Subgroups — C₄₁×#61435 #23837636

Order 10496.

1852 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3482	C₂	1	2	yes	maximal, complemented
2	C₄₁×#3395	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×D₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#3359	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3342	C₂	1	3	yes	maximal, complemented
6	C₄₁×#3302	C₂	1	6	yes	maximal, complemented
7	C₄₁×#3283	C₂	1	3	yes	maximal, complemented
8	C₄₁×#3170	C₂	1	3	yes	maximal, complemented
9	C₄₁×#3107	C₂	1	6	yes	maximal, complemented
10	C₈×#41×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#135×C₄₁	C₂	1	3	yes	maximal, complemented
12	C₂×#135×C₄₁	C₂²	1	3	yes	—
13	C₄₁×#557	C₂²	1	2	yes	—
14	C₄₁×#556	C₂²	1	6	yes	—
15	C₄₁×#552	—	2	6	no	—
16	D₄×Q₈×C₄₁	C₂²	1	2	yes	—
17	C₄₁×#548	—	2	2	no	—
18	C₄₁×#547	C₂²	1	6	yes	—
19	C₄₁×#533	C₂²	1	6	yes	—
20	C₄₁×#529	—	2	6	no	—
21	C₄×#41×C₄₁	C₂²	1	6	yes	—
22	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₄₁	—	2	2	no	—
24	C₄₁×#500	C₂²	1	3	yes	—
25	C₄₁×#494	C₂²	1	3	yes	—
26	C₄₁×#487	C₂²	1	6	yes	—
27	C₄₁×#485	C₂²	1	12	yes	—
28	C₄₁×#475	C₂²	1	6	yes	—
29	C₄₁×#474	C₂²	1	6	yes	—
30	C₄₁×#467	C₂²	1	6	yes	—
31	C₄₁×#467	C₂²	1	6	yes	—
32	C₄₁×#462	C₂²	1	6	yes	—
33	C₄₁×#461	C₂²	1	6	yes	—
34	C₄₁×#452	C₂²	1	12	yes	—
35	C₈×Q₈×C₄₁	C₂²	1	1	yes	characteristic
36	C₈×Q₈×C₄₁	C₂²	1	1	yes	characteristic
37	C₄×Q₁₆×C₄₁	C₂²	1	3	yes	—
38	C₄×Q₁₆×C₄₁	C₂²	1	6	yes	—
39	C₄×Q₁₆×C₄₁	C₂²	1	3	yes	—
40	C₄×SD₁₆×C₄₁	C₂²	1	6	yes	—
41	C₄×SD₁₆×C₄₁	C₂²	1	6	yes	—
42	C₄×D₈×C₄₁	C₂²	1	3	yes	—
43	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic
44	C₈×D₄×C₄₁	C₂²	1	3	yes	—
45	C₈×D₄×C₄₁	C₂²	1	3	yes	—
46	C₄₁×#431	C₂²	1	3	yes	—
47	C₄₁×#427	C₂²	1	3	yes	—
48	C₄₁×#416	C₂²	1	6	yes	—
49	C₂×C₄×C₈×C₄₁	C₂²	1	3	yes	—
50	C₂×#41×C₄₁	D₄	1	1	yes	characteristic
51	C₂×#41×C₄₁	C₂³	1	6	yes	—
52	C₂²×Q₈×C₄₁	—	2	2	no	—
53	#135×C₄₁	—	2	12	no	—
54	C₂×Q₁₆×C₄₁	C₂³	1	3	yes	—
55	C₂×Q₁₆×C₄₁	C₂³	1	6	yes	—
56	C₂×SD₁₆×C₄₁	C₂³	1	6	yes	—
57	C₂×D₈×C₄₁	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₄₁	C₂³	1	3	yes	—
59	C₂²×C₈×C₄₁	C₂³	1	3	yes	—
60	C₄⋊Q₈×C₄₁	C₂³	1	6	yes	—
61	C₄⋊Q₈×C₄₁	C₂³	1	6	yes	—
62	#126×C₄₁	—	2	12	no	—
63	#125×C₄₁	—	2	6	no	—
64	#125×C₄₁	—	2	6	no	—
65	#124×C₄₁	—	2	6	no	—
66	#123×C₄₁	—	2	12	no	—
67	C₂²⋊Q₈×C₄₁	—	2	6	no	—
68	C₂²⋊Q₈×C₄₁	—	2	6	no	—
69	C₂²⋊Q₈×C₄₁	C₂³	1	12	yes	—
70	#121×C₄₁	—	2	6	no	—
71	C₄×Q₈×C₄₁	—	2	2	no	—
72	C₄×Q₈×C₄₁	—	2	6	no	—
73	C₄×Q₈×C₄₁	—	2	6	no	—
74	C₄×Q₈×C₄₁	D₄	1	1	yes	characteristic
75	C₄×Q₈×C₄₁	C₂³	1	6	yes	—
76	C₄×Q₈×C₄₁	C₂³	1	6	yes	—
77	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
78	C₄×D₄×C₄₁	—	2	6	no	—
79	C₄×D₄×C₄₁	—	2	6	no	—
80	C₄×D₄×C₄₁	D₄	1	3	yes	—
81	C₄×D₄×C₄₁	C₂³	1	2	yes	—
82	C₄×D₄×C₄₁	C₂³	1	6	yes	—
83	C₄×D₄×C₄₁	C₂³	1	3	yes	—
84	#117×C₄₁	—	2	6	no	—
85	#117×C₄₁	—	2	6	no	—
86	#117×C₄₁	D₄	1	3	yes	—
87	#117×C₄₁	C₂³	1	6	yes	—
88	C₂×C₄⋊C₄×C₄₁	—	2	6	no	—
89	C₂×C₄²×C₄₁	—	2	6	no	—
90	C₂×C₄²×C₄₁	C₂³	1	3	yes	—
91	#107×C₄₁	C₂³	1	3	yes	—
92	#107×C₄₁	C₂³	1	6	yes	—
93	#107×C₄₁	C₂³	1	1	yes	characteristic
94	#106×C₄₁	C₂³	1	6	yes	—
95	C₄⋊C₈×C₄₁	C₂³	1	3	yes	—
96	C₄⋊C₈×C₄₁	C₂³	1	3	yes	—
97	#103×C₄₁	C₂³	1	6	yes	—
98	#103×C₄₁	C₂³	1	6	yes	—
99	#103×C₄₁	C₂³	1	12	yes	—
100	#102×C₄₁	C₂³	1	2	yes	—
101	#102×C₄₁	C₂³	1	6	yes	—
102	C₂²⋊C₈×C₄₁	C₂³	1	6	yes	—
103	C₄×C₈×C₄₁	C₂³	1	3	yes	—
104	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
105	C₄×C₈×C₄₁	C₂³	1	3	yes	—
106	C₄×C₈×C₄₁	C₂³	1	3	yes	—
107	#41×C₄₁	—	2	4	no	—
108	#41×C₄₁	—	2	12	no	—
109	#41×C₄₁	—	4	6	no	—
110	C₂×Q₈×C₄₁	—	2	6	no	—
111	C₂×Q₈×C₄₁	—	4	8	no	—
112	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
113	C₂×Q₈×C₄₁	C₂⁴	1	6	yes	—
114	C₂×D₄×C₄₁	—	2	6	no	—
115	C₂×D₄×C₄₁	C₂×D₄	1	3	yes	—
116	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
117	C₂²×C₄×C₄₁	—	2	6	no	—
118	C₂²×C₄×C₄₁	—	2	6	no	—
119	C₂²×C₄×C₄₁	—	2	2	no	—
120	C₂²×C₄×C₄₁	C₂×D₄	1	3	yes	—
121	C₂²×C₄×C₄₁	C₂×D₄	1	3	yes	—
122	C₂²×C₄×C₄₁	C₂⁴	1	3	yes	—
123	Q₁₆×C₄₁	—	2	6	no	—
124	Q₁₆×C₄₁	—	4	6	no	—
125	SD₁₆×C₄₁	—	2	12	no	—
126	D₈×C₄₁	#41	1	4	yes	complemented
127	C₂×C₈×C₄₁	—	2	6	no	—
128	C₂×C₈×C₄₁	—	4	3	no	—
129	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
130	C₂×C₈×C₄₁	C₂⁴	1	3	yes	—
131	C₂×C₈×C₄₁	C₂⁴	1	3	yes	—
132	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
133	C₄⋊C₄×C₄₁	—	2	6	no	—
134	C₄⋊C₄×C₄₁	—	2	12	no	—
135	C₄⋊C₄×C₄₁	—	2	6	no	—
136	C₄⋊C₄×C₄₁	—	2	6	no	—
137	C₄⋊C₄×C₄₁	—	2	6	no	—
138	C₄⋊C₄×C₄₁	—	2	6	no	—
139	C₄⋊C₄×C₄₁	C₂×D₄	1	3	yes	—
140	C₄⋊C₄×C₄₁	C₂×D₄	1	3	yes	—
141	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
142	C₄⋊C₄×C₄₁	C₂⁴	1	6	yes	—
143	C₂²⋊C₄×C₄₁	—	2	12	no	—
144	C₂²⋊C₄×C₄₁	—	2	6	no	—
145	C₂²⋊C₄×C₄₁	—	2	2	no	—
146	C₂²⋊C₄×C₄₁	—	2	6	no	—
147	C₂²⋊C₄×C₄₁	C₂×D₄	1	6	yes	—
148	C₄²×C₄₁	—	2	6	no	—
149	C₄²×C₄₁	—	2	6	no	—
150	C₄²×C₄₁	—	2	6	no	—
151	C₄²×C₄₁	C₂×D₄	1	3	yes	—
152	C₄²×C₄₁	C₂×D₄	1	3	yes	—
153	C₄²×C₄₁	C₂⁴	1	3	yes	—
154	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
155	C₂³×C₄₁	—	2	2	no	—
156	C₂³×C₄₁	C₂²×D₄	1	3	yes	—
157	Q₈×C₄₁	—	2	6	no	—
158	Q₈×C₄₁	—	2	6	no	—
159	Q₈×C₄₁	—	4	12	no	—
160	Q₈×C₄₁	#135	1	4	yes	complemented
161	D₄×C₄₁	—	2	6	no	—
162	D₄×C₄₁	—	2	2	no	—
163	D₄×C₄₁	—	4	12	no	—
164	D₄×C₄₁	C₂×#41	1	4	yes	—
165	C₂×C₄×C₄₁	—	2	6	no	—
166	C₂×C₄×C₄₁	—	2	6	no	—
167	C₂×C₄×C₄₁	—	2	3	no	—
168	C₂×C₄×C₄₁	—	2	3	no	—
169	C₂×C₄×C₄₁	—	2	2	no	—
170	C₂×C₄×C₄₁	—	2	6	no	—
171	C₂×C₄×C₄₁	—	2	6	no	—
172	C₂×C₄×C₄₁	—	4	12	no	—
173	C₂×C₄×C₄₁	—	4	12	no	—
174	C₂×C₄×C₄₁	—	4	4	no	—
175	C₂×C₄×C₄₁	C₂²×D₄	1	3	yes	—
176	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₁	C₂²×D₄	1	3	yes	—
178	C₂×C₄×C₄₁	C₂²×D₄	1	3	yes	—
179	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
181	C₈×C₄₁	—	2	3	no	—
182	C₈×C₄₁	—	2	1	no	—
183	C₈×C₄₁	—	2	3	no	—
184	C₈×C₄₁	C₂×#41	1	2	yes	—
185	#61435	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂²×C₄₁	—	2	3	no	—
187	C₂²×C₄₁	—	2	4	no	—
188	C₂²×C₄₁	—	2	3	no	—
189	C₂²×C₄₁	—	2	3	no	—
190	C₂²×C₄₁	—	4	2	no	—
191	C₂²×C₄₁	—	4	2	no	—
192	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
193	C₄×C₄₁	—	2	3	no	—
194	C₄×C₄₁	—	2	1	no	—
195	C₄×C₄₁	—	2	3	no	—
196	C₄×C₄₁	—	4	6	no	—
197	C₄×C₄₁	—	4	6	no	—
198	C₄×C₄₁	—	4	2	no	—
199	C₄×C₄₁	C₂×#135	1	6	yes	—
200	C₄×C₄₁	#578	1	2	yes	—
201	C₄×C₄₁	C₂²×#41	1	1	yes	characteristic
202	C₄×C₄₁	#585	1	1	yes	characteristic
203	#3482	C₂×C₄₁	1	2	yes	complemented
204	#3395	C₂×C₄₁	1	1	yes	characteristic, complemented
205	Q₈×D₈	C₂×C₄₁	1	1	yes	characteristic, complemented
206	#3359	C₂×C₄₁	1	2	yes	complemented
207	#3342	C₂×C₄₁	1	3	yes	complemented
208	#3302	C₂×C₄₁	1	6	yes	complemented
209	#3283	C₂×C₄₁	1	3	yes	complemented
210	#3170	C₂×C₄₁	1	3	yes	complemented
211	#3107	C₂×C₄₁	1	6	yes	complemented
212	C₈×#41	C₂×C₄₁	1	1	yes	characteristic, complemented
213	C₄×#135	C₂×C₄₁	1	3	yes	complemented
214	C₂×C₄₁	—	4	3	no	—
215	C₂×C₄₁	—	4	4	no	—
216	C₂×C₄₁	D₄×#41	1	1	yes	characteristic
217	C₂×C₄₁	C₂²×#135	1	1	yes	characteristic
218	C₂×C₄₁	C₂×#578	1	1	yes	characteristic
219	C₂×#135	C₂²×C₄₁	1	3	yes	—
220	#557	C₂²×C₄₁	1	2	yes	—
221	#556	C₂²×C₄₁	1	6	yes	—
222	#552	—	2	6	no	—
223	D₄×Q₈	C₂²×C₄₁	1	2	yes	—
224	#548	—	2	2	no	—
225	#547	C₂²×C₄₁	1	6	yes	—
226	#533	C₂²×C₄₁	1	6	yes	—
227	#529	—	2	6	no	—
228	C₄×#41	C₂²×C₄₁	1	6	yes	—
229	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
230	C₂×C₄×Q₈	—	2	2	no	—
231	#500	C₂²×C₄₁	1	3	yes	—
232	#494	C₂²×C₄₁	1	3	yes	—
233	#487	C₂²×C₄₁	1	6	yes	—
234	#485	C₂²×C₄₁	1	12	yes	—
235	#475	C₂²×C₄₁	1	6	yes	—
236	#474	C₂²×C₄₁	1	6	yes	—
237	#467	C₂²×C₄₁	1	6	yes	—
238	#467	C₂²×C₄₁	1	6	yes	—
239	#462	C₂²×C₄₁	1	6	yes	—
240	#461	C₂²×C₄₁	1	6	yes	—
241	#452	C₂²×C₄₁	1	12	yes	—
242	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic
243	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic
244	C₄×Q₁₆	C₂²×C₄₁	1	3	yes	—
245	C₄×Q₁₆	C₂²×C₄₁	1	6	yes	—
246	C₄×Q₁₆	C₂²×C₄₁	1	3	yes	—
247	C₄×SD₁₆	C₂²×C₄₁	1	6	yes	—
248	C₄×SD₁₆	C₂²×C₄₁	1	6	yes	—
249	C₄×D₈	C₂²×C₄₁	1	3	yes	—
250	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic
251	C₈×D₄	C₂²×C₄₁	1	3	yes	—
252	C₈×D₄	C₂²×C₄₁	1	3	yes	—
253	#431	C₂²×C₄₁	1	3	yes	—
254	#427	C₂²×C₄₁	1	3	yes	—
255	#416	C₂²×C₄₁	1	6	yes	—
256	C₂×C₄×C₈	C₂²×C₄₁	1	3	yes	—
257	C₄₁	#61435	1	1	yes	characteristic, direct product factor, Sylow
258	C₂×#41	D₄×C₄₁	1	1	yes	characteristic
259	C₂×#41	C₂³×C₄₁	1	6	yes	—
260	C₂²×Q₈	—	2	2	no	—
261	#135	—	2	12	no	—
262	C₂×Q₁₆	C₂³×C₄₁	1	3	yes	—
263	C₂×Q₁₆	C₂³×C₄₁	1	6	yes	—
264	C₂×SD₁₆	C₂³×C₄₁	1	6	yes	—
265	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
266	C₂²×C₈	C₂³×C₄₁	1	3	yes	—
267	C₂²×C₈	C₂³×C₄₁	1	3	yes	—
268	C₄⋊Q₈	C₂³×C₄₁	1	6	yes	—
269	C₄⋊Q₈	C₂³×C₄₁	1	6	yes	—
270	#126	—	2	12	no	—
271	#125	—	2	6	no	—
272	#125	—	2	6	no	—
273	#124	—	2	6	no	—
274	#123	—	2	12	no	—
275	C₂²⋊Q₈	—	2	6	no	—
276	C₂²⋊Q₈	—	2	6	no	—
277	C₂²⋊Q₈	C₂³×C₄₁	1	12	yes	—
278	#121	—	2	6	no	—
279	C₄×Q₈	—	2	2	no	—
280	C₄×Q₈	—	2	6	no	—
281	C₄×Q₈	—	2	6	no	—
282	C₄×Q₈	D₄×C₄₁	1	1	yes	characteristic
283	C₄×Q₈	C₂³×C₄₁	1	6	yes	—
284	C₄×Q₈	C₂³×C₄₁	1	6	yes	—
285	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
286	C₄×D₄	—	2	6	no	—
287	C₄×D₄	—	2	6	no	—
288	C₄×D₄	D₄×C₄₁	1	3	yes	—
289	C₄×D₄	C₂³×C₄₁	1	2	yes	—
290	C₄×D₄	C₂³×C₄₁	1	6	yes	—
291	C₄×D₄	C₂³×C₄₁	1	3	yes	—
292	#117	—	2	6	no	—
293	#117	—	2	6	no	—
294	#117	D₄×C₄₁	1	3	yes	—
295	#117	C₂³×C₄₁	1	6	yes	—
296	C₂×C₄⋊C₄	—	2	6	no	—
297	C₂×C₄²	—	2	6	no	—
298	C₂×C₄²	C₂³×C₄₁	1	3	yes	—
299	#107	C₂³×C₄₁	1	1	yes	characteristic
300	#107	C₂³×C₄₁	1	3	yes	—
301	#107	C₂³×C₄₁	1	6	yes	—
302	#106	C₂³×C₄₁	1	6	yes	—
303	C₄⋊C₈	C₂³×C₄₁	1	3	yes	—
304	C₄⋊C₈	C₂³×C₄₁	1	3	yes	—
305	#103	C₂³×C₄₁	1	6	yes	—
306	#103	C₂³×C₄₁	1	6	yes	—
307	#103	C₂³×C₄₁	1	12	yes	—
308	#102	C₂³×C₄₁	1	2	yes	—
309	#102	C₂³×C₄₁	1	6	yes	—
310	C₂²⋊C₈	C₂³×C₄₁	1	6	yes	—
311	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
312	C₄×C₈	C₂³×C₄₁	1	3	yes	—
313	C₄×C₈	C₂³×C₄₁	1	3	yes	—
314	C₄×C₈	C₂³×C₄₁	1	3	yes	—
315	#41	—	2	4	no	—
316	#41	—	2	12	no	—
317	#41	—	4	6	no	—
318	C₂×Q₈	—	2	6	no	—
319	C₂×Q₈	—	4	8	no	—
320	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
321	C₂×Q₈	C₂⁴×C₄₁	1	6	yes	—
322	C₂×D₄	—	2	6	no	—
323	C₂×D₄	C₂×D₄×C₄₁	1	3	yes	—
324	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	6	no	—
327	C₂²×C₄	—	2	6	no	—
328	C₂²×C₄	C₂×D₄×C₄₁	1	3	yes	—
329	C₂²×C₄	C₂×D₄×C₄₁	1	3	yes	—
330	C₂²×C₄	C₂⁴×C₄₁	1	3	yes	—
331	Q₁₆	—	2	6	no	—
332	Q₁₆	—	4	6	no	—
333	SD₁₆	—	2	12	no	—
334	D₈	#41×C₄₁	1	4	yes	complemented
335	C₂×C₈	—	2	6	no	—
336	C₂×C₈	—	4	3	no	—
337	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
338	C₂×C₈	C₂⁴×C₄₁	1	3	yes	—
339	C₂×C₈	C₂⁴×C₄₁	1	3	yes	—
340	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
341	C₄⋊C₄	—	2	6	no	—
342	C₄⋊C₄	—	2	12	no	—
343	C₄⋊C₄	—	2	6	no	—
344	C₄⋊C₄	—	2	6	no	—
345	C₄⋊C₄	—	2	6	no	—
346	C₄⋊C₄	—	2	6	no	—
347	C₄⋊C₄	C₂×D₄×C₄₁	1	3	yes	—
348	C₄⋊C₄	C₂×D₄×C₄₁	1	3	yes	—
349	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
350	C₄⋊C₄	C₂⁴×C₄₁	1	6	yes	—
351	C₂²⋊C₄	—	2	12	no	—
352	C₂²⋊C₄	—	2	6	no	—
353	C₂²⋊C₄	—	2	2	no	—
354	C₂²⋊C₄	—	2	6	no	—
355	C₂²⋊C₄	C₂×D₄×C₄₁	1	6	yes	—
356	C₄²	—	2	6	no	—
357	C₄²	—	2	6	no	—
358	C₄²	—	2	6	no	—
359	C₄²	C₂×D₄×C₄₁	1	3	yes	—
360	C₄²	C₂×D₄×C₄₁	1	3	yes	—
361	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
362	C₄²	C₂⁴×C₄₁	1	3	yes	—
363	C₂³	—	2	2	no	—
364	C₂³	C₂²×D₄×C₄₁	1	3	yes	—
365	Q₈	—	2	6	no	—
366	Q₈	—	2	6	no	—
367	Q₈	—	4	12	no	—
368	Q₈	#135×C₄₁	1	4	yes	complemented
369	D₄	—	2	6	no	—
370	D₄	—	2	2	no	—
371	D₄	—	4	12	no	—
372	D₄	C₂×#41×C₄₁	1	4	yes	—
373	C₂×C₄	—	2	6	no	—
374	C₂×C₄	—	2	6	no	—
375	C₂×C₄	—	2	3	no	—
376	C₂×C₄	—	2	3	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	6	no	—
379	C₂×C₄	—	2	6	no	—
380	C₂×C₄	—	4	12	no	—
381	C₂×C₄	—	4	12	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	C₂²×D₄×C₄₁	1	3	yes	—
384	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
385	C₂×C₄	C₂²×D₄×C₄₁	1	3	yes	—
386	C₂×C₄	C₂²×D₄×C₄₁	1	3	yes	—
387	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
388	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
389	C₈	—	2	3	no	—
390	C₈	—	2	1	no	—
391	C₈	—	2	3	no	—
392	C₈	C₂×#41×C₄₁	1	2	yes	—
393	C₂²	—	2	3	no	—
394	C₂²	—	2	3	no	—
395	C₂²	—	2	3	no	—
396	C₂²	—	2	4	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	2	3	no	—
402	C₄	—	2	3	no	—
403	C₄	—	4	6	no	—
404	C₄	—	4	2	no	—
405	C₄	—	4	6	no	—
406	C₄	C₂×#135×C₄₁	1	6	yes	—
407	C₄	C₄₁×#578	1	2	yes	—
408	C₄	C₂²×#41×C₄₁	1	1	yes	characteristic
409	C₄	C₄₁×#585	1	1	yes	characteristic
410	C₂	—	4	3	no	—
411	C₂	—	4	4	no	—
412	C₂	D₄×#41×C₄₁	1	1	yes	characteristic
413	C₂	C₂²×#135×C₄₁	1	1	yes	characteristic
414	C₂	C₂×C₄₁×#578	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3482	C₂	semidirect
2. C₄₁×#3395	C₂	semidirect
3. Q₈×D₈×C₄₁	C₂	semidirect
4. C₄₁×#3359	C₂	semidirect
5. C₄₁×#3342	C₂	semidirect
6. C₄₁×#3302	C₂	semidirect
7. C₄₁×#3283	C₂	semidirect
8. C₄₁×#3170	C₂	semidirect
9. C₄₁×#3107	C₂	semidirect
10. C₈×#41×C₄₁	C₂	semidirect
11. C₄×#135×C₄₁	C₂	semidirect
126. D₈×C₄₁	#41	semidirect
160. Q₈×C₄₁	#135	semidirect
185. #61435	C₄₁	direct (N × H)
203. #3482	C₂×C₄₁	semidirect
204. #3395	C₂×C₄₁	semidirect
205. Q₈×D₈	C₂×C₄₁	semidirect
206. #3359	C₂×C₄₁	semidirect
207. #3342	C₂×C₄₁	semidirect
208. #3302	C₂×C₄₁	semidirect
209. #3283	C₂×C₄₁	semidirect
210. #3170	C₂×C₄₁	semidirect
211. #3107	C₂×C₄₁	semidirect
212. C₈×#41	C₂×C₄₁	semidirect
213. C₄×#135	C₂×C₄₁	semidirect
257. C₄₁	#61435	direct (N × H)
334. D₈	#41×C₄₁	semidirect
368. Q₈	#135×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3482	2
C₄₁×#3395	2
Q₈×D₈×C₄₁	2
C₄₁×#3359	2
C₄₁×#3342	2
C₄₁×#3302	2
C₄₁×#3283	2
C₄₁×#3170	2
C₄₁×#3107	2
C₈×#41×C₄₁	2
C₄×#135×C₄₁	2
#61435	41

Subgroups — C41×#61435 #23837636

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61435 #23837636