Finite Group Databasebeta

← D61⋊#1359 #30605547

Subgroups — D61⋊#1359 #30605547

Order 15616.

442 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 88 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⋊#364C212yesmaximal, complemented
2#21460830C212yesmaximal, complemented
3#21460829C212yesmaximal, complemented
4#492×D61C211yesmaximal, characteristic
5D61⋊M32—22no—
6#16840685C2214yescomplemented
7#16840684—22no—
8C2×SD16×D61—22no—
9C4⋊Q8×D61C411yescharacteristic
10#127×D61C411yescharacteristic
11#16840136C2211yescharacteristic
12#16840135C411yescharacteristic
13#16840134C2211yescharacteristic
14#16840133—22no—
15C4×C8×D61C2211yescharacteristic
16C61×#492C411yescharacteristic
17#14519852—42no—
18#14519851—24no—
19D61⋊C16—42no—
20C2×Q8×D61—21no—
21C2×D4×D61—21no—
22C2×D4×D61—41no—
23C2×#11758190—22no—
24C2×#11758200—22no—
25C2×#11758201—22no—
26SD16×D61—42no—
27SD16×D61—42no—
28SD16×D61—42no—
29SD16×D61—42no—
30C2×C8×D61D412yes—
31#14519777C2×C411yescharacteristic
32#14519776—41no—
33#14519775—21no—
34#14519774C2×C411yescharacteristic
35#14519773—21no—
36#14519773—41no—
37C4⋊C4×D61—41no—
38C42×D61C2×C411yescharacteristic
39C4×#92418C2311yescharacteristic
40C8×Dic61D412yes—
41C2×SD16×C61—22no—
42C4⋊Q8×C61C2×C411yescharacteristic
43#127×C61C2×C411yescharacteristic
44C4×C8×C61C2×C411yescharacteristic
45C23×D61—41no—
46C2×Q8×C61—21no—
47C2×D4×C61—21no—
48C2×D4×C61—41no—
49C2×C22⋊D61—42no—
50C2×C22⋊D61—41no—
51Q8×D61—42no—
52Q8×D61—42no—
53D4×D61—42no—
54D4×D61—42no—
55D4×D61—84no—
56C2×D244—21no—
57C2×D244—41no—
58C2×C4×D61—21no—
59C2×C4×D61—41no—
60C2×C4×D61C22⋊C411yescharacteristic
61C2×Dic122—21no—
62C2×Dic122—41no—
63SD16×C61—42no—
64SD16×C61—42no—
65C2×C8×C61C22⋊C412yes—
66C4⋊C4×C61—41no—
67C42×C61C22×C411yescharacteristic
68#11758201—42no—
69#11758201—42no—
70#11758200—42no—
71#11758200—42no—
72C4⋊Dic61—41no—
73#11758196—42no—
74C4×Dic61—21no—
75C4×Dic61C22⋊C411yescharacteristic
76C2×#92418C2×D412yes—
77#11758190—42no—
78#11758190—42no—
79C8×D61D812yes—
80C8×D61D812yes—
81C8×D61SD1612yes—
82C8×D61SD1612yes—
83#11758187—44no—
84C23×C61—41no—
85C22×D61—41no—
86C22×D61—84no—
87C22×D61—81no—
88C22×D61—81no—
89C22×D61#10011yescharacteristic
90Q8×C61—42no—
91D4×C61—42no—
92D4×C61—82no—
93C2×C4×C61—21no—
94C2×C4×C61—41no—
95C2×C4×C61C2×C22⋊C411yescharacteristic
96C22⋊D61—84no—
97C22⋊D61—82no—
98C2×Dic61—21no—
99C2×Dic61—41no—
100C2×Dic61#10011yescharacteristic
101D244—42no—
102D244—82no—
103C4×D61—24no—
104C4×D61—81no—
105C4×D61—81no—
106C4×D61#10212yes—
107C4×D61#10212yes—
108Dic122—42no—
109Dic122—82no—
110C8×C61#10212yes—
111C8×C61#10212yes—
112#92418C2×D812yes—
113#92418C2×SD1612yes—
114C2×#1359—611nomaximal, Sylow
115C22×C61—82no—
116C22×C61—81no—
117C22×C61C2×#10011yescharacteristic
118C2×D61—22no—
119C2×D61—82no—
120C2×D61—81no—
121C2×D61—162no—
122C2×D61—162no—
123C2×D61#33111yescharacteristic
124C2×D61#33111yescharacteristic
125C4×C61—22no—
126C4×C61—81no—
127C4×C61C2×#10212yes—
128Dic61—22no—
129Dic61—81no—
130Dic61#33112yes—
131C2×#492—611no—
132C2×#364—612no—
133#1359—612no—
134#1359—612no—
135C2×C61—21no—
136C2×C61—161no—
137C2×C61C2×#33111yescharacteristic
138D61—21no—
139D61—161no—
140D61#135912yescomplemented
141C22×SD16—1222no—
142C2×C4⋊Q8—611no—
143C2×#127—611no—
144C2×M32—1222no—
145#492—611no—
146#492—611no—
147#492—611no—
148#492—1222no—
149#492#692311yescharacteristic
150C2×C4×C8—611no—
151#364—614no—
152#364—1222no—
153C61C2×#135911yescharacteristic, complemented, Sylow
154C22×Q8—1221no—
155C22×D4—1221no—
156C22×D4—2441no—
157C2×SD16—22no—
158C2×SD16—1222no—
159C2×SD16—1222no—
160C2×SD16—1222no—
161C2×SD16—2442no—
162C2×SD16—2442no—
163C2×SD16—2442no—
164C2×SD16—2442no—
165C22×C8—612no—
166C4⋊Q8—611no—
167C4⋊Q8—1221no—
168C4⋊Q8—2441no—
169C4⋊Q8C2×#692311yescharacteristic
170#127—611no—
171#127—1221no—
172#127—2441no—
173#127C2×#692311yescharacteristic
174C2×C4⋊C4—2441no—
175C2×C42—611no—
176M32—1224no—
177M32—2442no—
178C2×C16—2442no—
179C4×C8—612no—
180C4×C8—611no—
181C4×C8C2×#692311yescharacteristic
182C24—2441no—
183C2×Q8—21no—
184C2×Q8—1221no—
185C2×Q8—2441no—
186C2×Q8—2442no—
187C2×Q8—2442no—
188C2×D4—21no—
189C2×D4—41no—
190C2×D4—1221no—
191C2×D4—4884no—
192C2×D4—2441no—
193C2×D4—2442no—
194C2×D4—2442no—
195C2×D4—2441no—
196C2×D4—2442no—
197C22×C4—611no—
198C22×C4—1221no—
199C22×C4—2441no—
200SD16—42no—
201SD16—42no—
202SD16—2442no—
203SD16—2442no—
204SD16—2442no—
205SD16—2442no—
206SD16—2442no—
207SD16—2442no—
208C2×C8—612no—
209C2×C8—612no—
210C2×C8—612no—
211C2×C8—612no—
212C2×C8—612no—
213C2×C8C22⋊#692312yes—
214C4⋊C4—41no—
215C4⋊C4—2441no—
216C4⋊C4—2442no—
217C42—611no—
218C42—1221no—
219C42C22×#692311yescharacteristic
220C16—2444no—
221C23—41no—
222C23—611no—
223C23—4881no—
224C23—4881no—
225C23—4884no—
226C23—2441no—
227Q8—42no—
228Q8—4882no—
229Q8—2442no—
230D4—42no—
231D4—82no—
232D4—4882no—
233D4—4882no—
234D4—4884no—
235D4—2442no—
236C2×C4—21no—
237C2×C4—41no—
238C2×C4—611no—
239C2×C4—612no—
240C2×C4—612no—
241C2×C4—1224no—
242C2×C4—1221no—
243C2×C4—4881no—
244C2×C4—4881no—
245C2×C4—2441no—
246C2×C4C2×C22⋊#692311yescharacteristic
247C8—612no—
248C8—612no—
249C8#1451983912yes—
250C8#1451983912yes—
251C22—82no—
252C22—81no—
253C22—611no—
254C22—611no—
255C22—1222no—
256C22—9762no—
257C22—9762no—
258C22—4882no—
259C22—4881no—
260C22D61⋊#10011yescharacteristic
261C4—22no—
262C4—81no—
263C4—612no—
264C4—1222no—
265C4—4881no—
266C4C2×#1451983912yes—
267C2—21no—
268C2—161no—
269C2—612no—
270C2—1221no—
271C2—9761no—
272C2D61⋊#33111yescharacteristic
subgroupG/H
centerC2D61⋊#331
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#492C4
socleC2×C61C2×#331
prime radical#127×D61C4
cosocleC4×#92418C23
hypercenter#492#6923
hypocenterC61C2×#1359
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #492

Complements

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

NH ≅ G/Ntype
1. D61⋊#364C2semidirect
2. #21460830C2semidirect
3. #21460829C2semidirect
6. #16840685C22semidirect
140. D61#1359semidirect
153. C61C2×#1359semidirect

Maximal subgroups

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

subgroupindex
D61⋊#3642
#214608302
#214608292
#492×D612
C2×#135961