Finite Group Databasebeta

← #29646258

Subgroups — #29646258

Order 15616.

1002 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840475C211yesmaximal, characteristic
2#21454478C212yesmaximal, complemented
3#21444177C212yesmaximal, complemented
4#21444172C212yesmaximal, complemented
5#21444169C212yesmaximal, complemented
6#21444156C211yesmaximal, characteristic, complemented
7#21444152C211yesmaximal, characteristic, complemented
8#21444136C211yesmaximal, characteristic, complemented
9#21444133C211yesmaximal, characteristic, complemented
10#21444132C211yesmaximal, characteristic, complemented
11C61×#1464C211yesmaximal, characteristic, complemented
12#16840475—22no—
13#16840475—22no—
14#16840475—22no—
15#16840475—22no—
16C2×#14519776C411yescharacteristic
17C2×#14519765C411yescharacteristic
18C2×#14519765C2211yescharacteristic
19C2×#14519763C411yescharacteristic
20C2×#14519763C2211yescharacteristic
21C2×#14519752C411yescharacteristic
22C2×#14519751C411yescharacteristic
23C2×#14519750C411yescharacteristic
24C2×#14519750C2211yescharacteristic
25C2×#14519739C2211yescharacteristic
26C2×C4×C22⋊D61C411yescharacteristic
27C2×#14519735C2211yescharacteristic
28C2×#14519734C411yescharacteristic
29C2×#14519734C2211yescharacteristic
30#16839824—22no—
31#16839822—22no—
32#16839816C2212yes—
33#16839815C2212yes—
34#16839812C2212yes—
35#16839787—22no—
36#16839724C2212yes—
37C22⋊C8×D61C2212yes—
38#16839719—22no—
39#16839488C2211yescharacteristic
40#16839488C2211yescharacteristic
41#16839486C2212yes—
42#16839485C2212yes—
43#16839485C2212yes—
44#16839485C2212yes—
45#16839485C2212yes—
46C2×#117×C61C2211yescharacteristic
47C61×#432C2212yes—
48C61×#324C2211yescharacteristic
49C61×#324C2211yescharacteristic
50C61×#323C2212yes—
51C22×Dic122C2×C411yescharacteristic
52C22×Dic122C2×C411yescharacteristic
53C22×D244C2×C411yescharacteristic
54C22×D244C2×C411yescharacteristic
55C22×D244C2×C411yescharacteristic
56C22×C22⋊D61C2×C411yescharacteristic
57C22×C22⋊D61C2×C411yescharacteristic
58C22×C22⋊D61C2×C411yescharacteristic
59C22×C4×D61C2×C411yescharacteristic
60C22×C4×D61C2×C411yescharacteristic
61C22×C4×D61C2311yescharacteristic
62C2×#11758189—22no—
63C2×C8×D61—22no—
64#14519776—22no—
65#14519776—22no—
66#14519765—22no—
67#14519765—22no—
68#14519765—22no—
69#14519765—22no—
70#14519763—22no—
71#14519763—22no—
72#14519763—22no—
73#14519763—22no—
74#14519752—22no—
75#14519752—22no—
76#14519751—22no—
77#14519751—22no—
78#14519750—22no—
79#14519750—22no—
80#14519750—22no—
81#14519750—22no—
82#14519739—22no—
83#14519739—22no—
84C4×C22⋊D61—21no—
85C4×C22⋊D61—21no—
86C4×C22⋊D61—21no—
87C4×C22⋊D61—21no—
88#14519735—22no—
89#14519735—22no—
90#14519734—21no—
91#14519734—21no—
92#14519734—21no—
93#14519734—21no—
94#14519734D412yes—
95#14519734D412yes—
96#14519734D412yes—
97#14519734D412yes—
98C2×C4⋊Dic61C2×C411yescharacteristic
99C2×#11758196C2×C411yescharacteristic
100C2×#11758196C2×C411yescharacteristic
101C2×#11758196C2×C411yescharacteristic
102C2×C22⋊Dic61C2×C411yescharacteristic
103C2×#11758198C2×C411yescharacteristic
104C2×#11758198C2×C411yescharacteristic
105C2×#11758198C2×C411yescharacteristic
106C2×#11758198C2×C411yescharacteristic
107C2×#11758198C2×C411yescharacteristic
108C2×#11758198C2×C411yescharacteristic
109C2×#11758198C2×C411yescharacteristic
110C2×#11758198C2311yescharacteristic
111C2×#11758198C2311yescharacteristic
112C2×C4×Dic61C2×C411yescharacteristic
113C2×C4×Dic61C2×C411yescharacteristic
114C2×C4×Dic61C2311yescharacteristic
115C4⋊#92418—22no—
116#14519706—22no—
117#14519706—22no—
118C22⋊#92418C2312yes—
119C22⋊#92418C2312yes—
120#14519689—22no—
121#14519689—22no—
122#14519687—22no—
123C4×#92418—22no—
124C8×Dic61—22no—
125C23×C4×C61C2×C411yescharacteristic
126#117×C61—22no—
127#117×C61—22no—
128C2×C4⋊C4×C61C2×C411yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C22⋊C4×C61C2×C411yescharacteristic
131C2×C22⋊C4×C61C2311yescharacteristic
132C2×C42×C61C2×C411yescharacteristic
133C2×C42×C61C2311yescharacteristic
134C4⋊C8×C61—22no—
135C22⋊C8×C61C2312yes—
136C22⋊C8×C61C2312yes—
137#97×C61—22no—
138C24×C61C22×C411yescharacteristic
139C23×D61C22×C411yescharacteristic
140C23×D61C22×C411yescharacteristic
141C23×D61C22×C411yescharacteristic
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—22no—
145C22×C4×C61—41no—
146C22×C4×C61C22×C411yescharacteristic
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C2411yescharacteristic
152C2×C22⋊D61—22no—
153C2×C22⋊D61—21no—
154C2×C22⋊D61—21no—
155C2×C22⋊D61—22no—
156C2×C22⋊D61—42no—
157C2×C22⋊D61—81no—
158C2×C22⋊D61—81no—
159C22×Dic61C22×C411yescharacteristic
160C22×Dic61C22×C411yescharacteristic
161C22×Dic61C22×C411yescharacteristic
162C22×Dic61C22×C411yescharacteristic
163C22×Dic61C22×C411yescharacteristic
164C2×D244—22no—
165C2×D244—22no—
166C2×D244—22no—
167C2×D244—22no—
168C2×D244—41no—
169C2×D244—81no—
170C2×D244—81no—
171C2×C4×D61—22no—
172C2×C4×D61—21no—
173C2×C4×D61—21no—
174C2×C4×D61—21no—
175C2×C4×D61—21no—
176C2×C4×D61—42no—
177C2×C4×D61—41no—
178C2×C4×D61—42no—
179C2×C4×D61C2×D412yes—
180C2×C4×D61C2×D412yes—
181C2×Dic122—22no—
182C2×Dic122—22no—
183C2×Dic122—81no—
184C2×Dic122—81no—
185C2×C8×C61—22no—
186C2×C8×C61—22no—
187C4⋊C4×C61—22no—
188C4⋊C4×C61—22no—
189C22⋊C4×C61—22no—
190C22⋊C4×C61—22no—
191C42×C61—21no—
192C42×C61—21no—
193C42×C61C2×D412yes—
194C42×C61C2×D412yes—
195C22⋊Dic61—21no—
196C22⋊Dic61—21no—
197#11758198—22no—
198#11758198—21no—
199#11758198—21no—
200#11758198—21no—
201#11758198—21no—
202#11758198—22no—
203#11758198—22no—
204#11758198—21no—
205#11758198—21no—
206#11758198—22no—
207#11758198C22⋊C412yes—
208#11758198C22⋊C412yes—
209#11758198C22⋊C412yes—
210#11758198C22⋊C412yes—
211C4⋊Dic61—22no—
212#11758196—21no—
213#11758196—21no—
214#11758196C22⋊C411yescharacteristic
215#11758196C22⋊C411yescharacteristic
216#11758196C22⋊C411yescharacteristic
217#11758196C22⋊C411yescharacteristic
218#11758196C22⋊C412yes—
219#11758196C22⋊C412yes—
220C4×Dic61—21no—
221C4×Dic61—21no—
222C4×Dic61—21no—
223C4×Dic61—21no—
224C4×Dic61C2×D412yes—
225C4×Dic61C2×D412yes—
226C2×#92418—22no—
227C2×#92418—22no—
228#11758189—44no—
229C8×D61—44no—
230C23×C61—21no—
231C23×C61—21no—
232C23×C61—21no—
233C23×C61—41no—
234C23×C61—41no—
235C23×C61C23×C411yescharacteristic
236C22×D61—21no—
237C22×D61—21no—
238C22×D61—21no—
239C22×D61—21no—
240C22×D61—21no—
241C22×D61—21no—
242C22×D61—21no—
243C22×D61—21no—
244C22×D61—41no—
245C22×D61—41no—
246C22×D61—41no—
247C22×D61—41no—
248C22×D61—41no—
249C22×D61—41no—
250C22×D61C2×C22⋊C412yes—
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—41no—
258C2×C4×C61—41no—
259C2×C4×C61—42no—
260C2×C4×C61—42no—
261C2×C4×C61—41no—
262C2×C4×C61—41no—
263C2×C4×C61C2×C22⋊C411yescharacteristic
264C2×C4×C61C2×C22⋊C411yescharacteristic
265C2×C4×C61C2×C22⋊C412yes—
266C2×C4×C61#13112yes—
267C2×C4×C61C22×D412yes—
268C22⋊D61—42no—
269C22⋊D61—42no—
270C22⋊D61—82no—
271C22⋊D61—82no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61—22no—
275C2×Dic61—21no—
276C2×Dic61—21no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61C2×C22⋊C411yescharacteristic
281C2×Dic61C2×C22⋊C411yescharacteristic
282C2×Dic61C2×C22⋊C411yescharacteristic
283C2×Dic61C2×C22⋊C412yes—
284C2×Dic61C2×C22⋊C411yescharacteristic
285D244—44no—
286D244—82no—
287D244—82no—
288C4×D61—24no—
289C4×D61—42no—
290C4×D61—42no—
291C4×D61—42no—
292C4×D61—42no—
293C4×D61—42no—
294Dic122—82no—
295Dic122—82no—
296C8×C61—42no—
297C8×C61—42no—
298#92418—42no—
299#92418—42no—
300#17418—611nomaximal, Sylow
301C22×C61—21no—
302C22×C61—21no—
303C22×C61—41no—
304C22×C61—41no—
305C22×C61—41no—
306C22×C61—81no—
307C22×C61—81no—
308C22×C61C22×C22⋊C411yescharacteristic
309C22×C61C2×#13111yescharacteristic
310C22×C61#56811yescharacteristic
311C2×D61—22no—
312C2×D61—22no—
313C2×D61—22no—
314C2×D61—41no—
315C2×D61—41no—
316C2×D61—41no—
317C2×D61—41no—
318C2×D61—41no—
319C2×D61—41no—
320C2×D61—81no—
321C2×D61—81no—
322C2×D61—81no—
323C2×D61—81no—
324C2×D61—81no—
325C2×D61—81no—
326C4×C61—22no—
327C4×C61—21no—
328C4×C61—21no—
329C4×C61—22no—
330C4×C61—22no—
331C4×C61—41no—
332C4×C61—41no—
333Dic61—21no—
334Dic61—21no—
335Dic61—21no—
336Dic61—22no—
337Dic61—41no—
338Dic61—41no—
339Dic61#41012yes—
340C2×#555—611no—
341#2924—612no—
342#1471—612no—
343#1469—612no—
344#1469—612no—
345#1465—611no—
346#1464—611no—
347#1464D6111yescharacteristic, complemented
348#1459—611no—
349#1458—611no—
350#1458—611no—
351C2×C61—21no—
352C2×C61—21no—
353C2×C61—81no—
354C2×C61#288011yescharacteristic
355C2×C61C2×#41011yescharacteristic
356C2×C61#288811yescharacteristic
357D61—42no—
358D61—81no—
359D61—81no—
360#555—1222no—
361#555—1222no—
362#555—1222no—
363#555—1222no—
364C2×C4⋊Q8—611no—
365C2×#124—611no—
366C2×#124—611no—
367C2×#124—611no—
368C2×#124—611no—
369C2×#121—611no—
370C2×#121—611no—
371C2×#121—611no—
372C2×#121—611no—
373C2×C4×D4—611no—
374C2×C4×D4—611no—
375C2×#117—611no—
376C2×#117—611no—
377C2×#117—611no—
378C2×#117C2×D6111yescharacteristic
379#433—1222no—
380#433—1222no—
381#432—612no—
382#432C2×D6112yes—
383#431—612no—
384#431—612no—
385#424—1222no—
386#407—612no—
387C2×C22⋊C8—612no—
388#405—1222no—
389#324—611no—
390#324—611no—
391#324C2×D6111yescharacteristic
392#324C2×D6111yescharacteristic
393#323—612no—
394#323—612no—
395#323—612no—
396#323—612no—
397#323—612no—
398#323C2×D6112yes—
399C61#1741811yescharacteristic, complemented, Sylow
400C22×Q8—611no—
401C22×Q8—611no—
402C22×D4—611no—
403C22×D4—611no—
404C22×D4—611no—
405C22×D4—611no—
406C22×D4—611no—
407C22×D4—611no—
408C23×C4—611no—
409C23×C4—611no—
410C23×C4—611no—
411C23×C4C4×D6111yescharacteristic
412C2×M16—1222no—
413C22×C8—1222no—
414C4⋊Q8—1222no—
415C4⋊Q8—1222no—
416#124—1222no—
417#124—1222no—
418#124—1222no—
419#124—1222no—
420#124—1222no—
421#124—1222no—
422#124—1222no—
423#124—1222no—
424#121—1222no—
425#121—1222no—
426#121—1222no—
427#121—1222no—
428#121—1222no—
429#121—1222no—
430#121—1222no—
431#121—1222no—
432C4×D4—1222no—
433C4×D4—1222no—
434C4×D4—1221no—
435C4×D4—1221no—
436C4×D4—1221no—
437C4×D4—1221no—
438#117—22no—
439#117—22no—
440#117—612no—
441#117—612no—
442#117—612no—
443#117—612no—
444#117—1221no—
445#117—1221no—
446#117—1221no—
447#117—1221no—
448#117—1222no—
449#117—1222no—
450C2×C4⋊C4—611no—
451C2×C4⋊C4—611no—
452C2×C4⋊C4—611no—
453C2×C4⋊C4—611no—
454C2×C4⋊C4C4×D6111yescharacteristic
455C2×C4⋊C4C22×D6111yescharacteristic
456C2×C22⋊C4—611no—
457C2×C22⋊C4—611no—
458C2×C22⋊C4—611no—
459C2×C22⋊C4—611no—
460C2×C22⋊C4—611no—
461C2×C22⋊C4—611no—
462C2×C22⋊C4—611no—
463C2×C22⋊C4—611no—
464C2×C22⋊C4—611no—
465C2×C22⋊C4—611no—
466C2×C22⋊C4C4×D6111yescharacteristic
467C2×C22⋊C4C22×D6111yescharacteristic
468C2×C42—611no—
469C2×C42—611no—
470C2×C42—611no—
471C2×C42C4×D6111yescharacteristic
472C2×C42C22×D6111yescharacteristic
473C4⋊C8—22no—
474C4⋊C8—1222no—
475C4⋊C8—1222no—
476C4⋊C8—1222no—
477C22⋊C8—612no—
478C22⋊C8—612no—
479C22⋊C8—1222no—
480C22⋊C8—1222no—
481C22⋊C8C22×D6112yes—
482C22⋊C8C22×D6112yes—
483#97—22no—
484#97—1222no—
485C4×C8—1222no—
486C4×C8—1222no—
487C24—611no—
488C24—611no—
489C24—611no—
490C24C2×C4×D6111yescharacteristic
491C2×Q8—1222no—
492C2×Q8—1222no—
493C2×Q8—4881no—
494C2×Q8—4881no—
495C2×D4—1222no—
496C2×D4—1222no—
497C2×D4—1222no—
498C2×D4—1221no—
499C2×D4—1221no—
500C2×D4—1222no—
501C2×D4—1222no—
502C2×D4—1222no—
503C2×D4—4881no—
504C2×D4—4881no—
505C2×D4—4881no—
506C2×D4—4881no—
507C2×D4—2441no—
508C2×D4—2442no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—41no—
513C22×C4—611no—
514C22×C4—611no—
515C22×C4—611no—
516C22×C4—612no—
517C22×C4—612no—
518C22×C4—611no—
519C22×C4—611no—
520C22×C4—1221no—
521C22×C4—1221no—
522C22×C4—1221no—
523C22×C4—1221no—
524C22×C4—1222no—
525C22×C4—2441no—
526C22×C4—2442no—
527C22×C4—2442no—
528C22×C4C2×C4×D6111yescharacteristic
529C22×C4C2×C4×D6111yescharacteristic
530C22×C4C2×C4×D6111yescharacteristic
531C22×C4C2×C4×D6111yescharacteristic
532C22×C4C2×C4×D6111yescharacteristic
533C22×C4C23×D6111yescharacteristic
534M16—2444no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—1222no—
538C2×C8—1222no—
539C2×C8—2444no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—611no—
543C4⋊C4—611no—
544C4⋊C4—611no—
545C4⋊C4—611no—
546C4⋊C4—612no—
547C4⋊C4—612no—
548C4⋊C4—1221no—
549C4⋊C4—1221no—
550C4⋊C4—1222no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—612no—
554C22⋊C4—612no—
555C22⋊C4—612no—
556C22⋊C4—612no—
557C22⋊C4—1222no—
558C22⋊C4—1221no—
559C22⋊C4—1221no—
560C22⋊C4—1222no—
561C22⋊C4—1221no—
562C22⋊C4—1221no—
563C22⋊C4—1222no—
564C22⋊C4—1222no—
565C22⋊C4—1221no—
566C22⋊C4—1221no—
567C22⋊C4—1221no—
568C22⋊C4—1221no—
569C42—21no—
570C42—21no—
571C42—612no—
572C42—612no—
573C42—1221no—
574C42—1221no—
575C42—1221no—
576C42—1221no—
577C42D4×D6112yes—
578C42D4×D6112yes—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—41no—
583C23—41no—
584C23—612no—
585C23—1221no—
586C23—1221no—
587C23—1221no—
588C23—1221no—
589C23—1221no—
590C23—1221no—
591C23—1221no—
592C23—1221no—
593C23—2441no—
594C23—2441no—
595C23—2441no—
596C23—2441no—
597C23—2441no—
598C23—2441no—
599C23C22×C4×D6111yescharacteristic
600Q8—4882no—
601Q8—4882no—
602D4—4882no—
603D4—4882no—
604D4—4882no—
605D4—4882no—
606D4—2444no—
607D4—2442no—
608D4—2442no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—611no—
622C2×C4—611no—
623C2×C4—611no—
624C2×C4—612no—
625C2×C4—611no—
626C2×C4—1224no—
627C2×C4—1222no—
628C2×C4—1221no—
629C2×C4—1221no—
630C2×C4—1221no—
631C2×C4—1221no—
632C2×C4—2442no—
633C2×C4—2442no—
634C2×C4—2442no—
635C2×C4—2442no—
636C2×C4—2442no—
637C2×C4—2441no—
638C2×C4—2441no—
639C2×C4—2441no—
640C2×C4C22⋊C4×D6111yescharacteristic
641C2×C4C22⋊C4×D6111yescharacteristic
642C2×C4C22⋊C4×D6112yes—
643C2×C4#1451978512yes—
644C2×C4C2×D4×D6112yes—
645C8—42no—
646C8—42no—
647C8—2442no—
648C8—2442no—
649C22—21no—
650C22—21no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—81no—
655C22—81no—
656C22—1222no—
657C22—1222no—
658C22—1222no—
659C22—4881no—
660C22—4881no—
661C22—4881no—
662C22—4881no—
663C22—4881no—
664C22—4881no—
665C22—2441no—
666C22—2441no—
667C22—2441no—
668C22—2441no—
669C22—2441no—
670C22—2441no—
671C22C2×C22⋊C4×D6111yescharacteristic
672C22C2×#1451978511yescharacteristic
673C22#1684052811yescharacteristic
674C4—22no—
675C4—21no—
676C4—21no—
677C4—22no—
678C4—22no—
679C4—41no—
680C4—41no—
681C4—612no—
682C4—1221no—
683C4—1221no—
684C4—1221no—
685C4—1222no—
686C4—2441no—
687C4—2441no—
688C2—21no—
689C2—21no—
690C2—81no—
691C2—4881no—
692C2—4881no—
693C2—2442no—
694C2#2145426911yescharacteristic
695C2#410×D6111yescharacteristic
696C2#2145429611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1464C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840475C2
cosocleC22×C4×C61C24
hypercenter#1464D61
hypocenterC61#17418
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1464

Complements

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

NH ≅ G/Ntype
2. #21454478C2semidirect
3. #21444177C2semidirect
4. #21444172C2semidirect
5. #21444169C2semidirect
6. #21444156C2semidirect
7. #21444152C2semidirect
8. #21444136C2semidirect
9. #21444133C2semidirect
10. #21444132C2semidirect
11. C61×#1464C2semidirect
347. #1464D61semidirect
399. C61#17418semidirect

Maximal subgroups

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

subgroupindex
C2×#168404752
#214544782
#214441772
#214441722
#214441692
#214441562
#214441522
#214441362
#214441332
#214441322
C61×#14642
#1741861