Finite Group Databasebeta

← #30594026

Subgroups — #30594026

Order 15616.

240 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 44 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#21460755C212yesmaximal, complemented
2#21446617C211yesmaximal, characteristic
3C22⋊#11758187—22no—
4C2×C4×D244C411yescharacteristic
5C2×C4⋊#92418C2211yescharacteristic
6C2×#14519689—22no—
7C2×#97×C61C411yescharacteristic
8C2×#11758187—42no—
9C22×D244C811yescharacteristic
10C22×C4×D61—21no—
11C22×#92418D412yes—
12C4×D244—41no—
13C4×D244—41no—
14C2×C4⋊Dic61C811yescharacteristic
15C2×#11758198—21no—
16C4⋊#92418—41no—
17#14519689—44no—
18C22×C8×C61—21no—
19C2×C42×C61C2×C411yescharacteristic
20#97×C61—41no—
21C23×D61—21no—
22C22×C4×C61C22⋊C411yescharacteristic
23C22×C4×C61C2×C811yescharacteristic
24C22×C4×C61M1611yescharacteristic
25C22×Dic61—21no—
26C2×D244—41no—
27C2×D244—42no—
28C2×C4×D61—42no—
29C2×C4×D61—42no—
30C2×C4×D61—41no—
31C2×C4×D61—41no—
32C2×C8×C61—22no—
33C2×C8×C61—41no—
34C2×C8×C61—41no—
35C42×C61—21no—
36C42×C61—21no—
37#11758198—42no—
38C4⋊Dic61—41no—
39C2×#92418—22no—
40C2×#92418—42no—
41#11758187—82no—
42C23×C61C22⋊C811yescharacteristic
43C22×D61—22no—
44C22×D61—42no—
45C22×D61—41no—
46C22×D61—41no—
47C22×D61—42no—
48C2×C4×C61—21no—
49C2×C4×C61—21no—
50C2×C4×C61—21no—
51C2×C4×C61—21no—
52C2×C4×C61—22no—
53C2×C4×C61—41no—
54C2×C4×C61#9911yescharacteristic
55C2×C4×C61#10011yescharacteristic
56C2×Dic61—42no—
57C2×Dic61—41no—
58D244—42no—
59D244—42no—
60C4×D61—82no—
61C4×D61—81no—
62C4×D61—81no—
63C8×C61—42no—
64#92418—42no—
65#7060—611nomaximal, Sylow
66C22×C61—21no—
67C22×C61—21no—
68C22×C61#32311yescharacteristic
69C22×C61#35012yes—
70C2×D61—44no—
71C2×D61—42no—
72C2×D61—82no—
73C2×D61—81no—
74C2×D61—81no—
75C4×C61—21no—
76C4×C61—41no—
77C4×C61—41no—
78C4×C61#35311yescharacteristic
79C4×C61#35511yescharacteristic
80Dic61—81no—
81#1955—611no—
82#1322—612no—
83C2×C61—22no—
84C2×C61#131511yescharacteristic
85C2×C61#131811yescharacteristic
86C2×C61#132011yescharacteristic
87D61—82no—
88C2×C4×D4—611no—
89C2×C4⋊C8—611no—
90C2×C22⋊C8—1222no—
91C2×#97#692311yescharacteristic
92C22⋊C16—1222no—
93C61#706011yescharacteristic, complemented, Sylow
94C22×D4—611no—
95C23×C4—1221no—
96C22×C8—21no—
97C22×C8—612no—
98C4×D4—2441no—
99C4×D4—2441no—
100C2×C4⋊C4—611no—
101C2×C22⋊C4—1221no—
102C2×C42C2×#692311yescharacteristic
103C2×C16—2442no—
104C4⋊C8—2441no—
105C22⋊C8—2444no—
106#97—41no—
107C24—1221no—
108C2×D4—2441no—
109C2×D4—2442no—
110C22×C4—1221no—
111C22×C4—2442no—
112C22×C4—2442no—
113C22×C4—2441no—
114C22×C4—2441no—
115C22×C4D61⋊C811yescharacteristic
116C22×C4#1175821311yescharacteristic
117C22×C4C22⋊#692311yescharacteristic
118C2×C8—22no—
119C2×C8—41no—
120C2×C8—41no—
121C2×C8—1222no—
122C2×C8—2442no—
123C4⋊C4—2441no—
124C22⋊C4—2442no—
125C42—21no—
126C42—21no—
127C16—4882no—
128C23—1222no—
129C23—2442no—
130C23—2441no—
131C23—2441no—
132C23—2442no—
133C23#1451983411yescharacteristic
134D4—2442no—
135D4—2442no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—22no—
141C2×C4—41no—
142C2×C4—4882no—
143C2×C4—4881no—
144C2×C4—4881no—
145C2×C4—2442no—
146C2×C4—2441no—
147C2×C4#1451983611yescharacteristic
148C2×C4#1451983711yescharacteristic
149C8—42no—
150C8—2442no—
151C22—21no—
152C22—21no—
153C22—4882no—
154C22—4881no—
155C22—4881no—
156C22—2444no—
157C22—2442no—
158C22#1684060611yescharacteristic
159C22#1684066112yes—
160C4—21no—
161C4—41no—
162C4—41no—
163C4—4881no—
164C4#1684066711yescharacteristic
165C4#1684067111yescharacteristic
166C2—22no—
167C2—4882no—
168C2#2146074211yescharacteristic
169C2#2146074811yescharacteristic
170C2#2146075211yescharacteristic
subgroupG/H
centerC2×C4#14519836
commutatorC22×C4×C61C2×C8
FrattiniC2×C42C2×#6923
FittingC2×#97×C61C4
socleC22×C61#323
prime radicalC22×D244C8
cosocleC2×C4⋊#92418C22
hypercenterC2×#97#6923
hypocenterC61#7060
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
1. #21460755C2semidirect
93. C61#7060semidirect

Maximal subgroups

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

subgroupindex
#214607552
#214466172
#706061