Finite Group Databasebeta

← #29646346

Subgroups — #29646346

Order 15616.

1016 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840495C211yesmaximal, characteristic
2#21454855C212yesmaximal, complemented
3#21444169C212yesmaximal, complemented
4#21444168C212yesmaximal, complemented
5#21444164C212yesmaximal, complemented
6#21444161C211yesmaximal, characteristic, complemented
7#21444156C211yesmaximal, characteristic, complemented
8#21444141C211yesmaximal, characteristic, complemented
9#21444137C211yesmaximal, characteristic, complemented
10#21444136C211yesmaximal, characteristic, complemented
11C61×#1465C211yesmaximal, characteristic, complemented
12#16840495—22no—
13#16840495—22no—
14#16840495—22no—
15#16840495—22no—
16C2×#14519773C411yescharacteristic
17C2×#14519765C411yescharacteristic
18C2×#14519764C411yescharacteristic
19C2×#14519763C411yescharacteristic
20C2×#14519763C2211yescharacteristic
21C2×#14519760C411yescharacteristic
22C2×#14519760C2211yescharacteristic
23C2×#14519759C411yescharacteristic
24C2×#14519759C2211yescharacteristic
25C2×C4×Dic122C411yescharacteristic
26C2×#14519742C2211yescharacteristic
27C2×#14519739C2211yescharacteristic
28C2×C4×C22⋊D61C411yescharacteristic
29C2×C4×C22⋊D61C2211yescharacteristic
30#16839838—22no—
31#16839831—22no—
32#16839830—22no—
33#16839825—22no—
34#16839816C2212yes—
35#16839812C2212yes—
36#16839724C2212yes—
37C2×C22⋊#92418C2212yes—
38C22⋊C8×D61C2212yes—
39#16839488C2211yescharacteristic
40#16839488C2211yescharacteristic
41#16839487C2212yes—
42#16839487C2212yes—
43#16839486C2212yes—
44#16839485C2212yes—
45#16839485C2212yes—
46C2×C4×D4×C61C2211yescharacteristic
47C61×#407C2212yes—
48C61×#324C2211yescharacteristic
49C61×#324C2211yescharacteristic
50C61×#323C2212yes—
51C22×Dic122C2×C411yescharacteristic
52C22×Dic122C2×C411yescharacteristic
53C22×D244C2×C411yescharacteristic
54C22×C22⋊D61C2×C411yescharacteristic
55C22×C22⋊D61C2×C411yescharacteristic
56C22×C22⋊D61C2×C411yescharacteristic
57C22×C22⋊D61C2×C411yescharacteristic
58C22×C4×D61C2×C411yescharacteristic
59C22×C4×D61C2311yescharacteristic
60C2×#11758189—22no—
61C22×#92418—22no—
62C2×C8×D61—22no—
63#14519773—22no—
64#14519773—22no—
65#14519765—22no—
66#14519765—22no—
67#14519764—22no—
68#14519764—22no—
69#14519763—22no—
70#14519763—22no—
71#14519763—22no—
72#14519763—22no—
73#14519760—22no—
74#14519760—22no—
75#14519760—22no—
76#14519760—22no—
77#14519759—22no—
78#14519759—22no—
79#14519759—22no—
80#14519759—22no—
81C4×Dic122—21no—
82C4×Dic122—21no—
83C4×Dic122—21no—
84C4×Dic122—21no—
85#14519742—22no—
86#14519742—22no—
87#14519739—22no—
88#14519739—22no—
89C4×C22⋊D61—21no—
90C4×C22⋊D61—21no—
91C4×C22⋊D61—21no—
92C4×C22⋊D61—21no—
93C4×C22⋊D61D412yes—
94C4×C22⋊D61D412yes—
95C4×C22⋊D61D412yes—
96C4×C22⋊D61D412yes—
97C2×C4⋊Dic61C2×C411yescharacteristic
98C2×#11758196C2×C411yescharacteristic
99C2×#11758196C2×C411yescharacteristic
100C2×#11758196C2×C411yescharacteristic
101C2×#11758196C2311yescharacteristic
102C2×C22⋊Dic61C2×C411yescharacteristic
103C2×C22⋊Dic61C2×C411yescharacteristic
104C2×C22⋊Dic61C2×C411yescharacteristic
105C2×C22⋊Dic61C2×C411yescharacteristic
106C2×#11758198C2×C411yescharacteristic
107C2×#11758198C2×C411yescharacteristic
108C2×#11758198C2×C411yescharacteristic
109C2×#11758198C2×C411yescharacteristic
110C2×#11758198C2×C411yescharacteristic
111C2×#11758198C2311yescharacteristic
112C2×C4×Dic61C2×C411yescharacteristic
113C2×C4×Dic61C2×C411yescharacteristic
114C2×C4×Dic61C2×C411yescharacteristic
115C2×C4×Dic61C2311yescharacteristic
116#14519706—22no—
117#14519706—22no—
118C22⋊#92418—22no—
119C22⋊#92418C2312yes—
120C22⋊#92418C2312yes—
121#14519689—22no—
122#14519689—22no—
123#14519687—22no—
124C8×Dic61—22no—
125C22×D4×C61C2×C411yescharacteristic
126C23×C4×C61C2×C411yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C2×M16×C61—22no—
129C4×D4×C61—22no—
130C4×D4×C61—22no—
131C2×C4⋊C4×C61C2311yescharacteristic
132C2×C22⋊C4×C61C2×C411yescharacteristic
133C2×C22⋊C4×C61C2311yescharacteristic
134C2×C42×C61C2×C411yescharacteristic
135C22⋊C8×C61—22no—
136C22⋊C8×C61C2312yes—
137C22⋊C8×C61C2312yes—
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—81no—
148C22×C4×C61—81no—
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C2×D412yes—
154C22×C4×C61C2×D412yes—
155C22×C4×C61C2411yescharacteristic
156C2×C22⋊D61—22no—
157C2×C22⋊D61—22no—
158C2×C22⋊D61—21no—
159C2×C22⋊D61—21no—
160C2×C22⋊D61—42no—
161C2×C22⋊D61—42no—
162C2×C22⋊D61—81no—
163C2×C22⋊D61—81no—
164C2×C22⋊D61C22⋊C412yes—
165C2×C22⋊D61C22⋊C412yes—
166C22×Dic61C22×C411yescharacteristic
167C22×Dic61C22×C411yescharacteristic
168C22×Dic61C22×C411yescharacteristic
169C22×Dic61C22×C411yescharacteristic
170C22×Dic61C22×C411yescharacteristic
171C22×Dic61C22×C411yescharacteristic
172C2×D244—22no—
173C2×D244—22no—
174C2×D244—41no—
175C2×C4×D61—21no—
176C2×C4×D61—21no—
177C2×C4×D61—81no—
178C2×C4×D61—81no—
179C2×C4×D61C2×D412yes—
180C2×C4×D61C2×D412yes—
181C2×Dic122—22no—
182C2×Dic122—22no—
183C2×Dic122—21no—
184C2×Dic122—21no—
185C2×Dic122—41no—
186C2×Dic122—42no—
187M16×C61—82no—
188C2×C8×C61—22no—
189C2×C8×C61—22no—
190C4⋊C4×C61—22no—
191C22⋊C4×C61—22no—
192C22⋊C4×C61—22no—
193C42×C61—21no—
194C42×C61—21no—
195C22⋊Dic61—22no—
196C22⋊Dic61—21no—
197C22⋊Dic61—21no—
198C22⋊Dic61—22no—
199C22⋊Dic61C22⋊C412yes—
200C22⋊Dic61C22⋊C412yes—
201#11758198—22no—
202#11758198—22no—
203#11758198—21no—
204#11758198—21no—
205#11758198—22no—
206#11758198—22no—
207#11758198C22⋊C412yes—
208#11758198C22⋊C412yes—
209C4⋊Dic61—21no—
210C4⋊Dic61—21no—
211#11758196—21no—
212#11758196—21no—
213#11758196—22no—
214#11758196—22no—
215#11758196C22⋊C411yescharacteristic
216#11758196C22⋊C411yescharacteristic
217#11758196C22⋊C411yescharacteristic
218#11758196C22⋊C411yescharacteristic
219C4×Dic61—21no—
220C4×Dic61—21no—
221C4×Dic61—21no—
222C4×Dic61—21no—
223C4×Dic61—21no—
224C4×Dic61—21no—
225C4×Dic61C2×D412yes—
226C4×Dic61C2×D412yes—
227C2×#92418—22no—
228C2×#92418—22no—
229C2×#92418—82no—
230#11758189—82no—
231C8×D61—82no—
232C23×C61—21no—
233C23×C61—21no—
234C23×C61—21no—
235C23×C61—21no—
236C23×C61—21no—
237C23×C61—41no—
238C23×C61—41no—
239C23×C61—41no—
240C23×C61—41no—
241C23×C61C2×C22⋊C412yes—
242C23×C61C23×C411yescharacteristic
243C22×D61—21no—
244C22×D61—21no—
245C22×D61—21no—
246C22×D61—21no—
247C22×D61—21no—
248C22×D61—41no—
249C22×D61—41no—
250C22×D61—41no—
251C22×D61—41no—
252C22×D61C2×C22⋊C412yes—
253D4×C61—44no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—42no—
259C2×C4×C61—42no—
260C2×C4×C61—41no—
261C2×C4×C61—41no—
262C2×C4×C61—41no—
263C2×C4×C61—41no—
264C2×C4×C61—81no—
265C2×C4×C61—81no—
266C2×C4×C61C2×C22⋊C411yescharacteristic
267C2×C4×C61C2×C22⋊C411yescharacteristic
268C2×C4×C61#13112yes—
269C2×C4×C61C22×D412yes—
270C22⋊D61—24no—
271C22⋊D61—42no—
272C22⋊D61—42no—
273C22⋊D61—42no—
274C22⋊D61—82no—
275C22⋊D61—82no—
276C2×Dic61—21no—
277C2×Dic61—21no—
278C2×Dic61—22no—
279C2×Dic61—21no—
280C2×Dic61—21no—
281C2×Dic61—21no—
282C2×Dic61—21no—
283C2×Dic61—21no—
284C2×Dic61—41no—
285C2×Dic61—41no—
286C2×Dic61—41no—
287C2×Dic61C2×C22⋊C411yescharacteristic
288C2×Dic61C2×C22⋊C411yescharacteristic
289C2×Dic61C2×C22⋊C411yescharacteristic
290C2×Dic61C2×C22⋊C412yes—
291C2×Dic61C2×C22⋊C411yescharacteristic
292D244—44no—
293C4×D61—42no—
294C4×D61—42no—
295C4×D61—81no—
296C4×D61—81no—
297Dic122—44no—
298Dic122—42no—
299Dic122—42no—
300C8×C61—42no—
301C8×C61—42no—
302#92418—42no—
303#92418—42no—
304#17429—611nomaximal, Sylow
305C22×C61—21no—
306C22×C61—21no—
307C22×C61—22no—
308C22×C61—22no—
309C22×C61—22no—
310C22×C61—41no—
311C22×C61—41no—
312C22×C61—41no—
313C22×C61—81no—
314C22×C61—81no—
315C22×C61—81no—
316C22×C61—81no—
317C22×C61C22×C22⋊C411yescharacteristic
318C22×C61C2×#13111yescharacteristic
319C22×C61#56811yescharacteristic
320C2×D61—22no—
321C2×D61—22no—
322C2×D61—22no—
323C2×D61—41no—
324C2×D61—41no—
325C2×D61—41no—
326C2×D61—81no—
327C2×D61—81no—
328C2×D61—81no—
329C2×D61—81no—
330C4×C61—22no—
331C4×C61—22no—
332C4×C61—21no—
333C4×C61—21no—
334C4×C61—41no—
335C4×C61—41no—
336Dic61—22no—
337Dic61—21no—
338Dic61—21no—
339Dic61—21no—
340Dic61—41no—
341Dic61—41no—
342Dic61—41no—
343Dic61#41312yes—
344C2×#559—611no—
345#2974—612no—
346#1469—612no—
347#1468—612no—
348#1468—612no—
349#1467—611no—
350#1465—611no—
351#1465D6111yescharacteristic, complemented
352#1461—611no—
353#1459—611no—
354#1459—611no—
355C2×C61—21no—
356C2×C61—21no—
357C2×C61—42no—
358C2×C61—81no—
359C2×C61#288011yescharacteristic
360C2×C61#288311yescharacteristic
361C2×C61C2×#41311yescharacteristic
362D61—42no—
363D61—81no—
364#559—1222no—
365#559—1222no—
366#559—1222no—
367#559—1222no—
368C2×#127—611no—
369C2×#124—611no—
370C2×#124—611no—
371C2×#124—611no—
372C2×#124—611no—
373C2×#123—611no—
374C2×#123—611no—
375C2×#123—611no—
376C2×#123—611no—
377C2×C4×Q8—611no—
378C2×C4×Q8—611no—
379C2×C4×D4—611no—
380C2×C4×D4—611no—
381C2×C4×D4—611no—
382C2×C4×D4C2×D6111yescharacteristic
383#436—1222no—
384#435—1222no—
385#435—1222no—
386C8×D4—1222no—
387#432—612no—
388#431—612no—
389#407—612no—
390#407C2×D6112yes—
391C2×C22⋊C8—612no—
392C2×C22⋊C8—612no—
393#324—611no—
394#324—611no—
395#324—612no—
396#324—612no—
397#324C2×D6111yescharacteristic
398#324C2×D6111yescharacteristic
399#323—612no—
400#323—612no—
401#323—612no—
402#323C2×D6112yes—
403C61#1742911yescharacteristic, complemented, Sylow
404C22×Q8—611no—
405C22×Q8—611no—
406C22×D4—611no—
407C22×D4—611no—
408C22×D4—611no—
409C22×D4—611no—
410C22×D4—611no—
411C22×D4C4×D6111yescharacteristic
412C23×C4—611no—
413C23×C4—611no—
414C23×C4C4×D6111yescharacteristic
415C23×C4C22×D6111yescharacteristic
416C2×M16—22no—
417C2×M16—1222no—
418C22×C8—1222no—
419C22×C8—1222no—
420#127—1222no—
421#127—1222no—
422#124—1222no—
423#124—1222no—
424#124—1222no—
425#124—1222no—
426#124—1222no—
427#124—1222no—
428#124—1222no—
429#124—1222no—
430#123—1222no—
431#123—1222no—
432#123—1222no—
433#123—1222no—
434#123—1222no—
435#123—1222no—
436#123—1222no—
437#123—1222no—
438C4×Q8—1221no—
439C4×Q8—1221no—
440C4×Q8—1221no—
441C4×Q8—1221no—
442C4×Q8—1222no—
443C4×Q8—1222no—
444C4×D4—22no—
445C4×D4—22no—
446C4×D4—612no—
447C4×D4—612no—
448C4×D4—612no—
449C4×D4—612no—
450C4×D4—1222no—
451C4×D4—1222no—
452C4×D4—1221no—
453C4×D4—1221no—
454C4×D4—1221no—
455C4×D4—1221no—
456C2×C4⋊C4—611no—
457C2×C4⋊C4—611no—
458C2×C4⋊C4—611no—
459C2×C4⋊C4—611no—
460C2×C4⋊C4—611no—
461C2×C4⋊C4C22×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⋊C4—611no—
471C2×C22⋊C4—611no—
472C2×C22⋊C4C4×D6111yescharacteristic
473C2×C22⋊C4C22×D6111yescharacteristic
474C2×C42—611no—
475C2×C42—611no—
476C2×C42—611no—
477C2×C42—611no—
478C2×C42C4×D6111yescharacteristic
479C4⋊C8—1222no—
480C4⋊C8—1222no—
481C22⋊C8—22no—
482C22⋊C8—612no—
483C22⋊C8—612no—
484C22⋊C8—1222no—
485C22⋊C8—1222no—
486C22⋊C8—1222no—
487C22⋊C8C22×D6112yes—
488C22⋊C8C22×D6112yes—
489#97—1222no—
490C4×C8—1222no—
491C24—611no—
492C24—611no—
493C24C2×C4×D6111yescharacteristic
494C24C2×C4×D6111yescharacteristic
495C2×Q8—1222no—
496C2×Q8—1221no—
497C2×Q8—1221no—
498C2×Q8—1222no—
499C2×Q8—2441no—
500C2×Q8—2442no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—41no—
504C2×D4—612no—
505C2×D4—612no—
506C2×D4—1222no—
507C2×D4—1221no—
508C2×D4—1221no—
509C2×D4—1222no—
510C2×D4—1222no—
511C2×D4—1222no—
512C2×D4—4881no—
513C2×D4—4881no—
514C2×D4—2441no—
515C2×D4—2442no—
516C2×D4—2442no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—81no—
520C22×C4—81no—
521C22×C4—611no—
522C22×C4—611no—
523C22×C4—611no—
524C22×C4—612no—
525C22×C4—612no—
526C22×C4—611no—
527C22×C4—611no—
528C22×C4—611no—
529C22×C4—1221no—
530C22×C4—1221no—
531C22×C4—4881no—
532C22×C4—4881no—
533C22×C4C2×C4×D6111yescharacteristic
534C22×C4C2×C4×D6111yescharacteristic
535C22×C4C2×C4×D6111yescharacteristic
536C22×C4C2×C4×D6111yescharacteristic
537C22×C4D4×D6112yes—
538C22×C4D4×D6112yes—
539C22×C4C23×D6111yescharacteristic
540M16—82no—
541M16—4882no—
542C2×C8—22no—
543C2×C8—22no—
544C2×C8—1222no—
545C2×C8—1222no—
546C2×C8—4882no—
547C2×C8—4882no—
548C4⋊C4—22no—
549C4⋊C4—611no—
550C4⋊C4—611no—
551C4⋊C4—611no—
552C4⋊C4—611no—
553C4⋊C4—1222no—
554C4⋊C4—1221no—
555C4⋊C4—1221no—
556C4⋊C4—1222no—
557C4⋊C4—1221no—
558C4⋊C4—1221no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—612no—
562C22⋊C4—612no—
563C22⋊C4—612no—
564C22⋊C4—612no—
565C22⋊C4—1222no—
566C22⋊C4—1222no—
567C22⋊C4—1222no—
568C22⋊C4—1221no—
569C22⋊C4—1221no—
570C22⋊C4—1222no—
571C22⋊C4—1222no—
572C22⋊C4—1222no—
573C22⋊C4—1221no—
574C22⋊C4—1221no—
575C42—21no—
576C42—21no—
577C42—612no—
578C42—612no—
579C42—1221no—
580C42—1221no—
581C42—1221no—
582C42—1221no—
583C42—1221no—
584C42—1221no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—612no—
595C23—1221no—
596C23—1221no—
597C23—1221no—
598C23—1221no—
599C23—1221no—
600C23—2441no—
601C23—2441no—
602C23—2441no—
603C23—2441no—
604C23C22⋊C4×D6112yes—
605C23C22×C4×D6111yescharacteristic
606Q8—2444no—
607Q8—2442no—
608Q8—2442no—
609D4—44no—
610D4—1224no—
611D4—4882no—
612D4—4882no—
613D4—2444no—
614D4—2442no—
615D4—2442no—
616D4—2442no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—81no—
628C2×C4—81no—
629C2×C4—611no—
630C2×C4—611no—
631C2×C4—612no—
632C2×C4—611no—
633C2×C4—611no—
634C2×C4—1222no—
635C2×C4—1221no—
636C2×C4—1221no—
637C2×C4—1221no—
638C2×C4—1221no—
639C2×C4—1221no—
640C2×C4—1221no—
641C2×C4—1221no—
642C2×C4—4881no—
643C2×C4—4881no—
644C2×C4—2442no—
645C2×C4—2442no—
646C2×C4—2441no—
647C2×C4—2441no—
648C2×C4—2441no—
649C2×C4C22⋊C4×D6111yescharacteristic
650C2×C4C22⋊C4×D6111yescharacteristic
651C2×C4#1451978512yes—
652C2×C4C2×D4×D6112yes—
653C8—42no—
654C8—42no—
655C8—2442no—
656C8—2442no—
657C22—21no—
658C22—21no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22—1222no—
670C22—1222no—
671C22—1222no—
672C22—4881no—
673C22—4881no—
674C22—4881no—
675C22—4881no—
676C22—2441no—
677C22—2441no—
678C22—2441no—
679C22C2×C22⋊C4×D6111yescharacteristic
680C22C2×#1451978511yescharacteristic
681C22#1684052811yescharacteristic
682C4—22no—
683C4—22no—
684C4—21no—
685C4—21no—
686C4—41no—
687C4—41no—
688C4—612no—
689C4—1222no—
690C4—1221no—
691C4—1221no—
692C4—1221no—
693C4—2441no—
694C4—2441no—
695C4—2441no—
696C2—21no—
697C2—21no—
698C2—42no—
699C2—81no—
700C2—4881no—
701C2—2442no—
702C2#2145426911yescharacteristic
703C2#2145427711yescharacteristic
704C2#413×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1465C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519773C4
cosocleC22×C4×C61C24
hypercenter#1465D61
hypocenterC61#17429
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1465

Complements

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

NH ≅ G/Ntype
2. #21454855C2semidirect
3. #21444169C2semidirect
4. #21444168C2semidirect
5. #21444164C2semidirect
6. #21444161C2semidirect
7. #21444156C2semidirect
8. #21444141C2semidirect
9. #21444137C2semidirect
10. #21444136C2semidirect
11. C61×#1465C2semidirect
351. #1465D61semidirect
403. C61#17429semidirect

Maximal subgroups

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

subgroupindex
C2×#168404952
#214548552
#214441692
#214441682
#214441642
#214441612
#214441562
#214441412
#214441372
#214441362
C61×#14652
#1742961