Subgroups — C₂×C₂₃×#3242 #19208482

Order 5888.

1678 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#544	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#541	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3242	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₃×#501	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#499	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×#491	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×#487	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×#484	C₂	1	1	yes	maximal, characteristic
9	C₂×C₂₃×#485	C₂	1	1	yes	maximal, characteristic
10	C₂×C₂₃×#485	C₂	1	1	yes	maximal, characteristic
11	C₂×C₂₃×#483	C₂	1	1	yes	maximal, characteristic
12	C₂×C₂₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₂₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₃×#475	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×#433	C₂	1	1	yes	maximal, characteristic
17	C₂₃×#544	—	2	4	no	—
18	C₂₃×#544	C₂²	1	8	yes	—
19	C₂₃×#541	—	2	4	no	—
20	C₂₃×#541	C₂²	1	8	yes	—
21	C₂×C₂₃×C₄⋊Q₈	—	2	1	no	—
22	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#126	—	2	1	no	—
26	C₂×C₂₃×#126	—	2	1	no	—
27	C₂×C₂₃×#125	—	2	1	no	—
28	C₂×C₂₃×#125	—	2	1	no	—
29	C₂×C₂₃×#125	—	2	1	no	—
30	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
34	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
35	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
41	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
42	C₂₃×#501	C₂²	1	8	yes	complemented
43	C₂₃×#499	C₂²	1	8	yes	complemented
44	C₂₃×#491	C₂²	1	8	yes	complemented
45	C₂₃×#487	C₂²	1	8	yes	complemented
46	C₂₃×#485	C₂²	1	8	yes	—
47	C₂₃×#485	C₂²	1	8	yes	—
48	C₂₃×#484	C₂²	1	8	yes	—
49	C₂₃×#483	C₂²	1	8	yes	—
50	C₂₃×#479	C₂²	1	8	yes	complemented
51	C₂₃×#479	C₂²	1	8	yes	complemented
52	C₂₃×#477	C₂²	1	8	yes	complemented
53	C₂₃×#475	C₂²	1	8	yes	complemented
54	C₂₃×#433	C₂²	1	8	yes	—
55	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
56	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
57	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
58	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
59	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
60	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
61	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
62	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
63	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
64	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
66	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
67	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
68	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
69	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
70	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
71	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
72	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
73	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
74	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
76	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
77	C₂²×Q₈×C₂₃	—	2	1	no	—
78	C₂²×Q₈×C₂₃	—	2	1	no	—
79	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
80	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₂₃	—	2	1	no	—
82	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
87	C₂₃×C₄⋊Q₈	—	2	8	no	—
88	C₂₃×C₄⋊Q₈	—	2	2	no	—
89	C₂₃×C₄⋊Q₈	—	2	2	no	—
90	C₂₃×C₄⋊Q₈	—	2	2	no	—
91	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
92	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
93	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
94	C₂₃×#126	—	2	8	no	—
95	C₂₃×#126	—	2	8	no	—
96	C₂₃×#125	—	2	8	no	—
97	C₂₃×#125	—	2	8	no	—
98	C₂₃×#125	—	2	8	no	—
99	C₂₃×#125	—	2	2	no	—
100	C₂₃×#125	—	2	2	no	—
101	C₂₃×#125	—	2	2	no	—
102	C₂₃×#125	C₂³	1	4	yes	—
103	C₂₃×#125	C₂³	1	4	yes	—
104	C₂₃×#125	C₂³	1	4	yes	—
105	C₂₃×C₂²⋊Q₈	—	2	2	no	—
106	C₂₃×C₂²⋊Q₈	—	2	2	no	—
107	C₂₃×C₂²⋊Q₈	—	2	8	no	—
108	C₂₃×C₂²⋊Q₈	—	2	8	no	—
109	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
110	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
111	C₄×Q₈×C₂₃	—	2	2	no	—
112	C₄×Q₈×C₂₃	—	2	2	no	—
113	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
114	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
115	C₂₃×#117	—	2	2	no	—
116	C₂₃×#117	D₄	1	4	yes	—
117	C₂₃×#117	C₂³	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	1	no	—
122	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
123	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
124	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
125	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
126	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
127	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
128	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
129	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
130	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
131	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
132	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
133	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
134	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
135	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
145	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
146	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
147	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
148	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
149	C₂×C₄²×C₂₃	—	2	1	no	—
150	C₂×C₄²×C₂₃	—	2	1	no	—
151	C₂×C₄²×C₂₃	—	2	1	no	—
152	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
154	C₂₃×#107	C₂³	1	4	yes	—
155	C₂₃×#107	C₂³	1	4	yes	—
156	C₂₃×#107	C₂³	1	4	yes	—
157	C₂₃×#107	C₂³	1	4	yes	—
158	C₂₃×#106	C₂³	1	4	yes	—
159	C₂₃×#106	C₂³	1	4	yes	—
160	C₂₃×#106	C₂³	1	4	yes	—
161	C₂₃×#106	C₂³	1	4	yes	—
162	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
163	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
164	C₂₃×#103	C₂³	1	4	yes	—
165	C₂₃×#103	C₂³	1	4	yes	—
166	C₂₃×#103	C₂³	1	4	yes	—
167	C₂₃×#103	C₂³	1	4	yes	—
168	C₂₃×#103	C₂³	1	4	yes	—
169	C₂₃×#103	C₂³	1	4	yes	—
170	C₂₃×#103	C₂³	1	4	yes	—
171	C₂₃×#103	C₂³	1	4	yes	—
172	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
173	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
174	C₂₃×#97	C₂³	1	4	yes	—
175	C₄×C₈×C₂₃	C₂³	1	4	yes	—
176	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
177	C₂×Q₈×C₂₃	—	2	1	no	—
178	C₂×Q₈×C₂₃	—	2	1	no	—
179	C₂×Q₈×C₂₃	—	2	4	no	—
180	C₂×Q₈×C₂₃	—	2	4	no	—
181	C₂×Q₈×C₂₃	—	2	2	no	—
182	C₂×Q₈×C₂₃	—	2	2	no	—
183	C₂×Q₈×C₂₃	—	2	2	no	—
184	C₂×Q₈×C₂₃	—	2	2	no	—
185	C₂×Q₈×C₂₃	—	8	2	no	—
186	C₂×Q₈×C₂₃	—	8	2	no	—
187	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
188	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₂₃	—	2	2	no	—
190	C₂²×C₄×C₂₃	—	2	2	no	—
191	C₂²×C₄×C₂₃	—	2	1	no	—
192	C₂²×C₄×C₂₃	—	2	1	no	—
193	C₂²×C₄×C₂₃	—	2	1	no	—
194	C₂²×C₄×C₂₃	—	2	1	no	—
195	C₂²×C₄×C₂₃	—	2	1	no	—
196	C₂²×C₄×C₂₃	—	2	1	no	—
197	C₂²×C₄×C₂₃	—	2	1	no	—
198	C₂²×C₄×C₂₃	—	2	1	no	—
199	C₂²×C₄×C₂₃	—	2	4	no	—
200	C₂²×C₄×C₂₃	—	8	2	no	—
201	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
202	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
209	C₂×C₈×C₂₃	—	2	2	no	—
210	C₂×C₈×C₂₃	—	2	2	no	—
211	C₂×C₈×C₂₃	—	2	2	no	—
212	C₂×C₈×C₂₃	—	2	2	no	—
213	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
214	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
215	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
216	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
217	C₄⋊C₄×C₂₃	—	2	4	no	—
218	C₄⋊C₄×C₂₃	—	2	1	no	—
219	C₄⋊C₄×C₂₃	—	2	1	no	—
220	C₄⋊C₄×C₂₃	—	2	4	no	—
221	C₄⋊C₄×C₂₃	—	2	4	no	—
222	C₄⋊C₄×C₂₃	—	2	4	no	—
223	C₄⋊C₄×C₂₃	—	2	4	no	—
224	C₄⋊C₄×C₂₃	—	2	4	no	—
225	C₄⋊C₄×C₂₃	—	2	4	no	—
226	C₄⋊C₄×C₂₃	—	2	4	no	—
227	C₄⋊C₄×C₂₃	—	2	4	no	—
228	C₄⋊C₄×C₂₃	—	2	4	no	—
229	C₄⋊C₄×C₂₃	—	2	4	no	—
230	C₄⋊C₄×C₂₃	—	2	4	no	—
231	C₄⋊C₄×C₂₃	—	2	4	no	—
232	C₄⋊C₄×C₂₃	—	2	4	no	—
233	C₄⋊C₄×C₂₃	—	2	4	no	—
234	C₄⋊C₄×C₂₃	—	2	1	no	—
235	C₄⋊C₄×C₂₃	—	2	1	no	—
236	C₄⋊C₄×C₂₃	—	2	1	no	—
237	C₄⋊C₄×C₂₃	—	2	1	no	—
238	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
239	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
240	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
241	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
242	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
243	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
244	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
245	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
246	C₂²⋊C₄×C₂₃	—	2	4	no	—
247	C₂²⋊C₄×C₂₃	—	2	4	no	—
248	C₂²⋊C₄×C₂₃	—	2	4	no	—
249	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
250	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
251	C₄²×C₂₃	—	2	4	no	—
252	C₄²×C₂₃	—	2	4	no	—
253	C₄²×C₂₃	—	2	4	no	—
254	C₄²×C₂₃	C₂×D₄	1	2	yes	—
255	C₄²×C₂₃	C₂×D₄	1	2	yes	—
256	C₄²×C₂₃	C₂⁴	1	2	yes	—
257	C₄²×C₂₃	C₂⁴	1	2	yes	—
258	C₂×#3242	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
259	C₂³×C₂₃	—	2	2	no	—
260	C₂³×C₂₃	—	2	2	no	—
261	C₂³×C₂₃	—	2	2	no	—
262	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
263	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
264	Q₈×C₂₃	—	2	2	no	—
265	Q₈×C₂₃	—	2	2	no	—
266	Q₈×C₂₃	—	2	2	no	—
267	Q₈×C₂₃	—	2	2	no	—
268	Q₈×C₂₃	—	4	2	no	—
269	Q₈×C₂₃	—	4	2	no	—
270	Q₈×C₂₃	—	8	4	no	—
271	Q₈×C₂₃	—	8	4	no	—
272	C₂×C₄×C₂₃	—	2	2	no	—
273	C₂×C₄×C₂₃	—	2	2	no	—
274	C₂×C₄×C₂₃	—	2	2	no	—
275	C₂×C₄×C₂₃	—	2	2	no	—
276	C₂×C₄×C₂₃	—	2	2	no	—
277	C₂×C₄×C₂₃	—	2	4	no	—
278	C₂×C₄×C₂₃	—	2	2	no	—
279	C₂×C₄×C₂₃	—	2	2	no	—
280	C₂×C₄×C₂₃	—	2	2	no	—
281	C₂×C₄×C₂₃	—	2	2	no	—
282	C₂×C₄×C₂₃	—	2	2	no	—
283	C₂×C₄×C₂₃	—	2	2	no	—
284	C₂×C₄×C₂₃	—	2	2	no	—
285	C₂×C₄×C₂₃	—	2	2	no	—
286	C₂×C₄×C₂₃	—	2	2	no	—
287	C₂×C₄×C₂₃	—	2	2	no	—
288	C₂×C₄×C₂₃	—	4	2	no	—
289	C₂×C₄×C₂₃	—	4	2	no	—
290	C₂×C₄×C₂₃	—	4	2	no	—
291	C₂×C₄×C₂₃	—	4	2	no	—
292	C₂×C₄×C₂₃	—	4	2	no	—
293	C₂×C₄×C₂₃	—	4	2	no	—
294	C₂×C₄×C₂₃	—	4	2	no	—
295	C₂×C₄×C₂₃	—	4	2	no	—
296	C₂×C₄×C₂₃	—	8	4	no	—
297	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
298	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
299	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
300	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
301	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
302	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
303	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
304	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
305	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
306	C₈×C₂₃	—	2	2	no	—
307	C₈×C₂₃	—	2	2	no	—
308	C₈×C₂₃	—	2	2	no	—
309	C₈×C₂₃	—	2	2	no	—
310	C₂×#544	C₂×C₂₃	1	1	yes	characteristic
311	C₂×#541	C₂×C₂₃	1	1	yes	characteristic
312	#3242	C₂×C₂₃	1	16	yes	direct product factor
313	C₂×#501	C₂×C₂₃	1	1	yes	characteristic, complemented
314	C₂×#499	C₂×C₂₃	1	1	yes	characteristic, complemented
315	C₂×#491	C₂×C₂₃	1	1	yes	characteristic, complemented
316	C₂×#487	C₂×C₂₃	1	1	yes	characteristic, complemented
317	C₂×#484	C₂×C₂₃	1	1	yes	characteristic
318	C₂×#485	C₂×C₂₃	1	1	yes	characteristic
319	C₂×#485	C₂×C₂₃	1	1	yes	characteristic
320	C₂×#483	C₂×C₂₃	1	1	yes	characteristic
321	C₂×#479	C₂×C₂₃	1	1	yes	characteristic, complemented
322	C₂×#479	C₂×C₂₃	1	1	yes	characteristic, complemented
323	C₂×#477	C₂×C₂₃	1	1	yes	characteristic, complemented
324	C₂×#475	C₂×C₂₃	1	1	yes	characteristic, complemented
325	C₂×#433	C₂×C₂₃	1	1	yes	characteristic
326	C₂²×C₂₃	—	2	2	no	—
327	C₂²×C₂₃	—	2	2	no	—
328	C₂²×C₂₃	—	2	2	no	—
329	C₂²×C₂₃	—	4	4	no	—
330	C₂²×C₂₃	#536	1	2	yes	—
331	C₂²×C₂₃	#577	1	2	yes	—
332	C₂²×C₂₃	#578	1	2	yes	—
333	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
334	C₄×C₂₃	—	2	2	no	—
335	C₄×C₂₃	—	2	2	no	—
336	C₄×C₂₃	—	2	2	no	—
337	C₄×C₂₃	—	2	2	no	—
338	C₄×C₂₃	—	2	2	no	—
339	C₄×C₂₃	—	4	2	no	—
340	C₄×C₂₃	—	4	2	no	—
341	C₄×C₂₃	—	4	2	no	—
342	C₄×C₂₃	—	4	2	no	—
343	C₄×C₂₃	—	4	2	no	—
344	C₄×C₂₃	—	4	2	no	—
345	C₄×C₂₃	—	4	2	no	—
346	C₄×C₂₃	—	4	2	no	—
347	C₄×C₂₃	#536	1	2	yes	—
348	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
349	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
350	#544	—	2	4	no	—
351	#544	C₂²×C₂₃	1	8	yes	—
352	#541	—	2	4	no	—
353	#541	C₂²×C₂₃	1	8	yes	—
354	C₂×C₄⋊Q₈	—	2	1	no	—
355	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
356	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
357	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
358	C₂×#126	—	2	1	no	—
359	C₂×#126	—	2	1	no	—
360	C₂×#125	—	2	1	no	—
361	C₂×#125	—	2	1	no	—
362	C₂×#125	—	2	1	no	—
363	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
364	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
365	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
366	C₂×C₂²⋊Q₈	—	2	1	no	—
367	C₂×C₂²⋊Q₈	—	2	1	no	—
368	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
369	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
370	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
371	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
372	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
373	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
374	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
375	#501	C₂²×C₂₃	1	8	yes	complemented
376	#499	C₂²×C₂₃	1	8	yes	complemented
377	#491	C₂²×C₂₃	1	8	yes	complemented
378	#487	C₂²×C₂₃	1	8	yes	complemented
379	#485	C₂²×C₂₃	1	8	yes	—
380	#485	C₂²×C₂₃	1	8	yes	—
381	#484	C₂²×C₂₃	1	8	yes	—
382	#483	C₂²×C₂₃	1	8	yes	—
383	#479	C₂²×C₂₃	1	8	yes	complemented
384	#479	C₂²×C₂₃	1	8	yes	complemented
385	#477	C₂²×C₂₃	1	8	yes	complemented
386	#475	C₂²×C₂₃	1	8	yes	complemented
387	#433	C₂²×C₂₃	1	8	yes	—
388	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
389	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
390	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
391	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
392	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
393	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
394	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
395	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
396	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
397	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
398	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
399	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
400	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
401	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
402	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
403	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
404	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
405	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
406	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
407	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
408	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
409	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
410	C₂×C₂₃	—	4	2	no	—
411	C₂×C₂₃	#3242	1	4	yes	direct product factor
412	C₂×C₂₃	C₂×#536	1	1	yes	characteristic
413	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
414	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
415	C₂²×Q₈	—	2	1	no	—
416	C₂²×Q₈	—	2	1	no	—
417	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
418	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
419	C₂³×C₄	—	2	1	no	—
420	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
421	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
422	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
423	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
424	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
425	C₄⋊Q₈	—	2	8	no	—
426	C₄⋊Q₈	—	2	2	no	—
427	C₄⋊Q₈	—	2	2	no	—
428	C₄⋊Q₈	—	2	2	no	—
429	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
430	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
431	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
432	#126	—	2	8	no	—
433	#126	—	2	8	no	—
434	#125	—	2	8	no	—
435	#125	—	2	8	no	—
436	#125	—	2	8	no	—
437	#125	—	2	2	no	—
438	#125	—	2	2	no	—
439	#125	—	2	2	no	—
440	#125	C₂³×C₂₃	1	4	yes	—
441	#125	C₂³×C₂₃	1	4	yes	—
442	#125	C₂³×C₂₃	1	4	yes	—
443	C₂²⋊Q₈	—	2	2	no	—
444	C₂²⋊Q₈	—	2	2	no	—
445	C₂²⋊Q₈	—	2	8	no	—
446	C₂²⋊Q₈	—	2	8	no	—
447	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
448	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
449	C₄×Q₈	—	2	2	no	—
450	C₄×Q₈	—	2	2	no	—
451	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
452	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
453	#117	—	2	2	no	—
454	#117	D₄×C₂₃	1	4	yes	—
455	#117	C₂³×C₂₃	1	4	yes	—
456	#117	C₂³×C₂₃	1	4	yes	—
457	C₂×C₄⋊C₄	—	2	1	no	—
458	C₂×C₄⋊C₄	—	2	2	no	—
459	C₂×C₄⋊C₄	—	2	1	no	—
460	C₂×C₄⋊C₄	—	2	1	no	—
461	C₂×C₄⋊C₄	—	2	1	no	—
462	C₂×C₄⋊C₄	—	2	1	no	—
463	C₂×C₄⋊C₄	—	2	1	no	—
464	C₂×C₄⋊C₄	—	2	1	no	—
465	C₂×C₄⋊C₄	—	2	1	no	—
466	C₂×C₄⋊C₄	—	2	1	no	—
467	C₂×C₄⋊C₄	—	2	1	no	—
468	C₂×C₄⋊C₄	—	2	1	no	—
469	C₂×C₄⋊C₄	—	2	1	no	—
470	C₂×C₄⋊C₄	—	2	1	no	—
471	C₂×C₄⋊C₄	—	2	1	no	—
472	C₂×C₄⋊C₄	—	2	1	no	—
473	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
474	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
475	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
476	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
477	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
478	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
479	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
480	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
481	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
482	C₂×C₂²⋊C₄	—	2	1	no	—
483	C₂×C₂²⋊C₄	—	2	1	no	—
484	C₂×C₂²⋊C₄	—	2	1	no	—
485	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
486	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
487	C₂×C₄²	—	2	1	no	—
488	C₂×C₄²	—	2	1	no	—
489	C₂×C₄²	—	2	1	no	—
490	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
491	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
492	#107	C₂³×C₂₃	1	4	yes	—
493	#107	C₂³×C₂₃	1	4	yes	—
494	#107	C₂³×C₂₃	1	4	yes	—
495	#107	C₂³×C₂₃	1	4	yes	—
496	#106	C₂³×C₂₃	1	4	yes	—
497	#106	C₂³×C₂₃	1	4	yes	—
498	#106	C₂³×C₂₃	1	4	yes	—
499	#106	C₂³×C₂₃	1	4	yes	—
500	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
501	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
502	#103	C₂³×C₂₃	1	4	yes	—
503	#103	C₂³×C₂₃	1	4	yes	—
504	#103	C₂³×C₂₃	1	4	yes	—
505	#103	C₂³×C₂₃	1	4	yes	—
506	#103	C₂³×C₂₃	1	4	yes	—
507	#103	C₂³×C₂₃	1	4	yes	—
508	#103	C₂³×C₂₃	1	4	yes	—
509	#103	C₂³×C₂₃	1	4	yes	—
510	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
511	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
512	#97	C₂³×C₂₃	1	4	yes	—
513	C₄×C₈	C₂³×C₂₃	1	4	yes	—
514	C₂₃	C₂×#3242	1	1	yes	characteristic, direct product factor, Sylow
515	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
516	C₂×Q₈	—	2	1	no	—
517	C₂×Q₈	—	2	1	no	—
518	C₂×Q₈	—	2	4	no	—
519	C₂×Q₈	—	2	4	no	—
520	C₂×Q₈	—	2	2	no	—
521	C₂×Q₈	—	2	2	no	—
522	C₂×Q₈	—	2	2	no	—
523	C₂×Q₈	—	2	2	no	—
524	C₂×Q₈	—	8	2	no	—
525	C₂×Q₈	—	8	2	no	—
526	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
527	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	2	2	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	4	no	—
539	C₂²×C₄	—	8	2	no	—
540	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
541	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
542	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
543	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
544	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
545	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
546	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
547	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
548	C₂×C₈	—	2	2	no	—
549	C₂×C₈	—	2	2	no	—
550	C₂×C₈	—	2	2	no	—
551	C₂×C₈	—	2	2	no	—
552	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
553	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
554	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
555	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
556	C₄⋊C₄	—	2	4	no	—
557	C₄⋊C₄	—	2	1	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	2	4	no	—
560	C₄⋊C₄	—	2	4	no	—
561	C₄⋊C₄	—	2	4	no	—
562	C₄⋊C₄	—	2	4	no	—
563	C₄⋊C₄	—	2	4	no	—
564	C₄⋊C₄	—	2	4	no	—
565	C₄⋊C₄	—	2	4	no	—
566	C₄⋊C₄	—	2	4	no	—
567	C₄⋊C₄	—	2	4	no	—
568	C₄⋊C₄	—	2	4	no	—
569	C₄⋊C₄	—	2	4	no	—
570	C₄⋊C₄	—	2	4	no	—
571	C₄⋊C₄	—	2	4	no	—
572	C₄⋊C₄	—	2	4	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
578	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
579	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
580	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
581	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
582	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
583	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
584	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
585	C₂²⋊C₄	—	2	4	no	—
586	C₂²⋊C₄	—	2	4	no	—
587	C₂²⋊C₄	—	2	4	no	—
588	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
589	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
590	C₄²	—	2	4	no	—
591	C₄²	—	2	4	no	—
592	C₄²	—	2	4	no	—
593	C₄²	C₂×D₄×C₂₃	1	2	yes	—
594	C₄²	C₂×D₄×C₂₃	1	2	yes	—
595	C₄²	C₂⁴×C₂₃	1	2	yes	—
596	C₄²	C₂⁴×C₂₃	1	2	yes	—
597	C₂³	—	2	2	no	—
598	C₂³	—	2	2	no	—
599	C₂³	—	2	2	no	—
600	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
601	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
602	Q₈	—	2	2	no	—
603	Q₈	—	2	2	no	—
604	Q₈	—	2	2	no	—
605	Q₈	—	2	2	no	—
606	Q₈	—	4	2	no	—
607	Q₈	—	4	2	no	—
608	Q₈	—	8	4	no	—
609	Q₈	—	8	4	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	4	2	no	—
627	C₂×C₄	—	4	2	no	—
628	C₂×C₄	—	4	2	no	—
629	C₂×C₄	—	4	2	no	—
630	C₂×C₄	—	4	2	no	—
631	C₂×C₄	—	4	2	no	—
632	C₂×C₄	—	4	2	no	—
633	C₂×C₄	—	4	2	no	—
634	C₂×C₄	—	8	4	no	—
635	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
636	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
637	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
638	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
639	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
640	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
641	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
642	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
643	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
644	C₈	—	2	2	no	—
645	C₈	—	2	2	no	—
646	C₈	—	2	2	no	—
647	C₈	—	2	2	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	4	4	no	—
652	C₂²	C₂₃×#536	1	2	yes	—
653	C₂²	C₂₃×#577	1	2	yes	—
654	C₂²	C₂₃×#578	1	2	yes	—
655	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
656	C₄	—	2	2	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	2	no	—
660	C₄	—	2	2	no	—
661	C₄	—	4	2	no	—
662	C₄	—	4	2	no	—
663	C₄	—	4	2	no	—
664	C₄	—	4	2	no	—
665	C₄	—	4	2	no	—
666	C₄	—	4	2	no	—
667	C₄	—	4	2	no	—
668	C₄	—	4	2	no	—
669	C₄	C₂₃×#536	1	2	yes	—
670	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
671	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
672	C₂	—	4	2	no	—
673	C₂	C₂₃×#3242	1	4	yes	direct product factor
674	C₂	C₂×C₂₃×#536	1	1	yes	characteristic
675	C₂	C₂×C₂₃×#577	1	1	yes	characteristic
676	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	C₂⁴×C₂₃	C₂×D₄
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
3. C₂₃×#3242	C₂	direct (N × H)
4. C₂×C₂₃×#501	C₂	semidirect
5. C₂×C₂₃×#499	C₂	semidirect
6. C₂×C₂₃×#491	C₂	semidirect
7. C₂×C₂₃×#487	C₂	semidirect
12. C₂×C₂₃×#479	C₂	semidirect
13. C₂×C₂₃×#479	C₂	semidirect
14. C₂×C₂₃×#477	C₂	semidirect
15. C₂×C₂₃×#475	C₂	semidirect
42. C₂₃×#501	C₂²	semidirect
43. C₂₃×#499	C₂²	semidirect
44. C₂₃×#491	C₂²	semidirect
45. C₂₃×#487	C₂²	semidirect
50. C₂₃×#479	C₂²	semidirect
51. C₂₃×#479	C₂²	semidirect
52. C₂₃×#477	C₂²	semidirect
53. C₂₃×#475	C₂²	semidirect
258. C₂×#3242	C₂₃	direct (N × H)
312. #3242	C₂×C₂₃	direct (N × H)
313. C₂×#501	C₂×C₂₃	semidirect
314. C₂×#499	C₂×C₂₃	semidirect
315. C₂×#491	C₂×C₂₃	semidirect
316. C₂×#487	C₂×C₂₃	semidirect
321. C₂×#479	C₂×C₂₃	semidirect
322. C₂×#479	C₂×C₂₃	semidirect
323. C₂×#477	C₂×C₂₃	semidirect
324. C₂×#475	C₂×C₂₃	semidirect
375. #501	C₂²×C₂₃	semidirect
376. #499	C₂²×C₂₃	semidirect
377. #491	C₂²×C₂₃	semidirect
378. #487	C₂²×C₂₃	semidirect
383. #479	C₂²×C₂₃	semidirect
384. #479	C₂²×C₂₃	semidirect
385. #477	C₂²×C₂₃	semidirect
386. #475	C₂²×C₂₃	semidirect
411. C₂×C₂₃	#3242	direct (N × H)
514. C₂₃	C₂×#3242	direct (N × H)
673. C₂	C₂₃×#3242	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×C₂₃×#544	2
C₂×C₂₃×#541	2
C₂₃×#3242	2
C₂×C₂₃×#501	2
C₂×C₂₃×#499	2
C₂×C₂₃×#491	2
C₂×C₂₃×#487	2
C₂×C₂₃×#484	2
C₂×C₂₃×#485	2
C₂×C₂₃×#483	2
C₂×C₂₃×#479	2
C₂×C₂₃×#477	2
C₂×C₂₃×#475	2
C₂×C₂₃×#433	2
C₂×#3242	23

Subgroups — C2×C23×#3242 #19208482

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3242 #19208482