Finite Group Databasebeta

← #29688021

Subgroups — #29688021

Order 15616.

890 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840107C211yesmaximal, characteristic
2#21448566C211yesmaximal, characteristic, complemented
3#21448543C211yesmaximal, characteristic
4#21446790C211yesmaximal, characteristic, complemented
5#21446641C211yesmaximal, characteristic
6#21446516C211yesmaximal, characteristic, complemented
7#21446505C211yesmaximal, characteristic, complemented
8#21446501C211yesmaximal, characteristic, complemented
9#21445948C211yesmaximal, characteristic, complemented
10#21445646C211yesmaximal, characteristic, complemented
11#21445643C211yesmaximal, characteristic, complemented
12#102×Dic61C211yesmaximal, characteristic, complemented
13#21445633C211yesmaximal, characteristic, complemented
14#21445507C211yesmaximal, characteristic, complemented
15C61×#1936C211yesmaximal, characteristic, complemented
16C2×#14519776C2211yescharacteristic
17C2×#14519773C2211yescharacteristic
18C2×D4×Dic61C2211yescharacteristic
19C2×#14519739C2211yescharacteristic
20#16840107C418yescomplemented
21C2×#14519699C2211yescharacteristic
22C2×#14519699C2211yescharacteristic
23C2×#14519698C2211yescharacteristic
24C2×#14519698C2211yescharacteristic
25C2×#14519697C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×#14519687C2211yescharacteristic
28C2×#14519687C2211yescharacteristic
29C2×C4×#92418C2211yescharacteristic
30C2×C8×Dic61C2211yescharacteristic
31C2×C8×Dic61C2211yescharacteristic
32#16839667—21no—
33#16839666—21no—
34#16839664C2211yescharacteristic
35#16839660C2211yescharacteristic
36#16839644—21no—
37#16839643—21no—
38#16839639—21no—
39#16839639—21no—
40#16839638—21no—
41#16839638—21no—
42#16839627C2211yescharacteristic
43#16839627C2211yescharacteristic
44C4⋊C4×Dic61C2211yescharacteristic
45C4⋊C4×Dic61C2211yescharacteristic
46#16839608C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53C2×#102×C61C2211yescharacteristic
54C2×#102×C61C2211yescharacteristic
55C2×#97×C61C2211yescharacteristic
56C61×#390C2211yescharacteristic
57C61×#389C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C22×Dic122—21no—
61C22×D244C2311yescharacteristic
62C22×C22⋊D61—21no—
63C22×C22⋊D61—21no—
64C23×Dic61—21no—
65C22×C4×D61—21no—
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68#14519776—22no—
69#14519776C2×C414yescomplemented
70#14519773—22no—
71#14519773C2×C414yes—
72D4×Dic61—22no—
73D4×Dic61—22no—
74#14519739—22no—
75#14519739—22no—
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×#11758196—21no—
80C2×#11758196—21no—
81C2×C22⋊Dic61—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×#11758198—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61—21no—
87C2×C4×Dic61C2311yescharacteristic
88C2×C4×Dic61C2311yescharacteristic
89#14519699—22no—
90#14519699C2×C414yescomplemented
91#14519698—22no—
92#14519698C2×C414yescomplemented
93#14519697—22no—
94#14519697C2×C414yescomplemented
95#14519687—22no—
96#14519687—22no—
97C4×#92418—22no—
98C8×Dic61—22no—
99C8×Dic61C2×C414yescomplemented
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684D411yescharacteristic
108#14519684D411yescharacteristic
109#14519684D411yescharacteristic
110#14519684D411yescharacteristic
111C22×D4×C61C2311yescharacteristic
112C22×C8×C61C2311yescharacteristic
113C22×C8×C61C2311yescharacteristic
114C2×C4⋊C4×C61—21no—
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C22⋊C4×C61—21no—
119C2×C22⋊C4×C61—21no—
120C2×C42×C61C2311yescharacteristic
121#102×C61—22no—
122#102×C61C2×C414yescomplemented
123#97×C61—22no—
124#95×C61—21no—
125C24×C61—21no—
126C23×D61—21no—
127C2×D4×C61—21no—
128C2×D4×C61—21no—
129C2×D4×C61—21no—
130C2×D4×C61—21no—
131C2×D4×C61—21no—
132C2×D4×C61C22×C412yes—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2411yescharacteristic
139C2×C22⋊D61—24no—
140C2×C22⋊D61—24no—
141C2×C22⋊D61—81no—
142C2×C22⋊D61—81no—
143C2×C22⋊D61—81no—
144C2×C22⋊D61—81no—
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61—42no—
149C22×Dic61—81no—
150C22×Dic61—81no—
151C22×Dic61C2×D411yescharacteristic
152C22×Dic61C2×D411yescharacteristic
153C22×Dic61C2×D411yescharacteristic
154C22×Dic61C2×D411yescharacteristic
155C2×D244—21no—
156C2×D244—21no—
157C2×D244—21no—
158C2×D244—21no—
159C2×D244—21no—
160C2×D244C22×C412yes—
161C2×C4×D61—42no—
162C2×C4×D61—81no—
163C2×C4×D61—81no—
164C2×Dic122—24no—
165C2×Dic122—81no—
166C2×Dic122—81no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61C22×C412yes—
172C2×C8×C61#4112yes—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—81no—
179C4⋊C4×C61C22×C412yes—
180C22⋊C4×C61—81no—
181C22⋊C4×C61—81no—
182C42×C61—21no—
183C42×C61—21no—
184C22⋊Dic61—42no—
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⋊Dic61C22×C412yes—
194#11758196—24no—
195#11758196—81no—
196C4×Dic61—81no—
197C4×Dic61—81no—
198C4×Dic61C22×C412yes—
199C4×Dic61#4112yes—
200C4×Dic61#4112yes—
201C4×Dic61#4112yes—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418C22×C412yes—
207C2×#92418#4112yes—
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—22no—
217C22×D61—41no—
218C22×D61—41no—
219C22×D61—41no—
220C22×D61—41no—
221C22×D61—41no—
222C22×D61—41no—
223D4×C61—22no—
224D4×C61—22no—
225D4×C61—41no—
226D4×C61—41no—
227C2×C4×C61—22no—
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—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×C61C23×C411yescharacteristic
243C2×C4×C61C2×#4111yescharacteristic
244C2×C4×C61C2×#4111yescharacteristic
245C2×C4×C61C2×#4111yescharacteristic
246C2×C4×C61C2×#4111yescharacteristic
247C2×C4×C61C2×#4111yescharacteristic
248C22⋊D61—84no—
249C22⋊D61—84no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—22no—
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—84no—
268C2×Dic61C4×D412yes—
269C2×Dic61C4×D412yes—
270C2×Dic61#12412yes—
271C2×Dic61#12412yes—
272D244—22no—
273D244—22no—
274D244—41no—
275D244—41no—
276C4×D61—84no—
277Dic122—84no—
278C8×C61—22no—
279C8×C61—22no—
280#92418—22no—
281#92418—22no—
282#21644—611nomaximal, Sylow
283C22×C61—42no—
284C22×C61—42no—
285C22×C61—42no—
286C22×C61—81no—
287C22×C61—81no—
288C22×C61—81no—
289C22×C61—81no—
290C22×C61C2×C4×D411yescharacteristic
291C22×C61C2×#12411yescharacteristic
292C22×C61#53211yescharacteristic
293C22×C61#57611yescharacteristic
294C22×C61#57611yescharacteristic
295C22×C61#57711yescharacteristic
296C22×C61#57711yescharacteristic
297C2×D61—42no—
298C2×D61—42no—
299C2×D61—42no—
300C2×D61—81no—
301C2×D61—81no—
302C2×D61—81no—
303C2×D61—81no—
304C4×C61—41no—
305C4×C61—41no—
306C4×C61—42no—
307C4×C61—81no—
308C4×C61—81no—
309C4×C61C4×#4111yescharacteristic
310C4×C61C4×#4111yescharacteristic
311C4×C61#52911yescharacteristic
312C4×C61#52911yescharacteristic
313Dic61—22no—
314Dic61—22no—
315Dic61—22no—
316Dic61—22no—
317Dic61—42no—
318Dic61—81no—
319Dic61—81no—
320C2×#486—611no—
321#2331—611no—
322#2328—611no—
323#1993—611no—
324#1961—611no—
325#1936—611no—
326#1936D6111yescharacteristic, complemented
327#1934—611no—
328#1934—611no—
329#1835—611no—
330#1762—611no—
331#1762—611no—
332C4×#102—611no—
333C4×#102—611no—
334#1726—611no—
335C2×C61—82no—
336C2×C61C4×#12411yescharacteristic
337C2×C61#294811yescharacteristic
338C2×C61#294911yescharacteristic
339C2×C61#313611yescharacteristic
340C2×C61#313611yescharacteristic
341C2×C61#317911yescharacteristic
342C2×C61#317911yescharacteristic
343D61—82no—
344C2×C4⋊Q8—611no—
345C2×#127—611no—
346C2×C4×D4—611no—
347C2×C4×D4—611no—
348#486—618no—
349C2×#102—611no—
350C2×#102—611no—
351C2×#102—611no—
352C2×#102—611no—
353C2×#102—611no—
354C2×#102—611no—
355C2×#102C2×D6111yescharacteristic
356C2×#102C2×D6111yescharacteristic
357C2×#97—611no—
358C2×#97—611no—
359C2×#97C2×D6111yescharacteristic
360C2×C4×C8—611no—
361C2×C4×C8—611no—
362C2×C4×C8—611no—
363#391—1221no—
364#391—1221no—
365#390—611no—
366#390C2×D6111yescharacteristic
367#389—611no—
368#389C2×D6111yescharacteristic
369#387—1221no—
370#387—1221no—
371#386—1221no—
372#386—1221no—
373#386—1221no—
374#386—1221no—
375#382—611no—
376#382—611no—
377C4×C4⋊C4—611no—
378C4×C4⋊C4—611no—
379#376—611no—
380#340—611no—
381#340—611no—
382#340—611no—
383#340—611no—
384#340—611no—
385#340—611no—
386#340C2×D6111yescharacteristic
387#340C2×D6111yescharacteristic
388C61#2164411yescharacteristic, complemented, Sylow
389C22×Q8—1221no—
390C22×D4—611no—
391C22×D4—1221no—
392C22×D4—1221no—
393C22×D4C22×D6111yescharacteristic
394C23×C4—1221no—
395C23×C4—1221no—
396C22×C8—611no—
397C22×C8—611no—
398C22×C8C22×D6111yescharacteristic
399C22×C8C22×D6111yescharacteristic
400C4⋊Q8—614no—
401C4⋊Q8—1222no—
402#127—614no—
403#127—1222no—
404C4×D4—1222no—
405C4×D4—1222no—
406C4×D4—1222no—
407C4×D4—1222no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—611no—
410C2×C4⋊C4—611no—
411C2×C4⋊C4—611no—
412C2×C4⋊C4—1221no—
413C2×C4⋊C4—1221no—
414C2×C4⋊C4C22×D6111yescharacteristic
415C2×C4⋊C4C22×D6111yescharacteristic
416C2×C4⋊C4C22×D6111yescharacteristic
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—1221no—
420C2×C22⋊C4—1221no—
421C2×C22⋊C4—1221no—
422C2×C22⋊C4—1221no—
423C2×C42—611no—
424C2×C42—611no—
425C2×C42—1221no—
426C2×C42—1221no—
427C2×C42C22×D6111yescharacteristic
428#102—22no—
429#102—614no—
430#102—614no—
431#102—614no—
432#102—1222no—
433#102—1222no—
434#102—1222no—
435#102C4×D6114yescomplemented
436#97—22no—
437#97—1222no—
438#97—1222no—
439C4×C8—614no—
440C4×C8—1222no—
441C4×C8—1222no—
442#95—21no—
443#95—611no—
444#95—611no—
445#95—611no—
446#95—611no—
447#95—1221no—
448#95—1221no—
449#95—1221no—
450#95—1221no—
451#95—1221no—
452#95—1221no—
453#95—1221no—
454C24—21no—
455C24—1221no—
456C2×Q8—1224no—
457C2×Q8—4881no—
458C2×Q8—4881no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—612no—
465C2×D4—1224no—
466C2×D4—1224no—
467C2×D4—1221no—
468C2×D4—1221no—
469C2×D4—1221no—
470C2×D4—1221no—
471C2×D4—1221no—
472C2×D4—4881no—
473C2×D4—4881no—
474C2×D4—4881no—
475C2×D4—4881no—
476C2×D4C2×C4×D6112yes—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—611no—
483C22×C4—611no—
484C22×C4—1221no—
485C22×C4—1221no—
486C22×C4—1221no—
487C22×C4—4881no—
488C22×C4—4881no—
489C22×C4—4881no—
490C22×C4—4881no—
491C22×C4—2442no—
492C22×C4—2442no—
493C22×C4D4×D6111yescharacteristic
494C22×C4D4×D6111yescharacteristic
495C22×C4C23×D6111yescharacteristic
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—612no—
501C2×C8—612no—
502C2×C8—1221no—
503C2×C8—1221no—
504C2×C8—1221no—
505C2×C8—1221no—
506C2×C8C2×C4×D6112yes—
507C2×C8#1175822412yes—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—81no—
514C4⋊C4—612no—
515C4⋊C4—1224no—
516C4⋊C4—1221no—
517C4⋊C4—1221no—
518C4⋊C4—1221no—
519C4⋊C4—1221no—
520C4⋊C4—1221no—
521C4⋊C4—4881no—
522C4⋊C4C2×C4×D6112yes—
523C22⋊C4—81no—
524C22⋊C4—81no—
525C22⋊C4—4881no—
526C22⋊C4—4881no—
527C22⋊C4—2442no—
528C22⋊C4—2442no—
529C42—21no—
530C42—21no—
531C42—612no—
532C42—612no—
533C42—612no—
534C42—612no—
535C42—4881no—
536C42—4881no—
537C23—22no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—1222no—
545C23—2441no—
546C23—2441no—
547C23—2441no—
548C23—2441no—
549C23—2441no—
550C23—2441no—
551C23C2×D4×D6111yescharacteristic
552Q8—4884no—
553D4—22no—
554D4—22no—
555D4—41no—
556D4—41no—
557D4—1222no—
558D4—1222no—
559D4—4884no—
560D4—4884no—
561D4—2441no—
562D4—2441no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
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—612no—
579C2×C4—612no—
580C2×C4—612no—
581C2×C4—612no—
582C2×C4—1221no—
583C2×C4—1221no—
584C2×C4—1221no—
585C2×C4—1221no—
586C2×C4—1221no—
587C2×C4—1221no—
588C2×C4—1221no—
589C2×C4—1221no—
590C2×C4—1222no—
591C2×C4—4884no—
592C2×C4—4884no—
593C2×C4—2441no—
594C2×C4—2441no—
595C2×C4—2441no—
596C2×C4—2441no—
597C2×C4—2441no—
598C2×C4—2441no—
599C2×C4—2441no—
600C2×C4—2441no—
601C2×C4C22×C4×D6111yescharacteristic
602C2×C4#41×D6111yescharacteristic
603C2×C4#41×D6111yescharacteristic
604C2×C4#41×D6111yescharacteristic
605C2×C4#41×D6111yescharacteristic
606C2×C4C2×#1175822411yescharacteristic
607C8—22no—
608C8—22no—
609C8—1222no—
610C8—1222no—
611C22—42no—
612C22—42no—
613C22—42no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—4881no—
619C22—4881no—
620C22—4881no—
621C22—4881no—
622C22—2442no—
623C22—2442no—
624C22—2442no—
625C22C4×D4×D6111yescharacteristic
626C22#124×D6111yescharacteristic
627C22#1684030711yescharacteristic
628C22#1684056611yescharacteristic
629C22#1684056611yescharacteristic
630C22#1684057111yescharacteristic
631C22#1684057211yescharacteristic
632C4—42no—
633C4—41no—
634C4—41no—
635C4—81no—
636C4—81no—
637C4—1222no—
638C4—1222no—
639C4—1222no—
640C4—1222no—
641C4—4881no—
642C4—4881no—
643C4—2442no—
644C4C4×#1175822411yescharacteristic
645C4#1684023011yescharacteristic
646C4#1684028911yescharacteristic
647C4#1684029511yescharacteristic
648C2—82no—
649C2—4882no—
650C2#2144836011yescharacteristic
651C2#2145466811yescharacteristic
652C2#2145467511yescharacteristic
653C2#2145617011yescharacteristic
654C2#2145617411yescharacteristic
655C2#2145649511yescharacteristic
656C2#2145650311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1936C2
socleC23×C61C22×D4
prime radicalC2×#14519773C22
cosocleC22×C4×C61C24
hypercenter#1936D61
hypocenterC61#21644
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1936

Complements

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

NH ≅ G/Ntype
2. #21448566C2semidirect
4. #21446790C2semidirect
6. #21446516C2semidirect
7. #21446505C2semidirect
8. #21446501C2semidirect
9. #21445948C2semidirect
10. #21445646C2semidirect
11. #21445643C2semidirect
12. #102×Dic61C2semidirect
13. #21445633C2semidirect
14. #21445507C2semidirect
15. C61×#1936C2semidirect
20. #16840107C4semidirect
69. #14519776C2×C4semidirect
90. #14519699C2×C4semidirect
92. #14519698C2×C4semidirect
94. #14519697C2×C4semidirect
99. C8×Dic61C2×C4semidirect
122. #102×C61C2×C4semidirect
326. #1936D61semidirect
388. C61#21644semidirect
435. #102C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168401072
#214485662
#214485432
#214467902
#214466412
#214465162
#214465052
#214465012
#214459482
#214456462
#214456432
#102×Dic612
#214456332
#214455072
C61×#19362
#2164461