Finite Group Databasebeta

← #29591345

Subgroups — #29591345

Order 15616.

310 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 91 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#21447617C211yesmaximal, characteristic
3#335×D61C211yesmaximal, characteristic
4#21443878C211yesmaximal, characteristic, complemented
5#21443876C211yesmaximal, 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—
19C16×Dic61—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—21no—
96C4×D61—21no—
97C4×D61—41no—
98C4×D61SD3212yes—
99C4×D61Q3212yes—
100Dic122—82no—
101C8×C61—21no—
102C8×C61—81no—
103C8×C61#13511yescharacteristic
104C8×C61#13511yescharacteristic
105#92418—21no—
106#92418—21no—
107#92418—81no—
108#11949—611nomaximal, Sylow
109C22×C61C2×#10211yescharacteristic
110C2×D61—21no—
111C2×D61—21no—
112C2×D61#35812yes—
113C4×C61—21no—
114C4×C61—82no—
115C4×C61#41311yescharacteristic
116C4×C61#41611yescharacteristic
117C4×C61C2×SD3211yescharacteristic
118C4×C61C2×Q3211yescharacteristic
119Dic61—21no—
120Dic61—21no—
121Dic61—82no—
122Dic61#35812yes—
123#3170—611no—
124#2162—611no—
125C2×#335—611no—
126#1365—611no—
127#1365—611no—
128#1362—611no—
129#1362D6111yescharacteristic, complemented
130C2×C61#154011yescharacteristic
131C2×C61C2×#35811yescharacteristic
132C2×C61#214811yescharacteristic
133D61—22no—
134#533—1221no—
135#500—611no—
136#494C2×D6111yescharacteristic
137#487—1221no—
138#467—612no—
139#467—1221no—
140C4×Q16—612no—
141C4×Q16—1221no—
142C2×C4⋊C8—1221no—
143C2×C4×C8—611no—
144C4⋊C16—611no—
145C4⋊C16C2×D6111yescharacteristic
146C22⋊C16—1221no—
147C4×C16—1221no—
148#335—611no—
149#335—1221no—
150#335C2×D6111yescharacteristic
151C61#1194911yescharacteristic, complemented, Sylow
152C2×Q16—21no—
153C2×Q16C4×D6112yes—
154C22×C8—611no—
155C22×C8—611no—
156C22×C8—2441no—
157C4⋊Q8—21no—
158C4⋊Q8—1221no—
159#125—2441no—
160C22⋊Q8—1222no—
161C22⋊Q8—2441no—
162C4×Q8—1222no—
163C4×Q8—2441no—
164#117—2441no—
165C2×C42—611no—
166C2×C16—21no—
167C2×C16—1221no—
168#107—612no—
169#107—1221no—
170C4⋊C8—21no—
171C4⋊C8—1221no—
172C4⋊C8—2441no—
173#103—1222no—
174#103—1222no—
175C4×C8—611no—
176C4×C8—611no—
177C4×C8—611no—
178C4×C8C22×D6111yescharacteristic
179C2×Q8—22no—
180C2×Q8—2441no—
181C22×C4—611no—
182C22×C4—611no—
183C22×C4—611no—
184Q16—42no—
185Q16—41no—
186Q16—41no—
187C2×C8—41no—
188C2×C8—611no—
189C2×C8—611no—
190C2×C8—1221no—
191C2×C8—1221no—
192C2×C8—4882no—
193C2×C8—2441no—
194C2×C8—2441no—
195C2×C8C2×C4×D6111yescharacteristic
196C2×C8D4×D6111yescharacteristic
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—1222no—
200C4⋊C4—2442no—
201C4⋊C4—2442no—
202C4⋊C4—2441no—
203C22⋊C4—2442no—
204C42—611no—
205C42—611no—
206C42—611no—
207C42—2442no—
208C42D4×D6111yescharacteristic
209C16—41no—
210C16—2441no—
211C23—611no—
212Q8—42no—
213Q8—42no—
214Q8—4882no—
215C2×C4—42no—
216C2×C4—611no—
217C2×C4—612no—
218C2×C4—612no—
219C2×C4—611no—
220C2×C4—611no—
221C2×C4—1221no—
222C2×C4—1221no—
223C2×C4—2441no—
224C2×C4—2442no—
225C2×C4C22⋊C4×D6111yescharacteristic
226C2×C4D8×D6111yescharacteristic
227C2×C4SD16×D6111yescharacteristic
228C8—21no—
229C8—81no—
230C8—1221no—
231C8—1221no—
232C8—4881no—
233C8#1451979611yescharacteristic
234C8#1451979811yescharacteristic
235C22—612no—
236C22—1221no—
237C22—1221no—
238C22#102×D6111yescharacteristic
239C4—21no—
240C4—82no—
241C4—612no—
242C4—1221no—
243C4—1221no—
244C4—4882no—
245C4#1683974311yescharacteristic
246C4#1683975511yescharacteristic
247C4SD32×D6111yescharacteristic
248C4Q32×D6111yescharacteristic
249C2—1222no—
250C2#2144446511yescharacteristic
251C2#358×D6111yescharacteristic
252C2#2144756711yescharacteristic
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#11949
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. #21443878C2semidirect
5. #21443876C2semidirect
6. #21443868C2semidirect
7. C61×#1362C2semidirect
129. #1362D61semidirect
151. C61#11949semidirect

Maximal subgroups

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

subgroupindex
#214564032
#214476172
#335×D612
#214438782
#214438762
#214438682
C61×#13622
#1194961