Finite Group Databasebeta

← #34001246

Subgroups — #34001246

Order 18688.

126 conjugacy classes of subgroups; only the 22 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 22 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#22625073C211yesmaximal, characteristic
2#22624938C211yesmaximal, characteristic
3#22609260C211yesmaximal, characteristic
4#17989498—21no—
5#17989479—21no—
6C73⋊#564C411yescharacteristic
7#17988996—21no—
8#17988957C2211yescharacteristic
9#17988328—21no—
10#330×C73C411yescharacteristic
11#14556665—41no—
12#14556652—41no—
13#14556591D411yescharacteristic
14#14556583—21no—
15#14556582—41no—
16#14556581—41no—
17#14556581—41no—
18#14556525—41no—
19#14556523—41no—
20#14556514—41no—
21#14556502D411yescharacteristic
22#125×C73C2×C411yescharacteristic
23#97×C73—21no—
24#11924037—81no—
25#11924031—42no—
26C2×Dic146—21no—
27C2×#10596831—21no—
28C4⋊Dic73—21no—
29C4⋊Dic73—21no—
30C4⋊Dic73—41no—
31C4⋊Dic73—41no—
32#11924007—41no—
33#11924007—41no—
34#11924007—41no—
35#11924007—41no—
36C4×Dic73—41no—
37C2×C8×C73—41no—
38C4⋊C4×C73—21no—
39C4⋊C4×C73—41no—
40C42×C73C22⋊C411yescharacteristic
41C2×C4×C73—21no—
42C2×C4×C73—41no—
43C2×C4×C73#9911yescharacteristic
44C2×Dic73—41no—
45C2×Dic73—41no—
46C2×Dic73—41no—
47Dic146—81no—
48#10596833—161no—
49C8×C73—42no—
50#10596831—41no—
51C22×C73AΣL(1,𝔽16)11yescharacteristic
52C4×C73—21no—
53C4×C73—41no—
54C4×C73—81no—
55Dic73—81no—
56Dic73—81no—
57Dic73—81no—
58#7526—731nomaximal, Sylow
59C2×C73—21no—
60C2×C73#140411yescharacteristic
61#1663—731no—
62#1413—731no—
63#1356—731no—
64C73#752611yescharacteristic, complemented, Sylow
65#564—731no—
66#501—1461no—
67#491—731no—
68#356—1461no—
69#347—1461no—
70#330—1461no—
71#330#6440811yescharacteristic
72C4⋊Q8—731no—
73#125—2921no—
74#125—2921no—
75#125—2921no—
76#125—1461no—
77#125C2×#6440811yescharacteristic
78M32—2921no—
79#107—2921no—
80#106—2921no—
81#103—2921no—
82#101—2921no—
83#97—21no—
84#97—731no—
85C2×Q8—1461no—
86M16—5841no—
87C2×C8—41no—
88C2×C8—1461no—
89C4⋊C4—21no—
90C4⋊C4—41no—
91C4⋊C4—2921no—
92C4⋊C4—2921no—
93C4⋊C4—2921no—
94C4⋊C4—2921no—
95C4⋊C4—2921no—
96C4⋊C4—2921no—
97C4⋊C4—1461no—
98C4⋊C4—1461no—
99C42—2921no—
100C42C22⋊#6440811yescharacteristic
101C16—2922no—
102Q8—5841no—
103C2×C4—21no—
104C2×C4—41no—
105C2×C4—2921no—
106C2×C4—2921no—
107C2×C4—2921no—
108C2×C4#1455665011yescharacteristic
109C8—42no—
110C8—2921no—
111C8—11681no—
112C22#1798948811yescharacteristic
113C4—21no—
114C4—41no—
115C4—81no—
116C4—5841no—
117C4—5841no—
118C4—5841no—
119C2—21no—
120C2#2262505511yescharacteristic
subgroupG/H
centerC2#22625055
commutator#125×C73C2×C4
Frattini#125C2×#64408
Fitting#330×C73C4
socleC2×C73#1404
prime radicalC22×C73AΣL(1,𝔽16)
cosocle#17988957C22
hypercenter#330#64408
hypocenterC73#7526
LCSG ▷ #125×C73 ▷ C42×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #125 ◁ #330

Complements

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

NH ≅ G/Ntype
64. C73#7526semidirect

Maximal subgroups

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

subgroupindex
#226250732
#226249382
#226092602
#752673