Finite Group Databasebeta

← #29646231

Subgroups — #29646231

Order 15616.

1008 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840461C211yesmaximal, characteristic
2#21454478C212yesmaximal, complemented
3#21444189C212yesmaximal, complemented
4#21444185C212yesmaximal, complemented
5#21444177C212yesmaximal, complemented
6#21444158C211yesmaximal, characteristic, complemented
7#21444154C211yesmaximal, characteristic, complemented
8#21444140C211yesmaximal, characteristic, complemented
9#21444138C211yesmaximal, characteristic, complemented
10#21444134C211yesmaximal, characteristic, complemented
11C61×#1466C211yesmaximal, characteristic, complemented
12#16840461—22no—
13#16840461—22no—
14#16840461—22no—
15#16840461—22no—
16C2×#14519771C2211yescharacteristic
17C2×#14519770C2211yescharacteristic
18C2×#14519767C411yescharacteristic
19C2×#14519762C411yescharacteristic
20C2×#14519760C411yescharacteristic
21C2×#14519751C411yescharacteristic
22C2×#14519750C2211yescharacteristic
23C2×#14519749C411yescharacteristic
24C2×#14519749C411yescharacteristic
25C2×C4×C22⋊D61C411yescharacteristic
26C2×#14519737C2211yescharacteristic
27C2×#14519737C2211yescharacteristic
28C2×#14519734C2211yescharacteristic
29C22×#11758196C411yescharacteristic
30#16839824—22no—
31#16839822—22no—
32#16839816C2212yes—
33#16839815C2212yes—
34#16839812C2212yes—
35#16839787—22no—
36#16839724C2212yes—
37C22⋊C8×D61C2212yes—
38#16839719—22no—
39#16839487C2212yes—
40#16839487C2212yes—
41#16839486C2211yescharacteristic
42#16839486C2211yescharacteristic
43#16839486C2212yes—
44#16839485C2212yes—
45#16839485C2212yes—
46C2×C4×D4×C61C2211yescharacteristic
47C61×#432C2212yes—
48C61×#323C2211yescharacteristic
49C61×#323C2211yescharacteristic
50C61×#323C2212yes—
51C22×D244C2×C411yescharacteristic
52C22×C22⋊D61C2×C411yescharacteristic
53C22×C22⋊D61C2×C411yescharacteristic
54C22×C22⋊D61C2×C411yescharacteristic
55C22×C22⋊D61C2×C411yescharacteristic
56C23×Dic61C2×C411yescharacteristic
57C23×Dic61C2×C411yescharacteristic
58C22×C4×D61C2×C411yescharacteristic
59C22×C4×D61C2311yescharacteristic
60C2×#11758189—22no—
61C2×C8×D61—22no—
62#14519771—22no—
63#14519771—22no—
64#14519770—22no—
65#14519770—22no—
66#14519767—22no—
67#14519767—22no—
68#14519762—22no—
69#14519762—22no—
70#14519760—22no—
71#14519760—22no—
72#14519751—22no—
73#14519751—22no—
74#14519750—22no—
75#14519750—22no—
76#14519749—22no—
77#14519749—22no—
78#14519749—22no—
79#14519749—22no—
80C4×C22⋊D61—21no—
81C4×C22⋊D61—21no—
82C4×C22⋊D61—21no—
83C4×C22⋊D61—21no—
84#14519737—22no—
85#14519737—22no—
86#14519737—22no—
87#14519737—22no—
88#14519734D412yes—
89#14519734D412yes—
90#14519734D412yes—
91#14519734D412yes—
92C2×C4⋊Dic61C2×C411yescharacteristic
93C2×#11758196—21no—
94C2×#11758196—21no—
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196C2×C411yescharacteristic
98C2×#11758196C2×C411yescharacteristic
99C2×#11758196C2×C411yescharacteristic
100C2×#11758196C2×C411yescharacteristic
101C2×#11758196C2×C411yescharacteristic
102C2×#11758196C2×C411yescharacteristic
103C2×#11758196C2×C411yescharacteristic
104C2×#11758196C2311yescharacteristic
105C2×C22⋊Dic61C2×C411yescharacteristic
106C2×C22⋊Dic61C2×C411yescharacteristic
107C2×#11758198C2×C411yescharacteristic
108C2×#11758198C2×C411yescharacteristic
109C2×#11758198C2×C411yescharacteristic
110C2×#11758198C2×C411yescharacteristic
111C2×#11758198C2×C411yescharacteristic
112C2×#11758198C2311yescharacteristic
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—
125C22×D4×C61C2×C411yescharacteristic
126C23×C4×C61C2×C411yescharacteristic
127C23×C4×C61C2×C411yescharacteristic
128C4×D4×C61—22no—
129C4×D4×C61—22no—
130C2×C4⋊C4×C61C2×C411yescharacteristic
131C2×C22⋊C4×C61C2311yescharacteristic
132C2×C22⋊C4×C61C2311yescharacteristic
133C2×C42×C61C2311yescharacteristic
134C4⋊C8×C61—22no—
135C22⋊C8×C61C2312yes—
136C22⋊C8×C61C2312yes—
137#97×C61—22no—
138C24×C61C22×C411yescharacteristic
139C24×C61C22×C411yescharacteristic
140C23×D61C22×C411yescharacteristic
141C23×D61C22×C411yescharacteristic
142C2×D4×C61—22no—
143C2×D4×C61—22no—
144C2×D4×C61—41no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—81no—
150C22×C4×C61—81no—
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C2411yescharacteristic
156C2×C22⋊D61—22no—
157C2×C22⋊D61—22no—
158C2×C22⋊D61—22no—
159C2×C22⋊D61—22no—
160C2×C22⋊D61—22no—
161C2×C22⋊D61—21no—
162C2×C22⋊D61—21no—
163C2×C22⋊D61—41no—
164C2×C22⋊D61—41no—
165C2×C22⋊D61—42no—
166C2×C22⋊D61—81no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—42no—
172C22×Dic61—81no—
173C22×Dic61C22×C411yescharacteristic
174C22×Dic61C22×C411yescharacteristic
175C22×Dic61C22×C411yescharacteristic
176C22×Dic61C22×C411yescharacteristic
177C22×Dic61C22×C411yescharacteristic
178C22×Dic61C22×C411yescharacteristic
179C2×D244—22no—
180C2×D244—81no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—42no—
184C2×C4×D61—81no—
185C2×C4×D61C2×D412yes—
186C2×C4×D61C2×D412yes—
187C2×C8×C61—22no—
188C2×C8×C61—22no—
189C4⋊C4×C61—22no—
190C22⋊C4×C61—22no—
191C22⋊C4×C61—22no—
192C42×C61C2×D412yes—
193C42×C61C2×D412yes—
194C22⋊Dic61—21no—
195C22⋊Dic61—21no—
196C22⋊Dic61—22no—
197#11758198—22no—
198#11758198—21no—
199#11758198—21no—
200#11758198—22no—
201#11758198—22no—
202#11758198C22⋊C412yes—
203#11758198C22⋊C412yes—
204#11758198C22⋊C412yes—
205#11758198C22⋊C412yes—
206C4⋊Dic61—22no—
207#11758196—21no—
208#11758196—21no—
209#11758196—22no—
210#11758196—22no—
211#11758196—21no—
212#11758196—21no—
213#11758196—21no—
214#11758196—21no—
215#11758196—22no—
216#11758196C22⋊C411yescharacteristic
217#11758196C22⋊C411yescharacteristic
218#11758196C22⋊C411yescharacteristic
219#11758196C22⋊C411yescharacteristic
220#11758196C22⋊C412yes—
221#11758196C22⋊C412yes—
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—21no—
234C23×C61—21no—
235C23×C61—41no—
236C23×C61—41no—
237C23×C61—41no—
238C23×C61—41no—
239C23×C61#13112yes—
240C23×C61C23×C411yescharacteristic
241C22×D61—21no—
242C22×D61—21no—
243C22×D61—21no—
244C22×D61—21no—
245C22×D61—21no—
246C22×D61—41no—
247C22×D61—41no—
248C22×D61—41no—
249C22×D61—41no—
250C22×D61C2×C22⋊C412yes—
251D4×C61—44no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61—81no—
261C2×C4×C61—81no—
262C2×C4×C61—81no—
263C2×C4×C61—81no—
264C2×C4×C61C2×C22⋊C412yes—
265C2×C4×C61C2×C22⋊C411yescharacteristic
266C2×C4×C61C2×C22⋊C411yescharacteristic
267C2×C4×C61C22×D412yes—
268C22⋊D61—44no—
269C22⋊D61—42no—
270C22⋊D61—44no—
271C22⋊D61—42no—
272C22⋊D61—82no—
273C2×Dic61—21no—
274C2×Dic61—21no—
275C2×Dic61—22no—
276C2×Dic61—21no—
277C2×Dic61—21no—
278C2×Dic61—21no—
279C2×Dic61—21no—
280C2×Dic61—21no—
281C2×Dic61—41no—
282C2×Dic61—42no—
283C2×Dic61—42no—
284C2×Dic61—41no—
285C2×Dic61—41no—
286C2×Dic61—81no—
287C2×Dic61—81no—
288C2×Dic61C2×C22⋊C411yescharacteristic
289C2×Dic61C2×C22⋊C412yes—
290C2×Dic61C2×C22⋊C411yescharacteristic
291C2×Dic61C2×C22⋊C411yescharacteristic
292C2×Dic61C2×C22⋊C411yescharacteristic
293D244—82no—
294C4×D61—24no—
295C4×D61—42no—
296C4×D61—81no—
297C4×D61—81no—
298C8×C61—42no—
299C8×C61—42no—
300#92418—42no—
301#92418—42no—
302#17415—611nomaximal, Sylow
303C22×C61—21no—
304C22×C61—21no—
305C22×C61—22no—
306C22×C61—42no—
307C22×C61—42no—
308C22×C61—41no—
309C22×C61—41no—
310C22×C61—41no—
311C22×C61—41no—
312C22×C61—41no—
313C22×C61—81no—
314C22×C61—81no—
315C22×C61C22×C22⋊C411yescharacteristic
316C22×C61C2×#13111yescharacteristic
317C22×C61#56811yescharacteristic
318C2×D61—22no—
319C2×D61—22no—
320C2×D61—22no—
321C2×D61—41no—
322C2×D61—41no—
323C2×D61—41no—
324C2×D61—81no—
325C2×D61—81no—
326C2×D61—81no—
327C2×D61—81no—
328C4×C61—22no—
329C4×C61—22no—
330C4×C61—21no—
331C4×C61—21no—
332C4×C61—41no—
333C4×C61—41no—
334Dic61—22no—
335Dic61—21no—
336Dic61—21no—
337Dic61—21no—
338Dic61—41no—
339Dic61—41no—
340Dic61—41no—
341Dic61#41012yes—
342C2×#553—611no—
343#2924—612no—
344#1473—612no—
345#1473—612no—
346#1471—612no—
347#1466—611no—
348#1466D6111yescharacteristic, complemented
349#1465—611no—
350#1460—611no—
351#1460—611no—
352#1459—611no—
353C2×C61—21no—
354C2×C61—21no—
355C2×C61—42no—
356C2×C61—81no—
357C2×C61#288011yescharacteristic
358C2×C61C2×#41011yescharacteristic
359C2×C61#288811yescharacteristic
360D61—42no—
361D61—81no—
362#553—1222no—
363#553—1222no—
364#553—1222no—
365#553—1222no—
366C2×#126—611no—
367C2×#126—611no—
368C2×#125—611no—
369C2×#123—611no—
370C2×#123—611no—
371C2×#121—611no—
372C2×#121—611no—
373C2×#121—611no—
374C2×#121—611no—
375C2×C4×D4—611no—
376C2×C4×D4—611no—
377C2×C4×D4—611no—
378C2×C4×D4C2×D6111yescharacteristic
379C2×#117—611no—
380C22×C4⋊C4—611no—
381#433—1222no—
382#433—1222no—
383#432—612no—
384#432C2×D6112yes—
385#431—612no—
386#431—612no—
387#424—1222no—
388#407—612no—
389C2×C22⋊C8—612no—
390#405—1222no—
391#324—612no—
392#324—612no—
393#323—611no—
394#323—611no—
395#323—612no—
396#323—612no—
397#323—612no—
398#323C2×D6111yescharacteristic
399#323C2×D6111yescharacteristic
400#323C2×D6112yes—
401C61#1741511yescharacteristic, complemented, Sylow
402C22×D4—611no—
403C22×D4—611no—
404C22×D4—611no—
405C22×D4—611no—
406C22×D4—611no—
407C22×D4C4×D6111yescharacteristic
408C23×C4—611no—
409C23×C4—611no—
410C23×C4—611no—
411C23×C4—611no—
412C23×C4C4×D6111yescharacteristic
413C23×C4C4×D6111yescharacteristic
414C2×M16—1222no—
415C22×C8—1222no—
416#126—1222no—
417#126—1222no—
418#126—1222no—
419#126—1222no—
420#125—1222no—
421#125—1222no—
422#123—1222no—
423#123—1222no—
424#123—1222no—
425#123—1222no—
426#121—1222no—
427#121—1222no—
428#121—1222no—
429#121—1222no—
430#121—1222no—
431#121—1222no—
432#121—1222no—
433#121—1222no—
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—1222no—
437C4×D4—1222no—
438C4×D4—1222no—
439C4×D4—1222no—
440C4×D4—1221no—
441C4×D4—1221no—
442C4×D4—1221no—
443C4×D4—1221no—
444#117—612no—
445#117—612no—
446#117—612no—
447#117—612no—
448C2×C4⋊C4—611no—
449C2×C4⋊C4—611no—
450C2×C4⋊C4—611no—
451C2×C4⋊C4—611no—
452C2×C4⋊C4—611no—
453C2×C4⋊C4—611no—
454C2×C4⋊C4—611no—
455C2×C4⋊C4—611no—
456C2×C4⋊C4—611no—
457C2×C4⋊C4—1221no—
458C2×C4⋊C4—1221no—
459C2×C4⋊C4—1221no—
460C2×C4⋊C4—1221no—
461C2×C4⋊C4C4×D6111yescharacteristic
462C2×C22⋊C4—611no—
463C2×C22⋊C4—611no—
464C2×C22⋊C4—611no—
465C2×C22⋊C4—611no—
466C2×C22⋊C4—611no—
467C2×C22⋊C4—611no—
468C2×C22⋊C4—611no—
469C2×C22⋊C4—611no—
470C2×C22⋊C4C22×D6111yescharacteristic
471C2×C22⋊C4C22×D6111yescharacteristic
472C2×C42—611no—
473C2×C42—611no—
474C2×C42C22×D6111yescharacteristic
475C4⋊C8—22no—
476C4⋊C8—1222no—
477C4⋊C8—1222no—
478C4⋊C8—1222no—
479C22⋊C8—612no—
480C22⋊C8—612no—
481C22⋊C8—1222no—
482C22⋊C8—1222no—
483C22⋊C8C22×D6112yes—
484C22⋊C8C22×D6112yes—
485#97—22no—
486#97—1222no—
487C4×C8—1222no—
488C4×C8—1222no—
489C24—611no—
490C24—611no—
491C24C2×C4×D6111yescharacteristic
492C24C2×C4×D6111yescharacteristic
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—41no—
496C2×D4—1222no—
497C2×D4—1221no—
498C2×D4—1222no—
499C2×D4—1221no—
500C2×D4—1222no—
501C2×D4—1222no—
502C2×D4—1222no—
503C2×D4—1222no—
504C2×D4—4881no—
505C2×D4—4881no—
506C2×D4—2441no—
507C2×D4—2441no—
508C2×D4—2442no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—81no—
514C22×C4—81no—
515C22×C4—611no—
516C22×C4—611no—
517C22×C4—611no—
518C22×C4—612no—
519C22×C4—612no—
520C22×C4—611no—
521C22×C4—611no—
522C22×C4—611no—
523C22×C4—1221no—
524C22×C4—1221no—
525C22×C4—1221no—
526C22×C4—1221no—
527C22×C4—1221no—
528C22×C4—1221no—
529C22×C4—4881no—
530C22×C4—4881no—
531C22×C4—2442no—
532C22×C4—2442no—
533C22×C4C2×C4×D6111yescharacteristic
534C22×C4C2×C4×D6111yescharacteristic
535C22×C4C2×C4×D6111yescharacteristic
536C22×C4C2×C4×D6111yescharacteristic
537C22×C4C23×D6111yescharacteristic
538M16—2444no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—1222no—
542C2×C8—1222no—
543C2×C8—2444no—
544C4⋊C4—22no—
545C4⋊C4—611no—
546C4⋊C4—611no—
547C4⋊C4—611no—
548C4⋊C4—611no—
549C4⋊C4—612no—
550C4⋊C4—612no—
551C4⋊C4—1221no—
552C4⋊C4—1221no—
553C4⋊C4—1221no—
554C4⋊C4—1221no—
555C4⋊C4—1222no—
556C4⋊C4—1222no—
557C4⋊C4—1222no—
558C4⋊C4—1221no—
559C4⋊C4—1221no—
560C4⋊C4—1222no—
561C22⋊C4—22no—
562C22⋊C4—22no—
563C22⋊C4—612no—
564C22⋊C4—612no—
565C22⋊C4—612no—
566C22⋊C4—612no—
567C22⋊C4—1222no—
568C22⋊C4—1221no—
569C22⋊C4—1221no—
570C22⋊C4—1222no—
571C22⋊C4—1222no—
572C22⋊C4—1221no—
573C22⋊C4—1221no—
574C22⋊C4—1222no—
575C42—612no—
576C42—612no—
577C42—1221no—
578C42—1221no—
579C42D4×D6112yes—
580C42D4×D6112yes—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—612no—
591C23—1221no—
592C23—1221no—
593C23—1221no—
594C23—1221no—
595C23—1221no—
596C23—2441no—
597C23—2441no—
598C23—2441no—
599C23—2441no—
600C23#1451978512yes—
601C23C22×C4×D6111yescharacteristic
602D4—44no—
603D4—4882no—
604D4—4882no—
605D4—2442no—
606D4—2444no—
607D4—2442no—
608D4—2444no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—81no—
618C2×C4—81no—
619C2×C4—81no—
620C2×C4—81no—
621C2×C4—611no—
622C2×C4—612no—
623C2×C4—611no—
624C2×C4—611no—
625C2×C4—611no—
626C2×C4—1224no—
627C2×C4—1222no—
628C2×C4—1221no—
629C2×C4—1221no—
630C2×C4—1221no—
631C2×C4—1221no—
632C2×C4—1221no—
633C2×C4—1221no—
634C2×C4—1221no—
635C2×C4—4881no—
636C2×C4—4881no—
637C2×C4—4881no—
638C2×C4—4881no—
639C2×C4—2442no—
640C2×C4—2442no—
641C2×C4—2441no—
642C2×C4—2442no—
643C2×C4—2441no—
644C2×C4—2441no—
645C2×C4C22⋊C4×D6112yes—
646C2×C4C22⋊C4×D6111yescharacteristic
647C2×C4C22⋊C4×D6111yescharacteristic
648C2×C4C2×D4×D6112yes—
649C8—42no—
650C8—42no—
651C8—2442no—
652C8—2442no—
653C22—21no—
654C22—21no—
655C22—22no—
656C22—42no—
657C22—42no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—81no—
664C22—81no—
665C22—1222no—
666C22—1222no—
667C22—1222no—
668C22—4881no—
669C22—4881no—
670C22—4881no—
671C22—4881no—
672C22—2441no—
673C22—2441no—
674C22—2441no—
675C22C2×C22⋊C4×D6111yescharacteristic
676C22C2×#1451978511yescharacteristic
677C22#1684052811yescharacteristic
678C4—22no—
679C4—22no—
680C4—21no—
681C4—21no—
682C4—41no—
683C4—41no—
684C4—612no—
685C4—1222no—
686C4—1221no—
687C4—1221no—
688C4—1221no—
689C4—2441no—
690C4—2441no—
691C4—2441no—
692C2—21no—
693C2—21no—
694C2—42no—
695C2—81no—
696C2—4881no—
697C2—2442no—
698C2#2145426911yescharacteristic
699C2#410×D6111yescharacteristic
700C2#2145429511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1466C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840461C2
cosocleC22×C4×C61C24
hypercenter#1466D61
hypocenterC61#17415
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1466

Complements

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

NH ≅ G/Ntype
2. #21454478C2semidirect
3. #21444189C2semidirect
4. #21444185C2semidirect
5. #21444177C2semidirect
6. #21444158C2semidirect
7. #21444154C2semidirect
8. #21444140C2semidirect
9. #21444138C2semidirect
10. #21444134C2semidirect
11. C61×#1466C2semidirect
348. #1466D61semidirect
401. C61#17415semidirect

Maximal subgroups

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

subgroupindex
C2×#168404612
#214544782
#214441892
#214441852
#214441772
#214441582
#214441542
#214441402
#214441382
#214441342
C61×#14662
#1741561