Finite Group Databasebeta

← #24907138

Subgroups — #24907138

Order 10624.

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#19128104C211yesmaximal, characteristic
2#19128104C211yesmaximal, characteristic
3#19128097C211yesmaximal, characteristic
4#19128053C211yesmaximal, characteristic
5#19128052C211yesmaximal, characteristic
6#19127423C211yesmaximal, characteristic
7#494×C83C211yesmaximal, characteristic
8#14581792C2211yescharacteristic
9#14581792C2211yescharacteristic
10#14581725—22no—
11#14581725—22no—
12#14581723—22no—
13#14581717—22no—
14#14581715—22no—
15C4×C83⋊C8C2211yescharacteristic
16C4×C83⋊C8C2211yescharacteristic
17C2×Q16×C83—22no—
18C4⋊Q8×C83C2211yescharacteristic
19C4⋊Q8×C83C2211yescharacteristic
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—
31Q16×C83—44no—
32C2×C8×C83D412yes—
33C4⋊C4×C83—21no—
34C4⋊C4×C83—21no—
35C4⋊C4×C83—21no—
36C4⋊C4×C83—21no—
37C42×C83C2311yescharacteristic
38Q8×C83—42no—
39Q8×C83—42no—
40C2×C4×C83—41no—
41C2×C4×C83—41no—
42C2×C4×C83C2×D411yescharacteristic
43C2×C4×C83C2×D411yescharacteristic
44C2×C4×C83C2×D411yescharacteristic
45C2×Dic83—41no—
46C2×Dic83—41no—
47Dic166—42no—
48Dic166—42no—
49C8×C83—22no—
50C83⋊C8—22no—
51C83⋊C8Q1614yescomplemented
52C22×C83#12711yescharacteristic
53C4×C83—81no—
54C4×C83—81no—
55C4×C83C2×Q1612yes—
56C4×C83AGL(1,ℤ/8)12yes—
57C4×C83#13712yes—
58Dic83—81no—
59Dic83—81no—
60C2×C83#49411yescharacteristic
61C2×C83#49611yescharacteristic
62C2×C83#49711yescharacteristic
63#1723—831nomaximal, Sylow
64C83#172311yescharacteristic, complemented, Sylow
65#500—831no—
66#500—831no—
67#498—831no—
68#494D8311yescharacteristic
69#487—831no—
70#487—831no—
71#322—831no—
72C2×Q16—22no—
73C4⋊Q8—831no—
74C4⋊Q8—831no—
75C4⋊Q8C2×D8311yescharacteristic
76C4⋊Q8C2×D8311yescharacteristic
77#107—1662no—
78#107—1662no—
79#106—1662no—
80#103—1662no—
81#103—1662no—
82C4×C8—831no—
83C4×C8—831no—
84C4×C8C2×D8311yescharacteristic
85C2×Q8—21no—
86C2×Q8—21no—
87C2×Q8—1661no—
88C2×Q8—1661no—
89Q16—44no—
90C2×C8—832no—
91C2×C8—832no—
92C2×C8C22⋊D8312yes—
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—21no—
96C4⋊C4—21no—
97C4⋊C4—1661no—
98C4⋊C4—1661no—
99C4⋊C4—1661no—
100C4⋊C4—1661no—
101C42C22×D8311yescharacteristic
102Q8—42no—
103Q8—42no—
104Q8—3322no—
105Q8—3322no—
106C2×C4—41no—
107C2×C4—41no—
108C2×C4—3321no—
109C2×C4—3321no—
110C2×C4D4×D8311yescharacteristic
111C2×C4D4×D8311yescharacteristic
112C2×C4C2×C22⋊D8311yescharacteristic
113C8—22no—
114C8—834no—
115C8—1662no—
116C22#1458178811yescharacteristic
117C4—81no—
118C4—81no—
119C4—6641no—
120C4—6641no—
121C4Q16×D8312yes—
122C4#1458181812yes—
123C4#1458182412yes—
124C2#1912807911yescharacteristic
125C2#1912808811yescharacteristic
126C2#1912809411yescharacteristic
subgroupG/H
centerC22#14581788
commutator, cosocleC42×C83C23
FrattiniC42C22×D83
Fitting#494×C83C2
socle, prime radicalC22×C83#127
hypercenter#494D83
hypocenterC83#1723
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
51. C83⋊C8Q16semidirect
64. C83#1723semidirect

Maximal subgroups

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

subgroupindex
#191281042
#191280972
#191280532
#191280522
#191274232
#494×C832
#172383