Subgroups — C₄₁×#32677 #23808878

Order 10496.

758 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	C₄₁×#2592	C₂	1	2	yes	maximal, complemented
2	C₄₁×#2056	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#2054	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2015	C₂	1	2	yes	maximal, complemented
5	C₄₁×#2012	C₂	1	2	yes	maximal
6	C₄₁×#1985	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1973	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1928	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1925	C₂	1	2	yes	maximal, complemented
10	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
11	C₂²×SD₁₆×C₄₁	C₂²	1	2	yes	—
12	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×#124×C₄₁	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×#107×C₄₁	C₂²	1	2	yes	—
16	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
17	C₂×#103×C₄₁	C₂²	1	2	yes	—
18	C₂×#103×C₄₁	C₂²	1	2	yes	—
19	C₂×#102×C₄₁	C₂²	1	2	yes	—
20	C₂×#102×C₄₁	C₂²	1	2	yes	—
21	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
22	C₄₁×#397	—	2	2	no	—
23	C₄₁×#393	—	2	2	no	—
24	C₄₁×#391	C₂²	1	2	yes	—
25	C₄₁×#391	C₂²	1	2	yes	—
26	C₄₁×#390	C₂²	1	2	yes	—
27	C₄₁×#390	C₂²	1	2	yes	—
28	C₄₁×#388	—	2	2	no	—
29	C₄₁×#388	—	2	2	no	—
30	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
31	C₄₁×#340	C₂²	1	1	yes	characteristic
32	C₄₁×#340	C₂²	1	1	yes	characteristic
33	C₄₁×#336	C₂²	1	2	yes	—
34	C₄₁×#336	C₂²	1	2	yes	—
35	C₂²×Q₈×C₄₁	D₄	1	1	yes	characteristic
36	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
37	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
38	C₂×Q₁₆×C₄₁	—	4	2	no	—
39	C₂×Q₁₆×C₄₁	—	4	1	no	—
40	C₂×SD₁₆×C₄₁	—	2	4	no	—
41	C₂×SD₁₆×C₄₁	—	4	2	no	—
42	C₂×SD₁₆×C₄₁	—	4	2	no	—
43	C₂×D₈×C₄₁	—	4	2	no	—
44	C₂×D₈×C₄₁	—	4	1	no	—
45	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
48	#124×C₄₁	—	4	2	no	—
49	#124×C₄₁	—	4	2	no	—
50	C₄×Q₈×C₄₁	—	4	1	no	—
51	C₄×Q₈×C₄₁	—	4	1	no	—
52	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
54	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
56	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
62	C₂×C₄²×C₄₁	—	2	2	no	—
63	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
64	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
65	#107×C₄₁	—	4	2	no	—
66	C₄⋊C₈×C₄₁	—	4	1	no	—
67	#103×C₄₁	—	2	4	no	—
68	#103×C₄₁	—	4	2	no	—
69	#102×C₄₁	—	2	4	no	—
70	#102×C₄₁	—	4	2	no	—
71	#97×C₄₁	—	4	1	no	—
72	#95×C₄₁	—	2	2	no	—
73	#95×C₄₁	—	2	2	no	—
74	#95×C₄₁	—	2	2	no	—
75	#95×C₄₁	—	2	2	no	—
76	#95×C₄₁	—	2	2	no	—
77	C₂⁴×C₄₁	—	2	2	no	—
78	C₂×Q₈×C₄₁	—	2	2	no	—
79	C₂×Q₈×C₄₁	—	2	2	no	—
80	C₂×Q₈×C₄₁	—	2	2	no	—
81	C₂×Q₈×C₄₁	—	2	2	no	—
82	C₂×Q₈×C₄₁	—	2	2	no	—
83	C₂×Q₈×C₄₁	—	2	2	no	—
84	C₂×Q₈×C₄₁	—	4	1	no	—
85	C₂×Q₈×C₄₁	—	4	2	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	—	2	2	no	—
91	C₂×D₄×C₄₁	—	2	2	no	—
92	C₂²×C₄×C₄₁	—	2	2	no	—
93	C₂²×C₄×C₄₁	—	2	2	no	—
94	C₂²×C₄×C₄₁	—	2	2	no	—
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	1	yes	characteristic
98	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
100	Q₁₆×C₄₁	—	4	4	no	—
101	SD₁₆×C₄₁	—	4	8	no	—
102	D₈×C₄₁	—	4	4	no	—
103	C₂×C₈×C₄₁	—	2	2	no	—
104	C₂×C₈×C₄₁	—	2	2	no	—
105	C₂×C₈×C₄₁	—	2	2	no	—
106	C₂×C₈×C₄₁	—	2	2	no	—
107	C₂×C₈×C₄₁	—	2	1	no	—
108	C₂×C₈×C₄₁	—	2	1	no	—
109	C₂×C₈×C₄₁	#41	1	4	yes	—
110	C₄⋊C₄×C₄₁	—	2	2	no	—
111	C₄⋊C₄×C₄₁	—	2	2	no	—
112	C₄⋊C₄×C₄₁	—	2	2	no	—
113	C₄⋊C₄×C₄₁	—	2	2	no	—
114	C₄⋊C₄×C₄₁	—	4	1	no	—
115	C₄⋊C₄×C₄₁	—	4	2	no	—
116	C₂²⋊C₄×C₄₁	—	4	4	no	—
117	C₂²⋊C₄×C₄₁	—	4	4	no	—
118	C₂²⋊C₄×C₄₁	—	4	4	no	—
119	C₂²⋊C₄×C₄₁	—	4	4	no	—
120	C₂²⋊C₄×C₄₁	—	8	2	no	—
121	C₂²⋊C₄×C₄₁	—	8	2	no	—
122	C₄²×C₄₁	—	2	1	no	—
123	C₄²×C₄₁	—	2	1	no	—
124	C₄²×C₄₁	—	2	2	no	—
125	C₄²×C₄₁	—	2	2	no	—
126	C₄²×C₄₁	—	8	2	no	—
127	C₂³×C₄₁	—	4	2	no	—
128	C₂³×C₄₁	—	4	2	no	—
129	C₂³×C₄₁	—	4	2	no	—
130	C₂³×C₄₁	—	4	2	no	—
131	C₂³×C₄₁	—	4	2	no	—
132	C₂³×C₄₁	—	4	2	no	—
133	C₂³×C₄₁	—	4	2	no	—
134	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
135	Q₈×C₄₁	—	4	4	no	—
136	Q₈×C₄₁	—	4	2	no	—
137	Q₈×C₄₁	—	4	2	no	—
138	Q₈×C₄₁	—	4	2	no	—
139	Q₈×C₄₁	—	4	2	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	C₂×C₄×C₄₁	—	2	2	no	—
145	C₂×C₄×C₄₁	—	2	2	no	—
146	C₂×C₄×C₄₁	—	2	1	no	—
147	C₂×C₄×C₄₁	—	2	1	no	—
148	C₂×C₄×C₄₁	—	2	2	no	—
149	C₂×C₄×C₄₁	—	2	2	no	—
150	C₂×C₄×C₄₁	—	2	2	no	—
151	C₂×C₄×C₄₁	—	2	2	no	—
152	C₂×C₄×C₄₁	—	2	1	no	—
153	C₂×C₄×C₄₁	—	2	1	no	—
154	C₂×C₄×C₄₁	—	2	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	—	4	2	no	—
159	C₂×C₄×C₄₁	—	4	2	no	—
160	C₂×C₄×C₄₁	—	4	2	no	—
161	C₂×C₄×C₄₁	—	4	2	no	—
162	C₂×C₄×C₄₁	—	4	2	no	—
163	C₂×C₄×C₄₁	—	4	2	no	—
164	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
165	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
166	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
167	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
168	C₈×C₄₁	—	2	4	no	—
169	C₈×C₄₁	—	4	1	no	—
170	C₈×C₄₁	—	4	1	no	—
171	#32677	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂²×C₄₁	—	8	2	no	—
173	C₂²×C₄₁	—	8	2	no	—
174	C₂²×C₄₁	—	8	2	no	—
175	C₂²×C₄₁	—	8	2	no	—
176	C₂²×C₄₁	—	8	2	no	—
177	C₂²×C₄₁	—	8	2	no	—
178	C₂²×C₄₁	—	8	2	no	—
179	C₂²×C₄₁	#534	1	1	yes	characteristic
180	C₂²×C₄₁	#550	1	2	yes	—
181	C₂²×C₄₁	#575	1	2	yes	—
182	C₂²×C₄₁	#576	1	1	yes	characteristic
183	C₂²×C₄₁	#578	1	1	yes	characteristic
184	C₄×C₄₁	—	4	2	no	—
185	C₄×C₄₁	—	4	1	no	—
186	C₄×C₄₁	—	4	2	no	—
187	C₄×C₄₁	—	4	1	no	—
188	C₄×C₄₁	—	8	2	no	—
189	C₄×C₄₁	—	8	2	no	—
190	C₄×C₄₁	—	8	2	no	—
191	C₄×C₄₁	#538	1	2	yes	—
192	C₄×C₄₁	#555	1	1	yes	characteristic
193	C₄×C₄₁	H(3,𝔽₄)	1	1	yes	characteristic
194	#2592	C₂×C₄₁	1	2	yes	complemented
195	#2056	C₂×C₄₁	1	1	yes	characteristic, complemented
196	#2054	C₂×C₄₁	1	1	yes	characteristic
197	#2015	C₂×C₄₁	1	2	yes	complemented
198	#2012	C₂×C₄₁	1	2	yes	—
199	#1985	C₂×C₄₁	1	1	yes	characteristic, complemented
200	#1973	C₂×C₄₁	1	2	yes	complemented
201	#1928	C₂×C₄₁	1	2	yes	complemented
202	#1925	C₂×C₄₁	1	2	yes	complemented
203	C₂×C₄₁	—	16	2	no	—
204	C₂×C₄₁	#2733	1	1	yes	characteristic
205	C₂×C₄₁	#3197	1	1	yes	characteristic
206	C₂×C₄₁	#3203	1	1	yes	characteristic
207	C₂×C₄₁	#3402	1	2	yes	—
208	C₂×C₄₁	#3403	1	2	yes	—
209	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
210	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	—
211	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
212	C₂×#124	C₂²×C₄₁	1	2	yes	—
213	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
214	C₂×#107	C₂²×C₄₁	1	2	yes	—
215	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
216	C₂×#103	C₂²×C₄₁	1	2	yes	—
217	C₂×#103	C₂²×C₄₁	1	2	yes	—
218	C₂×#102	C₂²×C₄₁	1	2	yes	—
219	C₂×#102	C₂²×C₄₁	1	2	yes	—
220	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
221	#397	—	2	2	no	—
222	#393	—	2	2	no	—
223	#391	C₂²×C₄₁	1	2	yes	—
224	#391	C₂²×C₄₁	1	2	yes	—
225	#390	C₂²×C₄₁	1	2	yes	—
226	#390	C₂²×C₄₁	1	2	yes	—
227	#388	—	2	2	no	—
228	#388	—	2	2	no	—
229	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
230	#340	C₂²×C₄₁	1	1	yes	characteristic
231	#340	C₂²×C₄₁	1	1	yes	characteristic
232	#336	C₂²×C₄₁	1	2	yes	—
233	#336	C₂²×C₄₁	1	2	yes	—
234	C₄₁	#32677	1	1	yes	characteristic, direct product factor, Sylow
235	C₂²×Q₈	D₄×C₄₁	1	1	yes	characteristic
236	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
237	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
238	C₂×Q₁₆	—	4	2	no	—
239	C₂×Q₁₆	—	4	1	no	—
240	C₂×SD₁₆	—	2	4	no	—
241	C₂×SD₁₆	—	4	2	no	—
242	C₂×SD₁₆	—	4	2	no	—
243	C₂×D₈	—	4	2	no	—
244	C₂×D₈	—	4	1	no	—
245	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
246	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
247	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
248	#124	—	4	2	no	—
249	#124	—	4	2	no	—
250	C₄×Q₈	—	4	1	no	—
251	C₄×Q₈	—	4	1	no	—
252	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
253	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
254	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
255	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
256	C₂×C₂²⋊C₄	—	2	2	no	—
257	C₂×C₂²⋊C₄	—	2	2	no	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₄²	—	2	2	no	—
263	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
264	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
265	#107	—	4	2	no	—
266	C₄⋊C₈	—	4	1	no	—
267	#103	—	2	4	no	—
268	#103	—	4	2	no	—
269	#102	—	2	4	no	—
270	#102	—	4	2	no	—
271	#97	—	4	1	no	—
272	#95	—	2	2	no	—
273	#95	—	2	2	no	—
274	#95	—	2	2	no	—
275	#95	—	2	2	no	—
276	#95	—	2	2	no	—
277	C₂⁴	—	2	2	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	2	2	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	—	4	1	no	—
285	C₂×Q₈	—	4	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
297	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
299	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
300	Q₁₆	—	4	4	no	—
301	SD₁₆	—	4	8	no	—
302	D₈	—	4	4	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	#41×C₄₁	1	4	yes	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	4	1	no	—
315	C₄⋊C₄	—	4	2	no	—
316	C₂²⋊C₄	—	4	4	no	—
317	C₂²⋊C₄	—	4	4	no	—
318	C₂²⋊C₄	—	4	4	no	—
319	C₂²⋊C₄	—	4	4	no	—
320	C₂²⋊C₄	—	8	2	no	—
321	C₂²⋊C₄	—	8	2	no	—
322	C₄²	—	2	1	no	—
323	C₄²	—	2	1	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	8	2	no	—
327	C₂³	—	4	2	no	—
328	C₂³	—	4	2	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	2	no	—
334	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
335	Q₈	—	4	4	no	—
336	Q₈	—	4	2	no	—
337	Q₈	—	4	2	no	—
338	Q₈	—	4	2	no	—
339	Q₈	—	4	2	no	—
340	D₄	—	4	2	no	—
341	D₄	—	4	2	no	—
342	D₄	—	4	2	no	—
343	D₄	—	4	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
365	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
366	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
367	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
368	C₈	—	2	4	no	—
369	C₈	—	4	1	no	—
370	C₈	—	4	1	no	—
371	C₂²	—	8	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	2	no	—
377	C₂²	—	8	2	no	—
378	C₂²	C₄₁×#534	1	1	yes	characteristic
379	C₂²	C₄₁×#550	1	2	yes	—
380	C₂²	C₄₁×#575	1	2	yes	—
381	C₂²	C₄₁×#576	1	1	yes	characteristic
382	C₂²	C₄₁×#578	1	1	yes	characteristic
383	C₄	—	4	2	no	—
384	C₄	—	4	1	no	—
385	C₄	—	4	2	no	—
386	C₄	—	4	1	no	—
387	C₄	—	8	2	no	—
388	C₄	—	8	2	no	—
389	C₄	—	8	2	no	—
390	C₄	C₄₁×#538	1	2	yes	—
391	C₄	C₄₁×#555	1	1	yes	characteristic
392	C₄	C₄₁×H(3,𝔽₄)	1	1	yes	characteristic
393	C₂	—	16	2	no	—
394	C₂	C₄₁×#2733	1	1	yes	characteristic
395	C₂	C₄₁×#3197	1	1	yes	characteristic
396	C₂	C₄₁×#3203	1	1	yes	characteristic
397	C₂	C₄₁×#3402	1	2	yes	—
398	C₂	C₄₁×#3403	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂²×D₈×C₄₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂×C₄×Q₈×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#2592	C₂	semidirect
2. C₄₁×#2056	C₂	semidirect
4. C₄₁×#2015	C₂	semidirect
6. C₄₁×#1985	C₂	semidirect
7. C₄₁×#1973	C₂	semidirect
8. C₄₁×#1928	C₂	semidirect
9. C₄₁×#1925	C₂	semidirect
171. #32677	C₄₁	direct (N × H)
194. #2592	C₂×C₄₁	semidirect
195. #2056	C₂×C₄₁	semidirect
197. #2015	C₂×C₄₁	semidirect
199. #1985	C₂×C₄₁	semidirect
200. #1973	C₂×C₄₁	semidirect
201. #1928	C₂×C₄₁	semidirect
202. #1925	C₂×C₄₁	semidirect
234. C₄₁	#32677	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×#2592	2
C₄₁×#2056	2
C₄₁×#2054	2
C₄₁×#2015	2
C₄₁×#2012	2
C₄₁×#1985	2
C₄₁×#1973	2
C₄₁×#1928	2
C₄₁×#1925	2
#32677	41

Subgroups — C41×#32677 #23808878

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#32677 #23808878