Finite Group Databasebeta

← #30594947

Subgroups — #30594947

Order 15616.

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

normal subgroups only

This group has 282 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#21460913C211yesmaximal, characteristic
2#21460748C211yesmaximal, characteristic
3#21446904C211yesmaximal, characteristic
4C2×#14519836—21no—
5#16840607—21no—
6C22×#11758190—21no—
7C2×#14519777C411yescharacteristic, complemented
8C2×#14519702—21no—
9#16839664C2211yescharacteristic
10C61×#336C411yescharacteristic, complemented
11C2×C22⋊#6923—41no—
12#14519836—22no—
13#14519836—41no—
14C22⋊#92420—41no—
15C22×Dic122—21no—
16C22×D244D411yescharacteristic
17C2×#11758190—42no—
18C2×#11758190—42no—
19C2×#11758190—41no—
20C2×#11758190—41no—
21#14519777—42no—
22C2×C4⋊Dic61—41no—
23C2×C4⋊Dic61D411yescharacteristic
24C2×#11758198—41no—
25#14519702—42no—
26C22×C8×C61—21no—
27C2×C42×C61C2×C411yescharacteristic
28C23×D61—21no—
29C22×#6923—81no—
30C22×C4×C61—21no—
31C22×C4×C61C22⋊C411yescharacteristic
32C22×Dic61—21no—
33C22×Dic61—41no—
34C2×D244—21no—
35C2×D244—41no—
36C2×D244—41no—
37C2×D244D811yescharacteristic
38C2×D244SD1611yescharacteristic
39C2×Dic122—22no—
40C2×Dic122—41no—
41C2×Dic122—41no—
42C2×Dic122—41no—
43C2×Dic122—41no—
44C2×Dic122—41no—
45C22⋊#6923—42no—
46C22⋊#6923—81no—
47C2×#92420—81no—
48C2×C8×C61—22no—
49C2×C8×C61—41no—
50C2×C8×C61—41no—
51C42×C61—41no—
52#11758198—82no—
53C4⋊Dic61—42no—
54C4⋊Dic61—41no—
55C4⋊Dic61—42no—
56#11758190—44no—
57#11758190—44no—
58C23×C61#9911yescharacteristic
59C22×D61—21no—
60C22×D61—21no—
61C22×D61—41no—
62C22×D61—41no—
63C22×D61—81no—
64C22×D61—81no—
65C2×#6923—82no—
66C2×#6923—161no—
67C2×#6923—161no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—22no—
71C2×C4×C61—41no—
72C2×C4×C61—41no—
73C2×C4×C61#10211yescharacteristic
74C2×C4×C61#10411yescharacteristic
75C2×Dic61—42no—
76C2×Dic61—41no—
77C2×Dic61—81no—
78C2×Dic61—81no—
79C2×Dic61—81no—
80D244—41no—
81D244—41no—
82D244—81no—
83Dic122—42no—
84Dic122—42no—
85Dic122—81no—
86Dic122—81no—
87#92420—161no—
88C8×C61—42no—
89#7403—611nomaximal, Sylow
90C22×C61—21no—
91C22×C61—21no—
92C22×C61#32711yescharacteristic
93C22×C61AΣL(1,𝔽16)11yescharacteristic
94C22×C61#35311yescharacteristic
95C2×D61—41no—
96C2×D61—41no—
97C2×D61—81no—
98C2×D61—81no—
99C2×D61—81no—
100C2×D61—81no—
101C2×D61—161no—
102#6923—162no—
103C4×C61—21no—
104C4×C61—21no—
105C4×C61—42no—
106Dic61—82no—
107Dic61—81no—
108#2013—611no—
109#1393—611no—
110#1318—611no—
111C2×C61—21no—
112C2×C61—21no—
113C2×C61#134311yescharacteristic
114C2×C61#140711yescharacteristic
115C2×C61#140911yescharacteristic
116D61—81no—
117D61—81no—
118C22×SD16—1221no—
119C2×C4⋊Q8—611no—
120C2×#103—1221no—
121C2×#99—1221no—
122#390—611no—
123#336#692311yescharacteristic, complemented
124#324—1221no—
125C61#740311yescharacteristic, complemented, Sylow
126C22×Q8—1221no—
127C22×D4—611no—
128C2×SD16—2442no—
129C2×SD16—2441no—
130C2×SD16—2441no—
131C2×SD16—2442no—
132C22×C8—21no—
133C4⋊Q8—2442no—
134C2×C4⋊C4—611no—
135C2×C4⋊C4—2441no—
136C2×C22⋊C4—2441no—
137C2×C22⋊C4—2441no—
138C2×C42C2×#692311yescharacteristic
139#103—2442no—
140#99—1222no—
141#99—2441no—
142C22⋊C8—2441no—
143C24—1221no—
144C2×Q8—1222no—
145C2×Q8—2441no—
146C2×Q8—2441no—
147C2×Q8—2441no—
148C2×Q8—2441no—
149C2×Q8—2441no—
150C2×D4—611no—
151C2×D4—611no—
152C2×D4—1221no—
153C2×D4—2441no—
154C2×D4—2441no—
155C22×C4—21no—
156C22×C4—1221no—
157C22×C4—4881no—
158C22×C4—2441no—
159C22×C4C22⋊#692311yescharacteristic
160SD16—2444no—
161SD16—2444no—
162C2×C8—22no—
163C2×C8—41no—
164C2×C8—41no—
165C2×C8—4881no—
166C4⋊C4—2441no—
167C4⋊C4—2442no—
168C4⋊C4—2442no—
169C22⋊C4—4882no—
170C22⋊C4—4881no—
171C22⋊C4—2442no—
172C42—41no—
173C23—1221no—
174C23—1221no—
175C23—4881no—
176C23—4881no—
177C23—2441no—
178C23—2441no—
179C23#1451983611yescharacteristic
180Q8—4881no—
181Q8—4881no—
182Q8—2442no—
183Q8—2442no—
184D4—4881no—
185D4—2441no—
186D4—2441no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—9761no—
193C2×C4—9761no—
194C2×C4—4882no—
195C2×C4—4881no—
196C2×C4—4881no—
197C2×C4—4881no—
198C2×C4—2442no—
199C2×C4—2441no—
200C2×C4#1451983911yescharacteristic
201C2×C4#1451984211yescharacteristic
202C8—42no—
203C8—9761no—
204C22—21no—
205C22—21no—
206C22—9761no—
207C22—4881no—
208C22—4881no—
209C22—4881no—
210C22—4881no—
211C22—2441no—
212C22—2441no—
213C22#1684061411yescharacteristic
214C22#1684066311yescharacteristic
215C22#1684066711yescharacteristic
216C4—21no—
217C4—21no—
218C4—42no—
219C4—9762no—
220C4—4882no—
221C4—4881no—
222C2—21no—
223C2—21no—
224C2—4881no—
225C2—4881no—
226C2#2146079811yescharacteristic
227C2#2146094911yescharacteristic
228C2#2146095311yescharacteristic
subgroupG/H
centerC22#16840667
commutatorC2×C42×C61C2×C4
FrattiniC2×C42C2×#6923
FittingC61×#336C4
socleC22×C61#353
prime radicalC22×D244D4
cosocle#16839664C22
hypercenter#336#6923
hypocenterC61#7403
LCSG ▷ C2×C42×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
7. C2×#14519777C4semidirect
10. C61×#336C4semidirect
123. #336#6923semidirect
125. C61#7403semidirect

Maximal subgroups

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

subgroupindex
#214609132
#214607482
#214469042
#740361