Subgroups — C₂×C₄₁×#2194 #23809736

Order 10496.

1130 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#576	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#510	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×SD₃₂×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₁×#473	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2194	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄₁×#361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₁×#359	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₁×#350	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×H(5,𝔽₂)×C₄₁	—	2	1	no	—
10	C₄₁×#576	—	2	2	no	—
11	C₄₁×#576	—	2	2	no	—
12	C₄₁×#576	—	2	2	no	—
13	C₄₁×#576	C₂²	1	4	yes	—
14	C₂×#137×C₄₁	—	2	1	no	—
15	C₂×AGL(1,ℤ/8)×C₄₁	—	2	2	no	—
16	C₂×AGL(1,ℤ/8)×C₄₁	—	2	1	no	—
17	C₂×#135×C₄₁	—	2	1	no	—
18	C₂×#135×C₄₁	C₂²	1	1	yes	characteristic
19	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
20	C₂²×D₈×C₄₁	—	2	1	no	—
21	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×#131×C₄₁	C₂²	1	1	yes	characteristic
23	C₄₁×#510	—	2	2	no	—
24	C₄₁×#510	C₂²	1	4	yes	complemented
25	C₂×Q₃₂×C₄₁	—	2	1	no	—
26	C₂×SD₃₂×C₄₁	—	2	2	no	—
27	C₂×SD₃₂×C₄₁	—	2	2	no	—
28	C₂×SD₃₂×C₄₁	—	2	1	no	—
29	C₂×SD₃₂×C₄₁	C₂²	1	4	yes	complemented
30	C₂×M₃₂×C₄₁	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
32	C₄₁×#473	—	2	2	no	—
33	C₄₁×#473	C₂²	1	4	yes	complemented
34	C₂×#108×C₄₁	C₂²	1	1	yes	characteristic, complemented
35	C₂×#101×C₄₁	—	2	1	no	—
36	C₄₁×#361	C₂²	1	4	yes	complemented
37	C₄₁×#359	C₂²	1	4	yes	complemented
38	C₄₁×#350	C₂²	1	4	yes	complemented
39	H(5,𝔽₂)×C₄₁	—	2	4	no	—
40	H(5,𝔽₂)×C₄₁	—	2	4	no	—
41	H(5,𝔽₂)×C₄₁	—	4	2	no	—
42	H(5,𝔽₂)×C₄₁	—	4	2	no	—
43	C₂×#41×C₄₁	—	2	2	no	—
44	C₂×#41×C₄₁	—	2	1	no	—
45	C₂×#41×C₄₁	—	4	1	no	—
46	C₂×#41×C₄₁	D₄	1	1	yes	characteristic
47	C₂²×Q₈×C₄₁	—	2	1	no	—
48	C₂²×D₄×C₄₁	—	2	2	no	—
49	C₂²×D₄×C₄₁	—	2	1	no	—
50	C₂²×D₄×C₄₁	—	4	2	no	—
51	C₂²×D₄×C₄₁	—	4	1	no	—
52	#137×C₄₁	—	2	4	no	—
53	#137×C₄₁	—	4	2	no	—
54	AGL(1,ℤ/8)×C₄₁	—	2	4	no	—
55	AGL(1,ℤ/8)×C₄₁	—	2	8	no	—
56	AGL(1,ℤ/8)×C₄₁	—	2	8	no	—
57	AGL(1,ℤ/8)×C₄₁	—	2	4	no	—
58	#135×C₄₁	—	2	4	no	—
59	#135×C₄₁	—	2	4	no	—
60	#135×C₄₁	—	2	1	no	—
61	#135×C₄₁	—	2	1	no	—
62	#135×C₄₁	D₄	1	2	yes	—
63	#135×C₄₁	C₂³	1	2	yes	—
64	C₂×Q₁₆×C₄₁	—	2	1	no	—
65	C₂×Q₁₆×C₄₁	—	2	1	no	—
66	C₂×Q₁₆×C₄₁	—	2	1	no	—
67	C₂×Q₁₆×C₄₁	—	2	1	no	—
68	C₂×Q₁₆×C₄₁	—	2	1	no	—
69	C₂×Q₁₆×C₄₁	—	4	1	no	—
70	C₂×Q₁₆×C₄₁	D₄	1	1	yes	characteristic
71	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	complemented
72	C₂×SD₁₆×C₄₁	—	2	2	no	—
73	C₂×SD₁₆×C₄₁	—	2	1	no	—
74	C₂×SD₁₆×C₄₁	—	4	1	no	—
75	C₂×D₈×C₄₁	—	2	2	no	—
76	C₂×D₈×C₄₁	—	2	4	no	—
77	C₂×D₈×C₄₁	—	2	4	no	—
78	C₂×D₈×C₄₁	—	2	1	no	—
79	C₂×D₈×C₄₁	—	2	1	no	—
80	C₂×D₈×C₄₁	—	2	1	no	—
81	C₂×D₈×C₄₁	D₄	1	1	yes	characteristic
82	C₂×D₈×C₄₁	D₄	1	2	yes	—
83	C₂×D₈×C₄₁	D₄	1	2	yes	—
84	C₂×D₈×C₄₁	C₂³	1	2	yes	—
85	#131×C₄₁	—	2	1	no	—
86	#131×C₄₁	—	2	1	no	—
87	#131×C₄₁	D₄	1	2	yes	—
88	#131×C₄₁	C₂³	1	2	yes	—
89	C₂×M₁₆×C₄₁	—	2	1	no	—
90	C₂×M₁₆×C₄₁	—	2	1	no	—
91	C₂×M₁₆×C₄₁	D₄	1	1	yes	characteristic
92	C₂²×C₈×C₄₁	—	2	1	no	—
93	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
94	Q₃₂×C₄₁	—	2	4	no	—
95	SD₃₂×C₄₁	—	2	8	no	—
96	SD₃₂×C₄₁	—	2	4	no	—
97	M₃₂×C₄₁	—	2	1	no	—
98	M₃₂×C₄₁	C₂³	1	2	yes	complemented
99	C₂×C₁₆×C₄₁	—	2	1	no	—
100	C₂×C₁₆×C₄₁	—	2	1	no	—
101	C₂×C₁₆×C₄₁	—	2	1	no	—
102	C₂×C₁₆×C₄₁	C₂³	1	2	yes	complemented
103	#108×C₄₁	—	2	1	no	—
104	#108×C₄₁	C₂³	1	2	yes	complemented
105	#101×C₄₁	—	2	4	no	—
106	C₂⁴×C₄₁	—	4	2	no	—
107	C₂⁴×C₄₁	—	4	1	no	—
108	#41×C₄₁	—	2	1	no	—
109	#41×C₄₁	—	2	1	no	—
110	#41×C₄₁	—	2	8	no	—
111	#41×C₄₁	—	2	2	no	—
112	#41×C₄₁	—	2	2	no	—
113	#41×C₄₁	—	4	4	no	—
114	#41×C₄₁	—	4	4	no	—
115	#41×C₄₁	—	4	4	no	—
116	#41×C₄₁	—	4	1	no	—
117	#41×C₄₁	—	4	1	no	—
118	#41×C₄₁	D₈	1	2	yes	—
119	#41×C₄₁	C₂×D₄	1	2	yes	—
120	C₂×Q₈×C₄₁	—	2	1	no	—
121	C₂×Q₈×C₄₁	—	2	2	no	—
122	C₂×Q₈×C₄₁	—	4	1	no	—
123	C₂×Q₈×C₄₁	—	4	1	no	—
124	C₂×Q₈×C₄₁	—	4	1	no	—
125	C₂×Q₈×C₄₁	—	4	1	no	—
126	C₂×Q₈×C₄₁	—	4	1	no	—
127	C₂×Q₈×C₄₁	D₈	1	1	yes	characteristic
128	C₂×D₄×C₄₁	—	2	1	no	—
129	C₂×D₄×C₄₁	—	2	8	no	—
130	C₂×D₄×C₄₁	—	2	1	no	—
131	C₂×D₄×C₄₁	—	2	2	no	—
132	C₂×D₄×C₄₁	—	2	2	no	—
133	C₂×D₄×C₄₁	—	2	2	no	—
134	C₂×D₄×C₄₁	—	4	2	no	—
135	C₂×D₄×C₄₁	—	4	4	no	—
136	C₂×D₄×C₄₁	—	4	8	no	—
137	C₂×D₄×C₄₁	—	4	8	no	—
138	C₂×D₄×C₄₁	—	4	4	no	—
139	C₂×D₄×C₄₁	—	4	2	no	—
140	C₂×D₄×C₄₁	—	4	1	no	—
141	C₂×D₄×C₄₁	—	4	4	no	—
142	C₂×D₄×C₄₁	—	4	1	no	—
143	C₂×D₄×C₄₁	—	4	1	no	—
144	C₂×D₄×C₄₁	—	4	1	no	—
145	C₂×D₄×C₄₁	D₈	1	1	yes	characteristic
146	C₂²×C₄×C₄₁	—	2	1	no	—
147	C₂²×C₄×C₄₁	—	4	2	no	—
148	C₂²×C₄×C₄₁	—	4	1	no	—
149	C₂²×C₄×C₄₁	—	4	1	no	—
150	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
151	Q₁₆×C₄₁	—	2	1	no	—
152	Q₁₆×C₄₁	—	2	2	no	—
153	Q₁₆×C₄₁	—	2	2	no	—
154	Q₁₆×C₄₁	—	4	4	no	—
155	Q₁₆×C₄₁	—	4	1	no	—
156	Q₁₆×C₄₁	—	4	1	no	—
157	Q₁₆×C₄₁	C₂×D₄	1	2	yes	—
158	SD₁₆×C₄₁	—	2	8	no	—
159	SD₁₆×C₄₁	—	2	2	no	—
160	SD₁₆×C₄₁	—	2	2	no	—
161	SD₁₆×C₄₁	—	4	4	no	—
162	D₈×C₄₁	—	2	8	no	—
163	D₈×C₄₁	—	2	1	no	—
164	D₈×C₄₁	—	2	2	no	—
165	D₈×C₄₁	—	2	2	no	—
166	D₈×C₄₁	—	2	2	no	—
167	D₈×C₄₁	C₂×D₄	1	2	yes	—
168	D₈×C₄₁	C₂×D₄	1	4	yes	—
169	M₁₆×C₄₁	—	2	1	no	—
170	M₁₆×C₄₁	—	2	2	no	—
171	M₁₆×C₄₁	—	2	2	no	—
172	M₁₆×C₄₁	—	2	2	no	—
173	M₁₆×C₄₁	—	4	1	no	—
174	M₁₆×C₄₁	C₂×D₄	1	2	yes	—
175	C₂×C₈×C₄₁	—	2	1	no	—
176	C₂×C₈×C₄₁	—	2	2	no	—
177	C₂×C₈×C₄₁	—	2	2	no	—
178	C₂×C₈×C₄₁	—	4	1	no	—
179	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
180	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
181	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
183	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
185	C₁₆×C₄₁	—	2	2	no	—
186	C₁₆×C₄₁	—	2	2	no	—
187	C₂³×C₄₁	—	2	1	no	—
188	C₂³×C₄₁	—	4	8	no	—
189	C₂³×C₄₁	—	4	2	no	—
190	C₂³×C₄₁	—	4	1	no	—
191	C₂³×C₄₁	—	4	2	no	—
192	C₂³×C₄₁	—	4	2	no	—
193	C₂³×C₄₁	—	16	2	no	—
194	C₂³×C₄₁	—	16	4	no	—
195	C₂³×C₄₁	AGL(1,ℤ/8)	1	1	yes	characteristic
196	Q₈×C₄₁	—	2	1	no	—
197	Q₈×C₄₁	—	2	2	no	—
198	Q₈×C₄₁	—	4	1	no	—
199	Q₈×C₄₁	—	4	2	no	—
200	Q₈×C₄₁	—	4	2	no	—
201	Q₈×C₄₁	—	8	1	no	—
202	Q₈×C₄₁	—	8	1	no	—
203	Q₈×C₄₁	C₂×D₈	1	2	yes	—
204	D₄×C₄₁	—	2	2	no	—
205	D₄×C₄₁	—	2	2	no	—
206	D₄×C₄₁	—	2	2	no	—
207	D₄×C₄₁	—	2	4	no	—
208	D₄×C₄₁	—	2	1	no	—
209	D₄×C₄₁	—	4	8	no	—
210	D₄×C₄₁	—	4	8	no	—
211	D₄×C₄₁	—	4	2	no	—
212	D₄×C₄₁	—	4	2	no	—
213	D₄×C₄₁	—	4	2	no	—
214	D₄×C₄₁	—	4	1	no	—
215	D₄×C₄₁	—	4	2	no	—
216	D₄×C₄₁	—	4	2	no	—
217	D₄×C₄₁	C₂×D₈	1	2	yes	—
218	C₂×C₄×C₄₁	—	2	1	no	—
219	C₂×C₄×C₄₁	—	2	2	no	—
220	C₂×C₄×C₄₁	—	2	2	no	—
221	C₂×C₄×C₄₁	—	4	8	no	—
222	C₂×C₄×C₄₁	—	4	1	no	—
223	C₂×C₄×C₄₁	—	4	2	no	—
224	C₂×C₄×C₄₁	—	4	2	no	—
225	C₂×C₄×C₄₁	—	4	2	no	—
226	C₂×C₄×C₄₁	—	8	1	no	—
227	C₂×C₄×C₄₁	—	8	1	no	—
228	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
229	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
230	C₂×C₄×C₄₁	C₂×D₈	1	1	yes	characteristic
231	C₂×C₄×C₄₁	C₂×D₈	1	1	yes	characteristic
232	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	1	yes	characteristic
233	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
234	C₈×C₄₁	—	2	2	no	—
235	C₈×C₄₁	—	4	2	no	—
236	C₈×C₄₁	#120	1	1	yes	characteristic
237	C₈×C₄₁	#120	1	1	yes	characteristic
238	C₈×C₄₁	C₂²×D₄	1	1	yes	characteristic
239	C₈×C₄₁	C₂²×D₄	1	1	yes	characteristic
240	C₂×#2194	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
241	C₂²×C₄₁	—	2	2	no	—
242	C₂²×C₄₁	—	2	2	no	—
243	C₂²×C₄₁	—	4	2	no	—
244	C₂²×C₄₁	—	4	4	no	—
245	C₂²×C₄₁	—	4	2	no	—
246	C₂²×C₄₁	—	8	4	no	—
247	C₂²×C₄₁	—	8	2	no	—
248	C₂²×C₄₁	—	16	2	no	—
249	C₂²×C₄₁	—	16	2	no	—
250	C₂²×C₄₁	—	16	8	no	—
251	C₂²×C₄₁	#447	1	1	yes	characteristic
252	C₂²×C₄₁	#447	1	1	yes	characteristic
253	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
254	C₄×C₄₁	—	2	2	no	—
255	C₄×C₄₁	—	4	2	no	—
256	C₄×C₄₁	—	8	2	no	—
257	C₄×C₄₁	#447	1	1	yes	characteristic
258	C₄×C₄₁	#447	1	1	yes	characteristic
259	C₄×C₄₁	C₂×#120	1	1	yes	characteristic
260	C₄×C₄₁	C₂²×D₈	1	1	yes	characteristic
261	C₂×#576	C₂×C₄₁	1	1	yes	characteristic
262	C₂×#510	C₂×C₄₁	1	1	yes	characteristic, complemented
263	C₂²×SD₃₂	C₂×C₄₁	1	1	yes	characteristic, complemented
264	C₂×#473	C₂×C₄₁	1	1	yes	characteristic, complemented
265	#2194	C₂×C₄₁	1	8	yes	direct product factor
266	C₂×#361	C₂×C₄₁	1	1	yes	characteristic, complemented
267	C₂×#359	C₂×C₄₁	1	1	yes	characteristic, complemented
268	C₂×#350	C₂×C₄₁	1	1	yes	characteristic, complemented
269	C₂×C₄₁	—	2	1	no	—
270	C₂×C₄₁	—	2	1	no	—
271	C₂×C₄₁	—	4	2	no	—
272	C₂×C₄₁	—	8	4	no	—
273	C₂×C₄₁	—	8	2	no	—
274	C₂×C₄₁	#2194	1	2	yes	direct product factor
275	C₂×C₄₁	C₂×#447	1	1	yes	characteristic
276	C₂×H(5,𝔽₂)	—	2	1	no	—
277	#576	—	2	2	no	—
278	#576	—	2	2	no	—
279	#576	—	2	2	no	—
280	#576	C₂²×C₄₁	1	4	yes	—
281	C₂×#137	—	2	1	no	—
282	C₂×AGL(1,ℤ/8)	—	2	2	no	—
283	C₂×AGL(1,ℤ/8)	—	2	1	no	—
284	C₂×#135	—	2	1	no	—
285	C₂×#135	C₂²×C₄₁	1	1	yes	characteristic
286	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
287	C₂²×D₈	—	2	1	no	—
288	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
289	C₂×#131	C₂²×C₄₁	1	1	yes	characteristic
290	#510	—	2	2	no	—
291	#510	C₂²×C₄₁	1	4	yes	complemented
292	C₂×Q₃₂	—	2	1	no	—
293	C₂×SD₃₂	—	2	2	no	—
294	C₂×SD₃₂	—	2	2	no	—
295	C₂×SD₃₂	—	2	1	no	—
296	C₂×SD₃₂	C₂²×C₄₁	1	4	yes	complemented
297	C₂×M₃₂	C₂²×C₄₁	1	1	yes	characteristic, complemented
298	C₂²×C₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
299	#473	—	2	2	no	—
300	#473	C₂²×C₄₁	1	4	yes	complemented
301	C₂×#108	C₂²×C₄₁	1	1	yes	characteristic, complemented
302	C₂×#101	—	2	1	no	—
303	#361	C₂²×C₄₁	1	4	yes	complemented
304	#359	C₂²×C₄₁	1	4	yes	complemented
305	#350	C₂²×C₄₁	1	4	yes	complemented
306	C₄₁	C₂×#2194	1	1	yes	characteristic, direct product factor, Sylow
307	H(5,𝔽₂)	—	2	4	no	—
308	H(5,𝔽₂)	—	2	4	no	—
309	H(5,𝔽₂)	—	4	2	no	—
310	H(5,𝔽₂)	—	4	2	no	—
311	C₂×#41	—	2	2	no	—
312	C₂×#41	—	2	1	no	—
313	C₂×#41	—	4	1	no	—
314	C₂×#41	D₄×C₄₁	1	1	yes	characteristic
315	C₂²×Q₈	—	2	1	no	—
316	C₂²×D₄	—	2	2	no	—
317	C₂²×D₄	—	2	1	no	—
318	C₂²×D₄	—	4	2	no	—
319	C₂²×D₄	—	4	1	no	—
320	#137	—	2	4	no	—
321	#137	—	4	2	no	—
322	AGL(1,ℤ/8)	—	2	4	no	—
323	AGL(1,ℤ/8)	—	2	8	no	—
324	AGL(1,ℤ/8)	—	2	8	no	—
325	AGL(1,ℤ/8)	—	2	4	no	—
326	#135	—	2	4	no	—
327	#135	—	2	4	no	—
328	#135	—	2	1	no	—
329	#135	—	2	1	no	—
330	#135	D₄×C₄₁	1	2	yes	—
331	#135	C₂³×C₄₁	1	2	yes	—
332	C₂×Q₁₆	—	2	1	no	—
333	C₂×Q₁₆	—	2	1	no	—
334	C₂×Q₁₆	—	2	1	no	—
335	C₂×Q₁₆	—	2	1	no	—
336	C₂×Q₁₆	—	2	1	no	—
337	C₂×Q₁₆	—	4	1	no	—
338	C₂×Q₁₆	D₄×C₄₁	1	1	yes	characteristic
339	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	complemented
340	C₂×SD₁₆	—	2	2	no	—
341	C₂×SD₁₆	—	2	1	no	—
342	C₂×SD₁₆	—	4	1	no	—
343	C₂×D₈	—	2	2	no	—
344	C₂×D₈	—	2	4	no	—
345	C₂×D₈	—	2	4	no	—
346	C₂×D₈	—	2	1	no	—
347	C₂×D₈	—	2	1	no	—
348	C₂×D₈	—	2	1	no	—
349	C₂×D₈	D₄×C₄₁	1	1	yes	characteristic
350	C₂×D₈	D₄×C₄₁	1	2	yes	—
351	C₂×D₈	D₄×C₄₁	1	2	yes	—
352	C₂×D₈	C₂³×C₄₁	1	2	yes	—
353	#131	—	2	1	no	—
354	#131	—	2	1	no	—
355	#131	D₄×C₄₁	1	2	yes	—
356	#131	C₂³×C₄₁	1	2	yes	—
357	C₂×M₁₆	—	2	1	no	—
358	C₂×M₁₆	—	2	1	no	—
359	C₂×M₁₆	D₄×C₄₁	1	1	yes	characteristic
360	C₂²×C₈	—	2	1	no	—
361	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
362	Q₃₂	—	2	4	no	—
363	SD₃₂	—	2	8	no	—
364	SD₃₂	—	2	4	no	—
365	M₃₂	—	2	1	no	—
366	M₃₂	C₂³×C₄₁	1	2	yes	complemented
367	C₂×C₁₆	—	2	1	no	—
368	C₂×C₁₆	—	2	1	no	—
369	C₂×C₁₆	—	2	1	no	—
370	C₂×C₁₆	C₂³×C₄₁	1	2	yes	complemented
371	#108	—	2	1	no	—
372	#108	C₂³×C₄₁	1	2	yes	complemented
373	#101	—	2	4	no	—
374	C₂⁴	—	4	2	no	—
375	C₂⁴	—	4	1	no	—
376	#41	—	2	1	no	—
377	#41	—	2	1	no	—
378	#41	—	2	8	no	—
379	#41	—	2	2	no	—
380	#41	—	2	2	no	—
381	#41	—	4	4	no	—
382	#41	—	4	4	no	—
383	#41	—	4	4	no	—
384	#41	—	4	1	no	—
385	#41	—	4	1	no	—
386	#41	D₈×C₄₁	1	2	yes	—
387	#41	C₂×D₄×C₄₁	1	2	yes	—
388	C₂×Q₈	—	2	1	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	4	1	no	—
391	C₂×Q₈	—	4	1	no	—
392	C₂×Q₈	—	4	1	no	—
393	C₂×Q₈	—	4	1	no	—
394	C₂×Q₈	—	4	1	no	—
395	C₂×Q₈	D₈×C₄₁	1	1	yes	characteristic
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	8	no	—
398	C₂×D₄	—	2	1	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	4	2	no	—
403	C₂×D₄	—	4	4	no	—
404	C₂×D₄	—	4	8	no	—
405	C₂×D₄	—	4	8	no	—
406	C₂×D₄	—	4	4	no	—
407	C₂×D₄	—	4	2	no	—
408	C₂×D₄	—	4	1	no	—
409	C₂×D₄	—	4	4	no	—
410	C₂×D₄	—	4	1	no	—
411	C₂×D₄	—	4	1	no	—
412	C₂×D₄	—	4	1	no	—
413	C₂×D₄	D₈×C₄₁	1	1	yes	characteristic
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	4	2	no	—
416	C₂²×C₄	—	4	1	no	—
417	C₂²×C₄	—	4	1	no	—
418	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
419	Q₁₆	—	2	1	no	—
420	Q₁₆	—	2	2	no	—
421	Q₁₆	—	2	2	no	—
422	Q₁₆	—	4	4	no	—
423	Q₁₆	—	4	1	no	—
424	Q₁₆	—	4	1	no	—
425	Q₁₆	C₂×D₄×C₄₁	1	2	yes	—
426	SD₁₆	—	2	8	no	—
427	SD₁₆	—	2	2	no	—
428	SD₁₆	—	2	2	no	—
429	SD₁₆	—	4	4	no	—
430	D₈	—	2	8	no	—
431	D₈	—	2	1	no	—
432	D₈	—	2	2	no	—
433	D₈	—	2	2	no	—
434	D₈	—	2	2	no	—
435	D₈	C₂×D₄×C₄₁	1	2	yes	—
436	D₈	C₂×D₄×C₄₁	1	4	yes	—
437	M₁₆	—	2	1	no	—
438	M₁₆	—	2	2	no	—
439	M₁₆	—	2	2	no	—
440	M₁₆	—	2	2	no	—
441	M₁₆	—	4	1	no	—
442	M₁₆	C₂×D₄×C₄₁	1	2	yes	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	2	2	no	—
446	C₂×C₈	—	4	1	no	—
447	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
448	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
449	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
450	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
451	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
452	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
453	C₁₆	—	2	2	no	—
454	C₁₆	—	2	2	no	—
455	C₂³	—	2	1	no	—
456	C₂³	—	4	8	no	—
457	C₂³	—	4	2	no	—
458	C₂³	—	4	1	no	—
459	C₂³	—	4	2	no	—
460	C₂³	—	4	2	no	—
461	C₂³	—	16	2	no	—
462	C₂³	—	16	4	no	—
463	C₂³	AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
464	Q₈	—	2	1	no	—
465	Q₈	—	2	2	no	—
466	Q₈	—	4	1	no	—
467	Q₈	—	4	2	no	—
468	Q₈	—	4	2	no	—
469	Q₈	—	8	1	no	—
470	Q₈	—	8	1	no	—
471	Q₈	C₂×D₈×C₄₁	1	2	yes	—
472	D₄	—	2	2	no	—
473	D₄	—	2	2	no	—
474	D₄	—	2	2	no	—
475	D₄	—	2	4	no	—
476	D₄	—	2	1	no	—
477	D₄	—	4	8	no	—
478	D₄	—	4	8	no	—
479	D₄	—	4	2	no	—
480	D₄	—	4	2	no	—
481	D₄	—	4	2	no	—
482	D₄	—	4	1	no	—
483	D₄	—	4	2	no	—
484	D₄	—	4	2	no	—
485	D₄	C₂×D₈×C₄₁	1	2	yes	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	4	8	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	8	1	no	—
495	C₂×C₄	—	8	1	no	—
496	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
497	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
498	C₂×C₄	C₂×D₈×C₄₁	1	1	yes	characteristic
499	C₂×C₄	C₂×D₈×C₄₁	1	1	yes	characteristic
500	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
501	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
502	C₈	—	2	2	no	—
503	C₈	—	4	2	no	—
504	C₈	#120×C₄₁	1	1	yes	characteristic
505	C₈	#120×C₄₁	1	1	yes	characteristic
506	C₈	C₂²×D₄×C₄₁	1	1	yes	characteristic
507	C₈	C₂²×D₄×C₄₁	1	1	yes	characteristic
508	C₂²	—	2	2	no	—
509	C₂²	—	2	2	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	4	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	8	4	no	—
514	C₂²	—	8	2	no	—
515	C₂²	—	16	2	no	—
516	C₂²	—	16	2	no	—
517	C₂²	—	16	8	no	—
518	C₂²	C₄₁×#447	1	1	yes	characteristic
519	C₂²	C₄₁×#447	1	1	yes	characteristic
520	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
521	C₄	—	2	2	no	—
522	C₄	—	4	2	no	—
523	C₄	—	8	2	no	—
524	C₄	C₄₁×#447	1	1	yes	characteristic
525	C₄	C₄₁×#447	1	1	yes	characteristic
526	C₄	C₂×#120×C₄₁	1	1	yes	characteristic
527	C₄	C₂²×D₈×C₄₁	1	1	yes	characteristic
528	C₂	—	2	1	no	—
529	C₂	—	2	1	no	—
530	C₂	—	4	2	no	—
531	C₂	—	8	4	no	—
532	C₂	—	8	2	no	—
533	C₂	C₄₁×#2194	1	2	yes	direct product factor
534	C₂	C₂×C₄₁×#447	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	#447
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₄₁
prime radical	C₂×C₄₁×#576	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂²×C₄×C₄₁ ◁ C₂×#131×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#510	C₂	semidirect
3. C₂²×SD₃₂×C₄₁	C₂	semidirect
4. C₂×C₄₁×#473	C₂	semidirect
5. C₄₁×#2194	C₂	direct (N × H)
6. C₂×C₄₁×#361	C₂	semidirect
7. C₂×C₄₁×#359	C₂	semidirect
8. C₂×C₄₁×#350	C₂	semidirect
19. C₂²×Q₁₆×C₄₁	C₂²	semidirect
24. C₄₁×#510	C₂²	semidirect
29. C₂×SD₃₂×C₄₁	C₂²	semidirect
30. C₂×M₃₂×C₄₁	C₂²	semidirect
31. C₂²×C₁₆×C₄₁	C₂²	semidirect
33. C₄₁×#473	C₂²	semidirect
34. C₂×#108×C₄₁	C₂²	semidirect
36. C₄₁×#361	C₂²	semidirect
37. C₄₁×#359	C₂²	semidirect
38. C₄₁×#350	C₂²	semidirect
71. C₂×Q₁₆×C₄₁	C₂³	semidirect
98. M₃₂×C₄₁	C₂³	semidirect
102. C₂×C₁₆×C₄₁	C₂³	semidirect
104. #108×C₄₁	C₂³	semidirect
240. C₂×#2194	C₄₁	direct (N × H)
262. C₂×#510	C₂×C₄₁	semidirect
263. C₂²×SD₃₂	C₂×C₄₁	semidirect
264. C₂×#473	C₂×C₄₁	semidirect
265. #2194	C₂×C₄₁	direct (N × H)
266. C₂×#361	C₂×C₄₁	semidirect
267. C₂×#359	C₂×C₄₁	semidirect
268. C₂×#350	C₂×C₄₁	semidirect
274. C₂×C₄₁	#2194	direct (N × H)
286. C₂²×Q₁₆	C₂²×C₄₁	semidirect
291. #510	C₂²×C₄₁	semidirect
296. C₂×SD₃₂	C₂²×C₄₁	semidirect
297. C₂×M₃₂	C₂²×C₄₁	semidirect
298. C₂²×C₁₆	C₂²×C₄₁	semidirect
300. #473	C₂²×C₄₁	semidirect
301. C₂×#108	C₂²×C₄₁	semidirect
303. #361	C₂²×C₄₁	semidirect
304. #359	C₂²×C₄₁	semidirect
305. #350	C₂²×C₄₁	semidirect
306. C₄₁	C₂×#2194	direct (N × H)
339. C₂×Q₁₆	C₂³×C₄₁	semidirect
366. M₃₂	C₂³×C₄₁	semidirect
370. C₂×C₁₆	C₂³×C₄₁	semidirect
372. #108	C₂³×C₄₁	semidirect
533. C₂	C₄₁×#2194	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×#576	2
C₂×C₄₁×#510	2
C₂²×SD₃₂×C₄₁	2
C₂×C₄₁×#473	2
C₄₁×#2194	2
C₂×C₄₁×#361	2
C₂×C₄₁×#359	2
C₂×C₄₁×#350	2
C₂×#2194	41

Subgroups — C2×C41×#2194 #23809736

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#2194 #23809736