Finite Group Databasebeta

← #29568130

Subgroups — #29568130

Order 15616.

408 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519769C211yesmaximal, characteristic
2#21445936C211yesmaximal, characteristic
3#21443643C212yesmaximal
4#21443641C212yesmaximal
5C61×#1831C211yesmaximal, characteristic
6C2×#14519769C411yescharacteristic
7C2×C4⋊#92418—21no—
8#16839660C2211yescharacteristic
9#16839660C2211yescharacteristic
10#16839646—21no—
11#16839646—21no—
12#16839628C411yescharacteristic
13C4×#11758196—21no—
14C4×#11758196—21no—
15C4×C4⋊Dic61C411yescharacteristic
16C4×C4⋊Dic61C411yescharacteristic
17#16839517—21no—
18#16839517C2212yes—
19C2×C4⋊C8×C61—21no—
20C43×C61C2211yescharacteristic
21C61×#336—21no—
22C61×#336C2212yes—
23C22×#92418—22no—
24#14519769—22no—
25#14519769C814yescomplemented
26C2×C4⋊Dic61C2×C411yescharacteristic
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×C4⋊Dic61C2×C411yescharacteristic
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×#11758196—21no—
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×C4×Dic61—21no—
35C2×C4×Dic61—21no—
36C4⋊#92418—42no—
37#14519684—21no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43C22×C8×C61—22no—
44C2×C42×C61C2×C411yescharacteristic
45C2×C42×C61C2×C411yescharacteristic
46C2×C42×C61D411yescharacteristic
47C2×C42×C61D411yescharacteristic
48C2×C42×C61D411yescharacteristic
49C2×C42×C61D411yescharacteristic
50C2×C42×C61C2311yescharacteristic
51C4⋊C8×C61—42no—
52C22×C4×C61C22⋊C411yescharacteristic
53C22×C4×C61C22⋊C411yescharacteristic
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22×C411yescharacteristic
57C22×C4×C61C2×D411yescharacteristic
58C22×C4×C61C2×D411yescharacteristic
59C22×Dic61—21no—
60C22×Dic61—21no—
61C22×Dic61—21no—
62C22×Dic61—21no—
63C2×C8×C61—42no—
64C2×C8×C61—42no—
65C2×C8×C61—42no—
66C42×C61—22no—
67C42×C61—21no—
68C42×C61—21no—
69C42×C61—21no—
70C42×C61—21no—
71C42×C61—41no—
72C42×C61—41no—
73C42×C61—41no—
74C42×C61C2×C812yes—
75C42×C61M1612yes—
76C4⋊Dic61—21no—
77C4⋊Dic61—21no—
78C4⋊Dic61—41no—
79C4⋊Dic61—41no—
80C4⋊Dic61C2×C812yes—
81C4⋊Dic61C2×C812yes—
82#11758196—24no—
83#11758196—24no—
84#11758196—41no—
85#11758196—41no—
86#11758196—41no—
87#11758196—41no—
88C4×Dic61—42no—
89C4×Dic61—42no—
90C2×#92418—42no—
91C2×#92418—42no—
92C2×#92418—42no—
93C23×C61C2×C22⋊C411yescharacteristic
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—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61C22⋊C812yes—
110C2×C4×C61C22⋊C812yes—
111C2×C4×C61#10112yes—
112C2×C4×C61C22×C811yescharacteristic
113C2×C4×C61C2×M1611yescharacteristic
114C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
115C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
116C2×C4×C61#13711yescharacteristic
117C2×C4×C61#13711yescharacteristic
118C2×Dic61—22no—
119C2×Dic61—22no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C8×C61—82no—
131#92418—82no—
132#7602—611nomaximal, Sylow
133C22×C61C2×C22⋊C811yescharacteristic
134C22×C61#41011yescharacteristic
135C22×C61C2×#10111yescharacteristic
136C22×C61#41711yescharacteristic
137C22×C61#41711yescharacteristic
138C22×C61#42111yescharacteristic
139C22×C61#42111yescharacteristic
140C4×C61—21no—
141C4×C61—21no—
142C4×C61—22no—
143C4×C61—22no—
144C4×C61—21no—
145C4×C61—21no—
146C4×C61—21no—
147C4×C61—21no—
148C4×C61—22no—
149C4×C61—41no—
150Dic61—42no—
151Dic61—42no—
152Dic61—81no—
153Dic61—81no—
154C4×#125—611no—
155#1831—611no—
156#1831D6111yescharacteristic
157#1271—612no—
158#1271—612no—
159C2×C61#146111yescharacteristic
160C2×C61#147711yescharacteristic
161C2×C61#147711yescharacteristic
162C2×C61#151211yescharacteristic
163C2×C61#151211yescharacteristic
164C2×C61#153411yescharacteristic
165C2×C61#156111yescharacteristic
166C2×#125—611no—
167C2×C4⋊C8—21no—
168C2×C4⋊C8—1221no—
169#389—611no—
170#389—611no—
171#387—1221no—
172#387—1221no—
173#382—611no—
174C4×C4⋊C4—611no—
175C4×C4⋊C4—611no—
176C4×C4⋊C4—1221no—
177C4×C4⋊C4—1221no—
178C43C2×D6111yescharacteristic
179#336—21no—
180#336—612no—
181#336—1221no—
182#336C2×D6112yes—
183C61#760211yescharacteristic, complemented, Sylow
184C22×C8—22no—
185C22×C8—1222no—
186#125—614no—
187#125—1222no—
188C2×C4⋊C4—611no—
189C2×C4⋊C4—611no—
190C2×C4⋊C4—611no—
191C2×C4⋊C4—611no—
192C2×C4⋊C4—1221no—
193C2×C4⋊C4—1221no—
194C2×C4⋊C4—1221no—
195C2×C4⋊C4—1221no—
196C2×C42—1221no—
197C2×C42—1221no—
198C2×C42C4×D6111yescharacteristic
199C2×C42C4×D6111yescharacteristic
200C2×C42D24411yescharacteristic
201C2×C42D24411yescharacteristic
202C2×C42C22⋊D6111yescharacteristic
203C2×C42C22⋊D6111yescharacteristic
204C2×C42C22×D6111yescharacteristic
205C4⋊C8—42no—
206C4⋊C8—2442no—
207#95—1221no—
208#95—1221no—
209#95—1221no—
210#95—1221no—
211#95—1221no—
212#95—1221no—
213C22×C4—1221no—
214C22×C4—1221no—
215C22×C4—1221no—
216C22×C4—1221no—
217C22×C4#1175819811yescharacteristic
218C22×C4#1175819811yescharacteristic
219C22×C4#1175819811yescharacteristic
220C22×C4#1175819811yescharacteristic
221C22×C4C2×C4×D6111yescharacteristic
222C22×C4C2×D24411yescharacteristic
223C22×C4C2×C22⋊D6111yescharacteristic
224C2×C8—42no—
225C2×C8—42no—
226C2×C8—42no—
227C2×C8—2442no—
228C2×C8—2442no—
229C2×C8—2442no—
230C4⋊C4—612no—
231C4⋊C4—612no—
232C4⋊C4—1224no—
233C4⋊C4—1224no—
234C4⋊C4—1221no—
235C4⋊C4—1221no—
236C4⋊C4—2441no—
237C4⋊C4—2441no—
238C4⋊C4—2441no—
239C4⋊C4—2441no—
240C4⋊C4—2441no—
241C4⋊C4—2441no—
242C42—21no—
243C42—21no—
244C42—22no—
245C42—21no—
246C42—21no—
247C42—41no—
248C42—41no—
249C42—41no—
250C42—2442no—
251C42—2442no—
252C42C8×D6112yes—
253C42#1175818912yes—
254C23C2×#1175819811yescharacteristic
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
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—21no—
269C2×C4—21no—
270C2×C4—1222no—
271C2×C4—1222no—
272C2×C4—2441no—
273C2×C4—2441no—
274C2×C4—2441no—
275C2×C4—2441no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4—2441no—
279C2×C4—2441no—
280C2×C4—2441no—
281C2×C4—2441no—
282C2×C4#1451968912yes—
283C2×C4#1451968912yes—
284C2×C4#1451969512yes—
285C2×C4C2×C8×D6111yescharacteristic
286C2×C4C2×#1175818911yescharacteristic
287C2×C4#1451980311yescharacteristic
288C2×C4#1451980511yescharacteristic
289C2×C4#1451980811yescharacteristic
290C2×C4#1451981011yescharacteristic
291C8—82no—
292C8—4882no—
293C22C2×#1451968911yescharacteristic
294C22#1683973511yescharacteristic
295C22C2×#1451969511yescharacteristic
296C22#1683976111yescharacteristic
297C22#1683976411yescharacteristic
298C22#1683977811yescharacteristic
299C22#1683978011yescharacteristic
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—21no—
305C4—21no—
306C4—22no—
307C4—22no—
308C4—22no—
309C4—41no—
310C4—4881no—
311C4—4881no—
312C4—2442no—
313C4—2442no—
314C2#2144414211yescharacteristic
315C2#2144420411yescharacteristic
316C2#2144420711yescharacteristic
317C2#2144435511yescharacteristic
318C2#2144435811yescharacteristic
319C2#2144444511yescharacteristic
320C2#2144455611yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC61×#1831C2
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1831D61
hypocenterC61#7602
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C43 ◁ #1831

Complements

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

NH ≅ G/Ntype
25. #14519769C8semidirect
183. C61#7602semidirect

Maximal subgroups

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

subgroupindex
C4×#145197692
#214459362
#214436432
#214436412
C61×#18312
#760261