Finite Group Databasebeta

← #30605359

Subgroups — #30605359

Order 15616.

306 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 72 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#21462183C211yesmaximal, characteristic, complemented
2#21461744C211yesmaximal, characteristic, complemented
3#21460812C212yesmaximal, complemented
4#21460809C212yesmaximal
5#21456387C211yesmaximal, characteristic
6#16840767—21no—
7C4⋊#11758187—21no—
8#16840657C2212yes—
9#16840651—21no—
10#16840638—21no—
11#16840638C2212yes—
12#16840294—21no—
13#16840163C411yescharacteristic
14#16840145C411yescharacteristic
15#16840115—21no—
16#16840004C2211yescharacteristic
17#16839995C2211yescharacteristic
18#16839990—21no—
19C4×Dic244C411yescharacteristic
20C4×#11758200—21no—
21C4×C8×D61C2211yescharacteristic
22C4×D8×C61C411yescharacteristic
23C2×#11758213—22no—
24C2×#11758187—22no—
25#14519844—41no—
26#14519844—41no—
27C2×Dic244C2×C411yescharacteristic
28C2×#11758200—21no—
29C2×C8×D61D411yescharacteristic
30C2×C8×D61C2311yescharacteristic
31#14519770—41no—
32#14519768—21no—
33#14519764—21no—
34#14519759—41no—
35#14519757—21no—
36#14519748—21no—
37C4×Dic122—21no—
38C4×C22⋊D61—41no—
39#14519736—41no—
40C42×D61D411yescharacteristic
41#14519711C2×C411yescharacteristic
42#14519708—21no—
43#14519702—21no—
44#14519700—21no—
45#14519698—21no—
46C4×#92418D411yescharacteristic
47C8×Dic61C2×C411yescharacteristic
48C8×Dic61D411yescharacteristic
49C2×D8×C61C2×C411yescharacteristic
50C4×D4×C61—21no—
51#107×C61C2×C411yescharacteristic
52#102×C61—21no—
53C4×C8×C61C2×C411yescharacteristic
54C2×D4×C61—21no—
55C22×C4×C61—41no—
56C2×C22⋊D61—41no—
57C2×C4×D61SD1611yescharacteristic
58C2×C4×D61SD1611yescharacteristic
59C2×C4×D61C2×D411yescharacteristic
60C2×Dic122—21no—
61C2×#92420—42no—
62#11758213—42no—
63#11758213—42no—
64D8×C61—41no—
65C2×C8×C61C22⋊C411yescharacteristic
66C2×C8×C61C22×C411yescharacteristic
67C4⋊C4×C61—21no—
68C22⋊C4×C61—41no—
69C42×C61C22⋊C411yescharacteristic
70C22⋊Dic61—41no—
71C22⋊Dic61—41no—
72C22⋊Dic61—41no—
73#11758200—42no—
74#11758198—41no—
75C4⋊Dic61—21no—
76C4⋊Dic61—41no—
77C4⋊Dic61—41no—
78#11758196—41no—
79#11758196—41no—
80C4×Dic61—41no—
81C4×Dic61C22⋊C411yescharacteristic
82C4×Dic61D811yescharacteristic
83C4×Dic61D811yescharacteristic
84C2×#92418C22⋊C411yescharacteristic
85C2×#92418C2×D411yescharacteristic
86Dic244—41no—
87C8×D61—41no—
88C8×D61—41no—
89#11758187—42no—
90C23×C61—41no—
91C22×D61C2×SD1611yescharacteristic
92D4×C61—41no—
93D4×C61—41no—
94C2×C4×C61—41no—
95C2×C4×C61—82no—
96C2×C4×C61#10211yescharacteristic
97C2×C4×C61#10211yescharacteristic
98C2×C4×C61C2×C22⋊C411yescharacteristic
99C22⋊D61—82no—
100C2×Dic61—41no—
101C2×Dic61—41no—
102C2×Dic61#10211yescharacteristic
103C2×Dic61#10211yescharacteristic
104C2×Dic61C2×D811yescharacteristic
105C4×D61—21no—
106C4×D61—21no—
107C4×D61—41no—
108C4×D61—41no—
109Dic122—41no—
110Dic122—41no—
111#92420—82no—
112C8×C61—21no—
113C8×C61—21no—
114#92418—21no—
115#92418—21no—
116#11866—611nomaximal, Sylow
117C22×C61—81no—
118C22×C61—81no—
119C22×C61—81no—
120C22×C61C2×#10211yescharacteristic
121C2×D61—21no—
122C2×D61—21no—
123C2×D61—21no—
124C4×C61—21no—
125C4×C61—21no—
126C4×C61—81no—
127C4×C61#41011yescharacteristic
128C4×C61#42111yescharacteristic
129Dic61—21no—
130Dic61—21no—
131Dic61—21no—
132Dic61—81no—
133Dic61—81no—
134#3168—611no—
135#2163—611no—
136#1837—611no—
137#1350—612no—
138#1349—612no—
139C2×C61—161no—
140C2×C61#151711yescharacteristic
141C2×C61#214311yescharacteristic
142C2×C61#214811yescharacteristic
143D61—41no—
144#529—1221no—
145#499—611no—
146#495—611no—
147#488—1221no—
148#467—611no—
149#466—611no—
150#465—1221no—
151C4×Q16—611no—
152C4×SD16—1221no—
153C4×D8#692311yescharacteristic
154#423—1221no—
155C2×C4×C8—611no—
156C4⋊C16—1221no—
157C22⋊C16—612no—
158#346—1221no—
159#341—612no—
160#341—1221no—
161C61#1186611yescharacteristic, complemented, Sylow
162C2×Q16—611no—
163C2×SD16—1221no—
164C2×D8C2×#692311yescharacteristic
165C2×M16—1222no—
166C22×C8—611no—
167C22×C8—611no—
168#126—2441no—
169#125—1221no—
170#124—1221no—
171#123—2441no—
172C22⋊Q8—1221no—
173#121—1221no—
174C4×Q8—1221no—
175C4×D4—21no—
176C4×D4—2441no—
177#117—2441no—
178C2×C42—611no—
179C2×C16—1222no—
180#107—611no—
181#107C2×#692311yescharacteristic
182#106—1221no—
183C4⋊C8—2441no—
184C4⋊C8—2441no—
185#103—1221no—
186#103—1221no—
187#102—21no—
188#102—1221no—
189C4×C8—611no—
190C4×C8—611no—
191C4×C8—611no—
192C4×C8C2×#692311yescharacteristic
193C2×Q8—1221no—
194C2×D4—21no—
195C2×D4—2441no—
196C22×C4—41no—
197C22×C4—611no—
198C22×C4—611no—
199C22×C4—611no—
200Q16—2441no—
201SD16—2442no—
202D8—41no—
203M16—2442no—
204M16—2442no—
205C2×C8—611no—
206C2×C8—611no—
207C2×C8—2441no—
208C2×C8—2441no—
209C2×C8—2442no—
210C2×C8C22⋊#692311yescharacteristic
211C2×C8C22×#692311yescharacteristic
212C4⋊C4—21no—
213C4⋊C4—1221no—
214C4⋊C4—2441no—
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—2441no—
227C42C22⋊#692311yescharacteristic
228C16—2442no—
229C23—41no—
230C23—611no—
231Q8—2441no—
232Q8—2441no—
233D4—41no—
234D4—41no—
235D4—4882no—
236C2×C4—41no—
237C2×C4—82no—
238C2×C4—611no—
239C2×C4—611no—
240C2×C4—611no—
241C2×C4—1221no—
242C2×C4—1221no—
243C2×C4—2441no—
244C2×C4—2441no—
245C2×C4—2441no—
246C2×C4—2441no—
247C2×C4#1451983911yescharacteristic
248C2×C4#1451983911yescharacteristic
249C2×C4C2×C22⋊#692311yescharacteristic
250C8—21no—
251C8—21no—
252C8—1221no—
253C8—1221no—
254C8—4882no—
255C22—81no—
256C22—81no—
257C22—81no—
258C22—1221no—
259C22—1221no—
260C22—1221no—
261C22C2×#1451983911yescharacteristic
262C4—21no—
263C4—21no—
264C4—81no—
265C4—1221no—
266C4—1221no—
267C4—1221no—
268C4—4881no—
269C4—4881no—
270C4#1684074111yescharacteristic
271C4#1684075911yescharacteristic
272C2—161no—
273C2—2441no—
274C2#2146124911yescharacteristic
275C2#2146213411yescharacteristic
276C2#2146214611yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC4×D8×C61C4
socleC22×C61C2×#102
prime radical#16839995C22
cosocleC2×C8×D61C23
hypercenterC4×D8#6923
hypocenterC61#11866
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #21462183C2semidirect
2. #21461744C2semidirect
3. #21460812C2semidirect
161. C61#11866semidirect

Maximal subgroups

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

subgroupindex
#214621832
#214617442
#214608122
#214608092
#214563872
#1186661