Subgroups — C₄₁×#23047 #23799248

Order 10496.

840 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#473	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2950	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#2947	C₂	1	2	yes	maximal
4	C₄₁×#2912	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#1971	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1951	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1930	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1882	C₂	1	2	yes	maximal
9	C₄₁×#1857	C₂	1	2	yes	maximal, complemented
10	C₄₁×#1773	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1765	C₂	1	1	yes	maximal, characteristic
12	C₂×#137×C₄₁	C₂²	1	2	yes	—
13	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×#131×C₄₁	C₂²	1	1	yes	characteristic
15	C₄₁×#520	C₂²	1	2	yes	—
16	C₄₁×#519	C₂²	1	2	yes	—
17	C₄₁×#473	C₄	1	8	yes	complemented
18	C₄₁×#441	—	2	1	no	—
19	C₄₁×#441	—	2	1	no	—
20	C₄₁×#441	—	2	2	no	—
21	C₄₁×#440	—	2	2	no	—
22	C₄×Q₁₆×C₄₁	—	2	2	no	—
23	C₄×Q₁₆×C₄₁	—	2	2	no	—
24	C₄×SD₁₆×C₄₁	—	2	2	no	—
25	C₂×#108×C₄₁	C₂²	1	1	yes	characteristic
26	C₄₁×#428	—	2	2	no	—
27	C₄₁×#428	C₂²	1	2	yes	—
28	C₄₁×#428	C₂²	1	2	yes	—
29	C₄₁×#427	—	2	1	no	—
30	C₄₁×#427	C₂²	1	1	yes	characteristic
31	C₂×#106×C₄₁	—	2	1	no	—
32	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
33	C₂×#104×C₄₁	C₂²	1	1	yes	characteristic
34	C₄₁×#419	C₂²	1	2	yes	—
35	C₄₁×#416	C₂²	1	1	yes	characteristic
36	C₂×#103×C₄₁	C₂²	1	2	yes	—
37	C₂×#101×C₄₁	C₂²	1	2	yes	—
38	C₄₁×#405	C₂²	1	1	yes	characteristic
39	C₄₁×#405	C₂²	1	2	yes	—
40	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
41	C₄₁×#391	C₂²	1	2	yes	—
42	C₄₁×#343	C₂²	1	2	yes	—
43	C₄₁×#341	C₂²	1	1	yes	characteristic
44	C₄₁×#339	C₂²	1	1	yes	characteristic
45	C₄₁×#339	C₂²	1	2	yes	—
46	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
47	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
48	#137×C₄₁	—	2	4	no	—
49	#137×C₄₁	C₂×C₄	1	8	yes	—
50	C₂×Q₁₆×C₄₁	—	2	2	no	—
51	C₂×Q₁₆×C₄₁	—	2	1	no	—
52	C₂×Q₁₆×C₄₁	—	2	1	no	—
53	C₂×Q₁₆×C₄₁	—	2	2	no	—
54	C₂×Q₁₆×C₄₁	C₂×C₄	1	4	yes	complemented
55	C₂×SD₁₆×C₄₁	—	2	2	no	—
56	#131×C₄₁	—	2	2	no	—
57	#131×C₄₁	C₂×C₄	1	4	yes	—
58	C₂×M₁₆×C₄₁	—	2	1	no	—
59	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
60	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
61	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
62	C₂²×C₈×C₄₁	—	2	1	no	—
63	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
65	C₄×Q₈×C₄₁	—	2	2	no	—
66	C₄×Q₈×C₄₁	—	2	2	no	—
67	C₄×Q₈×C₄₁	—	2	2	no	—
68	C₄×Q₈×C₄₁	—	2	2	no	—
69	C₄×Q₈×C₄₁	—	2	2	no	—
70	C₄×D₄×C₄₁	—	2	2	no	—
71	C₄×D₄×C₄₁	—	4	2	no	—
72	#117×C₄₁	—	2	2	no	—
73	#117×C₄₁	—	4	2	no	—
74	#117×C₄₁	C₂³	1	1	yes	characteristic
75	#117×C₄₁	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
77	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
78	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
79	#108×C₄₁	C₂×C₄	1	4	yes	complemented
80	#107×C₄₁	—	2	2	no	—
81	#107×C₄₁	—	2	2	no	—
82	#107×C₄₁	D₄	1	2	yes	—
83	#106×C₄₁	—	2	1	no	—
84	#106×C₄₁	—	2	1	no	—
85	#106×C₄₁	—	2	2	no	—
86	#106×C₄₁	—	2	2	no	—
87	#106×C₄₁	D₄	1	1	yes	characteristic
88	#106×C₄₁	D₄	1	1	yes	characteristic
89	#104×C₄₁	—	2	2	no	—
90	#103×C₄₁	—	2	2	no	—
91	#103×C₄₁	—	2	2	no	—
92	#103×C₄₁	—	2	2	no	—
93	#103×C₄₁	—	2	2	no	—
94	#103×C₄₁	D₄	1	2	yes	—
95	#102×C₄₁	D₄	1	2	yes	—
96	#101×C₄₁	C₂×C₄	1	8	yes	complemented
97	#97×C₄₁	—	2	2	no	—
98	#97×C₄₁	—	2	1	no	—
99	#97×C₄₁	—	2	2	no	—
100	C₄×C₈×C₄₁	—	2	2	no	—
101	C₄×C₈×C₄₁	—	2	1	no	—
102	#95×C₄₁	—	4	2	no	—
103	#41×C₄₁	—	2	1	no	—
104	#41×C₄₁	—	2	1	no	—
105	#41×C₄₁	C₂²×C₄	1	2	yes	—
106	#41×C₄₁	#41	1	2	yes	—
107	C₂×Q₈×C₄₁	—	2	2	no	—
108	C₂×Q₈×C₄₁	—	2	2	no	—
109	C₂×Q₈×C₄₁	—	2	2	no	—
110	C₂×Q₈×C₄₁	—	2	2	no	—
111	C₂×Q₈×C₄₁	—	2	2	no	—
112	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	—
113	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
114	C₂×D₄×C₄₁	—	2	1	no	—
115	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₁	—	2	1	no	—
117	C₂²×C₄×C₄₁	—	2	2	no	—
118	C₂²×C₄×C₄₁	—	2	1	no	—
119	C₂²×C₄×C₄₁	—	2	2	no	—
120	C₂²×C₄×C₄₁	—	4	2	no	—
121	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
122	Q₁₆×C₄₁	—	2	8	no	—
123	Q₁₆×C₄₁	—	2	4	no	—
124	Q₁₆×C₄₁	—	2	4	no	—
125	SD₁₆×C₄₁	—	2	8	no	—
126	M₁₆×C₄₁	—	2	1	no	—
127	M₁₆×C₄₁	—	2	2	no	—
128	M₁₆×C₄₁	—	2	4	no	—
129	M₁₆×C₄₁	—	2	1	no	—
130	M₁₆×C₄₁	—	2	1	no	—
131	M₁₆×C₄₁	C₂²×C₄	1	2	yes	—
132	M₁₆×C₄₁	C₂²×C₄	1	4	yes	—
133	C₂×C₈×C₄₁	—	2	2	no	—
134	C₂×C₈×C₄₁	—	2	1	no	—
135	C₂×C₈×C₄₁	—	2	1	no	—
136	C₂×C₈×C₄₁	—	2	1	no	—
137	C₂×C₈×C₄₁	—	2	4	no	—
138	C₂×C₈×C₄₁	—	2	1	no	—
139	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
140	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₄₁	#41	1	2	yes	—
144	C₄⋊C₄×C₄₁	—	2	2	no	—
145	C₄⋊C₄×C₄₁	—	2	2	no	—
146	C₄⋊C₄×C₄₁	—	4	2	no	—
147	C₄⋊C₄×C₄₁	—	4	2	no	—
148	C₄⋊C₄×C₄₁	—	4	2	no	—
149	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
150	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
151	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
152	C₂²⋊C₄×C₄₁	—	2	1	no	—
153	C₂²⋊C₄×C₄₁	—	2	2	no	—
154	C₂²⋊C₄×C₄₁	—	4	2	no	—
155	C₄²×C₄₁	—	2	2	no	—
156	C₄²×C₄₁	—	2	1	no	—
157	C₄²×C₄₁	—	2	1	no	—
158	C₄²×C₄₁	—	2	1	no	—
159	C₄²×C₄₁	—	4	2	no	—
160	C₄²×C₄₁	—	4	2	no	—
161	C₄²×C₄₁	—	4	2	no	—
162	C₂³×C₄₁	—	2	1	no	—
163	C₂³×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
164	Q₈×C₄₁	—	2	1	no	—
165	Q₈×C₄₁	—	2	4	no	—
166	Q₈×C₄₁	—	2	4	no	—
167	Q₈×C₄₁	—	4	2	no	—
168	Q₈×C₄₁	—	4	2	no	—
169	Q₈×C₄₁	C₄×D₄	1	2	yes	—
170	D₄×C₄₁	—	2	2	no	—
171	D₄×C₄₁	—	2	2	no	—
172	D₄×C₄₁	—	2	1	no	—
173	D₄×C₄₁	C₄×D₄	1	2	yes	—
174	C₂×C₄×C₄₁	—	2	1	no	—
175	C₂×C₄×C₄₁	—	2	2	no	—
176	C₂×C₄×C₄₁	—	2	2	no	—
177	C₂×C₄×C₄₁	—	2	4	no	—
178	C₂×C₄×C₄₁	—	2	2	no	—
179	C₂×C₄×C₄₁	—	2	2	no	—
180	C₂×C₄×C₄₁	—	2	2	no	—
181	C₂×C₄×C₄₁	—	4	2	no	—
182	C₂×C₄×C₄₁	—	4	2	no	—
183	C₂×C₄×C₄₁	—	4	2	no	—
184	C₂×C₄×C₄₁	—	4	2	no	—
185	C₂×C₄×C₄₁	—	4	1	no	—
186	C₂×C₄×C₄₁	—	8	2	no	—
187	C₂×C₄×C₄₁	—	16	2	no	—
188	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
194	C₈×C₄₁	—	2	2	no	—
195	C₈×C₄₁	—	2	4	no	—
196	C₈×C₄₁	—	2	2	no	—
197	C₈×C₄₁	—	4	1	no	—
198	C₈×C₄₁	C₄×D₄	1	2	yes	—
199	C₈×C₄₁	C₄×D₄	1	2	yes	—
200	#23047	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
201	C₂²×C₄₁	—	2	2	no	—
202	C₂²×C₄₁	—	2	2	no	—
203	C₂²×C₄₁	—	4	2	no	—
204	C₂²×C₄₁	#520	1	1	yes	characteristic
205	C₂²×C₄₁	D₄²	1	1	yes	characteristic
206	C₂²×C₄₁	#553	1	1	yes	characteristic
207	C₄×C₄₁	—	2	2	no	—
208	C₄×C₄₁	—	4	4	no	—
209	C₄×C₄₁	—	4	2	no	—
210	C₄×C₄₁	—	4	2	no	—
211	C₄×C₄₁	—	4	2	no	—
212	C₄×C₄₁	—	8	1	no	—
213	C₄×C₄₁	—	8	2	no	—
214	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
215	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
216	C₄×C₄₁	#547	1	1	yes	characteristic
217	C₄×C₄₁	#548	1	1	yes	characteristic
218	C₂×#473	C₂×C₄₁	1	1	yes	characteristic
219	#2950	C₂×C₄₁	1	1	yes	characteristic, complemented
220	#2947	C₂×C₄₁	1	2	yes	—
221	#2912	C₂×C₄₁	1	1	yes	characteristic
222	#1971	C₂×C₄₁	1	1	yes	characteristic, complemented
223	#1951	C₂×C₄₁	1	1	yes	characteristic, complemented
224	#1930	C₂×C₄₁	1	2	yes	complemented
225	#1882	C₂×C₄₁	1	2	yes	—
226	#1857	C₂×C₄₁	1	2	yes	complemented
227	#1773	C₂×C₄₁	1	1	yes	characteristic, complemented
228	#1765	C₂×C₄₁	1	1	yes	characteristic
229	C₂×C₄₁	—	2	1	no	—
230	C₂×C₄₁	—	2	1	no	—
231	C₂×C₄₁	—	4	2	no	—
232	C₂×C₄₁	#2361	1	1	yes	characteristic
233	C₂×C₄₁	#3289	1	2	yes	—
234	C₂×#137	C₂²×C₄₁	1	2	yes	—
235	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
236	C₂×#131	C₂²×C₄₁	1	1	yes	characteristic
237	#520	C₂²×C₄₁	1	2	yes	—
238	#519	C₂²×C₄₁	1	2	yes	—
239	#473	C₄×C₄₁	1	8	yes	complemented
240	#441	—	2	1	no	—
241	#441	—	2	1	no	—
242	#441	—	2	2	no	—
243	#440	—	2	2	no	—
244	C₄×Q₁₆	—	2	2	no	—
245	C₄×Q₁₆	—	2	2	no	—
246	C₄×SD₁₆	—	2	2	no	—
247	C₂×#108	C₂²×C₄₁	1	1	yes	characteristic
248	#428	—	2	2	no	—
249	#428	C₂²×C₄₁	1	2	yes	—
250	#428	C₂²×C₄₁	1	2	yes	—
251	#427	—	2	1	no	—
252	#427	C₂²×C₄₁	1	1	yes	characteristic
253	C₂×#106	—	2	1	no	—
254	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
255	C₂×#104	C₂²×C₄₁	1	1	yes	characteristic
256	#419	C₂²×C₄₁	1	2	yes	—
257	#416	C₂²×C₄₁	1	1	yes	characteristic
258	C₂×#103	C₂²×C₄₁	1	2	yes	—
259	C₂×#101	C₂²×C₄₁	1	2	yes	—
260	#405	C₂²×C₄₁	1	2	yes	—
261	#405	C₂²×C₄₁	1	1	yes	characteristic
262	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
263	#391	C₂²×C₄₁	1	2	yes	—
264	#343	C₂²×C₄₁	1	2	yes	—
265	#341	C₂²×C₄₁	1	1	yes	characteristic
266	#339	C₂²×C₄₁	1	1	yes	characteristic
267	#339	C₂²×C₄₁	1	2	yes	—
268	C₄₁	#23047	1	1	yes	characteristic, direct product factor, Sylow
269	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
270	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
271	#137	—	2	4	no	—
272	#137	C₂×C₄×C₄₁	1	8	yes	—
273	C₂×Q₁₆	—	2	2	no	—
274	C₂×Q₁₆	—	2	1	no	—
275	C₂×Q₁₆	—	2	1	no	—
276	C₂×Q₁₆	—	2	2	no	—
277	C₂×Q₁₆	C₂×C₄×C₄₁	1	4	yes	complemented
278	C₂×SD₁₆	—	2	2	no	—
279	#131	—	2	2	no	—
280	#131	C₂×C₄×C₄₁	1	4	yes	—
281	C₂×M₁₆	—	2	1	no	—
282	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
283	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
284	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
285	C₂²×C₈	—	2	1	no	—
286	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
287	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
288	C₄×Q₈	—	2	2	no	—
289	C₄×Q₈	—	2	2	no	—
290	C₄×Q₈	—	2	2	no	—
291	C₄×Q₈	—	2	2	no	—
292	C₄×Q₈	—	2	2	no	—
293	C₄×D₄	—	2	2	no	—
294	C₄×D₄	—	4	2	no	—
295	#117	—	2	2	no	—
296	#117	—	4	2	no	—
297	#117	C₂³×C₄₁	1	1	yes	characteristic
298	#117	C₂³×C₄₁	1	2	yes	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
301	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
302	#108	C₂×C₄×C₄₁	1	4	yes	complemented
303	#107	—	2	2	no	—
304	#107	—	2	2	no	—
305	#107	D₄×C₄₁	1	2	yes	—
306	#106	—	2	1	no	—
307	#106	—	2	1	no	—
308	#106	—	2	2	no	—
309	#106	—	2	2	no	—
310	#106	D₄×C₄₁	1	1	yes	characteristic
311	#106	D₄×C₄₁	1	1	yes	characteristic
312	#104	—	2	2	no	—
313	#103	—	2	2	no	—
314	#103	—	2	2	no	—
315	#103	—	2	2	no	—
316	#103	—	2	2	no	—
317	#103	D₄×C₄₁	1	2	yes	—
318	#102	D₄×C₄₁	1	2	yes	—
319	#101	C₂×C₄×C₄₁	1	8	yes	complemented
320	#97	—	2	2	no	—
321	#97	—	2	1	no	—
322	#97	—	2	2	no	—
323	C₄×C₈	—	2	2	no	—
324	C₄×C₈	—	2	1	no	—
325	#95	—	4	2	no	—
326	#41	—	2	1	no	—
327	#41	—	2	1	no	—
328	#41	C₂²×C₄×C₄₁	1	2	yes	—
329	#41	#41×C₄₁	1	2	yes	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	—
336	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	4	2	no	—
344	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
345	Q₁₆	—	2	8	no	—
346	Q₁₆	—	2	4	no	—
347	Q₁₆	—	2	4	no	—
348	SD₁₆	—	2	8	no	—
349	M₁₆	—	2	1	no	—
350	M₁₆	—	2	2	no	—
351	M₁₆	—	2	4	no	—
352	M₁₆	—	2	1	no	—
353	M₁₆	—	2	1	no	—
354	M₁₆	C₂²×C₄×C₄₁	1	2	yes	—
355	M₁₆	C₂²×C₄×C₄₁	1	4	yes	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	4	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
363	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
364	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
365	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
366	C₂×C₈	#41×C₄₁	1	2	yes	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	4	2	no	—
370	C₄⋊C₄	—	4	2	no	—
371	C₄⋊C₄	—	4	2	no	—
372	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
373	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
374	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
375	C₂²⋊C₄	—	2	1	no	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	4	2	no	—
378	C₄²	—	2	2	no	—
379	C₄²	—	2	1	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	4	2	no	—
383	C₄²	—	4	2	no	—
384	C₄²	—	4	2	no	—
385	C₂³	—	2	1	no	—
386	C₂³	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
387	Q₈	—	2	1	no	—
388	Q₈	—	2	4	no	—
389	Q₈	—	2	4	no	—
390	Q₈	—	4	2	no	—
391	Q₈	—	4	2	no	—
392	Q₈	C₄×D₄×C₄₁	1	2	yes	—
393	D₄	—	2	2	no	—
394	D₄	—	2	2	no	—
395	D₄	—	2	1	no	—
396	D₄	C₄×D₄×C₄₁	1	2	yes	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	8	2	no	—
410	C₂×C₄	—	16	2	no	—
411	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
412	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
413	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
414	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
415	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
416	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
417	C₈	—	2	2	no	—
418	C₈	—	2	4	no	—
419	C₈	—	2	2	no	—
420	C₈	—	4	1	no	—
421	C₈	C₄×D₄×C₄₁	1	2	yes	—
422	C₈	C₄×D₄×C₄₁	1	2	yes	—
423	C₂²	—	2	2	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	4	2	no	—
426	C₂²	C₄₁×#520	1	1	yes	characteristic
427	C₂²	D₄²×C₄₁	1	1	yes	characteristic
428	C₂²	C₄₁×#553	1	1	yes	characteristic
429	C₄	—	2	2	no	—
430	C₄	—	4	4	no	—
431	C₄	—	4	2	no	—
432	C₄	—	4	2	no	—
433	C₄	—	4	2	no	—
434	C₄	—	8	1	no	—
435	C₄	—	8	2	no	—
436	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
437	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
438	C₄	C₄₁×#547	1	1	yes	characteristic
439	C₄	C₄₁×#548	1	1	yes	characteristic
440	C₂	—	2	1	no	—
441	C₂	—	2	1	no	—
442	C₂	—	4	2	no	—
443	C₂	C₄₁×#2361	1	1	yes	characteristic
444	C₂	C₄₁×#3289	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₁	D₄²
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×#41×C₄₁	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂²×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#2950	C₂	semidirect
5. C₄₁×#1971	C₂	semidirect
6. C₄₁×#1951	C₂	semidirect
7. C₄₁×#1930	C₂	semidirect
9. C₄₁×#1857	C₂	semidirect
10. C₄₁×#1773	C₂	semidirect
17. C₄₁×#473	C₄	semidirect
54. C₂×Q₁₆×C₄₁	C₂×C₄	semidirect
79. #108×C₄₁	C₂×C₄	semidirect
96. #101×C₄₁	C₂×C₄	semidirect
200. #23047	C₄₁	direct (N × H)
219. #2950	C₂×C₄₁	semidirect
222. #1971	C₂×C₄₁	semidirect
223. #1951	C₂×C₄₁	semidirect
224. #1930	C₂×C₄₁	semidirect
226. #1857	C₂×C₄₁	semidirect
227. #1773	C₂×C₄₁	semidirect
239. #473	C₄×C₄₁	semidirect
268. C₄₁	#23047	direct (N × H)
277. C₂×Q₁₆	C₂×C₄×C₄₁	semidirect
302. #108	C₂×C₄×C₄₁	semidirect
319. #101	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×#473	2
C₄₁×#2950	2
C₄₁×#2947	2
C₄₁×#2912	2
C₄₁×#1971	2
C₄₁×#1951	2
C₄₁×#1930	2
C₄₁×#1882	2
C₄₁×#1857	2
C₄₁×#1773	2
C₄₁×#1765	2
#23047	41

Subgroups — C41×#23047 #23799248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#23047 #23799248