Finite Group Databasebeta

← #24918088

Subgroups — #24918088

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#19128312C211yesmaximal, characteristic, complemented
2#19128305C211yesmaximal, characteristic
3#19128103C211yesmaximal, characteristic, complemented
4#19128069C211yesmaximal, characteristic, complemented
5#19128065C211yesmaximal, characteristic, complemented
6#19127944C212yesmaximal, complemented
7#19127927C212yesmaximal, complemented
8#19127802C212yesmaximal, complemented
9SD16×Dic83C212yesmaximal, complemented
10#19127655C211yesmaximal, characteristic, complemented
11#492×C83C211yesmaximal, characteristic, complemented
12C2×#13050573C2211yescharacteristic
13C2×C8×D83C2211yescharacteristic
14#14581787—22no—
15#14581784C2211yescharacteristic
16#14581784C2211yescharacteristic
17#14581782—22no—
18#14581773—22no—
19#14581768C2212yes—
20#14581764—22no—
21#14581763C2212yes—
22Q8×Dic83C2212yes—
23D4×Dic83C2212yes—
24#14581749C2211yescharacteristic
25#14581726C2212yes—
26#14581724C2212yes—
27#14581716C2212yes—
28#14581716C2212yes—
29#14581713C2212yes—
30#14581713C2212yes—
31#14581703C2211yescharacteristic
32#14581702C2211yescharacteristic
33C8×Dic83C2211yescharacteristic
34C2×SD16×C83C2212yes—
35C2×SD16×C83C2212yes—
36C4⋊Q8×C83C2211yescharacteristic
37#127×C83C2211yescharacteristic
38C4×C8×C83C2211yescharacteristic
39C2×C22⋊D83—22no—
40C22×Dic83—22no—
41C2×C4×D83C2311yescharacteristic
42#13050573—22no—
43C2×C83⋊C8C2311yescharacteristic
44C2×C83⋊C8C2311yescharacteristic
45C8×D83—22no—
46C4⋊Dic83—22no—
47C4⋊Dic83C2312yes—
48C4⋊Dic83C2312yes—
49Dic83⋊C4—22no—
50Dic83⋊C4—22no—
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×C83—22no—
61C2×D4×C83C2312yes—
62SD16×C83—24no—
63SD16×C83—24no—
64C2×C8×C83C2311yescharacteristic
65C2×C8×C83C2311yescharacteristic
66C4⋊C4×C83—22no—
67C42×C83C2311yescharacteristic
68C23×C83—22no—
69C22×D83C2×D411yescharacteristic
70Q8×C83—22no—
71Q8×C83—22no—
72D4×C83—22no—
73D4×C83—22no—
74D4×C83—82no—
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—
86C8×C83#4112yes—
87C8×C83#4112yes—
88C83⋊C8—21no—
89C83⋊C8—21no—
90C22×C83—42no—
91C22×C83—42no—
92C22×C83—42no—
93C22×C83C22×D411yescharacteristic
94C2×D83—21no—
95C2×D83—22no—
96C4×C83—22no—
97C4×C83—42no—
98C4×C83C2×#4111yescharacteristic
99C4×C83C2×#4111yescharacteristic
100Dic83—21no—
101Dic83—22no—
102Dic83—42no—
103Dic83—42no—
104C2×C83—82no—
105C2×C83#53211yescharacteristic
106C2×C83#57712yes—
107D83—41no—
108#3174—831nomaximal, Sylow
109C83#317411yescharacteristic, complemented, Sylow
110#541—831no—
111#540—831no—
112#499—831no—
113#492D8311yescharacteristic, complemented
114#491—831no—
115#490—831no—
116#468—832no—
117#465—832no—
118#440—832no—
119C4×SD16—832no—
120#405—831no—
121C2×SD16C2×D8312yes—
122C2×SD16C2×D8312yes—
123C2×M16—831no—
124C22×C8—831no—
125C4⋊Q8C2×D8311yescharacteristic
126#127C2×D8311yescharacteristic
127#126—1662no—
128#125—831no—
129#125—831no—
130#125—1662no—
131#123—1662no—
132C22⋊Q8—832no—
133#121—832no—
134#121—1662no—
135C4×Q8—832no—
136C4×D4—832no—
137#117—831no—
138#107—832no—
139#106—832no—
140#103—832no—
141#103—832no—
142#102—832no—
143#102—832no—
144#97—831no—
145#97—831no—
146C4×C8—831no—
147C4×C8C2×D8311yescharacteristic
148C2×Q8C22×D8312yes—
149C2×D4—22no—
150C2×D4—1662no—
151C2×D4C22×D8312yes—
152C22×C4—831no—
153C22×C4—1662no—
154SD16—24no—
155SD16—24no—
156M16—1662no—
157C2×C8—831no—
158C2×C8—831no—
159C2×C8—1662no—
160C2×C8C22×D8311yescharacteristic
161C2×C8C22×D8311yescharacteristic
162C4⋊C4—22no—
163C4⋊C4—832no—
164C4⋊C4—832no—
165C4⋊C4—832no—
166C4⋊C4—1662no—
167C4⋊C4—1662no—
168C4⋊C4—1662no—
169C4⋊C4—1662no—
170C22⋊C4—832no—
171C22⋊C4—1662no—
172C22⋊C4—1662no—
173C22⋊C4—1662no—
174C42—831no—
175C42—1662no—
176C42C22×D8311yescharacteristic
177C23—22no—
178C23—831no—
179Q8—22no—
180Q8—22no—
181D4—22no—
182D4—22no—
183D4—82no—
184D4—6642no—
185C2×C4—22no—
186C2×C4—832no—
187C2×C4—831no—
188C2×C4—6642no—
189C2×C4—1662no—
190C2×C4—1662no—
191C2×C4—1661no—
192C2×C4—1661no—
193C2×C4D4×D8312yes—
194C2×C4C23×D8311yescharacteristic
195C8—1661no—
196C8—1661no—
197C8#1305058912yes—
198C8#1305058912yes—
199C22—42no—
200C22—42no—
201C22—42no—
202C22—1661no—
203C22—1662no—
204C22C2×D4×D8311yescharacteristic
205C4—22no—
206C4—42no—
207C4—3322no—
208C4—3322no—
209C4—1661no—
210C4—1662no—
211C4C2×#1305058911yescharacteristic
212C4C2×#1305058911yescharacteristic
213C2—82no—
214C2—3321no—
215C2#1912824911yescharacteristic
216C2#1912850712yes—
subgroupG/H
centerC22C2×D4×D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#492×C83C2
socleC22×C83C22×D4
prime radical#19128305C2
hypercenter#492D83
hypocenterC83#3174
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #19128312C2semidirect
3. #19128103C2semidirect
4. #19128069C2semidirect
5. #19128065C2semidirect
6. #19127944C2semidirect
7. #19127927C2semidirect
8. #19127802C2semidirect
9. SD16×Dic83C2semidirect
10. #19127655C2semidirect
11. #492×C83C2semidirect
109. C83#3174semidirect
113. #492D83semidirect

Maximal subgroups

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

subgroupindex
#191283122
#191283052
#191281032
#191280692
#191280652
#191279442
#191279272
#191278022
SD16×Dic832
#191276552
#492×C832
#317483