Finite Group Databasebeta

← #29710902

Subgroups — #29710902

Order 15616.

608 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454760C211yesmaximal, characteristic, complemented
2#21454718C211yesmaximal, characteristic
3#21447402C211yesmaximal, characteristic, complemented
4#21447397C211yesmaximal, characteristic, complemented
5#21447271C211yesmaximal, characteristic, complemented
6#21447269C211yesmaximal, characteristic, complemented
7#21447124C211yesmaximal, characteristic
8#21447105C211yesmaximal, characteristic
9#21446988C211yesmaximal, characteristic, complemented
10#21445664C211yesmaximal, characteristic, complemented
11#21445660C211yesmaximal, characteristic, complemented
12#21445621C211yesmaximal, characteristic, complemented
13#21445618C211yesmaximal, characteristic, complemented
14#21445573C211yesmaximal, characteristic, complemented
15C61×#2031C211yesmaximal, characteristic, complemented
16#16840560C2211yescharacteristic
17C2×#14519785C2211yescharacteristic
18C2×#14519784C2211yescharacteristic
19#16839893—22no—
20#16839893—22no—
21#16839881—22no—
22#16839876—22no—
23#16839810C2211yescharacteristic
24#16839789C2211yescharacteristic
25#16839789C2211yescharacteristic
26#16839786C2211yescharacteristic
27#16839780C2211yescharacteristic
28C2×#14519705C2211yescharacteristic
29#16839758C2211yescharacteristic
30#16839756C2211yescharacteristic
31#16839746C2211yescharacteristic
32#16839744C2211yescharacteristic
33#16839735C2211yescharacteristic
34#16839720C2211yescharacteristic
35#16839718C2211yescharacteristic
36#16839718C2211yescharacteristic
37#16839718C2211yescharacteristic
38C2×#14519688C2211yescharacteristic
39#16839533C2211yescharacteristic
40#16839532C2211yescharacteristic
41#16839532C2211yescharacteristic
42#16839526C2211yescharacteristic
43#16839526C2211yescharacteristic
44#16839522C2211yescharacteristic
45#16839520C2211yescharacteristic
46#16839518C2211yescharacteristic
47#16839518C2211yescharacteristic
48C61×#533C2211yescharacteristic
49C61×#421C2211yescharacteristic
50C2×#104×C61C2211yescharacteristic
51C61×#410C2211yescharacteristic
52C61×#344C2211yescharacteristic
53C61×#339C2211yescharacteristic
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×#11758194C2311yescharacteristic
74C2×#11758189—21no—
75C22×#92418—21no—
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C2×C8×D61—21no—
79#14519736C2311yescharacteristic
80#14519712—22no—
81C4⋊#92418—22no—
82C4⋊#92418—22no—
83C4⋊#92418—22no—
84#14519705—22no—
85#14519705—21no—
86#14519705—21no—
87#14519701—21no—
88#14519700—21no—
89#14519698—21no—
90#14519697—21no—
91#14519696—21no—
92#14519695—21no—
93#14519694—21no—
94#14519693—21no—
95#14519691—22no—
96#14519688—21no—
97#14519688—21no—
98#14519688—21no—
99#14519688—21no—
100#14519688D412yes—
101#14519687—21no—
102C4×#92418—21no—
103C4×#92418—21no—
104C4×#92418D412yes—
105C8×Dic61—21no—
106C2×#41×C61C2311yescharacteristic
107C2×M16×C61C2311yescharacteristic
108C2×M16×C61C2311yescharacteristic
109C4⋊Q8×C61—21no—
110#125×C61—21no—
111C22⋊Q8×C61—22no—
112C4×Q8×C61—22no—
113#117×C61C2311yescharacteristic
114#117×C61C2311yescharacteristic
115#117×C61C2311yescharacteristic
116C2×C42×C61C2311yescharacteristic
117#104×C61—22no—
118#104×C61—21no—
119#104×C61—21no—
120#99×C61—22no—
121#41×C61—21no—
122#41×C61—21no—
123#41×C61—21no—
124#41×C61—21no—
125C2×Q8×C61—22no—
126C2×Q8×C61#4111yescharacteristic
127C2×D4×C61—21no—
128C2×D4×C61#4111yescharacteristic
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61C2411yescharacteristic
132C2×C22⋊D61—21no—
133#11758222—21no—
134#11758222—21no—
135#11758222—21no—
136#11758222—21no—
137C2×D244#4111yescharacteristic
138C2×C4×D61—21no—
139C2×Dic122#4111yescharacteristic
140M16×C61—21no—
141M16×C61—21no—
142M16×C61—21no—
143M16×C61—21no—
144C2×C8×C61—21no—
145C2×C8×C61—21no—
146C4⋊C4×C61—24no—
147C4⋊C4×C61—22no—
148C4⋊C4×C61—21no—
149C4⋊C4×C61—21no—
150C4⋊C4×C61—21no—
151C22⋊C4×C61—21no—
152C22⋊C4×C61—21no—
153C22⋊C4×C61#4112yes—
154C42×C61—21no—
155C42×C61—21no—
156C42×C61—21no—
157C42×C61C2×D412yes—
158C42×C61#4111yescharacteristic
159C42×C61#4111yescharacteristic
160C22⋊Dic61—21no—
161#11758202—22no—
162#11758201—22no—
163#11758200—22no—
164#11758199—22no—
165C4⋊Dic61—21no—
166C4×Dic61—21no—
167#11758194—21no—
168#11758194—21no—
169#11758194—21no—
170#11758194—21no—
171#11758194—21no—
172#11758194—21no—
173#11758194—21no—
174#11758194—21no—
175#11758194—41no—
176#11758194—41no—
177C2×#92418—21no—
178C2×#92418—21no—
179C2×#92418—21no—
180C2×#92418—21no—
181C2×#92418—21no—
182C2×#92418—21no—
183C2×#92418—41no—
184C2×#92418—41no—
185C2×#92418C2×D412yes—
186C2×#92418C2×D411yescharacteristic
187C2×#92418C2×D411yescharacteristic
188C2×#92418#4111yescharacteristic
189C2×#92418#4111yescharacteristic
190C2×#92418#4111yescharacteristic
191C2×#92418#4111yescharacteristic
192#11758189—41no—
193#11758189—41no—
194C8×D61—41no—
195C8×D61—41no—
196C23×C61—21no—
197C23×C61C2×#4111yescharacteristic
198C22×D61—21no—
199Q8×C61—21no—
200Q8×C61—21no—
201Q8×C61—82no—
202D4×C61—21no—
203D4×C61—21no—
204D4×C61—41no—
205D4×C61—41no—
206C2×C4×C61—21no—
207C2×C4×C61—21no—
208C2×C4×C61—22no—
209C2×C4×C61—22no—
210C2×C4×C61—21no—
211C2×C4×C61—41no—
212C2×C4×C61—41no—
213C2×C4×C61—41no—
214C2×C4×C61—81no—
215C2×C4×C61C22×D411yescharacteristic
216C2×C4×C61C2×#4111yescharacteristic
217C2×C4×C61C2×#4111yescharacteristic
218C2×C4×C61C2×#4111yescharacteristic
219C2×C4×C61C2×#4111yescharacteristic
220C2×C4×C61C2×#4111yescharacteristic
221C22⋊D61—41no—
222C22⋊D61—41no—
223C2×Dic61—21no—
224C2×Dic61—41no—
225D244—21no—
226D244—21no—
227C4×D61—41no—
228C4×D61—41no—
229Dic122—21no—
230Dic122—21no—
231C8×C61—41no—
232C8×C61—41no—
233#92418—22no—
234#92418—41no—
235#92418—41no—
236#92418—41no—
237#92418—41no—
238#92418#12411yescharacteristic
239#92418#12411yescharacteristic
240#92418#12411yescharacteristic
241#92418#12411yescharacteristic
242#23834—611nomaximal, Sylow
243C22×C61—41no—
244C22×C61—41no—
245C22×C61—81no—
246C22×C61#52511yescharacteristic
247C22×C61#52911yescharacteristic
248C22×C61#52911yescharacteristic
249C2×D61—41no—
250C2×D61—81no—
251C4×C61—41no—
252C4×C61—41no—
253C4×C61—42no—
254C4×C61—42no—
255C4×C61—41no—
256C4×C61—81no—
257C4×C61#52511yescharacteristic
258C4×C61C2×#12411yescharacteristic
259C4×C61#52911yescharacteristic
260C4×C61#52911yescharacteristic
261Dic61—41no—
262Dic61—81no—
263#2961—611no—
264#2955—611no—
265#2103—611no—
266#2102—611no—
267#2080—611no—
268#2080—611no—
269#2053—611no—
270#2050—611no—
271#2031—611no—
272#2031D6111yescharacteristic, complemented
273#1765—611no—
274#1765—611no—
275#1757—611no—
276#1757—611no—
277#1747—611no—
278C2×C61—21no—
279C2×C61—21no—
280C2×C61—21no—
281C2×C61—81no—
282C2×C61#239811yescharacteristic
283D61—81no—
284#575—611no—
285C2×#131—611no—
286C2×#131—611no—
287#533C2×D6111yescharacteristic
288#446—1222no—
289#446—1222no—
290#444—1222no—
291#443—1222no—
292#430—611no—
293#424—611no—
294#424—611no—
295#423—611no—
296#421—611no—
297#421C2×D6111yescharacteristic
298C2×#104—611no—
299C2×#104C2×D6111yescharacteristic
300#416—611no—
301#416—611no—
302#413—611no—
303#413—611no—
304#410—611no—
305#410C2×D6111yescharacteristic
306#405—611no—
307#405—611no—
308#405—611no—
309#405—611no—
310C2×#97—611no—
311#344—611no—
312#344—611no—
313#344—611no—
314#344C2×D6111yescharacteristic
315#341—611no—
316#341—611no—
317#339—611no—
318#339C2×D6111yescharacteristic
319#338—611no—
320H(3,ℤ/4)—611no—
321H(3,ℤ/4)—611no—
322H(3,ℤ/4)C2×D6111yescharacteristic
323C61#2383411yescharacteristic, complemented, Sylow
324C2×#41—611no—
325C2×#41C22×D6111yescharacteristic
326#137—1221no—
327#137—1221no—
328AGL(1,ℤ/8)—1221no—
329AGL(1,ℤ/8)—1221no—
330#135—1222no—
331#131—1221no—
332#131—1221no—
333#131—1221no—
334#131—1221no—
335#131—1221no—
336#131—1221no—
337#131—1221no—
338#131—1221no—
339C2×M16—611no—
340C2×M16—611no—
341C2×M16—611no—
342C2×M16—611no—
343C2×M16—1221no—
344C2×M16—1221no—
345C2×M16C22×D6111yescharacteristic
346C2×M16C22×D6111yescharacteristic
347C22×C8—611no—
348C22×C8—611no—
349C22×C8—1221no—
350C22×C8—1221no—
351C4⋊Q8—21no—
352#125—21no—
353C22⋊Q8—22no—
354C4×Q8—22no—
355#117—611no—
356#117C22×D6111yescharacteristic
357#117C22×D6111yescharacteristic
358#117C22×D6111yescharacteristic
359C2×C42C22×D6111yescharacteristic
360#108—1222no—
361C4⋊C8—1222no—
362C4⋊C8—1222no—
363C4⋊C8—1222no—
364#104—22no—
365#104—21no—
366#104—21no—
367#104—1222no—
368#104—1221no—
369#104—1221no—
370#103—1221no—
371#103—1221no—
372#102—1221no—
373#102—1221no—
374#101—1221no—
375#101—1221no—
376#100—1221no—
377#100—1221no—
378#99—22no—
379#99—1222no—
380#97—612no—
381#97—1221no—
382#97—1221no—
383#97—1221no—
384#97—1221no—
385#97—1221no—
386C4×C8—612no—
387C4×C8—1221no—
388C4×C8—1221no—
389C4×C8—1221no—
390#41—21no—
391#41—21no—
392#41—21no—
393#41—21no—
394#41—1221no—
395#41—1221no—
396#41—1221no—
397#41—1221no—
398C2×Q8—22no—
399C2×Q8—611no—
400C2×Q8#1175822611yescharacteristic
401C2×D4—21no—
402C2×D4—611no—
403C2×D4—1221no—
404C2×D4#1175822611yescharacteristic
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—1221no—
408C22×C4C23×D6111yescharacteristic
409Q16—1222no—
410SD16—1222no—
411SD16—1222no—
412D8—1222no—
413M16—21no—
414M16—21no—
415M16—21no—
416M16—21no—
417M16—1221no—
418M16—1221no—
419M16—1221no—
420M16—1221no—
421M16—1221no—
422M16—1221no—
423M16—1221no—
424M16—1221no—
425M16—2441no—
426M16—2441no—
427M16—2441no—
428M16—2441no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—611no—
432C2×C8—611no—
433C2×C8—611no—
434C2×C8—611no—
435C2×C8—611no—
436C2×C8—611no—
437C2×C8—612no—
438C2×C8—1221no—
439C2×C8—1221no—
440C2×C8—1221no—
441C2×C8—1221no—
442C2×C8—1221no—
443C2×C8—1221no—
444C2×C8—2441no—
445C2×C8—2441no—
446C2×C8—2441no—
447C2×C8—2441no—
448C4⋊C4—24no—
449C4⋊C4—22no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—1221no—
454C22⋊C4—21no—
455C22⋊C4—21no—
456C22⋊C4—1221no—
457C22⋊C4#1175822412yes—
458C42—21no—
459C42—21no—
460C42—21no—
461C42—1221no—
462C42D4×D6112yes—
463C42#1175822411yescharacteristic
464C42#1175822411yescharacteristic
465C23—21no—
466C23—1221no—
467C23C2×#1175822411yescharacteristic
468Q8—21no—
469Q8—21no—
470Q8—82no—
471Q8—1221no—
472Q8—1221no—
473D4—21no—
474D4—21no—
475D4—41no—
476D4—41no—
477D4—1221no—
478D4—1221no—
479D4—2441no—
480D4—2441no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—81no—
490C2×C4—1221no—
491C2×C4—2441no—
492C2×C4—2441no—
493C2×C4—2441no—
494C2×C4C2×D4×D6111yescharacteristic
495C2×C4#41×D6111yescharacteristic
496C2×C4#41×D6111yescharacteristic
497C2×C4#41×D6111yescharacteristic
498C2×C4C2×#1175822411yescharacteristic
499C2×C4C2×#1175822611yescharacteristic
500C8—41no—
501C8—41no—
502C8—611no—
503C8—611no—
504C8—611no—
505C8—611no—
506C8—1222no—
507C8—2441no—
508C8—2441no—
509C8—2441no—
510C8—2441no—
511C22—41no—
512C22—41no—
513C22—81no—
514C22—4881no—
515C22—2441no—
516C22#1684026811yescharacteristic
517C22#1684029111yescharacteristic
518C22#1684029811yescharacteristic
519C4—41no—
520C4—41no—
521C4—42no—
522C4—42no—
523C4—41no—
524C4—81no—
525C4—4881no—
526C4—2441no—
527C4#1684027511yescharacteristic
528C4#124×D6111yescharacteristic
529C4#1684029111yescharacteristic
530C4#1684029811yescharacteristic
531C2—21no—
532C2—21no—
533C2—21no—
534C2—81no—
535C2—4881no—
536C2#2144910111yescharacteristic
subgroupG/H
centerC4#124×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2031C2
socleC2×C61#2398
prime radical#16840560C22
hypercenter#2031D61
hypocenterC61#23834
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #2031

Complements

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

NH ≅ G/Ntype
1. #21454760C2semidirect
3. #21447402C2semidirect
4. #21447397C2semidirect
5. #21447271C2semidirect
6. #21447269C2semidirect
9. #21446988C2semidirect
10. #21445664C2semidirect
11. #21445660C2semidirect
12. #21445621C2semidirect
13. #21445618C2semidirect
14. #21445573C2semidirect
15. C61×#2031C2semidirect
272. #2031D61semidirect
323. C61#23834semidirect

Maximal subgroups

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

subgroupindex
#214547602
#214547182
#214474022
#214473972
#214472712
#214472692
#214471242
#214471052
#214469882
#214456642
#214456602
#214456212
#214456182
#214455732
C61×#20312
#2383461