Finite Group Databasebeta

← #29591522

Subgroups — #29591522

Order 15616.

308 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 85 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#21456403C211yesmaximal, characteristic
2#21447573C211yesmaximal, characteristic
3#21444576C211yesmaximal, characteristic
4#21443875C211yesmaximal, characteristic, complemented
5#21443873C211yesmaximal, characteristic, complemented
6#21443868C211yesmaximal, characteristic, complemented
7C61×#1362C211yesmaximal, characteristic, complemented
8#16840317—21no—
9C2×#14519716—21no—
10#16840167C2211yescharacteristic
11#16840112—21no—
12#16840000—21no—
13#16840000C412yes—
14Q16×Dic61—21no—
15Q16×Dic61C412yes—
16#16839784—21no—
17C4×C8×D61C2211yescharacteristic
18C4⋊#11758185C2211yescharacteristic
19#16839580—21no—
20#16839515C2211yescharacteristic
21#16839514—21no—
22C61×#494C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C61×#335C2211yescharacteristic
25C2×#11758189—41no—
26C2×C8×D61C2×C411yescharacteristic
27C2×C8×D61D411yescharacteristic
28#14519777—21no—
29#14519768—41no—
30#14519757—41no—
31#14519753—22no—
32Q8×Dic61—22no—
33#14519742—41no—
34#14519735—41no—
35C42×D61D411yescharacteristic
36#14519716—42no—
37C2×#11758185—21no—
38#14519711—21no—
39#14519711C2×C412yes—
40C4⋊#92418—21no—
41#14519706—41no—
42#14519701—22no—
43#14519701—22no—
44C4×#92418D411yescharacteristic
45C8×Dic61C2×C411yescharacteristic
46C8×Dic61D411yescharacteristic
47C2×Q16×C61—21no—
48C2×Q16×C61C2×C412yes—
49C4⋊Q8×C61—21no—
50C2×C16×C61—21no—
51C4⋊C8×C61—21no—
52C4×C8×C61C2311yescharacteristic
53C2×Q8×C61—22no—
54C2×C4×D61C22⋊C411yescharacteristic
55C2×C4×D61D811yescharacteristic
56C2×C4×D61SD1611yescharacteristic
57C2×Dic122—41no—
58Q16×C61—42no—
59Q16×C61—41no—
60Q16×C61—41no—
61C2×C8×C61—41no—
62C2×C8×C61C22×C411yescharacteristic
63C2×C8×C61C2×D411yescharacteristic
64C4⋊C4×C61—41no—
65C4⋊C4×C61—41no—
66C42×C61C2×D411yescharacteristic
67#11758198—42no—
68C4⋊Dic61—22no—
69C4⋊Dic61—41no—
70C4⋊Dic61—42no—
71#11758196—42no—
72C4×Dic61—42no—
73C4×Dic61C22⋊C411yescharacteristic
74C4×Dic61D811yescharacteristic
75C4×Dic61SD1611yescharacteristic
76C2×#92418—41no—
77C2×#92418C22⋊C411yescharacteristic
78C2×#92418C22⋊C411yescharacteristic
79#11758189—82no—
80C8×D61—21no—
81C8×D61—21no—
82C8×D61—41no—
83C16×C61—41no—
84#11758185—41no—
85C22×D61#10211yescharacteristic
86Q8×C61—42no—
87Q8×C61—42no—
88C2×C4×C61—42no—
89C2×C4×C61C2×C22⋊C411yescharacteristic
90C2×C4×C61C2×D811yescharacteristic
91C2×C4×C61C2×SD1611yescharacteristic
92C2×Dic61—42no—
93C2×Dic61#10211yescharacteristic
94C2×Dic61#10211yescharacteristic
95C2×Dic61#10211yescharacteristic
96C4×D61—21no—
97C4×D61—21no—
98C4×D61—21no—
99C4×D61—21no—
100C4×D61—22no—
101Dic122—81no—
102Dic122—81no—
103C8×C61—21no—
104C8×C61—81no—
105C8×C61AGL(1,ℤ/8)11yescharacteristic
106C8×C61#13711yescharacteristic
107#92418—21no—
108#92418—21no—
109#92418—81no—
110#11988—611nomaximal, Sylow
111C22×C61C2×#10211yescharacteristic
112C2×D61—21no—
113C2×D61—21no—
114C2×D61—21no—
115C4×C61—21no—
116C4×C61—82no—
117C4×C61#41311yescharacteristic
118C4×C61#41711yescharacteristic
119C4×C61#50911yescharacteristic
120C4×C61#51011yescharacteristic
121Dic61—21no—
122Dic61—21no—
123Dic61—82no—
124Dic61#36212yes—
125#3170—611no—
126#2150—611no—
127#1567—611no—
128#1364—611no—
129#1364—611no—
130#1362—611no—
131#1362D6111yescharacteristic, complemented
132C2×C61#154711yescharacteristic
133C2×C61#213911yescharacteristic
134C2×C61C2×#36211yescharacteristic
135D61—41no—
136#533—1221no—
137C2×M32—1221no—
138#500—611no—
139#494C2×D6111yescharacteristic
140#487—1221no—
141#467—612no—
142#467—1221no—
143C4×Q16—612no—
144C4×Q16—1221no—
145#423—1221no—
146C2×C4×C8—611no—
147C4⋊C16—611no—
148C4⋊C16—1221no—
149C4⋊C16C2×D6111yescharacteristic
150#335—611no—
151#335—1221no—
152#335C2×D6111yescharacteristic
153C61#1198811yescharacteristic, complemented, Sylow
154C2×Q16—21no—
155C2×Q16C4×D6112yes—
156C2×M16—2441no—
157C22×C8—611no—
158C22×C8—611no—
159C4⋊Q8—21no—
160C4⋊Q8—1221no—
161#125—2441no—
162C22⋊Q8—1222no—
163C22⋊Q8—2441no—
164C4×Q8—1222no—
165C4×Q8—2441no—
166#117—2441no—
167C2×C42—611no—
168M32—2442no—
169C2×C16—21no—
170C2×C16—1221no—
171#107—612no—
172#107—1221no—
173C4⋊C8—21no—
174C4⋊C8—1221no—
175C4⋊C8—2441no—
176#103—1222no—
177#103—1222no—
178C4×C8—611no—
179C4×C8—611no—
180C4×C8—611no—
181C4×C8C22×D6111yescharacteristic
182C2×Q8—22no—
183C2×Q8—2441no—
184C22×C4—611no—
185C22×C4—611no—
186C22×C4—611no—
187Q16—42no—
188Q16—41no—
189Q16—41no—
190M16—4882no—
191C2×C8—41no—
192C2×C8—611no—
193C2×C8—611no—
194C2×C8—1221no—
195C2×C8—1221no—
196C2×C8—2441no—
197C2×C8—2441no—
198C2×C8C2×C4×D6111yescharacteristic
199C2×C8D4×D6111yescharacteristic
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—1222no—
203C4⋊C4—2442no—
204C4⋊C4—2442no—
205C4⋊C4—2441no—
206C22⋊C4—2442no—
207C42—611no—
208C42—611no—
209C42—611no—
210C42—2442no—
211C42D4×D6111yescharacteristic
212C16—41no—
213C16—2441no—
214C23—611no—
215Q8—42no—
216Q8—42no—
217Q8—4881no—
218Q8—4881no—
219C2×C4—42no—
220C2×C4—611no—
221C2×C4—611no—
222C2×C4—611no—
223C2×C4—1222no—
224C2×C4—1221no—
225C2×C4—1221no—
226C2×C4—1221no—
227C2×C4—1221no—
228C2×C4—2442no—
229C2×C4C22⋊C4×D6111yescharacteristic
230C2×C4D8×D6111yescharacteristic
231C2×C4SD16×D6111yescharacteristic
232C8—21no—
233C8—81no—
234C8—1221no—
235C8—1221no—
236C8—4881no—
237C8#1451980111yescharacteristic
238C8#1451980611yescharacteristic
239C22—1221no—
240C22—1221no—
241C22—1221no—
242C22#102×D6111yescharacteristic
243C4—21no—
244C4—82no—
245C4—612no—
246C4—1221no—
247C4—1221no—
248C4—4882no—
249C4#1683974311yescharacteristic
250C4#1683976011yescharacteristic
251C4#1684019911yescharacteristic
252C4#1684020411yescharacteristic
253C2—2441no—
254C2#2144449311yescharacteristic
255C2#2144753011yescharacteristic
256C2#362×D6111yescharacteristic
subgroupG/H
centerC22#102×D61
commutatorC2×C8×C61C22×C4
FrattiniC4×C8C22×D61
FittingC61×#1362C2
socleC22×C61C2×#102
prime radicalC22×D61#102
cosocleC4×C8×C61C23
hypercenter#1362D61
hypocenterC61#11988
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
4. #21443875C2semidirect
5. #21443873C2semidirect
6. #21443868C2semidirect
7. C61×#1362C2semidirect
131. #1362D61semidirect
153. C61#11988semidirect

Maximal subgroups

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

subgroupindex
#214564032
#214475732
#214445762
#214438752
#214438732
#214438682
C61×#13622
#1198861