Finite Group Databasebeta

← C2×#14521184 #16854888

Subgroups — C2×#14521184 #16854888

Order 3968.

1048 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D31C211yesmaximal, characteristic, complemented
2C22×D248C211yesmaximal, characteristic, complemented
3C22×#92479C211yesmaximal, characteristic, complemented
4C2×#11758472C211yesmaximal, characteristic, complemented
5#14521184C218yesmaximal, direct product factor
6C2×#11758397C211yesmaximal, characteristic, complemented
7C2×(C2×D31)⋊C8C211yesmaximal, characteristic, complemented
8C2×C31×#102C211yesmaximal, characteristic, complemented
9C24×D31—21no—
10C22×D4×C31C2211yescharacteristic
11C22×C22⋊D31—21no—
12C2×D4×D31—24no—
13C2×D4×D31—24no—
14C2×D4×D31—22no—
15C2×D4×D31C2214yescomplemented
16C22×D124—21no—
17C22×D124C2211yescharacteristic
18C22×D124C2211yescharacteristic, complemented
19C22×C4×D31C2211yescharacteristic
20C22×C8×C31C2211yescharacteristic, complemented
21C2×C4⋊C4×C31C2211yescharacteristic, complemented
22C2×#92479—24no—
23C2×#92479C2214yescomplemented
24C2×(C2×D31)⋊C4—21no—
25C22×C31⋊C8C2211yescharacteristic, complemented
26C2×D248—24no—
27C2×D248C2214yescomplemented
28#11758472—22no—
29#11758472C2214yescomplemented
30C31×#102C2214yescomplemented
31(C2×D31)⋊C8C2214yescomplemented
32#11758397C2214yescomplemented
33C24×C31—21no—
34C23×D31—28no—
35C23×D31—21no—
36C23×D31—24no—
37C23×D31—21no—
38C23×D31—44no—
39C23×D31—44no—
40C23×D31D411yescharacteristic
41C2×D4×C31—21no—
42C2×D4×C31—22no—
43C2×D4×C31D414yescomplemented
44C2×D4×C31C2312yes—
45C22×C4×C31—21no—
46C22×C4×C31C2311yescharacteristic
47C2×C22⋊D31—28no—
48C2×C22⋊D31—24no—
49C22×Dic31D411yescharacteristic
50D4×D31—216no—
51D4×D31—28no—
52D4×D31—28no—
53C2×D124—21no—
54C2×D124—22no—
55C2×D124—22no—
56C2×D124—22no—
57C2×D124—24no—
58C2×D124—21no—
59C2×D124—44no—
60C2×D124D414yescomplemented
61C2×D124C2312yes—
62C2×D124C2312yescomplemented
63C2×C4×D31—22no—
64C2×C4×D31—22no—
65C2×C4×D31D412yes—
66C2×C4×D31C2312yes—
67C2×C8×C31—22no—
68C2×C8×C31C2312yescomplemented
69C4⋊C4×C31—21no—
70C4⋊C4×C31C2312yescomplemented
71#92479—28no—
72(C2×D31)⋊C4—24no—
73C2×C31⋊C8—22no—
74C2×C31⋊C8C2312yescomplemented
75D248—28no—
76C23×C31—24no—
77C23×C31—22no—
78C23×C31—42no—
79C23×C31—42no—
80C23×C31C2×D411yescharacteristic
81C22×D31—22no—
82C22×D31—22no—
83C22×D31—216no—
84C22×D31—24no—
85C22×D31—22no—
86C22×D31—22no—
87C22×D31—48no—
88C22×D31—432no—
89C22×D31—42no—
90C22×D31—42no—
91C22×D31—48no—
92C22×D31—42no—
93C22×D31—42no—
94C22×D31—42no—
95C22×D31D814yescomplemented
96C22×D31C2×D412yes—
97D4×C31—24no—
98D4×C31—22no—
99D4×C31C2×D414yescomplemented
100C2×C4×C31—22no—
101C2×C4×C31—42no—
102C2×C4×C31C2×D412yes—
103C2×C4×C31C2×D411yescharacteristic
104C2×C4×C31C2×D412yes—
105C2×C4×C31C2411yescharacteristic
106C22⋊D31—216no—
107C2×Dic31—22no—
108C2×Dic31C2×D412yes—
109D124—24no—
110D124—22no—
111D124—22no—
112D124—22no—
113D124—48no—
114D124—42no—
115D124C2×D414yescomplemented
116C4×D31—24no—
117C4×D31—22no—
118C4×D31—22no—
119C8×C31—22no—
120C31⋊C8—22no—
121C2×#447—311nomaximal, Sylow
122C22×C31—24no—
123C22×C31—42no—
124C22×C31—42no—
125C22×C31—48no—
126C22×C31#12012yes—
127C22×C31C2×D812yes—
128C22×C31AGL(1,ℤ/8)12yes—
129C22×C31C22×D411yescharacteristic
130C2×D31—22no—
131C2×D31—22no—
132C2×D31—28no—
133C2×D31—24no—
134C2×D31—432no—
135C2×D31—42no—
136C2×D31—42no—
137C2×D31—48no—
138C2×D31—42no—
139C2×D31—42no—
140C2×D31—42no—
141C2×D31—84no—
142C2×D31C2×D814yescomplemented
143C4×C31—42no—
144C4×C31#12012yes—
145C4×C31C22×D411yescharacteristic
146C4×C31C22×D411yescharacteristic
147Dic31—22no—
148C23×D4—311no—
149C22×D8—311no—
150C22×D8—311no—
151C2×#121—311no—
152#447—318no—
153C2×#102—311no—
154C2×#102D3111yescharacteristic, complemented
155C2×C22⋊C8—311no—
156C2×C31—44no—
157C2×C31#44714yescomplemented
158C2×C31C2×#12011yescharacteristic
159C2×C31C22×D811yescharacteristic
160C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
161D31—24no—
162D31—44no—
163D31—82no—
164C25—621no—
165C22×D4—314no—
166C22×D4—311no—
167C22×D4—311no—
168C22×D4—621no—
169C22×D4—622no—
170C22×D4—621no—
171C22×D4—624no—
172C22×D4—624no—
173C22×D4C2×D3111yescharacteristic
174C23×C4—311no—
175C2×D8—314no—
176C2×D8—314no—
177C2×D8—624no—
178C2×D8—624no—
179C22×C8—311no—
180C22×C8C2×D3111yescharacteristic, complemented
181#121—314no—
182#121—622no—
183C2×C4⋊C4C2×D3111yescharacteristic, complemented
184C2×C22⋊C4—621no—
185#102—314no—
186#102C2×D3114yescomplemented
187C22⋊C8—314no—
188C31C2×#44711yescharacteristic, complemented, Sylow
189C24—21no—
190C24—311no—
191C24—624no—
192C24—628no—
193C24—621no—
194C24—621no—
195C24—1244no—
196C24—1244no—
197C2×D4—21no—
198C2×D4—22no—
199C2×D4—314no—
200C2×D4—312no—
201C2×D4—312no—
202C2×D4—624no—
203C2×D4—624no—
204C2×D4—628no—
205C2×D4—6216no—
206C2×D4—628no—
207C2×D4—628no—
208C2×D4—622no—
209C2×D4—622no—
210C2×D4—621no—
211C2×D4—622no—
212C2×D4—621no—
213C2×D4—1244no—
214C2×D4D12414yescomplemented
215C2×D4C22×D3112yes—
216C22×C4—21no—
217C22×C4—311no—
218C22×C4—312no—
219C22×C4—312no—
220C22×C4—622no—
221C22×C4—622no—
222C22×C4C22×D3111yescharacteristic
223D8—628no—
224D8—628no—
225C2×C8—22no—
226C2×C8—312no—
227C2×C8—622no—
228C2×C8C22×D3112yescomplemented
229C4⋊C4—21no—
230C4⋊C4C22×D3112yescomplemented
231C22⋊C4—624no—
232C23—24no—
233C23—22no—
234C23—42no—
235C23—42no—
236C23—314no—
237C23—312no—
238C23—6216no—
239C23—622no—
240C23—622no—
241C23—624no—
242C23—622no—
243C23—622no—
244C23—1248no—
245C23—12432no—
246C23—1248no—
247C23—1242no—
248C23—1242no—
249C23—1242no—
250C23—1242no—
251C23—1242no—
252C23D4×D3111yescharacteristic
253D4—24no—
254D4—22no—
255D4—314no—
256D4—6216no—
257D4—624no—
258D4—622no—
259D4—622no—
260D4—622no—
261D4—1248no—
262D4—1242no—
263D4C2×D12414yescomplemented
264C2×C4—22no—
265C2×C4—42no—
266C2×C4—312no—
267C2×C4—622no—
268C2×C4—624no—
269C2×C4—622no—
270C2×C4—622no—
271C2×C4C2×D12412yes—
272C2×C4D4×D3111yescharacteristic
273C2×C4D4×D3112yes—
274C2×C4C23×D3111yescharacteristic
275C8—22no—
276C8—622no—
277C22—24no—
278C22—48no—
279C22—42no—
280C22—42no—
281C22—314no—
282C22—628no—
283C22—622no—
284C22—622no—
285C22—624no—
286C22—12432no—
287C22—1248no—
288C22—1242no—
289C22—1242no—
290C22—1242no—
291C22—1242no—
292C22—1242no—
293C22—2484no—
294C22#1175845912yes—
295C22D8×D3112yes—
296C22#1175849112yes—
297C22C2×D4×D3111yescharacteristic
298C4—42no—
299C4—622no—
300C4#1175845912yes—
301C4C22×D12411yescharacteristic
302C4C2×D4×D3111yescharacteristic
303C2—44no—
304C2—624no—
305C2—1244no—
306C2—2482no—
307C2#1452118414yesdirect product factor
308C2C2×#1175845911yescharacteristic
309C2C2×D8×D3111yescharacteristic
310C2C2×#1175849111yescharacteristic
subgroupG/H
centerC23D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC2×C31×#102C2
socleC23×C31C2×D4
hypercenterC2×#102D31
hypocenterC31C2×#447
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C22×D4×D31C2semidirect
2. C22×D248C2semidirect
3. C22×#92479C2semidirect
4. C2×#11758472C2semidirect
5. #14521184C2direct (N × H)
6. C2×#11758397C2semidirect
7. C2×(C2×D31)⋊C8C2semidirect
8. C2×C31×#102C2semidirect
15. C2×D4×D31C22semidirect
18. C22×D124C22semidirect
20. C22×C8×C31C22semidirect
21. C2×C4⋊C4×C31C22semidirect
23. C2×#92479C22semidirect
25. C22×C31⋊C8C22semidirect
27. C2×D248C22semidirect
29. #11758472C22semidirect
30. C31×#102C22semidirect
31. (C2×D31)⋊C8C22semidirect
32. #11758397C22semidirect
43. C2×D4×C31D4semidirect
60. C2×D124D4semidirect
62. C2×D124C23semidirect
68. C2×C8×C31C23semidirect
70. C4⋊C4×C31C23semidirect
74. C2×C31⋊C8C23semidirect
95. C22×D31D8semidirect
99. D4×C31C2×D4semidirect
115. D124C2×D4semidirect
142. C2×D31C2×D8semidirect
154. C2×#102D31semidirect
157. C2×C31#447semidirect
180. C22×C8C2×D31semidirect
183. C2×C4⋊C4C2×D31semidirect
186. #102C2×D31semidirect
188. C31C2×#447semidirect
214. C2×D4D124semidirect
228. C2×C8C22×D31semidirect
230. C4⋊C4C22×D31semidirect
263. D4C2×D124semidirect
307. C2#14521184direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D312
C22×D2482
C22×#924792
C2×#117584722
#145211842
C2×#117583972
C2×(C2×D31)⋊C82
C2×C31×#1022
C2×#44731