Finite Group Databasebeta

← #38752956

Subgroups — #38752956

Order 25216.

418 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 121 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#27161684C211yesmaximal, characteristic, complemented
2#27161553C211yesmaximal, characteristic, complemented
3#27161404C212yesmaximal, complemented
4#27161380C212yesmaximal, complemented
5#27161275C212yesmaximal, complemented
6#27161215C212yesmaximal, complemented
7#27161192C212yesmaximal, complemented
8C4×D1576C212yesmaximal, complemented
9#433×C197C211yesmaximal, characteristic, complemented
10C22×D788C2211yescharacteristic
11C2×D1576C2212yes—
12C2×D1576C2212yes—
13#20263323C2211yescharacteristic, complemented
14#20263318C2211yescharacteristic, complemented
15#20263311—22no—
16#20263300C2212yes—
17#20263299—22no—
18C4×D788C2212yes—
19C4×D788C2212yes—
20C4×D788C2212yescomplemented
21#20263288—22no—
22#20263285C2211yescharacteristic
23C22⋊C4×D197—22no—
24#20263260C2212yescomplemented
25#20263258C2212yescomplemented
26#20263248C2212yes—
27#20263248C2212yes—
28#20263248C2212yescomplemented
29#20263248C2212yescomplemented
30#117×C197C2211yescharacteristic
31C4⋊C8×C197C2212yescomplemented
32C22⋊C8×C197C2212yes—
33#97×C197C2211yescharacteristic, complemented
34C4×C8×C197C2211yescharacteristic, complemented
35C23×D197—21no—
36C2×D788—24no—
37C2×D788—21no—
38C2×D788—22no—
39C2×D788C2312yes—
40C2×D788C2312yes—
41C2×C22⋊D197—22no—
42C2×C4×D197—22no—
43C2×C4×D197—22no—
44C2×C4×D197—22no—
45D1576—24no—
46D1576—24no—
47C4⋊Dic197C2312yes—
48C4⋊Dic197C2312yes—
49#15691337—22no—
50C22⋊Dic197—21no—
51#15691335—22no—
52#15691335—22no—
53#15691335—22no—
54#15691335—22no—
55C4×Dic197—21no—
56C22×C4×C197C2311yescharacteristic
57C2×C8×C197C2312yes—
58C2×C8×C197C2312yes—
59C4⋊C4×C197D412yes—
60C22⋊C4×C197D412yes—
61C42×C197C2311yescharacteristic
62C42×C197C2311yescharacteristic
63C22×D197—22no—
64C22×D197—24no—
65C22×D197—22no—
66C22×D197—82no—
67D788—24no—
68D788—22no—
69D788—22no—
70D788—22no—
71D788—82no—
72D788#4114yes—
73C22⋊D197—82no—
74C2×Dic197—22no—
75C2×Dic197—22no—
76C4×D197—82no—
77C4×D197—82no—
78C4×D197—82no—
79C23×C197C2×D411yescharacteristic
80C2×C4×C197—22no—
81C2×C4×C197C2×D412yes—
82C2×C4×C197C2×D412yes—
83C2×C4×C197C2×D411yescharacteristic
84C2×C4×C197C2411yescharacteristic
85C8×C197—22no—
86C8×C197—22no—
87C22×C197—21no—
88C22×C197—22no—
89C22×C197C22×D411yescharacteristic
90C2×D197—24no—
91C2×D197—42no—
92C2×D197—42no—
93C2×D197—42no—
94C2×D197—42no—
95C2×D197—42no—
96C2×D197—84no—
97C4×C197—21no—
98C4×C197—22no—
99C4×C197—22no—
100C4×C197C2×#4112yes—
101Dic197—42no—
102Dic197—42no—
103C2×C197—41no—
104C2×C197#52511yescharacteristic
105C2×C197#57612yes—
106D197—44no—
107D197—82no—
108C197#312211yescharacteristic, complemented, Sylow
109#3122—1971nomaximal, Sylow
110#540—1971no—
111#518—1971no—
112#482—1972no—
113#478—1972no—
114#459—1972no—
115#447—1972no—
116#442—1972no—
117C4×D8—1972no—
118#433D19711yescharacteristic, complemented
119C22×D4—1971no—
120C2×D8—1972no—
121C2×D8—1972no—
122#127—1971no—
123#125—1971no—
124#123—3942no—
125#121—3942no—
126#121—1972no—
127C4×D4—3942no—
128C4×D4—1972no—
129C4×D4—1972no—
130C4×D4—1972no—
131#117—1971no—
132#117C2×D19711yescharacteristic
133C2×C22⋊C4—3942no—
134#107—1972no—
135#106—1972no—
136C4⋊C8C2×D19712yescomplemented
137#102—1972no—
138#102—1972no—
139#102—1972no—
140#102—1972no—
141C22⋊C8C2×D19712yes—
142#97C2×D19711yescharacteristic, complemented
143C4×C8C2×D19711yescharacteristic, complemented
144C24—3941no—
145C2×D4—3944no—
146C2×D4—3942no—
147C2×D4—3942no—
148C2×D4—3941no—
149C2×D4—1972no—
150C2×D4—1972no—
151C22×C4—3942no—
152C22×C4—3942no—
153C22×C4—3942no—
154C22×C4C22×D19711yescharacteristic
155D8—3944no—
156D8—3944no—
157C2×C8C22×D19712yes—
158C2×C8C22×D19712yes—
159C4⋊C4—3942no—
160C4⋊C4—1972no—
161C4⋊C4—1972no—
162C4⋊C4D78812yes—
163C22⋊C4—3941no—
164C22⋊C4—3942no—
165C22⋊C4—3942no—
166C22⋊C4—3942no—
167C22⋊C4—3942no—
168C22⋊C4D78812yes—
169C42—3941no—
170C42C22×D19711yescharacteristic
171C42C22×D19711yescharacteristic
172C23—15762no—
173C23—3944no—
174C23—3942no—
175C23—3942no—
176C23C2×D78811yescharacteristic
177D4—15762no—
178D4—15762no—
179D4—3944no—
180D4—3942no—
181D4—3942no—
182D4—3942no—
183D4—1974no—
184C2×C4—22no—
185C2×C4—15762no—
186C2×C4—15762no—
187C2×C4—15762no—
188C2×C4—3942no—
189C2×C4—3942no—
190C2×C4C2×D78811yescharacteristic
191C2×C4C2×D78812yes—
192C2×C4C2×D78812yes—
193C2×C4C23×D19711yescharacteristic
194C8—22no—
195C8—22no—
196C22—22no—
197C22—21no—
198C22—7882no—
199C22—7882no—
200C22—7882no—
201C22—7882no—
202C22—7882no—
203C22—15764no—
204C22—3944no—
205C22C22×D78811yescharacteristic
206C4—22no—
207C4—22no—
208C4—21no—
209C4—7882no—
210C4—7882no—
211C4#41×D19712yes—
212C2—41no—
213C2—7884no—
214C2—15762no—
215C2#2716159111yescharacteristic
216C2#2716188412yes—
subgroupG/H
centerC22C22×D788
commutator, cosocleC2×C4×C197C24
FrattiniC2×C4C23×D197
Fitting#433×C197C2
socleC22×C197C22×D4
hypercenter#433D197
hypocenterC197#3122
LCSG ▷ C2×C4×C197 ▷ C2×C197 ▷ C197
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #27161684C2semidirect
2. #27161553C2semidirect
3. #27161404C2semidirect
4. #27161380C2semidirect
5. #27161275C2semidirect
6. #27161215C2semidirect
7. #27161192C2semidirect
8. C4×D1576C2semidirect
9. #433×C197C2semidirect
13. #20263323C22semidirect
14. #20263318C22semidirect
20. C4×D788C22semidirect
24. #20263260C22semidirect
25. #20263258C22semidirect
28. #20263248C22semidirect
29. #20263248C22semidirect
31. C4⋊C8×C197C22semidirect
33. #97×C197C22semidirect
34. C4×C8×C197C22semidirect
108. C197#3122semidirect
118. #433D197semidirect
136. C4⋊C8C2×D197semidirect
142. #97C2×D197semidirect
143. C4×C8C2×D197semidirect

Maximal subgroups

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

subgroupindex
#271616842
#271615532
#271614042
#271613802
#271612752
#271612152
#271611922
C4×D15762
#433×C1972
#3122197