Finite Group Databasebeta

← #30594166

Subgroups — #30594166

Order 15616.

476 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 76 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#21460657C212yesmaximal
2#21444089C211yesmaximal, characteristic
3C2×C22⋊#92420—22no—
4C23×Dic122C411yescharacteristic
5C2×#14519684—22no—
6C2×#14519684C2211yescharacteristic
7C2×#95×C61C411yescharacteristic
8C22×#92420—42no—
9C22⋊#92420—24no—
10C22⋊#92420—42no—
11C22×Dic122—21no—
12C22×Dic122—41no—
13C22×Dic122—41no—
14C22×Dic122—44no—
15C22×Dic122C812yescomplemented
16C23×Dic61—21no—
17C23×Dic61D412yes—
18#14519684—41no—
19#14519684—44no—
20C23×C4×C61—21no—
21C23×C4×C61C2×C411yescharacteristic
22#95×C61—41no—
23C24×C61C22⋊C411yescharacteristic
24C22×C4×C61—21no—
25C22×C4×C61—21no—
26C22×C4×C61—22no—
27C22×C4×C61—42no—
28C22×C4×C61—41no—
29C22×C4×C61—42no—
30C22×C4×C61—41no—
31C22×C4×C61—42no—
32C22×C4×C61C2×C811yescharacteristic
33C22×C4×C61M1611yescharacteristic
34C22×Dic61—24no—
35C22×Dic61—22no—
36C22×Dic61—22no—
37C22×Dic61—22no—
38C22×Dic61—42no—
39C22×Dic61—41no—
40C22×Dic61—41no—
41C22×Dic61—42no—
42C22×Dic61—42no—
43C22×Dic61SD1612yes—
44C22×Dic61Q1612yes—
45C2×Dic122—44no—
46C2×Dic122—42no—
47C2×Dic122—44no—
48C2×Dic122—48no—
49C2×Dic122—42no—
50C2×Dic122—44no—
51C2×Dic122—44no—
52C2×#92420—44no—
53C2×#92420—82no—
54C2×#92420—82no—
55C23×C61—22no—
56C23×C61—21no—
57C23×C61—21no—
58C23×C61C22⋊C811yescharacteristic
59C23×C61#9911yescharacteristic
60C23×C61#10011yescharacteristic
61C23×C61#10312yes—
62C23×C61#10412yes—
63C2×C4×C61—21no—
64C2×C4×C61—21no—
65C2×C4×C61—42no—
66C2×C4×C61—42no—
67C2×C4×C61—41no—
68C2×C4×C61—41no—
69C2×C4×C61—42no—
70C2×C4×C61—44no—
71C2×C4×C61—81no—
72C2×C4×C61—82no—
73C2×C4×C61—81no—
74C2×Dic61—24no—
75C2×Dic61—22no—
76C2×Dic61—22no—
77C2×Dic61—42no—
78C2×Dic61—44no—
79C2×Dic61—42no—
80C2×Dic61—42no—
81C2×Dic61—44no—
82C2×Dic61—42no—
83C2×Dic61—42no—
84C2×Dic61—42no—
85C2×Dic61—82no—
86Dic122—48no—
87Dic122—44no—
88Dic122—44no—
89#92420—84no—
90#7131—611nomaximal, Sylow
91C22×C61—21no—
92C22×C61—21no—
93C22×C61—21no—
94C22×C61—21no—
95C22×C61—22no—
96C22×C61—22no—
97C22×C61—22no—
98C22×C61—22no—
99C22×C61#32311yescharacteristic
100C22×C61Q8⋊C812yes—
101C22×C61#32812yes—
102C22×C61#32911yescharacteristic
103C22×C61#33311yescharacteristic
104C22×C61AΣL(1,𝔽16)12yes—
105C22×C61#35411yescharacteristic
106C22×C61#35611yescharacteristic
107C4×C61—41no—
108C4×C61—41no—
109C4×C61—82no—
110Dic61—44no—
111Dic61—42no—
112Dic61—42no—
113#1446—611no—
114#1280—612no—
115C2×C61—21no—
116C2×C61—22no—
117C2×C61—21no—
118C2×C61#127211yescharacteristic
119C2×C61#131611yescharacteristic
120C2×C61#131911yescharacteristic
121C2×C61#135112yes—
122C2×C61#135412yes—
123C23×Q8—611no—
124C2×C22⋊C8—1222no—
125C2×#95—611no—
126C2×#95—1222no—
127C2×#95#692311yescharacteristic
128C61#713111yescharacteristic, complemented, Sylow
129C22×Q8—612no—
130C22×Q8—1221no—
131C22×Q8—2441no—
132C22×Q8—2441no—
133C22×Q8—2444no—
134C23×C4—21no—
135C23×C4—612no—
136C23×C4—1221no—
137C23×C4C2×#692311yescharacteristic
138C22×C8—2442no—
139C22⋊C8—1224no—
140C22⋊C8—2442no—
141#95—41no—
142#95—2441no—
143#95—2444no—
144C24C22⋊#692311yescharacteristic
145C2×Q8—2442no—
146C2×Q8—2442no—
147C2×Q8—2444no—
148C2×Q8—2444no—
149C2×Q8—2448no—
150C2×Q8—2444no—
151C2×Q8—2444no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—22no—
155C22×C4—42no—
156C22×C4—42no—
157C22×C4—41no—
158C22×C4—41no—
159C22×C4—42no—
160C22×C4—612no—
161C22×C4—612no—
162C22×C4—1222no—
163C22×C4—1224no—
164C22×C4—1222no—
165C22×C4—1222no—
166C22×C4—2442no—
167C22×C4—2442no—
168C22×C4—2442no—
169C22×C4—2441no—
170C22×C4—2441no—
171C22×C4D61⋊C811yescharacteristic
172C22×C4#1175821311yescharacteristic
173C2×C8—4882no—
174C2×C8—4882no—
175C2×C8—2444no—
176C23—22no—
177C23—21no—
178C23—21no—
179C23#1451983411yescharacteristic
180C23#1451983611yescharacteristic
181C23#1451983711yescharacteristic
182C23#1451984012yes—
183C23#1451984112yes—
184Q8—2444no—
185Q8—2448no—
186Q8—2444no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—42no—
194C2×C4—44no—
195C2×C4—81no—
196C2×C4—82no—
197C2×C4—81no—
198C2×C4—1224no—
199C2×C4—1222no—
200C2×C4—1222no—
201C2×C4—4882no—
202C2×C4—2444no—
203C2×C4—2442no—
204C2×C4—2442no—
205C2×C4—2442no—
206C2×C4—2444no—
207C2×C4—2442no—
208C2×C4—2442no—
209C2×C4—2442no—
210C8—4884no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—22no—
216C22—22no—
217C22—22no—
218C22—22no—
219C22#1684060611yescharacteristic
220C22#1684061212yes—
221C22#1684061512yes—
222C22#1684061711yescharacteristic
223C22#1684062211yescharacteristic
224C22#1684066312yes—
225C22#1684066911yescharacteristic
226C22#1684067311yescharacteristic
227C4—41no—
228C4—41no—
229C4—82no—
230C4—2444no—
231C4—2442no—
232C4—2442no—
233C2—21no—
234C2—22no—
235C2—21no—
236C2#2146064011yescharacteristic
237C2#2146074411yescharacteristic
238C2#2146075011yescharacteristic
239C2#2146081312yes—
240C2#2146081912yes—
subgroupG/H
centerC23#14519836
commutatorC22×C4×C61C2×C8
FrattiniC23×C4C2×#6923
FittingC2×#95×C61C4
socleC23×C61#99
prime radicalC24×C61C22⋊C4
cosocleC2×#14519684C22
hypercenterC2×#95#6923
hypocenterC61#7131
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
15. C22×Dic122C8semidirect
128. C61#7131semidirect

Maximal subgroups

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

subgroupindex
#214606572
#214440892
#713161