Finite Group Databasebeta

← #30594070

Subgroups — #30594070

Order 15616.

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

normal subgroups only

This group has 204 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#21460756C211yesmaximal, characteristic
2#21460684C211yesmaximal, characteristic
3#21447143C211yesmaximal, characteristic
4#16840783—21no—
5C22⋊#11758187—21no—
6C22×Dic244C411yescharacteristic
7C2×#14519706C2211yescharacteristic
8C2×#14519700—21no—
9#16839667—21no—
10C61×#340C411yescharacteristic
11C2×#11758187—41no—
12C4⋊#92420—41no—
13C22⋊#92420—41no—
14#14519832—22no—
15C22×Dic122—21no—
16C2×Dic244—41no—
17C2×Dic244—42no—
18C22×#92418D411yescharacteristic
19C2×C4×Dic61D411yescharacteristic
20#14519706—41no—
21#14519700—42no—
22#14519684—41no—
23#14519684—41no—
24C22×C8×C61C2×C411yescharacteristic
25C2×C4⋊C4×C61—21no—
26C22×C4×C61—41no—
27C22×C4×C61C22⋊C411yescharacteristic
28C22×Dic61—41no—
29C22×Dic61D811yescharacteristic
30C22×Dic61SD1611yescharacteristic
31C2×Dic122—22no—
32C2×Dic122—41no—
33C2×Dic122—41no—
34C2×Dic122—41no—
35C2×Dic122—41no—
36C2×Dic122—41no—
37C2×#92420—42no—
38C2×C8×C61—21no—
39C2×C8×C61—41no—
40C4⋊C4×C61—41no—
41C4⋊C4×C61—41no—
42C4×Dic61—21no—
43C4×Dic61—21no—
44C2×#92418—21no—
45C2×#92418—41no—
46Dic244—42no—
47Dic244—42no—
48#11758187—81no—
49C23×C61#10211yescharacteristic
50C2×C4×C61—21no—
51C2×C4×C61—21no—
52C2×C4×C61—81no—
53C2×C4×C61—81no—
54C2×C4×C61—81no—
55C2×C4×C61#9911yescharacteristic
56C2×C4×C61#10411yescharacteristic
57C2×Dic61—21no—
58C2×Dic61—21no—
59C2×Dic61—21no—
60C2×Dic61—21no—
61C2×Dic61—41no—
62C2×Dic61—42no—
63C2×Dic61—81no—
64C2×Dic61—81no—
65Dic122—42no—
66Dic122—42no—
67Dic122—81no—
68Dic122—81no—
69#92420—82no—
70C8×C61—41no—
71#92418—41no—
72#7082—611nomaximal, Sylow
73C22×C61—21no—
74C22×C61—21no—
75C22×C61#32711yescharacteristic
76C22×C61#35911yescharacteristic
77C22×C61#36211yescharacteristic
78C4×C61—21no—
79C4×C61—161no—
80C4×C61AΣL(1,𝔽16)11yescharacteristic
81C4×C61#35511yescharacteristic
82Dic61—41no—
83Dic61—41no—
84Dic61—82no—
85#2056—611no—
86#1322—611no—
87#1290—611no—
88C2×C61—21no—
89C2×C61—21no—
90C2×C61#134011yescharacteristic
91C2×C61#134511yescharacteristic
92C2×C61#135011yescharacteristic
93C22×Q16—611no—
94#432—1221no—
95C2×C4⋊C8—611no—
96C2×#103—1221no—
97#391—1221no—
98C22⋊C16—1221no—
99#340#692311yescharacteristic
100C61#708211yescharacteristic, complemented, Sylow
101C22×Q8—1221no—
102C2×Q16—2441no—
103C2×Q16—2442no—
104C22×C8—611no—
105C22×C8C2×#692311yescharacteristic
106C2×C4⋊C4—21no—
107C2×C42—611no—
108C2×C16—2441no—
109C4⋊C8—2441no—
110C4⋊C8—2441no—
111#103—2442no—
112C22⋊C8—2441no—
113#97—1222no—
114#95—2441no—
115#95—2441no—
116C2×Q8—1222no—
117C2×Q8—2441no—
118C2×Q8—2441no—
119C2×Q8—2441no—
120C2×Q8—2441no—
121C2×Q8—2441no—
122C22×C4—41no—
123C22×C4—611no—
124C22×C4—611no—
125C22×C4—2441no—
126C22×C4C22⋊#692311yescharacteristic
127Q16—2442no—
128Q16—2442no—
129C2×C8—21no—
130C2×C8—41no—
131C2×C8—1221no—
132C2×C8—2442no—
133C2×C8—2441no—
134C4⋊C4—41no—
135C4⋊C4—41no—
136C42—1221no—
137C42—1221no—
138C16—4881no—
139C23#1451983911yescharacteristic
140Q8—4881no—
141Q8—4881no—
142Q8—2442no—
143Q8—2442no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—81no—
147C2×C4—81no—
148C2×C4—81no—
149C2×C4—1221no—
150C2×C4—1221no—
151C2×C4—1221no—
152C2×C4—1221no—
153C2×C4—4881no—
154C2×C4—4881no—
155C2×C4—2442no—
156C2×C4—2441no—
157C2×C4#1451983611yescharacteristic
158C2×C4#1451984211yescharacteristic
159C8—41no—
160C8—4882no—
161C8—2441no—
162C22—21no—
163C22—21no—
164C22#1684061411yescharacteristic
165C22#1684067611yescharacteristic
166C22#1684068111yescharacteristic
167C4—21no—
168C4—161no—
169C4—4882no—
170C4—2441no—
171C4—2441no—
172C4#1684066311yescharacteristic
173C4#1684067111yescharacteristic
174C2—21no—
175C2—21no—
176C2#2146079211yescharacteristic
177C2#2146080211yescharacteristic
178C2#2146081211yescharacteristic
subgroupG/H
centerC22#16840614
commutatorC22×C8×C61C2×C4
FrattiniC22×C8C2×#6923
FittingC61×#340C4
socleC22×C61#327
prime radicalC23×C61#102
cosocleC2×#14519706C22
hypercenter#340#6923
hypocenterC61#7082
LCSG ▷ C22×C8×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #340

Complements

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

NH ≅ G/Ntype
100. C61#7082semidirect

Maximal subgroups

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

subgroupindex
#214607562
#214606842
#214471432
#708261