Finite Group Databasebeta

← #30605344

Subgroups — #30605344

Order 15616.

310 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 74 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#21462178C211yesmaximal, characteristic, complemented
2#21461744C211yesmaximal, characteristic, complemented
3#21460812C212yesmaximal, complemented
4#21460810C212yesmaximal
5#21456391C211yesmaximal, characteristic
6#16840767—21no—
7#16840683—21no—
8#16840657C2212yes—
9C4×#11758187—21no—
10#16840638—21no—
11#16840638C2212yes—
12#16840297—21no—
13#16840146C411yescharacteristic
14#16840119—21no—
15#16840004C2211yescharacteristic
16#16839999C2211yescharacteristic
17#16839992—21no—
18#16839856C411yescharacteristic
19#16839849—21no—
20#16839844C411yescharacteristic
21C4×C8×D61C2211yescharacteristic
22C61×#499C411yescharacteristic
23C2×#11758213—22no—
24C2×#11758187—22no—
25#14519844—41no—
26#14519844—41no—
27C2×Dic244C2×C411yescharacteristic
28C2×#11758190—21no—
29C2×D488C2×C411yescharacteristic
30C2×C8×D61D411yescharacteristic
31C2×C8×D61C2311yescharacteristic
32#14519772—41no—
33#14519765—21no—
34#14519762—41no—
35#14519757—21no—
36#14519752—21no—
37#14519742—21no—
38#14519739—21no—
39#14519739—41no—
40#14519735—41no—
41C42×D61D411yescharacteristic
42#14519700—21no—
43#14519700—21no—
44#14519697—21no—
45#14519697—21no—
46C4×#92418D411yescharacteristic
47C8×Dic61C2×C411yescharacteristic
48C8×Dic61D411yescharacteristic
49#125×C61—21no—
50#107×C61C2×C411yescharacteristic
51#107×C61C2×C411yescharacteristic
52#106×C61—21no—
53C4×C8×C61C2×C411yescharacteristic
54C2×D244—21no—
55C2×D244—41no—
56C2×C4×D61—41no—
57C2×C4×D61SD1611yescharacteristic
58C2×C4×D61SD1611yescharacteristic
59C2×C4×D61C2×D411yescharacteristic
60C2×Dic122—21no—
61C2×#92420—42no—
62#11758213—42no—
63#11758213—42no—
64C2×C8×C61C22⋊C411yescharacteristic
65C2×C8×C61C22×C411yescharacteristic
66C4⋊C4×C61—21no—
67C4⋊C4×C61—21no—
68C4⋊C4×C61—41no—
69C4⋊C4×C61—41no—
70C42×C61C22⋊C411yescharacteristic
71#11758198—41no—
72#11758198—41no—
73#11758198—41no—
74#11758198—41no—
75#11758198—41no—
76C4⋊Dic61—41no—
77#11758196—41no—
78C4×Dic61—41no—
79C4×Dic61C22⋊C411yescharacteristic
80C4×Dic61D811yescharacteristic
81C4×Dic61D811yescharacteristic
82C2×#92418C22⋊C411yescharacteristic
83C2×#92418C2×D411yescharacteristic
84Dic244—41no—
85D488—41no—
86#11758190—42no—
87C8×D61—41no—
88C8×D61—41no—
89#11758187—42no—
90C22×D61—41no—
91C22×D61C2×SD1611yescharacteristic
92C2×C4×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61#10211yescharacteristic
95C2×C4×C61#10211yescharacteristic
96C2×C4×C61C2×C22⋊C411yescharacteristic
97C2×Dic61—41no—
98C2×Dic61#10211yescharacteristic
99C2×Dic61#10211yescharacteristic
100C2×Dic61C2×D811yescharacteristic
101D244—41no—
102D244—41no—
103D244—82no—
104C4×D61—21no—
105C4×D61—21no—
106C4×D61—22no—
107C4×D61—41no—
108C4×D61—82no—
109Dic122—41no—
110Dic122—41no—
111#92420—82no—
112C8×C61—21no—
113C8×C61—21no—
114#92418—21no—
115#92418—21no—
116#11861—611nomaximal, Sylow
117C22×C61C2×#10211yescharacteristic
118C2×D61—21no—
119C2×D61—21no—
120C2×D61—21no—
121C2×D61—81no—
122C2×D61—81no—
123C2×D61—81no—
124C4×C61—21no—
125C4×C61—21no—
126C4×C61—81no—
127C4×C61—81no—
128C4×C61#41011yescharacteristic
129C4×C61#42111yescharacteristic
130Dic61—21no—
131Dic61—21no—
132Dic61—81no—
133Dic61#35912yes—
134#3168—611no—
135#2162—611no—
136#1837—611no—
137#1350—612no—
138#1349—612no—
139C2×C61#151711yescharacteristic
140C2×C61C2×#35911yescharacteristic
141C2×C61#214811yescharacteristic
142D61—41no—
143D61—161no—
144#529—1221no—
145#499#692311yescharacteristic
146#495—611no—
147#488—1221no—
148#467—611no—
149#466—611no—
150#465—1221no—
151C4×Q16—611no—
152C4×SD16—1221no—
153C4×D8—611no—
154#423—1221no—
155C2×C4×C8—611no—
156C4⋊C16—1221no—
157C22⋊C16—612no—
158C4×C16—1221no—
159#341—612no—
160#341—1221no—
161C61#1186111yescharacteristic, complemented, Sylow
162C2×Q16—611no—
163C2×SD16—1221no—
164C2×D8—611no—
165C2×M16—1222no—
166C22×C8—611no—
167C22×C8—611no—
168#126—2441no—
169#125—21no—
170#124—1221no—
171#123—2441no—
172C22⋊Q8—1221no—
173#121—1221no—
174C4×Q8—1221no—
175C4×D4—1221no—
176C4×D4—2441no—
177#117—2441no—
178C2×C42—611no—
179C2×C16—1222no—
180#107C2×#692311yescharacteristic
181#107C2×#692311yescharacteristic
182#106—21no—
183C4⋊C8—2441no—
184C4⋊C8—2441no—
185#103—1221no—
186#103—1221no—
187#102—1221no—
188#102—1221no—
189C4×C8—611no—
190C4×C8—611no—
191C4×C8—611no—
192C4×C8C2×#692311yescharacteristic
193C2×Q8—1221no—
194C2×D4—1221no—
195C2×D4—2441no—
196C22×C4—611no—
197C22×C4—611no—
198C22×C4—611no—
199C22×C4—2441no—
200Q16—2441no—
201SD16—2442no—
202D8—2441no—
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—21no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—2441no—
217C4⋊C4—2441no—
218C22⋊C4—2441no—
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—611no—
230C23—2441no—
231Q8—2441no—
232Q8—2441no—
233D4—4882no—
234D4—2441no—
235D4—2441no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—611no—
239C2×C4—611no—
240C2×C4—611no—
241C2×C4—1222no—
242C2×C4—1221no—
243C2×C4—1221no—
244C2×C4—4882no—
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—1221no—
256C22—1221no—
257C22—1221no—
258C22—4881no—
259C22—4881no—
260C22—4881no—
261C22C2×#1451983911yescharacteristic
262C4—21no—
263C4—21no—
264C4—81no—
265C4—81no—
266C4—612no—
267C4—1221no—
268C4—1221no—
269C4—4881no—
270C4#1684074311yescharacteristic
271C4#1684076111yescharacteristic
272C2—9761no—
273C2—2441no—
274C2#2146125011yescharacteristic
275C2D61⋊#35911yescharacteristic
276C2#2146214611yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#499C4
socleC22×C61C2×#102
prime radical#16839999C22
cosocleC2×C8×D61C23
hypercenter#499#6923
hypocenterC61#11861
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #499

Complements

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

NH ≅ G/Ntype
1. #21462178C2semidirect
2. #21461744C2semidirect
3. #21460812C2semidirect
161. C61#11861semidirect

Maximal subgroups

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

subgroupindex
#214621782
#214617442
#214608122
#214608102
#214563912
#1186161