Finite Group Databasebeta

← #30594568

Subgroups — #30594568

Order 15616.

318 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C2×#16840659C211yesmaximal, characteristic
2C2×#16840630C211yesmaximal, characteristic
3#21445858C211yesmaximal, characteristic
4C2×#14519856—21no—
5C2×#14519851—21no—
6#16840659—21no—
7#16840659C412yescomplemented
8#16840630—21no—
9#16840630C412yes—
10C22×#11758189C2211yescharacteristic
11C2×#14519713C411yescharacteristic, complemented
12#16839725—21no—
13#16839526—21no—
14C2×#108×C61C411yescharacteristic, complemented
15#14519856—22no—
16#14519856—22no—
17#14519856—41no—
18#14519856—41no—
19C2×C4⋊#6923—41no—
20C2×C22⋊#6923—41no—
21C2×C4×#6923—22no—
22#14519851—22no—
23#14519851—41no—
24C2×#11758187—41no—
25C22×C4×D61D411yescharacteristic
26C2×#11758194—21no—
27C2×#11758189—41no—
28C2×#11758189—41no—
29C2×#11758189C2×C411yescharacteristic
30C2×#11758189C2×C411yescharacteristic
31C2×#11758189D411yescharacteristic
32C2×#11758189Q811yescharacteristic
33C22×#92418D411yescharacteristic
34#14519713—41no—
35#14519689—41no—
36#14519689—41no—
37C2×M16×C61—21no—
38C22×C8×C61C2×C411yescharacteristic
39#108×C61—41no—
40C23×D61SD1611yescharacteristic
41C22×#6923—42no—
42C22×C4×C61C22⋊C411yescharacteristic
43C22×Dic61Q1611yescharacteristic
44C2×C4×D61—21no—
45C2×C4×D61—21no—
46C2×C4×D61—21no—
47C2×C4×D61—21no—
48C2×C4×D61C22⋊C411yescharacteristic
49C2×C4×D61C4⋊C411yescharacteristic
50C2×C4×D61D811yescharacteristic
51C2×C4×D61SD1611yescharacteristic
52C22⋊#6923—42no—
53C22⋊#6923—42no—
54C4⋊#6923—42no—
55C4⋊#6923—42no—
56C4×#6923—24no—
57C4×#6923—42no—
58M16×C61—41no—
59M16×C61—41no—
60C2×C8×C61—21no—
61C2×C8×C61—21no—
62C2×C8×C61—41no—
63C2×C8×C61C4211yescharacteristic
64C2×C8×C61C4⋊C411yescharacteristic
65#11758194—41no—
66#11758194—41no—
67C2×#92418—21no—
68C2×#92418—21no—
69C2×#92418—41no—
70C2×#92418C22⋊C411yescharacteristic
71C2×#92418C4⋊C411yescharacteristic
72#11758189—41no—
73#11758189—41no—
74#11758189—41no—
75#11758189—41no—
76#11758187—42no—
77C23×C61#10311yescharacteristic
78C22×D61—21no—
79C22×D61—21no—
80C22×D61—81no—
81C22×D61#10211yescharacteristic
82C22×D61#10611yescharacteristic
83C2×#6923—44no—
84C2×#6923—84no—
85C2×C4×C61#9511yescharacteristic
86C2×C4×C61#9911yescharacteristic
87C2×C4×C61#9911yescharacteristic
88C2×C4×C61#10211yescharacteristic
89C2×C4×C61#10411yescharacteristic
90C2×C4×C61#10411yescharacteristic
91C2×Dic61—21no—
92C2×Dic61—21no—
93C2×Dic61#10311yescharacteristic
94C2×Dic61#10711yescharacteristic
95C4×D61—21no—
96C4×D61—21no—
97C4×D61—21no—
98C4×D61—21no—
99C4×D61—21no—
100C4×D61—21no—
101C4×D61—21no—
102C4×D61—21no—
103C8×C61—21no—
104C8×C61—21no—
105C8×C61—81no—
106#92418—21no—
107#92418—21no—
108#92418—81no—
109#7256—611nomaximal, Sylow
110C22×C61—41no—
111C22×C61#32811yescharacteristic
112C22×C61#32811yescharacteristic
113C22×C61#34011yescharacteristic
114C2×D61—21no—
115C2×D61—21no—
116C2×D61—42no—
117C2×D61—41no—
118C2×D61—41no—
119C2×D61—81no—
120#6923—84no—
121C4×C61#32711yescharacteristic
122C4×C61#32711yescharacteristic
123C4×C61#33911yescharacteristic
124C4×C61#34211yescharacteristic
125Dic61—21no—
126Dic61—21no—
127C2×#349—611no—
128#1811—611no—
129C2×H(3,ℤ/4)—611no—
130C2×C61—21no—
131C2×C61—21no—
132C2×C61—21no—
133C2×C61#129411yescharacteristic
134D61—41no—
135D61—41no—
136C22×M16—611no—
137C2×#117—1221no—
138C2×M32—1221no—
139C2×#108—611no—
140C2×#108#692311yescharacteristic, complemented
141#407—1221no—
142#349—612no—
143#349—1221no—
144#341—1221no—
145H(3,ℤ/4)—612no—
146H(3,ℤ/4)—1221no—
147C61#725611yescharacteristic, complemented, Sylow
148C23×C4—611no—
149C2×M16—21no—
150C2×M16—611no—
151C2×M16—611no—
152C2×M16—611no—
153C2×M16—611no—
154C2×M16—1221no—
155C2×M16—2441no—
156C2×M16—2441no—
157C22×C8—611no—
158C22×C8C2×#692311yescharacteristic
159#117—1222no—
160#117—1222no—
161#117—2441no—
162#117—2441no—
163C2×C4⋊C4—2441no—
164C2×C22⋊C4—2441no—
165C2×C42—1222no—
166M32—1222no—
167M32—2441no—
168C2×C16—2441no—
169#108—41no—
170#108—2441no—
171C22⋊C8—2441no—
172C22⋊C8—2441no—
173C24—611no—
174C22×C4—611no—
175C22×C4—611no—
176C22×C4—611no—
177C22×C4—611no—
178C22×C4—611no—
179C22×C4—1221no—
180C22×C4—1221no—
181C22×C4—1221no—
182C22×C4—1221no—
183C22×C4—2442no—
184C22×C4C22⋊#692311yescharacteristic
185M16—41no—
186M16—41no—
187M16—2441no—
188M16—2441no—
189M16—2441no—
190M16—2441no—
191M16—2441no—
192M16—2441no—
193C2×C8—21no—
194C2×C8—21no—
195C2×C8—41no—
196C2×C8—611no—
197C2×C8—611no—
198C2×C8—1221no—
199C2×C8—1221no—
200C2×C8—2441no—
201C2×C8C4×#692311yescharacteristic
202C2×C8C4⋊#692311yescharacteristic
203C4⋊C4—2442no—
204C4⋊C4—2442no—
205C22⋊C4—2442no—
206C22⋊C4—2442no—
207C42—1224no—
208C42—2442no—
209C16—2442no—
210C23—611no—
211C23—611no—
212C23—1221no—
213C23—1221no—
214C23—4881no—
215C23#1451984011yescharacteristic
216C2×C4—611no—
217C2×C4—611no—
218C2×C4—1221no—
219C2×C4—1221no—
220C2×C4—1221no—
221C2×C4—1221no—
222C2×C4—1221no—
223C2×C4—1221no—
224C2×C4—1221no—
225C2×C4—1221no—
226C2×C4—1221no—
227C2×C4—1221no—
228C2×C4—4884no—
229C2×C4—2444no—
230C2×C4(C2×#6923)⋊C411yescharacteristic
231C2×C4#1451983511yescharacteristic
232C2×C4#1451983611yescharacteristic
233C2×C4#1451983911yescharacteristic
234C2×C4#1451984111yescharacteristic
235C2×C4#1451984211yescharacteristic
236C8—21no—
237C8—21no—
238C8—81no—
239C8—1221no—
240C8—1221no—
241C8—4881no—
242C22—41no—
243C22—1221no—
244C22—1221no—
245C22—4881no—
246C22—2441no—
247C22—2441no—
248C22—2442no—
249C22#1684061511yescharacteristic
250C22#1684061611yescharacteristic
251C22#1684063511yescharacteristic
252C4—1221no—
253C4—1221no—
254C4—4884no—
255C4#1684061311yescharacteristic
256C4#1684061411yescharacteristic
257C4#1684063211yescharacteristic
258C4#1684064011yescharacteristic
259C2—21no—
260C2—21no—
261C2—21no—
262C2—2441no—
263C2—2441no—
264C2#2146069211yescharacteristic
subgroupG/H
centerC4#16840613
commutatorC2×C8×C61C42
FrattiniC22×C8C2×#6923
FittingC2×#108×C61C4
socleC2×C61#1294
prime radicalC23×D61SD16
cosocleC22×#11758189C22
hypercenterC2×#108#6923
hypocenterC61#7256
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#108

Complements

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

NH ≅ G/Ntype
7. #16840659C4semidirect
11. C2×#14519713C4semidirect
14. C2×#108×C61C4semidirect
140. C2×#108#6923semidirect
147. C61#7256semidirect

Maximal subgroups

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

subgroupindex
C2×#168406592
C2×#168406302
#214458582
#725661