Subgroups — C₄₁×#11098 #23787299

Order 10496.

882 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#427	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#410	C₂	1	2	yes	maximal
3	C₂×C₄₁×#408	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#1735	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₁×H(3,ℤ/4)	C₂	1	2	yes	maximal, complemented
6	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
8	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
9	C₂×#117×C₄₁	C₂²	1	2	yes	—
10	C₂×#117×C₄₁	C₂²	1	2	yes	—
11	C₄₁×#427	—	2	4	no	—
12	C₂×#107×C₄₁	—	2	1	no	—
13	C₂×#106×C₄₁	—	2	1	no	—
14	C₄₁×#410	—	2	4	no	—
15	C₄₁×#410	—	2	4	no	—
16	C₂×#99×C₄₁	—	2	4	no	—
17	C₄₁×#408	—	2	2	no	—
18	C₄₁×#408	—	2	1	no	—
19	C₄₁×#408	—	2	1	no	—
20	C₂×C₂²⋊C₈×C₄₁	C₄	1	4	yes	complemented
21	C₄₁×#340	—	2	2	no	—
22	C₄₁×H(3,ℤ/4)	—	2	4	no	—
23	C₂×#41×C₄₁	—	2	1	no	—
24	C₂×#41×C₄₁	—	2	1	no	—
25	C₂×#41×C₄₁	—	2	2	no	—
26	C₂×#41×C₄₁	—	2	2	no	—
27	C₂×#41×C₄₁	—	2	1	no	—
28	C₂×#41×C₄₁	—	2	1	no	—
29	C₂×#41×C₄₁	—	2	2	no	—
30	C₂×#41×C₄₁	—	2	2	no	—
31	C₂²×Q₈×C₄₁	Q₈	1	1	yes	characteristic
32	C₂²×D₄×C₄₁	D₄	1	2	yes	—
33	C₂²×D₄×C₄₁	Q₈	1	1	yes	characteristic
34	C₂³×C₄×C₄₁	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
36	C₂×M₁₆×C₄₁	—	2	2	no	—
37	C₂×M₁₆×C₄₁	—	2	1	no	—
38	C₂×M₁₆×C₄₁	—	2	1	no	—
39	C₂×M₁₆×C₄₁	—	2	2	no	—
40	C₂²×C₈×C₄₁	—	2	2	no	—
41	C₂²×C₈×C₄₁	—	2	2	no	—
42	C₂²×C₈×C₄₁	C₂×C₄	1	2	yes	—
43	C₂²×C₈×C₄₁	C₂×C₄	1	2	yes	—
44	C₂²×C₈×C₄₁	D₄	1	2	yes	—
45	C₂²×C₈×C₄₁	D₄	1	1	yes	characteristic
46	C₂²×C₈×C₄₁	D₄	1	1	yes	characteristic
47	#117×C₄₁	—	2	2	no	—
48	#117×C₄₁	—	2	2	no	—
49	#117×C₄₁	—	2	2	no	—
50	#117×C₄₁	—	2	2	no	—
51	#117×C₄₁	—	2	2	no	—
52	#117×C₄₁	—	2	2	no	—
53	#117×C₄₁	D₄	1	4	yes	—
54	#117×C₄₁	D₄	1	4	yes	—
55	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
59	C₂×C₄²×C₄₁	—	2	2	no	—
60	C₂×C₄²×C₄₁	—	2	2	no	—
61	#107×C₄₁	—	2	4	no	—
62	#106×C₄₁	—	2	4	no	—
63	#99×C₄₁	—	2	16	no	—
64	C₂²⋊C₈×C₄₁	—	2	4	no	—
65	C₂²⋊C₈×C₄₁	—	2	4	no	—
66	C₂⁴×C₄₁	C₄⋊C₄	1	2	yes	—
67	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
68	#41×C₄₁	—	4	1	no	—
69	#41×C₄₁	—	4	2	no	—
70	#41×C₄₁	—	4	2	no	—
71	#41×C₄₁	—	4	2	no	—
72	#41×C₄₁	—	4	1	no	—
73	#41×C₄₁	—	4	2	no	—
74	#41×C₄₁	—	4	2	no	—
75	#41×C₄₁	—	4	1	no	—
76	#41×C₄₁	—	4	2	no	—
77	#41×C₄₁	—	4	1	no	—
78	C₂×Q₈×C₄₁	—	2	1	no	—
79	C₂×Q₈×C₄₁	—	2	1	no	—
80	C₂×Q₈×C₄₁	—	2	2	no	—
81	C₂×Q₈×C₄₁	—	2	2	no	—
82	C₂×D₄×C₄₁	—	2	4	no	—
83	C₂×D₄×C₄₁	—	2	2	no	—
84	C₂×D₄×C₄₁	—	2	2	no	—
85	C₂×D₄×C₄₁	—	2	4	no	—
86	C₂×D₄×C₄₁	—	2	2	no	—
87	C₂×D₄×C₄₁	—	2	1	no	—
88	C₂×D₄×C₄₁	—	2	1	no	—
89	C₂×D₄×C₄₁	—	2	2	no	—
90	C₂²×C₄×C₄₁	—	2	2	no	—
91	C₂²×C₄×C₄₁	—	2	2	no	—
92	C₂²×C₄×C₄₁	—	2	4	no	—
93	C₂²×C₄×C₄₁	—	2	4	no	—
94	C₂²×C₄×C₄₁	—	4	2	no	—
95	C₂²×C₄×C₄₁	—	4	2	no	—
96	C₂²×C₄×C₄₁	C₄⋊C₄	1	2	yes	—
97	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
102	C₂²×C₄×C₄₁	C₂×Q₈	1	1	yes	characteristic
103	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
104	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
105	C₂²×C₄×C₄₁	#41	1	2	yes	—
106	C₂²×C₄×C₄₁	#41	1	2	yes	—
107	M₁₆×C₄₁	—	4	2	no	—
108	M₁₆×C₄₁	—	4	1	no	—
109	M₁₆×C₄₁	—	4	1	no	—
110	C₂×C₈×C₄₁	—	2	4	no	—
111	C₂×C₈×C₄₁	—	2	1	no	—
112	C₂×C₈×C₄₁	—	2	1	no	—
113	C₂×C₈×C₄₁	—	2	4	no	—
114	C₂×C₈×C₄₁	—	2	1	no	—
115	C₂×C₈×C₄₁	—	2	1	no	—
116	C₂×C₈×C₄₁	—	2	2	no	—
117	C₂×C₈×C₄₁	—	2	4	no	—
118	C₂×C₈×C₄₁	C₂²⋊C₄	1	2	yes	—
119	C₂×C₈×C₄₁	C₂²⋊C₄	1	2	yes	—
120	C₄⋊C₄×C₄₁	—	2	4	no	—
121	C₄⋊C₄×C₄₁	—	2	4	no	—
122	C₄⋊C₄×C₄₁	—	4	2	no	—
123	C₄⋊C₄×C₄₁	—	4	2	no	—
124	C₂²⋊C₄×C₄₁	—	2	4	no	—
125	C₂²⋊C₄×C₄₁	—	2	4	no	—
126	C₂²⋊C₄×C₄₁	—	4	2	no	—
127	C₂²⋊C₄×C₄₁	—	4	2	no	—
128	C₄²×C₄₁	—	2	4	no	—
129	C₄²×C₄₁	—	2	4	no	—
130	C₄²×C₄₁	—	4	2	no	—
131	C₄²×C₄₁	—	4	2	no	—
132	C₂³×C₄₁	—	2	2	no	—
133	C₂³×C₄₁	—	2	4	no	—
134	C₂³×C₄₁	—	4	2	no	—
135	C₂³×C₄₁	—	4	4	no	—
136	C₂³×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂³×C₄₁	#120	1	2	yes	—
138	C₂³×C₄₁	#121	1	1	yes	characteristic
139	C₂³×C₄₁	#121	1	1	yes	characteristic
140	C₂³×C₄₁	#123	1	2	yes	—
141	Q₈×C₄₁	—	4	1	no	—
142	Q₈×C₄₁	—	4	2	no	—
143	Q₈×C₄₁	—	4	1	no	—
144	D₄×C₄₁	—	4	2	no	—
145	D₄×C₄₁	—	4	4	no	—
146	D₄×C₄₁	—	4	2	no	—
147	D₄×C₄₁	—	4	1	no	—
148	D₄×C₄₁	—	4	2	no	—
149	D₄×C₄₁	—	4	1	no	—
150	C₂×C₄×C₄₁	—	2	2	no	—
151	C₂×C₄×C₄₁	—	2	4	no	—
152	C₂×C₄×C₄₁	—	4	2	no	—
153	C₂×C₄×C₄₁	—	4	4	no	—
154	C₂×C₄×C₄₁	—	4	2	no	—
155	C₂×C₄×C₄₁	—	4	4	no	—
156	C₂×C₄×C₄₁	—	4	4	no	—
157	C₂×C₄×C₄₁	—	8	4	no	—
158	C₂×C₄×C₄₁	—	8	4	no	—
159	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₄₁	#117	1	1	yes	characteristic
161	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
162	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
163	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
164	C₂×C₄×C₄₁	#121	1	2	yes	—
165	C₂×C₄×C₄₁	#121	1	2	yes	—
166	C₂×C₄×C₄₁	#121	1	2	yes	—
167	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
168	C₂×C₄×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
169	C₂×C₄×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
170	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
171	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
172	C₂×C₄×C₄₁	#123	1	2	yes	—
173	C₂×C₄×C₄₁	#124	1	2	yes	—
174	C₂×C₄×C₄₁	#124	1	1	yes	characteristic
175	C₂×C₄×C₄₁	#126	1	2	yes	—
176	C₂×C₄×C₄₁	#127	1	1	yes	characteristic
177	C₈×C₄₁	—	2	2	no	—
178	C₈×C₄₁	—	2	2	no	—
179	C₈×C₄₁	—	4	2	no	—
180	#11098	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂²×C₄₁	—	2	2	no	—
182	C₂²×C₄₁	—	2	2	no	—
183	C₂²×C₄₁	—	2	2	no	—
184	C₂²×C₄₁	—	4	2	no	—
185	C₂²×C₄₁	—	4	2	no	—
186	C₂²×C₄₁	—	4	4	no	—
187	C₂²×C₄₁	—	4	2	no	—
188	C₂²×C₄₁	—	8	4	no	—
189	C₂²×C₄₁	#380	1	1	yes	characteristic
190	C₂²×C₄₁	#385	1	2	yes	—
191	C₂²×C₄₁	#392	1	1	yes	characteristic
192	C₂²×C₄₁	#394	1	2	yes	—
193	C₂²×C₄₁	#397	1	1	yes	characteristic
194	C₄×C₄₁	—	4	2	no	—
195	C₄×C₄₁	—	8	4	no	—
196	C₄×C₄₁	—	8	4	no	—
197	C₄×C₄₁	#386	1	1	yes	characteristic
198	C₄×C₄₁	#388	1	2	yes	—
199	C₄×C₄₁	#390	1	1	yes	characteristic
200	C₄×C₄₁	#393	1	1	yes	characteristic
201	C₄×C₄₁	#396	1	2	yes	—
202	C₄×C₄₁	#399	1	1	yes	characteristic
203	C₂×#427	C₂×C₄₁	1	1	yes	characteristic, complemented
204	C₂×#410	C₂×C₄₁	1	2	yes	—
205	C₂×#408	C₂×C₄₁	1	1	yes	characteristic
206	#1735	C₂×C₄₁	1	1	yes	characteristic, complemented
207	C₂×H(3,ℤ/4)	C₂×C₄₁	1	2	yes	complemented
208	C₂×C₄₁	—	2	1	no	—
209	C₂×C₄₁	—	2	2	no	—
210	C₂×C₄₁	—	2	2	no	—
211	C₂×C₄₁	—	2	1	no	—
212	C₂×C₄₁	—	8	2	no	—
213	C₂×C₄₁	#1439	1	1	yes	characteristic
214	C₂×C₄₁	#1812	1	2	yes	—
215	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
216	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
217	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
218	C₂×#117	C₂²×C₄₁	1	2	yes	—
219	C₂×#117	C₂²×C₄₁	1	2	yes	—
220	#427	—	2	4	no	—
221	C₂×#107	—	2	1	no	—
222	C₂×#106	—	2	1	no	—
223	#410	—	2	4	no	—
224	#410	—	2	4	no	—
225	C₂×#99	—	2	4	no	—
226	#408	—	2	2	no	—
227	#408	—	2	1	no	—
228	#408	—	2	1	no	—
229	C₂×C₂²⋊C₈	C₄×C₄₁	1	4	yes	complemented
230	#340	—	2	2	no	—
231	H(3,ℤ/4)	—	2	4	no	—
232	C₄₁	#11098	1	1	yes	characteristic, direct product factor, Sylow
233	C₂×#41	—	2	1	no	—
234	C₂×#41	—	2	1	no	—
235	C₂×#41	—	2	2	no	—
236	C₂×#41	—	2	2	no	—
237	C₂×#41	—	2	1	no	—
238	C₂×#41	—	2	1	no	—
239	C₂×#41	—	2	2	no	—
240	C₂×#41	—	2	2	no	—
241	C₂²×Q₈	Q₈×C₄₁	1	1	yes	characteristic
242	C₂²×D₄	D₄×C₄₁	1	2	yes	—
243	C₂²×D₄	Q₈×C₄₁	1	1	yes	characteristic
244	C₂³×C₄	C₂×C₄×C₄₁	1	2	yes	—
245	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
246	C₂×M₁₆	—	2	2	no	—
247	C₂×M₁₆	—	2	1	no	—
248	C₂×M₁₆	—	2	1	no	—
249	C₂×M₁₆	—	2	2	no	—
250	C₂²×C₈	—	2	2	no	—
251	C₂²×C₈	—	2	2	no	—
252	C₂²×C₈	C₂×C₄×C₄₁	1	2	yes	—
253	C₂²×C₈	C₂×C₄×C₄₁	1	2	yes	—
254	C₂²×C₈	D₄×C₄₁	1	2	yes	—
255	C₂²×C₈	D₄×C₄₁	1	1	yes	characteristic
256	C₂²×C₈	D₄×C₄₁	1	1	yes	characteristic
257	#117	—	2	2	no	—
258	#117	—	2	2	no	—
259	#117	—	2	2	no	—
260	#117	—	2	2	no	—
261	#117	—	2	2	no	—
262	#117	—	2	2	no	—
263	#117	D₄×C₄₁	1	4	yes	—
264	#117	D₄×C₄₁	1	4	yes	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₄²	—	2	2	no	—
270	C₂×C₄²	—	2	2	no	—
271	#107	—	2	4	no	—
272	#106	—	2	4	no	—
273	#99	—	2	16	no	—
274	C₂²⋊C₈	—	2	4	no	—
275	C₂²⋊C₈	—	2	4	no	—
276	C₂⁴	C₄⋊C₄×C₄₁	1	2	yes	—
277	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
278	#41	—	4	1	no	—
279	#41	—	4	2	no	—
280	#41	—	4	2	no	—
281	#41	—	4	2	no	—
282	#41	—	4	1	no	—
283	#41	—	4	2	no	—
284	#41	—	4	2	no	—
285	#41	—	4	1	no	—
286	#41	—	4	2	no	—
287	#41	—	4	1	no	—
288	C₂×Q₈	—	2	1	no	—
289	C₂×Q₈	—	2	1	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	4	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	4	2	no	—
305	C₂²×C₄	—	4	2	no	—
306	C₂²×C₄	C₄⋊C₄×C₄₁	1	2	yes	—
307	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
310	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
312	C₂²×C₄	C₂×Q₈×C₄₁	1	1	yes	characteristic
313	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
314	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
315	C₂²×C₄	#41×C₄₁	1	2	yes	—
316	C₂²×C₄	#41×C₄₁	1	2	yes	—
317	M₁₆	—	4	2	no	—
318	M₁₆	—	4	1	no	—
319	M₁₆	—	4	1	no	—
320	C₂×C₈	—	2	4	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	4	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	4	no	—
328	C₂×C₈	C₂²⋊C₄×C₄₁	1	2	yes	—
329	C₂×C₈	C₂²⋊C₄×C₄₁	1	2	yes	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	4	2	no	—
333	C₄⋊C₄	—	4	2	no	—
334	C₂²⋊C₄	—	2	4	no	—
335	C₂²⋊C₄	—	2	4	no	—
336	C₂²⋊C₄	—	4	2	no	—
337	C₂²⋊C₄	—	4	2	no	—
338	C₄²	—	2	4	no	—
339	C₄²	—	2	4	no	—
340	C₄²	—	4	2	no	—
341	C₄²	—	4	2	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	4	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	4	no	—
346	C₂³	C₂×C₄⋊C₄×C₄₁	1	1	yes	characteristic
347	C₂³	#120×C₄₁	1	2	yes	—
348	C₂³	#121×C₄₁	1	1	yes	characteristic
349	C₂³	#121×C₄₁	1	1	yes	characteristic
350	C₂³	#123×C₄₁	1	2	yes	—
351	Q₈	—	4	1	no	—
352	Q₈	—	4	2	no	—
353	Q₈	—	4	1	no	—
354	D₄	—	4	2	no	—
355	D₄	—	4	4	no	—
356	D₄	—	4	2	no	—
357	D₄	—	4	1	no	—
358	D₄	—	4	2	no	—
359	D₄	—	4	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	8	4	no	—
368	C₂×C₄	—	8	4	no	—
369	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
370	C₂×C₄	#117×C₄₁	1	1	yes	characteristic
371	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
372	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
373	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
374	C₂×C₄	#121×C₄₁	1	2	yes	—
375	C₂×C₄	#121×C₄₁	1	2	yes	—
376	C₂×C₄	#121×C₄₁	1	2	yes	—
377	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
378	C₂×C₄	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
379	C₂×C₄	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
380	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
381	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
382	C₂×C₄	#123×C₄₁	1	2	yes	—
383	C₂×C₄	#124×C₄₁	1	2	yes	—
384	C₂×C₄	#124×C₄₁	1	1	yes	characteristic
385	C₂×C₄	#126×C₄₁	1	2	yes	—
386	C₂×C₄	#127×C₄₁	1	1	yes	characteristic
387	C₈	—	2	2	no	—
388	C₈	—	2	2	no	—
389	C₈	—	4	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	4	4	no	—
396	C₂²	—	4	2	no	—
397	C₂²	—	8	4	no	—
398	C₂²	C₄₁×#380	1	1	yes	characteristic
399	C₂²	C₄₁×#385	1	2	yes	—
400	C₂²	C₄₁×#392	1	1	yes	characteristic
401	C₂²	C₄₁×#394	1	2	yes	—
402	C₂²	C₄₁×#397	1	1	yes	characteristic
403	C₄	—	4	2	no	—
404	C₄	—	8	4	no	—
405	C₄	—	8	4	no	—
406	C₄	C₄₁×#386	1	1	yes	characteristic
407	C₄	C₄₁×#388	1	2	yes	—
408	C₄	C₄₁×#390	1	1	yes	characteristic
409	C₄	C₄₁×#393	1	1	yes	characteristic
410	C₄	C₄₁×#396	1	2	yes	—
411	C₄	C₄₁×#399	1	1	yes	characteristic
412	C₂	—	2	1	no	—
413	C₂	—	2	2	no	—
414	C₂	—	2	2	no	—
415	C₂	—	2	1	no	—
416	C₂	—	8	2	no	—
417	C₂	C₄₁×#1439	1	1	yes	characteristic
418	C₂	C₄₁×#1812	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₄₁	#117
commutator	C₂²×C₄	C₂²×C₄×C₄₁
Frattini, cosocle	C₂³×C₄	C₂³×C₄₁
socle	C₂²×C₄₁	#380
prime radical	C₂²×#41×C₄₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁ ◁ C₂²×M₁₆×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#427	C₂	semidirect
4. C₄₁×#1735	C₂	semidirect
5. C₂×C₄₁×H(3,ℤ/4)	C₂	semidirect
20. C₂×C₂²⋊C₈×C₄₁	C₄	semidirect
180. #11098	C₄₁	direct (N × H)
203. C₂×#427	C₂×C₄₁	semidirect
206. #1735	C₂×C₄₁	semidirect
207. C₂×H(3,ℤ/4)	C₂×C₄₁	semidirect
229. C₂×C₂²⋊C₈	C₄×C₄₁	semidirect
232. C₄₁	#11098	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#427	2
C₂×C₄₁×#410	2
C₂×C₄₁×#408	2
C₄₁×#1735	2
C₂×C₄₁×H(3,ℤ/4)	2
#11098	41

Subgroups — C41×#11098 #23787299

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#11098 #23787299