Finite Group Databasebeta

← #27194787

Subgroups — #27194787

Order 13184.

164 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 57 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#20268194C211yesmaximal, characteristic
2#20268187C211yesmaximal, characteristic
3#20268143C211yesmaximal, characteristic
4#20268142C211yesmaximal, characteristic
5#20268141C211yesmaximal, characteristic
6#20267512C211yesmaximal, characteristic
7#487×C103C211yesmaximal, characteristic
8#15693021C2211yescharacteristic
9#15693021C2211yescharacteristic
10#15692954—22no—
11#15692952—22no—
12#15692946—22no—
13#15692945—22no—
14#15692944—22no—
15C4×C103⋊C8C2211yescharacteristic
16C4×C103⋊C8C2211yescharacteristic
17C4⋊Q8×C103C2211yescharacteristic
18C4⋊Q8×C103C2211yescharacteristic
19#103×C103—22no—
20C4×C8×C103C2211yescharacteristic
21C2×Dic206—21no—
22C2×Dic206—21no—
23C2×C103⋊C8D412yes—
24C2×C103⋊C8D412yes—
25C4⋊Dic103—21no—
26C4⋊Dic103—21no—
27C4⋊Dic103—21no—
28C4⋊Dic103—21no—
29C2×Q8×C103—21no—
30C2×Q8×C103—21no—
31C2×C8×C103D412yes—
32C4⋊C4×C103—21no—
33C4⋊C4×C103—21no—
34C4⋊C4×C103—21no—
35C4⋊C4×C103—21no—
36C42×C103C2311yescharacteristic
37Q8×C103—42no—
38Q8×C103—42no—
39C2×C4×C103—41no—
40C2×C4×C103—41no—
41C2×C4×C103C2×D411yescharacteristic
42C2×C4×C103C2×D411yescharacteristic
43C2×C4×C103C2×D411yescharacteristic
44C2×Dic103—41no—
45C2×Dic103—41no—
46Dic206—42no—
47Dic206—42no—
48C8×C103—22no—
49C103⋊C8—22no—
50C103⋊C8—22no—
51C22×C103#12711yescharacteristic
52C4×C103—81no—
53C4×C103—81no—
54C4×C103#13512yes—
55C4×C103#13712yes—
56C4×C103#13712yes—
57Dic103—81no—
58Dic103—81no—
59C2×C103#49511yescharacteristic
60C2×C103#49711yescharacteristic
61C2×C103#49711yescharacteristic
62#1718—1031nomaximal, Sylow
63C103#171811yescharacteristic, complemented, Sylow
64#500—1031no—
65#498—1031no—
66#487—1031no—
67#487—1031no—
68#487—1031no—
69#487D10311yescharacteristic
70#322—1031no—
71C4⋊Q8—1031no—
72C4⋊Q8—1031no—
73C4⋊Q8C2×D10311yescharacteristic
74C4⋊Q8C2×D10311yescharacteristic
75#107—2062no—
76#106—2062no—
77#103—22no—
78#103—2062no—
79#103—2062no—
80#103—2062no—
81C4×C8—1031no—
82C4×C8—1031no—
83C4×C8C2×D10311yescharacteristic
84C2×Q8—21no—
85C2×Q8—21no—
86C2×Q8—2061no—
87C2×Q8—2061no—
88C2×C8—1032no—
89C2×C8—1032no—
90C2×C8C22⋊D10312yes—
91C4⋊C4—21no—
92C4⋊C4—21no—
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—2061no—
96C4⋊C4—2061no—
97C4⋊C4—2061no—
98C4⋊C4—2061no—
99C42C22×D10311yescharacteristic
100Q8—42no—
101Q8—42no—
102Q8—4122no—
103Q8—4122no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—4121no—
107C2×C4—4121no—
108C2×C4D4×D10311yescharacteristic
109C2×C4D4×D10311yescharacteristic
110C2×C4C2×C22⋊D10311yescharacteristic
111C8—22no—
112C8—2062no—
113C8—2062no—
114C22#1569301711yescharacteristic
115C4—81no—
116C4—81no—
117C4—8241no—
118C4—8241no—
119C4#1569304112yes—
120C4#1569305012yes—
121C4#1569305312yes—
122C2#2026817311yescharacteristic
123C2#2026818211yescharacteristic
124C2#2026818411yescharacteristic
subgroupG/H
centerC22#15693017
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#487×C103C2
socle, prime radicalC22×C103#127
hypercenter#487D103
hypocenterC103#1718
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
63. C103#1718semidirect

Maximal subgroups

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

subgroupindex
#202681942
#202681872
#202681432
#202681422
#202681412
#202675122
#487×C1032
#1718103