Subgroups — C₄₁×#19255 #23795456

Order 10496.

798 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3169	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3036	C₂	1	2	yes	maximal, complemented
3	C₂×C₈×D₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1681	C₂	1	4	yes	maximal, complemented
5	C₄₁×#1673	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1667	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1567	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1547	C₂	1	2	yes	maximal, complemented
9	C₂×AGL(1,ℤ/8)×C₄₁	—	2	2	no	—
10	C₂³×C₈×C₄₁	—	2	1	no	—
11	C₄₁×#532	C₂²	1	2	yes	—
12	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
13	C₄₁×#500	C₂²	1	1	yes	characteristic, complemented
14	C₄₁×#493	C₂²	1	1	yes	characteristic, complemented
15	C₄₁×#486	C₂²	1	2	yes	complemented
16	C₄₁×#466	—	2	1	no	—
17	C₄₁×#466	—	2	1	no	—
18	C₄₁×#463	—	2	4	no	—
19	C₄₁×#461	C₂²	1	4	yes	—
20	C₄₁×#459	C₂²	1	4	yes	—
21	C₄×D₈×C₄₁	—	2	1	no	—
22	C₄×D₈×C₄₁	—	2	1	no	—
23	C₈×D₄×C₄₁	—	2	1	no	—
24	C₈×D₄×C₄₁	—	2	1	no	—
25	C₈×D₄×C₄₁	C₂²	1	2	yes	—
26	C₈×D₄×C₄₁	C₂²	1	2	yes	—
27	C₄₁×#423	C₂²	1	2	yes	—
28	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
29	C₄₁×#417	—	2	2	no	—
30	C₂×C₂²⋊C₈×C₄₁	—	2	1	no	—
31	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
32	C₄₁×#335	C₂²	1	2	yes	complemented
33	C₄₁×#335	C₂²	1	2	yes	complemented
34	C₄₁×#332	C₂²	1	4	yes	complemented
35	C₄₁×#331	C₂²	1	4	yes	complemented
36	C₂×#41×C₄₁	—	2	2	no	—
37	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₄₁	—	2	1	no	—
39	AGL(1,ℤ/8)×C₄₁	—	4	8	no	—
40	C₂×SD₁₆×C₄₁	—	2	4	no	—
41	C₂×D₈×C₄₁	—	2	4	no	—
42	C₂×D₈×C₄₁	—	2	1	no	—
43	C₂×D₈×C₄₁	—	2	1	no	—
44	C₂×M₁₆×C₄₁	—	2	2	no	—
45	C₂²×C₈×C₄₁	—	2	1	no	—
46	C₂²×C₈×C₄₁	—	2	2	no	—
47	C₂²×C₈×C₄₁	—	2	2	no	—
48	C₂²×C₈×C₄₁	—	4	4	no	—
49	C₂²×C₈×C₄₁	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₄₁	D₄	1	1	yes	characteristic
51	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
52	#127×C₄₁	C₂³	1	2	yes	—
53	#124×C₄₁	—	2	2	no	—
54	#121×C₄₁	—	2	2	no	—
55	#121×C₄₁	—	2	2	no	—
56	C₄×D₄×C₄₁	—	2	1	no	—
57	C₄×D₄×C₄₁	—	2	2	no	—
58	C₄×D₄×C₄₁	—	2	1	no	—
59	C₄×D₄×C₄₁	—	2	2	no	—
60	C₄×D₄×C₄₁	D₄	1	2	yes	—
61	C₄×D₄×C₄₁	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
63	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
64	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
65	#107×C₄₁	—	2	1	no	—
66	#107×C₄₁	—	2	1	no	—
67	C₄⋊C₈×C₄₁	—	2	1	no	—
68	C₄⋊C₈×C₄₁	—	2	2	no	—
69	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
70	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
71	#103×C₄₁	—	2	4	no	—
72	#102×C₄₁	—	2	2	no	—
73	#102×C₄₁	—	2	2	no	—
74	#102×C₄₁	—	2	4	no	—
75	C₂²⋊C₈×C₄₁	—	2	2	no	—
76	C₂²⋊C₈×C₄₁	—	2	2	no	—
77	C₄×C₈×C₄₁	D₄	1	1	yes	characteristic
78	C₄×C₈×C₄₁	D₄	1	1	yes	characteristic
79	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
80	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
81	C₂⁴×C₄₁	—	2	1	no	—
82	#41×C₄₁	—	4	4	no	—
83	#41×C₄₁	—	4	4	no	—
84	C₂×Q₈×C₄₁	—	2	2	no	—
85	C₂×D₄×C₄₁	—	2	1	no	—
86	C₂×D₄×C₄₁	—	2	2	no	—
87	C₂×D₄×C₄₁	—	2	2	no	—
88	C₂×D₄×C₄₁	—	2	2	no	—
89	C₂×D₄×C₄₁	—	2	2	no	—
90	C₂×D₄×C₄₁	—	4	2	no	—
91	C₂×D₄×C₄₁	D₈	1	4	yes	complemented
92	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₄₁	—	2	1	no	—
94	C₂²×C₄×C₄₁	—	2	2	no	—
95	C₂²×C₄×C₄₁	—	2	2	no	—
96	C₂²×C₄×C₄₁	—	4	2	no	—
97	C₂²×C₄×C₄₁	—	4	2	no	—
98	C₂²×C₄×C₄₁	—	4	2	no	—
99	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
102	SD₁₆×C₄₁	—	4	8	no	—
103	D₈×C₄₁	—	4	2	no	—
104	D₈×C₄₁	—	4	8	no	—
105	D₈×C₄₁	—	4	2	no	—
106	M₁₆×C₄₁	—	4	4	no	—
107	C₂×C₈×C₄₁	—	2	2	no	—
108	C₂×C₈×C₄₁	—	2	2	no	—
109	C₂×C₈×C₄₁	—	2	4	no	—
110	C₂×C₈×C₄₁	—	4	1	no	—
111	C₂×C₈×C₄₁	—	4	4	no	—
112	C₂×C₈×C₄₁	—	4	2	no	—
113	C₂×C₈×C₄₁	—	4	4	no	—
114	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
118	C₄⋊C₄×C₄₁	—	2	1	no	—
119	C₄⋊C₄×C₄₁	—	2	2	no	—
120	C₄⋊C₄×C₄₁	—	2	2	no	—
121	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
122	C₂²⋊C₄×C₄₁	—	2	2	no	—
123	C₂²⋊C₄×C₄₁	—	2	2	no	—
124	C₂²⋊C₄×C₄₁	—	4	2	no	—
125	C₂²⋊C₄×C₄₁	—	4	2	no	—
126	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₄₁	#41	1	1	yes	characteristic
129	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
130	C₂³×C₄₁	—	2	2	no	—
131	C₂³×C₄₁	—	2	4	no	—
132	C₂³×C₄₁	—	4	2	no	—
133	C₂³×C₄₁	—	4	2	no	—
134	C₂³×C₄₁	—	4	2	no	—
135	C₂³×C₄₁	#121	1	1	yes	characteristic
136	Q₈×C₄₁	—	4	2	no	—
137	Q₈×C₄₁	—	4	2	no	—
138	D₄×C₄₁	—	2	2	no	—
139	D₄×C₄₁	—	2	4	no	—
140	D₄×C₄₁	—	4	2	no	—
141	D₄×C₄₁	—	4	2	no	—
142	D₄×C₄₁	—	4	2	no	—
143	D₄×C₄₁	—	4	2	no	—
144	D₄×C₄₁	—	8	2	no	—
145	D₄×C₄₁	—	8	4	no	—
146	D₄×C₄₁	C₂×D₈	1	4	yes	—
147	C₂×C₄×C₄₁	—	2	1	no	—
148	C₂×C₄×C₄₁	—	2	1	no	—
149	C₂×C₄×C₄₁	—	2	2	no	—
150	C₂×C₄×C₄₁	—	4	1	no	—
151	C₂×C₄×C₄₁	—	4	4	no	—
152	C₂×C₄×C₄₁	—	4	2	no	—
153	C₂×C₄×C₄₁	—	4	2	no	—
154	C₂×C₄×C₄₁	—	4	2	no	—
155	C₂×C₄×C₄₁	—	4	2	no	—
156	C₂×C₄×C₄₁	—	8	4	no	—
157	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
158	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
159	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
160	C₂×C₄×C₄₁	C₂×D₈	1	2	yes	—
161	C₂×C₄×C₄₁	#135	1	2	yes	—
162	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
165	C₈×C₄₁	—	2	1	no	—
166	C₈×C₄₁	—	2	1	no	—
167	C₈×C₄₁	—	2	1	no	—
168	C₈×C₄₁	—	4	4	no	—
169	C₈×C₄₁	—	4	2	no	—
170	C₈×C₄₁	AGL(1,ℤ/8)	1	2	yes	complemented
171	#19255	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂²×C₄₁	—	2	1	no	—
173	C₂²×C₄₁	—	2	1	no	—
174	C₂²×C₄₁	—	2	4	no	—
175	C₂²×C₄₁	—	4	8	no	—
176	C₂²×C₄₁	—	4	2	no	—
177	C₂²×C₄₁	—	4	2	no	—
178	C₂²×C₄₁	—	8	2	no	—
179	C₂²×C₄₁	—	8	2	no	—
180	C₂²×C₄₁	—	8	2	no	—
181	C₂²×C₄₁	#466	1	2	yes	—
182	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
183	C₄×C₄₁	—	2	1	no	—
184	C₄×C₄₁	—	2	1	no	—
185	C₄×C₄₁	—	2	1	no	—
186	C₄×C₄₁	—	4	2	no	—
187	C₄×C₄₁	—	8	2	no	—
188	C₄×C₄₁	#466	1	2	yes	—
189	C₄×C₄₁	C₂²×D₈	1	1	yes	characteristic
190	C₄×C₄₁	C₂×#135	1	1	yes	characteristic
191	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
192	C₄×C₄₁	#575	1	1	yes	characteristic
193	#3169	C₂×C₄₁	1	1	yes	characteristic, complemented
194	#3036	C₂×C₄₁	1	2	yes	complemented
195	C₂×C₈×D₄	C₂×C₄₁	1	1	yes	characteristic, complemented
196	#1681	C₂×C₄₁	1	4	yes	complemented
197	#1673	C₂×C₄₁	1	2	yes	complemented
198	#1667	C₂×C₄₁	1	2	yes	complemented
199	#1567	C₂×C₄₁	1	1	yes	characteristic, complemented
200	#1547	C₂×C₄₁	1	2	yes	complemented
201	C₂×C₄₁	—	2	2	no	—
202	C₂×C₄₁	—	4	4	no	—
203	C₂×C₄₁	—	16	2	no	—
204	C₂×C₄₁	#3036	1	1	yes	characteristic
205	C₂×C₄₁	C₂×#466	1	1	yes	characteristic
206	C₂×C₄₁	#3067	1	1	yes	characteristic
207	C₂×AGL(1,ℤ/8)	—	2	2	no	—
208	C₂³×C₈	—	2	1	no	—
209	#532	C₂²×C₄₁	1	2	yes	—
210	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
211	#500	C₂²×C₄₁	1	1	yes	characteristic, complemented
212	#493	C₂²×C₄₁	1	1	yes	characteristic, complemented
213	#486	C₂²×C₄₁	1	2	yes	complemented
214	#466	—	2	1	no	—
215	#466	—	2	1	no	—
216	#463	—	2	4	no	—
217	#461	C₂²×C₄₁	1	4	yes	—
218	#459	C₂²×C₄₁	1	4	yes	—
219	C₄×D₈	—	2	1	no	—
220	C₄×D₈	—	2	1	no	—
221	C₈×D₄	—	2	1	no	—
222	C₈×D₄	—	2	1	no	—
223	C₈×D₄	C₂²×C₄₁	1	2	yes	—
224	C₈×D₄	C₂²×C₄₁	1	2	yes	—
225	#423	C₂²×C₄₁	1	2	yes	—
226	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
227	#417	—	2	2	no	—
228	C₂×C₂²⋊C₈	—	2	1	no	—
229	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
230	#335	C₂²×C₄₁	1	2	yes	complemented
231	#335	C₂²×C₄₁	1	2	yes	complemented
232	#332	C₂²×C₄₁	1	4	yes	complemented
233	#331	C₂²×C₄₁	1	4	yes	complemented
234	C₄₁	#19255	1	1	yes	characteristic, direct product factor, Sylow
235	C₂×#41	—	2	2	no	—
236	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
237	C₂³×C₄	—	2	1	no	—
238	AGL(1,ℤ/8)	—	4	8	no	—
239	C₂×SD₁₆	—	2	4	no	—
240	C₂×D₈	—	2	4	no	—
241	C₂×D₈	—	2	1	no	—
242	C₂×D₈	—	2	1	no	—
243	C₂×M₁₆	—	2	2	no	—
244	C₂²×C₈	—	2	1	no	—
245	C₂²×C₈	—	2	2	no	—
246	C₂²×C₈	—	2	2	no	—
247	C₂²×C₈	—	4	4	no	—
248	C₂²×C₈	D₄×C₄₁	1	1	yes	characteristic
249	C₂²×C₈	D₄×C₄₁	1	1	yes	characteristic
250	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
251	#127	C₂³×C₄₁	1	2	yes	—
252	#124	—	2	2	no	—
253	#121	—	2	2	no	—
254	#121	—	2	2	no	—
255	C₄×D₄	—	2	1	no	—
256	C₄×D₄	—	2	2	no	—
257	C₄×D₄	—	2	1	no	—
258	C₄×D₄	—	2	2	no	—
259	C₄×D₄	D₄×C₄₁	1	2	yes	—
260	C₄×D₄	C₂³×C₄₁	1	2	yes	—
261	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
262	C₂×C₂²⋊C₄	—	2	1	no	—
263	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
264	#107	—	2	1	no	—
265	#107	—	2	1	no	—
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	—	2	2	no	—
268	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
269	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
270	#103	—	2	4	no	—
271	#102	—	2	2	no	—
272	#102	—	2	2	no	—
273	#102	—	2	4	no	—
274	C₂²⋊C₈	—	2	2	no	—
275	C₂²⋊C₈	—	2	2	no	—
276	C₄×C₈	D₄×C₄₁	1	1	yes	characteristic
277	C₄×C₈	D₄×C₄₁	1	1	yes	characteristic
278	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
279	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
280	C₂⁴	—	2	1	no	—
281	#41	—	4	4	no	—
282	#41	—	4	4	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	4	2	no	—
290	C₂×D₄	D₈×C₄₁	1	4	yes	complemented
291	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	—	4	2	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
300	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
301	SD₁₆	—	4	8	no	—
302	D₈	—	4	2	no	—
303	D₈	—	4	8	no	—
304	D₈	—	4	2	no	—
305	M₁₆	—	4	4	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	4	no	—
309	C₂×C₈	—	4	1	no	—
310	C₂×C₈	—	4	4	no	—
311	C₂×C₈	—	4	2	no	—
312	C₂×C₈	—	4	4	no	—
313	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
314	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
315	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
316	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
321	C₂²⋊C₄	—	2	2	no	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	4	2	no	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
326	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
327	C₄²	#41×C₄₁	1	1	yes	characteristic
328	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
329	C₂³	—	2	2	no	—
330	C₂³	—	2	4	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	2	no	—
334	C₂³	#121×C₄₁	1	1	yes	characteristic
335	Q₈	—	4	2	no	—
336	Q₈	—	4	2	no	—
337	D₄	—	2	2	no	—
338	D₄	—	2	4	no	—
339	D₄	—	4	2	no	—
340	D₄	—	4	2	no	—
341	D₄	—	4	2	no	—
342	D₄	—	4	2	no	—
343	D₄	—	8	2	no	—
344	D₄	—	8	4	no	—
345	D₄	C₂×D₈×C₄₁	1	4	yes	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	8	4	no	—
356	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
357	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
358	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
359	C₂×C₄	C₂×D₈×C₄₁	1	2	yes	—
360	C₂×C₄	#135×C₄₁	1	2	yes	—
361	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
362	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
363	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
364	C₈	—	2	1	no	—
365	C₈	—	2	1	no	—
366	C₈	—	2	1	no	—
367	C₈	—	4	4	no	—
368	C₈	—	4	2	no	—
369	C₈	AGL(1,ℤ/8)×C₄₁	1	2	yes	complemented
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	4	no	—
373	C₂²	—	4	8	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	4	2	no	—
376	C₂²	—	8	2	no	—
377	C₂²	—	8	2	no	—
378	C₂²	—	8	2	no	—
379	C₂²	C₄₁×#466	1	2	yes	—
380	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	4	2	no	—
385	C₄	—	8	2	no	—
386	C₄	C₄₁×#466	1	2	yes	—
387	C₄	C₂²×D₈×C₄₁	1	1	yes	characteristic
388	C₄	C₂×#135×C₄₁	1	1	yes	characteristic
389	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
390	C₄	C₄₁×#575	1	1	yes	characteristic
391	C₂	—	2	2	no	—
392	C₂	—	4	4	no	—
393	C₂	—	16	2	no	—
394	C₂	C₄₁×#3036	1	1	yes	characteristic
395	C₂	C₂×C₄₁×#466	1	1	yes	characteristic
396	C₂	C₄₁×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₁
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3169	C₂	semidirect
2. C₄₁×#3036	C₂	semidirect
3. C₂×C₈×D₄×C₄₁	C₂	semidirect
4. C₄₁×#1681	C₂	semidirect
5. C₄₁×#1673	C₂	semidirect
6. C₄₁×#1667	C₂	semidirect
7. C₄₁×#1567	C₂	semidirect
8. C₄₁×#1547	C₂	semidirect
13. C₄₁×#500	C₂²	semidirect
14. C₄₁×#493	C₂²	semidirect
15. C₄₁×#486	C₂²	semidirect
32. C₄₁×#335	C₂²	semidirect
33. C₄₁×#335	C₂²	semidirect
34. C₄₁×#332	C₂²	semidirect
35. C₄₁×#331	C₂²	semidirect
91. C₂×D₄×C₄₁	D₈	semidirect
170. C₈×C₄₁	AGL(1,ℤ/8)	semidirect
171. #19255	C₄₁	direct (N × H)
193. #3169	C₂×C₄₁	semidirect
194. #3036	C₂×C₄₁	semidirect
195. C₂×C₈×D₄	C₂×C₄₁	semidirect
196. #1681	C₂×C₄₁	semidirect
197. #1673	C₂×C₄₁	semidirect
198. #1667	C₂×C₄₁	semidirect
199. #1567	C₂×C₄₁	semidirect
200. #1547	C₂×C₄₁	semidirect
211. #500	C₂²×C₄₁	semidirect
212. #493	C₂²×C₄₁	semidirect
213. #486	C₂²×C₄₁	semidirect
230. #335	C₂²×C₄₁	semidirect
231. #335	C₂²×C₄₁	semidirect
232. #332	C₂²×C₄₁	semidirect
233. #331	C₂²×C₄₁	semidirect
234. C₄₁	#19255	direct (N × H)
290. C₂×D₄	D₈×C₄₁	semidirect
369. C₈	AGL(1,ℤ/8)×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3169	2
C₄₁×#3036	2
C₂×C₈×D₄×C₄₁	2
C₄₁×#1681	2
C₄₁×#1673	2
C₄₁×#1667	2
C₄₁×#1567	2
C₄₁×#1547	2
#19255	41

Subgroups — C41×#19255 #23795456

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#19255 #23795456