Subgroups — C₂×C₂₃×#3377 #19208941

Order 5888.

1810 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#556	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3377	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
6	C₂×C₂₃×#488	C₂	1	1	yes	maximal, characteristic
7	C₂×C₂₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#478	C₂	1	1	yes	maximal, characteristic
10	C₂×C₂₃×#464	C₂	1	1	yes	maximal, characteristic
11	C₂×C₂₃×#464	C₂	1	1	yes	maximal, characteristic
12	C₂×C₂₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₃×#446	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₂₃×#441	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₃×#440	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄×Q₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
20	C₂₃×#557	—	2	4	no	—
21	C₂₃×#557	C₂²	1	8	yes	complemented
22	C₂₃×#556	—	2	4	no	—
23	C₂₃×#556	C₂²	1	8	yes	—
24	C₂×C₂₃×C₄⋊Q₈	—	2	1	no	—
25	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#126	—	2	1	no	—
28	C₂×C₂₃×#126	—	2	1	no	—
29	C₂×C₂₃×#125	—	2	1	no	—
30	C₂×C₂₃×#125	—	2	1	no	—
31	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
36	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
37	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
44	C₂×C₂₃×#117	—	2	1	no	—
45	C₂₃×#491	C₂²	1	8	yes	complemented
46	C₂₃×#489	C₂²	1	8	yes	—
47	C₂₃×#488	C₂²	1	8	yes	—
48	C₂₃×#479	C₂²	1	8	yes	complemented
49	C₂₃×#478	C₂²	1	8	yes	—
50	C₂₃×#477	C₂²	1	8	yes	complemented
51	C₂₃×#464	C₂²	1	8	yes	—
52	C₂₃×#464	C₂²	1	8	yes	—
53	C₂₃×#462	C₂²	1	8	yes	complemented
54	C₂₃×#446	C₂²	1	8	yes	complemented
55	C₂₃×#441	C₂²	1	8	yes	complemented
56	C₂₃×#440	C₂²	1	8	yes	—
57	C₄×Q₁₆×C₂₃	C₂²	1	8	yes	complemented
58	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
59	C₂×C₂₃×#107	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×#103	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×Q₈×C₂₃	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₂₃	—	2	1	no	—
84	C₂×Q₁₆×C₂₃	—	2	4	no	—
85	C₂×Q₁₆×C₂₃	—	2	4	no	—
86	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
87	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
88	C₂×SD₁₆×C₂₃	—	2	4	no	—
89	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
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	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
94	C₂₃×C₄⋊Q₈	—	2	8	no	—
95	C₂₃×C₄⋊Q₈	—	2	2	no	—
96	C₂₃×C₄⋊Q₈	—	2	2	no	—
97	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
98	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
99	C₂₃×#126	—	2	8	no	—
100	C₂₃×#126	—	2	8	no	—
101	C₂₃×#125	—	2	8	no	—
102	C₂₃×#125	—	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	C₄×Q₈×C₂₃	—	2	8	no	—
113	C₄×Q₈×C₂₃	—	2	2	no	—
114	C₄×Q₈×C₂₃	—	2	2	no	—
115	C₄×Q₈×C₂₃	—	2	2	no	—
116	C₄×Q₈×C₂₃	—	2	2	no	—
117	C₄×Q₈×C₂₃	—	2	2	no	—
118	C₄×Q₈×C₂₃	D₄	1	4	yes	—
119	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
120	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
121	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
122	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
123	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
124	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
125	C₄×D₄×C₂₃	—	2	2	no	—
126	C₄×D₄×C₂₃	C₂³	1	4	yes	—
127	C₂₃×#117	—	2	8	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	—	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	1	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×C₄²×C₂₃	—	2	1	no	—
153	C₂×C₄²×C₂₃	—	2	1	no	—
154	C₂×C₄²×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×#107	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×#103	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	C₂×Q₈×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	—	2	2	no	—
189	C₂×Q₈×C₂₃	—	4	2	no	—
190	C₂×Q₈×C₂₃	—	4	4	no	—
191	C₂×Q₈×C₂₃	C₂×D₄	1	4	yes	—
192	C₂×Q₈×C₂₃	#41	1	4	yes	—
193	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
194	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
195	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
196	C₂×D₄×C₂₃	—	2	1	no	—
197	C₂×D₄×C₂₃	—	2	2	no	—
198	C₂×D₄×C₂₃	—	2	2	no	—
199	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₂₃	—	2	1	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	—	4	4	no	—
209	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
216	Q₁₆×C₂₃	—	2	8	no	—
217	Q₁₆×C₂₃	—	2	8	no	—
218	SD₁₆×C₂₃	—	2	8	no	—
219	C₂×C₈×C₂₃	—	2	2	no	—
220	C₂×C₈×C₂₃	—	2	2	no	—
221	C₂×C₈×C₂₃	—	2	2	no	—
222	C₂×C₈×C₂₃	—	2	2	no	—
223	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
224	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
225	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
226	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
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	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	1	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	C₂×D₄	1	4	yes	—
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	C₂²⋊C₄×C₂₃	—	2	4	no	—
251	C₂²⋊C₄×C₂₃	—	2	4	no	—
252	C₂²⋊C₄×C₂₃	—	2	4	no	—
253	C₂²⋊C₄×C₂₃	—	2	4	no	—
254	C₂²⋊C₄×C₂₃	—	2	4	no	—
255	C₄²×C₂₃	—	2	4	no	—
256	C₄²×C₂₃	—	2	4	no	—
257	C₄²×C₂₃	—	2	4	no	—
258	C₄²×C₂₃	—	2	4	no	—
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	C₂×D₄	1	2	yes	—
263	C₄²×C₂₃	C₂⁴	1	2	yes	—
264	C₄²×C₂₃	C₂⁴	1	2	yes	—
265	C₄²×C₂₃	C₂⁴	1	2	yes	—
266	C₂×#3377	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
267	C₂³×C₂₃	—	2	2	no	—
268	C₂³×C₂₃	—	4	2	no	—
269	C₂³×C₂₃	—	4	2	no	—
270	C₂³×C₂₃	—	4	2	no	—
271	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
272	Q₈×C₂₃	—	2	4	no	—
273	Q₈×C₂₃	—	2	2	no	—
274	Q₈×C₂₃	—	2	2	no	—
275	Q₈×C₂₃	—	2	2	no	—
276	Q₈×C₂₃	—	2	2	no	—
277	Q₈×C₂₃	—	2	2	no	—
278	Q₈×C₂₃	—	4	4	no	—
279	Q₈×C₂₃	—	4	8	no	—
280	Q₈×C₂₃	—	4	2	no	—
281	Q₈×C₂₃	—	4	2	no	—
282	Q₈×C₂₃	C₂×#41	1	4	yes	—
283	D₄×C₂₃	—	2	2	no	—
284	D₄×C₂₃	—	2	2	no	—
285	D₄×C₂₃	—	4	2	no	—
286	C₂×C₄×C₂₃	—	2	4	no	—
287	C₂×C₄×C₂₃	—	2	2	no	—
288	C₂×C₄×C₂₃	—	2	2	no	—
289	C₂×C₄×C₂₃	—	2	2	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	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	—	4	8	no	—
301	C₂×C₄×C₂₃	—	4	2	no	—
302	C₂×C₄×C₂₃	—	4	2	no	—
303	C₂×C₄×C₂₃	—	4	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	C₂²×D₄	1	2	yes	—
308	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
309	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
310	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
311	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
312	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
313	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
314	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
315	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
316	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
317	C₈×C₂₃	—	2	2	no	—
318	C₈×C₂₃	—	2	2	no	—
319	C₈×C₂₃	—	2	2	no	—
320	C₈×C₂₃	—	2	2	no	—
321	C₂×#557	C₂×C₂₃	1	1	yes	characteristic, complemented
322	C₂×#556	C₂×C₂₃	1	1	yes	characteristic
323	#3377	C₂×C₂₃	1	16	yes	direct product factor
324	C₂×#491	C₂×C₂₃	1	1	yes	characteristic, complemented
325	C₂×#489	C₂×C₂₃	1	1	yes	characteristic
326	C₂×#488	C₂×C₂₃	1	1	yes	characteristic
327	C₂×#479	C₂×C₂₃	1	1	yes	characteristic, complemented
328	C₂×#477	C₂×C₂₃	1	1	yes	characteristic, complemented
329	C₂×#478	C₂×C₂₃	1	1	yes	characteristic
330	C₂×#464	C₂×C₂₃	1	1	yes	characteristic
331	C₂×#464	C₂×C₂₃	1	1	yes	characteristic
332	C₂×#462	C₂×C₂₃	1	1	yes	characteristic, complemented
333	C₂×#446	C₂×C₂₃	1	1	yes	characteristic, complemented
334	C₂×#441	C₂×C₂₃	1	1	yes	characteristic, complemented
335	C₂×#440	C₂×C₂₃	1	1	yes	characteristic
336	C₂×C₄×Q₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
337	C₂²×C₂₃	—	4	2	no	—
338	C₂²×C₂₃	—	4	2	no	—
339	C₂²×C₂₃	—	4	2	no	—
340	C₂²×C₂₃	—	8	4	no	—
341	C₂²×C₂₃	#548	1	2	yes	—
342	C₂²×C₂₃	#575	1	2	yes	—
343	C₂²×C₂₃	#578	1	2	yes	—
344	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
345	C₄×C₂₃	—	2	4	no	—
346	C₄×C₂₃	—	2	2	no	—
347	C₄×C₂₃	—	2	2	no	—
348	C₄×C₂₃	—	2	2	no	—
349	C₄×C₂₃	—	2	2	no	—
350	C₄×C₂₃	—	2	2	no	—
351	C₄×C₂₃	—	2	2	no	—
352	C₄×C₂₃	—	4	2	no	—
353	C₄×C₂₃	—	4	2	no	—
354	C₄×C₂₃	—	4	2	no	—
355	C₄×C₂₃	—	4	2	no	—
356	C₄×C₂₃	—	4	2	no	—
357	C₄×C₂₃	—	4	2	no	—
358	C₄×C₂₃	#548	1	2	yes	—
359	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
360	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
361	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
362	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
363	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
364	#557	—	2	4	no	—
365	#557	C₂²×C₂₃	1	8	yes	complemented
366	#556	—	2	4	no	—
367	#556	C₂²×C₂₃	1	8	yes	—
368	C₂×C₄⋊Q₈	—	2	1	no	—
369	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
370	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
371	C₂×#126	—	2	1	no	—
372	C₂×#126	—	2	1	no	—
373	C₂×#125	—	2	1	no	—
374	C₂×#125	—	2	1	no	—
375	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
376	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
377	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
378	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
379	C₂×C₂²⋊Q₈	—	2	1	no	—
380	C₂×C₄×Q₈	—	2	1	no	—
381	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
382	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
383	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
384	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
385	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
386	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
387	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
388	C₂×#117	—	2	1	no	—
389	#491	C₂²×C₂₃	1	8	yes	complemented
390	#489	C₂²×C₂₃	1	8	yes	—
391	#488	C₂²×C₂₃	1	8	yes	—
392	#479	C₂²×C₂₃	1	8	yes	complemented
393	#478	C₂²×C₂₃	1	8	yes	—
394	#477	C₂²×C₂₃	1	8	yes	complemented
395	#464	C₂²×C₂₃	1	8	yes	—
396	#464	C₂²×C₂₃	1	8	yes	—
397	#462	C₂²×C₂₃	1	8	yes	complemented
398	#446	C₂²×C₂₃	1	8	yes	complemented
399	#441	C₂²×C₂₃	1	8	yes	complemented
400	#440	C₂²×C₂₃	1	8	yes	—
401	C₄×Q₁₆	C₂²×C₂₃	1	8	yes	complemented
402	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
403	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
404	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
405	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
406	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
407	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
408	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
409	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
410	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
411	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
412	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
413	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
414	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
415	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
416	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
417	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
418	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
419	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
420	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
421	C₂×C₂₃	—	8	2	no	—
422	C₂×C₂₃	#3377	1	4	yes	direct product factor
423	C₂×C₂₃	C₂×#548	1	1	yes	characteristic
424	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
425	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
426	C₂²×Q₈	—	2	1	no	—
427	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
428	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
429	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
430	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
431	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
432	C₂³×C₄	—	2	1	no	—
433	C₂×Q₁₆	—	2	4	no	—
434	C₂×Q₁₆	—	2	4	no	—
435	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
436	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
437	C₂×SD₁₆	—	2	4	no	—
438	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
439	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
440	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
441	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
442	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
443	C₄⋊Q₈	—	2	8	no	—
444	C₄⋊Q₈	—	2	2	no	—
445	C₄⋊Q₈	—	2	2	no	—
446	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
447	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
448	#126	—	2	8	no	—
449	#126	—	2	8	no	—
450	#125	—	2	8	no	—
451	#125	—	2	8	no	—
452	#125	—	2	2	no	—
453	#125	—	2	2	no	—
454	#125	C₂³×C₂₃	1	4	yes	—
455	#125	C₂³×C₂₃	1	4	yes	—
456	#124	—	2	2	no	—
457	#124	—	2	2	no	—
458	#124	C₂³×C₂₃	1	4	yes	—
459	#124	C₂³×C₂₃	1	4	yes	—
460	C₂²⋊Q₈	—	2	8	no	—
461	C₄×Q₈	—	2	8	no	—
462	C₄×Q₈	—	2	2	no	—
463	C₄×Q₈	—	2	2	no	—
464	C₄×Q₈	—	2	2	no	—
465	C₄×Q₈	—	2	2	no	—
466	C₄×Q₈	—	2	2	no	—
467	C₄×Q₈	D₄×C₂₃	1	4	yes	—
468	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
469	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
470	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
471	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
472	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
473	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
474	C₄×D₄	—	2	2	no	—
475	C₄×D₄	C₂³×C₂₃	1	4	yes	—
476	#117	—	2	8	no	—
477	C₂×C₄⋊C₄	—	2	1	no	—
478	C₂×C₄⋊C₄	—	2	1	no	—
479	C₂×C₄⋊C₄	—	2	1	no	—
480	C₂×C₄⋊C₄	—	2	1	no	—
481	C₂×C₄⋊C₄	—	2	1	no	—
482	C₂×C₄⋊C₄	—	2	1	no	—
483	C₂×C₄⋊C₄	—	2	1	no	—
484	C₂×C₄⋊C₄	—	2	1	no	—
485	C₂×C₄⋊C₄	—	2	1	no	—
486	C₂×C₄⋊C₄	—	2	1	no	—
487	C₂×C₄⋊C₄	—	2	1	no	—
488	C₂×C₄⋊C₄	—	2	1	no	—
489	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
490	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
491	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
493	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
494	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
495	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
496	C₂×C₂²⋊C₄	—	2	1	no	—
497	C₂×C₂²⋊C₄	—	2	1	no	—
498	C₂×C₂²⋊C₄	—	2	1	no	—
499	C₂×C₂²⋊C₄	—	2	1	no	—
500	C₂×C₂²⋊C₄	—	2	1	no	—
501	C₂×C₄²	—	2	1	no	—
502	C₂×C₄²	—	2	1	no	—
503	C₂×C₄²	—	2	1	no	—
504	C₂×C₄²	—	2	1	no	—
505	C₂×C₄²	—	2	1	no	—
506	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
507	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
508	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
509	#107	C₂³×C₂₃	1	4	yes	—
510	#107	C₂³×C₂₃	1	4	yes	—
511	#106	C₂³×C₂₃	1	4	yes	—
512	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
513	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
514	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
515	#103	C₂³×C₂₃	1	4	yes	—
516	#103	C₂³×C₂₃	1	4	yes	—
517	#103	C₂³×C₂₃	1	4	yes	—
518	#103	C₂³×C₂₃	1	4	yes	—
519	#103	C₂³×C₂₃	1	4	yes	—
520	#103	C₂³×C₂₃	1	4	yes	—
521	#103	C₂³×C₂₃	1	4	yes	—
522	#102	C₂³×C₂₃	1	4	yes	—
523	#102	C₂³×C₂₃	1	4	yes	—
524	#102	C₂³×C₂₃	1	4	yes	—
525	#97	C₂³×C₂₃	1	4	yes	—
526	#97	C₂³×C₂₃	1	4	yes	—
527	C₄×C₈	C₂³×C₂₃	1	4	yes	—
528	C₂₃	C₂×#3377	1	1	yes	characteristic, direct product factor, Sylow
529	C₂⁴	—	2	1	no	—
530	C₂×Q₈	—	2	1	no	—
531	C₂×Q₈	—	2	1	no	—
532	C₂×Q₈	—	2	1	no	—
533	C₂×Q₈	—	2	4	no	—
534	C₂×Q₈	—	2	2	no	—
535	C₂×Q₈	—	2	2	no	—
536	C₂×Q₈	—	2	2	no	—
537	C₂×Q₈	—	2	2	no	—
538	C₂×Q₈	—	2	2	no	—
539	C₂×Q₈	—	4	2	no	—
540	C₂×Q₈	—	4	4	no	—
541	C₂×Q₈	C₂×D₄×C₂₃	1	4	yes	—
542	C₂×Q₈	#41×C₂₃	1	4	yes	—
543	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
544	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
545	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
546	C₂×D₄	—	2	1	no	—
547	C₂×D₄	—	2	2	no	—
548	C₂×D₄	—	2	2	no	—
549	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	4	no	—
558	C₂²×C₄	—	4	4	no	—
559	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
560	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
561	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
562	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
563	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
564	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
565	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
566	Q₁₆	—	2	8	no	—
567	Q₁₆	—	2	8	no	—
568	SD₁₆	—	2	8	no	—
569	C₂×C₈	—	2	2	no	—
570	C₂×C₈	—	2	2	no	—
571	C₂×C₈	—	2	2	no	—
572	C₂×C₈	—	2	2	no	—
573	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
574	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
575	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
576	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
577	C₄⋊C₄	—	2	4	no	—
578	C₄⋊C₄	—	2	4	no	—
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	—	2	4	no	—
581	C₄⋊C₄	—	2	4	no	—
582	C₄⋊C₄	—	2	4	no	—
583	C₄⋊C₄	—	2	4	no	—
584	C₄⋊C₄	—	2	4	no	—
585	C₄⋊C₄	—	2	4	no	—
586	C₄⋊C₄	—	2	4	no	—
587	C₄⋊C₄	—	2	4	no	—
588	C₄⋊C₄	—	2	4	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
594	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
595	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
596	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
597	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
598	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
599	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
600	C₂²⋊C₄	—	2	4	no	—
601	C₂²⋊C₄	—	2	4	no	—
602	C₂²⋊C₄	—	2	4	no	—
603	C₂²⋊C₄	—	2	4	no	—
604	C₂²⋊C₄	—	2	4	no	—
605	C₄²	—	2	4	no	—
606	C₄²	—	2	4	no	—
607	C₄²	—	2	4	no	—
608	C₄²	—	2	4	no	—
609	C₄²	—	2	4	no	—
610	C₄²	C₂×D₄×C₂₃	1	2	yes	—
611	C₄²	C₂×D₄×C₂₃	1	2	yes	—
612	C₄²	C₂×D₄×C₂₃	1	2	yes	—
613	C₄²	C₂⁴×C₂₃	1	2	yes	—
614	C₄²	C₂⁴×C₂₃	1	2	yes	—
615	C₄²	C₂⁴×C₂₃	1	2	yes	—
616	C₂³	—	2	2	no	—
617	C₂³	—	4	2	no	—
618	C₂³	—	4	2	no	—
619	C₂³	—	4	2	no	—
620	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
621	Q₈	—	2	4	no	—
622	Q₈	—	2	2	no	—
623	Q₈	—	2	2	no	—
624	Q₈	—	2	2	no	—
625	Q₈	—	2	2	no	—
626	Q₈	—	2	2	no	—
627	Q₈	—	4	4	no	—
628	Q₈	—	4	8	no	—
629	Q₈	—	4	2	no	—
630	Q₈	—	4	2	no	—
631	Q₈	C₂×#41×C₂₃	1	4	yes	—
632	D₄	—	2	2	no	—
633	D₄	—	2	2	no	—
634	D₄	—	4	2	no	—
635	C₂×C₄	—	2	4	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	4	8	no	—
650	C₂×C₄	—	4	2	no	—
651	C₂×C₄	—	4	2	no	—
652	C₂×C₄	—	4	2	no	—
653	C₂×C₄	—	4	2	no	—
654	C₂×C₄	—	4	2	no	—
655	C₂×C₄	—	4	2	no	—
656	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
657	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
658	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
659	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
660	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
661	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
662	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
663	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
664	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
665	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
666	C₈	—	2	2	no	—
667	C₈	—	2	2	no	—
668	C₈	—	2	2	no	—
669	C₈	—	2	2	no	—
670	C₂²	—	4	2	no	—
671	C₂²	—	4	2	no	—
672	C₂²	—	4	2	no	—
673	C₂²	—	8	4	no	—
674	C₂²	C₂₃×#548	1	2	yes	—
675	C₂²	C₂₃×#575	1	2	yes	—
676	C₂²	C₂₃×#578	1	2	yes	—
677	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
678	C₄	—	2	4	no	—
679	C₄	—	2	2	no	—
680	C₄	—	2	2	no	—
681	C₄	—	2	2	no	—
682	C₄	—	2	2	no	—
683	C₄	—	2	2	no	—
684	C₄	—	2	2	no	—
685	C₄	—	4	2	no	—
686	C₄	—	4	2	no	—
687	C₄	—	4	2	no	—
688	C₄	—	4	2	no	—
689	C₄	—	4	2	no	—
690	C₄	—	4	2	no	—
691	C₄	C₂₃×#548	1	2	yes	—
692	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
693	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
694	C₂	—	8	2	no	—
695	C₂	C₂₃×#3377	1	4	yes	direct product factor
696	C₂	C₂×C₂₃×#548	1	1	yes	characteristic
697	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
698	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×D₄×C₂₃	C₂³
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×#557	C₂	semidirect
3. C₂₃×#3377	C₂	direct (N × H)
4. C₂×C₂₃×#491	C₂	semidirect
7. C₂×C₂₃×#479	C₂	semidirect
8. C₂×C₂₃×#477	C₂	semidirect
12. C₂×C₂₃×#462	C₂	semidirect
13. C₂×C₂₃×#446	C₂	semidirect
14. C₂×C₂₃×#441	C₂	semidirect
16. C₂×C₄×Q₁₆×C₂₃	C₂	semidirect
21. C₂₃×#557	C₂²	semidirect
45. C₂₃×#491	C₂²	semidirect
48. C₂₃×#479	C₂²	semidirect
50. C₂₃×#477	C₂²	semidirect
53. C₂₃×#462	C₂²	semidirect
54. C₂₃×#446	C₂²	semidirect
55. C₂₃×#441	C₂²	semidirect
57. C₄×Q₁₆×C₂₃	C₂²	semidirect
266. C₂×#3377	C₂₃	direct (N × H)
321. C₂×#557	C₂×C₂₃	semidirect
323. #3377	C₂×C₂₃	direct (N × H)
324. C₂×#491	C₂×C₂₃	semidirect
327. C₂×#479	C₂×C₂₃	semidirect
328. C₂×#477	C₂×C₂₃	semidirect
332. C₂×#462	C₂×C₂₃	semidirect
333. C₂×#446	C₂×C₂₃	semidirect
334. C₂×#441	C₂×C₂₃	semidirect
336. C₂×C₄×Q₁₆	C₂×C₂₃	semidirect
365. #557	C₂²×C₂₃	semidirect
389. #491	C₂²×C₂₃	semidirect
392. #479	C₂²×C₂₃	semidirect
394. #477	C₂²×C₂₃	semidirect
397. #462	C₂²×C₂₃	semidirect
398. #446	C₂²×C₂₃	semidirect
399. #441	C₂²×C₂₃	semidirect
401. C₄×Q₁₆	C₂²×C₂₃	semidirect
422. C₂×C₂₃	#3377	direct (N × H)
528. C₂₃	C₂×#3377	direct (N × H)
695. C₂	C₂₃×#3377	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×#557	2
C₂×C₂₃×#556	2
C₂₃×#3377	2
C₂×C₂₃×#491	2
C₂×C₂₃×#489	2
C₂×C₂₃×#488	2
C₂×C₂₃×#479	2
C₂×C₂₃×#477	2
C₂×C₂₃×#478	2
C₂×C₂₃×#464	2
C₂×C₂₃×#462	2
C₂×C₂₃×#446	2
C₂×C₂₃×#441	2
C₂×C₂₃×#440	2
C₂×C₄×Q₁₆×C₂₃	2
C₂×#3377	23

Subgroups — C2×C23×#3377 #19208941

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3377 #19208941