Finite Group Databasebeta

← #29593398

Subgroups — #29593398

Order 15616.

280 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 55 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#21457220C211yesmaximal, characteristic
2#21448038C211yesmaximal, characteristic, complemented
3#21448033C211yesmaximal, characteristic
4#21443806C211yesmaximal, characteristic, complemented
5#21443803C211yesmaximal, characteristic
6#21443770C211yesmaximal, characteristic, complemented
7C61×#2102C211yesmaximal, characteristic, complemented
8#16840296—21no—
9#16840070—21no—
10#16840063—21no—
11#16840020C2211yescharacteristic
12#16840015C2211yescharacteristic
13#16840008—21no—
14#16839985—21no—
15#16839978—21no—
16#16839586—21no—
17#16839586—21no—
18#16839577—21no—
19#16839574—21no—
20#16839544C2211yescharacteristic
21#16839544C2211yescharacteristic
22C61×#430C2211yescharacteristic
23C61×#423C2211yescharacteristic
24C61×#344—21no—
25C61×#339—21no—
26C61×H(3,ℤ/4)C2211yescharacteristic
27C2×Dic244D411yescharacteristic
28C2×#11758190—21no—
29C2×D488D411yescharacteristic
30#14519771—41no—
31#14519769—21no—
32#14519765—21no—
33#14519760—41no—
34#14519756—21no—
35#14519751—21no—
36C4×Dic122—21no—
37C4×D244—21no—
38C4×C22⋊D61—41no—
39#14519734—41no—
40#14519717—21no—
41#14519717—21no—
42#14519711—21no—
43#14519709D411yescharacteristic
44#14519709D411yescharacteristic
45#14519702—21no—
46#14519702—21no—
47#14519699—21no—
48#14519699—21no—
49C2×M16×C61—21no—
50C2×M16×C61D411yescharacteristic
51C2×M16×C61C2311yescharacteristic
52#117×C61—21no—
53C2×C42×C61D411yescharacteristic
54#108×C61—21no—
55#108×C61—21no—
56C4⋊C8×C61—21no—
57C4⋊C8×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61C2×D411yescharacteristic
60C2×C22⋊D61—41no—
61C2×D244—21no—
62C2×C4×D61—41no—
63C2×Dic122—21no—
64M16×C61—41no—
65M16×C61—41no—
66M16×C61—41no—
67M16×C61—41no—
68C2×C8×C61—21no—
69C2×C8×C61—41no—
70C2×C8×C61C2×D411yescharacteristic
71C2×C8×C61C2×D411yescharacteristic
72C4⋊C4×C61—41no—
73C22⋊C4×C61—41no—
74C42×C61—21no—
75C42×C61—41no—
76C42×C61SD1611yescharacteristic
77C42×C61SD1611yescharacteristic
78C22⋊Dic61—41no—
79#11758198—41no—
80#11758198—41no—
81#11758198—41no—
82#11758198—41no—
83C4⋊Dic61—21no—
84C4⋊Dic61—21no—
85#11758196—41no—
86#11758196—41no—
87#11758196—41no—
88#11758196—41no—
89C4×Dic61—41no—
90Dic244—41no—
91D488—41no—
92#11758190—81no—
93#11758185—41no—
94#11758185—41no—
95C23×C61AGL(1,ℤ/8)11yescharacteristic
96C22×D61—41no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—81no—
102C2×C4×C61—81no—
103C2×C4×C61#12011yescharacteristic
104C2×C4×C61C2×SD1611yescharacteristic
105C22⋊D61—82no—
106C2×Dic61—41no—
107C2×Dic61—41no—
108C2×Dic61—41no—
109D244—41no—
110D244—41no—
111C4×D61—82no—
112Dic122—41no—
113Dic122—41no—
114C8×C61—21no—
115C8×C61—21no—
116C8×C61—41no—
117C8×C61—81no—
118#12309—611nomaximal, Sylow
119C22×C61—21no—
120C22×C61—41no—
121C22×C61#45011yescharacteristic
122C2×D61—81no—
123C2×D61—81no—
124C2×D61—81no—
125C4×C61—21no—
126C4×C61—41no—
127C4×C61—41no—
128C4×C61—161no—
129C4×C61#45411yescharacteristic
130C4×C61#45811yescharacteristic
131Dic61—81no—
132Dic61—81no—
133Dic61—81no—
134#3256—611no—
135#2239—611no—
136#2238—611no—
137#2102D6111yescharacteristic, complemented
138#1340—611no—
139#1339—611no—
140#1327—611no—
141C2×C61—21no—
142C2×C61—41no—
143C2×C61#161611yescharacteristic
144D61—161no—
145#529—1221no—
146#479—1221no—
147#478—1221no—
148#470—611no—
149#469—611no—
150#468—1221no—
151#464—1221no—
152#463—1221no—
153#430C2×D6111yescharacteristic
154#423C2×D6111yescharacteristic
155#365—1221no—
156#365—1221no—
157#362—1221no—
158#361—1221no—
159#349—611no—
160#349—611no—
161#344—21no—
162#339—21no—
163H(3,ℤ/4)C2×D6111yescharacteristic
164C61#1230911yescharacteristic, complemented, Sylow
165C2×Q16—611no—
166C2×SD16—1221no—
167C2×D8—611no—
168C2×M16—21no—
169C2×M16C22⋊D6111yescharacteristic
170C2×M16C22×D6111yescharacteristic
171#126—2441no—
172#125—1221no—
173#124—1221no—
174#123—2441no—
175C22⋊Q8—1221no—
176#121—1221no—
177C4×Q8—1221no—
178C4×D4—1221no—
179C4×D4—2441no—
180#117—21no—
181#117—2441no—
182C2×C42C22⋊D6111yescharacteristic
183M32—1221no—
184M32—1221no—
185#108—21no—
186#108—21no—
187#107—1221no—
188#106—611no—
189#106—611no—
190C4⋊C8—21no—
191C4⋊C8—21no—
192#103—1221no—
193#103—1221no—
194#102—1221no—
195#102—1221no—
196C2×Q8—1221no—
197C2×D4—1221no—
198C2×D4—2441no—
199C22×C4—21no—
200C22×C4—2441no—
201C22×C4C2×C22⋊D6111yescharacteristic
202Q16—2441no—
203SD16—4881no—
204D8—2441no—
205M16—41no—
206M16—41no—
207M16—41no—
208M16—41no—
209C2×C8—21no—
210C2×C8—41no—
211C2×C8D4×D6111yescharacteristic
212C2×C8D4×D6111yescharacteristic
213C4⋊C4—41no—
214C4⋊C4—1221no—
215C4⋊C4—1221no—
216C4⋊C4—2441no—
217C4⋊C4—2441no—
218C4⋊C4—2441no—
219C4⋊C4—2441no—
220C22⋊C4—41no—
221C22⋊C4—2441no—
222C22⋊C4—2441no—
223C22⋊C4—2441no—
224C22⋊C4—2441no—
225C22⋊C4—2441no—
226C42—21no—
227C42—41no—
228C42—2441no—
229C42#1175820111yescharacteristic
230C42#1175820111yescharacteristic
231C16—2441no—
232C16—2441no—
233C23—2441no—
234C23#1451980211yescharacteristic
235Q8—2441no—
236Q8—2441no—
237D4—4882no—
238D4—2441no—
239D4—2441no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—81no—
245C2×C4—81no—
246C2×C4—4882no—
247C2×C4—2441no—
248C2×C4—2441no—
249C2×C4—2441no—
250C2×C4#1451974511yescharacteristic
251C2×C4C2×#1175820111yescharacteristic
252C8—21no—
253C8—21no—
254C8—41no—
255C8—81no—
256C22—21no—
257C22—41no—
258C22—4881no—
259C22—4881no—
260C22—4881no—
261C22#1683991211yescharacteristic
262C4—21no—
263C4—41no—
264C4—41no—
265C4—161no—
266C4—4881no—
267C4—4881no—
268C4—4881no—
269C4#1683993411yescharacteristic
270C4#1683995111yescharacteristic
271C2—21no—
272C2—41no—
273C2—9761no—
274C2#2144485511yescharacteristic
subgroupG/H
centerC2#21444855
commutator, cosocleC2×M16×C61C23
FrattiniC2×M16C22×D61
FittingC61×#2102C2
socleC2×C61#1616
prime radical#16840015C22
hypercenter#2102D61
hypocenterC61#12309
LCSG ▷ C2×M16×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #2102

Complements

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

NH ≅ G/Ntype
2. #21448038C2semidirect
4. #21443806C2semidirect
6. #21443770C2semidirect
7. C61×#2102C2semidirect
137. #2102D61semidirect
164. C61#12309semidirect

Maximal subgroups

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

subgroupindex
#214572202
#214480382
#214480332
#214438062
#214438032
#214437702
C61×#21022
#1230961