Finite Group Databasebeta

← #29650712

Subgroups — #29650712

Order 15616.

592 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456385C211yesmaximal, characteristic
2#21454971C211yesmaximal, characteristic, complemented
3#21454963C211yesmaximal, characteristic, complemented
4#21444731C211yesmaximal, characteristic, complemented
5#21444726C211yesmaximal, characteristic, complemented
6#21444711C211yesmaximal, characteristic, complemented
7#21444640C211yesmaximal, characteristic, complemented
8#21444635C211yesmaximal, characteristic, complemented
9SD16×#92418C211yesmaximal, characteristic, complemented
10#21444618C211yesmaximal, characteristic, complemented
11#21444573C211yesmaximal, characteristic, complemented
12#21444283C211yesmaximal, characteristic, complemented
13#21444281C211yesmaximal, characteristic, complemented
14#21444101C211yesmaximal, characteristic, complemented
15C61×#1590C211yesmaximal, characteristic, complemented
16#16840299C2211yescharacteristic
17#16840294C2211yescharacteristic
18#16840162C411yescharacteristic
19#16840143C411yescharacteristic
20#16840118C411yescharacteristic
21#16840115C411yescharacteristic
22#16840002C411yescharacteristic
23#16839997C411yescharacteristic
24#16839992C411yescharacteristic
25#16839988C411yescharacteristic
26#16839892C2211yescharacteristic
27Q8×#92418C2211yescharacteristic
28#16839886C2211yescharacteristic
29C4×#11758202C2211yescharacteristic
30C4×#11758190C2211yescharacteristic
31C4×#11758199C2211yescharacteristic
32#16839841C2211yescharacteristic
33#16839839—21no—
34#16839838—21no—
35#16839835—21no—
36#16839830—21no—
37D4×#92418C2211yescharacteristic
38#16839827C2211yescharacteristic
39#16839824—21no—
40#16839820—21no—
41#16839813C2211yescharacteristic
42#16839813C2211yescharacteristic
43#16839790—21no—
44#16839787—21no—
45#16839784C2211yescharacteristic
46#16839784C2211yescharacteristic
47C4×C8×D61C2211yescharacteristic
48#16839513C2211yescharacteristic
49#16839512C2211yescharacteristic
50#16839512C2211yescharacteristic
51#16839494C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53#16839492C2211yescharacteristic
54#16839491C2211yescharacteristic
55D4⋊#92418C2211yescharacteristic
56#16839489C2211yescharacteristic
57#16839484C2211yescharacteristic
58#16839484C2211yescharacteristic
59C8×#92418C2211yescharacteristic
60C61×#446C2211yescharacteristic
61C4×SD16×C61C2211yescharacteristic
62C61×#436C2211yescharacteristic
63C61×#334C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C82×C61C2211yescharacteristic
67C2×#11758202C2×C411yescharacteristic
68C2×#11758190C2×C411yescharacteristic
69C2×#11758199C2×C411yescharacteristic
70C2×#11758189—21no—
71C2×#11758189—21no—
72C2×#11758189—21no—
73C22×#92418—21no—
74C2×C8×D61—21no—
75C2×C8×D61C2×C411yescharacteristic
76C2×C8×D61C2×C411yescharacteristic
77#14519772—21no—
78#14519770—21no—
79#14519768C2×C411yescharacteristic
80#14519768C2×C411yescharacteristic
81#14519766C2×C411yescharacteristic
82#14519764C2×C411yescharacteristic
83#14519762—21no—
84#14519759—21no—
85#14519757C2×C411yescharacteristic
86#14519753C2×C411yescharacteristic
87#14519752C2×C411yescharacteristic
88#14519748C2×C411yescharacteristic
89C4×Dic122C2311yescharacteristic
90C4×D244—21no—
91C4×D244C2311yescharacteristic
92C4×C22⋊D61—21no—
93#14519736—21no—
94#14519734—21no—
95C42×D61C2311yescharacteristic
96#14519710C2×C411yescharacteristic
97#14519710C2×C411yescharacteristic
98#14519709C2×C411yescharacteristic
99C4⋊#92418—21no—
100C4⋊#92418C2311yescharacteristic
101C4⋊#92418C2311yescharacteristic
102#14519706—21no—
103#14519706—21no—
104#14519706—21no—
105#14519706—21no—
106#14519706—21no—
107#14519706D411yescharacteristic
108#14519706D411yescharacteristic
109#14519702C2×C411yescharacteristic
110#14519701C2×C411yescharacteristic
111#14519700C2×C411yescharacteristic
112#14519699C2×C411yescharacteristic
113#14519698C2×C411yescharacteristic
114#14519697C2×C411yescharacteristic
115C22⋊#92418—21no—
116#14519689—21no—
117#14519689—21no—
118#14519689—21no—
119#14519689D411yescharacteristic
120#14519689D411yescharacteristic
121#14519687—21no—
122C4×#92418—21no—
123C4×#92418C2311yescharacteristic
124C4×#92418C2311yescharacteristic
125C4×#92418C2311yescharacteristic
126C8×Dic61—21no—
127C8×Dic61C2×C411yescharacteristic
128C8×Dic61C2×C411yescharacteristic
129C2×SD16×C61C2×C411yescharacteristic
130C2×M16×C61—21no—
131C4×Q8×C61C2311yescharacteristic
132C4×D4×C61C2311yescharacteristic
133#106×C61C2×C411yescharacteristic
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137#103×C61C2×C411yescharacteristic
138#102×C61C2×C411yescharacteristic
139C22⋊C8×C61—21no—
140#97×C61—21no—
141C4×C8×C61C2311yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61C22×C411yescharacteristic
145C2×D4×C61C22×C411yescharacteristic
146C22×C4×C61—21no—
147C2×C22⋊D61—21no—
148C2×D244—21no—
149C2×D244C22×C411yescharacteristic
150C2×C4×D61—21no—
151C2×C4×D61C22×C411yescharacteristic
152C2×C4×D61C2×D411yescharacteristic
153C2×C4×D61#4111yescharacteristic
154C2×Dic122C22×C411yescharacteristic
155SD16×C61—22no—
156M16×C61—81no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61C22×C411yescharacteristic
161C2×C8×C61C22×C411yescharacteristic
162C2×C8×C61C2×D411yescharacteristic
163C2×C8×C61C2×D411yescharacteristic
164C4⋊C4×C61—21no—
165C4⋊C4×C61C22×C411yescharacteristic
166C4⋊C4×C61C22×C411yescharacteristic
167C22⋊C4×C61—21no—
168C42×C61—21no—
169C42×C61C2411yescharacteristic
170C22⋊Dic61—21no—
171C22⋊Dic61—21no—
172C22⋊Dic61—21no—
173#11758202—22no—
174#11758199—22no—
175#11758198—21no—
176#11758198—21no—
177#11758198—21no—
178#11758198—21no—
179#11758198—21no—
180#11758198—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61C22×C411yescharacteristic
185C4⋊Dic61C22×C411yescharacteristic
186#11758196—21no—
187#11758196—21no—
188#11758196—21no—
189#11758196—21no—
190C4×Dic61—21no—
191C4×Dic61C22×C411yescharacteristic
192C4×Dic61C2×D411yescharacteristic
193C4×Dic61#4111yescharacteristic
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—81no—
198C2×#92418C22×C411yescharacteristic
199C2×#92418C22×C411yescharacteristic
200C2×#92418C2×D411yescharacteristic
201C2×#92418C2×D411yescharacteristic
202#11758190—22no—
203#11758189—81no—
204#11758189—81no—
205#11758189—81no—
206C8×D61—22no—
207C8×D61—22no—
208C8×D61—81no—
209C23×C61—21no—
210C22×D61—21no—
211C22×D61C4×D411yescharacteristic
212Q8×C61—21no—
213Q8×C61—21no—
214D4×C61—21no—
215D4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61C23×C411yescharacteristic
222C2×C4×C61C22×D411yescharacteristic
223C2×C4×C61C2×#4111yescharacteristic
224C22⋊D61—81no—
225C2×Dic61—21no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61C4×D411yescharacteristic
229C2×Dic61C4×D411yescharacteristic
230C2×Dic61C4×D411yescharacteristic
231D244—21no—
232D244—21no—
233D244—81no—
234C4×D61—21no—
235C4×D61—21no—
236C4×D61—21no—
237C4×D61—21no—
238C4×D61—41no—
239C4×D61—41no—
240C4×D61—41no—
241Dic122—21no—
242Dic122—21no—
243C8×C61—21no—
244C8×C61—21no—
245C8×C61—21no—
246C8×C61—41no—
247C8×C61—41no—
248C8×C61—41no—
249C8×C61#13112yes—
250#92418—21no—
251#92418—21no—
252#92418—21no—
253#92418—41no—
254#92418—41no—
255#92418—41no—
256#92418#13112yes—
257#17974—611nomaximal, Sylow
258C22×C61—41no—
259C22×C61—41no—
260C22×C61—41no—
261C22×C61C2×C4×D411yescharacteristic
262C2×D61—21no—
263C2×D61—21no—
264C2×D61—21no—
265C2×D61—41no—
266C2×D61—41no—
267C2×D61—41no—
268C4×C61—21no—
269C4×C61—41no—
270C4×C61—41no—
271C4×C61—41no—
272C4×C61C2×#13111yescharacteristic
273C4×C61C2×#13111yescharacteristic
274C4×C61#57711yescharacteristic
275C4×C61#57711yescharacteristic
276Dic61—21no—
277Dic61—21no—
278Dic61—21no—
279Dic61—41no—
280Dic61—41no—
281Dic61—41no—
282#3168—611no—
283#2993—611no—
284#2993—611no—
285#1594—611no—
286#1593—611no—
287#1590—611no—
288#1590D6111yescharacteristic, complemented
289#1580—611no—
290#1579—611no—
291C8×SD16—611no—
292C8×SD16—611no—
293#1566—611no—
294#1495—611no—
295#1495—611no—
296#1450—611no—
297C2×C61—81no—
298C2×C61#293111yescharacteristic
299C2×C61#295211yescharacteristic
300C2×C61#295711yescharacteristic
301D61—41no—
302D61—81no—
303#529—611no—
304#529—611no—
305#499—611no—
306#495—611no—
307#488—611no—
308#488—611no—
309#467—611no—
310#466—611no—
311#465—611no—
312#465—611no—
313#446—611no—
314#446C2×D6111yescharacteristic
315C8×Q8—611no—
316C8×Q8—611no—
317C4×Q16—611no—
318C4×SD16—611no—
319C4×SD16C2×D6111yescharacteristic
320C4×D8—611no—
321#436—611no—
322#436—1221no—
323#436—1221no—
324#436C2×D6111yescharacteristic
325#435—1221no—
326#435—1221no—
327C8×D4—611no—
328C8×D4—611no—
329#433—1221no—
330#433—1221no—
331#431—611no—
332#431—611no—
333#424—1221no—
334#424—1221no—
335#423—611no—
336#423—611no—
337C2×C4×C8—611no—
338#334—611no—
339#334—611no—
340#334—611no—
341#334C2×D6111yescharacteristic
342Q8⋊C8—611no—
343Q8⋊C8—611no—
344Q8⋊C8—611no—
345Q8⋊C8C2×D6111yescharacteristic
346D4⋊C8—611no—
347D4⋊C8—611no—
348D4⋊C8—611no—
349D4⋊C8C2×D6111yescharacteristic
350#322—611no—
351#322—611no—
352C82—611no—
353C82C2×D6111yescharacteristic
354C61#1797411yescharacteristic, complemented, Sylow
355C2×Q16—611no—
356C2×SD16—611no—
357C2×SD16C4×D6111yescharacteristic
358C2×D8—611no—
359C2×M16—21no—
360C2×M16—1221no—
361C2×M16—1221no—
362C2×M16—1221no—
363C22×C8—611no—
364C22×C8—611no—
365C22×C8—1221no—
366C22×C8—1221no—
367#126—1221no—
368#126—1221no—
369#125—611no—
370#125—611no—
371#124—611no—
372#124—611no—
373#123—1221no—
374#123—1221no—
375C22⋊Q8—611no—
376C22⋊Q8—611no—
377#121—611no—
378#121—611no—
379C4×Q8—611no—
380C4×Q8C22×D6111yescharacteristic
381C4×D4—611no—
382C4×D4—1221no—
383C4×D4—1221no—
384C4×D4C22×D6111yescharacteristic
385#117—1221no—
386#117—1221no—
387C2×C42—611no—
388#107—611no—
389#107—611no—
390#106—611no—
391#106C4×D6111yescharacteristic
392C4⋊C8—21no—
393C4⋊C8—611no—
394C4⋊C8—611no—
395C4⋊C8—611no—
396C4⋊C8—611no—
397C4⋊C8—1221no—
398C4⋊C8—1221no—
399C4⋊C8—1221no—
400C4⋊C8—1221no—
401C4⋊C8—1221no—
402C4⋊C8—1221no—
403C4⋊C8C22×D6111yescharacteristic
404C4⋊C8C22×D6111yescharacteristic
405#103—611no—
406#103—611no—
407#103—611no—
408#103C4×D6111yescharacteristic
409#102—611no—
410#102—611no—
411#102—611no—
412#102C4×D6111yescharacteristic
413C22⋊C8—21no—
414C22⋊C8—611no—
415C22⋊C8—611no—
416C22⋊C8—1221no—
417C22⋊C8—1221no—
418C22⋊C8—1221no—
419C22⋊C8—1221no—
420#97—21no—
421#97—1221no—
422C4×C8—611no—
423C4×C8—611no—
424C4×C8—611no—
425C4×C8—611no—
426C4×C8—611no—
427C4×C8—1221no—
428C4×C8—1221no—
429C4×C8C22×D6111yescharacteristic
430C4×C8C22×D6111yescharacteristic
431C4×C8C22×D6111yescharacteristic
432C2×Q8—611no—
433C2×Q8C2×C4×D6111yescharacteristic
434C2×D4—611no—
435C2×D4—1221no—
436C2×D4—1221no—
437C2×D4C2×C4×D6111yescharacteristic
438C22×C4—21no—
439C22×C4—611no—
440C22×C4—611no—
441C22×C4—611no—
442C22×C4—1221no—
443Q16—1222no—
444SD16—22no—
445SD16—1222no—
446D8—1222no—
447M16—81no—
448M16—4881no—
449M16—4881no—
450M16—4881no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—611no—
455C2×C8—611no—
456C2×C8—611no—
457C2×C8—611no—
458C2×C8—1222no—
459C2×C8—1222no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—1221no—
463C2×C8—4881no—
464C2×C8—4881no—
465C2×C8C2×C4×D6111yescharacteristic
466C2×C8C2×C4×D6111yescharacteristic
467C2×C8D4×D6111yescharacteristic
468C2×C8D4×D6111yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—611no—
471C4⋊C4—611no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C4⋊C4—1221no—
479C4⋊C4C2×C4×D6111yescharacteristic
480C4⋊C4C2×C4×D6111yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—1221no—
483C22⋊C4—1221no—
484C22⋊C4—1221no—
485C22⋊C4—1221no—
486C22⋊C4—1221no—
487C22⋊C4—1221no—
488C22⋊C4—1221no—
489C22⋊C4—1221no—
490C22⋊C4—1221no—
491C42—21no—
492C42—611no—
493C42—611no—
494C42—611no—
495C42—1221no—
496C42C23×D6111yescharacteristic
497C23—21no—
498C23—611no—
499C23—1221no—
500Q8—21no—
501Q8—21no—
502Q8—1221no—
503Q8—1221no—
504D4—21no—
505D4—21no—
506D4—1221no—
507D4—1221no—
508D4—4881no—
509D4—4881no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—611no—
516C2×C4—611no—
517C2×C4—611no—
518C2×C4—1221no—
519C2×C4—1221no—
520C2×C4—1221no—
521C2×C4—1221no—
522C2×C4—1221no—
523C2×C4—1221no—
524C2×C4—1221no—
525C2×C4—2441no—
526C2×C4—2441no—
527C2×C4—2441no—
528C2×C4C22×C4×D6111yescharacteristic
529C2×C4C2×D4×D6111yescharacteristic
530C2×C4#41×D6111yescharacteristic
531C8—21no—
532C8—21no—
533C8—21no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—612no—
538C8—1221no—
539C8—1221no—
540C8—1221no—
541C8—2441no—
542C8—2441no—
543C8—2441no—
544C8#1451978512yes—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—1221no—
549C22—1221no—
550C22—1221no—
551C22—2441no—
552C22—2441no—
553C22—2441no—
554C22C4×D4×D6111yescharacteristic
555C4—21no—
556C4—41no—
557C4—41no—
558C4—41no—
559C4—1221no—
560C4—1221no—
561C4—1221no—
562C4—2441no—
563C4—2441no—
564C4—2441no—
565C4#131×D6111yescharacteristic
566C4C2×#1451978511yescharacteristic
567C4#1684056811yescharacteristic
568C4#1684056911yescharacteristic
569C2—81no—
570C2—4881no—
571C2—2441no—
572C2#2145452811yescharacteristic
573C2#2145469711yescharacteristic
574C2#2145473111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1590C2
socleC22×C61C2×C4×D4
prime radical#16839997C4
cosocleC42×C61C24
hypercenter#1590D61
hypocenterC61#17974
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1590

Complements

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

NH ≅ G/Ntype
2. #21454971C2semidirect
3. #21454963C2semidirect
4. #21444731C2semidirect
5. #21444726C2semidirect
6. #21444711C2semidirect
7. #21444640C2semidirect
8. #21444635C2semidirect
9. SD16×#92418C2semidirect
10. #21444618C2semidirect
11. #21444573C2semidirect
12. #21444283C2semidirect
13. #21444281C2semidirect
14. #21444101C2semidirect
15. C61×#1590C2semidirect
288. #1590D61semidirect
354. C61#17974semidirect

Maximal subgroups

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

subgroupindex
#214563852
#214549712
#214549632
#214447312
#214447262
#214447112
#214446402
#214446352
SD16×#924182
#214446182
#214445732
#214442832
#214442812
#214441012
C61×#15902
#1797461