Subgroups — C₄₁×#11102 #23787303

Order 10496.

868 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×#2911	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#410	C₂	1	2	yes	maximal
3	C₄₁×#2879	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#1733	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₁×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
8	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
9	C₂×#117×C₄₁	C₂²	1	2	yes	—
10	C₂×#117×C₄₁	C₂²	1	2	yes	—
11	C₄₁×#428	—	2	4	no	—
12	C₄₁×#427	—	2	2	no	—
13	C₄₁×#410	—	2	4	no	—
14	C₄₁×#410	—	2	4	no	—
15	C₂×#99×C₄₁	—	2	4	no	—
16	C₄₁×#408	—	2	2	no	—
17	C₄₁×#408	—	2	2	no	—
18	C₄₁×#407	C₄	1	4	yes	complemented
19	C₄₁×#339	—	2	4	no	—
20	C₄₁×H(3,ℤ/4)	—	2	2	no	—
21	C₂×#41×C₄₁	—	2	1	no	—
22	C₂×#41×C₄₁	—	2	1	no	—
23	C₂×#41×C₄₁	—	2	2	no	—
24	C₂×#41×C₄₁	—	2	2	no	—
25	C₂×#41×C₄₁	—	2	1	no	—
26	C₂×#41×C₄₁	—	2	1	no	—
27	C₂×#41×C₄₁	—	2	2	no	—
28	C₂×#41×C₄₁	—	2	2	no	—
29	C₂²×Q₈×C₄₁	Q₈	1	1	yes	characteristic
30	C₂²×D₄×C₄₁	D₄	1	2	yes	—
31	C₂²×D₄×C₄₁	Q₈	1	1	yes	characteristic
32	C₂³×C₄×C₄₁	C₂×C₄	1	2	yes	—
33	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
34	C₂×M₁₆×C₄₁	—	2	2	no	—
35	C₂×M₁₆×C₄₁	—	2	2	no	—
36	C₂×M₁₆×C₄₁	—	2	1	no	—
37	C₂×M₁₆×C₄₁	—	2	2	no	—
38	C₂×M₁₆×C₄₁	—	2	2	no	—
39	C₂×M₁₆×C₄₁	C₂×C₄	1	2	yes	—
40	C₂×M₁₆×C₄₁	C₂×C₄	1	2	yes	—
41	C₂×M₁₆×C₄₁	D₄	1	2	yes	—
42	C₂²×C₈×C₄₁	—	2	1	no	—
43	C₂²×C₈×C₄₁	D₄	1	2	yes	—
44	#117×C₄₁	—	2	2	no	—
45	#117×C₄₁	—	2	2	no	—
46	#117×C₄₁	—	2	2	no	—
47	#117×C₄₁	—	2	2	no	—
48	#117×C₄₁	—	2	2	no	—
49	#117×C₄₁	—	2	2	no	—
50	#117×C₄₁	D₄	1	4	yes	—
51	#117×C₄₁	D₄	1	4	yes	—
52	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
53	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
54	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
55	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
56	C₂×C₄²×C₄₁	—	2	2	no	—
57	C₂×C₄²×C₄₁	—	2	2	no	—
58	#107×C₄₁	—	2	4	no	—
59	#106×C₄₁	—	2	4	no	—
60	#99×C₄₁	—	2	16	no	—
61	C₂²⋊C₈×C₄₁	—	2	8	no	—
62	C₂⁴×C₄₁	C₄⋊C₄	1	2	yes	—
63	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
64	#41×C₄₁	—	4	1	no	—
65	#41×C₄₁	—	4	2	no	—
66	#41×C₄₁	—	4	2	no	—
67	#41×C₄₁	—	4	2	no	—
68	#41×C₄₁	—	4	1	no	—
69	#41×C₄₁	—	4	2	no	—
70	#41×C₄₁	—	4	2	no	—
71	#41×C₄₁	—	4	1	no	—
72	#41×C₄₁	—	4	2	no	—
73	#41×C₄₁	—	4	1	no	—
74	C₂×Q₈×C₄₁	—	2	1	no	—
75	C₂×Q₈×C₄₁	—	2	1	no	—
76	C₂×Q₈×C₄₁	—	2	2	no	—
77	C₂×Q₈×C₄₁	—	2	2	no	—
78	C₂×D₄×C₄₁	—	2	4	no	—
79	C₂×D₄×C₄₁	—	2	2	no	—
80	C₂×D₄×C₄₁	—	2	2	no	—
81	C₂×D₄×C₄₁	—	2	4	no	—
82	C₂×D₄×C₄₁	—	2	2	no	—
83	C₂×D₄×C₄₁	—	2	1	no	—
84	C₂×D₄×C₄₁	—	2	1	no	—
85	C₂×D₄×C₄₁	—	2	2	no	—
86	C₂²×C₄×C₄₁	—	2	2	no	—
87	C₂²×C₄×C₄₁	—	2	2	no	—
88	C₂²×C₄×C₄₁	—	2	4	no	—
89	C₂²×C₄×C₄₁	—	2	4	no	—
90	C₂²×C₄×C₄₁	—	4	2	no	—
91	C₂²×C₄×C₄₁	—	4	2	no	—
92	C₂²×C₄×C₄₁	C₄⋊C₄	1	2	yes	—
93	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₄₁	C₂×Q₈	1	1	yes	characteristic
99	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
100	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
101	C₂²×C₄×C₄₁	#41	1	2	yes	—
102	C₂²×C₄×C₄₁	#41	1	2	yes	—
103	M₁₆×C₄₁	—	2	4	no	—
104	M₁₆×C₄₁	—	2	4	no	—
105	M₁₆×C₄₁	—	2	4	no	—
106	M₁₆×C₄₁	—	4	1	no	—
107	M₁₆×C₄₁	—	4	1	no	—
108	C₂×C₈×C₄₁	—	2	2	no	—
109	C₂×C₈×C₄₁	—	2	2	no	—
110	C₂×C₈×C₄₁	—	2	2	no	—
111	C₂×C₈×C₄₁	—	4	2	no	—
112	C₂×C₈×C₄₁	C₂²⋊C₄	1	4	yes	—
113	C₄⋊C₄×C₄₁	—	2	4	no	—
114	C₄⋊C₄×C₄₁	—	2	4	no	—
115	C₄⋊C₄×C₄₁	—	4	2	no	—
116	C₄⋊C₄×C₄₁	—	4	2	no	—
117	C₂²⋊C₄×C₄₁	—	2	4	no	—
118	C₂²⋊C₄×C₄₁	—	2	4	no	—
119	C₂²⋊C₄×C₄₁	—	4	2	no	—
120	C₂²⋊C₄×C₄₁	—	4	2	no	—
121	C₄²×C₄₁	—	2	4	no	—
122	C₄²×C₄₁	—	2	4	no	—
123	C₄²×C₄₁	—	4	2	no	—
124	C₄²×C₄₁	—	4	2	no	—
125	C₂³×C₄₁	—	2	2	no	—
126	C₂³×C₄₁	—	2	4	no	—
127	C₂³×C₄₁	—	8	1	no	—
128	C₂³×C₄₁	—	8	2	no	—
129	C₂³×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂³×C₄₁	#120	1	2	yes	—
131	C₂³×C₄₁	#121	1	1	yes	characteristic
132	C₂³×C₄₁	#121	1	1	yes	characteristic
133	C₂³×C₄₁	#123	1	2	yes	—
134	Q₈×C₄₁	—	4	1	no	—
135	Q₈×C₄₁	—	4	2	no	—
136	Q₈×C₄₁	—	4	1	no	—
137	D₄×C₄₁	—	4	2	no	—
138	D₄×C₄₁	—	4	4	no	—
139	D₄×C₄₁	—	4	2	no	—
140	D₄×C₄₁	—	4	1	no	—
141	D₄×C₄₁	—	4	2	no	—
142	D₄×C₄₁	—	4	1	no	—
143	C₂×C₄×C₄₁	—	2	2	no	—
144	C₂×C₄×C₄₁	—	2	4	no	—
145	C₂×C₄×C₄₁	—	4	2	no	—
146	C₂×C₄×C₄₁	—	4	4	no	—
147	C₂×C₄×C₄₁	—	4	2	no	—
148	C₂×C₄×C₄₁	—	4	4	no	—
149	C₂×C₄×C₄₁	—	4	4	no	—
150	C₂×C₄×C₄₁	—	8	4	no	—
151	C₂×C₄×C₄₁	—	8	4	no	—
152	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₄₁	#117	1	1	yes	characteristic
154	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
155	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
156	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
157	C₂×C₄×C₄₁	#121	1	2	yes	—
158	C₂×C₄×C₄₁	#121	1	2	yes	—
159	C₂×C₄×C₄₁	#121	1	2	yes	—
160	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
161	C₂×C₄×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
162	C₂×C₄×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
163	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
164	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
165	C₂×C₄×C₄₁	#123	1	2	yes	—
166	C₂×C₄×C₄₁	#124	1	2	yes	—
167	C₂×C₄×C₄₁	#124	1	1	yes	characteristic
168	C₂×C₄×C₄₁	#126	1	2	yes	—
169	C₂×C₄×C₄₁	#127	1	1	yes	characteristic
170	C₈×C₄₁	—	2	4	no	—
171	C₈×C₄₁	—	4	2	no	—
172	#11102	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂²×C₄₁	—	4	2	no	—
174	C₂²×C₄₁	—	4	2	no	—
175	C₂²×C₄₁	—	4	1	no	—
176	C₂²×C₄₁	—	4	1	no	—
177	C₂²×C₄₁	—	4	1	no	—
178	C₂²×C₄₁	—	4	4	no	—
179	C₂²×C₄₁	—	4	2	no	—
180	C₂²×C₄₁	—	8	4	no	—
181	C₂²×C₄₁	#380	1	1	yes	characteristic
182	C₂²×C₄₁	#385	1	2	yes	—
183	C₂²×C₄₁	#392	1	1	yes	characteristic
184	C₂²×C₄₁	#394	1	2	yes	—
185	C₂²×C₄₁	#397	1	1	yes	characteristic
186	C₄×C₄₁	—	4	2	no	—
187	C₄×C₄₁	—	8	4	no	—
188	C₄×C₄₁	—	8	4	no	—
189	C₄×C₄₁	#386	1	1	yes	characteristic
190	C₄×C₄₁	#388	1	2	yes	—
191	C₄×C₄₁	#390	1	1	yes	characteristic
192	C₄×C₄₁	#393	1	1	yes	characteristic
193	C₄×C₄₁	#396	1	2	yes	—
194	C₄×C₄₁	#399	1	1	yes	characteristic
195	#2911	C₂×C₄₁	1	1	yes	characteristic, complemented
196	C₂×#410	C₂×C₄₁	1	2	yes	—
197	#2879	C₂×C₄₁	1	1	yes	characteristic
198	#1733	C₂×C₄₁	1	2	yes	complemented
199	C₂×H(3,ℤ/4)	C₂×C₄₁	1	1	yes	characteristic, complemented
200	C₂×C₄₁	—	2	1	no	—
201	C₂×C₄₁	—	2	2	no	—
202	C₂×C₄₁	—	2	1	no	—
203	C₂×C₄₁	—	2	2	no	—
204	C₂×C₄₁	—	2	1	no	—
205	C₂×C₄₁	—	8	2	no	—
206	C₂×C₄₁	#1439	1	1	yes	characteristic
207	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
208	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
209	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
210	C₂×#117	C₂²×C₄₁	1	2	yes	—
211	C₂×#117	C₂²×C₄₁	1	2	yes	—
212	#428	—	2	4	no	—
213	#427	—	2	2	no	—
214	#410	—	2	4	no	—
215	#410	—	2	4	no	—
216	C₂×#99	—	2	4	no	—
217	#408	—	2	2	no	—
218	#408	—	2	2	no	—
219	#407	C₄×C₄₁	1	4	yes	complemented
220	#339	—	2	4	no	—
221	H(3,ℤ/4)	—	2	2	no	—
222	C₄₁	#11102	1	1	yes	characteristic, direct product factor, Sylow
223	C₂×#41	—	2	1	no	—
224	C₂×#41	—	2	1	no	—
225	C₂×#41	—	2	2	no	—
226	C₂×#41	—	2	2	no	—
227	C₂×#41	—	2	1	no	—
228	C₂×#41	—	2	1	no	—
229	C₂×#41	—	2	2	no	—
230	C₂×#41	—	2	2	no	—
231	C₂²×Q₈	Q₈×C₄₁	1	1	yes	characteristic
232	C₂²×D₄	D₄×C₄₁	1	2	yes	—
233	C₂²×D₄	Q₈×C₄₁	1	1	yes	characteristic
234	C₂³×C₄	C₂×C₄×C₄₁	1	2	yes	—
235	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
236	C₂×M₁₆	—	2	2	no	—
237	C₂×M₁₆	—	2	2	no	—
238	C₂×M₁₆	—	2	1	no	—
239	C₂×M₁₆	—	2	2	no	—
240	C₂×M₁₆	—	2	2	no	—
241	C₂×M₁₆	C₂×C₄×C₄₁	1	2	yes	—
242	C₂×M₁₆	C₂×C₄×C₄₁	1	2	yes	—
243	C₂×M₁₆	D₄×C₄₁	1	2	yes	—
244	C₂²×C₈	—	2	1	no	—
245	C₂²×C₈	D₄×C₄₁	1	2	yes	—
246	#117	—	2	2	no	—
247	#117	—	2	2	no	—
248	#117	—	2	2	no	—
249	#117	—	2	2	no	—
250	#117	—	2	2	no	—
251	#117	—	2	2	no	—
252	#117	D₄×C₄₁	1	4	yes	—
253	#117	D₄×C₄₁	1	4	yes	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₂²⋊C₄	—	2	2	no	—
257	C₂×C₂²⋊C₄	—	2	2	no	—
258	C₂×C₄²	—	2	2	no	—
259	C₂×C₄²	—	2	2	no	—
260	#107	—	2	4	no	—
261	#106	—	2	4	no	—
262	#99	—	2	16	no	—
263	C₂²⋊C₈	—	2	8	no	—
264	C₂⁴	C₄⋊C₄×C₄₁	1	2	yes	—
265	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
266	#41	—	4	1	no	—
267	#41	—	4	2	no	—
268	#41	—	4	2	no	—
269	#41	—	4	2	no	—
270	#41	—	4	1	no	—
271	#41	—	4	2	no	—
272	#41	—	4	2	no	—
273	#41	—	4	1	no	—
274	#41	—	4	2	no	—
275	#41	—	4	1	no	—
276	C₂×Q₈	—	2	1	no	—
277	C₂×Q₈	—	2	1	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×D₄	—	2	4	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	4	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	1	no	—
286	C₂×D₄	—	2	1	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	C₄⋊C₄×C₄₁	1	2	yes	—
295	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
299	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
300	C₂²×C₄	C₂×Q₈×C₄₁	1	1	yes	characteristic
301	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
302	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
303	C₂²×C₄	#41×C₄₁	1	2	yes	—
304	C₂²×C₄	#41×C₄₁	1	2	yes	—
305	M₁₆	—	2	4	no	—
306	M₁₆	—	2	4	no	—
307	M₁₆	—	2	4	no	—
308	M₁₆	—	4	1	no	—
309	M₁₆	—	4	1	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	4	2	no	—
314	C₂×C₈	C₂²⋊C₄×C₄₁	1	4	yes	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₄⋊C₄	—	4	2	no	—
319	C₂²⋊C₄	—	2	4	no	—
320	C₂²⋊C₄	—	2	4	no	—
321	C₂²⋊C₄	—	4	2	no	—
322	C₂²⋊C₄	—	4	2	no	—
323	C₄²	—	2	4	no	—
324	C₄²	—	2	4	no	—
325	C₄²	—	4	2	no	—
326	C₄²	—	4	2	no	—
327	C₂³	—	2	2	no	—
328	C₂³	—	2	4	no	—
329	C₂³	—	8	1	no	—
330	C₂³	—	8	2	no	—
331	C₂³	C₂×C₄⋊C₄×C₄₁	1	1	yes	characteristic
332	C₂³	#120×C₄₁	1	2	yes	—
333	C₂³	#121×C₄₁	1	1	yes	characteristic
334	C₂³	#121×C₄₁	1	1	yes	characteristic
335	C₂³	#123×C₄₁	1	2	yes	—
336	Q₈	—	4	1	no	—
337	Q₈	—	4	2	no	—
338	Q₈	—	4	1	no	—
339	D₄	—	4	2	no	—
340	D₄	—	4	4	no	—
341	D₄	—	4	2	no	—
342	D₄	—	4	1	no	—
343	D₄	—	4	2	no	—
344	D₄	—	4	1	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	—	8	4	no	—
353	C₂×C₄	—	8	4	no	—
354	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
355	C₂×C₄	#117×C₄₁	1	1	yes	characteristic
356	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
357	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
358	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
359	C₂×C₄	#121×C₄₁	1	2	yes	—
360	C₂×C₄	#121×C₄₁	1	2	yes	—
361	C₂×C₄	#121×C₄₁	1	2	yes	—
362	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
363	C₂×C₄	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
364	C₂×C₄	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
365	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
366	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
367	C₂×C₄	#123×C₄₁	1	2	yes	—
368	C₂×C₄	#124×C₄₁	1	2	yes	—
369	C₂×C₄	#124×C₄₁	1	1	yes	characteristic
370	C₂×C₄	#126×C₄₁	1	2	yes	—
371	C₂×C₄	#127×C₄₁	1	1	yes	characteristic
372	C₈	—	2	4	no	—
373	C₈	—	4	2	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	4	2	no	—
376	C₂²	—	4	1	no	—
377	C₂²	—	4	1	no	—
378	C₂²	—	4	1	no	—
379	C₂²	—	4	4	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	8	4	no	—
382	C₂²	C₄₁×#380	1	1	yes	characteristic
383	C₂²	C₄₁×#385	1	2	yes	—
384	C₂²	C₄₁×#392	1	1	yes	characteristic
385	C₂²	C₄₁×#394	1	2	yes	—
386	C₂²	C₄₁×#397	1	1	yes	characteristic
387	C₄	—	4	2	no	—
388	C₄	—	8	4	no	—
389	C₄	—	8	4	no	—
390	C₄	C₄₁×#386	1	1	yes	characteristic
391	C₄	C₄₁×#388	1	2	yes	—
392	C₄	C₄₁×#390	1	1	yes	characteristic
393	C₄	C₄₁×#393	1	1	yes	characteristic
394	C₄	C₄₁×#396	1	2	yes	—
395	C₄	C₄₁×#399	1	1	yes	characteristic
396	C₂	—	2	1	no	—
397	C₂	—	2	2	no	—
398	C₂	—	2	1	no	—
399	C₂	—	2	2	no	—
400	C₂	—	2	1	no	—
401	C₂	—	8	2	no	—
402	C₂	C₄₁×#1439	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₄₁	#390
commutator	C₂²×C₄	C₂²×C₄×C₄₁
Frattini, cosocle	C₂³×C₄	C₂³×C₄₁
socle	C₂×C₄₁	#1439
prime radical	C₂²×#41×C₄₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₄₁ ◁ C₂³×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#2911	C₂	semidirect
4. C₄₁×#1733	C₂	semidirect
5. C₂×C₄₁×H(3,ℤ/4)	C₂	semidirect
18. C₄₁×#407	C₄	semidirect
172. #11102	C₄₁	direct (N × H)
195. #2911	C₂×C₄₁	semidirect
198. #1733	C₂×C₄₁	semidirect
199. C₂×H(3,ℤ/4)	C₂×C₄₁	semidirect
219. #407	C₄×C₄₁	semidirect
222. C₄₁	#11102	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×#2911	2
C₂×C₄₁×#410	2
C₄₁×#2879	2
C₄₁×#1733	2
C₂×C₄₁×H(3,ℤ/4)	2
#11102	41

Subgroups — C41×#11102 #23787303

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#11102 #23787303