Finite Group Databasebeta

← #29589562

Subgroups — #29589562

Order 15616.

380 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 79 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#21450102C211yesmaximal, characteristic
2#21444153C211yesmaximal, characteristic
3#21443768C212yesmaximal
4#21443748C212yesmaximal
5C61×#1458C211yesmaximal, characteristic
6C22×#11758196C411yescharacteristic
7#16839819—21no—
8#16839700—21no—
9#16839693—21no—
10#16839646—21no—
11#16839646—21no—
12#16839634C411yescharacteristic
13#16839634C2211yescharacteristic
14#16839625C411yescharacteristic
15#16839623C411yescharacteristic
16#16839623C2211yescharacteristic
17#16839488—21no—
18#16839486C2212yes—
19C2×#117×C61C2211yescharacteristic
20C61×#431—21no—
21C61×#324—21no—
22C61×#323C2212yes—
23C23×Dic61C2×C411yescharacteristic
24C23×Dic61C2×C411yescharacteristic
25C2×#11758196—21no—
26C2×#11758196—21no—
27C2×#11758196—21no—
28C2×#11758196—21no—
29C2×#11758196—41no—
30C2×#11758196—41no—
31C2×C22⋊Dic61C2×C411yescharacteristic
32C2×C22⋊Dic61C2×C411yescharacteristic
33C4⋊#92418—41no—
34C22⋊#92418—22no—
35#14519688—41no—
36#14519684—21no—
37#14519684—21no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44C23×C4×C61C2×C411yescharacteristic
45#117×C61—41no—
46#117×C61—41no—
47C2×C4⋊C4×C61D411yescharacteristic
48C2×C4⋊C4×C61D411yescharacteristic
49C2×C22⋊C4×C61C2×C411yescharacteristic
50C2×C22⋊C4×C61C2311yescharacteristic
51C2×C42×C61D411yescharacteristic
52C2×C42×C61D411yescharacteristic
53C4⋊C8×C61—41no—
54C22⋊C8×C61—22no—
55C4×C8×C61—41no—
56C24×C61C22×C411yescharacteristic
57C22×C4×C61—22no—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—41no—
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C2×D411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—22no—
72C22×Dic61—42no—
73C22×Dic61—41no—
74C22×Dic61—41no—
75C22×Dic61—41no—
76C2×C8×C61—42no—
77C4⋊C4×C61—41no—
78C4⋊C4×C61—41no—
79C22⋊C4×C61—41no—
80C22⋊C4×C61—41no—
81C42×C61—21no—
82C42×C61—21no—
83C42×C61—21no—
84C42×C61—21no—
85C22⋊Dic61—22no—
86C22⋊Dic61—41no—
87#11758196—42no—
88#11758196—42no—
89#11758196—42no—
90#11758196—41no—
91#11758196—41no—
92C2×#92418—42no—
93C23×C61—21no—
94C23×C61—21no—
95C23×C61—41no—
96C23×C61—41no—
97C23×C61C2×C22⋊C411yescharacteristic
98C23×C61#13112yes—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—42no—
109C2×C4×C61—42no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61#9911yescharacteristic
115C2×C4×C61#9911yescharacteristic
116C2×Dic61—22no—
117C2×Dic61—41no—
118C2×Dic61—42no—
119C2×Dic61—41no—
120C2×Dic61—42no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—82no—
131C8×C61—82no—
132#92418—82no—
133#11548—611nomaximal, Sylow
134C22×C61—21no—
135C22×C61—21no—
136C22×C61—22no—
137C22×C61—42no—
138C22×C61—42no—
139C22×C61—41no—
140C22×C61—41no—
141C22×C61#40811yescharacteristic
142C22×C61C2×#9911yescharacteristic
143C22×C61#41311yescharacteristic
144C4×C61—21no—
145C4×C61—21no—
146C4×C61—41no—
147C4×C61—41no—
148C4×C61—41no—
149C4×C61—41no—
150C4×C61—41no—
151Dic61—42no—
152Dic61—81no—
153Dic61—81no—
154Dic61—81no—
155#2484—611no—
156#1464—611no—
157#1458D6111yescharacteristic
158#1326—612no—
159#1317—612no—
160C2×C61—21no—
161C2×C61—21no—
162C2×C61—42no—
163C2×C61#146811yescharacteristic
164C2×C61#212011yescharacteristic
165C2×C61#212311yescharacteristic
166C2×#117C2×D6111yescharacteristic
167C22×C4⋊C4—611no—
168#432—1221no—
169#431—21no—
170#400—1221no—
171#398—1221no—
172#387—1221no—
173#387—1221no—
174#385—611no—
175#385—611no—
176#381—611no—
177#381—611no—
178#381—611no—
179#324—21no—
180#324—1221no—
181#323—612no—
182#323C2×D6112yes—
183C61#1154811yescharacteristic, complemented, Sylow
184C23×C4—611no—
185C23×C4—611no—
186C23×C4C4×D6111yescharacteristic
187#117—41no—
188#117—41no—
189C2×C4⋊C4—1221no—
190C2×C4⋊C4—1221no—
191C2×C4⋊C4—1221no—
192C2×C4⋊C4—1221no—
193C2×C4⋊C4—2441no—
194C2×C4⋊C4—2441no—
195C2×C4⋊C4D24411yescharacteristic
196C2×C4⋊C4C22⋊D6111yescharacteristic
197C2×C22⋊C4—611no—
198C2×C22⋊C4—611no—
199C2×C22⋊C4C4×D6111yescharacteristic
200C2×C22⋊C4C22×D6111yescharacteristic
201C2×C42D24411yescharacteristic
202C2×C42C22⋊D6111yescharacteristic
203C4⋊C8—41no—
204C4⋊C8—2441no—
205C22⋊C8—22no—
206C22⋊C8—1222no—
207#97—2441no—
208C4×C8—41no—
209#95—1221no—
210#95—1221no—
211#95—1221no—
212#95—1221no—
213#95—1221no—
214#95—1221no—
215#95—1221no—
216#95—1221no—
217C24C2×C4×D6111yescharacteristic
218C22×C4—22no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—41no—
222C22×C4—1221no—
223C22×C4—1222no—
224C22×C4—1221no—
225C22×C4—1221no—
226C22×C4—1221no—
227C22×C4—2442no—
228C22×C4—2441no—
229C22×C4—2441no—
230C22×C4—2441no—
231C22×C4#1175819811yescharacteristic
232C22×C4#1175819811yescharacteristic
233C22×C4#1175819811yescharacteristic
234C22×C4#1175819811yescharacteristic
235C22×C4C2×D24411yescharacteristic
236C22×C4C2×C22⋊D6111yescharacteristic
237C2×C8—42no—
238C2×C8—2442no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—2442no—
242C4⋊C4—2442no—
243C4⋊C4—2442no—
244C4⋊C4—2441no—
245C4⋊C4—2441no—
246C22⋊C4—41no—
247C22⋊C4—41no—
248C22⋊C4—1222no—
249C22⋊C4—2441no—
250C42—21no—
251C42—21no—
252C42—21no—
253C42—21no—
254C23—21no—
255C23—21no—
256C23—41no—
257C23—41no—
258C23C2×#1175819811yescharacteristic
259C23#1451978312yes—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—1222no—
276C2×C4—4882no—
277C2×C4—2441no—
278C2×C4—2441no—
279C2×C4—2441no—
280C2×C4—2441no—
281C2×C4—2441no—
282C2×C4—2441no—
283C2×C4—2441no—
284C2×C4—2441no—
285C2×C4—2441no—
286C2×C4—2441no—
287C2×C4—2442no—
288C2×C4—2441no—
289C2×C4—2442no—
290C2×C4#1451969111yescharacteristic
291C2×C4#1451969111yescharacteristic
292C8—82no—
293C8—4882no—
294C22—21no—
295C22—21no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22#1683972811yescharacteristic
302C22C2×#1451969111yescharacteristic
303C22#1683974411yescharacteristic
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—4881no—
312C4—4881no—
313C4—4881no—
314C4—2442no—
315C2—21no—
316C2—21no—
317C2—42no—
318C2#2144416511yescharacteristic
319C2#2144746111yescharacteristic
320C2#2144747211yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutator, prime radicalC24×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1458C2
socleC22×C61C2×#99
cosocleC2×C22⋊C4×C61C23
hypercenter#1458D61
hypocenterC61#11548
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1458

Complements

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

NH ≅ G/Ntype
183. C61#11548semidirect

Maximal subgroups

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

subgroupindex
#214501022
#214441532
#214437682
#214437482
C61×#14582
#1154861