Subgroups — C₄₁×#22034 #23798235

Order 10496.

1176 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#435	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂²⋊C₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#120×C₄₁	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#1955	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1924	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1924	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1870	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1869	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1850	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1779	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1752	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
14	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×#120×C₄₁	C₄	1	1	yes	characteristic
17	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
19	C₄₁×#435	—	2	4	no	—
20	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	complemented
22	C₂×C₂²⋊C₈×C₄₁	—	2	4	no	—
23	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
28	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
29	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	complemented
31	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic, complemented
32	C₂×#97×C₄₁	C₂²	1	2	yes	complemented
33	C₄₁×#386	C₄	1	2	yes	—
34	C₄₁×#386	C₄	1	1	yes	characteristic
35	C₄₁×#385	C₄	1	1	yes	characteristic
36	C₄₁×#385	C₄	1	2	yes	—
37	C₄₁×#379	C₄	1	1	yes	characteristic
38	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
39	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
40	C₄₁×#336	C₂²	1	2	yes	complemented
41	C₄₁×#336	C₂²	1	2	yes	complemented
42	C₄₁×#336	C₂²	1	2	yes	complemented
43	C₂⁵×C₄₁	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
45	C₂²×D₄×C₄₁	C₂×C₄	1	2	yes	—
46	C₂³×C₄×C₄₁	—	2	2	no	—
47	C₂³×C₄×C₄₁	—	2	2	no	—
48	C₂³×C₄×C₄₁	—	4	2	no	—
49	C₂³×C₄×C₄₁	—	4	2	no	—
50	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₄₁	C₂×C₄	1	2	yes	—
52	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
54	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
55	C₂×M₁₆×C₄₁	—	2	2	no	—
56	C₂×M₁₆×C₄₁	—	4	2	no	—
57	C₂²×C₈×C₄₁	—	2	2	no	—
58	C₂²×C₈×C₄₁	—	4	2	no	—
59	C₂²×C₈×C₄₁	—	4	2	no	—
60	C₂²×C₈×C₄₁	D₄	1	4	yes	complemented
61	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
62	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
64	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
67	#120×C₄₁	—	2	4	no	—
68	C₄×D₄×C₄₁	—	2	2	no	—
69	C₄×D₄×C₄₁	—	2	2	no	—
70	C₄×D₄×C₄₁	—	4	2	no	—
71	C₄×D₄×C₄₁	—	4	2	no	—
72	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
74	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
76	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
77	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
78	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
80	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
81	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
82	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
84	C₄⋊C₈×C₄₁	—	2	2	no	—
85	C₄⋊C₈×C₄₁	—	4	2	no	—
86	C₂²⋊C₈×C₄₁	—	2	2	no	—
87	C₂²⋊C₈×C₄₁	—	2	2	no	—
88	C₂²⋊C₈×C₄₁	—	2	4	no	—
89	C₂²⋊C₈×C₄₁	—	2	4	no	—
90	C₂²⋊C₈×C₄₁	—	2	2	no	—
91	C₂²⋊C₈×C₄₁	—	4	2	no	—
92	C₂²⋊C₈×C₄₁	—	4	2	no	—
93	C₂²⋊C₈×C₄₁	—	4	2	no	—
94	#97×C₄₁	—	2	2	no	—
95	#97×C₄₁	—	4	2	no	—
96	#95×C₄₁	C₂×C₄	1	2	yes	—
97	#95×C₄₁	C₂×C₄	1	2	yes	—
98	#95×C₄₁	C₂×C₄	1	2	yes	—
99	C₂⁴×C₄₁	—	2	2	no	—
100	C₂⁴×C₄₁	—	2	2	no	—
101	C₂⁴×C₄₁	—	4	2	no	—
102	C₂⁴×C₄₁	—	4	2	no	—
103	C₂⁴×C₄₁	M₁₆	1	4	yes	complemented
104	C₂⁴×C₄₁	C₂²×C₄	1	1	yes	characteristic
105	C₂⁴×C₄₁	C₂²×C₄	1	2	yes	—
106	C₂⁴×C₄₁	C₂²×C₄	1	1	yes	characteristic
107	C₂×D₄×C₄₁	—	2	2	no	—
108	C₂×D₄×C₄₁	—	2	4	no	—
109	C₂×D₄×C₄₁	—	2	2	no	—
110	C₂×D₄×C₄₁	—	2	2	no	—
111	C₂×D₄×C₄₁	—	4	2	no	—
112	C₂×D₄×C₄₁	—	4	2	no	—
113	C₂²×C₄×C₄₁	—	2	2	no	—
114	C₂²×C₄×C₄₁	—	2	2	no	—
115	C₂²×C₄×C₄₁	—	2	2	no	—
116	C₂²×C₄×C₄₁	—	2	4	no	—
117	C₂²×C₄×C₄₁	—	2	2	no	—
118	C₂²×C₄×C₄₁	—	2	1	no	—
119	C₂²×C₄×C₄₁	—	2	1	no	—
120	C₂²×C₄×C₄₁	—	2	2	no	—
121	C₂²×C₄×C₄₁	—	2	2	no	—
122	C₂²×C₄×C₄₁	—	2	2	no	—
123	C₂²×C₄×C₄₁	—	2	2	no	—
124	C₂²×C₄×C₄₁	—	2	2	no	—
125	C₂²×C₄×C₄₁	—	2	2	no	—
126	C₂²×C₄×C₄₁	—	2	2	no	—
127	C₂²×C₄×C₄₁	—	4	2	no	—
128	C₂²×C₄×C₄₁	—	4	2	no	—
129	C₂²×C₄×C₄₁	—	4	2	no	—
130	C₂²×C₄×C₄₁	—	4	4	no	—
131	C₂²×C₄×C₄₁	—	4	4	no	—
132	C₂²×C₄×C₄₁	—	4	8	no	—
133	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
135	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
137	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
138	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₄₁	#41	1	2	yes	—
142	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
143	M₁₆×C₄₁	—	4	4	no	—
144	C₂×C₈×C₄₁	—	2	2	no	—
145	C₂×C₈×C₄₁	—	2	2	no	—
146	C₂×C₈×C₄₁	—	2	1	no	—
147	C₂×C₈×C₄₁	—	2	2	no	—
148	C₂×C₈×C₄₁	—	2	1	no	—
149	C₂×C₈×C₄₁	—	2	2	no	—
150	C₂×C₈×C₄₁	—	2	2	no	—
151	C₂×C₈×C₄₁	—	2	2	no	—
152	C₂×C₈×C₄₁	—	2	2	no	—
153	C₂×C₈×C₄₁	—	2	2	no	—
154	C₂×C₈×C₄₁	—	2	2	no	—
155	C₂×C₈×C₄₁	—	2	2	no	—
156	C₂×C₈×C₄₁	—	4	4	no	—
157	C₂×C₈×C₄₁	—	4	4	no	—
158	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
159	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
160	C₄⋊C₄×C₄₁	—	2	2	no	—
161	C₄⋊C₄×C₄₁	—	4	2	no	—
162	C₂²⋊C₄×C₄₁	—	2	2	no	—
163	C₂²⋊C₄×C₄₁	—	2	4	no	—
164	C₂²⋊C₄×C₄₁	—	2	2	no	—
165	C₂²⋊C₄×C₄₁	—	2	2	no	—
166	C₂²⋊C₄×C₄₁	—	2	2	no	—
167	C₂²⋊C₄×C₄₁	—	4	2	no	—
168	C₂²⋊C₄×C₄₁	—	4	2	no	—
169	C₂²⋊C₄×C₄₁	—	4	2	no	—
170	C₄²×C₄₁	—	2	1	no	—
171	C₄²×C₄₁	—	2	1	no	—
172	C₄²×C₄₁	—	2	2	no	—
173	C₄²×C₄₁	—	2	2	no	—
174	C₂³×C₄₁	—	2	2	no	—
175	C₂³×C₄₁	—	2	2	no	—
176	C₂³×C₄₁	—	2	2	no	—
177	C₂³×C₄₁	—	2	2	no	—
178	C₂³×C₄₁	—	2	2	no	—
179	C₂³×C₄₁	—	2	2	no	—
180	C₂³×C₄₁	—	2	2	no	—
181	C₂³×C₄₁	—	2	2	no	—
182	C₂³×C₄₁	—	2	8	no	—
183	C₂³×C₄₁	—	2	1	no	—
184	C₂³×C₄₁	—	2	2	no	—
185	C₂³×C₄₁	—	2	1	no	—
186	C₂³×C₄₁	—	2	1	no	—
187	C₂³×C₄₁	—	2	2	no	—
188	C₂³×C₄₁	—	4	8	no	—
189	C₂³×C₄₁	—	4	4	no	—
190	C₂³×C₄₁	—	4	4	no	—
191	C₂³×C₄₁	—	4	8	no	—
192	C₂³×C₄₁	C₄×D₄	1	2	yes	—
193	C₂³×C₄₁	C₂×M₁₆	1	4	yes	—
194	C₂³×C₄₁	C₂×M₁₆	1	2	yes	—
195	C₂³×C₄₁	#131	1	2	yes	—
196	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
197	D₄×C₄₁	—	4	8	no	—
198	D₄×C₄₁	—	4	4	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	—	2	1	no	—
204	C₂×C₄×C₄₁	—	2	1	no	—
205	C₂×C₄×C₄₁	—	2	1	no	—
206	C₂×C₄×C₄₁	—	2	2	no	—
207	C₂×C₄×C₄₁	—	2	2	no	—
208	C₂×C₄×C₄₁	—	2	2	no	—
209	C₂×C₄×C₄₁	—	2	2	no	—
210	C₂×C₄×C₄₁	—	2	2	no	—
211	C₂×C₄×C₄₁	—	2	2	no	—
212	C₂×C₄×C₄₁	—	2	1	no	—
213	C₂×C₄×C₄₁	—	2	2	no	—
214	C₂×C₄×C₄₁	—	2	2	no	—
215	C₂×C₄×C₄₁	—	2	1	no	—
216	C₂×C₄×C₄₁	—	2	2	no	—
217	C₂×C₄×C₄₁	—	2	2	no	—
218	C₂×C₄×C₄₁	—	2	2	no	—
219	C₂×C₄×C₄₁	—	4	8	no	—
220	C₂×C₄×C₄₁	—	4	4	no	—
221	C₂×C₄×C₄₁	—	4	1	no	—
222	C₂×C₄×C₄₁	—	4	2	no	—
223	C₂×C₄×C₄₁	—	4	1	no	—
224	C₂×C₄×C₄₁	—	4	2	no	—
225	C₂×C₄×C₄₁	—	4	2	no	—
226	C₂×C₄×C₄₁	—	4	2	no	—
227	C₂×C₄×C₄₁	—	4	2	no	—
228	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
229	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
232	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
233	C₈×C₄₁	—	2	2	no	—
234	C₈×C₄₁	—	2	2	no	—
235	C₈×C₄₁	—	4	1	no	—
236	C₈×C₄₁	—	4	1	no	—
237	C₈×C₄₁	—	4	2	no	—
238	C₈×C₄₁	—	4	2	no	—
239	#22034	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
240	C₂²×C₄₁	—	2	2	no	—
241	C₂²×C₄₁	—	2	2	no	—
242	C₂²×C₄₁	—	2	4	no	—
243	C₂²×C₄₁	—	2	4	no	—
244	C₂²×C₄₁	—	2	4	no	—
245	C₂²×C₄₁	—	2	4	no	—
246	C₂²×C₄₁	—	2	4	no	—
247	C₂²×C₄₁	—	4	16	no	—
248	C₂²×C₄₁	—	4	2	no	—
249	C₂²×C₄₁	—	4	2	no	—
250	C₂²×C₄₁	—	4	2	no	—
251	C₂²×C₄₁	—	4	2	no	—
252	C₂²×C₄₁	—	4	1	no	—
253	C₂²×C₄₁	—	4	1	no	—
254	C₂²×C₄₁	—	4	1	no	—
255	C₂²×C₄₁	—	4	2	no	—
256	C₂²×C₄₁	—	4	2	no	—
257	C₂²×C₄₁	#435	1	4	yes	—
258	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
259	C₂²×C₄₁	#518	1	2	yes	—
260	C₂²×C₄₁	C₂²×M₁₆	1	1	yes	characteristic
261	C₂²×C₄₁	C₂×#131	1	1	yes	characteristic
262	C₂²×C₄₁	#568	1	2	yes	—
263	C₄×C₄₁	—	2	2	no	—
264	C₄×C₄₁	—	4	1	no	—
265	C₄×C₄₁	—	4	2	no	—
266	C₄×C₄₁	—	4	1	no	—
267	C₄×C₄₁	—	4	1	no	—
268	C₄×C₄₁	—	4	2	no	—
269	C₄×C₄₁	—	4	2	no	—
270	C₄×C₄₁	#534	1	1	yes	characteristic
271	C₄×C₄₁	#535	1	1	yes	characteristic
272	C₄×C₄₁	#538	1	2	yes	—
273	C₂×#435	C₂×C₄₁	1	1	yes	characteristic, complemented
274	C₂²×C₂²⋊C₈	C₂×C₄₁	1	1	yes	characteristic, complemented
275	C₄×#120	C₂×C₄₁	1	1	yes	characteristic
276	#1955	C₂×C₄₁	1	2	yes	complemented
277	#1924	C₂×C₄₁	1	2	yes	complemented
278	#1924	C₂×C₄₁	1	2	yes	complemented
279	#1870	C₂×C₄₁	1	2	yes	complemented
280	#1869	C₂×C₄₁	1	1	yes	characteristic, complemented
281	#1850	C₂×C₄₁	1	1	yes	characteristic, complemented
282	#1779	C₂×C₄₁	1	1	yes	characteristic, complemented
283	#1752	C₂×C₄₁	1	1	yes	characteristic, complemented
284	C₂×C₄₁	—	2	4	no	—
285	C₂×C₄₁	—	4	4	no	—
286	C₂×C₄₁	—	8	1	no	—
287	C₂×C₄₁	#2321	1	1	yes	characteristic
288	C₂×C₄₁	C₂×#435	1	1	yes	characteristic
289	C₂×C₄₁	#2930	1	1	yes	characteristic
290	C₂×C₄₁	#2973	1	2	yes	—
291	C₂×C₄₁	#2976	1	2	yes	—
292	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
293	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
294	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
295	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
296	C₂×#120	C₄×C₄₁	1	1	yes	characteristic
297	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
298	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
299	#435	—	2	4	no	—
300	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
301	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	complemented
302	C₂×C₂²⋊C₈	—	2	4	no	—
303	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
304	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
305	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
306	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
307	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
308	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
309	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
310	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	complemented
311	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic, complemented
312	C₂×#97	C₂²×C₄₁	1	2	yes	complemented
313	#386	C₄×C₄₁	1	2	yes	—
314	#386	C₄×C₄₁	1	1	yes	characteristic
315	#385	C₄×C₄₁	1	1	yes	characteristic
316	#385	C₄×C₄₁	1	2	yes	—
317	#379	C₄×C₄₁	1	1	yes	characteristic
318	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
319	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
320	#336	C₂²×C₄₁	1	2	yes	complemented
321	#336	C₂²×C₄₁	1	2	yes	complemented
322	#336	C₂²×C₄₁	1	2	yes	complemented
323	C₄₁	#22034	1	1	yes	characteristic, direct product factor, Sylow
324	C₂⁵	C₂×C₄×C₄₁	1	1	yes	characteristic
325	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
326	C₂²×D₄	C₂×C₄×C₄₁	1	2	yes	—
327	C₂³×C₄	—	2	2	no	—
328	C₂³×C₄	—	2	2	no	—
329	C₂³×C₄	—	4	2	no	—
330	C₂³×C₄	—	4	2	no	—
331	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
332	C₂³×C₄	C₂×C₄×C₄₁	1	2	yes	—
333	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
334	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
335	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
336	C₂×M₁₆	—	2	2	no	—
337	C₂×M₁₆	—	4	2	no	—
338	C₂²×C₈	—	2	2	no	—
339	C₂²×C₈	—	4	2	no	—
340	C₂²×C₈	—	4	2	no	—
341	C₂²×C₈	D₄×C₄₁	1	4	yes	complemented
342	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
343	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
344	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
345	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
346	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
347	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
348	#120	—	2	4	no	—
349	C₄×D₄	—	2	2	no	—
350	C₄×D₄	—	2	2	no	—
351	C₄×D₄	—	4	2	no	—
352	C₄×D₄	—	4	2	no	—
353	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
354	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
355	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
356	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
357	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
358	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
359	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
360	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
361	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
362	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
363	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
364	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
365	C₄⋊C₈	—	2	2	no	—
366	C₄⋊C₈	—	4	2	no	—
367	C₂²⋊C₈	—	2	2	no	—
368	C₂²⋊C₈	—	2	2	no	—
369	C₂²⋊C₈	—	2	4	no	—
370	C₂²⋊C₈	—	2	4	no	—
371	C₂²⋊C₈	—	2	2	no	—
372	C₂²⋊C₈	—	4	2	no	—
373	C₂²⋊C₈	—	4	2	no	—
374	C₂²⋊C₈	—	4	2	no	—
375	#97	—	2	2	no	—
376	#97	—	4	2	no	—
377	#95	C₂×C₄×C₄₁	1	2	yes	—
378	#95	C₂×C₄×C₄₁	1	2	yes	—
379	#95	C₂×C₄×C₄₁	1	2	yes	—
380	C₂⁴	—	2	2	no	—
381	C₂⁴	—	2	2	no	—
382	C₂⁴	—	4	2	no	—
383	C₂⁴	—	4	2	no	—
384	C₂⁴	M₁₆×C₄₁	1	4	yes	complemented
385	C₂⁴	C₂²×C₄×C₄₁	1	1	yes	characteristic
386	C₂⁴	C₂²×C₄×C₄₁	1	2	yes	—
387	C₂⁴	C₂²×C₄×C₄₁	1	1	yes	characteristic
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	4	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	4	2	no	—
393	C₂×D₄	—	4	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	4	2	no	—
409	C₂²×C₄	—	4	2	no	—
410	C₂²×C₄	—	4	2	no	—
411	C₂²×C₄	—	4	4	no	—
412	C₂²×C₄	—	4	4	no	—
413	C₂²×C₄	—	4	8	no	—
414	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
415	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
416	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
417	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
418	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
419	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
420	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
421	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
422	C₂²×C₄	#41×C₄₁	1	2	yes	—
423	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
424	M₁₆	—	4	4	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	2	1	no	—
428	C₂×C₈	—	2	2	no	—
429	C₂×C₈	—	2	1	no	—
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	4	4	no	—
438	C₂×C₈	—	4	4	no	—
439	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
440	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	4	2	no	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₂²⋊C₄	—	2	4	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₂²⋊C₄	—	4	2	no	—
449	C₂²⋊C₄	—	4	2	no	—
450	C₂²⋊C₄	—	4	2	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	2	1	no	—
453	C₄²	—	2	2	no	—
454	C₄²	—	2	2	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	2	2	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	2	8	no	—
464	C₂³	—	2	1	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	2	1	no	—
467	C₂³	—	2	1	no	—
468	C₂³	—	2	2	no	—
469	C₂³	—	4	8	no	—
470	C₂³	—	4	4	no	—
471	C₂³	—	4	4	no	—
472	C₂³	—	4	8	no	—
473	C₂³	C₄×D₄×C₄₁	1	2	yes	—
474	C₂³	C₂×M₁₆×C₄₁	1	4	yes	—
475	C₂³	C₂×M₁₆×C₄₁	1	2	yes	—
476	C₂³	#131×C₄₁	1	2	yes	—
477	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
478	D₄	—	4	8	no	—
479	D₄	—	4	4	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	4	8	no	—
501	C₂×C₄	—	4	4	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
510	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
511	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
512	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
513	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
514	C₈	—	2	2	no	—
515	C₈	—	2	2	no	—
516	C₈	—	4	1	no	—
517	C₈	—	4	2	no	—
518	C₈	—	4	1	no	—
519	C₈	—	4	2	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	4	no	—
523	C₂²	—	2	4	no	—
524	C₂²	—	2	4	no	—
525	C₂²	—	2	4	no	—
526	C₂²	—	2	4	no	—
527	C₂²	—	4	16	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	1	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	4	2	no	—
537	C₂²	C₄₁×#435	1	4	yes	—
538	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
539	C₂²	C₄₁×#518	1	2	yes	—
540	C₂²	C₂²×M₁₆×C₄₁	1	1	yes	characteristic
541	C₂²	C₂×#131×C₄₁	1	1	yes	characteristic
542	C₂²	C₄₁×#568	1	2	yes	—
543	C₄	—	2	2	no	—
544	C₄	—	4	2	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	1	no	—
548	C₄	—	4	2	no	—
549	C₄	—	4	2	no	—
550	C₄	C₄₁×#534	1	1	yes	characteristic
551	C₄	C₄₁×#535	1	1	yes	characteristic
552	C₄	C₄₁×#538	1	2	yes	—
553	C₂	—	2	4	no	—
554	C₂	—	4	4	no	—
555	C₂	—	8	1	no	—
556	C₂	C₄₁×#2321	1	1	yes	characteristic
557	C₂	C₂×C₄₁×#435	1	1	yes	characteristic
558	C₂	C₄₁×#2930	1	1	yes	characteristic
559	C₂	C₄₁×#2973	1	2	yes	—
560	C₂	C₄₁×#2976	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₄₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
socle	C₂³×C₄₁	C₂³×C₄
prime radical	C₂×#120×C₄₁	C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#435	C₂	semidirect
2. C₂²×C₂²⋊C₈×C₄₁	C₂	semidirect
4. C₄₁×#1955	C₂	semidirect
5. C₄₁×#1924	C₂	semidirect
6. C₄₁×#1924	C₂	semidirect
7. C₄₁×#1870	C₂	semidirect
8. C₄₁×#1869	C₂	semidirect
9. C₄₁×#1850	C₂	semidirect
10. C₄₁×#1779	C₂	semidirect
11. C₄₁×#1752	C₂	semidirect
13. C₂²×M₁₆×C₄₁	C₂²	semidirect
20. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
21. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
29. C₂×C₂²⋊C₈×C₄₁	C₂²	semidirect
30. C₂×C₂²⋊C₈×C₄₁	C₂²	semidirect
31. C₂×#97×C₄₁	C₂²	semidirect
32. C₂×#97×C₄₁	C₂²	semidirect
40. C₄₁×#336	C₂²	semidirect
41. C₄₁×#336	C₂²	semidirect
42. C₄₁×#336	C₂²	semidirect
60. C₂²×C₈×C₄₁	D₄	semidirect
103. C₂⁴×C₄₁	M₁₆	semidirect
239. #22034	C₄₁	direct (N × H)
273. C₂×#435	C₂×C₄₁	semidirect
274. C₂²×C₂²⋊C₈	C₂×C₄₁	semidirect
276. #1955	C₂×C₄₁	semidirect
277. #1924	C₂×C₄₁	semidirect
278. #1924	C₂×C₄₁	semidirect
279. #1870	C₂×C₄₁	semidirect
280. #1869	C₂×C₄₁	semidirect
281. #1850	C₂×C₄₁	semidirect
282. #1779	C₂×C₄₁	semidirect
283. #1752	C₂×C₄₁	semidirect
293. C₂²×M₁₆	C₂²×C₄₁	semidirect
300. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
301. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
309. C₂×C₂²⋊C₈	C₂²×C₄₁	semidirect
310. C₂×C₂²⋊C₈	C₂²×C₄₁	semidirect
311. C₂×#97	C₂²×C₄₁	semidirect
312. C₂×#97	C₂²×C₄₁	semidirect
320. #336	C₂²×C₄₁	semidirect
321. #336	C₂²×C₄₁	semidirect
322. #336	C₂²×C₄₁	semidirect
323. C₄₁	#22034	direct (N × H)
341. C₂²×C₈	D₄×C₄₁	semidirect
384. C₂⁴	M₁₆×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×#435	2
C₂²×C₂²⋊C₈×C₄₁	2
C₄×#120×C₄₁	2
C₄₁×#1955	2
C₄₁×#1924	2
C₄₁×#1870	2
C₄₁×#1869	2
C₄₁×#1850	2
C₄₁×#1779	2
C₄₁×#1752	2
#22034	41

Subgroups — C41×#22034 #23798235

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#22034 #23798235