Finite Group Databasebeta

← #30604688

Subgroups — #30604688

Order 15616.

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

normal subgroups only

This group has 332 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#21461373C211yesmaximal, characteristic, complemented
3#21460779C212yesmaximal, complemented
4#21460778C212yesmaximal, complemented
5#21456390C211yesmaximal, characteristic
6C22×#11758187—21no—
7#16840765—21no—
8#16840651—21no—
9#16840651C2212yes—
10#16840624—21no—
11#16840623C2212yes—
12#16840298—21no—
13#16840163C411yescharacteristic
14#16840147C411yescharacteristic
15#16840118—21no—
16#16839998C411yescharacteristic
17#16839993—21no—
18Q16×Dic61C2211yescharacteristic
19#16839847—21no—
20#16839844C2211yescharacteristic
21C2×C8×Dic61C2211yescharacteristic
22C61×#467C411yescharacteristic
23C2×#11758217—41no—
24C2×#11758187—24no—
25C2×#11758187—22no—
26#14519844—41no—
27C4⋊#92420—22no—
28C2×#11758201—21no—
29C2×D488C2×C411yescharacteristic
30C22×#92418D411yescharacteristic
31#14519772—41no—
32#14519768—21no—
33#14519766—21no—
34#14519761—41no—
35#14519751—21no—
36Q8×Dic61—21no—
37#14519739—21no—
38#14519737—41no—
39#14519735—41no—
40C2×C4×Dic61D411yescharacteristic
41#14519711C2×C411yescharacteristic
42#14519708—21no—
43#14519701—21no—
44#14519699—21no—
45#14519697—21no—
46C8×Dic61C2×C411yescharacteristic
47C8×Dic61D411yescharacteristic
48C8×Dic61D411yescharacteristic
49C8×Dic61C2311yescharacteristic
50C2×Q16×C61C2×C411yescharacteristic
51C22×C8×C61C2×C411yescharacteristic
52C22⋊Q8×C61—21no—
53#107×C61C2×C411yescharacteristic
54#103×C61—21no—
55C2×Q8×C61—21no—
56C22×C4×C61C22⋊C411yescharacteristic
57C2×C22⋊D61—41no—
58C22×Dic61D811yescharacteristic
59C22×Dic61SD1611yescharacteristic
60C2×D244—21no—
61C2×C4×D61—41no—
62#11758217—82no—
63C2×#92420—42no—
64Q16×C61—22no—
65C2×C8×C61—22no—
66C2×C8×C61C22⋊C411yescharacteristic
67C2×C8×C61C22×C411yescharacteristic
68C4⋊C4×C61—21no—
69C4⋊C4×C61—41no—
70C22⋊C4×C61—41no—
71#11758201—42no—
72#11758198—41no—
73#11758198—41no—
74#11758198—41no—
75#11758198—41no—
76C4⋊Dic61—21no—
77C4⋊Dic61—41no—
78C4⋊Dic61—41no—
79#11758196—41no—
80C4×Dic61—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#10211yescharacteristic
91C22×D61—41no—
92Q8×C61—41no—
93Q8×C61—41no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—41no—
97C2×C4×C61—41no—
98C2×C4×C61#10211yescharacteristic
99C2×C4×C61C2×C22⋊C411yescharacteristic
100C22⋊D61—82no—
101C2×Dic61—22no—
102C2×Dic61—41no—
103C2×Dic61—41no—
104C2×Dic61#10211yescharacteristic
105C2×Dic61#10211yescharacteristic
106C2×Dic61C2×D811yescharacteristic
107C2×Dic61C2×SD1611yescharacteristic
108D244—41no—
109D244—41no—
110C4×D61—82no—
111#92420—82no—
112C8×C61—21no—
113C8×C61#13112yes—
114#92418—21no—
115#92418#10412yes—
116#11677—611nomaximal, Sylow
117C22×C61—21no—
118C22×C61—21no—
119C22×C61#36012yes—
120C22×C61C2×#10211yescharacteristic
121C2×D61—81no—
122C2×D61—81no—
123C2×D61—81no—
124C4×C61—21no—
125C4×C61—81no—
126C4×C61—81no—
127C4×C61#40811yescharacteristic
128C4×C61C2×#10411yescharacteristic
129Dic61—21no—
130Dic61—21no—
131Dic61—21no—
132Dic61—21no—
133Dic61—81no—
134#3168—611no—
135C2×#346—611no—
136#1566—611no—
137#1334—612no—
138#1333—612no—
139C2×C61—22no—
140C2×C61#149211yescharacteristic
141C2×C61C2×#36011yescharacteristic
142C2×C61#214811yescharacteristic
143D61—161no—
144#529—1221no—
145C22×C16—1221no—
146#499—611no—
147#495—611no—
148#488—1221no—
149#467#692311yescharacteristic
150#466—611no—
151#465—1221no—
152C4×Q16—611no—
153C4×SD16—1221no—
154C4×D8—611no—
155#423—1221no—
156C2×C4×C8—611no—
157#346—612no—
158#346—1221no—
159#334—612no—
160#334—1221no—
161C61#1167711yescharacteristic, complemented, Sylow
162C2×Q16C2×#692311yescharacteristic
163C2×SD16—1221no—
164C2×D8—611no—
165C2×M16—2441no—
166C22×C8—611no—
167C22×C8C2×#692311yescharacteristic
168#126—2441no—
169#125—1221no—
170#124—1221no—
171#123—2441no—
172C22⋊Q8—21no—
173#121—1221no—
174C4×Q8—1221no—
175C4×D4—1221no—
176C4×D4—2441no—
177#117—2441no—
178C2×C42—611no—
179C2×C16—1222no—
180C2×C16—1224no—
181#107—611no—
182#107C2×#692311yescharacteristic
183#106—1221no—
184C4⋊C8—1222no—
185C4⋊C8—2441no—
186#103—21no—
187#103—1221no—
188#102—1221no—
189#102—1221no—
190C4×C8—611no—
191C4×C8—611no—
192C4×C8—611no—
193C4×C8—611no—
194C2×Q8—21no—
195C2×D4—1221no—
196C2×D4—2441no—
197C22×C4—611no—
198C22×C4—611no—
199C22×C4—2441no—
200C22×C4C22⋊#692311yescharacteristic
201Q16—22no—
202SD16—2442no—
203D8—1222no—
204M16—4882no—
205C2×C8—22no—
206C2×C8—611no—
207C2×C8—611no—
208C2×C8—1222no—
209C2×C8—2442no—
210C2×C8C22⋊#692311yescharacteristic
211C2×C8C22×#692311yescharacteristic
212C4⋊C4—21no—
213C4⋊C4—41no—
214C4⋊C4—1221no—
215C4⋊C4—2441no—
216C4⋊C4—2441no—
217C4⋊C4—2441no—
218C22⋊C4—41no—
219C22⋊C4—2441no—
220C22⋊C4—2441no—
221C22⋊C4—2441no—
222C22⋊C4—2441no—
223C42—611no—
224C42—611no—
225C42—611no—
226C42—611no—
227C42—2441no—
228C16—1224no—
229C23—2441no—
230C23#1451983911yescharacteristic
231Q8—41no—
232Q8—41no—
233D4—4882no—
234D4—2441no—
235D4—2441no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—611no—
241C2×C4—611no—
242C2×C4—611no—
243C2×C4—611no—
244C2×C4—1222no—
245C2×C4—4882no—
246C2×C4—2441no—
247C2×C4—2441no—
248C2×C4#1451983911yescharacteristic
249C2×C4C2×C22⋊#692311yescharacteristic
250C8—21no—
251C8—612no—
252C8—1221no—
253C8—4882no—
254C8#1451986412yes—
255C22—21no—
256C22—21no—
257C22—4881no—
258C22—4881no—
259C22—4881no—
260C22#1684067912yes—
261C22C2×#1451983911yescharacteristic
262C4—21no—
263C4—81no—
264C4—81no—
265C4—1221no—
266C4—1221no—
267C4—1221no—
268C4—1221no—
269C4—4881no—
270C4#1684073511yescharacteristic
271C4D61⋊#10411yescharacteristic
272C2—22no—
273C2—9761no—
274C2#2146116411yescharacteristic
275C2C2×#1684067911yescharacteristic
276C2#2146214611yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#467C4
socleC22×C61C2×#102
prime radical#16839998C4
cosocleC8×Dic61C23
hypercenter#467#6923
hypocenterC61#11677
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #467

Complements

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

NH ≅ G/Ntype
1. C2×#16840651C2semidirect
2. #21461373C2semidirect
3. #21460779C2semidirect
4. #21460778C2semidirect
161. C61#11677semidirect

Maximal subgroups

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

subgroupindex
C2×#168406512
#214613732
#214607792
#214607782
#214563902
#1167761