Finite Group Databasebeta

← #24906504

Subgroups — #24906504

Order 10624.

202 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 53 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#19128332C211yesmaximal, characteristic
2#19128036C212yesmaximal
3#19127437C212yesmaximal
4#19127427C211yesmaximal, characteristic
5#400×C83C211yesmaximal, characteristic
6#14581791—22no—
7#14581783—22no—
8#14581771—21no—
9#14581771C2212yes—
10#14581751—21no—
11#14581725—22no—
12#14581715—22no—
13C22⋊(C83⋊C8)C2212yes—
14C2×C4⋊C4×C83C2211yescharacteristic
15C2×C4⋊C4×C83C2211yescharacteristic
16#95×C83—21no—
17#95×C83—21no—
18#95×C83C2211yescharacteristic
19C2×Dic166—21no—
20C2×Dic166D412yes—
21C2×C83⋊C8—22no—
22C4⋊Dic83—21no—
23C4⋊Dic83—21no—
24C4⋊Dic83—21no—
25C4⋊Dic83D412yes—
26Dic83⋊C4—22no—
27Dic83⋊C4—22no—
28C22⋊Dic83—22no—
29C4×Dic83—22no—
30C22×C4×C83—21no—
31C22×C4×C83—21no—
32C22×C4×C83D411yescharacteristic
33C22×C4×C83D411yescharacteristic
34C22×C4×C83C2311yescharacteristic
35C4⋊C4×C83—22no—
36C4⋊C4×C83—22no—
37C23×C83C2×D411yescharacteristic
38C2×C4×C83—21no—
39C2×C4×C83—21no—
40C2×C4×C83—21no—
41C2×C4×C83—41no—
42C2×C4×C83—41no—
43C2×C4×C83—41no—
44C2×C4×C83—41no—
45C2×C4×C83—42no—
46C2×C4×C83—41no—
47C2×C4×C83—41no—
48C2×C4×C83Q1612yes—
49C2×C4×C83C2×D412yes—
50C2×Dic83—22no—
51C2×Dic83—22no—
52Dic166—42no—
53Dic166—81no—
54C83⋊C8—42no—
55C22×C83—21no—
56C22×C83—21no—
57C22×C83#12011yescharacteristic
58C22×C83C2×Q1611yescharacteristic
59C22×C83#13711yescharacteristic
60C4×C83—22no—
61C4×C83—22no—
62C4×C83—41no—
63C4×C83—81no—
64C4×C83—81no—
65Dic83—42no—
66Dic83—42no—
67C2×C83—21no—
68C2×C83—21no—
69C2×C83#45111yescharacteristic
70C2×C83#45411yescharacteristic
71C2×C83#45811yescharacteristic
72#1617—831nomaximal, Sylow
73C83#161711yescharacteristic, complemented, Sylow
74#544—831no—
75#484—832no—
76#400D8311yescharacteristic
77#328—832no—
78#324—831no—
79C4⋊Q8—1662no—
80#125—1662no—
81C22⋊Q8—832no—
82C22⋊Q8—1661no—
83#117—1661no—
84C2×C4⋊C4C2×D8311yescharacteristic
85C2×C4⋊C4C2×D8311yescharacteristic
86#107—1662no—
87#103—1662no—
88C22⋊C8—832no—
89#95—21no—
90#95—21no—
91#95C2×D8311yescharacteristic
92C2×Q8—832no—
93C2×Q8—1661no—
94C22×C4—21no—
95C22×C4—21no—
96C22×C4C22⋊D8311yescharacteristic
97C22×C4C22⋊D8311yescharacteristic
98C22×C4C22×D8311yescharacteristic
99C2×C8—1662no—
100C4⋊C4—22no—
101C4⋊C4—22no—
102C4⋊C4—832no—
103C4⋊C4—1661no—
104C4⋊C4—1661no—
105C4⋊C4—1661no—
106C4⋊C4—1662no—
107C4⋊C4—1662no—
108C22⋊C4—1662no—
109C42—1662no—
110C23C2×C22⋊D8311yescharacteristic
111Q8—3322no—
112Q8—6641no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—42no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—1662no—
124C2×C4—1662no—
125C2×C4#1305058012yes—
126C2×C4D4×D8312yes—
127C8—3322no—
128C22—21no—
129C22—21no—
130C22#1458176011yescharacteristic
131C22C2×#1305058011yescharacteristic
132C22#1458182211yescharacteristic
133C4—22no—
134C4—22no—
135C4—41no—
136C4—81no—
137C4—81no—
138C4—3322no—
139C4—3322no—
140C2—21no—
141C2—21no—
142C2#1912785611yescharacteristic
143C2#1912787311yescharacteristic
144C2#1912789011yescharacteristic
subgroupG/H
centerC22#14581760
commutator, cosocleC22×C4×C83C23
FrattiniC22×C4C22×D83
Fitting#400×C83C2
socleC22×C83#120
prime radicalC23×C83C2×D4
hypercenter#400D83
hypocenterC83#1617
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ #400

Complements

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

NH ≅ G/Ntype
73. C83#1617semidirect

Maximal subgroups

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

subgroupindex
#191283322
#191280362
#191274372
#191274272
#400×C832
#161783