Finite Group Databasebeta

← #38742042

Subgroups — #38742042

Order 25216.

172 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C197⋊#564C211yesmaximal, characteristic
2#27161489C211yesmaximal, characteristic
3#27161488C211yesmaximal, characteristic
4#27161448C211yesmaximal, characteristic
5#27160820C211yesmaximal, characteristic
6#27160820C211yesmaximal, characteristic
7#330×C197C211yesmaximal, characteristic
8#20263326C2211yescharacteristic
9#20263318C2211yescharacteristic
10#20263318C2211yescharacteristic
11#20263317—21no—
12#20263317—21no—
13#20263316—21no—
14#20263316—21no—
15#20263316—21no—
16#20263316—21no—
17#20263260—21no—
18#20263259—21no—
19#20263258—21no—
20#20263257—21no—
21#20263251—21no—
22#20263251—21no—
23#20263237C2211yescharacteristic
24#125×C197C2211yescharacteristic
25#97×C197C2211yescharacteristic
26#97×C197C2211yescharacteristic
27C2×Dic394—21no—
28C2×#13096802—21no—
29C4⋊Dic197—21no—
30C4⋊Dic197—21no—
31C4⋊Dic197—21no—
32C4⋊Dic197—21no—
33C4⋊Dic197D411yescharacteristic
34C4⋊Dic197D411yescharacteristic
35C4⋊Dic197D411yescharacteristic
36C4⋊Dic197D411yescharacteristic
37#15691337—21no—
38#15691337—21no—
39#15691337—21no—
40#15691337—21no—
41#15691337—21no—
42#15691337—21no—
43#15691337—21no—
44#15691337—21no—
45C4×Dic197—21no—
46C4×Dic197—21no—
47C2×C8×C197—21no—
48C2×C8×C197—21no—
49C4⋊C4×C197—21no—
50C4⋊C4×C197—21no—
51C4⋊C4×C197D411yescharacteristic
52C4⋊C4×C197D411yescharacteristic
53C42×C197C2311yescharacteristic
54Dic394—42no—
55C2×Dic197—21no—
56C2×Dic197—21no—
57C2×Dic197—21no—
58C2×Dic197—21no—
59C2×Dic197—41no—
60#13096802—22no—
61C2×C4×C197—21no—
62C2×C4×C197—21no—
63C2×C4×C197C2×D411yescharacteristic
64C2×C4×C197C2×D411yescharacteristic
65C2×C4×C197C2×D411yescharacteristic
66C8×C197—22no—
67C8×C197—41no—
68C22×C197#12011yescharacteristic
69C4×C197—21no—
70C4×C197—21no—
71C4×C197—21no—
72C4×C197—41no—
73C4×C197—41no—
74Dic197—41no—
75Dic197—41no—
76Dic197—41no—
77Dic197—41no—
78Dic197—81no—
79C2×C197#45411yescharacteristic
80C2×C197#45611yescharacteristic
81C2×C197#45611yescharacteristic
82C197#166311yescharacteristic, complemented, Sylow
83#1663—1971nomaximal, Sylow
84#564—1971no—
85#501—1971no—
86#501—1971no—
87#491—1971no—
88#330—1971no—
89#330—1971no—
90#330D19711yescharacteristic
91C4⋊Q8—1971no—
92#125—3941no—
93#125—3941no—
94#125—3941no—
95#125—3941no—
96#125—3941no—
97#125—3941no—
98#125—1971no—
99#125—1971no—
100#125C2×D19711yescharacteristic
101#107—3941no—
102#107—3941no—
103#106—3941no—
104#106—3941no—
105#103—3941no—
106#103—3941no—
107#97—1971no—
108#97C2×D19711yescharacteristic
109#97C2×D19711yescharacteristic
110C2×Q8—3941no—
111C2×C8—21no—
112C2×C8—21no—
113C2×C8—3941no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—3941no—
117C4⋊C4—3941no—
118C4⋊C4—3941no—
119C4⋊C4—3941no—
120C4⋊C4—3941no—
121C4⋊C4—3941no—
122C4⋊C4—3941no—
123C4⋊C4—3941no—
124C4⋊C4—3941no—
125C4⋊C4—3941no—
126C4⋊C4—3941no—
127C4⋊C4—3941no—
128C4⋊C4—1971no—
129C4⋊C4—1971no—
130C4⋊C4—1971no—
131C4⋊C4—1971no—
132C4⋊C4D78811yescharacteristic
133C4⋊C4D78811yescharacteristic
134C42—3941no—
135C42—3941no—
136C42C22×D19711yescharacteristic
137Q8—7882no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—7881no—
141C2×C4—3941no—
142C2×C4—3941no—
143C2×C4—3941no—
144C2×C4—3941no—
145C2×C4D4×D19711yescharacteristic
146C2×C4D4×D19711yescharacteristic
147C2×C4C2×D78811yescharacteristic
148C8—22no—
149C8—41no—
150C8—3942no—
151C22#2026329611yescharacteristic
152C4—21no—
153C4—21no—
154C4—21no—
155C4—41no—
156C4—41no—
157C4—7881no—
158C4—7881no—
159C4—7881no—
160C4—7881no—
161C4—15761no—
162C2#2716125311yescharacteristic
163C2#2716126311yescharacteristic
164C2#2716126411yescharacteristic
subgroupG/H
centerC22#20263296
commutator, cosocleC42×C197C23
FrattiniC42C22×D197
Fitting#330×C197C2
socle, prime radicalC22×C197#120
hypercenter#330D197
hypocenterC197#1663
LCSG ▷ C42×C197 ▷ C22×C197 ▷ C197
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
82. C197#1663semidirect

Maximal subgroups

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

subgroupindex
C197⋊#5642
#271614892
#271614882
#271614482
#271608202
#330×C1972
#1663197