Subgroups — C₄₁×#33192 #23809393

Order 10496.

998 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#473	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#472	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₁×#471	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3040	C₂	1	2	yes	maximal, complemented
6	C₄×#131×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1979	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1978	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1977	C₂	1	2	yes	maximal, complemented
10	C₄₁×#1967	C₂	1	2	yes	maximal, complemented
11	C₄₁×#1848	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₄₁	C₂²	1	2	yes	—
13	C₂×AGL(1,ℤ/8)×C₄₁	C₂²	1	2	yes	—
14	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
15	C₂²×SD₁₆×C₄₁	C₂²	1	2	yes	—
16	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
17	C₂×#131×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×#131×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×#124×C₄₁	C₂²	1	2	yes	—
20	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
21	C₄₁×#495	—	2	1	no	—
22	C₄₁×#495	—	2	1	no	—
23	C₄₁×#495	—	2	1	no	—
24	C₄₁×#495	—	2	1	no	—
25	C₄₁×#473	—	2	4	no	—
26	C₄₁×#472	—	2	4	no	—
27	C₄₁×#471	—	2	8	no	—
28	C₄₁×#464	—	2	4	no	—
29	C₄₁×#463	—	2	4	no	—
30	C₂×#108×C₄₁	C₂²	1	2	yes	—
31	C₂×#108×C₄₁	C₂²	1	1	yes	characteristic
32	C₂×#108×C₄₁	C₂²	1	1	yes	characteristic
33	C₄₁×#423	C₂²	1	2	yes	—
34	C₄₁×#419	C₂²	1	2	yes	—
35	C₄₁×#418	C₂²	1	2	yes	—
36	C₂×#101×C₄₁	C₂²	1	2	yes	—
37	C₂×#101×C₄₁	C₂²	1	2	yes	—
38	C₂×#100×C₄₁	C₂²	1	2	yes	—
39	C₂×#100×C₄₁	C₂²	1	2	yes	—
40	C₄₁×#405	—	2	1	no	—
41	C₄₁×#405	—	2	1	no	—
42	C₄₁×#405	C₂²	1	1	yes	characteristic
43	C₄₁×#405	C₂²	1	1	yes	characteristic
44	C₄×M₁₆×C₄₁	—	2	1	no	—
45	C₄×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₄₁	—	2	1	no	—
47	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
48	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
49	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
50	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
51	#137×C₄₁	—	2	4	no	—
52	#137×C₄₁	—	2	4	no	—
53	AGL(1,ℤ/8)×C₄₁	—	2	4	no	—
54	AGL(1,ℤ/8)×C₄₁	—	2	4	no	—
55	C₂×Q₁₆×C₄₁	—	2	2	no	—
56	C₂×Q₁₆×C₄₁	—	2	2	no	—
57	C₂×Q₁₆×C₄₁	—	2	1	no	—
58	C₂×Q₁₆×C₄₁	—	2	1	no	—
59	C₂×Q₁₆×C₄₁	—	2	2	no	—
60	C₂×SD₁₆×C₄₁	—	2	2	no	—
61	C₂×SD₁₆×C₄₁	—	2	2	no	—
62	C₂×SD₁₆×C₄₁	—	2	4	no	—
63	C₂×SD₁₆×C₄₁	—	2	2	no	—
64	C₂×SD₁₆×C₄₁	—	2	2	no	—
65	C₂×SD₁₆×C₄₁	—	2	4	no	—
66	C₂×D₈×C₄₁	—	2	2	no	—
67	C₂×D₈×C₄₁	—	2	2	no	—
68	C₂×D₈×C₄₁	—	2	1	no	—
69	C₂×D₈×C₄₁	—	2	1	no	—
70	C₂×D₈×C₄₁	—	2	2	no	—
71	#131×C₄₁	—	2	2	no	—
72	#131×C₄₁	—	2	2	no	—
73	#131×C₄₁	D₄	1	4	yes	—
74	#131×C₄₁	D₄	1	4	yes	—
75	C₂×M₁₆×C₄₁	—	2	1	no	—
76	C₂×M₁₆×C₄₁	—	2	1	no	—
77	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
78	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
79	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
80	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₄₁	—	2	1	no	—
82	C₂²×C₈×C₄₁	—	2	1	no	—
83	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
85	#124×C₄₁	—	2	4	no	—
86	#124×C₄₁	—	2	2	no	—
87	#124×C₄₁	—	2	2	no	—
88	C₄×Q₈×C₄₁	D₄	1	2	yes	—
89	C₄×D₄×C₄₁	—	2	2	no	—
90	C₄×D₄×C₄₁	D₄	1	2	yes	—
91	#117×C₄₁	—	2	1	no	—
92	#117×C₄₁	C₂³	1	1	yes	characteristic
93	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
94	C₂×C₄²×C₄₁	—	2	1	no	—
95	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
96	#108×C₄₁	—	2	4	no	—
97	#108×C₄₁	—	2	2	no	—
98	#108×C₄₁	—	2	2	no	—
99	C₄⋊C₈×C₄₁	—	2	4	no	—
100	#103×C₄₁	—	2	4	no	—
101	#102×C₄₁	—	2	4	no	—
102	#101×C₄₁	—	2	4	no	—
103	#101×C₄₁	—	2	4	no	—
104	#100×C₄₁	—	2	4	no	—
105	#100×C₄₁	—	2	4	no	—
106	#97×C₄₁	—	2	1	no	—
107	#97×C₄₁	—	2	1	no	—
108	#97×C₄₁	—	2	1	no	—
109	C₄×C₈×C₄₁	—	2	1	no	—
110	C₄×C₈×C₄₁	—	2	1	no	—
111	C₄×C₈×C₄₁	—	2	1	no	—
112	C₄×C₈×C₄₁	D₄	1	1	yes	characteristic
113	C₄×C₈×C₄₁	D₄	1	1	yes	characteristic
114	C₄×C₈×C₄₁	D₄	1	1	yes	characteristic
115	C₄×C₈×C₄₁	D₄	1	1	yes	characteristic
116	C₂⁴×C₄₁	—	2	2	no	—
117	#41×C₄₁	—	2	1	no	—
118	#41×C₄₁	—	2	1	no	—
119	#41×C₄₁	C₂×D₄	1	2	yes	—
120	#41×C₄₁	C₂×D₄	1	2	yes	—
121	C₂×Q₈×C₄₁	—	2	2	no	—
122	C₂×Q₈×C₄₁	—	2	2	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	C₂×D₄	1	1	yes	characteristic
128	C₂×D₄×C₄₁	—	2	1	no	—
129	C₂×D₄×C₄₁	—	2	2	no	—
130	C₂×D₄×C₄₁	—	2	2	no	—
131	C₂×D₄×C₄₁	—	2	2	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	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₄₁	—	2	1	no	—
137	C₂²×C₄×C₄₁	—	2	2	no	—
138	C₂²×C₄×C₄₁	—	2	2	no	—
139	C₂²×C₄×C₄₁	#41	1	2	yes	—
140	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
141	Q₁₆×C₄₁	—	4	4	no	—
142	Q₁₆×C₄₁	—	4	2	no	—
143	Q₁₆×C₄₁	—	4	2	no	—
144	SD₁₆×C₄₁	—	4	4	no	—
145	SD₁₆×C₄₁	—	4	4	no	—
146	SD₁₆×C₄₁	—	4	4	no	—
147	SD₁₆×C₄₁	—	4	4	no	—
148	D₈×C₄₁	—	4	4	no	—
149	D₈×C₄₁	—	4	2	no	—
150	D₈×C₄₁	—	4	2	no	—
151	M₁₆×C₄₁	—	2	1	no	—
152	M₁₆×C₄₁	—	2	1	no	—
153	M₁₆×C₄₁	—	2	4	no	—
154	M₁₆×C₄₁	—	2	4	no	—
155	M₁₆×C₄₁	—	2	2	no	—
156	M₁₆×C₄₁	—	2	2	no	—
157	M₁₆×C₄₁	—	2	2	no	—
158	M₁₆×C₄₁	—	2	2	no	—
159	M₁₆×C₄₁	C₂×D₄	1	2	yes	—
160	M₁₆×C₄₁	C₂×D₄	1	2	yes	—
161	C₂×C₈×C₄₁	—	2	1	no	—
162	C₂×C₈×C₄₁	—	2	1	no	—
163	C₂×C₈×C₄₁	—	2	4	no	—
164	C₂×C₈×C₄₁	—	2	4	no	—
165	C₂×C₈×C₄₁	—	2	2	no	—
166	C₂×C₈×C₄₁	—	2	2	no	—
167	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
168	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
169	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
170	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
171	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
172	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
173	C₂×C₈×C₄₁	#41	1	2	yes	—
174	C₂×C₈×C₄₁	#41	1	2	yes	—
175	C₄⋊C₄×C₄₁	—	2	2	no	—
176	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
177	C₂²⋊C₄×C₄₁	—	2	1	no	—
178	C₂²⋊C₄×C₄₁	—	2	2	no	—
179	C₂²⋊C₄×C₄₁	—	4	4	no	—
180	C₂²⋊C₄×C₄₁	—	4	4	no	—
181	C₄²×C₄₁	—	2	2	no	—
182	C₄²×C₄₁	—	2	1	no	—
183	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
184	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₄₁	C₂×D₄	1	2	yes	—
186	C₂³×C₄₁	—	2	1	no	—
187	C₂³×C₄₁	—	4	2	no	—
188	C₂³×C₄₁	—	4	2	no	—
189	C₂³×C₄₁	—	4	2	no	—
190	C₂³×C₄₁	—	8	4	no	—
191	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
192	Q₈×C₄₁	—	2	1	no	—
193	Q₈×C₄₁	—	4	2	no	—
194	Q₈×C₄₁	—	4	2	no	—
195	Q₈×C₄₁	—	4	2	no	—
196	Q₈×C₄₁	—	4	2	no	—
197	Q₈×C₄₁	#127	1	2	yes	—
198	D₄×C₄₁	—	2	2	no	—
199	D₄×C₄₁	—	2	2	no	—
200	D₄×C₄₁	—	2	1	no	—
201	D₄×C₄₁	—	4	2	no	—
202	D₄×C₄₁	—	4	2	no	—
203	D₄×C₄₁	—	4	2	no	—
204	D₄×C₄₁	—	4	2	no	—
205	D₄×C₄₁	#127	1	2	yes	—
206	C₂×C₄×C₄₁	—	2	1	no	—
207	C₂×C₄×C₄₁	—	2	2	no	—
208	C₂×C₄×C₄₁	—	2	2	no	—
209	C₂×C₄×C₄₁	—	2	2	no	—
210	C₂×C₄×C₄₁	—	4	2	no	—
211	C₂×C₄×C₄₁	—	4	4	no	—
212	C₂×C₄×C₄₁	—	4	2	no	—
213	C₂×C₄×C₄₁	—	4	2	no	—
214	C₂×C₄×C₄₁	—	4	2	no	—
215	C₂×C₄×C₄₁	#121	1	2	yes	—
216	C₂×C₄×C₄₁	#121	1	2	yes	—
217	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
223	C₈×C₄₁	—	2	2	no	—
224	C₈×C₄₁	—	2	2	no	—
225	C₈×C₄₁	—	4	2	no	—
226	C₈×C₄₁	—	4	2	no	—
227	C₈×C₄₁	#121	1	2	yes	—
228	C₈×C₄₁	#121	1	2	yes	—
229	C₈×C₄₁	#121	1	2	yes	—
230	C₈×C₄₁	#121	1	2	yes	—
231	#33192	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂²×C₄₁	—	2	2	no	—
233	C₂²×C₄₁	—	2	2	no	—
234	C₂²×C₄₁	—	4	2	no	—
235	C₂²×C₄₁	—	8	2	no	—
236	C₂²×C₄₁	—	8	4	no	—
237	C₂²×C₄₁	—	16	2	no	—
238	C₂²×C₄₁	—	16	2	no	—
239	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
240	C₂²×C₄₁	#532	1	1	yes	characteristic
241	C₂²×C₄₁	#532	1	1	yes	characteristic
242	C₄×C₄₁	—	2	2	no	—
243	C₄×C₄₁	—	2	2	no	—
244	C₄×C₄₁	—	2	2	no	—
245	C₄×C₄₁	—	4	2	no	—
246	C₄×C₄₁	—	8	2	no	—
247	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
248	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
249	C₄×C₄₁	C₂×#127	1	1	yes	characteristic
250	C₄×C₄₁	#532	1	1	yes	characteristic
251	C₂×#495	C₂×C₄₁	1	1	yes	characteristic, complemented
252	C₂×#473	C₂×C₄₁	1	1	yes	characteristic, complemented
253	C₂×#472	C₂×C₄₁	1	1	yes	characteristic
254	C₂×#471	C₂×C₄₁	1	2	yes	complemented
255	#3040	C₂×C₄₁	1	2	yes	complemented
256	C₄×#131	C₂×C₄₁	1	1	yes	characteristic, complemented
257	#1979	C₂×C₄₁	1	1	yes	characteristic, complemented
258	#1978	C₂×C₄₁	1	1	yes	characteristic, complemented
259	#1977	C₂×C₄₁	1	2	yes	complemented
260	#1967	C₂×C₄₁	1	2	yes	complemented
261	#1848	C₂×C₄₁	1	1	yes	characteristic, complemented
262	C₂×C₄₁	—	2	1	no	—
263	C₂×C₄₁	—	2	1	no	—
264	C₂×C₄₁	—	4	2	no	—
265	C₂×C₄₁	—	16	2	no	—
266	C₂×C₄₁	#2856	1	1	yes	characteristic
267	C₂×C₄₁	#3067	1	2	yes	—
268	C₂×#137	C₂²×C₄₁	1	2	yes	—
269	C₂×AGL(1,ℤ/8)	C₂²×C₄₁	1	2	yes	—
270	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
271	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	—
272	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
273	C₂×#131	C₂²×C₄₁	1	1	yes	characteristic
274	C₂×#131	C₂²×C₄₁	1	1	yes	characteristic
275	C₂×#124	C₂²×C₄₁	1	2	yes	—
276	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
277	#495	—	2	1	no	—
278	#495	—	2	1	no	—
279	#495	—	2	1	no	—
280	#495	—	2	1	no	—
281	#473	—	2	4	no	—
282	#472	—	2	4	no	—
283	#471	—	2	8	no	—
284	#464	—	2	4	no	—
285	#463	—	2	4	no	—
286	C₂×#108	C₂²×C₄₁	1	2	yes	—
287	C₂×#108	C₂²×C₄₁	1	1	yes	characteristic
288	C₂×#108	C₂²×C₄₁	1	1	yes	characteristic
289	#423	C₂²×C₄₁	1	2	yes	—
290	#419	C₂²×C₄₁	1	2	yes	—
291	#418	C₂²×C₄₁	1	2	yes	—
292	C₂×#101	C₂²×C₄₁	1	2	yes	—
293	C₂×#101	C₂²×C₄₁	1	2	yes	—
294	C₂×#100	C₂²×C₄₁	1	2	yes	—
295	C₂×#100	C₂²×C₄₁	1	2	yes	—
296	#405	—	2	1	no	—
297	#405	—	2	1	no	—
298	#405	C₂²×C₄₁	1	1	yes	characteristic
299	#405	C₂²×C₄₁	1	1	yes	characteristic
300	C₄×M₁₆	—	2	1	no	—
301	C₄×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
302	C₂×C₄×C₈	—	2	1	no	—
303	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
304	C₄₁	#33192	1	1	yes	characteristic, direct product factor, Sylow
305	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
306	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
307	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
308	#137	—	2	4	no	—
309	#137	—	2	4	no	—
310	AGL(1,ℤ/8)	—	2	4	no	—
311	AGL(1,ℤ/8)	—	2	4	no	—
312	C₂×Q₁₆	—	2	2	no	—
313	C₂×Q₁₆	—	2	2	no	—
314	C₂×Q₁₆	—	2	1	no	—
315	C₂×Q₁₆	—	2	1	no	—
316	C₂×Q₁₆	—	2	2	no	—
317	C₂×SD₁₆	—	2	2	no	—
318	C₂×SD₁₆	—	2	2	no	—
319	C₂×SD₁₆	—	2	4	no	—
320	C₂×SD₁₆	—	2	2	no	—
321	C₂×SD₁₆	—	2	2	no	—
322	C₂×SD₁₆	—	2	4	no	—
323	C₂×D₈	—	2	2	no	—
324	C₂×D₈	—	2	2	no	—
325	C₂×D₈	—	2	1	no	—
326	C₂×D₈	—	2	1	no	—
327	C₂×D₈	—	2	2	no	—
328	#131	—	2	2	no	—
329	#131	—	2	2	no	—
330	#131	D₄×C₄₁	1	4	yes	—
331	#131	D₄×C₄₁	1	4	yes	—
332	C₂×M₁₆	—	2	1	no	—
333	C₂×M₁₆	—	2	1	no	—
334	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
335	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
336	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
337	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
338	C₂²×C₈	—	2	1	no	—
339	C₂²×C₈	—	2	1	no	—
340	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
341	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
342	#124	—	2	4	no	—
343	#124	—	2	2	no	—
344	#124	—	2	2	no	—
345	C₄×Q₈	D₄×C₄₁	1	2	yes	—
346	C₄×D₄	—	2	2	no	—
347	C₄×D₄	D₄×C₄₁	1	2	yes	—
348	#117	—	2	1	no	—
349	#117	C₂³×C₄₁	1	1	yes	characteristic
350	C₂×C₂²⋊C₄	—	2	4	no	—
351	C₂×C₄²	—	2	1	no	—
352	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
353	#108	—	2	4	no	—
354	#108	—	2	2	no	—
355	#108	—	2	2	no	—
356	C₄⋊C₈	—	2	4	no	—
357	#103	—	2	4	no	—
358	#102	—	2	4	no	—
359	#101	—	2	4	no	—
360	#101	—	2	4	no	—
361	#100	—	2	4	no	—
362	#100	—	2	4	no	—
363	#97	—	2	1	no	—
364	#97	—	2	1	no	—
365	#97	—	2	1	no	—
366	C₄×C₈	—	2	1	no	—
367	C₄×C₈	—	2	1	no	—
368	C₄×C₈	—	2	1	no	—
369	C₄×C₈	D₄×C₄₁	1	1	yes	characteristic
370	C₄×C₈	D₄×C₄₁	1	1	yes	characteristic
371	C₄×C₈	D₄×C₄₁	1	1	yes	characteristic
372	C₄×C₈	D₄×C₄₁	1	1	yes	characteristic
373	C₂⁴	—	2	2	no	—
374	#41	—	2	1	no	—
375	#41	—	2	1	no	—
376	#41	C₂×D₄×C₄₁	1	2	yes	—
377	#41	C₂×D₄×C₄₁	1	2	yes	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	2	2	no	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	—	2	2	no	—
383	C₂×Q₈	—	2	2	no	—
384	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
385	C₂×D₄	—	2	1	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	#41×C₄₁	1	2	yes	—
397	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
398	Q₁₆	—	4	4	no	—
399	Q₁₆	—	4	2	no	—
400	Q₁₆	—	4	2	no	—
401	SD₁₆	—	4	4	no	—
402	SD₁₆	—	4	4	no	—
403	SD₁₆	—	4	4	no	—
404	SD₁₆	—	4	4	no	—
405	D₈	—	4	4	no	—
406	D₈	—	4	2	no	—
407	D₈	—	4	2	no	—
408	M₁₆	—	2	1	no	—
409	M₁₆	—	2	1	no	—
410	M₁₆	—	2	4	no	—
411	M₁₆	—	2	4	no	—
412	M₁₆	—	2	2	no	—
413	M₁₆	—	2	2	no	—
414	M₁₆	—	2	2	no	—
415	M₁₆	—	2	2	no	—
416	M₁₆	C₂×D₄×C₄₁	1	2	yes	—
417	M₁₆	C₂×D₄×C₄₁	1	2	yes	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	4	no	—
421	C₂×C₈	—	2	4	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
425	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
426	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
427	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
428	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
429	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
430	C₂×C₈	#41×C₄₁	1	2	yes	—
431	C₂×C₈	#41×C₄₁	1	2	yes	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
434	C₂²⋊C₄	—	2	1	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	4	4	no	—
437	C₂²⋊C₄	—	4	4	no	—
438	C₄²	—	2	2	no	—
439	C₄²	—	2	1	no	—
440	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
441	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
442	C₄²	C₂×D₄×C₄₁	1	2	yes	—
443	C₂³	—	2	1	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	—	8	4	no	—
448	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
449	Q₈	—	2	1	no	—
450	Q₈	—	4	2	no	—
451	Q₈	—	4	2	no	—
452	Q₈	—	4	2	no	—
453	Q₈	—	4	2	no	—
454	Q₈	#127×C₄₁	1	2	yes	—
455	D₄	—	2	2	no	—
456	D₄	—	2	2	no	—
457	D₄	—	2	1	no	—
458	D₄	—	4	2	no	—
459	D₄	—	4	2	no	—
460	D₄	—	4	2	no	—
461	D₄	—	4	2	no	—
462	D₄	#127×C₄₁	1	2	yes	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	4	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	#121×C₄₁	1	2	yes	—
473	C₂×C₄	#121×C₄₁	1	2	yes	—
474	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
475	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
476	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
477	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
478	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
479	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
480	C₈	—	2	2	no	—
481	C₈	—	2	2	no	—
482	C₈	—	4	2	no	—
483	C₈	—	4	2	no	—
484	C₈	#121×C₄₁	1	2	yes	—
485	C₈	#121×C₄₁	1	2	yes	—
486	C₈	#121×C₄₁	1	2	yes	—
487	C₈	#121×C₄₁	1	2	yes	—
488	C₂²	—	2	2	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	8	4	no	—
492	C₂²	—	8	2	no	—
493	C₂²	—	16	2	no	—
494	C₂²	—	16	2	no	—
495	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
496	C₂²	C₄₁×#532	1	1	yes	characteristic
497	C₂²	C₄₁×#532	1	1	yes	characteristic
498	C₄	—	2	2	no	—
499	C₄	—	2	2	no	—
500	C₄	—	2	2	no	—
501	C₄	—	4	2	no	—
502	C₄	—	8	2	no	—
503	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
504	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
505	C₄	C₂×#127×C₄₁	1	1	yes	characteristic
506	C₄	C₄₁×#532	1	1	yes	characteristic
507	C₂	—	2	1	no	—
508	C₂	—	2	1	no	—
509	C₂	—	4	2	no	—
510	C₂	—	16	2	no	—
511	C₂	C₄₁×#2856	1	1	yes	characteristic
512	C₂	C₄₁×#3067	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×C₄₁×#472	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#495	C₂	semidirect
2. C₂×C₄₁×#473	C₂	semidirect
4. C₂×C₄₁×#471	C₂	semidirect
5. C₄₁×#3040	C₂	semidirect
6. C₄×#131×C₄₁	C₂	semidirect
7. C₄₁×#1979	C₂	semidirect
8. C₄₁×#1978	C₂	semidirect
9. C₄₁×#1977	C₂	semidirect
10. C₄₁×#1967	C₂	semidirect
11. C₄₁×#1848	C₂	semidirect
231. #33192	C₄₁	direct (N × H)
251. C₂×#495	C₂×C₄₁	semidirect
252. C₂×#473	C₂×C₄₁	semidirect
254. C₂×#471	C₂×C₄₁	semidirect
255. #3040	C₂×C₄₁	semidirect
256. C₄×#131	C₂×C₄₁	semidirect
257. #1979	C₂×C₄₁	semidirect
258. #1978	C₂×C₄₁	semidirect
259. #1977	C₂×C₄₁	semidirect
260. #1967	C₂×C₄₁	semidirect
261. #1848	C₂×C₄₁	semidirect
304. C₄₁	#33192	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×#495	2
C₂×C₄₁×#473	2
C₂×C₄₁×#472	2
C₂×C₄₁×#471	2
C₄₁×#3040	2
C₄×#131×C₄₁	2
C₄₁×#1979	2
C₄₁×#1978	2
C₄₁×#1977	2
C₄₁×#1967	2
C₄₁×#1848	2
#33192	41

Subgroups — C41×#33192 #23809393

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#33192 #23809393