Subgroups — C₄₁×#18683 #23794884

Order 10496.

1058 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3543	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#3238	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₁×#492	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1631	C₂	1	4	yes	maximal, complemented
5	C₄₁×#1630	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1629	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1555	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1494	C₂	1	2	yes	maximal, complemented
9	C₂²×SD₁₆×C₄₁	—	2	2	no	—
10	C₄₁×#560	—	2	2	no	—
11	C₄₁×#559	C₂²	1	1	yes	characteristic
12	C₄₁×#550	C₂²	1	2	yes	—
13	C₄₁×#546	—	2	2	no	—
14	D₄²×C₄₁	—	2	2	no	—
15	D₄²×C₄₁	C₂²	1	1	yes	characteristic
16	C₄₁×#540	—	2	2	no	—
17	C₄₁×#535	—	2	2	no	—
18	C₄₁×#534	—	2	2	no	—
19	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
20	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
21	C₄₁×#529	C₂²	1	2	yes	—
22	C₄₁×#501	—	2	2	no	—
23	C₄₁×#492	—	2	2	no	—
24	C₄₁×#492	C₂²	1	2	yes	—
25	C₄₁×#492	C₂²	1	2	yes	complemented
26	C₄₁×#489	—	2	2	no	—
27	C₄₁×#483	—	2	2	no	—
28	C₄₁×#480	—	2	2	no	—
29	C₄₁×#477	C₂²	1	4	yes	complemented
30	C₄₁×#476	C₂²	1	4	yes	complemented
31	C₄₁×#432	C₂²	1	2	yes	complemented
32	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
33	C₄₁×#331	C₂²	1	2	yes	—
34	C₄₁×#331	C₂²	1	2	yes	complemented
35	C₄₁×Q₈⋊C₈	C₂²	1	4	yes	complemented
36	C₄₁×D₄⋊C₈	C₂²	1	4	yes	complemented
37	C₂×#41×C₄₁	—	2	2	no	—
38	C₂²×Q₈×C₄₁	—	2	1	no	—
39	C₂²×D₄×C₄₁	—	2	2	no	—
40	C₂²×D₄×C₄₁	—	2	2	no	—
41	C₂²×D₄×C₄₁	—	2	2	no	—
42	C₂²×D₄×C₄₁	D₄	1	2	yes	—
43	C₂×SD₁₆×C₄₁	—	2	4	no	—
44	C₂×SD₁₆×C₄₁	—	2	4	no	—
45	C₂×SD₁₆×C₄₁	—	4	8	no	—
46	C₂²×C₈×C₄₁	—	2	1	no	—
47	C₄⋊Q₈×C₄₁	—	2	2	no	—
48	C₄⋊Q₈×C₄₁	—	2	1	no	—
49	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
50	#127×C₄₁	—	2	2	no	—
51	#127×C₄₁	—	2	2	no	—
52	#127×C₄₁	D₄	1	2	yes	—
53	#127×C₄₁	C₂³	1	1	yes	characteristic
54	#127×C₄₁	C₂³	1	1	yes	characteristic
55	#126×C₄₁	—	2	2	no	—
56	#125×C₄₁	D₄	1	2	yes	—
57	#124×C₄₁	—	2	2	no	—
58	#124×C₄₁	D₄	1	2	yes	—
59	#123×C₄₁	—	2	2	no	—
60	#123×C₄₁	—	2	4	no	—
61	#123×C₄₁	—	2	2	no	—
62	#123×C₄₁	—	2	2	no	—
63	C₂²⋊Q₈×C₄₁	D₄	1	2	yes	—
64	#121×C₄₁	—	2	4	no	—
65	#121×C₄₁	—	2	4	no	—
66	#121×C₄₁	—	2	4	no	—
67	#121×C₄₁	—	2	4	no	—
68	#121×C₄₁	—	2	2	no	—
69	#121×C₄₁	—	2	2	no	—
70	#121×C₄₁	D₄	1	2	yes	—
71	#120×C₄₁	—	2	2	no	—
72	#120×C₄₁	—	2	4	no	—
73	#120×C₄₁	—	2	4	no	—
74	#120×C₄₁	—	2	2	no	—
75	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
76	C₄×D₄×C₄₁	—	2	2	no	—
77	C₄×D₄×C₄₁	—	2	2	no	—
78	C₄×D₄×C₄₁	—	2	2	no	—
79	C₄×D₄×C₄₁	C₂³	1	2	yes	—
80	#117×C₄₁	—	2	2	no	—
81	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
83	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
84	#107×C₄₁	—	2	4	no	—
85	#106×C₄₁	—	2	4	no	—
86	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
87	#103×C₄₁	—	2	4	no	—
88	#102×C₄₁	—	2	4	no	—
89	C₂²⋊C₈×C₄₁	—	2	2	no	—
90	#97×C₄₁	—	2	2	no	—
91	C₄×C₈×C₄₁	—	2	1	no	—
92	C₄×C₈×C₄₁	C₂³	1	2	yes	—
93	C₂⁴×C₄₁	—	2	2	no	—
94	C₂⁴×C₄₁	—	2	2	no	—
95	#41×C₄₁	—	8	4	no	—
96	C₂×Q₈×C₄₁	—	2	2	no	—
97	C₂×Q₈×C₄₁	—	4	4	no	—
98	C₂×Q₈×C₄₁	—	4	1	no	—
99	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
100	C₂×D₄×C₄₁	—	2	2	no	—
101	C₂×D₄×C₄₁	—	2	4	no	—
102	C₂×D₄×C₄₁	—	2	4	no	—
103	C₂×D₄×C₄₁	—	2	4	no	—
104	C₂×D₄×C₄₁	—	2	2	no	—
105	C₂×D₄×C₄₁	—	2	4	no	—
106	C₂×D₄×C₄₁	—	2	2	no	—
107	C₂×D₄×C₄₁	—	2	2	no	—
108	C₂×D₄×C₄₁	—	4	4	no	—
109	C₂×D₄×C₄₁	—	8	4	no	—
110	C₂×D₄×C₄₁	—	8	4	no	—
111	C₂×D₄×C₄₁	—	8	4	no	—
112	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
113	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
114	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₄₁	—	2	4	no	—
116	C₂²×C₄×C₄₁	—	2	2	no	—
117	C₂²×C₄×C₄₁	—	2	2	no	—
118	C₂²×C₄×C₄₁	—	4	1	no	—
119	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
121	SD₁₆×C₄₁	—	4	8	no	—
122	SD₁₆×C₄₁	—	4	8	no	—
123	C₂×C₈×C₄₁	—	2	4	no	—
124	C₂×C₈×C₄₁	—	2	2	no	—
125	C₂×C₈×C₄₁	—	2	4	no	—
126	C₄⋊C₄×C₄₁	—	2	2	no	—
127	C₄⋊C₄×C₄₁	—	2	2	no	—
128	C₄⋊C₄×C₄₁	—	2	2	no	—
129	C₄⋊C₄×C₄₁	—	2	2	no	—
130	C₄⋊C₄×C₄₁	—	2	4	no	—
131	C₄⋊C₄×C₄₁	—	4	2	no	—
132	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
133	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
134	C₂²⋊C₄×C₄₁	—	2	2	no	—
135	C₂²⋊C₄×C₄₁	—	2	2	no	—
136	C₂²⋊C₄×C₄₁	—	2	4	no	—
137	C₂²⋊C₄×C₄₁	—	2	4	no	—
138	C₂²⋊C₄×C₄₁	—	2	2	no	—
139	C₂²⋊C₄×C₄₁	—	2	2	no	—
140	C₂²⋊C₄×C₄₁	—	2	2	no	—
141	C₂²⋊C₄×C₄₁	—	2	2	no	—
142	C₂²⋊C₄×C₄₁	—	2	2	no	—
143	C₄²×C₄₁	—	2	2	no	—
144	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₄₁	C₂×D₄	1	2	yes	—
146	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
147	C₂³×C₄₁	—	2	2	no	—
148	C₂³×C₄₁	—	2	2	no	—
149	C₂³×C₄₁	—	2	2	no	—
150	C₂³×C₄₁	—	4	4	no	—
151	C₂³×C₄₁	—	8	4	no	—
152	C₂³×C₄₁	—	8	4	no	—
153	C₂³×C₄₁	—	8	2	no	—
154	C₂³×C₄₁	#120	1	1	yes	characteristic
155	Q₈×C₄₁	—	2	4	no	—
156	Q₈×C₄₁	—	4	4	no	—
157	Q₈×C₄₁	—	8	2	no	—
158	D₄×C₄₁	—	2	4	no	—
159	D₄×C₄₁	—	4	2	no	—
160	D₄×C₄₁	—	4	2	no	—
161	D₄×C₄₁	—	4	4	no	—
162	D₄×C₄₁	—	4	4	no	—
163	D₄×C₄₁	—	4	4	no	—
164	D₄×C₄₁	—	8	2	no	—
165	D₄×C₄₁	—	8	4	no	—
166	D₄×C₄₁	—	8	4	no	—
167	D₄×C₄₁	—	8	4	no	—
168	D₄×C₄₁	—	8	4	no	—
169	C₂×C₄×C₄₁	—	2	2	no	—
170	C₂×C₄×C₄₁	—	2	4	no	—
171	C₂×C₄×C₄₁	—	2	2	no	—
172	C₂×C₄×C₄₁	—	2	2	no	—
173	C₂×C₄×C₄₁	—	2	2	no	—
174	C₂×C₄×C₄₁	—	4	4	no	—
175	C₂×C₄×C₄₁	—	4	2	no	—
176	C₂×C₄×C₄₁	—	8	2	no	—
177	C₂×C₄×C₄₁	—	8	4	no	—
178	C₂×C₄×C₄₁	—	8	2	no	—
179	C₂×C₄×C₄₁	#120	1	2	yes	—
180	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
181	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
183	C₈×C₄₁	—	2	4	no	—
184	C₈×C₄₁	—	4	4	no	—
185	#18683	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂²×C₄₁	—	2	2	no	—
187	C₂²×C₄₁	—	4	2	no	—
188	C₂²×C₄₁	—	4	4	no	—
189	C₂²×C₄₁	—	4	2	no	—
190	C₂²×C₄₁	—	4	4	no	—
191	C₂²×C₄₁	—	4	2	no	—
192	C₂²×C₄₁	—	4	2	no	—
193	C₂²×C₄₁	—	4	2	no	—
194	C₂²×C₄₁	—	16	4	no	—
195	C₂²×C₄₁	—	16	4	no	—
196	C₂²×C₄₁	#453	1	2	yes	—
197	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
198	C₄×C₄₁	—	2	2	no	—
199	C₄×C₄₁	—	2	1	no	—
200	C₄×C₄₁	—	2	1	no	—
201	C₄×C₄₁	—	4	2	no	—
202	C₄×C₄₁	—	4	2	no	—
203	C₄×C₄₁	—	4	2	no	—
204	C₄×C₄₁	—	8	2	no	—
205	C₄×C₄₁	#577	1	4	yes	—
206	#3543	C₂×C₄₁	1	1	yes	characteristic
207	#3238	C₂×C₄₁	1	2	yes	complemented
208	C₂×#492	C₂×C₄₁	1	1	yes	characteristic, complemented
209	#1631	C₂×C₄₁	1	4	yes	complemented
210	#1630	C₂×C₄₁	1	2	yes	complemented
211	#1629	C₂×C₄₁	1	2	yes	complemented
212	#1555	C₂×C₄₁	1	1	yes	characteristic, complemented
213	#1494	C₂×C₄₁	1	2	yes	complemented
214	C₂×C₄₁	—	2	2	no	—
215	C₂×C₄₁	—	8	2	no	—
216	C₂×C₄₁	—	8	2	no	—
217	C₂×C₄₁	—	8	2	no	—
218	C₂×C₄₁	#3009	1	2	yes	—
219	C₂×C₄₁	C₂×#453	1	1	yes	characteristic
220	C₂²×SD₁₆	—	2	2	no	—
221	#560	—	2	2	no	—
222	#559	C₂²×C₄₁	1	1	yes	characteristic
223	#550	C₂²×C₄₁	1	2	yes	—
224	#546	—	2	2	no	—
225	D₄²	—	2	2	no	—
226	D₄²	C₂²×C₄₁	1	1	yes	characteristic
227	#540	—	2	2	no	—
228	#535	—	2	2	no	—
229	#534	—	2	2	no	—
230	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
231	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
232	#529	C₂²×C₄₁	1	2	yes	—
233	#501	—	2	2	no	—
234	#492	—	2	2	no	—
235	#492	C₂²×C₄₁	1	2	yes	—
236	#492	C₂²×C₄₁	1	2	yes	complemented
237	#489	—	2	2	no	—
238	#483	—	2	2	no	—
239	#480	—	2	2	no	—
240	#477	C₂²×C₄₁	1	4	yes	complemented
241	#476	C₂²×C₄₁	1	4	yes	complemented
242	#432	C₂²×C₄₁	1	2	yes	complemented
243	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
244	#331	C₂²×C₄₁	1	2	yes	—
245	#331	C₂²×C₄₁	1	2	yes	complemented
246	Q₈⋊C₈	C₂²×C₄₁	1	4	yes	complemented
247	D₄⋊C₈	C₂²×C₄₁	1	4	yes	complemented
248	C₄₁	#18683	1	1	yes	characteristic, direct product factor, Sylow
249	C₂×#41	—	2	2	no	—
250	C₂²×Q₈	—	2	1	no	—
251	C₂²×D₄	—	2	2	no	—
252	C₂²×D₄	—	2	2	no	—
253	C₂²×D₄	—	2	2	no	—
254	C₂²×D₄	D₄×C₄₁	1	2	yes	—
255	C₂×SD₁₆	—	2	4	no	—
256	C₂×SD₁₆	—	2	4	no	—
257	C₂×SD₁₆	—	4	8	no	—
258	C₂²×C₈	—	2	1	no	—
259	C₄⋊Q₈	—	2	2	no	—
260	C₄⋊Q₈	—	2	1	no	—
261	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
262	#127	—	2	2	no	—
263	#127	—	2	2	no	—
264	#127	D₄×C₄₁	1	2	yes	—
265	#127	C₂³×C₄₁	1	1	yes	characteristic
266	#127	C₂³×C₄₁	1	1	yes	characteristic
267	#126	—	2	2	no	—
268	#125	D₄×C₄₁	1	2	yes	—
269	#124	—	2	2	no	—
270	#124	D₄×C₄₁	1	2	yes	—
271	#123	—	2	2	no	—
272	#123	—	2	4	no	—
273	#123	—	2	2	no	—
274	#123	—	2	2	no	—
275	C₂²⋊Q₈	D₄×C₄₁	1	2	yes	—
276	#121	—	2	4	no	—
277	#121	—	2	4	no	—
278	#121	—	2	4	no	—
279	#121	—	2	4	no	—
280	#121	—	2	2	no	—
281	#121	—	2	2	no	—
282	#121	D₄×C₄₁	1	2	yes	—
283	#120	—	2	2	no	—
284	#120	—	2	4	no	—
285	#120	—	2	4	no	—
286	#120	—	2	2	no	—
287	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
288	C₄×D₄	—	2	2	no	—
289	C₄×D₄	—	2	2	no	—
290	C₄×D₄	—	2	2	no	—
291	C₄×D₄	C₂³×C₄₁	1	2	yes	—
292	#117	—	2	2	no	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
296	#107	—	2	4	no	—
297	#106	—	2	4	no	—
298	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
299	#103	—	2	4	no	—
300	#102	—	2	4	no	—
301	C₂²⋊C₈	—	2	2	no	—
302	#97	—	2	2	no	—
303	C₄×C₈	—	2	1	no	—
304	C₄×C₈	C₂³×C₄₁	1	2	yes	—
305	C₂⁴	—	2	2	no	—
306	C₂⁴	—	2	2	no	—
307	#41	—	8	4	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	4	4	no	—
310	C₂×Q₈	—	4	1	no	—
311	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	4	no	—
314	C₂×D₄	—	2	4	no	—
315	C₂×D₄	—	2	4	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	4	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	4	4	no	—
321	C₂×D₄	—	8	4	no	—
322	C₂×D₄	—	8	4	no	—
323	C₂×D₄	—	8	4	no	—
324	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
325	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
326	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
332	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
333	SD₁₆	—	4	8	no	—
334	SD₁₆	—	4	8	no	—
335	C₂×C₈	—	2	4	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	4	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	4	no	—
343	C₄⋊C₄	—	4	2	no	—
344	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
345	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
346	C₂²⋊C₄	—	2	2	no	—
347	C₂²⋊C₄	—	2	2	no	—
348	C₂²⋊C₄	—	2	4	no	—
349	C₂²⋊C₄	—	2	4	no	—
350	C₂²⋊C₄	—	2	2	no	—
351	C₂²⋊C₄	—	2	2	no	—
352	C₂²⋊C₄	—	2	2	no	—
353	C₂²⋊C₄	—	2	2	no	—
354	C₂²⋊C₄	—	2	2	no	—
355	C₄²	—	2	2	no	—
356	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
357	C₄²	C₂×D₄×C₄₁	1	2	yes	—
358	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
359	C₂³	—	2	2	no	—
360	C₂³	—	2	2	no	—
361	C₂³	—	2	2	no	—
362	C₂³	—	4	4	no	—
363	C₂³	—	8	4	no	—
364	C₂³	—	8	4	no	—
365	C₂³	—	8	2	no	—
366	C₂³	#120×C₄₁	1	1	yes	characteristic
367	Q₈	—	2	4	no	—
368	Q₈	—	4	4	no	—
369	Q₈	—	8	2	no	—
370	D₄	—	2	4	no	—
371	D₄	—	4	2	no	—
372	D₄	—	4	2	no	—
373	D₄	—	4	4	no	—
374	D₄	—	4	4	no	—
375	D₄	—	4	4	no	—
376	D₄	—	8	2	no	—
377	D₄	—	8	4	no	—
378	D₄	—	8	4	no	—
379	D₄	—	8	4	no	—
380	D₄	—	8	4	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	8	2	no	—
389	C₂×C₄	—	8	4	no	—
390	C₂×C₄	—	8	2	no	—
391	C₂×C₄	#120×C₄₁	1	2	yes	—
392	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
393	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
394	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
395	C₈	—	2	4	no	—
396	C₈	—	4	4	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	4	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	4	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	4	2	no	—
404	C₂²	—	4	2	no	—
405	C₂²	—	16	4	no	—
406	C₂²	—	16	4	no	—
407	C₂²	C₄₁×#453	1	2	yes	—
408	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
409	C₄	—	2	2	no	—
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	4	2	no	—
413	C₄	—	4	2	no	—
414	C₄	—	4	2	no	—
415	C₄	—	8	2	no	—
416	C₄	C₄₁×#577	1	4	yes	—
417	C₂	—	2	2	no	—
418	C₂	—	8	2	no	—
419	C₂	—	8	2	no	—
420	C₂	—	8	2	no	—
421	C₂	C₄₁×#3009	1	2	yes	—
422	C₂	C₂×C₄₁×#453	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₁
prime radical	C₄₁×#3543	C₂
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
2. C₄₁×#3238	C₂	semidirect
3. C₂×C₄₁×#492	C₂	semidirect
4. C₄₁×#1631	C₂	semidirect
5. C₄₁×#1630	C₂	semidirect
6. C₄₁×#1629	C₂	semidirect
7. C₄₁×#1555	C₂	semidirect
8. C₄₁×#1494	C₂	semidirect
19. C₂×C₄⋊Q₈×C₄₁	C₂²	semidirect
25. C₄₁×#492	C₂²	semidirect
29. C₄₁×#477	C₂²	semidirect
30. C₄₁×#476	C₂²	semidirect
31. C₄₁×#432	C₂²	semidirect
32. C₂×C₄×C₈×C₄₁	C₂²	semidirect
34. C₄₁×#331	C₂²	semidirect
35. C₄₁×Q₈⋊C₈	C₂²	semidirect
36. C₄₁×D₄⋊C₈	C₂²	semidirect
185. #18683	C₄₁	direct (N × H)
207. #3238	C₂×C₄₁	semidirect
208. C₂×#492	C₂×C₄₁	semidirect
209. #1631	C₂×C₄₁	semidirect
210. #1630	C₂×C₄₁	semidirect
211. #1629	C₂×C₄₁	semidirect
212. #1555	C₂×C₄₁	semidirect
213. #1494	C₂×C₄₁	semidirect
230. C₂×C₄⋊Q₈	C₂²×C₄₁	semidirect
236. #492	C₂²×C₄₁	semidirect
240. #477	C₂²×C₄₁	semidirect
241. #476	C₂²×C₄₁	semidirect
242. #432	C₂²×C₄₁	semidirect
243. C₂×C₄×C₈	C₂²×C₄₁	semidirect
245. #331	C₂²×C₄₁	semidirect
246. Q₈⋊C₈	C₂²×C₄₁	semidirect
247. D₄⋊C₈	C₂²×C₄₁	semidirect
248. C₄₁	#18683	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×#3543	2
C₄₁×#3238	2
C₂×C₄₁×#492	2
C₄₁×#1631	2
C₄₁×#1630	2
C₄₁×#1629	2
C₄₁×#1555	2
C₄₁×#1494	2
#18683	41

Subgroups — C41×#18683 #23794884

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#18683 #23794884