Finite Group Databasebeta

← #30594494

Subgroups — #30594494

Order 15616.

292 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 66 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
1D61⋊(C22⋊C16)C211yesmaximal, characteristic
2#21461699C211yesmaximal, characteristic
3#21445843C211yesmaximal, characteristic
4C2×D61⋊C16C412yescomplemented
5C2×#14519848—21no—
6#16840733—21no—
7#16840657—21no—
8C22⋊#11758187—21no—
9#16840638C412yescomplemented
10C22×C8×D61C2211yescharacteristic
11C2×#14519708—21no—
12#16839619—21no—
13#16839525C411yescharacteristic
14C61×#340C411yescharacteristic
15C2×#11758213—22no—
16D61⋊C16—42no—
17C2×#11758187—22no—
18#14519848—42no—
19#14519834—41no—
20C22⋊#92420—41no—
21C22×C4×D61D411yescharacteristic
22C22×#92418D411yescharacteristic
23C2×C8×D61—42no—
24C2×C8×D61C2×C411yescharacteristic
25C2×C8×D61C2×C411yescharacteristic
26C2×C8×D61D411yescharacteristic
27C2×C8×D61Q811yescharacteristic
28C2×C4⋊Dic61—21no—
29C2×#11758198—41no—
30#14519708—42no—
31#14519684—41no—
32C22×C8×C61C2×C411yescharacteristic
33C2×C4⋊C4×C61—21no—
34C23×D61SD1611yescharacteristic
35C22×C4×C61—41no—
36C22×C4×C61C22⋊C411yescharacteristic
37C22×Dic61—41no—
38C22×Dic61D811yescharacteristic
39C2×C4×D61—41no—
40C2×C4×D61—41no—
41C2×C4×D61C22⋊C411yescharacteristic
42C2×C4×D61C4⋊C411yescharacteristic
43C2×C4×D61SD1611yescharacteristic
44C2×C4×D61Q1611yescharacteristic
45C2×#92420—42no—
46#11758213—42no—
47#11758213—42no—
48C2×C8×C61—41no—
49C2×C8×C61C4211yescharacteristic
50C2×C8×C61C4⋊C411yescharacteristic
51C4⋊C4×C61—41no—
52C4⋊C4×C61—41no—
53#11758198—82no—
54C4⋊Dic61—41no—
55C4⋊Dic61—41no—
56C2×#92418—22no—
57C2×#92418C22⋊C411yescharacteristic
58C2×#92418C4⋊C411yescharacteristic
59C8×D61—22no—
60C8×D61—22no—
61C8×D61—41no—
62C8×D61—41no—
63#11758187—42no—
64C23×C61#10211yescharacteristic
65C22×D61—21no—
66C22×D61—21no—
67C22×D61—22no—
68C22×D61—41no—
69C22×D61#10311yescharacteristic
70C22×D61#10611yescharacteristic
71C2×C4×C61—21no—
72C2×C4×C61—21no—
73C2×C4×C61—81no—
74C2×C4×C61—81no—
75C2×C4×C61—81no—
76C2×C4×C61#9511yescharacteristic
77C2×C4×C61#10311yescharacteristic
78C2×Dic61—41no—
79C2×Dic61—81no—
80C2×Dic61—81no—
81C2×Dic61—81no—
82C2×Dic61#10211yescharacteristic
83C2×Dic61#10711yescharacteristic
84C4×D61—21no—
85C4×D61—21no—
86C4×D61—21no—
87C4×D61—21no—
88C4×D61—41no—
89C4×D61—41no—
90#92420—82no—
91C8×C61—21no—
92C8×C61—21no—
93#92418—21no—
94#92418#9912yes—
95#7232—611nomaximal, Sylow
96C22×C61—21no—
97C22×C61—21no—
98C22×C61#34011yescharacteristic
99C22×C61#35911yescharacteristic
100C22×C61#35911yescharacteristic
101C2×D61—21no—
102C2×D61—21no—
103C2×D61—21no—
104C2×D61—21no—
105C2×D61—21no—
106C2×D61—42no—
107C2×D61—42no—
108C2×D61#36512yes—
109C4×C61—21no—
110C4×C61—161no—
111C4×C61H(3,ℤ/4)11yescharacteristic
112C4×C61#34211yescharacteristic
113Dic61—21no—
114Dic61—21no—
115Dic61—161no—
116C2×C22⋊C16—611no—
117#1810—611no—
118#1807—611no—
119C2×C61—21no—
120C2×C61—21no—
121C2×C61#128911yescharacteristic
122C2×C61#138211yescharacteristic
123C2×C61#138311yescharacteristic
124D61—22no—
125D61—41no—
126C23×C8—611no—
127C22×C16—612no—
128C2×#108—1221no—
129C2×#106—1221no—
130#407—1221no—
131#380—1221no—
132C22⋊C16—1221no—
133C22⋊C16—1221no—
134#341—612no—
135#340—611no—
136#340#692311yescharacteristic
137C61#723211yescharacteristic, complemented, Sylow
138C23×C4—611no—
139C2×M16—1222no—
140C22×C8—611no—
141C22×C8—611no—
142C22×C8—611no—
143C22×C8—611no—
144C22×C8—611no—
145C22×C8—2442no—
146C22×C8C2×#692311yescharacteristic
147C2×C4⋊C4—21no—
148C2×C4⋊C4—1221no—
149C2×C22⋊C4—2441no—
150C2×C16—1222no—
151C2×C16—2442no—
152#108—2442no—
153#106—2442no—
154C22⋊C8—2441no—
155C22⋊C8—2441no—
156#95—2441no—
157C24—611no—
158C22×C4—41no—
159C22×C4—611no—
160C22×C4—611no—
161C22×C4—611no—
162C22×C4—611no—
163C22×C4—611no—
164C22×C4—2441no—
165C22×C4—2441no—
166C22×C4—2441no—
167C22×C4C22⋊#692311yescharacteristic
168M16—2442no—
169M16—2442no—
170C2×C8—41no—
171C2×C8—611no—
172C2×C8—611no—
173C2×C8—1222no—
174C2×C8—1222no—
175C2×C8—1222no—
176C2×C8—2441no—
177C2×C8—2441no—
178C2×C8—2442no—
179C2×C8C4×#692311yescharacteristic
180C2×C8C4⋊#692311yescharacteristic
181C4⋊C4—41no—
182C4⋊C4—41no—
183C4⋊C4—2441no—
184C4⋊C4—2441no—
185C22⋊C4—4882no—
186C16—2442no—
187C23—611no—
188C23—611no—
189C23—1222no—
190C23—1221no—
191C23—1221no—
192C23—2441no—
193C23#1451983911yescharacteristic
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—81no—
197C2×C4—81no—
198C2×C4—81no—
199C2×C4—611no—
200C2×C4—611no—
201C2×C4—1221no—
202C2×C4—1221no—
203C2×C4—1221no—
204C2×C4—1221no—
205C2×C4—4881no—
206C2×C4—4881no—
207C2×C4—4881no—
208C2×C4—2441no—
209C2×C4—2441no—
210C2×C4—2441no—
211C2×C4(C2×#6923)⋊C411yescharacteristic
212C2×C4#1451984011yescharacteristic
213C8—21no—
214C8—21no—
215C8—612no—
216C8—1221no—
217C8—4882no—
218C22—21no—
219C22—21no—
220C22—612no—
221C22—1221no—
222C22—1221no—
223C22—1221no—
224C22—1221no—
225C22—1221no—
226C22—2442no—
227C22—2442no—
228C22#1684063511yescharacteristic
229C22#1684067611yescharacteristic
230C22#1684067711yescharacteristic
231C4—21no—
232C4—161no—
233C4—1221no—
234C4—1221no—
235C4—9761no—
236C4#1684062911yescharacteristic
237C4#1684063911yescharacteristic
238C2—21no—
239C2—21no—
240C2—1222no—
241C2—2441no—
242C2#2146068111yescharacteristic
243C2#2146088011yescharacteristic
244C2#2146088311yescharacteristic
subgroupG/H
centerC22#16840635
commutatorC2×C8×C61C42
FrattiniC22×C8C2×#6923
FittingC61×#340C4
socleC22×C61#340
prime radicalC23×D61SD16
cosocleC22×C8×D61C22
hypercenter#340#6923
hypocenterC61#7232
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #340

Complements

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

NH ≅ G/Ntype
4. C2×D61⋊C16C4semidirect
9. #16840638C4semidirect
137. C61#7232semidirect

Maximal subgroups

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

subgroupindex
D61⋊(C22⋊C16)2
#214616992
#214458432
#723261