Finite Group Databasebeta

← #29721420

Subgroups — #29721420

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×#16840061C211yesmaximal, characteristic, complemented
2C2×#16839820C211yesmaximal, characteristic, complemented
3#21451653C211yesmaximal, characteristic, complemented
4#21448508C211yesmaximal, characteristic
5#21447245C211yesmaximal, characteristic, complemented
6#21447009C211yesmaximal, characteristic
7#21447008C211yesmaximal, characteristic
8#21446773C211yesmaximal, characteristic, complemented
9#21446581C211yesmaximal, characteristic, complemented
10#21446561C211yesmaximal, characteristic, complemented
11#21446545C211yesmaximal, characteristic, complemented
12#21446514C211yesmaximal, characteristic, complemented
13#21446503C211yesmaximal, characteristic, complemented
14#21445818C211yesmaximal, characteristic, complemented
15C61×#2077C211yesmaximal, characteristic, complemented
16C2×#14519768C2211yescharacteristic
17C2×#14519751C2211yescharacteristic
18C2×#14519739C2211yescharacteristic
19C2×#14519736C2211yescharacteristic
20#16840061—24no—
21#16839820—24no—
22C2×#14519710C2211yescharacteristic
23C2×#14519709C2211yescharacteristic
24C2×#14519708C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26C2×#14519706C2211yescharacteristic
27C2×#14519699C2211yescharacteristic
28C2×#14519699C2211yescharacteristic
29C2×#14519697C2211yescharacteristic
30C2×#14519697C2211yescharacteristic
31C2×C22⋊#92418C2211yescharacteristic
32C2×#14519687C2211yescharacteristic
33C2×C8×Dic61C2211yescharacteristic
34#16839696—21no—
35#16839694—21no—
36#16839685—21no—
37#16839685—21no—
38#16839663C2211yescharacteristic
39#16839662—21no—
40#16839661C2211yescharacteristic
41#16839658C2211yescharacteristic
42#16839658C2211yescharacteristic
43#16839654—21no—
44#16839638—21no—
45#16839636—21no—
46#16839631C2211yescharacteristic
47#16839622C2211yescharacteristic
48C4⋊C4×Dic61C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54C2×#106×C61C2211yescharacteristic
55C2×C22⋊C8×C61C2211yescharacteristic
56C61×#380C2211yescharacteristic
57C61×#380C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C22×D244C2311yescharacteristic
62C22×C22⋊D61—21no—
63C22×C4×D61—21no—
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66#14519768—22no—
67#14519768—22no—
68#14519751—22no—
69#14519751—22no—
70#14519739—22no—
71#14519739—22no—
72#14519736—22no—
73#14519736—22no—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61D411yescharacteristic
77C2×C4⋊Dic61D411yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×#11758196—21no—
82C2×#11758196—21no—
83C2×#11758196—21no—
84C2×#11758196—21no—
85C2×#11758196—21no—
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61D411yescharacteristic
88C2×C22⋊Dic61D411yescharacteristic
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×C4×Dic61—21no—
94C2×C4×Dic61C2311yescharacteristic
95C2×C4×Dic61C2311yescharacteristic
96#14519710—22no—
97#14519709—22no—
98#14519708—22no—
99#14519706—22no—
100#14519706D414yescomplemented
101#14519699—22no—
102#14519699—22no—
103#14519697—22no—
104#14519697—22no—
105C22⋊#92418—22no—
106#14519687—22no—
107C8×Dic61—22no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113C23×C4×C61C2311yescharacteristic
114C22×C8×C61C2311yescharacteristic
115C22×C8×C61C2311yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C4⋊C4×C61C2311yescharacteristic
120C2×C22⋊C4×C61—21no—
121C2×C22⋊C4×C61—21no—
122#106×C61—22no—
123C22⋊C8×C61—22no—
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×C61C2411yescharacteristic
140C2×C22⋊D61—24no—
141C2×C22⋊D61—81no—
142C2×C22⋊D61—81no—
143C22×Dic61—21no—
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61C2×D411yescharacteristic
147C22×Dic61C2×D411yescharacteristic
148C22×Dic61C2×D411yescharacteristic
149C22×Dic61C2×D411yescharacteristic
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—
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—21no—
172C4⋊C4×C61—21no—
173C22⋊C4×C61—81no—
174C22⋊C4×C61—81no—
175C22⋊Dic61—22no—
176C22⋊Dic61—22no—
177C22⋊Dic61—81no—
178#11758198—24no—
179#11758198—42no—
180#11758198—81no—
181#11758198—81no—
182C4⋊Dic61—21no—
183C4⋊Dic61—22no—
184C4⋊Dic61—22no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—42no—
190C4⋊Dic61—81no—
191C4⋊Dic61#4112yes—
192#11758196—42no—
193#11758196—81no—
194#11758196—81no—
195#11758196—81no—
196#11758196—81no—
197C4×Dic61—21no—
198C4×Dic61—21no—
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—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—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—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—21no—
255C2×Dic61—22no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
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#12112yes—
269C2×Dic61#12112yes—
270D244—22no—
271D244—22no—
272D244—41no—
273D244—41no—
274C4×D61—84no—
275C8×C61—22no—
276C8×C61—41no—
277#92418—22no—
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—41no—
302C4×C61—81no—
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—41no—
315Dic61—81no—
316Dic61—81no—
317C2×#478—611no—
318C2×#433—611no—
319#2629—611no—
320#2324—611no—
321#2077D6111yescharacteristic, complemented
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×#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×#106C2×D6111yescharacteristic
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⋊C8C2×D6111yescharacteristic
359C2×#97—611no—
360C2×C4×C8—611no—
361#398—1221no—
362#398—1221no—
363#396—1221no—
364#396—1221no—
365#390—611no—
366#390—1221no—
367#389—611no—
368#389—611no—
369#389—611no—
370#388—1221no—
371#386—1221no—
372#385—1221no—
373#384—611no—
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#340C2×D6111yescharacteristic
384#340C2×D6111yescharacteristic
385#340C2×D6111yescharacteristic
386C61#2471711yescharacteristic, complemented, Sylow
387C22×D4—611no—
388C22×D4—1221no—
389C23×C4—1221no—
390C23×C4C22×D6111yescharacteristic
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—611no—
404C2×C4⋊C4—611no—
405C2×C4⋊C4—611no—
406C2×C4⋊C4—611no—
407C2×C4⋊C4—611no—
408C2×C4⋊C4—1221no—
409C2×C4⋊C4—1221no—
410C2×C4⋊C4—1221no—
411C2×C4⋊C4—1221no—
412C2×C4⋊C4—1221no—
413C2×C4⋊C4—1221no—
414C2×C4⋊C4—1221no—
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—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—611no—
430C2×C42—1221no—
431#107—1222no—
432#106—22no—
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—22no—
442C22⋊C8—1222no—
443#97—1222no—
444C4×C8—1222no—
445#95—21no—
446#95—21no—
447#95—1221no—
448#95—1221no—
449#95—1221no—
450#95—1221no—
451#95—1221no—
452C24—1221no—
453C24D4×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—611no—
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4—1221no—
480C22×C4—4881no—
481C22×C4—4881no—
482C22×C4—2442no—
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—21no—
504C4⋊C4—21no—
505C4⋊C4—612no—
506C4⋊C4—1222no—
507C4⋊C4—1222no—
508C4⋊C4—1221no—
509C4⋊C4—1221no—
510C4⋊C4—1221no—
511C4⋊C4—1221no—
512C4⋊C4—1221no—
513C4⋊C4—4881no—
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—1224no—
523C22⋊C4—1222no—
524C22⋊C4—1222no—
525C22⋊C4—4881no—
526C22⋊C4—4881no—
527C22⋊C4—4881no—
528C22⋊C4—2442no—
529C42—612no—
530C42—612no—
531C42—1221no—
532C42—1221no—
533C42—4881no—
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—
548C23C2×D4×D6111yescharacteristic
549D4—1222no—
550D4—1222no—
551D4—4884no—
552D4—2441no—
553D4—2441no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
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—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—612no—
574C2×C4—612no—
575C2×C4—1221no—
576C2×C4—1221no—
577C2×C4—1221no—
578C2×C4—1221no—
579C2×C4—1221no—
580C2×C4—1221no—
581C2×C4—1222no—
582C2×C4—1221no—
583C2×C4—1221no—
584C2×C4—1221no—
585C2×C4—1221no—
586C2×C4—4884no—
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×C4#41×D6111yescharacteristic
599C2×C4#1451982411yescharacteristic
600C2×C4#1451982411yescharacteristic
601C8—22no—
602C8—41no—
603C8—1222no—
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—
619C22#121×D6111yescharacteristic
620C22#1684027011yescharacteristic
621C22#1684033411yescharacteristic
622C22#1684056611yescharacteristic
623C22#1684056811yescharacteristic
624C22#1684056911yescharacteristic
625C22#1684057111yescharacteristic
626C4—41no—
627C4—81no—
628C4—81no—
629C4—81no—
630C4—81no—
631C4—1222no—
632C4—1222no—
633C4—4881no—
634C4—4881no—
635C4—2441no—
636C4—2441no—
637C4—2442no—
638C4#1684041011yescharacteristic
639C4#1684042011yescharacteristic
640C4#1684044811yescharacteristic
641C4#1684047911yescharacteristic
642C2—81no—
643C2—4882no—
644C2#2144924311yescharacteristic
645C2#2145547611yescharacteristic
646C2#2145549411yescharacteristic
647C2#2145601311yescharacteristic
648C2#2145606711yescharacteristic
649C2#2145707011yescharacteristic
650C2#2145712111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2077C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
hypercenter#2077D61
hypocenterC61#24717
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2077

Complements

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

NH ≅ G/Ntype
1. C2×#16840061C2semidirect
2. C2×#16839820C2semidirect
3. #21451653C2semidirect
5. #21447245C2semidirect
8. #21446773C2semidirect
9. #21446581C2semidirect
10. #21446561C2semidirect
11. #21446545C2semidirect
12. #21446514C2semidirect
13. #21446503C2semidirect
14. #21445818C2semidirect
15. C61×#2077C2semidirect
100. #14519706D4semidirect
321. #2077D61semidirect
386. C61#24717semidirect

Maximal subgroups

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

subgroupindex
C2×#168400612
C2×#168398202
#214516532
#214485082
#214472452
#214470092
#214470082
#214467732
#214465812
#214465612
#214465452
#214465142
#214465032
#214458182
C61×#20772
#2471761