Finite Group Databasebeta

← #30595201

Subgroups — #30595201

Order 15616.

294 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 46 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#21462092C212yesmaximal
2#21446646C211yesmaximal, characteristic
3#16840741—22no—
4#16840669C414yescomplemented
5#16840667—22no—
6#16840312C2211yescharacteristic
7C2×#14519703—22no—
8C42×Dic61C411yescharacteristic, complemented
9C61×#423C411yescharacteristic, complemented
10#14519856—42no—
11#14519836—24no—
12#14519835—42no—
13C2×#11758222D412yes—
14#14519777Q811yescharacteristic
15#14519774D411yescharacteristic
16#14519765C2×C412yes—
17#14519751—41no—
18C4×D244—41no—
19C2×C4×Dic61—21no—
20C2×C4×Dic61—41no—
21#14519703—44no—
22C2×M16×C61—21no—
23C2×C42×C61C2×C411yescharacteristic
24C4⋊C8×C61—41no—
25C22×C4×C61—21no—
26C22×C4×C61C22⋊C411yescharacteristic
27C2×C22⋊D61—22no—
28C22×Dic61—41no—
29#11758222—42no—
30#11758222—42no—
31C2×D244—41no—
32C2×D244C22⋊C412yes—
33C2×C4×D61—22no—
34C2×Dic122C4⋊C412yes—
35C22⋊#6923—44no—
36C4⋊#6923—82no—
37C4×#6923—82no—
38M16×C61—42no—
39C2×C8×C61—41no—
40C42×C61—21no—
41C42×C61C4211yescharacteristic
42C42×C61C4⋊C411yescharacteristic
43#11758198—42no—
44C4⋊Dic61—41no—
45C4×Dic61—22no—
46C4×Dic61—41no—
47C4×Dic61—44no—
48C23×C61#9911yescharacteristic
49C22×D61—22no—
50C2×#6923—84no—
51C2×C4×C61—21no—
52C2×C4×C61—21no—
53C2×C4×C61—21no—
54C2×C4×C61—21no—
55C2×C4×C61—42no—
56C2×C4×C61#9511yescharacteristic
57C2×C4×C61#9911yescharacteristic
58C22⋊D61—82no—
59C2×Dic61—22no—
60C2×Dic61—42no—
61C2×Dic61—44no—
62D244—42no—
63D244—82no—
64C4×D61—42no—
65C4×D61—42no—
66Dic122—42no—
67C8×C61—81no—
68#7500—611nomaximal, Sylow
69C22×C61—21no—
70C22×C61—41no—
71C22×C61#34211yescharacteristic
72C2×D61—42no—
73C2×D61—82no—
74#6923—164no—
75C4×C61—22no—
76C4×C61—21no—
77C4×C61—41no—
78C4×C61#35311yescharacteristic
79C4×C61#35411yescharacteristic
80Dic61—44no—
81Dic61—42no—
82#2126—612no—
83#1962—611no—
84C2×C61—21no—
85C2×C61—41no—
86C2×C61#139311yescharacteristic
87D61—82no—
88#532—611no—
89#423#692311yescharacteristic, complemented
90C2×#104—1222no—
91#410—1222no—
92C43—611no—
93#354—614no—
94#353—1222no—
95C61#750011yescharacteristic, complemented, Sylow
96C2×#41—612no—
97C2×M16—21no—
98C4⋊Q8—611no—
99#127—611no—
100#124—612no—
101#121—2441no—
102C4×D4—2441no—
103#117—2442no—
104C2×C42—1221no—
105C2×C42—2441no—
106C2×C42C2×#692311yescharacteristic
107C4⋊C8—41no—
108#104—2444no—
109#99—1224no—
110#99—2442no—
111#41—2442no—
112#41—2442no—
113C2×Q8—612no—
114C2×D4—612no—
115C2×D4—1222no—
116C2×D4—2441no—
117C22×C4—21no—
118C22×C4—1222no—
119C22×C4—2441no—
120C22×C4C22⋊#692311yescharacteristic
121M16—42no—
122C2×C8—41no—
123C4⋊C4—4882no—
124C4⋊C4—2441no—
125C22⋊C4—2442no—
126C22⋊C4—2444no—
127C42—21no—
128C42—1222no—
129C42—4882no—
130C42—2441no—
131C42—2444no—
132C42C4×#692311yescharacteristic
133C42C4⋊#692311yescharacteristic
134C23—1222no—
135C23#1451983611yescharacteristic
136Q8—2442no—
137D4—4882no—
138D4—4882no—
139D4—2442no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—42no—
145C2×C4—1222no—
146C2×C4—4884no—
147C2×C4—2442no—
148C2×C4—2444no—
149C2×C4—2442no—
150C2×C4—2442no—
151C2×C4(C2×#6923)⋊C411yescharacteristic
152C2×C4#1451983511yescharacteristic
153C8—81no—
154C22—21no—
155C22—41no—
156C22—4882no—
157C22—2442no—
158C22#1684064011yescharacteristic
159C4—22no—
160C4—21no—
161C4—41no—
162C4—9764no—
163C4—2444no—
164C4—2442no—
165C4#1684066611yescharacteristic
166C4#1684066811yescharacteristic
167C2—21no—
168C2—41no—
169C2—4882no—
170C2#2146091411yescharacteristic
subgroupG/H
centerC4#16840668
commutatorC42×C61C42
FrattiniC2×C42C2×#6923
FittingC61×#423C4
socleC2×C61#1393
prime radical, cosocle#16840312C22
hypercenter#423#6923
hypocenterC61#7500
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
4. #16840669C4semidirect
8. C42×Dic61C4semidirect
9. C61×#423C4semidirect
89. #423#6923semidirect
95. C61#7500semidirect

Maximal subgroups

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

subgroupindex
#214620922
#214466462
#750061