Subgroups — C₄₁×#33521 #23809722

Order 10496.

1140 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#135×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#510	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₁×#467	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2189	C₂	1	4	yes	maximal, complemented
5	C₄₁×#2188	C₂	1	2	yes	maximal, complemented
6	C₄₁×#2187	C₂	1	2	yes	maximal, complemented
7	C₄₁×#2139	C₂	1	2	yes	maximal, complemented
8	C₄₁×#2112	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₄₁	—	2	1	no	—
10	C₂×#135×C₄₁	—	2	8	no	—
11	C₂×#135×C₄₁	—	2	1	no	—
12	C₂×#135×C₄₁	—	2	1	no	—
13	C₂×#135×C₄₁	C₂²	1	2	yes	—
14	C₂×#135×C₄₁	C₂²	1	2	yes	—
15	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
16	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
17	C₂²×SD₁₆×C₄₁	—	2	1	no	—
18	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊Q₈×C₄₁	—	2	1	no	—
21	C₄₁×#510	—	2	8	no	—
22	C₂×Q₃₂×C₄₁	C₂²	1	4	yes	complemented
23	C₂×SD₃₂×C₄₁	C₂²	1	4	yes	complemented
24	C₂×M₃₂×C₄₁	C₂²	1	2	yes	complemented
25	C₄₁×#467	—	2	1	no	—
26	C₄₁×#467	—	2	1	no	—
27	C₄₁×#467	C₂²	1	2	yes	—
28	C₄₁×#467	C₂²	1	2	yes	complemented
29	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic, complemented
30	C₂×#103×C₄₁	—	2	1	no	—
31	C₄₁×#358	C₂²	1	4	yes	complemented
32	C₄₁×#357	C₂²	1	4	yes	complemented
33	C₄₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
34	C₄₁×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
35	C₂×#41×C₄₁	—	2	8	no	—
36	C₂×#41×C₄₁	—	2	2	no	—
37	C₂×#41×C₄₁	—	2	2	no	—
38	C₂×#41×C₄₁	—	4	4	no	—
39	C₂×#41×C₄₁	—	4	1	no	—
40	C₂×#41×C₄₁	—	4	1	no	—
41	C₂²×Q₈×C₄₁	—	2	1	no	—
42	C₂²×Q₈×C₄₁	—	2	1	no	—
43	C₂²×D₄×C₄₁	—	2	1	no	—
44	C₂²×D₄×C₄₁	—	4	1	no	—
45	C₂³×C₄×C₄₁	—	4	1	no	—
46	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
47	#135×C₄₁	—	2	8	no	—
48	#135×C₄₁	—	2	8	no	—
49	#135×C₄₁	—	2	4	no	—
50	#135×C₄₁	—	2	4	no	—
51	#135×C₄₁	—	2	4	no	—
52	#135×C₄₁	D₄	1	8	yes	—
53	C₂×Q₁₆×C₄₁	—	2	4	no	—
54	C₂×Q₁₆×C₄₁	—	2	1	no	—
55	C₂×Q₁₆×C₄₁	—	2	4	no	—
56	C₂×Q₁₆×C₄₁	—	2	1	no	—
57	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
58	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
59	C₂×SD₁₆×C₄₁	—	2	8	no	—
60	C₂×SD₁₆×C₄₁	—	2	2	no	—
61	C₂×SD₁₆×C₄₁	—	2	2	no	—
62	C₂×D₈×C₄₁	—	2	4	no	—
63	C₂×D₈×C₄₁	—	2	1	no	—
64	C₂×D₈×C₄₁	C₂³	1	2	yes	—
65	C₂²×C₈×C₄₁	—	2	4	no	—
66	C₂²×C₈×C₄₁	D₄	1	1	yes	characteristic
67	C₂²×C₈×C₄₁	D₄	1	1	yes	characteristic
68	C₂²×C₈×C₄₁	D₄	1	1	yes	characteristic
69	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
72	C₂²⋊Q₈×C₄₁	—	2	2	no	—
73	C₂²⋊Q₈×C₄₁	—	2	2	no	—
74	C₂²⋊Q₈×C₄₁	—	4	1	no	—
75	C₂²⋊Q₈×C₄₁	—	4	1	no	—
76	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
77	C₂×C₄⋊C₄×C₄₁	—	4	1	no	—
78	C₂×C₂²⋊C₄×C₄₁	—	4	1	no	—
79	Q₃₂×C₄₁	—	2	8	no	—
80	SD₃₂×C₄₁	—	2	8	no	—
81	M₃₂×C₄₁	—	2	4	no	—
82	C₂×C₁₆×C₄₁	C₂³	1	4	yes	—
83	#107×C₄₁	—	2	1	no	—
84	#107×C₄₁	C₂³	1	2	yes	—
85	#103×C₄₁	—	2	2	no	—
86	#103×C₄₁	—	2	2	no	—
87	C₂⁴×C₄₁	—	4	1	no	—
88	C₂⁴×C₄₁	D₈	1	1	yes	characteristic
89	#41×C₄₁	—	2	8	no	—
90	#41×C₄₁	—	2	8	no	—
91	#41×C₄₁	—	4	8	no	—
92	#41×C₄₁	—	4	4	no	—
93	#41×C₄₁	—	4	8	no	—
94	#41×C₄₁	—	4	4	no	—
95	C₂×Q₈×C₄₁	—	2	4	no	—
96	C₂×Q₈×C₄₁	—	2	2	no	—
97	C₂×Q₈×C₄₁	—	2	2	no	—
98	C₂×Q₈×C₄₁	—	4	2	no	—
99	C₂×Q₈×C₄₁	—	4	1	no	—
100	C₂×Q₈×C₄₁	—	4	1	no	—
101	C₂×Q₈×C₄₁	—	4	2	no	—
102	C₂×Q₈×C₄₁	—	4	2	no	—
103	C₂×D₄×C₄₁	—	2	4	no	—
104	C₂×D₄×C₄₁	—	2	2	no	—
105	C₂×D₄×C₄₁	—	4	2	no	—
106	C₂×D₄×C₄₁	—	4	8	no	—
107	C₂×D₄×C₄₁	—	4	2	no	—
108	C₂×D₄×C₄₁	—	4	2	no	—
109	C₂×D₄×C₄₁	—	4	1	no	—
110	C₂²×C₄×C₄₁	—	2	2	no	—
111	C₂²×C₄×C₄₁	—	2	2	no	—
112	C₂²×C₄×C₄₁	—	4	8	no	—
113	C₂²×C₄×C₄₁	—	4	1	no	—
114	C₂²×C₄×C₄₁	—	4	2	no	—
115	C₂²×C₄×C₄₁	—	4	2	no	—
116	C₂²×C₄×C₄₁	—	4	1	no	—
117	C₂²×C₄×C₄₁	—	4	1	no	—
118	C₂²×C₄×C₄₁	D₈	1	1	yes	characteristic
119	C₂²×C₄×C₄₁	D₈	1	1	yes	characteristic
120	C₂²×C₄×C₄₁	D₈	1	1	yes	characteristic
121	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
124	Q₁₆×C₄₁	—	2	4	no	—
125	Q₁₆×C₄₁	—	2	2	no	—
126	Q₁₆×C₄₁	—	2	4	no	—
127	Q₁₆×C₄₁	—	4	2	no	—
128	Q₁₆×C₄₁	C₂×D₄	1	4	yes	—
129	SD₁₆×C₄₁	—	2	8	no	—
130	SD₁₆×C₄₁	—	2	8	no	—
131	D₈×C₄₁	—	2	4	no	—
132	D₈×C₄₁	—	2	2	no	—
133	D₈×C₄₁	C₂×D₄	1	4	yes	—
134	C₂×C₈×C₄₁	—	2	2	no	—
135	C₂×C₈×C₄₁	—	2	2	no	—
136	C₂×C₈×C₄₁	—	2	2	no	—
137	C₂×C₈×C₄₁	—	2	2	no	—
138	C₂×C₈×C₄₁	—	2	2	no	—
139	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
143	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
144	C₄⋊C₄×C₄₁	—	2	2	no	—
145	C₄⋊C₄×C₄₁	—	4	1	no	—
146	C₄⋊C₄×C₄₁	—	4	2	no	—
147	C₄⋊C₄×C₄₁	—	4	2	no	—
148	C₂²⋊C₄×C₄₁	—	4	2	no	—
149	C₂²⋊C₄×C₄₁	—	4	2	no	—
150	C₁₆×C₄₁	—	2	4	no	—
151	C₂³×C₄₁	—	2	2	no	—
152	C₂³×C₄₁	—	2	2	no	—
153	C₂³×C₄₁	—	4	1	no	—
154	C₂³×C₄₁	—	4	4	no	—
155	C₂³×C₄₁	—	4	2	no	—
156	C₂³×C₄₁	—	8	2	no	—
157	C₂³×C₄₁	—	8	2	no	—
158	C₂³×C₄₁	C₂×D₈	1	1	yes	characteristic
159	C₂³×C₄₁	C₂×D₈	1	1	yes	characteristic
160	C₂³×C₄₁	C₂×D₈	1	1	yes	characteristic
161	Q₈×C₄₁	—	2	4	no	—
162	Q₈×C₄₁	—	4	4	no	—
163	Q₈×C₄₁	—	4	2	no	—
164	Q₈×C₄₁	—	4	2	no	—
165	Q₈×C₄₁	—	4	2	no	—
166	Q₈×C₄₁	—	8	2	no	—
167	D₄×C₄₁	—	2	4	no	—
168	D₄×C₄₁	—	4	4	no	—
169	D₄×C₄₁	—	4	8	no	—
170	D₄×C₄₁	—	4	8	no	—
171	D₄×C₄₁	—	4	2	no	—
172	C₂×C₄×C₄₁	—	2	2	no	—
173	C₂×C₄×C₄₁	—	2	1	no	—
174	C₂×C₄×C₄₁	—	2	1	no	—
175	C₂×C₄×C₄₁	—	2	1	no	—
176	C₂×C₄×C₄₁	—	2	1	no	—
177	C₂×C₄×C₄₁	—	2	2	no	—
178	C₂×C₄×C₄₁	—	2	2	no	—
179	C₂×C₄×C₄₁	—	4	8	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	2	no	—
184	C₂×C₄×C₄₁	—	4	2	no	—
185	C₂×C₄×C₄₁	—	8	2	no	—
186	C₂×C₄×C₄₁	—	8	2	no	—
187	C₂×C₄×C₄₁	#120	1	2	yes	—
188	C₂×C₄×C₄₁	C₂×D₈	1	1	yes	characteristic
189	C₂×C₄×C₄₁	C₂×D₈	1	1	yes	characteristic
190	C₂×C₄×C₄₁	C₂×D₈	1	1	yes	characteristic
191	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
192	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
193	C₈×C₄₁	—	2	1	no	—
194	C₈×C₄₁	—	2	1	no	—
195	C₈×C₄₁	#120	1	2	yes	—
196	C₈×C₄₁	C₂²×D₄	1	2	yes	—
197	#33521	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₂²×C₄₁	—	2	1	no	—
199	C₂²×C₄₁	—	2	1	no	—
200	C₂²×C₄₁	—	2	1	no	—
201	C₂²×C₄₁	—	2	1	no	—
202	C₂²×C₄₁	—	2	1	no	—
203	C₂²×C₄₁	—	2	1	no	—
204	C₂²×C₄₁	—	2	1	no	—
205	C₂²×C₄₁	—	4	4	no	—
206	C₂²×C₄₁	—	4	4	no	—
207	C₂²×C₄₁	—	8	8	no	—
208	C₂²×C₄₁	—	8	2	no	—
209	C₂²×C₄₁	—	8	2	no	—
210	C₂²×C₄₁	#447	1	2	yes	—
211	C₂²×C₄₁	#510	1	2	yes	complemented
212	C₂²×C₄₁	C₂²×D₈	1	1	yes	characteristic
213	C₄×C₄₁	—	2	1	no	—
214	C₄×C₄₁	—	2	1	no	—
215	C₄×C₄₁	—	4	4	no	—
216	C₄×C₄₁	—	8	2	no	—
217	C₄×C₄₁	—	8	2	no	—
218	C₄×C₄₁	#447	1	2	yes	—
219	C₄×C₄₁	C₂×#120	1	1	yes	characteristic
220	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
221	C₂²×#135	C₂×C₄₁	1	1	yes	characteristic
222	C₂×#510	C₂×C₄₁	1	2	yes	complemented
223	C₂×#467	C₂×C₄₁	1	1	yes	characteristic, complemented
224	#2189	C₂×C₄₁	1	4	yes	complemented
225	#2188	C₂×C₄₁	1	2	yes	complemented
226	#2187	C₂×C₄₁	1	2	yes	complemented
227	#2139	C₂×C₄₁	1	2	yes	complemented
228	#2112	C₂×C₄₁	1	1	yes	characteristic, complemented
229	C₂×C₄₁	—	2	2	no	—
230	C₂×C₄₁	—	2	2	no	—
231	C₂×C₄₁	—	4	1	no	—
232	C₂×C₄₁	—	8	4	no	—
233	C₂×C₄₁	C₂×#447	1	1	yes	characteristic
234	C₂×C₄₁	C₂×#510	1	1	yes	characteristic
235	C₂×C₄₁	#3414	1	1	yes	characteristic
236	C₂²×#41	—	2	1	no	—
237	C₂×#135	—	2	8	no	—
238	C₂×#135	—	2	1	no	—
239	C₂×#135	—	2	1	no	—
240	C₂×#135	C₂²×C₄₁	1	2	yes	—
241	C₂×#135	C₂²×C₄₁	1	2	yes	—
242	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
243	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
244	C₂²×SD₁₆	—	2	1	no	—
245	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
246	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
247	C₂×C₂²⋊Q₈	—	2	1	no	—
248	#510	—	2	8	no	—
249	C₂×Q₃₂	C₂²×C₄₁	1	4	yes	complemented
250	C₂×SD₃₂	C₂²×C₄₁	1	4	yes	complemented
251	C₂×M₃₂	C₂²×C₄₁	1	2	yes	complemented
252	#467	—	2	1	no	—
253	#467	—	2	1	no	—
254	#467	C₂²×C₄₁	1	2	yes	—
255	#467	C₂²×C₄₁	1	2	yes	complemented
256	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic, complemented
257	C₂×#103	—	2	1	no	—
258	#358	C₂²×C₄₁	1	4	yes	complemented
259	#357	C₂²×C₄₁	1	4	yes	complemented
260	C₂²⋊C₁₆	C₂²×C₄₁	1	2	yes	—
261	C₂²⋊C₁₆	C₂²×C₄₁	1	2	yes	complemented
262	C₄₁	#33521	1	1	yes	characteristic, direct product factor, Sylow
263	C₂×#41	—	2	8	no	—
264	C₂×#41	—	2	2	no	—
265	C₂×#41	—	2	2	no	—
266	C₂×#41	—	4	4	no	—
267	C₂×#41	—	4	1	no	—
268	C₂×#41	—	4	1	no	—
269	C₂²×Q₈	—	2	1	no	—
270	C₂²×Q₈	—	2	1	no	—
271	C₂²×D₄	—	2	1	no	—
272	C₂²×D₄	—	4	1	no	—
273	C₂³×C₄	—	4	1	no	—
274	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
275	#135	—	2	8	no	—
276	#135	—	2	8	no	—
277	#135	—	2	4	no	—
278	#135	—	2	4	no	—
279	#135	—	2	4	no	—
280	#135	D₄×C₄₁	1	8	yes	—
281	C₂×Q₁₆	—	2	4	no	—
282	C₂×Q₁₆	—	2	1	no	—
283	C₂×Q₁₆	—	2	4	no	—
284	C₂×Q₁₆	—	2	1	no	—
285	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
286	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
287	C₂×SD₁₆	—	2	8	no	—
288	C₂×SD₁₆	—	2	2	no	—
289	C₂×SD₁₆	—	2	2	no	—
290	C₂×D₈	—	2	4	no	—
291	C₂×D₈	—	2	1	no	—
292	C₂×D₈	C₂³×C₄₁	1	2	yes	—
293	C₂²×C₈	—	2	4	no	—
294	C₂²×C₈	D₄×C₄₁	1	1	yes	characteristic
295	C₂²×C₈	D₄×C₄₁	1	1	yes	characteristic
296	C₂²×C₈	D₄×C₄₁	1	1	yes	characteristic
297	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
298	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
299	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
300	C₂²⋊Q₈	—	2	2	no	—
301	C₂²⋊Q₈	—	2	2	no	—
302	C₂²⋊Q₈	—	4	1	no	—
303	C₂²⋊Q₈	—	4	1	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	4	1	no	—
306	C₂×C₂²⋊C₄	—	4	1	no	—
307	Q₃₂	—	2	8	no	—
308	SD₃₂	—	2	8	no	—
309	M₃₂	—	2	4	no	—
310	C₂×C₁₆	C₂³×C₄₁	1	4	yes	—
311	#107	—	2	1	no	—
312	#107	C₂³×C₄₁	1	2	yes	—
313	#103	—	2	2	no	—
314	#103	—	2	2	no	—
315	C₂⁴	—	4	1	no	—
316	C₂⁴	D₈×C₄₁	1	1	yes	characteristic
317	#41	—	2	8	no	—
318	#41	—	2	8	no	—
319	#41	—	4	8	no	—
320	#41	—	4	4	no	—
321	#41	—	4	8	no	—
322	#41	—	4	4	no	—
323	C₂×Q₈	—	2	4	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	4	2	no	—
327	C₂×Q₈	—	4	1	no	—
328	C₂×Q₈	—	4	1	no	—
329	C₂×Q₈	—	4	2	no	—
330	C₂×Q₈	—	4	2	no	—
331	C₂×D₄	—	2	4	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	4	2	no	—
334	C₂×D₄	—	4	8	no	—
335	C₂×D₄	—	4	2	no	—
336	C₂×D₄	—	4	2	no	—
337	C₂×D₄	—	4	1	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	4	8	no	—
341	C₂²×C₄	—	4	1	no	—
342	C₂²×C₄	—	4	2	no	—
343	C₂²×C₄	—	4	2	no	—
344	C₂²×C₄	—	4	1	no	—
345	C₂²×C₄	—	4	1	no	—
346	C₂²×C₄	D₈×C₄₁	1	1	yes	characteristic
347	C₂²×C₄	D₈×C₄₁	1	1	yes	characteristic
348	C₂²×C₄	D₈×C₄₁	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
352	Q₁₆	—	2	4	no	—
353	Q₁₆	—	2	2	no	—
354	Q₁₆	—	2	4	no	—
355	Q₁₆	—	4	2	no	—
356	Q₁₆	C₂×D₄×C₄₁	1	4	yes	—
357	SD₁₆	—	2	8	no	—
358	SD₁₆	—	2	8	no	—
359	D₈	—	2	4	no	—
360	D₈	—	2	2	no	—
361	D₈	C₂×D₄×C₄₁	1	4	yes	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
368	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
369	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
370	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
371	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	4	1	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₄⋊C₄	—	4	2	no	—
376	C₂²⋊C₄	—	4	2	no	—
377	C₂²⋊C₄	—	4	2	no	—
378	C₁₆	—	2	4	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	4	4	no	—
383	C₂³	—	4	2	no	—
384	C₂³	—	8	2	no	—
385	C₂³	—	8	2	no	—
386	C₂³	C₂×D₈×C₄₁	1	1	yes	characteristic
387	C₂³	C₂×D₈×C₄₁	1	1	yes	characteristic
388	C₂³	C₂×D₈×C₄₁	1	1	yes	characteristic
389	Q₈	—	2	4	no	—
390	Q₈	—	4	4	no	—
391	Q₈	—	4	2	no	—
392	Q₈	—	4	2	no	—
393	Q₈	—	4	2	no	—
394	Q₈	—	8	2	no	—
395	D₄	—	2	4	no	—
396	D₄	—	4	4	no	—
397	D₄	—	4	8	no	—
398	D₄	—	4	8	no	—
399	D₄	—	4	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	4	8	no	—
408	C₂×C₄	—	4	4	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	8	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	8	2	no	—
414	C₂×C₄	—	8	2	no	—
415	C₂×C₄	#120×C₄₁	1	2	yes	—
416	C₂×C₄	C₂×D₈×C₄₁	1	1	yes	characteristic
417	C₂×C₄	C₂×D₈×C₄₁	1	1	yes	characteristic
418	C₂×C₄	C₂×D₈×C₄₁	1	1	yes	characteristic
419	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
420	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
421	C₈	—	2	1	no	—
422	C₈	—	2	1	no	—
423	C₈	#120×C₄₁	1	2	yes	—
424	C₈	C₂²×D₄×C₄₁	1	2	yes	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	4	4	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	8	8	no	—
435	C₂²	—	8	2	no	—
436	C₂²	—	8	2	no	—
437	C₂²	C₄₁×#447	1	2	yes	—
438	C₂²	C₄₁×#510	1	2	yes	complemented
439	C₂²	C₂²×D₈×C₄₁	1	1	yes	characteristic
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	4	4	no	—
443	C₄	—	8	2	no	—
444	C₄	—	8	2	no	—
445	C₄	C₄₁×#447	1	2	yes	—
446	C₄	C₂×#120×C₄₁	1	1	yes	characteristic
447	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
448	C₂	—	2	2	no	—
449	C₂	—	2	2	no	—
450	C₂	—	4	1	no	—
451	C₂	—	8	4	no	—
452	C₂	C₂×C₄₁×#447	1	1	yes	characteristic
453	C₂	C₂×C₄₁×#510	1	1	yes	characteristic
454	C₂	C₄₁×#3414	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₄₁
prime radical	C₂²×#135×C₄₁	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂³×C₄×C₄₁ ◁ C₂³×C₈×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. C₂×C₄₁×#467	C₂	semidirect
4. C₄₁×#2189	C₂	semidirect
5. C₄₁×#2188	C₂	semidirect
6. C₄₁×#2187	C₂	semidirect
7. C₄₁×#2139	C₂	semidirect
8. C₄₁×#2112	C₂	semidirect
16. C₂²×Q₁₆×C₄₁	C₂²	semidirect
22. C₂×Q₃₂×C₄₁	C₂²	semidirect
23. C₂×SD₃₂×C₄₁	C₂²	semidirect
24. C₂×M₃₂×C₄₁	C₂²	semidirect
28. C₄₁×#467	C₂²	semidirect
29. C₂×#107×C₄₁	C₂²	semidirect
31. C₄₁×#358	C₂²	semidirect
32. C₄₁×#357	C₂²	semidirect
34. C₄₁×C₂²⋊C₁₆	C₂²	semidirect
197. #33521	C₄₁	direct (N × H)
211. C₂²×C₄₁	#510	semidirect
222. C₂×#510	C₂×C₄₁	semidirect
223. C₂×#467	C₂×C₄₁	semidirect
224. #2189	C₂×C₄₁	semidirect
225. #2188	C₂×C₄₁	semidirect
226. #2187	C₂×C₄₁	semidirect
227. #2139	C₂×C₄₁	semidirect
228. #2112	C₂×C₄₁	semidirect
243. C₂²×Q₁₆	C₂²×C₄₁	semidirect
249. C₂×Q₃₂	C₂²×C₄₁	semidirect
250. C₂×SD₃₂	C₂²×C₄₁	semidirect
251. C₂×M₃₂	C₂²×C₄₁	semidirect
255. #467	C₂²×C₄₁	semidirect
256. C₂×#107	C₂²×C₄₁	semidirect
258. #358	C₂²×C₄₁	semidirect
259. #357	C₂²×C₄₁	semidirect
261. C₂²⋊C₁₆	C₂²×C₄₁	semidirect
262. C₄₁	#33521	direct (N × H)
438. C₂²	C₄₁×#510	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#135×C₄₁	2
C₂×C₄₁×#510	2
C₂×C₄₁×#467	2
C₄₁×#2189	2
C₄₁×#2188	2
C₄₁×#2187	2
C₄₁×#2139	2
C₄₁×#2112	2
#33521	41

Subgroups — C41×#33521 #23809722

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#33521 #23809722