Subgroups — C₂₃×#60698 #19208324

Order 5888.

1970 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3460	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3184	C₂	1	2	yes	maximal, complemented
3	C₂₃×#3183	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3180	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3179	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3176	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3173	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3163	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3155	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3136	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3062	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3060	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3058	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₂₃×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2943	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#2875	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
19	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
23	C₂₃×#544	C₂²	1	2	yes	—
24	C₂₃×#542	—	2	2	no	—
25	C₂₃×#542	C₂²	1	4	yes	complemented
26	C₂₃×#540	—	2	2	no	—
27	C₂₃×#540	C₂²	1	4	yes	complemented
28	C₂₃×#538	—	2	4	no	—
29	C₂₃×#537	C₂²	1	2	yes	—
30	C₂₃×#535	C₂²	1	2	yes	—
31	C₂₃×#535	C₂²	1	2	yes	—
32	C₂₃×#532	—	2	2	no	—
33	C₂₃×#532	C₂²	1	4	yes	complemented
34	C₂₃×#529	—	2	2	no	—
35	C₂₃×#529	C₂²	1	4	yes	complemented
36	C₂₃×#525	—	2	4	no	—
37	C₄×#41×C₂₃	C₂²	1	2	yes	—
38	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
40	C₂₃×#501	C₂²	1	4	yes	complemented
41	C₂₃×#499	C₂²	1	2	yes	complemented
42	C₂₃×#498	C₂²	1	2	yes	complemented
43	C₂₃×#496	C₂²	1	4	yes	—
44	C₂₃×#495	C₂²	1	2	yes	—
45	C₂₃×#493	C₂²	1	2	yes	—
46	C₂₃×#490	C₂²	1	4	yes	complemented
47	C₂₃×#489	C₂²	1	4	yes	complemented
48	C₂₃×#488	C₂²	1	4	yes	complemented
49	C₂₃×#486	C₂²	1	4	yes	complemented
50	C₂₃×#470	C₂²	1	2	yes	complemented
51	C₂₃×#469	C₂²	1	2	yes	—
52	C₂₃×#469	C₂²	1	2	yes	—
53	C₂₃×#469	C₂²	1	2	yes	complemented
54	C₂₃×#469	C₂²	1	4	yes	complemented
55	C₂₃×#468	C₂²	1	4	yes	complemented
56	C₂₃×#466	C₂²	1	4	yes	—
57	C₂₃×#466	C₂²	1	4	yes	complemented
58	C₂₃×#465	C₂²	1	4	yes	complemented
59	C₂₃×#465	C₂²	1	4	yes	complemented
60	C₂₃×#442	C₂²	1	2	yes	—
61	C₂₃×#442	C₂²	1	2	yes	—
62	C₂₃×#442	C₂²	1	2	yes	—
63	C₂₃×#442	C₂²	1	2	yes	—
64	C₂₃×#442	C₂²	1	1	yes	characteristic, complemented
65	C₂₃×#442	C₂²	1	4	yes	complemented
66	C₂₃×#442	C₂²	1	1	yes	characteristic, complemented
67	C₂₃×#441	C₂²	1	1	yes	characteristic, complemented
68	C₂₃×#441	C₂²	1	1	yes	characteristic, complemented
69	C₂₃×#440	C₂²	1	2	yes	complemented
70	C₂₃×#440	C₂²	1	2	yes	complemented
71	C₂₃×#440	C₂²	1	4	yes	complemented
72	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
73	C₄×D₈×C₂₃	C₂²	1	4	yes	complemented
74	C₂₃×#428	C₂²	1	2	yes	—
75	C₂₃×#427	C₂²	1	1	yes	characteristic
76	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
77	C₂₃×#418	C₂²	1	2	yes	—
78	C₂₃×#417	C₂²	1	2	yes	—
79	C₂₃×#416	C₂²	1	2	yes	—
80	C₂×C₂₃×#102	C₂²	1	2	yes	—
81	C₂₃×#405	C₂²	1	1	yes	characteristic
82	C₂₃×#405	C₂²	1	1	yes	characteristic
83	C₂₃×#405	C₂²	1	2	yes	complemented
84	C₂₃×#405	C₂²	1	2	yes	complemented
85	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
86	C₄×M₁₆×C₂₃	C₂²	1	2	yes	complemented
87	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
88	C₂×C₂₃×#97	C₂²	1	2	yes	complemented
89	C₂×#41×C₂₃	—	2	4	no	—
90	C₂×#41×C₂₃	C₂³	1	2	yes	—
91	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
93	C₂³×C₄×C₂₃	—	2	2	no	—
94	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
95	C₂₃×#135	—	2	4	no	—
96	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
97	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
98	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
99	C₂×D₈×C₂₃	—	2	4	no	—
100	C₂×D₈×C₂₃	C₂³	1	2	yes	—
101	C₂×D₈×C₂₃	C₂³	1	2	yes	—
102	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
103	C₂×D₈×C₂₃	C₂³	1	4	yes	—
104	C₂₃×#131	—	2	4	no	—
105	C₂₃×#131	—	2	4	no	—
106	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
107	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
108	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
109	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
112	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
113	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
114	C₂₃×C₄⋊Q₈	—	2	2	no	—
115	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
116	C₂₃×#127	—	2	2	no	—
117	C₂₃×#127	C₂³	1	4	yes	—
118	C₂₃×#126	—	2	4	no	—
119	C₂₃×#126	—	2	4	no	—
120	C₂₃×#125	—	2	2	no	—
121	C₂₃×#125	C₂³	1	4	yes	—
122	C₂₃×#124	—	2	2	no	—
123	C₂₃×#124	—	2	4	no	—
124	C₂₃×#124	—	2	4	no	—
125	C₂₃×#124	C₂³	1	4	yes	—
126	C₂₃×#123	—	2	4	no	—
127	C₂₃×#123	—	2	4	no	—
128	C₂₃×#123	—	2	4	no	—
129	C₂₃×#123	—	2	4	no	—
130	C₂₃×C₂²⋊Q₈	—	2	2	no	—
131	C₂₃×C₂²⋊Q₈	—	2	4	no	—
132	C₂₃×C₂²⋊Q₈	—	2	4	no	—
133	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
134	C₂₃×#121	—	2	4	no	—
135	C₂₃×#121	—	2	2	no	—
136	C₂₃×#121	—	2	4	no	—
137	C₂₃×#121	—	2	2	no	—
138	C₂₃×#121	—	2	2	no	—
139	C₂₃×#121	—	2	4	no	—
140	C₂₃×#121	—	2	4	no	—
141	C₂₃×#121	C₂³	1	4	yes	—
142	C₂₃×#121	C₂³	1	4	yes	—
143	C₂₃×#121	C₂³	1	4	yes	—
144	C₂₃×#120	—	2	4	no	—
145	C₂₃×#120	—	2	4	no	—
146	C₄×Q₈×C₂₃	D₄	1	2	yes	—
147	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
148	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
149	C₄×D₄×C₂₃	—	2	2	no	—
150	C₄×D₄×C₂₃	—	2	2	no	—
151	C₄×D₄×C₂₃	—	2	4	no	—
152	C₄×D₄×C₂₃	—	2	2	no	—
153	C₄×D₄×C₂₃	—	2	2	no	—
154	C₄×D₄×C₂₃	—	2	4	no	—
155	C₄×D₄×C₂₃	D₄	1	4	yes	—
156	C₄×D₄×C₂₃	D₄	1	2	yes	—
157	C₄×D₄×C₂₃	C₂³	1	2	yes	—
158	C₄×D₄×C₂₃	C₂³	1	4	yes	—
159	C₄×D₄×C₂₃	C₂³	1	4	yes	—
160	C₄×D₄×C₂₃	C₂³	1	2	yes	—
161	C₂₃×#117	—	2	2	no	—
162	C₂₃×#117	—	2	4	no	—
163	C₂₃×#117	C₂³	1	2	yes	—
164	C₂₃×#117	C₂³	1	1	yes	characteristic
165	C₂₃×#117	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
168	C₂×C₄²×C₂₃	—	2	2	no	—
169	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
171	C₂₃×#107	C₂³	1	2	yes	—
172	C₂₃×#107	C₂³	1	4	yes	—
173	C₂₃×#106	C₂³	1	2	yes	—
174	C₂₃×#106	C₂³	1	2	yes	—
175	C₂₃×#106	C₂³	1	1	yes	characteristic
176	C₂₃×#106	C₂³	1	1	yes	characteristic
177	C₂₃×#106	C₂³	1	4	yes	—
178	C₂₃×#103	C₂³	1	2	yes	—
179	C₂₃×#103	C₂³	1	2	yes	—
180	C₂₃×#103	C₂³	1	4	yes	—
181	C₂₃×#102	C₂³	1	4	yes	—
182	C₂₃×#102	C₂³	1	4	yes	—
183	C₂₃×#102	C₂³	1	2	yes	—
184	C₂₃×#102	C₂³	1	2	yes	—
185	C₂₃×#102	C₂³	1	4	yes	—
186	C₂₃×#102	C₂³	1	4	yes	—
187	C₂₃×#102	C₂³	1	4	yes	—
188	C₂₃×#97	C₂³	1	1	yes	characteristic
189	C₂₃×#97	C₂³	1	1	yes	characteristic
190	C₂₃×#97	C₂³	1	1	yes	characteristic
191	C₂₃×#97	C₂³	1	1	yes	characteristic
192	C₂₃×#97	C₂³	1	2	yes	—
193	C₂₃×#97	C₂³	1	2	yes	—
194	C₂₃×#97	C₂³	1	2	yes	—
195	C₄×C₈×C₂₃	C₂³	1	2	yes	—
196	C₄×C₈×C₂₃	C₂³	1	2	yes	—
197	C₄×C₈×C₂₃	C₂³	1	2	yes	—
198	C₂⁴×C₂₃	—	2	2	no	—
199	#41×C₂₃	—	2	2	no	—
200	#41×C₂₃	—	2	2	no	—
201	#41×C₂₃	—	2	4	no	—
202	#41×C₂₃	—	2	4	no	—
203	#41×C₂₃	—	8	8	no	—
204	C₂×Q₈×C₂₃	—	2	4	no	—
205	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
206	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
207	C₂×D₄×C₂₃	—	2	2	no	—
208	C₂×D₄×C₂₃	—	2	4	no	—
209	C₂×D₄×C₂₃	—	2	4	no	—
210	C₂×D₄×C₂₃	—	2	4	no	—
211	C₂×D₄×C₂₃	—	2	2	no	—
212	C₂×D₄×C₂₃	—	2	4	no	—
213	C₂×D₄×C₂₃	—	2	4	no	—
214	C₂×D₄×C₂₃	—	2	4	no	—
215	C₂×D₄×C₂₃	—	2	4	no	—
216	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
217	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
218	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
219	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₂₃	—	2	2	no	—
221	C₂²×C₄×C₂₃	—	2	2	no	—
222	C₂²×C₄×C₂₃	—	2	2	no	—
223	C₂²×C₄×C₂₃	—	2	4	no	—
224	C₂²×C₄×C₂₃	—	2	2	no	—
225	C₂²×C₄×C₂₃	—	2	4	no	—
226	C₂²×C₄×C₂₃	—	8	4	no	—
227	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
228	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
229	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
231	Q₁₆×C₂₃	—	2	2	no	—
232	SD₁₆×C₂₃	—	2	4	no	—
233	SD₁₆×C₂₃	—	2	8	no	—
234	D₈×C₂₃	—	2	4	no	—
235	D₈×C₂₃	—	2	4	no	—
236	D₈×C₂₃	—	2	2	no	—
237	D₈×C₂₃	—	2	8	no	—
238	M₁₆×C₂₃	—	2	2	no	—
239	M₁₆×C₂₃	—	2	4	no	—
240	M₁₆×C₂₃	—	2	4	no	—
241	M₁₆×C₂₃	#41	1	4	yes	complemented
242	C₂×C₈×C₂₃	—	2	2	no	—
243	C₂×C₈×C₂₃	—	2	4	no	—
244	C₂×C₈×C₂₃	—	2	4	no	—
245	C₂×C₈×C₂₃	#41	1	4	yes	complemented
246	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
247	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
248	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
249	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
250	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
251	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
252	C₄⋊C₄×C₂₃	—	2	2	no	—
253	C₄⋊C₄×C₂₃	—	2	2	no	—
254	C₄⋊C₄×C₂₃	—	2	2	no	—
255	C₄⋊C₄×C₂₃	—	2	4	no	—
256	C₄⋊C₄×C₂₃	—	2	4	no	—
257	C₄⋊C₄×C₂₃	—	2	4	no	—
258	C₄⋊C₄×C₂₃	—	2	4	no	—
259	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
260	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
261	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
262	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
263	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
264	C₂²⋊C₄×C₂₃	—	2	2	no	—
265	C₂²⋊C₄×C₂₃	—	2	4	no	—
266	C₂²⋊C₄×C₂₃	—	2	4	no	—
267	C₂²⋊C₄×C₂₃	—	2	4	no	—
268	C₂²⋊C₄×C₂₃	—	2	2	no	—
269	C₂²⋊C₄×C₂₃	—	2	2	no	—
270	C₂²⋊C₄×C₂₃	—	2	4	no	—
271	C₂²⋊C₄×C₂₃	—	2	4	no	—
272	C₂²⋊C₄×C₂₃	—	2	4	no	—
273	C₂²⋊C₄×C₂₃	—	2	4	no	—
274	C₂²⋊C₄×C₂₃	—	2	4	no	—
275	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
276	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
277	C₄²×C₂₃	—	2	2	no	—
278	C₄²×C₂₃	—	2	2	no	—
279	C₄²×C₂₃	—	2	2	no	—
280	C₄²×C₂₃	C₂×D₄	1	2	yes	—
281	C₄²×C₂₃	C₂×D₄	1	4	yes	—
282	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
283	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
284	C₄²×C₂₃	C₂⁴	1	2	yes	—
285	#60698	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
286	C₂³×C₂₃	—	2	4	no	—
287	C₂³×C₂₃	—	2	2	no	—
288	C₂³×C₂₃	—	4	4	no	—
289	C₂³×C₂₃	—	8	2	no	—
290	C₂³×C₂₃	—	8	2	no	—
291	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
292	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
293	Q₈×C₂₃	—	2	2	no	—
294	Q₈×C₂₃	—	2	2	no	—
295	Q₈×C₂₃	—	2	2	no	—
296	Q₈×C₂₃	—	8	4	no	—
297	D₄×C₂₃	—	2	4	no	—
298	D₄×C₂₃	—	2	2	no	—
299	D₄×C₂₃	—	2	4	no	—
300	D₄×C₂₃	—	2	2	no	—
301	D₄×C₂₃	—	2	4	no	—
302	D₄×C₂₃	—	2	2	no	—
303	D₄×C₂₃	—	4	4	no	—
304	D₄×C₂₃	—	4	4	no	—
305	D₄×C₂₃	—	8	4	no	—
306	D₄×C₂₃	—	8	4	no	—
307	D₄×C₂₃	—	8	4	no	—
308	D₄×C₂₃	—	8	4	no	—
309	D₄×C₂₃	—	8	4	no	—
310	C₂×C₄×C₂₃	—	2	2	no	—
311	C₂×C₄×C₂₃	—	2	2	no	—
312	C₂×C₄×C₂₃	—	2	2	no	—
313	C₂×C₄×C₂₃	—	2	2	no	—
314	C₂×C₄×C₂₃	—	2	2	no	—
315	C₂×C₄×C₂₃	—	2	4	no	—
316	C₂×C₄×C₂₃	—	4	2	no	—
317	C₂×C₄×C₂₃	—	4	4	no	—
318	C₂×C₄×C₂₃	—	4	8	no	—
319	C₂×C₄×C₂₃	—	4	4	no	—
320	C₂×C₄×C₂₃	—	4	4	no	—
321	C₂×C₄×C₂₃	—	8	2	no	—
322	C₂×C₄×C₂₃	—	8	4	no	—
323	C₂×C₄×C₂₃	—	8	2	no	—
324	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
325	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
326	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
327	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
328	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
330	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
331	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
332	C₈×C₂₃	—	2	1	no	—
333	C₈×C₂₃	—	2	1	no	—
334	C₈×C₂₃	—	2	2	no	—
335	C₈×C₂₃	C₂×#41	1	2	yes	—
336	C₈×C₂₃	C₂×#41	1	4	yes	—
337	C₈×C₂₃	C₂×#41	1	2	yes	—
338	#3460	C₂×C₂₃	1	2	yes	complemented
339	#3184	C₂×C₂₃	1	2	yes	complemented
340	#3183	C₂×C₂₃	1	2	yes	complemented
341	#3180	C₂×C₂₃	1	4	yes	complemented
342	#3179	C₂×C₂₃	1	4	yes	complemented
343	#3176	C₂×C₂₃	1	2	yes	complemented
344	#3173	C₂×C₂₃	1	2	yes	complemented
345	#3163	C₂×C₂₃	1	1	yes	characteristic, complemented
346	#3155	C₂×C₂₃	1	1	yes	characteristic, complemented
347	#3136	C₂×C₂₃	1	2	yes	complemented
348	#3062	C₂×C₂₃	1	2	yes	complemented
349	#3060	C₂×C₂₃	1	1	yes	characteristic, complemented
350	#3058	C₂×C₂₃	1	1	yes	characteristic, complemented
351	C₄×AGL(1,ℤ/8)	C₂×C₂₃	1	2	yes	complemented
352	#2943	C₂×C₂₃	1	1	yes	characteristic, complemented
353	C₂×#442	C₂×C₂₃	1	1	yes	characteristic, complemented
354	#2875	C₂×C₂₃	1	1	yes	characteristic, complemented
355	C₂²×C₂₃	—	2	2	no	—
356	C₂²×C₂₃	—	2	4	no	—
357	C₂²×C₂₃	—	2	2	no	—
358	C₂²×C₂₃	—	4	4	no	—
359	C₂²×C₂₃	—	4	2	no	—
360	C₂²×C₂₃	—	4	2	no	—
361	C₂²×C₂₃	—	4	4	no	—
362	C₂²×C₂₃	—	4	2	no	—
363	C₂²×C₂₃	—	4	4	no	—
364	C₂²×C₂₃	—	8	8	no	—
365	C₂²×C₂₃	#532	1	2	yes	—
366	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
367	C₄×C₂₃	—	2	2	no	—
368	C₄×C₂₃	—	2	2	no	—
369	C₄×C₂₃	—	2	4	no	—
370	C₄×C₂₃	—	2	2	no	—
371	C₄×C₂₃	—	4	4	no	—
372	C₄×C₂₃	—	4	2	no	—
373	C₄×C₂₃	—	4	2	no	—
374	C₄×C₂₃	—	4	2	no	—
375	C₄×C₂₃	#532	1	2	yes	—
376	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
377	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
378	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	—
379	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
380	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
381	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
382	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
383	#544	C₂²×C₂₃	1	2	yes	—
384	#542	—	2	2	no	—
385	#542	C₂²×C₂₃	1	4	yes	complemented
386	#540	—	2	2	no	—
387	#540	C₂²×C₂₃	1	4	yes	complemented
388	#538	—	2	4	no	—
389	#537	C₂²×C₂₃	1	2	yes	—
390	#535	C₂²×C₂₃	1	2	yes	—
391	#535	C₂²×C₂₃	1	2	yes	—
392	#532	—	2	2	no	—
393	#532	C₂²×C₂₃	1	4	yes	complemented
394	#529	—	2	2	no	—
395	#529	C₂²×C₂₃	1	4	yes	complemented
396	#525	—	2	4	no	—
397	C₄×#41	C₂²×C₂₃	1	2	yes	—
398	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
399	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
400	#501	C₂²×C₂₃	1	4	yes	complemented
401	#499	C₂²×C₂₃	1	2	yes	complemented
402	#498	C₂²×C₂₃	1	2	yes	complemented
403	#496	C₂²×C₂₃	1	4	yes	—
404	#495	C₂²×C₂₃	1	2	yes	—
405	#493	C₂²×C₂₃	1	2	yes	—
406	#490	C₂²×C₂₃	1	4	yes	complemented
407	#489	C₂²×C₂₃	1	4	yes	complemented
408	#488	C₂²×C₂₃	1	4	yes	complemented
409	#486	C₂²×C₂₃	1	4	yes	complemented
410	#470	C₂²×C₂₃	1	2	yes	complemented
411	#469	C₂²×C₂₃	1	2	yes	—
412	#469	C₂²×C₂₃	1	2	yes	—
413	#469	C₂²×C₂₃	1	2	yes	complemented
414	#469	C₂²×C₂₃	1	4	yes	complemented
415	#468	C₂²×C₂₃	1	4	yes	complemented
416	#466	C₂²×C₂₃	1	4	yes	—
417	#466	C₂²×C₂₃	1	4	yes	complemented
418	#465	C₂²×C₂₃	1	4	yes	complemented
419	#465	C₂²×C₂₃	1	4	yes	complemented
420	#442	C₂²×C₂₃	1	2	yes	—
421	#442	C₂²×C₂₃	1	2	yes	—
422	#442	C₂²×C₂₃	1	2	yes	—
423	#442	C₂²×C₂₃	1	2	yes	—
424	#442	C₂²×C₂₃	1	1	yes	characteristic, complemented
425	#442	C₂²×C₂₃	1	4	yes	complemented
426	#442	C₂²×C₂₃	1	1	yes	characteristic, complemented
427	#441	C₂²×C₂₃	1	1	yes	characteristic, complemented
428	#441	C₂²×C₂₃	1	1	yes	characteristic, complemented
429	#440	C₂²×C₂₃	1	2	yes	complemented
430	#440	C₂²×C₂₃	1	2	yes	complemented
431	#440	C₂²×C₂₃	1	4	yes	complemented
432	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
433	C₄×D₈	C₂²×C₂₃	1	4	yes	complemented
434	#428	C₂²×C₂₃	1	2	yes	—
435	#427	C₂²×C₂₃	1	1	yes	characteristic
436	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
437	#418	C₂²×C₂₃	1	2	yes	—
438	#417	C₂²×C₂₃	1	2	yes	—
439	#416	C₂²×C₂₃	1	2	yes	—
440	C₂×#102	C₂²×C₂₃	1	2	yes	—
441	#405	C₂²×C₂₃	1	1	yes	characteristic
442	#405	C₂²×C₂₃	1	1	yes	characteristic
443	#405	C₂²×C₂₃	1	2	yes	complemented
444	#405	C₂²×C₂₃	1	2	yes	complemented
445	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
446	C₄×M₁₆	C₂²×C₂₃	1	2	yes	complemented
447	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
448	C₂×#97	C₂²×C₂₃	1	2	yes	complemented
449	C₂×C₂₃	—	2	2	no	—
450	C₂×C₂₃	—	4	2	no	—
451	C₂×C₂₃	—	8	2	no	—
452	C₂×C₂₃	—	8	4	no	—
453	C₂×C₂₃	C₂×#532	1	1	yes	characteristic
454	C₂×C₂₃	#3585	1	2	yes	—
455	C₂×#41	—	2	4	no	—
456	C₂×#41	C₂³×C₂₃	1	2	yes	—
457	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
458	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
459	C₂³×C₄	—	2	2	no	—
460	AGL(1,ℤ/8)	—	2	8	no	—
461	#135	—	2	4	no	—
462	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
463	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
464	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
465	C₂×D₈	—	2	4	no	—
466	C₂×D₈	C₂³×C₂₃	1	2	yes	—
467	C₂×D₈	C₂³×C₂₃	1	2	yes	—
468	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
469	C₂×D₈	C₂³×C₂₃	1	4	yes	—
470	#131	—	2	4	no	—
471	#131	—	2	4	no	—
472	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
473	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
474	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
475	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
476	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
477	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
478	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
479	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
480	C₄⋊Q₈	—	2	2	no	—
481	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
482	#127	—	2	2	no	—
483	#127	C₂³×C₂₃	1	4	yes	—
484	#126	—	2	4	no	—
485	#126	—	2	4	no	—
486	#125	—	2	2	no	—
487	#125	C₂³×C₂₃	1	4	yes	—
488	#124	—	2	2	no	—
489	#124	—	2	4	no	—
490	#124	—	2	4	no	—
491	#124	C₂³×C₂₃	1	4	yes	—
492	#123	—	2	4	no	—
493	#123	—	2	4	no	—
494	#123	—	2	4	no	—
495	#123	—	2	4	no	—
496	C₂²⋊Q₈	—	2	2	no	—
497	C₂²⋊Q₈	—	2	4	no	—
498	C₂²⋊Q₈	—	2	4	no	—
499	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
500	#121	—	2	4	no	—
501	#121	—	2	2	no	—
502	#121	—	2	4	no	—
503	#121	—	2	2	no	—
504	#121	—	2	2	no	—
505	#121	—	2	4	no	—
506	#121	—	2	4	no	—
507	#121	C₂³×C₂₃	1	4	yes	—
508	#121	C₂³×C₂₃	1	4	yes	—
509	#121	C₂³×C₂₃	1	4	yes	—
510	#120	—	2	4	no	—
511	#120	—	2	4	no	—
512	C₄×Q₈	D₄×C₂₃	1	2	yes	—
513	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
514	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
515	C₄×D₄	—	2	2	no	—
516	C₄×D₄	—	2	2	no	—
517	C₄×D₄	—	2	4	no	—
518	C₄×D₄	—	2	2	no	—
519	C₄×D₄	—	2	2	no	—
520	C₄×D₄	—	2	4	no	—
521	C₄×D₄	D₄×C₂₃	1	4	yes	—
522	C₄×D₄	D₄×C₂₃	1	2	yes	—
523	C₄×D₄	C₂³×C₂₃	1	4	yes	—
524	C₄×D₄	C₂³×C₂₃	1	4	yes	—
525	C₄×D₄	C₂³×C₂₃	1	2	yes	—
526	C₄×D₄	C₂³×C₂₃	1	2	yes	—
527	#117	—	2	2	no	—
528	#117	—	2	4	no	—
529	#117	C₂³×C₂₃	1	2	yes	—
530	#117	C₂³×C₂₃	1	1	yes	characteristic
531	#117	C₂³×C₂₃	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
533	C₂×C₂²⋊C₄	—	2	2	no	—
534	C₂×C₄²	—	2	2	no	—
535	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
536	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
537	#107	C₂³×C₂₃	1	2	yes	—
538	#107	C₂³×C₂₃	1	4	yes	—
539	#106	C₂³×C₂₃	1	2	yes	—
540	#106	C₂³×C₂₃	1	2	yes	—
541	#106	C₂³×C₂₃	1	1	yes	characteristic
542	#106	C₂³×C₂₃	1	1	yes	characteristic
543	#106	C₂³×C₂₃	1	4	yes	—
544	#103	C₂³×C₂₃	1	2	yes	—
545	#103	C₂³×C₂₃	1	2	yes	—
546	#103	C₂³×C₂₃	1	4	yes	—
547	#102	C₂³×C₂₃	1	4	yes	—
548	#102	C₂³×C₂₃	1	4	yes	—
549	#102	C₂³×C₂₃	1	2	yes	—
550	#102	C₂³×C₂₃	1	2	yes	—
551	#102	C₂³×C₂₃	1	4	yes	—
552	#102	C₂³×C₂₃	1	4	yes	—
553	#102	C₂³×C₂₃	1	4	yes	—
554	#97	C₂³×C₂₃	1	1	yes	characteristic
555	#97	C₂³×C₂₃	1	1	yes	characteristic
556	#97	C₂³×C₂₃	1	1	yes	characteristic
557	#97	C₂³×C₂₃	1	1	yes	characteristic
558	#97	C₂³×C₂₃	1	2	yes	—
559	#97	C₂³×C₂₃	1	2	yes	—
560	#97	C₂³×C₂₃	1	2	yes	—
561	C₄×C₈	C₂³×C₂₃	1	2	yes	—
562	C₄×C₈	C₂³×C₂₃	1	2	yes	—
563	C₄×C₈	C₂³×C₂₃	1	2	yes	—
564	C₂₃	#60698	1	1	yes	characteristic, direct product factor, Sylow
565	C₂⁴	—	2	2	no	—
566	#41	—	2	2	no	—
567	#41	—	2	2	no	—
568	#41	—	2	4	no	—
569	#41	—	2	4	no	—
570	#41	—	8	8	no	—
571	C₂×Q₈	—	2	4	no	—
572	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
573	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	2	4	no	—
576	C₂×D₄	—	2	4	no	—
577	C₂×D₄	—	2	4	no	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	2	4	no	—
580	C₂×D₄	—	2	4	no	—
581	C₂×D₄	—	2	4	no	—
582	C₂×D₄	—	2	4	no	—
583	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
584	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
585	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
586	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	2	no	—
589	C₂²×C₄	—	2	2	no	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	4	no	—
593	C₂²×C₄	—	8	4	no	—
594	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
595	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
596	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
598	Q₁₆	—	2	2	no	—
599	SD₁₆	—	2	4	no	—
600	SD₁₆	—	2	8	no	—
601	D₈	—	2	4	no	—
602	D₈	—	2	4	no	—
603	D₈	—	2	2	no	—
604	D₈	—	2	8	no	—
605	M₁₆	—	2	2	no	—
606	M₁₆	—	2	4	no	—
607	M₁₆	—	2	4	no	—
608	M₁₆	#41×C₂₃	1	4	yes	complemented
609	C₂×C₈	—	2	2	no	—
610	C₂×C₈	—	2	4	no	—
611	C₂×C₈	—	2	4	no	—
612	C₂×C₈	#41×C₂₃	1	4	yes	complemented
613	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
614	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
615	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
616	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
617	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
618	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
627	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
628	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
629	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
630	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
643	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
644	C₄²	—	2	2	no	—
645	C₄²	—	2	2	no	—
646	C₄²	—	2	2	no	—
647	C₄²	C₂×D₄×C₂₃	1	2	yes	—
648	C₄²	C₂×D₄×C₂₃	1	4	yes	—
649	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
650	C₄²	C₂⁴×C₂₃	1	2	yes	—
651	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
652	C₂³	—	2	4	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	4	4	no	—
655	C₂³	—	8	2	no	—
656	C₂³	—	8	2	no	—
657	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
658	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
659	Q₈	—	2	2	no	—
660	Q₈	—	2	2	no	—
661	Q₈	—	2	2	no	—
662	Q₈	—	8	4	no	—
663	D₄	—	2	4	no	—
664	D₄	—	2	4	no	—
665	D₄	—	2	2	no	—
666	D₄	—	2	4	no	—
667	D₄	—	2	2	no	—
668	D₄	—	2	2	no	—
669	D₄	—	4	4	no	—
670	D₄	—	4	4	no	—
671	D₄	—	8	4	no	—
672	D₄	—	8	4	no	—
673	D₄	—	8	4	no	—
674	D₄	—	8	4	no	—
675	D₄	—	8	4	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	4	no	—
682	C₂×C₄	—	4	2	no	—
683	C₂×C₄	—	4	4	no	—
684	C₂×C₄	—	4	8	no	—
685	C₂×C₄	—	4	4	no	—
686	C₂×C₄	—	4	4	no	—
687	C₂×C₄	—	8	4	no	—
688	C₂×C₄	—	8	2	no	—
689	C₂×C₄	—	8	2	no	—
690	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
691	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
692	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
693	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
694	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
695	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
696	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
697	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
698	C₈	—	2	1	no	—
699	C₈	—	2	1	no	—
700	C₈	—	2	2	no	—
701	C₈	C₂×#41×C₂₃	1	2	yes	—
702	C₈	C₂×#41×C₂₃	1	4	yes	—
703	C₈	C₂×#41×C₂₃	1	2	yes	—
704	C₂²	—	2	2	no	—
705	C₂²	—	2	2	no	—
706	C₂²	—	2	4	no	—
707	C₂²	—	4	2	no	—
708	C₂²	—	4	4	no	—
709	C₂²	—	4	4	no	—
710	C₂²	—	4	2	no	—
711	C₂²	—	4	2	no	—
712	C₂²	—	4	4	no	—
713	C₂²	—	8	8	no	—
714	C₂²	C₂₃×#532	1	2	yes	—
715	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
716	C₄	—	2	2	no	—
717	C₄	—	2	2	no	—
718	C₄	—	2	2	no	—
719	C₄	—	2	4	no	—
720	C₄	—	4	2	no	—
721	C₄	—	4	4	no	—
722	C₄	—	4	2	no	—
723	C₄	—	4	2	no	—
724	C₄	C₂₃×#532	1	2	yes	—
725	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
726	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
727	C₂	—	2	2	no	—
728	C₂	—	4	2	no	—
729	C₂	—	8	4	no	—
730	C₂	—	8	2	no	—
731	C₂	C₂×C₂₃×#532	1	1	yes	characteristic
732	C₂	C₂₃×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3460	C₂	semidirect
2. C₂₃×#3184	C₂	semidirect
3. C₂₃×#3183	C₂	semidirect
4. C₂₃×#3180	C₂	semidirect
5. C₂₃×#3179	C₂	semidirect
6. C₂₃×#3176	C₂	semidirect
7. C₂₃×#3173	C₂	semidirect
8. C₂₃×#3163	C₂	semidirect
9. C₂₃×#3155	C₂	semidirect
10. C₂₃×#3136	C₂	semidirect
11. C₂₃×#3062	C₂	semidirect
12. C₂₃×#3060	C₂	semidirect
13. C₂₃×#3058	C₂	semidirect
14. C₄×C₂₃×AGL(1,ℤ/8)	C₂	semidirect
15. C₂₃×#2943	C₂	semidirect
16. C₂×C₂₃×#442	C₂	semidirect
17. C₂₃×#2875	C₂	semidirect
25. C₂₃×#542	C₂²	semidirect
27. C₂₃×#540	C₂²	semidirect
33. C₂₃×#532	C₂²	semidirect
35. C₂₃×#529	C₂²	semidirect
40. C₂₃×#501	C₂²	semidirect
41. C₂₃×#499	C₂²	semidirect
42. C₂₃×#498	C₂²	semidirect
46. C₂₃×#490	C₂²	semidirect
47. C₂₃×#489	C₂²	semidirect
48. C₂₃×#488	C₂²	semidirect
49. C₂₃×#486	C₂²	semidirect
50. C₂₃×#470	C₂²	semidirect
53. C₂₃×#469	C₂²	semidirect
54. C₂₃×#469	C₂²	semidirect
55. C₂₃×#468	C₂²	semidirect
57. C₂₃×#466	C₂²	semidirect
58. C₂₃×#465	C₂²	semidirect
59. C₂₃×#465	C₂²	semidirect
64. C₂₃×#442	C₂²	semidirect
65. C₂₃×#442	C₂²	semidirect
66. C₂₃×#442	C₂²	semidirect
67. C₂₃×#441	C₂²	semidirect
68. C₂₃×#441	C₂²	semidirect
69. C₂₃×#440	C₂²	semidirect
70. C₂₃×#440	C₂²	semidirect
71. C₂₃×#440	C₂²	semidirect
72. C₄×SD₁₆×C₂₃	C₂²	semidirect
73. C₄×D₈×C₂₃	C₂²	semidirect
83. C₂₃×#405	C₂²	semidirect
84. C₂₃×#405	C₂²	semidirect
86. C₄×M₁₆×C₂₃	C₂²	semidirect
88. C₂×C₂₃×#97	C₂²	semidirect
241. M₁₆×C₂₃	#41	semidirect
245. C₂×C₈×C₂₃	#41	semidirect
285. #60698	C₂₃	direct (N × H)
338. #3460	C₂×C₂₃	semidirect
339. #3184	C₂×C₂₃	semidirect
340. #3183	C₂×C₂₃	semidirect
341. #3180	C₂×C₂₃	semidirect
342. #3179	C₂×C₂₃	semidirect
343. #3176	C₂×C₂₃	semidirect
344. #3173	C₂×C₂₃	semidirect
345. #3163	C₂×C₂₃	semidirect
346. #3155	C₂×C₂₃	semidirect
347. #3136	C₂×C₂₃	semidirect
348. #3062	C₂×C₂₃	semidirect
349. #3060	C₂×C₂₃	semidirect
350. #3058	C₂×C₂₃	semidirect
351. C₄×AGL(1,ℤ/8)	C₂×C₂₃	semidirect
352. #2943	C₂×C₂₃	semidirect
353. C₂×#442	C₂×C₂₃	semidirect
354. #2875	C₂×C₂₃	semidirect
385. #542	C₂²×C₂₃	semidirect
387. #540	C₂²×C₂₃	semidirect
393. #532	C₂²×C₂₃	semidirect
395. #529	C₂²×C₂₃	semidirect
400. #501	C₂²×C₂₃	semidirect
401. #499	C₂²×C₂₃	semidirect
402. #498	C₂²×C₂₃	semidirect
406. #490	C₂²×C₂₃	semidirect
407. #489	C₂²×C₂₃	semidirect
408. #488	C₂²×C₂₃	semidirect
409. #486	C₂²×C₂₃	semidirect
410. #470	C₂²×C₂₃	semidirect
413. #469	C₂²×C₂₃	semidirect
414. #469	C₂²×C₂₃	semidirect
415. #468	C₂²×C₂₃	semidirect
417. #466	C₂²×C₂₃	semidirect
418. #465	C₂²×C₂₃	semidirect
419. #465	C₂²×C₂₃	semidirect
424. #442	C₂²×C₂₃	semidirect
425. #442	C₂²×C₂₃	semidirect
426. #442	C₂²×C₂₃	semidirect
427. #441	C₂²×C₂₃	semidirect
428. #441	C₂²×C₂₃	semidirect
429. #440	C₂²×C₂₃	semidirect
430. #440	C₂²×C₂₃	semidirect
431. #440	C₂²×C₂₃	semidirect
432. C₄×SD₁₆	C₂²×C₂₃	semidirect
433. C₄×D₈	C₂²×C₂₃	semidirect
443. #405	C₂²×C₂₃	semidirect
444. #405	C₂²×C₂₃	semidirect
446. C₄×M₁₆	C₂²×C₂₃	semidirect
448. C₂×#97	C₂²×C₂₃	semidirect
564. C₂₃	#60698	direct (N × H)
608. M₁₆	#41×C₂₃	semidirect
612. 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
C₂₃×#3460	2
C₂₃×#3184	2
C₂₃×#3183	2
C₂₃×#3180	2
C₂₃×#3179	2
C₂₃×#3176	2
C₂₃×#3173	2
C₂₃×#3163	2
C₂₃×#3155	2
C₂₃×#3136	2
C₂₃×#3062	2
C₂₃×#3060	2
C₂₃×#3058	2
C₄×C₂₃×AGL(1,ℤ/8)	2
C₂₃×#2943	2
C₂×C₂₃×#442	2
C₂₃×#2875	2
#60698	23

Subgroups — C23×#60698 #19208324

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60698 #19208324