Finite Group Databasebeta

← #29577857

Subgroups — #29577857

Order 15616.

474 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 131 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#21451181C211yesmaximal, characteristic
2#21445815C211yesmaximal, characteristic
3#21444249C212yesmaximal
4#21443678C212yesmaximal
5C61×#2982C211yesmaximal, characteristic
6C2×C4×Dic122C2211yescharacteristic
7#16839786C2212yes—
8C2×#14519696—21no—
9#16839701C412yes—
10#16839682C412yes—
11#16839669—21no—
12#16839658—21no—
13#16839646—22no—
14#16839628C2211yescharacteristic
15#16839531—21no—
16#16839494—24no—
17C2×C4×Q8×C61C2211yescharacteristic
18C8×Q8×C61—24no—
19C61×#431—22no—
20C61×#431C2212yes—
21C22×Dic122C2×C411yescharacteristic
22C2×#11758194—22no—
23C4×Dic122—22no—
24C4×Dic122—22no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61C2×C411yescharacteristic
27C2×#11758196—22no—
28C2×#11758196—21no—
29C2×C4×Dic61—21no—
30C4⋊#92418—22no—
31C4⋊#92418—22no—
32#14519696—42no—
33#14519684—22no—
34#14519684—22no—
35#14519684—22no—
36#14519684—21no—
37#14519684C2×C412yes—
38C22×Q8×C61D411yescharacteristic
39C4×Q8×C61—22no—
40C4×Q8×C61—22no—
41C2×C4⋊C4×C61C2×C412yes—
42C2×C4⋊C4×C61D411yescharacteristic
43C2×C42×C61D412yes—
44C2×C42×C61C2311yescharacteristic
45C4⋊C8×C61—24no—
46C4⋊C8×C61—22no—
47C22⋊C8×C61—22no—
48C4×C8×C61—24no—
49C4×C8×C61D414yes—
50C2×Q8×C61—22no—
51C2×Q8×C61—22no—
52C2×Q8×C61SD1612yes—
53C2×Q8×C61Q1612yes—
54C22×C4×C61C22⋊C412yes—
55C22×C4×C61C22⋊C412yes—
56C22×C4×C61C22×C411yescharacteristic
57C22×C4×C61C2×D411yescharacteristic
58C22×C4×C61C2×D411yescharacteristic
59C22×Dic61—21no—
60C22×Dic61—22no—
61C22×Dic61—21no—
62C2×Dic122—22no—
63C2×Dic122—42no—
64C2×C8×C61—24no—
65C4⋊C4×C61—24no—
66C4⋊C4×C61—22no—
67C42×C61—22no—
68C42×C61—22no—
69C42×C61C2×D412yes—
70C42×C61#4112yes—
71C4⋊Dic61—22no—
72C4⋊Dic61—42no—
73#11758196—44no—
74#11758196—41no—
75#11758196—41no—
76C4×Dic61—42no—
77#11758194—42no—
78#11758194—42no—
79C2×#92418—42no—
80C23×C61C2×C22⋊C411yescharacteristic
81Q8×C61—24no—
82Q8×C61—24no—
83C2×C4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—41no—
87C2×C4×C61—41no—
88C2×C4×C61—42no—
89C2×C4×C61#10314yes—
90C2×C4×C61C4×D412yes—
91C2×C4×C61#12011yescharacteristic
92C2×C4×C61#12112yes—
93C2×C4×C61#12311yescharacteristic
94C2×C4×C61C2×SD1611yescharacteristic
95C2×C4×C61C2×Q1611yescharacteristic
96C2×C4×C61#13512yes—
97C2×Dic61—22no—
98C2×Dic61—41no—
99C2×Dic61—41no—
100C2×Dic61—42no—
101C2×Dic61—42no—
102C2×Dic61—42no—
103C2×Dic61—41no—
104C2×Dic61—42no—
105Dic122—24no—
106Dic122—42no—
107C8×C61—44no—
108#92418—82no—
109#9484—611nomaximal, Sylow
110C22×C61—21no—
111C22×C61—21no—
112C22×C61#38611yescharacteristic
113C22×C61C2×#10311yescharacteristic
114C22×C61#41611yescharacteristic
115C4×C61—22no—
116C4×C61—24no—
117C4×C61—21no—
118C4×C61—21no—
119C4×C61—42no—
120C4×C61#46512yes—
121C4×C61#46712yes—
122Dic61—42no—
123Dic61—82no—
124Dic61—81no—
125#2982D6111yescharacteristic
126#2581—611no—
127#1801—611no—
128#1487—612no—
129#1286—612no—
130C2×C61—21no—
131C2×C61—21no—
132C2×C61#189111yescharacteristic
133C2×C61#189211yescharacteristic
134C2×C61#191211yescharacteristic
135C2×C4×Q8—611no—
136C2×C4×Q8C2×D6111yescharacteristic
137C8×Q8—24no—
138#431—22no—
139#431C2×D6112yes—
140#423—612no—
141C2×#101—1221no—
142#400—612no—
143#395—612no—
144#391—1221no—
145#389—1221no—
146#387—1222no—
147#382—611no—
148#343—1221no—
149Q8⋊C8—1224no—
150C61#948411yescharacteristic, complemented, Sylow
151C22×Q8—611no—
152C22×Q8D24411yescharacteristic
153C2×M16—1222no—
154C4×Q8—22no—
155C4×Q8—22no—
156C4×Q8—1222no—
157C4×Q8—1222no—
158C2×C4⋊C4—611no—
159C2×C4⋊C4—1222no—
160C2×C4⋊C4—1221no—
161C2×C4⋊C4—1221no—
162C2×C4⋊C4C4×D6112yes—
163C2×C4⋊C4D24411yescharacteristic
164C2×C42—1221no—
165C2×C42C22⋊D6112yes—
166C2×C42C22×D6111yescharacteristic
167C4⋊C8—24no—
168C4⋊C8—22no—
169C4⋊C8—1222no—
170C4⋊C8—1222no—
171#101—2442no—
172C22⋊C8—22no—
173C4×C8—24no—
174C4×C8C22⋊D6114yes—
175#95—612no—
176#95—1222no—
177#95—1222no—
178#95—1222no—
179#95—1221no—
180C2×Q8—22no—
181C2×Q8—22no—
182C2×Q8—1222no—
183C2×Q8—2442no—
184C2×Q8#1175819012yes—
185C2×Q8Dic24412yes—
186C22×C4—1221no—
187C22×C4—1222no—
188C22×C4—1221no—
189C22×C4#1175819812yes—
190C22×C4#1175819812yes—
191C22×C4C2×C4×D6111yescharacteristic
192C22×C4C2×D24411yescharacteristic
193C22×C4C2×C22⋊D6111yescharacteristic
194M16—2442no—
195M16—2442no—
196C2×C8—24no—
197C2×C8—2442no—
198C4⋊C4—24no—
199C4⋊C4—22no—
200C4⋊C4—1222no—
201C4⋊C4—2444no—
202C4⋊C4—2441no—
203C4⋊C4—2441no—
204C4⋊C4—2442no—
205C42—22no—
206C42—22no—
207C42—2442no—
208C42#1175822212yes—
209C42C2×C22⋊D6112yes—
210C23C2×#1175819811yescharacteristic
211Q8—24no—
212Q8—24no—
213Q8—1224no—
214Q8—2442no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—42no—
221C2×C4—1222no—
222C2×C4—2442no—
223C2×C4—2442no—
224C2×C4—2442no—
225C2×C4—2442no—
226C2×C4—2441no—
227C2×C4—2441no—
228C2×C4—2441no—
229C2×C4#1451970214yes—
230C2×C4C4×C22⋊D6112yes—
231C2×C4#1451974611yescharacteristic
232C2×C4#1451975112yes—
233C2×C4#1451976011yescharacteristic
234C2×C4C2×#1175819011yescharacteristic
235C2×C4C2×Dic24411yescharacteristic
236C2×C4#1451979912yes—
237C8—44no—
238C8—4882no—
239C22—21no—
240C22—21no—
241C22#1683964111yescharacteristic
242C22C2×#1451970211yescharacteristic
243C22#1683975911yescharacteristic
244C4—22no—
245C4—24no—
246C4—21no—
247C4—21no—
248C4—42no—
249C4—4882no—
250C4—4881no—
251C4—2442no—
252C4#1683999112yes—
253C4#1684000312yes—
254C2—21no—
255C2—21no—
256C2#2144623711yescharacteristic
257C2#2144624211yescharacteristic
258C2#2144635611yescharacteristic
subgroupG/H
centerC22#16839641
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2982C2
socleC22×C61#386
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#2982D61
hypocenterC61#9484
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2982

Complements

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

NH ≅ G/Ntype
150. C61#9484semidirect

Maximal subgroups

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

subgroupindex
#214511812
#214458152
#214442492
#214436782
C61×#29822
#948461