Subgroups — C₂×C₂₃×#3376 #19208939

Order 5888.

1886 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3376	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₃×#491	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#489	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×#488	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×#475	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₂₃×#463	C₂	1	1	yes	maximal, characteristic
11	C₂×C₂₃×#463	C₂	1	1	yes	maximal, characteristic
12	C₂×C₂₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₃×#446	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₂₃×#442	C₂	1	1	yes	maximal, characteristic
15	C₂×C₂₃×#440	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×SD₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
20	C₂₃×#556	—	2	4	no	—
21	C₂₃×#556	C₂²	1	8	yes	complemented
22	C₂₃×#554	—	2	4	no	—
23	C₂₃×#554	C₂²	1	8	yes	complemented
24	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#126	—	2	1	no	—
27	C₂×C₂₃×#126	—	2	1	no	—
28	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
33	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
34	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
35	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
36	C₂×C₄×Q₈×C₂₃	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×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
43	C₂×C₂₃×#117	—	2	1	no	—
44	C₂²×C₄⋊C₄×C₂₃	—	2	1	no	—
45	C₂₃×#491	C₂²	1	8	yes	complemented
46	C₂₃×#489	C₂²	1	8	yes	complemented
47	C₂₃×#488	C₂²	1	8	yes	complemented
48	C₂₃×#479	C₂²	1	8	yes	complemented
49	C₂₃×#478	C₂²	1	8	yes	complemented
50	C₂₃×#475	C₂²	1	8	yes	complemented
51	C₂₃×#463	C₂²	1	8	yes	—
52	C₂₃×#463	C₂²	1	8	yes	—
53	C₂₃×#461	C₂²	1	8	yes	complemented
54	C₂₃×#446	C₂²	1	8	yes	complemented
55	C₂₃×#442	C₂²	1	8	yes	—
56	C₂₃×#440	C₂²	1	8	yes	complemented
57	C₄×SD₁₆×C₂₃	C₂²	1	8	yes	complemented
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×C₄⋊C₈	C₂²	1	1	yes	characteristic
62	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
63	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
64	C₂×C₂₃×#103	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×#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×#102	C₂²	1	1	yes	characteristic
74	C₂×C₂₃×#97	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	D₄	1	1	yes	characteristic
79	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
80	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₂₃	—	2	1	no	—
84	C₂³×C₄×C₂₃	—	2	1	no	—
85	C₂³×C₄×C₂₃	—	2	1	no	—
86	C₂³×C₄×C₂₃	—	2	1	no	—
87	C₂×SD₁₆×C₂₃	—	2	4	no	—
88	C₂×SD₁₆×C₂₃	—	2	4	no	—
89	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
90	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
91	C₂×D₈×C₂₃	—	2	4	no	—
92	C₂×D₈×C₂₃	C₂³	1	4	yes	—
93	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
97	C₂₃×C₄⋊Q₈	—	2	2	no	—
98	C₂₃×C₄⋊Q₈	—	2	2	no	—
99	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
100	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
101	C₂₃×#126	—	2	8	no	—
102	C₂₃×#126	—	2	8	no	—
103	C₂₃×#125	—	2	2	no	—
104	C₂₃×#125	—	2	2	no	—
105	C₂₃×#125	C₂³	1	4	yes	—
106	C₂₃×#125	C₂³	1	4	yes	—
107	C₂₃×#124	—	2	2	no	—
108	C₂₃×#124	—	2	2	no	—
109	C₂₃×#124	C₂³	1	4	yes	—
110	C₂₃×#124	C₂³	1	4	yes	—
111	C₂₃×C₂²⋊Q₈	—	2	8	no	—
112	C₂₃×C₂²⋊Q₈	—	2	8	no	—
113	C₂₃×C₂²⋊Q₈	—	2	8	no	—
114	C₂₃×C₂²⋊Q₈	—	2	8	no	—
115	C₄×Q₈×C₂₃	—	2	2	no	—
116	C₄×Q₈×C₂₃	—	2	2	no	—
117	C₄×Q₈×C₂₃	D₄	1	4	yes	—
118	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
119	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
120	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
121	C₄×D₄×C₂₃	—	2	2	no	—
122	C₄×D₄×C₂₃	—	2	2	no	—
123	C₄×D₄×C₂₃	—	2	2	no	—
124	C₄×D₄×C₂₃	—	2	2	no	—
125	C₄×D₄×C₂₃	C₂³	1	4	yes	—
126	C₄×D₄×C₂₃	C₂³	1	4	yes	—
127	C₄×D₄×C₂₃	C₂³	1	4	yes	—
128	C₄×D₄×C₂₃	C₂³	1	4	yes	—
129	C₂₃×#117	—	2	8	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	—	2	1	no	—
136	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
137	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
138	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
139	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
140	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
148	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
149	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
150	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
151	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
152	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
153	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
154	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
155	C₂×C₄²×C₂₃	—	2	1	no	—
156	C₂×C₄²×C₂₃	—	2	1	no	—
157	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
160	C₂₃×#107	C₂³	1	4	yes	—
161	C₂₃×#106	C₂³	1	4	yes	—
162	C₂₃×#106	C₂³	1	4	yes	—
163	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
164	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
165	C₂₃×C₄⋊C₈	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×#102	C₂³	1	4	yes	—
173	C₂₃×#102	C₂³	1	4	yes	—
174	C₂₃×#102	C₂³	1	4	yes	—
175	C₂₃×#102	C₂³	1	4	yes	—
176	C₂₃×#97	C₂³	1	4	yes	—
177	C₂₃×#97	C₂³	1	4	yes	—
178	C₄×C₈×C₂₃	C₂³	1	4	yes	—
179	C₂⁴×C₂₃	—	2	1	no	—
180	C₂⁴×C₂₃	—	2	1	no	—
181	C₂×Q₈×C₂₃	—	2	1	no	—
182	C₂×Q₈×C₂₃	—	2	1	no	—
183	C₂×Q₈×C₂₃	—	2	4	no	—
184	C₂×Q₈×C₂₃	—	2	2	no	—
185	C₂×Q₈×C₂₃	—	2	2	no	—
186	C₂×Q₈×C₂₃	—	2	2	no	—
187	C₂×Q₈×C₂₃	—	2	2	no	—
188	C₂×Q₈×C₂₃	—	4	2	no	—
189	C₂×Q₈×C₂₃	—	8	2	no	—
190	C₂×Q₈×C₂₃	C₂×D₄	1	4	yes	—
191	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
192	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
193	C₂×D₄×C₂₃	—	2	1	no	—
194	C₂×D₄×C₂₃	—	2	1	no	—
195	C₂×D₄×C₂₃	—	2	2	no	—
196	C₂×D₄×C₂₃	—	2	2	no	—
197	C₂×D₄×C₂₃	—	2	2	no	—
198	C₂×D₄×C₂₃	#41	1	4	yes	—
199	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
200	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
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	—	2	4	no	—
211	C₂²×C₄×C₂₃	—	4	4	no	—
212	C₂²×C₄×C₂₃	—	4	4	no	—
213	C₂²×C₄×C₂₃	—	8	2	no	—
214	C₂²×C₄×C₂₃	—	8	2	no	—
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	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
222	SD₁₆×C₂₃	—	2	8	no	—
223	SD₁₆×C₂₃	—	2	8	no	—
224	D₈×C₂₃	—	2	8	no	—
225	C₂×C₈×C₂₃	—	2	2	no	—
226	C₂×C₈×C₂₃	—	2	2	no	—
227	C₂×C₈×C₂₃	—	2	2	no	—
228	C₂×C₈×C₂₃	—	2	2	no	—
229	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
230	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
231	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
232	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
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	4	no	—
241	C₄⋊C₄×C₂₃	—	2	4	no	—
242	C₄⋊C₄×C₂₃	—	2	1	no	—
243	C₄⋊C₄×C₂₃	—	2	1	no	—
244	C₄⋊C₄×C₂₃	—	2	1	no	—
245	C₄⋊C₄×C₂₃	—	2	1	no	—
246	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
247	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
248	C₄⋊C₄×C₂₃	C₂×D₄	1	4	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	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
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	—	2	4	no	—
258	C₂²⋊C₄×C₂₃	—	2	4	no	—
259	C₂²⋊C₄×C₂₃	—	2	4	no	—
260	C₂²⋊C₄×C₂₃	—	2	4	no	—
261	C₄²×C₂₃	—	2	4	no	—
262	C₄²×C₂₃	—	2	4	no	—
263	C₄²×C₂₃	C₂×D₄	1	2	yes	—
264	C₄²×C₂₃	C₂×D₄	1	2	yes	—
265	C₄²×C₂₃	C₂×D₄	1	2	yes	—
266	C₄²×C₂₃	C₂⁴	1	2	yes	—
267	C₄²×C₂₃	C₂⁴	1	2	yes	—
268	C₄²×C₂₃	C₂⁴	1	2	yes	—
269	C₂×#3376	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
270	C₂³×C₂₃	—	2	4	no	—
271	C₂³×C₂₃	—	2	2	no	—
272	C₂³×C₂₃	—	2	2	no	—
273	C₂³×C₂₃	—	4	2	no	—
274	C₂³×C₂₃	—	4	2	no	—
275	C₂³×C₂₃	—	4	2	no	—
276	C₂³×C₂₃	—	4	2	no	—
277	C₂³×C₂₃	—	4	2	no	—
278	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
279	Q₈×C₂₃	—	2	2	no	—
280	Q₈×C₂₃	—	2	2	no	—
281	Q₈×C₂₃	—	2	2	no	—
282	Q₈×C₂₃	—	2	2	no	—
283	Q₈×C₂₃	—	4	4	no	—
284	Q₈×C₂₃	—	4	2	no	—
285	Q₈×C₂₃	—	4	2	no	—
286	Q₈×C₂₃	—	8	4	no	—
287	D₄×C₂₃	—	2	4	no	—
288	D₄×C₂₃	—	2	2	no	—
289	D₄×C₂₃	—	2	2	no	—
290	D₄×C₂₃	—	2	2	no	—
291	D₄×C₂₃	—	4	2	no	—
292	D₄×C₂₃	C₂×#41	1	4	yes	—
293	C₂×C₄×C₂₃	—	2	2	no	—
294	C₂×C₄×C₂₃	—	2	2	no	—
295	C₂×C₄×C₂₃	—	2	2	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	—	2	2	no	—
305	C₂×C₄×C₂₃	—	4	8	no	—
306	C₂×C₄×C₂₃	—	4	8	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	—	4	2	no	—
311	C₂×C₄×C₂₃	—	4	2	no	—
312	C₂×C₄×C₂₃	—	4	2	no	—
313	C₂×C₄×C₂₃	—	8	4	no	—
314	C₂×C₄×C₂₃	—	8	4	no	—
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	2	yes	—
319	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
320	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
321	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
322	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
323	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
324	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
325	C₈×C₂₃	—	2	2	no	—
326	C₈×C₂₃	—	2	2	no	—
327	C₈×C₂₃	—	2	2	no	—
328	C₈×C₂₃	—	2	2	no	—
329	C₂×#556	C₂×C₂₃	1	1	yes	characteristic, complemented
330	C₂×#554	C₂×C₂₃	1	1	yes	characteristic, complemented
331	#3376	C₂×C₂₃	1	16	yes	direct product factor
332	C₂×#491	C₂×C₂₃	1	1	yes	characteristic, complemented
333	C₂×#489	C₂×C₂₃	1	1	yes	characteristic, complemented
334	C₂×#488	C₂×C₂₃	1	1	yes	characteristic, complemented
335	C₂×#479	C₂×C₂₃	1	1	yes	characteristic, complemented
336	C₂×#475	C₂×C₂₃	1	1	yes	characteristic, complemented
337	C₂×#478	C₂×C₂₃	1	1	yes	characteristic, complemented
338	C₂×#463	C₂×C₂₃	1	1	yes	characteristic
339	C₂×#463	C₂×C₂₃	1	1	yes	characteristic
340	C₂×#461	C₂×C₂₃	1	1	yes	characteristic, complemented
341	C₂×#446	C₂×C₂₃	1	1	yes	characteristic, complemented
342	C₂×#442	C₂×C₂₃	1	1	yes	characteristic
343	C₂×#440	C₂×C₂₃	1	1	yes	characteristic, complemented
344	C₂×C₄×SD₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
345	C₂²×C₂₃	—	2	4	no	—
346	C₂²×C₂₃	—	4	8	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	#548	1	2	yes	—
354	C₂²×C₂₃	#575	1	2	yes	—
355	C₂²×C₂₃	#577	1	2	yes	—
356	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
357	C₄×C₂₃	—	2	2	no	—
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	#548	1	2	yes	—
370	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
371	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
372	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
373	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
374	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
375	#556	—	2	4	no	—
376	#556	C₂²×C₂₃	1	8	yes	complemented
377	#554	—	2	4	no	—
378	#554	C₂²×C₂₃	1	8	yes	complemented
379	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
380	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
381	C₂×#126	—	2	1	no	—
382	C₂×#126	—	2	1	no	—
383	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
384	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
385	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
386	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
387	C₂×C₂²⋊Q₈	—	2	1	no	—
388	C₂×C₂²⋊Q₈	—	2	1	no	—
389	C₂×C₂²⋊Q₈	—	2	1	no	—
390	C₂×C₂²⋊Q₈	—	2	1	no	—
391	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
392	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
393	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
394	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
395	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
396	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
397	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
398	C₂×#117	—	2	1	no	—
399	C₂²×C₄⋊C₄	—	2	1	no	—
400	#491	C₂²×C₂₃	1	8	yes	complemented
401	#489	C₂²×C₂₃	1	8	yes	complemented
402	#488	C₂²×C₂₃	1	8	yes	complemented
403	#479	C₂²×C₂₃	1	8	yes	complemented
404	#478	C₂²×C₂₃	1	8	yes	complemented
405	#475	C₂²×C₂₃	1	8	yes	complemented
406	#463	C₂²×C₂₃	1	8	yes	—
407	#463	C₂²×C₂₃	1	8	yes	—
408	#461	C₂²×C₂₃	1	8	yes	complemented
409	#446	C₂²×C₂₃	1	8	yes	complemented
410	#442	C₂²×C₂₃	1	8	yes	—
411	#440	C₂²×C₂₃	1	8	yes	complemented
412	C₄×SD₁₆	C₂²×C₂₃	1	8	yes	complemented
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×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
417	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
418	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
419	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
420	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
421	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
422	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
423	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
424	C₂×#103	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×#102	C₂²×C₂₃	1	1	yes	characteristic
429	C₂×#97	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	4	no	—
433	C₂×C₂₃	—	8	2	no	—
434	C₂×C₂₃	#3376	1	4	yes	direct product factor
435	C₂×C₂₃	C₂×#548	1	1	yes	characteristic
436	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
437	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
438	C₂²×Q₈	—	2	1	no	—
439	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
440	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
441	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
442	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
443	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
444	C₂³×C₄	—	2	1	no	—
445	C₂³×C₄	—	2	1	no	—
446	C₂³×C₄	—	2	1	no	—
447	C₂³×C₄	—	2	1	no	—
448	C₂×SD₁₆	—	2	4	no	—
449	C₂×SD₁₆	—	2	4	no	—
450	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
451	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
452	C₂×D₈	—	2	4	no	—
453	C₂×D₈	C₂³×C₂₃	1	4	yes	—
454	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
455	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
456	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
457	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
458	C₄⋊Q₈	—	2	2	no	—
459	C₄⋊Q₈	—	2	2	no	—
460	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
461	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
462	#126	—	2	8	no	—
463	#126	—	2	8	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	#124	—	2	2	no	—
469	#124	—	2	2	no	—
470	#124	C₂³×C₂₃	1	4	yes	—
471	#124	C₂³×C₂₃	1	4	yes	—
472	C₂²⋊Q₈	—	2	8	no	—
473	C₂²⋊Q₈	—	2	8	no	—
474	C₂²⋊Q₈	—	2	8	no	—
475	C₂²⋊Q₈	—	2	8	no	—
476	C₄×Q₈	—	2	2	no	—
477	C₄×Q₈	—	2	2	no	—
478	C₄×Q₈	D₄×C₂₃	1	4	yes	—
479	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
480	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
481	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
482	C₄×D₄	—	2	2	no	—
483	C₄×D₄	—	2	2	no	—
484	C₄×D₄	—	2	2	no	—
485	C₄×D₄	—	2	2	no	—
486	C₄×D₄	C₂³×C₂₃	1	4	yes	—
487	C₄×D₄	C₂³×C₂₃	1	4	yes	—
488	C₄×D₄	C₂³×C₂₃	1	4	yes	—
489	C₄×D₄	C₂³×C₂₃	1	4	yes	—
490	#117	—	2	8	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	—	2	1	no	—
498	C₂×C₄⋊C₄	—	2	1	no	—
499	C₂×C₄⋊C₄	—	2	1	no	—
500	C₂×C₄⋊C₄	—	2	8	no	—
501	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
502	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
503	C₂×C₄⋊C₄	D₄×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×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
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	—	2	1	no	—
512	C₂×C₂²⋊C₄	—	2	1	no	—
513	C₂×C₂²⋊C₄	—	2	1	no	—
514	C₂×C₂²⋊C₄	—	2	1	no	—
515	C₂×C₂²⋊C₄	—	2	1	no	—
516	C₂×C₄²	—	2	1	no	—
517	C₂×C₄²	—	2	1	no	—
518	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
519	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
520	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
521	#107	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	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
527	#103	C₂³×C₂₃	1	4	yes	—
528	#103	C₂³×C₂₃	1	4	yes	—
529	#103	C₂³×C₂₃	1	4	yes	—
530	#103	C₂³×C₂₃	1	4	yes	—
531	#103	C₂³×C₂₃	1	4	yes	—
532	#103	C₂³×C₂₃	1	4	yes	—
533	#102	C₂³×C₂₃	1	4	yes	—
534	#102	C₂³×C₂₃	1	4	yes	—
535	#102	C₂³×C₂₃	1	4	yes	—
536	#102	C₂³×C₂₃	1	4	yes	—
537	#97	C₂³×C₂₃	1	4	yes	—
538	#97	C₂³×C₂₃	1	4	yes	—
539	C₄×C₈	C₂³×C₂₃	1	4	yes	—
540	C₂₃	C₂×#3376	1	1	yes	characteristic, direct product factor, Sylow
541	C₂⁴	—	2	1	no	—
542	C₂⁴	—	2	1	no	—
543	C₂×Q₈	—	2	1	no	—
544	C₂×Q₈	—	2	1	no	—
545	C₂×Q₈	—	2	4	no	—
546	C₂×Q₈	—	2	2	no	—
547	C₂×Q₈	—	2	2	no	—
548	C₂×Q₈	—	2	2	no	—
549	C₂×Q₈	—	2	2	no	—
550	C₂×Q₈	—	4	2	no	—
551	C₂×Q₈	—	8	2	no	—
552	C₂×Q₈	C₂×D₄×C₂₃	1	4	yes	—
553	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
554	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	—	2	1	no	—
557	C₂×D₄	—	2	2	no	—
558	C₂×D₄	—	2	2	no	—
559	C₂×D₄	—	2	2	no	—
560	C₂×D₄	#41×C₂₃	1	4	yes	—
561	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
562	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
563	C₂²×C₄	—	2	1	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	4	no	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	—	2	4	no	—
572	C₂²×C₄	—	2	4	no	—
573	C₂²×C₄	—	4	4	no	—
574	C₂²×C₄	—	4	4	no	—
575	C₂²×C₄	—	8	2	no	—
576	C₂²×C₄	—	8	2	no	—
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	1	yes	characteristic
582	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
583	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
584	SD₁₆	—	2	8	no	—
585	SD₁₆	—	2	8	no	—
586	D₈	—	2	8	no	—
587	C₂×C₈	—	2	2	no	—
588	C₂×C₈	—	2	2	no	—
589	C₂×C₈	—	2	2	no	—
590	C₂×C₈	—	2	2	no	—
591	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
592	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
593	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
594	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
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	4	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
609	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
610	C₄⋊C₄	C₂×D₄×C₂₃	1	4	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	—	2	4	no	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₂²⋊C₄	—	2	4	no	—
623	C₄²	—	2	4	no	—
624	C₄²	—	2	4	no	—
625	C₄²	C₂×D₄×C₂₃	1	2	yes	—
626	C₄²	C₂×D₄×C₂₃	1	2	yes	—
627	C₄²	C₂×D₄×C₂₃	1	2	yes	—
628	C₄²	C₂⁴×C₂₃	1	2	yes	—
629	C₄²	C₂⁴×C₂₃	1	2	yes	—
630	C₄²	C₂⁴×C₂₃	1	2	yes	—
631	C₂³	—	2	4	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	4	2	no	—
635	C₂³	—	4	2	no	—
636	C₂³	—	4	2	no	—
637	C₂³	—	4	2	no	—
638	C₂³	—	4	2	no	—
639	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
640	Q₈	—	2	2	no	—
641	Q₈	—	2	2	no	—
642	Q₈	—	2	2	no	—
643	Q₈	—	2	2	no	—
644	Q₈	—	4	4	no	—
645	Q₈	—	4	2	no	—
646	Q₈	—	4	2	no	—
647	Q₈	—	8	4	no	—
648	D₄	—	2	4	no	—
649	D₄	—	2	2	no	—
650	D₄	—	2	2	no	—
651	D₄	—	2	2	no	—
652	D₄	—	4	2	no	—
653	D₄	C₂×#41×C₂₃	1	4	yes	—
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	2	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	8	no	—
667	C₂×C₄	—	4	8	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	—	4	2	no	—
673	C₂×C₄	—	4	2	no	—
674	C₂×C₄	—	8	4	no	—
675	C₂×C₄	—	8	4	no	—
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	2	yes	—
681	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
682	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
683	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
684	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
685	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
686	C₈	—	2	2	no	—
687	C₈	—	2	2	no	—
688	C₈	—	2	2	no	—
689	C₈	—	2	2	no	—
690	C₂²	—	2	4	no	—
691	C₂²	—	4	2	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	4	8	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	4	2	no	—
697	C₂²	—	8	4	no	—
698	C₂²	C₂₃×#548	1	2	yes	—
699	C₂²	C₂₃×#575	1	2	yes	—
700	C₂²	C₂₃×#577	1	2	yes	—
701	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
702	C₄	—	2	2	no	—
703	C₄	—	2	2	no	—
704	C₄	—	2	2	no	—
705	C₄	—	2	2	no	—
706	C₄	—	2	2	no	—
707	C₄	—	2	2	no	—
708	C₄	—	4	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	C₂₃×#548	1	2	yes	—
715	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
716	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
717	C₂	—	4	4	no	—
718	C₂	—	8	2	no	—
719	C₂	C₂₃×#3376	1	4	yes	direct product factor
720	C₂	C₂×C₂₃×#548	1	1	yes	characteristic
721	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
722	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	C₂²×D₈×C₂₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄×Q₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#556	C₂	semidirect
2. C₂×C₂₃×#554	C₂	semidirect
3. C₂₃×#3376	C₂	direct (N × H)
4. C₂×C₂₃×#491	C₂	semidirect
5. C₂×C₂₃×#489	C₂	semidirect
6. C₂×C₂₃×#488	C₂	semidirect
7. C₂×C₂₃×#479	C₂	semidirect
8. C₂×C₂₃×#475	C₂	semidirect
9. C₂×C₂₃×#478	C₂	semidirect
12. C₂×C₂₃×#461	C₂	semidirect
13. C₂×C₂₃×#446	C₂	semidirect
15. C₂×C₂₃×#440	C₂	semidirect
16. C₂×C₄×SD₁₆×C₂₃	C₂	semidirect
21. C₂₃×#556	C₂²	semidirect
23. C₂₃×#554	C₂²	semidirect
45. C₂₃×#491	C₂²	semidirect
46. C₂₃×#489	C₂²	semidirect
47. C₂₃×#488	C₂²	semidirect
48. C₂₃×#479	C₂²	semidirect
49. C₂₃×#478	C₂²	semidirect
50. C₂₃×#475	C₂²	semidirect
53. C₂₃×#461	C₂²	semidirect
54. C₂₃×#446	C₂²	semidirect
56. C₂₃×#440	C₂²	semidirect
57. C₄×SD₁₆×C₂₃	C₂²	semidirect
269. C₂×#3376	C₂₃	direct (N × H)
329. C₂×#556	C₂×C₂₃	semidirect
330. C₂×#554	C₂×C₂₃	semidirect
331. #3376	C₂×C₂₃	direct (N × H)
332. C₂×#491	C₂×C₂₃	semidirect
333. C₂×#489	C₂×C₂₃	semidirect
334. C₂×#488	C₂×C₂₃	semidirect
335. C₂×#479	C₂×C₂₃	semidirect
336. C₂×#475	C₂×C₂₃	semidirect
337. C₂×#478	C₂×C₂₃	semidirect
340. C₂×#461	C₂×C₂₃	semidirect
341. C₂×#446	C₂×C₂₃	semidirect
343. C₂×#440	C₂×C₂₃	semidirect
344. C₂×C₄×SD₁₆	C₂×C₂₃	semidirect
376. #556	C₂²×C₂₃	semidirect
378. #554	C₂²×C₂₃	semidirect
400. #491	C₂²×C₂₃	semidirect
401. #489	C₂²×C₂₃	semidirect
402. #488	C₂²×C₂₃	semidirect
403. #479	C₂²×C₂₃	semidirect
404. #478	C₂²×C₂₃	semidirect
405. #475	C₂²×C₂₃	semidirect
408. #461	C₂²×C₂₃	semidirect
409. #446	C₂²×C₂₃	semidirect
411. #440	C₂²×C₂₃	semidirect
412. C₄×SD₁₆	C₂²×C₂₃	semidirect
434. C₂×C₂₃	#3376	direct (N × H)
540. C₂₃	C₂×#3376	direct (N × H)
719. C₂	C₂₃×#3376	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×#556	2
C₂×C₂₃×#554	2
C₂₃×#3376	2
C₂×C₂₃×#491	2
C₂×C₂₃×#489	2
C₂×C₂₃×#488	2
C₂×C₂₃×#479	2
C₂×C₂₃×#475	2
C₂×C₂₃×#478	2
C₂×C₂₃×#463	2
C₂×C₂₃×#461	2
C₂×C₂₃×#446	2
C₂×C₂₃×#442	2
C₂×C₂₃×#440	2
C₂×C₄×SD₁₆×C₂₃	2
C₂×#3376	23

Subgroups — C2×C23×#3376 #19208939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3376 #19208939