Subgroups — C₄₁×#23060 #23799261

Order 10496.

854 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#474	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2365	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#2354	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#1990	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1947	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1934	C₂	1	2	yes	maximal
7	C₄₁×#1925	C₂	1	2	yes	maximal
8	C₄₁×#1918	C₂	1	2	yes	maximal, complemented
9	C₄×#107×C₄₁	C₂	1	2	yes	maximal, complemented
10	C₈×C₄⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#102×C₄₁	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₄₁	—	2	1	no	—
14	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×#117×C₄₁	—	2	1	no	—
16	C₄₁×#474	C₄	1	8	yes	complemented
17	C₂×#107×C₄₁	C₂²	1	2	yes	—
18	C₂×#107×C₄₁	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×#102×C₄₁	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
25	C₄₁×#391	—	2	1	no	—
26	C₄₁×#390	C₂²	1	2	yes	—
27	C₄₁×#389	C₂²	1	2	yes	—
28	C₄₁×#388	—	2	2	no	—
29	C₄₁×#387	—	2	2	no	—
30	C₄₁×#384	C₂²	1	1	yes	characteristic
31	C₄₁×#380	—	2	1	no	—
32	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
34	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
35	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
36	C₄₁×#340	C₂²	1	1	yes	characteristic
37	C₄₁×#340	C₂²	1	1	yes	characteristic
38	C₄₁×#340	C₂²	1	2	yes	—
39	C₄₁×#340	C₂²	1	2	yes	—
40	C₄₁×#340	C₂²	1	2	yes	—
41	C₄₁×#336	C₂²	1	2	yes	—
42	C₂²×Q₈×C₄₁	—	2	1	no	—
43	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₄₁	—	2	1	no	—
45	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
47	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
48	C₄⋊Q₈×C₄₁	—	2	2	no	—
49	C₄⋊Q₈×C₄₁	C₂×C₄	1	4	yes	—
50	C₄×Q₈×C₄₁	—	4	4	no	—
51	C₄×D₄×C₄₁	—	2	2	no	—
52	C₄×D₄×C₄₁	C₂×C₄	1	4	yes	—
53	#117×C₄₁	—	4	4	no	—
54	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
55	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
56	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
58	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
68	C₂×C₄²×C₄₁	—	2	2	no	—
69	C₂×C₄²×C₄₁	—	2	2	no	—
70	C₂×C₄²×C₄₁	—	2	1	no	—
71	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
72	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
73	#107×C₄₁	—	2	4	no	—
74	#107×C₄₁	C₂×C₄	1	8	yes	—
75	C₄⋊C₈×C₄₁	C₂×C₄	1	4	yes	—
76	#102×C₄₁	—	2	2	no	—
77	#102×C₄₁	—	2	2	no	—
78	#102×C₄₁	C₂×C₄	1	8	yes	—
79	C₄×C₈×C₄₁	—	2	4	no	—
80	C₄×C₈×C₄₁	—	2	2	no	—
81	#95×C₄₁	—	2	2	no	—
82	#95×C₄₁	—	2	1	no	—
83	#95×C₄₁	—	2	2	no	—
84	#95×C₄₁	—	2	2	no	—
85	#95×C₄₁	D₄	1	2	yes	—
86	C₂⁴×C₄₁	—	2	1	no	—
87	C₂×Q₈×C₄₁	—	2	4	no	—
88	C₂×Q₈×C₄₁	—	4	2	no	—
89	C₂×Q₈×C₄₁	—	4	2	no	—
90	C₂×D₄×C₄₁	—	2	1	no	—
91	C₂×D₄×C₄₁	—	2	1	no	—
92	C₂×D₄×C₄₁	—	2	1	no	—
93	C₂×D₄×C₄₁	—	2	1	no	—
94	C₂×D₄×C₄₁	—	2	1	no	—
95	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₄₁	—	2	1	no	—
97	C₂²×C₄×C₄₁	—	2	1	no	—
98	C₂²×C₄×C₄₁	—	2	2	no	—
99	C₂²×C₄×C₄₁	—	2	4	no	—
100	C₂²×C₄×C₄₁	—	2	1	no	—
101	C₂²×C₄×C₄₁	—	2	2	no	—
102	C₂²×C₄×C₄₁	—	4	2	no	—
103	C₂²×C₄×C₄₁	—	4	2	no	—
104	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
109	C₂×C₈×C₄₁	—	2	2	no	—
110	C₂×C₈×C₄₁	—	2	1	no	—
111	C₂×C₈×C₄₁	—	2	2	no	—
112	C₂×C₈×C₄₁	—	2	1	no	—
113	C₂×C₈×C₄₁	—	2	1	no	—
114	C₂×C₈×C₄₁	—	2	1	no	—
115	C₂×C₈×C₄₁	—	2	1	no	—
116	C₂×C₈×C₄₁	C₂²×C₄	1	4	yes	—
117	C₂×C₈×C₄₁	#41	1	2	yes	—
118	C₄⋊C₄×C₄₁	—	2	4	no	—
119	C₄⋊C₄×C₄₁	—	2	2	no	—
120	C₄⋊C₄×C₄₁	—	2	1	no	—
121	C₄⋊C₄×C₄₁	—	2	2	no	—
122	C₄⋊C₄×C₄₁	—	2	1	no	—
123	C₄⋊C₄×C₄₁	—	2	1	no	—
124	C₄⋊C₄×C₄₁	—	2	2	no	—
125	C₄⋊C₄×C₄₁	—	2	1	no	—
126	C₄⋊C₄×C₄₁	—	2	2	no	—
127	C₄⋊C₄×C₄₁	—	4	2	no	—
128	C₄⋊C₄×C₄₁	—	4	4	no	—
129	C₄⋊C₄×C₄₁	—	8	1	no	—
130	C₄⋊C₄×C₄₁	D₈	1	4	yes	—
131	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
132	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
133	C₄⋊C₄×C₄₁	#41	1	2	yes	—
134	C₂²⋊C₄×C₄₁	—	2	4	no	—
135	C₂²⋊C₄×C₄₁	—	4	4	no	—
136	C₂²⋊C₄×C₄₁	—	8	2	no	—
137	C₄²×C₄₁	—	2	2	no	—
138	C₄²×C₄₁	—	2	2	no	—
139	C₄²×C₄₁	—	4	4	no	—
140	C₄²×C₄₁	—	4	4	no	—
141	C₄²×C₄₁	—	4	2	no	—
142	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
143	C₄²×C₄₁	#41	1	2	yes	—
144	C₂³×C₄₁	—	2	2	no	—
145	C₂³×C₄₁	—	4	1	no	—
146	C₂³×C₄₁	—	4	1	no	—
147	C₂³×C₄₁	—	4	1	no	—
148	C₂³×C₄₁	—	4	1	no	—
149	C₂³×C₄₁	—	4	1	no	—
150	C₂³×C₄₁	—	4	1	no	—
151	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
152	Q₈×C₄₁	—	4	8	no	—
153	D₄×C₄₁	—	2	2	no	—
154	D₄×C₄₁	—	2	2	no	—
155	D₄×C₄₁	—	4	1	no	—
156	D₄×C₄₁	—	4	1	no	—
157	C₂×C₄×C₄₁	—	2	2	no	—
158	C₂×C₄×C₄₁	—	2	1	no	—
159	C₂×C₄×C₄₁	—	2	2	no	—
160	C₂×C₄×C₄₁	—	2	1	no	—
161	C₂×C₄×C₄₁	—	2	2	no	—
162	C₂×C₄×C₄₁	—	2	4	no	—
163	C₂×C₄×C₄₁	—	2	2	no	—
164	C₂×C₄×C₄₁	—	2	2	no	—
165	C₂×C₄×C₄₁	—	2	2	no	—
166	C₂×C₄×C₄₁	—	2	2	no	—
167	C₂×C₄×C₄₁	—	4	1	no	—
168	C₂×C₄×C₄₁	—	4	1	no	—
169	C₂×C₄×C₄₁	—	4	2	no	—
170	C₂×C₄×C₄₁	—	4	1	no	—
171	C₂×C₄×C₄₁	—	4	2	no	—
172	C₂×C₄×C₄₁	—	4	1	no	—
173	C₂×C₄×C₄₁	—	4	8	no	—
174	C₂×C₄×C₄₁	—	4	1	no	—
175	C₂×C₄×C₄₁	—	4	2	no	—
176	C₂×C₄×C₄₁	—	4	2	no	—
177	C₂×C₄×C₄₁	—	4	1	no	—
178	C₂×C₄×C₄₁	—	4	2	no	—
179	C₂×C₄×C₄₁	—	4	1	no	—
180	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
181	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
182	C₂×C₄×C₄₁	C₂×D₈	1	4	yes	—
183	C₂×C₄×C₄₁	C₂×D₈	1	2	yes	—
184	C₂×C₄×C₄₁	#135	1	2	yes	—
185	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
190	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
191	C₈×C₄₁	—	2	4	no	—
192	C₈×C₄₁	—	2	2	no	—
193	C₈×C₄₁	—	4	1	no	—
194	#23060	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂²×C₄₁	—	4	2	no	—
196	C₂²×C₄₁	—	4	2	no	—
197	C₂²×C₄₁	—	4	2	no	—
198	C₂²×C₄₁	—	8	1	no	—
199	C₂²×C₄₁	—	8	1	no	—
200	C₂²×C₄₁	—	8	1	no	—
201	C₂²×C₄₁	—	8	1	no	—
202	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
203	C₂²×C₄₁	#547	1	1	yes	characteristic
204	C₂²×C₄₁	#548	1	1	yes	characteristic
205	C₂²×C₄₁	C₂²×D₈	1	1	yes	characteristic
206	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
207	C₂²×C₄₁	#577	1	1	yes	characteristic
208	C₂²×C₄₁	#578	1	1	yes	characteristic
209	C₄×C₄₁	—	2	4	no	—
210	C₄×C₄₁	—	2	2	no	—
211	C₄×C₄₁	—	4	2	no	—
212	C₄×C₄₁	—	4	2	no	—
213	C₄×C₄₁	—	4	2	no	—
214	C₄×C₄₁	—	4	4	no	—
215	C₄×C₄₁	—	8	1	no	—
216	C₄×C₄₁	—	8	2	no	—
217	C₄×C₄₁	C₄×D₈	1	4	yes	—
218	C₄×C₄₁	C₄×#41	1	1	yes	characteristic
219	C₄×C₄₁	#519	1	1	yes	characteristic
220	C₄×C₄₁	#552	1	1	yes	characteristic
221	C₄×C₄₁	#556	1	1	yes	characteristic
222	C₂×#474	C₂×C₄₁	1	1	yes	characteristic
223	#2365	C₂×C₄₁	1	1	yes	characteristic, complemented
224	#2354	C₂×C₄₁	1	1	yes	characteristic
225	#1990	C₂×C₄₁	1	1	yes	characteristic, complemented
226	#1947	C₂×C₄₁	1	1	yes	characteristic, complemented
227	#1934	C₂×C₄₁	1	2	yes	—
228	#1925	C₂×C₄₁	1	2	yes	—
229	#1918	C₂×C₄₁	1	2	yes	complemented
230	C₄×#107	C₂×C₄₁	1	2	yes	complemented
231	C₈×C₄⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
232	C₄×#102	C₂×C₄₁	1	1	yes	characteristic
233	C₂×C₄₁	—	8	2	no	—
234	C₂×C₄₁	#2362	1	1	yes	characteristic
235	C₂×C₄₁	C₂×C₄×D₈	1	1	yes	characteristic
236	C₂×C₄₁	#2947	1	1	yes	characteristic
237	C₂×C₄₁	#3334	1	1	yes	characteristic
238	C₂×C₄₁	#3340	1	1	yes	characteristic
239	C₂×C₄₁	#3358	1	1	yes	characteristic
240	C₂×C₄₁	#3364	1	1	yes	characteristic
241	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
242	C₂×C₄×Q₈	—	2	1	no	—
243	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
244	C₂×#117	—	2	1	no	—
245	#474	C₄×C₄₁	1	8	yes	complemented
246	C₂×#107	C₂²×C₄₁	1	2	yes	—
247	C₂×#107	C₂²×C₄₁	1	2	yes	—
248	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
249	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
250	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
251	C₂×#102	C₂²×C₄₁	1	2	yes	—
252	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
253	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
254	#391	—	2	1	no	—
255	#390	C₂²×C₄₁	1	2	yes	—
256	#389	C₂²×C₄₁	1	2	yes	—
257	#388	—	2	2	no	—
258	#387	—	2	2	no	—
259	#384	C₂²×C₄₁	1	1	yes	characteristic
260	#380	—	2	1	no	—
261	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
262	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
263	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
264	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
265	#340	C₂²×C₄₁	1	1	yes	characteristic
266	#340	C₂²×C₄₁	1	2	yes	—
267	#340	C₂²×C₄₁	1	2	yes	—
268	#340	C₂²×C₄₁	1	2	yes	—
269	#340	C₂²×C₄₁	1	1	yes	characteristic
270	#336	C₂²×C₄₁	1	2	yes	—
271	C₄₁	#23060	1	1	yes	characteristic, direct product factor, Sylow
272	C₂²×Q₈	—	2	1	no	—
273	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
274	C₂³×C₄	—	2	1	no	—
275	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
276	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
277	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
278	C₄⋊Q₈	—	2	2	no	—
279	C₄⋊Q₈	C₂×C₄×C₄₁	1	4	yes	—
280	C₄×Q₈	—	4	4	no	—
281	C₄×D₄	—	2	2	no	—
282	C₄×D₄	C₂×C₄×C₄₁	1	4	yes	—
283	#117	—	4	4	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
289	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
294	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₄²	—	2	2	no	—
299	C₂×C₄²	—	2	2	no	—
300	C₂×C₄²	—	2	1	no	—
301	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
302	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
303	#107	—	2	4	no	—
304	#107	C₂×C₄×C₄₁	1	8	yes	—
305	C₄⋊C₈	C₂×C₄×C₄₁	1	4	yes	—
306	#102	—	2	2	no	—
307	#102	—	2	2	no	—
308	#102	C₂×C₄×C₄₁	1	8	yes	—
309	C₄×C₈	—	2	4	no	—
310	C₄×C₈	—	2	2	no	—
311	#95	—	2	2	no	—
312	#95	—	2	1	no	—
313	#95	—	2	2	no	—
314	#95	—	2	2	no	—
315	#95	D₄×C₄₁	1	2	yes	—
316	C₂⁴	—	2	1	no	—
317	C₂×Q₈	—	2	4	no	—
318	C₂×Q₈	—	4	2	no	—
319	C₂×Q₈	—	4	2	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	4	2	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
337	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
338	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	C₂²×C₄×C₄₁	1	4	yes	—
347	C₂×C₈	#41×C₄₁	1	2	yes	—
348	C₄⋊C₄	—	2	4	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	4	2	no	—
358	C₄⋊C₄	—	4	4	no	—
359	C₄⋊C₄	—	8	1	no	—
360	C₄⋊C₄	D₈×C₄₁	1	4	yes	—
361	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
362	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
363	C₄⋊C₄	#41×C₄₁	1	2	yes	—
364	C₂²⋊C₄	—	2	4	no	—
365	C₂²⋊C₄	—	4	4	no	—
366	C₂²⋊C₄	—	8	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	4	4	no	—
370	C₄²	—	4	4	no	—
371	C₄²	—	4	2	no	—
372	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
373	C₄²	#41×C₄₁	1	2	yes	—
374	C₂³	—	2	2	no	—
375	C₂³	—	4	1	no	—
376	C₂³	—	4	1	no	—
377	C₂³	—	4	1	no	—
378	C₂³	—	4	1	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	4	1	no	—
381	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
382	Q₈	—	4	8	no	—
383	D₄	—	2	2	no	—
384	D₄	—	2	2	no	—
385	D₄	—	4	1	no	—
386	D₄	—	4	1	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	8	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
411	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
412	C₂×C₄	C₂×D₈×C₄₁	1	4	yes	—
413	C₂×C₄	C₂×D₈×C₄₁	1	2	yes	—
414	C₂×C₄	#135×C₄₁	1	2	yes	—
415	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
416	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
417	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
418	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
419	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
420	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
421	C₈	—	2	4	no	—
422	C₈	—	2	2	no	—
423	C₈	—	4	1	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	8	1	no	—
428	C₂²	—	8	1	no	—
429	C₂²	—	8	1	no	—
430	C₂²	—	8	1	no	—
431	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
432	C₂²	C₄₁×#547	1	1	yes	characteristic
433	C₂²	C₄₁×#548	1	1	yes	characteristic
434	C₂²	C₂²×D₈×C₄₁	1	1	yes	characteristic
435	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
436	C₂²	C₄₁×#577	1	1	yes	characteristic
437	C₂²	C₄₁×#578	1	1	yes	characteristic
438	C₄	—	2	4	no	—
439	C₄	—	2	2	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	2	no	—
442	C₄	—	4	2	no	—
443	C₄	—	4	4	no	—
444	C₄	—	8	1	no	—
445	C₄	—	8	2	no	—
446	C₄	C₄×D₈×C₄₁	1	4	yes	—
447	C₄	C₄×#41×C₄₁	1	1	yes	characteristic
448	C₄	C₄₁×#519	1	1	yes	characteristic
449	C₄	C₄₁×#552	1	1	yes	characteristic
450	C₄	C₄₁×#556	1	1	yes	characteristic
451	C₂	—	8	2	no	—
452	C₂	C₄₁×#2362	1	1	yes	characteristic
453	C₂	C₂×C₄×D₈×C₄₁	1	1	yes	characteristic
454	C₂	C₄₁×#2947	1	1	yes	characteristic
455	C₂	C₄₁×#3334	1	1	yes	characteristic
456	C₂	C₄₁×#3340	1	1	yes	characteristic
457	C₂	C₄₁×#3358	1	1	yes	characteristic
458	C₂	C₄₁×#3364	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂²×D₄×C₄₁	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₄×C₄⋊C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#2365	C₂	semidirect
4. C₄₁×#1990	C₂	semidirect
5. C₄₁×#1947	C₂	semidirect
8. C₄₁×#1918	C₂	semidirect
9. C₄×#107×C₄₁	C₂	semidirect
10. C₈×C₄⋊C₄×C₄₁	C₂	semidirect
16. C₄₁×#474	C₄	semidirect
194. #23060	C₄₁	direct (N × H)
223. #2365	C₂×C₄₁	semidirect
225. #1990	C₂×C₄₁	semidirect
226. #1947	C₂×C₄₁	semidirect
229. #1918	C₂×C₄₁	semidirect
230. C₄×#107	C₂×C₄₁	semidirect
231. C₈×C₄⋊C₄	C₂×C₄₁	semidirect
245. #474	C₄×C₄₁	semidirect
271. C₄₁	#23060	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×#474	2
C₄₁×#2365	2
C₄₁×#2354	2
C₄₁×#1990	2
C₄₁×#1947	2
C₄₁×#1934	2
C₄₁×#1925	2
C₄₁×#1918	2
C₄×#107×C₄₁	2
C₈×C₄⋊C₄×C₄₁	2
C₄×#102×C₄₁	2
#23060	41

Subgroups — C41×#23060 #23799261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#23060 #23799261