Finite Group Databasebeta

← #28336141

Subgroups — #28336141

Order 13696.

176 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 61 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#20293032C211yesmaximal, characteristic
2#20293030C211yesmaximal, characteristic
3#20293023C211yesmaximal, characteristic
4#20293006C211yesmaximal, characteristic
5#20292979C211yesmaximal, characteristic
6#20292349C211yesmaximal, characteristic
7#487×C107C211yesmaximal, characteristic
8C2×#13133808—22no—
9#16812109C2211yescharacteristic
10#16812109C2211yescharacteristic
11#16812043—22no—
12#16812042—22no—
13#16812040—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—
23#13133808—44no—
24C2×C107⋊C8D412yes—
25C2×C107⋊C8D412yes—
26C4⋊Dic107—21no—
27C4⋊Dic107—21no—
28C4⋊Dic107—21no—
29C4⋊Dic107—21no—
30C2×Q8×C107—21no—
31C2×Q8×C107—21no—
32C2×C8×C107D412yes—
33C4⋊C4×C107—21no—
34C4⋊C4×C107—21no—
35C4⋊C4×C107—21no—
36C4⋊C4×C107—21no—
37C42×C107C2311yescharacteristic
38Q8×C107—42no—
39Q8×C107—42no—
40C2×C4×C107—41no—
41C2×C4×C107—41no—
42C2×C4×C107C2×D411yescharacteristic
43C2×C4×C107C2×D411yescharacteristic
44C2×C4×C107C2×D411yescharacteristic
45C2×Dic107—41no—
46C2×Dic107—41no—
47Dic214—42no—
48Dic214—42no—
49C8×C107—22no—
50C107⋊C8—22no—
51C107⋊C8Q1614yescomplemented
52C22×C107#12711yescharacteristic
53C4×C107—81no—
54C4×C107—81no—
55C4×C107C2×Q1612yes—
56C4×C107AGL(1,ℤ/8)12yes—
57C4×C107#13712yes—
58Dic107—81no—
59Dic107—81no—
60C2×C107#49411yescharacteristic
61C2×C107#49611yescharacteristic
62C2×C107#49711yescharacteristic
63#1723—1071nomaximal, Sylow
64C107#172311yescharacteristic, complemented, Sylow
65#500—1071no—
66#500—1071no—
67#498—1071no—
68#494—1071no—
69#487—1071no—
70#487D10711yescharacteristic
71#322—1071no—
72C2×Q16—2142no—
73C4⋊Q8—1071no—
74C4⋊Q8—1071no—
75C4⋊Q8C2×D10711yescharacteristic
76C4⋊Q8C2×D10711yescharacteristic
77#107—2142no—
78#107—2142no—
79#106—2142no—
80#103—22no—
81#103—2142no—
82C4×C8—1071no—
83C4×C8—1071no—
84C4×C8C2×D10711yescharacteristic
85C2×Q8—21no—
86C2×Q8—21no—
87C2×Q8—2141no—
88C2×Q8—2141no—
89Q16—4284no—
90C2×C8—1072no—
91C2×C8—1072no—
92C2×C8C22⋊D10712yes—
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—21no—
96C4⋊C4—21no—
97C4⋊C4—2141no—
98C4⋊C4—2141no—
99C4⋊C4—2141no—
100C4⋊C4—2141no—
101C42C22×D10711yescharacteristic
102Q8—42no—
103Q8—42no—
104Q8—4282no—
105Q8—4282no—
106C2×C4—41no—
107C2×C4—41no—
108C2×C4—4281no—
109C2×C4—4281no—
110C2×C4D4×D10711yescharacteristic
111C2×C4D4×D10711yescharacteristic
112C2×C4C2×C22⋊D10711yescharacteristic
113C8—22no—
114C8—1074no—
115C8—2142no—
116C22#1681210511yescharacteristic
117C4—81no—
118C4—81no—
119C4—8561no—
120C4—8561no—
121C4Q16×D10712yes—
122C4#1681213612yes—
123C4#1681213912yes—
124C2#2029300511yescharacteristic
125C2#2029301311yescharacteristic
126C2#2029302211yescharacteristic
subgroupG/H
centerC22#16812105
commutator, cosocleC42×C107C23
FrattiniC42C22×D107
Fitting#487×C107C2
socle, prime radicalC22×C107#127
hypercenter#487D107
hypocenterC107#1723
LCSG ▷ C42×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
51. C107⋊C8Q16semidirect
64. C107#1723semidirect

Maximal subgroups

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

subgroupindex
#202930322
#202930302
#202930232
#202930062
#202929792
#202923492
#487×C1072
#1723107