Finite Group Databasebeta

← #24915530

Subgroups — #24915530

Order 10624.

380 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×#14581784C211yesmaximal, characteristic
2#19127640C212yesmaximal
3#19127639C212yesmaximal
4#19127634C214yesmaximal
5#19127632C212yesmaximal
6#19127631C212yesmaximal
7#19127567C211yesmaximal, characteristic
8C2×#125×C83C211yesmaximal, characteristic
9#14581784—24no—
10C2×C4⋊Dic83C2211yescharacteristic
11C2×C4⋊Dic83C2211yescharacteristic
12C2×C4⋊Dic83C2212yes—
13C2×Dic83⋊C4C2212yes—
14C2×Dic83⋊C4C2212yes—
15C2×Dic83⋊C4C2214yes—
16C83⋊#95C2212yes—
17C83⋊#95C2212yes—
18C83⋊#95C2214yes—
19C83⋊#95C2214yes—
20C83⋊#95C2214yes—
21#125×C83—24no—
22C2×C4⋊C4×C83C2212yes—
23C2×C4⋊C4×C83C2211yescharacteristic
24C2×C4⋊C4×C83C2212yes—
25C2×C4⋊C4×C83C2211yescharacteristic
26C2×C42×C83C2211yescharacteristic
27C22×Dic83C2314yes—
28C22×Dic83C2312yes—
29C22×Dic83C2312yes—
30C4⋊Dic83—22no—
31C4⋊Dic83—22no—
32C4⋊Dic83—42no—
33Dic83⋊C4—24no—
34Dic83⋊C4—24no—
35Dic83⋊C4—44no—
36C22×C4×C83C2312yes—
37C22×C4×C83C2312yes—
38C22×C4×C83C2311yescharacteristic
39C22×C4×C83C2311yescharacteristic
40C22×C4×C83C2311yescharacteristic
41C4⋊C4×C83—22no—
42C4⋊C4×C83—24no—
43C4⋊C4×C83—22no—
44C4⋊C4×C83—24no—
45C42×C83D414yes—
46C23×C83C2411yescharacteristic
47C2×C4×C83—21no—
48C2×C4×C83—22no—
49C2×C4×C83—21no—
50C2×C4×C83—22no—
51C2×C4×C83—22no—
52C2×C4×C83—22no—
53C2×C4×C83—22no—
54C2×C4×C83—24no—
55C2×C4×C83—22no—
56C2×C4×C83C2×D412yes—
57C2×C4×C83C2×D412yes—
58C2×C4×C83C2×D412yes—
59C2×Dic83—22no—
60C2×Dic83—22no—
61C2×Dic83—22no—
62C2×Dic83—24no—
63C2×Dic83—22no—
64C2×Dic83—24no—
65C2×Dic83—24no—
66C2×Dic83—24no—
67C22×C83C22×D411yescharacteristic
68C22×C83H(5,𝔽2)11yescharacteristic
69C22×C832−1+412yes—
70C22×C832−1+411yescharacteristic
71C22×C832−1+412yes—
72C4×C83—22no—
73C4×C83—22no—
74C4×C83—22no—
75C4×C83—42no—
76C4×C83—42no—
77Dic83—42no—
78Dic83—42no—
79Dic83—44no—
80C2×C83#53611yescharacteristic
81C2×C83#53611yescharacteristic
82C2×C83#53711yescharacteristic
83C2×C83#56312yes—
84C2×C83#56412yes—
85#2822—831nomaximal, Sylow
86C83#282211yescharacteristic, complemented, Sylow
87C2×#125—831no—
88C2×#125D8311yescharacteristic
89#400—832no—
90#400—832no—
91#398—832no—
92#398—832no—
93#398—834no—
94#382—831no—
95#125—24no—
96#125—1664no—
97C2×C4⋊C4—832no—
98C2×C4⋊C4—834no—
99C2×C4⋊C4—832no—
100C2×C4⋊C4—831no—
101C2×C4⋊C4—832no—
102C2×C4⋊C4—831no—
103C2×C4⋊C4C2×D8312yes—
104C2×C4⋊C4C2×D8311yescharacteristic
105C2×C4⋊C4C2×D8312yes—
106C2×C4⋊C4C2×D8311yescharacteristic
107C2×C42C2×D8311yescharacteristic
108#95—832no—
109#95—832no—
110#95—834no—
111#95—834no—
112#95—834no—
113C22×C4—834no—
114C22×C4—832no—
115C22×C4—832no—
116C22×C4C22×D8312yes—
117C22×C4C22×D8312yes—
118C22×C4C22×D8311yescharacteristic
119C22×C4C22×D8311yescharacteristic
120C22×C4C22×D8311yescharacteristic
121C4⋊C4—24no—
122C4⋊C4—22no—
123C4⋊C4—24no—
124C4⋊C4—22no—
125C4⋊C4—3324no—
126C4⋊C4—3322no—
127C4⋊C4—1664no—
128C4⋊C4—1664no—
129C4⋊C4—1662no—
130C4⋊C4—1662no—
131C42C22⋊D8314yes—
132C23C23×D8311yescharacteristic
133C2×C4—21no—
134C2×C4—22no—
135C2×C4—21no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—24no—
141C2×C4—22no—
142C2×C4—1662no—
143C2×C4—1662no—
144C2×C4—1664no—
145C2×C4—1662no—
146C2×C4—1664no—
147C2×C4—1662no—
148C2×C4—1664no—
149C2×C4—1664no—
150C2×C4C2×C22⋊D8312yes—
151C2×C4C2×C22⋊D8312yes—
152C2×C4C2×C22⋊D8312yes—
153C22C22×C22⋊D8311yescharacteristic
154C22#1458183811yescharacteristic
155C22#1458183912yes—
156C22#1458183911yescharacteristic
157C22#1458184012yes—
158C4—22no—
159C4—22no—
160C4—22no—
161C4—42no—
162C4—42no—
163C4—3324no—
164C4—3322no—
165C4—3322no—
166C2#1912827211yescharacteristic
167C2#1912827511yescharacteristic
168C2#1912827911yescharacteristic
169C2#1912845512yes—
170C2C83⋊#56412yes—
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, prime radical, cosocleC23×C83C24
FittingC2×#125×C83C2
hypercenterC2×#125D83
hypocenterC83#2822
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
86. C83#2822semidirect

Maximal subgroups

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

subgroupindex
C2×#145817842
#191276402
#191276392
#191276342
#191276322
#191276312
#191275672
C2×#125×C832
#282283