Subgroups — C₂×C₂₃×#3046 #19208047

Order 5888.

2742 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂₃×#135	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#520	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3046	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₂₃×#464	C₂	1	2	yes	maximal, complemented
7	C₂×C₂₃×#462	C₂	1	2	yes	maximal, complemented
8	C₂×C₂₃×#463	C₂	1	2	yes	maximal, complemented
9	C₂×C₂₃×#461	C₂	1	2	yes	maximal, complemented
10	C₂×C₂₃×#424	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₃×#417	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₂₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
14	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
15	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic
16	C₂×C₂₃×#137	—	2	8	no	—
17	C₂×C₂₃×#137	C₂²	1	8	yes	complemented
18	C₂×C₂₃×#135	—	2	8	no	—
19	C₂×C₂₃×#135	C₂²	1	8	yes	—
20	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
21	C₂²×Q₁₆×C₂₃	C₂²	1	2	yes	—
22	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
23	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	—
24	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
25	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
26	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
27	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
28	C₂₃×#536	—	2	4	no	—
29	C₂₃×#536	C₂²	1	8	yes	complemented
30	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
31	C₂×C₂₃×#124	C₂²	1	2	yes	—
32	C₂×C₂₃×#123	—	2	2	no	—
33	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
34	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
35	C₂₃×#520	—	2	4	no	—
36	C₂₃×#520	C₂²	1	8	yes	complemented
37	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₂₃	—	2	2	no	—
39	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
40	C₂×C₂₃×#117	—	2	1	no	—
41	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
42	C₂²×C₄⋊C₄×C₂₃	—	2	1	no	—
43	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
44	C₂₃×#464	C₂²	1	16	yes	complemented
45	C₂₃×#463	C₂²	1	16	yes	complemented
46	C₂₃×#462	C₂²	1	16	yes	complemented
47	C₂₃×#461	C₂²	1	16	yes	complemented
48	C₂₃×#424	C₂²	1	8	yes	complemented
49	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
50	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
51	C₂₃×#417	C₂²	1	8	yes	complemented
52	C₂×C₂₃×#103	C₂²	1	2	yes	—
53	C₂×C₂₃×#103	C₂²	1	2	yes	—
54	C₂×C₂₃×#103	C₂²	1	2	yes	—
55	C₂×C₂₃×#103	C₂²	1	8	yes	complemented
56	C₂×C₂₃×#102	C₂²	1	2	yes	—
57	C₂×#41×C₂₃	—	2	2	no	—
58	C₂×#41×C₂₃	—	2	2	no	—
59	C₂×#41×C₂₃	—	2	4	no	—
60	C₂×#41×C₂₃	—	2	4	no	—
61	C₂×#41×C₂₃	—	2	4	no	—
62	C₂×#41×C₂₃	D₄	1	8	yes	—
63	C₂×#41×C₂₃	C₂³	1	4	yes	—
64	C₂×#41×C₂₃	C₂³	1	4	yes	—
65	C₂²×Q₈×C₂₃	—	2	1	no	—
66	C₂²×Q₈×C₂₃	—	2	2	no	—
67	C₂²×Q₈×C₂₃	—	2	4	no	—
68	C₂²×Q₈×C₂₃	—	2	4	no	—
69	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
70	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
72	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₂₃	—	2	1	no	—
74	C₂²×D₄×C₂₃	—	2	1	no	—
75	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
76	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₂₃	—	2	1	no	—
78	C₂³×C₄×C₂₃	—	2	1	no	—
79	C₂³×C₄×C₂₃	—	2	1	no	—
80	C₂³×C₄×C₂₃	—	2	1	no	—
81	C₂³×C₄×C₂₃	—	2	2	no	—
82	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
83	C₂₃×#137	—	2	32	no	—
84	C₂₃×#135	—	2	32	no	—
85	C₂×Q₁₆×C₂₃	—	2	4	no	—
86	C₂×Q₁₆×C₂₃	—	2	8	no	—
87	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
88	C₂×Q₁₆×C₂₃	C₂³	1	8	yes	—
89	C₂×SD₁₆×C₂₃	—	2	4	no	—
90	C₂×SD₁₆×C₂₃	—	2	4	no	—
91	C₂×SD₁₆×C₂₃	—	2	8	no	—
92	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
93	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
94	C₂×SD₁₆×C₂₃	C₂³	1	8	yes	—
95	C₂×D₈×C₂₃	—	2	4	no	—
96	C₂×D₈×C₂₃	C₂³	1	4	yes	—
97	C₂×M₁₆×C₂₃	—	2	4	no	—
98	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
99	C₂²×C₈×C₂₃	—	2	4	no	—
100	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
103	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
104	C₂₃×C₄⋊Q₈	—	2	4	no	—
105	C₂₃×C₄⋊Q₈	C₂³	1	8	yes	—
106	C₂₃×#124	—	2	4	no	—
107	C₂₃×#124	C₂³	1	8	yes	—
108	C₂₃×#123	—	2	16	no	—
109	C₂₃×C₂²⋊Q₈	—	2	8	no	—
110	C₂₃×C₂²⋊Q₈	—	2	8	no	—
111	C₄×Q₈×C₂₃	—	2	4	no	—
112	C₄×Q₈×C₂₃	C₂³	1	8	yes	—
113	C₄×D₄×C₂₃	—	2	16	no	—
114	C₄×D₄×C₂₃	—	2	4	no	—
115	C₄×D₄×C₂₃	C₂³	1	8	yes	—
116	C₂₃×#117	—	2	8	no	—
117	C₂₃×#117	D₄	1	4	yes	—
118	C₂₃×#117	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
120	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
121	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
122	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
123	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
124	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
125	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
130	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
131	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
132	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
133	C₂×C₄²×C₂₃	—	2	2	no	—
134	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
135	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
136	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
137	C₂₃×#103	C₂³	1	8	yes	—
138	C₂₃×#103	C₂³	1	8	yes	—
139	C₂₃×#103	C₂³	1	8	yes	—
140	C₂₃×#102	C₂³	1	8	yes	—
141	C₂⁴×C₂₃	—	2	1	no	—
142	C₂⁴×C₂₃	—	2	1	no	—
143	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
144	#41×C₂₃	—	2	16	no	—
145	#41×C₂₃	—	2	8	no	—
146	#41×C₂₃	—	2	8	no	—
147	#41×C₂₃	—	2	8	no	—
148	#41×C₂₃	—	4	8	no	—
149	#41×C₂₃	C₂×D₄	1	16	yes	—
150	C₂×Q₈×C₂₃	—	2	1	no	—
151	C₂×Q₈×C₂₃	—	2	4	no	—
152	C₂×Q₈×C₂₃	—	2	2	no	—
153	C₂×Q₈×C₂₃	—	2	1	no	—
154	C₂×Q₈×C₂₃	—	2	2	no	—
155	C₂×Q₈×C₂₃	—	2	4	no	—
156	C₂×Q₈×C₂₃	—	2	2	no	—
157	C₂×Q₈×C₂₃	—	2	8	no	—
158	C₂×Q₈×C₂₃	—	2	4	no	—
159	C₂×Q₈×C₂₃	—	2	8	no	—
160	C₂×Q₈×C₂₃	—	2	2	no	—
161	C₂×Q₈×C₂₃	—	4	4	no	—
162	C₂×Q₈×C₂₃	—	4	8	no	—
163	C₂×Q₈×C₂₃	C₂×D₄	1	4	yes	—
164	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
165	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
166	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
167	C₂×D₄×C₂₃	—	2	8	no	—
168	C₂×D₄×C₂₃	—	2	4	no	—
169	C₂×D₄×C₂₃	—	2	4	no	—
170	C₂×D₄×C₂₃	—	2	1	no	—
171	C₂×D₄×C₂₃	—	2	2	no	—
172	C₂×D₄×C₂₃	—	2	1	no	—
173	C₂×D₄×C₂₃	—	2	2	no	—
174	C₂×D₄×C₂₃	—	2	2	no	—
175	C₂×D₄×C₂₃	—	4	4	no	—
176	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
177	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
178	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₂₃	—	2	1	no	—
180	C₂²×C₄×C₂₃	—	2	8	no	—
181	C₂²×C₄×C₂₃	—	2	4	no	—
182	C₂²×C₄×C₂₃	—	2	4	no	—
183	C₂²×C₄×C₂₃	—	2	2	no	—
184	C₂²×C₄×C₂₃	—	2	2	no	—
185	C₂²×C₄×C₂₃	—	2	1	no	—
186	C₂²×C₄×C₂₃	—	2	4	no	—
187	C₂²×C₄×C₂₃	—	2	4	no	—
188	C₂²×C₄×C₂₃	—	2	8	no	—
189	C₂²×C₄×C₂₃	—	4	4	no	—
190	C₂²×C₄×C₂₃	—	4	4	no	—
191	C₂²×C₄×C₂₃	—	8	4	no	—
192	C₂²×C₄×C₂₃	—	8	2	no	—
193	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
194	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
195	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
196	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
198	C₂²×C₄×C₂₃	#41	1	4	yes	—
199	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
201	Q₁₆×C₂₃	—	2	8	no	—
202	Q₁₆×C₂₃	—	2	16	no	—
203	SD₁₆×C₂₃	—	2	8	no	—
204	SD₁₆×C₂₃	—	2	8	no	—
205	SD₁₆×C₂₃	—	2	16	no	—
206	D₈×C₂₃	—	2	8	no	—
207	M₁₆×C₂₃	—	2	8	no	—
208	C₂×C₈×C₂₃	—	2	2	no	—
209	C₂×C₈×C₂₃	—	2	2	no	—
210	C₂×C₈×C₂₃	—	2	8	no	—
211	C₂×C₈×C₂₃	—	2	4	no	—
212	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
213	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
214	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
215	C₄⋊C₄×C₂₃	—	2	4	no	—
216	C₄⋊C₄×C₂₃	—	2	8	no	—
217	C₄⋊C₄×C₂₃	—	2	2	no	—
218	C₄⋊C₄×C₂₃	—	2	8	no	—
219	C₄⋊C₄×C₂₃	—	2	8	no	—
220	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
221	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
222	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
223	C₂²⋊C₄×C₂₃	—	2	8	no	—
224	C₂²⋊C₄×C₂₃	—	2	8	no	—
225	C₂²⋊C₄×C₂₃	—	2	8	no	—
226	C₂²⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
227	C₄²×C₂₃	—	2	8	no	—
228	C₄²×C₂₃	C₂×D₄	1	4	yes	—
229	C₄²×C₂₃	C₂⁴	1	4	yes	—
230	C₂×#3046	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₂³×C₂₃	—	2	2	no	—
232	C₂³×C₂₃	—	2	2	no	—
233	C₂³×C₂₃	—	2	4	no	—
234	C₂³×C₂₃	—	2	2	no	—
235	C₂³×C₂₃	—	2	2	no	—
236	C₂³×C₂₃	—	4	2	no	—
237	C₂³×C₂₃	—	4	2	no	—
238	C₂³×C₂₃	—	4	2	no	—
239	C₂³×C₂₃	—	4	2	no	—
240	C₂³×C₂₃	—	4	2	no	—
241	C₂³×C₂₃	#121	1	4	yes	—
242	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
243	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
244	Q₈×C₂₃	—	2	4	no	—
245	Q₈×C₂₃	—	2	2	no	—
246	Q₈×C₂₃	—	2	4	no	—
247	Q₈×C₂₃	—	2	2	no	—
248	Q₈×C₂₃	—	2	4	no	—
249	Q₈×C₂₃	—	2	2	no	—
250	Q₈×C₂₃	—	4	8	no	—
251	Q₈×C₂₃	—	4	4	no	—
252	Q₈×C₂₃	—	4	2	no	—
253	Q₈×C₂₃	C₂²×D₄	1	4	yes	—
254	D₄×C₂₃	—	2	16	no	—
255	D₄×C₂₃	—	2	4	no	—
256	D₄×C₂₃	—	2	2	no	—
257	D₄×C₂₃	—	2	2	no	—
258	D₄×C₂₃	—	2	2	no	—
259	D₄×C₂₃	—	4	8	no	—
260	D₄×C₂₃	—	4	2	no	—
261	D₄×C₂₃	C₂²×D₄	1	4	yes	—
262	C₂×C₄×C₂₃	—	2	4	no	—
263	C₂×C₄×C₂₃	—	2	4	no	—
264	C₂×C₄×C₂₃	—	2	4	no	—
265	C₂×C₄×C₂₃	—	2	2	no	—
266	C₂×C₄×C₂₃	—	2	16	no	—
267	C₂×C₄×C₂₃	—	2	4	no	—
268	C₂×C₄×C₂₃	—	2	4	no	—
269	C₂×C₄×C₂₃	—	2	2	no	—
270	C₂×C₄×C₂₃	—	4	2	no	—
271	C₂×C₄×C₂₃	—	4	8	no	—
272	C₂×C₄×C₂₃	—	4	4	no	—
273	C₂×C₄×C₂₃	—	4	4	no	—
274	C₂×C₄×C₂₃	—	4	8	no	—
275	C₂×C₄×C₂₃	—	8	8	no	—
276	C₂×C₄×C₂₃	—	8	4	no	—
277	C₂×C₄×C₂₃	#121	1	4	yes	—
278	C₂×C₄×C₂₃	#121	1	8	yes	—
279	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
280	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
281	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
283	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
284	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
285	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
286	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
287	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
288	C₈×C₂₃	—	2	2	no	—
289	C₈×C₂₃	—	2	2	no	—
290	C₈×C₂₃	—	2	4	no	—
291	C₂²×#137	C₂×C₂₃	1	1	yes	characteristic, complemented
292	C₂²×#135	C₂×C₂₃	1	1	yes	characteristic
293	C₂×#536	C₂×C₂₃	1	1	yes	characteristic, complemented
294	C₂×#520	C₂×C₂₃	1	1	yes	characteristic, complemented
295	#3046	C₂×C₂₃	1	16	yes	direct product factor
296	C₂×#464	C₂×C₂₃	1	2	yes	complemented
297	C₂×#462	C₂×C₂₃	1	2	yes	complemented
298	C₂×#463	C₂×C₂₃	1	2	yes	complemented
299	C₂×#461	C₂×C₂₃	1	2	yes	complemented
300	C₂×#424	C₂×C₂₃	1	1	yes	characteristic, complemented
301	C₂×#417	C₂×C₂₃	1	1	yes	characteristic, complemented
302	C₂²×#103	C₂×C₂₃	1	1	yes	characteristic, complemented
303	C₂²×C₂₃	—	2	8	no	—
304	C₂²×C₂₃	—	2	2	no	—
305	C₂²×C₂₃	—	2	2	no	—
306	C₂²×C₂₃	—	2	4	no	—
307	C₂²×C₂₃	—	4	8	no	—
308	C₂²×C₂₃	—	4	2	no	—
309	C₂²×C₂₃	—	4	2	no	—
310	C₂²×C₂₃	—	4	2	no	—
311	C₂²×C₂₃	—	4	2	no	—
312	C₂²×C₂₃	—	4	2	no	—
313	C₂²×C₂₃	—	8	4	no	—
314	C₂²×C₂₃	C₂×#121	1	4	yes	—
315	C₂²×C₂₃	C₂×#121	1	2	yes	—
316	C₂²×C₂₃	#577	1	2	yes	—
317	C₂²×C₂₃	#578	1	2	yes	—
318	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
319	C₄×C₂₃	—	2	4	no	—
320	C₄×C₂₃	—	2	4	no	—
321	C₄×C₂₃	—	2	4	no	—
322	C₄×C₂₃	—	4	2	no	—
323	C₄×C₂₃	—	4	4	no	—
324	C₄×C₂₃	—	4	4	no	—
325	C₄×C₂₃	C₂×#121	1	4	yes	—
326	C₄×C₂₃	C₂×#121	1	2	yes	—
327	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
328	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
329	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
330	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
331	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
332	C₂×#137	—	2	8	no	—
333	C₂×#137	C₂²×C₂₃	1	8	yes	complemented
334	C₂×#135	—	2	8	no	—
335	C₂×#135	C₂²×C₂₃	1	8	yes	—
336	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
337	C₂²×Q₁₆	C₂²×C₂₃	1	2	yes	—
338	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
339	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	—
340	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
341	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
342	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
343	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
344	#536	—	2	4	no	—
345	#536	C₂²×C₂₃	1	8	yes	complemented
346	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
347	C₂×#124	C₂²×C₂₃	1	2	yes	—
348	C₂×#123	—	2	2	no	—
349	C₂×C₂²⋊Q₈	—	2	1	no	—
350	C₂×C₂²⋊Q₈	—	2	1	no	—
351	#520	—	2	4	no	—
352	#520	C₂²×C₂₃	1	8	yes	complemented
353	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
354	C₂×C₄×D₄	—	2	2	no	—
355	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
356	C₂×#117	—	2	1	no	—
357	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
358	C₂²×C₄⋊C₄	—	2	1	no	—
359	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
360	#464	C₂²×C₂₃	1	16	yes	complemented
361	#463	C₂²×C₂₃	1	16	yes	complemented
362	#462	C₂²×C₂₃	1	16	yes	complemented
363	#461	C₂²×C₂₃	1	16	yes	complemented
364	#424	C₂²×C₂₃	1	8	yes	complemented
365	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
366	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
367	#417	C₂²×C₂₃	1	8	yes	complemented
368	C₂×#103	C₂²×C₂₃	1	2	yes	—
369	C₂×#103	C₂²×C₂₃	1	2	yes	—
370	C₂×#103	C₂²×C₂₃	1	2	yes	—
371	C₂×#103	C₂²×C₂₃	1	8	yes	complemented
372	C₂×#102	C₂²×C₂₃	1	2	yes	—
373	C₂×C₂₃	—	2	4	no	—
374	C₂×C₂₃	—	4	4	no	—
375	C₂×C₂₃	—	8	2	no	—
376	C₂×C₂₃	#3046	1	4	yes	direct product factor
377	C₂×C₂₃	C₂²×#121	1	1	yes	characteristic
378	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
379	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
380	C₂×#41	—	2	2	no	—
381	C₂×#41	—	2	2	no	—
382	C₂×#41	—	2	4	no	—
383	C₂×#41	—	2	4	no	—
384	C₂×#41	—	2	4	no	—
385	C₂×#41	D₄×C₂₃	1	8	yes	—
386	C₂×#41	C₂³×C₂₃	1	4	yes	—
387	C₂×#41	C₂³×C₂₃	1	4	yes	—
388	C₂²×Q₈	—	2	1	no	—
389	C₂²×Q₈	—	2	2	no	—
390	C₂²×Q₈	—	2	4	no	—
391	C₂²×Q₈	—	2	4	no	—
392	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
393	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
394	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
395	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
396	C₂²×D₄	—	2	1	no	—
397	C₂²×D₄	—	2	1	no	—
398	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
399	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
400	C₂³×C₄	—	2	1	no	—
401	C₂³×C₄	—	2	1	no	—
402	C₂³×C₄	—	2	1	no	—
403	C₂³×C₄	—	2	1	no	—
404	C₂³×C₄	—	2	2	no	—
405	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
406	#137	—	2	32	no	—
407	#135	—	2	32	no	—
408	C₂×Q₁₆	—	2	4	no	—
409	C₂×Q₁₆	—	2	8	no	—
410	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
411	C₂×Q₁₆	C₂³×C₂₃	1	8	yes	—
412	C₂×SD₁₆	—	2	4	no	—
413	C₂×SD₁₆	—	2	4	no	—
414	C₂×SD₁₆	—	2	8	no	—
415	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
416	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
417	C₂×SD₁₆	C₂³×C₂₃	1	8	yes	—
418	C₂×D₈	—	2	4	no	—
419	C₂×D₈	C₂³×C₂₃	1	4	yes	—
420	C₂×M₁₆	—	2	4	no	—
421	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
422	C₂²×C₈	—	2	4	no	—
423	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
424	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
425	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
426	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
427	C₄⋊Q₈	—	2	4	no	—
428	C₄⋊Q₈	C₂³×C₂₃	1	8	yes	—
429	#124	—	2	4	no	—
430	#124	C₂³×C₂₃	1	8	yes	—
431	#123	—	2	16	no	—
432	C₂²⋊Q₈	—	2	8	no	—
433	C₂²⋊Q₈	—	2	8	no	—
434	C₄×Q₈	—	2	4	no	—
435	C₄×Q₈	C₂³×C₂₃	1	8	yes	—
436	C₄×D₄	—	2	16	no	—
437	C₄×D₄	—	2	4	no	—
438	C₄×D₄	C₂³×C₂₃	1	8	yes	—
439	#117	—	2	8	no	—
440	#117	D₄×C₂₃	1	4	yes	—
441	#117	C₂³×C₂₃	1	4	yes	—
442	C₂×C₄⋊C₄	—	2	1	no	—
443	C₂×C₄⋊C₄	—	2	2	no	—
444	C₂×C₄⋊C₄	—	2	2	no	—
445	C₂×C₄⋊C₄	—	2	2	no	—
446	C₂×C₄⋊C₄	—	2	2	no	—
447	C₂×C₄⋊C₄	—	2	8	no	—
448	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
449	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
451	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
452	C₂×C₂²⋊C₄	—	2	2	no	—
453	C₂×C₂²⋊C₄	—	2	2	no	—
454	C₂×C₂²⋊C₄	—	2	2	no	—
455	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
456	C₂×C₄²	—	2	2	no	—
457	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
458	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
459	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
460	#103	C₂³×C₂₃	1	8	yes	—
461	#103	C₂³×C₂₃	1	8	yes	—
462	#103	C₂³×C₂₃	1	8	yes	—
463	#102	C₂³×C₂₃	1	8	yes	—
464	C₂₃	C₂×#3046	1	1	yes	characteristic, direct product factor, Sylow
465	C₂⁴	—	2	1	no	—
466	C₂⁴	—	2	1	no	—
467	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
468	#41	—	2	16	no	—
469	#41	—	2	8	no	—
470	#41	—	2	8	no	—
471	#41	—	2	8	no	—
472	#41	—	4	8	no	—
473	#41	C₂×D₄×C₂₃	1	16	yes	—
474	C₂×Q₈	—	2	1	no	—
475	C₂×Q₈	—	2	4	no	—
476	C₂×Q₈	—	2	2	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	2	2	no	—
479	C₂×Q₈	—	2	4	no	—
480	C₂×Q₈	—	2	2	no	—
481	C₂×Q₈	—	2	8	no	—
482	C₂×Q₈	—	2	4	no	—
483	C₂×Q₈	—	2	8	no	—
484	C₂×Q₈	—	2	2	no	—
485	C₂×Q₈	—	4	4	no	—
486	C₂×Q₈	—	4	8	no	—
487	C₂×Q₈	C₂×D₄×C₂₃	1	4	yes	—
488	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
489	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
490	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
491	C₂×D₄	—	2	8	no	—
492	C₂×D₄	—	2	4	no	—
493	C₂×D₄	—	2	4	no	—
494	C₂×D₄	—	2	1	no	—
495	C₂×D₄	—	2	2	no	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	—	2	2	no	—
498	C₂×D₄	—	2	2	no	—
499	C₂×D₄	—	4	4	no	—
500	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
501	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
502	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	8	no	—
505	C₂²×C₄	—	2	4	no	—
506	C₂²×C₄	—	2	2	no	—
507	C₂²×C₄	—	2	2	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	4	no	—
510	C₂²×C₄	—	2	4	no	—
511	C₂²×C₄	—	2	4	no	—
512	C₂²×C₄	—	2	8	no	—
513	C₂²×C₄	—	4	4	no	—
514	C₂²×C₄	—	4	4	no	—
515	C₂²×C₄	—	8	4	no	—
516	C₂²×C₄	—	8	2	no	—
517	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
518	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
519	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
520	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
521	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
522	C₂²×C₄	#41×C₂₃	1	4	yes	—
523	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
524	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
525	Q₁₆	—	2	8	no	—
526	Q₁₆	—	2	16	no	—
527	SD₁₆	—	2	8	no	—
528	SD₁₆	—	2	8	no	—
529	SD₁₆	—	2	16	no	—
530	D₈	—	2	8	no	—
531	M₁₆	—	2	8	no	—
532	C₂×C₈	—	2	2	no	—
533	C₂×C₈	—	2	2	no	—
534	C₂×C₈	—	2	8	no	—
535	C₂×C₈	—	2	4	no	—
536	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
537	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
538	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
539	C₄⋊C₄	—	2	4	no	—
540	C₄⋊C₄	—	2	8	no	—
541	C₄⋊C₄	—	2	2	no	—
542	C₄⋊C₄	—	2	8	no	—
543	C₄⋊C₄	—	2	8	no	—
544	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
545	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
546	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
547	C₂²⋊C₄	—	2	8	no	—
548	C₂²⋊C₄	—	2	8	no	—
549	C₂²⋊C₄	—	2	8	no	—
550	C₂²⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
551	C₄²	—	2	8	no	—
552	C₄²	C₂×D₄×C₂₃	1	4	yes	—
553	C₄²	C₂⁴×C₂₃	1	4	yes	—
554	C₂³	—	2	2	no	—
555	C₂³	—	2	2	no	—
556	C₂³	—	2	2	no	—
557	C₂³	—	2	4	no	—
558	C₂³	—	2	2	no	—
559	C₂³	—	4	2	no	—
560	C₂³	—	4	2	no	—
561	C₂³	—	4	2	no	—
562	C₂³	—	4	2	no	—
563	C₂³	—	4	2	no	—
564	C₂³	C₂₃×#121	1	4	yes	—
565	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
566	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
567	Q₈	—	2	2	no	—
568	Q₈	—	2	4	no	—
569	Q₈	—	2	4	no	—
570	Q₈	—	2	2	no	—
571	Q₈	—	2	4	no	—
572	Q₈	—	2	2	no	—
573	Q₈	—	4	8	no	—
574	Q₈	—	4	4	no	—
575	Q₈	—	4	2	no	—
576	Q₈	C₂²×D₄×C₂₃	1	4	yes	—
577	D₄	—	2	16	no	—
578	D₄	—	2	2	no	—
579	D₄	—	2	2	no	—
580	D₄	—	2	2	no	—
581	D₄	—	2	4	no	—
582	D₄	—	4	8	no	—
583	D₄	—	4	2	no	—
584	D₄	C₂²×D₄×C₂₃	1	4	yes	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	4	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	16	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	4	4	no	—
594	C₂×C₄	—	4	2	no	—
595	C₂×C₄	—	4	8	no	—
596	C₂×C₄	—	4	4	no	—
597	C₂×C₄	—	4	8	no	—
598	C₂×C₄	—	8	8	no	—
599	C₂×C₄	—	8	4	no	—
600	C₂×C₄	C₂₃×#121	1	4	yes	—
601	C₂×C₄	C₂₃×#121	1	8	yes	—
602	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
603	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
604	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
605	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
606	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
607	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
608	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
609	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
610	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
611	C₈	—	2	2	no	—
612	C₈	—	2	2	no	—
613	C₈	—	2	4	no	—
614	C₂²	—	2	8	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	4	no	—
618	C₂²	—	4	8	no	—
619	C₂²	—	4	2	no	—
620	C₂²	—	4	2	no	—
621	C₂²	—	4	2	no	—
622	C₂²	—	4	2	no	—
623	C₂²	—	4	2	no	—
624	C₂²	—	8	4	no	—
625	C₂²	C₂×C₂₃×#121	1	4	yes	—
626	C₂²	C₂×C₂₃×#121	1	2	yes	—
627	C₂²	C₂₃×#577	1	2	yes	—
628	C₂²	C₂₃×#578	1	2	yes	—
629	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
630	C₄	—	2	4	no	—
631	C₄	—	2	4	no	—
632	C₄	—	2	4	no	—
633	C₄	—	4	2	no	—
634	C₄	—	4	4	no	—
635	C₄	—	4	4	no	—
636	C₄	C₂×C₂₃×#121	1	4	yes	—
637	C₄	C₂×C₂₃×#121	1	2	yes	—
638	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
639	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
640	C₂	—	2	4	no	—
641	C₂	—	4	4	no	—
642	C₂	—	8	2	no	—
643	C₂	C₂₃×#3046	1	4	yes	direct product factor
644	C₂	C₂²×C₂₃×#121	1	1	yes	characteristic
645	C₂	C₂×C₂₃×#577	1	1	yes	characteristic
646	C₂	C₂×C₂₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂²×C₂₃×#135	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₂₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₂₃×#137	C₂	semidirect
3. C₂×C₂₃×#536	C₂	semidirect
4. C₂×C₂₃×#520	C₂	semidirect
5. C₂₃×#3046	C₂	direct (N × H)
6. C₂×C₂₃×#464	C₂	semidirect
7. C₂×C₂₃×#462	C₂	semidirect
8. C₂×C₂₃×#463	C₂	semidirect
9. C₂×C₂₃×#461	C₂	semidirect
10. C₂×C₂₃×#424	C₂	semidirect
11. C₂×C₂₃×#417	C₂	semidirect
12. C₂²×C₂₃×#103	C₂	semidirect
17. C₂×C₂₃×#137	C₂²	semidirect
29. C₂₃×#536	C₂²	semidirect
36. C₂₃×#520	C₂²	semidirect
44. C₂₃×#464	C₂²	semidirect
45. C₂₃×#463	C₂²	semidirect
46. C₂₃×#462	C₂²	semidirect
47. C₂₃×#461	C₂²	semidirect
48. C₂₃×#424	C₂²	semidirect
51. C₂₃×#417	C₂²	semidirect
55. C₂×C₂₃×#103	C₂²	semidirect
230. C₂×#3046	C₂₃	direct (N × H)
291. C₂²×#137	C₂×C₂₃	semidirect
293. C₂×#536	C₂×C₂₃	semidirect
294. C₂×#520	C₂×C₂₃	semidirect
295. #3046	C₂×C₂₃	direct (N × H)
296. C₂×#464	C₂×C₂₃	semidirect
297. C₂×#462	C₂×C₂₃	semidirect
298. C₂×#463	C₂×C₂₃	semidirect
299. C₂×#461	C₂×C₂₃	semidirect
300. C₂×#424	C₂×C₂₃	semidirect
301. C₂×#417	C₂×C₂₃	semidirect
302. C₂²×#103	C₂×C₂₃	semidirect
333. C₂×#137	C₂²×C₂₃	semidirect
345. #536	C₂²×C₂₃	semidirect
352. #520	C₂²×C₂₃	semidirect
360. #464	C₂²×C₂₃	semidirect
361. #463	C₂²×C₂₃	semidirect
362. #462	C₂²×C₂₃	semidirect
363. #461	C₂²×C₂₃	semidirect
364. #424	C₂²×C₂₃	semidirect
367. #417	C₂²×C₂₃	semidirect
371. C₂×#103	C₂²×C₂₃	semidirect
376. C₂×C₂₃	#3046	direct (N × H)
464. C₂₃	C₂×#3046	direct (N × H)
643. C₂	C₂₃×#3046	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×C₂₃×#137	2
C₂²×C₂₃×#135	2
C₂×C₂₃×#536	2
C₂×C₂₃×#520	2
C₂₃×#3046	2
C₂×C₂₃×#464	2
C₂×C₂₃×#462	2
C₂×C₂₃×#463	2
C₂×C₂₃×#461	2
C₂×C₂₃×#424	2
C₂×C₂₃×#417	2
C₂²×C₂₃×#103	2
C₂×#3046	23

Subgroups — C2×C23×#3046 #19208047

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3046 #19208047