Finite Group Databasebeta

← #27196106

Subgroups — #27196106

Order 13184.

300 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 145 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×C4×C103⋊C8C211yesmaximal, characteristic
2#20267661C211yesmaximal, characteristic
3#20267553C214yesmaximal
4C2×C4⋊Q8×C103C211yesmaximal, characteristic
5C22×C103⋊C8C2212yes—
6C2×C4⋊Dic103—21no—
7C2×C4⋊Dic103—21no—
8C2×C4⋊Dic103C2212yes—
9C4×C103⋊C8—22no—
10C22×Q8×C103—21no—
11C4⋊Q8×C103—22no—
12C4⋊Q8×C103C414yescomplemented
13C2×C4⋊C4×C103—21no—
14C2×C4⋊C4×C103C2212yes—
15C2×C42×C103C2211yescharacteristic
16C22×Dic103—22no—
17C2×C103⋊C8—22no—
18C2×C103⋊C8—22no—
19C2×C103⋊C8Q814yescomplemented
20C4⋊Dic103—24no—
21C4⋊Dic103—42no—
22C4⋊Dic103—42no—
23C2×Q8×C103—24no—
24C2×Q8×C103—42no—
25C2×Q8×C103—42no—
26C22×C4×C103—22no—
27C22×C4×C103D411yescharacteristic
28C22×C4×C103D411yescharacteristic
29C22×C4×C103C2311yescharacteristic
30C4⋊C4×C103—24no—
31C4⋊C4×C103—22no—
32C4⋊C4×C103C2×C414yes—
33C42×C103C2×C412yes—
34C42×C103D412yes—
35C23×C103C2×D411yescharacteristic
36Q8×C103—48no—
37C2×C4×C103—24no—
38C2×C4×C103—42no—
39C2×C4×C103—42no—
40C2×C4×C103C22⋊C412yes—
41C2×C4×C103C22⋊C412yes—
42C2×C4×C103D812yes—
43C2×C4×C103SD1612yes—
44C2×C4×C103SD1612yes—
45C2×C4×C103Q1612yes—
46C2×C4×C103C22×C411yescharacteristic
47C2×C4×C103C2×D411yescharacteristic
48C2×C4×C103C2×Q812yes—
49C2×C4×C103#4112yes—
50C2×Dic103—42no—
51C2×Dic103—42no—
52C2×Dic103—42no—
53C103⋊C8—24no—
54C22×C103C2×C22⋊C411yescharacteristic
55C22×C103#12411yescharacteristic
56C22×C103C4⋊Q811yescharacteristic
57C22×C103C2×D811yescharacteristic
58C22×C103C2×SD1611yescharacteristic
59C22×C103C2×SD1611yescharacteristic
60C22×C103C2×Q1611yescharacteristic
61C4×C103—44no—
62C4×C103#10214yes—
63C4×C103#10314yes—
64C4×C103C4×Q812yes—
65C4×C103C22⋊Q812yes—
66Dic103—82no—
67C2×C103#39111yescharacteristic
68C2×C103C2×#10211yescharacteristic
69C2×C103C2×#10311yescharacteristic
70C2×C103#48611yescharacteristic
71C2×C103#48711yescharacteristic
72C2×C103#49811yescharacteristic
73C2×C103#50011yescharacteristic
74#1990—1031nomaximal, Sylow
75C103#199011yescharacteristic, complemented, Sylow
76C2×C4⋊Q8D10311yescharacteristic
77C2×C4×C8—1031no—
78#384—1031no—
79#340—1034no—
80C22×Q8—21no—
81C22×C8—1032no—
82C4⋊Q8—22no—
83C4⋊Q8Dic10314yescomplemented
84C2×C4⋊C4—21no—
85C2×C4⋊C4—1032no—
86C2×C4⋊C4—2061no—
87C2×C4⋊C4—2061no—
88C2×C4⋊C4C2×D10312yes—
89C2×C42C2×D10311yescharacteristic
90C4×C8—2062no—
91C2×Q8—24no—
92C2×Q8—42no—
93C2×Q8—42no—
94C22×C4—22no—
95C22×C4—2062no—
96C22×C4C22⋊D10311yescharacteristic
97C22×C4C22⋊D10311yescharacteristic
98C22×C4C22×D10311yescharacteristic
99C2×C8—1034no—
100C2×C8—2062no—
101C2×C8—2062no—
102C4⋊C4—24no—
103C4⋊C4—22no—
104C4⋊C4—4122no—
105C4⋊C4—4122no—
106C4⋊C4—2064no—
107C4⋊C4C2×Dic10314yes—
108C42C2×Dic10312yes—
109C42C22⋊D10312yes—
110C23C2×C22⋊D10311yescharacteristic
111Q8—48no—
112C2×C4—24no—
113C2×C4—42no—
114C2×C4—42no—
115C2×C4—4122no—
116C2×C4—4122no—
117C2×C4—4122no—
118C2×C4C22⋊Dic10312yes—
119C2×C4C22⋊Dic10312yes—
120C2×C4#1311009012yes—
121C2×C4#1311009212yes—
122C2×C4#1311009312yes—
123C2×C4#1311009512yes—
124C2×C4C22×Dic10311yescharacteristic
125C2×C4C2×C22⋊D10311yescharacteristic
126C2×C4Q8×D10312yes—
127C2×C4#1311010612yes—
128C8—2064no—
129C22C2×C22⋊Dic10311yescharacteristic
130C22#1569301011yescharacteristic
131C22#1569301911yescharacteristic
132C22C2×#1311009011yescharacteristic
133C22C2×#1311009211yescharacteristic
134C22C2×#1311009311yescharacteristic
135C22C2×#1311009511yescharacteristic
136C4—44no—
137C4—8242no—
138C4#1569294214yes—
139C4#1569294514yes—
140C4Q8×Dic10312yes—
141C4#1569299712yes—
142C2#2026769811yescharacteristic
143C2C2×#1569294211yescharacteristic
144C2C2×#1569294511yescharacteristic
145C2#2026813911yescharacteristic
146C2#2026814311yescharacteristic
147C2#2026818711yescharacteristic
148C2#2026819411yescharacteristic
subgroupG/H
centerC23C2×C22⋊D103
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
FittingC2×C4⋊Q8×C103C2
socle, prime radicalC23×C103C2×D4
cosocleC22×C4×C103C23
hypercenterC2×C4⋊Q8D103
hypocenterC103#1990
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
12. C4⋊Q8×C103C4semidirect
19. C2×C103⋊C8Q8semidirect
75. C103#1990semidirect
83. C4⋊Q8Dic103semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C103⋊C82
#202676612
#202675532
C2×C4⋊Q8×C1032
#1990103