Finite Group Databasebeta

← #30605607

Subgroups — #30605607

Order 15616.

316 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 80 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#21462177C211yesmaximal, characteristic, complemented
2C2×#16840624C211yesmaximal, characteristic, complemented
3#21460836C212yesmaximal, complemented
4#21460832C212yesmaximal, complemented
5#21456390C211yesmaximal, characteristic
6C2×C4⋊#92420—21no—
7#16840683C2212yes—
8C22⋊#11758187—21no—
9#16840648—21no—
10#16840624—21no—
11#16840624C2212yes—
12#16840298—21no—
13#16840163C2211yescharacteristic
14#16840147C2211yescharacteristic
15#16840118—21no—
16#16839998C411yescharacteristic
17#16839993—21no—
18Q16×Dic61C411yescharacteristic
19#16839847—21no—
20#16839844C411yescharacteristic
21C2×C8×Dic61C2211yescharacteristic
22C61×#467C411yescharacteristic
23C22×#92420—41no—
24C2×#11758187—22no—
25C4⋊#92420—22no—
26C4⋊#92420—41no—
27C2×#11758201—21no—
28C2×D488C2×C411yescharacteristic
29C22×#92418D411yescharacteristic
30#14519772—41no—
31#14519768—21no—
32#14519766—21no—
33#14519761—41no—
34#14519751—21no—
35Q8×Dic61—21no—
36#14519739—21no—
37#14519737—41no—
38#14519735—41no—
39C2×C4×Dic61D411yescharacteristic
40#14519711C2×C411yescharacteristic
41#14519708—21no—
42#14519701—21no—
43#14519699—21no—
44#14519697—21no—
45C8×Dic61C2×C411yescharacteristic
46C8×Dic61D411yescharacteristic
47C8×Dic61D411yescharacteristic
48C8×Dic61C2311yescharacteristic
49C2×Q16×C61C2×C411yescharacteristic
50C22×C8×C61C2×C411yescharacteristic
51C22⋊Q8×C61—21no—
52#107×C61C2×C411yescharacteristic
53#103×C61—21no—
54C2×Q8×C61—21no—
55C22×C4×C61C22⋊C411yescharacteristic
56C2×C22⋊D61—41no—
57C22×Dic61D811yescharacteristic
58C22×Dic61SD1611yescharacteristic
59C2×D244—21no—
60C2×C4×D61—41no—
61C2×#92420—42no—
62C2×#92420—82no—
63Q16×C61—41no—
64C2×C8×C61—41no—
65C2×C8×C61C22⋊C411yescharacteristic
66C2×C8×C61C22×C411yescharacteristic
67C4⋊C4×C61—21no—
68C4⋊C4×C61—41no—
69C22⋊C4×C61—41no—
70#11758201—42no—
71#11758198—41no—
72#11758198—41no—
73#11758198—41no—
74#11758198—41no—
75C4⋊Dic61—21no—
76C4⋊Dic61—41no—
77C4⋊Dic61—41no—
78#11758196—41no—
79C4×Dic61—41no—
80C4×Dic61C22⋊C411yescharacteristic
81C4×Dic61D811yescharacteristic
82C4×Dic61SD1611yescharacteristic
83C4×Dic61C2×D411yescharacteristic
84C2×#92418—22no—
85C2×#92418C22⋊C411yescharacteristic
86C2×#92418C2×D411yescharacteristic
87D488—41no—
88#11758187—42no—
89C23×C61#10211yescharacteristic
90C22×D61—41no—
91Q8×C61—41no—
92Q8×C61—41no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—41no—
96C2×C4×C61—41no—
97C2×C4×C61#10211yescharacteristic
98C2×C4×C61C2×C22⋊C411yescharacteristic
99C22⋊D61—82no—
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—41no—
103C2×Dic61#10211yescharacteristic
104C2×Dic61#10211yescharacteristic
105C2×Dic61C2×D811yescharacteristic
106C2×Dic61C2×SD1611yescharacteristic
107D244—41no—
108D244—41no—
109C4×D61—82no—
110#92420—82no—
111C8×C61—21no—
112C8×C61—21no—
113#92418—21no—
114#92418#13512yes—
115#11944—611nomaximal, Sylow
116C22×C61—21no—
117C22×C61—21no—
118C22×C61#35912yes—
119C22×C61C2×#10211yescharacteristic
120C2×D61—81no—
121C2×D61—81no—
122C2×D61—81no—
123C4×C61—21no—
124C4×C61—81no—
125C4×C61—81no—
126C4×C61#41311yescharacteristic
127C4×C61#41611yescharacteristic
128Dic61—21no—
129Dic61—21no—
130Dic61—21no—
131Dic61—81no—
132Dic61#36012yes—
133#3168—611no—
134#2162—611no—
135C2×#334—611no—
136#1363—612no—
137#1360—612no—
138C2×C61—22no—
139C2×C61#154011yescharacteristic
140C2×C61C2×#35911yescharacteristic
141C2×C61C2×#36011yescharacteristic
142D61—161no—
143#529—1221no—
144#499—611no—
145#495—611no—
146#488—1221no—
147#467#692311yescharacteristic
148#466—611no—
149#465—1221no—
150C4×Q16—611no—
151C4×SD16—1221no—
152C4×D8—611no—
153C2×C4⋊C8—1221no—
154C2×C4×C8—611no—
155C4⋊C16—612no—
156C22⋊C16—1221no—
157C4×C16—1221no—
158#334—612no—
159#334—1221no—
160C61#1194411yescharacteristic, complemented, Sylow
161C2×Q16C2×#692311yescharacteristic
162C2×SD16—1221no—
163C2×D8—611no—
164C22×C8—611no—
165C22×C8—2441no—
166C22×C8C2×#692311yescharacteristic
167#126—2441no—
168#125—1221no—
169#124—1221no—
170#123—2441no—
171C22⋊Q8—21no—
172#121—1221no—
173C4×Q8—1221no—
174C4×D4—1221no—
175C4×D4—2441no—
176#117—2441no—
177C2×C42—611no—
178C2×C16—1222no—
179#107—611no—
180#107C2×#692311yescharacteristic
181#106—1221no—
182C4⋊C8—1222no—
183C4⋊C8—2441no—
184#103—21no—
185#103—1221no—
186#102—1221no—
187#102—1221no—
188C4×C8—611no—
189C4×C8—611no—
190C4×C8—611no—
191C4×C8—611no—
192C2×Q8—21no—
193C2×D4—1221no—
194C2×D4—2441no—
195C22×C4—611no—
196C22×C4—611no—
197C22×C4—2441no—
198C22×C4C22⋊#692311yescharacteristic
199Q16—41no—
200SD16—2442no—
201D8—2441no—
202C2×C8—41no—
203C2×C8—611no—
204C2×C8—611no—
205C2×C8—1222no—
206C2×C8—4882no—
207C2×C8—2442no—
208C2×C8C22⋊#692311yescharacteristic
209C2×C8C22×#692311yescharacteristic
210C4⋊C4—21no—
211C4⋊C4—41no—
212C4⋊C4—1221no—
213C4⋊C4—2441no—
214C4⋊C4—2441no—
215C4⋊C4—2441no—
216C22⋊C4—41no—
217C22⋊C4—2441no—
218C22⋊C4—2441no—
219C22⋊C4—2441no—
220C22⋊C4—2441no—
221C42—611no—
222C42—611no—
223C42—611no—
224C42—611no—
225C42—2441no—
226C16—2442no—
227C23—2441no—
228C23#1451983911yescharacteristic
229Q8—41no—
230Q8—41no—
231D4—4882no—
232D4—2441no—
233D4—2441no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—611no—
239C2×C4—611no—
240C2×C4—611no—
241C2×C4—611no—
242C2×C4—1222no—
243C2×C4—1222no—
244C2×C4—4882no—
245C2×C4—2441no—
246C2×C4#1451983911yescharacteristic
247C2×C4C2×C22⋊#692311yescharacteristic
248C8—21no—
249C8—21no—
250C8—612no—
251C8—1221no—
252C8—4882no—
253C22—21no—
254C22—21no—
255C22—4881no—
256C22—4881no—
257C22—4881no—
258C22#1684067712yes—
259C22C2×#1451983911yescharacteristic
260C4—21no—
261C4—81no—
262C4—81no—
263C4—612no—
264C4—1221no—
265C4—1221no—
266C4—1221no—
267C4—4881no—
268C4#1684074911yescharacteristic
269C4#1684075211yescharacteristic
270C2—22no—
271C2—9761no—
272C2#2146131711yescharacteristic
273C2C2×#1684067711yescharacteristic
274C2D61⋊#36011yescharacteristic
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#11944
LCSG ▷ C2×C8×C61 ▷ C2×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. #21462177C2semidirect
2. C2×#16840624C2semidirect
3. #21460836C2semidirect
4. #21460832C2semidirect
160. C61#11944semidirect

Maximal subgroups

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

subgroupindex
#214621772
C2×#168406242
#214608362
#214608322
#214563902
#1194461