Subgroups — C₂₃×#26066 #19173692

Order 5888.

778 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#499	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#427	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2441	C₂	1	2	yes	maximal
4	C₂₃×#2084	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2059	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×#1845	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×#125	C₂²	1	2	yes	—
14	C₂×C₂₃×#117	C₂²	1	2	yes	—
15	C₂₃×#499	—	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×#399	—	2	2	no	—
28	C₂₃×#396	—	2	2	no	—
29	C₂₃×#389	—	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×#384	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	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₂₃	—	2	2	no	—
43	C₂²×C₈×C₂₃	—	2	2	no	—
44	C₂²×C₈×C₂₃	Q₈	1	4	yes	—
45	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
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	C₂₃×#125	—	2	4	no	—
50	C₂₃×#125	—	4	2	no	—
51	C₂₃×#117	—	2	4	no	—
52	C₂₃×#117	—	4	2	no	—
53	C₂×C₄⋊C₄×C₂₃	—	2	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	—	2	2	no	—
58	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
59	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
63	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₂₃	—	2	2	no	—
68	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
70	C₂₃×#107	—	2	2	no	—
71	C₂₃×#107	—	2	2	no	—
72	C₂₃×#107	—	2	2	no	—
73	C₂₃×#107	—	4	2	no	—
74	C₂₃×#107	D₄	1	4	yes	—
75	C₂₃×#106	—	2	4	no	—
76	C₂₃×#106	—	2	4	no	—
77	C₂₃×C₂²⋊C₈	Q₈	1	4	yes	—
78	C₄×C₈×C₂₃	—	2	2	no	—
79	C₄×C₈×C₂₃	—	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	C₂²×C₄×C₂₃	—	2	1	no	—
87	C₂²×C₄×C₂₃	—	2	1	no	—
88	C₂²×C₄×C₂₃	—	2	1	no	—
89	C₂²×C₄×C₂₃	—	2	1	no	—
90	C₂²×C₄×C₂₃	—	2	2	no	—
91	C₂²×C₄×C₂₃	—	2	2	no	—
92	C₂²×C₄×C₂₃	—	2	2	no	—
93	C₂²×C₄×C₂₃	—	2	2	no	—
94	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
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×Q₈	1	2	yes	—
100	C₂²×C₄×C₂₃	C₂×Q₈	1	2	yes	—
101	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
102	C₂×C₈×C₂₃	—	2	1	no	—
103	C₂×C₈×C₂₃	—	2	1	no	—
104	C₂×C₈×C₂₃	—	2	1	no	—
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	8	no	—
109	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
110	C₂×C₈×C₂₃	C₂×Q₈	1	2	yes	—
111	C₂×C₈×C₂₃	C₂×Q₈	1	2	yes	—
112	C₂×C₈×C₂₃	C₂×Q₈	1	2	yes	—
113	C₂×C₈×C₂₃	C₂×Q₈	1	2	yes	—
114	C₂×C₈×C₂₃	#41	1	2	yes	—
115	C₄⋊C₄×C₂₃	—	2	2	no	—
116	C₄⋊C₄×C₂₃	—	2	2	no	—
117	C₄⋊C₄×C₂₃	—	2	2	no	—
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	—	4	4	no	—
123	C₄⋊C₄×C₂₃	—	4	4	no	—
124	C₄⋊C₄×C₂₃	—	4	4	no	—
125	C₄⋊C₄×C₂₃	—	4	4	no	—
126	C₄⋊C₄×C₂₃	—	8	2	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	#26066	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	C₂×C₄×C₂₃	—	2	1	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	2	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	1	no	—
158	C₂×C₄×C₂₃	—	2	1	no	—
159	C₂×C₄×C₂₃	—	2	4	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	—	4	2	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	C₄⋊Q₈	1	2	yes	—
176	C₂×C₄×C₂₃	#135	1	2	yes	—
177	C₂×C₄×C₂₃	#135	1	2	yes	—
178	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₂₃	C₂²×Q₈	1	1	yes	characteristic
180	C₂×C₄×C₂₃	C₂²×Q₈	1	1	yes	characteristic
181	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
183	C₂×C₄×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
184	C₈×C₂₃	—	2	2	no	—
185	C₈×C₂₃	—	2	2	no	—
186	C₈×C₂₃	—	2	2	no	—
187	C₈×C₂₃	C₂²⋊Q₈	1	4	yes	—
188	C₂×#499	C₂×C₂₃	1	1	yes	characteristic, complemented
189	C₂×#427	C₂×C₂₃	1	1	yes	characteristic
190	#2441	C₂×C₂₃	1	2	yes	—
191	#2084	C₂×C₂₃	1	2	yes	complemented
192	#2059	C₂×C₂₃	1	2	yes	complemented
193	#1942	C₂×C₂₃	1	1	yes	characteristic, complemented
194	#1942	C₂×C₂₃	1	1	yes	characteristic, complemented
195	#1854	C₂×C₂₃	1	2	yes	—
196	#1845	C₂×C₂₃	1	1	yes	characteristic, complemented
197	#1808	C₂×C₂₃	1	1	yes	characteristic
198	C₈×C₂²⋊C₄	C₂×C₂₃	1	1	yes	characteristic
199	C₂²×C₂₃	—	2	2	no	—
200	C₂²×C₂₃	—	2	2	no	—
201	C₂²×C₂₃	—	2	2	no	—
202	C₂²×C₂₃	—	4	1	no	—
203	C₂²×C₂₃	—	4	1	no	—
204	C₂²×C₂₃	—	4	1	no	—
205	C₂²×C₂₃	—	4	1	no	—
206	C₂²×C₂₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
207	C₂²×C₂₃	D₄²	1	1	yes	characteristic
208	C₂²×C₂₃	#547	1	1	yes	characteristic
209	C₂²×C₂₃	C₂×#135	1	1	yes	characteristic
210	C₂²×C₂₃	C₂×#135	1	1	yes	characteristic
211	C₂²×C₂₃	#576	1	1	yes	characteristic
212	C₂²×C₂₃	#578	1	1	yes	characteristic
213	C₄×C₂₃	—	2	2	no	—
214	C₄×C₂₃	—	2	2	no	—
215	C₄×C₂₃	—	2	2	no	—
216	C₄×C₂₃	—	4	1	no	—
217	C₄×C₂₃	—	4	4	no	—
218	C₄×C₂₃	—	4	1	no	—
219	C₄×C₂₃	—	8	2	no	—
220	C₄×C₂₃	—	8	2	no	—
221	C₄×C₂₃	—	8	2	no	—
222	C₄×C₂₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
223	C₄×C₂₃	#544	1	1	yes	characteristic
224	C₄×C₂₃	D₄×Q₈	1	1	yes	characteristic
225	C₄×C₂₃	#554	1	1	yes	characteristic
226	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
227	C₂×#125	C₂²×C₂₃	1	2	yes	—
228	C₂×#117	C₂²×C₂₃	1	2	yes	—
229	#499	—	2	4	no	—
230	#427	—	2	4	no	—
231	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
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×#106	C₂²×C₂₃	1	2	yes	—
237	C₂×#106	C₂²×C₂₃	1	2	yes	—
238	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
239	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
240	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
241	#399	—	2	2	no	—
242	#396	—	2	2	no	—
243	#389	—	2	2	no	—
244	#389	C₂²×C₂₃	1	2	yes	—
245	#389	C₂²×C₂₃	1	2	yes	—
246	#387	—	2	2	no	—
247	#384	C₂²×C₂₃	1	2	yes	—
248	#380	C₂²×C₂₃	1	2	yes	—
249	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
250	#340	C₂²×C₂₃	1	2	yes	—
251	#340	C₂²×C₂₃	1	2	yes	—
252	#340	C₂²×C₂₃	1	2	yes	—
253	#336	C₂²×C₂₃	1	1	yes	characteristic
254	#336	C₂²×C₂₃	1	1	yes	characteristic
255	C₂×C₂₃	—	4	2	no	—
256	C₂×C₂₃	#2440	1	1	yes	characteristic
257	C₂×C₂₃	#3160	1	1	yes	characteristic
258	C₂×C₂₃	#3164	1	1	yes	characteristic
259	C₂×C₂₃	#3283	1	1	yes	characteristic
260	C₂×C₂₃	#3287	1	1	yes	characteristic
261	C₂×C₂₃	#3336	1	1	yes	characteristic
262	C₂×C₂₃	#3339	1	1	yes	characteristic
263	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
264	C₂²×C₈	—	2	2	no	—
265	C₂²×C₈	—	2	2	no	—
266	C₂²×C₈	Q₈×C₂₃	1	4	yes	—
267	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
268	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
269	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
270	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
271	#125	—	2	4	no	—
272	#125	—	4	2	no	—
273	#117	—	2	4	no	—
274	#117	—	4	2	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	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	—	2	2	no	—
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×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
288	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
289	C₂×C₄²	—	2	2	no	—
290	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
291	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
292	#107	—	2	2	no	—
293	#107	—	2	2	no	—
294	#107	—	2	2	no	—
295	#107	—	4	2	no	—
296	#107	D₄×C₂₃	1	4	yes	—
297	#106	—	2	4	no	—
298	#106	—	2	4	no	—
299	C₂²⋊C₈	Q₈×C₂₃	1	4	yes	—
300	C₄×C₈	—	2	2	no	—
301	C₄×C₈	—	2	2	no	—
302	#95	—	2	2	no	—
303	#95	—	2	2	no	—
304	#95	—	2	2	no	—
305	#95	D₄×C₂₃	1	1	yes	characteristic
306	#95	D₄×C₂₃	1	1	yes	characteristic
307	C₂₃	#26066	1	1	yes	characteristic, direct product factor, Sylow
308	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
322	C₂²×C₄	C₂×Q₈×C₂₃	1	2	yes	—
323	C₂²×C₄	C₂×Q₈×C₂₃	1	2	yes	—
324	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	8	no	—
332	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
333	C₂×C₈	C₂×Q₈×C₂₃	1	2	yes	—
334	C₂×C₈	C₂×Q₈×C₂₃	1	2	yes	—
335	C₂×C₈	C₂×Q₈×C₂₃	1	2	yes	—
336	C₂×C₈	C₂×Q₈×C₂₃	1	2	yes	—
337	C₂×C₈	#41×C₂₃	1	2	yes	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	4	4	no	—
346	C₄⋊C₄	—	4	4	no	—
347	C₄⋊C₄	—	4	4	no	—
348	C₄⋊C₄	—	4	4	no	—
349	C₄⋊C₄	—	8	2	no	—
350	C₄⋊C₄	—	8	2	no	—
351	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
352	C₂²⋊C₄	—	2	2	no	—
353	C₂²⋊C₄	—	2	2	no	—
354	C₂²⋊C₄	—	4	4	no	—
355	C₂²⋊C₄	—	8	2	no	—
356	C₄²	—	2	1	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	4	4	no	—
361	C₂³	—	2	1	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	C₂₃×C₄⋊Q₈	1	2	yes	—
368	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	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	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	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	4	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	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	C₂₃×C₄⋊Q₈	1	2	yes	—
398	C₂×C₄	C₂₃×#135	1	2	yes	—
399	C₂×C₄	C₂₃×#135	1	2	yes	—
400	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
401	C₂×C₄	C₂²×Q₈×C₂₃	1	1	yes	characteristic
402	C₂×C₄	C₂²×Q₈×C₂₃	1	1	yes	characteristic
403	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
404	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
405	C₂×C₄	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	2	2	no	—
408	C₈	—	2	2	no	—
409	C₈	C₂₃×C₂²⋊Q₈	1	4	yes	—
410	C₂²	—	2	2	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	4	1	no	—
417	C₂²	C₂×C₂₃×C₄⋊Q₈	1	1	yes	characteristic
418	C₂²	D₄²×C₂₃	1	1	yes	characteristic
419	C₂²	C₂₃×#547	1	1	yes	characteristic
420	C₂²	C₂×C₂₃×#135	1	1	yes	characteristic
421	C₂²	C₂×C₂₃×#135	1	1	yes	characteristic
422	C₂²	C₂₃×#576	1	1	yes	characteristic
423	C₂²	C₂₃×#578	1	1	yes	characteristic
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	2	2	no	—
427	C₄	—	4	1	no	—
428	C₄	—	4	4	no	—
429	C₄	—	4	1	no	—
430	C₄	—	8	2	no	—
431	C₄	—	8	2	no	—
432	C₄	—	8	2	no	—
433	C₄	C₂×C₂₃×C₂²⋊Q₈	1	1	yes	characteristic
434	C₄	C₂₃×#544	1	1	yes	characteristic
435	C₄	D₄×Q₈×C₂₃	1	1	yes	characteristic
436	C₄	C₂₃×#554	1	1	yes	characteristic
437	C₂	—	4	2	no	—
438	C₂	C₂₃×#2440	1	1	yes	characteristic
439	C₂	C₂₃×#3160	1	1	yes	characteristic
440	C₂	C₂₃×#3164	1	1	yes	characteristic
441	C₂	C₂₃×#3283	1	1	yes	characteristic
442	C₂	C₂₃×#3287	1	1	yes	characteristic
443	C₂	C₂₃×#3336	1	1	yes	characteristic
444	C₂	C₂₃×#3339	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×#499	C₂	semidirect
4. C₂₃×#2084	C₂	semidirect
5. C₂₃×#2059	C₂	semidirect
6. C₂₃×#1942	C₂	semidirect
7. C₂₃×#1942	C₂	semidirect
9. C₂₃×#1845	C₂	semidirect
138. #26066	C₂₃	direct (N × H)
188. C₂×#499	C₂×C₂₃	semidirect
191. #2084	C₂×C₂₃	semidirect
192. #2059	C₂×C₂₃	semidirect
193. #1942	C₂×C₂₃	semidirect
194. #1942	C₂×C₂₃	semidirect
196. #1845	C₂×C₂₃	semidirect
307. C₂₃	#26066	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×#499	2
C₂×C₂₃×#427	2
C₂₃×#2441	2
C₂₃×#2084	2
C₂₃×#2059	2
C₂₃×#1942	2
C₂₃×#1854	2
C₂₃×#1845	2
C₂₃×#1808	2
C₈×C₂²⋊C₄×C₂₃	2
#26066	23

Subgroups — C23×#26066 #19173692

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#26066 #19173692