Subgroups — C₂×C₂₃×#3241 #19208481

Order 5888.

1806 conjugacy classes of subgroups.

The subgroup lattice has 726 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, complemented
2	C₂×C₂₃×#540	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3241	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×#490	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×#486	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×#481	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₂₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₃×#480	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₂₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×#433	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#544	—	2	4	no	—
18	C₂₃×#544	C₂²	1	8	yes	complemented
19	C₂₃×#540	—	2	4	no	—
20	C₂₃×#540	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×#127	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#125	—	2	1	no	—
26	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#123	—	2	1	no	—
30	C₂×C₂₃×#123	—	2	1	no	—
31	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
32	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
33	C₂×C₂₃×#121	—	2	1	no	—
34	C₂×C₂₃×#121	—	2	1	no	—
35	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×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×#490	C₂²	1	8	yes	complemented
45	C₂₃×#486	C₂²	1	8	yes	complemented
46	C₂₃×#482	C₂²	1	8	yes	complemented
47	C₂₃×#482	C₂²	1	8	yes	complemented
48	C₂₃×#481	C₂²	1	8	yes	complemented
49	C₂₃×#480	C₂²	1	8	yes	complemented
50	C₂₃×#478	C₂²	1	8	yes	complemented
51	C₂₃×#478	C₂²	1	8	yes	complemented
52	C₂₃×#476	C₂²	1	8	yes	complemented
53	C₂₃×#474	C₂²	1	8	yes	complemented
54	C₂₃×#433	C₂²	1	8	yes	complemented
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×#102	C₂²	1	1	yes	characteristic
66	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
67	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
68	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
69	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
70	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
71	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
72	C₂×C₂₃×#102	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×D₄×C₂₃	—	2	1	no	—
80	C₂²×D₄×C₂₃	—	2	1	no	—
81	C₂²×D₄×C₂₃	—	2	1	no	—
82	C₂²×D₄×C₂₃	—	2	1	no	—
83	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₂₃	—	2	1	no	—
86	C₂³×C₄×C₂₃	—	2	1	no	—
87	C₂³×C₄×C₂₃	—	2	1	no	—
88	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
93	C₂₃×C₄⋊Q₈	—	2	8	no	—
94	C₂₃×C₄⋊Q₈	—	2	2	no	—
95	C₂₃×C₄⋊Q₈	—	2	2	no	—
96	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
97	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
98	C₂₃×#127	—	2	2	no	—
99	C₂₃×#127	C₂³	1	4	yes	—
100	C₂₃×#125	—	2	8	no	—
101	C₂₃×#125	—	2	2	no	—
102	C₂₃×#125	—	2	2	no	—
103	C₂₃×#125	—	2	2	no	—
104	C₂₃×#125	C₂³	1	4	yes	—
105	C₂₃×#125	C₂³	1	4	yes	—
106	C₂₃×#125	C₂³	1	4	yes	—
107	C₂₃×#123	—	2	8	no	—
108	C₂₃×#123	—	2	8	no	—
109	C₂₃×C₂²⋊Q₈	—	2	8	no	—
110	C₂₃×C₂²⋊Q₈	—	2	8	no	—
111	C₂₃×#121	—	2	2	no	—
112	C₂₃×#121	—	2	2	no	—
113	C₂₃×#121	—	2	8	no	—
114	C₂₃×#121	—	2	8	no	—
115	C₂₃×#121	C₂³	1	4	yes	—
116	C₂₃×#121	C₂³	1	4	yes	—
117	C₄×D₄×C₂₃	—	2	2	no	—
118	C₄×D₄×C₂₃	—	2	2	no	—
119	C₄×D₄×C₂₃	C₂³	1	4	yes	—
120	C₄×D₄×C₂₃	C₂³	1	4	yes	—
121	C₂₃×#117	—	2	2	no	—
122	C₂₃×#117	D₄	1	4	yes	—
123	C₂₃×#117	C₂³	1	4	yes	—
124	C₂₃×#117	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
126	C₂×C₄⋊C₄×C₂₃	—	2	2	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	—	2	1	no	—
148	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
149	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
150	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
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×#102	C₂³	1	4	yes	—
165	C₂₃×#102	C₂³	1	4	yes	—
166	C₂₃×#102	C₂³	1	4	yes	—
167	C₂₃×#102	C₂³	1	4	yes	—
168	C₂₃×#102	C₂³	1	4	yes	—
169	C₂₃×#102	C₂³	1	4	yes	—
170	C₂₃×#102	C₂³	1	4	yes	—
171	C₂₃×#102	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	—	2	1	no	—
177	C₂⁴×C₂₃	—	2	1	no	—
178	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
179	C₂×Q₈×C₂₃	—	2	4	no	—
180	C₂×Q₈×C₂₃	—	2	4	no	—
181	C₂×Q₈×C₂₃	—	8	2	no	—
182	C₂×Q₈×C₂₃	—	8	2	no	—
183	C₂×D₄×C₂₃	—	2	4	no	—
184	C₂×D₄×C₂₃	—	2	4	no	—
185	C₂×D₄×C₂₃	—	2	1	no	—
186	C₂×D₄×C₂₃	—	2	1	no	—
187	C₂×D₄×C₂₃	—	2	4	no	—
188	C₂×D₄×C₂₃	—	2	4	no	—
189	C₂×D₄×C₂₃	—	2	2	no	—
190	C₂×D₄×C₂₃	—	2	2	no	—
191	C₂×D₄×C₂₃	—	2	2	no	—
192	C₂×D₄×C₂₃	—	2	2	no	—
193	C₂×D₄×C₂₃	—	8	2	no	—
194	C₂×D₄×C₂₃	—	8	2	no	—
195	C₂×D₄×C₂₃	—	8	2	no	—
196	C₂×D₄×C₂₃	—	8	2	no	—
197	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
198	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₂₃	—	2	2	no	—
200	C₂²×C₄×C₂₃	—	2	2	no	—
201	C₂²×C₄×C₂₃	—	2	1	no	—
202	C₂²×C₄×C₂₃	—	2	1	no	—
203	C₂²×C₄×C₂₃	—	2	1	no	—
204	C₂²×C₄×C₂₃	—	2	1	no	—
205	C₂²×C₄×C₂₃	—	2	1	no	—
206	C₂²×C₄×C₂₃	—	2	1	no	—
207	C₂²×C₄×C₂₃	—	2	4	no	—
208	C₂²×C₄×C₂₃	—	2	4	no	—
209	C₂²×C₄×C₂₃	—	2	4	no	—
210	C₂²×C₄×C₂₃	—	8	2	no	—
211	C₂²×C₄×C₂₃	—	8	2	no	—
212	C₂²×C₄×C₂₃	—	8	2	no	—
213	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
214	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
221	C₂×C₈×C₂₃	—	2	2	no	—
222	C₂×C₈×C₂₃	—	2	2	no	—
223	C₂×C₈×C₂₃	—	2	2	no	—
224	C₂×C₈×C₂₃	—	2	2	no	—
225	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
226	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
227	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
228	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
229	C₄⋊C₄×C₂₃	—	2	4	no	—
230	C₄⋊C₄×C₂₃	—	2	1	no	—
231	C₄⋊C₄×C₂₃	—	2	1	no	—
232	C₄⋊C₄×C₂₃	—	2	4	no	—
233	C₄⋊C₄×C₂₃	—	2	4	no	—
234	C₄⋊C₄×C₂₃	—	2	4	no	—
235	C₄⋊C₄×C₂₃	—	2	4	no	—
236	C₄⋊C₄×C₂₃	—	2	4	no	—
237	C₄⋊C₄×C₂₃	—	2	4	no	—
238	C₄⋊C₄×C₂₃	—	2	4	no	—
239	C₄⋊C₄×C₂₃	—	2	4	no	—
240	C₄⋊C₄×C₂₃	—	2	1	no	—
241	C₄⋊C₄×C₂₃	—	2	1	no	—
242	C₄⋊C₄×C₂₃	—	2	1	no	—
243	C₄⋊C₄×C₂₃	—	2	1	no	—
244	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
245	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
246	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
247	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
248	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
249	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
250	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
251	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
252	C₂²⋊C₄×C₂₃	—	2	4	no	—
253	C₂²⋊C₄×C₂₃	—	2	4	no	—
254	C₂²⋊C₄×C₂₃	—	2	4	no	—
255	C₂²⋊C₄×C₂₃	—	2	4	no	—
256	C₂²⋊C₄×C₂₃	—	2	4	no	—
257	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
258	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
259	C₄²×C₂₃	—	2	4	no	—
260	C₄²×C₂₃	C₂×D₄	1	2	yes	—
261	C₄²×C₂₃	C₂×D₄	1	2	yes	—
262	C₄²×C₂₃	C₂⁴	1	2	yes	—
263	C₄²×C₂₃	C₂⁴	1	2	yes	—
264	C₂×#3241	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
265	C₂³×C₂₃	—	2	2	no	—
266	C₂³×C₂₃	—	2	2	no	—
267	C₂³×C₂₃	—	2	2	no	—
268	C₂³×C₂₃	—	2	2	no	—
269	C₂³×C₂₃	—	2	2	no	—
270	C₂³×C₂₃	—	4	2	no	—
271	C₂³×C₂₃	—	4	2	no	—
272	C₂³×C₂₃	—	4	2	no	—
273	C₂³×C₂₃	—	4	2	no	—
274	C₂³×C₂₃	—	4	2	no	—
275	C₂³×C₂₃	—	4	2	no	—
276	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
277	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
278	Q₈×C₂₃	—	8	4	no	—
279	Q₈×C₂₃	—	8	4	no	—
280	D₄×C₂₃	—	2	2	no	—
281	D₄×C₂₃	—	2	2	no	—
282	D₄×C₂₃	—	2	2	no	—
283	D₄×C₂₃	—	2	2	no	—
284	D₄×C₂₃	—	4	2	no	—
285	D₄×C₂₃	—	4	2	no	—
286	D₄×C₂₃	—	8	4	no	—
287	D₄×C₂₃	—	8	4	no	—
288	D₄×C₂₃	—	8	4	no	—
289	D₄×C₂₃	—	8	4	no	—
290	C₂×C₄×C₂₃	—	2	2	no	—
291	C₂×C₄×C₂₃	—	2	2	no	—
292	C₂×C₄×C₂₃	—	2	2	no	—
293	C₂×C₄×C₂₃	—	2	2	no	—
294	C₂×C₄×C₂₃	—	2	2	no	—
295	C₂×C₄×C₂₃	—	2	4	no	—
296	C₂×C₄×C₂₃	—	2	2	no	—
297	C₂×C₄×C₂₃	—	2	2	no	—
298	C₂×C₄×C₂₃	—	2	2	no	—
299	C₂×C₄×C₂₃	—	2	2	no	—
300	C₂×C₄×C₂₃	—	2	2	no	—
301	C₂×C₄×C₂₃	—	2	2	no	—
302	C₂×C₄×C₂₃	—	2	2	no	—
303	C₂×C₄×C₂₃	—	2	2	no	—
304	C₂×C₄×C₂₃	—	4	2	no	—
305	C₂×C₄×C₂₃	—	4	2	no	—
306	C₂×C₄×C₂₃	—	4	2	no	—
307	C₂×C₄×C₂₃	—	4	2	no	—
308	C₂×C₄×C₂₃	—	4	2	no	—
309	C₂×C₄×C₂₃	—	4	2	no	—
310	C₂×C₄×C₂₃	—	8	4	no	—
311	C₂×C₄×C₂₃	—	8	4	no	—
312	C₂×C₄×C₂₃	—	8	4	no	—
313	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
314	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
315	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
316	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
317	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
318	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
320	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
321	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
322	C₈×C₂₃	—	2	2	no	—
323	C₈×C₂₃	—	2	2	no	—
324	C₈×C₂₃	—	2	2	no	—
325	C₈×C₂₃	—	2	2	no	—
326	C₂×#544	C₂×C₂₃	1	1	yes	characteristic, complemented
327	C₂×#540	C₂×C₂₃	1	1	yes	characteristic
328	#3241	C₂×C₂₃	1	16	yes	direct product factor
329	C₂×#501	C₂×C₂₃	1	1	yes	characteristic, complemented
330	C₂×#499	C₂×C₂₃	1	1	yes	characteristic, complemented
331	C₂×#490	C₂×C₂₃	1	1	yes	characteristic, complemented
332	C₂×#486	C₂×C₂₃	1	1	yes	characteristic, complemented
333	C₂×#481	C₂×C₂₃	1	1	yes	characteristic, complemented
334	C₂×#482	C₂×C₂₃	1	1	yes	characteristic, complemented
335	C₂×#482	C₂×C₂₃	1	1	yes	characteristic, complemented
336	C₂×#480	C₂×C₂₃	1	1	yes	characteristic, complemented
337	C₂×#478	C₂×C₂₃	1	1	yes	characteristic, complemented
338	C₂×#478	C₂×C₂₃	1	1	yes	characteristic, complemented
339	C₂×#476	C₂×C₂₃	1	1	yes	characteristic, complemented
340	C₂×#474	C₂×C₂₃	1	1	yes	characteristic, complemented
341	C₂×#433	C₂×C₂₃	1	1	yes	characteristic, complemented
342	C₂²×C₂₃	—	2	2	no	—
343	C₂²×C₂₃	—	2	2	no	—
344	C₂²×C₂₃	—	2	2	no	—
345	C₂²×C₂₃	—	4	4	no	—
346	C₂²×C₂₃	—	4	2	no	—
347	C₂²×C₂₃	—	4	2	no	—
348	C₂²×C₂₃	—	4	2	no	—
349	C₂²×C₂₃	—	4	2	no	—
350	C₂²×C₂₃	—	4	2	no	—
351	C₂²×C₂₃	—	4	2	no	—
352	C₂²×C₂₃	—	8	4	no	—
353	C₂²×C₂₃	—	8	4	no	—
354	C₂²×C₂₃	#536	1	2	yes	—
355	C₂²×C₂₃	#576	1	2	yes	—
356	C₂²×C₂₃	#577	1	2	yes	—
357	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
358	C₄×C₂₃	—	2	2	no	—
359	C₄×C₂₃	—	2	2	no	—
360	C₄×C₂₃	—	2	2	no	—
361	C₄×C₂₃	—	2	2	no	—
362	C₄×C₂₃	—	2	2	no	—
363	C₄×C₂₃	—	4	2	no	—
364	C₄×C₂₃	—	4	2	no	—
365	C₄×C₂₃	—	4	2	no	—
366	C₄×C₂₃	—	4	2	no	—
367	C₄×C₂₃	—	4	2	no	—
368	C₄×C₂₃	—	4	2	no	—
369	C₄×C₂₃	#536	1	2	yes	—
370	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
371	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
372	#544	—	2	4	no	—
373	#544	C₂²×C₂₃	1	8	yes	complemented
374	#540	—	2	4	no	—
375	#540	C₂²×C₂₃	1	8	yes	—
376	C₂×C₄⋊Q₈	—	2	1	no	—
377	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
378	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
379	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
380	C₂×#125	—	2	1	no	—
381	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
382	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
383	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
384	C₂×#123	—	2	1	no	—
385	C₂×#123	—	2	1	no	—
386	C₂×C₂²⋊Q₈	—	2	1	no	—
387	C₂×C₂²⋊Q₈	—	2	1	no	—
388	C₂×#121	—	2	1	no	—
389	C₂×#121	—	2	1	no	—
390	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
391	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
392	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
393	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
394	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
395	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
396	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
397	#501	C₂²×C₂₃	1	8	yes	complemented
398	#499	C₂²×C₂₃	1	8	yes	complemented
399	#490	C₂²×C₂₃	1	8	yes	complemented
400	#486	C₂²×C₂₃	1	8	yes	complemented
401	#482	C₂²×C₂₃	1	8	yes	complemented
402	#482	C₂²×C₂₃	1	8	yes	complemented
403	#481	C₂²×C₂₃	1	8	yes	complemented
404	#480	C₂²×C₂₃	1	8	yes	complemented
405	#478	C₂²×C₂₃	1	8	yes	complemented
406	#478	C₂²×C₂₃	1	8	yes	complemented
407	#476	C₂²×C₂₃	1	8	yes	complemented
408	#474	C₂²×C₂₃	1	8	yes	complemented
409	#433	C₂²×C₂₃	1	8	yes	complemented
410	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
411	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
412	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
413	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
414	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
415	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
416	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
417	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
418	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
419	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
420	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
421	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
422	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
423	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
424	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
425	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
426	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
427	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
428	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
429	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
430	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
431	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
432	C₂×C₂₃	—	4	2	no	—
433	C₂×C₂₃	—	8	2	no	—
434	C₂×C₂₃	—	8	2	no	—
435	C₂×C₂₃	#3241	1	4	yes	direct product factor
436	C₂×C₂₃	C₂×#536	1	1	yes	characteristic
437	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
438	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
439	C₂²×Q₈	—	2	1	no	—
440	C₂²×Q₈	—	2	1	no	—
441	C₂²×D₄	—	2	1	no	—
442	C₂²×D₄	—	2	1	no	—
443	C₂²×D₄	—	2	1	no	—
444	C₂²×D₄	—	2	1	no	—
445	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
446	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
447	C₂³×C₄	—	2	1	no	—
448	C₂³×C₄	—	2	1	no	—
449	C₂³×C₄	—	2	1	no	—
450	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
451	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
452	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
453	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
454	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
455	C₄⋊Q₈	—	2	8	no	—
456	C₄⋊Q₈	—	2	2	no	—
457	C₄⋊Q₈	—	2	2	no	—
458	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
459	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
460	#127	—	2	2	no	—
461	#127	C₂³×C₂₃	1	4	yes	—
462	#125	—	2	8	no	—
463	#125	—	2	2	no	—
464	#125	—	2	2	no	—
465	#125	—	2	2	no	—
466	#125	C₂³×C₂₃	1	4	yes	—
467	#125	C₂³×C₂₃	1	4	yes	—
468	#125	C₂³×C₂₃	1	4	yes	—
469	#123	—	2	8	no	—
470	#123	—	2	8	no	—
471	C₂²⋊Q₈	—	2	8	no	—
472	C₂²⋊Q₈	—	2	8	no	—
473	#121	—	2	2	no	—
474	#121	—	2	2	no	—
475	#121	—	2	8	no	—
476	#121	—	2	8	no	—
477	#121	C₂³×C₂₃	1	4	yes	—
478	#121	C₂³×C₂₃	1	4	yes	—
479	C₄×D₄	—	2	2	no	—
480	C₄×D₄	—	2	2	no	—
481	C₄×D₄	C₂³×C₂₃	1	4	yes	—
482	C₄×D₄	C₂³×C₂₃	1	4	yes	—
483	#117	—	2	2	no	—
484	#117	D₄×C₂₃	1	4	yes	—
485	#117	C₂³×C₂₃	1	4	yes	—
486	#117	C₂³×C₂₃	1	4	yes	—
487	C₂×C₄⋊C₄	—	2	1	no	—
488	C₂×C₄⋊C₄	—	2	2	no	—
489	C₂×C₄⋊C₄	—	2	1	no	—
490	C₂×C₄⋊C₄	—	2	1	no	—
491	C₂×C₄⋊C₄	—	2	1	no	—
492	C₂×C₄⋊C₄	—	2	1	no	—
493	C₂×C₄⋊C₄	—	2	1	no	—
494	C₂×C₄⋊C₄	—	2	1	no	—
495	C₂×C₄⋊C₄	—	2	1	no	—
496	C₂×C₄⋊C₄	—	2	1	no	—
497	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
498	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
500	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
501	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
502	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
506	C₂×C₂²⋊C₄	—	2	1	no	—
507	C₂×C₂²⋊C₄	—	2	1	no	—
508	C₂×C₂²⋊C₄	—	2	1	no	—
509	C₂×C₂²⋊C₄	—	2	1	no	—
510	C₂×C₂²⋊C₄	—	2	1	no	—
511	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
512	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
513	C₂×C₄²	—	2	1	no	—
514	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
515	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
516	#107	C₂³×C₂₃	1	4	yes	—
517	#107	C₂³×C₂₃	1	4	yes	—
518	#107	C₂³×C₂₃	1	4	yes	—
519	#107	C₂³×C₂₃	1	4	yes	—
520	#106	C₂³×C₂₃	1	4	yes	—
521	#106	C₂³×C₂₃	1	4	yes	—
522	#106	C₂³×C₂₃	1	4	yes	—
523	#106	C₂³×C₂₃	1	4	yes	—
524	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
525	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
526	#102	C₂³×C₂₃	1	4	yes	—
527	#102	C₂³×C₂₃	1	4	yes	—
528	#102	C₂³×C₂₃	1	4	yes	—
529	#102	C₂³×C₂₃	1	4	yes	—
530	#102	C₂³×C₂₃	1	4	yes	—
531	#102	C₂³×C₂₃	1	4	yes	—
532	#102	C₂³×C₂₃	1	4	yes	—
533	#102	C₂³×C₂₃	1	4	yes	—
534	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
535	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
536	#97	C₂³×C₂₃	1	4	yes	—
537	C₄×C₈	C₂³×C₂₃	1	4	yes	—
538	C₂₃	C₂×#3241	1	1	yes	characteristic, direct product factor, Sylow
539	C₂⁴	—	2	1	no	—
540	C₂⁴	—	2	1	no	—
541	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
542	C₂×Q₈	—	2	4	no	—
543	C₂×Q₈	—	2	4	no	—
544	C₂×Q₈	—	8	2	no	—
545	C₂×Q₈	—	8	2	no	—
546	C₂×D₄	—	2	4	no	—
547	C₂×D₄	—	2	4	no	—
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	—	2	1	no	—
550	C₂×D₄	—	2	4	no	—
551	C₂×D₄	—	2	4	no	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	2	2	no	—
555	C₂×D₄	—	2	2	no	—
556	C₂×D₄	—	8	2	no	—
557	C₂×D₄	—	8	2	no	—
558	C₂×D₄	—	8	2	no	—
559	C₂×D₄	—	8	2	no	—
560	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
561	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	—	2	4	no	—
572	C₂²×C₄	—	2	4	no	—
573	C₂²×C₄	—	8	2	no	—
574	C₂²×C₄	—	8	2	no	—
575	C₂²×C₄	—	8	2	no	—
576	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
577	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
578	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
579	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
580	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
581	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
582	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
583	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
584	C₂×C₈	—	2	2	no	—
585	C₂×C₈	—	2	2	no	—
586	C₂×C₈	—	2	2	no	—
587	C₂×C₈	—	2	2	no	—
588	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
589	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
590	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
591	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
592	C₄⋊C₄	—	2	4	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	2	1	no	—
595	C₄⋊C₄	—	2	4	no	—
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
608	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
609	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
610	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
611	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
612	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
613	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
614	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₂²⋊C₄	—	2	4	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	4	no	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
621	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
622	C₄²	—	2	4	no	—
623	C₄²	C₂×D₄×C₂₃	1	2	yes	—
624	C₄²	C₂×D₄×C₂₃	1	2	yes	—
625	C₄²	C₂⁴×C₂₃	1	2	yes	—
626	C₄²	C₂⁴×C₂₃	1	2	yes	—
627	C₂³	—	2	2	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	2	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	4	2	no	—
633	C₂³	—	4	2	no	—
634	C₂³	—	4	2	no	—
635	C₂³	—	4	2	no	—
636	C₂³	—	4	2	no	—
637	C₂³	—	4	2	no	—
638	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
639	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
640	Q₈	—	8	4	no	—
641	Q₈	—	8	4	no	—
642	D₄	—	2	2	no	—
643	D₄	—	2	2	no	—
644	D₄	—	2	2	no	—
645	D₄	—	2	2	no	—
646	D₄	—	4	2	no	—
647	D₄	—	4	2	no	—
648	D₄	—	8	4	no	—
649	D₄	—	8	4	no	—
650	D₄	—	8	4	no	—
651	D₄	—	8	4	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	4	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	4	2	no	—
667	C₂×C₄	—	4	2	no	—
668	C₂×C₄	—	4	2	no	—
669	C₂×C₄	—	4	2	no	—
670	C₂×C₄	—	4	2	no	—
671	C₂×C₄	—	4	2	no	—
672	C₂×C₄	—	8	4	no	—
673	C₂×C₄	—	8	4	no	—
674	C₂×C₄	—	8	4	no	—
675	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
676	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
677	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
678	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
679	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
680	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
681	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
682	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
683	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
684	C₈	—	2	2	no	—
685	C₈	—	2	2	no	—
686	C₈	—	2	2	no	—
687	C₈	—	2	2	no	—
688	C₂²	—	2	2	no	—
689	C₂²	—	2	2	no	—
690	C₂²	—	2	2	no	—
691	C₂²	—	4	4	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	4	2	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	8	4	no	—
699	C₂²	—	8	4	no	—
700	C₂²	C₂₃×#536	1	2	yes	—
701	C₂²	C₂₃×#576	1	2	yes	—
702	C₂²	C₂₃×#577	1	2	yes	—
703	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
704	C₄	—	2	2	no	—
705	C₄	—	2	2	no	—
706	C₄	—	2	2	no	—
707	C₄	—	2	2	no	—
708	C₄	—	2	2	no	—
709	C₄	—	4	2	no	—
710	C₄	—	4	2	no	—
711	C₄	—	4	2	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	2	no	—
715	C₄	C₂₃×#536	1	2	yes	—
716	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
717	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
718	C₂	—	4	2	no	—
719	C₂	—	8	2	no	—
720	C₂	—	8	2	no	—
721	C₂	C₂₃×#3241	1	4	yes	direct product factor
722	C₂	C₂×C₂₃×#536	1	1	yes	characteristic
723	C₂	C₂×C₂₃×#576	1	1	yes	characteristic
724	C₂	C₂×C₂₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂×C₂₃×#540	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. C₂×C₂₃×#544	C₂	semidirect
3. C₂₃×#3241	C₂	direct (N × H)
4. C₂×C₂₃×#501	C₂	semidirect
5. C₂×C₂₃×#499	C₂	semidirect
6. C₂×C₂₃×#490	C₂	semidirect
7. C₂×C₂₃×#486	C₂	semidirect
8. C₂×C₂₃×#481	C₂	semidirect
9. C₂×C₂₃×#482	C₂	semidirect
10. C₂×C₂₃×#482	C₂	semidirect
11. C₂×C₂₃×#480	C₂	semidirect
12. C₂×C₂₃×#478	C₂	semidirect
13. C₂×C₂₃×#478	C₂	semidirect
14. C₂×C₂₃×#476	C₂	semidirect
15. C₂×C₂₃×#474	C₂	semidirect
16. C₂×C₂₃×#433	C₂	semidirect
18. C₂₃×#544	C₂²	semidirect
42. C₂₃×#501	C₂²	semidirect
43. C₂₃×#499	C₂²	semidirect
44. C₂₃×#490	C₂²	semidirect
45. C₂₃×#486	C₂²	semidirect
46. C₂₃×#482	C₂²	semidirect
47. C₂₃×#482	C₂²	semidirect
48. C₂₃×#481	C₂²	semidirect
49. C₂₃×#480	C₂²	semidirect
50. C₂₃×#478	C₂²	semidirect
51. C₂₃×#478	C₂²	semidirect
52. C₂₃×#476	C₂²	semidirect
53. C₂₃×#474	C₂²	semidirect
54. C₂₃×#433	C₂²	semidirect
264. C₂×#3241	C₂₃	direct (N × H)
326. C₂×#544	C₂×C₂₃	semidirect
328. #3241	C₂×C₂₃	direct (N × H)
329. C₂×#501	C₂×C₂₃	semidirect
330. C₂×#499	C₂×C₂₃	semidirect
331. C₂×#490	C₂×C₂₃	semidirect
332. C₂×#486	C₂×C₂₃	semidirect
333. C₂×#481	C₂×C₂₃	semidirect
334. C₂×#482	C₂×C₂₃	semidirect
335. C₂×#482	C₂×C₂₃	semidirect
336. C₂×#480	C₂×C₂₃	semidirect
337. C₂×#478	C₂×C₂₃	semidirect
338. C₂×#478	C₂×C₂₃	semidirect
339. C₂×#476	C₂×C₂₃	semidirect
340. C₂×#474	C₂×C₂₃	semidirect
341. C₂×#433	C₂×C₂₃	semidirect
373. #544	C₂²×C₂₃	semidirect
397. #501	C₂²×C₂₃	semidirect
398. #499	C₂²×C₂₃	semidirect
399. #490	C₂²×C₂₃	semidirect
400. #486	C₂²×C₂₃	semidirect
401. #482	C₂²×C₂₃	semidirect
402. #482	C₂²×C₂₃	semidirect
403. #481	C₂²×C₂₃	semidirect
404. #480	C₂²×C₂₃	semidirect
405. #478	C₂²×C₂₃	semidirect
406. #478	C₂²×C₂₃	semidirect
407. #476	C₂²×C₂₃	semidirect
408. #474	C₂²×C₂₃	semidirect
409. #433	C₂²×C₂₃	semidirect
435. C₂×C₂₃	#3241	direct (N × H)
538. C₂₃	C₂×#3241	direct (N × H)
721. C₂	C₂₃×#3241	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×#540	2
C₂₃×#3241	2
C₂×C₂₃×#501	2
C₂×C₂₃×#499	2
C₂×C₂₃×#490	2
C₂×C₂₃×#486	2
C₂×C₂₃×#481	2
C₂×C₂₃×#482	2
C₂×C₂₃×#480	2
C₂×C₂₃×#478	2
C₂×C₂₃×#476	2
C₂×C₂₃×#474	2
C₂×C₂₃×#433	2
C₂×#3241	23

Subgroups — C2×C23×#3241 #19208481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3241 #19208481