Subgroups — C₄₁×#24696 #23800897

Order 10496.

796 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#474	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#440	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2567	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2357	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#2071	C₂	1	2	yes	maximal
6	C₄₁×#2055	C₂	1	2	yes	maximal
7	C₄₁×#1993	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1947	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1940	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1928	C₂	1	2	yes	maximal, complemented
11	C₄₁×#1805	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×Q₈×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
16	C₄₁×#474	—	2	4	no	—
17	C₄₁×#440	—	2	4	no	—
18	C₂×#107×C₄₁	C₂²	1	2	yes	—
19	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
22	C₂×#103×C₄₁	C₂²	1	2	yes	—
23	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×#102×C₄₁	C₂²	1	2	yes	—
25	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
27	C₄₁×#395	—	2	1	no	—
28	C₄₁×#395	—	2	1	no	—
29	C₄₁×#391	C₂²	1	2	yes	—
30	C₄₁×#390	C₂²	1	2	yes	—
31	C₄₁×#389	—	2	2	no	—
32	C₄₁×#388	—	2	2	no	—
33	C₄₁×#384	C₂²	1	2	yes	—
34	C₄₁×#382	C₂²	1	1	yes	characteristic
35	C₄₁×#381	—	2	1	no	—
36	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
37	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
39	C₄₁×#340	C₂²	1	2	yes	—
40	C₄₁×#340	C₂²	1	2	yes	—
41	C₄₁×#340	C₂²	1	2	yes	—
42	C₄₁×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₄₁	—	2	1	no	—
44	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₄₁	—	2	1	no	—
47	C₂×SD₁₆×C₄₁	—	2	2	no	—
48	C₂×SD₁₆×C₄₁	—	2	2	no	—
49	C₂×SD₁₆×C₄₁	—	2	2	no	—
50	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
52	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
53	C₄⋊Q₈×C₄₁	—	2	2	no	—
54	C₄⋊Q₈×C₄₁	—	2	2	no	—
55	C₄×Q₈×C₄₁	—	2	2	no	—
56	C₄×Q₈×C₄₁	—	2	2	no	—
57	C₄×D₄×C₄₁	—	2	2	no	—
58	C₄×D₄×C₄₁	D₄	1	4	yes	—
59	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
60	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
64	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
68	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
71	C₂×C₄²×C₄₁	—	2	1	no	—
72	C₂×C₄²×C₄₁	—	2	2	no	—
73	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
74	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
75	#107×C₄₁	—	2	2	no	—
76	#107×C₄₁	—	2	4	no	—
77	C₄⋊C₈×C₄₁	—	2	4	no	—
78	C₄⋊C₈×C₄₁	—	2	2	no	—
79	#103×C₄₁	—	2	4	no	—
80	#103×C₄₁	—	2	2	no	—
81	#102×C₄₁	—	2	2	no	—
82	#102×C₄₁	—	2	4	no	—
83	#97×C₄₁	—	2	2	no	—
84	#95×C₄₁	—	2	1	no	—
85	#95×C₄₁	—	2	2	no	—
86	#95×C₄₁	—	2	1	no	—
87	#95×C₄₁	—	2	2	no	—
88	#95×C₄₁	—	2	2	no	—
89	#95×C₄₁	D₄	1	1	yes	characteristic
90	#95×C₄₁	D₄	1	1	yes	characteristic
91	C₂⁴×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	—	2	1	no	—
96	C₂×Q₈×C₄₁	—	2	1	no	—
97	C₂×Q₈×C₄₁	—	4	2	no	—
98	C₂×Q₈×C₄₁	—	8	2	no	—
99	C₂×Q₈×C₄₁	#41	1	2	yes	—
100	C₂×D₄×C₄₁	—	2	1	no	—
101	C₂×D₄×C₄₁	—	2	1	no	—
102	C₂×D₄×C₄₁	—	2	1	no	—
103	C₂×D₄×C₄₁	—	2	1	no	—
104	C₂×D₄×C₄₁	—	2	1	no	—
105	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₄₁	—	2	1	no	—
107	C₂²×C₄×C₄₁	—	2	1	no	—
108	C₂²×C₄×C₄₁	—	2	4	no	—
109	C₂²×C₄×C₄₁	—	2	2	no	—
110	C₂²×C₄×C₄₁	—	2	2	no	—
111	C₂²×C₄×C₄₁	—	2	1	no	—
112	C₂²×C₄×C₄₁	—	8	2	no	—
113	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
118	SD₁₆×C₄₁	—	2	8	no	—
119	C₂×C₈×C₄₁	—	2	1	no	—
120	C₂×C₈×C₄₁	—	2	1	no	—
121	C₂×C₈×C₄₁	—	2	1	no	—
122	C₂×C₈×C₄₁	—	2	2	no	—
123	C₂×C₈×C₄₁	—	2	2	no	—
124	C₂×C₈×C₄₁	—	2	2	no	—
125	C₂×C₈×C₄₁	—	2	1	no	—
126	C₂×C₈×C₄₁	—	2	1	no	—
127	C₂×C₈×C₄₁	#41	1	2	yes	—
128	C₄⋊C₄×C₄₁	—	2	4	no	—
129	C₄⋊C₄×C₄₁	—	2	1	no	—
130	C₄⋊C₄×C₄₁	—	2	1	no	—
131	C₄⋊C₄×C₄₁	—	2	2	no	—
132	C₄⋊C₄×C₄₁	—	2	2	no	—
133	C₄⋊C₄×C₄₁	—	2	1	no	—
134	C₄⋊C₄×C₄₁	—	2	2	no	—
135	C₄⋊C₄×C₄₁	—	2	2	no	—
136	C₄⋊C₄×C₄₁	—	4	2	no	—
137	C₄⋊C₄×C₄₁	—	4	2	no	—
138	C₄⋊C₄×C₄₁	—	8	2	no	—
139	C₄⋊C₄×C₄₁	—	8	2	no	—
140	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
141	C₂²⋊C₄×C₄₁	—	2	4	no	—
142	C₂²⋊C₄×C₄₁	—	4	4	no	—
143	C₂²⋊C₄×C₄₁	—	8	2	no	—
144	C₄²×C₄₁	—	2	2	no	—
145	C₄²×C₄₁	—	2	2	no	—
146	C₄²×C₄₁	—	4	2	no	—
147	C₄²×C₄₁	—	8	2	no	—
148	C₄²×C₄₁	C₂×D₄	1	2	yes	—
149	C₄²×C₄₁	#41	1	2	yes	—
150	C₂³×C₄₁	—	2	2	no	—
151	C₂³×C₄₁	—	4	1	no	—
152	C₂³×C₄₁	—	4	1	no	—
153	C₂³×C₄₁	—	4	2	no	—
154	C₂³×C₄₁	—	4	2	no	—
155	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
156	Q₈×C₄₁	—	2	2	no	—
157	Q₈×C₄₁	—	2	2	no	—
158	Q₈×C₄₁	—	4	1	no	—
159	Q₈×C₄₁	—	4	1	no	—
160	Q₈×C₄₁	—	8	4	no	—
161	D₄×C₄₁	—	2	2	no	—
162	D₄×C₄₁	—	2	2	no	—
163	D₄×C₄₁	—	4	1	no	—
164	D₄×C₄₁	—	4	1	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	—	2	2	no	—
169	C₂×C₄×C₄₁	—	2	2	no	—
170	C₂×C₄×C₄₁	—	2	2	no	—
171	C₂×C₄×C₄₁	—	2	2	no	—
172	C₂×C₄×C₄₁	—	2	2	no	—
173	C₂×C₄×C₄₁	—	2	2	no	—
174	C₂×C₄×C₄₁	—	4	1	no	—
175	C₂×C₄×C₄₁	—	4	1	no	—
176	C₂×C₄×C₄₁	—	4	2	no	—
177	C₂×C₄×C₄₁	—	4	1	no	—
178	C₂×C₄×C₄₁	—	4	2	no	—
179	C₂×C₄×C₄₁	—	4	2	no	—
180	C₂×C₄×C₄₁	—	4	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	—	8	4	no	—
186	C₂×C₄×C₄₁	#121	1	2	yes	—
187	C₂×C₄×C₄₁	#121	1	2	yes	—
188	C₂×C₄×C₄₁	#137	1	4	yes	—
189	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₄₁	C₂×#41	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	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
195	C₈×C₄₁	—	2	2	no	—
196	C₈×C₄₁	—	4	2	no	—
197	C₈×C₄₁	—	4	1	no	—
198	#24696	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂²×C₄₁	—	4	2	no	—
200	C₂²×C₄₁	—	4	2	no	—
201	C₂²×C₄₁	—	4	2	no	—
202	C₂²×C₄₁	—	8	2	no	—
203	C₂²×C₄₁	—	8	2	no	—
204	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
205	C₂²×C₄₁	#547	1	1	yes	characteristic
206	C₂²×C₄₁	#548	1	1	yes	characteristic
207	C₂²×C₄₁	C₂×#137	1	2	yes	—
208	C₂²×C₄₁	#576	1	2	yes	—
209	C₄×C₄₁	—	2	4	no	—
210	C₄×C₄₁	—	2	2	no	—
211	C₄×C₄₁	—	2	2	no	—
212	C₄×C₄₁	—	4	2	no	—
213	C₄×C₄₁	—	4	2	no	—
214	C₄×C₄₁	—	4	2	no	—
215	C₄×C₄₁	—	8	2	no	—
216	C₄×C₄₁	—	8	1	no	—
217	C₄×C₄₁	—	8	2	no	—
218	C₄×C₄₁	#525	1	1	yes	characteristic
219	C₄×C₄₁	#536	1	1	yes	characteristic
220	C₄×C₄₁	#552	1	1	yes	characteristic
221	C₄×C₄₁	#556	1	1	yes	characteristic
222	C₂×#474	C₂×C₄₁	1	1	yes	characteristic
223	C₂×#440	C₂×C₄₁	1	1	yes	characteristic
224	#2567	C₂×C₄₁	1	1	yes	characteristic, complemented
225	#2357	C₂×C₄₁	1	1	yes	characteristic
226	#2071	C₂×C₄₁	1	2	yes	—
227	#2055	C₂×C₄₁	1	2	yes	—
228	#1993	C₂×C₄₁	1	1	yes	characteristic, complemented
229	#1947	C₂×C₄₁	1	2	yes	complemented
230	#1940	C₂×C₄₁	1	1	yes	characteristic, complemented
231	#1928	C₂×C₄₁	1	2	yes	complemented
232	#1805	C₂×C₄₁	1	1	yes	characteristic, complemented
233	C₂×C₄₁	—	8	2	no	—
234	C₂×C₄₁	#2415	1	1	yes	characteristic
235	C₂×C₄₁	#3039	1	1	yes	characteristic
236	C₂×C₄₁	#3041	1	1	yes	characteristic
237	C₂×C₄₁	#3346	1	2	yes	—
238	C₂×C₄₁	#3375	1	2	yes	—
239	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
240	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
241	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
242	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
243	#474	—	2	4	no	—
244	#440	—	2	4	no	—
245	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
246	C₂×#107	C₂²×C₄₁	1	2	yes	—
247	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
248	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
249	C₂×#103	C₂²×C₄₁	1	2	yes	—
250	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
251	C₂×#102	C₂²×C₄₁	1	2	yes	—
252	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
253	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
254	#395	—	2	1	no	—
255	#395	—	2	1	no	—
256	#391	C₂²×C₄₁	1	2	yes	—
257	#390	C₂²×C₄₁	1	2	yes	—
258	#389	—	2	2	no	—
259	#388	—	2	2	no	—
260	#384	C₂²×C₄₁	1	2	yes	—
261	#382	C₂²×C₄₁	1	1	yes	characteristic
262	#381	—	2	1	no	—
263	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
264	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
265	C₄×C₂²⋊C₄	—	2	1	no	—
266	#340	C₂²×C₄₁	1	2	yes	—
267	#340	C₂²×C₄₁	1	2	yes	—
268	#340	C₂²×C₄₁	1	2	yes	—
269	#336	C₂²×C₄₁	1	2	yes	—
270	C₄₁	#24696	1	1	yes	characteristic, direct product factor, Sylow
271	C₂²×Q₈	—	2	1	no	—
272	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
273	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
274	C₂³×C₄	—	2	1	no	—
275	C₂×SD₁₆	—	2	2	no	—
276	C₂×SD₁₆	—	2	2	no	—
277	C₂×SD₁₆	—	2	2	no	—
278	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
279	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
280	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
281	C₄⋊Q₈	—	2	2	no	—
282	C₄⋊Q₈	—	2	2	no	—
283	C₄×Q₈	—	2	2	no	—
284	C₄×Q₈	—	2	2	no	—
285	C₄×D₄	—	2	2	no	—
286	C₄×D₄	D₄×C₄₁	1	4	yes	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
294	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
295	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
296	C₂×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	—	2	2	no	—
301	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
302	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
303	#107	—	2	2	no	—
304	#107	—	2	4	no	—
305	C₄⋊C₈	—	2	4	no	—
306	C₄⋊C₈	—	2	2	no	—
307	#103	—	2	4	no	—
308	#103	—	2	2	no	—
309	#102	—	2	2	no	—
310	#102	—	2	4	no	—
311	#97	—	2	2	no	—
312	#95	—	2	1	no	—
313	#95	—	2	2	no	—
314	#95	—	2	1	no	—
315	#95	—	2	2	no	—
316	#95	—	2	2	no	—
317	#95	D₄×C₄₁	1	1	yes	characteristic
318	#95	D₄×C₄₁	1	1	yes	characteristic
319	C₂⁴	—	2	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	4	2	no	—
326	C₂×Q₈	—	8	2	no	—
327	C₂×Q₈	#41×C₄₁	1	2	yes	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	8	2	no	—
341	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
342	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
344	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
345	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
346	SD₁₆	—	2	8	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	#41×C₄₁	1	2	yes	—
356	C₄⋊C₄	—	2	4	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	4	2	no	—
365	C₄⋊C₄	—	4	2	no	—
366	C₄⋊C₄	—	8	2	no	—
367	C₄⋊C₄	—	8	2	no	—
368	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
369	C₂²⋊C₄	—	2	4	no	—
370	C₂²⋊C₄	—	4	4	no	—
371	C₂²⋊C₄	—	8	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	4	2	no	—
375	C₄²	—	8	2	no	—
376	C₄²	C₂×D₄×C₄₁	1	2	yes	—
377	C₄²	#41×C₄₁	1	2	yes	—
378	C₂³	—	2	2	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	4	1	no	—
381	C₂³	—	4	2	no	—
382	C₂³	—	4	2	no	—
383	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
384	Q₈	—	2	2	no	—
385	Q₈	—	2	2	no	—
386	Q₈	—	4	1	no	—
387	Q₈	—	4	1	no	—
388	Q₈	—	8	4	no	—
389	D₄	—	2	2	no	—
390	D₄	—	2	2	no	—
391	D₄	—	4	1	no	—
392	D₄	—	4	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	8	4	no	—
414	C₂×C₄	#121×C₄₁	1	2	yes	—
415	C₂×C₄	#121×C₄₁	1	2	yes	—
416	C₂×C₄	#137×C₄₁	1	4	yes	—
417	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
418	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
419	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
420	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
421	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
422	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
423	C₈	—	2	2	no	—
424	C₈	—	4	2	no	—
425	C₈	—	4	1	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	8	2	no	—
430	C₂²	—	8	2	no	—
431	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
432	C₂²	C₄₁×#547	1	1	yes	characteristic
433	C₂²	C₄₁×#548	1	1	yes	characteristic
434	C₂²	C₂×#137×C₄₁	1	2	yes	—
435	C₂²	C₄₁×#576	1	2	yes	—
436	C₄	—	2	2	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	4	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	2	no	—
442	C₄	—	8	2	no	—
443	C₄	—	8	1	no	—
444	C₄	—	8	2	no	—
445	C₄	C₄₁×#525	1	1	yes	characteristic
446	C₄	C₄₁×#536	1	1	yes	characteristic
447	C₄	C₄₁×#552	1	1	yes	characteristic
448	C₄	C₄₁×#556	1	1	yes	characteristic
449	C₂	—	8	2	no	—
450	C₂	C₄₁×#2415	1	1	yes	characteristic
451	C₂	C₄₁×#3039	1	1	yes	characteristic
452	C₂	C₄₁×#3041	1	1	yes	characteristic
453	C₂	C₄₁×#3346	1	2	yes	—
454	C₂	C₄₁×#3375	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂²×D₄×C₄₁	C₂³
LCS	G ▷ C₂²×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×#2567	C₂	semidirect
7. C₄₁×#1993	C₂	semidirect
8. C₄₁×#1947	C₂	semidirect
9. C₄₁×#1940	C₂	semidirect
10. C₄₁×#1928	C₂	semidirect
11. C₄₁×#1805	C₂	semidirect
198. #24696	C₄₁	direct (N × H)
224. #2567	C₂×C₄₁	semidirect
228. #1993	C₂×C₄₁	semidirect
229. #1947	C₂×C₄₁	semidirect
230. #1940	C₂×C₄₁	semidirect
231. #1928	C₂×C₄₁	semidirect
232. #1805	C₂×C₄₁	semidirect
270. C₄₁	#24696	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×#474	2
C₂×C₄₁×#440	2
C₄₁×#2567	2
C₄₁×#2357	2
C₄₁×#2071	2
C₄₁×#2055	2
C₄₁×#1993	2
C₄₁×#1947	2
C₄₁×#1940	2
C₄₁×#1928	2
C₄₁×#1805	2
#24696	41

Subgroups — C41×#24696 #23800897

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#24696 #23800897