Finite Group Databasebeta

← #29589496

Subgroups — #29589496

Order 15616.

504 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 75 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#21448542C211yesmaximal, characteristic
2#21444156C212yesmaximal, complemented
3#21443763C211yesmaximal, characteristic, complemented
4#21443750C212yesmaximal, complemented
5C61×#1324C211yesmaximal, characteristic, complemented
6C2×#14519774C411yescharacteristic
7C2×#14519739C411yescharacteristic
8C2×#14519739C2211yescharacteristic
9#16839724—22no—
10#16839663C411yescharacteristic
11#16839663C2211yescharacteristic
12#16839640—22no—
13#16839640—22no—
14#16839608C411yescharacteristic
15#16839488C2212yes—
16#16839485—22no—
17C61×#382C2211yescharacteristic
18C61×#324C2212yes—
19C22×D244—22no—
20C22×D244C2×C411yescharacteristic
21C22×D244C2×C411yescharacteristic
22C22×C4×D61—21no—
23C22×C4×D61D412yes—
24C2×#11758189—42no—
25#14519774—22no—
26#14519774—22no—
27#14519739—42no—
28#14519739—42no—
29C2×#11758198—21no—
30C2×#11758198—22no—
31C2×#11758198—22no—
32C2×#11758198D412yes—
33C2×C4×Dic61C2×C411yescharacteristic
34C2×C4×Dic61C2×C411yescharacteristic
35C22⋊#92418—22no—
36#14519689—42no—
37#14519684—21no—
38#14519684—21no—
39C2×C4⋊C4×C61C2×C411yescharacteristic
40C2×C4⋊C4×C61C2311yescharacteristic
41C2×C42×C61C2×C411yescharacteristic
42C22⋊C8×C61—22no—
43#95×C61—22no—
44C23×D61—21no—
45C23×D61C22⋊C412yes—
46C22×C4×C61—21no—
47C22×C4×C61—21no—
48C22×C4×C61C22×C411yescharacteristic
49C22×C4×C61C2×D412yes—
50C22×Dic61—21no—
51C22×Dic61C22⋊C411yescharacteristic
52C22×Dic61C22⋊C411yescharacteristic
53C2×D244—21no—
54C2×D244—21no—
55C2×D244—21no—
56C2×D244—28no—
57C2×D244—41no—
58C2×D244—41no—
59C2×D244—41no—
60C2×D244—41no—
61C2×D244—82no—
62C2×D244—82no—
63C2×D244M1612yescomplemented
64C2×C4×D61—22no—
65C2×C4×D61—22no—
66C2×C4×D61—42no—
67C2×C4×D61—82no—
68C2×C4×D61—82no—
69C2×C8×C61—42no—
70C4⋊C4×C61—41no—
71C4⋊C4×C61—41no—
72C42×C61—21no—
73C42×C61M1612yescomplemented
74#11758198—42no—
75#11758198—42no—
76#11758198—82no—
77#11758198—82no—
78C4×Dic61—22no—
79C4×Dic61—41no—
80C2×#92418—42no—
81#11758189—84no—
82C23×C61C2×C22⋊C411yescharacteristic
83C22×D61—22no—
84C22×D61—22no—
85C22×D61—22no—
86C22×D61—22no—
87C22×D61—42no—
88C22×D61—42no—
89C22×D61—42no—
90C22×D61—42no—
91C22×D61—41no—
92C22×D61—41no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—22no—
96C2×C4×C61—22no—
97C2×C4×C61—41no—
98C2×C4×C61—41no—
99C2×C4×C61—42no—
100C2×C4×C61—42no—
101C2×C4×C61—41no—
102C2×C4×C61C2×M1611yescharacteristic
103C2×C4×C61C2×M1611yescharacteristic
104C2×Dic61—21no—
105C2×Dic61—41no—
106C2×Dic61—41no—
107C2×Dic61—41no—
108C2×Dic61—41no—
109C2×Dic61—41no—
110C2×Dic61#9912yes—
111D244—42no—
112D244—42no—
113D244—42no—
114D244—42no—
115D244—88no—
116C4×D61—44no—
117C4×D61—82no—
118C4×D61—84no—
119C8×C61—82no—
120#92418—82no—
121#11533—611nomaximal, Sylow
122C22×C61—21no—
123C22×C61—21no—
124C22×C61#40711yescharacteristic
125C22×C61C2×#9911yescharacteristic
126C22×C61#41311yescharacteristic
127C2×D61—44no—
128C2×D61—44no—
129C2×D61—42no—
130C2×D61—42no—
131C2×D61—42no—
132C2×D61—42no—
133C2×D61—82no—
134C2×D61—81no—
135C2×D61—81no—
136C2×D61—82no—
137C4×C61—21no—
138C4×C61—21no—
139C4×C61—42no—
140C4×C61—42no—
141C4×C61—81no—
142Dic61—22no—
143Dic61—41no—
144Dic61—81no—
145#2328—611no—
146#1465—612no—
147#1324—611no—
148#1324D6111yescharacteristic, complemented
149#1318—612no—
150C2×C61—21no—
151C2×C61—21no—
152C2×C61#146511yescharacteristic
153C2×C61#212711yescharacteristic
154C2×C61#213411yescharacteristic
155D61—82no—
156D61—82no—
157C2×#127—611no—
158C2×C4×D4—611no—
159C2×C4×D4—611no—
160#407—1222no—
161#390—611no—
162#390—611no—
163#386—1222no—
164#386—1222no—
165#382C2×D6111yescharacteristic
166#376—611no—
167#324—612no—
168#324C2×D6112yes—
169#323—1222no—
170C61#1153311yescharacteristic, complemented, Sylow
171C22×D4—611no—
172C22×D4—611no—
173C22×D4—1222no—
174C23×C4—612no—
175C23×C4—1221no—
176C2×M16—2442no—
177#127—1222no—
178#127—1222no—
179C4×D4—2442no—
180C4×D4—2442no—
181C2×C4⋊C4C4×D6111yescharacteristic
182C2×C4⋊C4C22×D6111yescharacteristic
183C2×C22⋊C4—612no—
184C2×C22⋊C4—1222no—
185C2×C22⋊C4—1222no—
186C2×C22⋊C4—1221no—
187C2×C42—611no—
188C2×C42—611no—
189C2×C42C4×D6111yescharacteristic
190C22⋊C8—22no—
191C22⋊C8—1222no—
192C22⋊C8—2442no—
193#95—22no—
194#95—1221no—
195#95—1221no—
196C24—612no—
197C24—1221no—
198C2×D4—612no—
199C2×D4—1228no—
200C2×D4—1221no—
201C2×D4—1221no—
202C2×D4—1221no—
203C2×D4—4882no—
204C2×D4—4882no—
205C2×D4—2441no—
206C2×D4—2441no—
207C2×D4—2441no—
208C2×D4—2441no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—611no—
212C22×C4—611no—
213C22×C4—1222no—
214C22×C4—1222no—
215C22×C4—1221no—
216C22×C4—4882no—
217C22×C4—4882no—
218C22×C4—2442no—
219C22×C4C2×C4×D6111yescharacteristic
220C22×C4D4×D6112yes—
221M16—4884no—
222C2×C8—42no—
223C2×C8—2442no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C22⋊C4—4882no—
227C22⋊C4—4882no—
228C22⋊C4—2442no—
229C22⋊C4—2442no—
230C42—21no—
231C42—1222no—
232C42—2441no—
233C42#1175818912yescomplemented
234C23—1222no—
235C23—1222no—
236C23—1222no—
237C23—1222no—
238C23—2442no—
239C23—2442no—
240C23—2442no—
241C23—2442no—
242C23—2441no—
243C23—2441no—
244C23C22⋊C4×D6111yescharacteristic
245D4—4888no—
246D4—2442no—
247D4—2442no—
248D4—2442no—
249D4—2442no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—41no—
259C2×C4—612no—
260C2×C4—1221no—
261C2×C4—4882no—
262C2×C4—4884no—
263C2×C4—2444no—
264C2×C4—2441no—
265C2×C4—2441no—
266C2×C4—2441no—
267C2×C4—2441no—
268C2×C4—2441no—
269C2×C4M16×D6111yescharacteristic
270C2×C4C2×#1175818911yescharacteristic
271C8—82no—
272C8—4882no—
273C22—21no—
274C22—21no—
275C22—4882no—
276C22—4882no—
277C22—4881no—
278C22—4881no—
279C22—2444no—
280C22—2444no—
281C22—2442no—
282C22—2442no—
283C22—2442no—
284C22—2442no—
285C22#1683972411yescharacteristic
286C22#99×D6111yescharacteristic
287C22#1683974511yescharacteristic
288C4—21no—
289C4—21no—
290C4—42no—
291C4—42no—
292C4—81no—
293C4—1222no—
294C4—4881no—
295C4—2441no—
296C2—21no—
297C2—21no—
298C2—4882no—
299C2—4882no—
300C2#2144415611yescharacteristic
301C2#2144748711yescharacteristic
302C2#2144750911yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1324C2
socleC22×C61C2×#99
prime radicalC2×#14519774C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1324D61
hypocenterC61#11533
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
2. #21444156C2semidirect
3. #21443763C2semidirect
4. #21443750C2semidirect
5. C61×#1324C2semidirect
63. C2×D244M16semidirect
73. C42×C61M16semidirect
148. #1324D61semidirect
170. C61#11533semidirect
233. C42#11758189semidirect

Maximal subgroups

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

subgroupindex
#214485422
#214441562
#214437632
#214437502
C61×#13242
#1153361