Finite Group Databasebeta

← #29667642

Subgroups — #29667642

Order 15616.

590 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457146C211yesmaximal, characteristic
2#21457042C211yesmaximal, characteristic, complemented
3#21456942C211yesmaximal, characteristic, complemented
4#21454981C211yesmaximal, characteristic, complemented
5#21445360C211yesmaximal, characteristic, complemented
6#21445353C211yesmaximal, characteristic, complemented
7#21445348C211yesmaximal, characteristic, complemented
8#21445343C211yesmaximal, characteristic, complemented
9#21445236C211yesmaximal, characteristic, complemented
10#21445229C211yesmaximal, characteristic, complemented
11#21445224C211yesmaximal, characteristic, complemented
12#21445219C211yesmaximal, characteristic, complemented
13#21444515C211yesmaximal, characteristic, complemented
14C2×#16839510C211yesmaximal, characteristic, complemented
15C61×#1573C211yesmaximal, characteristic, complemented
16#16840312C2211yescharacteristic
17C2×#14519777C2211yescharacteristic
18#16840296C2211yescharacteristic
19#16840171—21no—
20#16840167C2211yescharacteristic
21#16840167C2211yescharacteristic
22#16840122—21no—
23#16840109C2211yescharacteristic
24#16840109C2211yescharacteristic
25#16840093—21no—
26#16840076—21no—
27#16840076—21no—
28#16840076—21no—
29#16840063—21no—
30#16840058C2211yescharacteristic
31#16840058C2211yescharacteristic
32#16840058C2211yescharacteristic
33#16840053C2211yescharacteristic
34#16840053C2211yescharacteristic
35#16840053C2211yescharacteristic
36#16840043—21no—
37#16840043—21no—
38#16839998—21no—
39#16839991—21no—
40#16839978—21no—
41#16839963C2211yescharacteristic
42#16839958C2211yescharacteristic
43#16839892C2211yescharacteristic
44C8×Dic122C2211yescharacteristic
45#16839841C2211yescharacteristic
46#16839830—21no—
47C8×D244C2211yescharacteristic
48#16839825—21no—
49#16839822—21no—
50#16839787—21no—
51C2×C4⋊#92418C2211yescharacteristic
52#16839510C2211yescharacteristic
53#16839510C2211yescharacteristic
54#16839510C2211yescharacteristic
55#16839510C2211yescharacteristic
56#16839510C2211yescharacteristic
57#16839510C2211yescharacteristic
58#16839505C2211yescharacteristic
59#16839505C2211yescharacteristic
60C61×#432C2211yescharacteristic
61C61×#431C2211yescharacteristic
62C2×C4⋊C8×C61C2211yescharacteristic
63C61×#335C2211yescharacteristic
64C61×#335C2211yescharacteristic
65C61×#334C2211yescharacteristic
66C61×#334C2211yescharacteristic
67C2×#11758222—21no—
68C22×Dic122—21no—
69C2×#11758190—21no—
70C2×D488—21no—
71C2×#11758189—21no—
72C22×#92418—21no—
73C2×C8×D61—21no—
74#14519777—21no—
75#14519777—21no—
76#14519777—21no—
77#14519777C2311yescharacteristic
78#14519777C2311yescharacteristic
79#14519777C2311yescharacteristic
80#14519774C2311yescharacteristic
81#14519771—21no—
82#14519769D411yescharacteristic
83#14519765—21no—
84#14519765D411yescharacteristic
85#14519760—21no—
86#14519756D411yescharacteristic
87#14519751—21no—
88#14519751—21no—
89#14519751D411yescharacteristic
90C4×Dic122C2311yescharacteristic
91C4×D244—21no—
92C4×D244—21no—
93C4×D244C2311yescharacteristic
94C4×C22⋊D61—21no—
95#14519734—21no—
96C2×C4⋊Dic61—21no—
97C2×C4⋊Dic61—21no—
98#14519711—21no—
99#14519711—21no—
100#14519711—21no—
101#14519711—21no—
102#14519711—21no—
103#14519711—21no—
104#14519711—21no—
105#14519709—21no—
106#14519709—21no—
107#14519709—21no—
108C4⋊#92418—21no—
109C4⋊#92418C2311yescharacteristic
110C4⋊#92418C2311yescharacteristic
111#14519706—21no—
112#14519706—21no—
113#14519702—21no—
114#14519702—21no—
115#14519702—21no—
116#14519699—21no—
117#14519699—21no—
118#14519699—21no—
119#14519699—21no—
120#14519699—21no—
121#14519699—21no—
122#14519699—21no—
123#14519699—21no—
124#14519699—21no—
125#14519689—21no—
126#14519689—21no—
127#14519687—21no—
128C8×Dic61—21no—
129C22×C8×C61—21no—
130C2×C42×C61C2311yescharacteristic
131C4⋊C8×C61—21no—
132C4⋊C8×C61D411yescharacteristic
133C4⋊C8×C61D411yescharacteristic
134C4⋊C8×C61C2311yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138C22⋊C8×C61—21no—
139C22⋊C8×C61D411yescharacteristic
140C22⋊C8×C61D411yescharacteristic
141#97×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61#4111yescharacteristic
147C2×C22⋊D61—21no—
148C2×C22⋊D61—41no—
149C22×Dic61—41no—
150#11758222—82no—
151C2×D244—21no—
152C2×D244—21no—
153C2×D244—21no—
154C2×D244C2×D411yescharacteristic
155C2×C4×D61—21no—
156C2×C4×D61—41no—
157C2×Dic122—21no—
158C2×Dic122—21no—
159C2×Dic122—21no—
160C2×Dic122—41no—
161C2×Dic122—82no—
162C2×Dic122C2×D411yescharacteristic
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—81no—
168C2×C8×C61C2×D411yescharacteristic
169C2×C8×C61C2×D411yescharacteristic
170C2×C8×C61C2×D411yescharacteristic
171C2×C8×C61C2×D411yescharacteristic
172C42×C61C2×D411yescharacteristic
173C42×C61C2×D411yescharacteristic
174C42×C61#4111yescharacteristic
175C42×C61C2411yescharacteristic
176C22⋊Dic61—21no—
177#11758198—21no—
178#11758198—21no—
179#11758198—21no—
180#11758198—21no—
181#11758198—41no—
182#11758198—41no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—41no—
190C4⋊Dic61—41no—
191C4⋊Dic61C2×D411yescharacteristic
192C4⋊Dic61C2×D411yescharacteristic
193#11758196—21no—
194#11758196—21no—
195#11758196—21no—
196#11758196—21no—
197C4×Dic61—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—81no—
201D488—81no—
202#11758190—81no—
203#11758189—81no—
204C8×D61—81no—
205C23×C61#12111yescharacteristic
206C22×D61—21no—
207C22×D61—41no—
208C2×C4×C61—22no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61#12111yescharacteristic
214C2×C4×C61#12111yescharacteristic
215C2×C4×C61#12111yescharacteristic
216C2×C4×C61C22×D411yescharacteristic
217C2×C4×C61C22×D411yescharacteristic
218C2×C4×C61C2×#4111yescharacteristic
219C22⋊D61—42no—
220C22⋊D61—82no—
221C2×Dic61—21no—
222C2×Dic61—21no—
223C2×Dic61—21no—
224C2×Dic61—41no—
225C2×Dic61—41no—
226C2×Dic61—41no—
227C2×Dic61—82no—
228D244—21no—
229D244—21no—
230D244—41no—
231D244—41no—
232D244—41no—
233D244—41no—
234D244—81no—
235C4×D61—41no—
236C4×D61—41no—
237C4×D61—82no—
238Dic122—21no—
239Dic122—21no—
240Dic122—82no—
241Dic122—81no—
242Dic122—81no—
243Dic122—81no—
244C8×C61—21no—
245C8×C61—21no—
246C8×C61—21no—
247C8×C61—21no—
248C8×C61—41no—
249C8×C61—41no—
250C8×C61—41no—
251C8×C61—41no—
252#92418—41no—
253#92418—41no—
254#19591—611nomaximal, Sylow
255C22×C61—21no—
256C22×C61—21no—
257C22×C61#47212yes—
258C22×C61C2×#12111yescharacteristic
259C2×D61—41no—
260C2×D61—41no—
261C2×D61—41no—
262C2×D61—81no—
263C2×D61—81no—
264C2×D61—81no—
265C4×C61—21no—
266C4×C61—21no—
267C4×C61—21no—
268C4×C61—21no—
269C4×C61#57711yescharacteristic
270C4×C61#57711yescharacteristic
271C4×C61#57811yescharacteristic
272C4×C61#57811yescharacteristic
273Dic61—41no—
274Dic61—41no—
275Dic61—41no—
276Dic61—81no—
277Dic61—81no—
278Dic61—81no—
279#3247—611no—
280#3238—611no—
281#3226—611no—
282#2994—611no—
283#1698—611no—
284#1697—611no—
285#1696—611no—
286#1695—611no—
287#1678—611no—
288#1677—611no—
289#1676—611no—
290#1675—611no—
291#1573D6111yescharacteristic, complemented
292#1551—611no—
293C2×#333—611no—
294C2×C61—22no—
295C2×C61#304611yescharacteristic
296C2×C61#306311yescharacteristic
297C2×C61C2×#47211yescharacteristic
298D61—81no—
299D61—161no—
300#532—611no—
301C2×C4⋊Q8—611no—
302#529—611no—
303#501—1221no—
304#500—611no—
305#500—611no—
306#489—1221no—
307#486—611no—
308#486—611no—
309#483—1221no—
310#480—1221no—
311#480—1221no—
312#480—1221no—
313#478—1221no—
314#477—611no—
315#477—611no—
316#477—611no—
317#476—611no—
318#476—611no—
319#476—611no—
320#474—1221no—
321#474—1221no—
322#466—1221no—
323#465—1221no—
324#463—1221no—
325#460—611no—
326#459—611no—
327#446—611no—
328C8×Q8—611no—
329#436—611no—
330#435—1221no—
331C8×D4—611no—
332C8×D4—1221no—
333#433—1221no—
334#432C2×D6111yescharacteristic
335#431C2×D6111yescharacteristic
336#424—1221no—
337C2×C4⋊C8—611no—
338C2×C4⋊C8C2×D6111yescharacteristic
339#335C2×D6111yescharacteristic
340#335C2×D6111yescharacteristic
341#334C2×D6111yescharacteristic
342#334C2×D6111yescharacteristic
343#333—611no—
344#333—611no—
345#333—611no—
346#333—611no—
347#333—611no—
348#333—611no—
349#331—611no—
350#331—611no—
351C61#1959111yescharacteristic, complemented, Sylow
352C2×#41—1221no—
353C22×Q8—1221no—
354C2×SD16—1221no—
355C2×D8—1221no—
356C2×M16—1221no—
357C22×C8—21no—
358C22×C8—1221no—
359C22×C8—1221no—
360C4⋊Q8—611no—
361C4⋊Q8—611no—
362C4⋊Q8—611no—
363C4⋊Q8—1221no—
364C4⋊Q8—1221no—
365C4⋊Q8—1221no—
366#127—611no—
367#126—1221no—
368#125—611no—
369#124—611no—
370#124—1221no—
371#123—1221no—
372C22⋊Q8—611no—
373#121—611no—
374#121—1221no—
375#121—1221no—
376C4×Q8—611no—
377C4×D4—611no—
378C4×D4—1221no—
379C4×D4—1221no—
380C4×D4—1221no—
381#117—1221no—
382C2×C4⋊C4—1221no—
383C2×C4⋊C4—1221no—
384C2×C42C22×D6111yescharacteristic
385#107—1221no—
386#107—1221no—
387#107—1221no—
388#107—1221no—
389#107—1221no—
390#107—1221no—
391#107—1221no—
392#106—1221no—
393#106—1221no—
394#106—1221no—
395C4⋊C8—21no—
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—1221no—
399C4⋊C8—1221no—
400C4⋊C8—1221no—
401C4⋊C8D24411yescharacteristic
402C4⋊C8D24411yescharacteristic
403C4⋊C8C22×D6111yescharacteristic
404C4⋊C8C22×D6111yescharacteristic
405C4⋊C8C22×D6111yescharacteristic
406C4⋊C8C22×D6111yescharacteristic
407#103—1221no—
408#103—1221no—
409#103—1221no—
410#102—1221no—
411#102—1221no—
412#102—1221no—
413#102—1221no—
414#102—1221no—
415#102—1221no—
416#102—1221no—
417#102—1221no—
418#102—1221no—
419C22⋊C8—21no—
420C22⋊C8—1221no—
421C22⋊C8—1221no—
422C22⋊C8D24411yescharacteristic
423C22⋊C8D24411yescharacteristic
424#97—21no—
425#97—1221no—
426C4×C8—1221no—
427C4×C8C22×D6111yescharacteristic
428C4×C8C22×D6111yescharacteristic
429#41—4882no—
430C2×Q8—611no—
431C2×Q8—1221no—
432C2×Q8—1221no—
433C2×Q8—1221no—
434C2×Q8—4882no—
435C2×Q8—2441no—
436C2×D4—611no—
437C2×D4—1221no—
438C2×D4—1221no—
439C2×D4—1221no—
440C2×D4—1221no—
441C2×D4—2441no—
442C22×C4—1221no—
443C22×C4—2441no—
444C22×C4—2441no—
445C22×C4C2×D24411yescharacteristic
446C22×C4D4×D6111yescharacteristic
447C22×C4#1175822611yescharacteristic
448SD16—4881no—
449D8—4881no—
450M16—4881no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—81no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8—4881no—
459C2×C8—4881no—
460C2×C8C2×D24411yescharacteristic
461C2×C8C2×D24411yescharacteristic
462C2×C8C2×D24411yescharacteristic
463C2×C8C2×D24411yescharacteristic
464C4⋊C4—611no—
465C4⋊C4—611no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—2441no—
477C4⋊C4—2441no—
478C22⋊C4—1221no—
479C22⋊C4—1221no—
480C22⋊C4—1221no—
481C22⋊C4—1221no—
482C22⋊C4—1221no—
483C22⋊C4—2441no—
484C22⋊C4—2441no—
485C42—1221no—
486C42C2×D24411yescharacteristic
487C42D4×D6111yescharacteristic
488C42#1175822611yescharacteristic
489C42C23×D6111yescharacteristic
490C23—1221no—
491C23—2441no—
492C23#1451975211yescharacteristic
493Q8—1221no—
494Q8—1221no—
495Q8—4881no—
496Q8—4881no—
497Q8—4881no—
498Q8—4882no—
499D4—1221no—
500D4—1221no—
501D4—4881no—
502D4—4882no—
503D4—2442no—
504D4—2441no—
505D4—2441no—
506D4—2441no—
507D4—2441no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—1221no—
514C2×C4—1221no—
515C2×C4—1221no—
516C2×C4—4882no—
517C2×C4—4882no—
518C2×C4—2441no—
519C2×C4—2441no—
520C2×C4—2441no—
521C2×C4—2441no—
522C2×C4—2441no—
523C2×C4#1451975211yescharacteristic
524C2×C4#1451975211yescharacteristic
525C2×C4#1451975211yescharacteristic
526C2×C4C2×D4×D6111yescharacteristic
527C2×C4C22×D24411yescharacteristic
528C2×C4C2×#1175822611yescharacteristic
529C8—21no—
530C8—21no—
531C8—21no—
532C8—21no—
533C8—41no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—2441no—
538C8—2441no—
539C22—21no—
540C22—21no—
541C22—4881no—
542C22—4881no—
543C22—4881no—
544C22—2441no—
545C22—2441no—
546C22—2441no—
547C22#1684003312yes—
548C22C2×#1451975211yescharacteristic
549C4—21no—
550C4—21no—
551C4—21no—
552C4—21no—
553C4—4881no—
554C4—4881no—
555C4—4881no—
556C4—2441no—
557C4—2441no—
558C4—2441no—
559C4#1684057211yescharacteristic
560C4#1684057411yescharacteristic
561C4#1684057811yescharacteristic
562C4#1684057911yescharacteristic
563C2—22no—
564C2—9761no—
565C2—4881no—
566C2#2145537111yescharacteristic
567C2#2145551111yescharacteristic
568C2C2×#1684003311yescharacteristic
subgroupG/H
centerC22C2×#14519752
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1573C2
socleC22×C61C2×#121
prime radical#21457146C2
hypercenter#1573D61
hypocenterC61#19591
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1573

Complements

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

NH ≅ G/Ntype
2. #21457042C2semidirect
3. #21456942C2semidirect
4. #21454981C2semidirect
5. #21445360C2semidirect
6. #21445353C2semidirect
7. #21445348C2semidirect
8. #21445343C2semidirect
9. #21445236C2semidirect
10. #21445229C2semidirect
11. #21445224C2semidirect
12. #21445219C2semidirect
13. #21444515C2semidirect
14. C2×#16839510C2semidirect
15. C61×#1573C2semidirect
291. #1573D61semidirect
351. C61#19591semidirect

Maximal subgroups

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

subgroupindex
#214571462
#214570422
#214569422
#214549812
#214453602
#214453532
#214453482
#214453432
#214452362
#214452292
#214452242
#214452192
#214445152
C2×#168395102
C61×#15732
#1959161