Subgroups — C₂₃×#25185 #19172811

Order 5888.

1016 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#472	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3041	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#454	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3010	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2946	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2898	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2064	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2051	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2037	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2012	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1977	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1929	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1885	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1883	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1866	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
17	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
18	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
21	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
23	C₂₃×#535	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
25	C₂₃×#520	C₂²	1	1	yes	characteristic
26	C₂₃×#518	C₂²	1	1	yes	characteristic
27	C₂₃×#472	—	2	4	no	—
28	C₂₃×#463	—	2	1	no	—
29	C₂₃×#463	—	2	1	no	—
30	C₂₃×#459	—	2	1	no	—
31	C₂₃×#459	—	2	1	no	—
32	C₂₃×#454	—	2	4	no	—
33	C₂₃×#449	—	2	1	no	—
34	C₂₃×#449	—	2	1	no	—
35	C₂₃×#448	—	2	1	no	—
36	C₂₃×#448	—	2	1	no	—
37	C₂₃×#442	—	2	1	no	—
38	C₂₃×#440	—	2	1	no	—
39	C₄×SD₁₆×C₂₃	—	2	1	no	—
40	C₄×D₈×C₂₃	—	2	1	no	—
41	C₂×C₂₃×#108	C₂²	1	1	yes	characteristic
42	C₂×C₂₃×#108	C₂²	1	1	yes	characteristic
43	C₂₃×#428	C₂²	1	1	yes	characteristic
44	C₂₃×#424	C₂²	1	1	yes	characteristic
45	C₂×C₂₃×#104	C₂²	1	1	yes	characteristic
46	C₂×C₂₃×#104	C₂²	1	1	yes	characteristic
47	C₂₃×#419	—	2	1	no	—
48	C₂₃×#419	C₂²	1	1	yes	characteristic
49	C₂₃×#419	C₂²	1	1	yes	characteristic
50	C₂₃×#418	C₂²	1	1	yes	characteristic
51	C₂₃×#417	—	2	1	no	—
52	C₂₃×#417	C₂²	1	1	yes	characteristic
53	C₂₃×#416	—	2	1	no	—
54	C₂₃×#416	C₂²	1	1	yes	characteristic
55	C₂₃×#416	C₂²	1	1	yes	characteristic
56	C₂×C₂₃×#103	—	2	1	no	—
57	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
58	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
59	C₂×C₂₃×#101	C₂²	1	1	yes	characteristic
60	C₂×C₂₃×#100	C₂²	1	1	yes	characteristic
61	C₂×C₂₃×#100	C₂²	1	1	yes	characteristic
62	C₂₃×#408	C₂²	1	1	yes	characteristic
63	C₂₃×#405	C₂²	1	1	yes	characteristic
64	C₂₃×#390	C₂²	1	1	yes	characteristic
65	C₂₃×#343	C₂²	1	1	yes	characteristic
66	C₂₃×#339	C₂²	1	1	yes	characteristic
67	C₂₃×#339	C₂²	1	1	yes	characteristic
68	C₂₃×#336	C₂²	1	1	yes	characteristic
69	C₂₃×2₋¹⁺⁴	—	2	2	no	—
70	C₂₃×2₋¹⁺⁴	—	2	2	no	—
71	C₂₃×2₋¹⁺⁴	—	2	2	no	—
72	C₂₃×2₋¹⁺⁴	—	4	1	no	—
73	C₂×#41×C₂₃	—	2	1	no	—
74	C₂×#41×C₂₃	—	2	1	no	—
75	C₂×#41×C₂₃	—	4	1	no	—
76	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
77	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₂₃	—	2	1	no	—
79	C₂²×Q₈×C₂₃	—	2	1	no	—
80	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
83	C₂₃×AGL(1,ℤ/8)	—	2	2	no	—
84	C₂₃×AGL(1,ℤ/8)	—	2	2	no	—
85	C₂₃×AGL(1,ℤ/8)	—	2	2	no	—
86	C₂₃×AGL(1,ℤ/8)	—	2	2	no	—
87	C₂₃×AGL(1,ℤ/8)	—	4	1	no	—
88	C₂₃×AGL(1,ℤ/8)	D₄	1	4	yes	complemented
89	C₂×SD₁₆×C₂₃	—	2	1	no	—
90	C₂×SD₁₆×C₂₃	—	2	1	no	—
91	C₂×SD₁₆×C₂₃	—	2	1	no	—
92	C₂×SD₁₆×C₂₃	—	2	2	no	—
93	C₂×SD₁₆×C₂₃	—	2	1	no	—
94	C₂×SD₁₆×C₂₃	—	2	1	no	—
95	C₂×SD₁₆×C₂₃	—	4	1	no	—
96	C₂×D₈×C₂₃	—	2	1	no	—
97	C₂×D₈×C₂₃	—	2	2	no	—
98	C₂×D₈×C₂₃	—	2	1	no	—
99	C₂×D₈×C₂₃	—	2	1	no	—
100	C₂×D₈×C₂₃	—	2	1	no	—
101	C₂×D₈×C₂₃	—	2	1	no	—
102	C₂×D₈×C₂₃	—	4	1	no	—
103	C₂₃×#131	—	2	2	no	—
104	C₂₃×#131	—	4	1	no	—
105	C₂×M₁₆×C₂₃	—	2	1	no	—
106	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
107	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
108	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
109	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₂₃	—	2	1	no	—
111	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
113	C₂₃×#127	—	2	1	no	—
114	C₂₃×#124	—	2	1	no	—
115	C₂₃×#124	—	2	2	no	—
116	C₂₃×#124	—	2	2	no	—
117	C₂₃×#121	—	2	1	no	—
118	C₂₃×#121	—	2	1	no	—
119	C₂₃×#120	—	4	1	no	—
120	C₄×Q₈×C₂₃	—	2	1	no	—
121	C₄×D₄×C₂₃	—	2	1	no	—
122	C₄×D₄×C₂₃	—	2	1	no	—
123	C₄×D₄×C₂₃	—	2	1	no	—
124	C₄×D₄×C₂₃	—	2	1	no	—
125	C₄×D₄×C₂₃	—	2	1	no	—
126	C₄×D₄×C₂₃	—	4	1	no	—
127	C₂₃×#117	—	2	1	no	—
128	C₂₃×#117	C₂³	1	1	yes	characteristic
129	C₂₃×#117	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
131	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊C₄×C₂₃	—	4	1	no	—
133	C₂×C₂²⋊C₄×C₂₃	—	4	1	no	—
134	C₂×C₂²⋊C₄×C₂₃	—	4	1	no	—
135	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
136	C₂₃×#108	—	2	2	no	—
137	C₂₃×#108	—	4	1	no	—
138	C₂₃×#107	—	2	1	no	—
139	C₂₃×#106	—	2	1	no	—
140	C₂₃×C₄⋊C₈	—	2	1	no	—
141	C₂₃×C₄⋊C₈	—	2	1	no	—
142	C₂₃×#104	—	2	2	no	—
143	C₂₃×#104	—	2	2	no	—
144	C₂₃×#103	—	2	1	no	—
145	C₂₃×#103	—	2	1	no	—
146	C₂₃×#103	—	2	1	no	—
147	C₂₃×#103	—	2	1	no	—
148	C₂₃×#103	—	2	1	no	—
149	C₂₃×#103	—	2	1	no	—
150	C₂₃×#103	—	2	1	no	—
151	C₂₃×#103	D₄	1	1	yes	characteristic
152	C₂₃×#103	D₄	1	1	yes	characteristic
153	C₂₃×#103	D₄	1	1	yes	characteristic
154	C₂₃×#103	D₄	1	1	yes	characteristic
155	C₂₃×#102	—	2	1	no	—
156	C₂₃×#102	—	2	1	no	—
157	C₂₃×#102	—	2	1	no	—
158	C₂₃×#102	—	2	1	no	—
159	C₂₃×#102	—	2	1	no	—
160	C₂₃×#102	D₄	1	1	yes	characteristic
161	C₂₃×#102	D₄	1	1	yes	characteristic
162	C₂₃×#102	D₄	1	1	yes	characteristic
163	C₂₃×#102	D₄	1	1	yes	characteristic
164	C₂₃×#101	—	2	2	no	—
165	C₂₃×#100	—	2	2	no	—
166	C₂₃×#100	—	2	2	no	—
167	C₂₃×C₂²⋊C₈	—	2	1	no	—
168	C₂₃×C₂²⋊C₈	—	2	1	no	—
169	C₂₃×#97	—	2	1	no	—
170	C₄×C₈×C₂₃	—	2	1	no	—
171	C₂⁴×C₂₃	—	2	1	no	—
172	C₂⁴×C₂₃	—	2	1	no	—
173	#41×C₂₃	—	2	1	no	—
174	#41×C₂₃	—	2	1	no	—
175	#41×C₂₃	—	2	4	no	—
176	#41×C₂₃	—	2	1	no	—
177	#41×C₂₃	—	2	1	no	—
178	#41×C₂₃	—	2	1	no	—
179	#41×C₂₃	—	2	1	no	—
180	#41×C₂₃	—	4	2	no	—
181	#41×C₂₃	—	4	4	no	—
182	#41×C₂₃	—	4	2	no	—
183	#41×C₂₃	—	4	4	no	—
184	#41×C₂₃	—	4	2	no	—
185	#41×C₂₃	C₂×D₄	1	2	yes	—
186	#41×C₂₃	#41	1	2	yes	—
187	C₂×Q₈×C₂₃	—	2	1	no	—
188	C₂×Q₈×C₂₃	—	2	4	no	—
189	C₂×Q₈×C₂₃	—	2	1	no	—
190	C₂×Q₈×C₂₃	—	2	1	no	—
191	C₂×Q₈×C₂₃	—	2	1	no	—
192	C₂×Q₈×C₂₃	—	2	1	no	—
193	C₂×Q₈×C₂₃	—	4	1	no	—
194	C₂×Q₈×C₂₃	—	4	2	no	—
195	C₂×Q₈×C₂₃	—	4	2	no	—
196	C₂×Q₈×C₂₃	—	4	2	no	—
197	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
198	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
199	C₂×Q₈×C₂₃	#41	1	2	yes	—
200	C₂×D₄×C₂₃	—	2	1	no	—
201	C₂×D₄×C₂₃	—	2	1	no	—
202	C₂×D₄×C₂₃	—	2	1	no	—
203	C₂×D₄×C₂₃	—	2	1	no	—
204	C₂×D₄×C₂₃	—	2	1	no	—
205	C₂×D₄×C₂₃	—	2	1	no	—
206	C₂×D₄×C₂₃	—	2	1	no	—
207	C₂×D₄×C₂₃	—	2	1	no	—
208	C₂×D₄×C₂₃	—	2	1	no	—
209	C₂×D₄×C₂₃	—	2	1	no	—
210	C₂×D₄×C₂₃	—	2	1	no	—
211	C₂×D₄×C₂₃	—	2	1	no	—
212	C₂×D₄×C₂₃	—	2	1	no	—
213	C₂×D₄×C₂₃	—	4	1	no	—
214	C₂×D₄×C₂₃	—	4	1	no	—
215	C₂×D₄×C₂₃	—	4	1	no	—
216	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
217	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
218	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₂₃	—	2	1	no	—
220	C₂²×C₄×C₂₃	—	2	1	no	—
221	C₂²×C₄×C₂₃	—	2	1	no	—
222	C₂²×C₄×C₂₃	—	2	1	no	—
223	C₂²×C₄×C₂₃	—	2	1	no	—
224	C₂²×C₄×C₂₃	—	4	1	no	—
225	C₂²×C₄×C₂₃	—	4	1	no	—
226	C₂²×C₄×C₂₃	—	4	1	no	—
227	C₂²×C₄×C₂₃	—	4	1	no	—
228	C₂²×C₄×C₂₃	—	4	1	no	—
229	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
230	SD₁₆×C₂₃	—	2	4	no	—
231	SD₁₆×C₂₃	—	4	2	no	—
232	SD₁₆×C₂₃	—	4	2	no	—
233	SD₁₆×C₂₃	—	4	2	no	—
234	SD₁₆×C₂₃	—	4	2	no	—
235	D₈×C₂₃	—	2	4	no	—
236	D₈×C₂₃	—	4	2	no	—
237	D₈×C₂₃	—	4	2	no	—
238	D₈×C₂₃	—	4	2	no	—
239	D₈×C₂₃	—	4	2	no	—
240	M₁₆×C₂₃	—	2	1	no	—
241	M₁₆×C₂₃	—	2	1	no	—
242	M₁₆×C₂₃	—	2	1	no	—
243	M₁₆×C₂₃	—	2	1	no	—
244	M₁₆×C₂₃	—	2	1	no	—
245	M₁₆×C₂₃	—	2	1	no	—
246	M₁₆×C₂₃	—	2	1	no	—
247	M₁₆×C₂₃	—	4	2	no	—
248	M₁₆×C₂₃	C₂×D₄	1	2	yes	—
249	C₂×C₈×C₂₃	—	2	1	no	—
250	C₂×C₈×C₂₃	—	2	1	no	—
251	C₂×C₈×C₂₃	—	2	1	no	—
252	C₂×C₈×C₂₃	—	2	1	no	—
253	C₂×C₈×C₂₃	—	2	1	no	—
254	C₂×C₈×C₂₃	—	2	1	no	—
255	C₂×C₈×C₂₃	—	2	1	no	—
256	C₂×C₈×C₂₃	—	2	1	no	—
257	C₂×C₈×C₂₃	—	4	2	no	—
258	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
259	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
260	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
261	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
262	C₄⋊C₄×C₂₃	—	2	1	no	—
263	C₄⋊C₄×C₂₃	—	2	1	no	—
264	C₄⋊C₄×C₂₃	—	4	1	no	—
265	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
266	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
267	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
268	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
269	C₂²⋊C₄×C₂₃	—	2	1	no	—
270	C₂²⋊C₄×C₂₃	—	2	1	no	—
271	C₂²⋊C₄×C₂₃	—	4	1	no	—
272	C₂²⋊C₄×C₂₃	—	4	1	no	—
273	C₂²⋊C₄×C₂₃	—	4	1	no	—
274	C₂²⋊C₄×C₂₃	—	4	1	no	—
275	C₂²⋊C₄×C₂₃	—	4	4	no	—
276	C₂²⋊C₄×C₂₃	—	4	1	no	—
277	C₂²⋊C₄×C₂₃	—	8	2	no	—
278	C₄²×C₂₃	—	2	1	no	—
279	C₄²×C₂₃	—	2	1	no	—
280	C₄²×C₂₃	—	2	1	no	—
281	C₄²×C₂₃	—	2	1	no	—
282	C₄²×C₂₃	—	4	1	no	—
283	#25185	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
284	C₂³×C₂₃	—	2	1	no	—
285	C₂³×C₂₃	—	2	1	no	—
286	C₂³×C₂₃	—	2	2	no	—
287	C₂³×C₂₃	—	4	1	no	—
288	C₂³×C₂₃	—	4	1	no	—
289	C₂³×C₂₃	—	4	1	no	—
290	C₂³×C₂₃	—	4	1	no	—
291	C₂³×C₂₃	—	4	1	no	—
292	C₂³×C₂₃	—	8	1	no	—
293	C₂³×C₂₃	—	8	1	no	—
294	C₂³×C₂₃	—	8	1	no	—
295	C₂³×C₂₃	—	8	1	no	—
296	C₂³×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
297	Q₈×C₂₃	—	2	1	no	—
298	Q₈×C₂₃	—	2	1	no	—
299	Q₈×C₂₃	—	2	2	no	—
300	Q₈×C₂₃	—	2	1	no	—
301	Q₈×C₂₃	—	2	2	no	—
302	Q₈×C₂₃	—	4	4	no	—
303	Q₈×C₂₃	—	4	1	no	—
304	Q₈×C₂₃	—	4	1	no	—
305	Q₈×C₂₃	#121	1	2	yes	—
306	D₄×C₂₃	—	2	2	no	—
307	D₄×C₂₃	—	2	2	no	—
308	D₄×C₂₃	—	2	2	no	—
309	D₄×C₂₃	—	2	1	no	—
310	D₄×C₂₃	—	2	2	no	—
311	D₄×C₂₃	—	2	1	no	—
312	D₄×C₂₃	—	2	1	no	—
313	D₄×C₂₃	—	4	4	no	—
314	D₄×C₂₃	—	4	1	no	—
315	D₄×C₂₃	—	4	1	no	—
316	D₄×C₂₃	—	4	1	no	—
317	D₄×C₂₃	—	4	1	no	—
318	D₄×C₂₃	—	4	1	no	—
319	D₄×C₂₃	—	4	1	no	—
320	D₄×C₂₃	—	4	1	no	—
321	D₄×C₂₃	—	4	1	no	—
322	D₄×C₂₃	—	16	1	no	—
323	D₄×C₂₃	—	16	1	no	—
324	D₄×C₂₃	#121	1	2	yes	—
325	C₂×C₄×C₂₃	—	2	1	no	—
326	C₂×C₄×C₂₃	—	2	2	no	—
327	C₂×C₄×C₂₃	—	2	2	no	—
328	C₂×C₄×C₂₃	—	2	1	no	—
329	C₂×C₄×C₂₃	—	2	1	no	—
330	C₂×C₄×C₂₃	—	2	1	no	—
331	C₂×C₄×C₂₃	—	2	1	no	—
332	C₂×C₄×C₂₃	—	2	1	no	—
333	C₂×C₄×C₂₃	—	2	2	no	—
334	C₂×C₄×C₂₃	—	4	4	no	—
335	C₂×C₄×C₂₃	—	4	4	no	—
336	C₂×C₄×C₂₃	—	4	1	no	—
337	C₂×C₄×C₂₃	—	4	1	no	—
338	C₂×C₄×C₂₃	—	4	1	no	—
339	C₂×C₄×C₂₃	—	4	1	no	—
340	C₂×C₄×C₂₃	—	4	1	no	—
341	C₂×C₄×C₂₃	—	4	1	no	—
342	C₂×C₄×C₂₃	—	4	1	no	—
343	C₂×C₄×C₂₃	—	4	1	no	—
344	C₂×C₄×C₂₃	—	8	1	no	—
345	C₂×C₄×C₂₃	—	16	1	no	—
346	C₂×C₄×C₂₃	—	16	1	no	—
347	C₂×C₄×C₂₃	—	16	1	no	—
348	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
352	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
353	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
354	C₈×C₂₃	—	2	2	no	—
355	C₈×C₂₃	—	2	1	no	—
356	C₈×C₂₃	—	2	1	no	—
357	C₈×C₂₃	—	2	1	no	—
358	C₈×C₂₃	—	2	1	no	—
359	C₈×C₂₃	—	4	1	no	—
360	C₈×C₂₃	—	4	1	no	—
361	C₈×C₂₃	—	4	1	no	—
362	C₂×#472	C₂×C₂₃	1	1	yes	characteristic, complemented
363	#3041	C₂×C₂₃	1	1	yes	characteristic, complemented
364	C₂×#454	C₂×C₂₃	1	1	yes	characteristic, complemented
365	#3010	C₂×C₂₃	1	1	yes	characteristic, complemented
366	#2946	C₂×C₂₃	1	1	yes	characteristic, complemented
367	#2898	C₂×C₂₃	1	1	yes	characteristic, complemented
368	#2064	C₂×C₂₃	1	1	yes	characteristic, complemented
369	#2051	C₂×C₂₃	1	1	yes	characteristic, complemented
370	#2037	C₂×C₂₃	1	1	yes	characteristic, complemented
371	#2012	C₂×C₂₃	1	1	yes	characteristic, complemented
372	#1977	C₂×C₂₃	1	1	yes	characteristic, complemented
373	#1929	C₂×C₂₃	1	1	yes	characteristic, complemented
374	#1885	C₂×C₂₃	1	1	yes	characteristic, complemented
375	#1883	C₂×C₂₃	1	1	yes	characteristic, complemented
376	#1866	C₂×C₂₃	1	1	yes	characteristic, complemented
377	C₂²×C₂₃	—	2	1	no	—
378	C₂²×C₂₃	—	2	1	no	—
379	C₂²×C₂₃	—	2	2	no	—
380	C₂²×C₂₃	—	4	1	no	—
381	C₂²×C₂₃	—	4	1	no	—
382	C₂²×C₂₃	—	4	1	no	—
383	C₂²×C₂₃	—	4	2	no	—
384	C₂²×C₂₃	—	4	1	no	—
385	C₂²×C₂₃	—	4	1	no	—
386	C₂²×C₂₃	—	8	2	no	—
387	C₂²×C₂₃	—	8	2	no	—
388	C₂²×C₂₃	—	8	1	no	—
389	C₂²×C₂₃	—	8	1	no	—
390	C₂²×C₂₃	—	8	1	no	—
391	C₂²×C₂₃	—	8	1	no	—
392	C₂²×C₂₃	—	8	1	no	—
393	C₂²×C₂₃	—	16	1	no	—
394	C₂²×C₂₃	—	16	1	no	—
395	C₂²×C₂₃	#538	1	1	yes	characteristic
396	C₂²×C₂₃	D₄²	1	1	yes	characteristic
397	C₂²×C₂₃	#546	1	1	yes	characteristic
398	C₄×C₂₃	—	2	2	no	—
399	C₄×C₂₃	—	4	1	no	—
400	C₄×C₂₃	—	4	2	no	—
401	C₄×C₂₃	—	4	1	no	—
402	C₄×C₂₃	—	4	1	no	—
403	C₄×C₂₃	—	4	1	no	—
404	C₄×C₂₃	—	4	1	no	—
405	C₄×C₂₃	—	8	1	no	—
406	C₄×C₂₃	—	8	1	no	—
407	C₄×C₂₃	C₂×#121	1	1	yes	characteristic
408	C₄×C₂₃	#525	1	1	yes	characteristic
409	C₄×C₂₃	D₄²	1	1	yes	characteristic
410	C₄×C₂₃	#546	1	1	yes	characteristic
411	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	1	yes	characteristic
412	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
413	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
414	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
415	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
416	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
417	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
418	#535	C₂²×C₂₃	1	1	yes	characteristic
419	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
420	#520	C₂²×C₂₃	1	1	yes	characteristic
421	#518	C₂²×C₂₃	1	1	yes	characteristic
422	#472	—	2	4	no	—
423	#463	—	2	1	no	—
424	#463	—	2	1	no	—
425	#459	—	2	1	no	—
426	#459	—	2	1	no	—
427	#454	—	2	4	no	—
428	#449	—	2	1	no	—
429	#449	—	2	1	no	—
430	#448	—	2	1	no	—
431	#448	—	2	1	no	—
432	#442	—	2	1	no	—
433	#440	—	2	1	no	—
434	C₄×SD₁₆	—	2	1	no	—
435	C₄×D₈	—	2	1	no	—
436	C₂×#108	C₂²×C₂₃	1	1	yes	characteristic
437	C₂×#108	C₂²×C₂₃	1	1	yes	characteristic
438	#428	C₂²×C₂₃	1	1	yes	characteristic
439	#424	C₂²×C₂₃	1	1	yes	characteristic
440	C₂×#104	C₂²×C₂₃	1	1	yes	characteristic
441	C₂×#104	C₂²×C₂₃	1	1	yes	characteristic
442	#419	—	2	1	no	—
443	#419	C₂²×C₂₃	1	1	yes	characteristic
444	#419	C₂²×C₂₃	1	1	yes	characteristic
445	#418	C₂²×C₂₃	1	1	yes	characteristic
446	#417	—	2	1	no	—
447	#417	C₂²×C₂₃	1	1	yes	characteristic
448	#416	—	2	1	no	—
449	#416	C₂²×C₂₃	1	1	yes	characteristic
450	#416	C₂²×C₂₃	1	1	yes	characteristic
451	C₂×#103	—	2	1	no	—
452	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
453	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
454	C₂×#101	C₂²×C₂₃	1	1	yes	characteristic
455	C₂×#100	C₂²×C₂₃	1	1	yes	characteristic
456	C₂×#100	C₂²×C₂₃	1	1	yes	characteristic
457	#408	C₂²×C₂₃	1	1	yes	characteristic
458	#405	C₂²×C₂₃	1	1	yes	characteristic
459	#390	C₂²×C₂₃	1	1	yes	characteristic
460	#343	C₂²×C₂₃	1	1	yes	characteristic
461	#339	C₂²×C₂₃	1	1	yes	characteristic
462	#339	C₂²×C₂₃	1	1	yes	characteristic
463	#336	C₂²×C₂₃	1	1	yes	characteristic
464	C₂×C₂₃	—	2	1	no	—
465	C₂×C₂₃	—	2	1	no	—
466	C₂×C₂₃	—	4	2	no	—
467	C₂×C₂₃	—	8	1	no	—
468	C₂×C₂₃	—	8	2	no	—
469	C₂×C₂₃	—	16	1	no	—
470	C₂×C₂₃	#2424	1	1	yes	characteristic
471	C₂×C₂₃	#3288	1	1	yes	characteristic
472	C₂×C₂₃	#3290	1	1	yes	characteristic
473	2₋¹⁺⁴	—	2	2	no	—
474	2₋¹⁺⁴	—	2	2	no	—
475	2₋¹⁺⁴	—	2	2	no	—
476	2₋¹⁺⁴	—	4	1	no	—
477	C₂×#41	—	2	1	no	—
478	C₂×#41	—	2	1	no	—
479	C₂×#41	—	4	1	no	—
480	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
481	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
482	C₂²×Q₈	—	2	1	no	—
483	C₂²×Q₈	—	2	1	no	—
484	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
485	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
486	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
487	AGL(1,ℤ/8)	—	2	2	no	—
488	AGL(1,ℤ/8)	—	2	2	no	—
489	AGL(1,ℤ/8)	—	2	2	no	—
490	AGL(1,ℤ/8)	—	2	2	no	—
491	AGL(1,ℤ/8)	—	4	1	no	—
492	AGL(1,ℤ/8)	D₄×C₂₃	1	4	yes	complemented
493	C₂×SD₁₆	—	2	1	no	—
494	C₂×SD₁₆	—	2	1	no	—
495	C₂×SD₁₆	—	2	1	no	—
496	C₂×SD₁₆	—	2	2	no	—
497	C₂×SD₁₆	—	2	1	no	—
498	C₂×SD₁₆	—	2	1	no	—
499	C₂×SD₁₆	—	4	1	no	—
500	C₂×D₈	—	2	1	no	—
501	C₂×D₈	—	2	2	no	—
502	C₂×D₈	—	2	1	no	—
503	C₂×D₈	—	2	1	no	—
504	C₂×D₈	—	2	1	no	—
505	C₂×D₈	—	2	1	no	—
506	C₂×D₈	—	4	1	no	—
507	#131	—	2	2	no	—
508	#131	—	4	1	no	—
509	C₂×M₁₆	—	2	1	no	—
510	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
511	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
512	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
513	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
514	C₂²×C₈	—	2	1	no	—
515	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
516	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
517	#127	—	2	1	no	—
518	#124	—	2	1	no	—
519	#124	—	2	2	no	—
520	#124	—	2	2	no	—
521	#121	—	2	1	no	—
522	#121	—	2	1	no	—
523	#120	—	4	1	no	—
524	C₄×Q₈	—	2	1	no	—
525	C₄×D₄	—	2	1	no	—
526	C₄×D₄	—	2	1	no	—
527	C₄×D₄	—	2	1	no	—
528	C₄×D₄	—	2	1	no	—
529	C₄×D₄	—	2	1	no	—
530	C₄×D₄	—	4	1	no	—
531	#117	—	2	1	no	—
532	#117	C₂³×C₂₃	1	1	yes	characteristic
533	#117	C₂³×C₂₃	1	1	yes	characteristic
534	C₂×C₄⋊C₄	—	2	1	no	—
535	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
536	C₂×C₂²⋊C₄	—	4	1	no	—
537	C₂×C₂²⋊C₄	—	4	1	no	—
538	C₂×C₂²⋊C₄	—	4	1	no	—
539	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
540	#108	—	2	2	no	—
541	#108	—	4	1	no	—
542	#107	—	2	1	no	—
543	#106	—	2	1	no	—
544	C₄⋊C₈	—	2	1	no	—
545	C₄⋊C₈	—	2	1	no	—
546	#104	—	2	2	no	—
547	#104	—	2	2	no	—
548	#103	—	2	1	no	—
549	#103	—	2	1	no	—
550	#103	—	2	1	no	—
551	#103	—	2	1	no	—
552	#103	—	2	1	no	—
553	#103	—	2	1	no	—
554	#103	—	2	1	no	—
555	#103	D₄×C₂₃	1	1	yes	characteristic
556	#103	D₄×C₂₃	1	1	yes	characteristic
557	#103	D₄×C₂₃	1	1	yes	characteristic
558	#103	D₄×C₂₃	1	1	yes	characteristic
559	#102	—	2	1	no	—
560	#102	—	2	1	no	—
561	#102	—	2	1	no	—
562	#102	—	2	1	no	—
563	#102	—	2	1	no	—
564	#102	D₄×C₂₃	1	1	yes	characteristic
565	#102	D₄×C₂₃	1	1	yes	characteristic
566	#102	D₄×C₂₃	1	1	yes	characteristic
567	#102	D₄×C₂₃	1	1	yes	characteristic
568	#101	—	2	2	no	—
569	#100	—	2	2	no	—
570	#100	—	2	2	no	—
571	C₂²⋊C₈	—	2	1	no	—
572	C₂²⋊C₈	—	2	1	no	—
573	#97	—	2	1	no	—
574	C₄×C₈	—	2	1	no	—
575	C₂₃	#25185	1	1	yes	characteristic, direct product factor, Sylow
576	C₂⁴	—	2	1	no	—
577	C₂⁴	—	2	1	no	—
578	#41	—	2	1	no	—
579	#41	—	2	1	no	—
580	#41	—	2	4	no	—
581	#41	—	2	1	no	—
582	#41	—	2	1	no	—
583	#41	—	2	1	no	—
584	#41	—	2	1	no	—
585	#41	—	4	2	no	—
586	#41	—	4	4	no	—
587	#41	—	4	2	no	—
588	#41	—	4	4	no	—
589	#41	—	4	2	no	—
590	#41	C₂×D₄×C₂₃	1	2	yes	—
591	#41	#41×C₂₃	1	2	yes	—
592	C₂×Q₈	—	2	1	no	—
593	C₂×Q₈	—	2	4	no	—
594	C₂×Q₈	—	2	1	no	—
595	C₂×Q₈	—	2	1	no	—
596	C₂×Q₈	—	2	1	no	—
597	C₂×Q₈	—	2	1	no	—
598	C₂×Q₈	—	4	1	no	—
599	C₂×Q₈	—	4	2	no	—
600	C₂×Q₈	—	4	2	no	—
601	C₂×Q₈	—	4	2	no	—
602	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
603	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
604	C₂×Q₈	#41×C₂₃	1	2	yes	—
605	C₂×D₄	—	2	1	no	—
606	C₂×D₄	—	2	1	no	—
607	C₂×D₄	—	2	1	no	—
608	C₂×D₄	—	2	1	no	—
609	C₂×D₄	—	2	1	no	—
610	C₂×D₄	—	2	1	no	—
611	C₂×D₄	—	2	1	no	—
612	C₂×D₄	—	2	1	no	—
613	C₂×D₄	—	2	1	no	—
614	C₂×D₄	—	2	1	no	—
615	C₂×D₄	—	2	1	no	—
616	C₂×D₄	—	2	1	no	—
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	—	4	1	no	—
619	C₂×D₄	—	4	1	no	—
620	C₂×D₄	—	4	1	no	—
621	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
622	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
623	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	4	1	no	—
630	C₂²×C₄	—	4	1	no	—
631	C₂²×C₄	—	4	1	no	—
632	C₂²×C₄	—	4	1	no	—
633	C₂²×C₄	—	4	1	no	—
634	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
635	SD₁₆	—	2	4	no	—
636	SD₁₆	—	4	2	no	—
637	SD₁₆	—	4	2	no	—
638	SD₁₆	—	4	2	no	—
639	SD₁₆	—	4	2	no	—
640	D₈	—	2	4	no	—
641	D₈	—	4	2	no	—
642	D₈	—	4	2	no	—
643	D₈	—	4	2	no	—
644	D₈	—	4	2	no	—
645	M₁₆	—	2	1	no	—
646	M₁₆	—	2	1	no	—
647	M₁₆	—	2	1	no	—
648	M₁₆	—	2	1	no	—
649	M₁₆	—	2	1	no	—
650	M₁₆	—	2	1	no	—
651	M₁₆	—	2	1	no	—
652	M₁₆	—	4	2	no	—
653	M₁₆	C₂×D₄×C₂₃	1	2	yes	—
654	C₂×C₈	—	2	1	no	—
655	C₂×C₈	—	2	1	no	—
656	C₂×C₈	—	2	1	no	—
657	C₂×C₈	—	2	1	no	—
658	C₂×C₈	—	2	1	no	—
659	C₂×C₈	—	2	1	no	—
660	C₂×C₈	—	2	1	no	—
661	C₂×C₈	—	2	1	no	—
662	C₂×C₈	—	4	2	no	—
663	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
664	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
665	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
666	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	4	1	no	—
670	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
671	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
672	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
673	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
674	C₂²⋊C₄	—	2	1	no	—
675	C₂²⋊C₄	—	2	1	no	—
676	C₂²⋊C₄	—	4	1	no	—
677	C₂²⋊C₄	—	4	1	no	—
678	C₂²⋊C₄	—	4	1	no	—
679	C₂²⋊C₄	—	4	1	no	—
680	C₂²⋊C₄	—	4	4	no	—
681	C₂²⋊C₄	—	4	1	no	—
682	C₂²⋊C₄	—	8	2	no	—
683	C₄²	—	2	1	no	—
684	C₄²	—	2	1	no	—
685	C₄²	—	2	1	no	—
686	C₄²	—	2	1	no	—
687	C₄²	—	4	1	no	—
688	C₂³	—	2	1	no	—
689	C₂³	—	2	1	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	4	1	no	—
692	C₂³	—	4	1	no	—
693	C₂³	—	4	1	no	—
694	C₂³	—	4	1	no	—
695	C₂³	—	4	1	no	—
696	C₂³	—	8	1	no	—
697	C₂³	—	8	1	no	—
698	C₂³	—	8	1	no	—
699	C₂³	—	8	1	no	—
700	C₂³	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
701	Q₈	—	2	1	no	—
702	Q₈	—	2	1	no	—
703	Q₈	—	2	2	no	—
704	Q₈	—	2	1	no	—
705	Q₈	—	2	2	no	—
706	Q₈	—	4	4	no	—
707	Q₈	—	4	1	no	—
708	Q₈	—	4	1	no	—
709	Q₈	C₂₃×#121	1	2	yes	—
710	D₄	—	2	2	no	—
711	D₄	—	2	2	no	—
712	D₄	—	2	2	no	—
713	D₄	—	2	1	no	—
714	D₄	—	2	2	no	—
715	D₄	—	2	1	no	—
716	D₄	—	2	1	no	—
717	D₄	—	4	4	no	—
718	D₄	—	4	1	no	—
719	D₄	—	4	1	no	—
720	D₄	—	4	1	no	—
721	D₄	—	4	1	no	—
722	D₄	—	4	1	no	—
723	D₄	—	4	1	no	—
724	D₄	—	4	1	no	—
725	D₄	—	4	1	no	—
726	D₄	—	16	1	no	—
727	D₄	—	16	1	no	—
728	D₄	C₂₃×#121	1	2	yes	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	4	4	no	—
739	C₂×C₄	—	4	4	no	—
740	C₂×C₄	—	4	1	no	—
741	C₂×C₄	—	4	1	no	—
742	C₂×C₄	—	4	1	no	—
743	C₂×C₄	—	4	1	no	—
744	C₂×C₄	—	4	1	no	—
745	C₂×C₄	—	4	1	no	—
746	C₂×C₄	—	4	1	no	—
747	C₂×C₄	—	4	1	no	—
748	C₂×C₄	—	8	1	no	—
749	C₂×C₄	—	16	1	no	—
750	C₂×C₄	—	16	1	no	—
751	C₂×C₄	—	16	1	no	—
752	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
753	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
754	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
755	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
756	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
757	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
758	C₈	—	2	2	no	—
759	C₈	—	2	1	no	—
760	C₈	—	2	1	no	—
761	C₈	—	2	1	no	—
762	C₈	—	2	1	no	—
763	C₈	—	4	1	no	—
764	C₈	—	4	1	no	—
765	C₈	—	4	1	no	—
766	C₂²	—	2	1	no	—
767	C₂²	—	2	1	no	—
768	C₂²	—	2	2	no	—
769	C₂²	—	4	1	no	—
770	C₂²	—	4	1	no	—
771	C₂²	—	4	1	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	4	1	no	—
774	C₂²	—	4	1	no	—
775	C₂²	—	8	2	no	—
776	C₂²	—	8	2	no	—
777	C₂²	—	8	1	no	—
778	C₂²	—	8	1	no	—
779	C₂²	—	8	1	no	—
780	C₂²	—	8	1	no	—
781	C₂²	—	8	1	no	—
782	C₂²	—	16	1	no	—
783	C₂²	—	16	1	no	—
784	C₂²	C₂₃×#538	1	1	yes	characteristic
785	C₂²	D₄²×C₂₃	1	1	yes	characteristic
786	C₂²	C₂₃×#546	1	1	yes	characteristic
787	C₄	—	2	2	no	—
788	C₄	—	4	1	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	1	no	—
791	C₄	—	4	1	no	—
792	C₄	—	4	1	no	—
793	C₄	—	4	1	no	—
794	C₄	—	8	1	no	—
795	C₄	—	8	1	no	—
796	C₄	C₂×C₂₃×#121	1	1	yes	characteristic
797	C₄	C₂₃×#525	1	1	yes	characteristic
798	C₄	D₄²×C₂₃	1	1	yes	characteristic
799	C₄	C₂₃×#546	1	1	yes	characteristic
800	C₂	—	2	1	no	—
801	C₂	—	2	1	no	—
802	C₂	—	4	2	no	—
803	C₂	—	8	1	no	—
804	C₂	—	8	2	no	—
805	C₂	—	16	1	no	—
806	C₂	C₂₃×#2424	1	1	yes	characteristic
807	C₂	C₂₃×#3288	1	1	yes	characteristic
808	C₂	C₂₃×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#472	C₂	semidirect
2. C₂₃×#3041	C₂	semidirect
3. C₂×C₂₃×#454	C₂	semidirect
4. C₂₃×#3010	C₂	semidirect
5. C₂₃×#2946	C₂	semidirect
6. C₂₃×#2898	C₂	semidirect
7. C₂₃×#2064	C₂	semidirect
8. C₂₃×#2051	C₂	semidirect
9. C₂₃×#2037	C₂	semidirect
10. C₂₃×#2012	C₂	semidirect
11. C₂₃×#1977	C₂	semidirect
12. C₂₃×#1929	C₂	semidirect
13. C₂₃×#1885	C₂	semidirect
14. C₂₃×#1883	C₂	semidirect
15. C₂₃×#1866	C₂	semidirect
88. C₂₃×AGL(1,ℤ/8)	D₄	semidirect
283. #25185	C₂₃	direct (N × H)
362. C₂×#472	C₂×C₂₃	semidirect
363. #3041	C₂×C₂₃	semidirect
364. C₂×#454	C₂×C₂₃	semidirect
365. #3010	C₂×C₂₃	semidirect
366. #2946	C₂×C₂₃	semidirect
367. #2898	C₂×C₂₃	semidirect
368. #2064	C₂×C₂₃	semidirect
369. #2051	C₂×C₂₃	semidirect
370. #2037	C₂×C₂₃	semidirect
371. #2012	C₂×C₂₃	semidirect
372. #1977	C₂×C₂₃	semidirect
373. #1929	C₂×C₂₃	semidirect
374. #1885	C₂×C₂₃	semidirect
375. #1883	C₂×C₂₃	semidirect
376. #1866	C₂×C₂₃	semidirect
492. AGL(1,ℤ/8)	D₄×C₂₃	semidirect
575. C₂₃	#25185	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×#472	2
C₂₃×#3041	2
C₂×C₂₃×#454	2
C₂₃×#3010	2
C₂₃×#2946	2
C₂₃×#2898	2
C₂₃×#2064	2
C₂₃×#2051	2
C₂₃×#2037	2
C₂₃×#2012	2
C₂₃×#1977	2
C₂₃×#1929	2
C₂₃×#1885	2
C₂₃×#1883	2
C₂₃×#1866	2
#25185	23

Subgroups — C23×#25185 #19172811

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#25185 #19172811