Finite Group Databasebeta

← #30594495

Subgroups — #30594495

Order 15616.

292 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 68 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#21461698C211yesmaximal, characteristic
2#21461695C211yesmaximal, characteristic
3C2×#16839541C211yesmaximal, characteristic
4C2×#14519847—21no—
5C2×#14519845—21no—
6#16840733—21no—
7#16840704—21no—
8#16840638C412yescomplemented
9#16840636C412yes—
10C22×C8×D61C2211yescharacteristic
11C22×#11758185C411yescharacteristic, complemented
12#16839541—21no—
13#16839541—21no—
14C22×C16×C61C411yescharacteristic, complemented
15C2×#11758213—22no—
16C2×C4⋊#6923—22no—
17C2×C22⋊#6923—41no—
18#14519847—41no—
19#14519847—41no—
20#14519845—41no—
21#14519845—41no—
22#14519834—41no—
23C22⋊#92420—41no—
24(C2×#6923)⋊C4—41no—
25C22×C4×D61D411yescharacteristic
26C22×#92418Q811yescharacteristic
27C2×C8×D61—41no—
28C2×C8×D61—41no—
29C2×C8×D61C2×C411yescharacteristic
30C2×C8×D61C2×C411yescharacteristic
31C2×C8×D61D411yescharacteristic
32C2×C8×D61D411yescharacteristic
33C2×#11758185—21no—
34C2×#11758185—41no—
35C22×C8×C61C2×C411yescharacteristic
36C2×C16×C61—21no—
37C2×C16×C61—41no—
38C23×D61SD1611yescharacteristic
39C22×#6923—42no—
40C22×C4×C61C4⋊C411yescharacteristic
41C22×Dic61SD1611yescharacteristic
42C2×C4×D61—41no—
43C2×C4×D61—41no—
44C2×C4×D61C22⋊C411yescharacteristic
45C2×C4×D61C22⋊C411yescharacteristic
46C2×C4×D61D811yescharacteristic
47C2×C4×D61Q1611yescharacteristic
48C22⋊#6923—81no—
49C22⋊#6923—81no—
50C2×#92420—42no—
51C4⋊#6923—42no—
52C4⋊#6923—42no—
53#11758213—42no—
54#11758213—42no—
55C2×C8×C61—21no—
56C2×C8×C61—21no—
57C2×C8×C61C4211yescharacteristic
58C2×C8×C61C22⋊C411yescharacteristic
59C2×#92418—41no—
60C2×#92418C4⋊C411yescharacteristic
61C2×#92418C4⋊C411yescharacteristic
62C8×D61—21no—
63C8×D61—21no—
64C8×D61—21no—
65C8×D61—21no—
66C8×D61—41no—
67C8×D61—41no—
68C16×C61—41no—
69#11758185—41no—
70C23×C61#10611yescharacteristic
71C22×D61—21no—
72C22×D61—21no—
73C22×D61—22no—
74C22×D61—41no—
75C22×D61#10211yescharacteristic
76C22×D61#10311yescharacteristic
77C2×#6923—82no—
78C2×#6923—82no—
79C2×#6923—82no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61#9511yescharacteristic
83C2×C4×C61#10711yescharacteristic
84C2×Dic61—41no—
85C2×Dic61#10211yescharacteristic
86C2×Dic61#10311yescharacteristic
87C4×D61—21no—
88C4×D61—21no—
89C4×D61—21no—
90C4×D61—21no—
91C4×D61—41no—
92C4×D61—41no—
93#92420—82no—
94C8×C61—21no—
95C8×C61#9911yescharacteristic
96C8×C61#9911yescharacteristic
97#92418—21no—
98#92418—21no—
99#7232—611nomaximal, Sylow
100C22×C61—21no—
101C22×C61—21no—
102C22×C61#34011yescharacteristic
103C22×C61#36511yescharacteristic
104C22×C61#36511yescharacteristic
105C2×D61—21no—
106C2×D61—21no—
107C2×D61—21no—
108C2×D61—21no—
109C2×D61—21no—
110C2×D61—42no—
111C2×D61—42no—
112C2×D61#35912yes—
113#6923—162no—
114C4×C61—21no—
115C4×C61H(3,ℤ/4)11yescharacteristic
116C4×C61#34211yescharacteristic
117Dic61—21no—
118Dic61—21no—
119C2×C22⋊C16—611no—
120#1810—611no—
121#1807—611no—
122C2×C61—21no—
123C2×C61—21no—
124C2×C61#128911yescharacteristic
125C2×C61#138211yescharacteristic
126C2×C61#138311yescharacteristic
127D61—22no—
128D61—41no—
129C23×C8—611no—
130C22×C16—611no—
131C22×C16#692311yescharacteristic, complemented
132C2×#108—1221no—
133C2×#106—1221no—
134#407—1221no—
135#380—1221no—
136C22⋊C16—1221no—
137C22⋊C16—1221no—
138#341—612no—
139#340—612no—
140C61#723211yescharacteristic, complemented, Sylow
141C23×C4—611no—
142C2×M16—1222no—
143C22×C8—611no—
144C22×C8—611no—
145C22×C8—611no—
146C22×C8—611no—
147C22×C8—611no—
148C22×C8—2441no—
149C22×C8—2441no—
150C22×C8C2×#692311yescharacteristic
151C2×C4⋊C4—1222no—
152C2×C22⋊C4—2441no—
153C2×C16—21no—
154C2×C16—41no—
155C2×C16—1221no—
156C2×C16—2441no—
157#108—2441no—
158#108—2441no—
159#106—2441no—
160#106—2441no—
161C22⋊C8—2441no—
162C22⋊C8—2441no—
163#95—2441no—
164C24—611no—
165C22×C4—611no—
166C22×C4—611no—
167C22×C4—611no—
168C22×C4—611no—
169C22×C4—611no—
170C22×C4—2441no—
171C22×C4—2441no—
172C22×C4—2442no—
173C22×C4C4⋊#692311yescharacteristic
174M16—2442no—
175M16—2442no—
176C2×C8—21no—
177C2×C8—21no—
178C2×C8—611no—
179C2×C8—611no—
180C2×C8—1221no—
181C2×C8—1221no—
182C2×C8—1221no—
183C2×C8—1221no—
184C2×C8—2441no—
185C2×C8—2441no—
186C2×C8—2441no—
187C2×C8—2442no—
188C2×C8C4×#692311yescharacteristic
189C2×C8C22⋊#692311yescharacteristic
190C4⋊C4—2442no—
191C4⋊C4—2442no—
192C22⋊C4—4881no—
193C22⋊C4—4881no—
194C16—41no—
195C16—2441no—
196C23—611no—
197C23—611no—
198C23—1222no—
199C23—1221no—
200C23—1221no—
201C23—2441no—
202C23#1451984511yescharacteristic
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—611no—
206C2×C4—611no—
207C2×C4—1221no—
208C2×C4—1221no—
209C2×C4—1221no—
210C2×C4—1221no—
211C2×C4—4882no—
212C2×C4—4882no—
213C2×C4—4882no—
214C2×C4—2441no—
215C2×C4—2441no—
216C2×C4—2441no—
217C2×C4(C2×#6923)⋊C411yescharacteristic
218C2×C4#1451984611yescharacteristic
219C8—21no—
220C8—1221no—
221C8—1221no—
222C8—4882no—
223C8#1451983511yescharacteristic
224C8#1451983611yescharacteristic
225C22—21no—
226C22—21no—
227C22—612no—
228C22—1221no—
229C22—1221no—
230C22—1221no—
231C22—1221no—
232C22—1221no—
233C22—2442no—
234C22—2442no—
235C22#1684063611yescharacteristic
236C22#1684068611yescharacteristic
237C22#1684068711yescharacteristic
238C4—21no—
239C4—1221no—
240C4—1221no—
241C4—9762no—
242C4#1684063011yescharacteristic
243C4#1684064011yescharacteristic
244C2—21no—
245C2—21no—
246C2—1222no—
247C2—2441no—
248C2#2146068211yescharacteristic
249C2#2146088111yescharacteristic
250C2#2146088411yescharacteristic
subgroupG/H
centerC22#16840636
commutatorC2×C8×C61C42
FrattiniC22×C8C2×#6923
FittingC22×C16×C61C4
socleC22×C61#340
prime radicalC23×D61SD16
cosocleC22×C8×D61C22
hypercenterC22×C16#6923
hypocenterC61#7232
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

Complements

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

NH ≅ G/Ntype
8. #16840638C4semidirect
11. C22×#11758185C4semidirect
14. C22×C16×C61C4semidirect
131. C22×C16#6923semidirect
140. C61#7232semidirect

Maximal subgroups

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

subgroupindex
#214616982
#214616952
C2×#168395412
#723261