Finite Group Databasebeta

← #28336676

Subgroups — #28336676

Order 13696.

272 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 93 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#20292670C212yesmaximal
2C2×#16812028C211yesmaximal, characteristic
3#20292534C211yesmaximal, characteristic
4#20292386C212yesmaximal
5#519×C107C211yesmaximal, characteristic
6C2×#13133802C2212yes—
7C2×C4⋊Dic107C2211yescharacteristic
8C2×C4×Dic107C2211yescharacteristic
9#16812042—22no—
10#16812040—22no—
11#16812028C414yescomplemented
12C107⋊#95—22no—
13C22×Q8×C107C2211yescharacteristic
14C4×Q8×C107—22no—
15C4×Q8×C107—22no—
16#117×C107—22no—
17#117×C107C2212yes—
18C22×Dic107—21no—
19C22×Dic107—21no—
20#13133802—22no—
21#13133802C2×C414yes—
22C2×C107⋊C8—22no—
23C4⋊Dic107—22no—
24C4×Dic107—22no—
25C2×Q8×C107—22no—
26C2×Q8×C107—22no—
27C2×Q8×C107C2×C412yes—
28C2×Q8×C107Q812yes—
29C22×C4×C107D412yes—
30C22×C4×C107C2311yescharacteristic
31C4⋊C4×C107—22no—
32C4⋊C4×C107—22no—
33C4⋊C4×C107D412yes—
34C4⋊C4×C107D412yes—
35C22⋊C4×C107—22no—
36C42×C107—24no—
37C42×C107—22no—
38C23×C107C2×D411yescharacteristic
39Q8×C107—24no—
40Q8×C107—24no—
41C2×C4×C107—22no—
42C2×C4×C107—22no—
43C2×C4×C107—22no—
44C2×C4×C107—22no—
45C2×C4×C107C4⋊C414yes—
46C2×C4×C107C22×C411yescharacteristic
47C2×C4×C107C2×D412yes—
48C2×C4×C107C2×Q811yescharacteristic
49C2×C4×C107#4112yes—
50C2×Dic107—22no—
51C2×Dic107—41no—
52C2×Dic107—41no—
53C2×Dic107—42no—
54C2×Dic107—41no—
55C107⋊C8—24no—
56C22×C107—21no—
57C22×C107—21no—
58C22×C107C2×C4⋊C411yescharacteristic
59C22×C107#12011yescharacteristic
60C22×C107#12311yescharacteristic
61C4×C107—24no—
62C4×C107—42no—
63C4×C107—42no—
64C4×C107C4×D412yes—
65C4×C107C22⋊Q812yes—
66Dic107—42no—
67Dic107—81no—
68C2×C107—21no—
69C2×C107—21no—
70C2×C107#38511yescharacteristic
71C2×C107#45411yescharacteristic
72C2×C107#45611yescharacteristic
73#1857—1071nomaximal, Sylow
74C107#185711yescharacteristic, complemented, Sylow
75#519D10711yescharacteristic
76#428—1072no—
77C2×#101—1071no—
78#391—1071no—
79#339—1072no—
80C22×Q8C2×D10711yescharacteristic
81C2×M16—1072no—
82C4×Q8—22no—
83C4×Q8—22no—
84#117—22no—
85#117C2×D10712yes—
86C2×C4⋊C4—1071no—
87C2×C42—1071no—
88#107—2142no—
89#106—2142no—
90#101—1074no—
91#95—2142no—
92C2×Q8—22no—
93C2×Q8—22no—
94C2×Q8Dic21412yes—
95C2×Q8C4×D10712yes—
96C22×C4—2141no—
97C22×C4—2141no—
98C22×C4C22⋊D10712yes—
99C22×C4C22×D10711yescharacteristic
100M16—1074no—
101M16—2142no—
102C2×C8—2142no—
103C4⋊C4—22no—
104C4⋊C4—22no—
105C4⋊C4—2142no—
106C4⋊C4C22⋊D10712yes—
107C4⋊C4C22⋊D10712yes—
108C22⋊C4—22no—
109C42—24no—
110C42—22no—
111C42—2142no—
112C23C2×C22⋊D10711yescharacteristic
113Q8—24no—
114Q8—24no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—22no—
118C2×C4—22no—
119C2×C4—4282no—
120C2×C4—4281no—
121C2×C4—4281no—
122C2×C4—4281no—
123C2×C4—2142no—
124C2×C4Dic107⋊C414yes—
125C2×C4C2×C4×D10711yescharacteristic
126C2×C4C2×C22⋊D10712yes—
127C2×C4C2×Dic21411yescharacteristic
128C2×C4#1313381812yes—
129C8—2144no—
130C22—21no—
131C22—21no—
132C22C2×Dic107⋊C411yescharacteristic
133C22#1681207811yescharacteristic
134C22#1681209211yescharacteristic
135C4—24no—
136C4—42no—
137C4—42no—
138C4—8561no—
139C4—4282no—
140C4C4×C22⋊D10712yes—
141C4#1681208812yes—
142C2—21no—
143C2—21no—
144C2#2029250011yescharacteristic
145C2#2029280011yescharacteristic
146C2#2029281011yescharacteristic
subgroupG/H
centerC22#16812078
commutatorC2×C4×C107C22×C4
FrattiniC22×C4C22×D107
Fitting#519×C107C2
socleC22×C107#120
prime radicalC23×C107C2×D4
cosocleC22×C4×C107C23
hypercenter#519D107
hypocenterC107#1857
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #519

Complements

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

NH ≅ G/Ntype
11. #16812028C4semidirect
74. C107#1857semidirect

Maximal subgroups

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

subgroupindex
#202926702
C2×#168120282
#202925342
#202923862
#519×C1072
#1857107