Subgroups — C₄₁×#33165 #23809366

Order 10496.

1126 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	C₂×C₄₁×#464	C₂	1	4	yes	maximal, complemented
2	C₂×C₄₁×#462	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#460	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2858	C₂	1	1	yes	maximal, characteristic
5	C₄²×Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1983	C₂	1	4	yes	maximal, complemented
7	C₄₁×#1982	C₂	1	1	yes	maximal, characteristic
8	C₄₁×#1981	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1842	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×Q₁₆×C₄₁	C₂²	1	2	yes	—
11	C₂²×SD₁₆×C₄₁	C₂²	1	2	yes	—
12	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×#124×C₄₁	C₂²	1	4	yes	—
15	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
17	C₄₁×#464	—	2	16	no	—
18	C₄₁×#462	—	2	4	no	—
19	C₄₁×#460	—	2	4	no	—
20	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₄₁	C₂²	1	4	yes	—
23	C₂×#103×C₄₁	C₂²	1	4	yes	—
24	C₂×#103×C₄₁	C₂²	1	2	yes	—
25	C₂×#102×C₄₁	C₂²	1	4	yes	—
26	C₂×#102×C₄₁	C₂²	1	2	yes	—
27	C₄₁×#390	—	2	1	no	—
28	C₄₁×#390	—	2	1	no	—
29	C₄₁×#390	—	2	2	no	—
30	C₄×C₄⋊C₄×C₄₁	—	2	1	no	—
31	C₄×C₄⋊C₄×C₄₁	—	2	2	no	—
32	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
34	C₄³×C₄₁	—	2	1	no	—
35	C₄³×C₄₁	C₂²	1	1	yes	characteristic
36	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
37	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
38	C₂²×D₄×C₄₁	—	2	1	no	—
39	C₂²×D₄×C₄₁	—	2	1	no	—
40	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
41	C₂×Q₁₆×C₄₁	—	2	4	no	—
42	C₂×Q₁₆×C₄₁	—	2	8	no	—
43	C₂×SD₁₆×C₄₁	—	2	4	no	—
44	C₂×SD₁₆×C₄₁	—	2	8	no	—
45	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
46	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
47	C₄⋊Q₈×C₄₁	—	2	2	no	—
48	C₄⋊Q₈×C₄₁	—	2	2	no	—
49	#127×C₄₁	—	2	2	no	—
50	#127×C₄₁	—	2	2	no	—
51	#124×C₄₁	—	2	8	no	—
52	#124×C₄₁	—	2	8	no	—
53	C₄×Q₈×C₄₁	—	2	2	no	—
54	C₄×Q₈×C₄₁	—	2	4	no	—
55	C₄×Q₈×C₄₁	D₄	1	4	yes	—
56	C₄×Q₈×C₄₁	D₄	1	8	yes	complemented
57	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
58	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
60	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
63	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
64	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
65	C₂×C₄²×C₄₁	—	2	1	no	—
66	C₂×C₄²×C₄₁	—	2	2	no	—
67	C₂×C₄²×C₄₁	—	2	2	no	—
68	C₂×C₄²×C₄₁	—	2	1	no	—
69	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₄₁	D₄	1	2	yes	—
72	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
73	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
74	C₄⋊C₈×C₄₁	—	2	2	no	—
75	C₄⋊C₈×C₄₁	—	2	2	no	—
76	C₄⋊C₈×C₄₁	—	2	8	no	—
77	#103×C₄₁	—	2	4	no	—
78	#103×C₄₁	—	2	8	no	—
79	#102×C₄₁	—	2	4	no	—
80	#102×C₄₁	—	2	8	no	—
81	#95×C₄₁	—	2	2	no	—
82	#95×C₄₁	—	2	1	no	—
83	C₂⁴×C₄₁	—	2	2	no	—
84	C₂×Q₈×C₄₁	—	2	1	no	—
85	C₂×Q₈×C₄₁	—	2	2	no	—
86	C₂×Q₈×C₄₁	—	2	4	no	—
87	C₂×Q₈×C₄₁	—	2	2	no	—
88	C₂×Q₈×C₄₁	—	2	4	no	—
89	C₂×Q₈×C₄₁	—	2	2	no	—
90	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
91	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
92	C₂×D₄×C₄₁	—	2	4	no	—
93	C₂×D₄×C₄₁	—	2	2	no	—
94	C₂×D₄×C₄₁	—	2	4	no	—
95	C₂×D₄×C₄₁	—	2	2	no	—
96	C₂×D₄×C₄₁	—	4	4	no	—
97	C₂×D₄×C₄₁	—	4	2	no	—
98	C₂×D₄×C₄₁	—	4	2	no	—
99	C₂×D₄×C₄₁	—	4	2	no	—
100	C₂×D₄×C₄₁	—	4	2	no	—
101	C₂²×C₄×C₄₁	—	2	1	no	—
102	C₂²×C₄×C₄₁	—	2	2	no	—
103	C₂²×C₄×C₄₁	—	2	1	no	—
104	C₂²×C₄×C₄₁	—	2	2	no	—
105	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
110	Q₁₆×C₄₁	—	4	8	no	—
111	SD₁₆×C₄₁	—	4	8	no	—
112	C₂×C₈×C₄₁	—	2	2	no	—
113	C₂×C₈×C₄₁	—	2	4	no	—
114	C₂×C₈×C₄₁	—	2	4	no	—
115	C₂×C₈×C₄₁	—	2	2	no	—
116	C₄⋊C₄×C₄₁	—	2	4	no	—
117	C₄⋊C₄×C₄₁	—	2	8	no	—
118	C₄⋊C₄×C₄₁	—	2	2	no	—
119	C₄⋊C₄×C₄₁	—	2	1	no	—
120	C₄⋊C₄×C₄₁	—	4	2	no	—
121	C₄⋊C₄×C₄₁	—	4	2	no	—
122	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
123	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
124	C₂²⋊C₄×C₄₁	—	4	8	no	—
125	C₂²⋊C₄×C₄₁	—	4	8	no	—
126	C₄²×C₄₁	—	2	4	no	—
127	C₄²×C₄₁	—	2	8	no	—
128	C₄²×C₄₁	—	2	2	no	—
129	C₄²×C₄₁	—	2	2	no	—
130	C₄²×C₄₁	—	4	2	no	—
131	C₄²×C₄₁	—	4	4	no	—
132	C₄²×C₄₁	—	4	2	no	—
133	C₄²×C₄₁	C₂×D₄	1	2	yes	—
134	C₄²×C₄₁	C₂×D₄	1	4	yes	—
135	C₄²×C₄₁	#41	1	4	yes	—
136	C₄²×C₄₁	#41	1	2	yes	—
137	C₂³×C₄₁	—	4	4	no	—
138	C₂³×C₄₁	—	4	2	no	—
139	C₂³×C₄₁	—	4	2	no	—
140	C₂³×C₄₁	—	4	2	no	—
141	C₂³×C₄₁	—	4	4	no	—
142	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
143	Q₈×C₄₁	—	2	2	no	—
144	Q₈×C₄₁	—	2	4	no	—
145	Q₈×C₄₁	—	4	2	no	—
146	Q₈×C₄₁	—	4	4	no	—
147	Q₈×C₄₁	—	4	2	no	—
148	Q₈×C₄₁	#127	1	4	yes	—
149	D₄×C₄₁	—	4	2	no	—
150	D₄×C₄₁	—	4	4	no	—
151	D₄×C₄₁	—	4	2	no	—
152	D₄×C₄₁	—	8	4	no	—
153	D₄×C₄₁	—	8	4	no	—
154	C₂×C₄×C₄₁	—	2	2	no	—
155	C₂×C₄×C₄₁	—	2	4	no	—
156	C₂×C₄×C₄₁	—	2	2	no	—
157	C₂×C₄×C₄₁	—	2	2	no	—
158	C₂×C₄×C₄₁	—	2	2	no	—
159	C₂×C₄×C₄₁	—	2	2	no	—
160	C₂×C₄×C₄₁	—	2	2	no	—
161	C₂×C₄×C₄₁	—	2	4	no	—
162	C₂×C₄×C₄₁	—	2	2	no	—
163	C₂×C₄×C₄₁	—	4	2	no	—
164	C₂×C₄×C₄₁	—	4	2	no	—
165	C₂×C₄×C₄₁	—	4	2	no	—
166	C₂×C₄×C₄₁	—	4	4	no	—
167	C₂×C₄×C₄₁	—	4	2	no	—
168	C₂×C₄×C₄₁	#121	1	4	yes	—
169	C₂×C₄×C₄₁	#121	1	4	yes	—
170	C₂×C₄×C₄₁	#121	1	2	yes	—
171	C₂×C₄×C₄₁	#121	1	2	yes	—
172	C₂×C₄×C₄₁	#135	1	2	yes	—
173	C₂×C₄×C₄₁	#137	1	2	yes	—
174	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
176	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
177	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
178	C₈×C₄₁	—	4	2	no	—
179	C₈×C₄₁	—	4	2	no	—
180	#33165	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂²×C₄₁	—	8	2	no	—
182	C₂²×C₄₁	—	8	2	no	—
183	C₂²×C₄₁	—	8	4	no	—
184	C₂²×C₄₁	—	8	4	no	—
185	C₂²×C₄₁	—	8	2	no	—
186	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
187	C₂²×C₄₁	C₂×#121	1	2	yes	—
188	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
189	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
190	C₂²×C₄₁	#575	1	2	yes	—
191	C₄×C₄₁	—	2	4	no	—
192	C₄×C₄₁	—	2	4	no	—
193	C₄×C₄₁	—	2	4	no	—
194	C₄×C₄₁	—	2	2	no	—
195	C₄×C₄₁	—	4	4	no	—
196	C₄×C₄₁	—	4	2	no	—
197	C₄×C₄₁	—	8	2	no	—
198	C₄×C₄₁	#464	1	4	yes	complemented
199	C₄×C₄₁	C₂×#127	1	1	yes	characteristic
200	C₄×C₄₁	#532	1	1	yes	characteristic
201	C₄×C₄₁	#532	1	2	yes	—
202	C₂×#464	C₂×C₄₁	1	4	yes	complemented
203	C₂×#462	C₂×C₄₁	1	1	yes	characteristic, complemented
204	C₂×#460	C₂×C₄₁	1	1	yes	characteristic
205	#2858	C₂×C₄₁	1	1	yes	characteristic
206	C₄²×Q₈	C₂×C₄₁	1	1	yes	characteristic, complemented
207	#1983	C₂×C₄₁	1	4	yes	complemented
208	#1982	C₂×C₄₁	1	1	yes	characteristic
209	#1981	C₂×C₄₁	1	1	yes	characteristic, complemented
210	#1842	C₂×C₄₁	1	1	yes	characteristic, complemented
211	C₂×C₄₁	—	16	2	no	—
212	C₂×C₄₁	#2856	1	1	yes	characteristic
213	C₂×C₄₁	C₂×#464	1	1	yes	characteristic
214	C₂×C₄₁	#3035	1	2	yes	—
215	C₂×C₄₁	#3037	1	2	yes	—
216	C₂×C₄₁	#3040	1	1	yes	characteristic
217	C₂²×Q₁₆	C₂²×C₄₁	1	2	yes	—
218	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	—
219	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
220	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
221	C₂×#124	C₂²×C₄₁	1	4	yes	—
222	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
223	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
224	#464	—	2	16	no	—
225	#462	—	2	4	no	—
226	#460	—	2	4	no	—
227	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
228	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
229	C₂×C₄⋊C₈	C₂²×C₄₁	1	4	yes	—
230	C₂×#103	C₂²×C₄₁	1	4	yes	—
231	C₂×#103	C₂²×C₄₁	1	2	yes	—
232	C₂×#102	C₂²×C₄₁	1	4	yes	—
233	C₂×#102	C₂²×C₄₁	1	2	yes	—
234	#390	—	2	1	no	—
235	#390	—	2	1	no	—
236	#390	—	2	2	no	—
237	C₄×C₄⋊C₄	—	2	1	no	—
238	C₄×C₄⋊C₄	—	2	2	no	—
239	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
240	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
241	C₄³	—	2	1	no	—
242	C₄³	C₂²×C₄₁	1	1	yes	characteristic
243	C₄₁	#33165	1	1	yes	characteristic, direct product factor, Sylow
244	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
245	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
246	C₂²×D₄	—	2	1	no	—
247	C₂²×D₄	—	2	1	no	—
248	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
249	C₂×Q₁₆	—	2	4	no	—
250	C₂×Q₁₆	—	2	8	no	—
251	C₂×SD₁₆	—	2	4	no	—
252	C₂×SD₁₆	—	2	8	no	—
253	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
254	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
255	C₄⋊Q₈	—	2	2	no	—
256	C₄⋊Q₈	—	2	2	no	—
257	#127	—	2	2	no	—
258	#127	—	2	2	no	—
259	#124	—	2	8	no	—
260	#124	—	2	8	no	—
261	C₄×Q₈	—	2	2	no	—
262	C₄×Q₈	—	2	4	no	—
263	C₄×Q₈	D₄×C₄₁	1	4	yes	—
264	C₄×Q₈	D₄×C₄₁	1	8	yes	complemented
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
271	C₂×C₂²⋊C₄	—	2	4	no	—
272	C₂×C₂²⋊C₄	—	2	4	no	—
273	C₂×C₄²	—	2	1	no	—
274	C₂×C₄²	—	2	2	no	—
275	C₂×C₄²	—	2	2	no	—
276	C₂×C₄²	—	2	1	no	—
277	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
278	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
279	C₂×C₄²	D₄×C₄₁	1	2	yes	—
280	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
281	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
282	C₄⋊C₈	—	2	2	no	—
283	C₄⋊C₈	—	2	2	no	—
284	C₄⋊C₈	—	2	8	no	—
285	#103	—	2	4	no	—
286	#103	—	2	8	no	—
287	#102	—	2	4	no	—
288	#102	—	2	8	no	—
289	#95	—	2	2	no	—
290	#95	—	2	1	no	—
291	C₂⁴	—	2	2	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×Q₈	—	2	4	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	2	4	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
299	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
300	C₂×D₄	—	2	4	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	4	4	no	—
305	C₂×D₄	—	4	2	no	—
306	C₂×D₄	—	4	2	no	—
307	C₂×D₄	—	4	2	no	—
308	C₂×D₄	—	4	2	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
316	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
317	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
318	Q₁₆	—	4	8	no	—
319	SD₁₆	—	4	8	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	4	no	—
322	C₂×C₈	—	2	4	no	—
323	C₂×C₈	—	2	2	no	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	2	8	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	4	2	no	—
329	C₄⋊C₄	—	4	2	no	—
330	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
331	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
332	C₂²⋊C₄	—	4	8	no	—
333	C₂²⋊C₄	—	4	8	no	—
334	C₄²	—	2	4	no	—
335	C₄²	—	2	8	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	4	2	no	—
339	C₄²	—	4	4	no	—
340	C₄²	—	4	2	no	—
341	C₄²	C₂×D₄×C₄₁	1	2	yes	—
342	C₄²	C₂×D₄×C₄₁	1	4	yes	—
343	C₄²	#41×C₄₁	1	4	yes	—
344	C₄²	#41×C₄₁	1	2	yes	—
345	C₂³	—	4	4	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	4	no	—
350	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
351	Q₈	—	2	2	no	—
352	Q₈	—	2	4	no	—
353	Q₈	—	4	2	no	—
354	Q₈	—	4	4	no	—
355	Q₈	—	4	2	no	—
356	Q₈	#127×C₄₁	1	4	yes	—
357	D₄	—	4	2	no	—
358	D₄	—	4	4	no	—
359	D₄	—	4	2	no	—
360	D₄	—	8	4	no	—
361	D₄	—	8	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	#121×C₄₁	1	4	yes	—
377	C₂×C₄	#121×C₄₁	1	4	yes	—
378	C₂×C₄	#121×C₄₁	1	2	yes	—
379	C₂×C₄	#121×C₄₁	1	2	yes	—
380	C₂×C₄	#135×C₄₁	1	2	yes	—
381	C₂×C₄	#137×C₄₁	1	2	yes	—
382	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
383	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
384	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
385	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
386	C₈	—	4	2	no	—
387	C₈	—	4	2	no	—
388	C₂²	—	8	4	no	—
389	C₂²	—	8	2	no	—
390	C₂²	—	8	2	no	—
391	C₂²	—	8	2	no	—
392	C₂²	—	8	4	no	—
393	C₂²	C₂×#121×C₄₁	1	2	yes	—
394	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
395	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
396	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
397	C₂²	C₄₁×#575	1	2	yes	—
398	C₄	—	2	4	no	—
399	C₄	—	2	2	no	—
400	C₄	—	2	4	no	—
401	C₄	—	2	4	no	—
402	C₄	—	4	2	no	—
403	C₄	—	4	4	no	—
404	C₄	—	8	2	no	—
405	C₄	C₄₁×#464	1	4	yes	complemented
406	C₄	C₂×#127×C₄₁	1	1	yes	characteristic
407	C₄	C₄₁×#532	1	2	yes	—
408	C₄	C₄₁×#532	1	1	yes	characteristic
409	C₂	—	16	2	no	—
410	C₂	C₄₁×#2856	1	1	yes	characteristic
411	C₂	C₂×C₄₁×#464	1	1	yes	characteristic
412	C₂	C₄₁×#3035	1	2	yes	—
413	C₂	C₄₁×#3037	1	2	yes	—
414	C₂	C₄₁×#3040	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×#127×C₄₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₄³×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#464	C₂	semidirect
2. C₂×C₄₁×#462	C₂	semidirect
5. C₄²×Q₈×C₄₁	C₂	semidirect
6. C₄₁×#1983	C₂	semidirect
8. C₄₁×#1981	C₂	semidirect
9. C₄₁×#1842	C₂	semidirect
56. C₄×Q₈×C₄₁	D₄	semidirect
180. #33165	C₄₁	direct (N × H)
198. C₄×C₄₁	#464	semidirect
202. C₂×#464	C₂×C₄₁	semidirect
203. C₂×#462	C₂×C₄₁	semidirect
206. C₄²×Q₈	C₂×C₄₁	semidirect
207. #1983	C₂×C₄₁	semidirect
209. #1981	C₂×C₄₁	semidirect
210. #1842	C₂×C₄₁	semidirect
243. C₄₁	#33165	direct (N × H)
264. C₄×Q₈	D₄×C₄₁	semidirect
405. C₄	C₄₁×#464	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#464	2
C₂×C₄₁×#462	2
C₂×C₄₁×#460	2
C₄₁×#2858	2
C₄²×Q₈×C₄₁	2
C₄₁×#1983	2
C₄₁×#1982	2
C₄₁×#1981	2
C₄₁×#1842	2
#33165	41

Subgroups — C41×#33165 #23809366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#33165 #23809366