Finite Group Databasebeta

← #30605015

Subgroups — #30605015

Order 15616.

304 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 60 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#21462195C211yesmaximal, characteristic, complemented
2#21461541C211yesmaximal, characteristic, complemented
3#21460796C211yesmaximal, characteristic, complemented
4#21460793C211yesmaximal, characteristic
5#21460792C211yesmaximal, characteristic, complemented
6#21460789C211yesmaximal, characteristic
7#21456434C211yesmaximal, characteristic
8#16840725—21no—
9#16840685—21no—
10#16840659C2211yescharacteristic
11#16840659C2211yescharacteristic
12#16840655—21no—
13#16840631C2211yescharacteristic
14#16840630C2211yescharacteristic
15#16840629—21no—
16#16840377—21no—
17#16840159C411yescharacteristic, complemented
18#16840145C411yescharacteristic, complemented
19#16840120—21no—
20#16840021C2211yescharacteristic
21#16840012C2211yescharacteristic
22#16839990—21no—
23#16839870C411yescharacteristic, complemented
24C4×#11758200—21no—
25#16839719C2211yescharacteristic
26C61×#442C411yescharacteristic, complemented
27D61⋊M16—21no—
28#14519856—21no—
29#14519851—21no—
30#14519851—21no—
31#14519831—22no—
32C8×#6923—22no—
33C2×Dic244C2×C411yescharacteristic
34C2×#11758200—21no—
35C2×#11758189C2311yescharacteristic
36C2×C8×D61D411yescharacteristic
37#14519776—21no—
38#14519770—41no—
39#14519764—21no—
40#14519763—41no—
41#14519760—41no—
42#14519757—21no—
43#14519756—41no—
44#14519748—21no—
45C4×Dic122—21no—
46#14519734D411yescharacteristic
47#14519709C2×C411yescharacteristic
48#14519708—21no—
49#14519702—21no—
50#14519700—21no—
51#14519698—21no—
52#14519687D411yescharacteristic
53C4×#92418D411yescharacteristic
54C8×Dic61C2×C411yescharacteristic
55C2×D8×C61C2×C411yescharacteristic
56C4×D4×C61—21no—
57#106×C61C2×C411yescharacteristic
58#102×C61—21no—
59#97×C61C2×C411yescharacteristic
60C2×D4×C61—21no—
61C22×C4×C61—41no—
62C2×C22⋊D61—41no—
63C2×C4×D61C2×D411yescharacteristic
64C2×Dic122—21no—
65C2×Dic122—41no—
66C22⋊#6923—41no—
67#11758217—41no—
68C4⋊#6923—41no—
69C4×#6923—22no—
70#11758213—41no—
71D61⋊C8—22no—
72D8×C61—41no—
73C2×C8×C61C22⋊C411yescharacteristic
74C2×C8×C61C22×C411yescharacteristic
75C4⋊C4×C61—21no—
76C22⋊C4×C61—41no—
77C42×C61C22⋊C411yescharacteristic
78C22⋊Dic61—41no—
79C22⋊Dic61—41no—
80C22⋊Dic61—41no—
81#11758200—41no—
82#11758200—41no—
83#11758198—21no—
84#11758198—41no—
85C4⋊Dic61—21no—
86C4⋊Dic61—41no—
87#11758196—21no—
88#11758196—41no—
89#11758196—41no—
90C4×Dic61—41no—
91C4×Dic61C22⋊C411yescharacteristic
92C2×#92418C22⋊C411yescharacteristic
93C2×#92418C2×D411yescharacteristic
94Dic244—41no—
95#11758189—41no—
96C8×D61—21no—
97C8×D61—21no—
98#11758187—41no—
99#11758187—41no—
100C23×C61—41no—
101C22×D61AGL(1,ℤ/8)11yescharacteristic
102C2×#6923—42no—
103D4×C61—41no—
104D4×C61—41no—
105C2×C4×C61—21no—
106C2×C4×C61—41no—
107C2×C4×C61—161no—
108C2×C4×C61C2×C22⋊C411yescharacteristic
109C22⋊D61—161no—
110C2×Dic61—21no—
111C2×Dic61—41no—
112C2×Dic61—41no—
113C2×Dic61AGL(1,ℤ/8)11yescharacteristic
114C4×D61—21no—
115C4×D61—21no—
116Dic122—41no—
117Dic122—41no—
118Dic122—161no—
119#92420—42no—
120C8×C61—21no—
121C8×C61—21no—
122#92418—21no—
123#92418#10411yescharacteristic
124#92418#10411yescharacteristic
125#11769—611nomaximal, Sylow
126C22×C61—81no—
127C22×C61—81no—
128C22×C61—81no—
129C22×C61#41811yescharacteristic
130C2×D61—21no—
131C2×D61—41no—
132#6923—82no—
133C4×C61—41no—
134C4×C61—81no—
135C4×C61#41011yescharacteristic
136C4×C61C2×#10411yescharacteristic
137Dic61—21no—
138Dic61—41no—
139Dic61—81no—
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—161no—
150C2×C61#150511yescharacteristic
151D61—41no—
152#542—1221no—
153#498—611no—
154#495—611no—
155#489—1221no—
156#470—611no—
157#469—611no—
158#465—1221no—
159#442#692311yescharacteristic, complemented
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×D8C2×#692311yescharacteristic
175C2×M16—611no—
176C2×M16—1221no—
177C22×C8—611no—
178C4⋊Q8—1221no—
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—21no—
188#117—611no—
189#117—1221no—
190M32—1221no—
191M32—1221no—
192#106—611no—
193#106—1221no—
194#106C2×#692311yescharacteristic
195#103—1221no—
196#103—1221no—
197#102—21no—
198#102—1221no—
199#97—611no—
200#97—1222no—
201#97C2×#692311yescharacteristic
202C4×C8—611no—
203C4×C8—611no—
204C4×C8—1222no—
205C2×Q8—1221no—
206C2×Q8—2441no—
207C2×D4—21no—
208C2×D4—2441no—
209C22×C4—41no—
210C22×C4—611no—
211Q16—2441no—
212SD16—2441no—
213SD16—2441no—
214D8—41no—
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—1221no—
227C4⋊C4—1221no—
228C4⋊C4—2441no—
229C4⋊C4—2441no—
230C4⋊C4—2441no—
231C4⋊C4—2441no—
232C22⋊C4—41no—
233C22⋊C4—1221no—
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—41no—
246C23—611no—
247Q8—9761no—
248Q8—2441no—
249Q8—2441no—
250D4—41no—
251D4—41no—
252D4—9761no—
253C2×C4—21no—
254C2×C4—41no—
255C2×C4—161no—
256C2×C4—611no—
257C2×C4—1221no—
258C2×C4—1221no—
259C2×C4—1221no—
260C2×C4—2442no—
261C2×C4—2441no—
262C2×C4—2441no—
263C2×C4C2×C22⋊#692311yescharacteristic
264C8—21no—
265C8—21no—
266C8—611no—
267C8—611no—
268C8—1221no—
269C8—2442no—
270C22—81no—
271C22—81no—
272C22—81no—
273C22—1221no—
274C22—2441no—
275C22#1684075411yescharacteristic
276C4—41no—
277C4—81no—
278C4—1221no—
279C4—4881no—
280C4—4882no—
281C4—4881no—
282C4—2441no—
283C4#1684074111yescharacteristic
284C4D61⋊#10411yescharacteristic
285C2—21no—
286C2—161no—
287C2—2441no—
288C2#2146120911yescharacteristic
subgroupG/H
centerC2#21461209
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#442C4
socleC2×C61#1505
prime radical#16840012C22
cosocleC2×#11758189C23
hypercenter#442#6923
hypocenterC61#11769
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #21462195C2semidirect
2. #21461541C2semidirect
3. #21460796C2semidirect
5. #21460792C2semidirect
17. #16840159C4semidirect
18. #16840145C4semidirect
23. #16839870C4semidirect
26. C61×#442C4semidirect
159. #442#6923semidirect
171. C61#11769semidirect

Maximal subgroups

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

subgroupindex
#214621952
#214615412
#214607962
#214607932
#214607922
#214607892
#214564342
#1176961