Finite Group Databasebeta

← D61⋊#1409 #30608348

Subgroups — D61⋊#1409 #30608348

Order 15616.

474 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 58 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⋊#353C212yesmaximal
2#21460953C212yesmaximal, complemented
3#21460952C212yesmaximal, complemented
4#492×D61C211yesmaximal, characteristic
5D61⋊#99—22no—
6#16840667C2214yes—
7#16840666—22no—
8C2×SD16×D61—22no—
9C4⋊Q8×D61C411yescharacteristic, complemented
10#127×D61C2211yescharacteristic
11#16840136C2211yescharacteristic
12#16840135C2211yescharacteristic
13#16840134C411yescharacteristic, complemented
14#16840133—22no—
15C4×C8×D61C411yescharacteristic, complemented
16C61×#492C411yescharacteristic, complemented
17C2×C22⋊#6923—42no—
18#14519836—24no—
19#14519835—42no—
20C2×Q8×D61—21no—
21C2×D4×D61—41no—
22C2×D4×D61D412yes—
23C2×#11758190—22no—
24C2×#11758200—22no—
25C2×#11758201—22no—
26SD16×D61—44no—
27SD16×D61—44no—
28C2×C8×D61—21no—
29#14519777C2×C411yescharacteristic, complemented
30#14519776—41no—
31#14519775—21no—
32#14519774C2311yescharacteristic
33#14519773—41no—
34#14519773D412yes—
35C4⋊C4×D61—41no—
36C42×D61C2×C411yescharacteristic
37C4×#92418C2×C411yescharacteristic, complemented
38C8×Dic61—21no—
39C2×SD16×C61—22no—
40C4⋊Q8×C61C2×C411yescharacteristic, complemented
41#127×C61C2×C411yescharacteristic
42C4×C8×C61C2×C411yescharacteristic, complemented
43C23×D61—22no—
44C22×#6923—82no—
45C2×Q8×C61—21no—
46C2×D4×C61—41no—
47C2×D4×C61C22⋊C412yes—
48C2×C22⋊D61—22no—
49C2×C22⋊D61—42no—
50Q8×D61—42no—
51Q8×D61—42no—
52D4×D61—42no—
53D4×D61—42no—
54D4×D61—84no—
55C2×D244—41no—
56C2×D244C2×D412yes—
57C2×C4×D61—21no—
58C2×C4×D61—41no—
59C2×C4×D61C22⋊C411yescharacteristic
60C2×Dic122—21no—
61C2×Dic122—41no—
62C22⋊#6923—44no—
63C22⋊#6923—82no—
64SD16×C61—44no—
65C2×C8×C61—21no—
66C4⋊C4×C61—41no—
67C42×C61C22×C411yescharacteristic
68#11758201—44no—
69#11758200—44no—
70C4⋊Dic61—41no—
71#11758196—42no—
72C4×Dic61—21no—
73C4×Dic61C22⋊C411yescharacteristic
74C2×#92418—21no—
75#11758190—44no—
76C8×D61—22no—
77C8×D61—22no—
78C23×C61—22no—
79C22×D61—22no—
80C22×D61—42no—
81C22×D61—42no—
82C22×D61—84no—
83C22×D61#9911yescharacteristic
84C2×#6923—84no—
85C2×#6923—164no—
86Q8×C61—42no—
87D4×C61—42no—
88D4×C61—82no—
89C2×C4×C61—21no—
90C2×C4×C61—41no—
91C2×C4×C61C2×C22⋊C411yescharacteristic
92C22⋊D61—82no—
93C22⋊D61—84no—
94C2×Dic61—21no—
95C2×Dic61—41no—
96C2×Dic61#9911yescharacteristic
97D244—42no—
98D244—82no—
99C4×D61—24no—
100C4×D61—21no—
101C4×D61—21no—
102C4×D61—81no—
103C4×D61—81no—
104Dic122—42no—
105Dic122—82no—
106C8×C61—22no—
107#92418—22no—
108C2×#1409—611nomaximal, Sylow
109C22×C61—42no—
110C22×C61—82no—
111C22×C61C2×#9911yescharacteristic
112C2×D61—22no—
113C2×D61—42no—
114C2×D61—84no—
115C2×D61—82no—
116C2×D61—162no—
117C2×D61#35311yescharacteristic
118C2×D61#35311yescharacteristic
119#6923—164no—
120C4×C61—22no—
121C4×C61—21no—
122C4×C61—81no—
123Dic61—22no—
124Dic61—21no—
125Dic61—81no—
126C2×#492—611no—
127C2×#353—612no—
128#1409—612no—
129#1409—612no—
130C2×C61—21no—
131C2×C61—82no—
132C2×C61C2×#35311yescharacteristic
133D61—21no—
134D61—82no—
135D61#140912yescomplemented
136C22×SD16—1222no—
137C2×C4⋊Q8—611no—
138C2×#127—611no—
139#492—611no—
140#492—611no—
141#492—611no—
142#492—1222no—
143#492#692311yescharacteristic, complemented
144C2×#99—1222no—
145C2×C4×C8—611no—
146#353—614no—
147#353—1222no—
148C61C2×#140911yescharacteristic, complemented, Sylow
149C22×Q8—1221no—
150C22×D4—612no—
151C22×D4—2441no—
152C2×SD16—22no—
153C2×SD16—1222no—
154C2×SD16—1222no—
155C2×SD16—1222no—
156C2×SD16—2444no—
157C2×SD16—2444no—
158C22×C8—1221no—
159C4⋊Q8—611no—
160C4⋊Q8—1221no—
161C4⋊Q8—2441no—
162C4⋊Q8C2×#692311yescharacteristic, complemented
163#127—612no—
164#127—611no—
165#127—2441no—
166#127C2×#692311yescharacteristic
167C2×C4⋊C4—2441no—
168C2×C22⋊C4—2442no—
169C2×C42—611no—
170#99—1224no—
171#99—2442no—
172C4×C8—611no—
173C4×C8—1221no—
174C4×C8C2×#692311yescharacteristic, complemented
175C24—1222no—
176C2×Q8—21no—
177C2×Q8—1221no—
178C2×Q8—2441no—
179C2×Q8—2442no—
180C2×Q8—2442no—
181C2×D4—41no—
182C2×D4—612no—
183C2×D4—1222no—
184C2×D4—4884no—
185C2×D4—2441no—
186C2×D4—2442no—
187C2×D4—2442no—
188C2×D4—2442no—
189C2×D4C22⋊#692312yes—
190C22×C4—611no—
191C22×C4—1221no—
192C22×C4—4882no—
193C22×C4—2441no—
194SD16—44no—
195SD16—2444no—
196SD16—2444no—
197SD16—2444no—
198C2×C8—21no—
199C2×C8—1222no—
200C2×C8—1222no—
201C2×C8—1221no—
202C4⋊C4—41no—
203C4⋊C4—2441no—
204C4⋊C4—2442no—
205C22⋊C4—4882no—
206C22⋊C4—2444no—
207C42—611no—
208C42—1221no—
209C42C22×#692311yescharacteristic
210C23—22no—
211C23—611no—
212C23—1222no—
213C23—4884no—
214C23—2442no—
215C23—2442no—
216Q8—42no—
217Q8—4882no—
218Q8—2442no—
219D4—42no—
220D4—82no—
221D4—4882no—
222D4—4882no—
223D4—4884no—
224D4—2442no—
225C2×C4—21no—
226C2×C4—41no—
227C2×C4—611no—
228C2×C4—1221no—
229C2×C4—1221no—
230C2×C4—1224no—
231C2×C4—1221no—
232C2×C4—9764no—
233C2×C4—4881no—
234C2×C4—4881no—
235C2×C4—4884no—
236C2×C4—2441no—
237C2×C4C2×C22⋊#692311yescharacteristic
238C8—22no—
239C8—1222no—
240C22—42no—
241C22—82no—
242C22—611no—
243C22—611no—
244C22—1222no—
245C22—9762no—
246C22—4882no—
247C22—4884no—
248C22—2442no—
249C22D61⋊#9911yescharacteristic
250C4—22no—
251C4—21no—
252C4—81no—
253C4—1222no—
254C4—1221no—
255C4—9764no—
256C4—4881no—
257C2—21no—
258C2—82no—
259C2—612no—
260C2—1221no—
261C2—4882no—
262C2D61⋊#35311yescharacteristic
subgroupG/H
centerC2D61⋊#353
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#492C4
socleC2×C61C2×#353
prime radical#127×D61C22
cosocle#14519774C23
hypercenter#492#6923
hypocenterC61C2×#1409
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #492

Complements

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

NH ≅ G/Ntype
2. #21460953C2semidirect
3. #21460952C2semidirect
9. C4⋊Q8×D61C4semidirect
13. #16840134C4semidirect
15. C4×C8×D61C4semidirect
16. C61×#492C4semidirect
29. #14519777C2×C4semidirect
37. C4×#92418C2×C4semidirect
40. C4⋊Q8×C61C2×C4semidirect
42. C4×C8×C61C2×C4semidirect
135. D61#1409semidirect
143. #492#6923semidirect
148. C61C2×#1409semidirect
162. C4⋊Q8C2×#6923semidirect
174. C4×C8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
D61⋊#3532
#214609532
#214609522
#492×D612
C2×#140961