Subgroups — C₄₁×#61695 #23837896

Order 10496.

2018 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3501	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#547	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#3335	C₂	1	8	yes	maximal, complemented
4	C₄₁×#3298	C₂	1	8	yes	maximal, complemented
5	C₄₁×#3229	C₂	1	2	yes	maximal, complemented
6	C₄₁×#3187	C₂	1	4	yes	maximal, complemented
7	C₄₁×#3101	C₂	1	2	yes	maximal, complemented
8	C₂×C₄₁×#483	C₂	1	4	yes	maximal, complemented
9	C₄₁×#2972	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₄₁	—	2	1	no	—
11	C₄₁×#554	—	2	4	no	—
12	C₄₁×#554	C₂²	1	4	yes	complemented
13	D₄×Q₈×C₄₁	C₂²	1	4	yes	complemented
14	C₄₁×#547	—	2	4	no	—
15	C₄₁×#547	C₂²	1	8	yes	—
16	C₄₁×#544	—	2	1	no	—
17	C₄₁×#543	—	2	2	no	—
18	C₄₁×#533	C₂²	1	2	yes	—
19	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×#123×C₄₁	—	2	2	no	—
21	C₂×C₂²⋊Q₈×C₄₁	—	2	1	no	—
22	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	4	yes	—
23	C₂×#121×C₄₁	C₂²	1	2	yes	—
24	C₄₁×#518	—	2	1	no	—
25	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
28	C₄₁×#498	C₂²	1	4	yes	complemented
29	C₄₁×#487	C₂²	1	4	yes	complemented
30	C₄₁×#483	C₂²	1	4	yes	—
31	C₄₁×#483	C₂²	1	8	yes	—
32	C₄₁×#483	C₂²	1	16	yes	complemented
33	C₄₁×#481	C₂²	1	8	yes	complemented
34	C₄₁×#476	C₂²	1	4	yes	complemented
35	C₄₁×#475	C₂²	1	8	yes	complemented
36	C₄₁×#465	C₂²	1	16	yes	complemented
37	C₄₁×#461	C₂²	1	4	yes	complemented
38	C₄₁×#450	C₂²	1	4	yes	—
39	C₄₁×#448	C₂²	1	8	yes	complemented
40	C₄×SD₁₆×C₄₁	C₂²	1	8	yes	complemented
41	C₈×D₄×C₄₁	C₂²	1	8	yes	complemented
42	C₄₁×#431	C₂²	1	2	yes	—
43	C₂×#106×C₄₁	C₂²	1	8	yes	complemented
44	C₂×#103×C₄₁	C₂²	1	8	yes	complemented
45	C₂×C₂²⋊C₈×C₄₁	C₂²	1	4	yes	—
46	C₂×#41×C₄₁	—	2	8	no	—
47	C₂×#41×C₄₁	—	4	8	no	—
48	C₂²×Q₈×C₄₁	—	2	1	no	—
49	C₂²×Q₈×C₄₁	C₂³	1	4	yes	—
50	C₂²×D₄×C₄₁	—	2	2	no	—
51	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
52	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₄₁	—	2	2	no	—
54	C₂³×C₄×C₄₁	—	2	1	no	—
55	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
56	C₂×SD₁₆×C₄₁	C₂³	1	8	yes	—
57	C₂²×C₈×C₄₁	C₂³	1	8	yes	—
58	C₄⋊Q₈×C₄₁	—	2	4	no	—
59	C₄⋊Q₈×C₄₁	—	2	2	no	—
60	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
61	C₄⋊Q₈×C₄₁	C₂³	1	4	yes	—
62	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
63	#125×C₄₁	—	2	4	no	—
64	#125×C₄₁	—	2	2	no	—
65	#123×C₄₁	—	2	16	no	—
66	C₂²⋊Q₈×C₄₁	—	2	4	no	—
67	C₂²⋊Q₈×C₄₁	—	2	4	no	—
68	C₂²⋊Q₈×C₄₁	—	2	2	no	—
69	C₂²⋊Q₈×C₄₁	—	2	8	no	—
70	C₂²⋊Q₈×C₄₁	—	2	8	no	—
71	C₂²⋊Q₈×C₄₁	—	2	8	no	—
72	C₂²⋊Q₈×C₄₁	C₂³	1	4	yes	—
73	C₂²⋊Q₈×C₄₁	C₂³	1	8	yes	—
74	#121×C₄₁	—	2	4	no	—
75	#121×C₄₁	C₂³	1	8	yes	—
76	C₄×Q₈×C₄₁	—	2	2	no	—
77	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
78	C₄×D₄×C₄₁	—	2	4	no	—
79	C₄×D₄×C₄₁	—	2	4	no	—
80	C₄×D₄×C₄₁	—	2	2	no	—
81	C₄×D₄×C₄₁	D₄	1	4	yes	—
82	C₄×D₄×C₄₁	C₂³	1	4	yes	—
83	C₄×D₄×C₄₁	C₂³	1	4	yes	—
84	#117×C₄₁	—	2	2	no	—
85	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
86	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
87	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
88	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
89	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₄₁	C₂³	1	8	yes	—
93	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
94	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
95	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
98	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
99	#106×C₄₁	C₂³	1	8	yes	—
100	#106×C₄₁	C₂³	1	16	yes	—
101	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
102	#103×C₄₁	C₂³	1	8	yes	—
103	#103×C₄₁	C₂³	1	16	yes	—
104	#102×C₄₁	C₂³	1	8	yes	—
105	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
106	C₂²⋊C₈×C₄₁	C₂³	1	8	yes	—
107	C₄×C₈×C₄₁	C₂³	1	4	yes	—
108	C₂⁴×C₄₁	—	2	1	no	—
109	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
110	#41×C₄₁	—	4	32	no	—
111	C₂×Q₈×C₄₁	—	2	4	no	—
112	C₂×Q₈×C₄₁	—	2	2	no	—
113	C₂×Q₈×C₄₁	—	2	4	no	—
114	C₂×Q₈×C₄₁	—	4	8	no	—
115	C₂×Q₈×C₄₁	—	4	4	no	—
116	C₂×Q₈×C₄₁	C₂⁴	1	4	yes	—
117	C₂×D₄×C₄₁	—	2	8	no	—
118	C₂×D₄×C₄₁	—	2	1	no	—
119	C₂×D₄×C₄₁	—	4	2	no	—
120	C₂×D₄×C₄₁	—	4	8	no	—
121	C₂×D₄×C₄₁	SD₁₆	1	8	yes	complemented
122	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
123	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
124	C₂²×C₄×C₄₁	—	2	1	no	—
125	C₂²×C₄×C₄₁	—	2	2	no	—
126	C₂²×C₄×C₄₁	—	2	8	no	—
127	C₂²×C₄×C₄₁	—	2	4	no	—
128	C₂²×C₄×C₄₁	—	2	4	no	—
129	C₂²×C₄×C₄₁	—	2	4	no	—
130	C₂²×C₄×C₄₁	—	4	4	no	—
131	C₂²×C₄×C₄₁	—	4	8	no	—
132	C₂²×C₄×C₄₁	—	4	4	no	—
133	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
136	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
138	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
139	SD₁₆×C₄₁	—	4	8	no	—
140	C₂×C₈×C₄₁	—	4	8	no	—
141	C₂×C₈×C₄₁	C₂⁴	1	8	yes	—
142	C₄⋊C₄×C₄₁	—	2	1	no	—
143	C₄⋊C₄×C₄₁	—	2	2	no	—
144	C₄⋊C₄×C₄₁	—	2	8	no	—
145	C₄⋊C₄×C₄₁	—	2	4	no	—
146	C₄⋊C₄×C₄₁	—	2	8	no	—
147	C₄⋊C₄×C₄₁	—	2	4	no	—
148	C₄⋊C₄×C₄₁	—	2	4	no	—
149	C₄⋊C₄×C₄₁	—	2	2	no	—
150	C₄⋊C₄×C₄₁	—	2	2	no	—
151	C₄⋊C₄×C₄₁	—	2	2	no	—
152	C₄⋊C₄×C₄₁	—	2	4	no	—
153	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
154	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
155	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
156	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
157	C₂²⋊C₄×C₄₁	—	2	4	no	—
158	C₂²⋊C₄×C₄₁	—	2	8	no	—
159	C₂²⋊C₄×C₄₁	—	2	4	no	—
160	C₂²⋊C₄×C₄₁	—	2	8	no	—
161	C₂²⋊C₄×C₄₁	C₂×D₄	1	8	yes	—
162	C₄²×C₄₁	—	2	4	no	—
163	C₄²×C₄₁	C₂×D₄	1	2	yes	—
164	C₄²×C₄₁	C₂⁴	1	2	yes	—
165	C₂³×C₄₁	—	2	2	no	—
166	C₂³×C₄₁	—	4	2	no	—
167	C₂³×C₄₁	—	4	2	no	—
168	C₂³×C₄₁	—	4	2	no	—
169	C₂³×C₄₁	—	4	2	no	—
170	C₂³×C₄₁	—	4	2	no	—
171	C₂³×C₄₁	C₂×SD₁₆	1	8	yes	—
172	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
173	C₂³×C₄₁	C₂²×D₄	1	4	yes	—
174	Q₈×C₄₁	—	2	8	no	—
175	Q₈×C₄₁	—	4	8	no	—
176	Q₈×C₄₁	—	8	2	no	—
177	Q₈×C₄₁	—	8	4	no	—
178	D₄×C₄₁	—	2	4	no	—
179	D₄×C₄₁	—	4	2	no	—
180	D₄×C₄₁	—	4	16	no	—
181	D₄×C₄₁	C₂×SD₁₆	1	16	yes	—
182	C₂×C₄×C₄₁	—	2	8	no	—
183	C₂×C₄×C₄₁	—	2	2	no	—
184	C₂×C₄×C₄₁	—	2	4	no	—
185	C₂×C₄×C₄₁	—	2	4	no	—
186	C₂×C₄×C₄₁	—	2	2	no	—
187	C₂×C₄×C₄₁	—	2	4	no	—
188	C₂×C₄×C₄₁	—	4	4	no	—
189	C₂×C₄×C₄₁	—	4	2	no	—
190	C₂×C₄×C₄₁	—	4	1	no	—
191	C₂×C₄×C₄₁	—	4	2	no	—
192	C₂×C₄×C₄₁	—	4	4	no	—
193	C₂×C₄×C₄₁	—	4	16	no	—
194	C₂×C₄×C₄₁	—	4	8	no	—
195	C₂×C₄×C₄₁	—	8	4	no	—
196	C₂×C₄×C₄₁	—	8	4	no	—
197	C₂×C₄×C₄₁	C₂×SD₁₆	1	4	yes	—
198	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
200	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
201	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
202	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
203	C₈×C₄₁	—	2	8	no	—
204	#61695	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂²×C₄₁	—	2	1	no	—
206	C₂²×C₄₁	—	2	4	no	—
207	C₂²×C₄₁	—	2	1	no	—
208	C₂²×C₄₁	—	2	4	no	—
209	C₂²×C₄₁	—	4	8	no	—
210	C₂²×C₄₁	—	4	2	no	—
211	C₂²×C₄₁	—	4	2	no	—
212	C₂²×C₄₁	—	4	2	no	—
213	C₂²×C₄₁	—	8	4	no	—
214	C₂²×C₄₁	C₂²×SD₁₆	1	2	yes	—
215	C₂²×C₄₁	C₂²×SD₁₆	1	8	yes	—
216	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
217	C₄×C₄₁	—	2	2	no	—
218	C₄×C₄₁	—	2	1	no	—
219	C₄×C₄₁	—	2	4	no	—
220	C₄×C₄₁	—	4	4	no	—
221	C₄×C₄₁	—	4	4	no	—
222	C₄×C₄₁	—	4	2	no	—
223	C₄×C₄₁	—	4	4	no	—
224	C₄×C₄₁	C₂²×SD₁₆	1	4	yes	—
225	C₄×C₄₁	#585	1	2	yes	—
226	#3501	C₂×C₄₁	1	1	yes	characteristic, complemented
227	C₂×#547	C₂×C₄₁	1	1	yes	characteristic
228	#3335	C₂×C₄₁	1	8	yes	complemented
229	#3298	C₂×C₄₁	1	8	yes	complemented
230	#3229	C₂×C₄₁	1	2	yes	complemented
231	#3187	C₂×C₄₁	1	4	yes	complemented
232	#3101	C₂×C₄₁	1	2	yes	complemented
233	C₂×#483	C₂×C₄₁	1	4	yes	complemented
234	#2972	C₂×C₄₁	1	1	yes	characteristic, complemented
235	C₂×C₄₁	—	2	2	no	—
236	C₂×C₄₁	—	2	8	no	—
237	C₂×C₄₁	—	8	2	no	—
238	C₂×C₄₁	#3485	1	1	yes	characteristic
239	C₂×C₄₁	C₂³×SD₁₆	1	1	yes	characteristic
240	C₂×C₄₁	#3586	1	1	yes	characteristic
241	C₂²×#41	—	2	1	no	—
242	#554	—	2	4	no	—
243	#554	C₂²×C₄₁	1	4	yes	complemented
244	D₄×Q₈	C₂²×C₄₁	1	4	yes	complemented
245	#547	—	2	4	no	—
246	#547	C₂²×C₄₁	1	8	yes	—
247	#544	—	2	1	no	—
248	#543	—	2	2	no	—
249	#533	C₂²×C₄₁	1	2	yes	—
250	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
251	C₂×#123	—	2	2	no	—
252	C₂×C₂²⋊Q₈	—	2	1	no	—
253	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	4	yes	—
254	C₂×#121	C₂²×C₄₁	1	2	yes	—
255	#518	—	2	1	no	—
256	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
257	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
258	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
259	#498	C₂²×C₄₁	1	4	yes	complemented
260	#487	C₂²×C₄₁	1	4	yes	complemented
261	#483	C₂²×C₄₁	1	4	yes	—
262	#483	C₂²×C₄₁	1	8	yes	—
263	#483	C₂²×C₄₁	1	16	yes	complemented
264	#481	C₂²×C₄₁	1	8	yes	complemented
265	#476	C₂²×C₄₁	1	4	yes	complemented
266	#475	C₂²×C₄₁	1	8	yes	complemented
267	#465	C₂²×C₄₁	1	16	yes	complemented
268	#461	C₂²×C₄₁	1	4	yes	complemented
269	#450	C₂²×C₄₁	1	4	yes	—
270	#448	C₂²×C₄₁	1	8	yes	complemented
271	C₄×SD₁₆	C₂²×C₄₁	1	8	yes	complemented
272	C₈×D₄	C₂²×C₄₁	1	8	yes	complemented
273	#431	C₂²×C₄₁	1	2	yes	—
274	C₂×#106	C₂²×C₄₁	1	8	yes	complemented
275	C₂×#103	C₂²×C₄₁	1	8	yes	complemented
276	C₂×C₂²⋊C₈	C₂²×C₄₁	1	4	yes	—
277	C₄₁	#61695	1	1	yes	characteristic, direct product factor, Sylow
278	C₂×#41	—	2	8	no	—
279	C₂×#41	—	4	8	no	—
280	C₂²×Q₈	—	2	1	no	—
281	C₂²×Q₈	C₂³×C₄₁	1	4	yes	—
282	C₂²×D₄	—	2	2	no	—
283	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
284	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
285	C₂³×C₄	—	2	2	no	—
286	C₂³×C₄	—	2	1	no	—
287	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
288	C₂×SD₁₆	C₂³×C₄₁	1	8	yes	—
289	C₂²×C₈	C₂³×C₄₁	1	8	yes	—
290	C₄⋊Q₈	—	2	4	no	—
291	C₄⋊Q₈	—	2	2	no	—
292	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
293	C₄⋊Q₈	C₂³×C₄₁	1	4	yes	—
294	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
295	#125	—	2	4	no	—
296	#125	—	2	2	no	—
297	#123	—	2	16	no	—
298	C₂²⋊Q₈	—	2	4	no	—
299	C₂²⋊Q₈	—	2	4	no	—
300	C₂²⋊Q₈	—	2	2	no	—
301	C₂²⋊Q₈	—	2	8	no	—
302	C₂²⋊Q₈	—	2	8	no	—
303	C₂²⋊Q₈	—	2	8	no	—
304	C₂²⋊Q₈	C₂³×C₄₁	1	4	yes	—
305	C₂²⋊Q₈	C₂³×C₄₁	1	8	yes	—
306	#121	—	2	4	no	—
307	#121	C₂³×C₄₁	1	8	yes	—
308	C₄×Q₈	—	2	2	no	—
309	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
310	C₄×D₄	—	2	4	no	—
311	C₄×D₄	—	2	4	no	—
312	C₄×D₄	—	2	2	no	—
313	C₄×D₄	D₄×C₄₁	1	4	yes	—
314	C₄×D₄	C₂³×C₄₁	1	4	yes	—
315	C₄×D₄	C₂³×C₄₁	1	4	yes	—
316	#117	—	2	2	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	4	no	—
319	C₂×C₄⋊C₄	—	2	4	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
322	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
324	C₂×C₄⋊C₄	C₂³×C₄₁	1	8	yes	—
325	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
326	C₂×C₂²⋊C₄	—	2	4	no	—
327	C₂×C₂²⋊C₄	—	2	1	no	—
328	C₂×C₂²⋊C₄	—	2	2	no	—
329	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
330	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
331	#106	C₂³×C₄₁	1	8	yes	—
332	#106	C₂³×C₄₁	1	16	yes	—
333	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
334	#103	C₂³×C₄₁	1	8	yes	—
335	#103	C₂³×C₄₁	1	16	yes	—
336	#102	C₂³×C₄₁	1	8	yes	—
337	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
338	C₂²⋊C₈	C₂³×C₄₁	1	8	yes	—
339	C₄×C₈	C₂³×C₄₁	1	4	yes	—
340	C₂⁴	—	2	1	no	—
341	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
342	#41	—	4	32	no	—
343	C₂×Q₈	—	2	4	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	4	no	—
346	C₂×Q₈	—	4	8	no	—
347	C₂×Q₈	—	4	4	no	—
348	C₂×Q₈	C₂⁴×C₄₁	1	4	yes	—
349	C₂×D₄	—	2	8	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	4	2	no	—
352	C₂×D₄	—	4	8	no	—
353	C₂×D₄	SD₁₆×C₄₁	1	8	yes	complemented
354	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
355	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	8	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	4	4	no	—
363	C₂²×C₄	—	4	8	no	—
364	C₂²×C₄	—	4	4	no	—
365	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
367	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
368	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
369	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
370	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
371	SD₁₆	—	4	8	no	—
372	C₂×C₈	—	4	8	no	—
373	C₂×C₈	C₂⁴×C₄₁	1	8	yes	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	8	no	—
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	—	2	8	no	—
379	C₄⋊C₄	—	2	4	no	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	4	no	—
385	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
386	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
387	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
388	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
389	C₂²⋊C₄	—	2	4	no	—
390	C₂²⋊C₄	—	2	8	no	—
391	C₂²⋊C₄	—	2	4	no	—
392	C₂²⋊C₄	—	2	8	no	—
393	C₂²⋊C₄	C₂×D₄×C₄₁	1	8	yes	—
394	C₄²	—	2	4	no	—
395	C₄²	C₂×D₄×C₄₁	1	2	yes	—
396	C₄²	C₂⁴×C₄₁	1	2	yes	—
397	C₂³	—	2	2	no	—
398	C₂³	—	4	2	no	—
399	C₂³	—	4	2	no	—
400	C₂³	—	4	2	no	—
401	C₂³	—	4	2	no	—
402	C₂³	—	4	2	no	—
403	C₂³	C₂×SD₁₆×C₄₁	1	8	yes	—
404	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
405	C₂³	C₂²×D₄×C₄₁	1	4	yes	—
406	Q₈	—	2	8	no	—
407	Q₈	—	4	8	no	—
408	Q₈	—	8	4	no	—
409	Q₈	—	8	2	no	—
410	D₄	—	2	4	no	—
411	D₄	—	4	2	no	—
412	D₄	—	4	16	no	—
413	D₄	C₂×SD₁₆×C₄₁	1	16	yes	—
414	C₂×C₄	—	2	8	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	4	no	—
425	C₂×C₄	—	4	16	no	—
426	C₂×C₄	—	4	8	no	—
427	C₂×C₄	—	8	4	no	—
428	C₂×C₄	—	8	4	no	—
429	C₂×C₄	C₂×SD₁₆×C₄₁	1	4	yes	—
430	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
431	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
432	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
433	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
434	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
435	C₈	—	2	8	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	4	no	—
438	C₂²	—	2	1	no	—
439	C₂²	—	2	4	no	—
440	C₂²	—	4	8	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	8	4	no	—
445	C₂²	C₂²×SD₁₆×C₄₁	1	2	yes	—
446	C₂²	C₂²×SD₁₆×C₄₁	1	8	yes	—
447	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
448	C₄	—	2	2	no	—
449	C₄	—	2	1	no	—
450	C₄	—	2	4	no	—
451	C₄	—	4	2	no	—
452	C₄	—	4	4	no	—
453	C₄	—	4	4	no	—
454	C₄	—	4	4	no	—
455	C₄	C₂²×SD₁₆×C₄₁	1	4	yes	—
456	C₄	C₄₁×#585	1	2	yes	—
457	C₂	—	2	2	no	—
458	C₂	—	2	8	no	—
459	C₂	—	8	2	no	—
460	C₂	C₄₁×#3485	1	1	yes	characteristic
461	C₂	C₂³×SD₁₆×C₄₁	1	1	yes	characteristic
462	C₂	C₄₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
prime radical	C₂×C₄₁×#547	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂×C₄×D₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3501	C₂	semidirect
3. C₄₁×#3335	C₂	semidirect
4. C₄₁×#3298	C₂	semidirect
5. C₄₁×#3229	C₂	semidirect
6. C₄₁×#3187	C₂	semidirect
7. C₄₁×#3101	C₂	semidirect
8. C₂×C₄₁×#483	C₂	semidirect
9. C₄₁×#2972	C₂	semidirect
12. C₄₁×#554	C₂²	semidirect
13. D₄×Q₈×C₄₁	C₂²	semidirect
28. C₄₁×#498	C₂²	semidirect
29. C₄₁×#487	C₂²	semidirect
32. C₄₁×#483	C₂²	semidirect
33. C₄₁×#481	C₂²	semidirect
34. C₄₁×#476	C₂²	semidirect
35. C₄₁×#475	C₂²	semidirect
36. C₄₁×#465	C₂²	semidirect
37. C₄₁×#461	C₂²	semidirect
39. C₄₁×#448	C₂²	semidirect
40. C₄×SD₁₆×C₄₁	C₂²	semidirect
41. C₈×D₄×C₄₁	C₂²	semidirect
43. C₂×#106×C₄₁	C₂²	semidirect
44. C₂×#103×C₄₁	C₂²	semidirect
121. C₂×D₄×C₄₁	SD₁₆	semidirect
204. #61695	C₄₁	direct (N × H)
226. #3501	C₂×C₄₁	semidirect
228. #3335	C₂×C₄₁	semidirect
229. #3298	C₂×C₄₁	semidirect
230. #3229	C₂×C₄₁	semidirect
231. #3187	C₂×C₄₁	semidirect
232. #3101	C₂×C₄₁	semidirect
233. C₂×#483	C₂×C₄₁	semidirect
234. #2972	C₂×C₄₁	semidirect
243. #554	C₂²×C₄₁	semidirect
244. D₄×Q₈	C₂²×C₄₁	semidirect
259. #498	C₂²×C₄₁	semidirect
260. #487	C₂²×C₄₁	semidirect
263. #483	C₂²×C₄₁	semidirect
264. #481	C₂²×C₄₁	semidirect
265. #476	C₂²×C₄₁	semidirect
266. #475	C₂²×C₄₁	semidirect
267. #465	C₂²×C₄₁	semidirect
268. #461	C₂²×C₄₁	semidirect
270. #448	C₂²×C₄₁	semidirect
271. C₄×SD₁₆	C₂²×C₄₁	semidirect
272. C₈×D₄	C₂²×C₄₁	semidirect
274. C₂×#106	C₂²×C₄₁	semidirect
275. C₂×#103	C₂²×C₄₁	semidirect
277. C₄₁	#61695	direct (N × H)
353. C₂×D₄	SD₁₆×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3501	2
C₂×C₄₁×#547	2
C₄₁×#3335	2
C₄₁×#3298	2
C₄₁×#3229	2
C₄₁×#3187	2
C₄₁×#3101	2
C₂×C₄₁×#483	2
C₄₁×#2972	2
#61695	41

Subgroups — C41×#61695 #23837896

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61695 #23837896