Finite Group Databasebeta

← #29748089

Subgroups — #29748089

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#21450165C211yesmaximal, characteristic, complemented
2#21448831C211yesmaximal, characteristic, complemented
3#21447128C211yesmaximal, characteristic, complemented
4#21447006C211yesmaximal, characteristic, complemented
5#21446963C211yesmaximal, characteristic, complemented
6#21446816C211yesmaximal, characteristic
7#21446775C211yesmaximal, characteristic, complemented
8#21446502C211yesmaximal, characteristic, complemented
9#21446444C211yesmaximal, characteristic, complemented
10#21446425C211yesmaximal, characteristic, complemented
11#21446397C211yesmaximal, characteristic, complemented
12#21446167C211yesmaximal, characteristic, complemented
13#21446135C211yesmaximal, characteristic, complemented
14#21445908C211yesmaximal, characteristic, complemented
15C4×#102×C61C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C2×#14519768C2211yescharacteristic
18C2×#14519752C2211yescharacteristic
19C2×#14519748C2211yescharacteristic
20C2×C4×C22⋊D61—21no—
21C2×C4⋊C4×D61C2211yescharacteristic
22C2×#14519708C2211yescharacteristic
23C2×#14519706C2211yescharacteristic
24C2×#14519699C2211yescharacteristic
25C2×#14519699C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×#14519689C2211yescharacteristic
29C2×#14519689C2211yescharacteristic
30#16839689—21no—
31#16839680—21no—
32#16839665C2211yescharacteristic
33#16839664—21no—
34#16839664C2211yescharacteristic
35#16839663C2211yescharacteristic
36#16839660C2211yescharacteristic
37#16839656—21no—
38#16839653—21no—
39#16839638—21no—
40#16839635—21no—
41#16839619C2211yescharacteristic
42C4⋊C4×Dic61C2211yescharacteristic
43C4×#11758198C2211yescharacteristic
44#16839525C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×C4×D4×C61C2211yescharacteristic
53C2×#102×C61C2211yescharacteristic
54C2×#102×C61C2211yescharacteristic
55C2×C4×C8×C61C2211yescharacteristic
56C4×C4⋊C4×C61C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C22×D244—21no—
60C22×D244C2311yescharacteristic
61C22×C22⋊D61—21no—
62C22×C4×D61—21no—
63C22×C4×D61C2311yescharacteristic
64C2×#11758199—22no—
65C2×#11758199—41no—
66C2×#11758199—41no—
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69#14519768—22no—
70#14519768—41no—
71#14519752—22no—
72#14519752—41no—
73#14519748—22no—
74#14519748—22no—
75C4×C22⋊D61—44no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×#11758196—21no—
81C2×#11758196—21no—
82C2×#11758196—21no—
83C4⋊C4×D61—22no—
84C4⋊C4×D61—41no—
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198D411yescharacteristic
95C2×#11758198D411yescharacteristic
96C2×C4×Dic61—21no—
97C2×C4×Dic61C2311yescharacteristic
98#14519708—22no—
99#14519706—41no—
100#14519699—22no—
101#14519699—41no—
102#14519698—41no—
103#14519697—22no—
104#14519689—41no—
105#14519689—41no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684D411yescharacteristic
110#14519684D411yescharacteristic
111C22×D4×C61C2311yescharacteristic
112C23×C4×C61—21no—
113C22×C8×C61C2311yescharacteristic
114C22×C8×C61C2311yescharacteristic
115C4×D4×C61—22no—
116C4×D4×C61—41no—
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C4⋊C4×C61C2311yescharacteristic
120C2×C22⋊C4×C61—21no—
121C2×C42×C61—21no—
122C2×C42×C61C2311yescharacteristic
123#102×C61—22no—
124#102×C61—22no—
125C4×C8×C61—41no—
126#95×C61—21no—
127C24×C61—21no—
128C23×D61—21no—
129C23×D61C2×D411yescharacteristic
130C2×D4×C61—21no—
131C2×D4×C61—21no—
132C2×D4×C61—21no—
133C2×D4×C61—21no—
134C2×D4×C61—21no—
135C2×D4×C61#4112yes—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—42no—
140C22×C4×C61—42no—
141C22×C4×C61—81no—
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2411yescharacteristic
145C2×C22⋊D61—24no—
146C2×C22⋊D61—42no—
147C2×C22⋊D61—42no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151C22×Dic61C2×D411yescharacteristic
152C22×Dic61C2×D411yescharacteristic
153C22×Dic61C2×D411yescharacteristic
154C2×D244—21no—
155C2×D244—21no—
156C2×D244—21no—
157C2×D244—21no—
158C2×D244—21no—
159C2×D244—21no—
160C2×D244—42no—
161C2×D244—42no—
162C2×D244—81no—
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×C4×D61—21no—
166C2×C4×D61—21no—
167C2×C4×D61—21no—
168C2×C4×D61—21no—
169C2×C4×D61—42no—
170C2×C4×D61—42no—
171C2×C4×D61—81no—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61#4112yes—
183C4⋊C4×C61#4112yes—
184C22⋊C4×C61—42no—
185C42×C61—21no—
186C42×C61—21no—
187C42×C61—81no—
188C22⋊Dic61—24no—
189C22⋊Dic61—42no—
190C22⋊Dic61—81no—
191#11758199—44no—
192#11758198—22no—
193#11758198—22no—
194#11758198—42no—
195#11758198—42no—
196#11758198—81no—
197#11758198—81no—
198#11758198—81no—
199#11758198—81no—
200C4⋊Dic61—21no—
201C4⋊Dic61—21no—
202C4⋊Dic61—21no—
203C4⋊Dic61—21no—
204C4⋊Dic61—21no—
205C4⋊Dic61—42no—
206C4⋊Dic61#4112yes—
207#11758196—42no—
208#11758196—42no—
209#11758196—42no—
210C4×Dic61—21no—
211C4×Dic61—21no—
212C4×Dic61—42no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—21no—
217C2×#92418—21no—
218C2×#92418—21no—
219C23×C61—22no—
220C23×C61—41no—
221C23×C61—41no—
222C23×C61—41no—
223C23×C61—41no—
224C23×C61—41no—
225C23×C61—41no—
226C23×C61C22×D411yescharacteristic
227C22×D61—21no—
228C22×D61—21no—
229C22×D61—21no—
230C22×D61—21no—
231C22×D61—21no—
232C22×D61—21no—
233C22×D61—41no—
234C22×D61—41no—
235C22×D61—41no—
236C22×D61—41no—
237C22×D61—41no—
238C22×D61—41no—
239C22×D61—41no—
240C22×D61#13512yes—
241D4×C61—22no—
242D4×C61—22no—
243D4×C61—41no—
244D4×C61—41no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—22no—
248C2×C4×C61—22no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—84no—
260C2×C4×C61AGL(1,ℤ/8)12yes—
261C2×C4×C61C2×#4111yescharacteristic
262C2×C4×C61C2×#4111yescharacteristic
263C2×C4×C61C2×#4111yescharacteristic
264C2×C4×C61C2×#4111yescharacteristic
265C2×C4×C61H(5,𝔽2)11yescharacteristic
266C2×C4×C61H(5,𝔽2)11yescharacteristic
267C22⋊D61—48no—
268C2×Dic61—22no—
269C2×Dic61—21no—
270C2×Dic61—21no—
271C2×Dic61—21no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61—21no—
275C2×Dic61—21no—
276C2×Dic61—21no—
277C2×Dic61—21no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61—41no—
284C2×Dic61—41no—
285C2×Dic61—41no—
286D244—41no—
287D244—41no—
288D244—41no—
289D244—41no—
290D244—84no—
291C4×D61—41no—
292C4×D61—41no—
293C4×D61—41no—
294C4×D61—41no—
295C4×D61—84no—
296C8×C61—41no—
297C8×C61—41no—
298#92418—41no—
299#92418—41no—
300#26723—611nomaximal, Sylow
301C22×C61—42no—
302C22×C61—42no—
303C22×C61—42no—
304C22×C61—81no—
305C22×C61—81no—
306C22×C61—81no—
307C22×C61—81no—
308C22×C61#52511yescharacteristic
309C22×C61#54611yescharacteristic
310C22×C61#54611yescharacteristic
311C22×C61C2×#13511yescharacteristic
312C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
313C22×C61#57611yescharacteristic
314C22×C61#57711yescharacteristic
315C2×D61—22no—
316C2×D61—22no—
317C2×D61—22no—
318C2×D61—41no—
319C2×D61—41no—
320C2×D61—41no—
321C2×D61—41no—
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—42no—
331C4×C61—41no—
332C4×C61—42no—
333C4×C61—81no—
334C4×C61#52911yescharacteristic
335C4×C61#53811yescharacteristic
336C4×C61#55511yescharacteristic
337C4×C61#55911yescharacteristic
338Dic61—41no—
339Dic61—42no—
340Dic61—41no—
341Dic61—41no—
342Dic61—81no—
343Dic61—81no—
344#2490—611no—
345#2361—611no—
346#2054—611no—
347#2034—611no—
348#2025—611no—
349#1999—611no—
350#1989—611no—
351#1934—611no—
352#1926—611no—
353#1923—611no—
354#1919—611no—
355#1879—611no—
356#1874—611no—
357#1824—611no—
358C4×#102D6111yescharacteristic, complemented
359C2×C61—82no—
360C2×C61#245911yescharacteristic
361C2×C61#310511yescharacteristic
362C2×C61#311911yescharacteristic
363C2×C61#329711yescharacteristic
364C2×C61#330111yescharacteristic
365C2×C61#331811yescharacteristic
366C2×C61#333211yescharacteristic
367D61—42no—
368D61—161no—
369C22×D8—611no—
370C2×#125—611no—
371C2×#121—611no—
372C2×#121—611no—
373C2×C4×D4—1221no—
374C2×C4×D4C2×D6111yescharacteristic
375C22×C4⋊C4—611no—
376C2×#106—611no—
377C2×C4⋊C8—611no—
378C2×#102—611no—
379C2×#102—611no—
380C2×#102—611no—
381C2×#102—611no—
382C2×#102C2×D6111yescharacteristic
383C2×#102C2×D6111yescharacteristic
384C2×C22⋊C8—611no—
385C2×C22⋊C8—611no—
386C2×C4×C8C2×D6111yescharacteristic
387#397—1221no—
388#394—1221no—
389#390—611no—
390#390—611no—
391#390—611no—
392#390—1221no—
393#389—611no—
394#388—1221no—
395#388—1221no—
396#386—1221no—
397#385—1221no—
398#380—611no—
399C4×C4⋊C4—611no—
400C4×C4⋊C4C2×D6111yescharacteristic
401C4×C22⋊C4—611no—
402#340—611no—
403#340—611no—
404#340—611no—
405#340—611no—
406#340—611no—
407#340—611no—
408#340C2×D6111yescharacteristic
409#340C2×D6111yescharacteristic
410#336—611no—
411#336—611no—
412C61#2672311yescharacteristic, complemented, Sylow
413C22×D4—611no—
414C22×D4—1221no—
415C22×D4—1221no—
416C22×D4C22×D6111yescharacteristic
417C23×C4—21no—
418C23×C4—611no—
419C23×C4—1221no—
420C2×D8—1222no—
421C2×D8—2441no—
422C2×D8—2441no—
423C22×C8—611no—
424C22×C8—611no—
425C22×C8C22×D6111yescharacteristic
426C22×C8C22×D6111yescharacteristic
427#125—1222no—
428#125—2441no—
429#121—1222no—
430#121—1222no—
431#121—1222no—
432#121—2441no—
433C4×D4—22no—
434C4×D4—41no—
435C4×D4—2444no—
436C2×C4⋊C4—611no—
437C2×C4⋊C4—611no—
438C2×C4⋊C4—611no—
439C2×C4⋊C4—1222no—
440C2×C4⋊C4—1221no—
441C2×C4⋊C4—1221no—
442C2×C4⋊C4—1221no—
443C2×C4⋊C4—1221no—
444C2×C4⋊C4—2441no—
445C2×C4⋊C4C22×D6111yescharacteristic
446C2×C4⋊C4C22×D6111yescharacteristic
447C2×C4⋊C4C22×D6111yescharacteristic
448C2×C22⋊C4—21no—
449C2×C22⋊C4—611no—
450C2×C22⋊C4—611no—
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×C22⋊C4—1221no—
458C2×C22⋊C4—1221no—
459C2×C22⋊C4—1221no—
460C2×C42—21no—
461C2×C42—611no—
462C2×C42—1221no—
463C2×C42C22×D6111yescharacteristic
464#106—1222no—
465C4⋊C8—2441no—
466#102—22no—
467#102—22no—
468#102—1222no—
469#102—1222no—
470#102—2441no—
471#102—2441no—
472C22⋊C8—2441no—
473C22⋊C8—2441no—
474C4×C8—41no—
475#95—21no—
476#95—611no—
477#95—611no—
478#95—1221no—
479#95—1221no—
480#95—1221no—
481C24—21no—
482C24—611no—
483C24—1221no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—1224no—
490C2×D4—1221no—
491C2×D4—1221no—
492C2×D4—1221no—
493C2×D4—1221no—
494C2×D4—1221no—
495C2×D4—1221no—
496C2×D4—4881no—
497C2×D4—2442no—
498C2×D4—2442no—
499C2×D4—2442no—
500C2×D4—2442no—
501C2×D4#1175822212yes—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—81no—
508C22×C4—611no—
509C22×C4—611no—
510C22×C4—611no—
511C22×C4—1221no—
512C22×C4—1221no—
513C22×C4—1221no—
514C22×C4—1221no—
515C22×C4—1221no—
516C22×C4—1221no—
517C22×C4—1221no—
518C22×C4—1221no—
519C22×C4—1221no—
520C22×C4—4881no—
521C22×C4—2442no—
522C22×C4—2442no—
523C22×C4D4×D6111yescharacteristic
524C22×C4D4×D6111yescharacteristic
525C22×C4C23×D6111yescharacteristic
526D8—2444no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—1221no—
534C2×C8—1221no—
535C2×C8—1221no—
536C2×C8—1221no—
537C2×C8—1221no—
538C2×C8—1221no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—612no—
544C4⋊C4—1221no—
545C4⋊C4—1221no—
546C4⋊C4—1221no—
547C4⋊C4—1221no—
548C4⋊C4—1221no—
549C4⋊C4—2442no—
550C4⋊C4—2442no—
551C4⋊C4—2442no—
552C4⋊C4—2442no—
553C4⋊C4#1175822212yes—
554C4⋊C4#1175822212yes—
555C22⋊C4—42no—
556C22⋊C4—1222no—
557C22⋊C4—1224no—
558C22⋊C4—1222no—
559C22⋊C4—4881no—
560C22⋊C4—4881no—
561C22⋊C4—4881no—
562C22⋊C4—4881no—
563C22⋊C4—4881no—
564C22⋊C4—2442no—
565C22⋊C4—2442no—
566C22⋊C4—2442no—
567C42—21no—
568C42—21no—
569C42—81no—
570C42—1221no—
571C42—1221no—
572C42—2442no—
573C23—22no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—612no—
581C23—1221no—
582C23—1221no—
583C23—1221no—
584C23—1221no—
585C23—1221no—
586C23—1221no—
587C23—2441no—
588C23—2441no—
589C23—2441no—
590C23—2441no—
591C23—2441no—
592C23—2441no—
593C23—2441no—
594C23C2×D4×D6111yescharacteristic
595D4—22no—
596D4—22no—
597D4—41no—
598D4—41no—
599D4—4884no—
600D4—2448no—
601D4—2441no—
602D4—2441no—
603D4—2441no—
604D4—2441no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—84no—
620C2×C4—1221no—
621C2×C4—1222no—
622C2×C4—1221no—
623C2×C4—1221no—
624C2×C4—1221no—
625C2×C4—1221no—
626C2×C4—1221no—
627C2×C4—1221no—
628C2×C4—1221no—
629C2×C4—1221no—
630C2×C4—4884no—
631C2×C4—2441no—
632C2×C4—2441no—
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—2441no—
643C2×C4#1451980412yes—
644C2×C4#41×D6111yescharacteristic
645C2×C4C2×#1175822211yescharacteristic
646C2×C4C2×#1175822211yescharacteristic
647C2×C4C2×#1175822211yescharacteristic
648C2×C4#1451982211yescharacteristic
649C2×C4#1451982311yescharacteristic
650C8—41no—
651C8—41no—
652C8—2441no—
653C8—2441no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22—1222no—
662C22—1222no—
663C22—1222no—
664C22—4881no—
665C22—4881no—
666C22—4881no—
667C22—4881no—
668C22—4881no—
669C22—4881no—
670C22—4881no—
671C22—2441no—
672C22—2441no—
673C22—2441no—
674C22—2441no—
675C22#1684027111yescharacteristic
676C22#1684040211yescharacteristic
677C22#1684040811yescharacteristic
678C22#135×D6111yescharacteristic
679C22C2×#1451980411yescharacteristic
680C22#1684056311yescharacteristic
681C22#1684056911yescharacteristic
682C4—22no—
683C4—42no—
684C4—42no—
685C4—41no—
686C4—81no—
687C4—4881no—
688C4—4881no—
689C4—2441no—
690C4—2441no—
691C4—2441no—
692C4—2442no—
693C4#1684029611yescharacteristic
694C4#1684034511yescharacteristic
695C4#1684047511yescharacteristic
696C4#1684049511yescharacteristic
697C2—82no—
698C2—9761no—
699C2—2442no—
700C2#2144975611yescharacteristic
701C2#2145587011yescharacteristic
702C2#2145601411yescharacteristic
703C2#2145767411yescharacteristic
704C2#2145772211yescharacteristic
705C2#2145795611yescharacteristic
706C2#2145814811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC4×#102×C61C2
socleC23×C61C22×D4
prime radical#21446816C2
hypercenterC4×#102D61
hypocenterC61#26723
LCSG ▷ C22×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
1. #21450165C2semidirect
2. #21448831C2semidirect
3. #21447128C2semidirect
4. #21447006C2semidirect
5. #21446963C2semidirect
7. #21446775C2semidirect
8. #21446502C2semidirect
9. #21446444C2semidirect
10. #21446425C2semidirect
11. #21446397C2semidirect
12. #21446167C2semidirect
13. #21446135C2semidirect
14. #21445908C2semidirect
15. C4×#102×C61C2semidirect
358. C4×#102D61semidirect
412. C61#26723semidirect

Maximal subgroups

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

subgroupindex
#214501652
#214488312
#214471282
#214470062
#214469632
#214468162
#214467752
#214465022
#214464442
#214464252
#214463972
#214461672
#214461352
#214459082
C4×#102×C612
#2672361