Finite Group Databasebeta

← #29646165

Subgroups — #29646165

Order 15616.

952 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840354C211yesmaximal, characteristic
2#21454858C211yesmaximal, characteristic, complemented
3#21454846C211yesmaximal, characteristic, complemented
4#21444185C212yesmaximal, complemented
5#21444181C212yesmaximal, complemented
6#21444173C212yesmaximal, complemented
7#21444164C212yesmaximal, complemented
8#21444157C211yesmaximal, characteristic, complemented
9#21444148C211yesmaximal, characteristic, complemented
10#21444148C211yesmaximal, characteristic, complemented
11C61×#1465C211yesmaximal, characteristic, complemented
12#16840354—22no—
13#16840354—22no—
14#16840354—22no—
15#16840354—22no—
16C2×#14519771C411yescharacteristic
17C2×#14519770C2211yescharacteristic
18C2×#14519769C411yescharacteristic
19C2×#14519767C2211yescharacteristic
20C2×#14519761C411yescharacteristic
21C2×#14519760C411yescharacteristic
22C2×#14519759C2211yescharacteristic
23C2×#14519758C411yescharacteristic
24C2×#14519756C411yescharacteristic
25C2×#14519755C2211yescharacteristic
26C2×#14519754C411yescharacteristic
27C2×#14519749C411yescharacteristic
28C2×C4×C22⋊D61C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30#16839838—22no—
31#16839837—22no—
32#16839836—22no—
33#16839831—22no—
34#16839816C2212yes—
35#16839812C2212yes—
36#16839726C2211yescharacteristic
37#16839726C2211yescharacteristic
38#16839724C2212yes—
39C22⋊C8×D61C2212yes—
40#16839488C2212yes—
41#16839487C2212yes—
42#16839487C2212yes—
43#16839487C2212yes—
44#16839487C2212yes—
45#16839486C2212yes—
46C2×C4×D4×C61C2211yescharacteristic
47C61×#407C2211yescharacteristic
48C61×#407C2211yescharacteristic
49C61×#324C2212yes—
50C61×#323C2212yes—
51C22×Dic122C2×C411yescharacteristic
52C22×C22⋊D61C2×C411yescharacteristic
53C22×C22⋊D61C2×C411yescharacteristic
54C23×Dic61C2×C411yescharacteristic
55C23×Dic61C2×C411yescharacteristic
56C22×C4×D61C2311yescharacteristic
57C2×#11758194—21no—
58C2×#11758194—21no—
59C2×#11758189—22no—
60C2×C8×D61—22no—
61#14519771—22no—
62#14519771—22no—
63#14519770—22no—
64#14519770—22no—
65#14519769—22no—
66#14519769—22no—
67#14519767—22no—
68#14519767—22no—
69#14519761—22no—
70#14519761—22no—
71#14519760—22no—
72#14519760—22no—
73#14519759—22no—
74#14519759—22no—
75#14519758—22no—
76#14519758—22no—
77#14519756—22no—
78#14519756—22no—
79#14519755—22no—
80#14519755—22no—
81#14519754—22no—
82#14519754—22no—
83#14519749—22no—
84#14519749—22no—
85C4×C22⋊D61D412yes—
86C4×C22⋊D61D412yes—
87C4×C22⋊D61D412yes—
88C4×C22⋊D61D412yes—
89C2×C4⋊Dic61C2×C411yescharacteristic
90C2×C4⋊Dic61C2×C411yescharacteristic
91C2×C4⋊Dic61C2×C411yescharacteristic
92C2×#11758196—21no—
93C2×#11758196—21no—
94C2×#11758196—21no—
95C2×#11758196—21no—
96C2×#11758196C2×C411yescharacteristic
97C2×#11758196C2×C411yescharacteristic
98C2×#11758196C2×C411yescharacteristic
99C2×#11758196C2×C411yescharacteristic
100C2×#11758196C2×C411yescharacteristic
101C2×#11758196C2×C411yescharacteristic
102C2×#11758196C2×C411yescharacteristic
103C2×#11758196C2×C411yescharacteristic
104C2×#11758196C2311yescharacteristic
105C2×#11758196C2311yescharacteristic
106C2×C22⋊Dic61C2×C411yescharacteristic
107C2×C22⋊Dic61C2×C411yescharacteristic
108C2×C22⋊Dic61C2×C411yescharacteristic
109C2×C22⋊Dic61C2×C411yescharacteristic
110C2×#11758198C2×C411yescharacteristic
111C2×#11758198C2×C411yescharacteristic
112C2×#11758198C2×C411yescharacteristic
113C2×#11758198C2×C411yescharacteristic
114C2×C4×Dic61C2311yescharacteristic
115#14519706—22no—
116#14519706—22no—
117C22⋊#92418—21no—
118C22⋊#92418—21no—
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—21no—
129C2×M16×C61—21no—
130C4×D4×C61—21no—
131C4×D4×C61—21no—
132C4×D4×C61—21no—
133C4×D4×C61—21no—
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C22⋊C4×C61C2×C411yescharacteristic
136C2×C22⋊C4×C61C2311yescharacteristic
137C2×C42×C61C2×C411yescharacteristic
138C22⋊C8×C61—21no—
139C22⋊C8×C61—21no—
140C22⋊C8×C61C2312yes—
141C22⋊C8×C61C2312yes—
142C24×C61C22×C411yescharacteristic
143C24×C61C22×C411yescharacteristic
144C23×D61C22×C411yescharacteristic
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—42no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—81no—
151C22×C4×C61—81no—
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2411yescharacteristic
161C2×C22⋊D61—22no—
162C2×C22⋊D61—42no—
163C2×C22⋊D61—81no—
164C2×C22⋊D61C22⋊C412yes—
165C2×C22⋊D61C22⋊C412yes—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—42no—
171C22×Dic61—81no—
172C22×Dic61C22×C411yescharacteristic
173C22×Dic61C22×C411yescharacteristic
174C22×Dic61C22×C411yescharacteristic
175C22×Dic61C22×C411yescharacteristic
176C22×Dic61C22×C411yescharacteristic
177C22×Dic61C22×C411yescharacteristic
178C22×Dic61C22×C411yescharacteristic
179C2×C4×D61—81no—
180C2×C4×D61C2×D412yes—
181C2×C4×D61C2×D412yes—
182C2×Dic122—22no—
183C2×Dic122—81no—
184M16×C61—81no—
185M16×C61—81no—
186C2×C8×C61—22no—
187C2×C8×C61—22no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—21no—
190C22⋊C4×C61—21no—
191C22⋊C4×C61—21no—
192C22⋊C4×C61—21no—
193C22⋊C4×C61—21no—
194C42×C61—21no—
195C42×C61—21no—
196C22⋊Dic61—22no—
197C22⋊Dic61—22no—
198C22⋊Dic61—22no—
199C22⋊Dic61C22⋊C412yes—
200C22⋊Dic61C22⋊C412yes—
201#11758198—22no—
202#11758198—22no—
203#11758198—22no—
204#11758198C22⋊C412yes—
205#11758198C22⋊C412yes—
206C4⋊Dic61—22no—
207C4⋊Dic61—22no—
208C4⋊Dic61—22no—
209#11758196—21no—
210#11758196—21no—
211#11758196—21no—
212#11758196—21no—
213#11758196—21no—
214#11758196—21no—
215#11758196—21no—
216#11758196—21no—
217#11758196—22no—
218#11758196—22no—
219#11758196—22no—
220#11758196—22no—
221#11758196—22no—
222#11758196C22⋊C412yes—
223#11758196C22⋊C412yes—
224C4×Dic61C2×D412yes—
225C4×Dic61C2×D412yes—
226#11758194—81no—
227#11758194—81no—
228C2×#92418—22no—
229C2×#92418—22no—
230#11758189—82no—
231C8×D61—82no—
232C23×C61—22no—
233C23×C61—21no—
234C23×C61—22no—
235C23×C61—41no—
236C23×C61—41no—
237C23×C61—41no—
238C23×C61—41no—
239C23×C61C2×C22⋊C411yescharacteristic
240C23×C61C2×C22⋊C411yescharacteristic
241C23×C61C23×C411yescharacteristic
242C22×D61—22no—
243C22×D61—41no—
244C22×D61—41no—
245C22×D61C2×C22⋊C412yes—
246D4×C61—42no—
247D4×C61—42no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—22no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61—81no—
261C2×C4×C61—81no—
262C2×C4×C61C2×C22⋊C411yescharacteristic
263C2×C4×C61C2×C22⋊C411yescharacteristic
264C2×C4×C61C22×D411yescharacteristic
265C2×C4×C61C22×D411yescharacteristic
266C22⋊D61—42no—
267C22⋊D61—42no—
268C22⋊D61—82no—
269C2×Dic61—22no—
270C2×Dic61—21no—
271C2×Dic61—21no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61—22no—
275C2×Dic61—22no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278C2×Dic61—42no—
279C2×Dic61—42no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61—81no—
283C2×Dic61—81no—
284C2×Dic61C2×C22⋊C412yes—
285C2×Dic61C2×C22⋊C412yes—
286C2×Dic61C2×C22⋊C412yes—
287C4×D61—42no—
288C4×D61—42no—
289Dic122—82no—
290C8×C61—42no—
291C8×C61—42no—
292#92418—42no—
293#92418—42no—
294#17406—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—21no—
303C22×C61—44no—
304C22×C61—41no—
305C22×C61—41no—
306C22×C61—41no—
307C22×C61—82no—
308C22×C61C22×C22⋊C411yescharacteristic
309C22×C61#56812yes—
310C2×D61—22no—
311C2×D61—22no—
312C2×D61—22no—
313C2×D61—82no—
314C4×C61—21no—
315C4×C61—21no—
316C4×C61—21no—
317C4×C61—21no—
318C4×C61—41no—
319C4×C61—41no—
320C4×C61—41no—
321Dic61—22no—
322Dic61—22no—
323Dic61—22no—
324Dic61—41no—
325Dic61—41no—
326Dic61—41no—
327Dic61—41no—
328C2×#539—611no—
329#2975—611no—
330#2973—611no—
331#1473—612no—
332#1472—612no—
333#1470—612no—
334#1468—612no—
335#1465—611no—
336#1465D6111yescharacteristic, complemented
337#1463—611no—
338#1463—611no—
339C2×C61—22no—
340C2×C61—41no—
341C2×C61—41no—
342C2×C61—81no—
343C2×C61#287911yescharacteristic
344C2×C61#288311yescharacteristic
345C2×C61#288911yescharacteristic
346D61—42no—
347#539—1222no—
348#539—1222no—
349#539—1222no—
350#539—1222no—
351C2×#126—611no—
352C2×#126—611no—
353C2×#125—611no—
354C2×#125—611no—
355C2×#123—611no—
356C2×#123—611no—
357C2×#123—611no—
358C2×#123—611no—
359C2×C22⋊Q8—611no—
360C2×C22⋊Q8—611no—
361C2×C22⋊Q8—611no—
362C2×#121—611no—
363C2×C4×D4—611no—
364C2×C4×D4C2×D6111yescharacteristic
365C22×C4⋊C4—611no—
366#436—1222no—
367#436—1222no—
368#435—1222no—
369#435—1222no—
370#432—612no—
371#431—612no—
372#407—611no—
373#407—611no—
374#407—612no—
375#407C2×D6111yescharacteristic
376#407C2×D6111yescharacteristic
377C2×C22⋊C8—612no—
378#324—612no—
379#324—612no—
380#324—612no—
381#324—612no—
382#324—612no—
383#324C2×D6112yes—
384#323—612no—
385#323C2×D6112yes—
386C61#1740611yescharacteristic, complemented, Sylow
387C22×Q8—611no—
388C22×D4—611no—
389C22×D4—611no—
390C22×D4C4×D6111yescharacteristic
391C23×C4—611no—
392C23×C4—611no—
393C23×C4—611no—
394C23×C4C4×D6111yescharacteristic
395C23×C4C22×D6111yescharacteristic
396C2×M16—21no—
397C2×M16—21no—
398C2×M16—1222no—
399C2×M16—1221no—
400C2×M16—1221no—
401C22×C8—1222no—
402#126—1222no—
403#126—1222no—
404#126—1222no—
405#126—1222no—
406#125—1222no—
407#125—1222no—
408#125—1222no—
409#125—1222no—
410#123—1222no—
411#123—1222no—
412#123—1222no—
413#123—1222no—
414#123—1222no—
415#123—1222no—
416#123—1222no—
417#123—1222no—
418C22⋊Q8—1222no—
419C22⋊Q8—1222no—
420C22⋊Q8—1222no—
421C22⋊Q8—1222no—
422C22⋊Q8—1222no—
423C22⋊Q8—1222no—
424#121—1222no—
425#121—1222no—
426C4×D4—21no—
427C4×D4—21no—
428C4×D4—21no—
429C4×D4—21no—
430C4×D4—612no—
431C4×D4—612no—
432C4×D4—612no—
433C4×D4—612no—
434C2×C4⋊C4—611no—
435C2×C4⋊C4—611no—
436C2×C4⋊C4—611no—
437C2×C4⋊C4—611no—
438C2×C4⋊C4—611no—
439C2×C4⋊C4—611no—
440C2×C4⋊C4—611no—
441C2×C4⋊C4—611no—
442C2×C4⋊C4—611no—
443C2×C4⋊C4—611no—
444C2×C4⋊C4—611no—
445C2×C4⋊C4—611no—
446C2×C4⋊C4—611no—
447C2×C4⋊C4—1221no—
448C2×C4⋊C4—1221no—
449C2×C4⋊C4—1221no—
450C2×C4⋊C4—1221no—
451C2×C4⋊C4C22×D6111yescharacteristic
452C2×C22⋊C4—611no—
453C2×C22⋊C4—611no—
454C2×C22⋊C4—611no—
455C2×C22⋊C4—611no—
456C2×C22⋊C4—611no—
457C2×C22⋊C4—611no—
458C2×C22⋊C4—611no—
459C2×C22⋊C4—611no—
460C2×C22⋊C4C4×D6111yescharacteristic
461C2×C22⋊C4C22×D6111yescharacteristic
462C2×C42—611no—
463C2×C42C4×D6111yescharacteristic
464C4⋊C8—1222no—
465C4⋊C8—1222no—
466C22⋊C8—21no—
467C22⋊C8—21no—
468C22⋊C8—612no—
469C22⋊C8—612no—
470C22⋊C8—1222no—
471C22⋊C8—1222no—
472C22⋊C8—1221no—
473C22⋊C8—1221no—
474C22⋊C8C22×D6112yes—
475C22⋊C8C22×D6112yes—
476#97—1222no—
477C4×C8—1222no—
478C24—611no—
479C24C2×C4×D6111yescharacteristic
480C24C2×C4×D6111yescharacteristic
481C2×Q8—1222no—
482C2×Q8—4881no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—42no—
486C2×D4—612no—
487C2×D4—612no—
488C2×D4—1222no—
489C2×D4—4881no—
490C2×D4—2442no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—81no—
494C22×C4—81no—
495C22×C4—611no—
496C22×C4—611no—
497C22×C4—611no—
498C22×C4—612no—
499C22×C4—612no—
500C22×C4—611no—
501C22×C4—611no—
502C22×C4—611no—
503C22×C4—611no—
504C22×C4—1221no—
505C22×C4—1221no—
506C22×C4—1221no—
507C22×C4—1221no—
508C22×C4—4881no—
509C22×C4—4881no—
510C22×C4—2442no—
511C22×C4C2×C4×D6111yescharacteristic
512C22×C4C2×C4×D6111yescharacteristic
513C22×C4C2×C4×D6111yescharacteristic
514C22×C4C2×C4×D6111yescharacteristic
515C22×C4D4×D6111yescharacteristic
516C22×C4D4×D6111yescharacteristic
517C22×C4D4×D6111yescharacteristic
518C22×C4D4×D6111yescharacteristic
519C22×C4C23×D6111yescharacteristic
520M16—81no—
521M16—81no—
522M16—4882no—
523M16—4881no—
524M16—4881no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—1222no—
528C2×C8—1222no—
529C2×C8—4882no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—612no—
533C4⋊C4—612no—
534C4⋊C4—1222no—
535C4⋊C4—1222no—
536C4⋊C4—1222no—
537C4⋊C4—1222no—
538C4⋊C4—1222no—
539C4⋊C4—1222no—
540C4⋊C4—1222no—
541C4⋊C4—1222no—
542C4⋊C4—1221no—
543C4⋊C4—1221no—
544C4⋊C4—1221no—
545C4⋊C4—1221no—
546C4⋊C4—1221no—
547C4⋊C4—1221no—
548C4⋊C4—1221no—
549C4⋊C4—1221no—
550C22⋊C4—21no—
551C22⋊C4—21no—
552C22⋊C4—21no—
553C22⋊C4—21no—
554C22⋊C4—612no—
555C22⋊C4—612no—
556C22⋊C4—612no—
557C22⋊C4—612no—
558C22⋊C4—1222no—
559C22⋊C4—1222no—
560C22⋊C4—1222no—
561C22⋊C4—1222no—
562C22⋊C4—1222no—
563C22⋊C4—1222no—
564C42—21no—
565C42—21no—
566C42—612no—
567C42—612no—
568C23—22no—
569C23—21no—
570C23—22no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—612no—
576C23—1222no—
577C23—2441no—
578C23—2441no—
579C23C22⋊C4×D6111yescharacteristic
580C23C22⋊C4×D6111yescharacteristic
581C23C22×C4×D6111yescharacteristic
582Q8—4882no—
583D4—42no—
584D4—42no—
585D4—4882no—
586D4—2442no—
587D4—2442no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—81no—
601C2×C4—81no—
602C2×C4—612no—
603C2×C4—612no—
604C2×C4—612no—
605C2×C4—1222no—
606C2×C4—1221no—
607C2×C4—1221no—
608C2×C4—1221no—
609C2×C4—1221no—
610C2×C4—1222no—
611C2×C4—1222no—
612C2×C4—4881no—
613C2×C4—4881no—
614C2×C4—2442no—
615C2×C4—2442no—
616C2×C4—2441no—
617C2×C4—2441no—
618C2×C4—2442no—
619C2×C4—2442no—
620C2×C4—2441no—
621C2×C4—2441no—
622C2×C4C22⋊C4×D6111yescharacteristic
623C2×C4C22⋊C4×D6111yescharacteristic
624C2×C4C2×D4×D6111yescharacteristic
625C2×C4C2×D4×D6111yescharacteristic
626C8—42no—
627C8—42no—
628C8—2442no—
629C8—2442no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—21no—
634C22—21no—
635C22—21no—
636C22—21no—
637C22—21no—
638C22—44no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—82no—
643C22—1222no—
644C22—1222no—
645C22—1222no—
646C22—4882no—
647C22C2×C22⋊C4×D6111yescharacteristic
648C22#1684052812yes—
649C4—21no—
650C4—21no—
651C4—21no—
652C4—21no—
653C4—41no—
654C4—41no—
655C4—41no—
656C4—1222no—
657C4—1222no—
658C4—1222no—
659C4—2441no—
660C4—2441no—
661C4—2441no—
662C4—2441no—
663C2—22no—
664C2—41no—
665C2—41no—
666C2—81no—
667C2—2442no—
668C2#2145426211yescharacteristic
669C2#2145427711yescharacteristic
670C2#2145430011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1465C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519749C4
cosocleC22×C4×C61C24
hypercenter#1465D61
hypocenterC61#17406
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. #21454858C2semidirect
3. #21454846C2semidirect
4. #21444185C2semidirect
5. #21444181C2semidirect
6. #21444173C2semidirect
7. #21444164C2semidirect
8. #21444157C2semidirect
9. #21444148C2semidirect
10. #21444148C2semidirect
11. C61×#1465C2semidirect
336. #1465D61semidirect
386. C61#17406semidirect

Maximal subgroups

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

subgroupindex
C2×#168403542
#214548582
#214548462
#214441852
#214441812
#214441732
#214441642
#214441572
#214441482
C61×#14652
#1740661