Finite Group Databasebeta

← #29579137

Subgroups — #29579137

Order 15616.

856 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#21454162C211yesmaximal, characteristic
2#21445797C211yesmaximal, characteristic, complemented
3C2×#16839497C211yesmaximal, characteristic, complemented
4C2×#16839496C211yesmaximal, characteristic, complemented
5C2×#16839495C211yesmaximal, characteristic, complemented
6#95×Dic61C211yesmaximal, characteristic, complemented
7C2×C61×#327C211yesmaximal, characteristic, complemented
8C2×#14519773C411yescharacteristic, complemented
9C2×#14519751C2211yescharacteristic
10C2×#14519749—21no—
11C2×#14519749—21no—
12C22×C4×Dic61—21no—
13C22×C4×Dic61C2211yescharacteristic
14C2×#14519706—21no—
15C2×C22⋊#92418C2211yescharacteristic
16#16839665C411yescharacteristic, complemented
17#16839663C411yescharacteristic, complemented
18#16839662—21no—
19#16839662—21no—
20#16839631C411yescharacteristic, complemented
21C2×#14519684—21no—
22C2×#14519684C2211yescharacteristic
23#16839516—21no—
24#16839497—22no—
25#16839496—22no—
26#16839495—22no—
27C2×#121×C61C2211yescharacteristic
28C2×C22⋊C8×C61C2211yescharacteristic
29C2×#95×C61C2211yescharacteristic
30C61×#327—22no—
31C22×D244C2×C411yescharacteristic
32C22×C22⋊D61—21no—
33C22×C22⋊D61—21no—
34C22×C22⋊D61—21no—
35C23×Dic61—21no—
36C23×Dic61D411yescharacteristic
37C23×Dic61D411yescharacteristic
38C22×#92418—21no—
39#14519773—42no—
40#14519751—21no—
41#14519751—21no—
42#14519751—21no—
43#14519751—21no—
44#14519749—42no—
45#14519749—42no—
46#14519749—42no—
47#14519749—42no—
48C2×C4⋊Dic61C2×C411yescharacteristic
49C2×#11758196—21no—
50C2×#11758196—21no—
51C2×C22⋊Dic61—21no—
52C2×C22⋊Dic61—21no—
53C2×#11758198—21no—
54C2×#11758198—21no—
55C2×#11758198—21no—
56C2×C4×Dic61—24no—
57C2×C4×Dic61—42no—
58C2×C4×Dic61—42no—
59C2×C4×Dic61—42no—
60C2×C4×Dic61C2×C411yescharacteristic
61C2×C4×Dic61C2×C411yescharacteristic
62C2×C4×Dic61D411yescharacteristic
63C2×C4×Dic61D411yescharacteristic
64#14519706—42no—
65C22⋊#92418—21no—
66C22⋊#92418—21no—
67#14519684—24no—
68#14519684—21no—
69#14519684D412yescomplemented
70C22×D4×C61—21no—
71C22×D4×C61C2×C411yescharacteristic
72C23×C4×C61—21no—
73C23×C4×C61C2311yescharacteristic
74C22×C8×C61—21no—
75#121×C61—21no—
76#121×C61—21no—
77#121×C61—21no—
78#121×C61—21no—
79C2×C4⋊C4×C61C2×C411yescharacteristic
80C2×C22⋊C4×C61—21no—
81C22⋊C8×C61—21no—
82C22⋊C8×C61—21no—
83#95×C61—21no—
84#95×C61D412yescomplemented
85C24×C61—21no—
86C24×C61C2×D411yescharacteristic
87C23×D61—21no—
88C2×D4×C61—21no—
89C2×D4×C61—21no—
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C2×D4×C61—41no—
93C2×D4×C61—41no—
94C2×D4×C61—41no—
95C2×D4×C61—41no—
96C2×D4×C61—41no—
97C2×D4×C61—41no—
98C22×C4×C61—22no—
99C22×C4×C61—22no—
100C22×C4×C61—22no—
101C22×C4×C61—21no—
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×C61C22×C411yescharacteristic
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61#4111yescharacteristic
113C22×C4×C61#4111yescharacteristic
114C2×C22⋊D61—42no—
115C2×C22⋊D61—42no—
116C2×C22⋊D61—41no—
117C2×C22⋊D61—41no—
118C2×C22⋊D61—41no—
119C2×C22⋊D61—41no—
120C2×C22⋊D61—41no—
121C2×C22⋊D61—41no—
122C2×C22⋊D61—42no—
123C2×C22⋊D61—42no—
124C2×C22⋊D61—42no—
125C2×C22⋊D61—42no—
126C22×Dic61—22no—
127C22×Dic61—22no—
128C22×Dic61—22no—
129C22×Dic61—22no—
130C22×Dic61—22no—
131C22×Dic61—21no—
132C22×Dic61—21no—
133C22×Dic61—22no—
134C22×Dic61—21no—
135C22×Dic61—41no—
136C22×Dic61—41no—
137C22×Dic61—41no—
138C22×Dic61—41no—
139C22×Dic61—41no—
140C22×Dic61C22⋊C411yescharacteristic
141C22×Dic61C22⋊C411yescharacteristic
142C22×Dic61C22⋊C411yescharacteristic
143C22×Dic61C22⋊C411yescharacteristic
144C22×Dic61D812yes—
145C22×Dic61SD1612yes—
146C2×D244—21no—
147C2×D244—21no—
148C2×D244—41no—
149C2×D244—41no—
150C2×C8×C61—41no—
151C2×C8×C61—41no—
152C2×C8×C61—41no—
153C4⋊C4×C61—21no—
154C4⋊C4×C61—21no—
155C22⋊C4×C61—41no—
156C22⋊C4×C61—41no—
157C22⋊Dic61—42no—
158C22⋊Dic61—42no—
159#11758198—42no—
160#11758198—41no—
161#11758198—41no—
162#11758198—42no—
163C4⋊Dic61—21no—
164C4⋊Dic61—21no—
165#11758196—42no—
166#11758196—42no—
167C4×Dic61—22no—
168C4×Dic61—22no—
169C4×Dic61—41no—
170C4×Dic61—41no—
171C4×Dic61—48no—
172C2×#92418—41no—
173C2×#92418—41no—
174C2×#92418—41no—
175C23×C61—21no—
176C23×C61—21no—
177C23×C61—21no—
178C23×C61—21no—
179C23×C61—41no—
180C23×C61—41no—
181C23×C61—41no—
182C23×C61—41no—
183C23×C61—41no—
184C23×C61—41no—
185C23×C61—41no—
186C23×C61C2×C22⋊C411yescharacteristic
187C23×C61#12111yescharacteristic
188C23×C61#12111yescharacteristic
189C23×C61C2×D811yescharacteristic
190C23×C61C2×SD1611yescharacteristic
191C23×C61AGL(1,ℤ/8)11yescharacteristic
192C23×C61AGL(1,ℤ/8)11yescharacteristic
193C22×D61—41no—
194C22×D61—41no—
195C22×D61—41no—
196C22×D61—41no—
197C22×D61—41no—
198C22×D61—41no—
199C22×D61—41no—
200D4×C61—81no—
201D4×C61—81no—
202D4×C61—81no—
203D4×C61—81no—
204D4×C61—81no—
205D4×C61—81no—
206C2×C4×C61—21no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—24no—
211C2×C4×C61—41no—
212C2×C4×C61—41no—
213C2×C4×C61—41no—
214C2×C4×C61—41no—
215C2×C4×C61—42no—
216C2×C4×C61—42no—
217C2×C4×C61—42no—
218C2×C4×C61—42no—
219C2×C4×C61—42no—
220C2×C4×C61—42no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61C4×D411yescharacteristic
225C2×C4×C61C4×D411yescharacteristic
226C2×C4×C61#12411yescharacteristic
227C2×C4×C61#12711yescharacteristic
228C22⋊D61—84no—
229C22⋊D61—81no—
230C22⋊D61—81no—
231C22⋊D61—81no—
232C22⋊D61—81no—
233C22⋊D61—84no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—24no—
239C2×Dic61—24no—
240C2×Dic61—24no—
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—42no—
245C2×Dic61—42no—
246C2×Dic61—42no—
247C2×Dic61—42no—
248C2×Dic61—42no—
249C2×Dic61—42no—
250C2×Dic61—42no—
251C2×Dic61—42no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61#9912yes—
256C2×Dic61#10212yes—
257C2×Dic61#10212yes—
258C2×Dic61#10412yes—
259C2×Dic61#10412yes—
260D244—81no—
261D244—81no—
262C8×C61—81no—
263#92418—81no—
264#9712—611nomaximal, Sylow
265C22×C61—21no—
266C22×C61—21no—
267C22×C61—21no—
268C22×C61—21no—
269C22×C61—21no—
270C22×C61—21no—
271C22×C61—21no—
272C22×C61—21no—
273C22×C61—21no—
274C22×C61—21no—
275C22×C61—21no—
276C22×C61—21no—
277C22×C61—81no—
278C22×C61—81no—
279C22×C61—81no—
280C22×C61—81no—
281C22×C61—81no—
282C22×C61—81no—
283C22×C61—81no—
284C22×C61#39011yescharacteristic
285C22×C61C2×#9911yescharacteristic
286C22×C61#41011yescharacteristic
287C22×C61C2×#10211yescharacteristic
288C22×C61#41811yescharacteristic
289C22×C61C2×#10411yescharacteristic
290C22×C61C2×#10411yescharacteristic
291C22×C61#45911yescharacteristic
292C22×C61#45911yescharacteristic
293C22×C61#46011yescharacteristic
294C22×C61#46011yescharacteristic
295C2×D61—81no—
296C2×D61—81no—
297C2×D61—81no—
298C2×D61—81no—
299C2×D61—81no—
300C2×D61—81no—
301C2×D61—81no—
302C4×C61—21no—
303C4×C61—21no—
304C4×C61—21no—
305C4×C61—21no—
306C4×C61—44no—
307C4×C61—81no—
308Dic61—22no—
309Dic61—22no—
310Dic61—44no—
311Dic61—41no—
312Dic61—81no—
313Dic61#32714yescomplemented
314#2856—611no—
315#1797—611no—
316C2×#327—611no—
317C2×#327—611no—
318C2×#327—611no—
319C2×#327D6111yescharacteristic, complemented
320C4×#95—611no—
321C2×C61—21no—
322C2×C61—21no—
323C2×C61—21no—
324C2×C61—21no—
325C2×C61—161no—
326C2×C61C2×#32711yescharacteristic
327C2×C61#150211yescharacteristic
328C2×C61#150511yescharacteristic
329C2×C61#150711yescharacteristic
330C2×C61#196211yescharacteristic
331C2×C61#196411yescharacteristic
332C2×C61#198211yescharacteristic
333D61—161no—
334C2×#127—611no—
335C2×#121—611no—
336C2×#121—1221no—
337C2×#121—1221no—
338C2×#121C2×D6111yescharacteristic
339C22×C42—611no—
340C22×C42—1221no—
341C2×C4⋊C8—1221no—
342C2×C22⋊C8—611no—
343C2×C22⋊C8C2×D6111yescharacteristic
344#390—611no—
345#390—611no—
346#390—1221no—
347#390—1221no—
348#384—611no—
349C2×#95—611no—
350C2×#95—1221no—
351C2×#95C2×D6111yescharacteristic
352#336—1221no—
353#327—22no—
354#327—1222no—
355#327—1222no—
356#327—1222no—
357C61#971211yescharacteristic, complemented, Sylow
358C22×D4—21no—
359C22×D4—611no—
360C22×D4—1221no—
361C22×D4—1221no—
362C22×D4—1221no—
363C22×D4C4×D6111yescharacteristic
364C23×C4—21no—
365C23×C4—611no—
366C23×C4—611no—
367C23×C4—1221no—
368C23×C4C22×D6111yescharacteristic
369C22×C8—21no—
370C22×C8—1221no—
371#127—2442no—
372#121—21no—
373#121—21no—
374#121—21no—
375#121—21no—
376#121—1221no—
377#121—1221no—
378#121—1221no—
379#121—1221no—
380#121—2442no—
381#121—2442no—
382#121—2442no—
383#121—2442no—
384C2×C4⋊C4—611no—
385C2×C4⋊C4—1221no—
386C2×C4⋊C4—1221no—
387C2×C4⋊C4C4×D6111yescharacteristic
388C2×C22⋊C4—21no—
389C2×C22⋊C4—1221no—
390C2×C22⋊C4—1221no—
391C2×C22⋊C4—1221no—
392C2×C22⋊C4—1221no—
393C2×C22⋊C4—1221no—
394C2×C42—611no—
395C2×C42—611no—
396C2×C42—611no—
397C2×C42—611no—
398C2×C42—1224no—
399C2×C42—2442no—
400C2×C42—2442no—
401C2×C42—2442no—
402C4⋊C8—2442no—
403C22⋊C8—21no—
404C22⋊C8—21no—
405C22⋊C8—1221no—
406C22⋊C8—1221no—
407#95—21no—
408#95—612no—
409#95—1224no—
410#95—1221no—
411#95C22⋊D6112yescomplemented
412C24—21no—
413C24—1221no—
414C24D4×D6111yescharacteristic
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—1221no—
426C2×D4—1221no—
427C2×D4—2441no—
428C2×D4—2441no—
429C2×D4—2442no—
430C2×D4—2442no—
431C2×D4—2442no—
432C2×D4—2442no—
433C2×D4—2442no—
434C2×D4—2442no—
435C2×D4—2441no—
436C2×D4—2441no—
437C2×D4—2441no—
438C2×D4—2441no—
439C2×D4—2441no—
440C2×D4—2441no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—611no—
452C22×C4—611no—
453C22×C4—611no—
454C22×C4—612no—
455C22×C4—612no—
456C22×C4—611no—
457C22×C4—1222no—
458C22×C4—1222no—
459C22×C4—1222no—
460C22×C4—1222no—
461C22×C4—1222no—
462C22×C4—1222no—
463C22×C4—1221no—
464C22×C4—1221no—
465C22×C4—1221no—
466C22×C4—2441no—
467C22×C4—2441no—
468C22×C4—2441no—
469C22×C4—2441no—
470C22×C4—2441no—
471C22×C4C2×C4×D6111yescharacteristic
472C22×C4#1175822211yescharacteristic
473C22×C4D4×D6111yescharacteristic
474C22×C4D4×D6111yescharacteristic
475C22×C4#1175822411yescharacteristic
476C22×C4C2×C22⋊D6111yescharacteristic
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—2441no—
481C2×C8—2441no—
482C2×C8—2441no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—2442no—
488C4⋊C4—2442no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—2442no—
492C22⋊C4—2442no—
493C22⋊C4—2442no—
494C22⋊C4—2442no—
495C22⋊C4—2441no—
496C22⋊C4—2441no—
497C42—1222no—
498C42—1222no—
499C42—2441no—
500C42—2441no—
501C42—2448no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—2441no—
514C23—2441no—
515C23—2441no—
516C23—2441no—
517C23—2441no—
518C23—2441no—
519C23—2441no—
520C23C22⋊C4×D6111yescharacteristic
521C23#1451974911yescharacteristic
522C23#1451975011yescharacteristic
523C23D8×D6111yescharacteristic
524C23SD16×D6111yescharacteristic
525C23#1451980111yescharacteristic
526C23#1451980411yescharacteristic
527D4—81no—
528D4—81no—
529D4—81no—
530D4—81no—
531D4—81no—
532D4—81no—
533D4—4881no—
534D4—4881no—
535D4—4884no—
536D4—4884no—
537D4—4881no—
538D4—4881no—
539D4—4881no—
540D4—4881no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—24no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—612no—
560C2×C4—612no—
561C2×C4—612no—
562C2×C4—612no—
563C2×C4—612no—
564C2×C4—1224no—
565C2×C4—1224no—
566C2×C4—1221no—
567C2×C4—1221no—
568C2×C4—1221no—
569C2×C4—1221no—
570C2×C4—1224no—
571C2×C4—1221no—
572C2×C4—1221no—
573C2×C4—1221no—
574C2×C4—2442no—
575C2×C4—2442no—
576C2×C4—2441no—
577C2×C4—2441no—
578C2×C4—2441no—
579C2×C4—2442no—
580C2×C4—2442no—
581C2×C4—2442no—
582C2×C4—2442no—
583C2×C4—2442no—
584C2×C4—2442no—
585C2×C4#1451973711yescharacteristic
586C2×C4C4×C22⋊D6111yescharacteristic
587C2×C4#1451976311yescharacteristic
588C2×C4#1451977311yescharacteristic
589C8—81no—
590C8—4881no—
591C22—21no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—21no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22—4881no—
611C22—4881no—
612C22—4881no—
613C22—4881no—
614C22—4881no—
615C22—4881no—
616C22—4881no—
617C22#1683966211yescharacteristic
618C22#99×D6111yescharacteristic
619C22#1683973411yescharacteristic
620C22#102×D6111yescharacteristic
621C22#1683976511yescharacteristic
622C22#104×D6111yescharacteristic
623C22#104×D6111yescharacteristic
624C22#1683995511yescharacteristic
625C22#1683995611yescharacteristic
626C22#1683996011yescharacteristic
627C22#1683996111yescharacteristic
628C4—21no—
629C4—21no—
630C4—21no—
631C4—21no—
632C4—44no—
633C4—81no—
634C4—614no—
635C4—1222no—
636C4—1222no—
637C4—4881no—
638C4—2444no—
639C4—2441no—
640C2—21no—
641C2—21no—
642C2—21no—
643C2—21no—
644C2—161no—
645C2—9761no—
646C2#327×D6111yescharacteristic
647C2#2144431211yescharacteristic
648C2#2144432511yescharacteristic
649C2#2144433311yescharacteristic
650C2#2144664511yescharacteristic
651C2#2144665311yescharacteristic
652C2#2144674411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#327C2
socleC23×C61C2×C22⋊C4
prime radical#21454162C2
cosocleC23×C4×C61C23
hypercenterC2×#327D61
hypocenterC61#9712
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. #21445797C2semidirect
3. C2×#16839497C2semidirect
4. C2×#16839496C2semidirect
5. C2×#16839495C2semidirect
6. #95×Dic61C2semidirect
7. C2×C61×#327C2semidirect
8. C2×#14519773C4semidirect
16. #16839665C4semidirect
17. #16839663C4semidirect
20. #16839631C4semidirect
69. #14519684D4semidirect
84. #95×C61D4semidirect
313. Dic61#327semidirect
319. C2×#327D61semidirect
357. C61#9712semidirect
411. #95C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214541622
#214457972
C2×#168394972
C2×#168394962
C2×#168394952
#95×Dic612
C2×C61×#3272
#971261