Subgroups — C₄₁×#20947 #23797148

Order 10496.

1708 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#568	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3449	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₁×#421	C₂	1	2	yes	maximal, complemented
4	C₂×C₄₁×#410	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1884	C₂	1	8	yes	maximal, complemented
6	C₄₁×#1733	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
8	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
9	C₄₁×#568	—	2	2	no	—
10	C₄₁×#568	—	2	4	no	—
11	C₄₁×#568	C₂²	1	4	yes	complemented
12	C₂×#131×C₄₁	—	2	4	no	—
13	C₂²×M₁₆×C₄₁	—	2	2	no	—
14	C₂²×M₁₆×C₄₁	C₂²	1	2	yes	—
15	C₄₁×#537	—	2	2	no	—
16	C₄₁×#536	C₄	1	2	yes	complemented
17	C₄₁×#536	C₄	1	2	yes	complemented
18	C₄₁×#535	C₄	1	2	yes	complemented
19	C₄₁×#535	C₄	1	2	yes	complemented
20	C₄₁×#534	—	2	2	no	—
21	C₄₁×#532	C₂²	1	4	yes	—
22	C₄₁×#525	—	2	2	no	—
23	C₄₁×#525	—	2	2	no	—
24	C₂×#117×C₄₁	C₂²	1	2	yes	—
25	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
26	C₄₁×#421	—	2	4	no	—
27	C₄₁×#421	C₂²	1	8	yes	complemented
28	C₂×#104×C₄₁	—	2	4	no	—
29	C₄₁×#410	—	2	2	no	—
30	C₄₁×#410	C₂²	1	4	yes	complemented
31	C₂×#99×C₄₁	—	2	2	no	—
32	C₄₁×#339	C₂²	1	8	yes	complemented
33	C₂×#41×C₄₁	—	2	2	no	—
34	C₂×#41×C₄₁	—	2	2	no	—
35	C₂×#41×C₄₁	—	2	1	no	—
36	C₂×#41×C₄₁	—	2	1	no	—
37	C₂×#41×C₄₁	—	2	2	no	—
38	C₂×#41×C₄₁	—	2	2	no	—
39	C₂×#41×C₄₁	—	2	2	no	—
40	C₂×#41×C₄₁	—	2	2	no	—
41	C₂×#41×C₄₁	—	2	2	no	—
42	C₂×#41×C₄₁	—	2	2	no	—
43	C₂×#41×C₄₁	C₂×C₄	1	2	yes	—
44	C₂×#41×C₄₁	C₂×C₄	1	2	yes	—
45	C₂×#41×C₄₁	D₄	1	2	yes	—
46	C₂×#41×C₄₁	D₄	1	2	yes	—
47	C₂×#41×C₄₁	C₂³	1	2	yes	—
48	C₂×#41×C₄₁	C₂³	1	2	yes	—
49	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
50	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
51	C₂²×D₄×C₄₁	—	2	1	no	—
52	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
53	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
54	C₂²×D₄×C₄₁	D₄	1	2	yes	—
55	C₂³×C₄×C₄₁	—	2	1	no	—
56	C₂³×C₄×C₄₁	D₄	1	2	yes	—
57	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
58	#131×C₄₁	—	2	16	no	—
59	#131×C₄₁	—	2	16	no	—
60	C₂×M₁₆×C₄₁	—	2	4	no	—
61	C₂×M₁₆×C₄₁	—	2	8	no	—
62	C₂×M₁₆×C₄₁	—	2	2	no	—
63	C₂×M₁₆×C₄₁	—	2	8	no	—
64	C₂×M₁₆×C₄₁	—	2	2	no	—
65	C₂×M₁₆×C₄₁	—	2	2	no	—
66	C₂×M₁₆×C₄₁	D₄	1	4	yes	complemented
67	C₂×M₁₆×C₄₁	D₄	1	4	yes	complemented
68	C₂×M₁₆×C₄₁	C₂³	1	4	yes	—
69	C₂²×C₈×C₄₁	—	2	4	no	—
70	C₂²×C₈×C₄₁	—	2	2	no	—
71	C₄⋊Q₈×C₄₁	C₂×C₄	1	4	yes	complemented
72	#127×C₄₁	C₂×C₄	1	4	yes	complemented
73	#124×C₄₁	C₂×C₄	1	4	yes	complemented
74	#124×C₄₁	C₂×C₄	1	4	yes	complemented
75	#123×C₄₁	—	2	4	no	—
76	#123×C₄₁	—	2	4	no	—
77	C₂²⋊Q₈×C₄₁	—	2	4	no	—
78	C₂²⋊Q₈×C₄₁	—	2	4	no	—
79	#121×C₄₁	—	2	4	no	—
80	#121×C₄₁	—	2	8	no	—
81	#121×C₄₁	—	2	4	no	—
82	#120×C₄₁	—	2	4	no	—
83	#120×C₄₁	—	2	4	no	—
84	C₄×D₄×C₄₁	—	2	8	no	—
85	#117×C₄₁	—	2	1	no	—
86	#117×C₄₁	—	2	1	no	—
87	#117×C₄₁	—	2	2	no	—
88	#117×C₄₁	—	2	2	no	—
89	#117×C₄₁	—	2	2	no	—
90	#117×C₄₁	C₂×C₄	1	2	yes	—
91	#117×C₄₁	C₂×C₄	1	2	yes	—
92	#117×C₄₁	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
94	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
97	C₂×C₄²×C₄₁	—	2	2	no	—
98	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
99	#104×C₄₁	—	2	16	no	—
100	#99×C₄₁	—	2	8	no	—
101	C₂⁴×C₄₁	—	2	1	no	—
102	C₂⁴×C₄₁	C₂²⋊C₄	1	2	yes	—
103	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
104	#41×C₄₁	—	2	4	no	—
105	#41×C₄₁	—	2	4	no	—
106	#41×C₄₁	—	2	4	no	—
107	#41×C₄₁	—	2	4	no	—
108	#41×C₄₁	—	2	4	no	—
109	#41×C₄₁	—	2	4	no	—
110	#41×C₄₁	—	2	4	no	—
111	#41×C₄₁	—	2	4	no	—
112	#41×C₄₁	—	2	4	no	—
113	#41×C₄₁	—	2	4	no	—
114	#41×C₄₁	—	2	4	no	—
115	#41×C₄₁	—	2	4	no	—
116	#41×C₄₁	—	4	1	no	—
117	#41×C₄₁	—	4	1	no	—
118	#41×C₄₁	—	4	2	no	—
119	#41×C₄₁	—	4	2	no	—
120	#41×C₄₁	—	4	1	no	—
121	#41×C₄₁	—	4	1	no	—
122	C₂×Q₈×C₄₁	—	2	1	no	—
123	C₂×Q₈×C₄₁	—	2	2	no	—
124	C₂×Q₈×C₄₁	—	2	2	no	—
125	C₂×Q₈×C₄₁	—	2	2	no	—
126	C₂×Q₈×C₄₁	—	2	2	no	—
127	C₂×Q₈×C₄₁	C₂²⋊C₄	1	2	yes	—
128	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
129	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
130	C₂×D₄×C₄₁	—	2	4	no	—
131	C₂×D₄×C₄₁	—	2	4	no	—
132	C₂×D₄×C₄₁	—	2	2	no	—
133	C₂×D₄×C₄₁	—	2	2	no	—
134	C₂×D₄×C₄₁	—	2	8	no	—
135	C₂×D₄×C₄₁	—	2	1	no	—
136	C₂×D₄×C₄₁	—	2	2	no	—
137	C₂×D₄×C₄₁	—	2	2	no	—
138	C₂×D₄×C₄₁	—	2	2	no	—
139	C₂×D₄×C₄₁	—	2	2	no	—
140	C₂×D₄×C₄₁	—	4	2	no	—
141	C₂×D₄×C₄₁	—	4	2	no	—
142	C₂×D₄×C₄₁	C₂²⋊C₄	1	4	yes	—
143	C₂×D₄×C₄₁	C₂²⋊C₄	1	2	yes	—
144	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
145	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
146	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
147	C₂²×C₄×C₄₁	—	2	2	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	—	2	1	no	—
152	C₂²×C₄×C₄₁	—	2	2	no	—
153	C₂²×C₄×C₄₁	—	2	2	no	—
154	C₂²×C₄×C₄₁	—	2	2	no	—
155	C₂²×C₄×C₄₁	—	4	2	no	—
156	C₂²×C₄×C₄₁	—	4	2	no	—
157	C₂²×C₄×C₄₁	—	4	2	no	—
158	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
159	C₂²×C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
160	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
163	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₄₁	#41	1	2	yes	—
169	C₂²×C₄×C₄₁	#41	1	2	yes	—
170	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
171	M₁₆×C₄₁	—	2	16	no	—
172	M₁₆×C₄₁	—	2	4	no	—
173	M₁₆×C₄₁	—	2	4	no	—
174	M₁₆×C₄₁	—	2	4	no	—
175	M₁₆×C₄₁	C₂×D₄	1	8	yes	—
176	C₂×C₈×C₄₁	—	2	16	no	—
177	C₂×C₈×C₄₁	—	2	4	no	—
178	C₂×C₈×C₄₁	—	2	4	no	—
179	C₂×C₈×C₄₁	—	2	4	no	—
180	C₄⋊C₄×C₄₁	—	2	2	no	—
181	C₄⋊C₄×C₄₁	—	2	2	no	—
182	C₄⋊C₄×C₄₁	—	2	8	no	—
183	C₄⋊C₄×C₄₁	—	2	4	no	—
184	C₄⋊C₄×C₄₁	—	4	2	no	—
185	C₂²⋊C₄×C₄₁	—	2	2	no	—
186	C₂²⋊C₄×C₄₁	—	2	2	no	—
187	C₂²⋊C₄×C₄₁	—	2	8	no	—
188	C₂²⋊C₄×C₄₁	—	2	8	no	—
189	C₂²⋊C₄×C₄₁	—	2	4	no	—
190	C₂²⋊C₄×C₄₁	—	4	2	no	—
191	C₄²×C₄₁	—	2	2	no	—
192	C₄²×C₄₁	—	2	4	no	—
193	C₄²×C₄₁	—	4	2	no	—
194	C₄²×C₄₁	C₂²×C₄	1	4	yes	—
195	C₂³×C₄₁	—	2	2	no	—
196	C₂³×C₄₁	—	2	2	no	—
197	C₂³×C₄₁	—	2	2	no	—
198	C₂³×C₄₁	—	4	2	no	—
199	C₂³×C₄₁	—	8	1	no	—
200	C₂³×C₄₁	—	8	2	no	—
201	C₂³×C₄₁	—	8	2	no	—
202	C₂³×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
203	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂³×C₄₁	#121	1	2	yes	—
206	C₂³×C₄₁	#121	1	2	yes	—
207	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
208	Q₈×C₄₁	—	2	4	no	—
209	Q₈×C₄₁	—	2	4	no	—
210	Q₈×C₄₁	—	2	4	no	—
211	Q₈×C₄₁	—	4	1	no	—
212	Q₈×C₄₁	—	4	1	no	—
213	D₄×C₄₁	—	2	8	no	—
214	D₄×C₄₁	—	2	8	no	—
215	D₄×C₄₁	—	2	4	no	—
216	D₄×C₄₁	—	2	4	no	—
217	D₄×C₄₁	—	2	4	no	—
218	D₄×C₄₁	—	4	4	no	—
219	D₄×C₄₁	—	4	2	no	—
220	D₄×C₄₁	—	4	2	no	—
221	D₄×C₄₁	—	4	1	no	—
222	D₄×C₄₁	—	4	1	no	—
223	D₄×C₄₁	—	8	8	no	—
224	C₂×C₄×C₄₁	—	2	2	no	—
225	C₂×C₄×C₄₁	—	2	2	no	—
226	C₂×C₄×C₄₁	—	2	4	no	—
227	C₂×C₄×C₄₁	—	2	4	no	—
228	C₂×C₄×C₄₁	—	2	4	no	—
229	C₂×C₄×C₄₁	—	2	4	no	—
230	C₂×C₄×C₄₁	—	2	4	no	—
231	C₂×C₄×C₄₁	—	2	2	no	—
232	C₂×C₄×C₄₁	—	4	2	no	—
233	C₂×C₄×C₄₁	—	4	2	no	—
234	C₂×C₄×C₄₁	—	4	2	no	—
235	C₂×C₄×C₄₁	—	4	4	no	—
236	C₂×C₄×C₄₁	—	4	4	no	—
237	C₂×C₄×C₄₁	—	8	2	no	—
238	C₂×C₄×C₄₁	—	8	4	no	—
239	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
240	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
243	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
244	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
245	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
246	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
247	C₂×C₄×C₄₁	#120	1	2	yes	—
248	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
249	C₂×C₄×C₄₁	#121	1	2	yes	—
250	C₂×C₄×C₄₁	#121	1	2	yes	—
251	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
252	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
253	C₂×C₄×C₄₁	#123	1	2	yes	—
254	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
255	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
256	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
258	C₈×C₄₁	—	2	8	no	—
259	#20947	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
260	C₂²×C₄₁	—	2	4	no	—
261	C₂²×C₄₁	—	4	2	no	—
262	C₂²×C₄₁	—	4	1	no	—
263	C₂²×C₄₁	—	4	1	no	—
264	C₂²×C₄₁	—	4	1	no	—
265	C₂²×C₄₁	—	4	2	no	—
266	C₂²×C₄₁	—	4	4	no	—
267	C₂²×C₄₁	—	4	4	no	—
268	C₂²×C₄₁	—	4	4	no	—
269	C₂²×C₄₁	—	4	2	no	—
270	C₂²×C₄₁	—	8	2	no	—
271	C₂²×C₄₁	—	8	4	no	—
272	C₂²×C₄₁	#386	1	1	yes	characteristic
273	C₂²×C₄₁	#386	1	1	yes	characteristic
274	C₂²×C₄₁	#386	1	2	yes	—
275	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
276	C₂²×C₄₁	C₂×#121	1	2	yes	—
277	C₄×C₄₁	—	2	4	no	—
278	C₄×C₄₁	—	4	4	no	—
279	C₄×C₄₁	—	4	2	no	—
280	C₄×C₄₁	—	8	4	no	—
281	C₄×C₄₁	#386	1	1	yes	characteristic
282	C₄×C₄₁	#386	1	1	yes	characteristic
283	C₄×C₄₁	#386	1	2	yes	—
284	C₄×C₄₁	C₂×C₄×D₄	1	2	yes	—
285	C₄×C₄₁	C₂×#120	1	1	yes	characteristic
286	C₄×C₄₁	C₂×#123	1	1	yes	characteristic
287	C₂×#568	C₂×C₄₁	1	1	yes	characteristic, complemented
288	#3449	C₂×C₄₁	1	1	yes	characteristic
289	C₂×#421	C₂×C₄₁	1	2	yes	complemented
290	C₂×#410	C₂×C₄₁	1	1	yes	characteristic, complemented
291	#1884	C₂×C₄₁	1	8	yes	complemented
292	#1733	C₂×C₄₁	1	2	yes	complemented
293	C₂×C₄₁	—	2	1	no	—
294	C₂×C₄₁	—	2	2	no	—
295	C₂×C₄₁	—	2	1	no	—
296	C₂×C₄₁	—	2	1	no	—
297	C₂×C₄₁	—	2	2	no	—
298	C₂×C₄₁	—	4	4	no	—
299	C₂×C₄₁	—	8	2	no	—
300	C₂×C₄₁	C₂×#386	1	1	yes	characteristic
301	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
302	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
303	#568	—	2	2	no	—
304	#568	—	2	4	no	—
305	#568	C₂²×C₄₁	1	4	yes	complemented
306	C₂×#131	—	2	4	no	—
307	C₂²×M₁₆	—	2	2	no	—
308	C₂²×M₁₆	C₂²×C₄₁	1	2	yes	—
309	#537	—	2	2	no	—
310	#536	C₄×C₄₁	1	2	yes	complemented
311	#536	C₄×C₄₁	1	2	yes	complemented
312	#535	C₄×C₄₁	1	2	yes	complemented
313	#535	C₄×C₄₁	1	2	yes	complemented
314	#534	—	2	2	no	—
315	#532	C₂²×C₄₁	1	4	yes	—
316	#525	—	2	2	no	—
317	#525	—	2	2	no	—
318	C₂×#117	C₂²×C₄₁	1	2	yes	—
319	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
320	#421	—	2	4	no	—
321	#421	C₂²×C₄₁	1	8	yes	complemented
322	C₂×#104	—	2	4	no	—
323	#410	—	2	2	no	—
324	#410	C₂²×C₄₁	1	4	yes	complemented
325	C₂×#99	—	2	2	no	—
326	#339	C₂²×C₄₁	1	8	yes	complemented
327	C₄₁	#20947	1	1	yes	characteristic, direct product factor, Sylow
328	C₂×#41	—	2	2	no	—
329	C₂×#41	—	2	2	no	—
330	C₂×#41	—	2	1	no	—
331	C₂×#41	—	2	1	no	—
332	C₂×#41	—	2	2	no	—
333	C₂×#41	—	2	2	no	—
334	C₂×#41	—	2	2	no	—
335	C₂×#41	—	2	2	no	—
336	C₂×#41	—	2	2	no	—
337	C₂×#41	—	2	2	no	—
338	C₂×#41	C₂×C₄×C₄₁	1	2	yes	—
339	C₂×#41	C₂×C₄×C₄₁	1	2	yes	—
340	C₂×#41	D₄×C₄₁	1	2	yes	—
341	C₂×#41	D₄×C₄₁	1	2	yes	—
342	C₂×#41	C₂³×C₄₁	1	2	yes	—
343	C₂×#41	C₂³×C₄₁	1	2	yes	—
344	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
345	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
346	C₂²×D₄	—	2	1	no	—
347	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
348	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
349	C₂²×D₄	D₄×C₄₁	1	2	yes	—
350	C₂³×C₄	—	2	1	no	—
351	C₂³×C₄	D₄×C₄₁	1	2	yes	—
352	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
353	#131	—	2	16	no	—
354	#131	—	2	16	no	—
355	C₂×M₁₆	—	2	4	no	—
356	C₂×M₁₆	—	2	8	no	—
357	C₂×M₁₆	—	2	2	no	—
358	C₂×M₁₆	—	2	8	no	—
359	C₂×M₁₆	—	2	2	no	—
360	C₂×M₁₆	—	2	2	no	—
361	C₂×M₁₆	D₄×C₄₁	1	4	yes	complemented
362	C₂×M₁₆	D₄×C₄₁	1	4	yes	complemented
363	C₂×M₁₆	C₂³×C₄₁	1	4	yes	—
364	C₂²×C₈	—	2	4	no	—
365	C₂²×C₈	—	2	2	no	—
366	C₄⋊Q₈	C₂×C₄×C₄₁	1	4	yes	complemented
367	#127	C₂×C₄×C₄₁	1	4	yes	complemented
368	#124	C₂×C₄×C₄₁	1	4	yes	complemented
369	#124	C₂×C₄×C₄₁	1	4	yes	complemented
370	#123	—	2	4	no	—
371	#123	—	2	4	no	—
372	C₂²⋊Q₈	—	2	4	no	—
373	C₂²⋊Q₈	—	2	4	no	—
374	#121	—	2	4	no	—
375	#121	—	2	8	no	—
376	#121	—	2	4	no	—
377	#120	—	2	4	no	—
378	#120	—	2	4	no	—
379	C₄×D₄	—	2	8	no	—
380	#117	—	2	1	no	—
381	#117	—	2	1	no	—
382	#117	—	2	2	no	—
383	#117	—	2	2	no	—
384	#117	—	2	2	no	—
385	#117	C₂×C₄×C₄₁	1	2	yes	—
386	#117	C₂×C₄×C₄₁	1	2	yes	—
387	#117	C₂³×C₄₁	1	4	yes	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	C₂×C₄⋊C₄	—	2	2	no	—
390	C₂×C₂²⋊C₄	—	2	1	no	—
391	C₂×C₂²⋊C₄	—	2	2	no	—
392	C₂×C₄²	—	2	2	no	—
393	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
394	#104	—	2	16	no	—
395	#99	—	2	8	no	—
396	C₂⁴	—	2	1	no	—
397	C₂⁴	C₂²⋊C₄×C₄₁	1	2	yes	—
398	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
399	#41	—	2	4	no	—
400	#41	—	2	4	no	—
401	#41	—	2	4	no	—
402	#41	—	2	4	no	—
403	#41	—	2	4	no	—
404	#41	—	2	4	no	—
405	#41	—	2	4	no	—
406	#41	—	2	4	no	—
407	#41	—	2	4	no	—
408	#41	—	2	4	no	—
409	#41	—	2	4	no	—
410	#41	—	2	4	no	—
411	#41	—	4	1	no	—
412	#41	—	4	1	no	—
413	#41	—	4	2	no	—
414	#41	—	4	2	no	—
415	#41	—	4	1	no	—
416	#41	—	4	1	no	—
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	—	2	2	no	—
419	C₂×Q₈	—	2	2	no	—
420	C₂×Q₈	—	2	2	no	—
421	C₂×Q₈	—	2	2	no	—
422	C₂×Q₈	C₂²⋊C₄×C₄₁	1	2	yes	—
423	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
424	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
425	C₂×D₄	—	2	4	no	—
426	C₂×D₄	—	2	4	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	8	no	—
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	4	2	no	—
436	C₂×D₄	—	4	2	no	—
437	C₂×D₄	C₂²⋊C₄×C₄₁	1	4	yes	—
438	C₂×D₄	C₂²⋊C₄×C₄₁	1	2	yes	—
439	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
440	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
441	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	4	2	no	—
451	C₂²×C₄	—	4	2	no	—
452	C₂²×C₄	—	4	2	no	—
453	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
454	C₂²×C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
455	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
456	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
458	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
459	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
461	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
462	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
463	C₂²×C₄	#41×C₄₁	1	2	yes	—
464	C₂²×C₄	#41×C₄₁	1	2	yes	—
465	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
466	M₁₆	—	2	16	no	—
467	M₁₆	—	2	4	no	—
468	M₁₆	—	2	4	no	—
469	M₁₆	—	2	4	no	—
470	M₁₆	C₂×D₄×C₄₁	1	8	yes	—
471	C₂×C₈	—	2	16	no	—
472	C₂×C₈	—	2	4	no	—
473	C₂×C₈	—	2	4	no	—
474	C₂×C₈	—	2	4	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	—	2	8	no	—
478	C₄⋊C₄	—	2	4	no	—
479	C₄⋊C₄	—	4	2	no	—
480	C₂²⋊C₄	—	2	2	no	—
481	C₂²⋊C₄	—	2	2	no	—
482	C₂²⋊C₄	—	2	8	no	—
483	C₂²⋊C₄	—	2	8	no	—
484	C₂²⋊C₄	—	2	4	no	—
485	C₂²⋊C₄	—	4	2	no	—
486	C₄²	—	2	2	no	—
487	C₄²	—	2	4	no	—
488	C₄²	—	4	2	no	—
489	C₄²	C₂²×C₄×C₄₁	1	4	yes	—
490	C₂³	—	2	2	no	—
491	C₂³	—	2	2	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	4	2	no	—
494	C₂³	—	8	1	no	—
495	C₂³	—	8	2	no	—
496	C₂³	—	8	2	no	—
497	C₂³	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
498	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
499	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
500	C₂³	#121×C₄₁	1	2	yes	—
501	C₂³	#121×C₄₁	1	2	yes	—
502	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
503	Q₈	—	2	4	no	—
504	Q₈	—	2	4	no	—
505	Q₈	—	2	4	no	—
506	Q₈	—	4	1	no	—
507	Q₈	—	4	1	no	—
508	D₄	—	2	8	no	—
509	D₄	—	2	8	no	—
510	D₄	—	2	4	no	—
511	D₄	—	2	4	no	—
512	D₄	—	2	4	no	—
513	D₄	—	4	4	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	2	no	—
516	D₄	—	4	1	no	—
517	D₄	—	4	1	no	—
518	D₄	—	8	8	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	4	no	—
531	C₂×C₄	—	4	4	no	—
532	C₂×C₄	—	8	2	no	—
533	C₂×C₄	—	8	4	no	—
534	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
535	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
536	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
537	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
538	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
539	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
540	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
541	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
542	C₂×C₄	#120×C₄₁	1	2	yes	—
543	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
544	C₂×C₄	#121×C₄₁	1	2	yes	—
545	C₂×C₄	#121×C₄₁	1	2	yes	—
546	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
547	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
548	C₂×C₄	#123×C₄₁	1	2	yes	—
549	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
550	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
551	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
552	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
553	C₈	—	2	8	no	—
554	C₂²	—	2	4	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	4	no	—
561	C₂²	—	4	4	no	—
562	C₂²	—	4	4	no	—
563	C₂²	—	4	2	no	—
564	C₂²	—	8	2	no	—
565	C₂²	—	8	4	no	—
566	C₂²	C₄₁×#386	1	1	yes	characteristic
567	C₂²	C₄₁×#386	1	1	yes	characteristic
568	C₂²	C₄₁×#386	1	2	yes	—
569	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
570	C₂²	C₂×#121×C₄₁	1	2	yes	—
571	C₄	—	2	4	no	—
572	C₄	—	4	4	no	—
573	C₄	—	4	2	no	—
574	C₄	—	8	4	no	—
575	C₄	C₄₁×#386	1	1	yes	characteristic
576	C₄	C₄₁×#386	1	1	yes	characteristic
577	C₄	C₄₁×#386	1	2	yes	—
578	C₄	C₂×C₄×D₄×C₄₁	1	2	yes	—
579	C₄	C₂×#120×C₄₁	1	1	yes	characteristic
580	C₄	C₂×#123×C₄₁	1	1	yes	characteristic
581	C₂	—	2	1	no	—
582	C₂	—	2	2	no	—
583	C₂	—	2	1	no	—
584	C₂	—	2	1	no	—
585	C₂	—	2	2	no	—
586	C₂	—	4	4	no	—
587	C₂	—	8	2	no	—
588	C₂	C₂×C₄₁×#386	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₄₁	C₂×#120
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
socle	C₂×C₄₁	C₂×#386
prime radical	C₄₁×#3449	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₄₁ ◁ C₂³×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#568	C₂	semidirect
3. C₂×C₄₁×#421	C₂	semidirect
4. C₂×C₄₁×#410	C₂	semidirect
5. C₄₁×#1884	C₂	semidirect
6. C₄₁×#1733	C₂	semidirect
11. C₄₁×#568	C₂²	semidirect
16. C₄₁×#536	C₄	semidirect
17. C₄₁×#536	C₄	semidirect
18. C₄₁×#535	C₄	semidirect
19. C₄₁×#535	C₄	semidirect
27. C₄₁×#421	C₂²	semidirect
30. C₄₁×#410	C₂²	semidirect
32. C₄₁×#339	C₂²	semidirect
66. C₂×M₁₆×C₄₁	D₄	semidirect
67. C₂×M₁₆×C₄₁	D₄	semidirect
71. C₄⋊Q₈×C₄₁	C₂×C₄	semidirect
72. #127×C₄₁	C₂×C₄	semidirect
73. #124×C₄₁	C₂×C₄	semidirect
74. #124×C₄₁	C₂×C₄	semidirect
259. #20947	C₄₁	direct (N × H)
287. C₂×#568	C₂×C₄₁	semidirect
289. C₂×#421	C₂×C₄₁	semidirect
290. C₂×#410	C₂×C₄₁	semidirect
291. #1884	C₂×C₄₁	semidirect
292. #1733	C₂×C₄₁	semidirect
305. #568	C₂²×C₄₁	semidirect
310. #536	C₄×C₄₁	semidirect
311. #536	C₄×C₄₁	semidirect
312. #535	C₄×C₄₁	semidirect
313. #535	C₄×C₄₁	semidirect
321. #421	C₂²×C₄₁	semidirect
324. #410	C₂²×C₄₁	semidirect
326. #339	C₂²×C₄₁	semidirect
327. C₄₁	#20947	direct (N × H)
361. C₂×M₁₆	D₄×C₄₁	semidirect
362. C₂×M₁₆	D₄×C₄₁	semidirect
366. C₄⋊Q₈	C₂×C₄×C₄₁	semidirect
367. #127	C₂×C₄×C₄₁	semidirect
368. #124	C₂×C₄×C₄₁	semidirect
369. #124	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
C₂×C₄₁×#568	2
C₄₁×#3449	2
C₂×C₄₁×#421	2
C₂×C₄₁×#410	2
C₄₁×#1884	2
C₄₁×#1733	2
#20947	41

Subgroups — C41×#20947 #23797148

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#20947 #23797148