Finite Group Databasebeta

← #24918078

Subgroups — #24918078

Order 10624.

362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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#19128316C212yesmaximal, complemented
2#19128098C211yesmaximal, characteristic, complemented
3#19128084C211yesmaximal, characteristic, complemented
4#19128059C212yesmaximal, complemented
5#19127960C211yesmaximal, characteristic, complemented
6#19127951C211yesmaximal, characteristic
7#19127929C212yesmaximal, complemented
8#19127809C211yesmaximal, characteristic, complemented
9C4×#13050578C212yesmaximal, complemented
10#19127658C211yesmaximal, characteristic, complemented
11#442×C83C211yesmaximal, characteristic, complemented
12C2×Dic332C2211yescharacteristic
13C2×#13050578C2212yes—
14C2×#13050573C2211yescharacteristic
15C2×C8×D83C2211yescharacteristic
16#14581791C2212yes—
17#14581785—22no—
18#14581779C2212yes—
19#14581778—22no—
20#14581775—22no—
21#14581772C2212yes—
22#14581771—22no—
23#14581763C2212yes—
24C4×Dic166C2212yes—
25#14581749C2211yescharacteristic
26#14581724C2211yescharacteristic
27#14581723C2212yes—
28#14581717C2212yes—
29#14581715C2212yes—
30#14581713C2212yes—
31#14581702C2211yescharacteristic
32C4×C83⋊C8C2211yescharacteristic
33C8×Dic83C2211yescharacteristic
34C2×D8×C83C2211yescharacteristic
35C4×D4×C83C2212yes—
36#106×C83C2211yescharacteristic
37#102×C83C2212yes—
38#97×C83C2211yescharacteristic
39C2×Dic166—22no—
40C2×Dic166C2312yes—
41C2×C22⋊D83—22no—
42C2×C4×D83C2311yescharacteristic
43Dic332—22no—
44#13050578—24no—
45#13050573—22no—
46C2×C83⋊C8C2311yescharacteristic
47C2×C83⋊C8C2311yescharacteristic
48C8×D83—22no—
49C4⋊Dic83—22no—
50C4⋊Dic83C2312yes—
51Dic83⋊C4—22no—
52Dic83⋊C4—22no—
53Dic83⋊C4D412yes—
54C22⋊Dic83—22no—
55C22⋊Dic83—22no—
56C22⋊Dic83—22no—
57(C2×D83)⋊C4—22no—
58(C2×D83)⋊C4D412yes—
59C4×Dic83—22no—
60C4×Dic83C2311yescharacteristic
61C2×D4×C83C2312yes—
62C22×C4×C83—22no—
63D8×C83—22no—
64C2×C8×C83C2311yescharacteristic
65C2×C8×C83C2311yescharacteristic
66C4⋊C4×C83C2312yes—
67C22⋊C4×C83—22no—
68C42×C83C2311yescharacteristic
69C23×C83—22no—
70C22×D83C2×D411yescharacteristic
71D4×C83—22no—
72D4×C83—22no—
73C2×C4×C83—22no—
74C2×C4×C83—82no—
75C2×C4×C83C2×D412yes—
76C2×C4×C83C2411yescharacteristic
77C22⋊D83—82no—
78C2×Dic83—22no—
79C2×Dic83—22no—
80C2×Dic83C2×D412yes—
81C2×Dic83C2×D411yescharacteristic
82C4×D83—21no—
83C4×D83—21no—
84Dic166—22no—
85Dic166—22no—
86Dic166—82no—
87C8×C83—21no—
88C8×C83#4112yes—
89C83⋊C8—21no—
90C83⋊C8#4112yes—
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#495—831no—
114#489—832no—
115#470—831no—
116#469—831no—
117#465—832no—
118#442D8311yescharacteristic, complemented
119#441—831no—
120C4×SD16—832no—
121#405—831no—
122C2×Q16—831no—
123C2×SD16—832no—
124C2×D8C2×D8311yescharacteristic
125C2×M16—831no—
126C22×C8—831no—
127C4⋊Q8—832no—
128#126—1662no—
129#124—832no—
130#124—1662no—
131#123—1662no—
132C22⋊Q8—832no—
133C22⋊Q8—1662no—
134#121—832no—
135C4×Q8—832no—
136C4×D4C2×D8312yes—
137#117—831no—
138#106—831no—
139#106—832no—
140#106C2×D8311yescharacteristic
141#103—832no—
142#103—832no—
143#102—832no—
144#102C2×D8312yes—
145#97—831no—
146#97C2×D8311yescharacteristic
147C4×C8—831no—
148C4×C8—831no—
149C2×Q8—832no—
150C2×Q8—1662no—
151C2×D4—1662no—
152C2×D4C22×D8312yes—
153C22×C4—22no—
154C22×C4—831no—
155Q16—1662no—
156SD16—1664no—
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—1662no—
167C4⋊C4—1662no—
168C4⋊C4—1662no—
169C4⋊C4C22×D8312yes—
170C22⋊C4—22no—
171C22⋊C4—832no—
172C22⋊C4—1662no—
173C22⋊C4—1662no—
174C22⋊C4—1662no—
175C22⋊C4—1662no—
176C42—831no—
177C42—1662no—
178C42C22×D8311yescharacteristic
179C23—22no—
180C23—831no—
181Q8—6642no—
182Q8—1662no—
183Q8—1662no—
184D4—22no—
185D4—22no—
186D4—6642no—
187C2×C4—22no—
188C2×C4—82no—
189C2×C4—832no—
190C2×C4—831no—
191C2×C4—1662no—
192C2×C4—1662no—
193C2×C4—1661no—
194C2×C4—1661no—
195C2×C4D4×D8312yes—
196C2×C4C23×D8311yescharacteristic
197C8—21no—
198C8—832no—
199C8—1661no—
200C8#1305059012yes—
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—
213C4#41×D8311yescharacteristic
214C4C2×#1305059011yescharacteristic
215C2—82no—
216C2—3321no—
217C2#1912824811yescharacteristic
218C2#1912851112yes—
subgroupG/H
centerC22C2×D4×D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#442×C83C2
socleC22×C83C22×D4
prime radical#19127951C2
hypercenter#442D83
hypocenterC83#3173
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #19128316C2semidirect
2. #19128098C2semidirect
3. #19128084C2semidirect
4. #19128059C2semidirect
5. #19127960C2semidirect
7. #19127929C2semidirect
8. #19127809C2semidirect
9. C4×#13050578C2semidirect
10. #19127658C2semidirect
11. #442×C83C2semidirect
110. C83#3173semidirect
118. #442D83semidirect

Maximal subgroups

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

subgroupindex
#191283162
#191280982
#191280842
#191280592
#191279602
#191279512
#191279292
#191278092
C4×#130505782
#191276582
#442×C832
#317383