Finite Group Databasebeta

← D61⋊#1410 #30608365

Subgroups — D61⋊#1410 #30608365

Order 15616.

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

normal subgroups only

This group has 450 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⋊#356C212yesmaximal, complemented
2#21460955C212yesmaximal, complemented
3#21460954C212yesmaximal, complemented
4#492×D61C211yesmaximal, characteristic
5D61⋊#101—22no—
6#16840673C2214yescomplemented
7#16840672—22no—
8C2×SD16×D61—22no—
9C4⋊Q8×D61C2211yescharacteristic
10#127×D61C411yescharacteristic
11#16840136C411yescharacteristic
12#16840135C2211yescharacteristic
13#16840134C2211yescharacteristic
14#16840133—22no—
15C4×C8×D61C411yescharacteristic
16C61×#492C411yescharacteristic
17D61⋊M16—42no—
18#14519838—24no—
19#14519838—42no—
20C2×Q8×D61D412yes—
21C2×D4×D61—21no—
22C2×D4×D61—41no—
23C2×#11758190—22no—
24C2×#11758200—22no—
25C2×#11758201—22no—
26SD16×D61—44no—
27SD16×D61—44no—
28C2×C8×D61—21no—
29#14519777C2311yescharacteristic
30#14519776—41no—
31#14519775D412yes—
32#14519774C2×C411yescharacteristic
33#14519773—21no—
34#14519773—41no—
35C4⋊C4×D61—41no—
36C42×D61C2×C411yescharacteristic
37C4×#92418C2×C411yescharacteristic
38C8×Dic61—21no—
39C2×SD16×C61—22no—
40C4⋊Q8×C61C2×C411yescharacteristic
41#127×C61C2×C411yescharacteristic
42C4×C8×C61C2×C411yescharacteristic
43C23×D61—41no—
44C2×Q8×C61C22⋊C412yes—
45C2×D4×C61—21no—
46C2×D4×C61—41no—
47C2×C22⋊D61—42no—
48C2×C22⋊D61—41no—
49Q8×D61—42no—
50Q8×D61—42no—
51D4×D61—42no—
52D4×D61—42no—
53D4×D61—84no—
54C2×D244—21no—
55C2×D244—41no—
56C2×C4×D61—21no—
57C2×C4×D61—22no—
58C2×C4×D61C22⋊C411yescharacteristic
59C2×Dic122—22no—
60C2×Dic122C2×D412yes—
61#11758217—44no—
62#11758213—82no—
63D61⋊C8—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—41no—
79C22×D61—41no—
80C22×D61—84no—
81C22×D61—81no—
82C22×D61—81no—
83C22×D61#9911yescharacteristic
84Q8×C61—42no—
85D4×C61—42no—
86D4×C61—82no—
87C2×C4×C61—21no—
88C2×C4×C61—22no—
89C2×C4×C61C2×C22⋊C411yescharacteristic
90C22⋊D61—82no—
91C22⋊D61—84no—
92C2×Dic61—21no—
93C2×Dic61—22no—
94C2×Dic61#9911yescharacteristic
95D244—42no—
96D244—82no—
97C4×D61—24no—
98C4×D61—21no—
99C4×D61—21no—
100C4×D61—42no—
101C4×D61—42no—
102Dic122—42no—
103Dic122—82no—
104#92420—84no—
105C8×C61—22no—
106#92418—22no—
107C2×#1410—611nomaximal, Sylow
108C22×C61—82no—
109C22×C61—81no—
110C22×C61C2×#9911yescharacteristic
111C2×D61—22no—
112C2×D61—82no—
113C2×D61—81no—
114C2×D61—162no—
115C2×D61—162no—
116C2×D61#35311yescharacteristic
117C2×D61#35311yescharacteristic
118C4×C61—22no—
119C4×C61—21no—
120C4×C61—42no—
121Dic61—22no—
122Dic61—21no—
123Dic61—42no—
124C2×#492—611no—
125C2×#356—612no—
126#1410—612no—
127#1410—612no—
128C2×C61—21no—
129C2×C61—161no—
130C2×C61C2×#35311yescharacteristic
131D61—21no—
132D61—161no—
133D61#141012yescomplemented
134C22×SD16—1222no—
135C2×C4⋊Q8—611no—
136C2×#127—611no—
137#492—611no—
138#492—611no—
139#492—611no—
140#492—1222no—
141#492#692311yescharacteristic
142C2×#101—1222no—
143C2×C4×C8—611no—
144#356—614no—
145#356—1222no—
146C61C2×#141011yescharacteristic, complemented, Sylow
147C22×Q8—612no—
148C22×D4—1221no—
149C22×D4—2441no—
150C2×SD16—22no—
151C2×SD16—1222no—
152C2×SD16—1222no—
153C2×SD16—1222no—
154C2×SD16—2444no—
155C2×SD16—2444no—
156C2×M16—2442no—
157C22×C8—1221no—
158C4⋊Q8—612no—
159C4⋊Q8—611no—
160C4⋊Q8—2441no—
161C4⋊Q8C2×#692311yescharacteristic
162#127—611no—
163#127—1221no—
164#127—2441no—
165#127C2×#692311yescharacteristic
166C2×C4⋊C4—2441no—
167C2×C42—611no—
168#101—1224no—
169#101—2442no—
170C4×C8—611no—
171C4×C8—1221no—
172C4×C8C2×#692311yescharacteristic
173C24—2441no—
174C2×Q8—612no—
175C2×Q8—1222no—
176C2×Q8—2442no—
177C2×Q8—2442no—
178C2×Q8C22⋊#692312yes—
179C2×D4—21no—
180C2×D4—41no—
181C2×D4—1221no—
182C2×D4—4884no—
183C2×D4—2441no—
184C2×D4—2441no—
185C2×D4—2442no—
186C2×D4—2442no—
187C2×D4—2442no—
188C22×C4—611no—
189C22×C4—1221no—
190C22×C4—1222no—
191SD16—44no—
192SD16—2444no—
193SD16—2444no—
194SD16—2444no—
195M16—4882no—
196M16—2444no—
197C2×C8—21no—
198C2×C8—1222no—
199C2×C8—1222no—
200C2×C8—1221no—
201C2×C8—4882no—
202C4⋊C4—41no—
203C4⋊C4—2442no—
204C4⋊C4—2441no—
205C42—611no—
206C42—1221no—
207C42C22×#692311yescharacteristic
208C23—41no—
209C23—611no—
210C23—4881no—
211C23—4881no—
212C23—4884no—
213C23—2441no—
214Q8—42no—
215Q8—4882no—
216Q8—2442no—
217D4—42no—
218D4—82no—
219D4—4882no—
220D4—4884no—
221D4—4882no—
222D4—2442no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—611no—
226C2×C4—1221no—
227C2×C4—1221no—
228C2×C4—1224no—
229C2×C4—1221no—
230C2×C4—1222no—
231C2×C4—2442no—
232C2×C4—2442no—
233C2×C4C2×C22⋊#692311yescharacteristic
234C8—22no—
235C8—1222no—
236C8—4884no—
237C22—82no—
238C22—81no—
239C22—611no—
240C22—611no—
241C22—1222no—
242C22—9762no—
243C22—9762no—
244C22—4882no—
245C22—4881no—
246C22D61⋊#9911yescharacteristic
247C4—22no—
248C4—21no—
249C4—42no—
250C4—1222no—
251C4—1221no—
252C4—2442no—
253C2—21no—
254C2—161no—
255C2—612no—
256C2—1221no—
257C2—9761no—
258C2D61⋊#35311yescharacteristic
subgroupG/H
centerC2D61⋊#353
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#492C4
socleC2×C61C2×#353
prime radical#127×D61C4
cosocle#14519777C23
hypercenter#492#6923
hypocenterC61C2×#1410
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #492

Complements

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

NH ≅ G/Ntype
1. D61⋊#356C2semidirect
2. #21460955C2semidirect
3. #21460954C2semidirect
6. #16840673C22semidirect
133. D61#1410semidirect
146. C61C2×#1410semidirect

Maximal subgroups

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

subgroupindex
D61⋊#3562
#214609552
#214609542
#492×D612
C2×#141061