Subgroups — C₄₁×#21094 #23797295

Order 10496.

1122 conjugacy classes of subgroups.

The subgroup lattice has 438 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	1	yes	maximal, characteristic
2	C₂×C₄₁×#419	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×M₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2296	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄₁×#391	C₂	1	1	yes	maximal, characteristic
6	C₄₁×#1935	C₂	1	4	yes	maximal, complemented
7	C₄₁×#1933	C₂	1	4	yes	maximal, complemented
8	C₄₁×#1736	C₂	1	1	yes	maximal, characteristic
9	C₄₁×#1736	C₂	1	1	yes	maximal, characteristic
10	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
17	C₄₁×#419	—	2	4	no	—
18	C₄₁×#419	C₄	1	8	yes	complemented
19	C₂×#103×C₄₁	C₂²	1	4	yes	—
20	C₂×#103×C₄₁	C₂²	1	4	yes	—
21	C₄×M₁₆×C₄₁	—	2	4	no	—
22	C₂×#97×C₄₁	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
24	C₄₁×#391	—	2	2	no	—
25	C₄₁×#391	C₂²	1	2	yes	—
26	C₄₁×#391	C₂²	1	2	yes	—
27	C₄₁×#389	C₂²	1	2	yes	—
28	C₄₁×#389	C₂²	1	2	yes	—
29	C₄₁×#385	—	2	2	no	—
30	C₄×C₄⋊C₄×C₄₁	—	2	2	no	—
31	C₂×#95×C₄₁	—	2	2	no	—
32	C₄₁×#340	C₂²	1	4	yes	—
33	C₄₁×#340	C₂²	1	4	yes	—
34	C₂²×Q₈×C₄₁	—	2	1	no	—
35	C₂²×Q₈×C₄₁	—	2	2	no	—
36	C₂²×Q₈×C₄₁	—	2	2	no	—
37	C₂²×Q₈×C₄₁	—	2	2	no	—
38	C₂²×Q₈×C₄₁	—	2	2	no	—
39	C₂²×Q₈×C₄₁	—	2	2	no	—
40	C₂²×Q₈×C₄₁	C₂×C₄	1	4	yes	—
41	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
42	C₂³×C₄×C₄₁	—	2	1	no	—
43	C₂³×C₄×C₄₁	—	2	1	no	—
44	C₂³×C₄×C₄₁	D₄	1	2	yes	—
45	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₄₁	—	2	2	no	—
47	C₂×M₁₆×C₄₁	—	2	2	no	—
48	C₂×M₁₆×C₄₁	—	2	2	no	—
49	C₂×M₁₆×C₄₁	—	2	2	no	—
50	C₂×M₁₆×C₄₁	C₂×C₄	1	4	yes	—
51	C₂×M₁₆×C₄₁	D₄	1	4	yes	—
52	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
53	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
54	#117×C₄₁	—	2	2	no	—
55	#117×C₄₁	—	2	2	no	—
56	#117×C₄₁	—	2	2	no	—
57	#117×C₄₁	C₂×C₄	1	4	yes	—
58	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
68	C₂×C₄²×C₄₁	—	2	2	no	—
69	C₂×C₄²×C₄₁	—	2	1	no	—
70	C₂×C₄²×C₄₁	—	2	2	no	—
71	C₂×C₄²×C₄₁	—	2	1	no	—
72	C₂×C₄²×C₄₁	D₄	1	2	yes	—
73	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
75	#103×C₄₁	—	2	8	no	—
76	#103×C₄₁	C₂×C₄	1	16	yes	complemented
77	#97×C₄₁	—	2	4	no	—
78	C₄×C₈×C₄₁	—	2	4	no	—
79	#95×C₄₁	—	2	4	no	—
80	#95×C₄₁	—	2	4	no	—
81	#95×C₄₁	—	2	2	no	—
82	#95×C₄₁	—	2	2	no	—
83	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
84	C₂×Q₈×C₄₁	—	2	4	no	—
85	C₂×Q₈×C₄₁	—	2	2	no	—
86	C₂×Q₈×C₄₁	—	2	8	no	—
87	C₂×Q₈×C₄₁	—	2	8	no	—
88	C₂×Q₈×C₄₁	—	2	2	no	—
89	C₂×Q₈×C₄₁	—	2	2	no	—
90	C₂×Q₈×C₄₁	—	2	2	no	—
91	C₂×Q₈×C₄₁	—	2	2	no	—
92	C₂×Q₈×C₄₁	—	4	2	no	—
93	C₂×Q₈×C₄₁	—	4	4	no	—
94	C₂×Q₈×C₄₁	—	4	2	no	—
95	C₂×Q₈×C₄₁	—	4	4	no	—
96	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	—
97	C₂²×C₄×C₄₁	—	2	4	no	—
98	C₂²×C₄×C₄₁	—	2	4	no	—
99	C₂²×C₄×C₄₁	—	2	2	no	—
100	C₂²×C₄×C₄₁	—	2	2	no	—
101	C₂²×C₄×C₄₁	—	2	4	no	—
102	C₂²×C₄×C₄₁	—	2	2	no	—
103	C₂²×C₄×C₄₁	—	2	2	no	—
104	C₂²×C₄×C₄₁	—	4	2	no	—
105	C₂²×C₄×C₄₁	—	4	2	no	—
106	C₂²×C₄×C₄₁	—	4	2	no	—
107	C₂²×C₄×C₄₁	—	4	4	no	—
108	C₂²×C₄×C₄₁	—	4	2	no	—
109	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₄₁	#41	1	2	yes	—
115	C₂²×C₄×C₄₁	#41	1	2	yes	—
116	C₂²×C₄×C₄₁	#41	1	2	yes	—
117	C₂²×C₄×C₄₁	#41	1	2	yes	—
118	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
119	M₁₆×C₄₁	—	2	8	no	—
120	M₁₆×C₄₁	—	2	8	no	—
121	C₂×C₈×C₄₁	—	2	2	no	—
122	C₂×C₈×C₄₁	—	2	2	no	—
123	C₂×C₈×C₄₁	—	2	2	no	—
124	C₂×C₈×C₄₁	—	2	2	no	—
125	C₂×C₈×C₄₁	C₂²×C₄	1	4	yes	—
126	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
127	C₄⋊C₄×C₄₁	—	2	2	no	—
128	C₄⋊C₄×C₄₁	—	2	2	no	—
129	C₄⋊C₄×C₄₁	—	2	2	no	—
130	C₄⋊C₄×C₄₁	—	2	2	no	—
131	C₄⋊C₄×C₄₁	—	2	2	no	—
132	C₄⋊C₄×C₄₁	—	4	4	no	—
133	C₄⋊C₄×C₄₁	—	4	2	no	—
134	C₄⋊C₄×C₄₁	—	4	4	no	—
135	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
136	C₂²⋊C₄×C₄₁	—	2	4	no	—
137	C₂²⋊C₄×C₄₁	—	4	2	no	—
138	C₄²×C₄₁	—	2	4	no	—
139	C₄²×C₄₁	—	2	4	no	—
140	C₄²×C₄₁	—	2	1	no	—
141	C₄²×C₄₁	—	2	1	no	—
142	C₄²×C₄₁	—	2	1	no	—
143	C₄²×C₄₁	—	2	1	no	—
144	C₄²×C₄₁	—	4	2	no	—
145	C₂³×C₄₁	—	2	2	no	—
146	C₂³×C₄₁	—	2	2	no	—
147	C₂³×C₄₁	C₄×D₄	1	2	yes	—
148	C₂³×C₄₁	#121	1	2	yes	—
149	C₂³×C₄₁	#124	1	2	yes	—
150	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₄₁	—	2	4	no	—
152	Q₈×C₄₁	—	2	4	no	—
153	Q₈×C₄₁	—	4	2	no	—
154	Q₈×C₄₁	—	4	2	no	—
155	Q₈×C₄₁	—	4	8	no	—
156	C₂×C₄×C₄₁	—	2	2	no	—
157	C₂×C₄×C₄₁	—	2	2	no	—
158	C₂×C₄×C₄₁	—	2	4	no	—
159	C₂×C₄×C₄₁	—	2	4	no	—
160	C₂×C₄×C₄₁	—	2	2	no	—
161	C₂×C₄×C₄₁	—	2	2	no	—
162	C₂×C₄×C₄₁	—	2	2	no	—
163	C₂×C₄×C₄₁	—	4	8	no	—
164	C₂×C₄×C₄₁	—	4	2	no	—
165	C₂×C₄×C₄₁	—	4	2	no	—
166	C₂×C₄×C₄₁	—	4	2	no	—
167	C₂×C₄×C₄₁	—	4	2	no	—
168	C₂×C₄×C₄₁	—	4	8	no	—
169	C₂×C₄×C₄₁	—	4	2	no	—
170	C₂×C₄×C₄₁	—	4	2	no	—
171	C₂×C₄×C₄₁	—	4	2	no	—
172	C₂×C₄×C₄₁	—	4	2	no	—
173	C₂×C₄×C₄₁	—	4	4	no	—
174	C₂×C₄×C₄₁	—	8	4	no	—
175	C₂×C₄×C₄₁	#117	1	4	yes	—
176	C₂×C₄×C₄₁	C₄×D₄	1	4	yes	—
177	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
178	C₂×C₄×C₄₁	#121	1	2	yes	—
179	C₂×C₄×C₄₁	#123	1	4	yes	—
180	C₂×C₄×C₄₁	#124	1	2	yes	—
181	C₂×C₄×C₄₁	#126	1	4	yes	—
182	C₂×C₄×C₄₁	#137	1	4	yes	—
183	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
184	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
189	C₈×C₄₁	—	2	4	no	—
190	C₈×C₄₁	—	2	4	no	—
191	#21094	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂²×C₄₁	—	2	2	no	—
193	C₂²×C₄₁	—	2	2	no	—
194	C₂²×C₄₁	—	2	4	no	—
195	C₂²×C₄₁	—	2	4	no	—
196	C₂²×C₄₁	#388	1	4	yes	—
197	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
198	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
199	C₂²×C₄₁	C₂×#124	1	1	yes	characteristic
200	C₂²×C₄₁	C₂×#137	1	2	yes	—
201	C₂²×C₄₁	#575	1	2	yes	—
202	C₄×C₄₁	—	2	4	no	—
203	C₄×C₄₁	—	4	4	no	—
204	C₄×C₄₁	—	4	2	no	—
205	C₄×C₄₁	—	4	4	no	—
206	C₄×C₄₁	—	8	2	no	—
207	C₄×C₄₁	—	8	2	no	—
208	C₄×C₄₁	#388	1	4	yes	—
209	C₄×C₄₁	C₂×#117	1	1	yes	characteristic
210	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
211	C₄×C₄₁	C₂×#123	1	1	yes	characteristic
212	C₄×C₄₁	C₂×#126	1	1	yes	characteristic
213	C₂×#419	C₂×C₄₁	1	1	yes	characteristic
214	C₂×#419	C₂×C₄₁	1	1	yes	characteristic
215	C₂×C₄×M₁₆	C₂×C₄₁	1	1	yes	characteristic
216	#2296	C₂×C₄₁	1	1	yes	characteristic
217	C₂×#391	C₂×C₄₁	1	1	yes	characteristic
218	#1935	C₂×C₄₁	1	4	yes	complemented
219	#1933	C₂×C₄₁	1	4	yes	complemented
220	#1736	C₂×C₄₁	1	1	yes	characteristic
221	#1736	C₂×C₄₁	1	1	yes	characteristic
222	C₂×C₄₁	—	2	4	no	—
223	C₂×C₄₁	C₂×#388	1	1	yes	characteristic
224	C₂×C₄₁	C₄×#137	1	2	yes	—
225	C₂×C₄₁	#3056	1	2	yes	—
226	C₂×C₄₁	#3139	1	1	yes	characteristic
227	C₂×C₄₁	#3140	1	1	yes	characteristic
228	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
229	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
230	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
231	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
232	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
233	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
234	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
235	#419	—	2	4	no	—
236	#419	C₄×C₄₁	1	8	yes	complemented
237	C₂×#103	C₂²×C₄₁	1	4	yes	—
238	C₂×#103	C₂²×C₄₁	1	4	yes	—
239	C₄×M₁₆	—	2	4	no	—
240	C₂×#97	C₂²×C₄₁	1	2	yes	—
241	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
242	#391	—	2	2	no	—
243	#391	C₂²×C₄₁	1	2	yes	—
244	#391	C₂²×C₄₁	1	2	yes	—
245	#389	C₂²×C₄₁	1	2	yes	—
246	#389	C₂²×C₄₁	1	2	yes	—
247	#385	—	2	2	no	—
248	C₄×C₄⋊C₄	—	2	2	no	—
249	C₂×#95	—	2	2	no	—
250	#340	C₂²×C₄₁	1	4	yes	—
251	#340	C₂²×C₄₁	1	4	yes	—
252	C₄₁	#21094	1	1	yes	characteristic, direct product factor, Sylow
253	C₂²×Q₈	—	2	1	no	—
254	C₂²×Q₈	—	2	2	no	—
255	C₂²×Q₈	—	2	2	no	—
256	C₂²×Q₈	—	2	2	no	—
257	C₂²×Q₈	—	2	2	no	—
258	C₂²×Q₈	—	2	2	no	—
259	C₂²×Q₈	C₂×C₄×C₄₁	1	4	yes	—
260	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
261	C₂³×C₄	—	2	1	no	—
262	C₂³×C₄	—	2	1	no	—
263	C₂³×C₄	D₄×C₄₁	1	2	yes	—
264	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
265	C₂×M₁₆	—	2	2	no	—
266	C₂×M₁₆	—	2	2	no	—
267	C₂×M₁₆	—	2	2	no	—
268	C₂×M₁₆	—	2	2	no	—
269	C₂×M₁₆	C₂×C₄×C₄₁	1	4	yes	—
270	C₂×M₁₆	D₄×C₄₁	1	4	yes	—
271	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
272	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
273	#117	—	2	2	no	—
274	#117	—	2	2	no	—
275	#117	—	2	2	no	—
276	#117	C₂×C₄×C₄₁	1	4	yes	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
283	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
284	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
285	C₂×C₂²⋊C₄	—	2	1	no	—
286	C₂×C₂²⋊C₄	—	2	1	no	—
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	—	2	2	no	—
289	C₂×C₄²	—	2	2	no	—
290	C₂×C₄²	—	2	1	no	—
291	C₂×C₄²	D₄×C₄₁	1	2	yes	—
292	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
293	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
294	#103	—	2	8	no	—
295	#103	C₂×C₄×C₄₁	1	16	yes	complemented
296	#97	—	2	4	no	—
297	C₄×C₈	—	2	4	no	—
298	#95	—	2	4	no	—
299	#95	—	2	4	no	—
300	#95	—	2	2	no	—
301	#95	—	2	2	no	—
302	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
303	C₂×Q₈	—	2	4	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	8	no	—
306	C₂×Q₈	—	2	8	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	4	2	no	—
312	C₂×Q₈	—	4	4	no	—
313	C₂×Q₈	—	4	2	no	—
314	C₂×Q₈	—	4	4	no	—
315	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	4	2	no	—
324	C₂²×C₄	—	4	2	no	—
325	C₂²×C₄	—	4	2	no	—
326	C₂²×C₄	—	4	4	no	—
327	C₂²×C₄	—	4	2	no	—
328	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
329	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
330	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
331	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
333	C₂²×C₄	#41×C₄₁	1	2	yes	—
334	C₂²×C₄	#41×C₄₁	1	2	yes	—
335	C₂²×C₄	#41×C₄₁	1	2	yes	—
336	C₂²×C₄	#41×C₄₁	1	2	yes	—
337	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
338	M₁₆	—	2	8	no	—
339	M₁₆	—	2	8	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	C₂²×C₄×C₄₁	1	4	yes	—
345	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	4	4	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	—	4	4	no	—
354	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
355	C₂²⋊C₄	—	2	4	no	—
356	C₂²⋊C₄	—	4	2	no	—
357	C₄²	—	2	4	no	—
358	C₄²	—	2	4	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	2	1	no	—
362	C₄²	—	2	1	no	—
363	C₄²	—	4	2	no	—
364	C₂³	—	2	2	no	—
365	C₂³	—	2	2	no	—
366	C₂³	C₄×D₄×C₄₁	1	2	yes	—
367	C₂³	#121×C₄₁	1	2	yes	—
368	C₂³	#124×C₄₁	1	2	yes	—
369	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
370	Q₈	—	2	4	no	—
371	Q₈	—	2	4	no	—
372	Q₈	—	4	2	no	—
373	Q₈	—	4	2	no	—
374	Q₈	—	4	8	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	4	8	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	8	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	8	4	no	—
394	C₂×C₄	#117×C₄₁	1	4	yes	—
395	C₂×C₄	C₄×D₄×C₄₁	1	4	yes	—
396	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
397	C₂×C₄	#121×C₄₁	1	2	yes	—
398	C₂×C₄	#123×C₄₁	1	4	yes	—
399	C₂×C₄	#124×C₄₁	1	2	yes	—
400	C₂×C₄	#126×C₄₁	1	4	yes	—
401	C₂×C₄	#137×C₄₁	1	4	yes	—
402	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
403	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
404	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
405	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
406	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
407	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
408	C₈	—	2	4	no	—
409	C₈	—	2	4	no	—
410	C₂²	—	2	4	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	4	no	—
414	C₂²	C₄₁×#388	1	4	yes	—
415	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
416	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
417	C₂²	C₂×#124×C₄₁	1	1	yes	characteristic
418	C₂²	C₂×#137×C₄₁	1	2	yes	—
419	C₂²	C₄₁×#575	1	2	yes	—
420	C₄	—	2	4	no	—
421	C₄	—	4	2	no	—
422	C₄	—	4	4	no	—
423	C₄	—	4	4	no	—
424	C₄	—	8	2	no	—
425	C₄	—	8	2	no	—
426	C₄	C₄₁×#388	1	4	yes	—
427	C₄	C₂×#117×C₄₁	1	1	yes	characteristic
428	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
429	C₄	C₂×#123×C₄₁	1	1	yes	characteristic
430	C₄	C₂×#126×C₄₁	1	1	yes	characteristic
431	C₂	—	2	4	no	—
432	C₂	C₂×C₄₁×#388	1	1	yes	characteristic
433	C₂	C₄×#137×C₄₁	1	2	yes	—
434	C₂	C₄₁×#3056	1	2	yes	—
435	C₂	C₄₁×#3139	1	1	yes	characteristic
436	C₂	C₄₁×#3140	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
6. C₄₁×#1935	C₂	semidirect
7. C₄₁×#1933	C₂	semidirect
18. C₄₁×#419	C₄	semidirect
76. #103×C₄₁	C₂×C₄	semidirect
191. #21094	C₄₁	direct (N × H)
218. #1935	C₂×C₄₁	semidirect
219. #1933	C₂×C₄₁	semidirect
236. #419	C₄×C₄₁	semidirect
252. C₄₁	#21094	direct (N × H)
295. #103	C₂×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
C₂×C₄×M₁₆×C₄₁	2
C₄₁×#2296	2
C₂×C₄₁×#391	2
C₄₁×#1935	2
C₄₁×#1933	2
C₄₁×#1736	2
#21094	41

Subgroups — C41×#21094 #23797295

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#21094 #23797295