Subgroups — C₄₁×#11055 #23787256

Order 10496.

958 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#419	C₂	1	2	yes	maximal
2	C₄₁×#2316	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₁×#391	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₁×#343	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄₁×#339	C₂	1	2	yes	maximal
6	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₄₁	C₂²	1	2	yes	—
8	C₂×#117×C₄₁	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
10	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
11	C₄₁×#419	—	2	4	no	—
12	C₄₁×#419	—	2	4	no	—
13	C₂×#103×C₄₁	—	2	4	no	—
14	C₄₁×#391	—	2	2	no	—
15	C₄₁×#391	C₄	1	4	yes	complemented
16	C₄₁×#389	—	2	4	no	—
17	C₄₁×#380	—	2	2	no	—
18	C₂×#95×C₄₁	—	2	2	no	—
19	C₄₁×#343	—	2	2	no	—
20	C₄₁×#339	—	2	4	no	—
21	C₂²×Q₈×C₄₁	—	2	1	no	—
22	C₂²×Q₈×C₄₁	—	2	1	no	—
23	C₂²×Q₈×C₄₁	—	2	1	no	—
24	C₂²×Q₈×C₄₁	—	2	2	no	—
25	C₂²×Q₈×C₄₁	—	2	2	no	—
26	C₂²×Q₈×C₄₁	—	2	2	no	—
27	C₂²×Q₈×C₄₁	—	2	2	no	—
28	C₂²×Q₈×C₄₁	C₂×C₄	1	2	yes	—
29	C₂²×Q₈×C₄₁	D₄	1	2	yes	—
30	C₂²×Q₈×C₄₁	Q₈	1	2	yes	—
31	C₂³×C₄×C₄₁	—	2	1	no	—
32	C₂³×C₄×C₄₁	—	2	1	no	—
33	C₂³×C₄×C₄₁	D₄	1	2	yes	—
34	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
35	C₂×M₁₆×C₄₁	—	2	2	no	—
36	C₂×M₁₆×C₄₁	—	2	2	no	—
37	C₂×M₁₆×C₄₁	—	2	2	no	—
38	C₂×M₁₆×C₄₁	—	2	2	no	—
39	C₂×M₁₆×C₄₁	—	2	2	no	—
40	C₂×M₁₆×C₄₁	D₄	1	4	yes	—
41	C₂²×C₈×C₄₁	—	2	2	no	—
42	#117×C₄₁	—	2	2	no	—
43	#117×C₄₁	—	2	2	no	—
44	#117×C₄₁	—	2	2	no	—
45	#117×C₄₁	—	2	2	no	—
46	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
47	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
48	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
49	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
50	C₂×C₄⋊C₄×C₄₁	D₄	1	4	yes	—
51	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
52	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
53	C₂×C₄²×C₄₁	—	2	2	no	—
54	C₂×C₄²×C₄₁	—	2	2	no	—
55	C₂×C₄²×C₄₁	—	2	1	no	—
56	C₂×C₄²×C₄₁	—	2	2	no	—
57	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
58	#103×C₄₁	—	2	16	no	—
59	#95×C₄₁	—	2	4	no	—
60	#95×C₄₁	—	2	8	no	—
61	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
62	C₂×Q₈×C₄₁	—	2	2	no	—
63	C₂×Q₈×C₄₁	—	2	2	no	—
64	C₂×Q₈×C₄₁	—	2	2	no	—
65	C₂×Q₈×C₄₁	—	2	4	no	—
66	C₂×Q₈×C₄₁	—	2	4	no	—
67	C₂×Q₈×C₄₁	—	2	4	no	—
68	C₂×Q₈×C₄₁	—	2	4	no	—
69	C₂×Q₈×C₄₁	—	2	4	no	—
70	C₂×Q₈×C₄₁	—	2	4	no	—
71	C₂×Q₈×C₄₁	—	4	2	no	—
72	C₂×Q₈×C₄₁	—	4	2	no	—
73	C₂×Q₈×C₄₁	—	4	2	no	—
74	C₂×Q₈×C₄₁	—	4	2	no	—
75	C₂×Q₈×C₄₁	—	4	2	no	—
76	C₂×Q₈×C₄₁	—	4	2	no	—
77	C₂×Q₈×C₄₁	C₄⋊C₄	1	4	yes	complemented
78	C₂²×C₄×C₄₁	—	2	4	no	—
79	C₂²×C₄×C₄₁	—	2	2	no	—
80	C₂²×C₄×C₄₁	—	2	2	no	—
81	C₂²×C₄×C₄₁	—	2	2	no	—
82	C₂²×C₄×C₄₁	—	2	2	no	—
83	C₂²×C₄×C₄₁	—	2	2	no	—
84	C₂²×C₄×C₄₁	—	2	2	no	—
85	C₂²×C₄×C₄₁	—	2	4	no	—
86	C₂²×C₄×C₄₁	—	4	2	no	—
87	C₂²×C₄×C₄₁	—	4	1	no	—
88	C₂²×C₄×C₄₁	—	4	1	no	—
89	C₂²×C₄×C₄₁	—	4	1	no	—
90	C₂²×C₄×C₄₁	—	4	1	no	—
91	C₂²×C₄×C₄₁	—	4	1	no	—
92	C₂²×C₄×C₄₁	—	4	1	no	—
93	C₂²×C₄×C₄₁	—	4	4	no	—
94	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
95	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₁	C₂×Q₈	1	1	yes	characteristic
101	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
102	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
103	C₂²×C₄×C₄₁	#41	1	2	yes	—
104	C₂²×C₄×C₄₁	#41	1	2	yes	—
105	M₁₆×C₄₁	—	2	4	no	—
106	M₁₆×C₄₁	—	2	4	no	—
107	M₁₆×C₄₁	—	4	2	no	—
108	M₁₆×C₄₁	—	4	2	no	—
109	C₂×C₈×C₄₁	—	2	4	no	—
110	C₂×C₈×C₄₁	—	4	2	no	—
111	C₂×C₈×C₄₁	—	4	2	no	—
112	C₄⋊C₄×C₄₁	—	2	4	no	—
113	C₄⋊C₄×C₄₁	—	2	4	no	—
114	C₄⋊C₄×C₄₁	—	2	4	no	—
115	C₄⋊C₄×C₄₁	—	2	4	no	—
116	C₄⋊C₄×C₄₁	—	8	4	no	—
117	C₂²⋊C₄×C₄₁	—	4	2	no	—
118	C₂²⋊C₄×C₄₁	—	4	2	no	—
119	C₄²×C₄₁	—	2	4	no	—
120	C₄²×C₄₁	—	4	2	no	—
121	C₄²×C₄₁	—	4	2	no	—
122	C₄²×C₄₁	—	4	2	no	—
123	C₂³×C₄₁	—	2	2	no	—
124	C₂³×C₄₁	—	2	2	no	—
125	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
126	C₂³×C₄₁	#120	1	1	yes	characteristic
127	C₂³×C₄₁	#121	1	1	yes	characteristic
128	C₂³×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
129	C₂³×C₄₁	#123	1	1	yes	characteristic
130	C₂³×C₄₁	#124	1	1	yes	characteristic
131	C₂³×C₄₁	#127	1	1	yes	characteristic
132	Q₈×C₄₁	—	2	8	no	—
133	Q₈×C₄₁	—	4	4	no	—
134	Q₈×C₄₁	—	4	4	no	—
135	Q₈×C₄₁	—	4	4	no	—
136	C₂×C₄×C₄₁	—	2	4	no	—
137	C₂×C₄×C₄₁	—	2	4	no	—
138	C₂×C₄×C₄₁	—	2	4	no	—
139	C₂×C₄×C₄₁	—	4	2	no	—
140	C₂×C₄×C₄₁	—	4	4	no	—
141	C₂×C₄×C₄₁	—	4	4	no	—
142	C₂×C₄×C₄₁	—	4	2	no	—
143	C₂×C₄×C₄₁	—	4	2	no	—
144	C₂×C₄×C₄₁	—	4	2	no	—
145	C₂×C₄×C₄₁	—	4	2	no	—
146	C₂×C₄×C₄₁	—	4	2	no	—
147	C₂×C₄×C₄₁	—	4	2	no	—
148	C₂×C₄×C₄₁	—	4	2	no	—
149	C₂×C₄×C₄₁	—	4	4	no	—
150	C₂×C₄×C₄₁	—	4	4	no	—
151	C₂×C₄×C₄₁	—	4	4	no	—
152	C₂×C₄×C₄₁	—	4	4	no	—
153	C₂×C₄×C₄₁	—	4	4	no	—
154	C₂×C₄×C₄₁	—	8	2	no	—
155	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₄₁	#117	1	1	yes	characteristic
157	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
158	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
159	C₂×C₄×C₄₁	#120	1	2	yes	—
160	C₂×C₄×C₄₁	#121	1	2	yes	—
161	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
162	C₂×C₄×C₄₁	#121	1	2	yes	—
163	C₂×C₄×C₄₁	#121	1	2	yes	—
164	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
165	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
166	C₂×C₄×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
167	C₂×C₄×C₄₁	#123	1	2	yes	—
168	C₂×C₄×C₄₁	#123	1	2	yes	—
169	C₂×C₄×C₄₁	#124	1	2	yes	—
170	C₂×C₄×C₄₁	#126	1	2	yes	—
171	C₈×C₄₁	—	4	4	no	—
172	#11055	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂²×C₄₁	—	2	1	no	—
174	C₂²×C₄₁	—	2	1	no	—
175	C₂²×C₄₁	—	2	1	no	—
176	C₂²×C₄₁	—	2	1	no	—
177	C₂²×C₄₁	—	2	2	no	—
178	C₂²×C₄₁	—	2	2	no	—
179	C₂²×C₄₁	—	2	2	no	—
180	C₂²×C₄₁	—	2	2	no	—
181	C₂²×C₄₁	#380	1	1	yes	characteristic
182	C₂²×C₄₁	#386	1	1	yes	characteristic
183	C₂²×C₄₁	#390	1	1	yes	characteristic
184	C₂²×C₄₁	#392	1	1	yes	characteristic
185	C₂²×C₄₁	#393	1	1	yes	characteristic
186	C₂²×C₄₁	#397	1	1	yes	characteristic
187	C₂²×C₄₁	#399	1	1	yes	characteristic
188	C₂²×C₄₁	#455	1	2	yes	—
189	C₂²×C₄₁	#456	1	2	yes	—
190	C₄×C₄₁	—	4	4	no	—
191	C₄×C₄₁	—	4	4	no	—
192	C₄×C₄₁	—	4	4	no	—
193	C₄×C₄₁	—	8	4	no	—
194	C₄×C₄₁	#385	1	2	yes	—
195	C₄×C₄₁	#388	1	2	yes	—
196	C₄×C₄₁	#394	1	2	yes	—
197	C₄×C₄₁	#396	1	2	yes	—
198	C₂×#419	C₂×C₄₁	1	2	yes	—
199	#2316	C₂×C₄₁	1	1	yes	characteristic
200	C₂×#391	C₂×C₄₁	1	1	yes	characteristic
201	C₂×#343	C₂×C₄₁	1	1	yes	characteristic
202	C₂×#339	C₂×C₄₁	1	2	yes	—
203	C₂×C₄₁	—	2	1	no	—
204	C₂×C₄₁	—	2	1	no	—
205	C₂×C₄₁	—	2	1	no	—
206	C₂×C₄₁	—	2	1	no	—
207	C₂×C₄₁	#1439	1	1	yes	characteristic
208	C₂×C₄₁	#1885	1	1	yes	characteristic
209	C₂×C₄₁	#1886	1	1	yes	characteristic
210	C₂×C₄₁	#2007	1	2	yes	—
211	C₂×C₄₁	#2028	1	2	yes	—
212	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
213	C₂²×M₁₆	C₂²×C₄₁	1	2	yes	—
214	C₂×#117	C₂²×C₄₁	1	2	yes	—
215	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
216	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
217	#419	—	2	4	no	—
218	#419	—	2	4	no	—
219	C₂×#103	—	2	4	no	—
220	#391	—	2	2	no	—
221	#391	C₄×C₄₁	1	4	yes	complemented
222	#389	—	2	4	no	—
223	#380	—	2	2	no	—
224	C₂×#95	—	2	2	no	—
225	#343	—	2	2	no	—
226	#339	—	2	4	no	—
227	C₄₁	#11055	1	1	yes	characteristic, direct product factor, Sylow
228	C₂²×Q₈	—	2	1	no	—
229	C₂²×Q₈	—	2	1	no	—
230	C₂²×Q₈	—	2	1	no	—
231	C₂²×Q₈	—	2	2	no	—
232	C₂²×Q₈	—	2	2	no	—
233	C₂²×Q₈	—	2	2	no	—
234	C₂²×Q₈	—	2	2	no	—
235	C₂²×Q₈	C₂×C₄×C₄₁	1	2	yes	—
236	C₂²×Q₈	D₄×C₄₁	1	2	yes	—
237	C₂²×Q₈	Q₈×C₄₁	1	2	yes	—
238	C₂³×C₄	—	2	1	no	—
239	C₂³×C₄	—	2	1	no	—
240	C₂³×C₄	D₄×C₄₁	1	2	yes	—
241	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
242	C₂×M₁₆	—	2	2	no	—
243	C₂×M₁₆	—	2	2	no	—
244	C₂×M₁₆	—	2	2	no	—
245	C₂×M₁₆	—	2	2	no	—
246	C₂×M₁₆	—	2	2	no	—
247	C₂×M₁₆	D₄×C₄₁	1	4	yes	—
248	C₂²×C₈	—	2	2	no	—
249	#117	—	2	2	no	—
250	#117	—	2	2	no	—
251	#117	—	2	2	no	—
252	#117	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	4	no	—
256	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
257	C₂×C₄⋊C₄	D₄×C₄₁	1	4	yes	—
258	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₄²	—	2	2	no	—
261	C₂×C₄²	—	2	2	no	—
262	C₂×C₄²	—	2	2	no	—
263	C₂×C₄²	—	2	1	no	—
264	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
265	#103	—	2	16	no	—
266	#95	—	2	4	no	—
267	#95	—	2	8	no	—
268	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
269	C₂×Q₈	—	2	2	no	—
270	C₂×Q₈	—	2	2	no	—
271	C₂×Q₈	—	2	2	no	—
272	C₂×Q₈	—	2	4	no	—
273	C₂×Q₈	—	2	4	no	—
274	C₂×Q₈	—	2	4	no	—
275	C₂×Q₈	—	2	4	no	—
276	C₂×Q₈	—	2	4	no	—
277	C₂×Q₈	—	2	4	no	—
278	C₂×Q₈	—	4	2	no	—
279	C₂×Q₈	—	4	2	no	—
280	C₂×Q₈	—	4	2	no	—
281	C₂×Q₈	—	4	2	no	—
282	C₂×Q₈	—	4	2	no	—
283	C₂×Q₈	—	4	2	no	—
284	C₂×Q₈	C₄⋊C₄×C₄₁	1	4	yes	complemented
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	—	4	1	no	—
295	C₂²×C₄	—	4	1	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	—	4	1	no	—
298	C₂²×C₄	—	4	1	no	—
299	C₂²×C₄	—	4	1	no	—
300	C₂²×C₄	—	4	4	no	—
301	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
302	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
305	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
306	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
307	C₂²×C₄	C₂×Q₈×C₄₁	1	1	yes	characteristic
308	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
309	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
310	C₂²×C₄	#41×C₄₁	1	2	yes	—
311	C₂²×C₄	#41×C₄₁	1	2	yes	—
312	M₁₆	—	2	4	no	—
313	M₁₆	—	2	4	no	—
314	M₁₆	—	4	2	no	—
315	M₁₆	—	4	2	no	—
316	C₂×C₈	—	2	4	no	—
317	C₂×C₈	—	4	2	no	—
318	C₂×C₈	—	4	2	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	8	4	no	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₂²⋊C₄	—	4	2	no	—
326	C₄²	—	2	4	no	—
327	C₄²	—	4	2	no	—
328	C₄²	—	4	2	no	—
329	C₄²	—	4	2	no	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	2	no	—
332	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
333	C₂³	#120×C₄₁	1	1	yes	characteristic
334	C₂³	#121×C₄₁	1	1	yes	characteristic
335	C₂³	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
336	C₂³	#123×C₄₁	1	1	yes	characteristic
337	C₂³	#124×C₄₁	1	1	yes	characteristic
338	C₂³	#127×C₄₁	1	1	yes	characteristic
339	Q₈	—	2	8	no	—
340	Q₈	—	4	4	no	—
341	Q₈	—	4	4	no	—
342	Q₈	—	4	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	4	4	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	8	2	no	—
362	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	1	yes	characteristic
363	C₂×C₄	#117×C₄₁	1	1	yes	characteristic
364	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
365	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
366	C₂×C₄	#120×C₄₁	1	2	yes	—
367	C₂×C₄	#121×C₄₁	1	2	yes	—
368	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
369	C₂×C₄	#121×C₄₁	1	2	yes	—
370	C₂×C₄	#121×C₄₁	1	2	yes	—
371	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
372	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
373	C₂×C₄	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
374	C₂×C₄	#123×C₄₁	1	2	yes	—
375	C₂×C₄	#123×C₄₁	1	2	yes	—
376	C₂×C₄	#124×C₄₁	1	2	yes	—
377	C₂×C₄	#126×C₄₁	1	2	yes	—
378	C₈	—	4	4	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	C₄₁×#380	1	1	yes	characteristic
388	C₂²	C₄₁×#386	1	1	yes	characteristic
389	C₂²	C₄₁×#390	1	1	yes	characteristic
390	C₂²	C₄₁×#392	1	1	yes	characteristic
391	C₂²	C₄₁×#393	1	1	yes	characteristic
392	C₂²	C₄₁×#397	1	1	yes	characteristic
393	C₂²	C₄₁×#399	1	1	yes	characteristic
394	C₂²	C₄₁×#455	1	2	yes	—
395	C₂²	C₄₁×#456	1	2	yes	—
396	C₄	—	4	4	no	—
397	C₄	—	4	4	no	—
398	C₄	—	4	4	no	—
399	C₄	—	8	4	no	—
400	C₄	C₄₁×#385	1	2	yes	—
401	C₄	C₄₁×#388	1	2	yes	—
402	C₄	C₄₁×#394	1	2	yes	—
403	C₄	C₄₁×#396	1	2	yes	—
404	C₂	—	2	1	no	—
405	C₂	—	2	1	no	—
406	C₂	—	2	1	no	—
407	C₂	—	2	1	no	—
408	C₂	C₄₁×#1439	1	1	yes	characteristic
409	C₂	C₄₁×#1885	1	1	yes	characteristic
410	C₂	C₄₁×#1886	1	1	yes	characteristic
411	C₂	C₄₁×#2007	1	2	yes	—
412	C₂	C₄₁×#2028	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	#120
commutator	C₂²×C₄	C₂²×C₄×C₄₁
Frattini, cosocle	C₂³×C₄	C₂³×C₄₁
prime radical	C₂⁴×C₄₁	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂³×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
15. C₄₁×#391	C₄	semidirect
77. C₂×Q₈×C₄₁	C₄⋊C₄	semidirect
172. #11055	C₄₁	direct (N × H)
221. #391	C₄×C₄₁	semidirect
227. C₄₁	#11055	direct (N × H)
284. C₂×Q₈	C₄⋊C₄×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×#419	2
C₄₁×#2316	2
C₂×C₄₁×#391	2
C₂×C₄₁×#343	2
C₂×C₄₁×#339	2
#11055	41

Subgroups — C41×#11055 #23787256

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#11055 #23787256