Finite Group Databasebeta

← #30595126

Subgroups — #30595126

Order 15616.

284 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 46 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
1C2×#16840668C211yesmaximal, characteristic
2#21461300C211yesmaximal, characteristic
3#21446222C211yesmaximal, characteristic
4#16840782—21no—
5C2×#14519836—21no—
6#16840668—21no—
7#16840668C412yescomplemented
8#16840618—21no—
9#16840618C412yescomplemented
10C2×#14519766C2211yescharacteristic
11#16839766—21no—
12C2×#14519696C411yescharacteristic, complemented
13#16839521—21no—
14C61×#519C411yescharacteristic, complemented
15C2×C22⋊#6923—41no—
16#14519844—41no—
17#14519836—22no—
18#14519836—41no—
19C22⋊#92420—41no—
20#14519832—22no—
21C22×D244D411yescharacteristic
22C2×#11758194—21no—
23#14519766—41no—
24#14519766C2×C411yescharacteristic
25#14519766C2×C411yescharacteristic
26#14519766D411yescharacteristic
27#14519766Q811yescharacteristic
28C2×#11758198—41no—
29C2×C4×Dic61D411yescharacteristic
30#14519697—42no—
31#14519696—41no—
32C22×Q8×C61C2×C411yescharacteristic
33C4×Q8×C61—42no—
34#117×C61—21no—
35#117×C61—41no—
36C23×D61—21no—
37C22×#6923—81no—
38C2×Q8×C61—21no—
39C2×Q8×C61—41no—
40C2×Q8×C61—41no—
41C2×Q8×C61C4211yescharacteristic
42C2×Q8×C61C4⋊C411yescharacteristic
43C22×C4×C61—21no—
44C22×C4×C61C22⋊C411yescharacteristic
45C22×Dic61—21no—
46C2×D244—21no—
47C2×D244—41no—
48C2×D244—41no—
49C2×D244C22⋊C411yescharacteristic
50C2×D244C4⋊C411yescharacteristic
51C22⋊#6923—42no—
52C22⋊#6923—81no—
53C2×#92420—42no—
54C4⋊C4×C61—22no—
55C4⋊C4×C61—42no—
56C22⋊C4×C61—41no—
57C42×C61—41no—
58C42×C61—42no—
59#11758198—41no—
60#11758198—41no—
61#11758198—41no—
62#11758198—41no—
63C4×Dic61—21no—
64C4×Dic61C22⋊C411yescharacteristic
65C4×Dic61C4⋊C411yescharacteristic
66#11758194—41no—
67#11758194—41no—
68C2×#92418—41no—
69C23×C61#9911yescharacteristic
70C22×D61—21no—
71C22×D61—21no—
72C22×D61—41no—
73C22×D61—41no—
74C22×D61—82no—
75C2×#6923—82no—
76C2×#6923—162no—
77Q8×C61—42no—
78Q8×C61—41no—
79Q8×C61—41no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—41no—
85C2×C4×C61—41no—
86C2×C4×C61—42no—
87C2×C4×C61#9511yescharacteristic
88C2×C4×C61#9911yescharacteristic
89C2×Dic61—21no—
90C2×Dic61—21no—
91C2×Dic61—81no—
92D244—41no—
93D244—41no—
94D244—81no—
95#92420—82no—
96#92418—81no—
97#7481—611nomaximal, Sylow
98C22×C61—41no—
99C22×C61#34211yescharacteristic
100C22×C61AΣL(1,𝔽16)11yescharacteristic
101C22×C61#35211yescharacteristic
102C2×D61—41no—
103C2×D61—41no—
104C2×D61—82no—
105C2×D61—81no—
106C2×D61—81no—
107C2×D61—161no—
108#6923—162no—
109C4×C61—21no—
110C4×C61—21no—
111C4×C61—41no—
112C4×C61—41no—
113C4×C61—82no—
114Dic61—41no—
115Dic61—41no—
116C2×#354—611no—
117#1888—611no—
118#1533—611no—
119C2×C61—21no—
120C2×C61—21no—
121C2×C61—21no—
122C2×C61#139011yescharacteristic
123D61—81no—
124D61—81no—
125C2×#124—611no—
126#519#692311yescharacteristic, complemented
127#432—1221no—
128#418—1221no—
129C2×#101—611no—
130C2×#99—1221no—
131#354—612no—
132#354—1221no—
133#339—1221no—
134#329—612no—
135#329—1221no—
136C61#748111yescharacteristic, complemented, Sylow
137C22×Q8C2×#692311yescharacteristic
138C22×D4—611no—
139C2×M16—1221no—
140#124—611no—
141#124—611no—
142#124—611no—
143#124—611no—
144#124—2441no—
145C4×Q8—42no—
146#117—21no—
147#117—41no—
148C2×C22⋊C4—2441no—
149C2×C22⋊C4—2441no—
150C2×C42—611no—
151C4⋊C8—2441no—
152#102—2442no—
153#101—2441no—
154#99—1222no—
155#99—2441no—
156C22⋊C8—2441no—
157#97—1222no—
158C24—1221no—
159C2×Q8—21no—
160C2×Q8—41no—
161C2×Q8—41no—
162C2×Q8C4×#692311yescharacteristic
163C2×Q8C4⋊#692311yescharacteristic
164C2×D4—611no—
165C2×D4—611no—
166C2×D4—1221no—
167C2×D4—2441no—
168C2×D4—2441no—
169C22×C4—21no—
170C22×C4—1221no—
171C22×C4—4881no—
172C22×C4C22⋊#692311yescharacteristic
173M16—2441no—
174M16—2441no—
175C2×C8—2441no—
176C2×C8—2442no—
177C4⋊C4—22no—
178C4⋊C4—42no—
179C22⋊C4—41no—
180C22⋊C4—4881no—
181C22⋊C4—2441no—
182C22⋊C4—2441no—
183C22⋊C4—2441no—
184C22⋊C4—2441no—
185C22⋊C4—2442no—
186C42—41no—
187C42—42no—
188C42—611no—
189C42—611no—
190C42—1221no—
191C23—1221no—
192C23—1221no—
193C23—4882no—
194C23—2441no—
195C23—2441no—
196C23#1451983511yescharacteristic
197Q8—41no—
198Q8—41no—
199Q8—42no—
200D4—4881no—
201D4—2441no—
202D4—2441no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—42no—
210C2×C4—1221no—
211C2×C4—1221no—
212C2×C4—9762no—
213C2×C4—4882no—
214C2×C4—4881no—
215C2×C4(C2×#6923)⋊C411yescharacteristic
216C2×C4#1451983611yescharacteristic
217C8—4881no—
218C8—4882no—
219C22—41no—
220C22—9761no—
221C22—4881no—
222C22—4881no—
223C22—4882no—
224C22—2441no—
225C22—2441no—
226C22#1684064011yescharacteristic
227C22#1684066211yescharacteristic
228C22#1684066411yescharacteristic
229C4—21no—
230C4—21no—
231C4—41no—
232C4—41no—
233C4—82no—
234C4—9762no—
235C4—2441no—
236C4—2441no—
237C2—21no—
238C2—21no—
239C2—21no—
240C2—4881no—
241C2—4881no—
242C2#2146090311yescharacteristic
subgroupG/H
centerC2#21460903
commutatorC2×Q8×C61C42
FrattiniC22×Q8C2×#6923
FittingC61×#519C4
socleC2×C61#1390
prime radicalC22×D244D4
cosocleC2×#14519766C22
hypercenter#519#6923
hypocenterC61#7481
LCSG ▷ C2×Q8×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C22×Q8 ◁ #519

Complements

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

NH ≅ G/Ntype
7. #16840668C4semidirect
9. #16840618C4semidirect
12. C2×#14519696C4semidirect
14. C61×#519C4semidirect
126. #519#6923semidirect
136. C61#7481semidirect

Maximal subgroups

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

subgroupindex
C2×#168406682
#214613002
#214462222
#748161