Finite Group Databasebeta

← #49158417

Subgroups — #49158417

Order 37504.

176 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 61 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#34036525C211yesmaximal, characteristic
2#34036525C211yesmaximal, characteristic
3#34036508C211yesmaximal, characteristic
4#34036480C211yesmaximal, characteristic
5#34036479C211yesmaximal, characteristic
6#34035851C211yesmaximal, characteristic
7#498×C293C211yesmaximal, characteristic
8C2×#17989792—22no—
9#22627624C2211yescharacteristic
10#22627624C2211yescharacteristic
11#22627555—22no—
12#22627555—22no—
13#22627549—22no—
14#22627548—22no—
15C4×#14556873C2211yescharacteristic
16C4×#14556873C2211yescharacteristic
17C4⋊Q8×C293C2211yescharacteristic
18C4⋊Q8×C293C2211yescharacteristic
19#106×C293—22no—
20C4×C8×C293C2211yescharacteristic
21C2×Dic586—21no—
22C2×Dic586—21no—
23#17989792—44no—
24C2×#14556873D412yes—
25C2×#14556873D412yes—
26C4⋊Dic293—21no—
27C4⋊Dic293—21no—
28C4⋊Dic293—21no—
29C4⋊Dic293—21no—
30C2×Q8×C293—21no—
31C2×Q8×C293—21no—
32C2×C8×C293D412yes—
33C4⋊C4×C293—21no—
34C4⋊C4×C293—21no—
35C4⋊C4×C293—21no—
36C4⋊C4×C293—21no—
37C42×C293C2311yescharacteristic
38Dic586—42no—
39Dic586—42no—
40C2×Dic293—41no—
41C2×Dic293—41no—
42#14556873—22no—
43#14556873SD1614yes—
44Q8×C293—42no—
45Q8×C293—42no—
46C2×C4×C293—41no—
47C2×C4×C293—41no—
48C2×C4×C293C2×D411yescharacteristic
49C2×C4×C293C2×D411yescharacteristic
50C2×C4×C293C2×D411yescharacteristic
51C8×C293—22no—
52C22×C293#12711yescharacteristic
53C4×C293—81no—
54C4×C293—81no—
55C4×C293C2×SD1612yes—
56C4×C293#13712yes—
57C4×C293#13712yes—
58Dic293—81no—
59Dic293—81no—
60C2×C293#49211yescharacteristic
61C2×C293#49711yescharacteristic
62C2×C293#49711yescharacteristic
63C293#171611yescharacteristic, complemented, Sylow
64#1716—2931nomaximal, Sylow
65#498—2931no—
66#498—2931no—
67#498D29311yescharacteristic
68#494—2931no—
69#487—2931no—
70#487—2931no—
71#322—2931no—
72C2×Q16—5862no—
73C4⋊Q8—2931no—
74C4⋊Q8—2931no—
75C4⋊Q8C2×D29311yescharacteristic
76C4⋊Q8C2×D29311yescharacteristic
77#106—22no—
78#106—5862no—
79#106—5862no—
80#103—5862no—
81#103—5862no—
82C4×C8—2931no—
83C4×C8—2931no—
84C4×C8C2×D29311yescharacteristic
85C2×Q8—21no—
86C2×Q8—21no—
87C2×Q8—5861no—
88C2×Q8—5861no—
89Q16—11724no—
90C2×C8—2932no—
91C2×C8—2932no—
92C2×C8C22⋊D29312yes—
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—21no—
96C4⋊C4—21no—
97C4⋊C4—5861no—
98C4⋊C4—5861no—
99C4⋊C4—5861no—
100C4⋊C4—5861no—
101C42C22×D29311yescharacteristic
102Q8—42no—
103Q8—42no—
104Q8—11722no—
105Q8—11722no—
106C2×C4—41no—
107C2×C4—41no—
108C2×C4—11721no—
109C2×C4—11721no—
110C2×C4D4×D29311yescharacteristic
111C2×C4D4×D29311yescharacteristic
112C2×C4C2×C22⋊D29311yescharacteristic
113C8—22no—
114C8—2934no—
115C8—5862no—
116C22#2262762011yescharacteristic
117C4—81no—
118C4—81no—
119C4—23441no—
120C4—23441no—
121C4SD16×D29312yes—
122C4#2262765312yes—
123C4#2262765512yes—
124C2#3403650011yescharacteristic
125C2#3403652011yescharacteristic
126C2#3403652111yescharacteristic
subgroupG/H
centerC22#22627620
commutator, cosocleC42×C293C23
FrattiniC42C22×D293
Fitting#498×C293C2
socle, prime radicalC22×C293#127
hypercenter#498D293
hypocenterC293#1716
LCSG ▷ C42×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
63. C293#1716semidirect

Maximal subgroups

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

subgroupindex
#340365252
#340365082
#340364802
#340364792
#340358512
#498×C2932
#1716293