Finite Group Databasebeta

← #29579150

Subgroups — #29579150

Order 15616.

764 conjugacy classes of subgroups.

The subgroup lattice has 648 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#21444044C211yesmaximal, characteristic, complemented
7C2×C61×#327C211yesmaximal, characteristic, complemented
8C2×#14519773C411yescharacteristic, complemented
9C2×#14519751C2211yescharacteristic
10C2×#14519749—21no—
11C2×#14519749—21no—
12C22×C4×Dic61C2211yescharacteristic
13C2×#14519706—21no—
14C2×C22⋊#92418C2211yescharacteristic
15#16839665C411yescharacteristic, complemented
16#16839663C411yescharacteristic, complemented
17#16839662—21no—
18#16839662—21no—
19#16839631C411yescharacteristic, complemented
20C2×#14519684—21no—
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—42no—
57C2×C4×Dic61C2×C411yescharacteristic
58C2×C4×Dic61C2×C411yescharacteristic
59C2×C4×Dic61D411yescharacteristic
60C2×C4×Dic61D411yescharacteristic
61#14519706—42no—
62C22⋊#92418—21no—
63C22⋊#92418—21no—
64#14519684—21no—
65#14519684—42no—
66#14519684—42no—
67#14519684D412yescomplemented
68C22×D4×C61—21no—
69C22×D4×C61C2×C411yescharacteristic
70C23×C4×C61—21no—
71C23×C4×C61C2311yescharacteristic
72C22×C8×C61—21no—
73#121×C61—21no—
74#121×C61—21no—
75#121×C61—21no—
76#121×C61—21no—
77C2×C4⋊C4×C61C2×C411yescharacteristic
78C2×C22⋊C4×C61—21no—
79C22⋊C8×C61—21no—
80C22⋊C8×C61—21no—
81#95×C61—21no—
82#95×C61D412yescomplemented
83C24×C61—21no—
84C24×C61C2×D411yescharacteristic
85C23×D61—21no—
86C2×D4×C61—21no—
87C2×D4×C61—21no—
88C2×D4×C61—41no—
89C2×D4×C61—41no—
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C2×D4×C61—41no—
93C2×D4×C61—41no—
94C2×D4×C61—41no—
95C2×D4×C61—41no—
96C22×C4×C61—21no—
97C22×C4×C61—22no—
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×C61C22×C411yescharacteristic
107C22×C4×C61C2×D411yescharacteristic
108C22×C4×C61C2×D411yescharacteristic
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61#4111yescharacteristic
111C22×C4×C61#4111yescharacteristic
112C2×C22⋊D61—42no—
113C2×C22⋊D61—42no—
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—
124C22×Dic61—21no—
125C22×Dic61—21no—
126C22×Dic61—22no—
127C22×Dic61—21no—
128C22×Dic61—22no—
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—
138C22×Dic61C22⋊C411yescharacteristic
139C22×Dic61C22⋊C411yescharacteristic
140C22×Dic61C22⋊C411yescharacteristic
141C22×Dic61C22⋊C411yescharacteristic
142C22×Dic61D812yes—
143C22×Dic61SD1612yes—
144C2×D244—21no—
145C2×D244—21no—
146C2×D244—41no—
147C2×D244—41no—
148C2×C8×C61—41no—
149C2×C8×C61—41no—
150C2×C8×C61—41no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—21no—
153C22⋊C4×C61—41no—
154C22⋊C4×C61—41no—
155C22⋊Dic61—42no—
156C22⋊Dic61—42no—
157#11758198—42no—
158#11758198—41no—
159#11758198—41no—
160#11758198—42no—
161C4⋊Dic61—21no—
162C4⋊Dic61—21no—
163#11758196—42no—
164#11758196—42no—
165C4×Dic61—22no—
166C4×Dic61—22no—
167C4×Dic61—41no—
168C4×Dic61—41no—
169C2×#92418—41no—
170C2×#92418—41no—
171C2×#92418—41no—
172C23×C61—21no—
173C23×C61—21no—
174C23×C61—21no—
175C23×C61—21no—
176C23×C61—41no—
177C23×C61—41no—
178C23×C61—41no—
179C23×C61—41no—
180C23×C61—41no—
181C23×C61—41no—
182C23×C61—41no—
183C23×C61C2×C22⋊C411yescharacteristic
184C23×C61#12111yescharacteristic
185C23×C61#12111yescharacteristic
186C23×C61C2×D811yescharacteristic
187C23×C61C2×SD1611yescharacteristic
188C23×C61AGL(1,ℤ/8)11yescharacteristic
189C23×C61AGL(1,ℤ/8)11yescharacteristic
190C22×D61—41no—
191C22×D61—41no—
192C22×D61—41no—
193C22×D61—41no—
194C22×D61—41no—
195C22×D61—41no—
196C22×D61—41no—
197D4×C61—81no—
198D4×C61—81no—
199D4×C61—81no—
200D4×C61—81no—
201D4×C61—81no—
202D4×C61—81no—
203C2×C4×C61—21no—
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—21no—
207C2×C4×C61—41no—
208C2×C4×C61—41no—
209C2×C4×C61—41no—
210C2×C4×C61—41no—
211C2×C4×C61—42no—
212C2×C4×C61—42no—
213C2×C4×C61—41no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—42no—
217C2×C4×C61—81no—
218C2×C4×C61—81no—
219C2×C4×C61—81no—
220C2×C4×C61—81no—
221C2×C4×C61C4×D411yescharacteristic
222C2×C4×C61C4×D411yescharacteristic
223C2×C4×C61#12411yescharacteristic
224C2×C4×C61#12711yescharacteristic
225C22⋊D61—84no—
226C22⋊D61—84no—
227C22⋊D61—81no—
228C22⋊D61—81no—
229C22⋊D61—81no—
230C22⋊D61—81no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—42no—
241C2×Dic61—42no—
242C2×Dic61—42no—
243C2×Dic61—42no—
244C2×Dic61—42no—
245C2×Dic61—42no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—42no—
250C2×Dic61—81no—
251C2×Dic61—81no—
252C2×Dic61—81no—
253C2×Dic61—81no—
254C2×Dic61#9912yes—
255C2×Dic61#10212yes—
256C2×Dic61#10212yes—
257D244—81no—
258D244—81no—
259C8×C61—81no—
260#92418—81no—
261#9715—611nomaximal, Sylow
262C22×C61—21no—
263C22×C61—21no—
264C22×C61—21no—
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—81no—
275C22×C61—81no—
276C22×C61—81no—
277C22×C61—81no—
278C22×C61—81no—
279C22×C61—81no—
280C22×C61—81no—
281C22×C61#39011yescharacteristic
282C22×C61C2×#9911yescharacteristic
283C22×C61#41011yescharacteristic
284C22×C61C2×#10211yescharacteristic
285C22×C61#41811yescharacteristic
286C22×C61#42111yescharacteristic
287C22×C61#42111yescharacteristic
288C22×C61#45911yescharacteristic
289C22×C61#45911yescharacteristic
290C22×C61#46011yescharacteristic
291C22×C61#46011yescharacteristic
292C2×D61—81no—
293C2×D61—81no—
294C2×D61—81no—
295C2×D61—81no—
296C2×D61—81no—
297C2×D61—81no—
298C2×D61—81no—
299C4×C61—21no—
300C4×C61—21no—
301C4×C61—21no—
302C4×C61—21no—
303C4×C61—82no—
304C4×C61—81no—
305Dic61—22no—
306Dic61—22no—
307Dic61—22no—
308Dic61—41no—
309Dic61—82no—
310Dic61—81no—
311#2856—611no—
312#1797—611no—
313C2×#327—611no—
314C2×#327—611no—
315C2×#327—611no—
316C2×#327D6111yescharacteristic, complemented
317#1434—611no—
318C2×C61—21no—
319C2×C61—21no—
320C2×C61—21no—
321C2×C61—21no—
322C2×C61—161no—
323C2×C61#151011yescharacteristic
324C2×C61#151411yescharacteristic
325C2×C61#151711yescharacteristic
326C2×C61#151911yescharacteristic
327C2×C61#196311yescharacteristic
328C2×C61#196411yescharacteristic
329C2×C61#198211yescharacteristic
330D61—161no—
331C2×#127—611no—
332C2×#121—611no—
333C2×#121—1221no—
334C2×#121—1221no—
335C2×#121C2×D6111yescharacteristic
336C22×C42—611no—
337C2×C4⋊C8—1221no—
338C2×C22⋊C8—611no—
339C2×C22⋊C8C2×D6111yescharacteristic
340#390—611no—
341#390—611no—
342#390—1221no—
343#390—1221no—
344#384—611no—
345C2×#95—611no—
346C2×#95—1221no—
347C2×#95—1221no—
348C2×#95C2×D6111yescharacteristic
349#336—1221no—
350#327—22no—
351#327—1222no—
352#327—1222no—
353#327—1222no—
354C61#971511yescharacteristic, complemented, Sylow
355C22×D4—21no—
356C22×D4—611no—
357C22×D4—1221no—
358C22×D4—1221no—
359C22×D4—1221no—
360C22×D4C4×D6111yescharacteristic
361C23×C4—21no—
362C23×C4—611no—
363C23×C4—611no—
364C23×C4—1221no—
365C23×C4C22×D6111yescharacteristic
366C22×C8—21no—
367C22×C8—1221no—
368#127—2442no—
369#121—21no—
370#121—21no—
371#121—21no—
372#121—21no—
373#121—1221no—
374#121—1221no—
375#121—1221no—
376#121—1221no—
377#121—2442no—
378#121—2442no—
379#121—2442no—
380#121—2442no—
381C2×C4⋊C4—611no—
382C2×C4⋊C4—1221no—
383C2×C4⋊C4—1221no—
384C2×C4⋊C4C4×D6111yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—1221no—
387C2×C22⋊C4—1221no—
388C2×C22⋊C4—1221no—
389C2×C22⋊C4—1221no—
390C2×C22⋊C4—1221no—
391C2×C42—611no—
392C2×C42—611no—
393C2×C42—611no—
394C2×C42—611no—
395C2×C42—2442no—
396C4⋊C8—2442no—
397C22⋊C8—21no—
398C22⋊C8—21no—
399C22⋊C8—1221no—
400C22⋊C8—1221no—
401#95—21no—
402#95—612no—
403#95—1221no—
404#95—2442no—
405#95—2442no—
406#95C22⋊D6112yescomplemented
407C24—21no—
408C24—1221no—
409C24D4×D6111yescharacteristic
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—1221no—
421C2×D4—1221no—
422C2×D4—2441no—
423C2×D4—2441no—
424C2×D4—2442no—
425C2×D4—2442no—
426C2×D4—2442no—
427C2×D4—2442no—
428C2×D4—2442no—
429C2×D4—2442no—
430C2×D4—2441no—
431C2×D4—2441no—
432C2×D4—2441no—
433C2×D4—2441no—
434C2×D4—2441no—
435C2×D4—2441no—
436C22×C4—21no—
437C22×C4—22no—
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—611no—
447C22×C4—611no—
448C22×C4—611no—
449C22×C4—612no—
450C22×C4—612no—
451C22×C4—611no—
452C22×C4—1222no—
453C22×C4—1221no—
454C22×C4—1221no—
455C22×C4—1221no—
456C22×C4—1222no—
457C22×C4—2441no—
458C22×C4—2441no—
459C22×C4—2441no—
460C22×C4—2441no—
461C22×C4—2441no—
462C22×C4—2441no—
463C22×C4—2441no—
464C22×C4—2441no—
465C22×C4—2441no—
466C22×C4C2×C4×D6111yescharacteristic
467C22×C4#1175822211yescharacteristic
468C22×C4D4×D6111yescharacteristic
469C22×C4D4×D6111yescharacteristic
470C22×C4#1175822411yescharacteristic
471C22×C4C2×C22⋊D6111yescharacteristic
472C2×C8—41no—
473C2×C8—41no—
474C2×C8—41no—
475C2×C8—2441no—
476C2×C8—2441no—
477C2×C8—2441no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4—2442no—
483C4⋊C4—2442no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—2442no—
487C22⋊C4—2442no—
488C22⋊C4—2442no—
489C22⋊C4—2442no—
490C22⋊C4—2441no—
491C22⋊C4—2441no—
492C42—1222no—
493C42—1222no—
494C42—2441no—
495C42—2441no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—2441no—
508C23—2441no—
509C23—2441no—
510C23—2441no—
511C23—2441no—
512C23—2441no—
513C23—2441no—
514C23C22⋊C4×D6111yescharacteristic
515C23#1451974911yescharacteristic
516C23#1451975011yescharacteristic
517C23D8×D6111yescharacteristic
518C23SD16×D6111yescharacteristic
519C23#1451980111yescharacteristic
520C23#1451980411yescharacteristic
521D4—81no—
522D4—81no—
523D4—81no—
524D4—81no—
525D4—81no—
526D4—81no—
527D4—4881no—
528D4—4881no—
529D4—4884no—
530D4—4884no—
531D4—4881no—
532D4—4881no—
533D4—4881no—
534D4—4881no—
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—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—81no—
550C2×C4—81no—
551C2×C4—81no—
552C2×C4—81no—
553C2×C4—612no—
554C2×C4—612no—
555C2×C4—612no—
556C2×C4—1221no—
557C2×C4—1221no—
558C2×C4—1221no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—1221no—
562C2×C4—1221no—
563C2×C4—1221no—
564C2×C4—1221no—
565C2×C4—4881no—
566C2×C4—4881no—
567C2×C4—4881no—
568C2×C4—4881no—
569C2×C4—2442no—
570C2×C4—2442no—
571C2×C4—2442no—
572C2×C4—2442no—
573C2×C4—2442no—
574C2×C4—2442no—
575C2×C4—2442no—
576C2×C4—2441no—
577C2×C4—2441no—
578C2×C4—2441no—
579C2×C4#1451973711yescharacteristic
580C2×C4C4×C22⋊D6111yescharacteristic
581C2×C4#1451976311yescharacteristic
582C2×C4#1451977311yescharacteristic
583C8—81no—
584C8—4881no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—21no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—4881no—
605C22—4881no—
606C22—4881no—
607C22—4881no—
608C22—4881no—
609C22—4881no—
610C22—4881no—
611C22#1683966211yescharacteristic
612C22#99×D6111yescharacteristic
613C22#1683973411yescharacteristic
614C22#102×D6111yescharacteristic
615C22#1683976511yescharacteristic
616C22#1683977711yescharacteristic
617C22#1683977711yescharacteristic
618C22#1683995511yescharacteristic
619C22#1683995611yescharacteristic
620C22#1683996011yescharacteristic
621C22#1683996111yescharacteristic
622C4—21no—
623C4—21no—
624C4—21no—
625C4—21no—
626C4—82no—
627C4—81no—
628C4—1222no—
629C4—1222no—
630C4—1222no—
631C4—4882no—
632C4—4881no—
633C4—2441no—
634C2—21no—
635C2—21no—
636C2—21no—
637C2—21no—
638C2—161no—
639C2—9761no—
640C2#2144434611yescharacteristic
641C2#2144436411yescharacteristic
642C2#2144437711yescharacteristic
643C2#2144438511yescharacteristic
644C2#2144664911yescharacteristic
645C2#2144665311yescharacteristic
646C2#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#9715
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. #21444044C2semidirect
7. C2×C61×#327C2semidirect
8. C2×#14519773C4semidirect
15. #16839665C4semidirect
16. #16839663C4semidirect
19. #16839631C4semidirect
67. #14519684D4semidirect
82. #95×C61D4semidirect
316. C2×#327D61semidirect
354. C61#9715semidirect
406. #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
#214440442
C2×C61×#3272
#971561