Finite Group Databasebeta

← #46820385

Subgroups — #46820385

Order 34432.

526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C2×#22575479C211yesmaximal, characteristic, complemented
2#31771172C211yesmaximal, characteristic, complemented
3#31771080C211yesmaximal, characteristic, complemented
4#31770818C214yesmaximal, complemented
5#31770798C214yesmaximal, complemented
6#31770631C211yesmaximal, characteristic, complemented
7#31770610C211yesmaximal, characteristic, complemented
8#31770602C211yesmaximal, characteristic, complemented
9C22×D8×C269C211yesmaximal, characteristic, complemented
10C2×#16864402C2211yescharacteristic
11#22575479—24no—
12C2×#16864390C2212yescomplemented
13C2×#16864387C2212yescomplemented
14C2×#16864386C2211yescharacteristic
15#22575449C2212yescomplemented
16#22575440C2212yescomplemented
17#22575424—22no—
18#22575422—22no—
19D4×Dic269—22no—
20D4×Dic269C2214yescomplemented
21#22575412C2211yescharacteristic
22#22575412C2211yescharacteristic
23C2×C22⋊Dic269—22no—
24#22575382C2214yescomplemented
25#22575378C2212yescomplemented
26#22575375C2212yescomplemented
27#22575374C2214yescomplemented
28C22×D4×C269C2211yescharacteristic
29C22×D4×C269C2211yescharacteristic
30C2×D8×C269—24no—
31C2×D8×C269C2214yes—
32C22×C8×C269C2211yescharacteristic
33#16864402—22no—
34#16864402—22no—
35C2×Dic538C2311yescharacteristic
36C2×D1076C2311yescharacteristic
37C2×C22⋊D269—24no—
38C2×C22⋊D269—21no—
39C22×Dic269—24no—
40C2×C4×D269—21no—
41#16864390—24no—
42#16864387—24no—
43#16864386—22no—
44C2×#14524130C2312yes—
45C4⋊Dic269D412yes—
46C4⋊Dic269C2312yes—
47C22⋊Dic269—24no—
48C22⋊Dic269—24no—
49C22⋊Dic269—21no—
50C22⋊Dic269D412yes—
51C4×Dic269—21no—
52C4×Dic269C2312yes—
53C24×C269—21no—
54C24×C269—21no—
55C2×D4×C269—21no—
56C2×D4×C269—22no—
57C2×D4×C269—21no—
58C2×D4×C269—22no—
59C2×D4×C269—22no—
60C2×D4×C269D414yescomplemented
61C2×D4×C269C2312yes—
62C2×D4×C269C2312yes—
63C22×C4×C269C2311yescharacteristic
64D8×C269—28no—
65C2×C8×C269—22no—
66C2×C8×C269C2312yes—
67C22×D269—21no—
68Dic538—21no—
69Dic538—21no—
70D1076—21no—
71D1076—21no—
72C22⋊D269—42no—
73C22⋊D269—84no—
74C2×Dic269—22no—
75C2×Dic269—21no—
76C2×Dic269—84no—
77C2×Dic269C2×D414yes—
78C4×D269—42no—
79#14524130—22no—
80C23×C269—22no—
81C23×C269—24no—
82C23×C269—22no—
83C23×C269—42no—
84C23×C269—82no—
85C23×C269—82no—
86C23×C269C2×D411yescharacteristic
87D4×C269—24no—
88D4×C269—22no—
89D4×C269—22no—
90D4×C269—22no—
91D4×C269—42no—
92D4×C269C2×D414yes—
93C2×C4×C269C2×D411yescharacteristic
94C2×C4×C269C2×D412yes—
95C2×C4×C269#4112yes—
96C2×C4×C269C2411yescharacteristic
97C8×C269—22no—
98C22×C269—22no—
99C22×C269—24no—
100C22×C269—44no—
101C22×C269—42no—
102C22×C269—44no—
103C22×C269—84no—
104C22×C269—84no—
105C22×C269#12112yes—
106C22×C269C22×D411yescharacteristic
107C2×D269—41no—
108C2×D269—42no—
109C4×C269#12112yes—
110C4×C269C22×D411yescharacteristic
111C4×C269C2×#4111yescharacteristic
112Dic269—24no—
113Dic269—41no—
114Dic269—42no—
115C2×C269—22no—
116C2×C269—44no—
117C2×C269—82no—
118C2×C269C2×#12111yescharacteristic
119C2×C269#57612yes—
120D269—81no—
121C269#304111yescharacteristic, complemented, Sylow
122#3041—2691nomaximal, Sylow
123C2×AGL(1,ℤ/8)—2691no—
124C22×D8D26911yescharacteristic, complemented
125#535—2691no—
126#518—2691no—
127#463—2694no—
128#459—2694no—
129#424—2691no—
130#418—2691no—
131#416—2691no—
132C2×#41—2691no—
133C22×D4C2×D26911yescharacteristic
134C22×D4C2×D26911yescharacteristic
135AGL(1,ℤ/8)—5384no—
136C2×SD16—2692no—
137C2×D8—24no—
138C2×D8—2692no—
139C2×D8C2×D26914yes—
140C2×M16—2691no—
141C22×C8C2×D26911yescharacteristic
142#127—2692no—
143#124—2692no—
144#121—5382no—
145#120—5382no—
146C4×D4—2694no—
147C4×D4—5382no—
148#117—2691no—
149#117—2691no—
150C2×C22⋊C4—5382no—
151C4⋊C8—2694no—
152#103—2692no—
153#102—2694no—
154#102—2692no—
155C24—21no—
156C24—21no—
157#41—5382no—
158#41—5382no—
159C2×Q8—2691no—
160C2×D4—21no—
161C2×D4—21no—
162C2×D4—22no—
163C2×D4—22no—
164C2×D4—22no—
165C2×D4—2691no—
166C2×D4—5384no—
167C2×D4—5381no—
168C2×D4C22⋊D26914yescomplemented
169C2×D4C22×D26912yes—
170C2×D4C22×D26912yes—
171C22×C4—5384no—
172C22×C4—5381no—
173C22×C4C22×D26911yescharacteristic
174SD16—5384no—
175D8—28no—
176D8—5384no—
177M16—5382no—
178C2×C8—22no—
179C2×C8—2692no—
180C2×C8C22×D26912yes—
181C4⋊C4—2692no—
182C4⋊C4—2692no—
183C22⋊C4—2692no—
184C22⋊C4—5384no—
185C22⋊C4—5384no—
186C22⋊C4—5381no—
187C42—2692no—
188C42—5381no—
189C23—22no—
190C23—24no—
191C23—22no—
192C23—42no—
193C23—82no—
194C23—82no—
195C23—5381no—
196C23D4×D26911yescharacteristic
197Q8—5381no—
198Q8—5381no—
199D4—24no—
200D4—22no—
201D4—22no—
202D4—22no—
203D4—42no—
204D4—5381no—
205D4—5381no—
206D4—10762no—
207D4—21524no—
208D4C2×C22⋊D26914yes—
209C2×C4—2694no—
210C2×C4—5382no—
211C2×C4—5381no—
212C2×C4—10762no—
213C2×C4—21524no—
214C2×C4D4×D26911yescharacteristic
215C2×C4C2×C22⋊D26912yes—
216C2×C4#1686440112yes—
217C2×C4C23×D26911yescharacteristic
218C8—22no—
219C8—5382no—
220C22—22no—
221C22—24no—
222C22—44no—
223C22—44no—
224C22—42no—
225C22—84no—
226C22—84no—
227C22—10762no—
228C22—10761no—
229C22#2257542512yes—
230C22C2×D4×D26911yescharacteristic
231C4—5384no—
232C4—10762no—
233C4—10761no—
234C4#2257542512yes—
235C4C22×C22⋊D26911yescharacteristic
236C4C2×#1686440111yescharacteristic
237C2—22no—
238C2—44no—
239C2—82no—
240C2—21521no—
241C2C2×#2257542511yescharacteristic
242C2#3177140612yes—
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
FittingC22×D8×C269C2
socleC22×C269C22×D4
hypercenterC22×D8D269
hypocenterC269#3041
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×#22575479C2semidirect
2. #31771172C2semidirect
3. #31771080C2semidirect
4. #31770818C2semidirect
5. #31770798C2semidirect
6. #31770631C2semidirect
7. #31770610C2semidirect
8. #31770602C2semidirect
9. C22×D8×C269C2semidirect
12. C2×#16864390C22semidirect
13. C2×#16864387C22semidirect
15. #22575449C22semidirect
16. #22575440C22semidirect
20. D4×Dic269C22semidirect
24. #22575382C22semidirect
25. #22575378C22semidirect
26. #22575375C22semidirect
27. #22575374C22semidirect
60. C2×D4×C269D4semidirect
121. C269#3041semidirect
124. C22×D8D269semidirect
168. C2×D4C22⋊D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754792
#317711722
#317710802
#317708182
#317707982
#317706312
#317706102
#317706022
C22×D8×C2692
#3041269