Finite Group Databasebeta

← #34033052

Subgroups — #34033052

Order 18688.

164 conjugacy classes of subgroups; only the 29 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 29 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#22626971C212yesmaximal
2#22626118C211yesmaximal, characteristic
3#17989686—22no—
4#17989591C2211yescharacteristic
5#17989523C411yescharacteristic
6#17989457—22no—
7#17989143C411yescharacteristic
8#14556687—42no—
9C2×#11924038D412yes—
10C2×C4×#64408—21no—
11C4⋊#10596833—41no—
12(C2×#64408)⋊C4—41no—
13#14556590—21no—
14#14556583C811yescharacteristic
15#14556569—41no—
16#14556556—41no—
17#14556549—21no—
18C42×D73C2×C411yescharacteristic
19#125×C73C811yescharacteristic
20#11924040—82no—
21C22×#64408—41no—
22#11924038—42no—
23C2×#10596833—22no—
24C4×#64408—22no—
25C4×#64408—41no—
26C2×Dic146—41no—
27C2×C4×D73—21no—
28C2×C4×D73C22⋊C411yescharacteristic
29C4⋊Dic73—21no—
30#11924007—41no—
31#11924007—41no—
32#11924005—41no—
33C4×Dic73—21no—
34C4×Dic73—41no—
35C4×Dic73M1611yescharacteristic
36C4⋊C4×C73—21no—
37C4⋊C4×C73—41no—
38C42×C73C2×C811yescharacteristic
39C22×D73#10011yescharacteristic
40C2×#64408—42no—
41C2×#64408—82no—
42C2×C4×C73—21no—
43C2×C4×C73—41no—
44C2×C4×C73C22⋊C811yescharacteristic
45C2×Dic73—21no—
46C2×Dic73—41no—
47C2×Dic73#9911yescharacteristic
48C4×D73—21no—
49C4×D73—21no—
50C4×D73—81no—
51Dic146—82no—
52#10596833—42no—
53C22×C73#32311yescharacteristic
54C2×D73—21no—
55C2×D73—41no—
56#64408—82no—
57C4×C73—21no—
58C4×C73—41no—
59C4×C73—81no—
60Dic73—41no—
61Dic73—81no—
62Dic73#35411yescharacteristic
63Dic73#35611yescharacteristic
64#7360—731nomaximal, Sylow
65C2×C73—21no—
66C2×C73#131911yescharacteristic
67D73—41no—
68#1995—731no—
69#1327—732no—
70C73#736011yescharacteristic, complemented, Sylow
71#533—731no—
72#423—731no—
73#376—731no—
74#349—1462no—
75#339—1462no—
76C2×M16—732no—
77C4⋊Q8—1461no—
78#125—731no—
79#125#1059684211yescharacteristic
80C22⋊Q8—2921no—
81C4×Q8—2921no—
82#117—1461no—
83C2×C42—731no—
84C2×C42—1461no—
85M32—2922no—
86C4⋊C8—2921no—
87#95—2921no—
88C2×Q8—2921no—
89C22×C4—2921no—
90C22×C4—731no—
91C22×C4—1461no—
92M16—2922no—
93C2×C8—1462no—
94C4⋊C4—21no—
95C4⋊C4—41no—
96C4⋊C4—2921no—
97C4⋊C4—2921no—
98C4⋊C4—1461no—
99C22⋊C4—2921no—
100C42—2921no—
101C42—2921no—
102C42—731no—
103C42—1461no—
104C42—1462no—
105C42C2×#1059684211yescharacteristic
106C16—5842no—
107C23—731no—
108Q8—5842no—
109C2×C4—21no—
110C2×C4—41no—
111C2×C4—2922no—
112C2×C4—2921no—
113C2×C4—5841no—
114C2×C4—5842no—
115C2×C4—731no—
116C2×C4—1461no—
117C2×C4—1461no—
118C2×C4—1461no—
119C2×C4C22⋊#1059684211yescharacteristic
120C8—2922no—
121C22—2921no—
122C22—1461no—
123C22#1798967211yescharacteristic
124C4—21no—
125C4—41no—
126C4—81no—
127C4—2921no—
128C4—5841no—
129C4—5842no—
130C4—731no—
131C4—731no—
132C2—21no—
133C2—2921no—
134C2#2262695911yescharacteristic
subgroupG/H
centerC2#22626959
commutatorC42×C73C2×C8
FrattiniC42C2×#10596842
Fitting#125×C73C8
socleC2×C73#1319
prime radicalC22×D73#100
cosocle#17989591C22
hypercenter#125#10596842
hypocenterC73#7360
LCSG ▷ C42×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
70. C73#7360semidirect

Maximal subgroups

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

subgroupindex
#226269712
#226261182
#736073