Subgroups — C₄₁×#11073 #23787274

Order 10496.

1026 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#2905	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#418	C₂	1	2	yes	maximal
3	C₄₁×#2309	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#1740	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₁×H(3,ℤ/4)	C₂	1	2	yes	maximal, complemented
6	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₄₁	C₂²	1	2	yes	—
8	C₂×#117×C₄₁	C₂²	1	2	yes	—
9	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
10	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
11	C₄₁×#424	—	2	4	no	—
12	C₄₁×#423	—	2	2	no	—
13	C₄₁×#418	—	2	4	no	—
14	C₄₁×#418	—	2	4	no	—
15	C₂×#102×C₄₁	—	2	4	no	—
16	C₄₁×#390	—	2	2	no	—
17	C₄₁×#390	C₄	1	4	yes	complemented
18	C₄₁×#379	—	2	2	no	—
19	C₄₁×#342	—	2	2	no	—
20	C₄₁×H(3,ℤ/4)	—	2	4	no	—
21	C₂⁵×C₄₁	—	2	1	no	—
22	C₂²×D₄×C₄₁	—	2	2	no	—
23	C₂²×D₄×C₄₁	—	2	2	no	—
24	C₂²×D₄×C₄₁	—	2	1	no	—
25	C₂²×D₄×C₄₁	—	2	2	no	—
26	C₂²×D₄×C₄₁	—	2	2	no	—
27	C₂²×D₄×C₄₁	—	2	1	no	—
28	C₂²×D₄×C₄₁	—	2	1	no	—
29	C₂²×D₄×C₄₁	C₂×C₄	1	2	yes	—
30	C₂²×D₄×C₄₁	D₄	1	2	yes	—
31	C₂²×D₄×C₄₁	Q₈	1	2	yes	—
32	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
33	C₂×M₁₆×C₄₁	—	2	2	no	—
34	C₂×M₁₆×C₄₁	—	2	2	no	—
35	C₂×M₁₆×C₄₁	—	2	2	no	—
36	C₂×M₁₆×C₄₁	—	2	2	no	—
37	C₂×M₁₆×C₄₁	—	2	2	no	—
38	C₂×M₁₆×C₄₁	—	2	2	no	—
39	C₂²×C₈×C₄₁	D₄	1	4	yes	—
40	#117×C₄₁	—	2	2	no	—
41	#117×C₄₁	—	2	2	no	—
42	#117×C₄₁	—	2	2	no	—
43	#117×C₄₁	—	2	2	no	—
44	#117×C₄₁	—	2	2	no	—
45	#117×C₄₁	—	2	2	no	—
46	#117×C₄₁	—	2	2	no	—
47	#117×C₄₁	D₄	1	4	yes	—
48	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
49	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
50	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
51	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
52	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
53	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
54	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
55	C₂×C₄²×C₄₁	—	2	2	no	—
56	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₄₁	D₄	1	2	yes	—
58	C₄⋊C₈×C₄₁	—	2	8	no	—
59	#102×C₄₁	—	2	16	no	—
60	C₂⁴×C₄₁	—	2	2	no	—
61	C₂⁴×C₄₁	—	2	2	no	—
62	C₂⁴×C₄₁	—	2	2	no	—
63	C₂⁴×C₄₁	—	4	2	no	—
64	C₂⁴×C₄₁	—	4	2	no	—
65	C₂⁴×C₄₁	—	8	4	no	—
66	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
67	C₂×D₄×C₄₁	—	2	2	no	—
68	C₂×D₄×C₄₁	—	2	4	no	—
69	C₂×D₄×C₄₁	—	2	4	no	—
70	C₂×D₄×C₄₁	—	2	4	no	—
71	C₂×D₄×C₄₁	—	2	2	no	—
72	C₂×D₄×C₄₁	—	2	4	no	—
73	C₂×D₄×C₄₁	—	2	4	no	—
74	C₂×D₄×C₄₁	—	2	2	no	—
75	C₂×D₄×C₄₁	—	2	4	no	—
76	C₂×D₄×C₄₁	—	4	1	no	—
77	C₂×D₄×C₄₁	—	4	2	no	—
78	C₂×D₄×C₄₁	—	4	2	no	—
79	C₂×D₄×C₄₁	—	4	1	no	—
80	C₂×D₄×C₄₁	—	4	2	no	—
81	C₂×D₄×C₄₁	—	4	1	no	—
82	C₂×D₄×C₄₁	—	4	2	no	—
83	C₂×D₄×C₄₁	—	4	1	no	—
84	C₂×D₄×C₄₁	C₄⋊C₄	1	4	yes	—
85	C₂²×C₄×C₄₁	—	2	2	no	—
86	C₂²×C₄×C₄₁	—	4	2	no	—
87	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
88	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₁	C₂×Q₈	1	1	yes	characteristic
94	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
95	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
96	C₂²×C₄×C₄₁	#41	1	2	yes	—
97	C₂²×C₄×C₄₁	#41	1	2	yes	—
98	M₁₆×C₄₁	—	4	2	no	—
99	M₁₆×C₄₁	—	4	2	no	—
100	M₁₆×C₄₁	—	4	2	no	—
101	M₁₆×C₄₁	—	4	2	no	—
102	C₂×C₈×C₄₁	—	2	4	no	—
103	C₂×C₈×C₄₁	—	2	4	no	—
104	C₂×C₈×C₄₁	—	2	4	no	—
105	C₄⋊C₄×C₄₁	—	2	4	no	—
106	C₄⋊C₄×C₄₁	—	2	4	no	—
107	C₄⋊C₄×C₄₁	—	4	1	no	—
108	C₄⋊C₄×C₄₁	—	4	2	no	—
109	C₄⋊C₄×C₄₁	—	4	1	no	—
110	C₂²⋊C₄×C₄₁	—	2	4	no	—
111	C₂²⋊C₄×C₄₁	—	2	4	no	—
112	C₂²⋊C₄×C₄₁	—	4	2	no	—
113	C₂²⋊C₄×C₄₁	—	4	2	no	—
114	C₂²⋊C₄×C₄₁	—	8	8	no	—
115	C₄²×C₄₁	—	2	2	no	—
116	C₄²×C₄₁	—	2	2	no	—
117	C₄²×C₄₁	—	2	4	no	—
118	C₄²×C₄₁	—	2	4	no	—
119	C₄²×C₄₁	—	4	2	no	—
120	C₂³×C₄₁	—	2	4	no	—
121	C₂³×C₄₁	—	4	2	no	—
122	C₂³×C₄₁	—	4	8	no	—
123	C₂³×C₄₁	—	4	2	no	—
124	C₂³×C₄₁	—	4	2	no	—
125	C₂³×C₄₁	—	4	4	no	—
126	C₂³×C₄₁	—	4	4	no	—
127	C₂³×C₄₁	—	8	8	no	—
128	C₂³×C₄₁	—	8	4	no	—
129	C₂³×C₄₁	—	8	4	no	—
130	C₂³×C₄₁	—	8	8	no	—
131	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	C₂³×C₄₁	#121	1	2	yes	—
133	C₂³×C₄₁	#121	1	1	yes	characteristic
134	C₂³×C₄₁	#121	1	2	yes	—
135	C₂³×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
136	D₄×C₄₁	—	2	8	no	—
137	D₄×C₄₁	—	4	4	no	—
138	D₄×C₄₁	—	4	2	no	—
139	D₄×C₄₁	—	4	2	no	—
140	D₄×C₄₁	—	4	2	no	—
141	D₄×C₄₁	—	4	2	no	—
142	C₂×C₄×C₄₁	—	2	4	no	—
143	C₂×C₄×C₄₁	—	4	4	no	—
144	C₂×C₄×C₄₁	—	4	4	no	—
145	C₂×C₄×C₄₁	—	4	2	no	—
146	C₂×C₄×C₄₁	—	4	4	no	—
147	C₂×C₄×C₄₁	—	8	4	no	—
148	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₄₁	#117	1	1	yes	characteristic
150	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
151	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
152	C₂×C₄×C₄₁	#120	1	2	yes	—
153	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
154	C₂×C₄×C₄₁	#121	1	2	yes	—
155	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
156	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
157	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
158	C₂×C₄×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
159	C₂×C₄×C₄₁	#123	1	2	yes	—
160	C₂×C₄×C₄₁	#123	1	2	yes	—
161	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
162	C₂×C₄×C₄₁	#124	1	2	yes	—
163	C₂×C₄×C₄₁	#124	1	1	yes	characteristic
164	C₂×C₄×C₄₁	#126	1	2	yes	—
165	C₂×C₄×C₄₁	#127	1	1	yes	characteristic
166	C₈×C₄₁	—	4	4	no	—
167	#11073	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂²×C₄₁	—	2	2	no	—
169	C₂²×C₄₁	—	2	4	no	—
170	C₂²×C₄₁	—	4	2	no	—
171	C₂²×C₄₁	—	4	1	no	—
172	C₂²×C₄₁	—	4	1	no	—
173	C₂²×C₄₁	—	4	8	no	—
174	C₂²×C₄₁	—	4	4	no	—
175	C₂²×C₄₁	—	8	4	no	—
176	C₂²×C₄₁	—	8	8	no	—
177	C₂²×C₄₁	—	8	8	no	—
178	C₂²×C₄₁	—	8	4	no	—
179	C₂²×C₄₁	#380	1	1	yes	characteristic
180	C₂²×C₄₁	#386	1	1	yes	characteristic
181	C₂²×C₄₁	#390	1	1	yes	characteristic
182	C₂²×C₄₁	#394	1	2	yes	—
183	C₂²×C₄₁	#396	1	2	yes	—
184	C₄×C₄₁	—	4	4	no	—
185	C₄×C₄₁	—	8	2	no	—
186	C₄×C₄₁	—	8	4	no	—
187	C₄×C₄₁	#385	1	2	yes	—
188	C₄×C₄₁	#388	1	2	yes	—
189	C₄×C₄₁	#392	1	1	yes	characteristic
190	C₄×C₄₁	#393	1	1	yes	characteristic
191	C₄×C₄₁	#397	1	1	yes	characteristic
192	C₄×C₄₁	#399	1	1	yes	characteristic
193	#2905	C₂×C₄₁	1	1	yes	characteristic, complemented
194	C₂×#418	C₂×C₄₁	1	2	yes	—
195	#2309	C₂×C₄₁	1	1	yes	characteristic
196	#1740	C₂×C₄₁	1	1	yes	characteristic, complemented
197	C₂×H(3,ℤ/4)	C₂×C₄₁	1	2	yes	complemented
198	C₂×C₄₁	—	2	1	no	—
199	C₂×C₄₁	—	2	2	no	—
200	C₂×C₄₁	—	2	1	no	—
201	C₂×C₄₁	—	2	2	no	—
202	C₂×C₄₁	—	8	4	no	—
203	C₂×C₄₁	#1439	1	1	yes	characteristic
204	C₂×C₄₁	#1910	1	2	yes	—
205	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
206	C₂²×M₁₆	C₂²×C₄₁	1	2	yes	—
207	C₂×#117	C₂²×C₄₁	1	2	yes	—
208	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
209	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
210	#424	—	2	4	no	—
211	#423	—	2	2	no	—
212	#418	—	2	4	no	—
213	#418	—	2	4	no	—
214	C₂×#102	—	2	4	no	—
215	#390	—	2	2	no	—
216	#390	C₄×C₄₁	1	4	yes	complemented
217	#379	—	2	2	no	—
218	#342	—	2	2	no	—
219	H(3,ℤ/4)	—	2	4	no	—
220	C₄₁	#11073	1	1	yes	characteristic, direct product factor, Sylow
221	C₂⁵	—	2	1	no	—
222	C₂²×D₄	—	2	2	no	—
223	C₂²×D₄	—	2	2	no	—
224	C₂²×D₄	—	2	1	no	—
225	C₂²×D₄	—	2	2	no	—
226	C₂²×D₄	—	2	2	no	—
227	C₂²×D₄	—	2	1	no	—
228	C₂²×D₄	—	2	1	no	—
229	C₂²×D₄	C₂×C₄×C₄₁	1	2	yes	—
230	C₂²×D₄	D₄×C₄₁	1	2	yes	—
231	C₂²×D₄	Q₈×C₄₁	1	2	yes	—
232	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
233	C₂×M₁₆	—	2	2	no	—
234	C₂×M₁₆	—	2	2	no	—
235	C₂×M₁₆	—	2	2	no	—
236	C₂×M₁₆	—	2	2	no	—
237	C₂×M₁₆	—	2	2	no	—
238	C₂×M₁₆	—	2	2	no	—
239	C₂²×C₈	D₄×C₄₁	1	4	yes	—
240	#117	—	2	2	no	—
241	#117	—	2	2	no	—
242	#117	—	2	2	no	—
243	#117	—	2	2	no	—
244	#117	—	2	2	no	—
245	#117	—	2	2	no	—
246	#117	—	2	2	no	—
247	#117	D₄×C₄₁	1	4	yes	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
251	C₂×C₂²⋊C₄	—	2	2	no	—
252	C₂×C₂²⋊C₄	—	2	1	no	—
253	C₂×C₂²⋊C₄	—	2	8	no	—
254	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
255	C₂×C₄²	—	2	2	no	—
256	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
257	C₂×C₄²	D₄×C₄₁	1	2	yes	—
258	C₄⋊C₈	—	2	8	no	—
259	#102	—	2	16	no	—
260	C₂⁴	—	2	2	no	—
261	C₂⁴	—	2	2	no	—
262	C₂⁴	—	2	2	no	—
263	C₂⁴	—	4	2	no	—
264	C₂⁴	—	4	2	no	—
265	C₂⁴	—	8	4	no	—
266	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	2	4	no	—
269	C₂×D₄	—	2	4	no	—
270	C₂×D₄	—	2	4	no	—
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	—	2	4	no	—
273	C₂×D₄	—	2	4	no	—
274	C₂×D₄	—	2	2	no	—
275	C₂×D₄	—	2	4	no	—
276	C₂×D₄	—	4	1	no	—
277	C₂×D₄	—	4	2	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	—	4	1	no	—
280	C₂×D₄	—	4	2	no	—
281	C₂×D₄	—	4	1	no	—
282	C₂×D₄	—	4	2	no	—
283	C₂×D₄	—	4	1	no	—
284	C₂×D₄	C₄⋊C₄×C₄₁	1	4	yes	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
288	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
291	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
292	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
293	C₂²×C₄	C₂×Q₈×C₄₁	1	1	yes	characteristic
294	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
295	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
296	C₂²×C₄	#41×C₄₁	1	2	yes	—
297	C₂²×C₄	#41×C₄₁	1	2	yes	—
298	M₁₆	—	4	2	no	—
299	M₁₆	—	4	2	no	—
300	M₁₆	—	4	2	no	—
301	M₁₆	—	4	2	no	—
302	C₂×C₈	—	2	4	no	—
303	C₂×C₈	—	2	4	no	—
304	C₂×C₈	—	2	4	no	—
305	C₄⋊C₄	—	2	4	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	4	1	no	—
308	C₄⋊C₄	—	4	2	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₂²⋊C₄	—	2	4	no	—
311	C₂²⋊C₄	—	2	4	no	—
312	C₂²⋊C₄	—	4	2	no	—
313	C₂²⋊C₄	—	4	2	no	—
314	C₂²⋊C₄	—	8	8	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	2	2	no	—
317	C₄²	—	2	4	no	—
318	C₄²	—	2	4	no	—
319	C₄²	—	4	2	no	—
320	C₂³	—	2	4	no	—
321	C₂³	—	4	2	no	—
322	C₂³	—	4	8	no	—
323	C₂³	—	4	2	no	—
324	C₂³	—	4	2	no	—
325	C₂³	—	4	4	no	—
326	C₂³	—	4	4	no	—
327	C₂³	—	8	8	no	—
328	C₂³	—	8	4	no	—
329	C₂³	—	8	4	no	—
330	C₂³	—	8	8	no	—
331	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
332	C₂³	#121×C₄₁	1	2	yes	—
333	C₂³	#121×C₄₁	1	1	yes	characteristic
334	C₂³	#121×C₄₁	1	2	yes	—
335	C₂³	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
336	D₄	—	2	8	no	—
337	D₄	—	4	4	no	—
338	D₄	—	4	2	no	—
339	D₄	—	4	2	no	—
340	D₄	—	4	2	no	—
341	D₄	—	4	2	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	4	no	—
347	C₂×C₄	—	8	4	no	—
348	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	1	yes	characteristic
349	C₂×C₄	#117×C₄₁	1	1	yes	characteristic
350	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
351	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
352	C₂×C₄	#120×C₄₁	1	2	yes	—
353	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
354	C₂×C₄	#121×C₄₁	1	2	yes	—
355	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
356	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
357	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
358	C₂×C₄	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
359	C₂×C₄	#123×C₄₁	1	2	yes	—
360	C₂×C₄	#123×C₄₁	1	2	yes	—
361	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
362	C₂×C₄	#124×C₄₁	1	2	yes	—
363	C₂×C₄	#124×C₄₁	1	1	yes	characteristic
364	C₂×C₄	#126×C₄₁	1	2	yes	—
365	C₂×C₄	#127×C₄₁	1	1	yes	characteristic
366	C₈	—	4	4	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	2	4	no	—
369	C₂²	—	4	2	no	—
370	C₂²	—	4	1	no	—
371	C₂²	—	4	1	no	—
372	C₂²	—	4	8	no	—
373	C₂²	—	4	4	no	—
374	C₂²	—	8	4	no	—
375	C₂²	—	8	8	no	—
376	C₂²	—	8	8	no	—
377	C₂²	—	8	4	no	—
378	C₂²	C₄₁×#380	1	1	yes	characteristic
379	C₂²	C₄₁×#386	1	1	yes	characteristic
380	C₂²	C₄₁×#390	1	1	yes	characteristic
381	C₂²	C₄₁×#394	1	2	yes	—
382	C₂²	C₄₁×#396	1	2	yes	—
383	C₄	—	4	4	no	—
384	C₄	—	8	2	no	—
385	C₄	—	8	4	no	—
386	C₄	C₄₁×#385	1	2	yes	—
387	C₄	C₄₁×#388	1	2	yes	—
388	C₄	C₄₁×#392	1	1	yes	characteristic
389	C₄	C₄₁×#393	1	1	yes	characteristic
390	C₄	C₄₁×#397	1	1	yes	characteristic
391	C₄	C₄₁×#399	1	1	yes	characteristic
392	C₂	—	2	1	no	—
393	C₂	—	2	2	no	—
394	C₂	—	2	1	no	—
395	C₂	—	2	2	no	—
396	C₂	—	8	4	no	—
397	C₂	C₄₁×#1439	1	1	yes	characteristic
398	C₂	C₄₁×#1910	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₁	#386
commutator	C₂²×C₄	C₂²×C₄×C₄₁
Frattini, cosocle	C₂³×C₄	C₂³×C₄₁
prime radical	C₂³×D₄×C₄₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂³×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#2905	C₂	semidirect
4. C₄₁×#1740	C₂	semidirect
5. C₂×C₄₁×H(3,ℤ/4)	C₂	semidirect
17. C₄₁×#390	C₄	semidirect
167. #11073	C₄₁	direct (N × H)
193. #2905	C₂×C₄₁	semidirect
196. #1740	C₂×C₄₁	semidirect
197. C₂×H(3,ℤ/4)	C₂×C₄₁	semidirect
216. #390	C₄×C₄₁	semidirect
220. C₄₁	#11073	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×#2905	2
C₂×C₄₁×#418	2
C₄₁×#2309	2
C₄₁×#1740	2
C₂×C₄₁×H(3,ℤ/4)	2
#11073	41

Subgroups — C41×#11073 #23787274

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#11073 #23787274