Finite Group Databasebeta

← #24911746

Subgroups — #24911746

Order 10624.

512 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C22×Dic83⋊C4C211yesmaximal, characteristic
2#19127639C212yesmaximal, complemented
3#19127632C212yesmaximal, complemented
4#19127585C214yesmaximal, complemented
5#19127573C212yesmaximal
6#19127564C211yesmaximal, characteristic
7#19127562C212yesmaximal
8C2×#117×C83C211yesmaximal, characteristic
9C23×Dic83C2211yescharacteristic
10C23×Dic83C2211yescharacteristic
11C2×Dic83⋊C4—24no—
12C2×Dic83⋊C4C2214yes—
13C2×Dic83⋊C4C2212yes—
14C2×Dic83⋊C4C2212yes—
15C2×C22⋊Dic83C2212yes—
16C83⋊#95C2214yes—
17C83⋊#95C2214yes—
18C83⋊#95C2212yes—
19C83⋊#95C2212yes—
20C83⋊#95C2214yes—
21C23×C4×C83C2211yescharacteristic
22#117×C83—24no—
23C2×C4⋊C4×C83C2211yescharacteristic
24C2×C4⋊C4×C83C2211yescharacteristic
25C2×C22⋊C4×C83C2212yes—
26C2×C42×C83C2212yes—
27C22×Dic83—22no—
28C22×Dic83—24no—
29C22×Dic83—22no—
30C22×Dic83—24no—
31C22×Dic83C2312yes—
32C22×Dic83C2314yes—
33C22×Dic83C2312yes—
34Dic83⋊C4—24no—
35Dic83⋊C4—24no—
36Dic83⋊C4—28no—
37C22⋊Dic83—24no—
38C24×C83C2311yescharacteristic
39C22×C4×C83—24no—
40C22×C4×C83D414yes—
41C22×C4×C83C2312yes—
42C22×C4×C83C2312yes—
43C22×C4×C83C2311yescharacteristic
44C22×C4×C83C2311yescharacteristic
45C4⋊C4×C83—22no—
46C4⋊C4×C83—22no—
47C22⋊C4×C83—24no—
48C42×C83—24no—
49C23×C83—22no—
50C23×C83—22no—
51C23×C83C2×D412yes—
52C23×C83#4114yes—
53C23×C83C2411yescharacteristic
54C2×C4×C83—28no—
55C2×C4×C83—22no—
56C2×C4×C83—22no—
57C2×C4×C83—22no—
58C2×C4×C83—22no—
59C2×C4×C83—24no—
60C2×C4×C83—24no—
61C2×C4×C83C2×D412yes—
62C2×C4×C83C2×D412yes—
63C2×Dic83—28no—
64C2×Dic83—22no—
65C2×Dic83—22no—
66C2×Dic83—22no—
67C2×Dic83—24no—
68C2×Dic83—24no—
69C2×Dic83—24no—
70C2×Dic83—24no—
71C2×Dic83—44no—
72C2×Dic83#4114yes—
73C22×C83—22no—
74C22×C83—22no—
75C22×C83—28no—
76C22×C83#12314yes—
77C22×C83C22×D411yescharacteristic
78C22×C83C2×#4112yes—
79C22×C83C2×#4112yes—
80C22×C832−1+412yes—
81C4×C83—22no—
82C4×C83—22no—
83C4×C83—42no—
84C4×C83—42no—
85Dic83—24no—
86Dic83—42no—
87Dic83—44no—
88C2×C83—24no—
89C2×C83C2×#12311yescharacteristic
90C2×C83#52511yescharacteristic
91C2×C83#53611yescharacteristic
92C2×C83#55214yes—
93#2484—831nomaximal, Sylow
94C83#248411yescharacteristic, complemented, Sylow
95C2×#117D8311yescharacteristic
96C22×C4⋊C4—831no—
97#400—832no—
98#398—832no—
99#387—834no—
100#385—832no—
101#381—831no—
102#381—832no—
103C23×C4—831no—
104C23×C4—831no—
105C23×C4C2×D8311yescharacteristic
106#117—24no—
107C2×C4⋊C4—832no—
108C2×C4⋊C4—832no—
109C2×C4⋊C4—834no—
110C2×C4⋊C4—1664no—
111C2×C4⋊C4C2×D8311yescharacteristic
112C2×C4⋊C4C2×D8311yescharacteristic
113C2×C22⋊C4—832no—
114C2×C22⋊C4C2×D8312yes—
115C2×C42C2×D8312yes—
116#95—832no—
117#95—834no—
118#95—834no—
119#95—832no—
120#95—834no—
121C24C22×D8311yescharacteristic
122C22×C4—24no—
123C22×C4—832no—
124C22×C4—834no—
125C22×C4—832no—
126C22×C4—1662no—
127C22×C4—1664no—
128C22×C4—1664no—
129C22×C4—1662no—
130C22×C4C22⋊D8314yes—
131C22×C4C22×D8312yes—
132C22×C4C22×D8312yes—
133C22×C4C22×D8311yescharacteristic
134C22×C4C22×D8311yescharacteristic
135C4⋊C4—22no—
136C4⋊C4—22no—
137C4⋊C4—1668no—
138C4⋊C4—1664no—
139C4⋊C4—1664no—
140C22⋊C4—24no—
141C22⋊C4—1664no—
142C42—24no—
143C23—22no—
144C23—22no—
145C23C2×C22⋊D8312yes—
146C23#1305059014yes—
147C23C23×D8311yescharacteristic
148C2×C4—28no—
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—24no—
154C2×C4—24no—
155C2×C4—3324no—
156C2×C4—834no—
157C2×C4—1662no—
158C2×C4—1664no—
159C2×C4—1664no—
160C2×C4—1664no—
161C2×C4—1664no—
162C2×C4—1668no—
163C2×C4—1662no—
164C2×C4—1662no—
165C2×C4C2×C22⋊D8312yes—
166C2×C4C2×C22⋊D8312yes—
167C22—28no—
168C22—22no—
169C22—22no—
170C22#1458177514yes—
171C22C22×C22⋊D8311yescharacteristic
172C22#41×D8312yes—
173C22C2×#1305059012yes—
174C22#1458183912yes—
175C4—22no—
176C4—22no—
177C4—42no—
178C4—42no—
179C4—3324no—
180C4—3322no—
181C4—1664no—
182C2—24no—
183C2C2×#1458177511yescharacteristic
184C2#1912820811yescharacteristic
185C2#1912827211yescharacteristic
186C2#1912838414yes—
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
FittingC2×#117×C83C2
prime radicalC24×C83C23
hypercenterC2×#117D83
hypocenterC83#2484
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #19127639C2semidirect
3. #19127632C2semidirect
4. #19127585C2semidirect
94. C83#2484semidirect

Maximal subgroups

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

subgroupindex
C22×Dic83⋊C42
#191276392
#191276322
#191275852
#191275732
#191275642
#191275622
C2×#117×C832
#248483