Subgroups — C₂×C₄₁×#3117 #23836741

Order 10496.

2150 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#529	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3117	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₄₁×#484	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₁×#481	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄₁×#479	C₂	1	2	yes	maximal, complemented
7	C₂×C₄₁×#464	C₂	1	2	yes	maximal, complemented
8	C₂×C₄₁×#451	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₁×#448	C₂	1	1	yes	maximal, characteristic
10	C₂×C₄₁×#441	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₁×#440	C₂	1	2	yes	maximal, complemented
12	C₂×C₄₁×#432	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
14	C₂²×Q₁₆×C₄₁	C₂²	1	2	yes	—
15	C₂²×SD₁₆×C₄₁	C₂²	1	2	yes	—
16	C₄₁×#529	—	2	4	no	—
17	C₄₁×#529	C₂²	1	8	yes	—
18	C₂×#126×C₄₁	—	2	1	no	—
19	C₂×#125×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×#123×C₄₁	—	2	1	no	—
22	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₄₁	—	2	1	no	—
25	C₂×C₄×Q₈×C₄₁	—	2	1	no	—
26	C₂×C₄×Q₈×C₄₁	—	2	4	no	—
27	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₄₁	C₂²	1	8	yes	complemented
31	C₂×C₄×D₄×C₄₁	—	2	1	no	—
32	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
33	C₂×#117×C₄₁	—	2	1	no	—
34	C₂²×C₄⋊C₄×C₄₁	—	2	1	no	—
35	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₄₁	—	2	1	no	—
37	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
38	C₄₁×#484	C₂²	1	8	yes	complemented
39	C₄₁×#481	C₂²	1	8	yes	—
40	C₄₁×#479	C₂²	1	16	yes	complemented
41	C₄₁×#464	C₂²	1	16	yes	complemented
42	C₄₁×#451	C₂²	1	8	yes	complemented
43	C₄₁×#448	C₂²	1	8	yes	—
44	C₄₁×#441	C₂²	1	16	yes	complemented
45	C₄₁×#440	C₂²	1	16	yes	complemented
46	C₄₁×#432	C₂²	1	8	yes	complemented
47	C₂×#107×C₄₁	C₂²	1	2	yes	—
48	C₂×#106×C₄₁	C₂²	1	2	yes	—
49	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
50	C₂×#103×C₄₁	C₂²	1	2	yes	—
51	C₂×#103×C₄₁	C₂²	1	2	yes	—
52	C₂×#103×C₄₁	C₂²	1	2	yes	—
53	C₂×#102×C₄₁	C₂²	1	2	yes	—
54	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
55	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
56	C₂×#97×C₄₁	C₂²	1	2	yes	—
57	C₂²×Q₈×C₄₁	—	2	8	no	—
58	C₂²×Q₈×C₄₁	—	2	2	no	—
59	C₂²×Q₈×C₄₁	—	2	1	no	—
60	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
61	C₂²×Q₈×C₄₁	C₂³	1	4	yes	—
62	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
63	C₂²×D₄×C₄₁	—	2	1	no	—
64	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₄₁	—	2	1	no	—
66	C₂³×C₄×C₄₁	—	2	1	no	—
67	C₂³×C₄×C₄₁	—	2	1	no	—
68	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
69	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
70	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
71	C₂×Q₁₆×C₄₁	—	2	8	no	—
72	C₂×Q₁₆×C₄₁	C₂³	1	8	yes	—
73	C₂×SD₁₆×C₄₁	—	2	8	no	—
74	C₂×SD₁₆×C₄₁	C₂³	1	8	yes	—
75	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
76	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
77	#126×C₄₁	—	2	8	no	—
78	#125×C₄₁	—	2	2	no	—
79	#125×C₄₁	C₂³	1	4	yes	—
80	#124×C₄₁	—	2	2	no	—
81	#124×C₄₁	C₂³	1	4	yes	—
82	#123×C₄₁	—	2	8	no	—
83	C₂²⋊Q₈×C₄₁	—	2	2	no	—
84	C₂²⋊Q₈×C₄₁	C₂³	1	4	yes	—
85	#121×C₄₁	—	2	2	no	—
86	#121×C₄₁	C₂³	1	4	yes	—
87	C₄×Q₈×C₄₁	—	2	4	no	—
88	C₄×Q₈×C₄₁	—	2	4	no	—
89	C₄×Q₈×C₄₁	—	2	8	no	—
90	C₄×Q₈×C₄₁	—	2	8	no	—
91	C₄×Q₈×C₄₁	—	2	2	no	—
92	C₄×Q₈×C₄₁	C₂³	1	8	yes	—
93	C₄×Q₈×C₄₁	C₂³	1	8	yes	—
94	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
95	C₄×D₄×C₄₁	—	2	8	no	—
96	C₄×D₄×C₄₁	—	2	2	no	—
97	C₄×D₄×C₄₁	C₂³	1	4	yes	—
98	#117×C₄₁	—	2	8	no	—
99	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
100	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
101	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
102	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
103	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
104	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
105	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
106	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
107	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
108	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
110	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
112	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
117	C₂×C₄²×C₄₁	—	2	2	no	—
118	C₂×C₄²×C₄₁	—	2	2	no	—
119	C₂×C₄²×C₄₁	—	2	8	no	—
120	C₂×C₄²×C₄₁	—	2	1	no	—
121	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
122	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
123	C₂×C₄²×C₄₁	D₄	1	4	yes	—
124	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
127	#107×C₄₁	C₂³	1	8	yes	—
128	#106×C₄₁	C₂³	1	8	yes	—
129	C₄⋊C₈×C₄₁	C₂³	1	8	yes	—
130	#103×C₄₁	C₂³	1	8	yes	—
131	#103×C₄₁	C₂³	1	8	yes	—
132	#103×C₄₁	C₂³	1	8	yes	—
133	#102×C₄₁	C₂³	1	8	yes	—
134	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
135	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
136	#97×C₄₁	C₂³	1	8	yes	—
137	C₂⁴×C₄₁	—	2	1	no	—
138	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
139	C₂×Q₈×C₄₁	—	2	16	no	—
140	C₂×Q₈×C₄₁	—	2	8	no	—
141	C₂×Q₈×C₄₁	—	2	16	no	—
142	C₂×Q₈×C₄₁	—	2	4	no	—
143	C₂×Q₈×C₄₁	—	2	2	no	—
144	C₂×Q₈×C₄₁	—	2	1	no	—
145	C₂×Q₈×C₄₁	—	2	4	no	—
146	C₂×Q₈×C₄₁	—	2	4	no	—
147	C₂×Q₈×C₄₁	#41	1	8	yes	—
148	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
149	C₂×Q₈×C₄₁	C₂⁴	1	4	yes	—
150	C₂×D₄×C₄₁	—	2	4	no	—
151	C₂×D₄×C₄₁	—	2	1	no	—
152	C₂×D₄×C₄₁	—	2	4	no	—
153	C₂×D₄×C₄₁	—	4	4	no	—
154	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
155	C₂²×C₄×C₄₁	—	2	8	no	—
156	C₂²×C₄×C₄₁	—	2	4	no	—
157	C₂²×C₄×C₄₁	—	2	4	no	—
158	C₂²×C₄×C₄₁	—	2	2	no	—
159	C₂²×C₄×C₄₁	—	2	4	no	—
160	C₂²×C₄×C₄₁	—	2	4	no	—
161	C₂²×C₄×C₄₁	—	2	2	no	—
162	C₂²×C₄×C₄₁	—	2	1	no	—
163	C₂²×C₄×C₄₁	—	2	1	no	—
164	C₂²×C₄×C₄₁	—	2	1	no	—
165	C₂²×C₄×C₄₁	—	2	4	no	—
166	C₂²×C₄×C₄₁	—	4	2	no	—
167	C₂²×C₄×C₄₁	—	4	4	no	—
168	C₂²×C₄×C₄₁	—	4	4	no	—
169	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
170	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
177	C₂²×C₄×C₄₁	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
179	Q₁₆×C₄₁	—	2	16	no	—
180	SD₁₆×C₄₁	—	2	16	no	—
181	C₂×C₈×C₄₁	—	2	4	no	—
182	C₂×C₈×C₄₁	—	2	4	no	—
183	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
184	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
185	C₄⋊C₄×C₄₁	—	2	8	no	—
186	C₄⋊C₄×C₄₁	—	2	8	no	—
187	C₄⋊C₄×C₄₁	—	2	4	no	—
188	C₄⋊C₄×C₄₁	—	2	2	no	—
189	C₄⋊C₄×C₄₁	—	2	4	no	—
190	C₄⋊C₄×C₄₁	—	2	4	no	—
191	C₄⋊C₄×C₄₁	—	2	4	no	—
192	C₄⋊C₄×C₄₁	—	2	4	no	—
193	C₄⋊C₄×C₄₁	—	2	1	no	—
194	C₄⋊C₄×C₄₁	—	2	1	no	—
195	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
196	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
197	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
198	C₂²⋊C₄×C₄₁	—	2	4	no	—
199	C₂²⋊C₄×C₄₁	—	2	4	no	—
200	C₂²⋊C₄×C₄₁	—	2	4	no	—
201	C₂²⋊C₄×C₄₁	—	2	4	no	—
202	C₂²⋊C₄×C₄₁	—	2	4	no	—
203	C₄²×C₄₁	—	2	8	no	—
204	C₄²×C₄₁	—	2	8	no	—
205	C₄²×C₄₁	—	2	4	no	—
206	C₄²×C₄₁	C₂×D₄	1	4	yes	—
207	C₄²×C₄₁	C₂×D₄	1	2	yes	—
208	C₄²×C₄₁	C₂×D₄	1	2	yes	—
209	C₄²×C₄₁	C₂×D₄	1	4	yes	—
210	C₄²×C₄₁	C₂⁴	1	2	yes	—
211	C₄²×C₄₁	C₂⁴	1	2	yes	—
212	C₂³×C₄₁	—	2	2	no	—
213	C₂³×C₄₁	—	2	2	no	—
214	C₂³×C₄₁	—	2	2	no	—
215	C₂³×C₄₁	—	4	2	no	—
216	C₂³×C₄₁	—	4	2	no	—
217	C₂³×C₄₁	—	4	2	no	—
218	C₂³×C₄₁	#137	1	4	yes	—
219	C₂³×C₄₁	C₂²×D₄	1	2	yes	—
220	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
221	Q₈×C₄₁	—	2	16	no	—
222	Q₈×C₄₁	—	2	8	no	—
223	Q₈×C₄₁	—	2	4	no	—
224	Q₈×C₄₁	—	2	4	no	—
225	Q₈×C₄₁	—	4	2	no	—
226	Q₈×C₄₁	C₂×#41	1	8	yes	—
227	D₄×C₄₁	—	2	4	no	—
228	D₄×C₄₁	—	4	8	no	—
229	D₄×C₄₁	—	4	2	no	—
230	C₂×C₄×C₄₁	—	2	16	no	—
231	C₂×C₄×C₄₁	—	2	8	no	—
232	C₂×C₄×C₄₁	—	2	2	no	—
233	C₂×C₄×C₄₁	—	2	8	no	—
234	C₂×C₄×C₄₁	—	2	2	no	—
235	C₂×C₄×C₄₁	—	2	2	no	—
236	C₂×C₄×C₄₁	—	2	2	no	—
237	C₂×C₄×C₄₁	—	2	2	no	—
238	C₂×C₄×C₄₁	—	2	4	no	—
239	C₂×C₄×C₄₁	—	2	4	no	—
240	C₂×C₄×C₄₁	—	2	4	no	—
241	C₂×C₄×C₄₁	—	2	4	no	—
242	C₂×C₄×C₄₁	—	2	2	no	—
243	C₂×C₄×C₄₁	—	2	2	no	—
244	C₂×C₄×C₄₁	—	2	2	no	—
245	C₂×C₄×C₄₁	—	4	4	no	—
246	C₂×C₄×C₄₁	—	4	8	no	—
247	C₂×C₄×C₄₁	—	4	8	no	—
248	C₂×C₄×C₄₁	—	4	2	no	—
249	C₂×C₄×C₄₁	—	4	2	no	—
250	C₂×C₄×C₄₁	—	4	4	no	—
251	C₂×C₄×C₄₁	—	4	2	no	—
252	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
253	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
254	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
255	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
256	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
257	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
259	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
260	C₈×C₄₁	—	2	4	no	—
261	C₈×C₄₁	—	2	4	no	—
262	C₂×#3117	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
263	C₂²×C₄₁	—	2	8	no	—
264	C₂²×C₄₁	—	2	2	no	—
265	C₂²×C₄₁	—	2	2	no	—
266	C₂²×C₄₁	—	4	2	no	—
267	C₂²×C₄₁	—	4	2	no	—
268	C₂²×C₄₁	—	4	2	no	—
269	C₂²×C₄₁	—	8	4	no	—
270	C₂²×C₄₁	#525	1	2	yes	—
271	C₂²×C₄₁	C₂×#137	1	4	yes	—
272	C₂²×C₄₁	C₂×#137	1	2	yes	—
273	C₂²×C₄₁	#575	1	2	yes	—
274	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
275	C₄×C₄₁	—	2	8	no	—
276	C₄×C₄₁	—	2	2	no	—
277	C₄×C₄₁	—	2	2	no	—
278	C₄×C₄₁	—	2	2	no	—
279	C₄×C₄₁	—	2	2	no	—
280	C₄×C₄₁	—	2	2	no	—
281	C₄×C₄₁	—	4	2	no	—
282	C₄×C₄₁	—	4	2	no	—
283	C₄×C₄₁	—	4	4	no	—
284	C₄×C₄₁	—	4	2	no	—
285	C₄×C₄₁	#525	1	2	yes	—
286	C₄×C₄₁	C₂²×#41	1	2	yes	—
287	C₂×#529	C₂×C₄₁	1	1	yes	characteristic
288	C₂²×C₄×Q₈	C₂×C₄₁	1	1	yes	characteristic, complemented
289	#3117	C₂×C₄₁	1	16	yes	direct product factor
290	C₂×#484	C₂×C₄₁	1	1	yes	characteristic, complemented
291	C₂×#481	C₂×C₄₁	1	1	yes	characteristic
292	C₂×#479	C₂×C₄₁	1	2	yes	complemented
293	C₂×#464	C₂×C₄₁	1	2	yes	complemented
294	C₂×#451	C₂×C₄₁	1	1	yes	characteristic, complemented
295	C₂×#448	C₂×C₄₁	1	1	yes	characteristic
296	C₂×#441	C₂×C₄₁	1	2	yes	complemented
297	C₂×#440	C₂×C₄₁	1	2	yes	complemented
298	C₂×#432	C₂×C₄₁	1	1	yes	characteristic, complemented
299	C₂×C₄₁	—	2	4	no	—
300	C₂×C₄₁	—	8	2	no	—
301	C₂×C₄₁	#3117	1	4	yes	direct product factor
302	C₂×C₄₁	C₂×#525	1	1	yes	characteristic
303	C₂×C₄₁	C₂²×#137	1	1	yes	characteristic
304	C₂×C₄₁	C₂×#575	1	1	yes	characteristic
305	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
306	C₂²×Q₁₆	C₂²×C₄₁	1	2	yes	—
307	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	—
308	#529	—	2	4	no	—
309	#529	C₂²×C₄₁	1	8	yes	—
310	C₂×#126	—	2	1	no	—
311	C₂×#125	C₂²×C₄₁	1	1	yes	characteristic
312	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
313	C₂×#123	—	2	1	no	—
314	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
315	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
316	C₂×C₄×Q₈	—	2	1	no	—
317	C₂×C₄×Q₈	—	2	1	no	—
318	C₂×C₄×Q₈	—	2	4	no	—
319	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
320	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
321	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
322	C₂×C₄×Q₈	C₂²×C₄₁	1	8	yes	complemented
323	C₂×C₄×D₄	—	2	1	no	—
324	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
325	C₂×#117	—	2	1	no	—
326	C₂²×C₄⋊C₄	—	2	1	no	—
327	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
328	C₂²×C₄²	—	2	1	no	—
329	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
330	#484	C₂²×C₄₁	1	8	yes	complemented
331	#481	C₂²×C₄₁	1	8	yes	—
332	#479	C₂²×C₄₁	1	16	yes	complemented
333	#464	C₂²×C₄₁	1	16	yes	complemented
334	#451	C₂²×C₄₁	1	8	yes	complemented
335	#448	C₂²×C₄₁	1	8	yes	—
336	#441	C₂²×C₄₁	1	16	yes	complemented
337	#440	C₂²×C₄₁	1	16	yes	complemented
338	#432	C₂²×C₄₁	1	8	yes	complemented
339	C₂×#107	C₂²×C₄₁	1	2	yes	—
340	C₂×#106	C₂²×C₄₁	1	2	yes	—
341	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
342	C₂×#103	C₂²×C₄₁	1	2	yes	—
343	C₂×#103	C₂²×C₄₁	1	2	yes	—
344	C₂×#103	C₂²×C₄₁	1	2	yes	—
345	C₂×#102	C₂²×C₄₁	1	2	yes	—
346	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
347	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
348	C₂×#97	C₂²×C₄₁	1	2	yes	—
349	C₄₁	C₂×#3117	1	1	yes	characteristic, direct product factor, Sylow
350	C₂²×Q₈	—	2	8	no	—
351	C₂²×Q₈	—	2	1	no	—
352	C₂²×Q₈	—	2	2	no	—
353	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
354	C₂²×Q₈	C₂³×C₄₁	1	4	yes	—
355	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
356	C₂²×D₄	—	2	1	no	—
357	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
358	C₂³×C₄	—	2	1	no	—
359	C₂³×C₄	—	2	1	no	—
360	C₂³×C₄	—	2	1	no	—
361	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
362	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
363	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
364	C₂×Q₁₆	—	2	8	no	—
365	C₂×Q₁₆	C₂³×C₄₁	1	8	yes	—
366	C₂×SD₁₆	—	2	8	no	—
367	C₂×SD₁₆	C₂³×C₄₁	1	8	yes	—
368	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
369	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
370	#126	—	2	8	no	—
371	#125	—	2	2	no	—
372	#125	C₂³×C₄₁	1	4	yes	—
373	#124	—	2	2	no	—
374	#124	C₂³×C₄₁	1	4	yes	—
375	#123	—	2	8	no	—
376	C₂²⋊Q₈	—	2	2	no	—
377	C₂²⋊Q₈	C₂³×C₄₁	1	4	yes	—
378	#121	—	2	2	no	—
379	#121	C₂³×C₄₁	1	4	yes	—
380	C₄×Q₈	—	2	4	no	—
381	C₄×Q₈	—	2	4	no	—
382	C₄×Q₈	—	2	8	no	—
383	C₄×Q₈	—	2	8	no	—
384	C₄×Q₈	—	2	2	no	—
385	C₄×Q₈	C₂³×C₄₁	1	8	yes	—
386	C₄×Q₈	C₂³×C₄₁	1	8	yes	—
387	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
388	C₄×D₄	—	2	8	no	—
389	C₄×D₄	—	2	2	no	—
390	C₄×D₄	C₂³×C₄₁	1	4	yes	—
391	#117	—	2	8	no	—
392	C₂×C₄⋊C₄	—	2	2	no	—
393	C₂×C₄⋊C₄	—	2	2	no	—
394	C₂×C₄⋊C₄	—	2	8	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	—	2	2	no	—
397	C₂×C₄⋊C₄	—	2	1	no	—
398	C₂×C₄⋊C₄	—	2	1	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
402	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
403	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
405	C₂×C₂²⋊C₄	—	2	1	no	—
406	C₂×C₂²⋊C₄	—	2	1	no	—
407	C₂×C₂²⋊C₄	—	2	1	no	—
408	C₂×C₂²⋊C₄	—	2	1	no	—
409	C₂×C₂²⋊C₄	—	2	1	no	—
410	C₂×C₄²	—	2	1	no	—
411	C₂×C₄²	—	2	2	no	—
412	C₂×C₄²	—	2	2	no	—
413	C₂×C₄²	—	2	8	no	—
414	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
415	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
416	C₂×C₄²	D₄×C₄₁	1	4	yes	—
417	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
418	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
419	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
420	#107	C₂³×C₄₁	1	8	yes	—
421	#106	C₂³×C₄₁	1	8	yes	—
422	C₄⋊C₈	C₂³×C₄₁	1	8	yes	—
423	#103	C₂³×C₄₁	1	8	yes	—
424	#103	C₂³×C₄₁	1	8	yes	—
425	#103	C₂³×C₄₁	1	8	yes	—
426	#102	C₂³×C₄₁	1	8	yes	—
427	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
428	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
429	#97	C₂³×C₄₁	1	8	yes	—
430	C₂⁴	—	2	1	no	—
431	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
432	C₂×Q₈	—	2	16	no	—
433	C₂×Q₈	—	2	8	no	—
434	C₂×Q₈	—	2	16	no	—
435	C₂×Q₈	—	2	4	no	—
436	C₂×Q₈	—	2	2	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	—	2	4	no	—
439	C₂×Q₈	—	2	4	no	—
440	C₂×Q₈	#41×C₄₁	1	8	yes	—
441	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
442	C₂×Q₈	C₂⁴×C₄₁	1	4	yes	—
443	C₂×D₄	—	2	4	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	4	no	—
446	C₂×D₄	—	4	4	no	—
447	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
448	C₂²×C₄	—	2	8	no	—
449	C₂²×C₄	—	2	4	no	—
450	C₂²×C₄	—	2	4	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	4	no	—
453	C₂²×C₄	—	2	4	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	4	no	—
459	C₂²×C₄	—	4	2	no	—
460	C₂²×C₄	—	4	4	no	—
461	C₂²×C₄	—	4	4	no	—
462	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
463	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
464	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
465	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
466	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
467	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
468	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
470	C₂²×C₄	C₂⁴×C₄₁	1	2	yes	—
471	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
472	Q₁₆	—	2	16	no	—
473	SD₁₆	—	2	16	no	—
474	C₂×C₈	—	2	4	no	—
475	C₂×C₈	—	2	4	no	—
476	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
477	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
478	C₄⋊C₄	—	2	8	no	—
479	C₄⋊C₄	—	2	8	no	—
480	C₄⋊C₄	—	2	4	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	4	no	—
483	C₄⋊C₄	—	2	4	no	—
484	C₄⋊C₄	—	2	4	no	—
485	C₄⋊C₄	—	2	4	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
489	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
490	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
491	C₂²⋊C₄	—	2	4	no	—
492	C₂²⋊C₄	—	2	4	no	—
493	C₂²⋊C₄	—	2	4	no	—
494	C₂²⋊C₄	—	2	4	no	—
495	C₂²⋊C₄	—	2	4	no	—
496	C₄²	—	2	8	no	—
497	C₄²	—	2	8	no	—
498	C₄²	—	2	4	no	—
499	C₄²	C₂×D₄×C₄₁	1	4	yes	—
500	C₄²	C₂×D₄×C₄₁	1	2	yes	—
501	C₄²	C₂×D₄×C₄₁	1	2	yes	—
502	C₄²	C₂×D₄×C₄₁	1	4	yes	—
503	C₄²	C₂⁴×C₄₁	1	2	yes	—
504	C₄²	C₂⁴×C₄₁	1	2	yes	—
505	C₂³	—	2	2	no	—
506	C₂³	—	2	2	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	4	2	no	—
509	C₂³	—	4	2	no	—
510	C₂³	—	4	2	no	—
511	C₂³	#137×C₄₁	1	4	yes	—
512	C₂³	C₂²×D₄×C₄₁	1	2	yes	—
513	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
514	Q₈	—	2	16	no	—
515	Q₈	—	2	8	no	—
516	Q₈	—	2	4	no	—
517	Q₈	—	2	4	no	—
518	Q₈	—	4	2	no	—
519	Q₈	C₂×#41×C₄₁	1	8	yes	—
520	D₄	—	2	4	no	—
521	D₄	—	4	8	no	—
522	D₄	—	4	2	no	—
523	C₂×C₄	—	2	16	no	—
524	C₂×C₄	—	2	8	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	8	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	4	4	no	—
539	C₂×C₄	—	4	8	no	—
540	C₂×C₄	—	4	8	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	4	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
546	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
547	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
548	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
549	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
550	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
551	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
552	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
553	C₈	—	2	4	no	—
554	C₈	—	2	4	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	8	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	2	no	—
561	C₂²	—	8	4	no	—
562	C₂²	C₄₁×#525	1	2	yes	—
563	C₂²	C₂×#137×C₄₁	1	4	yes	—
564	C₂²	C₂×#137×C₄₁	1	2	yes	—
565	C₂²	C₄₁×#575	1	2	yes	—
566	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
567	C₄	—	2	2	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	2	no	—
570	C₄	—	2	2	no	—
571	C₄	—	2	8	no	—
572	C₄	—	2	2	no	—
573	C₄	—	4	2	no	—
574	C₄	—	4	4	no	—
575	C₄	—	4	2	no	—
576	C₄	—	4	2	no	—
577	C₄	C₄₁×#525	1	2	yes	—
578	C₄	C₂²×#41×C₄₁	1	2	yes	—
579	C₂	—	2	4	no	—
580	C₂	—	8	2	no	—
581	C₂	C₄₁×#3117	1	4	yes	direct product factor
582	C₂	C₂×C₄₁×#525	1	1	yes	characteristic
583	C₂	C₂²×#137×C₄₁	1	1	yes	characteristic
584	C₂	C₂×C₄₁×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
prime radical	C₂×#121×C₄₁	C₂²
LCS	G ▷ C₂×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
2. C₂²×C₄×Q₈×C₄₁	C₂	semidirect
3. C₄₁×#3117	C₂	direct (N × H)
4. C₂×C₄₁×#484	C₂	semidirect
6. C₂×C₄₁×#479	C₂	semidirect
7. C₂×C₄₁×#464	C₂	semidirect
8. C₂×C₄₁×#451	C₂	semidirect
10. C₂×C₄₁×#441	C₂	semidirect
11. C₂×C₄₁×#440	C₂	semidirect
12. C₂×C₄₁×#432	C₂	semidirect
30. C₂×C₄×Q₈×C₄₁	C₂²	semidirect
38. C₄₁×#484	C₂²	semidirect
40. C₄₁×#479	C₂²	semidirect
41. C₄₁×#464	C₂²	semidirect
42. C₄₁×#451	C₂²	semidirect
44. C₄₁×#441	C₂²	semidirect
45. C₄₁×#440	C₂²	semidirect
46. C₄₁×#432	C₂²	semidirect
262. C₂×#3117	C₄₁	direct (N × H)
288. C₂²×C₄×Q₈	C₂×C₄₁	semidirect
289. #3117	C₂×C₄₁	direct (N × H)
290. C₂×#484	C₂×C₄₁	semidirect
292. C₂×#479	C₂×C₄₁	semidirect
293. C₂×#464	C₂×C₄₁	semidirect
294. C₂×#451	C₂×C₄₁	semidirect
296. C₂×#441	C₂×C₄₁	semidirect
297. C₂×#440	C₂×C₄₁	semidirect
298. C₂×#432	C₂×C₄₁	semidirect
301. C₂×C₄₁	#3117	direct (N × H)
322. C₂×C₄×Q₈	C₂²×C₄₁	semidirect
330. #484	C₂²×C₄₁	semidirect
332. #479	C₂²×C₄₁	semidirect
333. #464	C₂²×C₄₁	semidirect
334. #451	C₂²×C₄₁	semidirect
336. #441	C₂²×C₄₁	semidirect
337. #440	C₂²×C₄₁	semidirect
338. #432	C₂²×C₄₁	semidirect
349. C₄₁	C₂×#3117	direct (N × H)
581. C₂	C₄₁×#3117	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×#529	2
C₂²×C₄×Q₈×C₄₁	2
C₄₁×#3117	2
C₂×C₄₁×#484	2
C₂×C₄₁×#481	2
C₂×C₄₁×#479	2
C₂×C₄₁×#464	2
C₂×C₄₁×#451	2
C₂×C₄₁×#448	2
C₂×C₄₁×#441	2
C₂×C₄₁×#440	2
C₂×C₄₁×#432	2
C₂×#3117	41

Subgroups — C2×C41×#3117 #23836741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#3117 #23836741