Finite Group Databasebeta

← #30595183

Subgroups — #30595183

Order 15616.

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

normal subgroups only

This group has 280 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×#16840670C211yesmaximal, characteristic
2#21461298C211yesmaximal, characteristic
3#21446205C211yesmaximal, characteristic
4#16840782—21no—
5C2×#14519838—21no—
6#16840670—21no—
7#16840670C412yescomplemented
8#16840617—21no—
9#16840617C412yescomplemented
10C2×#14519764C2211yescharacteristic
11#16840237C411yescharacteristic
12#16839772—21no—
13#16839523—21no—
14C2×#100×C61C411yescharacteristic
15C2×#11758217—41no—
16#14519844—41no—
17#14519838—22no—
18#14519838—41no—
19C22⋊#92420—41no—
20#14519832—22no—
21C22×Dic122D411yescharacteristic
22#14519764—41no—
23#14519764C2×C411yescharacteristic
24#14519764C2×C411yescharacteristic
25#14519764D411yescharacteristic
26#14519764Q811yescharacteristic
27D4×Dic61—42no—
28#14519736—21no—
29C2×C22⋊Dic61—41no—
30C2×C22⋊Dic61—41no—
31C2×C4×Dic61D411yescharacteristic
32#14519702—42no—
33C22×D4×C61C2×C411yescharacteristic
34C2×M16×C61—21no—
35#100×C61—41no—
36C24×C61—21no—
37C2×D4×C61—21no—
38C2×D4×C61—41no—
39C2×D4×C61—41no—
40C2×D4×C61C4211yescharacteristic
41C2×D4×C61C4⋊C411yescharacteristic
42C22×C4×C61C22⋊C411yescharacteristic
43C22×Dic61—21no—
44C22×Dic61—21no—
45C22×Dic61—42no—
46C2×Dic122—21no—
47C2×Dic122—41no—
48C2×Dic122—41no—
49C2×Dic122C22⋊C411yescharacteristic
50C2×Dic122C4⋊C411yescharacteristic
51#11758217—42no—
52#11758217—81no—
53C2×#92420—42no—
54C2×#92420—81no—
55M16×C61—41no—
56M16×C61—41no—
57C2×C8×C61—41no—
58C22⋊Dic61—41no—
59C22⋊Dic61—41no—
60C22⋊Dic61—41no—
61C22⋊Dic61—41no—
62C22⋊Dic61—41no—
63C22⋊Dic61—42no—
64C4⋊Dic61—22no—
65C4×Dic61—21no—
66C4×Dic61—41no—
67C4×Dic61C22⋊C411yescharacteristic
68C4×Dic61C4⋊C411yescharacteristic
69C23×C61—21no—
70C23×C61—21no—
71C23×C61—41no—
72C23×C61—41no—
73C23×C61—82no—
74C23×C61#9911yescharacteristic
75D4×C61—41no—
76D4×C61—41no—
77D4×C61—42no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61#9511yescharacteristic
81C2×C4×C61#9911yescharacteristic
82C2×Dic61—21no—
83C2×Dic61—21no—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—41no—
87C2×Dic61—41no—
88C2×Dic61—42no—
89C2×Dic61—81no—
90C2×Dic61—162no—
91Dic122—41no—
92Dic122—41no—
93Dic122—81no—
94#92420—82no—
95#92420—82no—
96C8×C61—81no—
97#7495—611nomaximal, Sylow
98C22×C61—41no—
99C22×C61—41no—
100C22×C61—41no—
101C22×C61—81no—
102C22×C61—81no—
103C22×C61—82no—
104C22×C61—161no—
105C22×C61#34211yescharacteristic
106C22×C61AΣL(1,𝔽16)11yescharacteristic
107C22×C61#35211yescharacteristic
108C4×C61—21no—
109C4×C61—21no—
110Dic61—41no—
111Dic61—41no—
112Dic61—41no—
113Dic61—41no—
114Dic61—82no—
115C2×#355—611no—
116#1885—611no—
117#1533—611no—
118C2×C61—21no—
119C2×C61—21no—
120C2×C61—21no—
121C2×C61—81no—
122C2×C61—81no—
123C2×C61#139011yescharacteristic
124C2×#124—611no—
125#518—611no—
126#432—1221no—
127#419—1221no—
128C2×#101—1221no—
129C2×#100#692311yescharacteristic
130#355—612no—
131#355—1221no—
132#339—1221no—
133#329—612no—
134#329—1221no—
135C61#749511yescharacteristic, complemented, Sylow
136C22×Q8—611no—
137C22×D4C2×#692311yescharacteristic
138C2×M16—21no—
139C2×M16—2441no—
140#124—611no—
141#124—611no—
142#124—611no—
143#124—611no—
144#124—2441no—
145C4×D4—2442no—
146#117—1221no—
147C2×C22⋊C4—2441no—
148C2×C22⋊C4—2441no—
149C2×C42—611no—
150C4⋊C8—2441no—
151#103—2442no—
152#101—1222no—
153#101—2441no—
154#100—41no—
155C22⋊C8—2441no—
156#97—1222no—
157C24—21no—
158C2×Q8—611no—
159C2×Q8—611no—
160C2×Q8—1221no—
161C2×Q8—2441no—
162C2×Q8—2441no—
163C2×D4—21no—
164C2×D4—41no—
165C2×D4—41no—
166C2×D4C4×#692311yescharacteristic
167C2×D4C4⋊#692311yescharacteristic
168C22×C4—1221no—
169C22×C4—1221no—
170C22×C4—2442no—
171C22×C4C22⋊#692311yescharacteristic
172M16—41no—
173M16—41no—
174M16—4881no—
175M16—2442no—
176C2×C8—41no—
177C2×C8—4881no—
178C2×C8—2442no—
179C4⋊C4—1222no—
180C22⋊C4—2441no—
181C22⋊C4—2441no—
182C22⋊C4—2441no—
183C22⋊C4—2441no—
184C22⋊C4—2441no—
185C22⋊C4—2442no—
186C42—611no—
187C42—611no—
188C42—1221no—
189C42—2441no—
190C23—21no—
191C23—21no—
192C23—41no—
193C23—41no—
194C23—82no—
195C23#1451983611yescharacteristic
196Q8—4881no—
197Q8—2441no—
198Q8—2441no—
199D4—41no—
200D4—41no—
201D4—42no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—1221no—
205C2×C4—1221no—
206C2×C4—1221no—
207C2×C4—1221no—
208C2×C4—9762no—
209C2×C4—4881no—
210C2×C4—2442no—
211C2×C4—2441no—
212C2×C4—2441no—
213C2×C4(C2×#6923)⋊C411yescharacteristic
214C2×C4#1451983511yescharacteristic
215C8—81no—
216C8—4882no—
217C8—4882no—
218C22—41no—
219C22—41no—
220C22—41no—
221C22—81no—
222C22—81no—
223C22—82no—
224C22—161no—
225C22#1684064011yescharacteristic
226C22#1684066311yescharacteristic
227C22#1684066511yescharacteristic
228C4—21no—
229C4—21no—
230C4—4882no—
231C4—2441no—
232C4—2441no—
233C4—2441no—
234C4—2441no—
235C2—21no—
236C2—21no—
237C2—21no—
238C2—81no—
239C2—81no—
240C2#2146090411yescharacteristic
subgroupG/H
centerC2#21460904
commutatorC2×D4×C61C42
FrattiniC22×D4C2×#6923
FittingC2×#100×C61C4
socleC2×C61#1390
prime radicalC22×D4×C61C2×C4
cosocleC2×#14519764C22
hypercenterC2×#100#6923
hypocenterC61#7495
LCSG ▷ C2×D4×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C22×D4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
7. #16840670C4semidirect
9. #16840617C4semidirect
135. C61#7495semidirect

Maximal subgroups

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

subgroupindex
C2×#168406702
#214612982
#214462052
#749561