Subgroups — C₂×C₂₃×#1649 #19166124

Order 5888.

1206 conjugacy classes of subgroups.

The subgroup lattice has 482 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
2	C₂×C₂₃×#500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#474	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1649	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
9	C₂³×Q₈×C₂₃	—	2	1	no	—
10	C₂²×Q₁₆×C₂₃	—	2	1	no	—
11	D₄×Q₈×C₂₃	—	2	2	no	—
12	D₄×Q₈×C₂₃	—	2	2	no	—
13	D₄×Q₈×C₂₃	—	2	2	no	—
14	D₄×Q₈×C₂₃	C₂²	1	4	yes	—
15	C₂×C₂₃×C₄⋊Q₈	—	2	1	no	—
16	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
19	C₂×C₂₃×C₂²⋊Q₈	—	2	2	no	—
20	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₂₃	—	2	1	no	—
22	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
23	C₂₃×#500	—	2	2	no	—
24	C₂₃×#500	C₂²	1	4	yes	complemented
25	C₂₃×#474	—	2	2	no	—
26	C₂₃×#474	C₂²	1	4	yes	—
27	C₂₃×#462	—	2	2	no	—
28	C₂₃×#462	C₂²	1	4	yes	complemented
29	C₂×C₂₃×#107	—	2	1	no	—
30	C₂×C₂₃×#107	—	2	2	no	—
31	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×#103	—	2	1	no	—
34	C₂×C₂₃×#102	—	2	1	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	—
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	—	2	1	no	—
44	C₂²×Q₈×C₂₃	—	4	4	no	—
45	C₂²×Q₈×C₂₃	—	4	4	no	—
46	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
47	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₂₃	—	2	2	no	—
49	C₂³×C₄×C₂₃	—	2	1	no	—
50	C₂×Q₁₆×C₂₃	—	2	4	no	—
51	C₂×Q₁₆×C₂₃	—	4	4	no	—
52	C₂²×C₈×C₂₃	—	2	1	no	—
53	C₂²×C₈×C₂₃	—	2	1	no	—
54	C₂²×C₈×C₂₃	—	2	1	no	—
55	C₂₃×C₄⋊Q₈	—	2	4	no	—
56	C₂₃×C₄⋊Q₈	—	2	4	no	—
57	C₂₃×C₄⋊Q₈	—	2	1	no	—
58	C₂₃×C₄⋊Q₈	—	2	1	no	—
59	C₂₃×C₄⋊Q₈	—	2	1	no	—
60	C₂₃×C₄⋊Q₈	—	2	1	no	—
61	C₂₃×C₄⋊Q₈	—	2	1	no	—
62	C₂₃×C₄⋊Q₈	D₄	1	2	yes	—
63	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
64	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
65	C₂₃×C₂²⋊Q₈	—	2	4	no	—
66	C₂₃×C₂²⋊Q₈	—	2	8	no	—
67	C₂₃×C₂²⋊Q₈	—	2	4	no	—
68	C₂₃×C₂²⋊Q₈	—	2	8	no	—
69	C₄×Q₈×C₂₃	—	2	1	no	—
70	C₄×Q₈×C₂₃	—	2	1	no	—
71	C₄×Q₈×C₂₃	D₄	1	2	yes	—
72	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
73	C₄×D₄×C₂₃	—	2	4	no	—
74	C₄×D₄×C₂₃	—	2	4	no	—
75	C₄×D₄×C₂₃	—	2	1	no	—
76	C₄×D₄×C₂₃	—	2	1	no	—
77	C₄×D₄×C₂₃	D₄	1	2	yes	—
78	C₄×D₄×C₂₃	C₂³	1	2	yes	—
79	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
80	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
81	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
82	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
83	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
84	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
87	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
89	C₂×C₄²×C₂₃	—	2	1	no	—
90	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
91	C₂₃×#107	—	2	4	no	—
92	C₂₃×#107	—	2	8	no	—
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×#103	—	2	4	no	—
98	C₂₃×#102	—	2	4	no	—
99	C₄×C₈×C₂₃	—	2	1	no	—
100	C₄×C₈×C₂₃	C₂³	1	2	yes	—
101	C₂⁴×C₂₃	—	2	1	no	—
102	C₂×Q₈×C₂₃	—	2	8	no	—
103	C₂×Q₈×C₂₃	—	2	1	no	—
104	C₂×Q₈×C₂₃	—	2	2	no	—
105	C₂×Q₈×C₂₃	—	2	2	no	—
106	C₂×Q₈×C₂₃	—	2	2	no	—
107	C₂×Q₈×C₂₃	—	2	2	no	—
108	C₂×Q₈×C₂₃	—	4	8	no	—
109	C₂×Q₈×C₂₃	—	4	8	no	—
110	C₂×Q₈×C₂₃	—	4	16	no	—
111	C₂×Q₈×C₂₃	—	4	8	no	—
112	C₂×Q₈×C₂₃	—	4	1	no	—
113	C₂×Q₈×C₂₃	—	4	2	no	—
114	C₂×Q₈×C₂₃	—	4	2	no	—
115	C₂×Q₈×C₂₃	—	4	2	no	—
116	C₂×Q₈×C₂₃	—	4	2	no	—
117	C₂×Q₈×C₂₃	D₈	1	4	yes	—
118	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
119	C₂×D₄×C₂₃	—	2	1	no	—
120	C₂×D₄×C₂₃	—	2	2	no	—
121	C₂×D₄×C₂₃	Q₁₆	1	4	yes	complemented
122	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₂₃	—	2	1	no	—
124	C₂²×C₄×C₂₃	—	2	8	no	—
125	C₂²×C₄×C₂₃	—	2	1	no	—
126	C₂²×C₄×C₂₃	—	2	2	no	—
127	C₂²×C₄×C₂₃	—	2	1	no	—
128	C₂²×C₄×C₂₃	—	2	2	no	—
129	C₂²×C₄×C₂₃	—	2	2	no	—
130	C₂²×C₄×C₂₃	—	4	8	no	—
131	C₂²×C₄×C₂₃	—	4	2	no	—
132	C₂²×C₄×C₂₃	—	4	2	no	—
133	C₂²×C₄×C₂₃	—	4	1	no	—
134	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
137	Q₁₆×C₂₃	—	4	8	no	—
138	C₂×C₈×C₂₃	—	2	4	no	—
139	C₂×C₈×C₂₃	—	2	2	no	—
140	C₂×C₈×C₂₃	—	2	2	no	—
141	C₂×C₈×C₂₃	—	2	2	no	—
142	C₂×C₈×C₂₃	—	4	2	no	—
143	C₂×C₈×C₂₃	—	4	2	no	—
144	C₄⋊C₄×C₂₃	—	2	8	no	—
145	C₄⋊C₄×C₂₃	—	2	2	no	—
146	C₄⋊C₄×C₂₃	—	2	2	no	—
147	C₄⋊C₄×C₂₃	—	2	1	no	—
148	C₄⋊C₄×C₂₃	—	2	1	no	—
149	C₄⋊C₄×C₂₃	—	2	2	no	—
150	C₄⋊C₄×C₂₃	—	2	2	no	—
151	C₄⋊C₄×C₂₃	—	2	2	no	—
152	C₄⋊C₄×C₂₃	—	2	2	no	—
153	C₄⋊C₄×C₂₃	—	2	2	no	—
154	C₄⋊C₄×C₂₃	—	4	1	no	—
155	C₄⋊C₄×C₂₃	—	4	1	no	—
156	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
157	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
158	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
159	C₂²⋊C₄×C₂₃	—	2	8	no	—
160	C₂²⋊C₄×C₂₃	—	2	2	no	—
161	C₂²⋊C₄×C₂₃	—	2	2	no	—
162	C₄²×C₂₃	—	2	2	no	—
163	C₄²×C₂₃	—	2	2	no	—
164	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
168	C₂×#1649	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₂³×C₂₃	—	2	2	no	—
170	C₂³×C₂₃	—	2	4	no	—
171	C₂³×C₂₃	—	4	2	no	—
172	C₂³×C₂₃	—	4	2	no	—
173	C₂³×C₂₃	#120	1	1	yes	characteristic
174	Q₈×C₂₃	—	2	2	no	—
175	Q₈×C₂₃	—	2	4	no	—
176	Q₈×C₂₃	—	4	16	no	—
177	Q₈×C₂₃	—	4	2	no	—
178	Q₈×C₂₃	—	4	2	no	—
179	Q₈×C₂₃	—	4	4	no	—
180	Q₈×C₂₃	—	4	2	no	—
181	Q₈×C₂₃	—	4	2	no	—
182	Q₈×C₂₃	—	8	2	no	—
183	Q₈×C₂₃	C₂×D₈	1	4	yes	—
184	D₄×C₂₃	—	2	2	no	—
185	D₄×C₂₃	—	2	4	no	—
186	D₄×C₂₃	C₂×Q₁₆	1	4	yes	complemented
187	C₂×C₄×C₂₃	—	2	2	no	—
188	C₂×C₄×C₂₃	—	2	4	no	—
189	C₂×C₄×C₂₃	—	2	2	no	—
190	C₂×C₄×C₂₃	—	2	2	no	—
191	C₂×C₄×C₂₃	—	2	4	no	—
192	C₂×C₄×C₂₃	—	2	2	no	—
193	C₂×C₄×C₂₃	—	4	16	no	—
194	C₂×C₄×C₂₃	—	4	4	no	—
195	C₂×C₄×C₂₃	—	4	2	no	—
196	C₂×C₄×C₂₃	—	4	2	no	—
197	C₂×C₄×C₂₃	—	4	2	no	—
198	C₂×C₄×C₂₃	—	4	2	no	—
199	C₂×C₄×C₂₃	—	4	4	no	—
200	C₂×C₄×C₂₃	—	4	2	no	—
201	C₂×C₄×C₂₃	—	8	2	no	—
202	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
203	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
204	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
205	C₂×C₄×C₂₃	C₂×D₈	1	2	yes	—
206	C₂×C₄×C₂₃	C₂×Q₁₆	1	2	yes	—
207	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
208	C₂×C₄×C₂₃	#137	1	2	yes	—
209	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
212	C₈×C₂₃	—	2	4	no	—
213	C₈×C₂₃	—	4	2	no	—
214	C₈×C₂₃	—	4	2	no	—
215	C₂×D₄×Q₈	C₂×C₂₃	1	1	yes	characteristic
216	C₂×#500	C₂×C₂₃	1	1	yes	characteristic, complemented
217	C₂×#474	C₂×C₂₃	1	1	yes	characteristic
218	C₂×#462	C₂×C₂₃	1	1	yes	characteristic, complemented
219	#1649	C₂×C₂₃	1	8	yes	direct product factor
220	C₂×#332	C₂×C₂₃	1	1	yes	characteristic, complemented
221	C₂×Q₈⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
222	C₂×D₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic
223	C₂²×C₂₃	—	2	4	no	—
224	C₂²×C₂₃	—	4	8	no	—
225	C₂²×C₂₃	—	4	2	no	—
226	C₂²×C₂₃	—	4	2	no	—
227	C₂²×C₂₃	#447	1	2	yes	—
228	C₂²×C₂₃	#451	1	2	yes	—
229	C₂²×C₂₃	#456	1	2	yes	—
230	C₂²×C₂₃	C₂×#120	1	1	yes	characteristic
231	C₄×C₂₃	—	2	4	no	—
232	C₄×C₂₃	—	2	1	no	—
233	C₄×C₂₃	—	2	1	no	—
234	C₄×C₂₃	—	4	4	no	—
235	C₄×C₂₃	—	4	2	no	—
236	C₄×C₂₃	—	4	2	no	—
237	C₄×C₂₃	—	8	2	no	—
238	C₄×C₂₃	#447	1	2	yes	—
239	C₄×C₂₃	#451	1	2	yes	—
240	C₄×C₂₃	C₂²×D₈	1	1	yes	characteristic
241	C₄×C₂₃	C₂²×Q₁₆	1	1	yes	characteristic
242	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
243	C₄×C₂₃	C₂×#137	1	1	yes	characteristic
244	C₂³×Q₈	—	2	1	no	—
245	C₂²×Q₁₆	—	2	1	no	—
246	D₄×Q₈	—	2	2	no	—
247	D₄×Q₈	—	2	2	no	—
248	D₄×Q₈	—	2	2	no	—
249	D₄×Q₈	C₂²×C₂₃	1	4	yes	—
250	C₂×C₄⋊Q₈	—	2	1	no	—
251	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
252	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
253	C₂×C₂²⋊Q₈	—	2	1	no	—
254	C₂×C₂²⋊Q₈	—	2	2	no	—
255	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
256	C₂×C₄×D₄	—	2	1	no	—
257	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
258	#500	—	2	2	no	—
259	#500	C₂²×C₂₃	1	4	yes	complemented
260	#474	—	2	2	no	—
261	#474	C₂²×C₂₃	1	4	yes	—
262	#462	—	2	2	no	—
263	#462	C₂²×C₂₃	1	4	yes	complemented
264	C₂×#107	—	2	2	no	—
265	C₂×#107	—	2	1	no	—
266	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
267	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
268	C₂×#103	—	2	1	no	—
269	C₂×#102	—	2	1	no	—
270	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
271	#332	C₂²×C₂₃	1	4	yes	complemented
272	Q₈⋊C₈	C₂²×C₂₃	1	4	yes	complemented
273	D₄⋊C₈	C₂²×C₂₃	1	4	yes	—
274	C₂×C₂₃	—	4	4	no	—
275	C₂×C₂₃	#1649	1	4	yes	direct product factor
276	C₂×C₂₃	C₂×#447	1	1	yes	characteristic
277	C₂×C₂₃	C₂×#451	1	1	yes	characteristic
278	C₂×C₂₃	C₂×#456	1	1	yes	characteristic
279	C₂²×Q₈	—	2	2	no	—
280	C₂²×Q₈	—	2	4	no	—
281	C₂²×Q₈	—	2	4	no	—
282	C₂²×Q₈	—	2	1	no	—
283	C₂²×Q₈	—	2	1	no	—
284	C₂²×Q₈	—	4	4	no	—
285	C₂²×Q₈	—	4	4	no	—
286	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
287	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
288	C₂³×C₄	—	2	2	no	—
289	C₂³×C₄	—	2	1	no	—
290	C₂×Q₁₆	—	2	4	no	—
291	C₂×Q₁₆	—	4	4	no	—
292	C₂²×C₈	—	2	1	no	—
293	C₂²×C₈	—	2	1	no	—
294	C₂²×C₈	—	2	1	no	—
295	C₄⋊Q₈	—	2	4	no	—
296	C₄⋊Q₈	—	2	4	no	—
297	C₄⋊Q₈	—	2	1	no	—
298	C₄⋊Q₈	—	2	1	no	—
299	C₄⋊Q₈	—	2	1	no	—
300	C₄⋊Q₈	—	2	1	no	—
301	C₄⋊Q₈	—	2	1	no	—
302	C₄⋊Q₈	D₄×C₂₃	1	2	yes	—
303	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
304	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
305	C₂²⋊Q₈	—	2	4	no	—
306	C₂²⋊Q₈	—	2	8	no	—
307	C₂²⋊Q₈	—	2	4	no	—
308	C₂²⋊Q₈	—	2	8	no	—
309	C₄×Q₈	—	2	1	no	—
310	C₄×Q₈	—	2	1	no	—
311	C₄×Q₈	D₄×C₂₃	1	2	yes	—
312	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
313	C₄×D₄	—	2	4	no	—
314	C₄×D₄	—	2	4	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	D₄×C₂₃	1	2	yes	—
318	C₄×D₄	C₂³×C₂₃	1	2	yes	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
325	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
326	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
327	C₂×C₂²⋊C₄	—	2	2	no	—
328	C₂×C₂²⋊C₄	—	2	1	no	—
329	C₂×C₄²	—	2	1	no	—
330	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
331	#107	—	2	4	no	—
332	#107	—	2	8	no	—
333	C₄⋊C₈	—	2	1	no	—
334	C₄⋊C₈	—	2	1	no	—
335	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
336	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
337	#103	—	2	4	no	—
338	#102	—	2	4	no	—
339	C₄×C₈	—	2	1	no	—
340	C₄×C₈	C₂³×C₂₃	1	2	yes	—
341	C₂₃	C₂×#1649	1	1	yes	characteristic, direct product factor, Sylow
342	C₂⁴	—	2	1	no	—
343	C₂×Q₈	—	2	8	no	—
344	C₂×Q₈	—	2	1	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	4	8	no	—
350	C₂×Q₈	—	4	8	no	—
351	C₂×Q₈	—	4	16	no	—
352	C₂×Q₈	—	4	8	no	—
353	C₂×Q₈	—	4	1	no	—
354	C₂×Q₈	—	4	2	no	—
355	C₂×Q₈	—	4	2	no	—
356	C₂×Q₈	—	4	2	no	—
357	C₂×Q₈	—	4	2	no	—
358	C₂×Q₈	D₈×C₂₃	1	4	yes	—
359	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	Q₁₆×C₂₃	1	4	yes	complemented
363	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	8	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	4	8	no	—
372	C₂²×C₄	—	4	2	no	—
373	C₂²×C₄	—	4	2	no	—
374	C₂²×C₄	—	4	1	no	—
375	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
378	Q₁₆	—	4	8	no	—
379	C₂×C₈	—	2	4	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	4	2	no	—
384	C₂×C₈	—	4	2	no	—
385	C₄⋊C₄	—	2	8	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	4	1	no	—
396	C₄⋊C₄	—	4	1	no	—
397	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
398	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
399	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
400	C₂²⋊C₄	—	2	8	no	—
401	C₂²⋊C₄	—	2	2	no	—
402	C₂²⋊C₄	—	2	2	no	—
403	C₄²	—	2	2	no	—
404	C₄²	—	2	2	no	—
405	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
406	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
407	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
408	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
409	C₂³	—	2	4	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	4	2	no	—
413	C₂³	C₂₃×#120	1	1	yes	characteristic
414	Q₈	—	2	2	no	—
415	Q₈	—	2	4	no	—
416	Q₈	—	4	16	no	—
417	Q₈	—	4	2	no	—
418	Q₈	—	4	2	no	—
419	Q₈	—	4	4	no	—
420	Q₈	—	4	2	no	—
421	Q₈	—	4	2	no	—
422	Q₈	—	8	2	no	—
423	Q₈	C₂×D₈×C₂₃	1	4	yes	—
424	D₄	—	2	2	no	—
425	D₄	—	2	4	no	—
426	D₄	C₂×Q₁₆×C₂₃	1	4	yes	complemented
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	4	16	no	—
434	C₂×C₄	—	4	4	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	4	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	8	2	no	—
442	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
443	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
444	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
445	C₂×C₄	C₂×D₈×C₂₃	1	2	yes	—
446	C₂×C₄	C₂×Q₁₆×C₂₃	1	2	yes	—
447	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
448	C₂×C₄	C₂₃×#137	1	2	yes	—
449	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
450	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
451	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
452	C₈	—	2	4	no	—
453	C₈	—	4	2	no	—
454	C₈	—	4	2	no	—
455	C₂²	—	2	4	no	—
456	C₂²	—	4	8	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	4	2	no	—
459	C₂²	C₂₃×#447	1	2	yes	—
460	C₂²	C₂₃×#451	1	2	yes	—
461	C₂²	C₂₃×#456	1	2	yes	—
462	C₂²	C₂×C₂₃×#120	1	1	yes	characteristic
463	C₄	—	2	4	no	—
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	4	4	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	2	no	—
469	C₄	—	8	2	no	—
470	C₄	C₂₃×#447	1	2	yes	—
471	C₄	C₂₃×#451	1	2	yes	—
472	C₄	C₂²×D₈×C₂₃	1	1	yes	characteristic
473	C₄	C₂²×Q₁₆×C₂₃	1	1	yes	characteristic
474	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
475	C₄	C₂×C₂₃×#137	1	1	yes	characteristic
476	C₂	—	4	4	no	—
477	C₂	C₂₃×#1649	1	4	yes	direct product factor
478	C₂	C₂×C₂₃×#447	1	1	yes	characteristic
479	C₂	C₂×C₂₃×#451	1	1	yes	characteristic
480	C₂	C₂×C₂₃×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₃
prime radical	C₂²×D₄×C₂₃	D₄
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
2. C₂×C₂₃×#500	C₂	semidirect
4. C₂×C₂₃×#462	C₂	semidirect
5. C₂₃×#1649	C₂	direct (N × H)
6. C₂×C₂₃×#332	C₂	semidirect
7. C₂×C₂₃×Q₈⋊C₈	C₂	semidirect
24. C₂₃×#500	C₂²	semidirect
28. C₂₃×#462	C₂²	semidirect
36. C₂₃×#332	C₂²	semidirect
37. C₂₃×Q₈⋊C₈	C₂²	semidirect
121. C₂×D₄×C₂₃	Q₁₆	semidirect
168. C₂×#1649	C₂₃	direct (N × H)
186. D₄×C₂₃	C₂×Q₁₆	semidirect
216. C₂×#500	C₂×C₂₃	semidirect
218. C₂×#462	C₂×C₂₃	semidirect
219. #1649	C₂×C₂₃	direct (N × H)
220. C₂×#332	C₂×C₂₃	semidirect
221. C₂×Q₈⋊C₈	C₂×C₂₃	semidirect
259. #500	C₂²×C₂₃	semidirect
263. #462	C₂²×C₂₃	semidirect
271. #332	C₂²×C₂₃	semidirect
272. Q₈⋊C₈	C₂²×C₂₃	semidirect
275. C₂×C₂₃	#1649	direct (N × H)
341. C₂₃	C₂×#1649	direct (N × H)
362. C₂×D₄	Q₁₆×C₂₃	semidirect
426. D₄	C₂×Q₁₆×C₂₃	semidirect
477. C₂	C₂₃×#1649	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×#500	2
C₂×C₂₃×#474	2
C₂×C₂₃×#462	2
C₂₃×#1649	2
C₂×C₂₃×#332	2
C₂×C₂₃×Q₈⋊C₈	2
C₂×C₂₃×D₄⋊C₈	2
C₂×#1649	23

Subgroups — C2×C23×#1649 #19166124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#1649 #19166124