Subgroups — C₄₁×#22481 #23798682

Order 10496.

1106 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#554	C₂	1	1	yes	maximal, characteristic
2	D₄×M₁₆×C₄₁	C₂	1	2	yes	maximal
3	C₄₁×#1997	C₂	1	2	yes	maximal, complemented
4	C₄₁×#1901	C₂	1	4	yes	maximal, complemented
5	C₄₁×#1821	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1801	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×#101×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₁×#343	C₂	1	2	yes	maximal, complemented
9	C₂²×M₁₆×C₄₁	C₂²	1	4	yes	—
10	C₄₁×#554	—	2	2	no	—
11	C₄₁×#554	—	2	4	no	—
12	C₄₁×#554	—	2	2	no	—
13	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×#125×C₄₁	C₄	1	2	yes	—
15	C₂×C₂²⋊Q₈×C₄₁	C₄	1	4	yes	—
16	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
17	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₄₁	C₄	1	2	yes	—
19	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
21	C₄₁×#436	—	2	2	no	—
22	C₄₁×#435	—	2	4	no	—
23	C₈×D₄×C₄₁	—	2	2	no	—
24	C₄₁×#423	C₂²	1	2	yes	—
25	C₂×#101×C₄₁	C₂²	1	2	yes	—
26	C₂×#101×C₄₁	C₂²	1	2	yes	—
27	C₄₁×#407	C₂²	1	4	yes	—
28	C₄×M₁₆×C₄₁	C₂²	1	2	yes	—
29	C₄₁×#343	C₂²	1	1	yes	characteristic
30	C₄₁×#343	C₂²	1	1	yes	characteristic
31	C₄₁×#343	C₂²	1	2	yes	—
32	C₄₁×#343	C₂²	1	4	yes	—
33	C₄₁×#343	C₂²	1	4	yes	—
34	C₂²×Q₈×C₄₁	C₂×C₄	1	2	yes	—
35	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
36	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₄₁	C₂×C₄	1	4	yes	—
38	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
39	C₂×M₁₆×C₄₁	—	2	4	no	—
40	C₂×M₁₆×C₄₁	—	2	8	no	—
41	C₂×M₁₆×C₄₁	—	4	4	no	—
42	C₂×M₁₆×C₄₁	C₂³	1	4	yes	—
43	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
44	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
45	C₂²×C₈×C₄₁	—	2	4	no	—
46	C₄⋊Q₈×C₄₁	—	2	2	no	—
47	C₄⋊Q₈×C₄₁	—	2	2	no	—
48	#125×C₄₁	—	2	4	no	—
49	#125×C₄₁	—	2	4	no	—
50	C₂²⋊Q₈×C₄₁	—	2	4	no	—
51	C₂²⋊Q₈×C₄₁	—	2	4	no	—
52	C₂²⋊Q₈×C₄₁	—	2	8	no	—
53	C₂²⋊Q₈×C₄₁	—	2	8	no	—
54	C₄×Q₈×C₄₁	—	2	2	no	—
55	C₄×Q₈×C₄₁	—	2	2	no	—
56	C₄×D₄×C₄₁	—	2	4	no	—
57	C₄×D₄×C₄₁	—	2	2	no	—
58	C₄×D₄×C₄₁	—	2	2	no	—
59	C₄×D₄×C₄₁	D₄	1	2	yes	—
60	C₄×D₄×C₄₁	D₄	1	4	yes	—
61	C₄×D₄×C₄₁	D₄	1	2	yes	—
62	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
63	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
64	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	4	yes	—
65	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
67	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	4	yes	—
68	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
71	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	4	yes	—
72	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
73	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
74	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
75	C₄⋊C₈×C₄₁	—	2	2	no	—
76	C₄⋊C₈×C₄₁	—	2	2	no	—
77	#101×C₄₁	—	2	4	no	—
78	#101×C₄₁	—	4	2	no	—
79	C₂²⋊C₈×C₄₁	—	2	4	no	—
80	C₂²⋊C₈×C₄₁	—	2	4	no	—
81	#97×C₄₁	—	2	2	no	—
82	C₄×C₈×C₄₁	—	2	2	no	—
83	C₂⁴×C₄₁	C₂²×C₄	1	2	yes	—
84	C₂×Q₈×C₄₁	—	2	4	no	—
85	C₂×Q₈×C₄₁	—	2	2	no	—
86	C₂×Q₈×C₄₁	—	2	2	no	—
87	C₂×Q₈×C₄₁	—	2	1	no	—
88	C₂×Q₈×C₄₁	—	2	1	no	—
89	C₂×Q₈×C₄₁	—	8	2	no	—
90	C₂×D₄×C₄₁	—	2	4	no	—
91	C₂×D₄×C₄₁	C₂²⋊C₄	1	2	yes	—
92	C₂×D₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
93	C₂×D₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₁	—	2	4	no	—
95	C₂²×C₄×C₄₁	—	2	2	no	—
96	C₂²×C₄×C₄₁	—	2	2	no	—
97	C₂²×C₄×C₄₁	—	2	4	no	—
98	C₂²×C₄×C₄₁	—	2	4	no	—
99	C₂²×C₄×C₄₁	—	8	4	no	—
100	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
105	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
107	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
108	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
109	M₁₆×C₄₁	—	2	2	no	—
110	M₁₆×C₄₁	—	2	2	no	—
111	M₁₆×C₄₁	—	2	4	no	—
112	M₁₆×C₄₁	—	2	4	no	—
113	M₁₆×C₄₁	—	2	2	no	—
114	M₁₆×C₄₁	—	4	8	no	—
115	M₁₆×C₄₁	#41	1	4	yes	—
116	C₂×C₈×C₄₁	—	2	2	no	—
117	C₂×C₈×C₄₁	—	2	2	no	—
118	C₂×C₈×C₄₁	—	2	4	no	—
119	C₂×C₈×C₄₁	—	4	8	no	—
120	C₄⋊C₄×C₄₁	—	2	8	no	—
121	C₄⋊C₄×C₄₁	—	2	2	no	—
122	C₄⋊C₄×C₄₁	—	2	2	no	—
123	C₄⋊C₄×C₄₁	—	2	4	no	—
124	C₄⋊C₄×C₄₁	—	2	8	no	—
125	C₄⋊C₄×C₄₁	—	2	2	no	—
126	C₄⋊C₄×C₄₁	—	2	4	no	—
127	C₄⋊C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
128	C₄⋊C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
129	C₂²⋊C₄×C₄₁	—	2	4	no	—
130	C₂²⋊C₄×C₄₁	—	2	4	no	—
131	C₂²⋊C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
132	C₂²⋊C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
133	C₄²×C₄₁	—	2	2	no	—
134	C₄²×C₄₁	—	2	2	no	—
135	C₄²×C₄₁	C₂×D₄	1	2	yes	—
136	C₄²×C₄₁	C₂×D₄	1	2	yes	—
137	C₂³×C₄₁	—	2	2	no	—
138	C₂³×C₄₁	—	2	2	no	—
139	C₂³×C₄₁	—	2	4	no	—
140	C₂³×C₄₁	—	4	2	no	—
141	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
142	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
143	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
144	Q₈×C₄₁	—	4	2	no	—
145	Q₈×C₄₁	—	4	2	no	—
146	Q₈×C₄₁	—	8	4	no	—
147	D₄×C₄₁	—	2	4	no	—
148	D₄×C₄₁	—	2	2	no	—
149	D₄×C₄₁	#101	1	4	yes	complemented
150	C₂×C₄×C₄₁	—	2	2	no	—
151	C₂×C₄×C₄₁	—	2	2	no	—
152	C₂×C₄×C₄₁	—	2	4	no	—
153	C₂×C₄×C₄₁	—	2	4	no	—
154	C₂×C₄×C₄₁	—	2	4	no	—
155	C₂×C₄×C₄₁	—	2	4	no	—
156	C₂×C₄×C₄₁	—	2	2	no	—
157	C₂×C₄×C₄₁	—	2	2	no	—
158	C₂×C₄×C₄₁	—	2	2	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	—	4	1	no	—
163	C₂×C₄×C₄₁	—	4	2	no	—
164	C₂×C₄×C₄₁	—	4	4	no	—
165	C₂×C₄×C₄₁	—	8	4	no	—
166	C₂×C₄×C₄₁	—	8	4	no	—
167	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
169	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
170	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
172	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
173	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
174	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
175	C₈×C₄₁	—	2	4	no	—
176	C₈×C₄₁	—	4	4	no	—
177	C₈×C₄₁	—	4	2	no	—
178	#22481	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂²×C₄₁	—	2	2	no	—
180	C₂²×C₄₁	—	2	1	no	—
181	C₂²×C₄₁	—	2	1	no	—
182	C₂²×C₄₁	—	2	2	no	—
183	C₂²×C₄₁	—	2	2	no	—
184	C₂²×C₄₁	—	2	2	no	—
185	C₂²×C₄₁	—	2	2	no	—
186	C₂²×C₄₁	—	4	4	no	—
187	C₂²×C₄₁	—	4	4	no	—
188	C₂²×C₄₁	C₂×#101	1	4	yes	—
189	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
190	C₂²×C₄₁	C₄×#41	1	1	yes	characteristic
191	C₂²×C₄₁	#520	1	1	yes	characteristic
192	C₄×C₄₁	—	2	4	no	—
193	C₄×C₄₁	—	2	1	no	—
194	C₄×C₄₁	—	2	2	no	—
195	C₄×C₄₁	—	4	2	no	—
196	C₄×C₄₁	—	4	2	no	—
197	C₄×C₄₁	—	4	4	no	—
198	C₄×C₄₁	C₂×#101	1	2	yes	—
199	C₄×C₄₁	#546	1	2	yes	—
200	C₄×C₄₁	#547	1	2	yes	—
201	C₂×#554	C₂×C₄₁	1	1	yes	characteristic
202	D₄×M₁₆	C₂×C₄₁	1	2	yes	—
203	#1997	C₂×C₄₁	1	2	yes	complemented
204	#1901	C₂×C₄₁	1	4	yes	complemented
205	#1821	C₂×C₄₁	1	2	yes	complemented
206	#1801	C₂×C₄₁	1	1	yes	characteristic, complemented
207	C₄×#101	C₂×C₄₁	1	1	yes	characteristic, complemented
208	C₂×#343	C₂×C₄₁	1	2	yes	complemented
209	C₂×C₄₁	—	2	1	no	—
210	C₂×C₄₁	—	2	1	no	—
211	C₂×C₄₁	—	2	4	no	—
212	C₂×C₄₁	—	4	2	no	—
213	C₂×C₄₁	#2339	1	1	yes	characteristic
214	C₂×C₄₁	C₂²×#101	1	1	yes	characteristic
215	C₂×C₄₁	#2888	1	1	yes	characteristic
216	C₂²×M₁₆	C₂²×C₄₁	1	4	yes	—
217	#554	—	2	2	no	—
218	#554	—	2	4	no	—
219	#554	—	2	2	no	—
220	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
221	C₂×#125	C₄×C₄₁	1	2	yes	—
222	C₂×C₂²⋊Q₈	C₄×C₄₁	1	4	yes	—
223	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
224	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
225	C₂×C₄×D₄	C₄×C₄₁	1	2	yes	—
226	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
227	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
228	#436	—	2	2	no	—
229	#435	—	2	4	no	—
230	C₈×D₄	—	2	2	no	—
231	#423	C₂²×C₄₁	1	2	yes	—
232	C₂×#101	C₂²×C₄₁	1	2	yes	—
233	C₂×#101	C₂²×C₄₁	1	2	yes	—
234	#407	C₂²×C₄₁	1	4	yes	—
235	C₄×M₁₆	C₂²×C₄₁	1	2	yes	—
236	#343	C₂²×C₄₁	1	2	yes	—
237	#343	C₂²×C₄₁	1	1	yes	characteristic
238	#343	C₂²×C₄₁	1	4	yes	—
239	#343	C₂²×C₄₁	1	4	yes	—
240	#343	C₂²×C₄₁	1	1	yes	characteristic
241	C₄₁	#22481	1	1	yes	characteristic, direct product factor, Sylow
242	C₂²×Q₈	C₂×C₄×C₄₁	1	2	yes	—
243	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
244	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
245	C₂³×C₄	C₂×C₄×C₄₁	1	4	yes	—
246	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
247	C₂×M₁₆	—	2	4	no	—
248	C₂×M₁₆	—	2	8	no	—
249	C₂×M₁₆	—	4	4	no	—
250	C₂×M₁₆	C₂³×C₄₁	1	4	yes	—
251	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
252	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
253	C₂²×C₈	—	2	4	no	—
254	C₄⋊Q₈	—	2	2	no	—
255	C₄⋊Q₈	—	2	2	no	—
256	#125	—	2	4	no	—
257	#125	—	2	4	no	—
258	C₂²⋊Q₈	—	2	4	no	—
259	C₂²⋊Q₈	—	2	4	no	—
260	C₂²⋊Q₈	—	2	8	no	—
261	C₂²⋊Q₈	—	2	8	no	—
262	C₄×Q₈	—	2	2	no	—
263	C₄×Q₈	—	2	2	no	—
264	C₄×D₄	—	2	4	no	—
265	C₄×D₄	—	2	2	no	—
266	C₄×D₄	—	2	2	no	—
267	C₄×D₄	D₄×C₄₁	1	2	yes	—
268	C₄×D₄	D₄×C₄₁	1	4	yes	—
269	C₄×D₄	D₄×C₄₁	1	2	yes	—
270	C₂×C₄⋊C₄	—	2	4	no	—
271	C₂×C₄⋊C₄	—	2	4	no	—
272	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	4	yes	—
273	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
274	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
275	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	4	yes	—
276	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
279	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	4	yes	—
280	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
281	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
282	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
283	C₄⋊C₈	—	2	2	no	—
284	C₄⋊C₈	—	2	2	no	—
285	#101	—	2	4	no	—
286	#101	—	4	2	no	—
287	C₂²⋊C₈	—	2	4	no	—
288	C₂²⋊C₈	—	2	4	no	—
289	#97	—	2	2	no	—
290	C₄×C₈	—	2	2	no	—
291	C₂⁴	C₂²×C₄×C₄₁	1	2	yes	—
292	C₂×Q₈	—	2	4	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	1	no	—
296	C₂×Q₈	—	2	1	no	—
297	C₂×Q₈	—	8	2	no	—
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	C₂²⋊C₄×C₄₁	1	2	yes	—
300	C₂×D₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
301	C₂×D₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	8	4	no	—
308	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
309	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
310	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
311	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
312	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
313	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
315	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
316	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
317	M₁₆	—	2	2	no	—
318	M₁₆	—	2	2	no	—
319	M₁₆	—	2	4	no	—
320	M₁₆	—	2	4	no	—
321	M₁₆	—	2	2	no	—
322	M₁₆	—	4	8	no	—
323	M₁₆	#41×C₄₁	1	4	yes	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	4	no	—
327	C₂×C₈	—	4	8	no	—
328	C₄⋊C₄	—	2	8	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	8	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	4	no	—
335	C₄⋊C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
336	C₄⋊C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
337	C₂²⋊C₄	—	2	4	no	—
338	C₂²⋊C₄	—	2	4	no	—
339	C₂²⋊C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
340	C₂²⋊C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
341	C₄²	—	2	2	no	—
342	C₄²	—	2	2	no	—
343	C₄²	C₂×D₄×C₄₁	1	2	yes	—
344	C₄²	C₂×D₄×C₄₁	1	2	yes	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	2	4	no	—
348	C₂³	—	4	2	no	—
349	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
350	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
351	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
352	Q₈	—	4	2	no	—
353	Q₈	—	4	2	no	—
354	Q₈	—	8	4	no	—
355	D₄	—	2	4	no	—
356	D₄	—	2	2	no	—
357	D₄	#101×C₄₁	1	4	yes	complemented
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	—	8	4	no	—
374	C₂×C₄	—	8	4	no	—
375	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
376	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
377	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
378	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
379	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
380	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
381	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
382	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
383	C₈	—	2	4	no	—
384	C₈	—	4	4	no	—
385	C₈	—	4	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	4	4	no	—
395	C₂²	C₂×#101×C₄₁	1	4	yes	—
396	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
397	C₂²	C₄×#41×C₄₁	1	1	yes	characteristic
398	C₂²	C₄₁×#520	1	1	yes	characteristic
399	C₄	—	2	4	no	—
400	C₄	—	2	1	no	—
401	C₄	—	2	2	no	—
402	C₄	—	4	2	no	—
403	C₄	—	4	2	no	—
404	C₄	—	4	4	no	—
405	C₄	C₂×#101×C₄₁	1	2	yes	—
406	C₄	C₄₁×#546	1	2	yes	—
407	C₄	C₄₁×#547	1	2	yes	—
408	C₂	—	2	1	no	—
409	C₂	—	2	1	no	—
410	C₂	—	2	4	no	—
411	C₂	—	4	2	no	—
412	C₂	C₄₁×#2339	1	1	yes	characteristic
413	C₂	C₂²×#101×C₄₁	1	1	yes	characteristic
414	C₂	C₄₁×#2888	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₄₁×#1997	C₂	semidirect
4. C₄₁×#1901	C₂	semidirect
5. C₄₁×#1821	C₂	semidirect
6. C₄₁×#1801	C₂	semidirect
7. C₄×#101×C₄₁	C₂	semidirect
8. C₂×C₄₁×#343	C₂	semidirect
149. D₄×C₄₁	#101	semidirect
178. #22481	C₄₁	direct (N × H)
203. #1997	C₂×C₄₁	semidirect
204. #1901	C₂×C₄₁	semidirect
205. #1821	C₂×C₄₁	semidirect
206. #1801	C₂×C₄₁	semidirect
207. C₄×#101	C₂×C₄₁	semidirect
208. C₂×#343	C₂×C₄₁	semidirect
241. C₄₁	#22481	direct (N × H)
357. D₄	#101×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×#554	2
D₄×M₁₆×C₄₁	2
C₄₁×#1997	2
C₄₁×#1901	2
C₄₁×#1821	2
C₄₁×#1801	2
C₄×#101×C₄₁	2
C₂×C₄₁×#343	2
#22481	41

Subgroups — C41×#22481 #23798682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#22481 #23798682