Subgroups — #2488×C₂₄₁ #44504155

Order 30848.

546 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#123×C₂₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂²⋊Q₈×C₂₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#400×C₂₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#400×C₂₄₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#397×C₂₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#393×C₂₄₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#391×C₂₄₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#388×C₂₄₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#388×C₂₄₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#386×C₂₄₁	C₂	1	1	yes	maximal, characteristic
11	#386×C₂₄₁	C₂	1	1	yes	maximal, characteristic
12	#382×C₂₄₁	C₂	1	1	yes	maximal, characteristic, complemented
13	#381×C₂₄₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₂²⋊C₄×C₂₄₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#95×C₂₄₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₈×C₂₄₁	C₂²	1	1	yes	characteristic
17	C₂²×D₄×C₂₄₁	C₂²	1	1	yes	characteristic
18	C₂³×C₄×C₂₄₁	C₂²	1	1	yes	characteristic
19	C₂³×C₄×C₂₄₁	C₂²	1	1	yes	characteristic
20	C₂³×C₄×C₂₄₁	C₂²	1	1	yes	characteristic
21	#123×C₂₄₁	—	2	4	no	—
22	C₂²⋊Q₈×C₂₄₁	—	2	4	no	—
23	C₂×C₄⋊C₄×C₂₄₁	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₄×C₂₄₁	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₄×C₂₄₁	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₄×C₂₄₁	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₄×C₂₄₁	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₄×C₂₄₁	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₄×C₂₄₁	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₄×C₂₄₁	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊C₄×C₂₄₁	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₄×C₂₄₁	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₄×C₂₄₁	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊C₄×C₂₄₁	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₄×C₂₄₁	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₄×C₂₄₁	C₂²	1	1	yes	characteristic
37	C₂×C₄²×C₂₄₁	C₂²	1	1	yes	characteristic
38	C₂×C₄²×C₂₄₁	C₂²	1	1	yes	characteristic
39	#95×C₂₄₁	C₂²	1	1	yes	characteristic
40	#95×C₂₄₁	C₂²	1	1	yes	characteristic
41	#95×C₂₄₁	C₂²	1	1	yes	characteristic
42	#95×C₂₄₁	C₂²	1	1	yes	characteristic
43	#95×C₂₄₁	C₂²	1	1	yes	characteristic
44	#95×C₂₄₁	C₂²	1	1	yes	characteristic
45	#95×C₂₄₁	C₂²	1	1	yes	characteristic
46	#95×C₂₄₁	C₂²	1	1	yes	characteristic
47	#95×C₂₄₁	C₂²	1	1	yes	characteristic
48	#95×C₂₄₁	C₂²	1	1	yes	characteristic
49	#95×C₂₄₁	C₂²	1	1	yes	characteristic
50	#95×C₂₄₁	C₂²	1	1	yes	characteristic
51	#95×C₂₄₁	C₂²	1	1	yes	characteristic
52	#95×C₂₄₁	C₂²	1	1	yes	characteristic
53	C₂⁴×C₂₄₁	C₂³	1	1	yes	characteristic
54	C₂⁴×C₂₄₁	C₂³	1	1	yes	characteristic
55	C₂×Q₈×C₂₄₁	—	2	2	no	—
56	C₂×Q₈×C₂₄₁	—	2	2	no	—
57	C₂×Q₈×C₂₄₁	—	4	1	no	—
58	C₂×D₄×C₂₄₁	—	2	2	no	—
59	C₂×D₄×C₂₄₁	—	2	2	no	—
60	C₂×D₄×C₂₄₁	—	2	2	no	—
61	C₂²×C₄×C₂₄₁	—	2	2	no	—
62	C₂²×C₄×C₂₄₁	—	2	2	no	—
63	C₂²×C₄×C₂₄₁	—	2	2	no	—
64	C₂²×C₄×C₂₄₁	—	2	2	no	—
65	C₂²×C₄×C₂₄₁	—	2	2	no	—
66	C₂²×C₄×C₂₄₁	—	2	2	no	—
67	C₂²×C₄×C₂₄₁	—	2	2	no	—
68	C₂²×C₄×C₂₄₁	—	4	1	no	—
69	C₂²×C₄×C₂₄₁	—	4	1	no	—
70	C₂²×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
72	C₂²×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
75	C₂²×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
76	C₂²×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
77	C₂²×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
78	C₂²×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
80	C₂²×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
82	C₂²×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
83	C₄⋊C₄×C₂₄₁	—	2	2	no	—
84	C₄⋊C₄×C₂₄₁	—	2	2	no	—
85	C₄⋊C₄×C₂₄₁	—	2	2	no	—
86	C₄⋊C₄×C₂₄₁	—	2	2	no	—
87	C₄⋊C₄×C₂₄₁	—	2	2	no	—
88	C₂²⋊C₄×C₂₄₁	—	2	2	no	—
89	C₂²⋊C₄×C₂₄₁	—	2	2	no	—
90	C₂²⋊C₄×C₂₄₁	—	2	2	no	—
91	C₂²⋊C₄×C₂₄₁	—	2	2	no	—
92	C₂²⋊C₄×C₂₄₁	—	2	2	no	—
93	C₂²⋊C₄×C₂₄₁	—	2	2	no	—
94	C₂²⋊C₄×C₂₄₁	—	4	1	no	—
95	C₂²⋊C₄×C₂₄₁	—	4	1	no	—
96	C₂²⋊C₄×C₂₄₁	D₄	1	4	yes	—
97	C₄²×C₂₄₁	—	2	2	no	—
98	C₄²×C₂₄₁	—	4	1	no	—
99	C₂³×C₂₄₁	—	2	1	no	—
100	C₂³×C₂₄₁	—	2	1	no	—
101	C₂³×C₂₄₁	—	2	1	no	—
102	C₂³×C₂₄₁	—	2	1	no	—
103	C₂³×C₂₄₁	—	2	1	no	—
104	C₂³×C₂₄₁	—	2	1	no	—
105	C₂³×C₂₄₁	—	2	1	no	—
106	C₂³×C₂₄₁	—	2	1	no	—
107	C₂³×C₂₄₁	—	2	1	no	—
108	C₂³×C₂₄₁	—	2	1	no	—
109	C₂³×C₂₄₁	—	2	1	no	—
110	C₂³×C₂₄₁	C₂×D₄	1	2	yes	—
111	C₂³×C₂₄₁	#41	1	2	yes	—
112	C₂³×C₂₄₁	#41	1	2	yes	—
113	C₂³×C₂₄₁	C₂⁴	1	1	yes	characteristic
114	Q₈×C₂₄₁	—	4	4	no	—
115	D₄×C₂₄₁	—	4	4	no	—
116	C₂×C₄×C₂₄₁	—	2	1	no	—
117	C₂×C₄×C₂₄₁	—	2	1	no	—
118	C₂×C₄×C₂₄₁	—	2	1	no	—
119	C₂×C₄×C₂₄₁	—	2	1	no	—
120	C₂×C₄×C₂₄₁	—	2	1	no	—
121	C₂×C₄×C₂₄₁	—	2	1	no	—
122	C₂×C₄×C₂₄₁	—	2	1	no	—
123	C₂×C₄×C₂₄₁	—	2	1	no	—
124	C₂×C₄×C₂₄₁	—	2	1	no	—
125	C₂×C₄×C₂₄₁	—	2	1	no	—
126	C₂×C₄×C₂₄₁	—	2	1	no	—
127	C₂×C₄×C₂₄₁	—	2	1	no	—
128	C₂×C₄×C₂₄₁	—	2	1	no	—
129	C₂×C₄×C₂₄₁	—	2	1	no	—
130	C₂×C₄×C₂₄₁	—	2	1	no	—
131	C₂×C₄×C₂₄₁	—	2	1	no	—
132	C₂×C₄×C₂₄₁	—	2	1	no	—
133	C₂×C₄×C₂₄₁	—	2	1	no	—
134	C₂×C₄×C₂₄₁	—	2	1	no	—
135	C₂×C₄×C₂₄₁	—	2	1	no	—
136	C₂×C₄×C₂₄₁	—	2	1	no	—
137	C₂×C₄×C₂₄₁	—	2	1	no	—
138	C₂×C₄×C₂₄₁	—	2	1	no	—
139	C₂×C₄×C₂₄₁	—	2	1	no	—
140	C₂×C₄×C₂₄₁	—	2	1	no	—
141	C₂×C₄×C₂₄₁	—	2	1	no	—
142	C₂×C₄×C₂₄₁	—	2	1	no	—
143	C₂×C₄×C₂₄₁	—	2	1	no	—
144	C₂×C₄×C₂₄₁	—	2	1	no	—
145	C₂×C₄×C₂₄₁	—	2	1	no	—
146	C₂×C₄×C₂₄₁	—	2	1	no	—
147	C₂×C₄×C₂₄₁	—	2	1	no	—
148	C₂×C₄×C₂₄₁	—	2	1	no	—
149	C₂×C₄×C₂₄₁	—	2	1	no	—
150	C₂×C₄×C₂₄₁	—	2	1	no	—
151	C₂×C₄×C₂₄₁	—	4	4	no	—
152	C₂×C₄×C₂₄₁	—	4	4	no	—
153	C₂×C₄×C₂₄₁	—	4	4	no	—
154	C₂×C₄×C₂₄₁	C₂×D₄	1	2	yes	—
155	C₂×C₄×C₂₄₁	C₂×D₄	1	2	yes	—
156	C₂×C₄×C₂₄₁	#41	1	2	yes	—
157	C₂×C₄×C₂₄₁	#41	1	2	yes	—
158	C₂²×C₂₄₁	—	2	2	no	—
159	C₂²×C₂₄₁	—	2	2	no	—
160	C₂²×C₂₄₁	—	2	2	no	—
161	C₂²×C₂₄₁	—	2	2	no	—
162	C₂²×C₂₄₁	—	2	2	no	—
163	C₂²×C₂₄₁	—	2	2	no	—
164	C₂²×C₂₄₁	—	4	1	no	—
165	C₂²×C₂₄₁	—	4	1	no	—
166	C₂²×C₂₄₁	—	4	1	no	—
167	C₂²×C₂₄₁	—	4	1	no	—
168	C₂²×C₂₄₁	—	4	1	no	—
169	C₂²×C₂₄₁	—	4	1	no	—
170	C₂²×C₂₄₁	—	4	1	no	—
171	C₂²×C₂₄₁	#124	1	4	yes	—
172	C₂²×C₂₄₁	C₂²×D₄	1	1	yes	characteristic
173	C₂²×C₂₄₁	C₂×#41	1	1	yes	characteristic
174	C₂²×C₂₄₁	C₂×#41	1	1	yes	characteristic
175	C₂²×C₂₄₁	C₂×#41	1	1	yes	characteristic
176	C₂²×C₂₄₁	C₂×#41	1	1	yes	characteristic
177	C₂²×C₂₄₁	H(5,𝔽₂)	1	1	yes	characteristic
178	C₂²×C₂₄₁	2₋¹⁺⁴	1	1	yes	characteristic
179	C₄×C₂₄₁	—	2	2	no	—
180	C₄×C₂₄₁	—	2	2	no	—
181	C₄×C₂₄₁	—	2	2	no	—
182	C₄×C₂₄₁	—	2	2	no	—
183	C₄×C₂₄₁	—	4	1	no	—
184	C₄×C₂₄₁	—	4	1	no	—
185	C₄×C₂₄₁	—	4	1	no	—
186	C₄×C₂₄₁	—	4	1	no	—
187	C₄×C₂₄₁	—	4	1	no	—
188	C₄×C₂₄₁	—	4	1	no	—
189	C₄×C₂₄₁	—	4	1	no	—
190	C₄×C₂₄₁	—	4	1	no	—
191	C₄×C₂₄₁	—	4	1	no	—
192	C₂×C₂₄₁	—	2	4	no	—
193	C₂×C₂₄₁	—	8	1	no	—
194	C₂×C₂₄₁	C₂×#124	1	1	yes	characteristic
195	C₂×C₂₄₁	#529	1	1	yes	characteristic
196	C₂×C₂₄₁	#539	1	1	yes	characteristic
197	C₂×C₂₄₁	#546	1	1	yes	characteristic
198	C₂×C₂₄₁	#547	1	1	yes	characteristic
199	C₂×C₂₄₁	#551	1	1	yes	characteristic
200	C₂×C₂₄₁	#552	1	1	yes	characteristic
201	C₂₄₁	#2488	1	1	yes	characteristic, direct product factor, Sylow
202	#2488	C₂₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₂×#123	C₂×C₂₄₁	1	1	yes	characteristic
204	C₂×C₂²⋊Q₈	C₂×C₂₄₁	1	1	yes	characteristic, complemented
205	#400	C₂×C₂₄₁	1	1	yes	characteristic, complemented
206	#400	C₂×C₂₄₁	1	1	yes	characteristic, complemented
207	#397	C₂×C₂₄₁	1	1	yes	characteristic, complemented
208	#393	C₂×C₂₄₁	1	1	yes	characteristic, complemented
209	#391	C₂×C₂₄₁	1	1	yes	characteristic, complemented
210	#388	C₂×C₂₄₁	1	1	yes	characteristic, complemented
211	#388	C₂×C₂₄₁	1	1	yes	characteristic, complemented
212	#386	C₂×C₂₄₁	1	1	yes	characteristic
213	#386	C₂×C₂₄₁	1	1	yes	characteristic
214	#382	C₂×C₂₄₁	1	1	yes	characteristic, complemented
215	#381	C₂×C₂₄₁	1	1	yes	characteristic, complemented
216	C₄×C₂²⋊C₄	C₂×C₂₄₁	1	1	yes	characteristic, complemented
217	C₂×#95	C₂×C₂₄₁	1	1	yes	characteristic, complemented
218	C₂²×Q₈	C₂²×C₂₄₁	1	1	yes	characteristic
219	C₂²×D₄	C₂²×C₂₄₁	1	1	yes	characteristic
220	C₂³×C₄	C₂²×C₂₄₁	1	1	yes	characteristic
221	C₂³×C₄	C₂²×C₂₄₁	1	1	yes	characteristic
222	C₂³×C₄	C₂²×C₂₄₁	1	1	yes	characteristic
223	#123	—	2	4	no	—
224	C₂²⋊Q₈	—	2	4	no	—
225	C₂×C₄⋊C₄	C₂²×C₂₄₁	1	1	yes	characteristic
226	C₂×C₄⋊C₄	C₂²×C₂₄₁	1	1	yes	characteristic
227	C₂×C₄⋊C₄	C₂²×C₂₄₁	1	1	yes	characteristic
228	C₂×C₄⋊C₄	C₂²×C₂₄₁	1	1	yes	characteristic
229	C₂×C₄⋊C₄	C₂²×C₂₄₁	1	1	yes	characteristic
230	C₂×C₂²⋊C₄	C₂²×C₂₄₁	1	1	yes	characteristic
231	C₂×C₂²⋊C₄	C₂²×C₂₄₁	1	1	yes	characteristic
232	C₂×C₂²⋊C₄	C₂²×C₂₄₁	1	1	yes	characteristic
233	C₂×C₂²⋊C₄	C₂²×C₂₄₁	1	1	yes	characteristic
234	C₂×C₂²⋊C₄	C₂²×C₂₄₁	1	1	yes	characteristic
235	C₂×C₂²⋊C₄	C₂²×C₂₄₁	1	1	yes	characteristic
236	C₂×C₂²⋊C₄	C₂²×C₂₄₁	1	1	yes	characteristic
237	C₂×C₂²⋊C₄	C₂²×C₂₄₁	1	1	yes	characteristic
238	C₂×C₂²⋊C₄	C₂²×C₂₄₁	1	1	yes	characteristic
239	C₂×C₄²	C₂²×C₂₄₁	1	1	yes	characteristic
240	C₂×C₄²	C₂²×C₂₄₁	1	1	yes	characteristic
241	#95	C₂²×C₂₄₁	1	1	yes	characteristic
242	#95	C₂²×C₂₄₁	1	1	yes	characteristic
243	#95	C₂²×C₂₄₁	1	1	yes	characteristic
244	#95	C₂²×C₂₄₁	1	1	yes	characteristic
245	#95	C₂²×C₂₄₁	1	1	yes	characteristic
246	#95	C₂²×C₂₄₁	1	1	yes	characteristic
247	#95	C₂²×C₂₄₁	1	1	yes	characteristic
248	#95	C₂²×C₂₄₁	1	1	yes	characteristic
249	#95	C₂²×C₂₄₁	1	1	yes	characteristic
250	#95	C₂²×C₂₄₁	1	1	yes	characteristic
251	#95	C₂²×C₂₄₁	1	1	yes	characteristic
252	#95	C₂²×C₂₄₁	1	1	yes	characteristic
253	#95	C₂²×C₂₄₁	1	1	yes	characteristic
254	#95	C₂²×C₂₄₁	1	1	yes	characteristic
255	C₂⁴	C₂³×C₂₄₁	1	1	yes	characteristic
256	C₂⁴	C₂³×C₂₄₁	1	1	yes	characteristic
257	C₂×Q₈	—	2	2	no	—
258	C₂×Q₈	—	2	2	no	—
259	C₂×Q₈	—	4	1	no	—
260	C₂×D₄	—	2	2	no	—
261	C₂×D₄	—	2	2	no	—
262	C₂×D₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	4	1	no	—
271	C₂²×C₄	—	4	1	no	—
272	C₂²×C₄	C₂³×C₂₄₁	1	1	yes	characteristic
273	C₂²×C₄	C₂³×C₂₄₁	1	1	yes	characteristic
274	C₂²×C₄	C₂³×C₂₄₁	1	1	yes	characteristic
275	C₂²×C₄	C₂³×C₂₄₁	1	1	yes	characteristic
276	C₂²×C₄	C₂³×C₂₄₁	1	1	yes	characteristic
277	C₂²×C₄	C₂³×C₂₄₁	1	1	yes	characteristic
278	C₂²×C₄	C₂³×C₂₄₁	1	1	yes	characteristic
279	C₂²×C₄	C₂³×C₂₄₁	1	1	yes	characteristic
280	C₂²×C₄	C₂³×C₂₄₁	1	1	yes	characteristic
281	C₂²×C₄	C₂³×C₂₄₁	1	1	yes	characteristic
282	C₂²×C₄	C₂³×C₂₄₁	1	1	yes	characteristic
283	C₂²×C₄	C₂³×C₂₄₁	1	1	yes	characteristic
284	C₂²×C₄	C₂³×C₂₄₁	1	1	yes	characteristic
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	2	2	no	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	—	2	2	no	—
290	C₂²⋊C₄	—	2	2	no	—
291	C₂²⋊C₄	—	2	2	no	—
292	C₂²⋊C₄	—	2	2	no	—
293	C₂²⋊C₄	—	2	2	no	—
294	C₂²⋊C₄	—	2	2	no	—
295	C₂²⋊C₄	—	2	2	no	—
296	C₂²⋊C₄	—	4	1	no	—
297	C₂²⋊C₄	—	4	1	no	—
298	C₂²⋊C₄	D₄×C₂₄₁	1	4	yes	—
299	C₄²	—	2	2	no	—
300	C₄²	—	4	1	no	—
301	C₂³	—	2	1	no	—
302	C₂³	—	2	1	no	—
303	C₂³	—	2	1	no	—
304	C₂³	—	2	1	no	—
305	C₂³	—	2	1	no	—
306	C₂³	—	2	1	no	—
307	C₂³	—	2	1	no	—
308	C₂³	—	2	1	no	—
309	C₂³	—	2	1	no	—
310	C₂³	—	2	1	no	—
311	C₂³	—	2	1	no	—
312	C₂³	C₂×D₄×C₂₄₁	1	2	yes	—
313	C₂³	#41×C₂₄₁	1	2	yes	—
314	C₂³	#41×C₂₄₁	1	2	yes	—
315	C₂³	C₂⁴×C₂₄₁	1	1	yes	characteristic
316	Q₈	—	4	4	no	—
317	D₄	—	4	4	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	C₂×D₄×C₂₄₁	1	2	yes	—
357	C₂×C₄	C₂×D₄×C₂₄₁	1	2	yes	—
358	C₂×C₄	#41×C₂₄₁	1	2	yes	—
359	C₂×C₄	#41×C₂₄₁	1	2	yes	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	4	1	no	—
367	C₂²	—	4	1	no	—
368	C₂²	—	4	1	no	—
369	C₂²	—	4	1	no	—
370	C₂²	—	4	1	no	—
371	C₂²	—	4	1	no	—
372	C₂²	—	4	1	no	—
373	C₂²	#124×C₂₄₁	1	4	yes	—
374	C₂²	C₂²×D₄×C₂₄₁	1	1	yes	characteristic
375	C₂²	C₂×#41×C₂₄₁	1	1	yes	characteristic
376	C₂²	C₂×#41×C₂₄₁	1	1	yes	characteristic
377	C₂²	C₂×#41×C₂₄₁	1	1	yes	characteristic
378	C₂²	C₂×#41×C₂₄₁	1	1	yes	characteristic
379	C₂²	H(5,𝔽₂)×C₂₄₁	1	1	yes	characteristic
380	C₂²	2₋¹⁺⁴×C₂₄₁	1	1	yes	characteristic
381	C₄	—	2	2	no	—
382	C₄	—	2	2	no	—
383	C₄	—	2	2	no	—
384	C₄	—	2	2	no	—
385	C₄	—	4	1	no	—
386	C₄	—	4	1	no	—
387	C₄	—	4	1	no	—
388	C₄	—	4	1	no	—
389	C₄	—	4	1	no	—
390	C₄	—	4	1	no	—
391	C₄	—	4	1	no	—
392	C₄	—	4	1	no	—
393	C₄	—	4	1	no	—
394	C₂	—	2	4	no	—
395	C₂	—	8	1	no	—
396	C₂	C₂×#124×C₂₄₁	1	1	yes	characteristic
397	C₂	#529×C₂₄₁	1	1	yes	characteristic
398	C₂	#539×C₂₄₁	1	1	yes	characteristic
399	C₂	#546×C₂₄₁	1	1	yes	characteristic
400	C₂	#547×C₂₄₁	1	1	yes	characteristic
401	C₂	#551×C₂₄₁	1	1	yes	characteristic
402	C₂	#552×C₂₄₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₄₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₄₁
prime radical	C₂²×D₄×C₂₄₁	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂²⋊Q₈×C₂₄₁	C₂	semidirect
3. #400×C₂₄₁	C₂	semidirect
4. #400×C₂₄₁	C₂	semidirect
5. #397×C₂₄₁	C₂	semidirect
6. #393×C₂₄₁	C₂	semidirect
7. #391×C₂₄₁	C₂	semidirect
8. #388×C₂₄₁	C₂	semidirect
9. #388×C₂₄₁	C₂	semidirect
12. #382×C₂₄₁	C₂	semidirect
13. #381×C₂₄₁	C₂	semidirect
14. C₄×C₂²⋊C₄×C₂₄₁	C₂	semidirect
15. C₂×#95×C₂₄₁	C₂	semidirect
201. C₂₄₁	#2488	direct (N × H)
202. #2488	C₂₄₁	direct (N × H)
204. C₂×C₂²⋊Q₈	C₂×C₂₄₁	semidirect
205. #400	C₂×C₂₄₁	semidirect
206. #400	C₂×C₂₄₁	semidirect
207. #397	C₂×C₂₄₁	semidirect
208. #393	C₂×C₂₄₁	semidirect
209. #391	C₂×C₂₄₁	semidirect
210. #388	C₂×C₂₄₁	semidirect
211. #388	C₂×C₂₄₁	semidirect
214. #382	C₂×C₂₄₁	semidirect
215. #381	C₂×C₂₄₁	semidirect
216. C₄×C₂²⋊C₄	C₂×C₂₄₁	semidirect
217. C₂×#95	C₂×C₂₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#123×C₂₄₁	2
C₂×C₂²⋊Q₈×C₂₄₁	2
#400×C₂₄₁	2
#397×C₂₄₁	2
#393×C₂₄₁	2
#391×C₂₄₁	2
#388×C₂₄₁	2
#386×C₂₄₁	2
#382×C₂₄₁	2
#381×C₂₄₁	2
C₄×C₂²⋊C₄×C₂₄₁	2
C₂×#95×C₂₄₁	2
#2488	241

Subgroups — #2488×C241 #44504155

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2488×C₂₄₁ #44504155