Subgroups — #2493×C₂₄₁ #44504160

Order 30848.

440 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#401×C₂₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	#400×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	#387×C₂₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#387×C₂₄₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#387×C₂₄₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#385×C₂₄₁	C₂	1	1	yes	maximal, characteristic
9	#385×C₂₄₁	C₂	1	1	yes	maximal, characteristic
10	#383×C₂₄₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#381×C₂₄₁	C₂	1	1	yes	maximal, characteristic
12	#381×C₂₄₁	C₂	1	1	yes	maximal, characteristic
13	#380×C₂₄₁	C₂	1	1	yes	maximal, characteristic
14	C₄×C₂²⋊C₄×C₂₄₁	C₂	1	1	yes	maximal, characteristic
15	C₂×#95×C₂₄₁	C₂	1	1	yes	maximal, characteristic
16	C₂³×C₄×C₂₄₁	C₂²	1	1	yes	characteristic
17	C₂³×C₄×C₂₄₁	C₂²	1	1	yes	characteristic
18	C₂³×C₄×C₂₄₁	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₄×C₂₄₁	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₄×C₂₄₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₄×C₂₄₁	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₄×C₂₄₁	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₄×C₂₄₁	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₄×C₂₄₁	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊C₄×C₂₄₁	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊C₄×C₂₄₁	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₄×C₂₄₁	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₄×C₂₄₁	C₂²	1	1	yes	characteristic
29	C₂×C₄²×C₂₄₁	C₂²	1	1	yes	characteristic
30	C₂×C₄²×C₂₄₁	C₂²	1	1	yes	characteristic
31	#95×C₂₄₁	C₂²	1	1	yes	characteristic
32	#95×C₂₄₁	C₂²	1	1	yes	characteristic
33	#95×C₂₄₁	C₂²	1	1	yes	characteristic
34	#95×C₂₄₁	C₂²	1	1	yes	characteristic
35	#95×C₂₄₁	C₂²	1	1	yes	characteristic
36	#95×C₂₄₁	C₂²	1	1	yes	characteristic
37	#95×C₂₄₁	C₂²	1	1	yes	characteristic
38	#95×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	C₂⁴×C₂₄₁	C₂³	1	1	yes	characteristic
52	C₂²×C₄×C₂₄₁	—	2	2	no	—
53	C₂²×C₄×C₂₄₁	—	2	2	no	—
54	C₂²×C₄×C₂₄₁	—	2	2	no	—
55	C₂²×C₄×C₂₄₁	—	2	2	no	—
56	C₂²×C₄×C₂₄₁	—	2	2	no	—
57	C₂²×C₄×C₂₄₁	—	2	2	no	—
58	C₂²×C₄×C₂₄₁	—	2	2	no	—
59	C₂²×C₄×C₂₄₁	—	4	1	no	—
60	C₂²×C₄×C₂₄₁	—	4	1	no	—
61	C₂²×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
62	C₂²×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
67	C₂²×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
68	C₂²×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
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	C₄⋊C₄×C₂₄₁	—	2	2	no	—
76	C₄⋊C₄×C₂₄₁	—	2	2	no	—
77	C₄⋊C₄×C₂₄₁	—	2	2	no	—
78	C₄⋊C₄×C₂₄₁	—	4	1	no	—
79	C₄⋊C₄×C₂₄₁	—	4	1	no	—
80	C₄⋊C₄×C₂₄₁	—	4	1	no	—
81	C₂²⋊C₄×C₂₄₁	—	2	2	no	—
82	C₂²⋊C₄×C₂₄₁	—	2	2	no	—
83	C₂²⋊C₄×C₂₄₁	—	2	2	no	—
84	C₂²⋊C₄×C₂₄₁	—	2	2	no	—
85	C₄²×C₂₄₁	—	2	2	no	—
86	C₄²×C₂₄₁	—	4	1	no	—
87	C₂³×C₂₄₁	—	2	1	no	—
88	C₂³×C₂₄₁	—	2	1	no	—
89	C₂³×C₂₄₁	—	2	1	no	—
90	C₂³×C₂₄₁	—	2	1	no	—
91	C₂³×C₂₄₁	#41	1	2	yes	—
92	C₂³×C₂₄₁	#41	1	2	yes	—
93	C₂³×C₂₄₁	#41	1	2	yes	—
94	C₂³×C₂₄₁	C₂⁴	1	1	yes	characteristic
95	C₂×C₄×C₂₄₁	—	2	1	no	—
96	C₂×C₄×C₂₄₁	—	2	1	no	—
97	C₂×C₄×C₂₄₁	—	2	1	no	—
98	C₂×C₄×C₂₄₁	—	2	1	no	—
99	C₂×C₄×C₂₄₁	—	2	1	no	—
100	C₂×C₄×C₂₄₁	—	2	1	no	—
101	C₂×C₄×C₂₄₁	—	2	1	no	—
102	C₂×C₄×C₂₄₁	—	2	1	no	—
103	C₂×C₄×C₂₄₁	—	2	1	no	—
104	C₂×C₄×C₂₄₁	—	2	1	no	—
105	C₂×C₄×C₂₄₁	—	2	1	no	—
106	C₂×C₄×C₂₄₁	—	2	1	no	—
107	C₂×C₄×C₂₄₁	—	2	1	no	—
108	C₂×C₄×C₂₄₁	—	2	1	no	—
109	C₂×C₄×C₂₄₁	—	2	1	no	—
110	C₂×C₄×C₂₄₁	—	2	1	no	—
111	C₂×C₄×C₂₄₁	—	2	1	no	—
112	C₂×C₄×C₂₄₁	—	2	1	no	—
113	C₂×C₄×C₂₄₁	—	2	1	no	—
114	C₂×C₄×C₂₄₁	—	2	1	no	—
115	C₂×C₄×C₂₄₁	—	2	1	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	—	4	4	no	—
136	C₂×C₄×C₂₄₁	—	4	4	no	—
137	C₂×C₄×C₂₄₁	—	4	4	no	—
138	C₂×C₄×C₂₄₁	#41	1	2	yes	—
139	C₂×C₄×C₂₄₁	#41	1	2	yes	—
140	C₂²×C₂₄₁	—	2	2	no	—
141	C₂²×C₂₄₁	—	2	2	no	—
142	C₂²×C₂₄₁	—	2	2	no	—
143	C₂²×C₂₄₁	—	2	2	no	—
144	C₂²×C₂₄₁	—	2	2	no	—
145	C₂²×C₂₄₁	—	2	2	no	—
146	C₂²×C₂₄₁	#126	1	4	yes	—
147	C₂²×C₂₄₁	C₂×#41	1	1	yes	characteristic
148	C₂²×C₂₄₁	C₂×#41	1	1	yes	characteristic
149	C₂²×C₂₄₁	C₂×#41	1	1	yes	characteristic
150	C₂²×C₂₄₁	C₂×#41	1	1	yes	characteristic
151	C₂²×C₂₄₁	C₂×#41	1	1	yes	characteristic
152	C₂²×C₂₄₁	H(5,𝔽₂)	1	1	yes	characteristic
153	C₂²×C₂₄₁	2₋¹⁺⁴	1	1	yes	characteristic
154	C₄×C₂₄₁	—	2	2	no	—
155	C₄×C₂₄₁	—	2	2	no	—
156	C₄×C₂₄₁	—	4	1	no	—
157	C₄×C₂₄₁	—	4	1	no	—
158	C₄×C₂₄₁	—	4	1	no	—
159	C₄×C₂₄₁	—	4	1	no	—
160	C₄×C₂₄₁	—	4	1	no	—
161	C₄×C₂₄₁	—	4	1	no	—
162	C₄×C₂₄₁	—	4	1	no	—
163	C₄×C₂₄₁	—	4	1	no	—
164	C₄×C₂₄₁	—	4	1	no	—
165	C₄×C₂₄₁	—	4	1	no	—
166	C₄×C₂₄₁	—	4	1	no	—
167	C₄×C₂₄₁	—	4	1	no	—
168	C₂×C₂₄₁	—	2	4	no	—
169	C₂×C₂₄₁	C₂×#126	1	1	yes	characteristic
170	C₂×C₂₄₁	#529	1	1	yes	characteristic
171	C₂×C₂₄₁	#539	1	1	yes	characteristic
172	C₂×C₂₄₁	#551	1	1	yes	characteristic
173	C₂×C₂₄₁	#551	1	1	yes	characteristic
174	C₂×C₂₄₁	#552	1	1	yes	characteristic
175	C₂×C₂₄₁	#552	1	1	yes	characteristic
176	C₂₄₁	#2493	1	1	yes	characteristic, direct product factor, Sylow
177	#2493	C₂₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	#401	C₂×C₂₄₁	1	1	yes	characteristic, complemented
179	#400	C₂×C₂₄₁	1	1	yes	characteristic, complemented
180	#400	C₂×C₂₄₁	1	1	yes	characteristic, complemented
181	#400	C₂×C₂₄₁	1	1	yes	characteristic, complemented
182	#387	C₂×C₂₄₁	1	1	yes	characteristic, complemented
183	#387	C₂×C₂₄₁	1	1	yes	characteristic, complemented
184	#387	C₂×C₂₄₁	1	1	yes	characteristic, complemented
185	#385	C₂×C₂₄₁	1	1	yes	characteristic
186	#385	C₂×C₂₄₁	1	1	yes	characteristic
187	#383	C₂×C₂₄₁	1	1	yes	characteristic, complemented
188	#381	C₂×C₂₄₁	1	1	yes	characteristic
189	#381	C₂×C₂₄₁	1	1	yes	characteristic
190	#380	C₂×C₂₄₁	1	1	yes	characteristic
191	C₄×C₂²⋊C₄	C₂×C₂₄₁	1	1	yes	characteristic
192	C₂×#95	C₂×C₂₄₁	1	1	yes	characteristic
193	C₂³×C₄	C₂²×C₂₄₁	1	1	yes	characteristic
194	C₂³×C₄	C₂²×C₂₄₁	1	1	yes	characteristic
195	C₂³×C₄	C₂²×C₂₄₁	1	1	yes	characteristic
196	C₂×C₄⋊C₄	C₂²×C₂₄₁	1	1	yes	characteristic
197	C₂×C₄⋊C₄	C₂²×C₂₄₁	1	1	yes	characteristic
198	C₂×C₄⋊C₄	C₂²×C₂₄₁	1	1	yes	characteristic
199	C₂×C₄⋊C₄	C₂²×C₂₄₁	1	1	yes	characteristic
200	C₂×C₄⋊C₄	C₂²×C₂₄₁	1	1	yes	characteristic
201	C₂×C₄⋊C₄	C₂²×C₂₄₁	1	1	yes	characteristic
202	C₂×C₂²⋊C₄	C₂²×C₂₄₁	1	1	yes	characteristic
203	C₂×C₂²⋊C₄	C₂²×C₂₄₁	1	1	yes	characteristic
204	C₂×C₂²⋊C₄	C₂²×C₂₄₁	1	1	yes	characteristic
205	C₂×C₂²⋊C₄	C₂²×C₂₄₁	1	1	yes	characteristic
206	C₂×C₄²	C₂²×C₂₄₁	1	1	yes	characteristic
207	C₂×C₄²	C₂²×C₂₄₁	1	1	yes	characteristic
208	#95	C₂²×C₂₄₁	1	1	yes	characteristic
209	#95	C₂²×C₂₄₁	1	1	yes	characteristic
210	#95	C₂²×C₂₄₁	1	1	yes	characteristic
211	#95	C₂²×C₂₄₁	1	1	yes	characteristic
212	#95	C₂²×C₂₄₁	1	1	yes	characteristic
213	#95	C₂²×C₂₄₁	1	1	yes	characteristic
214	#95	C₂²×C₂₄₁	1	1	yes	characteristic
215	#95	C₂²×C₂₄₁	1	1	yes	characteristic
216	#95	C₂²×C₂₄₁	1	1	yes	characteristic
217	#95	C₂²×C₂₄₁	1	1	yes	characteristic
218	#95	C₂²×C₂₄₁	1	1	yes	characteristic
219	#95	C₂²×C₂₄₁	1	1	yes	characteristic
220	#95	C₂²×C₂₄₁	1	1	yes	characteristic
221	#95	C₂²×C₂₄₁	1	1	yes	characteristic
222	#95	C₂²×C₂₄₁	1	1	yes	characteristic
223	#95	C₂²×C₂₄₁	1	1	yes	characteristic
224	#95	C₂²×C₂₄₁	1	1	yes	characteristic
225	#95	C₂²×C₂₄₁	1	1	yes	characteristic
226	#95	C₂²×C₂₄₁	1	1	yes	characteristic
227	#95	C₂²×C₂₄₁	1	1	yes	characteristic
228	C₂⁴	C₂³×C₂₄₁	1	1	yes	characteristic
229	C₂²×C₄	—	2	2	no	—
230	C₂²×C₄	—	2	2	no	—
231	C₂²×C₄	—	2	2	no	—
232	C₂²×C₄	—	2	2	no	—
233	C₂²×C₄	—	2	2	no	—
234	C₂²×C₄	—	2	2	no	—
235	C₂²×C₄	—	2	2	no	—
236	C₂²×C₄	—	4	1	no	—
237	C₂²×C₄	—	4	1	no	—
238	C₂²×C₄	C₂³×C₂₄₁	1	1	yes	characteristic
239	C₂²×C₄	C₂³×C₂₄₁	1	1	yes	characteristic
240	C₂²×C₄	C₂³×C₂₄₁	1	1	yes	characteristic
241	C₂²×C₄	C₂³×C₂₄₁	1	1	yes	characteristic
242	C₂²×C₄	C₂³×C₂₄₁	1	1	yes	characteristic
243	C₂²×C₄	C₂³×C₂₄₁	1	1	yes	characteristic
244	C₂²×C₄	C₂³×C₂₄₁	1	1	yes	characteristic
245	C₂²×C₄	C₂³×C₂₄₁	1	1	yes	characteristic
246	C₂²×C₄	C₂³×C₂₄₁	1	1	yes	characteristic
247	C₂²×C₄	C₂³×C₂₄₁	1	1	yes	characteristic
248	C₂²×C₄	C₂³×C₂₄₁	1	1	yes	characteristic
249	C₂²×C₄	C₂³×C₂₄₁	1	1	yes	characteristic
250	C₂²×C₄	C₂³×C₂₄₁	1	1	yes	characteristic
251	C₂²×C₄	C₂³×C₂₄₁	1	1	yes	characteristic
252	C₄⋊C₄	—	2	2	no	—
253	C₄⋊C₄	—	2	2	no	—
254	C₄⋊C₄	—	2	2	no	—
255	C₄⋊C₄	—	4	1	no	—
256	C₄⋊C₄	—	4	1	no	—
257	C₄⋊C₄	—	4	1	no	—
258	C₂²⋊C₄	—	2	2	no	—
259	C₂²⋊C₄	—	2	2	no	—
260	C₂²⋊C₄	—	2	2	no	—
261	C₂²⋊C₄	—	2	2	no	—
262	C₄²	—	2	2	no	—
263	C₄²	—	4	1	no	—
264	C₂³	—	2	1	no	—
265	C₂³	—	2	1	no	—
266	C₂³	—	2	1	no	—
267	C₂³	—	2	1	no	—
268	C₂³	#41×C₂₄₁	1	2	yes	—
269	C₂³	#41×C₂₄₁	1	2	yes	—
270	C₂³	#41×C₂₄₁	1	2	yes	—
271	C₂³	C₂⁴×C₂₄₁	1	1	yes	characteristic
272	C₂×C₄	—	2	1	no	—
273	C₂×C₄	—	2	1	no	—
274	C₂×C₄	—	2	1	no	—
275	C₂×C₄	—	2	1	no	—
276	C₂×C₄	—	2	1	no	—
277	C₂×C₄	—	2	1	no	—
278	C₂×C₄	—	2	1	no	—
279	C₂×C₄	—	2	1	no	—
280	C₂×C₄	—	2	1	no	—
281	C₂×C₄	—	2	1	no	—
282	C₂×C₄	—	2	1	no	—
283	C₂×C₄	—	2	1	no	—
284	C₂×C₄	—	2	1	no	—
285	C₂×C₄	—	2	1	no	—
286	C₂×C₄	—	2	1	no	—
287	C₂×C₄	—	2	1	no	—
288	C₂×C₄	—	2	1	no	—
289	C₂×C₄	—	2	1	no	—
290	C₂×C₄	—	2	1	no	—
291	C₂×C₄	—	2	1	no	—
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	1	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	4	4	no	—
313	C₂×C₄	—	4	4	no	—
314	C₂×C₄	—	4	4	no	—
315	C₂×C₄	#41×C₂₄₁	1	2	yes	—
316	C₂×C₄	#41×C₂₄₁	1	2	yes	—
317	C₂²	—	2	2	no	—
318	C₂²	—	2	2	no	—
319	C₂²	—	2	2	no	—
320	C₂²	—	2	2	no	—
321	C₂²	—	2	2	no	—
322	C₂²	—	2	2	no	—
323	C₂²	#126×C₂₄₁	1	4	yes	—
324	C₂²	C₂×#41×C₂₄₁	1	1	yes	characteristic
325	C₂²	C₂×#41×C₂₄₁	1	1	yes	characteristic
326	C₂²	C₂×#41×C₂₄₁	1	1	yes	characteristic
327	C₂²	C₂×#41×C₂₄₁	1	1	yes	characteristic
328	C₂²	C₂×#41×C₂₄₁	1	1	yes	characteristic
329	C₂²	H(5,𝔽₂)×C₂₄₁	1	1	yes	characteristic
330	C₂²	2₋¹⁺⁴×C₂₄₁	1	1	yes	characteristic
331	C₄	—	2	2	no	—
332	C₄	—	2	2	no	—
333	C₄	—	4	1	no	—
334	C₄	—	4	1	no	—
335	C₄	—	4	1	no	—
336	C₄	—	4	1	no	—
337	C₄	—	4	1	no	—
338	C₄	—	4	1	no	—
339	C₄	—	4	1	no	—
340	C₄	—	4	1	no	—
341	C₄	—	4	1	no	—
342	C₄	—	4	1	no	—
343	C₄	—	4	1	no	—
344	C₄	—	4	1	no	—
345	C₂	—	2	4	no	—
346	C₂	C₂×#126×C₂₄₁	1	1	yes	characteristic
347	C₂	#529×C₂₄₁	1	1	yes	characteristic
348	C₂	#539×C₂₄₁	1	1	yes	characteristic
349	C₂	#551×C₂₄₁	1	1	yes	characteristic
350	C₂	#551×C₂₄₁	1	1	yes	characteristic
351	C₂	#552×C₂₄₁	1	1	yes	characteristic
352	C₂	#552×C₂₄₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₄₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₄₁
prime radical	C₂⁴×C₂₄₁	C₂³
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
1. #401×C₂₄₁	C₂	semidirect
2. #400×C₂₄₁	C₂	semidirect
3. #400×C₂₄₁	C₂	semidirect
4. #400×C₂₄₁	C₂	semidirect
5. #387×C₂₄₁	C₂	semidirect
6. #387×C₂₄₁	C₂	semidirect
7. #387×C₂₄₁	C₂	semidirect
10. #383×C₂₄₁	C₂	semidirect
176. C₂₄₁	#2493	direct (N × H)
177. #2493	C₂₄₁	direct (N × H)
178. #401	C₂×C₂₄₁	semidirect
179. #400	C₂×C₂₄₁	semidirect
180. #400	C₂×C₂₄₁	semidirect
181. #400	C₂×C₂₄₁	semidirect
182. #387	C₂×C₂₄₁	semidirect
183. #387	C₂×C₂₄₁	semidirect
184. #387	C₂×C₂₄₁	semidirect
187. #383	C₂×C₂₄₁	semidirect

Maximal subgroups

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

subgroup	index
#401×C₂₄₁	2
#400×C₂₄₁	2
#387×C₂₄₁	2
#385×C₂₄₁	2
#383×C₂₄₁	2
#381×C₂₄₁	2
#380×C₂₄₁	2
C₄×C₂²⋊C₄×C₂₄₁	2
C₂×#95×C₂₄₁	2
#2493	241

Subgroups — #2493×C241 #44504160

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2493×C₂₄₁ #44504160