Finite Group Databasebeta

← #24907106

Subgroups — #24907106

Order 10624.

164 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 57 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#19128104C211yesmaximal, characteristic
2#19128097C211yesmaximal, characteristic
3#19128053C211yesmaximal, characteristic
4#19128052C211yesmaximal, characteristic
5#19128051C211yesmaximal, characteristic
6#19127422C211yesmaximal, characteristic
7#487×C83C211yesmaximal, characteristic
8#14581792C2211yescharacteristic
9#14581792C2211yescharacteristic
10#14581725—22no—
11#14581723—22no—
12#14581717—22no—
13#14581716—22no—
14#14581715—22no—
15C4×C83⋊C8C2211yescharacteristic
16C4×C83⋊C8C2211yescharacteristic
17C4⋊Q8×C83C2211yescharacteristic
18C4⋊Q8×C83C2211yescharacteristic
19#103×C83—22no—
20C4×C8×C83C2211yescharacteristic
21C2×Dic166—21no—
22C2×Dic166—21no—
23C2×C83⋊C8D412yes—
24C2×C83⋊C8D412yes—
25C4⋊Dic83—21no—
26C4⋊Dic83—21no—
27C4⋊Dic83—21no—
28C4⋊Dic83—21no—
29C2×Q8×C83—21no—
30C2×Q8×C83—21no—
31C2×C8×C83D412yes—
32C4⋊C4×C83—21no—
33C4⋊C4×C83—21no—
34C4⋊C4×C83—21no—
35C4⋊C4×C83—21no—
36C42×C83C2311yescharacteristic
37Q8×C83—42no—
38Q8×C83—42no—
39C2×C4×C83—41no—
40C2×C4×C83—41no—
41C2×C4×C83C2×D411yescharacteristic
42C2×C4×C83C2×D411yescharacteristic
43C2×C4×C83C2×D411yescharacteristic
44C2×Dic83—41no—
45C2×Dic83—41no—
46Dic166—42no—
47Dic166—42no—
48C8×C83—22no—
49C83⋊C8—22no—
50C83⋊C8—22no—
51C22×C83#12711yescharacteristic
52C4×C83—81no—
53C4×C83—81no—
54C4×C83#13512yes—
55C4×C83#13712yes—
56C4×C83#13712yes—
57Dic83—81no—
58Dic83—81no—
59C2×C83#49511yescharacteristic
60C2×C83#49711yescharacteristic
61C2×C83#49711yescharacteristic
62#1718—831nomaximal, Sylow
63C83#171811yescharacteristic, complemented, Sylow
64#500—831no—
65#498—831no—
66#487—831no—
67#487—831no—
68#487—831no—
69#487D8311yescharacteristic
70#322—831no—
71C4⋊Q8—831no—
72C4⋊Q8—831no—
73C4⋊Q8C2×D8311yescharacteristic
74C4⋊Q8C2×D8311yescharacteristic
75#107—1662no—
76#106—1662no—
77#103—22no—
78#103—1662no—
79#103—1662no—
80#103—1662no—
81C4×C8—831no—
82C4×C8—831no—
83C4×C8C2×D8311yescharacteristic
84C2×Q8—21no—
85C2×Q8—21no—
86C2×Q8—1661no—
87C2×Q8—1661no—
88C2×C8—832no—
89C2×C8—832no—
90C2×C8C22⋊D8312yes—
91C4⋊C4—21no—
92C4⋊C4—21no—
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—1661no—
96C4⋊C4—1661no—
97C4⋊C4—1661no—
98C4⋊C4—1661no—
99C42C22×D8311yescharacteristic
100Q8—42no—
101Q8—42no—
102Q8—3322no—
103Q8—3322no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—3321no—
107C2×C4—3321no—
108C2×C4D4×D8311yescharacteristic
109C2×C4D4×D8311yescharacteristic
110C2×C4C2×C22⋊D8311yescharacteristic
111C8—22no—
112C8—1662no—
113C8—1662no—
114C22#1458178811yescharacteristic
115C4—81no—
116C4—81no—
117C4—6641no—
118C4—6641no—
119C4#1458181212yes—
120C4#1458182112yes—
121C4#1458182412yes—
122C2#1912808311yescharacteristic
123C2#1912809211yescharacteristic
124C2#1912809411yescharacteristic
subgroupG/H
centerC22#14581788
commutator, cosocleC42×C83C23
FrattiniC42C22×D83
Fitting#487×C83C2
socle, prime radicalC22×C83#127
hypercenter#487D83
hypocenterC83#1718
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
63. C83#1718semidirect

Maximal subgroups

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

subgroupindex
#191281042
#191280972
#191280532
#191280522
#191280512
#191274222
#487×C832
#171883