Finite Group Databasebeta

← #30594843

Subgroups — #30594843

Order 15616.

202 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 36 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#21446651C211yesmaximal, characteristic
3#16840658—22no—
4#16840312C411yescharacteristic
5#16839786C2211yescharacteristic
6C2×#14519705—22no—
7C61×#376C411yescharacteristic
8#14519851—42no—
9C2×#11758222—21no—
10C2×#11758194D412yes—
11#14519777C811yescharacteristic
12#14519774C811yescharacteristic
13#14519765—21no—
14#14519751—41no—
15C4×D244—41no—
16C4⋊#92418—41no—
17#14519705—44no—
18C2×C42×C61—21no—
19C2×C42×C61C2×C411yescharacteristic
20#95×C61—41no—
21C22×C4×C61—21no—
22C22×C4×C61—41no—
23C22×C4×C61C22⋊C411yescharacteristic
24C2×C22⋊D61—41no—
25#11758222—42no—
26#11758222—42no—
27C2×D244—21no—
28C2×D244—41no—
29C2×C4×D61—41no—
30C2×Dic122—21no—
31C42×C61—21no—
32C42×C61—22no—
33C42×C61—41no—
34C42×C61C2×C811yescharacteristic
35C42×C61M1611yescharacteristic
36#11758198—42no—
37C4⋊Dic61—41no—
38#11758194—42no—
39C2×#92418—22no—
40#11758187—82no—
41C23×C61#10011yescharacteristic
42C22×D61—41no—
43C2×C4×C61—21no—
44C2×C4×C61—21no—
45C2×C4×C61—21no—
46C2×C4×C61—21no—
47C2×C4×C61—42no—
48C2×C4×C61—81no—
49C2×C4×C61—82no—
50C2×C4×C61C22⋊C811yescharacteristic
51C2×C4×C61#9911yescharacteristic
52C22⋊D61—82no—
53C2×Dic61—41no—
54D244—42no—
55D244—82no—
56C4×D61—81no—
57C4×D61—81no—
58Dic122—42no—
59#92418—42no—
60#7356—611nomaximal, Sylow
61C22×C61—21no—
62C22×C61—41no—
63C22×C61#32311yescharacteristic
64C2×D61—82no—
65C2×D61—81no—
66C4×C61—21no—
67C4×C61—41no—
68C4×C61—41no—
69C4×C61—82no—
70C4×C61#35311yescharacteristic
71C4×C61#35511yescharacteristic
72Dic61—81no—
73#1963—611no—
74#1327—612no—
75C2×C61—21no—
76C2×C61—41no—
77C2×C61#131811yescharacteristic
78D61—161no—
79#532—611no—
80#423—611no—
81C2×#104—1222no—
82#376#692311yescharacteristic
83#349—1222no—
84C61#735611yescharacteristic, complemented, Sylow
85C2×#41—1221no—
86C2×M16—612no—
87C4⋊Q8—611no—
88#127—611no—
89#124—1221no—
90#121—2441no—
91C4×D4—2441no—
92C2×C42—21no—
93C2×C42C2×#692311yescharacteristic
94M32—2442no—
95C4⋊C8—2441no—
96#104—2444no—
97#95—41no—
98#41—2442no—
99#41—2442no—
100C2×Q8—1221no—
101C2×D4—1221no—
102C2×D4—2441no—
103C2×D4—2441no—
104C22×C4—21no—
105C22×C4—41no—
106C22×C4—2441no—
107C22×C4C22⋊#692311yescharacteristic
108M16—2442no—
109C2×C8—1222no—
110C4⋊C4—2441no—
111C22⋊C4—2442no—
112C42—21no—
113C42—22no—
114C42—41no—
115C42D61⋊C811yescharacteristic
116C42#1175821311yescharacteristic
117C16—4882no—
118C23—2441no—
119C23#1451983711yescharacteristic
120Q8—2442no—
121D4—4882no—
122D4—4882no—
123D4—2442no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—42no—
129C2×C4—81no—
130C2×C4—82no—
131C2×C4—4881no—
132C2×C4—4881no—
133C2×C4—2441no—
134C2×C4#1451983411yescharacteristic
135C2×C4#1451983611yescharacteristic
136C8—2442no—
137C22—21no—
138C22—41no—
139C22—4882no—
140C22—4881no—
141C22#1684060611yescharacteristic
142C4—21no—
143C4—41no—
144C4—41no—
145C4—82no—
146C4—4881no—
147C4#1684066711yescharacteristic
148C4#1684067111yescharacteristic
149C2—21no—
150C2—41no—
151C2—9761no—
152C2#2146074811yescharacteristic
subgroupG/H
centerC4#16840667
commutatorC42×C61C2×C8
FrattiniC2×C42C2×#6923
FittingC61×#376C4
socleC2×C61#1318
prime radical#16840312C4
cosocle#16839786C22
hypercenter#376#6923
hypocenterC61#7356
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ #376

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
#214466512
#735661