Finite Group Databasebeta

← #27196814

Subgroups — #27196814

Order 13184.

270 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 55 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#20268354C211yesmaximal, characteristic
2#20267763C212yesmaximal, complemented
3#20267584C211yesmaximal, characteristic, complemented
4#20267583C212yesmaximal, complemented
5#353×C103C211yesmaximal, characteristic, complemented
6C2×#13110104C2211yescharacteristic
7C2×D4×D103C411yescharacteristic, complemented
8#15693017C2211yescharacteristic
9#15693009C411yescharacteristic, complemented
10#15693008C411yescharacteristic, complemented
11#15692993—22no—
12#15692989—22no—
13#15692978C411yescharacteristic, complemented
14#15692977—22no—
15#15692936C2212yescomplemented
16#15692935—22no—
17#127×C103C2211yescharacteristic
18#99×C103C2212yescomplemented
19C23×D103—21no—
20#13110104—42no—
21C2×Dic206C2×C411yescharacteristic
22C2×D412C2×C411yescharacteristic
23C2×C22⋊D103—22no—
24C2×C22⋊D103—21no—
25C2×C22⋊D103D412yes—
26D4×D103—42no—
27C22×Dic103D412yes—
28C2×C4×D103C2×C411yescharacteristic
29Dic103⋊C4—21no—
30Dic103⋊C4—42no—
31C22⋊Dic103—22no—
32C22⋊Dic103—22no—
33(C2×D103)⋊C4—21no—
34(C2×D103)⋊C4—22no—
35C4×Dic103—42no—
36C4×Dic103C2×C411yescharacteristic
37C2×D4×C103—22no—
38C2×D4×C103C2×C411yescharacteristic
39C2×D4×C103C2311yescharacteristic
40C22⋊C4×C103—22no—
41C42×C103C2×C411yescharacteristic
42C23×C103—21no—
43C23×C103C2×D412yes—
44C22×D103—21no—
45C22×D103—42no—
46C22×D103—82no—
47C22×D103C22⋊C411yescharacteristic
48D4×C103—41no—
49D4×C103—41no—
50D4×C103—82no—
51C2×C4×C103—21no—
52C2×C4×C103—42no—
53C2×C4×C103C22×C411yescharacteristic
54C22⋊D103—42no—
55C22⋊D103—42no—
56C22⋊D103—82no—
57C2×Dic103—22no—
58C2×Dic103—22no—
59C2×Dic103—21no—
60C2×Dic103—42no—
61C2×Dic103C22⋊C412yes—
62C2×Dic103C22⋊C411yescharacteristic
63D412—41no—
64C4×D103—22no—
65Dic206—41no—
66C22×C103—22no—
67C22×C103—42no—
68C22×C103—42no—
69C22×C103—41no—
70C22×C103C2×C22⋊C411yescharacteristic
71C2×D103—21no—
72C2×D103—41no—
73C2×D103—42no—
74C2×D103—41no—
75C2×D103—84no—
76C4×C103—21no—
77C4×C103—41no—
78C4×C103—82no—
79Dic103—22no—
80Dic103—41no—
81Dic103—82no—
82Dic103#9912yes—
83C2×C103—21no—
84C2×C103—42no—
85C2×C103—81no—
86C2×C103C2×#9911yescharacteristic
87D103—41no—
88D103—81no—
89#2128—1031nomaximal, Sylow
90C103#212811yescharacteristic, complemented, Sylow
91#535—1031no—
92#410—1032no—
93#353—1031no—
94#353—1032no—
95#353D10311yescharacteristic, complemented
96C2×#41—1031no—
97C22×D4—1031no—
98#127—1031no—
99#127C2×D10311yescharacteristic
100#124—1031no—
101#124—1031no—
102#121—2062no—
103#120—2062no—
104#117—1031no—
105#117—2062no—
106#99—1032no—
107#99—2062no—
108#99C2×D10312yescomplemented
109C24—2061no—
110#41—4122no—
111C2×Q8—1031no—
112C2×D4—22no—
113C2×D4—1032no—
114C2×D4—1031no—
115C2×D4—4122no—
116C2×D4—2061no—
117C2×D4—2062no—
118C2×D4C4×D10311yescharacteristic
119C2×D4C22×D10311yescharacteristic
120C22×C4—1032no—
121C22×C4—1031no—
122C4⋊C4—4122no—
123C4⋊C4—2061no—
124C22⋊C4—22no—
125C22⋊C4—2062no—
126C22⋊C4—2061no—
127C22⋊C4—2062no—
128C22⋊C4—2062no—
129C42—1031no—
130C42—4122no—
131C42C4×D10311yescharacteristic
132C23—21no—
133C23—8242no—
134C23—1031no—
135C23—4122no—
136C23—2061no—
137C23D4×D10312yes—
138Q8—4121no—
139D4—41no—
140D4—41no—
141D4—82no—
142D4—8242no—
143D4—4121no—
144D4—4122no—
145D4—4122no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—1031no—
149C2×C4—1032no—
150C2×C4—4122no—
151C2×C4—2062no—
152C2×C4—2062no—
153C2×C4—2062no—
154C2×C4—2061no—
155C2×C4C2×C4×D10311yescharacteristic
156C22—22no—
157C22—42no—
158C22—42no—
159C22—41no—
160C22—8244no—
161C22—4122no—
162C22—4121no—
163C22—4121no—
164C22—2061no—
165C22C22⋊C4×D10311yescharacteristic
166C4—21no—
167C4—41no—
168C4—82no—
169C4—8242no—
170C4—1032no—
171C4—4121no—
172C4—2062no—
173C2—21no—
174C2—42no—
175C2—81no—
176C2—8241no—
177C2—4121no—
178C2#99×D10311yescharacteristic
subgroupG/H
centerC2#99×D103
commutatorC2×C4×C103C22×C4
FrattiniC2×D4C22×D103
Fitting#353×C103C2
socleC2×C103C2×#99
prime radical#20268354C2
cosocleC2×D4×C103C23
hypercenter#353D103
hypocenterC103#2128
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #20267763C2semidirect
3. #20267584C2semidirect
4. #20267583C2semidirect
5. #353×C103C2semidirect
7. C2×D4×D103C4semidirect
9. #15693009C4semidirect
10. #15693008C4semidirect
13. #15692978C4semidirect
15. #15692936C22semidirect
18. #99×C103C22semidirect
90. C103#2128semidirect
95. #353D103semidirect
108. #99C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202683542
#202677632
#202675842
#202675832
#353×C1032
#2128103