Finite Group Databasebeta

← #30599361

Subgroups — #30599361

Order 15616.

398 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 72 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#21461718C212yesmaximal
2#21460722C214yesmaximal
3#21448419C211yesmaximal, characteristic
4#16840732C2214yes—
5#16840642—22no—
6#16840642—22no—
7C22×#11758196C2211yescharacteristic
8#16839646—22no—
9#16839644—22no—
10#16839623C2212yes—
11#16839620C412yes—
12C4×C22⋊Dic61C411yescharacteristic
13C4×C22⋊C4×C61C411yescharacteristic
14C2×#11758217—24no—
15C22⋊#92420—28no—
16C23×Dic61C2×C411yescharacteristic
17C23×Dic61C2311yescharacteristic
18C2×#11758196—24no—
19C2×#11758196—22no—
20C2×#11758196D412yes—
21C2×#11758196D412yes—
22C2×C22⋊Dic61C2×C412yes—
23C2×C4×Dic61—21no—
24#14519684—21no—
25#14519684—22no—
26#14519684—24no—
27C23×C4×C61C2×C411yescharacteristic
28C2×C22⋊C4×C61C2×C412yes—
29C2×C42×C61—21no—
30#95×C61—21no—
31C24×C61C22×C411yescharacteristic
32C22×C4×C61—22no—
33C22×C4×C61—22no—
34C22×C4×C61—81no—
35C22×C4×C61C22⋊C411yescharacteristic
36C22×C4×C61C22⋊C411yescharacteristic
37C22×Dic61—22no—
38C22×Dic61—22no—
39C22×Dic61—42no—
40C22×Dic61—81no—
41C22×Dic61C22⋊C412yes—
42C22×Dic61C2×D412yes—
43C22×Dic61#4114yes—
44#11758217—48no—
45C2×#92420—44no—
46C22⋊C4×C61—42no—
47C42×C61—81no—
48C22⋊Dic61—42no—
49#11758196—24no—
50#11758196—24no—
51#11758196—82no—
52C4×Dic61—81no—
53C23×C61—22no—
54C23×C61—41no—
55C23×C61—41no—
56C23×C61C2×C22⋊C411yescharacteristic
57C23×C61#11712yes—
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61—41no—
61C2×C4×C61—41no—
62C2×C4×C61—42no—
63C2×C4×C61—42no—
64C2×C4×C61—42no—
65C2×C4×C61—82no—
66C2×Dic61—24no—
67C2×Dic61—22no—
68C2×Dic61—44no—
69C2×Dic61—42no—
70C2×Dic61—42no—
71C2×Dic61—42no—
72C2×Dic61—42no—
73C2×Dic61—82no—
74C2×Dic61#12314yes—
75#92420—84no—
76#8755—611nomaximal, Sylow
77C22×C61—21no—
78C22×C61—21no—
79C22×C61—22no—
80C22×C61—22no—
81C22×C61—22no—
82C22×C61—44no—
83C22×C61#38111yescharacteristic
84C22×C61#41012yes—
85C4×C61—41no—
86C4×C61—41no—
87C4×C61—82no—
88Dic61—24no—
89Dic61—42no—
90Dic61—82no—
91#2313—611no—
92#1821—612no—
93#1306—614no—
94C2×C61—22no—
95C2×C61—42no—
96C2×C61#182011yescharacteristic
97C2×C61#182911yescharacteristic
98C2×C61#183011yescharacteristic
99C22×C4⋊C4—611no—
100#407—614no—
101#387—1222no—
102#387—1222no—
103#381—612no—
104#380—612no—
105C4×C22⋊C4—611no—
106C4×C22⋊C4#692311yescharacteristic
107#343—1222no—
108#343—1222no—
109C61#875511yescharacteristic, complemented, Sylow
110C23×C4—611no—
111C23×C4—611no—
112C23×C4C2×#692311yescharacteristic
113C2×M16—1224no—
114C2×C4⋊C4—612no—
115C2×C4⋊C4—612no—
116C2×C4⋊C4—1224no—
117C2×C4⋊C4—1222no—
118C2×C22⋊C4—612no—
119C2×C22⋊C4C2×#692312yes—
120C2×C42—21no—
121C2×C42—1221no—
122C22⋊C8—1228no—
123#95—21no—
124#95—1222no—
125#95—1224no—
126#95—1221no—
127C24C22×#692311yescharacteristic
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—81no—
131C22×C4—612no—
132C22×C4—614no—
133C22×C4—612no—
134C22×C4—1222no—
135C22×C4—1222no—
136C22×C4—4881no—
137C22×C4—2442no—
138C22×C4C22⋊#692311yescharacteristic
139C22×C4C22⋊#692311yescharacteristic
140M16—2448no—
141C2×C8—2444no—
142C4⋊C4—1224no—
143C4⋊C4—1224no—
144C4⋊C4—4882no—
145C22⋊C4—42no—
146C22⋊C4—2442no—
147C42—81no—
148C42—4881no—
149C23—22no—
150C23—41no—
151C23—41no—
152C23C2×C22⋊#692311yescharacteristic
153C23#1451985612yes—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—82no—
162C2×C4—614no—
163C2×C4—1224no—
164C2×C4—1222no—
165C2×C4—4882no—
166C2×C4—2444no—
167C2×C4—2442no—
168C2×C4—2442no—
169C2×C4—2442no—
170C2×C4—2442no—
171C8—4884no—
172C22—21no—
173C22—21no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—44no—
178C22#1684070511yescharacteristic
179C22#1684074112yes—
180C4—41no—
181C4—41no—
182C4—82no—
183C4—1224no—
184C4—4882no—
185C4—2442no—
186C2—22no—
187C2—42no—
188C2#2146171611yescharacteristic
189C2#2146173211yescharacteristic
190C2#2146173311yescharacteristic
subgroupG/H
centerC22#16840705
commutator, prime radicalC24×C61C22×C4
FrattiniC24C22×#6923
FittingC4×C22⋊C4×C61C4
socleC22×C61#381
cosocleC23×Dic61C23
hypercenterC4×C22⋊C4#6923
hypocenterC61#8755
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
109. C61#8755semidirect

Maximal subgroups

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

subgroupindex
#214617182
#214607222
#214484192
#875561