Finite Group Databasebeta

← #30599220

Subgroups — #30599220

Order 15616.

786 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 786 conjugacy classes of subgroups — too many to draw. Only its 108 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#21461642C212yesmaximal
2#21460657C214yesmaximal, complemented
3C2×#16839624C211yesmaximal, characteristic
4C2×#14519834—24no—
5C2×C22⋊#92420C2214yes—
6C23×C4×D61C2211yescharacteristic
7C22×#11758198C412yes—
8#16839624—24no—
9C2×#14519684C411yescharacteristic
10C2×#14519684C2212yes—
11C2×#95×C61C411yescharacteristic
12C22×#92420—24no—
13#14519834—48no—
14C22⋊#92420—28no—
15C24×D61C2×C411yescharacteristic
16C23×Dic61C2×C412yes—
17C23×Dic61C2311yescharacteristic
18C22×C4×D61—24no—
19C22×C4×D61—44no—
20C22×C4×D61D414yes—
21C2×#11758198—22no—
22C2×#11758198—22no—
23C2×#11758198—44no—
24#14519684—22no—
25#14519684—24no—
26C23×C4×C61C2×C412yes—
27C23×C4×C61C2×C411yescharacteristic
28#95×C61—22no—
29C24×C61C22×C411yescharacteristic
30C23×D61—22no—
31C23×D61—24no—
32C23×D61—22no—
33C23×D61—22no—
34C23×D61—42no—
35C23×D61C22⋊C412yes—
36C22×C4×C61—22no—
37C22×C4×C61—22no—
38C22×C4×C61—24no—
39C22×C4×C61—42no—
40C22×C4×C61—42no—
41C22×C4×C61—42no—
42C22×C4×C61C22⋊C412yes—
43C22×Dic61—22no—
44C22×Dic61—24no—
45C22×Dic61—42no—
46C22×Dic61—42no—
47C22×Dic61—42no—
48C22×Dic61C2×D412yes—
49C22×Dic61#4114yes—
50C2×C4×D61—28no—
51C2×C4×D61—28no—
52C2×C4×D61—44no—
53C2×C4×D61—416no—
54C2×#92420—48no—
55C2×#92420—44no—
56#11758198—44no—
57#11758198—44no—
58C23×C61—22no—
59C23×C61—22no—
60C23×C61C2×C22⋊C411yescharacteristic
61C23×C61#11712yes—
62C23×C61#13112yes—
63C23×C61#13112yes—
64C22×D61—28no—
65C22×D61—22no—
66C22×D61—22no—
67C22×D61—22no—
68C22×D61—22no—
69C22×D61—22no—
70C22×D61—22no—
71C22×D61—48no—
72C22×D61—48no—
73C22×D61—44no—
74C22×D61—44no—
75C22×D61#9914yes—
76C2×C4×C61—22no—
77C2×C4×C61—24no—
78C2×C4×C61—44no—
79C2×C4×C61—42no—
80C2×C4×C61—42no—
81C2×C4×C61—42no—
82C2×C4×C61—84no—
83C2×Dic61—24no—
84C2×Dic61—44no—
85C2×Dic61—42no—
86C2×Dic61—42no—
87C2×Dic61—42no—
88C2×Dic61—84no—
89C2×Dic61#12314yes—
90C4×D61—416no—
91#92420—84no—
92#8702—611nomaximal, Sylow
93C22×C61—22no—
94C22×C61—22no—
95C22×C61—24no—
96C22×C61—24no—
97C22×C61#38111yescharacteristic
98C22×C61#40811yescharacteristic
99C22×C61#40811yescharacteristic
100C22×C61C2×#9912yes—
101C22×C61#41312yes—
102C22×C61#43314yes—
103C2×D61—24no—
104C2×D61—24no—
105C2×D61—24no—
106C2×D61—416no—
107C2×D61—42no—
108C2×D61—42no—
109C2×D61—42no—
110C2×D61—42no—
111C4×C61—42no—
112C4×C61—82no—
113Dic61—24no—
114Dic61—82no—
115C2×#381—611no—
116#1779—612no—
117#1280—614no—
118C2×C61—24no—
119C2×C61#146812yes—
120C2×C61#146812yes—
121C2×C61#181811yescharacteristic
122C2×C61#181911yescharacteristic
123C2×C61#182211yescharacteristic
124D61—44no—
125C24×C4—611no—
126C22×C22⋊C4—612no—
127C2×C22⋊C8—614no—
128C2×C22⋊C8—1224no—
129#381—1224no—
130C2×#95—612no—
131C2×#95—611no—
132C2×#95#692311yescharacteristic
133C61#870211yescharacteristic, complemented, Sylow
134C25—611no—
135C23×C4—611no—
136C23×C4—614no—
137C23×C4—612no—
138C23×C4—1224no—
139C23×C4—2444no—
140C23×C4C2×#692312yes—
141C23×C4C2×#692311yescharacteristic
142C22×C8—1224no—
143C2×C22⋊C4—1222no—
144C2×C22⋊C4—1222no—
145C2×C22⋊C4—2444no—
146C22⋊C8—1228no—
147C22⋊C8—2448no—
148#95—22no—
149#95—1224no—
150#95—1222no—
151C24—612no—
152C24—1224no—
153C24—1222no—
154C24—1222no—
155C24—1222no—
156C24—2442no—
157C24C22×#692311yescharacteristic
158C22×C4—22no—
159C22×C4—22no—
160C22×C4—24no—
161C22×C4—42no—
162C22×C4—42no—
163C22×C4—42no—
164C22×C4—612no—
165C22×C4—614no—
166C22×C4—1228no—
167C22×C4—1228no—
168C22×C4—1224no—
169C22×C4—1222no—
170C22×C4—2444no—
171C22×C4—24416no—
172C22×C4—2442no—
173C22×C4—2442no—
174C22×C4—2442no—
175C22×C4C22⋊#692312yes—
176C2×C8—2444no—
177C2×C8—2448no—
178C22⋊C4—2444no—
179C22⋊C4—2444no—
180C23—22no—
181C23—22no—
182C23—614no—
183C23—1228no—
184C23—1222no—
185C23—1222no—
186C23—1222no—
187C23—1222no—
188C23—1222no—
189C23—1222no—
190C23—2448no—
191C23—2448no—
192C23—2444no—
193C23—2444no—
194C23C2×C22⋊#692311yescharacteristic
195C23#1451985612yes—
196C23#1451986412yes—
197C23#1451986512yes—
198C2×C4—22no—
199C2×C4—24no—
200C2×C4—44no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—84no—
205C2×C4—614no—
206C2×C4—1224no—
207C2×C4—4884no—
208C2×C4—24416no—
209C2×C4—2444no—
210C2×C4—2442no—
211C2×C4—2442no—
212C2×C4—2442no—
213C8—4884no—
214C22—24no—
215C22—24no—
216C22—22no—
217C22—22no—
218C22—1224no—
219C22—1224no—
220C22—1224no—
221C22—24416no—
222C22—2442no—
223C22—2442no—
224C22—2442no—
225C22—2442no—
226C22#1684070511yescharacteristic
227C22#1684073611yescharacteristic
228C22#1684073711yescharacteristic
229C22D61⋊#9912yes—
230C22#1684074812yes—
231C22#1684078714yes—
232C4—42no—
233C4—82no—
234C4—1224no—
235C4—4882no—
236C2—24no—
237C2—2444no—
238C2#2146108512yes—
239C2#2146108712yes—
240C2#2146171311yescharacteristic
241C2#2146171511yescharacteristic
242C2#2146172011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC2×#95×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×D61C2×C4
cosocleC23×Dic61C23
hypercenterC2×#95#6923
hypocenterC61#8702
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
2. #21460657C2semidirect
133. C61#8702semidirect

Maximal subgroups

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

subgroupindex
#214616422
#214606572
C2×#168396242
#870261