Finite Group Databasebeta

← #30594839

Subgroups — #30594839

Order 15616.

268 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 40 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#21460761C212yesmaximal, complemented
2#21446625C211yesmaximal, characteristic
3#16840607—22no—
4C2×#14519774C411yescharacteristic
5C2×#14519699—22no—
6#16839632C2211yescharacteristic
7C2×C4×C8×C61C411yescharacteristic
8C22⋊#92420—42no—
9C22×D244—21no—
10C22×D244—41no—
11#14519774—21no—
12#14519774—41no—
13#14519774C812yescomplemented
14C2×C4⋊Dic61—41no—
15C2×C4⋊Dic61D412yes—
16#14519699—44no—
17C22×C8×C61—21no—
18C2×C42×C61C2×C411yescharacteristic
19C4×C8×C61—41no—
20C23×D61—41no—
21C22×C4×C61—21no—
22C22×C4×C61C22⋊C411yescharacteristic
23C22×Dic61—22no—
24C2×D244—22no—
25C2×D244—42no—
26C2×D244—42no—
27C2×D244—42no—
28C2×D244—42no—
29C2×D244—41no—
30C2×D244—82no—
31C2×D244—82no—
32C2×#92420—82no—
33C2×C8×C61—22no—
34C2×C8×C61—41no—
35C2×C8×C61—41no—
36C42×C61—21no—
37C42×C61C2×C811yescharacteristic
38C42×C61M1611yescharacteristic
39C4⋊Dic61—42no—
40C4⋊Dic61—82no—
41C23×C61#9911yescharacteristic
42C22×D61—42no—
43C22×D61—82no—
44C22×D61—82no—
45C22×D61—81no—
46C22×D61—81no—
47C2×C4×C61—22no—
48C2×C4×C61—22no—
49C2×C4×C61—21no—
50C2×C4×C61—21no—
51C2×C4×C61—21no—
52C2×C4×C61—21no—
53C2×C4×C61C22⋊C811yescharacteristic
54C2×C4×C61#10011yescharacteristic
55C2×Dic61—42no—
56C2×Dic61—82no—
57D244—44no—
58D244—82no—
59D244—84no—
60D244—84no—
61#92420—162no—
62C8×C61—42no—
63#7354—611nomaximal, Sylow
64C22×C61—21no—
65C22×C61—21no—
66C22×C61#32311yescharacteristic
67C22×C61#35311yescharacteristic
68C22×C61#35511yescharacteristic
69C2×D61—84no—
70C2×D61—82no—
71C2×D61—162no—
72C2×D61—161no—
73C2×D61—161no—
74C4×C61—22no—
75C4×C61—22no—
76C4×C61—21no—
77C4×C61—21no—
78Dic61—82no—
79#1957—611no—
80#1325—612no—
81C2×C61—21no—
82C2×C61—21no—
83C2×C61#131811yescharacteristic
84C2×C61#140811yescharacteristic
85C2×C61#141011yescharacteristic
86D61—162no—
87C2×#127—611no—
88C2×#102—1222no—
89C2×C4×C8#692311yescharacteristic
90#384—611no—
91#324—1222no—
92C61#735411yescharacteristic, complemented, Sylow
93C22×D4—1221no—
94C22×D4—2441no—
95C22×C8—21no—
96#127—612no—
97#127—1221no—
98#127—2441no—
99C2×C4⋊C4—612no—
100C2×C4⋊C4—2441no—
101C2×C42C2×#692311yescharacteristic
102#102—2444no—
103C22⋊C8—2442no—
104C4×C8—41no—
105C24—2441no—
106C2×D4—1222no—
107C2×D4—4882no—
108C2×D4—4882no—
109C2×D4—2442no—
110C2×D4—2442no—
111C2×D4—2442no—
112C2×D4—2442no—
113C2×D4—2441no—
114C22×C4—21no—
115C22×C4—1222no—
116C22×C4C22⋊#692311yescharacteristic
117C2×C8—22no—
118C2×C8—41no—
119C2×C8—41no—
120C2×C8—4882no—
121C4⋊C4—4882no—
122C4⋊C4—2442no—
123C42—21no—
124C42D61⋊C811yescharacteristic
125C42#1175821311yescharacteristic
126C23—4882no—
127C23—4882no—
128C23—4881no—
129C23—4881no—
130C23—2442no—
131C23#1451983611yescharacteristic
132D4—4884no—
133D4—4884no—
134D4—4882no—
135D4—2444no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—4882no—
143C2×C4—2442no—
144C2×C4#1451983411yescharacteristic
145C2×C4#1451983711yescharacteristic
146C8—42no—
147C8—9762no—
148C22—21no—
149C22—21no—
150C22—9762no—
151C22—9761no—
152C22—9761no—
153C22—4884no—
154C22—4882no—
155C22#1684060611yescharacteristic
156C22#1684066711yescharacteristic
157C22#1684067111yescharacteristic
158C4—22no—
159C4—22no—
160C4—21no—
161C4—21no—
162C4—4882no—
163C2—21no—
164C2—21no—
165C2—9762no—
166C2#2146074811yescharacteristic
167C2#2146095111yescharacteristic
168C2#2146095511yescharacteristic
subgroupG/H
centerC22#16840667
commutatorC42×C61C2×C8
FrattiniC2×C42C2×#6923
FittingC2×C4×C8×C61C4
socleC22×C61#353
prime radicalC2×#14519774C4
cosocle#16839632C22
hypercenterC2×C4×C8#6923
hypocenterC61#7354
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
1. #21460761C2semidirect
13. #14519774C8semidirect
92. C61#7354semidirect

Maximal subgroups

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

subgroupindex
#214607612
#214466252
#735461