Finite Group Databasebeta

← #29710905

Subgroups — #29710905

Order 15616.

608 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454758C211yesmaximal, characteristic, complemented
2#21454718C211yesmaximal, characteristic
3#21447401C211yesmaximal, characteristic, complemented
4#21447396C211yesmaximal, characteristic, complemented
5#21447270C211yesmaximal, characteristic, complemented
6#21447123C211yesmaximal, characteristic
7#21447104C211yesmaximal, characteristic
8#21446990C211yesmaximal, characteristic, complemented
9#21446989C211yesmaximal, characteristic, complemented
10#21445666C211yesmaximal, characteristic, complemented
11#21445662C211yesmaximal, characteristic, complemented
12#21445622C211yesmaximal, characteristic, complemented
13#21445618C211yesmaximal, characteristic, complemented
14#21445573C211yesmaximal, characteristic, complemented
15C61×#2080C211yesmaximal, characteristic, complemented
16#16840560C2211yescharacteristic
17C2×#14519785C2211yescharacteristic
18C2×#14519784C2211yescharacteristic
19#16840315C2211yescharacteristic
20#16839891—22no—
21#16839889—22no—
22#16839881—22no—
23#16839876—22no—
24#16839810C2211yescharacteristic
25#16839788C2211yescharacteristic
26#16839785C2211yescharacteristic
27#16839780C2211yescharacteristic
28C2×#14519704C2211yescharacteristic
29C2×#14519703C2211yescharacteristic
30#16839759C2211yescharacteristic
31#16839744C2211yescharacteristic
32#16839736C2211yescharacteristic
33#16839735C2211yescharacteristic
34#16839720C2211yescharacteristic
35#16839720C2211yescharacteristic
36#16839718C2211yescharacteristic
37#16839718C2211yescharacteristic
38C2×#14519687C2211yescharacteristic
39#16839534C2211yescharacteristic
40#16839534C2211yescharacteristic
41#16839533C2211yescharacteristic
42#16839527C2211yescharacteristic
43#16839523C2211yescharacteristic
44#16839521C2211yescharacteristic
45#16839520C2211yescharacteristic
46#16839518C2211yescharacteristic
47#16839518C2211yescharacteristic
48C61×#424C2211yescharacteristic
49C61×#421C2211yescharacteristic
50C61×#416C2211yescharacteristic
51C61×#413C2211yescharacteristic
52C61×#344C2211yescharacteristic
53C61×#341C2211yescharacteristic
54C61×H(3,ℤ/4)C2211yescharacteristic
55C2×#11758222C2311yescharacteristic
56#14519808—21no—
57#14519807—21no—
58#14519803—21no—
59#14519802—21no—
60#14519797—22no—
61#14519785—21no—
62#14519785—21no—
63#14519785—21no—
64#14519785—21no—
65#14519784—21no—
66#14519784—21no—
67#14519784—21no—
68#14519784—21no—
69C2×#11758194—21no—
70C2×#11758194C2311yescharacteristic
71C2×#11758194C2311yescharacteristic
72C2×#11758194C2311yescharacteristic
73C2×#11758189—21no—
74C22×#92418—21no—
75C22×#92418C2311yescharacteristic
76C2×C8×D61—21no—
77#14519776—21no—
78#14519768—21no—
79#14519754—22no—
80C4×Dic122—22no—
81#14519736C2311yescharacteristic
82#14519736C2311yescharacteristic
83C2×C4×Dic61C2311yescharacteristic
84#14519712—22no—
85#14519706—22no—
86#14519706—22no—
87#14519705—22no—
88#14519704—21no—
89#14519704—21no—
90#14519703—21no—
91#14519703—21no—
92#14519702—21no—
93#14519699—21no—
94#14519695—21no—
95#14519693—21no—
96#14519692—22no—
97#14519691—22no—
98#14519688—21no—
99#14519688D412yes—
100#14519687—21no—
101#14519687—21no—
102#14519687—21no—
103#14519687—21no—
104C4×#92418—21no—
105C4×#92418D412yes—
106C8×Dic61—21no—
107C8×Dic61—21no—
108C2×#41×C61C2311yescharacteristic
109C2×M16×C61C2311yescharacteristic
110C2×M16×C61C2311yescharacteristic
111C2×M16×C61C2311yescharacteristic
112C22×C8×C61C2311yescharacteristic
113#117×C61C2311yescharacteristic
114#117×C61C2311yescharacteristic
115C4⋊C8×C61—22no—
116#104×C61—22no—
117#103×C61—21no—
118#102×C61—21no—
119#101×C61—21no—
120#100×C61—21no—
121#41×C61—21no—
122#41×C61—21no—
123#41×C61—21no—
124#41×C61—21no—
125C2×Q8×C61#4111yescharacteristic
126C2×D4×C61—21no—
127C2×D4×C61#4111yescharacteristic
128C22×C4×C61—21no—
129C22×C4×C61C2411yescharacteristic
130C2×C22⋊D61—21no—
131C22×Dic61—21no—
132#11758222—21no—
133#11758222—21no—
134#11758222—21no—
135#11758222—21no—
136C2×D244#4111yescharacteristic
137C2×C4×D61—21no—
138C2×Dic122—22no—
139C2×Dic122#4111yescharacteristic
140M16×C61—21no—
141M16×C61—21no—
142M16×C61—21no—
143M16×C61—21no—
144M16×C61—21no—
145M16×C61—21no—
146C2×C8×C61—21no—
147C2×C8×C61—21no—
148C2×C8×C61—21no—
149C2×C8×C61—21no—
150C2×C8×C61—21no—
151C2×C8×C61—21no—
152C4⋊C4×C61—21no—
153C4⋊C4×C61—21no—
154C22⋊C4×C61—21no—
155C22⋊C4×C61—21no—
156C42×C61—21no—
157C42×C61C2×D412yes—
158C22⋊Dic61—21no—
159C22⋊Dic61#4112yes—
160#11758202—22no—
161#11758201—22no—
162#11758200—22no—
163#11758199—22no—
164C4⋊Dic61—22no—
165C4⋊Dic61—21no—
166C4⋊Dic61—21no—
167#11758196—22no—
168#11758196—22no—
169C4×Dic61—21no—
170C4×Dic61—21no—
171C4×Dic61—21no—
172C4×Dic61#4111yescharacteristic
173C4×Dic61#4111yescharacteristic
174#11758194—21no—
175#11758194—21no—
176#11758194—21no—
177#11758194—21no—
178#11758194—21no—
179#11758194—21no—
180#11758194—41no—
181#11758194—41no—
182C2×#92418—21no—
183C2×#92418—21no—
184C2×#92418—41no—
185C2×#92418—41no—
186C2×#92418C2×D412yes—
187C2×#92418C2×D411yescharacteristic
188C2×#92418C2×D411yescharacteristic
189C2×#92418#4111yescharacteristic
190C2×#92418#4111yescharacteristic
191C2×#92418#4111yescharacteristic
192C2×#92418#4111yescharacteristic
193#11758189—41no—
194#11758189—41no—
195C8×D61—41no—
196C8×D61—41no—
197C23×C61—21no—
198C23×C61C2×#4111yescharacteristic
199C22×D61—21no—
200Q8×C61—21no—
201Q8×C61—21no—
202D4×C61—21no—
203D4×C61—21no—
204D4×C61—41no—
205D4×C61—41no—
206C2×C4×C61—22no—
207C2×C4×C61—21no—
208C2×C4×C61—41no—
209C2×C4×C61—41no—
210C2×C4×C61—41no—
211C2×C4×C61C22×D411yescharacteristic
212C2×C4×C61C2×#4111yescharacteristic
213C2×C4×C61C2×#4111yescharacteristic
214C2×C4×C61C2×#4111yescharacteristic
215C2×C4×C61C2×#4111yescharacteristic
216C2×C4×C61C2×#4111yescharacteristic
217C22⋊D61—41no—
218C22⋊D61—41no—
219C2×Dic61—21no—
220C2×Dic61—21no—
221C2×Dic61—22no—
222C2×Dic61—21no—
223C2×Dic61—41no—
224C2×Dic61—81no—
225D244—21no—
226D244—21no—
227C4×D61—41no—
228C4×D61—41no—
229Dic122—21no—
230Dic122—21no—
231Dic122—82no—
232C8×C61—41no—
233C8×C61—41no—
234C8×C61—41no—
235C8×C61—41no—
236#92418—22no—
237#92418—41no—
238#92418—41no—
239#92418#12411yescharacteristic
240#92418#12411yescharacteristic
241#92418#12411yescharacteristic
242#92418#12411yescharacteristic
243#23834—611nomaximal, Sylow
244C22×C61—41no—
245C22×C61—41no—
246C22×C61—81no—
247C22×C61#52511yescharacteristic
248C22×C61#52911yescharacteristic
249C22×C61#52911yescharacteristic
250C2×D61—41no—
251C2×D61—81no—
252C4×C61—42no—
253C4×C61—41no—
254C4×C61—81no—
255C4×C61#52511yescharacteristic
256C4×C61C2×#12411yescharacteristic
257C4×C61#52911yescharacteristic
258C4×C61#52911yescharacteristic
259Dic61—41no—
260Dic61—42no—
261Dic61—41no—
262Dic61—41no—
263Dic61—81no—
264#2961—611no—
265#2955—611no—
266#2103—611no—
267#2102—611no—
268#2080—611no—
269#2080D6111yescharacteristic, complemented
270#2053—611no—
271#2050—611no—
272#2031—611no—
273#2031—611no—
274#1765—611no—
275#1765—611no—
276#1757—611no—
277#1757—611no—
278#1747—611no—
279C2×C61—21no—
280C2×C61—21no—
281C2×C61—21no—
282C2×C61—81no—
283C2×C61#239811yescharacteristic
284D61—81no—
285#575—611no—
286C2×#131—611no—
287C2×#131—611no—
288#533—611no—
289#446—1222no—
290#446—1222no—
291#444—1222no—
292#443—1222no—
293#430—611no—
294#424—611no—
295#424C2×D6111yescharacteristic
296#423—611no—
297#421—611no—
298#421C2×D6111yescharacteristic
299C2×#104—611no—
300C2×#104—611no—
301#416—611no—
302#416C2×D6111yescharacteristic
303#413—611no—
304#413C2×D6111yescharacteristic
305#410—611no—
306#410—611no—
307#405—611no—
308#405—611no—
309#405—611no—
310#405—611no—
311C2×#97—611no—
312#344—611no—
313#344—611no—
314#344—611no—
315#344C2×D6111yescharacteristic
316#341—611no—
317#341C2×D6111yescharacteristic
318#339—611no—
319#339—611no—
320#338—611no—
321H(3,ℤ/4)—611no—
322H(3,ℤ/4)—611no—
323H(3,ℤ/4)C2×D6111yescharacteristic
324C61#2383411yescharacteristic, complemented, Sylow
325C2×#41—611no—
326C2×#41C22×D6111yescharacteristic
327#137—1221no—
328#137—1221no—
329AGL(1,ℤ/8)—1221no—
330AGL(1,ℤ/8)—1221no—
331#135—1222no—
332#131—1221no—
333#131—1221no—
334#131—1221no—
335#131—1221no—
336#131—1221no—
337#131—1221no—
338#131—1221no—
339#131—1221no—
340C2×M16—611no—
341C2×M16—611no—
342C2×M16—611no—
343C2×M16—1221no—
344C2×M16—1221no—
345C2×M16C22×D6111yescharacteristic
346C2×M16C22×D6111yescharacteristic
347C2×M16C22×D6111yescharacteristic
348C22×C8—611no—
349C22×C8—1221no—
350C22×C8—1221no—
351C22×C8C22×D6111yescharacteristic
352C4⋊Q8—1221no—
353#125—1221no—
354C22⋊Q8—1222no—
355C4×Q8—1222no—
356#117—611no—
357#117—611no—
358#117C22×D6111yescharacteristic
359#117C22×D6111yescharacteristic
360C2×C42—611no—
361#108—1222no—
362C4⋊C8—22no—
363C4⋊C8—1222no—
364C4⋊C8—1222no—
365#104—22no—
366#104—1221no—
367#104—1221no—
368#104—1221no—
369#104—1221no—
370#104—1222no—
371#103—21no—
372#103—1221no—
373#102—21no—
374#102—1221no—
375#101—21no—
376#101—1221no—
377#100—21no—
378#100—1221no—
379#99—1222no—
380#99—1222no—
381#97—612no—
382#97—1221no—
383#97—1221no—
384#97—1221no—
385#97—1221no—
386#97—1221no—
387C4×C8—612no—
388C4×C8—1221no—
389C4×C8—1221no—
390C4×C8—1221no—
391#41—21no—
392#41—21no—
393#41—21no—
394#41—21no—
395#41—1221no—
396#41—1221no—
397#41—1221no—
398#41—1221no—
399C2×Q8—611no—
400C2×Q8—1222no—
401C2×Q8#1175822411yescharacteristic
402C2×D4—21no—
403C2×D4—611no—
404C2×D4—1221no—
405C2×D4#1175822411yescharacteristic
406C22×C4—21no—
407C22×C4—1221no—
408C22×C4—1221no—
409C22×C4C23×D6111yescharacteristic
410Q16—1222no—
411SD16—1222no—
412SD16—1222no—
413D8—1222no—
414M16—21no—
415M16—21no—
416M16—21no—
417M16—21no—
418M16—21no—
419M16—21no—
420M16—1221no—
421M16—1221no—
422M16—1221no—
423M16—1221no—
424M16—1221no—
425M16—1221no—
426M16—2441no—
427M16—2441no—
428M16—2441no—
429M16—2441no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—611no—
437C2×C8—611no—
438C2×C8—611no—
439C2×C8—611no—
440C2×C8—611no—
441C2×C8—611no—
442C2×C8—612no—
443C2×C8—1221no—
444C2×C8—1221no—
445C2×C8—2441no—
446C2×C8—2441no—
447C2×C8—2441no—
448C2×C8—2441no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—1222no—
452C4⋊C4—1222no—
453C4⋊C4—1222no—
454C4⋊C4—1221no—
455C4⋊C4—1221no—
456C22⋊C4—21no—
457C22⋊C4—21no—
458C22⋊C4—612no—
459C22⋊C4—1221no—
460C42—21no—
461C42—611no—
462C42—611no—
463C42—1221no—
464C42—1221no—
465C42—1221no—
466C42D4×D6112yes—
467C23—21no—
468C23—1221no—
469C23#41×D6111yescharacteristic
470Q8—21no—
471Q8—21no—
472Q8—1221no—
473Q8—1221no—
474Q8—4882no—
475D4—21no—
476D4—21no—
477D4—41no—
478D4—41no—
479D4—1221no—
480D4—1221no—
481D4—2441no—
482D4—2441no—
483C2×C4—22no—
484C2×C4—21no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—1221no—
489C2×C4—1221no—
490C2×C4—1222no—
491C2×C4—1221no—
492C2×C4—4881no—
493C2×C4—2441no—
494C2×C4—2441no—
495C2×C4—2441no—
496C2×C4C2×D4×D6111yescharacteristic
497C2×C4#41×D6111yescharacteristic
498C2×C4#41×D6111yescharacteristic
499C2×C4#41×D6111yescharacteristic
500C2×C4#41×D6111yescharacteristic
501C2×C4C2×#1175822411yescharacteristic
502C8—41no—
503C8—41no—
504C8—41no—
505C8—41no—
506C8—611no—
507C8—611no—
508C8—611no—
509C8—611no—
510C8—1222no—
511C8—2441no—
512C8—2441no—
513C22—41no—
514C22—41no—
515C22—81no—
516C22—4881no—
517C22—2441no—
518C22#1684027011yescharacteristic
519C22#1684028911yescharacteristic
520C22#1684029511yescharacteristic
521C4—42no—
522C4—41no—
523C4—81no—
524C4—4881no—
525C4—2441no—
526C4—2441no—
527C4—2442no—
528C4—2441no—
529C4#1684027211yescharacteristic
530C4#124×D6111yescharacteristic
531C4#1684028911yescharacteristic
532C4#1684029511yescharacteristic
533C2—21no—
534C2—21no—
535C2—21no—
536C2—81no—
537C2—4881no—
538C2#2144910411yescharacteristic
subgroupG/H
centerC4#124×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2080C2
socleC2×C61#2398
prime radical#16840560C22
hypercenter#2080D61
hypocenterC61#23834
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #2080

Complements

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

NH ≅ G/Ntype
1. #21454758C2semidirect
3. #21447401C2semidirect
4. #21447396C2semidirect
5. #21447270C2semidirect
8. #21446990C2semidirect
9. #21446989C2semidirect
10. #21445666C2semidirect
11. #21445662C2semidirect
12. #21445622C2semidirect
13. #21445618C2semidirect
14. #21445573C2semidirect
15. C61×#2080C2semidirect
269. #2080D61semidirect
324. C61#23834semidirect

Maximal subgroups

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

subgroupindex
#214547582
#214547182
#214474012
#214473962
#214472702
#214471232
#214471042
#214469902
#214469892
#214456662
#214456622
#214456222
#214456182
#214455732
C61×#20802
#2383461