Finite Group Databasebeta

← #29595666

Subgroups — #29595666

Order 15616.

932 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×#135×D61C211yesmaximal, characteristic
2C2×#16839570C211yesmaximal, characteristic, complemented
3C2×#16839569C211yesmaximal, characteristic, complemented
4C2×#16839568C211yesmaximal, characteristic, complemented
5C2×#16839541C211yesmaximal, characteristic, complemented
6#21445854C211yesmaximal, characteristic, complemented
7C2×C61×#359C211yesmaximal, characteristic, complemented
8C2×#41×D61—21no—
9C2×#14519800C411yescharacteristic
10C2×#14519799C2211yescharacteristic
11C2×#14519798—21no—
12C2×#14519797—21no—
13C2×#14519796C411yescharacteristic
14#135×D61—22no—
15#135×D61—22no—
16#135×D61—22no—
17#135×D61—22no—
18C2×Q16×D61C411yescharacteristic
19C2×SD16×D61—21no—
20C2×D8×D61C411yescharacteristic
21C22×C8×D61C2211yescharacteristic
22C22×#11758185C2211yescharacteristic, complemented
23C2×#14519713C2211yescharacteristic, complemented
24#16839725—21no—
25#16839570—22no—
26#16839569—22no—
27#16839568—22no—
28#16839541—21no—
29#16839541—21no—
30#16839526—21no—
31C2×#135×C61C2211yescharacteristic
32C22×C16×C61C2211yescharacteristic, complemented
33C2×#108×C61C2211yescharacteristic, complemented
34C61×#359—22no—
35C2×#11758226—21no—
36C2×#11758222—21no—
37C2×#11758222—41no—
38C2×#11758224—21no—
39C2×#11758224—41no—
40#41×D61—24no—
41#41×D61—24no—
42#41×D61—42no—
43#41×D61—42no—
44C2×Q8×D61—21no—
45C2×D4×D61—21no—
46C2×D4×D61—41no—
47C22×C4×D61—41no—
48C22×C4×D61D411yescharacteristic
49#14519800—22no—
50#14519800—22no—
51#14519799—21no—
52#14519799—21no—
53#14519799D412yes—
54#14519799D412yes—
55#14519798—24no—
56#14519798—24no—
57#14519797—24no—
58#14519797—24no—
59#14519796—22no—
60#14519796—22no—
61C2×Dic244C2×C411yescharacteristic
62C2×#11758202—21no—
63Q16×D61—22no—
64Q16×D61—22no—
65C2×#11758190—21no—
66C2×#11758200—21no—
67C2×#11758201—21no—
68SD16×D61—24no—
69SD16×D61—24no—
70C2×D488C2×C411yescharacteristic
71C2×#11758199—21no—
72D8×D61—22no—
73D8×D61—22no—
74C2×#11758194—21no—
75C22×#92418D411yescharacteristic
76C2×C8×D61—21no—
77C2×C8×D61—21no—
78C2×C8×D61—21no—
79C2×C8×D61—21no—
80C2×C8×D61C2×C411yescharacteristic
81C2×C8×D61C2×C411yescharacteristic
82C2×C8×D61D411yescharacteristic
83C2×C8×D61D411yescharacteristic
84C2×#11758185—21no—
85C2×#11758185—21no—
86C2×#11758185—21no—
87#14519713—21no—
88#14519713—21no—
89#14519689—41no—
90#14519689—41no—
91C2×#41×C61—21no—
92#135×C61—21no—
93#135×C61—21no—
94#135×C61D412yes—
95#135×C61D412yes—
96C2×Q16×C61C2×C411yescharacteristic
97C2×SD16×C61—21no—
98C2×D8×C61C2×C411yescharacteristic
99C2×M16×C61—21no—
100C22×C8×C61C2311yescharacteristic
101C2×C16×C61—21no—
102C2×C16×C61—21no—
103C2×C16×C61—21no—
104#108×C61—21no—
105#108×C61—21no—
106C23×D61—41no—
107C23×D61SD1611yescharacteristic
108#41×C61—22no—
109#41×C61—22no—
110#41×C61—41no—
111#41×C61—41no—
112C2×Q8×C61—21no—
113C2×D4×C61—21no—
114C2×D4×C61—41no—
115C22×C4×C61—41no—
116C22×C4×C61C2×D411yescharacteristic
117C2×C22⋊D61—41no—
118C2×C22⋊D61—41no—
119C2×C22⋊D61—41no—
120C22×Dic61—41no—
121C22×Dic61SD1611yescharacteristic
122#11758226—24no—
123#11758226—42no—
124Q8×D61—24no—
125Q8×D61—42no—
126#11758224—24no—
127#11758224—42no—
128#11758224—44no—
129#11758224—44no—
130D4×D61—24no—
131D4×D61—42no—
132D4×D61—44no—
133D4×D61—44no—
134#11758222—22no—
135#11758222—22no—
136#11758222—44no—
137#11758222—44no—
138#11758222—41no—
139#11758222—41no—
140C2×D244—21no—
141C2×D244—41no—
142C2×C4×D61—21no—
143C2×C4×D61—21no—
144C2×C4×D61—21no—
145C2×C4×D61—21no—
146C2×C4×D61—44no—
147C2×C4×D61—44no—
148C2×C4×D61—41no—
149C2×C4×D61—41no—
150C2×C4×D61—41no—
151C2×C4×D61C22⋊C411yescharacteristic
152C2×C4×D61C22⋊C411yescharacteristic
153C2×C4×D61D811yescharacteristic
154C2×C4×D61D811yescharacteristic
155C2×Dic122—21no—
156C2×Dic122—41no—
157Q16×C61—21no—
158Q16×C61C22⋊C412yes—
159SD16×C61—22no—
160SD16×C61—22no—
161D8×C61—21no—
162D8×C61C22⋊C412yes—
163M16×C61—41no—
164M16×C61—41no—
165C2×C8×C61—41no—
166C2×C8×C61C22×C411yescharacteristic
167C2×C8×C61C2×D411yescharacteristic
168C2×C8×C61C2×D411yescharacteristic
169C2×C8×C61C2×D411yescharacteristic
170C2×C8×C61C2×D411yescharacteristic
171C2×C8×C61C2×D411yescharacteristic
172#11758202—24no—
173#11758201—24no—
174#11758200—24no—
175#11758199—24no—
176#11758194—41no—
177#11758194—41no—
178C2×#92418—21no—
179C2×#92418—21no—
180C2×#92418—41no—
181C2×#92418C22⋊C411yescharacteristic
182C2×#92418C22⋊C411yescharacteristic
183Dic244—21no—
184Dic244C22⋊C412yes—
185D488—21no—
186D488C22⋊C412yes—
187#11758190—22no—
188#11758190—22no—
189C8×D61—21no—
190C8×D61—21no—
191C8×D61—21no—
192C8×D61—21no—
193C8×D61—21no—
194C8×D61—21no—
195C8×D61—21no—
196C8×D61—21no—
197C16×C61—41no—
198#11758185—41no—
199C23×C61—41no—
200C23×C61C2×SD1611yescharacteristic
201C22×D61—21no—
202C22×D61—21no—
203C22×D61—22no—
204C22×D61—41no—
205C22×D61—44no—
206C22×D61—41no—
207C22×D61—82no—
208C22×D61—82no—
209C22×D61#10211yescharacteristic
210C22×D61#10211yescharacteristic
211Q8×C61—22no—
212Q8×C61—41no—
213D4×C61—22no—
214D4×C61—42no—
215D4×C61—42no—
216D4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—42no—
219C2×C4×C61—42no—
220C2×C4×C61C2×C22⋊C411yescharacteristic
221C2×C4×C61#12011yescharacteristic
222C2×C4×C61#12011yescharacteristic
223C2×C4×C61C2×D811yescharacteristic
224C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
225C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
226C22⋊D61—44no—
227C22⋊D61—44no—
228C22⋊D61—42no—
229C22⋊D61—42no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—44no—
233C2×Dic61—41no—
234C2×Dic61#10211yescharacteristic
235C2×Dic61#10211yescharacteristic
236D244—22no—
237D244—44no—
238D244—41no—
239C4×D61—21no—
240C4×D61—21no—
241C4×D61—21no—
242C4×D61—21no—
243C4×D61—21no—
244C4×D61—21no—
245C4×D61—21no—
246C4×D61—21no—
247C4×D61—44no—
248C4×D61—44no—
249C4×D61—42no—
250C4×D61—42no—
251Dic122—22no—
252Dic122—44no—
253Dic122—41no—
254C8×C61—81no—
255C8×C61C2×C22⋊C411yescharacteristic
256C8×C61C2×C22⋊C411yescharacteristic
257C8×C61#12011yescharacteristic
258C8×C61#12011yescharacteristic
259#92418—21no—
260#92418—21no—
261#92418—81no—
262#12734—611nomaximal, Sylow
263C22×C61—21no—
264C22×C61—21no—
265C22×C61—42no—
266C22×C61—81no—
267C22×C61—81no—
268C22×C61C2×#10211yescharacteristic
269C22×C61#45011yescharacteristic
270C22×C61#45011yescharacteristic
271C2×D61—21no—
272C2×D61—21no—
273C2×D61—21no—
274C2×D61—21no—
275C2×D61—21no—
276C2×D61—42no—
277C2×D61—42no—
278C2×D61—42no—
279C2×D61—88no—
280C2×D61—81no—
281C2×D61—81no—
282C2×D61#35912yescomplemented
283C4×C61—42no—
284C4×C61#37911yescharacteristic
285C4×C61#41811yescharacteristic
286C4×C61#44711yescharacteristic
287C4×C61#44711yescharacteristic
288Dic61—21no—
289Dic61—21no—
290Dic61—42no—
291C22×#135—611no—
292C2×#359—611no—
293C2×#359—611no—
294C2×#359—611no—
295C2×#359D6111yescharacteristic, complemented
296C2×C22⋊C16—611no—
297#1810—611no—
298C2×C61—21no—
299C2×C61—21no—
300C2×C61—82no—
301C2×C61#178611yescharacteristic
302C2×C61C2×#35911yescharacteristic
303C2×C61#214311yescharacteristic
304D61—22no—
305D61—41no—
306D61—82no—
307C22×#41—1221no—
308C2×#135—611no—
309C2×#135—611no—
310C2×#135—611no—
311C2×#135—1221no—
312C2×#135—1221no—
313C2×#135—1222no—
314C2×#135—1222no—
315C2×#135—1222no—
316C2×#135—1222no—
317C2×#135C2×D6111yescharacteristic
318C22×Q16—611no—
319C22×SD16—1221no—
320C22×D8—611no—
321C23×C8—611no—
322C22×C16—611no—
323C22×C16C2×D6111yescharacteristic, complemented
324C2×#108—611no—
325C2×#108C2×D6111yescharacteristic, complemented
326#407—1221no—
327#359—22no—
328#359—1222no—
329#359—1222no—
330#359—1222no—
331C22⋊C16—1221no—
332C22⋊C16—1221no—
333#341—1221no—
334C61#1273411yescharacteristic, complemented, Sylow
335C2×#41—21no—
336C2×#41—1221no—
337C2×#41—1221no—
338C2×#41—1224no—
339C2×#41—1224no—
340C2×#41—1221no—
341C2×#41—2441no—
342C2×#41—2441no—
343C2×#41—2442no—
344C2×#41—2442no—
345C22×Q8—1221no—
346C22×D4—1221no—
347C22×D4—2441no—
348C23×C4—611no—
349C23×C4—2441no—
350#135—21no—
351#135—21no—
352#135—612no—
353#135—612no—
354#135—1222no—
355#135—1222no—
356#135—1224no—
357#135—1224no—
358#135—1224no—
359#135—1224no—
360#135—1222no—
361#135—1222no—
362#135—1221no—
363#135—1221no—
364#135D24412yes—
365#135C22⋊D6112yes—
366C2×Q16—611no—
367C2×Q16—1221no—
368C2×Q16—1222no—
369C2×Q16—1222no—
370C2×Q16C4×D6111yescharacteristic
371C2×SD16—21no—
372C2×SD16—1221no—
373C2×SD16—1221no—
374C2×SD16—1224no—
375C2×SD16—1224no—
376C2×SD16—1221no—
377C2×D8—611no—
378C2×D8—1221no—
379C2×D8—1222no—
380C2×D8—1222no—
381C2×D8C4×D6111yescharacteristic
382C2×M16—21no—
383C2×M16—1221no—
384C22×C8—611no—
385C22×C8—611no—
386C22×C8—611no—
387C22×C8—611no—
388C22×C8—611no—
389C22×C8—1221no—
390C22×C8—1221no—
391C22×C8—1221no—
392C22×C8—1221no—
393C22×C8C22×D6111yescharacteristic
394C2×C16—21no—
395C2×C16—21no—
396C2×C16—21no—
397C2×C16—1221no—
398C2×C16—1221no—
399C2×C16—1221no—
400#108—21no—
401#108—21no—
402#108—1221no—
403#108—1221no—
404C22⋊C8—2441no—
405C22⋊C8—2441no—
406C24—611no—
407C24—2441no—
408#41—22no—
409#41—22no—
410#41—41no—
411#41—41no—
412#41—1224no—
413#41—1224no—
414#41—1222no—
415#41—1222no—
416#41—2444no—
417#41—2444no—
418#41—2444no—
419#41—2444no—
420#41—2442no—
421#41—2442no—
422#41—2441no—
423#41—2441no—
424C2×Q8—21no—
425C2×Q8—1224no—
426C2×Q8—1221no—
427C2×Q8—2441no—
428C2×Q8—2442no—
429C2×D4—21no—
430C2×D4—41no—
431C2×D4—1224no—
432C2×D4—1221no—
433C2×D4—2441no—
434C2×D4—2441no—
435C2×D4—2442no—
436C2×D4—2444no—
437C2×D4—2444no—
438C2×D4—2441no—
439C2×D4—2441no—
440C22×C4—41no—
441C22×C4—611no—
442C22×C4—611no—
443C22×C4—611no—
444C22×C4—611no—
445C22×C4—611no—
446C22×C4—1221no—
447C22×C4—1221no—
448C22×C4—1221no—
449C22×C4—1221no—
450C22×C4—2441no—
451C22×C4—2444no—
452C22×C4—2444no—
453C22×C4—2441no—
454C22×C4—2441no—
455C22×C4—2441no—
456C22×C4D4×D6111yescharacteristic
457Q16—21no—
458Q16—612no—
459Q16—1224no—
460Q16—1221no—
461Q16#1175819812yes—
462SD16—22no—
463SD16—22no—
464SD16—1224no—
465SD16—1224no—
466SD16—1222no—
467SD16—1222no—
468D8—21no—
469D8—612no—
470D8—1224no—
471D8—1221no—
472D8#1175819812yes—
473M16—41no—
474M16—41no—
475M16—2441no—
476M16—2441no—
477C2×C8—41no—
478C2×C8—611no—
479C2×C8—611no—
480C2×C8—1221no—
481C2×C8—1221no—
482C2×C8—1221no—
483C2×C8—1221no—
484C2×C8—1221no—
485C2×C8—1221no—
486C2×C8—1221no—
487C2×C8—1221no—
488C2×C8—1221no—
489C2×C8—1221no—
490C2×C8—2441no—
491C2×C8C2×C4×D6111yescharacteristic
492C2×C8C2×D24411yescharacteristic
493C2×C8D4×D6111yescharacteristic
494C2×C8D4×D6111yescharacteristic
495C2×C8D4×D6111yescharacteristic
496C2×C8C2×C22⋊D6111yescharacteristic
497C16—41no—
498C16—2441no—
499C23—41no—
500C23—611no—
501C23—611no—
502C23—1222no—
503C23—1221no—
504C23—1221no—
505C23—4882no—
506C23—4882no—
507C23—2441no—
508C23—2444no—
509C23—2441no—
510C23SD16×D6111yescharacteristic
511Q8—22no—
512Q8—41no—
513Q8—1222no—
514Q8—2444no—
515Q8—2441no—
516D4—22no—
517D4—42no—
518D4—42no—
519D4—41no—
520D4—1222no—
521D4—2444no—
522D4—2444no—
523D4—2444no—
524D4—2442no—
525D4—2442no—
526D4—2441no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—611no—
531C2×C4—611no—
532C2×C4—1221no—
533C2×C4—1221no—
534C2×C4—1221no—
535C2×C4—1221no—
536C2×C4—1221no—
537C2×C4—1221no—
538C2×C4—1221no—
539C2×C4—1221no—
540C2×C4—1221no—
541C2×C4—1221no—
542C2×C4—2444no—
543C2×C4—2444no—
544C2×C4—2444no—
545C2×C4—2441no—
546C2×C4—2442no—
547C2×C4—2442no—
548C2×C4C22⋊C4×D6111yescharacteristic
549C2×C4#1451974511yescharacteristic
550C2×C4#1451974711yescharacteristic
551C2×C4D8×D6111yescharacteristic
552C2×C4#1451980111yescharacteristic
553C2×C4#1451980411yescharacteristic
554C8—81no—
555C8—1221no—
556C8—1221no—
557C8—4881no—
558C8C22⋊C4×D6111yescharacteristic
559C8C2×#1175819811yescharacteristic
560C8#1451974511yescharacteristic
561C8#1451974711yescharacteristic
562C22—21no—
563C22—21no—
564C22—42no—
565C22—81no—
566C22—81no—
567C22—612no—
568C22—1221no—
569C22—1221no—
570C22—1221no—
571C22—1221no—
572C22—1221no—
573C22—4888no—
574C22—4881no—
575C22—4881no—
576C22—2442no—
577C22—2442no—
578C22—2442no—
579C22#102×D6111yescharacteristic
580C22#1683991111yescharacteristic
581C22#1683991411yescharacteristic
582C4—42no—
583C4—1221no—
584C4—1221no—
585C4—2442no—
586C4#1683961711yescharacteristic
587C4#1683976511yescharacteristic
588C4#1683989411yescharacteristic
589C4#1683989711yescharacteristic
590C2—21no—
591C2—21no—
592C2—82no—
593C2—1222no—
594C2—4882no—
595C2—2441no—
596C2#2144574811yescharacteristic
597C2#359×D6111yescharacteristic
598C2#2144754511yescharacteristic
subgroupG/H
centerC2×C4D8×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC2×C61×#359C2
socleC22×C61C2×#102
prime radicalC2×#135×D61C2
cosocleC22×C8×C61C23
hypercenterC2×#359D61
hypocenterC61#12734
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#359

Complements

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

NH ≅ G/Ntype
2. C2×#16839570C2semidirect
3. C2×#16839569C2semidirect
4. C2×#16839568C2semidirect
5. C2×#16839541C2semidirect
6. #21445854C2semidirect
7. C2×C61×#359C2semidirect
22. C22×#11758185C22semidirect
23. C2×#14519713C22semidirect
32. C22×C16×C61C22semidirect
33. C2×#108×C61C22semidirect
282. C2×D61#359semidirect
295. C2×#359D61semidirect
323. C22×C16C2×D61semidirect
325. C2×#108C2×D61semidirect
334. C61#12734semidirect

Maximal subgroups

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

subgroupindex
C2×#135×D612
C2×#168395702
C2×#168395692
C2×#168395682
C2×#168395412
#214458542
C2×C61×#3592
#1273461