Finite Group Databasebeta

← #30599206

Subgroups — #30599206

Order 15616.

384 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C4×#14519846C211yesmaximal, characteristic, complemented
2#21461380C211yesmaximal, characteristic, complemented
3#21461223C212yesmaximal
4#21460671C212yesmaximal, complemented
5#21454793C211yesmaximal, characteristic
6#16840784C2212yes—
7C2×#14519846—21no—
8C4×C4⋊#6923C2212yes—
9#16840636—21no—
10#16840625—21no—
11#16840623—21no—
12#16840616—22no—
13#16840614—22no—
14#16840299C2211yescharacteristic
15Q8×#92418C411yescharacteristic, complemented
16#16839841C411yescharacteristic, complemented
17#16839835—21no—
18#16839827—21no—
19#16839827C411yescharacteristic, complemented
20#16839822—21no—
21#16839818C2211yescharacteristic
22#16839719—21no—
23C4×C8×D61C2211yescharacteristic
24C61×#446C411yescharacteristic, complemented
25C2×C4⋊#6923—22no—
26C2×C4×#6923—22no—
27#14519846—24no—
28C4⋊#92420—22no—
29#14519834—22no—
30#14519832—22no—
31(C2×#6923)⋊C4—22no—
32C2×#11758189—21no—
33C2×C8×D61—21no—
34C2×C8×D61D411yescharacteristic
35C2×C8×D61D411yescharacteristic
36#14519772—21no—
37#14519768Q811yescharacteristic
38#14519766Q811yescharacteristic
39#14519762—21no—
40#14519753D411yescharacteristic
41#14519752D411yescharacteristic
42C4×D244—21no—
43C4×D244C2×C411yescharacteristic
44#14519734—21no—
45C42×D61C2311yescharacteristic
46C4⋊#92418—21no—
47C4⋊#92418C2×C411yescharacteristic
48#14519689—21no—
49#14519689—21no—
50#14519689—21no—
51#14519687—21no—
52C4×#92418—21no—
53C4×#92418C2×C411yescharacteristic
54C8×Dic61D411yescharacteristic
55C8×Dic61D411yescharacteristic
56C4×Q8×C61C2×C411yescharacteristic
57C4⋊C8×C61—21no—
58C4⋊C8×C61C2×C411yescharacteristic
59#97×C61—21no—
60C4×C8×C61C2×C411yescharacteristic
61C22×#6923—42no—
62C2×Q8×C61C4⋊C411yescharacteristic
63C2×D244—21no—
64C2×D244C4⋊C411yescharacteristic
65C2×C4×D61—21no—
66C2×C4×D61C2×D411yescharacteristic
67C2×C4×D61C2×D411yescharacteristic
68C2×C4×D61#4111yescharacteristic
69C2×#92420—42no—
70C4⋊#6923—24no—
71C4⋊#6923—42no—
72C4×#6923—82no—
73C2×C8×C61—21no—
74C2×C8×C61C22⋊C411yescharacteristic
75C2×C8×C61C22⋊C411yescharacteristic
76C4⋊C4×C61—21no—
77C4⋊C4×C61C4⋊C411yescharacteristic
78C42×C61—21no—
79C42×C61C22×C411yescharacteristic
80#11758198—21no—
81#11758198—21no—
82#11758198—21no—
83#11758198—21no—
84#11758198—21no—
85C4⋊Dic61—21no—
86C4⋊Dic61C4⋊C411yescharacteristic
87#11758196—21no—
88#11758196—21no—
89C4×Dic61C2×D411yescharacteristic
90C4×Dic61C2×Q811yescharacteristic
91C4×Dic61#4111yescharacteristic
92C2×#92418—21no—
93C2×#92418C22⋊C411yescharacteristic
94C2×#92418C22⋊C411yescharacteristic
95#11758189—42no—
96C8×D61—22no—
97C8×D61—41no—
98C8×D61—42no—
99C22×D61—21no—
100C22×D61#12111yescharacteristic
101C2×#6923—44no—
102C2×#6923—82no—
103C2×#6923—82no—
104Q8×C61—41no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61C2×C22⋊C411yescharacteristic
108C2×C4×C61C2×C4⋊C411yescharacteristic
109C2×C4×C61#11711yescharacteristic
110C2×Dic61—21no—
111C2×Dic61#12111yescharacteristic
112C2×Dic61C22⋊Q811yescharacteristic
113C2×Dic61C22⋊Q811yescharacteristic
114D244—41no—
115D244—41no—
116D244—41no—
117C4×D61—21no—
118C4×D61—21no—
119C4×D61—21no—
120C4×D61—21no—
121C4×D61—41no—
122C4×D61—41no—
123C4×D61—41no—
124#92420—82no—
125C8×C61—21no—
126C8×C61—41no—
127C8×C61#10412yes—
128#92418—21no—
129#92418—21no—
130#92418—41no—
131#8697—611nomaximal, Sylow
132C22×C61#38011yescharacteristic
133C2×D61—21no—
134C2×D61—21no—
135C2×D61—41no—
136C2×D61—41no—
137C2×D61—41no—
138C2×D61#47211yescharacteristic
139C2×D61#47311yescharacteristic
140#6923—84no—
141C4×C61—21no—
142C4×C61—21no—
143C4×C61—41no—
144C4×C61—41no—
145C4×C61C2×#10411yescharacteristic
146C4×C61#42111yescharacteristic
147Dic61—21no—
148Dic61—21no—
149Dic61—21no—
150Dic61—41no—
151#2966—611no—
152C4×#107—611no—
153#1568—611no—
154#1509—612no—
155#1285—612no—
156C2×C61#180611yescharacteristic
157C2×C61#181211yescharacteristic
158C2×C61#181611yescharacteristic
159D61—21no—
160D61—21no—
161D61—81no—
162#529—611no—
163#446#692311yescharacteristic, complemented
164C8×Q8—611no—
165#436—611no—
166#435—1221no—
167C8×D4—611no—
168C8×D4—1221no—
169#433—1221no—
170#432—611no—
171#432—612no—
172C2×#107—1221no—
173#405—1221no—
174C2×C4×C8—611no—
175C4×C4⋊C4—612no—
176#340—1221no—
177#335—1221no—
178#334—1221no—
179#328—1222no—
180#327—1222no—
181C61#869711yescharacteristic, complemented, Sylow
182C2×M16—1221no—
183C22×C8—611no—
184C22×C8—611no—
185C22×C8—1221no—
186#126—1221no—
187#125—611no—
188#124—611no—
189#123—1221no—
190C22⋊Q8—611no—
191#121—611no—
192C4×Q8C2×#692311yescharacteristic
193C4×D4—611no—
194C4×D4—1221no—
195#117—1221no—
196C2×C4⋊C4—1222no—
197C2×C42—611no—
198C2×C42—1222no—
199#107—1224no—
200C4⋊C8—21no—
201C4⋊C8—611no—
202C4⋊C8—1221no—
203C4⋊C8—1222no—
204C4⋊C8C2×#692311yescharacteristic
205C22⋊C8—1221no—
206C22⋊C8—1221no—
207C22⋊C8—1221no—
208C22⋊C8—1222no—
209#97—21no—
210#97—1221no—
211#97—1222no—
212C4×C8—611no—
213C4×C8—611no—
214C4×C8—611no—
215C4×C8—1221no—
216C4×C8C2×#692311yescharacteristic
217#95—1222no—
218C2×Q8C4⋊#692311yescharacteristic
219C2×D4—611no—
220C2×D4—1221no—
221C22×C4—611no—
222C22×C4—611no—
223C22×C4—611no—
224C22×C4—1221no—
225C22×C4—2442no—
226M16—2442no—
227C2×C8—21no—
228C2×C8—611no—
229C2×C8—611no—
230C2×C8—1222no—
231C2×C8—1221no—
232C2×C8—2441no—
233C2×C8—2442no—
234C2×C8—2442no—
235C2×C8C22⋊#692311yescharacteristic
236C2×C8C22⋊#692311yescharacteristic
237C4⋊C4—21no—
238C4⋊C4—611no—
239C4⋊C4—1221no—
240C4⋊C4—1221no—
241C4⋊C4—1221no—
242C4⋊C4—1224no—
243C4⋊C4—2442no—
244C4⋊C4C4⋊#692311yescharacteristic
245C22⋊C4—1221no—
246C22⋊C4—1221no—
247C22⋊C4—1221no—
248C22⋊C4—1221no—
249C22⋊C4—1221no—
250C42—21no—
251C42—611no—
252C42—611no—
253C42—611no—
254C42—4882no—
255C42C22×#692311yescharacteristic
256C23—611no—
257C23—1221no—
258Q8—41no—
259D4—2441no—
260D4—2441no—
261D4—2441no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—611no—
265C2×C4—611no—
266C2×C4—611no—
267C2×C4—1221no—
268C2×C4—1221no—
269C2×C4—1221no—
270C2×C4—1221no—
271C2×C4—1221no—
272C2×C4—4882no—
273C2×C4—4882no—
274C2×C4—2441no—
275C2×C4—2444no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4C2×C22⋊#692311yescharacteristic
279C2×C4C2×C4⋊#692311yescharacteristic
280C2×C4#1451985611yescharacteristic
281C8—21no—
282C8—41no—
283C8—1221no—
284C8—1221no—
285C8—4882no—
286C8—2441no—
287C8#1451984212yes—
288C22—611no—
289C22—611no—
290C22—1221no—
291C22—1221no—
292C22—2441no—
293C22—2441no—
294C22—2441no—
295C22#1684070411yescharacteristic
296C4—21no—
297C4—21no—
298C4—41no—
299C4—41no—
300C4—1221no—
301C4—1221no—
302C4—1221no—
303C4—4884no—
304C4—2441no—
305C4C2×#1451984211yescharacteristic
306C4#1684075911yescharacteristic
307C2—1221no—
308C2—1221no—
309C2—4881no—
310C2#2146169211yescharacteristic
311C2#2146170211yescharacteristic
312C2#2146170811yescharacteristic
subgroupG/H
centerC22#16840704
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#446C4
socleC22×C61#380
prime radical#14519752D4
cosocleC42×D61C23
hypercenter#446#6923
hypocenterC61#8697
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #446

Complements

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

NH ≅ G/Ntype
1. C4×#14519846C2semidirect
2. #21461380C2semidirect
4. #21460671C2semidirect
15. Q8×#92418C4semidirect
16. #16839841C4semidirect
19. #16839827C4semidirect
24. C61×#446C4semidirect
163. #446#6923semidirect
181. C61#8697semidirect

Maximal subgroups

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

subgroupindex
C4×#145198462
#214613802
#214612232
#214606712
#214547932
#869761