Finite Group Databasebeta

← #30604916

Subgroups — #30604916

Order 15616.

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

normal subgroups only

This group has 394 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
1#21462179C211yesmaximal, characteristic, complemented
2C4×#14519846C211yesmaximal, characteristic, complemented
3#21460806C214yesmaximal, complemented
4#21456399C211yesmaximal, characteristic
5C2×#14519846—21no—
6C4×C4⋊#6923—21no—
7C4⋊#11758187—21no—
8#16840657C2212yes—
9#16840648—21no—
10#16840636C2212yes—
11#16840313—21no—
12#16840139C411yescharacteristic, complemented
13#16840110—21no—
14#16839999—21no—
15#16839999C2212yes—
16#16839844—21no—
17#16839844C412yescomplemented
18C4×C8×D61C2211yescharacteristic
19C61×#500C411yescharacteristic, complemented
20C2×C4⋊#6923—22no—
21C2×C4×#6923—41no—
22C2×#11758187—22no—
23#14519846—24no—
24(C2×#6923)⋊C4—41no—
25C2×#11758226—41no—
26C2×D488—21no—
27C2×D488C2×C412yes—
28C2×C8×D61D411yescharacteristic
29C2×C8×D61C2311yescharacteristic
30#14519774—21no—
31#14519766—41no—
32#14519752—22no—
33#14519752—41no—
34#14519739—22no—
35#14519739—41no—
36C42×D61D411yescharacteristic
37#14519697—22no—
38#14519697—22no—
39C4×#92418D411yescharacteristic
40C8×Dic61C2×C411yescharacteristic
41C8×Dic61D411yescharacteristic
42C4⋊Q8×C61—21no—
43#107×C61—21no—
44#107×C61C2×C412yes—
45C4×C8×C61C2×C411yescharacteristic
46C22×#6923—42no—
47C2×Q8×C61—41no—
48#11758226—82no—
49#11758226—82no—
50C2×D244—22no—
51C2×D244—42no—
52C2×D244—41no—
53C2×D244—41no—
54C2×C4×D61—42no—
55C2×C4×D61D811yescharacteristic
56C2×C4×D61D811yescharacteristic
57C2×C4×D61C2×D411yescharacteristic
58C4⋊#6923—24no—
59C4⋊#6923—42no—
60C4×#6923—82no—
61C2×C8×C61C22⋊C411yescharacteristic
62C2×C8×C61C22×C411yescharacteristic
63C4⋊C4×C61—22no—
64C4⋊C4×C61—41no—
65C42×C61C22⋊C411yescharacteristic
66#11758198—42no—
67#11758198—42no—
68C4×Dic61C22⋊C411yescharacteristic
69C4×Dic61SD1611yescharacteristic
70C4×Dic61SD1611yescharacteristic
71C2×#92418C22⋊C411yescharacteristic
72C2×#92418C2×D411yescharacteristic
73D488—42no—
74D488—42no—
75C8×D61—22no—
76C8×D61—41no—
77#11758187—42no—
78C22×D61—42no—
79C22×D61C2×D811yescharacteristic
80C2×#6923—44no—
81C2×#6923—82no—
82C2×#6923—82no—
83Q8×C61—82no—
84C2×C4×C61—42no—
85C2×C4×C61#10211yescharacteristic
86C2×C4×C61#10211yescharacteristic
87C2×C4×C61C2×C22⋊C411yescharacteristic
88C2×Dic61#10211yescharacteristic
89C2×Dic61#10211yescharacteristic
90C2×Dic61C2×SD1611yescharacteristic
91D244—42no—
92D244—42no—
93D244—82no—
94D244—82no—
95D244—82no—
96D244—82no—
97C4×D61—21no—
98C4×D61—21no—
99C4×D61—41no—
100C4×D61—84no—
101C4×D61D1612yes—
102C4×D61SD3212yes—
103C8×C61—21no—
104C8×C61#10412yes—
105#92418—21no—
106#92418—21no—
107#11742—611nomaximal, Sylow
108C22×C61C2×#10211yescharacteristic
109C2×D61—21no—
110C2×D61—21no—
111C2×D61—82no—
112C2×D61—82no—
113C2×D61—82no—
114C2×D61C2×D1611yescharacteristic
115C2×D61C2×SD3211yescharacteristic
116#6923—84no—
117C4×C61—21no—
118C4×C61—82no—
119C4×C61#35712yes—
120C4×C61#41011yescharacteristic
121C4×C61C2×#10411yescharacteristic
122Dic61—21no—
123Dic61—21no—
124Dic61#35712yes—
125#3169—611no—
126#2162—611no—
127C4×#107—611no—
128#1347—614no—
129C2×C61#150211yescharacteristic
130C2×C61C2×#35711yescharacteristic
131C2×C61#214511yescharacteristic
132D61—21no—
133D61—21no—
134D61—162no—
135#532—1221no—
136#500#692311yescharacteristic, complemented
137#493—611no—
138#486—1221no—
139#466—612no—
140#466—1221no—
141C4×D8—612no—
142C4×D8—1221no—
143C2×#107—1221no—
144C2×C4×C8—611no—
145C4×C4⋊C4—1221no—
146C4⋊C16—1221no—
147C22⋊C16—612no—
148C4×C16—1221no—
149#340—612no—
150C61#1174211yescharacteristic, complemented, Sylow
151C2×#41—2441no—
152C2×D8—612no—
153C2×D8—1221no—
154C22×C8—611no—
155C22×C8—611no—
156C4⋊Q8—21no—
157#127—1221no—
158#124—2441no—
159#121—1222no—
160#121—2441no—
161C4×D4—1222no—
162C4×D4—2441no—
163C2×C4⋊C4—1222no—
164C2×C42—611no—
165C2×C42—2441no—
166C2×C16—1222no—
167#107—21no—
168#107—1224no—
169#107C2×#692312yes—
170#102—1222no—
171#102—1222no—
172C4×C8—611no—
173C4×C8—611no—
174C4×C8—611no—
175C4×C8C2×#692311yescharacteristic
176#95—2441no—
177#41—4882no—
178#41—4882no—
179C2×Q8—41no—
180C2×D4—1222no—
181C2×D4—2442no—
182C2×D4—2441no—
183C2×D4—2441no—
184C22×C4—611no—
185C22×C4—611no—
186C22×C4—611no—
187C22×C4—2442no—
188C22×C4—2442no—
189D8—2442no—
190D8—2442no—
191C2×C8—611no—
192C2×C8—611no—
193C2×C8—1222no—
194C2×C8—2441no—
195C2×C8C22⋊#692311yescharacteristic
196C2×C8C22×#692311yescharacteristic
197C4⋊C4—22no—
198C4⋊C4—41no—
199C4⋊C4—1224no—
200C4⋊C4—2442no—
201C22⋊C4—2442no—
202C22⋊C4—2442no—
203C42—611no—
204C42—611no—
205C42—611no—
206C42—4882no—
207C42C22⋊#692311yescharacteristic
208C16—2442no—
209C23—611no—
210C23—2442no—
211Q8—82no—
212D4—4882no—
213D4—4882no—
214D4—4882no—
215D4—4882no—
216D4—2442no—
217D4—2442no—
218C2×C4—42no—
219C2×C4—611no—
220C2×C4—612no—
221C2×C4—612no—
222C2×C4—611no—
223C2×C4—611no—
224C2×C4—1221no—
225C2×C4—1221no—
226C2×C4—4884no—
227C2×C4—4882no—
228C2×C4—4882no—
229C2×C4—2441no—
230C2×C4—2444no—
231C2×C4#1451983911yescharacteristic
232C2×C4#1451983911yescharacteristic
233C2×C4C2×C22⋊#692311yescharacteristic
234C8—21no—
235C8—1221no—
236C8—1221no—
237C8#1451984212yes—
238C22—611no—
239C22—611no—
240C22—1221no—
241C22—1221no—
242C22—4882no—
243C22—4882no—
244C22—4882no—
245C22C2×#1451983911yescharacteristic
246C4—21no—
247C4—82no—
248C4—612no—
249C4—1221no—
250C4—1221no—
251C4—4884no—
252C4#1684067412yes—
253C4#1684074311yescharacteristic
254C4C2×#1451984211yescharacteristic
255C2—1221no—
256C2—1221no—
257C2—9762no—
258C2#2146120011yescharacteristic
259C2C2×#1684067411yescharacteristic
260C2#2146214111yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#500C4
socleC22×C61C2×#102
prime radical#21456399C2
cosocleC2×C8×D61C23
hypercenter#500#6923
hypocenterC61#11742
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #500

Complements

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

NH ≅ G/Ntype
1. #21462179C2semidirect
2. C4×#14519846C2semidirect
3. #21460806C2semidirect
12. #16840139C4semidirect
17. #16839844C4semidirect
19. C61×#500C4semidirect
136. #500#6923semidirect
150. C61#11742semidirect

Maximal subgroups

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

subgroupindex
#214621792
C4×#145198462
#214608062
#214563992
#1174261