Finite Group Databasebeta

← #46819734

Subgroups — #46819734

Order 34432.

528 conjugacy classes of subgroups; only the 175 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 175 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×D8×D269C211yesmaximal, characteristic
2#31771077C212yesmaximal, complemented
3#31770718C211yesmaximal, characteristic, complemented
4#31770717C211yesmaximal, characteristic, complemented
5#31770716C211yesmaximal, characteristic, complemented
6C4×#16864387C212yesmaximal, complemented
7#31770685C212yesmaximal, complemented
8#31770640C211yesmaximal, characteristic, complemented
9#31770608C212yesmaximal, complemented
10#31770562C211yesmaximal, characteristic, complemented
11#442×C269C211yesmaximal, characteristic, complemented
12C2×D4×D269C2212yes—
13C2×D2152C2211yescharacteristic
14C2×#16864387C2212yes—
15D8×D269C418yescomplemented
16C2×#16864385C2211yescharacteristic
17C2×C8×D269C2211yescharacteristic
18C4×D1076C2212yescomplemented
19D4×Dic269C2212yescomplemented
20#22575415C2212yescomplemented
21C4×C22⋊D269—22no—
22#22575413—22no—
23#22575411C2212yes—
24#22575410C2211yescharacteristic
25C2×#16864379—22no—
26C22⋊C4×D269—22no—
27#22575386C2212yescomplemented
28#22575385C2211yescharacteristic, complemented
29#22575375C2212yescomplemented
30#22575374C2212yescomplemented
31#22575373C2212yescomplemented
32#22575363C2211yescharacteristic, complemented
33C4×#14524130C2211yescharacteristic, complemented
34C8×Dic269C2211yescharacteristic, complemented
35C2×D8×C269C2211yescharacteristic
36C4×D4×C269C2212yescomplemented
37#106×C269C2211yescharacteristic, complemented
38#102×C269C2212yescomplemented
39#97×C269C2211yescharacteristic, complemented
40C23×D269—22no—
41C2×D1076C2312yes—
42C2×C22⋊D269—22no—
43D4×D269—24no—
44D4×D269C2×C418yescomplemented
45C22×Dic269—22no—
46C2×C4×D269—22no—
47C2×C4×D269—22no—
48C2×C4×D269C2311yescharacteristic
49D2152C2×C414yescomplemented
50#16864387C2×C418yescomplemented
51#16864385—22no—
52C2×#14524130C2311yescharacteristic
53C2×#14524130C2311yescharacteristic
54C8×D269C2×C414yescomplemented
55C4⋊Dic269C2312yes—
56#16864381D412yes—
57C22⋊Dic269—22no—
58#16864379—22no—
59#16864379—22no—
60#16864379—22no—
61#16864379D412yes—
62C4×Dic269—22no—
63C4×Dic269C2311yescharacteristic
64C2×D4×C269C2312yes—
65C22×C4×C269—22no—
66D8×C269C2×C414yescomplemented
67C2×C8×C269C2311yescharacteristic
68C2×C8×C269C2311yescharacteristic
69C4⋊C4×C269C2312yes—
70C22⋊C4×C269—22no—
71C42×C269C2311yescharacteristic
72C22×D269—22no—
73C22×D269—28no—
74C22×D269—82no—
75C22×D269—82no—
76C22×D269C2×D411yescharacteristic
77D1076—22no—
78D1076C22×C414yes—
79C22⋊D269—28no—
80C2×Dic269—22no—
81C2×Dic269—82no—
82C2×Dic269C2×D412yes—
83C2×Dic269C2×D411yescharacteristic
84C4×D269—82no—
85C4×D269—82no—
86C4×D269C22×C412yes—
87C4×D269#4112yes—
88#14524130—21no—
89#14524130C22×C412yes—
90C23×C269—22no—
91D4×C269—22no—
92D4×C269C22×C414yes—
93C2×C4×C269—22no—
94C2×C4×C269—82no—
95C2×C4×C269C2×D412yes—
96C2×C4×C269C2411yescharacteristic
97C8×C269—21no—
98C8×C269C22×C412yes—
99C22×C269—24no—
100C22×C269—42no—
101C22×C269—42no—
102C22×C269C22×D411yescharacteristic
103C2×D269—22no—
104C2×D269—24no—
105C2×D269—42no—
106C2×D269—42no—
107C2×D269—88no—
108C2×D269C4×D412yes—
109C4×C269—22no—
110C4×C269—42no—
111C4×C269C23×C411yescharacteristic
112C4×C269C2×#4111yescharacteristic
113Dic269—22no—
114Dic269—42no—
115Dic269C4×D412yes—
116C2×C269—44no—
117C2×C269C2×C4×D411yescharacteristic
118C2×C269#57612yes—
119D269—22no—
120D269—44no—
121C269#294811yescharacteristic, complemented, Sylow
122#2948—2691nomaximal, Sylow
123C22×D8—2691no—
124#518—2692no—
125#442—2691no—
126#442—2691no—
127#442—2691no—
128#442D26911yescharacteristic, complemented
129C4×D8—2692no—
130C4×D8—2692no—
131#427—2691no—
132#418—2692no—
133#405—2691no—
134C22×D4—2692no—
135C2×D8—2692no—
136C2×D8—2698no—
137C2×D8—2691no—
138C2×D8C2×D26911yescharacteristic
139C2×M16—2691no—
140C22×C8—2691no—
141C4×D4—2692no—
142C4×D4—2692no—
143C4×D4—2692no—
144C4×D4—5382no—
145C4×D4—5382no—
146C4×D4C2×D26912yescomplemented
147#117—2691no—
148#117—2692no—
149C2×C22⋊C4—5382no—
150C2×C22⋊C4—5382no—
151#107—2692no—
152#106—2691no—
153#106C2×D26911yescharacteristic, complemented
154#102—2692no—
155#102—2692no—
156#102—2692no—
157#102C2×D26912yescomplemented
158#97—2691no—
159#97C2×D26911yescharacteristic, complemented
160C4×C8—2691no—
161C4×C8—2691no—
162C24—5382no—
163C2×D4—2698no—
164C2×D4—2692no—
165C2×D4—5384no—
166C2×D4—5382no—
167C2×D4C22×D26912yes—
168C22×C4—22no—
169C22×C4—2691no—
170C22×C4—5382no—
171C22×C4—5382no—
172C22×C4—5382no—
173D8—2698no—
174D8—2694no—
175D8C4×D26914yescomplemented
176M16—5382no—
177C2×C8—2691no—
178C2×C8—2694no—
179C2×C8—2691no—
180C2×C8C22×D26911yescharacteristic
181C2×C8C22×D26911yescharacteristic
182C4⋊C4—2692no—
183C4⋊C4—2692no—
184C4⋊C4C22×D26912yes—
185C22⋊C4—22no—
186C22⋊C4—2692no—
187C22⋊C4—5382no—
188C22⋊C4—5382no—
189C22⋊C4—5382no—
190C22⋊C4—5382no—
191C42—2691no—
192C42—5382no—
193C42C22×D26911yescharacteristic
194C23—22no—
195C23—2691no—
196C23—5388no—
197C23—5382no—
198C23—21522no—
199C23—21522no—
200D4—22no—
201D4—2694no—
202D4—5388no—
203D4—5382no—
204D4C2×C4×D26914yes—
205C2×C4—22no—
206C2×C4—82no—
207C2×C4—2691no—
208C2×C4—2692no—
209C2×C4—2692no—
210C2×C4—2692no—
211C2×C4—5382no—
212C2×C4—21522no—
213C2×C4—21522no—
214C2×C4—21522no—
215C2×C4D4×D26912yes—
216C2×C4C23×D26911yescharacteristic
217C8—21no—
218C8—2692no—
219C8—5381no—
220C8C2×C4×D26912yes—
221C22—24no—
222C22—42no—
223C22—42no—
224C22—2692no—
225C22—5382no—
226C22—5384no—
227C22—10762no—
228C22—10762no—
229C22—21528no—
230C22C2×D4×D26911yescharacteristic
231C4—22no—
232C4—42no—
233C4—2692no—
234C4—5382no—
235C4—10762no—
236C4C22×C4×D26911yescharacteristic
237C4#41×D26911yescharacteristic
238C2—44no—
239C2—5382no—
240C2—10764no—
241C2C4×D4×D26911yescharacteristic
242C2#3177140912yes—
subgroupG/H
centerC22C2×D4×D269
commutatorC4×C269C23×C4
FrattiniC2×C4C23×D269
Fitting#442×C269C2
socleC22×C269C22×D4
prime radicalC2×D8×D269C2
cosocleC2×C4×C269C24
hypercenter#442D269
hypocenterC269#2948
LCSG ▷ C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. #31771077C2semidirect
3. #31770718C2semidirect
4. #31770717C2semidirect
5. #31770716C2semidirect
6. C4×#16864387C2semidirect
7. #31770685C2semidirect
8. #31770640C2semidirect
9. #31770608C2semidirect
10. #31770562C2semidirect
11. #442×C269C2semidirect
15. D8×D269C4semidirect
18. C4×D1076C22semidirect
19. D4×Dic269C22semidirect
20. #22575415C22semidirect
27. #22575386C22semidirect
28. #22575385C22semidirect
29. #22575375C22semidirect
30. #22575374C22semidirect
31. #22575373C22semidirect
32. #22575363C22semidirect
33. C4×#14524130C22semidirect
34. C8×Dic269C22semidirect
36. C4×D4×C269C22semidirect
37. #106×C269C22semidirect
38. #102×C269C22semidirect
39. #97×C269C22semidirect
44. D4×D269C2×C4semidirect
49. D2152C2×C4semidirect
50. #16864387C2×C4semidirect
54. C8×D269C2×C4semidirect
66. D8×C269C2×C4semidirect
121. C269#2948semidirect
128. #442D269semidirect
146. C4×D4C2×D269semidirect
153. #106C2×D269semidirect
157. #102C2×D269semidirect
159. #97C2×D269semidirect
175. D8C4×D269semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D2692
#317710772
#317707182
#317707172
#317707162
C4×#168643872
#317706852
#317706402
#317706082
#317705622
#442×C2692
#2948269