Subgroups — C₄₁×#61936 #23838137

Order 10496.

1634 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3509	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#3398	C₂	1	4	yes	maximal, complemented
4	C₄₁×#3395	C₂	1	4	yes	maximal, complemented
5	C₄₁×#3374	C₂	1	4	yes	maximal, complemented
6	C₄₁×#3364	C₂	1	4	yes	maximal, complemented
7	C₄₁×#3223	C₂	1	4	yes	maximal
8	C₄₁×#3209	C₂	1	2	yes	maximal, complemented
9	C₄₁×#3127	C₂	1	4	yes	maximal, complemented
10	C₄₁×#3107	C₂	1	2	yes	maximal
11	C₄₁×#2986	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#564	—	2	2	no	—
13	C₄₁×#557	—	2	2	no	—
14	C₄₁×#557	C₂²	1	4	yes	—
15	C₄₁×#557	C₂²	1	4	yes	—
16	C₄₁×#557	C₂²	1	4	yes	—
17	C₄₁×#556	C₂²	1	4	yes	—
18	C₄₁×#552	—	2	4	no	—
19	C₄₁×#541	—	2	2	no	—
20	C₄₁×#541	—	2	4	no	—
21	C₄₁×#541	C₂²	1	4	yes	—
22	C₄₁×#536	C₂²	1	2	yes	—
23	C₄₁×#533	—	2	2	no	—
24	C₄₁×#533	C₂²	1	2	yes	—
25	C₄₁×#533	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
27	C₄₁×#519	C₂²	1	2	yes	—
28	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
29	C₄₁×#497	C₂²	1	4	yes	—
30	C₄₁×#494	C₂²	1	4	yes	—
31	C₄₁×#494	C₂²	1	4	yes	—
32	C₄₁×#491	C₂²	1	4	yes	—
33	C₄₁×#488	C₂²	1	4	yes	—
34	C₄₁×#487	C₂²	1	4	yes	—
35	C₄₁×#485	C₂²	1	4	yes	—
36	C₄₁×#479	C₂²	1	8	yes	—
37	C₄₁×#475	C₂²	1	2	yes	—
38	C₄₁×#474	C₂²	1	2	yes	—
39	C₄₁×#464	C₂²	1	8	yes	—
40	C₄₁×#462	C₂²	1	2	yes	—
41	C₄₁×#462	C₂²	1	4	yes	—
42	C₄₁×#462	C₂²	1	8	yes	—
43	C₄₁×#462	C₂²	1	4	yes	—
44	C₄₁×#462	C₂²	1	8	yes	—
45	C₄₁×#461	C₂²	1	2	yes	—
46	C₄₁×#452	C₂²	1	4	yes	—
47	C₄₁×#451	C₂²	1	8	yes	—
48	C₄₁×#446	C₂²	1	4	yes	—
49	C₈×Q₈×C₄₁	C₂²	1	4	yes	—
50	C₄₁×#441	C₂²	1	8	yes	—
51	C₄×Q₁₆×C₄₁	C₂²	1	4	yes	—
52	C₄×Q₁₆×C₄₁	C₂²	1	8	yes	—
53	C₄×SD₁₆×C₄₁	C₂²	1	4	yes	—
54	C₄₁×#433	C₂²	1	4	yes	—
55	C₄₁×#431	C₂²	1	2	yes	—
56	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
57	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
58	C₂×Q₁₆×C₄₁	C₂³	1	8	yes	—
59	C₂×Q₁₆×C₄₁	C₂³	1	4	yes	—
60	C₂×Q₁₆×C₄₁	C₂³	1	8	yes	—
61	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
62	C₄⋊Q₈×C₄₁	—	2	4	no	—
63	C₄⋊Q₈×C₄₁	—	2	1	no	—
64	C₄⋊Q₈×C₄₁	—	2	1	no	—
65	C₄⋊Q₈×C₄₁	D₄	1	2	yes	—
66	C₄⋊Q₈×C₄₁	C₂³	1	4	yes	—
67	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
68	C₄⋊Q₈×C₄₁	C₂³	1	4	yes	—
69	C₄⋊Q₈×C₄₁	C₂³	1	4	yes	—
70	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
71	#126×C₄₁	—	2	8	no	—
72	#126×C₄₁	—	2	8	no	—
73	#125×C₄₁	—	2	4	no	—
74	#125×C₄₁	—	2	8	no	—
75	#125×C₄₁	—	2	4	no	—
76	#125×C₄₁	—	2	8	no	—
77	#125×C₄₁	—	2	8	no	—
78	#125×C₄₁	—	2	8	no	—
79	#125×C₄₁	—	2	2	no	—
80	#125×C₄₁	D₄	1	2	yes	—
81	#125×C₄₁	C₂³	1	4	yes	—
82	#124×C₄₁	C₂³	1	4	yes	—
83	#123×C₄₁	—	2	4	no	—
84	C₂²⋊Q₈×C₄₁	—	2	4	no	—
85	C₂²⋊Q₈×C₄₁	—	2	2	no	—
86	C₂²⋊Q₈×C₄₁	—	2	4	no	—
87	C₂²⋊Q₈×C₄₁	D₄	1	4	yes	—
88	C₂²⋊Q₈×C₄₁	C₂³	1	4	yes	—
89	C₄×Q₈×C₄₁	—	2	4	no	—
90	C₄×Q₈×C₄₁	—	2	4	no	—
91	C₄×Q₈×C₄₁	—	2	4	no	—
92	C₄×Q₈×C₄₁	—	2	4	no	—
93	C₄×Q₈×C₄₁	—	2	2	no	—
94	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
95	C₄×Q₈×C₄₁	C₂³	1	8	yes	—
96	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
97	C₄×Q₈×C₄₁	C₂³	1	8	yes	—
98	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
99	C₄×D₄×C₄₁	—	2	2	no	—
100	C₄×D₄×C₄₁	C₂³	1	2	yes	—
101	#117×C₄₁	—	2	2	no	—
102	#117×C₄₁	—	2	4	no	—
103	#117×C₄₁	—	2	4	no	—
104	#117×C₄₁	—	2	1	no	—
105	#117×C₄₁	C₂³	1	1	yes	characteristic
106	#117×C₄₁	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
108	C₂×C₄²×C₄₁	—	2	1	no	—
109	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
110	#107×C₄₁	C₂³	1	4	yes	—
111	#106×C₄₁	C₂³	1	4	yes	—
112	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
113	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
114	C₄⋊C₈×C₄₁	C₂³	1	8	yes	—
115	#103×C₄₁	C₂³	1	4	yes	—
116	#103×C₄₁	C₂³	1	4	yes	—
117	#103×C₄₁	C₂³	1	8	yes	—
118	#103×C₄₁	C₂³	1	4	yes	—
119	#103×C₄₁	C₂³	1	8	yes	—
120	#102×C₄₁	C₂³	1	4	yes	—
121	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
122	#97×C₄₁	C₂³	1	4	yes	—
123	C₄×C₈×C₄₁	C₂³	1	4	yes	—
124	C₄×C₈×C₄₁	C₂³	1	4	yes	—
125	#41×C₄₁	—	4	2	no	—
126	C₂×Q₈×C₄₁	—	2	2	no	—
127	C₂×Q₈×C₄₁	—	2	2	no	—
128	C₂×Q₈×C₄₁	—	4	4	no	—
129	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
130	C₂×Q₈×C₄₁	C₂⁴	1	4	yes	—
131	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
132	C₂×Q₈×C₄₁	C₂⁴	1	4	yes	—
133	C₂×D₄×C₄₁	—	2	1	no	—
134	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
135	C₂²×C₄×C₄₁	—	2	2	no	—
136	C₂²×C₄×C₄₁	—	2	2	no	—
137	C₂²×C₄×C₄₁	—	2	1	no	—
138	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
140	Q₁₆×C₄₁	—	4	8	no	—
141	Q₁₆×C₄₁	—	4	8	no	—
142	Q₁₆×C₄₁	—	4	4	no	—
143	SD₁₆×C₄₁	—	4	4	no	—
144	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
145	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
146	C₄⋊C₄×C₄₁	—	2	4	no	—
147	C₄⋊C₄×C₄₁	—	2	4	no	—
148	C₄⋊C₄×C₄₁	—	2	2	no	—
149	C₄⋊C₄×C₄₁	—	2	8	no	—
150	C₄⋊C₄×C₄₁	—	2	2	no	—
151	C₄⋊C₄×C₄₁	—	2	2	no	—
152	C₄⋊C₄×C₄₁	—	2	2	no	—
153	C₄⋊C₄×C₄₁	—	2	8	no	—
154	C₄⋊C₄×C₄₁	—	2	4	no	—
155	C₄⋊C₄×C₄₁	—	2	8	no	—
156	C₄⋊C₄×C₄₁	—	2	8	no	—
157	C₄⋊C₄×C₄₁	—	2	4	no	—
158	C₄⋊C₄×C₄₁	—	2	8	no	—
159	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
160	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
161	C₄⋊C₄×C₄₁	C₂×D₄	1	8	yes	—
162	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
163	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
164	C₂²⋊C₄×C₄₁	—	2	1	no	—
165	C₂²⋊C₄×C₄₁	—	2	4	no	—
166	C₂²⋊C₄×C₄₁	—	2	2	no	—
167	C₂²⋊C₄×C₄₁	—	2	8	no	—
168	C₂²⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
169	C₄²×C₄₁	—	2	1	no	—
170	C₄²×C₄₁	—	2	2	no	—
171	C₄²×C₄₁	—	2	8	no	—
172	C₄²×C₄₁	—	2	4	no	—
173	C₄²×C₄₁	—	2	8	no	—
174	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₄₁	C₂⁴	1	2	yes	—
177	C₄²×C₄₁	C₂⁴	1	4	yes	—
178	C₂³×C₄₁	—	2	1	no	—
179	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
180	Q₈×C₄₁	—	2	8	no	—
181	Q₈×C₄₁	—	2	4	no	—
182	Q₈×C₄₁	—	2	4	no	—
183	Q₈×C₄₁	—	2	8	no	—
184	Q₈×C₄₁	—	2	2	no	—
185	Q₈×C₄₁	—	4	4	no	—
186	Q₈×C₄₁	—	4	4	no	—
187	D₄×C₄₁	—	2	2	no	—
188	D₄×C₄₁	—	4	2	no	—
189	C₂×C₄×C₄₁	—	2	4	no	—
190	C₂×C₄×C₄₁	—	2	2	no	—
191	C₂×C₄×C₄₁	—	2	2	no	—
192	C₂×C₄×C₄₁	—	2	4	no	—
193	C₂×C₄×C₄₁	—	2	4	no	—
194	C₂×C₄×C₄₁	—	2	4	no	—
195	C₂×C₄×C₄₁	—	2	1	no	—
196	C₂×C₄×C₄₁	—	4	2	no	—
197	C₂×C₄×C₄₁	—	4	4	no	—
198	C₂×C₄×C₄₁	—	4	4	no	—
199	C₂×C₄×C₄₁	C₂²×D₄	1	8	yes	—
200	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
202	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
203	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
204	C₈×C₄₁	—	2	4	no	—
205	C₈×C₄₁	—	2	4	no	—
206	#61936	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂²×C₄₁	—	2	1	no	—
208	C₂²×C₄₁	—	2	2	no	—
209	C₂²×C₄₁	—	4	1	no	—
210	C₂²×C₄₁	—	4	2	no	—
211	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
212	C₄×C₄₁	—	2	1	no	—
213	C₄×C₄₁	—	2	2	no	—
214	C₄×C₄₁	—	2	8	no	—
215	C₄×C₄₁	—	4	1	no	—
216	C₄×C₄₁	—	4	4	no	—
217	C₄×C₄₁	—	4	4	no	—
218	C₄×C₄₁	—	4	2	no	—
219	C₄×C₄₁	—	4	4	no	—
220	C₄×C₄₁	#578	1	4	yes	—
221	C₄×C₄₁	#585	1	2	yes	—
222	#3556	C₂×C₄₁	1	1	yes	characteristic, complemented
223	#3509	C₂×C₄₁	1	1	yes	characteristic
224	#3398	C₂×C₄₁	1	4	yes	complemented
225	#3395	C₂×C₄₁	1	4	yes	complemented
226	#3374	C₂×C₄₁	1	4	yes	complemented
227	#3364	C₂×C₄₁	1	4	yes	complemented
228	#3223	C₂×C₄₁	1	4	yes	—
229	#3209	C₂×C₄₁	1	2	yes	complemented
230	#3127	C₂×C₄₁	1	4	yes	complemented
231	#3107	C₂×C₄₁	1	2	yes	—
232	#2986	C₂×C₄₁	1	1	yes	characteristic, complemented
233	C₂×C₄₁	—	4	1	no	—
234	C₂×C₄₁	—	8	1	no	—
235	C₂×C₄₁	#3487	1	1	yes	characteristic
236	C₂×C₄₁	C₂×#578	1	2	yes	—
237	#564	—	2	2	no	—
238	#557	—	2	2	no	—
239	#557	C₂²×C₄₁	1	4	yes	—
240	#557	C₂²×C₄₁	1	4	yes	—
241	#557	C₂²×C₄₁	1	4	yes	—
242	#556	C₂²×C₄₁	1	4	yes	—
243	#552	—	2	4	no	—
244	#541	—	2	2	no	—
245	#541	—	2	4	no	—
246	#541	C₂²×C₄₁	1	4	yes	—
247	#536	C₂²×C₄₁	1	2	yes	—
248	#533	—	2	2	no	—
249	#533	C₂²×C₄₁	1	2	yes	—
250	#533	C₂²×C₄₁	1	1	yes	characteristic
251	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
252	#519	C₂²×C₄₁	1	2	yes	—
253	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
254	#497	C₂²×C₄₁	1	4	yes	—
255	#494	C₂²×C₄₁	1	4	yes	—
256	#494	C₂²×C₄₁	1	4	yes	—
257	#491	C₂²×C₄₁	1	4	yes	—
258	#488	C₂²×C₄₁	1	4	yes	—
259	#487	C₂²×C₄₁	1	4	yes	—
260	#485	C₂²×C₄₁	1	4	yes	—
261	#479	C₂²×C₄₁	1	8	yes	—
262	#475	C₂²×C₄₁	1	2	yes	—
263	#474	C₂²×C₄₁	1	2	yes	—
264	#464	C₂²×C₄₁	1	8	yes	—
265	#462	C₂²×C₄₁	1	2	yes	—
266	#462	C₂²×C₄₁	1	4	yes	—
267	#462	C₂²×C₄₁	1	8	yes	—
268	#462	C₂²×C₄₁	1	4	yes	—
269	#462	C₂²×C₄₁	1	8	yes	—
270	#461	C₂²×C₄₁	1	2	yes	—
271	#452	C₂²×C₄₁	1	4	yes	—
272	#451	C₂²×C₄₁	1	8	yes	—
273	#446	C₂²×C₄₁	1	4	yes	—
274	C₈×Q₈	C₂²×C₄₁	1	4	yes	—
275	#441	C₂²×C₄₁	1	8	yes	—
276	C₄×Q₁₆	C₂²×C₄₁	1	4	yes	—
277	C₄×Q₁₆	C₂²×C₄₁	1	8	yes	—
278	C₄×SD₁₆	C₂²×C₄₁	1	4	yes	—
279	#433	C₂²×C₄₁	1	4	yes	—
280	#431	C₂²×C₄₁	1	2	yes	—
281	C₄₁	#61936	1	1	yes	characteristic, direct product factor, Sylow
282	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
283	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
284	C₂×Q₁₆	C₂³×C₄₁	1	8	yes	—
285	C₂×Q₁₆	C₂³×C₄₁	1	4	yes	—
286	C₂×Q₁₆	C₂³×C₄₁	1	8	yes	—
287	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
288	C₄⋊Q₈	—	2	4	no	—
289	C₄⋊Q₈	—	2	1	no	—
290	C₄⋊Q₈	—	2	1	no	—
291	C₄⋊Q₈	D₄×C₄₁	1	2	yes	—
292	C₄⋊Q₈	C₂³×C₄₁	1	4	yes	—
293	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
294	C₄⋊Q₈	C₂³×C₄₁	1	4	yes	—
295	C₄⋊Q₈	C₂³×C₄₁	1	4	yes	—
296	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
297	#126	—	2	8	no	—
298	#126	—	2	8	no	—
299	#125	—	2	4	no	—
300	#125	—	2	8	no	—
301	#125	—	2	4	no	—
302	#125	—	2	8	no	—
303	#125	—	2	8	no	—
304	#125	—	2	8	no	—
305	#125	—	2	2	no	—
306	#125	D₄×C₄₁	1	2	yes	—
307	#125	C₂³×C₄₁	1	4	yes	—
308	#124	C₂³×C₄₁	1	4	yes	—
309	#123	—	2	4	no	—
310	C₂²⋊Q₈	—	2	4	no	—
311	C₂²⋊Q₈	—	2	2	no	—
312	C₂²⋊Q₈	—	2	4	no	—
313	C₂²⋊Q₈	D₄×C₄₁	1	4	yes	—
314	C₂²⋊Q₈	C₂³×C₄₁	1	4	yes	—
315	C₄×Q₈	—	2	4	no	—
316	C₄×Q₈	—	2	4	no	—
317	C₄×Q₈	—	2	4	no	—
318	C₄×Q₈	—	2	4	no	—
319	C₄×Q₈	—	2	2	no	—
320	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
321	C₄×Q₈	C₂³×C₄₁	1	8	yes	—
322	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
323	C₄×Q₈	C₂³×C₄₁	1	8	yes	—
324	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
325	C₄×D₄	—	2	2	no	—
326	C₄×D₄	C₂³×C₄₁	1	2	yes	—
327	#117	—	2	2	no	—
328	#117	—	2	4	no	—
329	#117	—	2	4	no	—
330	#117	—	2	1	no	—
331	#117	C₂³×C₄₁	1	1	yes	characteristic
332	#117	C₂³×C₄₁	1	2	yes	—
333	C₂×C₄⋊C₄	—	2	2	no	—
334	C₂×C₄²	—	2	1	no	—
335	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
336	#107	C₂³×C₄₁	1	4	yes	—
337	#106	C₂³×C₄₁	1	4	yes	—
338	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
339	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
340	C₄⋊C₈	C₂³×C₄₁	1	8	yes	—
341	#103	C₂³×C₄₁	1	4	yes	—
342	#103	C₂³×C₄₁	1	4	yes	—
343	#103	C₂³×C₄₁	1	8	yes	—
344	#103	C₂³×C₄₁	1	4	yes	—
345	#103	C₂³×C₄₁	1	8	yes	—
346	#102	C₂³×C₄₁	1	4	yes	—
347	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
348	#97	C₂³×C₄₁	1	4	yes	—
349	C₄×C₈	C₂³×C₄₁	1	4	yes	—
350	C₄×C₈	C₂³×C₄₁	1	4	yes	—
351	#41	—	4	2	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	4	4	no	—
355	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
356	C₂×Q₈	C₂⁴×C₄₁	1	4	yes	—
357	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
358	C₂×Q₈	C₂⁴×C₄₁	1	4	yes	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
365	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
366	Q₁₆	—	4	8	no	—
367	Q₁₆	—	4	8	no	—
368	Q₁₆	—	4	4	no	—
369	SD₁₆	—	4	4	no	—
370	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
371	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
372	C₄⋊C₄	—	2	4	no	—
373	C₄⋊C₄	—	2	4	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	8	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	8	no	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	8	no	—
382	C₄⋊C₄	—	2	8	no	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	2	8	no	—
385	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
386	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
387	C₄⋊C₄	C₂×D₄×C₄₁	1	8	yes	—
388	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
389	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
390	C₂²⋊C₄	—	2	1	no	—
391	C₂²⋊C₄	—	2	4	no	—
392	C₂²⋊C₄	—	2	2	no	—
393	C₂²⋊C₄	—	2	8	no	—
394	C₂²⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
395	C₄²	—	2	1	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	8	no	—
398	C₄²	—	2	4	no	—
399	C₄²	—	2	8	no	—
400	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
401	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
402	C₄²	C₂⁴×C₄₁	1	2	yes	—
403	C₄²	C₂⁴×C₄₁	1	4	yes	—
404	C₂³	—	2	1	no	—
405	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
406	Q₈	—	2	8	no	—
407	Q₈	—	2	4	no	—
408	Q₈	—	2	4	no	—
409	Q₈	—	2	8	no	—
410	Q₈	—	2	2	no	—
411	Q₈	—	4	4	no	—
412	Q₈	—	4	4	no	—
413	D₄	—	2	2	no	—
414	D₄	—	4	2	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	4	4	no	—
425	C₂×C₄	C₂²×D₄×C₄₁	1	8	yes	—
426	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
427	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
428	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
429	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
430	C₈	—	2	4	no	—
431	C₈	—	2	4	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	4	1	no	—
436	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
437	C₄	—	2	2	no	—
438	C₄	—	2	8	no	—
439	C₄	—	2	1	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	4	no	—
442	C₄	—	4	1	no	—
443	C₄	—	4	4	no	—
444	C₄	—	4	4	no	—
445	C₄	C₄₁×#578	1	4	yes	—
446	C₄	C₄₁×#585	1	2	yes	—
447	C₂	—	4	1	no	—
448	C₂	—	8	1	no	—
449	C₂	C₄₁×#3487	1	1	yes	characteristic
450	C₂	C₂×C₄₁×#578	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
prime radical	C₂×#41×C₄₁	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₄₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3556	C₂	semidirect
3. C₄₁×#3398	C₂	semidirect
4. C₄₁×#3395	C₂	semidirect
5. C₄₁×#3374	C₂	semidirect
6. C₄₁×#3364	C₂	semidirect
8. C₄₁×#3209	C₂	semidirect
9. C₄₁×#3127	C₂	semidirect
11. C₄₁×#2986	C₂	semidirect
206. #61936	C₄₁	direct (N × H)
222. #3556	C₂×C₄₁	semidirect
224. #3398	C₂×C₄₁	semidirect
225. #3395	C₂×C₄₁	semidirect
226. #3374	C₂×C₄₁	semidirect
227. #3364	C₂×C₄₁	semidirect
229. #3209	C₂×C₄₁	semidirect
230. #3127	C₂×C₄₁	semidirect
232. #2986	C₂×C₄₁	semidirect
281. C₄₁	#61936	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×#3556	2
C₄₁×#3509	2
C₄₁×#3398	2
C₄₁×#3395	2
C₄₁×#3374	2
C₄₁×#3364	2
C₄₁×#3223	2
C₄₁×#3209	2
C₄₁×#3127	2
C₄₁×#3107	2
C₄₁×#2986	2
#61936	41

Subgroups — C41×#61936 #23838137

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61936 #23838137