Finite Group Databasebeta

← #30616063

Subgroups — #30616063

Order 15616.

1054 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462276C211yesmaximal, characteristic, complemented
2C4×D4×#6923C211yesmaximal, characteristic, complemented
3#21461897C212yesmaximal, complemented
4#21461883C212yesmaximal, complemented
5#21461814C212yesmaximal
6#21461784C212yesmaximal, complemented
7C4×#14519845C211yesmaximal, characteristic, complemented
8C4×#14519839C211yesmaximal, characteristic, complemented
9C4×#14519839C211yesmaximal, characteristic, complemented
10#21461532C211yesmaximal, characteristic, complemented
11C4×D8×D61C211yesmaximal, characteristic
12C2×D4×#6923C2212yes—
13C2×#14519856—21no—
14C22×C4×#6923—21no—
15C2×#14519845C2212yes—
16C2×#14519839C2212yes—
17C2×#14519839C2212yes—
18C4×D61⋊C8C2211yescharacteristic
19#16840714C2212yes—
20#16840713C2212yes—
21#16840712—22no—
22C4⋊C4×#6923C2212yes—
23C4×C4⋊#6923C2211yescharacteristic
24C4×C4⋊#6923C2211yescharacteristic
25C22⋊C4×#6923—22no—
26C4×C22⋊#6923—21no—
27C4×C22⋊#6923—21no—
28C42×#6923C2211yescharacteristic
29#16840636C2212yes—
30#16840635C2212yes—
31#16840635C2212yes—
32(C2×#6923)⋊C8C2212yes—
33(C2×#6923)⋊C8C2212yes—
34C2×D8×D61C2211yescharacteristic
35C4×D4×D61C2211yescharacteristic
36C4×D4×D61C2211yescharacteristic
37C4×D488C411yescharacteristic, complemented
38D8×Dic61C411yescharacteristic, complemented
39#16839844C411yescharacteristic, complemented
40C4×#11758199C411yescharacteristic, complemented
41C4×#11758199C411yescharacteristic, complemented
42#16839842C411yescharacteristic, complemented
43#16839842C411yescharacteristic, complemented
44#107×D61C2211yescharacteristic
45#102×D61C2211yescharacteristic
46#102×D61C2211yescharacteristic
47C4×C8×D61C2211yescharacteristic
48C4×D8×C61C411yescharacteristic, complemented
49C23×#6923—22no—
50C2×D61⋊C8C2312yes—
51D4×#6923—24no—
52D4×#6923—24no—
53#14519856—44no—
54C2×C4⋊#6923—22no—
55C2×C4⋊#6923C2312yes—
56C2×C4⋊#6923C2312yes—
57C2×C22⋊#6923—22no—
58C2×C22⋊#6923—22no—
59C2×C22⋊#6923—22no—
60C2×C4×#6923—22no—
61C2×C4×#6923—21no—
62C2×C4×#6923—21no—
63C2×C4×#6923—44no—
64C2×C4×#6923D412yes—
65C2×C4×#6923D411yescharacteristic
66C2×C4×#6923D411yescharacteristic
67C2×C4×#6923C2312yes—
68#14519845—24no—
69#14519839—24no—
70#14519839—24no—
71C4×#92420—21no—
72C4×#92420—21no—
73(C2×#6923)⋊C4—22no—
74(C2×#6923)⋊C4—22no—
75(C2×#6923)⋊C4—21no—
76(C2×#6923)⋊C4—21no—
77C2×D4×D61C2311yescharacteristic
78C2×D4×D61C2311yescharacteristic
79C22×C4×D61—21no—
80C22×C4×D61—21no—
81C2×D488C2×C411yescharacteristic
82C2×#11758199C2×C411yescharacteristic
83C2×#11758199C2×C411yescharacteristic
84D8×D61—24no—
85C2×C8×D61C2311yescharacteristic
86C2×C8×D61C2311yescharacteristic
87C4×D244C2×C411yescharacteristic
88C4×D244C2×C411yescharacteristic, complemented
89D4×Dic61C2×C411yescharacteristic
90D4×Dic61C2×C411yescharacteristic, complemented
91#14519739C2×C411yescharacteristic
92#14519739C2×C411yescharacteristic, complemented
93C4×C22⋊D61—21no—
94C4×C22⋊D61—21no—
95#14519737—21no—
96#14519737—21no—
97C4⋊C4×D61C2311yescharacteristic
98C4⋊C4×D61C2311yescharacteristic
99C22⋊C4×D61—21no—
100C22⋊C4×D61—21no—
101C42×D61C2311yescharacteristic
102#14519711C2×C411yescharacteristic, complemented
103#14519710C2×C411yescharacteristic, complemented
104#14519710C2×C411yescharacteristic, complemented
105#14519699C2×C411yescharacteristic
106#14519699C2×C411yescharacteristic, complemented
107#14519698C2×C411yescharacteristic
108#14519698C2×C411yescharacteristic, complemented
109#14519697C2×C411yescharacteristic
110#14519697C2×C411yescharacteristic, complemented
111C4×#92418C2×C411yescharacteristic, complemented
112C8×Dic61C2×C411yescharacteristic, complemented
113C8×Dic61C2×C411yescharacteristic, complemented
114C2×D8×C61C2×C411yescharacteristic
115C4×D4×C61C2×C411yescharacteristic
116C4×D4×C61C2×C411yescharacteristic, complemented
117#107×C61C2×C411yescharacteristic, complemented
118#102×C61C2×C411yescharacteristic
119#102×C61C2×C411yescharacteristic, complemented
120C4×C8×C61C2×C411yescharacteristic, complemented
121C23×D61—21no—
122C23×D61—21no—
123C22×#6923—28no—
124C22×#6923—22no—
125C22×#6923—22no—
126C22×#6923—44no—
127C22×#6923—44no—
128C22×#6923C2×D412yes—
129C22×#6923C2×D412yes—
130C2×D4×C61C22×C411yescharacteristic
131C2×D4×C61C22×C411yescharacteristic
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C2×C22⋊D61—21no—
135C2×C22⋊D61—21no—
136C22×Dic61—21no—
137C22×Dic61—21no—
138D4×D61—22no—
139D4×D61—22no—
140D4×D61—22no—
141D4×D61#4114yes—
142C2×D244C22×C411yescharacteristic
143C2×D244C22×C411yescharacteristic
144C2×C4×D61—21no—
145C2×C4×D61—21no—
146C2×C4×D61—21no—
147C2×C4×D61—21no—
148C2×C4×D61—21no—
149C2×C4×D61—21no—
150C2×C4×D61—42no—
151C2×C4×D61—42no—
152C2×C4×D61—42no—
153C2×C4×D61—42no—
154C2×C4×D61C2×D411yescharacteristic
155C2×C4×D61C2×D411yescharacteristic
156C2×C4×D61C2411yescharacteristic
157C22⋊#6923—28no—
158C22⋊#6923—44no—
159C22⋊#6923—44no—
160C2×#92420—22no—
161C4⋊#6923—22no—
162C4⋊#6923—22no—
163C4⋊#6923—22no—
164C4⋊#6923—44no—
165C4⋊#6923#4114yes—
166C4×#6923—24no—
167C4×#6923—22no—
168C4×#6923—22no—
169C4×#6923—22no—
170C4×#6923—22no—
171C4×#6923—44no—
172C4×#6923—42no—
173C4×#6923—42no—
174D61⋊C8—22no—
175D61⋊C8—22no—
176D8×C61—22no—
177C2×C8×C61C22×C411yescharacteristic
178C2×C8×C61C22×C411yescharacteristic
179C4⋊C4×C61C22×C411yescharacteristic
180C4⋊C4×C61C22×C411yescharacteristic
181C22⋊C4×C61—21no—
182C22⋊C4×C61—21no—
183C42×C61C22×C411yescharacteristic
184C22⋊Dic61—21no—
185C22⋊Dic61—21no—
186#11758199—22no—
187#11758199—22no—
188#11758198—21no—
189#11758198—21no—
190#11758198—21no—
191#11758198—21no—
192C4⋊Dic61C22×C411yescharacteristic
193C4⋊Dic61C22×C411yescharacteristic
194#11758196—21no—
195#11758196—21no—
196C4×Dic61C22×C411yescharacteristic
197C4×Dic61#4111yescharacteristic
198C4×Dic61#4111yescharacteristic
199C2×#92418C22×C411yescharacteristic
200C2×#92418C22×C411yescharacteristic
201D488—22no—
202C8×D61—22no—
203C8×D61—22no—
204C23×C61—21no—
205C23×C61—21no—
206C22×D61—21no—
207C22×D61—24no—
208C22×D61—21no—
209C22×D61—42no—
210C22×D61—41no—
211C22×D61—41no—
212C22×D61—42no—
213C22×D61—42no—
214C22×D61—41no—
215C22×D61—41no—
216C22×D61C22×D411yescharacteristic
217C2×#6923—22no—
218C2×#6923—22no—
219C2×#6923—22no—
220C2×#6923—24no—
221C2×#6923—22no—
222C2×#6923—22no—
223C2×#6923—416no—
224C2×#6923—42no—
225C2×#6923—42no—
226C2×#6923—42no—
227C2×#6923—42no—
228C2×#6923—42no—
229C2×#6923#13514yes—
230D4×C61—21no—
231D4×C61—21no—
232D4×C61—21no—
233D4×C61#11712yescomplemented
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—42no—
237C2×C4×C61—42no—
238C2×C4×C61C4×D411yescharacteristic
239C2×C4×C61C4×D411yescharacteristic
240C2×C4×C61C23×C411yescharacteristic
241C22⋊D61—24no—
242C22⋊D61—42no—
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—42no—
246C2×Dic61—42no—
247C2×Dic61C4×D411yescharacteristic
248C2×Dic61C4×D411yescharacteristic
249C2×Dic61C2×#4111yescharacteristic
250D244—21no—
251D244—21no—
252D244—21no—
253D244#11712yescomplemented
254C4×D61—22no—
255C4×D61—41no—
256C4×D61—41no—
257C4×D61—41no—
258C4×D61—41no—
259C4×D61—42no—
260C4×D61—42no—
261C4×D61—42no—
262C4×D61—42no—
263C4×D61AGL(1,ℤ/8)12yes—
264C4×D61AGL(1,ℤ/8)12yes—
265C4×D61C2×#4112yes—
266C4×D61C2×#4112yes—
267#92420—42no—
268C8×C61—21no—
269C8×C61—21no—
270#92418—21no—
271#92418—21no—
272#21118—611nomaximal, Sylow
273C22×C61—22no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61—41no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61C2×C4×D411yescharacteristic
280C2×D61—22no—
281C2×D61—41no—
282C2×D61—41no—
283C2×D61—44no—
284C2×D61—44no—
285C2×D61—41no—
286C2×D61—41no—
287C2×D61—41no—
288C2×D61—82no—
289C2×D61—82no—
290C2×D61#52512yes—
291C2×D61C2×#13512yes—
292C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
293C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
294#6923—24no—
295#6923—44no—
296#6923—42no—
297#6923—82no—
298C4×C61—21no—
299C4×C61—41no—
300C4×C61—41no—
301C4×C61#44212yes—
302C4×C61C2×#11711yescharacteristic
303C4×C61C4×#4111yescharacteristic
304Dic61—21no—
305Dic61—41no—
306Dic61—41no—
307Dic61#44212yes—
308Dic61#52912yes—
309C2×C4×D8—611no—
310#2293—611no—
311C42×D4—611no—
312#1926—612no—
313#1921—612no—
314#1879—612no—
315#1864—612no—
316C4×#106—611no—
317C4×#102—611no—
318C4×#102—611no—
319#1744—611no—
320C2×C61—42no—
321C2×C61—81no—
322C2×C61#229011yescharacteristic
323C2×C61C4×#13511yescharacteristic
324C2×C61C2×#44211yescharacteristic
325D61—42no—
326D61—81no—
327D61#310512yes—
328D61#310612yes—
329C22×D8—611no—
330C2×C4×D4—611no—
331C2×C4×D4—611no—
332C2×C4×D4—612no—
333C2×#117—1221no—
334C22×C42—1221no—
335C4×D8—611no—
336C4×D8—611no—
337C4×D8—611no—
338C4×D8—611no—
339C4×D8—611no—
340C4×D8—611no—
341C4×D8—611no—
342C4×D8#692311yescharacteristic, complemented
343C2×#107—611no—
344C2×#106—612no—
345C2×#102—611no—
346C2×#102—611no—
347C2×#102—612no—
348C2×#102—612no—
349C2×C4×C8—611no—
350C2×C4×C8—611no—
351#390—612no—
352#389—612no—
353#388—1222no—
354C4×C4⋊C4—612no—
355C4×C4⋊C4—611no—
356C4×C4⋊C4—611no—
357C4×C22⋊C4—1221no—
358C4×C22⋊C4—1222no—
359C4×C22⋊C4—1221no—
360C43—611no—
361#340—612no—
362#340—612no—
363#340—612no—
364#336—612no—
365#336—612no—
366C61#2111811yescharacteristic, complemented, Sylow
367C22×D4—611no—
368C22×D4—611no—
369C23×C4—1221no—
370C23×C4—1221no—
371C23×C4—1222no—
372C2×D8—611no—
373C2×D8—611no—
374C2×D8—611no—
375C2×D8—1224no—
376C2×D8C2×#692311yescharacteristic
377C22×C8—611no—
378C22×C8—611no—
379C22×C8—612no—
380C4×D4—611no—
381C4×D4—611no—
382C4×D4—611no—
383C4×D4—611no—
384C4×D4—611no—
385C4×D4—611no—
386C4×D4—1221no—
387C4×D4—1221no—
388C4×D4—1221no—
389C4×D4—1221no—
390C4×D4—1224no—
391C4×D4—1224no—
392C4×D4C2×#692311yescharacteristic
393C4×D4C2×#692311yescharacteristic, complemented
394#117—2444no—
395C2×C4⋊C4—612no—
396C2×C4⋊C4—611no—
397C2×C4⋊C4—611no—
398C2×C4⋊C4—612no—
399C2×C4⋊C4—1222no—
400C2×C22⋊C4—1221no—
401C2×C22⋊C4—1221no—
402C2×C22⋊C4—1222no—
403C2×C22⋊C4—1222no—
404C2×C22⋊C4—1222no—
405C2×C42—611no—
406C2×C42—611no—
407C2×C42—612no—
408C2×C42—612no—
409C2×C42—611no—
410C2×C42—1221no—
411C2×C42—1221no—
412C2×C42—1222no—
413C2×C42—2444no—
414#107—611no—
415#107—611no—
416#107—611no—
417#107C2×#692311yescharacteristic, complemented
418#106—1224no—
419#102—611no—
420#102—611no—
421#102—611no—
422#102—611no—
423#102—611no—
424#102—611no—
425#102—1224no—
426#102—1224no—
427#102C2×#692311yescharacteristic
428#102C2×#692311yescharacteristic, complemented
429C4×C8—611no—
430C4×C8—611no—
431C4×C8—611no—
432C4×C8—1221no—
433C4×C8—1221no—
434C4×C8C2×#692311yescharacteristic, complemented
435#95—1221no—
436#95—1222no—
437#95—1222no—
438#95—1221no—
439C24—1221no—
440C24—1221no—
441C2×D4—614no—
442C2×D4—611no—
443C2×D4—611no—
444C2×D4—1222no—
445C2×D4—1222no—
446C2×D4—1222no—
447C2×D4—1221no—
448C2×D4—1221no—
449C2×D4C22×#692311yescharacteristic
450C2×D4C22×#692311yescharacteristic
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—611no—
454C22×C4—611no—
455C22×C4—612no—
456C22×C4—611no—
457C22×C4—612no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—1221no—
464C22×C4—1222no—
465C22×C4—1228no—
466C22×C4—1221no—
467C22×C4—1221no—
468C22×C4—1222no—
469C22×C4—2442no—
470C22×C4—2442no—
471C22×C4—2442no—
472C22×C4—2442no—
473C22×C4—2444no—
474C22×C4—2444no—
475D8—22no—
476D8—1222no—
477D8—1222no—
478D8—1222no—
479C2×C8—611no—
480C2×C8—611no—
481C2×C8—1222no—
482C2×C8—1222no—
483C2×C8—1222no—
484C2×C8—1222no—
485C2×C8—1222no—
486C2×C8C22×#692311yescharacteristic
487C2×C8C22×#692311yescharacteristic
488C4⋊C4—614no—
489C4⋊C4—611no—
490C4⋊C4—611no—
491C4⋊C4—1221no—
492C4⋊C4—1221no—
493C4⋊C4—1222no—
494C4⋊C4—1222no—
495C4⋊C4—1222no—
496C4⋊C4—2444no—
497C4⋊C4C22×#692311yescharacteristic
498C4⋊C4C22×#692311yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—1221no—
502C22⋊C4—1221no—
503C22⋊C4—1221no—
504C22⋊C4—1221no—
505C22⋊C4—1228no—
506C22⋊C4—1221no—
507C22⋊C4—1221no—
508C22⋊C4—2444no—
509C22⋊C4—2444no—
510C42—611no—
511C42—611no—
512C42—611no—
513C42—1222no—
514C42—1222no—
515C42—1222no—
516C42—1222no—
517C42—1224no—
518C42—2442no—
519C42—2442no—
520C42—2444no—
521C42C22×#692311yescharacteristic
522C23—21no—
523C23—21no—
524C23—611no—
525C23—1224no—
526C23—1221no—
527C23—1221no—
528C23—2441no—
529C23—2442no—
530C23—2441no—
531C23—2442no—
532C23—2441no—
533C23—2442no—
534C23—2441no—
535D4—21no—
536D4—21no—
537D4—21no—
538D4—612no—
539D4—1224no—
540D4—1221no—
541D4—1221no—
542D4—1221no—
543D4—2442no—
544D4#1451985612yescomplemented
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—611no—
550C2×C4—611no—
551C2×C4—612no—
552C2×C4—612no—
553C2×C4—612no—
554C2×C4—612no—
555C2×C4—614no—
556C2×C4—611no—
557C2×C4—1222no—
558C2×C4—1222no—
559C2×C4—1222no—
560C2×C4—1222no—
561C2×C4—1222no—
562C2×C4—1222no—
563C2×C4—1224no—
564C2×C4—1221no—
565C2×C4—1221no—
566C2×C4—2442no—
567C2×C4—2442no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4—2442no—
573C2×C4—2442no—
574C2×C4—24416no—
575C2×C4—2442no—
576C2×C4—2442no—
577C2×C4—2442no—
578C2×C4—2442no—
579C2×C4—2442no—
580C2×C4—2442no—
581C2×C4—2442no—
582C2×C4D4×#692311yescharacteristic
583C2×C4D4×#692311yescharacteristic
584C2×C4C23×#692311yescharacteristic
585C8—21no—
586C8—21no—
587C8—1221no—
588C8—1221no—
589C8—2442no—
590C22—22no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—612no—
597C22—612no—
598C22—611no—
599C22—611no—
600C22—1222no—
601C22—4882no—
602C22—4882no—
603C22—2444no—
604C22—2444no—
605C22—2441no—
606C22—2441no—
607C22—2441no—
608C22—2441no—
609C22—2441no—
610C22C2×D4×#692311yescharacteristic
611C4—21no—
612C4—41no—
613C4—41no—
614C4—612no—
615C4—612no—
616C4—1224no—
617C4—1221no—
618C4—4882no—
619C4—2442no—
620C4—2444no—
621C4—2441no—
622C4—2441no—
623C4#1684080312yes—
624C4C2×#1451985611yescharacteristic
625C4#41×#692311yescharacteristic
626C2—42no—
627C2—81no—
628C2—612no—
629C2—612no—
630C2—4881no—
631C2—2442no—
632C2#2146227311yescharacteristic
633C2#135×#692311yescharacteristic
634C2C2×#1684080311yescharacteristic
subgroupG/H
centerC2×C4D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC4×D8×C61C4
socleC22×C61C2×C4×D4
prime radicalC2×D8×D61C22
cosocleC2×C4×D61C24
hypercenterC4×D8#6923
hypocenterC61#21118
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #21462276C2semidirect
2. C4×D4×#6923C2semidirect
3. #21461897C2semidirect
4. #21461883C2semidirect
6. #21461784C2semidirect
7. C4×#14519845C2semidirect
8. C4×#14519839C2semidirect
9. C4×#14519839C2semidirect
10. #21461532C2semidirect
37. C4×D488C4semidirect
38. D8×Dic61C4semidirect
39. #16839844C4semidirect
40. C4×#11758199C4semidirect
41. C4×#11758199C4semidirect
42. #16839842C4semidirect
43. #16839842C4semidirect
48. C4×D8×C61C4semidirect
88. C4×D244C2×C4semidirect
90. D4×Dic61C2×C4semidirect
92. #14519739C2×C4semidirect
102. #14519711C2×C4semidirect
103. #14519710C2×C4semidirect
104. #14519710C2×C4semidirect
106. #14519699C2×C4semidirect
108. #14519698C2×C4semidirect
110. #14519697C2×C4semidirect
111. C4×#92418C2×C4semidirect
112. C8×Dic61C2×C4semidirect
113. C8×Dic61C2×C4semidirect
116. C4×D4×C61C2×C4semidirect
117. #107×C61C2×C4semidirect
119. #102×C61C2×C4semidirect
120. C4×C8×C61C2×C4semidirect
233. D4×C61#117semidirect
253. D244#117semidirect
342. C4×D8#6923semidirect
366. C61#21118semidirect
393. C4×D4C2×#6923semidirect
417. #107C2×#6923semidirect
428. #102C2×#6923semidirect
434. C4×C8C2×#6923semidirect
544. D4#14519856semidirect

Maximal subgroups

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

subgroupindex
#214622762
C4×D4×#69232
#214618972
#214618832
#214618142
#214617842
C4×#145198452
C4×#145198392
#214615322
C4×D8×D612
#2111861