Finite Group Databasebeta

← #29581336

Subgroups — #29581336

Order 15616.

600 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C2×#16840124C212yesmaximal, complemented
2#21453865C211yesmaximal, characteristic
3C2×#16839501C212yesmaximal, complemented
4#21443700C211yesmaximal, characteristic, complemented
5C61×#1960C211yesmaximal, characteristic, complemented
6C2×#14519765C2212yes—
7#16840124—24no—
8#16840124—24no—
9C2×#14519700—22no—
10C2×#14519697—22no—
11C2×#14519688C2212yes—
12#16839679—22no—
13#16839675—22no—
14#16839672—22no—
15#16839501—24no—
16C2×C4⋊Q8×C61C2211yescharacteristic
17C2×#103×C61—22no—
18C2×#97×C61C2211yescharacteristic
19C61×#382C2211yescharacteristic
20C22×Dic122D412yes—
21C22×D244—22no—
22C22×D244D412yes—
23C22×#92418—22no—
24#14519765—22no—
25#14519765—22no—
26#14519765—22no—
27#14519765—22no—
28C2×#11758198—22no—
29C2×#11758198—22no—
30C2×#11758198—24no—
31#14519700—28no—
32#14519697—28no—
33#14519688—22no—
34#14519688D414yescomplemented
35#14519684—22no—
36C22×Q8×C61—21no—
37C22×C8×C61—21no—
38C4⋊Q8×C61—22no—
39C4⋊Q8×C61—21no—
40C4⋊Q8×C61D412yescomplemented
41C2×C4⋊C4×C61—22no—
42C2×C4⋊C4×C61D412yes—
43C2×C42×C61C2311yescharacteristic
44#103×C61—44no—
45#97×C61—22no—
46#95×C61—22no—
47C23×D61—22no—
48C2×Q8×C61—22no—
49C2×Q8×C61—42no—
50C2×Q8×C61—42no—
51C2×Q8×C61—41no—
52C22×C4×C61—22no—
53C22×C4×C61—41no—
54C22×C4×C61C2×D412yes—
55C22×C4×C61C2×D411yescharacteristic
56C22×Dic61—22no—
57C2×D244—22no—
58C2×D244—22no—
59C2×D244—44no—
60C2×D244—82no—
61C2×D244—84no—
62C2×Dic122—22no—
63C2×Dic122—22no—
64C2×Dic122—44no—
65C2×C8×C61—22no—
66C2×C8×C61—41no—
67C2×C8×C61—41no—
68C4⋊C4×C61—24no—
69C4⋊C4×C61—42no—
70C4⋊C4×C61—42no—
71C42×C61C2×D411yescharacteristic
72C42×C61C2×D412yes—
73C42×C61#4111yescharacteristic
74#11758198—42no—
75#11758198—42no—
76#11758198—42no—
77#11758198—42no—
78#11758198—84no—
79C2×#92418—24no—
80C2×#92418—44no—
81C23×C61#12011yescharacteristic
82C22×D61—42no—
83C22×D61—42no—
84C22×D61—42no—
85C22×D61—44no—
86C22×D61—44no—
87Q8×C61—44no—
88Q8×C61—82no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—24no—
92C2×C4×C61—42no—
93C2×C4×C61—42no—
94C2×C4×C61—44no—
95C2×C4×C61—81no—
96C2×C4×C61—81no—
97C2×C4×C61#12012yes—
98C2×C4×C61#12112yes—
99C2×C4×C61#12111yescharacteristic
100C2×C4×C61#12711yescharacteristic
101C2×Dic61—42no—
102C2×Dic61—44no—
103D244—44no—
104D244—82no—
105D244—88no—
106Dic122—44no—
107Dic122—82no—
108C8×C61—42no—
109#92418—44no—
110#10085—611nomaximal, Sylow
111C22×C61#39211yescharacteristic
112C22×C61#45311yescharacteristic
113C22×C61#45411yescharacteristic
114C22×C61#45514yes—
115C2×D61—84no—
116C2×D61—84no—
117C2×D61—82no—
118C2×D61—82no—
119C2×D61—82no—
120C4×C61—22no—
121C4×C61—22no—
122C4×C61—21no—
123C4×C61—21no—
124C4×C61—82no—
125C4×C61—82no—
126Dic61—82no—
127C2×#489—612no—
128#2819—611no—
129#1960D6111yescharacteristic, complemented
130C2×#329—612no—
131#1295—611no—
132C2×C61#165912yes—
133C2×C61#166212yes—
134C2×C61#200412yes—
135C2×C61#200611yescharacteristic
136D61—162no—
137C2×C4⋊Q8C2×D6111yescharacteristic
138C2×#124—612no—
139#489—1224no—
140#489—1224no—
141C2×#103—22no—
142C2×#103—1222no—
143C2×#102—1222no—
144C2×#97—612no—
145C2×#97C2×D6111yescharacteristic
146#394—1222no—
147#393—1222no—
148#392—1222no—
149#382C2×D6111yescharacteristic
150#329—1224no—
151C61#1008511yescharacteristic, complemented, Sylow
152C22×Q8—21no—
153C22×Q8—612no—
154C22×D4—612no—
155C22×D4—1222no—
156C22×C8—21no—
157C22×C8—1222no—
158C4⋊Q8—21no—
159C4⋊Q8—22no—
160C4⋊Q8D24412yescomplemented
161#124—1222no—
162#124—1222no—
163#124—1222no—
164#124—1222no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4C22⋊D6112yes—
167C2×C22⋊C4—1224no—
168C2×C22⋊C4—1222no—
169C2×C22⋊C4—1222no—
170C2×C42C22×D6111yescharacteristic
171#103—44no—
172#103—1228no—
173#102—1228no—
174#97—22no—
175#97—614no—
176#97—1222no—
177#95—22no—
178#95—1222no—
179C24—1222no—
180C2×Q8—22no—
181C2×Q8—42no—
182C2×Q8—42no—
183C2×Q8—41no—
184C2×Q8—1222no—
185C2×Q8—1222no—
186C2×Q8—2444no—
187C2×D4—1222no—
188C2×D4—1222no—
189C2×D4—4884no—
190C2×D4—4882no—
191C2×D4—2444no—
192C22×C4—22no—
193C22×C4—41no—
194C22×C4—1222no—
195C22×C4D4×D6112yes—
196C22×C4C2×C22⋊D6111yescharacteristic
197C2×C8—22no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—1224no—
201C2×C8—2444no—
202C4⋊C4—24no—
203C4⋊C4—42no—
204C4⋊C4—42no—
205C22⋊C4—4884no—
206C22⋊C4—2442no—
207C22⋊C4—2442no—
208C22⋊C4—2442no—
209C22⋊C4—2442no—
210C42C2×D24411yescharacteristic
211C42#1175822211yescharacteristic
212C42D4×D6112yes—
213C23—2444no—
214C23—2444no—
215C23—2442no—
216C23—2442no—
217C23—2442no—
218C23#1451974511yescharacteristic
219Q8—44no—
220Q8—82no—
221Q8—4882no—
222Q8—2444no—
223D4—4882no—
224D4—4888no—
225D4—2444no—
226C2×C4—24no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—44no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—81no—
233C2×C4—81no—
234C2×C4—2444no—
235C2×C4—2442no—
236C2×C4#1451974712yes—
237C2×C4#1451975012yes—
238C2×C4#1451975111yescharacteristic
239C2×C4#1451977311yescharacteristic
240C8—42no—
241C8—2444no—
242C22—4884no—
243C22—4884no—
244C22—4882no—
245C22—4882no—
246C22—4882no—
247C22#1683967111yescharacteristic
248C22#1683992911yescharacteristic
249C22#1683993411yescharacteristic
250C22#1683993814yes—
251C4—22no—
252C4—22no—
253C4—21no—
254C4—21no—
255C4—82no—
256C4—82no—
257C4—4882no—
258C2—9762no—
259C2#2144512312yes—
260C2#2144514012yes—
261C2#2144684912yes—
262C2#2144686011yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1960C2
socleC23×C61#120
prime radical#21453865C2
hypercenter#1960D61
hypocenterC61#10085
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
1. C2×#16840124C2semidirect
3. C2×#16839501C2semidirect
4. #21443700C2semidirect
5. C61×#1960C2semidirect
34. #14519688D4semidirect
40. C4⋊Q8×C61D4semidirect
129. #1960D61semidirect
151. C61#10085semidirect
160. C4⋊Q8D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168401242
#214538652
C2×#168395012
#214437002
C61×#19602
#1008561