Finite Group Databasebeta

← #28335597

Subgroups — #28335597

Order 13696.

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

normal subgroups only

This group has 214 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#20293334C211yesmaximal, characteristic
2#20293007C211yesmaximal, characteristic, complemented
3#20292923C211yesmaximal, characteristic, complemented
4#20292917C211yesmaximal, characteristic
5#20292375C211yesmaximal, characteristic, complemented
6#20292359C211yesmaximal, characteristic, complemented
7D4⋊C8×C107C211yesmaximal, characteristic
8C2×Dic428—22no—
9#16812109C2211yescharacteristic
10#16812109C2211yescharacteristic
11#16812100—21no—
12#16812088—21no—
13#16812086—22no—
14C4×Dic214C2211yescharacteristic
15D4×Dic107—21no—
16C2×C4⋊Dic107—21no—
17#16812043—21no—
18#16812040—21no—
19C4⋊(C107⋊C8)C2211yescharacteristic
20#16812034—21no—
21#16812030—21no—
22C4×D4×C107C2211yescharacteristic
23C4⋊C8×C107C2211yescharacteristic
24C4×C8×C107C2211yescharacteristic
25C2×Dic214—21no—
26C2×Dic214D411yescharacteristic
27C2×Dic214D412yes—
28C22×Dic107—22no—
29Dic428—44no—
30C2×C107⋊C8—21no—
31C4⋊Dic107—22no—
32C4⋊Dic107—21no—
33C4⋊Dic107—21no—
34C4⋊Dic107—21no—
35C4⋊Dic107—21no—
36C4⋊Dic107D411yescharacteristic
37Dic107⋊C4—22no—
38Dic107⋊C4—21no—
39C22⋊Dic107—22no—
40C4×Dic107—21no—
41C2×D4×C107D411yescharacteristic
42C22×C4×C107—21no—
43C2×C8×C107—21no—
44C2×C8×C107—21no—
45C4⋊C4×C107D411yescharacteristic
46C22⋊C4×C107—21no—
47C42×C107C2311yescharacteristic
48C23×C107—21no—
49D4×C107—21no—
50D4×C107Q1612yescomplemented
51C2×C4×C107—21no—
52C2×C4×C107—41no—
53C2×C4×C107—41no—
54C2×C4×C107C2×D411yescharacteristic
55C2×C4×C107C2×D411yescharacteristic
56C2×C4×C107C2×D411yescharacteristic
57C2×Dic107—21no—
58C2×Dic107—21no—
59C2×Dic107—22no—
60C2×Dic107—41no—
61C2×Dic107—82no—
62Dic214—21no—
63Dic214—21no—
64Dic214—42no—
65Dic214—42no—
66C8×C107—22no—
67C8×C107—41no—
68C107⋊C8—41no—
69C22×C107—22no—
70C22×C107—41no—
71C22×C107—41no—
72C22×C107#12011yescharacteristic
73C4×C107—21no—
74C4×C107—41no—
75C4×C107C2×Q1611yescharacteristic
76C4×C107#13511yescharacteristic
77C4×C107#13711yescharacteristic
78C4×C107#13711yescharacteristic
79Dic107—41no—
80Dic107—42no—
81Dic107—41no—
82Dic107—81no—
83C2×C107—42no—
84C2×C107#45111yescharacteristic
85C2×C107#45211yescharacteristic
86C2×C107#45311yescharacteristic
87#1632—1071nomaximal, Sylow
88C107#163211yescharacteristic, complemented, Sylow
89#554—1071no—
90#494—1071no—
91#477—1071no—
92#476—1071no—
93#333—1071no—
94Q8⋊C8—1071no—
95D4⋊C8D10711yescharacteristic
96C2×Q16—2142no—
97C4⋊Q8—1071no—
98C4⋊Q8—1071no—
99#125—2141no—
100C22⋊Q8—2142no—
101C22⋊Q8—2141no—
102C4×Q8—1071no—
103C4×D4—2141no—
104C4×D4C2×D10711yescharacteristic
105C2×C4⋊C4—2141no—
106#107—2141no—
107#106—2141no—
108C4⋊C8—1071no—
109C4⋊C8C2×D10711yescharacteristic
110#103—2141no—
111#102—2141no—
112C4×C8C2×D10711yescharacteristic
113C2×Q8—1072no—
114C2×Q8—1071no—
115C2×Q8—2141no—
116C2×D4D42811yescharacteristic
117C22×C4—21no—
118C22×C4—2142no—
119Q16—4284no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—2141no—
123C4⋊C4—1071no—
124C4⋊C4—2142no—
125C4⋊C4—2142no—
126C4⋊C4—2141no—
127C4⋊C4—2141no—
128C4⋊C4—2141no—
129C4⋊C4—2141no—
130C4⋊C4—2141no—
131C4⋊C4D42811yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—2142no—
134C42—2141no—
135C42C22×D10711yescharacteristic
136C23—21no—
137Q8—4282no—
138Q8—4282no—
139Q8—2141no—
140Q8—2141no—
141D4—21no—
142D4Dic42812yescomplemented
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—8562no—
147C2×C4—4281no—
148C2×C4—2141no—
149C2×C4—2141no—
150C2×C4—2142no—
151C2×C4D4×D10711yescharacteristic
152C2×C4D4×D10711yescharacteristic
153C2×C4C2×D42811yescharacteristic
154C8—22no—
155C8—41no—
156C8—4281no—
157C22—22no—
158C22—41no—
159C22—41no—
160C22#1681207911yescharacteristic
161C4—21no—
162C4—41no—
163C4—8561no—
164C4—4281no—
165C4—4281no—
166C4—4282no—
167C4C2×Dic42811yescharacteristic
168C4#1681212811yescharacteristic
169C4#1681213811yescharacteristic
170C4#1681214211yescharacteristic
171C2—42no—
172C2#2029278511yescharacteristic
173C2#2029279011yescharacteristic
174C2#2029279611yescharacteristic
subgroupG/H
centerC22#16812079
commutator, cosocleC42×C107C23
FrattiniC42C22×D107
FittingD4⋊C8×C107C2
socleC22×C107#120
prime radicalC2×D4×C107D4
hypercenterD4⋊C8D107
hypocenterC107#1632
LCSG ▷ C42×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #20293007C2semidirect
3. #20292923C2semidirect
5. #20292375C2semidirect
6. #20292359C2semidirect
50. D4×C107Q16semidirect
88. C107#1632semidirect
142. D4Dic428semidirect

Maximal subgroups

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

subgroupindex
#202933342
#202930072
#202929232
#202929172
#202923752
#202923592
D4⋊C8×C1072
#1632107