Finite Group Databasebeta

← #30604874

Subgroups — #30604874

Order 15616.

442 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 68 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×#14519836C211yesmaximal, characteristic
2#21461056C211yesmaximal, characteristic
3#21460816C212yesmaximal, complemented
4#21460799C212yesmaximal, complemented
5#21451688C211yesmaximal, characteristic
6C2×#14519836—21no—
7D61⋊(C22⋊C8)—21no—
8C4×C22⋊#6923—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×D61⋊C8—41no—
24C2×C22⋊#6923—22no—
25C2×C4×#6923—41no—
26#14519836—24no—
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—22no—
70C2×D244—22no—
71C2×D244—41no—
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—81no—
77C2×C4×D61—81no—
78C22⋊#6923—24no—
79C22⋊#6923—42no—
80C2×#92420—42no—
81C4×#6923—82no—
82D61⋊C8—82no—
83C4⋊C4×C61—42no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—41no—
88C42×C61—21no—
89C42×C61—21no—
90#11758198—41no—
91#11758198—41no—
92#11758198—42no—
93#11758198—42no—
94#11758198—81no—
95#11758198—81no—
96C4⋊Dic61—41no—
97#11758196—81no—
98#11758196—81no—
99C23×C61C2×C22⋊C411yescharacteristic
100C22×D61—21no—
101C22×D61—21no—
102C22×D61—21no—
103C22×D61—21no—
104C22×D61—41no—
105C22×D61—41no—
106C22×D61—41no—
107C22×D61—41no—
108C22×D61#10412yes—
109C22×D61#13512yes—
110C2×#6923—44no—
111C2×#6923—82no—
112C2×#6923—82no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61#9911yescharacteristic
126C2×C4×C61#9911yescharacteristic
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137D244—44no—
138C4×D61—42no—
139C4×D61—42no—
140C4×D61—81no—
141C4×D61—81no—
142#92420—82no—
143#11732—611nomaximal, Sylow
144C22×C61—21no—
145C22×C61—21no—
146C22×C61C2×#9911yescharacteristic
147C22×C61#41611yescharacteristic
148C22×C61C2×#10411yescharacteristic
149C2×D61—22no—
150C2×D61—22no—
151C2×D61—41no—
152C2×D61—41no—
153C2×D61—41no—
154C2×D61—41no—
155C2×D61—42no—
156C2×D61—42no—
157C2×D61—81no—
158C2×D61—81no—
159#6923—84no—
160C4×C61—21no—
161C4×C61—21no—
162C4×C61—41no—
163C4×C61—41no—
164C4×C61—81no—
165C4×C61—81no—
166Dic61—41no—
167Dic61—41no—
168Dic61—81no—
169Dic61—81no—
170#2633—611no—
171C4×#99—611no—
172#1459—611no—
173#1352—612no—
174#1344—612no—
175C2×C61—21no—
176C2×C61—21no—
177C2×C61#150111yescharacteristic
178C2×C61#212311yescharacteristic
179C2×C61#212711yescharacteristic
180D61—42no—
181D61—42no—
182C2×#125#692311yescharacteristic, complemented
183C2×C4×D4—611no—
184C2×#99—1221no—
185C2×C22⋊C8—1221no—
186#399—611no—
187#399—611no—
188#398—1221no—
189#397—611no—
190#397—611no—
191#394—1221no—
192#385—1221no—
193#385—1221no—
194#383—611no—
195C4×C22⋊C4—1221no—
196#342—612no—
197#324—1221no—
198#323—612no—
199C61#1173211yescharacteristic, complemented, Sylow
200C22×D4—611no—
201C23×C4—611no—
202C23×C4—611no—
203C22×C8—2441no—
204#125—41no—
205#125—41no—
206C4×D4—2441no—
207C4×D4—2441no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—611no—
211C2×C4⋊C4—1221no—
212C2×C4⋊C4—1221no—
213C2×C4⋊C4C2×#692311yescharacteristic
214C2×C4⋊C4C2×#692311yescharacteristic
215C2×C22⋊C4—611no—
216C2×C22⋊C4—611no—
217C2×C22⋊C4—1222no—
218C2×C22⋊C4—1221no—
219C2×C22⋊C4—1221no—
220C2×C22⋊C4—1221no—
221C2×C22⋊C4—1221no—
222C2×C42—2441no—
223C2×C42C2×#692311yescharacteristic
224#99—1224no—
225C22⋊C8—1222no—
226C22⋊C8—2441no—
227#95—611no—
228#95—611no—
229#95—1221no—
230#95—1221no—
231#95—1221no—
232#95—1221no—
233#95—2441no—
234C24—611no—
235C24—611no—
236C2×D4—1222no—
237C2×D4—1222no—
238C2×D4—2441no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—611no—
242C22×C4—611no—
243C22×C4—1221no—
244C22×C4—1221no—
245C22×C4—1221no—
246C22×C4—1221no—
247C22×C4—1221no—
248C22×C4—1221no—
249C22×C4—4881no—
250C22×C4—4881no—
251C22×C4—2442no—
252C22×C4C22⋊#692311yescharacteristic
253C22×C4C22⋊#692311yescharacteristic
254C22×C4C22×#692311yescharacteristic
255C2×C8—4882no—
256C2×C8—2442no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—42no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—4881no—
263C4⋊C4—4881no—
264C4⋊C4—2441no—
265C22⋊C4—1224no—
266C22⋊C4—4881no—
267C22⋊C4—4881no—
268C22⋊C4—2441no—
269C22⋊C4—2441no—
270C22⋊C4—2442no—
271C22⋊C4—2442no—
272C22⋊C4—2442no—
273C42—21no—
274C42—21no—
275C42—4882no—
276C23—612no—
277C23—612no—
278C23—1221no—
279C23—1221no—
280C23—1221no—
281C23—1221no—
282C23—2441no—
283C23—2441no—
284C23—2441no—
285C23—2441no—
286C23C2×C22⋊#692311yescharacteristic
287D4—2444no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4—4881no—
303C2×C4—4881no—
304C2×C4—4882no—
305C2×C4—4882no—
306C2×C4—2442no—
307C2×C4—2442no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2444no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4#1451983511yescharacteristic
318C2×C4#1451983511yescharacteristic
319C8—4882no—
320C22—21no—
321C22—21no—
322C22—1222no—
323C22—1222no—
324C22—4881no—
325C22—4881no—
326C22—2442no—
327C22—2442no—
328C22—2441no—
329C22—2441no—
330C22—2441no—
331C22—2441no—
332C22C2×#1451983511yescharacteristic
333C22#1684075211yescharacteristic
334C22D61⋊#10411yescharacteristic
335C4—21no—
336C4—21no—
337C4—41no—
338C4—41no—
339C4—81no—
340C4—81no—
341C4—4881no—
342C4—4881no—
343C4—4884no—
344C4—2441no—
345C4—2441no—
346C2—21no—
347C2—21no—
348C2—2442no—
349C2—2442no—
350C2#2146119411yescharacteristic
351C2#2146208111yescharacteristic
352C2#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#11732
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
182. C2×#125#6923semidirect
199. C61#11732semidirect

Maximal subgroups

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

subgroupindex
C4×#145198362
#214610562
#214608162
#214607992
#214516882
#1173261