Finite Group Databasebeta

← #34070025

Subgroups — #34070025

Order 19328.

276 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C22×Dic604C211yesmaximal, characteristic
2C2×#18012675C211yesmaximal, characteristic
3#23752220C212yesmaximal
4C2×#18012657C212yesmaximal
5#405×C151C211yesmaximal, characteristic
6C22×Dic302C2212yes—
7C2×Dic604—21no—
8C2×Dic604—21no—
9C2×Dic604—22no—
10C2×Dic604C414yescomplemented
11C2×#14558988C2212yes—
12#18012675—22no—
13#18012662—24no—
14#18012657—24no—
15C2×M16×C151C2211yescharacteristic
16C22×C8×C151C2211yescharacteristic
17#117×C151C2211yescharacteristic
18#97×C151—21no—
19C4×C8×C151—21no—
20C2×Dic302—22no—
21C2×Dic302—22no—
22C2×Dic302—22no—
23C2×Dic302—22no—
24C2×Dic302—22no—
25C2×Dic302C2×C414yes—
26C22×Dic151—22no—
27Dic604—24no—
28Dic604—24no—
29#14558988—22no—
30#14558988—22no—
31C2×C151⋊C8—22no—
32C22×C4×C151C2311yescharacteristic
33M16×C151—21no—
34M16×C151D412yes—
35C2×C8×C151—21no—
36C2×C8×C151C2×C412yes—
37C2×C8×C151D411yescharacteristic
38C2×C8×C151D411yescharacteristic
39C2×C8×C151D412yes—
40C4⋊C4×C151D412yes—
41C22⋊C4×C151—21no—
42C42×C151—21no—
43Dic302—24no—
44Dic302—24no—
45Dic302—42no—
46Dic302—42no—
47C2×Dic151—24no—
48C2×Dic151—42no—
49C2×Dic151—42no—
50C151⋊C8—42no—
51C23×C151#4111yescharacteristic
52C2×C4×C151—22no—
53C2×C4×C151C22×C411yescharacteristic
54C2×C4×C151C2×D411yescharacteristic
55C2×C4×C151C2×D411yescharacteristic
56C2×C4×C151C2×D411yescharacteristic
57C2×C4×C151C2×D411yescharacteristic
58C2×C4×C151#4111yescharacteristic
59C8×C151—22no—
60C8×C151C22⋊C412yes—
61C8×C151C22⋊C412yes—
62C22×C151—22no—
63C22×C151C4×D411yescharacteristic
64C22×C151#12111yescharacteristic
65C22×C151#12411yescharacteristic
66C4×C151—42no—
67C4×C151C2×C22⋊C411yescharacteristic
68C4×C151C4×D411yescharacteristic
69C4×C151#12111yescharacteristic
70C4×C151#12711yescharacteristic
71Dic151—44no—
72C2×C151—21no—
73C2×C151—21no—
74C2×C151#39011yescharacteristic
75C2×C151#47312yes—
76C151#197911yescharacteristic, complemented, Sylow
77#1979—1511nomaximal, Sylow
78C22×Q16—1511no—
79C2×#108—1511no—
80#419—1512no—
81C2×#101—1512no—
82#405D15111yescharacteristic
83C22×Q8—1512no—
84C2×Q16—3021no—
85C2×Q16—3021no—
86C2×Q16—3022no—
87C2×Q16—1514no—
88C2×M16—1512no—
89C2×M16C2×D15111yescharacteristic
90C22×C8C2×D15111yescharacteristic
91#117C2×D15111yescharacteristic
92#108—3022no—
93#103—3024no—
94#101—3024no—
95#97—21no—
96C4×C8—21no—
97C2×Q8—3022no—
98C2×Q8—3022no—
99C2×Q8—3022no—
100C2×Q8—3022no—
101C2×Q8—3022no—
102C2×Q8—1514no—
103C22×C4—3022no—
104C22×C4C22×D15111yescharacteristic
105Q16—3024no—
106Q16—3024no—
107M16—21no—
108M16—3022no—
109M16—3022no—
110M16D60412yes—
111C2×C8—21no—
112C2×C8—3022no—
113C2×C8C4×D15112yes—
114C2×C8C22⋊D15111yescharacteristic
115C2×C8C22⋊D15111yescharacteristic
116C2×C8D60412yes—
117C4⋊C4D60412yes—
118C22⋊C4—21no—
119C42—21no—
120C23#1455900411yescharacteristic
121Q8—3024no—
122Q8—3024no—
123Q8—6042no—
124Q8—6042no—
125C2×C4—22no—
126C2×C4—3024no—
127C2×C4—6042no—
128C2×C4—6042no—
129C2×C4C2×C4×D15111yescharacteristic
130C2×C4C2×C22⋊D15111yescharacteristic
131C2×C4C2×D60411yescharacteristic
132C2×C4C2×D60411yescharacteristic
133C2×C4C2×D60411yescharacteristic
134C2×C4#1455900411yescharacteristic
135C8—22no—
136C8—6042no—
137C8(C2×D151)⋊C412yes—
138C8(C2×D151)⋊C412yes—
139C22—22no—
140C22C4×D60411yescharacteristic
141C22#1801271311yescharacteristic
142C22#1801272711yescharacteristic
143C4—42no—
144C4—6044no—
145C4C2×(C2×D151)⋊C411yescharacteristic
146C4C4×D60411yescharacteristic
147C4#1801271311yescharacteristic
148C4#1801273611yescharacteristic
149C2—21no—
150C2—21no—
151C2#2375211411yescharacteristic
152C2#2375248712yes—
subgroupG/H
centerC22#18012713
commutatorC2×C4×C151C22×C4
FrattiniC22×C4C22×D151
Fitting#405×C151C2
socleC22×C151#121
prime radicalC23×C151#41
cosocleC22×C4×C151C23
hypercenter#405D151
hypocenterC151#1979
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #405

Complements

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

NH ≅ G/Ntype
10. C2×Dic604C4semidirect
76. C151#1979semidirect

Maximal subgroups

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

subgroupindex
C22×Dic6042
C2×#180126752
#237522202
C2×#180126572
#405×C1512
#1979151