Finite Group Databasebeta

← #34070278

Subgroups — #34070278

Order 19328.

290 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 67 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#23752838C211yesmaximal, characteristic
2#23752073C211yesmaximal, characteristic
3#23752073C212yesmaximal
4#23751978C212yesmaximal
5#342×C151C211yesmaximal, characteristic
6C23×Dic151C2211yescharacteristic
7#18012718—22no—
8#18012716—24no—
9C2×C22⋊Dic151C2211yescharacteristic
10C2×C22⋊Dic151C2212yes—
11C151⋊#95—22no—
12C151⋊#95—24no—
13C2×C22⋊C4×C151C2212yes—
14C2×C22⋊C4×C151C2211yescharacteristic
15C2×Dic302—22no—
16C22×Dic151—22no—
17C22×Dic151—21no—
18C22×Dic151—21no—
19C22×Dic151—21no—
20C22×Dic151—22no—
21C22×Dic151D414yes—
22C22×Dic151Q812yescomplemented
23C4⋊Dic151—22no—
24Dic151⋊C4—24no—
25C22⋊Dic151—22no—
26C22⋊Dic151—22no—
27C22⋊Dic151—22no—
28C24×C151C2311yescharacteristic
29C22×C4×C151—22no—
30C22×C4×C151D412yes—
31C22⋊C4×C151—22no—
32C22⋊C4×C151—22no—
33C22⋊C4×C151—22no—
34Dic302—82no—
35C2×Dic151—24no—
36C2×Dic151—24no—
37C2×Dic151—22no—
38C2×Dic151—41no—
39C2×Dic151—42no—
40C2×Dic151—41no—
41C2×Dic151—44no—
42C2×Dic151—42no—
43C2×Dic151—41no—
44C23×C151—42no—
45C23×C151C2×D412yes—
46C23×C151C2×D411yescharacteristic
47C23×C151C2×Q811yescharacteristic
48C23×C151#4111yescharacteristic
49C23×C151#4112yes—
50C2×C4×C151—22no—
51C2×C4×C151—42no—
52C2×C4×C151—44no—
53C2×C4×C151—42no—
54C22×C151—24no—
55C22×C151—22no—
56C22×C151—41no—
57C22×C151—41no—
58C22×C151—42no—
59C22×C151#12011yescharacteristic
60C22×C151C22⋊Q812yes—
61C22×C151C22⋊Q811yescharacteristic
62C22×C151#12412yes—
63C22×C151#12411yescharacteristic
64C4×C151—42no—
65C4×C151—82no—
66Dic151—42no—
67Dic151—44no—
68Dic151—81no—
69C2×C151—21no—
70C2×C151—22no—
71C2×C151—22no—
72C2×C151—21no—
73C2×C151#39311yescharacteristic
74C2×C151#45812yes—
75C151#203011yescharacteristic, complemented, Sylow
76#2030—1511nomaximal, Sylow
77#543—1511no—
78#381—1512no—
79#381—1511no—
80#342—1512no—
81#342D15111yescharacteristic
82C23×C4—1511no—
83C22⋊Q8—3024no—
84C22⋊Q8—3022no—
85C2×C22⋊C4—1511no—
86C2×C22⋊C4—1512no—
87C2×C22⋊C4C2×D15112yes—
88C2×C22⋊C4C2×D15111yescharacteristic
89#95—3024no—
90#95—3022no—
91C24C22×D15111yescharacteristic
92C2×Q8—3022no—
93C22×C4—22no—
94C22×C4—3022no—
95C22×C4—3021no—
96C22×C4—3021no—
97C22×C4—3022no—
98C22×C4—3021no—
99C22×C4—1512no—
100C22×C4—1514no—
101C22×C4D60412yes—
102C4⋊C4—3024no—
103C4⋊C4—3022no—
104C22⋊C4—22no—
105C22⋊C4—22no—
106C22⋊C4—22no—
107C22⋊C4—3022no—
108C22⋊C4—3022no—
109C22⋊C4—3022no—
110C23—42no—
111C23D4×D15112yes—
112C23C2×D60411yescharacteristic
113C23Q8×D15111yescharacteristic
114C23#1455900311yescharacteristic
115C23#1455900412yes—
116Q8—12082no—
117C2×C4—22no—
118C2×C4—42no—
119C2×C4—44no—
120C2×C4—42no—
121C2×C4—3024no—
122C2×C4—3024no—
123C2×C4—3022no—
124C2×C4—6041no—
125C2×C4—6042no—
126C2×C4—6041no—
127C2×C4—6044no—
128C2×C4—6042no—
129C2×C4—6041no—
130C22—24no—
131C22—22no—
132C22—41no—
133C22—41no—
134C22—42no—
135C22#1801270911yescharacteristic
136C22#1801271712yes—
137C22#1801271911yescharacteristic
138C22#1801272512yes—
139C22#1801272711yescharacteristic
140C4—42no—
141C4—82no—
142C4—6042no—
143C4—6044no—
144C4—12081no—
145C2—22no—
146C2—21no—
147C2—22no—
148C2—21no—
149C2#2375212511yescharacteristic
150C2#2375240312yes—
subgroupG/H
centerC22#18012709
commutator, prime radical, cosocleC24×C151C23
FrattiniC24C22×D151
Fitting#342×C151C2
socleC22×C151#120
hypercenter#342D151
hypocenterC151#2030
LCSG ▷ C24×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
22. C22×Dic151Q8semidirect
75. C151#2030semidirect

Maximal subgroups

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

subgroupindex
#237528382
#237520732
#237519782
#342×C1512
#2030151