Finite Group Databasebeta

← #28335554

Subgroups — #28335554

Order 13696.

210 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 55 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#20293352C211yesmaximal, characteristic, complemented
2#20292824C211yesmaximal, characteristic
3#20292824C211yesmaximal, characteristic
4#20292373C211yesmaximal, characteristic, complemented
5#20292359C211yesmaximal, characteristic, complemented
6#20292359C211yesmaximal, characteristic, complemented
7#486×C107C211yesmaximal, characteristic
8C2×#13133806—21no—
9C2×#13133806—21no—
10#16812107—21no—
11#16812100—21no—
12#16812099—22no—
13Q8×Dic107—21no—
14C4×Dic214C2211yescharacteristic
15C4×Dic214C2211yescharacteristic
16#16812074—21no—
17C4⋊(C107⋊C8)C2211yescharacteristic
18C4⋊(C107⋊C8)C2211yescharacteristic
19#16812030—21no—
20#16812030—21no—
21C4⋊Q8×C107C2211yescharacteristic
22#127×C107C2211yescharacteristic
23#102×C107—22no—
24C4×C8×C107C2211yescharacteristic
25C2×Dic214D411yescharacteristic
26C2×Dic214D411yescharacteristic
27#13133806—42no—
28#13133806—42no—
29C2×C107⋊C8—21no—
30C2×C107⋊C8—21no—
31C4⋊Dic107—22no—
32C4⋊Dic107D411yescharacteristic
33C4⋊Dic107D411yescharacteristic
34Dic107⋊C4—22no—
35Dic107⋊C4—22no—
36Dic107⋊C4—21no—
37Dic107⋊C4—21no—
38C4×Dic107—22no—
39C4×Dic107—21no—
40C4×Dic107—21no—
41C2×Q8×C107—21no—
42C2×D4×C107—21no—
43C2×D4×C107—21no—
44C2×D4×C107—21no—
45C2×C8×C107—21no—
46C4⋊C4×C107—21no—
47C4⋊C4×C107D412yes—
48C42×C107C2311yescharacteristic
49C23×C107—41no—
50Q8×C107—41no—
51Q8×C107—41no—
52D4×C107—42no—
53D4×C107—41no—
54D4×C107—41no—
55D4×C107—41no—
56D4×C107—41no—
57C2×C4×C107—22no—
58C2×C4×C107C2×D411yescharacteristic
59C2×C4×C107C2×D411yescharacteristic
60C2×C4×C107C2×D411yescharacteristic
61C2×Dic107—21no—
62C2×Dic107—21no—
63C2×Dic107—21no—
64C2×Dic107—21no—
65Dic214—21no—
66Dic214—21no—
67Dic214—21no—
68Dic214SD1612yescomplemented
69C8×C107—41no—
70C107⋊C8—41no—
71C107⋊C8—41no—
72C22×C107—81no—
73C22×C107—81no—
74C22×C107—81no—
75C22×C107#12011yescharacteristic
76C4×C107—21no—
77C4×C107—42no—
78C4×C107C2×SD1611yescharacteristic
79C4×C107#13511yescharacteristic
80C4×C107AGL(1,ℤ/8)11yescharacteristic
81C4×C107#13711yescharacteristic
82Dic107—22no—
83Dic107—41no—
84Dic107—41no—
85Dic107—41no—
86C2×C107—161no—
87C2×C107#44811yescharacteristic
88C2×C107#44911yescharacteristic
89C2×C107#45411yescharacteristic
90#1626—1071nomaximal, Sylow
91C107#162611yescharacteristic, complemented, Sylow
92#557—1071no—
93#486D10711yescharacteristic
94#460—1071no—
95#460—1071no—
96#332—1071no—
97Q8⋊C8—1071no—
98Q8⋊C8—1071no—
99C2×SD16—2141no—
100C2×SD16—2141no—
101C4⋊Q8—2141no—
102C4⋊Q8C2×D10711yescharacteristic
103#127C2×D10711yescharacteristic
104#125—2141no—
105#125—2142no—
106C4×Q8—1071no—
107C4×Q8—1071no—
108C4×Q8—2141no—
109C4×Q8—2141no—
110C4⋊C8—1071no—
111C4⋊C8—1071no—
112#102—22no—
113#102—2141no—
114#102—2141no—
115C4×C8C2×D10711yescharacteristic
116C2×Q8—21no—
117C2×Q8—1071no—
118C2×Q8—1071no—
119C2×D4—21no—
120C2×D4—21no—
121C2×D4—21no—
122SD16—4282no—
123SD16—4282no—
124C2×C8—21no—
125C2×C8—2141no—
126C2×C8—2141no—
127C4⋊C4—21no—
128C4⋊C4—1071no—
129C4⋊C4—1071no—
130C4⋊C4—2142no—
131C4⋊C4—2142no—
132C4⋊C4—2142no—
133C4⋊C4—2141no—
134C4⋊C4—2141no—
135C4⋊C4C22⋊D10712yes—
136C42—2142no—
137C42—2141no—
138C42—2141no—
139C42C22×D10711yescharacteristic
140C23—41no—
141Q8—41no—
142Q8—41no—
143Q8—1072no—
144Q8—2141no—
145Q8—2141no—
146Q8—2141no—
147D4—42no—
148D4—41no—
149D4—41no—
150D4—41no—
151D4—41no—
152C2×C4—22no—
153C2×C4—2141no—
154C2×C4—2141no—
155C2×C4—2141no—
156C2×C4—2141no—
157C2×C4D4×D10711yescharacteristic
158C2×C4D4×D10711yescharacteristic
159C2×C4C2×C22⋊D10711yescharacteristic
160C8—41no—
161C8—4281no—
162C8—4281no—
163C22—81no—
164C22—81no—
165C22—81no—
166C22#1681207711yescharacteristic
167C4—21no—
168C4—42no—
169C4—4281no—
170C4—4281no—
171C4—4281no—
172C4—2142no—
173C4SD16×D10711yescharacteristic
174C4#1681212811yescharacteristic
175C4#1681213311yescharacteristic
176C4#1681213811yescharacteristic
177C2—161no—
178C2#2029276411yescharacteristic
179C2#2029276911yescharacteristic
180C2#2029279911yescharacteristic
subgroupG/H
centerC22#16812077
commutator, cosocleC42×C107C23
FrattiniC42C22×D107
Fitting#486×C107C2
socleC22×C107#120
prime radical#127×C107C22
hypercenter#486D107
hypocenterC107#1626
LCSG ▷ C42×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #20293352C2semidirect
4. #20292373C2semidirect
5. #20292359C2semidirect
6. #20292359C2semidirect
68. Dic214SD16semidirect
91. C107#1626semidirect

Maximal subgroups

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

subgroupindex
#202933522
#202928242
#202923732
#202923592
#486×C1072
#1626107