Finite Group Databasebeta

← #30594583

Subgroups — #30594583

Order 15616.

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

normal subgroups only

This group has 336 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
1D61⋊(C22⋊C16)C211yesmaximal, characteristic
2#21461699C211yesmaximal, characteristic
3#21445534C211yesmaximal, characteristic
4C2×D61⋊C16—21no—
5C2×#14519848C412yescomplemented
6#16840733—21no—
7#16840657C412yescomplemented
8C22⋊#11758187—21no—
9#16840638—21no—
10C22×C8×D61C2211yescharacteristic
11C2×#14519735—21no—
12#16839525C411yescharacteristic
13#16839524—21no—
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
28#14519735—24no—
29#14519735—42no—
30C2×C4⋊Dic61—21no—
31C2×#11758198—41no—
32C2×C4×Dic61—41no—
33C22×C8×C61C2×C411yescharacteristic
34C2×C4⋊C4×C61—21no—
35C23×D61SD1611yescharacteristic
36C22×C4×C61—41no—
37C22×C4×C61C22⋊C411yescharacteristic
38C22×Dic61—41no—
39C22×Dic61D811yescharacteristic
40C2×C4×D61—22no—
41C2×C4×D61—22no—
42C2×C4×D61C22⋊C411yescharacteristic
43C2×C4×D61C4⋊C411yescharacteristic
44C2×C4×D61SD1611yescharacteristic
45C2×C4×D61Q1611yescharacteristic
46C2×#92420—42no—
47#11758213—42no—
48#11758213—42no—
49C2×C8×C61—41no—
50C2×C8×C61C4211yescharacteristic
51C2×C8×C61C4⋊C411yescharacteristic
52C4⋊C4×C61—22no—
53C4⋊C4×C61—41no—
54#11758198—44no—
55C4⋊Dic61—22no—
56C4⋊Dic61—41no—
57C4×Dic61—44no—
58C2×#92418—41no—
59C2×#92418C22⋊C411yescharacteristic
60C2×#92418C4⋊C411yescharacteristic
61C8×D61—22no—
62C8×D61—22no—
63C8×D61—41no—
64C8×D61—41no—
65#11758187—42no—
66C23×C61#10211yescharacteristic
67C22×D61—21no—
68C22×D61—21no—
69C22×D61—22no—
70C22×D61—41no—
71C22×D61#10311yescharacteristic
72C22×D61#10611yescharacteristic
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—42no—
76C2×C4×C61—81no—
77C2×C4×C61—81no—
78C2×C4×C61#9511yescharacteristic
79C2×C4×C61#10311yescharacteristic
80C2×Dic61—22no—
81C2×Dic61—42no—
82C2×Dic61—81no—
83C2×Dic61—81no—
84C2×Dic61#10211yescharacteristic
85C2×Dic61#10711yescharacteristic
86C4×D61—22no—
87C4×D61—21no—
88C4×D61—21no—
89C4×D61—22no—
90C4×D61#9912yes—
91C4×D61#10412yes—
92#92420—82no—
93C8×C61—21no—
94C8×C61—21no—
95#92418—21no—
96#92418—21no—
97#7260—611nomaximal, Sylow
98C22×C61—21no—
99C22×C61—21no—
100C22×C61#34011yescharacteristic
101C22×C61#35911yescharacteristic
102C22×C61#35911yescharacteristic
103C2×D61—21no—
104C2×D61—21no—
105C2×D61—21no—
106C2×D61—21no—
107C2×D61—21no—
108C2×D61—42no—
109C2×D61—42no—
110C2×D61#32812yes—
111C4×C61—21no—
112C4×C61—82no—
113C4×C61#33911yescharacteristic
114C4×C61#34211yescharacteristic
115Dic61—21no—
116Dic61—82no—
117Dic61#32712yes—
118C2×C22⋊C16—611no—
119#1810—611no—
120#1735—611no—
121C2×C61—21no—
122C2×C61—21no—
123C2×C61#129411yescharacteristic
124C2×C61#138211yescharacteristic
125C2×C61#138911yescharacteristic
126D61—22no—
127D61—41no—
128C23×C8—611no—
129C2×#117—1221no—
130C22×C16—1221no—
131C2×#108—612no—
132#407—1221no—
133C22⋊C16—612no—
134C22⋊C16—1221no—
135#341—1221no—
136#340—611no—
137#340—1221no—
138#340#692311yescharacteristic
139C61#726011yescharacteristic, complemented, Sylow
140C23×C4—611no—
141C2×M16—1222no—
142C22×C8—611no—
143C22×C8—611no—
144C22×C8—611no—
145C22×C8—611no—
146C22×C8—611no—
147C22×C8—2442no—
148C22×C8C2×#692311yescharacteristic
149#117—1224no—
150#117—2442no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—1221no—
153C2×C22⋊C4—2441no—
154C2×C42—2441no—
155C2×C16—1222no—
156C2×C16—2442no—
157#108—2442no—
158C22⋊C8—2441no—
159C22⋊C8—2441no—
160C24—611no—
161C22×C4—41no—
162C22×C4—611no—
163C22×C4—611no—
164C22×C4—611no—
165C22×C4—611no—
166C22×C4—611no—
167C22×C4—1222no—
168C22×C4—1222no—
169C22×C4—2441no—
170C22×C4C22⋊#692311yescharacteristic
171M16—2442no—
172M16—2442no—
173C2×C8—41no—
174C2×C8—611no—
175C2×C8—611no—
176C2×C8—1222no—
177C2×C8—1222no—
178C2×C8—2441no—
179C2×C8—2441no—
180C2×C8—2441no—
181C2×C8—2442no—
182C2×C8C4×#692311yescharacteristic
183C2×C8C4⋊#692311yescharacteristic
184C4⋊C4—22no—
185C4⋊C4—41no—
186C4⋊C4—1222no—
187C4⋊C4—2441no—
188C22⋊C4—2444no—
189C42—2444no—
190C16—2442no—
191C23—611no—
192C23—611no—
193C23—1222no—
194C23—1221no—
195C23—1221no—
196C23—2441no—
197C23#1451983911yescharacteristic
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—42no—
201C2×C4—81no—
202C2×C4—81no—
203C2×C4—611no—
204C2×C4—612no—
205C2×C4—612no—
206C2×C4—611no—
207C2×C4—1222no—
208C2×C4—1222no—
209C2×C4—1222no—
210C2×C4—1221no—
211C2×C4—1221no—
212C2×C4—4881no—
213C2×C4—4881no—
214C2×C4—2442no—
215C2×C4(C2×#6923)⋊C411yescharacteristic
216C2×C4#1451984011yescharacteristic
217C8—21no—
218C8—21no—
219C8—1221no—
220C8—1221no—
221C8—4882no—
222C22—21no—
223C22—21no—
224C22—612no—
225C22—1221no—
226C22—1221no—
227C22—1221no—
228C22—1221no—
229C22—1221no—
230C22—2442no—
231C22—2442no—
232C22#1684063511yescharacteristic
233C22#1684067611yescharacteristic
234C22#1684067711yescharacteristic
235C4—21no—
236C4—82no—
237C4—612no—
238C4—1221no—
239C4—4882no—
240C4#1684063311yescharacteristic
241C4#1684063911yescharacteristic
242C2—21no—
243C2—21no—
244C2—1222no—
245C2—2441no—
246C2#2146069311yescharacteristic
247C2#2146088011yescharacteristic
248C2#2146090111yescharacteristic
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#7260
LCSG ▷ C2×C8×C61 ▷ C2×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
5. C2×#14519848C4semidirect
7. #16840657C4semidirect
139. C61#7260semidirect

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
#214455342
#726061