Finite Group Databasebeta

← #29577637

Subgroups — #29577637

Order 15616.

434 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 99 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#21456368C211yesmaximal, characteristic
2#21444446C211yesmaximal, characteristic
3#21444330C212yesmaximal
4#21443712C212yesmaximal
5C61×#2371C211yesmaximal, characteristic
6#16840319C2211yescharacteristic
7#16840172C414yescomplemented
8#16840161—22no—
9#16839819C2212yes—
10#16839802—22no—
11C4×#11758194C2211yescharacteristic
12#16839504—22no—
13#16839498—22no—
14#16839498—22no—
15C2×#125×C61C2211yescharacteristic
16C61×#387—22no—
17C61×#387—22no—
18C4×C4⋊C4×C61—22no—
19C61×#376C2212yes—
20C2×#11758194—21no—
21#14519777C2×C412yes—
22#14519769—21no—
23#14519756—22no—
24C4×Dic122—22no—
25#14519736—21no—
26#14519710—24no—
27#14519708—24no—
28C4⋊#92418—22no—
29C22⋊#92418—22no—
30#14519688—22no—
31#14519688C2×C412yes—
32C4×#92418—21no—
33#125×C61—22no—
34#125×C61C2×C412yes—
35#125×C61D412yes—
36C2×C4⋊C4×C61—22no—
37C2×C4⋊C4×C61—22no—
38C2×C4⋊C4×C61D412yes—
39C2×C42×C61—22no—
40C2×C42×C61—22no—
41C2×C42×C61C2311yescharacteristic
42#95×C61—22no—
43#95×C61—22no—
44#95×C61—22no—
45#95×C61D412yes—
46#95×C61D412yes—
47C22×C4×C61—22no—
48C22×C4×C61—22no—
49C22×C4×C61—22no—
50C22×C4×C61C2×D411yescharacteristic
51C22×C4×C61C2×D412yes—
52C2×Dic122—22no—
53C4⋊C4×C61—24no—
54C4⋊C4×C61—24no—
55C4⋊C4×C61—22no—
56C4⋊C4×C61—44no—
57C4⋊C4×C61C22⋊C414yes—
58C42×C61—44no—
59C42×C61—44no—
60C42×C61C22×C411yescharacteristic
61C42×C61C2×D411yescharacteristic
62C42×C61#4112yes—
63C22⋊Dic61—41no—
64C4⋊Dic61—22no—
65C4⋊Dic61—22no—
66#11758196—42no—
67C4×Dic61—41no—
68#11758194—24no—
69C2×#92418—22no—
70C2×#92418—42no—
71C23×C61#12011yescharacteristic
72C2×C4×C61—22no—
73C2×C4×C61—24no—
74C2×C4×C61—24no—
75C2×C4×C61—42no—
76C2×C4×C61—42no—
77C2×C4×C61—42no—
78C2×C4×C61—42no—
79C2×C4×C61—42no—
80C2×C4×C61—42no—
81C2×C4×C61—42no—
82C2×C4×C61—42no—
83C2×C4×C61C2×C22⋊C411yescharacteristic
84C2×C4×C61C4×D412yes—
85C2×C4×C61#12112yes—
86C2×C4×C61#12311yescharacteristic
87C2×Dic61—42no—
88Dic122—82no—
89#92418—24no—
90#92418—82no—
91#9440—611nomaximal, Sylow
92C22×C61—22no—
93C22×C61#38611yescharacteristic
94C22×C61#45612yes—
95C4×C61—21no—
96C4×C61—21no—
97C4×C61—22no—
98C4×C61—22no—
99C4×C61—44no—
100C4×C61—44no—
101C4×C61—82no—
102Dic61—82no—
103#3166—611no—
104#2371D6111yescharacteristic
105#1534—611no—
106#1506—612no—
107#1300—612no—
108C2×C61—22no—
109C2×C61#188611yescharacteristic
110C2×C61#190612yes—
111#533—611no—
112C2×#125C2×D6111yescharacteristic
113#501—614no—
114#499—1222no—
115#432—612no—
116#428—1222no—
117C4×M16—611no—
118#387—22no—
119#387—22no—
120C4×C4⋊C4—22no—
121#376C2×D6112yes—
122#330—1222no—
123#328—1222no—
124#328—1222no—
125C61#944011yescharacteristic, complemented, Sylow
126C2×M16—1221no—
127C4⋊Q8—612no—
128#125—22no—
129#125—1221no—
130#125C4×D6112yes—
131#125D24412yes—
132C22⋊Q8—1222no—
133C4×Q8—1222no—
134#117—1221no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4C22⋊D6112yes—
138C2×C42—22no—
139C2×C42—22no—
140C2×C42C22×D6111yescharacteristic
141#107—1224no—
142#106—1224no—
143C4⋊C8—1222no—
144C22⋊C8—1222no—
145#97—612no—
146#97—1222no—
147C4×C8—1221no—
148#95—22no—
149#95—22no—
150#95—22no—
151#95C22⋊D6112yes—
152#95C22⋊D6112yes—
153C2×Q8—1222no—
154C22×C4—22no—
155C22×C4—22no—
156C22×C4—22no—
157C22×C4C2×C22⋊D6111yescharacteristic
158C22×C4C2×C22⋊D6112yes—
159M16—1224no—
160C2×C8—1222no—
161C2×C8—2442no—
162C4⋊C4—24no—
163C4⋊C4—24no—
164C4⋊C4—22no—
165C4⋊C4—44no—
166C4⋊C4—1222no—
167C4⋊C4—1222no—
168C4⋊C4—2442no—
169C4⋊C4#1175819814yes—
170C22⋊C4—2441no—
171C42—44no—
172C42—44no—
173C42—2441no—
174C42C2×C4×D6111yescharacteristic
175C42C2×D24411yescharacteristic
176C42#1175822212yes—
177C23#1451974611yescharacteristic
178Q8—4882no—
179C2×C4—22no—
180C2×C4—24no—
181C2×C4—24no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—2442no—
191C2×C4C2×#1175819811yescharacteristic
192C2×C4C4×C22⋊D6112yes—
193C2×C4#1451975112yes—
194C2×C4#1451976011yescharacteristic
195C8—1224no—
196C8—4882no—
197C22—22no—
198C22#1683964111yescharacteristic
199C22#1683994512yes—
200C4—21no—
201C4—21no—
202C4—22no—
203C4—22no—
204C4—44no—
205C4—44no—
206C4—82no—
207C4—4882no—
208C2—22no—
209C2#2144621211yescharacteristic
210C2#2144632012yes—
subgroupG/H
centerC22#16839641
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2371C2
socleC22×C61#386
prime radicalC23×C61#120
cosocleC2×C42×C61C23
hypercenter#2371D61
hypocenterC61#9440
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2371

Complements

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

NH ≅ G/Ntype
7. #16840172C4semidirect
125. C61#9440semidirect

Maximal subgroups

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

subgroupindex
#214563682
#214444462
#214443302
#214437122
C61×#23712
#944061