Subgroups — C₄₁×#7606 #23783807

Order 10496.

892 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	C₂×C₄₁×#390	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#1817	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#1728	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1270	C₂	1	4	yes	maximal, complemented
5	C₂³×D₄×C₄₁	C₄	1	1	yes	characteristic
6	C₂²×M₁₆×C₄₁	—	2	1	no	—
7	C₂²×C₄⋊C₄×C₄₁	C₄	1	1	yes	characteristic
8	C₂²×C₂²⋊C₄×C₄₁	—	2	1	no	—
9	C₂²×C₂²⋊C₄×C₄₁	—	2	1	no	—
10	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
11	C₂×C₂²⋊C₈×C₄₁	—	2	1	no	—
12	C₄₁×#390	—	2	1	no	—
13	C₄₁×#390	—	2	1	no	—
14	C₄₁×#390	C₄	1	2	yes	—
15	C₄₁×#390	C₂²	1	2	yes	—
16	C₄₁×#336	—	2	1	no	—
17	C₄₁×#336	—	2	1	no	—
18	C₄₁×#336	C₂²	1	2	yes	complemented
19	C₄₁×#336	C₂²	1	2	yes	complemented
20	C₂⁵×C₄₁	—	2	1	no	—
21	C₂²×D₄×C₄₁	—	2	4	no	—
22	C₂²×D₄×C₄₁	—	2	1	no	—
23	C₂²×D₄×C₄₁	—	4	2	no	—
24	C₂²×D₄×C₄₁	—	4	2	no	—
25	C₂²×D₄×C₄₁	C₂×C₄	1	2	yes	—
26	C₂³×C₄×C₄₁	—	2	1	no	—
27	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
30	C₂×M₁₆×C₄₁	—	2	4	no	—
31	C₂×M₁₆×C₄₁	—	4	2	no	—
32	C₂×M₁₆×C₄₁	—	4	2	no	—
33	C₂²×C₈×C₄₁	—	2	2	no	—
34	C₂²×C₈×C₄₁	—	2	2	no	—
35	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
36	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
37	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
38	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
39	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
40	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
41	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
42	C₂×C₂²⋊C₄×C₄₁	—	4	4	no	—
43	C₂×C₂²⋊C₄×C₄₁	—	4	2	no	—
44	C₂×C₂²⋊C₄×C₄₁	—	4	2	no	—
45	C₂×C₄²×C₄₁	—	4	2	no	—
46	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
50	C₂²⋊C₈×C₄₁	—	4	2	no	—
51	C₂⁴×C₄₁	—	2	4	no	—
52	C₂⁴×C₄₁	—	2	2	no	—
53	C₂⁴×C₄₁	—	4	2	no	—
54	C₂⁴×C₄₁	—	4	2	no	—
55	C₂⁴×C₄₁	—	4	2	no	—
56	C₂⁴×C₄₁	—	4	2	no	—
57	C₂⁴×C₄₁	—	4	2	no	—
58	C₂⁴×C₄₁	—	4	2	no	—
59	C₂⁴×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
60	C₂×D₄×C₄₁	—	2	4	no	—
61	C₂×D₄×C₄₁	—	2	2	no	—
62	C₂×D₄×C₄₁	—	4	2	no	—
63	C₂×D₄×C₄₁	—	4	2	no	—
64	C₂×D₄×C₄₁	—	4	16	no	—
65	C₂×D₄×C₄₁	—	4	2	no	—
66	C₂×D₄×C₄₁	—	4	2	no	—
67	C₂×D₄×C₄₁	M₁₆	1	4	yes	complemented
68	C₂²×C₄×C₄₁	—	2	2	no	—
69	C₂²×C₄×C₄₁	—	2	2	no	—
70	C₂²×C₄×C₄₁	—	2	2	no	—
71	C₂²×C₄×C₄₁	—	2	2	no	—
72	C₂²×C₄×C₄₁	—	2	2	no	—
73	C₂²×C₄×C₄₁	—	2	2	no	—
74	C₂²×C₄×C₄₁	—	2	2	no	—
75	C₂²×C₄×C₄₁	—	2	2	no	—
76	C₂²×C₄×C₄₁	—	4	1	no	—
77	C₂²×C₄×C₄₁	—	4	2	no	—
78	C₂²×C₄×C₄₁	—	4	2	no	—
79	C₂²×C₄×C₄₁	—	4	2	no	—
80	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₁	D₈	1	2	yes	—
84	C₂²×C₄×C₄₁	SD₁₆	1	2	yes	—
85	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
88	M₁₆×C₄₁	—	4	8	no	—
89	C₂×C₈×C₄₁	—	2	4	no	—
90	C₂×C₈×C₄₁	—	4	2	no	—
91	C₂×C₈×C₄₁	—	4	2	no	—
92	C₂×C₈×C₄₁	—	4	2	no	—
93	C₂×C₈×C₄₁	—	4	2	no	—
94	C₂×C₈×C₄₁	—	4	2	no	—
95	C₄⋊C₄×C₄₁	—	4	2	no	—
96	C₄⋊C₄×C₄₁	—	4	2	no	—
97	C₂²⋊C₄×C₄₁	—	4	4	no	—
98	C₂²⋊C₄×C₄₁	—	4	4	no	—
99	C₂²⋊C₄×C₄₁	—	4	2	no	—
100	C₂²⋊C₄×C₄₁	—	4	2	no	—
101	C₂²⋊C₄×C₄₁	—	4	4	no	—
102	C₄²×C₄₁	—	4	1	no	—
103	C₄²×C₄₁	—	4	1	no	—
104	C₄²×C₄₁	—	4	1	no	—
105	C₄²×C₄₁	—	4	1	no	—
106	C₂³×C₄₁	—	2	1	no	—
107	C₂³×C₄₁	—	2	1	no	—
108	C₂³×C₄₁	—	2	1	no	—
109	C₂³×C₄₁	—	2	1	no	—
110	C₂³×C₄₁	—	2	4	no	—
111	C₂³×C₄₁	—	4	8	no	—
112	C₂³×C₄₁	—	4	8	no	—
113	C₂³×C₄₁	—	4	8	no	—
114	C₂³×C₄₁	—	4	2	no	—
115	C₂³×C₄₁	—	4	2	no	—
116	C₂³×C₄₁	—	4	2	no	—
117	C₂³×C₄₁	—	4	2	no	—
118	C₂³×C₄₁	—	4	2	no	—
119	C₂³×C₄₁	—	4	2	no	—
120	C₂³×C₄₁	—	8	4	no	—
121	C₂³×C₄₁	—	8	4	no	—
122	C₂³×C₄₁	—	8	4	no	—
123	C₂³×C₄₁	—	8	4	no	—
124	C₂³×C₄₁	#99	1	2	yes	—
125	C₂³×C₄₁	#102	1	2	yes	—
126	C₂³×C₄₁	#104	1	2	yes	—
127	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
128	D₄×C₄₁	—	4	4	no	—
129	D₄×C₄₁	—	4	8	no	—
130	D₄×C₄₁	—	4	4	no	—
131	C₂×C₄×C₄₁	—	2	8	no	—
132	C₂×C₄×C₄₁	—	2	4	no	—
133	C₂×C₄×C₄₁	—	2	4	no	—
134	C₂×C₄×C₄₁	—	2	1	no	—
135	C₂×C₄×C₄₁	—	2	1	no	—
136	C₂×C₄×C₄₁	—	2	1	no	—
137	C₂×C₄×C₄₁	—	2	1	no	—
138	C₂×C₄×C₄₁	—	2	1	no	—
139	C₂×C₄×C₄₁	—	2	1	no	—
140	C₂×C₄×C₄₁	—	2	1	no	—
141	C₂×C₄×C₄₁	—	2	1	no	—
142	C₂×C₄×C₄₁	—	2	1	no	—
143	C₂×C₄×C₄₁	—	2	1	no	—
144	C₂×C₄×C₄₁	—	2	1	no	—
145	C₂×C₄×C₄₁	—	2	1	no	—
146	C₂×C₄×C₄₁	—	2	1	no	—
147	C₂×C₄×C₄₁	—	4	4	no	—
148	C₂×C₄×C₄₁	—	4	2	no	—
149	C₂×C₄×C₄₁	—	4	2	no	—
150	C₂×C₄×C₄₁	—	4	2	no	—
151	C₂×C₄×C₄₁	—	8	4	no	—
152	C₂×C₄×C₄₁	#100	1	2	yes	—
153	C₂×C₄×C₄₁	#102	1	2	yes	—
154	C₂×C₄×C₄₁	C₂×M₁₆	1	2	yes	—
155	C₂×C₄×C₄₁	C₂×D₈	1	1	yes	characteristic
156	C₂×C₄×C₄₁	C₂×SD₁₆	1	1	yes	characteristic
157	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
158	C₈×C₄₁	—	4	4	no	—
159	C₈×C₄₁	—	8	2	no	—
160	#7606	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
161	C₂²×C₄₁	—	2	2	no	—
162	C₂²×C₄₁	—	2	2	no	—
163	C₂²×C₄₁	—	2	2	no	—
164	C₂²×C₄₁	—	2	2	no	—
165	C₂²×C₄₁	—	2	2	no	—
166	C₂²×C₄₁	—	2	2	no	—
167	C₂²×C₄₁	—	4	4	no	—
168	C₂²×C₄₁	—	4	4	no	—
169	C₂²×C₄₁	—	4	4	no	—
170	C₂²×C₄₁	—	8	16	no	—
171	C₂²×C₄₁	—	8	2	no	—
172	C₂²×C₄₁	—	8	2	no	—
173	C₂²×C₄₁	—	8	2	no	—
174	C₂²×C₄₁	—	8	2	no	—
175	C₂²×C₄₁	#327	1	4	yes	—
176	C₂²×C₄₁	#407	1	1	yes	characteristic
177	C₂²×C₄₁	C₂×#99	1	1	yes	characteristic
178	C₂²×C₄₁	C₂×#100	1	1	yes	characteristic
179	C₂²×C₄₁	C₂×#102	1	1	yes	characteristic
180	C₂²×C₄₁	#418	1	1	yes	characteristic
181	C₂²×C₄₁	C₂×#104	1	1	yes	characteristic
182	C₂²×C₄₁	#421	1	1	yes	characteristic
183	C₄×C₄₁	—	2	2	no	—
184	C₄×C₄₁	—	2	2	no	—
185	C₄×C₄₁	—	2	1	no	—
186	C₄×C₄₁	—	2	2	no	—
187	C₄×C₄₁	—	2	1	no	—
188	C₄×C₄₁	—	2	2	no	—
189	C₄×C₄₁	—	4	1	no	—
190	C₄×C₄₁	—	8	2	no	—
191	C₂×#390	C₂×C₄₁	1	1	yes	characteristic
192	#1817	C₂×C₄₁	1	1	yes	characteristic, complemented
193	#1728	C₂×C₄₁	1	1	yes	characteristic, complemented
194	#1270	C₂×C₄₁	1	4	yes	complemented
195	C₂×C₄₁	—	2	4	no	—
196	C₂×C₄₁	—	8	4	no	—
197	C₂×C₄₁	#1462	1	1	yes	characteristic
198	C₂×C₄₁	#1486	1	1	yes	characteristic
199	C₂×C₄₁	#1490	1	1	yes	characteristic
200	C₂×C₄₁	C₂×#327	1	1	yes	characteristic
201	C₂×C₄₁	#1510	1	1	yes	characteristic
202	C₂×C₄₁	#1527	1	1	yes	characteristic
203	C₂×C₄₁	#1545	1	1	yes	characteristic
204	C₂³×D₄	C₄×C₄₁	1	1	yes	characteristic
205	C₂²×M₁₆	—	2	1	no	—
206	C₂²×C₄⋊C₄	C₄×C₄₁	1	1	yes	characteristic
207	C₂²×C₂²⋊C₄	—	2	1	no	—
208	C₂²×C₂²⋊C₄	—	2	1	no	—
209	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
210	C₂×C₂²⋊C₈	—	2	1	no	—
211	#390	—	2	1	no	—
212	#390	—	2	1	no	—
213	#390	C₄×C₄₁	1	2	yes	—
214	#390	C₂²×C₄₁	1	2	yes	—
215	#336	—	2	1	no	—
216	#336	—	2	1	no	—
217	#336	C₂²×C₄₁	1	2	yes	complemented
218	#336	C₂²×C₄₁	1	2	yes	complemented
219	C₄₁	#7606	1	1	yes	characteristic, direct product factor, Sylow
220	C₂⁵	—	2	1	no	—
221	C₂²×D₄	—	2	4	no	—
222	C₂²×D₄	—	2	1	no	—
223	C₂²×D₄	—	4	2	no	—
224	C₂²×D₄	—	4	2	no	—
225	C₂²×D₄	C₂×C₄×C₄₁	1	2	yes	—
226	C₂³×C₄	—	2	1	no	—
227	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
228	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
229	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
230	C₂×M₁₆	—	2	4	no	—
231	C₂×M₁₆	—	4	2	no	—
232	C₂×M₁₆	—	4	2	no	—
233	C₂²×C₈	—	2	2	no	—
234	C₂²×C₈	—	2	2	no	—
235	C₂×C₄⋊C₄	—	2	1	no	—
236	C₂×C₄⋊C₄	—	4	2	no	—
237	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
238	C₂×C₂²⋊C₄	—	2	2	no	—
239	C₂×C₂²⋊C₄	—	2	2	no	—
240	C₂×C₂²⋊C₄	—	2	2	no	—
241	C₂×C₂²⋊C₄	—	2	2	no	—
242	C₂×C₂²⋊C₄	—	4	4	no	—
243	C₂×C₂²⋊C₄	—	4	2	no	—
244	C₂×C₂²⋊C₄	—	4	2	no	—
245	C₂×C₄²	—	4	2	no	—
246	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
247	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
248	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
249	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
250	C₂²⋊C₈	—	4	2	no	—
251	C₂⁴	—	2	4	no	—
252	C₂⁴	—	2	2	no	—
253	C₂⁴	—	4	2	no	—
254	C₂⁴	—	4	2	no	—
255	C₂⁴	—	4	2	no	—
256	C₂⁴	—	4	2	no	—
257	C₂⁴	—	4	2	no	—
258	C₂⁴	—	4	2	no	—
259	C₂⁴	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
260	C₂×D₄	—	2	4	no	—
261	C₂×D₄	—	2	2	no	—
262	C₂×D₄	—	4	2	no	—
263	C₂×D₄	—	4	2	no	—
264	C₂×D₄	—	4	16	no	—
265	C₂×D₄	—	4	2	no	—
266	C₂×D₄	—	4	2	no	—
267	C₂×D₄	M₁₆×C₄₁	1	4	yes	complemented
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	4	1	no	—
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	—	4	2	no	—
280	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
281	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
282	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
283	C₂²×C₄	D₈×C₄₁	1	2	yes	—
284	C₂²×C₄	SD₁₆×C₄₁	1	2	yes	—
285	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
286	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
288	M₁₆	—	4	8	no	—
289	C₂×C₈	—	2	4	no	—
290	C₂×C₈	—	4	2	no	—
291	C₂×C₈	—	4	2	no	—
292	C₂×C₈	—	4	2	no	—
293	C₂×C₈	—	4	2	no	—
294	C₂×C₈	—	4	2	no	—
295	C₄⋊C₄	—	4	2	no	—
296	C₄⋊C₄	—	4	2	no	—
297	C₂²⋊C₄	—	4	4	no	—
298	C₂²⋊C₄	—	4	4	no	—
299	C₂²⋊C₄	—	4	2	no	—
300	C₂²⋊C₄	—	4	2	no	—
301	C₂²⋊C₄	—	4	4	no	—
302	C₄²	—	4	1	no	—
303	C₄²	—	4	1	no	—
304	C₄²	—	4	1	no	—
305	C₄²	—	4	1	no	—
306	C₂³	—	2	1	no	—
307	C₂³	—	2	1	no	—
308	C₂³	—	2	1	no	—
309	C₂³	—	2	1	no	—
310	C₂³	—	2	4	no	—
311	C₂³	—	4	8	no	—
312	C₂³	—	4	8	no	—
313	C₂³	—	4	8	no	—
314	C₂³	—	4	2	no	—
315	C₂³	—	4	2	no	—
316	C₂³	—	4	2	no	—
317	C₂³	—	4	2	no	—
318	C₂³	—	4	2	no	—
319	C₂³	—	4	2	no	—
320	C₂³	—	8	4	no	—
321	C₂³	—	8	4	no	—
322	C₂³	—	8	4	no	—
323	C₂³	—	8	4	no	—
324	C₂³	#99×C₄₁	1	2	yes	—
325	C₂³	#102×C₄₁	1	2	yes	—
326	C₂³	#104×C₄₁	1	2	yes	—
327	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
328	D₄	—	4	4	no	—
329	D₄	—	4	8	no	—
330	D₄	—	4	4	no	—
331	C₂×C₄	—	2	8	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	8	4	no	—
352	C₂×C₄	#100×C₄₁	1	2	yes	—
353	C₂×C₄	#102×C₄₁	1	2	yes	—
354	C₂×C₄	C₂×M₁₆×C₄₁	1	2	yes	—
355	C₂×C₄	C₂×D₈×C₄₁	1	1	yes	characteristic
356	C₂×C₄	C₂×SD₁₆×C₄₁	1	1	yes	characteristic
357	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
358	C₈	—	4	4	no	—
359	C₈	—	8	2	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	4	4	no	—
367	C₂²	—	4	4	no	—
368	C₂²	—	4	4	no	—
369	C₂²	—	8	16	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	8	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	8	2	no	—
374	C₂²	C₄₁×#327	1	4	yes	—
375	C₂²	C₄₁×#407	1	1	yes	characteristic
376	C₂²	C₂×#99×C₄₁	1	1	yes	characteristic
377	C₂²	C₂×#100×C₄₁	1	1	yes	characteristic
378	C₂²	C₂×#102×C₄₁	1	1	yes	characteristic
379	C₂²	C₄₁×#418	1	1	yes	characteristic
380	C₂²	C₂×#104×C₄₁	1	1	yes	characteristic
381	C₂²	C₄₁×#421	1	1	yes	characteristic
382	C₄	—	2	2	no	—
383	C₄	—	2	2	no	—
384	C₄	—	2	2	no	—
385	C₄	—	2	1	no	—
386	C₄	—	2	2	no	—
387	C₄	—	2	1	no	—
388	C₄	—	4	1	no	—
389	C₄	—	8	2	no	—
390	C₂	—	2	4	no	—
391	C₂	—	8	4	no	—
392	C₂	C₄₁×#1462	1	1	yes	characteristic
393	C₂	C₄₁×#1486	1	1	yes	characteristic
394	C₂	C₄₁×#1490	1	1	yes	characteristic
395	C₂	C₂×C₄₁×#327	1	1	yes	characteristic
396	C₂	C₄₁×#1510	1	1	yes	characteristic
397	C₂	C₄₁×#1527	1	1	yes	characteristic
398	C₂	C₄₁×#1545	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₄₁
Frattini, cosocle	C₂×C₄²	C₂³×C₄₁
prime radical	C₂³×D₄×C₄₁	C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#1817	C₂	semidirect
3. C₄₁×#1728	C₂	semidirect
4. C₄₁×#1270	C₂	semidirect
18. C₄₁×#336	C₂²	semidirect
19. C₄₁×#336	C₂²	semidirect
67. C₂×D₄×C₄₁	M₁₆	semidirect
160. #7606	C₄₁	direct (N × H)
192. #1817	C₂×C₄₁	semidirect
193. #1728	C₂×C₄₁	semidirect
194. #1270	C₂×C₄₁	semidirect
217. #336	C₂²×C₄₁	semidirect
218. #336	C₂²×C₄₁	semidirect
219. C₄₁	#7606	direct (N × H)
267. C₂×D₄	M₁₆×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#390	2
C₄₁×#1817	2
C₄₁×#1728	2
C₄₁×#1270	2
#7606	41

Subgroups — C41×#7606 #23783807

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#7606 #23783807