Subgroups — C₂×C₄₁×#1639 #23794682

Order 10496.

1690 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄²×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#486	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#474	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₁×#461	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1639	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄₁×#331	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₁×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₁×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₄₁	—	2	1	no	—
10	C₂³×D₄×C₄₁	—	2	1	no	—
11	C₂²×SD₁₆×C₄₁	—	2	1	no	—
12	D₄²×C₄₁	—	2	2	no	—
13	D₄²×C₄₁	—	2	2	no	—
14	D₄²×C₄₁	—	2	2	no	—
15	D₄²×C₄₁	C₂²	1	4	yes	—
16	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
17	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×#121×C₄₁	—	2	1	no	—
19	C₂×#121×C₄₁	—	2	1	no	—
20	C₂×#120×C₄₁	—	2	2	no	—
21	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
23	C₄₁×#486	—	2	2	no	—
24	C₄₁×#486	C₂²	1	4	yes	complemented
25	C₄₁×#474	—	2	2	no	—
26	C₄₁×#474	C₂²	1	4	yes	complemented
27	C₄₁×#461	—	2	2	no	—
28	C₄₁×#461	C₂²	1	4	yes	complemented
29	C₂×#107×C₄₁	—	2	1	no	—
30	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
32	C₂×#103×C₄₁	—	2	1	no	—
33	C₂×#102×C₄₁	—	2	1	no	—
34	C₂×#102×C₄₁	—	2	2	no	—
35	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
36	C₄₁×#331	C₂²	1	4	yes	complemented
37	C₄₁×D₄⋊C₈	C₂²	1	4	yes	complemented
38	C₄₁×D₄⋊C₈	C₂²	1	4	yes	complemented
39	C₂⁵×C₄₁	—	2	2	no	—
40	C₂²×Q₈×C₄₁	—	2	1	no	—
41	C₂²×D₄×C₄₁	—	2	2	no	—
42	C₂²×D₄×C₄₁	—	2	2	no	—
43	C₂²×D₄×C₄₁	—	2	4	no	—
44	C₂²×D₄×C₄₁	—	2	4	no	—
45	C₂²×D₄×C₄₁	—	2	4	no	—
46	C₂²×D₄×C₄₁	—	2	4	no	—
47	C₂²×D₄×C₄₁	—	2	1	no	—
48	C₂²×D₄×C₄₁	—	2	1	no	—
49	C₂²×D₄×C₄₁	—	4	4	no	—
50	C₂²×D₄×C₄₁	—	4	4	no	—
51	C₂²×D₄×C₄₁	—	4	4	no	—
52	C₂²×D₄×C₄₁	—	4	4	no	—
53	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
54	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
55	C₂²×D₄×C₄₁	D₄	1	2	yes	—
56	C₂³×C₄×C₄₁	—	2	1	no	—
57	C₂³×C₄×C₄₁	—	2	1	no	—
58	C₂×SD₁₆×C₄₁	—	2	4	no	—
59	C₂×SD₁₆×C₄₁	—	4	4	no	—
60	C₂²×C₈×C₄₁	—	2	1	no	—
61	C₂²×C₈×C₄₁	—	2	1	no	—
62	C₂²×C₈×C₄₁	—	2	1	no	—
63	C₄⋊Q₈×C₄₁	—	2	1	no	—
64	C₄⋊Q₈×C₄₁	—	2	1	no	—
65	C₄⋊Q₈×C₄₁	—	2	1	no	—
66	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	complemented
67	#127×C₄₁	—	2	1	no	—
68	#127×C₄₁	—	2	1	no	—
69	#127×C₄₁	D₄	1	2	yes	—
70	#127×C₄₁	C₂³	1	2	yes	—
71	#121×C₄₁	—	2	4	no	—
72	#121×C₄₁	—	2	4	no	—
73	#121×C₄₁	—	2	4	no	—
74	#121×C₄₁	—	2	4	no	—
75	#120×C₄₁	—	2	8	no	—
76	#120×C₄₁	—	2	8	no	—
77	C₄×D₄×C₄₁	—	2	1	no	—
78	C₄×D₄×C₄₁	—	2	1	no	—
79	C₄×D₄×C₄₁	—	2	1	no	—
80	C₄×D₄×C₄₁	—	2	1	no	—
81	C₄×D₄×C₄₁	D₄	1	2	yes	—
82	C₄×D₄×C₄₁	D₄	1	2	yes	—
83	C₄×D₄×C₄₁	C₂³	1	2	yes	—
84	C₄×D₄×C₄₁	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
86	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
87	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
89	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
92	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
93	#107×C₄₁	—	2	4	no	—
94	C₄⋊C₈×C₄₁	—	2	1	no	—
95	C₄⋊C₈×C₄₁	—	2	1	no	—
96	C₄⋊C₈×C₄₁	C₂³	1	2	yes	complemented
97	C₄⋊C₈×C₄₁	C₂³	1	2	yes	complemented
98	#103×C₄₁	—	2	4	no	—
99	#102×C₄₁	—	2	4	no	—
100	#102×C₄₁	—	2	8	no	—
101	C₄×C₈×C₄₁	—	2	1	no	—
102	C₄×C₈×C₄₁	C₂³	1	2	yes	complemented
103	C₂⁴×C₄₁	—	2	1	no	—
104	C₂⁴×C₄₁	—	2	1	no	—
105	C₂⁴×C₄₁	—	2	8	no	—
106	C₂⁴×C₄₁	—	2	2	no	—
107	C₂⁴×C₄₁	—	4	8	no	—
108	C₂⁴×C₄₁	—	4	8	no	—
109	C₂⁴×C₄₁	—	8	4	no	—
110	C₂×Q₈×C₄₁	—	2	2	no	—
111	C₂×Q₈×C₄₁	—	4	1	no	—
112	C₂×Q₈×C₄₁	—	4	2	no	—
113	C₂×Q₈×C₄₁	—	4	2	no	—
114	C₂×D₄×C₄₁	—	2	8	no	—
115	C₂×D₄×C₄₁	—	2	8	no	—
116	C₂×D₄×C₄₁	—	2	1	no	—
117	C₂×D₄×C₄₁	—	2	1	no	—
118	C₂×D₄×C₄₁	—	2	2	no	—
119	C₂×D₄×C₄₁	—	2	2	no	—
120	C₂×D₄×C₄₁	—	2	2	no	—
121	C₂×D₄×C₄₁	—	2	2	no	—
122	C₂×D₄×C₄₁	—	2	2	no	—
123	C₂×D₄×C₄₁	—	2	2	no	—
124	C₂×D₄×C₄₁	—	2	2	no	—
125	C₂×D₄×C₄₁	—	4	4	no	—
126	C₂×D₄×C₄₁	—	4	8	no	—
127	C₂×D₄×C₄₁	—	4	8	no	—
128	C₂×D₄×C₄₁	—	4	16	no	—
129	C₂×D₄×C₄₁	—	4	16	no	—
130	C₂×D₄×C₄₁	—	4	8	no	—
131	C₂×D₄×C₄₁	—	4	8	no	—
132	C₂×D₄×C₄₁	—	4	8	no	—
133	C₂×D₄×C₄₁	—	4	8	no	—
134	C₂×D₄×C₄₁	—	4	2	no	—
135	C₂×D₄×C₄₁	—	4	2	no	—
136	C₂×D₄×C₄₁	—	4	2	no	—
137	C₂×D₄×C₄₁	—	4	2	no	—
138	C₂×D₄×C₄₁	D₈	1	4	yes	—
139	C₂×D₄×C₄₁	SD₁₆	1	4	yes	complemented
140	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
141	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
142	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
143	C₂²×C₄×C₄₁	—	2	1	no	—
144	C₂²×C₄×C₄₁	—	2	1	no	—
145	C₂²×C₄×C₄₁	—	2	2	no	—
146	C₂²×C₄×C₄₁	—	2	2	no	—
147	C₂²×C₄×C₄₁	—	2	2	no	—
148	C₂²×C₄×C₄₁	—	2	2	no	—
149	C₂²×C₄×C₄₁	—	4	2	no	—
150	C₂²×C₄×C₄₁	—	4	2	no	—
151	C₂²×C₄×C₄₁	—	4	2	no	—
152	C₂²×C₄×C₄₁	—	4	2	no	—
153	C₂²×C₄×C₄₁	—	4	1	no	—
154	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
157	SD₁₆×C₄₁	—	4	8	no	—
158	C₂×C₈×C₄₁	—	2	2	no	—
159	C₂×C₈×C₄₁	—	2	2	no	—
160	C₂×C₈×C₄₁	—	2	2	no	—
161	C₂×C₈×C₄₁	—	4	2	no	—
162	C₂×C₈×C₄₁	—	4	2	no	—
163	C₂×C₈×C₄₁	—	4	2	no	—
164	C₄⋊C₄×C₄₁	—	2	1	no	—
165	C₄⋊C₄×C₄₁	—	2	1	no	—
166	C₄⋊C₄×C₄₁	—	2	2	no	—
167	C₄⋊C₄×C₄₁	—	2	2	no	—
168	C₄⋊C₄×C₄₁	—	4	1	no	—
169	C₄⋊C₄×C₄₁	—	4	1	no	—
170	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
171	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
172	C₂²⋊C₄×C₄₁	—	2	8	no	—
173	C₂²⋊C₄×C₄₁	—	2	2	no	—
174	C₂²⋊C₄×C₄₁	—	2	2	no	—
175	C₂²⋊C₄×C₄₁	—	2	2	no	—
176	C₂²⋊C₄×C₄₁	—	2	2	no	—
177	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
181	C₂³×C₄₁	—	2	2	no	—
182	C₂³×C₄₁	—	2	2	no	—
183	C₂³×C₄₁	—	2	4	no	—
184	C₂³×C₄₁	—	2	4	no	—
185	C₂³×C₄₁	—	2	4	no	—
186	C₂³×C₄₁	—	4	16	no	—
187	C₂³×C₄₁	—	4	16	no	—
188	C₂³×C₄₁	—	4	2	no	—
189	C₂³×C₄₁	—	4	2	no	—
190	C₂³×C₄₁	—	4	2	no	—
191	C₂³×C₄₁	—	4	2	no	—
192	C₂³×C₄₁	—	4	4	no	—
193	C₂³×C₄₁	—	4	4	no	—
194	C₂³×C₄₁	—	4	4	no	—
195	C₂³×C₄₁	—	8	8	no	—
196	C₂³×C₄₁	—	8	32	no	—
197	C₂³×C₄₁	#120	1	1	yes	characteristic
198	Q₈×C₄₁	—	4	2	no	—
199	Q₈×C₄₁	—	4	2	no	—
200	Q₈×C₄₁	—	8	2	no	—
201	D₄×C₄₁	—	2	2	no	—
202	D₄×C₄₁	—	2	2	no	—
203	D₄×C₄₁	—	2	4	no	—
204	D₄×C₄₁	—	2	4	no	—
205	D₄×C₄₁	—	4	4	no	—
206	D₄×C₄₁	—	4	16	no	—
207	D₄×C₄₁	—	4	16	no	—
208	D₄×C₄₁	—	4	2	no	—
209	D₄×C₄₁	—	4	2	no	—
210	D₄×C₄₁	—	4	2	no	—
211	D₄×C₄₁	—	4	2	no	—
212	D₄×C₄₁	—	4	4	no	—
213	D₄×C₄₁	—	4	4	no	—
214	D₄×C₄₁	—	8	2	no	—
215	D₄×C₄₁	C₂×D₈	1	4	yes	—
216	D₄×C₄₁	C₂×SD₁₆	1	4	yes	complemented
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	—	4	2	no	—
221	C₂×C₄×C₄₁	—	4	2	no	—
222	C₂×C₄×C₄₁	—	4	2	no	—
223	C₂×C₄×C₄₁	—	4	2	no	—
224	C₂×C₄×C₄₁	—	4	2	no	—
225	C₂×C₄×C₄₁	—	4	2	no	—
226	C₂×C₄×C₄₁	—	4	4	no	—
227	C₂×C₄×C₄₁	—	4	4	no	—
228	C₂×C₄×C₄₁	—	4	2	no	—
229	C₂×C₄×C₄₁	—	8	2	no	—
230	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
231	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
232	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
233	C₂×C₄×C₄₁	C₂×D₈	1	2	yes	—
234	C₂×C₄×C₄₁	C₂×SD₁₆	1	2	yes	—
235	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
236	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
237	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
240	C₈×C₄₁	—	4	2	no	—
241	C₈×C₄₁	—	4	2	no	—
242	C₈×C₄₁	—	4	2	no	—
243	C₂×#1639	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
244	C₂²×C₄₁	—	2	4	no	—
245	C₂²×C₄₁	—	2	4	no	—
246	C₂²×C₄₁	—	4	8	no	—
247	C₂²×C₄₁	—	4	8	no	—
248	C₂²×C₄₁	—	4	2	no	—
249	C₂²×C₄₁	—	4	2	no	—
250	C₂²×C₄₁	—	4	2	no	—
251	C₂²×C₄₁	—	4	2	no	—
252	C₂²×C₄₁	—	4	4	no	—
253	C₂²×C₄₁	—	4	4	no	—
254	C₂²×C₄₁	—	4	4	no	—
255	C₂²×C₄₁	—	8	32	no	—
256	C₂²×C₄₁	—	8	8	no	—
257	C₂²×C₄₁	#447	1	2	yes	—
258	C₂²×C₄₁	#450	1	2	yes	—
259	C₂²×C₄₁	#455	1	2	yes	—
260	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
261	C₄×C₄₁	—	2	1	no	—
262	C₄×C₄₁	—	2	1	no	—
263	C₄×C₄₁	—	4	2	no	—
264	C₄×C₄₁	—	4	2	no	—
265	C₄×C₄₁	—	8	2	no	—
266	C₄×C₄₁	#447	1	2	yes	—
267	C₄×C₄₁	#450	1	2	yes	—
268	C₄×C₄₁	C₂²×D₈	1	1	yes	characteristic
269	C₄×C₄₁	C₂²×SD₁₆	1	1	yes	characteristic
270	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
271	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
272	C₂×D₄²	C₂×C₄₁	1	1	yes	characteristic
273	C₂×#486	C₂×C₄₁	1	1	yes	characteristic, complemented
274	C₂×#474	C₂×C₄₁	1	1	yes	characteristic, complemented
275	C₂×#461	C₂×C₄₁	1	1	yes	characteristic, complemented
276	#1639	C₂×C₄₁	1	8	yes	direct product factor
277	C₂×#331	C₂×C₄₁	1	1	yes	characteristic, complemented
278	C₂×D₄⋊C₈	C₂×C₄₁	1	1	yes	characteristic, complemented
279	C₂×D₄⋊C₈	C₂×C₄₁	1	1	yes	characteristic, complemented
280	C₂×C₄₁	—	4	4	no	—
281	C₂×C₄₁	—	4	4	no	—
282	C₂×C₄₁	—	8	4	no	—
283	C₂×C₄₁	#1639	1	4	yes	direct product factor
284	C₂×C₄₁	C₂×#447	1	1	yes	characteristic
285	C₂×C₄₁	C₂×#450	1	1	yes	characteristic
286	C₂×C₄₁	C₂×#455	1	1	yes	characteristic
287	C₂³×D₄	—	2	1	no	—
288	C₂³×D₄	—	2	1	no	—
289	C₂²×SD₁₆	—	2	1	no	—
290	D₄²	—	2	2	no	—
291	D₄²	—	2	2	no	—
292	D₄²	—	2	2	no	—
293	D₄²	C₂²×C₄₁	1	4	yes	—
294	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
295	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
296	C₂×#121	—	2	1	no	—
297	C₂×#121	—	2	1	no	—
298	C₂×#120	—	2	2	no	—
299	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
300	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
301	#486	—	2	2	no	—
302	#486	C₂²×C₄₁	1	4	yes	complemented
303	#474	—	2	2	no	—
304	#474	C₂²×C₄₁	1	4	yes	complemented
305	#461	—	2	2	no	—
306	#461	C₂²×C₄₁	1	4	yes	complemented
307	C₂×#107	—	2	1	no	—
308	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
309	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
310	C₂×#103	—	2	1	no	—
311	C₂×#102	—	2	2	no	—
312	C₂×#102	—	2	1	no	—
313	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
314	#331	C₂²×C₄₁	1	4	yes	complemented
315	D₄⋊C₈	C₂²×C₄₁	1	4	yes	complemented
316	D₄⋊C₈	C₂²×C₄₁	1	4	yes	complemented
317	C₄₁	C₂×#1639	1	1	yes	characteristic, direct product factor, Sylow
318	C₂⁵	—	2	2	no	—
319	C₂²×Q₈	—	2	1	no	—
320	C₂²×D₄	—	2	2	no	—
321	C₂²×D₄	—	2	2	no	—
322	C₂²×D₄	—	2	4	no	—
323	C₂²×D₄	—	2	4	no	—
324	C₂²×D₄	—	2	4	no	—
325	C₂²×D₄	—	2	4	no	—
326	C₂²×D₄	—	2	1	no	—
327	C₂²×D₄	—	2	1	no	—
328	C₂²×D₄	—	4	4	no	—
329	C₂²×D₄	—	4	4	no	—
330	C₂²×D₄	—	4	4	no	—
331	C₂²×D₄	—	4	4	no	—
332	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
333	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
334	C₂²×D₄	D₄×C₄₁	1	2	yes	—
335	C₂³×C₄	—	2	1	no	—
336	C₂³×C₄	—	2	1	no	—
337	C₂×SD₁₆	—	2	4	no	—
338	C₂×SD₁₆	—	4	4	no	—
339	C₂²×C₈	—	2	1	no	—
340	C₂²×C₈	—	2	1	no	—
341	C₂²×C₈	—	2	1	no	—
342	C₄⋊Q₈	—	2	1	no	—
343	C₄⋊Q₈	—	2	1	no	—
344	C₄⋊Q₈	—	2	1	no	—
345	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	complemented
346	#127	—	2	1	no	—
347	#127	—	2	1	no	—
348	#127	D₄×C₄₁	1	2	yes	—
349	#127	C₂³×C₄₁	1	2	yes	—
350	#121	—	2	4	no	—
351	#121	—	2	4	no	—
352	#121	—	2	4	no	—
353	#121	—	2	4	no	—
354	#120	—	2	8	no	—
355	#120	—	2	8	no	—
356	C₄×D₄	—	2	1	no	—
357	C₄×D₄	—	2	1	no	—
358	C₄×D₄	—	2	1	no	—
359	C₄×D₄	—	2	1	no	—
360	C₄×D₄	D₄×C₄₁	1	2	yes	—
361	C₄×D₄	D₄×C₄₁	1	2	yes	—
362	C₄×D₄	C₂³×C₄₁	1	2	yes	—
363	C₄×D₄	C₂³×C₄₁	1	2	yes	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄⋊C₄	—	2	1	no	—
366	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
367	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
368	C₂×C₂²⋊C₄	—	2	2	no	—
369	C₂×C₂²⋊C₄	—	2	1	no	—
370	C₂×C₂²⋊C₄	—	2	1	no	—
371	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
372	#107	—	2	4	no	—
373	C₄⋊C₈	—	2	1	no	—
374	C₄⋊C₈	—	2	1	no	—
375	C₄⋊C₈	C₂³×C₄₁	1	2	yes	complemented
376	C₄⋊C₈	C₂³×C₄₁	1	2	yes	complemented
377	#103	—	2	4	no	—
378	#102	—	2	4	no	—
379	#102	—	2	8	no	—
380	C₄×C₈	—	2	1	no	—
381	C₄×C₈	C₂³×C₄₁	1	2	yes	complemented
382	C₂⁴	—	2	1	no	—
383	C₂⁴	—	2	1	no	—
384	C₂⁴	—	2	8	no	—
385	C₂⁴	—	2	2	no	—
386	C₂⁴	—	4	8	no	—
387	C₂⁴	—	4	8	no	—
388	C₂⁴	—	8	4	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	4	1	no	—
391	C₂×Q₈	—	4	2	no	—
392	C₂×Q₈	—	4	2	no	—
393	C₂×D₄	—	2	8	no	—
394	C₂×D₄	—	2	8	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	4	4	no	—
405	C₂×D₄	—	4	8	no	—
406	C₂×D₄	—	4	8	no	—
407	C₂×D₄	—	4	16	no	—
408	C₂×D₄	—	4	16	no	—
409	C₂×D₄	—	4	8	no	—
410	C₂×D₄	—	4	8	no	—
411	C₂×D₄	—	4	8	no	—
412	C₂×D₄	—	4	8	no	—
413	C₂×D₄	—	4	2	no	—
414	C₂×D₄	—	4	2	no	—
415	C₂×D₄	—	4	2	no	—
416	C₂×D₄	—	4	2	no	—
417	C₂×D₄	D₈×C₄₁	1	4	yes	—
418	C₂×D₄	SD₁₆×C₄₁	1	4	yes	complemented
419	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
420	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
421	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	4	2	no	—
429	C₂²×C₄	—	4	2	no	—
430	C₂²×C₄	—	4	2	no	—
431	C₂²×C₄	—	4	2	no	—
432	C₂²×C₄	—	4	1	no	—
433	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
434	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
436	SD₁₆	—	4	8	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	4	2	no	—
441	C₂×C₈	—	4	2	no	—
442	C₂×C₈	—	4	2	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	4	1	no	—
448	C₄⋊C₄	—	4	1	no	—
449	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
450	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
451	C₂²⋊C₄	—	2	8	no	—
452	C₂²⋊C₄	—	2	2	no	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₂²⋊C₄	—	2	2	no	—
455	C₂²⋊C₄	—	2	2	no	—
456	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
457	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
458	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
459	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
460	C₂³	—	2	2	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	4	no	—
463	C₂³	—	2	4	no	—
464	C₂³	—	2	4	no	—
465	C₂³	—	4	16	no	—
466	C₂³	—	4	16	no	—
467	C₂³	—	4	2	no	—
468	C₂³	—	4	2	no	—
469	C₂³	—	4	2	no	—
470	C₂³	—	4	2	no	—
471	C₂³	—	4	4	no	—
472	C₂³	—	4	4	no	—
473	C₂³	—	4	4	no	—
474	C₂³	—	8	8	no	—
475	C₂³	—	8	32	no	—
476	C₂³	#120×C₄₁	1	1	yes	characteristic
477	Q₈	—	4	2	no	—
478	Q₈	—	4	2	no	—
479	Q₈	—	8	2	no	—
480	D₄	—	2	2	no	—
481	D₄	—	2	2	no	—
482	D₄	—	2	4	no	—
483	D₄	—	2	4	no	—
484	D₄	—	4	4	no	—
485	D₄	—	4	16	no	—
486	D₄	—	4	16	no	—
487	D₄	—	4	2	no	—
488	D₄	—	4	2	no	—
489	D₄	—	4	2	no	—
490	D₄	—	4	2	no	—
491	D₄	—	4	4	no	—
492	D₄	—	4	4	no	—
493	D₄	—	8	2	no	—
494	D₄	C₂×D₈×C₄₁	1	4	yes	—
495	D₄	C₂×SD₁₆×C₄₁	1	4	yes	complemented
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	4	no	—
506	C₂×C₄	—	4	4	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	8	2	no	—
509	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
510	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
511	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
512	C₂×C₄	C₂×D₈×C₄₁	1	2	yes	—
513	C₂×C₄	C₂×SD₁₆×C₄₁	1	2	yes	—
514	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
515	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
516	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
517	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
518	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
519	C₈	—	4	2	no	—
520	C₈	—	4	2	no	—
521	C₈	—	4	2	no	—
522	C₂²	—	2	4	no	—
523	C₂²	—	2	4	no	—
524	C₂²	—	4	8	no	—
525	C₂²	—	4	8	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	4	no	—
531	C₂²	—	4	4	no	—
532	C₂²	—	4	4	no	—
533	C₂²	—	8	32	no	—
534	C₂²	—	8	8	no	—
535	C₂²	C₄₁×#447	1	2	yes	—
536	C₂²	C₄₁×#450	1	2	yes	—
537	C₂²	C₄₁×#455	1	2	yes	—
538	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
539	C₄	—	2	1	no	—
540	C₄	—	2	1	no	—
541	C₄	—	4	2	no	—
542	C₄	—	4	2	no	—
543	C₄	—	8	2	no	—
544	C₄	C₄₁×#447	1	2	yes	—
545	C₄	C₄₁×#450	1	2	yes	—
546	C₄	C₂²×D₈×C₄₁	1	1	yes	characteristic
547	C₄	C₂²×SD₁₆×C₄₁	1	1	yes	characteristic
548	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
549	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
550	C₂	—	4	4	no	—
551	C₂	—	4	4	no	—
552	C₂	—	8	4	no	—
553	C₂	C₄₁×#1639	1	4	yes	direct product factor
554	C₂	C₂×C₄₁×#447	1	1	yes	characteristic
555	C₂	C₂×C₄₁×#450	1	1	yes	characteristic
556	C₂	C₂×C₄₁×#455	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₁
prime radical	C₂×D₄²×C₄₁	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#486	C₂	semidirect
3. C₂×C₄₁×#474	C₂	semidirect
4. C₂×C₄₁×#461	C₂	semidirect
5. C₄₁×#1639	C₂	direct (N × H)
6. C₂×C₄₁×#331	C₂	semidirect
7. C₂×C₄₁×D₄⋊C₈	C₂	semidirect
8. C₂×C₄₁×D₄⋊C₈	C₂	semidirect
16. C₂×C₄⋊Q₈×C₄₁	C₂²	semidirect
24. C₄₁×#486	C₂²	semidirect
26. C₄₁×#474	C₂²	semidirect
28. C₄₁×#461	C₂²	semidirect
30. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
31. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
35. C₂×C₄×C₈×C₄₁	C₂²	semidirect
36. C₄₁×#331	C₂²	semidirect
37. C₄₁×D₄⋊C₈	C₂²	semidirect
38. C₄₁×D₄⋊C₈	C₂²	semidirect
66. C₄⋊Q₈×C₄₁	C₂³	semidirect
96. C₄⋊C₈×C₄₁	C₂³	semidirect
97. C₄⋊C₈×C₄₁	C₂³	semidirect
102. C₄×C₈×C₄₁	C₂³	semidirect
139. C₂×D₄×C₄₁	SD₁₆	semidirect
216. D₄×C₄₁	C₂×SD₁₆	semidirect
243. C₂×#1639	C₄₁	direct (N × H)
273. C₂×#486	C₂×C₄₁	semidirect
274. C₂×#474	C₂×C₄₁	semidirect
275. C₂×#461	C₂×C₄₁	semidirect
276. #1639	C₂×C₄₁	direct (N × H)
277. C₂×#331	C₂×C₄₁	semidirect
278. C₂×D₄⋊C₈	C₂×C₄₁	semidirect
279. C₂×D₄⋊C₈	C₂×C₄₁	semidirect
283. C₂×C₄₁	#1639	direct (N × H)
294. C₂×C₄⋊Q₈	C₂²×C₄₁	semidirect
302. #486	C₂²×C₄₁	semidirect
304. #474	C₂²×C₄₁	semidirect
306. #461	C₂²×C₄₁	semidirect
308. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
309. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
313. C₂×C₄×C₈	C₂²×C₄₁	semidirect
314. #331	C₂²×C₄₁	semidirect
315. D₄⋊C₈	C₂²×C₄₁	semidirect
316. D₄⋊C₈	C₂²×C₄₁	semidirect
317. C₄₁	C₂×#1639	direct (N × H)
345. C₄⋊Q₈	C₂³×C₄₁	semidirect
375. C₄⋊C₈	C₂³×C₄₁	semidirect
376. C₄⋊C₈	C₂³×C₄₁	semidirect
381. C₄×C₈	C₂³×C₄₁	semidirect
418. C₂×D₄	SD₁₆×C₄₁	semidirect
495. D₄	C₂×SD₁₆×C₄₁	semidirect
553. C₂	C₄₁×#1639	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×D₄²×C₄₁	2
C₂×C₄₁×#486	2
C₂×C₄₁×#474	2
C₂×C₄₁×#461	2
C₄₁×#1639	2
C₂×C₄₁×#331	2
C₂×C₄₁×D₄⋊C₈	2
C₂×#1639	41

Subgroups — C2×C41×#1639 #23794682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#1639 #23794682