Subgroups — C₄₁×#23451 #23799652

Order 10496.

1294 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#416	C₂	1	2	yes	maximal
3	C₄₁×#2297	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2026	C₂	1	2	yes	maximal, complemented
5	C₄₁×#2025	C₂	1	2	yes	maximal, complemented
6	C₄₁×#2024	C₂	1	2	yes	maximal, complemented
7	C₄₁×#2023	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1735	C₂	1	2	yes	maximal, complemented
9	C₂×C₄₁×#336	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₄₁	C₂²	1	2	yes	—
12	C₄₁×#533	—	2	8	no	—
13	C₂×C₄⋊Q₈×C₄₁	C₂²	1	2	yes	—
14	C₂×#125×C₄₁	C₂²	1	2	yes	—
15	C₂×C₂²⋊Q₈×C₄₁	—	2	2	no	—
16	C₂×C₄×Q₈×C₄₁	—	2	2	no	—
17	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×#117×C₄₁	C₂²	1	2	yes	—
19	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
20	C₄₁×#416	—	2	8	no	—
21	C₂×#103×C₄₁	C₂²	1	4	yes	—
22	C₂×#102×C₄₁	C₂²	1	4	yes	—
23	C₄₁×#391	C₂²	1	1	yes	characteristic
24	C₄₁×#391	C₂²	1	1	yes	characteristic
25	C₄₁×#390	C₂²	1	1	yes	characteristic
26	C₄₁×#390	C₂²	1	1	yes	characteristic
27	C₄₁×#386	—	2	2	no	—
28	C₄×C₂²⋊C₄×C₄₁	—	2	2	no	—
29	C₄₁×#340	C₂²	1	4	yes	—
30	C₄₁×#340	C₂²	1	4	yes	—
31	C₄₁×#336	C₂²	1	2	yes	—
32	C₄₁×#336	C₂²	1	2	yes	—
33	C₂×#41×C₄₁	—	2	2	no	—
34	C₂×#41×C₄₁	—	2	4	no	—
35	C₂×#41×C₄₁	—	2	4	no	—
36	C₂×#41×C₄₁	Q₈	1	4	yes	complemented
37	C₂²×Q₈×C₄₁	—	2	2	no	—
38	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
39	C₂²×D₄×C₄₁	—	2	1	no	—
40	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₄₁	—	2	1	no	—
42	C₂³×C₄×C₄₁	D₄	1	2	yes	—
43	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₄₁	—	2	4	no	—
45	C₂²×C₈×C₄₁	—	2	4	no	—
46	C₂²×C₈×C₄₁	—	2	4	no	—
47	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
48	C₄⋊Q₈×C₄₁	—	2	8	no	—
49	#125×C₄₁	—	2	8	no	—
50	C₂²⋊Q₈×C₄₁	—	2	16	no	—
51	C₄×Q₈×C₄₁	—	2	16	no	—
52	#117×C₄₁	—	2	4	no	—
53	#117×C₄₁	—	2	4	no	—
54	#117×C₄₁	D₄	1	8	yes	—
55	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
56	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
60	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
62	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
64	C₂×C₄²×C₄₁	—	2	4	no	—
65	C₂×C₄²×C₄₁	—	2	2	no	—
66	C₂×C₄²×C₄₁	—	2	1	no	—
67	C₂×C₄²×C₄₁	D₄	1	2	yes	—
68	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
70	#103×C₄₁	—	2	8	no	—
71	#102×C₄₁	—	2	8	no	—
72	#95×C₄₁	—	2	2	no	—
73	#95×C₄₁	—	2	2	no	—
74	C₂⁴×C₄₁	—	2	1	no	—
75	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
76	#41×C₄₁	—	2	16	no	—
77	#41×C₄₁	—	4	8	no	—
78	C₂×Q₈×C₄₁	—	2	8	no	—
79	C₂×Q₈×C₄₁	—	2	1	no	—
80	C₂×Q₈×C₄₁	—	2	2	no	—
81	C₂×Q₈×C₄₁	—	2	2	no	—
82	C₂×Q₈×C₄₁	—	4	4	no	—
83	C₂×Q₈×C₄₁	—	4	4	no	—
84	C₂×Q₈×C₄₁	C₂×Q₈	1	2	yes	—
85	C₂×D₄×C₄₁	—	2	4	no	—
86	C₂×D₄×C₄₁	—	2	2	no	—
87	C₂×D₄×C₄₁	—	2	2	no	—
88	C₂×D₄×C₄₁	—	2	1	no	—
89	C₂×D₄×C₄₁	—	4	2	no	—
90	C₂×D₄×C₄₁	—	4	2	no	—
91	C₂×D₄×C₄₁	C₂×Q₈	1	2	yes	—
92	C₂²×C₄×C₄₁	—	2	4	no	—
93	C₂²×C₄×C₄₁	—	2	1	no	—
94	C₂²×C₄×C₄₁	—	2	4	no	—
95	C₂²×C₄×C₄₁	—	2	4	no	—
96	C₂²×C₄×C₄₁	—	2	4	no	—
97	C₂²×C₄×C₄₁	—	2	1	no	—
98	C₂²×C₄×C₄₁	—	2	1	no	—
99	C₂²×C₄×C₄₁	—	4	2	no	—
100	C₂²×C₄×C₄₁	—	4	2	no	—
101	C₂²×C₄×C₄₁	—	4	2	no	—
102	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
105	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
107	C₂²×C₄×C₄₁	#41	1	4	yes	—
108	C₂²×C₄×C₄₁	#41	1	2	yes	—
109	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
110	C₂×C₈×C₄₁	—	2	4	no	—
111	C₂×C₈×C₄₁	—	2	4	no	—
112	C₂×C₈×C₄₁	—	2	4	no	—
113	C₂×C₈×C₄₁	—	4	8	no	—
114	C₄⋊C₄×C₄₁	—	2	16	no	—
115	C₄⋊C₄×C₄₁	—	2	8	no	—
116	C₄⋊C₄×C₄₁	—	2	4	no	—
117	C₄⋊C₄×C₄₁	—	2	2	no	—
118	C₄⋊C₄×C₄₁	—	2	2	no	—
119	C₄⋊C₄×C₄₁	C₂×D₄	1	8	yes	—
120	C₂²⋊C₄×C₄₁	—	2	8	no	—
121	C₂²⋊C₄×C₄₁	—	4	4	no	—
122	C₂²⋊C₄×C₄₁	—	4	2	no	—
123	C₂²⋊C₄×C₄₁	—	4	4	no	—
124	C₄²×C₄₁	—	2	4	no	—
125	C₄²×C₄₁	—	2	8	no	—
126	C₄²×C₄₁	—	2	2	no	—
127	C₄²×C₄₁	—	2	2	no	—
128	C₄²×C₄₁	—	4	2	no	—
129	C₂³×C₄₁	—	2	2	no	—
130	C₂³×C₄₁	—	2	2	no	—
131	C₂³×C₄₁	—	2	2	no	—
132	C₂³×C₄₁	—	4	1	no	—
133	C₂³×C₄₁	—	4	1	no	—
134	C₂³×C₄₁	—	4	2	no	—
135	C₂³×C₄₁	—	4	2	no	—
136	C₂³×C₄₁	#120	1	2	yes	—
137	C₂³×C₄₁	C₂²⋊Q₈	1	2	yes	—
138	C₂³×C₄₁	#124	1	2	yes	—
139	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
140	Q₈×C₄₁	—	2	4	no	—
141	Q₈×C₄₁	—	4	16	no	—
142	Q₈×C₄₁	—	4	2	no	—
143	D₄×C₄₁	—	2	4	no	—
144	D₄×C₄₁	—	4	8	no	—
145	D₄×C₄₁	—	4	2	no	—
146	C₂×C₄×C₄₁	—	2	2	no	—
147	C₂×C₄×C₄₁	—	2	2	no	—
148	C₂×C₄×C₄₁	—	2	2	no	—
149	C₂×C₄×C₄₁	—	2	8	no	—
150	C₂×C₄×C₄₁	—	2	2	no	—
151	C₂×C₄×C₄₁	—	2	2	no	—
152	C₂×C₄×C₄₁	—	2	2	no	—
153	C₂×C₄×C₄₁	—	4	8	no	—
154	C₂×C₄×C₄₁	—	4	1	no	—
155	C₂×C₄×C₄₁	—	4	1	no	—
156	C₂×C₄×C₄₁	—	4	4	no	—
157	C₂×C₄×C₄₁	—	4	4	no	—
158	C₂×C₄×C₄₁	—	4	8	no	—
159	C₂×C₄×C₄₁	—	4	1	no	—
160	C₂×C₄×C₄₁	—	4	1	no	—
161	C₂×C₄×C₄₁	—	4	2	no	—
162	C₂×C₄×C₄₁	—	4	2	no	—
163	C₂×C₄×C₄₁	#120	1	2	yes	—
164	C₂×C₄×C₄₁	C₂²⋊Q₈	1	8	yes	—
165	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
166	C₂×C₄×C₄₁	#124	1	8	yes	—
167	C₂×C₄×C₄₁	#124	1	2	yes	—
168	C₂×C₄×C₄₁	#135	1	4	yes	—
169	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
170	C₂×C₄×C₄₁	C₂²×Q₈	1	1	yes	characteristic
171	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
172	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
173	C₈×C₄₁	—	4	4	no	—
174	#23451	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂²×C₄₁	—	2	4	no	—
176	C₂²×C₄₁	—	2	2	no	—
177	C₂²×C₄₁	—	2	2	no	—
178	C₂²×C₄₁	—	2	4	no	—
179	C₂²×C₄₁	—	4	4	no	—
180	C₂²×C₄₁	—	4	2	no	—
181	C₂²×C₄₁	—	8	1	no	—
182	C₂²×C₄₁	—	8	1	no	—
183	C₂²×C₄₁	—	8	2	no	—
184	C₂²×C₄₁	#393	1	4	yes	—
185	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
186	C₂²×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
187	C₂²×C₄₁	C₂×#124	1	1	yes	characteristic
188	C₂²×C₄₁	C₂×#135	1	2	yes	—
189	C₂²×C₄₁	#575	1	2	yes	—
190	C₄×C₄₁	—	2	4	no	—
191	C₄×C₄₁	—	4	2	no	—
192	C₄×C₄₁	—	4	2	no	—
193	C₄×C₄₁	—	4	8	no	—
194	C₄×C₄₁	—	8	1	no	—
195	C₄×C₄₁	—	8	1	no	—
196	C₄×C₄₁	#393	1	4	yes	—
197	C₄×C₄₁	C₂×C₂²⋊Q₈	1	2	yes	—
198	C₄×C₄₁	C₂×#124	1	2	yes	—
199	C₂×#533	C₂×C₄₁	1	1	yes	characteristic, complemented
200	C₂×#416	C₂×C₄₁	1	2	yes	—
201	#2297	C₂×C₄₁	1	1	yes	characteristic
202	#2026	C₂×C₄₁	1	2	yes	complemented
203	#2025	C₂×C₄₁	1	2	yes	complemented
204	#2024	C₂×C₄₁	1	2	yes	complemented
205	#2023	C₂×C₄₁	1	2	yes	complemented
206	#1735	C₂×C₄₁	1	2	yes	complemented
207	C₂×#336	C₂×C₄₁	1	1	yes	characteristic, complemented
208	C₂×C₄₁	—	2	4	no	—
209	C₂×C₄₁	—	8	2	no	—
210	C₂×C₄₁	C₂×#393	1	1	yes	characteristic
211	C₂×C₄₁	#3002	1	2	yes	—
212	C₂×C₄₁	#3076	1	2	yes	—
213	C₂×C₄₁	#3131	1	1	yes	characteristic
214	C₂×C₄₁	#3135	1	1	yes	characteristic
215	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
216	C₂³×C₈	C₂²×C₄₁	1	2	yes	—
217	#533	—	2	8	no	—
218	C₂×C₄⋊Q₈	C₂²×C₄₁	1	2	yes	—
219	C₂×#125	C₂²×C₄₁	1	2	yes	—
220	C₂×C₂²⋊Q₈	—	2	2	no	—
221	C₂×C₄×Q₈	—	2	2	no	—
222	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
223	C₂×#117	C₂²×C₄₁	1	2	yes	—
224	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
225	#416	—	2	8	no	—
226	C₂×#103	C₂²×C₄₁	1	4	yes	—
227	C₂×#102	C₂²×C₄₁	1	4	yes	—
228	#391	C₂²×C₄₁	1	1	yes	characteristic
229	#391	C₂²×C₄₁	1	1	yes	characteristic
230	#390	C₂²×C₄₁	1	1	yes	characteristic
231	#390	C₂²×C₄₁	1	1	yes	characteristic
232	#386	—	2	2	no	—
233	C₄×C₂²⋊C₄	—	2	2	no	—
234	#340	C₂²×C₄₁	1	4	yes	—
235	#340	C₂²×C₄₁	1	4	yes	—
236	#336	C₂²×C₄₁	1	2	yes	—
237	#336	C₂²×C₄₁	1	2	yes	—
238	C₄₁	#23451	1	1	yes	characteristic, direct product factor, Sylow
239	C₂×#41	—	2	2	no	—
240	C₂×#41	—	2	4	no	—
241	C₂×#41	—	2	4	no	—
242	C₂×#41	Q₈×C₄₁	1	4	yes	complemented
243	C₂²×Q₈	—	2	2	no	—
244	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
245	C₂²×D₄	—	2	1	no	—
246	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
247	C₂³×C₄	—	2	1	no	—
248	C₂³×C₄	D₄×C₄₁	1	2	yes	—
249	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
250	C₂²×C₈	—	2	4	no	—
251	C₂²×C₈	—	2	4	no	—
252	C₂²×C₈	—	2	4	no	—
253	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
254	C₄⋊Q₈	—	2	8	no	—
255	#125	—	2	8	no	—
256	C₂²⋊Q₈	—	2	16	no	—
257	C₄×Q₈	—	2	16	no	—
258	#117	—	2	4	no	—
259	#117	—	2	4	no	—
260	#117	D₄×C₄₁	1	8	yes	—
261	C₂×C₄⋊C₄	—	2	4	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
264	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
265	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	—	2	1	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₄²	—	2	2	no	—
271	C₂×C₄²	—	2	4	no	—
272	C₂×C₄²	—	2	1	no	—
273	C₂×C₄²	D₄×C₄₁	1	2	yes	—
274	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
276	#103	—	2	8	no	—
277	#102	—	2	8	no	—
278	#95	—	2	2	no	—
279	#95	—	2	2	no	—
280	C₂⁴	—	2	1	no	—
281	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
282	#41	—	2	16	no	—
283	#41	—	4	8	no	—
284	C₂×Q₈	—	2	8	no	—
285	C₂×Q₈	—	2	1	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	4	4	no	—
289	C₂×Q₈	—	4	4	no	—
290	C₂×Q₈	C₂×Q₈×C₄₁	1	2	yes	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂×D₄	C₂×Q₈×C₄₁	1	2	yes	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	4	2	no	—
306	C₂²×C₄	—	4	2	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
309	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
310	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
312	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
313	C₂²×C₄	#41×C₄₁	1	4	yes	—
314	C₂²×C₄	#41×C₄₁	1	2	yes	—
315	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
316	C₂×C₈	—	2	4	no	—
317	C₂×C₈	—	2	4	no	—
318	C₂×C₈	—	2	4	no	—
319	C₂×C₈	—	4	8	no	—
320	C₄⋊C₄	—	2	16	no	—
321	C₄⋊C₄	—	2	8	no	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	C₂×D₄×C₄₁	1	8	yes	—
326	C₂²⋊C₄	—	2	8	no	—
327	C₂²⋊C₄	—	4	4	no	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₂²⋊C₄	—	4	4	no	—
330	C₄²	—	2	4	no	—
331	C₄²	—	2	8	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	4	2	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	2	no	—
338	C₂³	—	4	1	no	—
339	C₂³	—	4	1	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	#120×C₄₁	1	2	yes	—
343	C₂³	C₂²⋊Q₈×C₄₁	1	2	yes	—
344	C₂³	#124×C₄₁	1	2	yes	—
345	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
346	Q₈	—	2	4	no	—
347	Q₈	—	4	16	no	—
348	Q₈	—	4	2	no	—
349	D₄	—	2	4	no	—
350	D₄	—	4	8	no	—
351	D₄	—	4	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	8	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	4	8	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	8	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	#120×C₄₁	1	2	yes	—
370	C₂×C₄	C₂²⋊Q₈×C₄₁	1	8	yes	—
371	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
372	C₂×C₄	#124×C₄₁	1	8	yes	—
373	C₂×C₄	#124×C₄₁	1	2	yes	—
374	C₂×C₄	#135×C₄₁	1	4	yes	—
375	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
376	C₂×C₄	C₂²×Q₈×C₄₁	1	1	yes	characteristic
377	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
378	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
379	C₈	—	4	4	no	—
380	C₂²	—	2	4	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	4	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	8	1	no	—
387	C₂²	—	8	1	no	—
388	C₂²	—	8	2	no	—
389	C₂²	C₄₁×#393	1	4	yes	—
390	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
391	C₂²	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
392	C₂²	C₂×#124×C₄₁	1	1	yes	characteristic
393	C₂²	C₂×#135×C₄₁	1	2	yes	—
394	C₂²	C₄₁×#575	1	2	yes	—
395	C₄	—	2	4	no	—
396	C₄	—	4	2	no	—
397	C₄	—	4	2	no	—
398	C₄	—	4	8	no	—
399	C₄	—	8	1	no	—
400	C₄	—	8	1	no	—
401	C₄	C₄₁×#393	1	4	yes	—
402	C₄	C₂×C₂²⋊Q₈×C₄₁	1	2	yes	—
403	C₄	C₂×#124×C₄₁	1	2	yes	—
404	C₂	—	2	4	no	—
405	C₂	—	8	2	no	—
406	C₂	C₂×C₄₁×#393	1	1	yes	characteristic
407	C₂	C₄₁×#3002	1	2	yes	—
408	C₂	C₄₁×#3076	1	2	yes	—
409	C₂	C₄₁×#3131	1	1	yes	characteristic
410	C₂	C₄₁×#3135	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₄₁	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
socle	C₂³×C₄₁	C₂²×D₄
prime radical	C₂²×#41×C₄₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#533	C₂	semidirect
4. C₄₁×#2026	C₂	semidirect
5. C₄₁×#2025	C₂	semidirect
6. C₄₁×#2024	C₂	semidirect
7. C₄₁×#2023	C₂	semidirect
8. C₄₁×#1735	C₂	semidirect
9. C₂×C₄₁×#336	C₂	semidirect
36. C₂×#41×C₄₁	Q₈	semidirect
174. #23451	C₄₁	direct (N × H)
199. C₂×#533	C₂×C₄₁	semidirect
202. #2026	C₂×C₄₁	semidirect
203. #2025	C₂×C₄₁	semidirect
204. #2024	C₂×C₄₁	semidirect
205. #2023	C₂×C₄₁	semidirect
206. #1735	C₂×C₄₁	semidirect
207. C₂×#336	C₂×C₄₁	semidirect
238. C₄₁	#23451	direct (N × H)
242. C₂×#41	Q₈×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×#533	2
C₂×C₄₁×#416	2
C₄₁×#2297	2
C₄₁×#2026	2
C₄₁×#2025	2
C₄₁×#2024	2
C₄₁×#2023	2
C₄₁×#1735	2
C₂×C₄₁×#336	2
#23451	41

Subgroups — C41×#23451 #23799652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#23451 #23799652