Finite Group Databasebeta

← #24917707

Subgroups — #24917707

Order 10624.

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

normal subgroups only

This group has 418 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, complemented
2#19128175C211yesmaximal, characteristic, complemented
3#19128026C212yesmaximal, complemented
4#19128002C212yesmaximal, complemented
5#19127897C212yesmaximal, complemented
6#19127837C212yesmaximal, complemented
7#19127814C212yesmaximal, complemented
8C4×D664C212yesmaximal, complemented
9#433×C83C211yesmaximal, characteristic, complemented
10C22×D332C2211yescharacteristic
11C2×D664C2212yes—
12C2×D664C2212yes—
13#14581789C2211yescharacteristic, complemented
14#14581784C2211yescharacteristic, complemented
15#14581777—22no—
16#14581766C2212yes—
17#14581765—22no—
18C4×D332C2212yes—
19C4×D332C2212yes—
20C4×D332C2212yescomplemented
21#14581754—22no—
22#14581751C2211yescharacteristic
23C22⋊C4×D83—22no—
24#14581726C2212yescomplemented
25#14581724C2212yescomplemented
26#14581714C2212yes—
27#14581714C2212yes—
28#14581714C2212yescomplemented
29#14581714C2212yescomplemented
30#117×C83C2211yescharacteristic
31C4⋊C8×C83C2212yescomplemented
32C22⋊C8×C83C2212yes—
33#97×C83C2211yescharacteristic, complemented
34C4×C8×C83C2211yescharacteristic, complemented
35C23×D83—21no—
36C2×D332—21no—
37C2×D332—24no—
38C2×D332—22no—
39C2×D332C2312yes—
40C2×D332C2312yes—
41C2×C22⋊D83—22no—
42C2×C4×D83—22no—
43C2×C4×D83—22no—
44C2×C4×D83—22no—
45D664—24no—
46D664—24no—
47C4⋊Dic83C2312yes—
48C4⋊Dic83C2312yes—
49Dic83⋊C4—22no—
50C22⋊Dic83—21no—
51(C2×D83)⋊C4—22no—
52(C2×D83)⋊C4—22no—
53(C2×D83)⋊C4—22no—
54(C2×D83)⋊C4—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—
65C22×D83—24no—
66C22×D83—22no—
67C22×D83—82no—
68C2×C4×C83—22no—
69C2×C4×C83C2×D412yes—
70C2×C4×C83C2×D412yes—
71C2×C4×C83C2×D411yescharacteristic
72C2×C4×C83C2411yescharacteristic
73C22⋊D83—82no—
74C2×Dic83—22no—
75C2×Dic83—22no—
76D332—24no—
77D332—22no—
78D332—22no—
79D332—22no—
80D332—82no—
81D332#4114yes—
82C4×D83—82no—
83C4×D83—82no—
84C4×D83—82no—
85C8×C83—22no—
86C8×C83—22no—
87C22×C83—21no—
88C22×C83—22no—
89C22×C83C22×D411yescharacteristic
90C2×D83—24no—
91C2×D83—42no—
92C2×D83—42no—
93C2×D83—42no—
94C2×D83—42no—
95C2×D83—42no—
96C2×D83—84no—
97C4×C83—21no—
98C4×C83—22no—
99C4×C83—22no—
100C4×C83C2×#4112yes—
101Dic83—42no—
102Dic83—42no—
103C2×C83—41no—
104C2×C83#52511yescharacteristic
105C2×C83#57612yes—
106D83—44no—
107D83—82no—
108#3122—831nomaximal, Sylow
109C83#312211yescharacteristic, complemented, Sylow
110#540—831no—
111#518—831no—
112#482—832no—
113#478—832no—
114#459—832no—
115#447—832no—
116#442—832no—
117C4×D8—832no—
118#433D8311yescharacteristic, complemented
119C22×D4—831no—
120C2×D8—832no—
121C2×D8—832no—
122#127—831no—
123#125—831no—
124#123—1662no—
125#121—832no—
126#121—1662no—
127C4×D4—832no—
128C4×D4—832no—
129C4×D4—832no—
130C4×D4—1662no—
131#117—831no—
132#117C2×D8311yescharacteristic
133C2×C22⋊C4—1662no—
134#107—832no—
135#106—832no—
136C4⋊C8C2×D8312yescomplemented
137#102—832no—
138#102—832no—
139#102—832no—
140#102—832no—
141C22⋊C8C2×D8312yes—
142#97C2×D8311yescharacteristic, complemented
143C4×C8C2×D8311yescharacteristic, complemented
144C24—1661no—
145C2×D4—832no—
146C2×D4—832no—
147C2×D4—1664no—
148C2×D4—1662no—
149C2×D4—1662no—
150C2×D4—1661no—
151C22×C4—1662no—
152C22×C4—1662no—
153C22×C4—1662no—
154C22×C4C22×D8311yescharacteristic
155D8—1664no—
156D8—1664no—
157C2×C8C22×D8312yes—
158C2×C8C22×D8312yes—
159C4⋊C4—832no—
160C4⋊C4—832no—
161C4⋊C4—1662no—
162C4⋊C4D33212yes—
163C22⋊C4—1661no—
164C22⋊C4—1662no—
165C22⋊C4—1662no—
166C22⋊C4—1662no—
167C22⋊C4—1662no—
168C22⋊C4D33212yes—
169C42—1661no—
170C42C22×D8311yescharacteristic
171C42C22×D8311yescharacteristic
172C23—6642no—
173C23—1664no—
174C23—1662no—
175C23—1662no—
176C23C2×D33211yescharacteristic
177D4—834no—
178D4—6642no—
179D4—6642no—
180D4—1664no—
181D4—1662no—
182D4—1662no—
183D4—1662no—
184C2×C4—22no—
185C2×C4—6642no—
186C2×C4—6642no—
187C2×C4—6642no—
188C2×C4—1662no—
189C2×C4—1662no—
190C2×C4C2×D33211yescharacteristic
191C2×C4C2×D33212yes—
192C2×C4C2×D33212yes—
193C2×C4C23×D8311yescharacteristic
194C8—22no—
195C8—22no—
196C22—21no—
197C22—22no—
198C22—3322no—
199C22—3322no—
200C22—3322no—
201C22—3322no—
202C22—3322no—
203C22—6644no—
204C22—1664no—
205C22C22×D33211yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—3322no—
210C4—3322no—
211C4#41×D8312yes—
212C2—41no—
213C2—3324no—
214C2—6642no—
215C2#1912821311yescharacteristic
216C2#1912850612yes—
subgroupG/H
centerC22C22×D332
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#433×C83C2
socleC22×C83C22×D4
hypercenter#433D83
hypocenterC83#3122
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
1. #19128306C2semidirect
2. #19128175C2semidirect
3. #19128026C2semidirect
4. #19128002C2semidirect
5. #19127897C2semidirect
6. #19127837C2semidirect
7. #19127814C2semidirect
8. C4×D664C2semidirect
9. #433×C83C2semidirect
13. #14581789C22semidirect
14. #14581784C22semidirect
20. C4×D332C22semidirect
24. #14581726C22semidirect
25. #14581724C22semidirect
28. #14581714C22semidirect
29. #14581714C22semidirect
31. C4⋊C8×C83C22semidirect
33. #97×C83C22semidirect
34. C4×C8×C83C22semidirect
109. C83#3122semidirect
118. #433D83semidirect
136. C4⋊C8C2×D83semidirect
142. #97C2×D83semidirect
143. C4×C8C2×D83semidirect

Maximal subgroups

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

subgroupindex
#191283062
#191281752
#191280262
#191280022
#191278972
#191278372
#191278142
C4×D6642
#433×C832
#312283