Finite Group Databasebeta

← #27193766

Subgroups — #27193766

Order 13184.

248 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 59 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#124×D103C211yesmaximal, characteristic
2#20267846C212yesmaximal, complemented
3#20267531C211yesmaximal, characteristic, complemented
4#20267530C212yesmaximal, complemented
5#329×C103C211yesmaximal, characteristic, complemented
6C2×Q8×D103C411yescharacteristic
7C2×D4×D103C411yescharacteristic
8#15693010C411yescharacteristic
9#15693009C2211yescharacteristic
10#15693008C411yescharacteristic
11#15693007—22no—
12C22⋊C4×D103—22no—
13C42×D103C2211yescharacteristic
14Dic103⋊C8—22no—
15(C2×D103)⋊C8—22no—
16#15692932C2212yescomplemented
17#124×C103C2211yescharacteristic
18#97×C103C2212yescomplemented
19C23×D103—21no—
20C2×Dic206—21no—
21C2×Dic206C2×C411yescharacteristic
22Q8×D103—42no—
23C2×D412C2×C411yescharacteristic
24C2×C22⋊D103—21no—
25D4×D103—42no—
26C2×C4×D103—21no—
27C2×C4×D103C2×C411yescharacteristic
28C2×C4×D103D412yes—
29C2×C103⋊C8—22no—
30C22⋊Dic103—22no—
31(C2×D103)⋊C4—22no—
32(C2×D103)⋊C4—22no—
33C4×Dic103C2×C411yescharacteristic
34C4×Dic103D412yes—
35C2×Q8×C103C2×C411yescharacteristic
36C2×D4×C103C2×C411yescharacteristic
37C2×C8×C103—22no—
38C22⋊C4×C103—22no—
39C42×C103C2311yescharacteristic
40C23×C103—21no—
41C22×D103—21no—
42C22×D103—44no—
43C22×D103—42no—
44C22×D103C22⋊C411yescharacteristic
45Q8×C103—41no—
46D4×C103—41no—
47C2×C4×C103—21no—
48C2×C4×C103C22×C411yescharacteristic
49C2×C4×C103C2×D412yes—
50C22⋊D103—42no—
51C2×Dic103—21no—
52C2×Dic103C22⋊C412yes—
53C2×Dic103C22⋊C411yescharacteristic
54D412—41no—
55C4×D103—22no—
56C4×D103—42no—
57C4×D103—42no—
58Dic206—42no—
59Dic206—41no—
60C8×C103—42no—
61C103⋊C8—42no—
62C22×C103—41no—
63C22×C103—42no—
64C22×C103C2×C22⋊C411yescharacteristic
65C2×D103—22no—
66C2×D103—41no—
67C2×D103—42no—
68C2×D103—84no—
69C2×D103#10012yes—
70C4×C103—21no—
71C4×C103—22no—
72C4×C103—41no—
73Dic103—21no—
74Dic103—22no—
75Dic103—41no—
76C2×C103—81no—
77C2×C103C2×#10011yescharacteristic
78C2×C103#42112yes—
79D103—22no—
80D103—81no—
81#1533—1031nomaximal, Sylow
82C103#153311yescharacteristic, complemented, Sylow
83C2×#124—1031no—
84#432—1032no—
85#329—1031no—
86#329—1032no—
87#329D10311yescharacteristic, complemented
88C22×Q8—1031no—
89C22×D4—1031no—
90#124—1031no—
91#124—1031no—
92#124—1031no—
93#124—2062no—
94#124C2×D10311yescharacteristic
95C2×C22⋊C4—2062no—
96C2×C42—1031no—
97C4⋊C8—2062no—
98C22⋊C8—2062no—
99#97—1032no—
100#97C2×D10312yescomplemented
101C24—2061no—
102C2×Q8—1031no—
103C2×Q8—4122no—
104C2×Q8—2061no—
105C2×Q8C4×D10311yescharacteristic
106C2×D4—1031no—
107C2×D4—4122no—
108C2×D4—2061no—
109C2×D4C4×D10311yescharacteristic
110C22×C4—1032no—
111C22×C4—1031no—
112C22×C4—2061no—
113C2×C8—22no—
114C2×C8—2062no—
115C22⋊C4—22no—
116C22⋊C4—2062no—
117C22⋊C4—2062no—
118C22⋊C4—2062no—
119C42—1031no—
120C42—1032no—
121C42C22×D10311yescharacteristic
122C23—21no—
123C23—1031no—
124C23—4122no—
125C23—4124no—
126C23—2061no—
127Q8—41no—
128Q8—4121no—
129Q8—4122no—
130D4—41no—
131D4—4121no—
132D4—4122no—
133C2×C4—21no—
134C2×C4—1032no—
135C2×C4—1031no—
136C2×C4—4122no—
137C2×C4—4122no—
138C2×C4—2062no—
139C2×C4—2061no—
140C2×C4C2×C4×D10311yescharacteristic
141C2×C4D4×D10312yes—
142C8—42no—
143C8—4122no—
144C22—42no—
145C22—41no—
146C22—8244no—
147C22—1032no—
148C22—4122no—
149C22—4121no—
150C22—2062no—
151C22C22⋊C4×D10311yescharacteristic
152C4—22no—
153C4—21no—
154C4—41no—
155C4—4121no—
156C4—2062no—
157C4—2061no—
158C2—81no—
159C2—8241no—
160C2—2062no—
161C2#100×D10311yescharacteristic
162C2#2026780612yes—
subgroupG/H
centerC22C22⋊C4×D103
commutatorC2×C4×C103C22×C4
FrattiniC42C22×D103
Fitting#329×C103C2
socleC22×C103C2×C22⋊C4
prime radicalC2×D4×D103C4
cosocleC42×C103C23
hypercenter#329D103
hypocenterC103#1533
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #20267846C2semidirect
3. #20267531C2semidirect
4. #20267530C2semidirect
5. #329×C103C2semidirect
16. #15692932C22semidirect
18. #97×C103C22semidirect
82. C103#1533semidirect
87. #329D103semidirect
100. #97C2×D103semidirect

Maximal subgroups

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

subgroupindex
#124×D1032
#202678462
#202675312
#202675302
#329×C1032
#1533103