Finite Group Databasebeta

← #29590588

Subgroups — #29590588

Order 15616.

480 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 87 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#21450811C211yesmaximal, characteristic
2C4×#14519692C211yesmaximal, characteristic
3#21443820C214yesmaximal, complemented
4C61×#1465C211yesmaximal, characteristic
5C2×#14519777C411yescharacteristic, complemented
6C2×#14519764—21no—
7C2×#14519692—21no—
8#16839687C412yescomplemented
9#16839687C2212yes—
10#16839667—21no—
11#16839622—21no—
12#16839622—21no—
13C4×C4⋊Dic61C411yescharacteristic, complemented
14C4×C22⋊Dic61—21no—
15#16839529C2212yes—
16C2×C4×D4×C61C2211yescharacteristic
17C61×#407—21no—
18C61×#324—21no—
19C61×#323C2212yes—
20C22×Dic122—21no—
21#14519777—41no—
22#14519777—41no—
23#14519764—44no—
24C2×C4⋊Dic61—21no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61C2×C412yes—
27C2×C22⋊Dic61—22no—
28C2×C22⋊Dic61—22no—
29C2×C22⋊Dic61—22no—
30C2×C4×Dic61—21no—
31C2×C4×Dic61—41no—
32#14519692—24no—
33#14519684—22no—
34#14519684—22no—
35#14519684—41no—
36#14519684C2×C412yes—
37C22×D4×C61D411yescharacteristic
38C23×C4×C61D411yescharacteristic
39C23×C4×C61D411yescharacteristic
40C2×M16×C61—41no—
41C4×D4×C61—41no—
42C4×D4×C61—41no—
43C2×C4⋊C4×C61D411yescharacteristic
44C2×C22⋊C4×C61C2×C411yescharacteristic
45C2×C22⋊C4×C61C2311yescharacteristic
46C2×C42×C61C2×C411yescharacteristic
47C22⋊C8×C61—22no—
48C22⋊C8×C61—41no—
49C24×C61C22⋊C411yescharacteristic
50C24×C61C2×D411yescharacteristic
51C2×D4×C61—22no—
52C2×D4×C61—22no—
53C2×D4×C61—41no—
54C22×C4×C61—21no—
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61—42no—
59C22×C4×C61—42no—
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22×C411yescharacteristic
64C22×C4×C61C2×D411yescharacteristic
65C22×Dic61—22no—
66C22×Dic61—22no—
67C22×Dic61—42no—
68C2×Dic122—42no—
69C2×Dic122—42no—
70C2×Dic122—42no—
71M16×C61—82no—
72C2×C8×C61—42no—
73C4⋊C4×C61—41no—
74C22⋊C4×C61—41no—
75C22⋊C4×C61—41no—
76C42×C61—21no—
77C42×C61—21no—
78C22⋊Dic61—24no—
79C22⋊Dic61—44no—
80C22⋊Dic61—42no—
81C22⋊Dic61—44no—
82C4⋊Dic61—42no—
83C4⋊Dic61—41no—
84C4⋊Dic61—41no—
85C4⋊Dic61—42no—
86C4×Dic61—42no—
87C4×Dic61—82no—
88C23×C61—21no—
89C23×C61—21no—
90C23×C61—21no—
91C23×C61—21no—
92C23×C61—21no—
93C23×C61—41no—
94C23×C61—41no—
95C23×C61—41no—
96C23×C61—41no—
97C23×C61C2×C22⋊C411yescharacteristic
98C23×C61AGL(1,ℤ/8)12yes—
99D4×C61—44no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—22no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—42no—
107C2×C4×C61—42no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—81no—
112C2×C4×C61—81no—
113C2×C4×C61#9911yescharacteristic
114C2×C4×C61#9911yescharacteristic
115C2×C4×C61#10412yes—
116C2×Dic61—42no—
117C2×Dic61—44no—
118C2×Dic61—42no—
119C2×Dic61—42no—
120C2×Dic61—42no—
121C2×Dic61—42no—
122C2×Dic61—42no—
123C2×Dic61—82no—
124C2×Dic61—82no—
125Dic122—84no—
126C8×C61—82no—
127#11777—611nomaximal, Sylow
128C22×C61—21no—
129C22×C61—21no—
130C22×C61—22no—
131C22×C61—42no—
132C22×C61—42no—
133C22×C61—41no—
134C22×C61—41no—
135C22×C61—41no—
136C22×C61—41no—
137C22×C61—41no—
138C22×C61—81no—
139C22×C61—81no—
140C22×C61C2×#9911yescharacteristic
141C22×C61#41811yescharacteristic
142C22×C61C2×#10411yescharacteristic
143C4×C61—21no—
144C4×C61—22no—
145C4×C61—41no—
146C4×C61—41no—
147C4×C61—41no—
148C4×C61#35412yes—
149Dic61—82no—
150Dic61—84no—
151Dic61—82no—
152#2547—611no—
153C4×#99—611no—
154#1465D6111yescharacteristic
155#1344—614no—
156C2×C61—21no—
157C2×C61—21no—
158C2×C61—42no—
159C2×C61—81no—
160C2×C61#150711yescharacteristic
161C2×C61#212311yescharacteristic
162C2×C61C2×#35411yescharacteristic
163C2×C4⋊Q8—611no—
164C2×#124—1221no—
165C2×C4×D4C2×D6111yescharacteristic
166C2×#99—1221no—
167#407—21no—
168#397—612no—
169#397—612no—
170#391—1221no—
171#380—1221no—
172#380—1221no—
173C4×C4⋊C4—611no—
174C4×C22⋊C4—1221no—
175#342—612no—
176#324—21no—
177#323C2×D6112yes—
178C61#1177711yescharacteristic, complemented, Sylow
179C22×Q8—1221no—
180C22×D4D24411yescharacteristic
181C23×C4D24411yescharacteristic
182C23×C4C22⋊D6111yescharacteristic
183C2×M16—41no—
184C4⋊Q8—2441no—
185C4⋊Q8—2441no—
186#124—2444no—
187C4×D4—41no—
188C4×D4—41no—
189C2×C4⋊C4—612no—
190C2×C4⋊C4—1221no—
191C2×C4⋊C4—1221no—
192C2×C4⋊C4C22⋊D6111yescharacteristic
193C2×C22⋊C4—1222no—
194C2×C22⋊C4—1222no—
195C2×C22⋊C4—1222no—
196C2×C22⋊C4C4×D6111yescharacteristic
197C2×C22⋊C4C22×D6111yescharacteristic
198C2×C42—1221no—
199C2×C42—2441no—
200C2×C42C4×D6111yescharacteristic
201#99—1224no—
202C22⋊C8—22no—
203C22⋊C8—41no—
204#95—612no—
205#95—1222no—
206#95—1222no—
207#95—2441no—
208C24#1175819811yescharacteristic
209C24C2×D24411yescharacteristic
210C2×Q8—2442no—
211C2×Q8—2442no—
212C2×Q8—2442no—
213C2×D4—22no—
214C2×D4—22no—
215C2×D4—41no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—1222no—
223C22×C4—1222no—
224C22×C4—2442no—
225C22×C4#1175819811yescharacteristic
226C22×C4#1175819811yescharacteristic
227C22×C4#1175819811yescharacteristic
228C22×C4C2×C4×D6111yescharacteristic
229C22×C4C2×C22⋊D6111yescharacteristic
230M16—82no—
231C2×C8—42no—
232C4⋊C4—41no—
233C4⋊C4—2442no—
234C4⋊C4—2442no—
235C4⋊C4—2441no—
236C4⋊C4—2441no—
237C22⋊C4—41no—
238C22⋊C4—41no—
239C22⋊C4—1224no—
240C22⋊C4—2444no—
241C22⋊C4—2442no—
242C22⋊C4—2444no—
243C42—21no—
244C42—21no—
245C42—4882no—
246C42—2442no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—41no—
253C23—41no—
254C23—41no—
255C23—41no—
256C23C2×#1175819811yescharacteristic
257C23#1451980512yes—
258Q8—4884no—
259D4—44no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—4882no—
274C2×C4—4882no—
275C2×C4—2444no—
276C2×C4—2442no—
277C2×C4—2442no—
278C2×C4—2442no—
279C2×C4—2442no—
280C2×C4—2442no—
281C2×C4—2442no—
282C2×C4#1451969111yescharacteristic
283C2×C4#1451969111yescharacteristic
284C2×C4#1451970312yes—
285C8—82no—
286C22—21no—
287C22—21no—
288C22—22no—
289C22—42no—
290C22—42no—
291C22—41no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—41no—
296C22—81no—
297C22—81no—
298C22C2×#1451969111yescharacteristic
299C22#1683976811yescharacteristic
300C22C2×#1451970311yescharacteristic
301C4—21no—
302C4—22no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—4882no—
307C4—4884no—
308C4—4882no—
309C4#1683955612yes—
310C2—21no—
311C2—21no—
312C2—42no—
313C2—81no—
314C2#2144433611yescharacteristic
315C2#2144747411yescharacteristic
316C2C2×#1683955611yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1465C2
socleC22×C61C2×#99
prime radicalC22×D4×C61D4
cosocleC2×C22⋊C4×C61C23
hypercenter#1465D61
hypocenterC61#11777
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
3. #21443820C2semidirect
5. C2×#14519777C4semidirect
8. #16839687C4semidirect
13. C4×C4⋊Dic61C4semidirect
178. C61#11777semidirect

Maximal subgroups

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

subgroupindex
#214508112
C4×#145196922
#214438202
C61×#14652
#1177761