Finite Group Databasebeta

← #29593761

Subgroups — #29593761

Order 15616.

292 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 65 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#21458779C211yesmaximal, characteristic
2#21448065C211yesmaximal, characteristic, complemented
3#21447865C211yesmaximal, characteristic
4#21445313C211yesmaximal, characteristic, complemented
5#21443870C211yesmaximal, characteristic, complemented
6#21443787C211yesmaximal, characteristic
7C61×#1338C211yesmaximal, characteristic, complemented
8#16840472—21no—
9C2×#14519722—21no—
10#16840171—21no—
11#16840164C2211yescharacteristic
12#16840142C2211yescharacteristic
13#16840063—21no—
14#16840063—21no—
15#16840047—21no—
16#16840043—21no—
17#16839875—21no—
18C4×D488C2211yescharacteristic
19#16839567—21no—
20#16839567—21no—
21#16839567—21no—
22#16839513C2211yescharacteristic
23#16839509—21no—
24C61×#446C2211yescharacteristic
25C61×C4⋊C16C2211yescharacteristic
26C61×#346C2211yescharacteristic
27C2×Dic244—21no—
28C2×Dic244—21no—
29C2×D488D411yescharacteristic
30#14519777—21no—
31#14519777—21no—
32#14519769—21no—
33#14519769—21no—
34#14519755—41no—
35#14519755—41no—
36#14519753—41no—
37C4×D244—21no—
38C4×D244—21no—
39C4×D244—21no—
40C4⋊C4×D61—41no—
41#14519722—42no—
42#14519711—21no—
43#14519711D411yescharacteristic
44#14519711D411yescharacteristic
45#14519711D411yescharacteristic
46#14519709—21no—
47#14519709—21no—
48#14519708—41no—
49C4⋊#92418—21no—
50#14519701—41no—
51#14519699—21no—
52#14519699—21no—
53#14519699—21no—
54C4×Q8×C61D411yescharacteristic
55C2×C16×C61—21no—
56C2×C16×C61—21no—
57C4⋊C8×C61—21no—
58C4⋊C8×C61D411yescharacteristic
59#97×C61—21no—
60C4×C8×C61C2311yescharacteristic
61C2×Q8×C61D811yescharacteristic
62C2×D244—21no—
63C2×C4×D61—41no—
64C2×C4×D61—41no—
65C2×C4×D61—41no—
66C2×Dic122—41no—
67C2×Dic122—41no—
68C2×C8×C61—21no—
69C2×C8×C61C2×D411yescharacteristic
70C2×C8×C61C2×D411yescharacteristic
71C4⋊C4×C61—21no—
72C4⋊C4×C61D811yescharacteristic
73C42×C61—21no—
74C42×C61C2×D411yescharacteristic
75#11758198—41no—
76#11758198—41no—
77#11758198—41no—
78C4⋊Dic61—21no—
79C4⋊Dic61—21no—
80C4⋊Dic61—21no—
81C4⋊Dic61—41no—
82C4⋊Dic61—41no—
83C4⋊Dic61—41no—
84#11758196—41no—
85#11758196—41no—
86#11758196—41no—
87#11758196—41no—
88C2×#92418—41no—
89Dic244—42no—
90Dic244—41no—
91Dic244—41no—
92D488—21no—
93D488SD1612yes—
94C16×C61—41no—
95C16×C61—41no—
96C22×D61—41no—
97Q8×C61—41no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61#12011yescharacteristic
101C2×C4×C61C2×D811yescharacteristic
102C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
103C2×Dic61—41no—
104C2×Dic61—41no—
105C2×Dic61—41no—
106C2×Dic61—81no—
107D244—22no—
108D244—41no—
109C4×D61—82no—
110C4×D61—161no—
111C4×D61—161no—
112Dic122—81no—
113Dic122—81no—
114Dic122—161no—
115C8×C61—21no—
116C8×C61—41no—
117C8×C61C2×SD1611yescharacteristic
118C8×C61#13711yescharacteristic
119#92418—81no—
120#12362—611nomaximal, Sylow
121C22×C61#44711yescharacteristic
122C2×D61—42no—
123C2×D61—81no—
124C2×D61—81no—
125C4×C61—21no—
126C4×C61—21no—
127C4×C61—41no—
128C4×C61—41no—
129C4×C61#44811yescharacteristic
130C4×C61#45411yescharacteristic
131Dic61—81no—
132Dic61—81no—
133Dic61—81no—
134Dic61—161no—
135#3389—611no—
136#2245—611no—
137#2208—611no—
138#1690—611no—
139#1363—611no—
140#1338D6111yescharacteristic, complemented
141#1333—611no—
142C2×C61#162711yescharacteristic
143C2×C61#219111yescharacteristic
144C2×C61#219411yescharacteristic
145D61—82no—
146#554—1221no—
147C2×SD32—1221no—
148#501—1221no—
149#499—611no—
150#494—611no—
151#478—1221no—
152#478—1221no—
153#475—1221no—
154#474—1221no—
155#446C2×D6111yescharacteristic
156#442—1221no—
157C4×D8—611no—
158C4⋊C16C2×D6111yescharacteristic
159#358—1221no—
160#358—1221no—
161#358—1221no—
162#346C2×D6111yescharacteristic
163#334—611no—
164#332—1221no—
165C61#1236211yescharacteristic, complemented, Sylow
166C2×Q16—1221no—
167C2×Q16—1221no—
168C2×D8—611no—
169C4⋊Q8—1221no—
170C4⋊Q8—1221no—
171#125—1221no—
172#125—1221no—
173C22⋊Q8—2441no—
174C22⋊Q8—2441no—
175C22⋊Q8—2441no—
176C4×Q8D24411yescharacteristic
177C4×D4—1221no—
178C4×D4—1221no—
179C4×D4—1221no—
180C2×C4⋊C4—2441no—
181SD32—2442no—
182C2×C16—21no—
183C2×C16—21no—
184#107—611no—
185#107—611no—
186#107—611no—
187#107—1221no—
188#106—1221no—
189#106—1221no—
190#106—2441no—
191C4⋊C8—21no—
192C4⋊C8—1221no—
193C4⋊C8D24411yescharacteristic
194#103—2441no—
195#102—1221no—
196#102—1221no—
197#102—1221no—
198#97—21no—
199C4×C8C22×D6111yescharacteristic
200C2×Q8—2441no—
201C2×Q8—2441no—
202C2×Q8D48811yescharacteristic
203C2×D4—1221no—
204C22×C4—2441no—
205C22×C4—2441no—
206C22×C4—2441no—
207Q16—2442no—
208Q16—2441no—
209Q16—2441no—
210D8—612no—
211D8—1221no—
212C2×C8—21no—
213C2×C8—2441no—
214C2×C8D4×D6111yescharacteristic
215C2×C8D4×D6111yescharacteristic
216C4⋊C4—21no—
217C4⋊C4—1221no—
218C4⋊C4—1221no—
219C4⋊C4—1221no—
220C4⋊C4—2441no—
221C4⋊C4—2441no—
222C4⋊C4—2441no—
223C4⋊C4—2441no—
224C4⋊C4—2441no—
225C4⋊C4—2441no—
226C4⋊C4—2441no—
227C4⋊C4D48811yescharacteristic
228C22⋊C4—2441no—
229C22⋊C4—2441no—
230C22⋊C4—2441no—
231C42—21no—
232C42C2×D24411yescharacteristic
233C16—41no—
234C16—41no—
235C23—2441no—
236Q8—41no—
237Q8—9761no—
238Q8—4881no—
239Q8—4881no—
240D4—1222no—
241D4—2441no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—9761no—
245C2×C4—9761no—
246C2×C4—4882no—
247C2×C4—4881no—
248C2×C4—2441no—
249C2×C4—2441no—
250C2×C4—2441no—
251C2×C4#1451974711yescharacteristic
252C2×C4C2×D48811yescharacteristic
253C2×C4#1451980511yescharacteristic
254C8—21no—
255C8—41no—
256C8—4881no—
257C8SD16×D6111yescharacteristic
258C8#1451980911yescharacteristic
259C22—4881no—
260C22—4881no—
261C22—2442no—
262C22#1683989811yescharacteristic
263C4—21no—
264C4—21no—
265C4—41no—
266C4—41no—
267C4—9761no—
268C4—4881no—
269C4—4881no—
270C4—4881no—
271C4#1683990211yescharacteristic
272C4#1683993611yescharacteristic
273C2—4882no—
274C2#2144492411yescharacteristic
275C2#2144777211yescharacteristic
276C2#2144779211yescharacteristic
subgroupG/H
centerC22#16839898
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1338C2
socleC22×C61#447
prime radicalC2×D488D4
hypercenter#1338D61
hypocenterC61#12362
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #446 ◁ #1338

Complements

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

NH ≅ G/Ntype
2. #21448065C2semidirect
4. #21445313C2semidirect
5. #21443870C2semidirect
7. C61×#1338C2semidirect
140. #1338D61semidirect
165. C61#12362semidirect

Maximal subgroups

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

subgroupindex
#214587792
#214480652
#214478652
#214453132
#214438702
#214437872
C61×#13382
#1236261