Finite Group Databasebeta

← #29646140

Subgroups — #29646140

Order 15616.

1240 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840309C211yesmaximal, characteristic
2#21454449C211yesmaximal, characteristic, complemented
3#432×D61C211yesmaximal, characteristic, complemented
4#21444177C214yesmaximal, complemented
5#21444169C214yesmaximal, complemented
6#21444160C211yesmaximal, characteristic, complemented
7#21444159C211yesmaximal, characteristic, complemented
8#21444159C211yesmaximal, characteristic, complemented
9C61×#1466C211yesmaximal, characteristic, complemented
10C22×#11758222C412yes—
11#16840309—21no—
12#16840309—21no—
13#16840309—21no—
14#16840309—21no—
15#16840309—21no—
16#16840309—21no—
17#16840309—21no—
18#16840309—21no—
19C2×#14519776C411yescharacteristic
20C2×#14519773C411yescharacteristic
21C2×#14519763C2212yes—
22C2×#14519752C411yescharacteristic
23C2×#14519750C2212yes—
24C2×#14519748C411yescharacteristic
25C2×C4×D244C2211yescharacteristic
26C2×C4×C22⋊D61C412yes—
27C2×C42×D61C2211yescharacteristic
28#16839819C2211yescharacteristic
29#16839819C2211yescharacteristic
30#16839818—21no—
31#16839817—21no—
32#16839817—21no—
33#16839816C2212yes—
34#16839814—21no—
35#16839812C2212yes—
36#16839784—21no—
37C4⋊C8×D61—21no—
38#16839724C2212yes—
39C22⋊C8×D61C2212yes—
40#16839714—21no—
41#97×D61—21no—
42#16839486C2214yes—
43#16839485C2214yes—
44#16839485C2214yes—
45C2×C4×D4×C61C2211yescharacteristic
46C61×#432C2211yescharacteristic
47C61×#432C2211yescharacteristic
48C61×#323C2214yes—
49C2×#11758222—22no—
50C2×#11758222—22no—
51C2×#11758222—22no—
52C2×#11758222—22no—
53C2×#11758222—48no—
54C22×Dic122C2×C412yes—
55C22×D244C2×C411yescharacteristic
56C22×D244C2×C412yes—
57C22×C22⋊D61C2×C412yes—
58C22×C22⋊D61C2×C412yes—
59C22×C22⋊D61C2×C412yes—
60C22×C4×D61C2×C411yescharacteristic
61C22×C4×D61C2×C412yes—
62C22×C4×D61C2×C411yescharacteristic
63C22×C4×D61C2311yescharacteristic
64C2×#11758189—22no—
65C2×C8×D61—22no—
66#14519776—21no—
67#14519776—21no—
68#14519776—21no—
69#14519776—21no—
70#14519773—21no—
71#14519773—21no—
72#14519773—21no—
73#14519773—21no—
74#14519763—22no—
75#14519763—22no—
76#14519763—22no—
77#14519763—22no—
78#14519752—21no—
79#14519752—21no—
80#14519752—21no—
81#14519752—21no—
82#14519750—22no—
83#14519750—22no—
84#14519750—22no—
85#14519750—22no—
86#14519748—21no—
87#14519748—21no—
88#14519748—21no—
89#14519748—21no—
90C4×D244—21no—
91C4×D244—21no—
92C4×D244—21no—
93C4×D244—21no—
94C4×C22⋊D61—22no—
95C4×C22⋊D61—22no—
96C4×C22⋊D61—22no—
97C4×C22⋊D61—22no—
98C2×C4⋊Dic61C2×C411yescharacteristic
99C2×#11758196C2×C412yes—
100C2×C22⋊Dic61C2×C412yes—
101C2×#11758198C2×C412yes—
102C2×#11758198C2312yes—
103C2×C4×Dic61C2×C411yescharacteristic
104C2×C4×Dic61C2×C411yescharacteristic
105C2×C4×Dic61C2311yescharacteristic
106C42×D61D411yescharacteristic
107C42×D61D411yescharacteristic
108C42×D61D411yescharacteristic
109C42×D61D411yescharacteristic
110C42×D61D411yescharacteristic
111C42×D61D411yescharacteristic
112C42×D61D411yescharacteristic
113C42×D61D411yescharacteristic
114C4⋊#92418—21no—
115C4⋊#92418—21no—
116#14519706—22no—
117#14519706—22no—
118C22⋊#92418C2312yes—
119C22⋊#92418C2312yes—
120#14519689—22no—
121#14519689—22no—
122#14519688—21no—
123#14519688—21no—
124#14519687—22no—
125C8×Dic61—22no—
126C22×D4×C61C2×C411yescharacteristic
127C23×C4×C61C2×C412yes—
128C4×D4×C61—21no—
129C4×D4×C61—21no—
130C4×D4×C61—21no—
131C4×D4×C61—21no—
132C2×C4⋊C4×C61C2×C411yescharacteristic
133C2×C22⋊C4×C61C2312yes—
134C2×C42×C61C2311yescharacteristic
135C4⋊C8×C61—21no—
136C4⋊C8×C61—21no—
137C22⋊C8×C61C2312yes—
138C22⋊C8×C61C2312yes—
139#97×C61—21no—
140#97×C61—21no—
141C24×C61C22×C412yes—
142C23×D61C22×C411yescharacteristic
143C23×D61C22×C412yes—
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61—42no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—44no—
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C412yes—
153C22×C4×C61C2411yescharacteristic
154C2×C22⋊D61—22no—
155C2×C22⋊D61—22no—
156C2×C22⋊D61—22no—
157C2×C22⋊D61—22no—
158C2×C22⋊D61—22no—
159C2×C22⋊D61—22no—
160C2×C22⋊D61—44no—
161C2×C22⋊D61—44no—
162C2×C22⋊D61—44no—
163C22×Dic61C22×C411yescharacteristic
164C22×Dic61C22×C411yescharacteristic
165C22×Dic61C22×C411yescharacteristic
166C22×Dic61C22×C412yes—
167#11758222—48no—
168#11758222—48no—
169#11758222—48no—
170#11758222—48no—
171C2×D244—22no—
172C2×D244—22no—
173C2×D244—21no—
174C2×D244—21no—
175C2×D244—42no—
176C2×D244—44no—
177C2×C4×D61—24no—
178C2×C4×D61—22no—
179C2×C4×D61—22no—
180C2×C4×D61—42no—
181C2×C4×D61—42no—
182C2×C4×D61—44no—
183C2×C4×D61C22⋊C411yescharacteristic
184C2×C4×D61C22⋊C411yescharacteristic
185C2×C4×D61C22⋊C411yescharacteristic
186C2×C4×D61C22⋊C411yescharacteristic
187C2×C4×D61C22⋊C411yescharacteristic
188C2×C4×D61C22⋊C411yescharacteristic
189C2×C4×D61C22⋊C411yescharacteristic
190C2×C4×D61C22⋊C411yescharacteristic
191C2×C4×D61C2×D411yescharacteristic
192C2×C4×D61C2×D411yescharacteristic
193C2×C4×D61C2×D411yescharacteristic
194C2×C4×D61C2×D411yescharacteristic
195C2×Dic122—22no—
196C2×Dic122—22no—
197C2×Dic122—44no—
198C2×C8×C61—22no—
199C2×C8×C61—22no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C22⋊C4×C61—22no—
203C22⋊C4×C61—22no—
204C42×C61C2×D411yescharacteristic
205C42×C61C2×D411yescharacteristic
206C42×C61C2×D411yescharacteristic
207C42×C61C2×D411yescharacteristic
208C22⋊Dic61—22no—
209C22⋊Dic61—22no—
210#11758198—22no—
211#11758198—22no—
212#11758198—22no—
213#11758198—22no—
214C4⋊Dic61—21no—
215C4⋊Dic61—21no—
216#11758196—22no—
217#11758196—22no—
218C4×Dic61C22⋊C411yescharacteristic
219C4×Dic61C22⋊C411yescharacteristic
220C4×Dic61C22⋊C411yescharacteristic
221C4×Dic61C22⋊C411yescharacteristic
222C4×Dic61C22⋊C411yescharacteristic
223C4×Dic61C22⋊C411yescharacteristic
224C4×Dic61C22⋊C411yescharacteristic
225C4×Dic61C22⋊C411yescharacteristic
226C4×Dic61C2×D411yescharacteristic
227C4×Dic61C2×D411yescharacteristic
228C4×Dic61C2×D411yescharacteristic
229C4×Dic61C2×D411yescharacteristic
230C2×#92418—22no—
231C2×#92418—22no—
232#11758189—44no—
233C8×D61—44no—
234C23×C61—22no—
235C23×C61—24no—
236C23×C61—42no—
237C23×C61—42no—
238C23×C61C23×C411yescharacteristic
239C22×D61—22no—
240C22×D61—22no—
241C22×D61—22no—
242C22×D61—24no—
243C22×D61—41no—
244C22×D61—42no—
245C22×D61—42no—
246C22×D61C2×C22⋊C411yescharacteristic
247C22×D61C2×C22⋊C411yescharacteristic
248D4×C61—42no—
249D4×C61—42no—
250C2×C4×C61—22no—
251C2×C4×C61—22no—
252C2×C4×C61—22no—
253C2×C4×C61—41no—
254C2×C4×C61—44no—
255C2×C4×C61—44no—
256C2×C4×C61—42no—
257C2×C4×C61C2×C22⋊C411yescharacteristic
258C2×C4×C61C2×C22⋊C411yescharacteristic
259C2×C4×C61C2×C22⋊C411yescharacteristic
260C2×C4×C61C2×C22⋊C411yescharacteristic
261C2×C4×C61C22×D411yescharacteristic
262C2×C4×C61C22×D411yescharacteristic
263C22⋊D61—44no—
264C22⋊D61—44no—
265C22⋊D61—44no—
266C22⋊D61—44no—
267C22⋊D61—44no—
268C22⋊D61—44no—
269C2×Dic61—22no—
270C2×Dic61—22no—
271C2×Dic61—22no—
272C2×Dic61—22no—
273C2×Dic61—42no—
274C2×Dic61C2×C22⋊C411yescharacteristic
275C2×Dic61C2×C22⋊C411yescharacteristic
276C2×Dic61C2×C22⋊C411yescharacteristic
277C2×Dic61C2×C22⋊C411yescharacteristic
278C2×Dic61C2×C22⋊C411yescharacteristic
279C2×Dic61C2×C22⋊C411yescharacteristic
280D244—42no—
281D244—42no—
282D244—44no—
283D244—44no—
284C4×D61—22no—
285C4×D61—22no—
286C4×D61—22no—
287C4×D61—22no—
288C4×D61—22no—
289C4×D61—41no—
290C4×D61—41no—
291C4×D61—41no—
292C4×D61—41no—
293C4×D61—41no—
294C4×D61—41no—
295C4×D61—44no—
296C4×D61—44no—
297C4×D61#10014yes—
298Dic122—44no—
299Dic122—44no—
300C8×C61—42no—
301C8×C61—42no—
302#92418—42no—
303#92418—42no—
304#17403—611nomaximal, Sylow
305C22×C61—21no—
306C22×C61—21no—
307C22×C61—42no—
308C22×C61—42no—
309C22×C61—42no—
310C22×C61—84no—
311C22×C61C22×C22⋊C411yescharacteristic
312C22×C61#56812yes—
313C2×D61—21no—
314C2×D61—21no—
315C2×D61—21no—
316C2×D61—21no—
317C2×D61—21no—
318C2×D61—44no—
319C2×D61—42no—
320C2×D61—42no—
321C2×D61—42no—
322C2×D61—84no—
323C2×D61C2×#10012yes—
324C4×C61—21no—
325C4×C61—21no—
326C4×C61—21no—
327C4×C61—21no—
328C4×C61—21no—
329C4×C61—42no—
330C4×C61C2×#10012yes—
331Dic61—21no—
332Dic61—21no—
333Dic61—21no—
334Dic61—21no—
335Dic61—42no—
336Dic61#41012yes—
337Dic61C2×#10012yes—
338C2×#532—611no—
339#2920—611no—
340C2×#432—611no—
341#1471—614no—
342#1469—614no—
343#1466—611no—
344#1466—611no—
345#1466—611no—
346#1466D6111yescharacteristic, complemented
347C2×C61—22no—
348C2×C61—82no—
349C2×C61#287911yescharacteristic
350C2×C61C2×#41011yescharacteristic
351C2×C61C22×#10011yescharacteristic
352D61—22no—
353D61—41no—
354D61—82no—
355C22×#41—612no—
356#532—1221no—
357#532—1221no—
358#532—1221no—
359#532—1221no—
360#532—1221no—
361#532—1221no—
362#532—1221no—
363#532—1221no—
364C2×C4⋊Q8—611no—
365C2×#127—611no—
366C2×#124—612no—
367C2×#121—611no—
368C2×#121—611no—
369C2×#121—612no—
370C2×C4×D4—612no—
371C2×C4×D4—611no—
372C2×C4×D4C2×D6111yescharacteristic
373C22×C42—611no—
374#432—611no—
375#432—611no—
376#432—612no—
377#432—1221no—
378#432—1221no—
379#432—1221no—
380#432C2×D6111yescharacteristic
381#432C2×D6111yescharacteristic
382#431—612no—
383#431—1221no—
384#423—1221no—
385C2×C4⋊C8—1221no—
386#407—612no—
387C2×C22⋊C8—612no—
388C4×M16—1221no—
389C2×#97—1221no—
390#323—614no—
391#323—614no—
392#323—614no—
393#323C2×D6114yes—
394C61#1740311yescharacteristic, complemented, Sylow
395C2×#41—1222no—
396C2×#41—1222no—
397C2×#41—1222no—
398C2×#41—1222no—
399C2×#41—2448no—
400C22×Q8—612no—
401C22×D4—612no—
402C22×D4—612no—
403C22×D4—612no—
404C22×D4—611no—
405C22×D4—612no—
406C22×D4C4×D6111yescharacteristic
407C23×C4—611no—
408C23×C4—611no—
409C23×C4—611no—
410C23×C4—612no—
411C23×C4C4×D6112yes—
412C2×M16—1222no—
413C22×C8—1222no—
414C4⋊Q8—1221no—
415C4⋊Q8—1221no—
416C4⋊Q8—1221no—
417C4⋊Q8—1221no—
418#127—1221no—
419#127—1221no—
420#127—1221no—
421#127—1221no—
422#124—1222no—
423#124—1222no—
424#124—1222no—
425#124—1222no—
426#121—1222no—
427#121—1222no—
428#121—1222no—
429#121—1222no—
430#121—1221no—
431#121—1221no—
432#121—1221no—
433#121—1221no—
434#121—1221no—
435#121—1221no—
436#121—1221no—
437#121—1221no—
438C4×D4—21no—
439C4×D4—21no—
440C4×D4—21no—
441C4×D4—21no—
442C4×D4—1222no—
443C4×D4—1222no—
444C4×D4—1222no—
445C4×D4—1222no—
446C4×D4—1221no—
447C4×D4—1221no—
448C4×D4—1221no—
449C4×D4—1221no—
450C2×C4⋊C4—612no—
451C2×C4⋊C4—611no—
452C2×C4⋊C4C4×D6111yescharacteristic
453C2×C22⋊C4—612no—
454C2×C22⋊C4—612no—
455C2×C22⋊C4—612no—
456C2×C22⋊C4C22×D6112yes—
457C2×C42—611no—
458C2×C42—611no—
459C2×C42—611no—
460C2×C42—611no—
461C2×C42—611no—
462C2×C42—611no—
463C2×C42—611no—
464C2×C42—611no—
465C2×C42—611no—
466C2×C42—611no—
467C2×C42—611no—
468C2×C42C22×D6111yescharacteristic
469C4⋊C8—21no—
470C4⋊C8—21no—
471C4⋊C8—1222no—
472C4⋊C8—1222no—
473C4⋊C8—1221no—
474C4⋊C8—1221no—
475C22⋊C8—612no—
476C22⋊C8—612no—
477C22⋊C8—1222no—
478C22⋊C8—1222no—
479C22⋊C8C22×D6112yes—
480C22⋊C8C22×D6112yes—
481#97—21no—
482#97—21no—
483#97—1222no—
484#97—1221no—
485#97—1221no—
486C4×C8—1222no—
487C24—611no—
488C24—612no—
489C24C2×C4×D6112yes—
490#41—2448no—
491#41—2448no—
492#41—2448no—
493#41—2448no—
494C2×Q8—1222no—
495C2×Q8—1222no—
496C2×Q8—2444no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—42no—
500C2×D4—1222no—
501C2×D4—1222no—
502C2×D4—1222no—
503C2×D4—1222no—
504C2×D4—1222no—
505C2×D4—1222no—
506C2×D4—1222no—
507C2×D4—1222no—
508C2×D4—1221no—
509C2×D4—1221no—
510C2×D4—2442no—
511C2×D4—2444no—
512C2×D4—2444no—
513C2×D4—2444no—
514C2×D4—2444no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—44no—
518C22×C4—611no—
519C22×C4—611no—
520C22×C4—611no—
521C22×C4—611no—
522C22×C4—611no—
523C22×C4—611no—
524C22×C4—611no—
525C22×C4—611no—
526C22×C4—611no—
527C22×C4—611no—
528C22×C4—611no—
529C22×C4—611no—
530C22×C4—611no—
531C22×C4—611no—
532C22×C4—611no—
533C22×C4—612no—
534C22×C4—1224no—
535C22×C4—1222no—
536C22×C4—1222no—
537C22×C4—2442no—
538C22×C4—2444no—
539C22×C4—2442no—
540C22×C4C2×C4×D6111yescharacteristic
541C22×C4C2×C4×D6111yescharacteristic
542C22×C4C2×C4×D6112yes—
543C22×C4C23×D6111yescharacteristic
544M16—2444no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—1222no—
548C2×C8—1222no—
549C2×C8—2444no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—1222no—
553C4⋊C4—1222no—
554C4⋊C4—1221no—
555C4⋊C4—1221no—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—1222no—
559C22⋊C4—1222no—
560C22⋊C4—1222no—
561C22⋊C4—1222no—
562C22⋊C4—1222no—
563C22⋊C4—1222no—
564C42—611no—
565C42—611no—
566C42—611no—
567C42—611no—
568C42—611no—
569C42—611no—
570C42—611no—
571C42—611no—
572C42—611no—
573C42—611no—
574C42—611no—
575C42—611no—
576C42D4×D6111yescharacteristic
577C42D4×D6111yescharacteristic
578C42D4×D6111yescharacteristic
579C42D4×D6111yescharacteristic
580C23—22no—
581C23—24no—
582C23—42no—
583C23—42no—
584C23—611no—
585C23—611no—
586C23—1222no—
587C23—1222no—
588C23—1224no—
589C23—1222no—
590C23—2441no—
591C23—2442no—
592C23—2442no—
593C23C22×C4×D6111yescharacteristic
594Q8—2444no—
595Q8—2444no—
596D4—42no—
597D4—42no—
598D4—2442no—
599D4—2442no—
600D4—2444no—
601D4—2444no—
602D4—2444no—
603D4—2444no—
604D4—2444no—
605D4—2444no—
606D4—2444no—
607D4—2444no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—41no—
612C2×C4—44no—
613C2×C4—44no—
614C2×C4—42no—
615C2×C4—611no—
616C2×C4—611no—
617C2×C4—614no—
618C2×C4—611no—
619C2×C4—611no—
620C2×C4—611no—
621C2×C4—611no—
622C2×C4—1222no—
623C2×C4—1222no—
624C2×C4—1222no—
625C2×C4—1222no—
626C2×C4—1222no—
627C2×C4—1222no—
628C2×C4—1222no—
629C2×C4—1222no—
630C2×C4—1222no—
631C2×C4—2441no—
632C2×C4—2441no—
633C2×C4—2441no—
634C2×C4—2441no—
635C2×C4—2441no—
636C2×C4—2441no—
637C2×C4—2444no—
638C2×C4—2444no—
639C2×C4—2442no—
640C2×C4C22⋊C4×D6111yescharacteristic
641C2×C4C22⋊C4×D6111yescharacteristic
642C2×C4C22⋊C4×D6111yescharacteristic
643C2×C4C22⋊C4×D6111yescharacteristic
644C2×C4C2×D4×D6111yescharacteristic
645C2×C4C2×D4×D6111yescharacteristic
646C8—42no—
647C8—42no—
648C8—2442no—
649C8—2442no—
650C22—21no—
651C22—21no—
652C22—42no—
653C22—42no—
654C22—42no—
655C22—84no—
656C22—612no—
657C22—1221no—
658C22—1221no—
659C22—1221no—
660C22—1221no—
661C22—1221no—
662C22—4884no—
663C22—2444no—
664C22—2442no—
665C22—2442no—
666C22—2442no—
667C22C2×C22⋊C4×D6111yescharacteristic
668C22#1684052812yes—
669C4—21no—
670C4—21no—
671C4—21no—
672C4—21no—
673C4—21no—
674C4—42no—
675C4—612no—
676C4—612no—
677C4—1221no—
678C4—1221no—
679C4—1221no—
680C4—1221no—
681C4—2442no—
682C4#100×D6112yes—
683C2—22no—
684C2—82no—
685C2—1222no—
686C2—4882no—
687C2—2441no—
688C2#2145426211yescharacteristic
689C2#410×D6111yescharacteristic
690C2C2×#100×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1466C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840309C2
cosocleC22×C4×C61C24
hypercenter#1466D61
hypocenterC61#17403
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. #21454449C2semidirect
3. #432×D61C2semidirect
4. #21444177C2semidirect
5. #21444169C2semidirect
6. #21444160C2semidirect
7. #21444159C2semidirect
8. #21444159C2semidirect
9. C61×#1466C2semidirect
346. #1466D61semidirect
394. C61#17403semidirect

Maximal subgroups

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

subgroupindex
C2×#168403092
#214544492
#432×D612
#214441772
#214441692
#214441602
#214441592
C61×#14662
#1740361