Finite Group Databasebeta

← #29593760

Subgroups — #29593760

Order 15616.

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

normal subgroups only

This group has 292 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#21458780C211yesmaximal, characteristic
2#21448066C211yesmaximal, characteristic, complemented
3#21447865C211yesmaximal, characteristic
4#21445314C211yesmaximal, characteristic, complemented
5#21443800C211yesmaximal, characteristic, complemented
6#21443785C211yesmaximal, characteristic
7C61×#1363C211yesmaximal, characteristic, complemented
8#16840468—21no—
9C2×#14519722—21no—
10#16840169—21no—
11#16840142C2211yescharacteristic
12#16840065—21no—
13#16840059—21no—
14#16840048—21no—
15#16840041—21no—
16#16839892C2211yescharacteristic
17#16839873—21no—
18C4×D488C2211yescharacteristic
19#16839567—21no—
20#16839565—21no—
21#16839565—21no—
22#16839538C2211yescharacteristic
23#16839507—21no—
24C61×#499C2211yescharacteristic
25C61×C4⋊C16C2211yescharacteristic
26C61×#334C2211yescharacteristic
27C2×Dic244—21no—
28C2×Dic244—21no—
29C2×D488D411yescharacteristic
30#14519777—21no—
31#14519776—21no—
32#14519768—21no—
33#14519757—41no—
34#14519755—41no—
35#14519755—41no—
36C4×Dic122D411yescharacteristic
37C4×D244—21no—
38#14519739—21no—
39#14519739—21no—
40C4⋊C4×D61—41no—
41#14519722—42no—
42C2×#11758185—21no—
43#14519711D411yescharacteristic
44#14519710—21no—
45#14519709—41no—
46#14519708—21no—
47C4⋊#92418D411yescharacteristic
48#14519706—21no—
49#14519702—41no—
50#14519699—21no—
51#14519697—21no—
52#14519697—21no—
53#14519687—21no—
54#125×C61—21no—
55C2×C16×C61—21no—
56#107×C61D411yescharacteristic
57#107×C61D411yescharacteristic
58#106×C61—21no—
59C4⋊C8×C61—21no—
60C4×C8×C61C2311yescharacteristic
61C2×D244—21no—
62C2×C4×D61—41no—
63C2×C4×D61—41no—
64C2×C4×D61—41no—
65C2×Dic122—41no—
66C2×Dic122—41no—
67C2×Dic122D811yescharacteristic
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—41no—
77#11758198—41no—
78#11758198—41no—
79C4⋊Dic61—21no—
80C4⋊Dic61—41no—
81C4⋊Dic61—41no—
82C4⋊Dic61—41no—
83C4⋊Dic61D811yescharacteristic
84#11758196—21no—
85#11758196—41no—
86#11758196—41no—
87C4×Dic61—21no—
88C2×#92418—21no—
89Dic244—42no—
90Dic244—41no—
91Dic244—41no—
92D488—21no—
93D488SD1612yes—
94C16×C61—41no—
95#11758185—41no—
96C22×D61—41no—
97C2×C4×C61—41no—
98C2×C4×C61—41no—
99C2×C4×C61#12011yescharacteristic
100C2×C4×C61C2×D811yescharacteristic
101C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
102C2×Dic61—21no—
103C2×Dic61—21no—
104C2×Dic61—41no—
105C2×Dic61—81no—
106D244—22no—
107D244—41no—
108C4×D61—82no—
109C4×D61—161no—
110C4×D61—161no—
111Dic122—41no—
112Dic122—81no—
113Dic122—81no—
114Dic122—161no—
115C8×C61—21no—
116C8×C61—81no—
117C8×C61C2×SD1611yescharacteristic
118C8×C61#13711yescharacteristic
119#92418—41no—
120#12362—611nomaximal, Sylow
121C22×C61#44711yescharacteristic
122C2×D61—42no—
123C2×D61—81no—
124C2×D61—81no—
125C4×C61—21no—
126C4×C61—21no—
127C4×C61—81no—
128C4×C61—81no—
129C4×C61#44811yescharacteristic
130C4×C61#45411yescharacteristic
131Dic61—41no—
132Dic61—41no—
133Dic61—81no—
134Dic61—161no—
135#3389—611no—
136#2245—611no—
137#2208—611no—
138#1690—611no—
139#1363D6111yescharacteristic, complemented
140#1338—611no—
141#1333—611no—
142C2×C61#162711yescharacteristic
143C2×C61#219111yescharacteristic
144C2×C61#219411yescharacteristic
145D61—82no—
146#554—1221no—
147C2×SD32—1221no—
148#501—1221no—
149#499C2×D6111yescharacteristic
150#494—611no—
151#478—1221no—
152#478—1221no—
153#475—1221no—
154#474—1221no—
155#446—611no—
156#442—1221no—
157C4×D8—611no—
158C4⋊C16C2×D6111yescharacteristic
159#358—1221no—
160#358—1221no—
161#358—1221no—
162#346—611no—
163#334C2×D6111yescharacteristic
164#332—1221no—
165C61#1236211yescharacteristic, complemented, Sylow
166C2×Q16—1221no—
167C2×Q16—1221no—
168C2×D8—611no—
169C4⋊Q8—1221no—
170C4⋊Q8—1221no—
171#125—21no—
172#125—1221no—
173C22⋊Q8—2441no—
174C22⋊Q8—2441no—
175C22⋊Q8—2441no—
176C4×Q8—611no—
177C4×D4—1221no—
178C4×D4—1221no—
179C4×D4—1221no—
180C2×C4⋊C4—2441no—
181SD32—2442no—
182C2×C16—21no—
183C2×C16—1221no—
184#107—611no—
185#107—1221no—
186#107D24411yescharacteristic
187#107D24411yescharacteristic
188#106—21no—
189#106—1221no—
190#106—2441no—
191C4⋊C8—21no—
192C4⋊C8—611no—
193C4⋊C8—1221no—
194#103—2441no—
195#102—1221no—
196#102—1221no—
197#102—1221no—
198#97—1221no—
199C4×C8C22×D6111yescharacteristic
200C2×Q8—611no—
201C2×Q8—2441no—
202C2×Q8—2441no—
203C2×D4—1221no—
204C22×C4—2441no—
205C22×C4—2441no—
206C22×C4—2441no—
207Q16—2442no—
208Q16—2441no—
209Q16—2441no—
210D8—612no—
211D8—1221no—
212C2×C8—41no—
213C2×C8—1221no—
214C2×C8C2×D24411yescharacteristic
215C2×C8D4×D6111yescharacteristic
216C4⋊C4—21no—
217C4⋊C4—21no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—611no—
221C4⋊C4—1221no—
222C4⋊C4—1221no—
223C4⋊C4—2441no—
224C4⋊C4—2441no—
225C4⋊C4—2441no—
226C4⋊C4—2441no—
227C4⋊C4—2441no—
228C22⋊C4—2441no—
229C22⋊C4—2441no—
230C22⋊C4—2441no—
231C42—1221no—
232C42D4×D6111yescharacteristic
233C16—41no—
234C16—2441no—
235C23—2441no—
236Q8—9761no—
237Q8—4881no—
238Q8—4881no—
239Q8—2441no—
240D4—1222no—
241D4—2441no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—1221no—
245C2×C4—1221no—
246C2×C4—9761no—
247C2×C4—9761no—
248C2×C4—4882no—
249C2×C4—4881no—
250C2×C4—2441no—
251C2×C4#1451974711yescharacteristic
252C2×C4D8×D6111yescharacteristic
253C2×C4#1451980411yescharacteristic
254C8—21no—
255C8—81no—
256C8—2441no—
257C8SD16×D6111yescharacteristic
258C8#1451980911yescharacteristic
259C22—4881no—
260C22—4881no—
261C22—2442no—
262C22#1683989711yescharacteristic
263C4—21no—
264C4—21no—
265C4—81no—
266C4—81no—
267C4—9761no—
268C4—4881no—
269C4—2441no—
270C4—2441no—
271C4#1683990211yescharacteristic
272C4#1683993711yescharacteristic
273C2—4882no—
274C2#2144492311yescharacteristic
275C2#2144777111yescharacteristic
276C2#2144779111yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1363C2
socleC22×C61#447
prime radicalC2×D488D4
hypercenter#1363D61
hypocenterC61#12362
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. #21448066C2semidirect
4. #21445314C2semidirect
5. #21443800C2semidirect
7. C61×#1363C2semidirect
139. #1363D61semidirect
165. C61#12362semidirect

Maximal subgroups

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

subgroupindex
#214587802
#214480662
#214478652
#214453142
#214438002
#214437852
C61×#13632
#1236261