Subgroups — C₂²×C₄₁×#386 #23810215

Order 10496.

11630 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₄×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂⁵×C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₂²⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×C₂²⋊C₄×C₄₁	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₁×#386	C₂	1	24	yes	maximal, direct product factor
6	C₂²×#95×C₄₁	C₂	1	2	yes	maximal, complemented
7	C₂⁶×C₄₁	C₂²	1	1	yes	characteristic
8	C₂⁶×C₄₁	C₂²	1	1	yes	characteristic
9	C₂³×D₄×C₄₁	—	2	8	no	—
10	C₂³×D₄×C₄₁	—	2	8	no	—
11	C₂³×D₄×C₄₁	C₄	1	16	yes	complemented
12	C₂³×D₄×C₄₁	C₂²	1	12	yes	—
13	C₂⁴×C₄×C₄₁	—	2	8	no	—
14	C₂⁴×C₄×C₄₁	—	2	16	no	—
15	C₂⁴×C₄×C₄₁	C₂²	1	2	yes	—
16	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₄₁	C₂²	1	2	yes	—
18	C₂⁴×C₄×C₄₁	C₂²	1	12	yes	complemented
19	C₂²×C₂²⋊C₄×C₄₁	—	2	8	no	—
20	C₂²×C₂²⋊C₄×C₄₁	—	2	16	no	—
21	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	12	yes	complemented
22	C₂²×C₂²⋊C₄×C₄₁	C₂²	1	24	yes	complemented
23	C₄₁×#386	C₂²	1	64	yes	direct product factor
24	C₂×#95×C₄₁	C₂²	1	24	yes	complemented
25	C₂⁵×C₄₁	—	2	8	no	—
26	C₂⁵×C₄₁	—	2	8	no	—
27	C₂⁵×C₄₁	—	2	8	no	—
28	C₂⁵×C₄₁	—	2	4	no	—
29	C₂⁵×C₄₁	—	2	4	no	—
30	C₂⁵×C₄₁	—	2	8	no	—
31	C₂⁵×C₄₁	C₂×C₄	1	8	yes	—
32	C₂⁵×C₄₁	C₂×C₄	1	8	yes	complemented
33	C₂⁵×C₄₁	D₄	1	8	yes	—
34	C₂⁵×C₄₁	D₄	1	8	yes	—
35	C₂⁵×C₄₁	C₂³	1	6	yes	—
36	C₂⁵×C₄₁	C₂³	1	6	yes	—
37	C₂⁵×C₄₁	C₂³	1	1	yes	characteristic
38	C₂²×D₄×C₄₁	—	2	128	no	—
39	C₂²×D₄×C₄₁	—	2	48	no	—
40	C₂²×D₄×C₄₁	—	2	48	no	—
41	C₂²×D₄×C₄₁	C₂×C₄	1	96	yes	complemented
42	C₂²×D₄×C₄₁	C₂³	1	16	yes	—
43	C₂³×C₄×C₄₁	—	2	128	no	—
44	C₂³×C₄×C₄₁	—	2	8	no	—
45	C₂³×C₄×C₄₁	—	2	8	no	—
46	C₂³×C₄×C₄₁	—	2	48	no	—
47	C₂³×C₄×C₄₁	—	2	4	no	—
48	C₂³×C₄×C₄₁	—	2	4	no	—
49	C₂³×C₄×C₄₁	—	2	96	no	—
50	C₂³×C₄×C₄₁	—	2	8	no	—
51	C₂³×C₄×C₄₁	—	2	8	no	—
52	C₂³×C₄×C₄₁	—	2	8	no	—
53	C₂³×C₄×C₄₁	C₂×C₄	1	8	yes	complemented
54	C₂³×C₄×C₄₁	D₄	1	16	yes	complemented
55	C₂³×C₄×C₄₁	C₂³	1	12	yes	—
56	C₂³×C₄×C₄₁	C₂³	1	6	yes	—
57	C₂³×C₄×C₄₁	C₂³	1	12	yes	—
58	C₂³×C₄×C₄₁	C₂³	1	16	yes	complemented
59	C₂×C₂²⋊C₄×C₄₁	—	2	48	no	—
60	C₂×C₂²⋊C₄×C₄₁	—	2	96	no	—
61	C₂×C₂²⋊C₄×C₄₁	C₂³	1	16	yes	complemented
62	C₂×C₂²⋊C₄×C₄₁	C₂³	1	32	yes	complemented
63	#95×C₄₁	C₂³	1	32	yes	complemented
64	C₂⁴×C₄₁	—	2	64	no	—
65	C₂⁴×C₄₁	—	2	32	no	—
66	C₂⁴×C₄₁	—	2	64	no	—
67	C₂⁴×C₄₁	—	2	32	no	—
68	C₂⁴×C₄₁	—	2	24	no	—
69	C₂⁴×C₄₁	—	2	24	no	—
70	C₂⁴×C₄₁	—	2	32	no	—
71	C₂⁴×C₄₁	—	2	64	no	—
72	C₂⁴×C₄₁	—	2	24	no	—
73	C₂⁴×C₄₁	—	2	12	no	—
74	C₂⁴×C₄₁	—	2	12	no	—
75	C₂⁴×C₄₁	—	2	24	no	—
76	C₂⁴×C₄₁	—	4	16	no	—
77	C₂⁴×C₄₁	—	4	32	no	—
78	C₂⁴×C₄₁	—	4	16	no	—
79	C₂⁴×C₄₁	C₂²⋊C₄	1	64	yes	complemented
80	C₂⁴×C₄₁	C₂²×C₄	1	24	yes	—
81	C₂⁴×C₄₁	C₂²×C₄	1	4	yes	—
82	C₂⁴×C₄₁	C₂²×C₄	1	24	yes	complemented
83	C₂⁴×C₄₁	C₂×D₄	1	24	yes	—
84	C₂⁴×C₄₁	C₂×D₄	1	24	yes	—
85	C₂⁴×C₄₁	C₂×D₄	1	4	yes	—
86	C₂⁴×C₄₁	C₂×D₄	1	4	yes	—
87	C₂⁴×C₄₁	C₂×D₄	1	8	yes	—
88	C₂⁴×C₄₁	#41	1	8	yes	—
89	C₂⁴×C₄₁	C₂⁴	1	4	yes	—
90	C₂⁴×C₄₁	C₂⁴	1	4	yes	—
91	C₂⁴×C₄₁	C₂⁴	1	3	yes	—
92	C₂×D₄×C₄₁	—	2	384	no	—
93	C₂×D₄×C₄₁	—	2	32	no	—
94	C₂×D₄×C₄₁	—	2	32	no	—
95	C₂×D₄×C₄₁	C₂²×C₄	1	64	yes	complemented
96	C₂²×C₄×C₄₁	—	2	384	no	—
97	C₂²×C₄×C₄₁	—	2	32	no	—
98	C₂²×C₄×C₄₁	—	2	64	no	—
99	C₂²×C₄×C₄₁	—	2	24	no	—
100	C₂²×C₄×C₄₁	—	2	24	no	—
101	C₂²×C₄×C₄₁	—	2	32	no	—
102	C₂²×C₄×C₄₁	—	2	12	no	—
103	C₂²×C₄×C₄₁	—	2	12	no	—
104	C₂²×C₄×C₄₁	—	2	64	no	—
105	C₂²×C₄×C₄₁	—	2	24	no	—
106	C₂²×C₄×C₄₁	—	2	24	no	—
107	C₂²×C₄×C₄₁	—	2	24	no	—
108	C₂²×C₄×C₄₁	—	4	32	no	—
109	C₂²×C₄×C₄₁	C₂²×C₄	1	24	yes	complemented
110	C₂²×C₄×C₄₁	C₂×D₄	1	48	yes	complemented
111	C₂²×C₄×C₄₁	C₂⁴	1	8	yes	—
112	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
113	C₂²×C₄×C₄₁	C₂⁴	1	8	yes	—
114	C₂²⋊C₄×C₄₁	—	2	32	no	—
115	C₂²⋊C₄×C₄₁	—	2	64	no	—
116	C₂³×C₄₁	—	2	96	no	—
117	C₂³×C₄₁	—	2	48	no	—
118	C₂³×C₄₁	—	2	96	no	—
119	C₂³×C₄₁	—	2	48	no	—
120	C₂³×C₄₁	—	2	8	no	—
121	C₂³×C₄₁	—	2	8	no	—
122	C₂³×C₄₁	—	2	256	no	—
123	C₂³×C₄₁	—	2	48	no	—
124	C₂³×C₄₁	—	2	96	no	—
125	C₂³×C₄₁	—	2	8	no	—
126	C₂³×C₄₁	—	2	4	no	—
127	C₂³×C₄₁	—	2	4	no	—
128	C₂³×C₄₁	—	2	8	no	—
129	C₂³×C₄₁	—	4	24	no	—
130	C₂³×C₄₁	—	4	48	no	—
131	C₂³×C₄₁	—	4	24	no	—
132	C₂³×C₄₁	—	4	128	no	—
133	C₂³×C₄₁	C₂×C₂²⋊C₄	1	16	yes	—
134	C₂³×C₄₁	C₂×C₂²⋊C₄	1	96	yes	complemented
135	C₂³×C₄₁	C₄×D₄	1	32	yes	—
136	C₂³×C₄₁	#120	1	16	yes	—
137	C₂³×C₄₁	#121	1	32	yes	—
138	C₂³×C₄₁	#123	1	16	yes	—
139	C₂³×C₄₁	C₂³×C₄	1	8	yes	—
140	C₂³×C₄₁	C₂³×C₄	1	6	yes	—
141	C₂³×C₄₁	C₂³×C₄	1	8	yes	complemented
142	C₂³×C₄₁	C₂²×D₄	1	8	yes	—
143	C₂³×C₄₁	C₂²×D₄	1	8	yes	—
144	C₂³×C₄₁	C₂²×D₄	1	6	yes	—
145	C₂³×C₄₁	C₂²×D₄	1	6	yes	—
146	C₂³×C₄₁	C₂²×D₄	1	12	yes	—
147	C₂³×C₄₁	C₂×#41	1	12	yes	—
148	C₂³×C₄₁	C₂⁵	1	1	yes	characteristic
149	D₄×C₄₁	—	2	128	no	—
150	C₂×C₄×C₄₁	—	2	128	no	—
151	C₂×C₄×C₄₁	—	2	48	no	—
152	C₂×C₄×C₄₁	—	2	96	no	—
153	C₂×C₄×C₄₁	—	2	8	no	—
154	C₂×C₄×C₄₁	—	2	8	no	—
155	C₂×C₄×C₄₁	—	2	4	no	—
156	C₂×C₄×C₄₁	—	2	4	no	—
157	C₂×C₄×C₄₁	—	2	8	no	—
158	C₂×C₄×C₄₁	—	2	8	no	—
159	C₂×C₄×C₄₁	—	2	8	no	—
160	C₂×C₄×C₄₁	—	4	48	no	—
161	C₂×C₄×C₄₁	C₂³×C₄	1	8	yes	complemented
162	C₂×C₄×C₄₁	C₂²×D₄	1	16	yes	complemented
163	C₂²×#386	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂²×C₄₁	—	2	16	no	—
165	C₂²×C₄₁	—	2	8	no	—
166	C₂²×C₄₁	—	2	16	no	—
167	C₂²×C₄₁	—	2	8	no	—
168	C₂²×C₄₁	—	2	192	no	—
169	C₂²×C₄₁	—	2	8	no	—
170	C₂²×C₄₁	—	2	16	no	—
171	C₂²×C₄₁	—	4	4	no	—
172	C₂²×C₄₁	—	4	8	no	—
173	C₂²×C₄₁	—	4	4	no	—
174	C₂²×C₄₁	—	4	96	no	—
175	C₂²×C₄₁	#386	1	64	yes	direct product factor
176	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	12	yes	—
177	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	16	yes	complemented
178	C₂²×C₄₁	C₂×C₄×D₄	1	24	yes	—
179	C₂²×C₄₁	C₂×#120	1	12	yes	—
180	C₂²×C₄₁	C₂×#121	1	24	yes	—
181	C₂²×C₄₁	C₂×#123	1	12	yes	—
182	C₂²×C₄₁	C₂⁴×C₄	1	1	yes	characteristic
183	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
184	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
185	C₂²×C₄₁	C₂³×D₄	1	2	yes	—
186	C₂²×C₄₁	C₂²×#41	1	2	yes	—
187	C₄×C₄₁	—	2	8	no	—
188	C₄×C₄₁	—	2	16	no	—
189	C₄×C₄₁	—	4	8	no	—
190	C₂⁴×D₄	C₂×C₄₁	1	1	yes	characteristic
191	C₂⁵×C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
192	C₂³×C₂²⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
193	C₂³×C₂²⋊C₄	C₂×C₄₁	1	2	yes	complemented
194	C₂×#386	C₂×C₄₁	1	24	yes	direct product factor
195	C₂²×#95	C₂×C₄₁	1	2	yes	complemented
196	C₂×C₄₁	—	2	16	no	—
197	C₂×C₄₁	—	4	8	no	—
198	C₂×C₄₁	C₂×#386	1	24	yes	direct product factor
199	C₂×C₄₁	C₂³×C₂²⋊C₄	1	1	yes	characteristic
200	C₂×C₄₁	C₂²×C₄×D₄	1	2	yes	—
201	C₂×C₄₁	C₂²×#120	1	1	yes	characteristic
202	C₂×C₄₁	C₂²×#121	1	2	yes	—
203	C₂×C₄₁	C₂²×#123	1	1	yes	characteristic
204	C₂⁶	C₂²×C₄₁	1	1	yes	characteristic
205	C₂⁶	C₂²×C₄₁	1	1	yes	characteristic
206	C₂³×D₄	—	2	8	no	—
207	C₂³×D₄	—	2	8	no	—
208	C₂³×D₄	C₄×C₄₁	1	16	yes	complemented
209	C₂³×D₄	C₂²×C₄₁	1	12	yes	—
210	C₂⁴×C₄	—	2	8	no	—
211	C₂⁴×C₄	—	2	16	no	—
212	C₂⁴×C₄	C₂²×C₄₁	1	2	yes	—
213	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
214	C₂⁴×C₄	C₂²×C₄₁	1	2	yes	—
215	C₂⁴×C₄	C₂²×C₄₁	1	12	yes	complemented
216	C₂²×C₂²⋊C₄	—	2	8	no	—
217	C₂²×C₂²⋊C₄	—	2	16	no	—
218	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	12	yes	complemented
219	C₂²×C₂²⋊C₄	C₂²×C₄₁	1	24	yes	complemented
220	#386	C₂²×C₄₁	1	64	yes	direct product factor
221	C₂×#95	C₂²×C₄₁	1	24	yes	complemented
222	C₄₁	C₂²×#386	1	1	yes	characteristic, direct product factor, Sylow
223	C₂⁵	—	2	8	no	—
224	C₂⁵	—	2	8	no	—
225	C₂⁵	—	2	8	no	—
226	C₂⁵	—	2	4	no	—
227	C₂⁵	—	2	4	no	—
228	C₂⁵	—	2	8	no	—
229	C₂⁵	C₂×C₄×C₄₁	1	8	yes	—
230	C₂⁵	C₂×C₄×C₄₁	1	8	yes	complemented
231	C₂⁵	D₄×C₄₁	1	8	yes	—
232	C₂⁵	D₄×C₄₁	1	8	yes	—
233	C₂⁵	C₂³×C₄₁	1	6	yes	—
234	C₂⁵	C₂³×C₄₁	1	6	yes	—
235	C₂⁵	C₂³×C₄₁	1	1	yes	characteristic
236	C₂²×D₄	—	2	128	no	—
237	C₂²×D₄	—	2	48	no	—
238	C₂²×D₄	—	2	48	no	—
239	C₂²×D₄	C₂×C₄×C₄₁	1	96	yes	complemented
240	C₂²×D₄	C₂³×C₄₁	1	16	yes	—
241	C₂³×C₄	—	2	128	no	—
242	C₂³×C₄	—	2	8	no	—
243	C₂³×C₄	—	2	8	no	—
244	C₂³×C₄	—	2	48	no	—
245	C₂³×C₄	—	2	4	no	—
246	C₂³×C₄	—	2	4	no	—
247	C₂³×C₄	—	2	96	no	—
248	C₂³×C₄	—	2	8	no	—
249	C₂³×C₄	—	2	8	no	—
250	C₂³×C₄	—	2	8	no	—
251	C₂³×C₄	C₂×C₄×C₄₁	1	8	yes	complemented
252	C₂³×C₄	D₄×C₄₁	1	16	yes	complemented
253	C₂³×C₄	C₂³×C₄₁	1	12	yes	—
254	C₂³×C₄	C₂³×C₄₁	1	6	yes	—
255	C₂³×C₄	C₂³×C₄₁	1	12	yes	—
256	C₂³×C₄	C₂³×C₄₁	1	16	yes	complemented
257	C₂×C₂²⋊C₄	—	2	48	no	—
258	C₂×C₂²⋊C₄	—	2	96	no	—
259	C₂×C₂²⋊C₄	C₂³×C₄₁	1	16	yes	complemented
260	C₂×C₂²⋊C₄	C₂³×C₄₁	1	32	yes	complemented
261	#95	C₂³×C₄₁	1	32	yes	complemented
262	C₂⁴	—	2	64	no	—
263	C₂⁴	—	2	32	no	—
264	C₂⁴	—	2	64	no	—
265	C₂⁴	—	2	32	no	—
266	C₂⁴	—	2	24	no	—
267	C₂⁴	—	2	24	no	—
268	C₂⁴	—	2	32	no	—
269	C₂⁴	—	2	64	no	—
270	C₂⁴	—	2	24	no	—
271	C₂⁴	—	2	12	no	—
272	C₂⁴	—	2	12	no	—
273	C₂⁴	—	2	24	no	—
274	C₂⁴	—	4	16	no	—
275	C₂⁴	—	4	32	no	—
276	C₂⁴	—	4	16	no	—
277	C₂⁴	C₂²⋊C₄×C₄₁	1	64	yes	complemented
278	C₂⁴	C₂²×C₄×C₄₁	1	24	yes	—
279	C₂⁴	C₂²×C₄×C₄₁	1	4	yes	—
280	C₂⁴	C₂²×C₄×C₄₁	1	24	yes	complemented
281	C₂⁴	C₂×D₄×C₄₁	1	24	yes	—
282	C₂⁴	C₂×D₄×C₄₁	1	24	yes	—
283	C₂⁴	C₂×D₄×C₄₁	1	4	yes	—
284	C₂⁴	C₂×D₄×C₄₁	1	4	yes	—
285	C₂⁴	C₂×D₄×C₄₁	1	8	yes	—
286	C₂⁴	#41×C₄₁	1	8	yes	—
287	C₂⁴	C₂⁴×C₄₁	1	4	yes	—
288	C₂⁴	C₂⁴×C₄₁	1	4	yes	—
289	C₂⁴	C₂⁴×C₄₁	1	3	yes	—
290	C₂×D₄	—	2	384	no	—
291	C₂×D₄	—	2	32	no	—
292	C₂×D₄	—	2	32	no	—
293	C₂×D₄	C₂²×C₄×C₄₁	1	64	yes	complemented
294	C₂²×C₄	—	2	384	no	—
295	C₂²×C₄	—	2	32	no	—
296	C₂²×C₄	—	2	64	no	—
297	C₂²×C₄	—	2	24	no	—
298	C₂²×C₄	—	2	24	no	—
299	C₂²×C₄	—	2	32	no	—
300	C₂²×C₄	—	2	12	no	—
301	C₂²×C₄	—	2	12	no	—
302	C₂²×C₄	—	2	64	no	—
303	C₂²×C₄	—	2	24	no	—
304	C₂²×C₄	—	2	24	no	—
305	C₂²×C₄	—	2	24	no	—
306	C₂²×C₄	—	4	32	no	—
307	C₂²×C₄	C₂²×C₄×C₄₁	1	24	yes	complemented
308	C₂²×C₄	C₂×D₄×C₄₁	1	48	yes	complemented
309	C₂²×C₄	C₂⁴×C₄₁	1	8	yes	—
310	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
311	C₂²×C₄	C₂⁴×C₄₁	1	8	yes	—
312	C₂²⋊C₄	—	2	32	no	—
313	C₂²⋊C₄	—	2	64	no	—
314	C₂³	—	2	96	no	—
315	C₂³	—	2	48	no	—
316	C₂³	—	2	96	no	—
317	C₂³	—	2	48	no	—
318	C₂³	—	2	8	no	—
319	C₂³	—	2	8	no	—
320	C₂³	—	2	256	no	—
321	C₂³	—	2	48	no	—
322	C₂³	—	2	96	no	—
323	C₂³	—	2	8	no	—
324	C₂³	—	2	4	no	—
325	C₂³	—	2	4	no	—
326	C₂³	—	2	8	no	—
327	C₂³	—	4	24	no	—
328	C₂³	—	4	48	no	—
329	C₂³	—	4	24	no	—
330	C₂³	—	4	128	no	—
331	C₂³	C₂×C₂²⋊C₄×C₄₁	1	16	yes	—
332	C₂³	C₂×C₂²⋊C₄×C₄₁	1	96	yes	complemented
333	C₂³	C₄×D₄×C₄₁	1	32	yes	—
334	C₂³	#120×C₄₁	1	16	yes	—
335	C₂³	#121×C₄₁	1	32	yes	—
336	C₂³	#123×C₄₁	1	16	yes	—
337	C₂³	C₂³×C₄×C₄₁	1	8	yes	—
338	C₂³	C₂³×C₄×C₄₁	1	6	yes	—
339	C₂³	C₂³×C₄×C₄₁	1	8	yes	complemented
340	C₂³	C₂²×D₄×C₄₁	1	8	yes	—
341	C₂³	C₂²×D₄×C₄₁	1	8	yes	—
342	C₂³	C₂²×D₄×C₄₁	1	6	yes	—
343	C₂³	C₂²×D₄×C₄₁	1	6	yes	—
344	C₂³	C₂²×D₄×C₄₁	1	12	yes	—
345	C₂³	C₂×#41×C₄₁	1	12	yes	—
346	C₂³	C₂⁵×C₄₁	1	1	yes	characteristic
347	D₄	—	2	128	no	—
348	C₂×C₄	—	2	128	no	—
349	C₂×C₄	—	2	48	no	—
350	C₂×C₄	—	2	96	no	—
351	C₂×C₄	—	2	8	no	—
352	C₂×C₄	—	2	8	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	8	no	—
356	C₂×C₄	—	2	8	no	—
357	C₂×C₄	—	2	8	no	—
358	C₂×C₄	—	4	48	no	—
359	C₂×C₄	C₂³×C₄×C₄₁	1	8	yes	complemented
360	C₂×C₄	C₂²×D₄×C₄₁	1	16	yes	complemented
361	C₂²	—	2	192	no	—
362	C₂²	—	2	16	no	—
363	C₂²	—	2	8	no	—
364	C₂²	—	2	16	no	—
365	C₂²	—	2	8	no	—
366	C₂²	—	2	8	no	—
367	C₂²	—	2	16	no	—
368	C₂²	—	4	96	no	—
369	C₂²	—	4	4	no	—
370	C₂²	—	4	8	no	—
371	C₂²	—	4	4	no	—
372	C₂²	C₄₁×#386	1	64	yes	direct product factor
373	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	12	yes	—
374	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	16	yes	complemented
375	C₂²	C₂×C₄×D₄×C₄₁	1	24	yes	—
376	C₂²	C₂×#120×C₄₁	1	12	yes	—
377	C₂²	C₂×#121×C₄₁	1	24	yes	—
378	C₂²	C₂×#123×C₄₁	1	12	yes	—
379	C₂²	C₂⁴×C₄×C₄₁	1	1	yes	characteristic
380	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
381	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
382	C₂²	C₂³×D₄×C₄₁	1	2	yes	—
383	C₂²	C₂²×#41×C₄₁	1	2	yes	—
384	C₄	—	2	8	no	—
385	C₄	—	2	16	no	—
386	C₄	—	4	8	no	—
387	C₂	—	2	16	no	—
388	C₂	—	4	8	no	—
389	C₂	C₂×C₄₁×#386	1	24	yes	direct product factor
390	C₂	C₂³×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
391	C₂	C₂²×C₄×D₄×C₄₁	1	2	yes	—
392	C₂	C₂²×#120×C₄₁	1	1	yes	characteristic
393	C₂	C₂²×#121×C₄₁	1	2	yes	—
394	C₂	C₂²×#123×C₄₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁵×C₄₁	C₂³
commutator	C₂²	C₂⁴×C₄×C₄₁
Frattini, cosocle	C₂³	C₂⁵×C₄₁
prime radical	C₂⁴×D₄×C₄₁	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁵×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂⁵×C₄×C₄₁	C₂	semidirect
3. C₂³×C₂²⋊C₄×C₄₁	C₂	semidirect
4. C₂³×C₂²⋊C₄×C₄₁	C₂	semidirect
5. C₂×C₄₁×#386	C₂	direct (N × H)
6. C₂²×#95×C₄₁	C₂	semidirect
11. C₂³×D₄×C₄₁	C₄	semidirect
18. C₂⁴×C₄×C₄₁	C₂²	semidirect
21. C₂²×C₂²⋊C₄×C₄₁	C₂²	semidirect
22. C₂²×C₂²⋊C₄×C₄₁	C₂²	semidirect
23. C₄₁×#386	C₂²	direct (N × H)
24. C₂×#95×C₄₁	C₂²	semidirect
32. C₂⁵×C₄₁	C₂×C₄	semidirect
41. C₂²×D₄×C₄₁	C₂×C₄	semidirect
53. C₂³×C₄×C₄₁	C₂×C₄	semidirect
54. C₂³×C₄×C₄₁	D₄	semidirect
58. C₂³×C₄×C₄₁	C₂³	semidirect
61. C₂×C₂²⋊C₄×C₄₁	C₂³	semidirect
62. C₂×C₂²⋊C₄×C₄₁	C₂³	semidirect
63. #95×C₄₁	C₂³	semidirect
79. C₂⁴×C₄₁	C₂²⋊C₄	semidirect
82. C₂⁴×C₄₁	C₂²×C₄	semidirect
95. C₂×D₄×C₄₁	C₂²×C₄	semidirect
109. C₂²×C₄×C₄₁	C₂²×C₄	semidirect
110. C₂²×C₄×C₄₁	C₂×D₄	semidirect
134. C₂³×C₄₁	C₂×C₂²⋊C₄	semidirect
141. C₂³×C₄₁	C₂³×C₄	semidirect
161. C₂×C₄×C₄₁	C₂³×C₄	semidirect
162. C₂×C₄×C₄₁	C₂²×D₄	semidirect
163. C₂²×#386	C₄₁	direct (N × H)
175. C₂²×C₄₁	#386	direct (N × H)
177. C₂²×C₄₁	C₂²×C₂²⋊C₄	semidirect
191. C₂⁵×C₄	C₂×C₄₁	semidirect
192. C₂³×C₂²⋊C₄	C₂×C₄₁	semidirect
193. C₂³×C₂²⋊C₄	C₂×C₄₁	semidirect
194. C₂×#386	C₂×C₄₁	direct (N × H)
195. C₂²×#95	C₂×C₄₁	semidirect
198. C₂×C₄₁	C₂×#386	direct (N × H)
208. C₂³×D₄	C₄×C₄₁	semidirect
215. C₂⁴×C₄	C₂²×C₄₁	semidirect
218. C₂²×C₂²⋊C₄	C₂²×C₄₁	semidirect
219. C₂²×C₂²⋊C₄	C₂²×C₄₁	semidirect
220. #386	C₂²×C₄₁	direct (N × H)
221. C₂×#95	C₂²×C₄₁	semidirect
222. C₄₁	C₂²×#386	direct (N × H)
230. C₂⁵	C₂×C₄×C₄₁	semidirect
239. C₂²×D₄	C₂×C₄×C₄₁	semidirect
251. C₂³×C₄	C₂×C₄×C₄₁	semidirect
252. C₂³×C₄	D₄×C₄₁	semidirect
256. C₂³×C₄	C₂³×C₄₁	semidirect
259. C₂×C₂²⋊C₄	C₂³×C₄₁	semidirect
260. C₂×C₂²⋊C₄	C₂³×C₄₁	semidirect
261. #95	C₂³×C₄₁	semidirect
277. C₂⁴	C₂²⋊C₄×C₄₁	semidirect
280. C₂⁴	C₂²×C₄×C₄₁	semidirect
293. C₂×D₄	C₂²×C₄×C₄₁	semidirect
307. C₂²×C₄	C₂²×C₄×C₄₁	semidirect
308. C₂²×C₄	C₂×D₄×C₄₁	semidirect
332. C₂³	C₂×C₂²⋊C₄×C₄₁	semidirect
339. C₂³	C₂³×C₄×C₄₁	semidirect
359. C₂×C₄	C₂³×C₄×C₄₁	semidirect
360. C₂×C₄	C₂²×D₄×C₄₁	semidirect
372. C₂²	C₄₁×#386	direct (N × H)
374. C₂²	C₂²×C₂²⋊C₄×C₄₁	semidirect
389. C₂	C₂×C₄₁×#386	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×D₄×C₄₁	2
C₂⁵×C₄×C₄₁	2
C₂³×C₂²⋊C₄×C₄₁	2
C₂×C₄₁×#386	2
C₂²×#95×C₄₁	2
C₂²×#386	41

Subgroups — C22×C41×#386 #23810215

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄₁×#386 #23810215