Finite Group Databasebeta

← #29591370

Subgroups — #29591370

Order 15616.

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

normal subgroups only

This group has 306 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#21447621C211yesmaximal, characteristic
3#335×D61C211yesmaximal, characteristic
4#21443875C211yesmaximal, characteristic, complemented
5#21443873C211yesmaximal, characteristic, complemented
6#21443868C211yesmaximal, characteristic, complemented
7C61×#1362C211yesmaximal, characteristic, complemented
8#16840317—21no—
9#16840167C2211yescharacteristic
10#16840112—21no—
11#16840000—21no—
12#16840000C412yes—
13Q16×Dic61—21no—
14Q16×Dic61C412yes—
15C4⋊C8×D61—21no—
16C4×C8×D61C2211yescharacteristic
17C4⋊#11758185C2211yescharacteristic
18#16839541—21no—
19#16839537—21no—
20#16839515C2211yescharacteristic
21#16839514—21no—
22C61×#494C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C61×#335C2211yescharacteristic
25C2×C8×D61—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
36C2×#11758185—21no—
37#14519711—21no—
38#14519711C2×C412yes—
39C4⋊#92418—21no—
40#14519706—41no—
41#14519701—22no—
42#14519701—22no—
43C4×#92418D411yescharacteristic
44C8×Dic61C2×C411yescharacteristic
45C8×Dic61D411yescharacteristic
46C2×Q16×C61—21no—
47C2×Q16×C61C2×C412yes—
48C4⋊Q8×C61—21no—
49C2×C16×C61—21no—
50C4⋊C8×C61—21no—
51C4×C8×C61C2311yescharacteristic
52C2×Q8×C61—22no—
53C2×C4×D61C22⋊C411yescharacteristic
54C2×C4×D61D811yescharacteristic
55C2×C4×D61SD1611yescharacteristic
56C2×Dic122—41no—
57Q16×C61—42no—
58Q16×C61—41no—
59Q16×C61—41no—
60C2×C8×C61—41no—
61C2×C8×C61C22×C411yescharacteristic
62C2×C8×C61C2×D411yescharacteristic
63C4⋊C4×C61—41no—
64C4⋊C4×C61—41no—
65C42×C61C2×D411yescharacteristic
66#11758198—42no—
67C4⋊Dic61—22no—
68C4⋊Dic61—41no—
69C4⋊Dic61—42no—
70#11758196—42no—
71C4×Dic61—42no—
72C4×Dic61C22⋊C411yescharacteristic
73C4×Dic61D811yescharacteristic
74C4×Dic61SD1611yescharacteristic
75C2×#92418—41no—
76C2×#92418C22⋊C411yescharacteristic
77C2×#92418C22⋊C411yescharacteristic
78C8×D61—21no—
79C8×D61—21no—
80C8×D61—41no—
81C8×D61—82no—
82C16×C61—41no—
83#11758185—41no—
84C22×D61#10211yescharacteristic
85Q8×C61—42no—
86Q8×C61—42no—
87C2×C4×C61—42no—
88C2×C4×C61C2×C22⋊C411yescharacteristic
89C2×C4×C61C2×D811yescharacteristic
90C2×C4×C61C2×SD1611yescharacteristic
91C2×Dic61—42no—
92C2×Dic61#10211yescharacteristic
93C2×Dic61#10211yescharacteristic
94C2×Dic61#10211yescharacteristic
95C4×D61—22no—
96C4×D61—21no—
97C4×D61—21no—
98C4×D61—21no—
99C4×D61—21no—
100Dic122—81no—
101Dic122—81no—
102C8×C61—21no—
103C8×C61—81no—
104C8×C61#13511yescharacteristic
105C8×C61#13511yescharacteristic
106#92418—21no—
107#92418—21no—
108#92418—81no—
109#11954—611nomaximal, Sylow
110C22×C61C2×#10211yescharacteristic
111C2×D61—21no—
112C2×D61—21no—
113C2×D61#36212yes—
114C4×C61—21no—
115C4×C61—82no—
116C4×C61#41311yescharacteristic
117C4×C61#41611yescharacteristic
118C4×C61#50911yescharacteristic
119C4×C61#51011yescharacteristic
120Dic61—21no—
121Dic61—21no—
122Dic61—21no—
123Dic61—82no—
124#3170—611no—
125#2163—611no—
126C2×#335—611no—
127#1364—611no—
128#1364—611no—
129#1362—611no—
130#1362D6111yescharacteristic, complemented
131C2×C61#154011yescharacteristic
132C2×C61#213911yescharacteristic
133C2×C61C2×#36211yescharacteristic
134D61—22no—
135#533—1221no—
136#500—611no—
137#494C2×D6111yescharacteristic
138#487—1221no—
139#467—612no—
140#467—1221no—
141C4×Q16—612no—
142C4×Q16—1221no—
143C2×C4⋊C8—1221no—
144C2×C4×C8—611no—
145C4⋊C16—611no—
146C4⋊C16C2×D6111yescharacteristic
147C22⋊C16—1221no—
148#346—1221no—
149#335—611no—
150#335—1221no—
151#335C2×D6111yescharacteristic
152C61#1195411yescharacteristic, complemented, Sylow
153C2×Q16—21no—
154C2×Q16C4×D6112yes—
155C22×C8—611no—
156C22×C8—611no—
157C22×C8—2441no—
158C4⋊Q8—21no—
159C4⋊Q8—1221no—
160#125—2441no—
161C22⋊Q8—1222no—
162C22⋊Q8—2441no—
163C4×Q8—1222no—
164C4×Q8—2441no—
165#117—2441no—
166C2×C42—611no—
167C2×C16—21no—
168C2×C16—1221no—
169#107—612no—
170#107—1221no—
171C4⋊C8—21no—
172C4⋊C8—1221no—
173C4⋊C8—2441no—
174#103—1222no—
175#103—1222no—
176C4×C8—611no—
177C4×C8—611no—
178C4×C8—611no—
179C4×C8C22×D6111yescharacteristic
180C2×Q8—22no—
181C2×Q8—2441no—
182C22×C4—611no—
183C22×C4—611no—
184C22×C4—611no—
185Q16—42no—
186Q16—41no—
187Q16—41no—
188C2×C8—41no—
189C2×C8—611no—
190C2×C8—611no—
191C2×C8—1221no—
192C2×C8—1221no—
193C2×C8—4882no—
194C2×C8—2441no—
195C2×C8—2441no—
196C2×C8C2×C4×D6111yescharacteristic
197C2×C8D4×D6111yescharacteristic
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—1222no—
201C4⋊C4—2442no—
202C4⋊C4—2442no—
203C4⋊C4—2441no—
204C22⋊C4—2442no—
205C42—611no—
206C42—611no—
207C42—611no—
208C42—2442no—
209C42D4×D6111yescharacteristic
210C16—41no—
211C16—2441no—
212C23—611no—
213Q8—42no—
214Q8—42no—
215Q8—4881no—
216Q8—4881no—
217C2×C4—42no—
218C2×C4—611no—
219C2×C4—611no—
220C2×C4—611no—
221C2×C4—1222no—
222C2×C4—1221no—
223C2×C4—1221no—
224C2×C4—1221no—
225C2×C4—1221no—
226C2×C4—2442no—
227C2×C4C22⋊C4×D6111yescharacteristic
228C2×C4D8×D6111yescharacteristic
229C2×C4SD16×D6111yescharacteristic
230C8—21no—
231C8—81no—
232C8—1221no—
233C8—1221no—
234C8—4881no—
235C8#1451979611yescharacteristic
236C8#1451979811yescharacteristic
237C22—612no—
238C22—1221no—
239C22—1221no—
240C22#102×D6111yescharacteristic
241C4—21no—
242C4—82no—
243C4—1221no—
244C4—1221no—
245C4—1221no—
246C4—4882no—
247C4#1683974311yescharacteristic
248C4#1683975511yescharacteristic
249C4#1684019911yescharacteristic
250C4#1684020411yescharacteristic
251C2—1222no—
252C2#2144446511yescharacteristic
253C2#2144753011yescharacteristic
254C2#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#11954
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
130. #1362D61semidirect
152. C61#11954semidirect

Maximal subgroups

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

subgroupindex
#214564032
#214476212
#335×D612
#214438752
#214438732
#214438682
C61×#13622
#1195461