Finite Group Databasebeta

← #29590353

Subgroups — #29590353

Order 15616.

470 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 87 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#21449103C211yesmaximal, characteristic
2C4×#14519692C211yesmaximal, characteristic
3#21443841C212yesmaximal, complemented
4#21443820C212yesmaximal, complemented
5C61×#1459C211yesmaximal, characteristic
6C2×C4×Dic122C411yescharacteristic, complemented
7C2×#14519692—21no—
8#16839700—21no—
9#16839687C411yescharacteristic, complemented
10#16839687C2211yescharacteristic
11#16839676—21no—
12#16839674C411yescharacteristic, complemented
13#16839674C2211yescharacteristic
14C4×C22⋊Dic61—21no—
15C4×C22⋊Dic61—21no—
16C4×C22⋊Dic61—21no—
17#16839608C411yescharacteristic, complemented
18#16839529C2212yes—
19C2×C4×D4×C61C2211yescharacteristic
20C2×C22⋊C8×C61—21no—
21C61×#324—21no—
22C61×#323C2212yes—
23C22×Dic122C2×C411yescharacteristic
24C4×Dic122—41no—
25C4×Dic122—41no—
26C2×C4⋊Dic61C2×C411yescharacteristic
27C2×#11758196—21no—
28C2×C22⋊Dic61—22no—
29C2×C22⋊Dic61—21no—
30C2×C22⋊Dic61—21no—
31C2×C22⋊Dic61—21no—
32C2×C22⋊Dic61—21no—
33C2×C4×Dic61—21no—
34C2×C4×Dic61—21no—
35C2×C4×Dic61—41no—
36#14519692—24no—
37#14519684—21no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684—41no—
43#14519684C2×C411yescharacteristic
44#14519684C2×C411yescharacteristic
45C22×D4×C61D411yescharacteristic
46C23×C4×C61D411yescharacteristic
47C23×C4×C61D411yescharacteristic
48C22×C8×C61—41no—
49C4×D4×C61—41no—
50C4×D4×C61—41no—
51C2×C4⋊C4×C61D411yescharacteristic
52C2×C22⋊C4×C61C2×C411yescharacteristic
53C2×C22⋊C4×C61C2311yescharacteristic
54C2×C42×C61C2×C411yescharacteristic
55C22⋊C8×C61—22no—
56C22⋊C8×C61—41no—
57C24×C61C22⋊C411yescharacteristic
58C24×C61C2×D411yescharacteristic
59C2×D4×C61—22no—
60C2×D4×C61—22no—
61C2×D4×C61—41no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—42no—
67C22×C4×C61—42no—
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22×C411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—42no—
78C2×Dic122—41no—
79C2×Dic122—42no—
80C2×C8×C61—42no—
81C2×C8×C61—82no—
82C4⋊C4×C61—41no—
83C22⋊C4×C61—41no—
84C22⋊C4×C61—41no—
85C42×C61—21no—
86C42×C61—21no—
87C22⋊Dic61—24no—
88C22⋊Dic61—42no—
89C22⋊Dic61—42no—
90C22⋊Dic61—42no—
91C22⋊Dic61—42no—
92C22⋊Dic61—42no—
93C4⋊Dic61—41no—
94#11758196—42no—
95C4×Dic61—42no—
96C4×Dic61—41no—
97C4×Dic61—41no—
98C4×Dic61—82no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—41no—
104C23×C61—41no—
105C23×C61—41no—
106C23×C61—41no—
107C23×C61#10412yes—
108C23×C61C2×C22⋊C411yescharacteristic
109C23×C61#13512yes—
110D4×C61—44no—
111C2×C4×C61—22no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—42no—
119C2×C4×C61—42no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—81no—
124C2×C4×C61—81no—
125C2×C4×C61#9911yescharacteristic
126C2×C4×C61#9911yescharacteristic
127C2×Dic61—22no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—44no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—82no—
141C2×Dic61—82no—
142Dic122—42no—
143Dic122—42no—
144C8×C61—82no—
145#11728—611nomaximal, Sylow
146C22×C61—21no—
147C22×C61—21no—
148C22×C61—22no—
149C22×C61—22no—
150C22×C61—42no—
151C22×C61—42no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61—81no—
157C22×C61—81no—
158C22×C61C2×#9911yescharacteristic
159C22×C61#41611yescharacteristic
160C22×C61C2×#10411yescharacteristic
161C4×C61—21no—
162C4×C61—41no—
163C4×C61—41no—
164C4×C61—41no—
165C4×C61—41no—
166C4×C61#35412yes—
167Dic61—42no—
168Dic61—81no—
169Dic61—81no—
170Dic61—84no—
171Dic61—81no—
172#2398—611no—
173C4×#99—611no—
174#1459D6111yescharacteristic
175#1351—612no—
176#1344—612no—
177C2×C61—21no—
178C2×C61—21no—
179C2×C61—42no—
180C2×C61—42no—
181C2×C61#150111yescharacteristic
182C2×C61#212011yescharacteristic
183C2×C61C2×#35411yescharacteristic
184C2×C4×Q8—611no—
185C2×C4×D4C2×D6111yescharacteristic
186C2×#99—1221no—
187C2×C22⋊C8—21no—
188#400—1221no—
189#397—611no—
190#397—611no—
191#394—1221no—
192#393—611no—
193#393—611no—
194C4×C22⋊C4—1221no—
195C4×C22⋊C4—1221no—
196C4×C22⋊C4—1221no—
197#376—611no—
198#342—612no—
199#324—21no—
200#323C2×D6112yes—
201C61#1172811yescharacteristic, complemented, Sylow
202C22×Q8—611no—
203C22×D4D24411yescharacteristic
204C23×C4D24411yescharacteristic
205C23×C4C22⋊D6111yescharacteristic
206C22×C8—41no—
207C4×Q8—2441no—
208C4×Q8—2441no—
209C4×D4—41no—
210C4×D4—41no—
211C2×C4⋊C4—611no—
212C2×C4⋊C4—1221no—
213C2×C4⋊C4C22⋊D6111yescharacteristic
214C2×C22⋊C4—1222no—
215C2×C22⋊C4—1221no—
216C2×C22⋊C4—1221no—
217C2×C22⋊C4—1221no—
218C2×C22⋊C4—1221no—
219C2×C22⋊C4C4×D6111yescharacteristic
220C2×C22⋊C4C22×D6111yescharacteristic
221C2×C42—1221no—
222C2×C42—1221no—
223C2×C42—2441no—
224C2×C42C4×D6111yescharacteristic
225#99—1224no—
226C22⋊C8—22no—
227C22⋊C8—41no—
228#95—611no—
229#95—611no—
230#95—1221no—
231#95—1221no—
232#95—1221no—
233#95—1221no—
234#95—1221no—
235#95—2441no—
236C24#1175819811yescharacteristic
237C24C2×D24411yescharacteristic
238C2×Q8—2441no—
239C2×Q8—2442no—
240C2×D4—22no—
241C2×D4—22no—
242C2×D4—41no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—2442no—
254C22×C4#1175819811yescharacteristic
255C22×C4#1175819811yescharacteristic
256C22×C4#1175819811yescharacteristic
257C22×C4C2×C4×D6111yescharacteristic
258C22×C4C2×C22⋊D6111yescharacteristic
259C2×C8—42no—
260C2×C8—82no—
261C4⋊C4—41no—
262C4⋊C4—2441no—
263C4⋊C4—2442no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C22⋊C4—1224no—
267C22⋊C4—2442no—
268C22⋊C4—2442no—
269C22⋊C4—2442no—
270C22⋊C4—2442no—
271C22⋊C4—2442no—
272C42—21no—
273C42—21no—
274C42—4882no—
275C42—2442no—
276C42—2441no—
277C42—2441no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23#1451970312yes—
287C23C2×#1175819811yescharacteristic
288C23#1451979912yes—
289Q8—2442no—
290Q8—2442no—
291D4—44no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—1222no—
307C2×C4—4882no—
308C2×C4—4882no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2444no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4#1451969111yescharacteristic
322C2×C4#1451969111yescharacteristic
323C8—82no—
324C22—21no—
325C22—21no—
326C22—22no—
327C22—22no—
328C22—42no—
329C22—42no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—81no—
335C22—81no—
336C22C2×#1451969111yescharacteristic
337C22#1683975911yescharacteristic
338C22C2×#1451970311yescharacteristic
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—4881no—
345C4—4881no—
346C4—4884no—
347C4—4881no—
348C4—2442no—
349C4#1683955612yes—
350C2—21no—
351C2—21no—
352C2—42no—
353C2—42no—
354C2#2144431111yescharacteristic
355C2#2144746111yescharacteristic
356C2C2×#1683955611yescharacteristic
subgroupG/H
centerC2×C4#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1459C2
socleC22×C61C2×#99
prime radicalC22×D4×C61D4
cosocleC2×C22⋊C4×C61C23
hypercenter#1459D61
hypocenterC61#11728
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
3. #21443841C2semidirect
4. #21443820C2semidirect
6. C2×C4×Dic122C4semidirect
9. #16839687C4semidirect
12. #16839674C4semidirect
17. #16839608C4semidirect
201. C61#11728semidirect

Maximal subgroups

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

subgroupindex
#214491032
C4×#145196922
#214438412
#214438202
C61×#14592
#1172861