Finite Group Databasebeta

← #29721422

Subgroups — #29721422

Order 15616.

794 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840064C211yesmaximal, characteristic, complemented
2C2×#16839821C211yesmaximal, characteristic, complemented
3#21451654C211yesmaximal, characteristic, complemented
4#21448515C211yesmaximal, characteristic
5#21447254C211yesmaximal, characteristic, complemented
6#21447246C211yesmaximal, characteristic, complemented
7#21447007C211yesmaximal, characteristic
8#21447006C211yesmaximal, characteristic
9#21446775C211yesmaximal, characteristic, complemented
10#21446581C211yesmaximal, characteristic, complemented
11#21446559C211yesmaximal, characteristic, complemented
12#21446547C211yesmaximal, characteristic, complemented
13#21446519C211yesmaximal, characteristic, complemented
14#21445817C211yesmaximal, characteristic, complemented
15C61×#1934C211yesmaximal, characteristic, complemented
16C2×#14519768C2211yescharacteristic
17C2×#14519748C2211yescharacteristic
18C2×D4×Dic61C2211yescharacteristic
19C2×#14519734C2211yescharacteristic
20#16840064—24no—
21#16839821—24no—
22C2×#14519710C2211yescharacteristic
23C2×#14519709C2211yescharacteristic
24C2×#14519709C2211yescharacteristic
25C2×#14519708C2211yescharacteristic
26C2×#14519706C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519689C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519688C2211yescharacteristic
33#16839696—21no—
34#16839693—21no—
35#16839686—21no—
36#16839684—21no—
37#16839662—21no—
38#16839660C2211yescharacteristic
39#16839660C2211yescharacteristic
40#16839650—21no—
41#16839639—21no—
42#16839634—21no—
43#16839631C2211yescharacteristic
44#16839619C2211yescharacteristic
45#16839619C2211yescharacteristic
46#16839619C2211yescharacteristic
47C4⋊C4×Dic61C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54C2×#102×C61C2211yescharacteristic
55C2×#102×C61C2211yescharacteristic
56C2×C4×C8×C61C2211yescharacteristic
57C61×#390C2211yescharacteristic
58C61×#389C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C22×C22⋊D61—21no—
62C23×Dic61—21no—
63C22×C4×D61C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66#14519768—22no—
67#14519768—22no—
68#14519748—22no—
69#14519748—22no—
70D4×Dic61—22no—
71D4×Dic61—22no—
72#14519734—22no—
73#14519734—22no—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×#11758196—21no—
80C2×#11758196—21no—
81C2×#11758196—21no—
82C2×#11758196—21no—
83C2×#11758196—21no—
84C2×#11758196D411yescharacteristic
85C2×#11758196D411yescharacteristic
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×#11758198D411yescharacteristic
92C2×#11758198D411yescharacteristic
93C2×C4×Dic61—21no—
94C2×C4×Dic61C2311yescharacteristic
95#14519710—22no—
96#14519709—22no—
97#14519709—22no—
98#14519708—22no—
99#14519706—22no—
100#14519706D414yescomplemented
101#14519698—22no—
102#14519698—22no—
103#14519689—22no—
104#14519689—22no—
105#14519688—22no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112C22×D4×C61C2311yescharacteristic
113C22×C8×C61C2311yescharacteristic
114C22×C8×C61C2311yescharacteristic
115C2×C4⋊C4×C61—21no—
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C22⋊C4×C61—21no—
120C2×C22⋊C4×C61—21no—
121C2×C42×C61C2311yescharacteristic
122#102×C61—22no—
123#102×C61—22no—
124C4×C8×C61—22no—
125#95×C61—21no—
126C24×C61—21no—
127C23×D61C2×D411yescharacteristic
128C2×D4×C61—21no—
129C2×D4×C61—21no—
130C2×D4×C61—21no—
131C2×D4×C61—21no—
132C2×D4×C61—21no—
133C2×D4×C61#4112yes—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2411yescharacteristic
140C2×C22⋊D61—24no—
141C2×C22⋊D61—81no—
142C2×C22⋊D61—81no—
143C22×Dic61—21no—
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61—42no—
148C22×Dic61—81no—
149C22×Dic61—81no—
150C22×Dic61C2×D411yescharacteristic
151C22×Dic61C2×D411yescharacteristic
152C22×Dic61C2×D411yescharacteristic
153C2×C4×D61—21no—
154C2×C4×D61—21no—
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61C2×D412yes—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—81no—
172C22⋊C4×C61—81no—
173C22⋊C4×C61—81no—
174C42×C61—21no—
175C42×C61—21no—
176C22⋊Dic61—24no—
177C22⋊Dic61—42no—
178#11758198—22no—
179#11758198—22no—
180#11758198—81no—
181#11758198—81no—
182#11758198—81no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—42no—
191C4⋊Dic61#4112yes—
192#11758196—22no—
193#11758196—22no—
194#11758196—42no—
195#11758196—81no—
196#11758196—81no—
197#11758196—81no—
198#11758196—81no—
199C4×Dic61—81no—
200C4×Dic61C2×D412yes—
201C4×Dic61#4112yes—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418C2×D412yes—
208C23×C61—22no—
209C23×C61—41no—
210C23×C61—41no—
211C23×C61—41no—
212C23×C61—41no—
213C23×C61—41no—
214C23×C61—41no—
215C23×C61C22×D411yescharacteristic
216C22×D61—21no—
217C22×D61—21no—
218C22×D61—21no—
219C22×D61—21no—
220C22×D61—21no—
221C22×D61—21no—
222C22×D61—21no—
223D4×C61—22no—
224D4×C61—22no—
225D4×C61—41no—
226D4×C61—41no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61C22×D411yescharacteristic
243C2×C4×C61C2×#4111yescharacteristic
244C2×C4×C61C2×#4111yescharacteristic
245C2×C4×C61C2×#4111yescharacteristic
246C2×C4×C612−1+411yescharacteristic
247C2×C4×C612−1+411yescharacteristic
248C22⋊D61—84no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—22no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—84no—
269C2×Dic61#12112yes—
270C2×Dic61#12112yes—
271C4×D61—41no—
272C4×D61—41no—
273C4×D61—41no—
274C4×D61—41no—
275C8×C61—22no—
276C8×C61—41no—
277#92418—22no—
278#92418—41no—
279#24717—611nomaximal, Sylow
280C22×C61—42no—
281C22×C61—42no—
282C22×C61—42no—
283C22×C61—81no—
284C22×C61—81no—
285C22×C61—81no—
286C22×C61—81no—
287C22×C61C2×#12111yescharacteristic
288C22×C61#52511yescharacteristic
289C22×C61#53611yescharacteristic
290C22×C61#57611yescharacteristic
291C22×C61#57711yescharacteristic
292C22×C61#57711yescharacteristic
293C22×C61#57711yescharacteristic
294C2×D61—41no—
295C2×D61—41no—
296C2×D61—41no—
297C2×D61—41no—
298C2×D61—41no—
299C2×D61—41no—
300C2×D61—41no—
301C4×C61—41no—
302C4×C61—41no—
303C4×C61—81no—
304C4×C61—81no—
305C4×C61—81no—
306C4×C61#54711yescharacteristic
307C4×C61#54811yescharacteristic
308C4×C61#55211yescharacteristic
309C4×C61#55611yescharacteristic
310Dic61—22no—
311Dic61—22no—
312Dic61—42no—
313Dic61—41no—
314Dic61—81no—
315Dic61—81no—
316Dic61—81no—
317C2×#478—611no—
318C2×#433—611no—
319#2629—611no—
320#2324—611no—
321#2077—611no—
322#2075—611no—
323#2034—611no—
324#2034—611no—
325#1989—611no—
326#1948—611no—
327#1944—611no—
328#1941—611no—
329#1936—611no—
330#1934D6111yescharacteristic, complemented
331#1802—611no—
332C2×C61—82no—
333C2×C61#241511yescharacteristic
334C2×C61#306011yescharacteristic
335C2×C61#306211yescharacteristic
336C2×C61#311911yescharacteristic
337C2×C61#312311yescharacteristic
338C2×C61#324111yescharacteristic
339C2×C61#324411yescharacteristic
340D61—81no—
341C2×#125—611no—
342C2×#121—611no—
343C2×C4×D4—611no—
344C2×#117—611no—
345#478—1224no—
346#433—1224no—
347C2×#107—611no—
348C2×#106—611no—
349C2×#106—611no—
350C2×#106—611no—
351C2×C4⋊C8—611no—
352C2×C4⋊C8—611no—
353C2×#102—611no—
354C2×#102—611no—
355C2×#102C2×D6111yescharacteristic
356C2×#102C2×D6111yescharacteristic
357C2×C22⋊C8—611no—
358C2×C22⋊C8—611no—
359C2×#97—611no—
360C2×C4×C8C2×D6111yescharacteristic
361#398—1221no—
362#398—1221no—
363#396—1221no—
364#396—1221no—
365#390—1221no—
366#390C2×D6111yescharacteristic
367#389—611no—
368#389—611no—
369#389C2×D6111yescharacteristic
370#388—1221no—
371#386—1221no—
372#385—1221no—
373#384—611no—
374#380—611no—
375#380—611no—
376#380—611no—
377C4×C4⋊C4—611no—
378#340—611no—
379#340—611no—
380#340—611no—
381#340—611no—
382#340—611no—
383#340—611no—
384#340C2×D6111yescharacteristic
385#340C2×D6111yescharacteristic
386C61#2471711yescharacteristic, complemented, Sylow
387C22×D4—1221no—
388C22×D4C22×D6111yescharacteristic
389C23×C4—611no—
390C23×C4—1221no—
391C22×C8—611no—
392C22×C8—611no—
393C22×C8C22×D6111yescharacteristic
394C22×C8C22×D6111yescharacteristic
395#125—1222no—
396#125—1222no—
397#121—1222no—
398#121—1222no—
399C4×D4—1222no—
400C4×D4—1222no—
401#117—1222no—
402#117—1222no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—611no—
405C2×C4⋊C4—611no—
406C2×C4⋊C4—611no—
407C2×C4⋊C4—611no—
408C2×C4⋊C4—611no—
409C2×C4⋊C4—611no—
410C2×C4⋊C4—1221no—
411C2×C4⋊C4—1221no—
412C2×C4⋊C4—1221no—
413C2×C4⋊C4—1221no—
414C2×C4⋊C4—1221no—
415C2×C4⋊C4—1221no—
416C2×C4⋊C4C22×D6111yescharacteristic
417C2×C4⋊C4C22×D6111yescharacteristic
418C2×C4⋊C4C22×D6111yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—611no—
422C2×C22⋊C4—611no—
423C2×C22⋊C4—1221no—
424C2×C22⋊C4—1221no—
425C2×C22⋊C4—1221no—
426C2×C22⋊C4—1221no—
427C2×C22⋊C4—1221no—
428C2×C42—611no—
429C2×C42—1221no—
430C2×C42C22×D6111yescharacteristic
431#107—1222no—
432#106—1222no—
433#106—1222no—
434#106—1222no—
435C4⋊C8—614no—
436C4⋊C8—1222no—
437#102—22no—
438#102—22no—
439#102—1222no—
440#102—1222no—
441C22⋊C8—1222no—
442C22⋊C8—1222no—
443#97—1222no—
444C4×C8—22no—
445#95—21no—
446#95—1221no—
447#95—1221no—
448#95—1221no—
449#95—1221no—
450#95—1221no—
451#95—1221no—
452C24—21no—
453C24—611no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—1224no—
460C2×D4—4881no—
461C2×D4—4881no—
462C2×D4#1175822212yes—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—611no—
467C22×C4—611no—
468C22×C4—611no—
469C22×C4—1221no—
470C22×C4—1221no—
471C22×C4—1221no—
472C22×C4—1221no—
473C22×C4—1221no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—1221no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4—4881no—
480C22×C4—4881no—
481C22×C4—2442no—
482C22×C4D4×D6111yescharacteristic
483C22×C4D4×D6111yescharacteristic
484C22×C4C23×D6111yescharacteristic
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—612no—
491C2×C8—1221no—
492C2×C8—1221no—
493C2×C8—1221no—
494C2×C8—1221no—
495C2×C8—1221no—
496C2×C8D4×D6112yes—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—81no—
504C4⋊C4—612no—
505C4⋊C4—1222no—
506C4⋊C4—1222no—
507C4⋊C4—1221no—
508C4⋊C4—1221no—
509C4⋊C4—1221no—
510C4⋊C4—1221no—
511C4⋊C4—1221no—
512C4⋊C4—1221no—
513C4⋊C4—1221no—
514C4⋊C4—4881no—
515C4⋊C4—4881no—
516C4⋊C4—4881no—
517C4⋊C4—4881no—
518C4⋊C4—2442no—
519C4⋊C4—2442no—
520C22⋊C4—81no—
521C22⋊C4—81no—
522C22⋊C4—1222no—
523C22⋊C4—1222no—
524C22⋊C4—1224no—
525C22⋊C4—4881no—
526C22⋊C4—4881no—
527C22⋊C4—4881no—
528C22⋊C4—2442no—
529C42—21no—
530C42—21no—
531C42—612no—
532C42—612no—
533C42—4881no—
534C23—22no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—1221no—
542C23—1221no—
543C23—1221no—
544C23—1221no—
545C23—1221no—
546C23—1221no—
547C23—1221no—
548C23C2×D4×D6111yescharacteristic
549D4—22no—
550D4—22no—
551D4—41no—
552D4—41no—
553D4—4884no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—612no—
570C2×C4—612no—
571C2×C4—1221no—
572C2×C4—1221no—
573C2×C4—1221no—
574C2×C4—1221no—
575C2×C4—1221no—
576C2×C4—1221no—
577C2×C4—1222no—
578C2×C4—1221no—
579C2×C4—4884no—
580C2×C4—2441no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4—2441no—
584C2×C4—2441no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4—2441no—
588C2×C4—2441no—
589C2×C4—2441no—
590C2×C4—2441no—
591C2×C4—2441no—
592C2×C4—2441no—
593C2×C4—2441no—
594C2×C4—2441no—
595C2×C4C2×D4×D6111yescharacteristic
596C2×C4#41×D6111yescharacteristic
597C2×C4#41×D6111yescharacteristic
598C2×C4C2×#1175822211yescharacteristic
599C2×C4#1451982411yescharacteristic
600C2×C4#1451982411yescharacteristic
601C8—22no—
602C8—41no—
603C8—1222no—
604C8—2441no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—2441no—
613C22—2441no—
614C22—2441no—
615C22—2441no—
616C22—2441no—
617C22—2441no—
618C22—2441no—
619C22#121×D6111yescharacteristic
620C22#1684027111yescharacteristic
621C22#1684033211yescharacteristic
622C22#1684056311yescharacteristic
623C22#1684056811yescharacteristic
624C22#1684056911yescharacteristic
625C22#1684056911yescharacteristic
626C4—41no—
627C4—41no—
628C4—81no—
629C4—81no—
630C4—81no—
631C4—1222no—
632C4—1222no—
633C4—4881no—
634C4—4881no—
635C4—4881no—
636C4—2441no—
637C4—2442no—
638C4#1684041011yescharacteristic
639C4#1684042111yescharacteristic
640C4#1684044511yescharacteristic
641C4#1684047911yescharacteristic
642C2—82no—
643C2—4881no—
644C2#2144924511yescharacteristic
645C2#2145547611yescharacteristic
646C2#2145549811yescharacteristic
647C2#2145601411yescharacteristic
648C2#2145606811yescharacteristic
649C2#2145706511yescharacteristic
650C2#2145711011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1934C2
socleC23×C61C22×D4
prime radicalC2×#14519748C22
hypercenter#1934D61
hypocenterC61#24717
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1934

Complements

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

NH ≅ G/Ntype
1. C2×#16840064C2semidirect
2. C2×#16839821C2semidirect
3. #21451654C2semidirect
5. #21447254C2semidirect
6. #21447246C2semidirect
9. #21446775C2semidirect
10. #21446581C2semidirect
11. #21446559C2semidirect
12. #21446547C2semidirect
13. #21446519C2semidirect
14. #21445817C2semidirect
15. C61×#1934C2semidirect
100. #14519706D4semidirect
330. #1934D61semidirect
386. C61#24717semidirect

Maximal subgroups

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

subgroupindex
C2×#168400642
C2×#168398212
#214516542
#214485152
#214472542
#214472462
#214470072
#214470062
#214467752
#214465812
#214465592
#214465472
#214465192
#214458172
C61×#19342
#2471761