Finite Group Databasebeta

← #30613206

Subgroups — #30613206

Order 15616.

670 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462655C211yesmaximal, characteristic, complemented
2D4×#11758213C211yesmaximal, characteristic, complemented
3#21461468C211yesmaximal, characteristic, complemented
4#21461454C211yesmaximal, characteristic, complemented
5#21461447C211yesmaximal, characteristic, complemented
6#21461438C211yesmaximal, characteristic, complemented
7#21461422C211yesmaximal, characteristic, complemented
8#21461419C211yesmaximal, characteristic, complemented
9#21461410C211yesmaximal, characteristic, complemented
10#21461399C211yesmaximal, characteristic, complemented
11#21461396C211yesmaximal, characteristic, complemented
12#21461177C211yesmaximal, characteristic, complemented
13#21461119C211yesmaximal, characteristic, complemented
14#21461037C211yesmaximal, characteristic, complemented
15#21455871C211yesmaximal, characteristic
16C22×#11758213—21no—
17#16840812C2211yescharacteristic, complemented
18#16840811C2211yescharacteristic, complemented
19#16840796—21no—
20#16840796C2211yescharacteristic
21#16840796C2211yescharacteristic
22#16840796C2211yescharacteristic, complemented
23#16840792—21no—
24#16840791—21no—
25#16840791—21no—
26#16840790C2211yescharacteristic, complemented
27D4×#92420C2211yescharacteristic
28D4×#92420C2211yescharacteristic
29#16840787—21no—
30#16840781C2211yescharacteristic
31#16840780C2211yescharacteristic
32#16840766C2211yescharacteristic
33#16840733—21no—
34#16840727—21no—
35C4×#11758213C2211yescharacteristic
36#16840626C2211yescharacteristic, complemented
37#16840626C2211yescharacteristic, complemented
38#16840623C2211yescharacteristic, complemented
39#16840623C2211yescharacteristic, complemented
40#16840612C2211yescharacteristic, complemented
41#16840612C2211yescharacteristic, complemented
42#16840610C2211yescharacteristic
43#16840610C2211yescharacteristic
44#16840610C2211yescharacteristic, complemented
45#16840610C2211yescharacteristic, complemented
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48#92420⋊C8C2211yescharacteristic, complemented
49#92420⋊C8C2211yescharacteristic, complemented
50#16840603C2211yescharacteristic, complemented
51C8×#92420C2211yescharacteristic, complemented
52#16840297C2211yescharacteristic
53C4×D4×D61C2211yescharacteristic
54#16840099C411yescharacteristic
55#16840082C411yescharacteristic
56#16840059C411yescharacteristic
57#16839978C411yescharacteristic
58#16839977C411yescharacteristic
59#16839914C411yescharacteristic
60#16839897C411yescharacteristic
61#16839853C2211yescharacteristic
62#16839849C2211yescharacteristic
63#16839844C2211yescharacteristic
64#16839842C2211yescharacteristic
65#16839814C2211yescharacteristic
66C61×#478C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758213—21no—
69C2×#11758213—21no—
70C2×#11758213—21no—
71C2×#11758213—44no—
72C2×#11758213D411yescharacteristic
73C2×#11758213D411yescharacteristic
74C2×D61⋊C8—21no—
75C22×#92420—21no—
76C22×#92420—21no—
77#14519844—21no—
78#14519844—21no—
79C4⋊#92420—21no—
80C4⋊#92420—21no—
81C4⋊#92420C2311yescharacteristic
82C4⋊#92420C2311yescharacteristic
83C4⋊#92420C2311yescharacteristic
84C4⋊#92420C2311yescharacteristic
85#14519834—21no—
86#14519834—21no—
87#14519834—21no—
88#14519834—21no—
89#14519834—21no—
90#14519834—21no—
91C22⋊#92420—21no—
92C22⋊#92420—21no—
93#14519832—21no—
94#14519832D411yescharacteristic
95#14519832D411yescharacteristic
96C4×#92420—21no—
97C4×#92420—21no—
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C4×#92420C2311yescharacteristic
102C2×D4×D61C2×C411yescharacteristic
103C22×C4×D61—21no—
104C2×#11758190C2×C411yescharacteristic
105C2×#11758200C2×C411yescharacteristic
106C2×D488C2×C411yescharacteristic
107C2×#11758199C2×C411yescharacteristic
108#14519772—21no—
109#14519765C2×C411yescharacteristic
110#14519762—21no—
111#14519757C2×C411yescharacteristic
112#14519752C2×C411yescharacteristic
113#14519742C2311yescharacteristic
114C4×D244C2×C411yescharacteristic
115D4×Dic61C2311yescharacteristic
116#14519739—21no—
117#14519739C2311yescharacteristic
118#14519739C2311yescharacteristic
119C4×C22⋊D61—21no—
120#14519737—21no—
121#14519735—21no—
122C4⋊C4×D61C2×C411yescharacteristic
123C22⋊C4×D61—21no—
124C42×D61C2311yescharacteristic
125#14519710C2×C411yescharacteristic
126#14519708C2×C411yescharacteristic
127C4⋊#92418C2×C411yescharacteristic
128#14519702C2×C411yescharacteristic
129#14519700C2×C411yescharacteristic
130#14519699C2×C411yescharacteristic
131#14519697C2×C411yescharacteristic
132#14519697C2×C411yescharacteristic
133#14519697C2×C411yescharacteristic
134#14519689C2×C411yescharacteristic
135#14519689C2×C411yescharacteristic
136C8×Dic61C2311yescharacteristic
137C8×Dic61C2311yescharacteristic
138#125×C61C2×C411yescharacteristic
139C4×D4×C61C2×C411yescharacteristic
140#107×C61C2×C411yescharacteristic
141#106×C61C2×C411yescharacteristic
142C4⋊C8×C61C2×C411yescharacteristic
143#102×C61C2×C411yescharacteristic
144#102×C61C2×C411yescharacteristic
145C23×D61—21no—
146C2×D4×C61C22×C411yescharacteristic
147C22×C4×C61—21no—
148C2×C22⋊D61—21no—
149C22×Dic61—21no—
150D4×D61—22no—
151D4×D61—41no—
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—42no—
160C2×C4×D61—42no—
161C2×C4×D61C22×C411yescharacteristic
162C2×C4×D61C2×D411yescharacteristic
163C2×C4×D61#4111yescharacteristic
164C2×Dic122C22×C411yescharacteristic
165C2×#92420—21no—
166C2×#92420—21no—
167C2×#92420—21no—
168C2×#92420—21no—
169C2×#92420—21no—
170C2×#92420—21no—
171C2×#92420—42no—
172C2×#92420—42no—
173C2×#92420C2×D411yescharacteristic
174C2×#92420C2×D411yescharacteristic
175C2×#92420C2×D411yescharacteristic
176C2×#92420C2×D411yescharacteristic
177#11758213—22no—
178#11758213—41no—
179#11758213—42no—
180#11758213—42no—
181#11758213—42no—
182#11758213—42no—
183D61⋊C8—42no—
184C2×C8×C61C22×C411yescharacteristic
185C2×C8×C61C22×C411yescharacteristic
186C4⋊C4×C61—21no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61C22×C411yescharacteristic
189C4⋊C4×C61C22×C411yescharacteristic
190C4⋊C4×C61C22×C411yescharacteristic
191C22⋊C4×C61—21no—
192C42×C61C22×C411yescharacteristic
193C22⋊Dic61—21no—
194#11758200—22no—
195#11758199—22no—
196#11758198—21no—
197#11758198—21no—
198#11758198—21no—
199#11758198—21no—
200#11758198—21no—
201#11758198—21no—
202#11758198—21no—
203C4⋊Dic61—21no—
204C4⋊Dic61C22×C411yescharacteristic
205#11758196—21no—
206#11758196—21no—
207C4×Dic61—21no—
208C4×Dic61C2×D411yescharacteristic
209C4×Dic61#4111yescharacteristic
210C4×Dic61C2411yescharacteristic
211C2×#92418C22×C411yescharacteristic
212C2×#92418C22×C411yescharacteristic
213D488—41no—
214#11758190—41no—
215C23×C61—21no—
216C22×D61—21no—
217C22×D61—21no—
218C22×D61—42no—
219C22×D61—42no—
220C22×D61—81no—
221C22×D61C4×D411yescharacteristic
222D4×C61—21no—
223D4×C61#13112yes—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—42no—
228C2×C4×C61C4×D411yescharacteristic
229C2×C4×C61C4×D411yescharacteristic
230C2×C4×C61C23×C411yescharacteristic
231C22⋊D61—42no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—41no—
235C2×Dic61—41no—
236C2×Dic61C4×D411yescharacteristic
237C2×Dic61C22×D411yescharacteristic
238C2×Dic61C2×#4111yescharacteristic
239D244—21no—
240D244—21no—
241D244—21no—
242D244—21no—
243D244—81no—
244C4×D61—21no—
245C4×D61—21no—
246C4×D61—21no—
247C4×D61—21no—
248C4×D61—41no—
249C4×D61—42no—
250C4×D61—42no—
251C4×D61—41no—
252C4×D61—41no—
253C4×D61—41no—
254C4×D61—41no—
255Dic122—21no—
256Dic122—21no—
257#92420—21no—
258#92420—21no—
259#92420—21no—
260#92420—41no—
261#92420—41no—
262#92420—41no—
263#92420—41no—
264#92420—41no—
265#92420—41no—
266#92420AGL(1,ℤ/8)12yes—
267C8×C61—21no—
268C8×C61—21no—
269#92418—21no—
270#92418—21no—
271#18006—611nomaximal, Sylow
272C22×C61—22no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61C2×C4×D411yescharacteristic
276C2×D61—21no—
277C2×D61—21no—
278C2×D61—21no—
279C2×D61—41no—
280C2×D61—41no—
281C2×D61—41no—
282C2×D61—41no—
283C2×D61—41no—
284C2×D61—41no—
285C2×D61—84no—
286C4×C61—21no—
287C4×C61—21no—
288C4×C61—41no—
289C4×C61—41no—
290C4×C61—41no—
291C4×C61C2×#13111yescharacteristic
292C4×C61#56811yescharacteristic
293Dic61—21no—
294Dic61—21no—
295Dic61—41no—
296Dic61—41no—
297Dic61C2×AGL(1,ℤ/8)11yescharacteristic
298Dic61#57511yescharacteristic
299#3105—611no—
300#2969—611no—
301D4×M16—611no—
302#1594—611no—
303#1590—611no—
304#1588—611no—
305#1586—611no—
306#1582—611no—
307#1581—611no—
308SD16⋊C8—611no—
309C8×D8—611no—
310#1574—611no—
311#1495—611no—
312#1478—611no—
313#1453—611no—
314C2×C61—42no—
315C2×C61#293311yescharacteristic
316C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
317C2×C61#295711yescharacteristic
318D61—41no—
319D61—81no—
320D61—81no—
321C22×M16—1221no—
322#529—611no—
323C2×C4×D4—611no—
324#484—611no—
325#481—611no—
326#478—611no—
327#478#692311yescharacteristic
328#463—611no—
329#463—611no—
330#450—611no—
331#447—611no—
332#446—611no—
333C8×Q8—611no—
334C4×SD16—611no—
335C4×SD16—611no—
336C4×D8—611no—
337C4×D8—611no—
338#436—611no—
339#436—611no—
340#436—611no—
341#436—1221no—
342#435—1221no—
343#435—1221no—
344#435—1221no—
345C8×D4—611no—
346C8×D4—611no—
347C8×D4—611no—
348#433—1221no—
349#431—611no—
350#431—611no—
351#431—611no—
352#423—611no—
353#407—1221no—
354#405—1221no—
355C4×M16—611no—
356#335—611no—
357#335—611no—
358#334—611no—
359#334—611no—
360Q8⋊C8—611no—
361Q8⋊C8—611no—
362D4⋊C8—611no—
363D4⋊C8—611no—
364D4⋊C8—611no—
365D4⋊C8—611no—
366D4⋊C8—611no—
367D4⋊C8—611no—
368#322—611no—
369#322—611no—
370#322—611no—
371C82—611no—
372C61#1800611yescharacteristic, complemented, Sylow
373C22×D4—611no—
374C23×C4—1221no—
375C2×SD16—611no—
376C2×SD16—611no—
377C2×D8—611no—
378C2×D8—611no—
379C2×M16—611no—
380C2×M16—611no—
381C2×M16—1221no—
382C2×M16—1221no—
383C2×M16—1221no—
384C2×M16—1221no—
385C2×M16—2444no—
386C22×C8—1221no—
387C22×C8—1221no—
388C22×C8—1221no—
389#126—1221no—
390#125C2×#692311yescharacteristic
391#124—611no—
392#123—1221no—
393C22⋊Q8—611no—
394#121—611no—
395C4×Q8—611no—
396C4×D4—611no—
397C4×D4—611no—
398C4×D4—611no—
399C4×D4—611no—
400C4×D4—1221no—
401C4×D4—1221no—
402C4×D4—1221no—
403C4×D4C2×#692311yescharacteristic
404#117—1221no—
405C2×C4⋊C4—611no—
406C2×C22⋊C4—1221no—
407C2×C42—611no—
408#107—611no—
409#107C2×#692311yescharacteristic
410#106—611no—
411#106C2×#692311yescharacteristic
412C4⋊C8—611no—
413C4⋊C8—611no—
414C4⋊C8—611no—
415C4⋊C8—611no—
416C4⋊C8—611no—
417C4⋊C8—1221no—
418C4⋊C8—1221no—
419C4⋊C8—1221no—
420C4⋊C8—1221no—
421C4⋊C8C2×#692311yescharacteristic
422#103—611no—
423#103—611no—
424#102—611no—
425#102—611no—
426#102—611no—
427#102—611no—
428#102C2×#692311yescharacteristic
429#102C2×#692311yescharacteristic
430C22⋊C8—611no—
431C22⋊C8—611no—
432C22⋊C8—1221no—
433C22⋊C8—1221no—
434C22⋊C8—1221no—
435C22⋊C8—1221no—
436C22⋊C8—1221no—
437C22⋊C8—1221no—
438C22⋊C8—1221no—
439C22⋊C8—1221no—
440#97—611no—
441#97—611no—
442#97—1221no—
443C4×C8—611no—
444C4×C8—611no—
445C4×C8—611no—
446C4×C8—611no—
447C4×C8—611no—
448C4×C8—611no—
449C4×C8—1221no—
450C4×C8—1221no—
451C24—1221no—
452C2×Q8—611no—
453C2×D4—611no—
454C2×D4—611no—
455C2×D4—1221no—
456C2×D4—1221no—
457C2×D4—1222no—
458C2×D4—2441no—
459C2×D4C22×#692311yescharacteristic
460C22×C4—21no—
461C22×C4—611no—
462C22×C4—611no—
463C22×C4—611no—
464C22×C4—1221no—
465C22×C4—1221no—
466C22×C4—1221no—
467C22×C4—1221no—
468C22×C4—1221no—
469C22×C4—2442no—
470C22×C4—2442no—
471SD16—1222no—
472SD16—2441no—
473D8—1222no—
474D8—2441no—
475M16—1222no—
476M16—2442no—
477M16—2441no—
478M16—2442no—
479M16—2442no—
480M16—2442no—
481C2×C8—611no—
482C2×C8—611no—
483C2×C8—611no—
484C2×C8—611no—
485C2×C8—611no—
486C2×C8—611no—
487C2×C8—1221no—
488C2×C8—1221no—
489C2×C8—1221no—
490C2×C8—1221no—
491C2×C8—1221no—
492C2×C8—1221no—
493C2×C8—2442no—
494C2×C8—2442no—
495C2×C8—2442no—
496C2×C8C22×#692311yescharacteristic
497C2×C8C22×#692311yescharacteristic
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—611no—
501C4⋊C4—1221no—
502C4⋊C4—1221no—
503C4⋊C4—1221no—
504C4⋊C4C22×#692311yescharacteristic
505C4⋊C4C22×#692311yescharacteristic
506C4⋊C4C22×#692311yescharacteristic
507C22⋊C4—21no—
508C22⋊C4—1221no—
509C22⋊C4—1221no—
510C22⋊C4—1221no—
511C22⋊C4—1221no—
512C22⋊C4—1221no—
513C22⋊C4—1221no—
514C22⋊C4—1221no—
515C22⋊C4—1221no—
516C42—611no—
517C42—611no—
518C42—611no—
519C42—1221no—
520C42C22×#692311yescharacteristic
521C23—21no—
522C23—611no—
523C23—1221no—
524C23—1221no—
525C23—4881no—
526C23—2442no—
527C23—2442no—
528Q8—1221no—
529Q8—1221no—
530D4—21no—
531D4—1221no—
532D4—1221no—
533D4—1221no—
534D4—1221no—
535D4—4881no—
536D4—2442no—
537D4#1451986512yes—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—42no—
542C2×C4—611no—
543C2×C4—611no—
544C2×C4—611no—
545C2×C4—1221no—
546C2×C4—1221no—
547C2×C4—1221no—
548C2×C4—1221no—
549C2×C4—1221no—
550C2×C4—1221no—
551C2×C4—2441no—
552C2×C4—2442no—
553C2×C4—2441no—
554C2×C4—2441no—
555C2×C4—2441no—
556C2×C4—2441no—
557C2×C4—2442no—
558C2×C4—2441no—
559C2×C4—2441no—
560C2×C4D4×#692311yescharacteristic
561C2×C4D4×#692311yescharacteristic
562C2×C4C23×#692311yescharacteristic
563C8—21no—
564C8—21no—
565C8—612no—
566C8—1221no—
567C8—1221no—
568C8—1221no—
569C8—1221no—
570C8—1221no—
571C8—2441no—
572C8—2441no—
573C8—2441no—
574C8—2441no—
575C8—2441no—
576C8—2441no—
577C22—22no—
578C22—41no—
579C22—41no—
580C22—1221no—
581C22—1221no—
582C22—1221no—
583C22—4884no—
584C22—2441no—
585C22—2441no—
586C22—2441no—
587C22—2441no—
588C22—2441no—
589C22—2441no—
590C22C2×D4×#692311yescharacteristic
591C4—21no—
592C4—21no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4—611no—
597C4—611no—
598C4—1221no—
599C4—1221no—
600C4—2441no—
601C4—2441no—
602C4C2×#1451986511yescharacteristic
603C4#1684084111yescharacteristic
604C2—42no—
605C2—4881no—
606C2—4881no—
607C2—2441no—
608C2#2146255211yescharacteristic
609C2AGL(1,ℤ/8)×#692311yescharacteristic
610C2#2146259811yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#478C4
socleC22×C61C2×C4×D4
prime radical#16839897C4
cosocleC4×Dic61C24
hypercenter#478#6923
hypocenterC61#18006
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #21462655C2semidirect
2. D4×#11758213C2semidirect
3. #21461468C2semidirect
4. #21461454C2semidirect
5. #21461447C2semidirect
6. #21461438C2semidirect
7. #21461422C2semidirect
8. #21461419C2semidirect
9. #21461410C2semidirect
10. #21461399C2semidirect
11. #21461396C2semidirect
12. #21461177C2semidirect
13. #21461119C2semidirect
14. #21461037C2semidirect
17. #16840812C22semidirect
18. #16840811C22semidirect
22. #16840796C22semidirect
26. #16840790C22semidirect
36. #16840626C22semidirect
37. #16840626C22semidirect
38. #16840623C22semidirect
39. #16840623C22semidirect
40. #16840612C22semidirect
41. #16840612C22semidirect
44. #16840610C22semidirect
45. #16840610C22semidirect
48. #92420⋊C8C22semidirect
49. #92420⋊C8C22semidirect
50. #16840603C22semidirect
51. C8×#92420C22semidirect
372. C61#18006semidirect

Maximal subgroups

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

subgroupindex
#214626552
D4×#117582132
#214614682
#214614542
#214614472
#214614382
#214614222
#214614192
#214614102
#214613992
#214613962
#214611772
#214611192
#214610372
#214558712
#1800661