Subgroups — C₂₃×#61109 #19208735

Order 5888.

2626 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3586	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3585	C₂	1	2	yes	maximal, complemented
3	C₂₃×#3290	C₂	1	8	yes	maximal, complemented
4	C₂₃×#3289	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3288	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3153	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#3069	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3068	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3018	C₂	1	2	yes	maximal, complemented
10	C₂×C₂₃×#454	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₃×#455	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#2956	C₂	1	2	yes	maximal, complemented
13	C₂₃×#585	C₂²	1	2	yes	complemented
14	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
16	C₂₃×#578	—	2	4	no	—
17	C₂₃×#578	C₂²	1	8	yes	complemented
18	C₂₃×#577	—	2	4	no	—
19	C₂₃×#577	—	2	4	no	—
20	C₂₃×#577	C₂²	1	8	yes	complemented
21	C₂₃×#577	C₂²	1	8	yes	complemented
22	C₂₃×#576	—	2	4	no	—
23	C₂₃×#576	C₂²	1	8	yes	complemented
24	C₂₃×#575	—	2	4	no	—
25	C₂₃×#575	—	2	4	no	—
26	C₂₃×#575	C₂²	1	2	yes	—
27	C₂₃×#575	C₂²	1	2	yes	—
28	C₂₃×#575	C₂²	1	2	yes	complemented
29	C₂×C₂₃×#137	—	2	4	no	—
30	C₂×C₂₃×#137	C₂²	1	2	yes	complemented
31	C₂×C₂₃×#137	C₂²	1	2	yes	complemented
32	C₂×C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
33	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
34	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
35	C₂₃×#568	C₂²	1	2	yes	complemented
36	C₂₃×#568	C₂²	1	2	yes	complemented
37	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic, complemented
39	C₂₃×#497	C₂²	1	2	yes	complemented
40	C₂₃×#496	C₂²	1	2	yes	complemented
41	C₂₃×#495	C₂²	1	4	yes	complemented
42	C₂₃×#473	C₂²	1	8	yes	complemented
43	C₂₃×#472	C₂²	1	8	yes	complemented
44	C₂₃×#471	C₂²	1	8	yes	complemented
45	C₂₃×#471	C₂²	1	8	yes	complemented
46	C₂₃×#456	C₂²	1	4	yes	complemented
47	C₂₃×#455	C₂²	1	4	yes	complemented
48	C₂₃×#455	C₂²	1	4	yes	complemented
49	C₂₃×#455	C₂²	1	4	yes	complemented
50	C₂₃×#454	C₂²	1	4	yes	complemented
51	C₂₃×#454	C₂²	1	4	yes	complemented
52	C₂₃×#454	C₂²	1	4	yes	complemented
53	C₂₃×#453	C₂²	1	4	yes	complemented
54	C₂₃×#444	C₂²	1	8	yes	complemented
55	C₂₃×#443	C₂²	1	8	yes	complemented
56	C₂₃×#430	C₂²	1	2	yes	complemented
57	C₂×C₂₃×#104	C₂²	1	2	yes	complemented
58	C₂×C₂₃×#104	C₂²	1	2	yes	complemented
59	C₂₃×#413	C₂²	1	2	yes	complemented
60	C₂×C₂₃×#101	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₂₃×#100	C₂²	1	1	yes	characteristic, complemented
62	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
63	C₂₃×2₋¹⁺⁴	—	2	4	no	—
64	C₂₃×2₋¹⁺⁴	—	2	2	no	—
65	C₂₃×2₋¹⁺⁴	—	2	2	no	—
66	C₂₃×2₋¹⁺⁴	—	4	1	no	—
67	C₂₃×2₋¹⁺⁴	C₂³	1	4	yes	—
68	C₂₃×2₋¹⁺⁴	C₂³	1	4	yes	complemented
69	C₂₃×H(5,𝔽₂)	—	2	4	no	—
70	C₂₃×H(5,𝔽₂)	—	2	2	no	—
71	C₂₃×H(5,𝔽₂)	—	2	2	no	—
72	C₂₃×H(5,𝔽₂)	—	4	2	no	—
73	C₂₃×H(5,𝔽₂)	—	4	1	no	—
74	C₂₃×H(5,𝔽₂)	C₂³	1	4	yes	—
75	C₂₃×H(5,𝔽₂)	C₂³	1	4	yes	—
76	C₂×#41×C₂₃	—	2	4	no	—
77	C₂×#41×C₂₃	—	2	4	no	—
78	C₂×#41×C₂₃	—	2	2	no	—
79	C₂×#41×C₂₃	—	2	2	no	—
80	C₂×#41×C₂₃	—	4	1	no	—
81	C₂×#41×C₂₃	—	4	2	no	—
82	C₂×#41×C₂₃	C₂³	1	2	yes	—
83	C₂×#41×C₂₃	C₂³	1	2	yes	—
84	C₂×#41×C₂₃	C₂³	1	2	yes	—
85	C₂²×Q₈×C₂₃	—	2	2	no	—
86	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₂₃	—	2	2	no	—
88	C₂²×D₄×C₂₃	—	4	1	no	—
89	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
90	C₂₃×#137	—	2	4	no	—
91	C₂₃×#137	—	2	2	no	—
92	C₂₃×#137	—	2	2	no	—
93	C₂₃×#137	—	2	8	no	—
94	C₂₃×#137	—	2	8	no	—
95	C₂₃×#137	—	2	8	no	—
96	C₂₃×#137	—	2	8	no	—
97	C₂₃×#137	—	2	4	no	—
98	C₂₃×#137	—	2	4	no	—
99	C₂₃×#137	D₄	1	4	yes	complemented
100	C₂₃×#137	D₄	1	4	yes	complemented
101	C₂₃×#137	C₂³	1	8	yes	—
102	C₂₃×#137	C₂³	1	4	yes	—
103	C₂₃×#137	C₂³	1	4	yes	complemented
104	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
105	C₂₃×AGL(1,ℤ/8)	—	2	2	no	—
106	C₂₃×AGL(1,ℤ/8)	—	2	2	no	—
107	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
108	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
109	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
110	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
111	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
112	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
113	C₂₃×AGL(1,ℤ/8)	D₄	1	4	yes	complemented
114	C₂₃×AGL(1,ℤ/8)	D₄	1	4	yes	complemented
115	C₂₃×AGL(1,ℤ/8)	C₂³	1	8	yes	—
116	C₂₃×AGL(1,ℤ/8)	C₂³	1	4	yes	—
117	C₂₃×AGL(1,ℤ/8)	C₂³	1	4	yes	complemented
118	C₂₃×#135	—	2	4	no	—
119	C₂₃×#135	—	2	4	no	—
120	C₂₃×#135	—	2	8	no	—
121	C₂₃×#135	—	2	8	no	—
122	C₂₃×#135	—	2	8	no	—
123	C₂₃×#135	—	2	8	no	—
124	C₂₃×#135	C₂³	1	8	yes	—
125	C₂×Q₁₆×C₂₃	—	2	2	no	—
126	C₂×Q₁₆×C₂₃	—	2	8	no	—
127	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	complemented
128	C₂×SD₁₆×C₂₃	—	2	2	no	—
129	C₂×SD₁₆×C₂₃	—	2	2	no	—
130	C₂×SD₁₆×C₂₃	—	2	8	no	—
131	C₂×SD₁₆×C₂₃	—	2	8	no	—
132	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
133	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	complemented
134	C₂×D₈×C₂₃	—	2	2	no	—
135	C₂×D₈×C₂₃	—	2	8	no	—
136	C₂×D₈×C₂₃	C₂³	1	4	yes	—
137	C₂₃×#131	—	2	4	no	—
138	C₂₃×#131	—	2	4	no	—
139	C₂₃×#131	C₂³	1	8	yes	—
140	C₂₃×#131	C₂³	1	8	yes	complemented
141	C₂×M₁₆×C₂₃	—	2	4	no	—
142	C₂×M₁₆×C₂₃	—	2	4	no	—
143	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
144	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
145	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
146	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
147	C₂₃×#127	C₂³	1	1	yes	characteristic, complemented
148	C₂₃×#124	—	4	1	no	—
149	C₂₃×#124	C₂³	1	2	yes	—
150	C₂₃×#124	C₂³	1	2	yes	—
151	C₂₃×#124	C₂³	1	2	yes	complemented
152	C₂₃×#121	—	4	1	no	—
153	C₄×D₄×C₂₃	—	4	1	no	—
154	C₂×C₂²⋊C₄×C₂₃	—	4	1	no	—
155	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
156	C₂₃×#108	C₂³	1	8	yes	complemented
157	C₂₃×#104	C₂³	1	4	yes	—
158	C₂₃×#104	C₂³	1	4	yes	—
159	C₂₃×#104	C₂³	1	4	yes	complemented
160	C₂₃×#104	C₂³	1	4	yes	complemented
161	C₂₃×#101	C₂³	1	4	yes	complemented
162	C₂₃×#101	C₂³	1	4	yes	complemented
163	C₂₃×#100	C₂³	1	4	yes	—
164	C₂₃×#100	C₂³	1	4	yes	complemented
165	C₂₃×#97	C₂³	1	2	yes	complemented
166	C₄×C₈×C₂₃	C₂³	1	2	yes	complemented
167	C₂⁴×C₂₃	—	2	1	no	—
168	C₂⁴×C₂₃	—	4	1	no	—
169	#41×C₂₃	—	2	2	no	—
170	#41×C₂₃	—	2	2	no	—
171	#41×C₂₃	—	2	2	no	—
172	#41×C₂₃	—	2	2	no	—
173	#41×C₂₃	—	2	4	no	—
174	#41×C₂₃	—	2	8	no	—
175	#41×C₂₃	—	2	4	no	—
176	#41×C₂₃	—	2	4	no	—
177	#41×C₂₃	—	2	8	no	—
178	#41×C₂₃	—	2	4	no	—
179	#41×C₂₃	—	2	2	no	—
180	#41×C₂₃	—	2	2	no	—
181	#41×C₂₃	—	2	2	no	—
182	#41×C₂₃	—	2	2	no	—
183	#41×C₂₃	—	4	4	no	—
184	#41×C₂₃	—	4	4	no	—
185	#41×C₂₃	—	4	4	no	—
186	#41×C₂₃	—	4	4	no	—
187	#41×C₂₃	—	4	4	no	—
188	#41×C₂₃	—	4	4	no	—
189	#41×C₂₃	—	4	4	no	—
190	#41×C₂₃	—	4	4	no	—
191	#41×C₂₃	—	4	2	no	—
192	#41×C₂₃	—	4	2	no	—
193	#41×C₂₃	C₂×D₄	1	4	yes	—
194	#41×C₂₃	C₂×D₄	1	4	yes	—
195	#41×C₂₃	C₂⁴	1	4	yes	—
196	#41×C₂₃	C₂⁴	1	4	yes	—
197	C₂×Q₈×C₂₃	—	2	1	no	—
198	C₂×Q₈×C₂₃	—	2	4	no	—
199	C₂×Q₈×C₂₃	—	2	8	no	—
200	C₂×Q₈×C₂₃	—	2	4	no	—
201	C₂×Q₈×C₂₃	—	2	2	no	—
202	C₂×Q₈×C₂₃	—	2	2	no	—
203	C₂×Q₈×C₂₃	—	4	1	no	—
204	C₂×Q₈×C₂₃	—	4	4	no	—
205	C₂×Q₈×C₂₃	—	4	2	no	—
206	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
207	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
208	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
209	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
210	C₂×D₄×C₂₃	—	2	2	no	—
211	C₂×D₄×C₂₃	—	2	2	no	—
212	C₂×D₄×C₂₃	—	2	4	no	—
213	C₂×D₄×C₂₃	—	2	8	no	—
214	C₂×D₄×C₂₃	—	2	4	no	—
215	C₂×D₄×C₂₃	—	2	2	no	—
216	C₂×D₄×C₂₃	—	2	2	no	—
217	C₂×D₄×C₂₃	—	2	2	no	—
218	C₂×D₄×C₂₃	—	2	1	no	—
219	C₂×D₄×C₂₃	—	4	4	no	—
220	C₂×D₄×C₂₃	—	4	2	no	—
221	C₂×D₄×C₂₃	—	4	1	no	—
222	C₂×D₄×C₂₃	—	4	4	no	—
223	C₂×D₄×C₂₃	—	4	4	no	—
224	C₂×D₄×C₂₃	—	4	4	no	—
225	C₂×D₄×C₂₃	—	4	2	no	—
226	C₂×D₄×C₂₃	—	4	4	no	—
227	C₂×D₄×C₂₃	—	4	4	no	—
228	C₂×D₄×C₂₃	—	4	1	no	—
229	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
230	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
231	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
232	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₂₃	—	2	2	no	—
234	C₂²×C₄×C₂₃	—	2	2	no	—
235	C₂²×C₄×C₂₃	—	2	1	no	—
236	C₂²×C₄×C₂₃	—	2	1	no	—
237	C₂²×C₄×C₂₃	—	2	2	no	—
238	C₂²×C₄×C₂₃	—	4	1	no	—
239	C₂²×C₄×C₂₃	—	4	4	no	—
240	C₂²×C₄×C₂₃	—	4	2	no	—
241	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
242	Q₁₆×C₂₃	—	2	8	no	—
243	Q₁₆×C₂₃	—	2	4	no	—
244	Q₁₆×C₂₃	—	2	4	no	—
245	Q₁₆×C₂₃	—	2	8	no	—
246	Q₁₆×C₂₃	C₂×D₄	1	8	yes	—
247	SD₁₆×C₂₃	—	2	8	no	—
248	SD₁₆×C₂₃	—	2	4	no	—
249	SD₁₆×C₂₃	—	2	4	no	—
250	SD₁₆×C₂₃	—	2	4	no	—
251	SD₁₆×C₂₃	—	2	8	no	—
252	SD₁₆×C₂₃	—	2	4	no	—
253	SD₁₆×C₂₃	—	2	8	no	—
254	SD₁₆×C₂₃	—	2	8	no	—
255	SD₁₆×C₂₃	C₂×D₄	1	8	yes	—
256	SD₁₆×C₂₃	C₂×D₄	1	8	yes	—
257	D₈×C₂₃	—	2	4	no	—
258	D₈×C₂₃	—	2	8	no	—
259	D₈×C₂₃	—	2	4	no	—
260	D₈×C₂₃	—	2	8	no	—
261	D₈×C₂₃	C₂×D₄	1	8	yes	—
262	M₁₆×C₂₃	—	2	2	no	—
263	M₁₆×C₂₃	—	2	2	no	—
264	M₁₆×C₂₃	—	2	8	no	—
265	M₁₆×C₂₃	—	2	8	no	—
266	M₁₆×C₂₃	C₂×D₄	1	4	yes	—
267	M₁₆×C₂₃	C₂×D₄	1	4	yes	—
268	M₁₆×C₂₃	C₂⁴	1	4	yes	—
269	M₁₆×C₂₃	C₂⁴	1	4	yes	—
270	C₂×C₈×C₂₃	—	2	2	no	—
271	C₂×C₈×C₂₃	—	2	2	no	—
272	C₂×C₈×C₂₃	—	2	8	no	—
273	C₂×C₈×C₂₃	—	2	8	no	—
274	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
275	C₄⋊C₄×C₂₃	—	4	1	no	—
276	C₂²⋊C₄×C₂₃	—	4	2	no	—
277	C₂²⋊C₄×C₂₃	—	4	2	no	—
278	C₂²⋊C₄×C₂₃	—	4	2	no	—
279	C₄²×C₂₃	—	2	1	no	—
280	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
281	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
282	#61109	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
283	C₂³×C₂₃	—	2	2	no	—
284	C₂³×C₂₃	—	2	2	no	—
285	C₂³×C₂₃	—	2	2	no	—
286	C₂³×C₂₃	—	2	2	no	—
287	C₂³×C₂₃	—	4	4	no	—
288	C₂³×C₂₃	—	4	4	no	—
289	C₂³×C₂₃	—	4	1	no	—
290	C₂³×C₂₃	—	4	1	no	—
291	C₂³×C₂₃	—	8	2	no	—
292	C₂³×C₂₃	—	16	2	no	—
293	C₂³×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
294	Q₈×C₂₃	—	2	2	no	—
295	Q₈×C₂₃	—	2	2	no	—
296	Q₈×C₂₃	—	2	2	no	—
297	Q₈×C₂₃	—	2	4	no	—
298	Q₈×C₂₃	—	2	2	no	—
299	Q₈×C₂₃	—	4	4	no	—
300	Q₈×C₂₃	—	4	4	no	—
301	Q₈×C₂₃	—	4	2	no	—
302	Q₈×C₂₃	C₂²×D₄	1	4	yes	—
303	Q₈×C₂₃	C₂²×D₄	1	4	yes	—
304	D₄×C₂₃	—	2	4	no	—
305	D₄×C₂₃	—	2	4	no	—
306	D₄×C₂₃	—	2	4	no	—
307	D₄×C₂₃	—	2	4	no	—
308	D₄×C₂₃	—	2	2	no	—
309	D₄×C₂₃	—	2	2	no	—
310	D₄×C₂₃	—	2	2	no	—
311	D₄×C₂₃	—	2	4	no	—
312	D₄×C₂₃	—	2	2	no	—
313	D₄×C₂₃	—	4	8	no	—
314	D₄×C₂₃	—	4	4	no	—
315	D₄×C₂₃	—	4	4	no	—
316	D₄×C₂₃	—	4	4	no	—
317	D₄×C₂₃	—	4	4	no	—
318	D₄×C₂₃	—	4	2	no	—
319	D₄×C₂₃	—	4	2	no	—
320	D₄×C₂₃	—	4	2	no	—
321	D₄×C₂₃	—	8	2	no	—
322	D₄×C₂₃	C₂²×D₄	1	4	yes	—
323	D₄×C₂₃	C₂²×D₄	1	4	yes	—
324	C₂×C₄×C₂₃	—	2	2	no	—
325	C₂×C₄×C₂₃	—	2	2	no	—
326	C₂×C₄×C₂₃	—	2	4	no	—
327	C₂×C₄×C₂₃	—	2	4	no	—
328	C₂×C₄×C₂₃	—	2	4	no	—
329	C₂×C₄×C₂₃	—	2	4	no	—
330	C₂×C₄×C₂₃	—	2	1	no	—
331	C₂×C₄×C₂₃	—	2	1	no	—
332	C₂×C₄×C₂₃	—	2	2	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	4	no	—
337	C₂×C₄×C₂₃	—	4	4	no	—
338	C₂×C₄×C₂₃	—	4	8	no	—
339	C₂×C₄×C₂₃	—	4	1	no	—
340	C₂×C₄×C₂₃	—	4	1	no	—
341	C₂×C₄×C₂₃	—	4	2	no	—
342	C₂×C₄×C₂₃	—	4	2	no	—
343	C₂×C₄×C₂₃	—	8	1	no	—
344	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
345	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
346	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
347	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
348	C₈×C₂₃	—	2	4	no	—
349	C₈×C₂₃	—	2	4	no	—
350	C₈×C₂₃	C₂²×D₄	1	8	yes	—
351	#3586	C₂×C₂₃	1	2	yes	complemented
352	#3585	C₂×C₂₃	1	2	yes	complemented
353	#3290	C₂×C₂₃	1	8	yes	complemented
354	#3289	C₂×C₂₃	1	4	yes	complemented
355	#3288	C₂×C₂₃	1	4	yes	complemented
356	#3153	C₂×C₂₃	1	1	yes	characteristic, complemented
357	#3069	C₂×C₂₃	1	2	yes	complemented
358	#3068	C₂×C₂₃	1	2	yes	complemented
359	#3018	C₂×C₂₃	1	2	yes	complemented
360	C₂×#454	C₂×C₂₃	1	1	yes	characteristic, complemented
361	C₂×#455	C₂×C₂₃	1	1	yes	characteristic, complemented
362	#2956	C₂×C₂₃	1	2	yes	complemented
363	C₂²×C₂₃	—	2	4	no	—
364	C₂²×C₂₃	—	2	4	no	—
365	C₂²×C₂₃	—	4	1	no	—
366	C₂²×C₂₃	—	4	2	no	—
367	C₂²×C₂₃	—	4	2	no	—
368	C₂²×C₂₃	—	8	2	no	—
369	C₂²×C₂₃	—	8	2	no	—
370	C₂²×C₂₃	—	8	2	no	—
371	C₂²×C₂₃	—	8	2	no	—
372	C₂²×C₂₃	—	8	2	no	—
373	C₂²×C₂₃	—	16	1	no	—
374	C₂²×C₂₃	—	16	4	no	—
375	C₂²×C₂₃	—	16	4	no	—
376	C₂²×C₂₃	D₄²	1	1	yes	characteristic
377	C₂²×C₂₃	D₄²	1	1	yes	characteristic
378	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
379	C₄×C₂₃	—	2	4	no	—
380	C₄×C₂₃	—	2	4	no	—
381	C₄×C₂₃	—	4	1	no	—
382	C₄×C₂₃	—	4	1	no	—
383	C₄×C₂₃	—	4	2	no	—
384	C₄×C₂₃	—	4	2	no	—
385	C₄×C₂₃	D₄²	1	2	yes	—
386	C₄×C₂₃	C₂³×D₄	1	2	yes	—
387	#585	C₂²×C₂₃	1	2	yes	complemented
388	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	1	yes	characteristic, complemented
389	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	1	yes	characteristic
390	#578	—	2	4	no	—
391	#578	C₂²×C₂₃	1	8	yes	complemented
392	#577	—	2	4	no	—
393	#577	—	2	4	no	—
394	#577	C₂²×C₂₃	1	8	yes	complemented
395	#577	C₂²×C₂₃	1	8	yes	complemented
396	#576	—	2	4	no	—
397	#576	C₂²×C₂₃	1	8	yes	complemented
398	#575	—	2	4	no	—
399	#575	—	2	4	no	—
400	#575	C₂²×C₂₃	1	2	yes	—
401	#575	C₂²×C₂₃	1	2	yes	—
402	#575	C₂²×C₂₃	1	2	yes	complemented
403	C₂×#137	—	2	4	no	—
404	C₂×#137	C₂²×C₂₃	1	2	yes	complemented
405	C₂×#137	C₂²×C₂₃	1	2	yes	complemented
406	C₂×AGL(1,ℤ/8)	—	2	4	no	—
407	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
408	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
409	#568	C₂²×C₂₃	1	2	yes	complemented
410	#568	C₂²×C₂₃	1	2	yes	complemented
411	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
412	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic, complemented
413	#497	C₂²×C₂₃	1	2	yes	complemented
414	#496	C₂²×C₂₃	1	2	yes	complemented
415	#495	C₂²×C₂₃	1	4	yes	complemented
416	#473	C₂²×C₂₃	1	8	yes	complemented
417	#472	C₂²×C₂₃	1	8	yes	complemented
418	#471	C₂²×C₂₃	1	8	yes	complemented
419	#471	C₂²×C₂₃	1	8	yes	complemented
420	#456	C₂²×C₂₃	1	4	yes	complemented
421	#455	C₂²×C₂₃	1	4	yes	complemented
422	#455	C₂²×C₂₃	1	4	yes	complemented
423	#455	C₂²×C₂₃	1	4	yes	complemented
424	#454	C₂²×C₂₃	1	4	yes	complemented
425	#454	C₂²×C₂₃	1	4	yes	complemented
426	#454	C₂²×C₂₃	1	4	yes	complemented
427	#453	C₂²×C₂₃	1	4	yes	complemented
428	#444	C₂²×C₂₃	1	8	yes	complemented
429	#443	C₂²×C₂₃	1	8	yes	complemented
430	#430	C₂²×C₂₃	1	2	yes	complemented
431	C₂×#104	C₂²×C₂₃	1	2	yes	complemented
432	C₂×#104	C₂²×C₂₃	1	2	yes	complemented
433	#413	C₂²×C₂₃	1	2	yes	complemented
434	C₂×#101	C₂²×C₂₃	1	1	yes	characteristic, complemented
435	C₂×#100	C₂²×C₂₃	1	1	yes	characteristic, complemented
436	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
437	C₂×C₂₃	—	2	1	no	—
438	C₂×C₂₃	—	2	1	no	—
439	C₂×C₂₃	—	2	1	no	—
440	C₂×C₂₃	—	4	4	no	—
441	C₂×C₂₃	—	4	4	no	—
442	C₂×C₂₃	—	8	2	no	—
443	C₂×C₂₃	—	8	2	no	—
444	C₂×C₂₃	C₂×D₄²	1	1	yes	characteristic
445	2₋¹⁺⁴	—	2	4	no	—
446	2₋¹⁺⁴	—	2	2	no	—
447	2₋¹⁺⁴	—	2	2	no	—
448	2₋¹⁺⁴	—	4	1	no	—
449	2₋¹⁺⁴	C₂³×C₂₃	1	4	yes	—
450	2₋¹⁺⁴	C₂³×C₂₃	1	4	yes	complemented
451	H(5,𝔽₂)	—	2	4	no	—
452	H(5,𝔽₂)	—	2	2	no	—
453	H(5,𝔽₂)	—	2	2	no	—
454	H(5,𝔽₂)	—	4	2	no	—
455	H(5,𝔽₂)	—	4	1	no	—
456	H(5,𝔽₂)	C₂³×C₂₃	1	4	yes	—
457	H(5,𝔽₂)	C₂³×C₂₃	1	4	yes	—
458	C₂×#41	—	2	4	no	—
459	C₂×#41	—	2	4	no	—
460	C₂×#41	—	2	2	no	—
461	C₂×#41	—	2	2	no	—
462	C₂×#41	—	4	1	no	—
463	C₂×#41	—	4	2	no	—
464	C₂×#41	C₂³×C₂₃	1	2	yes	—
465	C₂×#41	C₂³×C₂₃	1	2	yes	—
466	C₂×#41	C₂³×C₂₃	1	2	yes	—
467	C₂²×Q₈	—	2	2	no	—
468	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
469	C₂²×D₄	—	2	2	no	—
470	C₂²×D₄	—	4	1	no	—
471	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
472	#137	—	2	4	no	—
473	#137	—	2	2	no	—
474	#137	—	2	2	no	—
475	#137	—	2	8	no	—
476	#137	—	2	8	no	—
477	#137	—	2	8	no	—
478	#137	—	2	8	no	—
479	#137	—	2	4	no	—
480	#137	—	2	4	no	—
481	#137	D₄×C₂₃	1	4	yes	complemented
482	#137	D₄×C₂₃	1	4	yes	complemented
483	#137	C₂³×C₂₃	1	8	yes	—
484	#137	C₂³×C₂₃	1	4	yes	—
485	#137	C₂³×C₂₃	1	4	yes	complemented
486	AGL(1,ℤ/8)	—	2	4	no	—
487	AGL(1,ℤ/8)	—	2	2	no	—
488	AGL(1,ℤ/8)	—	2	2	no	—
489	AGL(1,ℤ/8)	—	2	8	no	—
490	AGL(1,ℤ/8)	—	2	8	no	—
491	AGL(1,ℤ/8)	—	2	8	no	—
492	AGL(1,ℤ/8)	—	2	8	no	—
493	AGL(1,ℤ/8)	—	2	4	no	—
494	AGL(1,ℤ/8)	—	2	4	no	—
495	AGL(1,ℤ/8)	D₄×C₂₃	1	4	yes	complemented
496	AGL(1,ℤ/8)	D₄×C₂₃	1	4	yes	complemented
497	AGL(1,ℤ/8)	C₂³×C₂₃	1	8	yes	—
498	AGL(1,ℤ/8)	C₂³×C₂₃	1	4	yes	—
499	AGL(1,ℤ/8)	C₂³×C₂₃	1	4	yes	complemented
500	#135	—	2	4	no	—
501	#135	—	2	4	no	—
502	#135	—	2	8	no	—
503	#135	—	2	8	no	—
504	#135	—	2	8	no	—
505	#135	—	2	8	no	—
506	#135	C₂³×C₂₃	1	8	yes	—
507	C₂×Q₁₆	—	2	2	no	—
508	C₂×Q₁₆	—	2	8	no	—
509	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	complemented
510	C₂×SD₁₆	—	2	2	no	—
511	C₂×SD₁₆	—	2	2	no	—
512	C₂×SD₁₆	—	2	8	no	—
513	C₂×SD₁₆	—	2	8	no	—
514	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
515	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	complemented
516	C₂×D₈	—	2	2	no	—
517	C₂×D₈	—	2	8	no	—
518	C₂×D₈	C₂³×C₂₃	1	4	yes	—
519	#131	—	2	4	no	—
520	#131	—	2	4	no	—
521	#131	C₂³×C₂₃	1	8	yes	—
522	#131	C₂³×C₂₃	1	8	yes	complemented
523	C₂×M₁₆	—	2	4	no	—
524	C₂×M₁₆	—	2	4	no	—
525	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
526	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
527	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
528	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic, complemented
529	#127	C₂³×C₂₃	1	1	yes	characteristic, complemented
530	#124	—	4	1	no	—
531	#124	C₂³×C₂₃	1	2	yes	—
532	#124	C₂³×C₂₃	1	2	yes	—
533	#124	C₂³×C₂₃	1	2	yes	complemented
534	#121	—	4	1	no	—
535	C₄×D₄	—	4	1	no	—
536	C₂×C₂²⋊C₄	—	4	1	no	—
537	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
538	#108	C₂³×C₂₃	1	8	yes	complemented
539	#104	C₂³×C₂₃	1	4	yes	—
540	#104	C₂³×C₂₃	1	4	yes	—
541	#104	C₂³×C₂₃	1	4	yes	complemented
542	#104	C₂³×C₂₃	1	4	yes	complemented
543	#101	C₂³×C₂₃	1	4	yes	complemented
544	#101	C₂³×C₂₃	1	4	yes	complemented
545	#100	C₂³×C₂₃	1	4	yes	—
546	#100	C₂³×C₂₃	1	4	yes	complemented
547	#97	C₂³×C₂₃	1	2	yes	complemented
548	C₄×C₈	C₂³×C₂₃	1	2	yes	complemented
549	C₂₃	#61109	1	1	yes	characteristic, direct product factor, Sylow
550	C₂⁴	—	2	1	no	—
551	C₂⁴	—	4	1	no	—
552	#41	—	2	2	no	—
553	#41	—	2	2	no	—
554	#41	—	2	2	no	—
555	#41	—	2	2	no	—
556	#41	—	2	4	no	—
557	#41	—	2	8	no	—
558	#41	—	2	4	no	—
559	#41	—	2	4	no	—
560	#41	—	2	8	no	—
561	#41	—	2	4	no	—
562	#41	—	2	2	no	—
563	#41	—	2	2	no	—
564	#41	—	2	2	no	—
565	#41	—	2	2	no	—
566	#41	—	4	4	no	—
567	#41	—	4	4	no	—
568	#41	—	4	4	no	—
569	#41	—	4	4	no	—
570	#41	—	4	4	no	—
571	#41	—	4	4	no	—
572	#41	—	4	4	no	—
573	#41	—	4	4	no	—
574	#41	—	4	2	no	—
575	#41	—	4	2	no	—
576	#41	C₂×D₄×C₂₃	1	4	yes	—
577	#41	C₂×D₄×C₂₃	1	4	yes	—
578	#41	C₂⁴×C₂₃	1	4	yes	—
579	#41	C₂⁴×C₂₃	1	4	yes	—
580	C₂×Q₈	—	2	1	no	—
581	C₂×Q₈	—	2	4	no	—
582	C₂×Q₈	—	2	8	no	—
583	C₂×Q₈	—	2	4	no	—
584	C₂×Q₈	—	2	2	no	—
585	C₂×Q₈	—	2	2	no	—
586	C₂×Q₈	—	4	1	no	—
587	C₂×Q₈	—	4	4	no	—
588	C₂×Q₈	—	4	2	no	—
589	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
590	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
591	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
592	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	—	2	2	no	—
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	—	2	8	no	—
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	2	2	no	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	2	no	—
601	C₂×D₄	—	2	1	no	—
602	C₂×D₄	—	4	4	no	—
603	C₂×D₄	—	4	2	no	—
604	C₂×D₄	—	4	1	no	—
605	C₂×D₄	—	4	4	no	—
606	C₂×D₄	—	4	4	no	—
607	C₂×D₄	—	4	4	no	—
608	C₂×D₄	—	4	2	no	—
609	C₂×D₄	—	4	4	no	—
610	C₂×D₄	—	4	4	no	—
611	C₂×D₄	—	4	1	no	—
612	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
613	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
614	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
615	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	4	1	no	—
622	C₂²×C₄	—	4	4	no	—
623	C₂²×C₄	—	4	2	no	—
624	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
625	Q₁₆	—	2	8	no	—
626	Q₁₆	—	2	4	no	—
627	Q₁₆	—	2	4	no	—
628	Q₁₆	—	2	8	no	—
629	Q₁₆	C₂×D₄×C₂₃	1	8	yes	—
630	SD₁₆	—	2	8	no	—
631	SD₁₆	—	2	4	no	—
632	SD₁₆	—	2	4	no	—
633	SD₁₆	—	2	4	no	—
634	SD₁₆	—	2	8	no	—
635	SD₁₆	—	2	4	no	—
636	SD₁₆	—	2	8	no	—
637	SD₁₆	—	2	8	no	—
638	SD₁₆	C₂×D₄×C₂₃	1	8	yes	—
639	SD₁₆	C₂×D₄×C₂₃	1	8	yes	—
640	D₈	—	2	4	no	—
641	D₈	—	2	8	no	—
642	D₈	—	2	4	no	—
643	D₈	—	2	8	no	—
644	D₈	C₂×D₄×C₂₃	1	8	yes	—
645	M₁₆	—	2	2	no	—
646	M₁₆	—	2	2	no	—
647	M₁₆	—	2	8	no	—
648	M₁₆	—	2	8	no	—
649	M₁₆	C₂×D₄×C₂₃	1	4	yes	—
650	M₁₆	C₂×D₄×C₂₃	1	4	yes	—
651	M₁₆	C₂⁴×C₂₃	1	4	yes	—
652	M₁₆	C₂⁴×C₂₃	1	4	yes	—
653	C₂×C₈	—	2	2	no	—
654	C₂×C₈	—	2	2	no	—
655	C₂×C₈	—	2	8	no	—
656	C₂×C₈	—	2	8	no	—
657	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
658	C₄⋊C₄	—	4	1	no	—
659	C₂²⋊C₄	—	4	2	no	—
660	C₂²⋊C₄	—	4	2	no	—
661	C₂²⋊C₄	—	4	2	no	—
662	C₄²	—	2	1	no	—
663	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
664	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
665	C₂³	—	2	2	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	4	4	no	—
670	C₂³	—	4	4	no	—
671	C₂³	—	4	1	no	—
672	C₂³	—	4	1	no	—
673	C₂³	—	8	2	no	—
674	C₂³	—	16	2	no	—
675	C₂³	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
676	Q₈	—	2	2	no	—
677	Q₈	—	2	2	no	—
678	Q₈	—	2	2	no	—
679	Q₈	—	2	4	no	—
680	Q₈	—	2	2	no	—
681	Q₈	—	4	4	no	—
682	Q₈	—	4	4	no	—
683	Q₈	—	4	2	no	—
684	Q₈	C₂²×D₄×C₂₃	1	4	yes	—
685	Q₈	C₂²×D₄×C₂₃	1	4	yes	—
686	D₄	—	2	4	no	—
687	D₄	—	2	4	no	—
688	D₄	—	2	4	no	—
689	D₄	—	2	4	no	—
690	D₄	—	2	2	no	—
691	D₄	—	2	4	no	—
692	D₄	—	2	2	no	—
693	D₄	—	2	2	no	—
694	D₄	—	2	2	no	—
695	D₄	—	4	8	no	—
696	D₄	—	4	4	no	—
697	D₄	—	4	4	no	—
698	D₄	—	4	4	no	—
699	D₄	—	4	4	no	—
700	D₄	—	4	2	no	—
701	D₄	—	4	2	no	—
702	D₄	—	4	2	no	—
703	D₄	—	8	2	no	—
704	D₄	C₂²×D₄×C₂₃	1	4	yes	—
705	D₄	C₂²×D₄×C₂₃	1	4	yes	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	4	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	4	4	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	4	4	no	—
719	C₂×C₄	—	4	4	no	—
720	C₂×C₄	—	4	8	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	2	no	—
724	C₂×C₄	—	4	2	no	—
725	C₂×C₄	—	8	1	no	—
726	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
727	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
728	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
729	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
730	C₈	—	2	4	no	—
731	C₈	—	2	4	no	—
732	C₈	C₂²×D₄×C₂₃	1	8	yes	—
733	C₂²	—	2	4	no	—
734	C₂²	—	2	4	no	—
735	C₂²	—	4	1	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	8	2	no	—
739	C₂²	—	8	2	no	—
740	C₂²	—	8	2	no	—
741	C₂²	—	8	2	no	—
742	C₂²	—	8	2	no	—
743	C₂²	—	16	1	no	—
744	C₂²	—	16	4	no	—
745	C₂²	—	16	4	no	—
746	C₂²	D₄²×C₂₃	1	1	yes	characteristic
747	C₂²	D₄²×C₂₃	1	1	yes	characteristic
748	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
749	C₄	—	2	4	no	—
750	C₄	—	2	4	no	—
751	C₄	—	4	1	no	—
752	C₄	—	4	1	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	2	no	—
755	C₄	D₄²×C₂₃	1	2	yes	—
756	C₄	C₂³×D₄×C₂₃	1	2	yes	—
757	C₂	—	2	1	no	—
758	C₂	—	2	1	no	—
759	C₂	—	2	1	no	—
760	C₂	—	4	4	no	—
761	C₂	—	4	4	no	—
762	C₂	—	8	2	no	—
763	C₂	—	8	2	no	—
764	C₂	C₂×D₄²×C₂₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₂₃	C₂×D₄²
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3586	C₂	semidirect
2. C₂₃×#3585	C₂	semidirect
3. C₂₃×#3290	C₂	semidirect
4. C₂₃×#3289	C₂	semidirect
5. C₂₃×#3288	C₂	semidirect
6. C₂₃×#3153	C₂	semidirect
7. C₂₃×#3069	C₂	semidirect
8. C₂₃×#3068	C₂	semidirect
9. C₂₃×#3018	C₂	semidirect
10. C₂×C₂₃×#454	C₂	semidirect
11. C₂×C₂₃×#455	C₂	semidirect
12. C₂₃×#2956	C₂	semidirect
13. C₂₃×#585	C₂²	semidirect
14. C₂×C₂₃×2₋¹⁺⁴	C₂²	semidirect
17. C₂₃×#578	C₂²	semidirect
20. C₂₃×#577	C₂²	semidirect
21. C₂₃×#577	C₂²	semidirect
23. C₂₃×#576	C₂²	semidirect
28. C₂₃×#575	C₂²	semidirect
30. C₂×C₂₃×#137	C₂²	semidirect
31. C₂×C₂₃×#137	C₂²	semidirect
33. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
34. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
35. C₂₃×#568	C₂²	semidirect
36. C₂₃×#568	C₂²	semidirect
37. C₂₃×#532	C₂²	semidirect
38. C₂×C₂₃×#124	C₂²	semidirect
39. C₂₃×#497	C₂²	semidirect
40. C₂₃×#496	C₂²	semidirect
41. C₂₃×#495	C₂²	semidirect
42. C₂₃×#473	C₂²	semidirect
43. C₂₃×#472	C₂²	semidirect
44. C₂₃×#471	C₂²	semidirect
45. C₂₃×#471	C₂²	semidirect
46. C₂₃×#456	C₂²	semidirect
47. C₂₃×#455	C₂²	semidirect
48. C₂₃×#455	C₂²	semidirect
49. C₂₃×#455	C₂²	semidirect
50. C₂₃×#454	C₂²	semidirect
51. C₂₃×#454	C₂²	semidirect
52. C₂₃×#454	C₂²	semidirect
53. C₂₃×#453	C₂²	semidirect
54. C₂₃×#444	C₂²	semidirect
55. C₂₃×#443	C₂²	semidirect
56. C₂₃×#430	C₂²	semidirect
57. C₂×C₂₃×#104	C₂²	semidirect
58. C₂×C₂₃×#104	C₂²	semidirect
59. C₂₃×#413	C₂²	semidirect
60. C₂×C₂₃×#101	C₂²	semidirect
61. C₂×C₂₃×#100	C₂²	semidirect
62. C₄×M₁₆×C₂₃	C₂²	semidirect
68. C₂₃×2₋¹⁺⁴	C₂³	semidirect
99. C₂₃×#137	D₄	semidirect
100. C₂₃×#137	D₄	semidirect
103. C₂₃×#137	C₂³	semidirect
113. C₂₃×AGL(1,ℤ/8)	D₄	semidirect
114. C₂₃×AGL(1,ℤ/8)	D₄	semidirect
117. C₂₃×AGL(1,ℤ/8)	C₂³	semidirect
127. C₂×Q₁₆×C₂₃	C₂³	semidirect
133. C₂×SD₁₆×C₂₃	C₂³	semidirect
140. C₂₃×#131	C₂³	semidirect
146. C₂₃×C₄⋊Q₈	C₂³	semidirect
147. C₂₃×#127	C₂³	semidirect
151. C₂₃×#124	C₂³	semidirect
156. C₂₃×#108	C₂³	semidirect
159. C₂₃×#104	C₂³	semidirect
160. C₂₃×#104	C₂³	semidirect
161. C₂₃×#101	C₂³	semidirect
162. C₂₃×#101	C₂³	semidirect
164. C₂₃×#100	C₂³	semidirect
165. C₂₃×#97	C₂³	semidirect
166. C₄×C₈×C₂₃	C₂³	semidirect
282. #61109	C₂₃	direct (N × H)
351. #3586	C₂×C₂₃	semidirect
352. #3585	C₂×C₂₃	semidirect
353. #3290	C₂×C₂₃	semidirect
354. #3289	C₂×C₂₃	semidirect
355. #3288	C₂×C₂₃	semidirect
356. #3153	C₂×C₂₃	semidirect
357. #3069	C₂×C₂₃	semidirect
358. #3068	C₂×C₂₃	semidirect
359. #3018	C₂×C₂₃	semidirect
360. C₂×#454	C₂×C₂₃	semidirect
361. C₂×#455	C₂×C₂₃	semidirect
362. #2956	C₂×C₂₃	semidirect
387. #585	C₂²×C₂₃	semidirect
388. C₂×2₋¹⁺⁴	C₂²×C₂₃	semidirect
391. #578	C₂²×C₂₃	semidirect
394. #577	C₂²×C₂₃	semidirect
395. #577	C₂²×C₂₃	semidirect
397. #576	C₂²×C₂₃	semidirect
402. #575	C₂²×C₂₃	semidirect
404. C₂×#137	C₂²×C₂₃	semidirect
405. C₂×#137	C₂²×C₂₃	semidirect
407. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
408. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
409. #568	C₂²×C₂₃	semidirect
410. #568	C₂²×C₂₃	semidirect
411. #532	C₂²×C₂₃	semidirect
412. C₂×#124	C₂²×C₂₃	semidirect
413. #497	C₂²×C₂₃	semidirect
414. #496	C₂²×C₂₃	semidirect
415. #495	C₂²×C₂₃	semidirect
416. #473	C₂²×C₂₃	semidirect
417. #472	C₂²×C₂₃	semidirect
418. #471	C₂²×C₂₃	semidirect
419. #471	C₂²×C₂₃	semidirect
420. #456	C₂²×C₂₃	semidirect
421. #455	C₂²×C₂₃	semidirect
422. #455	C₂²×C₂₃	semidirect
423. #455	C₂²×C₂₃	semidirect
424. #454	C₂²×C₂₃	semidirect
425. #454	C₂²×C₂₃	semidirect
426. #454	C₂²×C₂₃	semidirect
427. #453	C₂²×C₂₃	semidirect
428. #444	C₂²×C₂₃	semidirect
429. #443	C₂²×C₂₃	semidirect
430. #430	C₂²×C₂₃	semidirect
431. C₂×#104	C₂²×C₂₃	semidirect
432. C₂×#104	C₂²×C₂₃	semidirect
433. #413	C₂²×C₂₃	semidirect
434. C₂×#101	C₂²×C₂₃	semidirect
435. C₂×#100	C₂²×C₂₃	semidirect
436. C₄×M₁₆	C₂²×C₂₃	semidirect
450. 2₋¹⁺⁴	C₂³×C₂₃	semidirect
481. #137	D₄×C₂₃	semidirect
482. #137	D₄×C₂₃	semidirect
485. #137	C₂³×C₂₃	semidirect
495. AGL(1,ℤ/8)	D₄×C₂₃	semidirect
496. AGL(1,ℤ/8)	D₄×C₂₃	semidirect
499. AGL(1,ℤ/8)	C₂³×C₂₃	semidirect
509. C₂×Q₁₆	C₂³×C₂₃	semidirect
515. C₂×SD₁₆	C₂³×C₂₃	semidirect
522. #131	C₂³×C₂₃	semidirect
528. C₄⋊Q₈	C₂³×C₂₃	semidirect
529. #127	C₂³×C₂₃	semidirect
533. #124	C₂³×C₂₃	semidirect
538. #108	C₂³×C₂₃	semidirect
541. #104	C₂³×C₂₃	semidirect
542. #104	C₂³×C₂₃	semidirect
543. #101	C₂³×C₂₃	semidirect
544. #101	C₂³×C₂₃	semidirect
546. #100	C₂³×C₂₃	semidirect
547. #97	C₂³×C₂₃	semidirect
548. C₄×C₈	C₂³×C₂₃	semidirect
549. C₂₃	#61109	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#3586	2
C₂₃×#3585	2
C₂₃×#3290	2
C₂₃×#3289	2
C₂₃×#3288	2
C₂₃×#3153	2
C₂₃×#3069	2
C₂₃×#3068	2
C₂₃×#3018	2
C₂×C₂₃×#454	2
C₂×C₂₃×#455	2
C₂₃×#2956	2
#61109	23

Subgroups — C23×#61109 #19208735

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61109 #19208735