Finite Group Databasebeta

← #30601926

Subgroups — #30601926

Order 15616.

418 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 86 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#21461475C211yesmaximal, characteristic
2#21461380C211yesmaximal, characteristic
3#21461292C212yesmaximal
4#21461211C212yesmaximal
5#21456403C211yesmaximal, characteristic
6#16840784C2212yes—
7#16840721C2211yescharacteristic
8C2×#14519831—21no—
9C2×C8×#6923—21no—
10#16840698C2211yescharacteristic
11#16840625—21no—
12#16840623—21no—
13#16840619—24no—
14#16840615—24no—
15#16840317C2212yes—
16#16840167C411yescharacteristic, complemented
17#16840112C412yescomplemented
18#16840000—21no—
19#16840000—21no—
20Q16×Dic61—21no—
21Q16×Dic61—21no—
22C4×C8×D61C2211yescharacteristic
23C61×#494C411yescharacteristic, complemented
24C2×D61⋊C8—21no—
25C2×C4×#6923—21no—
26C4⋊#92420—22no—
27#14519834—22no—
28#14519832—22no—
29#14519832—21no—
30#14519832D412yes—
31#14519831—24no—
32C8×#6923—24no—
33(C2×#6923)⋊C4—21no—
34(C2×#6923)⋊C4D412yes—
35C2×C8×D61D411yescharacteristic
36C2×C8×D61D411yescharacteristic
37#14519777C2×C412yes—
38#14519768—22no—
39#14519757—22no—
40#14519753—22no—
41Q8×Dic61—22no—
42#14519742—22no—
43#14519735—22no—
44C42×D61C2311yescharacteristic
45#14519711—21no—
46#14519711—21no—
47#14519701—22no—
48#14519701—22no—
49C4×#92418C2×C411yescharacteristic
50C8×Dic61D411yescharacteristic
51C8×Dic61D411yescharacteristic
52C2×Q16×C61—21no—
53C2×Q16×C61—21no—
54C4⋊Q8×C61C2×C412yes—
55C4×C8×C61C2×C411yescharacteristic
56C22×#6923—22no—
57C2×Q8×C61—22no—
58C2×C4×D61C2×D411yescharacteristic
59C2×C4×D61C2×D411yescharacteristic
60C2×C4×D61#4111yescharacteristic
61C2×Dic122—22no—
62C2×#92420—22no—
63C2×#92420—42no—
64C4×#6923—22no—
65C4×#6923—22no—
66D61⋊C8—22no—
67D61⋊C8—22no—
68Q16×C61—42no—
69Q16×C61—42no—
70C2×C8×C61C22⋊C411yescharacteristic
71C2×C8×C61C22⋊C411yescharacteristic
72C4⋊C4×C61—22no—
73C4⋊C4×C61—22no—
74C42×C61C22×C411yescharacteristic
75#11758198—42no—
76C4⋊Dic61—22no—
77C4⋊Dic61—22no—
78C4⋊Dic61—42no—
79#11758196—42no—
80C4×Dic61—42no—
81C4×Dic61C2×D411yescharacteristic
82C4×Dic61C2×D411yescharacteristic
83C4×Dic61#4111yescharacteristic
84C2×#92418C22⋊C411yescharacteristic
85C2×#92418C22⋊C411yescharacteristic
86C8×D61—22no—
87C8×D61—22no—
88C22×D61#12111yescharacteristic
89C2×#6923—24no—
90C2×#6923—42no—
91C2×#6923—42no—
92Q8×C61—42no—
93Q8×C61—42no—
94C2×C4×C61—42no—
95C2×C4×C61C2×C22⋊C411yescharacteristic
96C2×C4×C61C4×D411yescharacteristic
97C2×C4×C61C4×D411yescharacteristic
98C2×Dic61—42no—
99C2×Dic61#12111yescharacteristic
100C2×Dic61#12411yescharacteristic
101C2×Dic61#12711yescharacteristic
102C4×D61—22no—
103C4×D61—21no—
104C4×D61—21no—
105C4×D61—41no—
106Dic122—82no—
107#92420—24no—
108#92420—82no—
109C8×C61#10412yes—
110C8×C61#10412yes—
111#92418—21no—
112#92418—21no—
113#9763—611nomaximal, Sylow
114C22×C61#39011yescharacteristic
115C2×D61—21no—
116C2×D61—21no—
117C2×D61#47312yes—
118#6923—44no—
119C4×C61—21no—
120C4×C61—21no—
121C4×C61—82no—
122C4×C61C2×#10411yescharacteristic
123C4×C61C2×#10411yescharacteristic
124Dic61—21no—
125Dic61—21no—
126Dic61—21no—
127Dic61—82no—
128#3170—611no—
129#1726—611no—
130#1568—611no—
131#1531—612no—
132#1506—612no—
133C2×C61#196211yescharacteristic
134C2×C61#197611yescharacteristic
135C2×C61#197911yescharacteristic
136D61—22no—
137#533—612no—
138#500—611no—
139#494#692311yescharacteristic, complemented
140#487—612no—
141#467—1221no—
142#467—1221no—
143C4×Q16—1221no—
144C4×Q16—1221no—
145#432—612no—
146C2×#97—611no—
147C2×#97—1221no—
148C2×C4×C8—611no—
149C2×C4×C8—1221no—
150#376—611no—
151#335—1221no—
152#334—1221no—
153#330—1224no—
154#328—1224no—
155C61#976311yescharacteristic, complemented, Sylow
156C2×Q16—21no—
157C2×Q16—21no—
158C22×C8—611no—
159C22×C8—611no—
160C22×C8—1221no—
161C4⋊Q8—612no—
162C4⋊Q8C2×#692312yes—
163#125—1222no—
164C22⋊Q8—1222no—
165C22⋊Q8—1222no—
166C4×Q8—1222no—
167C4×Q8—1222no—
168#117—1222no—
169C2×C42—611no—
170C2×C42—1221no—
171#107—1221no—
172#107—1221no—
173C4⋊C8—1222no—
174#103—1222no—
175#103—1222no—
176C22⋊C8—1222no—
177#97—612no—
178#97—1221no—
179#97—1222no—
180#97—1224no—
181C4×C8—611no—
182C4×C8—611no—
183C4×C8—611no—
184C4×C8—1224no—
185C4×C8C2×#692311yescharacteristic
186#95—612no—
187#95—1221no—
188C2×Q8—22no—
189C2×Q8—1222no—
190C22×C4—611no—
191C22×C4—611no—
192C22×C4—611no—
193C22×C4—1222no—
194Q16—42no—
195Q16—42no—
196C2×C8—611no—
197C2×C8—611no—
198C2×C8—1222no—
199C2×C8—1222no—
200C2×C8—1222no—
201C2×C8—1222no—
202C2×C8—1222no—
203C2×C8—2442no—
204C2×C8C22⋊#692311yescharacteristic
205C2×C8C22⋊#692311yescharacteristic
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—1222no—
209C4⋊C4—1222no—
210C4⋊C4—2442no—
211C4⋊C4—2442no—
212C22⋊C4—2442no—
213C42—611no—
214C42—611no—
215C42—611no—
216C42—1222no—
217C42—1222no—
218C42—2442no—
219C42C22×#692311yescharacteristic
220C23—611no—
221Q8—42no—
222Q8—42no—
223Q8—4882no—
224C2×C4—42no—
225C2×C4—611no—
226C2×C4—611no—
227C2×C4—611no—
228C2×C4—1222no—
229C2×C4—1221no—
230C2×C4—1221no—
231C2×C4—1224no—
232C2×C4—2441no—
233C2×C4—2442no—
234C2×C4—2442no—
235C2×C4—2442no—
236C2×C4C2×C22⋊#692311yescharacteristic
237C2×C4D4×#692311yescharacteristic
238C2×C4D4×#692311yescharacteristic
239C8—1224no—
240C8—1221no—
241C8—1221no—
242C8—4882no—
243C8#1451984112yes—
244C8#1451984112yes—
245C22—612no—
246C22—1221no—
247C22—1221no—
248C22#1684071411yescharacteristic
249C4—21no—
250C4—21no—
251C4—82no—
252C4—1221no—
253C4—1221no—
254C4—1221no—
255C4—4882no—
256C4—2444no—
257C4C2×#1451984111yescharacteristic
258C4C2×#1451984111yescharacteristic
259C2—1222no—
260C2#2146195311yescharacteristic
261C2#2146197811yescharacteristic
262C2#2146198111yescharacteristic
subgroupG/H
centerC22#16840714
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#494C4
socleC22×C61#390
prime radicalC22×D61#121
cosocleC42×D61C23
hypercenter#494#6923
hypocenterC61#9763
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
16. #16840167C4semidirect
17. #16840112C4semidirect
23. C61×#494C4semidirect
139. #494#6923semidirect
155. C61#9763semidirect

Maximal subgroups

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

subgroupindex
#214614752
#214613802
#214612922
#214612112
#214564032
#976361