Subgroups — C₂₃×#36607 #19184233

Order 5888.

2524 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2847	C₂	1	3	yes	maximal, complemented
2	C₂₃×#2569	C₂	1	3	yes	maximal, complemented
3	C₂₃×#2543	C₂	1	3	yes	maximal, complemented
4	C₂₃×#2510	C₂	1	6	yes	maximal, complemented
5	C₂₃×#2444	C₂	1	6	yes	maximal, complemented
6	C₂₃×#2364	C₂	1	3	yes	maximal, complemented
7	C₂₃×#2353	C₂	1	3	yes	maximal, complemented
8	C₄×C₂₃×#120	C₂	1	3	yes	maximal, complemented
9	C₂²×C₂₃×#95	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂⁴×C₄×C₂₃	C₂²	1	3	yes	—
11	C₂×C₂₃×#121	C₂²	1	3	yes	—
12	C₂×C₂₃×#121	C₂²	1	6	yes	—
13	C₂×C₂₃×#120	C₂²	1	3	yes	—
14	C₂×C₄×D₄×C₂₃	C₂²	1	3	yes	—
15	C₂×C₄×D₄×C₂₃	C₂²	1	6	yes	—
16	C₂₃×#401	C₂²	1	2	yes	complemented
17	C₂₃×#400	C₂²	1	6	yes	complemented
18	C₂₃×#398	C₂²	1	3	yes	complemented
19	C₂₃×#397	C₂²	1	6	yes	complemented
20	C₂₃×#397	C₂²	1	3	yes	complemented
21	C₂₃×#394	C₂²	1	3	yes	complemented
22	C₂₃×#392	C₂²	1	1	yes	characteristic, complemented
23	C₂₃×#388	C₂²	1	6	yes	complemented
24	C₂₃×#388	C₂²	1	6	yes	complemented
25	C₂₃×#387	C₂²	1	6	yes	complemented
26	C₂₃×#387	C₂²	1	6	yes	complemented
27	C₂₃×#386	C₂²	1	3	yes	—
28	C₂₃×#386	C₂²	1	6	yes	—
29	C₂₃×#386	C₂²	1	6	yes	—
30	C₂₃×#386	C₂²	1	6	yes	—
31	C₂₃×#386	C₂²	1	6	yes	—
32	C₂₃×#386	C₂²	1	6	yes	complemented
33	C₂₃×#385	C₂²	1	6	yes	—
34	C₂₃×#385	C₂²	1	3	yes	—
35	C₂₃×#383	C₂²	1	3	yes	complemented
36	C₂₃×#381	C₂²	1	3	yes	complemented
37	C₂₃×#380	C₂²	1	6	yes	—
38	C₂₃×#380	C₂²	1	3	yes	—
39	C₂₃×#379	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊C₄×C₂₃	C₂²	1	6	yes	—
41	C₄×C₂²⋊C₄×C₂₃	C₂²	1	3	yes	—
42	C₄×C₂²⋊C₄×C₂₃	C₂²	1	3	yes	complemented
43	C₂₃×#376	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₂₃×#95	C₂²	1	6	yes	—
45	C₂×C₂₃×#95	C₂²	1	3	yes	—
46	C₂×C₂₃×#95	C₂²	1	3	yes	—
47	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₂₃	C₂³	1	3	yes	—
49	C₂²×D₄×C₂₃	C₂³	1	6	yes	—
50	C₂²×D₄×C₂₃	C₂³	1	3	yes	—
51	C₂³×C₄×C₂₃	—	2	12	no	—
52	C₂³×C₄×C₂₃	—	4	12	no	—
53	C₂³×C₄×C₂₃	C₂³	1	6	yes	—
54	C₂³×C₄×C₂₃	C₂³	1	6	yes	—
55	C₂³×C₄×C₂₃	C₂³	1	3	yes	—
56	C₂³×C₄×C₂₃	C₂³	1	3	yes	—
57	C₂³×C₄×C₂₃	C₂³	1	3	yes	—
58	C₂₃×#121	—	2	12	no	—
59	C₂₃×#121	—	4	12	no	—
60	C₂₃×#120	—	2	12	no	—
61	C₄×D₄×C₂₃	—	2	12	no	—
62	C₄×D₄×C₂₃	—	4	12	no	—
63	C₂×C₄⋊C₄×C₂₃	C₂³	1	3	yes	—
64	C₂×C₄⋊C₄×C₂₃	C₂³	1	3	yes	—
65	C₂×C₄⋊C₄×C₂₃	C₂³	1	6	yes	—
66	C₂×C₄⋊C₄×C₂₃	C₂³	1	6	yes	—
67	C₂×C₂²⋊C₄×C₂₃	C₂³	1	3	yes	—
68	C₂×C₂²⋊C₄×C₂₃	C₂³	1	3	yes	—
69	C₂×C₂²⋊C₄×C₂₃	C₂³	1	6	yes	—
70	C₂×C₂²⋊C₄×C₂₃	C₂³	1	3	yes	—
71	C₂×C₂²⋊C₄×C₂₃	C₂³	1	6	yes	—
72	C₂×C₂²⋊C₄×C₂₃	C₂³	1	3	yes	—
73	C₂×C₂²⋊C₄×C₂₃	C₂³	1	6	yes	—
74	C₂×C₂²⋊C₄×C₂₃	C₂³	1	6	yes	—
75	C₂×C₂²⋊C₄×C₂₃	C₂³	1	6	yes	—
76	C₂×C₄²×C₂₃	C₂³	1	3	yes	—
77	C₂×C₄²×C₂₃	C₂³	1	6	yes	—
78	C₂₃×#95	C₂³	1	1	yes	characteristic
79	C₂₃×#95	C₂³	1	3	yes	—
80	C₂₃×#95	C₂³	1	6	yes	—
81	C₂₃×#95	C₂³	1	1	yes	characteristic
82	C₂₃×#95	C₂³	1	3	yes	—
83	C₂₃×#95	C₂³	1	2	yes	—
84	C₂₃×#95	C₂³	1	3	yes	—
85	C₂₃×#95	C₂³	1	6	yes	—
86	C₂₃×#95	C₂³	1	6	yes	—
87	C₂₃×#95	C₂³	1	6	yes	—
88	C₂₃×#95	C₂³	1	3	yes	—
89	C₂₃×#95	C₂³	1	6	yes	—
90	C₂₃×#95	C₂³	1	6	yes	—
91	C₂⁴×C₂₃	—	2	6	no	—
92	C₂⁴×C₂₃	—	2	6	no	—
93	C₂⁴×C₂₃	#41	1	4	yes	—
94	C₂⁴×C₂₃	C₂⁴	1	3	yes	—
95	C₂⁴×C₂₃	C₂⁴	1	3	yes	—
96	C₂×D₄×C₂₃	—	2	6	no	—
97	C₂×D₄×C₂₃	—	2	6	no	—
98	C₂×D₄×C₂₃	—	2	12	no	—
99	C₂×D₄×C₂₃	—	2	12	no	—
100	C₂×D₄×C₂₃	—	2	12	no	—
101	C₂×D₄×C₂₃	—	2	6	no	—
102	C₂×D₄×C₂₃	—	2	6	no	—
103	C₂×D₄×C₂₃	—	4	6	no	—
104	C₂²×C₄×C₂₃	—	2	6	no	—
105	C₂²×C₄×C₂₃	—	2	12	no	—
106	C₂²×C₄×C₂₃	—	2	12	no	—
107	C₂²×C₄×C₂₃	—	2	12	no	—
108	C₂²×C₄×C₂₃	—	2	12	no	—
109	C₂²×C₄×C₂₃	—	2	6	no	—
110	C₂²×C₄×C₂₃	—	4	6	no	—
111	C₂²×C₄×C₂₃	—	4	6	no	—
112	C₂²×C₄×C₂₃	—	4	6	no	—
113	C₂²×C₄×C₂₃	—	4	6	no	—
114	C₂²×C₄×C₂₃	—	4	6	no	—
115	C₂²×C₄×C₂₃	—	4	48	no	—
116	C₂²×C₄×C₂₃	#41	1	12	yes	—
117	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
118	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
119	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
120	C₂²×C₄×C₂₃	C₂⁴	1	6	yes	—
121	C₂²×C₄×C₂₃	C₂⁴	1	6	yes	—
122	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
123	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
124	C₄⋊C₄×C₂₃	—	2	6	no	—
125	C₄⋊C₄×C₂₃	—	2	6	no	—
126	C₄⋊C₄×C₂₃	—	4	6	no	—
127	C₄⋊C₄×C₂₃	—	4	6	no	—
128	C₂²⋊C₄×C₂₃	—	2	6	no	—
129	C₂²⋊C₄×C₂₃	—	2	12	no	—
130	C₂²⋊C₄×C₂₃	—	2	6	no	—
131	C₂²⋊C₄×C₂₃	—	2	6	no	—
132	C₂²⋊C₄×C₂₃	—	2	6	no	—
133	C₂²⋊C₄×C₂₃	—	2	12	no	—
134	C₂²⋊C₄×C₂₃	—	4	6	no	—
135	C₂²⋊C₄×C₂₃	—	4	6	no	—
136	C₂²⋊C₄×C₂₃	—	4	6	no	—
137	C₄²×C₂₃	—	2	6	no	—
138	C₄²×C₂₃	—	4	6	no	—
139	#36607	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂³×C₂₃	—	2	24	no	—
141	C₂³×C₂₃	—	2	8	no	—
142	C₂³×C₂₃	—	2	24	no	—
143	C₂³×C₂₃	—	2	6	no	—
144	C₂³×C₂₃	—	2	6	no	—
145	C₂³×C₂₃	—	2	3	no	—
146	C₂³×C₂₃	—	2	6	no	—
147	C₂³×C₂₃	—	2	3	no	—
148	C₂³×C₂₃	—	2	6	no	—
149	C₂³×C₂₃	—	2	3	no	—
150	C₂³×C₂₃	C₂×#41	1	6	yes	—
151	C₂³×C₂₃	C₂×#41	1	6	yes	—
152	C₂³×C₂₃	H(5,𝔽₂)	1	6	yes	—
153	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
154	D₄×C₂₃	—	4	12	no	—
155	D₄×C₂₃	—	4	24	no	—
156	D₄×C₂₃	—	8	6	no	—
157	C₂×C₄×C₂₃	—	2	6	no	—
158	C₂×C₄×C₂₃	—	2	6	no	—
159	C₂×C₄×C₂₃	—	2	3	no	—
160	C₂×C₄×C₂₃	—	2	3	no	—
161	C₂×C₄×C₂₃	—	2	3	no	—
162	C₂×C₄×C₂₃	—	2	6	no	—
163	C₂×C₄×C₂₃	—	2	3	no	—
164	C₂×C₄×C₂₃	—	2	6	no	—
165	C₂×C₄×C₂₃	—	2	6	no	—
166	C₂×C₄×C₂₃	—	2	6	no	—
167	C₂×C₄×C₂₃	—	2	6	no	—
168	C₂×C₄×C₂₃	—	2	3	no	—
169	C₂×C₄×C₂₃	—	2	6	no	—
170	C₂×C₄×C₂₃	—	2	6	no	—
171	C₂×C₄×C₂₃	—	4	12	no	—
172	C₂×C₄×C₂₃	—	4	24	no	—
173	C₂×C₄×C₂₃	—	4	24	no	—
174	C₂×C₄×C₂₃	—	4	12	no	—
175	C₂×C₄×C₂₃	—	8	6	no	—
176	C₂×C₄×C₂₃	C₂×#41	1	6	yes	—
177	C₂×C₄×C₂₃	C₂×#41	1	6	yes	—
178	#2847	C₂×C₂₃	1	3	yes	complemented
179	#2569	C₂×C₂₃	1	3	yes	complemented
180	#2543	C₂×C₂₃	1	3	yes	complemented
181	#2510	C₂×C₂₃	1	6	yes	complemented
182	#2444	C₂×C₂₃	1	6	yes	complemented
183	#2364	C₂×C₂₃	1	3	yes	complemented
184	#2353	C₂×C₂₃	1	3	yes	complemented
185	C₄×#120	C₂×C₂₃	1	3	yes	complemented
186	C₂²×#95	C₂×C₂₃	1	1	yes	characteristic, complemented
187	C₂²×C₂₃	—	2	32	no	—
188	C₂²×C₂₃	—	2	6	no	—
189	C₂²×C₂₃	—	2	12	no	—
190	C₂²×C₂₃	—	2	6	no	—
191	C₂²×C₂₃	—	2	12	no	—
192	C₂²×C₂₃	—	4	3	no	—
193	C₂²×C₂₃	—	4	3	no	—
194	C₂²×C₂₃	—	4	6	no	—
195	C₂²×C₂₃	—	4	3	no	—
196	C₂²×C₂₃	—	4	6	no	—
197	C₂²×C₂₃	#553	1	12	yes	—
198	C₂²×C₂₃	C₂²×#41	1	3	yes	—
199	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
200	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	3	yes	—
201	C₄×C₂₃	—	2	6	no	—
202	C₄×C₂₃	—	2	6	no	—
203	C₄×C₂₃	—	4	1	no	—
204	C₄×C₂₃	—	4	3	no	—
205	C₄×C₂₃	—	4	6	no	—
206	C₄×C₂₃	—	4	6	no	—
207	C₄×C₂₃	—	4	3	no	—
208	C₂⁴×C₄	C₂²×C₂₃	1	3	yes	—
209	C₂×#121	C₂²×C₂₃	1	3	yes	—
210	C₂×#121	C₂²×C₂₃	1	6	yes	—
211	C₂×#120	C₂²×C₂₃	1	3	yes	—
212	C₂×C₄×D₄	C₂²×C₂₃	1	3	yes	—
213	C₂×C₄×D₄	C₂²×C₂₃	1	6	yes	—
214	#401	C₂²×C₂₃	1	2	yes	complemented
215	#400	C₂²×C₂₃	1	6	yes	complemented
216	#398	C₂²×C₂₃	1	3	yes	complemented
217	#397	C₂²×C₂₃	1	6	yes	complemented
218	#397	C₂²×C₂₃	1	3	yes	complemented
219	#394	C₂²×C₂₃	1	3	yes	complemented
220	#392	C₂²×C₂₃	1	1	yes	characteristic, complemented
221	#388	C₂²×C₂₃	1	6	yes	complemented
222	#388	C₂²×C₂₃	1	6	yes	complemented
223	#387	C₂²×C₂₃	1	6	yes	complemented
224	#387	C₂²×C₂₃	1	6	yes	complemented
225	#386	C₂²×C₂₃	1	6	yes	—
226	#386	C₂²×C₂₃	1	6	yes	—
227	#386	C₂²×C₂₃	1	6	yes	—
228	#386	C₂²×C₂₃	1	3	yes	—
229	#386	C₂²×C₂₃	1	6	yes	—
230	#386	C₂²×C₂₃	1	6	yes	complemented
231	#385	C₂²×C₂₃	1	6	yes	—
232	#385	C₂²×C₂₃	1	3	yes	—
233	#383	C₂²×C₂₃	1	3	yes	complemented
234	#381	C₂²×C₂₃	1	3	yes	complemented
235	#380	C₂²×C₂₃	1	3	yes	—
236	#380	C₂²×C₂₃	1	6	yes	—
237	#379	C₂²×C₂₃	1	1	yes	characteristic
238	C₄×C₂²⋊C₄	C₂²×C₂₃	1	3	yes	—
239	C₄×C₂²⋊C₄	C₂²×C₂₃	1	6	yes	—
240	C₄×C₂²⋊C₄	C₂²×C₂₃	1	3	yes	complemented
241	#376	C₂²×C₂₃	1	1	yes	characteristic, complemented
242	C₂×#95	C₂²×C₂₃	1	3	yes	—
243	C₂×#95	C₂²×C₂₃	1	3	yes	—
244	C₂×#95	C₂²×C₂₃	1	6	yes	—
245	C₂×C₂₃	—	2	12	no	—
246	C₂×C₂₃	—	8	3	no	—
247	C₂×C₂₃	#3444	1	1	yes	characteristic
248	C₂×C₂₃	C₂×#553	1	3	yes	—
249	C₂×C₂₃	#3490	1	3	yes	—
250	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
251	C₂²×D₄	C₂³×C₂₃	1	3	yes	—
252	C₂²×D₄	C₂³×C₂₃	1	6	yes	—
253	C₂²×D₄	C₂³×C₂₃	1	3	yes	—
254	C₂³×C₄	—	2	12	no	—
255	C₂³×C₄	—	4	12	no	—
256	C₂³×C₄	C₂³×C₂₃	1	6	yes	—
257	C₂³×C₄	C₂³×C₂₃	1	6	yes	—
258	C₂³×C₄	C₂³×C₂₃	1	3	yes	—
259	C₂³×C₄	C₂³×C₂₃	1	3	yes	—
260	C₂³×C₄	C₂³×C₂₃	1	3	yes	—
261	#121	—	2	12	no	—
262	#121	—	4	12	no	—
263	#120	—	2	12	no	—
264	C₄×D₄	—	2	12	no	—
265	C₄×D₄	—	4	12	no	—
266	C₂×C₄⋊C₄	C₂³×C₂₃	1	3	yes	—
267	C₂×C₄⋊C₄	C₂³×C₂₃	1	3	yes	—
268	C₂×C₄⋊C₄	C₂³×C₂₃	1	6	yes	—
269	C₂×C₄⋊C₄	C₂³×C₂₃	1	6	yes	—
270	C₂×C₂²⋊C₄	C₂³×C₂₃	1	3	yes	—
271	C₂×C₂²⋊C₄	C₂³×C₂₃	1	3	yes	—
272	C₂×C₂²⋊C₄	C₂³×C₂₃	1	3	yes	—
273	C₂×C₂²⋊C₄	C₂³×C₂₃	1	3	yes	—
274	C₂×C₂²⋊C₄	C₂³×C₂₃	1	6	yes	—
275	C₂×C₂²⋊C₄	C₂³×C₂₃	1	6	yes	—
276	C₂×C₂²⋊C₄	C₂³×C₂₃	1	6	yes	—
277	C₂×C₂²⋊C₄	C₂³×C₂₃	1	6	yes	—
278	C₂×C₂²⋊C₄	C₂³×C₂₃	1	6	yes	—
279	C₂×C₄²	C₂³×C₂₃	1	3	yes	—
280	C₂×C₄²	C₂³×C₂₃	1	6	yes	—
281	#95	C₂³×C₂₃	1	1	yes	characteristic
282	#95	C₂³×C₂₃	1	3	yes	—
283	#95	C₂³×C₂₃	1	6	yes	—
284	#95	C₂³×C₂₃	1	1	yes	characteristic
285	#95	C₂³×C₂₃	1	3	yes	—
286	#95	C₂³×C₂₃	1	2	yes	—
287	#95	C₂³×C₂₃	1	3	yes	—
288	#95	C₂³×C₂₃	1	6	yes	—
289	#95	C₂³×C₂₃	1	6	yes	—
290	#95	C₂³×C₂₃	1	6	yes	—
291	#95	C₂³×C₂₃	1	3	yes	—
292	#95	C₂³×C₂₃	1	6	yes	—
293	#95	C₂³×C₂₃	1	6	yes	—
294	C₂₃	#36607	1	1	yes	characteristic, direct product factor, Sylow
295	C₂⁴	—	2	6	no	—
296	C₂⁴	—	2	6	no	—
297	C₂⁴	#41×C₂₃	1	4	yes	—
298	C₂⁴	C₂⁴×C₂₃	1	3	yes	—
299	C₂⁴	C₂⁴×C₂₃	1	3	yes	—
300	C₂×D₄	—	2	6	no	—
301	C₂×D₄	—	2	6	no	—
302	C₂×D₄	—	2	12	no	—
303	C₂×D₄	—	2	12	no	—
304	C₂×D₄	—	2	12	no	—
305	C₂×D₄	—	2	6	no	—
306	C₂×D₄	—	2	6	no	—
307	C₂×D₄	—	4	6	no	—
308	C₂²×C₄	—	2	6	no	—
309	C₂²×C₄	—	2	12	no	—
310	C₂²×C₄	—	2	12	no	—
311	C₂²×C₄	—	2	12	no	—
312	C₂²×C₄	—	2	12	no	—
313	C₂²×C₄	—	2	6	no	—
314	C₂²×C₄	—	4	6	no	—
315	C₂²×C₄	—	4	6	no	—
316	C₂²×C₄	—	4	6	no	—
317	C₂²×C₄	—	4	6	no	—
318	C₂²×C₄	—	4	6	no	—
319	C₂²×C₄	—	4	48	no	—
320	C₂²×C₄	#41×C₂₃	1	12	yes	—
321	C₂²×C₄	C₂⁴×C₂₃	1	6	yes	—
322	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
323	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
324	C₂²×C₄	C₂⁴×C₂₃	1	6	yes	—
325	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
326	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
327	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
328	C₄⋊C₄	—	2	6	no	—
329	C₄⋊C₄	—	2	6	no	—
330	C₄⋊C₄	—	4	6	no	—
331	C₄⋊C₄	—	4	6	no	—
332	C₂²⋊C₄	—	2	6	no	—
333	C₂²⋊C₄	—	2	6	no	—
334	C₂²⋊C₄	—	2	12	no	—
335	C₂²⋊C₄	—	2	6	no	—
336	C₂²⋊C₄	—	2	6	no	—
337	C₂²⋊C₄	—	2	12	no	—
338	C₂²⋊C₄	—	4	6	no	—
339	C₂²⋊C₄	—	4	6	no	—
340	C₂²⋊C₄	—	4	6	no	—
341	C₄²	—	2	6	no	—
342	C₄²	—	4	6	no	—
343	C₂³	—	2	24	no	—
344	C₂³	—	2	8	no	—
345	C₂³	—	2	24	no	—
346	C₂³	—	2	6	no	—
347	C₂³	—	2	6	no	—
348	C₂³	—	2	3	no	—
349	C₂³	—	2	6	no	—
350	C₂³	—	2	3	no	—
351	C₂³	—	2	6	no	—
352	C₂³	—	2	3	no	—
353	C₂³	C₂×#41×C₂₃	1	6	yes	—
354	C₂³	C₂×#41×C₂₃	1	6	yes	—
355	C₂³	C₂₃×H(5,𝔽₂)	1	6	yes	—
356	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
357	D₄	—	4	12	no	—
358	D₄	—	4	24	no	—
359	D₄	—	8	6	no	—
360	C₂×C₄	—	2	6	no	—
361	C₂×C₄	—	2	6	no	—
362	C₂×C₄	—	2	3	no	—
363	C₂×C₄	—	2	3	no	—
364	C₂×C₄	—	2	3	no	—
365	C₂×C₄	—	2	6	no	—
366	C₂×C₄	—	2	3	no	—
367	C₂×C₄	—	2	6	no	—
368	C₂×C₄	—	2	6	no	—
369	C₂×C₄	—	2	6	no	—
370	C₂×C₄	—	2	6	no	—
371	C₂×C₄	—	2	3	no	—
372	C₂×C₄	—	2	6	no	—
373	C₂×C₄	—	2	6	no	—
374	C₂×C₄	—	4	12	no	—
375	C₂×C₄	—	4	24	no	—
376	C₂×C₄	—	4	24	no	—
377	C₂×C₄	—	4	12	no	—
378	C₂×C₄	—	8	6	no	—
379	C₂×C₄	C₂×#41×C₂₃	1	6	yes	—
380	C₂×C₄	C₂×#41×C₂₃	1	6	yes	—
381	C₂²	—	2	32	no	—
382	C₂²	—	2	6	no	—
383	C₂²	—	2	12	no	—
384	C₂²	—	2	6	no	—
385	C₂²	—	2	12	no	—
386	C₂²	—	4	3	no	—
387	C₂²	—	4	3	no	—
388	C₂²	—	4	6	no	—
389	C₂²	—	4	3	no	—
390	C₂²	—	4	6	no	—
391	C₂²	C₂₃×#553	1	12	yes	—
392	C₂²	C₂²×#41×C₂₃	1	3	yes	—
393	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
394	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	3	yes	—
395	C₄	—	2	6	no	—
396	C₄	—	2	6	no	—
397	C₄	—	4	1	no	—
398	C₄	—	4	3	no	—
399	C₄	—	4	6	no	—
400	C₄	—	4	6	no	—
401	C₄	—	4	3	no	—
402	C₂	—	2	12	no	—
403	C₂	—	8	3	no	—
404	C₂	C₂₃×#3444	1	1	yes	characteristic
405	C₂	C₂×C₂₃×#553	1	3	yes	—
406	C₂	C₂₃×#3490	1	3	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#2847	C₂	semidirect
2. C₂₃×#2569	C₂	semidirect
3. C₂₃×#2543	C₂	semidirect
4. C₂₃×#2510	C₂	semidirect
5. C₂₃×#2444	C₂	semidirect
6. C₂₃×#2364	C₂	semidirect
7. C₂₃×#2353	C₂	semidirect
8. C₄×C₂₃×#120	C₂	semidirect
9. C₂²×C₂₃×#95	C₂	semidirect
16. C₂₃×#401	C₂²	semidirect
17. C₂₃×#400	C₂²	semidirect
18. C₂₃×#398	C₂²	semidirect
19. C₂₃×#397	C₂²	semidirect
20. C₂₃×#397	C₂²	semidirect
21. C₂₃×#394	C₂²	semidirect
22. C₂₃×#392	C₂²	semidirect
23. C₂₃×#388	C₂²	semidirect
24. C₂₃×#388	C₂²	semidirect
25. C₂₃×#387	C₂²	semidirect
26. C₂₃×#387	C₂²	semidirect
32. C₂₃×#386	C₂²	semidirect
35. C₂₃×#383	C₂²	semidirect
36. C₂₃×#381	C₂²	semidirect
42. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
43. C₂₃×#376	C₂²	semidirect
139. #36607	C₂₃	direct (N × H)
178. #2847	C₂×C₂₃	semidirect
179. #2569	C₂×C₂₃	semidirect
180. #2543	C₂×C₂₃	semidirect
181. #2510	C₂×C₂₃	semidirect
182. #2444	C₂×C₂₃	semidirect
183. #2364	C₂×C₂₃	semidirect
184. #2353	C₂×C₂₃	semidirect
185. C₄×#120	C₂×C₂₃	semidirect
186. C₂²×#95	C₂×C₂₃	semidirect
214. #401	C₂²×C₂₃	semidirect
215. #400	C₂²×C₂₃	semidirect
216. #398	C₂²×C₂₃	semidirect
217. #397	C₂²×C₂₃	semidirect
218. #397	C₂²×C₂₃	semidirect
219. #394	C₂²×C₂₃	semidirect
220. #392	C₂²×C₂₃	semidirect
221. #388	C₂²×C₂₃	semidirect
222. #388	C₂²×C₂₃	semidirect
223. #387	C₂²×C₂₃	semidirect
224. #387	C₂²×C₂₃	semidirect
230. #386	C₂²×C₂₃	semidirect
233. #383	C₂²×C₂₃	semidirect
234. #381	C₂²×C₂₃	semidirect
240. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
241. #376	C₂²×C₂₃	semidirect
294. C₂₃	#36607	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×#2847	2
C₂₃×#2569	2
C₂₃×#2543	2
C₂₃×#2510	2
C₂₃×#2444	2
C₂₃×#2364	2
C₂₃×#2353	2
C₄×C₂₃×#120	2
C₂²×C₂₃×#95	2
#36607	23

Subgroups — C23×#36607 #19184233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#36607 #19184233