Finite Group Databasebeta

← #34068409

Subgroups — #34068409

Order 19328.

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

normal subgroups only

This group has 206 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, complemented
2#23752602C211yesmaximal, characteristic
3#23752577C212yesmaximal, complemented
4#23751953C212yesmaximal, complemented
5#329×C151C211yesmaximal, characteristic, complemented
6C2×#14558991—21no—
7C2×#14558989—21no—
8#18012737—21no—
9#18012736C2211yescharacteristic
10#18012732—22no—
11#18012731C2212yes—
12#18012720—21no—
13#18012716—22no—
14#18012661—22no—
15#18012661—22no—
16#18012650C2211yescharacteristic
17#124×C151C2211yescharacteristic
18#97×C151C2212yes—
19C2×Dic302—21no—
20C2×D604—21no—
21C2×D604—22no—
22C22×Dic151—21no—
23#14558991—42no—
24#14558989—42no—
25C2×C151⋊C8—21no—
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
39C22×D151—41no—
40Dic302—81no—
41D604—41no—
42D604—41no—
43D604—44no—
44C2×Dic151—22no—
45C2×Dic151—22no—
46C2×Dic151—81no—
47C151⋊C8—22no—
48C23×C151—21no—
49Q8×C151—41no—
50D4×C151—41no—
51C2×C4×C151—21no—
52C2×C4×C151C2×D412yes—
53C2×C4×C151C2×D411yescharacteristic
54C8×C151—42no—
55C22×C151—41no—
56C22×C151—42no—
57C22×C151#12011yescharacteristic
58C2×D151—81no—
59C2×D151—82no—
60C4×C151—21no—
61C4×C151—22no—
62C4×C151—41no—
63Dic151—42no—
64Dic151—42no—
65C2×C151—81no—
66C2×C151#45311yescharacteristic
67C2×C151#45412yes—
68D151—161no—
69C151#165711yescharacteristic, complemented, Sylow
70#1657—1511nomaximal, Sylow
71#563—1511no—
72#496—1511no—
73#490—1512no—
74#330—1512no—
75#329D15111yescharacteristic, complemented
76C2×SD16—3021no—
77C2×D8—3021no—
78C4⋊Q8—3021no—
79#127—1511no—
80#126—3022no—
81#125—1512no—
82#124C2×D15111yescharacteristic
83#123—3021no—
84C22⋊Q8—3022no—
85#102—3022no—
86#102—3022no—
87#97—1511no—
88#97C2×D15112yes—
89C2×Q8—3021no—
90C2×Q8D60411yescharacteristic
91C2×D4—3022no—
92C2×D4—3021no—
93C2×D4D60411yescharacteristic
94C22×C4—3021no—
95SD16—6042no—
96D8—6042no—
97C2×C8—22no—
98C2×C8—3021no—
99C4⋊C4—3022no—
100C4⋊C4—3022no—
101C4⋊C4—3022no—
102C4⋊C4—1512no—
103C4⋊C4—1512no—
104C22⋊C4—22no—
105C22⋊C4—3022no—
106C22⋊C4—3021no—
107C42—3021no—
108C42C22×D15111yescharacteristic
109C23—21no—
110C23—6041no—
111Q8—41no—
112Q8—12081no—
113D4—41no—
114D4—6041no—
115D4—6041no—
116D4—6044no—
117C2×C4—21no—
118C2×C4—3022no—
119C2×C4—3022no—
120C2×C4—12081no—
121C2×C4D4×D15112yes—
122C2×C4C2×D60411yescharacteristic
123C8—42no—
124C8—3022no—
125C22—41no—
126C22—42no—
127C22—12081no—
128C22—12082no—
129C22#1801270911yescharacteristic
130C4—21no—
131C4—22no—
132C4—41no—
133C4—6042no—
134C4—6042no—
135C2—81no—
136C2—24161no—
137C2#2375238211yescharacteristic
138C2#2375238612yes—
subgroupG/H
centerC22#18012709
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#329×C151C2
socleC22×C151#120
prime radical#23752602C2
hypercenter#329D151
hypocenterC151#1657
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
1. #23752962C2semidirect
3. #23752577C2semidirect
4. #23751953C2semidirect
5. #329×C151C2semidirect
69. C151#1657semidirect
75. #329D151semidirect

Maximal subgroups

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

subgroupindex
#237529622
#237526022
#237525772
#237519532
#329×C1512
#1657151