Finite Group Databasebeta

← #29650097

Subgroups — #29650097

Order 15616.

638 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455879C211yesmaximal, characteristic
2#21454930C211yesmaximal, characteristic, complemented
3#21454897C211yesmaximal, characteristic, complemented
4#21444694C211yesmaximal, characteristic, complemented
5#21444680C211yesmaximal, characteristic, complemented
6#21444659C211yesmaximal, characteristic, complemented
7#21444645C211yesmaximal, characteristic, complemented
8#21444640C211yesmaximal, characteristic, complemented
9#21444634C211yesmaximal, characteristic, complemented
10#21444616C211yesmaximal, characteristic, complemented
11#21444611C211yesmaximal, characteristic, complemented
12#21444605C211yesmaximal, characteristic, complemented
13#21444219C211yesmaximal, characteristic, complemented
14#21444119C211yesmaximal, characteristic, complemented
15C61×#1488C211yesmaximal, characteristic, complemented
16#16840312C2211yescharacteristic
17#16840086C411yescharacteristic
18#16840086C411yescharacteristic
19#16840057C411yescharacteristic
20#16840052C411yescharacteristic
21#16839962C411yescharacteristic
22#16839957C411yescharacteristic
23#16839907C411yescharacteristic
24#16839907C411yescharacteristic
25Q8×#92418C2211yescharacteristic
26Q8×#92418C2211yescharacteristic
27C4×#11758201C2211yescharacteristic
28C4×#11758201C2211yescharacteristic
29C4×#11758199C2211yescharacteristic
30C4×#11758199C2211yescharacteristic
31#16839839C2211yescharacteristic
32#16839839C2211yescharacteristic
33#16839835—21no—
34#16839835—21no—
35D4×#92418—21no—
36D4×#92418—21no—
37D4×#92418C2211yescharacteristic
38D4×#92418C2211yescharacteristic
39#16839827C2211yescharacteristic
40#16839827C2211yescharacteristic
41#16839815—21no—
42#16839815C2211yescharacteristic
43#16839815C2211yescharacteristic
44C2×C4⋊#92418—21no—
45C2×C4⋊#92418C2211yescharacteristic
46#16839727—21no—
47#16839727—21no—
48#16839514C2211yescharacteristic
49#16839514C2211yescharacteristic
50#16839512C2211yescharacteristic
51#16839512C2211yescharacteristic
52#16839491C2211yescharacteristic
53#16839491C2211yescharacteristic
54#16839491C2211yescharacteristic
55#16839491C2211yescharacteristic
56#16839484C2211yescharacteristic
57#16839484C2211yescharacteristic
58#16839483C2211yescharacteristic
59C8×#92418C2211yescharacteristic
60C4×#41×C61C2211yescharacteristic
61C61×#432C2211yescharacteristic
62C61×#431C2211yescharacteristic
63C61×Q8⋊C8C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C61×D4⋊C8C2211yescharacteristic
67C2×#11758222—21no—
68C2×#11758201C2×C411yescharacteristic
69C2×#11758201C2×C411yescharacteristic
70C2×#11758199C2×C411yescharacteristic
71C2×#11758199C2×C411yescharacteristic
72C2×#11758189—21no—
73C2×#11758189—21no—
74C22×#92418—21no—
75C22×#92418—21no—
76C22×#92418—21no—
77C2×C8×D61—21no—
78C2×C8×D61—21no—
79#14519777C2×C411yescharacteristic
80#14519774C2×C411yescharacteristic
81#14519765—21no—
82#14519751—21no—
83#14519751C2×C411yescharacteristic
84#14519751C2×C411yescharacteristic
85C4×D244—21no—
86C4×D244C2311yescharacteristic
87C4×D244C2311yescharacteristic
88#14519710C2×C411yescharacteristic
89#14519710C2×C411yescharacteristic
90#14519708C2×C411yescharacteristic
91#14519708C2×C411yescharacteristic
92C4⋊#92418—21no—
93C4⋊#92418—21no—
94C4⋊#92418—21no—
95C4⋊#92418C2×C411yescharacteristic
96C4⋊#92418C2×C411yescharacteristic
97C4⋊#92418D411yescharacteristic
98C4⋊#92418D411yescharacteristic
99C4⋊#92418C2311yescharacteristic
100C4⋊#92418C2311yescharacteristic
101#14519701C2×C411yescharacteristic
102#14519701C2×C411yescharacteristic
103#14519698C2×C411yescharacteristic
104#14519698C2×C411yescharacteristic
105#14519697C2×C411yescharacteristic
106#14519697C2×C411yescharacteristic
107#14519697C2×C411yescharacteristic
108#14519697C2×C411yescharacteristic
109C22⋊#92418—21no—
110C22⋊#92418—21no—
111C22⋊#92418C2×C411yescharacteristic
112C22⋊#92418C2×C411yescharacteristic
113C22⋊#92418D411yescharacteristic
114C22⋊#92418D411yescharacteristic
115#14519689—21no—
116#14519689—21no—
117#14519689—21no—
118#14519689—21no—
119C4×#92418—21no—
120C4×#92418—21no—
121C4×#92418C2311yescharacteristic
122C4×#92418C2311yescharacteristic
123C4×#92418C2311yescharacteristic
124C4×#92418C2311yescharacteristic
125C2×#41×C61C2×C411yescharacteristic
126C4×Q8×C61C2×C411yescharacteristic
127C4×Q8×C61C2311yescharacteristic
128C4×D4×C61—21no—
129C4×D4×C61—21no—
130C4×D4×C61C2×C411yescharacteristic
131C4×D4×C61C2311yescharacteristic
132#117×C61—21no—
133#117×C61C2×C411yescharacteristic
134C2×C42×C61—21no—
135C2×C42×C61C2311yescharacteristic
136C4⋊C8×C61—21no—
137C4⋊C8×C61C2311yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139C22⋊C8×C61—21no—
140C22⋊C8×C61—21no—
141#97×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144#41×C61—22no—
145#41×C61—22no—
146C2×Q8×C61C22×C411yescharacteristic
147C2×D4×C61—21no—
148C2×D4×C61C22×C411yescharacteristic
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61#4111yescharacteristic
155C2×C22⋊D61—21no—
156C2×C22⋊D61—21no—
157#11758222—81no—
158#11758222—81no—
159C2×D244—21no—
160C2×D244—21no—
161C2×D244C22×C411yescharacteristic
162C2×D244C22×C411yescharacteristic
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×Dic122—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61C22×C411yescharacteristic
173C4⋊C4×C61C22×C411yescharacteristic
174C22⋊C4×C61—21no—
175C22⋊C4×C61—21no—
176C22⋊C4×C61—21no—
177C42×C61—21no—
178C42×C61—21no—
179C42×C61—21no—
180C42×C61C22×C411yescharacteristic
181C42×C61C2×D411yescharacteristic
182C42×C61#4111yescharacteristic
183C42×C61C2411yescharacteristic
184#11758201—22no—
185#11758201—22no—
186#11758199—22no—
187#11758199—22no—
188#11758198—21no—
189#11758198—21no—
190#11758198—21no—
191#11758198—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61C22×C411yescharacteristic
194C4⋊Dic61C22×C411yescharacteristic
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—81no—
198C2×#92418—81no—
199C2×#92418—81no—
200C2×#92418C22×C411yescharacteristic
201C2×#92418C22×C411yescharacteristic
202C2×#92418C22×C411yescharacteristic
203C2×#92418C22×C411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206C2×#92418C2×D411yescharacteristic
207C2×#92418C2×D411yescharacteristic
208#11758189—81no—
209#11758189—81no—
210C8×D61—81no—
211C8×D61—81no—
212C23×C61—21no—
213C23×C61C4×D411yescharacteristic
214C22×D61—21no—
215C22×D61—21no—
216Q8×C61—21no—
217Q8×C61#13112yes—
218D4×C61—24no—
219D4×C61—21no—
220D4×C61#13112yes—
221C2×C4×C61—24no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—81no—
233C2×C4×C61C4×D411yescharacteristic
234C2×C4×C61C4×D411yescharacteristic
235C2×C4×C61C4×D411yescharacteristic
236C2×C4×C61C23×C411yescharacteristic
237C2×C4×C61C22×D411yescharacteristic
238C2×C4×C61C2×#4111yescharacteristic
239C22⋊D61—81no—
240C22⋊D61—81no—
241C2×Dic61—21no—
242C2×Dic61—21no—
243D244—21no—
244D244—21no—
245D244—21no—
246D244—21no—
247D244—81no—
248D244—81no—
249C4×D61—41no—
250C4×D61—41no—
251C4×D61—41no—
252C4×D61—41no—
253Dic122—81no—
254C8×C61—41no—
255C8×C61—41no—
256C8×C61—41no—
257C8×C61—41no—
258#92418—21no—
259#92418—21no—
260#92418—21no—
261#92418—21no—
262#92418—21no—
263#92418—21no—
264#92418—21no—
265#92418—21no—
266#92418—41no—
267#92418—41no—
268#17920—611nomaximal, Sylow
269C22×C61—21no—
270C22×C61—22no—
271C22×C61—21no—
272C22×C61—21no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61C2×C4×D411yescharacteristic
276C2×D61—41no—
277C2×D61—41no—
278C2×D61—41no—
279C2×D61—41no—
280C2×D61—41no—
281C2×D61—41no—
282C4×C61—21no—
283C4×C61—22no—
284C4×C61—21no—
285C4×C61—21no—
286C4×C61—21no—
287C4×C61—41no—
288C4×C61—41no—
289C4×C61C2×#13111yescharacteristic
290C4×C61C2×#13111yescharacteristic
291C4×C61#57611yescharacteristic
292C4×C61#57711yescharacteristic
293Dic61—41no—
294Dic61—41no—
295#3106—611no—
296#2988—611no—
297#2981—611no—
298#1588—611no—
299#1586—611no—
300#1583—611no—
301#1581—611no—
302#1580—611no—
303SD16⋊C8—611no—
304C8×SD16—611no—
305C8×D8—611no—
306#1573—611no—
307#1488D6111yescharacteristic, complemented
308#1480—611no—
309#1454—611no—
310C2×C61—41no—
311C2×C61—42no—
312C2×C61#292911yescharacteristic
313C2×C61#294611yescharacteristic
314C2×C61#295711yescharacteristic
315D61—81no—
316D61—81no—
317#532—611no—
318C4×#41C2×D6111yescharacteristic
319#482—611no—
320#482—611no—
321#477—611no—
322#476—611no—
323#460—611no—
324#459—611no—
325#449—611no—
326#449—611no—
327C8×Q8—611no—
328C8×Q8—611no—
329C4×SD16—611no—
330C4×SD16—611no—
331C4×D8—611no—
332C4×D8—611no—
333#436—611no—
334#436—611no—
335#435—1221no—
336#435—1221no—
337C8×D4—611no—
338C8×D4—611no—
339C8×D4—611no—
340C8×D4—611no—
341C8×D4—1221no—
342C8×D4—1221no—
343#432C2×D6111yescharacteristic
344#431—611no—
345#431—611no—
346#431—1221no—
347#431C2×D6111yescharacteristic
348C2×C4⋊C8—611no—
349C2×C4⋊C8—1221no—
350#408—1221no—
351#408—1221no—
352#335—611no—
353#335—611no—
354#334—611no—
355#334—611no—
356Q8⋊C8C2×D6111yescharacteristic
357Q8⋊C8C2×D6111yescharacteristic
358D4⋊C8—611no—
359D4⋊C8—611no—
360D4⋊C8—611no—
361D4⋊C8—611no—
362D4⋊C8C2×D6111yescharacteristic
363D4⋊C8C2×D6111yescharacteristic
364#322—611no—
365#322—611no—
366#322—611no—
367C82—611no—
368C61#1792011yescharacteristic, complemented, Sylow
369C2×#41—1221no—
370C2×#41C4×D6111yescharacteristic
371C2×SD16—611no—
372C2×SD16—611no—
373C2×D8—611no—
374C2×D8—611no—
375C2×M16—1221no—
376C2×M16—1221no—
377C22×C8—1221no—
378C22×C8—1221no—
379C22×C8—1221no—
380C22×C8—1221no—
381C22×C8—1221no—
382C4⋊Q8—611no—
383#127—611no—
384#124—1221no—
385#121—611no—
386#121—611no—
387#121—1221no—
388C4×Q8C4×D6111yescharacteristic
389C4×Q8C22×D6111yescharacteristic
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—611no—
393C4×D4—611no—
394C4×D4—1221no—
395C4×D4C4×D6111yescharacteristic
396C4×D4C22×D6111yescharacteristic
397#117—21no—
398#117C4×D6111yescharacteristic
399C2×C42—21no—
400C2×C42C22×D6111yescharacteristic
401#107—611no—
402#107—611no—
403#106—611no—
404#106—611no—
405C4⋊C8—21no—
406C4⋊C8—611no—
407C4⋊C8—611no—
408C4⋊C8—611no—
409C4⋊C8—611no—
410C4⋊C8—611no—
411C4⋊C8—611no—
412C4⋊C8—1221no—
413C4⋊C8—1221no—
414C4⋊C8—1221no—
415C4⋊C8C22×D6111yescharacteristic
416C4⋊C8C22×D6111yescharacteristic
417#103—611no—
418#103—611no—
419#102—611no—
420#102—611no—
421#102—611no—
422#102—611no—
423#102—611no—
424#102—611no—
425C22⋊C8—21no—
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—
437#97—21no—
438C4×C8—611no—
439C4×C8—611no—
440C4×C8—611no—
441C4×C8—611no—
442C4×C8—1221no—
443C4×C8—1221no—
444C4×C8C22×D6111yescharacteristic
445C4×C8C22×D6111yescharacteristic
446#41—22no—
447#41—22no—
448#41—4881no—
449#41—4881no—
450C2×Q8—1221no—
451C2×Q8C2×C4×D6111yescharacteristic
452C2×D4—21no—
453C2×D4—611no—
454C2×D4—611no—
455C2×D4—1221no—
456C2×D4—1221no—
457C2×D4—1221no—
458C2×D4—1221no—
459C2×D4C2×C4×D6111yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—1221no—
464C22×C4—1221no—
465C22×C4C2×C4×D6111yescharacteristic
466C22×C4D4×D6111yescharacteristic
467C22×C4#1175822411yescharacteristic
468SD16—1222no—
469SD16—1222no—
470D8—1222no—
471D8—1222no—
472M16—4881no—
473M16—4881no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—611no—
479C2×C8—611no—
480C2×C8—611no—
481C2×C8—611no—
482C2×C8—611no—
483C2×C8—611no—
484C2×C8—611no—
485C2×C8—611no—
486C2×C8—1221no—
487C2×C8—1221no—
488C2×C8—4881no—
489C2×C8—4881no—
490C2×C8—4881no—
491C2×C8—4881no—
492C2×C8—4881no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—611no—
496C4⋊C4—611no—
497C4⋊C4—1221no—
498C4⋊C4C2×C4×D6111yescharacteristic
499C4⋊C4C2×C4×D6111yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—1221no—
504C22⋊C4—1221no—
505C22⋊C4—1221no—
506C22⋊C4—1221no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42C2×C4×D6111yescharacteristic
511C42D4×D6111yescharacteristic
512C42#1175822411yescharacteristic
513C42C23×D6111yescharacteristic
514C23—21no—
515C23—1221no—
516C23—1221no—
517C23#1451973711yescharacteristic
518Q8—21no—
519Q8—4881no—
520Q8#1451978512yes—
521D4—24no—
522D4—21no—
523D4—1221no—
524D4—1221no—
525D4—1221no—
526D4—1221no—
527D4—4881no—
528D4—4881no—
529D4—4881no—
530D4—4881no—
531D4#1451978512yes—
532C2×C4—24no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—81no—
544C2×C4—1221no—
545C2×C4—1221no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4—2441no—
549C2×C4—2441no—
550C2×C4#1451973711yescharacteristic
551C2×C4#1451973711yescharacteristic
552C2×C4#1451973711yescharacteristic
553C2×C4C22×C4×D6111yescharacteristic
554C2×C4C2×D4×D6111yescharacteristic
555C2×C4C2×#1175822411yescharacteristic
556C8—41no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8—1221no—
561C8—1221no—
562C8—1221no—
563C8—1221no—
564C8—1221no—
565C8—1221no—
566C8—1221no—
567C8—1221no—
568C8—2441no—
569C8—2441no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22—2441no—
577C22—2441no—
578C22—2441no—
579C22—2441no—
580C22—2441no—
581C22—2441no—
582C22C2×#1451973711yescharacteristic
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—22no—
588C4—41no—
589C4—41no—
590C4—2441no—
591C4—2441no—
592C4C2×#1451978511yescharacteristic
593C4C2×#1451978511yescharacteristic
594C4#1684056411yescharacteristic
595C4#1684056911yescharacteristic
596C2—41no—
597C2—42no—
598C2—4881no—
599C2—4881no—
600C2#2145450911yescharacteristic
601C2#2145465411yescharacteristic
602C2#2145473211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1488C2
socleC22×C61C2×C4×D4
prime radical#21455879C2
cosocleC42×C61C24
hypercenter#1488D61
hypocenterC61#17920
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1488

Complements

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

NH ≅ G/Ntype
2. #21454930C2semidirect
3. #21454897C2semidirect
4. #21444694C2semidirect
5. #21444680C2semidirect
6. #21444659C2semidirect
7. #21444645C2semidirect
8. #21444640C2semidirect
9. #21444634C2semidirect
10. #21444616C2semidirect
11. #21444611C2semidirect
12. #21444605C2semidirect
13. #21444219C2semidirect
14. #21444119C2semidirect
15. C61×#1488C2semidirect
307. #1488D61semidirect
368. C61#17920semidirect

Maximal subgroups

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

subgroupindex
#214558792
#214549302
#214548972
#214446942
#214446802
#214446592
#214446452
#214446402
#214446342
#214446162
#214446112
#214446052
#214442192
#214441192
C61×#14882
#1792061