Finite Group Databasebeta

← #29648083

Subgroups — #29648083

Order 15616.

962 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×D61C211yesmaximal, characteristic
2#21454450C211yesmaximal, characteristic
3#21454449C211yesmaximal, characteristic
4#21444444C214yesmaximal, complemented
5#21444422C211yesmaximal, characteristic, complemented
6#21444421C211yesmaximal, characteristic, complemented
7#21444420C211yesmaximal, characteristic, complemented
8#21444419C214yesmaximal, complemented
9C61×#1528C211yesmaximal, characteristic, complemented
10C2×#14519769C2211yescharacteristic
11C2×#14519768C411yescharacteristic
12C2×#14519768C411yescharacteristic
13C2×#14519767—21no—
14C2×#14519767—21no—
15#125×D61—21no—
16#125×D61—21no—
17#125×D61—21no—
18#125×D61—21no—
19#125×D61C412yes—
20#125×D61C412yes—
21#125×D61C2212yes—
22#125×D61C2212yes—
23C2×C4⋊C4×D61—21no—
24C2×C4⋊C4×D61—21no—
25C2×C4⋊C4×D61C411yescharacteristic
26C2×C4⋊C4×D61C411yescharacteristic
27C2×C42×D61C2211yescharacteristic
28#16839819C2211yescharacteristic
29#16839817C2212yes—
30#16839817C2212yes—
31#16839817C2212yes—
32#16839814—21no—
33#16839813—21no—
34#16839813—21no—
35#16839812—21no—
36#16839785—21no—
37#16839784—21no—
38#16839725—21no—
39#16839724—21no—
40C4×#11758194C2211yescharacteristic
41#16839714C2212yes—
42#16839504C2214yescomplemented
43#16839503C2214yescomplemented
44#16839503C2214yescomplemented
45C2×#125×C61C2211yescharacteristic
46C61×#432C2211yescharacteristic
47C4×M16×C61C2211yescharacteristic
48C61×#330C2214yescomplemented
49C22×C4×D61—21no—
50C22×C4×D61—21no—
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61D411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C2×#11758194—21no—
55C2×#11758189—22no—
56#14519769—21no—
57#14519769—21no—
58#14519769C2×C412yes—
59#14519769C2312yes—
60#14519768—21no—
61#14519768—21no—
62#14519768—21no—
63#14519768—21no—
64#14519768C2×C412yes—
65#14519768C2×C412yes—
66#14519768C2×C412yes—
67#14519768C2×C412yes—
68#14519767—22no—
69#14519767—22no—
70#14519767—22no—
71#14519767—22no—
72#14519767—22no—
73#14519767—22no—
74#14519767—22no—
75#14519767—22no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61C2×C411yescharacteristic
79C2×C4⋊Dic61C2×C411yescharacteristic
80C2×#11758196—21no—
81C2×#11758196—21no—
82C2×#11758196—21no—
83C2×#11758196—21no—
84C2×#11758196—21no—
85C2×#11758196—21no—
86C4⋊C4×D61—22no—
87C4⋊C4×D61—22no—
88C4⋊C4×D61—22no—
89C4⋊C4×D61—22no—
90C4⋊C4×D61—21no—
91C4⋊C4×D61—21no—
92C4⋊C4×D61—21no—
93C4⋊C4×D61—21no—
94C4⋊C4×D61—22no—
95C4⋊C4×D61—22no—
96C4⋊C4×D61—22no—
97C4⋊C4×D61—22no—
98C4⋊C4×D61C2×C412yes—
99C4⋊C4×D61C2×C412yes—
100C4⋊C4×D61C2×C412yes—
101C4⋊C4×D61C2×C412yes—
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—
114#14519706—22no—
115#14519706—22no—
116#14519706—22no—
117C22⋊#92418—21no—
118#14519689—22no—
119#14519689—22no—
120#14519689—22no—
121#14519688C2312yes—
122#14519688C2312yes—
123C4×#92418—21no—
124C8×Dic61—22no—
125C2×M16×C61—21no—
126#125×C61—21no—
127#125×C61—21no—
128#125×C61C2×C412yes—
129#125×C61C2312yes—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61C2×C411yescharacteristic
133C2×C4⋊C4×C61C2×C411yescharacteristic
134C2×C42×C61C2311yescharacteristic
135C4⋊C8×C61—21no—
136C22⋊C8×C61—21no—
137#97×C61C2312yes—
138#97×C61C2312yes—
139C4×C8×C61—21no—
140C23×D61C22⋊C411yescharacteristic
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61C22⋊C411yescharacteristic
149C22×Dic61C22⋊C411yescharacteristic
150C22×Dic61C22⋊C411yescharacteristic
151C2×C4×D61—24no—
152C2×C4×D61—22no—
153C2×C4×D61—22no—
154C2×C4×D61—22no—
155C2×C4×D61—22no—
156C2×C4×D61—42no—
157C2×C4×D61—42no—
158C2×C4×D61—44no—
159C2×C4×D61—44no—
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×D61C22×C411yescharacteristic
168C2×C4×D61C2×D411yescharacteristic
169C2×C4×D61C2×D411yescharacteristic
170C2×C4×D61C2×D411yescharacteristic
171C2×C4×D61C2×D411yescharacteristic
172M16×C61—42no—
173C2×C8×C61—22no—
174C2×C8×C61—22no—
175C4⋊C4×C61—22no—
176C4⋊C4×C61—22no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—22no—
180C4⋊C4×C61—22no—
181C4⋊C4×C61C22×C412yes—
182C4⋊C4×C61C22×C412yes—
183C42×C61C22×C411yescharacteristic
184C42×C61C2×D411yescharacteristic
185C42×C61C2×D411yescharacteristic
186C42×C61C2411yescharacteristic
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—22no—
190C4⋊Dic61—22no—
191C4⋊Dic61—22no—
192C4⋊Dic61—22no—
193C4⋊Dic61C22×C412yes—
194C4⋊Dic61C22×C412yes—
195#11758196—22no—
196#11758196—22no—
197#11758196—22no—
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—
207C4×Dic61C22⋊C411yescharacteristic
208C4×Dic61C22⋊C411yescharacteristic
209C4×Dic61C22⋊C411yescharacteristic
210C4×Dic61C22⋊C411yescharacteristic
211C4×Dic61C22⋊C411yescharacteristic
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C22×C411yescharacteristic
214C4×Dic61C22×C411yescharacteristic
215C4×Dic61C2×D411yescharacteristic
216C4×Dic61C2×D411yescharacteristic
217C4×Dic61C2×D411yescharacteristic
218C4×Dic61C2×D411yescharacteristic
219#11758194—42no—
220C2×#92418—22no—
221C2×#92418—22no—
222#11758189—44no—
223C23×C61C2×C22⋊C411yescharacteristic
224C22×D61—22no—
225C22×D61—22no—
226C22×D61—22no—
227C22×D61C2×C22⋊C411yescharacteristic
228C22×D61C2×C22⋊C411yescharacteristic
229C2×C4×C61—22no—
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—41no—
234C2×C4×C61—42no—
235C2×C4×C61—42no—
236C2×C4×C61C2×C22⋊C411yescharacteristic
237C2×C4×C61C2×C22⋊C411yescharacteristic
238C2×C4×C61C2×C22⋊C411yescharacteristic
239C2×C4×C61C23×C411yescharacteristic
240C2×C4×C61C22×D411yescharacteristic
241C2×C4×C61C22×D411yescharacteristic
242C2×Dic61—22no—
243C2×Dic61—22no—
244C2×Dic61—22no—
245C2×Dic61—22no—
246C2×Dic61—41no—
247C2×Dic61—42no—
248C2×Dic61—42no—
249C2×Dic61C2×C22⋊C411yescharacteristic
250C2×Dic61C2×C22⋊C411yescharacteristic
251C2×Dic61C2×C22⋊C411yescharacteristic
252C2×Dic61C2×C22⋊C411yescharacteristic
253C2×Dic61C2×C22⋊C411yescharacteristic
254C2×Dic61C2×C22⋊C411yescharacteristic
255C4×D61—22no—
256C4×D61—22no—
257C4×D61—22no—
258C4×D61—22no—
259C4×D61—22no—
260C4×D61—41no—
261C4×D61—41no—
262C4×D61—41no—
263C4×D61—41no—
264C4×D61—41no—
265C4×D61—41no—
266C4×D61—44no—
267C4×D61—44no—
268C4×D61—44no—
269C4×D61—44no—
270C4×D61#10114yes—
271C8×C61—42no—
272C8×C61—42no—
273#92418—42no—
274#92418—42no—
275#17667—611nomaximal, Sylow
276C22×C61—21no—
277C22×C61—21no—
278C22×C61#42112yes—
279C22×C61C22×C22⋊C411yescharacteristic
280C2×D61—28no—
281C2×D61—21no—
282C2×D61—21no—
283C2×D61—21no—
284C2×D61—21no—
285C2×D61C2×#10112yes—
286C2×D61#42112yes—
287C4×C61—21no—
288C4×C61—21no—
289C4×C61—21no—
290C4×C61—21no—
291C4×C61—21no—
292C4×C61—42no—
293C4×C61—42no—
294C4×C61C2×#10112yes—
295Dic61—21no—
296Dic61—21no—
297Dic61—21no—
298Dic61—21no—
299Dic61—21no—
300Dic61—42no—
301Dic61—42no—
302Dic61C2×#10112yes—
303C22×#125—611no—
304#2920—611no—
305#2920—611no—
306#1534—614no—
307#1528—611no—
308#1528—611no—
309#1528—614no—
310#1528—611no—
311#1528D6111yescharacteristic, complemented
312C2×C61—22no—
313C2×C61C22×#10111yescharacteristic
314C2×C61C2×#42111yescharacteristic
315C2×C61C2×#42111yescharacteristic
316D61—22no—
317D61—22no—
318C2×#125—612no—
319C2×#125—612no—
320C2×#125—612no—
321C2×#125—612no—
322C2×#125—611no—
323C2×#125—611no—
324C2×#125—611no—
325C2×#125—1221no—
326C2×#125—1221no—
327C2×#125—1221no—
328C2×#125—1221no—
329C2×#125—1221no—
330C2×#125—1221no—
331C2×#125C2×D6111yescharacteristic
332C22×C4⋊C4—611no—
333C22×C4⋊C4—611no—
334C22×C4⋊C4—1221no—
335C22×C4⋊C4—1221no—
336C22×C42—611no—
337#432—611no—
338#432—612no—
339#432—612no—
340#432—612no—
341#432C2×D6111yescharacteristic
342#431—1221no—
343#431—1221no—
344#431—1221no—
345#431—1221no—
346#423—1221no—
347#423—1221no—
348#407—1221no—
349#407—1221no—
350C4×M16—611no—
351C4×M16—612no—
352C4×M16C2×D6111yescharacteristic
353#330—614no—
354#330—614no—
355#330—614no—
356#330C2×D6114yescomplemented
357C61#1766711yescharacteristic, complemented, Sylow
358C23×C4—611no—
359C23×C4—611no—
360C23×C4—611no—
361C23×C4—1221no—
362C23×C4—1221no—
363C2×M16—21no—
364C2×M16—1222no—
365C2×M16—1221no—
366#125—21no—
367#125—21no—
368#125—612no—
369#125—612no—
370#125—612no—
371#125—612no—
372#125—612no—
373#125—612no—
374#125—1222no—
375#125—1222no—
376#125—1222no—
377#125—1222no—
378#125—1222no—
379#125—1222no—
380#125—1222no—
381#125—1222no—
382#125—1221no—
383#125—1221no—
384#125—1221no—
385#125—1221no—
386#125—1221no—
387#125—1221no—
388#125C4×D6112yes—
389#125C22×D6112yes—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—611no—
393C2×C4⋊C4—611no—
394C2×C4⋊C4—612no—
395C2×C4⋊C4—612no—
396C2×C4⋊C4—612no—
397C2×C4⋊C4—612no—
398C2×C4⋊C4—1221no—
399C2×C4⋊C4—1221no—
400C2×C4⋊C4—1221no—
401C2×C4⋊C4—1221no—
402C2×C4⋊C4—1222no—
403C2×C4⋊C4—1222no—
404C2×C4⋊C4—1222no—
405C2×C4⋊C4—1222no—
406C2×C4⋊C4—1222no—
407C2×C4⋊C4—1222no—
408C2×C4⋊C4—1222no—
409C2×C4⋊C4—1222no—
410C2×C4⋊C4—1221no—
411C2×C4⋊C4—1221no—
412C2×C4⋊C4—1221no—
413C2×C4⋊C4—1221no—
414C2×C4⋊C4—1221no—
415C2×C4⋊C4—1221no—
416C2×C4⋊C4—1221no—
417C2×C4⋊C4—1221no—
418C2×C4⋊C4C4×D6111yescharacteristic
419C2×C4⋊C4C4×D6111yescharacteristic
420C2×C42—611no—
421C2×C42—611no—
422C2×C42—611no—
423C2×C42—611no—
424C2×C42—611no—
425C2×C42—611no—
426C2×C42—611no—
427C2×C42—611no—
428C2×C42—611no—
429C2×C42—611no—
430C2×C42—611no—
431C2×C42C22×D6111yescharacteristic
432C4⋊C8—21no—
433C4⋊C8—1222no—
434C4⋊C8—1222no—
435C4⋊C8—1222no—
436C4⋊C8—1221no—
437C22⋊C8—21no—
438C22⋊C8—1222no—
439C22⋊C8—1222no—
440C22⋊C8—1222no—
441C22⋊C8—1221no—
442#97—612no—
443#97—612no—
444#97C22×D6112yes—
445#97C22×D6112yes—
446C4×C8—21no—
447C4×C8—1222no—
448C4×C8—1221no—
449C24—611no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—611no—
453C22×C4—611no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—611no—
457C22×C4—611no—
458C22×C4—611no—
459C22×C4—611no—
460C22×C4—611no—
461C22×C4—611no—
462C22×C4—611no—
463C22×C4—611no—
464C22×C4—611no—
465C22×C4—611no—
466C22×C4—611no—
467C22×C4—1224no—
468C22×C4—1222no—
469C22×C4—1222no—
470C22×C4—1222no—
471C22×C4—1222no—
472C22×C4—1221no—
473C22×C4—1221no—
474C22×C4—2442no—
475C22×C4—2442no—
476C22×C4—2444no—
477C22×C4—2444no—
478C22×C4C2×C4×D6111yescharacteristic
479C22×C4D4×D6111yescharacteristic
480C22×C4D4×D6111yescharacteristic
481M16—42no—
482M16—2444no—
483M16—2442no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—1222no—
487C2×C8—1222no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—612no—
495C4⋊C4—612no—
496C4⋊C4—1222no—
497C4⋊C4—1222no—
498C4⋊C4—1222no—
499C4⋊C4—1222no—
500C4⋊C4—1222no—
501C4⋊C4—1222no—
502C4⋊C4—1222no—
503C4⋊C4—1222no—
504C4⋊C4—1222no—
505C4⋊C4—1222no—
506C4⋊C4—1222no—
507C4⋊C4—1222no—
508C4⋊C4—1222no—
509C4⋊C4—1222no—
510C4⋊C4—1221no—
511C4⋊C4—1221no—
512C4⋊C4—1222no—
513C4⋊C4—1222no—
514C4⋊C4C2×C4×D6112yes—
515C4⋊C4C2×C4×D6112yes—
516C42—611no—
517C42—611no—
518C42—611no—
519C42—611no—
520C42—611no—
521C42—611no—
522C42—611no—
523C42—611no—
524C42—611no—
525C42—611no—
526C42—611no—
527C42—611no—
528C42C2×C4×D6111yescharacteristic
529C42D4×D6111yescharacteristic
530C42D4×D6111yescharacteristic
531C42C23×D6111yescharacteristic
532C23—611no—
533C23—611no—
534C23—1222no—
535C23—1222no—
536C23—1222no—
537C23C22⋊C4×D6111yescharacteristic
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—611no—
546C2×C4—614no—
547C2×C4—611no—
548C2×C4—611no—
549C2×C4—611no—
550C2×C4—611no—
551C2×C4—611no—
552C2×C4—1222no—
553C2×C4—1222no—
554C2×C4—1222no—
555C2×C4—1222no—
556C2×C4—1222no—
557C2×C4—1222no—
558C2×C4—1222no—
559C2×C4—1222no—
560C2×C4—1222no—
561C2×C4—2441no—
562C2×C4—2441no—
563C2×C4—2441no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4—2444no—
568C2×C4—2444no—
569C2×C4—2444no—
570C2×C4—2444no—
571C2×C4—2441no—
572C2×C4—2442no—
573C2×C4—2442no—
574C2×C4C22⋊C4×D6111yescharacteristic
575C2×C4C22⋊C4×D6111yescharacteristic
576C2×C4C22⋊C4×D6111yescharacteristic
577C2×C4C22×C4×D6111yescharacteristic
578C2×C4C2×D4×D6111yescharacteristic
579C2×C4C2×D4×D6111yescharacteristic
580C8—42no—
581C8—42no—
582C8—2442no—
583C8—2442no—
584C22—21no—
585C22—21no—
586C22—612no—
587C22—612no—
588C22—1228no—
589C22—1221no—
590C22—1221no—
591C22—1221no—
592C22—1221no—
593C22#1683977712yes—
594C22C2×C22⋊C4×D6111yescharacteristic
595C4—21no—
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—42no—
601C4—42no—
602C4—612no—
603C4—1221no—
604C4—1221no—
605C4—1221no—
606C4—1221no—
607C4—1221no—
608C4—2442no—
609C4—2442no—
610C4#101×D6112yes—
611C2—22no—
612C2—1222no—
613C2—1222no—
614C2C2×#101×D6111yescharacteristic
615C2#421×D6111yescharacteristic
616C2C2×#1683977711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1528C2
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC42×C61C24
hypercenter#1528D61
hypocenterC61#17667
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1528

Complements

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

NH ≅ G/Ntype
4. #21444444C2semidirect
5. #21444422C2semidirect
6. #21444421C2semidirect
7. #21444420C2semidirect
8. #21444419C2semidirect
9. C61×#1528C2semidirect
42. #16839504C22semidirect
43. #16839503C22semidirect
44. #16839503C22semidirect
48. C61×#330C22semidirect
311. #1528D61semidirect
356. #330C2×D61semidirect
357. C61#17667semidirect

Maximal subgroups

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

subgroupindex
C2×#125×D612
#214544502
#214544492
#214444442
#214444222
#214444212
#214444202
#214444192
C61×#15282
#1766761