Finite Group Databasebeta

← #46846413

Subgroups — #46846413

Order 34688.

454 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 129 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
1#31774431C211yesmaximal, characteristic, complemented
2C2×C4×D1084C211yesmaximal, characteristic, complemented
3#31774233C211yesmaximal, characteristic, complemented
4#31774216C211yesmaximal, characteristic, complemented
5#31774198C212yesmaximal, complemented
6#31774113C212yesmaximal, complemented
7#31774050C211yesmaximal, characteristic, complemented
8#31774033C211yesmaximal, characteristic
9C4×#16864643C212yesmaximal, complemented
10C4×D2168C212yesmaximal, complemented
11#431×C271C211yesmaximal, characteristic, complemented
12C22×D1084C2211yescharacteristic
13C22×C4×D271—21no—
14C2×#16864643C2212yes—
15C2×D2168C2212yes—
16#22576154—21no—
17#22576152C2211yescharacteristic, complemented
18#22576148C2211yescharacteristic, complemented
19#22576143—21no—
20#22576139C2211yescharacteristic
21#22576134C2211yescharacteristic
22C4×Dic542C2211yescharacteristic, complemented
23C4×D1084—21no—
24C4×D1084—21no—
25C4×D1084C2212yes—
26C4×D1084C2212yes—
27C4×D1084C2211yescharacteristic, complemented
28C4×C22⋊D271—21no—
29#22576117—21no—
30C2×C4⋊Dic271C2211yescharacteristic
31C2×(C2×D271)⋊C4—21no—
32#22576094C2212yescomplemented
33#22576092C2212yescomplemented
34#22576085C2212yescomplemented
35#22576082C2212yes—
36#22576082C2212yes—
37#22576082C2212yescomplemented
38C2×C42×C271C2211yescharacteristic
39C4⋊C8×C271C2212yescomplemented
40C22⋊C8×C271C2211yescharacteristic
41C22⋊C8×C271C2211yescharacteristic
42C4×C8×C271C2212yescomplemented
43C23×D271—21no—
44C2×Dic542C2311yescharacteristic
45C2×D1084—24no—
46C2×D1084—21no—
47C2×D1084C2311yescharacteristic
48C2×D1084C2312yes—
49C2×C22⋊D271—21no—
50C22×Dic271—21no—
51C2×C4×D271—22no—
52C2×C4×D271—22no—
53C2×C4×D271—21no—
54C2×C4×D271—44no—
55#16864643—24no—
56D2168—24no—
57C4⋊Dic271—21no—
58C4⋊Dic271C2311yescharacteristic
59C4⋊Dic271C2311yescharacteristic
60C4⋊Dic271C2312yes—
61Dic271⋊C4—21no—
62Dic271⋊C4—21no—
63Dic271⋊C4—21no—
64Dic271⋊C4—21no—
65C22⋊Dic271—21no—
66(C2×D271)⋊C4—21no—
67(C2×D271)⋊C4—21no—
68(C2×D271)⋊C4—21no—
69(C2×D271)⋊C4—21no—
70(C2×D271)⋊C4—22no—
71(C2×D271)⋊C4—22no—
72C4×Dic271—21no—
73C22×C4×C271D411yescharacteristic
74C22×C4×C271D411yescharacteristic
75C22×C4×C271C2311yescharacteristic
76C2×C8×C271C2312yes—
77C2×C8×C271C2312yes—
78C42×C271D411yescharacteristic
79C42×C271D411yescharacteristic
80C42×C271C2311yescharacteristic
81C42×C271C2311yescharacteristic
82C22×D271—24no—
83C22×D271—22no—
84C22×D271—21no—
85C22×D271—42no—
86C22×D271—42no—
87Dic542—22no—
88D1084—24no—
89D1084—22no—
90D1084—22no—
91D1084#4114yes—
92C22⋊D271—42no—
93C2×Dic271—21no—
94C2×Dic271—21no—
95C2×Dic271—22no—
96C2×Dic271—21no—
97C2×Dic271—42no—
98C4×D271—44no—
99C4×D271—42no—
100C4×D271—44no—
101C23×C271C2×D411yescharacteristic
102C2×C4×C271—22no—
103C2×C4×C271—22no—
104C2×C4×C271—22no—
105C2×C4×C271C2×D411yescharacteristic
106C2×C4×C271C2×D411yescharacteristic
107C2×C4×C271C2×D411yescharacteristic
108C2×C4×C271C2×D411yescharacteristic
109C2×C4×C271C2×D411yescharacteristic
110C2×C4×C271C2411yescharacteristic
111C8×C271—22no—
112C8×C271—22no—
113C22×C271—21no—
114C22×C271—21no—
115C22×C271#13512yes—
116C22×C271C22×D411yescharacteristic
117C2×D271—24no—
118C2×D271—48no—
119C2×D271—42no—
120C2×D271—42no—
121C2×D271—41no—
122C2×D271—41no—
123C2×D271—41no—
124C4×C271—21no—
125C4×C271—21no—
126C4×C271—21no—
127C4×C271—21no—
128C4×C271AGL(1,ℤ/8)12yes—
129C4×C271C2×#4112yes—
130Dic271—41no—
131Dic271—41no—
132Dic271—42no—
133Dic271—41no—
134C2×C271—22no—
135C2×C271#52511yescharacteristic
136C2×C271C2×#13511yescharacteristic
137C2×C271C2×AGL(1,ℤ/8)11yescharacteristic
138D271—44no—
139D271—81no—
140C271#310511yescharacteristic, complemented, Sylow
141#3105—2711nomaximal, Sylow
142#529—2711no—
143C2×C4×D4—2711no—
144#484—2711no—
145#481—2711no—
146#478—2712no—
147#463—2712no—
148#450—2711no—
149#447—2711no—
150C4×SD16—2712no—
151C4×D8—2712no—
152#431D27111yescharacteristic, complemented
153C22×D4—2711no—
154C23×C4—5421no—
155C2×SD16—2712no—
156C2×D8—2712no—
157#126—5421no—
158#125—2711no—
159#124—2711no—
160#123—5421no—
161C22⋊Q8—2711no—
162#121—2711no—
163C4×Q8—2711no—
164C4×D4—2712no—
165C4×D4—2712no—
166C4×D4—2711no—
167C4×D4—5421no—
168C4×D4—5421no—
169C4×D4—5421no—
170#117—5421no—
171C2×C4⋊C4—2711no—
172C2×C22⋊C4—5421no—
173C2×C42C2×D27111yescharacteristic
174#107—2712no—
175#106—2712no—
176C4⋊C8C2×D27112yescomplemented
177#103—2712no—
178#102—2712no—
179#102—2712no—
180#102—2712no—
181C22⋊C8C2×D27111yescharacteristic
182C22⋊C8C2×D27111yescharacteristic
183C4×C8C2×D27112yescomplemented
184C24—5421no—
185C2×Q8—2711no—
186C2×D4—2712no—
187C2×D4—2711no—
188C2×D4—5424no—
189C2×D4—5421no—
190C2×D4—5421no—
191C22×C4—5421no—
192C22×C4—5422no—
193C22×C4—5421no—
194C22×C4—5422no—
195C22×C4—10844no—
196C22×C4D108411yescharacteristic
197C22×C4D108411yescharacteristic
198C22×C4C22×D27111yescharacteristic
199SD16—5424no—
200D8—5424no—
201C2×C8C22×D27112yes—
202C2×C8C22×D27112yes—
203C4⋊C4—2711no—
204C4⋊C4—2711no—
205C4⋊C4—2712no—
206C4⋊C4—5421no—
207C4⋊C4—5421no—
208C4⋊C4—5421no—
209C4⋊C4—5421no—
210C4⋊C4—5421no—
211C22⋊C4—5421no—
212C22⋊C4—5422no—
213C22⋊C4—5422no—
214C22⋊C4—5421no—
215C22⋊C4—5421no—
216C22⋊C4—5421no—
217C22⋊C4—5421no—
218C42—5421no—
219C42D108411yescharacteristic
220C42D108411yescharacteristic
221C42C22×D27111yescharacteristic
222C42C22×D27111yescharacteristic
223C23—5424no—
224C23—5422no—
225C23—5421no—
226C23—10842no—
227C23—10842no—
228C23C2×D108411yescharacteristic
229Q8—5422no—
230D4—2714no—
231D4—5424no—
232D4—5422no—
233D4—5422no—
234D4—10842no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—5421no—
239C2×C4—5421no—
240C2×C4—5421no—
241C2×C4—5422no—
242C2×C4—10844no—
243C2×C4—10842no—
244C2×C4—10844no—
245C2×C4—10842no—
246C2×C4C2×D108411yescharacteristic
247C2×C4C2×D108411yescharacteristic
248C2×C4C2×D108411yescharacteristic
249C2×C4C2×D108411yescharacteristic
250C2×C4C2×D108411yescharacteristic
251C2×C4C23×D27111yescharacteristic
252C8—22no—
253C8—22no—
254C22—21no—
255C22—21no—
256C22—5424no—
257C22—10848no—
258C22—10842no—
259C22—10842no—
260C22—10841no—
261C22—10841no—
262C22—10841no—
263C22#2257618212yes—
264C22C22×D108411yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—10841no—
270C4—10841no—
271C4—10842no—
272C4—10841no—
273C4#2257618812yes—
274C4#41×D27112yes—
275C2—22no—
276C2—10844no—
277C2—21681no—
278C2#3177440911yescharacteristic
279C2C2×#2257618211yescharacteristic
280C2C2×#2257618811yescharacteristic
subgroupG/H
centerC2×C4C2×D1084
commutator, cosocleC2×C4×C271C24
FrattiniC2×C4C23×D271
Fitting#431×C271C2
socleC22×C271C22×D4
prime radical#31774033C2
hypercenter#431D271
hypocenterC271#3105
LCSG ▷ C2×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
1. #31774431C2semidirect
2. C2×C4×D1084C2semidirect
3. #31774233C2semidirect
4. #31774216C2semidirect
5. #31774198C2semidirect
6. #31774113C2semidirect
7. #31774050C2semidirect
9. C4×#16864643C2semidirect
10. C4×D2168C2semidirect
11. #431×C271C2semidirect
17. #22576152C22semidirect
18. #22576148C22semidirect
22. C4×Dic542C22semidirect
27. C4×D1084C22semidirect
32. #22576094C22semidirect
33. #22576092C22semidirect
34. #22576085C22semidirect
37. #22576082C22semidirect
39. C4⋊C8×C271C22semidirect
42. C4×C8×C271C22semidirect
140. C271#3105semidirect
152. #431D271semidirect
176. C4⋊C8C2×D271semidirect
183. C4×C8C2×D271semidirect

Maximal subgroups

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

subgroupindex
#317744312
C2×C4×D10842
#317742332
#317742162
#317741982
#317741132
#317740502
#317740332
C4×#168646432
C4×D21682
#431×C2712
#3105271