Finite Group Databasebeta

← #30608357

Subgroups — #30608357

Order 15616.

474 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 56 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#21460952C212yesmaximal, complemented
3#21460951C212yesmaximal, complemented
4#21456266C211yesmaximal, characteristic
5D61⋊#99—22no—
6#16840667C2214yes—
7#16840666—22no—
8C2×#14519804—22no—
9#16840313C411yescharacteristic, complemented
10#127×D61C2211yescharacteristic
11#16840148—22no—
12#16840139C2211yescharacteristic
13#16840138C411yescharacteristic, complemented
14#16840136C2211yescharacteristic
15C4×#11758189C411yescharacteristic, complemented
16C61×#492C411yescharacteristic, complemented
17C2×C22⋊#6923—42no—
18#14519836—24no—
19#14519835—42no—
20C2×#11758226—21no—
21C2×D4×D61—41no—
22C2×D4×D61D412yes—
23#14519804—44no—
24#14519804—44no—
25C2×#11758201—22no—
26C2×D488—22no—
27C2×#11758199—22no—
28C2×#11758189—21no—
29#14519774C2×C411yescharacteristic, complemented
30#14519774C2311yescharacteristic
31#14519773—41no—
32#14519773D412yes—
33#14519766—21no—
34#14519752—41no—
35#14519739—41no—
36C42×D61C2×C411yescharacteristic
37#14519687—21no—
38C4×#92418C2×C411yescharacteristic, complemented
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—
50#11758226—42no—
51#11758226—42no—
52D4×D61—42no—
53D4×D61—42no—
54D4×D61—84no—
55C2×D244—21no—
56C2×D244—41no—
57C2×D244—41no—
58C2×D244—41no—
59C2×D244C2×D412yes—
60C2×C4×D61—21no—
61C2×C4×D61—41no—
62C2×C4×D61C22⋊C411yescharacteristic
63C22⋊#6923—44no—
64C22⋊#6923—82no—
65SD16×C61—44no—
66C2×C8×C61—21no—
67C4⋊C4×C61—41no—
68C42×C61C22×C411yescharacteristic
69#11758201—44no—
70#11758199—44no—
71#11758198—42no—
72C4×Dic61—21no—
73C4×Dic61C22⋊C411yescharacteristic
74C2×#92418—21no—
75D488—44no—
76#11758189—24no—
77C23×C61—22no—
78C22×D61—22no—
79C22×D61—42no—
80C22×D61—42no—
81C22×D61—41no—
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#9911yescharacteristic
96D244—42no—
97D244—42no—
98D244—82no—
99D244—82no—
100D244—82no—
101C4×D61—22no—
102C4×D61—42no—
103C4×D61—81no—
104C4×D61—81no—
105C8×C61—22no—
106#92418—22no—
107#13584—611nomaximal, Sylow
108C22×C61—42no—
109C22×C61—82no—
110C22×C61C2×#9911yescharacteristic
111C2×D61—41no—
112C2×D61—42no—
113C2×D61—84no—
114C2×D61—82no—
115C2×D61—82no—
116C2×D61—81no—
117C2×D61—162no—
118C2×D61#35312yes—
119#6923—164no—
120C4×C61—22no—
121C4×C61—21no—
122C4×C61—81no—
123Dic61—21no—
124Dic61—41no—
125#3151—611no—
126C2×#353—612no—
127#1409—612no—
128#1408—612no—
129C2×C61—21no—
130C2×C61—82no—
131C2×C61C2×#35311yescharacteristic
132D61—22no—
133D61—82no—
134D61—161no—
135C2×AGL(1,ℤ/8)—1222no—
136#532—611no—
137C2×#127—611no—
138#496—1222no—
139#493—611no—
140#493—611no—
141#492—611no—
142#492#692311yescharacteristic, complemented
143C2×#99—1222no—
144C4×M16—611no—
145#353—614no—
146#353—1222no—
147C61#1358411yescharacteristic, complemented, Sylow
148C2×#41—1221no—
149C22×D4—612no—
150C22×D4—2441no—
151AGL(1,ℤ/8)—2444no—
152AGL(1,ℤ/8)—2444no—
153C2×SD16—22no—
154C2×SD16—1222no—
155C2×D8—1222no—
156C2×D8—1222no—
157C2×M16—1221no—
158C4⋊Q8C2×#692311yescharacteristic, complemented
159#127—612no—
160#127—611no—
161#127—611no—
162#127—2441no—
163#127C2×#692311yescharacteristic
164#124—1221no—
165#121—2441no—
166C4×D4—2441no—
167C2×C22⋊C4—2442no—
168C2×C42—611no—
169#99—1224no—
170#99—2442no—
171#97—1221no—
172C4×C8—611no—
173C4×C8C2×#692311yescharacteristic, complemented
174C24—1222no—
175#41—2442no—
176#41—2442no—
177C2×Q8—21no—
178C2×D4—41no—
179C2×D4—612no—
180C2×D4—1222no—
181C2×D4—1221no—
182C2×D4—4884no—
183C2×D4—2441no—
184C2×D4—2441no—
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—
196D8—2444no—
197D8—2444no—
198M16—1224no—
199C2×C8—21no—
200C2×C8—1221no—
201C4⋊C4—41no—
202C22⋊C4—4882no—
203C22⋊C4—2442no—
204C22⋊C4—2444no—
205C42—611no—
206C42—1221no—
207C42C22×#692311yescharacteristic
208C23—22no—
209C23—611no—
210C23—1222no—
211C23—4884no—
212C23—2442no—
213C23—2442no—
214C23—2441no—
215Q8—42no—
216D4—42no—
217D4—82no—
218D4—4882no—
219D4—4882no—
220D4—4882no—
221D4—4882no—
222D4—4884no—
223D4—2442no—
224D4—2442no—
225C2×C4—21no—
226C2×C4—41no—
227C2×C4—611no—
228C2×C4—1222no—
229C2×C4—1221no—
230C2×C4—9764no—
231C2×C4—4881no—
232C2×C4—4881no—
233C2×C4—4884no—
234C2×C4—2442no—
235C2×C4C2×C22⋊#692311yescharacteristic
236C8—22no—
237C8—1222no—
238C22—42no—
239C22—82no—
240C22—612no—
241C22—9762no—
242C22—4882no—
243C22—4882no—
244C22—4884no—
245C22—4881no—
246C22—2441no—
247C22—2442no—
248C22D61⋊#9911yescharacteristic
249C4—22no—
250C4—21no—
251C4—81no—
252C4—1221no—
253C4—9764no—
254C4—2441no—
255C2—21no—
256C2—82no—
257C2—1222no—
258C2—9761no—
259C2—4882no—
260C2D61⋊#35311yescharacteristic
subgroupG/H
centerC2D61⋊#353
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#492C4
socleC2×C61C2×#353
prime radical#21456266C2
cosocle#14519774C23
hypercenter#492#6923
hypocenterC61#13584
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
1. D61⋊#353C2semidirect
2. #21460952C2semidirect
3. #21460951C2semidirect
9. #16840313C4semidirect
13. #16840138C4semidirect
15. C4×#11758189C4semidirect
16. C61×#492C4semidirect
29. #14519774C2×C4semidirect
38. C4×#92418C2×C4semidirect
40. C4⋊Q8×C61C2×C4semidirect
42. C4×C8×C61C2×C4semidirect
142. #492#6923semidirect
147. C61#13584semidirect
158. C4⋊Q8C2×#6923semidirect
173. 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
#214609522
#214609512
#214562662
#1358461