Subgroups — C₂×C₄₁×#1872 #23797105

Order 10496.

2270 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×#103×C₄₁	C₂	1	2	yes	maximal, complemented
4	C₂²×C₂²⋊C₈×C₄₁	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#1872	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄₁×#340	C₂	1	2	yes	maximal, complemented
7	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
8	C₂⁴×C₄×C₄₁	—	2	1	no	—
9	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₄₁	C₂²	1	2	yes	—
11	C₂×C₂²⋊Q₈×C₄₁	—	2	4	no	—
12	C₂×C₂²⋊Q₈×C₄₁	—	2	2	no	—
13	C₂×C₂²⋊Q₈×C₄₁	C₄	1	8	yes	complemented
14	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	4	yes	—
15	C₂²×C₄⋊C₄×C₄₁	—	2	2	no	—
16	C₂²×C₄⋊C₄×C₄₁	—	2	1	no	—
17	C₂²×C₄⋊C₄×C₄₁	—	2	1	no	—
18	C₂²×C₄⋊C₄×C₄₁	—	2	8	no	—
19	C₂²×C₄⋊C₄×C₄₁	C₂²	1	4	yes	—
20	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
22	C₂²×C₂²⋊C₄×C₄₁	—	2	1	no	—
23	C₂×#103×C₄₁	—	2	8	no	—
24	C₂×#103×C₄₁	C₂²	1	8	yes	complemented
25	C₂×C₂²⋊C₈×C₄₁	—	2	4	no	—
26	C₂×C₂²⋊C₈×C₄₁	C₂²	1	4	yes	—
27	C₄₁×#340	C₂²	1	8	yes	complemented
28	C₂⁵×C₄₁	D₄	1	1	yes	characteristic
29	C₂²×Q₈×C₄₁	—	2	2	no	—
30	C₂²×Q₈×C₄₁	—	2	1	no	—
31	C₂²×Q₈×C₄₁	—	2	4	no	—
32	C₂²×Q₈×C₄₁	—	2	4	no	—
33	C₂²×Q₈×C₄₁	C₂×C₄	1	4	yes	complemented
34	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
35	C₂³×C₄×C₄₁	—	2	4	no	—
36	C₂³×C₄×C₄₁	—	2	4	no	—
37	C₂³×C₄×C₄₁	—	2	8	no	—
38	C₂³×C₄×C₄₁	—	2	4	no	—
39	C₂³×C₄×C₄₁	—	2	1	no	—
40	C₂³×C₄×C₄₁	—	2	1	no	—
41	C₂³×C₄×C₄₁	—	2	2	no	—
42	C₂³×C₄×C₄₁	—	4	4	no	—
43	C₂³×C₄×C₄₁	—	4	4	no	—
44	C₂³×C₄×C₄₁	C₂×C₄	1	4	yes	—
45	C₂³×C₄×C₄₁	D₄	1	2	yes	—
46	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₄₁	D₄	1	4	yes	—
48	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
49	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₄₁	—	2	4	no	—
51	C₂²×C₈×C₄₁	—	2	4	no	—
52	C₂²×C₈×C₄₁	—	2	4	no	—
53	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
54	C₂²⋊Q₈×C₄₁	—	2	16	no	—
55	C₂²⋊Q₈×C₄₁	—	2	8	no	—
56	C₂²⋊Q₈×C₄₁	C₂×C₄	1	16	yes	complemented
57	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
58	C₂×C₄⋊C₄×C₄₁	—	2	16	no	—
59	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
60	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
61	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
63	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
64	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
66	C₂×C₄⋊C₄×C₄₁	—	2	16	no	—
67	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	4	yes	complemented
68	C₂×C₄⋊C₄×C₄₁	D₄	1	8	yes	—
69	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
71	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
72	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
73	#103×C₄₁	—	2	16	no	—
74	C₂²⋊C₈×C₄₁	—	2	8	no	—
75	C₂⁴×C₄₁	—	2	2	no	—
76	C₂⁴×C₄₁	—	2	2	no	—
77	C₂⁴×C₄₁	—	2	2	no	—
78	C₂⁴×C₄₁	—	2	2	no	—
79	C₂⁴×C₄₁	C₂²⋊C₄	1	4	yes	—
80	C₂⁴×C₄₁	SD₁₆	1	4	yes	—
81	C₂⁴×C₄₁	Q₁₆	1	4	yes	—
82	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
83	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
84	C₂×Q₈×C₄₁	—	2	4	no	—
85	C₂×Q₈×C₄₁	—	2	2	no	—
86	C₂×Q₈×C₄₁	—	2	16	no	—
87	C₂×Q₈×C₄₁	—	2	4	no	—
88	C₂×Q₈×C₄₁	—	2	4	no	—
89	C₂×Q₈×C₄₁	—	4	2	no	—
90	C₂×Q₈×C₄₁	—	4	8	no	—
91	C₂×Q₈×C₄₁	—	4	2	no	—
92	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	complemented
93	C₂²×C₄×C₄₁	—	2	2	no	—
94	C₂²×C₄×C₄₁	—	2	2	no	—
95	C₂²×C₄×C₄₁	—	2	16	no	—
96	C₂²×C₄×C₄₁	—	2	4	no	—
97	C₂²×C₄×C₄₁	—	2	16	no	—
98	C₂²×C₄×C₄₁	—	2	4	no	—
99	C₂²×C₄×C₄₁	—	2	4	no	—
100	C₂²×C₄×C₄₁	—	2	4	no	—
101	C₂²×C₄×C₄₁	—	2	16	no	—
102	C₂²×C₄×C₄₁	—	2	4	no	—
103	C₂²×C₄×C₄₁	—	2	4	no	—
104	C₂²×C₄×C₄₁	—	2	8	no	—
105	C₂²×C₄×C₄₁	—	2	2	no	—
106	C₂²×C₄×C₄₁	—	2	2	no	—
107	C₂²×C₄×C₄₁	—	2	4	no	—
108	C₂²×C₄×C₄₁	—	4	8	no	—
109	C₂²×C₄×C₄₁	—	4	32	no	—
110	C₂²×C₄×C₄₁	—	4	2	no	—
111	C₂²×C₄×C₄₁	—	4	2	no	—
112	C₂²×C₄×C₄₁	—	4	8	no	—
113	C₂²×C₄×C₄₁	—	4	4	no	—
114	C₂²×C₄×C₄₁	—	4	2	no	—
115	C₂²×C₄×C₄₁	—	4	4	no	—
116	C₂²×C₄×C₄₁	—	4	2	no	—
117	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
118	C₂²×C₄×C₄₁	C₂²⋊C₄	1	8	yes	—
119	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
120	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
123	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
126	C₂²×C₄×C₄₁	#41	1	4	yes	—
127	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
128	C₂×C₈×C₄₁	—	2	4	no	—
129	C₂×C₈×C₄₁	—	2	4	no	—
130	C₂×C₈×C₄₁	—	2	4	no	—
131	C₂×C₈×C₄₁	—	4	8	no	—
132	C₄⋊C₄×C₄₁	—	2	16	no	—
133	C₄⋊C₄×C₄₁	—	2	16	no	—
134	C₄⋊C₄×C₄₁	—	2	4	no	—
135	C₄⋊C₄×C₄₁	—	2	8	no	—
136	C₄⋊C₄×C₄₁	—	2	4	no	—
137	C₄⋊C₄×C₄₁	—	2	2	no	—
138	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	complemented
139	C₄⋊C₄×C₄₁	C₂×D₄	1	8	yes	—
140	C₂²⋊C₄×C₄₁	—	2	16	no	—
141	C₂³×C₄₁	—	2	2	no	—
142	C₂³×C₄₁	—	2	2	no	—
143	C₂³×C₄₁	—	2	2	no	—
144	C₂³×C₄₁	—	2	2	no	—
145	C₂³×C₄₁	—	2	8	no	—
146	C₂³×C₄₁	—	2	8	no	—
147	C₂³×C₄₁	—	2	8	no	—
148	C₂³×C₄₁	—	2	8	no	—
149	C₂³×C₄₁	—	2	8	no	—
150	C₂³×C₄₁	—	2	8	no	—
151	C₂³×C₄₁	#103	1	16	yes	complemented
152	C₂³×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
153	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
154	C₂³×C₄₁	#120	1	2	yes	—
155	C₂³×C₄₁	#123	1	2	yes	—
156	C₂³×C₄₁	C₂×SD₁₆	1	4	yes	—
157	C₂³×C₄₁	C₂×SD₁₆	1	2	yes	—
158	C₂³×C₄₁	C₂×Q₁₆	1	4	yes	—
159	C₂³×C₄₁	C₂×Q₁₆	1	2	yes	—
160	C₂³×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
161	C₂³×C₄₁	#137	1	2	yes	—
162	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
163	Q₈×C₄₁	—	2	8	no	—
164	Q₈×C₄₁	—	4	4	no	—
165	Q₈×C₄₁	—	4	8	no	—
166	C₂×C₄×C₄₁	—	2	2	no	—
167	C₂×C₄×C₄₁	—	2	2	no	—
168	C₂×C₄×C₄₁	—	2	8	no	—
169	C₂×C₄×C₄₁	—	2	8	no	—
170	C₂×C₄×C₄₁	—	2	8	no	—
171	C₂×C₄×C₄₁	—	2	16	no	—
172	C₂×C₄×C₄₁	—	2	4	no	—
173	C₂×C₄×C₄₁	—	2	4	no	—
174	C₂×C₄×C₄₁	—	2	8	no	—
175	C₂×C₄×C₄₁	—	4	32	no	—
176	C₂×C₄×C₄₁	—	4	2	no	—
177	C₂×C₄×C₄₁	—	4	2	no	—
178	C₂×C₄×C₄₁	—	4	4	no	—
179	C₂×C₄×C₄₁	—	4	2	no	—
180	C₂×C₄×C₄₁	—	4	4	no	—
181	C₂×C₄×C₄₁	—	4	2	no	—
182	C₂×C₄×C₄₁	—	4	8	no	—
183	C₂×C₄×C₄₁	—	4	8	no	—
184	C₂×C₄×C₄₁	—	4	16	no	—
185	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
186	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
187	C₂×C₄×C₄₁	C₄×D₄	1	8	yes	—
188	C₂×C₄×C₄₁	#120	1	2	yes	—
189	C₂×C₄×C₄₁	#121	1	8	yes	—
190	C₂×C₄×C₄₁	#123	1	2	yes	—
191	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
192	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
193	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
195	C₈×C₄₁	—	4	4	no	—
196	C₂×#1872	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₂²×C₄₁	—	2	4	no	—
198	C₂²×C₄₁	—	2	4	no	—
199	C₂²×C₄₁	—	2	4	no	—
200	C₂²×C₄₁	—	2	32	no	—
201	C₂²×C₄₁	—	2	4	no	—
202	C₂²×C₄₁	—	2	4	no	—
203	C₂²×C₄₁	—	2	4	no	—
204	C₂²×C₄₁	#386	1	4	yes	—
205	C₂²×C₄₁	C₂×#103	1	4	yes	—
206	C₂²×C₄₁	C₂×#103	1	8	yes	complemented
207	C₂²×C₄₁	#417	1	4	yes	—
208	C₂²×C₄₁	#450	1	4	yes	—
209	C₂²×C₄₁	#451	1	4	yes	—
210	C₂²×C₄₁	#483	1	4	yes	—
211	C₂²×C₄₁	#484	1	4	yes	—
212	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
213	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
214	C₂²×C₄₁	C₂×#123	1	1	yes	characteristic
215	C₂²×C₄₁	C₂²×SD₁₆	1	1	yes	characteristic
216	C₂²×C₄₁	C₂²×Q₁₆	1	1	yes	characteristic
217	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
218	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
219	C₄×C₄₁	—	2	4	no	—
220	C₄×C₄₁	—	4	4	no	—
221	C₄×C₄₁	—	4	8	no	—
222	C₄×C₄₁	—	4	4	no	—
223	C₄×C₄₁	#386	1	4	yes	—
224	C₄×C₄₁	C₂×C₄×D₄	1	2	yes	—
225	C₄×C₄₁	C₂×#121	1	2	yes	—
226	C₂²×C₂²⋊Q₈	C₂×C₄₁	1	1	yes	characteristic
227	C₂³×C₄⋊C₄	C₂×C₄₁	1	1	yes	characteristic
228	C₂²×#103	C₂×C₄₁	1	2	yes	complemented
229	C₂²×C₂²⋊C₈	C₂×C₄₁	1	1	yes	characteristic
230	#1872	C₂×C₄₁	1	8	yes	direct product factor
231	C₂×#340	C₂×C₄₁	1	2	yes	complemented
232	C₂×C₄₁	—	2	8	no	—
233	C₂×C₄₁	#1872	1	8	yes	direct product factor
234	C₂×C₄₁	C₂×#386	1	1	yes	characteristic
235	C₂×C₄₁	C₂²×#103	1	1	yes	characteristic
236	C₂×C₄₁	C₂×#417	1	1	yes	characteristic
237	C₂×C₄₁	C₂×#450	1	1	yes	characteristic
238	C₂×C₄₁	C₂×#451	1	1	yes	characteristic
239	C₂×C₄₁	C₂×#483	1	1	yes	characteristic
240	C₂×C₄₁	C₂×#484	1	1	yes	characteristic
241	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
242	C₂⁴×C₄	—	2	1	no	—
243	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
244	C₂³×C₈	C₂²×C₄₁	1	2	yes	—
245	C₂×C₂²⋊Q₈	—	2	4	no	—
246	C₂×C₂²⋊Q₈	—	2	2	no	—
247	C₂×C₂²⋊Q₈	C₄×C₄₁	1	8	yes	complemented
248	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	4	yes	—
249	C₂²×C₄⋊C₄	—	2	1	no	—
250	C₂²×C₄⋊C₄	—	2	2	no	—
251	C₂²×C₄⋊C₄	—	2	1	no	—
252	C₂²×C₄⋊C₄	—	2	8	no	—
253	C₂²×C₄⋊C₄	C₂²×C₄₁	1	4	yes	—
254	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
255	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
256	C₂²×C₂²⋊C₄	—	2	1	no	—
257	C₂×#103	—	2	8	no	—
258	C₂×#103	C₂²×C₄₁	1	8	yes	complemented
259	C₂×C₂²⋊C₈	—	2	4	no	—
260	C₂×C₂²⋊C₈	C₂²×C₄₁	1	4	yes	—
261	#340	C₂²×C₄₁	1	8	yes	complemented
262	C₄₁	C₂×#1872	1	1	yes	characteristic, direct product factor, Sylow
263	C₂⁵	D₄×C₄₁	1	1	yes	characteristic
264	C₂²×Q₈	—	2	2	no	—
265	C₂²×Q₈	—	2	1	no	—
266	C₂²×Q₈	—	2	4	no	—
267	C₂²×Q₈	—	2	4	no	—
268	C₂²×Q₈	C₂×C₄×C₄₁	1	4	yes	complemented
269	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
270	C₂³×C₄	—	2	4	no	—
271	C₂³×C₄	—	2	4	no	—
272	C₂³×C₄	—	2	8	no	—
273	C₂³×C₄	—	2	1	no	—
274	C₂³×C₄	—	2	1	no	—
275	C₂³×C₄	—	2	4	no	—
276	C₂³×C₄	—	2	2	no	—
277	C₂³×C₄	—	4	4	no	—
278	C₂³×C₄	—	4	4	no	—
279	C₂³×C₄	C₂×C₄×C₄₁	1	4	yes	—
280	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
281	C₂³×C₄	D₄×C₄₁	1	2	yes	—
282	C₂³×C₄	D₄×C₄₁	1	4	yes	—
283	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
284	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
285	C₂²×C₈	—	2	4	no	—
286	C₂²×C₈	—	2	4	no	—
287	C₂²×C₈	—	2	4	no	—
288	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
289	C₂²⋊Q₈	—	2	16	no	—
290	C₂²⋊Q₈	—	2	8	no	—
291	C₂²⋊Q₈	C₂×C₄×C₄₁	1	16	yes	complemented
292	C₂×C₄⋊C₄	—	2	8	no	—
293	C₂×C₄⋊C₄	—	2	16	no	—
294	C₂×C₄⋊C₄	—	2	8	no	—
295	C₂×C₄⋊C₄	—	2	4	no	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₄⋊C₄	—	2	4	no	—
298	C₂×C₄⋊C₄	—	2	4	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	—	2	16	no	—
302	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	4	yes	complemented
303	C₂×C₄⋊C₄	D₄×C₄₁	1	8	yes	—
304	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
305	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
306	C₂×C₂²⋊C₄	—	2	8	no	—
307	C₂×C₂²⋊C₄	—	2	4	no	—
308	#103	—	2	16	no	—
309	C₂²⋊C₈	—	2	8	no	—
310	C₂⁴	—	2	2	no	—
311	C₂⁴	—	2	2	no	—
312	C₂⁴	—	2	2	no	—
313	C₂⁴	—	2	2	no	—
314	C₂⁴	C₂²⋊C₄×C₄₁	1	4	yes	—
315	C₂⁴	SD₁₆×C₄₁	1	4	yes	—
316	C₂⁴	Q₁₆×C₄₁	1	4	yes	—
317	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
318	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
319	C₂×Q₈	—	2	4	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	16	no	—
322	C₂×Q₈	—	2	4	no	—
323	C₂×Q₈	—	2	4	no	—
324	C₂×Q₈	—	4	2	no	—
325	C₂×Q₈	—	4	8	no	—
326	C₂×Q₈	—	4	2	no	—
327	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	complemented
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	16	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	16	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	2	16	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	8	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	4	8	no	—
344	C₂²×C₄	—	4	32	no	—
345	C₂²×C₄	—	4	2	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	—	4	8	no	—
348	C₂²×C₄	—	4	4	no	—
349	C₂²×C₄	—	4	4	no	—
350	C₂²×C₄	—	4	2	no	—
351	C₂²×C₄	—	4	2	no	—
352	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
353	C₂²×C₄	C₂²⋊C₄×C₄₁	1	8	yes	—
354	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
355	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
356	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
357	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
358	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
360	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
361	C₂²×C₄	#41×C₄₁	1	4	yes	—
362	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
363	C₂×C₈	—	2	4	no	—
364	C₂×C₈	—	2	4	no	—
365	C₂×C₈	—	2	4	no	—
366	C₂×C₈	—	4	8	no	—
367	C₄⋊C₄	—	2	16	no	—
368	C₄⋊C₄	—	2	16	no	—
369	C₄⋊C₄	—	2	4	no	—
370	C₄⋊C₄	—	2	8	no	—
371	C₄⋊C₄	—	2	4	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	complemented
374	C₄⋊C₄	C₂×D₄×C₄₁	1	8	yes	—
375	C₂²⋊C₄	—	2	16	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	2	2	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	8	no	—
381	C₂³	—	2	8	no	—
382	C₂³	—	2	8	no	—
383	C₂³	—	2	8	no	—
384	C₂³	—	2	8	no	—
385	C₂³	—	2	8	no	—
386	C₂³	#103×C₄₁	1	16	yes	complemented
387	C₂³	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
388	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
389	C₂³	#120×C₄₁	1	2	yes	—
390	C₂³	#123×C₄₁	1	2	yes	—
391	C₂³	C₂×SD₁₆×C₄₁	1	4	yes	—
392	C₂³	C₂×SD₁₆×C₄₁	1	2	yes	—
393	C₂³	C₂×Q₁₆×C₄₁	1	4	yes	—
394	C₂³	C₂×Q₁₆×C₄₁	1	2	yes	—
395	C₂³	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
396	C₂³	#137×C₄₁	1	2	yes	—
397	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
398	Q₈	—	2	8	no	—
399	Q₈	—	4	4	no	—
400	Q₈	—	4	8	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	8	no	—
404	C₂×C₄	—	2	8	no	—
405	C₂×C₄	—	2	8	no	—
406	C₂×C₄	—	2	16	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	8	no	—
410	C₂×C₄	—	4	32	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	8	no	—
418	C₂×C₄	—	4	8	no	—
419	C₂×C₄	—	4	16	no	—
420	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
421	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
422	C₂×C₄	C₄×D₄×C₄₁	1	8	yes	—
423	C₂×C₄	#120×C₄₁	1	2	yes	—
424	C₂×C₄	#121×C₄₁	1	8	yes	—
425	C₂×C₄	#123×C₄₁	1	2	yes	—
426	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
427	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
428	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
429	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
430	C₈	—	4	4	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	2	4	no	—
433	C₂²	—	2	4	no	—
434	C₂²	—	2	4	no	—
435	C₂²	—	2	32	no	—
436	C₂²	—	2	4	no	—
437	C₂²	—	2	4	no	—
438	C₂²	C₄₁×#386	1	4	yes	—
439	C₂²	C₂×#103×C₄₁	1	4	yes	—
440	C₂²	C₂×#103×C₄₁	1	8	yes	complemented
441	C₂²	C₄₁×#417	1	4	yes	—
442	C₂²	C₄₁×#450	1	4	yes	—
443	C₂²	C₄₁×#451	1	4	yes	—
444	C₂²	C₄₁×#483	1	4	yes	—
445	C₂²	C₄₁×#484	1	4	yes	—
446	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
447	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
448	C₂²	C₂×#123×C₄₁	1	1	yes	characteristic
449	C₂²	C₂²×SD₁₆×C₄₁	1	1	yes	characteristic
450	C₂²	C₂²×Q₁₆×C₄₁	1	1	yes	characteristic
451	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
452	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
453	C₄	—	2	4	no	—
454	C₄	—	4	4	no	—
455	C₄	—	4	4	no	—
456	C₄	—	4	8	no	—
457	C₄	C₄₁×#386	1	4	yes	—
458	C₄	C₂×C₄×D₄×C₄₁	1	2	yes	—
459	C₄	C₂×#121×C₄₁	1	2	yes	—
460	C₂	—	2	8	no	—
461	C₂	C₄₁×#1872	1	8	yes	direct product factor
462	C₂	C₂×C₄₁×#386	1	1	yes	characteristic
463	C₂	C₂²×#103×C₄₁	1	1	yes	characteristic
464	C₂	C₂×C₄₁×#417	1	1	yes	characteristic
465	C₂	C₂×C₄₁×#450	1	1	yes	characteristic
466	C₂	C₂×C₄₁×#451	1	1	yes	characteristic
467	C₂	C₂×C₄₁×#483	1	1	yes	characteristic
468	C₂	C₂×C₄₁×#484	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₄₁	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂⁵×C₄₁	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₁ ◁ C₂⁴×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂²×#103×C₄₁	C₂	semidirect
5. C₄₁×#1872	C₂	direct (N × H)
6. C₂×C₄₁×#340	C₂	semidirect
13. C₂×C₂²⋊Q₈×C₄₁	C₄	semidirect
24. C₂×#103×C₄₁	C₂²	semidirect
27. C₄₁×#340	C₂²	semidirect
33. C₂²×Q₈×C₄₁	C₂×C₄	semidirect
56. C₂²⋊Q₈×C₄₁	C₂×C₄	semidirect
67. C₂×C₄⋊C₄×C₄₁	C₂×C₄	semidirect
92. C₂×Q₈×C₄₁	C₂²×C₄	semidirect
138. C₄⋊C₄×C₄₁	C₂²×C₄	semidirect
151. C₂³×C₄₁	#103	semidirect
196. C₂×#1872	C₄₁	direct (N × H)
206. C₂²×C₄₁	C₂×#103	semidirect
228. C₂²×#103	C₂×C₄₁	semidirect
230. #1872	C₂×C₄₁	direct (N × H)
231. C₂×#340	C₂×C₄₁	semidirect
233. C₂×C₄₁	#1872	direct (N × H)
247. C₂×C₂²⋊Q₈	C₄×C₄₁	semidirect
258. C₂×#103	C₂²×C₄₁	semidirect
261. #340	C₂²×C₄₁	semidirect
262. C₄₁	C₂×#1872	direct (N × H)
268. C₂²×Q₈	C₂×C₄×C₄₁	semidirect
291. C₂²⋊Q₈	C₂×C₄×C₄₁	semidirect
302. C₂×C₄⋊C₄	C₂×C₄×C₄₁	semidirect
327. C₂×Q₈	C₂²×C₄×C₄₁	semidirect
373. C₄⋊C₄	C₂²×C₄×C₄₁	semidirect
386. C₂³	#103×C₄₁	semidirect
440. C₂²	C₂×#103×C₄₁	semidirect
461. C₂	C₄₁×#1872	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₂²⋊Q₈×C₄₁	2
C₂³×C₄⋊C₄×C₄₁	2
C₂²×#103×C₄₁	2
C₂²×C₂²⋊C₈×C₄₁	2
C₄₁×#1872	2
C₂×C₄₁×#340	2
C₂×#1872	41

Subgroups — C2×C41×#1872 #23797105

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#1872 #23797105