Finite Group Databasebeta

← #30598235

Subgroups — #30598235

Order 15616.

826 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 826 conjugacy classes of subgroups — too many to draw. Only its 120 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#21461546C212yesmaximal
2C2×#16840619C214yesmaximal, complemented
3C2×#125×D61C211yesmaximal, characteristic
4C2×#14519834—22no—
5C2×#14519832C2214yes—
6#16840628—22no—
7#16840619—28no—
8C2×#14519769C411yescharacteristic
9C2×#14519768C2212yes—
10C2×#14519767—22no—
11#125×D61—28no—
12C2×C4⋊C4×D61—22no—
13C2×C4⋊C4×D61C412yes—
14C2×C42×D61C2211yescharacteristic
15C2×#125×C61C411yescharacteristic
16C22×#92420—24no—
17#14519834—28no—
18#14519832—28no—
19C22×C4×D61—22no—
20C22×C4×D61C2×C411yescharacteristic
21C22×C4×D61D412yes—
22#14519769—24no—
23#14519768—24no—
24#14519768D418yes—
25#14519767—216no—
26C2×C4⋊Dic61—22no—
27C2×C4⋊Dic61C2×C412yes—
28C2×#11758196—22no—
29C2×#11758196—22no—
30C2×#11758196—22no—
31C4⋊C4×D61—216no—
32C4⋊C4×D61—24no—
33C4⋊C4×D61—24no—
34C2×C4×Dic61D412yes—
35C2×C4×Dic61C2311yescharacteristic
36C42×D61—24no—
37#125×C61—24no—
38C2×C4⋊C4×C61—22no—
39C2×C4⋊C4×C61C2×C412yes—
40C2×C42×C61C2×C411yescharacteristic
41C23×D61C22⋊C411yescharacteristic
42C22×C4×C61—22no—
43C22×C4×C61C22⋊C412yes—
44C22×C4×C61C22×C411yescharacteristic
45C22×Dic61—22no—
46C22×Dic61C22⋊C411yescharacteristic
47C22×Dic61C2×D412yes—
48C2×C4×D61—22no—
49C2×C4×D61—22no—
50C2×C4×D61—22no—
51C2×C4×D61—28no—
52C2×C4×D61—24no—
53C2×C4×D61—24no—
54C2×C4×D61—42no—
55C2×C4×D61—44no—
56C2×C4×D61—44no—
57C2×#92420—28no—
58C2×#92420—44no—
59C2×#92420—44no—
60C4⋊C4×C61—28no—
61C4⋊C4×C61—22no—
62C4⋊C4×C61C22⋊C414yes—
63C42×C61—22no—
64C4⋊Dic61—22no—
65C4⋊Dic61—28no—
66C4⋊Dic61C22⋊C414yes—
67#11758196—28no—
68#11758196—28no—
69#11758196—28no—
70C4×Dic61—24no—
71C4×Dic61C2×D414yes—
72C23×C61C2×C22⋊C411yescharacteristic
73C22×D61—21no—
74C22×D61—21no—
75C22×D61—22no—
76C22×D61#10112yes—
77C22×D61#10414yes—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—22no—
81C2×C4×C61—24no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61—42no—
85C2×C4×C61—42no—
86C2×C4×C61C2×C22⋊C412yes—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—24no—
92C2×Dic61—42no—
93C2×Dic61—42no—
94C2×Dic61#10112yes—
95C2×Dic61#12014yes—
96C4×D61—28no—
97C4×D61—48no—
98C4×D61—416no—
99#92420—48no—
100#8335—611nomaximal, Sylow
101C22×C61#37911yescharacteristic
102C22×C61C2×#10111yescharacteristic
103C22×C61C2×#10111yescharacteristic
104C22×C61C2×#10412yes—
105C22×C61#42112yes—
106C2×D61—24no—
107C2×D61—22no—
108C2×D61—24no—
109C2×D61—22no—
110C2×D61#33014yescomplemented
111C4×C61—22no—
112C4×C61—42no—
113C4×C61—44no—
114Dic61—22no—
115Dic61—24no—
116Dic61—44no—
117C22×#125—611no—
118#1749—612no—
119C2×#330—614no—
120C2×C61C2×#33011yescharacteristic
121C2×C61#152812yes—
122C2×C61#153411yescharacteristic
123C2×C61#178411yescharacteristic
124C2×C61#178912yes—
125D61—24no—
126C2×#125—612no—
127C2×#125—611no—
128C2×#125—1222no—
129C2×#125—1228no—
130C2×#125#692311yescharacteristic
131C22×C4⋊C4—612no—
132C22×C4⋊C4—1222no—
133C22×C42—611no—
134C2×C22⋊C8—1222no—
135C2×#97—614no—
136#336—1222no—
137#330—1228no—
138C61#833511yescharacteristic, complemented, Sylow
139C23×C4—611no—
140C23×C4—612no—
141C23×C4—1222no—
142C22×C8—1224no—
143#125—24no—
144#125—618no—
145#125—1224no—
146#125—1224no—
147#125—12216no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—612no—
150C2×C4⋊C4—1224no—
151C2×C4⋊C4—12216no—
152C2×C4⋊C4—1222no—
153C2×C4⋊C4—1222no—
154C2×C4⋊C4—1222no—
155C2×C4⋊C4—1222no—
156C2×C4⋊C4—1224no—
157C2×C4⋊C4C2×#692312yes—
158C2×C42—611no—
159C2×C42—612no—
160C2×C42—1224no—
161C2×C42C2×#692311yescharacteristic
162C22⋊C8—1228no—
163#97—1228no—
164C24—611no—
165C22×C4—22no—
166C22×C4—612no—
167C22×C4—611no—
168C22×C4—1222no—
169C22×C4—1224no—
170C22×C4—1222no—
171C22×C4—1224no—
172C22×C4—1228no—
173C22×C4—1222no—
174C22×C4—1222no—
175C22×C4—2442no—
176C22×C4—2444no—
177C22×C4—2444no—
178C22×C4C22⋊#692312yes—
179C22×C4C22×#692311yescharacteristic
180C2×C8—1228no—
181C2×C8—2444no—
182C2×C8—2444no—
183C4⋊C4—28no—
184C4⋊C4—22no—
185C4⋊C4—614no—
186C4⋊C4—1228no—
187C4⋊C4—1228no—
188C4⋊C4—1228no—
189C4⋊C4—1228no—
190C4⋊C4—1222no—
191C4⋊C4C22⋊#692314yes—
192C42—22no—
193C42—614no—
194C42—1224no—
195C23—612no—
196C23—614no—
197C23—1221no—
198C23—1222no—
199C23—1221no—
200C23C2×C22⋊#692311yescharacteristic
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—24no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—612no—
210C2×C4—614no—
211C2×C4—1228no—
212C2×C4—1221no—
213C2×C4—1222no—
214C2×C4—1222no—
215C2×C4—1221no—
216C2×C4—1224no—
217C2×C4—2448no—
218C2×C4—24416no—
219C2×C4—2442no—
220C2×C4—2442no—
221C2×C4C2×C22⋊#692312yes—
222C8—2448no—
223C22—614no—
224C22—1224no—
225C22—1222no—
226C22—1222no—
227C22—1224no—
228C22#1684070311yescharacteristic
229C22D61⋊#10111yescharacteristic
230C22D61⋊#10111yescharacteristic
231C22D61⋊#10412yes—
232C22#1684075912yes—
233C4—22no—
234C4—42no—
235C4—44no—
236C4—1222no—
237C4—1224no—
238C4—2444no—
239C2—1224no—
240C2D61⋊#33011yescharacteristic
241C2#2146128212yes—
242C2#2146130211yescharacteristic
243C2#2146165411yescharacteristic
244C2#2146166112yes—
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#125×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×#125#6923
hypocenterC61#8335
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. C2×#16840619C2semidirect
110. C2×D61#330semidirect
138. C61#8335semidirect

Maximal subgroups

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

subgroupindex
#214615462
C2×#168406192
C2×#125×D612
#833561