Finite Group Databasebeta

← #29583285

Subgroups — #29583285

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#21446137C211yesmaximal, characteristic, complemented
2#21446011C211yesmaximal, characteristic, complemented
3C2×#16839496C211yesmaximal, characteristic, complemented
4C2×#16839486C211yesmaximal, characteristic, complemented
5#21444064C211yesmaximal, characteristic, complemented
6#21443697C211yesmaximal, characteristic, complemented
7C61×#2617C211yesmaximal, characteristic
8C22×C4⋊Dic61C2211yescharacteristic
9C22×C22⋊Dic61—21no—
10C2×#14519708—21no—
11C2×#14519698—21no—
12C2×C22⋊#92418C2211yescharacteristic
13C2×C22⋊#92418C2211yescharacteristic
14C2×#14519684—21no—
15C2×#14519684C2211yescharacteristic
16#16839524—21no—
17#16839524—21no—
18#16839496—22no—
19#16839486—22no—
20C2×#121×C61C2211yescharacteristic
21C2×#120×C61—21no—
22C22×C22⋊C4×C61C2211yescharacteristic
23C61×#397—21no—
24C61×#394—21no—
25C61×#394—21no—
26C61×#392—21no—
27C61×#386—21no—
28C61×#380C2211yescharacteristic
29C23×Dic61—21no—
30C23×Dic61—21no—
31C22×#92418—21no—
32C22×#92418—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61—42no—
36C2×C22⋊Dic61—42no—
37C2×C22⋊Dic61—42no—
38C2×C22⋊Dic61—42no—
39#14519708—42no—
40#14519698—42no—
41C22⋊#92418—21no—
42C22⋊#92418—21no—
43C22⋊#92418—21no—
44C22⋊#92418D412yescomplemented
45#14519684—21no—
46#14519684—21no—
47#14519684—42no—
48C25×C61D411yescharacteristic
49C22×D4×C61—21no—
50C22×D4×C61—21no—
51C22×D4×C61—21no—
52C22×D4×C61D411yescharacteristic
53C23×C4×C61D411yescharacteristic
54C23×C4×C61C2311yescharacteristic
55#121×C61—21no—
56#121×C61—21no—
57#121×C61—21no—
58#121×C61—21no—
59#120×C61—42no—
60#120×C61—42no—
61C2×C4⋊C4×C61D411yescharacteristic
62C2×C4⋊C4×C61D411yescharacteristic
63C2×C4⋊C4×C61D411yescharacteristic
64C2×C22⋊C4×C61—21no—
65C2×C22⋊C4×C61—21no—
66C2×C22⋊C4×C61—21no—
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—21no—
74C2×C22⋊C4×C61—21no—
75C2×C22⋊C4×C61—21no—
76#95×C61—21no—
77#95×C61—21no—
78#95×C61—21no—
79C24×C61—21no—
80C24×C61—21no—
81C24×C61—21no—
82C24×C61—21no—
83C24×C61—21no—
84C24×C61—21no—
85C24×C61—21no—
86C24×C61—41no—
87C24×C61—41no—
88C24×C61—41no—
89C24×C61—41no—
90C24×C61SD1612yes—
91C24×C61C2×D411yescharacteristic
92C2×D4×C61—21no—
93C2×D4×C61—21no—
94C2×D4×C61—41no—
95C2×D4×C61—41no—
96C2×D4×C61—42no—
97C2×D4×C61—42no—
98C2×D4×C61—41no—
99C2×D4×C61—41no—
100C2×D4×C61—41no—
101C2×D4×C61—41no—
102C2×D4×C61—41no—
103C2×D4×C61—41no—
104C2×D4×C61—81no—
105C2×D4×C61—81no—
106C2×D4×C61—81no—
107C2×D4×C61—81no—
108C22×C4×C61—21no—
109C22×C4×C61—21no—
110C22×C4×C61—21no—
111C22×C4×C61—21no—
112C22×C4×C61—21no—
113C22×C4×C61—21no—
114C22×C4×C61—41no—
115C22×C4×C61—41no—
116C22×C4×C61—41no—
117C22×C4×C61—41no—
118C22×C4×C61C2×D411yescharacteristic
119C22×C4×C61C2×D411yescharacteristic
120C22×C4×C61C2×D411yescharacteristic
121C22×C4×C61#4111yescharacteristic
122C22×C4×C61#4111yescharacteristic
123C22×C4×C61#4111yescharacteristic
124C22×Dic61—22no—
125C22×Dic61—22no—
126C22×Dic61—41no—
127C22×Dic61—41no—
128C22×Dic61—41no—
129C22×Dic61—41no—
130C22×Dic61—41no—
131C22×Dic61—41no—
132C22×Dic61—41no—
133C22×Dic61—41no—
134C22×Dic61—41no—
135C22×Dic61—41no—
136C22×Dic61—41no—
137C22×Dic61—41no—
138C4⋊C4×C61—21no—
139C4⋊C4×C61—21no—
140C4⋊C4×C61—41no—
141C4⋊C4×C61—41no—
142C22⋊C4×C61—42no—
143C22⋊C4×C61—42no—
144C22⋊C4×C61—41no—
145C22⋊C4×C61—41no—
146C22⋊C4×C61—41no—
147C22⋊C4×C61—41no—
148C22⋊C4×C61—41no—
149C22⋊C4×C61—41no—
150C22⋊C4×C61—41no—
151C22⋊C4×C61—41no—
152C22⋊C4×C61—81no—
153C22⋊C4×C61—81no—
154C22⋊Dic61—48no—
155C4⋊Dic61—22no—
156C4⋊Dic61—22no—
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—41no—
187C23×C61—41no—
188C23×C61—41no—
189C23×C61—41no—
190C23×C61—41no—
191C23×C61—41no—
192C23×C61—41no—
193C23×C61—81no—
194C23×C61—81no—
195C23×C61—81no—
196C23×C61—81no—
197C23×C61—81no—
198C23×C61—81no—
199C23×C61#12011yescharacteristic
200C23×C61#12111yescharacteristic
201C23×C61#12311yescharacteristic
202C23×C61C2×SD1611yescharacteristic
203C23×C61#13511yescharacteristic
204C23×C61AGL(1,ℤ/8)11yescharacteristic
205C23×C61AGL(1,ℤ/8)11yescharacteristic
206D4×C61—42no—
207D4×C61—81no—
208D4×C61—84no—
209D4×C61—84no—
210D4×C61—81no—
211D4×C61—81no—
212D4×C61—81no—
213D4×C61—81no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—42no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—81no—
236C2×C4×C61#12111yescharacteristic
237C2×C4×C61#12111yescharacteristic
238C2×C4×C61#12311yescharacteristic
239C2×C4×C61#12411yescharacteristic
240C2×Dic61—42no—
241C2×Dic61—42no—
242C2×Dic61—42no—
243C2×Dic61—42no—
244C2×Dic61—42no—
245C2×Dic61—42no—
246C2×Dic61—81no—
247C2×Dic61—81no—
248C2×Dic61—81no—
249C2×Dic61—81no—
250C2×Dic61—81no—
251C2×Dic61—81no—
252C2×Dic61—81no—
253C2×Dic61—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—81no—
281C22×C61—81no—
282C22×C61—81no—
283C22×C61—81no—
284C22×C61—81no—
285C22×C61—81no—
286C22×C61—81no—
287C22×C61#39411yescharacteristic
288C22×C61#44911yescharacteristic
289C22×C61#45011yescharacteristic
290C22×C61#45311yescharacteristic
291C22×C61#45511yescharacteristic
292C22×C61B(4,𝔽2)11yescharacteristic
293C22×C61#45811yescharacteristic
294C22×C61#46511yescharacteristic
295C22×C61#46911yescharacteristic
296C22×C61#48111yescharacteristic
297C22×C61#48211yescharacteristic
298C4×C61—21no—
299C4×C61—21no—
300C4×C61—21no—
301C4×C61—21no—
302C4×C61—81no—
303C4×C61—81no—
304C4×C61—81no—
305C4×C61—81no—
306Dic61—82no—
307Dic61—82no—
308#2617D6111yescharacteristic
309#1874—611no—
310#1853—611no—
311C2×#327—611no—
312C2×#323—611no—
313#1439—611no—
314#1294—611no—
315C2×C61—21no—
316C2×C61—21no—
317C2×C61—21no—
318C2×C61—21no—
319C2×C61—82no—
320C2×C61—161no—
321C2×C61#160011yescharacteristic
322C2×C61#160111yescharacteristic
323C2×C61#161211yescharacteristic
324C2×C61#161311yescharacteristic
325C2×C61#203411yescharacteristic
326C2×C61#203711yescharacteristic
327C2×C61#204411yescharacteristic
328C2×#121C2×D6111yescharacteristic
329C2×#120—21no—
330C22×C4⋊C4—611no—
331C22×C22⋊C4—1221no—
332C22×C22⋊C4C2×D6111yescharacteristic
333C2×#106—1221no—
334C2×#102—1221no—
335C2×C22⋊C8—611no—
336C2×C22⋊C8—611no—
337#397—21no—
338#394—21no—
339#394—21no—
340#392—21no—
341#386—21no—
342#380C2×D6111yescharacteristic
343C2×#95—611no—
344C2×#95—1221no—
345#340—1221no—
346#340—1221no—
347#327—1222no—
348#323—1222no—
349C61#1039511yescharacteristic, complemented, Sylow
350C25C22⋊D6111yescharacteristic
351C22×D4—21no—
352C22×D4—21no—
353C22×D4—21no—
354C22×D4C22⋊D6111yescharacteristic
355C23×C4—1221no—
356C23×C4—1221no—
357C23×C4C22⋊D6111yescharacteristic
358C23×C4C22×D6111yescharacteristic
359C22×C8—1221no—
360C22×C8—1221no—
361#121—21no—
362#121—21no—
363#121—21no—
364#121—21no—
365#120—42no—
366#120—42no—
367C2×C4⋊C4—1221no—
368C2×C4⋊C4—1221no—
369C2×C4⋊C4—2442no—
370C2×C4⋊C4C22⋊D6111yescharacteristic
371C2×C4⋊C4C22⋊D6111yescharacteristic
372C2×C4⋊C4C22⋊D6111yescharacteristic
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—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—2442no—
386C2×C22⋊C4—2442no—
387C2×C22⋊C4—2442no—
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—21no—
397#95—1221no—
398#95—1221no—
399#95—2442no—
400C24—21no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—41no—
408C24—41no—
409C24—41no—
410C24—41no—
411C24#1175820012yes—
412C24C2×C22⋊D6111yescharacteristic
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—42no—
418C2×D4—42no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—81no—
426C2×D4—81no—
427C2×D4—81no—
428C2×D4—81no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—1222no—
440C22×C4—1222no—
441C22×C4—2441no—
442C22×C4—2441no—
443C22×C4—2441no—
444C22×C4—2441no—
445C22×C4—2441no—
446C22×C4—2441no—
447C22×C4—2441no—
448C22×C4—2441no—
449C22×C4—2441no—
450C22×C4—2441no—
451C22×C4—2441no—
452C22×C4—2441no—
453C22×C4D4×D6111yescharacteristic
454C22×C4#1175822411yescharacteristic
455C22×C4#1175822411yescharacteristic
456C22×C4#1175822411yescharacteristic
457C22×C4C2×C22⋊D6111yescharacteristic
458C22×C4C2×C22⋊D6111yescharacteristic
459C2×C8—1222no—
460C2×C8—2441no—
461C2×C8—2441no—
462C2×C8—2441no—
463C2×C8—2441no—
464C2×C8—2441no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—1222no—
470C4⋊C4—1222no—
471C4⋊C4—2441no—
472C4⋊C4—2441no—
473C22⋊C4—42no—
474C22⋊C4—42no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—81no—
484C22⋊C4—81no—
485C22⋊C4—2448no—
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—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—81no—
515C23—81no—
516C23—81no—
517C23—81no—
518C23—81no—
519C23—81no—
520C23#1451974611yescharacteristic
521C23#1451974911yescharacteristic
522C23#1451975811yescharacteristic
523C23C2×#1175820011yescharacteristic
524C23#1451979711yescharacteristic
525C23#1451980211yescharacteristic
526C23#1451980311yescharacteristic
527D4—42no—
528D4—81no—
529D4—84no—
530D4—84no—
531D4—81no—
532D4—81no—
533D4—81no—
534D4—81no—
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—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—81no—
557C2×C4—4881no—
558C2×C4—4881no—
559C2×C4—4881no—
560C2×C4—4881no—
561C2×C4—4881no—
562C2×C4—4881no—
563C2×C4—4881no—
564C2×C4—4881no—
565C2×C4—2442no—
566C2×C4—2442no—
567C2×C4—2442no—
568C2×C4—2442no—
569C2×C4—2442no—
570C2×C4—2442no—
571C2×C4#1451974811yescharacteristic
572C2×C4#1451974911yescharacteristic
573C2×C4#1451975811yescharacteristic
574C2×C4#1451976411yescharacteristic
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—81no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22#1683967611yescharacteristic
608C22#1683990711yescharacteristic
609C22#1683991311yescharacteristic
610C22#1683993011yescharacteristic
611C22#1683994011yescharacteristic
612C22#1683994911yescharacteristic
613C22#1683995211yescharacteristic
614C22#1683998911yescharacteristic
615C22#1684001311yescharacteristic
616C22#1684007811yescharacteristic
617C22#1684008311yescharacteristic
618C4—21no—
619C4—21no—
620C4—21no—
621C4—21no—
622C4—81no—
623C4—81no—
624C4—81no—
625C4—81no—
626C4—4882no—
627C4—4882no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—82no—
633C2—161no—
634C2#2144476511yescharacteristic
635C2#2144477111yescharacteristic
636C2#2144483311yescharacteristic
637C2#2144483911yescharacteristic
638C2#2144700511yescharacteristic
639C2#2144702611yescharacteristic
640C2#2144706711yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
Fitting, prime radicalC61×#2617C2
socleC23×C61#120
hypercenter#2617D61
hypocenterC61#10395
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2617

Complements

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

NH ≅ G/Ntype
1. #21446137C2semidirect
2. #21446011C2semidirect
3. C2×#16839496C2semidirect
4. C2×#16839486C2semidirect
5. #21444064C2semidirect
6. #21443697C2semidirect
44. C22⋊#92418D4semidirect
349. C61#10395semidirect

Maximal subgroups

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

subgroupindex
#214461372
#214460112
C2×#168394962
C2×#168394862
#214440642
#214436972
C61×#26172
#1039561