Finite Group Databasebeta

← #30604690

Subgroups — #30604690

Order 15616.

362 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 82 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
1C2×#16840651C211yesmaximal, characteristic, complemented
2#21461379C211yesmaximal, characteristic, complemented
3#21460778C212yesmaximal, complemented
4#21460777C212yesmaximal, complemented
5#21456393C211yesmaximal, characteristic
6C22×#11758187—21no—
7#16840783—21no—
8#16840651—21no—
9#16840651C2212yes—
10#16840626—21no—
11#16840623C2212yes—
12#16840307—21no—
13#16840166C411yescharacteristic
14#16840137C411yescharacteristic
15#16840107—21no—
16#16839998C411yescharacteristic
17#16839996—21no—
18D8×Dic61C2211yescharacteristic
19#16839844C2211yescharacteristic
20#16839842—21no—
21C2×C8×Dic61C2211yescharacteristic
22C61×#466C411yescharacteristic
23C2×#11758187—24no—
24C2×#11758187—22no—
25C4⋊#92420—22no—
26C22⋊#92420—41no—
27#14519832—41no—
28C2×#11758224—41no—
29C2×D488C2×C411yescharacteristic
30C2×#11758199—21no—
31C22×#92418D411yescharacteristic
32#14519776—21no—
33#14519773—21no—
34#14519763—41no—
35#14519751—21no—
36#14519749—41no—
37D4×Dic61—21no—
38#14519739—21no—
39#14519737—41no—
40C2×C4×Dic61D411yescharacteristic
41#14519711C2×C411yescharacteristic
42#14519710—21no—
43#14519699—21no—
44#14519698—21no—
45#14519697—21no—
46C8×Dic61C2×C411yescharacteristic
47C8×Dic61D411yescharacteristic
48C8×Dic61D411yescharacteristic
49C8×Dic61C2311yescharacteristic
50C2×D8×C61C2×C411yescharacteristic
51C22×C8×C61C2×C411yescharacteristic
52#121×C61—21no—
53#107×C61C2×C411yescharacteristic
54#102×C61—21no—
55C2×D4×C61—21no—
56C2×D4×C61—41no—
57C22×C4×C61C22⋊C411yescharacteristic
58C2×C22⋊D61—41no—
59C2×C22⋊D61—41no—
60C2×C22⋊D61—41no—
61C22×Dic61—41no—
62C22×Dic61D811yescharacteristic
63C22×Dic61SD1611yescharacteristic
64#11758224—84no—
65C2×D244—21no—
66C2×C4×D61—41no—
67C2×Dic122—41no—
68C2×#92420—42no—
69D8×C61—22no—
70C2×C8×C61—22no—
71C2×C8×C61C22⋊C411yescharacteristic
72C2×C8×C61C22×C411yescharacteristic
73C4⋊C4×C61—21no—
74C22⋊C4×C61—41no—
75C22⋊Dic61—41no—
76#11758199—42no—
77#11758198—41no—
78#11758198—41no—
79C4⋊Dic61—21no—
80#11758196—41no—
81C4×Dic61C22⋊C411yescharacteristic
82C4×Dic61D811yescharacteristic
83C4×Dic61SD1611yescharacteristic
84C4×Dic61C2×D411yescharacteristic
85C2×#92418—22no—
86C2×#92418C22⋊C411yescharacteristic
87C2×#92418C2×D411yescharacteristic
88D488—22no—
89#11758187—24no—
90C23×C61—41no—
91C23×C61#10211yescharacteristic
92C22×D61—41no—
93D4×C61—41no—
94D4×C61—41no—
95D4×C61—82no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—41no—
99C2×C4×C61#10211yescharacteristic
100C2×C4×C61C2×C22⋊C411yescharacteristic
101C22⋊D61—82no—
102C22⋊D61—82no—
103C22⋊D61—82no—
104C2×Dic61—22no—
105C2×Dic61—41no—
106C2×Dic61—41no—
107C2×Dic61—82no—
108C2×Dic61#10211yescharacteristic
109C2×Dic61#10211yescharacteristic
110C2×Dic61C2×D811yescharacteristic
111C2×Dic61C2×SD1611yescharacteristic
112D244—41no—
113D244—41no—
114C4×D61—82no—
115Dic122—82no—
116#92420—82no—
117C8×C61—21no—
118C8×C61#13112yes—
119#92418—21no—
120#92418#10412yes—
121#11678—611nomaximal, Sylow
122C22×C61—21no—
123C22×C61—21no—
124C22×C61—81no—
125C22×C61—81no—
126C22×C61—81no—
127C22×C61#36112yes—
128C22×C61C2×#10211yescharacteristic
129C2×D61—81no—
130C2×D61—81no—
131C2×D61—81no—
132C4×C61—21no—
133C4×C61—81no—
134C4×C61#40811yescharacteristic
135C4×C61C2×#10411yescharacteristic
136Dic61—21no—
137Dic61—21no—
138Dic61—21no—
139Dic61—21no—
140Dic61—81no—
141#3169—611no—
142C2×#346—611no—
143#1568—611no—
144#1333—612no—
145#1333—612no—
146C2×C61—22no—
147C2×C61—161no—
148C2×C61#149211yescharacteristic
149C2×C61#214511yescharacteristic
150C2×C61C2×#36111yescharacteristic
151D61—161no—
152#532—1221no—
153C22×C16—1221no—
154#500—611no—
155#493—611no—
156#486—1221no—
157#466—611no—
158#466—1221no—
159#466#692311yescharacteristic
160C4×D8—611no—
161C4×D8—611no—
162C4×D8—1221no—
163#432—1221no—
164C2×C4×C8—611no—
165#346—612no—
166#346—1221no—
167#335—1221no—
168#334—612no—
169C61#1167811yescharacteristic, complemented, Sylow
170C2×#41—2441no—
171C2×D8—611no—
172C2×D8—1221no—
173C2×D8C2×#692311yescharacteristic
174C22×C8—611no—
175C22×C8C2×#692311yescharacteristic
176C4⋊Q8—1221no—
177#127—1221no—
178#124—2441no—
179#121—21no—
180#121—1221no—
181#121—2441no—
182C4×D4—1221no—
183C4×D4—1221no—
184C4×D4—2441no—
185C2×C42—611no—
186C2×C16—1222no—
187C2×C16—1224no—
188#107—611no—
189#107—1221no—
190#107C2×#692311yescharacteristic
191C4⋊C8—1222no—
192#102—21no—
193#102—1221no—
194#102—1221no—
195#102—1221no—
196C22⋊C8—2441no—
197#97—2441no—
198C4×C8—611no—
199C4×C8—611no—
200C4×C8—611no—
201C4×C8—611no—
202#41—4884no—
203C2×Q8—2441no—
204C2×D4—21no—
205C2×D4—41no—
206C2×D4—1221no—
207C2×D4—2441no—
208C2×D4—2441no—
209C2×D4—2441no—
210C22×C4—611no—
211C22×C4—611no—
212C22×C4—2441no—
213C22×C4—2441no—
214C22×C4C22⋊#692311yescharacteristic
215D8—22no—
216D8—1222no—
217D8—2442no—
218C2×C8—22no—
219C2×C8—611no—
220C2×C8—611no—
221C2×C8—1222no—
222C2×C8—2442no—
223C2×C8C22⋊#692311yescharacteristic
224C2×C8C22×#692311yescharacteristic
225C4⋊C4—21no—
226C4⋊C4—1221no—
227C4⋊C4—2441no—
228C22⋊C4—41no—
229C22⋊C4—2441no—
230C22⋊C4—2441no—
231C22⋊C4—2441no—
232C42—611no—
233C42—611no—
234C42—611no—
235C42—611no—
236C16—1224no—
237C23—41no—
238C23—2441no—
239C23#1451983911yescharacteristic
240Q8—4882no—
241D4—41no—
242D4—41no—
243D4—82no—
244D4—4882no—
245D4—4882no—
246D4—4882no—
247D4—2441no—
248D4—2441no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—41no—
252C2×C4—611no—
253C2×C4—611no—
254C2×C4—611no—
255C2×C4—611no—
256C2×C4—1222no—
257C2×C4—4882no—
258C2×C4—4882no—
259C2×C4—2441no—
260C2×C4—2441no—
261C2×C4#1451983911yescharacteristic
262C2×C4C2×C22⋊#692311yescharacteristic
263C8—21no—
264C8—612no—
265C8—1221no—
266C8—4882no—
267C8#1451986412yes—
268C22—21no—
269C22—21no—
270C22—81no—
271C22—81no—
272C22—81no—
273C22—4881no—
274C22—4881no—
275C22—4881no—
276C22#1684068012yes—
277C22C2×#1451983911yescharacteristic
278C4—21no—
279C4—81no—
280C4—1221no—
281C4—1221no—
282C4—1221no—
283C4—1221no—
284C4—4881no—
285C4#1684073511yescharacteristic
286C4D61⋊#10411yescharacteristic
287C2—22no—
288C2—161no—
289C2—9761no—
290C2#2146116411yescharacteristic
291C2#2146213911yescharacteristic
292C2C2×#1684068011yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#466C4
socleC22×C61C2×#102
prime radical#21456393C2
cosocleC8×Dic61C23
hypercenter#466#6923
hypocenterC61#11678
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C2×#16840651C2semidirect
2. #21461379C2semidirect
3. #21460778C2semidirect
4. #21460777C2semidirect
169. C61#11678semidirect

Maximal subgroups

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

subgroupindex
C2×#168406512
#214613792
#214607782
#214607772
#214563932
#1167861