Finite Group Databasebeta

← #24910642

Subgroups — #24910642

Order 10624.

424 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 173 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×#14581790C211yesmaximal, characteristic
2#19127608C211yesmaximal, characteristic
3#19127605C212yesmaximal
4#19127588C212yesmaximal
5#19127585C212yesmaximal
6#19127583C212yesmaximal
7#19127582C212yesmaximal
8#19127568C212yesmaximal
9#391×C83C211yesmaximal, characteristic
10C22×Dic166C2211yescharacteristic
11#14581790C418yescomplemented
12C2×C4⋊Dic83C2211yescharacteristic
13C2×Dic83⋊C4C2212yes—
14C2×Dic83⋊C4C2212yes—
15C2×Dic83⋊C4C2212yes—
16C2×C4×Dic83C2212yes—
17C2×C4×Dic83C2211yescharacteristic
18C2×C4×Dic83C2211yescharacteristic
19C83⋊#95C2212yes—
20C83⋊#95C2212yes—
21C83⋊#95C2212yes—
22C83⋊#95C2212yes—
23C83⋊#95C2212yes—
24C83⋊#95C2212yes—
25C83⋊#95C2212yes—
26C83⋊#95C2212yes—
27C22×Q8×C83C2211yescharacteristic
28C2×C4⋊C4×C83C2211yescharacteristic
29C2×C42×C83C2211yescharacteristic
30#95×C83C2212yes—
31#95×C83C2212yes—
32C2×Dic166—41no—
33C2×Dic166—41no—
34C2×Dic166C2×C414yes—
35C22×Dic83C2312yes—
36C22×Dic83C2312yes—
37C22×Dic83C2312yes—
38C22×Dic83C2312yes—
39C4⋊Dic83—41no—
40Dic83⋊C4—42no—
41Dic83⋊C4C2×C418yes—
42Dic83⋊C4C2×C418yes—
43C4×Dic83—42no—
44C4×Dic83—41no—
45C4×Dic83C2×C414yes—
46C2×Q8×C83—41no—
47C2×Q8×C83—41no—
48C2×Q8×C83C2×C414yes—
49C22×C4×C83C2312yes—
50C22×C4×C83C2312yes—
51C22×C4×C83C2311yescharacteristic
52C22×C4×C83C2311yescharacteristic
53C22×C4×C83C2311yescharacteristic
54C4⋊C4×C83—41no—
55C42×C83—41no—
56C23×C83C2411yescharacteristic
57Q8×C83—44no—
58C2×C4×C83—21no—
59C2×C4×C83—21no—
60C2×C4×C83—21no—
61C2×C4×C83—21no—
62C2×C4×C83—21no—
63C2×C4×C83—21no—
64C2×C4×C83—22no—
65C2×C4×C83—22no—
66C2×C4×C83—22no—
67C2×C4×C83—24no—
68C2×C4×C83—22no—
69C2×C4×C83C22×C412yes—
70C2×C4×C83C22×C412yes—
71C2×C4×C83C22×C412yes—
72C2×Dic83—22no—
73C2×Dic83—22no—
74C2×Dic83—22no—
75C2×Dic83—22no—
76C2×Dic83—22no—
77C2×Dic83—22no—
78C2×Dic83—22no—
79C2×Dic83—22no—
80C2×Dic83—24no—
81C2×Dic83C22×C414yes—
82C2×Dic83C22×C414yes—
83Dic166—44no—
84C22×C83C23×C411yescharacteristic
85C22×C83H(5,𝔽2)11yescharacteristic
86C22×C83H(5,𝔽2)11yescharacteristic
87C22×C832−1+412yes—
88C22×C832−1+412yes—
89C4×C83—22no—
90C4×C83—22no—
91C4×C83—22no—
92C4×C83—42no—
93C4×C83—42no—
94Dic83—24no—
95Dic83—24no—
96Dic83—42no—
97Dic83—42no—
98C2×C83#51811yescharacteristic
99C2×C83#51912yes—
100C2×C83#56311yescharacteristic
101C2×C83#56311yescharacteristic
102C2×C83#56312yes—
103#2381—831nomaximal, Sylow
104C83#238111yescharacteristic, complemented, Sylow
105C2×C4⋊Q8—831no—
106#391—831no—
107#391—832no—
108#391D8311yescharacteristic
109#387—832no—
110#387—832no—
111#387—832no—
112#387—832no—
113#383—832no—
114C22×Q8—831no—
115C22×Q8C2×D8311yescharacteristic
116C4⋊Q8—838no—
117C2×C4⋊C4—832no—
118C2×C4⋊C4—831no—
119C2×C4⋊C4—832no—
120C2×C4⋊C4—832no—
121C2×C4⋊C4C2×D8311yescharacteristic
122C2×C42—832no—
123C2×C42—831no—
124C2×C42—831no—
125C2×C42C2×D8311yescharacteristic
126#95—832no—
127#95—832no—
128#95—832no—
129#95—832no—
130#95—832no—
131#95—832no—
132#95—832no—
133#95—832no—
134#95C2×D8312yes—
135#95C2×D8312yes—
136C2×Q8—41no—
137C2×Q8—41no—
138C2×Q8—3321no—
139C2×Q8—3321no—
140C2×Q8—834no—
141C2×Q8C4×D8314yes—
142C22×C4—832no—
143C22×C4—832no—
144C22×C4—832no—
145C22×C4—832no—
146C22×C4C22×D8312yes—
147C22×C4C22×D8312yes—
148C22×C4C22×D8311yescharacteristic
149C22×C4C22×D8311yescharacteristic
150C22×C4C22×D8311yescharacteristic
151C4⋊C4—41no—
152C4⋊C4—3322no—
153C4⋊C4—3321no—
154C4⋊C4—838no—
155C4⋊C4—838no—
156C42—41no—
157C42—3321no—
158C42—3322no—
159C42—834no—
160C23C23×D8311yescharacteristic
161Q8—44no—
162Q8—3324no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—24no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—834no—
175C2×C4—834no—
176C2×C4—1662no—
177C2×C4—1662no—
178C2×C4—1662no—
179C2×C4—1664no—
180C2×C4—1662no—
181C2×C4—1662no—
182C2×C4—1662no—
183C2×C4—1662no—
184C2×C4—1662no—
185C2×C4C2×C4×D8312yes—
186C2×C4C2×C4×D8312yes—
187C2×C4C2×C4×D8312yes—
188C22C22×C4×D8311yescharacteristic
189C22#1458183711yescharacteristic
190C22#1458183711yescharacteristic
191C22#1458183912yes—
192C22#1458184012yes—
193C4—22no—
194C4—22no—
195C4—22no—
196C4—42no—
197C4—42no—
198C4—3322no—
199C4—3322no—
200C4—1664no—
201C4—1664no—
202C2#1912817411yescharacteristic
203C2#1912817712yes—
204C2#1912845011yescharacteristic
205C2#1912845111yescharacteristic
206C2#1912845212yes—
subgroupG/H
center, FrattiniC23C23×D83
commutatorC22×C83C23×C4
Fitting#391×C83C2
socle, prime radical, cosocleC23×C83C24
hypercenter#391D83
hypocenterC83#2381
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
11. #14581790C4semidirect
104. C83#2381semidirect

Maximal subgroups

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

subgroupindex
C2×#145817902
#191276082
#191276052
#191275882
#191275852
#191275832
#191275822
#191275682
#391×C832
#238183