Finite Group Databasebeta

← #27196302

Subgroups — #27196302

Order 13184.

246 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 71 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#20267799C212yesmaximal
2#20267696C211yesmaximal, characteristic
3#20267560C211yesmaximal, characteristic
4#20267550C212yesmaximal
5#544×C103C211yesmaximal, characteristic
6C22×Dic206C2211yescharacteristic
7C2×#13110089C2212yes—
8C2×C4×Dic103C2211yescharacteristic
9#15692944—22no—
10#15692944—22no—
11C103⋊#95—22no—
12C4⋊Q8×C103—22no—
13#125×C103—22no—
14C22⋊Q8×C103—22no—
15#117×C103C2212yes—
16C2×C4⋊C4×C103C2211yescharacteristic
17C2×Dic206—22no—
18C2×Dic206—22no—
19C2×Dic206—21no—
20C2×Dic206Q812yescomplemented
21C22×Dic103—21no—
22C22×Dic103—21no—
23#13110089—22no—
24#13110089—22no—
25C2×C103⋊C8—22no—
26C4×Dic103—22no—
27C2×Q8×C103—22no—
28C22×C4×C103D412yes—
29C22×C4×C103C2311yescharacteristic
30C4⋊C4×C103—22no—
31C4⋊C4×C103—24no—
32C4⋊C4×C103—22no—
33C4⋊C4×C103D412yes—
34C4⋊C4×C103D412yes—
35C22⋊C4×C103—22no—
36C42×C103—22no—
37C23×C103C2×D411yescharacteristic
38Q8×C103—82no—
39C2×C4×C103—22no—
40C2×C4×C103—22no—
41C2×C4×C103—22no—
42C2×C4×C103—42no—
43C2×C4×C103C2×D412yes—
44C2×C4×C103C2×Q811yescharacteristic
45C2×C4×C103#4112yes—
46C2×C4×C103#4111yescharacteristic
47C2×Dic103—22no—
48C2×Dic103—22no—
49C2×Dic103—41no—
50C2×Dic103—41no—
51C2×Dic103—41no—
52C2×Dic103—41no—
53Dic206—24no—
54Dic206—42no—
55C103⋊C8—42no—
56C22×C103—21no—
57C22×C103—21no—
58C22×C103#12011yescharacteristic
59C22×C103C22⋊Q811yescharacteristic
60C22×C103#12411yescharacteristic
61C4×C103—42no—
62C4×C103—42no—
63C4×C103—42no—
64C4×C103C22⋊Q812yes—
65C4×C103#12412yes—
66Dic103—42no—
67Dic103—42no—
68C2×C103—21no—
69C2×C103—21no—
70C2×C103#39311yescharacteristic
71C2×C103#45511yescharacteristic
72C2×C103#45611yescharacteristic
73#2028—1031nomaximal, Sylow
74C103#202811yescharacteristic, complemented, Sylow
75#544D10311yescharacteristic
76#419—1032no—
77#391—1031no—
78#343—1031no—
79#339—1032no—
80C22×Q8—1031no—
81C2×M16—1032no—
82C4⋊Q8—22no—
83#125—22no—
84C22⋊Q8—22no—
85#117C2×D10312yes—
86C2×C4⋊C4C2×D10311yescharacteristic
87C2×C42—1031no—
88#103—2062no—
89#103—2062no—
90#95—2062no—
91C2×Q8—22no—
92C2×Q8—1032no—
93C2×Q8—2062no—
94C2×Q8—2062no—
95C2×Q8—2061no—
96C22×C4—2061no—
97C22×C4—2061no—
98C22×C4C22⋊D10312yes—
99C22×C4C22×D10311yescharacteristic
100M16—2062no—
101M16—2062no—
102C2×C8—2062no—
103C4⋊C4—22no—
104C4⋊C4—24no—
105C4⋊C4—22no—
106C4⋊C4C22⋊D10312yes—
107C4⋊C4C22⋊D10312yes—
108C22⋊C4—22no—
109C42—22no—
110C42—2062no—
111C23C2×C22⋊D10311yescharacteristic
112Q8—82no—
113Q8—4122no—
114Q8—2064no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—22no—
118C2×C4—42no—
119C2×C4—4121no—
120C2×C4—4121no—
121C2×C4—4121no—
122C2×C4—4121no—
123C2×C4—2062no—
124C2×C4—2062no—
125C2×C4C2×C22⋊D10312yes—
126C2×C4Q8×D10311yescharacteristic
127C2×C4#1311010612yes—
128C2×C4#1311010611yescharacteristic
129C8—4122no—
130C22—21no—
131C22—21no—
132C22#1569299011yescharacteristic
133C22#1569299711yescharacteristic
134C22#1569301011yescharacteristic
135C4—42no—
136C4—42no—
137C4—42no—
138C4—4122no—
139C4—4122no—
140C4#1569299712yes—
141C4#1569301012yes—
142C2—21no—
143C2—21no—
144C2#2026770211yescharacteristic
145C2#2026796911yescharacteristic
146C2#2026797411yescharacteristic
subgroupG/H
centerC22#15692990
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#544×C103C2
socleC22×C103#120
prime radicalC23×C103C2×D4
hypercenter#544D103
hypocenterC103#2028
LCSG ▷ C22×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
20. C2×Dic206Q8semidirect
74. C103#2028semidirect

Maximal subgroups

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

subgroupindex
#202677992
#202676962
#202675602
#202675502
#544×C1032
#2028103