Finite Group Databasebeta

← #29671307

Subgroups — #29671307

Order 15616.

738 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458452C211yesmaximal, characteristic, complemented
2#21457461C211yesmaximal, characteristic, complemented
3#21457435C211yesmaximal, characteristic, complemented
4#21445423C211yesmaximal, characteristic, complemented
5#21445306C211yesmaximal, characteristic, complemented
6#21445296C211yesmaximal, characteristic, complemented
7#21445260C211yesmaximal, characteristic, complemented
8#21445256C211yesmaximal, characteristic, complemented
9#21445011C211yesmaximal, characteristic, complemented
10#21444998C211yesmaximal, characteristic, complemented
11#21444921C211yesmaximal, characteristic, complemented
12#21444908C211yesmaximal, characteristic, complemented
13#21444704C211yesmaximal, characteristic, complemented
14C8×#11758200C211yesmaximal, characteristic, complemented
15C61×#3294C211yesmaximal, characteristic, complemented
16C2×#14519807—21no—
17C2×#14519803—21no—
18#16840433C2211yescharacteristic
19D4×Dic122C2211yescharacteristic, complemented
20#16840141C2211yescharacteristic, complemented
21#16840138C2211yescharacteristic
22#16840110C2211yescharacteristic, complemented
23#16840109C2211yescharacteristic, complemented
24#16840108C2211yescharacteristic
25#16840107—21no—
26#16840042C2211yescharacteristic
27#16840041—21no—
28#16840018—21no—
29#16840013—21no—
30#16839969C2211yescharacteristic, complemented
31#16839967C2211yescharacteristic
32#16839959C2211yescharacteristic
33#16839957C2211yescharacteristic
34#16839957C2211yescharacteristic, complemented
35#16839955—21no—
36#16839924—21no—
37#16839917—21no—
38#16839905—21no—
39#16839896—21no—
40C8×Dic122C2211yescharacteristic, complemented
41C4×#11758200C2211yescharacteristic
42#16839842—21no—
43#16839840C2211yescharacteristic
44#16839840C2211yescharacteristic, complemented
45#16839515C2211yescharacteristic, complemented
46#16839512C2211yescharacteristic, complemented
47#16839508C2211yescharacteristic, complemented
48#16839507C2211yescharacteristic, complemented
49#16839506C2211yescharacteristic
50#16839505C2211yescharacteristic, complemented
51#16839492C2211yescharacteristic, complemented
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic, complemented
55C8×#92418C2211yescharacteristic, complemented
56C61×#547C2211yescharacteristic
57D42×C61C2211yescharacteristic
58C61×#486C2211yescharacteristic
59C61×#480—21no—
60C61×#474C2211yescharacteristic
61C61×#466—21no—
62C61×#459C2211yescharacteristic
63C61×#447—21no—
64C4×D8×C61C2211yescharacteristic
65C8×D4×C61C2211yescharacteristic
66C2×#102×C61—21no—
67C2×#11758222—21no—
68C22×Dic122—21no—
69#14519807—44no—
70#14519803—44no—
71C2×#11758202—21no—
72C2×#11758202—21no—
73C2×#11758202—21no—
74C2×#11758200—21no—
75C2×#11758200—21no—
76C2×#11758200D411yescharacteristic
77C2×#11758199—21no—
78C2×#11758199—21no—
79C2×#11758199—21no—
80C2×#11758199—21no—
81C2×#11758194—21no—
82C2×#11758194—21no—
83#14519777C2311yescharacteristic
84#14519776—21no—
85#14519774C2311yescharacteristic
86#14519773—21no—
87#14519756—21no—
88#14519754—41no—
89#14519751—21no—
90#14519750—41no—
91C4×Dic122C2311yescharacteristic
92D4×Dic61—21no—
93#14519739—21no—
94#14519710—21no—
95#14519708D411yescharacteristic
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99#14519706—21no—
100#14519701—21no—
101#14519700—21no—
102#14519700D411yescharacteristic
103#14519699—21no—
104#14519699—21no—
105#14519698—21no—
106#14519698—21no—
107#14519698—41no—
108#14519698D411yescharacteristic
109#14519697—21no—
110#14519697—21no—
111#14519697—41no—
112C22⋊#92418—21no—
113C22⋊#92418—21no—
114C4×#92418C2311yescharacteristic
115C4×#92418C2311yescharacteristic
116C8×Dic61—21no—
117C2×#41×C61—21no—
118C22×D4×C61—21no—
119C22×D4×C61—21no—
120C2×D8×C61—21no—
121C2×D8×C61D411yescharacteristic
122C22×C8×C61—21no—
123C4⋊Q8×C61C2311yescharacteristic
124#127×C61C2311yescharacteristic
125#123×C61—41no—
126C22⋊Q8×C61—21no—
127#121×C61—21no—
128#121×C61—21no—
129#121×C61—21no—
130#120×C61—41no—
131C4×D4×C61C2311yescharacteristic
132C4×D4×C61C2311yescharacteristic
133C4×D4×C61C2311yescharacteristic
134C2×C4⋊C4×C61—21no—
135#107×C61—21no—
136#107×C61D411yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138#102×C61—21no—
139#102×C61—21no—
140#102×C61—21no—
141#102×C61—21no—
142#102×C61D411yescharacteristic
143#102×C61D411yescharacteristic
144C22⋊C8×C61—21no—
145C4×C8×C61C2311yescharacteristic
146C24×C61—41no—
147#41×C61—42no—
148#41×C61—81no—
149C2×Q8×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—41no—
154C2×D4×C61—41no—
155C2×D4×C61—42no—
156C2×D4×C61—42no—
157C2×D4×C61—41no—
158C2×D4×C61—81no—
159C2×D4×C61—81no—
160C2×D4×C61C2×D411yescharacteristic
161C2×D4×C61C2×D411yescharacteristic
162C2×D4×C61C2×D411yescharacteristic
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—41no—
167C2×C22⋊D61—41no—
168C2×C22⋊D61—41no—
169C22×Dic61—41no—
170#11758222—42no—
171#11758222—81no—
172C2×D244—21no—
173C2×D244—21no—
174C2×D244—21no—
175C2×C4×D61—41no—
176C2×Dic122—21no—
177C2×Dic122—42no—
178C2×Dic122—41no—
179C2×Dic122—81no—
180C2×Dic122C2×D411yescharacteristic
181D8×C61—41no—
182D8×C61—81no—
183C2×C8×C61—21no—
184C2×C8×C61—81no—
185C2×C8×C61C2×D411yescharacteristic
186C2×C8×C61C2×D411yescharacteristic
187C4⋊C4×C61—21no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—41no—
190C4⋊C4×C61C2×D411yescharacteristic
191C4⋊C4×C61C2×D411yescharacteristic
192C4⋊C4×C61C2×D411yescharacteristic
193C22⋊C4×C61—21no—
194C22⋊C4×C61—21no—
195C22⋊C4×C61—21no—
196C22⋊C4×C61—41no—
197C22⋊C4×C61—41no—
198C42×C61C2411yescharacteristic
199C22⋊Dic61—41no—
200#11758202—42no—
201#11758202—42no—
202#11758202—81no—
203#11758200—42no—
204#11758200—42no—
205#11758200D814yescomplemented
206#11758199—42no—
207#11758199—42no—
208#11758199—42no—
209#11758199—81no—
210#11758198—41no—
211C4⋊Dic61—21no—
212C4⋊Dic61—21no—
213C4⋊Dic61C2×D411yescharacteristic
214#11758196—21no—
215#11758196—41no—
216C4×Dic61—21no—
217#11758194—42no—
218#11758194—42no—
219C2×#92418—21no—
220C2×#92418—21no—
221C2×#92418—21no—
222C2×#92418—21no—
223C2×#92418C2×D411yescharacteristic
224C2×#92418C2×D411yescharacteristic
225C23×C61—21no—
226C23×C61—21no—
227C23×C61—21no—
228C23×C61—41no—
229C23×C61—82no—
230C23×C61—82no—
231C23×C61—161no—
232C22×D61—41no—
233Q8×C61—41no—
234Q8×C61—41no—
235D4×C61—21no—
236D4×C61—21no—
237D4×C61—21no—
238D4×C61—21no—
239D4×C61—21no—
240D4×C61—41no—
241D4×C61—41no—
242D4×C61—41no—
243D4×C61—41no—
244D4×C61—81no—
245D4×C61—82no—
246D4×C61—82no—
247D4×C61—82no—
248D4×C61C2×D812yes—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—82no—
260C2×C4×C61C22×D411yescharacteristic
261C2×C4×C61C22×D411yescharacteristic
262C2×C4×C61H(5,𝔽2)11yescharacteristic
263C22⋊D61—82no—
264C22⋊D61—161no—
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—41no—
268C2×Dic61—82no—
269D244—41no—
270D244—41no—
271D244—41no—
272D244—41no—
273D244—81no—
274C4×D61—82no—
275Dic122—21no—
276Dic122—41no—
277Dic122—41no—
278Dic122—82no—
279Dic122C2×D812yes—
280C8×C61—21no—
281C8×C61—21no—
282C8×C61—41no—
283#92418—21no—
284#92418—41no—
285#92418—41no—
286#92418—41no—
287#92418—41no—
288#92418C2×D812yes—
289#19886—611nomaximal, Sylow
290C22×C61—22no—
291C22×C61—41no—
292C22×C61—41no—
293C22×C61—41no—
294C22×C61—41no—
295C22×C61—41no—
296C22×C61—41no—
297C22×C61—41no—
298C22×C61—41no—
299C22×C61—81no—
300C22×C61—81no—
301C22×C61—81no—
302C22×C61—164no—
303C22×C61D4211yescharacteristic
304C2×D61—81no—
305C2×D61—81no—
306C2×D61—81no—
307C4×C61—21no—
308C4×C61—41no—
309C4×C61—41no—
310C4×C61—41no—
311C4×C61—81no—
312C4×C61C22×D811yescharacteristic
313C4×C61#57511yescharacteristic
314C4×C61#57611yescharacteristic
315C4×C61#57711yescharacteristic
316Dic61—22no—
317Dic61—41no—
318Dic61—81no—
319#3358—611no—
320#3294D6111yescharacteristic, complemented
321#3276—611no—
322#3274—611no—
323#1709—611no—
324#1689—611no—
325#1687—611no—
326#1682—611no—
327#1681—611no—
328#1641—611no—
329#1639—611no—
330#1627—611no—
331#1625—611no—
332#1589—611no—
333C8×SD16—611no—
334C2×C61—42no—
335C2×C61—81no—
336C2×C61—81no—
337C2×C61—161no—
338C2×C61#327511yescharacteristic
339C2×C61D4×D811yescharacteristic
340C2×C61#329011yescharacteristic
341D61—161no—
342C2×#137—1221no—
343C2×AGL(1,ℤ/8)—1221no—
344#550—611no—
345D4×Q8—611no—
346#547C2×D6111yescharacteristic
347D42C2×D6111yescharacteristic
348#494—611no—
349#493—611no—
350#486—611no—
351#486—611no—
352#486—611no—
353#486—1221no—
354#486C2×D6111yescharacteristic
355#480—21no—
356#474—611no—
357#474—1221no—
358#474C2×D6111yescharacteristic
359#470—1221no—
360#469—1221no—
361#466—21no—
362#462—611no—
363#461—611no—
364#460—611no—
365#459—611no—
366#459—611no—
367#459—1221no—
368#459C2×D6111yescharacteristic
369#452—1221no—
370#451—1221no—
371#449—1221no—
372#447—21no—
373#447—1221no—
374C8×Q8—611no—
375C4×SD16—611no—
376C4×D8—1221no—
377C4×D8C2×D6111yescharacteristic
378#436—611no—
379#436—611no—
380C8×D4C2×D6111yescharacteristic
381C2×#102—21no—
382#335—611no—
383#334—611no—
384#332—611no—
385#332—611no—
386#331—611no—
387#331—611no—
388Q8⋊C8—611no—
389D4⋊C8—611no—
390D4⋊C8—611no—
391D4⋊C8—611no—
392C82—611no—
393C61#1988611yescharacteristic, complemented, Sylow
394C2×#41—21no—
395C2×#41—1221no—
396C22×Q8—1221no—
397C22×D4—21no—
398C22×D4—21no—
399#137—2444no—
400AGL(1,ℤ/8)—2444no—
401C2×Q16—1221no—
402C2×Q16—1221no—
403C2×Q16—1221no—
404C2×SD16—611no—
405C2×SD16—1221no—
406C2×SD16—1221no—
407C2×D8—21no—
408C2×D8—1221no—
409C2×D8—1221no—
410C2×D8—1221no—
411C2×D8—1221no—
412C2×D8C22⋊D6111yescharacteristic
413C2×M16—1221no—
414C2×M16—1221no—
415C22×C8—21no—
416C4⋊Q8—611no—
417C4⋊Q8—1221no—
418C4⋊Q8C22×D6111yescharacteristic
419#127—611no—
420#127—1221no—
421#127C22×D6111yescharacteristic
422#123—41no—
423C22⋊Q8—21no—
424C22⋊Q8—1221no—
425C22⋊Q8—2441no—
426#121—21no—
427#121—21no—
428#121—21no—
429#121—1221no—
430#121—2441no—
431#120—41no—
432C4×Q8—611no—
433C4×D4—1221no—
434C4×D4—1221no—
435C4×D4C22×D6111yescharacteristic
436C4×D4C22×D6111yescharacteristic
437C4×D4C22×D6111yescharacteristic
438C2×C4⋊C4—21no—
439#107—21no—
440#107—1221no—
441#107C22⋊D6111yescharacteristic
442#106—611no—
443C4⋊C8—611no—
444C4⋊C8—611no—
445C4⋊C8—611no—
446C4⋊C8—1221no—
447C4⋊C8C22×D6111yescharacteristic
448#103—611no—
449#103—1221no—
450#103—1221no—
451#102—21no—
452#102—21no—
453#102—21no—
454#102—21no—
455#102—611no—
456#102—1221no—
457#102—1221no—
458#102—1221no—
459#102—1221no—
460#102—1221no—
461#102—1221no—
462#102—2441no—
463#102—2441no—
464#102C22⋊D6111yescharacteristic
465#102C22⋊D6111yescharacteristic
466C22⋊C8—21no—
467C22⋊C8—1221no—
468C22⋊C8—1221no—
469C4×C8—611no—
470C4×C8—611no—
471C4×C8—1221no—
472C4×C8C22×D6111yescharacteristic
473C24—41no—
474#41—42no—
475#41—81no—
476#41—4881no—
477#41—2442no—
478C2×Q8—21no—
479C2×Q8—611no—
480C2×Q8—1221no—
481C2×Q8—4881no—
482C2×Q8—2441no—
483C2×Q8—2442no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—41no—
488C2×D4—41no—
489C2×D4—42no—
490C2×D4—42no—
491C2×D4—41no—
492C2×D4—81no—
493C2×D4—81no—
494C2×D4—1221no—
495C2×D4—1221no—
496C2×D4—1221no—
497C2×D4—2441no—
498C2×D4—2441no—
499C2×D4D4×D6111yescharacteristic
500C2×D4C2×C22⋊D6111yescharacteristic
501C2×D4C2×C22⋊D6111yescharacteristic
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—41no—
506C22×C4—2441no—
507C22×C4—2441no—
508Q16—4881no—
509Q16—2442no—
510Q16—2442no—
511SD16—614no—
512SD16—2442no—
513SD16—2442no—
514D8—41no—
515D8—81no—
516D8—4881no—
517D8—2442no—
518D8—2442no—
519D8—2442no—
520M16—2442no—
521M16—2442no—
522C2×C8—21no—
523C2×C8—81no—
524C2×C8—611no—
525C2×C8—611no—
526C2×C8—1221no—
527C2×C8—1221no—
528C2×C8—1221no—
529C2×C8—1221no—
530C2×C8C2×C22⋊D6111yescharacteristic
531C2×C8C2×C22⋊D6111yescharacteristic
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—41no—
535C4⋊C4—611no—
536C4⋊C4—1221no—
537C4⋊C4—1221no—
538C4⋊C4—1221no—
539C4⋊C4—2441no—
540C4⋊C4D4×D6111yescharacteristic
541C4⋊C4C2×C22⋊D6111yescharacteristic
542C4⋊C4C2×C22⋊D6111yescharacteristic
543C22⋊C4—21no—
544C22⋊C4—21no—
545C22⋊C4—21no—
546C22⋊C4—41no—
547C22⋊C4—41no—
548C22⋊C4—2441no—
549C22⋊C4—2441no—
550C42—1221no—
551C42C23×D6111yescharacteristic
552C23—21no—
553C23—21no—
554C23—21no—
555C23—41no—
556C23—82no—
557C23—82no—
558C23—161no—
559C23—2441no—
560Q8—41no—
561Q8—41no—
562Q8—612no—
563Q8—1221no—
564Q8—4882no—
565Q8—2441no—
566Q8—2441no—
567D4—21no—
568D4—21no—
569D4—21no—
570D4—21no—
571D4—21no—
572D4—41no—
573D4—41no—
574D4—41no—
575D4—41no—
576D4—81no—
577D4—82no—
578D4—82no—
579D4—82no—
580D4—9761no—
581D4—4881no—
582D4—4882no—
583D4—2441no—
584D4—2441no—
585D4—2441no—
586D4—2441no—
587D4D8×D6112yes—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—82no—
599C2×C4—1221no—
600C2×C4—1221no—
601C2×C4—4882no—
602C2×C4—4882no—
603C2×C4—2441no—
604C2×C4C2×D4×D6111yescharacteristic
605C2×C4C22×C22⋊D6111yescharacteristic
606C2×C4#1451982211yescharacteristic
607C8—21no—
608C8—21no—
609C8—41no—
610C8—612no—
611C8—1221no—
612C8—2441no—
613C8—2441no—
614C8—2441no—
615C8—2441no—
616C22—22no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—164no—
629C22—4881no—
630C22—4881no—
631C22—4881no—
632C22D4×C22⋊D6111yescharacteristic
633C4—21no—
634C4—41no—
635C4—41no—
636C4—41no—
637C4—81no—
638C4—1222no—
639C4—4881no—
640C4—2441no—
641C4C2×D8×D6111yescharacteristic
642C4#1684056011yescharacteristic
643C4#1684056311yescharacteristic
644C4#1684057311yescharacteristic
645C2—42no—
646C2—81no—
647C2—81no—
648C2—161no—
649C2—9761no—
650C2#2145744611yescharacteristic
651C2D8×C22⋊D6111yescharacteristic
652C2#2145759911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3294C2
socleC22×C61D42
hypercenter#3294D61
hypocenterC61#19886
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3294

Complements

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

NH ≅ G/Ntype
1. #21458452C2semidirect
2. #21457461C2semidirect
3. #21457435C2semidirect
4. #21445423C2semidirect
5. #21445306C2semidirect
6. #21445296C2semidirect
7. #21445260C2semidirect
8. #21445256C2semidirect
9. #21445011C2semidirect
10. #21444998C2semidirect
11. #21444921C2semidirect
12. #21444908C2semidirect
13. #21444704C2semidirect
14. C8×#11758200C2semidirect
15. C61×#3294C2semidirect
19. D4×Dic122C22semidirect
20. #16840141C22semidirect
22. #16840110C22semidirect
23. #16840109C22semidirect
30. #16839969C22semidirect
34. #16839957C22semidirect
40. C8×Dic122C22semidirect
44. #16839840C22semidirect
45. #16839515C22semidirect
46. #16839512C22semidirect
47. #16839508C22semidirect
48. #16839507C22semidirect
50. #16839505C22semidirect
51. #16839492C22semidirect
54. D4⋊#92418C22semidirect
55. C8×#92418C22semidirect
205. #11758200D8semidirect
320. #3294D61semidirect
393. C61#19886semidirect

Maximal subgroups

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

subgroupindex
#214584522
#214574612
#214574352
#214454232
#214453062
#214452962
#214452602
#214452562
#214450112
#214449982
#214449212
#214449082
#214447042
C8×#117582002
C61×#32942
#1988661