Subgroups — C₂×C₄₁×#1909 #23797208

Order 10496.

1686 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#568	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#536	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₁×#419	C₂	1	2	yes	maximal, complemented
4	C₂×C₄₁×#410	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#1909	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄₁×H(3,ℤ/4)	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
8	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
9	C₄₁×#568	—	2	2	no	—
10	C₄₁×#568	—	2	4	no	—
11	C₄₁×#568	C₂²	1	4	yes	—
12	C₂×#131×C₄₁	—	2	4	no	—
13	C₂²×M₁₆×C₄₁	—	2	2	no	—
14	C₂²×M₁₆×C₄₁	C₂²	1	2	yes	—
15	C₄₁×#536	—	2	2	no	—
16	C₄₁×#536	—	2	2	no	—
17	C₄₁×#536	C₄	1	4	yes	complemented
18	C₄₁×#536	C₂²	1	4	yes	—
19	C₂×C₄⋊Q₈×C₄₁	C₄	1	2	yes	complemented
20	C₂×#124×C₄₁	C₄	1	2	yes	complemented
21	C₂×#123×C₄₁	—	2	2	no	—
22	C₂×C₂²⋊Q₈×C₄₁	—	2	2	no	—
23	C₂×#117×C₄₁	C₂²	1	2	yes	—
24	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
25	C₄₁×#419	—	2	4	no	—
26	C₄₁×#419	C₂²	1	8	yes	complemented
27	C₂×#103×C₄₁	—	2	4	no	—
28	C₄₁×#410	—	2	2	no	—
29	C₄₁×#410	C₂²	1	4	yes	—
30	C₂×#99×C₄₁	—	2	2	no	—
31	C₄₁×H(3,ℤ/4)	C₂²	1	8	yes	complemented
32	C₂×#41×C₄₁	—	2	2	no	—
33	C₂×#41×C₄₁	—	2	2	no	—
34	C₂×#41×C₄₁	—	2	2	no	—
35	C₂×#41×C₄₁	—	2	2	no	—
36	C₂×#41×C₄₁	C₂×C₄	1	2	yes	—
37	C₂×#41×C₄₁	D₄	1	2	yes	—
38	C₂×#41×C₄₁	D₄	1	2	yes	—
39	C₂×#41×C₄₁	C₂³	1	2	yes	—
40	C₂²×Q₈×C₄₁	—	2	1	no	—
41	C₂²×Q₈×C₄₁	—	2	1	no	—
42	C₂²×Q₈×C₄₁	—	2	1	no	—
43	C₂²×Q₈×C₄₁	—	2	2	no	—
44	C₂²×Q₈×C₄₁	—	2	2	no	—
45	C₂²×Q₈×C₄₁	—	2	2	no	—
46	C₂²×Q₈×C₄₁	—	2	2	no	—
47	C₂²×Q₈×C₄₁	C₂×C₄	1	2	yes	—
48	C₂²×Q₈×C₄₁	C₂×C₄	1	2	yes	—
49	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
50	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
51	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
52	C₂²×D₄×C₄₁	D₄	1	2	yes	—
53	C₂³×C₄×C₄₁	—	2	1	no	—
54	C₂³×C₄×C₄₁	D₄	1	2	yes	—
55	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
56	#131×C₄₁	—	2	16	no	—
57	#131×C₄₁	—	2	16	no	—
58	C₂×M₁₆×C₄₁	—	2	4	no	—
59	C₂×M₁₆×C₄₁	—	2	8	no	—
60	C₂×M₁₆×C₄₁	—	2	2	no	—
61	C₂×M₁₆×C₄₁	—	2	8	no	—
62	C₂×M₁₆×C₄₁	—	2	2	no	—
63	C₂×M₁₆×C₄₁	—	2	2	no	—
64	C₂×M₁₆×C₄₁	—	2	2	no	—
65	C₂×M₁₆×C₄₁	D₄	1	4	yes	—
66	C₂×M₁₆×C₄₁	C₂³	1	4	yes	—
67	C₂²×C₈×C₄₁	—	2	4	no	—
68	C₂²×C₈×C₄₁	D₄	1	4	yes	—
69	C₄⋊Q₈×C₄₁	—	2	4	no	—
70	C₄⋊Q₈×C₄₁	C₂×C₄	1	8	yes	complemented
71	#124×C₄₁	—	2	4	no	—
72	#124×C₄₁	C₂×C₄	1	8	yes	complemented
73	#123×C₄₁	—	2	8	no	—
74	#123×C₄₁	—	2	8	no	—
75	C₂²⋊Q₈×C₄₁	—	2	8	no	—
76	C₂²⋊Q₈×C₄₁	—	2	8	no	—
77	#117×C₄₁	—	2	1	no	—
78	#117×C₄₁	—	2	1	no	—
79	#117×C₄₁	—	2	2	no	—
80	#117×C₄₁	—	2	2	no	—
81	#117×C₄₁	—	2	2	no	—
82	#117×C₄₁	C₂×C₄	1	2	yes	—
83	#117×C₄₁	C₂³	1	4	yes	—
84	#117×C₄₁	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
86	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
87	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
89	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
91	C₂×C₄²×C₄₁	—	2	2	no	—
92	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
93	#103×C₄₁	—	2	16	no	—
94	#99×C₄₁	—	2	8	no	—
95	C₂⁴×C₄₁	C₂²⋊C₄	1	2	yes	—
96	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
97	#41×C₄₁	—	2	4	no	—
98	#41×C₄₁	—	2	4	no	—
99	#41×C₄₁	—	2	4	no	—
100	#41×C₄₁	—	2	4	no	—
101	#41×C₄₁	—	2	4	no	—
102	#41×C₄₁	—	2	4	no	—
103	#41×C₄₁	—	2	4	no	—
104	#41×C₄₁	—	2	4	no	—
105	C₂×Q₈×C₄₁	—	2	2	no	—
106	C₂×Q₈×C₄₁	—	2	2	no	—
107	C₂×Q₈×C₄₁	—	2	2	no	—
108	C₂×Q₈×C₄₁	—	2	2	no	—
109	C₂×Q₈×C₄₁	—	2	2	no	—
110	C₂×Q₈×C₄₁	—	2	4	no	—
111	C₂×Q₈×C₄₁	—	2	4	no	—
112	C₂×Q₈×C₄₁	—	2	4	no	—
113	C₂×Q₈×C₄₁	—	2	4	no	—
114	C₂×Q₈×C₄₁	—	2	4	no	—
115	C₂×Q₈×C₄₁	—	2	4	no	—
116	C₂×Q₈×C₄₁	—	4	2	no	—
117	C₂×Q₈×C₄₁	—	4	1	no	—
118	C₂×Q₈×C₄₁	—	4	1	no	—
119	C₂×Q₈×C₄₁	—	4	2	no	—
120	C₂×Q₈×C₄₁	—	4	2	no	—
121	C₂×Q₈×C₄₁	—	4	1	no	—
122	C₂×Q₈×C₄₁	—	4	2	no	—
123	C₂×Q₈×C₄₁	—	4	1	no	—
124	C₂×Q₈×C₄₁	C₂²⋊C₄	1	2	yes	—
125	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	—
126	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
127	C₂×D₄×C₄₁	—	2	4	no	—
128	C₂×D₄×C₄₁	—	2	4	no	—
129	C₂×D₄×C₄₁	—	2	2	no	—
130	C₂×D₄×C₄₁	—	2	2	no	—
131	C₂×D₄×C₄₁	C₂²⋊C₄	1	4	yes	—
132	C₂×D₄×C₄₁	C₂²⋊C₄	1	2	yes	—
133	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
134	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
135	C₂²×C₄×C₄₁	—	2	2	no	—
136	C₂²×C₄×C₄₁	—	2	2	no	—
137	C₂²×C₄×C₄₁	—	2	2	no	—
138	C₂²×C₄×C₄₁	—	2	2	no	—
139	C₂²×C₄×C₄₁	—	2	2	no	—
140	C₂²×C₄×C₄₁	—	2	2	no	—
141	C₂²×C₄×C₄₁	—	2	2	no	—
142	C₂²×C₄×C₄₁	—	2	2	no	—
143	C₂²×C₄×C₄₁	—	4	2	no	—
144	C₂²×C₄×C₄₁	—	4	2	no	—
145	C₂²×C₄×C₄₁	—	4	2	no	—
146	C₂²×C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
147	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
148	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
151	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
156	C₂²×C₄×C₄₁	#41	1	2	yes	—
157	C₂²×C₄×C₄₁	#41	1	2	yes	—
158	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
159	M₁₆×C₄₁	—	2	16	no	—
160	M₁₆×C₄₁	—	2	4	no	—
161	M₁₆×C₄₁	—	2	4	no	—
162	M₁₆×C₄₁	—	2	4	no	—
163	M₁₆×C₄₁	—	2	4	no	—
164	C₂×C₈×C₄₁	—	2	16	no	—
165	C₂×C₈×C₄₁	—	2	4	no	—
166	C₂×C₈×C₄₁	—	2	4	no	—
167	C₂×C₈×C₄₁	C₂×D₄	1	8	yes	—
168	C₄⋊C₄×C₄₁	—	2	2	no	—
169	C₄⋊C₄×C₄₁	—	2	16	no	—
170	C₄⋊C₄×C₄₁	—	2	2	no	—
171	C₄⋊C₄×C₄₁	—	2	4	no	—
172	C₄⋊C₄×C₄₁	—	4	2	no	—
173	C₂²⋊C₄×C₄₁	—	2	2	no	—
174	C₂²⋊C₄×C₄₁	—	2	16	no	—
175	C₂²⋊C₄×C₄₁	—	2	2	no	—
176	C₂²⋊C₄×C₄₁	—	2	4	no	—
177	C₂²⋊C₄×C₄₁	—	4	2	no	—
178	C₄²×C₄₁	—	2	2	no	—
179	C₄²×C₄₁	—	2	4	no	—
180	C₄²×C₄₁	—	4	2	no	—
181	C₄²×C₄₁	C₂²×C₄	1	4	yes	—
182	C₂³×C₄₁	—	2	2	no	—
183	C₂³×C₄₁	—	2	2	no	—
184	C₂³×C₄₁	—	4	2	no	—
185	C₂³×C₄₁	—	4	4	no	—
186	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
187	C₂³×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
188	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	C₂³×C₄₁	#121	1	2	yes	—
190	C₂³×C₄₁	#121	1	2	yes	—
191	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
192	Q₈×C₄₁	—	2	4	no	—
193	Q₈×C₄₁	—	2	4	no	—
194	Q₈×C₄₁	—	2	8	no	—
195	Q₈×C₄₁	—	4	2	no	—
196	Q₈×C₄₁	—	4	2	no	—
197	Q₈×C₄₁	—	4	2	no	—
198	Q₈×C₄₁	—	4	2	no	—
199	Q₈×C₄₁	—	4	4	no	—
200	D₄×C₄₁	—	2	8	no	—
201	D₄×C₄₁	—	2	8	no	—
202	D₄×C₄₁	—	2	4	no	—
203	D₄×C₄₁	—	2	4	no	—
204	C₂×C₄×C₄₁	—	2	2	no	—
205	C₂×C₄×C₄₁	—	2	2	no	—
206	C₂×C₄×C₄₁	—	2	4	no	—
207	C₂×C₄×C₄₁	—	2	4	no	—
208	C₂×C₄×C₄₁	—	2	4	no	—
209	C₂×C₄×C₄₁	—	2	4	no	—
210	C₂×C₄×C₄₁	—	2	4	no	—
211	C₂×C₄×C₄₁	—	2	4	no	—
212	C₂×C₄×C₄₁	—	4	4	no	—
213	C₂×C₄×C₄₁	—	4	4	no	—
214	C₂×C₄×C₄₁	—	4	2	no	—
215	C₂×C₄×C₄₁	—	4	4	no	—
216	C₂×C₄×C₄₁	—	4	2	no	—
217	C₂×C₄×C₄₁	—	4	4	no	—
218	C₂×C₄×C₄₁	—	8	4	no	—
219	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
220	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
223	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
224	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
225	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
226	C₂×C₄×C₄₁	#120	1	2	yes	—
227	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
228	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
229	C₂×C₄×C₄₁	#121	1	2	yes	—
230	C₂×C₄×C₄₁	#121	1	2	yes	—
231	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
232	C₂×C₄×C₄₁	#123	1	2	yes	—
233	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
234	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
235	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
236	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
238	C₈×C₄₁	—	2	8	no	—
239	C₂×#1909	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
240	C₂²×C₄₁	—	2	2	no	—
241	C₂²×C₄₁	—	2	4	no	—
242	C₂²×C₄₁	—	2	4	no	—
243	C₂²×C₄₁	—	4	1	no	—
244	C₂²×C₄₁	—	4	2	no	—
245	C₂²×C₄₁	—	4	1	no	—
246	C₂²×C₄₁	—	4	4	no	—
247	C₂²×C₄₁	—	4	4	no	—
248	C₂²×C₄₁	—	8	2	no	—
249	C₂²×C₄₁	#386	1	1	yes	characteristic
250	C₂²×C₄₁	#386	1	2	yes	—
251	C₂²×C₄₁	#386	1	1	yes	characteristic
252	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
253	C₂²×C₄₁	C₂×#121	1	2	yes	—
254	C₄×C₄₁	—	2	4	no	—
255	C₄×C₄₁	—	4	4	no	—
256	C₄×C₄₁	—	4	4	no	—
257	C₄×C₄₁	—	8	4	no	—
258	C₄×C₄₁	#386	1	1	yes	characteristic
259	C₄×C₄₁	#386	1	1	yes	characteristic
260	C₄×C₄₁	#386	1	2	yes	—
261	C₄×C₄₁	C₂×C₄×D₄	1	2	yes	—
262	C₄×C₄₁	C₂×#120	1	1	yes	characteristic
263	C₄×C₄₁	C₂×#123	1	1	yes	characteristic
264	C₂×#568	C₂×C₄₁	1	1	yes	characteristic
265	C₂×#536	C₂×C₄₁	1	1	yes	characteristic
266	C₂×#419	C₂×C₄₁	1	2	yes	complemented
267	C₂×#410	C₂×C₄₁	1	1	yes	characteristic
268	#1909	C₂×C₄₁	1	8	yes	direct product factor
269	C₂×H(3,ℤ/4)	C₂×C₄₁	1	2	yes	complemented
270	C₂×C₄₁	—	2	1	no	—
271	C₂×C₄₁	—	2	2	no	—
272	C₂×C₄₁	—	2	1	no	—
273	C₂×C₄₁	—	2	2	no	—
274	C₂×C₄₁	—	4	4	no	—
275	C₂×C₄₁	#1909	1	2	yes	direct product factor
276	C₂×C₄₁	C₂×#386	1	1	yes	characteristic
277	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
278	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
279	#568	—	2	2	no	—
280	#568	—	2	4	no	—
281	#568	C₂²×C₄₁	1	4	yes	—
282	C₂×#131	—	2	4	no	—
283	C₂²×M₁₆	—	2	2	no	—
284	C₂²×M₁₆	C₂²×C₄₁	1	2	yes	—
285	#536	—	2	2	no	—
286	#536	—	2	2	no	—
287	#536	C₄×C₄₁	1	4	yes	complemented
288	#536	C₂²×C₄₁	1	4	yes	—
289	C₂×C₄⋊Q₈	C₄×C₄₁	1	2	yes	complemented
290	C₂×#124	C₄×C₄₁	1	2	yes	complemented
291	C₂×#123	—	2	2	no	—
292	C₂×C₂²⋊Q₈	—	2	2	no	—
293	C₂×#117	C₂²×C₄₁	1	2	yes	—
294	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
295	#419	—	2	4	no	—
296	#419	C₂²×C₄₁	1	8	yes	complemented
297	C₂×#103	—	2	4	no	—
298	#410	—	2	2	no	—
299	#410	C₂²×C₄₁	1	4	yes	—
300	C₂×#99	—	2	2	no	—
301	H(3,ℤ/4)	C₂²×C₄₁	1	8	yes	complemented
302	C₄₁	C₂×#1909	1	1	yes	characteristic, direct product factor, Sylow
303	C₂×#41	—	2	2	no	—
304	C₂×#41	—	2	2	no	—
305	C₂×#41	—	2	2	no	—
306	C₂×#41	—	2	2	no	—
307	C₂×#41	C₂×C₄×C₄₁	1	2	yes	—
308	C₂×#41	D₄×C₄₁	1	2	yes	—
309	C₂×#41	D₄×C₄₁	1	2	yes	—
310	C₂×#41	C₂³×C₄₁	1	2	yes	—
311	C₂²×Q₈	—	2	1	no	—
312	C₂²×Q₈	—	2	1	no	—
313	C₂²×Q₈	—	2	1	no	—
314	C₂²×Q₈	—	2	2	no	—
315	C₂²×Q₈	—	2	2	no	—
316	C₂²×Q₈	—	2	2	no	—
317	C₂²×Q₈	—	2	2	no	—
318	C₂²×Q₈	C₂×C₄×C₄₁	1	2	yes	—
319	C₂²×Q₈	C₂×C₄×C₄₁	1	2	yes	—
320	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
321	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
322	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
323	C₂²×D₄	D₄×C₄₁	1	2	yes	—
324	C₂³×C₄	—	2	1	no	—
325	C₂³×C₄	D₄×C₄₁	1	2	yes	—
326	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
327	#131	—	2	16	no	—
328	#131	—	2	16	no	—
329	C₂×M₁₆	—	2	4	no	—
330	C₂×M₁₆	—	2	8	no	—
331	C₂×M₁₆	—	2	2	no	—
332	C₂×M₁₆	—	2	8	no	—
333	C₂×M₁₆	—	2	2	no	—
334	C₂×M₁₆	—	2	2	no	—
335	C₂×M₁₆	—	2	2	no	—
336	C₂×M₁₆	D₄×C₄₁	1	4	yes	—
337	C₂×M₁₆	C₂³×C₄₁	1	4	yes	—
338	C₂²×C₈	—	2	4	no	—
339	C₂²×C₈	D₄×C₄₁	1	4	yes	—
340	C₄⋊Q₈	—	2	4	no	—
341	C₄⋊Q₈	C₂×C₄×C₄₁	1	8	yes	complemented
342	#124	—	2	4	no	—
343	#124	C₂×C₄×C₄₁	1	8	yes	complemented
344	#123	—	2	8	no	—
345	#123	—	2	8	no	—
346	C₂²⋊Q₈	—	2	8	no	—
347	C₂²⋊Q₈	—	2	8	no	—
348	#117	—	2	1	no	—
349	#117	—	2	1	no	—
350	#117	—	2	2	no	—
351	#117	—	2	2	no	—
352	#117	—	2	2	no	—
353	#117	C₂×C₄×C₄₁	1	2	yes	—
354	#117	C₂³×C₄₁	1	4	yes	—
355	#117	C₂³×C₄₁	1	2	yes	—
356	C₂×C₄⋊C₄	—	2	4	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	2	no	—
359	C₂×C₂²⋊C₄	—	2	4	no	—
360	C₂×C₂²⋊C₄	—	2	1	no	—
361	C₂×C₂²⋊C₄	—	2	2	no	—
362	C₂×C₄²	—	2	2	no	—
363	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
364	#103	—	2	16	no	—
365	#99	—	2	8	no	—
366	C₂⁴	C₂²⋊C₄×C₄₁	1	2	yes	—
367	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
368	#41	—	2	4	no	—
369	#41	—	2	4	no	—
370	#41	—	2	4	no	—
371	#41	—	2	4	no	—
372	#41	—	2	4	no	—
373	#41	—	2	4	no	—
374	#41	—	2	4	no	—
375	#41	—	2	4	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	2	2	no	—
381	C₂×Q₈	—	2	4	no	—
382	C₂×Q₈	—	2	4	no	—
383	C₂×Q₈	—	2	4	no	—
384	C₂×Q₈	—	2	4	no	—
385	C₂×Q₈	—	2	4	no	—
386	C₂×Q₈	—	2	4	no	—
387	C₂×Q₈	—	4	1	no	—
388	C₂×Q₈	—	4	2	no	—
389	C₂×Q₈	—	4	1	no	—
390	C₂×Q₈	—	4	2	no	—
391	C₂×Q₈	—	4	2	no	—
392	C₂×Q₈	—	4	1	no	—
393	C₂×Q₈	—	4	1	no	—
394	C₂×Q₈	—	4	2	no	—
395	C₂×Q₈	C₂²⋊C₄×C₄₁	1	2	yes	—
396	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	—
397	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
398	C₂×D₄	—	2	4	no	—
399	C₂×D₄	—	2	4	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	C₂²⋊C₄×C₄₁	1	4	yes	—
403	C₂×D₄	C₂²⋊C₄×C₄₁	1	2	yes	—
404	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
405	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	4	2	no	—
415	C₂²×C₄	—	4	2	no	—
416	C₂²×C₄	—	4	2	no	—
417	C₂²×C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
418	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
419	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
420	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
421	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
422	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
423	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
424	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
425	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
426	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
427	C₂²×C₄	#41×C₄₁	1	2	yes	—
428	C₂²×C₄	#41×C₄₁	1	2	yes	—
429	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
430	M₁₆	—	2	16	no	—
431	M₁₆	—	2	4	no	—
432	M₁₆	—	2	4	no	—
433	M₁₆	—	2	4	no	—
434	M₁₆	—	2	4	no	—
435	C₂×C₈	—	2	16	no	—
436	C₂×C₈	—	2	4	no	—
437	C₂×C₈	—	2	4	no	—
438	C₂×C₈	C₂×D₄×C₄₁	1	8	yes	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	16	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	—	4	2	no	—
444	C₂²⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	—	2	16	no	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	2	4	no	—
448	C₂²⋊C₄	—	4	2	no	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	4	no	—
451	C₄²	—	4	2	no	—
452	C₄²	C₂²×C₄×C₄₁	1	4	yes	—
453	C₂³	—	2	2	no	—
454	C₂³	—	2	2	no	—
455	C₂³	—	4	2	no	—
456	C₂³	—	4	4	no	—
457	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
458	C₂³	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
459	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
460	C₂³	#121×C₄₁	1	2	yes	—
461	C₂³	#121×C₄₁	1	2	yes	—
462	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
463	Q₈	—	2	4	no	—
464	Q₈	—	2	4	no	—
465	Q₈	—	2	8	no	—
466	Q₈	—	4	2	no	—
467	Q₈	—	4	2	no	—
468	Q₈	—	4	2	no	—
469	Q₈	—	4	2	no	—
470	Q₈	—	4	4	no	—
471	D₄	—	2	8	no	—
472	D₄	—	2	8	no	—
473	D₄	—	2	4	no	—
474	D₄	—	2	4	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	4	4	no	—
484	C₂×C₄	—	4	4	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	4	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	4	no	—
489	C₂×C₄	—	8	4	no	—
490	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
491	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
492	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
493	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
494	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
495	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
496	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
497	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
498	C₂×C₄	#120×C₄₁	1	2	yes	—
499	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
500	C₂×C₄	#121×C₄₁	1	2	yes	—
501	C₂×C₄	#121×C₄₁	1	2	yes	—
502	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
503	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
504	C₂×C₄	#123×C₄₁	1	2	yes	—
505	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
506	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
507	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
508	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
509	C₈	—	2	8	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	2	4	no	—
512	C₂²	—	2	4	no	—
513	C₂²	—	4	1	no	—
514	C₂²	—	4	2	no	—
515	C₂²	—	4	1	no	—
516	C₂²	—	4	4	no	—
517	C₂²	—	4	4	no	—
518	C₂²	—	8	2	no	—
519	C₂²	C₄₁×#386	1	1	yes	characteristic
520	C₂²	C₄₁×#386	1	2	yes	—
521	C₂²	C₄₁×#386	1	1	yes	characteristic
522	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
523	C₂²	C₂×#121×C₄₁	1	2	yes	—
524	C₄	—	2	4	no	—
525	C₄	—	4	4	no	—
526	C₄	—	4	4	no	—
527	C₄	—	8	4	no	—
528	C₄	C₄₁×#386	1	1	yes	characteristic
529	C₄	C₄₁×#386	1	1	yes	characteristic
530	C₄	C₄₁×#386	1	2	yes	—
531	C₄	C₂×C₄×D₄×C₄₁	1	2	yes	—
532	C₄	C₂×#120×C₄₁	1	1	yes	characteristic
533	C₄	C₂×#123×C₄₁	1	1	yes	characteristic
534	C₂	—	2	1	no	—
535	C₂	—	2	2	no	—
536	C₂	—	2	1	no	—
537	C₂	—	2	2	no	—
538	C₂	—	4	4	no	—
539	C₂	C₄₁×#1909	1	2	yes	direct product factor
540	C₂	C₂×C₄₁×#386	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	#386
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂²×#41×C₄₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂³×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄₁×#419	C₂	semidirect
5. C₄₁×#1909	C₂	direct (N × H)
6. C₂×C₄₁×H(3,ℤ/4)	C₂	semidirect
17. C₄₁×#536	C₄	semidirect
19. C₂×C₄⋊Q₈×C₄₁	C₄	semidirect
20. C₂×#124×C₄₁	C₄	semidirect
26. C₄₁×#419	C₂²	semidirect
31. C₄₁×H(3,ℤ/4)	C₂²	semidirect
70. C₄⋊Q₈×C₄₁	C₂×C₄	semidirect
72. #124×C₄₁	C₂×C₄	semidirect
239. C₂×#1909	C₄₁	direct (N × H)
266. C₂×#419	C₂×C₄₁	semidirect
268. #1909	C₂×C₄₁	direct (N × H)
269. C₂×H(3,ℤ/4)	C₂×C₄₁	semidirect
275. C₂×C₄₁	#1909	direct (N × H)
287. #536	C₄×C₄₁	semidirect
289. C₂×C₄⋊Q₈	C₄×C₄₁	semidirect
290. C₂×#124	C₄×C₄₁	semidirect
296. #419	C₂²×C₄₁	semidirect
301. H(3,ℤ/4)	C₂²×C₄₁	semidirect
302. C₄₁	C₂×#1909	direct (N × H)
341. C₄⋊Q₈	C₂×C₄×C₄₁	semidirect
343. #124	C₂×C₄×C₄₁	semidirect
539. C₂	C₄₁×#1909	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×#568	2
C₂×C₄₁×#536	2
C₂×C₄₁×#419	2
C₂×C₄₁×#410	2
C₄₁×#1909	2
C₂×C₄₁×H(3,ℤ/4)	2
C₂×#1909	41

Subgroups — C2×C41×#1909 #23797208

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#1909 #23797208