Finite Group Databasebeta

← #29577877

Subgroups — #29577877

Order 15616.

454 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 115 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×#2983C211yesmaximal, 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
18C61×#446—24no—
19C61×#432—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—
48#97×C61—24no—
49C4×C8×C61D414yes—
50C2×Q8×C61—22no—
51C2×Q8×C61—21no—
52C2×Q8×C61—21no—
53C2×Q8×C61—22no—
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—41no—
73C4⋊Dic61—41no—
74#11758196—44no—
75#11758196—41no—
76#11758196—41no—
77C4×Dic61—42no—
78#11758194—42no—
79#11758194—42no—
80C2×#92418—42no—
81C23×C61C2×C22⋊C411yescharacteristic
82Q8×C61—42no—
83Q8×C61—42no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—41no—
89C2×C4×C61—41no—
90C2×C4×C61—42no—
91C2×C4×C61C4×D412yes—
92C2×C4×C61#12011yescharacteristic
93C2×C4×C61#12112yes—
94C2×C4×C61#12311yescharacteristic
95C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
96C2×C4×C61#13712yes—
97C2×C4×C61#13711yescharacteristic
98C2×Dic61—22no—
99C2×Dic61—41no—
100C2×Dic61—41no—
101C2×Dic61—42no—
102C2×Dic61—42no—
103C2×Dic61—42no—
104C2×Dic61—41no—
105C2×Dic61—42no—
106Dic122—24no—
107Dic122—42no—
108C8×C61—44no—
109#92418—82no—
110#9488—611nomaximal, Sylow
111C22×C61—21no—
112C22×C61—21no—
113C22×C61#38611yescharacteristic
114C22×C61#41711yescharacteristic
115C22×C61#41911yescharacteristic
116C4×C61—22no—
117C4×C61—21no—
118C4×C61—21no—
119C4×C61—42no—
120C4×C61—42no—
121C4×C61#46812yes—
122C4×C61#47012yes—
123Dic61—42no—
124Dic61—82no—
125Dic61—81no—
126#2983D6111yescharacteristic
127#2581—611no—
128#1801—611no—
129#1487—612no—
130#1286—612no—
131C2×C61—21no—
132C2×C61—21no—
133C2×C61#189111yescharacteristic
134C2×C61#189411yescharacteristic
135C2×C61#191211yescharacteristic
136C2×C4×Q8—611no—
137C2×C4×Q8C2×D6111yescharacteristic
138#446—24no—
139#432—22no—
140#431C2×D6112yes—
141#423—612no—
142C2×#101—1221no—
143#400—612no—
144#395—612no—
145#391—1221no—
146#389—1221no—
147#387—1222no—
148#382—611no—
149#343—1221no—
150Q8⋊C8—1224no—
151C61#948811yescharacteristic, complemented, Sylow
152C22×Q8—611no—
153C22×Q8D24411yescharacteristic
154C2×M16—1222no—
155C4×Q8—22no—
156C4×Q8—22no—
157C4×Q8—1222no—
158C4×Q8—1222no—
159C2×C4⋊C4—611no—
160C2×C4⋊C4—1222no—
161C2×C4⋊C4—1221no—
162C2×C4⋊C4—1221no—
163C2×C4⋊C4C4×D6112yes—
164C2×C4⋊C4D24411yescharacteristic
165C2×C42—1221no—
166C2×C42C22⋊D6112yes—
167C2×C42C22×D6111yescharacteristic
168C4⋊C8—24no—
169C4⋊C8—22no—
170C4⋊C8—1222no—
171C4⋊C8—1222no—
172#101—2442no—
173C22⋊C8—22no—
174#97—24no—
175C4×C8C22⋊D6114yes—
176#95—612no—
177#95—1222no—
178#95—1222no—
179#95—1222no—
180#95—1221no—
181C2×Q8—21no—
182C2×Q8—22no—
183C2×Q8—22no—
184C2×Q8—21no—
185C2×Q8—1222no—
186C2×Q8—2442no—
187C22×C4—1221no—
188C22×C4—1222no—
189C22×C4—1221no—
190C22×C4#1175819812yes—
191C22×C4#1175819812yes—
192C22×C4C2×C4×D6111yescharacteristic
193C22×C4C2×D24411yescharacteristic
194C22×C4C2×C22⋊D6111yescharacteristic
195M16—2442no—
196M16—2442no—
197C2×C8—24no—
198C2×C8—2442no—
199C4⋊C4—24no—
200C4⋊C4—22no—
201C4⋊C4—1222no—
202C4⋊C4—2444no—
203C4⋊C4—2441no—
204C4⋊C4—2441no—
205C4⋊C4—2441no—
206C4⋊C4—2441no—
207C42—22no—
208C42—22no—
209C42—2442no—
210C42#1175822212yes—
211C42C2×C22⋊D6112yes—
212C23C2×#1175819811yescharacteristic
213Q8—42no—
214Q8—42no—
215Q8—1224no—
216Q8—2442no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—1222no—
225C2×C4—2442no—
226C2×C4—2442no—
227C2×C4—2442no—
228C2×C4—2442no—
229C2×C4—2441no—
230C2×C4—2441no—
231C2×C4—2441no—
232C2×C4C4×C22⋊D6112yes—
233C2×C4#1451974611yescharacteristic
234C2×C4#1451975112yes—
235C2×C4#1451976011yescharacteristic
236C2×C4#1451980511yescharacteristic
237C2×C4#1451981012yes—
238C2×C4#1451981011yescharacteristic
239C8—44no—
240C8—4882no—
241C22—21no—
242C22—21no—
243C22#1683964111yescharacteristic
244C22#1683976411yescharacteristic
245C22#1683977211yescharacteristic
246C4—22no—
247C4—21no—
248C4—21no—
249C4—42no—
250C4—42no—
251C4—4882no—
252C4—4881no—
253C4—2442no—
254C4#1684000812yes—
255C4#1684002012yes—
256C2—21no—
257C2—21no—
258C2#2144623711yescharacteristic
259C2#2144625211yescharacteristic
260C2#2144635611yescharacteristic
subgroupG/H
centerC22#16839641
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2983C2
socleC22×C61#386
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#2983D61
hypocenterC61#9488
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
151. C61#9488semidirect

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×#29832
#948861