Finite Group Databasebeta

← #28335602

Subgroups — #28335602

Order 13696.

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

normal subgroups only

This group has 206 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#20293357C211yesmaximal, characteristic
2#20293006C211yesmaximal, characteristic
3#20292923C212yesmaximal
4#20292357C212yesmaximal
5#333×C107C211yesmaximal, characteristic
6C2×#13133808—22no—
7#16812109C2211yescharacteristic
8#16812108—22no—
9#16812107—22no—
10C4×Dic214C2212yes—
11#16812074—22no—
12#16812043—22no—
13#16812034—22no—
14C4×C107⋊C8C2211yescharacteristic
15C4⋊Q8×C107C2211yescharacteristic
16C4⋊C8×C107C2212yes—
17C2×Dic214—21no—
18C2×Dic214—22no—
19C2×Dic214D412yes—
20#13133808—44no—
21C2×C107⋊C8—21no—
22C4⋊Dic107—22no—
23C4⋊Dic107D412yes—
24Dic107⋊C4—24no—
25Dic107⋊C4—22no—
26C4×Dic107—22no—
27C4×Dic107—22no—
28C2×Q8×C107D412yes—
29C2×C8×C107—22no—
30C4⋊C4×C107—22no—
31C42×C107C2311yescharacteristic
32Q8×C107—42no—
33C2×C4×C107—22no—
34C2×C4×C107C2×D412yes—
35C2×C4×C107C2×D411yescharacteristic
36C2×Dic107—22no—
37C2×Dic107—22no—
38C2×Dic107—41no—
39Dic214—22no—
40Dic214—42no—
41Dic214—82no—
42Dic214Q1614yescomplemented
43C8×C107—42no—
44C107⋊C8—22no—
45C22×C107#12011yescharacteristic
46C4×C107—21no—
47C4×C107—42no—
48C4×C107C2×Q1612yes—
49C4×C107#13712yes—
50Dic107—24no—
51Dic107—42no—
52Dic107—81no—
53C2×C107#45112yes—
54C2×C107#45311yescharacteristic
55#1633—1071nomaximal, Sylow
56C107#163311yescharacteristic, complemented, Sylow
57Q82—1071no—
58#494—1071no—
59#477—1072no—
60#333D10711yescharacteristic
61Q8⋊C8—1072no—
62C2×Q16—2142no—
63C4⋊Q8—1071no—
64C4⋊Q8—2142no—
65C4⋊Q8—2142no—
66C4⋊Q8C2×D10711yescharacteristic
67C4×Q8—1072no—
68C4×Q8—2142no—
69#107—2142no—
70C4⋊C8C2×D10712yes—
71#103—2142no—
72C4×C8—1071no—
73C2×Q8—1072no—
74C2×Q8—2142no—
75C2×Q8—2141no—
76C2×Q8D42812yes—
77Q16—4284no—
78C2×C8—22no—
79C2×C8—2141no—
80C4⋊C4—22no—
81C4⋊C4—1072no—
82C4⋊C4—2144no—
83C4⋊C4—2142no—
84C4⋊C4—2142no—
85C42—2142no—
86C42—2142no—
87C42C22×D10711yescharacteristic
88Q8—42no—
89Q8—8562no—
90Q8—1074no—
91Q8—4282no—
92Q8—2142no—
93C2×C4—22no—
94C2×C4—4281no—
95C2×C4—2142no—
96C2×C4—2142no—
97C2×C4D4×D10712yes—
98C2×C4C2×D42811yescharacteristic
99C8—42no—
100C8—2142no—
101C22#1681207911yescharacteristic
102C4—21no—
103C4—42no—
104C4—8561no—
105C4—4282no—
106C4—2144no—
107C4Q16×D10712yes—
108C4#1681213812yes—
109C2#2029278412yes—
110C2#2029279711yescharacteristic
subgroupG/H
centerC22#16812079
commutator, cosocleC42×C107C23
FrattiniC42C22×D107
Fitting#333×C107C2
socle, prime radicalC22×C107#120
hypercenter#333D107
hypocenterC107#1633
LCSG ▷ C42×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
42. Dic214Q16semidirect
56. C107#1633semidirect

Maximal subgroups

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

subgroupindex
#202933572
#202930062
#202929232
#202923572
#333×C1072
#1633107