Finite Group Databasebeta

← #28344777

Subgroups — #28344777

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×#16812103C211yesmaximal, characteristic, complemented
2C2×C42×D107C211yesmaximal, characteristic, complemented
3#20292519C213yesmaximal, complemented
4#20292512C213yesmaximal, complemented
5#20292505C213yesmaximal
6#20292501C213yesmaximal, complemented
7#383×C107C211yesmaximal, characteristic, complemented
8C22×D428C2211yescharacteristic
9C22×C4×D107C2213yes—
10#16812103—24no—
11C2×C4⋊Dic107C2213yes—
12C2×Dic107⋊C4C2213yes—
13C2×(C2×D107)⋊C4C2213yes—
14C2×(C2×D107)⋊C4C2213yes—
15C2×(C2×D107)⋊C4C2213yes—
16C2×C4×Dic107C2213yes—
17C42×D107—24no—
18C107⋊#95C2213yes—
19C107⋊#95C2213yes—
20C2×C42×C107C2211yescharacteristic
21#95×C107C2213yes—
22#95×C107C2213yes—
23C23×D107C2311yescharacteristic
24C23×D107C2311yescharacteristic
25C2×D428—26no—
26C22×Dic107C2313yes—
27C22×Dic107C2313yes—
28C2×C4×D107—26no—
29C2×C4×D107—26no—
30C2×C4×D107—26no—
31C4⋊Dic107—26no—
32Dic107⋊C4—26no—
33(C2×D107)⋊C4—26no—
34(C2×D107)⋊C4—26no—
35(C2×D107)⋊C4—26no—
36C4×Dic107—26no—
37C22×C4×C107C2313yes—
38C22×C4×C107C2311yescharacteristic
39C22×C4×C107C2313yes—
40C42×C107D414yescomplemented
41C23×C107C2411yescharacteristic
42C22×D107—21no—
43C22×D107—23no—
44C22×D107—21no—
45C22×D107—23no—
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×C107—23no—
54C2×C4×C107C2×D416yes—
55C2×Dic107—23no—
56C2×Dic107—23no—
57C2×Dic107—23no—
58C2×Dic107—23no—
59C2×Dic107—23no—
60C2×Dic107#4116yes—
61D428—44no—
62C4×D107—224no—
63C22×C107C22×D411yescharacteristic
64C22×C107C2×#4113yes—
65C22×C107C2×#4113yes—
66C2×D107—26no—
67C2×D107—26no—
68C2×D107—43no—
69C2×D107—41no—
70C2×D107—43no—
71C2×D107#12614yescomplemented
72C4×C107—26no—
73C4×C107—41no—
74C4×C107—43no—
75Dic107—26no—
76Dic107—43no—
77C2×C107#52513yes—
78C2×C107C2×#12611yescharacteristic
79C2×C107#52913yes—
80D107—24no—
81D107—81no—
82#2852—1071nomaximal, Sylow
83C107#285211yescharacteristic, complemented, Sylow
84C2×#126—1071no—
85C22×C42—1071no—
86#388—1073no—
87#387—1073no—
88#386—1073no—
89#385—1073no—
90#383D10711yescharacteristic, complemented
91C22×D4—1071no—
92C23×C4—1073no—
93#126—2144no—
94C2×C4⋊C4—1073no—
95C2×C4⋊C4—1073no—
96C2×C22⋊C4—1073no—
97C2×C22⋊C4—1073no—
98C2×C22⋊C4—1073no—
99C2×C42—1073no—
100C2×C42—2144no—
101C2×C42C2×D10711yescharacteristic
102#95—1073no—
103#95—1073no—
104#95C2×D10713yes—
105#95C2×D10713yes—
106C24—1071no—
107C24—1071no—
108C2×D4—2146no—
109C22×C4—1073no—
110C22×C4—1073no—
111C22×C4—2146no—
112C22×C4—2146no—
113C22×C4—2146no—
114C22×C4C22×D10711yescharacteristic
115C22×C4C22×D10713yes—
116C22×C4C22×D10713yes—
117C4⋊C4—2146no—
118C4⋊C4—2146no—
119C22⋊C4—2146no—
120C22⋊C4—2146no—
121C22⋊C4—2146no—
122C42—2146no—
123C42D42814yescomplemented
124C23—1076no—
125C23—2141no—
126C23—2143no—
127C23—2143no—
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—23no—
138C2×C4—1076no—
139C2×C4—21424no—
140C2×C4—2143no—
141C2×C4—2143no—
142C2×C4—2143no—
143C2×C4—2143no—
144C2×C4—2143no—
145C2×C4C2×D42816yes—
146C22—1074no—
147C22—4283no—
148C22—4281no—
149C22—4283no—
150C22—2146no—
151C22—2146no—
152C22C22×D42811yescharacteristic
153C22#41×D10713yes—
154C22#41×D10713yes—
155C4—26no—
156C4—41no—
157C4—43no—
158C4—4283no—
159C4—2146no—
160C2—8561no—
161C2—2144no—
162C2#2029313913yes—
163C2#126×D10711yescharacteristic
164C2#2029316013yes—
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
Fitting#383×C107C2
prime radicalC22×D428C22
hypercenter#383D107
hypocenterC107#2852
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #383

Complements

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

NH ≅ G/Ntype
1. C2×#16812103C2semidirect
2. C2×C42×D107C2semidirect
3. #20292519C2semidirect
4. #20292512C2semidirect
6. #20292501C2semidirect
7. #383×C107C2semidirect
40. C42×C107D4semidirect
71. C2×D107#126semidirect
83. C107#2852semidirect
90. #383D107semidirect
123. C42D428semidirect

Maximal subgroups

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

subgroupindex
C2×#168121032
C2×C42×D1072
#202925192
#202925122
#202925052
#202925012
#383×C1072
#2852107