Finite Group Databasebeta

← #27197165

Subgroups — #27197165

Order 13184.

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

normal subgroups only

This group has 216 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#20267973C212yesmaximal, complemented
2#20267963C211yesmaximal, characteristic
3#20267590C212yesmaximal, complemented
4#20267588C211yesmaximal, characteristic, complemented
5#563×C103C211yesmaximal, characteristic, complemented
6#15693069C2211yescharacteristic
7#15693052—22no—
8#15693047—21no—
9#15692949—21no—
10#15692949—22no—
11#15692940C2212yes—
12#15692940C2211yescharacteristic
13C4⋊Q8×C103C2212yes—
14#126×C103—22no—
15#125×C103—21no—
16#124×C103C2211yescharacteristic
17#123×C103—21no—
18C22⋊Q8×C103—22no—
19#13110106—41no—
20#13110105—21no—
21#13110105—22no—
22Q8×D103—41no—
23#13110095—42no—
24#13110093—41no—
25#13110092—42no—
26#13110090—41no—
27#13110089—21no—
28#13110089—22no—
29C2×Q8×C103D412yes—
30C2×Q8×C103C2311yescharacteristic
31C2×D4×C103D411yescharacteristic
32C22×C4×C103—21no—
33C4⋊C4×C103—21no—
34C4⋊C4×C103—22no—
35C4⋊C4×C103—21no—
36C4⋊C4×C103—22no—
37C4⋊C4×C103—22no—
38C22⋊C4×C103—22no—
39C22⋊C4×C103—21no—
40C22⋊C4×C103—22no—
41C42×C103D411yescharacteristic
42C42×C103D412yes—
43C23×C103—21no—
44Q8×C103—41no—
45Q8×C103—42no—
46D4×C103—41no—
47C2×C4×C103—21no—
48C2×C4×C103—22no—
49C2×C4×C103—22no—
50C2×C4×C103—81no—
51C2×C4×C103C2×D412yes—
52C2×C4×C103C2×D411yescharacteristic
53C22⋊D103—41no—
54D412—21no—
55D412—22no—
56C4×D103—41no—
57C4×D103—42no—
58Dic206—21no—
59Dic206—22no—
60C103⋊C8—41no—
61C103⋊C8—42no—
62C22×C103—42no—
63C22×C103—41no—
64C22×C103#12011yescharacteristic
65C2×D103—41no—
66C4×C103—21no—
67C4×C103—22no—
68C4×C103—41no—
69C4×C103—42no—
70C4×C103—42no—
71Dic103—41no—
72C2×C103—21no—
73C2×C103—81no—
74C2×C103B(4,𝔽2)11yescharacteristic
75D103—81no—
76#2203—1031nomaximal, Sylow
77C103#220311yescharacteristic, complemented, Sylow
78#563D10311yescharacteristic, complemented
79#456—1032no—
80#454—1031no—
81#356—1032no—
82#355—1031no—
832−1+4—1031no—
84#137—2062no—
85AGL(1,ℤ/8)—2061no—
86C4⋊Q8C2×D10312yes—
87#126—22no—
88#125—21no—
89#124C2×D10311yescharacteristic
90#123—21no—
91C22⋊Q8—22no—
92#104—2061no—
93#104—2062no—
94#101—1032no—
95#101—1031no—
96#41—4121no—
97#41—2061no—
98#41—2062no—
99C2×Q8—4121no—
100C2×Q8C22⋊D10312yes—
101C2×Q8C22×D10311yescharacteristic
102C2×D4C22⋊D10311yescharacteristic
103C22×C4—21no—
104Q16—4122no—
105SD16—4121no—
106SD16—4122no—
107D8—4121no—
108M16—2061no—
109M16—2062no—
110C4⋊C4—21no—
111C4⋊C4—22no—
112C4⋊C4—21no—
113C4⋊C4—22no—
114C4⋊C4—22no—
115C22⋊C4—22no—
116C22⋊C4—21no—
117C22⋊C4—22no—
118C42C22⋊D10311yescharacteristic
119C42C22⋊D10312yes—
120C23—21no—
121Q8—41no—
122Q8—42no—
123Q8—2061no—
124Q8—2062no—
125D4—41no—
126D4—4121no—
127D4—2061no—
128D4—2062no—
129C2×C4—21no—
130C2×C4—22no—
131C2×C4—22no—
132C2×C4—81no—
133C2×C4—4121no—
134C2×C4—4122no—
135C2×C4C2×C22⋊D10312yes—
136C2×C4C2×C22⋊D10311yescharacteristic
137C8—4121no—
138C8—4122no—
139C22—42no—
140C22—41no—
141C22—4121no—
142C22#1569299011yescharacteristic
143C4—21no—
144C4—22no—
145C4—41no—
146C4—42no—
147C4—42no—
148C4—4121no—
149C2—21no—
150C2—81no—
151C2—8241no—
152C2#2026797811yescharacteristic
subgroupG/H
centerC2#20267978
commutator, cosocleC2×Q8×C103C23
FrattiniC2×Q8C22×D103
Fitting#563×C103C2
socleC2×C103B(4,𝔽2)
prime radical#20267963C2
hypercenter#563D103
hypocenterC103#2203
LCSG ▷ C2×Q8×C103 ▷ C22×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #563

Complements

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

NH ≅ G/Ntype
1. #20267973C2semidirect
3. #20267590C2semidirect
4. #20267588C2semidirect
5. #563×C103C2semidirect
77. C103#2203semidirect
78. #563D103semidirect

Maximal subgroups

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

subgroupindex
#202679732
#202679632
#202675902
#202675882
#563×C1032
#2203103