Finite Group Databasebeta

← #34070416

Subgroups — #34070416

Order 19328.

264 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 65 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#23753012C211yesmaximal, characteristic
2#23752209C212yesmaximal, complemented
3#23752185C212yesmaximal, complemented
4#23751969C211yesmaximal, characteristic, complemented
5#424×C151C211yesmaximal, characteristic, complemented
6C2×#14559004C2212yes—
7#18012772—22no—
8#18012767—22no—
9#18012761—22no—
10#18012698C2212yes—
11#18012664—22no—
12#18012661—22no—
13#18012653—24no—
14C2×M16×C151C2211yescharacteristic
15C22×C8×C151C2211yescharacteristic
16#117×C151C2211yescharacteristic
17C4⋊C8×C151—22no—
18#14559004—22no—
19#14559004—22no—
20#14559004—22no—
21#14559004—22no—
22C2×Dic302D412yes—
23C2×D604D412yes—
24C2×C22⋊D151—22no—
25C2×C4×D151—22no—
26Dic604—22no—
27#14558993—24no—
28D1208—22no—
29C4⋊Dic151—22no—
30C22⋊Dic151—22no—
31C4×Dic151—22no—
32C22×C4×C151C2311yescharacteristic
33M16×C151—22no—
34C2×C8×C151—21no—
35C2×C8×C151—22no—
36C2×C8×C151D412yes—
37C4⋊C4×C151—21no—
38C22⋊C4×C151D412yes—
39C42×C151—21no—
40C22×D151—22no—
41Dic302—22no—
42Dic302—22no—
43D604—22no—
44D604—22no—
45C22⋊D151—42no—
46C22⋊D151—42no—
47C2×Dic151—22no—
48C2×Dic151—42no—
49C4×D151—42no—
50C4×D151—42no—
51C23×C151C2×D411yescharacteristic
52C2×C4×C151—22no—
53C2×C4×C151C2×D412yes—
54C2×C4×C151C2×D411yescharacteristic
55C2×C4×C151#4111yescharacteristic
56C2×C4×C151#4112yes—
57C8×C151—22no—
58C8×C151—41no—
59C22×C151—41no—
60C22×C151#12111yescharacteristic
61C22×C151#12112yes—
62C2×D151—42no—
63C2×D151—82no—
64C4×C151—42no—
65C4×C151#12011yescharacteristic
66C4×C151#12312yes—
67C4×C151#12411yescharacteristic
68Dic151—42no—
69Dic151—82no—
70C2×C151—22no—
71C2×C151—21no—
72C2×C151#39411yescharacteristic
73D151—82no—
74C151#205311yescharacteristic, complemented, Sylow
75#2053—1511nomaximal, Sylow
76#575—1511no—
77#424D15111yescharacteristic, complemented
78#416—1512no—
79#410—1512no—
80H(3,ℤ/4)—1511no—
81C2×#41—1512no—
82#137—3022no—
83AGL(1,ℤ/8)—3022no—
84#135—3022no—
85C2×M16C2×D15111yescharacteristic
86C22×C8C2×D15111yescharacteristic
87#117—1512no—
88#117C2×D15111yescharacteristic
89C4⋊C8—22no—
90#103—3022no—
91#102—3022no—
92#99—3024no—
93#41—3022no—
94#41—3022no—
95#41—3022no—
96#41—3022no—
97C2×Q8—1512no—
98C2×D4—3022no—
99C2×D4—1512no—
100C22×C4—3022no—
101C22×C4C22×D15111yescharacteristic
102Q16—3022no—
103SD16—3024no—
104D8—3022no—
105M16—22no—
106C2×C8—22no—
107C2×C8—21no—
108C2×C8C22⋊D15112yes—
109C4⋊C4—21no—
110C4⋊C4—3022no—
111C22⋊C4—3022no—
112C22⋊C4D60412yes—
113C42—21no—
114C42—3022no—
115C23—3022no—
116C23C2×D60411yescharacteristic
117Q8—3022no—
118Q8—3022no—
119D4—3022no—
120D4—3022no—
121D4—6042no—
122D4—6042no—
123C2×C4—22no—
124C2×C4—3022no—
125C2×C4—6042no—
126C2×C4—6042no—
127C2×C4—6042no—
128C2×C4D4×D15112yes—
129C2×C4C2×C22⋊D15111yescharacteristic
130C2×C4#1455900411yescharacteristic
131C2×C4#1455900512yes—
132C8—22no—
133C8—41no—
134C22—41no—
135C22—6042no—
136C22—12082no—
137C22#1801271311yescharacteristic
138C22#1801271412yes—
139C4—42no—
140C4—6042no—
141C4—12082no—
142C4#1801270711yescharacteristic
143C4#1801272412yes—
144C4#1801272811yescharacteristic
145C2—21no—
146C2—22no—
147C2—12082no—
148C2#2375212911yescharacteristic
subgroupG/H
centerC4#18012728
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#424×C151C2
socleC2×C151#394
prime radical#23753012C2
hypercenter#424D151
hypocenterC151#2053
LCSG ▷ C22×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C4 ◁ C22×C4 ◁ #424

Complements

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

NH ≅ G/Ntype
2. #23752209C2semidirect
3. #23752185C2semidirect
4. #23751969C2semidirect
5. #424×C151C2semidirect
74. C151#2053semidirect
77. #424D151semidirect

Maximal subgroups

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

subgroupindex
#237530122
#237522092
#237521852
#237519692
#424×C1512
#2053151