Finite Group Databasebeta

← #29658601

Subgroups — #29658601

Order 15616.

1192 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×D244C211yesmaximal, characteristic, complemented
2#21456944C211yesmaximal, characteristic, complemented
3#21455279C211yesmaximal, characteristic
4#21445081C214yesmaximal, complemented
5#21444920C214yesmaximal, complemented
6#21444503C211yesmaximal, characteristic, complemented
7#21444248C211yesmaximal, characteristic, complemented
8#21444209C211yesmaximal, characteristic, complemented
9C61×#3103C211yesmaximal, characteristic, complemented
10C22×Q8×D61—21no—
11C2×#14519802—21no—
12Q8×D244—22no—
13Q8×D244—22no—
14Q8×D244—22no—
15Q8×D244C2214yes—
16C2×#14519777—21no—
17C2×#14519777C2211yescharacteristic
18C2×#14519757—22no—
19C2×#14519757—21no—
20C2×C4×D244—21no—
21C2×C4×D244C2211yescharacteristic
22#16840158C2212yescomplemented
23#16840108C2212yescomplemented
24#16840078—22no—
25#16840052—22no—
26#16839974—22no—
27#16839964C2212yes—
28#16839954C2212yes—
29#16839815C2211yescharacteristic
30#16839786C2211yescharacteristic
31#16839763—21no—
32#16839509C2214yescomplemented
33Q8⋊#92418C2214yescomplemented
34#16839489C2214yes—
35C61×#532C2211yescharacteristic
36C2×C4×Q8×C61C2211yescharacteristic
37C61×#481—21no—
38C61×#475C2212yescomplemented
39C61×#460C2212yescomplemented
40C61×#448—21no—
41C4×SD16×C61—22no—
42C61×#431C2211yescharacteristic
43C22×Dic122—22no—
44C22×Dic122—21no—
45C2×Q8×D61—24no—
46C2×Q8×D61—24no—
47C2×Q8×D61—48no—
48C22×D244D411yescharacteristic
49C22×C4×D61—22no—
50C22×C4×D61—21no—
51#14519802—44no—
52C2×#11758201—22no—
53C2×#11758199—22no—
54C2×#11758194—21no—
55#14519777—24no—
56#14519777—21no—
57#14519777—21no—
58#14519777—24no—
59#14519777D412yes—
60#14519777C2312yes—
61#14519757—24no—
62#14519757—28no—
63#14519757—24no—
64#14519757—28no—
65C4×D244—24no—
66C4×D244—24no—
67C4×D244—21no—
68C4×D244—21no—
69C4×D244D412yes—
70C4×D244C2312yes—
71C2×C4⋊Dic61—22no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61D411yescharacteristic
74C2×C4⋊Dic61D412yes—
75C2×#11758198—22no—
76C2×#11758198—21no—
77#14519708—24no—
78C4⋊#92418—21no—
79C4⋊#92418—21no—
80C4⋊#92418C2312yes—
81#14519701—22no—
82#14519698—22no—
83#14519698—24no—
84C22⋊#92418—21no—
85C4×#92418C2312yes—
86C2×#41×C61—21no—
87C22×Q8×C61D411yescharacteristic
88C2×SD16×C61—22no—
89C4⋊Q8×C61C2311yescharacteristic
90#127×C61C2311yescharacteristic
91#124×C61—21no—
92#121×C61—21no—
93#121×C61—21no—
94C4×Q8×C61—21no—
95C4×Q8×C61—21no—
96C4×Q8×C61D412yes—
97C4×Q8×C61C2312yes—
98C4×D4×C61—21no—
99C4×D4×C61—21no—
100C2×C4⋊C4×C61—21no—
101C2×C4⋊C4×C61D411yescharacteristic
102C2×C42×C61—21no—
103C2×C42×C61C2311yescharacteristic
104#106×C61—22no—
105C4⋊C8×C61C2312yes—
106#103×C61—22no—
107#102×C61—22no—
108C22⋊C8×C61—21no—
109C4×C8×C61—21no—
110C23×D61—21no—
111#41×C61—42no—
112#41×C61—42no—
113C2×Q8×C61—24no—
114C2×Q8×C61—21no—
115C2×Q8×C61—21no—
116C2×Q8×C61C2×D412yes—
117C2×D4×C61—21no—
118C2×D4×C61—21no—
119C2×D4×C61—21no—
120C2×D4×C61—41no—
121C22×C4×C61—21no—
122C22×C4×C61—21no—
123C22×C4×C61—41no—
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2×D411yescharacteristic
127C22×Dic61—22no—
128C22×Dic61—21no—
129Q8×D61—416no—
130Q8×D61—48no—
131Q8×D61—48no—
132C2×D244—21no—
133C2×D244—22no—
134C2×D244SD1614yescomplemented
135C2×D244C2×D412yes—
136C2×C4×D61—28no—
137C2×C4×D61—22no—
138C2×C4×D61—22no—
139C2×C4×D61—48no—
140C2×C4×D61—44no—
141C2×Dic122—28no—
142C2×Dic122—22no—
143C2×Dic122—22no—
144C2×Dic122—48no—
145C2×Dic122—44no—
146SD16×C61—44no—
147C2×C8×C61—22no—
148C4⋊C4×C61—22no—
149C4⋊C4×C61—21no—
150C4⋊C4×C61—22no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—21no—
153C4⋊C4×C61C2×D412yes—
154C22⋊C4×C61—41no—
155C22⋊C4×C61—41no—
156C42×C61—22no—
157C42×C61—22no—
158C42×C61C2×D411yescharacteristic
159C42×C61C2×D411yescharacteristic
160C42×C61C2×D411yescharacteristic
161C42×C61C2411yescharacteristic
162#11758201—44no—
163#11758199—44no—
164#11758198—28no—
165#11758198—22no—
166#11758198—22no—
167C4⋊Dic61—28no—
168C4⋊Dic61—22no—
169C4⋊Dic61—21no—
170C4⋊Dic61—22no—
171C4⋊Dic61—22no—
172C4⋊Dic61C2×D412yes—
173C4⋊Dic61C2×D414yes—
174#11758194—42no—
175C2×#92418—22no—
176C2×#92418—22no—
177C23×C61—41no—
178C23×C61#12011yescharacteristic
179C22×D61—22no—
180C22×D61—24no—
181C22×D61—42no—
182C22×D61—42no—
183Q8×C61—24no—
184Q8×C61—22no—
185Q8×C61—41no—
186Q8×C61—41no—
187Q8×C61AGL(1,ℤ/8)14yescomplemented
188D4×C61—42no—
189D4×C61—41no—
190D4×C61—42no—
191D4×C61—41no—
192D4×C61—82no—
193C2×C4×C61—24no—
194C2×C4×C61—22no—
195C2×C4×C61—22no—
196C2×C4×C61—22no—
197C2×C4×C61—41no—
198C2×C4×C61—42no—
199C2×C4×C61—41no—
200C2×C4×C61—82no—
201C2×C4×C61#12011yescharacteristic
202C2×C4×C61#12011yescharacteristic
203C2×C4×C61#12011yescharacteristic
204C2×C4×C61C2×SD1612yes—
205C2×C4×C61#13712yes—
206C2×C4×C61C22×D411yescharacteristic
207C2×C4×C61C22×D411yescharacteristic
208C2×C4×C61C22×D411yescharacteristic
209C2×Dic61—22no—
210C2×Dic61—24no—
211C2×Dic61—42no—
212C2×Dic61—44no—
213D244—22no—
214D244—24no—
215D244C2×SD1614yes—
216C4×D61—416no—
217C4×D61—44no—
218C4×D61—44no—
219Dic122—416no—
220Dic122—44no—
221Dic122—44no—
222C8×C61—42no—
223#92418—42no—
224#92418—42no—
225#18758—611nomaximal, Sylow
226C22×C61—21no—
227C22×C61—21no—
228C22×C61—81no—
229C22×C61—81no—
230C22×C61—81no—
231C22×C61#44812yes—
232C22×C61C2×#12011yescharacteristic
233C2×D61—24no—
234C2×D61—48no—
235C2×D61—42no—
236C2×D61—42no—
237C4×C61—24no—
238C4×C61—21no—
239C4×C61—21no—
240C4×C61—21no—
241C4×C61—42no—
242C4×C61—81no—
243C4×C61#44812yes—
244C4×C61C22×SD1611yescharacteristic
245C4×C61C2×AGL(1,ℤ/8)12yes—
246C4×C61C2×#13711yescharacteristic
247Dic61—42no—
248Dic61—44no—
249C2×D4×Q8—611no—
250#3227—611no—
251#3103D6111yescharacteristic, complemented
252#3036—611no—
253#1651—614no—
254#1627—614no—
255#1549—611no—
256#1487—611no—
257#1478—611no—
258C2×C61—22no—
259C2×C61—161no—
260C2×C61C2×#44811yescharacteristic
261C2×C61#300311yescharacteristic
262C2×C61#302011yescharacteristic
263D61—44no—
264C23×Q8—1221no—
265C2×AGL(1,ℤ/8)—1221no—
266D4×Q8—614no—
267D4×Q8—1222no—
268D4×Q8—1222no—
269D4×Q8—1222no—
270#532C2×D6111yescharacteristic
271C2×C4⋊Q8—611no—
272C2×C4⋊Q8—1221no—
273C2×C22⋊Q8—1222no—
274C2×C22⋊Q8—1221no—
275C2×C4×Q8C2×D6111yescharacteristic
276C2×C4×D4—611no—
277C2×C4×D4—1221no—
278#498—612no—
279#486—612no—
280#481—21no—
281#481—1222no—
282#476—1222no—
283#475C2×D6112yescomplemented
284#463—1222no—
285#461—612no—
286#460C2×D6112yescomplemented
287#459—612no—
288#448—21no—
289C4×SD16—22no—
290#431—611no—
291#431C2×D6111yescharacteristic
292#423—611no—
293#417—1221no—
294#332—614no—
295Q8⋊C8—614no—
296D4⋊C8—614no—
297C61#1875811yescharacteristic, complemented, Sylow
298C2×#41—21no—
299C22×Q8—1222no—
300C22×Q8—1224no—
301C22×Q8—1224no—
302C22×Q8—1221no—
303C22×Q8—2448no—
304C22×Q8C22⋊D6111yescharacteristic
305C22×D4—611no—
306C23×C4—1222no—
307C23×C4—1221no—
308AGL(1,ℤ/8)—2444no—
309C2×SD16—22no—
310C2×SD16—1222no—
311C2×D8—1222no—
312C2×M16—1221no—
313C4⋊Q8—612no—
314C4⋊Q8—612no—
315C4⋊Q8—1224no—
316C4⋊Q8—1224no—
317C4⋊Q8—1221no—
318C4⋊Q8—1221no—
319C4⋊Q8C22×D6111yescharacteristic
320#127C22×D6111yescharacteristic
321#124—21no—
322C22⋊Q8—1228no—
323C22⋊Q8—1224no—
324C22⋊Q8—1228no—
325C22⋊Q8—1224no—
326#121—21no—
327#121—21no—
328C4×Q8—21no—
329C4×Q8—21no—
330C4×Q8C22⋊D6112yes—
331C4×Q8C22×D6112yes—
332C4×D4—21no—
333C4×D4—21no—
334C4×D4—612no—
335C4×D4—612no—
336C4×D4—1224no—
337C4×D4—1224no—
338C4×D4—1221no—
339C4×D4—1221no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—611no—
342C2×C4⋊C4—612no—
343C2×C4⋊C4—1222no—
344C2×C4⋊C4—1221no—
345C2×C4⋊C4C22⋊D6111yescharacteristic
346C2×C22⋊C4—1222no—
347C2×C22⋊C4—1221no—
348C2×C42—21no—
349C2×C42C22×D6111yescharacteristic
350#106—22no—
351#106—1224no—
352C4⋊C8—612no—
353C4⋊C8—1221no—
354C4⋊C8—1221no—
355C4⋊C8C22×D6112yes—
356#103—22no—
357#103—1222no—
358#102—22no—
359#102—1222no—
360#102—1224no—
361C22⋊C8—21no—
362C22⋊C8—1221no—
363C4×C8—21no—
364C4×C8—612no—
365C24—1221no—
366#41—42no—
367#41—42no—
368C2×Q8—24no—
369C2×Q8—21no—
370C2×Q8—21no—
371C2×Q8—1228no—
372C2×Q8—1222no—
373C2×Q8—1222no—
374C2×Q8—2448no—
375C2×Q8—2444no—
376C2×Q8—24416no—
377C2×Q8—2448no—
378C2×Q8—2448no—
379C2×Q8C2×C22⋊D6112yes—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—41no—
384C2×D4—612no—
385C2×D4—614no—
386C2×D4—1221no—
387C2×D4—1222no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—41no—
391C22×C4—1228no—
392C22×C4—1222no—
393C22×C4—1221no—
394C22×C4—1222no—
395C22×C4—1222no—
396C22×C4—2448no—
397C22×C4—2444no—
398C22×C4D4×D6111yescharacteristic
399C22×C4D4×D6111yescharacteristic
400C22×C4C2×C22⋊D6111yescharacteristic
401SD16—44no—
402SD16—2444no—
403D8—2444no—
404M16—2442no—
405C2×C8—22no—
406C2×C8—1222no—
407C2×C8—1222no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—612no—
414C4⋊C4—614no—
415C4⋊C4—1228no—
416C4⋊C4—1222no—
417C4⋊C4—1221no—
418C4⋊C4—1222no—
419C4⋊C4—1222no—
420C4⋊C4C2×C22⋊D6112yes—
421C22⋊C4—41no—
422C22⋊C4—41no—
423C22⋊C4—1228no—
424C22⋊C4—1222no—
425C22⋊C4—1222no—
426C42—22no—
427C42—22no—
428C42D4×D6111yescharacteristic
429C42D4×D6111yescharacteristic
430C42C2×C22⋊D6111yescharacteristic
431C42C23×D6111yescharacteristic
432C23—41no—
433C23—1222no—
434C23—1224no—
435C23—2442no—
436C23—2442no—
437C23#1451974511yescharacteristic
438Q8—24no—
439Q8—22no—
440Q8—41no—
441Q8—41no—
442Q8—24416no—
443Q8—2444no—
444Q8—2444no—
445Q8#1451980214yescomplemented
446D4—42no—
447D4—41no—
448D4—42no—
449D4—41no—
450D4—82no—
451D4—614no—
452D4—1222no—
453D4—1224no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—41no—
459C2×C4—42no—
460C2×C4—41no—
461C2×C4—82no—
462C2×C4—1224no—
463C2×C4—1222no—
464C2×C4—24416no—
465C2×C4—2444no—
466C2×C4—2444no—
467C2×C4—2442no—
468C2×C4—2444no—
469C2×C4#1451974511yescharacteristic
470C2×C4#1451974511yescharacteristic
471C2×C4#1451974511yescharacteristic
472C2×C4SD16×D6112yes—
473C2×C4#1451980612yes—
474C2×C4C2×D4×D6111yescharacteristic
475C2×C4C2×D4×D6111yescharacteristic
476C2×C4C22×C22⋊D6111yescharacteristic
477C8—42no—
478C8—2442no—
479C8—2442no—
480C22—21no—
481C22—21no—
482C22—81no—
483C22—81no—
484C22—81no—
485C22—1224no—
486C22—2448no—
487C22—2442no—
488C22—2442no—
489C22#1683989912yes—
490C22C2×#1451974511yescharacteristic
491C4—21no—
492C4—21no—
493C4—24no—
494C4—21no—
495C4—42no—
496C4—81no—
497C4—2444no—
498C4—2442no—
499C4#1683989912yes—
500C4C2×SD16×D6111yescharacteristic
501C4C2×#1451980212yes—
502C4C2×#1451980611yescharacteristic
503C2—22no—
504C2—161no—
505C2—2444no—
506C2C2×#1683989911yescharacteristic
507C2#2145504511yescharacteristic
508C2#2145518111yescharacteristic
subgroupG/H
centerC22C2×#14519745
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3103C2
socleC22×C61C2×#120
prime radical#21455279C2
hypercenter#3103D61
hypocenterC61#18758
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3103

Complements

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

NH ≅ G/Ntype
1. C2×Q8×D244C2semidirect
2. #21456944C2semidirect
4. #21445081C2semidirect
5. #21444920C2semidirect
6. #21444503C2semidirect
7. #21444248C2semidirect
8. #21444209C2semidirect
9. C61×#3103C2semidirect
22. #16840158C22semidirect
23. #16840108C22semidirect
32. #16839509C22semidirect
33. Q8⋊#92418C22semidirect
38. C61×#475C22semidirect
39. C61×#460C22semidirect
134. C2×D244SD16semidirect
187. Q8×C61AGL(1,ℤ/8)semidirect
251. #3103D61semidirect
283. #475C2×D61semidirect
286. #460C2×D61semidirect
297. C61#18758semidirect
445. Q8#14519802semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×D2442
#214569442
#214552792
#214450812
#214449202
#214445032
#214442482
#214442092
C61×#31032
#1875861