Finite Group Databasebeta

← #28344773

Subgroups — #28344773

Order 13696.

582 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×C42×D107C211yesmaximal, characteristic, complemented
2#20292515C213yesmaximal, complemented
3#20292508C213yesmaximal, complemented
4#20292503C213yesmaximal
5#20292498C213yesmaximal, complemented
6#20292495C211yesmaximal, characteristic, complemented
7C2×#126×C107C211yesmaximal, characteristic, complemented
8C22×C22⋊D107C2211yescharacteristic
9C22×C4×D107C2213yes—
10C2×Dic107⋊C4C2213yes—
11C2×C22⋊Dic107C2213yes—
12C2×(C2×D107)⋊C4C2213yes—
13C2×C4×Dic107C2213yes—
14C42×D107—24no—
15C107⋊#95C2213yes—
16C107⋊#95C2213yes—
17C107⋊#95C2213yes—
18C107⋊#95C2213yes—
19#126×C107—24no—
20C2×C4⋊C4×C107C2213yes—
21C2×C22⋊C4×C107C2213yes—
22C2×C42×C107C2211yescharacteristic
23C23×D107C2311yescharacteristic
24C2×C22⋊D107—26no—
25C22×Dic107C2313yes—
26C22×Dic107C2311yescharacteristic
27C22×Dic107C2313yes—
28C2×C4×D107—26no—
29C2×C4×D107—26no—
30C2×C4×D107—26no—
31Dic107⋊C4—26no—
32C22⋊Dic107—26no—
33(C2×D107)⋊C4—26no—
34C4×Dic107—26no—
35C24×C107C2311yescharacteristic
36C22×C4×C107C2313yes—
37C22×C4×C107C2313yes—
38C4⋊C4×C107—26no—
39C22⋊C4×C107—26no—
40C42×C107D414yescomplemented
41C23×C107—21no—
42C23×C107—23no—
43C23×C107—23no—
44C23×C107C2411yescharacteristic
45C22×D107—21no—
46C22×D107—23no—
47C22×D107#4116yes—
48C2×C4×C107—23no—
49C2×C4×C107—23no—
50C2×C4×C107—23no—
51C2×C4×C107—23no—
52C2×C4×C107—23no—
53C2×C4×C107C2×D416yes—
54C22⋊D107—44no—
55C2×Dic107—23no—
56C2×Dic107—23no—
57C2×Dic107—23no—
58C2×Dic107—23no—
59C2×Dic107—23no—
60C2×Dic107—23no—
61C2×Dic107#4116yes—
62C4×D107—224no—
63C22×C107—43no—
64C22×C107—41no—
65C22×C107—43no—
66C22×C107C22×D411yescharacteristic
67C22×C107C2×#4113yes—
68C22×C107C2×#4113yes—
69C2×D107—26no—
70C2×D107—26no—
71C2×D107#12614yescomplemented
72C4×C107—26no—
73C4×C107—43no—
74Dic107—26no—
75Dic107—41no—
76Dic107—43no—
77C2×C107—81no—
78C2×C107#52513yes—
79C2×C107C2×#12611yescharacteristic
80C2×C107#52913yes—
81D107—24no—
82#2852—1071nomaximal, Sylow
83C107#285211yescharacteristic, complemented, Sylow
84C2×#126D10711yescharacteristic, complemented
85C22×C42—1071no—
86#388—1073no—
87#387—1073no—
88#386—1073no—
89#385—1073no—
90#383—1071no—
91C22×D4—1071no—
92C23×C4—1073no—
93#126—24no—
94C2×C4⋊C4—1073no—
95C2×C4⋊C4C2×D10713yes—
96C2×C22⋊C4—1073no—
97C2×C22⋊C4—1073no—
98C2×C22⋊C4C2×D10713yes—
99C2×C42—1073no—
100C2×C42—2144no—
101C2×C42C2×D10711yescharacteristic
102#95—1073no—
103#95—1073no—
104#95—1073no—
105#95—1073no—
106C24—1071no—
107C24C22×D10711yescharacteristic
108C2×D4—2146no—
109C22×C4—1073no—
110C22×C4—1071no—
111C22×C4—1073no—
112C22×C4—2146no—
113C22×C4—2146no—
114C22×C4—2146no—
115C22×C4C22×D10713yes—
116C22×C4C22×D10713yes—
117C4⋊C4—26no—
118C4⋊C4—2146no—
119C22⋊C4—26no—
120C22⋊C4—2146no—
121C22⋊C4—2146no—
122C42—2146no—
123C42C22⋊D10714yescomplemented
124C23—21no—
125C23—23no—
126C23—23no—
127C23—1076no—
128C23—2141no—
129C23—2143no—
130C23C23×D10711yescharacteristic
131D4—4284no—
132C2×C4—23no—
133C2×C4—23no—
134C2×C4—23no—
135C2×C4—23no—
136C2×C4—23no—
137C2×C4—1076no—
138C2×C4—21424no—
139C2×C4—2143no—
140C2×C4—2143no—
141C2×C4—2143no—
142C2×C4—2143no—
143C2×C4—2143no—
144C2×C4—2143no—
145C2×C4C2×C22⋊D10716yes—
146C22—43no—
147C22—41no—
148C22—43no—
149C22—1074no—
150C22—2146no—
151C22—2146no—
152C22C22×C22⋊D10711yescharacteristic
153C22#41×D10713yes—
154C22#41×D10713yes—
155C4—26no—
156C4—43no—
157C4—4281no—
158C4—4283no—
159C4—2146no—
160C2—81no—
161C2—2144no—
162C2#2029313413yes—
163C2#126×D10711yescharacteristic
164C2#2029316013yes—
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
FittingC2×#126×C107C2
prime radicalC22×C22⋊D107C22
hypercenterC2×#126D107
hypocenterC107#2852
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. C2×C42×D107C2semidirect
2. #20292515C2semidirect
3. #20292508C2semidirect
5. #20292498C2semidirect
6. #20292495C2semidirect
7. C2×#126×C107C2semidirect
40. C42×C107D4semidirect
71. C2×D107#126semidirect
83. C107#2852semidirect
84. C2×#126D107semidirect
123. C42C22⋊D107semidirect

Maximal subgroups

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

subgroupindex
C2×C42×D1072
#202925152
#202925082
#202925032
#202924982
#202924952
C2×#126×C1072
#2852107