Finite Group Databasebeta

← #34068251

Subgroups — #34068251

Order 19328.

206 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 57 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#23752942C211yesmaximal, characteristic
2#23752591C211yesmaximal, characteristic
3#23752508C212yesmaximal
4#23751942C212yesmaximal
5#333×C151C211yesmaximal, characteristic
6C2×#14558994—22no—
7#18012739C2211yescharacteristic
8#18012738—22no—
9#18012737—22no—
10C4×Dic302C2212yes—
11#18012704—22no—
12#18012673—22no—
13#18012664—22no—
14C4×C151⋊C8C2211yescharacteristic
15C4⋊Q8×C151C2211yescharacteristic
16C4⋊C8×C151C2212yes—
17C2×Dic302—22no—
18C2×Dic302—21no—
19C2×Dic302D412yes—
20#14558994—44no—
21C2×C151⋊C8—21no—
22C4⋊Dic151—22no—
23C4⋊Dic151D412yes—
24Dic151⋊C4—24no—
25Dic151⋊C4—22no—
26C4×Dic151—22no—
27C4×Dic151—22no—
28C2×Q8×C151D412yes—
29C2×C8×C151—22no—
30C4⋊C4×C151—22no—
31C42×C151C2311yescharacteristic
32Dic302—22no—
33Dic302—42no—
34Dic302—82no—
35Dic302Q1614yescomplemented
36C2×Dic151—22no—
37C2×Dic151—22no—
38C2×Dic151—41no—
39C151⋊C8—22no—
40Q8×C151—42no—
41C2×C4×C151—22no—
42C2×C4×C151C2×D412yes—
43C2×C4×C151C2×D411yescharacteristic
44C8×C151—42no—
45C22×C151#12011yescharacteristic
46C4×C151—21no—
47C4×C151—42no—
48C4×C151C2×Q1612yes—
49C4×C151#13712yes—
50Dic151—24no—
51Dic151—42no—
52Dic151—81no—
53C2×C151#45112yes—
54C2×C151#45311yescharacteristic
55C151#163311yescharacteristic, complemented, Sylow
56#1633—1511nomaximal, Sylow
57Q82—1511no—
58#494—1511no—
59#477—1512no—
60#333D15111yescharacteristic
61Q8⋊C8—1512no—
62C2×Q16—3022no—
63C4⋊Q8—3022no—
64C4⋊Q8—3022no—
65C4⋊Q8—1511no—
66C4⋊Q8C2×D15111yescharacteristic
67C4×Q8—3022no—
68C4×Q8—1512no—
69#107—3022no—
70C4⋊C8C2×D15112yes—
71#103—3022no—
72C4×C8—1511no—
73C2×Q8—3022no—
74C2×Q8—3021no—
75C2×Q8—1512no—
76C2×Q8D60412yes—
77Q16—6044no—
78C2×C8—22no—
79C2×C8—3021no—
80C4⋊C4—22no—
81C4⋊C4—3024no—
82C4⋊C4—3022no—
83C4⋊C4—3022no—
84C4⋊C4—1512no—
85C42—3022no—
86C42—3022no—
87C42C22×D15111yescharacteristic
88Q8—42no—
89Q8—3022no—
90Q8—6042no—
91Q8—1514no—
92Q8—12082no—
93C2×C4—22no—
94C2×C4—3022no—
95C2×C4—3022no—
96C2×C4—6041no—
97C2×C4D4×D15112yes—
98C2×C4C2×D60411yescharacteristic
99C8—42no—
100C8—3022no—
101C22#1801270911yescharacteristic
102C4—21no—
103C4—42no—
104C4—3024no—
105C4—6042no—
106C4—12081no—
107C4Q16×D15112yes—
108C4#1801276812yes—
109C2#2375236912yes—
110C2#2375238211yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#333×C151C2
socle, prime radicalC22×C151#120
hypercenter#333D151
hypocenterC151#1633
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
35. Dic302Q16semidirect
55. C151#1633semidirect

Maximal subgroups

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

subgroupindex
#237529422
#237525912
#237525082
#237519422
#333×C1512
#1633151