Finite Group Databasebeta

← #24918077

Subgroups — #24918077

Order 10624.

362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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#19128320C212yesmaximal, complemented
2#19128099C211yesmaximal, characteristic, complemented
3#19128060C212yesmaximal, complemented
4#19127956C211yesmaximal, characteristic, complemented
5#19127951C211yesmaximal, characteristic
6#19127927C212yesmaximal, complemented
7#19127813C211yesmaximal, characteristic, complemented
8#19127808C211yesmaximal, characteristic, complemented
9SD16×Dic83C212yesmaximal, complemented
10#19127655C211yesmaximal, characteristic, complemented
11#495×C83C211yesmaximal, characteristic, complemented
12C2×#13050573C2211yescharacteristic
13C2×C8×D83C2211yescharacteristic
14#14581792C2212yes—
15#14581785—22no—
16#14581778—22no—
17#14581776—22no—
18#14581769—22no—
19#14581768C2212yes—
20#14581763C2212yes—
21Q8×Dic83C2212yes—
22D4×Dic83C2212yes—
23#14581749C2211yescharacteristic
24#14581724C2211yescharacteristic
25#14581724C2211yescharacteristic
26#14581724C2212yes—
27#14581716C2212yes—
28#14581716C2212yes—
29#14581713C2212yes—
30#14581713C2212yes—
31#14581703C2211yescharacteristic
32#14581702C2211yescharacteristic
33C8×Dic83C2211yescharacteristic
34C2×Q16×C83C2211yescharacteristic
35C2×SD16×C83C2212yes—
36C2×D8×C83C2211yescharacteristic
37#124×C83C2212yes—
38C4×C8×C83C2211yescharacteristic
39C2×Dic166—22no—
40C2×C22⋊D83—22no—
41C22×Dic83—22no—
42C2×C4×D83C2311yescharacteristic
43#13050573—22no—
44C2×C83⋊C8C2311yescharacteristic
45C2×C83⋊C8C2311yescharacteristic
46C8×D83—22no—
47C4⋊Dic83—22no—
48C4⋊Dic83—22no—
49C4⋊Dic83C2312yes—
50C4⋊Dic83C2312yes—
51Dic83⋊C4—22no—
52Dic83⋊C4D412yes—
53C22⋊Dic83—22no—
54C22⋊Dic83—22no—
55(C2×D83)⋊C4—22no—
56(C2×D83)⋊C4D412yes—
57C4×Dic83—22no—
58C4×Dic83C2311yescharacteristic
59C2×Q8×C83C2312yes—
60C2×D4×C83C2312yes—
61Q16×C83—22no—
62SD16×C83—24no—
63D8×C83—22no—
64C2×C8×C83C2311yescharacteristic
65C2×C8×C83C2311yescharacteristic
66C22⋊C4×C83—22no—
67C22⋊C4×C83—22no—
68C42×C83C2311yescharacteristic
69C23×C83—22no—
70C22×D83C2×D411yescharacteristic
71Q8×C83—22no—
72Q8×C83—22no—
73D4×C83—22no—
74D4×C83—22no—
75C2×C4×C83—22no—
76C2×C4×C83C2×D412yes—
77C2×C4×C83C2411yescharacteristic
78C22⋊D83—82no—
79C2×Dic83—22no—
80C2×Dic83—22no—
81C2×Dic83—82no—
82C2×Dic83C2×D412yes—
83C2×Dic83C2×D411yescharacteristic
84C4×D83—21no—
85C4×D83—21no—
86Dic166—82no—
87C8×C83#4112yes—
88C8×C83#4112yes—
89C83⋊C8—21no—
90C83⋊C8—21no—
91C22×C83—42no—
92C22×C83—42no—
93C22×C83—42no—
94C22×C83C22×D411yescharacteristic
95C2×D83—21no—
96C2×D83—22no—
97C4×C83—22no—
98C4×C83—42no—
99C4×C83C2×#4111yescharacteristic
100C4×C83C2×#4111yescharacteristic
101Dic83—21no—
102Dic83—22no—
103Dic83—42no—
104Dic83—42no—
105C2×C83—82no—
106C2×C83#53211yescharacteristic
107C2×C83#57712yes—
108D83—41no—
109#3173—831nomaximal, Sylow
110C83#317311yescharacteristic, complemented, Sylow
111#542—832no—
112#498—831no—
113#495D8311yescharacteristic, complemented
114#489—832no—
115#470—831no—
116#469—831no—
117#465—832no—
118#442—831no—
119#441—831no—
120C4×SD16—832no—
121#405—831no—
122C2×Q16C2×D8311yescharacteristic
123C2×SD16C2×D8312yes—
124C2×D8C2×D8311yescharacteristic
125C2×M16—831no—
126C22×C8—831no—
127C4⋊Q8—832no—
128#126—1662no—
129#124—1662no—
130#124C2×D8312yes—
131#123—1662no—
132C22⋊Q8—832no—
133C22⋊Q8—1662no—
134#121—832no—
135C4×Q8—832no—
136C4×D4—832no—
137#117—831no—
138#106—832no—
139#106—831no—
140#106—831no—
141#103—832no—
142#103—832no—
143#102—832no—
144#102—832no—
145#97—831no—
146#97—831no—
147C4×C8—831no—
148C4×C8C2×D8311yescharacteristic
149C2×Q8—1662no—
150C2×Q8C22×D8312yes—
151C2×D4—1662no—
152C2×D4C22×D8312yes—
153C22×C4—831no—
154C22×C4—1662no—
155Q16—22no—
156SD16—24no—
157D8—22no—
158M16—1662no—
159C2×C8—831no—
160C2×C8—831no—
161C2×C8—1662no—
162C2×C8C22×D8311yescharacteristic
163C2×C8C22×D8311yescharacteristic
164C4⋊C4—832no—
165C4⋊C4—832no—
166C4⋊C4—832no—
167C4⋊C4—1662no—
168C4⋊C4—1662no—
169C4⋊C4—1662no—
170C22⋊C4—22no—
171C22⋊C4—22no—
172C22⋊C4—832no—
173C22⋊C4—1662no—
174C22⋊C4—1662no—
175C22⋊C4—1662no—
176C42—831no—
177C42—1662no—
178C42C22×D8311yescharacteristic
179C23—22no—
180C23—831no—
181Q8—22no—
182Q8—22no—
183Q8—6642no—
184D4—22no—
185D4—22no—
186D4—6642no—
187C2×C4—22no—
188C2×C4—832no—
189C2×C4—831no—
190C2×C4—6642no—
191C2×C4—1662no—
192C2×C4—1662no—
193C2×C4—1661no—
194C2×C4—1661no—
195C2×C4D4×D8312yes—
196C2×C4C23×D8311yescharacteristic
197C8—1661no—
198C8—1661no—
199C8#1305058912yes—
200C8#1305058912yes—
201C22—42no—
202C22—42no—
203C22—42no—
204C22—1661no—
205C22—1662no—
206C22C2×D4×D8311yescharacteristic
207C4—22no—
208C4—42no—
209C4—3322no—
210C4—3322no—
211C4—1661no—
212C4—1662no—
213C4C2×#1305058911yescharacteristic
214C4C2×#1305058911yescharacteristic
215C2—82no—
216C2—3321no—
217C2#1912824911yescharacteristic
218C2#1912850812yes—
subgroupG/H
centerC22C2×D4×D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#495×C83C2
socleC22×C83C22×D4
prime radical#19127951C2
hypercenter#495D83
hypocenterC83#3173
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #19128320C2semidirect
2. #19128099C2semidirect
3. #19128060C2semidirect
4. #19127956C2semidirect
6. #19127927C2semidirect
7. #19127813C2semidirect
8. #19127808C2semidirect
9. SD16×Dic83C2semidirect
10. #19127655C2semidirect
11. #495×C83C2semidirect
110. C83#3173semidirect
113. #495D83semidirect

Maximal subgroups

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

subgroupindex
#191283202
#191280992
#191280602
#191279562
#191279512
#191279272
#191278132
#191278082
SD16×Dic832
#191276552
#495×C832
#317383