Finite Group Databasebeta

← #29580870

Subgroups — #29580870

Order 15616.

696 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 103 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#21455823C212yesmaximal, complemented
2#21449100C211yesmaximal, characteristic
3#21444243C212yesmaximal, complemented
4#21443648C211yesmaximal, characteristic, complemented
5C61×#1995C211yesmaximal, characteristic, complemented
6C2×C4×D244—22no—
7C2×C4×D244C2212yes—
8#16840090—22no—
9#16840049—22no—
10#16839964—22no—
11#16839912—22no—
12C4×#11758201—24no—
13#16839815C2212yes—
14#16839699—22no—
15#16839672—22no—
16#16839489—24no—
17C61×#533C2211yescharacteristic
18C61×#423C2211yescharacteristic
19C61×#376C2211yescharacteristic
20C61×#339—22no—
21C22×D244—22no—
22C22×D244D412yes—
23C22×C4×D61—22no—
24C2×#11758201—24no—
25C4×D244—22no—
26C4×D244—22no—
27C4×D244—22no—
28C4×D244—22no—
29C4×D244—44no—
30C4×D244—44no—
31C2×C4⋊Dic61—22no—
32C2×C4⋊Dic61D412yes—
33C2×#11758198—24no—
34C2×#11758198—22no—
35#14519708—24no—
36C4⋊#92418—22no—
37#14519701—24no—
38#14519697—24no—
39C22⋊#92418—22no—
40C4×#92418D414yescomplemented
41C2×M16×C61—21no—
42C4⋊Q8×C61D412yescomplemented
43#125×C61—21no—
44C22⋊Q8×C61—22no—
45C4×Q8×C61—22no—
46#117×C61—21no—
47C2×C42×C61D412yes—
48C2×C42×C61C2311yescharacteristic
49C4⋊C8×C61—22no—
50#95×C61—22no—
51C23×D61—22no—
52C2×Q8×C61—22no—
53C22×C4×C61—22no—
54C22×C4×C61C2×D412yes—
55C22×C4×C61C2×D411yescharacteristic
56C22×Dic61—22no—
57C2×D244—22no—
58C2×D244—22no—
59C2×D244—44no—
60C2×D244—44no—
61C2×D244—48no—
62C2×C4×D61—42no—
63C2×C4×D61—42no—
64C2×C4×D61—44no—
65C2×C4×D61—44no—
66M16×C61—42no—
67C2×C8×C61—41no—
68C4⋊C4×C61—22no—
69C4⋊C4×C61—22no—
70C4⋊C4×C61—42no—
71C22⋊C4×C61—41no—
72C42×C61—22no—
73C42×C61—41no—
74C42×C61SD1614yescomplemented
75C42×C61C2×D411yescharacteristic
76C42×C61C2×D412yes—
77C42×C61#4111yescharacteristic
78#11758201—48no—
79#11758198—48no—
80#11758198—42no—
81#11758198—42no—
82C4⋊Dic61—22no—
83C4⋊Dic61—22no—
84C4⋊Dic61—44no—
85C2×#92418—24no—
86C23×C61#12011yescharacteristic
87C22×D61—24no—
88C22×D61—44no—
89C22×D61—42no—
90C22×D61—42no—
91C22×D61—44no—
92Q8×C61—44no—
93C2×C4×C61—24no—
94C2×C4×C61—42no—
95C2×C4×C61—44no—
96C2×C4×C61—42no—
97C2×C4×C61#12012yes—
98C2×C4×C61#12112yes—
99C2×C4×C61#12111yescharacteristic
100C2×C4×C61#12711yescharacteristic
101C2×C4×C61C2×SD1612yes—
102C2×C4×C61AGL(1,ℤ/8)12yes—
103C2×Dic61—42no—
104C2×Dic61—44no—
105D244—24no—
106D244—24no—
107D244—42no—
108D244—42no—
109D244—416no—
110C4×D61—84no—
111C4×D61—82no—
112C4×D61—82no—
113C8×C61—81no—
114#92418—44no—
115#10015—611nomaximal, Sylow
116C22×C61—22no—
117C22×C61#39211yescharacteristic
118C22×C61#45012yes—
119C2×D61—48no—
120C2×D61—44no—
121C2×D61—84no—
122C2×D61—82no—
123C2×D61—82no—
124C4×C61—22no—
125C4×C61—22no—
126C4×C61—44no—
127C4×C61—82no—
128C4×C61#46012yes—
129C4×C61#49211yescharacteristic
130C4×C61#49611yescharacteristic
131Dic61—82no—
132#3101—612no—
133#2397—611no—
134#1995D6111yescharacteristic, complemented
135#1486—612no—
136#1274—611no—
137C2×C61—22no—
138C2×C61#201012yes—
139C2×C61#201411yescharacteristic
140D61—84no—
141#533C2×D6111yescharacteristic
142C2×C4×D4—612no—
143C2×C4×D4—1222no—
144#483—1222no—
145#476—1222no—
146#461—1222no—
147#450—1222no—
148C4×SD16—1224no—
149#431—612no—
150#423C2×D6111yescharacteristic
151#399—1222no—
152#392—1222no—
153#376C2×D6111yescharacteristic
154#339—22no—
155D4⋊C8—1224no—
156C61#1001511yescharacteristic, complemented, Sylow
157C22×D4—612no—
158C22×D4—1222no—
159C23×C4—1222no—
160C2×SD16—1224no—
161C2×M16—21no—
162C4⋊Q8D24412yescomplemented
163#125—21no—
164C22⋊Q8—22no—
165C4×Q8—22no—
166C4×D4—1222no—
167C4×D4—1222no—
168C4×D4—1222no—
169C4×D4—1222no—
170C4×D4—2444no—
171C4×D4—2444no—
172#117—21no—
173C2×C4⋊C4—612no—
174C2×C4⋊C4—1222no—
175C2×C22⋊C4—1224no—
176C2×C22⋊C4—1222no—
177C2×C42C22⋊D6112yes—
178C2×C42C22×D6111yescharacteristic
179#106—1224no—
180C4⋊C8—22no—
181C4⋊C8—1222no—
182#103—1224no—
183#102—1224no—
184C22⋊C8—1222no—
185C4×C8—614no—
186#95—22no—
187C24—1222no—
188C2×Q8—22no—
189C2×D4—1222no—
190C2×D4—1222no—
191C2×D4—2444no—
192C2×D4—2444no—
193C2×D4—2448no—
194C22×C4—22no—
195C22×C4—1222no—
196C22×C4—2442no—
197C22×C4—2442no—
198C22×C4—2444no—
199C22×C4—2444no—
200C22×C4D4×D6112yes—
201C22×C4C2×C22⋊D6111yescharacteristic
202SD16—2448no—
203M16—42no—
204C2×C8—41no—
205C2×C8—1224no—
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—42no—
209C4⋊C4—1222no—
210C4⋊C4—1222no—
211C4⋊C4—2444no—
212C22⋊C4—41no—
213C22⋊C4—2448no—
214C22⋊C4—2442no—
215C22⋊C4—2442no—
216C42—22no—
217C42—41no—
218C42#1175820114yescomplemented
219C42C2×D24411yescharacteristic
220C42#1175822211yescharacteristic
221C42D4×D6112yes—
222C23—1224no—
223C23—2442no—
224C23—2444no—
225C23—2444no—
226C23—2442no—
227C23#1451974511yescharacteristic
228Q8—44no—
229D4—1224no—
230D4—1224no—
231D4—2442no—
232D4—2442no—
233D4—24416no—
234C2×C4—24no—
235C2×C4—42no—
236C2×C4—44no—
237C2×C4—42no—
238C2×C4—4884no—
239C2×C4—4882no—
240C2×C4—4882no—
241C2×C4—2444no—
242C2×C4—2442no—
243C2×C4#1451974712yes—
244C2×C4#1451975012yes—
245C2×C4#1451975111yescharacteristic
246C2×C4#1451977311yescharacteristic
247C2×C4C2×#1175820112yes—
248C2×C4#1451980212yes—
249C8—81no—
250C8—2444no—
251C22—22no—
252C22—4884no—
253C22—4882no—
254C22—4882no—
255C22—2448no—
256C22—2444no—
257C22#1683967111yescharacteristic
258C22#1683991212yes—
259C4—22no—
260C4—22no—
261C4—44no—
262C4—82no—
263C4—4882no—
264C4#1683996212yes—
265C4#1684013611yescharacteristic
266C4#1684015211yescharacteristic
267C2—22no—
268C2—4884no—
269C2#2144688512yes—
270C2#2144690611yescharacteristic
subgroupG/H
centerC2×C4#14519773
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1995C2
socleC22×C61#392
prime radical#21449100C2
hypercenter#1995D61
hypocenterC61#10015
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1995

Complements

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

NH ≅ G/Ntype
1. #21455823C2semidirect
3. #21444243C2semidirect
4. #21443648C2semidirect
5. C61×#1995C2semidirect
40. C4×#92418D4semidirect
42. C4⋊Q8×C61D4semidirect
74. C42×C61SD16semidirect
134. #1995D61semidirect
156. C61#10015semidirect
162. C4⋊Q8D244semidirect
218. C42#11758201semidirect

Maximal subgroups

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

subgroupindex
#214558232
#214491002
#214442432
#214436482
C61×#19952
#1001561