Finite Group Databasebeta

← #24917755

Subgroups — #24917755

Order 10624.

382 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 121 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#19128306C211yesmaximal, characteristic
2#19128178C211yesmaximal, characteristic, complemented
3#19128026C212yesmaximal, complemented
4#19128009C212yesmaximal, complemented
5#19127902C212yesmaximal, complemented
6#19127842C212yesmaximal, complemented
7#19127803C212yesmaximal, complemented
8C4×#13050579C212yesmaximal, complemented
9#433×C83C211yesmaximal, characteristic, complemented
10C22×Dic166C2211yescharacteristic
11C2×#13050579C2212yes—
12C2×#13050579C2212yes—
13#14581789C2211yescharacteristic
14#14581784C2211yescharacteristic
15#14581777—22no—
16#14581766C2212yes—
17#14581765—22no—
18C4×Dic166C2212yes—
19C4×Dic166C2212yes—
20#14581757—22no—
21C4×D332C2212yes—
22#14581751C2211yescharacteristic
23#14581748—22no—
24#14581726C2212yes—
25#14581724C2212yes—
26#14581717C2212yes—
27#14581717C2212yes—
28#14581714C2212yes—
29#14581714C2212yes—
30#117×C83C2211yescharacteristic
31C4⋊C8×C83C2212yes—
32C22⋊C8×C83C2212yes—
33#97×C83C2211yescharacteristic
34C4×C8×C83C2211yescharacteristic
35C2×Dic166—21no—
36C2×Dic166—24no—
37C2×Dic166C2312yes—
38C2×D332—22no—
39C2×D332C2312yes—
40C2×C22⋊D83—22no—
41C22×Dic83—21no—
42C2×C4×D83—22no—
43#13050579—24no—
44#13050579—24no—
45C4⋊Dic83C2312yes—
46C4⋊Dic83C2312yes—
47Dic83⋊C4—22no—
48Dic83⋊C4—22no—
49Dic83⋊C4—22no—
50C22⋊Dic83—21no—
51(C2×D83)⋊C4—22no—
52(C2×D83)⋊C4—22no—
53C4×Dic83—22no—
54C4×Dic83—22no—
55C4×Dic83—21no—
56C22×C4×C83C2311yescharacteristic
57C2×C8×C83C2312yes—
58C2×C8×C83C2312yes—
59C4⋊C4×C83D412yes—
60C22⋊C4×C83D412yes—
61C42×C83C2311yescharacteristic
62C42×C83C2311yescharacteristic
63C23×C83C2×D411yescharacteristic
64C22×D83—22no—
65C2×C4×C83—22no—
66C2×C4×C83C2×D412yes—
67C2×C4×C83C2×D412yes—
68C2×C4×C83C2×D411yescharacteristic
69C2×C4×C83C2411yescharacteristic
70C22⋊D83—82no—
71C2×Dic83—24no—
72C2×Dic83—22no—
73C2×Dic83—22no—
74C2×Dic83—22no—
75D332—22no—
76D332—22no—
77D332—82no—
78C4×D83—82no—
79Dic166—24no—
80Dic166—22no—
81Dic166#4114yes—
82C8×C83—22no—
83C8×C83—22no—
84C22×C83—21no—
85C22×C83—22no—
86C22×C83C22×D411yescharacteristic
87C2×D83—42no—
88C2×D83—42no—
89C2×D83—42no—
90C4×C83—21no—
91C4×C83—22no—
92C4×C83—22no—
93C4×C83C2×#4112yes—
94Dic83—24no—
95Dic83—42no—
96Dic83—42no—
97C2×C83—41no—
98C2×C83#52511yescharacteristic
99C2×C83#57712yes—
100D83—82no—
101#3126—831nomaximal, Sylow
102C83#312611yescharacteristic, complemented, Sylow
103#540—831no—
104#519—831no—
105#482—832no—
106#479—832no—
107#460—832no—
108#448—832no—
109#440—832no—
110C4×SD16—832no—
111#433D8311yescharacteristic, complemented
112C22×Q8—831no—
113C2×SD16—832no—
114C2×SD16—832no—
115#127—831no—
116#125—831no—
117#123—1662no—
118#121—832no—
119#121—1662no—
120C4×Q8—832no—
121C4×Q8—832no—
122C4×Q8—1662no—
123C4×D4—832no—
124#117—831no—
125#117—1662no—
126#117C2×D8311yescharacteristic
127#107—832no—
128#106—832no—
129C4⋊C8C2×D8312yes—
130#103—832no—
131#103—832no—
132#102—832no—
133#102—832no—
134C22⋊C8C2×D8312yes—
135#97C2×D8311yescharacteristic
136C4×C8C2×D8311yescharacteristic
137C2×Q8—832no—
138C2×Q8—1664no—
139C2×Q8—1661no—
140C2×D4—832no—
141C2×D4—1662no—
142C2×D4—1662no—
143C22×C4—1662no—
144C22×C4—1661no—
145C22×C4C22×D8311yescharacteristic
146SD16—1664no—
147SD16—1664no—
148C2×C8C22×D8312yes—
149C2×C8C22×D8312yes—
150C4⋊C4—832no—
151C4⋊C4—832no—
152C4⋊C4—1662no—
153C4⋊C4—1662no—
154C4⋊C4—1662no—
155C4⋊C4D33212yes—
156C22⋊C4—1661no—
157C22⋊C4—1662no—
158C22⋊C4—1662no—
159C22⋊C4D33212yes—
160C42—1661no—
161C42—1662no—
162C42—1662no—
163C42C22×D8311yescharacteristic
164C42C22×D8311yescharacteristic
165C23—1662no—
166C23C2×D33211yescharacteristic
167Q8—834no—
168Q8—1664no—
169Q8—1662no—
170D4—6642no—
171D4—6642no—
172D4—1662no—
173D4—1662no—
174C2×C4—22no—
175C2×C4—6642no—
176C2×C4—1662no—
177C2×C4—1662no—
178C2×C4—1664no—
179C2×C4—1662no—
180C2×C4C2×D33212yes—
181C2×C4C2×D33212yes—
182C2×C4C2×D33211yescharacteristic
183C2×C4C23×D8311yescharacteristic
184C8—22no—
185C8—22no—
186C22—21no—
187C22—22no—
188C22—3322no—
189C22—3322no—
190C22—3322no—
191C22C22×D33211yescharacteristic
192C4—21no—
193C4—22no—
194C4—22no—
195C4—3322no—
196C4—3322no—
197C4—1664no—
198C4#41×D8312yes—
199C2—41no—
200C2—6642no—
201C2#1912821311yescharacteristic
202C2#1912851312yes—
subgroupG/H
centerC22C22×D332
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#433×C83C2
socleC22×C83C22×D4
prime radical#19128306C2
hypercenter#433D83
hypocenterC83#3126
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #19128178C2semidirect
3. #19128026C2semidirect
4. #19128009C2semidirect
5. #19127902C2semidirect
6. #19127842C2semidirect
7. #19127803C2semidirect
8. C4×#13050579C2semidirect
9. #433×C83C2semidirect
102. C83#3126semidirect
111. #433D83semidirect

Maximal subgroups

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

subgroupindex
#191283062
#191281782
#191280262
#191280092
#191279022
#191278422
#191278032
C4×#130505792
#433×C832
#312683