Subgroups — C₂×C₄₁×#1940 #23797343

Order 10496.

1182 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊C₈×C₄₁	C₂	1	2	yes	maximal
2	C₂²×C₄⋊C₈×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×#97×C₄₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₄⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#1940	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄₁×#336	C₂	1	2	yes	maximal
7	C₂³×C₈×C₄₁	C₂²	1	2	yes	—
8	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
9	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₄₁	C₄	1	2	yes	—
11	C₂²×C₄²×C₄₁	C₂²	1	2	yes	—
12	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₈×C₄₁	—	2	8	no	—
14	C₂×C₄⋊C₈×C₄₁	—	2	4	no	—
15	C₂×C₄⋊C₈×C₄₁	C₂²	1	8	yes	—
16	C₂×C₄⋊C₈×C₄₁	C₂²	1	4	yes	—
17	C₂×#97×C₄₁	—	2	4	no	—
18	C₂×#97×C₄₁	C₂²	1	4	yes	—
19	C₄×C₄⋊C₄×C₄₁	C₄	1	4	yes	—
20	C₄×C₄⋊C₄×C₄₁	C₂²	1	4	yes	—
21	C₂×#95×C₄₁	C₄	1	1	yes	characteristic
22	C₂×#95×C₄₁	C₄	1	1	yes	characteristic
23	C₄₁×#336	C₂²	1	8	yes	—
24	C₂³×C₄×C₄₁	C₂×C₄	1	2	yes	—
25	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₄₁	C₂×C₄	1	2	yes	—
28	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
29	C₂²×C₈×C₄₁	—	2	2	no	—
30	C₂²×C₈×C₄₁	—	2	2	no	—
31	C₂²×C₈×C₄₁	—	2	2	no	—
32	C₂²×C₈×C₄₁	—	2	2	no	—
33	C₂²×C₈×C₄₁	—	2	4	no	—
34	C₂²×C₈×C₄₁	—	2	4	no	—
35	C₂²×C₈×C₄₁	—	2	4	no	—
36	C₂²×C₈×C₄₁	D₄	1	4	yes	—
37	C₂²×C₈×C₄₁	Q₈	1	4	yes	—
38	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
39	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
40	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
41	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
42	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	8	yes	—
43	C₂×C₄²×C₄₁	—	2	4	no	—
44	C₂×C₄²×C₄₁	—	2	4	no	—
45	C₂×C₄²×C₄₁	C₂×C₄	1	4	yes	—
46	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₄₁	D₄	1	4	yes	—
48	C₂×C₄²×C₄₁	Q₈	1	4	yes	—
49	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
50	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
51	C₄⋊C₈×C₄₁	—	2	16	no	—
52	C₄⋊C₈×C₄₁	—	2	8	no	—
53	#97×C₄₁	—	2	8	no	—
54	#95×C₄₁	C₂×C₄	1	4	yes	—
55	#95×C₄₁	C₂×C₄	1	4	yes	—
56	C₂⁴×C₄₁	C₂²×C₄	1	1	yes	characteristic
57	C₂²×C₄×C₄₁	—	2	4	no	—
58	C₂²×C₄×C₄₁	—	2	4	no	—
59	C₂²×C₄×C₄₁	—	2	4	no	—
60	C₂²×C₄×C₄₁	—	2	4	no	—
61	C₂²×C₄×C₄₁	—	2	4	no	—
62	C₂²×C₄×C₄₁	—	2	4	no	—
63	C₂²×C₄×C₄₁	—	2	4	no	—
64	C₂²×C₄×C₄₁	C₄⋊C₄	1	4	yes	—
65	C₂²×C₄×C₄₁	C₄⋊C₄	1	4	yes	—
66	C₂²×C₄×C₄₁	M₁₆	1	8	yes	—
67	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
68	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
69	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
70	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
71	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
73	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
74	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
75	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
76	C₂²×C₄×C₄₁	#41	1	2	yes	—
77	C₂²×C₄×C₄₁	#41	1	2	yes	—
78	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
79	C₂×C₈×C₄₁	—	2	8	no	—
80	C₂×C₈×C₄₁	—	2	8	no	—
81	C₂×C₈×C₄₁	—	2	2	no	—
82	C₂×C₈×C₄₁	—	2	2	no	—
83	C₂×C₈×C₄₁	—	2	2	no	—
84	C₂×C₈×C₄₁	—	2	2	no	—
85	C₂×C₈×C₄₁	—	2	4	no	—
86	C₂×C₈×C₄₁	—	2	4	no	—
87	C₂×C₈×C₄₁	—	2	4	no	—
88	C₂×C₈×C₄₁	—	4	8	no	—
89	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
90	C₂×C₈×C₄₁	C₂×Q₈	1	4	yes	—
91	C₄⋊C₄×C₄₁	—	2	16	no	—
92	C₄²×C₄₁	—	2	8	no	—
93	C₄²×C₄₁	—	2	4	no	—
94	C₄²×C₄₁	—	2	4	no	—
95	C₄²×C₄₁	C₄⋊C₄	1	8	yes	—
96	C₄²×C₄₁	C₂×D₄	1	4	yes	—
97	C₄²×C₄₁	C₂×Q₈	1	4	yes	—
98	C₂³×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
99	C₂³×C₄₁	C₄×D₄	1	2	yes	—
100	C₂³×C₄₁	C₄×Q₈	1	2	yes	—
101	C₂³×C₄₁	C₂×M₁₆	1	4	yes	—
102	C₂³×C₄₁	#131	1	4	yes	—
103	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
104	C₂×C₄×C₄₁	—	2	4	no	—
105	C₂×C₄×C₄₁	—	2	4	no	—
106	C₂×C₄×C₄₁	—	2	4	no	—
107	C₂×C₄×C₄₁	—	2	4	no	—
108	C₂×C₄×C₄₁	—	2	8	no	—
109	C₂×C₄×C₄₁	—	2	8	no	—
110	C₂×C₄×C₄₁	—	2	16	no	—
111	C₂×C₄×C₄₁	—	2	4	no	—
112	C₂×C₄×C₄₁	—	2	4	no	—
113	C₂×C₄×C₄₁	—	2	4	no	—
114	C₂×C₄×C₄₁	—	4	8	no	—
115	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	4	yes	—
116	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	4	yes	—
117	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
118	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
119	C₂×C₄×C₄₁	C₄×Q₈	1	2	yes	—
120	C₂×C₄×C₄₁	#121	1	4	yes	—
121	C₂×C₄×C₄₁	C₂²⋊Q₈	1	4	yes	—
122	C₂×C₄×C₄₁	#125	1	4	yes	—
123	C₂×C₄×C₄₁	C₄⋊Q₈	1	4	yes	—
124	C₂×C₄×C₄₁	C₂×M₁₆	1	8	yes	—
125	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
126	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
127	C₂×C₄×C₄₁	C₂²×Q₈	1	1	yes	characteristic
128	C₂×C₄×C₄₁	C₂²×Q₈	1	1	yes	characteristic
129	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
130	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
131	C₈×C₄₁	—	2	4	no	—
132	C₈×C₄₁	—	2	4	no	—
133	C₈×C₄₁	—	4	4	no	—
134	C₂×#1940	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
135	C₂²×C₄₁	#389	1	4	yes	—
136	C₂²×C₄₁	#423	1	4	yes	—
137	C₂²×C₄₁	#424	1	4	yes	—
138	C₂²×C₄₁	#435	1	8	yes	—
139	C₂²×C₄₁	#446	1	8	yes	—
140	C₂²×C₄₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
141	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
142	C₂²×C₄₁	C₂×C₄×Q₈	1	1	yes	characteristic
143	C₂²×C₄₁	C₂²×M₁₆	1	2	yes	—
144	C₂²×C₄₁	C₂×#131	1	2	yes	—
145	C₄×C₄₁	—	2	4	no	—
146	C₄×C₄₁	—	2	4	no	—
147	C₄×C₄₁	—	2	8	no	—
148	C₄×C₄₁	—	4	4	no	—
149	C₄×C₄₁	#389	1	4	yes	—
150	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
151	C₄×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
152	C₄×C₄₁	C₂×#125	1	1	yes	characteristic
153	C₄×C₄₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
154	C₂²×C₄⋊C₈	C₂×C₄₁	1	1	yes	characteristic
155	C₂²×C₄⋊C₈	C₂×C₄₁	1	2	yes	—
156	C₂²×#97	C₂×C₄₁	1	1	yes	characteristic
157	C₂×C₄×C₄⋊C₄	C₂×C₄₁	1	1	yes	characteristic
158	#1940	C₂×C₄₁	1	8	yes	direct product factor
159	C₂×#336	C₂×C₄₁	1	2	yes	—
160	C₂×C₄₁	#1940	1	8	yes	direct product factor
161	C₂×C₄₁	C₂×#389	1	1	yes	characteristic
162	C₂×C₄₁	C₂×#423	1	1	yes	characteristic
163	C₂×C₄₁	C₂×#424	1	1	yes	characteristic
164	C₂×C₄₁	C₂×#435	1	2	yes	—
165	C₂×C₄₁	C₂×#446	1	2	yes	—
166	C₂³×C₈	C₂²×C₄₁	1	2	yes	—
167	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
168	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
169	C₂²×C₄⋊C₄	C₄×C₄₁	1	2	yes	—
170	C₂²×C₄²	C₂²×C₄₁	1	2	yes	—
171	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
172	C₂×C₄⋊C₈	—	2	8	no	—
173	C₂×C₄⋊C₈	—	2	4	no	—
174	C₂×C₄⋊C₈	C₂²×C₄₁	1	8	yes	—
175	C₂×C₄⋊C₈	C₂²×C₄₁	1	4	yes	—
176	C₂×#97	—	2	4	no	—
177	C₂×#97	C₂²×C₄₁	1	4	yes	—
178	C₄×C₄⋊C₄	C₄×C₄₁	1	4	yes	—
179	C₄×C₄⋊C₄	C₂²×C₄₁	1	4	yes	—
180	C₂×#95	C₄×C₄₁	1	1	yes	characteristic
181	C₂×#95	C₄×C₄₁	1	1	yes	characteristic
182	#336	C₂²×C₄₁	1	8	yes	—
183	C₄₁	C₂×#1940	1	1	yes	characteristic, direct product factor, Sylow
184	C₂³×C₄	C₂×C₄×C₄₁	1	2	yes	—
185	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
186	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
187	C₂³×C₄	C₂×C₄×C₄₁	1	2	yes	—
188	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
189	C₂²×C₈	—	2	2	no	—
190	C₂²×C₈	—	2	2	no	—
191	C₂²×C₈	—	2	2	no	—
192	C₂²×C₈	—	2	2	no	—
193	C₂²×C₈	—	2	4	no	—
194	C₂²×C₈	—	2	4	no	—
195	C₂²×C₈	—	2	4	no	—
196	C₂²×C₈	D₄×C₄₁	1	4	yes	—
197	C₂²×C₈	Q₈×C₄₁	1	4	yes	—
198	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
199	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
200	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
201	C₂×C₄⋊C₄	—	2	8	no	—
202	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	8	yes	—
203	C₂×C₄²	—	2	4	no	—
204	C₂×C₄²	—	2	4	no	—
205	C₂×C₄²	C₂×C₄×C₄₁	1	4	yes	—
206	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
207	C₂×C₄²	D₄×C₄₁	1	4	yes	—
208	C₂×C₄²	Q₈×C₄₁	1	4	yes	—
209	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
210	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
211	C₄⋊C₈	—	2	16	no	—
212	C₄⋊C₈	—	2	8	no	—
213	#97	—	2	8	no	—
214	#95	C₂×C₄×C₄₁	1	4	yes	—
215	#95	C₂×C₄×C₄₁	1	4	yes	—
216	C₂⁴	C₂²×C₄×C₄₁	1	1	yes	characteristic
217	C₂²×C₄	—	2	4	no	—
218	C₂²×C₄	—	2	4	no	—
219	C₂²×C₄	—	2	4	no	—
220	C₂²×C₄	—	2	4	no	—
221	C₂²×C₄	—	2	4	no	—
222	C₂²×C₄	—	2	4	no	—
223	C₂²×C₄	—	2	4	no	—
224	C₂²×C₄	C₄⋊C₄×C₄₁	1	4	yes	—
225	C₂²×C₄	C₄⋊C₄×C₄₁	1	4	yes	—
226	C₂²×C₄	M₁₆×C₄₁	1	8	yes	—
227	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
228	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
229	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
230	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
231	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
232	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
233	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
234	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
235	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
236	C₂²×C₄	#41×C₄₁	1	2	yes	—
237	C₂²×C₄	#41×C₄₁	1	2	yes	—
238	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
239	C₂×C₈	—	2	8	no	—
240	C₂×C₈	—	2	8	no	—
241	C₂×C₈	—	2	2	no	—
242	C₂×C₈	—	2	2	no	—
243	C₂×C₈	—	2	2	no	—
244	C₂×C₈	—	2	2	no	—
245	C₂×C₈	—	2	4	no	—
246	C₂×C₈	—	2	4	no	—
247	C₂×C₈	—	2	4	no	—
248	C₂×C₈	—	4	8	no	—
249	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
250	C₂×C₈	C₂×Q₈×C₄₁	1	4	yes	—
251	C₄⋊C₄	—	2	16	no	—
252	C₄²	—	2	8	no	—
253	C₄²	—	2	4	no	—
254	C₄²	—	2	4	no	—
255	C₄²	C₄⋊C₄×C₄₁	1	8	yes	—
256	C₄²	C₂×D₄×C₄₁	1	4	yes	—
257	C₄²	C₂×Q₈×C₄₁	1	4	yes	—
258	C₂³	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
259	C₂³	C₄×D₄×C₄₁	1	2	yes	—
260	C₂³	C₄×Q₈×C₄₁	1	2	yes	—
261	C₂³	C₂×M₁₆×C₄₁	1	4	yes	—
262	C₂³	#131×C₄₁	1	4	yes	—
263	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
264	C₂×C₄	—	2	4	no	—
265	C₂×C₄	—	2	4	no	—
266	C₂×C₄	—	2	4	no	—
267	C₂×C₄	—	2	4	no	—
268	C₂×C₄	—	2	8	no	—
269	C₂×C₄	—	2	8	no	—
270	C₂×C₄	—	2	16	no	—
271	C₂×C₄	—	2	4	no	—
272	C₂×C₄	—	2	4	no	—
273	C₂×C₄	—	2	4	no	—
274	C₂×C₄	—	4	8	no	—
275	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	4	yes	—
276	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	4	yes	—
277	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
278	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
279	C₂×C₄	C₄×Q₈×C₄₁	1	2	yes	—
280	C₂×C₄	#121×C₄₁	1	4	yes	—
281	C₂×C₄	C₂²⋊Q₈×C₄₁	1	4	yes	—
282	C₂×C₄	#125×C₄₁	1	4	yes	—
283	C₂×C₄	C₄⋊Q₈×C₄₁	1	4	yes	—
284	C₂×C₄	C₂×M₁₆×C₄₁	1	8	yes	—
285	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
286	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
287	C₂×C₄	C₂²×Q₈×C₄₁	1	1	yes	characteristic
288	C₂×C₄	C₂²×Q₈×C₄₁	1	1	yes	characteristic
289	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
290	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
291	C₈	—	2	4	no	—
292	C₈	—	2	4	no	—
293	C₈	—	4	4	no	—
294	C₂²	C₄₁×#389	1	4	yes	—
295	C₂²	C₄₁×#423	1	4	yes	—
296	C₂²	C₄₁×#424	1	4	yes	—
297	C₂²	C₄₁×#435	1	8	yes	—
298	C₂²	C₄₁×#446	1	8	yes	—
299	C₂²	C₂²×C₄⋊C₄×C₄₁	1	1	yes	characteristic
300	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
301	C₂²	C₂×C₄×Q₈×C₄₁	1	1	yes	characteristic
302	C₂²	C₂²×M₁₆×C₄₁	1	2	yes	—
303	C₂²	C₂×#131×C₄₁	1	2	yes	—
304	C₄	—	2	4	no	—
305	C₄	—	2	4	no	—
306	C₄	—	2	8	no	—
307	C₄	—	4	4	no	—
308	C₄	C₄₁×#389	1	4	yes	—
309	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
310	C₄	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
311	C₄	C₂×#125×C₄₁	1	1	yes	characteristic
312	C₄	C₂×C₄⋊Q₈×C₄₁	1	1	yes	characteristic
313	C₂	C₄₁×#1940	1	8	yes	direct product factor
314	C₂	C₂×C₄₁×#389	1	1	yes	characteristic
315	C₂	C₂×C₄₁×#423	1	1	yes	characteristic
316	C₂	C₂×C₄₁×#424	1	1	yes	characteristic
317	C₂	C₂×C₄₁×#435	1	2	yes	—
318	C₂	C₂×C₄₁×#446	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄×C₄₁	C₂³
commutator	C₂³	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
socle, prime radical	C₂⁴×C₄₁	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₄₁×#1940	C₂	direct (N × H)
134. C₂×#1940	C₄₁	direct (N × H)
158. #1940	C₂×C₄₁	direct (N × H)
160. C₂×C₄₁	#1940	direct (N × H)
183. C₄₁	C₂×#1940	direct (N × H)
313. C₂	C₄₁×#1940	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊C₈×C₄₁	2
C₂²×#97×C₄₁	2
C₂×C₄×C₄⋊C₄×C₄₁	2
C₄₁×#1940	2
C₂×C₄₁×#336	2
C₂×#1940	41

Subgroups — C2×C41×#1940 #23797343

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#1940 #23797343