Finite Group Databasebeta

← #30604922

Subgroups — #30604922

Order 15616.

390 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 82 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#21462183C211yesmaximal, characteristic, complemented
2C4×#14519845C211yesmaximal, characteristic, complemented
3#21460806C214yesmaximal, complemented
4#21456399C211yesmaximal, characteristic
5C2×#14519845—21no—
6C4×C4⋊#6923—21no—
7C4⋊#11758187—21no—
8#16840657C2212yes—
9#16840651—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#14519845—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—84no—
49C2×D244—22no—
50C2×D244—42no—
51C2×D244—41no—
52C2×D244—41no—
53C2×C4×D61—42no—
54C2×C4×D61D811yescharacteristic
55C2×C4×D61D811yescharacteristic
56C2×C4×D61C2×D411yescharacteristic
57C4⋊#6923—24no—
58C4⋊#6923—42no—
59C4×#6923—82no—
60C2×C8×C61C22⋊C411yescharacteristic
61C2×C8×C61C22×C411yescharacteristic
62C4⋊C4×C61—22no—
63C4⋊C4×C61—41no—
64C42×C61C22⋊C411yescharacteristic
65#11758198—42no—
66#11758198—42no—
67C4×Dic61C22⋊C411yescharacteristic
68C4×Dic61SD1611yescharacteristic
69C4×Dic61SD1611yescharacteristic
70C2×#92418C22⋊C411yescharacteristic
71C2×#92418C2×D411yescharacteristic
72D488—42no—
73D488—42no—
74C8×D61—22no—
75C8×D61—41no—
76#11758187—42no—
77C22×D61—42no—
78C22×D61C2×D811yescharacteristic
79C2×#6923—44no—
80C2×#6923—82no—
81C2×#6923—82no—
82Q8×C61—82no—
83C2×C4×C61—42no—
84C2×C4×C61#10211yescharacteristic
85C2×C4×C61#10211yescharacteristic
86C2×C4×C61C2×C22⋊C411yescharacteristic
87C2×Dic61#10211yescharacteristic
88C2×Dic61#10211yescharacteristic
89C2×Dic61C2×SD1611yescharacteristic
90D244—42no—
91D244—42no—
92D244—82no—
93D244—84no—
94D244—82no—
95C4×D61—22no—
96C4×D61—22no—
97C4×D61—21no—
98C4×D61—21no—
99C4×D61—84no—
100C8×C61—21no—
101C8×C61#10412yes—
102#92418—21no—
103#92418—21no—
104#11744—611nomaximal, Sylow
105C22×C61C2×#10211yescharacteristic
106C2×D61—21no—
107C2×D61—21no—
108C2×D61—82no—
109C2×D61—82no—
110C2×D61—82no—
111C2×D61#50912yes—
112#6923—84no—
113C4×C61—21no—
114C4×C61—82no—
115C4×C61#36012yes—
116C4×C61#41011yescharacteristic
117C4×C61C2×#10411yescharacteristic
118Dic61—21no—
119Dic61—21no—
120Dic61—21no—
121#3169—611no—
122#2163—611no—
123C4×#106—611no—
124#1347—614no—
125C2×C61#150211yescharacteristic
126C2×C61#214011yescharacteristic
127C2×C61C2×#36011yescharacteristic
128D61—22no—
129D61—162no—
130#532—1221no—
131#500#692311yescharacteristic, complemented
132#493—611no—
133#486—1221no—
134#466—612no—
135#466—1221no—
136C4×D8—612no—
137C4×D8—1221no—
138C2×#106—1221no—
139C2×C4×C8—611no—
140C4×C4⋊C4—1221no—
141C4⋊C16—1221no—
142C22⋊C16—612no—
143#346—1221no—
144#340—612no—
145C61#1174411yescharacteristic, complemented, Sylow
146C2×#41—2441no—
147C2×D8—612no—
148C2×D8—1221no—
149C22×C8—611no—
150C22×C8—611no—
151C4⋊Q8—21no—
152#127—1221no—
153#124—2441no—
154#121—1222no—
155#121—2441no—
156C4×D4—1222no—
157C4×D4—2441no—
158C2×C4⋊C4—1222no—
159C2×C42—611no—
160C2×C42—2441no—
161C2×C16—1222no—
162#107—21no—
163#107C2×#692312yes—
164#106—1224no—
165#102—1222no—
166#102—1222no—
167C4×C8—611no—
168C4×C8—611no—
169C4×C8—611no—
170C4×C8C2×#692311yescharacteristic
171#95—2441no—
172#41—4884no—
173C2×Q8—41no—
174C2×D4—1222no—
175C2×D4—2442no—
176C2×D4—2441no—
177C2×D4—2441no—
178C22×C4—611no—
179C22×C4—611no—
180C22×C4—611no—
181C22×C4—2442no—
182C22×C4—2442no—
183D8—2442no—
184D8—2442no—
185C2×C8—611no—
186C2×C8—611no—
187C2×C8—1222no—
188C2×C8—2441no—
189C2×C8C22⋊#692311yescharacteristic
190C2×C8C22×#692311yescharacteristic
191C4⋊C4—22no—
192C4⋊C4—41no—
193C4⋊C4—1224no—
194C4⋊C4—2442no—
195C22⋊C4—2442no—
196C22⋊C4—2442no—
197C42—611no—
198C42—611no—
199C42—611no—
200C42—4882no—
201C42C22⋊#692311yescharacteristic
202C16—2442no—
203C23—611no—
204C23—2442no—
205Q8—82no—
206D4—4882no—
207D4—4884no—
208D4—4882no—
209D4—2442no—
210D4—2442no—
211C2×C4—42no—
212C2×C4—611no—
213C2×C4—611no—
214C2×C4—611no—
215C2×C4—1222no—
216C2×C4—1221no—
217C2×C4—1221no—
218C2×C4—1222no—
219C2×C4—4884no—
220C2×C4—4882no—
221C2×C4—4882no—
222C2×C4—2444no—
223C2×C4#1451983911yescharacteristic
224C2×C4#1451983911yescharacteristic
225C2×C4C2×C22⋊#692311yescharacteristic
226C8—21no—
227C8—1221no—
228C8—1221no—
229C8#1451984212yes—
230C22—612no—
231C22—1221no—
232C22—1221no—
233C22—4882no—
234C22—4882no—
235C22—4882no—
236C22C2×#1451983911yescharacteristic
237C4—21no—
238C4—82no—
239C4—1221no—
240C4—1221no—
241C4—1221no—
242C4—4884no—
243C4#1684067912yes—
244C4#1684074311yescharacteristic
245C4C2×#1451984211yescharacteristic
246C2—1222no—
247C2—9762no—
248C2#2146120011yescharacteristic
249C2#2146212811yescharacteristic
250C2C2×#1684067911yescharacteristic
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#11744
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. #21462183C2semidirect
2. C4×#14519845C2semidirect
3. #21460806C2semidirect
12. #16840139C4semidirect
17. #16839844C4semidirect
19. C61×#500C4semidirect
131. #500#6923semidirect
145. C61#11744semidirect

Maximal subgroups

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

subgroupindex
#214621832
C4×#145198452
#214608062
#214563992
#1174461