Finite Group Databasebeta

← #29575087

Subgroups — #29575087

Order 15616.

484 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 107 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#21449110C211yesmaximal, characteristic
2C4×#14519696C211yesmaximal, characteristic
3#21444265C212yesmaximal
4#21443711C212yesmaximal
5C61×#2983C211yesmaximal, characteristic
6C2×C4×Dic122C2211yescharacteristic
7C2×#14519696—21no—
8C4×#11758194C2212yes—
9#16839693—21no—
10#16839692C411yescharacteristic
11#16839692C411yescharacteristic
12#16839682C411yescharacteristic
13#16839682C411yescharacteristic
14#16839681—21no—
15C4×#11758196—21no—
16C4×#11758196—21no—
17#16839608C2211yescharacteristic
18#16839531—21no—
19#16839492—24no—
20C2×C4×Q8×C61C2211yescharacteristic
21C61×#446—24no—
22C61×#432—21no—
23C61×#432C2212yes—
24C61×#431—21no—
25C22×Dic122C2×C411yescharacteristic
26C2×#11758194—22no—
27C4×Dic122—22no—
28C4×Dic122—22no—
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×#11758196—21no—
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×C4×Dic61—21no—
36C2×C4×Dic61—21no—
37#14519696—24no—
38#14519688—22no—
39C4×#92418—22no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684C2×C411yescharacteristic
46#14519684C2×C411yescharacteristic
47C22×Q8×C61D411yescharacteristic
48C4×Q8×C61—22no—
49C4×Q8×C61—22no—
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C4⋊C4×C61D411yescharacteristic
53C2×C42×C61D411yescharacteristic
54C2×C42×C61D411yescharacteristic
55C2×C42×C61C2311yescharacteristic
56C4⋊C8×C61—22no—
57C4⋊C8×C61—22no—
58C4⋊C8×C61D414yes—
59C22⋊C8×C61—22no—
60#97×C61—22no—
61#97×C61—22no—
62C4×C8×C61—22no—
63C2×Q8×C61—22no—
64C2×Q8×C61—22no—
65C2×Q8×C61—41no—
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22×C411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C2×Dic122—22no—
78C2×Dic122—42no—
79C2×C8×C61—24no—
80C4⋊C4×C61—22no—
81C4⋊C4×C61—22no—
82C4⋊C4×C61—22no—
83C42×C61—21no—
84C42×C61—21no—
85C42×C61—21no—
86C42×C61—21no—
87C42×C61C2×D412yes—
88C42×C61#4112yes—
89C4⋊Dic61—22no—
90#11758196—42no—
91#11758196—42no—
92#11758196—42no—
93#11758196—42no—
94#11758196—42no—
95C4×Dic61—24no—
96C4×Dic61—41no—
97C4×Dic61—41no—
98#11758194—24no—
99#11758194—42no—
100C2×#92418—42no—
101C23×C61C2×C22⋊C411yescharacteristic
102Q8×C61—44no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—22no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61#10412yes—
117C2×C4×C61C4×D412yes—
118C2×C4×C61#12011yescharacteristic
119C2×C4×C61#12112yes—
120C2×C4×C61#12311yescharacteristic
121C2×Dic61—22no—
122C2×Dic61—22no—
123C2×Dic61—22no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133Dic122—24no—
134Dic122—42no—
135C8×C61—44no—
136#92418—44no—
137#9030—611nomaximal, Sylow
138C22×C61—21no—
139C22×C61—21no—
140C22×C61#38611yescharacteristic
141C22×C61C2×#10411yescharacteristic
142C22×C61#42111yescharacteristic
143C4×C61—22no—
144C4×C61—22no—
145C4×C61—21no—
146C4×C61—22no—
147C4×C61—41no—
148C4×C61—41no—
149C4×C61—41no—
150C4×C61#45612yes—
151Dic61—42no—
152Dic61—42no—
153Dic61—42no—
154Dic61—81no—
155#2983D6111yescharacteristic
156#2399—611no—
157C4×#101—611no—
158#1491—612no—
159#1300—612no—
160C2×C61—21no—
161C2×C61—21no—
162C2×C61#187111yescharacteristic
163C2×C61#188611yescharacteristic
164C2×C61#189111yescharacteristic
165C2×C4×Q8—611no—
166C2×C4×Q8C2×D6111yescharacteristic
167#446—24no—
168#432—21no—
169#432C2×D6112yes—
170#431—21no—
171C2×#101—1221no—
172C4×M16—612no—
173#398—611no—
174#398—611no—
175#398—1221no—
176#395—611no—
177#395—611no—
178#395—1221no—
179C4×C4⋊C4—1221no—
180C4×C4⋊C4—1221no—
181#376—611no—
182#343—1221no—
183Q8⋊C8—1224no—
184C61#903011yescharacteristic, complemented, Sylow
185C22×Q8—611no—
186C22×Q8D24411yescharacteristic
187C2×M16—1222no—
188C4×Q8—22no—
189C4×Q8—22no—
190C4×Q8—1222no—
191C4×Q8—1222no—
192C2×C4⋊C4—611no—
193C2×C4⋊C4—1221no—
194C2×C4⋊C4—1221no—
195C2×C4⋊C4—1221no—
196C2×C4⋊C4—1221no—
197C2×C4⋊C4—1221no—
198C2×C4⋊C4C4×D6111yescharacteristic
199C2×C4⋊C4C4×D6111yescharacteristic
200C2×C4⋊C4D24411yescharacteristic
201C2×C42—1221no—
202C2×C42—1221no—
203C2×C42C22⋊D6111yescharacteristic
204C2×C42C22⋊D6111yescharacteristic
205C2×C42C22×D6111yescharacteristic
206C4⋊C8—22no—
207C4⋊C8—22no—
208C4⋊C8C22⋊D6114yes—
209#101—1224no—
210C22⋊C8—22no—
211#97—22no—
212#97—22no—
213#97—1222no—
214C4×C8—22no—
215C4×C8—1222no—
216#95—611no—
217#95—611no—
218#95—1221no—
219#95—1221no—
220#95—1221no—
221#95—1221no—
222#95—1221no—
223C2×Q8—22no—
224C2×Q8—22no—
225C2×Q8—41no—
226C2×Q8—1222no—
227C2×Q8—2442no—
228C22×C4—1221no—
229C22×C4—1221no—
230C22×C4—1221no—
231C22×C4—1221no—
232C22×C4#1175819811yescharacteristic
233C22×C4#1175819811yescharacteristic
234C22×C4#1175819811yescharacteristic
235C22×C4#1175819811yescharacteristic
236C22×C4C2×C4×D6111yescharacteristic
237C22×C4C2×D24411yescharacteristic
238C22×C4C2×C22⋊D6111yescharacteristic
239M16—1224no—
240M16—2442no—
241C2×C8—24no—
242C2×C8—2442no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—1222no—
247C4⋊C4—2442no—
248C4⋊C4—2442no—
249C4⋊C4—2442no—
250C4⋊C4—2442no—
251C4⋊C4—2442no—
252C42—21no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—1224no—
257C42—2441no—
258C42—2441no—
259C42#1175822212yes—
260C42C2×C22⋊D6112yes—
261C23C2×#1175819811yescharacteristic
262Q8—44no—
263Q8—1224no—
264Q8—2442no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—1222no—
279C2×C4—1222no—
280C2×C4—1222no—
281C2×C4—2441no—
282C2×C4—2441no—
283C2×C4—2441no—
284C2×C4—2441no—
285C2×C4—2441no—
286C2×C4—2441no—
287C2×C4—2441no—
288C2×C4—2441no—
289C2×C4—2441no—
290C2×C4#1451970312yes—
291C2×C4C4×C22⋊D6112yes—
292C2×C4#1451974611yescharacteristic
293C2×C4#1451975112yes—
294C2×C4#1451976011yescharacteristic
295C8—44no—
296C8—2444no—
297C22—21no—
298C22—21no—
299C22#1683964111yescharacteristic
300C22C2×#1451970311yescharacteristic
301C22#1683977811yescharacteristic
302C4—21no—
303C4—22no—
304C4—22no—
305C4—22no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—4881no—
310C4—2442no—
311C4—2442no—
312C4—2442no—
313C4#1683994512yes—
314C2—21no—
315C2—21no—
316C2#2144612111yescharacteristic
317C2#2144621211yescharacteristic
318C2#2144623711yescharacteristic
subgroupG/H
centerC2×C4#14519746
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2983C2
socleC22×C61#386
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#2983D61
hypocenterC61#9030
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
184. C61#9030semidirect

Maximal subgroups

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

subgroupindex
#214491102
C4×#145196962
#214442652
#214437112
C61×#29832
#903061