Subgroups — C₄₁×#21376 #23797577

Order 10496.

1158 conjugacy classes of subgroups.

The subgroup lattice has 400 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	C₂×C₄×M₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1985	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1955	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1870	C₂	1	4	yes	maximal, complemented
7	C₄₁×#1750	C₂	1	4	yes	maximal, complemented
8	C₂²×M₁₆×C₄₁	C₂²	1	2	yes	—
9	C₄₁×#529	—	2	4	no	—
10	C₄₁×#529	—	2	4	no	—
11	C₂×#126×C₄₁	C₄	1	2	yes	—
12	C₂×#125×C₄₁	C₄	1	1	yes	characteristic
13	C₂×#124×C₄₁	C₄	1	1	yes	characteristic
14	C₂×#123×C₄₁	C₄	1	2	yes	—
15	C₂×C₂²⋊Q₈×C₄₁	C₄	1	1	yes	characteristic
16	C₂×#121×C₄₁	C₄	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×#117×C₄₁	C₂²	1	2	yes	—
21	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
22	C₄₁×#432	—	2	4	no	—
23	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
24	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₈×C₄₁	C₂²	1	8	yes	—
26	C₄×M₁₆×C₄₁	—	2	4	no	—
27	C₂×#97×C₄₁	C₂²	1	2	yes	—
28	C₂×#97×C₄₁	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
30	C₄₁×#336	C₂²	1	8	yes	—
31	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
32	C₂²×D₄×C₄₁	C₂×C₄	1	2	yes	—
33	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
37	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
38	C₂×M₁₆×C₄₁	—	2	4	no	—
39	C₂×M₁₆×C₄₁	—	2	8	no	—
40	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
41	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
42	#126×C₄₁	—	2	8	no	—
43	#125×C₄₁	—	2	4	no	—
44	#124×C₄₁	—	2	4	no	—
45	#123×C₄₁	—	2	8	no	—
46	C₂²⋊Q₈×C₄₁	—	2	4	no	—
47	#121×C₄₁	—	2	4	no	—
48	C₄×Q₈×C₄₁	—	2	2	no	—
49	C₄×Q₈×C₄₁	—	2	2	no	—
50	C₄×D₄×C₄₁	—	2	4	no	—
51	C₄×D₄×C₄₁	—	2	4	no	—
52	C₄×D₄×C₄₁	—	2	2	no	—
53	C₄×D₄×C₄₁	—	2	2	no	—
54	#117×C₄₁	—	2	4	no	—
55	#117×C₄₁	—	2	4	no	—
56	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
57	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
58	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
62	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
63	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
64	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
65	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
66	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₄₁	D₄	1	4	yes	—
70	C₂×C₄²×C₄₁	D₄	1	4	yes	—
71	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
72	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
74	C₄⋊C₈×C₄₁	—	2	4	no	—
75	C₂²⋊C₈×C₄₁	—	2	4	no	—
76	C₂²⋊C₈×C₄₁	—	2	16	no	—
77	#97×C₄₁	—	2	4	no	—
78	#97×C₄₁	—	2	4	no	—
79	C₄×C₈×C₄₁	—	2	4	no	—
80	C₂⁴×C₄₁	C₂²×C₄	1	2	yes	—
81	C₂⁴×C₄₁	C₂²×C₄	1	1	yes	characteristic
82	C₂×Q₈×C₄₁	—	2	2	no	—
83	C₂×Q₈×C₄₁	—	4	2	no	—
84	C₂×D₄×C₄₁	—	2	4	no	—
85	C₂×D₄×C₄₁	—	2	2	no	—
86	C₂×D₄×C₄₁	—	4	2	no	—
87	C₂×D₄×C₄₁	—	4	4	no	—
88	C₂²×C₄×C₄₁	—	2	4	no	—
89	C₂²×C₄×C₄₁	—	2	2	no	—
90	C₂²×C₄×C₄₁	—	2	2	no	—
91	C₂²×C₄×C₄₁	—	2	8	no	—
92	C₂²×C₄×C₄₁	—	4	2	no	—
93	C₂²×C₄×C₄₁	—	4	2	no	—
94	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
95	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
96	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
107	M₁₆×C₄₁	—	2	16	no	—
108	C₂×C₈×C₄₁	—	2	4	no	—
109	C₂×C₈×C₄₁	—	2	4	no	—
110	C₂×C₈×C₄₁	—	2	4	no	—
111	C₂×C₈×C₄₁	—	2	8	no	—
112	C₂×C₈×C₄₁	#41	1	8	yes	—
113	C₄⋊C₄×C₄₁	—	2	4	no	—
114	C₄⋊C₄×C₄₁	—	2	4	no	—
115	C₄⋊C₄×C₄₁	—	2	2	no	—
116	C₄⋊C₄×C₄₁	—	2	4	no	—
117	C₄⋊C₄×C₄₁	—	2	2	no	—
118	C₄⋊C₄×C₄₁	—	2	4	no	—
119	C₂²⋊C₄×C₄₁	—	2	4	no	—
120	C₂²⋊C₄×C₄₁	—	2	4	no	—
121	C₂²⋊C₄×C₄₁	—	2	4	no	—
122	C₂²⋊C₄×C₄₁	—	2	4	no	—
123	C₂²⋊C₄×C₄₁	—	2	4	no	—
124	C₄²×C₄₁	—	2	2	no	—
125	C₄²×C₄₁	—	2	2	no	—
126	C₄²×C₄₁	C₂²⋊C₄	1	4	yes	—
127	C₄²×C₄₁	C₂²⋊C₄	1	4	yes	—
128	C₄²×C₄₁	C₂×D₄	1	2	yes	—
129	C₄²×C₄₁	C₂×D₄	1	2	yes	—
130	C₄²×C₄₁	C₂×D₄	1	2	yes	—
131	C₄²×C₄₁	C₂×D₄	1	2	yes	—
132	C₂³×C₄₁	—	2	2	no	—
133	C₂³×C₄₁	—	2	2	no	—
134	C₂³×C₄₁	—	2	2	no	—
135	C₂³×C₄₁	—	2	2	no	—
136	C₂³×C₄₁	—	2	4	no	—
137	C₂³×C₄₁	—	2	4	no	—
138	C₂³×C₄₁	—	2	4	no	—
139	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
140	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
141	Q₈×C₄₁	—	4	4	no	—
142	D₄×C₄₁	—	4	4	no	—
143	D₄×C₄₁	—	4	8	no	—
144	C₂×C₄×C₄₁	—	2	2	no	—
145	C₂×C₄×C₄₁	—	2	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	4	no	—
150	C₂×C₄×C₄₁	—	2	4	no	—
151	C₂×C₄×C₄₁	—	2	2	no	—
152	C₂×C₄×C₄₁	—	2	2	no	—
153	C₂×C₄×C₄₁	—	2	2	no	—
154	C₂×C₄×C₄₁	—	2	4	no	—
155	C₂×C₄×C₄₁	—	2	4	no	—
156	C₂×C₄×C₄₁	—	2	4	no	—
157	C₂×C₄×C₄₁	—	4	4	no	—
158	C₂×C₄×C₄₁	—	4	4	no	—
159	C₂×C₄×C₄₁	—	4	4	no	—
160	C₂×C₄×C₄₁	—	4	4	no	—
161	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
162	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
163	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
164	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
169	C₈×C₄₁	—	2	8	no	—
170	C₈×C₄₁	—	4	4	no	—
171	#21376	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂²×C₄₁	—	2	2	no	—
173	C₂²×C₄₁	—	2	2	no	—
174	C₂²×C₄₁	—	2	2	no	—
175	C₂²×C₄₁	—	4	4	no	—
176	C₂²×C₄₁	—	4	2	no	—
177	C₂²×C₄₁	—	4	2	no	—
178	C₂²×C₄₁	—	4	8	no	—
179	C₂²×C₄₁	—	4	2	no	—
180	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
181	C₂²×C₄₁	C₄×#41	1	2	yes	—
182	C₂²×C₄₁	#568	1	2	yes	—
183	C₂²×C₄₁	#568	1	2	yes	—
184	C₄×C₄₁	—	2	2	no	—
185	C₄×C₄₁	—	2	2	no	—
186	C₄×C₄₁	—	2	2	no	—
187	C₄×C₄₁	—	2	2	no	—
188	C₄×C₄₁	—	2	2	no	—
189	C₄×C₄₁	—	4	2	no	—
190	C₄×C₄₁	—	4	2	no	—
191	C₄×C₄₁	—	4	2	no	—
192	C₄×C₄₁	#525	1	2	yes	—
193	C₄×C₄₁	#532	1	2	yes	—
194	C₂×#529	C₂×C₄₁	1	1	yes	characteristic
195	C₂×#432	C₂×C₄₁	1	1	yes	characteristic, complemented
196	C₂×C₄×M₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
197	#1985	C₂×C₄₁	1	2	yes	complemented
198	#1955	C₂×C₄₁	1	2	yes	complemented
199	#1870	C₂×C₄₁	1	4	yes	complemented
200	#1750	C₂×C₄₁	1	4	yes	complemented
201	C₂×C₄₁	—	4	2	no	—
202	C₂×C₄₁	—	8	2	no	—
203	C₂×C₄₁	#2297	1	1	yes	characteristic
204	C₂×C₄₁	#2879	1	1	yes	characteristic
205	C₂×C₄₁	#2879	1	1	yes	characteristic
206	C₂×C₄₁	#2967	1	4	yes	—
207	C₂²×M₁₆	C₂²×C₄₁	1	2	yes	—
208	#529	—	2	4	no	—
209	#529	—	2	4	no	—
210	C₂×#126	C₄×C₄₁	1	2	yes	—
211	C₂×#125	C₄×C₄₁	1	1	yes	characteristic
212	C₂×#124	C₄×C₄₁	1	1	yes	characteristic
213	C₂×#123	C₄×C₄₁	1	2	yes	—
214	C₂×C₂²⋊Q₈	C₄×C₄₁	1	1	yes	characteristic
215	C₂×#121	C₄×C₄₁	1	1	yes	characteristic
216	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
217	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
218	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
219	C₂×#117	C₂²×C₄₁	1	2	yes	—
220	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
221	#432	—	2	4	no	—
222	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
223	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
224	C₂×C₂²⋊C₈	C₂²×C₄₁	1	8	yes	—
225	C₄×M₁₆	—	2	4	no	—
226	C₂×#97	C₂²×C₄₁	1	2	yes	—
227	C₂×#97	C₂²×C₄₁	1	2	yes	—
228	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
229	#336	C₂²×C₄₁	1	8	yes	—
230	C₄₁	#21376	1	1	yes	characteristic, direct product factor, Sylow
231	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
232	C₂²×D₄	C₂×C₄×C₄₁	1	2	yes	—
233	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
234	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
235	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
236	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
237	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
238	C₂×M₁₆	—	2	4	no	—
239	C₂×M₁₆	—	2	8	no	—
240	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
241	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
242	#126	—	2	8	no	—
243	#125	—	2	4	no	—
244	#124	—	2	4	no	—
245	#123	—	2	8	no	—
246	C₂²⋊Q₈	—	2	4	no	—
247	#121	—	2	4	no	—
248	C₄×Q₈	—	2	2	no	—
249	C₄×Q₈	—	2	2	no	—
250	C₄×D₄	—	2	4	no	—
251	C₄×D₄	—	2	4	no	—
252	C₄×D₄	—	2	2	no	—
253	C₄×D₄	—	2	2	no	—
254	#117	—	2	4	no	—
255	#117	—	2	4	no	—
256	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
257	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
258	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
260	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
262	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
263	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
264	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
265	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
266	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
267	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
268	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
269	C₂×C₄²	D₄×C₄₁	1	4	yes	—
270	C₂×C₄²	D₄×C₄₁	1	4	yes	—
271	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
272	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
273	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
274	C₄⋊C₈	—	2	4	no	—
275	C₂²⋊C₈	—	2	4	no	—
276	C₂²⋊C₈	—	2	16	no	—
277	#97	—	2	4	no	—
278	#97	—	2	4	no	—
279	C₄×C₈	—	2	4	no	—
280	C₂⁴	C₂²×C₄×C₄₁	1	2	yes	—
281	C₂⁴	C₂²×C₄×C₄₁	1	1	yes	characteristic
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	4	2	no	—
284	C₂×D₄	—	2	4	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	4	2	no	—
287	C₂×D₄	—	4	4	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	8	no	—
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
295	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
296	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
297	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
298	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
299	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
300	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
301	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
302	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
303	C₂²×C₄	C₂²×C₄×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	C₂⁴×C₄₁	1	1	yes	characteristic
307	M₁₆	—	2	16	no	—
308	C₂×C₈	—	2	4	no	—
309	C₂×C₈	—	2	4	no	—
310	C₂×C₈	—	2	4	no	—
311	C₂×C₈	—	2	8	no	—
312	C₂×C₈	#41×C₄₁	1	8	yes	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₂²⋊C₄	—	2	4	no	—
320	C₂²⋊C₄	—	2	4	no	—
321	C₂²⋊C₄	—	2	4	no	—
322	C₂²⋊C₄	—	2	4	no	—
323	C₂²⋊C₄	—	2	4	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	C₂²⋊C₄×C₄₁	1	4	yes	—
327	C₄²	C₂²⋊C₄×C₄₁	1	4	yes	—
328	C₄²	C₂×D₄×C₄₁	1	2	yes	—
329	C₄²	C₂×D₄×C₄₁	1	2	yes	—
330	C₄²	C₂×D₄×C₄₁	1	2	yes	—
331	C₄²	C₂×D₄×C₄₁	1	2	yes	—
332	C₂³	—	2	2	no	—
333	C₂³	—	2	2	no	—
334	C₂³	—	2	2	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	2	4	no	—
337	C₂³	—	2	4	no	—
338	C₂³	—	2	4	no	—
339	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
340	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
341	Q₈	—	4	4	no	—
342	D₄	—	4	4	no	—
343	D₄	—	4	8	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	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	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
362	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
363	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
364	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
365	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
366	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
367	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
368	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
369	C₈	—	2	8	no	—
370	C₈	—	4	4	no	—
371	C₂²	—	2	2	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	4	4	no	—
375	C₂²	—	4	2	no	—
376	C₂²	—	4	2	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	8	no	—
379	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
380	C₂²	C₄×#41×C₄₁	1	2	yes	—
381	C₂²	C₄₁×#568	1	2	yes	—
382	C₂²	C₄₁×#568	1	2	yes	—
383	C₄	—	2	2	no	—
384	C₄	—	2	2	no	—
385	C₄	—	2	2	no	—
386	C₄	—	2	2	no	—
387	C₄	—	2	2	no	—
388	C₄	—	4	2	no	—
389	C₄	—	4	2	no	—
390	C₄	—	4	2	no	—
391	C₄	C₄₁×#525	1	2	yes	—
392	C₄	C₄₁×#532	1	2	yes	—
393	C₂	—	4	2	no	—
394	C₂	—	8	2	no	—
395	C₂	C₄₁×#2297	1	1	yes	characteristic
396	C₂	C₄₁×#2879	1	1	yes	characteristic
397	C₂	C₄₁×#2879	1	1	yes	characteristic
398	C₂	C₄₁×#2967	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₄₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
socle	C₂³×C₄₁	C₂³×C₄
prime radical	C₂×#121×C₄₁	C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×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. C₂×C₄×M₁₆×C₄₁	C₂	semidirect
4. C₄₁×#1985	C₂	semidirect
5. C₄₁×#1955	C₂	semidirect
6. C₄₁×#1870	C₂	semidirect
7. C₄₁×#1750	C₂	semidirect
171. #21376	C₄₁	direct (N × H)
195. C₂×#432	C₂×C₄₁	semidirect
196. C₂×C₄×M₁₆	C₂×C₄₁	semidirect
197. #1985	C₂×C₄₁	semidirect
198. #1955	C₂×C₄₁	semidirect
199. #1870	C₂×C₄₁	semidirect
200. #1750	C₂×C₄₁	semidirect
230. C₄₁	#21376	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
C₂×C₄×M₁₆×C₄₁	2
C₄₁×#1985	2
C₄₁×#1955	2
C₄₁×#1870	2
C₄₁×#1750	2
#21376	41

Subgroups — C41×#21376 #23797577

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#21376 #23797577