Subgroups — C₄₁×#21386 #23797587

Order 10496.

1538 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₄⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1988	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1982	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1874	C₂	1	4	yes	maximal, complemented
7	C₄×#102×C₄₁	C₂	1	4	yes	maximal, complemented
8	C₂²×#41×C₄₁	—	2	1	no	—
9	C₄₁×#532	—	2	4	no	—
10	C₄₁×#532	C₄	1	8	yes	complemented
11	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
12	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×#124×C₄₁	—	2	1	no	—
14	C₂×#121×C₄₁	—	2	1	no	—
15	C₂×#121×C₄₁	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₄₁	—	2	1	no	—
17	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
19	C₂²×C₄²×C₄₁	—	2	1	no	—
20	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
21	C₄₁×#431	—	2	4	no	—
22	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
23	C₂×#102×C₄₁	C₂²	1	8	yes	—
24	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
26	C₄×C₄⋊C₄×C₄₁	—	2	1	no	—
27	C₄×C₄⋊C₄×C₄₁	—	2	1	no	—
28	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
30	C₂×#95×C₄₁	—	2	1	no	—
31	C₄₁×#340	C₂²	1	8	yes	—
32	C₂×#41×C₄₁	—	2	8	no	—
33	C₂×#41×C₄₁	—	4	4	no	—
34	C₂×#41×C₄₁	—	4	4	no	—
35	C₂²×Q₈×C₄₁	—	2	1	no	—
36	C₂²×D₄×C₄₁	—	2	2	no	—
37	C₂²×D₄×C₄₁	—	2	1	no	—
38	C₂²×D₄×C₄₁	—	2	1	no	—
39	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
40	C₂³×C₄×C₄₁	—	2	2	no	—
41	C₂³×C₄×C₄₁	—	2	2	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	C₄⋊Q₈×C₄₁	—	2	2	no	—
47	C₄⋊Q₈×C₄₁	C₂×C₄	1	4	yes	complemented
48	#127×C₄₁	—	2	2	no	—
49	#127×C₄₁	C₂×C₄	1	4	yes	complemented
50	#124×C₄₁	—	2	8	no	—
51	#121×C₄₁	—	2	8	no	—
52	#121×C₄₁	—	2	4	no	—
53	#121×C₄₁	C₂×C₄	1	8	yes	—
54	C₄×D₄×C₄₁	—	2	8	no	—
55	C₄×D₄×C₄₁	—	2	4	no	—
56	C₄×D₄×C₄₁	C₂×C₄	1	8	yes	complemented
57	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
59	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
60	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
62	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
64	C₂×C₄²×C₄₁	—	2	2	no	—
65	C₂×C₄²×C₄₁	—	2	2	no	—
66	C₂×C₄²×C₄₁	—	4	4	no	—
67	C₂×C₄²×C₄₁	C₂×C₄	1	4	yes	—
68	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₄₁	D₄	1	4	yes	—
71	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
73	C₄⋊C₈×C₄₁	—	2	4	no	—
74	#102×C₄₁	—	2	16	no	—
75	C₂²⋊C₈×C₄₁	—	2	4	no	—
76	C₄×C₈×C₄₁	—	2	4	no	—
77	#95×C₄₁	—	2	2	no	—
78	#95×C₄₁	—	2	2	no	—
79	C₂⁴×C₄₁	—	2	2	no	—
80	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
81	#41×C₄₁	—	4	32	no	—
82	C₂×Q₈×C₄₁	—	2	4	no	—
83	C₂×Q₈×C₄₁	—	4	2	no	—
84	C₂×Q₈×C₄₁	—	4	2	no	—
85	C₂×D₄×C₄₁	—	2	8	no	—
86	C₂×D₄×C₄₁	—	2	4	no	—
87	C₂×D₄×C₄₁	—	2	4	no	—
88	C₂×D₄×C₄₁	—	2	2	no	—
89	C₂×D₄×C₄₁	—	2	8	no	—
90	C₂×D₄×C₄₁	—	4	4	no	—
91	C₂×D₄×C₄₁	—	4	4	no	—
92	C₂×D₄×C₄₁	—	4	4	no	—
93	C₂×D₄×C₄₁	—	4	2	no	—
94	C₂×D₄×C₄₁	—	4	2	no	—
95	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₄₁	—	2	4	no	—
97	C₂²×C₄×C₄₁	—	2	8	no	—
98	C₂²×C₄×C₄₁	—	2	4	no	—
99	C₂²×C₄×C₄₁	—	2	2	no	—
100	C₂²×C₄×C₄₁	—	2	8	no	—
101	C₂²×C₄×C₄₁	—	4	2	no	—
102	C₂²×C₄×C₄₁	—	4	4	no	—
103	C₂²×C₄×C₄₁	—	4	4	no	—
104	C₂²×C₄×C₄₁	—	4	4	no	—
105	C₂²×C₄×C₄₁	—	4	4	no	—
106	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
107	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
108	C₂²×C₄×C₄₁	D₈	1	4	yes	—
109	C₂²×C₄×C₄₁	SD₁₆	1	4	yes	—
110	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₁	C₂×D₄	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	C₂⁴	1	1	yes	characteristic
118	C₂×C₈×C₄₁	—	2	4	no	—
119	C₂×C₈×C₄₁	—	2	8	no	—
120	C₄⋊C₄×C₄₁	—	2	8	no	—
121	C₄⋊C₄×C₄₁	—	2	4	no	—
122	C₄⋊C₄×C₄₁	—	2	2	no	—
123	C₄⋊C₄×C₄₁	—	2	4	no	—
124	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
125	C₄⋊C₄×C₄₁	#41	1	8	yes	complemented
126	C₂²⋊C₄×C₄₁	—	2	8	no	—
127	C₂²⋊C₄×C₄₁	—	2	8	no	—
128	C₄²×C₄₁	—	4	4	no	—
129	C₄²×C₄₁	—	4	4	no	—
130	C₄²×C₄₁	C₂²⋊C₄	1	4	yes	—
131	C₄²×C₄₁	C₂²⋊C₄	1	4	yes	—
132	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
133	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
134	C₄²×C₄₁	C₂×D₄	1	2	yes	—
135	C₄²×C₄₁	C₂×D₄	1	2	yes	—
136	C₂³×C₄₁	—	2	2	no	—
137	C₂³×C₄₁	—	2	2	no	—
138	C₂³×C₄₁	—	2	4	no	—
139	C₂³×C₄₁	—	4	4	no	—
140	C₂³×C₄₁	—	4	2	no	—
141	C₂³×C₄₁	—	4	2	no	—
142	C₂³×C₄₁	—	4	4	no	—
143	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
144	C₂³×C₄₁	C₂×D₈	1	2	yes	—
145	C₂³×C₄₁	C₂×SD₁₆	1	2	yes	—
146	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
147	Q₈×C₄₁	—	4	8	no	—
148	D₄×C₄₁	—	2	8	no	—
149	D₄×C₄₁	—	4	8	no	—
150	D₄×C₄₁	—	4	16	no	—
151	D₄×C₄₁	—	4	4	no	—
152	D₄×C₄₁	—	4	8	no	—
153	C₂×C₄×C₄₁	—	2	2	no	—
154	C₂×C₄×C₄₁	—	2	2	no	—
155	C₂×C₄×C₄₁	—	2	2	no	—
156	C₂×C₄×C₄₁	—	2	4	no	—
157	C₂×C₄×C₄₁	—	2	4	no	—
158	C₂×C₄×C₄₁	—	2	4	no	—
159	C₂×C₄×C₄₁	—	2	8	no	—
160	C₂×C₄×C₄₁	—	4	4	no	—
161	C₂×C₄×C₄₁	—	4	16	no	—
162	C₂×C₄×C₄₁	—	4	4	no	—
163	C₂×C₄×C₄₁	—	4	2	no	—
164	C₂×C₄×C₄₁	—	4	2	no	—
165	C₂×C₄×C₄₁	—	4	4	no	—
166	C₂×C₄×C₄₁	—	4	16	no	—
167	C₂×C₄×C₄₁	#102	1	16	yes	complemented
168	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
169	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
170	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
171	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
172	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
173	C₂×C₄×C₄₁	C₂×D₈	1	2	yes	—
174	C₂×C₄×C₄₁	C₂×D₈	1	2	yes	—
175	C₂×C₄×C₄₁	C₂×SD₁₆	1	2	yes	—
176	C₂×C₄×C₄₁	C₂×SD₁₆	1	2	yes	—
177	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
178	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
180	C₈×C₄₁	—	4	4	no	—
181	#21386	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂²×C₄₁	—	2	4	no	—
183	C₂²×C₄₁	—	2	4	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	—	4	4	no	—
189	C₂²×C₄₁	—	8	4	no	—
190	C₂²×C₄₁	—	8	4	no	—
191	C₂²×C₄₁	C₂×#102	1	4	yes	—
192	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
193	C₂²×C₄₁	#525	1	2	yes	—
194	C₂²×C₄₁	C₂²×D₈	1	1	yes	characteristic
195	C₂²×C₄₁	C₂²×SD₁₆	1	1	yes	characteristic
196	C₂²×C₄₁	#575	1	2	yes	—
197	C₄×C₄₁	—	2	2	no	—
198	C₄×C₄₁	—	2	2	no	—
199	C₄×C₄₁	—	2	2	no	—
200	C₄×C₄₁	—	4	8	no	—
201	C₄×C₄₁	—	4	4	no	—
202	C₄×C₄₁	C₂×#102	1	4	yes	—
203	C₄×C₄₁	C₂×#102	1	4	yes	—
204	C₄×C₄₁	C₄×#41	1	2	yes	—
205	C₄×C₄₁	#532	1	2	yes	—
206	C₂×#532	C₂×C₄₁	1	1	yes	characteristic
207	C₂×#431	C₂×C₄₁	1	1	yes	characteristic, complemented
208	C₂×C₄×C₄⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
209	#1988	C₂×C₄₁	1	2	yes	complemented
210	#1982	C₂×C₄₁	1	2	yes	complemented
211	#1874	C₂×C₄₁	1	4	yes	complemented
212	C₄×#102	C₂×C₄₁	1	4	yes	complemented
213	C₂×C₄₁	—	2	4	no	—
214	C₂×C₄₁	—	8	4	no	—
215	C₂×C₄₁	#2297	1	1	yes	characteristic
216	C₂×C₄₁	C₂²×#102	1	1	yes	characteristic
217	C₂×C₄₁	#2896	1	1	yes	characteristic
218	C₂×C₄₁	#3100	1	2	yes	—
219	C₂×C₄₁	#3103	1	2	yes	—
220	C₂²×#41	—	2	1	no	—
221	#532	—	2	4	no	—
222	#532	C₄×C₄₁	1	8	yes	complemented
223	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
224	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
225	C₂×#124	—	2	1	no	—
226	C₂×#121	—	2	1	no	—
227	C₂×#121	C₂²×C₄₁	1	2	yes	—
228	C₂×C₄×D₄	—	2	1	no	—
229	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
230	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
231	C₂²×C₄²	—	2	1	no	—
232	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
233	#431	—	2	4	no	—
234	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
235	C₂×#102	C₂²×C₄₁	1	8	yes	—
236	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
237	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
238	C₄×C₄⋊C₄	—	2	1	no	—
239	C₄×C₄⋊C₄	—	2	1	no	—
240	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
241	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
242	C₂×#95	—	2	1	no	—
243	#340	C₂²×C₄₁	1	8	yes	—
244	C₄₁	#21386	1	1	yes	characteristic, direct product factor, Sylow
245	C₂×#41	—	2	8	no	—
246	C₂×#41	—	4	4	no	—
247	C₂×#41	—	4	4	no	—
248	C₂²×Q₈	—	2	1	no	—
249	C₂²×D₄	—	2	2	no	—
250	C₂²×D₄	—	2	1	no	—
251	C₂²×D₄	—	2	1	no	—
252	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
253	C₂³×C₄	—	2	2	no	—
254	C₂³×C₄	—	2	2	no	—
255	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
256	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
257	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
258	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
259	C₄⋊Q₈	—	2	2	no	—
260	C₄⋊Q₈	C₂×C₄×C₄₁	1	4	yes	complemented
261	#127	—	2	2	no	—
262	#127	C₂×C₄×C₄₁	1	4	yes	complemented
263	#124	—	2	8	no	—
264	#121	—	2	8	no	—
265	#121	—	2	4	no	—
266	#121	C₂×C₄×C₄₁	1	8	yes	—
267	C₄×D₄	—	2	8	no	—
268	C₄×D₄	—	2	4	no	—
269	C₄×D₄	C₂×C₄×C₄₁	1	8	yes	complemented
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	8	no	—
273	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
274	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₄²	—	2	2	no	—
278	C₂×C₄²	—	2	2	no	—
279	C₂×C₄²	—	4	4	no	—
280	C₂×C₄²	C₂×C₄×C₄₁	1	4	yes	—
281	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
282	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
283	C₂×C₄²	D₄×C₄₁	1	4	yes	—
284	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
285	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
286	C₄⋊C₈	—	2	4	no	—
287	#102	—	2	16	no	—
288	C₂²⋊C₈	—	2	4	no	—
289	C₄×C₈	—	2	4	no	—
290	#95	—	2	2	no	—
291	#95	—	2	2	no	—
292	C₂⁴	—	2	2	no	—
293	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
294	#41	—	4	32	no	—
295	C₂×Q₈	—	2	4	no	—
296	C₂×Q₈	—	4	2	no	—
297	C₂×Q₈	—	4	2	no	—
298	C₂×D₄	—	2	8	no	—
299	C₂×D₄	—	2	4	no	—
300	C₂×D₄	—	2	4	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	8	no	—
303	C₂×D₄	—	4	4	no	—
304	C₂×D₄	—	4	4	no	—
305	C₂×D₄	—	4	4	no	—
306	C₂×D₄	—	4	2	no	—
307	C₂×D₄	—	4	2	no	—
308	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	8	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	8	no	—
314	C₂²×C₄	—	4	2	no	—
315	C₂²×C₄	—	4	4	no	—
316	C₂²×C₄	—	4	4	no	—
317	C₂²×C₄	—	4	4	no	—
318	C₂²×C₄	—	4	4	no	—
319	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
320	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
321	C₂²×C₄	D₈×C₄₁	1	4	yes	—
322	C₂²×C₄	SD₁₆×C₄₁	1	4	yes	—
323	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
324	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
326	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
327	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
328	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
329	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
330	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
331	C₂×C₈	—	2	4	no	—
332	C₂×C₈	—	2	8	no	—
333	C₄⋊C₄	—	2	8	no	—
334	C₄⋊C₄	—	2	4	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	4	no	—
337	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
338	C₄⋊C₄	#41×C₄₁	1	8	yes	complemented
339	C₂²⋊C₄	—	2	8	no	—
340	C₂²⋊C₄	—	2	8	no	—
341	C₄²	—	4	4	no	—
342	C₄²	—	4	4	no	—
343	C₄²	C₂²⋊C₄×C₄₁	1	4	yes	—
344	C₄²	C₂²⋊C₄×C₄₁	1	4	yes	—
345	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
346	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
347	C₄²	C₂×D₄×C₄₁	1	2	yes	—
348	C₄²	C₂×D₄×C₄₁	1	2	yes	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	4	no	—
352	C₂³	—	4	4	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	4	no	—
356	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
357	C₂³	C₂×D₈×C₄₁	1	2	yes	—
358	C₂³	C₂×SD₁₆×C₄₁	1	2	yes	—
359	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
360	Q₈	—	4	8	no	—
361	D₄	—	2	8	no	—
362	D₄	—	4	8	no	—
363	D₄	—	4	16	no	—
364	D₄	—	4	4	no	—
365	D₄	—	4	8	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	8	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	4	16	no	—
375	C₂×C₄	—	4	4	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	—	4	16	no	—
380	C₂×C₄	#102×C₄₁	1	16	yes	complemented
381	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
382	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
383	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
384	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
385	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
386	C₂×C₄	C₂×D₈×C₄₁	1	2	yes	—
387	C₂×C₄	C₂×D₈×C₄₁	1	2	yes	—
388	C₂×C₄	C₂×SD₁₆×C₄₁	1	2	yes	—
389	C₂×C₄	C₂×SD₁₆×C₄₁	1	2	yes	—
390	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
391	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
392	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
393	C₈	—	4	4	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	4	no	—
396	C₂²	—	2	4	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	4	4	no	—
399	C₂²	—	4	4	no	—
400	C₂²	—	4	4	no	—
401	C₂²	—	8	4	no	—
402	C₂²	—	8	4	no	—
403	C₂²	C₂×#102×C₄₁	1	4	yes	—
404	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
405	C₂²	C₄₁×#525	1	2	yes	—
406	C₂²	C₂²×D₈×C₄₁	1	1	yes	characteristic
407	C₂²	C₂²×SD₁₆×C₄₁	1	1	yes	characteristic
408	C₂²	C₄₁×#575	1	2	yes	—
409	C₄	—	2	2	no	—
410	C₄	—	2	2	no	—
411	C₄	—	2	2	no	—
412	C₄	—	4	8	no	—
413	C₄	—	4	4	no	—
414	C₄	C₂×#102×C₄₁	1	4	yes	—
415	C₄	C₂×#102×C₄₁	1	4	yes	—
416	C₄	C₄×#41×C₄₁	1	2	yes	—
417	C₄	C₄₁×#532	1	2	yes	—
418	C₂	—	2	4	no	—
419	C₂	—	8	4	no	—
420	C₂	C₄₁×#2297	1	1	yes	characteristic
421	C₂	C₂²×#102×C₄₁	1	1	yes	characteristic
422	C₂	C₄₁×#2896	1	1	yes	characteristic
423	C₂	C₄₁×#3100	1	2	yes	—
424	C₂	C₄₁×#3103	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₄₁	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
socle	C₂³×C₄₁	C₂²×D₄
prime radical	C₂×C₄₁×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#431	C₂	semidirect
3. C₂×C₄×C₄⋊C₄×C₄₁	C₂	semidirect
4. C₄₁×#1988	C₂	semidirect
5. C₄₁×#1982	C₂	semidirect
6. C₄₁×#1874	C₂	semidirect
7. C₄×#102×C₄₁	C₂	semidirect
10. C₄₁×#532	C₄	semidirect
47. C₄⋊Q₈×C₄₁	C₂×C₄	semidirect
49. #127×C₄₁	C₂×C₄	semidirect
56. C₄×D₄×C₄₁	C₂×C₄	semidirect
125. C₄⋊C₄×C₄₁	#41	semidirect
167. C₂×C₄×C₄₁	#102	semidirect
181. #21386	C₄₁	direct (N × H)
207. C₂×#431	C₂×C₄₁	semidirect
208. C₂×C₄×C₄⋊C₄	C₂×C₄₁	semidirect
209. #1988	C₂×C₄₁	semidirect
210. #1982	C₂×C₄₁	semidirect
211. #1874	C₂×C₄₁	semidirect
212. C₄×#102	C₂×C₄₁	semidirect
222. #532	C₄×C₄₁	semidirect
244. C₄₁	#21386	direct (N × H)
260. C₄⋊Q₈	C₂×C₄×C₄₁	semidirect
262. #127	C₂×C₄×C₄₁	semidirect
269. C₄×D₄	C₂×C₄×C₄₁	semidirect
338. C₄⋊C₄	#41×C₄₁	semidirect
380. C₂×C₄	#102×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×#532	2
C₂×C₄₁×#431	2
C₂×C₄×C₄⋊C₄×C₄₁	2
C₄₁×#1988	2
C₄₁×#1982	2
C₄₁×#1874	2
C₄×#102×C₄₁	2
#21386	41

Subgroups — C41×#21386 #23797587

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#21386 #23797587