Finite Group Databasebeta

← #30594086

Subgroups — #30594086

Order 15616.

212 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 42 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#21460689C211yesmaximal, characteristic
3#21447143C211yesmaximal, characteristic
4#16840765—21no—
5C22⋊#11758187—21no—
6C22×Dic244C411yescharacteristic
7C2×#14519706C2211yescharacteristic
8C2×#14519700—21no—
9#16839667—21no—
10C61×#340C411yescharacteristic
11C2×#11758217—41no—
12C2×#11758187—41no—
13#14519844—22no—
14C4⋊#92420—41no—
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—
37#11758217—81no—
38#11758217—81no—
39C2×#92420—42no—
40C2×C8×C61—21no—
41C2×C8×C61—41no—
42C4⋊C4×C61—41no—
43C4⋊C4×C61—41no—
44C4×Dic61—21no—
45C4×Dic61—21no—
46C2×#92418—21no—
47C2×#92418—41no—
48Dic244—42no—
49Dic244—42no—
50#11758187—81no—
51C23×C61#10211yescharacteristic
52C2×C4×C61—21no—
53C2×C4×C61—21no—
54C2×C4×C61—81no—
55C2×C4×C61—81no—
56C2×C4×C61—81no—
57C2×C4×C61#9911yescharacteristic
58C2×C4×C61#10411yescharacteristic
59C2×Dic61—21no—
60C2×Dic61—21no—
61C2×Dic61—21no—
62C2×Dic61—41no—
63C2×Dic61—42no—
64C2×Dic61—81no—
65C2×Dic61—81no—
66C2×Dic61SD3211yescharacteristic
67C2×Dic61Q3211yescharacteristic
68Dic122—42no—
69Dic122—42no—
70Dic122—81no—
71Dic122—81no—
72#92420—82no—
73C8×C61—41no—
74#92418—41no—
75#7090—611nomaximal, Sylow
76C22×C61—21no—
77C22×C61—21no—
78C22×C61#32711yescharacteristic
79C22×C61#35811yescharacteristic
80C22×C61#36011yescharacteristic
81C4×C61—21no—
82C4×C61—161no—
83C4×C61AΣL(1,𝔽16)11yescharacteristic
84C4×C61#35511yescharacteristic
85Dic61—21no—
86Dic61—21no—
87Dic61—41no—
88Dic61—82no—
89#2056—611no—
90#1322—611no—
91#1292—611no—
92C2×C61—21no—
93C2×C61—21no—
94C2×C61#134211yescharacteristic
95C2×C61#134511yescharacteristic
96C2×C61#134811yescharacteristic
97C22×Q16—611no—
98#423—1221no—
99C2×C4⋊C8—611no—
100C2×#103—1221no—
101#391—1221no—
102C22⋊C16—1221no—
103#340#692311yescharacteristic
104C61#709011yescharacteristic, complemented, Sylow
105C22×Q8—1221no—
106C2×Q16—2441no—
107C2×Q16—2442no—
108C2×M16—2441no—
109C22×C8—611no—
110C22×C8C2×#692311yescharacteristic
111C2×C4⋊C4—21no—
112C2×C42—611no—
113C2×C16—2441no—
114C4⋊C8—1222no—
115C4⋊C8—2441no—
116C4⋊C8—2441no—
117#103—2442no—
118#95—2441no—
119#95—2441no—
120C2×Q8—1222no—
121C2×Q8—2441no—
122C2×Q8—2441no—
123C2×Q8—2441no—
124C2×Q8—2441no—
125C2×Q8—2441no—
126C22×C4—41no—
127C22×C4—611no—
128C22×C4—611no—
129C22×C4—2441no—
130C22×C4C22⋊#692311yescharacteristic
131Q16—2442no—
132Q16—2442no—
133M16—4881no—
134M16—4881no—
135C2×C8—21no—
136C2×C8—41no—
137C2×C8—1221no—
138C2×C8—2442no—
139C2×C8—2441no—
140C4⋊C4—41no—
141C4⋊C4—41no—
142C42—1221no—
143C42—1221no—
144C16—4881no—
145C23#1451983911yescharacteristic
146Q8—4881no—
147Q8—4881no—
148Q8—2442no—
149Q8—2442no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—81no—
153C2×C4—81no—
154C2×C4—81no—
155C2×C4—611no—
156C2×C4—611no—
157C2×C4—1221no—
158C2×C4—1221no—
159C2×C4—1221no—
160C2×C4—4881no—
161C2×C4—4881no—
162C2×C4—2442no—
163C2×C4—2441no—
164C2×C4#1451983611yescharacteristic
165C2×C4#1451984211yescharacteristic
166C8—41no—
167C8—4882no—
168C8—2441no—
169C22—21no—
170C22—21no—
171C22#1684061411yescharacteristic
172C22#1684067511yescharacteristic
173C22#1684067811yescharacteristic
174C4—21no—
175C4—161no—
176C4—1221no—
177C4—1221no—
178C4—4882no—
179C4—2441no—
180C4#1684066311yescharacteristic
181C4#1684067111yescharacteristic
182C2—21no—
183C2—21no—
184C2#2146079611yescharacteristic
185C2#2146080211yescharacteristic
186C2#2146080811yescharacteristic
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#7090
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
104. C61#7090semidirect

Maximal subgroups

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

subgroupindex
#214607562
#214606892
#214471432
#709061