Subgroups — C₂₃×#61290 #19208916

Order 5888.

1774 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3512	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3355	C₂	1	4	yes	maximal, complemented
3	C₂₃×#3352	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3337	C₂	1	8	yes	maximal, complemented
5	C₂×C₂₃×#499	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#3098	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3080	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3060	C₂	1	2	yes	maximal, complemented
9	C₄×C₂₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2931	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2912	C₂	1	2	yes	maximal, complemented
12	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
13	C₂×C₂₃×#131	C₂²	1	2	yes	—
14	C₂₃×#553	—	2	8	no	—
15	C₂₃×#553	C₂²	1	8	yes	—
16	C₂₃×#552	C₂²	1	8	yes	—
17	C₂₃×#541	—	2	2	no	—
18	C₂₃×#540	—	2	2	no	—
19	C₂₃×#537	C₂²	1	4	yes	—
20	C₂₃×#532	C₂²	1	1	yes	characteristic
21	C₂₃×#529	—	2	4	no	—
22	C₂×C₂₃×#125	C₂²	1	2	yes	—
23	C₂₃×#520	C₂²	1	4	yes	—
24	C₄×#41×C₂₃	C₂²	1	2	yes	—
25	C₂₃×#499	C₂²	1	4	yes	—
26	C₂₃×#499	C₂²	1	4	yes	—
27	C₂₃×#485	C₂²	1	8	yes	—
28	C₂₃×#484	C₂²	1	8	yes	—
29	C₂₃×#482	C₂²	1	8	yes	—
30	C₂₃×#480	C₂²	1	8	yes	—
31	C₂₃×#479	C₂²	1	8	yes	—
32	C₂₃×#478	C₂²	1	8	yes	—
33	C₂₃×#470	C₂²	1	4	yes	—
34	C₂₃×#469	C₂²	1	4	yes	—
35	C₂₃×#465	C₂²	1	8	yes	—
36	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
37	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	—
38	C₄×D₈×C₂₃	C₂²	1	2	yes	—
39	C₂₃×#436	C₂²	1	4	yes	—
40	C₈×D₄×C₂₃	C₂²	1	4	yes	—
41	C₂₃×#428	C₂²	1	4	yes	—
42	C₂₃×#428	C₂²	1	8	yes	—
43	C₂₃×#427	C₂²	1	1	yes	characteristic
44	C₂₃×#427	C₂²	1	4	yes	—
45	C₂×C₂₃×#107	C₂²	1	2	yes	—
46	C₂×C₂₃×#106	C₂²	1	2	yes	—
47	C₂×C₂₃×#106	C₂²	1	4	yes	—
48	C₂₃×#423	C₂²	1	1	yes	characteristic
49	C₂₃×#417	C₂²	1	4	yes	—
50	C₂₃×#416	C₂²	1	2	yes	—
51	C₂₃×#408	C₂²	1	2	yes	—
52	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
53	C₂×#41×C₂₃	C₂³	1	2	yes	—
54	C₂×#41×C₂₃	C₂³	1	2	yes	—
55	C₂₃×#135	—	2	4	no	—
56	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
57	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
58	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
59	C₂₃×#131	—	2	8	no	—
60	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
61	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
62	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
63	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
65	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
66	C₂₃×#127	D₄	1	1	yes	characteristic
67	C₂₃×#126	—	2	8	no	—
68	C₂₃×#126	—	2	8	no	—
69	C₂₃×#125	—	2	8	no	—
70	C₂₃×#125	—	2	2	no	—
71	C₂₃×#125	—	2	2	no	—
72	C₂₃×#125	C₂³	1	8	yes	—
73	C₂₃×#124	D₄	1	2	yes	—
74	C₂₃×#123	—	2	8	no	—
75	C₂₃×#123	—	2	8	no	—
76	C₂₃×C₂²⋊Q₈	—	2	4	no	—
77	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
78	C₂₃×#121	—	2	8	no	—
79	C₂₃×#121	—	2	8	no	—
80	C₂₃×#121	—	2	4	no	—
81	C₂₃×#121	D₄	1	4	yes	—
82	C₂₃×#121	C₂³	1	8	yes	—
83	C₄×Q₈×C₂₃	—	2	4	no	—
84	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
85	C₄×D₄×C₂₃	—	2	8	no	—
86	C₄×D₄×C₂₃	—	2	4	no	—
87	C₄×D₄×C₂₃	—	2	4	no	—
88	C₄×D₄×C₂₃	—	2	8	no	—
89	C₄×D₄×C₂₃	C₂³	1	4	yes	—
90	C₄×D₄×C₂₃	C₂³	1	4	yes	—
91	C₂₃×#117	—	2	8	no	—
92	C₂₃×#117	—	2	2	no	—
93	C₂₃×#117	C₂³	1	8	yes	—
94	C₂₃×#117	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
96	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
97	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
98	C₂×C₄²×C₂₃	—	2	2	no	—
99	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
100	C₂₃×#107	C₂³	1	4	yes	—
101	C₂₃×#107	C₂³	1	4	yes	—
102	C₂₃×#107	C₂³	1	2	yes	—
103	C₂₃×#107	C₂³	1	8	yes	—
104	C₂₃×#106	C₂³	1	2	yes	—
105	C₂₃×#106	C₂³	1	4	yes	—
106	C₂₃×#106	C₂³	1	4	yes	—
107	C₂₃×#106	C₂³	1	8	yes	—
108	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
109	C₂₃×#103	C₂³	1	4	yes	—
110	C₂₃×#103	C₂³	1	8	yes	—
111	C₂₃×#102	C₂³	1	4	yes	—
112	C₂₃×#102	C₂³	1	8	yes	—
113	C₂₃×C₂²⋊C₈	C₂³	1	8	yes	—
114	C₄×C₈×C₂₃	C₂³	1	2	yes	—
115	C₄×C₈×C₂₃	C₂³	1	2	yes	—
116	#41×C₂₃	—	2	4	no	—
117	#41×C₂₃	—	2	4	no	—
118	#41×C₂₃	—	2	4	no	—
119	#41×C₂₃	—	2	4	no	—
120	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
121	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
122	C₂×D₄×C₂₃	—	2	2	no	—
123	C₂×D₄×C₂₃	—	2	8	no	—
124	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
125	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
126	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
127	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
128	C₂²×C₄×C₂₃	—	2	4	no	—
129	C₂²×C₄×C₂₃	—	2	8	no	—
130	C₂²×C₄×C₂₃	—	2	2	no	—
131	C₂²×C₄×C₂₃	—	2	4	no	—
132	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
134	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
135	Q₁₆×C₂₃	—	2	2	no	—
136	SD₁₆×C₂₃	—	2	4	no	—
137	D₈×C₂₃	—	2	2	no	—
138	M₁₆×C₂₃	—	2	4	no	—
139	M₁₆×C₂₃	—	2	8	no	—
140	C₂×C₈×C₂₃	—	2	2	no	—
141	C₂×C₈×C₂₃	—	2	8	no	—
142	C₂×C₈×C₂₃	#41	1	4	yes	—
143	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
144	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
145	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
146	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
147	C₄⋊C₄×C₂₃	—	2	8	no	—
148	C₄⋊C₄×C₂₃	—	2	8	no	—
149	C₄⋊C₄×C₂₃	—	2	4	no	—
150	C₄⋊C₄×C₂₃	—	2	8	no	—
151	C₄⋊C₄×C₂₃	—	2	4	no	—
152	C₄⋊C₄×C₂₃	—	2	8	no	—
153	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
154	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
155	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
156	C₂²⋊C₄×C₂₃	—	2	8	no	—
157	C₂²⋊C₄×C₂₃	—	2	2	no	—
158	C₂²⋊C₄×C₂₃	—	2	8	no	—
159	C₂²⋊C₄×C₂₃	—	2	4	no	—
160	C₂²⋊C₄×C₂₃	—	2	8	no	—
161	C₂²⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
162	C₄²×C₂₃	—	2	4	no	—
163	C₄²×C₂₃	—	2	2	no	—
164	C₄²×C₂₃	—	2	8	no	—
165	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₂₃	C₂⁴	1	2	yes	—
168	#61290	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₂³×C₂₃	—	2	2	no	—
170	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
171	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
172	Q₈×C₂₃	—	2	4	no	—
173	Q₈×C₂₃	—	2	2	no	—
174	Q₈×C₂₃	—	2	2	no	—
175	D₄×C₂₃	—	2	8	no	—
176	D₄×C₂₃	—	2	4	no	—
177	D₄×C₂₃	—	2	2	no	—
178	D₄×C₂₃	—	2	2	no	—
179	D₄×C₂₃	—	4	4	no	—
180	D₄×C₂₃	—	4	4	no	—
181	D₄×C₂₃	—	8	8	no	—
182	C₂×C₄×C₂₃	—	2	4	no	—
183	C₂×C₄×C₂₃	—	2	4	no	—
184	C₂×C₄×C₂₃	—	2	4	no	—
185	C₂×C₄×C₂₃	—	2	2	no	—
186	C₂×C₄×C₂₃	—	2	8	no	—
187	C₂×C₄×C₂₃	—	4	2	no	—
188	C₂×C₄×C₂₃	—	4	4	no	—
189	C₂×C₄×C₂₃	—	8	4	no	—
190	C₂×C₄×C₂₃	—	8	8	no	—
191	C₂×C₄×C₂₃	—	8	4	no	—
192	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
193	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
194	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
195	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
197	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
198	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
199	C₈×C₂₃	—	2	4	no	—
200	C₈×C₂₃	—	2	2	no	—
201	C₈×C₂₃	C₂×#41	1	2	yes	—
202	C₈×C₂₃	C₂×#41	1	2	yes	—
203	#3512	C₂×C₂₃	1	2	yes	complemented
204	#3355	C₂×C₂₃	1	4	yes	complemented
205	#3352	C₂×C₂₃	1	4	yes	complemented
206	#3337	C₂×C₂₃	1	8	yes	complemented
207	C₂×#499	C₂×C₂₃	1	1	yes	characteristic, complemented
208	#3098	C₂×C₂₃	1	4	yes	complemented
209	#3080	C₂×C₂₃	1	2	yes	complemented
210	#3060	C₂×C₂₃	1	2	yes	complemented
211	C₄×#135	C₂×C₂₃	1	1	yes	characteristic, complemented
212	#2931	C₂×C₂₃	1	1	yes	characteristic, complemented
213	#2912	C₂×C₂₃	1	2	yes	complemented
214	C₂²×C₂₃	—	2	2	no	—
215	C₂²×C₂₃	—	2	8	no	—
216	C₂²×C₂₃	—	2	4	no	—
217	C₂²×C₂₃	—	4	4	no	—
218	C₂²×C₂₃	—	4	2	no	—
219	C₂²×C₂₃	#547	1	2	yes	—
220	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
221	C₄×C₂₃	—	2	2	no	—
222	C₄×C₂₃	—	2	2	no	—
223	C₄×C₂₃	—	2	4	no	—
224	C₄×C₂₃	—	4	4	no	—
225	C₄×C₂₃	—	4	8	no	—
226	C₄×C₂₃	—	4	2	no	—
227	C₄×C₂₃	#547	1	2	yes	—
228	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
229	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
230	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
231	C₂×#131	C₂²×C₂₃	1	2	yes	—
232	#553	—	2	8	no	—
233	#553	C₂²×C₂₃	1	8	yes	—
234	#552	C₂²×C₂₃	1	8	yes	—
235	#541	—	2	2	no	—
236	#540	—	2	2	no	—
237	#537	C₂²×C₂₃	1	4	yes	—
238	#532	C₂²×C₂₃	1	1	yes	characteristic
239	#529	—	2	4	no	—
240	C₂×#125	C₂²×C₂₃	1	2	yes	—
241	#520	C₂²×C₂₃	1	4	yes	—
242	C₄×#41	C₂²×C₂₃	1	2	yes	—
243	#499	C₂²×C₂₃	1	4	yes	—
244	#499	C₂²×C₂₃	1	4	yes	—
245	#485	C₂²×C₂₃	1	8	yes	—
246	#484	C₂²×C₂₃	1	8	yes	—
247	#482	C₂²×C₂₃	1	8	yes	—
248	#480	C₂²×C₂₃	1	8	yes	—
249	#479	C₂²×C₂₃	1	8	yes	—
250	#478	C₂²×C₂₃	1	8	yes	—
251	#470	C₂²×C₂₃	1	4	yes	—
252	#469	C₂²×C₂₃	1	4	yes	—
253	#465	C₂²×C₂₃	1	8	yes	—
254	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
255	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	—
256	C₄×D₈	C₂²×C₂₃	1	2	yes	—
257	#436	C₂²×C₂₃	1	4	yes	—
258	C₈×D₄	C₂²×C₂₃	1	4	yes	—
259	#428	C₂²×C₂₃	1	4	yes	—
260	#428	C₂²×C₂₃	1	8	yes	—
261	#427	C₂²×C₂₃	1	4	yes	—
262	#427	C₂²×C₂₃	1	1	yes	characteristic
263	C₂×#107	C₂²×C₂₃	1	2	yes	—
264	C₂×#106	C₂²×C₂₃	1	4	yes	—
265	C₂×#106	C₂²×C₂₃	1	2	yes	—
266	#423	C₂²×C₂₃	1	1	yes	characteristic
267	#417	C₂²×C₂₃	1	4	yes	—
268	#416	C₂²×C₂₃	1	2	yes	—
269	#408	C₂²×C₂₃	1	2	yes	—
270	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
271	C₂×C₂₃	—	2	2	no	—
272	C₂×C₂₃	—	4	4	no	—
273	C₂×C₂₃	—	8	2	no	—
274	C₂×C₂₃	C₂×#547	1	1	yes	characteristic
275	C₂×C₂₃	#3584	1	2	yes	—
276	C₂×#41	C₂³×C₂₃	1	2	yes	—
277	C₂×#41	C₂³×C₂₃	1	2	yes	—
278	#135	—	2	4	no	—
279	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
280	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
281	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
282	#131	—	2	8	no	—
283	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
284	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
285	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
286	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
287	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
288	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
289	#127	D₄×C₂₃	1	1	yes	characteristic
290	#126	—	2	8	no	—
291	#126	—	2	8	no	—
292	#125	—	2	8	no	—
293	#125	—	2	2	no	—
294	#125	—	2	2	no	—
295	#125	C₂³×C₂₃	1	8	yes	—
296	#124	D₄×C₂₃	1	2	yes	—
297	#123	—	2	8	no	—
298	#123	—	2	8	no	—
299	C₂²⋊Q₈	—	2	4	no	—
300	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
301	#121	—	2	4	no	—
302	#121	—	2	8	no	—
303	#121	—	2	8	no	—
304	#121	D₄×C₂₃	1	4	yes	—
305	#121	C₂³×C₂₃	1	8	yes	—
306	C₄×Q₈	—	2	4	no	—
307	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
308	C₄×D₄	—	2	4	no	—
309	C₄×D₄	—	2	8	no	—
310	C₄×D₄	—	2	4	no	—
311	C₄×D₄	—	2	8	no	—
312	C₄×D₄	C₂³×C₂₃	1	4	yes	—
313	C₄×D₄	C₂³×C₂₃	1	4	yes	—
314	#117	—	2	8	no	—
315	#117	—	2	2	no	—
316	#117	C₂³×C₂₃	1	2	yes	—
317	#117	C₂³×C₂₃	1	8	yes	—
318	C₂×C₄⋊C₄	—	2	4	no	—
319	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
320	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
321	C₂×C₄²	—	2	2	no	—
322	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
323	#107	C₂³×C₂₃	1	4	yes	—
324	#107	C₂³×C₂₃	1	4	yes	—
325	#107	C₂³×C₂₃	1	2	yes	—
326	#107	C₂³×C₂₃	1	8	yes	—
327	#106	C₂³×C₂₃	1	2	yes	—
328	#106	C₂³×C₂₃	1	4	yes	—
329	#106	C₂³×C₂₃	1	4	yes	—
330	#106	C₂³×C₂₃	1	8	yes	—
331	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
332	#103	C₂³×C₂₃	1	4	yes	—
333	#103	C₂³×C₂₃	1	8	yes	—
334	#102	C₂³×C₂₃	1	4	yes	—
335	#102	C₂³×C₂₃	1	8	yes	—
336	C₂²⋊C₈	C₂³×C₂₃	1	8	yes	—
337	C₄×C₈	C₂³×C₂₃	1	2	yes	—
338	C₄×C₈	C₂³×C₂₃	1	2	yes	—
339	C₂₃	#61290	1	1	yes	characteristic, direct product factor, Sylow
340	#41	—	2	4	no	—
341	#41	—	2	4	no	—
342	#41	—	2	4	no	—
343	#41	—	2	4	no	—
344	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
345	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	8	no	—
348	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
349	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
350	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
351	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	8	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
357	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
358	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
359	Q₁₆	—	2	2	no	—
360	SD₁₆	—	2	4	no	—
361	D₈	—	2	2	no	—
362	M₁₆	—	2	4	no	—
363	M₁₆	—	2	8	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	8	no	—
366	C₂×C₈	#41×C₂₃	1	4	yes	—
367	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
368	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
369	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
370	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
371	C₄⋊C₄	—	2	8	no	—
372	C₄⋊C₄	—	2	8	no	—
373	C₄⋊C₄	—	2	4	no	—
374	C₄⋊C₄	—	2	8	no	—
375	C₄⋊C₄	—	2	4	no	—
376	C₄⋊C₄	—	2	8	no	—
377	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
378	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
379	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
380	C₂²⋊C₄	—	2	8	no	—
381	C₂²⋊C₄	—	2	2	no	—
382	C₂²⋊C₄	—	2	8	no	—
383	C₂²⋊C₄	—	2	4	no	—
384	C₂²⋊C₄	—	2	8	no	—
385	C₂²⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
386	C₄²	—	2	4	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	2	8	no	—
389	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
390	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
391	C₄²	C₂⁴×C₂₃	1	2	yes	—
392	C₂³	—	2	2	no	—
393	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
394	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
395	Q₈	—	2	4	no	—
396	Q₈	—	2	2	no	—
397	Q₈	—	2	2	no	—
398	D₄	—	2	8	no	—
399	D₄	—	2	4	no	—
400	D₄	—	2	2	no	—
401	D₄	—	2	2	no	—
402	D₄	—	4	4	no	—
403	D₄	—	4	4	no	—
404	D₄	—	8	8	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	8	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	8	4	no	—
413	C₂×C₄	—	8	8	no	—
414	C₂×C₄	—	8	4	no	—
415	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
416	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
417	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
418	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
419	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
420	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
421	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
422	C₈	—	2	4	no	—
423	C₈	—	2	2	no	—
424	C₈	C₂×#41×C₂₃	1	2	yes	—
425	C₈	C₂×#41×C₂₃	1	2	yes	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	4	no	—
428	C₂²	—	2	8	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	4	no	—
431	C₂²	C₂₃×#547	1	2	yes	—
432	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
433	C₄	—	2	4	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	4	no	—
438	C₄	—	4	8	no	—
439	C₄	C₂₃×#547	1	2	yes	—
440	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
441	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
442	C₂	—	2	2	no	—
443	C₂	—	4	4	no	—
444	C₂	—	8	2	no	—
445	C₂	C₂×C₂₃×#547	1	1	yes	characteristic
446	C₂	C₂₃×#3584	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3512	C₂	semidirect
2. C₂₃×#3355	C₂	semidirect
3. C₂₃×#3352	C₂	semidirect
4. C₂₃×#3337	C₂	semidirect
5. C₂×C₂₃×#499	C₂	semidirect
6. C₂₃×#3098	C₂	semidirect
7. C₂₃×#3080	C₂	semidirect
8. C₂₃×#3060	C₂	semidirect
9. C₄×C₂₃×#135	C₂	semidirect
10. C₂₃×#2931	C₂	semidirect
11. C₂₃×#2912	C₂	semidirect
168. #61290	C₂₃	direct (N × H)
203. #3512	C₂×C₂₃	semidirect
204. #3355	C₂×C₂₃	semidirect
205. #3352	C₂×C₂₃	semidirect
206. #3337	C₂×C₂₃	semidirect
207. C₂×#499	C₂×C₂₃	semidirect
208. #3098	C₂×C₂₃	semidirect
209. #3080	C₂×C₂₃	semidirect
210. #3060	C₂×C₂₃	semidirect
211. C₄×#135	C₂×C₂₃	semidirect
212. #2931	C₂×C₂₃	semidirect
213. #2912	C₂×C₂₃	semidirect
339. C₂₃	#61290	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×#3512	2
C₂₃×#3355	2
C₂₃×#3352	2
C₂₃×#3337	2
C₂×C₂₃×#499	2
C₂₃×#3098	2
C₂₃×#3080	2
C₂₃×#3060	2
C₄×C₂₃×#135	2
C₂₃×#2931	2
C₂₃×#2912	2
#61290	23

Subgroups — C23×#61290 #19208916

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61290 #19208916