Finite Group Databasebeta

← #30594115

Subgroups — #30594115

Order 15616.

268 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 56 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#21460647C212yesmaximal, complemented
2#21446646C211yesmaximal, characteristic
3#16840778—22no—
4#16840312C411yescharacteristic
5C2×#14519703—22no—
6C42×Dic61C2211yescharacteristic
7C61×#423C411yescharacteristic
8C4⋊#92420—24no—
9C22⋊#92420—42no—
10C4×#92420—42no—
11C2×#11758222—21no—
12#14519777C811yescharacteristic, complemented
13#14519774C811yescharacteristic, complemented
14#14519765—21no—
15#14519751—41no—
16C4×D244—41no—
17C2×C4×Dic61—41no—
18C2×C4×Dic61D412yes—
19#14519703—42no—
20#14519703—42no—
21C2×M16×C61—21no—
22C2×C42×C61C2×C411yescharacteristic
23C4⋊C8×C61—41no—
24C22×C4×C61—21no—
25C22×C4×C61C22⋊C411yescharacteristic
26C2×C22⋊D61—41no—
27C22×Dic61—22no—
28#11758222—42no—
29#11758222—42no—
30C2×D244—21no—
31C2×D244—41no—
32C2×C4×D61—41no—
33C2×Dic122—21no—
34C2×#92420—44no—
35M16×C61—42no—
36C2×C8×C61—41no—
37C42×C61—21no—
38C42×C61C2×C811yescharacteristic
39C42×C61M1611yescharacteristic
40#11758198—42no—
41C4⋊Dic61—41no—
42C4×Dic61—22no—
43C4×Dic61—44no—
44C4×Dic61D812yes—
45C4×Dic61SD1612yes—
46C23×C61#9911yescharacteristic
47C22×D61—41no—
48C2×C4×C61—21no—
49C2×C4×C61—21no—
50C2×C4×C61—42no—
51C2×C4×C61C22⋊C811yescharacteristic
52C2×C4×C61#10011yescharacteristic
53C2×C4×C61#10212yes—
54C2×C4×C61#10412yes—
55C22⋊D61—82no—
56C2×Dic61—22no—
57C2×Dic61—22no—
58C2×Dic61—44no—
59C2×Dic61—41no—
60D244—42no—
61D244—82no—
62C4×D61—81no—
63C4×D61—81no—
64Dic122—42no—
65#92420—84no—
66C8×C61—81no—
67#7106—611nomaximal, Sylow
68C22×C61—41no—
69C22×C61#32311yescharacteristic
70C22×C61#32712yes—
71C2×D61—82no—
72C2×D61—81no—
73C4×C61—22no—
74C4×C61—41no—
75C4×C61D4⋊C812yes—
76C4×C61#32911yescharacteristic
77C4×C61#33111yescharacteristic
78Dic61—24no—
79Dic61—42no—
80Dic61—81no—
81#1962—611no—
82#1276—612no—
83C2×C61—22no—
84C2×C61—21no—
85C2×C61#127011yescharacteristic
86D61—161no—
87#532—611no—
88#431—1222no—
89#423#692311yescharacteristic
90C2×#104—1222no—
91C43—611no—
92C61#710611yescharacteristic, complemented, Sylow
93C2×#41—1221no—
94C2×M16—21no—
95C4⋊Q8—611no—
96#127—611no—
97#124—1221no—
98#121—2441no—
99C4×D4—2441no—
100C2×C42—612no—
101C2×C42—2441no—
102C2×C42C2×#692311yescharacteristic
103C4⋊C8—41no—
104C4⋊C8—1224no—
105#104—2442no—
106#104—2442no—
107C22⋊C8—2442no—
108C4×C8—2442no—
109#41—2442no—
110#41—2442no—
111C2×Q8—1221no—
112C2×D4—1221no—
113C2×D4—2441no—
114C2×D4—2441no—
115C22×C4—21no—
116C22×C4—1222no—
117C22×C4—2441no—
118C22×C4C22⋊#692311yescharacteristic
119M16—42no—
120C2×C8—41no—
121C2×C8—2444no—
122C4⋊C4—2441no—
123C22⋊C4—2442no—
124C42—21no—
125C42—612no—
126C42—612no—
127C42—1222no—
128C42—2444no—
129C42D61⋊C811yescharacteristic
130C42#1175821311yescharacteristic
131C23—2441no—
132C23#1451983611yescharacteristic
133Q8—2442no—
134D4—4882no—
135D4—4882no—
136D4—2442no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—42no—
140C2×C4—1222no—
141C2×C4—1222no—
142C2×C4—4881no—
143C2×C4—4881no—
144C2×C4—2444no—
145C2×C4—2441no—
146C2×C4#1451983411yescharacteristic
147C2×C4#1451983711yescharacteristic
148C2×C4#1451983912yes—
149C2×C4#1451984212yes—
150C8—81no—
151C8—4884no—
152C22—41no—
153C22—4882no—
154C22—4881no—
155C22#1684060611yescharacteristic
156C22#1684061412yes—
157C4—22no—
158C4—41no—
159C4—1224no—
160C4—4881no—
161C4—2442no—
162C4#1684061012yes—
163C4#1684061811yescharacteristic
164C4#1684062011yescharacteristic
165C2—21no—
166C2—22no—
167C2—9761no—
168C2#2146063611yescharacteristic
subgroupG/H
centerC4#16840620
commutatorC42×C61C2×C8
FrattiniC2×C42C2×#6923
FittingC61×#423C4
socleC2×C61#1270
prime radical#16840312C4
cosocleC42×Dic61C22
hypercenter#423#6923
hypocenterC61#7106
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
1. #21460647C2semidirect
12. #14519777C8semidirect
13. #14519774C8semidirect
92. C61#7106semidirect

Maximal subgroups

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

subgroupindex
#214606472
#214466462
#710661