Subgroups — C₂₃×#60432 #19208058

Order 5888.

2646 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#578	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₂₃×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3046	C₂	1	6	yes	maximal, complemented
5	C₂₃×#3044	C₂	1	6	yes	maximal, complemented
6	C₂₃×#3039	C₂	1	3	yes	maximal, complemented
7	C₂₃×#3037	C₂	1	3	yes	maximal, complemented
8	C₂₃×#3035	C₂	1	3	yes	maximal, complemented
9	C₂×C₂₃×#462	C₂	1	3	yes	maximal, complemented
10	C₂₃×#2906	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2898	C₂	1	2	yes	maximal, complemented
12	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	2	yes	—
13	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
14	C₂₃×#578	—	2	16	no	—
15	C₂×C₂₃×#137	C₂²	1	6	yes	—
16	C₂×C₂₃×#137	C₂²	1	6	yes	—
17	C₂×C₂₃×#135	C₂²	1	6	yes	—
18	C₂²×Q₁₆×C₂₃	C₂²	1	6	yes	—
19	C₂×C₂₃×#131	C₂²	1	2	yes	—
20	D₄×Q₈×C₂₃	—	2	1	no	—
21	D₄×Q₈×C₂₃	—	2	1	no	—
22	C₂₃×#547	—	2	3	no	—
23	C₂₃×#547	—	2	3	no	—
24	C₂₃×#536	C₂²	1	6	yes	—
25	C₂₃×#532	C₂²	1	3	yes	—
26	C₂×C₂₃×C₄⋊Q₈	C₂²	1	3	yes	—
27	C₂₃×#520	—	2	3	no	—
28	C₂₃×#520	C₂²	1	3	yes	—
29	C₂₃×#520	C₂²	1	1	yes	characteristic
30	C₂₃×#519	—	2	1	no	—
31	C₂₃×#519	C₂²	1	3	yes	—
32	C₄×#41×C₂₃	—	2	3	no	—
33	C₄×#41×C₂₃	C₂²	1	3	yes	—
34	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
36	C₂×C₄×Q₈×C₂₃	C₂²	1	3	yes	—
37	C₂₃×#464	C₂²	1	6	yes	—
38	C₂₃×#464	C₂²	1	12	yes	—
39	C₂₃×#463	C₂²	1	6	yes	—
40	C₂₃×#462	C₂²	1	3	yes	—
41	C₂₃×#462	C₂²	1	6	yes	—
42	C₂₃×#462	C₂²	1	12	yes	—
43	C₂₃×#462	C₂²	1	6	yes	—
44	C₂₃×#461	C₂²	1	3	yes	—
45	C₂₃×#461	C₂²	1	6	yes	—
46	C₂₃×#460	C₂²	1	3	yes	—
47	C₂₃×#459	C₂²	1	1	yes	characteristic
48	C₂₃×#424	C₂²	1	6	yes	—
49	C₂₃×#423	C₂²	1	3	yes	—
50	C₂×C₂₃×C₄⋊C₈	C₂²	1	3	yes	—
51	C₂₃×#419	C₂²	1	6	yes	—
52	C₂₃×#417	C₂²	1	6	yes	—
53	C₂₃×#416	C₂²	1	6	yes	—
54	C₂×C₂₃×#103	C₂²	1	6	yes	—
55	C₂₃×2₋¹⁺⁴	—	2	4	no	—
56	C₂₃×2₋¹⁺⁴	—	2	8	no	—
57	C₂₃×2₋¹⁺⁴	—	2	8	no	—
58	C₂₃×2₋¹⁺⁴	D₄	1	8	yes	complemented
59	C₂×#41×C₂₃	—	2	3	no	—
60	C₂×#41×C₂₃	—	2	6	no	—
61	C₂×#41×C₂₃	C₂³	1	6	yes	—
62	C₂×#41×C₂₃	C₂³	1	3	yes	—
63	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
64	C₂²×Q₈×C₂₃	—	2	1	no	—
65	C₂²×Q₈×C₂₃	—	2	2	no	—
66	C₂²×Q₈×C₂₃	C₂³	1	6	yes	—
67	C₂²×Q₈×C₂₃	C₂³	1	3	yes	—
68	C₂₃×#137	—	2	24	no	—
69	C₂₃×#137	—	2	24	no	—
70	C₂₃×#135	—	2	24	no	—
71	C₂×Q₁₆×C₂₃	—	2	24	no	—
72	C₂×Q₁₆×C₂₃	C₂³	1	6	yes	—
73	C₂×Q₁₆×C₂₃	C₂³	1	12	yes	—
74	C₂×SD₁₆×C₂₃	C₂³	1	6	yes	—
75	C₂×SD₁₆×C₂₃	C₂³	1	6	yes	—
76	C₂×D₈×C₂₃	C₂³	1	2	yes	—
77	C₂₃×#131	—	2	8	no	—
78	C₂×M₁₆×C₂₃	C₂³	1	6	yes	—
79	C₂²×C₈×C₂₃	C₂³	1	6	yes	—
80	C₂₃×C₄⋊Q₈	—	2	3	no	—
81	C₂₃×C₄⋊Q₈	—	2	3	no	—
82	C₂₃×C₄⋊Q₈	C₂³	1	3	yes	—
83	C₂₃×C₄⋊Q₈	C₂³	1	6	yes	—
84	C₂₃×#127	C₂³	1	1	yes	characteristic
85	C₂₃×#124	C₂³	1	6	yes	—
86	C₂₃×#123	—	2	12	no	—
87	C₂₃×C₂²⋊Q₈	—	2	6	no	—
88	C₂₃×C₂²⋊Q₈	—	2	6	no	—
89	C₂₃×#121	—	2	3	no	—
90	C₂₃×#121	—	2	3	no	—
91	C₄×Q₈×C₂₃	—	2	1	no	—
92	C₄×Q₈×C₂₃	—	2	3	no	—
93	C₄×Q₈×C₂₃	—	2	3	no	—
94	C₄×Q₈×C₂₃	—	2	3	no	—
95	C₄×Q₈×C₂₃	—	2	3	no	—
96	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
97	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
98	C₄×Q₈×C₂₃	C₂³	1	3	yes	—
99	C₄×Q₈×C₂₃	C₂³	1	6	yes	—
100	C₄×Q₈×C₂₃	C₂³	1	3	yes	—
101	C₄×D₄×C₂₃	—	2	3	no	—
102	C₄×D₄×C₂₃	—	2	3	no	—
103	C₄×D₄×C₂₃	—	2	3	no	—
104	C₄×D₄×C₂₃	—	2	6	no	—
105	C₄×D₄×C₂₃	—	2	3	no	—
106	C₄×D₄×C₂₃	—	2	3	no	—
107	C₄×D₄×C₂₃	D₄	1	3	yes	—
108	C₄×D₄×C₂₃	D₄	1	3	yes	—
109	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
110	C₄×D₄×C₂₃	C₂³	1	3	yes	—
111	C₂₃×#117	—	2	3	no	—
112	C₂₃×#117	—	2	6	no	—
113	C₂₃×#117	—	2	3	no	—
114	C₂₃×#117	C₂³	1	3	yes	—
115	C₂₃×#117	C₂³	1	3	yes	—
116	C₂×C₄⋊C₄×C₂₃	—	2	3	no	—
117	C₂×C₄⋊C₄×C₂₃	—	2	3	no	—
118	C₂×C₄⋊C₄×C₂₃	—	2	3	no	—
119	C₂×C₄⋊C₄×C₂₃	—	2	3	no	—
120	C₂×C₄⋊C₄×C₂₃	C₂³	1	3	yes	—
121	C₂×C₄²×C₂₃	—	2	3	no	—
122	C₂×C₄²×C₂₃	—	2	3	no	—
123	C₂×C₄²×C₂₃	C₂³	1	3	yes	—
124	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
125	C₂₃×C₄⋊C₈	C₂³	1	3	yes	—
126	C₂₃×C₄⋊C₈	C₂³	1	6	yes	—
127	C₂₃×C₄⋊C₈	C₂³	1	6	yes	—
128	C₂₃×#103	C₂³	1	6	yes	—
129	C₂₃×#103	C₂³	1	12	yes	—
130	C₂₃×#103	C₂³	1	6	yes	—
131	C₂₃×#102	C₂³	1	2	yes	—
132	C₂₃×#102	C₂³	1	6	yes	—
133	#41×C₂₃	—	2	24	no	—
134	#41×C₂₃	—	2	6	no	—
135	#41×C₂₃	—	2	12	no	—
136	#41×C₂₃	—	2	12	no	—
137	#41×C₂₃	—	4	24	no	—
138	#41×C₂₃	C₂×D₄	1	12	yes	—
139	#41×C₂₃	C₂×D₄	1	4	yes	—
140	#41×C₂₃	#41	1	4	yes	—
141	C₂×Q₈×C₂₃	—	2	8	no	—
142	C₂×Q₈×C₂₃	—	2	3	no	—
143	C₂×Q₈×C₂₃	—	2	6	no	—
144	C₂×Q₈×C₂₃	—	2	6	no	—
145	C₂×Q₈×C₂₃	—	2	12	no	—
146	C₂×Q₈×C₂₃	—	2	12	no	—
147	C₂×Q₈×C₂₃	—	4	8	no	—
148	C₂×Q₈×C₂₃	C₂×D₄	1	12	yes	—
149	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
150	C₂×Q₈×C₂₃	C₂⁴	1	6	yes	—
151	C₂×Q₈×C₂₃	C₂⁴	1	3	yes	—
152	C₂×D₄×C₂₃	—	2	3	no	—
153	C₂×D₄×C₂₃	—	2	6	no	—
154	C₂×D₄×C₂₃	—	2	1	no	—
155	C₂×D₄×C₂₃	—	2	1	no	—
156	C₂×D₄×C₂₃	C₂×D₄	1	3	yes	—
157	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
158	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
159	C₂²×C₄×C₂₃	—	2	3	no	—
160	C₂²×C₄×C₂₃	—	2	3	no	—
161	C₂²×C₄×C₂₃	—	2	6	no	—
162	C₂²×C₄×C₂₃	—	2	3	no	—
163	C₂²×C₄×C₂₃	—	2	1	no	—
164	C₂²×C₄×C₂₃	—	2	6	no	—
165	C₂²×C₄×C₂₃	—	2	3	no	—
166	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
167	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
168	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
169	Q₁₆×C₂₃	—	2	12	no	—
170	Q₁₆×C₂₃	—	2	24	no	—
171	SD₁₆×C₂₃	—	2	12	no	—
172	SD₁₆×C₂₃	—	2	12	no	—
173	D₈×C₂₃	—	2	4	no	—
174	M₁₆×C₂₃	—	2	12	no	—
175	C₂×C₈×C₂₃	—	2	12	no	—
176	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
177	C₂×C₈×C₂₃	C₂⁴	1	6	yes	—
178	C₄⋊C₄×C₂₃	—	2	6	no	—
179	C₄⋊C₄×C₂₃	—	2	3	no	—
180	C₄⋊C₄×C₂₃	—	2	3	no	—
181	C₄⋊C₄×C₂₃	—	2	3	no	—
182	C₄⋊C₄×C₂₃	—	2	3	no	—
183	C₄⋊C₄×C₂₃	—	2	6	no	—
184	C₄⋊C₄×C₂₃	—	2	6	no	—
185	C₄⋊C₄×C₂₃	—	2	3	no	—
186	C₄⋊C₄×C₂₃	C₂×D₄	1	3	yes	—
187	C₄⋊C₄×C₂₃	C₂×D₄	1	3	yes	—
188	C₄⋊C₄×C₂₃	C₂⁴	1	3	yes	—
189	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
190	C₂²⋊C₄×C₂₃	—	2	3	no	—
191	C₂²⋊C₄×C₂₃	—	2	1	no	—
192	C₂²⋊C₄×C₂₃	—	2	3	no	—
193	C₂²⋊C₄×C₂₃	—	2	6	no	—
194	C₂²⋊C₄×C₂₃	—	2	6	no	—
195	C₂²⋊C₄×C₂₃	C₂×D₄	1	6	yes	—
196	C₄²×C₂₃	—	2	3	no	—
197	C₄²×C₂₃	—	2	3	no	—
198	C₄²×C₂₃	—	2	6	no	—
199	C₄²×C₂₃	—	2	3	no	—
200	C₄²×C₂₃	C₂×D₄	1	3	yes	—
201	C₄²×C₂₃	C₂×D₄	1	3	yes	—
202	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
203	C₄²×C₂₃	C₂⁴	1	3	yes	—
204	#60432	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂³×C₂₃	—	2	1	no	—
206	C₂³×C₂₃	—	2	2	no	—
207	C₂³×C₂₃	C₂²×D₄	1	3	yes	—
208	Q₈×C₂₃	—	2	12	no	—
209	Q₈×C₂₃	—	2	3	no	—
210	Q₈×C₂₃	—	2	6	no	—
211	Q₈×C₂₃	—	2	6	no	—
212	Q₈×C₂₃	—	4	12	no	—
213	Q₈×C₂₃	#121	1	4	yes	—
214	Q₈×C₂₃	C₂²×D₄	1	6	yes	—
215	D₄×C₂₃	—	2	12	no	—
216	D₄×C₂₃	—	2	2	no	—
217	D₄×C₂₃	—	2	1	no	—
218	D₄×C₂₃	—	2	2	no	—
219	D₄×C₂₃	—	4	2	no	—
220	D₄×C₂₃	—	4	12	no	—
221	D₄×C₂₃	—	4	2	no	—
222	D₄×C₂₃	#121	1	12	yes	—
223	D₄×C₂₃	C₂²×D₄	1	2	yes	—
224	C₂×C₄×C₂₃	—	2	12	no	—
225	C₂×C₄×C₂₃	—	2	3	no	—
226	C₂×C₄×C₂₃	—	2	12	no	—
227	C₂×C₄×C₂₃	—	2	6	no	—
228	C₂×C₄×C₂₃	—	2	1	no	—
229	C₂×C₄×C₂₃	—	2	3	no	—
230	C₂×C₄×C₂₃	—	2	6	no	—
231	C₂×C₄×C₂₃	—	4	3	no	—
232	C₂×C₄×C₂₃	—	4	12	no	—
233	C₂×C₄×C₂₃	—	4	12	no	—
234	C₂×C₄×C₂₃	—	4	2	no	—
235	C₂×C₄×C₂₃	—	8	3	no	—
236	C₂×C₄×C₂₃	—	8	3	no	—
237	C₂×C₄×C₂₃	C₂²×D₄	1	3	yes	—
238	C₂×C₄×C₂₃	C₂²×D₄	1	3	yes	—
239	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₂₃	C₂²×D₄	1	3	yes	—
241	C₂×C₄×C₂₃	C₂²×D₄	1	6	yes	—
242	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₂₃	C₂×#41	1	6	yes	—
244	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
245	C₈×C₂₃	—	2	2	no	—
246	C₈×C₂₃	—	2	6	no	—
247	C₂×#578	C₂×C₂₃	1	2	yes	complemented
248	#3499	C₂×C₂₃	1	1	yes	characteristic, complemented
249	C₄×2₋¹⁺⁴	C₂×C₂₃	1	1	yes	characteristic, complemented
250	#3046	C₂×C₂₃	1	6	yes	complemented
251	#3044	C₂×C₂₃	1	6	yes	complemented
252	#3039	C₂×C₂₃	1	3	yes	complemented
253	#3037	C₂×C₂₃	1	3	yes	complemented
254	#3035	C₂×C₂₃	1	3	yes	complemented
255	C₂×#462	C₂×C₂₃	1	3	yes	complemented
256	#2906	C₂×C₂₃	1	1	yes	characteristic, complemented
257	#2898	C₂×C₂₃	1	2	yes	complemented
258	C₂²×C₂₃	—	2	3	no	—
259	C₂²×C₂₃	—	2	3	no	—
260	C₂²×C₂₃	—	2	2	no	—
261	C₂²×C₂₃	—	4	1	no	—
262	C₂²×C₂₃	—	4	1	no	—
263	C₂²×C₂₃	—	4	2	no	—
264	C₂²×C₂₃	—	4	2	no	—
265	C₂²×C₂₃	—	4	2	no	—
266	C₂²×C₂₃	C₂×#121	1	6	yes	—
267	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
268	C₄×C₂₃	—	2	1	no	—
269	C₄×C₂₃	—	2	3	no	—
270	C₄×C₂₃	—	2	6	no	—
271	C₄×C₂₃	—	2	3	no	—
272	C₄×C₂₃	—	4	3	no	—
273	C₄×C₂₃	—	4	6	no	—
274	C₄×C₂₃	—	4	1	no	—
275	C₄×C₂₃	C₂×#121	1	6	yes	—
276	C₄×C₂₃	#578	1	2	yes	complemented
277	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
278	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
279	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	2	yes	—
280	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	1	yes	characteristic
281	#578	—	2	16	no	—
282	C₂×#137	C₂²×C₂₃	1	6	yes	—
283	C₂×#137	C₂²×C₂₃	1	6	yes	—
284	C₂×#135	C₂²×C₂₃	1	6	yes	—
285	C₂²×Q₁₆	C₂²×C₂₃	1	6	yes	—
286	C₂×#131	C₂²×C₂₃	1	2	yes	—
287	D₄×Q₈	—	2	1	no	—
288	D₄×Q₈	—	2	1	no	—
289	#547	—	2	3	no	—
290	#547	—	2	3	no	—
291	#536	C₂²×C₂₃	1	6	yes	—
292	#532	C₂²×C₂₃	1	3	yes	—
293	C₂×C₄⋊Q₈	C₂²×C₂₃	1	3	yes	—
294	#520	—	2	3	no	—
295	#520	C₂²×C₂₃	1	3	yes	—
296	#520	C₂²×C₂₃	1	1	yes	characteristic
297	#519	—	2	1	no	—
298	#519	C₂²×C₂₃	1	3	yes	—
299	C₄×#41	—	2	3	no	—
300	C₄×#41	C₂²×C₂₃	1	3	yes	—
301	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
302	C₂×C₄×Q₈	—	2	1	no	—
303	C₂×C₄×Q₈	C₂²×C₂₃	1	3	yes	—
304	#464	C₂²×C₂₃	1	6	yes	—
305	#464	C₂²×C₂₃	1	12	yes	—
306	#463	C₂²×C₂₃	1	6	yes	—
307	#462	C₂²×C₂₃	1	3	yes	—
308	#462	C₂²×C₂₃	1	6	yes	—
309	#462	C₂²×C₂₃	1	12	yes	—
310	#462	C₂²×C₂₃	1	6	yes	—
311	#461	C₂²×C₂₃	1	3	yes	—
312	#461	C₂²×C₂₃	1	6	yes	—
313	#460	C₂²×C₂₃	1	3	yes	—
314	#459	C₂²×C₂₃	1	1	yes	characteristic
315	#424	C₂²×C₂₃	1	6	yes	—
316	#423	C₂²×C₂₃	1	3	yes	—
317	C₂×C₄⋊C₈	C₂²×C₂₃	1	3	yes	—
318	#419	C₂²×C₂₃	1	6	yes	—
319	#417	C₂²×C₂₃	1	6	yes	—
320	#416	C₂²×C₂₃	1	6	yes	—
321	C₂×#103	C₂²×C₂₃	1	6	yes	—
322	C₂×C₂₃	—	2	6	no	—
323	C₂×C₂₃	—	4	2	no	—
324	C₂×C₂₃	—	8	2	no	—
325	C₂×C₂₃	C₂²×#121	1	1	yes	characteristic
326	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
327	C₂×C₂₃	#3586	1	1	yes	characteristic
328	2₋¹⁺⁴	—	2	4	no	—
329	2₋¹⁺⁴	—	2	8	no	—
330	2₋¹⁺⁴	—	2	8	no	—
331	2₋¹⁺⁴	D₄×C₂₃	1	8	yes	complemented
332	C₂×#41	—	2	3	no	—
333	C₂×#41	—	2	6	no	—
334	C₂×#41	C₂³×C₂₃	1	6	yes	—
335	C₂×#41	C₂³×C₂₃	1	3	yes	—
336	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
337	C₂²×Q₈	—	2	1	no	—
338	C₂²×Q₈	—	2	2	no	—
339	C₂²×Q₈	C₂³×C₂₃	1	6	yes	—
340	C₂²×Q₈	C₂³×C₂₃	1	3	yes	—
341	#137	—	2	24	no	—
342	#137	—	2	24	no	—
343	#135	—	2	24	no	—
344	C₂×Q₁₆	—	2	24	no	—
345	C₂×Q₁₆	C₂³×C₂₃	1	6	yes	—
346	C₂×Q₁₆	C₂³×C₂₃	1	12	yes	—
347	C₂×SD₁₆	C₂³×C₂₃	1	6	yes	—
348	C₂×SD₁₆	C₂³×C₂₃	1	6	yes	—
349	C₂×D₈	C₂³×C₂₃	1	2	yes	—
350	#131	—	2	8	no	—
351	C₂×M₁₆	C₂³×C₂₃	1	6	yes	—
352	C₂²×C₈	C₂³×C₂₃	1	6	yes	—
353	C₄⋊Q₈	—	2	3	no	—
354	C₄⋊Q₈	—	2	3	no	—
355	C₄⋊Q₈	C₂³×C₂₃	1	3	yes	—
356	C₄⋊Q₈	C₂³×C₂₃	1	6	yes	—
357	#127	C₂³×C₂₃	1	1	yes	characteristic
358	#124	C₂³×C₂₃	1	6	yes	—
359	#123	—	2	12	no	—
360	C₂²⋊Q₈	—	2	6	no	—
361	C₂²⋊Q₈	—	2	6	no	—
362	#121	—	2	3	no	—
363	#121	—	2	3	no	—
364	C₄×Q₈	—	2	1	no	—
365	C₄×Q₈	—	2	3	no	—
366	C₄×Q₈	—	2	3	no	—
367	C₄×Q₈	—	2	3	no	—
368	C₄×Q₈	—	2	3	no	—
369	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
370	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
371	C₄×Q₈	C₂³×C₂₃	1	3	yes	—
372	C₄×Q₈	C₂³×C₂₃	1	6	yes	—
373	C₄×Q₈	C₂³×C₂₃	1	3	yes	—
374	C₄×D₄	—	2	3	no	—
375	C₄×D₄	—	2	3	no	—
376	C₄×D₄	—	2	3	no	—
377	C₄×D₄	—	2	6	no	—
378	C₄×D₄	—	2	3	no	—
379	C₄×D₄	—	2	3	no	—
380	C₄×D₄	D₄×C₂₃	1	3	yes	—
381	C₄×D₄	D₄×C₂₃	1	3	yes	—
382	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
383	C₄×D₄	C₂³×C₂₃	1	3	yes	—
384	#117	—	2	3	no	—
385	#117	—	2	6	no	—
386	#117	—	2	3	no	—
387	#117	C₂³×C₂₃	1	3	yes	—
388	#117	C₂³×C₂₃	1	3	yes	—
389	C₂×C₄⋊C₄	—	2	3	no	—
390	C₂×C₄⋊C₄	—	2	3	no	—
391	C₂×C₄⋊C₄	—	2	3	no	—
392	C₂×C₄⋊C₄	—	2	3	no	—
393	C₂×C₄⋊C₄	C₂³×C₂₃	1	3	yes	—
394	C₂×C₄²	—	2	3	no	—
395	C₂×C₄²	—	2	3	no	—
396	C₂×C₄²	C₂³×C₂₃	1	3	yes	—
397	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
398	C₄⋊C₈	C₂³×C₂₃	1	3	yes	—
399	C₄⋊C₈	C₂³×C₂₃	1	6	yes	—
400	C₄⋊C₈	C₂³×C₂₃	1	6	yes	—
401	#103	C₂³×C₂₃	1	6	yes	—
402	#103	C₂³×C₂₃	1	12	yes	—
403	#103	C₂³×C₂₃	1	6	yes	—
404	#102	C₂³×C₂₃	1	2	yes	—
405	#102	C₂³×C₂₃	1	6	yes	—
406	C₂₃	#60432	1	1	yes	characteristic, direct product factor, Sylow
407	#41	—	2	24	no	—
408	#41	—	2	6	no	—
409	#41	—	2	12	no	—
410	#41	—	2	12	no	—
411	#41	—	4	24	no	—
412	#41	C₂×D₄×C₂₃	1	12	yes	—
413	#41	C₂×D₄×C₂₃	1	4	yes	—
414	#41	#41×C₂₃	1	4	yes	—
415	C₂×Q₈	—	2	8	no	—
416	C₂×Q₈	—	2	3	no	—
417	C₂×Q₈	—	2	6	no	—
418	C₂×Q₈	—	2	6	no	—
419	C₂×Q₈	—	2	12	no	—
420	C₂×Q₈	—	2	12	no	—
421	C₂×Q₈	—	4	8	no	—
422	C₂×Q₈	C₂×D₄×C₂₃	1	12	yes	—
423	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
424	C₂×Q₈	C₂⁴×C₂₃	1	6	yes	—
425	C₂×Q₈	C₂⁴×C₂₃	1	3	yes	—
426	C₂×D₄	—	2	3	no	—
427	C₂×D₄	—	2	6	no	—
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	C₂×D₄×C₂₃	1	3	yes	—
431	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
432	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
433	C₂²×C₄	—	2	3	no	—
434	C₂²×C₄	—	2	3	no	—
435	C₂²×C₄	—	2	6	no	—
436	C₂²×C₄	—	2	3	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	6	no	—
439	C₂²×C₄	—	2	3	no	—
440	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
441	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
442	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
443	Q₁₆	—	2	12	no	—
444	Q₁₆	—	2	24	no	—
445	SD₁₆	—	2	12	no	—
446	SD₁₆	—	2	12	no	—
447	D₈	—	2	4	no	—
448	M₁₆	—	2	12	no	—
449	C₂×C₈	—	2	12	no	—
450	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
451	C₂×C₈	C₂⁴×C₂₃	1	6	yes	—
452	C₄⋊C₄	—	2	6	no	—
453	C₄⋊C₄	—	2	3	no	—
454	C₄⋊C₄	—	2	3	no	—
455	C₄⋊C₄	—	2	3	no	—
456	C₄⋊C₄	—	2	3	no	—
457	C₄⋊C₄	—	2	6	no	—
458	C₄⋊C₄	—	2	6	no	—
459	C₄⋊C₄	—	2	3	no	—
460	C₄⋊C₄	C₂×D₄×C₂₃	1	3	yes	—
461	C₄⋊C₄	C₂×D₄×C₂₃	1	3	yes	—
462	C₄⋊C₄	C₂⁴×C₂₃	1	3	yes	—
463	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
464	C₂²⋊C₄	—	2	3	no	—
465	C₂²⋊C₄	—	2	1	no	—
466	C₂²⋊C₄	—	2	3	no	—
467	C₂²⋊C₄	—	2	6	no	—
468	C₂²⋊C₄	—	2	6	no	—
469	C₂²⋊C₄	C₂×D₄×C₂₃	1	6	yes	—
470	C₄²	—	2	3	no	—
471	C₄²	—	2	3	no	—
472	C₄²	—	2	6	no	—
473	C₄²	—	2	3	no	—
474	C₄²	C₂×D₄×C₂₃	1	3	yes	—
475	C₄²	C₂×D₄×C₂₃	1	3	yes	—
476	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
477	C₄²	C₂⁴×C₂₃	1	3	yes	—
478	C₂³	—	2	1	no	—
479	C₂³	—	2	2	no	—
480	C₂³	C₂²×D₄×C₂₃	1	3	yes	—
481	Q₈	—	2	3	no	—
482	Q₈	—	2	12	no	—
483	Q₈	—	2	6	no	—
484	Q₈	—	2	6	no	—
485	Q₈	—	4	12	no	—
486	Q₈	C₂₃×#121	1	4	yes	—
487	Q₈	C₂²×D₄×C₂₃	1	6	yes	—
488	D₄	—	2	12	no	—
489	D₄	—	2	2	no	—
490	D₄	—	2	1	no	—
491	D₄	—	2	2	no	—
492	D₄	—	4	2	no	—
493	D₄	—	4	12	no	—
494	D₄	—	4	2	no	—
495	D₄	C₂₃×#121	1	12	yes	—
496	D₄	C₂²×D₄×C₂₃	1	2	yes	—
497	C₂×C₄	—	2	3	no	—
498	C₂×C₄	—	2	12	no	—
499	C₂×C₄	—	2	6	no	—
500	C₂×C₄	—	2	12	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	3	no	—
503	C₂×C₄	—	2	6	no	—
504	C₂×C₄	—	4	3	no	—
505	C₂×C₄	—	4	12	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	12	no	—
508	C₂×C₄	—	8	3	no	—
509	C₂×C₄	—	8	3	no	—
510	C₂×C₄	C₂²×D₄×C₂₃	1	3	yes	—
511	C₂×C₄	C₂²×D₄×C₂₃	1	3	yes	—
512	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
513	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
514	C₂×C₄	C₂²×D₄×C₂₃	1	6	yes	—
515	C₂×C₄	C₂²×D₄×C₂₃	1	3	yes	—
516	C₂×C₄	C₂×#41×C₂₃	1	6	yes	—
517	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
518	C₈	—	2	2	no	—
519	C₈	—	2	6	no	—
520	C₂²	—	2	3	no	—
521	C₂²	—	2	3	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	4	1	no	—
524	C₂²	—	4	1	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	2	no	—
528	C₂²	C₂×C₂₃×#121	1	6	yes	—
529	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
530	C₄	—	2	6	no	—
531	C₄	—	2	3	no	—
532	C₄	—	2	1	no	—
533	C₄	—	2	3	no	—
534	C₄	—	4	6	no	—
535	C₄	—	4	1	no	—
536	C₄	—	4	3	no	—
537	C₄	C₂×C₂₃×#121	1	6	yes	—
538	C₄	C₂₃×#578	1	2	yes	complemented
539	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
540	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
541	C₂	—	2	6	no	—
542	C₂	—	4	2	no	—
543	C₂	—	8	2	no	—
544	C₂	C₂²×C₂₃×#121	1	1	yes	characteristic
545	C₂	C₂×C₂₃×#578	1	1	yes	characteristic
546	C₂	C₂₃×#3586	1	1	yes	characteristic

	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 ◁ C₄×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#578	C₂	semidirect
2. C₂₃×#3499	C₂	semidirect
3. C₄×C₂₃×2₋¹⁺⁴	C₂	semidirect
4. C₂₃×#3046	C₂	semidirect
5. C₂₃×#3044	C₂	semidirect
6. C₂₃×#3039	C₂	semidirect
7. C₂₃×#3037	C₂	semidirect
8. C₂₃×#3035	C₂	semidirect
9. C₂×C₂₃×#462	C₂	semidirect
10. C₂₃×#2906	C₂	semidirect
11. C₂₃×#2898	C₂	semidirect
58. C₂₃×2₋¹⁺⁴	D₄	semidirect
204. #60432	C₂₃	direct (N × H)
247. C₂×#578	C₂×C₂₃	semidirect
248. #3499	C₂×C₂₃	semidirect
249. C₄×2₋¹⁺⁴	C₂×C₂₃	semidirect
250. #3046	C₂×C₂₃	semidirect
251. #3044	C₂×C₂₃	semidirect
252. #3039	C₂×C₂₃	semidirect
253. #3037	C₂×C₂₃	semidirect
254. #3035	C₂×C₂₃	semidirect
255. C₂×#462	C₂×C₂₃	semidirect
256. #2906	C₂×C₂₃	semidirect
257. #2898	C₂×C₂₃	semidirect
276. C₄×C₂₃	#578	semidirect
331. 2₋¹⁺⁴	D₄×C₂₃	semidirect
406. C₂₃	#60432	direct (N × H)
538. C₄	C₂₃×#578	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#578	2
C₂₃×#3499	2
C₄×C₂₃×2₋¹⁺⁴	2
C₂₃×#3046	2
C₂₃×#3044	2
C₂₃×#3039	2
C₂₃×#3037	2
C₂₃×#3035	2
C₂×C₂₃×#462	2
C₂₃×#2906	2
C₂₃×#2898	2
#60432	23

Subgroups — C23×#60432 #19208058

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60432 #19208058