Subgroups — C₄₁×#33121 #23809322

Order 10496.

872 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#481	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#483	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#2620	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2274	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1983	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1948	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1927	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1926	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1875	C₂	1	1	yes	maximal, characteristic
10	C₄₁×#1873	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1798	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
18	C₄₁×#483	—	2	4	no	—
19	C₄₁×#481	—	2	4	no	—
20	C₂×#106×C₄₁	C₂²	1	2	yes	—
21	C₂×#106×C₄₁	C₂²	1	2	yes	—
22	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
23	C₂×#103×C₄₁	C₂²	1	2	yes	—
24	C₂×#103×C₄₁	C₂²	1	2	yes	—
25	C₂×#102×C₄₁	C₂²	1	2	yes	—
26	C₂×#102×C₄₁	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
29	C₄₁×#396	—	2	2	no	—
30	C₄₁×#394	—	2	2	no	—
31	C₄₁×#391	C₂²	1	1	yes	characteristic
32	C₄₁×#390	C₂²	1	1	yes	characteristic
33	C₄₁×#384	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₄₁	—	2	2	no	—
35	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
36	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
37	C₄×C₂²⋊C₄×C₄₁	—	2	2	no	—
38	C₄₁×#340	C₂²	1	2	yes	—
39	C₄₁×#340	C₂²	1	2	yes	—
40	C₄₁×#336	C₂²	1	2	yes	—
41	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
42	C₂²×D₄×C₄₁	—	2	1	no	—
43	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₄₁	—	2	1	no	—
45	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
47	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
48	#124×C₄₁	—	2	4	no	—
49	C₂²⋊Q₈×C₄₁	—	2	2	no	—
50	C₂²⋊Q₈×C₄₁	—	2	2	no	—
51	#121×C₄₁	—	2	2	no	—
52	#121×C₄₁	—	2	2	no	—
53	#117×C₄₁	—	2	4	no	—
54	#117×C₄₁	—	2	4	no	—
55	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
56	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
58	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₄₁	D₄	1	4	yes	—
61	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
65	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
71	C₂×C₄²×C₄₁	—	2	1	no	—
72	C₂×C₄²×C₄₁	—	2	2	no	—
73	C₂×C₄²×C₄₁	—	2	2	no	—
74	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
76	#106×C₄₁	—	2	4	no	—
77	#106×C₄₁	—	2	4	no	—
78	C₄⋊C₈×C₄₁	—	2	4	no	—
79	#103×C₄₁	—	2	4	no	—
80	#103×C₄₁	—	2	4	no	—
81	#102×C₄₁	—	2	4	no	—
82	#102×C₄₁	—	2	4	no	—
83	C₂²⋊C₈×C₄₁	—	2	2	no	—
84	C₂²⋊C₈×C₄₁	—	2	2	no	—
85	#95×C₄₁	—	2	2	no	—
86	#95×C₄₁	—	2	2	no	—
87	#95×C₄₁	—	2	2	no	—
88	C₂⁴×C₄₁	—	2	1	no	—
89	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
90	C₂×Q₈×C₄₁	—	2	1	no	—
91	C₂×Q₈×C₄₁	—	2	2	no	—
92	C₂×Q₈×C₄₁	—	2	1	no	—
93	C₂×Q₈×C₄₁	—	2	2	no	—
94	C₂×D₄×C₄₁	—	2	1	no	—
95	C₂×D₄×C₄₁	—	2	2	no	—
96	C₂×D₄×C₄₁	—	2	1	no	—
97	C₂×D₄×C₄₁	—	2	2	no	—
98	C₂×D₄×C₄₁	—	4	2	no	—
99	C₂×D₄×C₄₁	—	8	2	no	—
100	C₂²×C₄×C₄₁	—	2	2	no	—
101	C₂²×C₄×C₄₁	—	2	2	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	1	no	—
106	C₂²×C₄×C₄₁	—	2	1	no	—
107	C₂²×C₄×C₄₁	—	2	1	no	—
108	C₂²×C₄×C₄₁	—	8	2	no	—
109	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₄₁	#41	1	2	yes	—
114	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
115	C₂×C₈×C₄₁	—	2	2	no	—
116	C₂×C₈×C₄₁	—	2	2	no	—
117	C₂×C₈×C₄₁	—	2	2	no	—
118	C₂×C₈×C₄₁	—	2	2	no	—
119	C₂×C₈×C₄₁	—	2	2	no	—
120	C₂×C₈×C₄₁	—	2	2	no	—
121	C₄⋊C₄×C₄₁	—	2	4	no	—
122	C₄⋊C₄×C₄₁	—	2	4	no	—
123	C₄⋊C₄×C₄₁	—	2	2	no	—
124	C₄⋊C₄×C₄₁	—	2	2	no	—
125	C₄⋊C₄×C₄₁	—	2	1	no	—
126	C₄⋊C₄×C₄₁	—	2	1	no	—
127	C₄⋊C₄×C₄₁	—	2	1	no	—
128	C₄⋊C₄×C₄₁	—	2	1	no	—
129	C₄⋊C₄×C₄₁	—	4	2	no	—
130	C₄⋊C₄×C₄₁	—	8	2	no	—
131	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
132	C₄⋊C₄×C₄₁	#41	1	4	yes	—
133	C₂²⋊C₄×C₄₁	—	2	4	no	—
134	C₂²⋊C₄×C₄₁	—	2	4	no	—
135	C₂²⋊C₄×C₄₁	—	4	2	no	—
136	C₂²⋊C₄×C₄₁	—	4	2	no	—
137	C₂²⋊C₄×C₄₁	—	4	4	no	—
138	C₂²⋊C₄×C₄₁	—	8	2	no	—
139	C₄²×C₄₁	—	2	4	no	—
140	C₄²×C₄₁	—	2	2	no	—
141	C₄²×C₄₁	—	8	2	no	—
142	C₄²×C₄₁	—	8	2	no	—
143	C₄²×C₄₁	#41	1	4	yes	—
144	C₂³×C₄₁	—	2	1	no	—
145	C₂³×C₄₁	—	2	1	no	—
146	C₂³×C₄₁	—	2	2	no	—
147	C₂³×C₄₁	—	2	2	no	—
148	C₂³×C₄₁	—	4	1	no	—
149	C₂³×C₄₁	—	4	1	no	—
150	C₂³×C₄₁	—	4	1	no	—
151	C₂³×C₄₁	—	4	2	no	—
152	C₂³×C₄₁	—	4	2	no	—
153	C₂³×C₄₁	#121	1	2	yes	—
154	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
155	Q₈×C₄₁	—	4	2	no	—
156	Q₈×C₄₁	—	4	2	no	—
157	D₄×C₄₁	—	4	2	no	—
158	D₄×C₄₁	—	4	2	no	—
159	D₄×C₄₁	—	8	4	no	—
160	C₂×C₄×C₄₁	—	2	1	no	—
161	C₂×C₄×C₄₁	—	2	1	no	—
162	C₂×C₄×C₄₁	—	2	2	no	—
163	C₂×C₄×C₄₁	—	2	2	no	—
164	C₂×C₄×C₄₁	—	2	4	no	—
165	C₂×C₄×C₄₁	—	2	4	no	—
166	C₂×C₄×C₄₁	—	2	4	no	—
167	C₂×C₄×C₄₁	—	2	2	no	—
168	C₂×C₄×C₄₁	—	2	4	no	—
169	C₂×C₄×C₄₁	—	2	2	no	—
170	C₂×C₄×C₄₁	—	2	2	no	—
171	C₂×C₄×C₄₁	—	4	2	no	—
172	C₂×C₄×C₄₁	—	4	2	no	—
173	C₂×C₄×C₄₁	—	4	2	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	—	4	1	no	—
178	C₂×C₄×C₄₁	—	4	1	no	—
179	C₂×C₄×C₄₁	—	4	1	no	—
180	C₂×C₄×C₄₁	—	4	2	no	—
181	C₂×C₄×C₄₁	—	4	2	no	—
182	C₂×C₄×C₄₁	—	8	4	no	—
183	C₂×C₄×C₄₁	#121	1	2	yes	—
184	C₂×C₄×C₄₁	#123	1	4	yes	—
185	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
188	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
189	C₈×C₄₁	—	4	2	no	—
190	C₈×C₄₁	—	4	2	no	—
191	#33121	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂²×C₄₁	—	2	2	no	—
193	C₂²×C₄₁	—	2	2	no	—
194	C₂²×C₄₁	—	2	2	no	—
195	C₂²×C₄₁	—	4	2	no	—
196	C₂²×C₄₁	—	4	2	no	—
197	C₂²×C₄₁	—	8	2	no	—
198	C₂²×C₄₁	—	8	1	no	—
199	C₂²×C₄₁	—	8	2	no	—
200	C₂²×C₄₁	—	8	1	no	—
201	C₂²×C₄₁	—	8	1	no	—
202	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
203	C₂²×C₄₁	C₂×#123	1	1	yes	characteristic
204	C₂²×C₄₁	#525	1	1	yes	characteristic
205	C₂²×C₄₁	#577	1	2	yes	—
206	C₂²×C₄₁	#577	1	2	yes	—
207	C₄×C₄₁	—	2	4	no	—
208	C₄×C₄₁	—	2	2	no	—
209	C₄×C₄₁	—	4	2	no	—
210	C₄×C₄₁	—	4	4	no	—
211	C₄×C₄₁	—	4	4	no	—
212	C₄×C₄₁	—	8	1	no	—
213	C₄×C₄₁	—	8	1	no	—
214	C₄×C₄₁	—	8	1	no	—
215	C₄×C₄₁	#529	1	2	yes	—
216	C₄×C₄₁	#532	1	2	yes	—
217	C₂×#481	C₂×C₄₁	1	1	yes	characteristic
218	C₂×#483	C₂×C₄₁	1	1	yes	characteristic, complemented
219	#2620	C₂×C₄₁	1	1	yes	characteristic
220	#2274	C₂×C₄₁	1	1	yes	characteristic, complemented
221	#1983	C₂×C₄₁	1	2	yes	complemented
222	#1948	C₂×C₄₁	1	2	yes	complemented
223	#1927	C₂×C₄₁	1	2	yes	complemented
224	#1926	C₂×C₄₁	1	2	yes	complemented
225	#1875	C₂×C₄₁	1	1	yes	characteristic
226	#1873	C₂×C₄₁	1	1	yes	characteristic, complemented
227	#1798	C₂×C₄₁	1	1	yes	characteristic, complemented
228	C₂×C₄₁	—	4	2	no	—
229	C₂×C₄₁	—	16	1	no	—
230	C₂×C₄₁	#2854	1	1	yes	characteristic
231	C₂×C₄₁	#3042	1	1	yes	characteristic
232	C₂×C₄₁	#3043	1	1	yes	characteristic
233	C₂×C₄₁	#3099	1	2	yes	—
234	C₂×C₄₁	#3125	1	2	yes	—
235	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
236	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
237	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
238	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
239	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
240	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
241	#483	—	2	4	no	—
242	#481	—	2	4	no	—
243	C₂×#106	C₂²×C₄₁	1	2	yes	—
244	C₂×#106	C₂²×C₄₁	1	2	yes	—
245	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
246	C₂×#103	C₂²×C₄₁	1	2	yes	—
247	C₂×#103	C₂²×C₄₁	1	2	yes	—
248	C₂×#102	C₂²×C₄₁	1	2	yes	—
249	C₂×#102	C₂²×C₄₁	1	2	yes	—
250	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
251	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
252	#396	—	2	2	no	—
253	#394	—	2	2	no	—
254	#391	C₂²×C₄₁	1	1	yes	characteristic
255	#390	C₂²×C₄₁	1	1	yes	characteristic
256	#384	C₂²×C₄₁	1	1	yes	characteristic
257	C₄×C₄⋊C₄	—	2	2	no	—
258	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
259	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
260	C₄×C₂²⋊C₄	—	2	2	no	—
261	#340	C₂²×C₄₁	1	2	yes	—
262	#340	C₂²×C₄₁	1	2	yes	—
263	#336	C₂²×C₄₁	1	2	yes	—
264	C₄₁	#33121	1	1	yes	characteristic, direct product factor, Sylow
265	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
266	C₂²×D₄	—	2	1	no	—
267	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
268	C₂³×C₄	—	2	1	no	—
269	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
270	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
271	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
272	#124	—	2	4	no	—
273	C₂²⋊Q₈	—	2	2	no	—
274	C₂²⋊Q₈	—	2	2	no	—
275	#121	—	2	2	no	—
276	#121	—	2	2	no	—
277	#117	—	2	4	no	—
278	#117	—	2	4	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
284	C₂×C₄⋊C₄	D₄×C₄₁	1	4	yes	—
285	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
289	C₂×C₂²⋊C₄	—	2	1	no	—
290	C₂×C₂²⋊C₄	—	2	1	no	—
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₂²⋊C₄	—	2	2	no	—
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	—	2	2	no	—
297	C₂×C₄²	—	2	2	no	—
298	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
299	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
300	#106	—	2	4	no	—
301	#106	—	2	4	no	—
302	C₄⋊C₈	—	2	4	no	—
303	#103	—	2	4	no	—
304	#103	—	2	4	no	—
305	#102	—	2	4	no	—
306	#102	—	2	4	no	—
307	C₂²⋊C₈	—	2	2	no	—
308	C₂²⋊C₈	—	2	2	no	—
309	#95	—	2	2	no	—
310	#95	—	2	2	no	—
311	#95	—	2	2	no	—
312	C₂⁴	—	2	1	no	—
313	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	4	2	no	—
323	C₂×D₄	—	8	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	8	2	no	—
333	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
336	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
337	C₂²×C₄	#41×C₄₁	1	2	yes	—
338	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	—	2	4	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₄⋊C₄	—	8	2	no	—
355	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
356	C₄⋊C₄	#41×C₄₁	1	4	yes	—
357	C₂²⋊C₄	—	2	4	no	—
358	C₂²⋊C₄	—	2	4	no	—
359	C₂²⋊C₄	—	4	2	no	—
360	C₂²⋊C₄	—	4	2	no	—
361	C₂²⋊C₄	—	4	4	no	—
362	C₂²⋊C₄	—	8	2	no	—
363	C₄²	—	2	4	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	8	2	no	—
366	C₄²	—	8	2	no	—
367	C₄²	#41×C₄₁	1	4	yes	—
368	C₂³	—	2	1	no	—
369	C₂³	—	2	1	no	—
370	C₂³	—	2	2	no	—
371	C₂³	—	2	2	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	1	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	4	2	no	—
377	C₂³	#121×C₄₁	1	2	yes	—
378	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
379	Q₈	—	4	2	no	—
380	Q₈	—	4	2	no	—
381	D₄	—	4	2	no	—
382	D₄	—	4	2	no	—
383	D₄	—	8	4	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	8	4	no	—
407	C₂×C₄	#121×C₄₁	1	2	yes	—
408	C₂×C₄	#123×C₄₁	1	4	yes	—
409	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
410	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
411	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
412	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
413	C₈	—	4	2	no	—
414	C₈	—	4	2	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	8	1	no	—
421	C₂²	—	8	1	no	—
422	C₂²	—	8	2	no	—
423	C₂²	—	8	1	no	—
424	C₂²	—	8	2	no	—
425	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
426	C₂²	C₂×#123×C₄₁	1	1	yes	characteristic
427	C₂²	C₄₁×#525	1	1	yes	characteristic
428	C₂²	C₄₁×#577	1	2	yes	—
429	C₂²	C₄₁×#577	1	2	yes	—
430	C₄	—	2	4	no	—
431	C₄	—	2	2	no	—
432	C₄	—	4	4	no	—
433	C₄	—	4	2	no	—
434	C₄	—	4	4	no	—
435	C₄	—	8	1	no	—
436	C₄	—	8	1	no	—
437	C₄	—	8	1	no	—
438	C₄	C₄₁×#529	1	2	yes	—
439	C₄	C₄₁×#532	1	2	yes	—
440	C₂	—	4	2	no	—
441	C₂	—	16	1	no	—
442	C₂	C₄₁×#2854	1	1	yes	characteristic
443	C₂	C₄₁×#3042	1	1	yes	characteristic
444	C₂	C₄₁×#3043	1	1	yes	characteristic
445	C₂	C₄₁×#3099	1	2	yes	—
446	C₂	C₄₁×#3125	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×#121×C₄₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂×#117×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#483	C₂	semidirect
4. C₄₁×#2274	C₂	semidirect
5. C₄₁×#1983	C₂	semidirect
6. C₄₁×#1948	C₂	semidirect
7. C₄₁×#1927	C₂	semidirect
8. C₄₁×#1926	C₂	semidirect
10. C₄₁×#1873	C₂	semidirect
11. C₄₁×#1798	C₂	semidirect
191. #33121	C₄₁	direct (N × H)
218. C₂×#483	C₂×C₄₁	semidirect
220. #2274	C₂×C₄₁	semidirect
221. #1983	C₂×C₄₁	semidirect
222. #1948	C₂×C₄₁	semidirect
223. #1927	C₂×C₄₁	semidirect
224. #1926	C₂×C₄₁	semidirect
226. #1873	C₂×C₄₁	semidirect
227. #1798	C₂×C₄₁	semidirect
264. C₄₁	#33121	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#481	2
C₂×C₄₁×#483	2
C₄₁×#2620	2
C₄₁×#2274	2
C₄₁×#1983	2
C₄₁×#1948	2
C₄₁×#1927	2
C₄₁×#1926	2
C₄₁×#1875	2
C₄₁×#1873	2
C₄₁×#1798	2
#33121	41

Subgroups — C41×#33121 #23809322

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#33121 #23809322