Finite Group Databasebeta

← #30595204

Subgroups — #30595204

Order 15616.

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

normal subgroups only

This group has 286 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#21462112C212yesmaximal
2#21446646C211yesmaximal, characteristic
3#16840748—22no—
4#16840673—22no—
5#16840671C414yescomplemented
6#16840312C2211yescharacteristic
7C2×#14519703—22no—
8C42×Dic61C411yescharacteristic
9C61×#423C411yescharacteristic
10D61⋊M16—42no—
11#14519838—24no—
12#14519837—42no—
13C2×#11758222D412yes—
14#14519777D411yescharacteristic
15#14519774Q811yescharacteristic
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×D244C4⋊C412yes—
33C2×C4×D61—22no—
34C2×Dic122C22⋊C412yes—
35#11758217—44no—
36#11758213—82no—
37D61⋊C8—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×C4×C61—21no—
51C2×C4×C61—21no—
52C2×C4×C61—21no—
53C2×C4×C61—21no—
54C2×C4×C61—42no—
55C2×C4×C61#9511yescharacteristic
56C2×C4×C61#9911yescharacteristic
57C22⋊D61—82no—
58C2×Dic61—22no—
59C2×Dic61—42no—
60C2×Dic61—44no—
61D244—42no—
62D244—82no—
63C4×D61—42no—
64C4×D61—42no—
65Dic122—42no—
66#92420—84no—
67C8×C61—81no—
68#7501—611nomaximal, Sylow
69C22×C61—21no—
70C22×C61—41no—
71C22×C61#34211yescharacteristic
72C2×D61—42no—
73C2×D61—82no—
74C4×C61—22no—
75C4×C61—21no—
76C4×C61—41no—
77C4×C61#35311yescharacteristic
78C4×C61#35411yescharacteristic
79Dic61—44no—
80Dic61—42no—
81#2132—612no—
82#1962—611no—
83C2×C61—21no—
84C2×C61—41no—
85C2×C61#139311yescharacteristic
86D61—82no—
87#532—611no—
88#423#692311yescharacteristic
89C2×#104—1222no—
90#413—1222no—
91C43—611no—
92#356—1222no—
93#355—614no—
94C61#750111yescharacteristic, complemented, Sylow
95C2×#41—612no—
96C2×M16—21no—
97C2×M16—2442no—
98C4⋊Q8—611no—
99#127—611no—
100#124—612no—
101#121—2441no—
102C4×D4—2441no—
103C2×C42—1221no—
104C2×C42—2441no—
105C2×C42C2×#692311yescharacteristic
106C4⋊C8—41no—
107#104—2444no—
108#101—1224no—
109#100—2442no—
110#41—2442no—
111#41—2442no—
112C2×Q8—612no—
113C2×D4—612no—
114C2×D4—1222no—
115C2×D4—2441no—
116C22×C4—21no—
117C22×C4—1222no—
118C22×C4—2441no—
119C22×C4C22⋊#692311yescharacteristic
120M16—42no—
121M16—4882no—
122M16—2444no—
123C2×C8—41no—
124C2×C8—4882no—
125C4⋊C4—2441no—
126C22⋊C4—2442no—
127C42—21no—
128C42—1222no—
129C42—2441no—
130C42—2444no—
131C42C4×#692311yescharacteristic
132C42C4⋊#692311yescharacteristic
133C23—1222no—
134C23#1451983611yescharacteristic
135Q8—2442no—
136D4—4882no—
137D4—4882no—
138D4—2442no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—42no—
144C2×C4—1222no—
145C2×C4—2442no—
146C2×C4—2444no—
147C2×C4—2442no—
148C2×C4—2442no—
149C2×C4(C2×#6923)⋊C411yescharacteristic
150C2×C4#1451983511yescharacteristic
151C8—81no—
152C8—4884no—
153C22—21no—
154C22—41no—
155C22—4882no—
156C22—2442no—
157C22#1684064011yescharacteristic
158C4—22no—
159C4—21no—
160C4—41no—
161C4—2444no—
162C4—2442no—
163C4#1684066611yescharacteristic
164C4#1684066811yescharacteristic
165C2—21no—
166C2—41no—
167C2—4882no—
168C2#2146091411yescharacteristic
subgroupG/H
centerC4#16840668
commutatorC42×C61C42
FrattiniC2×C42C2×#6923
FittingC61×#423C4
socleC2×C61#1393
prime radical, cosocle#16840312C22
hypercenter#423#6923
hypocenterC61#7501
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
5. #16840671C4semidirect
94. C61#7501semidirect

Maximal subgroups

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

subgroupindex
#214621122
#214466462
#750161