Finite Group Databasebeta

← #29684075

Subgroups — #29684075

Order 15616.

1650 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840311C211yesmaximal, characteristic
2C2×C4⋊C8×D61C211yesmaximal, characteristic, complemented
3C2×#16839757C212yesmaximal, complemented
4C2×#16839755C212yesmaximal, complemented
5C4×#14519735C211yesmaximal, characteristic, complemented
6#21446752C211yesmaximal, characteristic, complemented
7#21446751C211yesmaximal, characteristic, complemented
8#21446749C211yesmaximal, characteristic, complemented
9#21446744C212yesmaximal, complemented
10#21446740C212yesmaximal, complemented
11C61×#1983C211yesmaximal, characteristic, complemented
12C22×#11758226C2211yescharacteristic
13C22×#11758224C2211yescharacteristic
14C22×C8×D61C2212yes—
15#16840311—24no—
16#16840311C418yescomplemented
17C2×#14519775C2211yescharacteristic
18C2×#14519773C2211yescharacteristic
19C2×#14519765C2211yescharacteristic
20C2×#14519750—21no—
21C2×#14519750—21no—
22C2×#14519737—21no—
23C2×#14519737—21no—
24C2×#14519735C2212yes—
25C2×C42×D61C2211yescharacteristic
26C2×C4⋊#92418C2211yescharacteristic
27C2×#14519706C2212yes—
28C4⋊C8×D61—24no—
29#16839757—28no—
30#16839755—28no—
31C2×#14519702C2212yes—
32C2×#14519701C2212yes—
33C2×#14519700C2212yes—
34C2×#14519699C2212yes—
35C2×#14519698C2212yes—
36C2×#14519697C2212yes—
37C4⋊C4×Dic61C2212yes—
38C4×C4⋊Dic61C2211yescharacteristic
39C4×#11758198—21no—
40#16839609—21no—
41#16839607—21no—
42C42×Dic61—21no—
43C2×#124×C61C2211yescharacteristic
44C2×C4⋊C8×C61C2211yescharacteristic
45C2×#103×C61C2212yes—
46C2×#102×C61C2212yes—
47C4×C4⋊C4×C61C2211yescharacteristic
48C2×#11758226—22no—
49C2×#11758226—24no—
50C2×#11758226—24no—
51C2×#11758226C2×C414yes—
52C2×#11758224—24no—
53C2×#11758224—22no—
54C2×#11758224—24no—
55C2×#11758224C2×C414yes—
56C22×Dic122C2311yescharacteristic
57C22×D244—21no—
58C22×D244C2311yescharacteristic
59C22×C22⋊D61—21no—
60C22×C22⋊D61—21no—
61C22×C22⋊D61—21no—
62C23×Dic61—21no—
63C22×C4×D61—21no—
64C22×C4×D61D411yescharacteristic
65C22×C4×D61D411yescharacteristic
66C22×C4×D61C2311yescharacteristic
67C22×#92418C2312yes—
68C2×C8×D61—24no—
69C2×C8×D61—24no—
70C2×C8×D61—24no—
71#14519775—22no—
72#14519775C2×C414yes—
73#14519773—22no—
74#14519773C2×C414yes—
75#14519765—22no—
76#14519765C2×C414yes—
77#14519750—28no—
78#14519750—28no—
79#14519737—28no—
80#14519737—28no—
81#14519735—24no—
82#14519735D418yescomplemented
83C2×C4⋊Dic61C2312yes—
84C2×#11758196—21no—
85C2×#11758196—21no—
86C2×#11758198—22no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×C4×Dic61—22no—
90C2×C4×Dic61—21no—
91C2×C4×Dic61—22no—
92C2×C4×Dic61D411yescharacteristic
93C2×C4×Dic61D411yescharacteristic
94C2×C4×Dic61C2311yescharacteristic
95C42×D61C2×C414yes—
96C42×D61D414yes—
97C4⋊#92418—22no—
98#14519706—24no—
99#14519702—24no—
100#14519701—24no—
101#14519700—24no—
102#14519699—24no—
103#14519698—24no—
104#14519697—24no—
105#14519684—21no—
106#14519684—22no—
107C22×Q8×C61C2311yescharacteristic
108C22×D4×C61C2311yescharacteristic
109C22×C8×C61C2312yes—
110#124×C61—22no—
111#124×C61C2×C414yes—
112C2×C4⋊C4×C61C2312yes—
113C2×C22⋊C4×C61—21no—
114C2×C22⋊C4×C61—21no—
115C2×C42×C61—21no—
116C2×C42×C61C2311yescharacteristic
117C4⋊C8×C61—22no—
118#103×C61—24no—
119#102×C61—24no—
120#95×C61—21no—
121C24×C61—21no—
122C23×D61—21no—
123C23×D61C2×D411yescharacteristic
124C2×Q8×C61—21no—
125C2×Q8×C61—22no—
126C2×Q8×C61—22no—
127C2×Q8×C61C22×C412yes—
128C2×D4×C61—22no—
129C2×D4×C61—21no—
130C2×D4×C61—22no—
131C2×D4×C61C22×C412yes—
132C22×C4×C61—21no—
133C22×C4×C61—22no—
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2411yescharacteristic
137C2×C22⋊D61—24no—
138C2×C22⋊D61—24no—
139C2×C22⋊D61—24no—
140C2×C22⋊D61—42no—
141C2×C22⋊D61—42no—
142C2×C22⋊D61—44no—
143C2×C22⋊D61—44no—
144C22×Dic61—21no—
145C22×Dic61—22no—
146C22×Dic61—24no—
147C22×Dic61—44no—
148C22×Dic61C2×D411yescharacteristic
149C22×Dic61C2×D411yescharacteristic
150C22×Dic61C2×D411yescharacteristic
151#11758226—216no—
152#11758226—44no—
153#11758226—44no—
154#11758224—216no—
155#11758224—44no—
156#11758224—44no—
157C2×D244—22no—
158C2×D244—22no—
159C2×D244—24no—
160C2×D244—21no—
161C2×D244—44no—
162C2×D244C22×C412yes—
163C2×C4×D61—24no—
164C2×C4×D61—24no—
165C2×C4×D61—41no—
166C2×C4×D61—41no—
167C2×C4×D61—44no—
168C2×C4×D61C22⋊C414yes—
169C2×C4×D61C22⋊C414yes—
170C2×C4×D61C22×C412yes—
171C2×C4×D61C2×D414yes—
172C2×C4×D61C2×D412yes—
173C2×C4×D61#4114yes—
174C2×Dic122—22no—
175C2×Dic122—22no—
176C2×Dic122—21no—
177C2×Dic122C22×C412yes—
178C2×C8×C61—22no—
179C2×C8×C61—22no—
180C2×C8×C61—22no—
181C4⋊C4×C61—22no—
182C4⋊C4×C61C2×D414yes—
183C22⋊C4×C61—24no—
184C22⋊C4×C61—24no—
185C42×C61—42no—
186C42×C61C22×C412yes—
187C42×C61C2×D412yes—
188#11758198—28no—
189#11758198—24no—
190#11758198—24no—
191C4⋊Dic61—22no—
192C4⋊Dic61C2×D414yes—
193#11758196—24no—
194#11758196—24no—
195C4×Dic61—28no—
196C4×Dic61—42no—
197C4×Dic61—44no—
198C4×Dic61C22⋊C414yes—
199C4×Dic61C22⋊C414yes—
200C4×Dic61C22×C412yes—
201C4×Dic61C2×D412yes—
202C2×#92418—22no—
203C2×#92418—22no—
204C2×#92418—22no—
205C8×D61—48no—
206C23×C61—22no—
207C23×C61—42no—
208C23×C61—42no—
209C23×C61—41no—
210C23×C61—41no—
211C23×C61C22×D411yescharacteristic
212C22×D61—22no—
213C22×D61—21no—
214C22×D61—21no—
215C22×D61—22no—
216C22×D61—42no—
217C22×D61—42no—
218C22×D61—41no—
219C22×D61—41no—
220C22×D61C2×C22⋊C412yes—
221C22×D61#12114yes—
222Q8×C61—24no—
223Q8×C61—41no—
224Q8×C61—41no—
225D4×C61—24no—
226D4×C61—41no—
227D4×C61—41no—
228C2×C4×C61—22no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—22no—
232C2×C4×C61—24no—
233C2×C4×C61—42no—
234C2×C4×C61—42no—
235C2×C4×C61—42no—
236C2×C4×C61C2×C22⋊C412yes—
237C2×C4×C61C2×C22⋊C412yes—
238C2×C4×C61C23×C411yescharacteristic
239C2×C4×C61C22×D412yes—
240C2×C4×C61C22×D411yescharacteristic
241C2×C4×C61C2×#4112yes—
242C22⋊D61—48no—
243C22⋊D61—48no—
244C22⋊D61—48no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—22no—
248C2×Dic61—24no—
249C2×Dic61—42no—
250C2×Dic61—42no—
251C2×Dic61—42no—
252C2×Dic61—48no—
253C2×Dic61C2×C22⋊C412yes—
254C2×Dic61C2×C22⋊C412yes—
255C2×Dic61C2×C22⋊C412yes—
256C2×Dic61#12114yes—
257C2×Dic61#13514yes—
258D244—24no—
259D244—48no—
260D244—41no—
261D244—41no—
262C4×D61—28no—
263C4×D61—44no—
264C4×D61—48no—
265C4×D61C4×D418yes—
266C4×D61#12414yes—
267C4×D61#12714yes—
268Dic122—24no—
269Dic122—41no—
270Dic122—41no—
271C8×C61—42no—
272#92418—42no—
273#21257—611nomaximal, Sylow
274C22×C61—42no—
275C22×C61—42no—
276C22×C61—42no—
277C22×C61—82no—
278C22×C61—82no—
279C22×C61C22×C22⋊C411yescharacteristic
280C22×C61C2×#12112yes—
281C22×C61C2×#13512yes—
282C22×C61#57511yescharacteristic
283C22×C61#57511yescharacteristic
284C2×D61—22no—
285C2×D61—22no—
286C2×D61—24no—
287C2×D61—24no—
288C2×D61—42no—
289C2×D61—42no—
290C2×D61—42no—
291C2×D61—82no—
292C2×D61—82no—
293C2×D61#39014yes—
294C4×C61—22no—
295C4×C61—22no—
296C4×C61—44no—
297C4×C61—42no—
298C4×C61C2×C4×D412yes—
299C4×C61C2×#12411yescharacteristic
300C4×C61C2×#12711yescharacteristic
301Dic61—22no—
302Dic61—44no—
303Dic61—42no—
304Dic61#39014yes—
305Dic61#41614yescomplemented
306C2×#532—611no—
307C22×C4⋊C8—611no—
308C2×#416—612no—
309C2×#416—612no—
310C4×#117—611no—
311#1983—611no—
312#1983—611no—
313#1983—611no—
314#1983D6111yescharacteristic, complemented
315#1982—612no—
316#1981—612no—
317C2×C61—82no—
318C2×C61C2×#39011yescharacteristic
319C2×C61C2×#41611yescharacteristic
320C2×C61#289611yescharacteristic
321C2×C61#303512yes—
322C2×C61#303512yes—
323D61—24no—
324D61—82no—
325C22×#41—611no—
326C22×#41—611no—
327C23×C8—612no—
328#532—618no—
329#532—1224no—
330C2×C4⋊Q8—611no—
331C2×#127—611no—
332C2×#124—611no—
333C2×#124C2×D6111yescharacteristic
334C2×#121—1221no—
335C2×#121—1221no—
336C2×C4×D4—1221no—
337C2×C4×D4—1221no—
338C2×#117—612no—
339C22×C42—611no—
340C2×C4⋊C8—612no—
341C2×C4⋊C8—611no—
342C2×C4⋊C8—1224no—
343C2×C4⋊C8C2×D6111yescharacteristic
344#416—1228no—
345#416—1228no—
346C2×#103—612no—
347C2×#103—612no—
348C2×#103—612no—
349C2×#103C2×D6112yes—
350C2×#102—612no—
351C2×#102—612no—
352C2×#102—612no—
353C2×#102C2×D6112yes—
354C4×C4⋊C4—612no—
355C4×C4⋊C4—611no—
356C4×C4⋊C4C2×D6111yescharacteristic
357C4×C22⋊C4—1221no—
358C4×C22⋊C4—1221no—
359#376—1221no—
360C43—1221no—
361C61#2125711yescharacteristic, complemented, Sylow
362C2×#41—614no—
363C2×#41—614no—
364C2×#41—1222no—
365C2×#41—1222no—
366C2×#41—1224no—
367C2×#41—1224no—
368C2×#41—1224no—
369C2×#41—1224no—
370C22×Q8—611no—
371C22×Q8C22×D6111yescharacteristic
372C22×D4—611no—
373C22×D4—1221no—
374C22×D4—1221no—
375C22×D4—1221no—
376C22×D4—1221no—
377C22×D4C22×D6111yescharacteristic
378C23×C4—611no—
379C23×C4—611no—
380C23×C4—611no—
381C23×C4—1221no—
382C23×C4—1221no—
383C22×C8—612no—
384C22×C8—1224no—
385C22×C8—1224no—
386C22×C8—1224no—
387C22×C8C22×D6112yes—
388C4⋊Q8—614no—
389C4⋊Q8—1222no—
390#127—614no—
391#127—1222no—
392#124—22no—
393#124—614no—
394#124—1222no—
395#124C4×D6114yes—
396#121—1228no—
397#121—1228no—
398C4×D4—1228no—
399C4×D4—1228no—
400#117—618no—
401#117—1224no—
402C2×C4⋊C4—612no—
403C2×C4⋊C4—1221no—
404C2×C4⋊C4—1221no—
405C2×C4⋊C4C22×D6112yes—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—1222no—
409C2×C22⋊C4—1221no—
410C2×C22⋊C4—1221no—
411C2×C42—21no—
412C2×C42—611no—
413C2×C42—611no—
414C2×C42—611no—
415C2×C42—614no—
416C2×C42—614no—
417C2×C42—1222no—
418C2×C42—1222no—
419C2×C42—1221no—
420C2×C42C22×D6111yescharacteristic
421C4⋊C8—22no—
422C4⋊C8—1224no—
423C4⋊C8—1222no—
424#103—24no—
425#103—1224no—
426#103—1224no—
427#103—1224no—
428#102—24no—
429#102—1224no—
430#102—1224no—
431#102—1224no—
432#95—21no—
433#95—1222no—
434#95—1221no—
435C24—21no—
436C24—611no—
437C24—1221no—
438#41—12216no—
439#41—12216no—
440#41—2444no—
441#41—2444no—
442#41—2444no—
443#41—2444no—
444C2×Q8—21no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—612no—
448C2×Q8—1221no—
449C2×Q8—1222no—
450C2×Q8—1222no—
451C2×Q8C2×C4×D6112yes—
452C2×D4—22no—
453C2×D4—21no—
454C2×D4—22no—
455C2×D4—612no—
456C2×D4—1224no—
457C2×D4—1224no—
458C2×D4—1224no—
459C2×D4—1224no—
460C2×D4—1222no—
461C2×D4—1221no—
462C2×D4—1222no—
463C2×D4—2444no—
464C2×D4—2444no—
465C2×D4—2442no—
466C2×D4—2442no—
467C2×D4—2444no—
468C2×D4C2×C4×D6112yes—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—612no—
474C22×C4—612no—
475C22×C4—614no—
476C22×C4—614no—
477C22×C4—611no—
478C22×C4—614no—
479C22×C4—614no—
480C22×C4—1224no—
481C22×C4—1224no—
482C22×C4—1224no—
483C22×C4—1222no—
484C22×C4—1221no—
485C22×C4—2441no—
486C22×C4—2441no—
487C22×C4—2444no—
488C22×C4—2444no—
489C22×C4D4×D6111yescharacteristic
490C22×C4D4×D6111yescharacteristic
491C22×C4C23×D6111yescharacteristic
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—1222no—
496C2×C8—1222no—
497C2×C8—1222no—
498C2×C8—2448no—
499C4⋊C4—22no—
500C4⋊C4—614no—
501C4⋊C4—1224no—
502C4⋊C4—1224no—
503C4⋊C4—1222no—
504C4⋊C4D4×D6114yes—
505C22⋊C4—24no—
506C22⋊C4—24no—
507C22⋊C4—1228no—
508C22⋊C4—1224no—
509C22⋊C4—1224no—
510C42—42no—
511C42—612no—
512C42—612no—
513C42—614no—
514C42—614no—
515C42—1228no—
516C42—2442no—
517C42—2444no—
518C42C2×C4×D6112yes—
519C42D4×D6112yes—
520C23—22no—
521C23—42no—
522C23—42no—
523C23—41no—
524C23—41no—
525C23—612no—
526C23—614no—
527C23—1222no—
528C23—1221no—
529C23—1221no—
530C23—1222no—
531C23—2442no—
532C23—2442no—
533C23—2441no—
534C23—2441no—
535C23C2×D4×D6111yescharacteristic
536Q8—24no—
537Q8—41no—
538Q8—41no—
539Q8—1224no—
540Q8—2441no—
541Q8—2441no—
542D4—24no—
543D4—41no—
544D4—41no—
545D4—1224no—
546D4—2448no—
547D4—2448no—
548D4—2448no—
549D4—2448no—
550D4—2441no—
551D4—2441no—
552C2×C4—22no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—612no—
561C2×C4—612no—
562C2×C4—614no—
563C2×C4—614no—
564C2×C4—618no—
565C2×C4—614no—
566C2×C4—614no—
567C2×C4—612no—
568C2×C4—1228no—
569C2×C4—1221no—
570C2×C4—1221no—
571C2×C4—1222no—
572C2×C4—1224no—
573C2×C4—2444no—
574C2×C4—2448no—
575C2×C4—2448no—
576C2×C4—2442no—
577C2×C4—2442no—
578C2×C4—2442no—
579C2×C4C22⋊C4×D6112yes—
580C2×C4C22⋊C4×D6112yes—
581C2×C4C22×C4×D6111yescharacteristic
582C2×C4C2×D4×D6112yes—
583C2×C4C2×D4×D6111yescharacteristic
584C2×C4#41×D6112yes—
585C8—42no—
586C8—2442no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—82no—
591C22—82no—
592C22—614no—
593C22—1224no—
594C22—1224no—
595C22—1222no—
596C22—1222no—
597C22—4882no—
598C22—4882no—
599C22—2442no—
600C22—2442no—
601C22—2442no—
602C22C2×C22⋊C4×D6111yescharacteristic
603C22#121×D6112yes—
604C22#135×D6112yes—
605C22#1684055811yescharacteristic
606C22#1684056111yescharacteristic
607C4—22no—
608C4—22no—
609C4—42no—
610C4—44no—
611C4—614no—
612C4—614no—
613C4—1222no—
614C4—2442no—
615C4—2444no—
616C4C4×D4×D6112yes—
617C4#124×D6111yescharacteristic
618C4#127×D6111yescharacteristic
619C2—82no—
620C2—1224no—
621C2—4882no—
622C2#390×D6111yescharacteristic
623C2#416×D6111yescharacteristic
624C2#2145433511yescharacteristic
625C2#2145527112yes—
626C2#2145527312yes—
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1983C2
socleC23×C61C22×D4
prime radicalC2×#16840311C2
cosocleC22×C4×C61C24
hypercenter#1983D61
hypocenterC61#21257
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1983

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C8×D61C2semidirect
3. C2×#16839757C2semidirect
4. C2×#16839755C2semidirect
5. C4×#14519735C2semidirect
6. #21446752C2semidirect
7. #21446751C2semidirect
8. #21446749C2semidirect
9. #21446744C2semidirect
10. #21446740C2semidirect
11. C61×#1983C2semidirect
16. #16840311C4semidirect
82. #14519735D4semidirect
305. Dic61#416semidirect
314. #1983D61semidirect
361. C61#21257semidirect

Maximal subgroups

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

subgroupindex
C2×#168403112
C2×C4⋊C8×D612
C2×#168397572
C2×#168397552
C4×#145197352
#214467522
#214467512
#214467492
#214467442
#214467402
C61×#19832
#2125761