Subgroups — C₄₁×#17762 #23793963

Order 10496.

1028 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3508	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2989	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#2906	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1560	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1557	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1551	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1550	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1547	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1545	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1542	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₁×#331	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#131×C₄₁	—	2	1	no	—
13	C₄₁×#559	—	2	1	no	—
14	C₄₁×#559	C₄	1	2	yes	—
15	C₄₁×#550	—	2	1	no	—
16	C₄₁×#550	C₄	1	2	yes	—
17	C₄₁×#546	—	2	2	no	—
18	C₄₁×#546	C₄	1	4	yes	—
19	C₄₁×#540	—	2	2	no	—
20	C₄₁×#535	—	2	1	no	—
21	C₄₁×#533	C₂²	1	1	yes	characteristic
22	C₄₁×#532	C₂²	1	2	yes	—
23	C₄₁×#532	C₂²	1	2	yes	—
24	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
25	C₄₁×#518	—	2	1	no	—
26	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
27	C₄₁×#446	—	2	1	no	—
28	C₄₁×#436	—	2	1	no	—
29	C₄₁×#435	—	2	2	no	—
30	C₄₁×#432	C₂²	1	2	yes	complemented
31	C₄₁×#431	C₂²	1	1	yes	characteristic
32	C₄₁×#424	—	2	2	no	—
33	C₄₁×#424	—	2	1	no	—
34	C₄₁×#423	C₂²	1	1	yes	characteristic
35	C₄₁×#423	C₂²	1	2	yes	complemented
36	C₄₁×#423	C₂²	1	2	yes	complemented
37	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	complemented
40	C₄₁×#333	C₂²	1	1	yes	characteristic, complemented
41	C₄₁×#333	C₂²	1	1	yes	characteristic, complemented
42	C₄₁×#333	C₂²	1	2	yes	complemented
43	C₄₁×#332	C₂²	1	1	yes	characteristic, complemented
44	C₄₁×#332	C₂²	1	1	yes	characteristic, complemented
45	C₄₁×#332	C₂²	1	2	yes	complemented
46	C₄₁×#331	C₂²	1	2	yes	—
47	C₄₁×#331	C₂²	1	2	yes	—
48	C₄₁×#331	C₂²	1	2	yes	—
49	C₄₁×#331	C₂²	1	2	yes	—
50	C₂×#41×C₄₁	—	2	2	no	—
51	C₂×#41×C₄₁	C₂×C₄	1	4	yes	—
52	C₂×#41×C₄₁	D₄	1	1	yes	characteristic
53	C₂²×D₄×C₄₁	—	2	1	no	—
54	C₂²×D₄×C₄₁	—	2	1	no	—
55	C₂²×D₄×C₄₁	C₂×C₄	1	2	yes	—
56	#131×C₄₁	—	4	4	no	—
57	C₂×M₁₆×C₄₁	—	2	1	no	—
58	C₂×M₁₆×C₄₁	—	2	2	no	—
59	C₂×M₁₆×C₄₁	—	2	2	no	—
60	C₂²×C₈×C₄₁	—	2	1	no	—
61	C₂²×C₈×C₄₁	—	2	2	no	—
62	C₂²×C₈×C₄₁	—	2	1	no	—
63	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
64	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
65	#127×C₄₁	—	2	2	no	—
66	#127×C₄₁	—	2	1	no	—
67	#127×C₄₁	—	2	1	no	—
68	#127×C₄₁	C₂×C₄	1	2	yes	—
69	#127×C₄₁	C₂³	1	2	yes	—
70	#125×C₄₁	—	2	1	no	—
71	#124×C₄₁	—	2	2	no	—
72	#124×C₄₁	—	2	2	no	—
73	#124×C₄₁	C₂×C₄	1	4	yes	—
74	#123×C₄₁	—	2	4	no	—
75	#123×C₄₁	—	2	4	no	—
76	C₂²⋊Q₈×C₄₁	—	2	1	no	—
77	C₂²⋊Q₈×C₄₁	C₂×C₄	1	2	yes	—
78	#121×C₄₁	—	2	2	no	—
79	#121×C₄₁	—	2	2	no	—
80	#121×C₄₁	—	2	2	no	—
81	#121×C₄₁	—	2	4	no	—
82	#121×C₄₁	—	2	4	no	—
83	#121×C₄₁	C₂×C₄	1	4	yes	—
84	#120×C₄₁	—	2	4	no	—
85	C₄×Q₈×C₄₁	—	2	1	no	—
86	C₄×Q₈×C₄₁	C₂×C₄	1	2	yes	—
87	C₄×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
88	C₄×Q₈×C₄₁	D₄	1	1	yes	characteristic
89	C₄×D₄×C₄₁	—	2	2	no	—
90	C₄×D₄×C₄₁	—	2	2	no	—
91	C₄×D₄×C₄₁	—	2	2	no	—
92	C₄×D₄×C₄₁	—	2	2	no	—
93	C₄×D₄×C₄₁	—	2	2	no	—
94	C₄×D₄×C₄₁	C₂×C₄	1	4	yes	—
95	C₄×D₄×C₄₁	C₂×C₄	1	2	yes	—
96	C₄×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
97	C₄×D₄×C₄₁	D₄	1	2	yes	—
98	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
99	#117×C₄₁	—	2	1	no	—
100	#117×C₄₁	D₄	1	1	yes	characteristic
101	#117×C₄₁	D₄	1	2	yes	—
102	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
103	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
105	C₄⋊C₈×C₄₁	—	2	1	no	—
106	C₄⋊C₈×C₄₁	—	2	1	no	—
107	C₄⋊C₈×C₄₁	—	2	2	no	—
108	C₄⋊C₈×C₄₁	—	2	1	no	—
109	C₄⋊C₈×C₄₁	—	2	2	no	—
110	C₄⋊C₈×C₄₁	—	2	2	no	—
111	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
112	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
113	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
114	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
115	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
116	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
117	C₂²⋊C₈×C₄₁	—	2	1	no	—
118	C₂²⋊C₈×C₄₁	—	2	2	no	—
119	#97×C₄₁	—	2	2	no	—
120	C₄×C₈×C₄₁	—	2	1	no	—
121	C₂⁴×C₄₁	—	2	2	no	—
122	#41×C₄₁	—	2	2	no	—
123	#41×C₄₁	—	2	2	no	—
124	#41×C₄₁	—	8	2	no	—
125	#41×C₄₁	—	8	2	no	—
126	#41×C₄₁	—	8	4	no	—
127	C₂×Q₈×C₄₁	—	2	1	no	—
128	C₂×Q₈×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
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	2	no	—
135	C₂×D₄×C₄₁	—	2	2	no	—
136	C₂×D₄×C₄₁	—	2	2	no	—
137	C₂×D₄×C₄₁	—	4	2	no	—
138	C₂×D₄×C₄₁	—	4	2	no	—
139	C₂×D₄×C₄₁	—	8	1	no	—
140	C₂×D₄×C₄₁	—	8	1	no	—
141	C₂×D₄×C₄₁	—	8	2	no	—
142	C₂×D₄×C₄₁	C₂²⋊C₄	1	2	yes	—
143	C₂×D₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
144	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
145	C₂²×C₄×C₄₁	—	2	4	no	—
146	C₂²×C₄×C₄₁	—	2	4	no	—
147	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
148	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
153	M₁₆×C₄₁	—	4	4	no	—
154	M₁₆×C₄₁	—	4	2	no	—
155	M₁₆×C₄₁	—	8	2	no	—
156	C₂×C₈×C₄₁	—	2	1	no	—
157	C₂×C₈×C₄₁	—	2	1	no	—
158	C₂×C₈×C₄₁	—	2	2	no	—
159	C₂×C₈×C₄₁	—	2	1	no	—
160	C₂×C₈×C₄₁	—	2	1	no	—
161	C₂×C₈×C₄₁	—	2	2	no	—
162	C₂×C₈×C₄₁	—	4	4	no	—
163	C₂×C₈×C₄₁	—	4	2	no	—
164	C₂×C₈×C₄₁	—	8	1	no	—
165	C₄⋊C₄×C₄₁	—	2	2	no	—
166	C₄⋊C₄×C₄₁	—	2	2	no	—
167	C₄⋊C₄×C₄₁	—	2	1	no	—
168	C₄⋊C₄×C₄₁	—	2	1	no	—
169	C₄⋊C₄×C₄₁	—	2	1	no	—
170	C₄⋊C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
171	C₄⋊C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
172	C₄⋊C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
173	C₄⋊C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
174	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
175	C₂²⋊C₄×C₄₁	—	2	2	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	4	no	—
180	C₂²⋊C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
181	C₂²⋊C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
182	C₂²⋊C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
183	C₄²×C₄₁	—	2	2	no	—
184	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
185	C₄²×C₄₁	C₂²×C₄	1	1	yes	characteristic
186	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₄₁	C₂×D₄	1	2	yes	—
188	C₄²×C₄₁	C₂×D₄	1	2	yes	—
189	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
191	C₂³×C₄₁	—	2	4	no	—
192	C₂³×C₄₁	—	4	4	no	—
193	C₂³×C₄₁	—	8	2	no	—
194	C₂³×C₄₁	—	8	2	no	—
195	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
196	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
197	Q₈×C₄₁	—	2	2	no	—
198	Q₈×C₄₁	—	4	2	no	—
199	Q₈×C₄₁	—	4	1	no	—
200	Q₈×C₄₁	—	4	1	no	—
201	D₄×C₄₁	—	2	4	no	—
202	D₄×C₄₁	—	2	2	no	—
203	D₄×C₄₁	—	4	4	no	—
204	D₄×C₄₁	—	4	2	no	—
205	D₄×C₄₁	—	4	2	no	—
206	D₄×C₄₁	—	4	2	no	—
207	D₄×C₄₁	—	4	2	no	—
208	D₄×C₄₁	—	4	4	no	—
209	D₄×C₄₁	—	8	2	no	—
210	D₄×C₄₁	—	8	2	no	—
211	D₄×C₄₁	—	8	4	no	—
212	D₄×C₄₁	—	8	4	no	—
213	C₂×C₄×C₄₁	—	2	2	no	—
214	C₂×C₄×C₄₁	—	2	2	no	—
215	C₂×C₄×C₄₁	—	2	1	no	—
216	C₂×C₄×C₄₁	—	2	2	no	—
217	C₂×C₄×C₄₁	—	2	1	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	—	4	1	no	—
222	C₂×C₄×C₄₁	—	4	2	no	—
223	C₂×C₄×C₄₁	—	8	4	no	—
224	C₂×C₄×C₄₁	—	8	4	no	—
225	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
226	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
227	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
229	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
232	C₂×C₄×C₄₁	#137	1	2	yes	—
233	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
234	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
236	C₈×C₄₁	—	4	1	no	—
237	C₈×C₄₁	—	4	2	no	—
238	C₈×C₄₁	—	4	1	no	—
239	C₈×C₄₁	—	4	2	no	—
240	C₈×C₄₁	—	4	1	no	—
241	C₈×C₄₁	—	4	1	no	—
242	#17762	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
243	C₂²×C₄₁	—	2	1	no	—
244	C₂²×C₄₁	—	2	1	no	—
245	C₂²×C₄₁	—	2	2	no	—
246	C₂²×C₄₁	—	2	2	no	—
247	C₂²×C₄₁	—	2	2	no	—
248	C₂²×C₄₁	—	4	4	no	—
249	C₂²×C₄₁	—	4	4	no	—
250	C₂²×C₄₁	—	4	4	no	—
251	C₂²×C₄₁	—	16	4	no	—
252	C₂²×C₄₁	#417	1	2	yes	—
253	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
254	C₄×C₄₁	—	2	1	no	—
255	C₄×C₄₁	—	2	2	no	—
256	C₄×C₄₁	—	2	1	no	—
257	C₄×C₄₁	—	2	2	no	—
258	C₄×C₄₁	—	2	2	no	—
259	C₄×C₄₁	—	2	1	no	—
260	C₄×C₄₁	—	4	2	no	—
261	C₄×C₄₁	—	4	2	no	—
262	C₄×C₄₁	#417	1	2	yes	—
263	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
264	C₄×C₄₁	C₂×#137	1	1	yes	characteristic
265	C₄×C₄₁	#576	1	1	yes	characteristic
266	C₄×C₄₁	#577	1	1	yes	characteristic
267	#3508	C₂×C₄₁	1	1	yes	characteristic
268	#2989	C₂×C₄₁	1	1	yes	characteristic, complemented
269	#2906	C₂×C₄₁	1	1	yes	characteristic, complemented
270	#1560	C₂×C₄₁	1	2	yes	complemented
271	#1557	C₂×C₄₁	1	2	yes	complemented
272	#1551	C₂×C₄₁	1	2	yes	complemented
273	#1550	C₂×C₄₁	1	1	yes	characteristic, complemented
274	#1547	C₂×C₄₁	1	2	yes	complemented
275	#1545	C₂×C₄₁	1	1	yes	characteristic, complemented
276	#1542	C₂×C₄₁	1	1	yes	characteristic, complemented
277	C₂×#331	C₂×C₄₁	1	1	yes	characteristic, complemented
278	C₂×C₄₁	—	2	2	no	—
279	C₂×C₄₁	—	4	2	no	—
280	C₂×C₄₁	—	8	4	no	—
281	C₂×C₄₁	#2888	1	1	yes	characteristic
282	C₂×C₄₁	C₂×#417	1	1	yes	characteristic
283	C₂×C₄₁	#2897	1	1	yes	characteristic
284	C₂×#131	—	2	1	no	—
285	#559	—	2	1	no	—
286	#559	C₄×C₄₁	1	2	yes	—
287	#550	—	2	1	no	—
288	#550	C₄×C₄₁	1	2	yes	—
289	#546	—	2	2	no	—
290	#546	C₄×C₄₁	1	4	yes	—
291	#540	—	2	2	no	—
292	#535	—	2	1	no	—
293	#533	C₂²×C₄₁	1	1	yes	characteristic
294	#532	C₂²×C₄₁	1	2	yes	—
295	#532	C₂²×C₄₁	1	2	yes	—
296	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
297	#518	—	2	1	no	—
298	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
299	#446	—	2	1	no	—
300	#436	—	2	1	no	—
301	#435	—	2	2	no	—
302	#432	C₂²×C₄₁	1	2	yes	complemented
303	#431	C₂²×C₄₁	1	1	yes	characteristic
304	#424	—	2	2	no	—
305	#424	—	2	1	no	—
306	#423	C₂²×C₄₁	1	1	yes	characteristic
307	#423	C₂²×C₄₁	1	2	yes	complemented
308	#423	C₂²×C₄₁	1	2	yes	complemented
309	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
310	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
311	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	complemented
312	#333	C₂²×C₄₁	1	1	yes	characteristic, complemented
313	#333	C₂²×C₄₁	1	1	yes	characteristic, complemented
314	#333	C₂²×C₄₁	1	2	yes	complemented
315	#332	C₂²×C₄₁	1	1	yes	characteristic, complemented
316	#332	C₂²×C₄₁	1	1	yes	characteristic, complemented
317	#332	C₂²×C₄₁	1	2	yes	complemented
318	#331	C₂²×C₄₁	1	2	yes	—
319	#331	C₂²×C₄₁	1	2	yes	—
320	#331	C₂²×C₄₁	1	2	yes	—
321	#331	C₂²×C₄₁	1	2	yes	—
322	C₄₁	#17762	1	1	yes	characteristic, direct product factor, Sylow
323	C₂×#41	—	2	2	no	—
324	C₂×#41	C₂×C₄×C₄₁	1	4	yes	—
325	C₂×#41	D₄×C₄₁	1	1	yes	characteristic
326	C₂²×D₄	—	2	1	no	—
327	C₂²×D₄	—	2	1	no	—
328	C₂²×D₄	C₂×C₄×C₄₁	1	2	yes	—
329	#131	—	4	4	no	—
330	C₂×M₁₆	—	2	1	no	—
331	C₂×M₁₆	—	2	2	no	—
332	C₂×M₁₆	—	2	2	no	—
333	C₂²×C₈	—	2	1	no	—
334	C₂²×C₈	—	2	2	no	—
335	C₂²×C₈	—	2	1	no	—
336	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
337	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
338	#127	—	2	2	no	—
339	#127	—	2	1	no	—
340	#127	—	2	1	no	—
341	#127	C₂×C₄×C₄₁	1	2	yes	—
342	#127	C₂³×C₄₁	1	2	yes	—
343	#125	—	2	1	no	—
344	#124	—	2	2	no	—
345	#124	—	2	2	no	—
346	#124	C₂×C₄×C₄₁	1	4	yes	—
347	#123	—	2	4	no	—
348	#123	—	2	4	no	—
349	C₂²⋊Q₈	—	2	1	no	—
350	C₂²⋊Q₈	C₂×C₄×C₄₁	1	2	yes	—
351	#121	—	2	2	no	—
352	#121	—	2	2	no	—
353	#121	—	2	2	no	—
354	#121	—	2	4	no	—
355	#121	—	2	4	no	—
356	#121	C₂×C₄×C₄₁	1	4	yes	—
357	#120	—	2	4	no	—
358	C₄×Q₈	—	2	1	no	—
359	C₄×Q₈	C₂×C₄×C₄₁	1	2	yes	—
360	C₄×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
361	C₄×Q₈	D₄×C₄₁	1	1	yes	characteristic
362	C₄×D₄	—	2	2	no	—
363	C₄×D₄	—	2	2	no	—
364	C₄×D₄	—	2	2	no	—
365	C₄×D₄	—	2	2	no	—
366	C₄×D₄	—	2	2	no	—
367	C₄×D₄	C₂×C₄×C₄₁	1	4	yes	—
368	C₄×D₄	C₂×C₄×C₄₁	1	2	yes	—
369	C₄×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
370	C₄×D₄	D₄×C₄₁	1	2	yes	—
371	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
372	#117	—	2	1	no	—
373	#117	D₄×C₄₁	1	1	yes	characteristic
374	#117	D₄×C₄₁	1	2	yes	—
375	C₂×C₂²⋊C₄	—	2	4	no	—
376	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
377	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
378	C₄⋊C₈	—	2	1	no	—
379	C₄⋊C₈	—	2	1	no	—
380	C₄⋊C₈	—	2	2	no	—
381	C₄⋊C₈	—	2	1	no	—
382	C₄⋊C₈	—	2	2	no	—
383	C₄⋊C₈	—	2	2	no	—
384	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
385	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
386	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
387	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
388	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
389	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
390	C₂²⋊C₈	—	2	1	no	—
391	C₂²⋊C₈	—	2	2	no	—
392	#97	—	2	2	no	—
393	C₄×C₈	—	2	1	no	—
394	C₂⁴	—	2	2	no	—
395	#41	—	2	2	no	—
396	#41	—	2	2	no	—
397	#41	—	8	2	no	—
398	#41	—	8	2	no	—
399	#41	—	8	4	no	—
400	C₂×Q₈	—	2	1	no	—
401	C₂×Q₈	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
402	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
403	C₂×D₄	—	2	4	no	—
404	C₂×D₄	—	2	4	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	4	2	no	—
411	C₂×D₄	—	4	2	no	—
412	C₂×D₄	—	8	1	no	—
413	C₂×D₄	—	8	1	no	—
414	C₂×D₄	—	8	2	no	—
415	C₂×D₄	C₂²⋊C₄×C₄₁	1	2	yes	—
416	C₂×D₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
417	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
421	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
422	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
423	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
424	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
425	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
426	M₁₆	—	4	4	no	—
427	M₁₆	—	4	2	no	—
428	M₁₆	—	8	2	no	—
429	C₂×C₈	—	2	1	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	4	4	no	—
436	C₂×C₈	—	4	2	no	—
437	C₂×C₈	—	8	1	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
444	C₄⋊C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
445	C₄⋊C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
446	C₄⋊C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
447	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₂²⋊C₄	—	2	4	no	—
450	C₂²⋊C₄	—	2	4	no	—
451	C₂²⋊C₄	—	2	4	no	—
452	C₂²⋊C₄	—	2	4	no	—
453	C₂²⋊C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
454	C₂²⋊C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
455	C₂²⋊C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
456	C₄²	—	2	2	no	—
457	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
458	C₄²	C₂²×C₄×C₄₁	1	1	yes	characteristic
459	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
460	C₄²	C₂×D₄×C₄₁	1	2	yes	—
461	C₄²	C₂×D₄×C₄₁	1	2	yes	—
462	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
463	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
464	C₂³	—	2	4	no	—
465	C₂³	—	4	4	no	—
466	C₂³	—	8	2	no	—
467	C₂³	—	8	2	no	—
468	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
469	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
470	Q₈	—	2	2	no	—
471	Q₈	—	4	2	no	—
472	Q₈	—	4	1	no	—
473	Q₈	—	4	1	no	—
474	D₄	—	2	4	no	—
475	D₄	—	2	2	no	—
476	D₄	—	4	4	no	—
477	D₄	—	4	2	no	—
478	D₄	—	4	2	no	—
479	D₄	—	4	2	no	—
480	D₄	—	4	2	no	—
481	D₄	—	4	4	no	—
482	D₄	—	8	2	no	—
483	D₄	—	8	2	no	—
484	D₄	—	8	4	no	—
485	D₄	—	8	4	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	8	4	no	—
497	C₂×C₄	—	8	4	no	—
498	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
499	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
500	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
501	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
502	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
503	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
504	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
505	C₂×C₄	#137×C₄₁	1	2	yes	—
506	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
507	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
508	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
509	C₈	—	4	1	no	—
510	C₈	—	4	2	no	—
511	C₈	—	4	1	no	—
512	C₈	—	4	2	no	—
513	C₈	—	4	1	no	—
514	C₈	—	4	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	2	1	no	—
517	C₂²	—	2	2	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	4	4	no	—
521	C₂²	—	4	4	no	—
522	C₂²	—	4	4	no	—
523	C₂²	—	16	4	no	—
524	C₂²	C₄₁×#417	1	2	yes	—
525	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
526	C₄	—	2	1	no	—
527	C₄	—	2	2	no	—
528	C₄	—	2	1	no	—
529	C₄	—	2	2	no	—
530	C₄	—	2	2	no	—
531	C₄	—	2	1	no	—
532	C₄	—	4	2	no	—
533	C₄	—	4	2	no	—
534	C₄	C₄₁×#417	1	2	yes	—
535	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
536	C₄	C₂×#137×C₄₁	1	1	yes	characteristic
537	C₄	C₄₁×#576	1	1	yes	characteristic
538	C₄	C₄₁×#577	1	1	yes	characteristic
539	C₂	—	2	2	no	—
540	C₂	—	4	2	no	—
541	C₂	—	8	4	no	—
542	C₂	C₄₁×#2888	1	1	yes	characteristic
543	C₂	C₂×C₄₁×#417	1	1	yes	characteristic
544	C₂	C₄₁×#2897	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₄²	C₂⁴×C₄₁
prime radical	C₄₁×#3508	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₄×#41×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#2989	C₂	semidirect
3. C₄₁×#2906	C₂	semidirect
4. C₄₁×#1560	C₂	semidirect
5. C₄₁×#1557	C₂	semidirect
6. C₄₁×#1551	C₂	semidirect
7. C₄₁×#1550	C₂	semidirect
8. C₄₁×#1547	C₂	semidirect
9. C₄₁×#1545	C₂	semidirect
10. C₄₁×#1542	C₂	semidirect
11. C₂×C₄₁×#331	C₂	semidirect
30. C₄₁×#432	C₂²	semidirect
35. C₄₁×#423	C₂²	semidirect
36. C₄₁×#423	C₂²	semidirect
39. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
40. C₄₁×#333	C₂²	semidirect
41. C₄₁×#333	C₂²	semidirect
42. C₄₁×#333	C₂²	semidirect
43. C₄₁×#332	C₂²	semidirect
44. C₄₁×#332	C₂²	semidirect
45. C₄₁×#332	C₂²	semidirect
242. #17762	C₄₁	direct (N × H)
268. #2989	C₂×C₄₁	semidirect
269. #2906	C₂×C₄₁	semidirect
270. #1560	C₂×C₄₁	semidirect
271. #1557	C₂×C₄₁	semidirect
272. #1551	C₂×C₄₁	semidirect
273. #1550	C₂×C₄₁	semidirect
274. #1547	C₂×C₄₁	semidirect
275. #1545	C₂×C₄₁	semidirect
276. #1542	C₂×C₄₁	semidirect
277. C₂×#331	C₂×C₄₁	semidirect
302. #432	C₂²×C₄₁	semidirect
307. #423	C₂²×C₄₁	semidirect
308. #423	C₂²×C₄₁	semidirect
311. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
312. #333	C₂²×C₄₁	semidirect
313. #333	C₂²×C₄₁	semidirect
314. #333	C₂²×C₄₁	semidirect
315. #332	C₂²×C₄₁	semidirect
316. #332	C₂²×C₄₁	semidirect
317. #332	C₂²×C₄₁	semidirect
322. C₄₁	#17762	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×#3508	2
C₄₁×#2989	2
C₄₁×#2906	2
C₄₁×#1560	2
C₄₁×#1557	2
C₄₁×#1551	2
C₄₁×#1550	2
C₄₁×#1547	2
C₄₁×#1545	2
C₄₁×#1542	2
C₂×C₄₁×#331	2
#17762	41

Subgroups — C41×#17762 #23793963

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#17762 #23793963