Finite Group Databasebeta

← #29583530

Subgroups — #29583530

Order 15616.

630 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 125 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#21450735C211yesmaximal, characteristic
2#21445975C211yesmaximal, characteristic, complemented
3#21445820C212yesmaximal, complemented
4C2×#16839489C212yesmaximal, complemented
5C61×#1296C211yesmaximal, characteristic, complemented
6C2×#14519752—22no—
7C2×C4×D244C2212yes—
8C2×#14519708—22no—
9C2×#14519699—22no—
10C2×C4×#92418C2211yescharacteristic
11#16839679—22no—
12#16839632C2211yescharacteristic
13#16839619—22no—
14#16839525—22no—
15#16839489—24no—
16C2×C4⋊C8×C61C2212yes—
17C61×#384C2211yescharacteristic
18C22×D244—22no—
19C22×D244D412yes—
20C22×C4×D61—22no—
21C22×#92418—21no—
22#14519752—44no—
23#14519752—44no—
24C4×D244—22no—
25C4×D244—22no—
26C4×D244—22no—
27C4×D244—22no—
28C2×C4⋊Dic61—22no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61D412yes—
31C2×#11758198—24no—
32C2×#11758198—22no—
33#14519708—44no—
34#14519699—44no—
35C4×#92418—21no—
36C4×#92418D412yescomplemented
37#14519684—22no—
38C22×C8×C61—22no—
39C2×C4⋊C4×C61—22no—
40C2×C4⋊C4×C61D412yes—
41C2×C42×C61C2311yescharacteristic
42C4⋊C8×C61—22no—
43C4⋊C8×C61—22no—
44C23×D61—22no—
45C22×C4×C61—22no—
46C22×C4×C61C2×D411yescharacteristic
47C22×C4×C61C2×D412yes—
48C22×Dic61—22no—
49C22×Dic61—41no—
50C2×D244—22no—
51C2×D244—22no—
52C2×D244—22no—
53C2×D244—22no—
54C2×D244—22no—
55C2×D244—48no—
56C2×D244—82no—
57C2×D244SD1614yes—
58C2×C4×D61—42no—
59C2×C4×D61—42no—
60C2×C4×D61—42no—
61C2×C4×D61—42no—
62C2×C4×D61—42no—
63C2×C4×D61—42no—
64C2×C8×C61—42no—
65C2×C8×C61—42no—
66C2×C8×C61—42no—
67C4⋊C4×C61—42no—
68C4⋊C4×C61—42no—
69C4⋊C4×C61—42no—
70C42×C61C2×D411yescharacteristic
71C42×C61#4111yescharacteristic
72C42×C61#4112yes—
73#11758198—48no—
74#11758198—42no—
75#11758198—42no—
76C4⋊Dic61—22no—
77C4⋊Dic61—22no—
78C4⋊Dic61—42no—
79C4⋊Dic61—42no—
80C4⋊Dic61—42no—
81C2×#92418—22no—
82C2×#92418—22no—
83C2×#92418—22no—
84C23×C61#12011yescharacteristic
85C22×D61—24no—
86C22×D61—42no—
87C22×D61—42no—
88C22×D61—42no—
89C22×D61—42no—
90C22×D61—42no—
91C22×D61—42no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—44no—
95C2×C4×C61—42no—
96C2×C4×C61#12111yescharacteristic
97C2×C4×C61#12112yes—
98C2×C4×C61#12312yes—
99C2×C4×C61#12411yescharacteristic
100C2×C4×C61C2×SD1612yes—
101C2×C4×C61#13512yes—
102C2×C4×C61AGL(1,ℤ/8)12yes—
103C2×C4×C61AGL(1,ℤ/8)12yes—
104C2×Dic61—42no—
105C2×Dic61—42no—
106C2×Dic61—42no—
107C2×Dic61—82no—
108C2×Dic61—81no—
109D244—24no—
110D244—24no—
111D244—42no—
112D244—42no—
113D244—88no—
114C4×D61—82no—
115C4×D61—82no—
116C4×D61—82no—
117C4×D61—82no—
118C8×C61—82no—
119#92418—24no—
120#10432—611nomaximal, Sylow
121C22×C61#39411yescharacteristic
122C22×C61#44912yes—
123C22×C61#45012yes—
124C22×C61#45311yescharacteristic
125C22×C61#45611yescharacteristic
126C2×D61—44no—
127C2×D61—44no—
128C2×D61—44no—
129C2×D61—82no—
130C2×D61—82no—
131C2×D61—82no—
132C2×D61—82no—
133C4×C61—21no—
134C4×C61—21no—
135C4×C61—82no—
136C4×C61#46512yes—
137C4×C61#46912yes—
138C4×C61#48112yes—
139C4×C61#48212yes—
140Dic61—82no—
141Dic61—161no—
142#2537—611no—
143#1844—611no—
144#1802—612no—
145C2×D4⋊C8—612no—
146#1296D6111yescharacteristic, complemented
147C2×C61#162411yescharacteristic
148C2×C61#162911yescharacteristic
149C2×C61#165412yes—
150C2×C61#203412yes—
151C2×C61#203911yescharacteristic
152D61—84no—
153C2×#121—1222no—
154C2×C4×D4—612no—
155C2×#106—1222no—
156C2×C4⋊C8C2×D6112yes—
157C2×#102—1222no—
158C2×C4×C8—611no—
159#394—1222no—
160#384—611no—
161#384C2×D6111yescharacteristic
162#380—1222no—
163#340—1222no—
164D4⋊C8—1224no—
165C61#1043211yescharacteristic, complemented, Sylow
166C22×D4—612no—
167C22×D4—1222no—
168C23×C4—1222no—
169C22×C8—22no—
170C22×C8—1221no—
171#121—2444no—
172#121—2444no—
173C4×D4—1222no—
174C4×D4—1222no—
175C4×D4—1222no—
176C4×D4—1222no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—612no—
179C2×C4⋊C4—1221no—
180C2×C4⋊C4—1222no—
181C2×C4⋊C4D24412yes—
182C2×C22⋊C4—1224no—
183C2×C22⋊C4—1222no—
184C2×C42C22×D6111yescharacteristic
185#106—2444no—
186C4⋊C8—22no—
187C4⋊C8—22no—
188#102—2444no—
189C4×C8—612no—
190C4×C8—1221no—
191#95—1222no—
192C24—1222no—
193C2×D4—614no—
194C2×D4—1222no—
195C2×D4—1222no—
196C2×D4—1222no—
197C2×D4—1222no—
198C2×D4—1222no—
199C2×D4—4882no—
200C2×D4—2448no—
201C22×C4—22no—
202C22×C4—1222no—
203C22×C4—2441no—
204C22×C4—2442no—
205C22×C4—2442no—
206C22×C4—2442no—
207C22×C4—2442no—
208C22×C4—2442no—
209C22×C4—2442no—
210C22×C4C2×D24411yescharacteristic
211C22×C4D4×D6112yes—
212C2×C8—42no—
213C2×C8—42no—
214C2×C8—42no—
215C2×C8—1222no—
216C2×C8—1222no—
217C2×C8—1222no—
218C4⋊C4—42no—
219C4⋊C4—42no—
220C4⋊C4—42no—
221C4⋊C4—1222no—
222C4⋊C4—1222no—
223C4⋊C4—2442no—
224C4⋊C4—2442no—
225C4⋊C4—2442no—
226C22⋊C4—2448no—
227C22⋊C4—2442no—
228C22⋊C4—2442no—
229C42#1175822212yes—
230C42D4×D6111yescharacteristic
231C42#1175822611yescharacteristic
232C23—1224no—
233C23—2442no—
234C23—2442no—
235C23—2442no—
236C23—2442no—
237C23—2442no—
238C23—2442no—
239C23#1451974711yescharacteristic
240D4—1224no—
241D4—1224no—
242D4—4888no—
243D4—2442no—
244D4—2442no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—44no—
248C2×C4—42no—
249C2×C4—4882no—
250C2×C4—4881no—
251C2×C4—4882no—
252C2×C4—4882no—
253C2×C4—4882no—
254C2×C4—4882no—
255C2×C4—2442no—
256C2×C4—2442no—
257C2×C4—2442no—
258C2×C4#1451975012yes—
259C2×C4#1451975211yescharacteristic
260C2×C4#1451976212yes—
261C2×C4#1451976511yescharacteristic
262C2×C4SD16×D6112yes—
263C2×C4#1451980012yes—
264C2×C4#1451980112yes—
265C2×C4#1451980412yes—
266C8—82no—
267C8—1224no—
268C22—4882no—
269C22—4882no—
270C22—4882no—
271C22—4882no—
272C22—2444no—
273C22—2444no—
274C22—2444no—
275C22#1683968011yescharacteristic
276C22#1683991012yes—
277C22#1683991412yes—
278C22#1683993211yescharacteristic
279C22#1683994711yescharacteristic
280C4—21no—
281C4—21no—
282C4—82no—
283C4—9761no—
284C4—4882no—
285C4#1683999412yes—
286C4#1684001412yes—
287C4#1684008212yes—
288C4#1684008912yes—
289C2—4884no—
290C2#2144490311yescharacteristic
291C2#2144493611yescharacteristic
292C2#2144510412yes—
293C2#2144701112yes—
294C2#2144704411yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1296C2
socleC23×C61#120
prime radical#21450735C2
hypercenter#1296D61
hypocenterC61#10432
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
2. #21445975C2semidirect
3. #21445820C2semidirect
4. C2×#16839489C2semidirect
5. C61×#1296C2semidirect
36. C4×#92418D4semidirect
146. #1296D61semidirect
165. C61#10432semidirect

Maximal subgroups

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

subgroupindex
#214507352
#214459752
#214458202
C2×#168394892
C61×#12962
#1043261