Finite Group Databasebeta

← D61⋊#1408 #30608345

Subgroups — D61⋊#1408 #30608345

Order 15616.

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

normal subgroups only

This group has 526 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, complemented
2#21460951C212yesmaximal, complemented
3#21460950C212yesmaximal, complemented
4#493×D61C211yesmaximal, characteristic
5D61⋊#99—22no—
6#16840667C2214yescomplemented
7#16840666—22no—
8C2×D8×D61—22no—
9#127×D61C411yescharacteristic, complemented
10#127×D61C2211yescharacteristic
11#16840139C2211yescharacteristic
12#16840138C411yescharacteristic, complemented
13#16840138C2211yescharacteristic
14#16840137—22no—
15C4×C8×D61C411yescharacteristic, complemented
16C61×#493C411yescharacteristic, complemented
17C2×C22⋊#6923—42no—
18#14519836—24no—
19#14519835—42no—
20C2×D4×D61—21no—
21C2×D4×D61—41no—
22C2×D4×D61—41no—
23C2×D4×D61D412yes—
24C2×D488—22no—
25C2×#11758199—22no—
26C2×#11758199—22no—
27D8×D61—44no—
28D8×D61—44no—
29C2×C8×D61—21no—
30#14519774C2×C411yescharacteristic, complemented
31#14519774C2311yescharacteristic
32#14519773—21no—
33#14519773—41no—
34#14519773—41no—
35#14519773D412yes—
36C42×D61C2×C411yescharacteristic
37C4×#92418C2×C411yescharacteristic, complemented
38C8×Dic61—21no—
39C2×D8×C61—22no—
40#127×C61C2×C411yescharacteristic
41#127×C61C2×C411yescharacteristic, complemented
42C4×C8×C61C2×C411yescharacteristic, complemented
43C23×D61—22no—
44C23×D61—41no—
45C22×#6923—82no—
46C2×D4×C61—21no—
47C2×D4×C61—41no—
48C2×D4×C61—41no—
49C2×D4×C61C22⋊C412yes—
50C2×C22⋊D61—22no—
51C2×C22⋊D61—42no—
52C2×C22⋊D61—42no—
53C2×C22⋊D61—41no—
54D4×D61—42no—
55D4×D61—42no—
56D4×D61—42no—
57D4×D61—42no—
58D4×D61—84no—
59D4×D61—84no—
60C2×D244—21no—
61C2×D244—41no—
62C2×D244—41no—
63C2×D244C2×D412yes—
64C2×C4×D61—21no—
65C2×C4×D61C22⋊C411yescharacteristic
66C22⋊#6923—44no—
67C22⋊#6923—82no—
68D8×C61—44no—
69C2×C8×C61—21no—
70C42×C61C22×C411yescharacteristic
71#11758199—44no—
72#11758199—44no—
73C4×Dic61—21no—
74C4×Dic61C22⋊C411yescharacteristic
75C2×#92418—21no—
76D488—44no—
77C8×D61—22no—
78C8×D61—22no—
79C23×C61—22no—
80C23×C61—41no—
81C22×D61—22no—
82C22×D61—42no—
83C22×D61—42no—
84C22×D61—41no—
85C22×D61—84no—
86C22×D61—84no—
87C22×D61—81no—
88C22×D61—81no—
89C22×D61#9911yescharacteristic
90C2×#6923—84no—
91C2×#6923—164no—
92D4×C61—42no—
93D4×C61—42no—
94D4×C61—82no—
95D4×C61—82no—
96C2×C4×C61—21no—
97C2×C4×C61C2×C22⋊C411yescharacteristic
98C22⋊D61—82no—
99C22⋊D61—82no—
100C22⋊D61—84no—
101C22⋊D61—84no—
102C2×Dic61—21no—
103C2×Dic61#9911yescharacteristic
104D244—42no—
105D244—42no—
106D244—82no—
107D244—82no—
108C4×D61—24no—
109C4×D61—21no—
110C4×D61—21no—
111C8×C61—22no—
112#92418—22no—
113C2×#1408—611nomaximal, Sylow
114C22×C61—42no—
115C22×C61—82no—
116C22×C61—82no—
117C22×C61—81no—
118C22×C61C2×#9911yescharacteristic
119C2×D61—22no—
120C2×D61—42no—
121C2×D61—84no—
122C2×D61—82no—
123C2×D61—82no—
124C2×D61—81no—
125C2×D61—162no—
126C2×D61—162no—
127C2×D61—162no—
128C2×D61#35311yescharacteristic
129C2×D61#35311yescharacteristic
130#6923—164no—
131C4×C61—22no—
132C4×C61—21no—
133Dic61—22no—
134Dic61—21no—
135C2×#493—611no—
136C2×#353—612no—
137#1408—612no—
138#1408—612no—
139C2×C61—21no—
140C2×C61—82no—
141C2×C61—161no—
142C2×C61C2×#35311yescharacteristic
143D61—21no—
144D61—82no—
145D61—161no—
146D61#140812yescomplemented
147C22×D8—1222no—
148C2×#127—611no—
149C2×#127—611no—
150#493—611no—
151#493—611no—
152#493—611no—
153#493—1222no—
154#493#692311yescharacteristic, complemented
155C2×#99—1222no—
156C2×C4×C8—611no—
157#353—614no—
158#353—1222no—
159C61C2×#140811yescharacteristic, complemented, Sylow
160C22×D4—612no—
161C22×D4—1221no—
162C22×D4—2441no—
163C22×D4—2441no—
164C2×D8—22no—
165C2×D8—1222no—
166C2×D8—1222no—
167C2×D8—1222no—
168C2×D8—2444no—
169C2×D8—2444no—
170C22×C8—1221no—
171#127—612no—
172#127—611no—
173#127—611no—
174#127—1221no—
175#127—2441no—
176#127—2441no—
177#127C2×#692311yescharacteristic
178#127C2×#692311yescharacteristic, complemented
179C2×C22⋊C4—2442no—
180C2×C42—611no—
181#99—1224no—
182#99—2442no—
183C4×C8—611no—
184C4×C8—1221no—
185C4×C8C2×#692311yescharacteristic, complemented
186C24—1222no—
187C24—2441no—
188C2×D4—21no—
189C2×D4—41no—
190C2×D4—41no—
191C2×D4—612no—
192C2×D4—1222no—
193C2×D4—1221no—
194C2×D4—4884no—
195C2×D4—4884no—
196C2×D4—2441no—
197C2×D4—2441no—
198C2×D4—2441no—
199C2×D4—2442no—
200C2×D4—2442no—
201C2×D4—2442no—
202C2×D4—2442no—
203C2×D4—2442no—
204C2×D4—2442no—
205C2×D4C22⋊#692312yes—
206C22×C4—611no—
207C22×C4—1221no—
208C22×C4—4882no—
209D8—44no—
210D8—2444no—
211D8—2444no—
212D8—2444no—
213C2×C8—21no—
214C2×C8—1222no—
215C2×C8—1222no—
216C2×C8—1221no—
217C22⋊C4—4882no—
218C22⋊C4—2444no—
219C42—611no—
220C42—1221no—
221C42C22×#692311yescharacteristic
222C23—22no—
223C23—41no—
224C23—611no—
225C23—1222no—
226C23—4881no—
227C23—4881no—
228C23—4884no—
229C23—4884no—
230C23—2442no—
231C23—2442no—
232C23—2441no—
233D4—42no—
234D4—42no—
235D4—82no—
236D4—82no—
237D4—4882no—
238D4—4882no—
239D4—4882no—
240D4—4884no—
241D4—4884no—
242D4—4882no—
243D4—2442no—
244D4—2442no—
245C2×C4—21no—
246C2×C4—611no—
247C2×C4—1221no—
248C2×C4—1221no—
249C2×C4—1224no—
250C2×C4—1221no—
251C2×C4—9764no—
252C2×C4—4884no—
253C2×C4C2×C22⋊#692311yescharacteristic
254C8—22no—
255C8—1222no—
256C22—42no—
257C22—82no—
258C22—82no—
259C22—81no—
260C22—611no—
261C22—611no—
262C22—1222no—
263C22—9762no—
264C22—9762no—
265C22—9762no—
266C22—4882no—
267C22—4882no—
268C22—4884no—
269C22—4881no—
270C22—2442no—
271C22D61⋊#9911yescharacteristic
272C4—22no—
273C4—21no—
274C4—1222no—
275C4—1221no—
276C4—9764no—
277C2—21no—
278C2—82no—
279C2—161no—
280C2—612no—
281C2—1221no—
282C2—9761no—
283C2—4882no—
284C2D61⋊#35311yescharacteristic
subgroupG/H
centerC2D61⋊#353
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#493C4
socleC2×C61C2×#353
prime radical#493×D61C2
cosocle#14519774C23
hypercenter#493#6923
hypocenterC61C2×#1408
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #493

Complements

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

NH ≅ G/Ntype
1. D61⋊#353C2semidirect
2. #21460951C2semidirect
3. #21460950C2semidirect
6. #16840667C22semidirect
9. #127×D61C4semidirect
12. #16840138C4semidirect
15. C4×C8×D61C4semidirect
16. C61×#493C4semidirect
30. #14519774C2×C4semidirect
37. C4×#92418C2×C4semidirect
41. #127×C61C2×C4semidirect
42. C4×C8×C61C2×C4semidirect
146. D61#1408semidirect
154. #493#6923semidirect
159. C61C2×#1408semidirect
178. #127C2×#6923semidirect
185. 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
#214609512
#214609502
#493×D612
C2×#140861