Finite Group Databasebeta

← #30605520

Subgroups — #30605520

Order 15616.

284 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 62 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#21462194C211yesmaximal, characteristic, complemented
2#21462041C211yesmaximal, characteristic, complemented
3#21460826C211yesmaximal, characteristic, complemented
4#21460825C211yesmaximal, characteristic, complemented
5#21460823C211yesmaximal, characteristic, complemented
6#21460822C211yesmaximal, characteristic, complemented
7#21456449C211yesmaximal, characteristic
8D61⋊M32—21no—
9#16840684—21no—
10#16840659—21no—
11#16840655—21no—
12#16840654C2211yescharacteristic
13#16840654C2211yescharacteristic
14#16840654C2211yescharacteristic
15#16840654C2211yescharacteristic
16#16840375C411yescharacteristic
17#16840368C411yescharacteristic
18#16840135C411yescharacteristic
19#16840132C2211yescharacteristic
20#16840128C2211yescharacteristic
21#16840009—21no—
22#16839992—21no—
23#16839861—21no—
24#16839849—21no—
25#16839716C2211yescharacteristic
26C61×#499C411yescharacteristic
27#14519852—22no—
28#14519851—21no—
29#14519851—21no—
30#14519851—21no—
31#14519851—21no—
32D61⋊C16—22no—
33C2×#11758190—21no—
34C2×#11758190—21no—
35C2×#11758189D411yescharacteristic
36C2×C8×D61D411yescharacteristic
37#14519777C2×C411yescharacteristic
38#14519774C2×C411yescharacteristic
39#14519772—41no—
40#14519768—41no—
41#14519762—41no—
42#14519757—21no—
43#14519752—21no—
44#14519752—41no—
45#14519742—21no—
46#14519739—21no—
47#14519734C2×C411yescharacteristic
48#14519700—21no—
49#14519700—21no—
50#14519697—21no—
51#14519697—21no—
52#14519688C2311yescharacteristic
53#14519687D411yescharacteristic
54C8×Dic61D411yescharacteristic
55#125×C61C2×C411yescharacteristic
56#125×C61C2×C411yescharacteristic
57#107×C61—21no—
58#106×C61—21no—
59C4×C8×C61C2×C411yescharacteristic
60C2×D244—21no—
61C2×D244—41no—
62C2×D244—41no—
63C2×C4×D61—41no—
64C2×C4×D61C22⋊C411yescharacteristic
65C2×Dic122—21no—
66C2×C8×C61C22⋊C411yescharacteristic
67C2×C8×C61C22⋊C411yescharacteristic
68C4⋊C4×C61—21no—
69C4⋊C4×C61—21no—
70C4⋊C4×C61—41no—
71C4⋊C4×C61—41no—
72C42×C61C22×C411yescharacteristic
73#11758198—21no—
74#11758198—41no—
75#11758198—41no—
76#11758198—41no—
77C4⋊Dic61—41no—
78C4⋊Dic61—41no—
79#11758196—21no—
80#11758196—41no—
81C4×Dic61—41no—
82C4×Dic61C22⋊C411yescharacteristic
83C2×#92418C2×D411yescharacteristic
84C2×#92418C2×D411yescharacteristic
85#11758190—42no—
86#11758190—41no—
87#11758190—41no—
88#11758189—41no—
89C8×D61—21no—
90C8×D61—21no—
91#11758187—22no—
92#11758187—22no—
93#11758187—41no—
94#11758187—41no—
95C22×D61—41no—
96C22×D61#10011yescharacteristic
97C2×C4×C61—21no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61C2×C22⋊C411yescharacteristic
101C2×Dic61—21no—
102C2×Dic61—41no—
103C2×Dic61#10011yescharacteristic
104D244—41no—
105D244—41no—
106D244—161no—
107D244—161no—
108C4×D61—21no—
109C4×D61—21no—
110C4×D61—161no—
111Dic122—41no—
112Dic122—41no—
113C8×C61—21no—
114C8×C61#10411yescharacteristic
115C8×C61#10411yescharacteristic
116#92418—21no—
117#92418—21no—
118#11912—611nomaximal, Sylow
119C22×C61C2×#10011yescharacteristic
120C2×D61—21no—
121C2×D61—41no—
122C2×D61—81no—
123C2×D61—81no—
124C2×D61—81no—
125C4×C61—41no—
126C4×C61—81no—
127C4×C61—81no—
128C4×C61C2×#10411yescharacteristic
129C4×C61#42111yescharacteristic
130Dic61—21no—
131Dic61—41no—
132Dic61—81no—
133#3174—611no—
134#2166—611no—
135#2110—611no—
136#1356—611no—
137#1356—611no—
138#1355—611no—
139#1355—611no—
140C2×C61—21no—
141C2×C61#153011yescharacteristic
142D61—41no—
143D61—161no—
144#541—611no—
145#540—611no—
146C2×M32—1221no—
147#499#692311yescharacteristic
148#492—611no—
149#491—611no—
150#490—611no—
151#468—1221no—
152#465—1221no—
153#440—1221no—
154C4×SD16—1221no—
155#405—611no—
156#364—1221no—
157#349—1221no—
158#347—611no—
159#347—611no—
160#347—611no—
161#347—611no—
162#347—1221no—
163C61#1191211yescharacteristic, complemented, Sylow
164C2×SD16—1221no—
165C2×SD16—1221no—
166C2×M16—611no—
167C22×C8—611no—
168C4⋊Q8—611no—
169#127—611no—
170#126—2441no—
171#125—2441no—
172#125C2×#692311yescharacteristic
173#125C2×#692311yescharacteristic
174#123—2441no—
175C22⋊Q8—1221no—
176#121—1221no—
177#121—2441no—
178C4×Q8—1221no—
179C4×D4—1221no—
180#117—611no—
181M32—1221no—
182M32—1221no—
183M32—1222no—
184M32—1221no—
185M32—1221no—
186C2×C16—1222no—
187#107—21no—
188#106—21no—
189#103—1221no—
190#103—1221no—
191#102—1221no—
192#102—1221no—
193#97—611no—
194#97—611no—
195C4×C8—611no—
196C4×C8C2×#692311yescharacteristic
197C2×Q8—1221no—
198C2×D4—1221no—
199C2×D4—2441no—
200C2×D4—2441no—
201C22×C4—611no—
202C22×C4—2441no—
203SD16—2442no—
204SD16—2441no—
205SD16—2441no—
206M16—2441no—
207C2×C8—611no—
208C2×C8—611no—
209C2×C8—1221no—
210C2×C8—1221no—
211C2×C8C22⋊#692311yescharacteristic
212C2×C8C22⋊#692311yescharacteristic
213C4⋊C4—21no—
214C4⋊C4—21no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—1221no—
218C4⋊C4—2441no—
219C4⋊C4—2441no—
220C4⋊C4—2441no—
221C22⋊C4—1221no—
222C22⋊C4—2441no—
223C22⋊C4—2441no—
224C22⋊C4—2441no—
225C42—611no—
226C42—2441no—
227C42C22×#692311yescharacteristic
228C16—1222no—
229C16—1222no—
230C16—2441no—
231C16—2441no—
232C23—611no—
233C23—2441no—
234Q8—2441no—
235Q8—2441no—
236D4—9761no—
237D4—9761no—
238D4—2441no—
239D4—2441no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—611no—
244C2×C4—1221no—
245C2×C4—1221no—
246C2×C4—1221no—
247C2×C4—9761no—
248C2×C4—2441no—
249C2×C4C2×C22⋊#692311yescharacteristic
250C8—21no—
251C8—1221no—
252C8—1221no—
253C8#1451984211yescharacteristic
254C8#1451984211yescharacteristic
255C22—1221no—
256C22—4881no—
257C22—4881no—
258C22—4881no—
259C22—2441no—
260C22D61⋊#10011yescharacteristic
261C4—41no—
262C4—81no—
263C4—81no—
264C4—1221no—
265C4—4881no—
266C4—2441no—
267C4C2×#1451984211yescharacteristic
268C4#1684076111yescharacteristic
269C2—21no—
270C2—9761no—
271C2—2441no—
272C2#2146129011yescharacteristic
subgroupG/H
centerC2#21461290
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#499C4
socleC2×C61#1530
prime radical#16840368C4
cosocle#14519688C23
hypercenter#499#6923
hypocenterC61#11912
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #499

Complements

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

NH ≅ G/Ntype
1. #21462194C2semidirect
2. #21462041C2semidirect
3. #21460826C2semidirect
4. #21460825C2semidirect
5. #21460823C2semidirect
6. #21460822C2semidirect
163. C61#11912semidirect

Maximal subgroups

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

subgroupindex
#214621942
#214620412
#214608262
#214608252
#214608232
#214608222
#214564492
#1191261