Subgroups — C₂₃×#24100 #19171726

Order 5888.

1300 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#547	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#428	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2485	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2058	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2057	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2034	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2033	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1895	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1870	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1864	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1862	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1853	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1852	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1824	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₂₃	—	2	1	no	—
17	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
18	C₂₃×#547	—	2	4	no	—
19	C₂₃×#547	—	2	4	no	—
20	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#123	—	2	1	no	—
22	C₂×C₂₃×#123	—	2	1	no	—
23	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
24	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
30	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
31	C₂₃×#482	—	2	4	no	—
32	C₂₃×#428	—	2	4	no	—
33	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
42	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
43	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
44	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
45	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
46	C₂₃×#397	—	2	1	no	—
47	C₂₃×#394	—	2	1	no	—
48	C₂₃×#389	C₂²	1	1	yes	characteristic
49	C₂₃×#389	C₂²	1	1	yes	characteristic
50	C₂₃×#388	—	2	1	no	—
51	C₂₃×#387	—	2	1	no	—
52	C₂₃×#380	C₂²	1	1	yes	characteristic
53	C₂₃×#380	C₂²	1	1	yes	characteristic
54	C₂₃×#380	C₂²	1	1	yes	characteristic
55	C₂₃×#340	C₂²	1	1	yes	characteristic
56	C₂₃×#340	C₂²	1	1	yes	characteristic
57	C₂₃×#340	C₂²	1	1	yes	characteristic
58	C₂₃×#340	C₂²	1	1	yes	characteristic
59	C₂₃×#340	C₂²	1	1	yes	characteristic
60	C₂₃×#340	C₂²	1	1	yes	characteristic
61	C₂₃×#336	C₂²	1	1	yes	characteristic
62	C₂₃×#336	C₂²	1	1	yes	characteristic
63	C₂×#41×C₂₃	—	2	8	no	—
64	C₂×#41×C₂₃	—	4	4	no	—
65	C₂×#41×C₂₃	—	4	4	no	—
66	C₂²×Q₈×C₂₃	—	2	1	no	—
67	C₂²×D₄×C₂₃	—	2	1	no	—
68	C₂²×D₄×C₂₃	—	2	1	no	—
69	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
70	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₂₃	—	2	1	no	—
72	C₂³×C₄×C₂₃	—	2	1	no	—
73	C₂³×C₄×C₂₃	—	2	1	no	—
74	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
76	C₂×M₁₆×C₂₃	—	2	2	no	—
77	C₂×M₁₆×C₂₃	—	2	2	no	—
78	C₂×M₁₆×C₂₃	—	2	2	no	—
79	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
83	C₂₃×C₄⋊Q₈	—	2	2	no	—
84	C₂₃×C₄⋊Q₈	—	2	2	no	—
85	C₂₃×#123	—	2	8	no	—
86	C₂₃×#123	—	2	8	no	—
87	C₂₃×C₂²⋊Q₈	—	2	8	no	—
88	C₂₃×#121	—	2	2	no	—
89	C₂₃×#121	—	2	2	no	—
90	C₂₃×#121	—	2	2	no	—
91	C₂₃×#121	D₄	1	4	yes	—
92	C₄×D₄×C₂₃	—	2	2	no	—
93	C₄×D₄×C₂₃	—	2	2	no	—
94	C₄×D₄×C₂₃	—	2	2	no	—
95	C₄×D₄×C₂₃	—	2	2	no	—
96	C₂₃×#117	—	2	2	no	—
97	C₂₃×#117	—	2	2	no	—
98	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
99	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
100	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
101	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
102	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
103	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
104	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
105	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
106	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₂₃	D₄	1	4	yes	—
108	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
115	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
123	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
124	C₂×C₄²×C₂₃	—	2	1	no	—
125	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
126	C₂₃×#107	—	2	2	no	—
127	C₂₃×#107	—	2	2	no	—
128	C₂₃×#107	—	2	2	no	—
129	C₂₃×#106	—	2	2	no	—
130	C₂₃×#106	—	2	2	no	—
131	C₂₃×#106	—	2	2	no	—
132	C₂₃×#102	—	2	2	no	—
133	C₂₃×#102	—	2	2	no	—
134	C₂₃×#102	—	2	2	no	—
135	C₂₃×#102	—	2	2	no	—
136	C₂₃×C₂²⋊C₈	—	2	2	no	—
137	C₂₃×C₂²⋊C₈	—	2	2	no	—
138	C₂₃×C₂²⋊C₈	—	2	2	no	—
139	C₂₃×#95	—	2	1	no	—
140	C₂₃×#95	—	2	1	no	—
141	C₂₃×#95	—	2	1	no	—
142	C₂₃×#95	—	2	1	no	—
143	C₂₃×#95	—	2	1	no	—
144	C₂⁴×C₂₃	—	2	1	no	—
145	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
146	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
147	#41×C₂₃	—	4	32	no	—
148	C₂×Q₈×C₂₃	—	2	4	no	—
149	C₂×Q₈×C₂₃	—	4	2	no	—
150	C₂×Q₈×C₂₃	—	4	2	no	—
151	C₂×D₄×C₂₃	—	2	2	no	—
152	C₂×D₄×C₂₃	—	2	2	no	—
153	C₂×D₄×C₂₃	—	2	4	no	—
154	C₂×D₄×C₂₃	—	2	4	no	—
155	C₂×D₄×C₂₃	—	2	2	no	—
156	C₂×D₄×C₂₃	—	2	1	no	—
157	C₂×D₄×C₂₃	—	2	1	no	—
158	C₂×D₄×C₂₃	—	2	1	no	—
159	C₂×D₄×C₂₃	—	2	1	no	—
160	C₂×D₄×C₂₃	—	2	1	no	—
161	C₂×D₄×C₂₃	—	4	2	no	—
162	C₂×D₄×C₂₃	—	4	2	no	—
163	C₂×D₄×C₂₃	—	4	2	no	—
164	C₂×D₄×C₂₃	—	4	2	no	—
165	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₂₃	—	2	1	no	—
167	C₂²×C₄×C₂₃	—	2	1	no	—
168	C₂²×C₄×C₂₃	—	2	1	no	—
169	C₂²×C₄×C₂₃	—	2	1	no	—
170	C₂²×C₄×C₂₃	—	2	4	no	—
171	C₂²×C₄×C₂₃	—	2	4	no	—
172	C₂²×C₄×C₂₃	—	2	4	no	—
173	C₂²×C₄×C₂₃	—	2	1	no	—
174	C₂²×C₄×C₂₃	—	2	1	no	—
175	C₂²×C₄×C₂₃	—	2	1	no	—
176	C₂²×C₄×C₂₃	—	2	1	no	—
177	C₂²×C₄×C₂₃	—	2	1	no	—
178	C₂²×C₄×C₂₃	—	2	1	no	—
179	C₂²×C₄×C₂₃	—	2	1	no	—
180	C₂²×C₄×C₂₃	—	2	1	no	—
181	C₂²×C₄×C₂₃	—	2	1	no	—
182	C₂²×C₄×C₂₃	—	2	1	no	—
183	C₂²×C₄×C₂₃	—	2	1	no	—
184	C₂²×C₄×C₂₃	—	2	1	no	—
185	C₂²×C₄×C₂₃	—	2	1	no	—
186	C₂²×C₄×C₂₃	—	4	2	no	—
187	C₂²×C₄×C₂₃	—	4	2	no	—
188	C₂²×C₄×C₂₃	—	4	2	no	—
189	C₂²×C₄×C₂₃	—	4	2	no	—
190	C₂²×C₄×C₂₃	—	4	2	no	—
191	C₂²×C₄×C₂₃	—	4	2	no	—
192	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
196	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
197	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
199	M₁₆×C₂₃	—	2	8	no	—
200	C₂×C₈×C₂₃	—	2	1	no	—
201	C₂×C₈×C₂₃	—	2	1	no	—
202	C₂×C₈×C₂₃	—	2	1	no	—
203	C₂×C₈×C₂₃	—	2	1	no	—
204	C₂×C₈×C₂₃	—	2	1	no	—
205	C₂×C₈×C₂₃	—	2	1	no	—
206	C₂×C₈×C₂₃	—	2	1	no	—
207	C₂×C₈×C₂₃	—	2	1	no	—
208	C₂×C₈×C₂₃	—	2	1	no	—
209	C₂×C₈×C₂₃	—	2	1	no	—
210	C₂×C₈×C₂₃	#41	1	2	yes	complemented
211	C₂×C₈×C₂₃	#41	1	2	yes	complemented
212	C₄⋊C₄×C₂₃	—	2	4	no	—
213	C₄⋊C₄×C₂₃	—	2	4	no	—
214	C₄⋊C₄×C₂₃	—	2	4	no	—
215	C₄⋊C₄×C₂₃	—	2	2	no	—
216	C₄⋊C₄×C₂₃	—	2	1	no	—
217	C₄⋊C₄×C₂₃	—	2	1	no	—
218	C₄⋊C₄×C₂₃	—	2	1	no	—
219	C₄⋊C₄×C₂₃	—	2	1	no	—
220	C₄⋊C₄×C₂₃	—	2	1	no	—
221	C₄⋊C₄×C₂₃	—	2	1	no	—
222	C₄⋊C₄×C₂₃	—	2	1	no	—
223	C₄⋊C₄×C₂₃	—	2	1	no	—
224	C₄⋊C₄×C₂₃	—	2	1	no	—
225	C₄⋊C₄×C₂₃	—	2	1	no	—
226	C₄⋊C₄×C₂₃	—	2	1	no	—
227	C₄⋊C₄×C₂₃	—	4	2	no	—
228	C₄⋊C₄×C₂₃	—	8	1	no	—
229	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
230	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
231	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
232	C₂²⋊C₄×C₂₃	—	2	4	no	—
233	C₂²⋊C₄×C₂₃	—	2	4	no	—
234	C₂²⋊C₄×C₂₃	—	2	2	no	—
235	C₂²⋊C₄×C₂₃	—	2	4	no	—
236	C₂²⋊C₄×C₂₃	—	2	2	no	—
237	C₂²⋊C₄×C₂₃	—	4	2	no	—
238	C₂²⋊C₄×C₂₃	—	4	2	no	—
239	C₂²⋊C₄×C₂₃	—	8	1	no	—
240	C₂²⋊C₄×C₂₃	—	8	1	no	—
241	C₄²×C₂₃	—	2	1	no	—
242	C₄²×C₂₃	—	2	1	no	—
243	C₄²×C₂₃	—	4	2	no	—
244	#24100	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
245	C₂³×C₂₃	—	2	1	no	—
246	C₂³×C₂₃	—	2	1	no	—
247	C₂³×C₂₃	—	2	1	no	—
248	C₂³×C₂₃	—	2	1	no	—
249	C₂³×C₂₃	—	2	1	no	—
250	C₂³×C₂₃	—	2	1	no	—
251	C₂³×C₂₃	—	2	1	no	—
252	C₂³×C₂₃	—	2	1	no	—
253	C₂³×C₂₃	—	2	1	no	—
254	C₂³×C₂₃	—	2	1	no	—
255	C₂³×C₂₃	—	2	1	no	—
256	C₂³×C₂₃	—	2	1	no	—
257	C₂³×C₂₃	—	2	2	no	—
258	C₂³×C₂₃	—	4	1	no	—
259	C₂³×C₂₃	—	4	1	no	—
260	C₂³×C₂₃	—	4	1	no	—
261	C₂³×C₂₃	—	4	1	no	—
262	C₂³×C₂₃	—	4	1	no	—
263	C₂³×C₂₃	—	4	1	no	—
264	C₂³×C₂₃	#120	1	2	yes	—
265	C₂³×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
266	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
267	Q₈×C₂₃	—	4	8	no	—
268	D₄×C₂₃	—	2	8	no	—
269	D₄×C₂₃	—	2	2	no	—
270	D₄×C₂₃	—	2	2	no	—
271	D₄×C₂₃	—	4	8	no	—
272	D₄×C₂₃	—	4	8	no	—
273	D₄×C₂₃	—	4	1	no	—
274	D₄×C₂₃	—	4	1	no	—
275	C₂×C₄×C₂₃	—	2	1	no	—
276	C₂×C₄×C₂₃	—	2	1	no	—
277	C₂×C₄×C₂₃	—	2	1	no	—
278	C₂×C₄×C₂₃	—	2	1	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	1	no	—
284	C₂×C₄×C₂₃	—	2	1	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	—	2	1	no	—
289	C₂×C₄×C₂₃	—	2	1	no	—
290	C₂×C₄×C₂₃	—	2	1	no	—
291	C₂×C₄×C₂₃	—	2	1	no	—
292	C₂×C₄×C₂₃	—	4	8	no	—
293	C₂×C₄×C₂₃	—	4	8	no	—
294	C₂×C₄×C₂₃	—	4	8	no	—
295	C₂×C₄×C₂₃	—	4	1	no	—
296	C₂×C₄×C₂₃	—	4	1	no	—
297	C₂×C₄×C₂₃	—	4	1	no	—
298	C₂×C₄×C₂₃	—	4	1	no	—
299	C₂×C₄×C₂₃	—	4	1	no	—
300	C₂×C₄×C₂₃	—	4	1	no	—
301	C₂×C₄×C₂₃	—	4	1	no	—
302	C₂×C₄×C₂₃	—	4	1	no	—
303	C₂×C₄×C₂₃	—	4	1	no	—
304	C₂×C₄×C₂₃	—	4	1	no	—
305	C₂×C₄×C₂₃	—	4	1	no	—
306	C₂×C₄×C₂₃	—	4	1	no	—
307	C₂×C₄×C₂₃	—	4	1	no	—
308	C₂×C₄×C₂₃	—	4	1	no	—
309	C₂×C₄×C₂₃	—	4	1	no	—
310	C₂×C₄×C₂₃	—	4	1	no	—
311	C₂×C₄×C₂₃	—	4	1	no	—
312	C₂×C₄×C₂₃	—	4	1	no	—
313	C₂×C₄×C₂₃	—	4	1	no	—
314	C₂×C₄×C₂₃	—	4	1	no	—
315	C₂×C₄×C₂₃	—	4	1	no	—
316	C₂×C₄×C₂₃	—	4	1	no	—
317	C₂×C₄×C₂₃	#120	1	2	yes	—
318	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
319	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
322	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
323	C₂×C₄×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
324	C₂×C₄×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
325	C₈×C₂₃	—	2	2	no	—
326	C₈×C₂₃	—	2	2	no	—
327	C₈×C₂₃	—	4	1	no	—
328	C₈×C₂₃	—	4	1	no	—
329	C₂×#547	C₂×C₂₃	1	1	yes	characteristic
330	C₂×#482	C₂×C₂₃	1	1	yes	characteristic, complemented
331	C₂×#428	C₂×C₂₃	1	1	yes	characteristic, complemented
332	#2485	C₂×C₂₃	1	1	yes	characteristic, complemented
333	#2058	C₂×C₂₃	1	1	yes	characteristic, complemented
334	#2057	C₂×C₂₃	1	1	yes	characteristic, complemented
335	#2034	C₂×C₂₃	1	1	yes	characteristic, complemented
336	#2033	C₂×C₂₃	1	1	yes	characteristic, complemented
337	#1895	C₂×C₂₃	1	1	yes	characteristic, complemented
338	#1870	C₂×C₂₃	1	1	yes	characteristic, complemented
339	#1864	C₂×C₂₃	1	1	yes	characteristic, complemented
340	#1862	C₂×C₂₃	1	1	yes	characteristic, complemented
341	#1853	C₂×C₂₃	1	1	yes	characteristic, complemented
342	#1852	C₂×C₂₃	1	1	yes	characteristic, complemented
343	#1824	C₂×C₂₃	1	1	yes	characteristic, complemented
344	C₂²×C₂₃	—	2	2	no	—
345	C₂²×C₂₃	—	2	2	no	—
346	C₂²×C₂₃	—	2	2	no	—
347	C₂²×C₂₃	—	2	2	no	—
348	C₂²×C₂₃	—	2	2	no	—
349	C₂²×C₂₃	—	2	2	no	—
350	C₂²×C₂₃	—	4	1	no	—
351	C₂²×C₂₃	—	4	1	no	—
352	C₂²×C₂₃	—	4	1	no	—
353	C₂²×C₂₃	—	4	1	no	—
354	C₂²×C₂₃	—	4	1	no	—
355	C₂²×C₂₃	—	4	1	no	—
356	C₂²×C₂₃	—	4	1	no	—
357	C₂²×C₂₃	—	4	1	no	—
358	C₂²×C₂₃	—	4	2	no	—
359	C₂²×C₂₃	—	4	2	no	—
360	C₂²×C₂₃	—	4	2	no	—
361	C₂²×C₂₃	—	8	1	no	—
362	C₂²×C₂₃	—	8	1	no	—
363	C₂²×C₂₃	—	8	1	no	—
364	C₂²×C₂₃	—	8	1	no	—
365	C₂²×C₂₃	C₂×#120	1	1	yes	characteristic
366	C₂²×C₂₃	#547	1	1	yes	characteristic
367	C₂²×C₂₃	#547	1	1	yes	characteristic
368	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
369	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
370	C₂²×C₂₃	#577	1	1	yes	characteristic
371	C₂²×C₂₃	#578	1	1	yes	characteristic
372	C₄×C₂₃	—	2	2	no	—
373	C₄×C₂₃	—	2	2	no	—
374	C₄×C₂₃	—	4	1	no	—
375	C₄×C₂₃	—	4	2	no	—
376	C₄×C₂₃	—	4	2	no	—
377	C₄×C₂₃	—	4	2	no	—
378	C₄×C₂₃	—	4	1	no	—
379	C₄×C₂₃	—	8	1	no	—
380	C₄×C₂₃	—	8	1	no	—
381	C₄×C₂₃	—	8	1	no	—
382	C₄×C₂₃	—	8	1	no	—
383	C₄×C₂₃	#525	1	1	yes	characteristic
384	C₄×C₂₃	#536	1	1	yes	characteristic
385	C₄×C₂₃	#547	1	1	yes	characteristic
386	C₄×C₂₃	#547	1	1	yes	characteristic
387	C₂²×#41	—	2	1	no	—
388	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
389	#547	—	2	4	no	—
390	#547	—	2	4	no	—
391	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
392	C₂×#123	—	2	1	no	—
393	C₂×#123	—	2	1	no	—
394	C₂×C₂²⋊Q₈	—	2	1	no	—
395	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
396	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
397	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
398	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
399	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
400	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
401	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
402	#482	—	2	4	no	—
403	#428	—	2	4	no	—
404	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
405	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
406	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
407	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
408	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
409	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
410	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
411	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
412	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
413	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
414	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
415	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
416	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
417	#397	—	2	1	no	—
418	#394	—	2	1	no	—
419	#389	C₂²×C₂₃	1	1	yes	characteristic
420	#389	C₂²×C₂₃	1	1	yes	characteristic
421	#388	—	2	1	no	—
422	#387	—	2	1	no	—
423	#380	C₂²×C₂₃	1	1	yes	characteristic
424	#380	C₂²×C₂₃	1	1	yes	characteristic
425	#380	C₂²×C₂₃	1	1	yes	characteristic
426	#340	C₂²×C₂₃	1	1	yes	characteristic
427	#340	C₂²×C₂₃	1	1	yes	characteristic
428	#340	C₂²×C₂₃	1	1	yes	characteristic
429	#340	C₂²×C₂₃	1	1	yes	characteristic
430	#340	C₂²×C₂₃	1	1	yes	characteristic
431	#340	C₂²×C₂₃	1	1	yes	characteristic
432	#336	C₂²×C₂₃	1	1	yes	characteristic
433	#336	C₂²×C₂₃	1	1	yes	characteristic
434	C₂×C₂₃	—	4	2	no	—
435	C₂×C₂₃	—	4	2	no	—
436	C₂×C₂₃	—	8	2	no	—
437	C₂×C₂₃	#2406	1	1	yes	characteristic
438	C₂×C₂₃	#3003	1	1	yes	characteristic
439	C₂×C₂₃	#3013	1	1	yes	characteristic
440	C₂×C₂₃	#3343	1	1	yes	characteristic
441	C₂×C₂₃	#3345	1	1	yes	characteristic
442	C₂×C₂₃	#3353	1	1	yes	characteristic
443	C₂×C₂₃	#3354	1	1	yes	characteristic
444	C₂×#41	—	2	8	no	—
445	C₂×#41	—	4	4	no	—
446	C₂×#41	—	4	4	no	—
447	C₂²×Q₈	—	2	1	no	—
448	C₂²×D₄	—	2	1	no	—
449	C₂²×D₄	—	2	1	no	—
450	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
451	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
452	C₂³×C₄	—	2	1	no	—
453	C₂³×C₄	—	2	1	no	—
454	C₂³×C₄	—	2	1	no	—
455	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
456	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
457	C₂×M₁₆	—	2	2	no	—
458	C₂×M₁₆	—	2	2	no	—
459	C₂×M₁₆	—	2	2	no	—
460	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
461	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
462	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
463	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
464	C₄⋊Q₈	—	2	2	no	—
465	C₄⋊Q₈	—	2	2	no	—
466	#123	—	2	8	no	—
467	#123	—	2	8	no	—
468	C₂²⋊Q₈	—	2	8	no	—
469	#121	—	2	2	no	—
470	#121	—	2	2	no	—
471	#121	—	2	2	no	—
472	#121	D₄×C₂₃	1	4	yes	—
473	C₄×D₄	—	2	2	no	—
474	C₄×D₄	—	2	2	no	—
475	C₄×D₄	—	2	2	no	—
476	C₄×D₄	—	2	2	no	—
477	#117	—	2	2	no	—
478	#117	—	2	2	no	—
479	C₂×C₄⋊C₄	—	2	1	no	—
480	C₂×C₄⋊C₄	—	2	1	no	—
481	C₂×C₄⋊C₄	—	2	2	no	—
482	C₂×C₄⋊C₄	—	2	1	no	—
483	C₂×C₄⋊C₄	—	2	2	no	—
484	C₂×C₄⋊C₄	—	2	2	no	—
485	C₂×C₄⋊C₄	—	2	1	no	—
486	C₂×C₄⋊C₄	—	2	1	no	—
487	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
488	C₂×C₄⋊C₄	D₄×C₂₃	1	4	yes	—
489	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
491	C₂×C₄⋊C₄	C₂³×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×C₂²⋊C₄	—	2	1	no	—
502	C₂×C₂²⋊C₄	—	2	1	no	—
503	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
504	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
505	C₂×C₄²	—	2	1	no	—
506	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
507	#107	—	2	2	no	—
508	#107	—	2	2	no	—
509	#107	—	2	2	no	—
510	#106	—	2	2	no	—
511	#106	—	2	2	no	—
512	#106	—	2	2	no	—
513	#102	—	2	2	no	—
514	#102	—	2	2	no	—
515	#102	—	2	2	no	—
516	#102	—	2	2	no	—
517	C₂²⋊C₈	—	2	2	no	—
518	C₂²⋊C₈	—	2	2	no	—
519	C₂²⋊C₈	—	2	2	no	—
520	#95	—	2	1	no	—
521	#95	—	2	1	no	—
522	#95	—	2	1	no	—
523	#95	—	2	1	no	—
524	#95	—	2	1	no	—
525	C₂₃	#24100	1	1	yes	characteristic, direct product factor, Sylow
526	C₂⁴	—	2	1	no	—
527	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
528	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
529	#41	—	4	32	no	—
530	C₂×Q₈	—	2	4	no	—
531	C₂×Q₈	—	4	2	no	—
532	C₂×Q₈	—	4	2	no	—
533	C₂×D₄	—	2	2	no	—
534	C₂×D₄	—	2	2	no	—
535	C₂×D₄	—	2	4	no	—
536	C₂×D₄	—	2	4	no	—
537	C₂×D₄	—	2	2	no	—
538	C₂×D₄	—	2	1	no	—
539	C₂×D₄	—	2	1	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	—	2	1	no	—
543	C₂×D₄	—	4	2	no	—
544	C₂×D₄	—	4	2	no	—
545	C₂×D₄	—	4	2	no	—
546	C₂×D₄	—	4	2	no	—
547	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	4	no	—
553	C₂²×C₄	—	2	4	no	—
554	C₂²×C₄	—	2	4	no	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	1	no	—
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	—	4	2	no	—
569	C₂²×C₄	—	4	2	no	—
570	C₂²×C₄	—	4	2	no	—
571	C₂²×C₄	—	4	2	no	—
572	C₂²×C₄	—	4	2	no	—
573	C₂²×C₄	—	4	2	no	—
574	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
575	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
576	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
577	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
578	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
579	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
580	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
581	M₁₆	—	2	8	no	—
582	C₂×C₈	—	2	1	no	—
583	C₂×C₈	—	2	1	no	—
584	C₂×C₈	—	2	1	no	—
585	C₂×C₈	—	2	1	no	—
586	C₂×C₈	—	2	1	no	—
587	C₂×C₈	—	2	1	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	2	1	no	—
592	C₂×C₈	#41×C₂₃	1	2	yes	complemented
593	C₂×C₈	#41×C₂₃	1	2	yes	complemented
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	—	2	4	no	—
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	1	no	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	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	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	4	2	no	—
610	C₄⋊C₄	—	8	1	no	—
611	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
612	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
613	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
614	C₂²⋊C₄	—	2	4	no	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₂²⋊C₄	—	2	2	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	2	no	—
619	C₂²⋊C₄	—	4	2	no	—
620	C₂²⋊C₄	—	4	2	no	—
621	C₂²⋊C₄	—	8	1	no	—
622	C₂²⋊C₄	—	8	1	no	—
623	C₄²	—	2	1	no	—
624	C₄²	—	2	1	no	—
625	C₄²	—	4	2	no	—
626	C₂³	—	2	1	no	—
627	C₂³	—	2	1	no	—
628	C₂³	—	2	1	no	—
629	C₂³	—	2	1	no	—
630	C₂³	—	2	1	no	—
631	C₂³	—	2	1	no	—
632	C₂³	—	2	1	no	—
633	C₂³	—	2	1	no	—
634	C₂³	—	2	1	no	—
635	C₂³	—	2	1	no	—
636	C₂³	—	2	1	no	—
637	C₂³	—	2	1	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	4	1	no	—
640	C₂³	—	4	1	no	—
641	C₂³	—	4	1	no	—
642	C₂³	—	4	1	no	—
643	C₂³	—	4	1	no	—
644	C₂³	—	4	1	no	—
645	C₂³	C₂₃×#120	1	2	yes	—
646	C₂³	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
647	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
648	Q₈	—	4	8	no	—
649	D₄	—	2	8	no	—
650	D₄	—	2	2	no	—
651	D₄	—	2	2	no	—
652	D₄	—	4	8	no	—
653	D₄	—	4	8	no	—
654	D₄	—	4	1	no	—
655	D₄	—	4	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	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	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	4	8	no	—
674	C₂×C₄	—	4	8	no	—
675	C₂×C₄	—	4	8	no	—
676	C₂×C₄	—	4	1	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	4	1	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	C₂₃×#120	1	2	yes	—
699	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
700	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
701	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
702	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
703	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
704	C₂×C₄	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
705	C₂×C₄	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
706	C₈	—	2	2	no	—
707	C₈	—	2	2	no	—
708	C₈	—	4	1	no	—
709	C₈	—	4	1	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	2	2	no	—
713	C₂²	—	2	2	no	—
714	C₂²	—	2	2	no	—
715	C₂²	—	2	2	no	—
716	C₂²	—	4	1	no	—
717	C₂²	—	4	1	no	—
718	C₂²	—	4	1	no	—
719	C₂²	—	4	1	no	—
720	C₂²	—	4	1	no	—
721	C₂²	—	4	1	no	—
722	C₂²	—	4	1	no	—
723	C₂²	—	4	1	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	8	1	no	—
728	C₂²	—	8	1	no	—
729	C₂²	—	8	1	no	—
730	C₂²	—	8	1	no	—
731	C₂²	C₂×C₂₃×#120	1	1	yes	characteristic
732	C₂²	C₂₃×#547	1	1	yes	characteristic
733	C₂²	C₂₃×#547	1	1	yes	characteristic
734	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
735	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
736	C₂²	C₂₃×#577	1	1	yes	characteristic
737	C₂²	C₂₃×#578	1	1	yes	characteristic
738	C₄	—	2	2	no	—
739	C₄	—	2	2	no	—
740	C₄	—	4	1	no	—
741	C₄	—	4	2	no	—
742	C₄	—	4	2	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	1	no	—
745	C₄	—	8	1	no	—
746	C₄	—	8	1	no	—
747	C₄	—	8	1	no	—
748	C₄	—	8	1	no	—
749	C₄	C₂₃×#525	1	1	yes	characteristic
750	C₄	C₂₃×#536	1	1	yes	characteristic
751	C₄	C₂₃×#547	1	1	yes	characteristic
752	C₄	C₂₃×#547	1	1	yes	characteristic
753	C₂	—	4	2	no	—
754	C₂	—	4	2	no	—
755	C₂	—	8	2	no	—
756	C₂	C₂₃×#2406	1	1	yes	characteristic
757	C₂	C₂₃×#3003	1	1	yes	characteristic
758	C₂	C₂₃×#3013	1	1	yes	characteristic
759	C₂	C₂₃×#3343	1	1	yes	characteristic
760	C₂	C₂₃×#3345	1	1	yes	characteristic
761	C₂	C₂₃×#3353	1	1	yes	characteristic
762	C₂	C₂₃×#3354	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂×C₂₃×#547	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄×D₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#482	C₂	semidirect
3. C₂×C₂₃×#428	C₂	semidirect
4. C₂₃×#2485	C₂	semidirect
5. C₂₃×#2058	C₂	semidirect
6. C₂₃×#2057	C₂	semidirect
7. C₂₃×#2034	C₂	semidirect
8. C₂₃×#2033	C₂	semidirect
9. C₂₃×#1895	C₂	semidirect
10. C₂₃×#1870	C₂	semidirect
11. C₂₃×#1864	C₂	semidirect
12. C₂₃×#1862	C₂	semidirect
13. C₂₃×#1853	C₂	semidirect
14. C₂₃×#1852	C₂	semidirect
15. C₂₃×#1824	C₂	semidirect
210. C₂×C₈×C₂₃	#41	semidirect
211. C₂×C₈×C₂₃	#41	semidirect
244. #24100	C₂₃	direct (N × H)
330. C₂×#482	C₂×C₂₃	semidirect
331. C₂×#428	C₂×C₂₃	semidirect
332. #2485	C₂×C₂₃	semidirect
333. #2058	C₂×C₂₃	semidirect
334. #2057	C₂×C₂₃	semidirect
335. #2034	C₂×C₂₃	semidirect
336. #2033	C₂×C₂₃	semidirect
337. #1895	C₂×C₂₃	semidirect
338. #1870	C₂×C₂₃	semidirect
339. #1864	C₂×C₂₃	semidirect
340. #1862	C₂×C₂₃	semidirect
341. #1853	C₂×C₂₃	semidirect
342. #1852	C₂×C₂₃	semidirect
343. #1824	C₂×C₂₃	semidirect
525. C₂₃	#24100	direct (N × H)
592. C₂×C₈	#41×C₂₃	semidirect
593. C₂×C₈	#41×C₂₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₂₃×#547	2
C₂×C₂₃×#482	2
C₂×C₂₃×#428	2
C₂₃×#2485	2
C₂₃×#2058	2
C₂₃×#2057	2
C₂₃×#2034	2
C₂₃×#2033	2
C₂₃×#1895	2
C₂₃×#1870	2
C₂₃×#1864	2
C₂₃×#1862	2
C₂₃×#1853	2
C₂₃×#1852	2
C₂₃×#1824	2
#24100	23

Subgroups — C23×#24100 #19171726

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#24100 #19171726