Finite Group Databasebeta

← #29583288

Subgroups — #29583288

Order 15616.

772 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21451553C211yesmaximal, characteristic
2#21446136C211yesmaximal, characteristic, complemented
3#21446012C211yesmaximal, characteristic, complemented
4C2×#16839495C211yesmaximal, characteristic, complemented
5C2×#16839486C211yesmaximal, characteristic, complemented
6#21443698C211yesmaximal, characteristic, complemented
7C61×#1439C211yesmaximal, characteristic, complemented
8C2×#14519751C2211yescharacteristic
9C2×#14519746—21no—
10C2×#14519708—21no—
11C2×#14519697—21no—
12C2×C22⋊#92418C2211yescharacteristic
13C2×C22⋊#92418C2211yescharacteristic
14#16839687—21no—
15#16839678—21no—
16#16839678—21no—
17#16839671—21no—
18#16839641—21no—
19#16839622C2211yescharacteristic
20#16839524—21no—
21#16839524—21no—
22#16839495—22no—
23#16839486—22no—
24C22×C4⋊C4×C61C2211yescharacteristic
25C22×C22⋊C4×C61—21no—
26C22×C22⋊C4×C61C2211yescharacteristic
27C2×#95×C61—21no—
28C2×#95×C61C2211yescharacteristic
29C22×D244D411yescharacteristic
30C22×C22⋊D61—21no—
31C22×C22⋊D61—21no—
32C22×C22⋊D61—21no—
33C22×#92418—21no—
34C22×#92418—21no—
35#14519751—21no—
36#14519751—21no—
37#14519751—21no—
38#14519751—21no—
39#14519746—42no—
40#14519746—42no—
41C2×C4⋊Dic61D411yescharacteristic
42C2×C4⋊Dic61D411yescharacteristic
43C2×C4⋊Dic61D411yescharacteristic
44C2×C22⋊Dic61—21no—
45C2×C22⋊Dic61—21no—
46C2×C22⋊Dic61—21no—
47C2×#11758198—21no—
48C2×#11758198—21no—
49C2×#11758198—21no—
50#14519708—42no—
51#14519697—42no—
52C22⋊#92418—21no—
53C22⋊#92418—21no—
54C22⋊#92418—21no—
55C22⋊#92418D412yescomplemented
56#14519684—21no—
57#14519684—21no—
58#14519684—21no—
59C25×C61D411yescharacteristic
60C23×C4×C61—21no—
61C23×C4×C61—21no—
62C23×C4×C61D411yescharacteristic
63C23×C4×C61C2311yescharacteristic
64C2×C4⋊C4×C61—21no—
65C2×C4⋊C4×C61—21no—
66C2×C4⋊C4×C61—42no—
67C2×C22⋊C4×C61—21no—
68C2×C22⋊C4×C61—21no—
69C2×C22⋊C4×C61—21no—
70C2×C22⋊C4×C61—21no—
71C2×C22⋊C4×C61—21no—
72C2×C22⋊C4×C61—21no—
73C2×C22⋊C4×C61—42no—
74C2×C22⋊C4×C61—42no—
75C2×C22⋊C4×C61—42no—
76#95×C61—21no—
77#95×C61—21no—
78#95×C61—42no—
79C24×C61—21no—
80C24×C61—21no—
81C24×C61—21no—
82C24×C61—21no—
83C24×C61—21no—
84C24×C61—21no—
85C24×C61—41no—
86C24×C61—41no—
87C24×C61—41no—
88C24×C61—41no—
89C24×C61SD1612yes—
90C24×C61C2×D411yescharacteristic
91C23×D61—21no—
92C22×C4×C61—22no—
93C22×C4×C61—22no—
94C22×C4×C61—21no—
95C22×C4×C61—21no—
96C22×C4×C61—21no—
97C22×C4×C61—41no—
98C22×C4×C61—41no—
99C22×C4×C61—41no—
100C22×C4×C61—41no—
101C22×C4×C61—41no—
102C22×C4×C61—41no—
103C22×C4×C61—41no—
104C22×C4×C61—41no—
105C22×C4×C61—41no—
106C22×C4×C61—41no—
107C22×C4×C61—41no—
108C22×C4×C61—41no—
109C22×C4×C61—41no—
110C22×C4×C61—41no—
111C22×C4×C61—41no—
112C22×C4×C61—41no—
113C22×C4×C61C2×D411yescharacteristic
114C22×C4×C61C2×D411yescharacteristic
115C22×C4×C61C2×D411yescharacteristic
116C22×C4×C61#4111yescharacteristic
117C22×C4×C61#4111yescharacteristic
118C22×C4×C61#4111yescharacteristic
119C2×C22⋊D61—42no—
120C2×C22⋊D61—42no—
121C2×C22⋊D61—41no—
122C2×C22⋊D61—41no—
123C2×C22⋊D61—41no—
124C2×C22⋊D61—41no—
125C2×C22⋊D61—41no—
126C2×C22⋊D61—41no—
127C2×C22⋊D61—81no—
128C2×C22⋊D61—81no—
129C2×C22⋊D61—81no—
130C2×C22⋊D61—81no—
131C22×Dic61—21no—
132C22×Dic61—21no—
133C22×Dic61—21no—
134C2×D244—21no—
135C2×D244—21no—
136C2×D244—41no—
137C2×D244—41no—
138C4⋊C4×C61—22no—
139C4⋊C4×C61—22no—
140C4⋊C4×C61—41no—
141C4⋊C4×C61—41no—
142C22⋊C4×C61—48no—
143C22⋊C4×C61—41no—
144C22⋊C4×C61—41no—
145C22⋊C4×C61—41no—
146C22⋊C4×C61—41no—
147C22⋊Dic61—42no—
148C22⋊Dic61—42no—
149C22⋊Dic61—41no—
150C22⋊Dic61—41no—
151#11758198—41no—
152#11758198—41no—
153#11758198—81no—
154#11758198—81no—
155C4⋊Dic61—21no—
156C4⋊Dic61—21no—
157C4⋊Dic61—41no—
158C4⋊Dic61—41no—
159C2×#92418—22no—
160C2×#92418—41no—
161C2×#92418—41no—
162C2×#92418—41no—
163C2×#92418—41no—
164C2×#92418—41no—
165C23×C61—21no—
166C23×C61—21no—
167C23×C61—21no—
168C23×C61—21no—
169C23×C61—22no—
170C23×C61—22no—
171C23×C61—22no—
172C23×C61—42no—
173C23×C61—42no—
174C23×C61—42no—
175C23×C61—42no—
176C23×C61—42no—
177C23×C61—42no—
178C23×C61—41no—
179C23×C61—41no—
180C23×C61—41no—
181C23×C61—41no—
182C23×C61—41no—
183C23×C61—41no—
184C23×C61—41no—
185C23×C61—41no—
186C23×C61—81no—
187C23×C61—81no—
188C23×C61—81no—
189C23×C61—81no—
190C23×C61—81no—
191C23×C61—81no—
192C23×C61#12011yescharacteristic
193C23×C61#12111yescharacteristic
194C23×C61#12311yescharacteristic
195C23×C61C2×SD1611yescharacteristic
196C23×C61#13511yescharacteristic
197C23×C61AGL(1,ℤ/8)11yescharacteristic
198C23×C61AGL(1,ℤ/8)11yescharacteristic
199C22×D61—41no—
200C22×D61—41no—
201C22×D61—41no—
202C22×D61—41no—
203C22×D61—41no—
204C22×D61—41no—
205C22×D61—41no—
206C2×C4×C61—21no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—41no—
211C2×C4×C61—41no—
212C2×C4×C61—41no—
213C2×C4×C61—41no—
214C2×C4×C61—42no—
215C2×C4×C61—42no—
216C2×C4×C61—42no—
217C2×C4×C61—42no—
218C2×C4×C61—42no—
219C2×C4×C61—42no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—42no—
224C2×C4×C61—81no—
225C2×C4×C61—81no—
226C2×C4×C61—81no—
227C2×C4×C61—81no—
228C2×C4×C61—81no—
229C2×C4×C61—81no—
230C2×C4×C61—81no—
231C2×C4×C61—81no—
232C2×C4×C61—81no—
233C2×C4×C61#12111yescharacteristic
234C2×C4×C61#12111yescharacteristic
235C2×C4×C61#12311yescharacteristic
236C2×C4×C61#12411yescharacteristic
237C22⋊D61—84no—
238C22⋊D61—84no—
239C22⋊D61—81no—
240C22⋊D61—81no—
241C22⋊D61—81no—
242C22⋊D61—81no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252D244—42no—
253D244—81no—
254#92418—42no—
255#92418—81no—
256#10395—611nomaximal, Sylow
257C22×C61—21no—
258C22×C61—21no—
259C22×C61—21no—
260C22×C61—21no—
261C22×C61—21no—
262C22×C61—21no—
263C22×C61—21no—
264C22×C61—21no—
265C22×C61—21no—
266C22×C61—21no—
267C22×C61—21no—
268C22×C61—21no—
269C22×C61—44no—
270C22×C61—42no—
271C22×C61—42no—
272C22×C61—42no—
273C22×C61—82no—
274C22×C61—82no—
275C22×C61—82no—
276C22×C61—81no—
277C22×C61—81no—
278C22×C61—81no—
279C22×C61—81no—
280C22×C61#39411yescharacteristic
281C22×C61#44911yescharacteristic
282C22×C61#45011yescharacteristic
283C22×C61#45311yescharacteristic
284C22×C61#45511yescharacteristic
285C22×C61B(4,𝔽2)11yescharacteristic
286C22×C61#45811yescharacteristic
287C22×C61#46511yescharacteristic
288C22×C61#46911yescharacteristic
289C22×C61#48111yescharacteristic
290C22×C61#48211yescharacteristic
291C2×D61—81no—
292C2×D61—81no—
293C2×D61—81no—
294C2×D61—81no—
295C2×D61—81no—
296C2×D61—81no—
297C2×D61—81no—
298C4×C61—21no—
299C4×C61—21no—
300C4×C61—21no—
301C4×C61—21no—
302C4×C61—82no—
303C4×C61—82no—
304C4×C61—81no—
305Dic61—81no—
306Dic61—81no—
307Dic61—81no—
308#2617—611no—
309#1874—611no—
310#1853—611no—
311C2×#327—611no—
312C2×#323—611no—
313#1439D6111yescharacteristic, complemented
314#1294—611no—
315C2×C61—21no—
316C2×C61—21no—
317C2×C61—21no—
318C2×C61—21no—
319C2×C61—82no—
320C2×C61#160011yescharacteristic
321C2×C61#160111yescharacteristic
322C2×C61#161211yescharacteristic
323C2×C61#161311yescharacteristic
324C2×C61#203411yescharacteristic
325C2×C61#203711yescharacteristic
326C2×C61#204411yescharacteristic
327D61—161no—
328C2×#121—611no—
329C2×#120—1221no—
330C22×C4⋊C4C2×D6111yescharacteristic
331C22×C22⋊C4—21no—
332C22×C22⋊C4C2×D6111yescharacteristic
333C2×#106—1221no—
334C2×#102—1221no—
335C2×C22⋊C8—611no—
336C2×C22⋊C8—611no—
337#397—1221no—
338#394—1221no—
339#394—1221no—
340#392—1221no—
341#386—1221no—
342#380—611no—
343C2×#95—21no—
344C2×#95C2×D6111yescharacteristic
345#340—1221no—
346#340—1221no—
347#327—1222no—
348#323—1222no—
349C61#1039511yescharacteristic, complemented, Sylow
350C25C22⋊D6111yescharacteristic
351C22×D4—611no—
352C22×D4—1221no—
353C22×D4—1221no—
354C22×D4—1221no—
355C23×C4—21no—
356C23×C4—21no—
357C23×C4C22⋊D6111yescharacteristic
358C23×C4C22×D6111yescharacteristic
359C22×C8—1221no—
360C22×C8—1221no—
361#121—1221no—
362#121—1221no—
363#121—1221no—
364#121—1221no—
365#120—2442no—
366#120—2442no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—611no—
371C2×C4⋊C4—611no—
372C2×C4⋊C4—611no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—1221no—
383C2×C22⋊C4—1221no—
384C2×C22⋊C4—1221no—
385C2×C22⋊C4—1221no—
386C2×C22⋊C4—1221no—
387C2×C22⋊C4—1221no—
388#106—2442no—
389#102—2442no—
390C22⋊C8—612no—
391C22⋊C8—1221no—
392C22⋊C8—1221no—
393C22⋊C8—1221no—
394#95—21no—
395#95—21no—
396#95—42no—
397#95—1221no—
398#95—1221no—
399#95—1221no—
400C24—21no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—41no—
407C24—41no—
408C24—41no—
409C24—41no—
410C24—1221no—
411C24#1175820112yes—
412C24C2×C22⋊D6111yescharacteristic
413C2×D4—1221no—
414C2×D4—1221no—
415C2×D4—4881no—
416C2×D4—4881no—
417C2×D4—4881no—
418C2×D4—4881no—
419C2×D4—2441no—
420C2×D4—2441no—
421C2×D4—2442no—
422C2×D4—2442no—
423C2×D4—2441no—
424C2×D4—2441no—
425C2×D4—2441no—
426C2×D4—2441no—
427C2×D4—2441no—
428C2×D4—2441no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—1221no—
451C22×C4—1221no—
452C22×C4—1221no—
453C22×C4#1175822211yescharacteristic
454C22×C4#1175822211yescharacteristic
455C22×C4D4×D6111yescharacteristic
456C22×C4D4×D6111yescharacteristic
457C22×C4D4×D6111yescharacteristic
458C22×C4#1175822411yescharacteristic
459C2×C8—1222no—
460C2×C8—2441no—
461C2×C8—2441no—
462C2×C8—2441no—
463C2×C8—2441no—
464C2×C8—2441no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—2441no—
472C4⋊C4—2441no—
473C22⋊C4—48no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—4881no—
479C22⋊C4—4881no—
480C22⋊C4—2442no—
481C22⋊C4—2442no—
482C22⋊C4—2441no—
483C22⋊C4—2441no—
484C22⋊C4—2441no—
485C22⋊C4—2441no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—81no—
508C23—81no—
509C23—81no—
510C23—81no—
511C23—81no—
512C23—81no—
513C23—2441no—
514C23—2441no—
515C23—2441no—
516C23—2441no—
517C23—2441no—
518C23—2441no—
519C23—2441no—
520C23#1451974511yescharacteristic
521C23#1451974911yescharacteristic
522C23#1451976011yescharacteristic
523C23C2×#1175820111yescharacteristic
524C23#1451979711yescharacteristic
525C23#1451980211yescharacteristic
526C23#1451980311yescharacteristic
527D4—4881no—
528D4—4884no—
529D4—4884no—
530D4—4881no—
531D4—4881no—
532D4—4881no—
533D4—4881no—
534D4—2442no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—42no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—81no—
554C2×C4—81no—
555C2×C4—81no—
556C2×C4—81no—
557C2×C4—81no—
558C2×C4—81no—
559C2×C4—81no—
560C2×C4—81no—
561C2×C4—81no—
562C2×C4—2441no—
563C2×C4—2441no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4#1451975011yescharacteristic
572C2×C4#1451975011yescharacteristic
573C2×C4#1451975911yescharacteristic
574C2×C4#1451976311yescharacteristic
575C8—4881no—
576C8—2442no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—44no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—82no—
594C22—82no—
595C22—82no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—4881no—
601C22—4881no—
602C22—4881no—
603C22—4881no—
604C22—4881no—
605C22—4881no—
606C22—4881no—
607C22#1683967711yescharacteristic
608C22#1683990511yescharacteristic
609C22#1683991211yescharacteristic
610C22#1683992911yescharacteristic
611C22#1683993911yescharacteristic
612C22#1683994811yescharacteristic
613C22#1683995111yescharacteristic
614C22#1683999311yescharacteristic
615C22#1684001311yescharacteristic
616C22#1684008011yescharacteristic
617C22#1684008611yescharacteristic
618C4—21no—
619C4—21no—
620C4—21no—
621C4—21no—
622C4—82no—
623C4—81no—
624C4—82no—
625C4—4881no—
626C4—4881no—
627C4—4881no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—82no—
633C2—9761no—
634C2#2144476311yescharacteristic
635C2#2144477011yescharacteristic
636C2#2144483111yescharacteristic
637C2#2144483811yescharacteristic
638C2#2144700811yescharacteristic
639C2#2144702911yescharacteristic
640C2#2144706811yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1439C2
socleC23×C61#120
prime radical#21451553C2
hypercenter#1439D61
hypocenterC61#10395
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. #21446136C2semidirect
3. #21446012C2semidirect
4. C2×#16839495C2semidirect
5. C2×#16839486C2semidirect
6. #21443698C2semidirect
7. C61×#1439C2semidirect
55. C22⋊#92418D4semidirect
313. #1439D61semidirect
349. C61#10395semidirect

Maximal subgroups

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

subgroupindex
#214515532
#214461362
#214460122
C2×#168394952
C2×#168394862
#214436982
C61×#14392
#1039561