Subgroups — C₄₁×#21396 #23797597

Order 10496.

1182 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#529	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#117×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1989	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1983	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1875	C₂	1	2	yes	maximal
7	C₄₁×#1873	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1763	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1762	C₂	1	2	yes	maximal, complemented
10	C₄₁×#529	—	2	4	no	—
11	C₄₁×#529	C₄	1	8	yes	complemented
12	C₂×#126×C₄₁	—	2	1	no	—
13	C₂×#125×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×#123×C₄₁	—	2	1	no	—
16	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
17	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₄₁	—	2	1	no	—
20	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×#117×C₄₁	—	2	1	no	—
22	C₂×#117×C₄₁	C₂²	1	2	yes	—
23	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
24	C₄₁×#432	—	2	4	no	—
25	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
26	C₂×#103×C₄₁	C₂²	1	4	yes	—
27	C₂×#102×C₄₁	C₂²	1	4	yes	—
28	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
29	C₂×#97×C₄₁	C₂²	1	2	yes	—
30	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
31	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
32	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
33	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
34	C₄₁×#376	—	2	1	no	—
35	C₄³×C₄₁	—	2	1	no	—
36	C₄₁×#340	C₂²	1	4	yes	—
37	C₄₁×#340	C₂²	1	4	yes	—
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	1	yes	characteristic
43	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
46	#126×C₄₁	—	2	8	no	—
47	#125×C₄₁	—	2	2	no	—
48	#125×C₄₁	C₂×C₄	1	4	yes	—
49	#124×C₄₁	—	2	2	no	—
50	#124×C₄₁	C₂×C₄	1	4	yes	—
51	#123×C₄₁	—	2	8	no	—
52	C₂²⋊Q₈×C₄₁	—	2	2	no	—
53	C₂²⋊Q₈×C₄₁	C₂×C₄	1	4	yes	—
54	#121×C₄₁	—	2	2	no	—
55	#121×C₄₁	C₂×C₄	1	4	yes	—
56	C₄×Q₈×C₄₁	—	2	2	no	—
57	C₄×Q₈×C₄₁	C₂×C₄	1	4	yes	—
58	C₄×D₄×C₄₁	—	2	8	no	—
59	C₄×D₄×C₄₁	—	2	2	no	—
60	C₄×D₄×C₄₁	C₂×C₄	1	4	yes	—
61	#117×C₄₁	—	2	8	no	—
62	#117×C₄₁	—	2	8	no	—
63	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
70	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
76	C₂×C₄²×C₄₁	—	2	1	no	—
77	C₂×C₄²×C₄₁	—	2	2	no	—
78	C₂×C₄²×C₄₁	—	2	2	no	—
79	C₂×C₄²×C₄₁	—	2	2	no	—
80	C₂×C₄²×C₄₁	C₂×C₄	1	4	yes	—
81	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₄₁	D₄	1	4	yes	—
84	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₄₁	—	2	4	no	—
87	#103×C₄₁	—	2	8	no	—
88	#102×C₄₁	—	2	8	no	—
89	C₂²⋊C₈×C₄₁	—	2	4	no	—
90	#97×C₄₁	—	2	4	no	—
91	#95×C₄₁	—	2	2	no	—
92	#95×C₄₁	—	2	2	no	—
93	C₂⁴×C₄₁	—	2	1	no	—
94	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
95	C₂×Q₈×C₄₁	—	2	1	no	—
96	C₂×Q₈×C₄₁	—	2	4	no	—
97	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
98	C₂×D₄×C₄₁	—	2	4	no	—
99	C₂×D₄×C₄₁	—	2	1	no	—
100	C₂×D₄×C₄₁	—	2	4	no	—
101	C₂×D₄×C₄₁	—	4	4	no	—
102	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₄₁	—	2	4	no	—
104	C₂²×C₄×C₄₁	—	2	4	no	—
105	C₂²×C₄×C₄₁	—	2	1	no	—
106	C₂²×C₄×C₄₁	—	2	1	no	—
107	C₂²×C₄×C₄₁	—	2	1	no	—
108	C₂²×C₄×C₄₁	—	2	4	no	—
109	C₂²×C₄×C₄₁	—	4	2	no	—
110	C₂²×C₄×C₄₁	—	4	2	no	—
111	C₂²×C₄×C₄₁	—	4	4	no	—
112	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
113	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
114	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
115	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
122	C₂×C₈×C₄₁	—	2	4	no	—
123	C₂×C₈×C₄₁	—	2	4	no	—
124	C₂×C₈×C₄₁	—	2	4	no	—
125	C₄⋊C₄×C₄₁	—	2	4	no	—
126	C₄⋊C₄×C₄₁	—	2	4	no	—
127	C₄⋊C₄×C₄₁	—	2	4	no	—
128	C₄⋊C₄×C₄₁	—	2	4	no	—
129	C₄⋊C₄×C₄₁	—	2	1	no	—
130	C₄⋊C₄×C₄₁	—	2	1	no	—
131	C₄⋊C₄×C₄₁	—	2	4	no	—
132	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
133	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
134	C₄⋊C₄×C₄₁	#41	1	8	yes	—
135	C₂²⋊C₄×C₄₁	—	2	8	no	—
136	C₂²⋊C₄×C₄₁	—	2	4	no	—
137	C₂²⋊C₄×C₄₁	—	2	4	no	—
138	C₂²⋊C₄×C₄₁	—	2	4	no	—
139	C₂²⋊C₄×C₄₁	—	2	4	no	—
140	C₂²⋊C₄×C₄₁	—	2	4	no	—
141	C₄²×C₄₁	—	2	8	no	—
142	C₄²×C₄₁	—	2	4	no	—
143	C₄²×C₄₁	—	4	4	no	—
144	C₄²×C₄₁	—	4	4	no	—
145	C₄²×C₄₁	C₂²⋊C₄	1	4	yes	—
146	C₄²×C₄₁	C₂²⋊C₄	1	4	yes	—
147	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
148	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
149	C₄²×C₄₁	C₂×D₄	1	2	yes	—
150	C₄²×C₄₁	C₂×D₄	1	2	yes	—
151	C₂³×C₄₁	—	2	2	no	—
152	C₂³×C₄₁	—	2	2	no	—
153	C₂³×C₄₁	—	2	2	no	—
154	C₂³×C₄₁	—	2	2	no	—
155	C₂³×C₄₁	—	4	2	no	—
156	C₂³×C₄₁	—	4	2	no	—
157	C₂³×C₄₁	—	4	2	no	—
158	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
159	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
160	Q₈×C₄₁	—	2	4	no	—
161	Q₈×C₄₁	—	4	2	no	—
162	D₄×C₄₁	—	2	4	no	—
163	D₄×C₄₁	—	4	8	no	—
164	D₄×C₄₁	—	4	2	no	—
165	C₂×C₄×C₄₁	—	2	2	no	—
166	C₂×C₄×C₄₁	—	2	2	no	—
167	C₂×C₄×C₄₁	—	2	2	no	—
168	C₂×C₄×C₄₁	—	2	2	no	—
169	C₂×C₄×C₄₁	—	2	2	no	—
170	C₂×C₄×C₄₁	—	2	4	no	—
171	C₂×C₄×C₄₁	—	2	4	no	—
172	C₂×C₄×C₄₁	—	2	2	no	—
173	C₂×C₄×C₄₁	—	2	2	no	—
174	C₂×C₄×C₄₁	—	2	2	no	—
175	C₂×C₄×C₄₁	—	2	8	no	—
176	C₂×C₄×C₄₁	—	4	4	no	—
177	C₂×C₄×C₄₁	—	4	4	no	—
178	C₂×C₄×C₄₁	—	4	8	no	—
179	C₂×C₄×C₄₁	—	4	2	no	—
180	C₂×C₄×C₄₁	—	4	4	no	—
181	C₂×C₄×C₄₁	—	4	4	no	—
182	C₂×C₄×C₄₁	—	4	2	no	—
183	C₂×C₄×C₄₁	—	4	2	no	—
184	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
185	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
186	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
187	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
188	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
189	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
190	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
192	C₈×C₄₁	—	4	4	no	—
193	#21396	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₂²×C₄₁	—	2	2	no	—
195	C₂²×C₄₁	—	2	2	no	—
196	C₂²×C₄₁	—	2	2	no	—
197	C₂²×C₄₁	—	4	4	no	—
198	C₂²×C₄₁	—	4	2	no	—
199	C₂²×C₄₁	—	4	2	no	—
200	C₂²×C₄₁	—	4	2	no	—
201	C₂²×C₄₁	—	8	4	no	—
202	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
203	C₂²×C₄₁	#525	1	2	yes	—
204	C₂²×C₄₁	#575	1	2	yes	—
205	C₂²×C₄₁	#575	1	2	yes	—
206	C₄×C₄₁	—	2	2	no	—
207	C₄×C₄₁	—	2	2	no	—
208	C₄×C₄₁	—	2	2	no	—
209	C₄×C₄₁	—	2	2	no	—
210	C₄×C₄₁	—	2	2	no	—
211	C₄×C₄₁	—	4	8	no	—
212	C₄×C₄₁	—	4	2	no	—
213	C₄×C₄₁	—	4	2	no	—
214	C₄×C₄₁	—	4	2	no	—
215	C₄×C₄₁	C₄×#41	1	2	yes	—
216	C₄×C₄₁	#532	1	2	yes	—
217	C₂×#529	C₂×C₄₁	1	1	yes	characteristic
218	C₂×#432	C₂×C₄₁	1	1	yes	characteristic, complemented
219	C₄×#117	C₂×C₄₁	1	1	yes	characteristic, complemented
220	#1989	C₂×C₄₁	1	2	yes	complemented
221	#1983	C₂×C₄₁	1	2	yes	complemented
222	#1875	C₂×C₄₁	1	2	yes	—
223	#1873	C₂×C₄₁	1	2	yes	complemented
224	#1763	C₂×C₄₁	1	2	yes	complemented
225	#1762	C₂×C₄₁	1	2	yes	complemented
226	C₂×C₄₁	—	4	2	no	—
227	C₂×C₄₁	—	8	2	no	—
228	C₂×C₄₁	#2297	1	1	yes	characteristic
229	C₂×C₄₁	#2896	1	1	yes	characteristic
230	C₂×C₄₁	#2896	1	1	yes	characteristic
231	C₂×C₄₁	#3111	1	4	yes	—
232	#529	—	2	4	no	—
233	#529	C₄×C₄₁	1	8	yes	complemented
234	C₂×#126	—	2	1	no	—
235	C₂×#125	C₂²×C₄₁	1	1	yes	characteristic
236	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
237	C₂×#123	—	2	1	no	—
238	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
239	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
240	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
241	C₂×C₄×D₄	—	2	1	no	—
242	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
243	C₂×#117	—	2	1	no	—
244	C₂×#117	C₂²×C₄₁	1	2	yes	—
245	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
246	#432	—	2	4	no	—
247	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
248	C₂×#103	C₂²×C₄₁	1	4	yes	—
249	C₂×#102	C₂²×C₄₁	1	4	yes	—
250	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
251	C₂×#97	C₂²×C₄₁	1	2	yes	—
252	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
253	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
254	C₄×C₂²⋊C₄	—	2	1	no	—
255	C₄×C₂²⋊C₄	—	2	1	no	—
256	#376	—	2	1	no	—
257	C₄³	—	2	1	no	—
258	#340	C₂²×C₄₁	1	4	yes	—
259	#340	C₂²×C₄₁	1	4	yes	—
260	C₄₁	#21396	1	1	yes	characteristic, direct product factor, Sylow
261	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
262	C₂²×D₄	—	2	1	no	—
263	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
264	C₂³×C₄	—	2	1	no	—
265	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
266	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
267	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
268	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
269	#126	—	2	8	no	—
270	#125	—	2	2	no	—
271	#125	C₂×C₄×C₄₁	1	4	yes	—
272	#124	—	2	2	no	—
273	#124	C₂×C₄×C₄₁	1	4	yes	—
274	#123	—	2	8	no	—
275	C₂²⋊Q₈	—	2	2	no	—
276	C₂²⋊Q₈	C₂×C₄×C₄₁	1	4	yes	—
277	#121	—	2	2	no	—
278	#121	C₂×C₄×C₄₁	1	4	yes	—
279	C₄×Q₈	—	2	2	no	—
280	C₄×Q₈	C₂×C₄×C₄₁	1	4	yes	—
281	C₄×D₄	—	2	8	no	—
282	C₄×D₄	—	2	2	no	—
283	C₄×D₄	C₂×C₄×C₄₁	1	4	yes	—
284	#117	—	2	8	no	—
285	#117	—	2	8	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₂²⋊C₄	—	2	1	no	—
298	C₂×C₂²⋊C₄	—	2	1	no	—
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	—	2	2	no	—
301	C₂×C₄²	—	2	2	no	—
302	C₂×C₄²	—	2	2	no	—
303	C₂×C₄²	C₂×C₄×C₄₁	1	4	yes	—
304	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
305	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
306	C₂×C₄²	D₄×C₄₁	1	4	yes	—
307	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
308	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
309	C₄⋊C₈	—	2	4	no	—
310	#103	—	2	8	no	—
311	#102	—	2	8	no	—
312	C₂²⋊C₈	—	2	4	no	—
313	#97	—	2	4	no	—
314	#95	—	2	2	no	—
315	#95	—	2	2	no	—
316	C₂⁴	—	2	1	no	—
317	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	4	no	—
320	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
321	C₂×D₄	—	2	4	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	4	no	—
324	C₂×D₄	—	4	4	no	—
325	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	4	2	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	—	4	4	no	—
335	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
336	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
337	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
338	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
344	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
345	C₂×C₈	—	2	4	no	—
346	C₂×C₈	—	2	4	no	—
347	C₂×C₈	—	2	4	no	—
348	C₄⋊C₄	—	2	4	no	—
349	C₄⋊C₄	—	2	4	no	—
350	C₄⋊C₄	—	2	4	no	—
351	C₄⋊C₄	—	2	4	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	4	no	—
355	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
356	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
357	C₄⋊C₄	#41×C₄₁	1	8	yes	—
358	C₂²⋊C₄	—	2	8	no	—
359	C₂²⋊C₄	—	2	4	no	—
360	C₂²⋊C₄	—	2	4	no	—
361	C₂²⋊C₄	—	2	4	no	—
362	C₂²⋊C₄	—	2	4	no	—
363	C₂²⋊C₄	—	2	4	no	—
364	C₄²	—	2	8	no	—
365	C₄²	—	2	4	no	—
366	C₄²	—	4	4	no	—
367	C₄²	—	4	4	no	—
368	C₄²	C₂²⋊C₄×C₄₁	1	4	yes	—
369	C₄²	C₂²⋊C₄×C₄₁	1	4	yes	—
370	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
371	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
372	C₄²	C₂×D₄×C₄₁	1	2	yes	—
373	C₄²	C₂×D₄×C₄₁	1	2	yes	—
374	C₂³	—	2	2	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	2	2	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	4	2	no	—
380	C₂³	—	4	2	no	—
381	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
382	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
383	Q₈	—	2	4	no	—
384	Q₈	—	4	2	no	—
385	D₄	—	2	4	no	—
386	D₄	—	4	8	no	—
387	D₄	—	4	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	8	no	—
399	C₂×C₄	—	4	4	no	—
400	C₂×C₄	—	4	4	no	—
401	C₂×C₄	—	4	8	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
408	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
409	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
410	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
411	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
412	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
413	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
414	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
415	C₈	—	4	4	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	4	4	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	8	4	no	—
424	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
425	C₂²	C₄₁×#525	1	2	yes	—
426	C₂²	C₄₁×#575	1	2	yes	—
427	C₂²	C₄₁×#575	1	2	yes	—
428	C₄	—	2	2	no	—
429	C₄	—	2	2	no	—
430	C₄	—	2	2	no	—
431	C₄	—	2	2	no	—
432	C₄	—	2	2	no	—
433	C₄	—	4	2	no	—
434	C₄	—	4	8	no	—
435	C₄	—	4	2	no	—
436	C₄	—	4	2	no	—
437	C₄	C₄×#41×C₄₁	1	2	yes	—
438	C₄	C₄₁×#532	1	2	yes	—
439	C₂	—	4	2	no	—
440	C₂	—	8	2	no	—
441	C₂	C₄₁×#2297	1	1	yes	characteristic
442	C₂	C₄₁×#2896	1	1	yes	characteristic
443	C₂	C₄₁×#2896	1	1	yes	characteristic
444	C₂	C₄₁×#3111	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×#121×C₄₁	C₂²
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
2. C₂×C₄₁×#432	C₂	semidirect
3. C₄×#117×C₄₁	C₂	semidirect
4. C₄₁×#1989	C₂	semidirect
5. C₄₁×#1983	C₂	semidirect
7. C₄₁×#1873	C₂	semidirect
8. C₄₁×#1763	C₂	semidirect
9. C₄₁×#1762	C₂	semidirect
11. C₄₁×#529	C₄	semidirect
193. #21396	C₄₁	direct (N × H)
218. C₂×#432	C₂×C₄₁	semidirect
219. C₄×#117	C₂×C₄₁	semidirect
220. #1989	C₂×C₄₁	semidirect
221. #1983	C₂×C₄₁	semidirect
223. #1873	C₂×C₄₁	semidirect
224. #1763	C₂×C₄₁	semidirect
225. #1762	C₂×C₄₁	semidirect
233. #529	C₄×C₄₁	semidirect
260. C₄₁	#21396	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×#529	2
C₂×C₄₁×#432	2
C₄×#117×C₄₁	2
C₄₁×#1989	2
C₄₁×#1983	2
C₄₁×#1875	2
C₄₁×#1873	2
C₄₁×#1763	2
C₄₁×#1762	2
#21396	41

Subgroups — C41×#21396 #23797597

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#21396 #23797597