Finite Group Databasebeta

← #27193734

Subgroups — #27193734

Order 13184.

270 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 63 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#20268340C211yesmaximal, characteristic
2#20267743C212yesmaximal, complemented
3#20267531C211yesmaximal, characteristic, complemented
4#20267530C212yesmaximal, complemented
5#329×C103C211yesmaximal, characteristic, complemented
6C2×#13110106C411yescharacteristic
7C2×#13110104C411yescharacteristic
8C2×#13110088—22no—
9#15693019C411yescharacteristic
10#15693017C411yescharacteristic
11#15693009C2211yescharacteristic
12#15692994—22no—
13(C22⋊D103)⋊C4—22no—
14C42×D103C2211yescharacteristic
15#15692932C2212yes—
16C8×Dic103—22no—
17#124×C103C2211yescharacteristic
18#97×C103C2212yes—
19#13110106—42no—
20#13110104—42no—
21C2×Dic206C2×C411yescharacteristic
22C2×D412—21no—
23C2×D412C2×C411yescharacteristic
24C2×C22⋊D103—21no—
25C2×C22⋊D103—22no—
26C22×Dic103—21no—
27C2×C4×D103—21no—
28C2×C4×D103C2×C411yescharacteristic
29C2×C4×D103D412yes—
30#13110088—28no—
31C2×C103⋊C8—22no—
32Dic103⋊C4—22no—
33(C2×D103)⋊C4—22no—
34C4×Dic103C2×C411yescharacteristic
35C4×Dic103D412yes—
36C2×Q8×C103C2×C411yescharacteristic
37C2×D4×C103C2×C411yescharacteristic
38C2×C8×C103—22no—
39C22⋊C4×C103—22no—
40C42×C103C2311yescharacteristic
41C23×C103—21no—
42C22×D103—21no—
43C22×D103C22⋊C411yescharacteristic
44Q8×C103—41no—
45D4×C103—41no—
46C2×C4×C103—21no—
47C2×C4×C103C22×C411yescharacteristic
48C2×C4×C103C2×D412yes—
49C22⋊D103—42no—
50C22⋊D103—44no—
51C2×Dic103—21no—
52C2×Dic103—42no—
53C2×Dic103C22⋊C411yescharacteristic
54C2×Dic103C22⋊C412yes—
55D412—41no—
56D412—42no—
57C4×D103—22no—
58C4×D103—24no—
59C4×D103—42no—
60Dic206—41no—
61C8×C103—24no—
62C103⋊C8—24no—
63C22×C103—41no—
64C22×C103—42no—
65C22×C103C2×C22⋊C411yescharacteristic
66C2×D103—21no—
67C2×D103—22no—
68C2×D103—41no—
69C2×D103—42no—
70C4×C103—21no—
71C4×C103—22no—
72C4×C103—41no—
73Dic103—41no—
74Dic103#10012yes—
75Dic103#10414yes—
76C2×C103—81no—
77C2×C103C2×#10011yescharacteristic
78C2×C103C2×#10412yes—
79D103—41no—
80D103—81no—
81#1525—1031nomaximal, Sylow
82C103#152511yescharacteristic, complemented, Sylow
83#532—1031no—
84C4×M16—1032no—
85#329—1031no—
86#329—1032no—
87#329D10311yescharacteristic, complemented
88C2×#41—1031no—
89C2×#41—1031no—
90C2×M16—2062no—
91C4⋊Q8—1031no—
92#127—1031no—
93#124—1031no—
94#124C2×D10311yescharacteristic
95#121—2062no—
96C4×D4—2062no—
97C2×C42—1031no—
98#97—1032no—
99#97C2×D10312yes—
100C4×C8—2062no—
101#41—4122no—
102#41—4122no—
103C2×Q8—1031no—
104C2×Q8C4×D10311yescharacteristic
105C2×D4—1031no—
106C2×D4—2061no—
107C2×D4—2062no—
108C2×D4—2061no—
109C2×D4C4×D10311yescharacteristic
110C22×C4—1031no—
111C22×C4—1032no—
112C22×C4—2061no—
113C22×C4—2061no—
114M16—2068no—
115C2×C8—22no—
116C2×C8—2062no—
117C4⋊C4—2062no—
118C22⋊C4—22no—
119C22⋊C4—2062no—
120C42—1031no—
121C42—1032no—
122C42C22×D10311yescharacteristic
123C23—21no—
124C23—1031no—
125C23—2061no—
126Q8—41no—
127Q8—4121no—
128D4—41no—
129D4—4121no—
130D4—4122no—
131D4—4124no—
132D4—4122no—
133C2×C4—21no—
134C2×C4—1032no—
135C2×C4—1031no—
136C2×C4—4122no—
137C2×C4—4122no—
138C2×C4—2064no—
139C2×C4—2062no—
140C2×C4—2061no—
141C2×C4C2×C4×D10311yescharacteristic
142C2×C4D4×D10312yes—
143C8—24no—
144C8—2064no—
145C22—42no—
146C22—41no—
147C22—4122no—
148C22—4121no—
149C22—2062no—
150C22—2061no—
151C22C22⋊C4×D10311yescharacteristic
152C4—22no—
153C4—21no—
154C4—41no—
155C4—1034no—
156C4—1032no—
157C4—4121no—
158C2—81no—
159C2—8241no—
160C2—4121no—
161C2#100×D10311yescharacteristic
162C2#104×D10312yes—
subgroupG/H
centerC22C22⋊C4×D103
commutatorC2×C4×C103C22×C4
FrattiniC42C22×D103
Fitting#329×C103C2
socleC22×C103C2×C22⋊C4
prime radical#20268340C2
cosocleC42×C103C23
hypercenter#329D103
hypocenterC103#1525
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. #20267743C2semidirect
3. #20267531C2semidirect
4. #20267530C2semidirect
5. #329×C103C2semidirect
82. C103#1525semidirect
87. #329D103semidirect

Maximal subgroups

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

subgroupindex
#202683402
#202677432
#202675312
#202675302
#329×C1032
#1525103