Finite Group Databasebeta

← #46820378

Subgroups — #46820378

Order 34432.

500 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 133 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×#22575486C211yesmaximal, characteristic, complemented
2C2×#22575479C211yesmaximal, characteristic
3C2×#22575440C211yesmaximal, characteristic, complemented
4#31771073C211yesmaximal, characteristic, complemented
5#31770826C214yesmaximal, complemented
6#31770819C214yesmaximal, complemented
7#31770628C211yesmaximal, characteristic, complemented
8#31770613C211yesmaximal, characteristic, complemented
9#418×C269C211yesmaximal, characteristic, complemented
10C2×#16864402C2211yescharacteristic
11C22×Dic538C2211yescharacteristic
12#22575486—24no—
13#22575479—24no—
14C2×Dic1076C2212yescomplemented
15C2×#16864391C2212yescomplemented
16C2×#16864390C2212yes—
17C2×#16864387C2212yes—
18C2×#16864386C2211yescharacteristic
19#22575440—21no—
20#22575440—21no—
21#22575440C2214yes—
22#22575418C2212yescomplemented
23#22575415C2212yescomplemented
24#22575413—22no—
25#22575410—21no—
26C2×C22⋊Dic269—22no—
27C2×C4×Dic269C2211yescharacteristic
28C42×D269—21no—
29#22575382C2214yescomplemented
30#22575376C2214yescomplemented
31C22×D4×C269C2211yescharacteristic
32C2×M16×C269C2211yescharacteristic
33#117×C269C2211yescharacteristic
34#102×C269C2214yes—
35#16864402—22no—
36#16864402D414yes—
37C2×Dic538—21no—
38C2×Dic538—22no—
39C2×Dic538—22no—
40C2×Dic538C2312yes—
41C2×Dic538C2311yescharacteristic
42C2×D1076C2311yescharacteristic
43C2×C22⋊D269—21no—
44C22×Dic269—21no—
45C22×Dic269D412yes—
46C2×C4×D269—22no—
47C2×C4×D269—21no—
48Dic1076—24no—
49#16864391—24no—
50#16864390—24no—
51#16864387—24no—
52#16864386—22no—
53C2×#14524130C2312yes—
54#16864381—22no—
55C22⋊Dic269—24no—
56C22⋊Dic269—24no—
57#16864379—22no—
58C4×Dic269—22no—
59C4×Dic269D411yescharacteristic
60C4×Dic269D411yescharacteristic
61C4×Dic269C2312yes—
62C24×C269—21no—
63C2×D4×C269—22no—
64C2×D4×C269—21no—
65C2×D4×C269—22no—
66C2×D4×C269C2312yes—
67C22×C4×C269C2311yescharacteristic
68M16×C269—22no—
69C2×C8×C269C2312yes—
70C4⋊C4×C269C2312yes—
71C22⋊C4×C269—21no—
72C42×C269—21no—
73C22×D269—21no—
74Dic538—21no—
75Dic538—22no—
76Dic538—22no—
77Dic538—42no—
78Dic538C2×D412yes—
79D1076—21no—
80D1076C2×D412yes—
81C22⋊D269—24no—
82C2×Dic269—21no—
83C2×Dic269—22no—
84C2×Dic269—42no—
85C2×Dic269—42no—
86C2×Dic269C2×D412yes—
87C2×Dic269C2×D412yes—
88C4×D269—24no—
89C4×D269—44no—
90#14524130—22no—
91C23×C269—22no—
92C23×C269—44no—
93C23×C269—42no—
94C23×C269C2×D411yescharacteristic
95D4×C269—22no—
96D4×C269—22no—
97D4×C269—42no—
98C2×C4×C269—22no—
99C2×C4×C269C2×D411yescharacteristic
100C2×C4×C269C2×D412yes—
101C2×C4×C269#4112yes—
102C2×C4×C269C2411yescharacteristic
103C8×C269—22no—
104C22×C269—22no—
105C22×C269—42no—
106C22×C269—44no—
107C22×C269—84no—
108C22×C269#12112yes—
109C22×C269C22×D411yescharacteristic
110C2×D269—22no—
111C2×D269—42no—
112C4×C269—42no—
113C4×C269#12112yes—
114C4×C269C22×D411yescharacteristic
115C4×C269C2×#4111yescharacteristic
116Dic269—22no—
117Dic269—22no—
118Dic269—22no—
119Dic269—42no—
120C2×C269—22no—
121C2×C269—82no—
122C2×C269C2×#12111yescharacteristic
123C2×C269#57512yes—
124D269—42no—
125C269#304011yescharacteristic, complemented, Sylow
126#3040—2691nomaximal, Sylow
127C2×#137—2691no—
128C2×AGL(1,ℤ/8)—2691no—
129C2×#124—2691no—
130C4×#41—2691no—
131#464—2694no—
132#463—2694no—
133#423—2691no—
134#419—2691no—
135#418D26911yescharacteristic, complemented
136C2×#41—2691no—
137C22×Q8—2691no—
138C22×D4C2×D26911yescharacteristic
139#137—5384no—
140AGL(1,ℤ/8)—5384no—
141C2×Q16—2692no—
142C2×SD16—2692no—
143C2×SD16—2692no—
144C2×D8—2692no—
145C2×M16—2691no—
146C2×M16C2×D26911yescharacteristic
147#124—2694no—
148#124—5381no—
149#124—5381no—
150C4×Q8—2692no—
151C4×D4—2692no—
152C4×D4—5382no—
153#117—5381no—
154#117C2×D26911yescharacteristic
155C2×C22⋊C4—5382no—
156C2×C42—2691no—
157C2×C42—5381no—
158C4⋊C8—2694no—
159#103—2694no—
160#102C2×D26914yes—
161C24—21no—
162#41—2694no—
163#41—5382no—
164C2×Q8—2691no—
165C2×Q8—2692no—
166C2×Q8—5381no—
167C2×Q8—5382no—
168C2×Q8—5382no—
169C2×D4—22no—
170C2×D4—21no—
171C2×D4—22no—
172C2×D4—2691no—
173C2×D4—5381no—
174C2×D4C22×D26912yes—
175C22×C4—2692no—
176C22×C4—5382no—
177C22×C4—5381no—
178C22×C4—5381no—
179C22×C4C22×D26911yescharacteristic
180Q16—5384no—
181SD16—5384no—
182SD16—5384no—
183D8—5384no—
184M16—22no—
185M16—5382no—
186C2×C8—2692no—
187C2×C8C22×D26912yes—
188C4⋊C4—5382no—
189C4⋊C4C22×D26912yes—
190C22⋊C4—21no—
191C22⋊C4—5382no—
192C22⋊C4—5384no—
193C22⋊C4—5384no—
194C42—21no—
195C42—2691no—
196C42—2691no—
197C42—2692no—
198C42—5382no—
199C23—22no—
200C23—44no—
201C23—42no—
202C23—5381no—
203C23D4×D26911yescharacteristic
204Q8—2692no—
205Q8—5381no—
206Q8—5382no—
207Q8—5382no—
208Q8—10762no—
209D4—22no—
210D4—22no—
211D4—42no—
212D4—2692no—
213D4—5384no—
214D4—5381no—
215C2×C4—22no—
216C2×C4—2692no—
217C2×C4—2692no—
218C2×C4—5381no—
219C2×C4—5384no—
220C2×C4—5382no—
221C2×C4—10764no—
222C2×C4—10762no—
223C2×C4—10762no—
224C2×C4D4×D26911yescharacteristic
225C2×C4D4×D26912yes—
226C2×C4#1686440212yes—
227C2×C4C23×D26911yescharacteristic
228C8—22no—
229C8—5382no—
230C22—22no—
231C22—44no—
232C22—42no—
233C22—84no—
234C22—5382no—
235C22—10762no—
236C22#2257542612yes—
237C22C2×D4×D26911yescharacteristic
238C4—42no—
239C4—5382no—
240C4—5382no—
241C4—5382no—
242C4—10762no—
243C4#2257542612yes—
244C4C2×D4×D26911yescharacteristic
245C4C2×#1686440211yescharacteristic
246C2—22no—
247C2—82no—
248C2—10762no—
249C2C2×#2257542611yescharacteristic
250C2#3177140112yes—
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#418×C269C2
socleC22×C269C22×D4
prime radicalC2×#22575479C2
hypercenter#418D269
hypocenterC269#3040
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C2×#22575486C2semidirect
3. C2×#22575440C2semidirect
4. #31771073C2semidirect
5. #31770826C2semidirect
6. #31770819C2semidirect
7. #31770628C2semidirect
8. #31770613C2semidirect
9. #418×C269C2semidirect
14. C2×Dic1076C22semidirect
15. C2×#16864391C22semidirect
22. #22575418C22semidirect
23. #22575415C22semidirect
29. #22575382C22semidirect
30. #22575376C22semidirect
125. C269#3040semidirect
135. #418D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754862
C2×#225754792
C2×#225754402
#317710732
#317708262
#317708192
#317706282
#317706132
#418×C2692
#3040269