Finite Group Databasebeta

← #29647429

Subgroups — #29647429

Order 15616.

1070 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840298C211yesmaximal, characteristic
2C2×#16839816C211yesmaximal, characteristic, complemented
3#21448221C211yesmaximal, characteristic, complemented
4#21444391C211yesmaximal, characteristic, complemented
5#21444388C211yesmaximal, characteristic
6#21444386C211yesmaximal, characteristic
7#21444356C214yesmaximal, complemented
8#21444343C214yesmaximal, complemented
9C61×#1520C211yesmaximal, 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#16839816—21no—
31#16839816C2212yescomplemented
32#16839816C2212yescomplemented
33C2×#14519706—21no—
34C2×C22⋊#92418C2211yescharacteristic
35C2×#14519687—21no—
36#16839631—21no—
37#16839626C2212yescomplemented
38#16839622C2211yescharacteristic
39#16839620—21no—
40C4⋊C4×Dic61—21no—
41#16839613C2212yescomplemented
42#16839499C2214yescomplemented
43#16839497C2214yes—
44#16839495C2214yes—
45C2×C22⋊Q8×C61C2211yescharacteristic
46C2×C22⋊C8×C61C2211yescharacteristic
47C61×#380C2211yescharacteristic
48C61×#328C2214yescomplemented
49C22×D244C2×C411yescharacteristic
50C22×C22⋊D61—21no—
51C23×Dic61D411yescharacteristic
52C23×Dic61D411yescharacteristic
53C22×C4×D61—21no—
54C22×#92418—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—44no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61—21no—
94C2×C4⋊Dic61—21no—
95C2×C4⋊Dic61C2×C411yescharacteristic
96C2×#11758196—21no—
97C2×#11758196—22no—
98C2×#11758196—22no—
99C2×C22⋊Dic61—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
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—
123#14519687—22no—
124#14519684—22no—
125#14519684C2312yes—
126C22×Q8×C61C2×C411yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C22×C8×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×C61—21no—
135C2×C4⋊C4×C61C2×C411yescharacteristic
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×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—42no—
159C2×C22⋊D61—42no—
160C22×Dic61—22no—
161C22×Dic61—22no—
162C22×Dic61—21no—
163C22×Dic61—22no—
164C22×Dic61—42no—
165C22×Dic61C22⋊C411yescharacteristic
166C22×Dic61C22⋊C411yescharacteristic
167C22×Dic61C22⋊C411yescharacteristic
168C22×Dic61C22⋊C411yescharacteristic
169C22×Dic61C22⋊C411yescharacteristic
170C22×Dic61C22⋊C411yescharacteristic
171C22×Dic61C22⋊C411yescharacteristic
172C22×Dic61C22⋊C411yescharacteristic
173C22×Dic61C2×D411yescharacteristic
174C22×Dic61C2×D411yescharacteristic
175C22×Dic61C2×D411yescharacteristic
176C22×Dic61C2×D411yescharacteristic
177C2×D244—21no—
178C2×D244—42no—
179C2×D244C22×C412yes—
180C2×C4×D61—22no—
181C2×C4×D61—22no—
182C2×C4×D61—44no—
183C2×C8×C61—22no—
184C2×C8×C61—42no—
185C4⋊C4×C61—22no—
186C4⋊C4×C61—21no—
187C4⋊C4×C61—22no—
188C4⋊C4×C61—42no—
189C4⋊C4×C61C22×C412yes—
190C22⋊C4×C61—22no—
191C22⋊C4×C61—22no—
192C22⋊C4×C61—42no—
193C22⋊Dic61—42no—
194#11758198—22no—
195#11758198—22no—
196#11758198—22no—
197#11758198—22no—
198#11758198—22no—
199#11758198—22no—
200#11758198—22no—
201#11758198—22no—
202C4⋊Dic61—21no—
203C4⋊Dic61—22no—
204C4⋊Dic61—22no—
205C4⋊Dic61—22no—
206C4⋊Dic61—22no—
207C4⋊Dic61—42no—
208C4⋊Dic61C22×C412yes—
209#11758196—22no—
210#11758196—22no—
211#11758196—44no—
212#11758196—44no—
213C4×Dic61—22no—
214C4×Dic61—22no—
215C4×Dic61—44no—
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×Dic61C22×C411yescharacteristic
227C4×Dic61C22×C411yescharacteristic
228C4×Dic61C2×D411yescharacteristic
229C4×Dic61C2×D411yescharacteristic
230C4×Dic61C2×D411yescharacteristic
231C4×Dic61C2×D411yescharacteristic
232C2×#92418—22no—
233C2×#92418—42no—
234C23×C61—41no—
235C23×C61—41no—
236C23×C61C2×C22⋊C411yescharacteristic
237C23×C61C2×C22⋊C411yescharacteristic
238C23×C61AGL(1,ℤ/8)12yes—
239C23×C61#13712yes—
240C23×C61C22×D411yescharacteristic
241C22×D61—22no—
242C22×D61—42no—
243C22×D61—42no—
244C22×D61—42no—
245Q8×C61—42no—
246Q8×C61—42no—
247C2×C4×C61—22no—
248C2×C4×C61—22no—
249C2×C4×C61—22no—
250C2×C4×C61—22no—
251C2×C4×C61—22no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—42no—
256C2×C4×C61—42no—
257C2×C4×C61—42no—
258C2×C4×C61—42no—
259C2×C4×C61—42no—
260C2×C4×C61C2×C22⋊C411yescharacteristic
261C2×C4×C61C2×C22⋊C411yescharacteristic
262C2×C4×C61C23×C411yescharacteristic
263C2×C4×C61C22×D411yescharacteristic
264C22⋊D61—42no—
265C22⋊D61—42no—
266C22⋊D61—44no—
267C2×Dic61—21no—
268C2×Dic61—21no—
269C2×Dic61—21no—
270C2×Dic61—21no—
271C2×Dic61—22no—
272C2×Dic61—22no—
273C2×Dic61—22no—
274C2×Dic61—22no—
275C2×Dic61—22no—
276C2×Dic61—22no—
277C2×Dic61—22no—
278C2×Dic61—22no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61—42no—
283C2×Dic61—42no—
284C2×Dic61—42no—
285C2×Dic61—42no—
286C2×Dic61C2×C22⋊C411yescharacteristic
287C2×Dic61C2×C22⋊C411yescharacteristic
288C2×Dic61C2×C22⋊C411yescharacteristic
289C2×Dic61C2×C22⋊C411yescharacteristic
290C2×Dic61C2×C22⋊C411yescharacteristic
291C2×Dic61C2×C22⋊C411yescharacteristic
292C2×Dic61C2×C22⋊C411yescharacteristic
293C2×Dic61C2×C22⋊C411yescharacteristic
294D244—42no—
295D244—42no—
296C4×D61—44no—
297C4×D61—44no—
298C8×C61—42no—
299#92418—42no—
300#17581—611nomaximal, Sylow
301C22×C61—21no—
302C22×C61—21no—
303C22×C61—21no—
304C22×C61—21no—
305C22×C61—21no—
306C22×C61—21no—
307C22×C61—42no—
308C22×C61—42no—
309C22×C61#41712yes—
310C22×C61#41712yes—
311C22×C61C22×C22⋊C411yescharacteristic
312C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
313C22×C61C2×#13711yescharacteristic
314C2×D61—42no—
315C2×D61—42no—
316C2×D61—42no—
317C2×D61—84no—
318C4×C61—21no—
319C4×C61—21no—
320C4×C61—21no—
321C4×C61—42no—
322C4×C61—42no—
323C4×C61—82no—
324C4×C61#41012yes—
325Dic61—21no—
326Dic61—21no—
327Dic61—21no—
328Dic61—21no—
329Dic61—21no—
330Dic61—21no—
331Dic61—21no—
332Dic61—42no—
333Dic61—82no—
334Dic61#42112yes—
335C2×#529—611no—
336C2×#432—611no—
337#2285—611no—
338#1520—611no—
339#1520D6111yescharacteristic, complemented
340#1519—611no—
341#1519—611no—
342#1512—614no—
343#1509—614no—
344C2×C61—21no—
345C2×C61—22no—
346C2×C61—21no—
347C2×C61—22no—
348C2×C61C2×#41011yescharacteristic
349C2×C61C2×#41711yescharacteristic
350C2×C61C2×#42111yescharacteristic
351D61—82no—
352#529—612no—
353#529—612no—
354#529—612no—
355#529—612no—
356#529—1221no—
357#529—1221no—
358#529—1221no—
359#529—1221no—
360C2×#126—1221no—
361C2×#125—611no—
362C2×#124—611no—
363C2×#123—1221no—
364C2×C22⋊Q8C2×D6111yescharacteristic
365C2×#121—611no—
366C2×C4×Q8—611no—
367C2×C4×D4—611no—
368C2×C4×D4—1221no—
369C2×#117—1221no—
370C2×#117—1221no—
371C22×C42—611no—
372#432—612no—
373#432—612no—
374#432—1221no—
375#432—1221no—
376C2×C4⋊C8—1221no—
377C2×C22⋊C8—611no—
378C2×C22⋊C8C2×D6111yescharacteristic
379C2×#97—1221no—
380#384—1221no—
381#382—612no—
382#380—611no—
383#380—1221no—
384#380C2×D6111yescharacteristic
385C4×C4⋊C4—612no—
386C4×C4⋊C4—1221no—
387#328—614no—
388#328C2×D6114yescomplemented
389#327—614no—
390#327—614no—
391C61#1758111yescharacteristic, complemented, Sylow
392C22×Q8C4×D6111yescharacteristic
393C22×D4—611no—
394C22×D4—1221no—
395C23×C4—611no—
396C23×C4—611no—
397C23×C4—1221no—
398C23×C4C22×D6111yescharacteristic
399C22×C8—21no—
400C22×C8—1221no—
401#126—1222no—
402#126—1222no—
403#126—1222no—
404#126—1222no—
405#125—612no—
406#125—612no—
407#125—1221no—
408#125—1221no—
409#124—612no—
410#124—612no—
411#124—1221no—
412#124—1221no—
413#123—1222no—
414#123—1222no—
415#123—1222no—
416#123—1222no—
417C22⋊Q8—21no—
418C22⋊Q8—21no—
419C22⋊Q8C4×D6112yes—
420C22⋊Q8C22×D6112yes—
421#121—612no—
422#121—612no—
423#121—1221no—
424#121—1221no—
425C4×Q8—612no—
426C4×Q8—612no—
427C4×Q8—1221no—
428C4×Q8—1221no—
429C4×D4—612no—
430C4×D4—612no—
431C4×D4—1221no—
432C4×D4—1221no—
433C4×D4—1222no—
434C4×D4—1222no—
435C4×D4—1222no—
436C4×D4—1222no—
437#117—1222no—
438#117—1222no—
439#117—1222no—
440#117—1222no—
441#117—2444no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—611no—
445C2×C4⋊C4—1221no—
446C2×C4⋊C4—1221no—
447C2×C4⋊C4—1221no—
448C2×C4⋊C4—1222no—
449C2×C4⋊C4—1222no—
450C2×C4⋊C4—1221no—
451C2×C4⋊C4C4×D6111yescharacteristic
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—1221no—
455C2×C22⋊C4—1221no—
456C2×C22⋊C4—1221no—
457C2×C22⋊C4—1221no—
458C2×C22⋊C4—1221no—
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×C42—611no—
469C2×C42—611no—
470C2×C42—611no—
471C2×C42—1221no—
472C2×C42—1222no—
473C4⋊C8—1222no—
474C4⋊C8—1222no—
475C22⋊C8—21no—
476C22⋊C8—612no—
477C22⋊C8—1221no—
478C22⋊C8C22×D6112yes—
479#97—1222no—
480#97—1222no—
481#95—612no—
482#95—1222no—
483#95C22×D6112yes—
484C24—1221no—
485C24D4×D6111yescharacteristic
486C2×Q8—21no—
487C2×Q8—42no—
488C2×Q8C2×C4×D6112yes—
489C2×D4—612no—
490C2×D4—1222no—
491C2×D4—1222no—
492C2×D4—1221no—
493C2×D4—2442no—
494C2×D4—2442no—
495C2×D4—2442no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—42no—
500C22×C4—611no—
501C22×C4—611no—
502C22×C4—611no—
503C22×C4—611no—
504C22×C4—611no—
505C22×C4—611no—
506C22×C4—611no—
507C22×C4—611no—
508C22×C4—611no—
509C22×C4—611no—
510C22×C4—611no—
511C22×C4—611no—
512C22×C4—1222no—
513C22×C4—1222no—
514C22×C4—1222no—
515C22×C4—1222no—
516C22×C4—1221no—
517C22×C4—1222no—
518C22×C4—2444no—
519C22×C4—2442no—
520C22×C4C2×C4×D6111yescharacteristic
521C22×C4C2×C4×D6111yescharacteristic
522C22×C4D4×D6111yescharacteristic
523C22×C4D4×D6111yescharacteristic
524C22×C4D4×D6111yescharacteristic
525C22×C4C23×D6111yescharacteristic
526C2×C8—22no—
527C2×C8—42no—
528C2×C8—1222no—
529C2×C8—2442no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—21no—
533C4⋊C4—42no—
534C4⋊C4—612no—
535C4⋊C4—1222no—
536C4⋊C4—1222no—
537C4⋊C4—1222no—
538C4⋊C4—1222no—
539C4⋊C4—1222no—
540C4⋊C4—1222no—
541C4⋊C4—1221no—
542C4⋊C4—2442no—
543C4⋊C4—2444no—
544C4⋊C4—2444no—
545C4⋊C4C2×C4×D6112yes—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—42no—
549C22⋊C4—1222no—
550C22⋊C4—1222no—
551C22⋊C4—1222no—
552C22⋊C4—1222no—
553C22⋊C4—1222no—
554C22⋊C4—1222no—
555C22⋊C4—1222no—
556C22⋊C4—1222no—
557C22⋊C4—2442no—
558C42—611no—
559C42—611no—
560C42—611no—
561C42—611no—
562C42—611no—
563C42—611no—
564C42—611no—
565C42—611no—
566C42—611no—
567C42—611no—
568C42—611no—
569C42—611no—
570C42—611no—
571C42—611no—
572C42—611no—
573C42—611no—
574C42—1222no—
575C42—1222no—
576C42—2444no—
577C23—41no—
578C23—41no—
579C23—1222no—
580C23—2442no—
581C23—2442no—
582C23—2442no—
583C23C22⋊C4×D6111yescharacteristic
584C23C22⋊C4×D6111yescharacteristic
585C23#1451980412yes—
586C23#1451980912yes—
587C23C2×D4×D6111yescharacteristic
588Q8—42no—
589Q8—42no—
590D4—2442no—
591D4—2444no—
592D4—2442no—
593D4—2442no—
594D4—2442no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—611no—
609C2×C4—611no—
610C2×C4—611no—
611C2×C4—611no—
612C2×C4—611no—
613C2×C4—611no—
614C2×C4—611no—
615C2×C4—611no—
616C2×C4—1222no—
617C2×C4—1222no—
618C2×C4—1222no—
619C2×C4—1222no—
620C2×C4—1222no—
621C2×C4—1222no—
622C2×C4—1222no—
623C2×C4—1221no—
624C2×C4—1221no—
625C2×C4—1221no—
626C2×C4—1221no—
627C2×C4—1222no—
628C2×C4—2444no—
629C2×C4—2444no—
630C2×C4—2441no—
631C2×C4—2441no—
632C2×C4—2441no—
633C2×C4—2442no—
634C2×C4—2442no—
635C2×C4—2442no—
636C2×C4—2442no—
637C2×C4C22⋊C4×D6111yescharacteristic
638C2×C4C22⋊C4×D6111yescharacteristic
639C2×C4C22×C4×D6111yescharacteristic
640C2×C4C2×D4×D6111yescharacteristic
641C8—42no—
642C8—2442no—
643C22—21no—
644C22—21no—
645C22—21no—
646C22—21no—
647C22—21no—
648C22—21no—
649C22—42no—
650C22—42no—
651C22—4884no—
652C22—2442no—
653C22—2442no—
654C22—2442no—
655C22#1683976212yes—
656C22#1683976212yes—
657C22C2×C22⋊C4×D6111yescharacteristic
658C22C2×#1451980411yescharacteristic
659C22C2×#1451980911yescharacteristic
660C4—21no—
661C4—21no—
662C4—21no—
663C4—42no—
664C4—42no—
665C4—82no—
666C4—612no—
667C4—1221no—
668C4—1221no—
669C4—1221no—
670C4—1221no—
671C4—1221no—
672C4—1221no—
673C4—1221no—
674C4—4882no—
675C4—2442no—
676C4#1683973412yes—
677C2—21no—
678C2—22no—
679C2—22no—
680C2—21no—
681C2—4882no—
682C2C2×#1683973411yescharacteristic
683C2C2×#1683976211yescharacteristic
684C2#421×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1520C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519751C22
cosocleC22×C4×C61C24
hypercenter#1520D61
hypocenterC61#17581
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
2. C2×#16839816C2semidirect
3. #21448221C2semidirect
4. #21444391C2semidirect
7. #21444356C2semidirect
8. #21444343C2semidirect
9. C61×#1520C2semidirect
14. #16840298C4semidirect
15. #16840298C4semidirect
19. C2×#14519768C4semidirect
20. C2×#14519766C4semidirect
23. C2×Q8×Dic61C4semidirect
24. C2×#14519739C4semidirect
31. #16839816C22semidirect
32. #16839816C22semidirect
37. #16839626C22semidirect
41. #16839613C22semidirect
42. #16839499C22semidirect
48. C61×#328C22semidirect
339. #1520D61semidirect
388. #328C2×D61semidirect
391. C61#17581semidirect

Maximal subgroups

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

subgroupindex
C2×#168402982
C2×#168398162
#214482212
#214443912
#214443882
#214443862
#214443562
#214443432
C61×#15202
#1758161