Subgroups — C₄₁×#32984 #23809185

Order 10496.

1430 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#117×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#484	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#483	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2848	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#1873	C₂	1	4	yes	maximal, complemented
6	C₄₁×#1854	C₂	1	4	yes	maximal, complemented
7	C₄₁×#1824	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1823	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1779	C₂	1	1	yes	maximal, characteristic
10	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
11	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
12	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
13	C₂×#117×C₄₁	—	2	2	no	—
14	C₂×#117×C₄₁	—	2	4	no	—
15	C₂×#117×C₄₁	—	2	4	no	—
16	C₂×#117×C₄₁	C₂²	1	4	yes	—
17	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊C₄×C₄₁	—	2	1	no	—
20	C₂²×C₄²×C₄₁	—	2	1	no	—
21	C₄₁×#484	—	2	4	no	—
22	C₄₁×#483	—	2	4	no	—
23	C₂×#107×C₄₁	C₂²	1	2	yes	complemented
24	C₂×#106×C₄₁	C₂²	1	2	yes	complemented
25	C₂×#103×C₄₁	C₂²	1	2	yes	complemented
26	C₂×#103×C₄₁	C₂²	1	2	yes	complemented
27	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₈×C₄₁	C₂²	1	4	yes	—
30	C₄₁×#385	—	2	1	no	—
31	C₄₁×#385	—	2	2	no	—
32	C₄₁×#380	C₂²	1	1	yes	characteristic
33	C₄₁×#380	C₂²	1	2	yes	—
34	C₄₁×#379	—	2	1	no	—
35	C₄₁×#340	C₂²	1	4	yes	complemented
36	C₄₁×#340	C₂²	1	4	yes	complemented
37	C₂⁵×C₄₁	D₄	1	1	yes	characteristic
38	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₄₁	—	2	2	no	—
40	C₂³×C₄×C₄₁	—	2	2	no	—
41	C₂³×C₄×C₄₁	—	2	8	no	—
42	C₂³×C₄×C₄₁	—	2	1	no	—
43	C₂³×C₄×C₄₁	—	2	1	no	—
44	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₄₁	D₄	1	2	yes	—
46	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
48	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
49	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
50	C₂²⋊Q₈×C₄₁	—	2	2	no	—
51	C₂²⋊Q₈×C₄₁	—	2	2	no	—
52	C₂²⋊Q₈×C₄₁	—	2	8	no	—
53	#117×C₄₁	—	2	16	no	—
54	#117×C₄₁	—	2	8	no	—
55	#117×C₄₁	—	2	8	no	—
56	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
57	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
58	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₄₁	D₄	1	4	yes	—
63	C₂×C₄⋊C₄×C₄₁	D₄	1	4	yes	—
64	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
68	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
69	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
70	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
74	C₂×C₄²×C₄₁	—	2	8	no	—
75	C₂×C₄²×C₄₁	—	2	4	no	—
76	#107×C₄₁	—	2	4	no	—
77	#106×C₄₁	—	2	4	no	—
78	#103×C₄₁	—	2	4	no	—
79	#103×C₄₁	—	2	4	no	—
80	C₂²⋊C₈×C₄₁	—	2	2	no	—
81	C₂²⋊C₈×C₄₁	—	2	2	no	—
82	C₂²⋊C₈×C₄₁	—	2	8	no	—
83	#95×C₄₁	—	2	1	no	—
84	#95×C₄₁	—	2	2	no	—
85	C₂⁴×C₄₁	—	2	2	no	—
86	C₂⁴×C₄₁	—	2	4	no	—
87	C₂⁴×C₄₁	—	2	2	no	—
88	C₂⁴×C₄₁	—	2	2	no	—
89	C₂⁴×C₄₁	—	4	2	no	—
90	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
91	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
92	C₂×Q₈×C₄₁	—	2	1	no	—
93	C₂×Q₈×C₄₁	—	2	1	no	—
94	C₂×Q₈×C₄₁	—	2	4	no	—
95	C₂²×C₄×C₄₁	—	2	16	no	—
96	C₂²×C₄×C₄₁	—	2	16	no	—
97	C₂²×C₄×C₄₁	—	2	2	no	—
98	C₂²×C₄×C₄₁	—	2	4	no	—
99	C₂²×C₄×C₄₁	—	2	4	no	—
100	C₂²×C₄×C₄₁	—	2	4	no	—
101	C₂²×C₄×C₄₁	—	2	4	no	—
102	C₂²×C₄×C₄₁	—	2	2	no	—
103	C₂²×C₄×C₄₁	—	2	2	no	—
104	C₂²×C₄×C₄₁	—	2	4	no	—
105	C₂²×C₄×C₄₁	—	2	4	no	—
106	C₂²×C₄×C₄₁	—	2	4	no	—
107	C₂²×C₄×C₄₁	—	2	4	no	—
108	C₂²×C₄×C₄₁	—	2	2	no	—
109	C₂²×C₄×C₄₁	—	2	2	no	—
110	C₂²×C₄×C₄₁	—	2	1	no	—
111	C₂²×C₄×C₄₁	—	2	2	no	—
112	C₂²×C₄×C₄₁	—	2	1	no	—
113	C₂²×C₄×C₄₁	—	4	4	no	—
114	C₂²×C₄×C₄₁	—	4	2	no	—
115	C₂²×C₄×C₄₁	—	4	2	no	—
116	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₄₁	#41	1	8	yes	—
121	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
122	C₂×C₈×C₄₁	—	2	2	no	—
123	C₂×C₈×C₄₁	—	2	2	no	—
124	C₂×C₈×C₄₁	—	2	4	no	—
125	C₂×C₈×C₄₁	—	2	4	no	—
126	C₄⋊C₄×C₄₁	—	2	4	no	—
127	C₄⋊C₄×C₄₁	—	2	4	no	—
128	C₄⋊C₄×C₄₁	—	2	2	no	—
129	C₄⋊C₄×C₄₁	—	2	2	no	—
130	C₄⋊C₄×C₄₁	—	2	1	no	—
131	C₄⋊C₄×C₄₁	—	2	1	no	—
132	C₄⋊C₄×C₄₁	—	2	4	no	—
133	C₄⋊C₄×C₄₁	—	4	2	no	—
134	C₄⋊C₄×C₄₁	—	4	4	no	—
135	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
136	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
137	C₂²⋊C₄×C₄₁	—	2	16	no	—
138	C₂²⋊C₄×C₄₁	—	4	4	no	—
139	C₂²⋊C₄×C₄₁	—	4	2	no	—
140	C₂²⋊C₄×C₄₁	—	4	4	no	—
141	C₂²⋊C₄×C₄₁	—	4	2	no	—
142	C₄²×C₄₁	—	2	16	no	—
143	C₂³×C₄₁	—	2	2	no	—
144	C₂³×C₄₁	—	2	2	no	—
145	C₂³×C₄₁	—	2	8	no	—
146	C₂³×C₄₁	—	2	2	no	—
147	C₂³×C₄₁	—	2	2	no	—
148	C₂³×C₄₁	—	2	2	no	—
149	C₂³×C₄₁	—	2	2	no	—
150	C₂³×C₄₁	—	2	2	no	—
151	C₂³×C₄₁	—	2	2	no	—
152	C₂³×C₄₁	—	4	8	no	—
153	C₂³×C₄₁	—	4	8	no	—
154	C₂³×C₄₁	—	4	4	no	—
155	C₂³×C₄₁	—	4	4	no	—
156	C₂³×C₄₁	#120	1	2	yes	—
157	C₂³×C₄₁	#123	1	4	yes	—
158	C₂³×C₄₁	#135	1	2	yes	—
159	C₂³×C₄₁	#137	1	2	yes	—
160	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
161	Q₈×C₄₁	—	4	2	no	—
162	Q₈×C₄₁	—	4	2	no	—
163	C₂×C₄×C₄₁	—	2	16	no	—
164	C₂×C₄×C₄₁	—	2	8	no	—
165	C₂×C₄×C₄₁	—	2	2	no	—
166	C₂×C₄×C₄₁	—	2	2	no	—
167	C₂×C₄×C₄₁	—	2	2	no	—
168	C₂×C₄×C₄₁	—	2	4	no	—
169	C₂×C₄×C₄₁	—	2	4	no	—
170	C₂×C₄×C₄₁	—	2	8	no	—
171	C₂×C₄×C₄₁	—	2	8	no	—
172	C₂×C₄×C₄₁	—	2	4	no	—
173	C₂×C₄×C₄₁	—	2	4	no	—
174	C₂×C₄×C₄₁	—	4	8	no	—
175	C₂×C₄×C₄₁	—	4	2	no	—
176	C₂×C₄×C₄₁	—	4	2	no	—
177	C₂×C₄×C₄₁	—	4	4	no	—
178	C₂×C₄×C₄₁	—	4	8	no	—
179	C₂×C₄×C₄₁	—	4	1	no	—
180	C₂×C₄×C₄₁	—	4	1	no	—
181	C₂×C₄×C₄₁	—	4	2	no	—
182	C₂×C₄×C₄₁	—	4	2	no	—
183	C₂×C₄×C₄₁	—	4	2	no	—
184	C₂×C₄×C₄₁	—	4	2	no	—
185	C₂×C₄×C₄₁	—	4	2	no	—
186	C₂×C₄×C₄₁	#120	1	2	yes	—
187	C₂×C₄×C₄₁	#123	1	4	yes	—
188	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
191	C₈×C₄₁	—	4	2	no	—
192	C₈×C₄₁	—	4	2	no	—
193	#32984	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₂²×C₄₁	—	2	4	no	—
195	C₂²×C₄₁	—	2	4	no	—
196	C₂²×C₄₁	—	2	2	no	—
197	C₂²×C₄₁	—	2	2	no	—
198	C₂²×C₄₁	—	2	4	no	—
199	C₂²×C₄₁	—	2	4	no	—
200	C₂²×C₄₁	—	2	4	no	—
201	C₂²×C₄₁	—	4	16	no	—
202	C₂²×C₄₁	—	4	2	no	—
203	C₂²×C₄₁	—	4	2	no	—
204	C₂²×C₄₁	—	4	2	no	—
205	C₂²×C₄₁	—	4	2	no	—
206	C₂²×C₄₁	#452	1	4	yes	—
207	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
208	C₂²×C₄₁	C₂×#123	1	2	yes	—
209	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
210	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
211	C₂²×C₄₁	#575	1	2	yes	—
212	C₄×C₄₁	—	2	2	no	—
213	C₄×C₄₁	—	2	4	no	—
214	C₄×C₄₁	—	4	4	no	—
215	C₄×C₄₁	—	4	4	no	—
216	C₄×C₄₁	—	8	2	no	—
217	C₄×C₄₁	—	8	1	no	—
218	C₄×C₄₁	—	8	1	no	—
219	C₄×C₄₁	#525	1	2	yes	—
220	C₄×C₄₁	#525	1	2	yes	—
221	C₂²×#117	C₂×C₄₁	1	1	yes	characteristic
222	C₂×#484	C₂×C₄₁	1	1	yes	characteristic, complemented
223	C₂×#483	C₂×C₄₁	1	1	yes	characteristic, complemented
224	#2848	C₂×C₄₁	1	1	yes	characteristic
225	#1873	C₂×C₄₁	1	4	yes	complemented
226	#1854	C₂×C₄₁	1	4	yes	complemented
227	#1824	C₂×C₄₁	1	1	yes	characteristic, complemented
228	#1823	C₂×C₄₁	1	1	yes	characteristic, complemented
229	#1779	C₂×C₄₁	1	1	yes	characteristic
230	C₂×C₄₁	—	2	4	no	—
231	C₂×C₄₁	—	4	4	no	—
232	C₂×C₄₁	#2849	1	1	yes	characteristic
233	C₂×C₄₁	C₂×#452	1	1	yes	characteristic
234	C₂×C₄₁	#3005	1	1	yes	characteristic
235	C₂×C₄₁	#3091	1	2	yes	—
236	C₂×C₄₁	#3095	1	2	yes	—
237	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
238	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
239	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
240	C₂×#117	—	2	2	no	—
241	C₂×#117	—	2	4	no	—
242	C₂×#117	—	2	4	no	—
243	C₂×#117	C₂²×C₄₁	1	4	yes	—
244	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
245	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
246	C₂²×C₂²⋊C₄	—	2	1	no	—
247	C₂²×C₄²	—	2	1	no	—
248	#484	—	2	4	no	—
249	#483	—	2	4	no	—
250	C₂×#107	C₂²×C₄₁	1	2	yes	complemented
251	C₂×#106	C₂²×C₄₁	1	2	yes	complemented
252	C₂×#103	C₂²×C₄₁	1	2	yes	complemented
253	C₂×#103	C₂²×C₄₁	1	2	yes	complemented
254	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
255	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
256	C₂×C₂²⋊C₈	C₂²×C₄₁	1	4	yes	—
257	#385	—	2	2	no	—
258	#385	—	2	1	no	—
259	#380	C₂²×C₄₁	1	1	yes	characteristic
260	#380	C₂²×C₄₁	1	2	yes	—
261	#379	—	2	1	no	—
262	#340	C₂²×C₄₁	1	4	yes	complemented
263	#340	C₂²×C₄₁	1	4	yes	complemented
264	C₄₁	#32984	1	1	yes	characteristic, direct product factor, Sylow
265	C₂⁵	D₄×C₄₁	1	1	yes	characteristic
266	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
267	C₂³×C₄	—	2	2	no	—
268	C₂³×C₄	—	2	2	no	—
269	C₂³×C₄	—	2	8	no	—
270	C₂³×C₄	—	2	1	no	—
271	C₂³×C₄	—	2	1	no	—
272	C₂³×C₄	D₄×C₄₁	1	2	yes	—
273	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
274	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
275	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
276	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
277	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
278	C₂²⋊Q₈	—	2	2	no	—
279	C₂²⋊Q₈	—	2	2	no	—
280	C₂²⋊Q₈	—	2	8	no	—
281	#117	—	2	16	no	—
282	#117	—	2	8	no	—
283	#117	—	2	8	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	D₄×C₄₁	1	4	yes	—
291	C₂×C₄⋊C₄	D₄×C₄₁	1	4	yes	—
292	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
295	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
296	C₂×C₂²⋊C₄	—	2	8	no	—
297	C₂×C₂²⋊C₄	—	2	4	no	—
298	C₂×C₂²⋊C₄	—	2	1	no	—
299	C₂×C₂²⋊C₄	—	2	2	no	—
300	C₂×C₂²⋊C₄	—	2	2	no	—
301	C₂×C₂²⋊C₄	—	2	1	no	—
302	C₂×C₄²	—	2	8	no	—
303	C₂×C₄²	—	2	4	no	—
304	#107	—	2	4	no	—
305	#106	—	2	4	no	—
306	#103	—	2	4	no	—
307	#103	—	2	4	no	—
308	C₂²⋊C₈	—	2	2	no	—
309	C₂²⋊C₈	—	2	2	no	—
310	C₂²⋊C₈	—	2	8	no	—
311	#95	—	2	1	no	—
312	#95	—	2	2	no	—
313	C₂⁴	—	2	2	no	—
314	C₂⁴	—	2	4	no	—
315	C₂⁴	—	2	2	no	—
316	C₂⁴	—	2	2	no	—
317	C₂⁴	—	4	2	no	—
318	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
319	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	4	no	—
323	C₂²×C₄	—	2	16	no	—
324	C₂²×C₄	—	2	16	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	4	4	no	—
342	C₂²×C₄	—	4	2	no	—
343	C₂²×C₄	—	4	2	no	—
344	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
346	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
347	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
348	C₂²×C₄	#41×C₄₁	1	8	yes	—
349	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	4	no	—
353	C₂×C₈	—	2	4	no	—
354	C₄⋊C₄	—	2	4	no	—
355	C₄⋊C₄	—	2	4	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	4	2	no	—
362	C₄⋊C₄	—	4	4	no	—
363	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
364	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
365	C₂²⋊C₄	—	2	16	no	—
366	C₂²⋊C₄	—	4	4	no	—
367	C₂²⋊C₄	—	4	2	no	—
368	C₂²⋊C₄	—	4	4	no	—
369	C₂²⋊C₄	—	4	2	no	—
370	C₄²	—	2	16	no	—
371	C₂³	—	2	2	no	—
372	C₂³	—	2	2	no	—
373	C₂³	—	2	8	no	—
374	C₂³	—	2	2	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	2	2	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	4	8	no	—
381	C₂³	—	4	8	no	—
382	C₂³	—	4	4	no	—
383	C₂³	—	4	4	no	—
384	C₂³	#120×C₄₁	1	2	yes	—
385	C₂³	#123×C₄₁	1	4	yes	—
386	C₂³	#135×C₄₁	1	2	yes	—
387	C₂³	#137×C₄₁	1	2	yes	—
388	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
389	Q₈	—	4	2	no	—
390	Q₈	—	4	2	no	—
391	C₂×C₄	—	2	16	no	—
392	C₂×C₄	—	2	8	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	8	no	—
399	C₂×C₄	—	2	8	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	4	8	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	4	8	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	#120×C₄₁	1	2	yes	—
415	C₂×C₄	#123×C₄₁	1	4	yes	—
416	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
417	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
418	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
419	C₈	—	4	2	no	—
420	C₈	—	4	2	no	—
421	C₂²	—	2	4	no	—
422	C₂²	—	2	4	no	—
423	C₂²	—	2	2	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	4	no	—
426	C₂²	—	2	4	no	—
427	C₂²	—	2	4	no	—
428	C₂²	—	4	16	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	C₄₁×#452	1	4	yes	—
434	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
435	C₂²	C₂×#123×C₄₁	1	2	yes	—
436	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
437	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
438	C₂²	C₄₁×#575	1	2	yes	—
439	C₄	—	2	2	no	—
440	C₄	—	2	4	no	—
441	C₄	—	4	4	no	—
442	C₄	—	4	4	no	—
443	C₄	—	8	2	no	—
444	C₄	—	8	1	no	—
445	C₄	—	8	1	no	—
446	C₄	C₄₁×#525	1	2	yes	—
447	C₄	C₄₁×#525	1	2	yes	—
448	C₂	—	2	4	no	—
449	C₂	—	4	4	no	—
450	C₂	C₄₁×#2849	1	1	yes	characteristic
451	C₂	C₂×C₄₁×#452	1	1	yes	characteristic
452	C₂	C₄₁×#3005	1	1	yes	characteristic
453	C₂	C₄₁×#3091	1	2	yes	—
454	C₂	C₄₁×#3095	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂⁵×C₄₁	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂⁴×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#484	C₂	semidirect
3. C₂×C₄₁×#483	C₂	semidirect
5. C₄₁×#1873	C₂	semidirect
6. C₄₁×#1854	C₂	semidirect
7. C₄₁×#1824	C₂	semidirect
8. C₄₁×#1823	C₂	semidirect
23. C₂×#107×C₄₁	C₂²	semidirect
24. C₂×#106×C₄₁	C₂²	semidirect
25. C₂×#103×C₄₁	C₂²	semidirect
26. C₂×#103×C₄₁	C₂²	semidirect
35. C₄₁×#340	C₂²	semidirect
36. C₄₁×#340	C₂²	semidirect
193. #32984	C₄₁	direct (N × H)
222. C₂×#484	C₂×C₄₁	semidirect
223. C₂×#483	C₂×C₄₁	semidirect
225. #1873	C₂×C₄₁	semidirect
226. #1854	C₂×C₄₁	semidirect
227. #1824	C₂×C₄₁	semidirect
228. #1823	C₂×C₄₁	semidirect
250. C₂×#107	C₂²×C₄₁	semidirect
251. C₂×#106	C₂²×C₄₁	semidirect
252. C₂×#103	C₂²×C₄₁	semidirect
253. C₂×#103	C₂²×C₄₁	semidirect
262. #340	C₂²×C₄₁	semidirect
263. #340	C₂²×C₄₁	semidirect
264. C₄₁	#32984	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#117×C₄₁	2
C₂×C₄₁×#484	2
C₂×C₄₁×#483	2
C₄₁×#2848	2
C₄₁×#1873	2
C₄₁×#1854	2
C₄₁×#1824	2
C₄₁×#1823	2
C₄₁×#1779	2
#32984	41

Subgroups — C41×#32984 #23809185

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#32984 #23809185