Subgroups — C₄₁×#36708 #23812909

Order 10496.

2326 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂²⋊Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2848	C₂	1	2	yes	maximal
4	C₄₁×#2690	C₂	1	8	yes	maximal, complemented
5	C₄₁×#2677	C₂	1	8	yes	maximal, complemented
6	C₄₁×#2627	C₂	1	2	yes	maximal, complemented
7	C₄₁×#2561	C₂	1	2	yes	maximal
8	C₄₁×#2484	C₂	1	2	yes	maximal, complemented
9	C₄₁×#2482	C₂	1	2	yes	maximal
10	C₄₁×#2434	C₂	1	2	yes	maximal, complemented
11	C₄₁×#2313	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
14	C₄₁×#544	—	2	8	no	—
15	C₂×C₄⋊Q₈×C₄₁	C₂²	1	4	yes	complemented
16	C₂×C₄⋊Q₈×C₄₁	C₂²	1	4	yes	complemented
17	C₂×#125×C₄₁	C₂²	1	4	yes	complemented
18	C₂×C₂²⋊Q₈×C₄₁	—	2	8	no	—
19	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
20	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
21	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	8	yes	—
22	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	4	yes	—
23	C₂×#117×C₄₁	C₂²	1	2	yes	—
24	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
27	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
29	C₄₁×#400	C₂²	1	4	yes	complemented
30	C₄₁×#400	C₂²	1	4	yes	complemented
31	C₄₁×#399	C₂²	1	4	yes	—
32	C₄₁×#398	C₂²	1	8	yes	complemented
33	C₄₁×#398	C₂²	1	4	yes	complemented
34	C₄₁×#397	C₂²	1	4	yes	—
35	C₄₁×#397	C₂²	1	4	yes	—
36	C₄₁×#395	C₂²	1	4	yes	complemented
37	C₄₁×#395	C₂²	1	8	yes	complemented
38	C₄₁×#393	C₂²	1	4	yes	—
39	C₄₁×#391	C₂²	1	4	yes	complemented
40	C₄₁×#388	C₂²	1	8	yes	—
41	C₄₁×#388	C₂²	1	8	yes	—
42	C₄₁×#387	C₂²	1	8	yes	complemented
43	C₄₁×#387	C₂²	1	8	yes	complemented
44	C₄₁×#385	C₂²	1	8	yes	—
45	C₄₁×#385	C₂²	1	4	yes	—
46	C₄₁×#385	C₂²	1	4	yes	—
47	C₄₁×#381	C₂²	1	4	yes	—
48	C₄₁×#381	C₂²	1	2	yes	—
49	C₄₁×#380	C₂²	1	2	yes	—
50	C₄₁×#380	C₂²	1	4	yes	—
51	C₄₁×#379	C₂²	1	4	yes	—
52	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
53	C₂⁵×C₄₁	C₂³	1	1	yes	characteristic
54	C₂²×Q₈×C₄₁	—	2	4	no	—
55	C₂²×Q₈×C₄₁	—	4	4	no	—
56	C₂²×Q₈×C₄₁	C₂³	1	4	yes	—
57	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
58	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
59	C₂³×C₄×C₄₁	—	2	4	no	—
60	C₂³×C₄×C₄₁	—	4	4	no	—
61	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₄₁	C₂³	1	4	yes	—
64	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
68	C₄⋊Q₈×C₄₁	—	2	16	no	—
69	C₄⋊Q₈×C₄₁	—	4	8	no	—
70	#125×C₄₁	—	2	16	no	—
71	C₂²⋊Q₈×C₄₁	—	2	8	no	—
72	C₂²⋊Q₈×C₄₁	—	2	8	no	—
73	C₂²⋊Q₈×C₄₁	—	2	32	no	—
74	C₂²⋊Q₈×C₄₁	—	4	8	no	—
75	#117×C₄₁	—	2	8	no	—
76	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
77	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
78	C₂×C₄⋊C₄×C₄₁	D₄	1	8	yes	—
79	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
80	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
81	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
86	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
87	C₂×C₄⋊C₄×C₄₁	C₂³	1	8	yes	—
88	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
89	C₂×C₄⋊C₄×C₄₁	C₂³	1	8	yes	—
90	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
91	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
92	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
93	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
94	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
95	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
96	C₂×C₂²⋊C₄×C₄₁	C₂³	1	4	yes	—
97	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
98	C₂×C₂²⋊C₄×C₄₁	C₂³	1	8	yes	—
99	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
100	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
101	#95×C₄₁	C₂³	1	4	yes	—
102	#95×C₄₁	C₂³	1	4	yes	—
103	#95×C₄₁	C₂³	1	8	yes	—
104	#95×C₄₁	C₂³	1	4	yes	—
105	#95×C₄₁	C₂³	1	4	yes	—
106	#95×C₄₁	C₂³	1	8	yes	—
107	#95×C₄₁	C₂³	1	8	yes	—
108	#95×C₄₁	C₂³	1	8	yes	—
109	C₂⁴×C₄₁	—	2	2	no	—
110	C₂⁴×C₄₁	—	2	4	no	—
111	C₂⁴×C₄₁	—	2	4	no	—
112	C₂⁴×C₄₁	—	4	2	no	—
113	C₂⁴×C₄₁	C₂⁴	1	2	yes	—
114	C₂⁴×C₄₁	C₂⁴	1	1	yes	characteristic
115	C₂×Q₈×C₄₁	—	2	8	no	—
116	C₂×Q₈×C₄₁	—	2	4	no	—
117	C₂×Q₈×C₄₁	—	2	4	no	—
118	C₂×Q₈×C₄₁	—	2	8	no	—
119	C₂×Q₈×C₄₁	—	4	4	no	—
120	C₂×Q₈×C₄₁	—	4	4	no	—
121	C₂×Q₈×C₄₁	—	4	4	no	—
122	C₂×Q₈×C₄₁	—	4	16	no	—
123	C₂²×C₄×C₄₁	—	2	2	no	—
124	C₂²×C₄×C₄₁	—	2	4	no	—
125	C₂²×C₄×C₄₁	—	2	4	no	—
126	C₂²×C₄×C₄₁	—	2	2	no	—
127	C₂²×C₄×C₄₁	—	2	2	no	—
128	C₂²×C₄×C₄₁	—	2	4	no	—
129	C₂²×C₄×C₄₁	—	2	8	no	—
130	C₂²×C₄×C₄₁	—	2	8	no	—
131	C₂²×C₄×C₄₁	—	4	2	no	—
132	C₂²×C₄×C₄₁	—	4	4	no	—
133	C₂²×C₄×C₄₁	—	4	2	no	—
134	C₂²×C₄×C₄₁	—	4	2	no	—
135	C₂²×C₄×C₄₁	—	4	16	no	—
136	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
137	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
138	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
139	C₂²×C₄×C₄₁	C₂⁴	1	8	yes	—
140	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
141	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
142	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
143	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
144	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
145	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
146	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
147	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
148	C₄⋊C₄×C₄₁	—	2	8	no	—
149	C₄⋊C₄×C₄₁	—	2	8	no	—
150	C₄⋊C₄×C₄₁	—	2	4	no	—
151	C₄⋊C₄×C₄₁	—	2	4	no	—
152	C₄⋊C₄×C₄₁	—	2	4	no	—
153	C₄⋊C₄×C₄₁	—	2	4	no	—
154	C₄⋊C₄×C₄₁	—	2	8	no	—
155	C₄⋊C₄×C₄₁	—	2	8	no	—
156	C₄⋊C₄×C₄₁	—	2	16	no	—
157	C₄⋊C₄×C₄₁	—	4	4	no	—
158	C₄⋊C₄×C₄₁	—	4	8	no	—
159	C₄⋊C₄×C₄₁	C₂×D₄	1	16	yes	—
160	C₂²⋊C₄×C₄₁	—	2	8	no	—
161	C₂²⋊C₄×C₄₁	—	2	16	no	—
162	C₂²⋊C₄×C₄₁	—	2	8	no	—
163	C₂²⋊C₄×C₄₁	—	2	8	no	—
164	C₂²⋊C₄×C₄₁	—	2	8	no	—
165	C₂²⋊C₄×C₄₁	—	4	8	no	—
166	C₄²×C₄₁	—	2	8	no	—
167	C₄²×C₄₁	—	4	4	no	—
168	C₂³×C₄₁	—	2	2	no	—
169	C₂³×C₄₁	—	2	2	no	—
170	C₂³×C₄₁	—	2	8	no	—
171	C₂³×C₄₁	—	2	2	no	—
172	C₂³×C₄₁	—	2	4	no	—
173	C₂³×C₄₁	—	2	2	no	—
174	C₂³×C₄₁	—	2	4	no	—
175	C₂³×C₄₁	—	4	16	no	—
176	C₂³×C₄₁	—	4	4	no	—
177	C₂³×C₄₁	—	4	4	no	—
178	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
179	C₂³×C₄₁	2₋¹⁺⁴	1	4	yes	—
180	C₂³×C₄₁	2₋¹⁺⁴	1	4	yes	—
181	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
182	Q₈×C₄₁	—	4	16	no	—
183	Q₈×C₄₁	—	8	4	no	—
184	Q₈×C₄₁	—	8	4	no	—
185	C₂×C₄×C₄₁	—	2	8	no	—
186	C₂×C₄×C₄₁	—	2	8	no	—
187	C₂×C₄×C₄₁	—	2	2	no	—
188	C₂×C₄×C₄₁	—	2	4	no	—
189	C₂×C₄×C₄₁	—	2	4	no	—
190	C₂×C₄×C₄₁	—	2	2	no	—
191	C₂×C₄×C₄₁	—	2	4	no	—
192	C₂×C₄×C₄₁	—	2	4	no	—
193	C₂×C₄×C₄₁	—	2	4	no	—
194	C₂×C₄×C₄₁	—	2	2	no	—
195	C₂×C₄×C₄₁	—	2	2	no	—
196	C₂×C₄×C₄₁	—	2	8	no	—
197	C₂×C₄×C₄₁	—	2	8	no	—
198	C₂×C₄×C₄₁	—	2	4	no	—
199	C₂×C₄×C₄₁	—	2	8	no	—
200	C₂×C₄×C₄₁	—	2	8	no	—
201	C₂×C₄×C₄₁	—	2	8	no	—
202	C₂×C₄×C₄₁	—	2	4	no	—
203	C₂×C₄×C₄₁	—	4	4	no	—
204	C₂×C₄×C₄₁	—	4	4	no	—
205	C₂×C₄×C₄₁	—	4	16	no	—
206	C₂×C₄×C₄₁	—	4	4	no	—
207	C₂×C₄×C₄₁	—	4	4	no	—
208	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
209	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
210	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
211	C₂×C₄×C₄₁	H(5,𝔽₂)	1	4	yes	—
212	#36708	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₂²×C₄₁	—	2	2	no	—
214	C₂²×C₄₁	—	2	2	no	—
215	C₂²×C₄₁	—	2	8	no	—
216	C₂²×C₄₁	—	2	4	no	—
217	C₂²×C₄₁	—	2	8	no	—
218	C₂²×C₄₁	—	4	16	no	—
219	C₂²×C₄₁	—	4	2	no	—
220	C₂²×C₄₁	—	4	2	no	—
221	C₂²×C₄₁	—	4	4	no	—
222	C₂²×C₄₁	#536	1	4	yes	—
223	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
224	C₂²×C₄₁	C₂×H(5,𝔽₂)	1	2	yes	—
225	C₂²×C₄₁	C₂×2₋¹⁺⁴	1	2	yes	—
226	C₂²×C₄₁	C₂×2₋¹⁺⁴	1	2	yes	—
227	C₄×C₄₁	—	2	4	no	—
228	C₄×C₄₁	—	2	4	no	—
229	C₄×C₄₁	—	2	4	no	—
230	C₄×C₄₁	—	2	4	no	—
231	C₄×C₄₁	—	4	2	no	—
232	C₄×C₄₁	—	4	2	no	—
233	C₄×C₄₁	—	4	4	no	—
234	C₄×C₄₁	—	4	4	no	—
235	C₄×C₄₁	—	4	8	no	—
236	C₂×#544	C₂×C₄₁	1	1	yes	characteristic, complemented
237	C₂²×C₂²⋊Q₈	C₂×C₄₁	1	1	yes	characteristic
238	#2848	C₂×C₄₁	1	2	yes	—
239	#2690	C₂×C₄₁	1	8	yes	complemented
240	#2677	C₂×C₄₁	1	8	yes	complemented
241	#2627	C₂×C₄₁	1	2	yes	complemented
242	#2561	C₂×C₄₁	1	2	yes	—
243	#2484	C₂×C₄₁	1	2	yes	complemented
244	#2482	C₂×C₄₁	1	2	yes	—
245	#2434	C₂×C₄₁	1	2	yes	complemented
246	#2313	C₂×C₄₁	1	1	yes	characteristic, complemented
247	C₂×C₄₁	—	2	4	no	—
248	C₂×C₄₁	—	4	4	no	—
249	C₂×C₄₁	C₂×#536	1	1	yes	characteristic
250	C₂×C₄₁	#3484	1	1	yes	characteristic
251	C₂×C₄₁	#3486	1	1	yes	characteristic
252	C₂×C₄₁	#3538	1	4	yes	—
253	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
254	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
255	#544	—	2	8	no	—
256	C₂×C₄⋊Q₈	C₂²×C₄₁	1	4	yes	complemented
257	C₂×C₄⋊Q₈	C₂²×C₄₁	1	4	yes	complemented
258	C₂×#125	C₂²×C₄₁	1	4	yes	complemented
259	C₂×C₂²⋊Q₈	—	2	8	no	—
260	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
261	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
262	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	8	yes	—
263	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	4	yes	—
264	C₂×#117	C₂²×C₄₁	1	2	yes	—
265	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
266	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
267	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
268	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
269	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
270	#400	C₂²×C₄₁	1	4	yes	complemented
271	#400	C₂²×C₄₁	1	4	yes	complemented
272	#399	C₂²×C₄₁	1	4	yes	—
273	#398	C₂²×C₄₁	1	8	yes	complemented
274	#398	C₂²×C₄₁	1	4	yes	complemented
275	#397	C₂²×C₄₁	1	4	yes	—
276	#397	C₂²×C₄₁	1	4	yes	—
277	#395	C₂²×C₄₁	1	4	yes	complemented
278	#395	C₂²×C₄₁	1	8	yes	complemented
279	#393	C₂²×C₄₁	1	4	yes	—
280	#391	C₂²×C₄₁	1	4	yes	complemented
281	#388	C₂²×C₄₁	1	8	yes	—
282	#388	C₂²×C₄₁	1	8	yes	—
283	#387	C₂²×C₄₁	1	8	yes	complemented
284	#387	C₂²×C₄₁	1	8	yes	complemented
285	#385	C₂²×C₄₁	1	8	yes	—
286	#385	C₂²×C₄₁	1	4	yes	—
287	#385	C₂²×C₄₁	1	4	yes	—
288	#381	C₂²×C₄₁	1	4	yes	—
289	#381	C₂²×C₄₁	1	2	yes	—
290	#380	C₂²×C₄₁	1	2	yes	—
291	#380	C₂²×C₄₁	1	4	yes	—
292	#379	C₂²×C₄₁	1	4	yes	—
293	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
294	C₄₁	#36708	1	1	yes	characteristic, direct product factor, Sylow
295	C₂⁵	C₂³×C₄₁	1	1	yes	characteristic
296	C₂²×Q₈	—	2	4	no	—
297	C₂²×Q₈	—	4	4	no	—
298	C₂²×Q₈	C₂³×C₄₁	1	4	yes	—
299	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
300	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
301	C₂³×C₄	—	2	4	no	—
302	C₂³×C₄	—	4	4	no	—
303	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
304	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
305	C₂³×C₄	C₂³×C₄₁	1	4	yes	—
306	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
307	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
308	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
309	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
310	C₄⋊Q₈	—	2	16	no	—
311	C₄⋊Q₈	—	4	8	no	—
312	#125	—	2	16	no	—
313	C₂²⋊Q₈	—	2	8	no	—
314	C₂²⋊Q₈	—	2	8	no	—
315	C₂²⋊Q₈	—	2	32	no	—
316	C₂²⋊Q₈	—	4	8	no	—
317	#117	—	2	8	no	—
318	C₂×C₄⋊C₄	—	2	4	no	—
319	C₂×C₄⋊C₄	—	2	4	no	—
320	C₂×C₄⋊C₄	D₄×C₄₁	1	8	yes	—
321	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
322	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
323	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
324	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
325	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
326	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
327	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
328	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
329	C₂×C₄⋊C₄	C₂³×C₄₁	1	8	yes	—
330	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
331	C₂×C₄⋊C₄	C₂³×C₄₁	1	8	yes	—
332	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
333	C₂×C₂²⋊C₄	—	2	4	no	—
334	C₂×C₂²⋊C₄	—	2	4	no	—
335	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
336	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
337	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
338	C₂×C₂²⋊C₄	C₂³×C₄₁	1	4	yes	—
339	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
340	C₂×C₂²⋊C₄	C₂³×C₄₁	1	8	yes	—
341	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
342	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
343	#95	C₂³×C₄₁	1	4	yes	—
344	#95	C₂³×C₄₁	1	4	yes	—
345	#95	C₂³×C₄₁	1	8	yes	—
346	#95	C₂³×C₄₁	1	4	yes	—
347	#95	C₂³×C₄₁	1	4	yes	—
348	#95	C₂³×C₄₁	1	8	yes	—
349	#95	C₂³×C₄₁	1	8	yes	—
350	#95	C₂³×C₄₁	1	8	yes	—
351	C₂⁴	—	2	2	no	—
352	C₂⁴	—	2	4	no	—
353	C₂⁴	—	2	4	no	—
354	C₂⁴	—	4	2	no	—
355	C₂⁴	C₂⁴×C₄₁	1	2	yes	—
356	C₂⁴	C₂⁴×C₄₁	1	1	yes	characteristic
357	C₂×Q₈	—	2	8	no	—
358	C₂×Q₈	—	2	4	no	—
359	C₂×Q₈	—	2	4	no	—
360	C₂×Q₈	—	2	8	no	—
361	C₂×Q₈	—	4	4	no	—
362	C₂×Q₈	—	4	4	no	—
363	C₂×Q₈	—	4	4	no	—
364	C₂×Q₈	—	4	16	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	8	no	—
372	C₂²×C₄	—	2	8	no	—
373	C₂²×C₄	—	4	2	no	—
374	C₂²×C₄	—	4	4	no	—
375	C₂²×C₄	—	4	2	no	—
376	C₂²×C₄	—	4	2	no	—
377	C₂²×C₄	—	4	16	no	—
378	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
379	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
380	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
381	C₂²×C₄	C₂⁴×C₄₁	1	8	yes	—
382	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
383	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
384	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
385	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
386	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
387	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
388	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
389	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
390	C₄⋊C₄	—	2	8	no	—
391	C₄⋊C₄	—	2	8	no	—
392	C₄⋊C₄	—	2	4	no	—
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	—	2	4	no	—
396	C₄⋊C₄	—	2	8	no	—
397	C₄⋊C₄	—	2	8	no	—
398	C₄⋊C₄	—	2	16	no	—
399	C₄⋊C₄	—	4	4	no	—
400	C₄⋊C₄	—	4	8	no	—
401	C₄⋊C₄	C₂×D₄×C₄₁	1	16	yes	—
402	C₂²⋊C₄	—	2	8	no	—
403	C₂²⋊C₄	—	2	16	no	—
404	C₂²⋊C₄	—	2	8	no	—
405	C₂²⋊C₄	—	2	8	no	—
406	C₂²⋊C₄	—	2	8	no	—
407	C₂²⋊C₄	—	4	8	no	—
408	C₄²	—	2	8	no	—
409	C₄²	—	4	4	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	2	no	—
412	C₂³	—	2	8	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	2	4	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	2	4	no	—
417	C₂³	—	4	16	no	—
418	C₂³	—	4	4	no	—
419	C₂³	—	4	4	no	—
420	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
421	C₂³	2₋¹⁺⁴×C₄₁	1	4	yes	—
422	C₂³	2₋¹⁺⁴×C₄₁	1	4	yes	—
423	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
424	Q₈	—	4	16	no	—
425	Q₈	—	8	4	no	—
426	Q₈	—	8	4	no	—
427	C₂×C₄	—	2	8	no	—
428	C₂×C₄	—	2	8	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	8	no	—
439	C₂×C₄	—	2	8	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	8	no	—
442	C₂×C₄	—	2	8	no	—
443	C₂×C₄	—	2	8	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	4	4	no	—
446	C₂×C₄	—	4	4	no	—
447	C₂×C₄	—	4	16	no	—
448	C₂×C₄	—	4	4	no	—
449	C₂×C₄	—	4	4	no	—
450	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
451	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
452	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
453	C₂×C₄	H(5,𝔽₂)×C₄₁	1	4	yes	—
454	C₂²	—	2	2	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	8	no	—
457	C₂²	—	2	4	no	—
458	C₂²	—	2	8	no	—
459	C₂²	—	4	16	no	—
460	C₂²	—	4	2	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	4	no	—
463	C₂²	C₄₁×#536	1	4	yes	—
464	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
465	C₂²	C₂×H(5,𝔽₂)×C₄₁	1	2	yes	—
466	C₂²	C₂×2₋¹⁺⁴×C₄₁	1	2	yes	—
467	C₂²	C₂×2₋¹⁺⁴×C₄₁	1	2	yes	—
468	C₄	—	2	4	no	—
469	C₄	—	2	4	no	—
470	C₄	—	2	4	no	—
471	C₄	—	2	4	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	4	no	—
475	C₄	—	4	4	no	—
476	C₄	—	4	8	no	—
477	C₂	—	2	4	no	—
478	C₂	—	4	4	no	—
479	C₂	C₂×C₄₁×#536	1	1	yes	characteristic
480	C₂	C₄₁×#3484	1	1	yes	characteristic
481	C₂	C₄₁×#3486	1	1	yes	characteristic
482	C₂	C₄₁×#3538	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₁
prime radical	C₂⁵×C₄₁	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#544	C₂	semidirect
4. C₄₁×#2690	C₂	semidirect
5. C₄₁×#2677	C₂	semidirect
6. C₄₁×#2627	C₂	semidirect
8. C₄₁×#2484	C₂	semidirect
10. C₄₁×#2434	C₂	semidirect
11. C₄₁×#2313	C₂	semidirect
15. C₂×C₄⋊Q₈×C₄₁	C₂²	semidirect
16. C₂×C₄⋊Q₈×C₄₁	C₂²	semidirect
17. C₂×#125×C₄₁	C₂²	semidirect
29. C₄₁×#400	C₂²	semidirect
30. C₄₁×#400	C₂²	semidirect
32. C₄₁×#398	C₂²	semidirect
33. C₄₁×#398	C₂²	semidirect
36. C₄₁×#395	C₂²	semidirect
37. C₄₁×#395	C₂²	semidirect
39. C₄₁×#391	C₂²	semidirect
42. C₄₁×#387	C₂²	semidirect
43. C₄₁×#387	C₂²	semidirect
212. #36708	C₄₁	direct (N × H)
236. C₂×#544	C₂×C₄₁	semidirect
239. #2690	C₂×C₄₁	semidirect
240. #2677	C₂×C₄₁	semidirect
241. #2627	C₂×C₄₁	semidirect
243. #2484	C₂×C₄₁	semidirect
245. #2434	C₂×C₄₁	semidirect
246. #2313	C₂×C₄₁	semidirect
256. C₂×C₄⋊Q₈	C₂²×C₄₁	semidirect
257. C₂×C₄⋊Q₈	C₂²×C₄₁	semidirect
258. C₂×#125	C₂²×C₄₁	semidirect
270. #400	C₂²×C₄₁	semidirect
271. #400	C₂²×C₄₁	semidirect
273. #398	C₂²×C₄₁	semidirect
274. #398	C₂²×C₄₁	semidirect
277. #395	C₂²×C₄₁	semidirect
278. #395	C₂²×C₄₁	semidirect
280. #391	C₂²×C₄₁	semidirect
283. #387	C₂²×C₄₁	semidirect
284. #387	C₂²×C₄₁	semidirect
294. C₄₁	#36708	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#544	2
C₂²×C₂²⋊Q₈×C₄₁	2
C₄₁×#2848	2
C₄₁×#2690	2
C₄₁×#2677	2
C₄₁×#2627	2
C₄₁×#2561	2
C₄₁×#2484	2
C₄₁×#2482	2
C₄₁×#2434	2
C₄₁×#2313	2
#36708	41

Subgroups — C41×#36708 #23812909

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#36708 #23812909