Finite Group Databasebeta

← #28334970

Subgroups — #28334970

Order 13696.

272 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 73 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#20293177C211yesmaximal, characteristic
2#20292473C211yesmaximal, characteristic, complemented
3#20292362C214yesmaximal, complemented
4#432×C107C211yesmaximal, characteristic, complemented
5C2×#13133818—21no—
6#16812109C411yescharacteristic, complemented
7#16812106C411yescharacteristic, complemented
8#16812097—21no—
9#16812083—21no—
10#16812083C2212yes—
11C4×D428—21no—
12C4×D428C412yescomplemented
13C2×C4×Dic107—21no—
14C107⋊#95—21no—
15C107⋊#95C2212yes—
16C2×C42×C107C2211yescharacteristic
17C4⋊C8×C107—21no—
18C22⋊C8×C107C2212yes—
19#97×C107—21no—
20#13133818—44no—
21C2×Dic214—21no—
22C2×D428—21no—
23C2×D428—21no—
24C2×D428C2×C412yes—
25C2×C22⋊D107—22no—
26C22×Dic107—22no—
27C2×C4×D107—22no—
28C4⋊Dic107—21no—
29C4⋊Dic107C2×C412yes—
30(C2×D107)⋊C4—22no—
31(C2×D107)⋊C4—22no—
32C4×Dic107—24no—
33C22×C4×C107D411yescharacteristic
34C22×C4×C107D411yescharacteristic
35C22×C4×C107C2311yescharacteristic
36C2×C8×C107—22no—
37C42×C107C2×C411yescharacteristic
38C42×C107C2×C411yescharacteristic
39C42×C107D411yescharacteristic
40C42×C107D411yescharacteristic
41C23×C107C2×D411yescharacteristic
42C22×D107—22no—
43C2×C4×C107—22no—
44C2×C4×C107—22no—
45C2×C4×C107—41no—
46C2×C4×C107C22⋊C411yescharacteristic
47C2×C4×C107C22⋊C411yescharacteristic
48C2×C4×C107C22⋊C411yescharacteristic
49C2×C4×C107C22⋊C411yescharacteristic
50C2×C4×C107C22×C411yescharacteristic
51C2×C4×C107C2×D411yescharacteristic
52C22⋊D107—44no—
53C2×Dic107—24no—
54C2×Dic107—22no—
55C2×Dic107—42no—
56C2×Dic107—42no—
57D428—42no—
58D428—42no—
59D428—42no—
60C4×D107—44no—
61Dic214—42no—
62C8×C107—42no—
63C22×C107—21no—
64C22×C107—21no—
65C22×C107C2×C22⋊C411yescharacteristic
66C22×C107AGL(1,ℤ/8)12yes—
67C2×D107—42no—
68C2×D107—42no—
69C2×D107—42no—
70C4×C107—21no—
71C4×C107—21no—
72C4×C107—21no—
73C4×C107—21no—
74C4×C107—21no—
75C4×C107#10412yes—
76Dic107—44no—
77Dic107—42no—
78C2×C107—22no—
79C2×C107#41011yescharacteristic
80C2×C107#41811yescharacteristic
81C2×C107C2×#10411yescharacteristic
82D107—82no—
83#1505—1071nomaximal, Sylow
84C107#150511yescharacteristic, complemented, Sylow
85#532—1071no—
86#432D10711yescharacteristic, complemented
87#376—1071no—
88#327—1074no—
89C2×#41—2141no—
90C4⋊Q8—1071no—
91#127—1071no—
92#124—2141no—
93#121—1072no—
94#121—2141no—
95C4×D4—1072no—
96C4×D4—2141no—
97C2×C42—2141no—
98C2×C42C2×D10711yescharacteristic
99C4⋊C8—21no—
100C22⋊C8C2×D10712yes—
101#97—21no—
102#95—1072no—
103#95—2141no—
104#41—4284no—
105C2×Q8—2141no—
106C2×D4—1072no—
107C2×D4—2142no—
108C2×D4—2141no—
109C2×D4—2141no—
110C22×C4—2142no—
111C22×C4—2142no—
112C22×C4D42811yescharacteristic
113C22×C4D42811yescharacteristic
114C22×C4C22×D10711yescharacteristic
115C2×C8—22no—
116C4⋊C4—1072no—
117C4⋊C4—2141no—
118C22⋊C4—2142no—
119C22⋊C4—2142no—
120C42—2144no—
121C42C4×D10711yescharacteristic
122C42C4×D10711yescharacteristic
123C42C22⋊D10711yescharacteristic
124C42C22⋊D10711yescharacteristic
125C23—2142no—
126C23C2×D42811yescharacteristic
127Q8—4282no—
128D4—4282no—
129D4—4282no—
130D4—4284no—
131D4—4282no—
132C2×C4—22no—
133C2×C4—22no—
134C2×C4—41no—
135C2×C4—4284no—
136C2×C4—4282no—
137C2×C4—4282no—
138C2×C4—2144no—
139C2×C4—2142no—
140C2×C4(C2×D107)⋊C411yescharacteristic
141C2×C4(C2×D107)⋊C411yescharacteristic
142C2×C4(C2×D107)⋊C411yescharacteristic
143C2×C4(C2×D107)⋊C411yescharacteristic
144C2×C4C2×C4×D10711yescharacteristic
145C2×C4C2×C22⋊D10711yescharacteristic
146C8—42no—
147C22—21no—
148C22—21no—
149C22—4282no—
150C22—4282no—
151C22—4282no—
152C22C2×(C2×D107)⋊C411yescharacteristic
153C22#1681213712yes—
154C4—21no—
155C4—21no—
156C4—21no—
157C4—21no—
158C4—21no—
159C4—4284no—
160C4—4282no—
161C4#1681203512yes—
162C2—22no—
163C2—8562no—
164C2#2029260011yescharacteristic
165C2#2029263311yescharacteristic
166C2C2×#1681203511yescharacteristic
subgroupG/H
centerC22C2×(C2×D107)⋊C4
commutatorC2×C4×C107C22×C4
FrattiniC22×C4C22×D107
Fitting#432×C107C2
socleC22×C107C2×C22⋊C4
prime radical#20293177C2
cosocleC22×C4×C107C23
hypercenter#432D107
hypocenterC107#1505
LCSG ▷ C2×C4×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #20292473C2semidirect
3. #20292362C2semidirect
4. #432×C107C2semidirect
6. #16812109C4semidirect
7. #16812106C4semidirect
12. C4×D428C4semidirect
84. C107#1505semidirect
86. #432D107semidirect

Maximal subgroups

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

subgroupindex
#202931772
#202924732
#202923622
#432×C1072
#1505107