Subgroups — C₄₁×#17876 #23794077

Order 10496.

650 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#2988	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2983	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#137×C₄₁	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#1587	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1585	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1584	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1582	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1565	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1476	C₂	1	1	yes	maximal, characteristic
10	C₂×C₄₁×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₄₁	C₄	1	1	yes	characteristic
13	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
15	C₄₁×#446	—	2	1	no	—
16	C₄₁×#446	—	2	1	no	—
17	C₄₁×#446	C₂²	1	2	yes	—
18	C₄₁×#446	C₂²	1	2	yes	—
19	C₈×Q₈×C₄₁	C₂²	1	2	yes	—
20	C₄₁×#441	C₄	1	2	yes	—
21	C₄₁×#440	C₄	1	2	yes	—
22	C₄×Q₁₆×C₄₁	C₂²	1	2	yes	—
23	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	—
24	C₈×D₄×C₄₁	—	2	2	no	—
25	C₈×D₄×C₄₁	C₂²	1	2	yes	—
26	C₄₁×#432	—	2	2	no	—
27	C₄₁×#431	—	2	1	no	—
28	C₄₁×#431	C₂²	1	1	yes	characteristic
29	C₄₁×#431	C₂²	1	1	yes	characteristic
30	C₄₁×#428	C₄	1	1	yes	characteristic
31	C₂×C₄⋊C₈×C₄₁	—	2	1	no	—
32	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
33	C₄₁×#419	C₄	1	1	yes	characteristic
34	C₄₁×#417	C₄	1	1	yes	characteristic
35	C₄×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
37	C₄₁×#335	C₂²	1	2	yes	—
38	C₄₁×#334	C₂²	1	2	yes	—
39	C₄₁×Q₈⋊C₈	C₂²	1	2	yes	—
40	C₄₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
41	C₄₁×Q₈⋊C₈	C₂²	1	2	yes	—
42	C₄₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
43	C₄₁×D₄⋊C₈	C₂²	1	1	yes	characteristic
44	C₄₁×D₄⋊C₈	C₂²	1	1	yes	characteristic
45	C₄₁×#322	C₂²	1	2	yes	—
46	C₄₁×#322	C₂²	1	2	yes	—
47	C₂×#41×C₄₁	C₂×C₄	1	1	yes	characteristic
48	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
49	#137×C₄₁	—	2	4	no	—
50	C₂×Q₁₆×C₄₁	C₂×C₄	1	2	yes	—
51	C₂×SD₁₆×C₄₁	C₂×C₄	1	2	yes	—
52	C₂×M₁₆×C₄₁	C₂×C₄	1	1	yes	characteristic
53	C₂×M₁₆×C₄₁	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₈×C₄₁	—	2	1	no	—
55	C₂²×C₈×C₄₁	—	2	1	no	—
56	C₂²×C₈×C₄₁	—	2	2	no	—
57	C₄×Q₈×C₄₁	—	2	1	no	—
58	C₄×Q₈×C₄₁	—	2	1	no	—
59	C₄×Q₈×C₄₁	C₂×C₄	1	2	yes	—
60	C₄×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
61	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
62	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
63	C₄×D₄×C₄₁	—	2	1	no	—
64	C₄×D₄×C₄₁	—	2	1	no	—
65	C₄×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
66	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
67	#117×C₄₁	—	2	1	no	—
68	#117×C₄₁	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₄₁	—	2	1	no	—
72	C₂×C₄²×C₄₁	—	2	1	no	—
73	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
74	#107×C₄₁	C₂×C₄	1	2	yes	—
75	#106×C₄₁	C₂×C₄	1	2	yes	—
76	C₄⋊C₈×C₄₁	—	2	2	no	—
77	C₄⋊C₈×C₄₁	—	2	2	no	—
78	C₄⋊C₈×C₄₁	—	2	2	no	—
79	C₄⋊C₈×C₄₁	—	2	1	no	—
80	C₄⋊C₈×C₄₁	D₄	1	1	yes	characteristic
81	C₄⋊C₈×C₄₁	D₄	1	1	yes	characteristic
82	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
84	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
85	#103×C₄₁	C₂×C₄	1	2	yes	—
86	#103×C₄₁	C₂×C₄	1	2	yes	—
87	#103×C₄₁	C₂×C₄	1	2	yes	—
88	#102×C₄₁	C₂×C₄	1	2	yes	—
89	C₂²⋊C₈×C₄₁	—	2	1	no	—
90	C₂²⋊C₈×C₄₁	—	2	2	no	—
91	C₂²⋊C₈×C₄₁	D₄	1	2	yes	—
92	#97×C₄₁	—	2	2	no	—
93	#97×C₄₁	—	2	2	no	—
94	#97×C₄₁	C₂×C₄	1	2	yes	—
95	C₄×C₈×C₄₁	—	2	2	no	—
96	C₄×C₈×C₄₁	—	2	1	no	—
97	C₄×C₈×C₄₁	—	2	1	no	—
98	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₄₁	C₂³	1	2	yes	—
101	C₄×C₈×C₄₁	C₂³	1	2	yes	—
102	#41×C₄₁	—	2	2	no	—
103	#41×C₄₁	M₁₆	1	4	yes	—
104	C₂×Q₈×C₄₁	—	2	1	no	—
105	C₂×Q₈×C₄₁	—	2	2	no	—
106	C₂×Q₈×C₄₁	—	2	2	no	—
107	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
108	C₂×Q₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
109	C₂×D₄×C₄₁	—	2	1	no	—
110	C₂×D₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₁	—	2	1	no	—
112	C₂²×C₄×C₄₁	—	2	1	no	—
113	C₂²×C₄×C₄₁	—	2	1	no	—
114	C₂²×C₄×C₄₁	—	2	1	no	—
115	C₂²×C₄×C₄₁	—	2	1	no	—
116	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
119	Q₁₆×C₄₁	—	2	4	no	—
120	SD₁₆×C₄₁	—	2	4	no	—
121	M₁₆×C₄₁	—	2	2	no	—
122	M₁₆×C₄₁	—	2	2	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	2	no	—
127	C₂×C₈×C₄₁	—	2	1	no	—
128	C₂×C₈×C₄₁	—	4	2	no	—
129	C₂×C₈×C₄₁	—	8	2	no	—
130	C₂×C₈×C₄₁	—	8	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	C₂×D₄	1	2	yes	—
135	C₄⋊C₄×C₄₁	—	2	2	no	—
136	C₄⋊C₄×C₄₁	—	2	1	no	—
137	C₄⋊C₄×C₄₁	—	2	1	no	—
138	C₄⋊C₄×C₄₁	—	2	2	no	—
139	C₄⋊C₄×C₄₁	—	2	1	no	—
140	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
141	C₄⋊C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
142	C₄⋊C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
143	C₂²⋊C₄×C₄₁	—	2	1	no	—
144	C₂²⋊C₄×C₄₁	—	2	1	no	—
145	C₂²⋊C₄×C₄₁	—	2	1	no	—
146	C₄²×C₄₁	—	2	1	no	—
147	C₄²×C₄₁	—	2	1	no	—
148	C₄²×C₄₁	—	2	2	no	—
149	C₄²×C₄₁	—	2	1	no	—
150	C₄²×C₄₁	—	2	2	no	—
151	C₄²×C₄₁	C₂²×C₄	1	1	yes	characteristic
152	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₄₁	#41	1	1	yes	characteristic
154	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
155	C₂³×C₄₁	—	2	1	no	—
156	C₂³×C₄₁	C₄×D₄	1	1	yes	characteristic
157	Q₈×C₄₁	—	2	1	no	—
158	Q₈×C₄₁	—	2	2	no	—
159	Q₈×C₄₁	—	2	2	no	—
160	Q₈×C₄₁	—	4	2	no	—
161	Q₈×C₄₁	C₂×M₁₆	1	2	yes	—
162	D₄×C₄₁	—	2	4	no	—
163	D₄×C₄₁	—	2	1	no	—
164	D₄×C₄₁	C₂×M₁₆	1	2	yes	—
165	C₂×C₄×C₄₁	—	2	1	no	—
166	C₂×C₄×C₄₁	—	2	1	no	—
167	C₂×C₄×C₄₁	—	2	1	no	—
168	C₂×C₄×C₄₁	—	2	4	no	—
169	C₂×C₄×C₄₁	—	2	1	no	—
170	C₂×C₄×C₄₁	—	2	1	no	—
171	C₂×C₄×C₄₁	—	2	2	no	—
172	C₂×C₄×C₄₁	—	2	2	no	—
173	C₂×C₄×C₄₁	—	4	1	no	—
174	C₂×C₄×C₄₁	—	4	2	no	—
175	C₂×C₄×C₄₁	—	4	1	no	—
176	C₂×C₄×C₄₁	—	4	1	no	—
177	C₂×C₄×C₄₁	—	8	1	no	—
178	C₂×C₄×C₄₁	—	8	1	no	—
179	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
180	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₄₁	C₂×M₁₆	1	2	yes	—
183	C₂×C₄×C₄₁	#131	1	2	yes	—
184	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
187	C₈×C₄₁	—	2	2	no	—
188	C₈×C₄₁	—	2	2	no	—
189	C₈×C₄₁	—	2	2	no	—
190	C₈×C₄₁	—	2	2	no	—
191	C₈×C₄₁	—	2	2	no	—
192	C₈×C₄₁	—	4	1	no	—
193	C₈×C₄₁	—	4	1	no	—
194	C₈×C₄₁	—	4	2	no	—
195	C₈×C₄₁	—	4	1	no	—
196	#17876	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₂²×C₄₁	—	2	1	no	—
198	C₂²×C₄₁	—	2	1	no	—
199	C₂²×C₄₁	—	2	2	no	—
200	C₂²×C₄₁	—	4	1	no	—
201	C₂²×C₄₁	—	4	1	no	—
202	C₂²×C₄₁	#435	1	2	yes	—
203	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
204	C₄×C₄₁	—	2	2	no	—
205	C₄×C₄₁	—	2	1	no	—
206	C₄×C₄₁	—	2	1	no	—
207	C₄×C₄₁	—	2	1	no	—
208	C₄×C₄₁	—	4	2	no	—
209	C₄×C₄₁	—	4	1	no	—
210	C₄×C₄₁	—	4	1	no	—
211	C₄×C₄₁	—	4	2	no	—
212	C₄×C₄₁	#435	1	2	yes	—
213	C₄×C₄₁	C₂²×M₁₆	1	1	yes	characteristic
214	C₄×C₄₁	C₂×#131	1	1	yes	characteristic
215	C₄×C₄₁	#577	1	1	yes	characteristic
216	C₄×C₄₁	#578	1	1	yes	characteristic
217	#2988	C₂×C₄₁	1	1	yes	characteristic
218	#2983	C₂×C₄₁	1	1	yes	characteristic, complemented
219	C₄×#137	C₂×C₄₁	1	1	yes	characteristic
220	#1587	C₂×C₄₁	1	2	yes	complemented
221	#1585	C₂×C₄₁	1	2	yes	complemented
222	#1584	C₂×C₄₁	1	2	yes	complemented
223	#1582	C₂×C₄₁	1	2	yes	complemented
224	#1565	C₂×C₄₁	1	1	yes	characteristic, complemented
225	#1476	C₂×C₄₁	1	1	yes	characteristic
226	C₂×Q₈⋊C₈	C₂×C₄₁	1	1	yes	characteristic, complemented
227	#1451	C₂×C₄₁	1	1	yes	characteristic, complemented
228	C₂×C₄₁	—	2	2	no	—
229	C₂×C₄₁	—	4	2	no	—
230	C₂×C₄₁	C₂×#435	1	1	yes	characteristic
231	C₂×C₄₁	#2947	1	1	yes	characteristic
232	C₂×C₄₁	#2956	1	1	yes	characteristic
233	C₂×#137	C₄×C₄₁	1	1	yes	characteristic
234	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
235	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
236	#446	—	2	1	no	—
237	#446	—	2	1	no	—
238	#446	C₂²×C₄₁	1	2	yes	—
239	#446	C₂²×C₄₁	1	2	yes	—
240	C₈×Q₈	C₂²×C₄₁	1	2	yes	—
241	#441	C₄×C₄₁	1	2	yes	—
242	#440	C₄×C₄₁	1	2	yes	—
243	C₄×Q₁₆	C₂²×C₄₁	1	2	yes	—
244	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	—
245	C₈×D₄	—	2	2	no	—
246	C₈×D₄	C₂²×C₄₁	1	2	yes	—
247	#432	—	2	2	no	—
248	#431	—	2	1	no	—
249	#431	C₂²×C₄₁	1	1	yes	characteristic
250	#431	C₂²×C₄₁	1	1	yes	characteristic
251	#428	C₄×C₄₁	1	1	yes	characteristic
252	C₂×C₄⋊C₈	—	2	1	no	—
253	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
254	#419	C₄×C₄₁	1	1	yes	characteristic
255	#417	C₄×C₄₁	1	1	yes	characteristic
256	C₄×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
257	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
258	#335	C₂²×C₄₁	1	2	yes	—
259	#334	C₂²×C₄₁	1	2	yes	—
260	Q₈⋊C₈	C₂²×C₄₁	1	2	yes	—
261	Q₈⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
262	Q₈⋊C₈	C₂²×C₄₁	1	2	yes	—
263	Q₈⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
264	D₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
265	D₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
266	#322	C₂²×C₄₁	1	2	yes	—
267	#322	C₂²×C₄₁	1	2	yes	—
268	C₄₁	#17876	1	1	yes	characteristic, direct product factor, Sylow
269	C₂×#41	C₂×C₄×C₄₁	1	1	yes	characteristic
270	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
271	#137	—	2	4	no	—
272	C₂×Q₁₆	C₂×C₄×C₄₁	1	2	yes	—
273	C₂×SD₁₆	C₂×C₄×C₄₁	1	2	yes	—
274	C₂×M₁₆	C₂×C₄×C₄₁	1	1	yes	characteristic
275	C₂×M₁₆	C₂×C₄×C₄₁	1	1	yes	characteristic
276	C₂²×C₈	—	2	1	no	—
277	C₂²×C₈	—	2	1	no	—
278	C₂²×C₈	—	2	2	no	—
279	C₄×Q₈	—	2	1	no	—
280	C₄×Q₈	—	2	1	no	—
281	C₄×Q₈	C₂×C₄×C₄₁	1	2	yes	—
282	C₄×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
283	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
284	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
285	C₄×D₄	—	2	1	no	—
286	C₄×D₄	—	2	1	no	—
287	C₄×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
288	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
289	#117	—	2	1	no	—
290	#117	C₂×C₄×C₄₁	1	1	yes	characteristic
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
293	C₂×C₄²	—	2	1	no	—
294	C₂×C₄²	—	2	1	no	—
295	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
296	#107	C₂×C₄×C₄₁	1	2	yes	—
297	#106	C₂×C₄×C₄₁	1	2	yes	—
298	C₄⋊C₈	—	2	2	no	—
299	C₄⋊C₈	—	2	2	no	—
300	C₄⋊C₈	—	2	2	no	—
301	C₄⋊C₈	—	2	1	no	—
302	C₄⋊C₈	D₄×C₄₁	1	1	yes	characteristic
303	C₄⋊C₈	D₄×C₄₁	1	1	yes	characteristic
304	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
305	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
306	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
307	#103	C₂×C₄×C₄₁	1	2	yes	—
308	#103	C₂×C₄×C₄₁	1	2	yes	—
309	#103	C₂×C₄×C₄₁	1	2	yes	—
310	#102	C₂×C₄×C₄₁	1	2	yes	—
311	C₂²⋊C₈	—	2	1	no	—
312	C₂²⋊C₈	—	2	2	no	—
313	C₂²⋊C₈	D₄×C₄₁	1	2	yes	—
314	#97	—	2	2	no	—
315	#97	—	2	2	no	—
316	#97	C₂×C₄×C₄₁	1	2	yes	—
317	C₄×C₈	—	2	2	no	—
318	C₄×C₈	—	2	1	no	—
319	C₄×C₈	—	2	1	no	—
320	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
321	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
322	C₄×C₈	C₂³×C₄₁	1	2	yes	—
323	C₄×C₈	C₂³×C₄₁	1	2	yes	—
324	#41	—	2	2	no	—
325	#41	M₁₆×C₄₁	1	4	yes	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
330	C₂×Q₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
340	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
341	Q₁₆	—	2	4	no	—
342	SD₁₆	—	2	4	no	—
343	M₁₆	—	2	2	no	—
344	M₁₆	—	2	2	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	4	2	no	—
351	C₂×C₈	—	8	2	no	—
352	C₂×C₈	—	8	1	no	—
353	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
354	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
355	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
356	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
363	C₄⋊C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
364	C₄⋊C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
365	C₂²⋊C₄	—	2	1	no	—
366	C₂²⋊C₄	—	2	1	no	—
367	C₂²⋊C₄	—	2	1	no	—
368	C₄²	—	2	1	no	—
369	C₄²	—	2	1	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	2	1	no	—
372	C₄²	—	2	2	no	—
373	C₄²	C₂²×C₄×C₄₁	1	1	yes	characteristic
374	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
375	C₄²	#41×C₄₁	1	1	yes	characteristic
376	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
377	C₂³	—	2	1	no	—
378	C₂³	C₄×D₄×C₄₁	1	1	yes	characteristic
379	Q₈	—	2	1	no	—
380	Q₈	—	2	2	no	—
381	Q₈	—	2	2	no	—
382	Q₈	—	4	2	no	—
383	Q₈	C₂×M₁₆×C₄₁	1	2	yes	—
384	D₄	—	2	4	no	—
385	D₄	—	2	1	no	—
386	D₄	C₂×M₁₆×C₄₁	1	2	yes	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	8	1	no	—
400	C₂×C₄	—	8	1	no	—
401	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
402	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
403	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
404	C₂×C₄	C₂×M₁₆×C₄₁	1	2	yes	—
405	C₂×C₄	#131×C₄₁	1	2	yes	—
406	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
407	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
408	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
409	C₈	—	2	2	no	—
410	C₈	—	2	2	no	—
411	C₈	—	2	2	no	—
412	C₈	—	2	2	no	—
413	C₈	—	2	2	no	—
414	C₈	—	4	1	no	—
415	C₈	—	4	2	no	—
416	C₈	—	4	1	no	—
417	C₈	—	4	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	4	1	no	—
423	C₂²	C₄₁×#435	1	2	yes	—
424	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
425	C₄	—	2	2	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	1	no	—
431	C₄	—	4	1	no	—
432	C₄	—	4	2	no	—
433	C₄	C₄₁×#435	1	2	yes	—
434	C₄	C₂²×M₁₆×C₄₁	1	1	yes	characteristic
435	C₄	C₂×#131×C₄₁	1	1	yes	characteristic
436	C₄	C₄₁×#577	1	1	yes	characteristic
437	C₄	C₄₁×#578	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	4	2	no	—
440	C₂	C₂×C₄₁×#435	1	1	yes	characteristic
441	C₂	C₄₁×#2947	1	1	yes	characteristic
442	C₂	C₄₁×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₄²	C₂⁴×C₄₁
socle	C₂²×C₄₁	C₂×C₄×D₄
prime radical	C₂×#41×C₄₁	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁ ◁ C₄₁×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#2983	C₂	semidirect
4. C₄₁×#1587	C₂	semidirect
5. C₄₁×#1585	C₂	semidirect
6. C₄₁×#1584	C₂	semidirect
7. C₄₁×#1582	C₂	semidirect
8. C₄₁×#1565	C₂	semidirect
10. C₂×C₄₁×Q₈⋊C₈	C₂	semidirect
11. C₄₁×#1451	C₂	semidirect
196. #17876	C₄₁	direct (N × H)
218. #2983	C₂×C₄₁	semidirect
220. #1587	C₂×C₄₁	semidirect
221. #1585	C₂×C₄₁	semidirect
222. #1584	C₂×C₄₁	semidirect
223. #1582	C₂×C₄₁	semidirect
224. #1565	C₂×C₄₁	semidirect
226. C₂×Q₈⋊C₈	C₂×C₄₁	semidirect
227. #1451	C₂×C₄₁	semidirect
268. C₄₁	#17876	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×#2988	2
C₄₁×#2983	2
C₄×#137×C₄₁	2
C₄₁×#1587	2
C₄₁×#1585	2
C₄₁×#1584	2
C₄₁×#1582	2
C₄₁×#1565	2
C₄₁×#1476	2
C₂×C₄₁×Q₈⋊C₈	2
C₄₁×#1451	2
#17876	41

Subgroups — C41×#17876 #23794077

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#17876 #23794077