Subgroups — C₄₁×#33358 #23809559

Order 10496.

1252 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3449	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#410	C₂	1	2	yes	maximal, complemented
3	C₄₁×#2129	C₂	1	2	yes	maximal, complemented
4	C₄₁×#2128	C₂	1	2	yes	maximal, complemented
5	C₄₁×#2127	C₂	1	4	yes	maximal, complemented
6	C₄₁×#2126	C₂	1	4	yes	maximal, complemented
7	C₂²×#41×C₄₁	C₄	1	1	yes	characteristic, complemented
8	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
9	C₄₁×#537	—	2	2	no	—
10	C₄₁×#536	C₄	1	2	yes	complemented
11	C₄₁×#536	C₄	1	1	yes	characteristic, complemented
12	C₄₁×#536	C₂²	1	1	yes	characteristic
13	C₄₁×#535	C₄	1	1	yes	characteristic, complemented
14	C₄₁×#535	C₂²	1	2	yes	—
15	C₄₁×#535	C₂²	1	1	yes	characteristic
16	C₄₁×#534	—	2	2	no	—
17	C₄₁×#532	C₄	1	2	yes	complemented
18	C₄₁×#532	C₂²	1	2	yes	—
19	C₄₁×#525	—	2	2	no	—
20	C₄₁×#525	—	2	2	no	—
21	C₂×#117×C₄₁	—	2	2	no	—
22	C₂×#117×C₄₁	C₄	1	1	yes	characteristic, complemented
23	C₄₁×#410	—	2	2	no	—
24	C₄₁×#410	—	2	2	no	—
25	C₄₁×#410	C₂²	1	4	yes	—
26	C₄₁×#410	C₂²	1	4	yes	complemented
27	C₂×#99×C₄₁	—	2	2	no	—
28	C₂×#99×C₄₁	C₂²	1	4	yes	complemented
29	C₄₁×#354	C₂²	1	8	yes	complemented
30	C₄₁×#353	C₂²	1	8	yes	complemented
31	C₂×#41×C₄₁	—	2	1	no	—
32	C₂×#41×C₄₁	—	2	1	no	—
33	C₂×#41×C₄₁	—	4	2	no	—
34	C₂×#41×C₄₁	—	4	2	no	—
35	C₂×#41×C₄₁	—	4	2	no	—
36	C₂×#41×C₄₁	—	4	2	no	—
37	C₂×#41×C₄₁	C₂×C₄	1	2	yes	—
38	C₂×#41×C₄₁	C₂×C₄	1	1	yes	characteristic
39	C₂×#41×C₄₁	C₂×C₄	1	1	yes	characteristic
40	C₂×#41×C₄₁	C₂×C₄	1	2	yes	complemented
41	C₂×#41×C₄₁	D₄	1	2	yes	—
42	C₂×#41×C₄₁	D₄	1	2	yes	—
43	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
44	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
45	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
46	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic, complemented
47	C₂²×D₄×C₄₁	—	2	1	no	—
48	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic, complemented
49	C₂²×D₄×C₄₁	D₄	1	2	yes	—
50	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₄₁	—	2	1	no	—
52	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
53	C₂³×C₄×C₄₁	D₄	1	2	yes	—
54	C₄⋊Q₈×C₄₁	C₂×C₄	1	2	yes	complemented
55	C₄⋊Q₈×C₄₁	C₂×C₄	1	2	yes	complemented
56	#127×C₄₁	C₂×C₄	1	2	yes	—
57	#127×C₄₁	C₂³	1	2	yes	—
58	#124×C₄₁	C₂×C₄	1	2	yes	—
59	#124×C₄₁	C₂×C₄	1	2	yes	complemented
60	#124×C₄₁	C₂×C₄	1	2	yes	complemented
61	#124×C₄₁	C₂³	1	2	yes	—
62	#123×C₄₁	—	2	2	no	—
63	#123×C₄₁	—	2	2	no	—
64	#123×C₄₁	—	2	4	no	—
65	C₂²⋊Q₈×C₄₁	—	2	4	no	—
66	C₂²⋊Q₈×C₄₁	—	2	2	no	—
67	C₂²⋊Q₈×C₄₁	—	2	2	no	—
68	#121×C₄₁	—	2	4	no	—
69	#121×C₄₁	—	2	4	no	—
70	#121×C₄₁	—	2	4	no	—
71	#121×C₄₁	—	2	2	no	—
72	#121×C₄₁	—	2	2	no	—
73	#120×C₄₁	—	2	4	no	—
74	#120×C₄₁	—	2	2	no	—
75	#120×C₄₁	—	2	2	no	—
76	C₄×D₄×C₄₁	—	2	4	no	—
77	C₄×D₄×C₄₁	—	2	4	no	—
78	#117×C₄₁	—	2	1	no	—
79	#117×C₄₁	—	2	1	no	—
80	#117×C₄₁	—	2	4	no	—
81	#117×C₄₁	—	2	4	no	—
82	#117×C₄₁	—	4	2	no	—
83	#117×C₄₁	—	4	2	no	—
84	#117×C₄₁	C₂×C₄	1	2	yes	—
85	#117×C₄₁	C₂×C₄	1	1	yes	characteristic, complemented
86	#117×C₄₁	C₂×C₄	1	1	yes	characteristic, complemented
87	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
88	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
89	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
91	C₂×C₄²×C₄₁	—	4	2	no	—
92	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	complemented
93	#99×C₄₁	—	2	4	no	—
94	#99×C₄₁	—	2	4	no	—
95	#99×C₄₁	—	2	4	no	—
96	#99×C₄₁	C₂³	1	8	yes	—
97	C₂⁴×C₄₁	—	2	1	no	—
98	C₂⁴×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
99	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
100	#41×C₄₁	—	4	2	no	—
101	#41×C₄₁	—	4	1	no	—
102	#41×C₄₁	—	4	1	no	—
103	#41×C₄₁	—	4	2	no	—
104	#41×C₄₁	—	4	2	no	—
105	#41×C₄₁	—	4	2	no	—
106	#41×C₄₁	—	4	2	no	—
107	#41×C₄₁	—	4	2	no	—
108	#41×C₄₁	—	4	1	no	—
109	#41×C₄₁	—	4	1	no	—
110	#41×C₄₁	—	4	4	no	—
111	#41×C₄₁	—	4	4	no	—
112	#41×C₄₁	—	4	2	no	—
113	#41×C₄₁	—	4	2	no	—
114	#41×C₄₁	—	4	2	no	—
115	#41×C₄₁	—	4	2	no	—
116	C₂×Q₈×C₄₁	—	2	1	no	—
117	C₂×Q₈×C₄₁	—	4	2	no	—
118	C₂×Q₈×C₄₁	—	4	2	no	—
119	C₂×Q₈×C₄₁	C₂²⋊C₄	1	2	yes	—
120	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
121	C₂×Q₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
122	C₂×Q₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
123	C₂×D₄×C₄₁	—	2	2	no	—
124	C₂×D₄×C₄₁	—	2	2	no	—
125	C₂×D₄×C₄₁	—	2	4	no	—
126	C₂×D₄×C₄₁	—	2	4	no	—
127	C₂×D₄×C₄₁	—	2	1	no	—
128	C₂×D₄×C₄₁	—	4	2	no	—
129	C₂×D₄×C₄₁	—	4	2	no	—
130	C₂×D₄×C₄₁	—	4	2	no	—
131	C₂×D₄×C₄₁	—	4	2	no	—
132	C₂×D₄×C₄₁	—	4	4	no	—
133	C₂×D₄×C₄₁	C₂²⋊C₄	1	2	yes	—
134	C₂×D₄×C₄₁	C₂²⋊C₄	1	2	yes	—
135	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
136	C₂×D₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
137	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
138	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
139	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
140	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
141	C₂²×C₄×C₄₁	—	2	2	no	—
142	C₂²×C₄×C₄₁	—	2	2	no	—
143	C₂²×C₄×C₄₁	—	2	2	no	—
144	C₂²×C₄×C₄₁	—	2	2	no	—
145	C₂²×C₄×C₄₁	—	2	2	no	—
146	C₂²×C₄×C₄₁	—	2	2	no	—
147	C₂²×C₄×C₄₁	—	2	1	no	—
148	C₂²×C₄×C₄₁	—	2	2	no	—
149	C₂²×C₄×C₄₁	—	2	2	no	—
150	C₂²×C₄×C₄₁	—	2	2	no	—
151	C₂²×C₄×C₄₁	—	4	2	no	—
152	C₂²×C₄×C₄₁	—	4	2	no	—
153	C₂²×C₄×C₄₁	—	4	4	no	—
154	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
155	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
156	C₂²×C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
157	C₂²×C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
158	C₂²×C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
159	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
160	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
164	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
165	C₄⋊C₄×C₄₁	—	2	2	no	—
166	C₄⋊C₄×C₄₁	—	2	1	no	—
167	C₄⋊C₄×C₄₁	—	2	1	no	—
168	C₄⋊C₄×C₄₁	—	2	4	no	—
169	C₄⋊C₄×C₄₁	—	2	4	no	—
170	C₄⋊C₄×C₄₁	—	4	4	no	—
171	C₄⋊C₄×C₄₁	—	4	4	no	—
172	C₂²⋊C₄×C₄₁	—	2	2	no	—
173	C₂²⋊C₄×C₄₁	—	2	1	no	—
174	C₂²⋊C₄×C₄₁	—	2	1	no	—
175	C₂²⋊C₄×C₄₁	—	2	4	no	—
176	C₂²⋊C₄×C₄₁	—	2	4	no	—
177	C₂²⋊C₄×C₄₁	—	2	4	no	—
178	C₂²⋊C₄×C₄₁	—	2	4	no	—
179	C₂²⋊C₄×C₄₁	—	2	8	no	—
180	C₂²⋊C₄×C₄₁	—	4	4	no	—
181	C₄²×C₄₁	—	2	2	no	—
182	C₄²×C₄₁	—	4	4	no	—
183	C₄²×C₄₁	—	4	4	no	—
184	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
185	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
186	C₂³×C₄₁	—	2	2	no	—
187	C₂³×C₄₁	—	2	2	no	—
188	C₂³×C₄₁	—	2	2	no	—
189	C₂³×C₄₁	—	2	2	no	—
190	C₂³×C₄₁	—	4	2	no	—
191	C₂³×C₄₁	—	8	2	no	—
192	C₂³×C₄₁	—	8	1	no	—
193	C₂³×C₄₁	—	8	2	no	—
194	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
196	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
197	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
198	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
199	Q₈×C₄₁	—	4	2	no	—
200	Q₈×C₄₁	—	4	1	no	—
201	Q₈×C₄₁	—	4	1	no	—
202	Q₈×C₄₁	—	4	2	no	—
203	Q₈×C₄₁	—	4	2	no	—
204	D₄×C₄₁	—	4	2	no	—
205	D₄×C₄₁	—	4	2	no	—
206	D₄×C₄₁	—	4	1	no	—
207	D₄×C₄₁	—	4	2	no	—
208	D₄×C₄₁	—	4	2	no	—
209	D₄×C₄₁	—	4	2	no	—
210	D₄×C₄₁	—	4	1	no	—
211	D₄×C₄₁	—	4	2	no	—
212	D₄×C₄₁	—	4	4	no	—
213	D₄×C₄₁	—	4	4	no	—
214	D₄×C₄₁	—	4	2	no	—
215	D₄×C₄₁	—	8	4	no	—
216	D₄×C₄₁	—	8	4	no	—
217	C₂×C₄×C₄₁	—	2	2	no	—
218	C₂×C₄×C₄₁	—	2	2	no	—
219	C₂×C₄×C₄₁	—	2	2	no	—
220	C₂×C₄×C₄₁	—	2	2	no	—
221	C₂×C₄×C₄₁	—	2	2	no	—
222	C₂×C₄×C₄₁	—	2	2	no	—
223	C₂×C₄×C₄₁	—	2	1	no	—
224	C₂×C₄×C₄₁	—	2	2	no	—
225	C₂×C₄×C₄₁	—	2	2	no	—
226	C₂×C₄×C₄₁	—	2	2	no	—
227	C₂×C₄×C₄₁	—	2	2	no	—
228	C₂×C₄×C₄₁	—	2	2	no	—
229	C₂×C₄×C₄₁	—	2	1	no	—
230	C₂×C₄×C₄₁	—	2	2	no	—
231	C₂×C₄×C₄₁	—	2	1	no	—
232	C₂×C₄×C₄₁	—	2	2	no	—
233	C₂×C₄×C₄₁	—	2	1	no	—
234	C₂×C₄×C₄₁	—	2	2	no	—
235	C₂×C₄×C₄₁	—	2	2	no	—
236	C₂×C₄×C₄₁	—	2	2	no	—
237	C₂×C₄×C₄₁	—	4	4	no	—
238	C₂×C₄×C₄₁	—	4	2	no	—
239	C₂×C₄×C₄₁	—	4	2	no	—
240	C₂×C₄×C₄₁	—	4	2	no	—
241	C₂×C₄×C₄₁	—	4	8	no	—
242	C₂×C₄×C₄₁	—	8	2	no	—
243	C₂×C₄×C₄₁	—	8	8	no	—
244	C₂×C₄×C₄₁	#99	1	2	yes	—
245	C₂×C₄×C₄₁	#99	1	2	yes	—
246	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
247	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
248	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
249	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
251	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
252	#33358	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
253	C₂²×C₄₁	—	2	2	no	—
254	C₂²×C₄₁	—	2	1	no	—
255	C₂²×C₄₁	—	2	1	no	—
256	C₂²×C₄₁	—	2	2	no	—
257	C₂²×C₄₁	—	4	1	no	—
258	C₂²×C₄₁	—	4	1	no	—
259	C₂²×C₄₁	—	4	2	no	—
260	C₂²×C₄₁	—	4	2	no	—
261	C₂²×C₄₁	—	4	1	no	—
262	C₂²×C₄₁	—	4	4	no	—
263	C₂²×C₄₁	—	4	4	no	—
264	C₂²×C₄₁	—	4	2	no	—
265	C₂²×C₄₁	—	8	2	no	—
266	C₂²×C₄₁	—	8	2	no	—
267	C₂²×C₄₁	—	8	4	no	—
268	C₂²×C₄₁	C₂×#99	1	2	yes	—
269	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
270	C₄×C₄₁	—	2	1	no	—
271	C₄×C₄₁	—	2	2	no	—
272	C₄×C₄₁	—	2	2	no	—
273	C₄×C₄₁	—	2	1	no	—
274	C₄×C₄₁	—	4	2	no	—
275	C₄×C₄₁	—	4	2	no	—
276	C₄×C₄₁	—	4	2	no	—
277	C₄×C₄₁	—	8	8	no	—
278	C₄×C₄₁	C₂×#99	1	1	yes	characteristic
279	C₄×C₄₁	C₂×#99	1	2	yes	—
280	C₄×C₄₁	C₂×#99	1	1	yes	characteristic
281	#3449	C₂×C₄₁	1	1	yes	characteristic
282	C₂×#410	C₂×C₄₁	1	2	yes	complemented
283	#2129	C₂×C₄₁	1	2	yes	complemented
284	#2128	C₂×C₄₁	1	2	yes	complemented
285	#2127	C₂×C₄₁	1	4	yes	complemented
286	#2126	C₂×C₄₁	1	4	yes	complemented
287	C₂×C₄₁	—	2	1	no	—
288	C₂×C₄₁	—	2	2	no	—
289	C₂×C₄₁	—	4	2	no	—
290	C₂×C₄₁	—	4	2	no	—
291	C₂×C₄₁	—	4	1	no	—
292	C₂×C₄₁	—	4	1	no	—
293	C₂×C₄₁	—	8	2	no	—
294	C₂×C₄₁	C₂²×#99	1	1	yes	characteristic
295	C₂²×#41	C₄×C₄₁	1	1	yes	characteristic, complemented
296	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
297	#537	—	2	2	no	—
298	#536	C₄×C₄₁	1	2	yes	complemented
299	#536	C₄×C₄₁	1	1	yes	characteristic, complemented
300	#536	C₂²×C₄₁	1	1	yes	characteristic
301	#535	C₄×C₄₁	1	1	yes	characteristic, complemented
302	#535	C₂²×C₄₁	1	2	yes	—
303	#535	C₂²×C₄₁	1	1	yes	characteristic
304	#534	—	2	2	no	—
305	#532	C₄×C₄₁	1	2	yes	complemented
306	#532	C₂²×C₄₁	1	2	yes	—
307	#525	—	2	2	no	—
308	#525	—	2	2	no	—
309	C₂×#117	—	2	2	no	—
310	C₂×#117	C₄×C₄₁	1	1	yes	characteristic, complemented
311	#410	—	2	2	no	—
312	#410	—	2	2	no	—
313	#410	C₂²×C₄₁	1	4	yes	—
314	#410	C₂²×C₄₁	1	4	yes	complemented
315	C₂×#99	—	2	2	no	—
316	C₂×#99	C₂²×C₄₁	1	4	yes	complemented
317	#354	C₂²×C₄₁	1	8	yes	complemented
318	#353	C₂²×C₄₁	1	8	yes	complemented
319	C₄₁	#33358	1	1	yes	characteristic, direct product factor, Sylow
320	C₂×#41	—	2	1	no	—
321	C₂×#41	—	2	1	no	—
322	C₂×#41	—	4	2	no	—
323	C₂×#41	—	4	2	no	—
324	C₂×#41	—	4	2	no	—
325	C₂×#41	—	4	2	no	—
326	C₂×#41	C₂×C₄×C₄₁	1	2	yes	—
327	C₂×#41	C₂×C₄×C₄₁	1	1	yes	characteristic
328	C₂×#41	C₂×C₄×C₄₁	1	1	yes	characteristic
329	C₂×#41	C₂×C₄×C₄₁	1	2	yes	complemented
330	C₂×#41	D₄×C₄₁	1	2	yes	—
331	C₂×#41	D₄×C₄₁	1	2	yes	—
332	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
333	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
334	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
335	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic, complemented
336	C₂²×D₄	—	2	1	no	—
337	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic, complemented
338	C₂²×D₄	D₄×C₄₁	1	2	yes	—
339	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
340	C₂³×C₄	—	2	1	no	—
341	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
342	C₂³×C₄	D₄×C₄₁	1	2	yes	—
343	C₄⋊Q₈	C₂×C₄×C₄₁	1	2	yes	complemented
344	C₄⋊Q₈	C₂×C₄×C₄₁	1	2	yes	complemented
345	#127	C₂×C₄×C₄₁	1	2	yes	—
346	#127	C₂³×C₄₁	1	2	yes	—
347	#124	C₂×C₄×C₄₁	1	2	yes	—
348	#124	C₂×C₄×C₄₁	1	2	yes	complemented
349	#124	C₂×C₄×C₄₁	1	2	yes	complemented
350	#124	C₂³×C₄₁	1	2	yes	—
351	#123	—	2	2	no	—
352	#123	—	2	2	no	—
353	#123	—	2	4	no	—
354	C₂²⋊Q₈	—	2	4	no	—
355	C₂²⋊Q₈	—	2	2	no	—
356	C₂²⋊Q₈	—	2	2	no	—
357	#121	—	2	4	no	—
358	#121	—	2	4	no	—
359	#121	—	2	4	no	—
360	#121	—	2	2	no	—
361	#121	—	2	2	no	—
362	#120	—	2	4	no	—
363	#120	—	2	2	no	—
364	#120	—	2	2	no	—
365	C₄×D₄	—	2	4	no	—
366	C₄×D₄	—	2	4	no	—
367	#117	—	2	1	no	—
368	#117	—	2	1	no	—
369	#117	—	2	4	no	—
370	#117	—	2	4	no	—
371	#117	—	4	2	no	—
372	#117	—	4	2	no	—
373	#117	C₂×C₄×C₄₁	1	2	yes	—
374	#117	C₂×C₄×C₄₁	1	1	yes	characteristic, complemented
375	#117	C₂×C₄×C₄₁	1	1	yes	characteristic, complemented
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	—	4	2	no	—
378	C₂×C₂²⋊C₄	—	2	1	no	—
379	C₂×C₂²⋊C₄	—	2	4	no	—
380	C₂×C₄²	—	4	2	no	—
381	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	complemented
382	#99	—	2	4	no	—
383	#99	—	2	4	no	—
384	#99	—	2	4	no	—
385	#99	C₂³×C₄₁	1	8	yes	—
386	C₂⁴	—	2	1	no	—
387	C₂⁴	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
388	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
389	#41	—	4	2	no	—
390	#41	—	4	1	no	—
391	#41	—	4	1	no	—
392	#41	—	4	2	no	—
393	#41	—	4	2	no	—
394	#41	—	4	2	no	—
395	#41	—	4	2	no	—
396	#41	—	4	1	no	—
397	#41	—	4	2	no	—
398	#41	—	4	1	no	—
399	#41	—	4	4	no	—
400	#41	—	4	4	no	—
401	#41	—	4	2	no	—
402	#41	—	4	2	no	—
403	#41	—	4	2	no	—
404	#41	—	4	2	no	—
405	C₂×Q₈	—	2	1	no	—
406	C₂×Q₈	—	4	2	no	—
407	C₂×Q₈	—	4	2	no	—
408	C₂×Q₈	C₂²⋊C₄×C₄₁	1	2	yes	—
409	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
410	C₂×Q₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
411	C₂×Q₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	4	no	—
415	C₂×D₄	—	2	4	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	4	2	no	—
418	C₂×D₄	—	4	2	no	—
419	C₂×D₄	—	4	2	no	—
420	C₂×D₄	—	4	2	no	—
421	C₂×D₄	—	4	4	no	—
422	C₂×D₄	C₂²⋊C₄×C₄₁	1	2	yes	—
423	C₂×D₄	C₂²⋊C₄×C₄₁	1	2	yes	—
424	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
425	C₂×D₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
426	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
427	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
428	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
429	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	4	2	no	—
441	C₂²×C₄	—	4	2	no	—
442	C₂²×C₄	—	4	4	no	—
443	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
444	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
445	C₂²×C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
446	C₂²×C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
447	C₂²×C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
448	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
449	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
450	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
451	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
453	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	4	no	—
458	C₄⋊C₄	—	2	4	no	—
459	C₄⋊C₄	—	4	4	no	—
460	C₄⋊C₄	—	4	4	no	—
461	C₂²⋊C₄	—	2	2	no	—
462	C₂²⋊C₄	—	2	1	no	—
463	C₂²⋊C₄	—	2	1	no	—
464	C₂²⋊C₄	—	2	4	no	—
465	C₂²⋊C₄	—	2	4	no	—
466	C₂²⋊C₄	—	2	4	no	—
467	C₂²⋊C₄	—	2	4	no	—
468	C₂²⋊C₄	—	2	8	no	—
469	C₂²⋊C₄	—	4	4	no	—
470	C₄²	—	2	2	no	—
471	C₄²	—	4	4	no	—
472	C₄²	—	4	4	no	—
473	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
474	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	4	2	no	—
480	C₂³	—	8	2	no	—
481	C₂³	—	8	1	no	—
482	C₂³	—	8	2	no	—
483	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
484	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
485	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
486	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
487	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
488	Q₈	—	4	2	no	—
489	Q₈	—	4	1	no	—
490	Q₈	—	4	1	no	—
491	Q₈	—	4	2	no	—
492	Q₈	—	4	2	no	—
493	D₄	—	4	2	no	—
494	D₄	—	4	2	no	—
495	D₄	—	4	1	no	—
496	D₄	—	4	2	no	—
497	D₄	—	4	2	no	—
498	D₄	—	4	2	no	—
499	D₄	—	4	1	no	—
500	D₄	—	4	2	no	—
501	D₄	—	4	4	no	—
502	D₄	—	4	4	no	—
503	D₄	—	4	2	no	—
504	D₄	—	8	4	no	—
505	D₄	—	8	4	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	4	4	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	8	no	—
531	C₂×C₄	—	8	2	no	—
532	C₂×C₄	—	8	8	no	—
533	C₂×C₄	#99×C₄₁	1	2	yes	—
534	C₂×C₄	#99×C₄₁	1	2	yes	—
535	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
536	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
537	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
538	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
539	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
540	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
541	C₂²	—	2	2	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	4	1	no	—
546	C₂²	—	4	1	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	4	no	—
551	C₂²	—	4	4	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	8	2	no	—
554	C₂²	—	8	2	no	—
555	C₂²	—	8	4	no	—
556	C₂²	C₂×#99×C₄₁	1	2	yes	—
557	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
558	C₄	—	2	1	no	—
559	C₄	—	2	2	no	—
560	C₄	—	2	2	no	—
561	C₄	—	2	1	no	—
562	C₄	—	4	2	no	—
563	C₄	—	4	2	no	—
564	C₄	—	4	2	no	—
565	C₄	—	8	8	no	—
566	C₄	C₂×#99×C₄₁	1	1	yes	characteristic
567	C₄	C₂×#99×C₄₁	1	1	yes	characteristic
568	C₄	C₂×#99×C₄₁	1	2	yes	—
569	C₂	—	2	1	no	—
570	C₂	—	2	2	no	—
571	C₂	—	4	2	no	—
572	C₂	—	4	2	no	—
573	C₂	—	4	1	no	—
574	C₂	—	4	1	no	—
575	C₂	—	8	2	no	—
576	C₂	C₂²×#99×C₄₁	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₄₁	C₂×#99
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂×D₄	C₂⁴×C₄₁
socle	C₂×C₄₁	C₂²×#99
prime radical	C₄₁×#3449	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₄₁ ◁ C₂²×C₄×C₄₁ ◁ C₂²×#41×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#410	C₂	semidirect
3. C₄₁×#2129	C₂	semidirect
4. C₄₁×#2128	C₂	semidirect
5. C₄₁×#2127	C₂	semidirect
6. C₄₁×#2126	C₂	semidirect
7. C₂²×#41×C₄₁	C₄	semidirect
10. C₄₁×#536	C₄	semidirect
11. C₄₁×#536	C₄	semidirect
13. C₄₁×#535	C₄	semidirect
17. C₄₁×#532	C₄	semidirect
22. C₂×#117×C₄₁	C₄	semidirect
26. C₄₁×#410	C₂²	semidirect
28. C₂×#99×C₄₁	C₂²	semidirect
29. C₄₁×#354	C₂²	semidirect
30. C₄₁×#353	C₂²	semidirect
40. C₂×#41×C₄₁	C₂×C₄	semidirect
46. C₂²×Q₈×C₄₁	C₂×C₄	semidirect
48. C₂²×D₄×C₄₁	C₂×C₄	semidirect
54. C₄⋊Q₈×C₄₁	C₂×C₄	semidirect
55. C₄⋊Q₈×C₄₁	C₂×C₄	semidirect
59. #124×C₄₁	C₂×C₄	semidirect
60. #124×C₄₁	C₂×C₄	semidirect
85. #117×C₄₁	C₂×C₄	semidirect
86. #117×C₄₁	C₂×C₄	semidirect
92. C₂×C₄²×C₄₁	C₂×C₄	semidirect
252. #33358	C₄₁	direct (N × H)
282. C₂×#410	C₂×C₄₁	semidirect
283. #2129	C₂×C₄₁	semidirect
284. #2128	C₂×C₄₁	semidirect
285. #2127	C₂×C₄₁	semidirect
286. #2126	C₂×C₄₁	semidirect
295. C₂²×#41	C₄×C₄₁	semidirect
298. #536	C₄×C₄₁	semidirect
299. #536	C₄×C₄₁	semidirect
301. #535	C₄×C₄₁	semidirect
305. #532	C₄×C₄₁	semidirect
310. C₂×#117	C₄×C₄₁	semidirect
314. #410	C₂²×C₄₁	semidirect
316. C₂×#99	C₂²×C₄₁	semidirect
317. #354	C₂²×C₄₁	semidirect
318. #353	C₂²×C₄₁	semidirect
319. C₄₁	#33358	direct (N × H)
329. C₂×#41	C₂×C₄×C₄₁	semidirect
335. C₂²×Q₈	C₂×C₄×C₄₁	semidirect
337. C₂²×D₄	C₂×C₄×C₄₁	semidirect
343. C₄⋊Q₈	C₂×C₄×C₄₁	semidirect
344. C₄⋊Q₈	C₂×C₄×C₄₁	semidirect
348. #124	C₂×C₄×C₄₁	semidirect
349. #124	C₂×C₄×C₄₁	semidirect
374. #117	C₂×C₄×C₄₁	semidirect
375. #117	C₂×C₄×C₄₁	semidirect
381. C₂×C₄²	C₂×C₄×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3449	2
C₂×C₄₁×#410	2
C₄₁×#2129	2
C₄₁×#2128	2
C₄₁×#2127	2
C₄₁×#2126	2
#33358	41

Subgroups — C41×#33358 #23809559

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#33358 #23809559