Subgroups — C₂×C₂₃×#2436 #19182327

Order 5888.

5630 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	C₂⁴×Q₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂₃×#124	C₂	1	2	yes	maximal, complemented
3	C₂²×C₂₃×#121	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#2436	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₂₃×#393	C₂	1	4	yes	maximal, complemented
6	C₂×C₂₃×#391	C₂	1	2	yes	maximal, complemented
7	C₂×C₂₃×#386	C₂	1	4	yes	maximal, complemented
8	C₂×C₄×C₂²⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×Q₈×C₂₃	—	2	16	no	—
10	C₂³×Q₈×C₂₃	—	2	8	no	—
11	C₂³×Q₈×C₂₃	C₂²	1	2	yes	—
12	C₂³×Q₈×C₂₃	C₂²	1	2	yes	—
13	C₂³×Q₈×C₂₃	C₂²	1	8	yes	complemented
14	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₂₃	C₂²	1	2	yes	—
16	C₂⁴×C₄×C₂₃	C₂²	1	2	yes	—
17	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
18	C₂×C₂₃×#124	—	2	16	no	—
19	C₂×C₂₃×#124	C₂²	1	16	yes	complemented
20	C₂×C₂₃×#121	—	2	8	no	—
21	C₂×C₂₃×#121	C₂²	1	8	yes	—
22	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	8	yes	—
25	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
26	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
27	C₂₃×#393	C₂²	1	32	yes	complemented
28	C₂₃×#391	C₂²	1	16	yes	complemented
29	C₂₃×#386	C₂²	1	32	yes	complemented
30	C₄×C₂²⋊C₄×C₂₃	C₂²	1	8	yes	complemented
31	C₂×C₂₃×#95	C₂²	1	2	yes	—
32	C₂×C₂₃×#95	C₂²	1	8	yes	—
33	C₂⁵×C₂₃	C₂³	1	2	yes	—
34	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
35	C₂²×Q₈×C₂₃	—	2	128	no	—
36	C₂²×Q₈×C₂₃	—	2	64	no	—
37	C₂²×Q₈×C₂₃	—	2	16	no	—
38	C₂²×Q₈×C₂₃	—	2	8	no	—
39	C₂²×Q₈×C₂₃	—	2	8	no	—
40	C₂²×Q₈×C₂₃	—	2	8	no	—
41	C₂²×Q₈×C₂₃	—	2	32	no	—
42	C₂²×Q₈×C₂₃	D₄	1	16	yes	complemented
43	C₂²×Q₈×C₂₃	C₂³	1	8	yes	—
44	C₂²×Q₈×C₂₃	C₂³	1	8	yes	—
45	C₂²×D₄×C₂₃	—	2	8	no	—
46	C₂²×D₄×C₂₃	—	2	16	no	—
47	C₂²×D₄×C₂₃	—	2	4	no	—
48	C₂²×D₄×C₂₃	—	2	8	no	—
49	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
50	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
51	C₂³×C₄×C₂₃	—	2	8	no	—
52	C₂³×C₄×C₂₃	—	2	16	no	—
53	C₂³×C₄×C₂₃	—	2	8	no	—
54	C₂³×C₄×C₂₃	D₄	1	8	yes	—
55	C₂³×C₄×C₂₃	C₂³	1	8	yes	—
56	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
57	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
58	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
59	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
60	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
62	C₂₃×#124	—	2	64	no	—
63	C₂₃×#121	—	2	32	no	—
64	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
65	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
66	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
67	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
68	C₂×C₂²⋊C₄×C₂₃	—	2	32	no	—
69	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
70	C₂×C₂²⋊C₄×C₂₃	C₂³	1	32	yes	—
71	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
72	C₂×C₄²×C₂₃	—	2	8	no	—
73	C₂×C₄²×C₂₃	C₂³	1	8	yes	—
74	C₂₃×#95	C₂³	1	8	yes	—
75	C₂₃×#95	C₂³	1	32	yes	—
76	C₂⁴×C₂₃	—	2	4	no	—
77	C₂⁴×C₂₃	—	2	4	no	—
78	C₂⁴×C₂₃	—	2	8	no	—
79	C₂⁴×C₂₃	—	2	4	no	—
80	C₂⁴×C₂₃	—	2	8	no	—
81	C₂⁴×C₂₃	—	2	8	no	—
82	C₂⁴×C₂₃	C₂×D₄	1	4	yes	—
83	C₂⁴×C₂₃	#41	1	8	yes	—
84	C₂⁴×C₂₃	C₂⁴	1	4	yes	—
85	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
86	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
87	C₂×Q₈×C₂₃	—	2	256	no	—
88	C₂×Q₈×C₂₃	—	2	64	no	—
89	C₂×Q₈×C₂₃	—	2	64	no	—
90	C₂×Q₈×C₂₃	—	2	32	no	—
91	C₂×Q₈×C₂₃	—	2	16	no	—
92	C₂×Q₈×C₂₃	—	2	16	no	—
93	C₂×Q₈×C₂₃	—	2	16	no	—
94	C₂×Q₈×C₂₃	C₂×D₄	1	32	yes	complemented
95	C₂×D₄×C₂₃	—	2	16	no	—
96	C₂×D₄×C₂₃	—	2	32	no	—
97	C₂×D₄×C₂₃	—	2	8	no	—
98	C₂×D₄×C₂₃	—	2	16	no	—
99	C₂×D₄×C₂₃	—	4	32	no	—
100	C₂×D₄×C₂₃	—	4	16	no	—
101	C₂²×C₄×C₂₃	—	2	64	no	—
102	C₂²×C₄×C₂₃	—	2	16	no	—
103	C₂²×C₄×C₂₃	—	2	8	no	—
104	C₂²×C₄×C₂₃	—	2	8	no	—
105	C₂²×C₄×C₂₃	—	2	4	no	—
106	C₂²×C₄×C₂₃	—	2	32	no	—
107	C₂²×C₄×C₂₃	—	2	32	no	—
108	C₂²×C₄×C₂₃	—	2	16	no	—
109	C₂²×C₄×C₂₃	—	2	8	no	—
110	C₂²×C₄×C₂₃	—	2	4	no	—
111	C₂²×C₄×C₂₃	—	2	8	no	—
112	C₂²×C₄×C₂₃	—	2	8	no	—
113	C₂²×C₄×C₂₃	—	2	8	no	—
114	C₂²×C₄×C₂₃	C₂×D₄	1	16	yes	—
115	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
116	C₂²×C₄×C₂₃	C₂×D₄	1	16	yes	—
117	C₂²×C₄×C₂₃	C₂×D₄	1	8	yes	—
118	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
119	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
120	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
121	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
122	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
123	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
124	C₄⋊C₄×C₂₃	—	2	8	no	—
125	C₂²⋊C₄×C₂₃	—	2	16	no	—
126	C₂²⋊C₄×C₂₃	—	2	16	no	—
127	C₂²⋊C₄×C₂₃	—	2	64	no	—
128	C₄²×C₂₃	—	2	16	no	—
129	C₂×#2436	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂³×C₂₃	—	2	8	no	—
131	C₂³×C₂₃	—	2	8	no	—
132	C₂³×C₂₃	—	2	32	no	—
133	C₂³×C₂₃	—	2	4	no	—
134	C₂³×C₂₃	—	2	4	no	—
135	C₂³×C₂₃	—	2	8	no	—
136	C₂³×C₂₃	—	2	4	no	—
137	C₂³×C₂₃	—	2	8	no	—
138	C₂³×C₂₃	—	2	8	no	—
139	C₂³×C₂₃	—	4	8	no	—
140	C₂³×C₂₃	—	4	8	no	—
141	C₂³×C₂₃	—	4	8	no	—
142	C₂³×C₂₃	—	4	32	no	—
143	C₂³×C₂₃	#124	1	16	yes	complemented
144	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
145	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
146	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
147	C₂³×C₂₃	C₂×#41	1	8	yes	—
148	C₂³×C₂₃	C₂×#41	1	4	yes	—
149	C₂³×C₂₃	2₋¹⁺⁴	1	4	yes	—
150	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
151	Q₈×C₂₃	—	2	64	no	—
152	Q₈×C₂₃	—	2	64	no	—
153	D₄×C₂₃	—	4	32	no	—
154	D₄×C₂₃	—	4	16	no	—
155	C₂×C₄×C₂₃	—	2	64	no	—
156	C₂×C₄×C₂₃	—	2	32	no	—
157	C₂×C₄×C₂₃	—	2	8	no	—
158	C₂×C₄×C₂₃	—	2	8	no	—
159	C₂×C₄×C₂₃	—	2	8	no	—
160	C₂×C₄×C₂₃	—	2	4	no	—
161	C₂×C₄×C₂₃	—	2	32	no	—
162	C₂×C₄×C₂₃	—	2	8	no	—
163	C₂×C₄×C₂₃	—	2	4	no	—
164	C₂×C₄×C₂₃	—	2	8	no	—
165	C₂×C₄×C₂₃	—	2	8	no	—
166	C₂×C₄×C₂₃	—	2	8	no	—
167	C₂×C₄×C₂₃	—	4	8	no	—
168	C₂×C₄×C₂₃	—	4	16	no	—
169	C₂×C₄×C₂₃	#120	1	16	yes	—
170	C₂×C₄×C₂₃	C₂²×D₄	1	16	yes	—
171	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
172	C₂×C₄×C₂₃	C₂²×D₄	1	8	yes	—
173	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
174	C₂⁴×Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
175	C₂²×#124	C₂×C₂₃	1	2	yes	complemented
176	C₂²×#121	C₂×C₂₃	1	1	yes	characteristic
177	#2436	C₂×C₂₃	1	16	yes	direct product factor
178	C₂×#393	C₂×C₂₃	1	4	yes	complemented
179	C₂×#391	C₂×C₂₃	1	2	yes	complemented
180	C₂×#386	C₂×C₂₃	1	4	yes	complemented
181	C₂×C₄×C₂²⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
182	C₂²×C₂₃	—	2	4	no	—
183	C₂²×C₂₃	—	2	4	no	—
184	C₂²×C₂₃	—	2	32	no	—
185	C₂²×C₂₃	—	2	16	no	—
186	C₂²×C₂₃	—	4	4	no	—
187	C₂²×C₂₃	—	4	4	no	—
188	C₂²×C₂₃	—	4	4	no	—
189	C₂²×C₂₃	—	4	16	no	—
190	C₂²×C₂₃	—	8	16	no	—
191	C₂²×C₂₃	C₂×#120	1	4	yes	—
192	C₂²×C₂₃	C₂×#124	1	4	yes	—
193	C₂²×C₂₃	C₂×#124	1	8	yes	complemented
194	C₂²×C₂₃	#536	1	4	yes	—
195	C₂²×C₂₃	#548	1	16	yes	—
196	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
197	C₂²×C₂₃	C₂³×D₄	1	2	yes	—
198	C₂²×C₂₃	C₂²×#41	1	2	yes	—
199	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
200	C₄×C₂₃	—	2	16	no	—
201	C₄×C₂₃	—	2	4	no	—
202	C₄×C₂₃	—	4	4	no	—
203	C₄×C₂₃	—	4	8	no	—
204	C₄×C₂₃	C₂×#120	1	8	yes	—
205	C₂³×Q₈	—	2	16	no	—
206	C₂³×Q₈	—	2	8	no	—
207	C₂³×Q₈	C₂²×C₂₃	1	2	yes	—
208	C₂³×Q₈	C₂²×C₂₃	1	2	yes	—
209	C₂³×Q₈	C₂²×C₂₃	1	8	yes	complemented
210	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
211	C₂³×D₄	C₂²×C₂₃	1	2	yes	—
212	C₂⁴×C₄	C₂²×C₂₃	1	2	yes	—
213	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
214	C₂×#124	—	2	16	no	—
215	C₂×#124	C₂²×C₂₃	1	16	yes	complemented
216	C₂×#121	—	2	8	no	—
217	C₂×#121	C₂²×C₂₃	1	8	yes	—
218	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
219	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
220	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	8	yes	—
221	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
222	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
223	#393	C₂²×C₂₃	1	32	yes	complemented
224	#391	C₂²×C₂₃	1	16	yes	complemented
225	#386	C₂²×C₂₃	1	32	yes	complemented
226	C₄×C₂²⋊C₄	C₂²×C₂₃	1	8	yes	complemented
227	C₂×#95	C₂²×C₂₃	1	2	yes	—
228	C₂×#95	C₂²×C₂₃	1	8	yes	—
229	C₂×C₂₃	—	2	8	no	—
230	C₂×C₂₃	—	8	4	no	—
231	C₂×C₂₃	#2436	1	8	yes	direct product factor
232	C₂×C₂₃	C₂²×#120	1	1	yes	characteristic
233	C₂×C₂₃	C₂²×#124	1	1	yes	characteristic
234	C₂×C₂₃	C₂×#536	1	1	yes	characteristic
235	C₂×C₂₃	C₂×#548	1	4	yes	—
236	C₂⁵	C₂³×C₂₃	1	2	yes	—
237	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
238	C₂²×Q₈	—	2	128	no	—
239	C₂²×Q₈	—	2	64	no	—
240	C₂²×Q₈	—	2	16	no	—
241	C₂²×Q₈	—	2	8	no	—
242	C₂²×Q₈	—	2	8	no	—
243	C₂²×Q₈	—	2	8	no	—
244	C₂²×Q₈	—	2	32	no	—
245	C₂²×Q₈	D₄×C₂₃	1	16	yes	complemented
246	C₂²×Q₈	C₂³×C₂₃	1	8	yes	—
247	C₂²×Q₈	C₂³×C₂₃	1	8	yes	—
248	C₂²×D₄	—	2	8	no	—
249	C₂²×D₄	—	2	16	no	—
250	C₂²×D₄	—	2	4	no	—
251	C₂²×D₄	—	2	8	no	—
252	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
253	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
254	C₂³×C₄	—	2	8	no	—
255	C₂³×C₄	—	2	16	no	—
256	C₂³×C₄	—	2	8	no	—
257	C₂³×C₄	D₄×C₂₃	1	8	yes	—
258	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
259	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
260	C₂³×C₄	C₂³×C₂₃	1	8	yes	—
261	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
262	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
263	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
264	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
265	#124	—	2	64	no	—
266	#121	—	2	32	no	—
267	C₂×C₄⋊C₄	—	2	4	no	—
268	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
269	C₂×C₂²⋊C₄	—	2	8	no	—
270	C₂×C₂²⋊C₄	—	2	8	no	—
271	C₂×C₂²⋊C₄	—	2	32	no	—
272	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
273	C₂×C₂²⋊C₄	C₂³×C₂₃	1	32	yes	—
274	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
275	C₂×C₄²	—	2	8	no	—
276	C₂×C₄²	C₂³×C₂₃	1	8	yes	—
277	#95	C₂³×C₂₃	1	8	yes	—
278	#95	C₂³×C₂₃	1	32	yes	—
279	C₂₃	C₂×#2436	1	1	yes	characteristic, direct product factor, Sylow
280	C₂⁴	—	2	4	no	—
281	C₂⁴	—	2	4	no	—
282	C₂⁴	—	2	8	no	—
283	C₂⁴	—	2	4	no	—
284	C₂⁴	—	2	8	no	—
285	C₂⁴	—	2	8	no	—
286	C₂⁴	C₂×D₄×C₂₃	1	4	yes	—
287	C₂⁴	#41×C₂₃	1	8	yes	—
288	C₂⁴	C₂⁴×C₂₃	1	4	yes	—
289	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
290	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
291	C₂×Q₈	—	2	256	no	—
292	C₂×Q₈	—	2	64	no	—
293	C₂×Q₈	—	2	64	no	—
294	C₂×Q₈	—	2	32	no	—
295	C₂×Q₈	—	2	16	no	—
296	C₂×Q₈	—	2	16	no	—
297	C₂×Q₈	—	2	16	no	—
298	C₂×Q₈	C₂×D₄×C₂₃	1	32	yes	complemented
299	C₂×D₄	—	2	16	no	—
300	C₂×D₄	—	2	32	no	—
301	C₂×D₄	—	2	8	no	—
302	C₂×D₄	—	2	16	no	—
303	C₂×D₄	—	4	32	no	—
304	C₂×D₄	—	4	16	no	—
305	C₂²×C₄	—	2	64	no	—
306	C₂²×C₄	—	2	16	no	—
307	C₂²×C₄	—	2	8	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	8	no	—
310	C₂²×C₄	—	2	32	no	—
311	C₂²×C₄	—	2	32	no	—
312	C₂²×C₄	—	2	16	no	—
313	C₂²×C₄	—	2	8	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	8	no	—
316	C₂²×C₄	—	2	8	no	—
317	C₂²×C₄	—	2	8	no	—
318	C₂²×C₄	C₂×D₄×C₂₃	1	16	yes	—
319	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
320	C₂²×C₄	C₂×D₄×C₂₃	1	16	yes	—
321	C₂²×C₄	C₂×D₄×C₂₃	1	8	yes	—
322	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
323	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
324	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
325	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
326	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
327	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
328	C₄⋊C₄	—	2	8	no	—
329	C₂²⋊C₄	—	2	16	no	—
330	C₂²⋊C₄	—	2	16	no	—
331	C₂²⋊C₄	—	2	64	no	—
332	C₄²	—	2	16	no	—
333	C₂³	—	2	32	no	—
334	C₂³	—	2	4	no	—
335	C₂³	—	2	4	no	—
336	C₂³	—	2	8	no	—
337	C₂³	—	2	8	no	—
338	C₂³	—	2	8	no	—
339	C₂³	—	2	4	no	—
340	C₂³	—	2	8	no	—
341	C₂³	—	2	8	no	—
342	C₂³	—	4	32	no	—
343	C₂³	—	4	8	no	—
344	C₂³	—	4	8	no	—
345	C₂³	—	4	8	no	—
346	C₂³	C₂₃×#124	1	16	yes	complemented
347	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
348	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
349	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
350	C₂³	C₂×#41×C₂₃	1	8	yes	—
351	C₂³	C₂×#41×C₂₃	1	4	yes	—
352	C₂³	C₂₃×2₋¹⁺⁴	1	4	yes	—
353	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
354	Q₈	—	2	64	no	—
355	Q₈	—	2	64	no	—
356	D₄	—	4	32	no	—
357	D₄	—	4	16	no	—
358	C₂×C₄	—	2	64	no	—
359	C₂×C₄	—	2	8	no	—
360	C₂×C₄	—	2	8	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	32	no	—
363	C₂×C₄	—	2	8	no	—
364	C₂×C₄	—	2	32	no	—
365	C₂×C₄	—	2	8	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	8	no	—
368	C₂×C₄	—	2	8	no	—
369	C₂×C₄	—	2	8	no	—
370	C₂×C₄	—	4	16	no	—
371	C₂×C₄	—	4	8	no	—
372	C₂×C₄	C₂₃×#120	1	16	yes	—
373	C₂×C₄	C₂²×D₄×C₂₃	1	16	yes	—
374	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
375	C₂×C₄	C₂²×D₄×C₂₃	1	8	yes	—
376	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
377	C₂²	—	2	4	no	—
378	C₂²	—	2	4	no	—
379	C₂²	—	2	32	no	—
380	C₂²	—	2	16	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	4	4	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	4	16	no	—
385	C₂²	—	8	16	no	—
386	C₂²	C₂×C₂₃×#120	1	4	yes	—
387	C₂²	C₂×C₂₃×#124	1	4	yes	—
388	C₂²	C₂×C₂₃×#124	1	8	yes	complemented
389	C₂²	C₂₃×#536	1	4	yes	—
390	C₂²	C₂₃×#548	1	16	yes	—
391	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
392	C₂²	C₂³×D₄×C₂₃	1	2	yes	—
393	C₂²	C₂²×#41×C₂₃	1	2	yes	—
394	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
395	C₄	—	2	16	no	—
396	C₄	—	2	4	no	—
397	C₄	—	4	4	no	—
398	C₄	—	4	8	no	—
399	C₄	C₂×C₂₃×#120	1	8	yes	—
400	C₂	—	2	8	no	—
401	C₂	—	8	4	no	—
402	C₂	C₂₃×#2436	1	8	yes	direct product factor
403	C₂	C₂²×C₂₃×#120	1	1	yes	characteristic
404	C₂	C₂²×C₂₃×#124	1	1	yes	characteristic
405	C₂	C₂×C₂₃×#536	1	1	yes	characteristic
406	C₂	C₂×C₂₃×#548	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂²×C₂₃×#121	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂⁴×Q₈×C₂₃	C₂	semidirect
2. C₂²×C₂₃×#124	C₂	semidirect
4. C₂₃×#2436	C₂	direct (N × H)
5. C₂×C₂₃×#393	C₂	semidirect
6. C₂×C₂₃×#391	C₂	semidirect
7. C₂×C₂₃×#386	C₂	semidirect
8. C₂×C₄×C₂²⋊C₄×C₂₃	C₂	semidirect
13. C₂³×Q₈×C₂₃	C₂²	semidirect
19. C₂×C₂₃×#124	C₂²	semidirect
27. C₂₃×#393	C₂²	semidirect
28. C₂₃×#391	C₂²	semidirect
29. C₂₃×#386	C₂²	semidirect
30. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
42. C₂²×Q₈×C₂₃	D₄	semidirect
94. C₂×Q₈×C₂₃	C₂×D₄	semidirect
129. C₂×#2436	C₂₃	direct (N × H)
143. C₂³×C₂₃	#124	semidirect
174. C₂⁴×Q₈	C₂×C₂₃	semidirect
175. C₂²×#124	C₂×C₂₃	semidirect
177. #2436	C₂×C₂₃	direct (N × H)
178. C₂×#393	C₂×C₂₃	semidirect
179. C₂×#391	C₂×C₂₃	semidirect
180. C₂×#386	C₂×C₂₃	semidirect
181. C₂×C₄×C₂²⋊C₄	C₂×C₂₃	semidirect
193. C₂²×C₂₃	C₂×#124	semidirect
209. C₂³×Q₈	C₂²×C₂₃	semidirect
215. C₂×#124	C₂²×C₂₃	semidirect
223. #393	C₂²×C₂₃	semidirect
224. #391	C₂²×C₂₃	semidirect
225. #386	C₂²×C₂₃	semidirect
226. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
231. C₂×C₂₃	#2436	direct (N × H)
245. C₂²×Q₈	D₄×C₂₃	semidirect
279. C₂₃	C₂×#2436	direct (N × H)
298. C₂×Q₈	C₂×D₄×C₂₃	semidirect
346. C₂³	C₂₃×#124	semidirect
388. C₂²	C₂×C₂₃×#124	semidirect
402. C₂	C₂₃×#2436	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×Q₈×C₂₃	2
C₂²×C₂₃×#124	2
C₂²×C₂₃×#121	2
C₂₃×#2436	2
C₂×C₂₃×#393	2
C₂×C₂₃×#391	2
C₂×C₂₃×#386	2
C₂×C₄×C₂²⋊C₄×C₂₃	2
C₂×#2436	23

Subgroups — C2×C23×#2436 #19182327

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#2436 #19182327