Finite Group Databasebeta

← #29721427

Subgroups — #29721427

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×#16840059C211yesmaximal, characteristic, complemented
2C2×#16839823C211yesmaximal, characteristic, complemented
3#21448512C211yesmaximal, characteristic
4#21447255C211yesmaximal, characteristic, complemented
5#21447245C211yesmaximal, characteristic, complemented
6#21447008C211yesmaximal, characteristic
7#21447008C211yesmaximal, characteristic
8#21446777C211yesmaximal, characteristic, complemented
9#21446580C211yesmaximal, characteristic, complemented
10#21446559C211yesmaximal, characteristic, complemented
11#21446544C211yesmaximal, characteristic, complemented
12#21446515C211yesmaximal, characteristic, complemented
13#21446501C211yesmaximal, characteristic, complemented
14#21445816C211yesmaximal, characteristic, complemented
15C61×#2629C211yesmaximal, characteristic, complemented
16C2×#14519751C2211yescharacteristic
17C2×C4×D244C2211yescharacteristic
18#16840059—24no—
19#16839823—24no—
20C2×#14519710C2211yescharacteristic
21C2×#14519708C2211yescharacteristic
22C2×#14519708C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×C4⋊#92418C2211yescharacteristic
25C2×C4⋊#92418C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29C2×#14519697C2211yescharacteristic
30C2×C22⋊#92418C2211yescharacteristic
31C2×C22⋊#92418C2211yescharacteristic
32C2×#14519688C2211yescharacteristic
33C2×C4×#92418C2211yescharacteristic
34#16839664C2211yescharacteristic
35#16839662—21no—
36#16839660C2211yescharacteristic
37#16839652—21no—
38#16839638—21no—
39#16839633—21no—
40#16839622C2211yescharacteristic
41C4×C4⋊Dic61C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50C2×#125×C61C2211yescharacteristic
51C2×#117×C61C2211yescharacteristic
52C61×#398—21no—
53C61×#398—21no—
54C61×#396—21no—
55C61×#396—21no—
56C61×#389C2211yescharacteristic
57C61×#389C2211yescharacteristic
58C61×#384C2211yescharacteristic
59C61×#380C2211yescharacteristic
60C61×#380C2211yescharacteristic
61C22×D244C2311yescharacteristic
62C22×C22⋊D61—21no—
63C22×C4×D61—21no—
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68#14519751—22no—
69#14519751—22no—
70C4×D244—22no—
71C4×D244—22no—
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×#11758196—21no—
76C2×C22⋊Dic61—21no—
77C2×#11758198—21no—
78C2×#11758198—21no—
79C2×#11758198—21no—
80C2×#11758198—21no—
81C2×C4×Dic61—21no—
82#14519710—22no—
83#14519708—22no—
84#14519708—22no—
85#14519708—22no—
86C4⋊#92418—22no—
87C4⋊#92418D414yescomplemented
88#14519697—22no—
89#14519697—22no—
90#14519697—22no—
91#14519697—22no—
92C22⋊#92418—22no—
93C22⋊#92418—22no—
94#14519688—22no—
95C4×#92418—22no—
96#14519684—21no—
97#14519684—21no—
98#14519684—21no—
99C23×C4×C61C2311yescharacteristic
100#125×C61—22no—
101#125×C61—22no—
102#117×C61—22no—
103#117×C61—22no—
104C2×C4⋊C4×C61—21no—
105C2×C4⋊C4×C61—21no—
106C2×C4⋊C4×C61—21no—
107C2×C4⋊C4×C61—21no—
108C2×C4⋊C4×C61—21no—
109C2×C4⋊C4×C61—21no—
110C2×C4⋊C4×C61D411yescharacteristic
111C2×C4⋊C4×C61D411yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C22⋊C4×C61—21no—
117C2×C22⋊C4×C61—21no—
118C2×C22⋊C4×C61D411yescharacteristic
119C2×C22⋊C4×C61D411yescharacteristic
120C2×C42×C61C2311yescharacteristic
121C2×C42×C61C2311yescharacteristic
122#95×C61—21no—
123#95×C61—21no—
124#95×C61—21no—
125#95×C61—21no—
126C24×C61C2×D411yescharacteristic
127C23×D61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2×D411yescharacteristic
141C22×C4×C61C2×D411yescharacteristic
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2411yescharacteristic
144C2×C22⋊D61—24no—
145C2×C22⋊D61—81no—
146C2×C22⋊D61—81no—
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150C2×D244—21no—
151C2×D244—21no—
152C2×D244—21no—
153C2×D244—21no—
154C2×D244—21no—
155C2×D244#4112yes—
156C2×C4×D61—42no—
157C2×C4×D61—81no—
158C2×C4×D61—81no—
159C4⋊C4×C61—22no—
160C4⋊C4×C61—22no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—42no—
170C4⋊C4×C61—42no—
171C4⋊C4×C61—81no—
172C4⋊C4×C61—81no—
173C4⋊C4×C61—81no—
174C4⋊C4×C61—81no—
175C22⋊C4×C61—22no—
176C22⋊C4×C61—22no—
177C22⋊C4×C61—81no—
178C22⋊C4×C61—81no—
179C42×C61—21no—
180C42×C61—21no—
181C42×C61C2×D412yes—
182C42×C61#4112yes—
183C22⋊Dic61—81no—
184#11758198—24no—
185#11758198—42no—
186#11758198—81no—
187#11758198—81no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61#4112yes—
194#11758196—81no—
195C4×Dic61—81no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418C2×D412yes—
207C2×#92418C2×D412yes—
208C23×C61—21no—
209C23×C61—21no—
210C23×C61—21no—
211C23×C61—21no—
212C23×C61—21no—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61C22×D411yescharacteristic
216C22×D61—22no—
217C22×D61—41no—
218C22×D61—41no—
219C22×D61—41no—
220C22×D61—41no—
221C22×D61—41no—
222C22×D61—41no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
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—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
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×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61#12112yes—
253C2×C4×C61#12112yes—
254C2×C4×C61C22×D411yescharacteristic
255C2×C4×C61C2×#4111yescharacteristic
256C2×C4×C61C2×#4111yescharacteristic
257C2×C4×C61C2×#4111yescharacteristic
258C2×C4×C612−1+411yescharacteristic
259C2×C4×C612−1+411yescharacteristic
260C22⋊D61—84no—
261C2×Dic61—22no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270D244—22no—
271D244—22no—
272D244—41no—
273D244—41no—
274C4×D61—84no—
275#92418—22no—
276#92418—22no—
277#92418—41no—
278#92418—41no—
279#24717—611nomaximal, Sylow
280C22×C61—41no—
281C22×C61—41no—
282C22×C61—41no—
283C22×C61—41no—
284C22×C61—41no—
285C22×C61—41no—
286C22×C61—41no—
287C22×C61C2×#12111yescharacteristic
288C22×C61#52511yescharacteristic
289C22×C61#53611yescharacteristic
290C22×C61#57611yescharacteristic
291C22×C61#57711yescharacteristic
292C22×C61#57711yescharacteristic
293C22×C61#57711yescharacteristic
294C2×D61—42no—
295C2×D61—42no—
296C2×D61—42no—
297C2×D61—81no—
298C2×D61—81no—
299C2×D61—81no—
300C2×D61—81no—
301C4×C61—22no—
302C4×C61—22no—
303C4×C61—41no—
304C4×C61—41no—
305C4×C61—41no—
306C4×C61—81no—
307C4×C61—81no—
308C4×C61—81no—
309C4×C61—81no—
310C4×C61#54711yescharacteristic
311C4×C61#54811yescharacteristic
312C4×C61#55211yescharacteristic
313C4×C61#55611yescharacteristic
314Dic61—42no—
315Dic61—81no—
316Dic61—81no—
317C2×#478—611no—
318C2×#433—611no—
319#2629D6111yescharacteristic, complemented
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#1934—611no—
331#1802—611no—
332C2×C61—81no—
333C2×C61#241511yescharacteristic
334C2×C61#306011yescharacteristic
335C2×C61#306211yescharacteristic
336C2×C61#311911yescharacteristic
337C2×C61#312311yescharacteristic
338C2×C61#324111yescharacteristic
339C2×C61#324411yescharacteristic
340D61—82no—
341C2×#125C2×D6111yescharacteristic
342C2×#121—611no—
343C2×C4×D4—611no—
344C2×#117C2×D6111yescharacteristic
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×#102—611no—
356C2×#102—611no—
357C2×C22⋊C8—611no—
358C2×C22⋊C8—611no—
359C2×#97—611no—
360C2×C4×C8—611no—
361#398—21no—
362#398—21no—
363#396—21no—
364#396—21no—
365#390—611no—
366#390—1221no—
367#389—611no—
368#389C2×D6111yescharacteristic
369#389C2×D6111yescharacteristic
370#388—1221no—
371#386—1221no—
372#385—1221no—
373#384C2×D6111yescharacteristic
374#380—611no—
375#380C2×D6111yescharacteristic
376#380C2×D6111yescharacteristic
377C4×C4⋊C4—611no—
378#340—611no—
379#340—611no—
380#340—611no—
381#340—611no—
382#340—611no—
383#340—611no—
384#340—611no—
385#340—611no—
386C61#2471711yescharacteristic, complemented, Sylow
387C22×D4—611no—
388C22×D4—1221no—
389C23×C4—1221no—
390C23×C4C22×D6111yescharacteristic
391C22×C8—611no—
392C22×C8—611no—
393C22×C8—611no—
394C22×C8—611no—
395#125—22no—
396#125—22no—
397#121—1222no—
398#121—1222no—
399C4×D4—1222no—
400C4×D4—1222no—
401#117—22no—
402#117—22no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—611no—
410C2×C4⋊C4—611no—
411C2×C4⋊C4—611no—
412C2×C4⋊C4—1221no—
413C2×C4⋊C4C22⋊D6111yescharacteristic
414C2×C4⋊C4C22⋊D6111yescharacteristic
415C2×C4⋊C4C22×D6111yescharacteristic
416C2×C4⋊C4C22×D6111yescharacteristic
417C2×C4⋊C4C22×D6111yescharacteristic
418C2×C4⋊C4C22×D6111yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—1221no—
422C2×C22⋊C4—1221no—
423C2×C22⋊C4—1221no—
424C2×C22⋊C4—1221no—
425C2×C22⋊C4—1221no—
426C2×C22⋊C4C22⋊D6111yescharacteristic
427C2×C22⋊C4C22⋊D6111yescharacteristic
428C2×C42—1221no—
429C2×C42C22×D6111yescharacteristic
430C2×C42C22×D6111yescharacteristic
431#107—1222no—
432#106—1222no—
433#106—1222no—
434#106—1222no—
435C4⋊C8—614no—
436C4⋊C8—1222no—
437#102—1222no—
438#102—1222no—
439#102—1222no—
440#102—1222no—
441C22⋊C8—1222no—
442C22⋊C8—1222no—
443#97—1222no—
444C4×C8—1222no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—1221no—
450#95—1221no—
451#95—1221no—
452C24—1221no—
453C24C2×C22⋊D6111yescharacteristic
454C2×D4—612no—
455C2×D4—1224no—
456C2×D4—1221no—
457C2×D4—1221no—
458C2×D4—1221no—
459C2×D4—1221no—
460C2×D4—1221no—
461C2×D4—4881no—
462C2×D4—4881no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—1221no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—4881no—
477C22×C4—4881no—
478C22×C4—2442no—
479C22×C4C2×C22⋊D6111yescharacteristic
480C22×C4C2×C22⋊D6111yescharacteristic
481C22×C4C2×C22⋊D6111yescharacteristic
482C22×C4C2×C22⋊D6111yescharacteristic
483C22×C4C2×C22⋊D6111yescharacteristic
484C22×C4C23×D6111yescharacteristic
485C2×C8—612no—
486C2×C8—612no—
487C2×C8—1221no—
488C2×C8—1221no—
489C2×C8—1221no—
490C2×C8—1221no—
491C2×C8—1221no—
492C2×C8—1221no—
493C2×C8—1221no—
494C2×C8—1221no—
495C2×C8—1221no—
496C2×C8—1221no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—42no—
508C4⋊C4—42no—
509C4⋊C4—81no—
510C4⋊C4—81no—
511C4⋊C4—81no—
512C4⋊C4—81no—
513C4⋊C4—612no—
514C4⋊C4—1221no—
515C4⋊C4—1221no—
516C4⋊C4—1221no—
517C4⋊C4—1221no—
518C4⋊C4—1221no—
519C4⋊C4—4881no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—81no—
523C22⋊C4—81no—
524C22⋊C4—1224no—
525C22⋊C4—4881no—
526C22⋊C4—4881no—
527C22⋊C4—4881no—
528C22⋊C4—2442no—
529C42—21no—
530C42—21no—
531C42—4881no—
532C42D4×D6112yes—
533C42#1175822412yes—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—1222no—
542C23—2441no—
543C23—2441no—
544C23—2441no—
545C23—2441no—
546C23—2441no—
547C23—2441no—
548C23C22×C22⋊D6111yescharacteristic
549D4—1222no—
550D4—1222no—
551D4—4884no—
552D4—2441no—
553D4—2441no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—1222no—
584C2×C4—4884no—
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#1451974912yes—
594C2×C4#1451974912yes—
595C2×C4C2×D4×D6111yescharacteristic
596C2×C4#41×D6111yescharacteristic
597C2×C4#41×D6111yescharacteristic
598C2×C4C2×#1175822411yescharacteristic
599C2×C4#1451982511yescharacteristic
600C2×C4#1451982511yescharacteristic
601C8—1222no—
602C8—1222no—
603C8—2441no—
604C8—2441no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—4881no—
613C22—4881no—
614C22—4881no—
615C22—4881no—
616C22—2442no—
617C22—2442no—
618C22—2442no—
619C22C2×#1451974911yescharacteristic
620C22#1684026911yescharacteristic
621C22#1684033611yescharacteristic
622C22#1684056511yescharacteristic
623C22#1684057011yescharacteristic
624C22#1684057011yescharacteristic
625C22#1684057311yescharacteristic
626C4—22no—
627C4—22no—
628C4—41no—
629C4—41no—
630C4—41no—
631C4—81no—
632C4—81no—
633C4—81no—
634C4—81no—
635C4—4881no—
636C4—4881no—
637C4—2442no—
638C4#1684041411yescharacteristic
639C4#1684042211yescharacteristic
640C4#1684044611yescharacteristic
641C4#1684048311yescharacteristic
642C2—81no—
643C2—4882no—
644C2#2144924911yescharacteristic
645C2#2145547811yescharacteristic
646C2#2145550111yescharacteristic
647C2#2145601211yescharacteristic
648C2#2145606611yescharacteristic
649C2#2145707211yescharacteristic
650C2#2145711711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2629C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
hypercenter#2629D61
hypocenterC61#24717
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2629

Complements

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

NH ≅ G/Ntype
1. C2×#16840059C2semidirect
2. C2×#16839823C2semidirect
4. #21447255C2semidirect
5. #21447245C2semidirect
8. #21446777C2semidirect
9. #21446580C2semidirect
10. #21446559C2semidirect
11. #21446544C2semidirect
12. #21446515C2semidirect
13. #21446501C2semidirect
14. #21445816C2semidirect
15. C61×#2629C2semidirect
87. C4⋊#92418D4semidirect
319. #2629D61semidirect
386. C61#24717semidirect

Maximal subgroups

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

subgroupindex
C2×#168400592
C2×#168398232
#214485122
#214472552
#214472452
#214470082
#214467772
#214465802
#214465592
#214465442
#214465152
#214465012
#214458162
C61×#26292
#2471761