Finite Group Databasebeta

← #34070271

Subgroups — #34070271

Order 19328.

246 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 69 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#23752843C211yesmaximal, characteristic
2#23752221C212yesmaximal
3#23751981C211yesmaximal, characteristic
4#23751972C212yesmaximal
5#391×C151C211yesmaximal, characteristic
6C2×#14558988C2212yes—
7#18012738—22no—
8#18012730—22no—
9#18012718—22no—
10#18012698C2212yes—
11#18012663—22no—
12#18012663—22no—
13C22×Q8×C151C2211yescharacteristic
14C2×C4⋊C4×C151C2211yescharacteristic
15C2×C42×C151C2211yescharacteristic
16#95×C151—22no—
17C2×Dic302—22no—
18#14558988—22no—
19#14558988—22no—
20C2×C151⋊C8—22no—
21C4⋊Dic151—22no—
22C4⋊Dic151D412yes—
23C4⋊Dic151D412yes—
24Dic151⋊C4—24no—
25C22⋊Dic151—22no—
26C4×Dic151—22no—
27C2×Q8×C151—21no—
28C2×Q8×C151—22no—
29C2×Q8×C151—22no—
30C2×Q8×C151Q812yescomplemented
31C22×C4×C151—21no—
32C22×C4×C151—21no—
33C22×C4×C151D412yes—
34C22×C4×C151C2311yescharacteristic
35C4⋊C4×C151—22no—
36C42×C151—22no—
37Dic302—82no—
38C2×Dic151—22no—
39C2×Dic151—22no—
40C151⋊C8—42no—
41C23×C151C2×D411yescharacteristic
42Q8×C151—24no—
43Q8×C151—42no—
44C2×C4×C151—22no—
45C2×C4×C151—22no—
46C2×C4×C151—22no—
47C2×C4×C151—41no—
48C2×C4×C151—41no—
49C2×C4×C151—41no—
50C2×C4×C151—41no—
51C2×C4×C151—42no—
52C2×C4×C151C2×D412yes—
53C2×C4×C151C2×Q811yescharacteristic
54C2×C4×C151#4112yes—
55C2×C4×C151#4111yescharacteristic
56C22×C151—21no—
57C22×C151—21no—
58C22×C151#12011yescharacteristic
59C22×C151C22⋊Q811yescharacteristic
60C22×C151#12411yescharacteristic
61C4×C151—42no—
62C4×C151—42no—
63C4×C151—42no—
64C4×C151C22⋊Q812yes—
65C4×C151#12412yes—
66Dic151—42no—
67Dic151—42no—
68C2×C151—21no—
69C2×C151—21no—
70C2×C151#39311yescharacteristic
71C2×C151#45511yescharacteristic
72C2×C151#45611yescharacteristic
73C151#202811yescharacteristic, complemented, Sylow
74#2028—1511nomaximal, Sylow
75#544—1511no—
76#419—1512no—
77#391D15111yescharacteristic
78#343—1511no—
79#339—1512no—
80C22×Q8C2×D15111yescharacteristic
81C2×M16—1512no—
82C4⋊Q8—3022no—
83#125—3022no—
84C22⋊Q8—3022no—
85#117—1512no—
86C2×C4⋊C4C2×D15111yescharacteristic
87C2×C42C2×D15111yescharacteristic
88#103—3022no—
89#103—3022no—
90#95—22no—
91C2×Q8—21no—
92C2×Q8—22no—
93C2×Q8—22no—
94C2×Q8—3022no—
95C2×Q8Dic30212yescomplemented
96C22×C4—21no—
97C22×C4—21no—
98C22×C4C22⋊D15112yes—
99C22×C4C22×D15111yescharacteristic
100M16—3022no—
101M16—3022no—
102C2×C8—3022no—
103C4⋊C4—22no—
104C4⋊C4—3024no—
105C4⋊C4—3022no—
106C4⋊C4—1512no—
107C4⋊C4—1512no—
108C22⋊C4—3022no—
109C42—22no—
110C42—3022no—
111C23C2×C22⋊D15111yescharacteristic
112Q8—24no—
113Q8—42no—
114Q8—12082no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—22no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—41no—
122C2×C4—42no—
123C2×C4—3022no—
124C2×C4—3022no—
125C2×C4D4×D15112yes—
126C2×C4C2×Dic30211yescharacteristic
127C2×C4#1455900312yes—
128C2×C4#1455900411yescharacteristic
129C8—6042no—
130C22—21no—
131C22—21no—
132C22#1801270711yescharacteristic
133C22#1801271811yescharacteristic
134C22#1801272611yescharacteristic
135C4—42no—
136C4—42no—
137C4—42no—
138C4—6042no—
139C4—6042no—
140C4#1801271612yes—
141C4#1801272512yes—
142C2—21no—
143C2—21no—
144C2#2375212411yescharacteristic
145C2#2375238911yescharacteristic
146C2#2375239411yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#391×C151C2
socleC22×C151#120
prime radicalC23×C151C2×D4
hypercenter#391D151
hypocenterC151#2028
LCSG ▷ C22×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
30. C2×Q8×C151Q8semidirect
73. C151#2028semidirect
95. C2×Q8Dic302semidirect

Maximal subgroups

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

subgroupindex
#237528432
#237522212
#237519812
#237519722
#391×C1512
#2028151