Finite Group Databasebeta

← #30605281

Subgroups — #30605281

Order 15616.

432 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 66 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#21461716C211yesmaximal, characteristic, complemented
2#21461052C211yesmaximal, characteristic, complemented
3#21460813C212yesmaximal, complemented
4#21460798C212yesmaximal
5#21451500C211yesmaximal, characteristic
6#16840778—21no—
7#16840705—21no—
8#16840640—21no—
9#16840640C2212yes—
10#16840608—21no—
11#16840606C2212yes—
12C2×#14519765C411yescharacteristic, complemented
13C2×#14519734C2211yescharacteristic
14#16839683C411yescharacteristic, complemented
15#16839680C411yescharacteristic, complemented
16#16839675C2211yescharacteristic
17#16839672C2211yescharacteristic
18#16839664—21no—
19#16839654—21no—
20#16839653—21no—
21#16839640—21no—
22C61×#376C411yescharacteristic, complemented
23C2×C22⋊#6923—22no—
24C4⋊#92420—41no—
25C22⋊#92420—22no—
26C4×#92420—41no—
27(C2×#6923)⋊C4—41no—
28(C2×#6923)⋊C4—41no—
29C22×Dic122C2×C411yescharacteristic
30C22×D244—21no—
31C22×D244C2×C411yescharacteristic
32C22×C4×D61D411yescharacteristic
33#14519765—41no—
34#14519765—41no—
35#14519734—41no—
36#14519734—41no—
37C2×C4⋊Dic61—21no—
38C2×#11758196C2×C411yescharacteristic
39C2×#11758196D411yescharacteristic
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198D411yescharacteristic
47C2×#11758198C2311yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49#14519684—21no—
50#14519684—21no—
51C2×C42×C61—21no—
52C2×C42×C61C2×C411yescharacteristic
53#95×C61—21no—
54#95×C61C2×C411yescharacteristic
55#95×C61C2×C411yescharacteristic
56C23×D61—21no—
57C23×D61C2×D411yescharacteristic
58C22×#6923—42no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22×C411yescharacteristic
64C22×Dic61—21no—
65C22×Dic61C22⋊C411yescharacteristic
66C22×Dic61C22⋊C411yescharacteristic
67C22×Dic61C2×D411yescharacteristic
68C2×D244—42no—
69C2×D244—41no—
70C2×D244—42no—
71C2×D244—81no—
72C2×D244—81no—
73C2×C4×D61—22no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—41no—
77C2×Dic122—41no—
78C2×Dic122—81no—
79C22⋊#6923—42no—
80C22⋊#6923—42no—
81C2×#92420—42no—
82C42×C61—21no—
83C42×C61—21no—
84C42×C61—42no—
85#11758198—41no—
86#11758198—41no—
87#11758198—42no—
88#11758198—42no—
89#11758198—42no—
90#11758198—41no—
91#11758198—41no—
92#11758198—81no—
93#11758198—81no—
94C4⋊Dic61—81no—
95#11758196—41no—
96#11758196—41no—
97C4×Dic61—21no—
98C4×Dic61—21no—
99C23×C61C2×C22⋊C411yescharacteristic
100C22×D61—21no—
101C22×D61—21no—
102C22×D61—41no—
103C22×D61—41no—
104C22×D61—41no—
105C22×D61—41no—
106C22×D61—41no—
107C22×D61—41no—
108C22×D61—41no—
109C22×D61—41no—
110C22×D61—41no—
111C22×D61#13512yes—
112C2×#6923—82no—
113C2×#6923—82no—
114C2×#6923—82no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—22no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61#9911yescharacteristic
128C2×C4×C61#9911yescharacteristic
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139D244—84no—
140D244—82no—
141C4×D61—42no—
142C4×D61—42no—
143Dic122—82no—
144#92420—82no—
145#11844—611nomaximal, Sylow
146C22×C61—21no—
147C22×C61—21no—
148C22×C61C2×#9911yescharacteristic
149C22×C61#41611yescharacteristic
150C22×C61#42111yescharacteristic
151C2×D61—22no—
152C2×D61—41no—
153C2×D61—41no—
154C2×D61—42no—
155C2×D61—81no—
156C2×D61—81no—
157C2×D61—81no—
158C2×D61—81no—
159C2×D61—81no—
160C2×D61—81no—
161C2×D61—81no—
162C2×D61—81no—
163#6923—162no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—42no—
167C4×C61—41no—
168C4×C61—41no—
169C4×C61—81no—
170Dic61—41no—
171Dic61—41no—
172Dic61—41no—
173Dic61—81no—
174#2610—611no—
175#1820—611no—
176#1458—611no—
177#1351—612no—
178#1343—612no—
179C2×C61—21no—
180C2×C61—21no—
181C2×C61#151611yescharacteristic
182C2×C61#212211yescharacteristic
183C2×C61#212611yescharacteristic
184D61—42no—
185D61—161no—
186C2×#124—611no—
187C2×#117—611no—
188#431—1221no—
189#395—611no—
190#394—611no—
191#393—611no—
192#392—611no—
193#390—1221no—
194#388—1221no—
195#388—1221no—
196#386—1221no—
197#381—1221no—
198#376#692311yescharacteristic, complemented
199#342—612no—
200#342—1221no—
201#324—1221no—
202#323—612no—
203C61#1184411yescharacteristic, complemented, Sylow
204C22×Q8—611no—
205C22×D4—611no—
206C22×D4—1221no—
207C23×C4—611no—
208#124—2441no—
209#124—2441no—
210#117—2441no—
211#117—2441no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4—1221no—
215C2×C22⋊C4—611no—
216C2×C22⋊C4—611no—
217C2×C22⋊C4—1221no—
218C2×C22⋊C4—1221no—
219C2×C22⋊C4—1221no—
220C2×C22⋊C4—1221no—
221C2×C22⋊C4—1221no—
222C2×C22⋊C4—1221no—
223C2×C22⋊C4—1222no—
224C2×C42—21no—
225C2×C42—611no—
226C2×C42C2×#692311yescharacteristic
227C4⋊C8—2441no—
228C22⋊C8—1222no—
229C4×C8—2441no—
230#95—21no—
231#95—1221no—
232#95—1221no—
233#95—2441no—
234#95—2441no—
235#95C2×#692311yescharacteristic
236#95C2×#692311yescharacteristic
237C24—611no—
238C24—1221no—
239C2×Q8—4881no—
240C2×Q8—2441no—
241C2×D4—4881no—
242C2×D4—4881no—
243C2×D4—2441no—
244C2×D4—2442no—
245C2×D4—2442no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4—611no—
251C22×C4—1222no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—2441no—
256C22×C4—2442no—
257C22×C4C22⋊#692311yescharacteristic
258C22×C4C22⋊#692311yescharacteristic
259C22×C4C22×#692311yescharacteristic
260C2×C8—2442no—
261C4⋊C4—4881no—
262C4⋊C4—2441no—
263C4⋊C4—2441no—
264C22⋊C4—4881no—
265C22⋊C4—4881no—
266C22⋊C4—2441no—
267C22⋊C4—2441no—
268C22⋊C4—2442no—
269C22⋊C4—2442no—
270C22⋊C4—2442no—
271C22⋊C4—2442no—
272C22⋊C4—2442no—
273C22⋊C4—2441no—
274C22⋊C4—2441no—
275C42—21no—
276C42—21no—
277C42—42no—
278C42—1221no—
279C42—1221no—
280C23—612no—
281C23—1221no—
282C23—1221no—
283C23—2441no—
284C23—2441no—
285C23—2441no—
286C23—2441no—
287C23—2441no—
288C23—2441no—
289C23—2441no—
290C23—2441no—
291C23—2441no—
292C23C2×C22⋊#692311yescharacteristic
293Q8—4882no—
294D4—4882no—
295D4—4884no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—4882no—
314C2×C4—4882no—
315C2×C4—4882no—
316C2×C4—2442no—
317C2×C4—2442no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4#1451983611yescharacteristic
324C2×C4#1451983611yescharacteristic
325C8—4882no—
326C22—21no—
327C22—21no—
328C22—1222no—
329C22—4881no—
330C22—4881no—
331C22—4881no—
332C22—4881no—
333C22—4881no—
334C22—4881no—
335C22—4881no—
336C22—4881no—
337C22—2442no—
338C22—2441no—
339C22—2441no—
340C22C2×#1451983611yescharacteristic
341C22#1684075211yescharacteristic
342C22#1684075911yescharacteristic
343C4—21no—
344C4—21no—
345C4—42no—
346C4—41no—
347C4—41no—
348C4—81no—
349C4—9762no—
350C4—4881no—
351C4—2441no—
352C4—2441no—
353C4—2441no—
354C2—21no—
355C2—21no—
356C2—9761no—
357C2—2442no—
358C2#2146124711yescharacteristic
359C2#2146208011yescharacteristic
360C2#2146209211yescharacteristic
subgroupG/H
centerC22C2×#14519836
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#376C4
socleC22×C61C2×#99
prime radical#16839672C22
cosocleC2×#11758198C23
hypercenter#376#6923
hypocenterC61#11844
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ #376

Complements

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

NH ≅ G/Ntype
1. #21461716C2semidirect
2. #21461052C2semidirect
3. #21460813C2semidirect
12. C2×#14519765C4semidirect
14. #16839683C4semidirect
15. #16839680C4semidirect
22. C61×#376C4semidirect
198. #376#6923semidirect
203. C61#11844semidirect

Maximal subgroups

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

subgroupindex
#214617162
#214610522
#214608132
#214607982
#214515002
#1184461