Finite Group Databasebeta

← #29594018

Subgroups — #29594018

Order 15616.

286 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 61 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#21458423C211yesmaximal, characteristic
2#21448106C211yesmaximal, characteristic, complemented
3#21447957C211yesmaximal, characteristic, complemented
4#21445343C211yesmaximal, characteristic, complemented
5#21443785C211yesmaximal, characteristic, complemented
6#21443776C211yesmaximal, characteristic, complemented
7C61×#1363C211yesmaximal, characteristic, complemented
8#16840465—21no—
9#16840167C2211yescharacteristic
10#16840089—21no—
11#16840077—21no—
12#16840059—21no—
13#16840053—21no—
14#16840016—21no—
15C4×D488C2211yescharacteristic
16#16839841C2211yescharacteristic
17#16839801—21no—
18#16839589—21no—
19#16839588—21no—
20#16839587—21no—
21#16839564—21no—
22#16839538C2211yescharacteristic
23#16839510—21no—
24C61×#499C2211yescharacteristic
25C61×C4⋊C16C2211yescharacteristic
26C61×#334C2211yescharacteristic
27C2×D488D411yescharacteristic
28C2×#11758189—21no—
29#14519777—21no—
30#14519772—41no—
31#14519762—41no—
32#14519752—21no—
33#14519752—21no—
34#14519752—41no—
35C4×D244—21no—
36C4×D244D411yescharacteristic
37#14519739—41no—
38#14519735—21no—
39C4⋊C4×D61—21no—
40C2×#11758185—21no—
41#14519711—21no—
42#14519711—21no—
43#14519711D411yescharacteristic
44#14519710—21no—
45#14519709—41no—
46#14519708—21no—
47C4⋊#92418D411yescharacteristic
48#14519699—21no—
49#14519699—41no—
50#14519697—21no—
51#14519697—21no—
52#14519689—21no—
53#125×C61—21no—
54C2×C16×C61—21no—
55#107×C61D411yescharacteristic
56#107×C61D411yescharacteristic
57#106×C61—21no—
58C4⋊C8×C61—21no—
59C4×C8×C61C2311yescharacteristic
60C2×D244—21no—
61C2×D244—41no—
62C2×D244—41no—
63C2×D244D811yescharacteristic
64C2×C4×D61—21no—
65C2×C4×D61—41no—
66C2×C4×D61—41no—
67C2×Dic122—41no—
68C2×C8×C61—41no—
69C2×C8×C61C2×D411yescharacteristic
70C2×C8×C61C2×D411yescharacteristic
71C4⋊C4×C61—21no—
72C4⋊C4×C61—21no—
73C4⋊C4×C61—41no—
74C4⋊C4×C61—41no—
75C42×C61C2×D411yescharacteristic
76#11758198—21no—
77#11758198—41no—
78#11758198—41no—
79#11758198—41no—
80#11758198—41no—
81C4⋊Dic61—21no—
82C4⋊Dic61—41no—
83C4⋊Dic61—41no—
84C4⋊Dic61D811yescharacteristic
85#11758196—41no—
86C4×Dic61—41no—
87C2×#92418—21no—
88D488—21no—
89D488—21no—
90#11758189—41no—
91#11758189—41no—
92C16×C61—41no—
93#11758185—22no—
94C22×D61—21no—
95C22×D61—41no—
96C2×C4×C61—41no—
97C2×C4×C61—41no—
98C2×C4×C61#12011yescharacteristic
99C2×C4×C61C2×D811yescharacteristic
100C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
101C2×Dic61—21no—
102C2×Dic61—41no—
103C2×Dic61—81no—
104D244—41no—
105D244—41no—
106D244—41no—
107D244—82no—
108D244—161no—
109C4×D61—41no—
110C4×D61—41no—
111C4×D61—161no—
112C4×D61—161no—
113Dic122—161no—
114C8×C61—21no—
115C8×C61—81no—
116C8×C61#13511yescharacteristic
117C8×C61#13711yescharacteristic
118#92418—41no—
119#12400—611nomaximal, Sylow
120C22×C61#44711yescharacteristic
121C2×D61—41no—
122C2×D61—41no—
123C2×D61—41no—
124C2×D61—81no—
125C2×D61—81no—
126C2×D61—81no—
127C4×C61—21no—
128C4×C61—21no—
129C4×C61—81no—
130C4×C61—81no—
131C4×C61#45211yescharacteristic
132C4×C61#45611yescharacteristic
133Dic61—41no—
134Dic61—81no—
135Dic61—161no—
136#3355—611no—
137#2255—611no—
138#2224—611no—
139#1695—611no—
140#1363D6111yescharacteristic, complemented
141#1333—611no—
142#1330—611no—
143C2×C61#164711yescharacteristic
144C2×C61#219111yescharacteristic
145C2×C61#219211yescharacteristic
146D61—81no—
147D61—161no—
148#553—1221no—
149#500—611no—
150#499C2×D6111yescharacteristic
151#482—1221no—
152#480—1221no—
153#478—1221no—
154#476—1221no—
155#469—1221no—
156C4×D8—611no—
157#436—611no—
158#428—1221no—
159#367—1221no—
160#366—1221no—
161#366—1221no—
162C4⋊C16C2×D6111yescharacteristic
163#357—1221no—
164#346—611no—
165#334C2×D6111yescharacteristic
166#333—1221no—
167C61#1240011yescharacteristic, complemented, Sylow
168C2×D8—611no—
169C2×M16—1221no—
170C4⋊Q8—1221no—
171#126—2441no—
172#125—21no—
173#123—2441no—
174#121—1221no—
175#121—1221no—
176#121—2441no—
177C4×D4—611no—
178C4×D4—1221no—
179C4×D4—2441no—
180#117—1221no—
181C2×C4⋊C4—1221no—
182C2×C16—21no—
183C2×C16—1221no—
184#107—611no—
185#107—1221no—
186#107—1221no—
187#107—1221no—
188#107D24411yescharacteristic
189#107D24411yescharacteristic
190#106—21no—
191#106—1221no—
192#106—2441no—
193C4⋊C8—21no—
194C4⋊C8—611no—
195#102—1221no—
196#102—1221no—
197#102—1221no—
198#102—2441no—
199C22⋊C8—1221no—
200C4×C8C22×D6111yescharacteristic
201C2×Q8—2441no—
202C2×D4—611no—
203C2×D4—1221no—
204C2×D4—2441no—
205C2×D4—2441no—
206C22×C4—1221no—
207C22×C4—2441no—
208C22×C4—2441no—
209D8—1221no—
210D8—1221no—
211M16—2441no—
212M16—2441no—
213C2×C8—41no—
214C2×C8—1221no—
215C2×C8C2×D24411yescharacteristic
216C2×C8D4×D6111yescharacteristic
217C4⋊C4—21no—
218C4⋊C4—21no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—611no—
222C4⋊C4—1221no—
223C4⋊C4—2441no—
224C4⋊C4—2441no—
225C4⋊C4—2441no—
226C22⋊C4—1221no—
227C22⋊C4—2441no—
228C22⋊C4—2441no—
229C22⋊C4—2441no—
230C22⋊C4—2441no—
231C42—2441no—
232C42D4×D6111yescharacteristic
233C16—41no—
234C16—1222no—
235C23—1221no—
236C23—2441no—
237Q8—9761no—
238D4—9761no—
239D4—4882no—
240D4—2441no—
241D4—2441no—
242D4—2441no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—1221no—
246C2×C4—9761no—
247C2×C4—9761no—
248C2×C4—4881no—
249C2×C4—2441no—
250C2×C4—2441no—
251C2×C4—2441no—
252C2×C4#1451974711yescharacteristic
253C2×C4D8×D6111yescharacteristic
254C2×C4#1451980411yescharacteristic
255C8—21no—
256C8—81no—
257C8—2441no—
258C8#1451979811yescharacteristic
259C8#1451980911yescharacteristic
260C22—4881no—
261C22—4881no—
262C22—4881no—
263C22—2441no—
264C22—2441no—
265C22—2441no—
266C22#1683989711yescharacteristic
267C4—21no—
268C4—21no—
269C4—81no—
270C4—81no—
271C4—9761no—
272C4—4881no—
273C4—2441no—
274C4#1683992711yescharacteristic
275C4#1683994711yescharacteristic
276C2—9761no—
277C2—4881no—
278C2#2144505511yescharacteristic
279C2#2144777111yescharacteristic
280C2#2144777711yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1363C2
socleC22×C61#447
prime radical#21458423C2
hypercenter#1363D61
hypocenterC61#12400
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1363

Complements

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

NH ≅ G/Ntype
2. #21448106C2semidirect
3. #21447957C2semidirect
4. #21445343C2semidirect
5. #21443785C2semidirect
6. #21443776C2semidirect
7. C61×#1363C2semidirect
140. #1363D61semidirect
167. C61#12400semidirect

Maximal subgroups

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

subgroupindex
#214584232
#214481062
#214479572
#214453432
#214437852
#214437762
C61×#13632
#1240061