Finite Group Databasebeta

← #27195527

Subgroups — #27195527

Order 13184.

332 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 89 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#20268337C211yesmaximal, characteristic
2#20267807C212yesmaximal, complemented
3#20267765C211yesmaximal, characteristic, complemented
4#20267552C212yesmaximal, complemented
5#568×C103C211yesmaximal, characteristic, complemented
6C2×#13110105C2211yescharacteristic
7#15693019C411yescharacteristic, complemented
8#15693017C411yescharacteristic, complemented
9#15693010C411yescharacteristic, complemented
10#15693008C411yescharacteristic, complemented
11#15692993—22no—
12C4×C22⋊D103—22no—
13#15692980C2212yes—
14C2×C4×Dic103C2211yescharacteristic
15#15692947—24no—
16#15692936—22no—
17C2×#41×C103C2211yescharacteristic
18#131×C103—24no—
19C2×M16×C103—22no—
20C2×M16×C103C2212yes—
21#13110105—22no—
22#13110105—22no—
23C2×Dic206C2×C411yescharacteristic
24C2×D412C2×C411yescharacteristic
25C2×C22⋊D103—22no—
26C2×C22⋊D103—21no—
27C22×Dic103—21no—
28C2×C4×D103—21no—
29C4⋊Dic103—22no—
30Dic103⋊C4—22no—
31C22⋊Dic103—22no—
32C22⋊Dic103—22no—
33(C2×D103)⋊C4—22no—
34C4×Dic103—21no—
35C4×Dic103—22no—
36C4×Dic103C2×C411yescharacteristic
37C4×Dic103C2×C411yescharacteristic
38#41×C103—22no—
39#41×C103—22no—
40C2×Q8×C103C2×C411yescharacteristic
41C2×D4×C103C2×C411yescharacteristic
42C2×D4×C103D412yes—
43C22×C4×C103D412yes—
44C22×C4×C103C2311yescharacteristic
45M16×C103—24no—
46M16×C103—22no—
47M16×C103D414yescomplemented
48C2×C8×C103—24no—
49C2×C8×C103—22no—
50C23×C103C22⋊C412yes—
51C23×C103C2×D411yescharacteristic
52C22×D103—21no—
53Q8×C103—22no—
54D4×C103—24no—
55D4×C103—22no—
56C2×C4×C103—22no—
57C2×C4×C103—22no—
58C2×C4×C103C22⋊C412yes—
59C2×C4×C103C22×C411yescharacteristic
60C2×C4×C103C2×D412yes—
61C2×C4×C103C2×D411yescharacteristic
62C2×C4×C103#4112yes—
63C22⋊D103—44no—
64C22⋊D103—42no—
65C2×Dic103—21no—
66C2×Dic103—21no—
67C2×Dic103—21no—
68C2×Dic103—42no—
69C2×Dic103—42no—
70D412—22no—
71C4×D103—41no—
72C4×D103—41no—
73Dic206—22no—
74C8×C103—24no—
75C22×C103—22no—
76C22×C103—41no—
77C22×C103—42no—
78C22×C103C2×C22⋊C411yescharacteristic
79C22×C103#12112yes—
80C2×D103—42no—
81C2×D103—41no—
82C4×C103—22no—
83C4×C103C4×D412yes—
84C4×C103#12011yescharacteristic
85C4×C103#12311yescharacteristic
86Dic103—22no—
87Dic103—41no—
88Dic103—41no—
89Dic103—82no—
90C2×C103—21no—
91C2×C103—22no—
92C2×C103—42no—
93C2×C103#38611yescharacteristic
94D103—81no—
95#1884—1031nomaximal, Sylow
96C103#188411yescharacteristic, complemented, Sylow
97#568D10311yescharacteristic, complemented
98#532—1031no—
99#421—1032no—
100#410—1031no—
101#339—1032no—
102C2×#41—1031no—
103C2×#41C2×D10311yescharacteristic
104#131—24no—
105C2×M16—22no—
106C2×M16C2×D10312yes—
107C4⋊Q8—1031no—
108#127—1031no—
109#124—1031no—
110#124—1031no—
111#121—2062no—
112C4×D4—2062no—
113#117—1032no—
114C2×C42—1031no—
115#104—2064no—
116#99—2062no—
117#41—22no—
118#41—22no—
119#41—2062no—
120#41—2062no—
121C2×Q8—1031no—
122C2×Q8C4×D10311yescharacteristic
123C2×D4—1031no—
124C2×D4—2062no—
125C2×D4—2061no—
126C2×D4C4×D10311yescharacteristic
127C2×D4D41212yes—
128C22×C4—2061no—
129C22×C4—2061no—
130C22×C4C22⋊D10312yes—
131C22×C4C22×D10311yescharacteristic
132M16—24no—
133M16—22no—
134M16C22⋊D10314yescomplemented
135C2×C8—24no—
136C2×C8—22no—
137C4⋊C4—2062no—
138C4⋊C4—2062no—
139C22⋊C4—2062no—
140C22⋊C4—2062no—
141C22⋊C4—2062no—
142C42—1031no—
143C42—1031no—
144C42—2062no—
145C42—2061no—
146C23—2061no—
147C23(C2×D103)⋊C412yes—
148C23C2×D41211yescharacteristic
149Q8—22no—
150Q8—2062no—
151D4—24no—
152D4—22no—
153D4—4122no—
154D4—4124no—
155D4—2062no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—4122no—
159C2×C4—4122no—
160C2×C4—4121no—
161C2×C4—4121no—
162C2×C4—2061no—
163C2×C4—2061no—
164C2×C4—2061no—
165C2×C4(C2×D103)⋊C412yes—
166C2×C4C2×C4×D10311yescharacteristic
167C2×C4C2×C22⋊D10312yes—
168C2×C4C2×C22⋊D10311yescharacteristic
169C2×C4#1311010512yes—
170C8—24no—
171C22—22no—
172C22—41no—
173C22—42no—
174C22—4122no—
175C22—4121no—
176C22C2×(C2×D103)⋊C411yescharacteristic
177C22#1569299512yes—
178C4—22no—
179C4—8242no—
180C4—4121no—
181C4—4121no—
182C4—2062no—
183C4C4×C22⋊D10312yes—
184C4#1569299011yescharacteristic
185C4#1569300411yescharacteristic
186C2—22no—
187C2—21no—
188C2—42no—
189C2—8241no—
190C2#2026767011yescharacteristic
subgroupG/H
centerC4#15692990
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#568×C103C2
socleC2×C103#386
prime radical#20268337C2
cosocleC22×C4×C103C23
hypercenter#568D103
hypocenterC103#1884
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C4 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #20267807C2semidirect
3. #20267765C2semidirect
4. #20267552C2semidirect
5. #568×C103C2semidirect
7. #15693019C4semidirect
8. #15693017C4semidirect
9. #15693010C4semidirect
10. #15693008C4semidirect
47. M16×C103D4semidirect
96. C103#1884semidirect
97. #568D103semidirect
134. M16C22⋊D103semidirect

Maximal subgroups

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

subgroupindex
#202683372
#202678072
#202677652
#202675522
#568×C1032
#1884103