Finite Group Databasebeta

← #32973820

Subgroups — #32973820

Order 18688.

142 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 25 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#22609069C211yesmaximal, characteristic
2#22607970C211yesmaximal, characteristic
3C73×#1411C211yesmaximal, characteristic
4#17989317C411yescharacteristic
5#17988879—21no—
6#17988408—21no—
7#17988336C411yescharacteristic
8#17988319—21no—
9#494×C73C2211yescharacteristic
10#356×C73—21no—
11#14556590—41no—
12#14556589—41no—
13C4×Dic146—21no—
14#14556556—41no—
15#14556531—41no—
16#14556524—41no—
17C4⋊#10596831—21no—
18#14556514—41no—
19C2×Q16×C73—41no—
20C4⋊Q8×C73C2×C411yescharacteristic
21C4⋊Q8×C73D411yescharacteristic
22#101×C73—41no—
23C4×C8×C73D411yescharacteristic
24C2×Dic146—21no—
25C2×Dic146—41no—
26C2×#10596831—41no—
27C4⋊Dic73—21no—
28#11924007—42no—
29#11924007—41no—
30C4×Dic73—41no—
31C4×Dic73—41no—
32#11924003—81no—
33C2×Q8×C73—21no—
34C2×Q8×C73—21no—
35Q16×C73—81no—
36Q16×C73—81no—
37M16×C73—81no—
38C2×C8×C73—21no—
39C4⋊C4×C73—41no—
40C4⋊C4×C73—41no—
41C42×C73C22⋊C411yescharacteristic
42Q8×C73—81no—
43Q8×C73—81no—
44C2×C4×C73—21no—
45C2×C4×C73—41no—
46C2×C4×C73—41no—
47C2×C4×C73#9911yescharacteristic
48C2×Dic73—41no—
49C2×Dic73—41no—
50Dic146—22no—
51Dic146—41no—
52Dic146—161no—
53C8×C73—21no—
54C8×C73—21no—
55C8×C73—161no—
56#10596831—81no—
57C22×C73AΣL(1,𝔽16)11yescharacteristic
58C4×C73—21no—
59C4×C73—21no—
60C4×C73—21no—
61C4×C73—81no—
62C4×C73—81no—
63Dic73—42no—
64Dic73—81no—
65#7522—731nomaximal, Sylow
66C2×C73—21no—
67C2×C73#140211yescharacteristic
68#1633—731no—
69#1411D7311yescharacteristic
70#1358—731no—
71C73#752211yescharacteristic, complemented, Sylow
72Q82—731no—
73#494C2×D7311yescharacteristic
74#477—1461no—
75#364—1461no—
76#356—21no—
77#333—731no—
78Q8⋊C8—1461no—
79C2×Q16—41no—
80C4⋊Q8—2921no—
81C4⋊Q8—2921no—
82C4⋊Q8C4×D7311yescharacteristic
83C4⋊Q8C22⋊D7311yescharacteristic
84C4×Q8—2921no—
85C4×Q8—1461no—
86M32—2921no—
87#107—2921no—
88C4⋊C8—1461no—
89#103—2921no—
90#101—41no—
91C4×C8D29211yescharacteristic
92C2×Q8—21no—
93C2×Q8—21no—
94C2×Q8—2921no—
95C2×Q8—1461no—
96Q16—81no—
97Q16—81no—
98M16—81no—
99C2×C8—21no—
100C2×C8—2921no—
101C4⋊C4—41no—
102C4⋊C4—41no—
103C4⋊C4—2922no—
104C4⋊C4—2921no—
105C4⋊C4—1461no—
106C42—2921no—
107C42—2921no—
108C42#1192400511yescharacteristic
109C16—5841no—
110Q8—81no—
111Q8—81no—
112Q8—2921no—
113Q8—11681no—
114Q8—1462no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—2921no—
119C2×C4—2921no—
120C2×C4#1455650511yescharacteristic
121C8—21no—
122C8—21no—
123C8—161no—
124C8—5841no—
125C22#1798837311yescharacteristic
126C4—21no—
127C4—21no—
128C4—21no—
129C4—81no—
130C4—81no—
131C4—2922no—
132C4—5841no—
133C2—21no—
134C2#2260807511yescharacteristic
subgroupG/H
centerC2#22608075
commutatorC4⋊Q8×C73C2×C4
Frattini#494C2×D73
FittingC73×#1411C2
socleC2×C73#1402
prime radicalC22×C73AΣL(1,𝔽16)
cosocle#494×C73C22
hypercenter#1411D73
hypocenterC73#7522
LCSG ▷ C4⋊Q8×C73 ▷ C42×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #494 ◁ #1411

Complements

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

NH ≅ G/Ntype
71. C73#7522semidirect

Maximal subgroups

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

subgroupindex
#226090692
#226079702
C73×#14112
#752273