Subgroups — C₄₁×#62000 #23838201

Order 10496.

1818 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3482	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#3395	C₂	1	2	yes	maximal, complemented
4	C₄₁×#3359	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3328	C₂	1	6	yes	maximal, complemented
6	C₄₁×#3276	C₂	1	6	yes	maximal, complemented
7	C₄₁×#3255	C₂	1	3	yes	maximal, complemented
8	C₄₁×#3209	C₂	1	3	yes	maximal, complemented
9	C₄₁×#3107	C₂	1	3	yes	maximal, complemented
10	C₄₁×#3039	C₂	1	3	yes	maximal, complemented
11	C₄₁×#2991	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₄₁	C₂²	1	6	yes	—
13	Q₈²×C₄₁	—	2	1	no	—
14	C₄₁×#557	C₂²	1	2	yes	—
15	C₄₁×#557	C₂²	1	1	yes	characteristic
16	C₄₁×#556	C₂²	1	3	yes	—
17	C₄₁×#554	—	2	3	no	—
18	C₄₁×#552	—	2	3	no	—
19	D₄×Q₈×C₄₁	C₂²	1	6	yes	—
20	D₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
21	C₄₁×#548	—	2	1	no	—
22	C₄₁×#547	C₂²	1	3	yes	—
23	C₄₁×#544	—	2	3	no	—
24	C₄₁×#533	C₂²	1	3	yes	—
25	C₄₁×#533	C₂²	1	3	yes	—
26	C₂×C₄⋊Q₈×C₄₁	C₂²	1	3	yes	—
27	C₄₁×#529	—	2	3	no	—
28	C₄₁×#520	—	2	1	no	—
29	C₄×#41×C₄₁	C₂²	1	3	yes	—
30	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₄₁	—	2	1	no	—
32	C₄₁×#494	C₂²	1	6	yes	—
33	C₄₁×#487	C₂²	1	6	yes	—
34	C₄₁×#485	C₂²	1	6	yes	—
35	C₄₁×#475	C₂²	1	6	yes	—
36	C₄₁×#475	C₂²	1	3	yes	—
37	C₄₁×#474	C₂²	1	1	yes	characteristic
38	C₄₁×#470	C₂²	1	12	yes	—
39	C₄₁×#462	C₂²	1	6	yes	—
40	C₄₁×#462	C₂²	1	6	yes	—
41	C₄₁×#462	C₂²	1	3	yes	—
42	C₄₁×#462	C₂²	1	6	yes	—
43	C₄₁×#461	C₂²	1	3	yes	—
44	C₄₁×#461	C₂²	1	6	yes	—
45	C₄₁×#452	C₂²	1	6	yes	—
46	C₄₁×#451	C₂²	1	12	yes	—
47	C₈×Q₈×C₄₁	C₂²	1	2	yes	—
48	C₄×Q₁₆×C₄₁	C₂²	1	6	yes	—
49	C₄×SD₁₆×C₄₁	C₂²	1	6	yes	—
50	C₄₁×#436	C₂²	1	6	yes	—
51	C₄₁×#431	C₂²	1	3	yes	—
52	C₄₁×#423	C₂²	1	3	yes	—
53	C₄₁×#419	C₂²	1	6	yes	—
54	C₂×#41×C₄₁	D₄	1	1	yes	characteristic
55	C₂×#41×C₄₁	C₂³	1	3	yes	—
56	C₂²×Q₈×C₄₁	—	2	1	no	—
57	C₂²×Q₈×C₄₁	C₂³	1	6	yes	—
58	#137×C₄₁	—	4	12	no	—
59	C₂×Q₁₆×C₄₁	C₂³	1	12	yes	—
60	C₂×Q₁₆×C₄₁	C₂³	1	6	yes	—
61	C₂×SD₁₆×C₄₁	C₂³	1	6	yes	—
62	C₂×M₁₆×C₄₁	C₂³	1	6	yes	—
63	C₄⋊Q₈×C₄₁	—	2	6	no	—
64	C₄⋊Q₈×C₄₁	—	2	3	no	—
65	C₄⋊Q₈×C₄₁	—	2	3	no	—
66	C₄⋊Q₈×C₄₁	C₂³	1	3	yes	—
67	C₄⋊Q₈×C₄₁	C₂³	1	6	yes	—
68	C₄⋊Q₈×C₄₁	C₂³	1	3	yes	—
69	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
70	C₄⋊Q₈×C₄₁	C₂³	1	3	yes	—
71	#126×C₄₁	—	2	6	no	—
72	#125×C₄₁	—	2	3	no	—
73	#125×C₄₁	—	2	6	no	—
74	#125×C₄₁	—	2	3	no	—
75	#125×C₄₁	—	2	3	no	—
76	#124×C₄₁	—	2	3	no	—
77	#123×C₄₁	—	2	6	no	—
78	C₂²⋊Q₈×C₄₁	—	2	3	no	—
79	C₂²⋊Q₈×C₄₁	—	2	3	no	—
80	C₂²⋊Q₈×C₄₁	—	2	3	no	—
81	C₂²⋊Q₈×C₄₁	—	2	12	no	—
82	C₂²⋊Q₈×C₄₁	C₂³	1	6	yes	—
83	C₂²⋊Q₈×C₄₁	C₂³	1	6	yes	—
84	#121×C₄₁	—	2	3	no	—
85	C₄×Q₈×C₄₁	—	2	1	no	—
86	C₄×Q₈×C₄₁	—	2	2	no	—
87	C₄×Q₈×C₄₁	—	2	3	no	—
88	C₄×Q₈×C₄₁	—	2	3	no	—
89	C₄×Q₈×C₄₁	—	2	3	no	—
90	C₄×Q₈×C₄₁	D₄	1	1	yes	characteristic
91	C₄×Q₈×C₄₁	C₂³	1	3	yes	—
92	C₄×Q₈×C₄₁	C₂³	1	3	yes	—
93	C₄×Q₈×C₄₁	C₂³	1	6	yes	—
94	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
95	C₄×D₄×C₄₁	—	2	6	no	—
96	C₄×D₄×C₄₁	—	2	3	no	—
97	C₄×D₄×C₄₁	—	2	3	no	—
98	C₄×D₄×C₄₁	D₄	1	3	yes	—
99	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
100	C₄×D₄×C₄₁	C₂³	1	3	yes	—
101	C₄×D₄×C₄₁	C₂³	1	3	yes	—
102	#117×C₄₁	—	2	3	no	—
103	#117×C₄₁	—	2	3	no	—
104	#117×C₄₁	—	2	3	no	—
105	#117×C₄₁	D₄	1	3	yes	—
106	#117×C₄₁	C₂³	1	3	yes	—
107	C₂×C₄⋊C₄×C₄₁	—	2	3	no	—
108	C₂×C₄⋊C₄×C₄₁	—	2	3	no	—
109	C₂×C₄⋊C₄×C₄₁	—	2	3	no	—
110	C₂×C₄²×C₄₁	—	2	3	no	—
111	C₂×C₄²×C₄₁	C₂³	1	3	yes	—
112	#107×C₄₁	C₂³	1	2	yes	—
113	#106×C₄₁	C₂³	1	6	yes	—
114	C₄⋊C₈×C₄₁	C₂³	1	3	yes	—
115	C₄⋊C₈×C₄₁	C₂³	1	6	yes	—
116	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
117	#103×C₄₁	C₂³	1	6	yes	—
118	#103×C₄₁	C₂³	1	12	yes	—
119	#103×C₄₁	C₂³	1	6	yes	—
120	#103×C₄₁	C₂³	1	6	yes	—
121	#102×C₄₁	C₂³	1	2	yes	—
122	C₂²⋊C₈×C₄₁	C₂³	1	6	yes	—
123	C₄×C₈×C₄₁	C₂³	1	6	yes	—
124	#41×C₄₁	—	2	4	no	—
125	#41×C₄₁	—	2	6	no	—
126	#41×C₄₁	—	4	3	no	—
127	C₂×Q₈×C₄₁	—	2	1	no	—
128	C₂×Q₈×C₄₁	—	2	3	no	—
129	C₂×Q₈×C₄₁	—	2	6	no	—
130	C₂×Q₈×C₄₁	—	4	6	no	—
131	C₂×Q₈×C₄₁	—	4	6	no	—
132	C₂×Q₈×C₄₁	—	4	4	no	—
133	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
134	C₂×Q₈×C₄₁	C₂⁴	1	6	yes	—
135	C₂×Q₈×C₄₁	C₂⁴	1	3	yes	—
136	C₂×D₄×C₄₁	—	2	3	no	—
137	C₂×D₄×C₄₁	C₂×D₄	1	3	yes	—
138	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
139	C₂²×C₄×C₄₁	—	2	6	no	—
140	C₂²×C₄×C₄₁	—	2	1	no	—
141	C₂²×C₄×C₄₁	—	2	3	no	—
142	C₂²×C₄×C₄₁	—	2	3	no	—
143	C₂²×C₄×C₄₁	C₂×D₄	1	3	yes	—
144	C₂²×C₄×C₄₁	C₂×D₄	1	3	yes	—
145	C₂²×C₄×C₄₁	C₂⁴	1	3	yes	—
146	Q₁₆×C₄₁	—	4	6	no	—
147	Q₁₆×C₄₁	—	4	12	no	—
148	SD₁₆×C₄₁	—	2	12	no	—
149	M₁₆×C₄₁	—	4	6	no	—
150	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
151	C₂×C₈×C₄₁	C₂⁴	1	6	yes	—
152	C₄⋊C₄×C₄₁	—	2	3	no	—
153	C₄⋊C₄×C₄₁	—	2	3	no	—
154	C₄⋊C₄×C₄₁	—	2	6	no	—
155	C₄⋊C₄×C₄₁	—	2	3	no	—
156	C₄⋊C₄×C₄₁	—	2	6	no	—
157	C₄⋊C₄×C₄₁	—	2	6	no	—
158	C₄⋊C₄×C₄₁	—	2	1	no	—
159	C₄⋊C₄×C₄₁	—	2	3	no	—
160	C₄⋊C₄×C₄₁	—	2	3	no	—
161	C₄⋊C₄×C₄₁	—	2	3	no	—
162	C₄⋊C₄×C₄₁	—	2	3	no	—
163	C₄⋊C₄×C₄₁	—	2	6	no	—
164	C₄⋊C₄×C₄₁	—	2	6	no	—
165	C₄⋊C₄×C₄₁	C₂×D₄	1	3	yes	—
166	C₄⋊C₄×C₄₁	C₂×D₄	1	3	yes	—
167	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
168	C₄⋊C₄×C₄₁	C₂⁴	1	3	yes	—
169	C₄⋊C₄×C₄₁	C₂⁴	1	1	yes	characteristic
170	C₂²⋊C₄×C₄₁	—	2	6	no	—
171	C₂²⋊C₄×C₄₁	—	2	6	no	—
172	C₂²⋊C₄×C₄₁	—	2	3	no	—
173	C₂²⋊C₄×C₄₁	—	2	1	no	—
174	C₂²⋊C₄×C₄₁	—	2	3	no	—
175	C₂²⋊C₄×C₄₁	C₂×D₄	1	6	yes	—
176	C₄²×C₄₁	—	2	3	no	—
177	C₄²×C₄₁	—	2	3	no	—
178	C₄²×C₄₁	—	2	3	no	—
179	C₄²×C₄₁	—	2	6	no	—
180	C₄²×C₄₁	C₂×D₄	1	3	yes	—
181	C₄²×C₄₁	C₂×D₄	1	3	yes	—
182	C₄²×C₄₁	C₂⁴	1	3	yes	—
183	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
184	C₂³×C₄₁	—	2	1	no	—
185	C₂³×C₄₁	C₂²×D₄	1	3	yes	—
186	Q₈×C₄₁	—	2	6	no	—
187	Q₈×C₄₁	—	2	3	no	—
188	Q₈×C₄₁	—	2	3	no	—
189	Q₈×C₄₁	—	2	6	no	—
190	Q₈×C₄₁	—	4	6	no	—
191	Q₈×C₄₁	—	4	2	no	—
192	Q₈×C₄₁	—	8	6	no	—
193	Q₈×C₄₁	#137	1	4	yes	complemented
194	D₄×C₄₁	—	2	6	no	—
195	D₄×C₄₁	—	2	1	no	—
196	D₄×C₄₁	—	4	6	no	—
197	D₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
198	C₂×C₄×C₄₁	—	2	6	no	—
199	C₂×C₄×C₄₁	—	2	6	no	—
200	C₂×C₄×C₄₁	—	2	3	no	—
201	C₂×C₄×C₄₁	—	2	3	no	—
202	C₂×C₄×C₄₁	—	2	1	no	—
203	C₂×C₄×C₄₁	—	2	2	no	—
204	C₂×C₄×C₄₁	—	2	3	no	—
205	C₂×C₄×C₄₁	—	2	3	no	—
206	C₂×C₄×C₄₁	—	2	6	no	—
207	C₂×C₄×C₄₁	—	4	6	no	—
208	C₂×C₄×C₄₁	—	4	6	no	—
209	C₂×C₄×C₄₁	—	4	2	no	—
210	C₂×C₄×C₄₁	—	8	6	no	—
211	C₂×C₄×C₄₁	C₂²×D₄	1	3	yes	—
212	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₄₁	C₂²×D₄	1	3	yes	—
214	C₂×C₄×C₄₁	C₂²×D₄	1	3	yes	—
215	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
217	C₈×C₄₁	—	2	6	no	—
218	C₈×C₄₁	—	2	2	no	—
219	#62000	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₂²×C₄₁	—	2	3	no	—
221	C₂²×C₄₁	—	2	2	no	—
222	C₂²×C₄₁	—	2	3	no	—
223	C₂²×C₄₁	—	2	3	no	—
224	C₂²×C₄₁	—	4	1	no	—
225	C₂²×C₄₁	—	4	1	no	—
226	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
227	C₄×C₄₁	—	2	3	no	—
228	C₄×C₄₁	—	2	1	no	—
229	C₄×C₄₁	—	2	3	no	—
230	C₄×C₄₁	—	4	3	no	—
231	C₄×C₄₁	—	4	6	no	—
232	C₄×C₄₁	—	4	3	no	—
233	C₄×C₄₁	—	4	1	no	—
234	C₄×C₄₁	—	4	2	no	—
235	C₄×C₄₁	C₂×#137	1	6	yes	—
236	C₄×C₄₁	#578	1	2	yes	—
237	C₄×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
238	C₄×C₄₁	#585	1	1	yes	characteristic
239	#3503	C₂×C₄₁	1	1	yes	characteristic, complemented
240	#3482	C₂×C₄₁	1	1	yes	characteristic
241	#3395	C₂×C₄₁	1	2	yes	complemented
242	#3359	C₂×C₄₁	1	2	yes	complemented
243	#3328	C₂×C₄₁	1	6	yes	complemented
244	#3276	C₂×C₄₁	1	6	yes	complemented
245	#3255	C₂×C₄₁	1	3	yes	complemented
246	#3209	C₂×C₄₁	1	3	yes	complemented
247	#3107	C₂×C₄₁	1	3	yes	complemented
248	#3039	C₂×C₄₁	1	3	yes	complemented
249	#2991	C₂×C₄₁	1	1	yes	characteristic, complemented
250	C₂×C₄₁	—	4	3	no	—
251	C₂×C₄₁	—	4	2	no	—
252	C₂×C₄₁	#3488	1	1	yes	characteristic
253	C₂×C₄₁	C₂²×#137	1	1	yes	characteristic
254	C₂×C₄₁	C₂×#578	1	1	yes	characteristic
255	C₂×#137	C₂²×C₄₁	1	6	yes	—
256	Q₈²	—	2	1	no	—
257	#557	C₂²×C₄₁	1	2	yes	—
258	#557	C₂²×C₄₁	1	1	yes	characteristic
259	#556	C₂²×C₄₁	1	3	yes	—
260	#554	—	2	3	no	—
261	#552	—	2	3	no	—
262	D₄×Q₈	C₂²×C₄₁	1	6	yes	—
263	D₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
264	#548	—	2	1	no	—
265	#547	C₂²×C₄₁	1	3	yes	—
266	#544	—	2	3	no	—
267	#533	C₂²×C₄₁	1	3	yes	—
268	#533	C₂²×C₄₁	1	3	yes	—
269	C₂×C₄⋊Q₈	C₂²×C₄₁	1	3	yes	—
270	#529	—	2	3	no	—
271	#520	—	2	1	no	—
272	C₄×#41	C₂²×C₄₁	1	3	yes	—
273	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
274	C₂×C₄×Q₈	—	2	1	no	—
275	#494	C₂²×C₄₁	1	6	yes	—
276	#487	C₂²×C₄₁	1	6	yes	—
277	#485	C₂²×C₄₁	1	6	yes	—
278	#475	C₂²×C₄₁	1	6	yes	—
279	#475	C₂²×C₄₁	1	3	yes	—
280	#474	C₂²×C₄₁	1	1	yes	characteristic
281	#470	C₂²×C₄₁	1	12	yes	—
282	#462	C₂²×C₄₁	1	6	yes	—
283	#462	C₂²×C₄₁	1	3	yes	—
284	#462	C₂²×C₄₁	1	6	yes	—
285	#462	C₂²×C₄₁	1	6	yes	—
286	#461	C₂²×C₄₁	1	6	yes	—
287	#461	C₂²×C₄₁	1	3	yes	—
288	#452	C₂²×C₄₁	1	6	yes	—
289	#451	C₂²×C₄₁	1	12	yes	—
290	C₈×Q₈	C₂²×C₄₁	1	2	yes	—
291	C₄×Q₁₆	C₂²×C₄₁	1	6	yes	—
292	C₄×SD₁₆	C₂²×C₄₁	1	6	yes	—
293	#436	C₂²×C₄₁	1	6	yes	—
294	#431	C₂²×C₄₁	1	3	yes	—
295	#423	C₂²×C₄₁	1	3	yes	—
296	#419	C₂²×C₄₁	1	6	yes	—
297	C₄₁	#62000	1	1	yes	characteristic, direct product factor, Sylow
298	C₂×#41	D₄×C₄₁	1	1	yes	characteristic
299	C₂×#41	C₂³×C₄₁	1	3	yes	—
300	C₂²×Q₈	—	2	1	no	—
301	C₂²×Q₈	C₂³×C₄₁	1	6	yes	—
302	#137	—	4	12	no	—
303	C₂×Q₁₆	C₂³×C₄₁	1	12	yes	—
304	C₂×Q₁₆	C₂³×C₄₁	1	6	yes	—
305	C₂×SD₁₆	C₂³×C₄₁	1	6	yes	—
306	C₂×M₁₆	C₂³×C₄₁	1	6	yes	—
307	C₄⋊Q₈	—	2	6	no	—
308	C₄⋊Q₈	—	2	3	no	—
309	C₄⋊Q₈	—	2	3	no	—
310	C₄⋊Q₈	C₂³×C₄₁	1	3	yes	—
311	C₄⋊Q₈	C₂³×C₄₁	1	6	yes	—
312	C₄⋊Q₈	C₂³×C₄₁	1	3	yes	—
313	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
314	C₄⋊Q₈	C₂³×C₄₁	1	3	yes	—
315	#126	—	2	6	no	—
316	#125	—	2	3	no	—
317	#125	—	2	6	no	—
318	#125	—	2	3	no	—
319	#125	—	2	3	no	—
320	#124	—	2	3	no	—
321	#123	—	2	6	no	—
322	C₂²⋊Q₈	—	2	3	no	—
323	C₂²⋊Q₈	—	2	3	no	—
324	C₂²⋊Q₈	—	2	3	no	—
325	C₂²⋊Q₈	—	2	12	no	—
326	C₂²⋊Q₈	C₂³×C₄₁	1	6	yes	—
327	C₂²⋊Q₈	C₂³×C₄₁	1	6	yes	—
328	#121	—	2	3	no	—
329	C₄×Q₈	—	2	1	no	—
330	C₄×Q₈	—	2	2	no	—
331	C₄×Q₈	—	2	3	no	—
332	C₄×Q₈	—	2	3	no	—
333	C₄×Q₈	—	2	3	no	—
334	C₄×Q₈	D₄×C₄₁	1	1	yes	characteristic
335	C₄×Q₈	C₂³×C₄₁	1	3	yes	—
336	C₄×Q₈	C₂³×C₄₁	1	3	yes	—
337	C₄×Q₈	C₂³×C₄₁	1	6	yes	—
338	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
339	C₄×D₄	—	2	6	no	—
340	C₄×D₄	—	2	3	no	—
341	C₄×D₄	—	2	3	no	—
342	C₄×D₄	D₄×C₄₁	1	3	yes	—
343	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
344	C₄×D₄	C₂³×C₄₁	1	3	yes	—
345	C₄×D₄	C₂³×C₄₁	1	3	yes	—
346	#117	—	2	3	no	—
347	#117	—	2	3	no	—
348	#117	—	2	3	no	—
349	#117	D₄×C₄₁	1	3	yes	—
350	#117	C₂³×C₄₁	1	3	yes	—
351	C₂×C₄⋊C₄	—	2	3	no	—
352	C₂×C₄⋊C₄	—	2	3	no	—
353	C₂×C₄⋊C₄	—	2	3	no	—
354	C₂×C₄²	—	2	3	no	—
355	C₂×C₄²	C₂³×C₄₁	1	3	yes	—
356	#107	C₂³×C₄₁	1	2	yes	—
357	#106	C₂³×C₄₁	1	6	yes	—
358	C₄⋊C₈	C₂³×C₄₁	1	3	yes	—
359	C₄⋊C₈	C₂³×C₄₁	1	6	yes	—
360	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
361	#103	C₂³×C₄₁	1	6	yes	—
362	#103	C₂³×C₄₁	1	12	yes	—
363	#103	C₂³×C₄₁	1	6	yes	—
364	#103	C₂³×C₄₁	1	6	yes	—
365	#102	C₂³×C₄₁	1	2	yes	—
366	C₂²⋊C₈	C₂³×C₄₁	1	6	yes	—
367	C₄×C₈	C₂³×C₄₁	1	6	yes	—
368	#41	—	2	4	no	—
369	#41	—	2	6	no	—
370	#41	—	4	3	no	—
371	C₂×Q₈	—	2	1	no	—
372	C₂×Q₈	—	2	3	no	—
373	C₂×Q₈	—	2	6	no	—
374	C₂×Q₈	—	4	6	no	—
375	C₂×Q₈	—	4	6	no	—
376	C₂×Q₈	—	4	4	no	—
377	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
378	C₂×Q₈	C₂⁴×C₄₁	1	6	yes	—
379	C₂×Q₈	C₂⁴×C₄₁	1	3	yes	—
380	C₂×D₄	—	2	3	no	—
381	C₂×D₄	C₂×D₄×C₄₁	1	3	yes	—
382	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
383	C₂²×C₄	—	2	6	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	3	no	—
386	C₂²×C₄	—	2	3	no	—
387	C₂²×C₄	C₂×D₄×C₄₁	1	3	yes	—
388	C₂²×C₄	C₂×D₄×C₄₁	1	3	yes	—
389	C₂²×C₄	C₂⁴×C₄₁	1	3	yes	—
390	Q₁₆	—	4	6	no	—
391	Q₁₆	—	4	12	no	—
392	SD₁₆	—	2	12	no	—
393	M₁₆	—	4	6	no	—
394	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
395	C₂×C₈	C₂⁴×C₄₁	1	6	yes	—
396	C₄⋊C₄	—	2	3	no	—
397	C₄⋊C₄	—	2	3	no	—
398	C₄⋊C₄	—	2	6	no	—
399	C₄⋊C₄	—	2	3	no	—
400	C₄⋊C₄	—	2	6	no	—
401	C₄⋊C₄	—	2	6	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	3	no	—
404	C₄⋊C₄	—	2	3	no	—
405	C₄⋊C₄	—	2	3	no	—
406	C₄⋊C₄	—	2	3	no	—
407	C₄⋊C₄	—	2	6	no	—
408	C₄⋊C₄	—	2	6	no	—
409	C₄⋊C₄	C₂×D₄×C₄₁	1	3	yes	—
410	C₄⋊C₄	C₂×D₄×C₄₁	1	3	yes	—
411	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
412	C₄⋊C₄	C₂⁴×C₄₁	1	3	yes	—
413	C₄⋊C₄	C₂⁴×C₄₁	1	1	yes	characteristic
414	C₂²⋊C₄	—	2	6	no	—
415	C₂²⋊C₄	—	2	6	no	—
416	C₂²⋊C₄	—	2	3	no	—
417	C₂²⋊C₄	—	2	1	no	—
418	C₂²⋊C₄	—	2	3	no	—
419	C₂²⋊C₄	C₂×D₄×C₄₁	1	6	yes	—
420	C₄²	—	2	3	no	—
421	C₄²	—	2	3	no	—
422	C₄²	—	2	3	no	—
423	C₄²	—	2	6	no	—
424	C₄²	C₂×D₄×C₄₁	1	3	yes	—
425	C₄²	C₂×D₄×C₄₁	1	3	yes	—
426	C₄²	C₂⁴×C₄₁	1	3	yes	—
427	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
428	C₂³	—	2	1	no	—
429	C₂³	C₂²×D₄×C₄₁	1	3	yes	—
430	Q₈	—	2	6	no	—
431	Q₈	—	2	3	no	—
432	Q₈	—	2	3	no	—
433	Q₈	—	2	6	no	—
434	Q₈	—	4	6	no	—
435	Q₈	—	4	2	no	—
436	Q₈	—	8	6	no	—
437	Q₈	#137×C₄₁	1	4	yes	complemented
438	D₄	—	2	6	no	—
439	D₄	—	2	1	no	—
440	D₄	—	4	6	no	—
441	D₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
442	C₂×C₄	—	2	6	no	—
443	C₂×C₄	—	2	6	no	—
444	C₂×C₄	—	2	3	no	—
445	C₂×C₄	—	2	3	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	3	no	—
449	C₂×C₄	—	2	3	no	—
450	C₂×C₄	—	2	6	no	—
451	C₂×C₄	—	4	6	no	—
452	C₂×C₄	—	4	6	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	8	6	no	—
455	C₂×C₄	C₂²×D₄×C₄₁	1	3	yes	—
456	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
457	C₂×C₄	C₂²×D₄×C₄₁	1	3	yes	—
458	C₂×C₄	C₂²×D₄×C₄₁	1	3	yes	—
459	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
460	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
461	C₈	—	2	6	no	—
462	C₈	—	2	2	no	—
463	C₂²	—	2	3	no	—
464	C₂²	—	2	3	no	—
465	C₂²	—	2	3	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	4	1	no	—
468	C₂²	—	4	1	no	—
469	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
470	C₄	—	2	1	no	—
471	C₄	—	2	3	no	—
472	C₄	—	2	3	no	—
473	C₄	—	4	3	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	3	no	—
477	C₄	—	4	6	no	—
478	C₄	C₂×#137×C₄₁	1	6	yes	—
479	C₄	C₄₁×#578	1	2	yes	—
480	C₄	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
481	C₄	C₄₁×#585	1	1	yes	characteristic
482	C₂	—	4	3	no	—
483	C₂	—	4	2	no	—
484	C₂	C₄₁×#3488	1	1	yes	characteristic
485	C₂	C₂²×#137×C₄₁	1	1	yes	characteristic
486	C₂	C₂×C₄₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
prime radical	C₄₁×#3482	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₄×#41×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3503	C₂	semidirect
3. C₄₁×#3395	C₂	semidirect
4. C₄₁×#3359	C₂	semidirect
5. C₄₁×#3328	C₂	semidirect
6. C₄₁×#3276	C₂	semidirect
7. C₄₁×#3255	C₂	semidirect
8. C₄₁×#3209	C₂	semidirect
9. C₄₁×#3107	C₂	semidirect
10. C₄₁×#3039	C₂	semidirect
11. C₄₁×#2991	C₂	semidirect
193. Q₈×C₄₁	#137	semidirect
219. #62000	C₄₁	direct (N × H)
239. #3503	C₂×C₄₁	semidirect
241. #3395	C₂×C₄₁	semidirect
242. #3359	C₂×C₄₁	semidirect
243. #3328	C₂×C₄₁	semidirect
244. #3276	C₂×C₄₁	semidirect
245. #3255	C₂×C₄₁	semidirect
246. #3209	C₂×C₄₁	semidirect
247. #3107	C₂×C₄₁	semidirect
248. #3039	C₂×C₄₁	semidirect
249. #2991	C₂×C₄₁	semidirect
297. C₄₁	#62000	direct (N × H)
437. Q₈	#137×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3503	2
C₄₁×#3482	2
C₄₁×#3395	2
C₄₁×#3359	2
C₄₁×#3328	2
C₄₁×#3276	2
C₄₁×#3255	2
C₄₁×#3209	2
C₄₁×#3107	2
C₄₁×#3039	2
C₄₁×#2991	2
#62000	41

Subgroups — C41×#62000 #23838201

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#62000 #23838201