Finite Group Databasebeta

← #30605262

Subgroups — #30605262

Order 15616.

446 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 64 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#21461717C211yesmaximal, characteristic, complemented
2#21461053C211yesmaximal, characteristic, complemented
3#21460815C212yesmaximal, complemented
4#21460797C212yesmaximal
5#21451380C211yesmaximal, characteristic
6#16840779—21no—
7#16840705—21no—
8#16840640—21no—
9#16840640C2212yes—
10#16840607—21no—
11#16840606C2212yes—
12C2×D4×Dic61C411yescharacteristic, complemented
13C2×#14519735C2211yescharacteristic
14#16839701C411yescharacteristic, complemented
15#16839699C2211yescharacteristic
16#16839670C2211yescharacteristic
17#16839655—21no—
18#16839639—21no—
19#16839638—21no—
20#16839637—21no—
21#16839629C411yescharacteristic, complemented
22C61×#394C411yescharacteristic, complemented
23C2×C22⋊#6923—22no—
24#14519844—41no—
25C22⋊#92420—22no—
26C4×#92420—41no—
27(C2×#6923)⋊C4—41no—
28(C2×#6923)⋊C4—41no—
29C22×C22⋊D61—21no—
30C23×Dic61—21no—
31C22×C4×D61D411yescharacteristic
32D4×Dic61—41no—
33D4×Dic61—41no—
34#14519735—41no—
35#14519735—41no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×C4⋊Dic61D411yescharacteristic
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×#11758198—21no—
42C2×#11758198D411yescharacteristic
43C2×#11758198C2311yescharacteristic
44C2×C4×Dic61C2×C411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684C2×C411yescharacteristic
51C22×D4×C61C2×C411yescharacteristic
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C22⋊C4×C61—21no—
54C2×C22⋊C4×C61—21no—
55#95×C61C2×C411yescharacteristic
56C24×C61—21no—
57C23×D61C2×D411yescharacteristic
58C22×#6923—42no—
59C2×D4×C61—41no—
60C2×D4×C61—42no—
61C22×C4×C61—21no—
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22×C411yescharacteristic
65C2×C22⋊D61—42no—
66C2×C22⋊D61—42no—
67C2×C22⋊D61—81no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—42no—
71C22×Dic61—81no—
72C22×Dic61—81no—
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C2×D411yescharacteristic
76C2×C4×D61—22no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—41no—
80C22⋊#6923—42no—
81C22⋊#6923—42no—
82C2×#92420—42no—
83C4⋊C4×C61—41no—
84C22⋊C4×C61—42no—
85C22⋊C4×C61—42no—
86C22⋊Dic61—41no—
87C22⋊Dic61—41no—
88C22⋊Dic61—81no—
89#11758198—41no—
90#11758198—41no—
91#11758198—81no—
92C4⋊Dic61—41no—
93C4⋊Dic61—41no—
94C4⋊Dic61—81no—
95C4×Dic61—21no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—21no—
99C23×C61—22no—
100C23×C61—41no—
101C23×C61—41no—
102C23×C61—41no—
103C23×C61—41no—
104C23×C61—41no—
105C23×C61—41no—
106C23×C61C2×C22⋊C411yescharacteristic
107C22×D61—21no—
108C22×D61—21no—
109C22×D61—41no—
110C22×D61—41no—
111C22×D61#13512yes—
112C2×#6923—82no—
113C2×#6923—82no—
114C2×#6923—82no—
115D4×C61—42no—
116D4×C61—42no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C22⋊D61—84no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—84no—
141C2×Dic61#9911yescharacteristic
142C2×Dic61#9911yescharacteristic
143C4×D61—42no—
144C4×D61—42no—
145#92420—82no—
146#11840—611nomaximal, Sylow
147C22×C61—21no—
148C22×C61—21no—
149C22×C61—42no—
150C22×C61—42no—
151C22×C61—42no—
152C22×C61—81no—
153C22×C61—81no—
154C22×C61—81no—
155C22×C61—81no—
156C22×C61C2×#9911yescharacteristic
157C22×C61#41611yescharacteristic
158C22×C61#42111yescharacteristic
159C2×D61—22no—
160C2×D61—41no—
161C2×D61—41no—
162C2×D61—42no—
163C2×D61—81no—
164#6923—162no—
165C4×C61—41no—
166C4×C61—41no—
167C4×C61—41no—
168C4×C61—81no—
169Dic61—21no—
170Dic61—21no—
171Dic61—41no—
172Dic61—41no—
173Dic61—81no—
174Dic61—81no—
175#2598—611no—
176#1820—611no—
177#1458—611no—
178#1352—612no—
179#1343—612no—
180C2×C61—21no—
181C2×C61—21no—
182C2×C61—82no—
183C2×C61#151611yescharacteristic
184C2×C61#212011yescharacteristic
185C2×C61#212811yescharacteristic
186D61—42no—
187C2×C4×D4—611no—
188C2×#117—611no—
189#431—1221no—
190#400—611no—
191#399—611no—
192#394#692311yescharacteristic, complemented
193#392—611no—
194#388—1221no—
195#386—1221no—
196#386—1221no—
197#385—1221no—
198#383—611no—
199#381—1221no—
200#342—612no—
201#342—1221no—
202#324—1221no—
203#323—612no—
204C61#1184011yescharacteristic, complemented, Sylow
205C22×D4—1221no—
206C22×D4C2×#692311yescharacteristic
207C23×C4—611no—
208C23×C4—1221no—
209C4×D4—2441no—
210C4×D4—2441no—
211#117—2441no—
212#117—2441no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4—611no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4C2×#692311yescharacteristic
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—611no—
220C2×C22⋊C4—611no—
221C2×C22⋊C4—1221no—
222C2×C22⋊C4—1221no—
223C2×C22⋊C4—1221no—
224C2×C22⋊C4—1222no—
225C2×C42—611no—
226C2×C42—611no—
227C4⋊C8—2441no—
228C22⋊C8—1222no—
229C4×C8—2441no—
230#95—611no—
231#95—1221no—
232#95—1221no—
233#95—1221no—
234#95—1221no—
235#95—2441no—
236#95—2441no—
237#95C2×#692311yescharacteristic
238C24—21no—
239C24—611no—
240C2×D4—41no—
241C2×D4—42no—
242C2×D4—4881no—
243C2×D4—2442no—
244C2×D4—2442no—
245C22×C4—21no—
246C22×C4—611no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4—1222no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—4881no—
255C22×C4—4881no—
256C22×C4—2441no—
257C22×C4—2442no—
258C22×C4—2442no—
259C22×C4C22⋊#692311yescharacteristic
260C22×C4C22⋊#692311yescharacteristic
261C22×C4C22×#692311yescharacteristic
262C2×C8—2442no—
263C4⋊C4—41no—
264C4⋊C4—4881no—
265C4⋊C4—2441no—
266C4⋊C4—2441no—
267C22⋊C4—42no—
268C22⋊C4—42no—
269C22⋊C4—4881no—
270C22⋊C4—4881no—
271C22⋊C4—2441no—
272C22⋊C4—2441no—
273C22⋊C4—2441no—
274C22⋊C4—2441no—
275C22⋊C4—2442no—
276C22⋊C4—2442no—
277C42—1221no—
278C42—1221no—
279C42—1221no—
280C42—1221no—
281C23—22no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—612no—
289C23—1221no—
290C23—1221no—
291C23—2441no—
292C23—2441no—
293C23C2×C22⋊#692311yescharacteristic
294D4—42no—
295D4—42no—
296D4—4884no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—611no—
308C2×C4—611no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—4882no—
314C2×C4—4882no—
315C2×C4—4882no—
316C2×C4—4884no—
317C2×C4—2442no—
318C2×C4—2442no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C8—4882no—
328C22—21no—
329C22—21no—
330C22—42no—
331C22—42no—
332C22—42no—
333C22—81no—
334C22—81no—
335C22—81no—
336C22—81no—
337C22—1222no—
338C22—4881no—
339C22—2442no—
340C22—2441no—
341C22—2441no—
342C22D61⋊#9911yescharacteristic
343C22#1684075211yescharacteristic
344C22#1684076011yescharacteristic
345C4—41no—
346C4—41no—
347C4—41no—
348C4—81no—
349C4—1221no—
350C4—1221no—
351C4—9762no—
352C4—4881no—
353C4—4881no—
354C4—2441no—
355C4—2441no—
356C2—21no—
357C2—21no—
358C2—82no—
359C2—2442no—
360C2#2146124411yescharacteristic
361C2#2146207111yescharacteristic
362C2#2146209911yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#394C4
socleC22×C61C2×#99
prime radical#16839670C22
cosocleC2×#11758198C23
hypercenter#394#6923
hypocenterC61#11840
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #21461717C2semidirect
2. #21461053C2semidirect
3. #21460815C2semidirect
12. C2×D4×Dic61C4semidirect
14. #16839701C4semidirect
21. #16839629C4semidirect
22. C61×#394C4semidirect
192. #394#6923semidirect
204. C61#11840semidirect

Maximal subgroups

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

subgroupindex
#214617172
#214610532
#214608152
#214607972
#214513802
#1184061