₃	—	4	16	no	—
186	Q₈×C₂₃	—	4	2	no	—
187	Q₈×C₂₃	—	4	2	no	—
188	Q₈×C₂₃	—	4	4	no	—
189	Q₈×C₂₃	C₂×D₈	1	4	yes	complemented
190	D₄×C₂₃	—	2	2	no	—
191	D₄×C₂₃	—	2	4	no	—
192	D₄×C₂₃	—	4	4	no	—
193	D₄×C₂₃	—	4	2	no	—
194	D₄×C₂₃	—	4	2	no	—
195	D₄×C₂₃	—	4	2	no	—
196	D₄×C₂₃	—	4	2	no	—
197	D₄×C₂₃	—	8	2	no	—
198	D₄×C₂₃	—	8	2	no	—
199	D₄×C₂₃	—	8	2	no	—
200	D₄×C₂₃	C₂×SD₁₆	1	4	yes	complemented
201	C₂×C₄×C₂₃	—	2	2	no	—
202	C₂×C₄×C₂₃	—	2	4	no	—
203	C₂×C₄×C₂₃	—	2	2	no	—
204	C₂×C₄×C₂₃	—	2	2	no	—
205	C₂×C₄×C₂₃	—	2	4	no	—
206	C₂×C₄×C₂₃	—	2	2	no	—
207	C₂×C₄×C₂₃	—	4	16	no	—
208	C₂×C₄×C₂₃	—	4	4	no	—
209	C₂×C₄×C₂₃	—	4	2	no	—
210	C₂×C₄×C₂₃	—	4	2	no	—
211	C₂×C₄×C₂₃	—	4	2	no	—
212	C₂×C₄×C₂₃	—	4	2	no	—
213	C₂×C₄×C₂₃	—	4	4	no	—
214	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
215	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
216	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
217	C₂×C₄×C₂₃	C₂×D₈	1	2	yes	—
218	C₂×C₄×C₂₃	C₂×SD₁₆	1	2	yes	—
219	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
220	C₂×C₄×C₂₃	#137	1	2	yes	—
221	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
224	C₈×C₂₃	—	4	2	no	—
225	C₈×C₂₃	—	4	2	no	—
226	C₈×C₂₃	—	4	2	no	—
227	C₂×D₄×Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
228	C₂×#486	C₂×C₂₃	1	1	yes	characteristic, complemented
229	C₂×#460	C₂×C₂₃	1	1	yes	characteristic, complemented
230	C₂×#459	C₂×C₂₃	1	1	yes	characteristic
231	#1627	C₂×C₂₃	1	8	yes	direct product factor
232	C₂×#332	C₂×C₂₃	1	1	yes	characteristic, complemented
233	C₂×Q₈⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
234	C₂×D₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
235	C₂²×C₂₃	—	2	4	no	—
236	C₂²×C₂₃	—	4	8	no	—
237	C₂²×C₂₃	—	4	2	no	—
238	C₂²×C₂₃	—	4	2	no	—
239	C₂²×C₂₃	—	8	2	no	—
240	C₂²×C₂₃	—	8	2	no	—
241	C₂²×C₂₃	—	8	2	no	—
242	C₂²×C₂₃	—	16	4	no	—
243	C₂²×C₂₃	#447	1	2	yes	—
244	C₂²×C₂₃	#448	1	2	yes	—
245	C₂²×C₂₃	#454	1	2	yes	—
246	C₂²×C₂₃	C₂×#120	1	1	yes	characteristic
247	C₄×C₂₃	—	2	4	no	—
248	C₄×C₂₃	—	2	1	no	—
249	C₄×C₂₃	—	2	1	no	—
250	C₄×C₂₃	—	4	4	no	—
251	C₄×C₂₃	—	4	2	no	—
252	C₄×C₂₃	—	4	2	no	—
253	C₄×C₂₃	#447	1	2	yes	—
254	C₄×C₂₃	#448	1	2	yes	—
255	C₄×C₂₃	C₂²×D₈	1	1	yes	characteristic
256	C₄×C₂₃	C₂²×SD₁₆	1	1	yes	characteristic
257	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
258	C₄×C₂₃	C₂×#137	1	1	yes	characteristic
259	C₂³×Q₈	—	2	1	no	—
260	C₂²×SD₁₆	—	2	1	no	—
261	C₂²×D₈	—	2	1	no	—
262	D₄×Q₈	—	2	2	no	—
263	D₄×Q₈	—	2	2	no	—
264	D₄×Q₈	—	2	2	no	—
265	D₄×Q₈	C₂²×C₂₃	1	4	yes	complemented
266	C₂×C₄⋊Q₈	—	2	1	no	—
267	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
268	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
269	C₂×C₂²⋊Q₈	—	2	1	no	—
270	C₂×C₂²⋊Q₈	—	2	2	no	—
271	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
272	C₂×C₄×D₄	—	2	1	no	—
273	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
274	#486	—	2	2	no	—
275	#486	C₂²×C₂₃	1	4	yes	complemented
276	#460	—	2	2	no	—
277	#460	C₂²×C₂₃	1	4	yes	complemented
278	#459	—	2	2	no	—
279	#459	C₂²×C₂₃	1	4	yes	—
280	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
281	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
282	C₂×#102	—	2	2	no	—
283	C₂×#102	—	2	1	no	—
284	C₂×#102	—	2	1	no	—
285	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
286	#332	C₂²×C₂₃	1	4	yes	complemented
287	Q₈⋊C₈	C₂²×C₂₃	1	4	yes	complemented
288	D₄⋊C₈	C₂²×C₂₃	1	4	yes	complemented
289	C₂×C₂₃	—	4	4	no	—
290	C₂×C₂₃	—	16	2	no	—
291	C₂×C₂₃	#1627	1	4	yes	direct product factor
292	C₂×C₂₃	C₂×#447	1	1	yes	characteristic
293	C₂×C₂₃	C₂×#448	1	1	yes	characteristic
294	C₂×C₂₃	C₂×#454	1	1	yes	characteristic
295	C₂²×Q₈	—	2	2	no	—
296	C₂²×Q₈	—	2	4	no	—
297	C₂²×Q₈	—	2	4	no	—
298	C₂²×Q₈	—	2	1	no	—
299	C₂²×Q₈	—	4	4	no	—
300	C₂²×Q₈	—	4	4	no	—
301	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
302	C₂²×D₄	—	2	1	no	—
303	C₂²×D₄	—	2	1	no	—
304	C₂²×D₄	—	2	1	no	—
305	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
306	C₂³×C₄	—	2	2	no	—
307	C₂³×C₄	—	2	1	no	—
308	C₂×SD₁₆	—	2	4	no	—
309	C₂×SD₁₆	—	4	4	no	—
310	C₂×D₈	—	2	4	no	—
311	C₂×D₈	—	4	4	no	—
312	C₂²×C₈	—	2	1	no	—
313	C₂²×C₈	—	2	1	no	—
314	C₂²×C₈	—	2	1	no	—
315	C₄⋊Q₈	—	2	4	no	—
316	C₄⋊Q₈	—	2	4	no	—
317	C₄⋊Q₈	—	2	1	no	—
318	C₄⋊Q₈	—	2	1	no	—
319	C₄⋊Q₈	D₄×C₂₃	1	2	yes	—
320	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
321	#127	—	2	1	no	—
322	#127	—	2	1	no	—
323	#127	—	2	1	no	—
324	#127	C₂³×C₂₃	1	2	yes	—
325	C₂²⋊Q₈	—	2	4	no	—
326	C₂²⋊Q₈	—	2	8	no	—
327	C₂²⋊Q₈	—	2	4	no	—
328	C₂²⋊Q₈	—	2	8	no	—
329	C₄×Q₈	—	2	1	no	—
330	C₄×Q₈	—	2	1	no	—
331	C₄×Q₈	D₄×C₂₃	1	2	yes	—
332	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
333	C₄×D₄	—	2	4	no	—
334	C₄×D₄	—	2	4	no	—
335	C₄×D₄	—	2	1	no	—
336	C₄×D₄	—	2	1	no	—
337	C₄×D₄	D₄×C₂₃	1	2	yes	—
338	C₄×D₄	C₂³×C₂₃	1	2	yes	—
339	C₂×C₄⋊C₄	—	2	2	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
343	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
344	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
345	C₂×C₂²⋊C₄	—	2	2	no	—
346	C₂×C₂²⋊C₄	—	2	1	no	—
347	C₂×C₄²	—	2	1	no	—
348	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
349	C₄⋊C₈	—	2	1	no	—
350	C₄⋊C₈	—	2	1	no	—
351	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
352	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
353	#102	—	2	4	no	—
354	#102	—	2	4	no	—
355	#102	—	2	8	no	—
356	C₄×C₈	—	2	1	no	—
357	C₄×C₈	C₂³×C₂₃	1	2	yes	—
358	C₂₃	C₂×#1627	1	1	yes	characteristic, direct product factor, Sylow
359	C₂⁴	—	2	1	no	—
360	C₂⁴	—	4	1	no	—
361	C₂×Q₈	—	2	8	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	—	4	8	no	—
367	C₂×Q₈	—	4	8	no	—
368	C₂×Q₈	—	4	16	no	—
369	C₂×Q₈	—	4	8	no	—
370	C₂×Q₈	—	4	2	no	—
371	C₂×Q₈	—	4	2	no	—
372	C₂×Q₈	D₈×C₂₃	1	4	yes	complemented
373	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	4	4	no	—
380	C₂×D₄	—	4	1	no	—
381	C₂×D₄	—	4	1	no	—
382	C₂×D₄	—	4	1	no	—
383	C₂×D₄	—	4	2	no	—
384	C₂×D₄	—	4	2	no	—
385	C₂×D₄	—	4	2	no	—
386	C₂×D₄	—	4	2	no	—
387	C₂×D₄	SD₁₆×C₂₃	1	4	yes	complemented
388	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	8	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	4	8	no	—
397	C₂²×C₄	—	4	2	no	—
398	C₂²×C₄	—	4	2	no	—
399	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
401	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
402	SD₁₆	—	4	8	no	—
403	D₈	—	4	8	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	4	2	no	—
408	C₂×C₈	—	4	2	no	—
409	C₂×C₈	—	4	2	no	—
410	C₄⋊C₄	—	2	8	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
419	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
420	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
421	C₂²⋊C₄	—	2	8	no	—
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	2	2	no	—
426	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
427	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
428	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
429	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
430	C₂³	—	2	4	no	—
431	C₂³	—	2	2	no	—
432	C₂³	—	4	2	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	4	2	no	—
435	C₂³	—	8	2	no	—
436	C₂³	—	8	2	no	—
437	C₂³	—	8	2	no	—
438	C₂³	C₂₃×#120	1	1	yes	characteristic
439	Q₈	—	2	2	no	—
440	Q₈	—	2	4	no	—
441	Q₈	—	4	16	no	—
442	Q₈	—	4	2	no	—
443	Q₈	—	4	2	no	—
444	Q₈	—	4	4	no	—
445	Q₈	C₂×D₈×C₂₃	1	4	yes	complemented
446	D₄	—	2	2	no	—
447	D₄	—	2	4	no	—
448	D₄	—	4	4	no	—
449	D₄	—	4	2	no	—
450	D₄	—	4	2	no	—
451	D₄	—	4	2	no	—
452	D₄	—	4	2	no	—
453	D₄	—	8	2	no	—
454	D₄	—	8	2	no	—
455	D₄	—	8	2	no	—
456	D₄	C₂×SD₁₆×C₂₃	1	4	yes	complemented
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	4	16	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	4	no	—
470	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
471	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
472	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
473	C₂×C₄	C₂×D₈×C₂₃	1	2	yes	—
474	C₂×C₄	C₂×SD₁₆×C₂₃	1	2	yes	—
475	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
476	C₂×C₄	C₂₃×#137	1	2	yes	—
477	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
478	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
479	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
480	C₈	—	4	2	no	—
481	C₈	—	4	2	no	—
482	C₈	—	4	2	no	—
483	C₂²	—	2	4	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	8	no	—
487	C₂²	—	8	2	no	—
488	C₂²	—	8	2	no	—
489	C₂²	—	8	2	no	—
490	C₂²	—	16	4	no	—
491	C₂²	C₂₃×#447	1	2	yes	—
492	C₂²	C₂₃×#448	1	2	yes	—
493	C₂²	C₂₃×#454	1	2	yes	—
494	C₂²	C₂×C₂₃×#120	1	1	yes	characteristic
495	C₄	—	2	4	no	—
496	C₄	—	2	1	no	—
497	C₄	—	2	1	no	—
498	C₄	—	4	4	no	—
499	C₄	—	4	2	no	—
500	C₄	—	4	2	no	—
501	C₄	C₂₃×#447	1	2	yes	—
502	C₄	C₂₃×#448	1	2	yes	—
503	C₄	C₂²×D₈×C₂₃	1	1	yes	characteristic
504	C₄	C₂²×SD₁₆×C₂₃	1	1	yes	characteristic
505	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
506	C₄	C₂×C₂₃×#137	1	1	yes	characteristic
507	C₂	—	4	4	no	—
508	C₂	—	16	2	no	—
509	C₂	C₂₃×#1627	1	4	yes	direct product factor
510	C₂	C₂×C₂₃×#447	1	1	yes	characteristic
511	C₂	C₂×C₂₃×#448	1	1	yes	characteristic
512	C₂	C₂×C₂₃×#454	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₃
prime radical	C₂×C₂₃×#459	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×D₄×Q₈×C₂₃	C₂	semidirect
2. C₂×C₂₃×#486	C₂	semidirect
3. C₂×C₂₃×#460	C₂	semidirect
5. C₂₃×#1627	C₂	direct (N × H)
6. C₂×C₂₃×#332	C₂	semidirect
7. C₂×C₂₃×Q₈⋊C₈	C₂	semidirect
8. C₂×C₂₃×D₄⋊C₈	C₂	semidirect
15. D₄×Q₈×C₂₃	C₂²	semidirect
25. C₂₃×#486	C₂²	semidirect
27. C₂₃×#460	C₂²	semidirect
36. C₂₃×#332	C₂²	semidirect
37. C₂₃×Q₈⋊C₈	C₂²	semidirect
38. C₂₃×D₄⋊C₈	C₂²	semidirect
115. C₂×Q₈×C₂₃	D₈	semidirect
130. C₂×D₄×C₂₃	SD₁₆	semidirect
173. C₂×#1627	C₂₃	direct (N × H)
189. Q₈×C₂₃	C₂×D₈	semidirect
200. D₄×C₂₃	C₂×SD₁₆	semidirect
227. C₂×D₄×Q₈	C₂×C₂₃	semidirect
228. C₂×#486	C₂×C₂₃	semidirect
229. C₂×#460	C₂×C₂₃	semidirect
231. #1627	C₂×C₂₃	direct (N × H)
232. C₂×#332	C₂×C₂₃	semidirect
233. C₂×Q₈⋊C₈	C₂×C₂₃	semidirect
234. C₂×D₄⋊C₈	C₂×C₂₃	semidirect
265. D₄×Q₈	C₂²×C₂₃	semidirect
275. #486	C₂²×C₂₃	semidirect
277. #460	C₂²×C₂₃	semidirect
286. #332	C₂²×C₂₃	semidirect
287. Q₈⋊C₈	C₂²×C₂₃	semidirect
288. D₄⋊C₈	C₂²×C₂₃	semidirect
291. C₂×C₂₃	#1627	direct (N × H)
358. C₂₃	C₂×#1627	direct (N × H)
372. C₂×Q₈	D₈×C₂₃	semidirect
387. C₂×D₄	SD₁₆×C₂₃	semidirect
445. Q₈	C₂×D₈×C₂₃	semidirect
456. D₄	C₂×SD₁₆×C₂₃	semidirect
509. C₂	C₂₃×#1627	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×D₄×Q₈×C₂₃	2
C₂×C₂₃×#486	2
C₂×C₂₃×#460	2
C₂×C₂₃×#459	2
C₂₃×#1627	2
C₂×C₂₃×#332	2
C₂×C₂₃×Q₈⋊C₈	2
C₂×C₂₃×D₄⋊C₈	2
C₂×#1627	23

Subgroups — C2×C23×#1627 #19166114

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#1627 #19166114