Finite Group Databasebeta

← #29595653

Subgroups — #29595653

Order 15616.

1190 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D8×D61C211yesmaximal, characteristic
2C2×#16839564C211yesmaximal, characteristic, complemented
3C2×#16839563C211yesmaximal, characteristic, complemented
4C2×#16839562C211yesmaximal, characteristic, complemented
5C2×#16839541C211yesmaximal, characteristic, complemented
6#21445845C211yesmaximal, characteristic, complemented
7C2×C61×#357C211yesmaximal, characteristic, complemented
8C22×D4×D61—21no—
9C22×D488C2211yescharacteristic
10C22×#11758199—21no—
11C2×D8×D61—22no—
12C2×D8×D61—22no—
13C2×D8×D61—22no—
14C2×D8×D61—22no—
15C2×D8×D61—22no—
16C2×D8×D61C414yescomplemented
17C22×C8×D61C2211yescharacteristic
18C22×#11758185C2211yescharacteristic, complemented
19C2×#14519711C2211yescharacteristic, complemented
20#16839619—21no—
21#16839564—22no—
22#16839563—22no—
23#16839562—22no—
24#16839541—22no—
25#16839524—21no—
26C22×D8×C61C2211yescharacteristic
27C22×C16×C61C2211yescharacteristic, complemented
28C2×#107×C61C2211yescharacteristic, complemented
29C61×#357—22no—
30C24×D61—41no—
31C22×D244—21no—
32C22×C22⋊D61—41no—
33C2×D4×D61—24no—
34C2×D4×D61—24no—
35C2×D4×D61—24no—
36C2×D4×D61—42no—
37C2×D4×D61—42no—
38C2×D4×D61—42no—
39C22×C4×D61D411yescharacteristic
40C2×D488—21no—
41C2×D488—21no—
42C2×D488—21no—
43C2×D488C2×C412yes—
44C2×D488D412yes—
45C2×D488D412yes—
46C2×#11758199—24no—
47C2×#11758199—24no—
48C2×#11758199—24no—
49D8×D61—28no—
50D8×D61—28no—
51D8×D61—28no—
52D8×D61—28no—
53C22×#92418D411yescharacteristic
54C2×C8×D61—21no—
55C2×C8×D61—21no—
56C2×C8×D61—21no—
57C2×C8×D61—21no—
58C2×C8×D61C2×C412yes—
59C2×C8×D61D412yes—
60C2×C4⋊Dic61—21no—
61C2×#11758198—41no—
62C2×#11758185—21no—
63C2×#11758185—21no—
64C2×#11758185—21no—
65#14519711—21no—
66#14519711—21no—
67#14519684—41no—
68C22×D4×C61—21no—
69C2×D8×C61—21no—
70C2×D8×C61—21no—
71C2×D8×C61—21no—
72C2×D8×C61C2×C412yes—
73C2×D8×C61D412yes—
74C2×D8×C61D412yes—
75C22×C8×C61C2311yescharacteristic
76C2×C4⋊C4×C61—21no—
77C2×C16×C61—21no—
78C2×C16×C61—21no—
79C2×C16×C61—21no—
80#107×C61—21no—
81#107×C61—21no—
82C24×C61—41no—
83C23×D61—44no—
84C23×D61—44no—
85C23×D61—41no—
86C23×D61—44no—
87C23×D61—82no—
88C23×D61—82no—
89C23×D61—82no—
90C23×D61—82no—
91C23×D61D811yescharacteristic
92C2×D4×C61—22no—
93C2×D4×C61—22no—
94C2×D4×C61—22no—
95C2×D4×C61—41no—
96C2×D4×C61—41no—
97C2×D4×C61—41no—
98C22×C4×C61—41no—
99C22×C4×C61C2×D411yescharacteristic
100C2×C22⋊D61—44no—
101C2×C22⋊D61—44no—
102C2×C22⋊D61—44no—
103C22×Dic61—41no—
104C22×Dic61D811yescharacteristic
105D4×D61—216no—
106D4×D61—48no—
107D4×D61—48no—
108D4×D61—48no—
109C2×D244—22no—
110C2×D244—22no—
111C2×D244—22no—
112C2×D244—41no—
113C2×D244—41no—
114C2×D244—41no—
115C2×C4×D61—21no—
116C2×C4×D61—21no—
117C2×C4×D61—21no—
118C2×C4×D61—21no—
119C2×C4×D61C22⋊C412yes—
120C2×C4×D61SD1612yes—
121D8×C61—22no—
122D8×C61—22no—
123D8×C61—22no—
124D8×C61C22⋊C414yescomplemented
125C2×C8×C61C22×C411yescharacteristic
126C2×C8×C61C2×D411yescharacteristic
127C2×C8×C61C2×D411yescharacteristic
128C2×C8×C61C2×D411yescharacteristic
129C2×C8×C61C2×D411yescharacteristic
130C2×C8×C61C2×D411yescharacteristic
131C4⋊C4×C61—41no—
132C4⋊C4×C61—41no—
133#11758199—216no—
134#11758198—82no—
135C4⋊Dic61—41no—
136C4⋊Dic61—41no—
137C2×#92418—21no—
138C2×#92418—21no—
139C2×#92418C22⋊C412yes—
140D488—22no—
141D488—22no—
142D488—22no—
143D488C22⋊C414yescomplemented
144C8×D61—22no—
145C8×D61—22no—
146C8×D61—22no—
147C8×D61—22no—
148C16×C61—41no—
149#11758185—41no—
150C23×C61—42no—
151C23×C61—42no—
152C23×C61—42no—
153C23×C61—81no—
154C23×C61—81no—
155C23×C61—81no—
156C23×C61—81no—
157C23×C61C2×D811yescharacteristic
158C22×D61—21no—
159C22×D61—21no—
160C22×D61—21no—
161C22×D61—21no—
162C22×D61—416no—
163C22×D61—42no—
164C22×D61—42no—
165C22×D61—42no—
166C22×D61—88no—
167C22×D61—88no—
168C22×D61—88no—
169C22×D61—88no—
170C22×D61—88no—
171C22×D61—81no—
172C22×D61—81no—
173C22×D61—81no—
174C22×D61—81no—
175C22×D61—88no—
176C22×D61#10212yes—
177C22×D61D1612yes—
178C22×D61SD3212yes—
179D4×C61—24no—
180D4×C61—42no—
181D4×C61—42no—
182D4×C61—42no—
183C2×C4×C61—81no—
184C2×C4×C61—81no—
185C2×C4×C61—81no—
186C2×C4×C61C2×C22⋊C411yescharacteristic
187C2×C4×C61#12011yescharacteristic
188C2×C4×C61#12011yescharacteristic
189C2×C4×C61C2×SD1611yescharacteristic
190C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
191C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
192C22⋊D61—416no—
193C2×Dic61—21no—
194C2×Dic61—21no—
195C2×Dic61—81no—
196C2×Dic61—81no—
197C2×Dic61—81no—
198C2×Dic61#10212yes—
199D244—24no—
200D244—42no—
201D244—42no—
202D244—42no—
203C4×D61—22no—
204C4×D61—22no—
205C4×D61—22no—
206C4×D61—22no—
207C8×C61C2×C22⋊C411yescharacteristic
208C8×C61C2×C22⋊C411yescharacteristic
209C8×C61#12011yescharacteristic
210C8×C61#12011yescharacteristic
211#92418—22no—
212#12731—611nomaximal, Sylow
213C22×C61—44no—
214C22×C61—82no—
215C22×C61—82no—
216C22×C61—82no—
217C22×C61—82no—
218C22×C61—82no—
219C22×C61—82no—
220C22×C61C2×#10211yescharacteristic
221C22×C61#44711yescharacteristic
222C22×C61#44711yescharacteristic
223C22×C61C2×D1611yescharacteristic
224C22×C61C2×SD3211yescharacteristic
225C22×C61#50911yescharacteristic
226C22×C61#50911yescharacteristic
227C2×D61—22no—
228C2×D61—22no—
229C2×D61—22no—
230C2×D61—22no—
231C2×D61—22no—
232C2×D61—22no—
233C2×D61—44no—
234C2×D61—832no—
235C2×D61—82no—
236C2×D61—82no—
237C2×D61—82no—
238C2×D61—82no—
239C2×D61—82no—
240C2×D61—82no—
241C2×D61#35714yescomplemented
242C4×C61—161no—
243C4×C61#37911yescharacteristic
244C4×C61#41811yescharacteristic
245C4×C61#45011yescharacteristic
246C4×C61#45011yescharacteristic
247Dic61—22no—
248Dic61—161no—
249C23×D8—611no—
250C2×#357—611no—
251C2×#357—611no—
252C2×#357—611no—
253C2×#357D6111yescharacteristic, complemented
254C2×C22⋊C16—611no—
255#1808—611no—
256C2×C61—84no—
257C2×C61#178611yescharacteristic
258C2×C61C2×#35711yescharacteristic
259C2×C61#214011yescharacteristic
260C2×C61#218411yescharacteristic
261C2×C61#218411yescharacteristic
262C2×C61#218711yescharacteristic
263C2×C61#218711yescharacteristic
264D61—24no—
265D61—84no—
266C23×D4—1221no—
267C22×D8—614no—
268C22×D8—611no—
269C22×D8—1222no—
270C22×D8—1221no—
271C22×D8—1222no—
272C22×D8—1222no—
273C22×D8—1222no—
274C22×D8—1222no—
275C22×D8C2×D6111yescharacteristic
276C23×C8—611no—
277C22×C16—611no—
278C22×C16C2×D6111yescharacteristic, complemented
279C2×#107—611no—
280C2×#107C2×D6111yescharacteristic, complemented
281#380—1221no—
282#357—22no—
283#357—1222no—
284#357—1222no—
285#357—1222no—
286C22⋊C16—1222no—
287#340—1221no—
288C61#1273111yescharacteristic, complemented, Sylow
289C25—2441no—
290C22×D4—21no—
291C22×D4—1224no—
292C22×D4—1224no—
293C22×D4—1224no—
294C22×D4—1221no—
295C22×D4—2442no—
296C22×D4—2441no—
297C22×D4—2442no—
298C22×D4—2442no—
299C23×C4—611no—
300C2×D8—21no—
301C2×D8—21no—
302C2×D8—21no—
303C2×D8—612no—
304C2×D8—612no—
305C2×D8—612no—
306C2×D8—1224no—
307C2×D8—1228no—
308C2×D8—1228no—
309C2×D8—1228no—
310C2×D8—1224no—
311C2×D8—1224no—
312C2×D8—1228no—
313C2×D8—1221no—
314C2×D8—1221no—
315C2×D8—1221no—
316C2×D8C4×D6112yes—
317C2×D8D24412yes—
318C2×D8C22⋊D6112yes—
319C22×C8—611no—
320C22×C8—612no—
321C22×C8—612no—
322C22×C8—1221no—
323C22×C8—1221no—
324C22×C8—1221no—
325C22×C8—1221no—
326C22×C8C22×D6111yescharacteristic
327C2×C4⋊C4—21no—
328C2×C4⋊C4—1221no—
329C2×C22⋊C4—2441no—
330C2×C16—21no—
331C2×C16—21no—
332C2×C16—21no—
333C2×C16—1221no—
334C2×C16—1221no—
335C2×C16—1221no—
336#107—21no—
337#107—21no—
338#107—1221no—
339#107—1221no—
340#95—2441no—
341C24—41no—
342C24—611no—
343C24—4882no—
344C24—4882no—
345C24—4882no—
346C24—4882no—
347C24—2444no—
348C24—2444no—
349C24—2444no—
350C24—2441no—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—22no—
354C2×D4—41no—
355C2×D4—41no—
356C2×D4—41no—
357C2×D4—12216no—
358C2×D4—1222no—
359C2×D4—1222no—
360C2×D4—1222no—
361C2×D4—2444no—
362C2×D4—2448no—
363C2×D4—2448no—
364C2×D4—2448no—
365C2×D4—2444no—
366C2×D4—2444no—
367C2×D4—2441no—
368C2×D4—2441no—
369C2×D4—2441no—
370C22×C4—41no—
371C22×C4—611no—
372C22×C4—612no—
373C22×C4—612no—
374C22×C4—1221no—
375C22×C4—1221no—
376C22×C4—1221no—
377C22×C4—1221no—
378C22×C4—2441no—
379C22×C4D4×D6111yescharacteristic
380D8—22no—
381D8—22no—
382D8—22no—
383D8—614no—
384D8—12216no—
385D8—1222no—
386D8—1222no—
387D8—1222no—
388D8#1175819814yescomplemented
389C2×C8—612no—
390C2×C8—1221no—
391C2×C8—1221no—
392C2×C8—1222no—
393C2×C8—1222no—
394C2×C8—1222no—
395C2×C8—1222no—
396C2×C8C2×C4×D6111yescharacteristic
397C2×C8C2×D24411yescharacteristic
398C2×C8D4×D6111yescharacteristic
399C2×C8D4×D6111yescharacteristic
400C2×C8D4×D6111yescharacteristic
401C2×C8C2×C22⋊D6111yescharacteristic
402C4⋊C4—41no—
403C4⋊C4—41no—
404C4⋊C4—2441no—
405C4⋊C4—2441no—
406C22⋊C4—4882no—
407C16—41no—
408C16—2441no—
409C23—42no—
410C23—42no—
411C23—42no—
412C23—81no—
413C23—81no—
414C23—81no—
415C23—81no—
416C23—612no—
417C23—612no—
418C23—612no—
419C23—1221no—
420C23—1221no—
421C23—1221no—
422C23—1221no—
423C23—4888no—
424C23—4888no—
425C23—4888no—
426C23—4888no—
427C23—4888no—
428C23—4888no—
429C23—4881no—
430C23—4881no—
431C23—4881no—
432C23—4881no—
433C23—24416no—
434C23—2442no—
435C23—2442no—
436C23—2442no—
437C23D8×D6111yescharacteristic
438D4—24no—
439D4—42no—
440D4—42no—
441D4—42no—
442D4—1224no—
443D4—24416no—
444D4—2442no—
445D4—2442no—
446D4—2442no—
447C2×C4—81no—
448C2×C4—81no—
449C2×C4—81no—
450C2×C4—612no—
451C2×C4—1221no—
452C2×C4—1221no—
453C2×C4—1222no—
454C2×C4—1222no—
455C2×C4—1222no—
456C2×C4—1222no—
457C2×C4—4881no—
458C2×C4—4881no—
459C2×C4—4881no—
460C2×C4C22⋊C4×D6111yescharacteristic
461C2×C4#1451974511yescharacteristic
462C2×C4#1451974711yescharacteristic
463C2×C4SD16×D6111yescharacteristic
464C2×C4#1451980111yescharacteristic
465C2×C4#1451980411yescharacteristic
466C8—1222no—
467C8C22⋊C4×D6111yescharacteristic
468C8C2×#1175819811yescharacteristic
469C8#1451974511yescharacteristic
470C8#1451974711yescharacteristic
471C22—44no—
472C22—82no—
473C22—82no—
474C22—82no—
475C22—82no—
476C22—82no—
477C22—82no—
478C22—614no—
479C22—1222no—
480C22—1222no—
481C22—1222no—
482C22—1222no—
483C22—1222no—
484C22—1222no—
485C22—48832no—
486C22—4882no—
487C22—4882no—
488C22—4882no—
489C22—4882no—
490C22—4882no—
491C22—4882no—
492C22—2444no—
493C22#102×D6111yescharacteristic
494C22#1683989411yescharacteristic
495C22#1683989711yescharacteristic
496C22D16×D6111yescharacteristic
497C22SD32×D6111yescharacteristic
498C22#1684019611yescharacteristic
499C22#1684019911yescharacteristic
500C4—161no—
501C4—1222no—
502C4—9761no—
503C4#1683961711yescharacteristic
504C4#1683976511yescharacteristic
505C4#1683991111yescharacteristic
506C4#1683991411yescharacteristic
507C2—84no—
508C2—1224no—
509C2—4884no—
510C2#2144574811yescharacteristic
511C2#357×D6111yescharacteristic
512C2#2144753311yescharacteristic
513C2#2144772911yescharacteristic
514C2#2144773211yescharacteristic
515C2#2144774611yescharacteristic
516C2#2144774911yescharacteristic
subgroupG/H
centerC23D8×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC2×C61×#357C2
socleC23×C61C2×D8
prime radicalC22×D8×D61C2
cosocleC22×C8×C61C23
hypercenterC2×#357D61
hypocenterC61#12731
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
2. C2×#16839564C2semidirect
3. C2×#16839563C2semidirect
4. C2×#16839562C2semidirect
5. C2×#16839541C2semidirect
6. #21445845C2semidirect
7. C2×C61×#357C2semidirect
16. C2×D8×D61C4semidirect
18. C22×#11758185C22semidirect
19. C2×#14519711C22semidirect
27. C22×C16×C61C22semidirect
28. C2×#107×C61C22semidirect
124. D8×C61C22⋊C4semidirect
143. D488C22⋊C4semidirect
241. C2×D61#357semidirect
253. C2×#357D61semidirect
278. C22×C16C2×D61semidirect
280. C2×#107C2×D61semidirect
288. C61#12731semidirect
388. D8#11758198semidirect

Maximal subgroups

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

subgroupindex
C22×D8×D612
C2×#168395642
C2×#168395632
C2×#168395622
C2×#168395412
#214458452
C2×C61×#3572
#1273161