Subgroups — C₄₁×#22806 #23799007

Order 10496.

814 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×SD₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2357	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2356	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1968	C₂	1	2	yes	maximal
5	C₄₁×#1928	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1925	C₂	1	2	yes	maximal
7	C₄₁×#1846	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1805	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1804	C₂	1	1	yes	maximal, characteristic
10	C₄×#106×C₄₁	C₂	1	2	yes	maximal, complemented
11	C₈×C₄⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
15	C₄×SD₁₆×C₄₁	C₄	1	8	yes	complemented
16	C₂×#107×C₄₁	C₂²	1	2	yes	—
17	C₂×#106×C₄₁	C₂²	1	2	yes	—
18	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×#103×C₄₁	C₂²	1	2	yes	—
21	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×#102×C₄₁	C₂²	1	2	yes	—
23	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
26	C₄₁×#391	C₂²	1	2	yes	—
27	C₄₁×#390	C₂²	1	2	yes	—
28	C₄₁×#388	—	2	2	no	—
29	C₄₁×#387	—	2	2	no	—
30	C₄₁×#383	—	2	1	no	—
31	C₄₁×#382	C₂²	1	1	yes	characteristic
32	C₄₁×#382	C₂²	1	1	yes	characteristic
33	C₄₁×#381	—	2	1	no	—
34	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
35	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
36	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
37	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
38	C₄₁×#376	—	2	1	no	—
39	C₄₁×#340	C₂²	1	2	yes	—
40	C₄₁×#340	C₂²	1	2	yes	—
41	C₄₁×#336	C₂²	1	2	yes	—
42	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
43	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₄₁	—	2	1	no	—
45	C₂×SD₁₆×C₄₁	—	2	2	no	—
46	C₂×SD₁₆×C₄₁	—	2	2	no	—
47	C₂×SD₁₆×C₄₁	C₂×C₄	1	4	yes	—
48	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
49	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
51	C₄×Q₈×C₄₁	—	2	2	no	—
52	C₄×Q₈×C₄₁	C₂×C₄	1	4	yes	—
53	C₄×D₄×C₄₁	—	2	2	no	—
54	C₄×D₄×C₄₁	C₂×C₄	1	4	yes	—
55	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
56	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
57	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
61	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
62	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
64	C₂×C₄²×C₄₁	—	2	1	no	—
65	C₂×C₄²×C₄₁	—	2	2	no	—
66	C₂×C₄²×C₄₁	—	2	2	no	—
67	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
68	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
69	#107×C₄₁	—	4	2	no	—
70	#106×C₄₁	—	2	4	no	—
71	#106×C₄₁	C₂×C₄	1	4	yes	—
72	C₄⋊C₈×C₄₁	—	2	2	no	—
73	#103×C₄₁	—	4	2	no	—
74	#103×C₄₁	C₂×C₄	1	4	yes	—
75	#102×C₄₁	—	4	2	no	—
76	#102×C₄₁	C₂×C₄	1	4	yes	—
77	C₄×C₈×C₄₁	—	2	4	no	—
78	C₄×C₈×C₄₁	C₂×C₄	1	4	yes	—
79	#95×C₄₁	—	2	1	no	—
80	#95×C₄₁	—	2	2	no	—
81	#95×C₄₁	—	2	1	no	—
82	#95×C₄₁	—	2	2	no	—
83	#95×C₄₁	—	2	2	no	—
84	#95×C₄₁	—	2	1	no	—
85	#95×C₄₁	—	2	1	no	—
86	#95×C₄₁	—	2	2	no	—
87	#95×C₄₁	D₄	1	1	yes	characteristic
88	#95×C₄₁	D₄	1	1	yes	characteristic
89	C₂⁴×C₄₁	—	2	1	no	—
90	C₂×Q₈×C₄₁	—	2	1	no	—
91	C₂×Q₈×C₄₁	—	2	1	no	—
92	C₂×Q₈×C₄₁	—	2	1	no	—
93	C₂×Q₈×C₄₁	—	2	1	no	—
94	C₂×Q₈×C₄₁	—	2	1	no	—
95	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
96	C₂×D₄×C₄₁	—	2	1	no	—
97	C₂×D₄×C₄₁	—	2	1	no	—
98	C₂×D₄×C₄₁	—	2	1	no	—
99	C₂×D₄×C₄₁	—	2	1	no	—
100	C₂×D₄×C₄₁	—	2	1	no	—
101	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₄₁	—	2	1	no	—
103	C₂²×C₄×C₄₁	—	2	1	no	—
104	C₂²×C₄×C₄₁	—	2	1	no	—
105	C₂²×C₄×C₄₁	—	2	4	no	—
106	C₂²×C₄×C₄₁	—	2	2	no	—
107	C₂²×C₄×C₄₁	—	2	2	no	—
108	C₂²×C₄×C₄₁	—	8	2	no	—
109	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
114	SD₁₆×C₄₁	—	2	8	no	—
115	C₂×C₈×C₄₁	—	2	1	no	—
116	C₂×C₈×C₄₁	—	2	1	no	—
117	C₂×C₈×C₄₁	—	2	2	no	—
118	C₂×C₈×C₄₁	—	2	2	no	—
119	C₂×C₈×C₄₁	—	2	2	no	—
120	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
121	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
122	C₂×C₈×C₄₁	#41	1	2	yes	—
123	C₂×C₈×C₄₁	#41	1	2	yes	—
124	C₄⋊C₄×C₄₁	—	2	4	no	—
125	C₄⋊C₄×C₄₁	—	2	4	no	—
126	C₄⋊C₄×C₄₁	—	2	1	no	—
127	C₄⋊C₄×C₄₁	—	2	1	no	—
128	C₄⋊C₄×C₄₁	—	2	2	no	—
129	C₄⋊C₄×C₄₁	—	2	2	no	—
130	C₄⋊C₄×C₄₁	—	2	2	no	—
131	C₄⋊C₄×C₄₁	—	2	2	no	—
132	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
133	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
134	C₂²⋊C₄×C₄₁	—	2	4	no	—
135	C₂²⋊C₄×C₄₁	—	4	4	no	—
136	C₂²⋊C₄×C₄₁	—	8	2	no	—
137	C₄²×C₄₁	—	2	4	no	—
138	C₄²×C₄₁	—	2	2	no	—
139	C₄²×C₄₁	—	2	2	no	—
140	C₄²×C₄₁	—	4	4	no	—
141	C₄²×C₄₁	—	8	2	no	—
142	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
143	C₄²×C₄₁	#41	1	2	yes	—
144	C₂³×C₄₁	—	2	2	no	—
145	C₂³×C₄₁	—	4	1	no	—
146	C₂³×C₄₁	—	4	1	no	—
147	C₂³×C₄₁	—	4	2	no	—
148	C₂³×C₄₁	—	4	2	no	—
149	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
150	Q₈×C₄₁	—	2	2	no	—
151	Q₈×C₄₁	—	2	2	no	—
152	Q₈×C₄₁	—	4	1	no	—
153	Q₈×C₄₁	—	4	1	no	—
154	D₄×C₄₁	—	2	2	no	—
155	D₄×C₄₁	—	2	2	no	—
156	D₄×C₄₁	—	4	1	no	—
157	D₄×C₄₁	—	4	1	no	—
158	C₂×C₄×C₄₁	—	2	2	no	—
159	C₂×C₄×C₄₁	—	2	2	no	—
160	C₂×C₄×C₄₁	—	2	2	no	—
161	C₂×C₄×C₄₁	—	2	2	no	—
162	C₂×C₄×C₄₁	—	2	2	no	—
163	C₂×C₄×C₄₁	—	2	2	no	—
164	C₂×C₄×C₄₁	—	2	2	no	—
165	C₂×C₄×C₄₁	—	2	2	no	—
166	C₂×C₄×C₄₁	—	2	2	no	—
167	C₂×C₄×C₄₁	—	2	2	no	—
168	C₂×C₄×C₄₁	—	4	1	no	—
169	C₂×C₄×C₄₁	—	4	1	no	—
170	C₂×C₄×C₄₁	—	4	2	no	—
171	C₂×C₄×C₄₁	—	4	2	no	—
172	C₂×C₄×C₄₁	—	4	2	no	—
173	C₂×C₄×C₄₁	—	4	2	no	—
174	C₂×C₄×C₄₁	—	4	2	no	—
175	C₂×C₄×C₄₁	—	4	2	no	—
176	C₂×C₄×C₄₁	—	4	2	no	—
177	C₂×C₄×C₄₁	—	4	2	no	—
178	C₂×C₄×C₄₁	—	8	4	no	—
179	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
180	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
181	C₂×C₄×C₄₁	#135	1	4	yes	—
182	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
185	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
187	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
188	C₈×C₄₁	—	2	2	no	—
189	C₈×C₄₁	—	4	2	no	—
190	C₈×C₄₁	#117	1	4	yes	—
191	#22806	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂²×C₄₁	—	4	2	no	—
193	C₂²×C₄₁	—	4	2	no	—
194	C₂²×C₄₁	—	4	2	no	—
195	C₂²×C₄₁	—	8	2	no	—
196	C₂²×C₄₁	—	8	2	no	—
197	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
198	C₂²×C₄₁	#547	1	1	yes	characteristic
199	C₂²×C₄₁	#550	1	1	yes	characteristic
200	C₂²×C₄₁	C₂×#135	1	2	yes	—
201	C₂²×C₄₁	#577	1	2	yes	—
202	C₄×C₄₁	—	2	4	no	—
203	C₄×C₄₁	—	2	2	no	—
204	C₄×C₄₁	—	2	2	no	—
205	C₄×C₄₁	—	4	2	no	—
206	C₄×C₄₁	—	4	2	no	—
207	C₄×C₄₁	—	4	2	no	—
208	C₄×C₄₁	—	4	2	no	—
209	C₄×C₄₁	—	8	2	no	—
210	C₄×C₄₁	—	8	2	no	—
211	C₄×C₄₁	C₂×#117	1	1	yes	characteristic
212	C₄×C₄₁	#520	1	1	yes	characteristic
213	C₄×C₄₁	#555	1	1	yes	characteristic
214	C₄×C₄₁	#556	1	1	yes	characteristic
215	C₂×C₄×SD₁₆	C₂×C₄₁	1	1	yes	characteristic
216	#2357	C₂×C₄₁	1	1	yes	characteristic
217	#2356	C₂×C₄₁	1	1	yes	characteristic, complemented
218	#1968	C₂×C₄₁	1	2	yes	—
219	#1928	C₂×C₄₁	1	2	yes	complemented
220	#1925	C₂×C₄₁	1	2	yes	—
221	#1846	C₂×C₄₁	1	1	yes	characteristic, complemented
222	#1805	C₂×C₄₁	1	1	yes	characteristic, complemented
223	#1804	C₂×C₄₁	1	1	yes	characteristic
224	C₄×#106	C₂×C₄₁	1	2	yes	complemented
225	C₈×C₄⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
226	C₂×C₄₁	—	8	2	no	—
227	C₂×C₄₁	#2354	1	1	yes	characteristic
228	C₂×C₄₁	C₄×#135	1	1	yes	characteristic
229	C₂×C₄₁	#2949	1	1	yes	characteristic
230	C₂×C₄₁	#3337	1	2	yes	—
231	C₂×C₄₁	#3394	1	2	yes	—
232	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
233	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
234	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
235	C₄×SD₁₆	C₄×C₄₁	1	8	yes	complemented
236	C₂×#107	C₂²×C₄₁	1	2	yes	—
237	C₂×#106	C₂²×C₄₁	1	2	yes	—
238	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
239	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
240	C₂×#103	C₂²×C₄₁	1	2	yes	—
241	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
242	C₂×#102	C₂²×C₄₁	1	2	yes	—
243	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
244	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
245	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
246	#391	C₂²×C₄₁	1	2	yes	—
247	#390	C₂²×C₄₁	1	2	yes	—
248	#388	—	2	2	no	—
249	#387	—	2	2	no	—
250	#383	—	2	1	no	—
251	#382	C₂²×C₄₁	1	1	yes	characteristic
252	#382	C₂²×C₄₁	1	1	yes	characteristic
253	#381	—	2	1	no	—
254	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
255	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
256	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
257	C₄×C₂²⋊C₄	—	2	1	no	—
258	#376	—	2	1	no	—
259	#340	C₂²×C₄₁	1	2	yes	—
260	#340	C₂²×C₄₁	1	2	yes	—
261	#336	C₂²×C₄₁	1	2	yes	—
262	C₄₁	#22806	1	1	yes	characteristic, direct product factor, Sylow
263	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
264	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
265	C₂³×C₄	—	2	1	no	—
266	C₂×SD₁₆	—	2	2	no	—
267	C₂×SD₁₆	—	2	2	no	—
268	C₂×SD₁₆	C₂×C₄×C₄₁	1	4	yes	—
269	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
270	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
271	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
272	C₄×Q₈	—	2	2	no	—
273	C₄×Q₈	C₂×C₄×C₄₁	1	4	yes	—
274	C₄×D₄	—	2	2	no	—
275	C₄×D₄	C₂×C₄×C₄₁	1	4	yes	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
278	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
279	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
280	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
282	C₂×C₂²⋊C₄	—	2	1	no	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₄²	—	2	1	no	—
286	C₂×C₄²	—	2	2	no	—
287	C₂×C₄²	—	2	2	no	—
288	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
289	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
290	#107	—	4	2	no	—
291	#106	—	2	4	no	—
292	#106	C₂×C₄×C₄₁	1	4	yes	—
293	C₄⋊C₈	—	2	2	no	—
294	#103	—	4	2	no	—
295	#103	C₂×C₄×C₄₁	1	4	yes	—
296	#102	—	4	2	no	—
297	#102	C₂×C₄×C₄₁	1	4	yes	—
298	C₄×C₈	—	2	4	no	—
299	C₄×C₈	C₂×C₄×C₄₁	1	4	yes	—
300	#95	—	2	1	no	—
301	#95	—	2	2	no	—
302	#95	—	2	1	no	—
303	#95	—	2	2	no	—
304	#95	—	2	2	no	—
305	#95	—	2	1	no	—
306	#95	—	2	1	no	—
307	#95	—	2	2	no	—
308	#95	D₄×C₄₁	1	1	yes	characteristic
309	#95	D₄×C₄₁	1	1	yes	characteristic
310	C₂⁴	—	2	1	no	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	—	2	1	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	8	2	no	—
330	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
331	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
334	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
335	SD₁₆	—	2	8	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
342	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
343	C₂×C₈	#41×C₄₁	1	2	yes	—
344	C₂×C₈	#41×C₄₁	1	2	yes	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	—	2	4	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
354	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
355	C₂²⋊C₄	—	2	4	no	—
356	C₂²⋊C₄	—	4	4	no	—
357	C₂²⋊C₄	—	8	2	no	—
358	C₄²	—	2	4	no	—
359	C₄²	—	2	2	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	4	4	no	—
362	C₄²	—	8	2	no	—
363	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
364	C₄²	#41×C₄₁	1	2	yes	—
365	C₂³	—	2	2	no	—
366	C₂³	—	4	1	no	—
367	C₂³	—	4	1	no	—
368	C₂³	—	4	2	no	—
369	C₂³	—	4	2	no	—
370	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
371	Q₈	—	2	2	no	—
372	Q₈	—	2	2	no	—
373	Q₈	—	4	1	no	—
374	Q₈	—	4	1	no	—
375	D₄	—	2	2	no	—
376	D₄	—	2	2	no	—
377	D₄	—	4	1	no	—
378	D₄	—	4	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	8	4	no	—
400	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
401	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
402	C₂×C₄	#135×C₄₁	1	4	yes	—
403	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
404	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
405	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
406	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
407	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
408	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
409	C₈	—	2	2	no	—
410	C₈	—	4	2	no	—
411	C₈	#117×C₄₁	1	4	yes	—
412	C₂²	—	4	2	no	—
413	C₂²	—	4	2	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	8	2	no	—
417	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
418	C₂²	C₄₁×#547	1	1	yes	characteristic
419	C₂²	C₄₁×#550	1	1	yes	characteristic
420	C₂²	C₂×#135×C₄₁	1	2	yes	—
421	C₂²	C₄₁×#577	1	2	yes	—
422	C₄	—	2	4	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	2	no	—
425	C₄	—	4	2	no	—
426	C₄	—	4	2	no	—
427	C₄	—	4	2	no	—
428	C₄	—	4	2	no	—
429	C₄	—	8	2	no	—
430	C₄	—	8	2	no	—
431	C₄	C₂×#117×C₄₁	1	1	yes	characteristic
432	C₄	C₄₁×#520	1	1	yes	characteristic
433	C₄	C₄₁×#555	1	1	yes	characteristic
434	C₄	C₄₁×#556	1	1	yes	characteristic
435	C₂	—	8	2	no	—
436	C₂	C₄₁×#2354	1	1	yes	characteristic
437	C₂	C₄×#135×C₄₁	1	1	yes	characteristic
438	C₂	C₄₁×#2949	1	1	yes	characteristic
439	C₂	C₄₁×#3337	1	2	yes	—
440	C₂	C₄₁×#3394	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂²×D₄×C₄₁	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₄×C₄⋊C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄₁×#2356	C₂	semidirect
5. C₄₁×#1928	C₂	semidirect
7. C₄₁×#1846	C₂	semidirect
8. C₄₁×#1805	C₂	semidirect
10. C₄×#106×C₄₁	C₂	semidirect
11. C₈×C₄⋊C₄×C₄₁	C₂	semidirect
15. C₄×SD₁₆×C₄₁	C₄	semidirect
191. #22806	C₄₁	direct (N × H)
217. #2356	C₂×C₄₁	semidirect
219. #1928	C₂×C₄₁	semidirect
221. #1846	C₂×C₄₁	semidirect
222. #1805	C₂×C₄₁	semidirect
224. C₄×#106	C₂×C₄₁	semidirect
225. C₈×C₄⋊C₄	C₂×C₄₁	semidirect
235. C₄×SD₁₆	C₄×C₄₁	semidirect
262. C₄₁	#22806	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×C₄×SD₁₆×C₄₁	2
C₄₁×#2357	2
C₄₁×#2356	2
C₄₁×#1968	2
C₄₁×#1928	2
C₄₁×#1925	2
C₄₁×#1846	2
C₄₁×#1805	2
C₄₁×#1804	2
C₄×#106×C₄₁	2
C₈×C₄⋊C₄×C₄₁	2
#22806	41

Subgroups — C41×#22806 #23799007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#22806 #23799007