Finite Group Databasebeta

← #34033036

Subgroups — #34033036

Order 18688.

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

normal subgroups only

This group has 178 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#22626961C212yesmaximal
2#22625832C211yesmaximal, characteristic
3#17989685—22no—
4#17989559C411yescharacteristic
5#17989559C2211yescharacteristic
6#17989467—22no—
7C2×#14556548C411yescharacteristic
8#14556687—42no—
9C2×#11924037—21no—
10C2×#11924037D412yes—
11#14556648—41no—
12#14556648—41no—
13C22×C4×D73C2×C411yescharacteristic
14#14556548—41no—
15#14556548—41no—
16C2×#11924007—21no—
17C2×#11924005—21no—
18C2×C4×Dic73C811yescharacteristic
19C2×C42×C73C811yescharacteristic
20#11924040—82no—
21#11924037—42no—
22#11924037—42no—
23C2×#10596833—22no—
24C2×#10596833—41no—
25C23×D73M1611yescharacteristic
26C22×Dic73—21no—
27C22×Dic73C22⋊C411yescharacteristic
28C2×C4×D73—21no—
29C2×C4×D73—21no—
30C2×C4×D73—42no—
31#11924007—41no—
32#11924007—41no—
33#11924005—42no—
34C4×Dic73—41no—
35C22×C4×C73—21no—
36C22×C4×C73C2×C811yescharacteristic
37C42×C73—41no—
38C23×C73C22⋊C811yescharacteristic
39C22×D73—21no—
40C22×D73—41no—
41C22×D73—81no—
42C2×C4×C73—21no—
43C2×C4×C73—41no—
44C2×C4×C73—41no—
45C2×C4×C73—81no—
46C2×Dic73—22no—
47C2×Dic73—41no—
48C2×Dic73—81no—
49C2×Dic73#9911yescharacteristic
50C2×Dic73#10011yescharacteristic
51C4×D73—42no—
52C4×D73—42no—
53#10596833—42no—
54#10596833—81no—
55C22×C73—21no—
56C22×C73—41no—
57C22×C73#32311yescharacteristic
58C2×D73—42no—
59C2×D73—41no—
60C2×D73—82no—
61C4×C73—41no—
62C4×C73—81no—
63Dic73—21no—
64Dic73—81no—
65Dic73#35212yes—
66#7350—731nomaximal, Sylow
67C2×C73—21no—
68C2×C73—41no—
69C2×C73#131711yescharacteristic
70D73—81no—
71#1822—731no—
72#1320—732no—
73C73#735011yescharacteristic, complemented, Sylow
74C2×#117—731no—
75#407—731no—
76#407—731no—
77#349—1462no—
78#343—1462no—
79C23×C4—731no—
80C2×M16—732no—
81C2×M16—1461no—
82#117—2921no—
83#117—2921no—
84C2×C4⋊C4—1461no—
85C2×C22⋊C4—1461no—
86C2×C42—731no—
87C2×C42#1059684211yescharacteristic
88M32—2922no—
89C22⋊C8—2921no—
90C22⋊C8—2921no—
91C24—731no—
92C22×C4—21no—
93C22×C4—2922no—
94C22×C4—731no—
95C22×C4—1461no—
96C22×C4—1461no—
97C22×C4—1461no—
98C22×C4C2×#1059684211yescharacteristic
99M16—2922no—
100M16—2922no—
101C2×C8—2921no—
102C2×C8—1462no—
103C4⋊C4—2921no—
104C4⋊C4—2921no—
105C22⋊C4—2922no—
106C42—41no—
107C42—2921no—
108C16—5842no—
109C23—2921no—
110C23—5841no—
111C23—1461no—
112C23C22⋊#1059684211yescharacteristic
113C2×C4—21no—
114C2×C4—41no—
115C2×C4—41no—
116C2×C4—81no—
117C2×C4—2922no—
118C2×C4—2922no—
119C2×C4—2921no—
120C2×C4—5841no—
121C2×C4—731no—
122C2×C4—731no—
123C2×C4—1462no—
124C8—2922no—
125C8—5841no—
126C22—21no—
127C22—41no—
128C22—2922no—
129C22—2921no—
130C22—5842no—
131C22#1798967211yescharacteristic
132C4—41no—
133C4—81no—
134C4—5841no—
135C4—732no—
136C4—1461no—
137C2—21no—
138C2—41no—
139C2—5841no—
140C2#2262695711yescharacteristic
subgroupG/H
centerC2#22626957
commutatorC22×C4×C73C2×C8
FrattiniC22×C4C2×#10596842
FittingC2×C42×C73C8
socleC2×C73#1317
prime radicalC23×D73M16
cosocle#17989559C22
hypercenterC2×C42#10596842
hypocenterC73#7350
LCSG ▷ C22×C4×C73 ▷ C23×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
73. C73#7350semidirect

Maximal subgroups

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

subgroupindex
#226269612
#226258322
#735073