Subgroups — C₂×C₄₁×#1978 #23797447

Order 10496.

1694 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₈×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×#108×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#418	C₂	1	2	yes	maximal, complemented
4	C₂²×#100×C₄₁	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₁×#405	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1978	C₂	1	8	yes	maximal, direct product factor
7	C₂³×D₄×C₄₁	C₂²	1	2	yes	—
8	C₂²×D₈×C₄₁	—	2	1	no	—
9	C₂²×D₈×C₄₁	—	2	1	no	—
10	C₂²×D₈×C₄₁	—	2	2	no	—
11	C₂²×D₈×C₄₁	—	2	4	no	—
12	C₂²×D₈×C₄₁	C₄	1	8	yes	complemented
13	C₂²×D₈×C₄₁	C₂²	1	4	yes	—
14	C₂²×M₁₆×C₄₁	C₂²	1	2	yes	—
15	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
17	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×#108×C₄₁	—	2	4	no	—
19	C₂×#108×C₄₁	C₂²	1	4	yes	complemented
20	C₄₁×#418	—	2	4	no	—
21	C₄₁×#418	C₂²	1	8	yes	complemented
22	C₂×#102×C₄₁	—	2	4	no	—
23	C₂×#100×C₄₁	—	2	8	no	—
24	C₂×#100×C₄₁	C₂²	1	8	yes	complemented
25	C₄₁×#405	—	2	2	no	—
26	C₄₁×#405	C₂²	1	4	yes	complemented
27	C₂×#97×C₄₁	—	2	1	no	—
28	C₂×C₄×C₈×C₄₁	—	2	1	no	—
29	C₂⁵×C₄₁	—	2	2	no	—
30	C₂²×D₄×C₄₁	—	2	2	no	—
31	C₂²×D₄×C₄₁	—	2	2	no	—
32	C₂²×D₄×C₄₁	—	2	4	no	—
33	C₂²×D₄×C₄₁	—	2	2	no	—
34	C₂²×D₄×C₄₁	—	2	2	no	—
35	C₂²×D₄×C₄₁	—	2	4	no	—
36	C₂²×D₄×C₄₁	—	2	4	no	—
37	C₂²×D₄×C₄₁	—	2	2	no	—
38	C₂²×D₄×C₄₁	C₂×C₄	1	8	yes	—
39	C₂²×D₄×C₄₁	C₂³	1	4	yes	—
40	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
41	C₂×D₈×C₄₁	—	2	8	no	—
42	C₂×D₈×C₄₁	—	2	8	no	—
43	C₂×D₈×C₄₁	—	2	16	no	—
44	C₂×D₈×C₄₁	—	2	4	no	—
45	C₂×D₈×C₄₁	—	2	4	no	—
46	C₂×D₈×C₄₁	—	2	8	no	—
47	C₂×D₈×C₄₁	C₂×C₄	1	16	yes	complemented
48	C₂×M₁₆×C₄₁	—	2	1	no	—
49	C₂×M₁₆×C₄₁	—	2	2	no	—
50	C₂×M₁₆×C₄₁	—	2	2	no	—
51	C₂×M₁₆×C₄₁	—	2	4	no	—
52	C₂×M₁₆×C₄₁	—	2	4	no	—
53	C₂×M₁₆×C₄₁	D₄	1	4	yes	—
54	C₂×M₁₆×C₄₁	C₂³	1	4	yes	—
55	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
56	C₂²×C₈×C₄₁	—	2	1	no	—
57	C₂²×C₈×C₄₁	—	2	2	no	—
58	C₂²×C₈×C₄₁	C₂×C₄	1	4	yes	—
59	C₂²×C₈×C₄₁	D₄	1	1	yes	characteristic
60	C₂²×C₈×C₄₁	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₄₁	D₄	1	2	yes	—
62	C₂²×C₈×C₄₁	D₄	1	4	yes	—
63	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
64	#117×C₄₁	—	2	1	no	—
65	#117×C₄₁	—	2	1	no	—
66	#117×C₄₁	D₄	1	2	yes	—
67	#117×C₄₁	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
69	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
70	C₂×C₄²×C₄₁	—	2	1	no	—
71	#108×C₄₁	—	2	8	no	—
72	#102×C₄₁	—	2	16	no	—
73	#100×C₄₁	—	2	16	no	—
74	#97×C₄₁	—	2	4	no	—
75	C₄×C₈×C₄₁	—	2	4	no	—
76	C₂⁴×C₄₁	—	2	8	no	—
77	C₂⁴×C₄₁	—	2	4	no	—
78	C₂⁴×C₄₁	—	4	2	no	—
79	C₂⁴×C₄₁	—	4	2	no	—
80	C₂⁴×C₄₁	—	4	4	no	—
81	C₂⁴×C₄₁	—	8	8	no	—
82	C₂⁴×C₄₁	#41	1	1	yes	characteristic
83	C₂×D₄×C₄₁	—	2	8	no	—
84	C₂×D₄×C₄₁	—	2	8	no	—
85	C₂×D₄×C₄₁	—	2	8	no	—
86	C₂×D₄×C₄₁	—	2	8	no	—
87	C₂×D₄×C₄₁	—	2	8	no	—
88	C₂×D₄×C₄₁	—	2	4	no	—
89	C₂×D₄×C₄₁	—	2	4	no	—
90	C₂×D₄×C₄₁	—	2	4	no	—
91	C₂×D₄×C₄₁	—	2	4	no	—
92	C₂×D₄×C₄₁	—	2	4	no	—
93	C₂×D₄×C₄₁	—	4	4	no	—
94	C₂×D₄×C₄₁	—	4	4	no	—
95	C₂×D₄×C₄₁	—	4	2	no	—
96	C₂×D₄×C₄₁	—	4	2	no	—
97	C₂×D₄×C₄₁	—	4	4	no	—
98	C₂×D₄×C₄₁	—	4	4	no	—
99	C₂×D₄×C₄₁	—	4	4	no	—
100	C₂×D₄×C₄₁	C₂²×C₄	1	8	yes	—
101	C₂²×C₄×C₄₁	—	2	2	no	—
102	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
110	C₂²×C₄×C₄₁	#41	1	2	yes	—
111	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
112	D₈×C₄₁	—	2	16	no	—
113	D₈×C₄₁	—	2	16	no	—
114	M₁₆×C₄₁	—	2	4	no	—
115	M₁₆×C₄₁	—	2	2	no	—
116	M₁₆×C₄₁	—	2	4	no	—
117	M₁₆×C₄₁	—	2	4	no	—
118	M₁₆×C₄₁	—	4	4	no	—
119	M₁₆×C₄₁	C₂×D₄	1	4	yes	—
120	C₂×C₈×C₄₁	—	2	4	no	—
121	C₂×C₈×C₄₁	—	2	2	no	—
122	C₂×C₈×C₄₁	—	2	4	no	—
123	C₂×C₈×C₄₁	—	4	4	no	—
124	C₂×C₈×C₄₁	C₂²⋊C₄	1	4	yes	—
125	C₂×C₈×C₄₁	C₂²⋊C₄	1	4	yes	—
126	C₂×C₈×C₄₁	C₂²⋊C₄	1	8	yes	—
127	C₂×C₈×C₄₁	C₂²×C₄	1	4	yes	—
128	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
131	C₄⋊C₄×C₄₁	—	2	2	no	—
132	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
133	C₂²⋊C₄×C₄₁	—	2	2	no	—
134	C₂²⋊C₄×C₄₁	—	2	2	no	—
135	C₄²×C₄₁	—	2	2	no	—
136	C₄²×C₄₁	—	2	2	no	—
137	C₂³×C₄₁	—	2	4	no	—
138	C₂³×C₄₁	—	2	8	no	—
139	C₂³×C₄₁	—	4	4	no	—
140	C₂³×C₄₁	—	4	4	no	—
141	C₂³×C₄₁	—	4	8	no	—
142	C₂³×C₄₁	—	4	8	no	—
143	C₂³×C₄₁	—	8	16	no	—
144	C₂³×C₄₁	—	8	8	no	—
145	C₂³×C₄₁	—	8	16	no	—
146	C₂³×C₄₁	—	8	8	no	—
147	C₂³×C₄₁	—	8	8	no	—
148	C₂³×C₄₁	C₄×D₄	1	2	yes	—
149	C₂³×C₄₁	#121	1	1	yes	characteristic
150	C₂³×C₄₁	#121	1	1	yes	characteristic
151	C₂³×C₄₁	#124	1	2	yes	—
152	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
153	D₄×C₄₁	—	2	8	no	—
154	D₄×C₄₁	—	2	8	no	—
155	D₄×C₄₁	—	4	4	no	—
156	D₄×C₄₁	—	4	4	no	—
157	D₄×C₄₁	—	4	8	no	—
158	D₄×C₄₁	—	4	8	no	—
159	C₂×C₄×C₄₁	—	2	4	no	—
160	C₂×C₄×C₄₁	—	4	4	no	—
161	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
162	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
163	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
164	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
165	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
166	C₂×C₄×C₄₁	#121	1	2	yes	—
167	C₂×C₄×C₄₁	#121	1	2	yes	—
168	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
169	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
170	C₂×C₄×C₄₁	#124	1	2	yes	—
171	C₂×C₄×C₄₁	#127	1	2	yes	—
172	C₂×C₄×C₄₁	#127	1	2	yes	—
173	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
179	C₈×C₄₁	—	2	4	no	—
180	C₈×C₄₁	—	4	4	no	—
181	C₈×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
182	C₈×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
183	C₂×#1978	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂²×C₄₁	—	2	4	no	—
185	C₂²×C₄₁	—	2	4	no	—
186	C₂²×C₄₁	—	2	2	no	—
187	C₂²×C₄₁	—	2	2	no	—
188	C₂²×C₄₁	—	4	8	no	—
189	C₂²×C₄₁	—	8	8	no	—
190	C₂²×C₄₁	—	8	8	no	—
191	C₂²×C₄₁	—	8	16	no	—
192	C₂²×C₄₁	—	8	16	no	—
193	C₂²×C₄₁	—	8	8	no	—
194	C₂²×C₄₁	#390	1	2	yes	—
195	C₂²×C₄₁	#390	1	2	yes	—
196	C₂²×C₄₁	#472	1	4	yes	—
197	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
198	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
199	C₂²×C₄₁	C₂×#124	1	1	yes	characteristic
200	C₄×C₄₁	—	4	4	no	—
201	C₄×C₄₁	#390	1	2	yes	—
202	C₄×C₄₁	#390	1	2	yes	—
203	C₄×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
204	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
205	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
206	C₄×C₄₁	C₂×#127	1	1	yes	characteristic
207	C₂³×D₈	C₂×C₄₁	1	1	yes	characteristic
208	C₂²×#108	C₂×C₄₁	1	1	yes	characteristic, complemented
209	C₂×#418	C₂×C₄₁	1	2	yes	complemented
210	C₂²×#100	C₂×C₄₁	1	2	yes	complemented
211	C₂×#405	C₂×C₄₁	1	1	yes	characteristic, complemented
212	#1978	C₂×C₄₁	1	8	yes	direct product factor
213	C₂×C₄₁	—	2	1	no	—
214	C₂×C₄₁	—	2	1	no	—
215	C₂×C₄₁	—	2	2	no	—
216	C₂×C₄₁	—	8	8	no	—
217	C₂×C₄₁	#1978	1	4	yes	direct product factor
218	C₂×C₄₁	C₂×#390	1	1	yes	characteristic
219	C₂×C₄₁	C₂×#472	1	2	yes	—
220	C₂³×D₄	C₂²×C₄₁	1	2	yes	—
221	C₂²×D₈	—	2	1	no	—
222	C₂²×D₈	—	2	1	no	—
223	C₂²×D₈	—	2	2	no	—
224	C₂²×D₈	—	2	4	no	—
225	C₂²×D₈	C₄×C₄₁	1	8	yes	complemented
226	C₂²×D₈	C₂²×C₄₁	1	4	yes	—
227	C₂²×M₁₆	C₂²×C₄₁	1	2	yes	—
228	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
229	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
230	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
231	C₂×#108	—	2	4	no	—
232	C₂×#108	C₂²×C₄₁	1	4	yes	complemented
233	#418	—	2	4	no	—
234	#418	C₂²×C₄₁	1	8	yes	complemented
235	C₂×#102	—	2	4	no	—
236	C₂×#100	—	2	8	no	—
237	C₂×#100	C₂²×C₄₁	1	8	yes	complemented
238	#405	—	2	2	no	—
239	#405	C₂²×C₄₁	1	4	yes	complemented
240	C₂×#97	—	2	1	no	—
241	C₂×C₄×C₈	—	2	1	no	—
242	C₄₁	C₂×#1978	1	1	yes	characteristic, direct product factor, Sylow
243	C₂⁵	—	2	2	no	—
244	C₂²×D₄	—	2	2	no	—
245	C₂²×D₄	—	2	2	no	—
246	C₂²×D₄	—	2	4	no	—
247	C₂²×D₄	—	2	2	no	—
248	C₂²×D₄	—	2	2	no	—
249	C₂²×D₄	—	2	4	no	—
250	C₂²×D₄	—	2	4	no	—
251	C₂²×D₄	—	2	2	no	—
252	C₂²×D₄	C₂×C₄×C₄₁	1	8	yes	—
253	C₂²×D₄	C₂³×C₄₁	1	4	yes	—
254	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
255	C₂×D₈	—	2	8	no	—
256	C₂×D₈	—	2	8	no	—
257	C₂×D₈	—	2	16	no	—
258	C₂×D₈	—	2	4	no	—
259	C₂×D₈	—	2	4	no	—
260	C₂×D₈	—	2	8	no	—
261	C₂×D₈	C₂×C₄×C₄₁	1	16	yes	complemented
262	C₂×M₁₆	—	2	1	no	—
263	C₂×M₁₆	—	2	2	no	—
264	C₂×M₁₆	—	2	2	no	—
265	C₂×M₁₆	—	2	4	no	—
266	C₂×M₁₆	—	2	4	no	—
267	C₂×M₁₆	D₄×C₄₁	1	4	yes	—
268	C₂×M₁₆	C₂³×C₄₁	1	4	yes	—
269	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
270	C₂²×C₈	—	2	1	no	—
271	C₂²×C₈	—	2	2	no	—
272	C₂²×C₈	C₂×C₄×C₄₁	1	4	yes	—
273	C₂²×C₈	D₄×C₄₁	1	1	yes	characteristic
274	C₂²×C₈	D₄×C₄₁	1	1	yes	characteristic
275	C₂²×C₈	D₄×C₄₁	1	2	yes	—
276	C₂²×C₈	D₄×C₄₁	1	4	yes	—
277	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
278	#117	—	2	1	no	—
279	#117	—	2	1	no	—
280	#117	D₄×C₄₁	1	2	yes	—
281	#117	C₂³×C₄₁	1	2	yes	—
282	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
283	C₂×C₂²⋊C₄	—	2	1	no	—
284	C₂×C₄²	—	2	1	no	—
285	#108	—	2	8	no	—
286	#102	—	2	16	no	—
287	#100	—	2	16	no	—
288	#97	—	2	4	no	—
289	C₄×C₈	—	2	4	no	—
290	C₂⁴	—	2	8	no	—
291	C₂⁴	—	2	4	no	—
292	C₂⁴	—	4	2	no	—
293	C₂⁴	—	4	2	no	—
294	C₂⁴	—	4	4	no	—
295	C₂⁴	—	8	8	no	—
296	C₂⁴	#41×C₄₁	1	1	yes	characteristic
297	C₂×D₄	—	2	8	no	—
298	C₂×D₄	—	2	8	no	—
299	C₂×D₄	—	2	8	no	—
300	C₂×D₄	—	2	8	no	—
301	C₂×D₄	—	2	8	no	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	—	2	4	no	—
307	C₂×D₄	—	4	4	no	—
308	C₂×D₄	—	4	4	no	—
309	C₂×D₄	—	4	2	no	—
310	C₂×D₄	—	4	2	no	—
311	C₂×D₄	—	4	4	no	—
312	C₂×D₄	—	4	4	no	—
313	C₂×D₄	—	4	4	no	—
314	C₂×D₄	C₂²×C₄×C₄₁	1	8	yes	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
317	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
320	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
323	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
324	C₂²×C₄	#41×C₄₁	1	2	yes	—
325	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
326	D₈	—	2	16	no	—
327	D₈	—	2	16	no	—
328	M₁₆	—	2	4	no	—
329	M₁₆	—	2	2	no	—
330	M₁₆	—	2	4	no	—
331	M₁₆	—	2	4	no	—
332	M₁₆	—	4	4	no	—
333	M₁₆	C₂×D₄×C₄₁	1	4	yes	—
334	C₂×C₈	—	2	4	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	4	no	—
337	C₂×C₈	—	4	4	no	—
338	C₂×C₈	C₂²⋊C₄×C₄₁	1	4	yes	—
339	C₂×C₈	C₂²⋊C₄×C₄₁	1	4	yes	—
340	C₂×C₈	C₂²⋊C₄×C₄₁	1	8	yes	—
341	C₂×C₈	C₂²×C₄×C₄₁	1	4	yes	—
342	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
343	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
344	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
347	C₂²⋊C₄	—	2	2	no	—
348	C₂²⋊C₄	—	2	2	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	2	2	no	—
351	C₂³	—	2	4	no	—
352	C₂³	—	2	8	no	—
353	C₂³	—	4	4	no	—
354	C₂³	—	4	4	no	—
355	C₂³	—	4	8	no	—
356	C₂³	—	4	8	no	—
357	C₂³	—	8	8	no	—
358	C₂³	—	8	16	no	—
359	C₂³	—	8	8	no	—
360	C₂³	—	8	16	no	—
361	C₂³	—	8	8	no	—
362	C₂³	C₄×D₄×C₄₁	1	2	yes	—
363	C₂³	#121×C₄₁	1	1	yes	characteristic
364	C₂³	#121×C₄₁	1	1	yes	characteristic
365	C₂³	#124×C₄₁	1	2	yes	—
366	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
367	D₄	—	2	8	no	—
368	D₄	—	2	8	no	—
369	D₄	—	4	4	no	—
370	D₄	—	4	4	no	—
371	D₄	—	4	8	no	—
372	D₄	—	4	8	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
376	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
377	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
378	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
379	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
380	C₂×C₄	#121×C₄₁	1	2	yes	—
381	C₂×C₄	#121×C₄₁	1	2	yes	—
382	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
383	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
384	C₂×C₄	#124×C₄₁	1	2	yes	—
385	C₂×C₄	#127×C₄₁	1	2	yes	—
386	C₂×C₄	#127×C₄₁	1	2	yes	—
387	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
388	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
389	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
390	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
391	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
392	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
393	C₈	—	2	4	no	—
394	C₈	—	4	4	no	—
395	C₈	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
396	C₈	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	4	no	—
400	C₂²	—	2	4	no	—
401	C₂²	—	4	8	no	—
402	C₂²	—	8	8	no	—
403	C₂²	—	8	8	no	—
404	C₂²	—	8	16	no	—
405	C₂²	—	8	8	no	—
406	C₂²	—	8	16	no	—
407	C₂²	C₄₁×#390	1	2	yes	—
408	C₂²	C₄₁×#390	1	2	yes	—
409	C₂²	C₄₁×#472	1	4	yes	—
410	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
411	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
412	C₂²	C₂×#124×C₄₁	1	1	yes	characteristic
413	C₄	—	4	4	no	—
414	C₄	C₄₁×#390	1	2	yes	—
415	C₄	C₄₁×#390	1	2	yes	—
416	C₄	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
417	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
418	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
419	C₄	C₂×#127×C₄₁	1	1	yes	characteristic
420	C₂	—	2	1	no	—
421	C₂	—	2	1	no	—
422	C₂	—	2	2	no	—
423	C₂	—	8	8	no	—
424	C₂	C₄₁×#1978	1	4	yes	direct product factor
425	C₂	C₂×C₄₁×#390	1	1	yes	characteristic
426	C₂	C₂×C₄₁×#472	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	#121
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂³×D₈×C₄₁	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂³×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#108×C₄₁	C₂	semidirect
3. C₂×C₄₁×#418	C₂	semidirect
4. C₂²×#100×C₄₁	C₂	semidirect
5. C₂×C₄₁×#405	C₂	semidirect
6. C₄₁×#1978	C₂	direct (N × H)
12. C₂²×D₈×C₄₁	C₄	semidirect
19. C₂×#108×C₄₁	C₂²	semidirect
21. C₄₁×#418	C₂²	semidirect
24. C₂×#100×C₄₁	C₂²	semidirect
26. C₄₁×#405	C₂²	semidirect
47. C₂×D₈×C₄₁	C₂×C₄	semidirect
183. C₂×#1978	C₄₁	direct (N × H)
208. C₂²×#108	C₂×C₄₁	semidirect
209. C₂×#418	C₂×C₄₁	semidirect
210. C₂²×#100	C₂×C₄₁	semidirect
211. C₂×#405	C₂×C₄₁	semidirect
212. #1978	C₂×C₄₁	direct (N × H)
217. C₂×C₄₁	#1978	direct (N × H)
225. C₂²×D₈	C₄×C₄₁	semidirect
232. C₂×#108	C₂²×C₄₁	semidirect
234. #418	C₂²×C₄₁	semidirect
237. C₂×#100	C₂²×C₄₁	semidirect
239. #405	C₂²×C₄₁	semidirect
242. C₄₁	C₂×#1978	direct (N × H)
261. C₂×D₈	C₂×C₄×C₄₁	semidirect
424. C₂	C₄₁×#1978	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×D₈×C₄₁	2
C₂²×#108×C₄₁	2
C₂×C₄₁×#418	2
C₂²×#100×C₄₁	2
C₂×C₄₁×#405	2
C₄₁×#1978	2
C₂×#1978	41

Subgroups — C2×C41×#1978 #23797447

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#1978 #23797447