Finite Group Databasebeta

← #29650072

Subgroups — #29650072

Order 15616.

648 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455870C211yesmaximal, characteristic
2#21454971C211yesmaximal, characteristic, complemented
3#21454840C211yesmaximal, characteristic, complemented
4#21444685C211yesmaximal, characteristic, complemented
5#21444653C211yesmaximal, characteristic, complemented
6#21444648C211yesmaximal, characteristic, complemented
7#21444640C211yesmaximal, characteristic, complemented
8#21444634C211yesmaximal, characteristic, complemented
9SD16×#92418C211yesmaximal, characteristic, complemented
10#21444613C211yesmaximal, characteristic, complemented
11#21444609C211yesmaximal, characteristic, complemented
12#21444242C211yesmaximal, characteristic, complemented
13#21444226C211yesmaximal, characteristic, complemented
14#21444120C211yesmaximal, characteristic, complemented
15C61×#1585C211yesmaximal, characteristic, complemented
16#16840299C2211yescharacteristic
17C4×D4×D61C2211yescharacteristic
18#16840096C411yescharacteristic
19#16840082C411yescharacteristic
20#16840061C411yescharacteristic
21#16840060C411yescharacteristic
22#16839980C411yescharacteristic
23#16839979C411yescharacteristic
24#16839911C411yescharacteristic
25#16839897C411yescharacteristic
26Q8×#92418C2211yescharacteristic, complemented
27C4×#11758201C2211yescharacteristic
28C4×D488C2211yescharacteristic
29C4×#11758199C2211yescharacteristic
30#16839841C2211yescharacteristic, complemented
31#16839839—21no—
32#16839835—21no—
33C8×D244C2211yescharacteristic
34D4×#92418C2211yescharacteristic
35#16839827C2211yescharacteristic
36#16839827C2211yescharacteristic, complemented
37C8×C22⋊D61—21no—
38#16839825—21no—
39#16839824—21no—
40#16839814C2211yescharacteristic
41#16839813C2211yescharacteristic
42#16839813C2211yescharacteristic
43#16839813C2211yescharacteristic
44#16839787—21no—
45#16839784C2211yescharacteristic
46C2×#14519689—21no—
47C22⋊C8×D61—21no—
48#16839514C2211yescharacteristic, complemented
49#16839513C2211yescharacteristic, complemented
50#16839512C2211yescharacteristic, complemented
51Q8⋊#92418C2211yescharacteristic, complemented
52#16839491C2211yescharacteristic
53#16839491C2211yescharacteristic, complemented
54D4⋊#92418C2211yescharacteristic
55#16839489C2211yescharacteristic
56#16839489C2211yescharacteristic, complemented
57#16839484C2211yescharacteristic, complemented
58#16839483C2211yescharacteristic, complemented
59C8×#92418C2211yescharacteristic, complemented
60C61×#446C2211yescharacteristic, complemented
61C4×SD16×C61C2211yescharacteristic
62C8×D4×C61C2211yescharacteristic
63C61×#335C2211yescharacteristic, complemented
64C61×Q8⋊C8C2211yescharacteristic, complemented
65C61×D4⋊C8C2211yescharacteristic
66C61×#322C2211yescharacteristic, complemented
67C2×D4×D61C2×C411yescharacteristic
68C22×C4×D61—21no—
69C2×#11758201C2×C411yescharacteristic
70C2×D488C2×C411yescharacteristic
71C2×#11758199C2×C411yescharacteristic
72C2×#11758189—21no—
73C2×#11758189—21no—
74C22×#92418—21no—
75C2×C8×D61—21no—
76C2×C8×D61—21no—
77C2×C8×D61—21no—
78#14519772—21no—
79#14519768C2×C411yescharacteristic
80#14519766C2×C411yescharacteristic
81#14519762—21no—
82#14519753C2×C411yescharacteristic
83#14519752C2×C411yescharacteristic
84C4×D244—21no—
85C4×D244C2311yescharacteristic
86C4×D244C2311yescharacteristic
87D4×Dic61C2×C411yescharacteristic
88#14519739C2×C411yescharacteristic
89C4×C22⋊D61—21no—
90#14519737—21no—
91#14519734—21no—
92C4⋊C4×D61C2×C411yescharacteristic
93C22⋊C4×D61—21no—
94C42×D61C2311yescharacteristic
95#14519711C2×C411yescharacteristic
96#14519710C2×C411yescharacteristic
97#14519708C2×C411yescharacteristic
98C4⋊#92418—21no—
99C4⋊#92418C2311yescharacteristic
100C4⋊#92418C2311yescharacteristic
101#14519706—21no—
102#14519706—21no—
103#14519706C2×C411yescharacteristic
104#14519706C2×C411yescharacteristic
105#14519706D411yescharacteristic
106#14519706D411yescharacteristic
107#14519701C2×C411yescharacteristic
108#14519699C2×C411yescharacteristic
109#14519699C2×C411yescharacteristic
110#14519698C2×C411yescharacteristic
111#14519697C2×C411yescharacteristic
112#14519697C2×C411yescharacteristic
113C22⋊#92418—21no—
114#14519689—21no—
115#14519689—21no—
116#14519689—21no—
117#14519689—21no—
118#14519689—21no—
119#14519689—21no—
120#14519689C2×C411yescharacteristic
121#14519689C2×C411yescharacteristic
122#14519689D411yescharacteristic
123#14519689D411yescharacteristic
124C4×#92418—21no—
125C4×#92418C2311yescharacteristic
126C4×#92418C2311yescharacteristic
127C4×#92418C2311yescharacteristic
128C8×Dic61—21no—
129C2×SD16×C61C2×C411yescharacteristic
130C22×C8×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
144C23×D61—21no—
145C2×Q8×C61C22×C411yescharacteristic
146C2×D4×C61C22×C411yescharacteristic
147C22×C4×C61—21no—
148C2×C22⋊D61—21no—
149C22×Dic61—21no—
150D4×D61—22no—
151D4×D61—22no—
152C2×D244—21no—
153C2×D244C22×C411yescharacteristic
154C2×D244C22×C411yescharacteristic
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61—81no—
160C2×C4×D61—81no—
161C2×C4×D61C22×C411yescharacteristic
162C2×C4×D61C2×D411yescharacteristic
163C2×C4×D61#4111yescharacteristic
164SD16×C61—22no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—81no—
169C2×C8×C61C22×C411yescharacteristic
170C2×C8×C61C22×C411yescharacteristic
171C2×C8×C61C2×D411yescharacteristic
172C2×C8×C61C2×D411yescharacteristic
173C4⋊C4×C61—21no—
174C4⋊C4×C61C22×C411yescharacteristic
175C4⋊C4×C61C22×C411yescharacteristic
176C22⋊C4×C61—21no—
177C42×C61—21no—
178C42×C61C2411yescharacteristic
179C22⋊Dic61—21no—
180#11758201—22no—
181#11758199—22no—
182#11758198—21no—
183#11758198—21no—
184#11758198—21no—
185#11758198—21no—
186#11758198—21no—
187#11758198—21no—
188#11758198—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61C22×C411yescharacteristic
191C4⋊Dic61C22×C411yescharacteristic
192#11758196—21no—
193#11758196—21no—
194#11758196—21no—
195C4×Dic61C22×C411yescharacteristic
196C4×Dic61C2×D411yescharacteristic
197C4×Dic61#4111yescharacteristic
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—81no—
202C2×#92418C22×C411yescharacteristic
203C2×#92418C22×C411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206D488—22no—
207#11758189—81no—
208#11758189—81no—
209C8×D61—81no—
210C8×D61—81no—
211C8×D61—81no—
212C23×C61—21no—
213C22×D61—21no—
214C22×D61—24no—
215C22×D61—21no—
216C22×D61—81no—
217C22×D61—81no—
218C22×D61C4×D411yescharacteristic
219Q8×C61—21no—
220Q8×C61—21no—
221D4×C61—21no—
222D4×C61#13112yes—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61C23×C411yescharacteristic
229C2×C4×C61C22×D411yescharacteristic
230C2×C4×C61C2×#4111yescharacteristic
231C22⋊D61—24no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—81no—
235C2×Dic61C4×D411yescharacteristic
236C2×Dic61C4×D411yescharacteristic
237C2×Dic61C4×D411yescharacteristic
238D244—21no—
239D244—21no—
240D244—21no—
241D244—81no—
242D244#13112yes—
243C4×D61—21no—
244C4×D61—21no—
245C4×D61—21no—
246C4×D61—21no—
247C4×D61—41no—
248C4×D61—41no—
249C4×D61—41no—
250C4×D61—41no—
251C4×D61—41no—
252C4×D61—81no—
253C4×D61—81no—
254C8×C61—21no—
255C8×C61—21no—
256C8×C61—21no—
257C8×C61—21no—
258C8×C61—41no—
259C8×C61—41no—
260C8×C61—41no—
261#92418—21no—
262#92418—21no—
263#92418—21no—
264#92418—21no—
265#92418—41no—
266#92418—41no—
267#92418—41no—
268#17918—611nomaximal, Sylow
269C22×C61—22no—
270C22×C61—41no—
271C22×C61—41no—
272C22×C61C2×C4×D411yescharacteristic
273C2×D61—21no—
274C2×D61—22no—
275C2×D61—21no—
276C2×D61—21no—
277C2×D61—41no—
278C2×D61—41no—
279C2×D61—41no—
280C2×D61—41no—
281C2×D61—41no—
282C2×D61—84no—
283C4×C61—21no—
284C4×C61—41no—
285C4×C61—41no—
286C4×C61—41no—
287C4×C61C2×#13111yescharacteristic
288C4×C61C2×#13111yescharacteristic
289C4×C61#57611yescharacteristic
290C4×C61#57711yescharacteristic
291Dic61—21no—
292Dic61—21no—
293Dic61—21no—
294Dic61—41no—
295Dic61—41no—
296#3105—611no—
297#2993—611no—
298#2972—611no—
299#1586—611no—
300#1585D6111yescharacteristic, complemented
301#1582—611no—
302#1581—611no—
303#1580—611no—
304SD16⋊C8—611no—
305C8×SD16—611no—
306C8×D8—611no—
307#1574—611no—
308#1486—611no—
309#1482—611no—
310#1454—611no—
311C2×C61—42no—
312C2×C61#292911yescharacteristic
313C2×C61#294611yescharacteristic
314C2×C61#295711yescharacteristic
315D61—41no—
316D61—42no—
317D61—81no—
318#529—611no—
319C2×C4×D4—611no—
320#484—611no—
321#481—611no—
322#478—611no—
323#478—611no—
324#463—611no—
325#463—611no—
326#450—611no—
327#447—611no—
328#446C2×D6111yescharacteristic, complemented
329C8×Q8—611no—
330C4×SD16—611no—
331C4×SD16C2×D6111yescharacteristic
332C4×D8—611no—
333C4×D8—611no—
334#436—611no—
335#436—1221no—
336#435—1221no—
337C8×D4—611no—
338C8×D4—611no—
339C8×D4—611no—
340C8×D4—611no—
341C8×D4—1221no—
342C8×D4—1221no—
343C8×D4C2×D6111yescharacteristic
344#433—1221no—
345#431—611no—
346#431—611no—
347#431—611no—
348#431—611no—
349#424—1221no—
350#423—611no—
351C2×C22⋊C8—1221no—
352C2×C22⋊C8—1221no—
353#335—611no—
354#335C2×D6111yescharacteristic, complemented
355#334—611no—
356#334—611no—
357Q8⋊C8—611no—
358Q8⋊C8C2×D6111yescharacteristic, complemented
359D4⋊C8—611no—
360D4⋊C8—611no—
361D4⋊C8—611no—
362D4⋊C8—611no—
363D4⋊C8—611no—
364D4⋊C8C2×D6111yescharacteristic
365#322—611no—
366#322—611no—
367#322C2×D6111yescharacteristic, complemented
368C82—611no—
369C61#1791811yescharacteristic, complemented, Sylow
370C22×D4—611no—
371C23×C4—1221no—
372C2×SD16—611no—
373C2×SD16C4×D6111yescharacteristic
374C2×D8—611no—
375C2×D8—611no—
376C2×M16—1221no—
377C2×M16—1221no—
378C22×C8—21no—
379C22×C8—1221no—
380C22×C8—1221no—
381C22×C8—1221no—
382C22×C8—1221no—
383#126—1221no—
384#125—611no—
385#124—611no—
386#123—1221no—
387C22⋊Q8—611no—
388#121—611no—
389C4×Q8C22×D6111yescharacteristic
390C4×D4—611no—
391C4×D4—611no—
392C4×D4—611no—
393C4×D4—611no—
394C4×D4—1221no—
395C4×D4—1221no—
396C4×D4—1221no—
397C4×D4C22×D6111yescharacteristic
398#117—1221no—
399C2×C4⋊C4—611no—
400C2×C22⋊C4—1221no—
401C2×C42—611no—
402#107—611no—
403#107—611no—
404#106—611no—
405#106C4×D6111yescharacteristic
406C4⋊C8—21no—
407C4⋊C8—611no—
408C4⋊C8—611no—
409C4⋊C8—611no—
410C4⋊C8—611no—
411C4⋊C8—611no—
412C4⋊C8—611no—
413C4⋊C8—1221no—
414C4⋊C8—1221no—
415C4⋊C8—1221no—
416C4⋊C8C22×D6111yescharacteristic
417C4⋊C8C22×D6111yescharacteristic
418#103—611no—
419#103C4×D6111yescharacteristic
420#102—611no—
421#102—611no—
422#102—611no—
423#102—611no—
424#102—611no—
425#102C4×D6111yescharacteristic
426C22⋊C8—21no—
427C22⋊C8—611no—
428C22⋊C8—611no—
429C22⋊C8—611no—
430C22⋊C8—611no—
431C22⋊C8—1221no—
432C22⋊C8—1221no—
433C22⋊C8—1221no—
434C22⋊C8—1221no—
435C22⋊C8—1221no—
436C22⋊C8—1221no—
437C22⋊C8—1221no—
438#97—21no—
439C4×C8—611no—
440C4×C8—611no—
441C4×C8—611no—
442C4×C8—1221no—
443C4×C8—1221no—
444C4×C8C22×D6111yescharacteristic
445C4×C8C22×D6111yescharacteristic
446C4×C8C22×D6111yescharacteristic
447C24—1221no—
448C2×Q8C2×C4×D6111yescharacteristic
449C2×D4—611no—
450C2×D4—611no—
451C2×D4—1221no—
452C2×D4—1221no—
453C2×D4—1222no—
454C2×D4—1222no—
455C2×D4C2×C4×D6111yescharacteristic
456C22×C4—21no—
457C22×C4—611no—
458C22×C4—611no—
459C22×C4—611no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—1221no—
464C22×C4—1221no—
465C22×C4—4881no—
466C22×C4—4881no—
467SD16—22no—
468SD16—1222no—
469D8—1222no—
470D8—1222no—
471M16—4881no—
472M16—4881no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—81no—
477C2×C8—611no—
478C2×C8—611no—
479C2×C8—611no—
480C2×C8—611no—
481C2×C8—1221no—
482C2×C8—1221no—
483C2×C8—1221no—
484C2×C8—4881no—
485C2×C8—4881no—
486C2×C8—4881no—
487C2×C8—4881no—
488C2×C8C2×C4×D6111yescharacteristic
489C2×C8C2×C4×D6111yescharacteristic
490C2×C8D4×D6111yescharacteristic
491C2×C8D4×D6111yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—611no—
494C4⋊C4—611no—
495C4⋊C4—1221no—
496C4⋊C4—1221no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C4⋊C4C2×C4×D6111yescharacteristic
500C4⋊C4C2×C4×D6111yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—1221no—
503C22⋊C4—1221no—
504C22⋊C4—1221no—
505C22⋊C4—1221no—
506C22⋊C4—1221no—
507C22⋊C4—1221no—
508C22⋊C4—1221no—
509C22⋊C4—1221no—
510C42—21no—
511C42—611no—
512C42—611no—
513C42—611no—
514C42C23×D6111yescharacteristic
515C23—21no—
516C23—611no—
517C23—1224no—
518C23—1221no—
519C23—1221no—
520C23—4881no—
521C23—4881no—
522Q8—21no—
523Q8—21no—
524D4—21no—
525D4—612no—
526D4—1224no—
527D4—1221no—
528D4—1221no—
529D4—1221no—
530D4—4881no—
531D4#1451978512yes—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—611no—
538C2×C4—611no—
539C2×C4—611no—
540C2×C4—1221no—
541C2×C4—1221no—
542C2×C4—1221no—
543C2×C4—1221no—
544C2×C4—1221no—
545C2×C4—1221no—
546C2×C4—4881no—
547C2×C4—4881no—
548C2×C4—4881no—
549C2×C4—2441no—
550C2×C4—2441no—
551C2×C4—2441no—
552C2×C4—2441no—
553C2×C4—2441no—
554C2×C4C22×C4×D6111yescharacteristic
555C2×C4C2×D4×D6111yescharacteristic
556C2×C4#41×D6111yescharacteristic
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—1221no—
565C8—1221no—
566C8—1221no—
567C8—1221no—
568C8—2441no—
569C8—2441no—
570C8—2441no—
571C22—22no—
572C22—41no—
573C22—41no—
574C22—1221no—
575C22—1221no—
576C22—1221no—
577C22—1222no—
578C22—4884no—
579C22—2441no—
580C22—2441no—
581C22—2441no—
582C22—2441no—
583C22—2441no—
584C22C4×D4×D6111yescharacteristic
585C4—21no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—1221no—
590C4—1221no—
591C4—1221no—
592C4—2441no—
593C4—2441no—
594C4#131×D6111yescharacteristic
595C4C2×#1451978511yescharacteristic
596C4#1684056611yescharacteristic
597C4#1684057111yescharacteristic
598C2—42no—
599C2—4881no—
600C2—2441no—
601C2—2442no—
602C2#2145451011yescharacteristic
603C2#2145465011yescharacteristic
604C2#2145473111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1585C2
socleC22×C61C2×C4×D4
prime radical#16839897C4
cosocleC42×C61C24
hypercenter#1585D61
hypocenterC61#17918
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1585

Complements

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

NH ≅ G/Ntype
2. #21454971C2semidirect
3. #21454840C2semidirect
4. #21444685C2semidirect
5. #21444653C2semidirect
6. #21444648C2semidirect
7. #21444640C2semidirect
8. #21444634C2semidirect
9. SD16×#92418C2semidirect
10. #21444613C2semidirect
11. #21444609C2semidirect
12. #21444242C2semidirect
13. #21444226C2semidirect
14. #21444120C2semidirect
15. C61×#1585C2semidirect
26. Q8×#92418C22semidirect
30. #16839841C22semidirect
36. #16839827C22semidirect
48. #16839514C22semidirect
49. #16839513C22semidirect
50. #16839512C22semidirect
51. Q8⋊#92418C22semidirect
53. #16839491C22semidirect
56. #16839489C22semidirect
57. #16839484C22semidirect
58. #16839483C22semidirect
59. C8×#92418C22semidirect
60. C61×#446C22semidirect
63. C61×#335C22semidirect
64. C61×Q8⋊C8C22semidirect
66. C61×#322C22semidirect
300. #1585D61semidirect
328. #446C2×D61semidirect
354. #335C2×D61semidirect
358. Q8⋊C8C2×D61semidirect
367. #322C2×D61semidirect
369. C61#17918semidirect

Maximal subgroups

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

subgroupindex
#214558702
#214549712
#214548402
#214446852
#214446532
#214446482
#214446402
#214446342
SD16×#924182
#214446132
#214446092
#214442422
#214442262
#214441202
C61×#15852
#1791861