Finite Group Databasebeta

← #29593816

Subgroups — #29593816

Order 15616.

356 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 69 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#21457541C211yesmaximal, characteristic
2#21448047C211yesmaximal, characteristic, complemented
3#21447957C211yesmaximal, characteristic, complemented
4#21445208C211yesmaximal, characteristic, complemented
5#21443869C211yesmaximal, characteristic, complemented
6#21443781C211yesmaximal, characteristic, complemented
7C61×D4⋊C16C211yesmaximal, characteristic, complemented
8C2×#14519799—21no—
9#16840417—21no—
10#16840167C2211yescharacteristic
11#16840142C2211yescharacteristic
12#16840003—21no—
13#16839968—21no—
14#16839967—21no—
15#16839926—22no—
16C4×D488C2211yescharacteristic
17#16839588—21no—
18#16839567—22no—
19#16839564—21no—
20#16839515C2211yescharacteristic
21#16839507—21no—
22C8×D4×C61C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C4×C16×C61C2211yescharacteristic
25C2×#11758222—22no—
26#14519799—42no—
27#14519799—42no—
28C2×Dic244—21no—
29C2×Dic244D412yes—
30C2×#11758190—22no—
31C2×#11758200—41no—
32C2×D488D411yescharacteristic
33#14519777—21no—
34#14519777—21no—
35#14519759—42no—
36#14519756—22no—
37#14519748—41no—
38C4×D244—21no—
39C4⋊C4×D61—41no—
40#14519711—21no—
41#14519711—21no—
42#14519711D411yescharacteristic
43C4⋊#92418—21no—
44#14519702—22no—
45#14519700—41no—
46#14519699—21no—
47C22×C8×C61—21no—
48C4×D4×C61D411yescharacteristic
49C2×C16×C61—21no—
50C2×C16×C61—21no—
51C4⋊C8×C61D411yescharacteristic
52C22⋊C8×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×D4×C61D811yescharacteristic
55C22×C4×C61—21no—
56C2×C22⋊D61—42no—
57#11758222—44no—
58#11758222—82no—
59C2×D244—21no—
60C2×C4×D61—42no—
61C2×C4×D61—41no—
62C2×Dic122—22no—
63C2×Dic122—41no—
64C2×C8×C61—21no—
65C2×C8×C61—41no—
66C2×C8×C61—41no—
67C2×C8×C61C2×D411yescharacteristic
68C2×C8×C61C2×D411yescharacteristic
69C4⋊C4×C61D811yescharacteristic
70C22⋊C4×C61—21no—
71C42×C61C2×D411yescharacteristic
72C22⋊Dic61—42no—
73#11758200—82no—
74#11758198—41no—
75C4⋊Dic61—21no—
76C4⋊Dic61—41no—
77C4⋊Dic61—41no—
78C4⋊Dic61—41no—
79C4⋊Dic61—41no—
80#11758196—42no—
81C2×#92418—41no—
82Dic244—42no—
83Dic244—41no—
84Dic244—41no—
85D488—21no—
86D488SD1612yescomplemented
87#11758190—44no—
88C16×C61—41no—
89C16×C61—41no—
90C23×C61—21no—
91C22×D61—41no—
92D4×C61—21no—
93D4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—41no—
96C2×C4×C61—41no—
97C2×C4×C61#12011yescharacteristic
98C2×C4×C61C2×D811yescharacteristic
99C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
100C22⋊D61—84no—
101C2×Dic61—41no—
102C2×Dic61—42no—
103C2×Dic61—81no—
104D244—22no—
105D244—41no—
106C4×D61—84no—
107C4×D61—81no—
108C4×D61—81no—
109Dic122—42no—
110Dic122—42no—
111Dic122—81no—
112Dic122—81no—
113C8×C61—21no—
114C8×C61—41no—
115C8×C61C2×SD1611yescharacteristic
116C8×C61AGL(1,ℤ/8)11yescharacteristic
117#92418—81no—
118#12371—611nomaximal, Sylow
119C22×C61—41no—
120C22×C61—41no—
121C22×C61—41no—
122C22×C61#44711yescharacteristic
123C2×D61—42no—
124C2×D61—81no—
125C2×D61—81no—
126C4×C61—21no—
127C4×C61—41no—
128C4×C61#45011yescharacteristic
129C4×C61#45511yescharacteristic
130C4×C61#50811yescharacteristic
131C4×C61#50911yescharacteristic
132Dic61—82no—
133Dic61—81no—
134Dic61—161no—
135#3283—611no—
136#2241—611no—
137#2224—611no—
138#1673—611no—
139#1362—611no—
140#1331—611no—
141D4⋊C16D6111yescharacteristic, complemented
142C2×C61—81no—
143C2×C61#163911yescharacteristic
144C2×C61#218611yescharacteristic
145C2×C61#219511yescharacteristic
146D61—82no—
147C2×#135—1221no—
148#547—1221no—
149#500—611no—
150#494—611no—
151#467—1221no—
152#461—1221no—
153#461—1221no—
154#452—1222no—
155C4×D8—611no—
156C8×D4C2×D6111yescharacteristic
157#366—1221no—
158C4⋊C16C2×D6111yescharacteristic
159#358—1222no—
160#357—1221no—
161C4×C16C2×D6111yescharacteristic
162#335—611no—
163#332—1221no—
164C61#1237111yescharacteristic, complemented, Sylow
165C2×#41—1222no—
166#135—2442no—
167#135—2442no—
168C2×Q16—612no—
169C2×Q16—1221no—
170C2×SD16—1222no—
171C2×SD16—2441no—
172C2×D8—611no—
173C22×C8—21no—
174C4⋊Q8—1221no—
175C4⋊Q8—1221no—
176#123—2442no—
177C22⋊Q8—1222no—
178#121—2441no—
179C4×D4—1221no—
180C4×D4D24411yescharacteristic
181C2×C4⋊C4—2441no—
182C2×C16—21no—
183C2×C16—21no—
184#107—611no—
185#107—1221no—
186#107—1221no—
187C4⋊C8—1221no—
188C4⋊C8D24411yescharacteristic
189#103—1222no—
190#103—2441no—
191#102—1221no—
192C22⋊C8—21no—
193C4×C8C22×D6111yescharacteristic
194#41—4882no—
195#41—2444no—
196C2×Q8—1222no—
197C2×Q8—2441no—
198C2×D4—1221no—
199C2×D4—2442no—
200C2×D4D48811yescharacteristic
201C22×C4—21no—
202C22×C4—2442no—
203C22×C4—2441no—
204Q16—2442no—
205Q16—2441no—
206Q16—2441no—
207SD16—4882no—
208SD16—2444no—
209D8—612no—
210D8—1221no—
211C2×C8—21no—
212C2×C8—41no—
213C2×C8—41no—
214C2×C8—2441no—
215C2×C8D4×D6111yescharacteristic
216C2×C8D4×D6111yescharacteristic
217C4⋊C4—1221no—
218C4⋊C4—2442no—
219C4⋊C4—2441no—
220C4⋊C4—2441no—
221C4⋊C4—2441no—
222C4⋊C4—2441no—
223C4⋊C4D48811yescharacteristic
224C22⋊C4—21no—
225C22⋊C4—2442no—
226C22⋊C4—2441no—
227C42C2×D24411yescharacteristic
228C16—41no—
229C16—41no—
230C23—21no—
231C23—2441no—
232Q8—4881no—
233Q8—4881no—
234Q8—2442no—
235Q8—2442no—
236D4—21no—
237D4—21no—
238D4—1222no—
239D4—4884no—
240D4—2441no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—4884no—
245C2×C4—4881no—
246C2×C4—4881no—
247C2×C4—4881no—
248C2×C4—2441no—
249C2×C4—2442no—
250C2×C4#1451974711yescharacteristic
251C2×C4C2×D48811yescharacteristic
252C2×C4#1451980511yescharacteristic
253C8—21no—
254C8—41no—
255C8—4881no—
256C8SD16×D6111yescharacteristic
257C8#1451980111yescharacteristic
258C22—41no—
259C22—41no—
260C22—41no—
261C22—4881no—
262C22—4881no—
263C22—2442no—
264C22#1683989811yescharacteristic
265C4—21no—
266C4—41no—
267C4—9761no—
268C4—4881no—
269C4—4882no—
270C4#1683991411yescharacteristic
271C4#1683994111yescharacteristic
272C4#1684019411yescharacteristic
273C4#1684020011yescharacteristic
274C2—81no—
275C2—4882no—
276C2#2144500011yescharacteristic
277C2#2144774411yescharacteristic
278C2#2144779911yescharacteristic
subgroupG/H
centerC22#16839898
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×D4⋊C16C2
socleC22×C61#447
prime radical#21457541C2
hypercenterD4⋊C16D61
hypocenterC61#12371
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ D4⋊C16

Complements

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

NH ≅ G/Ntype
2. #21448047C2semidirect
3. #21447957C2semidirect
4. #21445208C2semidirect
5. #21443869C2semidirect
6. #21443781C2semidirect
7. C61×D4⋊C16C2semidirect
86. D488SD16semidirect
141. D4⋊C16D61semidirect
164. C61#12371semidirect

Maximal subgroups

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

subgroupindex
#214575412
#214480472
#214479572
#214452082
#214438692
#214437812
C61×D4⋊C162
#1237161