Finite Group Databasebeta

← #29568104

Subgroups — #29568104

Order 15616.

406 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448296C211yesmaximal, characteristic
2#21445962C211yesmaximal, characteristic
3#21443644C212yesmaximal
4#21443643C212yesmaximal
5C61×#1831C211yesmaximal, characteristic
6C2×C4×Dic122C411yescharacteristic
7#16839668C411yescharacteristic
8#16839668C2211yescharacteristic
9#16839660C411yescharacteristic
10#16839660C2211yescharacteristic
11#16839646—21no—
12#16839646—21no—
13C4×#11758196—21no—
14C4×C4⋊Dic61C411yescharacteristic
15#16839608—21no—
16#16839517—21no—
17#16839517—21no—
18#16839517C2212yes—
19C2×C4⋊C8×C61—21no—
20C43×C61C2211yescharacteristic
21C61×#336—21no—
22C61×#336C2212yes—
23C22×Dic122C2×C411yescharacteristic
24C22×#92418—22no—
25C4×Dic122—22no—
26C4×Dic122C814yescomplemented
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×C4⋊Dic61C2×C411yescharacteristic
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×#11758196—21no—
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×C4×Dic61—21no—
34C2×C4×Dic61—21no—
35#14519684—21no—
36#14519684—21no—
37#14519684—21no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42C22×C8×C61—22no—
43C2×C42×C61C2×C411yescharacteristic
44C2×C42×C61C2×C411yescharacteristic
45C2×C42×C61D411yescharacteristic
46C2×C42×C61D411yescharacteristic
47C2×C42×C61D411yescharacteristic
48C2×C42×C61D411yescharacteristic
49C2×C42×C61C2311yescharacteristic
50C4⋊C8×C61—42no—
51C22×C4×C61C22⋊C411yescharacteristic
52C22×C4×C61C22⋊C411yescharacteristic
53C22×C4×C61C22⋊C411yescharacteristic
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C22×C411yescharacteristic
56C22×C4×C61C2×D411yescharacteristic
57C22×C4×C61C2×D411yescharacteristic
58C22×Dic61—21no—
59C22×Dic61—21no—
60C22×Dic61—21no—
61C22×Dic61—21no—
62C2×Dic122—21no—
63C2×Dic122—41no—
64C2×Dic122—41no—
65C2×Dic122C2×C812yes—
66C2×C8×C61—42no—
67C2×C8×C61—42no—
68C2×C8×C61—42no—
69C42×C61—21no—
70C42×C61—21no—
71C42×C61—22no—
72C42×C61—41no—
73C42×C61—41no—
74C42×C61—41no—
75C42×C61—41no—
76C42×C61C2×C812yes—
77C42×C61M1612yes—
78C4⋊Dic61—21no—
79C4⋊Dic61—41no—
80C4⋊Dic61—41no—
81C4⋊Dic61C2×C812yes—
82#11758196—24no—
83#11758196—42no—
84#11758196—41no—
85#11758196—41no—
86C4×Dic61—24no—
87C4×Dic61—42no—
88C2×#92418—42no—
89C2×#92418—42no—
90C2×#92418—42no—
91C23×C61C2×C22⋊C411yescharacteristic
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—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×C61C22⋊C812yes—
109C2×C4×C61C22⋊C812yes—
110C2×C4×C61C22×C811yescharacteristic
111C2×C4×C61C2×M1611yescharacteristic
112C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
113C2×C4×C61#13711yescharacteristic
114C2×C4×C61#13712yes—
115C2×Dic61—22no—
116C2×Dic61—22no—
117C2×Dic61—41no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127Dic122—42no—
128Dic122—42no—
129C8×C61—82no—
130#92418—82no—
131#7596—611nomaximal, Sylow
132C22×C61C2×C22⋊C811yescharacteristic
133C22×C61#41011yescharacteristic
134C22×C61#41311yescharacteristic
135C22×C61#41711yescharacteristic
136C22×C61#41911yescharacteristic
137C22×C61#42111yescharacteristic
138C22×C61#42111yescharacteristic
139C4×C61—21no—
140C4×C61—21no—
141C4×C61—22no—
142C4×C61—22no—
143C4×C61—21no—
144C4×C61—21no—
145C4×C61—22no—
146C4×C61—41no—
147C4×C61—41no—
148Dic61—42no—
149Dic61—42no—
150Dic61—81no—
151Dic61—81no—
152#2295—611no—
153#1839—611no—
154#1831D6111yescharacteristic
155#1272—612no—
156#1271—612no—
157C2×C61#145811yescharacteristic
158C2×C61#147711yescharacteristic
159C2×C61#147911yescharacteristic
160C2×C61#151211yescharacteristic
161C2×C61#151511yescharacteristic
162C2×C61#153511yescharacteristic
163C2×C61#155911yescharacteristic
164C2×C4×Q8—611no—
165C2×C4⋊C8—21no—
166#391—611no—
167#391—611no—
168#389—611no—
169#389—611no—
170#387—1221no—
171#387—1221no—
172C4×C4⋊C4—611no—
173C4×C4⋊C4—1221no—
174#376—1221no—
175C43C2×D6111yescharacteristic
176#336—21no—
177#336—612no—
178#336—1221no—
179#336—1221no—
180#336C2×D6112yes—
181C61#759611yescharacteristic, complemented, Sylow
182C22×Q8—611no—
183C22×C8—22no—
184C22×C8—1222no—
185C4×Q8—614no—
186C4×Q8—1222no—
187C2×C4⋊C4—611no—
188C2×C4⋊C4—611no—
189C2×C4⋊C4—611no—
190C2×C4⋊C4—1221no—
191C2×C4⋊C4—1221no—
192C2×C4⋊C4—1221no—
193C2×C42—1221no—
194C2×C42—1221no—
195C2×C42C4×D6111yescharacteristic
196C2×C42C4×D6111yescharacteristic
197C2×C42D24411yescharacteristic
198C2×C42D24411yescharacteristic
199C2×C42C22⋊D6111yescharacteristic
200C2×C42C22⋊D6111yescharacteristic
201C2×C42C22×D6111yescharacteristic
202C4⋊C8—42no—
203#95—1221no—
204#95—1221no—
205#95—1221no—
206#95—1221no—
207#95—1221no—
208#95—1221no—
209#95—1221no—
210C2×Q8—612no—
211C2×Q8—1221no—
212C2×Q8—2441no—
213C2×Q8—2441no—
214C22×C4—1221no—
215C22×C4—1221no—
216C22×C4—1221no—
217C22×C4—1221no—
218C22×C4#1175819811yescharacteristic
219C22×C4#1175819811yescharacteristic
220C22×C4#1175819811yescharacteristic
221C22×C4#1175819811yescharacteristic
222C22×C4C2×C4×D6111yescharacteristic
223C22×C4C2×D24411yescharacteristic
224C22×C4C2×C22⋊D6111yescharacteristic
225C2×C8—42no—
226C2×C8—42no—
227C2×C8—42no—
228C2×C8—2442no—
229C2×C8—2442no—
230C2×C8—2442no—
231C4⋊C4—612no—
232C4⋊C4—1224no—
233C4⋊C4—1221no—
234C4⋊C4—2441no—
235C4⋊C4—2441no—
236C4⋊C4—2442no—
237C4⋊C4—2441no—
238C4⋊C4—2441no—
239C42—21no—
240C42—22no—
241C42—21no—
242C42—41no—
243C42—41no—
244C42—41no—
245C42—41no—
246C42—1224no—
247C42—2442no—
248C42C8×D6112yes—
249C42#1175818912yes—
250C23C2×#1175819811yescharacteristic
251Q8—2442no—
252Q8—2442no—
253C2×C4—21no—
254C2×C4—21no—
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—1222no—
270C2×C4—1222no—
271C2×C4—2441no—
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#1451968912yes—
282C2×C4#1451968912yes—
283C2×C4C2×C8×D6111yescharacteristic
284C2×C4C2×#1175818911yescharacteristic
285C2×C4#1451980311yescharacteristic
286C2×C4#1451980811yescharacteristic
287C2×C4#1451981012yes—
288C8—82no—
289C8—4882no—
290C22C2×#1451968911yescharacteristic
291C22#1683973511yescharacteristic
292C22#1683974411yescharacteristic
293C22#1683976111yescharacteristic
294C22#1683977211yescharacteristic
295C22#1683977811yescharacteristic
296C22#1683978011yescharacteristic
297C4—21no—
298C4—21no—
299C4—22no—
300C4—21no—
301C4—21no—
302C4—22no—
303C4—22no—
304C4—41no—
305C4—41no—
306C4—4881no—
307C4—4881no—
308C4—2442no—
309C4—2442no—
310C2#2144413111yescharacteristic
311C2#2144420411yescharacteristic
312C2#2144421511yescharacteristic
313C2#2144435511yescharacteristic
314C2#2144437111yescharacteristic
315C2#2144444811yescharacteristic
316C2#2144454711yescharacteristic
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#7596
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
26. C4×Dic122C8semidirect
181. C61#7596semidirect

Maximal subgroups

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

subgroupindex
#214482962
#214459622
#214436442
#214436432
C61×#18312
#759661