Finite Group Databasebeta

← #29576041

Subgroups — #29576041

Order 15616.

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

normal subgroups only

This group has 478 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#21451585C211yesmaximal, characteristic
2#21444492C212yesmaximal, complemented
3#21444133C211yesmaximal, characteristic
4#21443679C212yesmaximal, complemented
5C61×#2921C211yesmaximal, characteristic
6C2×#14519777C2211yescharacteristic
7C2×#14519756—21no—
8#16839815C2212yes—
9#16839692—21no—
10#16839692C412yes—
11#16839687—21no—
12#16839687C412yes—
13#16839668—21no—
14#16839628C2211yescharacteristic
15#16839509—24no—
16#16839488—21no—
17#16839486—21no—
18C2×#117×C61C2211yescharacteristic
19C61×#433—24no—
20C61×#423C2212yes—
21C61×#407—21no—
22C4×M16×C61—21no—
23C22×Dic122—21no—
24#14519777—22no—
25#14519777—22no—
26#14519756—44no—
27C2×C4⋊Dic61—21no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61C2×C412yes—
30C2×#11758196—22no—
31C2×C22⋊Dic61—22no—
32C4⋊#92418—22no—
33C22⋊#92418—22no—
34C4×#92418—22no—
35#14519684—22no—
36#14519684—22no—
37#14519684—21no—
38#14519684C2×C412yes—
39C23×C4×C61D411yescharacteristic
40C2×M16×C61—22no—
41#117×C61—22no—
42#117×C61—22no—
43C2×C4⋊C4×C61C2×C411yescharacteristic
44C2×C4⋊C4×C61D411yescharacteristic
45C2×C22⋊C4×C61C2×C411yescharacteristic
46C2×C22⋊C4×C61D411yescharacteristic
47C2×C42×C61D411yescharacteristic
48C2×C42×C61C2311yescharacteristic
49C4⋊C8×C61—22no—
50C4⋊C8×C61D414yes—
51C22⋊C8×C61—24no—
52#97×C61—22no—
53C4×C8×C61—22no—
54C24×C61C22⋊C411yescharacteristic
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61—22no—
58C22×C4×C61—22no—
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22×C411yescharacteristic
63C22×C4×C61C2×D411yescharacteristic
64C22×C4×C61C2×D411yescharacteristic
65C22×Dic61—22no—
66C22×Dic61—22no—
67C2×Dic122—41no—
68C2×Dic122—41no—
69C2×Dic122—42no—
70C2×Dic122—42no—
71M16×C61—42no—
72M16×C61—42no—
73C2×C8×C61—24no—
74C4⋊C4×C61—22no—
75C4⋊C4×C61—22no—
76C22⋊C4×C61—22no—
77C22⋊C4×C61—22no—
78C42×C61—21no—
79C42×C61—21no—
80C42×C61C2×D412yes—
81C42×C61#4112yes—
82C22⋊Dic61—44no—
83C4⋊Dic61—24no—
84C4⋊Dic61—42no—
85C4⋊Dic61—42no—
86#11758196—44no—
87C2×#92418—42no—
88C23×C61—21no—
89C23×C61—21no—
90C23×C61—21no—
91C23×C61—41no—
92C23×C61—41no—
93C23×C61C2×C22⋊C411yescharacteristic
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61—42no—
102C2×C4×C61—42no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61C4×D412yes—
106C2×C4×C61#12011yescharacteristic
107C2×C4×C61#12112yes—
108C2×C4×C61#12311yescharacteristic
109C2×C4×C61#13512yes—
110C2×C4×C61AGL(1,ℤ/8)12yes—
111C2×Dic61—42no—
112C2×Dic61—42no—
113C2×Dic61—42no—
114C2×Dic61—42no—
115C2×Dic61—42no—
116C2×Dic61—42no—
117Dic122—82no—
118Dic122—82no—
119C8×C61—44no—
120#92418—82no—
121#9196—611nomaximal, Sylow
122C22×C61—21no—
123C22×C61—21no—
124C22×C61—42no—
125C22×C61—41no—
126C22×C61—41no—
127C22×C61—41no—
128C22×C61—81no—
129C22×C61#38611yescharacteristic
130C22×C61#41611yescharacteristic
131C22×C61#41811yescharacteristic
132C4×C61—22no—
133C4×C61—22no—
134C4×C61—41no—
135C4×C61—41no—
136C4×C61—41no—
137C4×C61#44912yes—
138C4×C61#48212yes—
139Dic61—82no—
140Dic61—82no—
141#2921D6111yescharacteristic
142#2621—611no—
143#1546—612no—
144#1458—611no—
145#1286—612no—
146C2×C61—21no—
147C2×C61—21no—
148C2×C61—81no—
149C2×C61#187511yescharacteristic
150C2×C61#190911yescharacteristic
151C2×C61#191511yescharacteristic
152C2×C4⋊Q8—611no—
153C2×C22⋊Q8—1221no—
154C2×#117C2×D6111yescharacteristic
155#433—24no—
156#431—612no—
157#423C2×D6112yes—
158#407—21no—
159C4×M16—21no—
160#398—612no—
161#398—1221no—
162#397—612no—
163#397—1221no—
164#391—1221no—
165#382—611no—
166#332—1224no—
167#324—1221no—
168#323—1221no—
169C61#919611yescharacteristic, complemented, Sylow
170C22×Q8—1221no—
171C23×C4C22⋊D6111yescharacteristic
172C2×M16—22no—
173C4⋊Q8—1222no—
174C4⋊Q8—1222no—
175C22⋊Q8—2444no—
176#117—22no—
177#117—22no—
178C2×C4⋊C4—612no—
179C2×C4⋊C4—1222no—
180C2×C4⋊C4—1221no—
181C2×C4⋊C4—1221no—
182C2×C4⋊C4C4×D6111yescharacteristic
183C2×C4⋊C4D24411yescharacteristic
184C2×C22⋊C4—1222no—
185C2×C22⋊C4C4×D6111yescharacteristic
186C2×C22⋊C4D24411yescharacteristic
187C2×C42C22⋊D6111yescharacteristic
188C2×C42C22×D6111yescharacteristic
189C4⋊C8—22no—
190C4⋊C8—1222no—
191C4⋊C8C22⋊D6114yes—
192C22⋊C8—24no—
193C22⋊C8—1222no—
194#97—22no—
195C4×C8—22no—
196C4×C8—1222no—
197#95—612no—
198#95—1222no—
199#95—1222no—
200#95—1221no—
201C24#1175819811yescharacteristic
202C2×Q8—2441no—
203C2×Q8—2441no—
204C2×Q8—2442no—
205C2×Q8—2442no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—1222no—
211C22×C4—1222no—
212C22×C4#1175819811yescharacteristic
213C22×C4#1175819811yescharacteristic
214C22×C4#1175819811yescharacteristic
215C22×C4C2×C4×D6111yescharacteristic
216C22×C4C2×D24411yescharacteristic
217C22×C4C2×C22⋊D6111yescharacteristic
218M16—42no—
219M16—42no—
220C2×C8—24no—
221C2×C8—2442no—
222C4⋊C4—22no—
223C4⋊C4—22no—
224C4⋊C4—1224no—
225C4⋊C4—2444no—
226C4⋊C4—2442no—
227C4⋊C4—2442no—
228C22⋊C4—22no—
229C22⋊C4—22no—
230C22⋊C4—2444no—
231C42—21no—
232C42—21no—
233C42#1175822212yes—
234C42C2×C22⋊D6112yes—
235C23—21no—
236C23—21no—
237C23—21no—
238C23—41no—
239C23—41no—
240C23C2×#1175819811yescharacteristic
241Q8—4882no—
242Q8—4882no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—2442no—
255C2×C4—2442no—
256C2×C4—2442no—
257C2×C4—2442no—
258C2×C4—2442no—
259C2×C4—2442no—
260C2×C4C4×C22⋊D6112yes—
261C2×C4#1451974611yescharacteristic
262C2×C4#1451975112yes—
263C2×C4#1451976011yescharacteristic
264C2×C4#1451979712yes—
265C2×C4#1451980212yes—
266C8—44no—
267C8—4882no—
268C22—21no—
269C22—21no—
270C22—42no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—81no—
275C22#1683964111yescharacteristic
276C22#1683975611yescharacteristic
277C22#1683976611yescharacteristic
278C4—22no—
279C4—22no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—4882no—
284C4—4882no—
285C4#1683990712yes—
286C4#1684008612yes—
287C2—21no—
288C2—21no—
289C2—81no—
290C2#2144614111yescharacteristic
291C2#2144634111yescharacteristic
292C2#2144637111yescharacteristic
subgroupG/H
centerC22#16839641
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2921C2
socleC22×C61#386
prime radicalC24×C61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#2921D61
hypocenterC61#9196
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2921

Complements

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

NH ≅ G/Ntype
2. #21444492C2semidirect
4. #21443679C2semidirect
169. C61#9196semidirect

Maximal subgroups

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

subgroupindex
#214515852
#214444922
#214441332
#214436792
C61×#29212
#919661