Finite Group Databasebeta

← #34068421

Subgroups — #34068421

Order 19328.

196 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 49 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#23752622C212yesmaximal, complemented
2#23752607C211yesmaximal, characteristic
3#23751954C212yesmaximal, complemented
4#23751952C211yesmaximal, characteristic
5#563×C151C211yesmaximal, characteristic
6C2×#14558994—21no—
7C2×#14558992—21no—
8#18012739C2211yescharacteristic
9#18012672—22no—
10#18012670—22no—
11#18012650C2212yes—
12#18012650C2211yescharacteristic
13C4⋊Q8×C151—21no—
14#126×C151—22no—
15#125×C151C2212yes—
16#124×C151C2211yescharacteristic
17#123×C151—21no—
18C22⋊Q8×C151—22no—
19C2×Dic302—21no—
20#14558994—42no—
21#14558992—42no—
22C2×C151⋊C8—22no—
23C2×C151⋊C8—21no—
24C4⋊Dic151—22no—
25C2×Q8×C151—21no—
26C2×Q8×C151D411yescharacteristic
27C2×D4×C151D411yescharacteristic
28C22×C4×C151—21no—
29C4⋊C4×C151—22no—
30C4⋊C4×C151—22no—
31C4⋊C4×C151—22no—
32C4⋊C4×C151D412yes—
33C4⋊C4×C151D412yes—
34C22⋊C4×C151—22no—
35C22⋊C4×C151—21no—
36C22⋊C4×C151—22no—
37C42×C151—21no—
38C42×C151C2311yescharacteristic
39Dic302—41no—
40Dic302—41no—
41C2×Dic151—41no—
42C151⋊C8—24no—
43C151⋊C8—22no—
44C23×C151—21no—
45Q8×C151—41no—
46Q8×C151—81no—
47D4×C151—41no—
48C2×C4×C151—21no—
49C2×C4×C151—22no—
50C2×C4×C151—22no—
51C2×C4×C151—81no—
52C2×C4×C151C2×D411yescharacteristic
53C2×C4×C151C2×D412yes—
54C22×C151—41no—
55C22×C151—42no—
56C22×C151#12011yescharacteristic
57C4×C151—21no—
58C4×C151—22no—
59C4×C151—42no—
60C4×C151—41no—
61C4×C151—42no—
62Dic151—81no—
63C2×C151—81no—
64C2×C151#45311yescharacteristic
65C2×C151#45612yes—
66C151#166011yescharacteristic, complemented, Sylow
67#1660—1511nomaximal, Sylow
68#563D15111yescharacteristic
69#501—1512no—
70#497—1511no—
71#330—1512no—
72#329—1511no—
73C2×Q16—3021no—
74C2×SD16—3021no—
75C4⋊Q8—21no—
76C4⋊Q8—1511no—
77#126—22no—
78#125C2×D15112yes—
79#124C2×D15111yescharacteristic
80#123—21no—
81C22⋊Q8—22no—
82#107—3022no—
83#106—3022no—
84#97—1512no—
85#97—1511no—
86C2×Q8—21no—
87C2×Q8—3021no—
88C2×Q8C22⋊D15111yescharacteristic
89C2×D4C22⋊D15111yescharacteristic
90C22×C4—21no—
91Q16—6042no—
92SD16—6042no—
93C2×C8—3022no—
94C2×C8—3021no—
95C4⋊C4—22no—
96C4⋊C4—22no—
97C4⋊C4—22no—
98C4⋊C4—3022no—
99C4⋊C4C22⋊D15112yes—
100C4⋊C4C22⋊D15112yes—
101C22⋊C4—22no—
102C22⋊C4—21no—
103C22⋊C4—22no—
104C42—21no—
105C42C22×D15111yescharacteristic
106C23—21no—
107Q8—41no—
108Q8—81no—
109Q8—6041no—
110Q8—6041no—
111D4—41no—
112C2×C4—22no—
113C2×C4—21no—
114C2×C4—22no—
115C2×C4—81no—
116C2×C4—6041no—
117C2×C4C2×C22⋊D15112yes—
118C2×C4C2×C22⋊D15111yescharacteristic
119C8—3022no—
120C8—3024no—
121C22—41no—
122C22—42no—
123C22#1801270811yescharacteristic
124C4—21no—
125C4—22no—
126C4—42no—
127C4—41no—
128C4—42no—
129C4—12081no—
130C2—81no—
131C2#2375238011yescharacteristic
132C2#2375239512yes—
subgroupG/H
centerC22#18012708
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#563×C151C2
socleC22×C151#120
prime radicalC2×D4×C151D4
hypercenter#563D151
hypocenterC151#1660
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #563

Complements

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

NH ≅ G/Ntype
1. #23752622C2semidirect
3. #23751954C2semidirect
66. C151#1660semidirect

Maximal subgroups

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

subgroupindex
#237526222
#237526072
#237519542
#237519522
#563×C1512
#1660151