Finite Group Databasebeta

← #29684376

Subgroups — #29684376

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#21448462C211yesmaximal, characteristic, complemented
3#21448457C211yesmaximal, characteristic, complemented
4#21446692C211yesmaximal, characteristic
5#21446682C211yesmaximal, characteristic
6#21446561C211yesmaximal, characteristic, complemented
7#21446546C211yesmaximal, characteristic, complemented
8#21446517C211yesmaximal, characteristic, complemented
9#21446513C211yesmaximal, characteristic, complemented
10#21446503C211yesmaximal, characteristic, complemented
11#21446499C211yesmaximal, characteristic, complemented
12#21445717C211yesmaximal, characteristic, complemented
13C4×#14519699C211yesmaximal, characteristic, complemented
14#21445505C211yesmaximal, characteristic, complemented
15C4×#102×C61C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C2×C4×D244C2211yescharacteristic
18#16839872C418yescomplemented
19C2×#14519710C2211yescharacteristic
20C2×#14519708C2211yescharacteristic
21C2×#14519708C2211yescharacteristic
22C2×#14519699C2211yescharacteristic
23C2×#14519699C2211yescharacteristic
24C2×#14519698C2211yescharacteristic
25C2×#14519697C2211yescharacteristic
26C2×#14519688C2211yescharacteristic
27C2×#14519687C2211yescharacteristic
28C2×#14519687C2211yescharacteristic
29C2×C8×Dic61C2211yescharacteristic
30C2×C8×Dic61C2211yescharacteristic
31#16839665C2211yescharacteristic
32#16839665C2211yescharacteristic
33#16839663C2211yescharacteristic
34#16839663C2211yescharacteristic
35#16839661C2211yescharacteristic
36#16839661C2211yescharacteristic
37#16839658C2211yescharacteristic
38#16839658C2211yescharacteristic
39#16839655—21no—
40#16839655—21no—
41#16839653—21no—
42#16839653—21no—
43#16839625—21no—
44#16839624—21no—
45#16839622—21no—
46#16839621—21no—
47C4×C4⋊Dic61C2211yescharacteristic
48#16839608C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53C2×C4×D4×C61C2211yescharacteristic
54C2×#102×C61C2211yescharacteristic
55C2×#102×C61C2211yescharacteristic
56C2×C4×C8×C61C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C22×D244C2311yescharacteristic
61C22×C4×D61—21no—
62C2×#11758199—22no—
63C2×#11758199—22no—
64C2×#11758199C2×C414yes—
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C4×D244—22no—
68C4×D244C2×C414yes—
69C2×C4⋊Dic61—21no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×#11758196—21no—
75C2×#11758196—21no—
76C2×C22⋊Dic61—21no—
77C2×C22⋊Dic61—21no—
78C2×C22⋊Dic61—21no—
79C2×C22⋊Dic61—21no—
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×#11758198—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61C2311yescharacteristic
87C2×C4×Dic61C2311yescharacteristic
88#14519710—22no—
89#14519708—22no—
90#14519708C2×C414yes—
91#14519699—22no—
92#14519699—22no—
93#14519698C2×C414yes—
94#14519697C2×C414yes—
95#14519688C2×C414yes—
96#14519687—22no—
97#14519687—22no—
98C8×Dic61—22no—
99C8×Dic61—22no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684D411yescharacteristic
106#14519684D411yescharacteristic
107#14519684D411yescharacteristic
108#14519684D411yescharacteristic
109C22×D4×C61C2311yescharacteristic
110C23×C4×C61—21no—
111C22×C8×C61C2311yescharacteristic
112C22×C8×C61C2311yescharacteristic
113C4×D4×C61—22no—
114C4×D4×C61C2×C414yes—
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C22⋊C4×C61—21no—
119C2×C42×C61—21no—
120C2×C42×C61C2311yescharacteristic
121#102×C61—22no—
122#102×C61—22no—
123C4×C8×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—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×C61C2411yescharacteristic
142C22×Dic61—21no—
143C22×Dic61—21no—
144C22×Dic61—21no—
145C22×Dic61C2×D411yescharacteristic
146C22×Dic61C2×D411yescharacteristic
147C22×Dic61C2×D411yescharacteristic
148C22×Dic61C2×D411yescharacteristic
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—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61#4112yes—
163C2×C8×C61#4112yes—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61C22×C412yes—
170C22⋊C4×C61—24no—
171C42×C61—81no—
172C42×C61C22×C412yes—
173C42×C61#4112yes—
174C22⋊Dic61—81no—
175C22⋊Dic61—81no—
176C22⋊Dic61—81no—
177C22⋊Dic61—81no—
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⋊Dic61—81no—
190C4⋊Dic61—81no—
191C4⋊Dic61C22×C412yes—
192#11758196—81no—
193#11758196—81no—
194C4×Dic61—21no—
195C4×Dic61—21no—
196C4×Dic61—21no—
197C4×Dic61—21no—
198C4×Dic61—81no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418C22×C412yes—
202C2×#92418C22×C412yes—
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—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—84no—
238C2×C4×C61C4×D412yes—
239C2×C4×C61C4×D412yes—
240C2×C4×C61C23×C411yescharacteristic
241C2×C4×C61C2×#4111yescharacteristic
242C2×C4×C61C2×#4111yescharacteristic
243C2×C4×C61C2×#4111yescharacteristic
244C2×C4×C61C2×#4111yescharacteristic
245C2×C4×C61C2×#4111yescharacteristic
246C2×Dic61—22no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—21no—
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—21no—
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—
272C8×C61—22no—
273C8×C61—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—42no—
301C4×C61—81no—
302C4×C61—81no—
303C4×C61C2×#11711yescharacteristic
304C4×C61C4×#4111yescharacteristic
305C4×C61#52911yescharacteristic
306C4×C61#52911yescharacteristic
307Dic61—41no—
308Dic61—41no—
309Dic61—41no—
310Dic61—41no—
311Dic61—42no—
312Dic61—81no—
313Dic61—81no—
314C2×#442—611no—
315#2319—611no—
316#2319—611no—
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×#102D6111yescharacteristic, complemented
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×#102C2×D6111yescharacteristic
350C2×#102C2×D6111yescharacteristic
351C2×#97—611no—
352C2×#97—611no—
353C2×#97—611no—
354C2×C4×C8—611no—
355C2×C4×C8—611no—
356C2×C4×C8C2×D6111yescharacteristic
357#390—611no—
358#390—611no—
359#390—611no—
360#390—611no—
361#389—611no—
362#389—611no—
363#389—611no—
364#389—611no—
365#388—1221no—
366#388—1221no—
367#388—1221no—
368#388—1221no—
369#381—1221no—
370#381—1221no—
371#380—1221no—
372#380—1221no—
373C4×C4⋊C4—611no—
374C4×C4⋊C4C2×D6111yescharacteristic
375#376—611no—
376#340—611no—
377#340—611no—
378#340—611no—
379#340—611no—
380#340C2×D6111yescharacteristic
381#340C2×D6111yescharacteristic
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×C8C22×D6111yescharacteristic
393C22×C8C22×D6111yescharacteristic
394C4×D4—22no—
395C4×D4—614no—
396C4×D4—1222no—
397C4×D4C4×D6114yes—
398C2×C4⋊C4—611no—
399C2×C4⋊C4—611no—
400C2×C4⋊C4—611no—
401C2×C4⋊C4—1221no—
402C2×C4⋊C4—1221no—
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—1221no—
410C2×C22⋊C4—1221no—
411C2×C22⋊C4—1221no—
412C2×C22⋊C4—1221no—
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—611no—
420C2×C42—611no—
421C2×C42—1221no—
422C2×C42C22×D6111yescharacteristic
423#107—1222no—
424#106—614no—
425#106—1222no—
426#102—22no—
427#102—22no—
428#102—614no—
429#102—614no—
430#102—1222no—
431#102—1222no—
432#97—614no—
433#97—1222no—
434#97—1222no—
435C4×C8—22no—
436C4×C8—1222no—
437C4×C8—1222no—
438#95—21no—
439#95—611no—
440#95—611no—
441#95—611no—
442#95—611no—
443#95—1221no—
444#95—1221no—
445#95—1221no—
446#95—1221no—
447#95—1221no—
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—611no—
469C22×C4—611no—
470C22×C4—611no—
471C22×C4—611no—
472C22×C4—1221no—
473C22×C4—1224no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—4881no—
477C22×C4—4881no—
478C22×C4D4×D6111yescharacteristic
479C22×C4D4×D6111yescharacteristic
480C22×C4C23×D6111yescharacteristic
481D8—1228no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—612no—
487C2×C8—612no—
488C2×C8—612no—
489C2×C8—612no—
490C2×C8—1221no—
491C2×C8—1221no—
492C2×C8#1175822212yes—
493C2×C8#1175822212yes—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—612no—
500C4⋊C4—1221no—
501C4⋊C4—1221no—
502C4⋊C4—1221no—
503C4⋊C4—1221no—
504C4⋊C4—1221no—
505C4⋊C4—4881no—
506C4⋊C4—4881no—
507C4⋊C4—4881no—
508C4⋊C4—4881no—
509C4⋊C4C2×C4×D6112yes—
510C22⋊C4—24no—
511C22⋊C4—1224no—
512C22⋊C4—4881no—
513C22⋊C4—4881no—
514C22⋊C4—4881no—
515C22⋊C4—4881no—
516C22⋊C4—4881no—
517C22⋊C4—4881no—
518C22⋊C4—4881no—
519C22⋊C4—4881no—
520C42—81no—
521C42—1221no—
522C42—1221no—
523C42—1221no—
524C42—1221no—
525C42—4881no—
526C42C2×C4×D6112yes—
527C42#1175822412yes—
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—
542C23C2×D4×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—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—84no—
565C2×C4—1222no—
566C2×C4—1221no—
567C2×C4—1221no—
568C2×C4—1221no—
569C2×C4—1221no—
570C2×C4—1221no—
571C2×C4—1221no—
572C2×C4—1221no—
573C2×C4—1221no—
574C2×C4—1221no—
575C2×C4—1221no—
576C2×C4—1221no—
577C2×C4—1221no—
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×C4#1451973712yes—
588C2×C4#1451973712yes—
589C2×C4C22×C4×D6111yescharacteristic
590C2×C4#41×D6111yescharacteristic
591C2×C4#41×D6111yescharacteristic
592C2×C4C2×#1175822411yescharacteristic
593C2×C4C2×#1175822211yescharacteristic
594C2×C4C2×#1175822211yescharacteristic
595C8—22no—
596C8—22no—
597C8—614no—
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×#1451973711yescharacteristic
614C22#1684030911yescharacteristic
615C22#1684030911yescharacteristic
616C22#1684056311yescharacteristic
617C22#1684056411yescharacteristic
618C22#1684056811yescharacteristic
619C22#1684056911yescharacteristic
620C4—22no—
621C4—22no—
622C4—42no—
623C4—81no—
624C4—81no—
625C4—4881no—
626C4—4881no—
627C4—2441no—
628C4—2442no—
629C4—2441no—
630C4—2441no—
631C4—2441no—
632C4#117×D6111yescharacteristic
633C4C4×#1175822211yescharacteristic
634C4#1684029211yescharacteristic
635C4#1684029211yescharacteristic
636C2—82no—
637C2—4882no—
638C2#2144828211yescharacteristic
639C2#2145464511yescharacteristic
640C2#2145465411yescharacteristic
641C2#2145643211yescharacteristic
642C2#2145646511yescharacteristic
643C2#2145649811yescharacteristic
644C2#2145650611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC4×#102×C61C2
socleC23×C61C22×D4
prime radicalC22×#11758199C22
cosocleC22×C4×C61C24
hypercenterC4×#102D61
hypocenterC61#21290
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. #21448462C2semidirect
3. #21448457C2semidirect
6. #21446561C2semidirect
7. #21446546C2semidirect
8. #21446517C2semidirect
9. #21446513C2semidirect
10. #21446503C2semidirect
11. #21446499C2semidirect
12. #21445717C2semidirect
13. C4×#14519699C2semidirect
14. #21445505C2semidirect
15. C4×#102×C61C2semidirect
18. #16839872C4semidirect
327. C4×#102D61semidirect
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
#214484622
#214484572
#214466922
#214466822
#214465612
#214465462
#214465172
#214465132
#214465032
#214464992
#214457172
C4×#145196992
#214455052
C4×#102×C612
#2129061