Finite Group Databasebeta

← #29684372

Subgroups — #29684372

Order 15616.

862 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839872C211yesmaximal, characteristic
2#21448463C211yesmaximal, characteristic, complemented
3#21446694C211yesmaximal, characteristic
4#21446684C211yesmaximal, characteristic
5#21446559C211yesmaximal, characteristic, complemented
6#21446544C211yesmaximal, characteristic, complemented
7#21446519C211yesmaximal, characteristic, complemented
8#21446515C211yesmaximal, characteristic, complemented
9#21446505C211yesmaximal, characteristic, complemented
10#21446501C211yesmaximal, characteristic, complemented
11#21445717C211yesmaximal, characteristic, complemented
12C4×#14519697C211yesmaximal, characteristic, complemented
13C4×#14519698C211yesmaximal, characteristic, complemented
14#21445506C211yesmaximal, characteristic, complemented
15C61×#2319C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C2×C4×D244C2211yescharacteristic
18#16839872C418yescomplemented
19C2×#14519710C2211yescharacteristic
20C2×#14519708C2211yescharacteristic
21C2×#14519708C2211yescharacteristic
22C2×#14519698C2211yescharacteristic
23C2×#14519698C2211yescharacteristic
24C2×#14519698C2211yescharacteristic
25C2×#14519697C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×#14519688C2211yescharacteristic
29C2×#14519688C2211yescharacteristic
30C2×#14519688C2211yescharacteristic
31C2×C4×#92418C2211yescharacteristic
32C2×C4×#92418C2211yescharacteristic
33C2×C4×#92418C2211yescharacteristic
34#16839664C2211yescharacteristic
35#16839664C2211yescharacteristic
36#16839660C2211yescharacteristic
37#16839660C2211yescharacteristic
38#16839651—21no—
39#16839651—21no—
40#16839624—21no—
41#16839621—21no—
42C4×C4⋊Dic61C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49C2×C4×D4×C61C2211yescharacteristic
50C61×#390C2211yescharacteristic
51C61×#390C2211yescharacteristic
52C61×#389C2211yescharacteristic
53C61×#389C2211yescharacteristic
54C61×#388—21no—
55C61×#388—21no—
56C61×#381—21no—
57C61×#380—21no—
58C4×C4⋊C4×C61C2211yescharacteristic
59C61×#376C2211yescharacteristic
60C22×D244C2311yescharacteristic
61C22×C4×D61—21no—
62C2×#11758199—22no—
63C2×#11758199—22no—
64C2×#11758199C2×C414yes—
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C4×D244—22no—
70C4×D244C2×C414yes—
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×#11758196—21no—
75C2×#11758196—21no—
76C2×#11758198—21no—
77C2×#11758198—21no—
78C2×#11758198—21no—
79C2×#11758198—21no—
80C2×#11758198—21no—
81C2×C4×Dic61—21no—
82#14519710—22no—
83#14519708—22no—
84#14519708C2×C414yes—
85#14519698—22no—
86#14519698—22no—
87#14519698C2×C414yes—
88#14519697—22no—
89#14519697—22no—
90#14519697C2×C414yes—
91#14519688—22no—
92#14519688—22no—
93#14519688C2×C414yes—
94C4×#92418—22no—
95C4×#92418—22no—
96C4×#92418—22no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100C22×D4×C61C2311yescharacteristic
101C23×C4×C61—21no—
102C4×D4×C61—22no—
103C4×D4×C61C2×C414yes—
104C2×C4⋊C4×C61—21no—
105C2×C4⋊C4×C61—21no—
106C2×C4⋊C4×C61C2311yescharacteristic
107C2×C4⋊C4×C61C2311yescharacteristic
108C2×C4⋊C4×C61C2311yescharacteristic
109C2×C22⋊C4×C61—21no—
110C2×C22⋊C4×C61—21no—
111C2×C22⋊C4×C61—21no—
112C2×C22⋊C4×C61—21no—
113C2×C22⋊C4×C61—21no—
114C2×C42×C61—21no—
115C2×C42×C61C2311yescharacteristic
116C2×C42×C61C2311yescharacteristic
117C2×C42×C61C2311yescharacteristic
118#95×C61—21no—
119#95×C61—21no—
120#95×C61—21no—
121#95×C61D411yescharacteristic
122#95×C61D411yescharacteristic
123#95×C61D411yescharacteristic
124#95×C61D411yescharacteristic
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—24no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61—81no—
138C22×C4×C61—81no—
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2×D411yescharacteristic
141C22×C4×C61C2×D411yescharacteristic
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2411yescharacteristic
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61—21no—
149C2×D244—21no—
150C2×D244—21no—
151C2×D244—21no—
152C2×D244—21no—
153C2×D244—21no—
154C2×D244C22×C412yes—
155C2×C4×D61—24no—
156C2×C4×D61—81no—
157C2×C4×D61—81no—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—81no—
164C4⋊C4×C61—81no—
165C4⋊C4×C61C22×C412yes—
166C22⋊C4×C61—24no—
167C22⋊C4×C61—81no—
168C22⋊C4×C61—81no—
169C22⋊C4×C61—81no—
170C22⋊C4×C61—81no—
171C42×C61—21no—
172C42×C61—21no—
173C42×C61—21no—
174C42×C61—21no—
175C42×C61—81no—
176C42×C61C22×C412yes—
177C42×C61#4112yes—
178#11758199—28no—
179#11758198—24no—
180#11758198—81no—
181#11758198—81no—
182#11758198—81no—
183#11758198—81no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61C22×C412yes—
190#11758196—81no—
191#11758196—81no—
192C4×Dic61—81no—
193C2×#92418—21no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418C22×C412yes—
200C2×#92418C22×C412yes—
201C2×#92418#4112yes—
202C2×#92418#4112yes—
203C2×#92418#4112yes—
204C2×#92418#4112yes—
205C23×C61—22no—
206C23×C61—41no—
207C23×C61—41no—
208C23×C61—41no—
209C23×C61—41no—
210C23×C61—41no—
211C23×C61—41no—
212C23×C61C22×D411yescharacteristic
213C22×D61—22no—
214C22×D61—41no—
215C22×D61—41no—
216C22×D61—41no—
217C22×D61—41no—
218C22×D61—41no—
219C22×D61—41no—
220D4×C61—22no—
221D4×C61—22no—
222D4×C61—41no—
223D4×C61—41no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—22no—
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—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
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—84no—
250C2×C4×C61C4×D412yes—
251C2×C4×C61C4×D412yes—
252C2×C4×C61C23×C411yescharacteristic
253C2×C4×C61C2×#4111yescharacteristic
254C2×C4×C61C2×#4111yescharacteristic
255C2×C4×C61C2×#4111yescharacteristic
256C2×C4×C61C2×#4111yescharacteristic
257C2×C4×C61C2×#4111yescharacteristic
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—
267D244—22no—
268D244—22no—
269D244—41no—
270D244—41no—
271C4×D61—84no—
272#92418—22no—
273#92418—22no—
274#92418—22no—
275#92418#11714yes—
276#21290—611nomaximal, Sylow
277C22×C61—42no—
278C22×C61—42no—
279C22×C61—42no—
280C22×C61—81no—
281C22×C61—81no—
282C22×C61—81no—
283C22×C61—81no—
284C22×C61C2×C4×D411yescharacteristic
285C22×C61#53211yescharacteristic
286C22×C61#53211yescharacteristic
287C22×C61#57611yescharacteristic
288C22×C61#57611yescharacteristic
289C22×C61#57711yescharacteristic
290C22×C61#57711yescharacteristic
291C2×D61—42no—
292C2×D61—42no—
293C2×D61—42no—
294C2×D61—81no—
295C2×D61—81no—
296C2×D61—81no—
297C2×D61—81no—
298C4×C61—22no—
299C4×C61—22no—
300C4×C61—41no—
301C4×C61—41no—
302C4×C61—41no—
303C4×C61—41no—
304C4×C61—42no—
305C4×C61—81no—
306C4×C61—81no—
307C4×C61C2×#11711yescharacteristic
308C4×C61C4×#4111yescharacteristic
309C4×C61#52911yescharacteristic
310C4×C61#52911yescharacteristic
311Dic61—42no—
312Dic61—81no—
313Dic61—81no—
314C2×#442—611no—
315#2319—611no—
316#2319D6111yescharacteristic, complemented
317#1972—611no—
318#1970—611no—
319#1944—611no—
320#1941—611no—
321#1936—611no—
322#1936—611no—
323#1934—611no—
324#1934—611no—
325#1776—611no—
326C4×#102—611no—
327C4×#102—611no—
328#1726—611no—
329C2×C61—82no—
330C2×C61#229311yescharacteristic
331C2×C61#294611yescharacteristic
332C2×C61#294611yescharacteristic
333C2×C61#317311yescharacteristic
334C2×C61#317611yescharacteristic
335C2×C61#317911yescharacteristic
336C2×C61#317911yescharacteristic
337D61—82no—
338C22×D8—611no—
339C2×C4×D4—611no—
340C2×C4×D4C2×D6111yescharacteristic
341#442—618no—
342C2×#107—611no—
343C2×#106—611no—
344C2×#106—611no—
345C2×#102—611no—
346C2×#102—611no—
347C2×#102—611no—
348C2×#102—611no—
349C2×#102—611no—
350C2×#102—611no—
351C2×#97—611no—
352C2×#97—611no—
353C2×#97—611no—
354C2×C4×C8—611no—
355C2×C4×C8—611no—
356C2×C4×C8—611no—
357#390—611no—
358#390—611no—
359#390C2×D6111yescharacteristic
360#390C2×D6111yescharacteristic
361#389—611no—
362#389—611no—
363#389C2×D6111yescharacteristic
364#389C2×D6111yescharacteristic
365#388—21no—
366#388—21no—
367#388—1221no—
368#388—1221no—
369#381—21no—
370#381—1221no—
371#380—21no—
372#380—1221no—
373C4×C4⋊C4—611no—
374C4×C4⋊C4C2×D6111yescharacteristic
375#376C2×D6111yescharacteristic
376#340—611no—
377#340—611no—
378#340—611no—
379#340—611no—
380#340—611no—
381#340—611no—
382C61#2129011yescharacteristic, complemented, Sylow
383C22×D4—611no—
384C22×D4C22×D6111yescharacteristic
385C23×C4—21no—
386C23×C4—1221no—
387C2×D8—614no—
388C2×D8—1222no—
389C2×D8—1222no—
390C22×C8—611no—
391C22×C8—611no—
392C22×C8—611no—
393C22×C8—611no—
394C4×D4—22no—
395C4×D4—614no—
396C4×D4—1222no—
397C4×D4C4×D6114yes—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—611no—
401C2×C4⋊C4—611no—
402C2×C4⋊C4—611no—
403C2×C4⋊C4—1221no—
404C2×C4⋊C4—1221no—
405C2×C4⋊C4C22×D6111yescharacteristic
406C2×C4⋊C4C22×D6111yescharacteristic
407C2×C4⋊C4C22×D6111yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—1221no—
414C2×C22⋊C4—1221no—
415C2×C22⋊C4—1221no—
416C2×C22⋊C4—1221no—
417C2×C22⋊C4—1221no—
418C2×C42—21no—
419C2×C42—1221no—
420C2×C42C22×D6111yescharacteristic
421C2×C42C22×D6111yescharacteristic
422C2×C42C22×D6111yescharacteristic
423#107—1222no—
424#106—614no—
425#106—1222no—
426#102—614no—
427#102—614no—
428#102—1222no—
429#102—1222no—
430#102—1222no—
431#102—1222no—
432#97—614no—
433#97—1222no—
434#97—1222no—
435C4×C8—1222no—
436C4×C8—1222no—
437C4×C8—1222no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—1221no—
442#95—1221no—
443#95—1221no—
444#95C22⋊D6111yescharacteristic
445#95C22⋊D6111yescharacteristic
446#95C22⋊D6111yescharacteristic
447#95C22⋊D6111yescharacteristic
448C24—21no—
449C24—1221no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—612no—
456C2×D4—1221no—
457C2×D4—1221no—
458C2×D4—1221no—
459C2×D4—1221no—
460C2×D4—1221no—
461C2×D4C2×C4×D6112yes—
462C22×C4—21no—
463C22×C4—24no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—81no—
467C22×C4—81no—
468C22×C4—1221no—
469C22×C4—1224no—
470C22×C4—1221no—
471C22×C4—1221no—
472C22×C4—4881no—
473C22×C4—4881no—
474C22×C4C2×C22⋊D6111yescharacteristic
475C22×C4C2×C22⋊D6111yescharacteristic
476C22×C4C2×C22⋊D6111yescharacteristic
477C22×C4C2×C22⋊D6111yescharacteristic
478C22×C4C2×C22⋊D6111yescharacteristic
479C22×C4C2×C22⋊D6111yescharacteristic
480C22×C4C23×D6111yescharacteristic
481D8—1228no—
482C2×C8—612no—
483C2×C8—612no—
484C2×C8—612no—
485C2×C8—612no—
486C2×C8—612no—
487C2×C8—612no—
488C2×C8—1221no—
489C2×C8—1221no—
490C2×C8—1221no—
491C2×C8—1221no—
492C2×C8—1221no—
493C2×C8—1221no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—81no—
500C4⋊C4—81no—
501C4⋊C4—612no—
502C4⋊C4—1221no—
503C4⋊C4—1221no—
504C4⋊C4—1221no—
505C4⋊C4—1221no—
506C4⋊C4—1221no—
507C4⋊C4—4881no—
508C4⋊C4—4881no—
509C4⋊C4C2×C4×D6112yes—
510C22⋊C4—24no—
511C22⋊C4—81no—
512C22⋊C4—81no—
513C22⋊C4—81no—
514C22⋊C4—81no—
515C22⋊C4—1224no—
516C22⋊C4—4881no—
517C22⋊C4—4881no—
518C22⋊C4—4881no—
519C22⋊C4—4881no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—81no—
525C42—4881no—
526C42C2×C4×D6112yes—
527C42#1175822212yes—
528C23—22no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—1222no—
536C23—2441no—
537C23—2441no—
538C23—2441no—
539C23—2441no—
540C23—2441no—
541C23—2441no—
542C23C22×C22⋊D6111yescharacteristic
543D4—22no—
544D4—22no—
545D4—41no—
546D4—41no—
547D4—1222no—
548D4—1222no—
549D4—2441no—
550D4—2441no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—22no—
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—21no—
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—84no—
577C2×C4—1222no—
578C2×C4—4884no—
579C2×C4—2441no—
580C2×C4—2441no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4—2441no—
584C2×C4—2441no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4C4×C22⋊D6112yes—
588C2×C4C4×C22⋊D6112yes—
589C2×C4C22×C4×D6111yescharacteristic
590C2×C4#41×D6111yescharacteristic
591C2×C4#41×D6111yescharacteristic
592C2×C4#41×D6111yescharacteristic
593C2×C4#41×D6111yescharacteristic
594C2×C4C2×#1175822211yescharacteristic
595C8—614no—
596C8—1222no—
597C8—1222no—
598C8—1222no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—4881no—
607C22—4881no—
608C22—4881no—
609C22—4881no—
610C22—2442no—
611C22—2442no—
612C22—2442no—
613C22C2×C4×C22⋊D6111yescharacteristic
614C22#1684030811yescharacteristic
615C22#1684030811yescharacteristic
616C22#1684056511yescharacteristic
617C22#1684056511yescharacteristic
618C22#1684057011yescharacteristic
619C22#1684057311yescharacteristic
620C4—22no—
621C4—22no—
622C4—41no—
623C4—42no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—81no—
628C4—81no—
629C4—4881no—
630C4—4881no—
631C4—2442no—
632C4#117×D6111yescharacteristic
633C4#1684023011yescharacteristic
634C4#1684029011yescharacteristic
635C4#1684029011yescharacteristic
636C2—82no—
637C2—4882no—
638C2#2144827811yescharacteristic
639C2#2145464711yescharacteristic
640C2#2145465111yescharacteristic
641C2#2145643011yescharacteristic
642C2#2145646311yescharacteristic
643C2#2145649611yescharacteristic
644C2#2145650411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2319C2
socleC23×C61C22×D4
prime radicalC22×#11758199C22
cosocleC22×C4×C61C24
hypercenter#2319D61
hypocenterC61#21290
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ #376 ◁ #2319

Complements

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

NH ≅ G/Ntype
2. #21448463C2semidirect
5. #21446559C2semidirect
6. #21446544C2semidirect
7. #21446519C2semidirect
8. #21446515C2semidirect
9. #21446505C2semidirect
10. #21446501C2semidirect
11. #21445717C2semidirect
12. C4×#14519697C2semidirect
13. C4×#14519698C2semidirect
14. #21445506C2semidirect
15. C61×#2319C2semidirect
18. #16839872C4semidirect
316. #2319D61semidirect
382. C61#21290semidirect

Maximal subgroups

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

subgroupindex
C2×#168398722
#214484632
#214466942
#214466842
#214465592
#214465442
#214465192
#214465152
#214465052
#214465012
#214457172
C4×#145196972
C4×#145196982
#214455062
C61×#23192
#2129061