Subgroups — C₂×C₂₃×#1970 #19168849

Order 5888.

2046 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₈×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₂₃×#102	C₂	1	2	yes	maximal, complemented
4	C₂²×C₄×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#390	C₂	1	2	yes	maximal, complemented
6	C₂₃×#1970	C₂	1	8	yes	maximal, direct product factor
7	C₂³×D₄×C₂₃	C₂²	1	2	yes	—
8	C₂²×D₈×C₂₃	—	2	4	no	—
9	C₂²×D₈×C₂₃	—	2	4	no	—
10	C₂²×D₈×C₂₃	C₄	1	8	yes	complemented
11	C₂²×D₈×C₂₃	C₂²	1	4	yes	—
12	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
15	C₂²×C₂²⋊C₄×C₂₃	—	2	4	no	—
16	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
17	C₂×C₂₃×#107	—	2	4	no	—
18	C₂×C₂₃×#107	C₂²	1	4	yes	complemented
19	C₂×C₂₃×#102	—	2	8	no	—
20	C₂×C₂₃×#102	C₂²	1	8	yes	complemented
21	C₂×C₄×C₈×C₂₃	—	2	4	no	—
22	C₂×C₄×C₈×C₂₃	C₂²	1	4	yes	complemented
23	C₂₃×#390	—	2	4	no	—
24	C₂₃×#390	C₂²	1	8	yes	complemented
25	C₂⁵×C₂₃	—	2	2	no	—
26	C₂²×D₄×C₂₃	—	2	4	no	—
27	C₂²×D₄×C₂₃	—	2	4	no	—
28	C₂²×D₄×C₂₃	—	2	4	no	—
29	C₂²×D₄×C₂₃	—	2	2	no	—
30	C₂²×D₄×C₂₃	—	2	4	no	—
31	C₂²×D₄×C₂₃	—	2	4	no	—
32	C₂²×D₄×C₂₃	C₂×C₄	1	8	yes	—
33	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
34	C₂³×C₄×C₂₃	—	2	2	no	—
35	C₂³×C₄×C₂₃	D₄	1	2	yes	—
36	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
37	C₂×D₈×C₂₃	—	2	32	no	—
38	C₂×D₈×C₂₃	—	2	8	no	—
39	C₂×D₈×C₂₃	—	2	8	no	—
40	C₂×D₈×C₂₃	C₂×C₄	1	16	yes	complemented
41	C₂²×C₈×C₂₃	—	2	2	no	—
42	C₂²×C₈×C₂₃	—	2	2	no	—
43	C₂²×C₈×C₂₃	C₂×C₄	1	4	yes	—
44	C₂²×C₈×C₂₃	D₄	1	4	yes	—
45	C₂²×C₈×C₂₃	D₄	1	4	yes	—
46	C₂²×C₈×C₂₃	D₄	1	4	yes	—
47	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
48	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
49	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
50	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
51	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
52	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
53	C₂×C₂²⋊C₄×C₂₃	—	2	16	no	—
54	C₂×C₂²⋊C₄×C₂₃	—	4	16	no	—
55	C₂×C₄²×C₂₃	—	2	2	no	—
56	C₂×C₄²×C₂₃	—	2	2	no	—
57	C₂×C₄²×C₂₃	D₄	1	2	yes	—
58	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
59	C₂₃×#107	—	2	8	no	—
60	C₂₃×#102	—	2	16	no	—
61	C₄×C₈×C₂₃	—	2	8	no	—
62	C₂⁴×C₂₃	—	2	8	no	—
63	C₂⁴×C₂₃	—	2	4	no	—
64	C₂⁴×C₂₃	—	4	4	no	—
65	C₂⁴×C₂₃	—	4	4	no	—
66	C₂⁴×C₂₃	—	4	8	no	—
67	C₂⁴×C₂₃	—	4	8	no	—
68	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
69	C₂×D₄×C₂₃	—	2	16	no	—
70	C₂×D₄×C₂₃	—	2	16	no	—
71	C₂×D₄×C₂₃	—	2	8	no	—
72	C₂×D₄×C₂₃	—	2	4	no	—
73	C₂×D₄×C₂₃	—	2	4	no	—
74	C₂×D₄×C₂₃	—	2	4	no	—
75	C₂×D₄×C₂₃	—	2	4	no	—
76	C₂×D₄×C₂₃	—	2	4	no	—
77	C₂×D₄×C₂₃	—	4	8	no	—
78	C₂×D₄×C₂₃	—	4	4	no	—
79	C₂×D₄×C₂₃	—	4	8	no	—
80	C₂×D₄×C₂₃	—	4	4	no	—
81	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
82	C₂²×C₄×C₂₃	—	2	4	no	—
83	C₂²×C₄×C₂₃	—	2	4	no	—
84	C₂²×C₄×C₂₃	—	2	4	no	—
85	C₂²×C₄×C₂₃	—	4	4	no	—
86	C₂²×C₄×C₂₃	—	4	8	no	—
87	C₂²×C₄×C₂₃	D₈	1	8	yes	complemented
88	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
90	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₂₃	#41	1	2	yes	—
95	C₂²×C₄×C₂₃	#41	1	2	yes	—
96	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
97	D₈×C₂₃	—	2	32	no	—
98	C₂×C₈×C₂₃	—	2	8	no	—
99	C₂×C₈×C₂₃	—	2	2	no	—
100	C₂×C₈×C₂₃	—	2	2	no	—
101	C₂×C₈×C₂₃	C₂²⋊C₄	1	16	yes	complemented
102	C₂×C₈×C₂₃	C₂²×C₄	1	4	yes	—
103	C₂×C₈×C₂₃	C₂×D₄	1	4	yes	—
104	C₂×C₈×C₂₃	C₂×D₄	1	4	yes	—
105	C₂×C₈×C₂₃	C₂×D₄	1	4	yes	—
106	C₄⋊C₄×C₂₃	—	2	4	no	—
107	C₄⋊C₄×C₂₃	—	2	4	no	—
108	C₄⋊C₄×C₂₃	—	4	4	no	—
109	C₂²⋊C₄×C₂₃	—	4	32	no	—
110	C₄²×C₂₃	—	2	4	no	—
111	C₄²×C₂₃	—	2	2	no	—
112	C₄²×C₂₃	—	2	2	no	—
113	C₂×#1970	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
114	C₂³×C₂₃	—	2	8	no	—
115	C₂³×C₂₃	—	4	4	no	—
116	C₂³×C₂₃	—	4	4	no	—
117	C₂³×C₂₃	—	4	8	no	—
118	C₂³×C₂₃	—	4	8	no	—
119	C₂³×C₂₃	—	4	16	no	—
120	C₂³×C₂₃	—	4	32	no	—
121	C₂³×C₂₃	—	8	16	no	—
122	C₂³×C₂₃	—	8	8	no	—
123	C₂³×C₂₃	—	8	8	no	—
124	C₂³×C₂₃	C₄×D₄	1	2	yes	—
125	C₂³×C₂₃	#121	1	2	yes	—
126	C₂³×C₂₃	#127	1	2	yes	—
127	C₂³×C₂₃	C₂×D₈	1	4	yes	—
128	C₂³×C₂₃	#135	1	4	yes	—
129	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
130	D₄×C₂₃	—	2	8	no	—
131	D₄×C₂₃	—	2	8	no	—
132	D₄×C₂₃	—	4	4	no	—
133	D₄×C₂₃	—	4	4	no	—
134	D₄×C₂₃	—	4	16	no	—
135	C₂×C₄×C₂₃	—	2	4	no	—
136	C₂×C₄×C₂₃	—	2	4	no	—
137	C₂×C₄×C₂₃	—	2	16	no	—
138	C₂×C₄×C₂₃	—	4	4	no	—
139	C₂×C₄×C₂₃	—	4	8	no	—
140	C₂×C₄×C₂₃	—	8	8	no	—
141	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	4	yes	—
142	C₂×C₄×C₂₃	C₄×D₄	1	4	yes	—
143	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
144	C₂×C₄×C₂₃	#121	1	4	yes	—
145	C₂×C₄×C₂₃	#121	1	2	yes	—
146	C₂×C₄×C₂₃	#124	1	4	yes	—
147	C₂×C₄×C₂₃	#127	1	2	yes	—
148	C₂×C₄×C₂₃	C₂×D₈	1	8	yes	complemented
149	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
150	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
154	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
155	C₈×C₂₃	—	2	4	no	—
156	C₈×C₂₃	C₂×C₂²⋊C₄	1	8	yes	complemented
157	C₂³×D₈	C₂×C₂₃	1	1	yes	characteristic
158	C₂²×#107	C₂×C₂₃	1	1	yes	characteristic, complemented
159	C₂²×#102	C₂×C₂₃	1	2	yes	complemented
160	C₂²×C₄×C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
161	C₂×#390	C₂×C₂₃	1	2	yes	complemented
162	#1970	C₂×C₂₃	1	8	yes	direct product factor
163	C₂²×C₂₃	—	4	16	no	—
164	C₂²×C₂₃	—	4	8	no	—
165	C₂²×C₂₃	—	8	4	no	—
166	C₂²×C₂₃	—	8	4	no	—
167	C₂²×C₂₃	—	8	32	no	—
168	C₂²×C₂₃	—	8	8	no	—
169	C₂²×C₂₃	#390	1	4	yes	—
170	C₂²×C₂₃	C₄×D₈	1	8	yes	—
171	C₂²×C₂₃	#466	1	8	yes	—
172	C₂²×C₂₃	#493	1	4	yes	—
173	C₂²×C₂₃	#495	1	4	yes	—
174	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
175	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
176	C₂²×C₂₃	C₂×#127	1	1	yes	characteristic
177	C₂²×C₂₃	C₂²×D₈	1	2	yes	—
178	C₂²×C₂₃	C₂×#135	1	2	yes	—
179	C₄×C₂₃	—	2	8	no	—
180	C₄×C₂₃	—	8	4	no	—
181	C₄×C₂₃	#390	1	4	yes	—
182	C₄×C₂₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
183	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
184	C₄×C₂₃	C₂×#121	1	1	yes	characteristic
185	C₄×C₂₃	C₂×#124	1	1	yes	characteristic
186	C₂³×D₄	C₂²×C₂₃	1	2	yes	—
187	C₂²×D₈	—	2	4	no	—
188	C₂²×D₈	—	2	4	no	—
189	C₂²×D₈	C₄×C₂₃	1	8	yes	complemented
190	C₂²×D₈	C₂²×C₂₃	1	4	yes	—
191	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
192	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
193	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
194	C₂²×C₂²⋊C₄	—	2	4	no	—
195	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
196	C₂×#107	—	2	4	no	—
197	C₂×#107	C₂²×C₂₃	1	4	yes	complemented
198	C₂×#102	—	2	8	no	—
199	C₂×#102	C₂²×C₂₃	1	8	yes	complemented
200	C₂×C₄×C₈	—	2	4	no	—
201	C₂×C₄×C₈	C₂²×C₂₃	1	4	yes	complemented
202	#390	—	2	4	no	—
203	#390	C₂²×C₂₃	1	8	yes	complemented
204	C₂×C₂₃	—	8	8	no	—
205	C₂×C₂₃	#1970	1	8	yes	direct product factor
206	C₂×C₂₃	C₂×#390	1	1	yes	characteristic
207	C₂×C₂₃	C₂×C₄×D₈	1	2	yes	—
208	C₂×C₂₃	C₂×#466	1	2	yes	—
209	C₂×C₂₃	C₂×#493	1	1	yes	characteristic
210	C₂×C₂₃	C₂×#495	1	1	yes	characteristic
211	C₂⁵	—	2	2	no	—
212	C₂²×D₄	—	2	4	no	—
213	C₂²×D₄	—	2	4	no	—
214	C₂²×D₄	—	2	4	no	—
215	C₂²×D₄	—	2	2	no	—
216	C₂²×D₄	—	2	4	no	—
217	C₂²×D₄	—	2	4	no	—
218	C₂²×D₄	C₂×C₄×C₂₃	1	8	yes	—
219	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
220	C₂³×C₄	—	2	2	no	—
221	C₂³×C₄	D₄×C₂₃	1	2	yes	—
222	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
223	C₂×D₈	—	2	32	no	—
224	C₂×D₈	—	2	8	no	—
225	C₂×D₈	—	2	8	no	—
226	C₂×D₈	C₂×C₄×C₂₃	1	16	yes	complemented
227	C₂²×C₈	—	2	2	no	—
228	C₂²×C₈	—	2	2	no	—
229	C₂²×C₈	C₂×C₄×C₂₃	1	4	yes	—
230	C₂²×C₈	D₄×C₂₃	1	4	yes	—
231	C₂²×C₈	D₄×C₂₃	1	4	yes	—
232	C₂²×C₈	D₄×C₂₃	1	4	yes	—
233	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
234	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
235	C₂×C₄⋊C₄	—	2	4	no	—
236	C₂×C₄⋊C₄	—	2	4	no	—
237	C₂×C₄⋊C₄	—	2	2	no	—
238	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
239	C₂×C₂²⋊C₄	—	2	16	no	—
240	C₂×C₂²⋊C₄	—	4	16	no	—
241	C₂×C₄²	—	2	2	no	—
242	C₂×C₄²	—	2	2	no	—
243	C₂×C₄²	D₄×C₂₃	1	2	yes	—
244	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
245	#107	—	2	8	no	—
246	#102	—	2	16	no	—
247	C₄×C₈	—	2	8	no	—
248	C₂₃	C₂×#1970	1	1	yes	characteristic, direct product factor, Sylow
249	C₂⁴	—	2	8	no	—
250	C₂⁴	—	2	4	no	—
251	C₂⁴	—	4	4	no	—
252	C₂⁴	—	4	4	no	—
253	C₂⁴	—	4	8	no	—
254	C₂⁴	—	4	8	no	—
255	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
256	C₂×D₄	—	2	16	no	—
257	C₂×D₄	—	2	16	no	—
258	C₂×D₄	—	2	8	no	—
259	C₂×D₄	—	2	4	no	—
260	C₂×D₄	—	2	4	no	—
261	C₂×D₄	—	2	4	no	—
262	C₂×D₄	—	2	4	no	—
263	C₂×D₄	—	2	4	no	—
264	C₂×D₄	—	4	4	no	—
265	C₂×D₄	—	4	8	no	—
266	C₂×D₄	—	4	8	no	—
267	C₂×D₄	—	4	4	no	—
268	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	4	4	no	—
273	C₂²×C₄	—	4	8	no	—
274	C₂²×C₄	D₈×C₂₃	1	8	yes	complemented
275	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
276	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
277	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
278	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
279	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
280	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
281	C₂²×C₄	#41×C₂₃	1	2	yes	—
282	C₂²×C₄	#41×C₂₃	1	2	yes	—
283	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
284	D₈	—	2	32	no	—
285	C₂×C₈	—	2	8	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	C₂²⋊C₄×C₂₃	1	16	yes	complemented
289	C₂×C₈	C₂²×C₄×C₂₃	1	4	yes	—
290	C₂×C₈	C₂×D₄×C₂₃	1	4	yes	—
291	C₂×C₈	C₂×D₄×C₂₃	1	4	yes	—
292	C₂×C₈	C₂×D₄×C₂₃	1	4	yes	—
293	C₄⋊C₄	—	2	4	no	—
294	C₄⋊C₄	—	2	4	no	—
295	C₄⋊C₄	—	4	4	no	—
296	C₂²⋊C₄	—	4	32	no	—
297	C₄²	—	2	4	no	—
298	C₄²	—	2	2	no	—
299	C₄²	—	2	2	no	—
300	C₂³	—	2	8	no	—
301	C₂³	—	4	8	no	—
302	C₂³	—	4	8	no	—
303	C₂³	—	4	16	no	—
304	C₂³	—	4	32	no	—
305	C₂³	—	4	4	no	—
306	C₂³	—	4	4	no	—
307	C₂³	—	8	16	no	—
308	C₂³	—	8	8	no	—
309	C₂³	—	8	8	no	—
310	C₂³	C₄×D₄×C₂₃	1	2	yes	—
311	C₂³	C₂₃×#121	1	2	yes	—
312	C₂³	C₂₃×#127	1	2	yes	—
313	C₂³	C₂×D₈×C₂₃	1	4	yes	—
314	C₂³	C₂₃×#135	1	4	yes	—
315	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
316	D₄	—	2	8	no	—
317	D₄	—	2	8	no	—
318	D₄	—	4	16	no	—
319	D₄	—	4	4	no	—
320	D₄	—	4	4	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	16	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	4	8	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	8	8	no	—
327	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	4	yes	—
328	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
329	C₂×C₄	C₄×D₄×C₂₃	1	4	yes	—
330	C₂×C₄	C₂₃×#121	1	2	yes	—
331	C₂×C₄	C₂₃×#121	1	4	yes	—
332	C₂×C₄	C₂₃×#124	1	4	yes	—
333	C₂×C₄	C₂₃×#127	1	2	yes	—
334	C₂×C₄	C₂×D₈×C₂₃	1	8	yes	complemented
335	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
336	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
337	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
338	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
339	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
340	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
341	C₈	—	2	4	no	—
342	C₈	C₂×C₂²⋊C₄×C₂₃	1	8	yes	complemented
343	C₂²	—	4	16	no	—
344	C₂²	—	4	8	no	—
345	C₂²	—	8	32	no	—
346	C₂²	—	8	8	no	—
347	C₂²	—	8	4	no	—
348	C₂²	—	8	4	no	—
349	C₂²	C₂₃×#390	1	4	yes	—
350	C₂²	C₄×D₈×C₂₃	1	8	yes	—
351	C₂²	C₂₃×#466	1	8	yes	—
352	C₂²	C₂₃×#493	1	4	yes	—
353	C₂²	C₂₃×#495	1	4	yes	—
354	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
355	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
356	C₂²	C₂×C₂₃×#127	1	1	yes	characteristic
357	C₂²	C₂²×D₈×C₂₃	1	2	yes	—
358	C₂²	C₂×C₂₃×#135	1	2	yes	—
359	C₄	—	2	8	no	—
360	C₄	—	8	4	no	—
361	C₄	C₂₃×#390	1	4	yes	—
362	C₄	C₂²×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
363	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
364	C₄	C₂×C₂₃×#121	1	1	yes	characteristic
365	C₄	C₂×C₂₃×#124	1	1	yes	characteristic
366	C₂	—	8	8	no	—
367	C₂	C₂₃×#1970	1	8	yes	direct product factor
368	C₂	C₂×C₂₃×#390	1	1	yes	characteristic
369	C₂	C₂×C₄×D₈×C₂₃	1	2	yes	—
370	C₂	C₂×C₂₃×#466	1	2	yes	—
371	C₂	C₂×C₂₃×#493	1	1	yes	characteristic
372	C₂	C₂×C₂₃×#495	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₂₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂³×D₈×C₂₃	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₂₃×#107	C₂	semidirect
3. C₂²×C₂₃×#102	C₂	semidirect
4. C₂²×C₄×C₈×C₂₃	C₂	semidirect
5. C₂×C₂₃×#390	C₂	semidirect
6. C₂₃×#1970	C₂	direct (N × H)
10. C₂²×D₈×C₂₃	C₄	semidirect
18. C₂×C₂₃×#107	C₂²	semidirect
20. C₂×C₂₃×#102	C₂²	semidirect
22. C₂×C₄×C₈×C₂₃	C₂²	semidirect
24. C₂₃×#390	C₂²	semidirect
40. C₂×D₈×C₂₃	C₂×C₄	semidirect
87. C₂²×C₄×C₂₃	D₈	semidirect
101. C₂×C₈×C₂₃	C₂²⋊C₄	semidirect
113. C₂×#1970	C₂₃	direct (N × H)
148. C₂×C₄×C₂₃	C₂×D₈	semidirect
156. C₈×C₂₃	C₂×C₂²⋊C₄	semidirect
158. C₂²×#107	C₂×C₂₃	semidirect
159. C₂²×#102	C₂×C₂₃	semidirect
160. C₂²×C₄×C₈	C₂×C₂₃	semidirect
161. C₂×#390	C₂×C₂₃	semidirect
162. #1970	C₂×C₂₃	direct (N × H)
189. C₂²×D₈	C₄×C₂₃	semidirect
197. C₂×#107	C₂²×C₂₃	semidirect
199. C₂×#102	C₂²×C₂₃	semidirect
201. C₂×C₄×C₈	C₂²×C₂₃	semidirect
203. #390	C₂²×C₂₃	semidirect
205. C₂×C₂₃	#1970	direct (N × H)
226. C₂×D₈	C₂×C₄×C₂₃	semidirect
248. C₂₃	C₂×#1970	direct (N × H)
274. C₂²×C₄	D₈×C₂₃	semidirect
288. C₂×C₈	C₂²⋊C₄×C₂₃	semidirect
334. C₂×C₄	C₂×D₈×C₂₃	semidirect
342. C₈	C₂×C₂²⋊C₄×C₂₃	semidirect
367. C₂	C₂₃×#1970	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×D₈×C₂₃	2
C₂²×C₂₃×#107	2
C₂²×C₂₃×#102	2
C₂²×C₄×C₈×C₂₃	2
C₂×C₂₃×#390	2
C₂₃×#1970	2
C₂×#1970	23

Subgroups — C2×C23×#1970 #19168849

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#1970 #19168849