Subgroups — C₄₁×#23172 #23799373

Order 10496.

626 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3162	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2962	C₂	1	2	yes	maximal
3	C₄₁×#1986	C₂	1	2	yes	maximal
4	C₄₁×#1946	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#1945	C₂	1	1	yes	maximal, characteristic
6	C₄₁×#1922	C₂	1	2	yes	maximal
7	C₄₁×#1922	C₂	1	2	yes	maximal
8	C₄₁×#1778	C₂	1	1	yes	maximal, characteristic
9	C₄₁×#1773	C₂	1	1	yes	maximal, characteristic
10	C₄₁×#1772	C₂	1	1	yes	maximal, characteristic
11	C₄₁×#1771	C₂	1	1	yes	maximal, characteristic
12	C₄₁×#533	C₂²	1	2	yes	—
13	C₄₁×#501	C₄	1	2	yes	complemented
14	C₄₁×#501	C₄	1	2	yes	complemented
15	C₄₁×#501	C₄	1	2	yes	complemented
16	C₄₁×#501	C₄	1	2	yes	complemented
17	C₄₁×#446	—	2	2	no	—
18	C₄₁×#446	—	2	2	no	—
19	C₄₁×#446	—	2	2	no	—
20	C₈×Q₈×C₄₁	—	2	2	no	—
21	C₂×#108×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×#108×C₄₁	C₂²	1	1	yes	characteristic
23	C₄₁×#427	C₂²	1	1	yes	characteristic
24	C₄₁×#427	C₂²	1	1	yes	characteristic
25	C₄₁×#427	C₂²	1	2	yes	—
26	C₄₁×#424	C₂²	1	2	yes	—
27	C₄₁×#424	C₂²	1	2	yes	—
28	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
29	C₄₁×#405	C₂²	1	2	yes	—
30	C₄₁×#405	C₂²	1	2	yes	—
31	C₄×M₁₆×C₄₁	C₂²	1	2	yes	—
32	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
33	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
36	C₄₁×#341	C₂²	1	2	yes	—
37	C₄₁×#339	C₂²	1	2	yes	—
38	C₄₁×#339	C₂²	1	2	yes	—
39	C₄₁×#339	C₂²	1	2	yes	—
40	C₄₁×#339	C₂²	1	2	yes	—
41	C₄₁×#336	C₂²	1	1	yes	characteristic
42	C₄₁×#336	C₂²	1	1	yes	characteristic
43	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
44	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
45	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
49	C₄⋊Q₈×C₄₁	C₂×C₄	1	2	yes	—
50	C₄⋊Q₈×C₄₁	C₂×C₄	1	2	yes	—
51	#125×C₄₁	C₂×C₄	1	2	yes	—
52	#125×C₄₁	C₂×C₄	1	2	yes	—
53	C₂²⋊Q₈×C₄₁	—	2	2	no	—
54	C₂²⋊Q₈×C₄₁	—	2	2	no	—
55	C₄×Q₈×C₄₁	—	2	2	no	—
56	C₄×Q₈×C₄₁	—	2	2	no	—
57	#117×C₄₁	C₂³	1	2	yes	—
58	#117×C₄₁	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
60	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
63	#108×C₄₁	—	2	2	no	—
64	#108×C₄₁	Q₈	1	4	yes	complemented
65	#107×C₄₁	C₂×C₄	1	2	yes	—
66	#107×C₄₁	C₂×C₄	1	2	yes	—
67	#107×C₄₁	C₂×C₄	1	1	yes	characteristic
68	#107×C₄₁	C₂×C₄	1	1	yes	characteristic
69	#107×C₄₁	C₂×C₄	1	1	yes	characteristic
70	#107×C₄₁	C₂×C₄	1	1	yes	characteristic
71	#106×C₄₁	C₂×C₄	1	2	yes	—
72	#106×C₄₁	C₂×C₄	1	2	yes	—
73	#106×C₄₁	C₂×C₄	1	2	yes	—
74	#106×C₄₁	C₂×C₄	1	2	yes	—
75	C₄⋊C₈×C₄₁	—	2	2	no	—
76	C₄⋊C₈×C₄₁	—	2	2	no	—
77	C₄⋊C₈×C₄₁	—	2	2	no	—
78	C₄⋊C₈×C₄₁	—	2	2	no	—
79	C₄⋊C₈×C₄₁	D₄	1	2	yes	—
80	C₄⋊C₈×C₄₁	D₄	1	2	yes	—
81	#97×C₄₁	—	2	2	no	—
82	#97×C₄₁	—	2	2	no	—
83	#97×C₄₁	—	2	2	no	—
84	#97×C₄₁	—	2	2	no	—
85	#97×C₄₁	C₂×C₄	1	2	yes	—
86	#97×C₄₁	C₂×C₄	1	2	yes	—
87	C₄×C₈×C₄₁	—	2	2	no	—
88	C₄×C₈×C₄₁	—	2	2	no	—
89	C₄×C₈×C₄₁	—	2	2	no	—
90	C₄×C₈×C₄₁	—	2	2	no	—
91	#95×C₄₁	—	2	1	no	—
92	C₂×Q₈×C₄₁	—	2	2	no	—
93	C₂×Q₈×C₄₁	—	2	2	no	—
94	C₂²×C₄×C₄₁	—	2	1	no	—
95	C₂²×C₄×C₄₁	—	2	1	no	—
96	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
97	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
98	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
99	M₁₆×C₄₁	—	2	2	no	—
100	M₁₆×C₄₁	—	2	2	no	—
101	M₁₆×C₄₁	—	2	2	no	—
102	M₁₆×C₄₁	C₂×Q₈	1	4	yes	—
103	C₂×C₈×C₄₁	—	2	2	no	—
104	C₂×C₈×C₄₁	—	2	1	no	—
105	C₂×C₈×C₄₁	—	2	1	no	—
106	C₂×C₈×C₄₁	—	2	1	no	—
107	C₂×C₈×C₄₁	—	2	1	no	—
108	C₂×C₈×C₄₁	—	2	1	no	—
109	C₂×C₈×C₄₁	—	2	1	no	—
110	C₂×C₈×C₄₁	—	2	2	no	—
111	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
112	C₂×C₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
116	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₄₁	C₂×Q₈	1	2	yes	—
118	C₂×C₈×C₄₁	#41	1	2	yes	—
119	C₄⋊C₄×C₄₁	—	2	2	no	—
120	C₄⋊C₄×C₄₁	—	2	2	no	—
121	C₄⋊C₄×C₄₁	—	2	2	no	—
122	C₄⋊C₄×C₄₁	—	2	2	no	—
123	C₄⋊C₄×C₄₁	—	2	2	no	—
124	C₄⋊C₄×C₄₁	—	2	2	no	—
125	C₄⋊C₄×C₄₁	—	4	2	no	—
126	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
127	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
128	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
129	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
130	C₂²⋊C₄×C₄₁	—	2	2	no	—
131	C₂²⋊C₄×C₄₁	—	2	2	no	—
132	C₄²×C₄₁	—	2	2	no	—
133	C₄²×C₄₁	—	2	2	no	—
134	C₄²×C₄₁	—	2	1	no	—
135	C₄²×C₄₁	—	2	1	no	—
136	C₄²×C₄₁	—	2	1	no	—
137	C₄²×C₄₁	—	2	1	no	—
138	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
139	C₄²×C₄₁	C₂×D₄	1	2	yes	—
140	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
141	Q₈×C₄₁	—	4	4	no	—
142	Q₈×C₄₁	—	8	2	no	—
143	C₂×C₄×C₄₁	—	2	2	no	—
144	C₂×C₄×C₄₁	—	2	2	no	—
145	C₂×C₄×C₄₁	—	2	2	no	—
146	C₂×C₄×C₄₁	—	2	2	no	—
147	C₂×C₄×C₄₁	—	2	2	no	—
148	C₂×C₄×C₄₁	—	4	1	no	—
149	C₂×C₄×C₄₁	—	4	1	no	—
150	C₂×C₄×C₄₁	—	4	1	no	—
151	C₂×C₄×C₄₁	—	4	1	no	—
152	C₂×C₄×C₄₁	—	4	1	no	—
153	C₂×C₄×C₄₁	—	4	1	no	—
154	C₂×C₄×C₄₁	—	4	1	no	—
155	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
156	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
157	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₄₁	C₂²×Q₈	1	1	yes	characteristic
160	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
161	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
162	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
163	C₈×C₄₁	—	2	2	no	—
164	C₈×C₄₁	—	2	1	no	—
165	C₈×C₄₁	—	2	1	no	—
166	C₈×C₄₁	—	2	2	no	—
167	C₈×C₄₁	—	2	4	no	—
168	C₈×C₄₁	—	4	2	no	—
169	C₈×C₄₁	C₄×Q₈	1	2	yes	—
170	C₈×C₄₁	C₄×Q₈	1	2	yes	—
171	#23172	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	C₂×C₄×D₄	1	1	yes	characteristic
175	C₂²×C₄₁	#556	1	1	yes	characteristic
176	C₂²×C₄₁	#557	1	1	yes	characteristic
177	C₄×C₄₁	—	2	2	no	—
178	C₄×C₄₁	—	2	2	no	—
179	C₄×C₄₁	—	4	2	no	—
180	C₄×C₄₁	—	4	2	no	—
181	C₄×C₄₁	—	4	2	no	—
182	C₄×C₄₁	—	4	2	no	—
183	C₄×C₄₁	—	4	2	no	—
184	C₄×C₄₁	—	8	1	no	—
185	C₄×C₄₁	C₂×C₄×Q₈	1	1	yes	characteristic
186	C₄×C₄₁	#519	1	1	yes	characteristic
187	C₄×C₄₁	#547	1	1	yes	characteristic
188	C₄×C₄₁	D₄×Q₈	1	1	yes	characteristic
189	#3162	C₂×C₄₁	1	1	yes	characteristic
190	#2962	C₂×C₄₁	1	2	yes	—
191	#1986	C₂×C₄₁	1	2	yes	—
192	#1946	C₂×C₄₁	1	1	yes	characteristic
193	#1945	C₂×C₄₁	1	1	yes	characteristic
194	#1922	C₂×C₄₁	1	2	yes	—
195	#1922	C₂×C₄₁	1	2	yes	—
196	#1778	C₂×C₄₁	1	1	yes	characteristic
197	#1773	C₂×C₄₁	1	1	yes	characteristic
198	#1772	C₂×C₄₁	1	1	yes	characteristic
199	#1771	C₂×C₄₁	1	1	yes	characteristic
200	C₂×C₄₁	—	2	1	no	—
201	C₂×C₄₁	—	2	1	no	—
202	C₂×C₄₁	#2365	1	1	yes	characteristic
203	C₂×C₄₁	#2955	1	1	yes	characteristic
204	C₂×C₄₁	#2956	1	1	yes	characteristic
205	#533	C₂²×C₄₁	1	2	yes	—
206	#501	C₄×C₄₁	1	2	yes	complemented
207	#501	C₄×C₄₁	1	2	yes	complemented
208	#501	C₄×C₄₁	1	2	yes	complemented
209	#501	C₄×C₄₁	1	2	yes	complemented
210	#446	—	2	2	no	—
211	#446	—	2	2	no	—
212	#446	—	2	2	no	—
213	C₈×Q₈	—	2	2	no	—
214	C₂×#108	C₂²×C₄₁	1	1	yes	characteristic
215	C₂×#108	C₂²×C₄₁	1	1	yes	characteristic
216	#427	C₂²×C₄₁	1	2	yes	—
217	#427	C₂²×C₄₁	1	1	yes	characteristic
218	#427	C₂²×C₄₁	1	1	yes	characteristic
219	#424	C₂²×C₄₁	1	2	yes	—
220	#424	C₂²×C₄₁	1	2	yes	—
221	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
222	#405	C₂²×C₄₁	1	2	yes	—
223	#405	C₂²×C₄₁	1	2	yes	—
224	C₄×M₁₆	C₂²×C₄₁	1	2	yes	—
225	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
226	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
227	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
228	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
229	#341	C₂²×C₄₁	1	2	yes	—
230	#339	C₂²×C₄₁	1	2	yes	—
231	#339	C₂²×C₄₁	1	2	yes	—
232	#339	C₂²×C₄₁	1	2	yes	—
233	#339	C₂²×C₄₁	1	2	yes	—
234	#336	C₂²×C₄₁	1	1	yes	characteristic
235	#336	C₂²×C₄₁	1	1	yes	characteristic
236	C₄₁	#23172	1	1	yes	characteristic, direct product factor, Sylow
237	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
238	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
239	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
240	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
241	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
242	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
243	C₄⋊Q₈	C₂×C₄×C₄₁	1	2	yes	—
244	C₄⋊Q₈	C₂×C₄×C₄₁	1	2	yes	—
245	#125	C₂×C₄×C₄₁	1	2	yes	—
246	#125	C₂×C₄×C₄₁	1	2	yes	—
247	C₂²⋊Q₈	—	2	2	no	—
248	C₂²⋊Q₈	—	2	2	no	—
249	C₄×Q₈	—	2	2	no	—
250	C₄×Q₈	—	2	2	no	—
251	#117	C₂³×C₄₁	1	2	yes	—
252	#117	C₂³×C₄₁	1	2	yes	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
255	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
256	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
257	#108	—	2	2	no	—
258	#108	Q₈×C₄₁	1	4	yes	complemented
259	#107	C₂×C₄×C₄₁	1	2	yes	—
260	#107	C₂×C₄×C₄₁	1	2	yes	—
261	#107	C₂×C₄×C₄₁	1	1	yes	characteristic
262	#107	C₂×C₄×C₄₁	1	1	yes	characteristic
263	#107	C₂×C₄×C₄₁	1	1	yes	characteristic
264	#107	C₂×C₄×C₄₁	1	1	yes	characteristic
265	#106	C₂×C₄×C₄₁	1	2	yes	—
266	#106	C₂×C₄×C₄₁	1	2	yes	—
267	#106	C₂×C₄×C₄₁	1	2	yes	—
268	#106	C₂×C₄×C₄₁	1	2	yes	—
269	C₄⋊C₈	—	2	2	no	—
270	C₄⋊C₈	—	2	2	no	—
271	C₄⋊C₈	—	2	2	no	—
272	C₄⋊C₈	—	2	2	no	—
273	C₄⋊C₈	D₄×C₄₁	1	2	yes	—
274	C₄⋊C₈	D₄×C₄₁	1	2	yes	—
275	#97	—	2	2	no	—
276	#97	—	2	2	no	—
277	#97	—	2	2	no	—
278	#97	—	2	2	no	—
279	#97	C₂×C₄×C₄₁	1	2	yes	—
280	#97	C₂×C₄×C₄₁	1	2	yes	—
281	C₄×C₈	—	2	2	no	—
282	C₄×C₈	—	2	2	no	—
283	C₄×C₈	—	2	2	no	—
284	C₄×C₈	—	2	2	no	—
285	#95	—	2	1	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
291	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
292	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
293	M₁₆	—	2	2	no	—
294	M₁₆	—	2	2	no	—
295	M₁₆	—	2	2	no	—
296	M₁₆	C₂×Q₈×C₄₁	1	4	yes	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
306	C₂×C₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
307	C₂×C₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
308	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
309	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
310	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
311	C₂×C₈	C₂×Q₈×C₄₁	1	2	yes	—
312	C₂×C₈	#41×C₄₁	1	2	yes	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	4	2	no	—
320	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
321	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
322	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
323	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
324	C₂²⋊C₄	—	2	2	no	—
325	C₂²⋊C₄	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	2	1	no	—
329	C₄²	—	2	1	no	—
330	C₄²	—	2	1	no	—
331	C₄²	—	2	1	no	—
332	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
333	C₄²	C₂×D₄×C₄₁	1	2	yes	—
334	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
335	Q₈	—	4	4	no	—
336	Q₈	—	8	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
350	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
351	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
352	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
353	C₂×C₄	C₂²×Q₈×C₄₁	1	1	yes	characteristic
354	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
355	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
356	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
357	C₈	—	2	2	no	—
358	C₈	—	2	1	no	—
359	C₈	—	2	1	no	—
360	C₈	—	2	2	no	—
361	C₈	—	2	4	no	—
362	C₈	—	4	2	no	—
363	C₈	C₄×Q₈×C₄₁	1	2	yes	—
364	C₈	C₄×Q₈×C₄₁	1	2	yes	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
368	C₂²	C₄₁×#556	1	1	yes	characteristic
369	C₂²	C₄₁×#557	1	1	yes	characteristic
370	C₄	—	2	2	no	—
371	C₄	—	2	2	no	—
372	C₄	—	4	2	no	—
373	C₄	—	4	2	no	—
374	C₄	—	4	2	no	—
375	C₄	—	4	2	no	—
376	C₄	—	4	2	no	—
377	C₄	—	8	1	no	—
378	C₄	C₂×C₄×Q₈×C₄₁	1	1	yes	characteristic
379	C₄	C₄₁×#519	1	1	yes	characteristic
380	C₄	C₄₁×#547	1	1	yes	characteristic
381	C₄	D₄×Q₈×C₄₁	1	1	yes	characteristic
382	C₂	—	2	1	no	—
383	C₂	—	2	1	no	—
384	C₂	C₄₁×#2365	1	1	yes	characteristic
385	C₂	C₄₁×#2955	1	1	yes	characteristic
386	C₂	C₄₁×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
socle	C₂²×C₄₁	C₂×C₄×D₄
prime radical	C₂³×C₄₁	C₂×#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁ ◁ C₂×C₄⋊C₈×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
13. C₄₁×#501	C₄	semidirect
14. C₄₁×#501	C₄	semidirect
15. C₄₁×#501	C₄	semidirect
16. C₄₁×#501	C₄	semidirect
64. #108×C₄₁	Q₈	semidirect
171. #23172	C₄₁	direct (N × H)
206. #501	C₄×C₄₁	semidirect
207. #501	C₄×C₄₁	semidirect
208. #501	C₄×C₄₁	semidirect
209. #501	C₄×C₄₁	semidirect
236. C₄₁	#23172	direct (N × H)
258. #108	Q₈×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3162	2
C₄₁×#2962	2
C₄₁×#1986	2
C₄₁×#1946	2
C₄₁×#1945	2
C₄₁×#1922	2
C₄₁×#1778	2
C₄₁×#1773	2
C₄₁×#1772	2
C₄₁×#1771	2
#23172	41

Subgroups — C41×#23172 #23799373

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#23172 #23799373