Finite Group Databasebeta

← #29595456

Subgroups — #29595456

Order 15616.

936 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#131×D61C211yesmaximal, characteristic
2C2×#16839547C211yesmaximal, characteristic, complemented
3C2×#16839546C211yesmaximal, characteristic, complemented
4C2×#16839545C211yesmaximal, characteristic, complemented
5#21447429C211yesmaximal, characteristic, complemented
6C2×#16839541C211yesmaximal, characteristic, complemented
7C2×C61×#350C211yesmaximal, characteristic, complemented
8C2×#41×D61C411yescharacteristic
9C2×#14519785—21no—
10C2×#14519785C411yescharacteristic
11C2×#14519784C411yescharacteristic
12C2×#14519783—21no—
13C2×#14519783C2211yescharacteristic
14#131×D61—22no—
15#131×D61—22no—
16#131×D61—22no—
17#131×D61—22no—
18C2×M16×D61—21no—
19C2×M16×D61C411yescharacteristic
20C22×C8×D61—21no—
21C22×C8×D61C2211yescharacteristic
22C2×#14519717C2211yescharacteristic, complemented
23C22×#11758185C2211yescharacteristic, complemented
24#16839547—22no—
25#16839546—22no—
26#16839545—22no—
27#16839541—21no—
28#16839541—21no—
29#16839541—21no—
30#16839541—21no—
31C2×#131×C61C2211yescharacteristic
32C2×M32×C61C2211yescharacteristic, complemented
33C22×C16×C61C2211yescharacteristic, complemented
34C61×#350—22no—
35C2×#11758226C811yescharacteristic
36C2×#11758222—21no—
37C2×#11758222C2×C411yescharacteristic
38C2×#11758224—21no—
39C2×#11758224C811yescharacteristic
40#41×D61—22no—
41#41×D61—22no—
42#41×D61—22no—
43#41×D61—22no—
44C2×Q8×D61C811yescharacteristic
45C2×D4×D61—21no—
46C2×D4×D61C811yescharacteristic
47C22×C4×D61—21no—
48C22×C4×D61C2×C411yescharacteristic
49#14519785—24no—
50#14519785—24no—
51#14519785—22no—
52#14519785—22no—
53#14519784—22no—
54#14519784—22no—
55#14519783—24no—
56#14519783—24no—
57#14519783—21no—
58#14519783—21no—
59#14519783D412yes—
60#14519783D412yes—
61C2×#11758194—21no—
62C2×#11758194C2×C411yescharacteristic
63C2×#11758189—21no—
64C2×#11758189—21no—
65C2×#11758189—21no—
66M16×D61—24no—
67M16×D61—24no—
68M16×D61—22no—
69M16×D61—22no—
70C22×#92418—21no—
71C22×#92418C2×C411yescharacteristic
72C2×C8×D61—24no—
73C2×C8×D61—24no—
74C2×C8×D61—21no—
75C2×C8×D61—21no—
76C2×C8×D61—21no—
77C2×C8×D61—21no—
78C2×C8×D61—21no—
79C2×C8×D61—21no—
80C2×C8×D61—21no—
81C2×C8×D61D411yescharacteristic
82C2×C8×D61D411yescharacteristic
83C2×C8×D61D411yescharacteristic
84C2×C8×D61D411yescharacteristic
85#14519717—21no—
86#14519717—21no—
87C2×#11758185—21no—
88C2×#11758185—21no—
89C2×#11758185—21no—
90C2×#11758185—21no—
91C2×#41×C61C2×C411yescharacteristic
92#131×C61—21no—
93#131×C61—21no—
94#131×C61D412yes—
95#131×C61D412yes—
96C2×M16×C61—21no—
97C2×M16×C61C2×C411yescharacteristic
98C22×C8×C61—21no—
99C22×C8×C61C2311yescharacteristic
100M32×C61—21no—
101M32×C61—21no—
102C2×C16×C61—21no—
103C2×C16×C61—21no—
104C2×C16×C61—21no—
105C2×C16×C61—21no—
106C23×D61—21no—
107C23×D61M1611yescharacteristic
108#41×C61—21no—
109#41×C61—21no—
110#41×C61C22⋊C412yes—
111#41×C61M1612yes—
112C2×Q8×C61C2×C811yescharacteristic
113C2×D4×C61—21no—
114C2×D4×C61C2×C811yescharacteristic
115C22×C4×C61—21no—
116C22×C4×C61C22×C411yescharacteristic
117C2×C22⋊D61—21no—
118C2×C22⋊D61—21no—
119C2×C22⋊D61—21no—
120C22×Dic61—21no—
121C22×Dic61M1611yescharacteristic
122#11758226—22no—
123#11758226—22no—
124Q8×D61—22no—
125Q8×D61—22no—
126#11758224—24no—
127#11758224—24no—
128#11758224—22no—
129#11758224—22no—
130D4×D61—24no—
131D4×D61—24no—
132D4×D61—22no—
133D4×D61—22no—
134#11758222—24no—
135#11758222—24no—
136#11758222—21no—
137#11758222—21no—
138#11758222C22⋊C412yes—
139#11758222M1612yes—
140C2×D244—21no—
141C2×D244C2×C811yescharacteristic
142C2×C4×D61—24no—
143C2×C4×D61—24no—
144C2×C4×D61—21no—
145C2×C4×D61—21no—
146C2×C4×D61—21no—
147C2×C4×D61—21no—
148C2×C4×D61—21no—
149C2×C4×D61—21no—
150C2×C4×D61—21no—
151C2×C4×D61C22⋊C411yescharacteristic
152C2×C4×D61C22⋊C411yescharacteristic
153C2×C4×D61C2×C811yescharacteristic
154C2×C4×D61C2×C811yescharacteristic
155C2×Dic122—21no—
156C2×Dic122C2×C811yescharacteristic
157M16×C61—21no—
158M16×C61—22no—
159M16×C61—22no—
160M16×C61C22⋊C412yes—
161C2×C8×C61—21no—
162C2×C8×C61—22no—
163C2×C8×C61—22no—
164C2×C8×C61C2×D411yescharacteristic
165C2×C8×C61C2×D411yescharacteristic
166C2×C8×C61C2×D411yescharacteristic
167C2×C8×C61C2×D411yescharacteristic
168C2×C8×C61C2×D411yescharacteristic
169C2×C8×C61C2×D411yescharacteristic
170#11758194—24no—
171#11758194—21no—
172#11758194C22⋊C412yes—
173C2×#92418—24no—
174C2×#92418—21no—
175C2×#92418—21no—
176C2×#92418—21no—
177C2×#92418C22⋊C411yescharacteristic
178C2×#92418C22⋊C411yescharacteristic
179#11758189—24no—
180#11758189—24no—
181#11758189—22no—
182#11758189—22no—
183C8×D61—24no—
184C8×D61—24no—
185C8×D61—21no—
186C8×D61—21no—
187C8×D61—22no—
188C8×D61—22no—
189C8×D61—21no—
190C8×D61—21no—
191C8×D61—21no—
192C8×D61—21no—
193C8×D61—21no—
194C8×D61—21no—
195C16×C61—41no—
196C16×C61—41no—
197#11758185—41no—
198#11758185—41no—
199C23×C61—21no—
200C23×C61C2×M1611yescharacteristic
201C22×D61—24no—
202C22×D61—21no—
203C22×D61—21no—
204C22×D61—21no—
205C22×D61—22no—
206C22×D61—41no—
207C22×D61—42no—
208C22×D61—42no—
209C22×D61C22⋊C811yescharacteristic
210C22×D61C22⋊C811yescharacteristic
211Q8×C61—21no—
212Q8×C61C22⋊C812yes—
213D4×C61—22no—
214D4×C61—22no—
215D4×C61—21no—
216D4×C61C22⋊C812yes—
217C2×C4×C61—21no—
218C2×C4×C61—22no—
219C2×C4×C61—22no—
220C2×C4×C61C2×C22⋊C411yescharacteristic
221C2×C4×C61C2×C22⋊C411yescharacteristic
222C2×C4×C61C2×C22⋊C411yescharacteristic
223C2×C4×C61C22×C811yescharacteristic
224C2×C4×C61C2×M1611yescharacteristic
225C2×C4×C61C2×M1611yescharacteristic
226C22⋊D61—24no—
227C22⋊D61—24no—
228C22⋊D61—22no—
229C22⋊D61—22no—
230C2×Dic61—24no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61C22⋊C811yescharacteristic
235C2×Dic61C22⋊C811yescharacteristic
236D244—24no—
237D244—21no—
238D244C22⋊C812yes—
239C4×D61—24no—
240C4×D61—24no—
241C4×D61—21no—
242C4×D61—22no—
243C4×D61—21no—
244C4×D61—21no—
245C4×D61—21no—
246C4×D61—21no—
247C4×D61—21no—
248C4×D61—21no—
249C4×D61—22no—
250C4×D61—21no—
251Dic122—24no—
252Dic122—21no—
253Dic122C22⋊C812yes—
254C8×C61—22no—
255C8×C61#12011yescharacteristic
256C8×C61#12011yescharacteristic
257C8×C61#12011yescharacteristic
258C8×C61#12011yescharacteristic
259#92418—21no—
260#92418—22no—
261#92418—21no—
262#12683—611nomaximal, Sylow
263C22×C61—21no—
264C22×C61—21no—
265C22×C61—22no—
266C22×C61—41no—
267C22×C61—41no—
268C22×C61C2×C22⋊C811yescharacteristic
269C22×C61#40711yescharacteristic
270C22×C61#40711yescharacteristic
271C2×D61—21no—
272C2×D61—21no—
273C2×D61—21no—
274C2×D61—21no—
275C2×D61—21no—
276C2×D61—22no—
277C2×D61—42no—
278C2×D61—42no—
279C2×D61—48no—
280C2×D61—41no—
281C2×D61—41no—
282C2×D61#35012yescomplemented
283C4×C61—22no—
284C4×C61#37911yescharacteristic
285C4×C61C2×C22⋊C811yescharacteristic
286C4×C61C2×C22⋊C811yescharacteristic
287C4×C61#40711yescharacteristic
288Dic61—21no—
289Dic61—22no—
290Dic61—21no—
291C22×#131—611no—
292C2×#350—611no—
293C2×#350—611no—
294C2×#350—611no—
295C2×#350D6111yescharacteristic, complemented
296#2112—611no—
297C2×C22⋊C16—611no—
298C2×C61—21no—
299C2×C61—21no—
300C2×C61—42no—
301C2×C61#177911yescharacteristic
302C2×C61C2×#35011yescharacteristic
303C2×C61#211711yescharacteristic
304D61—22no—
305D61—41no—
306D61—42no—
307C22×#41—611no—
308C2×#131—611no—
309C2×#131—611no—
310C2×#131—611no—
311C2×#131—1221no—
312C2×#131—1221no—
313C2×#131—1222no—
314C2×#131—1222no—
315C2×#131—1222no—
316C2×#131—1222no—
317C2×#131C2×D6111yescharacteristic
318C22×M16—611no—
319C22×M16—1221no—
320C23×C8—611no—
321C23×C8—1221no—
322C2×M32—611no—
323C2×M32C2×D6111yescharacteristic, complemented
324C22×C16—611no—
325C22×C16C2×D6111yescharacteristic, complemented
326#350—22no—
327#350—1222no—
328#350—1222no—
329#350—1222no—
330C22⋊C16—1221no—
331C22⋊C16—1221no—
332C22⋊C16—1221no—
333C22⋊C16—1221no—
334C61#1268311yescharacteristic, complemented, Sylow
335C2×#41—611no—
336C2×#41—611no—
337C2×#41—611no—
338C2×#41—1221no—
339C2×#41—1221no—
340C2×#41—1222no—
341C2×#41—1222no—
342C2×#41—1222no—
343C2×#41—1222no—
344C2×#41C4×D6111yescharacteristic
345C22×Q8—611no—
346C22×D4—611no—
347C22×D4—1221no—
348C23×C4—611no—
349C23×C4—1221no—
350#131—21no—
351#131—21no—
352#131—612no—
353#131—612no—
354#131—1224no—
355#131—1224no—
356#131—1222no—
357#131—1224no—
358#131—1224no—
359#131—1222no—
360#131—1222no—
361#131—1222no—
362#131—1221no—
363#131—1221no—
364#131D24412yes—
365#131C22⋊D6112yes—
366C2×M16—21no—
367C2×M16—611no—
368C2×M16—1221no—
369C2×M16—1221no—
370C2×M16—1221no—
371C2×M16—1222no—
372C2×M16—1224no—
373C2×M16—1224no—
374C2×M16—1222no—
375C2×M16—1221no—
376C2×M16C4×D6111yescharacteristic
377C22×C8—21no—
378C22×C8—611no—
379C22×C8—611no—
380C22×C8—611no—
381C22×C8—611no—
382C22×C8—611no—
383C22×C8—1221no—
384C22×C8—1221no—
385C22×C8—1224no—
386C22×C8—1224no—
387C22×C8—1221no—
388C22×C8—1221no—
389C22×C8—1221no—
390C22×C8—1221no—
391C22×C8—1221no—
392C22×C8—1221no—
393C22×C8C22×D6111yescharacteristic
394M32—21no—
395M32—21no—
396M32—1221no—
397M32—1221no—
398C2×C16—21no—
399C2×C16—21no—
400C2×C16—21no—
401C2×C16—21no—
402C2×C16—1221no—
403C2×C16—1221no—
404C2×C16—1221no—
405C2×C16—1221no—
406C24—611no—
407C24—1221no—
408#41—21no—
409#41—21no—
410#41—612no—
411#41—612no—
412#41—1224no—
413#41—1224no—
414#41—1222no—
415#41—1224no—
416#41—1224no—
417#41—1222no—
418#41—1222no—
419#41—1222no—
420#41—1221no—
421#41—1221no—
422#41#1175818912yes—
423#41#1175819812yes—
424C2×Q8—611no—
425C2×Q8—1221no—
426C2×Q8—1222no—
427C2×Q8—1222no—
428C2×Q8C8×D6111yescharacteristic
429C2×D4—21no—
430C2×D4—611no—
431C2×D4—1221no—
432C2×D4—1221no—
433C2×D4—1222no—
434C2×D4—1224no—
435C2×D4—1224no—
436C2×D4—1221no—
437C2×D4—1221no—
438C2×D4—1222no—
439C2×D4C8×D6111yescharacteristic
440C22×C4—21no—
441C22×C4—611no—
442C22×C4—611no—
443C22×C4—611no—
444C22×C4—611no—
445C22×C4—611no—
446C22×C4—1221no—
447C22×C4—1221no—
448C22×C4—1224no—
449C22×C4—1224no—
450C22×C4—1221no—
451C22×C4—1221no—
452C22×C4—1221no—
453C22×C4—1221no—
454C22×C4—1221no—
455C22×C4—1221no—
456C22×C4C2×C4×D6111yescharacteristic
457M16—21no—
458M16—22no—
459M16—22no—
460M16—612no—
461M16—1224no—
462M16—1224no—
463M16—1224no—
464M16—1221no—
465M16—1222no—
466M16—1222no—
467M16#1175819812yes—
468C2×C8—21no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—611no—
472C2×C8—611no—
473C2×C8—1224no—
474C2×C8—1224no—
475C2×C8—1224no—
476C2×C8—1221no—
477C2×C8—1221no—
478C2×C8—1221no—
479C2×C8—1221no—
480C2×C8—1221no—
481C2×C8—1221no—
482C2×C8—1221no—
483C2×C8—1222no—
484C2×C8—1221no—
485C2×C8—1221no—
486C2×C8—1221no—
487C2×C8—1221no—
488C2×C8—1222no—
489C2×C8C2×D24411yescharacteristic
490C2×C8D4×D6111yescharacteristic
491C2×C8D4×D6111yescharacteristic
492C2×C8D4×D6111yescharacteristic
493C2×C8D4×D6111yescharacteristic
494C2×C8C2×C22⋊D6111yescharacteristic
495C16—41no—
496C16—41no—
497C16—2441no—
498C16—2441no—
499C23—21no—
500C23—611no—
501C23—611no—
502C23—1222no—
503C23—1224no—
504C23—1221no—
505C23—1221no—
506C23—1221no—
507C23—2441no—
508C23—2442no—
509C23—2442no—
510C23M16×D6111yescharacteristic
511Q8—21no—
512Q8—612no—
513Q8—1224no—
514Q8—1221no—
515Q8#1451968912yes—
516D4—22no—
517D4—22no—
518D4—21no—
519D4—612no—
520D4—1224no—
521D4—1224no—
522D4—1224no—
523D4—1222no—
524D4—1222no—
525D4—1221no—
526D4#1451968912yes—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—611no—
531C2×C4—611no—
532C2×C4—1224no—
533C2×C4—1224no—
534C2×C4—1224no—
535C2×C4—1221no—
536C2×C4—1221no—
537C2×C4—1221no—
538C2×C4—1221no—
539C2×C4—1221no—
540C2×C4—1221no—
541C2×C4—1221no—
542C2×C4—1221no—
543C2×C4—1221no—
544C2×C4—1222no—
545C2×C4—1221no—
546C2×C4—1221no—
547C2×C4—1222no—
548C2×C4C22⋊C4×D6111yescharacteristic
549C2×C4C22⋊C4×D6111yescharacteristic
550C2×C4C2×#1175819811yescharacteristic
551C2×C4C2×C8×D6111yescharacteristic
552C2×C4M16×D6111yescharacteristic
553C2×C4C2×#1175818911yescharacteristic
554C8—22no—
555C8—1221no—
556C8—1221no—
557C8—1222no—
558C8#1451974511yescharacteristic
559C8#1451974511yescharacteristic
560C8#1451974711yescharacteristic
561C8#1451974711yescharacteristic
562C22—21no—
563C22—21no—
564C22—22no—
565C22—41no—
566C22—41no—
567C22—612no—
568C22—1221no—
569C22—1221no—
570C22—1221no—
571C22—1221no—
572C22—1222no—
573C22—1221no—
574C22—2442no—
575C22—2442no—
576C22—2448no—
577C22—2441no—
578C22—2441no—
579C22C22⋊C8×D6111yescharacteristic
580C22#1683972411yescharacteristic
581C22#1683972511yescharacteristic
582C4—22no—
583C4—1221no—
584C4—1221no—
585C4—1222no—
586C4#1683961711yescharacteristic
587C4C22⋊C8×D6111yescharacteristic
588C4C2×#1451968911yescharacteristic
589C4#1683972411yescharacteristic
590C2—21no—
591C2—21no—
592C2—42no—
593C2—1222no—
594C2—2441no—
595C2—2442no—
596C2#2144572811yescharacteristic
597C2#350×D6111yescharacteristic
598C2#2144744511yescharacteristic
subgroupG/H
centerC2×C8D4×D61
commutatorC2×C4×C61C22×C8
FrattiniC22×C8C22×D61
FittingC2×C61×#350C2
socleC22×C61C2×C22⋊C8
prime radicalC2×#41×D61C4
cosocleC22×C8×C61C23
hypercenterC2×#350D61
hypocenterC61#12683
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#350

Complements

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

NH ≅ G/Ntype
2. C2×#16839547C2semidirect
3. C2×#16839546C2semidirect
4. C2×#16839545C2semidirect
5. #21447429C2semidirect
6. C2×#16839541C2semidirect
7. C2×C61×#350C2semidirect
22. C2×#14519717C22semidirect
23. C22×#11758185C22semidirect
32. C2×M32×C61C22semidirect
33. C22×C16×C61C22semidirect
282. C2×D61#350semidirect
295. C2×#350D61semidirect
323. C2×M32C2×D61semidirect
325. C22×C16C2×D61semidirect
334. C61#12683semidirect

Maximal subgroups

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

subgroupindex
C2×#131×D612
C2×#168395472
C2×#168395462
C2×#168395452
#214474292
C2×#168395412
C2×C61×#3502
#1268361