Finite Group Databasebeta

← #28336678

Subgroups — #28336678

Order 13696.

272 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 97 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#20293105C211yesmaximal, characteristic
2#20292669C212yesmaximal
3#20292534C211yesmaximal, characteristic
4#20292388C212yesmaximal
5C2×#101×C107C211yesmaximal, characteristic
6Q8×Dic107—22no—
7Q8×Dic107—22no—
8#16812068—22no—
9#16812068C2212yes—
10C2×C4⋊Dic107C2211yescharacteristic
11C2×C4×Dic107C2211yescharacteristic
12#16812043—22no—
13#16812041—22no—
14C107⋊#95—22no—
15C22×Q8×C107C2211yescharacteristic
16C2×M16×C107C2212yes—
17#101×C107C414yescomplemented
18C22×Dic107—21no—
19C22×Dic107—21no—
20C4⋊Dic107—22no—
21C4⋊Dic107—22no—
22C4⋊Dic107—22no—
23C4⋊Dic107D412yes—
24C4⋊Dic107D412yes—
25C22⋊Dic107—22no—
26C4×Dic107—24no—
27C4×Dic107—22no—
28C4×Dic107—22no—
29C2×Q8×C107—22no—
30C2×Q8×C107—22no—
31C2×Q8×C107C2×C412yes—
32C2×Q8×C107Q812yes—
33C22×C4×C107D412yes—
34C22×C4×C107C2311yescharacteristic
35M16×C107—22no—
36M16×C107C2×C414yes—
37C2×C8×C107—22no—
38C23×C107C2×D411yescharacteristic
39Q8×C107—24no—
40Q8×C107—24no—
41C2×C4×C107—22no—
42C2×C4×C107—22no—
43C2×C4×C107C4⋊C414yes—
44C2×C4×C107C22×C411yescharacteristic
45C2×C4×C107C2×D412yes—
46C2×C4×C107C2×Q811yescharacteristic
47C2×C4×C107#4112yes—
48C2×Dic107—22no—
49C2×Dic107—22no—
50C2×Dic107—22no—
51C2×Dic107—41no—
52C2×Dic107—41no—
53C2×Dic107—42no—
54C2×Dic107—41no—
55C8×C107—24no—
56C22×C107—21no—
57C22×C107—21no—
58C22×C107C2×C4⋊C411yescharacteristic
59C22×C107#12011yescharacteristic
60C22×C107#12311yescharacteristic
61C4×C107—24no—
62C4×C107C4×D412yes—
63C4×C107C22⋊Q812yes—
64Dic107—42no—
65Dic107—42no—
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#519—1071no—
76#428—1072no—
77C2×#101D10711yescharacteristic
78#391—1071no—
79#339—1072no—
80C22×Q8C2×D10711yescharacteristic
81C2×M16C2×D10712yes—
82C4×Q8—2142no—
83C4×Q8—2142no—
84#117—1072no—
85#117—2142no—
86C2×C4⋊C4—1071no—
87C2×C42—1071no—
88#107—2142no—
89#106—2142no—
90#101Dic10714yescomplemented
91#95—2142no—
92C2×Q8—22no—
93C2×Q8—22no—
94C2×Q8Dic21412yes—
95C2×Q8C2×Dic10712yes—
96C22×C4—2141no—
97C22×C4—2141no—
98C22×C4D42812yes—
99C22×C4C22×D10711yescharacteristic
100M16—22no—
101M16C2×Dic10714yes—
102C2×C8—22no—
103C4⋊C4—1072no—
104C4⋊C4—1072no—
105C4⋊C4—2142no—
106C4⋊C4—2142no—
107C4⋊C4—2142no—
108C22⋊C4—2142no—
109C42—2144no—
110C42—2142no—
111C42—2142no—
112C23C2×D42811yescharacteristic
113Q8—24no—
114Q8—24no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—4282no—
118C2×C4—4281no—
119C2×C4—4281no—
120C2×C4—4281no—
121C2×C4—2142no—
122C2×C4—2142no—
123C2×C4—2142no—
124C2×C4C4⋊Dic10714yes—
125C2×C4C22×Dic10711yescharacteristic
126C2×C4D4×D10712yes—
127C2×C4C2×Dic21411yescharacteristic
128C2×C4#1313381712yes—
129C8—24no—
130C22—21no—
131C22—21no—
132C22C2×C4⋊Dic10711yescharacteristic
133C22#1681207911yescharacteristic
134C22#1681209311yescharacteristic
135C4—24no—
136C4—8561no—
137C4—4282no—
138C4—4282no—
139C4—4282no—
140C4D4×Dic10712yes—
141C4#1681208612yes—
142C2—21no—
143C2—21no—
144C2#2029250211yescharacteristic
145C2#2029280211yescharacteristic
146C2#2029281211yescharacteristic
subgroupG/H
centerC22#16812079
commutatorC2×C4×C107C22×C4
FrattiniC22×C4C22×D107
FittingC2×#101×C107C2
socleC22×C107#120
prime radicalC23×C107C2×D4
cosocleC22×C4×C107C23
hypercenterC2×#101D107
hypocenterC107#1857
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
17. #101×C107C4semidirect
74. C107#1857semidirect
90. #101Dic107semidirect

Maximal subgroups

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

subgroupindex
#202931052
#202926692
#202925342
#202923882
C2×#101×C1072
#1857107