Finite Group Databasebeta

← #29590546

Subgroups — #29590546

Order 15616.

304 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 65 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#21456431C211yesmaximal, characteristic
2#21447632C211yesmaximal, characteristic, complemented
3#21445573C211yesmaximal, characteristic, complemented
4#21443814C211yesmaximal, characteristic, complemented
5#21443810C211yesmaximal, characteristic
6#21443806C211yesmaximal, characteristic, complemented
7C61×#1339C211yesmaximal, characteristic
8#16840379—21no—
9#16840159C411yescharacteristic, complemented
10#16840145C411yescharacteristic, complemented
11#16840120—21no—
12#16840020C2211yescharacteristic
13#16839989—21no—
14#16839874C411yescharacteristic, complemented
15#16839868C411yescharacteristic, complemented
16#16839853—21no—
17#16839720C2211yescharacteristic
18#16839718—21no—
19#16839582—21no—
20#16839544C2211yescharacteristic
21#16839539—21no—
22#16839520C2211yescharacteristic
23#16839518—21no—
24C61×#469C2211yescharacteristic
25C61×#349C2211yescharacteristic
26C61×H(3,ℤ/4)C2211yescharacteristic
27C2×Dic244C2×C411yescharacteristic
28C2×#11758200—21no—
29C2×#11758194—21no—
30C22×#92418D411yescharacteristic
31#14519776—21no—
32#14519770—41no—
33#14519764—21no—
34#14519764—41no—
35#14519758—41no—
36#14519756—21no—
37#14519754—41no—
38#14519742—21no—
39D4×Dic61—21no—
40#14519736D411yescharacteristic
41#14519717—21no—
42#14519709C2×C411yescharacteristic
43#14519708—21no—
44#14519702—21no—
45#14519700—21no—
46#14519698—21no—
47#14519688—22no—
48#14519687C2×C411yescharacteristic
49#14519687D411yescharacteristic
50C4×#92418—22no—
51C8×Dic61C2×C411yescharacteristic
52C8×Dic61D411yescharacteristic
53C2×D8×C61C2×C411yescharacteristic
54C2×M16×C61C2311yescharacteristic
55#121×C61—21no—
56#117×C61—21no—
57M32×C61—21no—
58#106×C61C2×C411yescharacteristic
59#102×C61—21no—
60C2×D4×C61—21no—
61C2×D4×C61—41no—
62C22×C4×C61C2×D411yescharacteristic
63C22×Dic61—41no—
64C2×Dic122—21no—
65C2×Dic122—41no—
66D8×C61—41no—
67M16×C61—41no—
68C2×C8×C61C22×C411yescharacteristic
69C2×C8×C61C2×D411yescharacteristic
70C4⋊C4×C61—21no—
71C4⋊C4×C61—41no—
72C22⋊C4×C61—41no—
73C22⋊C4×C61—41no—
74C42×C61—22no—
75C22⋊Dic61—21no—
76C22⋊Dic61—41no—
77C22⋊Dic61—41no—
78C22⋊Dic61—41no—
79C22⋊Dic61—41no—
80#11758200—41no—
81#11758200—41no—
82C4⋊Dic61—21no—
83C4⋊Dic61—21no—
84#11758196—41no—
85#11758196—41no—
86#11758196—41no—
87C4×Dic61—41no—
88C4×Dic61C22⋊C411yescharacteristic
89C4×Dic61C22⋊C411yescharacteristic
90#11758194—41no—
91#11758194—41no—
92C2×#92418—21no—
93C2×#92418—21no—
94C2×#92418—22no—
95C2×#92418C22⋊C411yescharacteristic
96C2×#92418C22⋊C411yescharacteristic
97Dic244—41no—
98C16×C61—41no—
99#11758185—41no—
100C23×C61—41no—
101C23×C61AGL(1,ℤ/8)11yescharacteristic
102D4×C61—41no—
103D4×C61—41no—
104D4×C61—161no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—42no—
108C2×C4×C61—41no—
109C2×C4×C61C2×C22⋊C411yescharacteristic
110C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—41no—
114C2×Dic61—41no—
115C2×Dic61—161no—
116Dic122—41no—
117Dic122—41no—
118Dic122—161no—
119C8×C61—21no—
120C8×C61—21no—
121#92418—21no—
122#92418—42no—
123#92418#10411yescharacteristic
124#92418#10411yescharacteristic
125#11769—611nomaximal, Sylow
126C22×C61—21no—
127C22×C61—41no—
128C22×C61—81no—
129C22×C61—81no—
130C22×C61—81no—
131C22×C61#41811yescharacteristic
132C4×C61—21no—
133C4×C61—81no—
134C4×C61—82no—
135C4×C61#41011yescharacteristic
136C4×C61C2×#10411yescharacteristic
137Dic61—41no—
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#1339D6111yescharacteristic
148C2×C61—21no—
149C2×C61—41no—
150C2×C61—161no—
151C2×C61#150511yescharacteristic
152#542—1221no—
153#498—611no—
154#495—611no—
155#489—1221no—
156#470—611no—
157#469C2×D6111yescharacteristic
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#349C2×D6111yescharacteristic
167#347—1221no—
168#338—611no—
169H(3,ℤ/4)—1221no—
170H(3,ℤ/4)C2×D6111yescharacteristic
171C61#1176911yescharacteristic, complemented, Sylow
172C2×Q16—611no—
173C2×SD16—1221no—
174C2×D8C4×D6111yescharacteristic
175C2×M16—1221no—
176C2×M16C22×D6111yescharacteristic
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—21no—
186C4×Q8—1221no—
187C4×D4—1221no—
188#117—21no—
189#117—611no—
190M32—21no—
191M32—1221no—
192#106—611no—
193#106—1221no—
194#106C4×D6111yescharacteristic
195#103—1221no—
196#103—1221no—
197#102—21no—
198#102—1221no—
199#97—611no—
200#97—611no—
201#97—1222no—
202C4×C8—611no—
203C4×C8—611no—
204C4×C8—1222no—
205C2×Q8—1221no—
206C2×Q8—2441no—
207C2×D4—21no—
208C2×D4—41no—
209C22×C4—2441no—
210C22×C4D4×D6111yescharacteristic
211Q16—2441no—
212SD16—2441no—
213SD16—2441no—
214D8—41no—
215M16—41no—
216M16—2441no—
217M16—2441no—
218C2×C8—611no—
219C2×C8—611no—
220C2×C8—1221no—
221C2×C8—1221no—
222C2×C8—1222no—
223C2×C8C2×C4×D6111yescharacteristic
224C2×C8D4×D6111yescharacteristic
225C4⋊C4—21no—
226C4⋊C4—41no—
227C4⋊C4—1221no—
228C4⋊C4—1221no—
229C4⋊C4—2441no—
230C4⋊C4—2441no—
231C4⋊C4—2441no—
232C22⋊C4—41no—
233C22⋊C4—41no—
234C22⋊C4—1221no—
235C22⋊C4—2441no—
236C22⋊C4—2441no—
237C22⋊C4—2441no—
238C22⋊C4—2441no—
239C42—22no—
240C42—611no—
241C42—611no—
242C42—2441no—
243C16—41no—
244C16—2441no—
245C23—41no—
246C23#1451980111yescharacteristic
247Q8—9761no—
248Q8—2441no—
249Q8—2441no—
250D4—41no—
251D4—41no—
252D4—161no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—42no—
256C2×C4—41no—
257C2×C4—1221no—
258C2×C4—1221no—
259C2×C4—9761no—
260C2×C4—2441no—
261C2×C4—2441no—
262C2×C4C22⋊C4×D6111yescharacteristic
263C2×C4#1451980411yescharacteristic
264C8—21no—
265C8—21no—
266C8—611no—
267C8—611no—
268C8—1221no—
269C8—2442no—
270C22—21no—
271C22—41no—
272C22—81no—
273C22—81no—
274C22—81no—
275C22#1683976511yescharacteristic
276C4—21no—
277C4—81no—
278C4—82no—
279C4—4881no—
280C4—4881no—
281C4—2441no—
282C4—2441no—
283C4#1683973411yescharacteristic
284C4#104×D6111yescharacteristic
285C2—21no—
286C2—41no—
287C2—161no—
288C2#2144432511yescharacteristic
subgroupG/H
centerC2#21444325
commutatorC2×C8×C61C22×C4
FrattiniC2×M16C22×D61
FittingC61×#1339C2
socleC2×C61#1505
prime radicalC61×#469C22
cosocleC2×M16×C61C23
hypercenter#1339D61
hypocenterC61#11769
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #1339

Complements

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

NH ≅ G/Ntype
2. #21447632C2semidirect
3. #21445573C2semidirect
4. #21443814C2semidirect
6. #21443806C2semidirect
9. #16840159C4semidirect
10. #16840145C4semidirect
14. #16839874C4semidirect
15. #16839868C4semidirect
171. C61#11769semidirect

Maximal subgroups

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

subgroupindex
#214564312
#214476322
#214455732
#214438142
#214438102
#214438062
C61×#13392
#1176961