Finite Group Databasebeta

← #29686811

Subgroups — #29686811

Order 15616.

958 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455399C211yesmaximal, characteristic
2C2×#16839881C211yesmaximal, characteristic, complemented
3#21454516C211yesmaximal, characteristic, complemented
4#21454512C211yesmaximal, characteristic, complemented
5C2×#97×D61C211yesmaximal, characteristic, complemented
6#21446711C211yesmaximal, characteristic, complemented
7#21446569C211yesmaximal, characteristic, complemented
8#21446530C211yesmaximal, characteristic, complemented
9#21446261C211yesmaximal, characteristic, complemented
10#21446259C211yesmaximal, characteristic, complemented
11#21445856C211yesmaximal, characteristic, complemented
12#21445702C211yesmaximal, characteristic, complemented
13#21445666C211yesmaximal, characteristic, complemented
14#21445662C211yesmaximal, characteristic, complemented
15C61×#1938C211yesmaximal, characteristic, complemented
16C2×#14519797C2211yescharacteristic
17C2×#14519785C2211yescharacteristic
18C2×#14519784C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20C22×C8×D61C2211yescharacteristic
21#16840274C2211yescharacteristic
22#16840269C2211yescharacteristic
23C2×C42×D61C2211yescharacteristic
24#16840002C412yescomplemented
25#16839997C412yescomplemented
26#16839994C412yescomplemented
27#16839990C412yescomplemented
28#16839881—24no—
29#16839836—22no—
30#16839832—22no—
31#16839827—22no—
32#16839825—22no—
33C2×#14519712C2211yescharacteristic
34C2×#14519712C2211yescharacteristic
35#16839798C2211yescharacteristic
36#16839788C2211yescharacteristic
37C2×#14519705C2211yescharacteristic
38C2×#14519704C2211yescharacteristic
39C2×#14519703C2211yescharacteristic
40#16839759C2211yescharacteristic
41#16839728C2211yescharacteristic
42#16839725C2211yescharacteristic
43#16839725C2211yescharacteristic
44#16839720C2211yescharacteristic
45#16839718C2211yescharacteristic
46C2×#14519688C2211yescharacteristic
47C2×#14519687C2211yescharacteristic
48C2×#14519687C2211yescharacteristic
49#97×D61—24no—
50#16839527C2211yescharacteristic
51#16839523C2211yescharacteristic
52#16839522C2211yescharacteristic
53#16839521C2211yescharacteristic
54C61×#424C2211yescharacteristic
55C2×#104×C61C2211yescharacteristic
56C61×#416C2211yescharacteristic
57C61×#408C2211yescharacteristic
58C2×#97×C61C2211yescharacteristic
59C61×#341C2211yescharacteristic
60C61×#339C2211yescharacteristic
61C2×#11758222C2311yescharacteristic
62C22×C4×D61—21no—
63C22×C4×D61C2311yescharacteristic
64#14519797—22no—
65#14519797—22no—
66C2×#11758202C2×C411yescharacteristic, complemented
67C2×#11758200C2×C411yescharacteristic, complemented
68C2×#11758201C2×C411yescharacteristic, complemented
69C2×#11758199C2×C411yescharacteristic, complemented
70#14519785—22no—
71#14519785—22no—
72#14519784—22no—
73#14519784—22no—
74C2×#11758194—21no—
75C2×#11758194C2311yescharacteristic
76C2×#11758194C2311yescharacteristic
77C2×#11758189—21no—
78C22×#92418—21no—
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81C2×C8×D61—22no—
82C2×C8×D61—22no—
83C2×C8×D61—22no—
84C2×C8×D61—22no—
85C2×C8×D61—21no—
86C2×C8×D61C2×C412yes—
87C2×C8×D61C2×C412yes—
88C2×C8×D61D412yes—
89C2×C8×D61D412yes—
90#14519761—21no—
91#14519758—21no—
92#14519757C2×C412yes—
93#14519753C2×C412yes—
94#14519752C2×C412yes—
95#14519748C2×C412yes—
96#14519747—21no—
97#14519745—21no—
98C4×D244—22no—
99C4×C22⋊D61—22no—
100#14519736C2311yescharacteristic
101C2×C4×Dic61—21no—
102C2×C4×Dic61C2311yescharacteristic
103C42×D61—22no—
104C42×D61—22no—
105#14519712—22no—
106#14519712—22no—
107#14519710C2×C412yescomplemented
108#14519708C2×C412yescomplemented
109#14519706—22no—
110#14519705—22no—
111#14519704—22no—
112#14519703—22no—
113#14519702C2×C412yescomplemented
114#14519699C2×C412yescomplemented
115#14519689—22no—
116#14519689—22no—
117#14519689—22no—
118#14519688—21no—
119#14519688D414yescomplemented
120#14519687—22no—
121#14519687—22no—
122#14519687—21no—
123C4×#92418—21no—
124C8×Dic61—21no—
125C2×#41×C61C2311yescharacteristic
126C2×M16×C61C2311yescharacteristic
127C2×M16×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129C22×C8×C61C2311yescharacteristic
130#117×C61C2311yescharacteristic
131C2×C42×C61C2311yescharacteristic
132C4⋊C8×C61—22no—
133#104×C61—22no—
134#103×C61C2×C412yescomplemented
135#102×C61C2×C412yescomplemented
136C22⋊C8×C61—22no—
137#97×C61—22no—
138C23×D61#4111yescharacteristic
139#41×C61—21no—
140#41×C61—21no—
141#41×C61—21no—
142#41×C61—21no—
143C2×Q8×C61C22×C411yescharacteristic
144C2×D4×C61—21no—
145C2×D4×C61C22×C411yescharacteristic
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61C2411yescharacteristic
149C2×C22⋊D61—21no—
150C2×C22⋊D61—22no—
151C22×Dic61—21no—
152C22×Dic61#4111yescharacteristic
153#11758222—21no—
154#11758222—21no—
155#11758222—21no—
156#11758222—21no—
157C2×D244—22no—
158C2×D244C22×C411yescharacteristic
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C4×D61—21no—
163C2×C4×D61—24no—
164C2×C4×D61—21no—
165C2×C4×D61—44no—
166C2×C4×D61C22×C412yes—
167C2×C4×D61C2×D412yes—
168C2×Dic122C22×C411yescharacteristic
169M16×C61—21no—
170M16×C61—21no—
171M16×C61—21no—
172M16×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C2×C8×C61—21no—
179C2×C8×C61C22×C412yes—
180C2×C8×C61C2×D412yes—
181C4⋊C4×C61C22×C412yes—
182C22⋊C4×C61—21no—
183C42×C61—21no—
184C42×C61—21no—
185C42×C61C2×D412yes—
186C22⋊Dic61—21no—
187C22⋊Dic61—22no—
188#11758202—22no—
189#11758201—22no—
190#11758200—22no—
191#11758199—22no—
192#11758198—22no—
193#11758198—22no—
194#11758198—22no—
195C4⋊Dic61—22no—
196C4⋊Dic61C22×C412yes—
197#11758196—22no—
198C4×Dic61—24no—
199C4×Dic61—21no—
200C4×Dic61—21no—
201C4×Dic61#4112yes—
202#11758194—21no—
203#11758194—21no—
204#11758194—21no—
205#11758194—21no—
206#11758194—42no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—42no—
210C2×#92418C22×C411yescharacteristic
211C2×#92418C22×C411yescharacteristic
212C2×#92418C2×D412yes—
213C2×#92418C2×D411yescharacteristic
214C2×#92418C2×D411yescharacteristic
215C2×#92418C2×D412yes—
216C2×#92418#4112yes—
217C2×#92418#4112yes—
218#11758189—42no—
219C8×D61—24no—
220C8×D61—24no—
221C8×D61—24no—
222C8×D61—24no—
223C8×D61—42no—
224C23×C61—21no—
225C23×C61C2×#4111yescharacteristic
226C22×D61—21no—
227C22×D61—21no—
228C22×D61—24no—
229C22×D61—21no—
230C22×D61C4×D412yes—
231Q8×C61—21no—
232Q8×C61—21no—
233D4×C61—21no—
234D4×C61—21no—
235D4×C61—41no—
236D4×C61—41no—
237C2×C4×C61—21no—
238C2×C4×C61—22no—
239C2×C4×C61—22no—
240C2×C4×C61—42no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61C23×C411yescharacteristic
244C2×C4×C61C22×D411yescharacteristic
245C2×C4×C61C22×D411yescharacteristic
246C2×C4×C61C2×#4111yescharacteristic
247C2×C4×C61C2×#4111yescharacteristic
248C2×C4×C61C2×#4111yescharacteristic
249C22⋊D61—41no—
250C22⋊D61—41no—
251C22⋊D61—44no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—22no—
255C2×Dic61—21no—
256C2×Dic61—22no—
257C2×Dic61—42no—
258C2×Dic61C4×D412yes—
259D244—21no—
260D244—21no—
261D244—44no—
262C4×D61—22no—
263C4×D61—22no—
264C4×D61—22no—
265C4×D61—22no—
266C4×D61—48no—
267C4×D61—41no—
268C4×D61—41no—
269Dic122—21no—
270Dic122—21no—
271C8×C61—22no—
272C8×C61—22no—
273C8×C61—41no—
274C8×C61—41no—
275#92418—41no—
276#92418—41no—
277#92418C4×D412yes—
278#92418C4×D412yes—
279#92418#12112yes—
280#92418#12112yes—
281#21546—611nomaximal, Sylow
282C22×C61—22no—
283C22×C61—42no—
284C22×C61—41no—
285C22×C61C2×C4×D411yescharacteristic
286C22×C61#52511yescharacteristic
287C22×C61#52911yescharacteristic
288C2×D61—24no—
289C2×D61—24no—
290C2×D61—22no—
291C2×D61—22no—
292C2×D61—42no—
293C2×D61—41no—
294C2×D61#44414yescomplemented
295C4×C61—42no—
296C4×C61—42no—
297C4×C61—41no—
298C4×C61C2×C4×D411yescharacteristic
299C4×C61C4×#4111yescharacteristic
300C4×C61C2×#12111yescharacteristic
301C4×C61#53211yescharacteristic
302Dic61—22no—
303Dic61—42no—
304Dic61—42no—
305Dic61—41no—
306#3050—611no—
307C2×#444—611no—
308#2929—611no—
309#2929—611no—
310C22×#97—611no—
311#1975—611no—
312#1946—611no—
313#1938—611no—
314#1938D6111yescharacteristic, complemented
315#1896—611no—
316#1896—611no—
317#1810—611no—
318#1773—611no—
319#1765—611no—
320#1765—611no—
321C2×C61—21no—
322C2×C61—21no—
323C2×C61—81no—
324C2×C61C4×#12111yescharacteristic
325C2×C61C2×#44412yes—
326D61—24no—
327D61—81no—
328C2×#135—611no—
329C2×#131—611no—
330C2×#131—611no—
331C23×C8—611no—
332C23×C8—611no—
333#525—611no—
334#525—611no—
335C22×C42—611no—
336#467—612no—
337#466—612no—
338#465—612no—
339#465—612no—
340#444—1224no—
341#435—1222no—
342#435—1222no—
343C8×D4—1222no—
344C8×D4—1222no—
345C2×#108—611no—
346C2×#108—611no—
347#427—611no—
348#424—611no—
349#424C2×D6111yescharacteristic
350C2×#104—611no—
351C2×#104—611no—
352C2×#104—611no—
353C2×#104C2×D6111yescharacteristic
354#416—611no—
355#416C2×D6111yescharacteristic
356#408—611no—
357#408C2×D6111yescharacteristic
358#407—611no—
359#407—611no—
360#405—611no—
361#405—611no—
362C2×#97—611no—
363C2×#97—611no—
364C2×#97—611no—
365C2×#97—1224no—
366C2×#97C2×D6111yescharacteristic
367#341—611no—
368#341C2×D6111yescharacteristic
369#339—611no—
370#339—611no—
371#339—611no—
372#339C2×D6111yescharacteristic
373C61#2154611yescharacteristic, complemented, Sylow
374C2×#41—611no—
375C2×#41C22×D6111yescharacteristic
376C23×C4—611no—
377C23×C4—1221no—
378#135—1222no—
379#135—1222no—
380C2×Q16—611no—
381C2×SD16—611no—
382C2×SD16—611no—
383C2×D8—611no—
384#131—1222no—
385#131—1222no—
386#131—1222no—
387#131—1222no—
388C2×M16—611no—
389C2×M16—611no—
390C2×M16—1221no—
391C2×M16—1221no—
392C2×M16C22×D6111yescharacteristic
393C2×M16C22×D6111yescharacteristic
394C22×C8—611no—
395C22×C8—611no—
396C22×C8—612no—
397C22×C8—612no—
398C22×C8—612no—
399C22×C8—612no—
400C22×C8—1222no—
401C22×C8—1222no—
402C22×C8—1222no—
403C22×C8—1222no—
404C22×C8—1221no—
405C22×C8—1221no—
406C22×C8C22×D6111yescharacteristic
407C22×C8C22×D6111yescharacteristic
408#123—1221no—
409#123—1221no—
410C22⋊Q8—612no—
411C22⋊Q8—612no—
412#121—612no—
413#121—612no—
414#120—1221no—
415#120—1221no—
416C4×D4—1222no—
417C4×D4—1222no—
418#117—611no—
419#117C22×D6111yescharacteristic
420C2×C42—611no—
421C2×C42—1222no—
422C2×C42—1221no—
423C2×C42—1222no—
424C2×C42C22×D6111yescharacteristic
425#108—1222no—
426#108—1222no—
427#107—612no—
428#106—612no—
429C4⋊C8—22no—
430C4⋊C8—1222no—
431#104—22no—
432#104—1222no—
433#104—1222no—
434#104—1222no—
435#103—612no—
436#103C4×D6112yescomplemented
437#102—612no—
438#102C4×D6112yescomplemented
439C22⋊C8—22no—
440C22⋊C8—1222no—
441C22⋊C8—1222no—
442C22⋊C8—1222no—
443#97—22no—
444#97—614no—
445#97—1221no—
446#97—1222no—
447#97—1222no—
448#97—1221no—
449C4×C8—1221no—
450C4×C8—1221no—
451C24—611no—
452#41—21no—
453#41—21no—
454#41—21no—
455#41—21no—
456#41—1221no—
457#41—1221no—
458#41—1221no—
459#41—1221no—
460C2×Q8—611no—
461C2×Q8C2×C4×D6111yescharacteristic
462C2×D4—21no—
463C2×D4—611no—
464C2×D4—1222no—
465C2×D4—1222no—
466C2×D4—1221no—
467C2×D4C2×C4×D6111yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—611no—
471C22×C4—612no—
472C22×C4—612no—
473C22×C4—1224no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—1221no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4—1221no—
480C22×C4—2444no—
481C22×C4C23×D6111yescharacteristic
482Q16—1222no—
483SD16—1222no—
484SD16—1222no—
485D8—1222no—
486M16—21no—
487M16—21no—
488M16—21no—
489M16—21no—
490M16—1221no—
491M16—1221no—
492M16—1221no—
493M16—1221no—
494M16—2442no—
495M16—2442no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—611no—
503C2×C8—611no—
504C2×C8—612no—
505C2×C8—612no—
506C2×C8—611no—
507C2×C8—611no—
508C2×C8—612no—
509C2×C8—612no—
510C2×C8—1224no—
511C2×C8—1224no—
512C2×C8—1224no—
513C2×C8—1224no—
514C2×C8—1221no—
515C2×C8—1221no—
516C2×C8—2442no—
517C2×C8—2442no—
518C2×C8C2×C4×D6112yes—
519C2×C8D4×D6112yes—
520C4⋊C4—612no—
521C4⋊C4—1222no—
522C4⋊C4—1222no—
523C4⋊C4C2×C4×D6112yes—
524C22⋊C4—21no—
525C22⋊C4—1222no—
526C22⋊C4—1222no—
527C22⋊C4—1222no—
528C22⋊C4—1222no—
529C22⋊C4—1221no—
530C42—21no—
531C42—21no—
532C42—612no—
533C42—1224no—
534C42—1221no—
535C42—1221no—
536C42D4×D6112yes—
537C23—21no—
538C23—612no—
539C23—1224no—
540C23—1221no—
541C23—1221no—
542C23—1221no—
543C23#41×D6111yescharacteristic
544Q8—21no—
545Q8—21no—
546Q8—1221no—
547Q8—1221no—
548D4—21no—
549D4—21no—
550D4—41no—
551D4—41no—
552D4—1221no—
553D4—1221no—
554D4—2444no—
555D4—2444no—
556D4—2441no—
557D4—2441no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—42no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—612no—
565C2×C4—1221no—
566C2×C4—1221no—
567C2×C4—1222no—
568C2×C4—1222no—
569C2×C4—1222no—
570C2×C4—1222no—
571C2×C4—1222no—
572C2×C4—1221no—
573C2×C4—1222no—
574C2×C4—2448no—
575C2×C4—2442no—
576C2×C4—2441no—
577C2×C4—2441no—
578C2×C4C22×C4×D6111yescharacteristic
579C2×C4C2×D4×D6111yescharacteristic
580C2×C4C2×D4×D6111yescharacteristic
581C2×C4#41×D6111yescharacteristic
582C2×C4#41×D6111yescharacteristic
583C2×C4#41×D6111yescharacteristic
584C8—22no—
585C8—22no—
586C8—41no—
587C8—41no—
588C8—612no—
589C8—612no—
590C8—612no—
591C8—612no—
592C8—2441no—
593C8—2441no—
594C22—22no—
595C22—42no—
596C22—41no—
597C22—614no—
598C22—1224no—
599C22—1224no—
600C22—1222no—
601C22—1222no—
602C22—2442no—
603C22—2441no—
604C22C4×D4×D6111yescharacteristic
605C22#1684027011yescharacteristic
606C22#1684029511yescharacteristic
607C4—42no—
608C4—42no—
609C4—41no—
610C4—1222no—
611C4—2442no—
612C4—2442no—
613C4—2441no—
614C4C4×D4×D6111yescharacteristic
615C4#1684023011yescharacteristic
616C4#121×D6111yescharacteristic
617C4#1684031111yescharacteristic
618C2—21no—
619C2—21no—
620C2—81no—
621C2—1224no—
622C2—4881no—
623C2#2144833111yescharacteristic
624C2#444×D6112yes—
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1938C2
socleC22×C61C2×C4×D4
prime radical#21455399C2
cosocleC22×C4×C61C24
hypercenter#1938D61
hypocenterC61#21546
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1938

Complements

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

NH ≅ G/Ntype
2. C2×#16839881C2semidirect
3. #21454516C2semidirect
4. #21454512C2semidirect
5. C2×#97×D61C2semidirect
6. #21446711C2semidirect
7. #21446569C2semidirect
8. #21446530C2semidirect
9. #21446261C2semidirect
10. #21446259C2semidirect
11. #21445856C2semidirect
12. #21445702C2semidirect
13. #21445666C2semidirect
14. #21445662C2semidirect
15. C61×#1938C2semidirect
24. #16840002C4semidirect
25. #16839997C4semidirect
26. #16839994C4semidirect
27. #16839990C4semidirect
66. C2×#11758202C2×C4semidirect
67. C2×#11758200C2×C4semidirect
68. C2×#11758201C2×C4semidirect
69. C2×#11758199C2×C4semidirect
107. #14519710C2×C4semidirect
108. #14519708C2×C4semidirect
113. #14519702C2×C4semidirect
114. #14519699C2×C4semidirect
119. #14519688D4semidirect
134. #103×C61C2×C4semidirect
135. #102×C61C2×C4semidirect
294. C2×D61#444semidirect
314. #1938D61semidirect
373. C61#21546semidirect
436. #103C4×D61semidirect
438. #102C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214553992
C2×#168398812
#214545162
#214545122
C2×#97×D612
#214467112
#214465692
#214465302
#214462612
#214462592
#214458562
#214457022
#214456662
#214456622
C61×#19382
#2154661