Subgroups — C₂₃×#26064 #19173690

Order 5888.

794 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	C₂×C₂₃×#500	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#427	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2439	C₂	1	2	yes	maximal
4	C₂₃×#2085	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2058	C₂	1	2	yes	maximal, complemented
6	C₂₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1854	C₂	1	2	yes	maximal
9	C₂₃×#1846	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1808	C₂	1	1	yes	maximal, characteristic
11	C₈×C₂²⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
13	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₂₃×#117	C₂²	1	2	yes	—
15	C₂₃×#500	—	2	4	no	—
16	C₂₃×#427	—	2	4	no	—
17	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
18	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
20	C₂×C₂₃×#107	C₂²	1	2	yes	—
21	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#106	C₂²	1	2	yes	—
23	C₂×C₂₃×#106	C₂²	1	2	yes	—
24	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
27	C₂₃×#396	—	2	2	no	—
28	C₂₃×#393	—	2	2	no	—
29	C₂₃×#391	—	2	2	no	—
30	C₂₃×#389	C₂²	1	2	yes	—
31	C₂₃×#389	C₂²	1	2	yes	—
32	C₂₃×#387	—	2	2	no	—
33	C₂₃×#382	C₂²	1	2	yes	—
34	C₂₃×#380	C₂²	1	2	yes	—
35	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
36	C₂₃×#340	C₂²	1	2	yes	—
37	C₂₃×#340	C₂²	1	2	yes	—
38	C₂₃×#340	C₂²	1	2	yes	—
39	C₂₃×#336	C₂²	1	1	yes	characteristic
40	C₂₃×#336	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₂₃	—	2	2	no	—
42	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₂₃	—	2	2	no	—
44	C₂²×C₈×C₂₃	—	2	2	no	—
45	C₂²×C₈×C₂₃	Q₈	1	4	yes	complemented
46	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
50	C₂₃×C₄⋊Q₈	—	2	4	no	—
51	C₂₃×C₄⋊Q₈	—	4	2	no	—
52	C₂₃×#117	—	2	4	no	—
53	C₂₃×#117	—	4	2	no	—
54	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
55	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
56	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
57	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
61	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₂₃	—	2	2	no	—
66	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
68	C₂₃×#107	—	2	2	no	—
69	C₂₃×#107	—	2	2	no	—
70	C₂₃×#107	—	2	2	no	—
71	C₂₃×#107	—	2	4	no	—
72	C₂₃×#107	D₄	1	4	yes	—
73	C₂₃×#106	—	2	4	no	—
74	C₂₃×#106	—	4	2	no	—
75	C₂₃×C₂²⋊C₈	Q₈	1	4	yes	complemented
76	C₄×C₈×C₂₃	—	2	2	no	—
77	C₄×C₈×C₂₃	—	2	2	no	—
78	C₂₃×#95	—	2	2	no	—
79	C₂₃×#95	—	2	2	no	—
80	C₂₃×#95	—	2	2	no	—
81	C₂₃×#95	—	2	2	no	—
82	C₂₃×#95	—	2	2	no	—
83	C₂₃×#95	D₄	1	1	yes	characteristic
84	C₂₃×#95	D₄	1	1	yes	characteristic
85	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
86	C₂×Q₈×C₂₃	—	4	4	no	—
87	C₂×Q₈×C₂₃	—	4	4	no	—
88	C₂×Q₈×C₂₃	—	8	2	no	—
89	C₂²×C₄×C₂₃	—	2	1	no	—
90	C₂²×C₄×C₂₃	—	2	1	no	—
91	C₂²×C₄×C₂₃	—	2	1	no	—
92	C₂²×C₄×C₂₃	—	2	1	no	—
93	C₂²×C₄×C₂₃	—	2	2	no	—
94	C₂²×C₄×C₂₃	—	2	2	no	—
95	C₂²×C₄×C₂₃	—	2	2	no	—
96	C₂²×C₄×C₂₃	—	2	2	no	—
97	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₂₃	C₂×Q₈	1	2	yes	—
103	C₂²×C₄×C₂₃	C₂×Q₈	1	2	yes	—
104	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
105	C₂×C₈×C₂₃	—	2	1	no	—
106	C₂×C₈×C₂₃	—	2	1	no	—
107	C₂×C₈×C₂₃	—	2	1	no	—
108	C₂×C₈×C₂₃	—	2	1	no	—
109	C₂×C₈×C₂₃	—	2	1	no	—
110	C₂×C₈×C₂₃	—	2	1	no	—
111	C₂×C₈×C₂₃	—	2	8	no	—
112	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
113	C₂×C₈×C₂₃	C₂×Q₈	1	2	yes	—
114	C₂×C₈×C₂₃	C₂×Q₈	1	2	yes	—
115	C₂×C₈×C₂₃	C₂×Q₈	1	2	yes	—
116	C₂×C₈×C₂₃	C₂×Q₈	1	2	yes	—
117	C₂×C₈×C₂₃	#41	1	2	yes	—
118	C₄⋊C₄×C₂₃	—	2	2	no	—
119	C₄⋊C₄×C₂₃	—	2	2	no	—
120	C₄⋊C₄×C₂₃	—	2	2	no	—
121	C₄⋊C₄×C₂₃	—	2	2	no	—
122	C₄⋊C₄×C₂₃	—	2	2	no	—
123	C₄⋊C₄×C₂₃	—	2	2	no	—
124	C₄⋊C₄×C₂₃	—	2	2	no	—
125	C₄⋊C₄×C₂₃	—	4	4	no	—
126	C₄⋊C₄×C₂₃	—	4	4	no	—
127	C₄⋊C₄×C₂₃	—	8	2	no	—
128	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
129	C₂²⋊C₄×C₂₃	—	2	2	no	—
130	C₂²⋊C₄×C₂₃	—	2	2	no	—
131	C₂²⋊C₄×C₂₃	—	4	4	no	—
132	C₂²⋊C₄×C₂₃	—	8	2	no	—
133	C₄²×C₂₃	—	2	1	no	—
134	C₄²×C₂₃	—	2	1	no	—
135	C₄²×C₂₃	—	2	1	no	—
136	C₄²×C₂₃	—	2	1	no	—
137	C₄²×C₂₃	—	4	4	no	—
138	#26064	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂³×C₂₃	—	2	1	no	—
140	C₂³×C₂₃	—	2	1	no	—
141	C₂³×C₂₃	—	2	1	no	—
142	C₂³×C₂₃	—	2	1	no	—
143	C₂³×C₂₃	—	2	1	no	—
144	C₂³×C₂₃	—	2	1	no	—
145	C₂³×C₂₃	C₄⋊Q₈	1	2	yes	—
146	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
147	Q₈×C₂₃	—	8	8	no	—
148	C₂×C₄×C₂₃	—	2	1	no	—
149	C₂×C₄×C₂₃	—	2	1	no	—
150	C₂×C₄×C₂₃	—	2	1	no	—
151	C₂×C₄×C₂₃	—	2	1	no	—
152	C₂×C₄×C₂₃	—	2	1	no	—
153	C₂×C₄×C₂₃	—	2	1	no	—
154	C₂×C₄×C₂₃	—	2	2	no	—
155	C₂×C₄×C₂₃	—	2	2	no	—
156	C₂×C₄×C₂₃	—	2	2	no	—
157	C₂×C₄×C₂₃	—	2	2	no	—
158	C₂×C₄×C₂₃	—	2	4	no	—
159	C₂×C₄×C₂₃	—	2	1	no	—
160	C₂×C₄×C₂₃	—	2	1	no	—
161	C₂×C₄×C₂₃	—	2	1	no	—
162	C₂×C₄×C₂₃	—	2	1	no	—
163	C₂×C₄×C₂₃	—	2	1	no	—
164	C₂×C₄×C₂₃	—	2	1	no	—
165	C₂×C₄×C₂₃	—	4	2	no	—
166	C₂×C₄×C₂₃	—	4	2	no	—
167	C₂×C₄×C₂₃	—	4	2	no	—
168	C₂×C₄×C₂₃	—	4	2	no	—
169	C₂×C₄×C₂₃	—	4	2	no	—
170	C₂×C₄×C₂₃	—	4	2	no	—
171	C₂×C₄×C₂₃	—	4	2	no	—
172	C₂×C₄×C₂₃	—	4	2	no	—
173	C₂×C₄×C₂₃	—	4	2	no	—
174	C₂×C₄×C₂₃	—	4	2	no	—
175	C₂×C₄×C₂₃	—	4	2	no	—
176	C₂×C₄×C₂₃	C₄⋊Q₈	1	2	yes	—
177	C₂×C₄×C₂₃	#135	1	2	yes	—
178	C₂×C₄×C₂₃	#135	1	2	yes	—
179	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₂₃	C₂²×Q₈	1	1	yes	characteristic
181	C₂×C₄×C₂₃	C₂²×Q₈	1	1	yes	characteristic
182	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
184	C₂×C₄×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
185	C₈×C₂₃	—	2	2	no	—
186	C₈×C₂₃	—	2	2	no	—
187	C₈×C₂₃	—	2	2	no	—
188	C₈×C₂₃	C₂²⋊Q₈	1	4	yes	—
189	C₂×#500	C₂×C₂₃	1	1	yes	characteristic, complemented
190	C₂×#427	C₂×C₂₃	1	1	yes	characteristic
191	#2439	C₂×C₂₃	1	2	yes	—
192	#2085	C₂×C₂₃	1	2	yes	complemented
193	#2058	C₂×C₂₃	1	2	yes	complemented
194	#1942	C₂×C₂₃	1	1	yes	characteristic, complemented
195	#1942	C₂×C₂₃	1	1	yes	characteristic, complemented
196	#1854	C₂×C₂₃	1	2	yes	—
197	#1846	C₂×C₂₃	1	1	yes	characteristic, complemented
198	#1808	C₂×C₂₃	1	1	yes	characteristic
199	C₈×C₂²⋊C₄	C₂×C₂₃	1	1	yes	characteristic
200	C₂²×C₂₃	—	2	2	no	—
201	C₂²×C₂₃	—	2	2	no	—
202	C₂²×C₂₃	—	2	2	no	—
203	C₂²×C₂₃	—	4	1	no	—
204	C₂²×C₂₃	—	4	1	no	—
205	C₂²×C₂₃	—	4	1	no	—
206	C₂²×C₂₃	—	4	1	no	—
207	C₂²×C₂₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
208	C₂²×C₂₃	D₄²	1	1	yes	characteristic
209	C₂²×C₂₃	#547	1	1	yes	characteristic
210	C₂²×C₂₃	C₂×#135	1	1	yes	characteristic
211	C₂²×C₂₃	C₂×#135	1	1	yes	characteristic
212	C₂²×C₂₃	#576	1	1	yes	characteristic
213	C₂²×C₂₃	#578	1	1	yes	characteristic
214	C₄×C₂₃	—	2	2	no	—
215	C₄×C₂₃	—	2	2	no	—
216	C₄×C₂₃	—	2	2	no	—
217	C₄×C₂₃	—	4	1	no	—
218	C₄×C₂₃	—	4	1	no	—
219	C₄×C₂₃	—	4	4	no	—
220	C₄×C₂₃	—	8	2	no	—
221	C₄×C₂₃	—	8	2	no	—
222	C₄×C₂₃	—	8	2	no	—
223	C₄×C₂₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
224	C₄×C₂₃	#544	1	1	yes	characteristic
225	C₄×C₂₃	D₄×Q₈	1	1	yes	characteristic
226	C₄×C₂₃	#554	1	1	yes	characteristic
227	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
228	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
229	C₂×#117	C₂²×C₂₃	1	2	yes	—
230	#500	—	2	4	no	—
231	#427	—	2	4	no	—
232	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
233	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
234	C₂×#107	C₂²×C₂₃	1	2	yes	—
235	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
236	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
237	C₂×#106	C₂²×C₂₃	1	2	yes	—
238	C₂×#106	C₂²×C₂₃	1	2	yes	—
239	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
240	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
241	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
242	#396	—	2	2	no	—
243	#393	—	2	2	no	—
244	#391	—	2	2	no	—
245	#389	C₂²×C₂₃	1	2	yes	—
246	#389	C₂²×C₂₃	1	2	yes	—
247	#387	—	2	2	no	—
248	#382	C₂²×C₂₃	1	2	yes	—
249	#380	C₂²×C₂₃	1	2	yes	—
250	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
251	#340	C₂²×C₂₃	1	2	yes	—
252	#340	C₂²×C₂₃	1	2	yes	—
253	#340	C₂²×C₂₃	1	2	yes	—
254	#336	C₂²×C₂₃	1	1	yes	characteristic
255	#336	C₂²×C₂₃	1	1	yes	characteristic
256	C₂×C₂₃	—	4	2	no	—
257	C₂×C₂₃	#2440	1	1	yes	characteristic
258	C₂×C₂₃	#3160	1	1	yes	characteristic
259	C₂×C₂₃	#3164	1	1	yes	characteristic
260	C₂×C₂₃	#3280	1	1	yes	characteristic
261	C₂×C₂₃	#3285	1	1	yes	characteristic
262	C₂×C₂₃	#3341	1	1	yes	characteristic
263	C₂×C₂₃	#3342	1	1	yes	characteristic
264	C₂²×Q₈	—	2	2	no	—
265	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
266	C₂²×C₈	—	2	2	no	—
267	C₂²×C₈	—	2	2	no	—
268	C₂²×C₈	Q₈×C₂₃	1	4	yes	complemented
269	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
270	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
271	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
272	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
273	C₄⋊Q₈	—	2	4	no	—
274	C₄⋊Q₈	—	4	2	no	—
275	#117	—	2	4	no	—
276	#117	—	4	2	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
281	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
282	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
283	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
287	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
288	C₂×C₄²	—	2	2	no	—
289	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
290	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
291	#107	—	2	2	no	—
292	#107	—	2	2	no	—
293	#107	—	2	2	no	—
294	#107	—	2	4	no	—
295	#107	D₄×C₂₃	1	4	yes	—
296	#106	—	2	4	no	—
297	#106	—	4	2	no	—
298	C₂²⋊C₈	Q₈×C₂₃	1	4	yes	complemented
299	C₄×C₈	—	2	2	no	—
300	C₄×C₈	—	2	2	no	—
301	#95	—	2	2	no	—
302	#95	—	2	2	no	—
303	#95	—	2	2	no	—
304	#95	—	2	2	no	—
305	#95	—	2	2	no	—
306	#95	D₄×C₂₃	1	1	yes	characteristic
307	#95	D₄×C₂₃	1	1	yes	characteristic
308	C₂₃	#26064	1	1	yes	characteristic, direct product factor, Sylow
309	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
310	C₂×Q₈	—	4	4	no	—
311	C₂×Q₈	—	4	4	no	—
312	C₂×Q₈	—	8	2	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
323	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
324	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
326	C₂²×C₄	C₂×Q₈×C₂₃	1	2	yes	—
327	C₂²×C₄	C₂×Q₈×C₂₃	1	2	yes	—
328	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	8	no	—
336	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
337	C₂×C₈	C₂×Q₈×C₂₃	1	2	yes	—
338	C₂×C₈	C₂×Q₈×C₂₃	1	2	yes	—
339	C₂×C₈	C₂×Q₈×C₂₃	1	2	yes	—
340	C₂×C₈	C₂×Q₈×C₂₃	1	2	yes	—
341	C₂×C₈	#41×C₂₃	1	2	yes	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	4	4	no	—
350	C₄⋊C₄	—	4	4	no	—
351	C₄⋊C₄	—	8	2	no	—
352	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
353	C₂²⋊C₄	—	2	2	no	—
354	C₂²⋊C₄	—	2	2	no	—
355	C₂²⋊C₄	—	4	4	no	—
356	C₂²⋊C₄	—	8	2	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	4	4	no	—
362	C₂³	—	2	1	no	—
363	C₂³	—	2	1	no	—
364	C₂³	—	2	1	no	—
365	C₂³	—	2	1	no	—
366	C₂³	—	2	1	no	—
367	C₂³	—	2	1	no	—
368	C₂³	C₂₃×C₄⋊Q₈	1	2	yes	—
369	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
370	Q₈	—	8	8	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	C₂₃×C₄⋊Q₈	1	2	yes	—
400	C₂×C₄	C₂₃×#135	1	2	yes	—
401	C₂×C₄	C₂₃×#135	1	2	yes	—
402	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
403	C₂×C₄	C₂²×Q₈×C₂₃	1	1	yes	characteristic
404	C₂×C₄	C₂²×Q₈×C₂₃	1	1	yes	characteristic
405	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
406	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
407	C₂×C₄	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
408	C₈	—	2	2	no	—
409	C₈	—	2	2	no	—
410	C₈	—	2	2	no	—
411	C₈	C₂₃×C₂²⋊Q₈	1	4	yes	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	4	1	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	4	1	no	—
419	C₂²	C₂×C₂₃×C₄⋊Q₈	1	1	yes	characteristic
420	C₂²	D₄²×C₂₃	1	1	yes	characteristic
421	C₂²	C₂₃×#547	1	1	yes	characteristic
422	C₂²	C₂×C₂₃×#135	1	1	yes	characteristic
423	C₂²	C₂×C₂₃×#135	1	1	yes	characteristic
424	C₂²	C₂₃×#576	1	1	yes	characteristic
425	C₂²	C₂₃×#578	1	1	yes	characteristic
426	C₄	—	2	2	no	—
427	C₄	—	2	2	no	—
428	C₄	—	2	2	no	—
429	C₄	—	4	4	no	—
430	C₄	—	4	1	no	—
431	C₄	—	4	1	no	—
432	C₄	—	8	2	no	—
433	C₄	—	8	2	no	—
434	C₄	—	8	2	no	—
435	C₄	C₂×C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
436	C₄	C₂₃×#544	1	1	yes	characteristic
437	C₄	D₄×Q₈×C₂₃	1	1	yes	characteristic
438	C₄	C₂₃×#554	1	1	yes	characteristic
439	C₂	—	4	2	no	—
440	C₂	C₂₃×#2440	1	1	yes	characteristic
441	C₂	C₂₃×#3160	1	1	yes	characteristic
442	C₂	C₂₃×#3164	1	1	yes	characteristic
443	C₂	C₂₃×#3280	1	1	yes	characteristic
444	C₂	C₂₃×#3285	1	1	yes	characteristic
445	C₂	C₂₃×#3341	1	1	yes	characteristic
446	C₂	C₂₃×#3342	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#500	C₂	semidirect
4. C₂₃×#2085	C₂	semidirect
5. C₂₃×#2058	C₂	semidirect
6. C₂₃×#1942	C₂	semidirect
7. C₂₃×#1942	C₂	semidirect
9. C₂₃×#1846	C₂	semidirect
45. C₂²×C₈×C₂₃	Q₈	semidirect
75. C₂₃×C₂²⋊C₈	Q₈	semidirect
138. #26064	C₂₃	direct (N × H)
189. C₂×#500	C₂×C₂₃	semidirect
192. #2085	C₂×C₂₃	semidirect
193. #2058	C₂×C₂₃	semidirect
194. #1942	C₂×C₂₃	semidirect
195. #1942	C₂×C₂₃	semidirect
197. #1846	C₂×C₂₃	semidirect
268. C₂²×C₈	Q₈×C₂₃	semidirect
298. C₂²⋊C₈	Q₈×C₂₃	semidirect
308. C₂₃	#26064	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×#500	2
C₂×C₂₃×#427	2
C₂₃×#2439	2
C₂₃×#2085	2
C₂₃×#2058	2
C₂₃×#1942	2
C₂₃×#1854	2
C₂₃×#1846	2
C₂₃×#1808	2
C₈×C₂²⋊C₄×C₂₃	2
#26064	23

Subgroups — C23×#26064 #19173690

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#26064 #19173690