Subgroups — C₄₁×#21071 #23797272

Order 10496.

1050 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#430	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#104×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2896	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2879	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#2873	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1929	C₂	1	8	yes	maximal, complemented
7	C₂×C₄₁×#339	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1728	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×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	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
16	C₄₁×#430	—	2	4	no	—
17	C₂×#108×C₄₁	C₂²	1	4	yes	complemented
18	C₂×#104×C₄₁	—	2	4	no	—
19	C₂×#104×C₄₁	C₂²	1	4	yes	—
20	C₄₁×#419	C₄	1	2	yes	complemented
21	C₄₁×#418	C₄	1	2	yes	complemented
22	C₄₁×#417	C₄	1	4	yes	complemented
23	C₄₁×#416	C₂²	1	4	yes	—
24	C₄₁×#408	—	2	2	no	—
25	C₄₁×#408	C₂²	1	4	yes	—
26	C₄₁×#407	—	2	2	no	—
27	C₄₁×#405	—	2	2	no	—
28	C₄₁×#405	C₂²	1	4	yes	complemented
29	C₄×M₁₆×C₄₁	—	2	2	no	—
30	C₄₁×#339	C₂²	1	4	yes	complemented
31	C₄₁×#336	C₂²	1	4	yes	complemented
32	C₂×#41×C₄₁	—	2	1	no	—
33	C₂×#41×C₄₁	—	2	1	no	—
34	C₂×#41×C₄₁	—	2	2	no	—
35	C₂×#41×C₄₁	—	2	2	no	—
36	C₂×#41×C₄₁	—	2	2	no	—
37	C₂×#41×C₄₁	—	2	2	no	—
38	C₂×#41×C₄₁	C₂×C₄	1	2	yes	—
39	C₂×#41×C₄₁	C₂³	1	2	yes	—
40	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
41	C₂²×D₄×C₄₁	—	2	1	no	—
42	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₄₁	—	2	1	no	—
44	C₂³×C₄×C₄₁	—	2	1	no	—
45	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₄₁	—	2	1	no	—
47	C₂×M₁₆×C₄₁	—	2	2	no	—
48	C₂×M₁₆×C₄₁	—	2	2	no	—
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	1	no	—
53	C₂×M₁₆×C₄₁	—	2	2	no	—
54	C₂×M₁₆×C₄₁	—	2	2	no	—
55	C₂×M₁₆×C₄₁	C₂×C₄	1	2	yes	—
56	C₂×M₁₆×C₄₁	C₂×C₄	1	2	yes	—
57	C₂×M₁₆×C₄₁	D₄	1	4	yes	—
58	C₂×M₁₆×C₄₁	D₄	1	2	yes	—
59	C₂×M₁₆×C₄₁	D₄	1	2	yes	—
60	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
61	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
62	C₂²×C₈×C₄₁	—	2	1	no	—
63	C₂²×C₈×C₄₁	—	2	1	no	—
64	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
65	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
66	#117×C₄₁	—	2	1	no	—
67	#117×C₄₁	—	2	1	no	—
68	#117×C₄₁	C₂×C₄	1	2	yes	—
69	#117×C₄₁	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
71	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
72	C₂×C₄²×C₄₁	—	2	1	no	—
73	C₂×C₄²×C₄₁	—	2	2	no	—
74	C₂×C₄²×C₄₁	—	2	2	no	—
75	C₂×C₄²×C₄₁	—	2	1	no	—
76	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
77	#108×C₄₁	—	2	8	no	—
78	#104×C₄₁	—	2	8	no	—
79	#103×C₄₁	C₂×C₄	1	8	yes	complemented
80	#102×C₄₁	C₂×C₄	1	8	yes	complemented
81	C₂²⋊C₈×C₄₁	—	2	8	no	—
82	#97×C₄₁	—	2	4	no	—
83	C₄×C₈×C₄₁	—	2	4	no	—
84	C₂⁴×C₄₁	—	2	1	no	—
85	C₂⁴×C₄₁	#41	1	1	yes	characteristic
86	#41×C₄₁	—	2	4	no	—
87	#41×C₄₁	—	2	4	no	—
88	#41×C₄₁	—	2	2	no	—
89	#41×C₄₁	—	2	2	no	—
90	#41×C₄₁	—	2	2	no	—
91	#41×C₄₁	—	2	2	no	—
92	#41×C₄₁	—	4	2	no	—
93	#41×C₄₁	—	4	2	no	—
94	#41×C₄₁	—	4	2	no	—
95	#41×C₄₁	—	4	2	no	—
96	C₂×Q₈×C₄₁	—	2	1	no	—
97	C₂×Q₈×C₄₁	—	2	2	no	—
98	C₂×Q₈×C₄₁	—	2	2	no	—
99	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
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	1	no	—
105	C₂×D₄×C₄₁	—	4	2	no	—
106	C₂×D₄×C₄₁	—	4	2	no	—
107	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₄₁	—	2	1	no	—
109	C₂²×C₄×C₄₁	—	2	2	no	—
110	C₂²×C₄×C₄₁	—	2	2	no	—
111	C₂²×C₄×C₄₁	—	2	2	no	—
112	C₂²×C₄×C₄₁	—	2	2	no	—
113	C₂²×C₄×C₄₁	—	4	4	no	—
114	C₂²×C₄×C₄₁	—	4	2	no	—
115	C₂²×C₄×C₄₁	—	4	2	no	—
116	C₂²×C₄×C₄₁	—	4	2	no	—
117	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₁	#41	1	2	yes	—
123	C₂²×C₄×C₄₁	#41	1	2	yes	—
124	C₂²×C₄×C₄₁	#41	1	2	yes	—
125	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
126	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
127	M₁₆×C₄₁	—	2	4	no	—
128	M₁₆×C₄₁	—	2	4	no	—
129	M₁₆×C₄₁	—	2	4	no	—
130	M₁₆×C₄₁	—	2	4	no	—
131	M₁₆×C₄₁	—	2	4	no	—
132	M₁₆×C₄₁	—	2	2	no	—
133	M₁₆×C₄₁	—	2	2	no	—
134	M₁₆×C₄₁	—	2	2	no	—
135	M₁₆×C₄₁	—	4	2	no	—
136	M₁₆×C₄₁	C₂×D₄	1	4	yes	—
137	C₂×C₈×C₄₁	—	2	4	no	—
138	C₂×C₈×C₄₁	—	2	2	no	—
139	C₂×C₈×C₄₁	—	2	2	no	—
140	C₂×C₈×C₄₁	—	2	2	no	—
141	C₂×C₈×C₄₁	—	2	2	no	—
142	C₂×C₈×C₄₁	—	2	2	no	—
143	C₂×C₈×C₄₁	—	2	2	no	—
144	C₂×C₈×C₄₁	—	4	2	no	—
145	C₂×C₈×C₄₁	C₂²×C₄	1	4	yes	—
146	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
147	C₄⋊C₄×C₄₁	—	2	2	no	—
148	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
149	C₂²⋊C₄×C₄₁	—	2	2	no	—
150	C₂²⋊C₄×C₄₁	—	2	2	no	—
151	C₄²×C₄₁	—	2	2	no	—
152	C₄²×C₄₁	—	2	2	no	—
153	C₄²×C₄₁	—	2	2	no	—
154	C₄²×C₄₁	—	2	2	no	—
155	C₄²×C₄₁	—	4	2	no	—
156	C₂³×C₄₁	—	2	2	no	—
157	C₂³×C₄₁	—	4	2	no	—
158	C₂³×C₄₁	—	4	2	no	—
159	C₂³×C₄₁	—	8	2	no	—
160	C₂³×C₄₁	C₄×D₄	1	1	yes	characteristic
161	C₂³×C₄₁	C₄×D₄	1	1	yes	characteristic
162	C₂³×C₄₁	#124	1	2	yes	—
163	C₂³×C₄₁	#126	1	2	yes	—
164	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
165	Q₈×C₄₁	—	2	2	no	—
166	Q₈×C₄₁	—	2	2	no	—
167	Q₈×C₄₁	—	4	2	no	—
168	D₄×C₄₁	—	2	2	no	—
169	D₄×C₄₁	—	2	2	no	—
170	D₄×C₄₁	—	4	2	no	—
171	D₄×C₄₁	—	4	2	no	—
172	D₄×C₄₁	—	4	4	no	—
173	D₄×C₄₁	—	4	2	no	—
174	C₂×C₄×C₄₁	—	2	4	no	—
175	C₂×C₄×C₄₁	—	2	4	no	—
176	C₂×C₄×C₄₁	—	2	2	no	—
177	C₂×C₄×C₄₁	—	4	2	no	—
178	C₂×C₄×C₄₁	—	4	8	no	—
179	C₂×C₄×C₄₁	—	4	2	no	—
180	C₂×C₄×C₄₁	—	4	2	no	—
181	C₂×C₄×C₄₁	—	4	2	no	—
182	C₂×C₄×C₄₁	—	4	2	no	—
183	C₂×C₄×C₄₁	—	4	4	no	—
184	C₂×C₄×C₄₁	—	8	2	no	—
185	C₂×C₄×C₄₁	#117	1	2	yes	—
186	C₂×C₄×C₄₁	#117	1	2	yes	—
187	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
188	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
189	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
190	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
191	C₂×C₄×C₄₁	#121	1	2	yes	—
192	C₂×C₄×C₄₁	#121	1	2	yes	—
193	C₂×C₄×C₄₁	#123	1	2	yes	—
194	C₂×C₄×C₄₁	#123	1	2	yes	—
195	C₂×C₄×C₄₁	#124	1	2	yes	—
196	C₂×C₄×C₄₁	#126	1	2	yes	—
197	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
198	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
203	C₈×C₄₁	—	2	4	no	—
204	C₈×C₄₁	—	2	4	no	—
205	C₈×C₄₁	—	2	4	no	—
206	C₈×C₄₁	—	4	2	no	—
207	#21071	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂²×C₄₁	—	2	2	no	—
209	C₂²×C₄₁	—	2	2	no	—
210	C₂²×C₄₁	—	2	2	no	—
211	C₂²×C₄₁	—	4	2	no	—
212	C₂²×C₄₁	—	4	2	no	—
213	C₂²×C₄₁	—	4	4	no	—
214	C₂²×C₄₁	—	4	2	no	—
215	C₂²×C₄₁	—	8	4	no	—
216	C₂²×C₄₁	#388	1	2	yes	—
217	C₂²×C₄₁	#388	1	2	yes	—
218	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
219	C₂²×C₄₁	C₂×#124	1	1	yes	characteristic
220	C₂²×C₄₁	C₂×#126	1	1	yes	characteristic
221	C₄×C₄₁	—	4	4	no	—
222	C₄×C₄₁	—	4	4	no	—
223	C₄×C₄₁	—	4	2	no	—
224	C₄×C₄₁	#388	1	2	yes	—
225	C₄×C₄₁	#388	1	2	yes	—
226	C₄×C₄₁	C₂×#117	1	1	yes	characteristic
227	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
228	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
229	C₄×C₄₁	C₂×#123	1	1	yes	characteristic
230	C₂×#430	C₂×C₄₁	1	1	yes	characteristic, complemented
231	C₂²×#104	C₂×C₄₁	1	1	yes	characteristic
232	#2896	C₂×C₄₁	1	1	yes	characteristic
233	#2879	C₂×C₄₁	1	1	yes	characteristic
234	#2873	C₂×C₄₁	1	1	yes	characteristic, complemented
235	#1929	C₂×C₄₁	1	8	yes	complemented
236	C₂×#339	C₂×C₄₁	1	1	yes	characteristic, complemented
237	#1728	C₂×C₄₁	1	1	yes	characteristic, complemented
238	C₂×C₄₁	—	2	1	no	—
239	C₂×C₄₁	—	2	2	no	—
240	C₂×C₄₁	—	2	1	no	—
241	C₂×C₄₁	—	2	2	no	—
242	C₂×C₄₁	—	8	2	no	—
243	C₂×C₄₁	C₂×#388	1	1	yes	characteristic
244	C₂×C₄₁	#2956	1	2	yes	—
245	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
246	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
247	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
248	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
249	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
250	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
251	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
252	#430	—	2	4	no	—
253	C₂×#108	C₂²×C₄₁	1	4	yes	complemented
254	C₂×#104	—	2	4	no	—
255	C₂×#104	C₂²×C₄₁	1	4	yes	—
256	#419	C₄×C₄₁	1	2	yes	complemented
257	#418	C₄×C₄₁	1	2	yes	complemented
258	#417	C₄×C₄₁	1	4	yes	complemented
259	#416	C₂²×C₄₁	1	4	yes	—
260	#408	—	2	2	no	—
261	#408	C₂²×C₄₁	1	4	yes	—
262	#407	—	2	2	no	—
263	#405	—	2	2	no	—
264	#405	C₂²×C₄₁	1	4	yes	complemented
265	C₄×M₁₆	—	2	2	no	—
266	#339	C₂²×C₄₁	1	4	yes	complemented
267	#336	C₂²×C₄₁	1	4	yes	complemented
268	C₄₁	#21071	1	1	yes	characteristic, direct product factor, Sylow
269	C₂×#41	—	2	1	no	—
270	C₂×#41	—	2	1	no	—
271	C₂×#41	—	2	2	no	—
272	C₂×#41	—	2	2	no	—
273	C₂×#41	—	2	2	no	—
274	C₂×#41	—	2	2	no	—
275	C₂×#41	C₂×C₄×C₄₁	1	2	yes	—
276	C₂×#41	C₂³×C₄₁	1	2	yes	—
277	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
278	C₂²×D₄	—	2	1	no	—
279	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
280	C₂³×C₄	—	2	1	no	—
281	C₂³×C₄	—	2	1	no	—
282	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
283	C₂×M₁₆	—	2	1	no	—
284	C₂×M₁₆	—	2	2	no	—
285	C₂×M₁₆	—	2	2	no	—
286	C₂×M₁₆	—	2	2	no	—
287	C₂×M₁₆	—	2	2	no	—
288	C₂×M₁₆	—	2	2	no	—
289	C₂×M₁₆	—	2	1	no	—
290	C₂×M₁₆	—	2	2	no	—
291	C₂×M₁₆	—	2	2	no	—
292	C₂×M₁₆	C₂×C₄×C₄₁	1	2	yes	—
293	C₂×M₁₆	C₂×C₄×C₄₁	1	2	yes	—
294	C₂×M₁₆	D₄×C₄₁	1	4	yes	—
295	C₂×M₁₆	D₄×C₄₁	1	2	yes	—
296	C₂×M₁₆	D₄×C₄₁	1	2	yes	—
297	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
298	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
299	C₂²×C₈	—	2	1	no	—
300	C₂²×C₈	—	2	1	no	—
301	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
302	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
303	#117	—	2	1	no	—
304	#117	—	2	1	no	—
305	#117	C₂×C₄×C₄₁	1	2	yes	—
306	#117	C₂³×C₄₁	1	2	yes	—
307	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₄²	—	2	1	no	—
310	C₂×C₄²	—	2	2	no	—
311	C₂×C₄²	—	2	2	no	—
312	C₂×C₄²	—	2	1	no	—
313	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
314	#108	—	2	8	no	—
315	#104	—	2	8	no	—
316	#103	C₂×C₄×C₄₁	1	8	yes	complemented
317	#102	C₂×C₄×C₄₁	1	8	yes	complemented
318	C₂²⋊C₈	—	2	8	no	—
319	#97	—	2	4	no	—
320	C₄×C₈	—	2	4	no	—
321	C₂⁴	—	2	1	no	—
322	C₂⁴	#41×C₄₁	1	1	yes	characteristic
323	#41	—	2	4	no	—
324	#41	—	2	4	no	—
325	#41	—	2	2	no	—
326	#41	—	2	2	no	—
327	#41	—	2	2	no	—
328	#41	—	2	2	no	—
329	#41	—	4	2	no	—
330	#41	—	4	2	no	—
331	#41	—	4	2	no	—
332	#41	—	4	2	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	4	2	no	—
343	C₂×D₄	—	4	2	no	—
344	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	4	4	no	—
351	C₂²×C₄	—	4	2	no	—
352	C₂²×C₄	—	4	2	no	—
353	C₂²×C₄	—	4	2	no	—
354	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
355	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
357	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
359	C₂²×C₄	#41×C₄₁	1	2	yes	—
360	C₂²×C₄	#41×C₄₁	1	2	yes	—
361	C₂²×C₄	#41×C₄₁	1	2	yes	—
362	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
363	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
364	M₁₆	—	2	4	no	—
365	M₁₆	—	2	4	no	—
366	M₁₆	—	2	4	no	—
367	M₁₆	—	2	4	no	—
368	M₁₆	—	2	4	no	—
369	M₁₆	—	2	2	no	—
370	M₁₆	—	2	2	no	—
371	M₁₆	—	2	2	no	—
372	M₁₆	—	4	2	no	—
373	M₁₆	C₂×D₄×C₄₁	1	4	yes	—
374	C₂×C₈	—	2	4	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	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	—	4	2	no	—
382	C₂×C₈	C₂²×C₄×C₄₁	1	4	yes	—
383	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
386	C₂²⋊C₄	—	2	2	no	—
387	C₂²⋊C₄	—	2	2	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	4	2	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	8	2	no	—
397	C₂³	C₄×D₄×C₄₁	1	1	yes	characteristic
398	C₂³	C₄×D₄×C₄₁	1	1	yes	characteristic
399	C₂³	#124×C₄₁	1	2	yes	—
400	C₂³	#126×C₄₁	1	2	yes	—
401	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
402	Q₈	—	2	2	no	—
403	Q₈	—	2	2	no	—
404	Q₈	—	4	2	no	—
405	D₄	—	2	2	no	—
406	D₄	—	2	2	no	—
407	D₄	—	4	2	no	—
408	D₄	—	4	2	no	—
409	D₄	—	4	4	no	—
410	D₄	—	4	2	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	8	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	8	2	no	—
422	C₂×C₄	#117×C₄₁	1	2	yes	—
423	C₂×C₄	#117×C₄₁	1	2	yes	—
424	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
425	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
426	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
427	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
428	C₂×C₄	#121×C₄₁	1	2	yes	—
429	C₂×C₄	#121×C₄₁	1	2	yes	—
430	C₂×C₄	#123×C₄₁	1	2	yes	—
431	C₂×C₄	#123×C₄₁	1	2	yes	—
432	C₂×C₄	#124×C₄₁	1	2	yes	—
433	C₂×C₄	#126×C₄₁	1	2	yes	—
434	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
435	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
436	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
437	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
438	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
439	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
440	C₈	—	2	4	no	—
441	C₈	—	2	4	no	—
442	C₈	—	2	4	no	—
443	C₈	—	4	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	4	2	no	—
450	C₂²	—	4	4	no	—
451	C₂²	—	8	4	no	—
452	C₂²	C₄₁×#388	1	2	yes	—
453	C₂²	C₄₁×#388	1	2	yes	—
454	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
455	C₂²	C₂×#124×C₄₁	1	1	yes	characteristic
456	C₂²	C₂×#126×C₄₁	1	1	yes	characteristic
457	C₄	—	4	4	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	4	no	—
460	C₄	C₄₁×#388	1	2	yes	—
461	C₄	C₄₁×#388	1	2	yes	—
462	C₄	C₂×#117×C₄₁	1	1	yes	characteristic
463	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
464	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
465	C₄	C₂×#123×C₄₁	1	1	yes	characteristic
466	C₂	—	2	1	no	—
467	C₂	—	2	2	no	—
468	C₂	—	2	1	no	—
469	C₂	—	2	2	no	—
470	C₂	—	8	2	no	—
471	C₂	C₂×C₄₁×#388	1	1	yes	characteristic
472	C₂	C₄₁×#2956	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
socle	C₂²×C₄₁	C₂×C₄×D₄
prime radical	C₂²×#41×C₄₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁ ◁ C₂²×M₁₆×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#430	C₂	semidirect
5. C₄₁×#2873	C₂	semidirect
6. C₄₁×#1929	C₂	semidirect
7. C₂×C₄₁×#339	C₂	semidirect
8. C₄₁×#1728	C₂	semidirect
17. C₂×#108×C₄₁	C₂²	semidirect
20. C₄₁×#419	C₄	semidirect
21. C₄₁×#418	C₄	semidirect
22. C₄₁×#417	C₄	semidirect
28. C₄₁×#405	C₂²	semidirect
30. C₄₁×#339	C₂²	semidirect
31. C₄₁×#336	C₂²	semidirect
79. #103×C₄₁	C₂×C₄	semidirect
80. #102×C₄₁	C₂×C₄	semidirect
207. #21071	C₄₁	direct (N × H)
230. C₂×#430	C₂×C₄₁	semidirect
234. #2873	C₂×C₄₁	semidirect
235. #1929	C₂×C₄₁	semidirect
236. C₂×#339	C₂×C₄₁	semidirect
237. #1728	C₂×C₄₁	semidirect
253. C₂×#108	C₂²×C₄₁	semidirect
256. #419	C₄×C₄₁	semidirect
257. #418	C₄×C₄₁	semidirect
258. #417	C₄×C₄₁	semidirect
264. #405	C₂²×C₄₁	semidirect
266. #339	C₂²×C₄₁	semidirect
267. #336	C₂²×C₄₁	semidirect
268. C₄₁	#21071	direct (N × H)
316. #103	C₂×C₄×C₄₁	semidirect
317. #102	C₂×C₄×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#430	2
C₂²×#104×C₄₁	2
C₄₁×#2896	2
C₄₁×#2879	2
C₄₁×#2873	2
C₄₁×#1929	2
C₂×C₄₁×#339	2
C₄₁×#1728	2
#21071	41

Subgroups — C41×#21071 #23797272

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#21071 #23797272