Finite Group Databasebeta

← #29567045

Subgroups — #29567045

Order 15616.

422 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 75 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#21445899C211yesmaximal, characteristic
2#21444051C211yesmaximal, characteristic
3C61×#1463C211yesmaximal, characteristic
4C22×C4×Dic61C411yescharacteristic
5#16839726—21no—
6C2×#14519684—21no—
7C2×#14519684—21no—
8C2×#14519684C411yescharacteristic
9#16839531—21no—
10#16839531C412yescomplemented
11C22×C4⋊C4×C61C2211yescharacteristic
12C61×#407—21no—
13C61×#324—21no—
14C61×#324C412yescomplemented
15C23×Dic61—21no—
16C23×Dic61—21no—
17C2×#11758194—22no—
18C2×C4×Dic61—41no—
19C2×C4×Dic61—42no—
20C22⋊#92418—41no—
21C22⋊#92418—41no—
22#14519684—24no—
23#14519684—42no—
24#14519684—41no—
25C23×C4×C61C2×C411yescharacteristic
26C23×C4×C61D411yescharacteristic
27C23×C4×C61D411yescharacteristic
28C2×M16×C61—41no—
29C2×C4⋊C4×C61—41no—
30C2×C4⋊C4×C61—41no—
31C2×C4⋊C4×C61C2×C411yescharacteristic
32C2×C4⋊C4×C61C2×C411yescharacteristic
33C2×C4⋊C4×C61D411yescharacteristic
34C2×C4⋊C4×C61Q811yescharacteristic
35C22⋊C8×C61—22no—
36C22⋊C8×C61—41no—
37C24×C61C22⋊C411yescharacteristic
38C22×C4×C61—21no—
39C22×C4×C61—21no—
40C22×C4×C61—21no—
41C22×C4×C61—21no—
42C22×C4×C61—21no—
43C22×C4×C61—21no—
44C22×C4×C61—22no—
45C22×C4×C61—41no—
46C22×C4×C61—41no—
47C22×C4×C61—41no—
48C22×C4×C61—41no—
49C22×C4×C61—41no—
50C22×C4×C61C4211yescharacteristic
51C22×C4×C61C22⋊C411yescharacteristic
52C22×C4×C61C22⋊C411yescharacteristic
53C22×C4×C61C4⋊C411yescharacteristic
54C22×C4×C61C4⋊C411yescharacteristic
55C22×C4×C61C4⋊C411yescharacteristic
56C22×Dic61—22no—
57C22×Dic61—22no—
58C22×Dic61—22no—
59C22×Dic61—22no—
60C22×Dic61—41no—
61C22×Dic61—41no—
62C22×Dic61—41no—
63C22×Dic61—41no—
64C22×Dic61—41no—
65C22×Dic61—41no—
66C22×Dic61—41no—
67C22×Dic61—41no—
68C22×Dic61—41no—
69C22×Dic61—41no—
70M16×C61—81no—
71M16×C61—81no—
72C2×C8×C61—42no—
73C4⋊C4×C61—41no—
74C4⋊C4×C61—41no—
75C4⋊C4×C61—41no—
76C4⋊C4×C61—41no—
77C4×Dic61—42no—
78C4×Dic61—42no—
79#11758194—42no—
80#11758194—42no—
81C2×#92418—42no—
82C23×C61—21no—
83C23×C61—21no—
84C23×C61—21no—
85C23×C61—21no—
86C23×C61—21no—
87C23×C61—21no—
88C23×C61#9511yescharacteristic
89C23×C61#9911yescharacteristic
90C23×C61#9911yescharacteristic
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—42no—
101C2×C4×C61—42no—
102C2×C4×C61—42no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—81no—
112C2×C4×C61#10412yes—
113C2×Dic61—24no—
114C2×Dic61—42no—
115C2×Dic61—42no—
116C2×Dic61—42no—
117C2×Dic61—42no—
118C2×Dic61—42no—
119C2×Dic61—42no—
120C2×Dic61—42no—
121C2×Dic61—42no—
122C2×Dic61—42no—
123C2×Dic61—81no—
124C2×Dic61—81no—
125C2×Dic61—81no—
126C2×Dic61—81no—
127C8×C61—82no—
128#92418—82no—
129#7215—611nomaximal, Sylow
130C22×C61—21no—
131C22×C61—21no—
132C22×C61—21no—
133C22×C61—21no—
134C22×C61—21no—
135C22×C61—21no—
136C22×C61—21no—
137C22×C61—21no—
138C22×C61—21no—
139C22×C61—21no—
140C22×C61—21no—
141C22×C61—21no—
142C22×C61—21no—
143C22×C61—21no—
144C22×C61H(3,ℤ/4)11yescharacteristic
145C22×C61#33911yescharacteristic
146C22×C61#34211yescharacteristic
147C22×C61AΣL(1,𝔽16)11yescharacteristic
148C22×C61#35211yescharacteristic
149C22×C61#35511yescharacteristic
150C22×C61#35611yescharacteristic
151C4×C61—22no—
152C4×C61—41no—
153C4×C61—41no—
154C4×C61—41no—
155C4×C61—41no—
156C4×C61—41no—
157Dic61—44no—
158Dic61—82no—
159#1821—611no—
160#1463D6111yescharacteristic
161#1436—611no—
162C2×C61—21no—
163C2×C61—21no—
164C2×C61—21no—
165C2×C61—21no—
166C2×C61—21no—
167C2×C61—21no—
168C2×C61#128411yescharacteristic
169C2×C61#139011yescharacteristic
170C2×C61#139411yescharacteristic
171C22×C4⋊C4C2×D6111yescharacteristic
172C22×C42—611no—
173#407—21no—
174#407—1221no—
175C2×#95—611no—
176C2×#95—1221no—
177C2×#95—1221no—
178#343—612no—
179#343—1221no—
180#324—21no—
181#324Dic6112yescomplemented
182C61#721511yescharacteristic, complemented, Sylow
183C23×C4—1221no—
184C23×C4—1221no—
185C23×C4C4×D6111yescharacteristic
186C23×C4D24411yescharacteristic
187C23×C4C22⋊D6111yescharacteristic
188C2×M16—41no—
189C2×M16—1222no—
190C2×C4⋊C4—41no—
191C2×C4⋊C4—41no—
192C2×C4⋊C4Dic12211yescharacteristic
193C2×C4⋊C4C4×D6111yescharacteristic
194C2×C4⋊C4C2×Dic6111yescharacteristic
195C2×C4⋊C4C22⋊D6111yescharacteristic
196C2×C42—2441no—
197C2×C42—2442no—
198C22⋊C8—22no—
199C22⋊C8—41no—
200C22⋊C8—2441no—
201C22⋊C8—2441no—
202#95—1224no—
203#95—2441no—
204#95—2442no—
205C24#1175819811yescharacteristic
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—22no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4—41no—
218C22×C4—1222no—
219C22×C4—1222no—
220C22×C4—1222no—
221C22×C4—1222no—
222C22×C4—2441no—
223C22×C4—2441no—
224C22×C4—2441no—
225C22×C4—2441no—
226C22×C4—2441no—
227C22×C4—2441no—
228C22×C4—2441no—
229C22×C4—2441no—
230C22×C4—2441no—
231C22×C4—2441no—
232C22×C4C4×Dic6111yescharacteristic
233C22×C4#1175819611yescharacteristic
234C22×C4#1175819611yescharacteristic
235C22×C4C4⋊Dic6111yescharacteristic
236C22×C4#1175819811yescharacteristic
237C22×C4C22⋊Dic6111yescharacteristic
238M16—81no—
239M16—81no—
240M16—2442no—
241M16—2442no—
242C2×C8—42no—
243C2×C8—2442no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C42—2442no—
249C42—2442no—
250C23—21no—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23#1451968411yescharacteristic
257C23#1451969111yescharacteristic
258C23#1451969111yescharacteristic
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—81no—
280C2×C4—1224no—
281C2×C4—4881no—
282C2×C4—4881no—
283C2×C4—4881no—
284C2×C4—4881no—
285C2×C4—2442no—
286C2×C4—2442no—
287C2×C4—2442no—
288C2×C4—2442no—
289C2×C4—2442no—
290C2×C4—2442no—
291C2×C4—2442no—
292C2×C4—2442no—
293C2×C4—2442no—
294C2×C4#1451970312yes—
295C8—82no—
296C8—4882no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22#1683951911yescharacteristic
312C22#1683952311yescharacteristic
313C22#1683952811yescharacteristic
314C22#1683954811yescharacteristic
315C22#1683955111yescharacteristic
316C22#1683955811yescharacteristic
317C22#1683956011yescharacteristic
318C4—22no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—4882no—
325C4—2444no—
326C2—21no—
327C2—21no—
328C2—21no—
329C2—21no—
330C2—21no—
331C2—21no—
332C2#2144367311yescharacteristic
333C2#2144393611yescharacteristic
334C2#2144394511yescharacteristic
subgroupG/H
centerC22#16839528
commutatorC22×C4×C61C42
FrattiniC22×C4⋊C4C2×D61
FittingC61×#1463C2
socleC22×C61#342
prime radicalC24×C61C22⋊C4
cosocleC22×C4⋊C4×C61C22
hypercenter#1463D61
hypocenterC61#7215
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
10. #16839531C4semidirect
14. C61×#324C4semidirect
181. #324Dic61semidirect
182. C61#7215semidirect

Maximal subgroups

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

subgroupindex
#214458992
#214440512
C61×#14632
#721561