Finite Group Databasebeta

← #30594569

Subgroups — #30594569

Order 15616.

318 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 62 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⋊#349C211yesmaximal, characteristic
2#21461700C211yesmaximal, characteristic
3H(3,ℤ/4)×D61C211yesmaximal, characteristic
4D61⋊M32—21no—
5C2×#14519848C411yescharacteristic, complemented
6C2×#14519847C411yescharacteristic, complemented
7#16840733—21no—
8#16840659C412yescomplemented
9#16840658—21no—
10#16840638—21no—
11C2×M16×D61C2211yescharacteristic
12#117×D61—21no—
13#16839519C411yescharacteristic
14#16839518—21no—
15C61×H(3,ℤ/4)C411yescharacteristic
16C2×#11758213—21no—
17C2×#11758213—21no—
18#14519852—41no—
19#14519851—22no—
20D61⋊C16—41no—
21#14519848—41no—
22#14519847—41no—
23#14519834—41no—
24C22⋊#92420—41no—
25C22×C4×D61D411yescharacteristic
26C2×#11758194D411yescharacteristic
27C2×#11758189C2×C411yescharacteristic
28C2×#11758189Q811yescharacteristic
29M16×D61—41no—
30M16×D61—41no—
31C2×C8×D61C2×C411yescharacteristic
32C2×C8×D61D411yescharacteristic
33#14519736—21no—
34#14519735—41no—
35#14519734—22no—
36#14519733—41no—
37C4⋊C4×D61—41no—
38C22⋊C4×D61—41no—
39C42×D61—22no—
40C2×M16×C61C2×C411yescharacteristic
41#117×C61—21no—
42C23×D61SD1611yescharacteristic
43C22×C4×C61C22⋊C411yescharacteristic
44C22×Dic61D811yescharacteristic
45C2×C4×D61—21no—
46C2×C4×D61—21no—
47C2×C4×D61—21no—
48C2×C4×D61—21no—
49C2×C4×D61—42no—
50C2×C4×D61C22⋊C411yescharacteristic
51C2×C4×D61C4⋊C411yescharacteristic
52C2×C4×D61SD1611yescharacteristic
53C2×C4×D61Q1611yescharacteristic
54C2×#92420—41no—
55C2×#92420—41no—
56#11758213—41no—
57#11758213—41no—
58#11758213—41no—
59#11758213—41no—
60M16×C61—41no—
61C2×C8×C61C4211yescharacteristic
62C2×C8×C61C4⋊C411yescharacteristic
63C4⋊C4×C61—41no—
64C22⋊C4×C61—41no—
65C42×C61—22no—
66C22⋊Dic61—41no—
67#11758198—42no—
68C4⋊Dic61—41no—
69#11758196—42no—
70C4×Dic61—22no—
71C4×Dic61—42no—
72#11758194—41no—
73C2×#92418C22⋊C411yescharacteristic
74C2×#92418C4⋊C411yescharacteristic
75#11758189—41no—
76#11758189—41no—
77C8×D61—21no—
78C8×D61—21no—
79C8×D61—21no—
80C8×D61—21no—
81#11758187—42no—
82C23×C61#10211yescharacteristic
83C22×D61—21no—
84C22×D61—21no—
85C22×D61—81no—
86C22×D61#10311yescharacteristic
87C22×D61#10611yescharacteristic
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—42no—
91C2×C4×C61#9511yescharacteristic
92C2×C4×C61#10311yescharacteristic
93C2×Dic61—21no—
94C2×Dic61—21no—
95C2×Dic61—42no—
96C2×Dic61#10211yescharacteristic
97C2×Dic61#10711yescharacteristic
98C4×D61—21no—
99C4×D61—21no—
100C4×D61—21no—
101C4×D61—21no—
102C4×D61—21no—
103C4×D61—21no—
104C4×D61—84no—
105C4×D61#9911yescharacteristic
106C4×D61#9911yescharacteristic
107C4×D61#10411yescharacteristic
108C4×D61#10411yescharacteristic
109#92420—81no—
110#92420—81no—
111C8×C61—21no—
112C8×C61—21no—
113#92418—21no—
114#92418—21no—
115#7256—611nomaximal, Sylow
116C22×C61—21no—
117C22×C61—41no—
118C22×C61#34011yescharacteristic
119C2×D61—21no—
120C2×D61—41no—
121C2×D61—42no—
122C2×D61—41no—
123C2×D61—81no—
124C2×D61#32811yescharacteristic
125C2×D61#32811yescharacteristic
126C4×C61—21no—
127C4×C61—82no—
128C4×C61#33911yescharacteristic
129C4×C61#34211yescharacteristic
130Dic61—21no—
131Dic61—82no—
132Dic61#32711yescharacteristic
133Dic61#32711yescharacteristic
134C2×#349—611no—
135#1811—611no—
136C2×H(3,ℤ/4)—611no—
137C2×C61—21no—
138C2×C61—41no—
139C2×C61#129411yescharacteristic
140D61—21no—
141D61—21no—
142D61—41no—
143C22×M16—611no—
144C2×#117—1221no—
145C2×M32—1221no—
146C2×#108—611no—
147C2×#108—611no—
148#407—1221no—
149#349—612no—
150#349—1221no—
151#341—1221no—
152H(3,ℤ/4)—611no—
153H(3,ℤ/4)—1221no—
154H(3,ℤ/4)#692311yescharacteristic
155C61#725611yescharacteristic, complemented, Sylow
156C23×C4—611no—
157C2×M16—611no—
158C2×M16—611no—
159C2×M16—611no—
160C2×M16—1221no—
161C2×M16—1221no—
162C2×M16—2441no—
163C2×M16—2441no—
164C2×M16C2×#692311yescharacteristic
165C22×C8—611no—
166C22×C8—611no—
167#117—21no—
168#117—1222no—
169#117—1221no—
170#117—2441no—
171#117—2441no—
172C2×C4⋊C4—2441no—
173C2×C22⋊C4—2441no—
174C2×C42—1222no—
175M32—1222no—
176M32—2441no—
177C2×C16—2441no—
178#108—2441no—
179#108—2441no—
180C22⋊C8—2441no—
181C22⋊C8—2441no—
182C24—611no—
183C22×C4—611no—
184C22×C4—611no—
185C22×C4—611no—
186C22×C4—611no—
187C22×C4—611no—
188C22×C4—1221no—
189C22×C4—1221no—
190C22×C4—1221no—
191C22×C4—1221no—
192C22×C4—2442no—
193C22×C4C22⋊#692311yescharacteristic
194M16—41no—
195M16—2441no—
196M16—2441no—
197M16—2441no—
198M16—2441no—
199M16—2441no—
200M16—2441no—
201M16—2441no—
202C2×C8—611no—
203C2×C8—611no—
204C2×C8—1221no—
205C2×C8—1221no—
206C2×C8—1221no—
207C2×C8—1221no—
208C2×C8—2441no—
209C2×C8—2441no—
210C2×C8C4×#692311yescharacteristic
211C2×C8C4⋊#692311yescharacteristic
212C4⋊C4—41no—
213C4⋊C4—2441no—
214C4⋊C4—2442no—
215C22⋊C4—41no—
216C22⋊C4—2442no—
217C22⋊C4—2441no—
218C42—22no—
219C42—1222no—
220C42—2442no—
221C16—2442no—
222C23—611no—
223C23—611no—
224C23—1221no—
225C23—1221no—
226C23—4881no—
227C23#1451983911yescharacteristic
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—42no—
231C2×C4—611no—
232C2×C4—611no—
233C2×C4—611no—
234C2×C4—611no—
235C2×C4—611no—
236C2×C4—611no—
237C2×C4—1221no—
238C2×C4—1221no—
239C2×C4—1221no—
240C2×C4—1221no—
241C2×C4—1221no—
242C2×C4—1221no—
243C2×C4—1221no—
244C2×C4—1221no—
245C2×C4—4884no—
246C2×C4—2442no—
247C2×C4(C2×#6923)⋊C411yescharacteristic
248C2×C4#1451984011yescharacteristic
249C8—21no—
250C8—21no—
251C8—1221no—
252C8—1221no—
253C8—4881no—
254C8—4881no—
255C22—21no—
256C22—41no—
257C22—611no—
258C22—611no—
259C22—1221no—
260C22—4881no—
261C22—2441no—
262C22—2441no—
263C22—2442no—
264C22#1684063511yescharacteristic
265C4—21no—
266C4—82no—
267C4—611no—
268C4—611no—
269C4—1221no—
270C4—4882no—
271C4#1684063311yescharacteristic
272C4#1684063911yescharacteristic
273C2—21no—
274C2—41no—
275C2—1221no—
276C2—1221no—
277C2—2441no—
278C2#2146069311yescharacteristic
subgroupG/H
centerC2#21460693
commutatorC2×C8×C61C42
FrattiniC2×M16C2×#6923
FittingC61×H(3,ℤ/4)C4
socleC2×C61#1294
prime radicalC23×D61SD16
cosocleC2×M16×D61C22
hypercenterH(3,ℤ/4)#6923
hypocenterC61#7256
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
5. C2×#14519848C4semidirect
6. C2×#14519847C4semidirect
8. #16840659C4semidirect
155. C61#7256semidirect

Maximal subgroups

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

subgroupindex
D61⋊#3492
#214617002
H(3,ℤ/4)×D612
#725661