Finite Group Databasebeta

← #29647181

Subgroups — #29647181

Order 15616.

1108 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459114C211yesmaximal, characteristic
2#432×D61C211yesmaximal, characteristic, complemented
3#21448158C211yesmaximal, characteristic, complemented
4#21444341C214yesmaximal, complemented
5#21444332C211yesmaximal, characteristic, complemented
6#21444330C211yesmaximal, characteristic, complemented
7#21444327C211yesmaximal, characteristic, complemented
8#21444307C214yesmaximal, complemented
9C61×#1505C211yesmaximal, characteristic, complemented
10#16840319C2211yescharacteristic
11#16840317C411yescharacteristic, complemented
12#16840317C411yescharacteristic, complemented
13#16840310C411yescharacteristic, complemented
14#16840310C411yescharacteristic, complemented
15#16840294—21no—
16#16840294C412yescomplemented
17#16840293—21no—
18#16840293C2212yes—
19#16840291—21no—
20#16840291—21no—
21#16840272—21no—
22#16840272C2212yes—
23#16840269—21no—
24#41×Dic61—21no—
25C4×#11758224—21no—
26C4×#11758224C412yescomplemented
27C2×#14519734—21no—
28C2×C42×D61C2211yescharacteristic
29#16839819C2211yescharacteristic
30#16839818—21no—
31#16839817—21no—
32#16839816C2212yes—
33C4⋊C8×D61—21no—
34C22⋊C8×D61C2212yes—
35#97×D61—21no—
36#16839613—21no—
37#16839613C2212yes—
38#16839609—21no—
39#16839609C2212yes—
40#16839608C2211yescharacteristic
41C42×Dic61—21no—
42#16839500C2214yes—
43#16839498C2214yes—
44#16839496C2214yes—
45C61×#532C2211yescharacteristic
46C61×#432C2211yescharacteristic
47C61×#376C2211yescharacteristic
48C61×#327C2214yes—
49C2×#11758224—21no—
50C2×#11758224C2×C412yes—
51C22×C4×D61D411yescharacteristic
52C22×C4×D61D411yescharacteristic
53C22×C4×D61C2311yescharacteristic
54C2×C8×D61—22no—
55#14519777C2×C411yescharacteristic
56#14519777C2×C411yescharacteristic
57#14519770—22no—
58#14519770—22no—
59#14519769—21no—
60#14519768—21no—
61#14519768C2×C412yes—
62#14519764—21no—
63#14519764C2×C412yes—
64#14519759—22no—
65#14519759—22no—
66#14519758—22no—
67#14519757—21no—
68#14519757C2×C412yes—
69#14519756—21no—
70#14519756C2312yes—
71#14519753—21no—
72#14519753—21no—
73#14519748—21no—
74#14519748—21no—
75#14519748—21no—
76#14519748C2×C412yes—
77#14519745—22no—
78Q8×Dic61—21no—
79Q8×Dic61—21no—
80C4×Dic122—21no—
81C4×Dic122C2×C412yes—
82#14519742—21no—
83#14519742C2×C412yes—
84D4×Dic61—22no—
85D4×Dic61—22no—
86D4×Dic61—21no—
87D4×Dic61—21no—
88D4×Dic61—21no—
89D4×Dic61C2×C412yes—
90C4×C22⋊D61—22no—
91C4×C22⋊D61—22no—
92#14519737—22no—
93#14519737—22no—
94#14519736—21no—
95#14519736—22no—
96#14519735—21no—
97#14519735C2×C412yes—
98#14519734—28no—
99#14519733—22no—
100#14519733—22no—
101C2×#11758196—22no—
102C2×#11758198—22no—
103C2×C4×Dic61—21no—
104C2×C4×Dic61—22no—
105C2×C4×Dic61—22no—
106C2×C4×Dic61—22no—
107C2×C4×Dic61D411yescharacteristic
108C2×C4×Dic61D411yescharacteristic
109C2×C4×Dic61C2311yescharacteristic
110C42×D61C2×C411yescharacteristic
111C42×D61C2×C411yescharacteristic
112C42×D61C2×C411yescharacteristic
113C42×D61C2×C411yescharacteristic
114C42×D61D411yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C4⋊#92418—21no—
119#14519706—22no—
120C22⋊#92418C2312yes—
121#14519689—22no—
122#14519688—21no—
123#14519687—22no—
124#14519684—21no—
125#14519684C2312yes—
126C2×#41×C61—21no—
127C4⋊Q8×C61C2×C411yescharacteristic
128#127×C61C2×C411yescharacteristic
129#124×C61—21no—
130#121×C61—21no—
131#121×C61C2312yes—
132C4×D4×C61—21no—
133C4×D4×C61C2×C412yes—
134C2×C42×C61—21no—
135C2×C42×C61C2311yescharacteristic
136C4⋊C8×C61—21no—
137C22⋊C8×C61C2312yes—
138#97×C61—21no—
139#95×C61—21no—
140#95×C61C2312yes—
141C23×D61C2×D411yescharacteristic
142#41×C61—44no—
143C2×Q8×C61—21no—
144C2×D4×C61—22no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61C22×C412yes—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2411yescharacteristic
153C2×C22⋊D61—22no—
154C2×C22⋊D61—22no—
155C22×Dic61—22no—
156C22×Dic61—22no—
157C22×Dic61—22no—
158C22×Dic61C2×D411yescharacteristic
159C22×Dic61C2×D411yescharacteristic
160C22×Dic61C2×D411yescharacteristic
161#11758224—44no—
162#11758224—44no—
163C2×C4×D61—24no—
164C2×C4×D61—42no—
165C2×C4×D61—42no—
166C2×C4×D61C22⋊C411yescharacteristic
167C2×C4×D61C22⋊C411yescharacteristic
168C2×C4×D61C22⋊C411yescharacteristic
169C2×C4×D61C22⋊C411yescharacteristic
170C2×C4×D61C22⋊C411yescharacteristic
171C2×C4×D61C22⋊C411yescharacteristic
172C2×C4×D61C22⋊C411yescharacteristic
173C2×C4×D61C22⋊C411yescharacteristic
174C2×C4×D61C22×C411yescharacteristic
175C2×C4×D61C22×C411yescharacteristic
176C2×C4×D61C2×D411yescharacteristic
177C2×C4×D61C2×D411yescharacteristic
178C2×Dic122—21no—
179C2×Dic122C22×C412yes—
180C2×C8×C61—22no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61C22×C412yes—
183C22⋊C4×C61—22no—
184C22⋊C4×C61—22no—
185C42×C61—24no—
186C42×C61C22×C411yescharacteristic
187C42×C61C22×C411yescharacteristic
188C42×C61C2×D411yescharacteristic
189C42×C61C2×D411yescharacteristic
190C22⋊Dic61—22no—
191C22⋊Dic61—22no—
192C22⋊Dic61—22no—
193C22⋊Dic61—22no—
194C22⋊Dic61—22no—
195#11758198—28no—
196#11758198—22no—
197#11758198—22no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—22no—
202C4⋊Dic61—22no—
203C4⋊Dic61C22×C412yes—
204#11758196—28no—
205#11758196—22no—
206#11758196—22no—
207#11758196—22no—
208#11758196—22no—
209C4×Dic61—24no—
210C4×Dic61—22no—
211C4×Dic61—22no—
212C4×Dic61—22no—
213C4×Dic61—44no—
214C4×Dic61—44no—
215C4×Dic61C22⋊C411yescharacteristic
216C4×Dic61C22⋊C411yescharacteristic
217C4×Dic61C22⋊C411yescharacteristic
218C4×Dic61C22⋊C411yescharacteristic
219C4×Dic61C22⋊C411yescharacteristic
220C4×Dic61C22⋊C411yescharacteristic
221C4×Dic61C22⋊C411yescharacteristic
222C4×Dic61C22⋊C411yescharacteristic
223C4×Dic61C22×C411yescharacteristic
224C4×Dic61C22×C411yescharacteristic
225C4×Dic61C2×D411yescharacteristic
226C4×Dic61C2×D411yescharacteristic
227C2×#92418—22no—
228C8×D61—44no—
229C23×C61—22no—
230C23×C61C22×D411yescharacteristic
231C22×D61—22no—
232C22×D61—22no—
233C22×D61—41no—
234C22×D61C2×C22⋊C411yescharacteristic
235C22×D61C2×C22⋊C411yescharacteristic
236Q8×C61—42no—
237D4×C61—42no—
238D4×C61—42no—
239D4×C61—44no—
240D4×C61—42no—
241C2×C4×C61—22no—
242C2×C4×C61—22no—
243C2×C4×C61—24no—
244C2×C4×C61—22no—
245C2×C4×C61—41no—
246C2×C4×C61—44no—
247C2×C4×C61—42no—
248C2×C4×C61—42no—
249C2×C4×C61C2×C22⋊C411yescharacteristic
250C2×C4×C61C2×C22⋊C411yescharacteristic
251C2×C4×C61C2×C22⋊C411yescharacteristic
252C2×C4×C61C2×C22⋊C411yescharacteristic
253C2×C4×C61C23×C411yescharacteristic
254C2×C4×C61C22×D411yescharacteristic
255C22⋊D61—44no—
256C22⋊D61—44no—
257C2×Dic61—22no—
258C2×Dic61—22no—
259C2×Dic61—22no—
260C2×Dic61—24no—
261C2×Dic61—22no—
262C2×Dic61—22no—
263C2×Dic61—42no—
264C2×Dic61—42no—
265C2×Dic61—44no—
266C2×Dic61—44no—
267C2×Dic61C2×C22⋊C411yescharacteristic
268C2×Dic61C2×C22⋊C411yescharacteristic
269C2×Dic61C2×C22⋊C411yescharacteristic
270C2×Dic61C2×C22⋊C411yescharacteristic
271C2×Dic61C2×C22⋊C411yescharacteristic
272C2×Dic61C2×C22⋊C411yescharacteristic
273C4×D61—22no—
274C4×D61—22no—
275C4×D61—22no—
276C4×D61—22no—
277C4×D61—22no—
278C4×D61—41no—
279C4×D61—41no—
280C4×D61—41no—
281C4×D61—41no—
282C4×D61—41no—
283C4×D61—41no—
284C4×D61#10414yes—
285Dic122—42no—
286Dic122—42no—
287C8×C61—42no—
288#92418—42no—
289#17543—611nomaximal, Sylow
290C22×C61—21no—
291C22×C61—21no—
292C22×C61—42no—
293C22×C61—42no—
294C22×C61—42no—
295C22×C61C22×C22⋊C411yescharacteristic
296C22×C61#57512yes—
297C2×D61—21no—
298C2×D61—21no—
299C2×D61—21no—
300C2×D61—21no—
301C2×D61—21no—
302C2×D61—44no—
303C2×D61C2×#10412yes—
304C4×C61—21no—
305C4×C61—21no—
306C4×C61—21no—
307C4×C61—21no—
308C4×C61—21no—
309C4×C61—44no—
310C4×C61—42no—
311C4×C61C2×#10412yes—
312Dic61—21no—
313Dic61—21no—
314Dic61—21no—
315Dic61—21no—
316Dic61—44no—
317Dic61—42no—
318Dic61—42no—
319Dic61#41012yes—
320Dic61C2×#10412yes—
321#3444—611no—
322C2×#432—611no—
323C4×#117—611no—
324#1509—614no—
325#1506—611no—
326#1506—611no—
327#1505—611no—
328#1505D6111yescharacteristic, complemented
329#1501—614no—
330C2×C61—22no—
331C2×C61—82no—
332C2×C61C2×#41011yescharacteristic
333C2×C61#289611yescharacteristic
334C2×C61C22×#10411yescharacteristic
335D61—22no—
336D61—41no—
337#533—611no—
338#533—611no—
339#533—611no—
340#532—611no—
341#532—611no—
342#532C2×D6111yescharacteristic
343#529—612no—
344#529—612no—
345#529—1221no—
346#529—1221no—
347#529—1221no—
348#529—1221no—
349#525—612no—
350#525—1221no—
351#525—1221no—
352C4×#41—612no—
353C4×#41—1221no—
354C4×#41—1221no—
355C2×#117—1221no—
356C22×C42—611no—
357#432—611no—
358#432—612no—
359#432—1221no—
360#432—1221no—
361#432C2×D6111yescharacteristic
362C2×C4⋊C8—1221no—
363C2×C22⋊C8—612no—
364C2×#97—1221no—
365C4×C4⋊C4—612no—
366C4×C4⋊C4—1221no—
367C4×C22⋊C4—612no—
368C4×C22⋊C4—1221no—
369#376—611no—
370#376C2×D6111yescharacteristic
371C43—1221no—
372#328—614no—
373#328—614no—
374#327—614no—
375#327C2×D6114yes—
376C61#1754311yescharacteristic, complemented, Sylow
377C2×#41—21no—
378C2×#41—612no—
379C2×#41—1221no—
380C23×C4—611no—
381C23×C4—611no—
382C23×C4—611no—
383C22×C8—1222no—
384C4⋊Q8—611no—
385C4⋊Q8—611no—
386C4⋊Q8C4×D6111yescharacteristic
387#127C4×D6111yescharacteristic
388#126—1222no—
389#126—1222no—
390#125—612no—
391#125—1221no—
392#125—1221no—
393#124—21no—
394#124—612no—
395#124—1221no—
396#123—1222no—
397#123—1222no—
398#123—1222no—
399C22⋊Q8—612no—
400C22⋊Q8—612no—
401C22⋊Q8—1221no—
402C22⋊Q8—1221no—
403C22⋊Q8—1221no—
404C22⋊Q8—1221no—
405#121—21no—
406#121—612no—
407#121—1221no—
408#121—1221no—
409#121—1221no—
410#121C22×D6112yes—
411#120—1222no—
412C4×Q8—612no—
413C4×Q8—612no—
414C4×Q8—1221no—
415C4×Q8—1221no—
416C4×Q8—1221no—
417C4×Q8—1221no—
418C4×D4—21no—
419C4×D4—612no—
420C4×D4—1221no—
421C4×D4—1221no—
422C4×D4—1221no—
423C4×D4—1222no—
424C4×D4—1222no—
425C4×D4—1222no—
426C4×D4—1222no—
427C4×D4—1222no—
428C4×D4—1222no—
429C4×D4C4×D6112yes—
430#117—612no—
431#117—1228no—
432#117—1222no—
433#117—1222no—
434#117—1222no—
435#117—1221no—
436#117—1221no—
437C2×C4⋊C4—1222no—
438C2×C22⋊C4—1222no—
439C2×C42—21no—
440C2×C42—611no—
441C2×C42—611no—
442C2×C42—611no—
443C2×C42—611no—
444C2×C42—611no—
445C2×C42—611no—
446C2×C42—611no—
447C2×C42—611no—
448C2×C42—611no—
449C2×C42—611no—
450C2×C42—611no—
451C2×C42—1222no—
452C2×C42—1221no—
453C2×C42—1222no—
454C2×C42—1222no—
455C2×C42C22×D6111yescharacteristic
456C4⋊C8—21no—
457C4⋊C8—1222no—
458C4⋊C8—1221no—
459C22⋊C8—612no—
460C22⋊C8—1222no—
461C22⋊C8C22×D6112yes—
462#97—21no—
463#97—1222no—
464#97—1221no—
465#95—21no—
466#95—612no—
467#95—1221no—
468#95C22×D6112yes—
469C24—611no—
470#41—44no—
471#41—2444no—
472#41—2444no—
473C2×Q8—21no—
474C2×Q8—612no—
475C2×Q8—1221no—
476C2×D4—22no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—1222no—
480C2×D4—1222no—
481C2×D4C2×C4×D6112yes—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—611no—
488C22×C4—611no—
489C22×C4—611no—
490C22×C4—611no—
491C22×C4—611no—
492C22×C4—611no—
493C22×C4—611no—
494C22×C4—611no—
495C22×C4—611no—
496C22×C4—611no—
497C22×C4—611no—
498C22×C4—611no—
499C22×C4—1224no—
500C22×C4—1222no—
501C22×C4—1222no—
502C22×C4—1222no—
503C22×C4—2442no—
504C22×C4—2442no—
505C22×C4D4×D6111yescharacteristic
506C22×C4D4×D6111yescharacteristic
507C22×C4C23×D6111yescharacteristic
508C2×C8—22no—
509C2×C8—1222no—
510C2×C8—2444no—
511C4⋊C4—21no—
512C4⋊C4—612no—
513C4⋊C4—1222no—
514C4⋊C4—1222no—
515C4⋊C4—1222no—
516C4⋊C4—1222no—
517C4⋊C4—1228no—
518C4⋊C4—1222no—
519C4⋊C4—1222no—
520C4⋊C4—1221no—
521C4⋊C4—1221no—
522C4⋊C4—1221no—
523C4⋊C4C2×C4×D6112yes—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—1222no—
527C22⋊C4—1222no—
528C22⋊C4—1228no—
529C22⋊C4—1222no—
530C22⋊C4—1222no—
531C22⋊C4—1222no—
532C22⋊C4—1222no—
533C22⋊C4—1222no—
534C42—24no—
535C42—611no—
536C42—611no—
537C42—611no—
538C42—611no—
539C42—611no—
540C42—611no—
541C42—611no—
542C42—611no—
543C42—611no—
544C42—611no—
545C42—611no—
546C42—611no—
547C42—1222no—
548C42—1222no—
549C42—1224no—
550C42—1222no—
551C42—2444no—
552C42—2444no—
553C42C2×C4×D6111yescharacteristic
554C42C2×C4×D6111yescharacteristic
555C42D4×D6111yescharacteristic
556C42D4×D6111yescharacteristic
557C23—22no—
558C23—611no—
559C23—611no—
560C23—1222no—
561C23—1222no—
562C23—2441no—
563C23C2×D4×D6111yescharacteristic
564Q8—42no—
565Q8—2442no—
566Q8—2442no—
567D4—42no—
568D4—42no—
569D4—44no—
570D4—42no—
571D4—2444no—
572D4—2444no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—24no—
576C2×C4—22no—
577C2×C4—41no—
578C2×C4—44no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—611no—
582C2×C4—611no—
583C2×C4—614no—
584C2×C4—611no—
585C2×C4—611no—
586C2×C4—611no—
587C2×C4—611no—
588C2×C4—1222no—
589C2×C4—1222no—
590C2×C4—1222no—
591C2×C4—1222no—
592C2×C4—1222no—
593C2×C4—1222no—
594C2×C4—1222no—
595C2×C4—1222no—
596C2×C4—1224no—
597C2×C4—1222no—
598C2×C4—1222no—
599C2×C4—2441no—
600C2×C4—2441no—
601C2×C4—2441no—
602C2×C4—2441no—
603C2×C4—2441no—
604C2×C4—2441no—
605C2×C4—2444no—
606C2×C4—2444no—
607C2×C4—2442no—
608C2×C4—2442no—
609C2×C4C22⋊C4×D6111yescharacteristic
610C2×C4C22⋊C4×D6111yescharacteristic
611C2×C4C22⋊C4×D6111yescharacteristic
612C2×C4C22⋊C4×D6111yescharacteristic
613C2×C4C22×C4×D6111yescharacteristic
614C2×C4C2×D4×D6111yescharacteristic
615C8—42no—
616C8—2442no—
617C22—21no—
618C22—21no—
619C22—42no—
620C22—42no—
621C22—42no—
622C22—612no—
623C22—1221no—
624C22—1221no—
625C22—1221no—
626C22—1221no—
627C22—1221no—
628C22—2444no—
629C22C2×C22⋊C4×D6111yescharacteristic
630C22#1684055812yes—
631C4—21no—
632C4—21no—
633C4—21no—
634C4—21no—
635C4—21no—
636C4—44no—
637C4—42no—
638C4—612no—
639C4—612no—
640C4—1221no—
641C4—1221no—
642C4—1221no—
643C4—1221no—
644C4—2444no—
645C4—2442no—
646C4—2442no—
647C4#104×D6112yes—
648C2—22no—
649C2—82no—
650C2—1222no—
651C2—2441no—
652C2#410×D6111yescharacteristic
653C2#2145433311yescharacteristic
654C2C2×#104×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1505C2
socleC22×C61C22×C22⋊C4
prime radical#21459114C2
cosocleC22×C4×C61C24
hypercenter#1505D61
hypocenterC61#17543
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1505

Complements

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

NH ≅ G/Ntype
2. #432×D61C2semidirect
3. #21448158C2semidirect
4. #21444341C2semidirect
5. #21444332C2semidirect
6. #21444330C2semidirect
7. #21444327C2semidirect
8. #21444307C2semidirect
9. C61×#1505C2semidirect
11. #16840317C4semidirect
12. #16840317C4semidirect
13. #16840310C4semidirect
14. #16840310C4semidirect
16. #16840294C4semidirect
26. C4×#11758224C4semidirect
328. #1505D61semidirect
376. C61#17543semidirect

Maximal subgroups

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

subgroupindex
#214591142
#432×D612
#214481582
#214443412
#214443322
#214443302
#214443272
#214443072
C61×#15052
#1754361