Finite Group Databasebeta

← #29570949

Subgroups — #29570949

Order 15616.

488 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
1C4×#14519769C211yesmaximal, characteristic
2#21445568C211yesmaximal, characteristic
3C2×#16839503C212yesmaximal
4#21443701C212yesmaximal
5C4×#97×C61C211yesmaximal, characteristic
6C2×#14519769C2211yescharacteristic
7C2×#14519688C2212yes—
8#16839660C411yescharacteristic
9#16839660C411yescharacteristic
10#16839646—21no—
11#16839646—21no—
12#16839628C2211yescharacteristic
13C4×#11758196—21no—
14C4×#11758196—21no—
15C4×C4⋊Dic61C411yescharacteristic
16C4×C4⋊Dic61C411yescharacteristic
17#16839517—21no—
18#16839517—21no—
19#16839503C418yescomplemented
20C2×#97×C61—21no—
21C2×#97×C61C2212yes—
22C2×C4×C8×C61—21no—
23C43×C61C2211yescharacteristic
24C22×#92418—22no—
25#14519769—22no—
26#14519769C2×C414yes—
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×C4⋊Dic61C2×C411yescharacteristic
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×C4⋊Dic61C2×C411yescharacteristic
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×C4×Dic61—21no—
36C2×C4×Dic61—21no—
37#14519688—22no—
38#14519688C2×C414yes—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45C22×C8×C61—22no—
46C2×C42×C61C2×C411yescharacteristic
47C2×C42×C61C2×C411yescharacteristic
48C2×C42×C61D411yescharacteristic
49C2×C42×C61D411yescharacteristic
50C2×C42×C61D411yescharacteristic
51C2×C42×C61D411yescharacteristic
52C2×C42×C61C2311yescharacteristic
53#97×C61—24no—
54#97×C61—22no—
55#97×C61C2×C414yes—
56C4×C8×C61—24no—
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22×C411yescharacteristic
62C22×C4×C61C2×D411yescharacteristic
63C22×C4×C61C2×D411yescharacteristic
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61—21no—
67C22×Dic61—21no—
68C2×C8×C61—24no—
69C2×C8×C61—24no—
70C2×C8×C61—24no—
71C42×C61—22no—
72C42×C61—22no—
73C42×C61—22no—
74C42×C61—41no—
75C42×C61—41no—
76C42×C61—41no—
77C42×C61C22×C412yes—
78C42×C61#4112yes—
79C4⋊Dic61—21no—
80C4⋊Dic61—21no—
81C4⋊Dic61—41no—
82C4⋊Dic61—41no—
83C4⋊Dic61C4212yes—
84C4⋊Dic61C4212yes—
85#11758196—24no—
86#11758196—24no—
87#11758196—42no—
88#11758196—42no—
89C4×Dic61—42no—
90C4×Dic61—42no—
91C2×#92418—24no—
92C2×#92418—42no—
93C2×#92418—42no—
94C23×C61C2×C22⋊C411yescharacteristic
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×C61—21no—
110C2×C4×C61#10112yes—
111C2×C4×C61#10412yes—
112C2×C4×C61#10412yes—
113C2×C4×C61C2×C4211yescharacteristic
114C2×C4×C61#11711yescharacteristic
115C2×C4×C61C4×D412yes—
116C2×C4×C61C4×D412yes—
117C2×Dic61—22no—
118C2×Dic61—22no—
119C2×Dic61—41no—
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—
129C8×C61—28no—
130#92418—44no—
131#8227—611nomaximal, Sylow
132C22×C61C4×C22⋊C411yescharacteristic
133C22×C61C2×#10111yescharacteristic
134C22×C61#41311yescharacteristic
135C22×C61C2×#10411yescharacteristic
136C22×C61C2×#10411yescharacteristic
137C22×C61#42111yescharacteristic
138C22×C61#42111yescharacteristic
139C4×C61—21no—
140C4×C61—21no—
141C4×C61—22no—
142C4×C61—22no—
143C4×C61—22no—
144C4×C61—22no—
145C4×C61—22no—
146C4×C61—41no—
147Dic61—42no—
148Dic61—42no—
149Dic61—81no—
150Dic61—81no—
151C4×#125—611no—
152#1745—611no—
153C4×#97D6111yescharacteristic
154C2×#330—612no—
155#1295—612no—
156C2×C61#152811yescharacteristic
157C2×C61#152911yescharacteristic
158C2×C61#153111yescharacteristic
159C2×C61#153211yescharacteristic
160C2×C61C4×#10111yescharacteristic
161C2×C61C4×#10411yescharacteristic
162C2×C61#175911yescharacteristic
163C2×#125—611no—
164C2×#97—21no—
165C2×#97—612no—
166C2×#97C2×D6112yes—
167C2×C4×C8—21no—
168#389—611no—
169#389—611no—
170#387—1221no—
171#387—1221no—
172#382—611no—
173C4×C4⋊C4—611no—
174C4×C4⋊C4—611no—
175C4×C4⋊C4—1221no—
176C4×C4⋊C4—1221no—
177C43C2×D6111yescharacteristic
178#336—1221no—
179#336—1221no—
180#330—618no—
181C61#822711yescharacteristic, complemented, Sylow
182C22×C8—22no—
183C22×C8—1222no—
184#125—614no—
185#125—1222no—
186C2×C4⋊C4—611no—
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×C4⋊C4—1221no—
194C2×C42—1221no—
195C2×C42—1221no—
196C2×C42C4×D6111yescharacteristic
197C2×C42C4×D6111yescharacteristic
198C2×C42D24411yescharacteristic
199C2×C42D24411yescharacteristic
200C2×C42C22⋊D6111yescharacteristic
201C2×C42C22⋊D6111yescharacteristic
202C2×C42C22×D6111yescharacteristic
203#97—24no—
204#97—22no—
205#97—614no—
206#97—1222no—
207#97C4×D6114yes—
208C4×C8—24no—
209#95—1221no—
210#95—1221no—
211#95—1221no—
212#95—1221no—
213#95—1221no—
214#95—1221no—
215C22×C4—1221no—
216C22×C4—1221no—
217C22×C4—1221no—
218C22×C4—1221no—
219C22×C4#1175819811yescharacteristic
220C22×C4#1175819811yescharacteristic
221C22×C4#1175819811yescharacteristic
222C22×C4#1175819811yescharacteristic
223C22×C4C2×C4×D6111yescharacteristic
224C22×C4C2×D24411yescharacteristic
225C22×C4C2×C22⋊D6111yescharacteristic
226C2×C8—24no—
227C2×C8—24no—
228C2×C8—24no—
229C2×C8—1224no—
230C2×C8—2442no—
231C2×C8—2442no—
232C4⋊C4—612no—
233C4⋊C4—612no—
234C4⋊C4—1221no—
235C4⋊C4—1221no—
236C4⋊C4—1224no—
237C4⋊C4—1224no—
238C4⋊C4—2441no—
239C4⋊C4—2441no—
240C4⋊C4—2442no—
241C4⋊C4—2442no—
242C42—22no—
243C42—22no—
244C42—22no—
245C42—41no—
246C42—41no—
247C42—41no—
248C42—2442no—
249C42—2442no—
250C42C2×C4×D6112yes—
251C42#1175822212yes—
252C23C2×#1175819811yescharacteristic
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—1222no—
269C2×C4—1222no—
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—2441no—
280C2×C4#1451969512yes—
281C2×C4#1451970512yes—
282C2×C4#1451970512yes—
283C2×C4C42×D6111yescharacteristic
284C2×C4#1451973411yescharacteristic
285C2×C4C4×C22⋊D6112yes—
286C2×C4C4×D24412yes—
287C8—28no—
288C8—2444no—
289C22C4×#1175819811yescharacteristic
290C22C2×#1451969511yescharacteristic
291C22#1683974411yescharacteristic
292C22C2×#1451970511yescharacteristic
293C22C2×#1451970511yescharacteristic
294C22#1683977811yescharacteristic
295C22#1683977811yescharacteristic
296C4—22no—
297C4—22no—
298C4—22no—
299C4—22no—
300C4—21no—
301C4—21no—
302C4—22no—
303C4—41no—
304C4—4881no—
305C4—4881no—
306C4—2442no—
307C4—2442no—
308C2#2144442011yescharacteristic
309C2#2144442411yescharacteristic
310C2#2144443311yescharacteristic
311C2#2144443711yescharacteristic
312C2C4×#1451969511yescharacteristic
313C2C4×#1451970511yescharacteristic
314C2#2144563211yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC2×C4×C61C2×C42
FrattiniC2×C42C22×D61
FittingC4×#97×C61C2
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenterC4×#97D61
hypocenterC61#8227
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C43 ◁ C4×#97

Complements

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

NH ≅ G/Ntype
19. #16839503C4semidirect
181. C61#8227semidirect

Maximal subgroups

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

subgroupindex
C4×#145197692
#214455682
C2×#168395032
#214437012
C4×#97×C612
#822761