Subgroups — C₄₁×#23137 #23799338

Order 10496.

966 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#466	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2363	C₂	1	2	yes	maximal, complemented
3	C₄₁×#1936	C₂	1	2	yes	maximal, complemented
4	C₄₁×#1918	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1879	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1875	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1762	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1752	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1735	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
12	C₂×#121×C₄₁	C₂²	1	2	yes	—
13	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
14	C₂×#117×C₄₁	C₂²	1	2	yes	—
15	C₄₁×#466	C₄	1	8	yes	complemented
16	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
17	C₂×#102×C₄₁	C₂²	1	2	yes	—
18	C₂×#102×C₄₁	C₂²	1	2	yes	—
19	C₂×#102×C₄₁	C₂²	1	2	yes	—
20	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×#97×C₄₁	C₂²	1	2	yes	—
22	C₄₁×#390	—	2	2	no	—
23	C₄₁×#390	C₂²	1	2	yes	—
24	C₄₁×#389	C₂²	1	2	yes	—
25	C₄₁×#388	—	2	2	no	—
26	C₄₁×#386	—	2	2	no	—
27	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
28	C₄×C₂²⋊C₄×C₄₁	—	2	2	no	—
29	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
30	C₄₁×#340	C₂²	1	1	yes	characteristic
31	C₄₁×#340	C₂²	1	2	yes	—
32	C₄₁×#340	C₂²	1	2	yes	—
33	C₄₁×#340	C₂²	1	2	yes	—
34	C₄₁×#340	C₂²	1	1	yes	characteristic
35	C₄₁×#336	C₂²	1	2	yes	—
36	C₂²×D₄×C₄₁	—	2	2	no	—
37	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
38	C₂³×C₄×C₄₁	—	2	2	no	—
39	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
40	C₂×D₈×C₄₁	—	4	2	no	—
41	C₂×D₈×C₄₁	C₂×C₄	1	4	yes	—
42	C₂²×C₈×C₄₁	—	4	2	no	—
43	C₂²×C₈×C₄₁	C₂×C₄	1	4	yes	complemented
44	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
45	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
47	#121×C₄₁	—	2	4	no	—
48	#121×C₄₁	C₂×C₄	1	8	yes	complemented
49	C₄×D₄×C₄₁	—	2	4	no	—
50	C₄×D₄×C₄₁	—	4	2	no	—
51	#117×C₄₁	—	2	4	no	—
52	#117×C₄₁	—	4	2	no	—
53	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
54	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
57	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
63	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₄₁	—	2	2	no	—
65	C₂×C₄²×C₄₁	—	2	2	no	—
66	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
67	#107×C₄₁	C₂×C₄	1	4	yes	complemented
68	#102×C₄₁	—	2	4	no	—
69	#102×C₄₁	—	4	2	no	—
70	#102×C₄₁	C₂×C₄	1	8	yes	complemented
71	C₂²⋊C₈×C₄₁	—	2	2	no	—
72	#97×C₄₁	—	4	2	no	—
73	#95×C₄₁	—	2	2	no	—
74	#95×C₄₁	—	2	2	no	—
75	#95×C₄₁	D₄	1	2	yes	—
76	C₂⁴×C₄₁	—	2	2	no	—
77	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
78	C₂×D₄×C₄₁	—	2	8	no	—
79	C₂×D₄×C₄₁	—	2	2	no	—
80	C₂×D₄×C₄₁	—	2	2	no	—
81	C₂×D₄×C₄₁	—	2	2	no	—
82	C₂×D₄×C₄₁	—	2	2	no	—
83	C₂×D₄×C₄₁	—	2	2	no	—
84	C₂×D₄×C₄₁	—	8	2	no	—
85	C₂×D₄×C₄₁	—	8	2	no	—
86	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
87	C₂²×C₄×C₄₁	—	2	2	no	—
88	C₂²×C₄×C₄₁	—	2	2	no	—
89	C₂²×C₄×C₄₁	—	2	2	no	—
90	C₂²×C₄×C₄₁	—	2	2	no	—
91	C₂²×C₄×C₄₁	—	2	2	no	—
92	C₂²×C₄×C₄₁	—	4	4	no	—
93	C₂²×C₄×C₄₁	—	4	4	no	—
94	C₂²×C₄×C₄₁	—	8	2	no	—
95	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₁	#41	1	2	yes	—
100	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
101	D₈×C₄₁	—	4	4	no	—
102	C₂×C₈×C₄₁	—	2	2	no	—
103	C₂×C₈×C₄₁	—	2	2	no	—
104	C₂×C₈×C₄₁	—	2	2	no	—
105	C₂×C₈×C₄₁	—	2	2	no	—
106	C₂×C₈×C₄₁	—	2	2	no	—
107	C₂×C₈×C₄₁	—	4	4	no	—
108	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
109	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
110	C₄⋊C₄×C₄₁	—	2	2	no	—
111	C₄⋊C₄×C₄₁	—	2	2	no	—
112	C₄⋊C₄×C₄₁	—	2	2	no	—
113	C₄⋊C₄×C₄₁	—	2	2	no	—
114	C₄⋊C₄×C₄₁	—	8	2	no	—
115	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
116	C₄⋊C₄×C₄₁	#41	1	4	yes	—
117	C₂²⋊C₄×C₄₁	—	2	8	no	—
118	C₂²⋊C₄×C₄₁	—	4	1	no	—
119	C₂²⋊C₄×C₄₁	—	4	1	no	—
120	C₂²⋊C₄×C₄₁	—	4	4	no	—
121	C₂²⋊C₄×C₄₁	—	4	4	no	—
122	C₂²⋊C₄×C₄₁	—	4	4	no	—
123	C₂²⋊C₄×C₄₁	—	8	2	no	—
124	C₄²×C₄₁	—	2	2	no	—
125	C₄²×C₄₁	—	2	2	no	—
126	C₄²×C₄₁	—	4	4	no	—
127	C₄²×C₄₁	—	8	2	no	—
128	C₂³×C₄₁	—	2	2	no	—
129	C₂³×C₄₁	—	2	1	no	—
130	C₂³×C₄₁	—	2	1	no	—
131	C₂³×C₄₁	—	2	2	no	—
132	C₂³×C₄₁	—	2	4	no	—
133	C₂³×C₄₁	—	4	2	no	—
134	C₂³×C₄₁	—	4	2	no	—
135	C₂³×C₄₁	—	4	2	no	—
136	C₂³×C₄₁	—	4	2	no	—
137	C₂³×C₄₁	—	4	2	no	—
138	C₂³×C₄₁	—	4	2	no	—
139	C₂³×C₄₁	C₄×D₄	1	2	yes	—
140	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
141	D₄×C₄₁	—	2	4	no	—
142	D₄×C₄₁	—	2	4	no	—
143	D₄×C₄₁	—	4	2	no	—
144	D₄×C₄₁	—	4	2	no	—
145	D₄×C₄₁	—	8	8	no	—
146	C₂×C₄×C₄₁	—	2	2	no	—
147	C₂×C₄×C₄₁	—	2	2	no	—
148	C₂×C₄×C₄₁	—	2	2	no	—
149	C₂×C₄×C₄₁	—	2	4	no	—
150	C₂×C₄×C₄₁	—	2	4	no	—
151	C₂×C₄×C₄₁	—	2	2	no	—
152	C₂×C₄×C₄₁	—	2	2	no	—
153	C₂×C₄×C₄₁	—	2	4	no	—
154	C₂×C₄×C₄₁	—	2	2	no	—
155	C₂×C₄×C₄₁	—	2	2	no	—
156	C₂×C₄×C₄₁	—	2	2	no	—
157	C₂×C₄×C₄₁	—	2	2	no	—
158	C₂×C₄×C₄₁	—	4	2	no	—
159	C₂×C₄×C₄₁	—	4	2	no	—
160	C₂×C₄×C₄₁	—	4	2	no	—
161	C₂×C₄×C₄₁	—	4	2	no	—
162	C₂×C₄×C₄₁	—	4	2	no	—
163	C₂×C₄×C₄₁	—	4	2	no	—
164	C₂×C₄×C₄₁	—	4	2	no	—
165	C₂×C₄×C₄₁	—	8	8	no	—
166	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
169	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
171	C₈×C₄₁	—	2	2	no	—
172	C₈×C₄₁	—	2	2	no	—
173	C₈×C₄₁	—	4	2	no	—
174	#23137	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂²×C₄₁	—	2	2	no	—
176	C₂²×C₄₁	—	2	2	no	—
177	C₂²×C₄₁	—	2	2	no	—
178	C₂²×C₄₁	—	4	2	no	—
179	C₂²×C₄₁	—	4	2	no	—
180	C₂²×C₄₁	—	4	4	no	—
181	C₂²×C₄₁	—	4	4	no	—
182	C₂²×C₄₁	—	4	4	no	—
183	C₂²×C₄₁	—	8	2	no	—
184	C₂²×C₄₁	—	8	2	no	—
185	C₂²×C₄₁	—	8	2	no	—
186	C₂²×C₄₁	—	8	2	no	—
187	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
188	C₂²×C₄₁	#546	1	2	yes	—
189	C₂²×C₄₁	#575	1	1	yes	characteristic
190	C₂²×C₄₁	#575	1	1	yes	characteristic
191	C₂²×C₄₁	#576	1	2	yes	—
192	C₄×C₄₁	—	2	2	no	—
193	C₄×C₄₁	—	4	4	no	—
194	C₄×C₄₁	—	4	2	no	—
195	C₄×C₄₁	—	4	2	no	—
196	C₄×C₄₁	—	4	4	no	—
197	C₄×C₄₁	—	8	2	no	—
198	C₄×C₄₁	C₄×#41	1	1	yes	characteristic
199	C₄×C₄₁	#518	1	1	yes	characteristic
200	C₄×C₄₁	#553	1	2	yes	—
201	C₂×#466	C₂×C₄₁	1	1	yes	characteristic
202	#2363	C₂×C₄₁	1	2	yes	complemented
203	#1936	C₂×C₄₁	1	2	yes	complemented
204	#1918	C₂×C₄₁	1	2	yes	complemented
205	#1879	C₂×C₄₁	1	2	yes	complemented
206	#1875	C₂×C₄₁	1	2	yes	complemented
207	#1762	C₂×C₄₁	1	2	yes	complemented
208	#1752	C₂×C₄₁	1	1	yes	characteristic, complemented
209	#1735	C₂×C₄₁	1	1	yes	characteristic, complemented
210	C₂×C₄₁	—	4	2	no	—
211	C₂×C₄₁	—	8	4	no	—
212	C₂×C₄₁	#2364	1	1	yes	characteristic
213	C₂×C₄₁	#2943	1	1	yes	characteristic
214	C₂×C₄₁	#2948	1	1	yes	characteristic
215	C₂×C₄₁	#3309	1	2	yes	—
216	C₂×C₄₁	#3319	1	2	yes	—
217	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
218	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
219	C₂×#121	C₂²×C₄₁	1	2	yes	—
220	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
221	C₂×#117	C₂²×C₄₁	1	2	yes	—
222	#466	C₄×C₄₁	1	8	yes	complemented
223	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
224	C₂×#102	C₂²×C₄₁	1	2	yes	—
225	C₂×#102	C₂²×C₄₁	1	2	yes	—
226	C₂×#102	C₂²×C₄₁	1	2	yes	—
227	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
228	C₂×#97	C₂²×C₄₁	1	2	yes	—
229	#390	—	2	2	no	—
230	#390	C₂²×C₄₁	1	2	yes	—
231	#389	C₂²×C₄₁	1	2	yes	—
232	#388	—	2	2	no	—
233	#386	—	2	2	no	—
234	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
235	C₄×C₂²⋊C₄	—	2	2	no	—
236	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
237	#340	C₂²×C₄₁	1	2	yes	—
238	#340	C₂²×C₄₁	1	2	yes	—
239	#340	C₂²×C₄₁	1	2	yes	—
240	#340	C₂²×C₄₁	1	1	yes	characteristic
241	#340	C₂²×C₄₁	1	1	yes	characteristic
242	#336	C₂²×C₄₁	1	2	yes	—
243	C₄₁	#23137	1	1	yes	characteristic, direct product factor, Sylow
244	C₂²×D₄	—	2	2	no	—
245	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
246	C₂³×C₄	—	2	2	no	—
247	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
248	C₂×D₈	—	4	2	no	—
249	C₂×D₈	C₂×C₄×C₄₁	1	4	yes	—
250	C₂²×C₈	—	4	2	no	—
251	C₂²×C₈	C₂×C₄×C₄₁	1	4	yes	complemented
252	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
253	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
254	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
255	#121	—	2	4	no	—
256	#121	C₂×C₄×C₄₁	1	8	yes	complemented
257	C₄×D₄	—	2	4	no	—
258	C₄×D₄	—	4	2	no	—
259	#117	—	2	4	no	—
260	#117	—	4	2	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
271	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
272	C₂×C₄²	—	2	2	no	—
273	C₂×C₄²	—	2	2	no	—
274	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
275	#107	C₂×C₄×C₄₁	1	4	yes	complemented
276	#102	—	2	4	no	—
277	#102	—	4	2	no	—
278	#102	C₂×C₄×C₄₁	1	8	yes	complemented
279	C₂²⋊C₈	—	2	2	no	—
280	#97	—	4	2	no	—
281	#95	—	2	2	no	—
282	#95	—	2	2	no	—
283	#95	D₄×C₄₁	1	2	yes	—
284	C₂⁴	—	2	2	no	—
285	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
286	C₂×D₄	—	2	8	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	8	2	no	—
293	C₂×D₄	—	8	2	no	—
294	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	4	4	no	—
301	C₂²×C₄	—	4	4	no	—
302	C₂²×C₄	—	8	2	no	—
303	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
305	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
306	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
307	C₂²×C₄	#41×C₄₁	1	2	yes	—
308	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
309	D₈	—	4	4	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	4	4	no	—
316	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
317	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	8	2	no	—
323	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
324	C₄⋊C₄	#41×C₄₁	1	4	yes	—
325	C₂²⋊C₄	—	2	8	no	—
326	C₂²⋊C₄	—	4	1	no	—
327	C₂²⋊C₄	—	4	1	no	—
328	C₂²⋊C₄	—	4	4	no	—
329	C₂²⋊C₄	—	4	4	no	—
330	C₂²⋊C₄	—	4	4	no	—
331	C₂²⋊C₄	—	8	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	4	4	no	—
335	C₄²	—	8	2	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	2	no	—
340	C₂³	—	2	4	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	C₄×D₄×C₄₁	1	2	yes	—
348	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
349	D₄	—	2	4	no	—
350	D₄	—	2	4	no	—
351	D₄	—	4	2	no	—
352	D₄	—	4	2	no	—
353	D₄	—	8	8	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	8	8	no	—
374	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
375	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
376	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
377	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
378	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
379	C₈	—	2	2	no	—
380	C₈	—	2	2	no	—
381	C₈	—	4	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	4	no	—
388	C₂²	—	4	4	no	—
389	C₂²	—	4	4	no	—
390	C₂²	—	8	2	no	—
391	C₂²	—	8	2	no	—
392	C₂²	—	8	2	no	—
393	C₂²	—	8	2	no	—
394	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
395	C₂²	C₄₁×#546	1	2	yes	—
396	C₂²	C₄₁×#575	1	1	yes	characteristic
397	C₂²	C₄₁×#575	1	1	yes	characteristic
398	C₂²	C₄₁×#576	1	2	yes	—
399	C₄	—	2	2	no	—
400	C₄	—	4	2	no	—
401	C₄	—	4	2	no	—
402	C₄	—	4	4	no	—
403	C₄	—	4	4	no	—
404	C₄	—	8	2	no	—
405	C₄	C₄×#41×C₄₁	1	1	yes	characteristic
406	C₄	C₄₁×#518	1	1	yes	characteristic
407	C₄	C₄₁×#553	1	2	yes	—
408	C₂	—	4	2	no	—
409	C₂	—	8	4	no	—
410	C₂	C₄₁×#2364	1	1	yes	characteristic
411	C₂	C₄₁×#2943	1	1	yes	characteristic
412	C₂	C₄₁×#2948	1	1	yes	characteristic
413	C₂	C₄₁×#3309	1	2	yes	—
414	C₂	C₄₁×#3319	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×C₄₁×#466	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₄×C₂²⋊C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#2363	C₂	semidirect
3. C₄₁×#1936	C₂	semidirect
4. C₄₁×#1918	C₂	semidirect
5. C₄₁×#1879	C₂	semidirect
6. C₄₁×#1875	C₂	semidirect
7. C₄₁×#1762	C₂	semidirect
8. C₄₁×#1752	C₂	semidirect
9. C₄₁×#1735	C₂	semidirect
15. C₄₁×#466	C₄	semidirect
43. C₂²×C₈×C₄₁	C₂×C₄	semidirect
48. #121×C₄₁	C₂×C₄	semidirect
67. #107×C₄₁	C₂×C₄	semidirect
70. #102×C₄₁	C₂×C₄	semidirect
174. #23137	C₄₁	direct (N × H)
202. #2363	C₂×C₄₁	semidirect
203. #1936	C₂×C₄₁	semidirect
204. #1918	C₂×C₄₁	semidirect
205. #1879	C₂×C₄₁	semidirect
206. #1875	C₂×C₄₁	semidirect
207. #1762	C₂×C₄₁	semidirect
208. #1752	C₂×C₄₁	semidirect
209. #1735	C₂×C₄₁	semidirect
222. #466	C₄×C₄₁	semidirect
243. C₄₁	#23137	direct (N × H)
251. C₂²×C₈	C₂×C₄×C₄₁	semidirect
256. #121	C₂×C₄×C₄₁	semidirect
275. #107	C₂×C₄×C₄₁	semidirect
278. #102	C₂×C₄×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×#466	2
C₄₁×#2363	2
C₄₁×#1936	2
C₄₁×#1918	2
C₄₁×#1879	2
C₄₁×#1875	2
C₄₁×#1762	2
C₄₁×#1752	2
C₄₁×#1735	2
#23137	41

Subgroups — C41×#23137 #23799338

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#23137 #23799338