Subgroups — C₂×C₄₁×#1686 #23795344

Order 10496.

766 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#492	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#460	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₁×#446	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1686	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄₁×#335	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₁×#332	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₁×#331	C₂	1	1	yes	maximal, characteristic
9	C₂²×SD₁₆×C₄₁	—	2	1	no	—
10	C₂²×SD₁₆×C₄₁	—	2	1	no	—
11	C₂²×SD₁₆×C₄₁	—	2	1	no	—
12	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
15	C₄₁×#492	—	2	2	no	—
16	C₄₁×#492	C₂²	1	4	yes	—
17	C₄₁×#475	—	2	2	no	—
18	C₄₁×#475	C₂²	1	4	yes	complemented
19	C₄₁×#460	—	2	2	no	—
20	C₄₁×#460	C₂²	1	4	yes	—
21	C₄₁×#446	—	2	2	no	—
22	C₄₁×#446	C₂²	1	4	yes	complemented
23	C₂×#106×C₄₁	—	2	1	no	—
24	C₂×C₄⋊C₈×C₄₁	—	2	1	no	—
25	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
28	C₂×#103×C₄₁	—	2	1	no	—
29	C₂×#102×C₄₁	—	2	1	no	—
30	C₂×#97×C₄₁	—	2	1	no	—
31	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
32	C₄₁×#335	C₂²	1	4	yes	complemented
33	C₄₁×#332	C₂²	1	4	yes	complemented
34	C₄₁×#331	C₂²	1	4	yes	—
35	C₂²×Q₈×C₄₁	—	2	1	no	—
36	C₂²×Q₈×C₄₁	D₄	1	1	yes	characteristic
37	C₂²×D₄×C₄₁	—	2	1	no	—
38	C₂²×D₄×C₄₁	—	2	1	no	—
39	C₂²×D₄×C₄₁	—	2	1	no	—
40	C₂×SD₁₆×C₄₁	—	2	4	no	—
41	C₂×SD₁₆×C₄₁	—	2	4	no	—
42	C₂×SD₁₆×C₄₁	—	2	4	no	—
43	C₂×SD₁₆×C₄₁	—	4	4	no	—
44	C₂×SD₁₆×C₄₁	—	4	4	no	—
45	C₂×SD₁₆×C₄₁	—	4	4	no	—
46	C₂²×C₈×C₄₁	—	2	1	no	—
47	C₂²×C₈×C₄₁	—	2	1	no	—
48	C₂²×C₈×C₄₁	—	2	1	no	—
49	C₂²×C₈×C₄₁	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₄₁	D₄	1	1	yes	characteristic
51	C₄⋊Q₈×C₄₁	—	2	1	no	—
52	C₄⋊Q₈×C₄₁	—	2	1	no	—
53	C₄⋊Q₈×C₄₁	—	2	1	no	—
54	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
55	#127×C₄₁	—	2	1	no	—
56	#127×C₄₁	—	2	1	no	—
57	#127×C₄₁	—	2	1	no	—
58	#127×C₄₁	C₂³	1	2	yes	—
59	C₄×Q₈×C₄₁	—	2	1	no	—
60	C₄×Q₈×C₄₁	—	2	1	no	—
61	C₄×Q₈×C₄₁	D₄	1	2	yes	—
62	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₄₁	—	2	1	no	—
68	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
69	#106×C₄₁	—	2	4	no	—
70	C₄⋊C₈×C₄₁	—	2	4	no	—
71	C₄⋊C₈×C₄₁	—	2	1	no	—
72	C₄⋊C₈×C₄₁	—	2	1	no	—
73	C₄⋊C₈×C₄₁	—	2	1	no	—
74	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
75	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
76	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
77	#103×C₄₁	—	2	4	no	—
78	#102×C₄₁	—	2	4	no	—
79	#97×C₄₁	—	2	4	no	—
80	C₄×C₈×C₄₁	D₄	1	2	yes	—
81	C₄×C₈×C₄₁	C₂³	1	2	yes	—
82	C₂⁴×C₄₁	—	4	1	no	—
83	C₂×Q₈×C₄₁	—	2	1	no	—
84	C₂×Q₈×C₄₁	—	2	2	no	—
85	C₂×Q₈×C₄₁	—	2	2	no	—
86	C₂×Q₈×C₄₁	—	2	2	no	—
87	C₂×Q₈×C₄₁	—	4	1	no	—
88	C₂×Q₈×C₄₁	—	4	2	no	—
89	C₂×Q₈×C₄₁	—	4	2	no	—
90	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
91	C₂×D₄×C₄₁	—	2	2	no	—
92	C₂×D₄×C₄₁	—	2	2	no	—
93	C₂×D₄×C₄₁	—	2	2	no	—
94	C₂×D₄×C₄₁	—	4	1	no	—
95	C₂×D₄×C₄₁	—	4	1	no	—
96	C₂×D₄×C₄₁	—	4	1	no	—
97	C₂×D₄×C₄₁	—	4	2	no	—
98	C₂×D₄×C₄₁	—	4	2	no	—
99	C₂×D₄×C₄₁	—	4	2	no	—
100	C₂×D₄×C₄₁	—	4	2	no	—
101	C₂×D₄×C₄₁	—	8	2	no	—
102	C₂²×C₄×C₄₁	—	2	1	no	—
103	C₂²×C₄×C₄₁	—	2	1	no	—
104	C₂²×C₄×C₄₁	—	4	1	no	—
105	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
108	SD₁₆×C₄₁	—	4	8	no	—
109	SD₁₆×C₄₁	—	4	8	no	—
110	SD₁₆×C₄₁	—	4	8	no	—
111	C₂×C₈×C₄₁	—	2	2	no	—
112	C₂×C₈×C₄₁	—	2	2	no	—
113	C₂×C₈×C₄₁	—	2	2	no	—
114	C₂×C₈×C₄₁	—	2	2	no	—
115	C₂×C₈×C₄₁	—	4	2	no	—
116	C₂×C₈×C₄₁	—	4	2	no	—
117	C₂×C₈×C₄₁	—	4	2	no	—
118	C₂×C₈×C₄₁	SD₁₆	1	4	yes	complemented
119	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
120	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
121	C₄⋊C₄×C₄₁	—	2	2	no	—
122	C₄⋊C₄×C₄₁	—	2	1	no	—
123	C₄⋊C₄×C₄₁	—	2	2	no	—
124	C₄⋊C₄×C₄₁	—	2	2	no	—
125	C₄⋊C₄×C₄₁	—	2	2	no	—
126	C₄⋊C₄×C₄₁	—	4	1	no	—
127	C₄⋊C₄×C₄₁	—	4	1	no	—
128	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
129	C₄²×C₄₁	—	2	2	no	—
130	C₄²×C₄₁	—	2	2	no	—
131	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₄₁	#41	1	1	yes	characteristic
134	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
135	C₂³×C₄₁	—	4	2	no	—
136	C₂³×C₄₁	—	8	2	no	—
137	C₂³×C₄₁	—	8	2	no	—
138	C₂³×C₄₁	—	8	2	no	—
139	C₂³×C₄₁	#121	1	1	yes	characteristic
140	Q₈×C₄₁	—	2	2	no	—
141	Q₈×C₄₁	—	2	2	no	—
142	Q₈×C₄₁	—	4	2	no	—
143	Q₈×C₄₁	—	4	2	no	—
144	Q₈×C₄₁	—	4	2	no	—
145	Q₈×C₄₁	—	8	2	no	—
146	D₄×C₄₁	—	4	2	no	—
147	D₄×C₄₁	—	4	2	no	—
148	D₄×C₄₁	—	4	2	no	—
149	D₄×C₄₁	—	4	2	no	—
150	D₄×C₄₁	—	8	2	no	—
151	D₄×C₄₁	—	8	2	no	—
152	D₄×C₄₁	—	8	2	no	—
153	D₄×C₄₁	—	8	2	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	—	4	2	no	—
158	C₂×C₄×C₄₁	—	4	2	no	—
159	C₂×C₄×C₄₁	—	4	2	no	—
160	C₂×C₄×C₄₁	—	8	2	no	—
161	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
162	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
163	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
164	C₂×C₄×C₄₁	C₂×SD₁₆	1	2	yes	—
165	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
166	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
167	C₂×C₄×C₄₁	#137	1	2	yes	—
168	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
171	C₈×C₄₁	—	2	2	no	—
172	C₈×C₄₁	—	4	2	no	—
173	C₈×C₄₁	—	4	2	no	—
174	C₈×C₄₁	—	4	2	no	—
175	C₈×C₄₁	C₂×SD₁₆	1	4	yes	complemented
176	C₂×#1686	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂²×C₄₁	—	8	2	no	—
178	C₂²×C₄₁	—	8	2	no	—
179	C₂²×C₄₁	—	8	2	no	—
180	C₂²×C₄₁	—	16	4	no	—
181	C₂²×C₄₁	#460	1	2	yes	—
182	C₂²×C₄₁	#468	1	2	yes	—
183	C₂²×C₄₁	#471	1	2	yes	—
184	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
185	C₄×C₄₁	—	2	1	no	—
186	C₄×C₄₁	—	2	1	no	—
187	C₄×C₄₁	—	4	2	no	—
188	C₄×C₄₁	—	4	2	no	—
189	C₄×C₄₁	—	8	2	no	—
190	C₄×C₄₁	#460	1	2	yes	—
191	C₄×C₄₁	#468	1	2	yes	—
192	C₄×C₄₁	C₂²×SD₁₆	1	1	yes	characteristic
193	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
194	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
195	C₄×C₄₁	C₂×#137	1	1	yes	characteristic
196	C₂×#492	C₂×C₄₁	1	1	yes	characteristic
197	C₂×#475	C₂×C₄₁	1	1	yes	characteristic, complemented
198	C₂×#460	C₂×C₄₁	1	1	yes	characteristic
199	C₂×#446	C₂×C₄₁	1	1	yes	characteristic, complemented
200	#1686	C₂×C₄₁	1	8	yes	direct product factor
201	C₂×#335	C₂×C₄₁	1	1	yes	characteristic, complemented
202	C₂×#332	C₂×C₄₁	1	1	yes	characteristic, complemented
203	C₂×#331	C₂×C₄₁	1	1	yes	characteristic
204	C₂×C₄₁	—	16	2	no	—
205	C₂×C₄₁	#1686	1	4	yes	direct product factor
206	C₂×C₄₁	C₂×#460	1	1	yes	characteristic
207	C₂×C₄₁	C₂×#468	1	1	yes	characteristic
208	C₂×C₄₁	C₂×#471	1	1	yes	characteristic
209	C₂²×SD₁₆	—	2	1	no	—
210	C₂²×SD₁₆	—	2	1	no	—
211	C₂²×SD₁₆	—	2	1	no	—
212	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
213	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
214	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
215	#492	—	2	2	no	—
216	#492	C₂²×C₄₁	1	4	yes	—
217	#475	—	2	2	no	—
218	#475	C₂²×C₄₁	1	4	yes	complemented
219	#460	—	2	2	no	—
220	#460	C₂²×C₄₁	1	4	yes	—
221	#446	—	2	2	no	—
222	#446	C₂²×C₄₁	1	4	yes	complemented
223	C₂×#106	—	2	1	no	—
224	C₂×C₄⋊C₈	—	2	1	no	—
225	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
226	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
227	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
228	C₂×#103	—	2	1	no	—
229	C₂×#102	—	2	1	no	—
230	C₂×#97	—	2	1	no	—
231	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
232	#335	C₂²×C₄₁	1	4	yes	complemented
233	#332	C₂²×C₄₁	1	4	yes	complemented
234	#331	C₂²×C₄₁	1	4	yes	—
235	C₄₁	C₂×#1686	1	1	yes	characteristic, direct product factor, Sylow
236	C₂²×Q₈	—	2	1	no	—
237	C₂²×Q₈	D₄×C₄₁	1	1	yes	characteristic
238	C₂²×D₄	—	2	1	no	—
239	C₂²×D₄	—	2	1	no	—
240	C₂²×D₄	—	2	1	no	—
241	C₂×SD₁₆	—	2	4	no	—
242	C₂×SD₁₆	—	2	4	no	—
243	C₂×SD₁₆	—	2	4	no	—
244	C₂×SD₁₆	—	4	4	no	—
245	C₂×SD₁₆	—	4	4	no	—
246	C₂×SD₁₆	—	4	4	no	—
247	C₂²×C₈	—	2	1	no	—
248	C₂²×C₈	—	2	1	no	—
249	C₂²×C₈	—	2	1	no	—
250	C₂²×C₈	D₄×C₄₁	1	1	yes	characteristic
251	C₂²×C₈	D₄×C₄₁	1	1	yes	characteristic
252	C₄⋊Q₈	—	2	1	no	—
253	C₄⋊Q₈	—	2	1	no	—
254	C₄⋊Q₈	—	2	1	no	—
255	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
256	#127	—	2	1	no	—
257	#127	—	2	1	no	—
258	#127	—	2	1	no	—
259	#127	C₂³×C₄₁	1	2	yes	—
260	C₄×Q₈	—	2	1	no	—
261	C₄×Q₈	—	2	1	no	—
262	C₄×Q₈	D₄×C₄₁	1	2	yes	—
263	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
268	C₂×C₄²	—	2	1	no	—
269	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
270	#106	—	2	4	no	—
271	C₄⋊C₈	—	2	4	no	—
272	C₄⋊C₈	—	2	1	no	—
273	C₄⋊C₈	—	2	1	no	—
274	C₄⋊C₈	—	2	1	no	—
275	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
276	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
277	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
278	#103	—	2	4	no	—
279	#102	—	2	4	no	—
280	#97	—	2	4	no	—
281	C₄×C₈	D₄×C₄₁	1	2	yes	—
282	C₄×C₈	C₂³×C₄₁	1	2	yes	—
283	C₂⁴	—	4	1	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	4	1	no	—
289	C₂×Q₈	—	4	2	no	—
290	C₂×Q₈	—	4	2	no	—
291	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	—	4	2	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂×D₄	—	4	2	no	—
302	C₂×D₄	—	8	2	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
308	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
309	SD₁₆	—	4	8	no	—
310	SD₁₆	—	4	8	no	—
311	SD₁₆	—	4	8	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	4	2	no	—
317	C₂×C₈	—	4	2	no	—
318	C₂×C₈	—	4	2	no	—
319	C₂×C₈	SD₁₆×C₄₁	1	4	yes	complemented
320	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
321	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	2	no	—
332	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
333	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
334	C₄²	#41×C₄₁	1	1	yes	characteristic
335	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
336	C₂³	—	4	2	no	—
337	C₂³	—	8	2	no	—
338	C₂³	—	8	2	no	—
339	C₂³	—	8	2	no	—
340	C₂³	#121×C₄₁	1	1	yes	characteristic
341	Q₈	—	2	2	no	—
342	Q₈	—	2	2	no	—
343	Q₈	—	4	2	no	—
344	Q₈	—	4	2	no	—
345	Q₈	—	4	2	no	—
346	Q₈	—	8	2	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	2	no	—
350	D₄	—	4	2	no	—
351	D₄	—	8	2	no	—
352	D₄	—	8	2	no	—
353	D₄	—	8	2	no	—
354	D₄	—	8	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	8	2	no	—
362	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
363	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
364	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
365	C₂×C₄	C₂×SD₁₆×C₄₁	1	2	yes	—
366	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
367	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
368	C₂×C₄	#137×C₄₁	1	2	yes	—
369	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
370	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
371	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
372	C₈	—	2	2	no	—
373	C₈	—	4	2	no	—
374	C₈	—	4	2	no	—
375	C₈	—	4	2	no	—
376	C₈	C₂×SD₁₆×C₄₁	1	4	yes	complemented
377	C₂²	—	8	2	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	16	4	no	—
381	C₂²	C₄₁×#460	1	2	yes	—
382	C₂²	C₄₁×#468	1	2	yes	—
383	C₂²	C₄₁×#471	1	2	yes	—
384	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	4	2	no	—
388	C₄	—	4	2	no	—
389	C₄	—	8	2	no	—
390	C₄	C₄₁×#460	1	2	yes	—
391	C₄	C₄₁×#468	1	2	yes	—
392	C₄	C₂²×SD₁₆×C₄₁	1	1	yes	characteristic
393	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
394	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
395	C₄	C₂×#137×C₄₁	1	1	yes	characteristic
396	C₂	—	16	2	no	—
397	C₂	C₄₁×#1686	1	4	yes	direct product factor
398	C₂	C₂×C₄₁×#460	1	1	yes	characteristic
399	C₂	C₂×C₄₁×#468	1	1	yes	characteristic
400	C₂	C₂×C₄₁×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₁
prime radical	C₂×#127×C₄₁	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#475	C₂	semidirect
4. C₂×C₄₁×#446	C₂	semidirect
5. C₄₁×#1686	C₂	direct (N × H)
6. C₂×C₄₁×#335	C₂	semidirect
7. C₂×C₄₁×#332	C₂	semidirect
18. C₄₁×#475	C₂²	semidirect
22. C₄₁×#446	C₂²	semidirect
32. C₄₁×#335	C₂²	semidirect
33. C₄₁×#332	C₂²	semidirect
118. C₂×C₈×C₄₁	SD₁₆	semidirect
175. C₈×C₄₁	C₂×SD₁₆	semidirect
176. C₂×#1686	C₄₁	direct (N × H)
197. C₂×#475	C₂×C₄₁	semidirect
199. C₂×#446	C₂×C₄₁	semidirect
200. #1686	C₂×C₄₁	direct (N × H)
201. C₂×#335	C₂×C₄₁	semidirect
202. C₂×#332	C₂×C₄₁	semidirect
205. C₂×C₄₁	#1686	direct (N × H)
218. #475	C₂²×C₄₁	semidirect
222. #446	C₂²×C₄₁	semidirect
232. #335	C₂²×C₄₁	semidirect
233. #332	C₂²×C₄₁	semidirect
235. C₄₁	C₂×#1686	direct (N × H)
319. C₂×C₈	SD₁₆×C₄₁	semidirect
376. C₈	C₂×SD₁₆×C₄₁	semidirect
397. C₂	C₄₁×#1686	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×#492	2
C₂×C₄₁×#475	2
C₂×C₄₁×#460	2
C₂×C₄₁×#446	2
C₄₁×#1686	2
C₂×C₄₁×#335	2
C₂×C₄₁×#332	2
C₂×C₄₁×#331	2
C₂×#1686	41

Subgroups — C2×C41×#1686 #23795344

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#1686 #23795344