Finite Group Databasebeta

← #27193737

Subgroups — #27193737

Order 13184.

226 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 63 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#20268347C211yesmaximal, characteristic
2#20267743C212yesmaximal
3#20267533C211yesmaximal, characteristic, complemented
4#20267532C212yesmaximal, complemented
5#330×C103C211yesmaximal, characteristic, complemented
6C2×#13110088—22no—
7#15693020C412yes—
8#15693013C2211yescharacteristic
9#15692999—22no—
10#15692986—22no—
11#15692979C412yes—
12C42×D103C2211yescharacteristic
13#15692932C2212yes—
14C8×Dic103—22no—
15#125×C103C2211yescharacteristic
16#97×C103C2212yes—
17C2×Dic206—22no—
18C2×C4×D103C2×C411yescharacteristic
19C2×C4×D103D412yes—
20#13110088—28no—
21C2×C103⋊C8—22no—
22C4⋊Dic103C2×C412yes—
23Dic103⋊C4—22no—
24Dic103⋊C4—22no—
25(C2×D103)⋊C4—22no—
26C4×Dic103—22no—
27C4×Dic103C2×C411yescharacteristic
28C4×Dic103D412yes—
29C2×C8×C103—22no—
30C4⋊C4×C103—22no—
31C4⋊C4×C103C2×C412yes—
32C42×C103C2311yescharacteristic
33C22×D103C22⋊C411yescharacteristic
34C2×C4×C103—22no—
35C2×C4×C103C22×C411yescharacteristic
36C2×C4×C103C2×D412yes—
37C2×Dic103—22no—
38C2×Dic103C22⋊C411yescharacteristic
39C2×Dic103C22⋊C412yes—
40C4×D103—22no—
41C4×D103—24no—
42Dic206—44no—
43C8×C103—24no—
44C103⋊C8—24no—
45C22×C103C2×C22⋊C411yescharacteristic
46C2×D103—21no—
47C2×D103—22no—
48C4×C103—21no—
49C4×C103—22no—
50C4×C103—42no—
51Dic103—42no—
52Dic103#10112yes—
53Dic103#10414yes—
54C2×C103C2×#10111yescharacteristic
55C2×C103C2×#10412yes—
56D103—41no—
57#1526—1031nomaximal, Sylow
58C103#152611yescharacteristic, complemented, Sylow
59#533—1031no—
60C4×M16—1032no—
61#330—1031no—
62#330—1032no—
63#330D10311yescharacteristic, complemented
64C2×M16—2062no—
65C4⋊Q8—1032no—
66#125—1031no—
67#125C2×D10311yescharacteristic
68C22⋊Q8—2062no—
69C4×Q8—2062no—
70#117—1032no—
71C2×C42—1031no—
72#97—1032no—
73#97C2×D10312yes—
74C4×C8—2062no—
75C2×Q8—2062no—
76C22×C4—1031no—
77C22×C4—1032no—
78M16—2068no—
79C2×C8—22no—
80C2×C8—2062no—
81C4⋊C4—22no—
82C4⋊C4—1032no—
83C4⋊C4—2062no—
84C4⋊C4—2062no—
85C4⋊C4C4×D10312yes—
86C22⋊C4—2062no—
87C42—1031no—
88C42—1032no—
89C42—2062no—
90C42C22×D10311yescharacteristic
91C23—1031no—
92Q8—4124no—
93C2×C4—22no—
94C2×C4—1031no—
95C2×C4—1032no—
96C2×C4—2064no—
97C2×C4—2062no—
98C2×C4—2062no—
99C2×C4C2×C4×D10311yescharacteristic
100C2×C4D4×D10312yes—
101C8—24no—
102C8—2064no—
103C22—2062no—
104C22—2061no—
105C22C22⋊C4×D10311yescharacteristic
106C4—22no—
107C4—21no—
108C4—42no—
109C4—1034no—
110C4—1032no—
111C4—4122no—
112C2—4121no—
113C2#101×D10311yescharacteristic
114C2#104×D10312yes—
subgroupG/H
centerC22C22⋊C4×D103
commutatorC2×C4×C103C22×C4
FrattiniC42C22×D103
Fitting#330×C103C2
socleC22×C103C2×C22⋊C4
prime radicalC22×D103C22⋊C4
cosocleC42×C103C23
hypercenter#330D103
hypocenterC103#1526
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
3. #20267533C2semidirect
4. #20267532C2semidirect
5. #330×C103C2semidirect
58. C103#1526semidirect
63. #330D103semidirect

Maximal subgroups

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

subgroupindex
#202683472
#202677432
#202675332
#202675322
#330×C1032
#1526103