Finite Group Databasebeta

← #29669435

Subgroups — #29669435

Order 15616.

702 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458450C211yesmaximal, characteristic, complemented
2#21458162C211yesmaximal, characteristic, complemented
3#21457466C211yesmaximal, characteristic, complemented
4#21445488C211yesmaximal, characteristic, complemented
5#21445281C211yesmaximal, characteristic, complemented
6#21445254C211yesmaximal, characteristic, complemented
7#21445211C211yesmaximal, characteristic, complemented
8#21445184C211yesmaximal, characteristic, complemented
9#21445066C211yesmaximal, characteristic, complemented
10#21445054C211yesmaximal, characteristic, complemented
11#21445012C211yesmaximal, characteristic, complemented
12#21444906C211yesmaximal, characteristic, complemented
13#21444648C211yesmaximal, characteristic, complemented
14SD16⋊#92418C211yesmaximal, characteristic, complemented
15C61×#3284C211yesmaximal, characteristic, complemented
16C2×#14519806—21no—
17Q8×D244C2211yescharacteristic
18#16840416C2211yescharacteristic
19#16840165C2211yescharacteristic
20#16840165C2211yescharacteristic
21#16840142C2211yescharacteristic
22#16840108—21no—
23#16840108C2211yescharacteristic
24#16840108C2211yescharacteristic
25#16840075—21no—
26#16840073—21no—
27#16840042—21no—
28#16840042C2211yescharacteristic
29#16840042C2211yescharacteristic
30#16840039C2211yescharacteristic
31#16840021—21no—
32#16839996—21no—
33#16839972C2211yescharacteristic
34#16839967C2211yescharacteristic
35#16839954—21no—
36#16839954C2211yescharacteristic
37#16839925—21no—
38#16839919—21no—
39Q8×#92418C2211yescharacteristic
40C4×#11758199—21no—
41C4×#11758199C2211yescharacteristic
42#16839841C2211yescharacteristic
43D4×#92418C2211yescharacteristic
44C2×#14519710—21no—
45#16839515C2211yescharacteristic
46#16839514C2211yescharacteristic
47#16839509C2211yescharacteristic
48#16839509C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839506C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54#16839489C2211yescharacteristic
55#16839483C2211yescharacteristic
56C2×#135×C61—21no—
57C61×#550C2211yescharacteristic
58C61×#547C2211yescharacteristic
59C61×#492C2211yescharacteristic
60C61×#465—21no—
61C61×#462C2211yescharacteristic
62C61×#459C2211yescharacteristic
63C61×#452—21no—
64C61×#449—21no—
65C4×SD16×C61C2211yescharacteristic
66C8×D4×C61C2211yescharacteristic
67C2×#11758224—21no—
68C2×Q8×D61—21no—
69#14519806—44no—
70C2×Dic244—21no—
71C2×Dic244—21no—
72C2×#11758202—21no—
73C2×#11758200—21no—
74C2×#11758199—21no—
75C2×#11758199D411yescharacteristic
76C2×#11758189—21no—
77C22×#92418—21no—
78#14519777—21no—
79#14519777C2311yescharacteristic
80#14519777C2311yescharacteristic
81#14519761—41no—
82#14519757—21no—
83#14519757—21no—
84#14519757—41no—
85#14519751—21no—
86C4×D244—21no—
87C4×D244C2311yescharacteristic
88C2×C4⋊Dic61—21no—
89#14519710—21no—
90#14519710—21no—
91#14519710—21no—
92#14519710—21no—
93#14519710—21no—
94#14519710—41no—
95#14519710D411yescharacteristic
96C4⋊#92418—21no—
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99C4⋊#92418C2311yescharacteristic
100#14519700—21no—
101#14519700—21no—
102#14519698—21no—
103#14519698—21no—
104#14519698—21no—
105#14519698—21no—
106#14519698—21no—
107#14519698—41no—
108#14519698D411yescharacteristic
109#14519697—21no—
110#14519697D411yescharacteristic
111C22⋊#92418—21no—
112#14519689—21no—
113C4×#92418—21no—
114C4×#92418C2311yescharacteristic
115C4×#92418C2311yescharacteristic
116C2×#41×C61—21no—
117C2×#41×C61—21no—
118#135×C61—44no—
119C2×Q16×C61—21no—
120C2×SD16×C61—21no—
121C2×SD16×C61—21no—
122C2×SD16×C61D411yescharacteristic
123C2×D8×C61—21no—
124C22×C8×C61—21no—
125C4⋊Q8×C61C2311yescharacteristic
126#127×C61—21no—
127#127×C61C2311yescharacteristic
128#123×C61—41no—
129C22⋊Q8×C61—21no—
130#121×C61—21no—
131#121×C61—21no—
132#121×C61—41no—
133C4×Q8×C61C2311yescharacteristic
134C4×D4×C61—21no—
135C4×D4×C61C2311yescharacteristic
136C4×D4×C61C2311yescharacteristic
137C2×C4⋊C4×C61—21no—
138#106×C61D411yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140#103×C61—21no—
141#103×C61D411yescharacteristic
142#102×C61—21no—
143#102×C61D411yescharacteristic
144C22⋊C8×C61—21no—
145C4×C8×C61C2311yescharacteristic
146#41×C61—42no—
147#41×C61—42no—
148#41×C61—81no—
149#41×C61—81no—
150C2×Q8×C61—21no—
151C2×Q8×C61C2×D411yescharacteristic
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—41no—
156C2×D4×C61—41no—
157C2×D4×C61—41no—
158C2×D4×C61C2×D411yescharacteristic
159C2×D4×C61C2×D411yescharacteristic
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—41no—
163C22×C4×C61—41no—
164C2×C22⋊D61—41no—
165C22×Dic61—41no—
166Q8×D61—42no—
167Q8×D61—81no—
168#11758224—42no—
169#11758224—81no—
170C2×D244C2×D411yescharacteristic
171C2×C4×D61—21no—
172C2×C4×D61—41no—
173C2×Dic122—21no—
174C2×Dic122—21no—
175C2×Dic122—41no—
176Q16×C61—42no—
177SD16×C61—42no—
178SD16×C61—81no—
179SD16×C61D814yescomplemented
180D8×C61—42no—
181C2×C8×C61—21no—
182C2×C8×C61—42no—
183C2×C8×C61C2×D411yescharacteristic
184C2×C8×C61C2×D411yescharacteristic
185C4⋊C4×C61—21no—
186C4⋊C4×C61—21no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61—41no—
189C4⋊C4×C61C2×D411yescharacteristic
190C4⋊C4×C61C2×D411yescharacteristic
191C4⋊C4×C61C2×D411yescharacteristic
192C22⋊C4×C61—21no—
193C22⋊C4×C61—21no—
194C22⋊C4×C61—41no—
195C22⋊C4×C61—41no—
196C42×C61—21no—
197C42×C61C2411yescharacteristic
198#11758202—42no—
199#11758200—42no—
200#11758199—41no—
201#11758199—42no—
202#11758198—21no—
203#11758198—41no—
204#11758198—41no—
205C4⋊Dic61—21no—
206C4⋊Dic61—21no—
207C4⋊Dic61—21no—
208C4⋊Dic61—21no—
209C4⋊Dic61—41no—
210C4⋊Dic61—41no—
211C4⋊Dic61C2×D411yescharacteristic
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—42no—
217C2×#92418C2×D411yescharacteristic
218C2×#92418C2×D411yescharacteristic
219Dic244—42no—
220Dic244—81no—
221#11758189—42no—
222C23×C61—21no—
223C23×C61—21no—
224C23×C61—41no—
225C22×D61—21no—
226Q8×C61—21no—
227Q8×C61—41no—
228Q8×C61—41no—
229Q8×C61C2×D812yes—
230D4×C61—21no—
231D4×C61—21no—
232D4×C61—21no—
233D4×C61—41no—
234D4×C61—41no—
235D4×C61—41no—
236D4×C61—41no—
237D4×C61—82no—
238D4×C61—81no—
239D4×C61—82no—
240D4×C61—161no—
241D4×C61C2×D812yes—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—82no—
252C2×C4×C61—82no—
253C2×C4×C61C22×D411yescharacteristic
254C2×C4×C61C22×D411yescharacteristic
255C2×C4×C61H(5,𝔽2)11yescharacteristic
256C22⋊D61—82no—
257C2×Dic61—21no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—82no—
261D244—21no—
262D244—21no—
263C4×D61—41no—
264C4×D61—41no—
265C4×D61—82no—
266Dic122—41no—
267Dic122—41no—
268Dic122—41no—
269Dic122—41no—
270Dic122—82no—
271C8×C61—21no—
272C8×C61—41no—
273C8×C61C2×D812yes—
274#92418—21no—
275#92418—21no—
276#92418—41no—
277#92418—41no—
278#92418—41no—
279#92418—41no—
280#19760—611nomaximal, Sylow
281C22×C61—22no—
282C22×C61—41no—
283C22×C61—41no—
284C22×C61—41no—
285C22×C61—41no—
286C22×C61—41no—
287C22×C61—81no—
288C22×C61—81no—
289C22×C61—81no—
290C22×C61D4211yescharacteristic
291C2×D61—41no—
292C2×D61—41no—
293C2×D61—41no—
294C4×C61—22no—
295C4×C61—21no—
296C4×C61—41no—
297C4×C61—41no—
298C4×C61—41no—
299C4×C61—81no—
300C4×C61C22×D811yescharacteristic
301C4×C61#57511yescharacteristic
302C4×C61#57611yescharacteristic
303C4×C61#57811yescharacteristic
304Dic61—41no—
305Dic61—81no—
306Dic61—81no—
307#3358—611no—
308#3334—611no—
309#3284D6111yescharacteristic, complemented
310#3276—611no—
311#1722—611no—
312#1685—611no—
313#1681—611no—
314#1674—611no—
315#1669—611no—
316#1649—611no—
317#1647—611no—
318#1641—611no—
319#1625—611no—
320#1581—611no—
321SD16⋊C8—611no—
322C2×C61—42no—
323C2×C61—81no—
324C2×C61—161no—
325C2×C61#326911yescharacteristic
326C2×C61D4×D811yescharacteristic
327C2×C61#328911yescharacteristic
328D61—81no—
329C2×#137—1221no—
330C2×#135—21no—
331#550C2×D6111yescharacteristic
332D4×Q8—611no—
333#547—611no—
334#547C2×D6111yescharacteristic
335#500—611no—
336#500—611no—
337#494—611no—
338#492C2×D6111yescharacteristic
339#486—611no—
340#486—611no—
341#486—1221no—
342#480—1221no—
343#480—1221no—
344#474—611no—
345#474—611no—
346#474—611no—
347#474—1221no—
348#470—1221no—
349#466—1221no—
350#465—21no—
351#462—611no—
352#462C2×D6111yescharacteristic
353#461—611no—
354#459—611no—
355#459—1221no—
356#459C2×D6111yescharacteristic
357#452—21no—
358#452—1221no—
359#451—1221no—
360#449—21no—
361C8×Q8—611no—
362C4×SD16C2×D6111yescharacteristic
363C4×D8—611no—
364C4×D8—1221no—
365#436—611no—
366C8×D4—611no—
367C8×D4C2×D6111yescharacteristic
368C2×#107—1221no—
369#335—611no—
370#335—611no—
371#332—611no—
372#332—611no—
373#332—611no—
374#331—611no—
375Q8⋊C8—611no—
376D4⋊C8—611no—
377D4⋊C8—611no—
378D4⋊C8—611no—
379#322—611no—
380C61#1976011yescharacteristic, complemented, Sylow
381C2×#41—21no—
382C2×#41—21no—
383C2×#41—1221no—
384C22×Q8—1221no—
385#137—2444no—
386#135—44no—
387C2×Q16—21no—
388C2×Q16—1221no—
389C2×Q16—1221no—
390C2×Q16—1221no—
391C2×SD16—21no—
392C2×SD16—21no—
393C2×SD16—1221no—
394C2×SD16C22⋊D6111yescharacteristic
395C2×D8—21no—
396C2×D8—611no—
397C2×D8—1221no—
398C2×M16—1221no—
399C22×C8—21no—
400C22×C8—1221no—
401C4⋊Q8—611no—
402C4⋊Q8—611no—
403C4⋊Q8—1221no—
404C4⋊Q8C22×D6111yescharacteristic
405#127—21no—
406#127C22×D6111yescharacteristic
407#123—41no—
408#123—2441no—
409C22⋊Q8—21no—
410C22⋊Q8—1221no—
411C22⋊Q8—1221no—
412C22⋊Q8—2441no—
413#121—21no—
414#121—21no—
415#121—41no—
416#121—1221no—
417C4×Q8C22×D6111yescharacteristic
418C4×D4—21no—
419C4×D4—611no—
420C4×D4—1221no—
421C4×D4C22×D6111yescharacteristic
422C4×D4C22×D6111yescharacteristic
423C2×C4⋊C4—21no—
424C2×C4⋊C4—1221no—
425#107—611no—
426#107—1221no—
427#107—1221no—
428#107—1221no—
429#107—1221no—
430#107—1221no—
431#107—2441no—
432#106C22⋊D6111yescharacteristic
433C4⋊C8—611no—
434C4⋊C8—611no—
435C4⋊C8—611no—
436C4⋊C8—1221no—
437C4⋊C8C22×D6111yescharacteristic
438#103—21no—
439#103—1221no—
440#103—1221no—
441#103C22⋊D6111yescharacteristic
442#102—21no—
443#102—611no—
444#102—611no—
445#102—1221no—
446#102—1221no—
447#102—1221no—
448#102—1221no—
449#102—1221no—
450#102—1221no—
451#102—2441no—
452#102C22⋊D6111yescharacteristic
453C22⋊C8—21no—
454C22⋊C8—1221no—
455C22⋊C8—1221no—
456C4×C8—611no—
457C4×C8—611no—
458C4×C8—1221no—
459C4×C8C22×D6111yescharacteristic
460#41—42no—
461#41—42no—
462#41—81no—
463#41—81no—
464#41—4881no—
465#41—2442no—
466C2×Q8—21no—
467C2×Q8—1221no—
468C2×Q8—1221no—
469C2×Q8—4881no—
470C2×Q8—2441no—
471C2×Q8—2442no—
472C2×Q8C2×C22⋊D6111yescharacteristic
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—41no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4—611no—
480C2×D4—2441no—
481C2×D4D4×D6111yescharacteristic
482C2×D4C2×C22⋊D6111yescharacteristic
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—1221no—
488C22×C4—2441no—
489C22×C4—2441no—
490Q16—42no—
491Q16—4881no—
492Q16—2442no—
493Q16—2442no—
494SD16—42no—
495SD16—81no—
496SD16—2442no—
497SD16#1175819914yescomplemented
498D8—42no—
499D8—2441no—
500D8—2442no—
501M16—2442no—
502C2×C8—21no—
503C2×C8—42no—
504C2×C8—611no—
505C2×C8—611no—
506C2×C8—1221no—
507C2×C8—1221no—
508C2×C8—1221no—
509C2×C8—1221no—
510C2×C8—2442no—
511C2×C8C2×C22⋊D6111yescharacteristic
512C2×C8C2×C22⋊D6111yescharacteristic
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—41no—
517C4⋊C4—611no—
518C4⋊C4—1221no—
519C4⋊C4—1221no—
520C4⋊C4—1221no—
521C4⋊C4—1221no—
522C4⋊C4—2441no—
523C4⋊C4—2441no—
524C4⋊C4D4×D6111yescharacteristic
525C4⋊C4C2×C22⋊D6111yescharacteristic
526C4⋊C4C2×C22⋊D6111yescharacteristic
527C22⋊C4—21no—
528C22⋊C4—21no—
529C22⋊C4—41no—
530C22⋊C4—41no—
531C22⋊C4—1221no—
532C22⋊C4—2441no—
533C22⋊C4—2441no—
534C42—21no—
535C42C23×D6111yescharacteristic
536C23—21no—
537C23—21no—
538C23—41no—
539C23—1221no—
540Q8—21no—
541Q8—41no—
542Q8—41no—
543Q8—4882no—
544Q8—2441no—
545Q8—2441no—
546Q8—2441no—
547Q8—2441no—
548Q8C2×#1175819912yes—
549D4—21no—
550D4—21no—
551D4—21no—
552D4—41no—
553D4—41no—
554D4—41no—
555D4—41no—
556D4—82no—
557D4—81no—
558D4—82no—
559D4—161no—
560D4—1221no—
561D4—1221no—
562D4—4882no—
563D4C2×#1175819912yes—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—82no—
574C2×C4—82no—
575C2×C4—1221no—
576C2×C4—4882no—
577C2×C4—4882no—
578C2×C4—2441no—
579C2×C4—2441no—
580C2×C4—2441no—
581C2×C4—2441no—
582C2×C4C2×D4×D6111yescharacteristic
583C2×C4C22×C22⋊D6111yescharacteristic
584C2×C4#1451982211yescharacteristic
585C8—21no—
586C8—41no—
587C8—1221no—
588C8—1221no—
589C8—2441no—
590C8—2441no—
591C8—2441no—
592C8—2441no—
593C8C2×#1175819912yes—
594C22—22no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22—2441no—
604C22—2441no—
605C22—2441no—
606C22D4×C22⋊D6111yescharacteristic
607C4—22no—
608C4—21no—
609C4—41no—
610C4—41no—
611C4—41no—
612C4—81no—
613C4—4881no—
614C4—4881no—
615C4—2441no—
616C4C22×#1175819911yescharacteristic
617C4#1684055911yescharacteristic
618C4#1684056511yescharacteristic
619C4#1684057611yescharacteristic
620C2—42no—
621C2—81no—
622C2—161no—
623C2—4881no—
624C2#2145737411yescharacteristic
625C2D4×#1175819911yescharacteristic
626C2#2145759211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3284C2
socleC22×C61D42
hypercenter#3284D61
hypocenterC61#19760
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3284

Complements

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

NH ≅ G/Ntype
1. #21458450C2semidirect
2. #21458162C2semidirect
3. #21457466C2semidirect
4. #21445488C2semidirect
5. #21445281C2semidirect
6. #21445254C2semidirect
7. #21445211C2semidirect
8. #21445184C2semidirect
9. #21445066C2semidirect
10. #21445054C2semidirect
11. #21445012C2semidirect
12. #21444906C2semidirect
13. #21444648C2semidirect
14. SD16⋊#92418C2semidirect
15. C61×#3284C2semidirect
179. SD16×C61D8semidirect
309. #3284D61semidirect
380. C61#19760semidirect
497. SD16#11758199semidirect

Maximal subgroups

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

subgroupindex
#214584502
#214581622
#214574662
#214454882
#214452812
#214452542
#214452112
#214451842
#214450662
#214450542
#214450122
#214449062
#214446482
SD16⋊#924182
C61×#32842
#1976061