Finite Group Databasebeta

← #29662433

Subgroups — #29662433

Order 15616.

672 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456374C211yesmaximal, characteristic, complemented
2#21455609C211yesmaximal, characteristic, complemented
3#21455268C211yesmaximal, characteristic
4#21454775C211yesmaximal, characteristic, complemented
5#21445252C211yesmaximal, characteristic, complemented
6#21445245C211yesmaximal, characteristic, complemented
7#21445234C211yesmaximal, characteristic, complemented
8#21445227C211yesmaximal, characteristic, complemented
9#21445200C211yesmaximal, characteristic, complemented
10#21445193C211yesmaximal, characteristic, complemented
11#21445166C211yesmaximal, characteristic, complemented
12#21445159C211yesmaximal, characteristic, complemented
13C2×#16839512C211yesmaximal, characteristic, complemented
14#21444474C211yesmaximal, characteristic, complemented
15C61×#1540C211yesmaximal, characteristic, complemented
16C2×#14519797—21no—
17#16840319C2211yescharacteristic
18C4×#11758222C2211yescharacteristic
19#16840158C2211yescharacteristic
20#16840134C2211yescharacteristic
21#16840114C2211yescharacteristic
22#16840108C2211yescharacteristic
23#16840070—21no—
24#16840063—21no—
25#16840058C2211yescharacteristic
26#16840053C2211yescharacteristic
27#16840048C2211yescharacteristic
28#16840043C2211yescharacteristic
29#16839989—21no—
30#16839989—21no—
31#16839981—21no—
32#16839974—21no—
33#16839969C2211yescharacteristic
34#16839964C2211yescharacteristic
35#16839959C2211yescharacteristic
36#16839954C2211yescharacteristic
37#16839886C2211yescharacteristic
38#16839886C2211yescharacteristic
39C4×#11758200—21no—
40C4×#11758200—21no—
41#16839827C2211yescharacteristic
42#16839827C2211yescharacteristic
43#16839825—21no—
44#16839825—21no—
45#16839813—21no—
46#16839800—21no—
47C2×C4⋊#92418C2211yescharacteristic
48#16839759—21no—
49#16839758—21no—
50C2×C4×#92418C2211yescharacteristic
51C4×C8×D61—21no—
52#16839512C2211yescharacteristic
53#16839512C2211yescharacteristic
54#16839512C2211yescharacteristic
55#16839512C2211yescharacteristic
56#16839510C2211yescharacteristic
57#16839510C2211yescharacteristic
58#16839509C2211yescharacteristic
59#16839509C2211yescharacteristic
60C61×#532C2211yescharacteristic
61C61×#431C2211yescharacteristic
62C2×C4⋊C8×C61C2211yescharacteristic
63C61×#332C2211yescharacteristic
64C61×#332C2211yescharacteristic
65C61×#331C2211yescharacteristic
66C61×#331C2211yescharacteristic
67C2×#11758222D411yescharacteristic
68#14519797—44no—
69C2×#11758202—21no—
70C2×#11758200—21no—
71C2×#11758200—21no—
72C2×#11758200—21no—
73C2×#11758201—21no—
74C2×#11758199—21no—
75C22×#92418—21no—
76C22×#92418D411yescharacteristic
77C22×#92418D411yescharacteristic
78C2×C8×D61—21no—
79C2×C8×D61—21no—
80#14519777C2311yescharacteristic
81#14519777C2311yescharacteristic
82#14519769—21no—
83#14519756—21no—
84#14519756—21no—
85C4×Dic122—21no—
86C4×Dic122—21no—
87C4×Dic122D411yescharacteristic
88C4×Dic122C2311yescharacteristic
89C4×D244D411yescharacteristic
90C4×D244C2311yescharacteristic
91C4×C22⋊D61—21no—
92C4×C22⋊D61—21no—
93#14519736—21no—
94#14519736D411yescharacteristic
95#14519734—21no—
96C42×D61—21no—
97#14519711—21no—
98#14519711—21no—
99#14519709—21no—
100#14519709—21no—
101#14519708—21no—
102#14519708—21no—
103C4⋊#92418—21no—
104C4⋊#92418C2311yescharacteristic
105C4⋊#92418C2311yescharacteristic
106#14519706—21no—
107#14519706—21no—
108#14519702—21no—
109#14519702—21no—
110#14519701—21no—
111#14519701—21no—
112#14519700—21no—
113#14519700—21no—
114#14519699—21no—
115#14519699—21no—
116#14519698—21no—
117#14519698—21no—
118#14519698—21no—
119#14519698—21no—
120#14519689—21no—
121#14519689—21no—
122C4×#92418D411yescharacteristic
123C4×#92418D411yescharacteristic
124C4×#92418C2311yescharacteristic
125C4×#92418C2311yescharacteristic
126C8×Dic61—21no—
127C8×Dic61—21no—
128C2×#41×C61—21no—
129C22×C8×C61—21no—
130C4⋊Q8×C61C2311yescharacteristic
131#127×C61C2311yescharacteristic
132#124×C61—21no—
133#121×C61—21no—
134#121×C61—21no—
135C4×D4×C61—21no—
136C4×D4×C61—21no—
137C2×C42×C61C2311yescharacteristic
138C4⋊C8×C61—21no—
139C4⋊C8×C61C2311yescharacteristic
140C4⋊C8×C61C2311yescharacteristic
141C4⋊C8×C61C2311yescharacteristic
142C4⋊C8×C61C2311yescharacteristic
143C22⋊C8×C61—21no—
144C4×C8×C61—21no—
145#41×C61—42no—
146#41×C61—42no—
147C2×Q8×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—41no—
152C22×C4×C61—41no—
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61#4111yescharacteristic
156C2×C22⋊D61—21no—
157#11758222—22no—
158#11758222SD1614yescomplemented
159C2×D244C2×D411yescharacteristic
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C4×D61—21no—
163C2×Dic122—21no—
164C2×Dic122—21no—
165C2×Dic122C2×D411yescharacteristic
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—42no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C22⋊C4×C61—41no—
174C22⋊C4×C61—41no—
175C42×C61C2×D411yescharacteristic
176C42×C61C2×D411yescharacteristic
177C42×C61#4111yescharacteristic
178C42×C61C2411yescharacteristic
179C22⋊Dic61—21no—
180C22⋊Dic61—41no—
181#11758202—42no—
182#11758201—42no—
183#11758200—42no—
184#11758200—42no—
185#11758200—42no—
186#11758199—42no—
187#11758198—21no—
188#11758198—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61C2×D411yescharacteristic
194C4⋊Dic61C2×D411yescharacteristic
195#11758196—21no—
196#11758196—21no—
197#11758196—41no—
198#11758196—41no—
199C4×Dic61—21no—
200C4×Dic61—21no—
201C4×Dic61—21no—
202C4×Dic61—41no—
203C2×#92418—22no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—41no—
207C2×#92418—42no—
208C2×#92418C2×D411yescharacteristic
209C2×#92418C2×D411yescharacteristic
210C2×#92418C2×D411yescharacteristic
211C2×#92418C2×D411yescharacteristic
212C8×D61—42no—
213C8×D61—42no—
214C23×C61—41no—
215C23×C61#12111yescharacteristic
216C22×D61—21no—
217Q8×C61—41no—
218Q8×C61—41no—
219D4×C61—41no—
220D4×C61—41no—
221D4×C61—41no—
222D4×C61—41no—
223D4×C61—81no—
224D4×C61—82no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—82no—
230C2×C4×C61#12111yescharacteristic
231C2×C4×C61#12111yescharacteristic
232C2×C4×C61#12111yescharacteristic
233C2×C4×C61C2×SD1612yes—
234C2×C4×C61#13512yes—
235C2×C4×C61C22×D411yescharacteristic
236C2×C4×C61C22×D411yescharacteristic
237C2×C4×C61C2×#4111yescharacteristic
238C22⋊D61—24no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244D244—21no—
245D244C2×SD1612yes—
246C4×D61—24no—
247C4×D61—42no—
248C4×D61—41no—
249C4×D61—41no—
250Dic122—21no—
251Dic122—41no—
252Dic122—41no—
253Dic122—81no—
254Dic122C2×SD1612yes—
255C8×C61—41no—
256C8×C61—41no—
257C8×C61—41no—
258C8×C61—41no—
259#92418—21no—
260#92418—21no—
261#92418—21no—
262#92418—41no—
263#92418—41no—
264#92418#13512yescomplemented
265#19124—611nomaximal, Sylow
266C22×C61—21no—
267C22×C61—21no—
268C22×C61—81no—
269C22×C61—81no—
270C22×C61—81no—
271C22×C61#46512yes—
272C22×C61C2×#12111yescharacteristic
273C2×D61—22no—
274C2×D61—41no—
275C2×D61—41no—
276C4×C61—21no—
277C4×C61—21no—
278C4×C61—21no—
279C4×C61—81no—
280C4×C61#46512yes—
281C4×C61C22×SD1611yescharacteristic
282C4×C61C2×#13511yescharacteristic
283C4×C61C2×#13511yescharacteristic
284C4×C61#57511yescharacteristic
285Dic61—22no—
286Dic61—41no—
287Dic61—41no—
288Dic61—81no—
289Dic61—81no—
290#3167—611no—
291#3076—611no—
292#3035—611no—
293C8×#41—611no—
294#1680—611no—
295#1679—611no—
296#1678—611no—
297#1677—611no—
298#1672—611no—
299#1671—611no—
300#1666—611no—
301#1665—611no—
302C2×#334—611no—
303#1542—611no—
304#1540D6111yescharacteristic, complemented
305C2×C61—22no—
306C2×C61—161no—
307C2×C61#303511yescharacteristic
308C2×C61C2×#46511yescharacteristic
309C2×C61#306711yescharacteristic
310D61—42no—
311C2×#135—1221no—
312#533—611no—
313#532C2×D6111yescharacteristic
314C4×#41—611no—
315#498—611no—
316#492—611no—
317#487—611no—
318#486—611no—
319#479—1221no—
320#478—1221no—
321#477—611no—
322#476—611no—
323#475—611no—
324#474—611no—
325#465—1221no—
326#465—1221no—
327#464—1221no—
328#463—1221no—
329#462—611no—
330#461—611no—
331#460—611no—
332#459—611no—
333C8×Q8—611no—
334C8×Q8—611no—
335C4×SD16—1221no—
336C4×SD16—1221no—
337C8×D4—611no—
338C8×D4—611no—
339C8×D4—1221no—
340C8×D4—1221no—
341#431—1221no—
342#431C2×D6111yescharacteristic
343#427—1221no—
344C2×C4⋊C8—611no—
345C2×C4⋊C8C2×D6111yescharacteristic
346#416—1221no—
347#416—1221no—
348C2×C4×C8—611no—
349C2×C4×C8—1221no—
350#334—611no—
351#334—611no—
352#334—611no—
353#334—611no—
354#333—611no—
355#333—611no—
356#332—611no—
357#332—611no—
358#332C2×D6111yescharacteristic
359#332C2×D6111yescharacteristic
360#331C2×D6111yescharacteristic
361#331C2×D6111yescharacteristic
362C61#1912411yescharacteristic, complemented, Sylow
363C2×#41—21no—
364C2×#41—611no—
365#135—2444no—
366C2×Q16—1221no—
367C2×SD16—1221no—
368C2×SD16—1221no—
369C2×SD16—1221no—
370C2×SD16—1221no—
371C2×D8—1221no—
372C22×C8—21no—
373C22×C8—611no—
374C22×C8—611no—
375C22×C8—1221no—
376C22×C8—1221no—
377C22×C8—1221no—
378C4⋊Q8—611no—
379C4⋊Q8—611no—
380C4⋊Q8C22×D6111yescharacteristic
381#127C22×D6111yescharacteristic
382#125—1221no—
383#124—21no—
384C22⋊Q8—1221no—
385C22⋊Q8—1221no—
386#121—21no—
387#121—21no—
388C4×Q8—611no—
389C4×Q8—611no—
390C4×Q8—1221no—
391C4×Q8—1221no—
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—611no—
395C4×D4—611no—
396C4×D4—1221no—
397C4×D4—1221no—
398#117—611no—
399#117—1221no—
400#117—1221no—
401C2×C42—1221no—
402C2×C42C22×D6111yescharacteristic
403#107—1221no—
404#107—1221no—
405#106—1221no—
406#106—1221no—
407#106—1221no—
408#106—1221no—
409C4⋊C8—21no—
410C4⋊C8—611no—
411C4⋊C8—611no—
412C4⋊C8—1221no—
413C4⋊C8—1221no—
414C4⋊C8—1221no—
415C4⋊C8C22×D6111yescharacteristic
416C4⋊C8C22×D6111yescharacteristic
417C4⋊C8C22×D6111yescharacteristic
418C4⋊C8C22×D6111yescharacteristic
419#103—1221no—
420#103—1221no—
421#103—1221no—
422#103—1221no—
423#103—1221no—
424#103—1221no—
425#102—1221no—
426#102—1221no—
427#102—1221no—
428#102—1221no—
429#102—1221no—
430#102—1221no—
431C22⋊C8—21no—
432C22⋊C8—1221no—
433C22⋊C8—1221no—
434C4×C8—21no—
435C4×C8—611no—
436C4×C8—611no—
437C4×C8—611no—
438C4×C8—611no—
439C4×C8—1221no—
440C4×C8—1221no—
441#41—42no—
442#41—42no—
443#41—614no—
444#41—1222no—
445C2×Q8—21no—
446C2×Q8—611no—
447C2×Q8—1221no—
448C2×Q8—1221no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—41no—
453C2×D4—611no—
454C2×D4—1221no—
455C22×C4—41no—
456C22×C4—1221no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4#1175822211yescharacteristic
460C22×C4D4×D6111yescharacteristic
461C22×C4D4×D6111yescharacteristic
462Q16—2442no—
463SD16—2442no—
464SD16—2442no—
465SD16—2442no—
466SD16—2442no—
467D8—2442no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—42no—
473C2×C8—611no—
474C2×C8—611no—
475C2×C8—611no—
476C2×C8—611no—
477C2×C8—1222no—
478C2×C8—1221no—
479C2×C8—1221no—
480C2×C8—2442no—
481C2×C8—2442no—
482C2×C8—2441no—
483C2×C8—2442no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—611no—
487C4⋊C4—611no—
488C4⋊C4—1221no—
489C4⋊C4—1221no—
490C4⋊C4—1221no—
491C4⋊C4—1221no—
492C4⋊C4—1221no—
493C4⋊C4—1221no—
494C4⋊C4—2441no—
495C4⋊C4—2441no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—1221no—
499C22⋊C4—1221no—
500C22⋊C4—1221no—
501C22⋊C4—2441no—
502C42—1221no—
503C42—1221no—
504C42—1221no—
505C42—2441no—
506C42#1175822211yescharacteristic
507C42D4×D6111yescharacteristic
508C42D4×D6111yescharacteristic
509C42C23×D6111yescharacteristic
510C23—41no—
511C23—1221no—
512C23#1451975011yescharacteristic
513Q8—41no—
514Q8—41no—
515Q8—612no—
516Q8—1221no—
517Q8—4881no—
518Q8—2441no—
519Q8—2441no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—81no—
525D4—82no—
526D4—612no—
527D4—1224no—
528D4—1221no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—82no—
534C2×C4—1221no—
535C2×C4—1224no—
536C2×C4—1221no—
537C2×C4—1221no—
538C2×C4—2442no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4#1451975011yescharacteristic
544C2×C4#1451975011yescharacteristic
545C2×C4#1451975011yescharacteristic
546C2×C4SD16×D6112yes—
547C2×C4#1451979612yes—
548C2×C4C2×D4×D6111yescharacteristic
549C2×C4C2×D4×D6111yescharacteristic
550C2×C4C2×#1175822211yescharacteristic
551C8—41no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—612no—
556C8—1221no—
557C8—1221no—
558C8—1221no—
559C8—2441no—
560C8—2441no—
561C22—21no—
562C22—21no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—1222no—
567C22—2441no—
568C22—2441no—
569C22#1683999012yes—
570C22C2×#1451975011yescharacteristic
571C4—21no—
572C4—21no—
573C4—21no—
574C4—81no—
575C4—1222no—
576C4—4881no—
577C4—4881no—
578C4—2441no—
579C4—2441no—
580C4#1683999012yes—
581C4C2×SD16×D6111yescharacteristic
582C4#135×D6111yescharacteristic
583C4C2×#1451979611yescharacteristic
584C4#1684055911yescharacteristic
585C2—22no—
586C2—161no—
587C2—2442no—
588C2#2145527211yescharacteristic
589C2C2×#1683999011yescharacteristic
590C2#2145553811yescharacteristic
subgroupG/H
centerC2×C4#14519750
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1540C2
socleC22×C61C2×#121
prime radical#21455268C2
hypercenter#1540D61
hypocenterC61#19124
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1540

Complements

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

NH ≅ G/Ntype
1. #21456374C2semidirect
2. #21455609C2semidirect
4. #21454775C2semidirect
5. #21445252C2semidirect
6. #21445245C2semidirect
7. #21445234C2semidirect
8. #21445227C2semidirect
9. #21445200C2semidirect
10. #21445193C2semidirect
11. #21445166C2semidirect
12. #21445159C2semidirect
13. C2×#16839512C2semidirect
14. #21444474C2semidirect
15. C61×#1540C2semidirect
158. #11758222SD16semidirect
264. #92418#135semidirect
304. #1540D61semidirect
362. C61#19124semidirect

Maximal subgroups

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

subgroupindex
#214563742
#214556092
#214552682
#214547752
#214452522
#214452452
#214452342
#214452272
#214452002
#214451932
#214451662
#214451592
C2×#168395122
#214444742
C61×#15402
#1912461