Subgroups — C₄₁×#23186 #23799387

Order 10496.

1038 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#495	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×D₈×C₄₁	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2367	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1983	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1970	C₂	1	1	yes	maximal, characteristic
7	C₄₁×#1969	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1880	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1877	C₂	1	2	yes	maximal, complemented
10	C₄×#107×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₄⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₄₁	C₂²	1	2	yes	—
14	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×#124×C₄₁	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
18	C₄₁×#495	C₄	1	8	yes	complemented
19	C₄×Q₁₆×C₄₁	—	2	4	no	—
20	C₄×D₈×C₄₁	—	2	4	no	—
21	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×#103×C₄₁	C₂²	1	2	yes	—
25	C₂×#103×C₄₁	C₂²	1	2	yes	—
26	C₂×#102×C₄₁	C₂²	1	2	yes	—
27	C₂×#102×C₄₁	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
31	C₄₁×#391	C₂²	1	2	yes	—
32	C₄₁×#390	C₂²	1	2	yes	—
33	C₄₁×#388	—	2	2	no	—
34	C₄₁×#388	—	2	2	no	—
35	C₄₁×#385	—	2	2	no	—
36	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
37	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊C₄×C₄₁	—	2	2	no	—
39	C₄₁×#340	C₂²	1	2	yes	—
40	C₄₁×#336	C₂²	1	1	yes	characteristic
41	C₄₁×#336	C₂²	1	1	yes	characteristic
42	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
43	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
44	C₂³×C₄×C₄₁	—	2	2	no	—
45	C₂×Q₁₆×C₄₁	—	2	2	no	—
46	C₂×Q₁₆×C₄₁	—	2	2	no	—
47	C₂×Q₁₆×C₄₁	C₂×C₄	1	4	yes	complemented
48	C₂×SD₁₆×C₄₁	—	4	2	no	—
49	C₂×SD₁₆×C₄₁	—	4	2	no	—
50	C₂×SD₁₆×C₄₁	C₂×C₄	1	8	yes	complemented
51	C₂×D₈×C₄₁	—	2	2	no	—
52	C₂×D₈×C₄₁	—	2	2	no	—
53	C₂×D₈×C₄₁	C₂×C₄	1	4	yes	—
54	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
58	#124×C₄₁	—	2	4	no	—
59	#124×C₄₁	C₂×C₄	1	8	yes	complemented
60	C₄×Q₈×C₄₁	—	2	4	no	—
61	C₄×Q₈×C₄₁	—	4	2	no	—
62	C₄×D₄×C₄₁	—	2	4	no	—
63	C₄×D₄×C₄₁	—	4	2	no	—
64	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
69	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
74	C₂×C₄²×C₄₁	—	2	2	no	—
75	C₂×C₄²×C₄₁	—	2	2	no	—
76	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
79	#107×C₄₁	—	2	2	no	—
80	#107×C₄₁	D₄	1	4	yes	—
81	C₄⋊C₈×C₄₁	—	2	2	no	—
82	#103×C₄₁	—	2	4	no	—
83	#103×C₄₁	—	4	2	no	—
84	#102×C₄₁	—	2	4	no	—
85	#102×C₄₁	—	4	2	no	—
86	C₄×C₈×C₄₁	—	2	2	no	—
87	C₄×C₈×C₄₁	—	2	2	no	—
88	C₄×C₈×C₄₁	C₂×C₄	1	4	yes	complemented
89	#95×C₄₁	—	2	2	no	—
90	#95×C₄₁	—	2	2	no	—
91	#95×C₄₁	—	2	2	no	—
92	#95×C₄₁	D₄	1	1	yes	characteristic
93	#95×C₄₁	D₄	1	1	yes	characteristic
94	C₂⁴×C₄₁	—	2	2	no	—
95	C₂×Q₈×C₄₁	—	2	2	no	—
96	C₂×Q₈×C₄₁	—	2	2	no	—
97	C₂×Q₈×C₄₁	—	2	2	no	—
98	C₂×Q₈×C₄₁	—	2	2	no	—
99	C₂×Q₈×C₄₁	—	2	2	no	—
100	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	—
101	C₂×D₄×C₄₁	—	2	2	no	—
102	C₂×D₄×C₄₁	—	2	2	no	—
103	C₂×D₄×C₄₁	—	2	2	no	—
104	C₂×D₄×C₄₁	—	2	2	no	—
105	C₂×D₄×C₄₁	—	2	2	no	—
106	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
107	C₂²×C₄×C₄₁	—	2	2	no	—
108	C₂²×C₄×C₄₁	—	2	2	no	—
109	C₂²×C₄×C₄₁	—	2	2	no	—
110	C₂²×C₄×C₄₁	—	4	4	no	—
111	C₂²×C₄×C₄₁	—	4	4	no	—
112	C₂²×C₄×C₄₁	—	8	2	no	—
113	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
120	Q₁₆×C₄₁	—	2	8	no	—
121	SD₁₆×C₄₁	—	4	8	no	—
122	D₈×C₄₁	—	2	8	no	—
123	C₂×C₈×C₄₁	—	2	1	no	—
124	C₂×C₈×C₄₁	—	2	1	no	—
125	C₂×C₈×C₄₁	—	2	1	no	—
126	C₂×C₈×C₄₁	—	2	1	no	—
127	C₂×C₈×C₄₁	—	2	1	no	—
128	C₂×C₈×C₄₁	—	2	1	no	—
129	C₂×C₈×C₄₁	—	2	1	no	—
130	C₂×C₈×C₄₁	—	2	1	no	—
131	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
132	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₄₁	#41	1	2	yes	—
135	C₄⋊C₄×C₄₁	—	2	2	no	—
136	C₄⋊C₄×C₄₁	—	2	2	no	—
137	C₄⋊C₄×C₄₁	—	2	2	no	—
138	C₄⋊C₄×C₄₁	—	2	2	no	—
139	C₄⋊C₄×C₄₁	—	2	2	no	—
140	C₄⋊C₄×C₄₁	—	4	4	no	—
141	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
142	C₂²⋊C₄×C₄₁	—	2	8	no	—
143	C₂²⋊C₄×C₄₁	—	2	8	no	—
144	C₂²⋊C₄×C₄₁	—	4	4	no	—
145	C₂²⋊C₄×C₄₁	—	4	4	no	—
146	C₂²⋊C₄×C₄₁	—	8	2	no	—
147	C₄²×C₄₁	—	2	1	no	—
148	C₄²×C₄₁	—	2	1	no	—
149	C₄²×C₄₁	—	2	1	no	—
150	C₄²×C₄₁	—	2	1	no	—
151	C₄²×C₄₁	—	4	4	no	—
152	C₄²×C₄₁	—	8	2	no	—
153	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
154	C₄²×C₄₁	#41	1	2	yes	—
155	C₂³×C₄₁	—	2	4	no	—
156	C₂³×C₄₁	—	4	2	no	—
157	C₂³×C₄₁	—	4	2	no	—
158	C₂³×C₄₁	—	4	2	no	—
159	C₂³×C₄₁	—	4	2	no	—
160	C₂³×C₄₁	—	4	2	no	—
161	C₂³×C₄₁	—	4	2	no	—
162	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
163	Q₈×C₄₁	—	2	4	no	—
164	Q₈×C₄₁	—	2	4	no	—
165	Q₈×C₄₁	—	4	2	no	—
166	Q₈×C₄₁	—	4	2	no	—
167	D₄×C₄₁	—	2	4	no	—
168	D₄×C₄₁	—	2	4	no	—
169	D₄×C₄₁	—	4	2	no	—
170	D₄×C₄₁	—	4	2	no	—
171	C₂×C₄×C₄₁	—	2	1	no	—
172	C₂×C₄×C₄₁	—	2	1	no	—
173	C₂×C₄×C₄₁	—	2	1	no	—
174	C₂×C₄×C₄₁	—	2	1	no	—
175	C₂×C₄×C₄₁	—	2	1	no	—
176	C₂×C₄×C₄₁	—	2	1	no	—
177	C₂×C₄×C₄₁	—	2	1	no	—
178	C₂×C₄×C₄₁	—	2	1	no	—
179	C₂×C₄×C₄₁	—	2	4	no	—
180	C₂×C₄×C₄₁	—	2	1	no	—
181	C₂×C₄×C₄₁	—	2	1	no	—
182	C₂×C₄×C₄₁	—	2	4	no	—
183	C₂×C₄×C₄₁	—	2	1	no	—
184	C₂×C₄×C₄₁	—	2	1	no	—
185	C₂×C₄×C₄₁	—	2	1	no	—
186	C₂×C₄×C₄₁	—	2	1	no	—
187	C₂×C₄×C₄₁	—	4	2	no	—
188	C₂×C₄×C₄₁	—	4	2	no	—
189	C₂×C₄×C₄₁	—	4	2	no	—
190	C₂×C₄×C₄₁	—	4	2	no	—
191	C₂×C₄×C₄₁	—	4	2	no	—
192	C₂×C₄×C₄₁	—	4	2	no	—
193	C₂×C₄×C₄₁	—	4	2	no	—
194	C₂×C₄×C₄₁	—	8	8	no	—
195	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
196	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
197	C₂×C₄×C₄₁	#135	1	2	yes	—
198	C₂×C₄×C₄₁	#135	1	2	yes	—
199	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
200	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
204	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
205	C₈×C₄₁	—	2	2	no	—
206	C₈×C₄₁	—	4	1	no	—
207	C₈×C₄₁	—	4	1	no	—
208	C₈×C₄₁	C₄×D₄	1	4	yes	—
209	#23186	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂²×C₄₁	—	4	4	no	—
211	C₂²×C₄₁	—	4	4	no	—
212	C₂²×C₄₁	—	4	4	no	—
213	C₂²×C₄₁	—	8	2	no	—
214	C₂²×C₄₁	—	8	2	no	—
215	C₂²×C₄₁	—	8	2	no	—
216	C₂²×C₄₁	—	8	2	no	—
217	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
218	C₂²×C₄₁	D₄²	1	1	yes	characteristic
219	C₂²×C₄₁	#550	1	1	yes	characteristic
220	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
221	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
222	C₂²×C₄₁	#576	1	1	yes	characteristic
223	C₂²×C₄₁	#578	1	1	yes	characteristic
224	C₄×C₄₁	—	2	2	no	—
225	C₄×C₄₁	—	2	2	no	—
226	C₄×C₄₁	—	2	2	no	—
227	C₄×C₄₁	—	2	2	no	—
228	C₄×C₄₁	—	4	4	no	—
229	C₄×C₄₁	—	4	1	no	—
230	C₄×C₄₁	—	4	4	no	—
231	C₄×C₄₁	—	4	1	no	—
232	C₄×C₄₁	—	8	2	no	—
233	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
234	C₄×C₄₁	#518	1	1	yes	characteristic
235	C₄×C₄₁	#550	1	1	yes	characteristic
236	C₄×C₄₁	#559	1	1	yes	characteristic
237	C₂×#495	C₂×C₄₁	1	1	yes	characteristic
238	C₂×C₄×Q₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
239	C₂×C₄×D₈	C₂×C₄₁	1	1	yes	characteristic
240	#2367	C₂×C₄₁	1	2	yes	complemented
241	#1983	C₂×C₄₁	1	2	yes	complemented
242	#1970	C₂×C₄₁	1	1	yes	characteristic
243	#1969	C₂×C₄₁	1	1	yes	characteristic, complemented
244	#1880	C₂×C₄₁	1	2	yes	complemented
245	#1877	C₂×C₄₁	1	2	yes	complemented
246	C₄×#107	C₂×C₄₁	1	1	yes	characteristic, complemented
247	C₈×C₄⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
248	C₂×C₄₁	—	8	4	no	—
249	C₂×C₄₁	#2366	1	1	yes	characteristic
250	C₂×C₄₁	C₄×#135	1	1	yes	characteristic
251	C₂×C₄₁	#2951	1	1	yes	characteristic
252	C₂×C₄₁	#3280	1	1	yes	characteristic
253	C₂×C₄₁	#3285	1	1	yes	characteristic
254	C₂×C₄₁	#3393	1	1	yes	characteristic
255	C₂×C₄₁	#3396	1	1	yes	characteristic
256	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
257	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	—
258	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
259	C₂×#124	C₂²×C₄₁	1	2	yes	—
260	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
261	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
262	#495	C₄×C₄₁	1	8	yes	complemented
263	C₄×Q₁₆	—	2	4	no	—
264	C₄×D₈	—	2	4	no	—
265	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
266	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
267	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
268	C₂×#103	C₂²×C₄₁	1	2	yes	—
269	C₂×#103	C₂²×C₄₁	1	2	yes	—
270	C₂×#102	C₂²×C₄₁	1	2	yes	—
271	C₂×#102	C₂²×C₄₁	1	2	yes	—
272	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
273	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
274	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
275	#391	C₂²×C₄₁	1	2	yes	—
276	#390	C₂²×C₄₁	1	2	yes	—
277	#388	—	2	2	no	—
278	#388	—	2	2	no	—
279	#385	—	2	2	no	—
280	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
281	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
282	C₄×C₂²⋊C₄	—	2	2	no	—
283	#340	C₂²×C₄₁	1	2	yes	—
284	#336	C₂²×C₄₁	1	1	yes	characteristic
285	#336	C₂²×C₄₁	1	1	yes	characteristic
286	C₄₁	#23186	1	1	yes	characteristic, direct product factor, Sylow
287	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
288	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
289	C₂³×C₄	—	2	2	no	—
290	C₂×Q₁₆	—	2	2	no	—
291	C₂×Q₁₆	—	2	2	no	—
292	C₂×Q₁₆	C₂×C₄×C₄₁	1	4	yes	complemented
293	C₂×SD₁₆	—	4	2	no	—
294	C₂×SD₁₆	—	4	2	no	—
295	C₂×SD₁₆	C₂×C₄×C₄₁	1	8	yes	complemented
296	C₂×D₈	—	2	2	no	—
297	C₂×D₈	—	2	2	no	—
298	C₂×D₈	C₂×C₄×C₄₁	1	4	yes	—
299	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
300	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
301	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
302	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
303	#124	—	2	4	no	—
304	#124	C₂×C₄×C₄₁	1	8	yes	complemented
305	C₄×Q₈	—	2	4	no	—
306	C₄×Q₈	—	4	2	no	—
307	C₄×D₄	—	2	4	no	—
308	C₄×D₄	—	4	2	no	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
311	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
312	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
313	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₂²⋊C₄	—	2	2	no	—
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₄²	—	2	2	no	—
320	C₂×C₄²	—	2	2	no	—
321	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
322	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
323	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
324	#107	—	2	2	no	—
325	#107	D₄×C₄₁	1	4	yes	—
326	C₄⋊C₈	—	2	2	no	—
327	#103	—	2	4	no	—
328	#103	—	4	2	no	—
329	#102	—	2	4	no	—
330	#102	—	4	2	no	—
331	C₄×C₈	—	2	2	no	—
332	C₄×C₈	—	2	2	no	—
333	C₄×C₈	C₂×C₄×C₄₁	1	4	yes	complemented
334	#95	—	2	2	no	—
335	#95	—	2	2	no	—
336	#95	—	2	2	no	—
337	#95	D₄×C₄₁	1	1	yes	characteristic
338	#95	D₄×C₄₁	1	1	yes	characteristic
339	C₂⁴	—	2	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	4	4	no	—
356	C₂²×C₄	—	4	4	no	—
357	C₂²×C₄	—	8	2	no	—
358	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
364	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
365	Q₁₆	—	2	8	no	—
366	SD₁₆	—	4	8	no	—
367	D₈	—	2	8	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
377	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
378	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
379	C₂×C₈	#41×C₄₁	1	2	yes	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	4	4	no	—
386	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
387	C₂²⋊C₄	—	2	8	no	—
388	C₂²⋊C₄	—	2	8	no	—
389	C₂²⋊C₄	—	4	4	no	—
390	C₂²⋊C₄	—	4	4	no	—
391	C₂²⋊C₄	—	8	2	no	—
392	C₄²	—	2	1	no	—
393	C₄²	—	2	1	no	—
394	C₄²	—	2	1	no	—
395	C₄²	—	2	1	no	—
396	C₄²	—	4	4	no	—
397	C₄²	—	8	2	no	—
398	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
399	C₄²	#41×C₄₁	1	2	yes	—
400	C₂³	—	2	4	no	—
401	C₂³	—	4	2	no	—
402	C₂³	—	4	2	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
408	Q₈	—	2	4	no	—
409	Q₈	—	2	4	no	—
410	Q₈	—	4	2	no	—
411	Q₈	—	4	2	no	—
412	D₄	—	2	4	no	—
413	D₄	—	2	4	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	2	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	8	8	no	—
440	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
441	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
442	C₂×C₄	#135×C₄₁	1	2	yes	—
443	C₂×C₄	#135×C₄₁	1	2	yes	—
444	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
445	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
446	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
447	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
448	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
449	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
450	C₈	—	2	2	no	—
451	C₈	—	4	1	no	—
452	C₈	—	4	1	no	—
453	C₈	C₄×D₄×C₄₁	1	4	yes	—
454	C₂²	—	4	4	no	—
455	C₂²	—	4	4	no	—
456	C₂²	—	4	4	no	—
457	C₂²	—	8	2	no	—
458	C₂²	—	8	2	no	—
459	C₂²	—	8	2	no	—
460	C₂²	—	8	2	no	—
461	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
462	C₂²	D₄²×C₄₁	1	1	yes	characteristic
463	C₂²	C₄₁×#550	1	1	yes	characteristic
464	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
465	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
466	C₂²	C₄₁×#576	1	1	yes	characteristic
467	C₂²	C₄₁×#578	1	1	yes	characteristic
468	C₄	—	2	2	no	—
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	4	4	no	—
473	C₄	—	4	1	no	—
474	C₄	—	4	4	no	—
475	C₄	—	4	1	no	—
476	C₄	—	8	2	no	—
477	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
478	C₄	C₄₁×#518	1	1	yes	characteristic
479	C₄	C₄₁×#550	1	1	yes	characteristic
480	C₄	C₄₁×#559	1	1	yes	characteristic
481	C₂	—	8	4	no	—
482	C₂	C₄₁×#2366	1	1	yes	characteristic
483	C₂	C₄×#135×C₄₁	1	1	yes	characteristic
484	C₂	C₄₁×#2951	1	1	yes	characteristic
485	C₂	C₄₁×#3280	1	1	yes	characteristic
486	C₂	C₄₁×#3285	1	1	yes	characteristic
487	C₂	C₄₁×#3393	1	1	yes	characteristic
488	C₂	C₄₁×#3396	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×D₈×C₄₁	C₂²
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. C₂×C₄×Q₁₆×C₄₁	C₂	semidirect
4. C₄₁×#2367	C₂	semidirect
5. C₄₁×#1983	C₂	semidirect
7. C₄₁×#1969	C₂	semidirect
8. C₄₁×#1880	C₂	semidirect
9. C₄₁×#1877	C₂	semidirect
10. C₄×#107×C₄₁	C₂	semidirect
11. C₈×C₄⋊C₄×C₄₁	C₂	semidirect
18. C₄₁×#495	C₄	semidirect
47. C₂×Q₁₆×C₄₁	C₂×C₄	semidirect
50. C₂×SD₁₆×C₄₁	C₂×C₄	semidirect
59. #124×C₄₁	C₂×C₄	semidirect
88. C₄×C₈×C₄₁	C₂×C₄	semidirect
209. #23186	C₄₁	direct (N × H)
238. C₂×C₄×Q₁₆	C₂×C₄₁	semidirect
240. #2367	C₂×C₄₁	semidirect
241. #1983	C₂×C₄₁	semidirect
243. #1969	C₂×C₄₁	semidirect
244. #1880	C₂×C₄₁	semidirect
245. #1877	C₂×C₄₁	semidirect
246. C₄×#107	C₂×C₄₁	semidirect
247. C₈×C₄⋊C₄	C₂×C₄₁	semidirect
262. #495	C₄×C₄₁	semidirect
286. C₄₁	#23186	direct (N × H)
292. C₂×Q₁₆	C₂×C₄×C₄₁	semidirect
295. C₂×SD₁₆	C₂×C₄×C₄₁	semidirect
304. #124	C₂×C₄×C₄₁	semidirect
333. C₄×C₈	C₂×C₄×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#495	2
C₂×C₄×Q₁₆×C₄₁	2
C₂×C₄×D₈×C₄₁	2
C₄₁×#2367	2
C₄₁×#1983	2
C₄₁×#1970	2
C₄₁×#1969	2
C₄₁×#1880	2
C₄₁×#1877	2
C₄×#107×C₄₁	2
C₈×C₄⋊C₄×C₄₁	2
#23186	41

Subgroups — C41×#23186 #23799387

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#23186 #23799387