Finite Group Databasebeta

← #30594842

Subgroups — #30594842

Order 15616.

202 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 38 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#21460765C212yesmaximal, complemented
2#21446652C211yesmaximal, characteristic
3#16840658—22no—
4#16839786C2211yescharacteristic
5C2×#14519704—22no—
6#16839608C411yescharacteristic
7C61×#532C411yescharacteristic
8#14519851—42no—
9C2×#11758194D412yes—
10C2×C4×Dic61—21no—
11C4⋊#92418—41no—
12#14519704—44no—
13#14519684—41no—
14C2×#41×C61—21no—
15C4⋊Q8×C61C811yescharacteristic
16#127×C61C811yescharacteristic
17#124×C61—21no—
18#121×C61—41no—
19C4×D4×C61—41no—
20C2×C42×C61C2×C411yescharacteristic
21#41×C61—42no—
22#41×C61—42no—
23C2×Q8×C61—21no—
24C2×D4×C61—21no—
25C2×D4×C61—41no—
26C2×D4×C61—41no—
27C22×C4×C61—21no—
28C22×C4×C61—41no—
29C22×C4×C61C22⋊C411yescharacteristic
30C22×Dic61—41no—
31C4⋊C4×C61—41no—
32C22⋊C4×C61—42no—
33C42×C61—21no—
34C42×C61C2×C811yescharacteristic
35C42×C61M1611yescharacteristic
36C4×Dic61—22no—
37C4×Dic61—41no—
38#11758194—42no—
39C2×#92418—22no—
40#11758187—82no—
41C23×C61—41no—
42C23×C61#10011yescharacteristic
43Q8×C61—42no—
44D4×C61—42no—
45D4×C61—82no—
46D4×C61—82no—
47C2×C4×C61—21no—
48C2×C4×C61—21no—
49C2×C4×C61—21no—
50C2×C4×C61—21no—
51C2×C4×C61—41no—
52C2×C4×C61—81no—
53C2×C4×C61—81no—
54C2×C4×C61—81no—
55C2×C4×C61C22⋊C811yescharacteristic
56C2×C4×C61#9911yescharacteristic
57C2×Dic61—42no—
58C2×Dic61—82no—
59#92418—42no—
60#7356—611nomaximal, Sylow
61C22×C61—21no—
62C22×C61—41no—
63C22×C61—82no—
64C22×C61—81no—
65C22×C61#32311yescharacteristic
66C4×C61—21no—
67C4×C61—41no—
68C4×C61—41no—
69C4×C61—81no—
70C4×C61#35311yescharacteristic
71C4×C61#35511yescharacteristic
72Dic61—82no—
73#1963—611no—
74#1327—612no—
75C2×C61—21no—
76C2×C61—41no—
77C2×C61—161no—
78C2×C61#131811yescharacteristic
79#532#692311yescharacteristic
80#423—611no—
81C2×#104—1222no—
82#376—611no—
83#349—1222no—
84C61#735611yescharacteristic, complemented, Sylow
85C2×#41—21no—
86C2×M16—612no—
87C4⋊Q8#9242011yescharacteristic
88#127#9242011yescharacteristic
89#124—21no—
90#121—41no—
91C4×D4—41no—
92C2×C42—1221no—
93C2×C42C2×#692311yescharacteristic
94M32—2442no—
95C4⋊C8—2441no—
96#104—2444no—
97#95—2441no—
98#41—42no—
99#41—42no—
100C2×Q8—21no—
101C2×D4—21no—
102C2×D4—41no—
103C2×D4—41no—
104C22×C4—21no—
105C22×C4—41no—
106C22×C4—2441no—
107C22×C4C22⋊#692311yescharacteristic
108M16—2442no—
109C2×C8—1222no—
110C4⋊C4—41no—
111C22⋊C4—42no—
112C42—21no—
113C42—1222no—
114C42—2441no—
115C42C2×#9242011yescharacteristic
116C42#1175821711yescharacteristic
117C16—4882no—
118C23—41no—
119C23#1451983711yescharacteristic
120Q8—42no—
121D4—42no—
122D4—82no—
123D4—82no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—41no—
129C2×C4—81no—
130C2×C4—81no—
131C2×C4—81no—
132C2×C4—4882no—
133C2×C4—2442no—
134C2×C4C22⋊#9242011yescharacteristic
135C2×C4#1451983511yescharacteristic
136C8—2442no—
137C22—21no—
138C22—41no—
139C22—82no—
140C22—81no—
141C22#1684060511yescharacteristic
142C4—21no—
143C4—41no—
144C4—41no—
145C4—81no—
146C4—4882no—
147C4#1684066611yescharacteristic
148C4#1684067011yescharacteristic
149C2—21no—
150C2—41no—
151C2—161no—
152C2#2146074711yescharacteristic
subgroupG/H
centerC4#16840666
commutatorC42×C61C2×C8
FrattiniC2×C42C2×#6923
Fitting, prime radicalC61×#532C4
socleC2×C61#1318
cosocle#16839786C22
hypercenter#532#6923
hypocenterC61#7356
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #21460765C2semidirect
84. C61#7356semidirect

Maximal subgroups

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

subgroupindex
#214607652
#214466522
#735661