Finite Group Databasebeta

← #29753189

Subgroups — #29753189

Order 15616.

874 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450416C211yesmaximal, characteristic, complemented
2#21447340C211yesmaximal, characteristic, complemented
3#21447129C211yesmaximal, characteristic, complemented
4#21447050C211yesmaximal, characteristic, complemented
5#21446890C211yesmaximal, characteristic
6#21446684C211yesmaximal, characteristic, complemented
7#21446446C211yesmaximal, characteristic, complemented
8#21446443C211yesmaximal, characteristic, complemented
9#21446411C211yesmaximal, characteristic, complemented
10#21446378C211yesmaximal, characteristic, complemented
11#21446167C211yesmaximal, characteristic, complemented
12#21446167C211yesmaximal, characteristic, complemented
13#21445829C211yesmaximal, characteristic, complemented
14C4×#14519698C211yesmaximal, characteristic, complemented
15C61×#2366C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C2×#14519710C2211yescharacteristic
19C2×#14519708C2211yescharacteristic
20C2×C4⋊#92418C2211yescharacteristic
21C2×#14519698C2211yescharacteristic
22C2×#14519698C2211yescharacteristic
23C2×#14519698C2211yescharacteristic
24C2×#14519698C2211yescharacteristic
25C2×#14519698C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29C2×C4×#92418C2211yescharacteristic
30#16839691—21no—
31#16839688—21no—
32#16839664C2211yescharacteristic
33#16839664C2211yescharacteristic
34#16839664C2211yescharacteristic
35#16839660C2211yescharacteristic
36#16839652—21no—
37#16839651—21no—
38#16839628C2211yescharacteristic
39C4×C4⋊Dic61C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839517C2211yescharacteristic
45#16839517C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48C2×#127×C61C2211yescharacteristic
49C2×C4×D4×C61—21no—
50C2×C4×D4×C61C2211yescharacteristic
51C2×C4×D4×C61C2211yescharacteristic
52C61×#390—21no—
53C61×#390C2211yescharacteristic
54C61×#390C2211yescharacteristic
55C61×#386—21no—
56C61×#386—21no—
57C4×C4⋊C4×C61C2211yescharacteristic
58C4×C4⋊C4×C61C2211yescharacteristic
59C22×D244C2311yescharacteristic
60C2×#11758199—22no—
61C2×#11758199—22no—
62C2×#11758199—22no—
63C2×#11758199—41no—
64C2×#11758199—41no—
65C2×#11758199—41no—
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70C2×C4⋊Dic61C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×#11758196—21no—
74C2×#11758198—21no—
75C2×#11758198—21no—
76C2×#11758198—21no—
77C2×#11758198—21no—
78C2×#11758198—21no—
79C2×#11758198—21no—
80C2×C4×Dic61—21no—
81#14519710—22no—
82#14519708—41no—
83C4⋊#92418—41no—
84#14519698—22no—
85#14519698—22no—
86#14519698—22no—
87#14519698—41no—
88#14519698—41no—
89#14519698—41no—
90#14519697—22no—
91#14519697—41no—
92C4×#92418—41no—
93#14519684—21no—
94#14519684—21no—
95#14519684—21no—
96#14519684—21no—
97C22×D4×C61—21no—
98C22×D4×C61—21no—
99C22×D4×C61C2311yescharacteristic
100C22×D4×C61C2311yescharacteristic
101C23×C4×C61—21no—
102C23×C4×C61—21no—
103#127×C61—22no—
104#127×C61—22no—
105C4×D4×C61—22no—
106C4×D4×C61—22no—
107C4×D4×C61—41no—
108C4×D4×C61—41no—
109C4×D4×C61—44no—
110C2×C4⋊C4×C61D411yescharacteristic
111C2×C4⋊C4×C61D411yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C22⋊C4×C61—21no—
115C2×C22⋊C4×C61—21no—
116C2×C22⋊C4×C61—21no—
117C2×C22⋊C4×C61—21no—
118C2×C22⋊C4×C61—21no—
119C2×C22⋊C4×C61—21no—
120C2×C42×C61—21no—
121C2×C42×C61C2311yescharacteristic
122C2×C42×C61C2311yescharacteristic
123C2×C42×C61C2311yescharacteristic
124#95×C61—21no—
125#95×C61D411yescharacteristic
126#95×C61D411yescharacteristic
127C24×C61—21no—
128C24×C61—21no—
129C23×D61—21no—
130C2×D4×C61—24no—
131C2×D4×C61—24no—
132C2×D4×C61—21no—
133C2×D4×C61—21no—
134C2×D4×C61—21no—
135C2×D4×C61—21no—
136C2×D4×C61—21no—
137C2×D4×C61—21no—
138C2×D4×C61—21no—
139C2×D4×C61—21no—
140C2×D4×C61—21no—
141C2×D4×C61—21no—
142C2×D4×C61—42no—
143C2×D4×C61—42no—
144C2×D4×C61—81no—
145C2×D4×C61—81no—
146C2×D4×C61#4112yes—
147C2×D4×C61#4112yes—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—42no—
151C22×C4×C61—42no—
152C22×C4×C61—42no—
153C22×C4×C61—42no—
154C22×C4×C61—81no—
155C22×C4×C61—81no—
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2411yescharacteristic
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C2×D244—21no—
167C2×D244—21no—
168C2×D244—21no—
169C2×D244—21no—
170C2×D244—21no—
171C2×D244—21no—
172C4⋊C4×C61—22no—
173C4⋊C4×C61—22no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61#4112yes—
178C22⋊C4×C61—42no—
179C22⋊C4×C61—42no—
180C22⋊C4×C61—42no—
181C22⋊C4×C61—42no—
182C22⋊C4×C61—81no—
183C22⋊C4×C61—81no—
184C42×C61—21no—
185C42×C61—21no—
186C42×C61—21no—
187C42×C61—21no—
188C42×C61—21no—
189C42×C61—21no—
190C42×C61—42no—
191#11758199—44no—
192#11758199—44no—
193#11758198—42no—
194#11758198—42no—
195#11758198—81no—
196#11758198—81no—
197#11758198—81no—
198#11758198—81no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—21no—
202C4⋊Dic61—21no—
203C4⋊Dic61—21no—
204C4⋊Dic61—21no—
205#11758196—81no—
206C4×Dic61—81no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—21no—
217C2×#92418—21no—
218C2×#92418#4112yes—
219C23×C61—22no—
220C23×C61—22no—
221C23×C61—41no—
222C23×C61—41no—
223C23×C61—41no—
224C23×C61—41no—
225C23×C61—41no—
226C23×C61—41no—
227C23×C61—41no—
228C23×C61—41no—
229C23×C61—41no—
230C23×C61—41no—
231C23×C61—41no—
232C23×C61—41no—
233C23×C61C22×D411yescharacteristic
234C22×D61—41no—
235C22×D61—41no—
236C22×D61—41no—
237C22×D61—41no—
238C22×D61—41no—
239C22×D61—41no—
240C22×D61—41no—
241D4×C61—22no—
242D4×C61—22no—
243D4×C61—22no—
244D4×C61—22no—
245D4×C61—48no—
246D4×C61—41no—
247D4×C61—41no—
248D4×C61—41no—
249D4×C61—41no—
250D4×C61—84no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—22no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—41no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—84no—
274C2×C4×C61—84no—
275C2×C4×C61#13512yes—
276C2×C4×C61AGL(1,ℤ/8)12yes—
277C2×C4×C61C2×#4111yescharacteristic
278C2×C4×C61C2×#4111yescharacteristic
279C2×C4×C61C2×#4111yescharacteristic
280C2×C4×C61C2×#4111yescharacteristic
281C2×C4×C61H(5,𝔽2)11yescharacteristic
282C2×C4×C61H(5,𝔽2)11yescharacteristic
283C2×Dic61—41no—
284C2×Dic61—41no—
285C2×Dic61—41no—
286C2×Dic61—41no—
287C2×Dic61—41no—
288C2×Dic61—41no—
289C2×Dic61—41no—
290C2×Dic61—41no—
291C2×Dic61—41no—
292D244—41no—
293D244—41no—
294D244—41no—
295D244—41no—
296#92418—22no—
297#92418—41no—
298#92418—41no—
299#92418—41no—
300#27065—611nomaximal, Sylow
301C22×C61—42no—
302C22×C61—42no—
303C22×C61—42no—
304C22×C61—42no—
305C22×C61—42no—
306C22×C61—42no—
307C22×C61—81no—
308C22×C61—81no—
309C22×C61—81no—
310C22×C61—81no—
311C22×C61—81no—
312C22×C61—81no—
313C22×C61—81no—
314C22×C61—81no—
315C22×C61#52511yescharacteristic
316C22×C61#54611yescharacteristic
317C22×C61#55011yescharacteristic
318C22×C61C2×#13511yescharacteristic
319C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
320C22×C61#57611yescharacteristic
321C22×C61#57611yescharacteristic
322C2×D61—81no—
323C2×D61—81no—
324C2×D61—81no—
325C2×D61—81no—
326C2×D61—81no—
327C2×D61—81no—
328C2×D61—81no—
329C4×C61—22no—
330C4×C61—22no—
331C4×C61—41no—
332C4×C61—41no—
333C4×C61—41no—
334C4×C61—41no—
335C4×C61—42no—
336C4×C61—81no—
337C4×C61#52911yescharacteristic
338C4×C61#53811yescharacteristic
339C4×C61#55111yescharacteristic
340C4×C61#55311yescharacteristic
341Dic61—81no—
342Dic61—81no—
343Dic61—81no—
344#2513—611no—
345#2366D6111yescharacteristic, complemented
346#2092—611no—
347#2054—611no—
348#2041—611no—
349#2011—611no—
350#1970—611no—
351#1926—611no—
352#1926—611no—
353#1921—611no—
354#1916—611no—
355#1879—611no—
356#1879—611no—
357#1804—611no—
358C4×#102—611no—
359C2×C61—82no—
360C2×C61—82no—
361C2×C61#246711yescharacteristic
362C2×C61#310511yescharacteristic
363C2×C61#312211yescharacteristic
364C2×C61#330511yescharacteristic
365C2×C61#331811yescharacteristic
366C2×C61#339611yescharacteristic
367C2×C61#339911yescharacteristic
368D61—161no—
369C22×D8—611no—
370C22×D8—611no—
371C2×#127C2×D6111yescharacteristic
372C2×C4×D4—21no—
373C2×C4×D4C2×D6111yescharacteristic
374C2×C4×D4C2×D6111yescharacteristic
375C2×#107—611no—
376C2×#106—611no—
377C2×C4⋊C8—611no—
378C2×#102—611no—
379C2×#102—611no—
380C2×#102—611no—
381C2×#102—611no—
382C2×#102—611no—
383C2×#102—611no—
384C2×#102—611no—
385C2×#102—611no—
386C2×C4×C8—611no—
387#397—1221no—
388#397—1221no—
389#390—21no—
390#390—611no—
391#390—611no—
392#390—611no—
393#390C2×D6111yescharacteristic
394#390C2×D6111yescharacteristic
395#389—611no—
396#388—1221no—
397#388—1221no—
398#386—21no—
399#386—21no—
400#382—611no—
401C4×C4⋊C4—611no—
402C4×C4⋊C4C2×D6111yescharacteristic
403C4×C4⋊C4C2×D6111yescharacteristic
404#340—611no—
405#340—611no—
406#340—611no—
407#340—611no—
408#336—611no—
409#336—611no—
410#336—611no—
411#336—611no—
412C61#2706511yescharacteristic, complemented, Sylow
413C22×D4—21no—
414C22×D4—21no—
415C22×D4—611no—
416C22×D4C22×D6111yescharacteristic
417C22×D4C22×D6111yescharacteristic
418C23×C4—21no—
419C23×C4—21no—
420C2×D8—1222no—
421C2×D8—1222no—
422C2×D8—1222no—
423C2×D8—2441no—
424C2×D8—2441no—
425C2×D8—2441no—
426C22×C8—611no—
427C22×C8—611no—
428C22×C8—611no—
429C22×C8—611no—
430#127—22no—
431#127—22no—
432C4×D4—22no—
433C4×D4—22no—
434C4×D4—41no—
435C4×D4—41no—
436C4×D4—44no—
437C2×C4⋊C4—611no—
438C2×C4⋊C4—611no—
439C2×C4⋊C4—611no—
440C2×C4⋊C4—1221no—
441C2×C4⋊C4C22⋊D6111yescharacteristic
442C2×C4⋊C4C22⋊D6111yescharacteristic
443C2×C4⋊C4C22×D6111yescharacteristic
444C2×C4⋊C4C22×D6111yescharacteristic
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—1221no—
452C2×C22⋊C4—1221no—
453C2×C22⋊C4—1221no—
454C2×C22⋊C4—1221no—
455C2×C22⋊C4—1221no—
456C2×C22⋊C4—1221no—
457C2×C42—21no—
458C2×C42—1221no—
459C2×C42C22×D6111yescharacteristic
460C2×C42C22×D6111yescharacteristic
461C2×C42C22×D6111yescharacteristic
462#107—1222no—
463#106—2441no—
464C4⋊C8—2441no—
465#102—1222no—
466#102—1222no—
467#102—1222no—
468#102—1222no—
469#102—2441no—
470#102—2441no—
471#102—2441no—
472#102—2441no—
473C4×C8—2441no—
474#95—21no—
475#95—1221no—
476#95—1221no—
477#95—1221no—
478#95—1221no—
479#95C22⋊D6111yescharacteristic
480#95C22⋊D6111yescharacteristic
481C24—21no—
482C24—21no—
483C24—1221no—
484C2×D4—24no—
485C2×D4—24no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—81no—
499C2×D4—81no—
500C2×D4—1221no—
501C2×D4—1221no—
502C2×D4—1221no—
503C2×D4—1221no—
504C2×D4—1221no—
505C2×D4—1221no—
506C2×D4#1175822212yes—
507C2×D4#1175822212yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—81no—
515C22×C4—81no—
516C22×C4—1221no—
517C22×C4—1221no—
518C22×C4—1221no—
519C22×C4C2×C22⋊D6111yescharacteristic
520C22×C4C2×C22⋊D6111yescharacteristic
521C22×C4C2×C22⋊D6111yescharacteristic
522C22×C4C2×C22⋊D6111yescharacteristic
523C22×C4C2×C22⋊D6111yescharacteristic
524C22×C4C2×C22⋊D6111yescharacteristic
525C22×C4C23×D6111yescharacteristic
526D8—2444no—
527D8—2444no—
528C2×C8—612no—
529C2×C8—1221no—
530C2×C8—1221no—
531C2×C8—1221no—
532C2×C8—1221no—
533C2×C8—1221no—
534C2×C8—1221no—
535C2×C8—1221no—
536C2×C8—1221no—
537C2×C8—1221no—
538C2×C8—1221no—
539C2×C8—1221no—
540C4⋊C4—21no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—1221no—
546C4⋊C4—1221no—
547C4⋊C4—1221no—
548C4⋊C4—1221no—
549C4⋊C4—1221no—
550C4⋊C4—1221no—
551C4⋊C4—4881no—
552C4⋊C4#1175822412yes—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—81no—
558C22⋊C4—81no—
559C22⋊C4—4881no—
560C22⋊C4—4881no—
561C22⋊C4—4881no—
562C22⋊C4—4881no—
563C22⋊C4—2442no—
564C22⋊C4—2442no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—42no—
572C42—4881no—
573C23—22no—
574C23—22no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—2441no—
588C23—2441no—
589C23—2441no—
590C23—2441no—
591C23—2441no—
592C23—2441no—
593C23—2441no—
594C23C22×C22⋊D6111yescharacteristic
595D4—22no—
596D4—22no—
597D4—22no—
598D4—22no—
599D4—48no—
600D4—41no—
601D4—41no—
602D4—41no—
603D4—41no—
604D4—84no—
605D4—2441no—
606D4—2441no—
607D4—2441no—
608D4—2441no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—22no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—84no—
632C2×C4—84no—
633C2×C4—2441no—
634C2×C4—2441no—
635C2×C4—2441no—
636C2×C4—2441no—
637C2×C4—2441no—
638C2×C4—2441no—
639C2×C4—2441no—
640C2×C4—2441no—
641C2×C4—2441no—
642C2×C4#1451979712yes—
643C2×C4#1451980312yes—
644C2×C4#41×D6111yescharacteristic
645C2×C4C2×#1175822411yescharacteristic
646C2×C4C2×#1175822211yescharacteristic
647C2×C4C2×#1175822211yescharacteristic
648C2×C4#1451982211yescharacteristic
649C2×C4#1451982311yescharacteristic
650C8—1222no—
651C8—2441no—
652C8—2441no—
653C8—2441no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—42no—
659C22—42no—
660C22—81no—
661C22—81no—
662C22—81no—
663C22—81no—
664C22—81no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—4881no—
669C22—4881no—
670C22—4881no—
671C22—4881no—
672C22—4881no—
673C22—4881no—
674C22—4881no—
675C22#1684027311yescharacteristic
676C22#1684040611yescharacteristic
677C22#1684043111yescharacteristic
678C22C2×#1451979711yescharacteristic
679C22C2×#1451980311yescharacteristic
680C22#1684056511yescharacteristic
681C22#1684056511yescharacteristic
682C4—22no—
683C4—22no—
684C4—41no—
685C4—42no—
686C4—41no—
687C4—41no—
688C4—41no—
689C4—81no—
690C4—4881no—
691C4—4881no—
692C4—4881no—
693C4#1684029211yescharacteristic
694C4#1684034511yescharacteristic
695C4#1684044111yescharacteristic
696C4#1684045811yescharacteristic
697C2—82no—
698C2—82no—
699C2—9761no—
700C2#2144986411yescharacteristic
701C2#2145586611yescharacteristic
702C2#2145606211yescharacteristic
703C2#2145776911yescharacteristic
704C2#2145796011yescharacteristic
705C2#2145882711yescharacteristic
706C2#2145886111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2366C2
socleC23×C61C22×D4
prime radical#21446890C2
hypercenter#2366D61
hypocenterC61#27065
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2366

Complements

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

NH ≅ G/Ntype
1. #21450416C2semidirect
2. #21447340C2semidirect
3. #21447129C2semidirect
4. #21447050C2semidirect
6. #21446684C2semidirect
7. #21446446C2semidirect
8. #21446443C2semidirect
9. #21446411C2semidirect
10. #21446378C2semidirect
11. #21446167C2semidirect
12. #21446167C2semidirect
13. #21445829C2semidirect
14. C4×#14519698C2semidirect
15. C61×#2366C2semidirect
345. #2366D61semidirect
412. C61#27065semidirect

Maximal subgroups

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

subgroupindex
#214504162
#214473402
#214471292
#214470502
#214468902
#214466842
#214464462
#214464432
#214464112
#214463782
#214461672
#214458292
C4×#145196982
C61×#23662
#2706561