Finite Group Databasebeta

← #30594014

Subgroups — #30594014

Order 15616.

476 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 50 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#21460739C212yesmaximal, complemented
2#21445728C211yesmaximal, characteristic
3C22⋊#11758187—22no—
4C23×C4×D61C411yescharacteristic
5C2×C22⋊#92418C2211yescharacteristic
6C2×#14519689—22no—
7C2×C22⋊C8×C61C411yescharacteristic
8C2×#11758187—42no—
9C24×D61C811yescharacteristic
10C23×Dic61C811yescharacteristic
11C22×C4×D61—21no—
12C22×C4×D61—21no—
13C22×C4×D61—44no—
14C22×C4×D61—41no—
15C22×C4×D61—41no—
16C22×#92418D412yes—
17C22⋊#92418—41no—
18#14519689—44no—
19C23×C4×C61C2×C411yescharacteristic
20C22×C8×C61—21no—
21C22⋊C8×C61—41no—
22C24×C61C2×C811yescharacteristic
23C23×D61—21no—
24C23×D61—21no—
25C23×D61—42no—
26C23×D61—42no—
27C23×D61—41no—
28C23×D61—41no—
29C23×D61C1612yescomplemented
30C22×C4×C61—21no—
31C22×C4×C61—21no—
32C22×C4×C61—42no—
33C22×C4×C61C22⋊C411yescharacteristic
34C22×C4×C61M1611yescharacteristic
35C22×Dic61—21no—
36C22×Dic61—42no—
37C22×Dic61—41no—
38C2×C4×D61—24no—
39C2×C4×D61—42no—
40C2×C4×D61—42no—
41C2×C4×D61—42no—
42C2×C4×D61—42no—
43C2×C4×D61—44no—
44C2×C4×D61—44no—
45C2×C4×D61—44no—
46C2×C4×D61—41no—
47C2×C4×D61—41no—
48C2×C4×D61—44no—
49C2×C8×C61—42no—
50C2×C8×C61—41no—
51C2×#92418—22no—
52C2×#92418—42no—
53#11758187—82no—
54C23×C61—21no—
55C23×C61—21no—
56C23×C61—41no—
57C23×C61—41no—
58C23×C61C22⋊C811yescharacteristic
59C23×C61C2×C1611yescharacteristic
60C23×C61M3211yescharacteristic
61C22×D61—22no—
62C22×D61—22no—
63C22×D61—22no—
64C22×D61—44no—
65C22×D61—44no—
66C22×D61—41no—
67C22×D61—41no—
68C22×D61—42no—
69C22×D61—42no—
70C22×D61—48no—
71C22×D61—42no—
72C22×D61—41no—
73C22×D61—41no—
74C22×D61—42no—
75C22×D61—42no—
76C22×D61—42no—
77C2×C4×C61—22no—
78C2×C4×C61—21no—
79C2×C4×C61—42no—
80C2×C4×C61—42no—
81C2×C4×C61—41no—
82C2×C4×C61#9911yescharacteristic
83C2×C4×C61#10011yescharacteristic
84C2×Dic61—22no—
85C2×Dic61—41no—
86C2×Dic61—42no—
87C2×Dic61—41no—
88C2×Dic61—42no—
89C4×D61—44no—
90C4×D61—48no—
91C4×D61—44no—
92C8×C61—81no—
93#92418—42no—
94#7054—611nomaximal, Sylow
95C22×C61—21no—
96C22×C61—21no—
97C22×C61—21no—
98C22×C61—21no—
99C22×C61—41no—
100C22×C61—41no—
101C22×C61—42no—
102C22×C61—41no—
103C22×C61—41no—
104C22×C61#32311yescharacteristic
105C22×C61C22⋊C1611yescharacteristic
106C22×C61#34911yescharacteristic
107C2×D61—24no—
108C2×D61—42no—
109C2×D61—42no—
110C2×D61—42no—
111C2×D61—44no—
112C2×D61—44no—
113C2×D61—44no—
114C2×D61—42no—
115C2×D61—42no—
116C2×D61—42no—
117C2×D61—44no—
118C4×C61—21no—
119C4×C61—41no—
120C4×C61AΣL(1,𝔽16)12yes—
121Dic61—42no—
122#1779—611no—
123#1314—612no—
124C2×C61—21no—
125C2×C61—21no—
126C2×C61—41no—
127C2×C61—41no—
128C2×C61#131411yescharacteristic
129C2×C61#131611yescharacteristic
130C2×C61#132011yescharacteristic
131D61—44no—
132C24×C4—611no—
133C2×C22⋊C8—611no—
134C2×C22⋊C8—1222no—
135C2×C22⋊C8#692311yescharacteristic
136C22⋊C16—1222no—
137C61#705411yescharacteristic, complemented, Sylow
138C25—611no—
139C23×C4—611no—
140C23×C4—1221no—
141C23×C4—1221no—
142C23×C4—2441no—
143C23×C4—2441no—
144C23×C4—2444no—
145C23×C4C2×#692311yescharacteristic
146C22×C8—21no—
147C22×C8—612no—
148C2×C16—2442no—
149C22⋊C8—41no—
150C22⋊C8—2444no—
151C22⋊C8—2441no—
152C24—612no—
153C24—1221no—
154C24—1221no—
155C24—2441no—
156C24—2441no—
157C24—2442no—
158C24—2442no—
159C24D61⋊C811yescharacteristic
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—42no—
163C22×C4—1224no—
164C22×C4—1221no—
165C22×C4—2442no—
166C22×C4—2442no—
167C22×C4—2442no—
168C22×C4—2442no—
169C22×C4—2444no—
170C22×C4—2444no—
171C22×C4—2444no—
172C22×C4—2444no—
173C22×C4—2442no—
174C22×C4—2441no—
175C22×C4—2441no—
176C22×C4—2441no—
177C22×C4#1175821311yescharacteristic
178C22×C4C22⋊#692311yescharacteristic
179C2×C8—42no—
180C2×C8—41no—
181C2×C8—1222no—
182C2×C8—2442no—
183C16—4882no—
184C23—21no—
185C23—21no—
186C23—41no—
187C23—41no—
188C23—1222no—
189C23—1222no—
190C23—1222no—
191C23—2442no—
192C23—2441no—
193C23—2441no—
194C23—2442no—
195C23—2444no—
196C23—2444no—
197C23—2442no—
198C23—2442no—
199C23—2442no—
200C23—2448no—
201C23—2442no—
202C23—2441no—
203C23—2441no—
204C23#1451983411yescharacteristic
205C23D61⋊C1611yescharacteristic
206C23#1451985211yescharacteristic
207C2×C4—22no—
208C2×C4—21no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—1222no—
213C2×C4—2444no—
214C2×C4—2448no—
215C2×C4—2441no—
216C2×C4—2442no—
217C2×C4—2441no—
218C2×C4—2444no—
219C2×C4—2442no—
220C2×C4#1451983611yescharacteristic
221C2×C4#1451983711yescharacteristic
222C8—81no—
223C8—2442no—
224C22—21no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—41no—
229C22—41no—
230C22—42no—
231C22—41no—
232C22—41no—
233C22—1224no—
234C22—2442no—
235C22—2442no—
236C22—2442no—
237C22—2444no—
238C22—2444no—
239C22—2444no—
240C22—2444no—
241C22—2442no—
242C22—2442no—
243C22—2442no—
244C22#1684060611yescharacteristic
245C22#1684065711yescharacteristic
246C22#1684065911yescharacteristic
247C4—21no—
248C4—41no—
249C4—2442no—
250C4#1684066312yes—
251C2—21no—
252C2—21no—
253C2—41no—
254C2—41no—
255C2—2444no—
256C2#2146074011yescharacteristic
257C2#2146074411yescharacteristic
258C2#2146075211yescharacteristic
subgroupG/H
centerC2×C4#14519836
commutatorC23×C61C2×C16
FrattiniC23×C4C2×#6923
FittingC2×C22⋊C8×C61C4
socleC22×C61#323
prime radicalC24×D61C8
cosocleC2×C22⋊#92418C22
hypercenterC2×C22⋊C8#6923
hypocenterC61#7054
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #21460739C2semidirect
29. C23×D61C16semidirect
137. C61#7054semidirect

Maximal subgroups

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

subgroupindex
#214607392
#214457282
#705461