Finite Group Databasebeta

← #29650196

Subgroups — #29650196

Order 15616.

620 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455839C211yesmaximal, characteristic
2#21454970C211yesmaximal, characteristic, complemented
3#21454927C211yesmaximal, characteristic, complemented
4#21444692C211yesmaximal, characteristic, complemented
5#21444685C211yesmaximal, characteristic, complemented
6#21444664C211yesmaximal, characteristic, complemented
7#21444657C211yesmaximal, characteristic, complemented
8#21444644C211yesmaximal, characteristic, complemented
9#21444639C211yesmaximal, characteristic, complemented
10C8×#11758190C211yesmaximal, characteristic, complemented
11C8×#11758190C211yesmaximal, characteristic, complemented
12#21444590C211yesmaximal, characteristic, complemented
13#21444259C211yesmaximal, characteristic, complemented
14#21444233C211yesmaximal, characteristic, complemented
15C61×#1453C211yesmaximal, characteristic, complemented
16#16840296C2211yescharacteristic
17C4×#11758222C2211yescharacteristic
18#16840104C411yescharacteristic
19#16840087C411yescharacteristic
20#16840070C411yescharacteristic
21#16840063C411yescharacteristic
22#16839985C411yescharacteristic
23#16839978C411yescharacteristic
24#16839926C411yescharacteristic
25#16839909C411yescharacteristic
26#16839892C2211yescharacteristic
27C8×Dic122C2211yescharacteristic
28C8×Dic122C2211yescharacteristic
29C8×Dic122C2211yescharacteristic
30C4×Dic244C2211yescharacteristic
31C4×#11758190C2211yescharacteristic
32C4×#11758190C2211yescharacteristic
33C4×D488C2211yescharacteristic
34#16839841C2211yescharacteristic
35#16839837—21no—
36#16839836—21no—
37C8×D244C2211yescharacteristic
38C8×D244C2211yescharacteristic
39C8×D244C2211yescharacteristic
40#16839825—21no—
41#16839825—21no—
42#16839822—21no—
43#16839814—21no—
44#16839787—21no—
45#16839786C2211yescharacteristic
46C2×C4⋊#92418C2211yescharacteristic
47C4⋊C8×D61—21no—
48#16839513C2211yescharacteristic
49#16839513C2211yescharacteristic
50#16839513C2211yescharacteristic
51#16839513C2211yescharacteristic
52#16839494C2211yescharacteristic
53#16839494C2211yescharacteristic
54#16839494C2211yescharacteristic
55#16839494C2211yescharacteristic
56#16839491C2211yescharacteristic
57#16839491C2211yescharacteristic
58#16839491C2211yescharacteristic
59#16839491C2211yescharacteristic
60C61×#431C2211yescharacteristic
61C61×#431C2211yescharacteristic
62C4×M16×C61C2211yescharacteristic
63C61×#322C2211yescharacteristic
64C61×#322C2211yescharacteristic
65C61×#322C2211yescharacteristic
66C82×C61C2211yescharacteristic
67C2×#11758222C2×C411yescharacteristic
68C2×Dic244C2×C411yescharacteristic
69C2×#11758190C2×C411yescharacteristic
70C2×#11758190C2×C411yescharacteristic
71C2×D488C2×C411yescharacteristic
72C2×#11758194—21no—
73C2×#11758189—21no—
74C22×#92418—21no—
75C2×C8×D61—21no—
76C2×C8×D61—21no—
77C2×C8×D61—21no—
78#14519771—21no—
79#14519769C2×C411yescharacteristic
80#14519765C2×C411yescharacteristic
81#14519760—21no—
82#14519756C2×C411yescharacteristic
83#14519751C2×C411yescharacteristic
84C4×Dic122C2×C411yescharacteristic
85C4×Dic122C2311yescharacteristic
86C4×Dic122C2311yescharacteristic
87C4×D244C2×C411yescharacteristic
88C4×D244C2311yescharacteristic
89C4×D244C2311yescharacteristic
90C4×C22⋊D61—21no—
91C4×C22⋊D61—21no—
92C4×C22⋊D61—21no—
93#14519736C2×C411yescharacteristic
94#14519734—21no—
95#14519734—21no—
96C42×D61—21no—
97#14519711C2×C411yescharacteristic
98#14519711C2×C411yescharacteristic
99#14519709C2×C411yescharacteristic
100#14519709C2×C411yescharacteristic
101C4⋊#92418—21no—
102C4⋊#92418—21no—
103C4⋊#92418C2311yescharacteristic
104C4⋊#92418C2311yescharacteristic
105C4⋊#92418C2311yescharacteristic
106C4⋊#92418C2311yescharacteristic
107#14519706—21no—
108#14519706—21no—
109#14519706—21no—
110#14519706—21no—
111#14519702C2×C411yescharacteristic
112#14519702C2×C411yescharacteristic
113#14519702C2×C411yescharacteristic
114#14519702C2×C411yescharacteristic
115#14519699C2×C411yescharacteristic
116#14519699C2×C411yescharacteristic
117#14519699C2×C411yescharacteristic
118#14519699C2×C411yescharacteristic
119#14519689—21no—
120#14519689—21no—
121#14519689—21no—
122#14519689—21no—
123#14519687—21no—
124C8×Dic61—21no—
125C8×Dic61—21no—
126C8×Dic61—21no—
127C2×M16×C61—21no—
128C2×C42×C61C2311yescharacteristic
129C4⋊C8×C61C2×C411yescharacteristic
130C4⋊C8×C61C2×C411yescharacteristic
131C4⋊C8×C61D411yescharacteristic
132C4⋊C8×C61D411yescharacteristic
133C22⋊C8×C61C2×C411yescharacteristic
134C22⋊C8×C61C2×C411yescharacteristic
135C22⋊C8×C61D411yescharacteristic
136C22⋊C8×C61D411yescharacteristic
137#97×C61—21no—
138C4×C8×C61C2311yescharacteristic
139C4×C8×C61C2311yescharacteristic
140C4×C8×C61C2311yescharacteristic
141C4×C8×C61C2311yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C22×C4×C61C22×C411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61#4111yescharacteristic
147C2×C22⋊D61—21no—
148C2×C22⋊D61—21no—
149#11758222—22no—
150#11758222—22no—
151C2×D244C22×C411yescharacteristic
152C2×D244C22×C411yescharacteristic
153C2×C4×D61—21no—
154C2×C4×D61—21no—
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×Dic122C22×C411yescharacteristic
158C2×Dic122C22×C411yescharacteristic
159M16×C61—42no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61C22×C411yescharacteristic
163C2×C8×C61C22×C411yescharacteristic
164C2×C8×C61C22×C411yescharacteristic
165C2×C8×C61C22×C411yescharacteristic
166C2×C8×C61C2×D411yescharacteristic
167C2×C8×C61C2×D411yescharacteristic
168C2×C8×C61C2×D411yescharacteristic
169C2×C8×C61C2×D411yescharacteristic
170C42×C61C22×C411yescharacteristic
171C42×C61C2×D411yescharacteristic
172C42×C61#4111yescharacteristic
173C42×C61C2411yescharacteristic
174C22⋊Dic61—21no—
175C22⋊Dic61—21no—
176#11758198—21no—
177#11758198—21no—
178#11758198—21no—
179#11758198—21no—
180#11758198—21no—
181#11758198—21no—
182C4⋊Dic61C22×C411yescharacteristic
183C4⋊Dic61C22×C411yescharacteristic
184C4⋊Dic61C22×C411yescharacteristic
185C4⋊Dic61C22×C411yescharacteristic
186#11758196—21no—
187#11758196—21no—
188#11758196—21no—
189#11758196—21no—
190#11758196—21no—
191#11758196—21no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61—21no—
196#11758194—81no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—81no—
202Dic244—22no—
203D488—22no—
204#11758190—22no—
205#11758190—22no—
206#11758189—81no—
207C8×D61—81no—
208C8×D61—81no—
209C8×D61—81no—
210C23×C61C4×D411yescharacteristic
211C22×D61—21no—
212C22×D61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—41no—
218C2×C4×C61C4×D411yescharacteristic
219C2×C4×C61C4×D411yescharacteristic
220C2×C4×C61C4×D411yescharacteristic
221C2×C4×C61C23×C411yescharacteristic
222C2×C4×C61C22×D411yescharacteristic
223C2×C4×C61C2×#4111yescharacteristic
224C22⋊D61—24no—
225C22⋊D61—81no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232D244—21no—
233D244—21no—
234D244—21no—
235D244#13112yes—
236C4×D61—24no—
237C4×D61—41no—
238C4×D61—41no—
239C4×D61—41no—
240C4×D61—41no—
241C4×D61—81no—
242Dic122—21no—
243Dic122—21no—
244Dic122—21no—
245Dic122#13112yes—
246C8×C61—22no—
247C8×C61—21no—
248C8×C61—21no—
249C8×C61—21no—
250C8×C61—21no—
251C8×C61—21no—
252C8×C61—21no—
253C8×C61—21no—
254C8×C61—21no—
255C8×C61—41no—
256#92418—41no—
257#92418—41no—
258#92418—41no—
259#92418—41no—
260#17927—611nomaximal, Sylow
261C22×C61—21no—
262C22×C61—21no—
263C22×C61—21no—
264C22×C61C2×C4×D411yescharacteristic
265C2×D61—22no—
266C2×D61—41no—
267C2×D61—41no—
268C2×D61—41no—
269C2×D61—41no—
270C2×D61—41no—
271C4×C61—21no—
272C4×C61—21no—
273C4×C61—21no—
274C4×C61—21no—
275C4×C61C2×#13111yescharacteristic
276C4×C61C2×#13111yescharacteristic
277C4×C61#57711yescharacteristic
278C4×C61#57711yescharacteristic
279Dic61—22no—
280Dic61—41no—
281Dic61—41no—
282Dic61—41no—
283Dic61—41no—
284Dic61—41no—
285#3102—611no—
286#2993—611no—
287#2988—611no—
288#1587—611no—
289#1586—611no—
290#1583—611no—
291#1582—611no—
292#1580—611no—
293#1579—611no—
294C8×SD16—611no—
295C8×SD16—611no—
296#1570—611no—
297#1489—611no—
298#1483—611no—
299#1453D6111yescharacteristic, complemented
300C2×C61—41no—
301C2×C61#292911yescharacteristic
302C2×C61#295211yescharacteristic
303C2×C61#295611yescharacteristic
304D61—42no—
305D61—81no—
306#529—611no—
307C4×#41—611no—
308#485—611no—
309#482—611no—
310#479—611no—
311#478—611no—
312#464—611no—
313#463—611no—
314#452—611no—
315#449—611no—
316#446—611no—
317C8×Q8—611no—
318C8×Q8—611no—
319C8×Q8—611no—
320C4×Q16—611no—
321C4×SD16—611no—
322C4×SD16—611no—
323C4×D8—611no—
324#436—611no—
325#436—1221no—
326#435—1221no—
327C8×D4—611no—
328C8×D4—611no—
329C8×D4—611no—
330C8×D4—1221no—
331C8×D4—1221no—
332#433—1221no—
333#431—1221no—
334#431C2×D6111yescharacteristic
335#431C2×D6111yescharacteristic
336#424—1221no—
337#423—611no—
338C2×C4⋊C8—611no—
339C2×C4⋊C8—1221no—
340C4×M16C2×D6111yescharacteristic
341#334—611no—
342#334—611no—
343#334—611no—
344#334—611no—
345Q8⋊C8—611no—
346Q8⋊C8—611no—
347Q8⋊C8—611no—
348Q8⋊C8—611no—
349D4⋊C8—611no—
350D4⋊C8—611no—
351D4⋊C8—611no—
352D4⋊C8—611no—
353#322C2×D6111yescharacteristic
354#322C2×D6111yescharacteristic
355#322C2×D6111yescharacteristic
356C82C2×D6111yescharacteristic
357C61#1792711yescharacteristic, complemented, Sylow
358C2×#41—611no—
359C2×Q16—611no—
360C2×SD16—611no—
361C2×SD16—611no—
362C2×D8—611no—
363C2×M16—21no—
364C2×M16—1221no—
365C2×M16—1221no—
366C22×C8—1221no—
367C22×C8—1221no—
368C22×C8—1221no—
369C22×C8—1221no—
370#126—1221no—
371#125—611no—
372#124—611no—
373#123—1221no—
374C22⋊Q8—611no—
375#121—611no—
376C4×Q8—611no—
377C4×Q8—611no—
378C4×Q8—611no—
379C4×D4—611no—
380C4×D4—611no—
381C4×D4—611no—
382C4×D4—1221no—
383C4×D4—1221no—
384C4×D4—1221no—
385#117—611no—
386#117—1221no—
387#117—1221no—
388C2×C42—1221no—
389C2×C42C22×D6111yescharacteristic
390#107—611no—
391#107—611no—
392#106—611no—
393#106—611no—
394C4⋊C8—611no—
395C4⋊C8—611no—
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—1221no—
399C4⋊C8—1221no—
400C4⋊C8—1221no—
401C4⋊C8—1221no—
402C4⋊C8—1221no—
403C4⋊C8—1221no—
404C4⋊C8C4×D6111yescharacteristic
405C4⋊C8C4×D6111yescharacteristic
406C4⋊C8D24411yescharacteristic
407C4⋊C8D24411yescharacteristic
408#103—611no—
409#103—611no—
410#103—611no—
411#103—611no—
412#102—611no—
413#102—611no—
414#102—611no—
415#102—611no—
416C22⋊C8—1221no—
417C22⋊C8—1221no—
418C22⋊C8—1221no—
419C22⋊C8—1221no—
420C22⋊C8C4×D6111yescharacteristic
421C22⋊C8C4×D6111yescharacteristic
422C22⋊C8D24411yescharacteristic
423C22⋊C8D24411yescharacteristic
424#97—21no—
425#97—1221no—
426C4×C8—1221no—
427C4×C8—1221no—
428C4×C8—1221no—
429C4×C8C22×D6111yescharacteristic
430C4×C8C22×D6111yescharacteristic
431C4×C8C22×D6111yescharacteristic
432C4×C8C22×D6111yescharacteristic
433C4×C8C22×D6111yescharacteristic
434C4×C8C22×D6111yescharacteristic
435#41—1222no—
436#41—1222no—
437C2×Q8—611no—
438C2×Q8—611no—
439C2×D4—611no—
440C2×D4—611no—
441C2×D4—1221no—
442C2×D4—1221no—
443C22×C4—1221no—
444C22×C4—1221no—
445C22×C4—1221no—
446C22×C4—1221no—
447C22×C4C2×C4×D6111yescharacteristic
448C22×C4C2×D24411yescharacteristic
449C22×C4#1175822211yescharacteristic
450Q16—1222no—
451SD16—1222no—
452SD16—1222no—
453D8—1222no—
454M16—42no—
455M16—4881no—
456M16—4881no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—1221no—
463C2×C8—4881no—
464C2×C8—4881no—
465C2×C8—4881no—
466C2×C8—4881no—
467C2×C8C2×C4×D6111yescharacteristic
468C2×C8C2×C4×D6111yescharacteristic
469C2×C8C2×C4×D6111yescharacteristic
470C2×C8C2×C4×D6111yescharacteristic
471C2×C8C2×D24411yescharacteristic
472C2×C8C2×D24411yescharacteristic
473C2×C8C2×D24411yescharacteristic
474C2×C8C2×D24411yescharacteristic
475C4⋊C4—611no—
476C4⋊C4—611no—
477C4⋊C4—611no—
478C4⋊C4—611no—
479C4⋊C4—1221no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C4⋊C4—1221no—
484C4⋊C4—1221no—
485C22⋊C4—1221no—
486C22⋊C4—1221no—
487C22⋊C4—1221no—
488C22⋊C4—1221no—
489C22⋊C4—1221no—
490C22⋊C4—1221no—
491C22⋊C4—1221no—
492C22⋊C4—1221no—
493C42—1221no—
494C42—1221no—
495C42—1221no—
496C42—1221no—
497C42C2×C4×D6111yescharacteristic
498C42C2×D24411yescharacteristic
499C42#1175822211yescharacteristic
500C42C23×D6111yescharacteristic
501C23—1221no—
502C23—1221no—
503C23C4×D24411yescharacteristic
504Q8—612no—
505Q8—1221no—
506Q8—1221no—
507Q8—1221no—
508D4—612no—
509D4—1224no—
510D4—1221no—
511D4—1221no—
512D4—1221no—
513D4—4881no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—1224no—
520C2×C4—1221no—
521C2×C4—1221no—
522C2×C4—1221no—
523C2×C4—1221no—
524C2×C4—1221no—
525C2×C4—1221no—
526C2×C4—4881no—
527C2×C4—2441no—
528C2×C4—2441no—
529C2×C4—2441no—
530C2×C4—2441no—
531C2×C4C4×D24411yescharacteristic
532C2×C4C4×D24411yescharacteristic
533C2×C4C4×D24411yescharacteristic
534C2×C4C22×C4×D6111yescharacteristic
535C2×C4C22×D24411yescharacteristic
536C2×C4C2×#1175822211yescharacteristic
537C8—22no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—21no—
542C8—21no—
543C8—21no—
544C8—21no—
545C8—21no—
546C8—41no—
547C8—2441no—
548C8—2441no—
549C8—2441no—
550C8—2441no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—1222no—
555C22—2441no—
556C22—2441no—
557C22—2441no—
558C22—2441no—
559C22—2441no—
560C22C2×C4×D24411yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—1222no—
566C4—2441no—
567C4—2441no—
568C4—2441no—
569C4—2441no—
570C4—2441no—
571C4#131×D6111yescharacteristic
572C4#131×D6111yescharacteristic
573C4#1684057411yescharacteristic
574C4#1684057411yescharacteristic
575C2—41no—
576C2—4881no—
577C2—2442no—
578C2#2145451511yescharacteristic
579C2#2145470411yescharacteristic
580C2#2145473011yescharacteristic
subgroupG/H
centerC2×C4C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1453C2
socleC22×C61C2×C4×D4
prime radical#16839909C4
cosocleC42×C61C24
hypercenter#1453D61
hypocenterC61#17927
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1453

Complements

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

NH ≅ G/Ntype
2. #21454970C2semidirect
3. #21454927C2semidirect
4. #21444692C2semidirect
5. #21444685C2semidirect
6. #21444664C2semidirect
7. #21444657C2semidirect
8. #21444644C2semidirect
9. #21444639C2semidirect
10. C8×#11758190C2semidirect
11. C8×#11758190C2semidirect
12. #21444590C2semidirect
13. #21444259C2semidirect
14. #21444233C2semidirect
15. C61×#1453C2semidirect
299. #1453D61semidirect
357. C61#17927semidirect

Maximal subgroups

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

subgroupindex
#214558392
#214549702
#214549272
#214446922
#214446852
#214446642
#214446572
#214446442
#214446392
C8×#117581902
#214445902
#214442592
#214442332
C61×#14532
#1792761