Subgroups — C₄₁×#24129 #23800330

Order 10496.

1204 conjugacy classes of subgroups.

The subgroup lattice has 564 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×C₄₁×#474	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#442	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2535	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2033	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1999	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1993	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1955	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1875	C₂	1	2	yes	maximal, complemented
10	C₄₁×#1854	C₂	1	2	yes	maximal, complemented
11	C₄₁×#1804	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₄₁×#555	—	2	4	no	—
14	C₄₁×#555	—	2	4	no	—
15	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×#124×C₄₁	—	2	2	no	—
17	C₂×#121×C₄₁	—	2	1	no	—
18	C₂×#121×C₄₁	C₂²	1	2	yes	—
19	C₂×#121×C₄₁	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×#117×C₄₁	—	2	1	no	—
24	C₂×#117×C₄₁	C₂²	1	2	yes	—
25	C₄₁×#474	—	2	4	no	—
26	C₄₁×#442	—	2	4	no	—
27	C₂×#107×C₄₁	C₂²	1	2	yes	—
28	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
30	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×#102×C₄₁	C₂²	1	2	yes	—
32	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
33	C₂×#102×C₄₁	C₂²	1	2	yes	—
34	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
35	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
36	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
37	C₄₁×#397	—	2	1	no	—
38	C₄₁×#392	—	2	1	no	—
39	C₄₁×#386	—	2	2	no	—
40	C₄₁×#382	C₂²	1	1	yes	characteristic
41	C₄₁×#380	C₂²	1	2	yes	—
42	C₄₁×#340	C₂²	1	2	yes	—
43	C₄₁×#340	C₂²	1	2	yes	—
44	C₄₁×#340	C₂²	1	2	yes	—
45	C₂²×Q₈×C₄₁	—	2	1	no	—
46	C₂²×D₄×C₄₁	—	2	2	no	—
47	C₂²×D₄×C₄₁	—	2	2	no	—
48	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
49	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₄₁	—	2	1	no	—
52	C₂³×C₄×C₄₁	—	2	1	no	—
53	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
54	C₂×D₈×C₄₁	—	2	2	no	—
55	C₂×D₈×C₄₁	—	2	2	no	—
56	C₂×D₈×C₄₁	—	2	2	no	—
57	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
59	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
60	C₄⋊Q₈×C₄₁	—	2	2	no	—
61	C₄⋊Q₈×C₄₁	D₄	1	4	yes	complemented
62	#124×C₄₁	—	2	16	no	—
63	#121×C₄₁	—	2	8	no	—
64	#121×C₄₁	—	2	4	no	—
65	#121×C₄₁	—	2	4	no	—
66	#121×C₄₁	—	2	4	no	—
67	#121×C₄₁	—	4	2	no	—
68	C₄×D₄×C₄₁	—	2	2	no	—
69	C₄×D₄×C₄₁	—	2	2	no	—
70	C₄×D₄×C₄₁	—	2	2	no	—
71	C₄×D₄×C₄₁	—	2	2	no	—
72	C₄×D₄×C₄₁	—	2	2	no	—
73	C₄×D₄×C₄₁	D₄	1	4	yes	complemented
74	#117×C₄₁	—	2	8	no	—
75	#117×C₄₁	—	2	4	no	—
76	#117×C₄₁	—	2	4	no	—
77	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
78	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
83	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
89	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
90	C₂×C₄²×C₄₁	—	2	2	no	—
91	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
92	#107×C₄₁	—	2	4	no	—
93	#106×C₄₁	—	2	2	no	—
94	C₄⋊C₈×C₄₁	—	2	2	no	—
95	#102×C₄₁	—	2	2	no	—
96	#102×C₄₁	—	2	2	no	—
97	#102×C₄₁	—	2	4	no	—
98	#102×C₄₁	—	4	2	no	—
99	C₂²⋊C₈×C₄₁	—	2	4	no	—
100	C₂²⋊C₈×C₄₁	—	4	2	no	—
101	#97×C₄₁	—	2	2	no	—
102	#95×C₄₁	—	2	2	no	—
103	#95×C₄₁	—	2	1	no	—
104	#95×C₄₁	—	2	1	no	—
105	C₂⁴×C₄₁	—	2	1	no	—
106	C₂⁴×C₄₁	—	2	1	no	—
107	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
108	C₂×Q₈×C₄₁	—	2	4	no	—
109	C₂×Q₈×C₄₁	—	8	2	no	—
110	C₂×D₄×C₄₁	—	2	8	no	—
111	C₂×D₄×C₄₁	—	2	2	no	—
112	C₂×D₄×C₄₁	—	2	1	no	—
113	C₂×D₄×C₄₁	—	2	1	no	—
114	C₂×D₄×C₄₁	—	2	1	no	—
115	C₂×D₄×C₄₁	—	2	1	no	—
116	C₂×D₄×C₄₁	—	2	1	no	—
117	C₂×D₄×C₄₁	—	2	1	no	—
118	C₂×D₄×C₄₁	—	2	1	no	—
119	C₂×D₄×C₄₁	—	2	1	no	—
120	C₂×D₄×C₄₁	—	2	1	no	—
121	C₂×D₄×C₄₁	—	2	1	no	—
122	C₂×D₄×C₄₁	—	4	2	no	—
123	C₂×D₄×C₄₁	—	4	4	no	—
124	C₂×D₄×C₄₁	—	4	4	no	—
125	C₂×D₄×C₄₁	—	8	2	no	—
126	C₂×D₄×C₄₁	—	8	2	no	—
127	C₂×D₄×C₄₁	—	8	2	no	—
128	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
129	C₂×D₄×C₄₁	#41	1	2	yes	—
130	C₂²×C₄×C₄₁	—	2	1	no	—
131	C₂²×C₄×C₄₁	—	2	2	no	—
132	C₂²×C₄×C₄₁	—	2	4	no	—
133	C₂²×C₄×C₄₁	—	2	2	no	—
134	C₂²×C₄×C₄₁	—	2	2	no	—
135	C₂²×C₄×C₄₁	—	2	2	no	—
136	C₂²×C₄×C₄₁	—	2	2	no	—
137	C₂²×C₄×C₄₁	—	2	2	no	—
138	C₂²×C₄×C₄₁	—	2	2	no	—
139	C₂²×C₄×C₄₁	—	2	2	no	—
140	C₂²×C₄×C₄₁	—	2	1	no	—
141	C₂²×C₄×C₄₁	—	4	4	no	—
142	C₂²×C₄×C₄₁	—	4	2	no	—
143	C₂²×C₄×C₄₁	—	8	2	no	—
144	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
148	D₈×C₄₁	—	2	8	no	—
149	C₂×C₈×C₄₁	—	2	1	no	—
150	C₂×C₈×C₄₁	—	2	1	no	—
151	C₂×C₈×C₄₁	—	2	1	no	—
152	C₂×C₈×C₄₁	—	2	2	no	—
153	C₂×C₈×C₄₁	—	2	2	no	—
154	C₂×C₈×C₄₁	—	2	1	no	—
155	C₂×C₈×C₄₁	—	2	2	no	—
156	C₂×C₈×C₄₁	—	2	1	no	—
157	C₂×C₈×C₄₁	#41	1	2	yes	—
158	C₄⋊C₄×C₄₁	—	2	4	no	—
159	C₄⋊C₄×C₄₁	—	2	2	no	—
160	C₄⋊C₄×C₄₁	—	2	1	no	—
161	C₄⋊C₄×C₄₁	—	2	2	no	—
162	C₄⋊C₄×C₄₁	—	2	1	no	—
163	C₄⋊C₄×C₄₁	—	2	1	no	—
164	C₄⋊C₄×C₄₁	—	2	2	no	—
165	C₄⋊C₄×C₄₁	—	2	2	no	—
166	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
167	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
168	C₂²⋊C₄×C₄₁	—	2	8	no	—
169	C₂²⋊C₄×C₄₁	—	2	8	no	—
170	C₂²⋊C₄×C₄₁	—	2	4	no	—
171	C₂²⋊C₄×C₄₁	—	2	4	no	—
172	C₂²⋊C₄×C₄₁	—	4	4	no	—
173	C₂²⋊C₄×C₄₁	—	4	2	no	—
174	C₂²⋊C₄×C₄₁	—	8	2	no	—
175	C₄²×C₄₁	—	2	8	no	—
176	C₄²×C₄₁	C₂×D₄	1	2	yes	—
177	C₄²×C₄₁	C₂×D₄	1	2	yes	—
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	2	no	—
183	C₂³×C₄₁	—	2	2	no	—
184	C₂³×C₄₁	—	2	2	no	—
185	C₂³×C₄₁	—	2	2	no	—
186	C₂³×C₄₁	—	2	2	no	—
187	C₂³×C₄₁	—	4	1	no	—
188	C₂³×C₄₁	—	4	1	no	—
189	C₂³×C₄₁	—	4	1	no	—
190	C₂³×C₄₁	—	4	1	no	—
191	C₂³×C₄₁	—	4	2	no	—
192	C₂³×C₄₁	—	4	2	no	—
193	C₂³×C₄₁	—	4	2	no	—
194	C₂³×C₄₁	—	4	2	no	—
195	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
196	Q₈×C₄₁	—	8	4	no	—
197	D₄×C₄₁	—	2	2	no	—
198	D₄×C₄₁	—	2	2	no	—
199	D₄×C₄₁	—	2	2	no	—
200	D₄×C₄₁	—	2	2	no	—
201	D₄×C₄₁	—	4	4	no	—
202	D₄×C₄₁	—	4	1	no	—
203	D₄×C₄₁	—	4	1	no	—
204	D₄×C₄₁	—	4	1	no	—
205	D₄×C₄₁	—	4	1	no	—
206	D₄×C₄₁	—	8	8	no	—
207	D₄×C₄₁	—	8	8	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	4	no	—
213	C₂×C₄×C₄₁	—	2	2	no	—
214	C₂×C₄×C₄₁	—	2	2	no	—
215	C₂×C₄×C₄₁	—	4	8	no	—
216	C₂×C₄×C₄₁	—	4	2	no	—
217	C₂×C₄×C₄₁	—	4	2	no	—
218	C₂×C₄×C₄₁	—	4	2	no	—
219	C₂×C₄×C₄₁	—	4	2	no	—
220	C₂×C₄×C₄₁	—	4	2	no	—
221	C₂×C₄×C₄₁	—	4	2	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	—	8	4	no	—
229	C₂×C₄×C₄₁	#120	1	2	yes	—
230	C₂×C₄×C₄₁	#120	1	2	yes	—
231	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
235	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
236	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
237	C₈×C₄₁	—	2	2	no	—
238	C₈×C₄₁	—	4	1	no	—
239	C₈×C₄₁	—	4	2	no	—
240	#24129	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
241	C₂²×C₄₁	—	4	2	no	—
242	C₂²×C₄₁	—	4	2	no	—
243	C₂²×C₄₁	—	4	2	no	—
244	C₂²×C₄₁	—	4	2	no	—
245	C₂²×C₄₁	—	4	2	no	—
246	C₂²×C₄₁	—	4	2	no	—
247	C₂²×C₄₁	—	4	2	no	—
248	C₂²×C₄₁	—	4	2	no	—
249	C₂²×C₄₁	—	4	2	no	—
250	C₂²×C₄₁	—	4	2	no	—
251	C₂²×C₄₁	—	4	4	no	—
252	C₂²×C₄₁	—	4	2	no	—
253	C₂²×C₄₁	—	8	2	no	—
254	C₂²×C₄₁	—	8	2	no	—
255	C₂²×C₄₁	—	8	1	no	—
256	C₂²×C₄₁	—	8	1	no	—
257	C₂²×C₄₁	—	8	2	no	—
258	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
259	C₂²×C₄₁	#546	1	1	yes	characteristic
260	C₂²×C₄₁	#547	1	1	yes	characteristic
261	C₂²×C₄₁	#575	1	2	yes	—
262	C₂²×C₄₁	#576	1	2	yes	—
263	C₄×C₄₁	—	2	2	no	—
264	C₄×C₄₁	—	2	2	no	—
265	C₄×C₄₁	—	4	2	no	—
266	C₄×C₄₁	—	4	2	no	—
267	C₄×C₄₁	—	4	4	no	—
268	C₄×C₄₁	—	8	1	no	—
269	C₄×C₄₁	—	8	2	no	—
270	C₄×C₄₁	#525	1	1	yes	characteristic
271	C₄×C₄₁	#537	1	1	yes	characteristic
272	C₄×C₄₁	#548	1	1	yes	characteristic
273	C₄×C₄₁	#550	1	1	yes	characteristic
274	C₂×#555	C₂×C₄₁	1	1	yes	characteristic, complemented
275	C₂×#474	C₂×C₄₁	1	1	yes	characteristic, complemented
276	C₂×#442	C₂×C₄₁	1	1	yes	characteristic, complemented
277	#2535	C₂×C₄₁	1	1	yes	characteristic, complemented
278	#2033	C₂×C₄₁	1	2	yes	complemented
279	#1999	C₂×C₄₁	1	2	yes	complemented
280	#1993	C₂×C₄₁	1	1	yes	characteristic, complemented
281	#1955	C₂×C₄₁	1	1	yes	characteristic, complemented
282	#1875	C₂×C₄₁	1	2	yes	complemented
283	#1854	C₂×C₄₁	1	2	yes	complemented
284	#1804	C₂×C₄₁	1	1	yes	characteristic, complemented
285	C₂×C₄₁	—	8	2	no	—
286	C₂×C₄₁	—	8	2	no	—
287	C₂×C₄₁	—	8	2	no	—
288	C₂×C₄₁	#2407	1	1	yes	characteristic
289	C₂×C₄₁	#3005	1	1	yes	characteristic
290	C₂×C₄₁	#3008	1	1	yes	characteristic
291	C₂×C₄₁	#3319	1	2	yes	—
292	C₂×C₄₁	#3347	1	2	yes	—
293	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
294	#555	—	2	4	no	—
295	#555	—	2	4	no	—
296	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
297	C₂×#124	—	2	2	no	—
298	C₂×#121	—	2	1	no	—
299	C₂×#121	C₂²×C₄₁	1	2	yes	—
300	C₂×#121	C₂²×C₄₁	1	2	yes	—
301	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
302	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
303	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
304	C₂×#117	—	2	1	no	—
305	C₂×#117	C₂²×C₄₁	1	2	yes	—
306	#474	—	2	4	no	—
307	#442	—	2	4	no	—
308	C₂×#107	C₂²×C₄₁	1	2	yes	—
309	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
310	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
311	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
312	C₂×#102	C₂²×C₄₁	1	2	yes	—
313	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
314	C₂×#102	C₂²×C₄₁	1	2	yes	—
315	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
316	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
317	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
318	#397	—	2	1	no	—
319	#392	—	2	1	no	—
320	#386	—	2	2	no	—
321	#382	C₂²×C₄₁	1	1	yes	characteristic
322	#380	C₂²×C₄₁	1	2	yes	—
323	#340	C₂²×C₄₁	1	2	yes	—
324	#340	C₂²×C₄₁	1	2	yes	—
325	#340	C₂²×C₄₁	1	2	yes	—
326	C₄₁	#24129	1	1	yes	characteristic, direct product factor, Sylow
327	C₂²×Q₈	—	2	1	no	—
328	C₂²×D₄	—	2	2	no	—
329	C₂²×D₄	—	2	2	no	—
330	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
331	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
332	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
333	C₂³×C₄	—	2	1	no	—
334	C₂³×C₄	—	2	1	no	—
335	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
336	C₂×D₈	—	2	2	no	—
337	C₂×D₈	—	2	2	no	—
338	C₂×D₈	—	2	2	no	—
339	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
340	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
341	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
342	C₄⋊Q₈	—	2	2	no	—
343	C₄⋊Q₈	D₄×C₄₁	1	4	yes	complemented
344	#124	—	2	16	no	—
345	#121	—	2	8	no	—
346	#121	—	2	4	no	—
347	#121	—	2	4	no	—
348	#121	—	2	4	no	—
349	#121	—	4	2	no	—
350	C₄×D₄	—	2	2	no	—
351	C₄×D₄	—	2	2	no	—
352	C₄×D₄	—	2	2	no	—
353	C₄×D₄	—	2	2	no	—
354	C₄×D₄	—	2	2	no	—
355	C₄×D₄	D₄×C₄₁	1	4	yes	complemented
356	#117	—	2	8	no	—
357	#117	—	2	4	no	—
358	#117	—	2	4	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
363	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
365	C₂×C₂²⋊C₄	—	2	2	no	—
366	C₂×C₂²⋊C₄	—	2	2	no	—
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₂²⋊C₄	—	2	1	no	—
369	C₂×C₂²⋊C₄	—	2	2	no	—
370	C₂×C₂²⋊C₄	—	2	2	no	—
371	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
372	C₂×C₄²	—	2	2	no	—
373	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
374	#107	—	2	4	no	—
375	#106	—	2	2	no	—
376	C₄⋊C₈	—	2	2	no	—
377	#102	—	2	2	no	—
378	#102	—	2	2	no	—
379	#102	—	2	4	no	—
380	#102	—	4	2	no	—
381	C₂²⋊C₈	—	2	4	no	—
382	C₂²⋊C₈	—	4	2	no	—
383	#97	—	2	2	no	—
384	#95	—	2	2	no	—
385	#95	—	2	1	no	—
386	#95	—	2	1	no	—
387	C₂⁴	—	2	1	no	—
388	C₂⁴	—	2	1	no	—
389	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
390	C₂×Q₈	—	2	4	no	—
391	C₂×Q₈	—	8	2	no	—
392	C₂×D₄	—	2	8	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	1	no	—
399	C₂×D₄	—	2	1	no	—
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	—	2	1	no	—
402	C₂×D₄	—	2	1	no	—
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	—	4	2	no	—
405	C₂×D₄	—	4	4	no	—
406	C₂×D₄	—	4	4	no	—
407	C₂×D₄	—	8	2	no	—
408	C₂×D₄	—	8	2	no	—
409	C₂×D₄	—	8	2	no	—
410	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
411	C₂×D₄	#41×C₄₁	1	2	yes	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	4	4	no	—
424	C₂²×C₄	—	4	2	no	—
425	C₂²×C₄	—	8	2	no	—
426	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
427	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
429	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
430	D₈	—	2	8	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	#41×C₄₁	1	2	yes	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
449	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
450	C₂²⋊C₄	—	2	8	no	—
451	C₂²⋊C₄	—	2	8	no	—
452	C₂²⋊C₄	—	2	4	no	—
453	C₂²⋊C₄	—	2	4	no	—
454	C₂²⋊C₄	—	4	4	no	—
455	C₂²⋊C₄	—	4	2	no	—
456	C₂²⋊C₄	—	8	2	no	—
457	C₄²	—	2	8	no	—
458	C₄²	C₂×D₄×C₄₁	1	2	yes	—
459	C₄²	C₂×D₄×C₄₁	1	2	yes	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	2	2	no	—
469	C₂³	—	4	1	no	—
470	C₂³	—	4	1	no	—
471	C₂³	—	4	1	no	—
472	C₂³	—	4	1	no	—
473	C₂³	—	4	2	no	—
474	C₂³	—	4	2	no	—
475	C₂³	—	4	2	no	—
476	C₂³	—	4	2	no	—
477	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
478	Q₈	—	8	4	no	—
479	D₄	—	2	2	no	—
480	D₄	—	2	2	no	—
481	D₄	—	2	2	no	—
482	D₄	—	2	2	no	—
483	D₄	—	4	4	no	—
484	D₄	—	4	1	no	—
485	D₄	—	4	1	no	—
486	D₄	—	4	1	no	—
487	D₄	—	4	1	no	—
488	D₄	—	8	8	no	—
489	D₄	—	8	8	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	4	8	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	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	—	4	2	no	—
510	C₂×C₄	—	8	4	no	—
511	C₂×C₄	#120×C₄₁	1	2	yes	—
512	C₂×C₄	#120×C₄₁	1	2	yes	—
513	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
514	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
515	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
516	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
517	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
518	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
519	C₈	—	2	2	no	—
520	C₈	—	4	1	no	—
521	C₈	—	4	2	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	4	4	no	—
524	C₂²	—	4	2	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	8	2	no	—
535	C₂²	—	8	2	no	—
536	C₂²	—	8	2	no	—
537	C₂²	—	8	1	no	—
538	C₂²	—	8	1	no	—
539	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
540	C₂²	C₄₁×#546	1	1	yes	characteristic
541	C₂²	C₄₁×#547	1	1	yes	characteristic
542	C₂²	C₄₁×#575	1	2	yes	—
543	C₂²	C₄₁×#576	1	2	yes	—
544	C₄	—	2	2	no	—
545	C₄	—	2	2	no	—
546	C₄	—	4	2	no	—
547	C₄	—	4	2	no	—
548	C₄	—	4	4	no	—
549	C₄	—	8	2	no	—
550	C₄	—	8	1	no	—
551	C₄	C₄₁×#525	1	1	yes	characteristic
552	C₄	C₄₁×#537	1	1	yes	characteristic
553	C₄	C₄₁×#548	1	1	yes	characteristic
554	C₄	C₄₁×#550	1	1	yes	characteristic
555	C₂	—	8	2	no	—
556	C₂	—	8	2	no	—
557	C₂	—	8	2	no	—
558	C₂	C₄₁×#2407	1	1	yes	characteristic
559	C₂	C₄₁×#3005	1	1	yes	characteristic
560	C₂	C₄₁×#3008	1	1	yes	characteristic
561	C₂	C₄₁×#3319	1	2	yes	—
562	C₂	C₄₁×#3347	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
LCS	G ▷ C₂²×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×C₄₁×#474	C₂	semidirect
3. C₂×C₄₁×#442	C₂	semidirect
4. C₄₁×#2535	C₂	semidirect
5. C₄₁×#2033	C₂	semidirect
6. C₄₁×#1999	C₂	semidirect
7. C₄₁×#1993	C₂	semidirect
8. C₄₁×#1955	C₂	semidirect
9. C₄₁×#1875	C₂	semidirect
10. C₄₁×#1854	C₂	semidirect
11. C₄₁×#1804	C₂	semidirect
61. C₄⋊Q₈×C₄₁	D₄	semidirect
73. C₄×D₄×C₄₁	D₄	semidirect
240. #24129	C₄₁	direct (N × H)
274. C₂×#555	C₂×C₄₁	semidirect
275. C₂×#474	C₂×C₄₁	semidirect
276. C₂×#442	C₂×C₄₁	semidirect
277. #2535	C₂×C₄₁	semidirect
278. #2033	C₂×C₄₁	semidirect
279. #1999	C₂×C₄₁	semidirect
280. #1993	C₂×C₄₁	semidirect
281. #1955	C₂×C₄₁	semidirect
282. #1875	C₂×C₄₁	semidirect
283. #1854	C₂×C₄₁	semidirect
284. #1804	C₂×C₄₁	semidirect
326. C₄₁	#24129	direct (N × H)
343. C₄⋊Q₈	D₄×C₄₁	semidirect
355. C₄×D₄	D₄×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×#555	2
C₂×C₄₁×#474	2
C₂×C₄₁×#442	2
C₄₁×#2535	2
C₄₁×#2033	2
C₄₁×#1999	2
C₄₁×#1993	2
C₄₁×#1955	2
C₄₁×#1875	2
C₄₁×#1854	2
C₄₁×#1804	2
#24129	41

Subgroups — C41×#24129 #23800330

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#24129 #23800330