Subgroups — C₂₃×#61416 #19209042

Order 5888.

1850 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3507	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3401	C₂	1	8	yes	maximal, complemented
3	C₂₃×#3398	C₂	1	8	yes	maximal, complemented
4	C₂₃×#3156	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3150	C₂	1	1	yes	maximal, characteristic
6	C₂₃×#3046	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3037	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2961	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2952	C₂	1	2	yes	maximal, complemented
10	C₂×C₂₃×#441	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₃×#137	C₂²	1	4	yes	—
12	C₂×C₂₃×#135	C₂²	1	2	yes	—
13	C₂×C₂₃×#135	C₂²	1	2	yes	—
14	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
15	C₂₃×#559	C₂²	1	4	yes	—
16	C₂₃×#557	C₂²	1	4	yes	—
17	C₂₃×#556	—	2	2	no	—
18	C₂₃×#556	C₂²	1	8	yes	—
19	C₂₃×#554	—	2	2	no	—
20	C₂₃×#552	—	2	4	no	—
21	C₂₃×#539	—	2	4	no	—
22	C₂₃×#536	C₂²	1	4	yes	—
23	C₂₃×#533	C₂²	1	1	yes	characteristic
24	C₂₃×#532	C₂²	1	2	yes	—
25	C₂₃×#529	—	2	4	no	—
26	C₂₃×#520	C₂²	1	4	yes	—
27	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
28	C₂₃×#497	C₂²	1	4	yes	—
29	C₂₃×#497	C₂²	1	8	yes	—
30	C₂₃×#496	C₂²	1	4	yes	—
31	C₂₃×#495	C₂²	1	4	yes	—
32	C₂₃×#494	C₂²	1	4	yes	—
33	C₂₃×#464	C₂²	1	8	yes	—
34	C₂₃×#464	C₂²	1	8	yes	—
35	C₂₃×#463	C₂²	1	8	yes	—
36	C₂₃×#462	C₂²	1	4	yes	—
37	C₂₃×#462	C₂²	1	8	yes	—
38	C₂₃×#461	C₂²	1	8	yes	—
39	C₂₃×#460	C₂²	1	4	yes	—
40	C₂₃×#446	C₂²	1	8	yes	—
41	C₂₃×#442	C₂²	1	4	yes	—
42	C₂₃×#441	C₂²	1	8	yes	—
43	C₂₃×#441	C₂²	1	4	yes	—
44	C₄×SD₁₆×C₂₃	C₂²	1	8	yes	—
45	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
46	C₂₃×#424	C₂²	1	2	yes	—
47	C₂₃×#423	C₂²	1	1	yes	characteristic
48	C₂₃×#417	C₂²	1	4	yes	—
49	C₂×C₂₃×#103	C₂²	1	2	yes	—
50	C₂₃×#405	C₂²	1	2	yes	—
51	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
52	C₂×#41×C₂₃	C₂³	1	4	yes	—
53	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
54	C₂₃×#137	—	4	8	no	—
55	C₂₃×#135	—	2	8	no	—
56	C₂₃×#135	—	4	4	no	—
57	C₂×Q₁₆×C₂₃	—	2	4	no	—
58	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
59	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
60	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
61	C₂×Q₁₆×C₂₃	C₂³	1	8	yes	—
62	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
63	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
64	C₂×SD₁₆×C₂₃	C₂³	1	8	yes	—
65	C₂×D₈×C₂₃	C₂³	1	2	yes	—
66	C₂×D₈×C₂₃	C₂³	1	2	yes	—
67	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
68	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
70	C₂₃×C₄⋊Q₈	D₄	1	2	yes	—
71	C₂₃×C₄⋊Q₈	C₂³	1	8	yes	—
72	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
73	C₂₃×#127	C₂³	1	2	yes	—
74	C₂₃×#126	—	2	8	no	—
75	C₂₃×#126	—	2	8	no	—
76	C₂₃×#125	—	2	8	no	—
77	C₂₃×#125	—	2	4	no	—
78	C₂₃×#125	D₄	1	2	yes	—
79	C₂₃×#124	—	2	4	no	—
80	C₂₃×#124	C₂³	1	4	yes	—
81	C₂₃×#124	C₂³	1	8	yes	—
82	C₂₃×#123	—	2	8	no	—
83	C₂₃×#123	—	2	8	no	—
84	C₂₃×C₂²⋊Q₈	—	2	8	no	—
85	C₂₃×C₂²⋊Q₈	—	2	4	no	—
86	C₂₃×C₂²⋊Q₈	—	2	4	no	—
87	C₂₃×C₂²⋊Q₈	D₄	1	4	yes	—
88	C₂₃×#121	—	2	2	no	—
89	C₂₃×#121	—	2	2	no	—
90	C₄×Q₈×C₂₃	—	2	4	no	—
91	C₄×Q₈×C₂₃	—	2	2	no	—
92	C₄×Q₈×C₂₃	—	2	2	no	—
93	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
94	C₄×Q₈×C₂₃	C₂³	1	8	yes	—
95	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
96	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
97	C₄×D₄×C₂₃	—	2	4	no	—
98	C₄×D₄×C₂₃	—	2	8	no	—
99	C₄×D₄×C₂₃	—	2	2	no	—
100	C₄×D₄×C₂₃	—	2	2	no	—
101	C₄×D₄×C₂₃	C₂³	1	8	yes	—
102	C₂₃×#117	—	2	4	no	—
103	C₂₃×#117	—	2	8	no	—
104	C₂₃×#117	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
106	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
107	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
108	C₂×C₄²×C₂₃	—	2	2	no	—
109	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
110	C₂₃×#106	C₂³	1	4	yes	—
111	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
112	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
113	C₂₃×#103	C₂³	1	8	yes	—
114	C₂₃×#103	C₂³	1	8	yes	—
115	C₂₃×#102	C₂³	1	8	yes	—
116	C₂₃×#97	C₂³	1	4	yes	—
117	C₂₃×#97	C₂³	1	4	yes	—
118	C₄×C₈×C₂₃	C₂³	1	4	yes	—
119	#41×C₂₃	—	2	8	no	—
120	#41×C₂₃	—	2	8	no	—
121	C₂×Q₈×C₂₃	—	2	2	no	—
122	C₂×Q₈×C₂₃	—	2	4	no	—
123	C₂×Q₈×C₂₃	—	2	4	no	—
124	C₂×Q₈×C₂₃	C₂×D₄	1	4	yes	—
125	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
126	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
127	C₂×D₄×C₂₃	—	2	4	no	—
128	C₂×D₄×C₂₃	—	2	2	no	—
129	C₂×D₄×C₂₃	—	2	2	no	—
130	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
131	C₂²×C₄×C₂₃	—	2	2	no	—
132	C₂²×C₄×C₂₃	—	2	2	no	—
133	C₂²×C₄×C₂₃	—	2	4	no	—
134	C₂²×C₄×C₂₃	—	2	8	no	—
135	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
137	Q₁₆×C₂₃	—	2	8	no	—
138	Q₁₆×C₂₃	—	2	4	no	—
139	Q₁₆×C₂₃	—	4	2	no	—
140	Q₁₆×C₂₃	—	4	8	no	—
141	SD₁₆×C₂₃	—	2	8	no	—
142	SD₁₆×C₂₃	—	4	4	no	—
143	SD₁₆×C₂₃	—	4	8	no	—
144	D₈×C₂₃	—	2	4	no	—
145	D₈×C₂₃	—	4	2	no	—
146	M₁₆×C₂₃	—	2	4	no	—
147	C₂×C₈×C₂₃	—	2	2	no	—
148	C₂×C₈×C₂₃	#41	1	4	yes	—
149	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
150	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
151	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
152	C₄⋊C₄×C₂₃	—	2	2	no	—
153	C₄⋊C₄×C₂₃	—	2	8	no	—
154	C₄⋊C₄×C₂₃	—	2	4	no	—
155	C₄⋊C₄×C₂₃	—	2	4	no	—
156	C₄⋊C₄×C₂₃	—	2	8	no	—
157	C₄⋊C₄×C₂₃	—	2	2	no	—
158	C₄⋊C₄×C₂₃	—	2	2	no	—
159	C₄⋊C₄×C₂₃	—	2	8	no	—
160	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
161	C₄⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
162	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
163	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
164	C₂²⋊C₄×C₂₃	—	2	4	no	—
165	C₂²⋊C₄×C₂₃	—	2	8	no	—
166	C₂²⋊C₄×C₂₃	—	2	8	no	—
167	C₂²⋊C₄×C₂₃	—	2	4	no	—
168	C₂²⋊C₄×C₂₃	—	2	8	no	—
169	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
170	C₄²×C₂₃	—	2	4	no	—
171	C₄²×C₂₃	—	2	4	no	—
172	C₄²×C₂₃	—	2	8	no	—
173	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₂₃	C₂⁴	1	2	yes	—
176	C₄²×C₂₃	C₂⁴	1	4	yes	—
177	#61416	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂³×C₂₃	—	2	4	no	—
179	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
180	Q₈×C₂₃	—	2	4	no	—
181	Q₈×C₂₃	—	2	4	no	—
182	Q₈×C₂₃	—	2	4	no	—
183	Q₈×C₂₃	—	2	4	no	—
184	Q₈×C₂₃	—	4	4	no	—
185	Q₈×C₂₃	—	4	4	no	—
186	D₄×C₂₃	—	2	4	no	—
187	D₄×C₂₃	—	2	4	no	—
188	D₄×C₂₃	—	4	4	no	—
189	D₄×C₂₃	—	4	8	no	—
190	D₄×C₂₃	—	8	2	no	—
191	C₂×C₄×C₂₃	—	2	4	no	—
192	C₂×C₄×C₂₃	—	2	4	no	—
193	C₂×C₄×C₂₃	—	2	4	no	—
194	C₂×C₄×C₂₃	—	4	2	no	—
195	C₂×C₄×C₂₃	—	4	4	no	—
196	C₂×C₄×C₂₃	—	4	8	no	—
197	C₂×C₄×C₂₃	—	8	8	no	—
198	C₂×C₄×C₂₃	—	8	2	no	—
199	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
200	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
201	C₂×C₄×C₂₃	C₂²×D₄	1	8	yes	—
202	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
204	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
205	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
206	C₈×C₂₃	—	2	2	no	—
207	C₈×C₂₃	—	2	4	no	—
208	C₈×C₂₃	C₂×#41	1	4	yes	—
209	#3507	C₂×C₂₃	1	2	yes	complemented
210	#3401	C₂×C₂₃	1	8	yes	complemented
211	#3398	C₂×C₂₃	1	8	yes	complemented
212	#3156	C₂×C₂₃	1	2	yes	complemented
213	#3150	C₂×C₂₃	1	1	yes	characteristic
214	#3046	C₂×C₂₃	1	4	yes	complemented
215	#3037	C₂×C₂₃	1	2	yes	complemented
216	#2961	C₂×C₂₃	1	1	yes	characteristic, complemented
217	#2952	C₂×C₂₃	1	2	yes	complemented
218	C₂×#441	C₂×C₂₃	1	1	yes	characteristic, complemented
219	C₂²×C₂₃	—	2	2	no	—
220	C₂²×C₂₃	—	4	4	no	—
221	C₂²×C₂₃	—	4	4	no	—
222	C₂²×C₂₃	—	4	4	no	—
223	C₂²×C₂₃	#550	1	2	yes	—
224	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
225	C₄×C₂₃	—	2	2	no	—
226	C₄×C₂₃	—	2	2	no	—
227	C₄×C₂₃	—	2	8	no	—
228	C₄×C₂₃	—	4	4	no	—
229	C₄×C₂₃	—	4	4	no	—
230	C₄×C₂₃	—	4	4	no	—
231	C₄×C₂₃	#550	1	2	yes	—
232	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
233	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
234	C₂×#137	C₂²×C₂₃	1	4	yes	—
235	C₂×#135	C₂²×C₂₃	1	2	yes	—
236	C₂×#135	C₂²×C₂₃	1	2	yes	—
237	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
238	#559	C₂²×C₂₃	1	4	yes	—
239	#557	C₂²×C₂₃	1	4	yes	—
240	#556	—	2	2	no	—
241	#556	C₂²×C₂₃	1	8	yes	—
242	#554	—	2	2	no	—
243	#552	—	2	4	no	—
244	#539	—	2	4	no	—
245	#536	C₂²×C₂₃	1	4	yes	—
246	#533	C₂²×C₂₃	1	1	yes	characteristic
247	#532	C₂²×C₂₃	1	2	yes	—
248	#529	—	2	4	no	—
249	#520	C₂²×C₂₃	1	4	yes	—
250	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
251	#497	C₂²×C₂₃	1	4	yes	—
252	#497	C₂²×C₂₃	1	8	yes	—
253	#496	C₂²×C₂₃	1	4	yes	—
254	#495	C₂²×C₂₃	1	4	yes	—
255	#494	C₂²×C₂₃	1	4	yes	—
256	#464	C₂²×C₂₃	1	8	yes	—
257	#464	C₂²×C₂₃	1	8	yes	—
258	#463	C₂²×C₂₃	1	8	yes	—
259	#462	C₂²×C₂₃	1	4	yes	—
260	#462	C₂²×C₂₃	1	8	yes	—
261	#461	C₂²×C₂₃	1	8	yes	—
262	#460	C₂²×C₂₃	1	4	yes	—
263	#446	C₂²×C₂₃	1	8	yes	—
264	#442	C₂²×C₂₃	1	4	yes	—
265	#441	C₂²×C₂₃	1	4	yes	—
266	#441	C₂²×C₂₃	1	8	yes	—
267	C₄×SD₁₆	C₂²×C₂₃	1	8	yes	—
268	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
269	#424	C₂²×C₂₃	1	2	yes	—
270	#423	C₂²×C₂₃	1	1	yes	characteristic
271	#417	C₂²×C₂₃	1	4	yes	—
272	C₂×#103	C₂²×C₂₃	1	2	yes	—
273	#405	C₂²×C₂₃	1	2	yes	—
274	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
275	C₂×C₂₃	—	2	2	no	—
276	C₂×C₂₃	—	8	4	no	—
277	C₂×C₂₃	C₂×#550	1	1	yes	characteristic
278	C₂×C₂₃	#3586	1	2	yes	—
279	C₂×#41	C₂³×C₂₃	1	4	yes	—
280	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
281	#137	—	4	8	no	—
282	#135	—	2	8	no	—
283	#135	—	4	4	no	—
284	C₂×Q₁₆	—	2	4	no	—
285	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
286	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
287	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
288	C₂×Q₁₆	C₂³×C₂₃	1	8	yes	—
289	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
290	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
291	C₂×SD₁₆	C₂³×C₂₃	1	8	yes	—
292	C₂×D₈	C₂³×C₂₃	1	2	yes	—
293	C₂×D₈	C₂³×C₂₃	1	2	yes	—
294	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
295	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
296	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
297	C₄⋊Q₈	D₄×C₂₃	1	2	yes	—
298	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
299	C₄⋊Q₈	C₂³×C₂₃	1	8	yes	—
300	#127	C₂³×C₂₃	1	2	yes	—
301	#126	—	2	8	no	—
302	#126	—	2	8	no	—
303	#125	—	2	4	no	—
304	#125	—	2	8	no	—
305	#125	D₄×C₂₃	1	2	yes	—
306	#124	—	2	4	no	—
307	#124	C₂³×C₂₃	1	4	yes	—
308	#124	C₂³×C₂₃	1	8	yes	—
309	#123	—	2	8	no	—
310	#123	—	2	8	no	—
311	C₂²⋊Q₈	—	2	8	no	—
312	C₂²⋊Q₈	—	2	4	no	—
313	C₂²⋊Q₈	—	2	4	no	—
314	C₂²⋊Q₈	D₄×C₂₃	1	4	yes	—
315	#121	—	2	2	no	—
316	#121	—	2	2	no	—
317	C₄×Q₈	—	2	4	no	—
318	C₄×Q₈	—	2	2	no	—
319	C₄×Q₈	—	2	2	no	—
320	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
321	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
322	C₄×Q₈	C₂³×C₂₃	1	8	yes	—
323	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
324	C₄×D₄	—	2	4	no	—
325	C₄×D₄	—	2	8	no	—
326	C₄×D₄	—	2	2	no	—
327	C₄×D₄	—	2	2	no	—
328	C₄×D₄	C₂³×C₂₃	1	8	yes	—
329	#117	—	2	4	no	—
330	#117	—	2	8	no	—
331	#117	C₂³×C₂₃	1	2	yes	—
332	C₂×C₄⋊C₄	—	2	2	no	—
333	C₂×C₄⋊C₄	—	2	4	no	—
334	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
335	C₂×C₄²	—	2	2	no	—
336	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
337	#106	C₂³×C₂₃	1	4	yes	—
338	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
339	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
340	#103	C₂³×C₂₃	1	8	yes	—
341	#103	C₂³×C₂₃	1	8	yes	—
342	#102	C₂³×C₂₃	1	8	yes	—
343	#97	C₂³×C₂₃	1	4	yes	—
344	#97	C₂³×C₂₃	1	4	yes	—
345	C₄×C₈	C₂³×C₂₃	1	4	yes	—
346	C₂₃	#61416	1	1	yes	characteristic, direct product factor, Sylow
347	#41	—	2	8	no	—
348	#41	—	2	8	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	4	no	—
351	C₂×Q₈	—	2	4	no	—
352	C₂×Q₈	C₂×D₄×C₂₃	1	4	yes	—
353	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
354	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
355	C₂×D₄	—	2	4	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	8	no	—
363	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
364	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
365	Q₁₆	—	2	8	no	—
366	Q₁₆	—	2	4	no	—
367	Q₁₆	—	4	2	no	—
368	Q₁₆	—	4	8	no	—
369	SD₁₆	—	2	8	no	—
370	SD₁₆	—	4	4	no	—
371	SD₁₆	—	4	8	no	—
372	D₈	—	2	4	no	—
373	D₈	—	4	2	no	—
374	M₁₆	—	2	4	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	#41×C₂₃	1	4	yes	—
377	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
378	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
379	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	8	no	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	2	8	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	8	no	—
388	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
389	C₄⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
390	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
391	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
392	C₂²⋊C₄	—	2	4	no	—
393	C₂²⋊C₄	—	2	8	no	—
394	C₂²⋊C₄	—	2	8	no	—
395	C₂²⋊C₄	—	2	4	no	—
396	C₂²⋊C₄	—	2	8	no	—
397	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
398	C₄²	—	2	4	no	—
399	C₄²	—	2	4	no	—
400	C₄²	—	2	8	no	—
401	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
402	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
403	C₄²	C₂⁴×C₂₃	1	4	yes	—
404	C₄²	C₂⁴×C₂₃	1	2	yes	—
405	C₂³	—	2	4	no	—
406	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
407	Q₈	—	2	4	no	—
408	Q₈	—	2	4	no	—
409	Q₈	—	2	4	no	—
410	Q₈	—	2	4	no	—
411	Q₈	—	4	4	no	—
412	Q₈	—	4	4	no	—
413	D₄	—	2	4	no	—
414	D₄	—	2	4	no	—
415	D₄	—	4	4	no	—
416	D₄	—	4	8	no	—
417	D₄	—	8	2	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	4	8	no	—
424	C₂×C₄	—	8	8	no	—
425	C₂×C₄	—	8	2	no	—
426	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
427	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
428	C₂×C₄	C₂²×D₄×C₂₃	1	8	yes	—
429	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
430	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
431	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
432	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
433	C₈	—	2	2	no	—
434	C₈	—	2	4	no	—
435	C₈	C₂×#41×C₂₃	1	4	yes	—
436	C₂²	—	2	2	no	—
437	C₂²	—	4	4	no	—
438	C₂²	—	4	4	no	—
439	C₂²	—	4	4	no	—
440	C₂²	C₂₃×#550	1	2	yes	—
441	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
442	C₄	—	2	2	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	8	no	—
445	C₄	—	4	4	no	—
446	C₄	—	4	4	no	—
447	C₄	—	4	4	no	—
448	C₄	C₂₃×#550	1	2	yes	—
449	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
450	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
451	C₂	—	2	2	no	—
452	C₂	—	8	4	no	—
453	C₂	C₂×C₂₃×#550	1	1	yes	characteristic
454	C₂	C₂₃×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3150	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3507	C₂	semidirect
2. C₂₃×#3401	C₂	semidirect
3. C₂₃×#3398	C₂	semidirect
4. C₂₃×#3156	C₂	semidirect
6. C₂₃×#3046	C₂	semidirect
7. C₂₃×#3037	C₂	semidirect
8. C₂₃×#2961	C₂	semidirect
9. C₂₃×#2952	C₂	semidirect
10. C₂×C₂₃×#441	C₂	semidirect
177. #61416	C₂₃	direct (N × H)
209. #3507	C₂×C₂₃	semidirect
210. #3401	C₂×C₂₃	semidirect
211. #3398	C₂×C₂₃	semidirect
212. #3156	C₂×C₂₃	semidirect
214. #3046	C₂×C₂₃	semidirect
215. #3037	C₂×C₂₃	semidirect
216. #2961	C₂×C₂₃	semidirect
217. #2952	C₂×C₂₃	semidirect
218. C₂×#441	C₂×C₂₃	semidirect
346. C₂₃	#61416	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×#3507	2
C₂₃×#3401	2
C₂₃×#3398	2
C₂₃×#3156	2
C₂₃×#3150	2
C₂₃×#3046	2
C₂₃×#3037	2
C₂₃×#2961	2
C₂₃×#2952	2
C₂×C₂₃×#441	2
#61416	23

Subgroups — C23×#61416 #19209042

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61416 #19209042