Subgroups — C₂₃×#36572 #19184198

Order 5888.

2446 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2848	C₂	1	3	yes	maximal, complemented
2	C₂₃×#2564	C₂	1	3	yes	maximal, complemented
3	C₂₃×#2549	C₂	1	3	yes	maximal, complemented
4	C₂₃×#2505	C₂	1	6	yes	maximal, complemented
5	C₂₃×#2450	C₂	1	6	yes	maximal, complemented
6	C₂₃×#2368	C₂	1	3	yes	maximal, complemented
7	C₂₃×#2349	C₂	1	3	yes	maximal, complemented
8	C₄×C₂₃×#120	C₂	1	3	yes	maximal
9	C₂²×C₂₃×#95	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂⁴×C₄×C₂₃	C₂²	1	3	yes	—
11	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	3	yes	—
12	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	6	yes	—
13	C₂×C₂₃×#120	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₂₃	C₂²	1	3	yes	—
15	C₂×C₄×D₄×C₂₃	C₂²	1	6	yes	—
16	C₂₃×#400	C₂²	1	6	yes	complemented
17	C₂₃×#400	C₂²	1	3	yes	complemented
18	C₂₃×#399	C₂²	1	1	yes	characteristic, complemented
19	C₂₃×#398	C₂²	1	6	yes	complemented
20	C₂₃×#396	C₂²	1	2	yes	complemented
21	C₂₃×#395	C₂²	1	3	yes	complemented
22	C₂₃×#393	C₂²	1	3	yes	complemented
23	C₂₃×#391	C₂²	1	6	yes	complemented
24	C₂₃×#389	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×#385	C₂²	1	6	yes	—
30	C₂₃×#385	C₂²	1	6	yes	—
31	C₂₃×#385	C₂²	1	3	yes	—
32	C₂₃×#385	C₂²	1	6	yes	—
33	C₂₃×#385	C₂²	1	6	yes	—
34	C₂₃×#385	C₂²	1	6	yes	complemented
35	C₂₃×#382	C₂²	1	3	yes	complemented
36	C₂₃×#380	C₂²	1	6	yes	—
37	C₂₃×#380	C₂²	1	3	yes	—
38	C₂₃×#380	C₂²	1	3	yes	complemented
39	C₂₃×#379	C₂²	1	3	yes	—
40	C₄×C₄⋊C₄×C₂₃	C₂²	1	3	yes	complemented
41	C₄×C₂²⋊C₄×C₂₃	C₂²	1	6	yes	—
42	C₄×C₂²⋊C₄×C₂₃	C₂²	1	3	yes	—
43	C₂×C₂₃×#95	C₂²	1	6	yes	—
44	C₂×C₂₃×#95	C₂²	1	3	yes	—
45	C₂×C₂₃×#95	C₂²	1	3	yes	—
46	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic, complemented
47	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
48	C₂²×Q₈×C₂₃	C₂³	1	3	yes	—
49	C₂²×D₄×C₂₃	C₂³	1	3	yes	—
50	C₂³×C₄×C₂₃	—	2	12	no	—
51	C₂³×C₄×C₂₃	—	4	12	no	—
52	C₂³×C₄×C₂₃	C₂³	1	6	yes	—
53	C₂³×C₄×C₂₃	C₂³	1	6	yes	—
54	C₂³×C₄×C₂₃	C₂³	1	3	yes	—
55	C₂³×C₄×C₂₃	C₂³	1	3	yes	—
56	C₂³×C₄×C₂₃	C₂³	1	3	yes	—
57	C₂₃×C₂²⋊Q₈	—	2	12	no	—
58	C₂₃×C₂²⋊Q₈	—	4	12	no	—
59	C₂₃×#120	Q₈	1	8	yes	complemented
60	C₄×D₄×C₂₃	—	2	12	no	—
61	C₄×D₄×C₂₃	—	4	12	no	—
62	C₂×C₄⋊C₄×C₂₃	C₂³	1	6	yes	—
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×C₄⋊C₄×C₂₃	C₂³	1	6	yes	—
68	C₂×C₄⋊C₄×C₂₃	C₂³	1	6	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	3	yes	—
72	C₂×C₂²⋊C₄×C₂₃	C₂³	1	6	yes	—
73	C₂×C₂²⋊C₄×C₂₃	C₂³	1	3	yes	—
74	C₂×C₂²⋊C₄×C₂₃	C₂³	1	6	yes	—
75	C₂×C₂²⋊C₄×C₂₃	C₂³	1	3	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	3	yes	—
82	C₂₃×#95	C₂³	1	1	yes	characteristic
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	C₂×Q₈	1	4	yes	—
94	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
95	C₂⁴×C₂₃	C₂⁴	1	3	yes	—
96	C₂×Q₈×C₂₃	—	2	6	no	—
97	C₂×Q₈×C₂₃	—	4	6	no	—
98	C₂×D₄×C₂₃	—	2	6	no	—
99	C₂×D₄×C₂₃	—	2	6	no	—
100	C₂×D₄×C₂₃	C₂×Q₈	1	12	yes	—
101	C₂²×C₄×C₂₃	—	2	6	no	—
102	C₂²×C₄×C₂₃	—	2	12	no	—
103	C₂²×C₄×C₂₃	—	2	12	no	—
104	C₂²×C₄×C₂₃	—	2	12	no	—
105	C₂²×C₄×C₂₃	—	2	12	no	—
106	C₂²×C₄×C₂₃	—	2	6	no	—
107	C₂²×C₄×C₂₃	—	4	6	no	—
108	C₂²×C₄×C₂₃	—	4	6	no	—
109	C₂²×C₄×C₂₃	—	4	6	no	—
110	C₂²×C₄×C₂₃	—	4	6	no	—
111	C₂²×C₄×C₂₃	—	4	6	no	—
112	C₂²×C₄×C₂₃	—	4	48	no	—
113	C₂²×C₄×C₂₃	#41	1	12	yes	—
114	C₂²×C₄×C₂₃	C₂⁴	1	6	yes	—
115	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
116	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
117	C₂²×C₄×C₂₃	C₂⁴	1	6	yes	—
118	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
119	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
120	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
121	C₄⋊C₄×C₂₃	—	2	6	no	—
122	C₄⋊C₄×C₂₃	—	2	6	no	—
123	C₄⋊C₄×C₂₃	—	2	12	no	—
124	C₄⋊C₄×C₂₃	—	4	6	no	—
125	C₄⋊C₄×C₂₃	—	4	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	12	no	—
131	C₂²⋊C₄×C₂₃	—	2	6	no	—
132	C₂²⋊C₄×C₂₃	—	2	6	no	—
133	C₂²⋊C₄×C₂₃	—	4	6	no	—
134	C₂²⋊C₄×C₂₃	C₂×Q₈	1	12	yes	—
135	C₄²×C₂₃	—	2	6	no	—
136	C₄²×C₂₃	—	4	6	no	—
137	#36572	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
138	C₂³×C₂₃	—	2	24	no	—
139	C₂³×C₂₃	—	2	8	no	—
140	C₂³×C₂₃	—	2	24	no	—
141	C₂³×C₂₃	—	2	6	no	—
142	C₂³×C₂₃	—	2	6	no	—
143	C₂³×C₂₃	—	2	3	no	—
144	C₂³×C₂₃	—	2	3	no	—
145	C₂³×C₂₃	C₂²×Q₈	1	2	yes	—
146	C₂³×C₂₃	C₂²×Q₈	1	6	yes	—
147	C₂³×C₂₃	C₂×#41	1	6	yes	—
148	C₂³×C₂₃	H(5,𝔽₂)	1	6	yes	—
149	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
150	Q₈×C₂₃	—	8	6	no	—
151	D₄×C₂₃	—	2	24	no	—
152	C₂×C₄×C₂₃	—	2	3	no	—
153	C₂×C₄×C₂₃	—	2	3	no	—
154	C₂×C₄×C₂₃	—	2	6	no	—
155	C₂×C₄×C₂₃	—	2	6	no	—
156	C₂×C₄×C₂₃	—	2	3	no	—
157	C₂×C₄×C₂₃	—	2	6	no	—
158	C₂×C₄×C₂₃	—	2	3	no	—
159	C₂×C₄×C₂₃	—	2	6	no	—
160	C₂×C₄×C₂₃	—	2	6	no	—
161	C₂×C₄×C₂₃	—	2	6	no	—
162	C₂×C₄×C₂₃	—	2	6	no	—
163	C₂×C₄×C₂₃	—	2	6	no	—
164	C₂×C₄×C₂₃	—	2	6	no	—
165	C₂×C₄×C₂₃	—	2	6	no	—
166	C₂×C₄×C₂₃	—	4	12	no	—
167	C₂×C₄×C₂₃	—	4	24	no	—
168	C₂×C₄×C₂₃	—	4	24	no	—
169	C₂×C₄×C₂₃	—	4	12	no	—
170	C₂×C₄×C₂₃	—	8	6	no	—
171	C₂×C₄×C₂₃	C₂²×Q₈	1	6	yes	—
172	C₂×C₄×C₂₃	C₂×#41	1	6	yes	—
173	C₂×C₄×C₂₃	C₂×#41	1	6	yes	—
174	#2848	C₂×C₂₃	1	3	yes	complemented
175	#2564	C₂×C₂₃	1	3	yes	complemented
176	#2549	C₂×C₂₃	1	3	yes	complemented
177	#2505	C₂×C₂₃	1	6	yes	complemented
178	#2450	C₂×C₂₃	1	6	yes	complemented
179	#2368	C₂×C₂₃	1	3	yes	complemented
180	#2349	C₂×C₂₃	1	3	yes	complemented
181	C₄×#120	C₂×C₂₃	1	3	yes	—
182	C₂²×#95	C₂×C₂₃	1	1	yes	characteristic, complemented
183	C₂²×C₂₃	—	2	32	no	—
184	C₂²×C₂₃	—	2	6	no	—
185	C₂²×C₂₃	—	2	12	no	—
186	C₂²×C₂₃	—	2	6	no	—
187	C₂²×C₂₃	—	2	12	no	—
188	C₂²×C₂₃	—	2	6	no	—
189	C₂²×C₂₃	—	4	1	no	—
190	C₂²×C₂₃	—	4	3	no	—
191	C₂²×C₂₃	#554	1	12	yes	—
192	C₂²×C₂₃	C₂³×Q₈	1	1	yes	characteristic
193	C₂²×C₂₃	C₂²×#41	1	3	yes	—
194	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	3	yes	—
195	C₄×C₂₃	—	2	6	no	—
196	C₄×C₂₃	—	2	6	no	—
197	C₄×C₂₃	—	2	6	no	—
198	C₄×C₂₃	—	4	3	no	—
199	C₄×C₂₃	—	4	6	no	—
200	C₄×C₂₃	—	4	3	no	—
201	C₄×C₂₃	—	4	6	no	—
202	C₂⁴×C₄	C₂²×C₂₃	1	3	yes	—
203	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	3	yes	—
204	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	6	yes	—
205	C₂×#120	C₂²×C₂₃	1	1	yes	characteristic
206	C₂×C₄×D₄	C₂²×C₂₃	1	3	yes	—
207	C₂×C₄×D₄	C₂²×C₂₃	1	6	yes	—
208	#400	C₂²×C₂₃	1	3	yes	complemented
209	#400	C₂²×C₂₃	1	6	yes	complemented
210	#399	C₂²×C₂₃	1	1	yes	characteristic, complemented
211	#398	C₂²×C₂₃	1	6	yes	complemented
212	#396	C₂²×C₂₃	1	2	yes	complemented
213	#395	C₂²×C₂₃	1	3	yes	complemented
214	#393	C₂²×C₂₃	1	3	yes	complemented
215	#391	C₂²×C₂₃	1	6	yes	complemented
216	#389	C₂²×C₂₃	1	6	yes	complemented
217	#387	C₂²×C₂₃	1	6	yes	complemented
218	#387	C₂²×C₂₃	1	6	yes	complemented
219	#386	C₂²×C₂₃	1	6	yes	—
220	#386	C₂²×C₂₃	1	3	yes	—
221	#385	C₂²×C₂₃	1	6	yes	—
222	#385	C₂²×C₂₃	1	6	yes	—
223	#385	C₂²×C₂₃	1	6	yes	—
224	#385	C₂²×C₂₃	1	3	yes	—
225	#385	C₂²×C₂₃	1	6	yes	—
226	#385	C₂²×C₂₃	1	6	yes	complemented
227	#382	C₂²×C₂₃	1	3	yes	complemented
228	#380	C₂²×C₂₃	1	6	yes	—
229	#380	C₂²×C₂₃	1	3	yes	—
230	#380	C₂²×C₂₃	1	3	yes	complemented
231	#379	C₂²×C₂₃	1	3	yes	—
232	C₄×C₄⋊C₄	C₂²×C₂₃	1	3	yes	complemented
233	C₄×C₂²⋊C₄	C₂²×C₂₃	1	6	yes	—
234	C₄×C₂²⋊C₄	C₂²×C₂₃	1	3	yes	—
235	C₂×#95	C₂²×C₂₃	1	3	yes	—
236	C₂×#95	C₂²×C₂₃	1	3	yes	—
237	C₂×#95	C₂²×C₂₃	1	6	yes	—
238	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic, complemented
239	C₂×C₂₃	—	2	12	no	—
240	C₂×C₂₃	—	4	2	no	—
241	C₂×C₂₃	#3444	1	1	yes	characteristic
242	C₂×C₂₃	C₂×#554	1	3	yes	—
243	C₂×C₂₃	#3490	1	3	yes	—
244	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
245	C₂²×Q₈	C₂³×C₂₃	1	3	yes	—
246	C₂²×D₄	C₂³×C₂₃	1	3	yes	—
247	C₂³×C₄	—	2	12	no	—
248	C₂³×C₄	—	4	12	no	—
249	C₂³×C₄	C₂³×C₂₃	1	6	yes	—
250	C₂³×C₄	C₂³×C₂₃	1	6	yes	—
251	C₂³×C₄	C₂³×C₂₃	1	3	yes	—
252	C₂³×C₄	C₂³×C₂₃	1	3	yes	—
253	C₂³×C₄	C₂³×C₂₃	1	3	yes	—
254	C₂²⋊Q₈	—	2	12	no	—
255	C₂²⋊Q₈	—	4	12	no	—
256	#120	Q₈×C₂₃	1	8	yes	complemented
257	C₄×D₄	—	2	12	no	—
258	C₄×D₄	—	4	12	no	—
259	C₂×C₄⋊C₄	C₂³×C₂₃	1	3	yes	—
260	C₂×C₄⋊C₄	C₂³×C₂₃	1	6	yes	—
261	C₂×C₄⋊C₄	C₂³×C₂₃	1	3	yes	—
262	C₂×C₄⋊C₄	C₂³×C₂₃	1	6	yes	—
263	C₂×C₄⋊C₄	C₂³×C₂₃	1	6	yes	—
264	C₂×C₄⋊C₄	C₂³×C₂₃	1	6	yes	—
265	C₂×C₄⋊C₄	C₂³×C₂₃	1	6	yes	—
266	C₂×C₂²⋊C₄	C₂³×C₂₃	1	6	yes	—
267	C₂×C₂²⋊C₄	C₂³×C₂₃	1	3	yes	—
268	C₂×C₂²⋊C₄	C₂³×C₂₃	1	3	yes	—
269	C₂×C₂²⋊C₄	C₂³×C₂₃	1	3	yes	—
270	C₂×C₂²⋊C₄	C₂³×C₂₃	1	6	yes	—
271	C₂×C₂²⋊C₄	C₂³×C₂₃	1	6	yes	—
272	C₂×C₂²⋊C₄	C₂³×C₂₃	1	3	yes	—
273	C₂×C₄²	C₂³×C₂₃	1	3	yes	—
274	C₂×C₄²	C₂³×C₂₃	1	6	yes	—
275	#95	C₂³×C₂₃	1	1	yes	characteristic
276	#95	C₂³×C₂₃	1	3	yes	—
277	#95	C₂³×C₂₃	1	6	yes	—
278	#95	C₂³×C₂₃	1	3	yes	—
279	#95	C₂³×C₂₃	1	1	yes	characteristic
280	#95	C₂³×C₂₃	1	2	yes	—
281	#95	C₂³×C₂₃	1	3	yes	—
282	#95	C₂³×C₂₃	1	6	yes	—
283	#95	C₂³×C₂₃	1	6	yes	—
284	#95	C₂³×C₂₃	1	6	yes	—
285	#95	C₂³×C₂₃	1	3	yes	—
286	#95	C₂³×C₂₃	1	6	yes	—
287	#95	C₂³×C₂₃	1	6	yes	—
288	C₂₃	#36572	1	1	yes	characteristic, direct product factor, Sylow
289	C₂⁴	—	2	6	no	—
290	C₂⁴	—	2	6	no	—
291	C₂⁴	C₂×Q₈×C₂₃	1	4	yes	—
292	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
293	C₂⁴	C₂⁴×C₂₃	1	3	yes	—
294	C₂×Q₈	—	2	6	no	—
295	C₂×Q₈	—	4	6	no	—
296	C₂×D₄	—	2	6	no	—
297	C₂×D₄	—	2	6	no	—
298	C₂×D₄	C₂×Q₈×C₂₃	1	12	yes	—
299	C₂²×C₄	—	2	6	no	—
300	C₂²×C₄	—	2	12	no	—
301	C₂²×C₄	—	2	12	no	—
302	C₂²×C₄	—	2	12	no	—
303	C₂²×C₄	—	2	12	no	—
304	C₂²×C₄	—	2	6	no	—
305	C₂²×C₄	—	4	6	no	—
306	C₂²×C₄	—	4	6	no	—
307	C₂²×C₄	—	4	6	no	—
308	C₂²×C₄	—	4	6	no	—
309	C₂²×C₄	—	4	6	no	—
310	C₂²×C₄	—	4	48	no	—
311	C₂²×C₄	#41×C₂₃	1	12	yes	—
312	C₂²×C₄	C₂⁴×C₂₃	1	6	yes	—
313	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
314	C₂²×C₄	C₂⁴×C₂₃	1	6	yes	—
315	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
316	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
317	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
318	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
319	C₄⋊C₄	—	2	6	no	—
320	C₄⋊C₄	—	2	6	no	—
321	C₄⋊C₄	—	2	12	no	—
322	C₄⋊C₄	—	4	6	no	—
323	C₄⋊C₄	—	4	6	no	—
324	C₄⋊C₄	—	4	6	no	—
325	C₄⋊C₄	—	4	6	no	—
326	C₂²⋊C₄	—	2	6	no	—
327	C₂²⋊C₄	—	2	12	no	—
328	C₂²⋊C₄	—	2	12	no	—
329	C₂²⋊C₄	—	2	6	no	—
330	C₂²⋊C₄	—	2	6	no	—
331	C₂²⋊C₄	—	4	6	no	—
332	C₂²⋊C₄	C₂×Q₈×C₂₃	1	12	yes	—
333	C₄²	—	2	6	no	—
334	C₄²	—	4	6	no	—
335	C₂³	—	2	24	no	—
336	C₂³	—	2	8	no	—
337	C₂³	—	2	24	no	—
338	C₂³	—	2	6	no	—
339	C₂³	—	2	6	no	—
340	C₂³	—	2	3	no	—
341	C₂³	—	2	3	no	—
342	C₂³	C₂²×Q₈×C₂₃	1	2	yes	—
343	C₂³	C₂²×Q₈×C₂₃	1	6	yes	—
344	C₂³	C₂×#41×C₂₃	1	6	yes	—
345	C₂³	C₂₃×H(5,𝔽₂)	1	6	yes	—
346	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
347	Q₈	—	8	6	no	—
348	D₄	—	2	24	no	—
349	C₂×C₄	—	2	3	no	—
350	C₂×C₄	—	2	3	no	—
351	C₂×C₄	—	2	6	no	—
352	C₂×C₄	—	2	6	no	—
353	C₂×C₄	—	2	3	no	—
354	C₂×C₄	—	2	6	no	—
355	C₂×C₄	—	2	3	no	—
356	C₂×C₄	—	2	6	no	—
357	C₂×C₄	—	2	6	no	—
358	C₂×C₄	—	2	6	no	—
359	C₂×C₄	—	2	6	no	—
360	C₂×C₄	—	2	6	no	—
361	C₂×C₄	—	2	6	no	—
362	C₂×C₄	—	2	6	no	—
363	C₂×C₄	—	4	12	no	—
364	C₂×C₄	—	4	24	no	—
365	C₂×C₄	—	4	24	no	—
366	C₂×C₄	—	4	12	no	—
367	C₂×C₄	—	8	6	no	—
368	C₂×C₄	C₂²×Q₈×C₂₃	1	6	yes	—
369	C₂×C₄	C₂×#41×C₂₃	1	6	yes	—
370	C₂×C₄	C₂×#41×C₂₃	1	6	yes	—
371	C₂²	—	2	32	no	—
372	C₂²	—	2	6	no	—
373	C₂²	—	2	12	no	—
374	C₂²	—	2	6	no	—
375	C₂²	—	2	12	no	—
376	C₂²	—	2	6	no	—
377	C₂²	—	4	1	no	—
378	C₂²	—	4	3	no	—
379	C₂²	C₂₃×#554	1	12	yes	—
380	C₂²	C₂³×Q₈×C₂₃	1	1	yes	characteristic
381	C₂²	C₂²×#41×C₂₃	1	3	yes	—
382	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	3	yes	—
383	C₄	—	2	6	no	—
384	C₄	—	2	6	no	—
385	C₄	—	2	6	no	—
386	C₄	—	4	3	no	—
387	C₄	—	4	6	no	—
388	C₄	—	4	3	no	—
389	C₄	—	4	6	no	—
390	C₂	—	2	12	no	—
391	C₂	—	4	2	no	—
392	C₂	C₂₃×#3444	1	1	yes	characteristic
393	C₂	C₂×C₂₃×#554	1	3	yes	—
394	C₂	C₂₃×#3490	1	3	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂×C₂₃×#120	C₂²
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×#2848	C₂	semidirect
2. C₂₃×#2564	C₂	semidirect
3. C₂₃×#2549	C₂	semidirect
4. C₂₃×#2505	C₂	semidirect
5. C₂₃×#2450	C₂	semidirect
6. C₂₃×#2368	C₂	semidirect
7. C₂₃×#2349	C₂	semidirect
9. C₂²×C₂₃×#95	C₂	semidirect
16. C₂₃×#400	C₂²	semidirect
17. C₂₃×#400	C₂²	semidirect
18. C₂₃×#399	C₂²	semidirect
19. C₂₃×#398	C₂²	semidirect
20. C₂₃×#396	C₂²	semidirect
21. C₂₃×#395	C₂²	semidirect
22. C₂₃×#393	C₂²	semidirect
23. C₂₃×#391	C₂²	semidirect
24. C₂₃×#389	C₂²	semidirect
25. C₂₃×#387	C₂²	semidirect
26. C₂₃×#387	C₂²	semidirect
34. C₂₃×#385	C₂²	semidirect
35. C₂₃×#382	C₂²	semidirect
38. C₂₃×#380	C₂²	semidirect
40. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
46. C₂×C₂₃×#95	C₂²	semidirect
59. C₂₃×#120	Q₈	semidirect
137. #36572	C₂₃	direct (N × H)
174. #2848	C₂×C₂₃	semidirect
175. #2564	C₂×C₂₃	semidirect
176. #2549	C₂×C₂₃	semidirect
177. #2505	C₂×C₂₃	semidirect
178. #2450	C₂×C₂₃	semidirect
179. #2368	C₂×C₂₃	semidirect
180. #2349	C₂×C₂₃	semidirect
182. C₂²×#95	C₂×C₂₃	semidirect
208. #400	C₂²×C₂₃	semidirect
209. #400	C₂²×C₂₃	semidirect
210. #399	C₂²×C₂₃	semidirect
211. #398	C₂²×C₂₃	semidirect
212. #396	C₂²×C₂₃	semidirect
213. #395	C₂²×C₂₃	semidirect
214. #393	C₂²×C₂₃	semidirect
215. #391	C₂²×C₂₃	semidirect
216. #389	C₂²×C₂₃	semidirect
217. #387	C₂²×C₂₃	semidirect
218. #387	C₂²×C₂₃	semidirect
226. #385	C₂²×C₂₃	semidirect
227. #382	C₂²×C₂₃	semidirect
230. #380	C₂²×C₂₃	semidirect
232. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
238. C₂×#95	C₂²×C₂₃	semidirect
256. #120	Q₈×C₂₃	semidirect
288. C₂₃	#36572	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×#2848	2
C₂₃×#2564	2
C₂₃×#2549	2
C₂₃×#2505	2
C₂₃×#2450	2
C₂₃×#2368	2
C₂₃×#2349	2
C₄×C₂₃×#120	2
C₂²×C₂₃×#95	2
#36572	23

Subgroups — C23×#36572 #19184198

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#36572 #19184198