Subgroups — C₂₃×#62824 #19210450

Order 5888.

7330 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3561	C₂	1	8	yes	maximal, complemented
2	C₂₃×#3558	C₂	1	8	yes	maximal, complemented
3	C₂₃×#3545	C₂	1	8	yes	maximal, complemented
4	C₂₃×#3514	C₂	1	16	yes	maximal, complemented
5	C₂₃×#3510	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3500	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3490	C₂	1	8	yes	maximal, complemented
8	C₂₃×#3486	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3484	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3444	C₂	1	2	yes	maximal, complemented
11	C₂²×C₂₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	2	yes	complemented
13	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	2	yes	complemented
14	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
15	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
16	C₂₃×#563	C₂²	1	8	yes	complemented
17	C₂₃×#562	C₂²	1	16	yes	complemented
18	C₂₃×H(3,𝔽₄)	C₂²	1	8	yes	complemented
19	C₂₃×#559	C₂²	1	16	yes	complemented
20	C₂₃×#556	C₂²	1	16	yes	complemented
21	C₂₃×#555	C₂²	1	16	yes	complemented
22	C₂₃×#551	C₂²	1	32	yes	complemented
23	C₂₃×#551	C₂²	1	32	yes	complemented
24	C₂₃×#551	C₂²	1	16	yes	complemented
25	D₄×Q₈×C₂₃	C₂²	1	16	yes	complemented
26	C₂₃×#548	C₂²	1	16	yes	complemented
27	C₂₃×#548	C₂²	1	16	yes	complemented
28	C₂₃×#546	C₂²	1	16	yes	complemented
29	C₂₃×#546	C₂²	1	32	yes	complemented
30	C₂₃×#546	C₂²	1	32	yes	complemented
31	C₂₃×#546	C₂²	1	16	yes	complemented
32	D₄²×C₂₃	C₂²	1	16	yes	complemented
33	C₂₃×#543	C₂²	1	8	yes	complemented
34	C₂₃×#542	C₂²	1	16	yes	complemented
35	C₂₃×#542	C₂²	1	32	yes	complemented
36	C₂₃×#538	C₂²	1	16	yes	complemented
37	C₂₃×#538	C₂²	1	16	yes	complemented
38	C₂₃×#538	C₂²	1	32	yes	complemented
39	C₂₃×#536	C₂²	1	4	yes	complemented
40	C₂₃×#536	C₂²	1	8	yes	complemented
41	C₂₃×#536	C₂²	1	8	yes	complemented
42	C₂₃×#535	C₂²	1	4	yes	—
43	C₂₃×#535	C₂²	1	8	yes	complemented
44	C₂₃×#534	C₂²	1	8	yes	complemented
45	C₂₃×#534	C₂²	1	8	yes	complemented
46	C₂₃×#533	C₂²	1	2	yes	complemented
47	C₂₃×#533	C₂²	1	4	yes	complemented
48	C₂₃×#532	C₂²	1	2	yes	complemented
49	C₂₃×#532	C₂²	1	4	yes	complemented
50	C₂₃×#532	C₂²	1	8	yes	complemented
51	C₂₃×#529	C₂²	1	8	yes	complemented
52	C₂₃×#529	C₂²	1	8	yes	complemented
53	C₂₃×#529	C₂²	1	8	yes	complemented
54	C₂₃×#529	C₂²	1	16	yes	complemented
55	C₂×C₂₃×#124	C₂²	1	4	yes	complemented
56	C₂×C₂₃×#124	C₂²	1	8	yes	complemented
57	C₂×C₂₃×#124	C₂²	1	4	yes	complemented
58	C₂×C₂₃×#124	C₂²	1	8	yes	complemented
59	C₂×C₂₃×#124	C₂²	1	8	yes	complemented
60	C₂₃×#525	C₂²	1	4	yes	complemented
61	C₂₃×#525	C₂²	1	8	yes	complemented
62	C₂₃×#525	C₂²	1	8	yes	complemented
63	C₂×C₂₃×#120	C₂²	1	8	yes	complemented
64	C₂₃×#519	C₂²	1	2	yes	complemented
65	C₂₃×#518	C₂²	1	2	yes	complemented
66	C₂₃×#518	C₂²	1	16	yes	complemented
67	C₄×#41×C₂₃	C₂²	1	4	yes	complemented
68	C₄×#41×C₂₃	C₂²	1	8	yes	complemented
69	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	complemented
70	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic, complemented
71	C₂⁵×C₂₃	C₂³	1	2	yes	—
72	C₂₃×2₋¹⁺⁴	—	4	8	no	—
73	C₂₃×H(5,𝔽₂)	—	4	8	no	—
74	C₂×#41×C₂₃	C₂³	1	4	yes	—
75	C₂×#41×C₂₃	C₂³	1	8	yes	—
76	C₂×#41×C₂₃	C₂³	1	8	yes	—
77	C₂×#41×C₂₃	C₂³	1	8	yes	—
78	C₂×#41×C₂₃	C₂³	1	8	yes	complemented
79	C₂²×Q₈×C₂₃	—	4	4	no	—
80	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
81	C₂²×Q₈×C₂₃	C₂³	1	8	yes	—
82	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
83	C₂²×Q₈×C₂₃	C₂³	1	8	yes	complemented
84	C₂²×D₄×C₂₃	—	4	4	no	—
85	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
86	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
87	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
88	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
89	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
90	C₂²×D₄×C₂₃	C₂³	1	16	yes	—
91	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
93	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
94	C₂₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
95	C₂₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
96	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	complemented
97	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
98	C₂₃×#127	C₂³	1	8	yes	—
99	C₂₃×#127	C₂³	1	2	yes	complemented
100	C₂₃×#126	C₂³	1	32	yes	complemented
101	C₂₃×#126	C₂³	1	32	yes	complemented
102	C₂₃×#126	C₂³	1	16	yes	complemented
103	C₂₃×#125	C₂³	1	8	yes	complemented
104	C₂₃×#125	C₂³	1	4	yes	complemented
105	C₂₃×#124	C₂³	1	16	yes	—
106	C₂₃×#124	C₂³	1	8	yes	—
107	C₂₃×#124	C₂³	1	8	yes	—
108	C₂₃×#124	C₂³	1	8	yes	—
109	C₂₃×#124	C₂³	1	8	yes	—
110	C₂₃×#124	C₂³	1	8	yes	—
111	C₂₃×#124	C₂³	1	16	yes	—
112	C₂₃×#124	C₂³	1	16	yes	complemented
113	C₂₃×#124	C₂³	1	8	yes	complemented
114	C₂₃×#124	C₂³	1	32	yes	complemented
115	C₂₃×#124	C₂³	1	32	yes	complemented
116	C₂₃×#124	C₂³	1	8	yes	complemented
117	C₂₃×#124	C₂³	1	4	yes	complemented
118	C₂₃×#123	C₂³	1	16	yes	—
119	C₂₃×#123	C₂³	1	16	yes	—
120	C₂₃×#123	C₂³	1	16	yes	—
121	C₂₃×#123	C₂³	1	8	yes	—
122	C₂₃×#123	C₂³	1	32	yes	complemented
123	C₂₃×#123	C₂³	1	32	yes	complemented
124	C₂₃×#123	C₂³	1	32	yes	complemented
125	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
126	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
127	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
128	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
129	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
130	C₂₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
131	C₂₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
132	C₂₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
133	C₂₃×#121	C₂³	1	8	yes	—
134	C₂₃×#121	C₂³	1	16	yes	—
135	C₂₃×#121	C₂³	1	16	yes	—
136	C₂₃×#121	C₂³	1	32	yes	—
137	C₂₃×#121	C₂³	1	8	yes	—
138	C₂₃×#121	C₂³	1	8	yes	—
139	C₂₃×#121	C₂³	1	32	yes	complemented
140	C₂₃×#121	C₂³	1	32	yes	complemented
141	C₂₃×#120	C₂³	1	16	yes	—
142	C₂₃×#120	C₂³	1	16	yes	—
143	C₂₃×#120	C₂³	1	32	yes	—
144	C₂₃×#120	C₂³	1	8	yes	—
145	C₂₃×#120	C₂³	1	32	yes	complemented
146	C₄×Q₈×C₂₃	C₂³	1	8	yes	complemented
147	C₄×Q₈×C₂₃	C₂³	1	16	yes	complemented
148	C₄×Q₈×C₂₃	C₂³	1	8	yes	complemented
149	C₄×Q₈×C₂₃	C₂³	1	8	yes	complemented
150	C₄×D₄×C₂₃	C₂³	1	32	yes	—
151	C₄×D₄×C₂₃	C₂³	1	16	yes	—
152	C₄×D₄×C₂₃	C₂³	1	16	yes	—
153	C₄×D₄×C₂₃	C₂³	1	16	yes	—
154	C₄×D₄×C₂₃	C₂³	1	16	yes	—
155	C₄×D₄×C₂₃	C₂³	1	8	yes	complemented
156	C₄×D₄×C₂₃	C₂³	1	32	yes	complemented
157	C₄×D₄×C₂₃	C₂³	1	32	yes	complemented
158	C₄×D₄×C₂₃	C₂³	1	8	yes	complemented
159	C₄×D₄×C₂₃	C₂³	1	8	yes	complemented
160	C₂₃×#117	C₂³	1	8	yes	—
161	C₂₃×#117	C₂³	1	8	yes	—
162	C₂₃×#117	C₂³	1	4	yes	—
163	C₂₃×#117	C₂³	1	16	yes	complemented
164	C₂₃×#117	C₂³	1	32	yes	complemented
165	C₂₃×#117	C₂³	1	8	yes	complemented
166	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
167	C₂×C₂²⋊C₄×C₂₃	C₂³	1	16	yes	—
168	C₂×C₂²⋊C₄×C₂₃	C₂³	1	16	yes	—
169	C₂×C₂²⋊C₄×C₂₃	C₂³	1	16	yes	—
170	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
171	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
172	C₂×C₂²⋊C₄×C₂₃	C₂³	1	32	yes	complemented
173	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
174	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
175	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
176	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
177	C₂×C₄²×C₂₃	C₂³	1	8	yes	complemented
178	C₂⁴×C₂₃	—	4	4	no	—
179	C₂⁴×C₂₃	—	4	8	no	—
180	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
181	C₂⁴×C₂₃	C₂⁴	1	4	yes	—
182	C₂⁴×C₂₃	C₂⁴	1	8	yes	—
183	C₂⁴×C₂₃	C₂⁴	1	8	yes	—
184	#41×C₂₃	—	2	16	no	—
185	#41×C₂₃	—	4	16	no	—
186	#41×C₂₃	—	4	16	no	—
187	#41×C₂₃	—	4	16	no	—
188	#41×C₂₃	—	4	16	no	—
189	C₂×Q₈×C₂₃	—	2	8	no	—
190	C₂×Q₈×C₂₃	—	4	4	no	—
191	C₂×Q₈×C₂₃	—	4	16	no	—
192	C₂×Q₈×C₂₃	—	4	16	no	—
193	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
194	C₂×Q₈×C₂₃	C₂⁴	1	8	yes	—
195	C₂×Q₈×C₂₃	C₂⁴	1	8	yes	—
196	C₂×Q₈×C₂₃	C₂⁴	1	8	yes	—
197	C₂×Q₈×C₂₃	C₂⁴	1	8	yes	—
198	C₂×D₄×C₂₃	—	2	8	no	—
199	C₂×D₄×C₂₃	—	4	16	no	—
200	C₂×D₄×C₂₃	—	4	16	no	—
201	C₂×D₄×C₂₃	—	4	4	no	—
202	C₂×D₄×C₂₃	—	4	32	no	—
203	C₂×D₄×C₂₃	—	4	16	no	—
204	C₂×D₄×C₂₃	C₂⁴	1	16	yes	—
205	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
206	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
207	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
208	C₂×D₄×C₂₃	C₂⁴	1	32	yes	—
209	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
210	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
211	C₂×D₄×C₂₃	C₂⁴	1	16	yes	—
212	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
213	C₂²×C₄×C₂₃	—	2	4	no	—
214	C₂²×C₄×C₂₃	—	4	4	no	—
215	C₂²×C₄×C₂₃	—	4	4	no	—
216	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
217	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
218	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
220	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
221	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
223	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₂₃	C₂⁴	1	16	yes	—
225	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
226	C₂²×C₄×C₂₃	C₂⁴	1	16	yes	—
227	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
228	C₂²×C₄×C₂₃	C₂⁴	1	16	yes	—
229	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
230	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
231	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
232	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
233	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
234	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
235	C₄⋊C₄×C₂₃	C₂⁴	1	32	yes	—
236	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
237	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
238	C₂²⋊C₄×C₂₃	C₂⁴	1	32	yes	—
239	C₂²⋊C₄×C₂₃	C₂⁴	1	32	yes	—
240	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
241	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
242	C₂²⋊C₄×C₂₃	C₂⁴	1	32	yes	—
243	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
244	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
245	C₂²⋊C₄×C₂₃	C₂⁴	1	32	yes	—
246	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
247	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
248	C₄²×C₂₃	C₂⁴	1	2	yes	—
249	C₄²×C₂₃	C₂⁴	1	2	yes	—
250	C₄²×C₂₃	C₂⁴	1	2	yes	—
251	C₄²×C₂₃	C₂⁴	1	4	yes	—
252	C₄²×C₂₃	C₂⁴	1	4	yes	—
253	C₄²×C₂₃	C₂⁴	1	2	yes	—
254	C₄²×C₂₃	C₂⁴	1	16	yes	—
255	C₄²×C₂₃	C₂⁴	1	8	yes	—
256	C₄²×C₂₃	C₂⁴	1	16	yes	—
257	#62824	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
258	C₂³×C₂₃	—	2	2	no	—
259	C₂³×C₂₃	—	2	4	no	—
260	C₂³×C₂₃	—	2	8	no	—
261	C₂³×C₂₃	—	2	16	no	—
262	C₂³×C₂₃	—	4	8	no	—
263	C₂³×C₂₃	—	4	8	no	—
264	C₂³×C₂₃	—	4	8	no	—
265	C₂³×C₂₃	—	4	8	no	—
266	C₂³×C₂₃	—	4	16	no	—
267	C₂³×C₂₃	—	8	16	no	—
268	C₂³×C₂₃	C₂⁵	1	8	yes	—
269	C₂³×C₂₃	C₂⁵	1	8	yes	—
270	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
271	C₂³×C₂₃	C₂⁵	1	2	yes	—
272	Q₈×C₂₃	—	2	16	no	—
273	Q₈×C₂₃	—	2	8	no	—
274	Q₈×C₂₃	—	4	8	no	—
275	Q₈×C₂₃	—	4	8	no	—
276	Q₈×C₂₃	—	4	8	no	—
277	D₄×C₂₃	—	2	16	no	—
278	D₄×C₂₃	—	2	32	no	—
279	D₄×C₂₃	—	2	16	no	—
280	D₄×C₂₃	—	2	8	no	—
281	D₄×C₂₃	—	4	8	no	—
282	D₄×C₂₃	—	4	16	no	—
283	D₄×C₂₃	—	4	32	no	—
284	D₄×C₂₃	—	4	8	no	—
285	D₄×C₂₃	—	4	8	no	—
286	C₂×C₄×C₂₃	—	2	2	no	—
287	C₂×C₄×C₂₃	—	2	8	no	—
288	C₂×C₄×C₂₃	—	2	8	no	—
289	C₂×C₄×C₂₃	—	2	8	no	—
290	C₂×C₄×C₂₃	—	2	16	no	—
291	C₂×C₄×C₂₃	—	4	2	no	—
292	C₂×C₄×C₂₃	—	4	4	no	—
293	C₂×C₄×C₂₃	—	4	2	no	—
294	C₂×C₄×C₂₃	—	4	8	no	—
295	C₂×C₄×C₂₃	—	4	16	no	—
296	C₂×C₄×C₂₃	—	4	8	no	—
297	C₂×C₄×C₂₃	—	4	16	no	—
298	C₂×C₄×C₂₃	—	4	16	no	—
299	C₂×C₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
300	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
301	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
302	C₂×C₄×C₂₃	C₂⁵	1	16	yes	—
303	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
304	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
305	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
306	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
307	#3561	C₂×C₂₃	1	8	yes	complemented
308	#3558	C₂×C₂₃	1	8	yes	complemented
309	#3545	C₂×C₂₃	1	8	yes	complemented
310	#3514	C₂×C₂₃	1	16	yes	complemented
311	#3510	C₂×C₂₃	1	4	yes	complemented
312	#3500	C₂×C₂₃	1	4	yes	complemented
313	#3490	C₂×C₂₃	1	8	yes	complemented
314	#3486	C₂×C₂₃	1	2	yes	complemented
315	#3484	C₂×C₂₃	1	2	yes	complemented
316	#3444	C₂×C₂₃	1	2	yes	complemented
317	C₂²×#124	C₂×C₂₃	1	1	yes	characteristic, complemented
318	C₂²×C₂₃	—	2	8	no	—
319	C₂²×C₂₃	—	2	2	no	—
320	C₂²×C₂₃	—	2	2	no	—
321	C₂²×C₂₃	—	2	2	no	—
322	C₂²×C₂₃	—	2	8	no	—
323	C₂²×C₂₃	—	2	8	no	—
324	C₂²×C₂₃	—	2	16	no	—
325	C₂²×C₂₃	—	2	16	no	—
326	C₂²×C₂₃	—	8	8	no	—
327	C₂²×C₂₃	—	8	16	no	—
328	C₂²×C₂₃	—	16	8	no	—
329	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
330	C₂²×C₂₃	#585	1	4	yes	—
331	C₂²×C₂₃	C₂⁶	1	1	yes	characteristic
332	C₄×C₂₃	—	2	2	no	—
333	C₄×C₂₃	—	2	8	no	—
334	C₄×C₂₃	—	2	8	no	—
335	C₄×C₂₃	—	2	4	no	—
336	C₄×C₂₃	—	2	4	no	—
337	C₄×C₂₃	—	2	16	no	—
338	C₄×C₂₃	C₂×H(5,𝔽₂)	1	4	yes	—
339	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	2	yes	complemented
340	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	2	yes	complemented
341	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
342	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
343	#563	C₂²×C₂₃	1	8	yes	complemented
344	#562	C₂²×C₂₃	1	16	yes	complemented
345	H(3,𝔽₄)	C₂²×C₂₃	1	8	yes	complemented
346	#559	C₂²×C₂₃	1	16	yes	complemented
347	#556	C₂²×C₂₃	1	16	yes	complemented
348	#555	C₂²×C₂₃	1	16	yes	complemented
349	#551	C₂²×C₂₃	1	32	yes	complemented
350	#551	C₂²×C₂₃	1	32	yes	complemented
351	#551	C₂²×C₂₃	1	16	yes	complemented
352	D₄×Q₈	C₂²×C₂₃	1	16	yes	complemented
353	#548	C₂²×C₂₃	1	16	yes	complemented
354	#548	C₂²×C₂₃	1	16	yes	complemented
355	#546	C₂²×C₂₃	1	16	yes	complemented
356	#546	C₂²×C₂₃	1	32	yes	complemented
357	#546	C₂²×C₂₃	1	32	yes	complemented
358	#546	C₂²×C₂₃	1	16	yes	complemented
359	D₄²	C₂²×C₂₃	1	16	yes	complemented
360	#543	C₂²×C₂₃	1	8	yes	complemented
361	#542	C₂²×C₂₃	1	16	yes	complemented
362	#542	C₂²×C₂₃	1	32	yes	complemented
363	#538	C₂²×C₂₃	1	16	yes	complemented
364	#538	C₂²×C₂₃	1	16	yes	complemented
365	#538	C₂²×C₂₃	1	32	yes	complemented
366	#536	C₂²×C₂₃	1	4	yes	complemented
367	#536	C₂²×C₂₃	1	8	yes	complemented
368	#536	C₂²×C₂₃	1	8	yes	complemented
369	#535	C₂²×C₂₃	1	4	yes	—
370	#535	C₂²×C₂₃	1	8	yes	complemented
371	#534	C₂²×C₂₃	1	8	yes	complemented
372	#534	C₂²×C₂₃	1	8	yes	complemented
373	#533	C₂²×C₂₃	1	2	yes	complemented
374	#533	C₂²×C₂₃	1	4	yes	complemented
375	#532	C₂²×C₂₃	1	2	yes	complemented
376	#532	C₂²×C₂₃	1	4	yes	complemented
377	#532	C₂²×C₂₃	1	8	yes	complemented
378	#529	C₂²×C₂₃	1	8	yes	complemented
379	#529	C₂²×C₂₃	1	8	yes	complemented
380	#529	C₂²×C₂₃	1	8	yes	complemented
381	#529	C₂²×C₂₃	1	16	yes	complemented
382	C₂×#124	C₂²×C₂₃	1	4	yes	complemented
383	C₂×#124	C₂²×C₂₃	1	8	yes	complemented
384	C₂×#124	C₂²×C₂₃	1	4	yes	complemented
385	C₂×#124	C₂²×C₂₃	1	8	yes	complemented
386	C₂×#124	C₂²×C₂₃	1	8	yes	complemented
387	#525	C₂²×C₂₃	1	4	yes	complemented
388	#525	C₂²×C₂₃	1	8	yes	complemented
389	#525	C₂²×C₂₃	1	8	yes	complemented
390	C₂×#120	C₂²×C₂₃	1	8	yes	complemented
391	#519	C₂²×C₂₃	1	2	yes	complemented
392	#518	C₂²×C₂₃	1	2	yes	complemented
393	#518	C₂²×C₂₃	1	16	yes	complemented
394	C₄×#41	C₂²×C₂₃	1	4	yes	complemented
395	C₄×#41	C₂²×C₂₃	1	8	yes	complemented
396	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	complemented
397	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic, complemented
398	C₂×C₂₃	—	2	2	no	—
399	C₂×C₂₃	—	2	4	no	—
400	C₂×C₂₃	—	4	8	no	—
401	C₂×C₂₃	—	4	8	no	—
402	C₂×C₂₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
403	C₂×C₂₃	C₂×#585	1	2	yes	—
404	C₂⁵	C₂³×C₂₃	1	2	yes	—
405	2₋¹⁺⁴	—	4	8	no	—
406	H(5,𝔽₂)	—	4	8	no	—
407	C₂×#41	C₂³×C₂₃	1	4	yes	—
408	C₂×#41	C₂³×C₂₃	1	8	yes	—
409	C₂×#41	C₂³×C₂₃	1	8	yes	—
410	C₂×#41	C₂³×C₂₃	1	8	yes	—
411	C₂×#41	C₂³×C₂₃	1	8	yes	complemented
412	C₂²×Q₈	—	4	4	no	—
413	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
414	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
415	C₂²×Q₈	C₂³×C₂₃	1	8	yes	—
416	C₂²×Q₈	C₂³×C₂₃	1	8	yes	complemented
417	C₂²×D₄	—	4	4	no	—
418	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
419	C₂²×D₄	C₂³×C₂₃	1	16	yes	—
420	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
421	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
422	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
423	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
424	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
425	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
426	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
427	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	complemented
428	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	complemented
429	C₄⋊Q₈	C₂³×C₂₃	1	8	yes	complemented
430	C₄⋊Q₈	C₂³×C₂₃	1	16	yes	complemented
431	#127	C₂³×C₂₃	1	8	yes	—
432	#127	C₂³×C₂₃	1	2	yes	complemented
433	#126	C₂³×C₂₃	1	16	yes	complemented
434	#126	C₂³×C₂₃	1	32	yes	complemented
435	#126	C₂³×C₂₃	1	32	yes	complemented
436	#125	C₂³×C₂₃	1	4	yes	complemented
437	#125	C₂³×C₂₃	1	8	yes	complemented
438	#124	C₂³×C₂₃	1	8	yes	—
439	#124	C₂³×C₂₃	1	8	yes	—
440	#124	C₂³×C₂₃	1	16	yes	—
441	#124	C₂³×C₂₃	1	16	yes	—
442	#124	C₂³×C₂₃	1	8	yes	—
443	#124	C₂³×C₂₃	1	8	yes	—
444	#124	C₂³×C₂₃	1	8	yes	—
445	#124	C₂³×C₂₃	1	4	yes	complemented
446	#124	C₂³×C₂₃	1	8	yes	complemented
447	#124	C₂³×C₂₃	1	32	yes	complemented
448	#124	C₂³×C₂₃	1	8	yes	complemented
449	#124	C₂³×C₂₃	1	16	yes	complemented
450	#124	C₂³×C₂₃	1	32	yes	complemented
451	#123	C₂³×C₂₃	1	8	yes	—
452	#123	C₂³×C₂₃	1	16	yes	—
453	#123	C₂³×C₂₃	1	16	yes	—
454	#123	C₂³×C₂₃	1	16	yes	—
455	#123	C₂³×C₂₃	1	32	yes	complemented
456	#123	C₂³×C₂₃	1	32	yes	complemented
457	#123	C₂³×C₂₃	1	32	yes	complemented
458	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
459	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
460	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
461	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
462	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	complemented
463	C₂²⋊Q₈	C₂³×C₂₃	1	32	yes	complemented
464	C₂²⋊Q₈	C₂³×C₂₃	1	32	yes	complemented
465	C₂²⋊Q₈	C₂³×C₂₃	1	32	yes	complemented
466	#121	C₂³×C₂₃	1	8	yes	—
467	#121	C₂³×C₂₃	1	8	yes	—
468	#121	C₂³×C₂₃	1	8	yes	—
469	#121	C₂³×C₂₃	1	16	yes	—
470	#121	C₂³×C₂₃	1	16	yes	—
471	#121	C₂³×C₂₃	1	32	yes	—
472	#121	C₂³×C₂₃	1	32	yes	complemented
473	#121	C₂³×C₂₃	1	32	yes	complemented
474	#120	C₂³×C₂₃	1	8	yes	—
475	#120	C₂³×C₂₃	1	16	yes	—
476	#120	C₂³×C₂₃	1	32	yes	—
477	#120	C₂³×C₂₃	1	16	yes	—
478	#120	C₂³×C₂₃	1	32	yes	complemented
479	C₄×Q₈	C₂³×C₂₃	1	8	yes	complemented
480	C₄×Q₈	C₂³×C₂₃	1	8	yes	complemented
481	C₄×Q₈	C₂³×C₂₃	1	8	yes	complemented
482	C₄×Q₈	C₂³×C₂₃	1	16	yes	complemented
483	C₄×D₄	C₂³×C₂₃	1	16	yes	—
484	C₄×D₄	C₂³×C₂₃	1	16	yes	—
485	C₄×D₄	C₂³×C₂₃	1	16	yes	—
486	C₄×D₄	C₂³×C₂₃	1	32	yes	—
487	C₄×D₄	C₂³×C₂₃	1	16	yes	—
488	C₄×D₄	C₂³×C₂₃	1	8	yes	complemented
489	C₄×D₄	C₂³×C₂₃	1	8	yes	complemented
490	C₄×D₄	C₂³×C₂₃	1	8	yes	complemented
491	C₄×D₄	C₂³×C₂₃	1	32	yes	complemented
492	C₄×D₄	C₂³×C₂₃	1	32	yes	complemented
493	#117	C₂³×C₂₃	1	4	yes	—
494	#117	C₂³×C₂₃	1	8	yes	—
495	#117	C₂³×C₂₃	1	8	yes	—
496	#117	C₂³×C₂₃	1	8	yes	complemented
497	#117	C₂³×C₂₃	1	16	yes	complemented
498	#117	C₂³×C₂₃	1	32	yes	complemented
499	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
500	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₂₃	1	16	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₂₃	1	16	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₂₃	1	16	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₂₃	1	32	yes	complemented
506	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
507	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
508	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
509	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
510	C₂×C₄²	C₂³×C₂₃	1	8	yes	complemented
511	C₂₃	#62824	1	1	yes	characteristic, direct product factor, Sylow
512	C₂⁴	—	4	4	no	—
513	C₂⁴	—	4	8	no	—
514	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
515	C₂⁴	C₂⁴×C₂₃	1	4	yes	—
516	C₂⁴	C₂⁴×C₂₃	1	8	yes	—
517	C₂⁴	C₂⁴×C₂₃	1	8	yes	—
518	#41	—	2	16	no	—
519	#41	—	4	16	no	—
520	#41	—	4	16	no	—
521	#41	—	4	16	no	—
522	#41	—	4	16	no	—
523	C₂×Q₈	—	2	8	no	—
524	C₂×Q₈	—	4	4	no	—
525	C₂×Q₈	—	4	16	no	—
526	C₂×Q₈	—	4	16	no	—
527	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
528	C₂×Q₈	C₂⁴×C₂₃	1	8	yes	—
529	C₂×Q₈	C₂⁴×C₂₃	1	8	yes	—
530	C₂×Q₈	C₂⁴×C₂₃	1	8	yes	—
531	C₂×Q₈	C₂⁴×C₂₃	1	8	yes	—
532	C₂×D₄	—	2	8	no	—
533	C₂×D₄	—	4	16	no	—
534	C₂×D₄	—	4	16	no	—
535	C₂×D₄	—	4	4	no	—
536	C₂×D₄	—	4	16	no	—
537	C₂×D₄	—	4	32	no	—
538	C₂×D₄	C₂⁴×C₂₃	1	16	yes	—
539	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
540	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
541	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
542	C₂×D₄	C₂⁴×C₂₃	1	32	yes	—
543	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
544	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
545	C₂×D₄	C₂⁴×C₂₃	1	16	yes	—
546	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
547	C₂²×C₄	—	2	4	no	—
548	C₂²×C₄	—	4	4	no	—
549	C₂²×C₄	—	4	4	no	—
550	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
551	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
552	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
553	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
554	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
555	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
556	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
557	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
558	C₂²×C₄	C₂⁴×C₂₃	1	16	yes	—
559	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
560	C₂²×C₄	C₂⁴×C₂₃	1	16	yes	—
561	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
562	C₂²×C₄	C₂⁴×C₂₃	1	16	yes	—
563	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
564	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
565	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
566	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
567	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
568	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
569	C₄⋊C₄	C₂⁴×C₂₃	1	32	yes	—
570	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
571	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
572	C₂²⋊C₄	C₂⁴×C₂₃	1	32	yes	—
573	C₂²⋊C₄	C₂⁴×C₂₃	1	32	yes	—
574	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
575	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
576	C₂²⋊C₄	C₂⁴×C₂₃	1	32	yes	—
577	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
578	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
579	C₂²⋊C₄	C₂⁴×C₂₃	1	32	yes	—
580	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
581	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
582	C₄²	C₂⁴×C₂₃	1	2	yes	—
583	C₄²	C₂⁴×C₂₃	1	2	yes	—
584	C₄²	C₂⁴×C₂₃	1	2	yes	—
585	C₄²	C₂⁴×C₂₃	1	4	yes	—
586	C₄²	C₂⁴×C₂₃	1	4	yes	—
587	C₄²	C₂⁴×C₂₃	1	2	yes	—
588	C₄²	C₂⁴×C₂₃	1	16	yes	—
589	C₄²	C₂⁴×C₂₃	1	8	yes	—
590	C₄²	C₂⁴×C₂₃	1	16	yes	—
591	C₂³	—	2	2	no	—
592	C₂³	—	2	4	no	—
593	C₂³	—	2	8	no	—
594	C₂³	—	2	16	no	—
595	C₂³	—	4	8	no	—
596	C₂³	—	4	8	no	—
597	C₂³	—	4	8	no	—
598	C₂³	—	4	8	no	—
599	C₂³	—	4	16	no	—
600	C₂³	—	8	16	no	—
601	C₂³	C₂⁵×C₂₃	1	8	yes	—
602	C₂³	C₂⁵×C₂₃	1	8	yes	—
603	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
604	C₂³	C₂⁵×C₂₃	1	2	yes	—
605	Q₈	—	2	16	no	—
606	Q₈	—	2	8	no	—
607	Q₈	—	4	8	no	—
608	Q₈	—	4	8	no	—
609	Q₈	—	4	8	no	—
610	D₄	—	2	16	no	—
611	D₄	—	2	32	no	—
612	D₄	—	2	16	no	—
613	D₄	—	2	8	no	—
614	D₄	—	4	8	no	—
615	D₄	—	4	16	no	—
616	D₄	—	4	32	no	—
617	D₄	—	4	8	no	—
618	D₄	—	4	8	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	8	no	—
621	C₂×C₄	—	2	8	no	—
622	C₂×C₄	—	2	8	no	—
623	C₂×C₄	—	2	16	no	—
624	C₂×C₄	—	4	8	no	—
625	C₂×C₄	—	4	2	no	—
626	C₂×C₄	—	4	4	no	—
627	C₂×C₄	—	4	2	no	—
628	C₂×C₄	—	4	8	no	—
629	C₂×C₄	—	4	16	no	—
630	C₂×C₄	—	4	16	no	—
631	C₂×C₄	—	4	16	no	—
632	C₂×C₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
633	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
634	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
635	C₂×C₄	C₂⁵×C₂₃	1	16	yes	—
636	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
637	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
638	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
639	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
640	C₂²	—	2	8	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	8	no	—
645	C₂²	—	2	8	no	—
646	C₂²	—	2	16	no	—
647	C₂²	—	2	16	no	—
648	C₂²	—	8	8	no	—
649	C₂²	—	8	16	no	—
650	C₂²	—	16	8	no	—
651	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
652	C₂²	C₂₃×#585	1	4	yes	—
653	C₂²	C₂⁶×C₂₃	1	1	yes	characteristic
654	C₄	—	2	2	no	—
655	C₄	—	2	8	no	—
656	C₄	—	2	8	no	—
657	C₄	—	2	4	no	—
658	C₄	—	2	4	no	—
659	C₄	—	2	16	no	—
660	C₄	C₂×C₂₃×H(5,𝔽₂)	1	4	yes	—
661	C₂	—	2	2	no	—
662	C₂	—	2	4	no	—
663	C₂	—	4	8	no	—
664	C₂	—	4	8	no	—
665	C₂	C₂²×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
666	C₂	C₂×C₂₃×#585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₂₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3561	C₂	semidirect
2. C₂₃×#3558	C₂	semidirect
3. C₂₃×#3545	C₂	semidirect
4. C₂₃×#3514	C₂	semidirect
5. C₂₃×#3510	C₂	semidirect
6. C₂₃×#3500	C₂	semidirect
7. C₂₃×#3490	C₂	semidirect
8. C₂₃×#3486	C₂	semidirect
9. C₂₃×#3484	C₂	semidirect
10. C₂₃×#3444	C₂	semidirect
11. C₂²×C₂₃×#124	C₂	semidirect
12. C₂×C₂₃×2₋¹⁺⁴	C₂²	semidirect
13. C₂×C₂₃×H(5,𝔽₂)	C₂²	semidirect
14. C₂³×Q₈×C₂₃	C₂²	semidirect
16. C₂₃×#563	C₂²	semidirect
17. C₂₃×#562	C₂²	semidirect
18. C₂₃×H(3,𝔽₄)	C₂²	semidirect
19. C₂₃×#559	C₂²	semidirect
20. C₂₃×#556	C₂²	semidirect
21. C₂₃×#555	C₂²	semidirect
22. C₂₃×#551	C₂²	semidirect
23. C₂₃×#551	C₂²	semidirect
24. C₂₃×#551	C₂²	semidirect
25. D₄×Q₈×C₂₃	C₂²	semidirect
26. C₂₃×#548	C₂²	semidirect
27. C₂₃×#548	C₂²	semidirect
28. C₂₃×#546	C₂²	semidirect
29. C₂₃×#546	C₂²	semidirect
30. C₂₃×#546	C₂²	semidirect
31. C₂₃×#546	C₂²	semidirect
32. D₄²×C₂₃	C₂²	semidirect
33. C₂₃×#543	C₂²	semidirect
34. C₂₃×#542	C₂²	semidirect
35. C₂₃×#542	C₂²	semidirect
36. C₂₃×#538	C₂²	semidirect
37. C₂₃×#538	C₂²	semidirect
38. C₂₃×#538	C₂²	semidirect
39. C₂₃×#536	C₂²	semidirect
40. C₂₃×#536	C₂²	semidirect
41. C₂₃×#536	C₂²	semidirect
43. C₂₃×#535	C₂²	semidirect
44. C₂₃×#534	C₂²	semidirect
45. C₂₃×#534	C₂²	semidirect
46. C₂₃×#533	C₂²	semidirect
47. C₂₃×#533	C₂²	semidirect
48. C₂₃×#532	C₂²	semidirect
49. C₂₃×#532	C₂²	semidirect
50. C₂₃×#532	C₂²	semidirect
51. C₂₃×#529	C₂²	semidirect
52. C₂₃×#529	C₂²	semidirect
53. C₂₃×#529	C₂²	semidirect
54. C₂₃×#529	C₂²	semidirect
55. C₂×C₂₃×#124	C₂²	semidirect
56. C₂×C₂₃×#124	C₂²	semidirect
57. C₂×C₂₃×#124	C₂²	semidirect
58. C₂×C₂₃×#124	C₂²	semidirect
59. C₂×C₂₃×#124	C₂²	semidirect
60. C₂₃×#525	C₂²	semidirect
61. C₂₃×#525	C₂²	semidirect
62. C₂₃×#525	C₂²	semidirect
63. C₂×C₂₃×#120	C₂²	semidirect
64. C₂₃×#519	C₂²	semidirect
65. C₂₃×#518	C₂²	semidirect
66. C₂₃×#518	C₂²	semidirect
67. C₄×#41×C₂₃	C₂²	semidirect
68. C₄×#41×C₂₃	C₂²	semidirect
69. C₂²×C₂²⋊C₄×C₂₃	C₂²	semidirect
70. C₂²×C₄²×C₂₃	C₂²	semidirect
78. C₂×#41×C₂₃	C₂³	semidirect
83. C₂²×Q₈×C₂₃	C₂³	semidirect
94. C₂₃×C₄⋊Q₈	C₂³	semidirect
95. C₂₃×C₄⋊Q₈	C₂³	semidirect
96. C₂₃×C₄⋊Q₈	C₂³	semidirect
97. C₂₃×C₄⋊Q₈	C₂³	semidirect
99. C₂₃×#127	C₂³	semidirect
100. C₂₃×#126	C₂³	semidirect
101. C₂₃×#126	C₂³	semidirect
102. C₂₃×#126	C₂³	semidirect
103. C₂₃×#125	C₂³	semidirect
104. C₂₃×#125	C₂³	semidirect
112. C₂₃×#124	C₂³	semidirect
113. C₂₃×#124	C₂³	semidirect
114. C₂₃×#124	C₂³	semidirect
115. C₂₃×#124	C₂³	semidirect
116. C₂₃×#124	C₂³	semidirect
117. C₂₃×#124	C₂³	semidirect
122. C₂₃×#123	C₂³	semidirect
123. C₂₃×#123	C₂³	semidirect
124. C₂₃×#123	C₂³	semidirect
129. C₂₃×C₂²⋊Q₈	C₂³	semidirect
130. C₂₃×C₂²⋊Q₈	C₂³	semidirect
131. C₂₃×C₂²⋊Q₈	C₂³	semidirect
132. C₂₃×C₂²⋊Q₈	C₂³	semidirect
139. C₂₃×#121	C₂³	semidirect
140. C₂₃×#121	C₂³	semidirect
145. C₂₃×#120	C₂³	semidirect
146. C₄×Q₈×C₂₃	C₂³	semidirect
147. C₄×Q₈×C₂₃	C₂³	semidirect
148. C₄×Q₈×C₂₃	C₂³	semidirect
149. C₄×Q₈×C₂₃	C₂³	semidirect
155. C₄×D₄×C₂₃	C₂³	semidirect
156. C₄×D₄×C₂₃	C₂³	semidirect
157. C₄×D₄×C₂₃	C₂³	semidirect
158. C₄×D₄×C₂₃	C₂³	semidirect
159. C₄×D₄×C₂₃	C₂³	semidirect
163. C₂₃×#117	C₂³	semidirect
164. C₂₃×#117	C₂³	semidirect
165. C₂₃×#117	C₂³	semidirect
172. C₂×C₂²⋊C₄×C₂₃	C₂³	semidirect
177. C₂×C₄²×C₂₃	C₂³	semidirect
257. #62824	C₂₃	direct (N × H)
307. #3561	C₂×C₂₃	semidirect
308. #3558	C₂×C₂₃	semidirect
309. #3545	C₂×C₂₃	semidirect
310. #3514	C₂×C₂₃	semidirect
311. #3510	C₂×C₂₃	semidirect
312. #3500	C₂×C₂₃	semidirect
313. #3490	C₂×C₂₃	semidirect
314. #3486	C₂×C₂₃	semidirect
315. #3484	C₂×C₂₃	semidirect
316. #3444	C₂×C₂₃	semidirect
317. C₂²×#124	C₂×C₂₃	semidirect
339. C₂×2₋¹⁺⁴	C₂²×C₂₃	semidirect
340. C₂×H(5,𝔽₂)	C₂²×C₂₃	semidirect
341. C₂³×Q₈	C₂²×C₂₃	semidirect
343. #563	C₂²×C₂₃	semidirect
344. #562	C₂²×C₂₃	semidirect
345. H(3,𝔽₄)	C₂²×C₂₃	semidirect
346. #559	C₂²×C₂₃	semidirect
347. #556	C₂²×C₂₃	semidirect
348. #555	C₂²×C₂₃	semidirect
349. #551	C₂²×C₂₃	semidirect
350. #551	C₂²×C₂₃	semidirect
351. #551	C₂²×C₂₃	semidirect
352. D₄×Q₈	C₂²×C₂₃	semidirect
353. #548	C₂²×C₂₃	semidirect
354. #548	C₂²×C₂₃	semidirect
355. #546	C₂²×C₂₃	semidirect
356. #546	C₂²×C₂₃	semidirect
357. #546	C₂²×C₂₃	semidirect
358. #546	C₂²×C₂₃	semidirect
359. D₄²	C₂²×C₂₃	semidirect
360. #543	C₂²×C₂₃	semidirect
361. #542	C₂²×C₂₃	semidirect
362. #542	C₂²×C₂₃	semidirect
363. #538	C₂²×C₂₃	semidirect
364. #538	C₂²×C₂₃	semidirect
365. #538	C₂²×C₂₃	semidirect
366. #536	C₂²×C₂₃	semidirect
367. #536	C₂²×C₂₃	semidirect
368. #536	C₂²×C₂₃	semidirect
370. #535	C₂²×C₂₃	semidirect
371. #534	C₂²×C₂₃	semidirect
372. #534	C₂²×C₂₃	semidirect
373. #533	C₂²×C₂₃	semidirect
374. #533	C₂²×C₂₃	semidirect
375. #532	C₂²×C₂₃	semidirect
376. #532	C₂²×C₂₃	semidirect
377. #532	C₂²×C₂₃	semidirect
378. #529	C₂²×C₂₃	semidirect
379. #529	C₂²×C₂₃	semidirect
380. #529	C₂²×C₂₃	semidirect
381. #529	C₂²×C₂₃	semidirect
382. C₂×#124	C₂²×C₂₃	semidirect
383. C₂×#124	C₂²×C₂₃	semidirect
384. C₂×#124	C₂²×C₂₃	semidirect
385. C₂×#124	C₂²×C₂₃	semidirect
386. C₂×#124	C₂²×C₂₃	semidirect
387. #525	C₂²×C₂₃	semidirect
388. #525	C₂²×C₂₃	semidirect
389. #525	C₂²×C₂₃	semidirect
390. C₂×#120	C₂²×C₂₃	semidirect
391. #519	C₂²×C₂₃	semidirect
392. #518	C₂²×C₂₃	semidirect
393. #518	C₂²×C₂₃	semidirect
394. C₄×#41	C₂²×C₂₃	semidirect
395. C₄×#41	C₂²×C₂₃	semidirect
396. C₂²×C₂²⋊C₄	C₂²×C₂₃	semidirect
397. C₂²×C₄²	C₂²×C₂₃	semidirect
411. C₂×#41	C₂³×C₂₃	semidirect
416. C₂²×Q₈	C₂³×C₂₃	semidirect
427. C₄⋊Q₈	C₂³×C₂₃	semidirect
428. C₄⋊Q₈	C₂³×C₂₃	semidirect
429. C₄⋊Q₈	C₂³×C₂₃	semidirect
430. C₄⋊Q₈	C₂³×C₂₃	semidirect
432. #127	C₂³×C₂₃	semidirect
433. #126	C₂³×C₂₃	semidirect
434. #126	C₂³×C₂₃	semidirect
435. #126	C₂³×C₂₃	semidirect
436. #125	C₂³×C₂₃	semidirect
437. #125	C₂³×C₂₃	semidirect
445. #124	C₂³×C₂₃	semidirect
446. #124	C₂³×C₂₃	semidirect
447. #124	C₂³×C₂₃	semidirect
448. #124	C₂³×C₂₃	semidirect
449. #124	C₂³×C₂₃	semidirect
450. #124	C₂³×C₂₃	semidirect
455. #123	C₂³×C₂₃	semidirect
456. #123	C₂³×C₂₃	semidirect
457. #123	C₂³×C₂₃	semidirect
462. C₂²⋊Q₈	C₂³×C₂₃	semidirect
463. C₂²⋊Q₈	C₂³×C₂₃	semidirect
464. C₂²⋊Q₈	C₂³×C₂₃	semidirect
465. C₂²⋊Q₈	C₂³×C₂₃	semidirect
472. #121	C₂³×C₂₃	semidirect
473. #121	C₂³×C₂₃	semidirect
478. #120	C₂³×C₂₃	semidirect
479. C₄×Q₈	C₂³×C₂₃	semidirect
480. C₄×Q₈	C₂³×C₂₃	semidirect
481. C₄×Q₈	C₂³×C₂₃	semidirect
482. C₄×Q₈	C₂³×C₂₃	semidirect
488. C₄×D₄	C₂³×C₂₃	semidirect
489. C₄×D₄	C₂³×C₂₃	semidirect
490. C₄×D₄	C₂³×C₂₃	semidirect
491. C₄×D₄	C₂³×C₂₃	semidirect
492. C₄×D₄	C₂³×C₂₃	semidirect
496. #117	C₂³×C₂₃	semidirect
497. #117	C₂³×C₂₃	semidirect
498. #117	C₂³×C₂₃	semidirect
505. C₂×C₂²⋊C₄	C₂³×C₂₃	semidirect
510. C₂×C₄²	C₂³×C₂₃	semidirect
511. C₂₃	#62824	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×#3561	2
C₂₃×#3558	2
C₂₃×#3545	2
C₂₃×#3514	2
C₂₃×#3510	2
C₂₃×#3500	2
C₂₃×#3490	2
C₂₃×#3486	2
C₂₃×#3484	2
C₂₃×#3444	2
C₂²×C₂₃×#124	2
#62824	23

Subgroups — C23×#62824 #19210450

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#62824 #19210450