Finite Group Databasebeta

← #30601916

Subgroups — #30601916

Order 15616.

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

normal subgroups only

This group has 478 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, complemented
2#21461250C214yesmaximal, complemented
3#21461033C211yesmaximal, characteristic, complemented
4#21456248C211yesmaximal, characteristic
5#16840780C2212yes—
6#16840706C2212yes—
7#16840636—22no—
8#16840614—28no—
9#92420⋊C8—22no—
10C2×#14519800—22no—
11#16840313C2212yes—
12#16840147—22no—
13#16840139C411yescharacteristic, complemented
14#16840136C412yescomplemented
15C4×C8×D61C2211yescharacteristic
16C61×#494C411yescharacteristic, complemented
17C2×C4⋊#6923—22no—
18#14519844—22no—
19#14519834D414yes—
20C4×#92420—22no—
21(C2×#6923)⋊C4—24no—
22C2×#11758226—22no—
23#14519800—48no—
24C2×#11758201—24no—
25C2×D488—22no—
26C2×C8×D61D412yes—
27#14519774C2×C412yes—
28#14519766—22no—
29#14519752—24no—
30#14519739—24no—
31C42×D61C2311yescharacteristic
32C4×#92418C2×C411yescharacteristic
33C8×Dic61D412yes—
34C2×Q16×C61—22no—
35C4⋊Q8×C61C2×C412yes—
36C4×C8×C61C2×C411yescharacteristic
37C22×#6923—42no—
38C2×Q8×C61—22no—
39#11758226—48no—
40C2×D244—22no—
41C2×D244—24no—
42C2×D244—42no—
43C2×C4×D61—42no—
44C2×C4×D61C2×D412yes—
45C2×C4×D61C2×D411yescharacteristic
46C2×#92420—24no—
47C4⋊#6923—44no—
48Q16×C61—44no—
49C2×C8×C61C22⋊C412yes—
50C4⋊C4×C61—24no—
51C42×C61C22×C411yescharacteristic
52#11758201—48no—
53#11758198—44no—
54C4×Dic61C2×D411yescharacteristic
55C4×Dic61#4112yes—
56C2×#92418C22⋊C412yes—
57D488—44no—
58C8×D61—24no—
59C22×D61—42no—
60C22×D61#12711yescharacteristic
61C2×#6923—84no—
62C2×#6923—82no—
63Q8×C61—44no—
64C2×C4×C61—42no—
65C2×C4×C61C2×C22⋊C411yescharacteristic
66C2×C4×C61C4×D412yes—
67C2×Dic61#12112yes—
68C2×Dic61#12411yescharacteristic
69D244—44no—
70D244—84no—
71D244—84no—
72C4×D61—42no—
73C4×D61—84no—
74C4×D61AGL(1,ℤ/8)14yes—
75#92420—44no—
76C8×C61—22no—
77#92418—22no—
78#9760—611nomaximal, Sylow
79C22×C61#39011yescharacteristic
80C2×D61—22no—
81C2×D61—82no—
82C2×D61—84no—
83C2×D61#49612yes—
84#6923—162no—
85C4×C61—22no—
86C4×C61—82no—
87C4×C61#41812yes—
88Dic61—22no—
89Dic61#49012yes—
90#3147—611no—
91#1835—611no—
92#1517—614no—
93#1452—611no—
94C2×C61#196111yescharacteristic
95C2×C61#197612yes—
96D61—22no—
97D61—162no—
98C2×#135—1222no—
99#532—612no—
100#495—1222no—
101#494#692311yescharacteristic, complemented
102#493—611no—
103#492—612no—
104#431—612no—
105C2×C4×C8—611no—
106#382—612no—
107#340—1222no—
108#327—1228no—
109#322—1222no—
110C61#976011yescharacteristic, complemented, Sylow
111C2×#41—1222no—
112#135—2448no—
113C2×Q16—22no—
114C2×SD16—1224no—
115C2×D8—1222no—
116C22×C8—612no—
117C4⋊Q8C2×#692312yes—
118#127—612no—
119#124—1222no—
120#121—1224no—
121C4×D4—1224no—
122C2×C4⋊C4—1222no—
123C2×C42—611no—
124C4⋊C8—1222no—
125C22⋊C8—614no—
126C4×C8—612no—
127C4×C8—611no—
128C4×C8—1222no—
129C4×C8C2×#692311yescharacteristic
130#95—1224no—
131#41—2448no—
132C2×Q8—22no—
133C2×D4—1222no—
134C2×D4—1224no—
135C2×D4—2442no—
136C22×C4—611no—
137C22×C4—612no—
138C22×C4—2442no—
139C22×C4—2442no—
140Q16—44no—
141SD16—2448no—
142D8—2444no—
143C2×C8—612no—
144C2×C8—1224no—
145C2×C8—1224no—
146C2×C8C22⋊#692312yes—
147C4⋊C4—24no—
148C4⋊C4—2444no—
149C22⋊C4—2444no—
150C42—611no—
151C42—612no—
152C42C22×#692311yescharacteristic
153C23—611no—
154C23—2442no—
155Q8—44no—
156D4—4884no—
157D4—4884no—
158D4—2444no—
159C2×C4—42no—
160C2×C4—611no—
161C2×C4—614no—
162C2×C4—612no—
163C2×C4—4884no—
164C2×C4—4882no—
165C2×C4—4884no—
166C2×C4—2442no—
167C2×C4C2×C22⋊#692311yescharacteristic
168C2×C4D4×#692312yes—
169C8—22no—
170C8—1222no—
171C8—2444no—
172C22—612no—
173C22—1222no—
174C22—4882no—
175C22—4884no—
176C22#1684071411yescharacteristic
177C4—22no—
178C4—82no—
179C4—612no—
180C4—1222no—
181C4—9762no—
182C4#1684075412yes—
183C2—1222no—
184C2—9762no—
185C2#2146195111yescharacteristic
186C2#2146197812yes—
subgroupG/H
centerC22#16840714
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#494C4
socleC22×C61#390
prime radical#21456248C2
cosocleC42×D61C23
hypercenter#494#6923
hypocenterC61#9760
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
1. #21461741C2semidirect
2. #21461250C2semidirect
3. #21461033C2semidirect
13. #16840139C4semidirect
14. #16840136C4semidirect
16. C61×#494C4semidirect
101. #494#6923semidirect
110. C61#9760semidirect

Maximal subgroups

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

subgroupindex
#214617412
#214612502
#214610332
#214562482
#976061