Subgroups — C₄₁×#21384 #23797585

Order 10496.

1094 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3455	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2873	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#2298	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1986	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1980	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1871	C₂	1	4	yes	maximal, complemented
7	C₄₁×#1759	C₂	1	2	yes	maximal, complemented
8	C₄×#104×C₄₁	C₂	1	2	yes	maximal, complemented
9	C₂²×M₁₆×C₄₁	C₂²	1	2	yes	—
10	C₄₁×#542	C₄	1	4	yes	complemented
11	C₄₁×#541	C₄	1	2	yes	complemented
12	C₄₁×#540	C₄	1	2	yes	complemented
13	C₄₁×#539	—	2	2	no	—
14	C₄₁×#538	—	2	2	no	—
15	C₄₁×#533	C₂²	1	1	yes	characteristic
16	C₄₁×#532	C₂²	1	1	yes	characteristic
17	C₄₁×#529	—	2	4	no	—
18	C₄₁×#525	C₂²	1	2	yes	—
19	C₄×#41×C₄₁	C₂²	1	2	yes	—
20	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×#104×C₄₁	C₂²	1	4	yes	—
22	C₂×#104×C₄₁	C₂²	1	4	yes	—
23	C₄₁×#405	—	2	4	no	—
24	C₄×M₁₆×C₄₁	C₂²	1	2	yes	—
25	C₄×M₁₆×C₄₁	C₂²	1	2	yes	—
26	C₄₁×#388	—	2	2	no	—
27	C₄₁×#387	—	2	2	no	—
28	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
29	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
30	C₄₁×#376	C₂²	1	1	yes	characteristic
31	C₄³×C₄₁	C₂²	1	1	yes	characteristic
32	C₄₁×#339	C₂²	1	4	yes	—
33	C₄₁×#339	C₂²	1	4	yes	—
34	C₂×#41×C₄₁	C₂³	1	2	yes	—
35	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
36	C₂×M₁₆×C₄₁	—	2	2	no	—
37	C₂×M₁₆×C₄₁	—	2	8	no	—
38	C₂×M₁₆×C₄₁	C₂³	1	4	yes	—
39	C₂²×C₈×C₄₁	—	2	2	no	—
40	C₄⋊Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
41	C₄⋊Q₈×C₄₁	C₂×C₄	1	2	yes	—
42	#127×C₄₁	C₂×C₄	1	1	yes	characteristic
43	#126×C₄₁	—	2	4	no	—
44	#126×C₄₁	—	2	4	no	—
45	#125×C₄₁	—	2	4	no	—
46	#125×C₄₁	C₂×C₄	1	2	yes	—
47	#124×C₄₁	—	2	4	no	—
48	#124×C₄₁	C₂×C₄	1	2	yes	—
49	#123×C₄₁	—	2	2	no	—
50	#123×C₄₁	—	2	4	no	—
51	#123×C₄₁	—	2	4	no	—
52	C₂²⋊Q₈×C₄₁	—	2	2	no	—
53	C₂²⋊Q₈×C₄₁	—	2	4	no	—
54	C₂²⋊Q₈×C₄₁	C₂×C₄	1	4	yes	—
55	#121×C₄₁	—	2	2	no	—
56	#121×C₄₁	—	2	4	no	—
57	#121×C₄₁	C₂×C₄	1	4	yes	—
58	#120×C₄₁	—	2	2	no	—
59	C₄×Q₈×C₄₁	—	2	2	no	—
60	C₄×Q₈×C₄₁	C₂×C₄	1	4	yes	—
61	C₄×D₄×C₄₁	—	2	4	no	—
62	C₄×D₄×C₄₁	—	2	4	no	—
63	C₄×D₄×C₄₁	—	2	2	no	—
64	C₄×D₄×C₄₁	C₂×C₄	1	4	yes	—
65	#117×C₄₁	—	2	2	no	—
66	#117×C₄₁	C₂×C₄	1	2	yes	—
67	#117×C₄₁	C₂×C₄	1	2	yes	—
68	#117×C₄₁	D₄	1	4	yes	—
69	#117×C₄₁	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
71	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
72	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
74	C₂×C₄²×C₄₁	—	2	2	no	—
75	C₂×C₄²×C₄₁	—	2	2	no	—
76	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
77	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
78	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
80	#104×C₄₁	—	2	8	no	—
81	#104×C₄₁	—	2	8	no	—
82	#97×C₄₁	—	2	2	no	—
83	#97×C₄₁	—	2	2	no	—
84	C₄×C₈×C₄₁	—	2	2	no	—
85	C₄×C₈×C₄₁	—	2	2	no	—
86	#95×C₄₁	—	2	2	no	—
87	#95×C₄₁	—	2	2	no	—
88	#95×C₄₁	—	2	2	no	—
89	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
90	#41×C₄₁	—	2	4	no	—
91	#41×C₄₁	—	2	4	no	—
92	C₂×Q₈×C₄₁	—	2	2	no	—
93	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
94	C₂×D₄×C₄₁	—	2	2	no	—
95	C₂×D₄×C₄₁	—	2	4	no	—
96	C₂×D₄×C₄₁	—	2	2	no	—
97	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₄₁	—	2	4	no	—
99	C₂²×C₄×C₄₁	—	2	2	no	—
100	C₂²×C₄×C₄₁	—	2	2	no	—
101	C₂²×C₄×C₄₁	—	2	4	no	—
102	C₂²×C₄×C₄₁	—	2	2	no	—
103	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
109	M₁₆×C₄₁	—	2	8	no	—
110	M₁₆×C₄₁	—	2	4	no	—
111	M₁₆×C₄₁	#41	1	8	yes	—
112	C₂×C₈×C₄₁	—	2	8	no	—
113	C₂×C₈×C₄₁	—	2	4	no	—
114	C₄⋊C₄×C₄₁	—	2	4	no	—
115	C₄⋊C₄×C₄₁	—	2	2	no	—
116	C₄⋊C₄×C₄₁	—	2	4	no	—
117	C₄⋊C₄×C₄₁	—	2	4	no	—
118	C₄⋊C₄×C₄₁	—	2	2	no	—
119	C₄⋊C₄×C₄₁	—	4	4	no	—
120	C₄⋊C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
121	C₄⋊C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
122	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
123	C₂²⋊C₄×C₄₁	—	2	4	no	—
124	C₂²⋊C₄×C₄₁	—	2	2	no	—
125	C₂²⋊C₄×C₄₁	—	2	4	no	—
126	C₂²⋊C₄×C₄₁	—	2	4	no	—
127	C₂²⋊C₄×C₄₁	—	2	4	no	—
128	C₂²⋊C₄×C₄₁	—	4	4	no	—
129	C₂²⋊C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
130	C₂²⋊C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
131	C₄²×C₄₁	—	2	4	no	—
132	C₄²×C₄₁	—	2	2	no	—
133	C₄²×C₄₁	—	2	4	no	—
134	C₄²×C₄₁	—	2	4	no	—
135	C₄²×C₄₁	—	4	4	no	—
136	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
137	C₄²×C₄₁	C₂²×C₄	1	1	yes	characteristic
138	C₄²×C₄₁	C₂²×C₄	1	1	yes	characteristic
139	C₄²×C₄₁	C₂×D₄	1	2	yes	—
140	C₄²×C₄₁	C₂×D₄	1	2	yes	—
141	C₂³×C₄₁	—	2	2	no	—
142	C₂³×C₄₁	—	2	2	no	—
143	C₂³×C₄₁	—	4	2	no	—
144	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
145	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
146	Q₈×C₄₁	—	2	2	no	—
147	Q₈×C₄₁	—	2	2	no	—
148	Q₈×C₄₁	—	8	2	no	—
149	D₄×C₄₁	—	2	2	no	—
150	D₄×C₄₁	—	2	2	no	—
151	D₄×C₄₁	—	4	4	no	—
152	D₄×C₄₁	—	8	2	no	—
153	D₄×C₄₁	—	8	4	no	—
154	C₂×C₄×C₄₁	—	2	2	no	—
155	C₂×C₄×C₄₁	—	2	4	no	—
156	C₂×C₄×C₄₁	—	2	2	no	—
157	C₂×C₄×C₄₁	—	2	2	no	—
158	C₂×C₄×C₄₁	—	2	4	no	—
159	C₂×C₄×C₄₁	—	2	2	no	—
160	C₂×C₄×C₄₁	—	2	4	no	—
161	C₂×C₄×C₄₁	—	4	2	no	—
162	C₂×C₄×C₄₁	—	4	2	no	—
163	C₂×C₄×C₄₁	—	4	2	no	—
164	C₂×C₄×C₄₁	—	4	2	no	—
165	C₂×C₄×C₄₁	—	4	4	no	—
166	C₂×C₄×C₄₁	—	4	2	no	—
167	C₂×C₄×C₄₁	—	4	2	no	—
168	C₂×C₄×C₄₁	—	4	2	no	—
169	C₂×C₄×C₄₁	—	8	4	no	—
170	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
171	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
172	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
173	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
174	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
177	C₈×C₄₁	—	2	8	no	—
178	#21384	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂²×C₄₁	—	2	2	no	—
180	C₂²×C₄₁	—	2	4	no	—
181	C₂²×C₄₁	—	2	2	no	—
182	C₂²×C₄₁	—	4	4	no	—
183	C₂²×C₄₁	—	4	2	no	—
184	C₂²×C₄₁	—	8	2	no	—
185	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
186	C₂²×C₄₁	#532	1	2	yes	—
187	C₄×C₄₁	—	2	4	no	—
188	C₄×C₄₁	—	2	2	no	—
189	C₄×C₄₁	—	2	2	no	—
190	C₄×C₄₁	—	2	2	no	—
191	C₄×C₄₁	—	4	4	no	—
192	C₄×C₄₁	—	4	4	no	—
193	C₄×C₄₁	—	4	2	no	—
194	C₄×C₄₁	—	8	2	no	—
195	C₄×C₄₁	C₄×#41	1	2	yes	—
196	C₄×C₄₁	#525	1	2	yes	—
197	#3455	C₂×C₄₁	1	1	yes	characteristic
198	#2873	C₂×C₄₁	1	1	yes	characteristic, complemented
199	#2298	C₂×C₄₁	1	1	yes	characteristic, complemented
200	#1986	C₂×C₄₁	1	2	yes	complemented
201	#1980	C₂×C₄₁	1	2	yes	complemented
202	#1871	C₂×C₄₁	1	4	yes	complemented
203	#1759	C₂×C₄₁	1	2	yes	complemented
204	C₄×#104	C₂×C₄₁	1	2	yes	complemented
205	C₂×C₄₁	—	2	2	no	—
206	C₂×C₄₁	—	4	2	no	—
207	C₂×C₄₁	—	8	2	no	—
208	C₂×C₄₁	#2297	1	1	yes	characteristic
209	C₂×C₄₁	#2901	1	2	yes	—
210	C₂²×M₁₆	C₂²×C₄₁	1	2	yes	—
211	#542	C₄×C₄₁	1	4	yes	complemented
212	#541	C₄×C₄₁	1	2	yes	complemented
213	#540	C₄×C₄₁	1	2	yes	complemented
214	#539	—	2	2	no	—
215	#538	—	2	2	no	—
216	#533	C₂²×C₄₁	1	1	yes	characteristic
217	#532	C₂²×C₄₁	1	1	yes	characteristic
218	#529	—	2	4	no	—
219	#525	C₂²×C₄₁	1	2	yes	—
220	C₄×#41	C₂²×C₄₁	1	2	yes	—
221	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
222	C₂×#104	C₂²×C₄₁	1	4	yes	—
223	C₂×#104	C₂²×C₄₁	1	4	yes	—
224	#405	—	2	4	no	—
225	C₄×M₁₆	C₂²×C₄₁	1	2	yes	—
226	C₄×M₁₆	C₂²×C₄₁	1	2	yes	—
227	#388	—	2	2	no	—
228	#387	—	2	2	no	—
229	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
230	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
231	#376	C₂²×C₄₁	1	1	yes	characteristic
232	C₄³	C₂²×C₄₁	1	1	yes	characteristic
233	#339	C₂²×C₄₁	1	4	yes	—
234	#339	C₂²×C₄₁	1	4	yes	—
235	C₄₁	#21384	1	1	yes	characteristic, direct product factor, Sylow
236	C₂×#41	C₂³×C₄₁	1	2	yes	—
237	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
238	C₂×M₁₆	—	2	2	no	—
239	C₂×M₁₆	—	2	8	no	—
240	C₂×M₁₆	C₂³×C₄₁	1	4	yes	—
241	C₂²×C₈	—	2	2	no	—
242	C₄⋊Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
243	C₄⋊Q₈	C₂×C₄×C₄₁	1	2	yes	—
244	#127	C₂×C₄×C₄₁	1	1	yes	characteristic
245	#126	—	2	4	no	—
246	#126	—	2	4	no	—
247	#125	—	2	4	no	—
248	#125	C₂×C₄×C₄₁	1	2	yes	—
249	#124	—	2	4	no	—
250	#124	C₂×C₄×C₄₁	1	2	yes	—
251	#123	—	2	2	no	—
252	#123	—	2	4	no	—
253	#123	—	2	4	no	—
254	C₂²⋊Q₈	—	2	2	no	—
255	C₂²⋊Q₈	—	2	4	no	—
256	C₂²⋊Q₈	C₂×C₄×C₄₁	1	4	yes	—
257	#121	—	2	2	no	—
258	#121	—	2	4	no	—
259	#121	C₂×C₄×C₄₁	1	4	yes	—
260	#120	—	2	2	no	—
261	C₄×Q₈	—	2	2	no	—
262	C₄×Q₈	C₂×C₄×C₄₁	1	4	yes	—
263	C₄×D₄	—	2	4	no	—
264	C₄×D₄	—	2	4	no	—
265	C₄×D₄	—	2	2	no	—
266	C₄×D₄	C₂×C₄×C₄₁	1	4	yes	—
267	#117	—	2	2	no	—
268	#117	C₂×C₄×C₄₁	1	2	yes	—
269	#117	C₂×C₄×C₄₁	1	2	yes	—
270	#117	D₄×C₄₁	1	4	yes	—
271	#117	C₂³×C₄₁	1	2	yes	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
276	C₂×C₄²	—	2	2	no	—
277	C₂×C₄²	—	2	2	no	—
278	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
279	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
280	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
281	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
282	#104	—	2	8	no	—
283	#104	—	2	8	no	—
284	#97	—	2	2	no	—
285	#97	—	2	2	no	—
286	C₄×C₈	—	2	2	no	—
287	C₄×C₈	—	2	2	no	—
288	#95	—	2	2	no	—
289	#95	—	2	2	no	—
290	#95	—	2	2	no	—
291	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
292	#41	—	2	4	no	—
293	#41	—	2	4	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
306	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
308	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
309	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
310	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
311	M₁₆	—	2	8	no	—
312	M₁₆	—	2	4	no	—
313	M₁₆	#41×C₄₁	1	8	yes	—
314	C₂×C₈	—	2	8	no	—
315	C₂×C₈	—	2	4	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	4	4	no	—
322	C₄⋊C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
323	C₄⋊C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
324	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
325	C₂²⋊C₄	—	2	4	no	—
326	C₂²⋊C₄	—	2	2	no	—
327	C₂²⋊C₄	—	2	4	no	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₂²⋊C₄	—	2	4	no	—
330	C₂²⋊C₄	—	4	4	no	—
331	C₂²⋊C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
332	C₂²⋊C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
333	C₄²	—	2	4	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	2	4	no	—
336	C₄²	—	2	4	no	—
337	C₄²	—	4	4	no	—
338	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
339	C₄²	C₂²×C₄×C₄₁	1	1	yes	characteristic
340	C₄²	C₂²×C₄×C₄₁	1	1	yes	characteristic
341	C₄²	C₂×D₄×C₄₁	1	2	yes	—
342	C₄²	C₂×D₄×C₄₁	1	2	yes	—
343	C₂³	—	2	2	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
347	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
348	Q₈	—	2	2	no	—
349	Q₈	—	2	2	no	—
350	Q₈	—	8	2	no	—
351	D₄	—	2	2	no	—
352	D₄	—	2	2	no	—
353	D₄	—	4	4	no	—
354	D₄	—	8	2	no	—
355	D₄	—	8	4	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	8	4	no	—
372	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
373	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
374	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
375	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
376	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
377	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
378	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
379	C₈	—	2	8	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	4	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	8	2	no	—
386	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
387	C₂²	C₄₁×#532	1	2	yes	—
388	C₄	—	2	2	no	—
389	C₄	—	2	4	no	—
390	C₄	—	2	2	no	—
391	C₄	—	2	2	no	—
392	C₄	—	4	4	no	—
393	C₄	—	4	2	no	—
394	C₄	—	4	4	no	—
395	C₄	—	8	2	no	—
396	C₄	C₄×#41×C₄₁	1	2	yes	—
397	C₄	C₄₁×#525	1	2	yes	—
398	C₂	—	2	2	no	—
399	C₂	—	4	2	no	—
400	C₂	—	8	2	no	—
401	C₂	C₄₁×#2297	1	1	yes	characteristic
402	C₂	C₄₁×#2901	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
socle	C₂²×C₄₁	C₂²×C₂²⋊C₄
prime radical	C₄₁×#3455	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁ ◁ C₂×#117×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#2873	C₂	semidirect
3. C₄₁×#2298	C₂	semidirect
4. C₄₁×#1986	C₂	semidirect
5. C₄₁×#1980	C₂	semidirect
6. C₄₁×#1871	C₂	semidirect
7. C₄₁×#1759	C₂	semidirect
8. C₄×#104×C₄₁	C₂	semidirect
10. C₄₁×#542	C₄	semidirect
11. C₄₁×#541	C₄	semidirect
12. C₄₁×#540	C₄	semidirect
178. #21384	C₄₁	direct (N × H)
198. #2873	C₂×C₄₁	semidirect
199. #2298	C₂×C₄₁	semidirect
200. #1986	C₂×C₄₁	semidirect
201. #1980	C₂×C₄₁	semidirect
202. #1871	C₂×C₄₁	semidirect
203. #1759	C₂×C₄₁	semidirect
204. C₄×#104	C₂×C₄₁	semidirect
211. #542	C₄×C₄₁	semidirect
212. #541	C₄×C₄₁	semidirect
213. #540	C₄×C₄₁	semidirect
235. C₄₁	#21384	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄₁×#3455	2
C₄₁×#2873	2
C₄₁×#2298	2
C₄₁×#1986	2
C₄₁×#1980	2
C₄₁×#1871	2
C₄₁×#1759	2
C₄×#104×C₄₁	2
#21384	41

Subgroups — C41×#21384 #23797585

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#21384 #23797585