Finite Group Databasebeta

← #34070452

Subgroups — #34070452

Order 19328.

246 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 75 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#23752255C212yesmaximal
2#23752081C211yesmaximal, characteristic
3#23751981C211yesmaximal, characteristic
4#23751971C212yesmaximal
5#544×C151C211yesmaximal, characteristic
6C2×#14558988C2212yes—
7C2×C4⋊Dic151C2211yescharacteristic
8C2×Dic151⋊C4—22no—
9C2×C4×Dic151C2211yescharacteristic
10#18012672—22no—
11#18012670—22no—
12C4⋊Q8×C151—22no—
13#125×C151—22no—
14C22⋊Q8×C151—22no—
15#117×C151C2212yes—
16C2×C4⋊C4×C151C2211yescharacteristic
17C22×Dic151—21no—
18C22×Dic151—21no—
19#14558988—22no—
20#14558988Q814yescomplemented
21C2×C151⋊C8—22no—
22C4⋊Dic151—22no—
23Dic151⋊C4—44no—
24C4×Dic151—21no—
25C4×Dic151Q812yescomplemented
26C2×Q8×C151—22no—
27C22×C4×C151D412yes—
28C22×C4×C151C2311yescharacteristic
29C4⋊C4×C151—22no—
30C4⋊C4×C151—24no—
31C4⋊C4×C151—22no—
32C4⋊C4×C151D412yes—
33C4⋊C4×C151D412yes—
34C22⋊C4×C151—22no—
35C42×C151—22no—
36C2×Dic151—22no—
37C2×Dic151—22no—
38C2×Dic151—22no—
39C2×Dic151—42no—
40C2×Dic151—41no—
41C151⋊C8—24no—
42C23×C151C2×D411yescharacteristic
43Q8×C151—82no—
44C2×C4×C151—22no—
45C2×C4×C151—22no—
46C2×C4×C151—22no—
47C2×C4×C151—42no—
48C2×C4×C151C2×D412yes—
49C2×C4×C151C2×Q812yes—
50C2×C4×C151C2×Q811yescharacteristic
51C2×C4×C151#4111yescharacteristic
52C22×C151—21no—
53C22×C151—21no—
54C22×C151#12011yescharacteristic
55C22×C151C22⋊Q811yescharacteristic
56C22×C151C4⋊Q811yescharacteristic
57C4×C151—42no—
58C4×C151—42no—
59C4×C151—42no—
60C4×C151C22⋊Q812yes—
61C4×C151C4⋊Q812yes—
62Dic151—24no—
63Dic151—81no—
64C2×C151—21no—
65C2×C151—21no—
66C2×C151#39511yescharacteristic
67C2×C151#45311yescharacteristic
68C2×C151#45611yescharacteristic
69C151#206011yescharacteristic, complemented, Sylow
70#2060—1511nomaximal, Sylow
71#544D15111yescharacteristic
72#428—1512no—
73#384—1511no—
74#343—1511no—
75#339—1512no—
76C2×M16—1512no—
77C4⋊Q8—22no—
78#125—22no—
79C22⋊Q8—22no—
80#117C2×D15112yes—
81C2×C4⋊C4—3022no—
82C2×C4⋊C4—1511no—
83C2×C4⋊C4C2×D15111yescharacteristic
84C2×C42—1511no—
85#107—3022no—
86#106—3022no—
87C2×Q8—22no—
88C22×C4—3021no—
89C22×C4—3021no—
90C22×C4C22⋊D15112yes—
91C22×C4C22×D15111yescharacteristic
92M16—3022no—
93M16—1514no—
94C2×C8—3022no—
95C4⋊C4—22no—
96C4⋊C4—24no—
97C4⋊C4—22no—
98C4⋊C4—3022no—
99C4⋊C4—6044no—
100C4⋊C4C22⋊D15112yes—
101C4⋊C4C22⋊D15112yes—
102C22⋊C4—22no—
103C42—22no—
104C42—3021no—
105C42—1512no—
106C23C2×C22⋊D15111yescharacteristic
107Q8—82no—
108C2×C4—22no—
109C2×C4—22no—
110C2×C4—22no—
111C2×C4—42no—
112C2×C4—3022no—
113C2×C4—3022no—
114C2×C4—3022no—
115C2×C4—6042no—
116C2×C4—6041no—
117C2×C4C2×C22⋊D15112yes—
118C2×C4Q8×D15112yes—
119C2×C4Q8×D15111yescharacteristic
120C2×C4#1455900511yescharacteristic
121C8—3024no—
122C22—21no—
123C22—21no—
124C22#1801270811yescharacteristic
125C22#1801271511yescharacteristic
126C22#1801273711yescharacteristic
127C4—42no—
128C4—42no—
129C4—42no—
130C4—3024no—
131C4—12081no—
132C4#1801271512yes—
133C4#1801273712yes—
134C2—21no—
135C2—21no—
136C2#2375213111yescharacteristic
137C2#2375238011yescharacteristic
138C2#2375239511yescharacteristic
subgroupG/H
centerC22#18012708
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#544×C151C2
socleC22×C151#120
prime radicalC23×C151C2×D4
hypercenter#544D151
hypocenterC151#2060
LCSG ▷ C22×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
20. #14558988Q8semidirect
25. C4×Dic151Q8semidirect
69. C151#2060semidirect

Maximal subgroups

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

subgroupindex
#237522552
#237520812
#237519812
#237519712
#544×C1512
#2060151