Finite Group Databasebeta

← #29597404

Subgroups — #29597404

Order 15616.

510 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M32×D61C211yesmaximal, characteristic, complemented
2#21455401C211yesmaximal, characteristic
3C2×#16839573C211yesmaximal, characteristic, complemented
4C2×#16839571C211yesmaximal, characteristic, complemented
5#21445841C211yesmaximal, characteristic, complemented
6#21443924C211yesmaximal, characteristic, complemented
7C61×#1386C211yesmaximal, characteristic, complemented
8C2×#14519799C2211yescharacteristic
9C22×C8×D61C2211yescharacteristic
10#16840274—21no—
11C2×#14519717C2211yescharacteristic
12C2×#14519716—21no—
13M32×D61—22no—
14M32×D61—22no—
15C2×C16×D61—21no—
16#16840004C411yescharacteristic, complemented
17#16840004C411yescharacteristic, complemented
18#16839999C411yescharacteristic, complemented
19#16839999C411yescharacteristic, complemented
20#16839992—21no—
21#16839992—21no—
22C2×#14519709C2211yescharacteristic
23#16839756—21no—
24#16839619—21no—
25#16839573—22no—
26#16839571—22no—
27#16839524—21no—
28C2×M32×C61C2211yescharacteristic
29C61×#427C2211yescharacteristic
30C2×#106×C61C2211yescharacteristic
31C2×#11758222—21no—
32C22×C4×D61D411yescharacteristic
33#14519799—21no—
34#14519799—21no—
35#14519799—21no—
36#14519799—21no—
37C2×Dic244C2×C411yescharacteristic
38C2×#11758190—21no—
39C2×D488C2×C411yescharacteristic
40C22×#92418D411yescharacteristic
41C2×C8×D61—21no—
42C2×C8×D61—21no—
43C2×C8×D61—21no—
44C2×C8×D61—21no—
45C2×C8×D61C2×C411yescharacteristic
46C2×C8×D61C2×C411yescharacteristic
47C2×C8×D61D411yescharacteristic
48C2×C8×D61D411yescharacteristic
49#14519761—41no—
50#14519757—21no—
51#14519757—21no—
52#14519752—21no—
53#14519752—21no—
54#14519747—41no—
55C4×D244—41no—
56C4×D244—41no—
57C2×C4⋊Dic61—21no—
58C2×#11758198—41no—
59#14519717—21no—
60#14519717D412yescomplemented
61#14519716—24no—
62C2×#11758185—21no—
63C16×D61—24no—
64#14519709—21no—
65#14519709—21no—
66#14519700—21no—
67#14519700—21no—
68#14519697—21no—
69#14519697—21no—
70#14519684—41no—
71C22×C8×C61C2311yescharacteristic
72#117×C61—21no—
73C2×C4⋊C4×C61—21no—
74M32×C61—21no—
75M32×C61D412yescomplemented
76C2×C16×C61—21no—
77#107×C61C2×C411yescharacteristic
78#107×C61C2×C411yescharacteristic
79#106×C61—21no—
80#106×C61—21no—
81#106×C61—21no—
82C23×D61D811yescharacteristic
83C22×C4×C61—41no—
84C22×C4×C61C2×D411yescharacteristic
85C2×C22⋊D61—41no—
86C22×Dic61—41no—
87C22×Dic61D811yescharacteristic
88#11758222—41no—
89#11758222—41no—
90#11758222—41no—
91#11758222—41no—
92C2×D244—21no—
93C2×D244—41no—
94C2×D244—41no—
95C2×C4×D61—21no—
96C2×C4×D61—21no—
97C2×C4×D61—21no—
98C2×C4×D61—21no—
99C2×C4×D61—41no—
100C2×C4×D61C22⋊C411yescharacteristic
101C2×C4×D61C22⋊C411yescharacteristic
102C2×C4×D61SD1611yescharacteristic
103C2×C4×D61SD1611yescharacteristic
104C2×Dic122—21no—
105C2×C8×C61C22×C411yescharacteristic
106C2×C8×C61C2×D411yescharacteristic
107C2×C8×C61C2×D411yescharacteristic
108C2×C8×C61C2×D411yescharacteristic
109C2×C8×C61#4111yescharacteristic
110C2×C8×C61#4111yescharacteristic
111C4⋊C4×C61—21no—
112C4⋊C4×C61—21no—
113C4⋊C4×C61—41no—
114C4⋊C4×C61—41no—
115C22⋊C4×C61—41no—
116C42×C61—41no—
117#11758198—41no—
118#11758198—41no—
119#11758198—41no—
120#11758198—41no—
121#11758198—82no—
122C4⋊Dic61—41no—
123C4⋊Dic61—41no—
124C4⋊Dic61—41no—
125C4⋊Dic61—41no—
126C2×#92418—21no—
127C2×#92418—21no—
128C2×#92418C22⋊C411yescharacteristic
129C2×#92418C22⋊C411yescharacteristic
130Dic244—21no—
131Dic244—21no—
132D488—21no—
133D488—21no—
134#11758190—41no—
135#11758190—41no—
136C8×D61—21no—
137C8×D61—21no—
138C8×D61—21no—
139C8×D61—21no—
140C8×D61—21no—
141C8×D61—21no—
142C8×D61—21no—
143C8×D61—21no—
144C16×C61—22no—
145#11758185—22no—
146C23×C61C2×D811yescharacteristic
147C22×D61—21no—
148C22×D61—21no—
149C22×D61—22no—
150C22×D61—41no—
151C22×D61—41no—
152C22×D61#10211yescharacteristic
153C22×D61#10211yescharacteristic
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—81no—
157C2×C4×C61—81no—
158C2×C4×C61—81no—
159C2×C4×C61C2×C22⋊C411yescharacteristic
160C2×C4×C61#12111yescharacteristic
161C2×C4×C61#12111yescharacteristic
162C2×C4×C61C2×SD1611yescharacteristic
163C2×C4×C61#13511yescharacteristic
164C2×C4×C61#13511yescharacteristic
165C22⋊D61—81no—
166C22⋊D61—81no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—41no—
170C2×Dic61—81no—
171C2×Dic61—81no—
172C2×Dic61—81no—
173C2×Dic61#10211yescharacteristic
174C2×Dic61#10211yescharacteristic
175D244—41no—
176D244—41no—
177D244—82no—
178D244—82no—
179C4×D61—21no—
180C4×D61—21no—
181C4×D61—21no—
182C4×D61—21no—
183C4×D61—21no—
184C4×D61—21no—
185C4×D61—21no—
186C4×D61—21no—
187C4×D61—81no—
188C4×D61—81no—
189Dic122—41no—
190Dic122—41no—
191C8×C61C4×D411yescharacteristic
192C8×C61C4×D411yescharacteristic
193C8×C61#12011yescharacteristic
194C8×C61#12311yescharacteristic
195#92418—21no—
196#92418—21no—
197#13065—611nomaximal, Sylow
198C22×C61—21no—
199C22×C61—21no—
200C22×C61C2×#10211yescharacteristic
201C22×C61#46611yescharacteristic
202C22×C61#46611yescharacteristic
203C2×D61—21no—
204C2×D61—21no—
205C2×D61—21no—
206C2×D61—21no—
207C2×D61—21no—
208C2×D61—42no—
209C2×D61—42no—
210C2×D61—81no—
211C2×D61—81no—
212C2×D61—81no—
213C2×D61#36012yescomplemented
214C4×C61—81no—
215C4×C61—81no—
216C4×C61—161no—
217C4×C61#38611yescharacteristic
218C4×C61#41611yescharacteristic
219C4×C61#46511yescharacteristic
220C4×C61#46511yescharacteristic
221Dic61—21no—
222Dic61—21no—
223Dic61—81no—
224Dic61—161no—
225C22×M32—611no—
226#3050—611no—
227C2×#360—611no—
228C2×#360—611no—
229#1807—611no—
230#1386—611no—
231#1386D6111yescharacteristic, complemented
232C2×C61—21no—
233C2×C61—21no—
234C2×C61#189311yescharacteristic
235C2×C61C2×#36011yescharacteristic
236C2×C61#214511yescharacteristic
237D61—22no—
238D61—41no—
239D61—161no—
240C2×#135—611no—
241C23×C8—611no—
242#525—1221no—
243C2×M32—611no—
244C2×M32—1221no—
245C2×M32—1222no—
246C2×M32—1222no—
247C2×M32C2×D6111yescharacteristic
248C22×C16—1221no—
249#467—611no—
250#467—611no—
251#466—611no—
252#466—611no—
253#465—1221no—
254#465—1221no—
255#427C2×D6111yescharacteristic
256C2×#106—611no—
257C2×#106C2×D6111yescharacteristic
258#416—1221no—
259#380—1221no—
260#360—1222no—
261#360—1222no—
262#340—1221no—
263C61#1306511yescharacteristic, complemented, Sylow
264C2×#41—1221no—
265C23×C4—611no—
266#135—1221no—
267#135—1221no—
268#135—1221no—
269#135—1221no—
270C2×Q16—611no—
271C2×SD16—1221no—
272C2×D8—611no—
273C22×C8—611no—
274C22×C8—611no—
275C22×C8—611no—
276C22×C8—611no—
277C22×C8—611no—
278C22×C8—1221no—
279C22×C8—1221no—
280C22×C8—1221no—
281C22×C8—1221no—
282C22×C8C22×D6111yescharacteristic
283#123—2441no—
284C22⋊Q8—1221no—
285C22⋊Q8—1221no—
286#121—1221no—
287#121—1221no—
288#120—2441no—
289C4×D4—2441no—
290C4×D4—2441no—
291#117—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—1221no—
294C2×C22⋊C4—2441no—
295M32—21no—
296M32—612no—
297M32—1224no—
298M32—1221no—
299M32D24412yescomplemented
300C2×C16—21no—
301C2×C16—1224no—
302C2×C16—1221no—
303#107C4×D6111yescharacteristic
304#107C4×D6111yescharacteristic
305#106—21no—
306#106—21no—
307#106—21no—
308#106—1221no—
309#106—1221no—
310#103—1221no—
311#103—1221no—
312#102—1221no—
313#102—1221no—
314#95—2441no—
315C24—611no—
316#41—2441no—
317#41—2441no—
318#41—2441no—
319#41—2441no—
320C2×Q8—1221no—
321C2×D4—1221no—
322C2×D4—2441no—
323C2×D4—2441no—
324C2×D4—2441no—
325C22×C4—41no—
326C22×C4—611no—
327C22×C4—611no—
328C22×C4—611no—
329C22×C4—611no—
330C22×C4—611no—
331C22×C4—1221no—
332C22×C4—1221no—
333C22×C4—1221no—
334C22×C4—1221no—
335C22×C4—2441no—
336C22×C4—2441no—
337C22×C4D4×D6111yescharacteristic
338Q16—1221no—
339Q16—1221no—
340SD16—2441no—
341SD16—2441no—
342D8—1221no—
343D8—1221no—
344C2×C8—611no—
345C2×C8—611no—
346C2×C8—1221no—
347C2×C8—1221no—
348C2×C8—1221no—
349C2×C8—1221no—
350C2×C8—1221no—
351C2×C8—1221no—
352C2×C8—1221no—
353C2×C8—1221no—
354C2×C8—1221no—
355C2×C8—1221no—
356C2×C8C2×C4×D6111yescharacteristic
357C2×C8C2×D24411yescharacteristic
358C2×C8#1175822211yescharacteristic
359C2×C8D4×D6111yescharacteristic
360C2×C8D4×D6111yescharacteristic
361C2×C8#1175822611yescharacteristic
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—2441no—
367C4⋊C4—2441no—
368C4⋊C4—2441no—
369C4⋊C4—2441no—
370C22⋊C4—41no—
371C22⋊C4—4882no—
372C22⋊C4—2441no—
373C22⋊C4—2441no—
374C22⋊C4—2441no—
375C22⋊C4—2441no—
376C42—41no—
377C16—22no—
378C16—1222no—
379C23—611no—
380C23—611no—
381C23—1222no—
382C23—1221no—
383C23—1221no—
384C23—2441no—
385C23—2441no—
386C23D8×D6111yescharacteristic
387Q8—2441no—
388Q8—2441no—
389D4—4882no—
390D4—4882no—
391D4—4881no—
392D4—4881no—
393D4—2441no—
394D4—2441no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—611no—
401C2×C4—611no—
402C2×C4—1221no—
403C2×C4—1221no—
404C2×C4—1221no—
405C2×C4—1221no—
406C2×C4—1221no—
407C2×C4—1221no—
408C2×C4—1221no—
409C2×C4—1221no—
410C2×C4—1221no—
411C2×C4—1221no—
412C2×C4—4881no—
413C2×C4—4881no—
414C2×C4—4881no—
415C2×C4—4881no—
416C2×C4—4881no—
417C2×C4—2441no—
418C2×C4C22⋊C4×D6111yescharacteristic
419C2×C4#1451975011yescharacteristic
420C2×C4#1451975211yescharacteristic
421C2×C4SD16×D6111yescharacteristic
422C2×C4#1451979811yescharacteristic
423C2×C4#1451980011yescharacteristic
424C8—1221no—
425C8—1221no—
426C8#1451973911yescharacteristic
427C8C4×D24411yescharacteristic
428C8#1451974711yescharacteristic
429C8#1451976211yescharacteristic
430C22—21no—
431C22—21no—
432C22—612no—
433C22—1221no—
434C22—1221no—
435C22—1221no—
436C22—1221no—
437C22—1221no—
438C22—4881no—
439C22—4881no—
440C22—4881no—
441C22—2442no—
442C22—2442no—
443C22#102×D6111yescharacteristic
444C22#1683999711yescharacteristic
445C22#1683999911yescharacteristic
446C4—81no—
447C4—81no—
448C4—161no—
449C4—1221no—
450C4—1221no—
451C4—9761no—
452C4—4881no—
453C4#1683964011yescharacteristic
454C4#1683975711yescharacteristic
455C4#1683999211yescharacteristic
456C4#1683999411yescharacteristic
457C2—21no—
458C2—21no—
459C2—1222no—
460C2—9761no—
461C2—2441no—
462C2#2144624611yescharacteristic
463C2#360×D6111yescharacteristic
464C2#2144755311yescharacteristic
subgroupG/H
centerC22#102×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#1386C2
socleC22×C61C2×#102
prime radical#21455401C2
cosocleC22×C8×C61C23
hypercenter#1386D61
hypocenterC61#13065
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1386

Complements

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

NH ≅ G/Ntype
1. C2×M32×D61C2semidirect
3. C2×#16839573C2semidirect
4. C2×#16839571C2semidirect
5. #21445841C2semidirect
6. #21443924C2semidirect
7. C61×#1386C2semidirect
16. #16840004C4semidirect
17. #16840004C4semidirect
18. #16839999C4semidirect
19. #16839999C4semidirect
60. #14519717D4semidirect
75. M32×C61D4semidirect
213. C2×D61#360semidirect
231. #1386D61semidirect
263. C61#13065semidirect
299. M32D244semidirect

Maximal subgroups

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

subgroupindex
C2×M32×D612
#214554012
C2×#168395732
C2×#168395712
#214458412
#214439242
C61×#13862
#1306561