Finite Group Databasebeta

← #29658296

Subgroups — #29658296

Order 15616.

884 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 884 conjugacy classes of subgroups — too many to draw. Only its 163 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#21460314C211yesmaximal, characteristic, complemented
2#21456760C212yesmaximal
3#21444912C218yesmaximal, complemented
4#21444484C211yesmaximal, characteristic, complemented
5#21444241C212yesmaximal, complemented
6C61×#3138C211yesmaximal, characteristic
7C61⋊#564—22no—
8#16840491—22no—
9#16840490—22no—
10#16840487C2214yescomplemented
11#16840374—22no—
12#16840372—24no—
13#16840319C2212yes—
14#16840134—22no—
15#16840108—22no—
16#16839959C2218yes—
17#16839913—24no—
18#16839815C2212yes—
19#16839508C2214yescomplemented
20#16839494C2218yescomplemented
21C61×#533C2211yescharacteristic
22C2×#127×C61C2211yescharacteristic
23C61×#490—22no—
24C61×#486C2214yes—
25C61×#418—22no—
26C4×M16×C61C2211yescharacteristic
27C2×#11758200—28no—
28#14519777—22no—
29#14519777D412yes—
30#14519777D412yes—
31#14519775—24no—
32#14519770—28no—
33#14519769—22no—
34#14519769—22no—
35#14519768—28no—
36#14519768—24no—
37#14519767—28no—
38#14519767—28no—
39#14519756—22no—
40#14519756D414yes—
41Q8×Dic61—24no—
42C4×Dic122—24no—
43C4×Dic122—22no—
44C4×Dic122C2314yes—
45#14519742—24no—
46#14519736—22no—
47C4⋊#92418C2314yes—
48#14519698—28no—
49C22⋊#92418—22no—
50C4×#92418—22no—
51C22×D4×C61—21no—
52C22×D4×C61—22no—
53C2×M16×C61—21no—
54C4⋊Q8×C61C2312yes—
55#127×C61—22no—
56#127×C61—21no—
57#127×C61C2312yes—
58#125×C61D412yes—
59C22⋊Q8×C61—22no—
60C4×Q8×C61—22no—
61#117×C61D412yes—
62C2×C42×C61C2311yescharacteristic
63#102×C61—28no—
64#97×C61—21no—
65C4×C8×C61C2312yes—
66C24×C61—41no—
67C2×Q8×C61—22no—
68C2×D4×C61—22no—
69C2×D4×C61—24no—
70C2×D4×C61—44no—
71C2×D4×C61—42no—
72C2×D4×C61—41no—
73C2×D4×C61—84no—
74C22×C4×C61C2×D412yes—
75C22×C4×C61C2×D411yescharacteristic
76C2×Dic122—22no—
77C2×Dic122C2×D414yes—
78M16×C61—42no—
79C2×C8×C61—22no—
80C4⋊C4×C61—24no—
81C4⋊C4×C61—22no—
82C4⋊C4×C61C2×D414yes—
83C22⋊C4×C61—22no—
84C42×C61—22no—
85C42×C61C2×D412yes—
86C42×C61C2×D411yescharacteristic
87C42×C61C2411yescharacteristic
88C22⋊Dic61—24no—
89#11758200—88no—
90C4⋊Dic61—28no—
91C4⋊Dic61—22no—
92C4⋊Dic61—22no—
93C4⋊Dic61—22no—
94C4⋊Dic61C2×D414yes—
95#11758196—28no—
96#11758196—28no—
97#11758196—24no—
98#11758196—24no—
99C4×Dic61—28no—
100C4×Dic61—24no—
101C2×#92418—24no—
102C23×C61—42no—
103C23×C61—82no—
104C23×C61—84no—
105C23×C61#12011yescharacteristic
106Q8×C61—44no—
107D4×C61—44no—
108D4×C61—48no—
109D4×C61—84no—
110D4×C61—82no—
111C2×C4×C61—24no—
112C2×C4×C61—22no—
113C2×C4×C61—24no—
114C2×C4×C61#12012yes—
115C2×C4×C61#12011yescharacteristic
116C2×C4×C61C22×D411yescharacteristic
117C2×C4×C61C22×D412yes—
118C2×Dic61—24no—
119C2×Dic61—24no—
120Dic122—28no—
121Dic122—44no—
122C8×C61—42no—
123#92418—44no—
124#18731—611nomaximal, Sylow
125C22×C61—22no—
126C22×C61—21no—
127C22×C61—84no—
128C22×C61—82no—
129C22×C61—164no—
130C22×C61C2×#12011yescharacteristic
131C4×C61—22no—
132C4×C61—21no—
133C4×C61—44no—
134C4×C61#45412yes—
135C4×C61#57714yes—
136Dic61—44no—
137Dic61—44no—
138#3556—611no—
139#3208—612no—
140#3138D6111yescharacteristic
141#1626—618no—
142#1544—611no—
143#1485—612no—
144C2×C61—41no—
145C2×C61—162no—
146C2×C61#301012yes—
147C2×C61C2×#45411yescharacteristic
148#564—1222no—
149#557—614no—
150#557—1222no—
151#557—1222no—
152#541—1224no—
153#541—1222no—
154#533—612no—
155#533C2×D6111yescharacteristic
156C2×#127C2×D6111yescharacteristic
157#492—1222no—
158#490—22no—
159#486—1222no—
160#486C2×D6114yes—
161#460—618no—
162#450—1224no—
163#431—612no—
164#418—22no—
165C4×M16C2×D6111yescharacteristic
166#332—614no—
167Q8⋊C8—618no—
168C61#1873111yescharacteristic, complemented, Sylow
169C22×D4—22no—
170C22×D4—21no—
171C2×SD16—1228no—
172C2×M16—21no—
173C4⋊Q8—612no—
174C4⋊Q8—612no—
175C4⋊Q8—1222no—
176C4⋊Q8—1224no—
177C4⋊Q8C22×D6112yes—
178#127—22no—
179#127—21no—
180#127C22×D6112yes—
181#126—1228no—
182#125—1222no—
183#125—1224no—
184#125—1228no—
185#125—1228no—
186#125—1228no—
187#125—1222no—
188#125C22⋊D6112yes—
189C22⋊Q8—22no—
190C22⋊Q8—614no—
191C22⋊Q8—1222no—
192C4×Q8—22no—
193C4×Q8—614no—
194C4×Q8—1224no—
195C4×Q8—1224no—
196C4×Q8—1224no—
197C4×Q8—1222no—
198#117—1222no—
199#117C22⋊D6112yes—
200C2×C42C22×D6111yescharacteristic
201C4⋊C8—614no—
202#102—28no—
203#102—1228no—
204C22⋊C8—1222no—
205#97—21no—
206C4×C8—1222no—
207C4×C8C22×D6112yes—
208C24—41no—
209C2×Q8—22no—
210C2×Q8—614no—
211C2×Q8—1222no—
212C2×D4—24no—
213C2×D4—22no—
214C2×D4—44no—
215C2×D4—42no—
216C2×D4—41no—
217C2×D4—84no—
218C22×C4D4×D6112yes—
219C22×C4C2×C22⋊D6111yescharacteristic
220SD16—4888no—
221M16—42no—
222C2×C8—22no—
223C2×C8—1224no—
224C4⋊C4—22no—
225C4⋊C4—24no—
226C4⋊C4—614no—
227C4⋊C4—1228no—
228C4⋊C4—1228no—
229C4⋊C4—1228no—
230C4⋊C4—1224no—
231C4⋊C4—1224no—
232C4⋊C4—1222no—
233C4⋊C4—1222no—
234C4⋊C4—1222no—
235C4⋊C4C2×C22⋊D6114yes—
236C22⋊C4—22no—
237C22⋊C4—1224no—
238C42—22no—
239C42—1228no—
240C42—1224no—
241C42D4×D6112yes—
242C42C2×C22⋊D6111yescharacteristic
243C42C23×D6111yescharacteristic
244C23—42no—
245C23—82no—
246C23—84no—
247C23#1451974511yescharacteristic
248Q8—44no—
249Q8—1228no—
250Q8—2444no—
251D4—44no—
252D4—48no—
253D4—84no—
254D4—82no—
255C2×C4—24no—
256C2×C4—22no—
257C2×C4—24no—
258C2×C4—1224no—
259C2×C4—1224no—
260C2×C4#1451974512yes—
261C2×C4#1451974511yescharacteristic
262C2×C4C2×D4×D6112yes—
263C2×C4C22×C22⋊D6111yescharacteristic
264C8—42no—
265C8—2444no—
266C22—22no—
267C22—21no—
268C22—84no—
269C22—82no—
270C22—164no—
271C22C2×#1451974511yescharacteristic
272C4—22no—
273C4—21no—
274C4—44no—
275C4—2444no—
276C4—2444no—
277C4#1683993412yes—
278C4#1684057214yes—
279C2—41no—
280C2—162no—
281C2#2145510412yes—
282C2C2×#1683993411yescharacteristic
subgroupG/H
centerC22C2×#14519745
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3138C2
socleC22×C61C2×#120
prime radicalC2×#127×C61C22
hypercenter#3138D61
hypocenterC61#18731
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3138

Complements

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

NH ≅ G/Ntype
1. #21460314C2semidirect
3. #21444912C2semidirect
4. #21444484C2semidirect
5. #21444241C2semidirect
10. #16840487C22semidirect
19. #16839508C22semidirect
20. #16839494C22semidirect
168. C61#18731semidirect

Maximal subgroups

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

subgroupindex
#214603142
#214567602
#214449122
#214444842
#214442412
C61×#31382
#1873161