Finite Group Databasebeta

← #28344784

Subgroups — #28344784

Order 13696.

582 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 157 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×#16812092C211yesmaximal, characteristic
2C22×C4×Dic107C211yesmaximal, characteristic, complemented
3#20292519C214yesmaximal, complemented
4#20292512C214yesmaximal, complemented
5#20292504C212yesmaximal
6#20292502C212yesmaximal, complemented
7#381×C107C211yesmaximal, characteristic, complemented
8C22×C22⋊D107C2211yescharacteristic
9C23×Dic107C2212yes—
10#16812092—24no—
11C2×C4⋊Dic107C2214yes—
12C2×Dic107⋊C4C2212yes—
13C2×C22⋊Dic107C2211yescharacteristic
14C2×(C2×D107)⋊C4C2212yes—
15C2×(C2×D107)⋊C4C2214yes—
16C2×C4×Dic107—24no—
17C2×C4×Dic107C2214yes—
18C107⋊#95C2214yes—
19C107⋊#95C2214yes—
20C23×C4×C107C2211yescharacteristic
21C2×C22⋊C4×C107C2212yes—
22#95×C107C2214yes—
23C23×D107C2311yescharacteristic
24C2×C22⋊D107—22no—
25C2×C22⋊D107—24no—
26C22×Dic107—24no—
27C22×Dic107—28no—
28C22×Dic107C2312yes—
29C22×Dic107C2311yescharacteristic
30C22×Dic107C2314yes—
31C4⋊Dic107—28no—
32Dic107⋊C4—24no—
33C22⋊Dic107—22no—
34(C2×D107)⋊C4—24no—
35(C2×D107)⋊C4—28no—
36C4×Dic107—28no—
37C24×C107C2311yescharacteristic
38C22×C4×C107—24no—
39C22×C4×C107D414yes—
40C22×C4×C107C2314yes—
41C22×C4×C107C2312yes—
42C22⋊C4×C107—24no—
43C23×C107—24no—
44C23×C107C2×D412yes—
45C23×C107#4114yes—
46C23×C107C2411yescharacteristic
47C22×D107—21no—
48C22×D107—24no—
49C22×D107—22no—
50C2×C4×C107—28no—
51C2×C4×C107—24no—
52C2×C4×C107—24no—
53C2×C4×C107—24no—
54C2×C4×C107—24no—
55C2×C4×C107C2×D414yes—
56C22⋊D107—44no—
57C2×Dic107—216no—
58C2×Dic107—24no—
59C2×Dic107—24no—
60C2×Dic107—22no—
61C2×Dic107—21no—
62C2×Dic107—24no—
63C2×Dic107—22no—
64C2×Dic107#4118yes—
65C22×C107—24no—
66C22×C107—28no—
67C22×C107#12314yes—
68C22×C107C22×D411yescharacteristic
69C22×C107C2×#4114yes—
70C22×C107C2×#4112yes—
71C2×D107—41no—
72C2×D107—42no—
73C2×D107—44no—
74C4×C107—24no—
75C4×C107—44no—
76Dic107—28no—
77Dic107—41no—
78Dic107—42no—
79C2×C107—24no—
80C2×C107C2×#12311yescharacteristic
81C2×C107#52512yes—
82C2×C107#52914yes—
83D107—81no—
84#2853—1071nomaximal, Sylow
85C107#285311yescharacteristic, complemented, Sylow
86C2×#123—1071no—
87C22×C42—1071no—
88#388—1074no—
89#387—1074no—
90#386—1072no—
91#385—1072no—
92#381D10711yescharacteristic, complemented
93C22×D4—1071no—
94C23×C4—1072no—
95C23×C4C2×D10711yescharacteristic
96#123—2144no—
97C2×C4⋊C4—1072no—
98C2×C4⋊C4—1074no—
99C2×C22⋊C4—1071no—
100C2×C22⋊C4—1072no—
101C2×C22⋊C4—1074no—
102C2×C22⋊C4C2×D10712yes—
103C2×C42—1074no—
104C2×C42—2144no—
105#95—1074no—
106#95—1074no—
107#95C2×D10714yes—
108C24—1071no—
109C24C22×D10711yescharacteristic
110C2×D4—2142no—
111C2×D4—2144no—
112C22×C4—24no—
113C22×C4—1074no—
114C22×C4—1071no—
115C22×C4—1072no—
116C22×C4—2148no—
117C22×C4—2144no—
118C22×C4D42814yes—
119C22×C4C22×D10714yes—
120C22×C4C22×D10712yes—
121C4⋊C4—2148no—
122C4⋊C4—2144no—
123C22⋊C4—24no—
124C22⋊C4—2148no—
125C22⋊C4—2142no—
126C22⋊C4—2144no—
127C42—2148no—
128C23—24no—
129C23—2141no—
130C23—2144no—
131C23—2142no—
132C23C2×D42812yes—
133C23#1313381714yes—
134C23C23×D10711yescharacteristic
135D4—4284no—
136C2×C4—28no—
137C2×C4—24no—
138C2×C4—24no—
139C2×C4—24no—
140C2×C4—24no—
141C2×C4—1078no—
142C2×C4—2142no—
143C2×C4—2141no—
144C2×C4—2144no—
145C2×C4—2142no—
146C2×C4—21416no—
147C2×C4—2144no—
148C2×C4—2144no—
149C2×C4C2×D42814yes—
150C22—24no—
151C22—28no—
152C22—4281no—
153C22—4282no—
154C22—4284no—
155C22#1681209314yes—
156C22C22×D42811yescharacteristic
157C22#41×D10714yes—
158C22C2×#1313381712yes—
159C4—24no—
160C4—44no—
161C4—4281no—
162C4—4282no—
163C4—2148no—
164C2—24no—
165C2—8561no—
166C2C2×#1681209311yescharacteristic
167C2#2029313912yes—
168C2#2029315414yes—
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
Fitting#381×C107C2
prime radicalC22×C22⋊D107C22
hypercenter#381D107
hypocenterC107#2853
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic107C2semidirect
3. #20292519C2semidirect
4. #20292512C2semidirect
6. #20292502C2semidirect
7. #381×C107C2semidirect
85. C107#2853semidirect
92. #381D107semidirect

Maximal subgroups

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

subgroupindex
C2×#168120922
C22×C4×Dic1072
#202925192
#202925122
#202925042
#202925022
#381×C1072
#2853107