Subgroups — C₂₃×#61049 #19208675

Order 5888.

3074 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#576	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3484	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3280	C₂	1	4	yes	maximal, complemented
5	D₄×D₈×C₂₃	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3264	C₂	1	8	yes	maximal, complemented
7	C₂₃×#3155	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3058	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3050	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3041	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3008	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3003	C₂	1	2	yes	maximal, complemented
13	C₂₃×#2948	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#2929	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	2	yes	complemented
16	C₂³×D₄×C₂₃	C₂²	1	2	yes	complemented
17	C₂₃×#576	—	2	8	no	—
18	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
19	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
20	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
21	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₂₃×#135	C₂²	1	2	yes	complemented
23	C₂²×D₈×C₂₃	—	2	8	no	—
24	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
25	C₂²×D₈×C₂₃	C₂²	1	2	yes	complemented
26	C₂²×D₈×C₂₃	C₂²	1	4	yes	complemented
27	C₂²×D₈×C₂₃	C₂²	1	4	yes	complemented
28	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
29	C₂²×D₈×C₂₃	C₂²	1	2	yes	complemented
30	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic, complemented
31	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
32	C₂₃×#546	—	2	4	no	—
33	C₂₃×#546	C₂²	1	8	yes	complemented
34	D₄²×C₂₃	—	2	4	no	—
35	D₄²×C₂₃	C₂²	1	8	yes	complemented
36	C₂₃×#535	C₂²	1	2	yes	complemented
37	C₂₃×#535	C₂²	1	2	yes	complemented
38	C₂₃×#534	—	2	4	no	—
39	C₂₃×#525	C₂²	1	1	yes	characteristic
40	C₂₃×#525	C₂²	1	2	yes	complemented
41	C₂×C₂₃×#120	—	2	4	no	—
42	C₂₃×#518	C₂²	1	2	yes	complemented
43	C₂₃×#496	C₂²	1	4	yes	complemented
44	C₂₃×#495	C₂²	1	2	yes	complemented
45	C₂₃×#493	C₂²	1	2	yes	complemented
46	C₂₃×#469	C₂²	1	4	yes	complemented
47	C₂₃×#467	C₂²	1	2	yes	complemented
48	C₂₃×#466	C₂²	1	2	yes	complemented
49	C₂₃×#466	C₂²	1	4	yes	complemented
50	C₂₃×#465	C₂²	1	4	yes	complemented
51	C₂₃×#463	C₂²	1	8	yes	complemented
52	C₂₃×#459	C₂²	1	8	yes	complemented
53	C₂₃×#450	C₂²	1	8	yes	complemented
54	C₂₃×#449	C₂²	1	8	yes	complemented
55	C₂₃×#447	C₂²	1	8	yes	complemented
56	C₂₃×#447	C₂²	1	8	yes	complemented
57	C₂₃×#442	C₂²	1	4	yes	complemented
58	C₄×D₈×C₂₃	C₂²	1	4	yes	complemented
59	C₂₃×#435	C₂²	1	4	yes	complemented
60	C₈×D₄×C₂₃	C₂²	1	4	yes	complemented
61	C₂₃×#427	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#424	C₂²	1	1	yes	characteristic, complemented
63	C₂₃×#418	C₂²	1	2	yes	complemented
64	C₂₃×#418	C₂²	1	2	yes	complemented
65	C₂₃×#416	C₂²	1	2	yes	complemented
66	C₂₃×#408	C₂²	1	1	yes	characteristic, complemented
67	C₂₃×#407	C₂²	1	1	yes	characteristic, complemented
68	C₂₃×#405	C₂²	1	1	yes	characteristic, complemented
69	C₂⁵×C₂₃	—	2	2	no	—
70	C₂₃×H(5,𝔽₂)	—	2	8	no	—
71	C₂₃×H(5,𝔽₂)	—	4	4	no	—
72	C₂×#41×C₂₃	—	2	2	no	—
73	C₂×#41×C₂₃	C₂³	1	2	yes	—
74	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
75	C₂×#41×C₂₃	C₂³	1	4	yes	complemented
76	C₂²×D₄×C₂₃	—	2	8	no	—
77	C₂²×D₄×C₂₃	—	2	4	no	—
78	C₂²×D₄×C₂₃	—	2	2	no	—
79	C₂²×D₄×C₂₃	—	2	8	no	—
80	C₂²×D₄×C₂₃	—	2	2	no	—
81	C₂²×D₄×C₂₃	—	2	4	no	—
82	C₂²×D₄×C₂₃	—	4	4	no	—
83	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
84	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
85	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
86	C₂²×D₄×C₂₃	C₂³	1	4	yes	complemented
87	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
88	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
89	C₂₃×AGL(1,ℤ/8)	—	2	16	no	—
90	C₂₃×AGL(1,ℤ/8)	—	4	4	no	—
91	C₂₃×#135	—	2	8	no	—
92	C₂₃×#135	—	2	4	no	—
93	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic, complemented
94	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	complemented
95	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	complemented
96	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	complemented
97	C₂×D₈×C₂₃	—	2	8	no	—
98	C₂×D₈×C₂₃	—	2	16	no	—
99	C₂×D₈×C₂₃	—	2	16	no	—
100	C₂×D₈×C₂₃	—	2	8	no	—
101	C₂×D₈×C₂₃	—	2	4	no	—
102	C₂×D₈×C₂₃	D₄	1	8	yes	complemented
103	C₂×D₈×C₂₃	C₂³	1	8	yes	—
104	C₂×D₈×C₂₃	C₂³	1	2	yes	—
105	C₂×D₈×C₂₃	C₂³	1	2	yes	—
106	C₂×D₈×C₂₃	C₂³	1	2	yes	—
107	C₂×D₈×C₂₃	C₂³	1	2	yes	—
108	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic, complemented
109	C₂×D₈×C₂₃	C₂³	1	4	yes	complemented
110	C₂×D₈×C₂₃	C₂³	1	4	yes	complemented
111	C₂₃×#131	—	2	4	no	—
112	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
113	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
114	C₂×M₁₆×C₂₃	C₂³	1	2	yes	complemented
115	C₂²×C₈×C₂₃	—	2	4	no	—
116	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
117	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
118	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
119	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₂₃	C₂³	1	2	yes	complemented
121	C₂₃×#127	—	2	2	no	—
122	C₂₃×#127	C₂³	1	4	yes	complemented
123	C₂₃×#124	—	2	2	no	—
124	C₂₃×#124	C₂³	1	4	yes	complemented
125	C₂₃×#123	—	2	2	no	—
126	C₂₃×#123	—	2	8	no	—
127	C₂₃×#123	D₄	1	2	yes	—
128	C₂₃×C₂²⋊Q₈	D₄	1	2	yes	—
129	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
130	C₂₃×#121	—	2	8	no	—
131	C₂₃×#121	—	2	4	no	—
132	C₂₃×#121	—	2	8	no	—
133	C₂₃×#121	D₄	1	2	yes	—
134	C₂₃×#121	C₂³	1	4	yes	—
135	C₂₃×#121	C₂³	1	8	yes	complemented
136	C₂₃×#120	—	2	2	no	—
137	C₂₃×#120	—	2	4	no	—
138	C₂₃×#120	—	2	8	no	—
139	C₂₃×#120	—	2	4	no	—
140	C₂₃×#120	—	2	8	no	—
141	C₂₃×#120	—	2	8	no	—
142	C₂₃×#120	D₄	1	2	yes	—
143	C₄×D₄×C₂₃	—	2	4	no	—
144	C₄×D₄×C₂₃	—	2	4	no	—
145	C₄×D₄×C₂₃	C₂³	1	4	yes	—
146	C₄×D₄×C₂₃	C₂³	1	8	yes	complemented
147	C₂₃×#117	C₂³	1	2	yes	—
148	C₂₃×#117	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
150	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
151	C₂₃×#107	C₂³	1	2	yes	complemented
152	C₂₃×#106	C₂³	1	2	yes	complemented
153	C₂₃×C₄⋊C₈	C₂³	1	4	yes	complemented
154	C₂₃×#103	C₂³	1	4	yes	complemented
155	C₂₃×#102	C₂³	1	4	yes	complemented
156	C₂₃×#102	C₂³	1	8	yes	complemented
157	C₂₃×#102	C₂³	1	8	yes	complemented
158	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
159	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	complemented
160	C₂₃×#97	C₂³	1	2	yes	complemented
161	C₄×C₈×C₂₃	C₂³	1	2	yes	complemented
162	C₂⁴×C₂₃	—	2	2	no	—
163	C₂⁴×C₂₃	—	2	8	no	—
164	C₂⁴×C₂₃	—	2	2	no	—
165	C₂⁴×C₂₃	—	2	4	no	—
166	C₂⁴×C₂₃	—	4	8	no	—
167	C₂⁴×C₂₃	—	8	8	no	—
168	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
169	#41×C₂₃	—	2	2	no	—
170	#41×C₂₃	—	2	2	no	—
171	#41×C₂₃	—	2	8	no	—
172	#41×C₂₃	—	2	4	no	—
173	#41×C₂₃	—	2	4	no	—
174	#41×C₂₃	—	4	4	no	—
175	#41×C₂₃	—	4	8	no	—
176	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
177	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
178	C₂×D₄×C₂₃	—	2	16	no	—
179	C₂×D₄×C₂₃	—	2	8	no	—
180	C₂×D₄×C₂₃	—	2	4	no	—
181	C₂×D₄×C₂₃	—	2	2	no	—
182	C₂×D₄×C₂₃	—	2	4	no	—
183	C₂×D₄×C₂₃	—	2	8	no	—
184	C₂×D₄×C₂₃	—	2	2	no	—
185	C₂×D₄×C₂₃	—	2	4	no	—
186	C₂×D₄×C₂₃	—	2	4	no	—
187	C₂×D₄×C₂₃	—	2	8	no	—
188	C₂×D₄×C₂₃	—	2	2	no	—
189	C₂×D₄×C₂₃	—	2	8	no	—
190	C₂×D₄×C₂₃	—	2	4	no	—
191	C₂×D₄×C₂₃	—	2	4	no	—
192	C₂×D₄×C₂₃	—	4	8	no	—
193	C₂×D₄×C₂₃	—	4	4	no	—
194	C₂×D₄×C₂₃	—	4	16	no	—
195	C₂×D₄×C₂₃	—	4	8	no	—
196	C₂×D₄×C₂₃	—	4	8	no	—
197	C₂×D₄×C₂₃	—	4	16	no	—
198	C₂×D₄×C₂₃	—	8	16	no	—
199	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
200	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
201	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
202	C₂×D₄×C₂₃	C₂×D₄	1	8	yes	complemented
203	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
204	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
205	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
206	C₂²×C₄×C₂₃	—	2	2	no	—
207	C₂²×C₄×C₂₃	—	2	2	no	—
208	C₂²×C₄×C₂₃	—	2	4	no	—
209	C₂²×C₄×C₂₃	—	2	2	no	—
210	C₂²×C₄×C₂₃	—	2	8	no	—
211	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
212	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
216	Q₁₆×C₂₃	—	2	2	no	—
217	SD₁₆×C₂₃	—	2	8	no	—
218	SD₁₆×C₂₃	—	2	4	no	—
219	SD₁₆×C₂₃	—	4	4	no	—
220	D₈×C₂₃	—	2	16	no	—
221	D₈×C₂₃	—	2	8	no	—
222	D₈×C₂₃	—	2	4	no	—
223	D₈×C₂₃	—	2	4	no	—
224	D₈×C₂₃	—	2	2	no	—
225	D₈×C₂₃	—	4	4	no	—
226	D₈×C₂₃	C₂×D₄	1	8	yes	complemented
227	D₈×C₂₃	C₂×D₄	1	8	yes	complemented
228	M₁₆×C₂₃	—	2	2	no	—
229	M₁₆×C₂₃	—	2	2	no	—
230	M₁₆×C₂₃	—	2	4	no	—
231	C₂×C₈×C₂₃	—	2	2	no	—
232	C₂×C₈×C₂₃	—	2	4	no	—
233	C₂×C₈×C₂₃	—	2	4	no	—
234	C₂×C₈×C₂₃	—	2	4	no	—
235	C₂×C₈×C₂₃	C₂×D₄	1	4	yes	complemented
236	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
237	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
238	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
239	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
240	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
241	C₄⋊C₄×C₂₃	—	2	4	no	—
242	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
243	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
244	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
245	C₂²⋊C₄×C₂₃	—	2	2	no	—
246	C₂²⋊C₄×C₂₃	—	2	4	no	—
247	C₂²⋊C₄×C₂₃	—	2	8	no	—
248	C₂²⋊C₄×C₂₃	—	2	8	no	—
249	C₂²⋊C₄×C₂₃	—	2	8	no	—
250	C₂²⋊C₄×C₂₃	—	2	4	no	—
251	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
252	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
253	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
254	C₄²×C₂₃	—	2	2	no	—
255	C₄²×C₂₃	C₂⁴	1	2	yes	—
256	#61049	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
257	C₂³×C₂₃	—	2	2	no	—
258	C₂³×C₂₃	—	2	4	no	—
259	C₂³×C₂₃	—	2	4	no	—
260	C₂³×C₂₃	—	2	8	no	—
261	C₂³×C₂₃	—	2	4	no	—
262	C₂³×C₂₃	—	2	2	no	—
263	C₂³×C₂₃	—	4	16	no	—
264	C₂³×C₂₃	—	4	8	no	—
265	C₂³×C₂₃	—	4	4	no	—
266	C₂³×C₂₃	—	4	16	no	—
267	C₂³×C₂₃	—	8	4	no	—
268	C₂³×C₂₃	—	8	8	no	—
269	C₂³×C₂₃	—	8	4	no	—
270	C₂³×C₂₃	—	8	8	no	—
271	C₂³×C₂₃	—	8	32	no	—
272	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
273	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
274	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
275	Q₈×C₂₃	—	2	2	no	—
276	Q₈×C₂₃	—	2	2	no	—
277	Q₈×C₂₃	—	2	2	no	—
278	D₄×C₂₃	—	2	4	no	—
279	D₄×C₂₃	—	2	8	no	—
280	D₄×C₂₃	—	2	8	no	—
281	D₄×C₂₃	—	2	2	no	—
282	D₄×C₂₃	—	2	4	no	—
283	D₄×C₂₃	—	2	2	no	—
284	D₄×C₂₃	—	2	4	no	—
285	D₄×C₂₃	—	2	2	no	—
286	D₄×C₂₃	—	2	4	no	—
287	D₄×C₂₃	—	4	16	no	—
288	D₄×C₂₃	—	4	8	no	—
289	D₄×C₂₃	—	4	8	no	—
290	D₄×C₂₃	—	4	4	no	—
291	D₄×C₂₃	—	4	8	no	—
292	D₄×C₂₃	—	4	4	no	—
293	D₄×C₂₃	—	8	8	no	—
294	D₄×C₂₃	—	8	8	no	—
295	D₄×C₂₃	C₂²×D₄	1	8	yes	—
296	C₂×C₄×C₂₃	—	2	2	no	—
297	C₂×C₄×C₂₃	—	2	4	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	4	no	—
303	C₂×C₄×C₂₃	—	2	2	no	—
304	C₂×C₄×C₂₃	—	4	8	no	—
305	C₂×C₄×C₂₃	—	4	4	no	—
306	C₂×C₄×C₂₃	—	8	8	no	—
307	C₂×C₄×C₂₃	C₂²×D₄	1	4	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	1	yes	characteristic
311	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
312	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
313	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
314	C₈×C₂₃	—	2	2	no	—
315	C₈×C₂₃	—	2	2	no	—
316	C₈×C₂₃	—	2	2	no	—
317	C₈×C₂₃	C₂²×D₄	1	2	yes	—
318	C₈×C₂₃	C₂²×D₄	1	2	yes	—
319	C₂×#576	C₂×C₂₃	1	1	yes	characteristic, complemented
320	C₂³×D₈	C₂×C₂₃	1	1	yes	characteristic, complemented
321	#3484	C₂×C₂₃	1	2	yes	complemented
322	#3280	C₂×C₂₃	1	4	yes	complemented
323	D₄×D₈	C₂×C₂₃	1	4	yes	complemented
324	#3264	C₂×C₂₃	1	8	yes	complemented
325	#3155	C₂×C₂₃	1	1	yes	characteristic, complemented
326	#3058	C₂×C₂₃	1	1	yes	characteristic, complemented
327	#3050	C₂×C₂₃	1	1	yes	characteristic, complemented
328	#3041	C₂×C₂₃	1	2	yes	complemented
329	#3008	C₂×C₂₃	1	2	yes	complemented
330	#3003	C₂×C₂₃	1	2	yes	complemented
331	#2948	C₂×C₂₃	1	1	yes	characteristic, complemented
332	#2929	C₂×C₂₃	1	1	yes	characteristic, complemented
333	C₂²×C₂₃	—	2	8	no	—
334	C₂²×C₂₃	—	2	2	no	—
335	C₂²×C₂₃	—	2	2	no	—
336	C₂²×C₂₃	—	2	2	no	—
337	C₂²×C₂₃	—	2	2	no	—
338	C₂²×C₂₃	—	2	8	no	—
339	C₂²×C₂₃	—	2	4	no	—
340	C₂²×C₂₃	—	4	8	no	—
341	C₂²×C₂₃	—	4	2	no	—
342	C₂²×C₂₃	—	4	4	no	—
343	C₂²×C₂₃	—	4	4	no	—
344	C₂²×C₂₃	—	4	8	no	—
345	C₂²×C₂₃	—	8	8	no	—
346	C₂²×C₂₃	—	8	32	no	—
347	C₂²×C₂₃	—	8	8	no	—
348	C₂²×C₂₃	—	16	8	no	—
349	C₂²×C₂₃	D₄²	1	2	yes	—
350	C₂²×C₂₃	#576	1	4	yes	complemented
351	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
352	C₄×C₂₃	—	2	2	no	—
353	C₄×C₂₃	—	2	2	no	—
354	C₄×C₂₃	—	2	4	no	—
355	C₄×C₂₃	—	4	2	no	—
356	C₄×C₂₃	—	4	4	no	—
357	C₄×C₂₃	D₄²	1	2	yes	—
358	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
359	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
360	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	2	yes	complemented
361	C₂³×D₄	C₂²×C₂₃	1	2	yes	complemented
362	#576	—	2	8	no	—
363	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
364	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
365	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	4	yes	complemented
366	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic, complemented
367	C₂×#135	C₂²×C₂₃	1	2	yes	complemented
368	C₂²×D₈	—	2	8	no	—
369	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
370	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
371	C₂²×D₈	C₂²×C₂₃	1	2	yes	complemented
372	C₂²×D₈	C₂²×C₂₃	1	4	yes	complemented
373	C₂²×D₈	C₂²×C₂₃	1	4	yes	complemented
374	C₂²×D₈	C₂²×C₂₃	1	2	yes	complemented
375	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic, complemented
376	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
377	#546	—	2	4	no	—
378	#546	C₂²×C₂₃	1	8	yes	complemented
379	D₄²	—	2	4	no	—
380	D₄²	C₂²×C₂₃	1	8	yes	complemented
381	#535	C₂²×C₂₃	1	2	yes	complemented
382	#535	C₂²×C₂₃	1	2	yes	complemented
383	#534	—	2	4	no	—
384	#525	C₂²×C₂₃	1	1	yes	characteristic
385	#525	C₂²×C₂₃	1	2	yes	complemented
386	C₂×#120	—	2	4	no	—
387	#518	C₂²×C₂₃	1	2	yes	complemented
388	#496	C₂²×C₂₃	1	4	yes	complemented
389	#495	C₂²×C₂₃	1	2	yes	complemented
390	#493	C₂²×C₂₃	1	2	yes	complemented
391	#469	C₂²×C₂₃	1	4	yes	complemented
392	#467	C₂²×C₂₃	1	2	yes	complemented
393	#466	C₂²×C₂₃	1	2	yes	complemented
394	#466	C₂²×C₂₃	1	4	yes	complemented
395	#465	C₂²×C₂₃	1	4	yes	complemented
396	#463	C₂²×C₂₃	1	8	yes	complemented
397	#459	C₂²×C₂₃	1	8	yes	complemented
398	#450	C₂²×C₂₃	1	8	yes	complemented
399	#449	C₂²×C₂₃	1	8	yes	complemented
400	#447	C₂²×C₂₃	1	8	yes	complemented
401	#447	C₂²×C₂₃	1	8	yes	complemented
402	#442	C₂²×C₂₃	1	4	yes	complemented
403	C₄×D₈	C₂²×C₂₃	1	4	yes	complemented
404	#435	C₂²×C₂₃	1	4	yes	complemented
405	C₈×D₄	C₂²×C₂₃	1	4	yes	complemented
406	#427	C₂²×C₂₃	1	1	yes	characteristic, complemented
407	#424	C₂²×C₂₃	1	1	yes	characteristic, complemented
408	#418	C₂²×C₂₃	1	2	yes	complemented
409	#418	C₂²×C₂₃	1	2	yes	complemented
410	#416	C₂²×C₂₃	1	2	yes	complemented
411	#408	C₂²×C₂₃	1	1	yes	characteristic, complemented
412	#407	C₂²×C₂₃	1	1	yes	characteristic, complemented
413	#405	C₂²×C₂₃	1	1	yes	characteristic, complemented
414	C₂×C₂₃	—	2	2	no	—
415	C₂×C₂₃	—	2	4	no	—
416	C₂×C₂₃	—	4	2	no	—
417	C₂×C₂₃	—	4	8	no	—
418	C₂×C₂₃	—	8	4	no	—
419	C₂×C₂₃	—	8	2	no	—
420	C₂×C₂₃	C₂×D₄²	1	1	yes	characteristic
421	C₂×C₂₃	C₂×#576	1	2	yes	—
422	C₂⁵	—	2	2	no	—
423	H(5,𝔽₂)	—	2	8	no	—
424	H(5,𝔽₂)	—	4	4	no	—
425	C₂×#41	—	2	2	no	—
426	C₂×#41	C₂³×C₂₃	1	2	yes	—
427	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
428	C₂×#41	C₂³×C₂₃	1	4	yes	complemented
429	C₂²×D₄	—	2	8	no	—
430	C₂²×D₄	—	2	4	no	—
431	C₂²×D₄	—	2	2	no	—
432	C₂²×D₄	—	2	8	no	—
433	C₂²×D₄	—	2	2	no	—
434	C₂²×D₄	—	2	4	no	—
435	C₂²×D₄	—	4	4	no	—
436	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
437	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
438	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
439	C₂²×D₄	C₂³×C₂₃	1	4	yes	complemented
440	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
441	AGL(1,ℤ/8)	—	2	8	no	—
442	AGL(1,ℤ/8)	—	2	16	no	—
443	AGL(1,ℤ/8)	—	4	4	no	—
444	#135	—	2	8	no	—
445	#135	—	2	4	no	—
446	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic, complemented
447	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	complemented
448	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	complemented
449	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	complemented
450	C₂×D₈	—	2	8	no	—
451	C₂×D₈	—	2	16	no	—
452	C₂×D₈	—	2	16	no	—
453	C₂×D₈	—	2	8	no	—
454	C₂×D₈	—	2	4	no	—
455	C₂×D₈	D₄×C₂₃	1	8	yes	complemented
456	C₂×D₈	C₂³×C₂₃	1	8	yes	—
457	C₂×D₈	C₂³×C₂₃	1	2	yes	—
458	C₂×D₈	C₂³×C₂₃	1	2	yes	—
459	C₂×D₈	C₂³×C₂₃	1	2	yes	—
460	C₂×D₈	C₂³×C₂₃	1	2	yes	—
461	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic, complemented
462	C₂×D₈	C₂³×C₂₃	1	4	yes	complemented
463	C₂×D₈	C₂³×C₂₃	1	4	yes	complemented
464	#131	—	2	4	no	—
465	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
466	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
467	C₂×M₁₆	C₂³×C₂₃	1	2	yes	complemented
468	C₂²×C₈	—	2	4	no	—
469	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
470	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
471	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
472	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
473	C₂²×C₈	C₂³×C₂₃	1	2	yes	complemented
474	#127	—	2	2	no	—
475	#127	C₂³×C₂₃	1	4	yes	complemented
476	#124	—	2	2	no	—
477	#124	C₂³×C₂₃	1	4	yes	complemented
478	#123	—	2	2	no	—
479	#123	—	2	8	no	—
480	#123	D₄×C₂₃	1	2	yes	—
481	C₂²⋊Q₈	D₄×C₂₃	1	2	yes	—
482	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
483	#121	—	2	8	no	—
484	#121	—	2	4	no	—
485	#121	—	2	8	no	—
486	#121	D₄×C₂₃	1	2	yes	—
487	#121	C₂³×C₂₃	1	4	yes	—
488	#121	C₂³×C₂₃	1	8	yes	complemented
489	#120	—	2	2	no	—
490	#120	—	2	4	no	—
491	#120	—	2	8	no	—
492	#120	—	2	4	no	—
493	#120	—	2	8	no	—
494	#120	—	2	8	no	—
495	#120	D₄×C₂₃	1	2	yes	—
496	C₄×D₄	—	2	4	no	—
497	C₄×D₄	—	2	4	no	—
498	C₄×D₄	C₂³×C₂₃	1	4	yes	—
499	C₄×D₄	C₂³×C₂₃	1	8	yes	complemented
500	#117	C₂³×C₂₃	1	2	yes	—
501	#117	C₂³×C₂₃	1	1	yes	characteristic
502	C₂×C₂²⋊C₄	—	2	4	no	—
503	C₂×C₂²⋊C₄	—	2	8	no	—
504	#107	C₂³×C₂₃	1	2	yes	complemented
505	#106	C₂³×C₂₃	1	2	yes	complemented
506	C₄⋊C₈	C₂³×C₂₃	1	4	yes	complemented
507	#103	C₂³×C₂₃	1	4	yes	complemented
508	#102	C₂³×C₂₃	1	4	yes	complemented
509	#102	C₂³×C₂₃	1	8	yes	complemented
510	#102	C₂³×C₂₃	1	8	yes	complemented
511	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
512	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	complemented
513	#97	C₂³×C₂₃	1	2	yes	complemented
514	C₄×C₈	C₂³×C₂₃	1	2	yes	complemented
515	C₂₃	#61049	1	1	yes	characteristic, direct product factor, Sylow
516	C₂⁴	—	2	2	no	—
517	C₂⁴	—	2	8	no	—
518	C₂⁴	—	2	2	no	—
519	C₂⁴	—	2	4	no	—
520	C₂⁴	—	4	8	no	—
521	C₂⁴	—	8	8	no	—
522	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
523	#41	—	2	2	no	—
524	#41	—	2	2	no	—
525	#41	—	2	8	no	—
526	#41	—	2	4	no	—
527	#41	—	2	4	no	—
528	#41	—	4	4	no	—
529	#41	—	4	8	no	—
530	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
531	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
532	C₂×D₄	—	2	16	no	—
533	C₂×D₄	—	2	8	no	—
534	C₂×D₄	—	2	4	no	—
535	C₂×D₄	—	2	2	no	—
536	C₂×D₄	—	2	4	no	—
537	C₂×D₄	—	2	8	no	—
538	C₂×D₄	—	2	2	no	—
539	C₂×D₄	—	2	4	no	—
540	C₂×D₄	—	2	4	no	—
541	C₂×D₄	—	2	8	no	—
542	C₂×D₄	—	2	2	no	—
543	C₂×D₄	—	2	8	no	—
544	C₂×D₄	—	2	4	no	—
545	C₂×D₄	—	2	4	no	—
546	C₂×D₄	—	4	8	no	—
547	C₂×D₄	—	4	4	no	—
548	C₂×D₄	—	4	16	no	—
549	C₂×D₄	—	4	8	no	—
550	C₂×D₄	—	4	8	no	—
551	C₂×D₄	—	4	16	no	—
552	C₂×D₄	—	8	16	no	—
553	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
554	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
555	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
556	C₂×D₄	C₂×D₄×C₂₃	1	8	yes	complemented
557	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
558	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
559	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	4	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	8	no	—
565	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
566	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
567	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
568	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
569	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
570	Q₁₆	—	2	2	no	—
571	SD₁₆	—	2	8	no	—
572	SD₁₆	—	2	4	no	—
573	SD₁₆	—	4	4	no	—
574	D₈	—	2	16	no	—
575	D₈	—	2	8	no	—
576	D₈	—	2	4	no	—
577	D₈	—	2	4	no	—
578	D₈	—	2	2	no	—
579	D₈	—	4	4	no	—
580	D₈	C₂×D₄×C₂₃	1	8	yes	complemented
581	D₈	C₂×D₄×C₂₃	1	8	yes	complemented
582	M₁₆	—	2	2	no	—
583	M₁₆	—	2	2	no	—
584	M₁₆	—	2	4	no	—
585	C₂×C₈	—	2	2	no	—
586	C₂×C₈	—	2	4	no	—
587	C₂×C₈	—	2	4	no	—
588	C₂×C₈	—	2	4	no	—
589	C₂×C₈	C₂×D₄×C₂₃	1	4	yes	complemented
590	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
591	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
592	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
593	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
594	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
595	C₄⋊C₄	—	2	4	no	—
596	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
597	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
598	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
599	C₂²⋊C₄	—	2	2	no	—
600	C₂²⋊C₄	—	2	4	no	—
601	C₂²⋊C₄	—	2	8	no	—
602	C₂²⋊C₄	—	2	8	no	—
603	C₂²⋊C₄	—	2	8	no	—
604	C₂²⋊C₄	—	2	4	no	—
605	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
606	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
607	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
608	C₄²	—	2	2	no	—
609	C₄²	C₂⁴×C₂₃	1	2	yes	—
610	C₂³	—	2	4	no	—
611	C₂³	—	2	2	no	—
612	C₂³	—	2	4	no	—
613	C₂³	—	2	8	no	—
614	C₂³	—	2	4	no	—
615	C₂³	—	2	2	no	—
616	C₂³	—	4	16	no	—
617	C₂³	—	4	8	no	—
618	C₂³	—	4	16	no	—
619	C₂³	—	4	4	no	—
620	C₂³	—	8	4	no	—
621	C₂³	—	8	8	no	—
622	C₂³	—	8	4	no	—
623	C₂³	—	8	8	no	—
624	C₂³	—	8	32	no	—
625	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
626	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
627	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
628	Q₈	—	2	2	no	—
629	Q₈	—	2	2	no	—
630	Q₈	—	2	2	no	—
631	D₄	—	2	8	no	—
632	D₄	—	2	4	no	—
633	D₄	—	2	4	no	—
634	D₄	—	2	2	no	—
635	D₄	—	2	4	no	—
636	D₄	—	2	2	no	—
637	D₄	—	2	4	no	—
638	D₄	—	2	8	no	—
639	D₄	—	2	2	no	—
640	D₄	—	4	16	no	—
641	D₄	—	4	8	no	—
642	D₄	—	4	8	no	—
643	D₄	—	4	8	no	—
644	D₄	—	4	4	no	—
645	D₄	—	4	4	no	—
646	D₄	—	8	8	no	—
647	D₄	—	8	8	no	—
648	D₄	C₂²×D₄×C₂₃	1	8	yes	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	4	no	—
655	C₂×C₄	—	2	4	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	4	8	no	—
658	C₂×C₄	—	4	4	no	—
659	C₂×C₄	—	8	8	no	—
660	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
661	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
662	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
663	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
664	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
665	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
666	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
667	C₈	—	2	2	no	—
668	C₈	—	2	2	no	—
669	C₈	—	2	2	no	—
670	C₈	C₂²×D₄×C₂₃	1	2	yes	—
671	C₈	C₂²×D₄×C₂₃	1	2	yes	—
672	C₂²	—	2	8	no	—
673	C₂²	—	2	2	no	—
674	C₂²	—	2	2	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	8	no	—
678	C₂²	—	2	4	no	—
679	C₂²	—	4	8	no	—
680	C₂²	—	4	2	no	—
681	C₂²	—	4	4	no	—
682	C₂²	—	4	4	no	—
683	C₂²	—	4	8	no	—
684	C₂²	—	8	8	no	—
685	C₂²	—	8	32	no	—
686	C₂²	—	8	8	no	—
687	C₂²	—	16	8	no	—
688	C₂²	D₄²×C₂₃	1	2	yes	—
689	C₂²	C₂₃×#576	1	4	yes	complemented
690	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
691	C₄	—	2	2	no	—
692	C₄	—	2	2	no	—
693	C₄	—	2	4	no	—
694	C₄	—	4	2	no	—
695	C₄	—	4	4	no	—
696	C₄	D₄²×C₂₃	1	2	yes	—
697	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
698	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
699	C₂	—	2	4	no	—
700	C₂	—	2	2	no	—
701	C₂	—	4	2	no	—
702	C₂	—	4	8	no	—
703	C₂	—	8	4	no	—
704	C₂	—	8	2	no	—
705	C₂	C₂×D₄²×C₂₃	1	1	yes	characteristic
706	C₂	C₂×C₂₃×#576	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 ◁ C₂₃×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#576	C₂	semidirect
2. C₂³×D₈×C₂₃	C₂	semidirect
3. C₂₃×#3484	C₂	semidirect
4. C₂₃×#3280	C₂	semidirect
5. D₄×D₈×C₂₃	C₂	semidirect
6. C₂₃×#3264	C₂	semidirect
7. C₂₃×#3155	C₂	semidirect
8. C₂₃×#3058	C₂	semidirect
9. C₂₃×#3050	C₂	semidirect
10. C₂₃×#3041	C₂	semidirect
11. C₂₃×#3008	C₂	semidirect
12. C₂₃×#3003	C₂	semidirect
13. C₂₃×#2948	C₂	semidirect
14. C₂₃×#2929	C₂	semidirect
15. C₂×C₂₃×H(5,𝔽₂)	C₂²	semidirect
16. C₂³×D₄×C₂₃	C₂²	semidirect
18. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
19. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
20. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
21. C₂×C₂₃×#135	C₂²	semidirect
22. C₂×C₂₃×#135	C₂²	semidirect
25. C₂²×D₈×C₂₃	C₂²	semidirect
26. C₂²×D₈×C₂₃	C₂²	semidirect
27. C₂²×D₈×C₂₃	C₂²	semidirect
28. C₂²×D₈×C₂₃	C₂²	semidirect
29. C₂²×D₈×C₂₃	C₂²	semidirect
30. C₂×C₂₃×#131	C₂²	semidirect
31. C₂³×C₈×C₂₃	C₂²	semidirect
33. C₂₃×#546	C₂²	semidirect
35. D₄²×C₂₃	C₂²	semidirect
36. C₂₃×#535	C₂²	semidirect
37. C₂₃×#535	C₂²	semidirect
40. C₂₃×#525	C₂²	semidirect
42. C₂₃×#518	C₂²	semidirect
43. C₂₃×#496	C₂²	semidirect
44. C₂₃×#495	C₂²	semidirect
45. C₂₃×#493	C₂²	semidirect
46. C₂₃×#469	C₂²	semidirect
47. C₂₃×#467	C₂²	semidirect
48. C₂₃×#466	C₂²	semidirect
49. C₂₃×#466	C₂²	semidirect
50. C₂₃×#465	C₂²	semidirect
51. C₂₃×#463	C₂²	semidirect
52. C₂₃×#459	C₂²	semidirect
53. C₂₃×#450	C₂²	semidirect
54. C₂₃×#449	C₂²	semidirect
55. C₂₃×#447	C₂²	semidirect
56. C₂₃×#447	C₂²	semidirect
57. C₂₃×#442	C₂²	semidirect
58. C₄×D₈×C₂₃	C₂²	semidirect
59. C₂₃×#435	C₂²	semidirect
60. C₈×D₄×C₂₃	C₂²	semidirect
61. C₂₃×#427	C₂²	semidirect
62. C₂₃×#424	C₂²	semidirect
63. C₂₃×#418	C₂²	semidirect
64. C₂₃×#418	C₂²	semidirect
65. C₂₃×#416	C₂²	semidirect
66. C₂₃×#408	C₂²	semidirect
67. C₂₃×#407	C₂²	semidirect
68. C₂₃×#405	C₂²	semidirect
75. C₂×#41×C₂₃	C₂³	semidirect
86. C₂²×D₄×C₂₃	C₂³	semidirect
93. C₂×Q₁₆×C₂₃	C₂³	semidirect
94. C₂×SD₁₆×C₂₃	C₂³	semidirect
95. C₂×SD₁₆×C₂₃	C₂³	semidirect
96. C₂×SD₁₆×C₂₃	C₂³	semidirect
102. C₂×D₈×C₂₃	D₄	semidirect
108. C₂×D₈×C₂₃	C₂³	semidirect
109. C₂×D₈×C₂₃	C₂³	semidirect
110. C₂×D₈×C₂₃	C₂³	semidirect
114. C₂×M₁₆×C₂₃	C₂³	semidirect
120. C₂²×C₈×C₂₃	C₂³	semidirect
122. C₂₃×#127	C₂³	semidirect
124. C₂₃×#124	C₂³	semidirect
135. C₂₃×#121	C₂³	semidirect
146. C₄×D₄×C₂₃	C₂³	semidirect
151. C₂₃×#107	C₂³	semidirect
152. C₂₃×#106	C₂³	semidirect
153. C₂₃×C₄⋊C₈	C₂³	semidirect
154. C₂₃×#103	C₂³	semidirect
155. C₂₃×#102	C₂³	semidirect
156. C₂₃×#102	C₂³	semidirect
157. C₂₃×#102	C₂³	semidirect
159. C₂₃×C₂²⋊C₈	C₂³	semidirect
160. C₂₃×#97	C₂³	semidirect
161. C₄×C₈×C₂₃	C₂³	semidirect
202. C₂×D₄×C₂₃	C₂×D₄	semidirect
226. D₈×C₂₃	C₂×D₄	semidirect
227. D₈×C₂₃	C₂×D₄	semidirect
235. C₂×C₈×C₂₃	C₂×D₄	semidirect
256. #61049	C₂₃	direct (N × H)
319. C₂×#576	C₂×C₂₃	semidirect
320. C₂³×D₈	C₂×C₂₃	semidirect
321. #3484	C₂×C₂₃	semidirect
322. #3280	C₂×C₂₃	semidirect
323. D₄×D₈	C₂×C₂₃	semidirect
324. #3264	C₂×C₂₃	semidirect
325. #3155	C₂×C₂₃	semidirect
326. #3058	C₂×C₂₃	semidirect
327. #3050	C₂×C₂₃	semidirect
328. #3041	C₂×C₂₃	semidirect
329. #3008	C₂×C₂₃	semidirect
330. #3003	C₂×C₂₃	semidirect
331. #2948	C₂×C₂₃	semidirect
332. #2929	C₂×C₂₃	semidirect
350. C₂²×C₂₃	#576	semidirect
360. C₂×H(5,𝔽₂)	C₂²×C₂₃	semidirect
361. C₂³×D₄	C₂²×C₂₃	semidirect
363. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
364. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
365. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
366. C₂×#135	C₂²×C₂₃	semidirect
367. C₂×#135	C₂²×C₂₃	semidirect
370. C₂²×D₈	C₂²×C₂₃	semidirect
371. C₂²×D₈	C₂²×C₂₃	semidirect
372. C₂²×D₈	C₂²×C₂₃	semidirect
373. C₂²×D₈	C₂²×C₂₃	semidirect
374. C₂²×D₈	C₂²×C₂₃	semidirect
375. C₂×#131	C₂²×C₂₃	semidirect
376. C₂³×C₈	C₂²×C₂₃	semidirect
378. #546	C₂²×C₂₃	semidirect
380. D₄²	C₂²×C₂₃	semidirect
381. #535	C₂²×C₂₃	semidirect
382. #535	C₂²×C₂₃	semidirect
385. #525	C₂²×C₂₃	semidirect
387. #518	C₂²×C₂₃	semidirect
388. #496	C₂²×C₂₃	semidirect
389. #495	C₂²×C₂₃	semidirect
390. #493	C₂²×C₂₃	semidirect
391. #469	C₂²×C₂₃	semidirect
392. #467	C₂²×C₂₃	semidirect
393. #466	C₂²×C₂₃	semidirect
394. #466	C₂²×C₂₃	semidirect
395. #465	C₂²×C₂₃	semidirect
396. #463	C₂²×C₂₃	semidirect
397. #459	C₂²×C₂₃	semidirect
398. #450	C₂²×C₂₃	semidirect
399. #449	C₂²×C₂₃	semidirect
400. #447	C₂²×C₂₃	semidirect
401. #447	C₂²×C₂₃	semidirect
402. #442	C₂²×C₂₃	semidirect
403. C₄×D₈	C₂²×C₂₃	semidirect
404. #435	C₂²×C₂₃	semidirect
405. C₈×D₄	C₂²×C₂₃	semidirect
406. #427	C₂²×C₂₃	semidirect
407. #424	C₂²×C₂₃	semidirect
408. #418	C₂²×C₂₃	semidirect
409. #418	C₂²×C₂₃	semidirect
410. #416	C₂²×C₂₃	semidirect
411. #408	C₂²×C₂₃	semidirect
412. #407	C₂²×C₂₃	semidirect
413. #405	C₂²×C₂₃	semidirect
428. C₂×#41	C₂³×C₂₃	semidirect
439. C₂²×D₄	C₂³×C₂₃	semidirect
446. C₂×Q₁₆	C₂³×C₂₃	semidirect
447. C₂×SD₁₆	C₂³×C₂₃	semidirect
448. C₂×SD₁₆	C₂³×C₂₃	semidirect
449. C₂×SD₁₆	C₂³×C₂₃	semidirect
455. C₂×D₈	D₄×C₂₃	semidirect
461. C₂×D₈	C₂³×C₂₃	semidirect
462. C₂×D₈	C₂³×C₂₃	semidirect
463. C₂×D₈	C₂³×C₂₃	semidirect
467. C₂×M₁₆	C₂³×C₂₃	semidirect
473. C₂²×C₈	C₂³×C₂₃	semidirect
475. #127	C₂³×C₂₃	semidirect
477. #124	C₂³×C₂₃	semidirect
488. #121	C₂³×C₂₃	semidirect
499. C₄×D₄	C₂³×C₂₃	semidirect
504. #107	C₂³×C₂₃	semidirect
505. #106	C₂³×C₂₃	semidirect
506. C₄⋊C₈	C₂³×C₂₃	semidirect
507. #103	C₂³×C₂₃	semidirect
508. #102	C₂³×C₂₃	semidirect
509. #102	C₂³×C₂₃	semidirect
510. #102	C₂³×C₂₃	semidirect
512. C₂²⋊C₈	C₂³×C₂₃	semidirect
513. #97	C₂³×C₂₃	semidirect
514. C₄×C₈	C₂³×C₂₃	semidirect
515. C₂₃	#61049	direct (N × H)
556. C₂×D₄	C₂×D₄×C₂₃	semidirect
580. D₈	C₂×D₄×C₂₃	semidirect
581. D₈	C₂×D₄×C₂₃	semidirect
589. C₂×C₈	C₂×D₄×C₂₃	semidirect
689. C₂²	C₂₃×#576	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#576	2
C₂³×D₈×C₂₃	2
C₂₃×#3484	2
C₂₃×#3280	2
D₄×D₈×C₂₃	2
C₂₃×#3264	2
C₂₃×#3155	2
C₂₃×#3058	2
C₂₃×#3050	2
C₂₃×#3041	2
C₂₃×#3008	2
C₂₃×#3003	2
C₂₃×#2948	2
C₂₃×#2929	2
#61049	23

Subgroups — C23×#61049 #19208675

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61049 #19208675