Finite Group Databasebeta

← #29590858

Subgroups — #29590858

Order 15616.

324 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 63 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#21456552C211yesmaximal, characteristic
2#21447628C211yesmaximal, characteristic, complemented
3#21445966C211yesmaximal, characteristic, complemented
4#21443811C211yesmaximal, characteristic, complemented
5#21443810C211yesmaximal, characteristic, complemented
6#21443803C211yesmaximal, characteristic, complemented
7C61×#1339C211yesmaximal, characteristic, complemented
8#16840307—21no—
9#16840159C411yescharacteristic, complemented
10#16840137C411yescharacteristic, complemented
11#16840107—21no—
12#16840015C2211yescharacteristic
13#16840013—21no—
14#16839874C411yescharacteristic, complemented
15#16839873C411yescharacteristic, complemented
16#16839871—21no—
17M16×Dic61C2211yescharacteristic
18#16839582—21no—
19#16839544C2211yescharacteristic
20#16839539—21no—
21#16839532—21no—
22#16839521—21no—
23#16839520C2211yescharacteristic
24C61×#469C2211yescharacteristic
25C61×#349C2211yescharacteristic
26C61×H(3,ℤ/4)C2211yescharacteristic
27C2×#11758224—41no—
28C2×D488C2×C411yescharacteristic
29C2×#11758199—21no—
30C2×#11758194—21no—
31C2×#11758194D411yescharacteristic
32#14519776—21no—
33#14519773—21no—
34#14519763—41no—
35#14519751—21no—
36#14519749—41no—
37D4×Dic61—21no—
38#14519739—21no—
39#14519737—41no—
40C2×C4×Dic61D411yescharacteristic
41#14519717—21no—
42#14519709C2×C411yescharacteristic
43#14519708—21no—
44#14519699—21no—
45#14519698—21no—
46#14519697—21no—
47#14519687C2×C411yescharacteristic
48#14519687D411yescharacteristic
49C8×Dic61C2×C411yescharacteristic
50C8×Dic61D411yescharacteristic
51C2×D8×C61C2×C411yescharacteristic
52C2×M16×C61C2311yescharacteristic
53#121×C61—21no—
54#117×C61—21no—
55M32×C61—21no—
56#106×C61C2×C411yescharacteristic
57#102×C61—21no—
58C2×D4×C61—21no—
59C2×D4×C61—41no—
60C22×C4×C61C2×D411yescharacteristic
61C2×C22⋊D61—41no—
62C2×C22⋊D61—41no—
63C2×C22⋊D61—41no—
64C22×Dic61—21no—
65C22×Dic61—41no—
66#11758224—84no—
67C2×D244—21no—
68C2×C4×D61—41no—
69C2×Dic122—41no—
70D8×C61—41no—
71M16×C61—41no—
72C2×C8×C61C22×C411yescharacteristic
73C2×C8×C61C2×D411yescharacteristic
74C4⋊C4×C61—21no—
75C4⋊C4×C61—41no—
76C22⋊C4×C61—41no—
77C22⋊C4×C61—41no—
78C42×C61—41no—
79C22⋊Dic61—41no—
80#11758199—42no—
81#11758198—41no—
82#11758198—41no—
83C4⋊Dic61—21no—
84#11758196—41no—
85C4×Dic61—21no—
86C4×Dic61C22⋊C411yescharacteristic
87C4×Dic61C22⋊C411yescharacteristic
88#11758194—41no—
89#11758194—41no—
90#11758194—41no—
91C2×#92418—41no—
92C2×#92418C22⋊C411yescharacteristic
93C2×#92418C22⋊C411yescharacteristic
94D488—41no—
95C16×C61—41no—
96#11758185—41no—
97C23×C61—41no—
98C23×C61AGL(1,ℤ/8)11yescharacteristic
99C22×D61—41no—
100D4×C61—41no—
101D4×C61—41no—
102D4×C61—82no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—41no—
106C2×C4×C61—81no—
107C2×C4×C61C2×C22⋊C411yescharacteristic
108C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
109C22⋊D61—82no—
110C22⋊D61—82no—
111C22⋊D61—82no—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—42no—
115C2×Dic61—41no—
116C2×Dic61—82no—
117D244—41no—
118D244—41no—
119C4×D61—82no—
120Dic122—82no—
121C8×C61—21no—
122C8×C61—21no—
123#92418—21no—
124#92418—21no—
125#92418—81no—
126#11837—611nomaximal, Sylow
127C22×C61—21no—
128C22×C61—41no—
129C22×C61—81no—
130C22×C61—81no—
131C22×C61—81no—
132C22×C61#41811yescharacteristic
133C2×D61—81no—
134C2×D61—81no—
135C2×D61—81no—
136C4×C61—21no—
137C4×C61—81no—
138C4×C61—161no—
139C4×C61#41011yescharacteristic
140C4×C61#42111yescharacteristic
141Dic61—22no—
142Dic61—41no—
143Dic61—81no—
144#3184—611no—
145#2165—611no—
146#1841—611no—
147#1341—611no—
148#1341—611no—
149#1339—611no—
150#1339D6111yescharacteristic, complemented
151C2×C61—21no—
152C2×C61—41no—
153C2×C61—161no—
154C2×C61#151411yescharacteristic
155D61—161no—
156#532—1221no—
157#498—611no—
158#493—611no—
159#486—1221no—
160#469—611no—
161#469—1221no—
162#469C2×D6111yescharacteristic
163#442—611no—
164#442—611no—
165#442—1221no—
166C4×M16—611no—
167#364—1221no—
168#349—611no—
169#349C2×D6111yescharacteristic
170#347—1221no—
171#344—1221no—
172#339—1221no—
173#338—611no—
174H(3,ℤ/4)C2×D6111yescharacteristic
175C61#1183711yescharacteristic, complemented, Sylow
176C2×#41—2441no—
177C2×D8—611no—
178C2×D8—1221no—
179C2×D8C4×D6111yescharacteristic
180C2×M16—611no—
181C2×M16—1221no—
182C2×M16C22×D6111yescharacteristic
183C4⋊Q8—1221no—
184#127—1221no—
185#124—2441no—
186#121—21no—
187#121—1221no—
188#121—2441no—
189C4×D4—1221no—
190C4×D4—1221no—
191C4×D4—2441no—
192#117—21no—
193C2×C42—611no—
194M32—21no—
195M32—1221no—
196#106—611no—
197#106—1221no—
198#106C4×D6111yescharacteristic
199#102—21no—
200#102—1221no—
201#102—1221no—
202#102—1221no—
203#97—611no—
204#97—611no—
205C4×C8—611no—
206C4×C8—611no—
207#41—4884no—
208C2×Q8—2441no—
209C2×D4—21no—
210C2×D4—41no—
211C2×D4—1221no—
212C2×D4—2441no—
213C2×D4—2441no—
214C2×D4—2441no—
215C22×C4—1221no—
216C22×C4—2441no—
217C22×C4—2441no—
218C22×C4D4×D6111yescharacteristic
219D8—41no—
220D8—2441no—
221D8—2442no—
222M16—41no—
223M16—2441no—
224M16—2441no—
225M16—2441no—
226C2×C8—611no—
227C2×C8—611no—
228C2×C8—2441no—
229C2×C8C2×C4×D6111yescharacteristic
230C2×C8D4×D6111yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—41no—
233C4⋊C4—1221no—
234C4⋊C4—2441no—
235C22⋊C4—41no—
236C22⋊C4—41no—
237C22⋊C4—2441no—
238C22⋊C4—2441no—
239C22⋊C4—2441no—
240C42—41no—
241C42—611no—
242C42—611no—
243C42—1221no—
244C16—41no—
245C16—2441no—
246C23—41no—
247C23—2441no—
248C23#1451980111yescharacteristic
249Q8—4882no—
250D4—41no—
251D4—41no—
252D4—82no—
253D4—4882no—
254D4—4882no—
255D4—4882no—
256D4—2441no—
257D4—2441no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—41no—
261C2×C4—81no—
262C2×C4—1221no—
263C2×C4—1221no—
264C2×C4—4882no—
265C2×C4—4882no—
266C2×C4—2442no—
267C2×C4—2441no—
268C2×C4C22⋊C4×D6111yescharacteristic
269C2×C4#1451980411yescharacteristic
270C8—21no—
271C8—21no—
272C8—1221no—
273C8—1221no—
274C8—4881no—
275C22—21no—
276C22—41no—
277C22—81no—
278C22—81no—
279C22—81no—
280C22—4881no—
281C22—4881no—
282C22—4881no—
283C22#1683976511yescharacteristic
284C4—21no—
285C4—81no—
286C4—161no—
287C4—1222no—
288C4—4881no—
289C4—2441no—
290C4#1683973411yescharacteristic
291C4#1683977711yescharacteristic
292C2—21no—
293C2—41no—
294C2—161no—
295C2—9761no—
296C2#2144436411yescharacteristic
subgroupG/H
centerC2#21444364
commutatorC2×C8×C61C22×C4
FrattiniC2×M16C22×D61
FittingC61×#1339C2
socleC2×C61#1514
prime radical#21456552C2
cosocleC2×M16×C61C23
hypercenter#1339D61
hypocenterC61#11837
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. #21447628C2semidirect
3. #21445966C2semidirect
4. #21443811C2semidirect
5. #21443810C2semidirect
6. #21443803C2semidirect
7. C61×#1339C2semidirect
9. #16840159C4semidirect
10. #16840137C4semidirect
14. #16839874C4semidirect
15. #16839873C4semidirect
150. #1339D61semidirect
175. C61#11837semidirect

Maximal subgroups

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

subgroupindex
#214565522
#214476282
#214459662
#214438112
#214438102
#214438032
C61×#13392
#1183761