Finite Group Databasebeta

← #29568304

Subgroups — #29568304

Order 15616.

402 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448296C211yesmaximal, characteristic
2#21445936C211yesmaximal, characteristic
3#21443644C212yesmaximal
4#21443643C212yesmaximal
5C61×#1839C211yesmaximal, characteristic
6C2×C4×Dic122C411yescharacteristic
7C2×C4⋊#92418—21no—
8#16839668C411yescharacteristic
9#16839668C2211yescharacteristic
10#16839660C411yescharacteristic
11#16839660C2211yescharacteristic
12#16839646—21no—
13#16839646—21no—
14C4×#11758196—21no—
15C4×C4⋊Dic61C411yescharacteristic
16#16839608—21no—
17#16839517—21no—
18#16839517C2212yes—
19C43×C61C2211yescharacteristic
20C61×#336—21no—
21C61×#336—21no—
22C61×#336C2212yes—
23C22×Dic122C2×C411yescharacteristic
24C22×#92418—22no—
25C4×Dic122—22no—
26C4×Dic122—22no—
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—
35C4⋊#92418—42no—
36#14519684—21no—
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
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×Dic122M1612yes—
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×C61SD1612yes—
77C42×C61Q1612yes—
78C4⋊Dic61—21no—
79C4⋊Dic61—41no—
80C4⋊Dic61—41no—
81C4⋊Dic61M1612yes—
82#11758196—24no—
83#11758196—42no—
84#11758196—42no—
85C4×Dic61—24no—
86C4×Dic61—42no—
87C2×#92418—42no—
88C2×#92418—42no—
89C2×#92418—42no—
90C23×C61C2×C22⋊C411yescharacteristic
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—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#10312yes—
108C2×C4×C61#10312yes—
109C2×C4×C61C2×M1611yescharacteristic
110C2×C4×C61C2×M1611yescharacteristic
111C2×C4×C61C2×SD1611yescharacteristic
112C2×C4×C61C2×Q1611yescharacteristic
113C2×C4×C61#13512yes—
114C2×Dic61—22no—
115C2×Dic61—22no—
116C2×Dic61—41no—
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—
126Dic122—42no—
127Dic122—42no—
128C8×C61—82no—
129#92418—82no—
130#7644—611nomaximal, Sylow
131C22×C61#40711yescharacteristic
132C22×C61#41011yescharacteristic
133C22×C61#41311yescharacteristic
134C22×C61C2×#10311yescharacteristic
135C22×C61#41611yescharacteristic
136C22×C61#42111yescharacteristic
137C22×C61#42111yescharacteristic
138C4×C61—22no—
139C4×C61—21no—
140C4×C61—21no—
141C4×C61—22no—
142C4×C61—21no—
143C4×C61—21no—
144C4×C61—22no—
145C4×C61—41no—
146C4×C61—41no—
147Dic61—42no—
148Dic61—42no—
149Dic61—81no—
150Dic61—81no—
151#2295—611no—
152#1839D6111yescharacteristic
153#1831—611no—
154#1272—612no—
155#1271—612no—
156C2×C61#146411yescharacteristic
157C2×C61#148711yescharacteristic
158C2×C61#148811yescharacteristic
159C2×C61#151811yescharacteristic
160C2×C61#152111yescharacteristic
161C2×C61#153511yescharacteristic
162C2×C61#154211yescharacteristic
163C2×C4×Q8—611no—
164C2×C4⋊C8—1221no—
165#391—611no—
166#391—611no—
167#389—611no—
168#389—611no—
169#387—1221no—
170#387—1221no—
171C4×C4⋊C4—611no—
172C4×C4⋊C4—1221no—
173#376—1221no—
174C43C2×D6111yescharacteristic
175#336—21no—
176#336—21no—
177#336—612no—
178#336—1221no—
179#336C2×D6112yes—
180C61#764411yescharacteristic, complemented, Sylow
181C22×Q8—611no—
182C22×C8—22no—
183C22×C8—1222no—
184C4×Q8—1222no—
185C4×Q8—1222no—
186C2×C4⋊C4—611no—
187C2×C4⋊C4—611no—
188C2×C4⋊C4—611no—
189C2×C4⋊C4—1221no—
190C2×C4⋊C4—1221no—
191C2×C4⋊C4—1221no—
192C2×C42—1221no—
193C2×C42—1221no—
194C2×C42C4×D6111yescharacteristic
195C2×C42C4×D6111yescharacteristic
196C2×C42D24411yescharacteristic
197C2×C42D24411yescharacteristic
198C2×C42C22⋊D6111yescharacteristic
199C2×C42C22⋊D6111yescharacteristic
200C2×C42C22×D6111yescharacteristic
201C4⋊C8—2442no—
202#95—1221no—
203#95—1221no—
204#95—1221no—
205#95—1221no—
206#95—1221no—
207#95—1221no—
208#95—1221no—
209C2×Q8—612no—
210C2×Q8—1221no—
211C2×Q8—2441no—
212C2×Q8—2441no—
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—1224no—
232C4⋊C4—1221no—
233C4⋊C4—2441no—
234C4⋊C4—2441no—
235C4⋊C4—2442no—
236C4⋊C4—2442no—
237C42—21no—
238C42—21no—
239C42—22no—
240C42—41no—
241C42—41no—
242C42—41no—
243C42—41no—
244C42—1224no—
245C42—2442no—
246C42#1175819012yes—
247C42Dic24412yes—
248C23C2×#1175819811yescharacteristic
249Q8—2442no—
250Q8—2442no—
251C2×C4—21no—
252C2×C4—21no—
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—1222no—
268C2×C4—1222no—
269C2×C4—2441no—
270C2×C4—2441no—
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#1451970212yes—
280C2×C4#1451970212yes—
281C2×C4M16×D6111yescharacteristic
282C2×C4M16×D6111yescharacteristic
283C2×C4C2×#1175819011yescharacteristic
284C2×C4C2×Dic24411yescharacteristic
285C2×C4#1451979712yes—
286C8—82no—
287C8—4882no—
288C22#1683972511yescharacteristic
289C22#1683973511yescharacteristic
290C22#1683974411yescharacteristic
291C22C2×#1451970211yescharacteristic
292C22#1683975611yescharacteristic
293C22#1683977811yescharacteristic
294C22#1683978011yescharacteristic
295C4—21no—
296C4—21no—
297C4—22no—
298C4—21no—
299C4—21no—
300C4—22no—
301C4—22no—
302C4—41no—
303C4—41no—
304C4—4881no—
305C4—4881no—
306C4—2442no—
307C4—2442no—
308C2#2144415111yescharacteristic
309C2#2144424911yescharacteristic
310C2#2144425111yescharacteristic
311C2#2144438411yescharacteristic
312C2#2144439411yescharacteristic
313C2#2144444811yescharacteristic
314C2#2144447411yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1839C2
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1839D61
hypocenterC61#7644
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C43 ◁ #1839

Complements

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

NH ≅ G/Ntype
180. C61#7644semidirect

Maximal subgroups

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

subgroupindex
#214482962
#214459362
#214436442
#214436432
C61×#18392
#764461