Subgroups — C₂×C₄₁×#1490 #23793645

Order 10496.

1734 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₄₁	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×#1490	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₄₁×D₄⋊C₈	C₂	1	4	yes	maximal, complemented
6	C₂³×D₄×C₄₁	C₄	1	1	yes	characteristic
7	C₂⁴×C₄×C₄₁	—	2	1	no	—
8	C₂²×M₁₆×C₄₁	—	2	1	no	—
9	C₂×C₄×D₄×C₄₁	—	2	1	no	—
10	C₂×C₄×D₄×C₄₁	—	2	2	no	—
11	C₂×C₄×D₄×C₄₁	—	2	2	no	—
12	C₂×C₄×D₄×C₄₁	—	2	1	no	—
13	C₂×C₄×D₄×C₄₁	C₄	1	4	yes	—
14	C₂×C₄×D₄×C₄₁	C₄	1	2	yes	—
15	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₄₁	C₂²	1	4	yes	—
17	C₂²×C₄⋊C₄×C₄₁	C₄	1	1	yes	characteristic
18	C₂²×C₂²⋊C₄×C₄₁	—	2	1	no	—
19	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
20	C₄₁×#432	—	2	2	no	—
21	C₄₁×#432	C₂²	1	4	yes	complemented
22	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	complemented
23	C₂×C₂²⋊C₈×C₄₁	—	2	1	no	—
24	C₄×M₁₆×C₄₁	—	2	2	no	—
25	C₄×M₁₆×C₄₁	C₂²	1	4	yes	complemented
26	C₂×#97×C₄₁	—	2	1	no	—
27	C₂×#97×C₄₁	—	2	1	no	—
28	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	complemented
29	C₄₁×D₄⋊C₈	C₂²	1	16	yes	complemented
30	C₂⁵×C₄₁	—	2	1	no	—
31	C₂²×D₄×C₄₁	—	2	8	no	—
32	C₂²×D₄×C₄₁	—	2	1	no	—
33	C₂²×D₄×C₄₁	—	2	2	no	—
34	C₂²×D₄×C₄₁	C₂×C₄	1	4	yes	—
35	C₂²×D₄×C₄₁	C₂×C₄	1	2	yes	—
36	C₂³×C₄×C₄₁	—	2	1	no	—
37	C₂³×C₄×C₄₁	—	2	4	no	—
38	C₂³×C₄×C₄₁	—	2	2	no	—
39	C₂³×C₄×C₄₁	—	2	4	no	—
40	C₂³×C₄×C₄₁	—	2	2	no	—
41	C₂³×C₄×C₄₁	—	4	8	no	—
42	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
45	C₂×M₁₆×C₄₁	—	2	8	no	—
46	C₂×M₁₆×C₄₁	—	2	4	no	—
47	C₂²×C₈×C₄₁	—	2	2	no	—
48	C₂²×C₈×C₄₁	—	2	2	no	—
49	C₄×D₄×C₄₁	—	2	4	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	4	no	—
54	C₄×D₄×C₄₁	—	2	4	no	—
55	C₄×D₄×C₄₁	—	2	2	no	—
56	C₄×D₄×C₄₁	C₂×C₄	1	4	yes	—
57	C₄×D₄×C₄₁	C₂×C₄	1	8	yes	—
58	C₄×D₄×C₄₁	C₂³	1	4	yes	—
59	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
60	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	4	yes	—
62	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
63	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
64	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
67	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
68	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₄₁	D₄	1	2	yes	—
71	C₂×C₄²×C₄₁	D₄	1	2	yes	—
72	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
74	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
75	C₄⋊C₈×C₄₁	—	2	2	no	—
76	C₄⋊C₈×C₄₁	C₂³	1	4	yes	complemented
77	C₂²⋊C₈×C₄₁	—	2	4	no	—
78	#97×C₄₁	—	2	4	no	—
79	#97×C₄₁	—	2	4	no	—
80	C₄×C₈×C₄₁	—	2	2	no	—
81	C₄×C₈×C₄₁	C₂³	1	4	yes	complemented
82	C₂⁴×C₄₁	—	2	8	no	—
83	C₂⁴×C₄₁	—	2	4	no	—
84	C₂⁴×C₄₁	—	2	2	no	—
85	C₂⁴×C₄₁	—	4	4	no	—
86	C₂⁴×C₄₁	—	4	4	no	—
87	C₂⁴×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
88	C₂×D₄×C₄₁	—	2	8	no	—
89	C₂×D₄×C₄₁	—	2	16	no	—
90	C₂×D₄×C₄₁	—	2	16	no	—
91	C₂×D₄×C₄₁	—	2	4	no	—
92	C₂×D₄×C₄₁	—	2	2	no	—
93	C₂×D₄×C₄₁	—	2	4	no	—
94	C₂×D₄×C₄₁	M₁₆	1	8	yes	complemented
95	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₄₁	—	2	4	no	—
97	C₂²×C₄×C₄₁	—	2	4	no	—
98	C₂²×C₄×C₄₁	—	2	4	no	—
99	C₂²×C₄×C₄₁	—	2	4	no	—
100	C₂²×C₄×C₄₁	—	2	2	no	—
101	C₂²×C₄×C₄₁	—	2	8	no	—
102	C₂²×C₄×C₄₁	—	2	4	no	—
103	C₂²×C₄×C₄₁	—	2	4	no	—
104	C₂²×C₄×C₄₁	—	4	8	no	—
105	C₂²×C₄×C₄₁	—	4	16	no	—
106	C₂²×C₄×C₄₁	—	4	16	no	—
107	C₂²×C₄×C₄₁	—	4	4	no	—
108	C₂²×C₄×C₄₁	—	4	8	no	—
109	C₂²×C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
110	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
113	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
115	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
121	M₁₆×C₄₁	—	2	16	no	—
122	C₂×C₈×C₄₁	—	2	8	no	—
123	C₂×C₈×C₄₁	—	2	4	no	—
124	C₂×C₈×C₄₁	—	2	4	no	—
125	C₂×C₈×C₄₁	—	4	4	no	—
126	C₄⋊C₄×C₄₁	—	2	4	no	—
127	C₄⋊C₄×C₄₁	—	2	2	no	—
128	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
129	C₂²⋊C₄×C₄₁	—	2	8	no	—
130	C₂²⋊C₄×C₄₁	—	2	4	no	—
131	C₂²⋊C₄×C₄₁	—	2	4	no	—
132	C₄²×C₄₁	C₂²⋊C₄	1	2	yes	—
133	C₄²×C₄₁	C₂²⋊C₄	1	2	yes	—
134	C₄²×C₄₁	C₂²⋊C₄	1	2	yes	—
135	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
136	C₄²×C₄₁	C₂²×C₄	1	1	yes	characteristic
137	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₄₁	C₂×D₄	1	2	yes	—
139	C₄²×C₄₁	C₂×D₄	1	2	yes	—
140	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
142	C₂³×C₄₁	—	2	2	no	—
143	C₂³×C₄₁	—	2	2	no	—
144	C₂³×C₄₁	—	2	16	no	—
145	C₂³×C₄₁	—	2	4	no	—
146	C₂³×C₄₁	—	2	8	no	—
147	C₂³×C₄₁	—	4	8	no	—
148	C₂³×C₄₁	—	4	32	no	—
149	C₂³×C₄₁	—	4	4	no	—
150	C₂³×C₄₁	—	4	8	no	—
151	C₂³×C₄₁	—	4	4	no	—
152	C₂³×C₄₁	#104	1	4	yes	—
153	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
154	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	D₄×C₄₁	—	2	16	no	—
156	D₄×C₄₁	—	2	4	no	—
157	D₄×C₄₁	—	2	8	no	—
158	D₄×C₄₁	C₂×M₁₆	1	8	yes	complemented
159	C₂×C₄×C₄₁	—	2	2	no	—
160	C₂×C₄×C₄₁	—	2	2	no	—
161	C₂×C₄×C₄₁	—	2	2	no	—
162	C₂×C₄×C₄₁	—	2	4	no	—
163	C₂×C₄×C₄₁	—	2	4	no	—
164	C₂×C₄×C₄₁	—	2	2	no	—
165	C₂×C₄×C₄₁	—	2	4	no	—
166	C₂×C₄×C₄₁	—	2	4	no	—
167	C₂×C₄×C₄₁	—	2	4	no	—
168	C₂×C₄×C₄₁	—	2	4	no	—
169	C₂×C₄×C₄₁	—	2	4	no	—
170	C₂×C₄×C₄₁	—	4	16	no	—
171	C₂×C₄×C₄₁	—	4	8	no	—
172	C₂×C₄×C₄₁	—	4	4	no	—
173	C₂×C₄×C₄₁	—	4	8	no	—
174	C₂×C₄×C₄₁	—	4	8	no	—
175	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
176	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
178	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
179	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₄₁	C₂×M₁₆	1	4	yes	—
182	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	4	yes	—
183	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
184	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
186	C₈×C₄₁	—	2	8	no	—
187	C₈×C₄₁	—	4	4	no	—
188	C₂×#1490	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₂²×C₄₁	—	2	2	no	—
190	C₂²×C₄₁	—	2	2	no	—
191	C₂²×C₄₁	—	2	8	no	—
192	C₂²×C₄₁	—	2	8	no	—
193	C₂²×C₄₁	—	4	32	no	—
194	C₂²×C₄₁	—	4	4	no	—
195	C₂²×C₄₁	—	4	4	no	—
196	C₂²×C₄₁	—	4	16	no	—
197	C₂²×C₄₁	#407	1	2	yes	—
198	C₂²×C₄₁	#418	1	2	yes	—
199	C₂²×C₄₁	C₂×#104	1	4	yes	—
200	C₂²×C₄₁	C₂×#104	1	2	yes	—
201	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
202	C₄×C₄₁	—	2	2	no	—
203	C₄×C₄₁	—	2	2	no	—
204	C₄×C₄₁	—	2	1	no	—
205	C₄×C₄₁	—	2	1	no	—
206	C₄×C₄₁	—	2	2	no	—
207	C₄×C₄₁	—	4	4	no	—
208	C₄×C₄₁	#407	1	2	yes	—
209	C₄×C₄₁	#418	1	2	yes	—
210	C₄×C₄₁	C₂²×M₁₆	1	2	yes	—
211	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
212	C₂²×C₄×D₄	C₂×C₄₁	1	1	yes	characteristic
213	C₂×#432	C₂×C₄₁	1	1	yes	characteristic, complemented
214	C₂×C₄×M₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
215	#1490	C₂×C₄₁	1	8	yes	direct product factor
216	C₂×D₄⋊C₈	C₂×C₄₁	1	4	yes	complemented
217	C₂×C₄₁	—	2	4	no	—
218	C₂×C₄₁	—	4	8	no	—
219	C₂×C₄₁	#1490	1	4	yes	direct product factor
220	C₂×C₄₁	C₂×#407	1	1	yes	characteristic
221	C₂×C₄₁	C₂×#418	1	1	yes	characteristic
222	C₂×C₄₁	C₂²×#104	1	1	yes	characteristic
223	C₂³×D₄	C₄×C₄₁	1	1	yes	characteristic
224	C₂⁴×C₄	—	2	1	no	—
225	C₂²×M₁₆	—	2	1	no	—
226	C₂×C₄×D₄	—	2	1	no	—
227	C₂×C₄×D₄	—	2	1	no	—
228	C₂×C₄×D₄	—	2	2	no	—
229	C₂×C₄×D₄	—	2	2	no	—
230	C₂×C₄×D₄	C₄×C₄₁	1	4	yes	—
231	C₂×C₄×D₄	C₄×C₄₁	1	2	yes	—
232	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
233	C₂×C₄×D₄	C₂²×C₄₁	1	4	yes	—
234	C₂²×C₄⋊C₄	C₄×C₄₁	1	1	yes	characteristic
235	C₂²×C₂²⋊C₄	—	2	1	no	—
236	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
237	#432	—	2	2	no	—
238	#432	C₂²×C₄₁	1	4	yes	complemented
239	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	complemented
240	C₂×C₂²⋊C₈	—	2	1	no	—
241	C₄×M₁₆	—	2	2	no	—
242	C₄×M₁₆	C₂²×C₄₁	1	4	yes	complemented
243	C₂×#97	—	2	1	no	—
244	C₂×#97	—	2	1	no	—
245	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	complemented
246	D₄⋊C₈	C₂²×C₄₁	1	16	yes	complemented
247	C₄₁	C₂×#1490	1	1	yes	characteristic, direct product factor, Sylow
248	C₂⁵	—	2	1	no	—
249	C₂²×D₄	—	2	8	no	—
250	C₂²×D₄	—	2	1	no	—
251	C₂²×D₄	—	2	2	no	—
252	C₂²×D₄	C₂×C₄×C₄₁	1	4	yes	—
253	C₂²×D₄	C₂×C₄×C₄₁	1	2	yes	—
254	C₂³×C₄	—	2	1	no	—
255	C₂³×C₄	—	2	4	no	—
256	C₂³×C₄	—	2	2	no	—
257	C₂³×C₄	—	2	4	no	—
258	C₂³×C₄	—	2	2	no	—
259	C₂³×C₄	—	4	8	no	—
260	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
261	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
262	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
263	C₂×M₁₆	—	2	8	no	—
264	C₂×M₁₆	—	2	4	no	—
265	C₂²×C₈	—	2	2	no	—
266	C₂²×C₈	—	2	2	no	—
267	C₄×D₄	—	2	4	no	—
268	C₄×D₄	—	2	4	no	—
269	C₄×D₄	—	2	4	no	—
270	C₄×D₄	—	2	2	no	—
271	C₄×D₄	—	2	4	no	—
272	C₄×D₄	—	2	4	no	—
273	C₄×D₄	—	2	2	no	—
274	C₄×D₄	C₂×C₄×C₄₁	1	4	yes	—
275	C₄×D₄	C₂×C₄×C₄₁	1	8	yes	—
276	C₄×D₄	C₂³×C₄₁	1	4	yes	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	4	yes	—
280	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
281	C₂×C₂²⋊C₄	—	2	4	no	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₂²⋊C₄	—	2	4	no	—
285	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
286	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
287	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
288	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
289	C₂×C₄²	D₄×C₄₁	1	2	yes	—
290	C₂×C₄²	D₄×C₄₁	1	2	yes	—
291	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
292	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
293	C₄⋊C₈	—	2	2	no	—
294	C₄⋊C₈	C₂³×C₄₁	1	4	yes	complemented
295	C₂²⋊C₈	—	2	4	no	—
296	#97	—	2	4	no	—
297	#97	—	2	4	no	—
298	C₄×C₈	—	2	2	no	—
299	C₄×C₈	C₂³×C₄₁	1	4	yes	complemented
300	C₂⁴	—	2	8	no	—
301	C₂⁴	—	2	4	no	—
302	C₂⁴	—	2	2	no	—
303	C₂⁴	—	4	4	no	—
304	C₂⁴	—	4	4	no	—
305	C₂⁴	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
306	C₂×D₄	—	2	8	no	—
307	C₂×D₄	—	2	16	no	—
308	C₂×D₄	—	2	16	no	—
309	C₂×D₄	—	2	4	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	4	no	—
312	C₂×D₄	M₁₆×C₄₁	1	8	yes	complemented
313	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	8	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	4	8	no	—
323	C₂²×C₄	—	4	16	no	—
324	C₂²×C₄	—	4	16	no	—
325	C₂²×C₄	—	4	4	no	—
326	C₂²×C₄	—	4	8	no	—
327	C₂²×C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
328	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
329	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
330	C₂²×C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
331	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
332	C₂²×C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
333	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
334	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
336	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
338	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
339	M₁₆	—	2	16	no	—
340	C₂×C₈	—	2	8	no	—
341	C₂×C₈	—	2	4	no	—
342	C₂×C₈	—	2	4	no	—
343	C₂×C₈	—	4	4	no	—
344	C₄⋊C₄	—	2	4	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
347	C₂²⋊C₄	—	2	8	no	—
348	C₂²⋊C₄	—	2	4	no	—
349	C₂²⋊C₄	—	2	4	no	—
350	C₄²	C₂²⋊C₄×C₄₁	1	2	yes	—
351	C₄²	C₂²⋊C₄×C₄₁	1	2	yes	—
352	C₄²	C₂²⋊C₄×C₄₁	1	2	yes	—
353	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
354	C₄²	C₂²×C₄×C₄₁	1	1	yes	characteristic
355	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
356	C₄²	C₂×D₄×C₄₁	1	2	yes	—
357	C₄²	C₂×D₄×C₄₁	1	2	yes	—
358	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
359	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
360	C₂³	—	2	2	no	—
361	C₂³	—	2	2	no	—
362	C₂³	—	2	16	no	—
363	C₂³	—	2	4	no	—
364	C₂³	—	2	8	no	—
365	C₂³	—	4	8	no	—
366	C₂³	—	4	32	no	—
367	C₂³	—	4	4	no	—
368	C₂³	—	4	8	no	—
369	C₂³	—	4	4	no	—
370	C₂³	#104×C₄₁	1	4	yes	—
371	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
372	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
373	D₄	—	2	16	no	—
374	D₄	—	2	4	no	—
375	D₄	—	2	8	no	—
376	D₄	C₂×M₁₆×C₄₁	1	8	yes	complemented
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	4	16	no	—
389	C₂×C₄	—	4	8	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	8	no	—
392	C₂×C₄	—	4	8	no	—
393	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
394	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
395	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
396	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
397	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
398	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
399	C₂×C₄	C₂×M₁₆×C₄₁	1	4	yes	—
400	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	4	yes	—
401	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
402	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
403	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
404	C₈	—	2	8	no	—
405	C₈	—	4	4	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	8	no	—
409	C₂²	—	2	8	no	—
410	C₂²	—	4	32	no	—
411	C₂²	—	4	4	no	—
412	C₂²	—	4	4	no	—
413	C₂²	—	4	16	no	—
414	C₂²	C₄₁×#407	1	2	yes	—
415	C₂²	C₄₁×#418	1	2	yes	—
416	C₂²	C₂×#104×C₄₁	1	4	yes	—
417	C₂²	C₂×#104×C₄₁	1	2	yes	—
418	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
419	C₄	—	2	2	no	—
420	C₄	—	2	2	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	2	no	—
424	C₄	—	4	4	no	—
425	C₄	C₄₁×#407	1	2	yes	—
426	C₄	C₄₁×#418	1	2	yes	—
427	C₄	C₂²×M₁₆×C₄₁	1	2	yes	—
428	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	2	yes	—
429	C₂	—	2	4	no	—
430	C₂	—	4	8	no	—
431	C₂	C₄₁×#1490	1	4	yes	direct product factor
432	C₂	C₂×C₄₁×#407	1	1	yes	characteristic
433	C₂	C₂×C₄₁×#418	1	1	yes	characteristic
434	C₂	C₂²×#104×C₄₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₄₁	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₄²	C₂⁴×C₄₁
socle	C₂³×C₄₁	C₂×C₂²⋊C₄
prime radical	C₂³×D₄×C₄₁	C₄
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×#432	C₂	semidirect
3. C₂×C₄×M₁₆×C₄₁	C₂	semidirect
4. C₄₁×#1490	C₂	direct (N × H)
5. C₂×C₄₁×D₄⋊C₈	C₂	semidirect
21. C₄₁×#432	C₂²	semidirect
22. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
25. C₄×M₁₆×C₄₁	C₂²	semidirect
28. C₂×C₄×C₈×C₄₁	C₂²	semidirect
29. C₄₁×D₄⋊C₈	C₂²	semidirect
76. C₄⋊C₈×C₄₁	C₂³	semidirect
81. C₄×C₈×C₄₁	C₂³	semidirect
94. C₂×D₄×C₄₁	M₁₆	semidirect
158. D₄×C₄₁	C₂×M₁₆	semidirect
188. C₂×#1490	C₄₁	direct (N × H)
213. C₂×#432	C₂×C₄₁	semidirect
214. C₂×C₄×M₁₆	C₂×C₄₁	semidirect
215. #1490	C₂×C₄₁	direct (N × H)
216. C₂×D₄⋊C₈	C₂×C₄₁	semidirect
219. C₂×C₄₁	#1490	direct (N × H)
238. #432	C₂²×C₄₁	semidirect
239. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
242. C₄×M₁₆	C₂²×C₄₁	semidirect
245. C₂×C₄×C₈	C₂²×C₄₁	semidirect
246. D₄⋊C₈	C₂²×C₄₁	semidirect
247. C₄₁	C₂×#1490	direct (N × H)
294. C₄⋊C₈	C₂³×C₄₁	semidirect
299. C₄×C₈	C₂³×C₄₁	semidirect
312. C₂×D₄	M₁₆×C₄₁	semidirect
376. D₄	C₂×M₁₆×C₄₁	semidirect
431. C₂	C₄₁×#1490	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×C₄×D₄×C₄₁	2
C₂×C₄₁×#432	2
C₂×C₄×M₁₆×C₄₁	2
C₄₁×#1490	2
C₂×C₄₁×D₄⋊C₈	2
C₂×#1490	41

Subgroups — C2×C41×#1490 #23793645

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#1490 #23793645