Finite Group Databasebeta

← #29646558

Subgroups — #29646558

Order 15616.

988 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840316C211yesmaximal, characteristic
2#21454447C211yesmaximal, characteristic
3#431×D61C211yesmaximal, characteristic
4#21444238C214yesmaximal, complemented
5#21444220C214yesmaximal, complemented
6#21444215C211yesmaximal, characteristic, complemented
7#21444214C211yesmaximal, characteristic, complemented
8#21444213C211yesmaximal, characteristic, complemented
9C61×#1479C211yesmaximal, characteristic, complemented
10#16840316—21no—
11#16840316—21no—
12#16840316—21no—
13#16840316—21no—
14#16840316C412yes—
15#16840316C412yes—
16#16840316C2212yes—
17#16840316C2212yes—
18C2×#14519776C411yescharacteristic
19C2×#14519775C411yescharacteristic
20C2×#14519767—21no—
21C2×#14519757C411yescharacteristic
22C2×#14519755—21no—
23C2×#14519753C411yescharacteristic
24C2×C4×Dic122—21no—
25C2×C4×Dic122C2211yescharacteristic
26C2×#14519734—21no—
27C2×C42×D61C2211yescharacteristic
28#16839818—21no—
29#16839816—21no—
30#16839815C2211yescharacteristic
31#16839815C2211yescharacteristic
32#16839814C2212yes—
33#16839813—21no—
34#16839813C2212yes—
35#16839812—21no—
36#16839784—21no—
37C4⋊C8×D61C2212yes—
38#16839724—21no—
39C22⋊C8×D61—21no—
40C4×#11758189C2212yes—
41C4×C8×D61—21no—
42#16839494C2214yescomplemented
43Q8⋊#92418C2214yescomplemented
44#16839492C2214yescomplemented
45C2×C4×Q8×C61C2211yescharacteristic
46C61×#431C2211yescharacteristic
47C61×#431C2211yescharacteristic
48C61×Q8⋊C8C2214yescomplemented
49C22×Dic122—21no—
50C22×Dic122C2×C411yescharacteristic
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61D411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C2×#11758189—22no—
55C2×C8×D61—22no—
56#14519776—21no—
57#14519776—21no—
58#14519776C2×C412yes—
59#14519776C2×C412yes—
60#14519775—21no—
61#14519775—21no—
62#14519775C2×C412yes—
63#14519775C2×C412yes—
64#14519767—22no—
65#14519767—22no—
66#14519767—22no—
67#14519767—22no—
68#14519757—21no—
69#14519757—21no—
70#14519757C2×C412yes—
71#14519757C2×C412yes—
72#14519755—22no—
73#14519755—22no—
74#14519755—22no—
75#14519755—22no—
76#14519753—21no—
77#14519753—21no—
78#14519753C2×C412yes—
79#14519753C2×C412yes—
80C4×Dic122—21no—
81C4×Dic122—21no—
82C4×Dic122—22no—
83C4×Dic122—22no—
84C4×Dic122—22no—
85C4×Dic122—22no—
86C4×Dic122C2×C412yes—
87C4×Dic122C2312yes—
88#14519734—22no—
89#14519734—22no—
90#14519734—22no—
91#14519734—22no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61C2×C411yescharacteristic
94C2×#11758196—21no—
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×C4×Dic61—21no—
102C2×C4×Dic61C2×C411yescharacteristic
103C2×C4×Dic61D411yescharacteristic
104C2×C4×Dic61D411yescharacteristic
105C42×D61C2×C411yescharacteristic
106C42×D61C2×C411yescharacteristic
107C42×D61D411yescharacteristic
108C42×D61D411yescharacteristic
109C42×D61D411yescharacteristic
110C42×D61D411yescharacteristic
111C42×D61C2311yescharacteristic
112C42×D61C2311yescharacteristic
113C4⋊#92418—21no—
114C4⋊#92418C2312yes—
115#14519706—22no—
116#14519706—22no—
117C22⋊#92418—21no—
118C22⋊#92418—21no—
119#14519689—22no—
120#14519689—22no—
121#14519687—22no—
122C4×#92418—21no—
123C4×#92418C2312yes—
124C8×Dic61—22no—
125C22×Q8×C61C2×C411yescharacteristic
126C4×Q8×C61—21no—
127C4×Q8×C61—21no—
128C4×Q8×C61C2×C412yes—
129C4×Q8×C61C2312yes—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61C2×C411yescharacteristic
132C2×C42×C61—21no—
133C2×C42×C61C2311yescharacteristic
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2312yes—
136C22⋊C8×C61—21no—
137C22⋊C8×C61—21no—
138C4×C8×C61—21no—
139C4×C8×C61C2312yes—
140C23×D61C22⋊C411yescharacteristic
141C2×Q8×C61—21no—
142C2×Q8×C61—22no—
143C2×Q8×C61—22no—
144C2×Q8×C61C22×C412yes—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×Dic61—21no—
151C22×Dic61—21no—
152C22×Dic61C22⋊C411yescharacteristic
153C22×Dic61C22⋊C411yescharacteristic
154C22×Dic61C22⋊C411yescharacteristic
155C2×C4×D61—22no—
156C2×C4×D61—22no—
157C2×C4×D61—24no—
158C2×C4×D61—42no—
159C2×C4×D61C22⋊C411yescharacteristic
160C2×C4×D61C22⋊C411yescharacteristic
161C2×C4×D61C22⋊C411yescharacteristic
162C2×C4×D61C22⋊C411yescharacteristic
163C2×C4×D61C22⋊C411yescharacteristic
164C2×C4×D61C22⋊C411yescharacteristic
165C2×C4×D61C22×C411yescharacteristic
166C2×C4×D61C22×C411yescharacteristic
167C2×C4×D61C2×D411yescharacteristic
168C2×C4×D61C2×D411yescharacteristic
169C2×C4×D61C2×D411yescharacteristic
170C2×C4×D61C2×D411yescharacteristic
171C2×Dic122—22no—
172C2×Dic122—22no—
173C2×Dic122—21no—
174C2×Dic122—22no—
175C2×Dic122—22no—
176C2×Dic122—44no—
177C2×Dic122C22×C412yes—
178C2×C8×C61—22no—
179C2×C8×C61—22no—
180C4⋊C4×C61—22no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—22no—
183C4⋊C4×C61C22×C412yes—
184C42×C61—22no—
185C42×C61—22no—
186C42×C61C22×C411yescharacteristic
187C42×C61C2×D411yescharacteristic
188C42×C61C2×D411yescharacteristic
189C42×C61C2411yescharacteristic
190#11758198—22no—
191#11758198—22no—
192#11758198—22no—
193#11758198—22no—
194C4⋊Dic61—21no—
195C4⋊Dic61—22no—
196C4⋊Dic61—22no—
197C4⋊Dic61C22×C412yes—
198#11758196—22no—
199#11758196—22no—
200#11758196—22no—
201#11758196—22no—
202#11758196—22no—
203#11758196—22no—
204#11758196—22no—
205#11758196—22no—
206#11758196—22no—
207#11758196—22no—
208C4×Dic61—22no—
209C4×Dic61—22no—
210C4×Dic61C22⋊C411yescharacteristic
211C4×Dic61C22⋊C411yescharacteristic
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C22⋊C411yescharacteristic
214C4×Dic61C22⋊C411yescharacteristic
215C4×Dic61C22⋊C411yescharacteristic
216C4×Dic61C22×C411yescharacteristic
217C4×Dic61C22×C411yescharacteristic
218C4×Dic61C2×D411yescharacteristic
219C4×Dic61C2×D411yescharacteristic
220C4×Dic61C2×D411yescharacteristic
221C4×Dic61C2×D411yescharacteristic
222C2×#92418—22no—
223C2×#92418—22no—
224#11758189—44no—
225C8×D61—44no—
226C23×C61C2×C22⋊C411yescharacteristic
227C22×D61—22no—
228C22×D61—22no—
229C22×D61—41no—
230C22×D61C2×C22⋊C411yescharacteristic
231C22×D61C2×C22⋊C411yescharacteristic
232Q8×C61—22no—
233Q8×C61—22no—
234Q8×C61—42no—
235C2×C4×C61—22no—
236C2×C4×C61—22no—
237C2×C4×C61—22no—
238C2×C4×C61—41no—
239C2×C4×C61—42no—
240C2×C4×C61—42no—
241C2×C4×C61C2×C22⋊C411yescharacteristic
242C2×C4×C61C2×C22⋊C411yescharacteristic
243C2×C4×C61C2×C22⋊C411yescharacteristic
244C2×C4×C61#13112yes—
245C2×C4×C61#13112yes—
246C2×C4×C61C23×C411yescharacteristic
247C2×C4×C61C22×D411yescharacteristic
248C2×C4×C61C22×D411yescharacteristic
249C2×Dic61—22no—
250C2×Dic61—22no—
251C2×Dic61—22no—
252C2×Dic61—22no—
253C2×Dic61—22no—
254C2×Dic61—42no—
255C2×Dic61—42no—
256C2×Dic61C2×C22⋊C411yescharacteristic
257C2×Dic61C2×C22⋊C411yescharacteristic
258C2×Dic61C2×C22⋊C411yescharacteristic
259C2×Dic61C2×C22⋊C411yescharacteristic
260C2×Dic61C2×C22⋊C411yescharacteristic
261C2×Dic61C2×C22⋊C411yescharacteristic
262C4×D61—22no—
263C4×D61—21no—
264C4×D61—21no—
265C4×D61—21no—
266C4×D61—21no—
267C4×D61—22no—
268C4×D61—22no—
269C4×D61—22no—
270C4×D61—22no—
271C4×D61—22no—
272C4×D61—22no—
273C4×D61—41no—
274C4×D61—41no—
275C4×D61#13714yes—
276Dic122—22no—
277Dic122—22no—
278Dic122—44no—
279Dic122—42no—
280Dic122—44no—
281C8×C61—42no—
282C8×C61—42no—
283#92418—42no—
284#92418—42no—
285#17464—611nomaximal, Sylow
286C22×C61—21no—
287C22×C61—21no—
288C22×C61#40812yes—
289C22×C61C22×C22⋊C411yescharacteristic
290C2×D61—21no—
291C2×D61—21no—
292C2×D61—21no—
293C2×D61—21no—
294C2×D61—21no—
295C2×D61—44no—
296C2×D61#41912yes—
297C4×C61—21no—
298C4×C61—21no—
299C4×C61—21no—
300C4×C61—42no—
301C4×C61—42no—
302C4×C61#40812yes—
303C4×C61C2×#13111yescharacteristic
304C4×C61C2×#13111yescharacteristic
305C4×C61C2×#13712yes—
306Dic61—21no—
307Dic61—21no—
308Dic61—21no—
309Dic61—21no—
310Dic61—42no—
311Dic61—42no—
312Dic61#41912yes—
313Dic61#42112yes—
314C2×#533—611no—
315#2920—611no—
316C2×#431—611no—
317#1485—614no—
318#1481—614no—
319#1479—611no—
320#1479—611no—
321#1479—611no—
322#1479D6111yescharacteristic, complemented
323C2×C61—22no—
324C2×C61C2×#40811yescharacteristic
325C2×C61C2×#41911yescharacteristic
326C2×C61C2×#42111yescharacteristic
327D61—22no—
328D61—41no—
329#533—612no—
330#533—612no—
331#533—612no—
332#533—612no—
333#533—1221no—
334#533—1221no—
335#533—1221no—
336#533—1221no—
337C2×C4⋊Q8—611no—
338C2×C4⋊Q8—611no—
339C2×#125—1221no—
340C2×C22⋊Q8—611no—
341C2×C22⋊Q8—611no—
342C2×C22⋊Q8—1221no—
343C2×C4×Q8—611no—
344C2×C4×Q8—1221no—
345C2×C4×Q8C2×D6111yescharacteristic
346C2×#117—1221no—
347C22×C42—611no—
348#432—1221no—
349#432—1221no—
350#431—611no—
351#431—612no—
352#431—611no—
353#431—612no—
354#431—1221no—
355#431—1221no—
356#431C2×D6111yescharacteristic
357#431C2×D6111yescharacteristic
358#423—1221no—
359C2×C4⋊C8—612no—
360#407—1221no—
361C2×C22⋊C8—1221no—
362C4×M16—612no—
363C2×C4×C8—1221no—
364Q8⋊C8—614no—
365Q8⋊C8—614no—
366Q8⋊C8—614no—
367Q8⋊C8C2×D6114yescomplemented
368C61#1746411yescharacteristic, complemented, Sylow
369C22×Q8—611no—
370C22×Q8—1221no—
371C22×Q8C4×D6111yescharacteristic
372C23×C4—611no—
373C23×C4—611no—
374C23×C4—611no—
375C2×M16—1222no—
376C22×C8—1222no—
377C4⋊Q8—612no—
378C4⋊Q8—612no—
379C4⋊Q8—612no—
380C4⋊Q8—612no—
381C4⋊Q8—1221no—
382C4⋊Q8—1221no—
383C4⋊Q8—1221no—
384C4⋊Q8—1221no—
385#125—1222no—
386#125—1222no—
387#125—1222no—
388#125—1222no—
389C22⋊Q8—612no—
390C22⋊Q8—612no—
391C22⋊Q8—612no—
392C22⋊Q8—612no—
393C22⋊Q8—1221no—
394C22⋊Q8—1221no—
395C22⋊Q8—1222no—
396C22⋊Q8—1222no—
397C22⋊Q8—1222no—
398C22⋊Q8—1222no—
399C22⋊Q8—1221no—
400C22⋊Q8—1221no—
401C4×Q8—21no—
402C4×Q8—21no—
403C4×Q8—612no—
404C4×Q8—612no—
405C4×Q8—1222no—
406C4×Q8—1222no—
407C4×Q8—1222no—
408C4×Q8—1222no—
409C4×Q8—1221no—
410C4×Q8—1221no—
411C4×Q8C4×D6112yes—
412C4×Q8C22×D6112yes—
413#117—1222no—
414#117—1222no—
415#117—1222no—
416#117—1222no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—611no—
419C2×C4⋊C4—1221no—
420C2×C4⋊C4—1221no—
421C2×C4⋊C4—1221no—
422C2×C4⋊C4—1221no—
423C2×C4⋊C4—1221no—
424C2×C4⋊C4—1221no—
425C2×C4⋊C4C4×D6111yescharacteristic
426C2×C22⋊C4—1221no—
427C2×C22⋊C4—1221no—
428C2×C42—21no—
429C2×C42—611no—
430C2×C42—611no—
431C2×C42—611no—
432C2×C42—611no—
433C2×C42—611no—
434C2×C42—611no—
435C2×C42—611no—
436C2×C42—611no—
437C2×C42—611no—
438C2×C42—611no—
439C2×C42—611no—
440C2×C42—1221no—
441C2×C42C22×D6111yescharacteristic
442C4⋊C8—21no—
443C4⋊C8—612no—
444C4⋊C8—1222no—
445C4⋊C8—1222no—
446C4⋊C8—1221no—
447C4⋊C8C22×D6112yes—
448C22⋊C8—21no—
449C22⋊C8—21no—
450C22⋊C8—1222no—
451C22⋊C8—1222no—
452C22⋊C8—1221no—
453C22⋊C8—1221no—
454#97—1222no—
455C4×C8—21no—
456C4×C8—612no—
457C4×C8—1222no—
458C4×C8—1221no—
459C4×C8C22×D6112yes—
460C24—611no—
461C2×Q8—21no—
462C2×Q8—22no—
463C2×Q8—22no—
464C2×Q8—612no—
465C2×Q8—1222no—
466C2×Q8—1222no—
467C2×Q8—1221no—
468C2×Q8—1222no—
469C2×Q8—1222no—
470C2×Q8—2444no—
471C2×Q8C2×C4×D6112yes—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—611no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—611no—
488C22×C4—611no—
489C22×C4—1224no—
490C22×C4—1222no—
491C22×C4—1222no—
492C22×C4—1221no—
493C22×C4—1221no—
494C22×C4—2442no—
495C22×C4C2×C4×D6111yescharacteristic
496C22×C4D4×D6111yescharacteristic
497C22×C4D4×D6111yescharacteristic
498M16—2444no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—1222no—
502C2×C8—1222no—
503C2×C8—2444no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—612no—
508C4⋊C4—1222no—
509C4⋊C4—1222no—
510C4⋊C4—1222no—
511C4⋊C4—1222no—
512C4⋊C4—1222no—
513C4⋊C4—1222no—
514C4⋊C4—1222no—
515C4⋊C4—1222no—
516C4⋊C4—1222no—
517C4⋊C4—1222no—
518C4⋊C4—1222no—
519C4⋊C4—1221no—
520C4⋊C4—1222no—
521C4⋊C4C2×C4×D6112yes—
522C22⋊C4—1222no—
523C22⋊C4—1222no—
524C22⋊C4—1222no—
525C22⋊C4—1222no—
526C42—22no—
527C42—22no—
528C42—611no—
529C42—611no—
530C42—611no—
531C42—611no—
532C42—611no—
533C42—611no—
534C42—611no—
535C42—611no—
536C42—611no—
537C42—611no—
538C42—611no—
539C42—611no—
540C42—1222no—
541C42—1222no—
542C42C2×C4×D6111yescharacteristic
543C42D4×D6111yescharacteristic
544C42D4×D6111yescharacteristic
545C42C23×D6111yescharacteristic
546C23—611no—
547C23—611no—
548C23—1222no—
549C23—1222no—
550C23—2441no—
551C23C22⋊C4×D6111yescharacteristic
552Q8—22no—
553Q8—22no—
554Q8—42no—
555Q8—1222no—
556Q8—1222no—
557Q8—2444no—
558Q8—2444no—
559Q8—2442no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—611no—
567C2×C4—611no—
568C2×C4—614no—
569C2×C4—611no—
570C2×C4—611no—
571C2×C4—611no—
572C2×C4—611no—
573C2×C4—1222no—
574C2×C4—1222no—
575C2×C4—1222no—
576C2×C4—1222no—
577C2×C4—1222no—
578C2×C4—1222no—
579C2×C4—1222no—
580C2×C4—1222no—
581C2×C4—1222no—
582C2×C4—1221no—
583C2×C4—1221no—
584C2×C4—1221no—
585C2×C4—1221no—
586C2×C4—1222no—
587C2×C4—1222no—
588C2×C4—1222no—
589C2×C4—2441no—
590C2×C4—2441no—
591C2×C4—2442no—
592C2×C4—2442no—
593C2×C4C22⋊C4×D6111yescharacteristic
594C2×C4C22⋊C4×D6111yescharacteristic
595C2×C4C22⋊C4×D6111yescharacteristic
596C2×C4#1451978312yes—
597C2×C4#1451978512yes—
598C2×C4C22×C4×D6111yescharacteristic
599C2×C4C2×D4×D6111yescharacteristic
600C2×C4C2×D4×D6111yescharacteristic
601C8—42no—
602C8—42no—
603C8—2442no—
604C8—2442no—
605C22—21no—
606C22—21no—
607C22—612no—
608C22—1221no—
609C22—1221no—
610C22—1221no—
611C22—1221no—
612C22—1221no—
613C22—2444no—
614C22#1683972712yes—
615C22C2×C22⋊C4×D6111yescharacteristic
616C4—21no—
617C4—21no—
618C4—21no—
619C4—42no—
620C4—42no—
621C4—612no—
622C4—612no—
623C4—1221no—
624C4—1221no—
625C4—1221no—
626C4—1221no—
627C4—2442no—
628C4—2442no—
629C4#1683972712yes—
630C4C2×#1451978311yescharacteristic
631C4C2×#1451978511yescharacteristic
632C4#137×D6112yes—
633C2—22no—
634C2—1222no—
635C2—2441no—
636C2C2×#1683972711yescharacteristic
637C2#419×D6111yescharacteristic
638C2#421×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1479C2
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC42×C61C24
hypercenter#1479D61
hypocenterC61#17464
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
4. #21444238C2semidirect
5. #21444220C2semidirect
6. #21444215C2semidirect
7. #21444214C2semidirect
8. #21444213C2semidirect
9. C61×#1479C2semidirect
42. #16839494C22semidirect
43. Q8⋊#92418C22semidirect
44. #16839492C22semidirect
48. C61×Q8⋊C8C22semidirect
322. #1479D61semidirect
367. Q8⋊C8C2×D61semidirect
368. C61#17464semidirect

Maximal subgroups

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

subgroupindex
C2×#168403162
#214544472
#431×D612
#214442382
#214442202
#214442152
#214442142
#214442132
C61×#14792
#1746461