Subgroups — C₄₁×#17778 #23793979

Order 10496.

868 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3509	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2991	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2990	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#1561	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1559	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1554	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1550	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1548	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1548	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1544	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1542	C₂	1	2	yes	maximal, complemented
12	C₄₁×#557	—	2	1	no	—
13	C₄₁×#557	—	2	1	no	—
14	C₄₁×#556	—	2	1	no	—
15	C₄₁×#556	—	2	1	no	—
16	C₄₁×#552	—	2	2	no	—
17	C₄₁×#552	—	2	2	no	—
18	C₄₁×#541	C₄	1	4	yes	—
19	C₄₁×#536	C₄	1	2	yes	—
20	C₄₁×#533	C₂²	1	2	yes	—
21	C₄₁×#533	C₂²	1	2	yes	—
22	C₄₁×#533	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
24	C₄₁×#519	C₄	1	2	yes	—
25	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
26	C₄₁×#446	—	2	1	no	—
27	C₈×Q₈×C₄₁	—	2	1	no	—
28	C₄₁×#436	—	2	2	no	—
29	C₄₁×#436	—	2	1	no	—
30	C₄₁×#435	—	2	2	no	—
31	C₈×D₄×C₄₁	—	2	1	no	—
32	C₄₁×#432	C₂²	1	2	yes	—
33	C₄₁×#431	C₂²	1	2	yes	—
34	C₄₁×#431	C₂²	1	1	yes	characteristic
35	C₄₁×#431	C₂²	1	1	yes	characteristic
36	C₄₁×#423	C₂²	1	1	yes	characteristic
37	C₄₁×#423	C₂²	1	1	yes	characteristic
38	C₄₁×#423	C₂²	1	2	yes	—
39	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
40	C₄₁×#333	C₂²	1	2	yes	—
41	C₄₁×#333	C₂²	1	2	yes	—
42	C₄₁×#333	C₂²	1	2	yes	—
43	C₄₁×#333	C₂²	1	2	yes	—
44	C₄₁×#332	C₂²	1	1	yes	characteristic
45	C₄₁×#332	C₂²	1	2	yes	—
46	C₄₁×#332	C₂²	1	1	yes	characteristic
47	C₄₁×#332	C₂²	1	1	yes	characteristic
48	C₄₁×#332	C₂²	1	1	yes	characteristic
49	C₄₁×#332	C₂²	1	2	yes	—
50	C₂×#41×C₄₁	C₂×C₄	1	1	yes	characteristic
51	C₂²×Q₈×C₄₁	C₂×C₄	1	2	yes	—
52	C₂×M₁₆×C₄₁	—	2	1	no	—
53	C₂×M₁₆×C₄₁	—	2	1	no	—
54	C₂×M₁₆×C₄₁	—	2	2	no	—
55	C₂²×C₈×C₄₁	—	2	2	no	—
56	C₄⋊Q₈×C₄₁	—	2	2	no	—
57	C₄⋊Q₈×C₄₁	—	2	1	no	—
58	C₄⋊Q₈×C₄₁	—	2	1	no	—
59	C₄⋊Q₈×C₄₁	C₂×C₄	1	2	yes	—
60	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
61	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
62	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
63	#126×C₄₁	—	2	4	no	—
64	#126×C₄₁	—	2	4	no	—
65	#125×C₄₁	—	2	4	no	—
66	#125×C₄₁	—	2	4	no	—
67	#125×C₄₁	—	2	2	no	—
68	#125×C₄₁	—	2	2	no	—
69	#125×C₄₁	C₂×C₄	1	2	yes	—
70	#124×C₄₁	—	2	2	no	—
71	#123×C₄₁	—	2	4	no	—
72	C₂²⋊Q₈×C₄₁	—	2	1	no	—
73	C₂²⋊Q₈×C₄₁	—	2	1	no	—
74	C₂²⋊Q₈×C₄₁	—	2	2	no	—
75	C₂²⋊Q₈×C₄₁	—	2	2	no	—
76	C₂²⋊Q₈×C₄₁	C₂×C₄	1	4	yes	—
77	C₂²⋊Q₈×C₄₁	C₂×C₄	1	4	yes	—
78	C₄×Q₈×C₄₁	—	2	2	no	—
79	C₄×Q₈×C₄₁	—	2	2	no	—
80	C₄×Q₈×C₄₁	—	2	2	no	—
81	C₄×Q₈×C₄₁	—	2	2	no	—
82	C₄×Q₈×C₄₁	—	2	1	no	—
83	C₄×Q₈×C₄₁	—	2	1	no	—
84	C₄×Q₈×C₄₁	C₂×C₄	1	4	yes	—
85	C₄×Q₈×C₄₁	C₂×C₄	1	4	yes	—
86	C₄×Q₈×C₄₁	D₄	1	1	yes	characteristic
87	C₄×Q₈×C₄₁	D₄	1	1	yes	characteristic
88	C₄×D₄×C₄₁	D₄	1	2	yes	—
89	C₄×D₄×C₄₁	D₄	1	2	yes	—
90	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
91	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
92	#117×C₄₁	—	2	2	no	—
93	#117×C₄₁	—	2	2	no	—
94	#117×C₄₁	—	2	4	no	—
95	#117×C₄₁	C₂×C₄	1	2	yes	—
96	#117×C₄₁	C₂×C₄	1	1	yes	characteristic
97	#117×C₄₁	C₂×C₄	1	2	yes	—
98	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
99	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
100	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
102	C₄⋊C₈×C₄₁	—	2	2	no	—
103	C₄⋊C₈×C₄₁	—	2	1	no	—
104	C₄⋊C₈×C₄₁	—	2	2	no	—
105	C₄⋊C₈×C₄₁	—	2	1	no	—
106	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
107	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
108	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
109	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
110	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
111	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
112	C₂²⋊C₈×C₄₁	—	2	1	no	—
113	C₂²⋊C₈×C₄₁	—	2	1	no	—
114	C₂²⋊C₈×C₄₁	—	2	2	no	—
115	C₂²⋊C₈×C₄₁	—	2	2	no	—
116	#97×C₄₁	—	2	2	no	—
117	C₄×C₈×C₄₁	—	2	1	no	—
118	C₄×C₈×C₄₁	—	2	2	no	—
119	C₄×C₈×C₄₁	—	2	1	no	—
120	#41×C₄₁	—	4	2	no	—
121	C₂×Q₈×C₄₁	—	2	2	no	—
122	C₂×Q₈×C₄₁	—	2	1	no	—
123	C₂×Q₈×C₄₁	—	2	1	no	—
124	C₂×Q₈×C₄₁	—	4	4	no	—
125	C₂×Q₈×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
126	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	—
127	C₂×D₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
128	C₂×D₄×C₄₁	C₂²⋊C₄	1	2	yes	—
129	C₂²×C₄×C₄₁	—	2	2	no	—
130	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
132	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
136	M₁₆×C₄₁	—	8	1	no	—
137	M₁₆×C₄₁	—	8	1	no	—
138	M₁₆×C₄₁	—	8	2	no	—
139	C₂×C₈×C₄₁	—	2	1	no	—
140	C₂×C₈×C₄₁	—	2	1	no	—
141	C₂×C₈×C₄₁	—	2	1	no	—
142	C₂×C₈×C₄₁	—	2	2	no	—
143	C₂×C₈×C₄₁	—	2	1	no	—
144	C₂×C₈×C₄₁	—	2	2	no	—
145	C₂×C₈×C₄₁	—	8	2	no	—
146	C₄⋊C₄×C₄₁	—	2	2	no	—
147	C₄⋊C₄×C₄₁	—	2	2	no	—
148	C₄⋊C₄×C₄₁	—	2	4	no	—
149	C₄⋊C₄×C₄₁	—	2	4	no	—
150	C₄⋊C₄×C₄₁	—	2	2	no	—
151	C₄⋊C₄×C₄₁	—	2	2	no	—
152	C₄⋊C₄×C₄₁	—	2	4	no	—
153	C₄⋊C₄×C₄₁	—	2	4	no	—
154	C₄⋊C₄×C₄₁	—	2	2	no	—
155	C₄⋊C₄×C₄₁	—	2	2	no	—
156	C₄⋊C₄×C₄₁	—	2	1	no	—
157	C₄⋊C₄×C₄₁	—	2	1	no	—
158	C₄⋊C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
159	C₄⋊C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
160	C₄⋊C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
161	C₄⋊C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
162	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
163	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
164	C₂²⋊C₄×C₄₁	—	2	2	no	—
165	C₂²⋊C₄×C₄₁	—	2	4	no	—
166	C₂²⋊C₄×C₄₁	—	2	4	no	—
167	C₂²⋊C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
168	C₂²⋊C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
169	C₂²⋊C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
170	C₄²×C₄₁	—	2	4	no	—
171	C₄²×C₄₁	—	2	4	no	—
172	C₄²×C₄₁	—	2	2	no	—
173	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
174	C₄²×C₄₁	C₂²×C₄	1	1	yes	characteristic
175	C₄²×C₄₁	C₂×D₄	1	2	yes	—
176	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₄₁	C₂×D₄	1	2	yes	—
179	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
180	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
181	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	Q₈×C₄₁	—	2	2	no	—
183	Q₈×C₄₁	—	4	4	no	—
184	Q₈×C₄₁	—	4	1	no	—
185	Q₈×C₄₁	—	4	1	no	—
186	Q₈×C₄₁	—	4	1	no	—
187	Q₈×C₄₁	—	4	1	no	—
188	Q₈×C₄₁	—	4	4	no	—
189	D₄×C₄₁	—	2	2	no	—
190	D₄×C₄₁	—	4	2	no	—
191	C₂×C₄×C₄₁	—	2	2	no	—
192	C₂×C₄×C₄₁	—	2	1	no	—
193	C₂×C₄×C₄₁	—	2	1	no	—
194	C₂×C₄×C₄₁	—	2	2	no	—
195	C₂×C₄×C₄₁	—	2	1	no	—
196	C₂×C₄×C₄₁	—	2	1	no	—
197	C₂×C₄×C₄₁	—	2	2	no	—
198	C₂×C₄×C₄₁	—	2	2	no	—
199	C₂×C₄×C₄₁	—	2	2	no	—
200	C₂×C₄×C₄₁	—	2	2	no	—
201	C₂×C₄×C₄₁	—	2	2	no	—
202	C₂×C₄×C₄₁	—	2	4	no	—
203	C₂×C₄×C₄₁	—	4	2	no	—
204	C₂×C₄×C₄₁	—	4	4	no	—
205	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
206	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
207	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
210	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
212	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
214	C₈×C₄₁	—	4	1	no	—
215	C₈×C₄₁	—	4	2	no	—
216	C₈×C₄₁	—	4	2	no	—
217	C₈×C₄₁	—	4	1	no	—
218	C₈×C₄₁	—	4	1	no	—
219	C₈×C₄₁	—	4	1	no	—
220	#17778	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
221	C₂²×C₄₁	—	2	1	no	—
222	C₂²×C₄₁	—	2	2	no	—
223	C₂²×C₄₁	—	2	2	no	—
224	C₂²×C₄₁	—	2	2	no	—
225	C₂²×C₄₁	—	2	1	no	—
226	C₂²×C₄₁	—	2	1	no	—
227	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
228	C₄×C₄₁	—	2	1	no	—
229	C₄×C₄₁	—	2	2	no	—
230	C₄×C₄₁	—	2	2	no	—
231	C₄×C₄₁	—	2	2	no	—
232	C₄×C₄₁	—	2	1	no	—
233	C₄×C₄₁	—	2	1	no	—
234	C₄×C₄₁	—	4	4	no	—
235	C₄×C₄₁	—	4	2	no	—
236	C₄×C₄₁	—	4	2	no	—
237	C₄×C₄₁	#413	1	2	yes	—
238	C₄×C₄₁	#577	1	1	yes	characteristic
239	C₄×C₄₁	#577	1	1	yes	characteristic
240	C₄×C₄₁	#578	1	1	yes	characteristic
241	C₄×C₄₁	#578	1	1	yes	characteristic
242	#3509	C₂×C₄₁	1	1	yes	characteristic
243	#2991	C₂×C₄₁	1	1	yes	characteristic
244	#2990	C₂×C₄₁	1	1	yes	characteristic
245	#1561	C₂×C₄₁	1	1	yes	characteristic, complemented
246	#1559	C₂×C₄₁	1	2	yes	complemented
247	#1554	C₂×C₄₁	1	2	yes	complemented
248	#1550	C₂×C₄₁	1	2	yes	complemented
249	#1548	C₂×C₄₁	1	1	yes	characteristic, complemented
250	#1548	C₂×C₄₁	1	1	yes	characteristic, complemented
251	#1544	C₂×C₄₁	1	1	yes	characteristic, complemented
252	#1542	C₂×C₄₁	1	2	yes	complemented
253	C₂×C₄₁	—	4	1	no	—
254	C₂×C₄₁	—	4	2	no	—
255	C₂×C₄₁	C₂×#413	1	1	yes	characteristic
256	C₂×C₄₁	#2898	1	1	yes	characteristic
257	C₂×C₄₁	#2898	1	1	yes	characteristic
258	#557	—	2	1	no	—
259	#557	—	2	1	no	—
260	#556	—	2	1	no	—
261	#556	—	2	1	no	—
262	#552	—	2	2	no	—
263	#552	—	2	2	no	—
264	#541	C₄×C₄₁	1	4	yes	—
265	#536	C₄×C₄₁	1	2	yes	—
266	#533	C₂²×C₄₁	1	2	yes	—
267	#533	C₂²×C₄₁	1	2	yes	—
268	#533	C₂²×C₄₁	1	1	yes	characteristic
269	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
270	#519	C₄×C₄₁	1	2	yes	—
271	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
272	#446	—	2	1	no	—
273	C₈×Q₈	—	2	1	no	—
274	#436	—	2	2	no	—
275	#436	—	2	1	no	—
276	#435	—	2	2	no	—
277	C₈×D₄	—	2	1	no	—
278	#432	C₂²×C₄₁	1	2	yes	—
279	#431	C₂²×C₄₁	1	2	yes	—
280	#431	C₂²×C₄₁	1	1	yes	characteristic
281	#431	C₂²×C₄₁	1	1	yes	characteristic
282	#423	C₂²×C₄₁	1	1	yes	characteristic
283	#423	C₂²×C₄₁	1	1	yes	characteristic
284	#423	C₂²×C₄₁	1	2	yes	—
285	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
286	#333	C₂²×C₄₁	1	2	yes	—
287	#333	C₂²×C₄₁	1	2	yes	—
288	#333	C₂²×C₄₁	1	2	yes	—
289	#333	C₂²×C₄₁	1	2	yes	—
290	#332	C₂²×C₄₁	1	1	yes	characteristic
291	#332	C₂²×C₄₁	1	2	yes	—
292	#332	C₂²×C₄₁	1	1	yes	characteristic
293	#332	C₂²×C₄₁	1	1	yes	characteristic
294	#332	C₂²×C₄₁	1	1	yes	characteristic
295	#332	C₂²×C₄₁	1	2	yes	—
296	C₄₁	#17778	1	1	yes	characteristic, direct product factor, Sylow
297	C₂×#41	C₂×C₄×C₄₁	1	1	yes	characteristic
298	C₂²×Q₈	C₂×C₄×C₄₁	1	2	yes	—
299	C₂×M₁₆	—	2	1	no	—
300	C₂×M₁₆	—	2	1	no	—
301	C₂×M₁₆	—	2	2	no	—
302	C₂²×C₈	—	2	2	no	—
303	C₄⋊Q₈	—	2	2	no	—
304	C₄⋊Q₈	—	2	1	no	—
305	C₄⋊Q₈	—	2	1	no	—
306	C₄⋊Q₈	C₂×C₄×C₄₁	1	2	yes	—
307	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
308	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
309	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
310	#126	—	2	4	no	—
311	#126	—	2	4	no	—
312	#125	—	2	4	no	—
313	#125	—	2	4	no	—
314	#125	—	2	2	no	—
315	#125	—	2	2	no	—
316	#125	C₂×C₄×C₄₁	1	2	yes	—
317	#124	—	2	2	no	—
318	#123	—	2	4	no	—
319	C₂²⋊Q₈	—	2	1	no	—
320	C₂²⋊Q₈	—	2	1	no	—
321	C₂²⋊Q₈	—	2	2	no	—
322	C₂²⋊Q₈	—	2	2	no	—
323	C₂²⋊Q₈	C₂×C₄×C₄₁	1	4	yes	—
324	C₂²⋊Q₈	C₂×C₄×C₄₁	1	4	yes	—
325	C₄×Q₈	—	2	2	no	—
326	C₄×Q₈	—	2	2	no	—
327	C₄×Q₈	—	2	2	no	—
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	—	2	1	no	—
330	C₄×Q₈	—	2	1	no	—
331	C₄×Q₈	C₂×C₄×C₄₁	1	4	yes	—
332	C₄×Q₈	C₂×C₄×C₄₁	1	4	yes	—
333	C₄×Q₈	D₄×C₄₁	1	1	yes	characteristic
334	C₄×Q₈	D₄×C₄₁	1	1	yes	characteristic
335	C₄×D₄	D₄×C₄₁	1	2	yes	—
336	C₄×D₄	D₄×C₄₁	1	2	yes	—
337	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
338	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
339	#117	—	2	2	no	—
340	#117	—	2	2	no	—
341	#117	—	2	4	no	—
342	#117	C₂×C₄×C₄₁	1	2	yes	—
343	#117	C₂×C₄×C₄₁	1	1	yes	characteristic
344	#117	C₂×C₄×C₄₁	1	2	yes	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
348	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
349	C₄⋊C₈	—	2	2	no	—
350	C₄⋊C₈	—	2	1	no	—
351	C₄⋊C₈	—	2	2	no	—
352	C₄⋊C₈	—	2	1	no	—
353	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
354	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
355	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
356	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
357	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
358	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
359	C₂²⋊C₈	—	2	1	no	—
360	C₂²⋊C₈	—	2	1	no	—
361	C₂²⋊C₈	—	2	2	no	—
362	C₂²⋊C₈	—	2	2	no	—
363	#97	—	2	2	no	—
364	C₄×C₈	—	2	1	no	—
365	C₄×C₈	—	2	2	no	—
366	C₄×C₈	—	2	1	no	—
367	#41	—	4	2	no	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	—	2	1	no	—
371	C₂×Q₈	—	4	4	no	—
372	C₂×Q₈	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
373	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	—
374	C₂×D₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
375	C₂×D₄	C₂²⋊C₄×C₄₁	1	2	yes	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
378	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
379	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
382	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
383	M₁₆	—	8	1	no	—
384	M₁₆	—	8	1	no	—
385	M₁₆	—	8	2	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	8	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	4	no	—
396	C₄⋊C₄	—	2	4	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	4	no	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
406	C₄⋊C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
407	C₄⋊C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
408	C₄⋊C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
409	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
410	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	2	4	no	—
413	C₂²⋊C₄	—	2	4	no	—
414	C₂²⋊C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
415	C₂²⋊C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
416	C₂²⋊C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
417	C₄²	—	2	4	no	—
418	C₄²	—	2	4	no	—
419	C₄²	—	2	2	no	—
420	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
421	C₄²	C₂²×C₄×C₄₁	1	1	yes	characteristic
422	C₄²	C₂×D₄×C₄₁	1	2	yes	—
423	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
424	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
425	C₄²	C₂×D₄×C₄₁	1	2	yes	—
426	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
427	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
428	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
429	Q₈	—	2	2	no	—
430	Q₈	—	4	4	no	—
431	Q₈	—	4	1	no	—
432	Q₈	—	4	1	no	—
433	Q₈	—	4	1	no	—
434	Q₈	—	4	1	no	—
435	Q₈	—	4	4	no	—
436	D₄	—	2	2	no	—
437	D₄	—	4	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	4	no	—
452	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
453	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
454	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
455	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
456	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
457	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
458	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
459	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
460	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
461	C₈	—	4	1	no	—
462	C₈	—	4	2	no	—
463	C₈	—	4	2	no	—
464	C₈	—	4	1	no	—
465	C₈	—	4	1	no	—
466	C₈	—	4	1	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	2	1	no	—
473	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
474	C₄	—	2	1	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	2	2	no	—
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	4	4	no	—
481	C₄	—	4	2	no	—
482	C₄	—	4	2	no	—
483	C₄	C₄₁×#413	1	2	yes	—
484	C₄	C₄₁×#577	1	1	yes	characteristic
485	C₄	C₄₁×#577	1	1	yes	characteristic
486	C₄	C₄₁×#578	1	1	yes	characteristic
487	C₄	C₄₁×#578	1	1	yes	characteristic
488	C₂	—	4	1	no	—
489	C₂	—	4	2	no	—
490	C₂	C₂×C₄₁×#413	1	1	yes	characteristic
491	C₂	C₄₁×#2898	1	1	yes	characteristic
492	C₂	C₄₁×#2898	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₄²	C₂⁴×C₄₁
prime radical	C₂×#41×C₄₁	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ 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
4. C₄₁×#1561	C₂	semidirect
5. C₄₁×#1559	C₂	semidirect
6. C₄₁×#1554	C₂	semidirect
7. C₄₁×#1550	C₂	semidirect
8. C₄₁×#1548	C₂	semidirect
9. C₄₁×#1548	C₂	semidirect
10. C₄₁×#1544	C₂	semidirect
11. C₄₁×#1542	C₂	semidirect
220. #17778	C₄₁	direct (N × H)
245. #1561	C₂×C₄₁	semidirect
246. #1559	C₂×C₄₁	semidirect
247. #1554	C₂×C₄₁	semidirect
248. #1550	C₂×C₄₁	semidirect
249. #1548	C₂×C₄₁	semidirect
250. #1548	C₂×C₄₁	semidirect
251. #1544	C₂×C₄₁	semidirect
252. #1542	C₂×C₄₁	semidirect
296. C₄₁	#17778	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×#3509	2
C₄₁×#2991	2
C₄₁×#2990	2
C₄₁×#1561	2
C₄₁×#1559	2
C₄₁×#1554	2
C₄₁×#1550	2
C₄₁×#1548	2
C₄₁×#1544	2
C₄₁×#1542	2
#17778	41

Subgroups — C41×#17778 #23793979

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#17778 #23793979