Finite Group Databasebeta

← #30602118

Subgroups — #30602118

Order 15616.

514 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 112 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#21461760C211yesmaximal, characteristic, complemented
2#21461166C212yesmaximal, complemented
3#21461165C212yesmaximal, complemented
4#21461013C211yesmaximal, characteristic, complemented
5#21456242C211yesmaximal, characteristic
6C2×#14519848—22no—
7#16840766C2212yes—
8C4×D61⋊C8C2212yes—
9#16840610—24no—
10D4⋊#92420—24no—
11#16840603—22no—
12C2×#14519798—22no—
13#16840313C2211yescharacteristic
14#16840310C2211yescharacteristic
15#16840143—22no—
16#16840141C411yescharacteristic
17#16840138C411yescharacteristic
18#16840135C411yescharacteristic
19C4×C8×D61C2211yescharacteristic
20C61×#492C411yescharacteristic
21C2×#11758213—22no—
22C2×D61⋊C8—22no—
23#14519848—44no—
24C4⋊#92420—22no—
25C4⋊#92420—22no—
26C4×#92420—22no—
27C4×#92420D414yes—
28C2×#11758226—21no—
29C2×#11758224—21no—
30#14519798—44no—
31#14519798—44no—
32C2×#11758202—22no—
33C2×#11758190—22no—
34C2×#11758199—22no—
35C2×C8×D61D412yes—
36#14519777C2×C411yescharacteristic
37#14519774C2×C411yescharacteristic
38#14519766—21no—
39#14519764—21no—
40#14519752—22no—
41#14519748—22no—
42D4×Dic61—22no—
43#14519739—22no—
44C42×D61C2311yescharacteristic
45C4×#92418C2×C411yescharacteristic
46C8×Dic61D412yes—
47C2×SD16×C61—22no—
48C4⋊Q8×C61C2×C411yescharacteristic
49#127×C61C2×C411yescharacteristic
50C4×C8×C61C2×C411yescharacteristic
51C2×Q8×C61—21no—
52C2×D4×C61—21no—
53C2×D4×C61—22no—
54C2×C22⋊D61—41no—
55C22×Dic61—41no—
56#11758226—42no—
57#11758226—42no—
58#11758224—42no—
59#11758224—42no—
60C2×D244—21no—
61C2×D244—22no—
62C2×D244—41no—
63C2×C4×D61—41no—
64C2×C4×D61C2×D411yescharacteristic
65C2×C4×D61#4112yes—
66C2×Dic122—21no—
67C2×#92420—24no—
68C2×#92420—42no—
69#11758213—44no—
70D61⋊C8—44no—
71SD16×C61—44no—
72C2×C8×C61C22⋊C412yes—
73C4⋊C4×C61—22no—
74C42×C61C22×C411yescharacteristic
75C22⋊Dic61—42no—
76#11758202—44no—
77#11758199—44no—
78#11758198—42no—
79C4⋊Dic61—22no—
80C4×Dic61C2×D411yescharacteristic
81C4×Dic61C2×D412yes—
82C2×#92418C22⋊C412yes—
83#11758190—44no—
84C8×D61D814yes—
85C8×D61SD1614yes—
86C23×C61—41no—
87C22×D61—41no—
88C22×D61#12411yescharacteristic
89Q8×C61—42no—
90D4×C61—42no—
91D4×C61—44no—
92C2×C4×C61—41no—
93C2×C4×C61C2×C22⋊C411yescharacteristic
94C2×C4×C61C4×D412yes—
95C22⋊D61—82no—
96C2×Dic61—41no—
97C2×Dic61—81no—
98C2×Dic61—81no—
99C2×Dic61#12112yes—
100C2×Dic61#12711yescharacteristic
101D244—42no—
102D244—44no—
103D244—82no—
104C4×D61—24no—
105C4×D61—81no—
106C4×D61—81no—
107C4×D61C2×D812yes—
108C4×D61C2×SD1612yes—
109Dic122—42no—
110#92420—44no—
111#92420—82no—
112C8×C61#10214yes—
113#92418#10214yes—
114#9862—611nomaximal, Sylow
115C22×C61—81no—
116C22×C61—82no—
117C22×C61#39011yescharacteristic
118C2×D61—22no—
119C2×D61—81no—
120C2×D61—82no—
121C2×D61#48612yes—
122C4×C61—81no—
123C4×C61C2×#10212yes—
124C4×C61#44414yes—
125Dic61—22no—
126Dic61—81no—
127Dic61#49211yescharacteristic
128Dic61#49311yescharacteristic
129#3147—611no—
130#1848—611no—
131#1492—612no—
132#1492—612no—
133C2×#322—611no—
134C2×C61—161no—
135C2×C61#195711yescharacteristic
136C2×C61#197512yes—
137D61—22no—
138D61—161no—
139C2×#135—1222no—
140#532—611no—
141#532—611no—
142#495—1222no—
143#494—611no—
144#493—611no—
145#492—611no—
146#492#692311yescharacteristic
147C2×#108—1222no—
148#423—612no—
149C2×C4×C8—611no—
150C2×C4×C8—612no—
151D4⋊C8—1224no—
152D4⋊C8—1224no—
153#322—1222no—
154C61#986211yescharacteristic, complemented, Sylow
155C2×#41—1221no—
156C2×#41—1221no—
157#135—2444no—
158#135—2444no—
159C2×Q16—1222no—
160C2×SD16—22no—
161C2×SD16—1222no—
162C2×D8—1222no—
163C2×M16—1222no—
164C22×C8—612no—
165C22×C8—1222no—
166C4⋊Q8—611no—
167C4⋊Q8C2×#692311yescharacteristic
168#127—611no—
169#127C2×#692311yescharacteristic
170#124—1221no—
171#124—1221no—
172#121—1222no—
173#121—1222no—
174C4×D4—1222no—
175C4×D4—1222no—
176C2×C42—611no—
177#108—2444no—
178C4⋊C8—1222no—
179C4⋊C8—1222no—
180C4×C8—612no—
181C4×C8—614no—
182C4×C8—611no—
183C4×C8—1222no—
184C4×C8C2×#692311yescharacteristic
185#41—2442no—
186#41—2442no—
187#41—2442no—
188#41—2442no—
189C2×Q8—21no—
190C2×Q8—1221no—
191C2×D4—21no—
192C2×D4—22no—
193C2×D4—1221no—
194C2×D4—1222no—
195C2×D4—2441no—
196C2×D4—2441no—
197C22×C4—611no—
198C22×C4—612no—
199C22×C4—2441no—
200C22×C4—2441no—
201Q16—2444no—
202SD16—44no—
203SD16—2444no—
204D8—2444no—
205M16—2444no—
206C2×C8—612no—
207C2×C8—614no—
208C2×C8—614no—
209C2×C8—1224no—
210C2×C8—2442no—
211C2×C8—2444no—
212C2×C8C22⋊#692312yes—
213C4⋊C4—22no—
214C4⋊C4—1222no—
215C22⋊C4—2442no—
216C22⋊C4—2442no—
217C42—611no—
218C42—612no—
219C42C22×#692311yescharacteristic
220C23—41no—
221C23—611no—
222C23—2441no—
223Q8—42no—
224Q8—2442no—
225D4—42no—
226D4—44no—
227D4—4882no—
228D4—4882no—
229D4—2442no—
230D4—2444no—
231C2×C4—41no—
232C2×C4—611no—
233C2×C4—612no—
234C2×C4—612no—
235C2×C4—612no—
236C2×C4—1224no—
237C2×C4—4881no—
238C2×C4—4881no—
239C2×C4—4881no—
240C2×C4—4881no—
241C2×C4—2441no—
242C2×C4C2×C22⋊#692311yescharacteristic
243C2×C4D4×#692312yes—
244C8—614no—
245C8—4882no—
246C8—2444no—
247C8#1451983914yes—
248C22—81no—
249C22—82no—
250C22—612no—
251C22—1222no—
252C22—4881no—
253C22—4882no—
254C22#1684071411yescharacteristic
255C4—81no—
256C4—611no—
257C4—611no—
258C4—1222no—
259C4—4881no—
260C4C2×#1451983912yes—
261C4#1684080714yes—
262C2—161no—
263C2—1222no—
264C2—9761no—
265C2#2146194711yescharacteristic
266C2#2146197512yes—
subgroupG/H
centerC22#16840714
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#492C4
socleC22×C61#390
prime radical#21456242C2
cosocleC42×D61C23
hypercenter#492#6923
hypocenterC61#9862
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #21461760C2semidirect
2. #21461166C2semidirect
3. #21461165C2semidirect
4. #21461013C2semidirect
154. C61#9862semidirect

Maximal subgroups

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

subgroupindex
#214617602
#214611662
#214611652
#214610132
#214562422
#986261