Finite Group Databasebeta

← #30595198

Subgroups — #30595198

Order 15616.

272 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 50 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
1C2×#16840673C212yesmaximal
2#21446620C211yesmaximal, characteristic
3C2×#14519838—22no—
4#16840673—22no—
5#16840673C414yescomplemented
6C2×#14519777C2211yescharacteristic
7C2×#14519700—22no—
8C2×C4×#92418C411yescharacteristic
9C61×#384C411yescharacteristic
10C2×#11758217—42no—
11#14519838—24no—
12#14519838—42no—
13C22×Dic122D412yes—
14C22×#92418—21no—
15#14519777—41no—
16#14519777C2×C412yes—
17#14519777D411yescharacteristic
18#14519777Q811yescharacteristic
19C2×C4⋊Dic61—41no—
20#14519700—44no—
21C4×#92418—41no—
22C2×C4⋊C4×C61—21no—
23C2×C4⋊C4×C61—41no—
24C2×C42×C61C2×C411yescharacteristic
25C22×C4×C61—21no—
26C22×C4×C61—41no—
27C22×C4×C61C22⋊C411yescharacteristic
28C22×Dic61—22no—
29C2×Dic122—22no—
30C2×Dic122—42no—
31C2×Dic122—42no—
32C2×Dic122C22⋊C412yes—
33C2×Dic122C4⋊C412yes—
34#11758217—44no—
35#11758217—82no—
36C2×#92420—82no—
37C4⋊C4×C61—42no—
38C4⋊C4×C61—82no—
39C42×C61—21no—
40C42×C61C4211yescharacteristic
41C42×C61C4⋊C411yescharacteristic
42C4⋊Dic61—42no—
43C4⋊Dic61—41no—
44C4⋊Dic61—41no—
45C2×#92418—22no—
46C2×#92418—41no—
47C2×#92418—41no—
48C23×C61#9911yescharacteristic
49C2×C4×C61—22no—
50C2×C4×C61—22no—
51C2×C4×C61—21no—
52C2×C4×C61—21no—
53C2×C4×C61—21no—
54C2×C4×C61—21no—
55C2×C4×C61—82no—
56C2×C4×C61—81no—
57C2×C4×C61#9511yescharacteristic
58C2×C4×C61#9911yescharacteristic
59C2×Dic61—22no—
60C2×Dic61—22no—
61C2×Dic61—42no—
62C2×Dic61—42no—
63Dic122—42no—
64Dic122—42no—
65Dic122—82no—
66#92420—84no—
67#92418—42no—
68#7499—611nomaximal, Sylow
69C22×C61—21no—
70C22×C61—21no—
71C22×C61#34211yescharacteristic
72C22×C61#35311yescharacteristic
73C22×C61#35411yescharacteristic
74C4×C61—22no—
75C4×C61—22no—
76C4×C61—21no—
77C4×C61—21no—
78C4×C61—161no—
79Dic61—42no—
80Dic61—42no—
81C2×#356—612no—
82#1956—611no—
83C2×C61—21no—
84C2×C61—21no—
85C2×C61#139311yescharacteristic
86C2×C61#141011yescharacteristic
87C2×C61#141111yescharacteristic
88C2×C4⋊Q8—611no—
89C2×#103—1222no—
90C2×#101—1222no—
91C2×C4×C8—611no—
92#384#692311yescharacteristic
93#356—614no—
94#356—1222no—
95C61#749911yescharacteristic, complemented, Sylow
96C22×Q8—612no—
97C2×M16—2442no—
98C22×C8—1221no—
99C4⋊Q8—612no—
100C4⋊Q8—611no—
101C4⋊Q8—611no—
102C4⋊Q8—2441no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—41no—
105C2×C4⋊C4—2441no—
106C2×C42C2×#692311yescharacteristic
107#103—2444no—
108#101—1224no—
109#101—2442no—
110C4×C8—2441no—
111C2×Q8—612no—
112C2×Q8—612no—
113C2×Q8—1222no—
114C2×Q8—2442no—
115C2×Q8—2442no—
116C22×C4—21no—
117C22×C4—41no—
118C22×C4—1222no—
119C22×C4C22⋊#692311yescharacteristic
120M16—4882no—
121M16—2444no—
122C2×C8—1222no—
123C2×C8—4882no—
124C2×C8—2441no—
125C2×C8—2441no—
126C4⋊C4—42no—
127C4⋊C4—82no—
128C4⋊C4—2442no—
129C4⋊C4—2441no—
130C4⋊C4—2441no—
131C42—21no—
132C42C4×#692311yescharacteristic
133C42C4⋊#692311yescharacteristic
134C23#1451983511yescharacteristic
135Q8—4882no—
136Q8—2442no—
137Q8—2442no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—82no—
145C2×C4—81no—
146C2×C4—1222no—
147C2×C4—1222no—
148C2×C4—2442no—
149C2×C4—2442no—
150C2×C4(C2×#6923)⋊C411yescharacteristic
151C2×C4#1451983611yescharacteristic
152C8—4884no—
153C8—2442no—
154C22—21no—
155C22—21no—
156C22#1684064011yescharacteristic
157C22#1684066611yescharacteristic
158C22#1684066811yescharacteristic
159C4—22no—
160C4—22no—
161C4—21no—
162C4—21no—
163C4—161no—
164C4—2442no—
165C4—2442no—
166C2—21no—
167C2—21no—
168C2#2146091411yescharacteristic
169C2#2146095411yescharacteristic
170C2#2146095611yescharacteristic
subgroupG/H
centerC22#16840666
commutatorC42×C61C42
FrattiniC2×C42C2×#6923
FittingC61×#384C4
socleC22×C61#353
prime radicalC23×C61#99
cosocleC2×#14519777C22
hypercenter#384#6923
hypocenterC61#7499
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
5. #16840673C4semidirect
95. C61#7499semidirect

Maximal subgroups

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

subgroupindex
C2×#168406732
#214466202
#749961