Finite Group Databasebeta

← #30595220

Subgroups — #30595220

Order 15616.

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

normal subgroups only

This group has 274 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#21446651C211yesmaximal, characteristic
3#16840741—22no—
4#16840669C414yescomplemented
5#16840667—22no—
6#16840312C2211yescharacteristic
7#16839786C411yescharacteristic, complemented
8C2×#14519705—22no—
9C61×#376C411yescharacteristic, complemented
10#14519856—42no—
11#14519836—24no—
12#14519835—42no—
13C2×#11758222D412yes—
14C2×#11758194—21no—
15#14519777Q811yescharacteristic
16#14519774D411yescharacteristic
17#14519765C2×C412yes—
18#14519751—41no—
19C4×D244—41no—
20C4⋊#92418—41no—
21#14519705—44no—
22C2×C42×C61—21no—
23C2×C42×C61C2×C411yescharacteristic
24#95×C61—41no—
25C22×C4×C61—21no—
26C22×C4×C61—41no—
27C22×C4×C61C22⋊C411yescharacteristic
28C2×C22⋊D61—22no—
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—
38C42×C61—21no—
39C42×C61—22no—
40C42×C61—41no—
41C42×C61C4211yescharacteristic
42C42×C61C4⋊C411yescharacteristic
43#11758198—42no—
44C4⋊Dic61—41no—
45#11758194—42no—
46C2×#92418—41no—
47C23×C61#9911yescharacteristic
48C22×D61—22no—
49C2×#6923—84no—
50C2×C4×C61—21no—
51C2×C4×C61—21no—
52C2×C4×C61—21no—
53C2×C4×C61—21no—
54C2×C4×C61—42no—
55C2×C4×C61—81no—
56C2×C4×C61—82no—
57C2×C4×C61#9511yescharacteristic
58C2×C4×C61#9911yescharacteristic
59C22⋊D61—82no—
60C2×Dic61—22no—
61D244—42no—
62D244—82no—
63C4×D61—42no—
64C4×D61—42no—
65Dic122—42no—
66#92418—81no—
67#7506—611nomaximal, Sylow
68C22×C61—21no—
69C22×C61—41no—
70C22×C61#34211yescharacteristic
71C2×D61—42no—
72C2×D61—82no—
73#6923—164no—
74C4×C61—21no—
75C4×C61—41no—
76C4×C61—41no—
77C4×C61—82no—
78C4×C61#35311yescharacteristic
79C4×C61#35411yescharacteristic
80Dic61—42no—
81#2126—612no—
82#1963—611no—
83C2×C61—21no—
84C2×C61—41no—
85C2×C61#139311yescharacteristic
86D61—82no—
87#532—611no—
88#423—611no—
89C2×#104—1222no—
90#410—1222no—
91#376#692311yescharacteristic, complemented
92#354—614no—
93#353—1222no—
94C61#750611yescharacteristic, complemented, Sylow
95C2×#41—612no—
96C2×M16—1221no—
97C4⋊Q8—611no—
98#127—611no—
99#124—612no—
100#121—2441no—
101C4×D4—2441no—
102#117—2442no—
103C2×C42—21no—
104C2×C42C2×#692311yescharacteristic
105C4⋊C8—2441no—
106#104—2444no—
107#99—1224no—
108#99—2442no—
109#95—41no—
110#41—2442no—
111#41—2442no—
112C2×Q8—612no—
113C2×D4—612no—
114C2×D4—1222no—
115C2×D4—2441no—
116C22×C4—21no—
117C22×C4—41no—
118C22×C4—1222no—
119C22×C4C22⋊#692311yescharacteristic
120M16—2442no—
121C2×C8—2441no—
122C4⋊C4—4882no—
123C4⋊C4—2441no—
124C22⋊C4—2442no—
125C22⋊C4—2444no—
126C42—21no—
127C42—22no—
128C42—41no—
129C42—4882no—
130C42C4×#692311yescharacteristic
131C42C4⋊#692311yescharacteristic
132C23—1222no—
133C23#1451983511yescharacteristic
134Q8—2442no—
135D4—4882no—
136D4—4882no—
137D4—2442no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—42no—
143C2×C4—81no—
144C2×C4—82no—
145C2×C4—1222no—
146C2×C4—4884no—
147C2×C4—2442no—
148C2×C4—2442no—
149C2×C4(C2×#6923)⋊C411yescharacteristic
150C2×C4#1451983611yescharacteristic
151C8—4881no—
152C22—21no—
153C22—41no—
154C22—4882no—
155C22—2442no—
156C22#1684064011yescharacteristic
157C4—21no—
158C4—41no—
159C4—41no—
160C4—82no—
161C4—9764no—
162C4—2442no—
163C4#1684066711yescharacteristic
164C4#1684066911yescharacteristic
165C2—21no—
166C2—41no—
167C2—4882no—
168C2#2146091311yescharacteristic
subgroupG/H
centerC4#16840667
commutatorC42×C61C42
FrattiniC2×C42C2×#6923
FittingC61×#376C4
socleC2×C61#1393
prime radical, cosocle#16840312C22
hypercenter#376#6923
hypocenterC61#7506
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ #376

Complements

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

NH ≅ G/Ntype
4. #16840669C4semidirect
7. #16839786C4semidirect
9. C61×#376C4semidirect
91. #376#6923semidirect
94. C61#7506semidirect

Maximal subgroups

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

subgroupindex
#214620922
#214466512
#750661