Subgroups — C₂×C₄₁×#3325 #23837346

Order 10496.

2630 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄²×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3325	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₄₁×#486	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₁×#482	C₂	1	2	yes	maximal, complemented
6	C₂×C₄₁×#476	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₁×#469	C₂	1	2	yes	maximal, complemented
8	C₂×C₄₁×#459	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₁×#447	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×D₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₁×#436	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄₁×#418	C₂	1	2	yes	maximal, complemented
13	C₂³×D₄×C₄₁	—	2	1	no	—
14	C₂³×D₄×C₄₁	C₂²	1	2	yes	—
15	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
16	C₂²×D₈×C₄₁	C₂²	1	2	yes	complemented
17	C₂²×M₁₆×C₄₁	C₂²	1	2	yes	complemented
18	C₄₁×#555	—	2	4	no	—
19	C₄₁×#555	C₂²	1	8	yes	complemented
20	D₄²×C₄₁	—	2	4	no	—
21	D₄²×C₄₁	C₂²	1	8	yes	complemented
22	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
23	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×#124×C₄₁	—	2	2	no	—
25	C₂×#121×C₄₁	—	2	1	no	—
26	C₂×#121×C₄₁	—	2	1	no	—
27	C₂×#121×C₄₁	C₂²	1	2	yes	—
28	C₂×#121×C₄₁	C₂²	1	2	yes	complemented
29	C₂×#120×C₄₁	—	2	2	no	—
30	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic, complemented
33	C₂×#117×C₄₁	—	2	1	no	—
34	C₂×#117×C₄₁	C₂²	1	2	yes	complemented
35	C₄₁×#486	C₂²	1	8	yes	complemented
36	C₄₁×#482	C₂²	1	16	yes	complemented
37	C₄₁×#476	C₂²	1	8	yes	complemented
38	C₄₁×#469	C₂²	1	16	yes	complemented
39	C₄₁×#459	C₂²	1	8	yes	complemented
40	C₄₁×#447	C₂²	1	16	yes	complemented
41	C₄×D₈×C₄₁	C₂²	1	8	yes	complemented
42	C₄₁×#436	C₂²	1	8	yes	complemented
43	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic, complemented
44	C₂×#106×C₄₁	C₂²	1	2	yes	complemented
45	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
46	C₄₁×#418	C₂²	1	16	yes	complemented
47	C₂×#102×C₄₁	C₂²	1	2	yes	—
48	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
49	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic, complemented
50	C₂×#102×C₄₁	C₂²	1	2	yes	complemented
51	C₂×#102×C₄₁	C₂²	1	2	yes	complemented
52	C₂×#102×C₄₁	C₂²	1	2	yes	complemented
53	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	complemented
54	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
55	C₂⁵×C₄₁	—	2	2	no	—
56	C₂²×Q₈×C₄₁	—	2	1	no	—
57	C₂²×D₄×C₄₁	—	2	8	no	—
58	C₂²×D₄×C₄₁	—	2	2	no	—
59	C₂²×D₄×C₄₁	—	2	2	no	—
60	C₂²×D₄×C₄₁	—	2	8	no	—
61	C₂²×D₄×C₄₁	—	2	2	no	—
62	C₂²×D₄×C₄₁	—	2	1	no	—
63	C₂²×D₄×C₄₁	—	2	4	no	—
64	C₂²×D₄×C₄₁	—	2	1	no	—
65	C₂²×D₄×C₄₁	—	4	4	no	—
66	C₂²×D₄×C₄₁	—	4	8	no	—
67	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
68	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
70	C₂²×D₄×C₄₁	C₂³	1	8	yes	—
71	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₄₁	—	2	1	no	—
73	C₂³×C₄×C₄₁	—	2	1	no	—
74	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
75	C₂×D₈×C₄₁	—	2	4	no	—
76	C₂×D₈×C₄₁	—	4	4	no	—
77	C₂×D₈×C₄₁	C₂³	1	4	yes	—
78	C₂×D₈×C₄₁	C₂³	1	8	yes	complemented
79	C₂×M₁₆×C₄₁	—	4	4	no	—
80	C₂×M₁₆×C₄₁	C₂³	1	8	yes	complemented
81	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
83	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
84	C₄⋊Q₈×C₄₁	—	2	2	no	—
85	C₄⋊Q₈×C₄₁	C₂³	1	4	yes	complemented
86	#127×C₄₁	—	2	2	no	—
87	#127×C₄₁	C₂³	1	4	yes	—
88	#124×C₄₁	—	2	16	no	—
89	#121×C₄₁	—	2	8	no	—
90	#121×C₄₁	—	2	4	no	—
91	#121×C₄₁	—	2	4	no	—
92	#121×C₄₁	—	2	8	no	—
93	#121×C₄₁	C₂³	1	8	yes	—
94	#121×C₄₁	C₂³	1	8	yes	complemented
95	#120×C₄₁	—	2	16	no	—
96	C₄×D₄×C₄₁	—	2	2	no	—
97	C₄×D₄×C₄₁	—	2	2	no	—
98	C₄×D₄×C₄₁	D₄	1	4	yes	—
99	C₄×D₄×C₄₁	C₂³	1	4	yes	—
100	C₄×D₄×C₄₁	C₂³	1	4	yes	—
101	C₄×D₄×C₄₁	C₂³	1	4	yes	complemented
102	#117×C₄₁	—	2	4	no	—
103	#117×C₄₁	—	2	8	no	—
104	#117×C₄₁	C₂³	1	8	yes	complemented
105	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
106	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
110	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
111	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
112	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
115	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
116	C₂×C₄²×C₄₁	—	2	2	no	—
117	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
118	#107×C₄₁	C₂³	1	4	yes	complemented
119	#106×C₄₁	C₂³	1	8	yes	complemented
120	C₄⋊C₈×C₄₁	C₂³	1	4	yes	complemented
121	#102×C₄₁	C₂³	1	4	yes	—
122	#102×C₄₁	C₂³	1	8	yes	—
123	#102×C₄₁	C₂³	1	8	yes	complemented
124	#102×C₄₁	C₂³	1	8	yes	complemented
125	#102×C₄₁	C₂³	1	4	yes	complemented
126	#102×C₄₁	C₂³	1	8	yes	complemented
127	C₂²⋊C₈×C₄₁	C₂³	1	8	yes	complemented
128	C₄×C₈×C₄₁	C₂³	1	4	yes	complemented
129	C₂⁴×C₄₁	—	2	1	no	—
130	C₂⁴×C₄₁	—	2	1	no	—
131	C₂⁴×C₄₁	—	2	2	no	—
132	C₂⁴×C₄₁	—	2	8	no	—
133	C₂⁴×C₄₁	—	4	8	no	—
134	C₂⁴×C₄₁	—	4	8	no	—
135	C₂⁴×C₄₁	—	8	4	no	—
136	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
137	C₂×Q₈×C₄₁	—	2	4	no	—
138	C₂×Q₈×C₄₁	—	8	2	no	—
139	C₂×D₄×C₄₁	—	2	16	no	—
140	C₂×D₄×C₄₁	—	2	8	no	—
141	C₂×D₄×C₄₁	—	2	8	no	—
142	C₂×D₄×C₄₁	—	2	4	no	—
143	C₂×D₄×C₄₁	—	2	1	no	—
144	C₂×D₄×C₄₁	—	2	1	no	—
145	C₂×D₄×C₄₁	—	2	8	no	—
146	C₂×D₄×C₄₁	—	2	2	no	—
147	C₂×D₄×C₄₁	—	2	4	no	—
148	C₂×D₄×C₄₁	—	2	4	no	—
149	C₂×D₄×C₄₁	—	2	2	no	—
150	C₂×D₄×C₄₁	—	2	4	no	—
151	C₂×D₄×C₄₁	—	2	2	no	—
152	C₂×D₄×C₄₁	—	2	2	no	—
153	C₂×D₄×C₄₁	—	2	4	no	—
154	C₂×D₄×C₄₁	—	4	8	no	—
155	C₂×D₄×C₄₁	—	4	16	no	—
156	C₂×D₄×C₄₁	—	4	8	no	—
157	C₂×D₄×C₄₁	—	4	32	no	—
158	C₂×D₄×C₄₁	—	4	8	no	—
159	C₂×D₄×C₄₁	—	4	4	no	—
160	C₂×D₄×C₄₁	—	8	2	no	—
161	C₂×D₄×C₄₁	—	8	4	no	—
162	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
163	C₂×D₄×C₄₁	#41	1	4	yes	—
164	C₂×D₄×C₄₁	C₂⁴	1	4	yes	—
165	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
166	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
167	C₂²×C₄×C₄₁	—	2	4	no	—
168	C₂²×C₄×C₄₁	—	2	4	no	—
169	C₂²×C₄×C₄₁	—	2	1	no	—
170	C₂²×C₄×C₄₁	—	2	2	no	—
171	C₂²×C₄×C₄₁	—	2	1	no	—
172	C₂²×C₄×C₄₁	—	2	4	no	—
173	C₂²×C₄×C₄₁	—	2	4	no	—
174	C₂²×C₄×C₄₁	—	4	4	no	—
175	C₂²×C₄×C₄₁	—	4	4	no	—
176	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
177	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
178	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
181	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
182	D₈×C₄₁	—	2	8	no	—
183	D₈×C₄₁	—	4	8	no	—
184	M₁₆×C₄₁	—	4	8	no	—
185	C₂×C₈×C₄₁	—	2	2	no	—
186	C₂×C₈×C₄₁	—	2	2	no	—
187	C₂×C₈×C₄₁	—	2	4	no	—
188	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
189	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
190	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
191	C₄⋊C₄×C₄₁	—	2	4	no	—
192	C₄⋊C₄×C₄₁	—	2	1	no	—
193	C₄⋊C₄×C₄₁	—	2	2	no	—
194	C₄⋊C₄×C₄₁	—	2	1	no	—
195	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
196	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
197	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
198	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
199	C₂²⋊C₄×C₄₁	—	2	8	no	—
200	C₂²⋊C₄×C₄₁	—	2	8	no	—
201	C₂²⋊C₄×C₄₁	—	2	4	no	—
202	C₂²⋊C₄×C₄₁	—	2	4	no	—
203	C₂²⋊C₄×C₄₁	—	2	8	no	—
204	C₂²⋊C₄×C₄₁	C₂×D₄	1	8	yes	—
205	C₄²×C₄₁	—	2	8	no	—
206	C₄²×C₄₁	C₂×D₄	1	2	yes	—
207	C₄²×C₄₁	C₂⁴	1	2	yes	—
208	C₂³×C₄₁	—	2	4	no	—
209	C₂³×C₄₁	—	2	4	no	—
210	C₂³×C₄₁	—	2	4	no	—
211	C₂³×C₄₁	—	2	4	no	—
212	C₂³×C₄₁	—	2	2	no	—
213	C₂³×C₄₁	—	2	2	no	—
214	C₂³×C₄₁	—	2	4	no	—
215	C₂³×C₄₁	—	4	16	no	—
216	C₂³×C₄₁	—	4	16	no	—
217	C₂³×C₄₁	—	4	2	no	—
218	C₂³×C₄₁	—	4	2	no	—
219	C₂³×C₄₁	—	4	4	no	—
220	C₂³×C₄₁	—	4	2	no	—
221	C₂³×C₄₁	—	4	2	no	—
222	C₂³×C₄₁	—	4	4	no	—
223	C₂³×C₄₁	—	4	2	no	—
224	C₂³×C₄₁	—	4	4	no	—
225	C₂³×C₄₁	—	8	8	no	—
226	C₂³×C₄₁	—	8	32	no	—
227	C₂³×C₄₁	C₂²×D₄	1	4	yes	—
228	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
229	Q₈×C₄₁	—	8	4	no	—
230	D₄×C₄₁	—	2	4	no	—
231	D₄×C₄₁	—	2	8	no	—
232	D₄×C₄₁	—	2	2	no	—
233	D₄×C₄₁	—	2	4	no	—
234	D₄×C₄₁	—	2	2	no	—
235	D₄×C₄₁	—	2	2	no	—
236	D₄×C₄₁	—	2	4	no	—
237	D₄×C₄₁	—	4	16	no	—
238	D₄×C₄₁	—	4	16	no	—
239	D₄×C₄₁	—	4	2	no	—
240	D₄×C₄₁	—	4	4	no	—
241	D₄×C₄₁	—	4	8	no	—
242	D₄×C₄₁	—	8	4	no	—
243	D₄×C₄₁	—	8	8	no	—
244	D₄×C₄₁	C₂×#41	1	4	yes	—
245	C₂×C₄×C₄₁	—	2	4	no	—
246	C₂×C₄×C₄₁	—	2	2	no	—
247	C₂×C₄×C₄₁	—	2	8	no	—
248	C₂×C₄×C₄₁	—	2	4	no	—
249	C₂×C₄×C₄₁	—	2	4	no	—
250	C₂×C₄×C₄₁	—	2	2	no	—
251	C₂×C₄×C₄₁	—	2	4	no	—
252	C₂×C₄×C₄₁	—	2	2	no	—
253	C₂×C₄×C₄₁	—	4	2	no	—
254	C₂×C₄×C₄₁	—	4	2	no	—
255	C₂×C₄×C₄₁	—	4	4	no	—
256	C₂×C₄×C₄₁	—	4	8	no	—
257	C₂×C₄×C₄₁	—	4	8	no	—
258	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	4	yes	—
259	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
260	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
261	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
263	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
264	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
265	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
266	C₈×C₄₁	—	2	2	no	—
267	C₈×C₄₁	—	2	2	no	—
268	C₈×C₄₁	—	2	4	no	—
269	C₂×#3325	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
270	C₂²×C₄₁	—	2	4	no	—
271	C₂²×C₄₁	—	2	4	no	—
272	C₂²×C₄₁	—	2	4	no	—
273	C₂²×C₄₁	—	2	4	no	—
274	C₂²×C₄₁	—	4	2	no	—
275	C₂²×C₄₁	—	4	8	no	—
276	C₂²×C₄₁	—	4	8	no	—
277	C₂²×C₄₁	—	4	2	no	—
278	C₂²×C₄₁	—	4	4	no	—
279	C₂²×C₄₁	—	4	2	no	—
280	C₂²×C₄₁	—	4	2	no	—
281	C₂²×C₄₁	—	4	4	no	—
282	C₂²×C₄₁	—	4	2	no	—
283	C₂²×C₄₁	—	4	4	no	—
284	C₂²×C₄₁	—	8	32	no	—
285	C₂²×C₄₁	—	8	4	no	—
286	C₂²×C₄₁	—	8	8	no	—
287	C₂²×C₄₁	#546	1	2	yes	—
288	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
289	C₂²×C₄₁	#576	1	2	yes	—
290	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
291	C₄×C₄₁	—	2	4	no	—
292	C₄×C₄₁	—	2	2	no	—
293	C₄×C₄₁	—	4	2	no	—
294	C₄×C₄₁	—	4	2	no	—
295	C₄×C₄₁	—	4	4	no	—
296	C₄×C₄₁	#546	1	2	yes	—
297	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	4	yes	—
298	C₄×C₄₁	C₂²×#41	1	1	yes	characteristic
299	C₄×C₄₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
300	C₂×#555	C₂×C₄₁	1	1	yes	characteristic, complemented
301	C₂×D₄²	C₂×C₄₁	1	1	yes	characteristic, complemented
302	#3325	C₂×C₄₁	1	16	yes	direct product factor
303	C₂×#486	C₂×C₄₁	1	1	yes	characteristic, complemented
304	C₂×#482	C₂×C₄₁	1	2	yes	complemented
305	C₂×#476	C₂×C₄₁	1	1	yes	characteristic, complemented
306	C₂×#469	C₂×C₄₁	1	2	yes	complemented
307	C₂×#459	C₂×C₄₁	1	1	yes	characteristic, complemented
308	C₂×#447	C₂×C₄₁	1	2	yes	complemented
309	C₂×C₄×D₈	C₂×C₄₁	1	1	yes	characteristic, complemented
310	C₂×#436	C₂×C₄₁	1	1	yes	characteristic, complemented
311	C₂×#418	C₂×C₄₁	1	2	yes	complemented
312	C₂×C₄₁	—	4	4	no	—
313	C₂×C₄₁	—	4	4	no	—
314	C₂×C₄₁	—	8	2	no	—
315	C₂×C₄₁	—	8	4	no	—
316	C₂×C₄₁	#3325	1	4	yes	direct product factor
317	C₂×C₄₁	C₂×#546	1	1	yes	characteristic
318	C₂×C₄₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
319	C₂×C₄₁	C₂×#576	1	1	yes	characteristic
320	C₂³×D₄	—	2	1	no	—
321	C₂³×D₄	C₂²×C₄₁	1	2	yes	—
322	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
323	C₂²×D₈	C₂²×C₄₁	1	2	yes	complemented
324	C₂²×M₁₆	C₂²×C₄₁	1	2	yes	complemented
325	#555	—	2	4	no	—
326	#555	C₂²×C₄₁	1	8	yes	complemented
327	D₄²	—	2	4	no	—
328	D₄²	C₂²×C₄₁	1	8	yes	complemented
329	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
330	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
331	C₂×#124	—	2	2	no	—
332	C₂×#121	—	2	1	no	—
333	C₂×#121	—	2	1	no	—
334	C₂×#121	C₂²×C₄₁	1	2	yes	—
335	C₂×#121	C₂²×C₄₁	1	2	yes	complemented
336	C₂×#120	—	2	2	no	—
337	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
338	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
339	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic, complemented
340	C₂×#117	—	2	1	no	—
341	C₂×#117	C₂²×C₄₁	1	2	yes	complemented
342	#486	C₂²×C₄₁	1	8	yes	complemented
343	#482	C₂²×C₄₁	1	16	yes	complemented
344	#476	C₂²×C₄₁	1	8	yes	complemented
345	#469	C₂²×C₄₁	1	16	yes	complemented
346	#459	C₂²×C₄₁	1	8	yes	complemented
347	#447	C₂²×C₄₁	1	16	yes	complemented
348	C₄×D₈	C₂²×C₄₁	1	8	yes	complemented
349	#436	C₂²×C₄₁	1	8	yes	complemented
350	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic, complemented
351	C₂×#106	C₂²×C₄₁	1	2	yes	complemented
352	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
353	#418	C₂²×C₄₁	1	16	yes	complemented
354	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
355	C₂×#102	C₂²×C₄₁	1	2	yes	—
356	C₂×#102	C₂²×C₄₁	1	2	yes	complemented
357	C₂×#102	C₂²×C₄₁	1	2	yes	complemented
358	C₂×#102	C₂²×C₄₁	1	2	yes	complemented
359	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic, complemented
360	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	complemented
361	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
362	C₄₁	C₂×#3325	1	1	yes	characteristic, direct product factor, Sylow
363	C₂⁵	—	2	2	no	—
364	C₂²×Q₈	—	2	1	no	—
365	C₂²×D₄	—	2	8	no	—
366	C₂²×D₄	—	2	2	no	—
367	C₂²×D₄	—	2	2	no	—
368	C₂²×D₄	—	2	8	no	—
369	C₂²×D₄	—	2	2	no	—
370	C₂²×D₄	—	2	1	no	—
371	C₂²×D₄	—	2	4	no	—
372	C₂²×D₄	—	2	1	no	—
373	C₂²×D₄	—	4	4	no	—
374	C₂²×D₄	—	4	8	no	—
375	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
376	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
377	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
378	C₂²×D₄	C₂³×C₄₁	1	8	yes	—
379	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
380	C₂³×C₄	—	2	1	no	—
381	C₂³×C₄	—	2	1	no	—
382	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
383	C₂×D₈	—	2	4	no	—
384	C₂×D₈	—	4	4	no	—
385	C₂×D₈	C₂³×C₄₁	1	4	yes	—
386	C₂×D₈	C₂³×C₄₁	1	8	yes	complemented
387	C₂×M₁₆	—	4	4	no	—
388	C₂×M₁₆	C₂³×C₄₁	1	8	yes	complemented
389	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
390	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
391	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
392	C₄⋊Q₈	—	2	2	no	—
393	C₄⋊Q₈	C₂³×C₄₁	1	4	yes	complemented
394	#127	—	2	2	no	—
395	#127	C₂³×C₄₁	1	4	yes	—
396	#124	—	2	16	no	—
397	#121	—	2	8	no	—
398	#121	—	2	4	no	—
399	#121	—	2	4	no	—
400	#121	—	2	8	no	—
401	#121	C₂³×C₄₁	1	8	yes	—
402	#121	C₂³×C₄₁	1	8	yes	complemented
403	#120	—	2	16	no	—
404	C₄×D₄	—	2	2	no	—
405	C₄×D₄	—	2	2	no	—
406	C₄×D₄	D₄×C₄₁	1	4	yes	—
407	C₄×D₄	C₂³×C₄₁	1	4	yes	—
408	C₄×D₄	C₂³×C₄₁	1	4	yes	—
409	C₄×D₄	C₂³×C₄₁	1	4	yes	complemented
410	#117	—	2	4	no	—
411	#117	—	2	8	no	—
412	#117	C₂³×C₄₁	1	8	yes	complemented
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
417	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
418	C₂×C₂²⋊C₄	—	2	2	no	—
419	C₂×C₂²⋊C₄	—	2	2	no	—
420	C₂×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₂²⋊C₄	—	2	1	no	—
422	C₂×C₂²⋊C₄	—	2	2	no	—
423	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
424	C₂×C₄²	—	2	2	no	—
425	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
426	#107	C₂³×C₄₁	1	4	yes	complemented
427	#106	C₂³×C₄₁	1	8	yes	complemented
428	C₄⋊C₈	C₂³×C₄₁	1	4	yes	complemented
429	#102	C₂³×C₄₁	1	4	yes	—
430	#102	C₂³×C₄₁	1	8	yes	—
431	#102	C₂³×C₄₁	1	8	yes	complemented
432	#102	C₂³×C₄₁	1	8	yes	complemented
433	#102	C₂³×C₄₁	1	4	yes	complemented
434	#102	C₂³×C₄₁	1	8	yes	complemented
435	C₂²⋊C₈	C₂³×C₄₁	1	8	yes	complemented
436	C₄×C₈	C₂³×C₄₁	1	4	yes	complemented
437	C₂⁴	—	2	1	no	—
438	C₂⁴	—	2	1	no	—
439	C₂⁴	—	2	2	no	—
440	C₂⁴	—	2	8	no	—
441	C₂⁴	—	4	8	no	—
442	C₂⁴	—	4	8	no	—
443	C₂⁴	—	8	4	no	—
444	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
445	C₂×Q₈	—	2	4	no	—
446	C₂×Q₈	—	8	2	no	—
447	C₂×D₄	—	2	16	no	—
448	C₂×D₄	—	2	8	no	—
449	C₂×D₄	—	2	8	no	—
450	C₂×D₄	—	2	4	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	8	no	—
454	C₂×D₄	—	2	2	no	—
455	C₂×D₄	—	2	4	no	—
456	C₂×D₄	—	2	4	no	—
457	C₂×D₄	—	2	2	no	—
458	C₂×D₄	—	2	4	no	—
459	C₂×D₄	—	2	2	no	—
460	C₂×D₄	—	2	2	no	—
461	C₂×D₄	—	2	4	no	—
462	C₂×D₄	—	4	8	no	—
463	C₂×D₄	—	4	16	no	—
464	C₂×D₄	—	4	8	no	—
465	C₂×D₄	—	4	32	no	—
466	C₂×D₄	—	4	8	no	—
467	C₂×D₄	—	4	4	no	—
468	C₂×D₄	—	8	2	no	—
469	C₂×D₄	—	8	4	no	—
470	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
471	C₂×D₄	#41×C₄₁	1	4	yes	—
472	C₂×D₄	C₂⁴×C₄₁	1	4	yes	—
473	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
474	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	4	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	4	no	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	—	4	4	no	—
483	C₂²×C₄	—	4	4	no	—
484	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
485	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
486	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
487	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
488	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
489	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
490	D₈	—	2	8	no	—
491	D₈	—	4	8	no	—
492	M₁₆	—	4	8	no	—
493	C₂×C₈	—	2	2	no	—
494	C₂×C₈	—	2	2	no	—
495	C₂×C₈	—	2	4	no	—
496	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
497	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
498	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
499	C₄⋊C₄	—	2	4	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
504	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
505	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
506	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
507	C₂²⋊C₄	—	2	8	no	—
508	C₂²⋊C₄	—	2	8	no	—
509	C₂²⋊C₄	—	2	4	no	—
510	C₂²⋊C₄	—	2	4	no	—
511	C₂²⋊C₄	—	2	8	no	—
512	C₂²⋊C₄	C₂×D₄×C₄₁	1	8	yes	—
513	C₄²	—	2	8	no	—
514	C₄²	C₂×D₄×C₄₁	1	2	yes	—
515	C₄²	C₂⁴×C₄₁	1	2	yes	—
516	C₂³	—	2	4	no	—
517	C₂³	—	2	4	no	—
518	C₂³	—	2	4	no	—
519	C₂³	—	2	4	no	—
520	C₂³	—	2	2	no	—
521	C₂³	—	2	2	no	—
522	C₂³	—	2	4	no	—
523	C₂³	—	4	16	no	—
524	C₂³	—	4	16	no	—
525	C₂³	—	4	2	no	—
526	C₂³	—	4	2	no	—
527	C₂³	—	4	4	no	—
528	C₂³	—	4	2	no	—
529	C₂³	—	4	2	no	—
530	C₂³	—	4	4	no	—
531	C₂³	—	4	2	no	—
532	C₂³	—	4	4	no	—
533	C₂³	—	8	8	no	—
534	C₂³	—	8	32	no	—
535	C₂³	C₂²×D₄×C₄₁	1	4	yes	—
536	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
537	Q₈	—	8	4	no	—
538	D₄	—	2	4	no	—
539	D₄	—	2	8	no	—
540	D₄	—	2	2	no	—
541	D₄	—	2	4	no	—
542	D₄	—	2	2	no	—
543	D₄	—	2	2	no	—
544	D₄	—	2	4	no	—
545	D₄	—	4	16	no	—
546	D₄	—	4	16	no	—
547	D₄	—	4	4	no	—
548	D₄	—	4	2	no	—
549	D₄	—	4	8	no	—
550	D₄	—	8	4	no	—
551	D₄	—	8	8	no	—
552	D₄	C₂×#41×C₄₁	1	4	yes	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	8	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	4	4	no	—
564	C₂×C₄	—	4	8	no	—
565	C₂×C₄	—	4	8	no	—
566	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	4	yes	—
567	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
568	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
569	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
570	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
571	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
572	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
573	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
574	C₈	—	2	2	no	—
575	C₈	—	2	2	no	—
576	C₈	—	2	4	no	—
577	C₂²	—	2	4	no	—
578	C₂²	—	2	4	no	—
579	C₂²	—	2	4	no	—
580	C₂²	—	2	4	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	4	8	no	—
583	C₂²	—	4	8	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	4	no	—
587	C₂²	—	4	2	no	—
588	C₂²	—	4	4	no	—
589	C₂²	—	4	4	no	—
590	C₂²	—	4	2	no	—
591	C₂²	—	8	32	no	—
592	C₂²	—	8	8	no	—
593	C₂²	—	8	4	no	—
594	C₂²	C₄₁×#546	1	2	yes	—
595	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	2	yes	—
596	C₂²	C₄₁×#576	1	2	yes	—
597	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
598	C₄	—	2	2	no	—
599	C₄	—	2	4	no	—
600	C₄	—	4	2	no	—
601	C₄	—	4	2	no	—
602	C₄	—	4	4	no	—
603	C₄	C₄₁×#546	1	2	yes	—
604	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	4	yes	—
605	C₄	C₂²×#41×C₄₁	1	1	yes	characteristic
606	C₄	C₂×H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
607	C₂	—	4	4	no	—
608	C₂	—	4	4	no	—
609	C₂	—	8	4	no	—
610	C₂	—	8	2	no	—
611	C₂	C₄₁×#3325	1	4	yes	direct product factor
612	C₂	C₂×C₄₁×#546	1	1	yes	characteristic
613	C₂	C₂²×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
614	C₂	C₂×C₄₁×#576	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#555	C₂	semidirect
2. C₂×D₄²×C₄₁	C₂	semidirect
3. C₄₁×#3325	C₂	direct (N × H)
4. C₂×C₄₁×#486	C₂	semidirect
5. C₂×C₄₁×#482	C₂	semidirect
6. C₂×C₄₁×#476	C₂	semidirect
7. C₂×C₄₁×#469	C₂	semidirect
8. C₂×C₄₁×#459	C₂	semidirect
9. C₂×C₄₁×#447	C₂	semidirect
10. C₂×C₄×D₈×C₄₁	C₂	semidirect
11. C₂×C₄₁×#436	C₂	semidirect
12. C₂×C₄₁×#418	C₂	semidirect
16. C₂²×D₈×C₄₁	C₂²	semidirect
17. C₂²×M₁₆×C₄₁	C₂²	semidirect
19. C₄₁×#555	C₂²	semidirect
21. D₄²×C₄₁	C₂²	semidirect
22. C₂×C₄⋊Q₈×C₄₁	C₂²	semidirect
28. C₂×#121×C₄₁	C₂²	semidirect
32. C₂×C₄×D₄×C₄₁	C₂²	semidirect
34. C₂×#117×C₄₁	C₂²	semidirect
35. C₄₁×#486	C₂²	semidirect
36. C₄₁×#482	C₂²	semidirect
37. C₄₁×#476	C₂²	semidirect
38. C₄₁×#469	C₂²	semidirect
39. C₄₁×#459	C₂²	semidirect
40. C₄₁×#447	C₂²	semidirect
41. C₄×D₈×C₄₁	C₂²	semidirect
42. C₄₁×#436	C₂²	semidirect
43. C₂×#107×C₄₁	C₂²	semidirect
44. C₂×#106×C₄₁	C₂²	semidirect
45. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
46. C₄₁×#418	C₂²	semidirect
49. C₂×#102×C₄₁	C₂²	semidirect
50. C₂×#102×C₄₁	C₂²	semidirect
51. C₂×#102×C₄₁	C₂²	semidirect
52. C₂×#102×C₄₁	C₂²	semidirect
53. C₂×C₂²⋊C₈×C₄₁	C₂²	semidirect
54. C₂×C₄×C₈×C₄₁	C₂²	semidirect
78. C₂×D₈×C₄₁	C₂³	semidirect
80. C₂×M₁₆×C₄₁	C₂³	semidirect
85. C₄⋊Q₈×C₄₁	C₂³	semidirect
94. #121×C₄₁	C₂³	semidirect
101. C₄×D₄×C₄₁	C₂³	semidirect
104. #117×C₄₁	C₂³	semidirect
118. #107×C₄₁	C₂³	semidirect
119. #106×C₄₁	C₂³	semidirect
120. C₄⋊C₈×C₄₁	C₂³	semidirect
123. #102×C₄₁	C₂³	semidirect
124. #102×C₄₁	C₂³	semidirect
125. #102×C₄₁	C₂³	semidirect
126. #102×C₄₁	C₂³	semidirect
127. C₂²⋊C₈×C₄₁	C₂³	semidirect
128. C₄×C₈×C₄₁	C₂³	semidirect
269. C₂×#3325	C₄₁	direct (N × H)
300. C₂×#555	C₂×C₄₁	semidirect
301. C₂×D₄²	C₂×C₄₁	semidirect
302. #3325	C₂×C₄₁	direct (N × H)
303. C₂×#486	C₂×C₄₁	semidirect
304. C₂×#482	C₂×C₄₁	semidirect
305. C₂×#476	C₂×C₄₁	semidirect
306. C₂×#469	C₂×C₄₁	semidirect
307. C₂×#459	C₂×C₄₁	semidirect
308. C₂×#447	C₂×C₄₁	semidirect
309. C₂×C₄×D₈	C₂×C₄₁	semidirect
310. C₂×#436	C₂×C₄₁	semidirect
311. C₂×#418	C₂×C₄₁	semidirect
316. C₂×C₄₁	#3325	direct (N × H)
323. C₂²×D₈	C₂²×C₄₁	semidirect
324. C₂²×M₁₆	C₂²×C₄₁	semidirect
326. #555	C₂²×C₄₁	semidirect
328. D₄²	C₂²×C₄₁	semidirect
329. C₂×C₄⋊Q₈	C₂²×C₄₁	semidirect
335. C₂×#121	C₂²×C₄₁	semidirect
339. C₂×C₄×D₄	C₂²×C₄₁	semidirect
341. C₂×#117	C₂²×C₄₁	semidirect
342. #486	C₂²×C₄₁	semidirect
343. #482	C₂²×C₄₁	semidirect
344. #476	C₂²×C₄₁	semidirect
345. #469	C₂²×C₄₁	semidirect
346. #459	C₂²×C₄₁	semidirect
347. #447	C₂²×C₄₁	semidirect
348. C₄×D₈	C₂²×C₄₁	semidirect
349. #436	C₂²×C₄₁	semidirect
350. C₂×#107	C₂²×C₄₁	semidirect
351. C₂×#106	C₂²×C₄₁	semidirect
352. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
353. #418	C₂²×C₄₁	semidirect
356. C₂×#102	C₂²×C₄₁	semidirect
357. C₂×#102	C₂²×C₄₁	semidirect
358. C₂×#102	C₂²×C₄₁	semidirect
359. C₂×#102	C₂²×C₄₁	semidirect
360. C₂×C₂²⋊C₈	C₂²×C₄₁	semidirect
361. C₂×C₄×C₈	C₂²×C₄₁	semidirect
362. C₄₁	C₂×#3325	direct (N × H)
386. C₂×D₈	C₂³×C₄₁	semidirect
388. C₂×M₁₆	C₂³×C₄₁	semidirect
393. C₄⋊Q₈	C₂³×C₄₁	semidirect
402. #121	C₂³×C₄₁	semidirect
409. C₄×D₄	C₂³×C₄₁	semidirect
412. #117	C₂³×C₄₁	semidirect
426. #107	C₂³×C₄₁	semidirect
427. #106	C₂³×C₄₁	semidirect
428. C₄⋊C₈	C₂³×C₄₁	semidirect
431. #102	C₂³×C₄₁	semidirect
432. #102	C₂³×C₄₁	semidirect
433. #102	C₂³×C₄₁	semidirect
434. #102	C₂³×C₄₁	semidirect
435. C₂²⋊C₈	C₂³×C₄₁	semidirect
436. C₄×C₈	C₂³×C₄₁	semidirect
611. C₂	C₄₁×#3325	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×#555	2
C₂×D₄²×C₄₁	2
C₄₁×#3325	2
C₂×C₄₁×#486	2
C₂×C₄₁×#482	2
C₂×C₄₁×#476	2
C₂×C₄₁×#469	2
C₂×C₄₁×#459	2
C₂×C₄₁×#447	2
C₂×C₄×D₈×C₄₁	2
C₂×C₄₁×#436	2
C₂×C₄₁×#418	2
C₂×#3325	41

Subgroups — C2×C41×#3325 #23837346

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#3325 #23837346