Finite Group Databasebeta

← #34068422

Subgroups — #34068422

Order 19328.

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

normal subgroups only

This group has 196 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#23752962C211yesmaximal, characteristic
2#23752621C212yesmaximal, complemented
3#23752607C211yesmaximal, characteristic
4#23751953C212yesmaximal, complemented
5#329×C151C211yesmaximal, characteristic
6C2×#14558994—21no—
7C2×#14558992—21no—
8#18012739C2211yescharacteristic
9#18012737—21no—
10#18012732—22no—
11#18012731C2212yes—
12#18012720—21no—
13#18012716—22no—
14#18012673—22no—
15#18012671—22no—
16#18012650C2211yescharacteristic
17#124×C151C2211yescharacteristic
18#97×C151C2212yes—
19C2×Dic302—21no—
20C2×Dic302—21no—
21C22×Dic151—21no—
22#14558994—42no—
23#14558992—42no—
24C2×C151⋊C8—21no—
25C4⋊Dic151—22no—
26C4⋊Dic151D412yes—
27C4⋊Dic151D412yes—
28Dic151⋊C4—22no—
29Dic151⋊C4—22no—
30Dic151⋊C4—22no—
31C22⋊Dic151—22no—
32C22⋊Dic151—21no—
33C4×Dic151—21no—
34C2×Q8×C151D411yescharacteristic
35C2×D4×C151D411yescharacteristic
36C2×C8×C151—22no—
37C22⋊C4×C151—22no—
38C42×C151C2311yescharacteristic
39Dic302—41no—
40Dic302—41no—
41Dic302—81no—
42C2×Dic151—22no—
43C2×Dic151—22no—
44C2×Dic151—41no—
45C2×Dic151—81no—
46C151⋊C8—22no—
47C23×C151—21no—
48Q8×C151—41no—
49D4×C151—41no—
50C2×C4×C151—21no—
51C2×C4×C151C2×D412yes—
52C2×C4×C151C2×D411yescharacteristic
53C8×C151—24no—
54C22×C151—41no—
55C22×C151—42no—
56C22×C151#12011yescharacteristic
57C4×C151—21no—
58C4×C151—22no—
59C4×C151—41no—
60Dic151—42no—
61Dic151—42no—
62Dic151—81no—
63C2×C151—81no—
64C2×C151#45311yescharacteristic
65C2×C151#45612yes—
66C151#166011yescharacteristic, complemented, Sylow
67#1660—1511nomaximal, Sylow
68#563—1511no—
69#501—1512no—
70#497—1511no—
71#330—1512no—
72#329D15111yescharacteristic
73C2×Q16—3021no—
74C2×SD16—3021no—
75C4⋊Q8—3021no—
76C4⋊Q8—1511no—
77#126—3022no—
78#125—1512no—
79#124C2×D15111yescharacteristic
80#123—3021no—
81C22⋊Q8—3022no—
82#107—3022no—
83#106—3022no—
84#97—1511no—
85#97C2×D15112yes—
86C2×Q8—3021no—
87C2×Q8—3021no—
88C2×Q8D60411yescharacteristic
89C2×D4D60411yescharacteristic
90C22×C4—3021no—
91Q16—6042no—
92SD16—6042no—
93C2×C8—22no—
94C2×C8—3021no—
95C4⋊C4—3022no—
96C4⋊C4—3022no—
97C4⋊C4—3022no—
98C4⋊C4—3022no—
99C4⋊C4—1512no—
100C4⋊C4—1512no—
101C22⋊C4—22no—
102C22⋊C4—3022no—
103C22⋊C4—3021no—
104C42—3021no—
105C42C22×D15111yescharacteristic
106C23—21no—
107Q8—41no—
108Q8—6041no—
109Q8—6041no—
110Q8—12081no—
111D4—41no—
112C2×C4—21no—
113C2×C4—3022no—
114C2×C4—3022no—
115C2×C4—6041no—
116C2×C4—12081no—
117C2×C4D4×D15112yes—
118C2×C4C2×D60411yescharacteristic
119C8—24no—
120C8—3022no—
121C22—41no—
122C22—42no—
123C22#1801270911yescharacteristic
124C4—21no—
125C4—22no—
126C4—41no—
127C4—6042no—
128C4—6042no—
129C4—12081no—
130C2—81no—
131C2#2375238211yescharacteristic
132C2#2375239612yes—
subgroupG/H
centerC22#18012709
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#329×C151C2
socleC22×C151#120
prime radicalC2×D4×C151D4
hypercenter#329D151
hypocenterC151#1660
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. #23752621C2semidirect
4. #23751953C2semidirect
66. C151#1660semidirect

Maximal subgroups

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

subgroupindex
#237529622
#237526212
#237526072
#237519532
#329×C1512
#1660151