Finite Group Databasebeta

← #30605016

Subgroups — #30605016

Order 15616.

304 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 62 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#21462194C211yesmaximal, characteristic, complemented
2#21461540C211yesmaximal, characteristic, complemented
3#21460796C211yesmaximal, characteristic, complemented
4#21460794C211yesmaximal, characteristic
5#21460792C211yesmaximal, characteristic, complemented
6#21460790C211yesmaximal, characteristic
7#21456438C211yesmaximal, characteristic
8#16840725—21no—
9#16840684—21no—
10#16840659C2211yescharacteristic
11#16840659C2211yescharacteristic
12#16840654—21no—
13#16840631C2211yescharacteristic
14#16840630C2211yescharacteristic
15#16840629—21no—
16#16840386—21no—
17#16840146C411yescharacteristic, complemented
18#16840124—21no—
19#16840021C2211yescharacteristic
20#16840016C2211yescharacteristic
21#16839992—21no—
22#16839873C411yescharacteristic, complemented
23#16839868C411yescharacteristic, complemented
24#16839849—21no—
25#16839716C2211yescharacteristic
26C61×#498C411yescharacteristic, complemented
27D61⋊M16—21no—
28#14519856—21no—
29#14519851—21no—
30#14519851—21no—
31#14519831—22no—
32C8×#6923—22no—
33C2×Dic244C2×C411yescharacteristic
34C2×#11758190—21no—
35C2×D488C2×C411yescharacteristic
36C2×#11758189C2311yescharacteristic
37C2×C8×D61D411yescharacteristic
38#14519772—41no—
39#14519766—41no—
40#14519765—21no—
41#14519762—41no—
42#14519757—21no—
43#14519753—41no—
44#14519752—21no—
45#14519742—21no—
46#14519739—21no—
47#14519734D411yescharacteristic
48#14519700—21no—
49#14519700—21no—
50#14519697—21no—
51#14519697—21no—
52#14519688D411yescharacteristic
53#14519687C2×C411yescharacteristic
54C8×Dic61D411yescharacteristic
55C4⋊Q8×C61—21no—
56#106×C61—21no—
57#106×C61C2×C411yescharacteristic
58#106×C61C2×C411yescharacteristic
59C4×C8×C61C2×C411yescharacteristic
60C2×Q8×C61—41no—
61C2×D244—21no—
62C2×D244—41no—
63C2×C4×D61—41no—
64C2×C4×D61C2×D411yescharacteristic
65C2×Dic122—21no—
66C22⋊#6923—41no—
67#11758217—41no—
68C4⋊#6923—41no—
69C4×#6923—22no—
70#11758213—41no—
71D61⋊C8—22no—
72C2×C8×C61C22⋊C411yescharacteristic
73C2×C8×C61C22×C411yescharacteristic
74C4⋊C4×C61—21no—
75C4⋊C4×C61—21no—
76C4⋊C4×C61—41no—
77C42×C61C22⋊C411yescharacteristic
78#11758198—21no—
79#11758198—41no—
80#11758198—41no—
81#11758198—41no—
82#11758198—41no—
83#11758198—41no—
84C4⋊Dic61—41no—
85#11758196—21no—
86#11758196—41no—
87C4×Dic61—41no—
88C4×Dic61C22⋊C411yescharacteristic
89C2×#92418C22⋊C411yescharacteristic
90C2×#92418C2×D411yescharacteristic
91Dic244—41no—
92D488—41no—
93#11758190—41no—
94#11758190—41no—
95#11758189—41no—
96C8×D61—21no—
97C8×D61—21no—
98#11758187—41no—
99#11758187—41no—
100C22×D61—41no—
101C22×D61AGL(1,ℤ/8)11yescharacteristic
102C2×#6923—42no—
103Q8×C61—161no—
104C2×C4×C61—21no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61C2×C22⋊C411yescharacteristic
108C2×Dic61—21no—
109C2×Dic61—41no—
110C2×Dic61AGL(1,ℤ/8)11yescharacteristic
111D244—41no—
112D244—41no—
113D244—161no—
114C4×D61—21no—
115C4×D61—21no—
116C4×D61—161no—
117Dic122—41no—
118Dic122—41no—
119#92420—42no—
120C8×C61—21no—
121C8×C61#10411yescharacteristic
122C8×C61#10411yescharacteristic
123#92418—21no—
124#92418—21no—
125#11769—611nomaximal, Sylow
126C22×C61#41811yescharacteristic
127C2×D61—21no—
128C2×D61—41no—
129C2×D61—81no—
130C2×D61—81no—
131C2×D61—81no—
132#6923—82no—
133C4×C61—41no—
134C4×C61—81no—
135C4×C61—81no—
136C4×C61#41011yescharacteristic
137C4×C61C2×#10411yescharacteristic
138Dic61—21no—
139Dic61—41no—
140Dic61—81no—
141#3173—611no—
142#2166—611no—
143#1747—611no—
144#1342—611no—
145#1341—611no—
146#1340—611no—
147#1339—611no—
148C2×C61—21no—
149C2×C61#150511yescharacteristic
150D61—41no—
151D61—161no—
152#542—1221no—
153#498#692311yescharacteristic, complemented
154#495—611no—
155#489—1221no—
156#470—611no—
157#469—611no—
158#465—1221no—
159#442—611no—
160#441—611no—
161C4×SD16—1221no—
162#405—611no—
163#405—1221no—
164#364—1221no—
165#349—611no—
166#349—611no—
167#347—1221no—
168#338—611no—
169H(3,ℤ/4)—611no—
170H(3,ℤ/4)—1221no—
171C61#1176911yescharacteristic, complemented, Sylow
172C2×Q16—611no—
173C2×SD16—1221no—
174C2×D8—611no—
175C2×M16—611no—
176C2×M16—1221no—
177C22×C8—611no—
178C4⋊Q8—21no—
179#126—2441no—
180#124—1221no—
181#124—2441no—
182#123—2441no—
183C22⋊Q8—1221no—
184C22⋊Q8—2441no—
185#121—1221no—
186C4×Q8—1221no—
187C4×D4—1221no—
188#117—611no—
189#117—1221no—
190M32—1221no—
191M32—1221no—
192#106—21no—
193#106C2×#692311yescharacteristic
194#106C2×#692311yescharacteristic
195#103—1221no—
196#103—1221no—
197#102—1221no—
198#102—1221no—
199#97—611no—
200#97—611no—
201#97—1222no—
202C4×C8—611no—
203C4×C8—1222no—
204C4×C8C2×#692311yescharacteristic
205C2×Q8—41no—
206C2×Q8—1221no—
207C2×D4—1221no—
208C2×D4—2441no—
209C22×C4—611no—
210C22×C4—2441no—
211Q16—2441no—
212SD16—2441no—
213SD16—2441no—
214D8—2441no—
215M16—2441no—
216M16—2441no—
217M16—2441no—
218C2×C8—611no—
219C2×C8—611no—
220C2×C8—1221no—
221C2×C8—1221no—
222C2×C8—1222no—
223C2×C8C22⋊#692311yescharacteristic
224C2×C8C22×#692311yescharacteristic
225C4⋊C4—21no—
226C4⋊C4—21no—
227C4⋊C4—41no—
228C4⋊C4—1221no—
229C4⋊C4—2441no—
230C4⋊C4—2441no—
231C4⋊C4—2441no—
232C22⋊C4—1221no—
233C22⋊C4—2441no—
234C22⋊C4—2441no—
235C22⋊C4—2441no—
236C22⋊C4—2441no—
237C22⋊C4—2441no—
238C22⋊C4—2441no—
239C42—611no—
240C42—1222no—
241C42—2441no—
242C42C22⋊#692311yescharacteristic
243C16—2441no—
244C16—2441no—
245C23—611no—
246C23—2441no—
247Q8—161no—
248Q8—2441no—
249Q8—2441no—
250D4—9761no—
251D4—2441no—
252D4—2441no—
253C2×C4—21no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—611no—
257C2×C4—1221no—
258C2×C4—1221no—
259C2×C4—1221no—
260C2×C4—9761no—
261C2×C4—2442no—
262C2×C4—2441no—
263C2×C4C2×C22⋊#692311yescharacteristic
264C8—21no—
265C8—1221no—
266C8—1221no—
267C8—2442no—
268C8#1451984211yescharacteristic
269C8#1451984211yescharacteristic
270C22—1221no—
271C22—4881no—
272C22—4881no—
273C22—4881no—
274C22—2441no—
275C22#1684075411yescharacteristic
276C4—41no—
277C4—81no—
278C4—81no—
279C4—1221no—
280C4—4882no—
281C4—4881no—
282C4—2441no—
283C4#1684074311yescharacteristic
284C4C2×#1451984211yescharacteristic
285C2—21no—
286C2—9761no—
287C2—2441no—
288C2#2146121011yescharacteristic
subgroupG/H
centerC2#21461210
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#498C4
socleC2×C61#1505
prime radical#16840016C22
cosocleC2×#11758189C23
hypercenter#498#6923
hypocenterC61#11769
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #498

Complements

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

NH ≅ G/Ntype
1. #21462194C2semidirect
2. #21461540C2semidirect
3. #21460796C2semidirect
5. #21460792C2semidirect
17. #16840146C4semidirect
22. #16839873C4semidirect
23. #16839868C4semidirect
26. C61×#498C4semidirect
153. #498#6923semidirect
171. C61#11769semidirect

Maximal subgroups

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

subgroupindex
#214621942
#214615402
#214607962
#214607942
#214607922
#214607902
#214564382
#1176961