Subgroups — C₄×C₂₃×#467 #19169148

Order 5888.

1054 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#467	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic
4	C₄×C₂₃×C₂²⋊Q₈	C₂	1	2	yes	maximal
5	C₂₃×#1969	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1933	C₂	1	2	yes	maximal, complemented
8	C₂₃×#1892	C₂	1	2	yes	maximal
9	C₂₃×#1808	C₂	1	1	yes	maximal, characteristic
10	C₄×C₂₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₂₃×#103	C₂	1	2	yes	maximal, complemented
12	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
15	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
17	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
18	C₂₃×#467	C₄	1	8	yes	direct product factor
19	C₄×Q₁₆×C₂₃	—	2	4	no	—
20	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×#103	C₂²	1	2	yes	—
24	C₂×C₂₃×#103	C₂²	1	2	yes	—
25	C₂×C₂₃×#103	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₂₃	—	2	4	no	—
27	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
31	C₂₃×#391	C₂²	1	2	yes	—
32	C₂₃×#389	C₂²	1	2	yes	—
33	C₂₃×#387	—	2	2	no	—
34	C₂₃×#385	—	2	2	no	—
35	C₂₃×#380	C₂²	1	2	yes	—
36	C₄×C₄⋊C₄×C₂₃	—	2	2	no	—
37	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
38	C₄×C₂²⋊C₄×C₂₃	—	2	2	no	—
39	C₂₃×#340	C₂²	1	2	yes	—
40	C₂₃×#340	C₂²	1	2	yes	—
41	C₂₃×#340	C₂²	1	2	yes	—
42	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
43	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
46	C₂×Q₁₆×C₂₃	—	2	2	no	—
47	C₂×Q₁₆×C₂₃	—	2	2	no	—
48	C₂×Q₁₆×C₂₃	C₂×C₄	1	4	yes	complemented
49	C₂²×C₈×C₂₃	—	2	2	no	—
50	C₂²×C₈×C₂₃	—	2	2	no	—
51	C₂²×C₈×C₂₃	—	2	2	no	—
52	C₂²×C₈×C₂₃	—	2	2	no	—
53	C₂²×C₈×C₂₃	—	2	2	no	—
54	C₂²×C₈×C₂₃	C₂×C₄	1	4	yes	—
55	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
59	C₂₃×C₂²⋊Q₈	—	2	4	no	—
60	C₂₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
61	C₄×Q₈×C₂₃	—	2	4	no	—
62	C₄×Q₈×C₂₃	—	2	4	no	—
63	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
64	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
65	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
66	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
69	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
71	C₂×C₄²×C₂₃	—	2	2	no	—
72	C₂×C₄²×C₂₃	—	2	2	no	—
73	C₂×C₄²×C₂₃	—	2	2	no	—
74	C₂×C₄²×C₂₃	—	2	2	no	—
75	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
79	C₂₃×#107	—	2	2	no	—
80	C₂₃×#107	—	2	2	no	—
81	C₂₃×#107	C₂×C₄	1	4	yes	complemented
82	C₂₃×#103	—	2	4	no	—
83	C₂₃×#103	—	2	4	no	—
84	C₂₃×#103	C₂×C₄	1	8	yes	complemented
85	C₄×C₈×C₂₃	—	2	2	no	—
86	C₄×C₈×C₂₃	—	2	2	no	—
87	C₄×C₈×C₂₃	—	2	2	no	—
88	C₄×C₈×C₂₃	D₄	1	4	yes	—
89	C₂₃×#95	—	2	2	no	—
90	C₂₃×#95	—	2	2	no	—
91	C₂₃×#95	—	2	2	no	—
92	C₂₃×#95	—	2	2	no	—
93	C₂₃×#95	—	2	2	no	—
94	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
95	C₂×Q₈×C₂₃	—	2	2	no	—
96	C₂×Q₈×C₂₃	—	2	2	no	—
97	C₂×Q₈×C₂₃	—	2	2	no	—
98	C₂×Q₈×C₂₃	—	2	2	no	—
99	C₂×Q₈×C₂₃	—	2	2	no	—
100	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
101	C₂²×C₄×C₂₃	—	2	2	no	—
102	C₂²×C₄×C₂₃	—	2	2	no	—
103	C₂²×C₄×C₂₃	—	2	2	no	—
104	C₂²×C₄×C₂₃	—	2	2	no	—
105	C₂²×C₄×C₂₃	—	2	2	no	—
106	C₂²×C₄×C₂₃	—	2	1	no	—
107	C₂²×C₄×C₂₃	—	2	1	no	—
108	C₂²×C₄×C₂₃	—	2	1	no	—
109	C₂²×C₄×C₂₃	—	2	1	no	—
110	C₂²×C₄×C₂₃	—	2	2	no	—
111	C₂²×C₄×C₂₃	—	2	2	no	—
112	C₂²×C₄×C₂₃	—	2	2	no	—
113	C₂²×C₄×C₂₃	—	2	2	no	—
114	C₂²×C₄×C₂₃	Q₁₆	1	4	yes	complemented
115	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₂₃	#41	1	2	yes	—
122	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
123	Q₁₆×C₂₃	—	2	8	no	—
124	C₂×C₈×C₂₃	—	2	8	no	—
125	C₂×C₈×C₂₃	—	2	1	no	—
126	C₂×C₈×C₂₃	—	2	1	no	—
127	C₂×C₈×C₂₃	—	2	1	no	—
128	C₂×C₈×C₂₃	—	2	1	no	—
129	C₂×C₈×C₂₃	—	2	1	no	—
130	C₂×C₈×C₂₃	—	2	1	no	—
131	C₂×C₈×C₂₃	—	2	8	no	—
132	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
136	C₂×C₈×C₂₃	#41	1	2	yes	—
137	C₂×C₈×C₂₃	#41	1	2	yes	—
138	C₄⋊C₄×C₂₃	—	2	8	no	—
139	C₄⋊C₄×C₂₃	—	2	2	no	—
140	C₄⋊C₄×C₂₃	—	2	2	no	—
141	C₄⋊C₄×C₂₃	—	2	2	no	—
142	C₄⋊C₄×C₂₃	—	2	2	no	—
143	C₄⋊C₄×C₂₃	—	2	2	no	—
144	C₄⋊C₄×C₂₃	—	4	4	no	—
145	C₄⋊C₄×C₂₃	—	4	4	no	—
146	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
147	C₂²⋊C₄×C₂₃	—	2	8	no	—
148	C₂²⋊C₄×C₂₃	—	4	4	no	—
149	C₄²×C₂₃	—	2	2	no	—
150	C₄²×C₂₃	—	2	2	no	—
151	C₄²×C₂₃	—	2	1	no	—
152	C₄²×C₂₃	—	2	1	no	—
153	C₄²×C₂₃	—	4	4	no	—
154	C₄²×C₂₃	—	4	4	no	—
155	C₄²×C₂₃	C₂×D₄	1	2	yes	—
156	C₄²×C₂₃	#41	1	2	yes	—
157	C₄×#467	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
158	C₂³×C₂₃	—	2	1	no	—
159	C₂³×C₂₃	—	2	1	no	—
160	C₂³×C₂₃	—	2	1	no	—
161	C₂³×C₂₃	—	2	1	no	—
162	C₂³×C₂₃	C₄×D₄	1	2	yes	—
163	C₂³×C₂₃	C₂×Q₁₆	1	2	yes	—
164	C₂³×C₂₃	#135	1	2	yes	—
165	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
166	Q₈×C₂₃	—	2	4	no	—
167	Q₈×C₂₃	—	2	4	no	—
168	Q₈×C₂₃	—	4	2	no	—
169	Q₈×C₂₃	—	4	2	no	—
170	C₂×C₄×C₂₃	—	2	8	no	—
171	C₂×C₄×C₂₃	—	2	1	no	—
172	C₂×C₄×C₂₃	—	2	1	no	—
173	C₂×C₄×C₂₃	—	2	1	no	—
174	C₂×C₄×C₂₃	—	2	1	no	—
175	C₂×C₄×C₂₃	—	2	1	no	—
176	C₂×C₄×C₂₃	—	2	1	no	—
177	C₂×C₄×C₂₃	—	2	1	no	—
178	C₂×C₄×C₂₃	—	2	1	no	—
179	C₂×C₄×C₂₃	—	2	2	no	—
180	C₂×C₄×C₂₃	—	2	2	no	—
181	C₂×C₄×C₂₃	—	2	2	no	—
182	C₂×C₄×C₂₃	—	2	2	no	—
183	C₂×C₄×C₂₃	—	2	8	no	—
184	C₂×C₄×C₂₃	—	2	4	no	—
185	C₂×C₄×C₂₃	—	2	4	no	—
186	C₂×C₄×C₂₃	—	4	2	no	—
187	C₂×C₄×C₂₃	—	4	2	no	—
188	C₂×C₄×C₂₃	—	4	2	no	—
189	C₂×C₄×C₂₃	—	4	2	no	—
190	C₂×C₄×C₂₃	—	4	2	no	—
191	C₂×C₄×C₂₃	—	4	2	no	—
192	C₂×C₄×C₂₃	—	4	2	no	—
193	C₂×C₄×C₂₃	—	4	2	no	—
194	C₂×C₄×C₂₃	—	4	2	no	—
195	C₂×C₄×C₂₃	—	4	2	no	—
196	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
197	C₂×C₄×C₂₃	#121	1	2	yes	—
198	C₂×C₄×C₂₃	#121	1	2	yes	—
199	C₂×C₄×C₂₃	C₂×Q₁₆	1	2	yes	—
200	C₂×C₄×C₂₃	C₂×Q₁₆	1	2	yes	—
201	C₂×C₄×C₂₃	#135	1	2	yes	—
202	C₂×C₄×C₂₃	#135	1	2	yes	—
203	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
204	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
207	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
209	C₈×C₂₃	—	2	2	no	—
210	C₈×C₂₃	—	2	2	no	—
211	C₈×C₂₃	—	2	2	no	—
212	C₈×C₂₃	C₄×D₄	1	4	yes	—
213	C₂×#467	C₂×C₂₃	1	1	yes	characteristic
214	C₂×C₄×Q₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
215	C₂²×C₄×C₈	C₂×C₂₃	1	1	yes	characteristic
216	C₄×C₂²⋊Q₈	C₂×C₂₃	1	2	yes	—
217	#1969	C₂×C₂₃	1	1	yes	characteristic, complemented
218	#1942	C₂×C₂₃	1	1	yes	characteristic, complemented
219	#1933	C₂×C₂₃	1	2	yes	complemented
220	#1892	C₂×C₂₃	1	2	yes	—
221	#1808	C₂×C₂₃	1	1	yes	characteristic
222	C₄×#107	C₂×C₂₃	1	1	yes	characteristic, complemented
223	C₄×#103	C₂×C₂₃	1	2	yes	complemented
224	C₂²×C₂₃	—	2	2	no	—
225	C₂²×C₂₃	—	2	2	no	—
226	C₂²×C₂₃	—	2	2	no	—
227	C₂²×C₂₃	—	2	2	no	—
228	C₂²×C₂₃	—	2	2	no	—
229	C₂²×C₂₃	—	2	2	no	—
230	C₂²×C₂₃	C₄×Q₁₆	1	4	yes	complemented
231	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
232	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
233	C₂²×C₂₃	#532	1	1	yes	characteristic
234	C₂²×C₂₃	C₂²×Q₁₆	1	1	yes	characteristic
235	C₂²×C₂₃	C₂×#135	1	1	yes	characteristic
236	C₂²×C₂₃	C₂×#135	1	1	yes	characteristic
237	C₂²×C₂₃	C₂×#135	1	1	yes	characteristic
238	C₄×C₂₃	—	2	2	no	—
239	C₄×C₂₃	—	2	2	no	—
240	C₄×C₂₃	—	2	2	no	—
241	C₄×C₂₃	—	2	2	no	—
242	C₄×C₂₃	—	4	4	no	—
243	C₄×C₂₃	—	4	4	no	—
244	C₄×C₂₃	—	8	2	no	—
245	C₄×C₂₃	—	8	2	no	—
246	C₄×C₂₃	#467	1	4	yes	direct product factor
247	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
248	C₄×C₂₃	C₄×#41	1	1	yes	characteristic
249	C₄×C₂₃	#525	1	1	yes	characteristic
250	C₄×C₂₃	#529	1	1	yes	characteristic
251	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
252	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
253	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
254	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
255	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
256	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
257	#467	C₄×C₂₃	1	8	yes	direct product factor
258	C₄×Q₁₆	—	2	4	no	—
259	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
260	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
261	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
262	C₂×#103	C₂²×C₂₃	1	2	yes	—
263	C₂×#103	C₂²×C₂₃	1	2	yes	—
264	C₂×#103	C₂²×C₂₃	1	2	yes	—
265	C₂×C₄×C₈	—	2	4	no	—
266	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
267	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
268	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
269	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
270	#391	C₂²×C₂₃	1	2	yes	—
271	#389	C₂²×C₂₃	1	2	yes	—
272	#387	—	2	2	no	—
273	#385	—	2	2	no	—
274	#380	C₂²×C₂₃	1	2	yes	—
275	C₄×C₄⋊C₄	—	2	2	no	—
276	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
277	C₄×C₂²⋊C₄	—	2	2	no	—
278	#340	C₂²×C₂₃	1	2	yes	—
279	#340	C₂²×C₂₃	1	2	yes	—
280	#340	C₂²×C₂₃	1	2	yes	—
281	C₂×C₂₃	—	2	4	no	—
282	C₂×C₂₃	C₄×#121	1	1	yes	characteristic
283	C₂×C₂₃	C₂×C₄×Q₁₆	1	1	yes	characteristic
284	C₂×C₂₃	C₄×#135	1	1	yes	characteristic
285	C₂×C₂₃	C₂×#467	1	1	yes	characteristic
286	C₂×C₂₃	#3050	1	1	yes	characteristic
287	C₂×C₂₃	#3168	1	1	yes	characteristic
288	C₂×C₂₃	#3170	1	1	yes	characteristic
289	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
290	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
291	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
292	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
293	C₂×Q₁₆	—	2	2	no	—
294	C₂×Q₁₆	—	2	2	no	—
295	C₂×Q₁₆	C₂×C₄×C₂₃	1	4	yes	complemented
296	C₂²×C₈	—	2	2	no	—
297	C₂²×C₈	—	2	2	no	—
298	C₂²×C₈	—	2	2	no	—
299	C₂²×C₈	—	2	2	no	—
300	C₂²×C₈	—	2	2	no	—
301	C₂²×C₈	C₂×C₄×C₂₃	1	4	yes	—
302	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
303	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
304	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
306	C₂²⋊Q₈	—	2	4	no	—
307	C₂²⋊Q₈	C₂×C₄×C₂₃	1	8	yes	—
308	C₄×Q₈	—	2	4	no	—
309	C₄×Q₈	—	2	4	no	—
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	—	2	2	no	—
313	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
314	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
315	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₂²⋊C₄	—	2	2	no	—
318	C₂×C₄²	—	2	2	no	—
319	C₂×C₄²	—	2	2	no	—
320	C₂×C₄²	—	2	2	no	—
321	C₂×C₄²	—	2	2	no	—
322	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
323	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
324	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
325	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
326	#107	—	2	2	no	—
327	#107	—	2	2	no	—
328	#107	C₂×C₄×C₂₃	1	4	yes	complemented
329	#103	—	2	4	no	—
330	#103	—	2	4	no	—
331	#103	C₂×C₄×C₂₃	1	8	yes	complemented
332	C₄×C₈	—	2	2	no	—
333	C₄×C₈	—	2	2	no	—
334	C₄×C₈	—	2	2	no	—
335	C₄×C₈	D₄×C₂₃	1	4	yes	—
336	#95	—	2	2	no	—
337	#95	—	2	2	no	—
338	#95	—	2	2	no	—
339	#95	—	2	2	no	—
340	#95	—	2	2	no	—
341	C₂₃	C₄×#467	1	1	yes	characteristic, direct product factor, Sylow
342	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	Q₁₆×C₂₃	1	4	yes	complemented
363	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
364	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
369	C₂²×C₄	#41×C₂₃	1	2	yes	—
370	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
371	Q₁₆	—	2	8	no	—
372	C₂×C₈	—	2	8	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	8	no	—
380	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
381	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
382	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
383	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
384	C₂×C₈	#41×C₂₃	1	2	yes	—
385	C₂×C₈	#41×C₂₃	1	2	yes	—
386	C₄⋊C₄	—	2	8	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	4	4	no	—
393	C₄⋊C₄	—	4	4	no	—
394	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
395	C₂²⋊C₄	—	2	8	no	—
396	C₂²⋊C₄	—	4	4	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	2	1	no	—
400	C₄²	—	2	1	no	—
401	C₄²	—	4	4	no	—
402	C₄²	—	4	4	no	—
403	C₄²	C₂×D₄×C₂₃	1	2	yes	—
404	C₄²	#41×C₂₃	1	2	yes	—
405	C₂³	—	2	1	no	—
406	C₂³	—	2	1	no	—
407	C₂³	—	2	1	no	—
408	C₂³	—	2	1	no	—
409	C₂³	C₄×D₄×C₂₃	1	2	yes	—
410	C₂³	C₂×Q₁₆×C₂₃	1	2	yes	—
411	C₂³	C₂₃×#135	1	2	yes	—
412	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
413	Q₈	—	2	4	no	—
414	Q₈	—	2	4	no	—
415	Q₈	—	4	2	no	—
416	Q₈	—	4	2	no	—
417	C₂×C₄	—	2	8	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	8	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
444	C₂×C₄	C₂₃×#121	1	2	yes	—
445	C₂×C₄	C₂₃×#121	1	2	yes	—
446	C₂×C₄	C₂×Q₁₆×C₂₃	1	2	yes	—
447	C₂×C₄	C₂×Q₁₆×C₂₃	1	2	yes	—
448	C₂×C₄	C₂₃×#135	1	2	yes	—
449	C₂×C₄	C₂₃×#135	1	2	yes	—
450	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
451	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
452	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
453	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
454	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
455	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
456	C₈	—	2	2	no	—
457	C₈	—	2	2	no	—
458	C₈	—	2	2	no	—
459	C₈	C₄×D₄×C₂₃	1	4	yes	—
460	C₂²	—	2	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	2	2	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	2	2	no	—
466	C₂²	C₄×Q₁₆×C₂₃	1	4	yes	complemented
467	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
468	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
469	C₂²	C₂₃×#532	1	1	yes	characteristic
470	C₂²	C₂²×Q₁₆×C₂₃	1	1	yes	characteristic
471	C₂²	C₂×C₂₃×#135	1	1	yes	characteristic
472	C₂²	C₂×C₂₃×#135	1	1	yes	characteristic
473	C₂²	C₂×C₂₃×#135	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	2	2	no	—
478	C₄	—	4	4	no	—
479	C₄	—	4	4	no	—
480	C₄	—	8	2	no	—
481	C₄	—	8	2	no	—
482	C₄	C₂₃×#467	1	4	yes	direct product factor
483	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
484	C₄	C₄×#41×C₂₃	1	1	yes	characteristic
485	C₄	C₂₃×#525	1	1	yes	characteristic
486	C₄	C₂₃×#529	1	1	yes	characteristic
487	C₂	—	2	4	no	—
488	C₂	C₄×C₂₃×#121	1	1	yes	characteristic
489	C₂	C₂×C₄×Q₁₆×C₂₃	1	1	yes	characteristic
490	C₂	C₄×C₂₃×#135	1	1	yes	characteristic
491	C₂	C₂×C₂₃×#467	1	1	yes	characteristic
492	C₂	C₂₃×#3050	1	1	yes	characteristic
493	C₂	C₂₃×#3168	1	1	yes	characteristic
494	C₂	C₂₃×#3170	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
socle	C₂³×C₂₃	C₂²×D₄
prime radical	C₂⁴×C₂₃	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Q₁₆×C₂₃	C₂	semidirect
5. C₂₃×#1969	C₂	semidirect
6. C₂₃×#1942	C₂	semidirect
7. C₂₃×#1933	C₂	semidirect
10. C₄×C₂₃×#107	C₂	semidirect
11. C₄×C₂₃×#103	C₂	semidirect
18. C₂₃×#467	C₄	direct (N × H)
48. C₂×Q₁₆×C₂₃	C₂×C₄	semidirect
81. C₂₃×#107	C₂×C₄	semidirect
84. C₂₃×#103	C₂×C₄	semidirect
114. C₂²×C₄×C₂₃	Q₁₆	semidirect
157. C₄×#467	C₂₃	direct (N × H)
214. C₂×C₄×Q₁₆	C₂×C₂₃	semidirect
217. #1969	C₂×C₂₃	semidirect
218. #1942	C₂×C₂₃	semidirect
219. #1933	C₂×C₂₃	semidirect
222. C₄×#107	C₂×C₂₃	semidirect
223. C₄×#103	C₂×C₂₃	semidirect
230. C₂²×C₂₃	C₄×Q₁₆	semidirect
246. C₄×C₂₃	#467	direct (N × H)
257. #467	C₄×C₂₃	direct (N × H)
295. C₂×Q₁₆	C₂×C₄×C₂₃	semidirect
328. #107	C₂×C₄×C₂₃	semidirect
331. #103	C₂×C₄×C₂₃	semidirect
341. C₂₃	C₄×#467	direct (N × H)
362. C₂²×C₄	Q₁₆×C₂₃	semidirect
466. C₂²	C₄×Q₁₆×C₂₃	semidirect
482. C₄	C₂₃×#467	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#467	2
C₂×C₄×Q₁₆×C₂₃	2
C₂²×C₄×C₈×C₂₃	2
C₄×C₂₃×C₂²⋊Q₈	2
C₂₃×#1969	2
C₂₃×#1942	2
C₂₃×#1933	2
C₂₃×#1892	2
C₂₃×#1808	2
C₄×C₂₃×#107	2
C₄×C₂₃×#103	2
C₄×#467	23

Subgroups — C4×C23×#467 #19169148

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₂₃×#467 #19169148