Finite Group Databasebeta

← #29583529

Subgroups — #29583529

Order 15616.

630 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 127 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#21445816C212yesmaximal, complemented
3C2×#16839491C212yesmaximal, complemented
4#21443702C211yesmaximal, characteristic, complemented
5C61×#1844C211yesmaximal, characteristic, complemented
6C2×#14519752—22no—
7C2×C4×D244C2212yes—
8C2×C4⋊#92418C2212yes—
9C2×#14519697—22no—
10#16839679—22no—
11#16839619—22no—
12#16839524—22no—
13#16839491—24no—
14C2×#106×C61—22no—
15C2×C4×C8×C61C2211yescharacteristic
16C61×#384C2211yescharacteristic
17C61×#384C2211yescharacteristic
18C22×D244—22no—
19C22×D244D412yes—
20C22×C4×D61—22no—
21C22×#92418—22no—
22#14519752—44no—
23#14519752—44no—
24C4×D244—22no—
25C4×D244—22no—
26C4×D244—22no—
27C4×D244—22no—
28C2×C4⋊Dic61D412yes—
29C2×#11758198—24no—
30C2×#11758198—22no—
31C4⋊#92418—22no—
32C4⋊#92418—22no—
33#14519697—44no—
34#14519684—22no—
35C22×C8×C61—21no—
36C2×C4⋊C4×C61—22no—
37C2×C4⋊C4×C61—22no—
38C2×C4⋊C4×C61—21no—
39C2×C4⋊C4×C61D412yes—
40C2×C42×C61C2311yescharacteristic
41#106×C61—44no—
42C4×C8×C61—21no—
43C4×C8×C61D412yescomplemented
44C23×D61—22no—
45C22×C4×C61—22no—
46C22×C4×C61—41no—
47C22×C4×C61C2×D411yescharacteristic
48C22×C4×C61C2×D412yes—
49C22×Dic61—22no—
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—22no—
65C2×C8×C61—22no—
66C2×C8×C61—22no—
67C4⋊C4×C61—42no—
68C4⋊C4×C61—42no—
69C4⋊C4×C61—42no—
70C4⋊C4×C61—42no—
71C4⋊C4×C61—42no—
72C4⋊C4×C61—42no—
73C42×C61C2×D411yescharacteristic
74C42×C61#4111yescharacteristic
75C42×C61#4112yes—
76#11758198—48no—
77#11758198—42no—
78#11758198—42no—
79C4⋊Dic61—22no—
80C4⋊Dic61—22no—
81C2×#92418—42no—
82C2×#92418—42no—
83C2×#92418—42no—
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—82no—
97C2×C4×C61—81no—
98C2×C4×C61#12111yescharacteristic
99C2×C4×C61#12112yes—
100C2×C4×C61#12312yes—
101C2×C4×C61#12411yescharacteristic
102C2×C4×C61C2×SD1612yes—
103C2×C4×C61#13512yes—
104C2×C4×C61AGL(1,ℤ/8)12yes—
105C2×C4×C61AGL(1,ℤ/8)12yes—
106C2×Dic61—42no—
107C2×Dic61—42no—
108C2×Dic61—42no—
109D244—24no—
110D244—24no—
111D244—42no—
112D244—42no—
113D244—88no—
114C4×D61—82no—
115C4×D61—82no—
116C4×D61—82no—
117C4×D61—82no—
118C8×C61—24no—
119#92418—82no—
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—161no—
137C4×C61#46512yes—
138C4×C61#46912yes—
139C4×C61#48112yes—
140C4×C61#48212yes—
141Dic61—82no—
142#2537—611no—
143#1844D6111yescharacteristic, complemented
144#1802—612no—
145C2×D4⋊C8—612no—
146#1296—611no—
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—22no—
156C2×C4⋊C8—612no—
157C2×#102—1222no—
158C2×C4×C8C2×D6111yescharacteristic
159#394—1222no—
160#384C2×D6111yescharacteristic
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—21no—
170C22×C8—1222no—
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—22no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—612no—
181C2×C4⋊C4C22⋊D6112yes—
182C2×C22⋊C4—1224no—
183C2×C22⋊C4—1222no—
184C2×C42C22×D6111yescharacteristic
185#106—44no—
186C4⋊C8—1222no—
187C4⋊C8—1222no—
188#102—2444no—
189C4×C8—21no—
190C4×C8D24412yescomplemented
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—41no—
203C22×C4—1222no—
204C22×C4—2442no—
205C22×C4—2442no—
206C22×C4—2442no—
207C22×C4—2442no—
208C22×C4—2442no—
209C22×C4—2442no—
210C22×C4D4×D6112yes—
211C22×C4C2×C22⋊D6111yescharacteristic
212C2×C8—22no—
213C2×C8—22no—
214C2×C8—22no—
215C2×C8—2442no—
216C2×C8—2442no—
217C2×C8—2442no—
218C4⋊C4—42no—
219C4⋊C4—42no—
220C4⋊C4—42no—
221C4⋊C4—42no—
222C4⋊C4—42no—
223C4⋊C4—42no—
224C4⋊C4—1222no—
225C4⋊C4—1222no—
226C22⋊C4—2448no—
227C22⋊C4—2442no—
228C22⋊C4—2442no—
229C42C2×D24411yescharacteristic
230C42#1175822211yescharacteristic
231C42#1175822612yes—
232C23—1224no—
233C23—2442no—
234C23—2442no—
235C23—2442no—
236C23—2442no—
237C23—2442no—
238C23—2442no—
239C23#1451974511yescharacteristic
240D4—1224no—
241D4—1224no—
242D4—4888no—
243D4—2442no—
244D4—2442no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—44no—
248C2×C4—42no—
249C2×C4—82no—
250C2×C4—81no—
251C2×C4—4882no—
252C2×C4—4882no—
253C2×C4—4882no—
254C2×C4—4882no—
255C2×C4—2442no—
256C2×C4—2442no—
257C2×C4—2442no—
258C2×C4#1451975111yescharacteristic
259C2×C4#1451975212yes—
260C2×C4#1451976212yes—
261C2×C4#1451976611yescharacteristic
262C2×C4SD16×D6112yes—
263C2×C4#1451979812yes—
264C2×C4#1451980412yes—
265C2×C4#1451980412yes—
266C8—24no—
267C8—4882no—
268C22—4882no—
269C22—4882no—
270C22—4882no—
271C22—4882no—
272C22—2444no—
273C22—2444no—
274C22—2444no—
275C22#1683967911yescharacteristic
276C22#1683990612yes—
277C22#1683991112yes—
278C22#1683992911yescharacteristic
279C22#1683994411yescharacteristic
280C4—21no—
281C4—21no—
282C4—82no—
283C4—161no—
284C4—4882no—
285C4#1683999212yes—
286C4#1684001612yes—
287C4#1684008212yes—
288C4#1684008812yes—
289C2—4884no—
290C2#2144490011yescharacteristic
291C2#2144493311yescharacteristic
292C2#2144510012yes—
293C2#2144701012yes—
294C2#2144704311yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1844C2
socleC23×C61#120
prime radical#21450735C2
hypercenter#1844D61
hypocenterC61#10432
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1844

Complements

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

NH ≅ G/Ntype
2. #21445816C2semidirect
3. C2×#16839491C2semidirect
4. #21443702C2semidirect
5. C61×#1844C2semidirect
43. C4×C8×C61D4semidirect
143. #1844D61semidirect
165. C61#10432semidirect
190. C4×C8D244semidirect

Maximal subgroups

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

subgroupindex
#214507352
#214458162
C2×#168394912
#214437022
C61×#18442
#1043261