Subgroups — C₄₁×#23618 #23799819

Order 10496.

1318 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#428	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#423	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#418	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₁×#418	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#2296	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄₁×#390	C₂	1	1	yes	maximal, characteristic
7	C₄₁×#2067	C₂	1	4	yes	maximal, complemented
8	C₄₁×#2065	C₂	1	4	yes	maximal, complemented
9	C₄₁×#1736	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
16	C₂²×C₂²⋊C₄×C₄₁	—	2	2	no	—
17	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
18	C₄₁×#428	—	2	4	no	—
19	C₂×#107×C₄₁	C₂²	1	2	yes	complemented
20	C₂×#106×C₄₁	C₂²	1	2	yes	complemented
21	C₄₁×#423	—	2	4	no	—
22	C₂×C₄⋊C₈×C₄₁	C₂²	1	4	yes	complemented
23	C₄₁×#418	—	2	4	no	—
24	C₄₁×#418	—	2	4	no	—
25	C₂×#102×C₄₁	C₂²	1	2	yes	—
26	C₂×#102×C₄₁	C₂²	1	4	yes	—
27	C₂×#102×C₄₁	C₂²	1	2	yes	—
28	C₄₁×#390	—	2	1	no	—
29	C₄₁×#390	—	2	1	no	—
30	C₄₁×#390	C₂²	1	4	yes	—
31	C₄₁×#389	C₂²	1	2	yes	complemented
32	C₄₁×#389	C₂²	1	2	yes	complemented
33	C₄₁×#385	—	2	2	no	—
34	C₄×C₄⋊C₄×C₄₁	—	2	1	no	—
35	C₄×C₄⋊C₄×C₄₁	—	2	1	no	—
36	C₄₁×#340	C₂²	1	4	yes	complemented
37	C₂⁵×C₄₁	—	2	1	no	—
38	C₂²×D₄×C₄₁	—	2	2	no	—
39	C₂²×D₄×C₄₁	—	2	2	no	—
40	C₂²×D₄×C₄₁	—	2	1	no	—
41	C₂²×D₄×C₄₁	—	2	2	no	—
42	C₂²×D₄×C₄₁	—	2	2	no	—
43	C₂²×D₄×C₄₁	—	2	2	no	—
44	C₂²×D₄×C₄₁	Q₈	1	4	yes	—
45	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
46	C₂³×C₄×C₄₁	—	2	1	no	—
47	C₂³×C₄×C₄₁	D₄	1	2	yes	—
48	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
49	C₂×M₁₆×C₄₁	—	2	2	no	—
50	C₂×M₁₆×C₄₁	—	2	2	no	—
51	C₂×M₁₆×C₄₁	—	2	2	no	—
52	C₂×M₁₆×C₄₁	—	2	2	no	—
53	C₂×M₁₆×C₄₁	—	2	2	no	—
54	C₂×M₁₆×C₄₁	D₄	1	4	yes	—
55	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
56	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
57	#117×C₄₁	—	2	2	no	—
58	#117×C₄₁	—	2	2	no	—
59	#117×C₄₁	—	2	2	no	—
60	#117×C₄₁	D₄	1	4	yes	—
61	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
66	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
74	C₂×C₂²⋊C₄×C₄₁	—	4	8	no	—
75	C₂×C₄²×C₄₁	—	2	2	no	—
76	C₂×C₄²×C₄₁	—	2	1	no	—
77	C₂×C₄²×C₄₁	—	2	2	no	—
78	C₂×C₄²×C₄₁	—	2	1	no	—
79	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
82	#107×C₄₁	—	2	4	no	—
83	#106×C₄₁	—	2	4	no	—
84	C₄⋊C₈×C₄₁	—	2	8	no	—
85	#102×C₄₁	—	2	8	no	—
86	#102×C₄₁	—	2	4	no	—
87	#102×C₄₁	—	2	4	no	—
88	#95×C₄₁	—	2	2	no	—
89	#95×C₄₁	—	2	2	no	—
90	C₂⁴×C₄₁	—	2	4	no	—
91	C₂⁴×C₄₁	—	2	2	no	—
92	C₂⁴×C₄₁	—	4	4	no	—
93	C₂⁴×C₄₁	—	4	4	no	—
94	C₂⁴×C₄₁	—	4	2	no	—
95	C₂⁴×C₄₁	—	4	2	no	—
96	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
97	C₂×D₄×C₄₁	—	2	8	no	—
98	C₂×D₄×C₄₁	—	2	8	no	—
99	C₂×D₄×C₄₁	—	2	4	no	—
100	C₂×D₄×C₄₁	—	2	2	no	—
101	C₂×D₄×C₄₁	—	2	2	no	—
102	C₂×D₄×C₄₁	—	2	2	no	—
103	C₂×D₄×C₄₁	—	2	2	no	—
104	C₂×D₄×C₄₁	—	2	2	no	—
105	C₂×D₄×C₄₁	—	4	4	no	—
106	C₂×D₄×C₄₁	—	4	2	no	—
107	C₂×D₄×C₄₁	—	4	2	no	—
108	C₂×D₄×C₄₁	—	4	4	no	—
109	C₂×D₄×C₄₁	C₂×Q₈	1	4	yes	—
110	C₂²×C₄×C₄₁	—	2	4	no	—
111	C₂²×C₄×C₄₁	—	2	1	no	—
112	C₂²×C₄×C₄₁	—	2	1	no	—
113	C₂²×C₄×C₄₁	—	2	4	no	—
114	C₂²×C₄×C₄₁	—	2	2	no	—
115	C₂²×C₄×C₄₁	—	2	2	no	—
116	C₂²×C₄×C₄₁	—	4	2	no	—
117	C₂²×C₄×C₄₁	—	4	4	no	—
118	C₂²×C₄×C₄₁	—	4	2	no	—
119	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
125	C₂²×C₄×C₄₁	#41	1	2	yes	—
126	C₂²×C₄×C₄₁	#41	1	2	yes	—
127	C₂²×C₄×C₄₁	#41	1	2	yes	—
128	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
129	M₁₆×C₄₁	—	2	8	no	—
130	M₁₆×C₄₁	—	4	4	no	—
131	C₂×C₈×C₄₁	—	2	2	no	—
132	C₂×C₈×C₄₁	—	2	2	no	—
133	C₂×C₈×C₄₁	—	2	2	no	—
134	C₂×C₈×C₄₁	—	2	2	no	—
135	C₂×C₈×C₄₁	—	2	2	no	—
136	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
137	C₄⋊C₄×C₄₁	—	2	1	no	—
138	C₄⋊C₄×C₄₁	—	2	1	no	—
139	C₄⋊C₄×C₄₁	—	2	2	no	—
140	C₄⋊C₄×C₄₁	—	2	2	no	—
141	C₄⋊C₄×C₄₁	—	2	2	no	—
142	C₄⋊C₄×C₄₁	—	2	2	no	—
143	C₄⋊C₄×C₄₁	—	4	4	no	—
144	C₄⋊C₄×C₄₁	—	4	2	no	—
145	C₄⋊C₄×C₄₁	—	4	4	no	—
146	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
147	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
148	C₂²⋊C₄×C₄₁	—	2	4	no	—
149	C₂²⋊C₄×C₄₁	—	4	8	no	—
150	C₂²⋊C₄×C₄₁	—	4	2	no	—
151	C₂²⋊C₄×C₄₁	—	4	8	no	—
152	C₄²×C₄₁	—	2	2	no	—
153	C₄²×C₄₁	—	2	2	no	—
154	C₄²×C₄₁	—	2	4	no	—
155	C₄²×C₄₁	—	2	2	no	—
156	C₄²×C₄₁	—	2	2	no	—
157	C₄²×C₄₁	—	4	2	no	—
158	C₂³×C₄₁	—	2	2	no	—
159	C₂³×C₄₁	—	2	2	no	—
160	C₂³×C₄₁	—	2	4	no	—
161	C₂³×C₄₁	—	4	16	no	—
162	C₂³×C₄₁	—	4	2	no	—
163	C₂³×C₄₁	—	4	2	no	—
164	C₂³×C₄₁	—	4	4	no	—
165	C₂³×C₄₁	—	4	4	no	—
166	C₂³×C₄₁	—	4	8	no	—
167	C₂³×C₄₁	—	8	4	no	—
168	C₂³×C₄₁	—	8	4	no	—
169	C₂³×C₄₁	—	8	8	no	—
170	C₂³×C₄₁	#121	1	2	yes	—
171	C₂³×C₄₁	#121	1	2	yes	—
172	C₂³×C₄₁	C₂²⋊Q₈	1	2	yes	—
173	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
174	D₄×C₄₁	—	2	4	no	—
175	D₄×C₄₁	—	2	4	no	—
176	D₄×C₄₁	—	4	2	no	—
177	D₄×C₄₁	—	4	2	no	—
178	D₄×C₄₁	—	4	8	no	—
179	C₂×C₄×C₄₁	—	2	2	no	—
180	C₂×C₄×C₄₁	—	2	2	no	—
181	C₂×C₄×C₄₁	—	2	2	no	—
182	C₂×C₄×C₄₁	—	2	2	no	—
183	C₂×C₄×C₄₁	—	2	2	no	—
184	C₂×C₄×C₄₁	—	2	2	no	—
185	C₂×C₄×C₄₁	—	2	2	no	—
186	C₂×C₄×C₄₁	—	4	8	no	—
187	C₂×C₄×C₄₁	—	4	2	no	—
188	C₂×C₄×C₄₁	—	4	2	no	—
189	C₂×C₄×C₄₁	—	4	2	no	—
190	C₂×C₄×C₄₁	—	4	2	no	—
191	C₂×C₄×C₄₁	—	4	4	no	—
192	C₂×C₄×C₄₁	—	4	2	no	—
193	C₂×C₄×C₄₁	—	4	2	no	—
194	C₂×C₄×C₄₁	—	8	4	no	—
195	C₂×C₄×C₄₁	#121	1	4	yes	—
196	C₂×C₄×C₄₁	#121	1	2	yes	—
197	C₂×C₄×C₄₁	#121	1	2	yes	—
198	C₂×C₄×C₄₁	C₂²⋊Q₈	1	4	yes	—
199	C₂×C₄×C₄₁	C₂²⋊Q₈	1	4	yes	—
200	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
201	C₂×C₄×C₄₁	#126	1	4	yes	—
202	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	4	yes	—
203	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₄₁	C₂²×Q₈	1	1	yes	characteristic
206	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
207	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
209	C₈×C₄₁	—	2	4	no	—
210	C₈×C₄₁	—	4	2	no	—
211	#23618	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
212	C₂²×C₄₁	—	2	4	no	—
213	C₂²×C₄₁	—	2	2	no	—
214	C₂²×C₄₁	—	2	2	no	—
215	C₂²×C₄₁	—	2	4	no	—
216	C₂²×C₄₁	—	4	8	no	—
217	C₂²×C₄₁	—	4	4	no	—
218	C₂²×C₄₁	—	8	16	no	—
219	C₂²×C₄₁	—	8	2	no	—
220	C₂²×C₄₁	—	8	2	no	—
221	C₂²×C₄₁	—	8	4	no	—
222	C₂²×C₄₁	#396	1	4	yes	—
223	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
224	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
225	C₂²×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
226	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
227	C₂²×C₄₁	#575	1	2	yes	—
228	C₄×C₄₁	—	2	4	no	—
229	C₄×C₄₁	—	4	2	no	—
230	C₄×C₄₁	—	4	2	no	—
231	C₄×C₄₁	—	4	2	no	—
232	C₄×C₄₁	—	8	2	no	—
233	C₄×C₄₁	—	8	2	no	—
234	C₄×C₄₁	#396	1	4	yes	—
235	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
236	C₄×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
237	C₄×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
238	C₄×C₄₁	C₂×#126	1	1	yes	characteristic
239	C₂×#428	C₂×C₄₁	1	1	yes	characteristic, complemented
240	C₂×#423	C₂×C₄₁	1	1	yes	characteristic, complemented
241	C₂×#418	C₂×C₄₁	1	1	yes	characteristic
242	C₂×#418	C₂×C₄₁	1	1	yes	characteristic
243	#2296	C₂×C₄₁	1	1	yes	characteristic, complemented
244	C₂×#390	C₂×C₄₁	1	1	yes	characteristic
245	#2067	C₂×C₄₁	1	4	yes	complemented
246	#2065	C₂×C₄₁	1	4	yes	complemented
247	#1736	C₂×C₄₁	1	1	yes	characteristic, complemented
248	C₂×C₄₁	—	2	4	no	—
249	C₂×C₄₁	—	8	4	no	—
250	C₂×C₄₁	C₂×#396	1	1	yes	characteristic
251	C₂×C₄₁	#3038	1	1	yes	characteristic
252	C₂×C₄₁	#3040	1	1	yes	characteristic
253	C₂×C₄₁	#3055	1	2	yes	—
254	C₂×C₄₁	#3077	1	2	yes	—
255	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
256	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
257	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
258	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
259	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
260	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
261	C₂²×C₂²⋊C₄	—	2	2	no	—
262	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
263	#428	—	2	4	no	—
264	C₂×#107	C₂²×C₄₁	1	2	yes	complemented
265	C₂×#106	C₂²×C₄₁	1	2	yes	complemented
266	#423	—	2	4	no	—
267	C₂×C₄⋊C₈	C₂²×C₄₁	1	4	yes	complemented
268	#418	—	2	4	no	—
269	#418	—	2	4	no	—
270	C₂×#102	C₂²×C₄₁	1	2	yes	—
271	C₂×#102	C₂²×C₄₁	1	4	yes	—
272	C₂×#102	C₂²×C₄₁	1	2	yes	—
273	#390	—	2	1	no	—
274	#390	—	2	1	no	—
275	#390	C₂²×C₄₁	1	4	yes	—
276	#389	C₂²×C₄₁	1	2	yes	complemented
277	#389	C₂²×C₄₁	1	2	yes	complemented
278	#385	—	2	2	no	—
279	C₄×C₄⋊C₄	—	2	1	no	—
280	C₄×C₄⋊C₄	—	2	1	no	—
281	#340	C₂²×C₄₁	1	4	yes	complemented
282	C₄₁	#23618	1	1	yes	characteristic, direct product factor, Sylow
283	C₂⁵	—	2	1	no	—
284	C₂²×D₄	—	2	2	no	—
285	C₂²×D₄	—	2	2	no	—
286	C₂²×D₄	—	2	1	no	—
287	C₂²×D₄	—	2	2	no	—
288	C₂²×D₄	—	2	2	no	—
289	C₂²×D₄	—	2	2	no	—
290	C₂²×D₄	Q₈×C₄₁	1	4	yes	—
291	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
292	C₂³×C₄	—	2	1	no	—
293	C₂³×C₄	D₄×C₄₁	1	2	yes	—
294	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
295	C₂×M₁₆	—	2	2	no	—
296	C₂×M₁₆	—	2	2	no	—
297	C₂×M₁₆	—	2	2	no	—
298	C₂×M₁₆	—	2	2	no	—
299	C₂×M₁₆	—	2	2	no	—
300	C₂×M₁₆	D₄×C₄₁	1	4	yes	—
301	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
302	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
303	#117	—	2	2	no	—
304	#117	—	2	2	no	—
305	#117	—	2	2	no	—
306	#117	D₄×C₄₁	1	4	yes	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
313	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
314	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
315	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
316	C₂×C₂²⋊C₄	—	2	1	no	—
317	C₂×C₂²⋊C₄	—	2	1	no	—
318	C₂×C₂²⋊C₄	—	2	4	no	—
319	C₂×C₂²⋊C₄	—	2	4	no	—
320	C₂×C₂²⋊C₄	—	4	8	no	—
321	C₂×C₄²	—	2	1	no	—
322	C₂×C₄²	—	2	2	no	—
323	C₂×C₄²	—	2	2	no	—
324	C₂×C₄²	—	2	1	no	—
325	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
326	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
327	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
328	#107	—	2	4	no	—
329	#106	—	2	4	no	—
330	C₄⋊C₈	—	2	8	no	—
331	#102	—	2	8	no	—
332	#102	—	2	4	no	—
333	#102	—	2	4	no	—
334	#95	—	2	2	no	—
335	#95	—	2	2	no	—
336	C₂⁴	—	2	4	no	—
337	C₂⁴	—	2	2	no	—
338	C₂⁴	—	4	4	no	—
339	C₂⁴	—	4	4	no	—
340	C₂⁴	—	4	2	no	—
341	C₂⁴	—	4	2	no	—
342	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
343	C₂×D₄	—	2	8	no	—
344	C₂×D₄	—	2	8	no	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	4	4	no	—
352	C₂×D₄	—	4	2	no	—
353	C₂×D₄	—	4	2	no	—
354	C₂×D₄	—	4	4	no	—
355	C₂×D₄	C₂×Q₈×C₄₁	1	4	yes	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	4	2	no	—
363	C₂²×C₄	—	4	4	no	—
364	C₂²×C₄	—	4	2	no	—
365	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
366	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
367	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
370	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
371	C₂²×C₄	#41×C₄₁	1	2	yes	—
372	C₂²×C₄	#41×C₄₁	1	2	yes	—
373	C₂²×C₄	#41×C₄₁	1	2	yes	—
374	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
375	M₁₆	—	2	8	no	—
376	M₁₆	—	4	4	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	4	4	no	—
390	C₄⋊C₄	—	4	2	no	—
391	C₄⋊C₄	—	4	4	no	—
392	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
393	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
394	C₂²⋊C₄	—	2	4	no	—
395	C₂²⋊C₄	—	4	8	no	—
396	C₂²⋊C₄	—	4	2	no	—
397	C₂²⋊C₄	—	4	8	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	2	4	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	2	2	no	—
403	C₄²	—	4	2	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	2	4	no	—
407	C₂³	—	4	16	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	4	2	no	—
410	C₂³	—	4	4	no	—
411	C₂³	—	4	4	no	—
412	C₂³	—	4	8	no	—
413	C₂³	—	8	4	no	—
414	C₂³	—	8	4	no	—
415	C₂³	—	8	8	no	—
416	C₂³	#121×C₄₁	1	2	yes	—
417	C₂³	#121×C₄₁	1	2	yes	—
418	C₂³	C₂²⋊Q₈×C₄₁	1	2	yes	—
419	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
420	D₄	—	2	4	no	—
421	D₄	—	2	4	no	—
422	D₄	—	4	2	no	—
423	D₄	—	4	2	no	—
424	D₄	—	4	8	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	4	8	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	4	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	8	4	no	—
441	C₂×C₄	#121×C₄₁	1	4	yes	—
442	C₂×C₄	#121×C₄₁	1	2	yes	—
443	C₂×C₄	#121×C₄₁	1	2	yes	—
444	C₂×C₄	C₂²⋊Q₈×C₄₁	1	4	yes	—
445	C₂×C₄	C₂²⋊Q₈×C₄₁	1	4	yes	—
446	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
447	C₂×C₄	#126×C₄₁	1	4	yes	—
448	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	4	yes	—
449	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
450	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
451	C₂×C₄	C₂²×Q₈×C₄₁	1	1	yes	characteristic
452	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
453	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
454	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
455	C₈	—	2	4	no	—
456	C₈	—	4	2	no	—
457	C₂²	—	2	2	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	2	4	no	—
460	C₂²	—	2	4	no	—
461	C₂²	—	4	8	no	—
462	C₂²	—	4	4	no	—
463	C₂²	—	8	16	no	—
464	C₂²	—	8	2	no	—
465	C₂²	—	8	2	no	—
466	C₂²	—	8	4	no	—
467	C₂²	C₄₁×#396	1	4	yes	—
468	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
469	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
470	C₂²	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
471	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	2	yes	—
472	C₂²	C₄₁×#575	1	2	yes	—
473	C₄	—	2	4	no	—
474	C₄	—	4	2	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	2	no	—
477	C₄	—	8	2	no	—
478	C₄	—	8	2	no	—
479	C₄	C₄₁×#396	1	4	yes	—
480	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
481	C₄	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
482	C₄	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
483	C₄	C₂×#126×C₄₁	1	1	yes	characteristic
484	C₂	—	2	4	no	—
485	C₂	—	8	4	no	—
486	C₂	C₂×C₄₁×#396	1	1	yes	characteristic
487	C₂	C₄₁×#3038	1	1	yes	characteristic
488	C₂	C₄₁×#3040	1	1	yes	characteristic
489	C₂	C₄₁×#3055	1	2	yes	—
490	C₂	C₄₁×#3077	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂³×D₄×C₄₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#428	C₂	semidirect
2. C₂×C₄₁×#423	C₂	semidirect
5. C₄₁×#2296	C₂	semidirect
7. C₄₁×#2067	C₂	semidirect
8. C₄₁×#2065	C₂	semidirect
9. C₄₁×#1736	C₂	semidirect
19. C₂×#107×C₄₁	C₂²	semidirect
20. C₂×#106×C₄₁	C₂²	semidirect
22. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
31. C₄₁×#389	C₂²	semidirect
32. C₄₁×#389	C₂²	semidirect
36. C₄₁×#340	C₂²	semidirect
211. #23618	C₄₁	direct (N × H)
239. C₂×#428	C₂×C₄₁	semidirect
240. C₂×#423	C₂×C₄₁	semidirect
243. #2296	C₂×C₄₁	semidirect
245. #2067	C₂×C₄₁	semidirect
246. #2065	C₂×C₄₁	semidirect
247. #1736	C₂×C₄₁	semidirect
264. C₂×#107	C₂²×C₄₁	semidirect
265. C₂×#106	C₂²×C₄₁	semidirect
267. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
276. #389	C₂²×C₄₁	semidirect
277. #389	C₂²×C₄₁	semidirect
281. #340	C₂²×C₄₁	semidirect
282. C₄₁	#23618	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×#428	2
C₂×C₄₁×#423	2
C₂×C₄₁×#418	2
C₄₁×#2296	2
C₂×C₄₁×#390	2
C₄₁×#2067	2
C₄₁×#2065	2
C₄₁×#1736	2
#23618	41

Subgroups — C41×#23618 #23799819

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#23618 #23799819