Finite Group Databasebeta

← #30594078

Subgroups — #30594078

Order 15616.

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

normal subgroups only

This group has 264 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#21460740C211yesmaximal, characteristic
2#21460691C211yesmaximal, characteristic
3#21446830C211yesmaximal, characteristic
4#16840733—21no—
5C22⋊#11758187—21no—
6C22×Dic244C411yescharacteristic
7C2×#14519757—21no—
8C2×#14519700—21no—
9C2×#14519689C2211yescharacteristic
10C61×#340C411yescharacteristic
11C2×#11758213—41no—
12C2×#11758187—41no—
13#14519834—22no—
14C22⋊#92420—41no—
15C22×Dic122—21no—
16C22×C4×D61D411yescharacteristic
17C2×Dic244—41no—
18C2×Dic244—42no—
19C22×#92418D411yescharacteristic
20#14519757—42no—
21#14519757—42no—
22C2×C4⋊Dic61—41no—
23C2×#11758198—41no—
24#14519700—42no—
25#14519689—41no—
26C22×C8×C61C2×C411yescharacteristic
27C2×C4⋊C4×C61—21no—
28C23×D61SD1611yescharacteristic
29C22×C4×C61—41no—
30C22×C4×C61C22⋊C411yescharacteristic
31C22×Dic61—41no—
32C22×Dic61D811yescharacteristic
33C2×C4×D61—21no—
34C2×C4×D61—21no—
35C2×C4×D61—41no—
36C2×C4×D61—41no—
37C2×Dic122—22no—
38C2×Dic122—41no—
39C2×Dic122—41no—
40C2×Dic122—41no—
41C2×Dic122—41no—
42C2×Dic122—41no—
43C2×#92420—42no—
44#11758213—81no—
45#11758213—81no—
46C2×C8×C61—21no—
47C2×C8×C61—41no—
48C4⋊C4×C61—22no—
49C4⋊C4×C61—41no—
50#11758198—44no—
51C4⋊Dic61—44no—
52C2×#92418—21no—
53C2×#92418—41no—
54Dic244—42no—
55Dic244—42no—
56#11758187—81no—
57C23×C61#10211yescharacteristic
58C22×D61—21no—
59C22×D61—21no—
60C22×D61—21no—
61C22×D61—41no—
62C22×D61—41no—
63C2×C4×C61—21no—
64C2×C4×C61—21no—
65C2×C4×C61—42no—
66C2×C4×C61—81no—
67C2×C4×C61—81no—
68C2×C4×C61#9911yescharacteristic
69C2×C4×C61#10411yescharacteristic
70C2×Dic61—21no—
71C2×Dic61—41no—
72C2×Dic61—42no—
73C2×Dic61—81no—
74C2×Dic61—81no—
75C4×D61—41no—
76C4×D61—41no—
77C4×D61—81no—
78Dic122—42no—
79Dic122—42no—
80Dic122—81no—
81Dic122—81no—
82#92420—82no—
83C8×C61—41no—
84#92418—41no—
85#7086—611nomaximal, Sylow
86C22×C61—21no—
87C22×C61—21no—
88C22×C61#32711yescharacteristic
89C22×C61#35911yescharacteristic
90C22×C61#36211yescharacteristic
91C2×D61—42no—
92C2×D61—41no—
93C2×D61—41no—
94C2×D61—41no—
95C2×D61—81no—
96C4×C61—21no—
97C4×C61—82no—
98C4×C61AΣL(1,𝔽16)11yescharacteristic
99C4×C61#35311yescharacteristic
100Dic61—41no—
101Dic61—82no—
102#2001—611no—
103#1314—611no—
104#1293—611no—
105C2×C61—21no—
106C2×C61—21no—
107C2×C61#134211yescharacteristic
108C2×C61#134311yescharacteristic
109C2×C61#135011yescharacteristic
110D61—81no—
111C22×Q16—611no—
112C2×C22⋊Q8—1221no—
113C2×#103—1221no—
114#407—1221no—
115C2×C22⋊C8—611no—
116C22⋊C16—1221no—
117#340#692311yescharacteristic
118C61#708611yescharacteristic, complemented, Sylow
119C22×Q8—1221no—
120C23×C4—611no—
121C2×Q16—2441no—
122C2×Q16—2442no—
123C2×M16—2441no—
124C22×C8—611no—
125C22×C8C2×#692311yescharacteristic
126C22⋊Q8—2442no—
127C22⋊Q8—2442no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—2441no—
130C2×C22⋊C4—2441no—
131C2×C16—2441no—
132#103—2442no—
133C22⋊C8—1222no—
134C22⋊C8—2441no—
135C22⋊C8—2441no—
136C24—611no—
137C2×Q8—1222no—
138C2×Q8—2441no—
139C2×Q8—2441no—
140C2×Q8—2441no—
141C2×Q8—2441no—
142C2×Q8—2441no—
143C22×C4—41no—
144C22×C4—611no—
145C22×C4—1221no—
146C22×C4—1221no—
147C22×C4—2441no—
148C22×C4—2441no—
149C22×C4—2441no—
150C22×C4C22⋊#692311yescharacteristic
151Q16—2442no—
152Q16—2442no—
153M16—4881no—
154M16—4881no—
155C2×C8—21no—
156C2×C8—41no—
157C2×C8—1221no—
158C2×C8—2442no—
159C2×C8—2441no—
160C4⋊C4—22no—
161C4⋊C4—41no—
162C4⋊C4—2444no—
163C22⋊C4—2444no—
164C16—4881no—
165C23—1221no—
166C23—1221no—
167C23—1221no—
168C23—2441no—
169C23—2441no—
170C23#1451983911yescharacteristic
171Q8—4881no—
172Q8—4881no—
173Q8—2442no—
174Q8—2442no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—42no—
178C2×C4—81no—
179C2×C4—81no—
180C2×C4—1221no—
181C2×C4—4881no—
182C2×C4—4881no—
183C2×C4—4881no—
184C2×C4—2442no—
185C2×C4—2441no—
186C2×C4—2441no—
187C2×C4—2441no—
188C2×C4#1451983611yescharacteristic
189C2×C4#1451984211yescharacteristic
190C8—41no—
191C8—4882no—
192C8—2441no—
193C22—21no—
194C22—21no—
195C22—4881no—
196C22—2442no—
197C22—2441no—
198C22—2441no—
199C22—2441no—
200C22#1684061411yescharacteristic
201C22#1684067611yescharacteristic
202C22#1684068111yescharacteristic
203C4—21no—
204C4—82no—
205C4—4882no—
206C4—2441no—
207C4#1684066311yescharacteristic
208C4#1684066711yescharacteristic
209C2—21no—
210C2—21no—
211C2—4881no—
212C2#2146079611yescharacteristic
213C2#2146079811yescharacteristic
214C2#2146081211yescharacteristic
subgroupG/H
centerC22#16840614
commutatorC22×C8×C61C2×C4
FrattiniC22×C8C2×#6923
FittingC61×#340C4
socleC22×C61#327
prime radicalC23×D61SD16
cosocleC2×#14519689C22
hypercenter#340#6923
hypocenterC61#7086
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
118. C61#7086semidirect

Maximal subgroups

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

subgroupindex
#214607402
#214606912
#214468302
#708661