Finite Group Databasebeta

← #29577855

Subgroups — #29577855

Order 15616.

474 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 127 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#21454900C211yesmaximal, characteristic
2#21451181C211yesmaximal, characteristic
3#21444247C212yesmaximal
4#21443679C212yesmaximal
5C61×#1801C211yesmaximal, characteristic
6C2×C4×Dic122C2211yescharacteristic
7Q8×#92418—24no—
8#16839815—22no—
9#16839815C2212yes—
10#16839701C412yes—
11#16839682C412yes—
12#16839669—21no—
13#16839658—21no—
14#16839646—22no—
15#16839628C2211yescharacteristic
16#16839492—24no—
17C2×C4×Q8×C61C2211yescharacteristic
18C61×#423C2212yes—
19C2×#101×C61—21no—
20C61×#343—21no—
21C22×Dic122C2×C411yescharacteristic
22C4×Dic122—22no—
23C4×Dic122—22no—
24C2×C4⋊Dic61—21no—
25C2×C4⋊Dic61C2×C411yescharacteristic
26C2×#11758196—22no—
27C2×#11758196—21no—
28C2×C4×Dic61—21no—
29C4⋊#92418—24no—
30C4⋊#92418—22no—
31C22⋊#92418—22no—
32C4×#92418—24no—
33C4×#92418D414yes—
34#14519684—22no—
35#14519684—22no—
36#14519684—22no—
37#14519684—21no—
38#14519684C2×C412yes—
39C22×Q8×C61D411yescharacteristic
40C2×M16×C61—22no—
41C4×Q8×C61—22no—
42C4×Q8×C61—22no—
43C2×C4⋊C4×C61C2×C412yes—
44C2×C4⋊C4×C61D411yescharacteristic
45C2×C42×C61D412yes—
46C2×C42×C61C2311yescharacteristic
47C4⋊C8×C61—22no—
48C4⋊C8×C61—22no—
49#101×C61—42no—
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—
64M16×C61—42no—
65M16×C61—42no—
66C2×C8×C61—42no—
67C4⋊C4×C61—24no—
68C4⋊C4×C61—22no—
69C42×C61—22no—
70C42×C61—22no—
71C42×C61C2×D412yes—
72C42×C61#4112yes—
73C4⋊Dic61—22no—
74C4⋊Dic61—42no—
75#11758196—44no—
76#11758196—41no—
77#11758196—41no—
78C4×Dic61—42no—
79C2×#92418—24no—
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—82no—
108#92418—44no—
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#2982—611no—
126#2581—611no—
127#1801D6111yescharacteristic
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—1224no—
138#431—612no—
139#431—1222no—
140#423C2×D6112yes—
141C2×#101—21no—
142#400—612no—
143#395—612no—
144#391—1221no—
145#389—1221no—
146#387—1222no—
147#382—611no—
148#343—21no—
149Q8⋊C8—1224no—
150C61#948411yescharacteristic, complemented, Sylow
151C22×Q8—611no—
152C22×Q8C22⋊D6111yescharacteristic
153C2×M16—22no—
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⋊C4C22⋊D6111yescharacteristic
164C2×C42—1221no—
165C2×C42D24412yes—
166C2×C42C22×D6111yescharacteristic
167C4⋊C8—22no—
168C4⋊C8—22no—
169C4⋊C8—1224no—
170C4⋊C8—1222no—
171#101—42no—
172C22⋊C8—1222no—
173C4×C8—614no—
174C4×C8—1224no—
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#1175820012yes—
185C2×Q8#1175820212yes—
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—42no—
195M16—42no—
196C2×C8—42no—
197C2×C8—1224no—
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—
208C42D4×D6112yes—
209C42#1175822412yes—
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#1451970014yes—
230C2×C4#1451973712yes—
231C2×C4#1451974711yescharacteristic
232C2×C4#1451974912yes—
233C2×C4#1451976111yescharacteristic
234C2×C4C2×#1175820011yescharacteristic
235C2×C4C2×#1175820211yescharacteristic
236C2×C4#1451979712yes—
237C8—82no—
238C8—2444no—
239C22—21no—
240C22—21no—
241C22#1683963911yescharacteristic
242C22C2×#1451970011yescharacteristic
243C22#1683975611yescharacteristic
244C4—22no—
245C4—24no—
246C4—21no—
247C4—21no—
248C4—42no—
249C4—4882no—
250C4—4881no—
251C4—2442no—
252C4#1683998912yes—
253C4#1684000112yes—
254C2—21no—
255C2—21no—
256C2#2144623511yescharacteristic
257C2#2144624011yescharacteristic
258C2#2144635411yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1801C2
socleC22×C61#386
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1801D61
hypocenterC61#9484
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1801

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
#214549002
#214511812
#214442472
#214436792
C61×#18012
#948461