Subgroups — C₄₁×#17770 #23793971

Order 10496.

1248 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×#3498	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2990	C₂	1	2	yes	maximal, complemented
3	C₄₁×#1560	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1555	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1551	C₂	1	4	yes	maximal, complemented
6	C₄₁×#1545	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1543	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₁×#331	C₂	1	2	yes	maximal, complemented
9	C₂×H(5,𝔽₂)×C₄₁	C₄	1	2	yes	—
10	C₄₁×#550	—	2	2	no	—
11	D₄²×C₄₁	—	2	2	no	—
12	D₄²×C₄₁	—	2	4	no	—
13	C₄₁×#535	C₄	1	4	yes	—
14	C₄₁×#535	C₄	1	2	yes	—
15	C₄₁×#532	C₂²	1	1	yes	characteristic
16	C₄₁×#532	C₂²	1	2	yes	—
17	C₂×#127×C₄₁	C₂²	1	2	yes	—
18	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
19	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
20	C₄₁×#446	—	2	2	no	—
21	C₄₁×#435	—	2	4	no	—
22	C₈×D₄×C₄₁	—	2	2	no	—
23	C₄₁×#432	C₂²	1	4	yes	complemented
24	C₄₁×#431	C₂²	1	2	yes	complemented
25	C₄₁×#423	C₂²	1	2	yes	complemented
26	C₂×C₄⋊C₈×C₄₁	C₂²	1	4	yes	complemented
27	C₄₁×#333	C₂²	1	2	yes	complemented
28	C₄₁×#333	C₂²	1	2	yes	complemented
29	C₄₁×#331	C₂²	1	1	yes	characteristic, complemented
30	C₄₁×#331	C₂²	1	4	yes	complemented
31	C₄₁×#331	C₂²	1	2	yes	complemented
32	C₄₁×#331	C₂²	1	1	yes	characteristic, complemented
33	C₄₁×#331	C₂²	1	4	yes	complemented
34	H(5,𝔽₂)×C₄₁	—	4	8	no	—
35	C₂×#41×C₄₁	—	2	2	no	—
36	C₂×#41×C₄₁	C₂×C₄	1	4	yes	—
37	C₂×#41×C₄₁	C₂×C₄	1	2	yes	—
38	C₂×#41×C₄₁	C₂×C₄	1	1	yes	characteristic
39	C₂²×D₄×C₄₁	—	2	4	no	—
40	C₂²×D₄×C₄₁	—	2	2	no	—
41	C₂²×D₄×C₄₁	—	2	4	no	—
42	C₂²×D₄×C₄₁	—	2	2	no	—
43	C₂²×D₄×C₄₁	C₂×C₄	1	4	yes	—
44	C₂²×D₄×C₄₁	C₂×C₄	1	2	yes	—
45	C₂×M₁₆×C₄₁	—	2	2	no	—
46	C₂²×C₈×C₄₁	—	2	4	no	—
47	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
48	#127×C₄₁	—	2	2	no	—
49	#127×C₄₁	—	2	4	no	—
50	#127×C₄₁	C₂×C₄	1	4	yes	—
51	#127×C₄₁	C₂×C₄	1	2	yes	—
52	#127×C₄₁	C₂³	1	1	yes	characteristic
53	#127×C₄₁	C₂³	1	2	yes	—
54	#124×C₄₁	C₂×C₄	1	2	yes	—
55	#124×C₄₁	C₂×C₄	1	4	yes	—
56	#121×C₄₁	—	2	4	no	—
57	#121×C₄₁	—	2	2	no	—
58	#121×C₄₁	—	2	8	no	—
59	#121×C₄₁	—	2	4	no	—
60	#120×C₄₁	—	2	4	no	—
61	#120×C₄₁	—	2	8	no	—
62	C₄×Q₈×C₄₁	D₄	1	2	yes	—
63	C₄×D₄×C₄₁	—	2	2	no	—
64	C₄×D₄×C₄₁	—	2	4	no	—
65	C₄×D₄×C₄₁	D₄	1	2	yes	—
66	C₄×D₄×C₄₁	D₄	1	4	yes	—
67	#117×C₄₁	C₂×C₄	1	1	yes	characteristic
68	#117×C₄₁	C₂×C₄	1	2	yes	—
69	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
70	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
71	C₄⋊C₈×C₄₁	—	2	4	no	—
72	C₄⋊C₈×C₄₁	—	2	2	no	—
73	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
74	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
75	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
76	C₂²⋊C₈×C₄₁	—	2	2	no	—
77	C₂²⋊C₈×C₄₁	—	2	4	no	—
78	#97×C₄₁	—	2	4	no	—
79	C₄×C₈×C₄₁	—	2	2	no	—
80	C₂⁴×C₄₁	—	2	2	no	—
81	C₂⁴×C₄₁	—	2	4	no	—
82	#41×C₄₁	—	2	4	no	—
83	#41×C₄₁	—	4	8	no	—
84	#41×C₄₁	—	4	4	no	—
85	#41×C₄₁	—	4	8	no	—
86	C₂×Q₈×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
87	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
88	C₂×D₄×C₄₁	—	2	2	no	—
89	C₂×D₄×C₄₁	—	2	4	no	—
90	C₂×D₄×C₄₁	—	2	4	no	—
91	C₂×D₄×C₄₁	—	2	2	no	—
92	C₂×D₄×C₄₁	—	2	4	no	—
93	C₂×D₄×C₄₁	—	2	8	no	—
94	C₂×D₄×C₄₁	—	2	2	no	—
95	C₂×D₄×C₄₁	—	2	4	no	—
96	C₂×D₄×C₄₁	—	4	8	no	—
97	C₂×D₄×C₄₁	—	4	4	no	—
98	C₂×D₄×C₄₁	—	4	16	no	—
99	C₂×D₄×C₄₁	—	4	8	no	—
100	C₂×D₄×C₄₁	—	8	4	no	—
101	C₂×D₄×C₄₁	—	8	2	no	—
102	C₂×D₄×C₄₁	—	8	4	no	—
103	C₂×D₄×C₄₁	—	8	2	no	—
104	C₂×D₄×C₄₁	C₂²⋊C₄	1	2	yes	—
105	C₂×D₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
106	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
107	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
108	C₂²×C₄×C₄₁	—	2	4	no	—
109	C₂²×C₄×C₄₁	—	2	2	no	—
110	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
113	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
114	M₁₆×C₄₁	—	8	2	no	—
115	C₂×C₈×C₄₁	—	2	2	no	—
116	C₂×C₈×C₄₁	—	2	2	no	—
117	C₂×C₈×C₄₁	—	2	4	no	—
118	C₂×C₈×C₄₁	—	8	4	no	—
119	C₄⋊C₄×C₄₁	—	2	2	no	—
120	C₄⋊C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
121	C₄⋊C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
122	C₂²⋊C₄×C₄₁	—	2	4	no	—
123	C₂²⋊C₄×C₄₁	—	2	8	no	—
124	C₂²⋊C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
125	C₂²⋊C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
126	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
127	C₄²×C₄₁	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₄₁	C₂×D₄	1	2	yes	—
129	C₄²×C₄₁	C₂×D₄	1	4	yes	—
130	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
131	C₂³×C₄₁	—	2	4	no	—
132	C₂³×C₄₁	—	2	2	no	—
133	C₂³×C₄₁	—	4	4	no	—
134	C₂³×C₄₁	—	4	8	no	—
135	C₂³×C₄₁	—	8	8	no	—
136	C₂³×C₄₁	—	8	4	no	—
137	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
138	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
139	Q₈×C₄₁	—	2	2	no	—
140	Q₈×C₄₁	—	4	2	no	—
141	D₄×C₄₁	—	2	4	no	—
142	D₄×C₄₁	—	4	2	no	—
143	D₄×C₄₁	—	4	4	no	—
144	D₄×C₄₁	—	4	8	no	—
145	D₄×C₄₁	—	4	4	no	—
146	D₄×C₄₁	—	4	8	no	—
147	D₄×C₄₁	—	4	2	no	—
148	D₄×C₄₁	—	4	4	no	—
149	D₄×C₄₁	—	4	2	no	—
150	D₄×C₄₁	—	4	4	no	—
151	D₄×C₄₁	—	4	4	no	—
152	D₄×C₄₁	—	8	8	no	—
153	D₄×C₄₁	—	8	4	no	—
154	D₄×C₄₁	#100	1	4	yes	—
155	C₂×C₄×C₄₁	—	2	4	no	—
156	C₂×C₄×C₄₁	—	2	4	no	—
157	C₂×C₄×C₄₁	—	2	2	no	—
158	C₂×C₄×C₄₁	—	2	4	no	—
159	C₂×C₄×C₄₁	—	2	2	no	—
160	C₂×C₄×C₄₁	—	2	2	no	—
161	C₂×C₄×C₄₁	—	2	2	no	—
162	C₂×C₄×C₄₁	—	4	8	no	—
163	C₂×C₄×C₄₁	—	4	4	no	—
164	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
166	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
170	C₈×C₄₁	—	4	2	no	—
171	C₈×C₄₁	—	4	4	no	—
172	C₈×C₄₁	—	4	2	no	—
173	#17770	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂²×C₄₁	—	2	4	no	—
175	C₂²×C₄₁	—	2	1	no	—
176	C₂²×C₄₁	—	2	2	no	—
177	C₂²×C₄₁	—	4	4	no	—
178	C₂²×C₄₁	—	4	2	no	—
179	C₂²×C₄₁	—	4	4	no	—
180	C₂²×C₄₁	—	4	8	no	—
181	C₂²×C₄₁	—	16	8	no	—
182	C₂²×C₄₁	—	16	4	no	—
183	C₂²×C₄₁	C₂×#100	1	4	yes	—
184	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
185	C₄×C₄₁	—	2	1	no	—
186	C₄×C₄₁	—	2	2	no	—
187	C₄×C₄₁	—	2	4	no	—
188	C₄×C₄₁	—	2	2	no	—
189	C₄×C₄₁	—	4	2	no	—
190	C₄×C₄₁	C₂×#100	1	2	yes	—
191	C₄×C₄₁	#576	1	2	yes	—
192	C₄×C₄₁	#577	1	2	yes	—
193	#3498	C₂×C₄₁	1	1	yes	characteristic
194	#2990	C₂×C₄₁	1	2	yes	complemented
195	#1560	C₂×C₄₁	1	1	yes	characteristic, complemented
196	#1555	C₂×C₄₁	1	2	yes	complemented
197	#1551	C₂×C₄₁	1	4	yes	complemented
198	#1545	C₂×C₄₁	1	2	yes	complemented
199	#1543	C₂×C₄₁	1	1	yes	characteristic, complemented
200	C₂×#331	C₂×C₄₁	1	2	yes	complemented
201	C₂×C₄₁	—	2	4	no	—
202	C₂×C₄₁	—	4	1	no	—
203	C₂×C₄₁	—	8	2	no	—
204	C₂×C₄₁	—	8	4	no	—
205	C₂×C₄₁	C₂²×#100	1	1	yes	characteristic
206	C₂×C₄₁	#2897	1	2	yes	—
207	C₂×H(5,𝔽₂)	C₄×C₄₁	1	2	yes	—
208	#550	—	2	2	no	—
209	D₄²	—	2	2	no	—
210	D₄²	—	2	4	no	—
211	#535	C₄×C₄₁	1	4	yes	—
212	#535	C₄×C₄₁	1	2	yes	—
213	#532	C₂²×C₄₁	1	1	yes	characteristic
214	#532	C₂²×C₄₁	1	2	yes	—
215	C₂×#127	C₂²×C₄₁	1	2	yes	—
216	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
217	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
218	#446	—	2	2	no	—
219	#435	—	2	4	no	—
220	C₈×D₄	—	2	2	no	—
221	#432	C₂²×C₄₁	1	4	yes	complemented
222	#431	C₂²×C₄₁	1	2	yes	complemented
223	#423	C₂²×C₄₁	1	2	yes	complemented
224	C₂×C₄⋊C₈	C₂²×C₄₁	1	4	yes	complemented
225	#333	C₂²×C₄₁	1	2	yes	complemented
226	#333	C₂²×C₄₁	1	2	yes	complemented
227	#331	C₂²×C₄₁	1	1	yes	characteristic, complemented
228	#331	C₂²×C₄₁	1	4	yes	complemented
229	#331	C₂²×C₄₁	1	2	yes	complemented
230	#331	C₂²×C₄₁	1	1	yes	characteristic, complemented
231	#331	C₂²×C₄₁	1	4	yes	complemented
232	C₄₁	#17770	1	1	yes	characteristic, direct product factor, Sylow
233	H(5,𝔽₂)	—	4	8	no	—
234	C₂×#41	—	2	2	no	—
235	C₂×#41	C₂×C₄×C₄₁	1	4	yes	—
236	C₂×#41	C₂×C₄×C₄₁	1	2	yes	—
237	C₂×#41	C₂×C₄×C₄₁	1	1	yes	characteristic
238	C₂²×D₄	—	2	4	no	—
239	C₂²×D₄	—	2	2	no	—
240	C₂²×D₄	—	2	4	no	—
241	C₂²×D₄	—	2	2	no	—
242	C₂²×D₄	C₂×C₄×C₄₁	1	4	yes	—
243	C₂²×D₄	C₂×C₄×C₄₁	1	2	yes	—
244	C₂×M₁₆	—	2	2	no	—
245	C₂²×C₈	—	2	4	no	—
246	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
247	#127	—	2	2	no	—
248	#127	—	2	4	no	—
249	#127	C₂×C₄×C₄₁	1	4	yes	—
250	#127	C₂×C₄×C₄₁	1	2	yes	—
251	#127	C₂³×C₄₁	1	1	yes	characteristic
252	#127	C₂³×C₄₁	1	2	yes	—
253	#124	C₂×C₄×C₄₁	1	2	yes	—
254	#124	C₂×C₄×C₄₁	1	4	yes	—
255	#121	—	2	4	no	—
256	#121	—	2	2	no	—
257	#121	—	2	8	no	—
258	#121	—	2	4	no	—
259	#120	—	2	4	no	—
260	#120	—	2	8	no	—
261	C₄×Q₈	D₄×C₄₁	1	2	yes	—
262	C₄×D₄	—	2	2	no	—
263	C₄×D₄	—	2	4	no	—
264	C₄×D₄	D₄×C₄₁	1	2	yes	—
265	C₄×D₄	D₄×C₄₁	1	4	yes	—
266	#117	C₂×C₄×C₄₁	1	1	yes	characteristic
267	#117	C₂×C₄×C₄₁	1	2	yes	—
268	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
269	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
270	C₄⋊C₈	—	2	4	no	—
271	C₄⋊C₈	—	2	2	no	—
272	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
273	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
274	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
275	C₂²⋊C₈	—	2	2	no	—
276	C₂²⋊C₈	—	2	4	no	—
277	#97	—	2	4	no	—
278	C₄×C₈	—	2	2	no	—
279	C₂⁴	—	2	2	no	—
280	C₂⁴	—	2	4	no	—
281	#41	—	2	4	no	—
282	#41	—	4	8	no	—
283	#41	—	4	4	no	—
284	#41	—	4	8	no	—
285	C₂×Q₈	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
286	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	4	no	—
289	C₂×D₄	—	2	4	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	8	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	4	no	—
295	C₂×D₄	—	4	8	no	—
296	C₂×D₄	—	4	4	no	—
297	C₂×D₄	—	4	16	no	—
298	C₂×D₄	—	4	8	no	—
299	C₂×D₄	—	8	4	no	—
300	C₂×D₄	—	8	2	no	—
301	C₂×D₄	—	8	4	no	—
302	C₂×D₄	—	8	2	no	—
303	C₂×D₄	C₂²⋊C₄×C₄₁	1	2	yes	—
304	C₂×D₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
305	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
306	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
310	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
312	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
313	M₁₆	—	8	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	4	no	—
317	C₂×C₈	—	8	4	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
320	C₄⋊C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
321	C₂²⋊C₄	—	2	4	no	—
322	C₂²⋊C₄	—	2	8	no	—
323	C₂²⋊C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
324	C₂²⋊C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
325	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
326	C₄²	C₂²×C₄×C₄₁	1	1	yes	characteristic
327	C₄²	C₂×D₄×C₄₁	1	2	yes	—
328	C₄²	C₂×D₄×C₄₁	1	4	yes	—
329	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
330	C₂³	—	2	4	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	4	4	no	—
333	C₂³	—	4	8	no	—
334	C₂³	—	8	8	no	—
335	C₂³	—	8	4	no	—
336	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
337	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
338	Q₈	—	2	2	no	—
339	Q₈	—	4	2	no	—
340	D₄	—	2	4	no	—
341	D₄	—	4	2	no	—
342	D₄	—	4	4	no	—
343	D₄	—	4	8	no	—
344	D₄	—	4	4	no	—
345	D₄	—	4	8	no	—
346	D₄	—	4	2	no	—
347	D₄	—	4	4	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	4	no	—
350	D₄	—	4	4	no	—
351	D₄	—	8	8	no	—
352	D₄	—	8	4	no	—
353	D₄	#100×C₄₁	1	4	yes	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	4	8	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
364	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
365	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
366	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
367	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
368	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
369	C₈	—	4	2	no	—
370	C₈	—	4	4	no	—
371	C₈	—	4	2	no	—
372	C₂²	—	2	4	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	4	4	no	—
376	C₂²	—	4	2	no	—
377	C₂²	—	4	4	no	—
378	C₂²	—	4	8	no	—
379	C₂²	—	16	8	no	—
380	C₂²	—	16	4	no	—
381	C₂²	C₂×#100×C₄₁	1	4	yes	—
382	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
383	C₄	—	2	1	no	—
384	C₄	—	2	2	no	—
385	C₄	—	2	4	no	—
386	C₄	—	2	2	no	—
387	C₄	—	4	2	no	—
388	C₄	C₂×#100×C₄₁	1	2	yes	—
389	C₄	C₄₁×#576	1	2	yes	—
390	C₄	C₄₁×#577	1	2	yes	—
391	C₂	—	2	4	no	—
392	C₂	—	4	1	no	—
393	C₂	—	8	2	no	—
394	C₂	—	8	4	no	—
395	C₂	C₂²×#100×C₄₁	1	1	yes	characteristic
396	C₂	C₄₁×#2897	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₄²	C₂⁴×C₄₁
prime radical	C₄₁×#3498	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₄×#41×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#2990	C₂	semidirect
3. C₄₁×#1560	C₂	semidirect
4. C₄₁×#1555	C₂	semidirect
5. C₄₁×#1551	C₂	semidirect
6. C₄₁×#1545	C₂	semidirect
7. C₄₁×#1543	C₂	semidirect
8. C₂×C₄₁×#331	C₂	semidirect
23. C₄₁×#432	C₂²	semidirect
24. C₄₁×#431	C₂²	semidirect
25. C₄₁×#423	C₂²	semidirect
26. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
27. C₄₁×#333	C₂²	semidirect
28. C₄₁×#333	C₂²	semidirect
29. C₄₁×#331	C₂²	semidirect
30. C₄₁×#331	C₂²	semidirect
31. C₄₁×#331	C₂²	semidirect
32. C₄₁×#331	C₂²	semidirect
33. C₄₁×#331	C₂²	semidirect
173. #17770	C₄₁	direct (N × H)
194. #2990	C₂×C₄₁	semidirect
195. #1560	C₂×C₄₁	semidirect
196. #1555	C₂×C₄₁	semidirect
197. #1551	C₂×C₄₁	semidirect
198. #1545	C₂×C₄₁	semidirect
199. #1543	C₂×C₄₁	semidirect
200. C₂×#331	C₂×C₄₁	semidirect
221. #432	C₂²×C₄₁	semidirect
222. #431	C₂²×C₄₁	semidirect
223. #423	C₂²×C₄₁	semidirect
224. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
225. #333	C₂²×C₄₁	semidirect
226. #333	C₂²×C₄₁	semidirect
227. #331	C₂²×C₄₁	semidirect
228. #331	C₂²×C₄₁	semidirect
229. #331	C₂²×C₄₁	semidirect
230. #331	C₂²×C₄₁	semidirect
231. #331	C₂²×C₄₁	semidirect
232. C₄₁	#17770	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×#3498	2
C₄₁×#2990	2
C₄₁×#1560	2
C₄₁×#1555	2
C₄₁×#1551	2
C₄₁×#1545	2
C₄₁×#1543	2
C₂×C₄₁×#331	2
#17770	41

Subgroups — C41×#17770 #23793971

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#17770 #23793971