Finite Group Databasebeta

← #30605255

Subgroups — #30605255

Order 15616.

280 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 58 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#21462190C211yesmaximal, characteristic
2#21461750C211yesmaximal, characteristic
3#21460796C211yesmaximal, characteristic
4#21460795C211yesmaximal, characteristic
5#21460792C211yesmaximal, characteristic
6#21460791C211yesmaximal, characteristic
7#21456561C211yesmaximal, characteristic
8#16840684—21no—
9#16840659C2211yescharacteristic
10#16840659C2211yescharacteristic
11#16840654—21no—
12#16840644—21no—
13#16840633—21no—
14#16840631C2211yescharacteristic
15#16840630C2211yescharacteristic
16#16840316—21no—
17#16840159C411yescharacteristic, complemented
18#16840140C411yescharacteristic, complemented
19#16840111—21no—
20#16840021C2211yescharacteristic
21#16840019—21no—
22#16840017C2211yescharacteristic
23#16839870C411yescharacteristic, complemented
24#16839867—21no—
25#16839714C2211yescharacteristic
26C61×#441C411yescharacteristic, complemented
27D61⋊M16—21no—
28#14519856—21no—
29#14519851—21no—
30#14519851—21no—
31C2×Dic244C2×C411yescharacteristic
32C2×#11758202—21no—
33C2×#11758189D411yescharacteristic
34C2×#11758189C2311yescharacteristic
35#14519776—21no—
36#14519775—21no—
37#14519767—41no—
38#14519757—21no—
39#14519755—41no—
40#14519753—21no—
41C4×Dic122—21no—
42C4×Dic122—41no—
43#14519734—41no—
44C42×D61D411yescharacteristic
45#14519709C2×C411yescharacteristic
46#14519708—21no—
47#14519702—21no—
48#14519701—21no—
49#14519700—21no—
50#14519688D411yescharacteristic
51C8×Dic61C2×C411yescharacteristic
52C8×Dic61D411yescharacteristic
53C2×Q16×C61C2×C411yescharacteristic
54C4×Q8×C61—21no—
55#106×C61C2×C411yescharacteristic
56#103×C61—21no—
57#97×C61C2×C411yescharacteristic
58C2×Q8×C61—21no—
59C2×C4×D61—21no—
60C2×C4×D61C2×D411yescharacteristic
61C2×Dic122—21no—
62C2×Dic122—41no—
63C22⋊#6923—41no—
64#11758217—41no—
65C4⋊#6923—41no—
66C4×#6923—41no—
67#11758213—41no—
68D61⋊C8—41no—
69Q16×C61—41no—
70C2×C8×C61C22⋊C411yescharacteristic
71C2×C8×C61C22×C411yescharacteristic
72C4⋊C4×C61—21no—
73C4⋊C4×C61—41no—
74C42×C61—41no—
75C42×C61C22⋊C411yescharacteristic
76#11758202—42no—
77#11758198—41no—
78#11758198—41no—
79C4⋊Dic61—21no—
80C4⋊Dic61—41no—
81#11758196—41no—
82#11758196—41no—
83#11758196—41no—
84#11758196—41no—
85#11758196—41no—
86C4×Dic61—21no—
87C4×Dic61—41no—
88C4×Dic61C22⋊C411yescharacteristic
89C2×#92418C22⋊C411yescharacteristic
90C2×#92418C2×D411yescharacteristic
91Dic244—41no—
92#11758189—41no—
93#11758189—41no—
94#11758187—41no—
95#11758187—41no—
96C22×D61AGL(1,ℤ/8)11yescharacteristic
97C2×#6923—81no—
98Q8×C61—41no—
99Q8×C61—41no—
100C2×C4×C61—21no—
101C2×C4×C61—41no—
102C2×C4×C61—41no—
103C2×C4×C61C2×C22⋊C411yescharacteristic
104C2×Dic61—21no—
105C2×Dic61—41no—
106C2×Dic61—41no—
107C2×Dic61AGL(1,ℤ/8)11yescharacteristic
108C4×D61—21no—
109C4×D61—21no—
110C4×D61—42no—
111Dic122—41no—
112Dic122—41no—
113Dic122—82no—
114#92420—81no—
115C8×C61—21no—
116C8×C61—21no—
117#92418—21no—
118#92418—21no—
119#11838—611nomaximal, Sylow
120C22×C61#41811yescharacteristic
121C2×D61—21no—
122C2×D61—41no—
123#6923—161no—
124C4×C61—41no—
125C4×C61—81no—
126C4×C61—81no—
127C4×C61#41011yescharacteristic
128C4×C61#42111yescharacteristic
129Dic61—22no—
130Dic61—21no—
131Dic61—81no—
132Dic61—81no—
133#3185—611no—
134#2165—611no—
135#1841—611no—
136#1342—611no—
137#1342—611no—
138#1340—611no—
139#1340—611no—
140C2×C61—21no—
141C2×C61#151411yescharacteristic
142D61—41no—
143#533—1221no—
144#498—611no—
145#494—611no—
146#487—1221no—
147#470—611no—
148#470—611no—
149#470—1221no—
150#441—611no—
151#441—1221no—
152#441#692311yescharacteristic, complemented
153C4×M16—611no—
154#364—1221no—
155#349—611no—
156#349—611no—
157#347—1221no—
158#344—1221no—
159#339—1221no—
160#338—611no—
161H(3,ℤ/4)—611no—
162C61#1183811yescharacteristic, complemented, Sylow
163C2×Q16—611no—
164C2×Q16—1221no—
165C2×Q16C2×#692311yescharacteristic
166C2×M16—611no—
167C2×M16—611no—
168C2×M16—1221no—
169C4⋊Q8—1221no—
170C4⋊Q8—1221no—
171#125—2441no—
172C22⋊Q8—1221no—
173C22⋊Q8—1221no—
174C22⋊Q8—2441no—
175C4×Q8—21no—
176C4×Q8—1221no—
177C4×Q8—2441no—
178#117—1221no—
179#117—2441no—
180C2×C42—611no—
181M32—1221no—
182M32—1221no—
183#106—611no—
184#106—1221no—
185#106C2×#692311yescharacteristic
186#103—21no—
187#103—1221no—
188#103—1221no—
189#103—1221no—
190#97—611no—
191#97C2×#692311yescharacteristic
192C4×C8—611no—
193C4×C8—611no—
194C2×Q8—21no—
195C2×Q8—1221no—
196C2×Q8—2441no—
197C22×C4—611no—
198C22×C4—1221no—
199Q16—41no—
200Q16—2441no—
201Q16—2442no—
202M16—2441no—
203M16—2441no—
204M16—2441no—
205M16—2441no—
206C2×C8—611no—
207C2×C8—611no—
208C2×C8—2441no—
209C2×C8C22⋊#692311yescharacteristic
210C2×C8C22×#692311yescharacteristic
211C4⋊C4—21no—
212C4⋊C4—41no—
213C4⋊C4—1221no—
214C4⋊C4—2441no—
215C4⋊C4—2441no—
216C4⋊C4—2441no—
217C4⋊C4—2441no—
218C4⋊C4—2441no—
219C4⋊C4—2441no—
220C4⋊C4—2441no—
221C22⋊C4—2441no—
222C22⋊C4—2441no—
223C22⋊C4—2441no—
224C42—41no—
225C42—611no—
226C42—1221no—
227C42—2441no—
228C42—2441no—
229C42C22⋊#692311yescharacteristic
230C16—2441no—
231C16—2441no—
232C23—611no—
233Q8—41no—
234Q8—41no—
235Q8—4882no—
236Q8—2441no—
237Q8—2441no—
238C2×C4—21no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—611no—
242C2×C4—1221no—
243C2×C4—1221no—
244C2×C4—1221no—
245C2×C4—4881no—
246C2×C4—2442no—
247C2×C4—2441no—
248C2×C4—2441no—
249C2×C4C2×C22⋊#692311yescharacteristic
250C8—21no—
251C8—21no—
252C8—1221no—
253C8—1221no—
254C8—4881no—
255C22—1221no—
256C22—2441no—
257C22#1684075411yescharacteristic
258C4—41no—
259C4—81no—
260C4—81no—
261C4—1222no—
262C4—1221no—
263C4—9761no—
264C4—4881no—
265C4—4881no—
266C4#1684074111yescharacteristic
267C4#1684075911yescharacteristic
268C2—21no—
269C2—2441no—
270C2#2146123811yescharacteristic
subgroupG/H
centerC2#21461238
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#441C4
socleC2×C61#1514
prime radicalC22×D61AGL(1,ℤ/8)
cosocleC2×#11758189C23
hypercenter#441#6923
hypocenterC61#11838
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #441

Complements

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

NH ≅ G/Ntype
17. #16840159C4semidirect
18. #16840140C4semidirect
23. #16839870C4semidirect
26. C61×#441C4semidirect
152. #441#6923semidirect
162. C61#11838semidirect

Maximal subgroups

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

subgroupindex
#214621902
#214617502
#214607962
#214607952
#214607922
#214607912
#214565612
#1183861