Finite Group Databasebeta

← #28336104

Subgroups — #28336104

Order 13696.

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#20293030C211yesmaximal, characteristic
2#20293023C211yesmaximal, characteristic
3#20292979C211yesmaximal, characteristic
4#20292978C211yesmaximal, characteristic
5#20292977C211yesmaximal, characteristic
6#20292348C211yesmaximal, characteristic
7#487×C107C211yesmaximal, characteristic
8#16812109C2211yescharacteristic
9#16812109C2211yescharacteristic
10#16812042—22no—
11#16812040—22no—
12#16812034—22no—
13#16812033—22no—
14#16812032—22no—
15C4×C107⋊C8C2211yescharacteristic
16C4×C107⋊C8C2211yescharacteristic
17C4⋊Q8×C107C2211yescharacteristic
18C4⋊Q8×C107C2211yescharacteristic
19#103×C107—22no—
20C4×C8×C107C2211yescharacteristic
21C2×Dic214—21no—
22C2×Dic214—21no—
23C2×C107⋊C8D412yes—
24C2×C107⋊C8D412yes—
25C4⋊Dic107—21no—
26C4⋊Dic107—21no—
27C4⋊Dic107—21no—
28C4⋊Dic107—21no—
29C2×Q8×C107—21no—
30C2×Q8×C107—21no—
31C2×C8×C107D412yes—
32C4⋊C4×C107—21no—
33C4⋊C4×C107—21no—
34C4⋊C4×C107—21no—
35C4⋊C4×C107—21no—
36C42×C107C2311yescharacteristic
37Q8×C107—42no—
38Q8×C107—42no—
39C2×C4×C107—41no—
40C2×C4×C107—41no—
41C2×C4×C107C2×D411yescharacteristic
42C2×C4×C107C2×D411yescharacteristic
43C2×C4×C107C2×D411yescharacteristic
44C2×Dic107—41no—
45C2×Dic107—41no—
46Dic214—42no—
47Dic214—42no—
48C8×C107—22no—
49C107⋊C8—22no—
50C107⋊C8—22no—
51C22×C107#12711yescharacteristic
52C4×C107—81no—
53C4×C107—81no—
54C4×C107#13512yes—
55C4×C107#13712yes—
56C4×C107#13712yes—
57Dic107—81no—
58Dic107—81no—
59C2×C107#49511yescharacteristic
60C2×C107#49711yescharacteristic
61C2×C107#49711yescharacteristic
62#1718—1071nomaximal, Sylow
63C107#171811yescharacteristic, complemented, Sylow
64#500—1071no—
65#498—1071no—
66#487—1071no—
67#487—1071no—
68#487—1071no—
69#487D10711yescharacteristic
70#322—1071no—
71C4⋊Q8—1071no—
72C4⋊Q8—1071no—
73C4⋊Q8C2×D10711yescharacteristic
74C4⋊Q8C2×D10711yescharacteristic
75#107—2142no—
76#106—2142no—
77#103—22no—
78#103—2142no—
79#103—2142no—
80#103—2142no—
81C4×C8—1071no—
82C4×C8—1071no—
83C4×C8C2×D10711yescharacteristic
84C2×Q8—21no—
85C2×Q8—21no—
86C2×Q8—2141no—
87C2×Q8—2141no—
88C2×C8—1072no—
89C2×C8—1072no—
90C2×C8C22⋊D10712yes—
91C4⋊C4—21no—
92C4⋊C4—21no—
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—2141no—
96C4⋊C4—2141no—
97C4⋊C4—2141no—
98C4⋊C4—2141no—
99C42C22×D10711yescharacteristic
100Q8—42no—
101Q8—42no—
102Q8—4282no—
103Q8—4282no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—4281no—
107C2×C4—4281no—
108C2×C4D4×D10711yescharacteristic
109C2×C4D4×D10711yescharacteristic
110C2×C4C2×C22⋊D10711yescharacteristic
111C8—22no—
112C8—2142no—
113C8—2142no—
114C22#1681210511yescharacteristic
115C4—81no—
116C4—81no—
117C4—8561no—
118C4—8561no—
119C4#1681212912yes—
120C4#1681213812yes—
121C4#1681214112yes—
122C2#2029300911yescharacteristic
123C2#2029301811yescharacteristic
124C2#2029302011yescharacteristic
subgroupG/H
centerC22#16812105
commutator, cosocleC42×C107C23
FrattiniC42C22×D107
Fitting#487×C107C2
socle, prime radicalC22×C107#127
hypercenter#487D107
hypocenterC107#1718
LCSG ▷ C42×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
63. C107#1718semidirect

Maximal subgroups

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

subgroupindex
#202930302
#202930232
#202929792
#202929782
#202929772
#202923482
#487×C1072
#1718107