Subgroups — C₂×C₂₃×#2403 #19182271

Order 5888.

11518 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₄×C₂₃	C₂	1	2	yes	maximal, complemented
2	C₂²×C₂₃×#120	C₂	1	4	yes	maximal, complemented
3	C₂₃×#2403	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₃×#392	C₂	1	4	yes	maximal, complemented
5	C₂×C₂₃×#386	C₂	1	4	yes	maximal, complemented
6	C₂×C₂₃×#379	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂⁶×C₂₃	C₂²	1	1	yes	characteristic
8	C₂⁶×C₂₃	C₂²	1	2	yes	complemented
9	C₂³×D₄×C₂₃	—	2	16	no	—
10	C₂³×D₄×C₂₃	—	2	32	no	—
11	C₂³×D₄×C₂₃	C₂²	1	4	yes	—
12	C₂³×D₄×C₂₃	C₂²	1	4	yes	complemented
13	C₂³×D₄×C₂₃	C₂²	1	4	yes	complemented
14	C₂³×D₄×C₂₃	C₂²	1	16	yes	complemented
15	C₂⁴×C₄×C₂₃	C₂²	1	2	yes	complemented
16	C₂×C₂₃×#120	—	2	32	no	—
17	C₂×C₂₃×#120	C₂²	1	32	yes	complemented
18	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	complemented
19	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	8	yes	complemented
20	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
21	C₂₃×#392	C₂²	1	32	yes	complemented
22	C₂₃×#386	C₂²	1	32	yes	complemented
23	C₂₃×#379	C₂²	1	8	yes	complemented
24	C₂×C₂₃×#95	C₂²	1	4	yes	complemented
25	C₂⁵×C₂₃	—	2	16	no	—
26	C₂⁵×C₂₃	—	2	8	no	—
27	C₂⁵×C₂₃	—	2	16	no	—
28	C₂⁵×C₂₃	—	2	16	no	—
29	C₂⁵×C₂₃	—	4	4	no	—
30	C₂⁵×C₂₃	—	4	8	no	—
31	C₂⁵×C₂₃	D₄	1	8	yes	complemented
32	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
33	C₂⁵×C₂₃	C₂³	1	4	yes	—
34	C₂⁵×C₂₃	C₂³	1	4	yes	—
35	C₂⁵×C₂₃	C₂³	1	2	yes	—
36	C₂⁵×C₂₃	C₂³	1	8	yes	complemented
37	C₂²×D₄×C₂₃	—	2	256	no	—
38	C₂²×D₄×C₂₃	—	2	16	no	—
39	C₂²×D₄×C₂₃	—	2	16	no	—
40	C₂²×D₄×C₂₃	—	2	16	no	—
41	C₂²×D₄×C₂₃	—	2	16	no	—
42	C₂²×D₄×C₂₃	—	2	64	no	—
43	C₂²×D₄×C₂₃	—	2	128	no	—
44	C₂²×D₄×C₂₃	—	2	32	no	—
45	C₂²×D₄×C₂₃	—	2	16	no	—
46	C₂²×D₄×C₂₃	—	4	8	no	—
47	C₂²×D₄×C₂₃	D₄	1	32	yes	complemented
48	C₂²×D₄×C₂₃	C₂³	1	16	yes	—
49	C₂²×D₄×C₂₃	C₂³	1	16	yes	complemented
50	C₂²×D₄×C₂₃	C₂³	1	16	yes	complemented
51	C₂³×C₄×C₂₃	—	2	8	no	—
52	C₂³×C₄×C₂₃	—	2	16	no	—
53	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
54	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
55	C₂³×C₄×C₂₃	C₂³	1	8	yes	complemented
56	C₂₃×#120	—	2	128	no	—
57	C₂×C₂²⋊C₄×C₂₃	—	2	16	no	—
58	C₂×C₂²⋊C₄×C₂₃	—	2	32	no	—
59	C₂×C₂²⋊C₄×C₂₃	—	4	4	no	—
60	C₂×C₂²⋊C₄×C₂₃	C₂³	1	16	yes	complemented
61	C₂×C₂²⋊C₄×C₂₃	C₂³	1	32	yes	complemented
62	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	complemented
63	C₂₃×#95	C₂³	1	16	yes	complemented
64	C₂⁴×C₂₃	—	2	8	no	—
65	C₂⁴×C₂₃	—	2	8	no	—
66	C₂⁴×C₂₃	—	2	64	no	—
67	C₂⁴×C₂₃	—	2	64	no	—
68	C₂⁴×C₂₃	—	2	16	no	—
69	C₂⁴×C₂₃	—	2	32	no	—
70	C₂⁴×C₂₃	—	2	8	no	—
71	C₂⁴×C₂₃	—	2	8	no	—
72	C₂⁴×C₂₃	—	2	8	no	—
73	C₂⁴×C₂₃	—	2	16	no	—
74	C₂⁴×C₂₃	—	2	32	no	—
75	C₂⁴×C₂₃	—	2	4	no	—
76	C₂⁴×C₂₃	—	2	16	no	—
77	C₂⁴×C₂₃	—	2	32	no	—
78	C₂⁴×C₂₃	—	4	16	no	—
79	C₂⁴×C₂₃	—	4	8	no	—
80	C₂⁴×C₂₃	—	4	16	no	—
81	C₂⁴×C₂₃	—	4	64	no	—
82	C₂⁴×C₂₃	—	4	128	no	—
83	C₂⁴×C₂₃	—	4	32	no	—
84	C₂⁴×C₂₃	—	4	32	no	—
85	C₂⁴×C₂₃	C₂×D₄	1	4	yes	—
86	C₂⁴×C₂₃	C₂×D₄	1	16	yes	—
87	C₂⁴×C₂₃	C₂×D₄	1	8	yes	—
88	C₂⁴×C₂₃	C₂×D₄	1	16	yes	complemented
89	C₂⁴×C₂₃	C₂×D₄	1	16	yes	complemented
90	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
91	C₂⁴×C₂₃	C₂⁴	1	8	yes	—
92	C₂⁴×C₂₃	C₂⁴	1	4	yes	—
93	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
94	C₂×D₄×C₂₃	—	2	512	no	—
95	C₂×D₄×C₂₃	—	2	128	no	—
96	C₂×D₄×C₂₃	—	2	128	no	—
97	C₂×D₄×C₂₃	—	2	32	no	—
98	C₂×D₄×C₂₃	—	2	32	no	—
99	C₂×D₄×C₂₃	—	2	32	no	—
100	C₂×D₄×C₂₃	—	2	32	no	—
101	C₂×D₄×C₂₃	—	2	64	no	—
102	C₂×D₄×C₂₃	—	2	32	no	—
103	C₂×D₄×C₂₃	—	4	16	no	—
104	C₂×D₄×C₂₃	—	4	64	no	—
105	C₂×D₄×C₂₃	C₂×D₄	1	64	yes	complemented
106	C₂²×C₄×C₂₃	—	2	64	no	—
107	C₂²×C₄×C₂₃	—	2	8	no	—
108	C₂²×C₄×C₂₃	—	2	8	no	—
109	C₂²×C₄×C₂₃	—	2	16	no	—
110	C₂²×C₄×C₂₃	—	2	32	no	—
111	C₂²×C₄×C₂₃	—	2	16	no	—
112	C₂²×C₄×C₂₃	—	2	8	no	—
113	C₂²×C₄×C₂₃	C₂×D₄	1	16	yes	complemented
114	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
115	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
116	C₂²⋊C₄×C₂₃	—	2	32	no	—
117	C₂²⋊C₄×C₂₃	—	2	64	no	—
118	C₂²⋊C₄×C₂₃	—	4	8	no	—
119	C₂×#2403	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂³×C₂₃	—	2	16	no	—
121	C₂³×C₂₃	—	2	16	no	—
122	C₂³×C₂₃	—	2	64	no	—
123	C₂³×C₂₃	—	2	8	no	—
124	C₂³×C₂₃	—	2	8	no	—
125	C₂³×C₂₃	—	2	64	no	—
126	C₂³×C₂₃	—	2	16	no	—
127	C₂³×C₂₃	—	2	32	no	—
128	C₂³×C₂₃	—	2	64	no	—
129	C₂³×C₂₃	—	2	8	no	—
130	C₂³×C₂₃	—	2	64	no	—
131	C₂³×C₂₃	—	2	16	no	—
132	C₂³×C₂₃	—	2	8	no	—
133	C₂³×C₂₃	—	2	8	no	—
134	C₂³×C₂₃	—	2	8	no	—
135	C₂³×C₂₃	—	2	4	no	—
136	C₂³×C₂₃	—	2	16	no	—
137	C₂³×C₂₃	—	4	16	no	—
138	C₂³×C₂₃	—	4	128	no	—
139	C₂³×C₂₃	—	4	64	no	—
140	C₂³×C₂₃	—	4	128	no	—
141	C₂³×C₂₃	—	4	256	no	—
142	C₂³×C₂₃	—	4	32	no	—
143	C₂³×C₂₃	—	4	16	no	—
144	C₂³×C₂₃	—	4	32	no	—
145	C₂³×C₂₃	—	4	16	no	—
146	C₂³×C₂₃	—	4	32	no	—
147	C₂³×C₂₃	—	4	16	no	—
148	C₂³×C₂₃	#120	1	32	yes	complemented
149	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
150	C₂³×C₂₃	C₂²×D₄	1	16	yes	—
151	C₂³×C₂₃	C₂²×D₄	1	8	yes	—
152	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
153	C₂³×C₂₃	C₂²×D₄	1	8	yes	—
154	C₂³×C₂₃	C₂²×D₄	1	16	yes	complemented
155	C₂³×C₂₃	H(5,𝔽₂)	1	4	yes	—
156	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
157	D₄×C₂₃	—	2	128	no	—
158	D₄×C₂₃	—	2	128	no	—
159	D₄×C₂₃	—	4	64	no	—
160	C₂×C₄×C₂₃	—	2	64	no	—
161	C₂×C₄×C₂₃	—	2	32	no	—
162	C₂×C₄×C₂₃	—	2	8	no	—
163	C₂×C₄×C₂₃	—	2	8	no	—
164	C₂×C₄×C₂₃	—	2	16	no	—
165	C₂×C₄×C₂₃	—	2	8	no	—
166	C₂×C₄×C₂₃	—	4	16	no	—
167	C₂×C₄×C₂₃	C₂²×D₄	1	16	yes	complemented
168	C₂⁴×D₄	C₂×C₂₃	1	2	yes	complemented
169	C₂²×#120	C₂×C₂₃	1	4	yes	complemented
170	#2403	C₂×C₂₃	1	16	yes	direct product factor
171	C₂×#392	C₂×C₂₃	1	4	yes	complemented
172	C₂×#386	C₂×C₂₃	1	4	yes	complemented
173	C₂×#379	C₂×C₂₃	1	1	yes	characteristic, complemented
174	C₂²×C₂₃	—	2	64	no	—
175	C₂²×C₂₃	—	2	8	no	—
176	C₂²×C₂₃	—	2	8	no	—
177	C₂²×C₂₃	—	2	32	no	—
178	C₂²×C₂₃	—	2	8	no	—
179	C₂²×C₂₃	—	2	16	no	—
180	C₂²×C₂₃	—	2	4	no	—
181	C₂²×C₂₃	—	2	32	no	—
182	C₂²×C₂₃	—	4	64	no	—
183	C₂²×C₂₃	—	4	128	no	—
184	C₂²×C₂₃	—	4	16	no	—
185	C₂²×C₂₃	—	4	64	no	—
186	C₂²×C₂₃	—	4	8	no	—
187	C₂²×C₂₃	—	4	8	no	—
188	C₂²×C₂₃	—	4	16	no	—
189	C₂²×C₂₃	—	4	8	no	—
190	C₂²×C₂₃	C₂×#120	1	8	yes	—
191	C₂²×C₂₃	C₂×#120	1	16	yes	complemented
192	C₂²×C₂₃	#534	1	4	yes	—
193	C₂²×C₂₃	D₄²	1	16	yes	—
194	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
195	C₂²×C₂₃	C₂³×D₄	1	4	yes	—
196	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
197	C₄×C₂₃	—	2	16	no	—
198	C₄×C₂₃	—	4	8	no	—
199	C₂⁶	C₂²×C₂₃	1	1	yes	characteristic
200	C₂⁶	C₂²×C₂₃	1	2	yes	complemented
201	C₂³×D₄	—	2	16	no	—
202	C₂³×D₄	—	2	32	no	—
203	C₂³×D₄	C₂²×C₂₃	1	4	yes	—
204	C₂³×D₄	C₂²×C₂₃	1	4	yes	complemented
205	C₂³×D₄	C₂²×C₂₃	1	4	yes	complemented
206	C₂³×D₄	C₂²×C₂₃	1	16	yes	complemented
207	C₂⁴×C₄	C₂²×C₂₃	1	2	yes	complemented
208	C₂×#120	—	2	32	no	—
209	C₂×#120	C₂²×C₂₃	1	32	yes	complemented
210	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	8	yes	complemented
211	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	complemented
212	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
213	#392	C₂²×C₂₃	1	32	yes	complemented
214	#386	C₂²×C₂₃	1	32	yes	complemented
215	#379	C₂²×C₂₃	1	8	yes	complemented
216	C₂×#95	C₂²×C₂₃	1	4	yes	complemented
217	C₂×C₂₃	—	2	16	no	—
218	C₂×C₂₃	—	4	4	no	—
219	C₂×C₂₃	—	4	16	no	—
220	C₂×C₂₃	#2403	1	8	yes	direct product factor
221	C₂×C₂₃	C₂²×#120	1	2	yes	—
222	C₂×C₂₃	C₂×#534	1	1	yes	characteristic
223	C₂×C₂₃	C₂×D₄²	1	4	yes	—
224	C₂⁵	—	2	16	no	—
225	C₂⁵	—	2	8	no	—
226	C₂⁵	—	2	16	no	—
227	C₂⁵	—	2	16	no	—
228	C₂⁵	—	4	4	no	—
229	C₂⁵	—	4	8	no	—
230	C₂⁵	D₄×C₂₃	1	8	yes	complemented
231	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
232	C₂⁵	C₂³×C₂₃	1	4	yes	—
233	C₂⁵	C₂³×C₂₃	1	4	yes	—
234	C₂⁵	C₂³×C₂₃	1	2	yes	—
235	C₂⁵	C₂³×C₂₃	1	8	yes	complemented
236	C₂²×D₄	—	2	256	no	—
237	C₂²×D₄	—	2	16	no	—
238	C₂²×D₄	—	2	16	no	—
239	C₂²×D₄	—	2	16	no	—
240	C₂²×D₄	—	2	16	no	—
241	C₂²×D₄	—	2	64	no	—
242	C₂²×D₄	—	2	128	no	—
243	C₂²×D₄	—	2	32	no	—
244	C₂²×D₄	—	2	16	no	—
245	C₂²×D₄	—	4	8	no	—
246	C₂²×D₄	D₄×C₂₃	1	32	yes	complemented
247	C₂²×D₄	C₂³×C₂₃	1	16	yes	—
248	C₂²×D₄	C₂³×C₂₃	1	16	yes	complemented
249	C₂²×D₄	C₂³×C₂₃	1	16	yes	complemented
250	C₂³×C₄	—	2	8	no	—
251	C₂³×C₄	—	2	16	no	—
252	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
253	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
254	C₂³×C₄	C₂³×C₂₃	1	8	yes	complemented
255	#120	—	2	128	no	—
256	C₂×C₂²⋊C₄	—	2	16	no	—
257	C₂×C₂²⋊C₄	—	2	32	no	—
258	C₂×C₂²⋊C₄	—	4	4	no	—
259	C₂×C₂²⋊C₄	C₂³×C₂₃	1	16	yes	complemented
260	C₂×C₂²⋊C₄	C₂³×C₂₃	1	32	yes	complemented
261	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	complemented
262	#95	C₂³×C₂₃	1	16	yes	complemented
263	C₂₃	C₂×#2403	1	1	yes	characteristic, direct product factor, Sylow
264	C₂⁴	—	2	8	no	—
265	C₂⁴	—	2	8	no	—
266	C₂⁴	—	2	64	no	—
267	C₂⁴	—	2	64	no	—
268	C₂⁴	—	2	16	no	—
269	C₂⁴	—	2	32	no	—
270	C₂⁴	—	2	8	no	—
271	C₂⁴	—	2	8	no	—
272	C₂⁴	—	2	8	no	—
273	C₂⁴	—	2	16	no	—
274	C₂⁴	—	2	32	no	—
275	C₂⁴	—	2	4	no	—
276	C₂⁴	—	2	16	no	—
277	C₂⁴	—	2	32	no	—
278	C₂⁴	—	4	16	no	—
279	C₂⁴	—	4	8	no	—
280	C₂⁴	—	4	16	no	—
281	C₂⁴	—	4	64	no	—
282	C₂⁴	—	4	128	no	—
283	C₂⁴	—	4	32	no	—
284	C₂⁴	—	4	32	no	—
285	C₂⁴	C₂×D₄×C₂₃	1	4	yes	—
286	C₂⁴	C₂×D₄×C₂₃	1	16	yes	—
287	C₂⁴	C₂×D₄×C₂₃	1	8	yes	—
288	C₂⁴	C₂×D₄×C₂₃	1	16	yes	complemented
289	C₂⁴	C₂×D₄×C₂₃	1	16	yes	complemented
290	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
291	C₂⁴	C₂⁴×C₂₃	1	8	yes	—
292	C₂⁴	C₂⁴×C₂₃	1	4	yes	—
293	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
294	C₂×D₄	—	2	512	no	—
295	C₂×D₄	—	2	128	no	—
296	C₂×D₄	—	2	128	no	—
297	C₂×D₄	—	2	32	no	—
298	C₂×D₄	—	2	32	no	—
299	C₂×D₄	—	2	32	no	—
300	C₂×D₄	—	2	32	no	—
301	C₂×D₄	—	2	64	no	—
302	C₂×D₄	—	2	32	no	—
303	C₂×D₄	—	4	16	no	—
304	C₂×D₄	—	4	64	no	—
305	C₂×D₄	C₂×D₄×C₂₃	1	64	yes	complemented
306	C₂²×C₄	—	2	64	no	—
307	C₂²×C₄	—	2	8	no	—
308	C₂²×C₄	—	2	8	no	—
309	C₂²×C₄	—	2	16	no	—
310	C₂²×C₄	—	2	32	no	—
311	C₂²×C₄	—	2	16	no	—
312	C₂²×C₄	—	2	8	no	—
313	C₂²×C₄	C₂×D₄×C₂₃	1	16	yes	complemented
314	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
315	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
316	C₂²⋊C₄	—	2	32	no	—
317	C₂²⋊C₄	—	2	64	no	—
318	C₂²⋊C₄	—	4	8	no	—
319	C₂³	—	2	8	no	—
320	C₂³	—	2	8	no	—
321	C₂³	—	2	16	no	—
322	C₂³	—	2	16	no	—
323	C₂³	—	2	64	no	—
324	C₂³	—	2	64	no	—
325	C₂³	—	2	16	no	—
326	C₂³	—	2	8	no	—
327	C₂³	—	2	8	no	—
328	C₂³	—	2	8	no	—
329	C₂³	—	2	4	no	—
330	C₂³	—	2	16	no	—
331	C₂³	—	2	16	no	—
332	C₂³	—	2	32	no	—
333	C₂³	—	2	64	no	—
334	C₂³	—	2	8	no	—
335	C₂³	—	2	64	no	—
336	C₂³	—	4	16	no	—
337	C₂³	—	4	128	no	—
338	C₂³	—	4	64	no	—
339	C₂³	—	4	128	no	—
340	C₂³	—	4	256	no	—
341	C₂³	—	4	32	no	—
342	C₂³	—	4	16	no	—
343	C₂³	—	4	32	no	—
344	C₂³	—	4	16	no	—
345	C₂³	—	4	32	no	—
346	C₂³	—	4	16	no	—
347	C₂³	C₂₃×#120	1	32	yes	complemented
348	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
349	C₂³	C₂²×D₄×C₂₃	1	16	yes	—
350	C₂³	C₂²×D₄×C₂₃	1	8	yes	—
351	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
352	C₂³	C₂²×D₄×C₂₃	1	8	yes	—
353	C₂³	C₂²×D₄×C₂₃	1	16	yes	complemented
354	C₂³	C₂₃×H(5,𝔽₂)	1	4	yes	—
355	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
356	D₄	—	2	128	no	—
357	D₄	—	2	128	no	—
358	D₄	—	4	64	no	—
359	C₂×C₄	—	2	64	no	—
360	C₂×C₄	—	2	8	no	—
361	C₂×C₄	—	2	8	no	—
362	C₂×C₄	—	2	32	no	—
363	C₂×C₄	—	2	16	no	—
364	C₂×C₄	—	2	8	no	—
365	C₂×C₄	—	4	16	no	—
366	C₂×C₄	C₂²×D₄×C₂₃	1	16	yes	complemented
367	C₂²	—	2	64	no	—
368	C₂²	—	2	8	no	—
369	C₂²	—	2	8	no	—
370	C₂²	—	2	32	no	—
371	C₂²	—	2	8	no	—
372	C₂²	—	2	16	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	2	32	no	—
375	C₂²	—	4	64	no	—
376	C₂²	—	4	128	no	—
377	C₂²	—	4	16	no	—
378	C₂²	—	4	64	no	—
379	C₂²	—	4	8	no	—
380	C₂²	—	4	8	no	—
381	C₂²	—	4	16	no	—
382	C₂²	—	4	8	no	—
383	C₂²	C₂×C₂₃×#120	1	8	yes	—
384	C₂²	C₂×C₂₃×#120	1	16	yes	complemented
385	C₂²	C₂₃×#534	1	4	yes	—
386	C₂²	D₄²×C₂₃	1	16	yes	—
387	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
388	C₂²	C₂³×D₄×C₂₃	1	4	yes	—
389	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
390	C₄	—	2	16	no	—
391	C₄	—	4	8	no	—
392	C₂	—	2	16	no	—
393	C₂	—	4	4	no	—
394	C₂	—	4	16	no	—
395	C₂	C₂₃×#2403	1	8	yes	direct product factor
396	C₂	C₂²×C₂₃×#120	1	2	yes	—
397	C₂	C₂×C₂₃×#534	1	1	yes	characteristic
398	C₂	C₂×D₄²×C₂₃	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
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×D₄×C₂₃	C₂	semidirect
2. C₂²×C₂₃×#120	C₂	semidirect
3. C₂₃×#2403	C₂	direct (N × H)
4. C₂×C₂₃×#392	C₂	semidirect
5. C₂×C₂₃×#386	C₂	semidirect
6. C₂×C₂₃×#379	C₂	semidirect
8. C₂⁶×C₂₃	C₂²	semidirect
12. C₂³×D₄×C₂₃	C₂²	semidirect
13. C₂³×D₄×C₂₃	C₂²	semidirect
14. C₂³×D₄×C₂₃	C₂²	semidirect
15. C₂⁴×C₄×C₂₃	C₂²	semidirect
17. C₂×C₂₃×#120	C₂²	semidirect
18. C₂²×C₂²⋊C₄×C₂₃	C₂²	semidirect
19. C₂²×C₂²⋊C₄×C₂₃	C₂²	semidirect
20. C₂²×C₂²⋊C₄×C₂₃	C₂²	semidirect
21. C₂₃×#392	C₂²	semidirect
22. C₂₃×#386	C₂²	semidirect
23. C₂₃×#379	C₂²	semidirect
24. C₂×C₂₃×#95	C₂²	semidirect
31. C₂⁵×C₂₃	D₄	semidirect
36. C₂⁵×C₂₃	C₂³	semidirect
47. C₂²×D₄×C₂₃	D₄	semidirect
49. C₂²×D₄×C₂₃	C₂³	semidirect
50. C₂²×D₄×C₂₃	C₂³	semidirect
55. C₂³×C₄×C₂₃	C₂³	semidirect
60. C₂×C₂²⋊C₄×C₂₃	C₂³	semidirect
61. C₂×C₂²⋊C₄×C₂₃	C₂³	semidirect
62. C₂×C₂²⋊C₄×C₂₃	C₂³	semidirect
63. C₂₃×#95	C₂³	semidirect
88. C₂⁴×C₂₃	C₂×D₄	semidirect
89. C₂⁴×C₂₃	C₂×D₄	semidirect
105. C₂×D₄×C₂₃	C₂×D₄	semidirect
113. C₂²×C₄×C₂₃	C₂×D₄	semidirect
119. C₂×#2403	C₂₃	direct (N × H)
148. C₂³×C₂₃	#120	semidirect
154. C₂³×C₂₃	C₂²×D₄	semidirect
167. C₂×C₄×C₂₃	C₂²×D₄	semidirect
168. C₂⁴×D₄	C₂×C₂₃	semidirect
169. C₂²×#120	C₂×C₂₃	semidirect
170. #2403	C₂×C₂₃	direct (N × H)
171. C₂×#392	C₂×C₂₃	semidirect
172. C₂×#386	C₂×C₂₃	semidirect
173. C₂×#379	C₂×C₂₃	semidirect
191. C₂²×C₂₃	C₂×#120	semidirect
200. C₂⁶	C₂²×C₂₃	semidirect
204. C₂³×D₄	C₂²×C₂₃	semidirect
205. C₂³×D₄	C₂²×C₂₃	semidirect
206. C₂³×D₄	C₂²×C₂₃	semidirect
207. C₂⁴×C₄	C₂²×C₂₃	semidirect
209. C₂×#120	C₂²×C₂₃	semidirect
210. C₂²×C₂²⋊C₄	C₂²×C₂₃	semidirect
211. C₂²×C₂²⋊C₄	C₂²×C₂₃	semidirect
212. C₂²×C₂²⋊C₄	C₂²×C₂₃	semidirect
213. #392	C₂²×C₂₃	semidirect
214. #386	C₂²×C₂₃	semidirect
215. #379	C₂²×C₂₃	semidirect
216. C₂×#95	C₂²×C₂₃	semidirect
220. C₂×C₂₃	#2403	direct (N × H)
230. C₂⁵	D₄×C₂₃	semidirect
235. C₂⁵	C₂³×C₂₃	semidirect
246. C₂²×D₄	D₄×C₂₃	semidirect
248. C₂²×D₄	C₂³×C₂₃	semidirect
249. C₂²×D₄	C₂³×C₂₃	semidirect
254. C₂³×C₄	C₂³×C₂₃	semidirect
259. C₂×C₂²⋊C₄	C₂³×C₂₃	semidirect
260. C₂×C₂²⋊C₄	C₂³×C₂₃	semidirect
261. C₂×C₂²⋊C₄	C₂³×C₂₃	semidirect
262. #95	C₂³×C₂₃	semidirect
263. C₂₃	C₂×#2403	direct (N × H)
288. C₂⁴	C₂×D₄×C₂₃	semidirect
289. C₂⁴	C₂×D₄×C₂₃	semidirect
305. C₂×D₄	C₂×D₄×C₂₃	semidirect
313. C₂²×C₄	C₂×D₄×C₂₃	semidirect
347. C₂³	C₂₃×#120	semidirect
353. C₂³	C₂²×D₄×C₂₃	semidirect
366. C₂×C₄	C₂²×D₄×C₂₃	semidirect
384. C₂²	C₂×C₂₃×#120	semidirect
395. C₂	C₂₃×#2403	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×D₄×C₂₃	2
C₂²×C₂₃×#120	2
C₂₃×#2403	2
C₂×C₂₃×#392	2
C₂×C₂₃×#386	2
C₂×C₂₃×#379	2
C₂×#2403	23

Subgroups — C2×C23×#2403 #19182271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#2403 #19182271