Finite Group Databasebeta

← #30605020

Subgroups — #30605020

Order 15616.

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

normal subgroups only

This group has 316 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#21461540C211yesmaximal, characteristic, complemented
3#21460794C212yesmaximal, complemented
4#21460790C212yesmaximal, complemented
5#21456470C211yesmaximal, characteristic
6#16840725—21no—
7#16840684—21no—
8#16840659C2212yes—
9#16840654—21no—
10#16840631C2211yescharacteristic
11#16840630C2211yescharacteristic
12#16840629—21no—
13#16840368—21no—
14#16840139C411yescharacteristic, complemented
15#16840128—21no—
16#16840016C2212yes—
17#16839999—21no—
18#16839873C412yescomplemented
19#16839844—21no—
20#16839716C2211yescharacteristic
21C61×#499C411yescharacteristic, complemented
22D61⋊M16—21no—
23#14519856—21no—
24#14519851—22no—
25#14519831—22no—
26C8×#6923—22no—
27C2×D488—21no—
28C2×D488C2×C412yes—
29C2×#11758189C2311yescharacteristic
30C2×C8×D61D411yescharacteristic
31#14519774—21no—
32#14519762—42no—
33#14519752—22no—
34#14519752—42no—
35#14519739—22no—
36#14519734D411yescharacteristic
37#14519697—22no—
38#14519697—22no—
39#14519688D411yescharacteristic
40#14519687C2×C411yescharacteristic
41C8×Dic61D411yescharacteristic
42#125×C61—21no—
43#107×C61—21no—
44#106×C61C2×C412yes—
45C4×C8×C61C2×C411yescharacteristic
46C2×D244—22no—
47C2×D244—42no—
48C2×D244—42no—
49C2×C4×D61—42no—
50C2×C4×D61C2×D411yescharacteristic
51C22⋊#6923—41no—
52#11758217—41no—
53C4⋊#6923—41no—
54C4×#6923—22no—
55#11758213—41no—
56D61⋊C8—22no—
57C2×C8×C61C22⋊C411yescharacteristic
58C2×C8×C61C22×C411yescharacteristic
59C4⋊C4×C61—22no—
60C4⋊C4×C61—42no—
61C42×C61C22⋊C411yescharacteristic
62#11758198—21no—
63#11758198—42no—
64#11758198—42no—
65#11758196—21no—
66C4×Dic61C22⋊C411yescharacteristic
67C2×#92418C22⋊C411yescharacteristic
68C2×#92418C2×D411yescharacteristic
69D488—42no—
70D488—41no—
71D488—41no—
72#11758189—41no—
73C8×D61—21no—
74C8×D61—21no—
75#11758187—42no—
76C22×D61—42no—
77C22×D61AGL(1,ℤ/8)11yescharacteristic
78C2×#6923—42no—
79C2×C4×C61—21no—
80C2×C4×C61—42no—
81C2×C4×C61C2×C22⋊C411yescharacteristic
82C2×Dic61—21no—
83C2×Dic61AGL(1,ℤ/8)11yescharacteristic
84D244—42no—
85D244—42no—
86D244—162no—
87D244—162no—
88C4×D61—21no—
89C4×D61—21no—
90C4×D61—162no—
91#92420—42no—
92C8×C61—21no—
93C8×C61#10411yescharacteristic
94C8×C61#10411yescharacteristic
95#92418—21no—
96#92418—21no—
97#11770—611nomaximal, Sylow
98C22×C61#41811yescharacteristic
99C2×D61—21no—
100C2×D61—41no—
101C2×D61—82no—
102C2×D61—82no—
103C2×D61—82no—
104#6923—82no—
105C4×C61—41no—
106C4×C61—82no—
107C4×C61#41011yescharacteristic
108C4×C61C2×#10411yescharacteristic
109Dic61—21no—
110Dic61—41no—
111#3176—611no—
112#2166—611no—
113#1747—611no—
114#1341—612no—
115#1339—612no—
116C2×C61—21no—
117C2×C61#150511yescharacteristic
118D61—41no—
119D61—162no—
120#540—1221no—
121#499#692311yescharacteristic, complemented
122#493—611no—
123#490—1221no—
124#469—612no—
125#466—1221no—
126#442—612no—
127C4×D8—1221no—
128#405—611no—
129#405—1221no—
130#364—1221no—
131#349—612no—
132#347—1221no—
133#338—611no—
134H(3,ℤ/4)—611no—
135H(3,ℤ/4)—1221no—
136C61#1177011yescharacteristic, complemented, Sylow
137C2×D8—612no—
138C2×D8—1221no—
139C2×M16—611no—
140C2×M16—1221no—
141C22×C8—611no—
142#127—1221no—
143#125—21no—
144#123—2442no—
145#121—1222no—
146#121—2442no—
147C4×D4—1222no—
148#117—611no—
149#117—1221no—
150M32—1222no—
151#107—21no—
152#106C2×#692312yes—
153#102—1222no—
154#102—1222no—
155#97—611no—
156#97—611no—
157#97—1222no—
158C4×C8—611no—
159C4×C8—1222no—
160C4×C8C2×#692311yescharacteristic
161C2×D4—1222no—
162C2×D4—2442no—
163C2×D4—2442no—
164C22×C4—611no—
165C22×C4—2442no—
166D8—2442no—
167D8—2441no—
168D8—2441no—
169M16—2441no—
170M16—2441no—
171M16—2441no—
172C2×C8—611no—
173C2×C8—611no—
174C2×C8—1221no—
175C2×C8—1221no—
176C2×C8—1222no—
177C2×C8C22⋊#692311yescharacteristic
178C2×C8C22×#692311yescharacteristic
179C4⋊C4—22no—
180C4⋊C4—42no—
181C4⋊C4—1221no—
182C4⋊C4—2441no—
183C22⋊C4—1221no—
184C22⋊C4—2442no—
185C22⋊C4—2442no—
186C22⋊C4—2441no—
187C42—611no—
188C42—1222no—
189C42C22⋊#692311yescharacteristic
190C16—2442no—
191C23—611no—
192C23—2442no—
193D4—9762no—
194D4—9762no—
195D4—2442no—
196D4—2442no—
197C2×C4—21no—
198C2×C4—42no—
199C2×C4—611no—
200C2×C4—1221no—
201C2×C4—1221no—
202C2×C4—1221no—
203C2×C4—9762no—
204C2×C4—2442no—
205C2×C4C2×C22⋊#692311yescharacteristic
206C8—21no—
207C8—1221no—
208C8—1221no—
209C8—2442no—
210C8#1451984211yescharacteristic
211C8#1451984211yescharacteristic
212C22—1221no—
213C22—4882no—
214C22—4882no—
215C22—4882no—
216C22—2441no—
217C22#1684075411yescharacteristic
218C4—41no—
219C4—82no—
220C4—1221no—
221C4—4882no—
222C4—2441no—
223C4#1684074311yescharacteristic
224C4C2×#1451984211yescharacteristic
225C2—21no—
226C2—9762no—
227C2—2441no—
228C2#2146121011yescharacteristic
subgroupG/H
centerC2#21461210
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#499C4
socleC2×C61#1505
prime radical#21456470C2
cosocleC2×#11758189C23
hypercenter#499#6923
hypocenterC61#11770
LCSG ▷ C2×C8×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. #21461540C2semidirect
3. #21460794C2semidirect
4. #21460790C2semidirect
14. #16840139C4semidirect
18. #16839873C4semidirect
21. C61×#499C4semidirect
121. #499#6923semidirect
136. C61#11770semidirect

Maximal subgroups

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

subgroupindex
#214621942
#214615402
#214607942
#214607902
#214564702
#1177061