Finite Group Databasebeta

← #28338445

Subgroups — #28338445

Order 13696.

354 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 45 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#20292813C212yesmaximal, complemented
2#20292794C211yesmaximal, characteristic, complemented
3#20292420C211yesmaximal, characteristic, complemented
4#20292414C212yesmaximal, complemented
5D42×C107C211yesmaximal, characteristic, complemented
6#16812154C2211yescharacteristic, complemented
7#16812135—21no—
8#16812078—22no—
9#16812037—21no—
10#16812026C2211yescharacteristic, complemented
11#16812024C2212yescomplemented
12#16812023—22no—
13C22×D4×C107—22no—
14#127×C107C2211yescharacteristic
15#121×C107—22no—
16#120×C107—21no—
17#120×C107C2212yes—
18C4×D4×C107—21no—
19#13133818—21no—
20#13133817—41no—
21C2×C22⋊D107—22no—
22C2×C22⋊D107—42no—
23D4×D107—41no—
24#13133806—41no—
25#13133803—41no—
26#13133802—21no—
27C22⋊Dic107—22no—
28C22⋊Dic107—42no—
29C24×C107—21no—
30C24×C107D412yescomplemented
31C2×D4×C107—21no—
32C2×D4×C107—22no—
33C2×D4×C107—22no—
34C2×D4×C107—22no—
35C2×D4×C107—48no—
36C2×D4×C107D411yescharacteristic, complemented
37C2×D4×C107C2311yescharacteristic
38C22×C4×C107—22no—
39C4⋊C4×C107—21no—
40C22⋊C4×C107—21no—
41C22⋊C4×C107—22no—
42C22⋊C4×C107D412yescomplemented
43C42×C107D411yescharacteristic, complemented
44C23×C107—22no—
45C23×C107—21no—
46C23×C107—44no—
47C23×C107—42no—
48C23×C107—44no—
49C23×C107—81no—
50C23×C107C2×D412yes—
51C22×D107—22no—
52D4×C107—24no—
53D4×C107—41no—
54D4×C107—41no—
55D4×C107—44no—
56D4×C107—44no—
57D4×C107—44no—
58C2×C4×C107—21no—
59C2×C4×C107—22no—
60C2×C4×C107—44no—
61C2×C4×C107C2×D411yescharacteristic
62C22⋊D107—42no—
63C22⋊D107—41no—
64C22⋊D107—84no—
65C2×Dic107—22no—
66C2×Dic107—42no—
67D428—21no—
68C4×D107—41no—
69Dic214—21no—
70C107⋊C8—41no—
71C22×C107—24no—
72C22×C107—22no—
73C22×C107—42no—
74C22×C107—42no—
75C22×C107—42no—
76C22×C107—44no—
77C22×C107—42no—
78C22×C107—41no—
79C22×C107—82no—
80C22×C107—84no—
81C22×C107#12011yescharacteristic
82C2×D107—41no—
83C2×D107—82no—
84C4×C107—22no—
85C4×C107—21no—
86C4×C107—42no—
87Dic107—41no—
88Dic107—82no—
89C2×C107—21no—
90C2×C107—42no—
91C2×C107—44no—
92C2×C107—81no—
93C2×C107B(4,𝔽2)11yescharacteristic
94D107—81no—
95#2196—1071nomaximal, Sylow
96C107#219611yescharacteristic, complemented, Sylow
97D42D10711yescharacteristic, complemented
98B(4,𝔽2)—1072no—
99#453—1071no—
100#353—1071no—
101AΣL(1,𝔽16)—1072no—
102H(5,𝔽2)—1071no—
103C22×D4—22no—
104AGL(1,ℤ/8)—2141no—
105#127C2×D10711yescharacteristic
106#121—22no—
107#120—21no—
108#120—2142no—
109#120C2×D10712yes—
110C4×D4—21no—
111#104—2141no—
112#100—1071no—
113#99—1072no—
114#99—2142no—
115C24—21no—
116C24C22⋊D10712yescomplemented
117#41—4281no—
118#41—2141no—
119C2×D4—21no—
120C2×D4—22no—
121C2×D4—22no—
122C2×D4—22no—
123C2×D4—48no—
124C2×D4—4281no—
125C2×D4—4282no—
126C2×D4—2142no—
127C2×D4C22⋊D10711yescharacteristic, complemented
128C2×D4C22×D10711yescharacteristic
129C22×C4—22no—
130SD16—4281no—
131D8—4281no—
132M16—2141no—
133C4⋊C4—21no—
134C22⋊C4—21no—
135C22⋊C4—22no—
136C22⋊C4—4282no—
137C22⋊C4—2142no—
138C22⋊C4C22⋊D10712yescomplemented
139C42C22⋊D10711yescharacteristic, complemented
140C23—22no—
141C23—21no—
142C23—42no—
143C23—44no—
144C23—44no—
145C23—81no—
146C23—2142no—
147C23C2×C22⋊D10712yes—
148Q8—2141no—
149D4—24no—
150D4—41no—
151D4—41no—
152D4—44no—
153D4—44no—
154D4—44no—
155D4—8564no—
156D4—4282no—
157D4—4281no—
158D4—2141no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—44no—
162C2×C4—4281no—
163C2×C4—4282no—
164C2×C4—2142no—
165C2×C4C2×C22⋊D10711yescharacteristic
166C8—4281no—
167C22—24no—
168C22—22no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22—44no—
173C22—42no—
174C22—41no—
175C22—82no—
176C22—84no—
177C22—8562no—
178C22—4281no—
179C22#1681207811yescharacteristic
180C4—22no—
181C4—21no—
182C4—42no—
183C4—8562no—
184C4—4281no—
185C2—21no—
186C2—42no—
187C2—44no—
188C2—81no—
189C2—8561no—
190C2#2029281411yescharacteristic
subgroupG/H
centerC2#20292814
commutator, cosocleC2×D4×C107C23
FrattiniC2×D4C22×D107
FittingD42×C107C2
socleC2×C107B(4,𝔽2)
hypercenterD42D107
hypocenterC107#2196
LCSG ▷ C2×D4×C107 ▷ C22×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #20292813C2semidirect
2. #20292794C2semidirect
3. #20292420C2semidirect
4. #20292414C2semidirect
5. D42×C107C2semidirect
6. #16812154C22semidirect
10. #16812026C22semidirect
11. #16812024C22semidirect
30. C24×C107D4semidirect
36. C2×D4×C107D4semidirect
42. C22⋊C4×C107D4semidirect
43. C42×C107D4semidirect
96. C107#2196semidirect
97. D42D107semidirect
116. C24C22⋊D107semidirect
127. C2×D4C22⋊D107semidirect
138. C22⋊C4C22⋊D107semidirect
139. C42C22⋊D107semidirect

Maximal subgroups

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

subgroupindex
#202928132
#202927942
#202924202
#202924142
D42×C1072
#2196107