Finite Group Databasebeta

← #30598141

Subgroups — #30598141

Order 15616.

1154 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 132 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#21461710C212yesmaximal, complemented
2C2×#16840606C214yesmaximal, complemented
3C22×#14519766C211yesmaximal, characteristic
4C2×C22⋊#92420C2214yes—
5#16840628—24no—
6#16840606—28no—
7C23×D244C411yescharacteristic
8C2×#14519766—28no—
9C2×#14519766—24no—
10C22×#11758198C412yes—
11C22×#11758198C2212yes—
12C22×C4×Dic61C2211yescharacteristic
13C23×Q8×C61C411yescharacteristic
14C22×#92420—24no—
15C22⋊#92420—28no—
16C24×D61C2×C412yes—
17C22×D244—24no—
18C22×D244—22no—
19C22×D244—44no—
20C23×Dic61C2×C411yescharacteristic
21C23×Dic61C2311yescharacteristic
22#14519766—232no—
23C2×#11758198—24no—
24C2×#11758198—24no—
25C2×#11758198—24no—
26C2×#11758198—24no—
27C2×#11758198—24no—
28C2×#11758198D418yes—
29C2×C4×Dic61—24no—
30C2×C4×Dic61D414yes—
31C22×Q8×C61—24no—
32C22×Q8×C61—22no—
33C22×Q8×C61—44no—
34C23×C4×C61C2×C412yes—
35C23×C4×C61C2×C411yescharacteristic
36C24×C61C22×C411yescharacteristic
37C23×D61—22no—
38C23×D61—22no—
39C23×D61—28no—
40C23×D61—44no—
41C23×D61—44no—
42C23×D61C22⋊C414yes—
43C2×Q8×C61—28no—
44C2×Q8×C61—416no—
45C2×Q8×C61—44no—
46C2×Q8×C61—44no—
47C22×C4×C61—22no—
48C22×C4×C61—24no—
49C22×C4×C61—22no—
50C22×C4×C61—22no—
51C22×C4×C61—44no—
52C22×C4×C61C22⋊C412yes—
53C22×C4×C61C22⋊C414yes—
54C22×Dic61—22no—
55C22×Dic61—24no—
56C22×Dic61—42no—
57C22×Dic61C22⋊C412yes—
58C22×Dic61C2×D412yes—
59C22×Dic61C2×D414yes—
60C2×D244—28no—
61C2×D244—416no—
62C2×D244—44no—
63C2×D244—44no—
64C2×#92420—48no—
65C2×#92420—44no—
66#11758198—216no—
67#11758198—216no—
68C4×Dic61—28no—
69C23×C61—22no—
70C23×C61—22no—
71C23×C61C2×C22⋊C412yes—
72C23×C61C2×C22⋊C411yescharacteristic
73C23×C61#13114yes—
74C22×D61—24no—
75C22×D61—28no—
76C22×D61—44no—
77C22×D61—44no—
78C22×D61—44no—
79C22×D61—44no—
80C22×D61—44no—
81C22×D61—44no—
82C22×D61—44no—
83C22×D61—44no—
84C22×D61—816no—
85Q8×C61—416no—
86C2×C4×C61—28no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—24no—
90C2×C4×C61—44no—
91C2×C4×C61—44no—
92C2×C4×C61—44no—
93C2×C4×C61#10014yes—
94C2×Dic61—24no—
95C2×Dic61—22no—
96C2×Dic61—24no—
97C2×Dic61—44no—
98C2×Dic61—44no—
99C2×Dic61#12014yes—
100D244—416no—
101#92420—84no—
102#8305—611nomaximal, Sylow
103C22×C61—28no—
104C22×C61—22no—
105C22×C61—22no—
106C22×C61#37911yescharacteristic
107C22×C61#40814yes—
108C22×C61#40812yes—
109C22×C61#41012yes—
110C22×C61C2×#10012yes—
111C2×D61—44no—
112C2×D61—44no—
113C2×D61—44no—
114C2×D61—88no—
115C2×D61—88no—
116C2×D61—88no—
117C4×C61—24no—
118C4×C61—44no—
119Dic61—24no—
120Dic61—42no—
121C22×#124—611no—
122#1817—612no—
123C2×#323—614no—
124C2×C61—24no—
125C2×C61#146914yes—
126C2×C61#178011yescharacteristic
127C2×C61#178211yescharacteristic
128C2×C61#178311yescharacteristic
129D61—84no—
130C23×Q8#692311yescharacteristic
131C23×D4—611no—
132C2×#124—1224no—
133C2×#124—1228no—
134C22×C22⋊C4—612no—
135C22×C22⋊C4—612no—
136C22×C42—611no—
137C2×C22⋊C8—614no—
138#336—1224no—
139#323—1228no—
140C61#830511yescharacteristic, complemented, Sylow
141C25—612no—
142C22×Q8—24no—
143C22×Q8—22no—
144C22×Q8—44no—
145C22×D4—1224no—
146C22×D4—1222no—
147C22×D4—2444no—
148C23×C4—611no—
149C23×C4—611no—
150C23×C4C2×#692312yes—
151C23×C4C2×#692311yescharacteristic
152C22×C8—1224no—
153#124—12232no—
154C2×C22⋊C4—618no—
155C2×C22⋊C4—1224no—
156C2×C22⋊C4—1224no—
157C2×C22⋊C4—1224no—
158C2×C22⋊C4—1224no—
159C2×C22⋊C4—1224no—
160C2×C42—614no—
161C2×C42—1224no—
162C22⋊C8—1228no—
163C24—614no—
164C24—1228no—
165C24—1222no—
166C24—1222no—
167C24—2444no—
168C24—2444no—
169C24C22×#692311yescharacteristic
170C2×Q8—28no—
171C2×Q8—416no—
172C2×Q8—44no—
173C2×Q8—44no—
174C2×D4—1228no—
175C2×D4—24416no—
176C2×D4—2444no—
177C2×D4—2444no—
178C22×C4—22no—
179C22×C4—24no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—44no—
183C22×C4—612no—
184C22×C4—614no—
185C22×C4—612no—
186C22×C4—1222no—
187C22×C4—1224no—
188C22×C4—2442no—
189C22×C4C22⋊#692312yes—
190C22×C4C22⋊#692314yes—
191C2×C8—2444no—
192C2×C8—2448no—
193C22⋊C4—12216no—
194C22⋊C4—12216no—
195C42—1228no—
196C23—22no—
197C23—22no—
198C23—1228no—
199C23—1224no—
200C23—48816no—
201C23—2444no—
202C23—2444no—
203C23—2444no—
204C23—2444no—
205C23—2444no—
206C23—2444no—
207C23—2444no—
208C23—2444no—
209C23C2×C22⋊#692312yes—
210C23C2×C22⋊#692311yescharacteristic
211C23#1451986514yes—
212Q8—416no—
213D4—24416no—
214C2×C4—28no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—24no—
218C2×C4—44no—
219C2×C4—44no—
220C2×C4—44no—
221C2×C4—614no—
222C2×C4—1224no—
223C2×C4—1224no—
224C2×C4—1222no—
225C2×C4—2444no—
226C2×C4—2444no—
227C2×C4#1451983714yes—
228C8—4884no—
229C22—28no—
230C22—22no—
231C22—22no—
232C22—4888no—
233C22—4888no—
234C22—4888no—
235C22—2444no—
236C22—2444no—
237C22—2444no—
238C22#1684070311yescharacteristic
239C22#1684073714yes—
240C22#1684073712yes—
241C22#1684074312yes—
242C22C2×#1451983712yes—
243C4—24no—
244C4—44no—
245C4—1224no—
246C4—2442no—
247C2—24no—
248C2—4884no—
249C2#2146109014yes—
250C2#2146164411yescharacteristic
251C2#2146165011yescharacteristic
252C2#2146165111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC23×Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D244C4
cosocleC23×Dic61C23
hypercenterC23×Q8#6923
hypocenterC61#8305
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×Q8

Complements

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

NH ≅ G/Ntype
1. #21461710C2semidirect
2. C2×#16840606C2semidirect
140. C61#8305semidirect

Maximal subgroups

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

subgroupindex
#214617102
C2×#168406062
C22×#145197662
#830561