Finite Group Databasebeta

← #30594591

Subgroups — #30594591

Order 15616.

336 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 76 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#21462048C211yesmaximal, characteristic
2#21461511C211yesmaximal, characteristic
3#21445841C211yesmaximal, characteristic
4C2×D61⋊M16—21no—
5C2×#14519851—21no—
6#16840657—21no—
7#16840657C412yescomplemented
8#16840638—21no—
9#16840638C412yescomplemented
10C22×C8×D61C2211yescharacteristic
11C2×#14519709C411yescharacteristic
12#16839619—21no—
13#16839524—21no—
14C2×#106×C61C411yescharacteristic
15C2×#11758213—22no—
16D61⋊M16—22no—
17D61⋊M16—22no—
18D61⋊M16—41no—
19D61⋊M16—41no—
20C2×#11758217—41no—
21C2×D61⋊C8—41no—
22#14519851—41no—
23#14519851—41no—
24C2×#11758187—22no—
25C22×C4×D61D411yescharacteristic
26C22×#92418D411yescharacteristic
27C2×C8×D61—41no—
28C2×C8×D61—41no—
29C2×C8×D61C2×C411yescharacteristic
30C2×C8×D61C2×C411yescharacteristic
31C2×C8×D61D411yescharacteristic
32C2×C8×D61Q811yescharacteristic
33C2×C4⋊Dic61—21no—
34C2×#11758198—41no—
35#14519709—41no—
36#14519684—41no—
37C22×C8×C61C2×C411yescharacteristic
38C2×C4⋊C4×C61—21no—
39#106×C61—41no—
40C23×D61SD1611yescharacteristic
41C22×C4×C61—41no—
42C22×C4×C61C22⋊C411yescharacteristic
43C22×Dic61—41no—
44C22×Dic61D811yescharacteristic
45C2×C4×D61—21no—
46C2×C4×D61—21no—
47C2×C4×D61—21no—
48C2×C4×D61—21no—
49C2×C4×D61C22⋊C411yescharacteristic
50C2×C4×D61C4⋊C411yescharacteristic
51C2×C4×D61SD1611yescharacteristic
52C2×C4×D61Q1611yescharacteristic
53#11758217—42no—
54#11758217—42no—
55C2×#92420—42no—
56#11758213—24no—
57#11758213—42no—
58D61⋊C8—42no—
59D61⋊C8—42no—
60C2×C8×C61—21no—
61C2×C8×C61—21no—
62C2×C8×C61C4211yescharacteristic
63C2×C8×C61C4⋊C411yescharacteristic
64C4⋊C4×C61—41no—
65C4⋊C4×C61—41no—
66#11758198—82no—
67C4⋊Dic61—41no—
68C4⋊Dic61—41no—
69C2×#92418—21no—
70C2×#92418—21no—
71C2×#92418C22⋊C411yescharacteristic
72C2×#92418C4⋊C411yescharacteristic
73C8×D61—41no—
74C8×D61—41no—
75C8×D61—41no—
76C8×D61—41no—
77#11758187—42no—
78C23×C61#10211yescharacteristic
79C22×D61—21no—
80C22×D61—21no—
81C22×D61—22no—
82C22×D61—41no—
83C22×D61#10311yescharacteristic
84C22×D61#10611yescharacteristic
85C2×C4×C61—81no—
86C2×C4×C61—81no—
87C2×C4×C61—81no—
88C2×C4×C61#9511yescharacteristic
89C2×C4×C61#9911yescharacteristic
90C2×C4×C61#9911yescharacteristic
91C2×C4×C61#10311yescharacteristic
92C2×C4×C61#10411yescharacteristic
93C2×C4×C61#10411yescharacteristic
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—81no—
97C2×Dic61—81no—
98C2×Dic61—81no—
99C2×Dic61#10211yescharacteristic
100C2×Dic61#10711yescharacteristic
101C4×D61—21no—
102C4×D61—21no—
103C4×D61—21no—
104C4×D61—21no—
105C4×D61—21no—
106C4×D61—21no—
107C4×D61—21no—
108C4×D61—21no—
109#92420—44no—
110C8×C61—21no—
111C8×C61—21no—
112#92418—21no—
113#92418—21no—
114#7263—611nomaximal, Sylow
115C22×C61—21no—
116C22×C61—21no—
117C22×C61#32711yescharacteristic
118C22×C61#32711yescharacteristic
119C22×C61#34011yescharacteristic
120C2×D61—21no—
121C2×D61—21no—
122C2×D61—21no—
123C2×D61—21no—
124C2×D61—21no—
125C2×D61—42no—
126C2×D61—42no—
127C2×D61#36512yes—
128C4×C61—161no—
129C4×C61#32811yescharacteristic
130C4×C61#32811yescharacteristic
131C4×C61#33911yescharacteristic
132C4×C61#34211yescharacteristic
133Dic61—21no—
134Dic61—21no—
135Dic61—161no—
136#2112—611no—
137#1807—611no—
138C2×#341—611no—
139C2×C61—21no—
140C2×C61—21no—
141C2×C61#129411yescharacteristic
142C2×C61#138311yescharacteristic
143C2×C61#138911yescharacteristic
144D61—22no—
145D61—41no—
146C22×M16—1221no—
147C23×C8—611no—
148C2×M32—1221no—
149C2×#106—611no—
150C2×#106#692311yescharacteristic
151#380—1221no—
152C22⋊C16—612no—
153C22⋊C16—1221no—
154#341—612no—
155#341—1221no—
156#340—1221no—
157C61#726311yescharacteristic, complemented, Sylow
158C23×C4—611no—
159C2×M16—1222no—
160C2×M16—1222no—
161C2×M16—1222no—
162C2×M16—2441no—
163C2×M16—2441no—
164C2×M16—2441no—
165C22×C8—611no—
166C22×C8—611no—
167C22×C8—611no—
168C22×C8—611no—
169C22×C8—611no—
170C22×C8—2441no—
171C22×C8—2441no—
172C22×C8—2441no—
173C22×C8C2×#692311yescharacteristic
174C2×C4⋊C4—21no—
175C2×C4⋊C4—1221no—
176C2×C22⋊C4—2441no—
177M32—2441no—
178M32—2441no—
179C2×C16—1222no—
180#106—41no—
181#106—2441no—
182#95—2441no—
183C24—611no—
184C22×C4—41no—
185C22×C4—611no—
186C22×C4—611no—
187C22×C4—611no—
188C22×C4—611no—
189C22×C4—611no—
190C22×C4—1221no—
191C22×C4—1221no—
192C22×C4—1221no—
193C22×C4—1221no—
194C22×C4—2441no—
195C22×C4C22⋊#692311yescharacteristic
196M16—1224no—
197M16—2442no—
198M16—2442no—
199M16—2442no—
200C2×C8—21no—
201C2×C8—21no—
202C2×C8—611no—
203C2×C8—611no—
204C2×C8—1221no—
205C2×C8—1221no—
206C2×C8—2441no—
207C2×C8—2441no—
208C2×C8—2441no—
209C2×C8—2441no—
210C2×C8—2442no—
211C2×C8—2442no—
212C2×C8—2442no—
213C2×C8C4×#692311yescharacteristic
214C2×C8C4⋊#692311yescharacteristic
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—2441no—
218C4⋊C4—2441no—
219C22⋊C4—4882no—
220C16—2442no—
221C23—611no—
222C23—611no—
223C23—1222no—
224C23—1221no—
225C23—1221no—
226C23—2441no—
227C23#1451983911yescharacteristic
228C2×C4—81no—
229C2×C4—81no—
230C2×C4—81no—
231C2×C4—611no—
232C2×C4—611no—
233C2×C4—1221no—
234C2×C4—1221no—
235C2×C4—1221no—
236C2×C4—1221no—
237C2×C4—1221no—
238C2×C4—1221no—
239C2×C4—1221no—
240C2×C4—1221no—
241C2×C4—1221no—
242C2×C4—1221no—
243C2×C4—4881no—
244C2×C4—4881no—
245C2×C4—4881no—
246C2×C4(C2×#6923)⋊C411yescharacteristic
247C2×C4#1451983511yescharacteristic
248C2×C4#1451983611yescharacteristic
249C2×C4#1451984011yescharacteristic
250C2×C4#1451984111yescharacteristic
251C2×C4#1451984211yescharacteristic
252C8—21no—
253C8—21no—
254C8—1221no—
255C8—1221no—
256C8—2444no—
257C22—21no—
258C22—21no—
259C22—612no—
260C22—1221no—
261C22—1221no—
262C22—1221no—
263C22—1221no—
264C22—1221no—
265C22—2442no—
266C22—2442no—
267C22#1684061311yescharacteristic
268C22#1684061411yescharacteristic
269C22#1684063511yescharacteristic
270C4—161no—
271C4—1221no—
272C4—1221no—
273C4—9761no—
274C4#1684061511yescharacteristic
275C4#1684061611yescharacteristic
276C4#1684063211yescharacteristic
277C4#1684064011yescharacteristic
278C2—21no—
279C2—21no—
280C2—1222no—
281C2—2441no—
282C2#2146069211yescharacteristic
283C2#2146088311yescharacteristic
284C2#2146090111yescharacteristic
subgroupG/H
centerC22#16840635
commutatorC2×C8×C61C42
FrattiniC22×C8C2×#6923
FittingC2×#106×C61C4
socleC22×C61#340
prime radicalC23×D61SD16
cosocleC22×C8×D61C22
hypercenterC2×#106#6923
hypocenterC61#7263
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
7. #16840657C4semidirect
9. #16840638C4semidirect
157. C61#7263semidirect

Maximal subgroups

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

subgroupindex
#214620482
#214615112
#214458412
#726361