Finite Group Databasebeta

← #29593825

Subgroups — #29593825

Order 15616.

360 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 67 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#21457577C211yesmaximal, characteristic
2#21447968C211yesmaximal, characteristic, complemented
3#21445215C211yesmaximal, characteristic, complemented
4#21443865C211yesmaximal, characteristic, complemented
5#21443784C211yesmaximal, characteristic, complemented
6#21443775C211yesmaximal, characteristic, complemented
7C61×#2240C211yesmaximal, characteristic, complemented
8C2×#14519796—21no—
9#16840432—21no—
10#16840049—21no—
11#16839995—21no—
12#16839959—21no—
13#16839904—22no—
14C4×Dic244C2211yescharacteristic
15C8×D244C2211yescharacteristic
16#16839587—21no—
17C4⋊#11758185C2211yescharacteristic
18#16839565—21no—
19#16839515C2211yescharacteristic
20#16839511—21no—
21C61×#500C2211yescharacteristic
22C61×#493C2211yescharacteristic
23C61×#357—22no—
24C4×C16×C61C2211yescharacteristic
25C2×#11758224—22no—
26#14519796—42no—
27#14519796—42no—
28C2×Dic244D411yescharacteristic
29C2×#11758200—22no—
30C2×C8×D61—21no—
31#14519773—41no—
32#14519749—42no—
33#14519748—22no—
34C4×Dic122—21no—
35C4×D244D411yescharacteristic
36D4×Dic61—41no—
37C2×#11758185—21no—
38#14519711D411yescharacteristic
39#14519708—41no—
40C4⋊#92418—21no—
41C4⋊#92418D411yescharacteristic
42#14519702—21no—
43#14519698—22no—
44#14519697—41no—
45#14519689—21no—
46C2×D8×C61—21no—
47C2×D8×C61D412yes—
48C4⋊Q8×C61—21no—
49#127×C61—21no—
50C2×C16×C61—21no—
51#107×C61—21no—
52#107×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×Q8×C61—41no—
55C2×D4×C61—22no—
56C2×D4×C61—41no—
57C2×D4×C61—41no—
58C2×C22⋊D61—42no—
59C2×C22⋊D61—42no—
60C22×Dic61—42no—
61#11758224—44no—
62#11758224—82no—
63C2×D244D811yescharacteristic
64C2×C4×D61—21no—
65C2×Dic122—21no—
66D8×C61—42no—
67D8×C61—41no—
68D8×C61—41no—
69C2×C8×C61C2×D411yescharacteristic
70C2×C8×C61C2×D411yescharacteristic
71C4⋊C4×C61—41no—
72C4⋊C4×C61—41no—
73C42×C61C2×D411yescharacteristic
74C22⋊Dic61—42no—
75#11758200—44no—
76#11758198—21no—
77C4⋊Dic61—21no—
78C4⋊Dic61D811yescharacteristic
79#11758196—41no—
80C4×Dic61—41no—
81C2×#92418—21no—
82C2×#92418—41no—
83Dic244—21no—
84Dic244SD1612yes—
85C8×D61—41no—
86C8×D61—41no—
87C16×C61—41no—
88#11758185—41no—
89C23×C61—42no—
90C22×D61—21no—
91Q8×C61—161no—
92D4×C61—42no—
93D4×C61—42no—
94D4×C61—81no—
95D4×C61—81no—
96D4×C61—161no—
97C2×C4×C61—81no—
98C2×C4×C61#12011yescharacteristic
99C2×C4×C61C2×D811yescharacteristic
100C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
101C22⋊D61—84no—
102C22⋊D61—162no—
103C2×Dic61—21no—
104C2×Dic61—41no—
105C2×Dic61—41no—
106C2×Dic61—84no—
107D244—21no—
108D244—21no—
109C4×D61—41no—
110C4×D61—41no—
111Dic122—22no—
112Dic122—41no—
113C8×C61—21no—
114C8×C61C2×SD1611yescharacteristic
115C8×C61AGL(1,ℤ/8)11yescharacteristic
116#92418—41no—
117#92418—81no—
118#12373—611nomaximal, Sylow
119C22×C61—82no—
120C22×C61—82no—
121C22×C61—82no—
122C22×C61#44711yescharacteristic
123C2×D61—41no—
124C2×D61—41no—
125C2×D61—41no—
126C4×C61—21no—
127C4×C61—161no—
128C4×C61#45011yescharacteristic
129C4×C61#45511yescharacteristic
130C4×C61#50811yescharacteristic
131C4×C61#51011yescharacteristic
132Dic61—42no—
133Dic61—41no—
134Dic61—81no—
135#3287—611no—
136#2240D6111yescharacteristic, complemented
137#2227—611no—
138#1675—611no—
139#1361—611no—
140#1332—611no—
141D4⋊C16—611no—
142C2×C61—162no—
143C2×C61#163911yescharacteristic
144C2×C61#218911yescharacteristic
145C2×C61#219211yescharacteristic
146D61—81no—
147C2×#135—1221no—
148#550—1221no—
149#500C2×D6111yescharacteristic
150#493C2×D6111yescharacteristic
151#476—1221no—
152#466—1221no—
153#460—1221no—
154#449—1222no—
155C4×Q16—611no—
156C8×D4—611no—
157#366—1221no—
158C4⋊C16—611no—
159#358—1221no—
160#357—22no—
161C4×C16C2×D6111yescharacteristic
162#335—611no—
163#333—1221no—
164C61#1237311yescharacteristic, complemented, Sylow
165C2×#41—1222no—
166#135—2442no—
167#135—2442no—
168C2×Q16—611no—
169C2×SD16—1222no—
170C2×D8—21no—
171C2×D8C22⋊D6112yes—
172C22×C8—1221no—
173C4⋊Q8—21no—
174#127—21no—
175#127—2441no—
176#121—1222no—
177#121—2442no—
178C4×Q8—1221no—
179C4×D4—611no—
180C4×D4—2441no—
181C2×C16—21no—
182C2×C16—1221no—
183#107—21no—
184#107—21no—
185#107—611no—
186#106—2441no—
187C4⋊C8—611no—
188C4⋊C8—1221no—
189#103—1221no—
190#102—1222no—
191#102—2441no—
192C22⋊C8—1221no—
193C4×C8C22×D6111yescharacteristic
194#41—4882no—
195#41—2444no—
196C2×Q8—41no—
197C2×Q8—1221no—
198C2×D4—22no—
199C2×D4—41no—
200C2×D4—41no—
201C2×D4—611no—
202C2×D4—2442no—
203C2×D4—2442no—
204C22×C4—1221no—
205C22×C4—2442no—
206Q16—612no—
207Q16—1221no—
208SD16—2444no—
209D8—42no—
210D8—41no—
211D8—41no—
212C2×C8—1221no—
213C2×C8—2441no—
214C2×C8—2441no—
215C2×C8—2441no—
216C2×C8D4×D6111yescharacteristic
217C2×C8C2×C22⋊D6111yescharacteristic
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—611no—
221C4⋊C4—1221no—
222C4⋊C4—2441no—
223C22⋊C4—1221no—
224C22⋊C4—2442no—
225C42—2441no—
226C42D4×D6111yescharacteristic
227C16—41no—
228C16—2441no—
229C23—42no—
230C23—1221no—
231Q8—161no—
232Q8—1222no—
233Q8—2441no—
234D4—42no—
235D4—42no—
236D4—81no—
237D4—81no—
238D4—161no—
239D4—1221no—
240D4—1221no—
241D4—9762no—
242D4—4884no—
243C2×C4—81no—
244C2×C4—1221no—
245C2×C4—4884no—
246C2×C4—2441no—
247C2×C4—2441no—
248C2×C4—2441no—
249C2×C4—2441no—
250C2×C4#1451974511yescharacteristic
251C2×C4D8×D6111yescharacteristic
252C2×C4#1451980111yescharacteristic
253C8—21no—
254C8—4881no—
255C8—2441no—
256C8SD16×D6111yescharacteristic
257C8#1451980411yescharacteristic
258C22—82no—
259C22—82no—
260C22—82no—
261C22—2441no—
262C22—2441no—
263C22—2441no—
264C22#1683989411yescharacteristic
265C4—21no—
266C4—161no—
267C4—4881no—
268C4—2441no—
269C4—2442no—
270C4#1683991111yescharacteristic
271C4#1683993911yescharacteristic
272C4#1684019311yescharacteristic
273C4#1684020111yescharacteristic
274C2—162no—
275C2—4881no—
276C2#2144499511yescharacteristic
277C2#2144775611yescharacteristic
278C2#2144777511yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2240C2
socleC22×C61#447
prime radical#21457577C2
hypercenter#2240D61
hypocenterC61#12373
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2240

Complements

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

NH ≅ G/Ntype
2. #21447968C2semidirect
3. #21445215C2semidirect
4. #21443865C2semidirect
5. #21443784C2semidirect
6. #21443775C2semidirect
7. C61×#2240C2semidirect
136. #2240D61semidirect
164. C61#12373semidirect

Maximal subgroups

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

subgroupindex
#214575772
#214479682
#214452152
#214438652
#214437842
#214437752
C61×#22402
#1237361