Finite Group Databasebeta

← #29583484

Subgroups — #29583484

Order 15616.

534 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 89 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#21453865C211yesmaximal, characteristic
2#21446635C212yesmaximal, complemented
3#21445988C211yesmaximal, characteristic, complemented
4C2×#16839501C212yesmaximal, complemented
5C61×#1295C211yesmaximal, characteristic, complemented
6C2×#14519765C2212yes—
7C2×#14519710—21no—
8C2×#14519708—21no—
9C2×#14519702—22no—
10C2×#14519699—22no—
11C2×#14519688C2211yescharacteristic
12#16839679—21no—
13#16839679—21no—
14#16839675—22no—
15#16839672—22no—
16#16839632C2211yescharacteristic
17#16839501—24no—
18C2×#97×C61C2212yes—
19C61×#382C2211yescharacteristic
20C22×Dic122D412yes—
21C22×D244—21no—
22C22×D244—21no—
23C22×D244D412yes—
24C22×#92418—21no—
25#14519765—22no—
26#14519765—22no—
27#14519765—22no—
28#14519765—22no—
29C2×C4⋊Dic61—22no—
30C2×C4⋊Dic61—21no—
31C2×#11758198—22no—
32C2×#11758198—22no—
33C2×#11758198—22no—
34C2×#11758198—22no—
35#14519710—42no—
36#14519708—42no—
37#14519702—44no—
38#14519699—44no—
39#14519688—21no—
40#14519688D412yescomplemented
41#14519684—21no—
42#14519684—21no—
43C22×C8×C61—22no—
44C2×C4⋊C4×C61D411yescharacteristic
45C2×C4⋊C4×C61D411yescharacteristic
46C2×C42×C61C2311yescharacteristic
47#97×C61—22no—
48#97×C61—22no—
49#95×C61—22no—
50C23×D61—22no—
51C22×C4×C61—21no—
52C22×C4×C61—21no—
53C22×C4×C61C2×D412yes—
54C22×C4×C61C2×D411yescharacteristic
55C22×Dic61—22no—
56C22×Dic61—41no—
57C2×D244—22no—
58C2×D244—22no—
59C2×D244—42no—
60C2×D244—42no—
61C2×D244—82no—
62C2×D244—81no—
63C2×D244—81no—
64C2×D244—82no—
65C2×Dic122—22no—
66C2×Dic122—22no—
67C2×Dic122—42no—
68C2×Dic122—42no—
69C2×C8×C61—24no—
70C2×C8×C61—42no—
71C2×C8×C61—42no—
72C4⋊C4×C61—41no—
73C4⋊C4×C61—41no—
74C42×C61C2×D411yescharacteristic
75C42×C61#4111yescharacteristic
76C42×C61#4112yes—
77#11758198—42no—
78#11758198—42no—
79#11758198—42no—
80#11758198—42no—
81#11758198—82no—
82#11758198—82no—
83C4⋊Dic61—42no—
84C4⋊Dic61—42no—
85C4⋊Dic61—41no—
86C4⋊Dic61—41no—
87C2×#92418—22no—
88C2×#92418—22no—
89C2×#92418—22no—
90C23×C61#12011yescharacteristic
91C22×D61—42no—
92C22×D61—42no—
93C22×D61—42no—
94C22×D61—42no—
95C22×D61—42no—
96C22×D61—42no—
97C22×D61—42no—
98C2×C4×C61—21no—
99C2×C4×C61—22no—
100C2×C4×C61—22no—
101C2×C4×C61—21no—
102C2×C4×C61—42no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61—42no—
106C2×C4×C61#12112yes—
107C2×C4×C61#12111yescharacteristic
108C2×C4×C61#12312yes—
109C2×C4×C61#12411yescharacteristic
110C2×Dic61—42no—
111C2×Dic61—42no—
112C2×Dic61—42no—
113C2×Dic61—82no—
114C2×Dic61—81no—
115D244—44no—
116D244—82no—
117D244—84no—
118D244—84no—
119Dic122—44no—
120Dic122—82no—
121C8×C61—44no—
122#92418—24no—
123#10424—611nomaximal, Sylow
124C22×C61#39411yescharacteristic
125C22×C61#45312yes—
126C22×C61#45311yescharacteristic
127C22×C61#45512yes—
128C22×C61#45611yescharacteristic
129C2×D61—82no—
130C2×D61—82no—
131C2×D61—82no—
132C2×D61—82no—
133C2×D61—82no—
134C2×D61—82no—
135C2×D61—82no—
136C4×C61—22no—
137C4×C61—22no—
138C4×C61—21no—
139C4×C61—21no—
140C4×C61—81no—
141C4×C61—81no—
142Dic61—82no—
143Dic61—161no—
144#2819—611no—
145#1959—612no—
146#1847—611no—
147C2×#329—612no—
148#1295D6111yescharacteristic, complemented
149C2×C61#165511yescharacteristic
150C2×C61#165911yescharacteristic
151C2×C61#166112yes—
152C2×C61#203712yes—
153C2×C61#203911yescharacteristic
154D61—162no—
155C2×#124—612no—
156C2×#107—1221no—
157C2×#106—1221no—
158C2×#103—1222no—
159C2×#102—1222no—
160C2×#97—611no—
161C2×#97C2×D6112yes—
162#394—1221no—
163#394—1221no—
164#393—1222no—
165#392—1222no—
166#384—611no—
167#382C2×D6111yescharacteristic
168#329—1224no—
169C61#1042411yescharacteristic, complemented, Sylow
170C22×Q8—612no—
171C22×D4—612no—
172C22×D4—1221no—
173C22×D4—1221no—
174C22×C8—22no—
175C22×C8—1221no—
176#124—1222no—
177#124—1222no—
178#124—1222no—
179#124—1222no—
180C2×C4⋊C4—1221no—
181C2×C4⋊C4—1222no—
182C2×C4⋊C4D24411yescharacteristic
183C2×C4⋊C4D24411yescharacteristic
184C2×C22⋊C4—1222no—
185C2×C22⋊C4—1222no—
186C2×C22⋊C4—1222no—
187C2×C22⋊C4—1222no—
188C2×C42C22×D6111yescharacteristic
189#107—2442no—
190#106—2442no—
191#103—2444no—
192#102—2444no—
193#97—22no—
194#97—22no—
195#97—612no—
196#97—1221no—
197#95—22no—
198#95—1221no—
199#95—1221no—
200C24—1222no—
201C2×Q8—1222no—
202C2×Q8—1222no—
203C2×Q8—2442no—
204C2×Q8—2442no—
205C2×D4—1222no—
206C2×D4—1222no—
207C2×D4—4882no—
208C2×D4—4882no—
209C2×D4—4881no—
210C2×D4—4881no—
211C2×D4—2442no—
212C2×D4—2442no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—1222no—
216C22×C4—2441no—
217C22×C4C2×D24411yescharacteristic
218C22×C4D4×D6112yes—
219C2×C8—24no—
220C2×C8—42no—
221C2×C8—42no—
222C2×C8—1222no—
223C2×C8—1222no—
224C2×C8—1222no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—2442no—
228C4⋊C4—2442no—
229C4⋊C4—2441no—
230C4⋊C4—2441no—
231C22⋊C4—4882no—
232C22⋊C4—4882no—
233C22⋊C4—2442no—
234C22⋊C4—2442no—
235C22⋊C4—2442no—
236C22⋊C4—2442no—
237C42#1175822212yes—
238C42D4×D6111yescharacteristic
239C42#1175822611yescharacteristic
240C23—2442no—
241C23—2442no—
242C23—2442no—
243C23—2442no—
244C23—2442no—
245C23—2442no—
246C23—2442no—
247C23#1451974711yescharacteristic
248Q8—4882no—
249Q8—2444no—
250D4—4882no—
251D4—4884no—
252D4—4884no—
253D4—2444no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—4882no—
263C2×C4—4881no—
264C2×C4—2442no—
265C2×C4—2442no—
266C2×C4—2442no—
267C2×C4#1451975012yes—
268C2×C4#1451975211yescharacteristic
269C2×C4#1451976212yes—
270C2×C4#1451976511yescharacteristic
271C8—44no—
272C8—1224no—
273C22—4882no—
274C22—4882no—
275C22—4882no—
276C22—4882no—
277C22—4882no—
278C22—4882no—
279C22—4882no—
280C22#1683968011yescharacteristic
281C22#1683993112yes—
282C22#1683993211yescharacteristic
283C22#1683994112yes—
284C22#1683994711yescharacteristic
285C4—22no—
286C4—22no—
287C4—21no—
288C4—21no—
289C4—81no—
290C4—81no—
291C4—9761no—
292C4—4882no—
293C2—9762no—
294C2#2144510911yescharacteristic
295C2#2144512611yescharacteristic
296C2#2144513812yes—
297C2#2144703212yes—
298C2#2144704411yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1295C2
socleC23×C61#120
prime radical#21453865C2
hypercenter#1295D61
hypocenterC61#10424
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
2. #21446635C2semidirect
3. #21445988C2semidirect
4. C2×#16839501C2semidirect
5. C61×#1295C2semidirect
40. #14519688D4semidirect
148. #1295D61semidirect
169. C61#10424semidirect

Maximal subgroups

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

subgroupindex
#214538652
#214466352
#214459882
C2×#168395012
C61×#12952
#1042461