Finite Group Databasebeta

← #29647146

Subgroups — #29647146

Order 15616.

1116 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840298C211yesmaximal, characteristic
2#21454448C211yesmaximal, characteristic, complemented
3C4×#14519733C211yesmaximal, characteristic, complemented
4#21444343C214yesmaximal, complemented
5#21444339C211yesmaximal, characteristic, complemented
6#21444336C211yesmaximal, characteristic
7#21444334C211yesmaximal, characteristic
8#21444304C214yesmaximal, complemented
9C61×#1508C211yesmaximal, characteristic, complemented
10#16840298—21no—
11#16840298—21no—
12#16840298—21no—
13#16840298—21no—
14#16840298C412yescomplemented
15#16840298C412yescomplemented
16#16840298C2212yes—
17#16840298C2212yes—
18C2×#14519772—21no—
19C2×#14519768C411yescharacteristic, complemented
20C2×#14519766C411yescharacteristic, complemented
21C2×#14519761—21no—
22C2×#14519751C2211yescharacteristic
23C2×Q8×Dic61C411yescharacteristic, complemented
24C2×#14519739C411yescharacteristic, complemented
25C2×#14519737—21no—
26C2×#14519735—21no—
27C2×#14519733—21no—
28C22×C4×Dic61C2211yescharacteristic
29#16839816—21no—
30#16839816C2212yescomplemented
31#16839812—21no—
32#16839812C2212yescomplemented
33#16839785—21no—
34#16839726C2211yescharacteristic
35M16×Dic61—21no—
36C4×#11758196—21no—
37#16839613C2212yescomplemented
38C22⋊C4×Dic61—21no—
39C4×C22⋊Dic61C2211yescharacteristic
40#16839607C2212yescomplemented
41C42×Dic61—21no—
42#16839499C2214yescomplemented
43#16839497C2214yes—
44#16839495C2214yes—
45C2×C22⋊Q8×C61C2211yescharacteristic
46C61×#407C2211yescharacteristic
47C4×C22⋊C4×C61C2211yescharacteristic
48C61×#328C2214yescomplemented
49C22×D244C2×C411yescharacteristic
50C22×C22⋊D61—21no—
51C23×Dic61D411yescharacteristic
52C23×Dic61D411yescharacteristic
53C22×C4×D61—21no—
54C2×#11758194—21no—
55#14519772—22no—
56#14519772—22no—
57#14519772—22no—
58#14519772—22no—
59#14519768—21no—
60#14519768—21no—
61#14519768C2×C412yes—
62#14519768C2×C412yes—
63#14519766—21no—
64#14519766—21no—
65#14519766C2×C412yes—
66#14519766C2×C412yes—
67#14519761—22no—
68#14519761—22no—
69#14519761—22no—
70#14519761—22no—
71#14519751—21no—
72#14519751—21no—
73#14519751C2×C412yes—
74#14519751C2312yes—
75Q8×Dic61—21no—
76Q8×Dic61—21no—
77Q8×Dic61C2×C412yes—
78Q8×Dic61C2×C412yes—
79#14519739—21no—
80#14519739—21no—
81#14519739C2×C412yes—
82#14519739C2×C412yes—
83#14519737—22no—
84#14519737—22no—
85#14519737—22no—
86#14519737—22no—
87#14519735—22no—
88#14519735—22no—
89#14519735—22no—
90#14519735—22no—
91#14519733—28no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61—21no—
94C2×C4⋊Dic61C2×C411yescharacteristic
95C2×#11758196—21no—
96C2×#11758196—22no—
97C2×C22⋊Dic61—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×C4×Dic61—21no—
103C2×C4×Dic61—22no—
104C2×C4×Dic61—21no—
105C2×C4×Dic61—22no—
106C2×C4×Dic61C2×C411yescharacteristic
107C2×C4×Dic61C2×C411yescharacteristic
108C2×C4×Dic61C2×C411yescharacteristic
109C2×C4×Dic61C2×C411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61D411yescharacteristic
112C2×C4×Dic61D411yescharacteristic
113C2×C4×Dic61D411yescharacteristic
114C2×C4×Dic61D411yescharacteristic
115C2×C4×Dic61D411yescharacteristic
116C2×C4×Dic61C2311yescharacteristic
117C2×C4×Dic61C2311yescharacteristic
118#14519706—22no—
119#14519706—22no—
120C22⋊#92418—21no—
121C22⋊#92418C2312yes—
122#14519687—22no—
123C8×Dic61—22no—
124#14519684—22no—
125#14519684C2312yes—
126C22×Q8×C61C2×C411yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C2×M16×C61—21no—
129C22⋊Q8×C61—21no—
130C22⋊Q8×C61—21no—
131C22⋊Q8×C61C2×C412yes—
132C22⋊Q8×C61C2312yes—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61C2×C411yescharacteristic
135C2×C22⋊C4×C61—21no—
136C2×C22⋊C4×C61—21no—
137C2×C42×C61—21no—
138C22⋊C8×C61—21no—
139C22⋊C8×C61C2312yes—
140#95×C61C2312yes—
141C24×C61C2×D411yescharacteristic
142C23×D61—21no—
143C2×Q8×C61—21no—
144C2×Q8×C61—42no—
145C2×Q8×C61C22×C412yes—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—22no—
149C22×C4×C61—42no—
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2411yescharacteristic
156C2×C22⋊D61—22no—
157C2×C22⋊D61—22no—
158C2×C22⋊D61—44no—
159C22×Dic61—24no—
160C22×Dic61—21no—
161C22×Dic61—22no—
162C22×Dic61—42no—
163C22×Dic61C22⋊C411yescharacteristic
164C22×Dic61C22⋊C411yescharacteristic
165C22×Dic61C22⋊C411yescharacteristic
166C22×Dic61C22⋊C411yescharacteristic
167C22×Dic61C22⋊C411yescharacteristic
168C22×Dic61C22⋊C411yescharacteristic
169C22×Dic61C22⋊C411yescharacteristic
170C22×Dic61C22⋊C411yescharacteristic
171C22×Dic61C2×D411yescharacteristic
172C22×Dic61C2×D411yescharacteristic
173C22×Dic61C2×D411yescharacteristic
174C22×Dic61C2×D411yescharacteristic
175C2×D244—21no—
176C2×D244—42no—
177C2×D244C22×C412yes—
178C2×C4×D61—22no—
179C2×C4×D61—22no—
180C2×C4×D61—44no—
181M16×C61—42no—
182C2×C8×C61—22no—
183C4⋊C4×C61—22no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—22no—
186C4⋊C4×C61C22×C412yes—
187C22⋊C4×C61—24no—
188C22⋊C4×C61—22no—
189C22⋊C4×C61—22no—
190C42×C61—42no—
191C22⋊Dic61—24no—
192#11758198—22no—
193#11758198—22no—
194#11758198—22no—
195#11758198—22no—
196#11758198—22no—
197#11758198—22no—
198#11758198—22no—
199#11758198—22no—
200C4⋊Dic61—21no—
201C4⋊Dic61—22no—
202C4⋊Dic61—22no—
203C4⋊Dic61—22no—
204C4⋊Dic61—22no—
205C4⋊Dic61C22×C412yes—
206#11758196—28no—
207#11758196—22no—
208#11758196—22no—
209C4×Dic61—28no—
210C4×Dic61—22no—
211C4×Dic61—22no—
212C4×Dic61—44no—
213C4×Dic61—42no—
214C4×Dic61C22⋊C411yescharacteristic
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×Dic61C22×C411yescharacteristic
226C4×Dic61C2×D411yescharacteristic
227C4×Dic61C2×D411yescharacteristic
228C4×Dic61C2×D411yescharacteristic
229C4×Dic61C2×D411yescharacteristic
230#11758194—42no—
231C2×#92418—22no—
232C23×C61—22no—
233C23×C61—22no—
234C23×C61—41no—
235C23×C61C2×C22⋊C411yescharacteristic
236C23×C61C2×C22⋊C411yescharacteristic
237C23×C61C22×D411yescharacteristic
238C22×D61—22no—
239C22×D61—42no—
240C22×D61—42no—
241C22×D61—42no—
242Q8×C61—42no—
243Q8×C61—42no—
244C2×C4×C61—22no—
245C2×C4×C61—22no—
246C2×C4×C61—22no—
247C2×C4×C61—24no—
248C2×C4×C61—22no—
249C2×C4×C61—22no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—42no—
254C2×C4×C61—42no—
255C2×C4×C61—42no—
256C2×C4×C61—42no—
257C2×C4×C61C2×C22⋊C411yescharacteristic
258C2×C4×C61C2×C22⋊C411yescharacteristic
259C2×C4×C61C23×C411yescharacteristic
260C2×C4×C61C22×D411yescharacteristic
261C22⋊D61—44no—
262C22⋊D61—44no—
263C2×Dic61—22no—
264C2×Dic61—22no—
265C2×Dic61—22no—
266C2×Dic61—22no—
267C2×Dic61—22no—
268C2×Dic61—22no—
269C2×Dic61—22no—
270C2×Dic61—24no—
271C2×Dic61—22no—
272C2×Dic61—41no—
273C2×Dic61—41no—
274C2×Dic61—41no—
275C2×Dic61—41no—
276C2×Dic61—42no—
277C2×Dic61—42no—
278C2×Dic61—42no—
279C2×Dic61#10414yes—
280C2×Dic61C2×C22⋊C411yescharacteristic
281C2×Dic61C2×C22⋊C411yescharacteristic
282C2×Dic61C2×C22⋊C411yescharacteristic
283C2×Dic61C2×C22⋊C411yescharacteristic
284C2×Dic61C2×C22⋊C411yescharacteristic
285C2×Dic61C2×C22⋊C411yescharacteristic
286C2×Dic61C2×C22⋊C411yescharacteristic
287C2×Dic61C2×C22⋊C411yescharacteristic
288D244—42no—
289D244—42no—
290C4×D61—44no—
291C4×D61—44no—
292C8×C61—42no—
293#92418—42no—
294#17537—611nomaximal, Sylow
295C22×C61—21no—
296C22×C61—21no—
297C22×C61—21no—
298C22×C61—21no—
299C22×C61—21no—
300C22×C61—21no—
301C22×C61—21no—
302C22×C61—44no—
303C22×C61C2×#10412yes—
304C22×C61C22×C22⋊C411yescharacteristic
305C22×C61#57512yes—
306C2×D61—42no—
307C2×D61—42no—
308C2×D61—42no—
309C2×D61—84no—
310C4×C61—21no—
311C4×C61—21no—
312C4×C61—21no—
313C4×C61—44no—
314C4×C61—42no—
315C4×C61—42no—
316C4×C61#41012yes—
317Dic61—21no—
318Dic61—21no—
319Dic61—21no—
320Dic61—21no—
321Dic61—21no—
322Dic61—21no—
323Dic61—44no—
324Dic61—42no—
325Dic61C2×#10412yes—
326Dic61C2×#10412yes—
327C2×#529—611no—
328#2920—611no—
329C4×#117—611no—
330#1509—614no—
331#1508—611no—
332#1508D6111yescharacteristic, complemented
333#1507—611no—
334#1507—611no—
335#1500—614no—
336C2×C61—22no—
337C2×C61—22no—
338C2×C61—41no—
339C2×C61C2×#41011yescharacteristic
340C2×C61#289611yescharacteristic
341C2×C61C22×#10411yescharacteristic
342D61—82no—
343#529—612no—
344#529—612no—
345#529—612no—
346#529—612no—
347#529—1221no—
348#529—1221no—
349#529—1221no—
350#529—1221no—
351C2×#126—1221no—
352C2×#125—611no—
353C2×#124—611no—
354C2×#123—1221no—
355C2×C22⋊Q8C2×D6111yescharacteristic
356C2×#121—611no—
357C2×C4×Q8—611no—
358C2×C4×D4—611no—
359C2×C4×D4—1221no—
360C2×#117—1221no—
361C2×#117—1221no—
362C22×C42—611no—
363#432—612no—
364#432—1221no—
365#431—612no—
366#431—1221no—
367#423—1221no—
368#407—611no—
369#407C2×D6111yescharacteristic
370C4×M16—1221no—
371C4×C4⋊C4—612no—
372C4×C4⋊C4—1221no—
373C4×C22⋊C4—611no—
374C4×C22⋊C4—1221no—
375C4×C22⋊C4C2×D6111yescharacteristic
376#376—612no—
377C43—1221no—
378#328—614no—
379#328C2×D6114yescomplemented
380#327—614no—
381#327—614no—
382C61#1753711yescharacteristic, complemented, Sylow
383C22×Q8C4×D6111yescharacteristic
384C22×D4—611no—
385C22×D4—1221no—
386C23×C4—611no—
387C23×C4—611no—
388C23×C4—1221no—
389C23×C4C22×D6111yescharacteristic
390C2×M16—21no—
391C2×M16—1221no—
392#126—1222no—
393#126—1222no—
394#126—1222no—
395#126—1222no—
396#125—612no—
397#125—612no—
398#125—1221no—
399#125—1221no—
400#124—612no—
401#124—612no—
402#124—1221no—
403#124—1221no—
404#123—1222no—
405#123—1222no—
406#123—1222no—
407#123—1222no—
408C22⋊Q8—21no—
409C22⋊Q8—21no—
410C22⋊Q8C4×D6112yes—
411C22⋊Q8C22×D6112yes—
412#121—612no—
413#121—612no—
414#121—1221no—
415#121—1221no—
416C4×Q8—612no—
417C4×Q8—612no—
418C4×Q8—1221no—
419C4×Q8—1221no—
420C4×D4—612no—
421C4×D4—612no—
422C4×D4—1221no—
423C4×D4—1221no—
424C4×D4—1222no—
425C4×D4—1222no—
426C4×D4—1222no—
427C4×D4—1222no—
428#117—1222no—
429#117—1222no—
430#117—1222no—
431#117—1222no—
432#117—1228no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—611no—
435C2×C4⋊C4—1221no—
436C2×C4⋊C4—1222no—
437C2×C4⋊C4—1221no—
438C2×C4⋊C4—1221no—
439C2×C4⋊C4C4×D6111yescharacteristic
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—1221no—
443C2×C22⋊C4—1221no—
444C2×C22⋊C4—1221no—
445C2×C22⋊C4—1221no—
446C2×C22⋊C4—1221no—
447C2×C42—21no—
448C2×C42—611no—
449C2×C42—611no—
450C2×C42—611no—
451C2×C42—611no—
452C2×C42—611no—
453C2×C42—611no—
454C2×C42—611no—
455C2×C42—611no—
456C2×C42—611no—
457C2×C42—611no—
458C2×C42—611no—
459C2×C42—611no—
460C2×C42—1221no—
461C2×C42—1222no—
462C2×C42—1222no—
463C2×C42—1221no—
464C4⋊C8—1222no—
465C4⋊C8—1222no—
466C22⋊C8—21no—
467C22⋊C8—612no—
468C22⋊C8—1221no—
469C22⋊C8C22×D6112yes—
470#97—1222no—
471C4×C8—1222no—
472#95—612no—
473#95—1222no—
474#95C22×D6112yes—
475C24—1221no—
476C24D4×D6111yescharacteristic
477C2×Q8—21no—
478C2×Q8—42no—
479C2×Q8C2×C4×D6112yes—
480C2×D4—612no—
481C2×D4—1222no—
482C2×D4—1222no—
483C2×D4—1221no—
484C2×D4—2442no—
485C2×D4—2444no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—42no—
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—611no—
500C22×C4—611no—
501C22×C4—611no—
502C22×C4—1222no—
503C22×C4—1222no—
504C22×C4—1224no—
505C22×C4—1222no—
506C22×C4—1221no—
507C22×C4—2444no—
508C22×C4—2442no—
509C22×C4C2×C4×D6111yescharacteristic
510C22×C4C2×C4×D6111yescharacteristic
511C22×C4D4×D6111yescharacteristic
512C22×C4D4×D6111yescharacteristic
513C22×C4D4×D6111yescharacteristic
514C22×C4C23×D6111yescharacteristic
515M16—42no—
516M16—2442no—
517C2×C8—22no—
518C2×C8—1222no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—21no—
522C4⋊C4—612no—
523C4⋊C4—1222no—
524C4⋊C4—1222no—
525C4⋊C4—1222no—
526C4⋊C4—1222no—
527C4⋊C4—1222no—
528C4⋊C4—1222no—
529C4⋊C4—1228no—
530C4⋊C4—1221no—
531C4⋊C4C2×C4×D6112yes—
532C22⋊C4—24no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—1222no—
536C22⋊C4—1222no—
537C22⋊C4—1222no—
538C22⋊C4—1222no—
539C22⋊C4—1222no—
540C22⋊C4—1222no—
541C22⋊C4—1224no—
542C22⋊C4—1222no—
543C22⋊C4—1222no—
544C42—42no—
545C42—611no—
546C42—611no—
547C42—611no—
548C42—611no—
549C42—611no—
550C42—611no—
551C42—611no—
552C42—611no—
553C42—611no—
554C42—611no—
555C42—611no—
556C42—611no—
557C42—611no—
558C42—611no—
559C42—611no—
560C42—611no—
561C42—1222no—
562C42—1222no—
563C42—1228no—
564C42—2442no—
565C42—2444no—
566C23—22no—
567C23—22no—
568C23—41no—
569C23—1222no—
570C23—2442no—
571C23—2442no—
572C23—2442no—
573C23C22⋊C4×D6111yescharacteristic
574C23C22⋊C4×D6111yescharacteristic
575C23C2×D4×D6111yescharacteristic
576Q8—42no—
577Q8—42no—
578D4—2442no—
579D4—2444no—
580D4—2444no—
581D4—2442no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—611no—
596C2×C4—611no—
597C2×C4—614no—
598C2×C4—611no—
599C2×C4—611no—
600C2×C4—611no—
601C2×C4—611no—
602C2×C4—611no—
603C2×C4—611no—
604C2×C4—1222no—
605C2×C4—1222no—
606C2×C4—1222no—
607C2×C4—1222no—
608C2×C4—1222no—
609C2×C4—1222no—
610C2×C4—1222no—
611C2×C4—1224no—
612C2×C4—1222no—
613C2×C4—2444no—
614C2×C4—2444no—
615C2×C4—2441no—
616C2×C4—2441no—
617C2×C4—2441no—
618C2×C4—2441no—
619C2×C4—2442no—
620C2×C4—2442no—
621C2×C4—2442no—
622C2×C4C22⋊C4×D6111yescharacteristic
623C2×C4C22⋊C4×D6111yescharacteristic
624C2×C4C22×C4×D6111yescharacteristic
625C2×C4C2×D4×D6111yescharacteristic
626C8—42no—
627C8—2442no—
628C22—21no—
629C22—21no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—21no—
634C22—21no—
635C22—44no—
636C22—4884no—
637C22—2442no—
638C22—2442no—
639C22—2442no—
640C22#104×D6112yes—
641C22C2×C22⋊C4×D6111yescharacteristic
642C22#1684056112yes—
643C4—21no—
644C4—21no—
645C4—21no—
646C4—44no—
647C4—42no—
648C4—42no—
649C4—612no—
650C4—612no—
651C4—1221no—
652C4—1221no—
653C4—1221no—
654C4—1221no—
655C4—1221no—
656C4—1221no—
657C4—2444no—
658C4—2442no—
659C4#1683973412yes—
660C2—22no—
661C2—22no—
662C2—41no—
663C2—4882no—
664C2C2×#1683973411yescharacteristic
665C2#2145433711yescharacteristic
666C2C2×#104×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1508C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519751C22
cosocleC22×C4×C61C24
hypercenter#1508D61
hypocenterC61#17537
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1508

Complements

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

NH ≅ G/Ntype
2. #21454448C2semidirect
3. C4×#14519733C2semidirect
4. #21444343C2semidirect
5. #21444339C2semidirect
8. #21444304C2semidirect
9. C61×#1508C2semidirect
14. #16840298C4semidirect
15. #16840298C4semidirect
19. C2×#14519768C4semidirect
20. C2×#14519766C4semidirect
23. C2×Q8×Dic61C4semidirect
24. C2×#14519739C4semidirect
30. #16839816C22semidirect
32. #16839812C22semidirect
37. #16839613C22semidirect
40. #16839607C22semidirect
42. #16839499C22semidirect
48. C61×#328C22semidirect
332. #1508D61semidirect
379. #328C2×D61semidirect
382. C61#17537semidirect

Maximal subgroups

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

subgroupindex
C2×#168402982
#214544482
C4×#145197332
#214443432
#214443392
#214443362
#214443342
#214443042
C61×#15082
#1753761