Finite Group Databasebeta

← #30601915

Subgroups — #30601915

Order 15616.

370 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 84 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#21461741C211yesmaximal, characteristic
2#21461253C212yesmaximal
3#21461251C212yesmaximal
4#21461033C211yesmaximal, characteristic
5#21456330C211yesmaximal, characteristic
6#16840780C2211yescharacteristic
7#16840780C2211yescharacteristic
8#16840706C2212yes—
9#16840636—22no—
10#16840616—24no—
11#16840615—24no—
12#92420⋊C8—22no—
13#16840317C2212yes—
14#16840167C411yescharacteristic, complemented
15#16840163—22no—
16#16840158C412yescomplemented
17#16839799—22no—
18C4×C8×D61C2211yescharacteristic
19C61×#500C411yescharacteristic, complemented
20C2×C4⋊#6923—22no—
21#14519844—21no—
22#14519844—21no—
23#14519834D412yes—
24#14519834D412yes—
25C4×#92420—21no—
26C4×#92420—21no—
27(C2×#6923)⋊C4—22no—
28(C2×#6923)⋊C4—22no—
29C2×C8×D61D412yes—
30#14519777C2×C412yes—
31#14519768—22no—
32#14519757—22no—
33#14519753—22no—
34Q8×Dic61—22no—
35#14519742—22no—
36#14519735—22no—
37C42×D61C2311yescharacteristic
38#14519711—22no—
39#14519708—24no—
40C4×#92418C2×C411yescharacteristic
41C8×Dic61D412yes—
42C4⋊Q8×C61C2×C412yes—
43#107×C61—22no—
44C4×C8×C61C2×C411yescharacteristic
45C22×#6923—42no—
46C2×Q8×C61—22no—
47C2×C4×D61C2×D411yescharacteristic
48C2×C4×D61C2×D411yescharacteristic
49C2×C4×D61C2×D411yescharacteristic
50C2×Dic122—22no—
51C2×#92420—22no—
52C2×#92420—22no—
53C4⋊#6923—44no—
54C2×C8×C61C22⋊C412yes—
55C4⋊C4×C61—22no—
56C4⋊C4×C61—22no—
57C42×C61C22×C411yescharacteristic
58#11758198—42no—
59C4⋊Dic61—22no—
60C4⋊Dic61—22no—
61C4⋊Dic61—42no—
62#11758196—42no—
63C4×Dic61—42no—
64C4×Dic61C2×D411yescharacteristic
65C4×Dic61#4111yescharacteristic
66C4×Dic61#4111yescharacteristic
67C2×#92418C22⋊C412yes—
68C8×D61—24no—
69C22×D61#12711yescharacteristic
70C2×#6923—82no—
71C2×#6923—82no—
72C2×#6923—82no—
73Q8×C61—82no—
74C2×C4×C61—42no—
75C2×C4×C61C2×C22⋊C411yescharacteristic
76C2×C4×C61C4×D411yescharacteristic
77C2×C4×C61C4×D411yescharacteristic
78C2×Dic61—42no—
79C2×Dic61#12111yescharacteristic
80C2×Dic61#12111yescharacteristic
81C2×Dic61#12411yescharacteristic
82C4×D61—41no—
83C4×D61—41no—
84C4×D61#13714yes—
85Dic122—82no—
86#92420—42no—
87#92420—42no—
88C8×C61—22no—
89#92418—22no—
90#9759—611nomaximal, Sylow
91C22×C61#39011yescharacteristic
92C2×D61—21no—
93C2×D61—21no—
94C2×D61#49712yes—
95#6923—162no—
96C4×C61—21no—
97C4×C61—21no—
98C4×C61—82no—
99C4×C61#41912yes—
100Dic61—21no—
101Dic61—21no—
102Dic61—82no—
103Dic61#49112yes—
104#3160—611no—
105#1835—611no—
106#1518—612no—
107#1518—612no—
108#1452—611no—
109C2×C61#196011yescharacteristic
110C2×C61#197611yescharacteristic
111C2×C61#197611yescharacteristic
112D61—22no—
113#533—612no—
114#500—611no—
115#500#692311yescharacteristic, complemented
116#499—1222no—
117#498—612no—
118#431—611no—
119#431—611no—
120#427—1222no—
121C2×C4×C8—611no—
122#382—612no—
123#340—1222no—
124#328—1224no—
125#328—1224no—
126#322—1222no—
127C61#975911yescharacteristic, complemented, Sylow
128C22×C8—612no—
129C4⋊Q8—612no—
130C4⋊Q8C2×#692312yes—
131#125—1222no—
132C22⋊Q8—1222no—
133C22⋊Q8—1222no—
134C4×Q8—1222no—
135C4×Q8—1222no—
136#117—1222no—
137C2×C4⋊C4—1222no—
138C2×C42—611no—
139#107—22no—
140#107—1222no—
141#106—1224no—
142C4⋊C8—1221no—
143C4⋊C8—1221no—
144C22⋊C8—612no—
145C22⋊C8—612no—
146C4×C8—612no—
147C4×C8—611no—
148C4×C8—1221no—
149C4×C8—1221no—
150C4×C8C2×#692311yescharacteristic
151#95—1222no—
152#95—1222no—
153C2×Q8—22no—
154C2×Q8—1222no—
155C22×C4—611no—
156C22×C4—611no—
157C22×C4—611no—
158C22×C4—2442no—
159C2×C8—612no—
160C2×C8—1224no—
161C2×C8—1222no—
162C2×C8—1222no—
163C2×C8C22⋊#692312yes—
164C4⋊C4—22no—
165C4⋊C4—22no—
166C4⋊C4—1222no—
167C4⋊C4—1222no—
168C4⋊C4—2442no—
169C4⋊C4—2442no—
170C4⋊C4—2444no—
171C22⋊C4—2442no—
172C42—611no—
173C42—611no—
174C42—611no—
175C42—2442no—
176C42C22×#692311yescharacteristic
177C23—611no—
178Q8—82no—
179Q8—4882no—
180C2×C4—42no—
181C2×C4—611no—
182C2×C4—614no—
183C2×C4—611no—
184C2×C4—611no—
185C2×C4—4882no—
186C2×C4—4882no—
187C2×C4—4882no—
188C2×C4—2441no—
189C2×C4—2441no—
190C2×C4—2442no—
191C2×C4C2×C22⋊#692311yescharacteristic
192C2×C4D4×#692311yescharacteristic
193C2×C4D4×#692311yescharacteristic
194C8—22no—
195C8—1222no—
196C8—2442no—
197C8—2442no—
198C22—612no—
199C22—1221no—
200C22—1221no—
201C22#1684071411yescharacteristic
202C4—21no—
203C4—21no—
204C4—82no—
205C4—612no—
206C4—1221no—
207C4—1221no—
208C4—9762no—
209C4—4882no—
210C4#1684075512yes—
211C2—1222no—
212C2#2146195011yescharacteristic
213C2#2146197611yescharacteristic
214C2#2146197811yescharacteristic
subgroupG/H
centerC22#16840714
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#500C4
socleC22×C61#390
prime radicalC22×D61#127
cosocleC42×D61C23
hypercenter#500#6923
hypocenterC61#9759
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
14. #16840167C4semidirect
16. #16840158C4semidirect
19. C61×#500C4semidirect
115. #500#6923semidirect
127. C61#9759semidirect

Maximal subgroups

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

subgroupindex
#214617412
#214612532
#214612512
#214610332
#214563302
#975961