Finite Group Databasebeta

← #29580643

Subgroups — #29580643

Order 15616.

492 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 85 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#21456594C211yesmaximal, characteristic
2#21455768C212yesmaximal
3#21445888C211yesmaximal, characteristic
4#21444184C212yesmaximal
5C61×#1293C211yesmaximal, characteristic
6C2×#14519756C2212yes—
7C2×#14519736C2211yescharacteristic
8#16840104—24no—
9#16840098—22no—
10#16840098—22no—
11#16840093—22no—
12#16840003—22no—
13#16839920—22no—
14#16839804—22no—
15#16839772—22no—
16C2×C22⋊#92418C2211yescharacteristic
17#16839516—22no—
18#16839487—24no—
19C61×#407C2212yes—
20C2×C22⋊C8×C61C2211yescharacteristic
21C22×Dic122D412yes—
22C2×Dic244—22no—
23C22×#92418—21no—
24#14519756—22no—
25#14519756—22no—
26#14519756—22no—
27#14519756—22no—
28#14519736—22no—
29#14519736—22no—
30C2×C4⋊Dic61D411yescharacteristic
31C2×C4⋊Dic61D411yescharacteristic
32C2×C4⋊Dic61D412yes—
33C2×#11758196—22no—
34C2×C22⋊Dic61—21no—
35C2×C22⋊Dic61—22no—
36C2×C4×Dic61—21no—
37#14519711—22no—
38#14519711—24no—
39#14519709—24no—
40#14519702—24no—
41#14519702—24no—
42#14519702—24no—
43C22⋊#92418—22no—
44C23×C4×C61C2311yescharacteristic
45C2×M16×C61—22no—
46C22×C8×C61D412yes—
47C22⋊C8×C61—22no—
48C22⋊C8×C61—22no—
49C22⋊C8×C61D414yes—
50C24×C61#4111yescharacteristic
51C22×C4×C61—42no—
52C22×C4×C61C2×D412yes—
53C22×C4×C61C2×D411yescharacteristic
54C22×C4×C61C2×D411yescharacteristic
55C22×C4×C61C2×D412yes—
56C22×Dic61—21no—
57C22×Dic61—21no—
58C22×Dic61—22no—
59C22×Dic61—22no—
60C2×Dic122—22no—
61C2×Dic122—22no—
62C2×Dic122—44no—
63M16×C61—44no—
64C2×C8×C61—22no—
65C2×C8×C61—24no—
66C2×C8×C61—42no—
67C22⋊Dic61—42no—
68C22⋊Dic61—42no—
69C22⋊Dic61—42no—
70C4⋊Dic61—22no—
71C4⋊Dic61—22no—
72C4⋊Dic61—22no—
73C4⋊Dic61—22no—
74#11758196—42no—
75#11758196—42no—
76C4×Dic61—41no—
77C4×Dic61—41no—
78C2×#92418—42no—
79C2×#92418—41no—
80Dic244—82no—
81C23×C61—22no—
82C23×C61—41no—
83C23×C61—41no—
84C23×C61#12112yes—
85C23×C61#12111yescharacteristic
86C2×C4×C61—22no—
87C2×C4×C61—24no—
88C2×C4×C61—42no—
89C2×C4×C61—41no—
90C2×C4×C61#12012yes—
91C2×C4×C61#12011yescharacteristic
92C2×C4×C61#12711yescharacteristic
93C2×Dic61—42no—
94C2×Dic61—44no—
95C2×Dic61—41no—
96C2×Dic61—41no—
97C2×Dic61—42no—
98C2×Dic61—42no—
99C2×Dic61—42no—
100C2×Dic61—82no—
101Dic122—44no—
102Dic122—44no—
103C8×C61—44no—
104C8×C61—42no—
105#92418—81no—
106#9979—611nomaximal, Sylow
107C22×C61—21no—
108C22×C61—21no—
109C22×C61—22no—
110C22×C61—22no—
111C22×C61—22no—
112C22×C61—82no—
113C22×C61#39211yescharacteristic
114C22×C61#47312yes—
115C4×C61—21no—
116C4×C61—22no—
117C4×C61#45812yes—
118Dic61—81no—
119Dic61—82no—
120Dic61—81no—
121Dic61—82no—
122#3189—611no—
123#3095—612no—
124#1818—611no—
125#1472—612no—
126#1293D6111yescharacteristic
127C2×C61—22no—
128C2×C61—42no—
129C2×C61#201711yescharacteristic
130C2×C61#202011yescharacteristic
131C2×C61#202211yescharacteristic
132C2×C22⋊Q8—612no—
133C2×#117—611no—
134#485—1224no—
135#484—1222no—
136#484—1222no—
137#483—1222no—
138#467—1222no—
139#451—1222no—
140#428—1222no—
141#419—1222no—
142#407C2×D6112yes—
143C2×C22⋊C8—611no—
144C2×C22⋊C8C2×D6111yescharacteristic
145#336—1222no—
146#324—1224no—
147C61#997911yescharacteristic, complemented, Sylow
148C22×Q8—612no—
149C23×C4C22×D6111yescharacteristic
150C2×Q16—1222no—
151C2×M16—22no—
152C22×C8—1221no—
153C22×C8D24412yes—
154C22⋊Q8—1222no—
155C22⋊Q8—1222no—
156C22⋊Q8—1222no—
157C22⋊Q8—1222no—
158#117—1222no—
159#117—1222no—
160C2×C4⋊C4—611no—
161C2×C4⋊C4—611no—
162C2×C4⋊C4—612no—
163C2×C4⋊C4—1222no—
164C2×C22⋊C4—1221no—
165C2×C22⋊C4—1222no—
166C2×C42—1221no—
167#107—1224no—
168#107—1222no—
169#106—1224no—
170#103—1224no—
171#103—1224no—
172#103—1224no—
173C22⋊C8—22no—
174C22⋊C8—22no—
175C22⋊C8—1222no—
176C22⋊C8D24414yes—
177C24#1175822611yescharacteristic
178C2×Q8—1222no—
179C2×Q8—1222no—
180C2×Q8—2444no—
181C22×C4—42no—
182C22×C4—1222no—
183C22×C4—1221no—
184C22×C4—1221no—
185C22×C4—1222no—
186C22×C4C2×D24411yescharacteristic
187C22×C4C2×D24412yes—
188C22×C4D4×D6112yes—
189C22×C4D4×D6111yescharacteristic
190Q16—4882no—
191M16—44no—
192C2×C8—22no—
193C2×C8—24no—
194C2×C8—42no—
195C2×C8—2442no—
196C2×C8—2441no—
197C4⋊C4—1222no—
198C4⋊C4—1222no—
199C4⋊C4—1222no—
200C4⋊C4—1222no—
201C4⋊C4—2442no—
202C4⋊C4—2442no—
203C22⋊C4—2442no—
204C22⋊C4—2442no—
205C22⋊C4—2442no—
206C42—2441no—
207C42—2441no—
208C23—22no—
209C23—41no—
210C23—41no—
211C23#1451975212yes—
212C23#1451975211yescharacteristic
213Q8—2444no—
214Q8—2444no—
215C2×C4—22no—
216C2×C4—24no—
217C2×C4—42no—
218C2×C4—41no—
219C2×C4—4882no—
220C2×C4—2442no—
221C2×C4—2444no—
222C2×C4—2442no—
223C2×C4—2441no—
224C2×C4—2441no—
225C2×C4—2442no—
226C2×C4—2442no—
227C2×C4#1451974712yes—
228C2×C4#1451974711yescharacteristic
229C2×C4#1451977411yescharacteristic
230C8—44no—
231C8—42no—
232C8—4881no—
233C22—21no—
234C22—21no—
235C22—22no—
236C22—22no—
237C22—22no—
238C22—82no—
239C22#1683967211yescharacteristic
240C22#1684003812yes—
241C4—22no—
242C4—21no—
243C4—4881no—
244C4—4882no—
245C4—4881no—
246C4—4882no—
247C4#1683995312yes—
248C2—22no—
249C2—42no—
250C2#2144692411yescharacteristic
251C2#2144694111yescharacteristic
252C2#2144695111yescharacteristic
subgroupG/H
centerC22#16839672
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1293C2
socleC22×C61#392
prime radicalC24×C61#41
hypercenter#1293D61
hypocenterC61#9979
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1293

Complements

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

NH ≅ G/Ntype
147. C61#9979semidirect

Maximal subgroups

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

subgroupindex
#214565942
#214557682
#214458882
#214441842
C61×#12932
#997961