Finite Group Databasebeta

← #29721336

Subgroups — #29721336

Order 15616.

828 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840055C211yesmaximal, characteristic, complemented
2C2×#16839817C211yesmaximal, characteristic
3#21454170C211yesmaximal, characteristic
4#21448357C211yesmaximal, characteristic
5#21447246C211yesmaximal, characteristic
6#21447244C211yesmaximal, characteristic
7#21447014C211yesmaximal, characteristic
8#21447013C211yesmaximal, characteristic
9#21446765C211yesmaximal, characteristic, complemented
10#21446581C211yesmaximal, characteristic, complemented
11#21446562C211yesmaximal, characteristic, complemented
12#21446559C211yesmaximal, characteristic, complemented
13#21446512C211yesmaximal, characteristic, complemented
14#21445822C211yesmaximal, characteristic, complemented
15C61×#1935C211yesmaximal, characteristic, complemented
16C2×#14519776C2211yescharacteristic
17C2×#14519755—21no—
18C2×#14519753C2211yescharacteristic
19C2×Q8×Dic61C2211yescharacteristic
20C2×C42×D61C2211yescharacteristic
21#16840055—24no—
22#16839817—24no—
23C2×#14519711C2211yescharacteristic
24C2×#14519710C2211yescharacteristic
25C2×#14519709C2211yescharacteristic
26C2×#14519708C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28C2×#14519706C2211yescharacteristic
29C2×#14519701C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519688C2211yescharacteristic
34#16839666—21no—
35#16839660C2211yescharacteristic
36#16839660C2211yescharacteristic
37#16839657—21no—
38#16839649—21no—
39#16839636—21no—
40#16839631C2211yescharacteristic
41#16839621—21no—
42#16839619C2211yescharacteristic
43#16839619C2211yescharacteristic
44#16839619C2211yescharacteristic
45C4⋊C4×Dic61C2211yescharacteristic
46#16839613—21no—
47#16839609—21no—
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54C2×#103×C61C2211yescharacteristic
55C2×#103×C61C2211yescharacteristic
56C2×#97×C61C2211yescharacteristic
57C61×#391C2211yescharacteristic
58C61×#389C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C22×Dic122—21no—
62C22×C4×D61D411yescharacteristic
63C22×C4×D61D411yescharacteristic
64C22×C4×D61C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67#14519776—22no—
68#14519776—22no—
69#14519755—44no—
70#14519753—22no—
71#14519753—22no—
72Q8×Dic61—22no—
73Q8×Dic61—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×#11758196—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×C4×Dic61—21no—
90C2×C4×Dic61—21no—
91C2×C4×Dic61D411yescharacteristic
92C2×C4×Dic61D411yescharacteristic
93C2×C4×Dic61C2311yescharacteristic
94C42×D61—22no—
95C42×D61—22no—
96#14519711—22no—
97#14519710—22no—
98#14519709—22no—
99#14519708—22no—
100#14519706—22no—
101#14519706D414yes—
102#14519701—22no—
103#14519701—22no—
104#14519689—22no—
105#14519689—22no—
106#14519688—22no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113C22×Q8×C61C2311yescharacteristic
114C22×C8×C61C2311yescharacteristic
115C22×C8×C61C2311yescharacteristic
116C2×C4⋊C4×C61—21no—
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C4⋊C4×C61C2311yescharacteristic
120C2×C42×C61C2311yescharacteristic
121#103×C61—22no—
122#103×C61—22no—
123#97×C61—22no—
124#95×C61—21no—
125#95×C61—21no—
126#95×C61—21no—
127C23×D61C2×D411yescharacteristic
128C2×Q8×C61—21no—
129C2×Q8×C61—21no—
130C2×Q8×C61—21no—
131C2×Q8×C61—21no—
132C2×Q8×C61—21no—
133C2×Q8×C61#4112yes—
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×C61C2411yescharacteristic
141C22×Dic61—21no—
142C22×Dic61—21no—
143C22×Dic61—21no—
144C22×Dic61—21no—
145C22×Dic61C2×D411yescharacteristic
146C22×Dic61C2×D411yescharacteristic
147C22×Dic61C2×D411yescharacteristic
148C2×C4×D61—22no—
149C2×C4×D61—21no—
150C2×C4×D61—21no—
151C2×C4×D61—21no—
152C2×C4×D61—21no—
153C2×C4×D61—21no—
154C2×C4×D61—21no—
155C2×C4×D61—22no—
156C2×C4×D61—22no—
157C2×C4×D61—22no—
158C2×C4×D61—22no—
159C2×C4×D61—41no—
160C2×Dic122—42no—
161C2×Dic122—42no—
162C2×Dic122—42no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61C2×D412yes—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—42no—
176C42×C61—21no—
177C42×C61—21no—
178#11758198—24no—
179#11758198—42no—
180#11758198—42no—
181#11758198—42no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—42no—
190C4⋊Dic61#4112yes—
191#11758196—24no—
192#11758196—42no—
193#11758196—42no—
194#11758196—42no—
195#11758196—42no—
196#11758196—42no—
197C4×Dic61—22no—
198C4×Dic61—22no—
199C4×Dic61—42no—
200C4×Dic61—42no—
201C4×Dic61C2×D412yes—
202C4×Dic61#4112yes—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418C2×D412yes—
209C23×C61C22×D411yescharacteristic
210C22×D61—21no—
211C22×D61—21no—
212C22×D61—21no—
213C22×D61—21no—
214C22×D61—21no—
215C22×D61—21no—
216C22×D61AGL(1,ℤ/8)12yes—
217Q8×C61—22no—
218Q8×C61—22no—
219Q8×C61—41no—
220Q8×C61—41no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—22no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
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×C61C22×D411yescharacteristic
240C2×C4×C61C2×#4111yescharacteristic
241C2×C4×C61C2×#4111yescharacteristic
242C2×C4×C61C2×#4111yescharacteristic
243C2×C4×C612−1+411yescharacteristic
244C2×C4×C612−1+411yescharacteristic
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—22no—
250C2×Dic61—21no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61#12112yes—
263C2×Dic61#12112yes—
264C2×Dic61#13712yes—
265C2×Dic61#13712yes—
266C4×D61—44no—
267C4×D61—41no—
268C4×D61—41no—
269C4×D61—41no—
270C4×D61—41no—
271C4×D61—44no—
272Dic122—84no—
273C8×C61—22no—
274C8×C61—41no—
275#92418—22no—
276#92418—41no—
277#24711—611nomaximal, Sylow
278C22×C61C2×#12111yescharacteristic
279C22×C61#52511yescharacteristic
280C22×C61#53611yescharacteristic
281C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
282C22×C61C2×#13711yescharacteristic
283C22×C61C2×#13711yescharacteristic
284C22×C61#57511yescharacteristic
285C2×D61—22no—
286C2×D61—22no—
287C2×D61—22no—
288C2×D61—41no—
289C2×D61—41no—
290C2×D61—41no—
291C2×D61—41no—
292C4×C61—42no—
293C4×C61—41no—
294C4×C61—41no—
295C4×C61—81no—
296C4×C61—81no—
297C4×C61—81no—
298C4×C61#54711yescharacteristic
299C4×C61#54811yescharacteristic
300C4×C61#55211yescharacteristic
301C4×C61#55611yescharacteristic
302Dic61—22no—
303Dic61—42no—
304Dic61—41no—
305Dic61—81no—
306Dic61—81no—
307Dic61—81no—
308Dic61#47014yes—
309C2×#477—611no—
310C2×#432—611no—
311#2857—611no—
312C4×C22⋊Q8—611no—
313#2075—611no—
314#2075—611no—
315#2035—611no—
316#2035—611no—
317#1987—611no—
318#1948—611no—
319#1944—611no—
320#1944—611no—
321#1935—611no—
322#1935D6111yescharacteristic, complemented
323#1803—611no—
324C2×C61#241511yescharacteristic
325C2×C61C2×#47011yescharacteristic
326C2×C61#305511yescharacteristic
327C2×C61#311211yescharacteristic
328C2×C61#311611yescharacteristic
329C2×C61#323711yescharacteristic
330C2×C61#323811yescharacteristic
331D61—42no—
332C2×C4⋊Q8—611no—
333C2×C22⋊Q8—611no—
334C2×C22⋊Q8—1221no—
335C2×C4×Q8—611no—
336C22×C42—611no—
337#477—1224no—
338#432—1224no—
339C2×#107—611no—
340C2×#107—611no—
341C2×#106—611no—
342C2×#106—611no—
343C2×C4⋊C8—611no—
344C2×C4⋊C8—611no—
345C2×#103—611no—
346C2×#103—611no—
347C2×#103C2×D6111yescharacteristic
348C2×#103C2×D6111yescharacteristic
349C2×C22⋊C8—611no—
350C2×C22⋊C8—611no—
351C2×#97—611no—
352C2×#97C2×D6111yescharacteristic
353#391—1221no—
354#391C2×D6111yescharacteristic
355#389—611no—
356#389—611no—
357#389—1221no—
358#389C2×D6111yescharacteristic
359#387—1221no—
360#385—1221no—
361#384—611no—
362#380—611no—
363#380—611no—
364#380—611no—
365#380—1221no—
366C4×C4⋊C4—611no—
367C4×C4⋊C4—1221no—
368C4×C22⋊C4—1221no—
369#340—611no—
370#340—611no—
371#340—611no—
372#340—611no—
373#340—611no—
374#340—611no—
375#340C2×D6111yescharacteristic
376#340C2×D6111yescharacteristic
377C61#2471111yescharacteristic, complemented, Sylow
378C22×Q8—1221no—
379C22×Q8C22×D6111yescharacteristic
380C23×C4—611no—
381C23×C4—611no—
382C23×C4—611no—
383C22×C8—611no—
384C22×C8—611no—
385C22×C8C22×D6111yescharacteristic
386C22×C8C22×D6111yescharacteristic
387C4⋊Q8—1222no—
388C4⋊Q8—1222no—
389C22⋊Q8—1222no—
390C22⋊Q8—1222no—
391C22⋊Q8—2444no—
392C4×Q8—1222no—
393C4×Q8—1222no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—611no—
396C2×C4⋊C4—611no—
397C2×C4⋊C4—611no—
398C2×C4⋊C4—611no—
399C2×C4⋊C4—1221no—
400C2×C4⋊C4—1221no—
401C2×C4⋊C4—1221no—
402C2×C4⋊C4—1221no—
403C2×C4⋊C4—1221no—
404C2×C4⋊C4—1221no—
405C2×C4⋊C4—1221no—
406C2×C4⋊C4C22×D6111yescharacteristic
407C2×C4⋊C4C22×D6111yescharacteristic
408C2×C4⋊C4C22×D6111yescharacteristic
409C2×C22⋊C4—1221no—
410C2×C22⋊C4—1221no—
411C2×C22⋊C4—1221no—
412C2×C22⋊C4—1221no—
413C2×C42—611no—
414C2×C42—611no—
415C2×C42—611no—
416C2×C42—1222no—
417C2×C42—1222no—
418C2×C42—1221no—
419C2×C42—1221no—
420C2×C42C22×D6111yescharacteristic
421#107—1222no—
422#107—1222no—
423#106—1222no—
424#106—1222no—
425C4⋊C8—614no—
426C4⋊C8—1222no—
427#103—22no—
428#103—22no—
429#103—1222no—
430#103—1222no—
431C22⋊C8—1222no—
432C22⋊C8—1222no—
433#97—22no—
434#97—1222no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—1221no—
439#95—1221no—
440#95—1221no—
441#95—1221no—
442#95—1221no—
443#95—1221no—
444C24—611no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—2442no—
451C2×Q8—2442no—
452C2×Q8—2442no—
453C2×Q8#1175822212yes—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—611no—
459C22×C4—611no—
460C22×C4—611no—
461C22×C4—1222no—
462C22×C4—1222no—
463C22×C4—1222no—
464C22×C4—1222no—
465C22×C4—1222no—
466C22×C4—1221no—
467C22×C4—1221no—
468C22×C4—1221no—
469C22×C4—1221no—
470C22×C4—1221no—
471C22×C4—1221no—
472C22×C4—1221no—
473C22×C4—1221no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—2441no—
477C22×C4D4×D6111yescharacteristic
478C22×C4D4×D6111yescharacteristic
479C22×C4C23×D6111yescharacteristic
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—612no—
486C2×C8—1221no—
487C2×C8—1221no—
488C2×C8—1221no—
489C2×C8—1221no—
490C2×C8—1221no—
491C2×C8D4×D6112yes—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—42no—
499C4⋊C4—612no—
500C4⋊C4—1224no—
501C4⋊C4—1221no—
502C4⋊C4—1221no—
503C4⋊C4—1221no—
504C4⋊C4—1221no—
505C4⋊C4—1221no—
506C4⋊C4—1221no—
507C4⋊C4—1221no—
508C4⋊C4—2442no—
509C4⋊C4—2442no—
510C4⋊C4—2442no—
511C4⋊C4—2442no—
512C4⋊C4—2442no—
513C4⋊C4—2442no—
514C22⋊C4—1224no—
515C22⋊C4—2442no—
516C22⋊C4—2442no—
517C22⋊C4—2442no—
518C42—21no—
519C42—21no—
520C42—612no—
521C42—612no—
522C42—1222no—
523C42—1222no—
524C42—2442no—
525C42—2442no—
526C23—612no—
527C23—1221no—
528C23—1221no—
529C23—1221no—
530C23—1221no—
531C23—1221no—
532C23—1221no—
533C23C2×D4×D6111yescharacteristic
534Q8—22no—
535Q8—22no—
536Q8—41no—
537Q8—41no—
538Q8—4884no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—22no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—612no—
558C2×C4—612no—
559C2×C4—612no—
560C2×C4—612no—
561C2×C4—1221no—
562C2×C4—1221no—
563C2×C4—1221no—
564C2×C4—1222no—
565C2×C4—1221no—
566C2×C4—1221no—
567C2×C4—2444no—
568C2×C4—2444no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4—2441no—
574C2×C4—2441no—
575C2×C4—2441no—
576C2×C4—2441no—
577C2×C4—2441no—
578C2×C4—2441no—
579C2×C4—2441no—
580C2×C4—2441no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4—2441no—
584C2×C4C2×D4×D6111yescharacteristic
585C2×C4#41×D6111yescharacteristic
586C2×C4#41×D6111yescharacteristic
587C2×C4C2×#1175822211yescharacteristic
588C2×C4#1451982411yescharacteristic
589C2×C4#1451982411yescharacteristic
590C8—22no—
591C8—41no—
592C8—1222no—
593C8—2441no—
594C22—1222no—
595C22—1222no—
596C22—1222no—
597C22—2441no—
598C22—2441no—
599C22—2441no—
600C22—2441no—
601C22#121×D6111yescharacteristic
602C22#1684027111yescharacteristic
603C22#1684033211yescharacteristic
604C22AGL(1,ℤ/8)×D6111yescharacteristic
605C22#137×D6111yescharacteristic
606C22#137×D6111yescharacteristic
607C22#1684056111yescharacteristic
608C4—42no—
609C4—41no—
610C4—41no—
611C4—81no—
612C4—81no—
613C4—81no—
614C4—614no—
615C4—1222no—
616C4—4881no—
617C4—4881no—
618C4—4881no—
619C4—2441no—
620C4—2442no—
621C4#1684041011yescharacteristic
622C4#1684042111yescharacteristic
623C4#1684044511yescharacteristic
624C4#1684047911yescharacteristic
625C2—2442no—
626C2#2144924511yescharacteristic
627C2#470×D6111yescharacteristic
628C2#2145543311yescharacteristic
629C2#2145593911yescharacteristic
630C2#2145597911yescharacteristic
631C2#2145702811yescharacteristic
632C2#2145703611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1935C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
hypercenter#1935D61
hypocenterC61#24711
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1935

Complements

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

NH ≅ G/Ntype
1. C2×#16840055C2semidirect
9. #21446765C2semidirect
10. #21446581C2semidirect
11. #21446562C2semidirect
12. #21446559C2semidirect
13. #21446512C2semidirect
14. #21445822C2semidirect
15. C61×#1935C2semidirect
322. #1935D61semidirect
377. C61#24711semidirect

Maximal subgroups

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

subgroupindex
C2×#168400552
C2×#168398172
#214541702
#214483572
#214472462
#214472442
#214470142
#214470132
#214467652
#214465812
#214465622
#214465592
#214465122
#214458222
C61×#19352
#2471161