Finite Group Databasebeta

← #28335635

Subgroups — #28335635

Order 13696.

194 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 53 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#20293347C211yesmaximal, characteristic
2#20292978C211yesmaximal, characteristic, complemented
3#20292923C211yesmaximal, characteristic, complemented
4#20292917C211yesmaximal, characteristic
5#20292372C211yesmaximal, characteristic, complemented
6#20292359C211yesmaximal, characteristic, complemented
7D4⋊C8×C107C211yesmaximal, characteristic
8#16812109C2211yescharacteristic
9#16812109C2211yescharacteristic
10#16812102—22no—
11#16812096—21no—
12#16812088—21no—
13C4×Dic214C2211yescharacteristic
14#16812074—21no—
15#16812068—21no—
16#16812043—21no—
17#16812040—21no—
18C4⋊(C107⋊C8)C2211yescharacteristic
19#16812034—21no—
20#16812034—22no—
21#16812030—21no—
22C4×D4×C107C2211yescharacteristic
23C4⋊C8×C107C2211yescharacteristic
24C4×C8×C107C2211yescharacteristic
25C2×Dic214—21no—
26C2×Dic214—21no—
27C2×Dic214D411yescharacteristic
28C2×C107⋊C8—21no—
29C4⋊Dic107—21no—
30C4⋊Dic107—21no—
31C4⋊Dic107—21no—
32C4⋊Dic107D412yes—
33C4⋊Dic107D411yescharacteristic
34Dic107⋊C4—22no—
35Dic107⋊C4—21no—
36C22⋊Dic107—22no—
37C22⋊Dic107—22no—
38C4×Dic107—22no—
39C4×Dic107—21no—
40C2×D4×C107D411yescharacteristic
41C22×C4×C107—21no—
42C2×C8×C107—21no—
43C2×C8×C107—21no—
44C4⋊C4×C107D411yescharacteristic
45C22⋊C4×C107—21no—
46C42×C107C2311yescharacteristic
47C23×C107—21no—
48D4×C107—21no—
49D4×C107—21no—
50C2×C4×C107—21no—
51C2×C4×C107—41no—
52C2×C4×C107—41no—
53C2×C4×C107C2×D411yescharacteristic
54C2×C4×C107C2×D411yescharacteristic
55C2×C4×C107C2×D411yescharacteristic
56C2×Dic107—21no—
57C2×Dic107—21no—
58C2×Dic107—22no—
59C2×Dic107—41no—
60Dic214—21no—
61Dic214—21no—
62Dic214—41no—
63Dic214—41no—
64Dic214—42no—
65C8×C107—41no—
66C8×C107—41no—
67C107⋊C8—41no—
68C22×C107—41no—
69C22×C107—41no—
70C22×C107—41no—
71C22×C107#12011yescharacteristic
72C4×C107—21no—
73C4×C107—41no—
74C4×C107#13511yescharacteristic
75C4×C107#13511yescharacteristic
76C4×C107#13711yescharacteristic
77C4×C107#13711yescharacteristic
78Dic107—41no—
79Dic107—42no—
80Dic107—41no—
81Dic107—81no—
82C2×C107—81no—
83C2×C107#45211yescharacteristic
84C2×C107#45211yescharacteristic
85C2×C107#45411yescharacteristic
86#1638—1071nomaximal, Sylow
87C107#163811yescharacteristic, complemented, Sylow
88#556—1071no—
89#487—1071no—
90#477—1071no—
91#476—1071no—
92#332—1071no—
93Q8⋊C8—1071no—
94D4⋊C8D10711yescharacteristic
95C4⋊Q8—1071no—
96C4⋊Q8—1071no—
97#126—2142no—
98#124—2141no—
99C22⋊Q8—2141no—
100C4×Q8—1071no—
101C4×Q8—2141no—
102C4×D4C2×D10711yescharacteristic
103#117—2141no—
104#107—2141no—
105#106—2141no—
106C4⋊C8—1071no—
107C4⋊C8C2×D10711yescharacteristic
108#103—2142no—
109#103—2141no—
110#102—2141no—
111C4×C8C2×D10711yescharacteristic
112C2×Q8—1071no—
113C2×Q8—2141no—
114C2×Q8—2141no—
115C2×D4D42811yescharacteristic
116C22×C4—21no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—2141no—
120C4⋊C4—1072no—
121C4⋊C4—1071no—
122C4⋊C4—2142no—
123C4⋊C4—2141no—
124C4⋊C4—2141no—
125C4⋊C4—2141no—
126C4⋊C4—2141no—
127C4⋊C4D42811yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—2142no—
130C22⋊C4—2142no—
131C42—2142no—
132C42—2141no—
133C42C22×D10711yescharacteristic
134C23—21no—
135Q8—4282no—
136Q8—4281no—
137Q8—4281no—
138Q8—2141no—
139Q8—2141no—
140D4—21no—
141D4—21no—
142C2×C4—21no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—4281no—
146C2×C4—2141no—
147C2×C4—2142no—
148C2×C4—2141no—
149C2×C4D4×D10711yescharacteristic
150C2×C4D4×D10711yescharacteristic
151C2×C4C2×D42811yescharacteristic
152C8—41no—
153C8—41no—
154C8—4281no—
155C22—41no—
156C22—41no—
157C22—41no—
158C22#1681207911yescharacteristic
159C4—21no—
160C4—41no—
161C4—8561no—
162C4—4281no—
163C4—4282no—
164C4—4281no—
165C4#1681212811yescharacteristic
166C4#1681213111yescharacteristic
167C4#1681213811yescharacteristic
168C4#1681214211yescharacteristic
169C2—81no—
170C2#2029279011yescharacteristic
171C2#2029279111yescharacteristic
172C2#2029280111yescharacteristic
subgroupG/H
centerC22#16812079
commutator, cosocleC42×C107C23
FrattiniC42C22×D107
FittingD4⋊C8×C107C2
socleC22×C107#120
prime radicalC2×D4×C107D4
hypercenterD4⋊C8D107
hypocenterC107#1638
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. #20292978C2semidirect
3. #20292923C2semidirect
5. #20292372C2semidirect
6. #20292359C2semidirect
87. C107#1638semidirect

Maximal subgroups

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

subgroupindex
#202933472
#202929782
#202929232
#202929172
#202923722
#202923592
D4⋊C8×C1072
#1638107