Finite Group Databasebeta

← #27194448

Subgroups — #27194448

Order 13184.

228 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 45 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#20268533C211yesmaximal, characteristic
2#20268153C212yesmaximal, complemented
3#20267531C211yesmaximal, characteristic, complemented
4#20267530C212yesmaximal, complemented
5#497×C103C211yesmaximal, characteristic, complemented
6#15693010—21no—
7#15693009C2212yes—
8#15693007—22no—
9#15692991—22no—
10#15692989—21no—
11#15692944—22no—
12#15692941—22no—
13#15692932C2212yescomplemented
14C2×Q16×C103—21no—
15C2×SD16×C103—21no—
16C4⋊Q8×C103C2211yescharacteristic, complemented
17#124×C103C2211yescharacteristic
18#97×C103C2211yescharacteristic, complemented
19C23×D103—21no—
20C2×Dic206D412yes—
21C2×D412—21no—
22C2×D412D412yes—
23C2×C22⋊D103—22no—
24C2×C103⋊C8—22no—
25C22⋊Dic103—21no—
26(C2×D103)⋊C4—22no—
27(C2×D103)⋊C4—22no—
28(C2×D103)⋊C4—22no—
29C4×Dic103—21no—
30C2×Q8×C103—21no—
31C2×Q8×C103D411yescharacteristic
32C2×D4×C103D411yescharacteristic
33Q16×C103—42no—
34SD16×C103—42no—
35C2×C8×C103—21no—
36C4⋊C4×C103—22no—
37C22⋊C4×C103—22no—
38C42×C103C2311yescharacteristic
39C23×C103—21no—
40C22×D103—22no—
41C22×D103—81no—
42C22×D103—82no—
43Q8×C103—41no—
44Q8×C103—41no—
45Q8×C103—41no—
46D4×C103—41no—
47C2×C4×C103—21no—
48C2×C4×C103—41no—
49C2×C4×C103C2×D412yes—
50C2×C4×C103C2×D411yescharacteristic
51C22⋊D103—82no—
52C2×Dic103—22no—
53D412—42no—
54D412—81no—
55Dic206—42no—
56C8×C103—22no—
57C103⋊C8—42no—
58C22×C103—41no—
59C22×C103—42no—
60C22×C103#12011yescharacteristic
61C2×D103—42no—
62C2×D103—42no—
63C2×D103—42no—
64C2×D103—84no—
65C4×C103—21no—
66C4×C103—22no—
67C4×C103—41no—
68C4×C103—81no—
69Dic103—42no—
70C2×C103—81no—
71C2×C103#45311yescharacteristic
72C2×C103#45512yes—
73D103—82no—
74#1659—1031nomaximal, Sylow
75C103#165911yescharacteristic, complemented, Sylow
76H(3,𝔽4)—1031no—
77#497D10311yescharacteristic, complemented
78#489—1032no—
79#329—1031no—
80#329—1032no—
81C2×Q16—21no—
82C2×SD16—21no—
83C4⋊Q8C2×D10311yescharacteristic, complemented
84#124—1032no—
85#124—2062no—
86#124—2061no—
87#124C2×D10311yescharacteristic
88#120—2062no—
89#120—2061no—
90#103—2062no—
91#102—2062no—
92#97—1032no—
93#97C2×D10311yescharacteristic, complemented
94C24—2061no—
95C2×Q8—21no—
96C2×Q8—1032no—
97C2×Q8C22⋊D10311yescharacteristic
98C2×D4—1032no—
99C2×D4—2061no—
100C2×D4—2062no—
101C2×D4C22⋊D10311yescharacteristic
102Q16—42no—
103SD16—42no—
104C2×C8—21no—
105C2×C8—2062no—
106C4⋊C4—22no—
107C22⋊C4—22no—
108C22⋊C4—2062no—
109C22⋊C4—2061no—
110C22⋊C4—2062no—
111C22⋊C4—2062no—
112C42—2061no—
113C42C22×D10311yescharacteristic
114C23—21no—
115C23—8241no—
116C23—8242no—
117C23—2062no—
118Q8—41no—
119Q8—41no—
120Q8—41no—
121Q8—4122no—
122D4—41no—
123D4—8241no—
124D4—8242no—
125D4—4122no—
126C2×C4—21no—
127C2×C4—41no—
128C2×C4—2062no—
129C2×C4D4×D10312yes—
130C2×C4C2×C22⋊D10311yescharacteristic
131C8—22no—
132C8—4122no—
133C22—41no—
134C22—42no—
135C22—8244no—
136C22—4122no—
137C22—4122no—
138C22—4122no—
139C22#1569298911yescharacteristic
140C4—21no—
141C4—22no—
142C4—41no—
143C4—81no—
144C4—4122no—
145C2—81no—
146C2—8242no—
147C2#2026795811yescharacteristic
148C2#2026796712yes—
subgroupG/H
centerC22#15692989
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#497×C103C2
socleC22×C103#120
prime radical#20268533C2
hypercenter#497D103
hypocenterC103#1659
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
2. #20268153C2semidirect
3. #20267531C2semidirect
4. #20267530C2semidirect
5. #497×C103C2semidirect
13. #15692932C22semidirect
16. C4⋊Q8×C103C22semidirect
18. #97×C103C22semidirect
75. C103#1659semidirect
77. #497D103semidirect
83. C4⋊Q8C2×D103semidirect
93. #97C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202685332
#202681532
#202675312
#202675302
#497×C1032
#1659103