Finite Group Databasebeta

← #29590244

Subgroups — #29590244

Order 15616.

504 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455400C211yesmaximal, characteristic
2#21447430C211yesmaximal, characteristic, complemented
3#21443830C212yesmaximal, complemented
4#21443827C212yesmaximal, complemented
5C2×C61×#340C211yesmaximal, characteristic, complemented
6C2×#14519799C411yescharacteristic, complemented
7#16840273—21no—
8C2×#14519717—21no—
9#16840003C411yescharacteristic, complemented
10#16840003C2211yescharacteristic
11#16839998C411yescharacteristic, complemented
12#16839998C2211yescharacteristic
13#16839991—21no—
14#16839991—21no—
15#16839800C411yescharacteristic, complemented
16#16839759—21no—
17C22⋊#11758185—21no—
18C22⋊#11758185C2212yes—
19C23×C8×C61C2211yescharacteristic
20C22×C4⋊C4×C61—21no—
21C61×#340—21no—
22C61×#340C2212yes—
23C2×#11758222—21no—
24#14519799—42no—
25C2×Dic244C2×C411yescharacteristic, complemented
26C2×#11758190—21no—
27C2×D488C2×C411yescharacteristic, complemented
28#14519760—41no—
29#14519756—21no—
30#14519756—21no—
31#14519751—21no—
32#14519751—21no—
33#14519746—41no—
34C4×C22⋊D61—41no—
35C4×C22⋊D61—41no—
36#14519736—21no—
37#14519717—42no—
38C2×#11758185—22no—
39#14519711C2×C411yescharacteristic, complemented
40#14519711C2×C411yescharacteristic, complemented
41#14519709—21no—
42#14519702—21no—
43#14519702—21no—
44#14519699—21no—
45#14519699—21no—
46C23×C4×C61—41no—
47C23×C4×C61D411yescharacteristic
48C22×C8×C61—42no—
49C22×C8×C61C2×C411yescharacteristic
50C22×C8×C61C2×C411yescharacteristic
51C22×C8×C61D411yescharacteristic
52C22×C8×C61D411yescharacteristic
53C22×C8×C61D411yescharacteristic
54C22×C8×C61C2311yescharacteristic
55C2×C4⋊C4×C61—24no—
56C2×C4⋊C4×C61—22no—
57C2×C4⋊C4×C61—42no—
58C2×C4⋊C4×C61—41no—
59C24×C61D811yescharacteristic
60C22×C4×C61—22no—
61C22×C4×C61—22no—
62C22×C4×C61—44no—
63C22×C4×C61—42no—
64C22×C4×C61—82no—
65C22×C4×C61—82no—
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61D811yescharacteristic
69C22×C4×C61SD1611yescharacteristic
70C22×C4×C61SD1611yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C2×C22⋊D61—41no—
73C2×C22⋊D61—41no—
74C2×C22⋊D61—41no—
75#11758222—42no—
76#11758222—42no—
77C2×D244—21no—
78C2×C4×D61—41no—
79C2×Dic122—21no—
80C2×C8×C61—22no—
81C2×C8×C61—22no—
82C2×C8×C61—41no—
83C2×C8×C61—41no—
84C2×C8×C61—41no—
85C2×C8×C61—41no—
86C2×C8×C61C22⋊C411yescharacteristic
87C2×C8×C61C22⋊C411yescharacteristic
88C2×C8×C61C22×C411yescharacteristic
89C2×C8×C61C2×D411yescharacteristic
90C4⋊C4×C61—24no—
91C4⋊C4×C61—44no—
92C4⋊C4×C61—42no—
93C22⋊Dic61—41no—
94C22⋊Dic61—41no—
95C22⋊Dic61—41no—
96#11758198—41no—
97#11758198—41no—
98C4⋊Dic61—21no—
99C4⋊Dic61—21no—
100#11758196—41no—
101#11758196—41no—
102C4×Dic61—41no—
103Dic244—41no—
104D488—41no—
105#11758190—42no—
106#11758185—42no—
107C23×C61—22no—
108C23×C61—22no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61#10211yescharacteristic
112C23×C61#10211yescharacteristic
113C23×C61C2×D811yescharacteristic
114C22×D61—41no—
115C2×C4×C61—22no—
116C2×C4×C61—22no—
117C2×C4×C61—22no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—44no—
123C2×C4×C61—88no—
124C2×C4×C61—82no—
125C2×C4×C61—82no—
126C2×C4×C61#9912yes—
127C2×C4×C61#10211yescharacteristic
128C2×C4×C61#10211yescharacteristic
129C2×C4×C61#10412yes—
130C2×C4×C61C2×C22⋊C411yescharacteristic
131C2×C4×C61C2×SD1611yescharacteristic
132C22⋊D61—82no—
133C22⋊D61—82no—
134C22⋊D61—81no—
135C22⋊D61—81no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139D244—41no—
140D244—41no—
141C4×D61—82no—
142Dic122—41no—
143Dic122—41no—
144C8×C61—21no—
145C8×C61—21no—
146C8×C61—21no—
147C8×C61—21no—
148#11704—611nomaximal, Sylow
149C22×C61—24no—
150C22×C61—24no—
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61#32712yes—
158C22×C61#36012yes—
159C22×C61C2×#10211yescharacteristic
160C22×C61#50911yescharacteristic
161C22×C61#51011yescharacteristic
162C2×D61—81no—
163C2×D61—81no—
164C2×D61—81no—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—84no—
168C4×C61#32712yes—
169C4×C61C2×#9911yescharacteristic
170C4×C61C2×#10411yescharacteristic
171Dic61—81no—
172Dic61—81no—
173Dic61—81no—
174#3050—611no—
175#2112—611no—
176C2×#340D6111yescharacteristic, complemented
177#1348—612no—
178#1347—612no—
179C2×C61—21no—
180C2×C61—22no—
181C2×C61—22no—
182C2×C61—21no—
183C2×C61C2×#32711yescharacteristic
184C2×C61#213911yescharacteristic
185C2×C61C2×#36011yescharacteristic
186D61—161no—
187C2×#135—611no—
188C23×C8C2×D6111yescharacteristic
189#525—1221no—
190C22×C4⋊C4—21no—
191C2×M32—1221no—
192#467—611no—
193#467—611no—
194#466—611no—
195#466—611no—
196#465—1221no—
197#465—1221no—
198#427—611no—
199#416—1221no—
200C22⋊C16—612no—
201C22⋊C16—1221no—
202#340—21no—
203#340C2×D6112yes—
204C61#1170411yescharacteristic, complemented, Sylow
205C2×#41—1221no—
206C23×C4—41no—
207C23×C4C22⋊D6111yescharacteristic
208#135—2442no—
209C2×Q16—611no—
210C2×SD16—1221no—
211C2×D8—611no—
212C22×C8—42no—
213C22×C8C4×D6111yescharacteristic
214C22×C8C4×D6111yescharacteristic
215C22×C8D24411yescharacteristic
216C22×C8D24411yescharacteristic
217C22×C8C22⋊D6111yescharacteristic
218C22×C8C22×D6111yescharacteristic
219#123—2441no—
220C22⋊Q8—1221no—
221C22⋊Q8—1221no—
222#121—1221no—
223#121—1221no—
224#120—2441no—
225C4×D4—2441no—
226C4×D4—2441no—
227#117—1221no—
228C2×C4⋊C4—24no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—42no—
231C2×C4⋊C4—41no—
232M32—2442no—
233C2×C16—1222no—
234#107—611no—
235#107—611no—
236#106—1221no—
237#103—1221no—
238#103—1221no—
239#102—1221no—
240#102—1221no—
241C24#1175819911yescharacteristic
242#41—2442no—
243#41—2442no—
244C2×Q8—1221no—
245C2×D4—1221no—
246C2×D4—2441no—
247C2×D4—2441no—
248C2×D4—2441no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—44no—
252C22×C4—42no—
253C22×C4—82no—
254C22×C4—82no—
255C22×C4—2441no—
256C22×C4#1175819811yescharacteristic
257C22×C4#1175819811yescharacteristic
258C22×C4#1175819911yescharacteristic
259C22×C4#1175820111yescharacteristic
260C22×C4#1175820111yescharacteristic
261C22×C4C2×C22⋊D6111yescharacteristic
262Q16—2441no—
263SD16—2442no—
264D8—2441no—
265C2×C8—22no—
266C2×C8—22no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8#1175819811yescharacteristic
272C2×C8#1175819811yescharacteristic
273C2×C8C2×C4×D6111yescharacteristic
274C2×C8C2×D24411yescharacteristic
275C4⋊C4—24no—
276C4⋊C4—42no—
277C4⋊C4—44no—
278C4⋊C4—1221no—
279C4⋊C4—1221no—
280C4⋊C4—2441no—
281C4⋊C4—2441no—
282C22⋊C4—2441no—
283C22⋊C4—2441no—
284C22⋊C4—2441no—
285C22⋊C4—2441no—
286C22⋊C4—2441no—
287C42—2441no—
288C16—2442no—
289C23—21no—
290C23—21no—
291C23—22no—
292C23—22no—
293C23—2441no—
294C23#1451969711yescharacteristic
295C23#1451969711yescharacteristic
296C23C2×#1175819911yescharacteristic
297Q8—2441no—
298Q8—2441no—
299D4—4881no—
300D4—4881no—
301D4—4882no—
302D4—4882no—
303D4—2441no—
304D4—2441no—
305C2×C4—22no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—44no—
313C2×C4—88no—
314C2×C4—82no—
315C2×C4—82no—
316C2×C4—4882no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4#1451969112yes—
321C2×C4#1451969711yescharacteristic
322C2×C4#1451969711yescharacteristic
323C2×C4#1451970512yes—
324C2×C4C2×#1175819811yescharacteristic
325C2×C4C2×#1175820111yescharacteristic
326C8—21no—
327C8—21no—
328C8—21no—
329C8—21no—
330C22—24no—
331C22—24no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—4881no—
339C22—4881no—
340C22—4881no—
341C22#1683949512yes—
342C22#1683957112yes—
343C22C2×#1451969711yescharacteristic
344C22#1684019811yescharacteristic
345C22#1684020311yescharacteristic
346C4—21no—
347C4—21no—
348C4—84no—
349C4—4881no—
350C4—4881no—
351C4—4881no—
352C4#1683949512yes—
353C4C2×#1451969111yescharacteristic
354C4C2×#1451970511yescharacteristic
355C2—21no—
356C2—21no—
357C2—22no—
358C2—22no—
359C2—9761no—
360C2C2×#1683949511yescharacteristic
361C2#2144752911yescharacteristic
362C2C2×#1683957111yescharacteristic
subgroupG/H
centerC22C2×#14519697
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC2×C61×#340C2
socleC22×C61C2×#102
prime radical#21455400C2
cosocleC22×C8×C61C23
hypercenterC2×#340D61
hypocenterC61#11704
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
2. #21447430C2semidirect
3. #21443830C2semidirect
4. #21443827C2semidirect
5. C2×C61×#340C2semidirect
6. C2×#14519799C4semidirect
9. #16840003C4semidirect
11. #16839998C4semidirect
15. #16839800C4semidirect
25. C2×Dic244C2×C4semidirect
27. C2×D488C2×C4semidirect
39. #14519711C2×C4semidirect
40. #14519711C2×C4semidirect
176. C2×#340D61semidirect
204. C61#11704semidirect

Maximal subgroups

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

subgroupindex
#214554002
#214474302
#214438302
#214438272
C2×C61×#3402
#1170461