Subgroups — C₄₁×#33031 #23809232

Order 10496.

978 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	C₂×C₄₁×#477	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#460	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2858	C₂	1	1	yes	maximal, characteristic
4	C₄²×Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1987	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1982	C₂	1	1	yes	maximal, characteristic
7	C₄₁×#1925	C₂	1	4	yes	maximal, complemented
8	C₄₁×#1880	C₂	1	4	yes	maximal, complemented
9	C₄₁×#1831	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₄₁	C₂²	1	2	yes	—
11	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
12	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×#124×C₄₁	—	2	2	no	—
14	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
16	C₄₁×#477	—	2	4	no	—
17	C₄₁×#460	—	2	4	no	—
18	C₂×#107×C₄₁	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×#103×C₄₁	C₂²	1	2	yes	—
22	C₂×#102×C₄₁	C₂²	1	4	yes	—
23	C₂×#102×C₄₁	C₂²	1	2	yes	—
24	C₄₁×#390	—	2	1	no	—
25	C₄₁×#390	—	2	1	no	—
26	C₄₁×#390	C₂²	1	4	yes	—
27	C₄×C₄⋊C₄×C₄₁	—	2	2	no	—
28	C₄×C₄⋊C₄×C₄₁	—	2	1	no	—
29	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
30	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
31	C₄³×C₄₁	—	2	1	no	—
32	C₄³×C₄₁	C₂²	1	1	yes	characteristic
33	C₄₁×#340	C₂²	1	4	yes	—
34	C₄₁×#336	C₂²	1	4	yes	—
35	C₂²×Q₈×C₄₁	—	2	1	no	—
36	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
37	C₂²×D₄×C₄₁	—	2	1	no	—
38	C₂²×D₄×C₄₁	—	2	1	no	—
39	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
40	C₂×SD₁₆×C₄₁	—	2	4	no	—
41	C₂×SD₁₆×C₄₁	—	2	8	no	—
42	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
43	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
44	C₄⋊Q₈×C₄₁	—	2	2	no	—
45	C₄⋊Q₈×C₄₁	—	2	2	no	—
46	#127×C₄₁	—	2	2	no	—
47	#127×C₄₁	—	2	2	no	—
48	#124×C₄₁	—	4	8	no	—
49	C₄×Q₈×C₄₁	—	2	4	no	—
50	C₄×Q₈×C₄₁	—	2	4	no	—
51	C₄×Q₈×C₄₁	—	2	2	no	—
52	C₄×Q₈×C₄₁	D₄	1	4	yes	—
53	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
54	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
55	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
56	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
59	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
60	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
61	C₂×C₄²×C₄₁	—	2	2	no	—
62	C₂×C₄²×C₄₁	—	2	1	no	—
63	C₂×C₄²×C₄₁	—	2	1	no	—
64	C₂×C₄²×C₄₁	—	2	2	no	—
65	C₂×C₄²×C₄₁	D₄	1	2	yes	—
66	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
69	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
70	#107×C₄₁	—	2	4	no	—
71	C₄⋊C₈×C₄₁	—	2	2	no	—
72	C₄⋊C₈×C₄₁	—	2	2	no	—
73	#103×C₄₁	—	2	4	no	—
74	#102×C₄₁	—	2	4	no	—
75	#102×C₄₁	—	2	8	no	—
76	#95×C₄₁	—	2	2	no	—
77	#95×C₄₁	—	2	1	no	—
78	C₂⁴×C₄₁	—	2	2	no	—
79	C₂×Q₈×C₄₁	—	2	1	no	—
80	C₂×Q₈×C₄₁	—	2	2	no	—
81	C₂×Q₈×C₄₁	—	4	4	no	—
82	C₂×Q₈×C₄₁	—	4	2	no	—
83	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
84	C₂×Q₈×C₄₁	#41	1	4	yes	—
85	C₂×D₄×C₄₁	—	2	2	no	—
86	C₂×D₄×C₄₁	—	2	4	no	—
87	C₂×D₄×C₄₁	—	2	2	no	—
88	C₂×D₄×C₄₁	—	2	4	no	—
89	C₂×D₄×C₄₁	—	4	4	no	—
90	C₂×D₄×C₄₁	—	4	2	no	—
91	C₂×D₄×C₄₁	—	4	2	no	—
92	C₂×D₄×C₄₁	—	4	2	no	—
93	C₂×D₄×C₄₁	—	4	2	no	—
94	C₂²×C₄×C₄₁	—	2	1	no	—
95	C₂²×C₄×C₄₁	—	2	1	no	—
96	C₂²×C₄×C₄₁	—	2	2	no	—
97	C₂²×C₄×C₄₁	—	2	2	no	—
98	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
103	SD₁₆×C₄₁	—	4	8	no	—
104	C₂×C₈×C₄₁	—	2	2	no	—
105	C₂×C₈×C₄₁	—	2	2	no	—
106	C₂×C₈×C₄₁	—	2	4	no	—
107	C₂×C₈×C₄₁	—	2	4	no	—
108	C₄⋊C₄×C₄₁	—	2	8	no	—
109	C₄⋊C₄×C₄₁	—	2	4	no	—
110	C₄⋊C₄×C₄₁	—	2	1	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	2	no	—
115	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
116	C₄⋊C₄×C₄₁	#41	1	4	yes	—
117	C₂²⋊C₄×C₄₁	—	4	8	no	—
118	C₂²⋊C₄×C₄₁	—	4	8	no	—
119	C₄²×C₄₁	—	2	8	no	—
120	C₄²×C₄₁	—	2	4	no	—
121	C₄²×C₄₁	—	2	2	no	—
122	C₄²×C₄₁	—	2	4	no	—
123	C₄²×C₄₁	—	2	2	no	—
124	C₄²×C₄₁	—	2	2	no	—
125	C₄²×C₄₁	—	2	2	no	—
126	C₄²×C₄₁	—	4	2	no	—
127	C₄²×C₄₁	—	4	4	no	—
128	C₄²×C₄₁	C₂×D₄	1	2	yes	—
129	C₄²×C₄₁	#41	1	2	yes	—
130	C₂³×C₄₁	—	4	2	no	—
131	C₂³×C₄₁	—	4	4	no	—
132	C₂³×C₄₁	—	4	2	no	—
133	C₂³×C₄₁	—	4	4	no	—
134	C₂³×C₄₁	—	4	2	no	—
135	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
136	Q₈×C₄₁	—	2	4	no	—
137	Q₈×C₄₁	—	2	2	no	—
138	Q₈×C₄₁	—	8	4	no	—
139	Q₈×C₄₁	#124	1	4	yes	complemented
140	D₄×C₄₁	—	4	2	no	—
141	D₄×C₄₁	—	4	4	no	—
142	D₄×C₄₁	—	4	2	no	—
143	D₄×C₄₁	—	8	4	no	—
144	D₄×C₄₁	—	8	4	no	—
145	C₂×C₄×C₄₁	—	2	2	no	—
146	C₂×C₄×C₄₁	—	2	2	no	—
147	C₂×C₄×C₄₁	—	2	4	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	4	no	—
153	C₂×C₄×C₄₁	—	2	2	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	4	no	—
160	C₂×C₄×C₄₁	#121	1	2	yes	—
161	C₂×C₄×C₄₁	#121	1	2	yes	—
162	C₂×C₄×C₄₁	#135	1	2	yes	—
163	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	4	yes	—
164	C₂×C₄×C₄₁	#137	1	2	yes	—
165	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
167	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
168	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
169	C₈×C₄₁	—	4	2	no	—
170	C₈×C₄₁	—	4	2	no	—
171	#33031	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂²×C₄₁	—	8	2	no	—
173	C₂²×C₄₁	—	8	4	no	—
174	C₂²×C₄₁	—	8	4	no	—
175	C₂²×C₄₁	—	8	2	no	—
176	C₂²×C₄₁	—	8	2	no	—
177	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
178	C₂²×C₄₁	#525	1	2	yes	—
179	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
180	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
181	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
182	C₄×C₄₁	—	2	4	no	—
183	C₄×C₄₁	—	2	4	no	—
184	C₄×C₄₁	—	2	2	no	—
185	C₄×C₄₁	—	4	2	no	—
186	C₄×C₄₁	—	4	4	no	—
187	C₄×C₄₁	—	4	2	no	—
188	C₄×C₄₁	—	8	2	no	—
189	C₄×C₄₁	#464	1	4	yes	—
190	C₄×C₄₁	C₂×#124	1	1	yes	characteristic
191	C₄×C₄₁	#529	1	2	yes	—
192	C₄×C₄₁	#532	1	1	yes	characteristic
193	C₂×#477	C₂×C₄₁	1	1	yes	characteristic, complemented
194	C₂×#460	C₂×C₄₁	1	1	yes	characteristic
195	#2858	C₂×C₄₁	1	1	yes	characteristic
196	C₄²×Q₈	C₂×C₄₁	1	1	yes	characteristic, complemented
197	#1987	C₂×C₄₁	1	1	yes	characteristic, complemented
198	#1982	C₂×C₄₁	1	1	yes	characteristic
199	#1925	C₂×C₄₁	1	4	yes	complemented
200	#1880	C₂×C₄₁	1	4	yes	complemented
201	#1831	C₂×C₄₁	1	1	yes	characteristic, complemented
202	C₂×C₄₁	—	16	2	no	—
203	C₂×C₄₁	#2850	1	1	yes	characteristic
204	C₂×C₄₁	C₂×#464	1	1	yes	characteristic
205	C₂×C₄₁	#3038	1	1	yes	characteristic
206	C₂×C₄₁	#3106	1	2	yes	—
207	C₂×C₄₁	#3112	1	2	yes	—
208	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	—
209	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
210	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
211	C₂×#124	—	2	2	no	—
212	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
213	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
214	#477	—	2	4	no	—
215	#460	—	2	4	no	—
216	C₂×#107	C₂²×C₄₁	1	2	yes	—
217	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
218	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
219	C₂×#103	C₂²×C₄₁	1	2	yes	—
220	C₂×#102	C₂²×C₄₁	1	4	yes	—
221	C₂×#102	C₂²×C₄₁	1	2	yes	—
222	#390	—	2	1	no	—
223	#390	—	2	1	no	—
224	#390	C₂²×C₄₁	1	4	yes	—
225	C₄×C₄⋊C₄	—	2	2	no	—
226	C₄×C₄⋊C₄	—	2	1	no	—
227	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
228	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
229	C₄³	—	2	1	no	—
230	C₄³	C₂²×C₄₁	1	1	yes	characteristic
231	#340	C₂²×C₄₁	1	4	yes	—
232	#336	C₂²×C₄₁	1	4	yes	—
233	C₄₁	#33031	1	1	yes	characteristic, direct product factor, Sylow
234	C₂²×Q₈	—	2	1	no	—
235	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
236	C₂²×D₄	—	2	1	no	—
237	C₂²×D₄	—	2	1	no	—
238	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
239	C₂×SD₁₆	—	2	4	no	—
240	C₂×SD₁₆	—	2	8	no	—
241	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
242	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
243	C₄⋊Q₈	—	2	2	no	—
244	C₄⋊Q₈	—	2	2	no	—
245	#127	—	2	2	no	—
246	#127	—	2	2	no	—
247	#124	—	4	8	no	—
248	C₄×Q₈	—	2	4	no	—
249	C₄×Q₈	—	2	4	no	—
250	C₄×Q₈	—	2	2	no	—
251	C₄×Q₈	D₄×C₄₁	1	4	yes	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
256	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
258	C₂×C₂²⋊C₄	—	2	4	no	—
259	C₂×C₂²⋊C₄	—	2	4	no	—
260	C₂×C₄²	—	2	2	no	—
261	C₂×C₄²	—	2	1	no	—
262	C₂×C₄²	—	2	1	no	—
263	C₂×C₄²	—	2	2	no	—
264	C₂×C₄²	D₄×C₄₁	1	2	yes	—
265	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
266	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
267	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
268	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
269	#107	—	2	4	no	—
270	C₄⋊C₈	—	2	2	no	—
271	C₄⋊C₈	—	2	2	no	—
272	#103	—	2	4	no	—
273	#102	—	2	4	no	—
274	#102	—	2	8	no	—
275	#95	—	2	2	no	—
276	#95	—	2	1	no	—
277	C₂⁴	—	2	2	no	—
278	C₂×Q₈	—	2	1	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	4	4	no	—
281	C₂×Q₈	—	4	2	no	—
282	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
283	C₂×Q₈	#41×C₄₁	1	4	yes	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	4	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	4	no	—
288	C₂×D₄	—	4	4	no	—
289	C₂×D₄	—	4	2	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	—	4	2	no	—
292	C₂×D₄	—	4	2	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
298	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
300	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
301	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
302	SD₁₆	—	4	8	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	4	no	—
306	C₂×C₈	—	2	4	no	—
307	C₄⋊C₄	—	2	8	no	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
315	C₄⋊C₄	#41×C₄₁	1	4	yes	—
316	C₂²⋊C₄	—	4	8	no	—
317	C₂²⋊C₄	—	4	8	no	—
318	C₄²	—	2	8	no	—
319	C₄²	—	2	4	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	4	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	4	2	no	—
326	C₄²	—	4	4	no	—
327	C₄²	C₂×D₄×C₄₁	1	2	yes	—
328	C₄²	#41×C₄₁	1	2	yes	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	4	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	4	no	—
333	C₂³	—	4	2	no	—
334	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
335	Q₈	—	2	4	no	—
336	Q₈	—	2	2	no	—
337	Q₈	—	8	4	no	—
338	Q₈	#124×C₄₁	1	4	yes	complemented
339	D₄	—	4	2	no	—
340	D₄	—	4	4	no	—
341	D₄	—	4	2	no	—
342	D₄	—	8	4	no	—
343	D₄	—	8	4	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	#121×C₄₁	1	2	yes	—
360	C₂×C₄	#121×C₄₁	1	2	yes	—
361	C₂×C₄	#135×C₄₁	1	2	yes	—
362	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	4	yes	—
363	C₂×C₄	#137×C₄₁	1	2	yes	—
364	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
365	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
366	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
367	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
368	C₈	—	4	2	no	—
369	C₈	—	4	2	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	8	2	no	—
372	C₂²	—	8	4	no	—
373	C₂²	—	8	4	no	—
374	C₂²	—	8	2	no	—
375	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
376	C₂²	C₄₁×#525	1	2	yes	—
377	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
378	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	2	yes	—
379	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
380	C₄	—	2	2	no	—
381	C₄	—	2	4	no	—
382	C₄	—	2	4	no	—
383	C₄	—	4	2	no	—
384	C₄	—	4	2	no	—
385	C₄	—	4	4	no	—
386	C₄	—	8	2	no	—
387	C₄	C₄₁×#464	1	4	yes	—
388	C₄	C₂×#124×C₄₁	1	1	yes	characteristic
389	C₄	C₄₁×#529	1	2	yes	—
390	C₄	C₄₁×#532	1	1	yes	characteristic
391	C₂	—	16	2	no	—
392	C₂	C₄₁×#2850	1	1	yes	characteristic
393	C₂	C₂×C₄₁×#464	1	1	yes	characteristic
394	C₂	C₄₁×#3038	1	1	yes	characteristic
395	C₂	C₄₁×#3106	1	2	yes	—
396	C₂	C₄₁×#3112	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×#127×C₄₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₄³×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#477	C₂	semidirect
4. C₄²×Q₈×C₄₁	C₂	semidirect
5. C₄₁×#1987	C₂	semidirect
7. C₄₁×#1925	C₂	semidirect
8. C₄₁×#1880	C₂	semidirect
9. C₄₁×#1831	C₂	semidirect
139. Q₈×C₄₁	#124	semidirect
171. #33031	C₄₁	direct (N × H)
193. C₂×#477	C₂×C₄₁	semidirect
196. C₄²×Q₈	C₂×C₄₁	semidirect
197. #1987	C₂×C₄₁	semidirect
199. #1925	C₂×C₄₁	semidirect
200. #1880	C₂×C₄₁	semidirect
201. #1831	C₂×C₄₁	semidirect
233. C₄₁	#33031	direct (N × H)
338. Q₈	#124×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#477	2
C₂×C₄₁×#460	2
C₄₁×#2858	2
C₄²×Q₈×C₄₁	2
C₄₁×#1987	2
C₄₁×#1982	2
C₄₁×#1925	2
C₄₁×#1880	2
C₄₁×#1831	2
#33031	41

Subgroups — C41×#33031 #23809232

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#33031 #23809232