Finite Group Databasebeta

← #34068417

Subgroups — #34068417

Order 19328.

228 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 45 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#23752954C211yesmaximal, characteristic
2#23752607C211yesmaximal, characteristic, complemented
3#23752572C212yesmaximal, complemented
4#23751951C212yesmaximal, complemented
5#329×C151C211yesmaximal, characteristic, complemented
6C2×#14558994—21no—
7C2×#14558992—21no—
8#18012739C2211yescharacteristic, complemented
9#18012728—21no—
10#18012727C2212yes—
11#18012725—22no—
12#18012709—22no—
13#18012707—21no—
14#18012664—22no—
15#18012661—22no—
16#18012650C2211yescharacteristic, complemented
17#124×C151C2211yescharacteristic
18#97×C151C2212yescomplemented
19C23×D151—21no—
20C2×Dic302—21no—
21C2×Dic302D412yes—
22C2×D604—21no—
23C2×D604D412yes—
24C2×C22⋊D151—22no—
25#14558994—42no—
26#14558992—42no—
27C2×C151⋊C8—21no—
28C4⋊Dic151—22no—
29C22⋊Dic151—21no—
30(C2×D151)⋊C4—22no—
31(C2×D151)⋊C4—22no—
32(C2×D151)⋊C4—22no—
33C4×Dic151—21no—
34C2×Q8×C151D411yescharacteristic
35C2×D4×C151D411yescharacteristic
36C2×C8×C151—22no—
37C22⋊C4×C151—22no—
38C42×C151C2311yescharacteristic
39C22×D151—22no—
40C22×D151—81no—
41C22×D151—82no—
42Dic302—42no—
43Dic302—41no—
44Dic302—41no—
45D604—42no—
46D604—81no—
47C22⋊D151—82no—
48C2×Dic151—22no—
49C2×Dic151—41no—
50C151⋊C8—22no—
51C23×C151—21no—
52Q8×C151—41no—
53D4×C151—41no—
54C2×C4×C151—21no—
55C2×C4×C151C2×D412yes—
56C2×C4×C151C2×D411yescharacteristic
57C8×C151—42no—
58C22×C151—41no—
59C22×C151—42no—
60C22×C151#12011yescharacteristic
61C2×D151—42no—
62C2×D151—42no—
63C2×D151—42no—
64C2×D151—84no—
65C4×C151—21no—
66C4×C151—22no—
67C4×C151—41no—
68Dic151—42no—
69Dic151—81no—
70C2×C151—81no—
71C2×C151#45311yescharacteristic
72C2×C151#45512yes—
73D151—82no—
74C151#165911yescharacteristic, complemented, Sylow
75#1659—1511nomaximal, Sylow
76H(3,𝔽4)—1511no—
77#497—1511no—
78#489—1512no—
79#329—1512no—
80#329D15111yescharacteristic, complemented
81C2×Q16—3021no—
82C2×SD16—3021no—
83C4⋊Q8—1511no—
84#124—3022no—
85#124—3021no—
86#124—1512no—
87#124C2×D15111yescharacteristic
88#120—3022no—
89#120—3021no—
90#103—3022no—
91#102—3022no—
92#97—1511no—
93#97C2×D15112yescomplemented
94C24—3021no—
95C2×Q8—3021no—
96C2×Q8—1512no—
97C2×Q8D60411yescharacteristic
98C2×D4—3021no—
99C2×D4—3022no—
100C2×D4—1512no—
101C2×D4D60411yescharacteristic
102Q16—6042no—
103SD16—6042no—
104C2×C8—22no—
105C2×C8—3021no—
106C4⋊C4—3022no—
107C22⋊C4—22no—
108C22⋊C4—3022no—
109C22⋊C4—3021no—
110C22⋊C4—3022no—
111C22⋊C4—3022no—
112C42—3021no—
113C42C22×D15111yescharacteristic
114C23—21no—
115C23—3022no—
116C23—12081no—
117C23—12082no—
118Q8—41no—
119Q8—6042no—
120Q8—6041no—
121Q8—6041no—
122D4—41no—
123D4—6042no—
124D4—12081no—
125D4—12082no—
126C2×C4—21no—
127C2×C4—3022no—
128C2×C4—6041no—
129C2×C4D4×D15112yes—
130C2×C4C2×D60411yescharacteristic
131C8—42no—
132C8—3022no—
133C22—41no—
134C22—42no—
135C22—6042no—
136C22—6042no—
137C22—6042no—
138C22—12084no—
139C22#1801270911yescharacteristic
140C4—21no—
141C4—22no—
142C4—41no—
143C4—6042no—
144C4—12081no—
145C2—81no—
146C2—12082no—
147C2#2375238211yescharacteristic
148C2#2375239112yes—
subgroupG/H
centerC22#18012709
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#329×C151C2
socleC22×C151#120
prime radical#23752954C2
hypercenter#329D151
hypocenterC151#1659
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #23752607C2semidirect
3. #23752572C2semidirect
4. #23751951C2semidirect
5. #329×C151C2semidirect
8. #18012739C22semidirect
16. #18012650C22semidirect
18. #97×C151C22semidirect
74. C151#1659semidirect
80. #329D151semidirect
93. #97C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237529542
#237526072
#237525722
#237519512
#329×C1512
#1659151