Finite Group Databasebeta

← #30605212

Subgroups — #30605212

Order 15616.

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

normal subgroups only

This group has 418 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#21461680C211yesmaximal, characteristic
2#21461076C211yesmaximal, characteristic
3#21460816C212yesmaximal, complemented
4#21460799C212yesmaximal, complemented
5#21451688C211yesmaximal, characteristic
6C2×#14519836—21no—
7#16840733—21no—
8#16840704—21no—
9#16840640C2212yes—
10#16840607—21no—
11#16840606C2212yes—
12C2×C4×D244C2211yescharacteristic
13#16839697C411yescharacteristic, complemented
14#16839697C2211yescharacteristic
15#16839692—21no—
16#16839688C411yescharacteristic, complemented
17#16839688C2211yescharacteristic
18#16839679—21no—
19#16839633—21no—
20#16839633—21no—
21#16839630C411yescharacteristic, complemented
22C2×#125×C61C411yescharacteristic, complemented
23C2×#11758213—41no—
24C2×C4⋊#6923—41no—
25C2×C22⋊#6923—22no—
26#14519836—42no—
27#14519834—41no—
28C22⋊#92420—22no—
29(C2×#6923)⋊C4—41no—
30C22×D244D411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C4×D244—41no—
34C4×D244—41no—
35C2×C4⋊Dic61D411yescharacteristic
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198C2×C411yescharacteristic
43C2×#11758198C2311yescharacteristic
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684C2×C411yescharacteristic
49#14519684C2×C411yescharacteristic
50#125×C61—41no—
51#125×C61—41no—
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C42×C61C2×C411yescharacteristic
57C23×D61C22⋊C411yescharacteristic
58C23×D61C2×D411yescharacteristic
59C22×#6923—42no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22×C411yescharacteristic
65C22×Dic61—21no—
66C22×Dic61—21no—
67C22×Dic61C22⋊C411yescharacteristic
68C22×Dic61C2×D411yescharacteristic
69C2×D244—21no—
70C2×D244—21no—
71C2×D244—41no—
72C2×D244—41no—
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—81no—
78C2×C4×D61—81no—
79C22⋊#6923—42no—
80C22⋊#6923—42no—
81C2×#92420—42no—
82C4⋊#6923—82no—
83#11758213—82no—
84C4⋊C4×C61—42no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—41no—
88C4⋊C4×C61—41no—
89C42×C61—21no—
90C42×C61—21no—
91#11758198—41no—
92#11758198—41no—
93#11758198—42no—
94#11758198—41no—
95#11758198—41no—
96#11758198—81no—
97#11758198—81no—
98C4⋊Dic61—41no—
99#11758196—81no—
100#11758196—81no—
101C23×C61C2×C22⋊C411yescharacteristic
102C22×D61—21no—
103C22×D61—21no—
104C22×D61—21no—
105C22×D61—21no—
106C22×D61—21no—
107C22×D61—41no—
108C22×D61—41no—
109C22×D61—41no—
110C22×D61—41no—
111C22×D61AGL(1,ℤ/8)11yescharacteristic
112C22×D61#13711yescharacteristic
113C2×#6923—82no—
114C2×#6923—82no—
115C2×#6923—82no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
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—41no—
128C2×C4×C61#9911yescharacteristic
129C2×C4×C61#9911yescharacteristic
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—
140D244—42no—
141D244—42no—
142C4×D61—42no—
143C4×D61—42no—
144C4×D61—81no—
145C4×D61—81no—
146#92420—82no—
147#11827—611nomaximal, Sylow
148C22×C61—21no—
149C22×C61—21no—
150C22×C61C2×#9911yescharacteristic
151C22×C61#41711yescharacteristic
152C22×C61#42111yescharacteristic
153C2×D61—21no—
154C2×D61—21no—
155C2×D61—41no—
156C2×D61—41no—
157C2×D61—41no—
158C2×D61—41no—
159C2×D61—42no—
160C2×D61—41no—
161C2×D61—41no—
162C2×D61—41no—
163C2×D61—81no—
164C2×D61—81no—
165#6923—162no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—41no—
169C4×C61—41no—
170C4×C61—81no—
171C4×C61—81no—
172Dic61—41no—
173Dic61—41no—
174Dic61—81no—
175Dic61—81no—
176#2633—611no—
177#1799—611no—
178#1465—611no—
179#1352—612no—
180#1344—612no—
181C2×C61—21no—
182C2×C61—21no—
183C2×C61#151311yescharacteristic
184C2×C61#212311yescharacteristic
185C2×C61#212711yescharacteristic
186D61—41no—
187D61—41no—
188D61—81no—
189C2×#125#692311yescharacteristic, complemented
190C2×C4×D4—611no—
191C2×#99—1221no—
192#407—1221no—
193#399—611no—
194#399—611no—
195#398—1221no—
196#397—611no—
197#397—611no—
198#394—1221no—
199#385—1221no—
200#385—1221no—
201#383—611no—
202#380—1221no—
203#342—612no—
204#324—1221no—
205#323—612no—
206C61#1182711yescharacteristic, complemented, Sylow
207C22×D4—611no—
208C23×C4—611no—
209C23×C4—611no—
210C2×M16—2441no—
211#125—41no—
212#125—41no—
213C4×D4—2441no—
214C4×D4—2441no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—611no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4—1221no—
220C2×C4⋊C4—2441no—
221C2×C4⋊C4C2×#692311yescharacteristic
222C2×C4⋊C4C2×#692311yescharacteristic
223C2×C22⋊C4—611no—
224C2×C22⋊C4—611no—
225C2×C22⋊C4—1221no—
226C2×C22⋊C4—1221no—
227C2×C22⋊C4—1221no—
228C2×C22⋊C4—1221no—
229C2×C22⋊C4—1222no—
230C2×C42C2×#692311yescharacteristic
231#99—2442no—
232C22⋊C8—1222no—
233C22⋊C8—2441no—
234#95—611no—
235#95—611no—
236#95—1221no—
237#95—1221no—
238#95—1221no—
239#95—1221no—
240#95—2441no—
241C24—611no—
242C24—611no—
243C2×D4—1221no—
244C2×D4—1221no—
245C2×D4—2441no—
246C2×D4—2441no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—611no—
250C22×C4—611no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—4881no—
258C22×C4—4881no—
259C22×C4—2442no—
260C22×C4C22⋊#692311yescharacteristic
261C22×C4C22⋊#692311yescharacteristic
262C22×C4C22×#692311yescharacteristic
263M16—4882no—
264C2×C8—2442no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—42no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—4881no—
271C4⋊C4—4881no—
272C4⋊C4—4882no—
273C4⋊C4—2441no—
274C22⋊C4—4881no—
275C22⋊C4—4881no—
276C22⋊C4—2441no—
277C22⋊C4—2441no—
278C22⋊C4—2441no—
279C22⋊C4—2441no—
280C22⋊C4—2442no—
281C22⋊C4—2442no—
282C22⋊C4—2442no—
283C42—21no—
284C42—21no—
285C23—611no—
286C23—611no—
287C23—1221no—
288C23—1221no—
289C23—1221no—
290C23—1221no—
291C23—1221no—
292C23—2441no—
293C23—2441no—
294C23—2441no—
295C23—2441no—
296C23C2×C22⋊#692311yescharacteristic
297D4—2442no—
298D4—2442no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—4881no—
314C2×C4—4881no—
315C2×C4—4882no—
316C2×C4—4882no—
317C2×C4—4882no—
318C2×C4—2442no—
319C2×C4—2442no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4#1451983511yescharacteristic
329C2×C4#1451983511yescharacteristic
330C8—4882no—
331C22—21no—
332C22—21no—
333C22—1221no—
334C22—1221no—
335C22—4881no—
336C22—4881no—
337C22—2442no—
338C22—2441no—
339C22—2441no—
340C22—2441no—
341C22—2441no—
342C22—2441no—
343C22—2441no—
344C22—2441no—
345C22C2×#1451983511yescharacteristic
346C22#1684075311yescharacteristic
347C22#1684075911yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—81no—
353C4—81no—
354C4—9762no—
355C4—4881no—
356C4—4881no—
357C4—2441no—
358C4—2441no—
359C2—21no—
360C2—21no—
361C2—4881no—
362C2—2441no—
363C2—2441no—
364C2#2146123411yescharacteristic
365C2#2146208111yescharacteristic
366C2#2146209411yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#125×C61C4
socleC22×C61C2×#99
prime radicalC22×D244D4
cosocleC2×#11758198C23
hypercenterC2×#125#6923
hypocenterC61#11827
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
3. #21460816C2semidirect
4. #21460799C2semidirect
13. #16839697C4semidirect
16. #16839688C4semidirect
21. #16839630C4semidirect
22. C2×#125×C61C4semidirect
189. C2×#125#6923semidirect
206. C61#11827semidirect

Maximal subgroups

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

subgroupindex
#214616802
#214610762
#214608162
#214607992
#214516882
#1182761