Finite Group Databasebeta

← #29721406

Subgroups — #29721406

Order 15616.

802 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839822C211yesmaximal, characteristic, complemented
2#21451641C211yesmaximal, characteristic, complemented
3#21448506C211yesmaximal, characteristic
4#21447253C211yesmaximal, characteristic, complemented
5#21447253C211yesmaximal, characteristic, complemented
6#21447007C211yesmaximal, characteristic
7#21447000C211yesmaximal, characteristic
8#21446772C211yesmaximal, characteristic, complemented
9#21446589C211yesmaximal, characteristic, complemented
10#21446555C211yesmaximal, characteristic, complemented
11#21446545C211yesmaximal, characteristic, complemented
12#21446513C211yesmaximal, characteristic, complemented
13#21446499C211yesmaximal, characteristic, complemented
14#21445829C211yesmaximal, characteristic, complemented
15C2×C61×#476C211yesmaximal, characteristic, complemented
16C2×#14519748C2211yescharacteristic
17C2×#14519734C2211yescharacteristic
18#16839822—24no—
19C2×#14519711C2211yescharacteristic
20C2×#14519709C2211yescharacteristic
21C2×C4⋊#92418C2211yescharacteristic
22C2×#14519698C2211yescharacteristic
23C2×#14519698C2211yescharacteristic
24C2×#14519689C2211yescharacteristic
25C2×#14519689C2211yescharacteristic
26C2×#14519687C2211yescharacteristic
27C2×C8×Dic61C2211yescharacteristic
28#16839700—21no—
29#16839697—21no—
30#16839681—21no—
31#16839673—21no—
32#16839665C2211yescharacteristic
33#16839662—21no—
34#16839658C2211yescharacteristic
35#16839658C2211yescharacteristic
36#16839658C2211yescharacteristic
37#16839656—21no—
38#16839641—21no—
39#16839635—21no—
40#16839628C2211yescharacteristic
41#16839619C2211yescharacteristic
42#16839619C2211yescharacteristic
43#16839619C2211yescharacteristic
44C4×C4⋊Dic61C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53C2×C4⋊Q8×C61C2211yescharacteristic
54C2×C4×D4×C61C2211yescharacteristic
55C61×#476—24no—
56C2×#106×C61C2211yescharacteristic
57C2×#106×C61C2211yescharacteristic
58C2×C4⋊C8×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C22×C22⋊D61—21no—
62C22×C4×D61C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65#14519748—22no—
66#14519748—22no—
67#14519734—22no—
68#14519734—22no—
69C2×C4⋊Dic61C2311yescharacteristic
70C2×C4⋊Dic61C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×#11758196—21no—
74C2×#11758196—21no—
75C2×#11758196—21no—
76C2×#11758196D411yescharacteristic
77C2×#11758196D411yescharacteristic
78C2×C22⋊Dic61—21no—
79C2×C22⋊Dic61—21no—
80C2×C22⋊Dic61—21no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×#11758198D411yescharacteristic
85C2×#11758198D411yescharacteristic
86C2×C4×Dic61—21no—
87C2×C4×Dic61C2311yescharacteristic
88#14519711—22no—
89#14519709—22no—
90C4⋊#92418—22no—
91#14519698—22no—
92#14519698—22no—
93#14519689—22no—
94#14519689—22no—
95#14519687—22no—
96C8×Dic61—22no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106C22×Q8×C61—21no—
107C22×D4×C61C2311yescharacteristic
108C23×C4×C61—21no—
109C22×C8×C61C2311yescharacteristic
110C22×C8×C61C2311yescharacteristic
111C4⋊Q8×C61—22no—
112C4⋊Q8×C61—22no—
113C4×D4×C61—22no—
114C4×D4×C61—22no—
115C2×C4⋊C4×C61—21no—
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C22⋊C4×C61—21no—
120C2×C42×C61C2311yescharacteristic
121#106×C61—22no—
122#106×C61—22no—
123C4⋊C8×C61D414yescomplemented
124#102×C61—22no—
125#102×C61—22no—
126C24×C61—21no—
127C23×D61C2×D411yescharacteristic
128C2×Q8×C61—42no—
129C2×Q8×C61—81no—
130C2×Q8×C61—81no—
131C2×D4×C61—21no—
132C2×D4×C61—21no—
133C2×D4×C61—21no—
134C2×D4×C61—21no—
135C2×D4×C61—21no—
136C2×D4×C61#4112yes—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—42no—
141C22×C4×C61—81no—
142C22×C4×C61—81no—
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2411yescharacteristic
146C2×C22⋊D61—24no—
147C2×C22⋊D61—81no—
148C2×C22⋊D61—81no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153C22×Dic61C2×D411yescharacteristic
154C22×Dic61C2×D411yescharacteristic
155C22×Dic61C2×D411yescharacteristic
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61C2×D412yes—
167C2×C8×C61C2×D412yes—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—42no—
175C22⋊C4×C61—42no—
176C42×C61C2×D412yes—
177C42×C61#4112yes—
178C22⋊Dic61—24no—
179C22⋊Dic61—81no—
180C22⋊Dic61—81no—
181#11758198—22no—
182#11758198—22no—
183#11758198—81no—
184#11758198—81no—
185#11758198—81no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61#4112yes—
194#11758196—22no—
195#11758196—22no—
196#11758196—81no—
197#11758196—81no—
198#11758196—81no—
199C4×Dic61—21no—
200C4×Dic61—21no—
201C4×Dic61—81no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
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—
223Q8×C61—84no—
224D4×C61—22no—
225D4×C61—22no—
226D4×C61—41no—
227D4×C61—41no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
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—84no—
242C2×C4×C61#12112yes—
243C2×C4×C61#12112yes—
244C2×C4×C61C22×D411yescharacteristic
245C2×C4×C61C2×#4111yescharacteristic
246C2×C4×C61C2×#4111yescharacteristic
247C2×C4×C61C2×#4111yescharacteristic
248C2×C4×C612−1+411yescharacteristic
249C2×C4×C612−1+411yescharacteristic
250C22⋊D61—84no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—22no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61—41no—
272C4×D61—41no—
273C4×D61—41no—
274C4×D61—41no—
275C4×D61—41no—
276C8×C61—22no—
277C8×C61—22no—
278#92418—41no—
279#92418—41no—
280#24716—611nomaximal, Sylow
281C22×C61—42no—
282C22×C61—42no—
283C22×C61—42no—
284C22×C61—81no—
285C22×C61—81no—
286C22×C61—81no—
287C22×C61—81no—
288C22×C61C2×#12111yescharacteristic
289C22×C61#52511yescharacteristic
290C22×C61#53611yescharacteristic
291C22×C61#57611yescharacteristic
292C22×C61#57711yescharacteristic
293C22×C61#57711yescharacteristic
294C22×C61#57711yescharacteristic
295C2×D61—41no—
296C2×D61—41no—
297C2×D61—41no—
298C2×D61—41no—
299C2×D61—41no—
300C2×D61—41no—
301C2×D61—41no—
302C4×C61—22no—
303C4×C61—22no—
304C4×C61—81no—
305C4×C61—81no—
306C4×C61—81no—
307C4×C61#54711yescharacteristic
308C4×C61#54811yescharacteristic
309C4×C61#55211yescharacteristic
310C4×C61#55611yescharacteristic
311Dic61—42no—
312Dic61—41no—
313Dic61—41no—
314Dic61—41no—
315Dic61—81no—
316Dic61—81no—
317Dic61—81no—
318C2×#476D6111yescharacteristic, complemented
319C2×#433—611no—
320#2628—611no—
321#2324—611no—
322#2077—611no—
323#2077—611no—
324#2034—611no—
325#2033—611no—
326#1988—611no—
327#1949—611no—
328#1943—611no—
329#1941—611no—
330#1936—611no—
331#1934—611no—
332#1804—611no—
333C2×C61—82no—
334C2×C61#241511yescharacteristic
335C2×C61#305711yescharacteristic
336C2×C61#306211yescharacteristic
337C2×C61#311811yescharacteristic
338C2×C61#312511yescharacteristic
339C2×C61#324111yescharacteristic
340C2×C61#324411yescharacteristic
341D61—81no—
342C2×C4⋊Q8C2×D6111yescharacteristic
343C2×#121—611no—
344C2×C4×D4C2×D6111yescharacteristic
345C2×#117—611no—
346#476—24no—
347#433—1224no—
348C2×#107—611no—
349C2×#106—611no—
350C2×#106C2×D6111yescharacteristic
351C2×#106C2×D6111yescharacteristic
352C2×C4⋊C8—611no—
353C2×C4⋊C8C2×D6111yescharacteristic
354C2×#102—611no—
355C2×#102—611no—
356C2×#102C2×D6111yescharacteristic
357C2×#102C2×D6111yescharacteristic
358C2×C22⋊C8—611no—
359C2×C22⋊C8—611no—
360C2×#97—611no—
361C2×C4×C8—611no—
362#400—1221no—
363#399—1221no—
364#395—1221no—
365#393—1221no—
366#390—611no—
367#390—1221no—
368#389—611no—
369#389—611no—
370#389—611no—
371#388—1221no—
372#386—1221no—
373#385—1221no—
374#382—611no—
375#380—611no—
376#380—611no—
377#380—611no—
378C4×C4⋊C4—611no—
379#340—611no—
380#340—611no—
381#340—611no—
382#340—611no—
383#340—611no—
384#340—611no—
385#340—611no—
386#340—611no—
387C61#2471611yescharacteristic, complemented, Sylow
388C22×Q8—21no—
389C22×D4—1221no—
390C22×D4C22×D6111yescharacteristic
391C23×C4—21no—
392C23×C4—611no—
393C22×C8—611no—
394C22×C8—611no—
395C22×C8C22×D6111yescharacteristic
396C22×C8C22×D6111yescharacteristic
397C4⋊Q8—22no—
398C4⋊Q8—22no—
399#121—1222no—
400#121—1222no—
401C4×D4—22no—
402C4×D4—22no—
403#117—1222no—
404#117—1222no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—611no—
407C2×C4⋊C4—611no—
408C2×C4⋊C4—611no—
409C2×C4⋊C4—611no—
410C2×C4⋊C4—611no—
411C2×C4⋊C4—611no—
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×C22⋊C4—21no—
419C2×C22⋊C4—611no—
420C2×C22⋊C4—611no—
421C2×C22⋊C4—1221no—
422C2×C22⋊C4—1221no—
423C2×C22⋊C4—1221no—
424C2×C22⋊C4—1221no—
425C2×C22⋊C4—1221no—
426C2×C22⋊C4—1221no—
427C2×C42—611no—
428C2×C42—1221no—
429C2×C42C22×D6111yescharacteristic
430#107—1222no—
431#106—22no—
432#106—22no—
433#106—1222no—
434C4⋊C8—1222no—
435C4⋊C8C22⋊D6114yescomplemented
436#102—22no—
437#102—22no—
438#102—1222no—
439#102—1222no—
440C22⋊C8—1222no—
441C22⋊C8—1222no—
442#97—1222no—
443C4×C8—1222no—
444#95—1221no—
445#95—1221no—
446#95—1221no—
447#95—1221no—
448#95—1221no—
449#95—1221no—
450#95—1221no—
451#95—1221no—
452#95—1221no—
453C24—21no—
454C24—611no—
455C2×Q8—42no—
456C2×Q8—81no—
457C2×Q8—81no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—1224no—
464C2×D4—4881no—
465C2×D4—4881no—
466C2×D4#1175822612yes—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—42no—
471C22×C4—81no—
472C22×C4—81no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—1221no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—1221no—
482C22×C4—1221no—
483C22×C4—1221no—
484C22×C4—1221no—
485C22×C4—1221no—
486C22×C4D4×D6111yescharacteristic
487C22×C4D4×D6111yescharacteristic
488C22×C4C23×D6111yescharacteristic
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—1221no—
494C2×C8—1221no—
495C2×C8—1221no—
496C2×C8—1221no—
497C2×C8—1221no—
498C2×C8—1221no—
499C2×C8C2×C22⋊D6112yes—
500C2×C8C2×C22⋊D6112yes—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—42no—
508C4⋊C4—612no—
509C4⋊C4—1221no—
510C4⋊C4—1222no—
511C4⋊C4—1222no—
512C4⋊C4—1221no—
513C4⋊C4—1221no—
514C4⋊C4—1221no—
515C4⋊C4—1221no—
516C4⋊C4—1221no—
517C4⋊C4—1221no—
518C4⋊C4—4881no—
519C4⋊C4—4881no—
520C4⋊C4—4881no—
521C22⋊C4—42no—
522C22⋊C4—1224no—
523C22⋊C4—1222no—
524C22⋊C4—1222no—
525C22⋊C4—4881no—
526C22⋊C4—4881no—
527C22⋊C4—4881no—
528C22⋊C4—4881no—
529C22⋊C4—4881no—
530C42—1221no—
531C42—1221no—
532C42—4881no—
533C42#1175822412yes—
534C42C2×C22⋊D6112yes—
535C23—22no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—1221no—
543C23—1221no—
544C23—1221no—
545C23—1221no—
546C23—1221no—
547C23—1221no—
548C23—1221no—
549C23C2×D4×D6111yescharacteristic
550Q8—84no—
551D4—22no—
552D4—22no—
553D4—41no—
554D4—41no—
555D4—4884no—
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—84no—
570C2×C4—1221no—
571C2×C4—1221no—
572C2×C4—1221no—
573C2×C4—1221no—
574C2×C4—1222no—
575C2×C4—1221no—
576C2×C4—1221no—
577C2×C4—1221no—
578C2×C4—1221no—
579C2×C4—1221no—
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×C4#1451974812yes—
596C2×C4#1451974812yes—
597C2×C4C22×C22⋊D6111yescharacteristic
598C2×C4#41×D6111yescharacteristic
599C2×C4C2×#1175822411yescharacteristic
600C2×C4C2×#1175822611yescharacteristic
601C2×C4#1451982411yescharacteristic
602C2×C4#1451982511yescharacteristic
603C8—22no—
604C8—22no—
605C8—2441no—
606C8—2441no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—2441no—
615C22—2441no—
616C22—2441no—
617C22—2441no—
618C22—2441no—
619C22—2441no—
620C22—2441no—
621C22C2×#1451974811yescharacteristic
622C22#1684027511yescharacteristic
623C22#1684033511yescharacteristic
624C22#1684056611yescharacteristic
625C22#1684056811yescharacteristic
626C22#1684056811yescharacteristic
627C22#1684057211yescharacteristic
628C4—22no—
629C4—22no—
630C4—81no—
631C4—81no—
632C4—81no—
633C4—4881no—
634C4—4881no—
635C4—4881no—
636C4—2441no—
637C4—2441no—
638C4—2441no—
639C4—2442no—
640C4#1684041111yescharacteristic
641C4#1684042311yescharacteristic
642C4#1684045411yescharacteristic
643C4#1684048311yescharacteristic
644C2—82no—
645C2—4881no—
646C2#2144924411yescharacteristic
647C2#2145545411yescharacteristic
648C2#2145549311yescharacteristic
649C2#2145600811yescharacteristic
650C2#2145610111yescharacteristic
651C2#2145707111yescharacteristic
652C2#2145711411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#476C2
socleC23×C61C22×D4
prime radicalC2×#14519748C22
hypercenterC2×#476D61
hypocenterC61#24716
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#16839822C2semidirect
2. #21451641C2semidirect
4. #21447253C2semidirect
5. #21447253C2semidirect
8. #21446772C2semidirect
9. #21446589C2semidirect
10. #21446555C2semidirect
11. #21446545C2semidirect
12. #21446513C2semidirect
13. #21446499C2semidirect
14. #21445829C2semidirect
15. C2×C61×#476C2semidirect
123. C4⋊C8×C61D4semidirect
318. C2×#476D61semidirect
387. C61#24716semidirect
435. C4⋊C8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398222
#214516412
#214485062
#214472532
#214470072
#214470002
#214467722
#214465892
#214465552
#214465452
#214465132
#214464992
#214458292
C2×C61×#4762
#2471661