Subgroups — C₄₁×#19191 #23795392

Order 10496.

662 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3227	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#3206	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₁×#498	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2931	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#1691	C₂	1	4	yes	maximal, complemented
6	C₄₁×#1671	C₂	1	4	yes	maximal, complemented
7	C₄₁×#1564	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1549	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1548	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#131×C₄₁	—	2	1	no	—
11	C₄₁×#532	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
14	C₄₁×#498	—	2	1	no	—
15	C₄₁×#498	—	2	1	no	—
16	C₄₁×#498	—	2	1	no	—
17	C₄₁×#498	C₂²	1	2	yes	—
18	C₄₁×#498	C₂²	1	2	yes	—
19	C₄₁×#492	—	2	1	no	—
20	C₄₁×#487	—	2	1	no	—
21	C₄₁×#486	—	2	1	no	—
22	C₄₁×#481	—	2	2	no	—
23	C₄₁×#476	C₂²	1	4	yes	—
24	C₄₁×#461	C₂²	1	4	yes	—
25	C₄₁×#448	—	2	2	no	—
26	C₄₁×#436	—	2	1	no	—
27	C₄₁×#436	C₂²	1	2	yes	—
28	C₈×D₄×C₄₁	—	2	1	no	—
29	C₈×D₄×C₄₁	C₂²	1	2	yes	—
30	C₄₁×#431	C₂²	1	1	yes	characteristic
31	C₄₁×#431	C₂²	1	1	yes	characteristic
32	C₂×#106×C₄₁	—	2	1	no	—
33	C₂×#106×C₄₁	—	2	1	no	—
34	C₄₁×#423	C₂²	1	1	yes	characteristic
35	C₄₁×#408	—	2	1	no	—
36	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
37	C₄₁×#335	C₂²	1	2	yes	—
38	C₄₁×#334	C₂²	1	2	yes	—
39	C₄₁×#333	C₂²	1	4	yes	—
40	C₄₁×#332	C₂²	1	4	yes	—
41	C₂×#41×C₄₁	—	2	1	no	—
42	C₂²×Q₈×C₄₁	—	2	1	no	—
43	C₂²×Q₈×C₄₁	—	2	1	no	—
44	C₂×SD₁₆×C₄₁	—	2	4	no	—
45	#131×C₄₁	—	4	4	no	—
46	C₂×M₁₆×C₄₁	—	2	1	no	—
47	C₂×M₁₆×C₄₁	—	2	2	no	—
48	C₂²×C₈×C₄₁	—	2	2	no	—
49	C₂²×C₈×C₄₁	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₄₁	D₄	1	1	yes	characteristic
51	C₄⋊Q₈×C₄₁	—	2	1	no	—
52	C₄⋊Q₈×C₄₁	—	2	1	no	—
53	C₄⋊Q₈×C₄₁	—	2	1	no	—
54	C₄⋊Q₈×C₄₁	—	2	1	no	—
55	C₄⋊Q₈×C₄₁	—	2	1	no	—
56	C₄⋊Q₈×C₄₁	—	2	1	no	—
57	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
58	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
59	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
60	#127×C₄₁	D₄	1	1	yes	characteristic
61	#124×C₄₁	—	2	1	no	—
62	#121×C₄₁	—	2	1	no	—
63	#121×C₄₁	D₄	1	2	yes	—
64	C₄×D₄×C₄₁	—	2	1	no	—
65	C₄×D₄×C₄₁	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
68	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
69	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
70	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
71	#106×C₄₁	—	2	2	no	—
72	#106×C₄₁	—	2	2	no	—
73	#106×C₄₁	—	2	2	no	—
74	#106×C₄₁	—	2	2	no	—
75	#106×C₄₁	—	2	4	no	—
76	C₄⋊C₈×C₄₁	—	2	1	no	—
77	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
78	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
79	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
80	#103×C₄₁	—	2	4	no	—
81	#102×C₄₁	—	2	4	no	—
82	C₂²⋊C₈×C₄₁	—	2	1	no	—
83	C₂²⋊C₈×C₄₁	—	2	1	no	—
84	C₂²⋊C₈×C₄₁	—	2	2	no	—
85	C₂²⋊C₈×C₄₁	—	2	2	no	—
86	C₄×C₈×C₄₁	—	2	1	no	—
87	C₄×C₈×C₄₁	—	2	1	no	—
88	C₄×C₈×C₄₁	D₄	1	1	yes	characteristic
89	C₄×C₈×C₄₁	D₄	1	1	yes	characteristic
90	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
92	#41×C₄₁	—	4	2	no	—
93	#41×C₄₁	—	4	2	no	—
94	C₂×Q₈×C₄₁	—	2	1	no	—
95	C₂×Q₈×C₄₁	—	2	2	no	—
96	C₂×Q₈×C₄₁	—	2	2	no	—
97	C₂×Q₈×C₄₁	—	4	1	no	—
98	C₂×Q₈×C₄₁	—	4	1	no	—
99	C₂×Q₈×C₄₁	—	8	2	no	—
100	C₂×Q₈×C₄₁	—	8	2	no	—
101	C₂×D₄×C₄₁	—	2	2	no	—
102	C₂×D₄×C₄₁	—	2	1	no	—
103	C₂×D₄×C₄₁	—	2	1	no	—
104	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₁	—	2	2	no	—
106	C₂²×C₄×C₄₁	—	4	1	no	—
107	C₂²×C₄×C₄₁	—	4	1	no	—
108	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
111	SD₁₆×C₄₁	—	8	4	no	—
112	M₁₆×C₄₁	—	4	2	no	—
113	M₁₆×C₄₁	—	4	4	no	—
114	C₂×C₈×C₄₁	—	2	2	no	—
115	C₂×C₈×C₄₁	—	2	2	no	—
116	C₂×C₈×C₄₁	—	2	2	no	—
117	C₂×C₈×C₄₁	—	2	2	no	—
118	C₂×C₈×C₄₁	—	4	4	no	—
119	C₂×C₈×C₄₁	SD₁₆	1	4	yes	complemented
120	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
124	C₄⋊C₄×C₄₁	—	2	1	no	—
125	C₄⋊C₄×C₄₁	—	2	2	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	—	4	1	no	—
130	C₄⋊C₄×C₄₁	—	4	1	no	—
131	C₄⋊C₄×C₄₁	—	4	1	no	—
132	C₄⋊C₄×C₄₁	—	4	1	no	—
133	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
134	C₂²⋊C₄×C₄₁	—	2	2	no	—
135	C₂²⋊C₄×C₄₁	—	2	2	no	—
136	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₄₁	#41	1	1	yes	characteristic
139	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
140	C₂³×C₄₁	—	2	2	no	—
141	C₂³×C₄₁	#121	1	1	yes	characteristic
142	Q₈×C₄₁	—	4	2	no	—
143	Q₈×C₄₁	—	4	4	no	—
144	Q₈×C₄₁	—	8	2	no	—
145	Q₈×C₄₁	—	8	2	no	—
146	Q₈×C₄₁	—	8	2	no	—
147	D₄×C₄₁	—	2	4	no	—
148	D₄×C₄₁	—	4	4	no	—
149	D₄×C₄₁	—	4	2	no	—
150	D₄×C₄₁	—	4	2	no	—
151	C₂×C₄×C₄₁	—	2	2	no	—
152	C₂×C₄×C₄₁	—	2	2	no	—
153	C₂×C₄×C₄₁	—	2	2	no	—
154	C₂×C₄×C₄₁	—	4	2	no	—
155	C₂×C₄×C₄₁	—	4	2	no	—
156	C₂×C₄×C₄₁	—	4	2	no	—
157	C₂×C₄×C₄₁	—	4	2	no	—
158	C₂×C₄×C₄₁	—	8	2	no	—
159	C₂×C₄×C₄₁	—	8	2	no	—
160	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
161	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
162	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
163	C₂×C₄×C₄₁	C₂×SD₁₆	1	2	yes	—
164	C₂×C₄×C₄₁	#137	1	2	yes	—
165	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
168	C₈×C₄₁	—	2	1	no	—
169	C₈×C₄₁	—	2	1	no	—
170	C₈×C₄₁	—	4	2	no	—
171	C₈×C₄₁	—	4	2	no	—
172	C₈×C₄₁	—	4	2	no	—
173	C₈×C₄₁	C₂×SD₁₆	1	2	yes	—
174	C₈×C₄₁	C₂×SD₁₆	1	2	yes	—
175	#19191	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₂²×C₄₁	—	2	1	no	—
177	C₂²×C₄₁	—	2	1	no	—
178	C₂²×C₄₁	—	4	2	no	—
179	C₂²×C₄₁	—	4	2	no	—
180	C₂²×C₄₁	—	4	2	no	—
181	C₂²×C₄₁	#461	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	—	4	2	no	—
186	C₄×C₄₁	—	8	2	no	—
187	C₄×C₄₁	—	8	2	no	—
188	C₄×C₄₁	#461	1	2	yes	—
189	C₄×C₄₁	#471	1	2	yes	—
190	C₄×C₄₁	C₂²×SD₁₆	1	1	yes	characteristic
191	C₄×C₄₁	C₂×#137	1	1	yes	characteristic
192	C₄×C₄₁	#577	1	2	yes	—
193	#3227	C₂×C₄₁	1	1	yes	characteristic
194	#3206	C₂×C₄₁	1	1	yes	characteristic
195	C₂×#498	C₂×C₄₁	1	1	yes	characteristic, complemented
196	#2931	C₂×C₄₁	1	1	yes	characteristic
197	#1691	C₂×C₄₁	1	4	yes	complemented
198	#1671	C₂×C₄₁	1	4	yes	complemented
199	#1564	C₂×C₄₁	1	1	yes	characteristic, complemented
200	#1549	C₂×C₄₁	1	1	yes	characteristic, complemented
201	#1548	C₂×C₄₁	1	1	yes	characteristic, complemented
202	C₂×C₄₁	—	2	2	no	—
203	C₂×C₄₁	—	8	2	no	—
204	C₂×C₄₁	C₂×#461	1	1	yes	characteristic
205	C₂×C₄₁	#3057	1	1	yes	characteristic
206	C₂×C₄₁	C₂×#471	1	1	yes	characteristic
207	C₂×#131	—	2	1	no	—
208	#532	C₂²×C₄₁	1	1	yes	characteristic
209	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
210	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
211	#498	—	2	1	no	—
212	#498	—	2	1	no	—
213	#498	—	2	1	no	—
214	#498	C₂²×C₄₁	1	2	yes	—
215	#498	C₂²×C₄₁	1	2	yes	—
216	#492	—	2	1	no	—
217	#487	—	2	1	no	—
218	#486	—	2	1	no	—
219	#481	—	2	2	no	—
220	#476	C₂²×C₄₁	1	4	yes	—
221	#461	C₂²×C₄₁	1	4	yes	—
222	#448	—	2	2	no	—
223	#436	—	2	1	no	—
224	#436	C₂²×C₄₁	1	2	yes	—
225	C₈×D₄	—	2	1	no	—
226	C₈×D₄	C₂²×C₄₁	1	2	yes	—
227	#431	C₂²×C₄₁	1	1	yes	characteristic
228	#431	C₂²×C₄₁	1	1	yes	characteristic
229	C₂×#106	—	2	1	no	—
230	C₂×#106	—	2	1	no	—
231	#423	C₂²×C₄₁	1	1	yes	characteristic
232	#408	—	2	1	no	—
233	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
234	#335	C₂²×C₄₁	1	2	yes	—
235	#334	C₂²×C₄₁	1	2	yes	—
236	#333	C₂²×C₄₁	1	4	yes	—
237	#332	C₂²×C₄₁	1	4	yes	—
238	C₄₁	#19191	1	1	yes	characteristic, direct product factor, Sylow
239	C₂×#41	—	2	1	no	—
240	C₂²×Q₈	—	2	1	no	—
241	C₂²×Q₈	—	2	1	no	—
242	C₂×SD₁₆	—	2	4	no	—
243	#131	—	4	4	no	—
244	C₂×M₁₆	—	2	1	no	—
245	C₂×M₁₆	—	2	2	no	—
246	C₂²×C₈	—	2	2	no	—
247	C₂²×C₈	D₄×C₄₁	1	1	yes	characteristic
248	C₂²×C₈	D₄×C₄₁	1	1	yes	characteristic
249	C₄⋊Q₈	—	2	1	no	—
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	—	2	1	no	—
252	C₄⋊Q₈	—	2	1	no	—
253	C₄⋊Q₈	—	2	1	no	—
254	C₄⋊Q₈	—	2	1	no	—
255	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
256	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
257	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
258	#127	D₄×C₄₁	1	1	yes	characteristic
259	#124	—	2	1	no	—
260	#121	—	2	1	no	—
261	#121	D₄×C₄₁	1	2	yes	—
262	C₄×D₄	—	2	1	no	—
263	C₄×D₄	C₂³×C₄₁	1	2	yes	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
269	#106	—	2	2	no	—
270	#106	—	2	2	no	—
271	#106	—	2	2	no	—
272	#106	—	2	2	no	—
273	#106	—	2	4	no	—
274	C₄⋊C₈	—	2	1	no	—
275	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
276	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
277	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
278	#103	—	2	4	no	—
279	#102	—	2	4	no	—
280	C₂²⋊C₈	—	2	1	no	—
281	C₂²⋊C₈	—	2	1	no	—
282	C₂²⋊C₈	—	2	2	no	—
283	C₂²⋊C₈	—	2	2	no	—
284	C₄×C₈	—	2	1	no	—
285	C₄×C₈	—	2	1	no	—
286	C₄×C₈	D₄×C₄₁	1	1	yes	characteristic
287	C₄×C₈	D₄×C₄₁	1	1	yes	characteristic
288	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
289	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
290	#41	—	4	2	no	—
291	#41	—	4	2	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	4	1	no	—
296	C₂×Q₈	—	4	1	no	—
297	C₂×Q₈	—	8	2	no	—
298	C₂×Q₈	—	8	2	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
308	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
309	SD₁₆	—	8	4	no	—
310	M₁₆	—	4	2	no	—
311	M₁₆	—	4	4	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	4	4	no	—
317	C₂×C₈	SD₁₆×C₄₁	1	4	yes	complemented
318	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
319	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
320	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
321	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₄⋊C₄	—	4	1	no	—
330	C₄⋊C₄	—	4	1	no	—
331	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
332	C₂²⋊C₄	—	2	2	no	—
333	C₂²⋊C₄	—	2	2	no	—
334	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
335	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
336	C₄²	#41×C₄₁	1	1	yes	characteristic
337	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
338	C₂³	—	2	2	no	—
339	C₂³	#121×C₄₁	1	1	yes	characteristic
340	Q₈	—	4	2	no	—
341	Q₈	—	4	4	no	—
342	Q₈	—	8	2	no	—
343	Q₈	—	8	2	no	—
344	Q₈	—	8	2	no	—
345	D₄	—	2	4	no	—
346	D₄	—	4	4	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	8	2	no	—
357	C₂×C₄	—	8	2	no	—
358	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
359	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
360	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
361	C₂×C₄	C₂×SD₁₆×C₄₁	1	2	yes	—
362	C₂×C₄	#137×C₄₁	1	2	yes	—
363	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
364	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
365	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
366	C₈	—	2	1	no	—
367	C₈	—	2	1	no	—
368	C₈	—	4	2	no	—
369	C₈	—	4	2	no	—
370	C₈	—	4	2	no	—
371	C₈	C₂×SD₁₆×C₄₁	1	2	yes	—
372	C₈	C₂×SD₁₆×C₄₁	1	2	yes	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	4	2	no	—
376	C₂²	—	4	2	no	—
377	C₂²	—	4	2	no	—
378	C₂²	C₄₁×#461	1	2	yes	—
379	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	4	2	no	—
383	C₄	—	8	2	no	—
384	C₄	—	8	2	no	—
385	C₄	C₄₁×#461	1	2	yes	—
386	C₄	C₄₁×#471	1	2	yes	—
387	C₄	C₂²×SD₁₆×C₄₁	1	1	yes	characteristic
388	C₄	C₂×#137×C₄₁	1	1	yes	characteristic
389	C₄	C₄₁×#577	1	2	yes	—
390	C₂	—	2	2	no	—
391	C₂	—	8	2	no	—
392	C₂	C₂×C₄₁×#461	1	1	yes	characteristic
393	C₂	C₄₁×#3057	1	1	yes	characteristic
394	C₂	C₂×C₄₁×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₁
prime radical	C₄₁×#532	C₂²
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
3. C₂×C₄₁×#498	C₂	semidirect
5. C₄₁×#1691	C₂	semidirect
6. C₄₁×#1671	C₂	semidirect
7. C₄₁×#1564	C₂	semidirect
8. C₄₁×#1549	C₂	semidirect
9. C₄₁×#1548	C₂	semidirect
119. C₂×C₈×C₄₁	SD₁₆	semidirect
175. #19191	C₄₁	direct (N × H)
195. C₂×#498	C₂×C₄₁	semidirect
197. #1691	C₂×C₄₁	semidirect
198. #1671	C₂×C₄₁	semidirect
199. #1564	C₂×C₄₁	semidirect
200. #1549	C₂×C₄₁	semidirect
201. #1548	C₂×C₄₁	semidirect
238. C₄₁	#19191	direct (N × H)
317. C₂×C₈	SD₁₆×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3227	2
C₄₁×#3206	2
C₂×C₄₁×#498	2
C₄₁×#2931	2
C₄₁×#1691	2
C₄₁×#1671	2
C₄₁×#1564	2
C₄₁×#1549	2
C₄₁×#1548	2
#19191	41

Subgroups — C41×#19191 #23795392

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#19191 #23795392