Finite Group Databasebeta

← #27195664

Subgroups — #27195664

Order 13184.

312 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 85 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#20268558C211yesmaximal, characteristic
2#20268362C211yesmaximal, characteristic
3#20267799C212yesmaximal, complemented
4#20267547C212yesmaximal, complemented
5#410×C103C211yesmaximal, characteristic
6C22×Dic206C2211yescharacteristic
7#15693028—24no—
8C2×#13110089—22no—
9C2×#13110089C2212yes—
10#15693019C412yescomplemented
11#15693008C412yescomplemented
12#15693002—22no—
13#15693000—22no—
14#15692980C2211yescharacteristic
15#15692944—24no—
16C2×#41×C103C2211yescharacteristic
17#117×C103C2212yes—
18#99×C103—22no—
19C2×Dic206—22no—
20C2×Dic206—22no—
21C2×Dic206—21no—
22C2×Dic206C2×C412yes—
23C22×Dic103—21no—
24#13110089—24no—
25#13110089—22no—
26#13110089—22no—
27C2×C103⋊C8—24no—
28C2×C103⋊C8D414yes—
29C4⋊Dic103—21no—
30Dic103⋊C4—24no—
31C22⋊Dic103—24no—
32C22⋊Dic103—21no—
33C4×Dic103C2×C412yes—
34#41×C103—22no—
35#41×C103—22no—
36C2×Q8×C103C2×C411yescharacteristic
37C2×D4×C103C2×C411yescharacteristic
38C2×D4×C103D412yes—
39C22×C4×C103D412yes—
40C22×C4×C103C2311yescharacteristic
41C4⋊C4×C103—22no—
42C22⋊C4×C103—22no—
43C42×C103—22no—
44C23×C103C22⋊C412yes—
45C23×C103C2×D411yescharacteristic
46Q8×C103—22no—
47D4×C103—24no—
48D4×C103—22no—
49C2×C4×C103—22no—
50C2×C4×C103—22no—
51C2×C4×C103—42no—
52C2×C4×C103C22⋊C412yes—
53C2×C4×C103C22×C411yescharacteristic
54C2×C4×C103C2×D412yes—
55C2×C4×C103C2×D411yescharacteristic
56C2×C4×C103#4112yes—
57C2×Dic103—22no—
58C2×Dic103—22no—
59C2×Dic103—42no—
60Dic206—24no—
61Dic206—41no—
62Dic206—41no—
63C103⋊C8—24no—
64C22×C103—22no—
65C22×C103—41no—
66C22×C103—42no—
67C22×C103C2×C22⋊C411yescharacteristic
68C22×C103#12112yes—
69C4×C103—22no—
70C4×C103—82no—
71C4×C103C4×D412yes—
72C4×C103#12011yescharacteristic
73C4×C103#12311yescharacteristic
74Dic103—42no—
75Dic103—42no—
76C2×C103—21no—
77C2×C103—22no—
78C2×C103—42no—
79C2×C103#38611yescharacteristic
80#1909—1031nomaximal, Sylow
81C103#190911yescharacteristic, complemented, Sylow
82#568—1031no—
83#536—1031no—
84#419—1032no—
85#410D10311yescharacteristic
86H(3,ℤ/4)—1032no—
87C2×#41C2×D10311yescharacteristic
88C22×Q8—1031no—
89#131—2064no—
90C2×M16—1032no—
91C2×M16—2062no—
92C4⋊Q8—1032no—
93#124—1032no—
94#123—2062no—
95C22⋊Q8—2062no—
96#117—1031no—
97#117C2×D10312yes—
98#103—2064no—
99#99—22no—
100#41—22no—
101#41—22no—
102C2×Q8—1032no—
103C2×Q8—2062no—
104C2×Q8—2062no—
105C2×Q8—2061no—
106C2×Q8C4×D10311yescharacteristic
107C2×D4C4×D10311yescharacteristic
108C2×D4C22⋊D10312yes—
109C22×C4—2061no—
110C22×C4D41212yes—
111C22×C4C22×D10311yescharacteristic
112M16—2064no—
113M16—2062no—
114M16—2062no—
115C2×C8—1034no—
116C2×C8—2064no—
117C4⋊C4—22no—
118C4⋊C4—2064no—
119C4⋊C4—2061no—
120C22⋊C4—22no—
121C22⋊C4—2064no—
122C22⋊C4—2061no—
123C42—22no—
124C42—1032no—
125C23(C2×D103)⋊C412yes—
126C23C2×C22⋊D10311yescharacteristic
127Q8—22no—
128Q8—4121no—
129Q8—4121no—
130Q8—2064no—
131D4—24no—
132D4—22no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—42no—
136C2×C4—4122no—
137C2×C4—2062no—
138C2×C4—2062no—
139C2×C4(C2×D103)⋊C412yes—
140C2×C4C2×C4×D10311yescharacteristic
141C2×C4D4×D10312yes—
142C2×C4C2×D41211yescharacteristic
143C2×C4#1311010412yes—
144C8—2064no—
145C22—22no—
146C22—41no—
147C22—42no—
148C22C2×(C2×D103)⋊C411yescharacteristic
149C22#1569299312yes—
150C4—22no—
151C4—82no—
152C4—4122no—
153C4—4122no—
154C4(C22⋊D103)⋊C412yes—
155C4#1569299111yescharacteristic
156C4#1569300511yescharacteristic
157C2—22no—
158C2—21no—
159C2—42no—
160C2#2026766811yescharacteristic
subgroupG/H
centerC2#20267668
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#410×C103C2
socleC2×C103#386
prime radicalC2×#41×C103C22
cosocleC22×C4×C103C23
hypercenter#410D103
hypocenterC103#1909
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
3. #20267799C2semidirect
4. #20267547C2semidirect
10. #15693019C4semidirect
11. #15693008C4semidirect
81. C103#1909semidirect

Maximal subgroups

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

subgroupindex
#202685582
#202683622
#202677992
#202675472
#410×C1032
#1909103