Finite Group Databasebeta

← #29646166

Subgroups — #29646166

Order 15616.

952 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840353C211yesmaximal, characteristic
2#21454859C211yesmaximal, characteristic, complemented
3#21454847C211yesmaximal, characteristic, complemented
4#21444188C211yesmaximal, characteristic, complemented
5#21444181C212yesmaximal, complemented
6#21444176C211yesmaximal, characteristic, complemented
7#21444174C211yesmaximal, characteristic, complemented
8#21444164C212yesmaximal, complemented
9#21444154C212yesmaximal, complemented
10#21444147C212yesmaximal, complemented
11C61×#1473C211yesmaximal, characteristic, complemented
12#16840353—22no—
13#16840353—22no—
14#16840353—22no—
15#16840353—22no—
16C2×#14519772C411yescharacteristic
17C2×#14519769C2211yescharacteristic
18C2×#14519768C411yescharacteristic
19C2×#14519762C411yescharacteristic
20C2×#14519761C411yescharacteristic
21C2×#14519759C411yescharacteristic
22C2×#14519759C2211yescharacteristic
23C2×#14519757C411yescharacteristic
24C2×#14519755C2211yescharacteristic
25C2×#14519754C411yescharacteristic
26C2×#14519750C411yescharacteristic
27C2×C4×D244C2211yescharacteristic
28C2×#14519737C2211yescharacteristic
29C2×C4⋊C4×D61C2211yescharacteristic
30#16839841—22no—
31#16839839—22no—
32#16839835—22no—
33#16839832—22no—
34#16839819C2211yescharacteristic
35#16839815C2211yescharacteristic
36#16839724C2212yes—
37#16839724C2212yes—
38#16839724C2212yes—
39C22⋊C8×D61C2212yes—
40#16839488C2212yes—
41#16839487C2212yes—
42#16839487C2212yes—
43#16839487C2212yes—
44#16839487C2212yes—
45#16839486C2212yes—
46C2×#126×C61C2211yescharacteristic
47C61×#432C2211yescharacteristic
48C61×#431C2211yescharacteristic
49C61×#324C2212yes—
50C61×#323C2212yes—
51C22×Dic122C2×C411yescharacteristic
52C22×D244C2×C411yescharacteristic
53C22×C22⋊D61C2×C411yescharacteristic
54C22×C22⋊D61C2×C411yescharacteristic
55C23×Dic61C2×C411yescharacteristic
56C22×C4×D61C2×C411yescharacteristic
57C22×C4×D61C2×C411yescharacteristic
58C22×C4×D61C2311yescharacteristic
59C22×C4×D61C2311yescharacteristic
60C2×#11758189—22no—
61C2×#11758189—22no—
62C2×#11758189—22no—
63C2×C8×D61—22no—
64#14519772—22no—
65#14519772—22no—
66#14519769—21no—
67#14519769—21no—
68#14519769—21no—
69#14519769—21no—
70#14519768—22no—
71#14519768—22no—
72#14519762—22no—
73#14519762—22no—
74#14519761—22no—
75#14519761—22no—
76#14519759—22no—
77#14519759—22no—
78#14519759—22no—
79#14519759—22no—
80#14519757—22no—
81#14519757—22no—
82#14519755—22no—
83#14519755—22no—
84#14519754—22no—
85#14519754—22no—
86#14519750—22no—
87#14519750—22no—
88C4×D244D412yes—
89C4×D244D412yes—
90C4×D244D412yes—
91C4×D244D412yes—
92#14519737—22no—
93#14519737—22no—
94C2×C4⋊Dic61C2×C411yescharacteristic
95C2×C4⋊Dic61C2×C411yescharacteristic
96C2×C4⋊Dic61C2×C411yescharacteristic
97C2×C4⋊Dic61C2×C411yescharacteristic
98C2×C4⋊Dic61C2×C411yescharacteristic
99C2×#11758196C2×C411yescharacteristic
100C2×#11758196C2×C411yescharacteristic
101C2×#11758196C2×C411yescharacteristic
102C2×#11758196C2×C411yescharacteristic
103C2×#11758196C2311yescharacteristic
104C2×#11758196C2311yescharacteristic
105C4⋊C4×D61—22no—
106C4⋊C4×D61—22no—
107C2×C22⋊Dic61C2×C411yescharacteristic
108C2×#11758198C2×C411yescharacteristic
109C2×#11758198C2×C411yescharacteristic
110C2×#11758198C2×C411yescharacteristic
111C2×#11758198C2×C411yescharacteristic
112C2×#11758198C2×C411yescharacteristic
113C2×#11758198C2×C411yescharacteristic
114C2×C4×Dic61C2×C411yescharacteristic
115C4⋊#92418—21no—
116C4⋊#92418—21no—
117C22⋊#92418C2312yes—
118C22⋊#92418C2312yes—
119#14519689—22no—
120#14519689—22no—
121#14519689—22no—
122#14519689—22no—
123#14519688—21no—
124C4×#92418—21no—
125#126×C61—21no—
126#126×C61—21no—
127#126×C61—21no—
128#126×C61—21no—
129C2×C4⋊C4×C61C2×C411yescharacteristic
130C2×C4⋊C4×C61C2×C411yescharacteristic
131C2×C4⋊C4×C61C2311yescharacteristic
132C2×C22⋊C4×C61C2×C411yescharacteristic
133C2×C22⋊C4×C61C2×C411yescharacteristic
134C2×C22⋊C4×C61C2311yescharacteristic
135C2×C42×C61C2311yescharacteristic
136C4⋊C8×C61—21no—
137C4⋊C8×C61—21no—
138C22⋊C8×C61C2312yes—
139C22⋊C8×C61C2312yes—
140#97×C61—21no—
141C4×C8×C61—21no—
142C24×C61C22×C411yescharacteristic
143C23×D61C22×C411yescharacteristic
144C23×D61C22×C411yescharacteristic
145C22×C4×C61C22×C411yescharacteristic
146C22×C4×C61C22×C411yescharacteristic
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C2411yescharacteristic
151C2×C22⋊D61—22no—
152C2×C22⋊D61—22no—
153C2×C22⋊D61—42no—
154C2×C22⋊D61—81no—
155C22×Dic61—22no—
156C22×Dic61—81no—
157C22×Dic61C22×C411yescharacteristic
158C22×Dic61C22×C411yescharacteristic
159C22×Dic61C22×C411yescharacteristic
160C22×Dic61C22×C411yescharacteristic
161C22×Dic61C22×C411yescharacteristic
162C22×Dic61C22×C411yescharacteristic
163C2×D244—42no—
164C2×D244C22⋊C412yes—
165C2×D244C22⋊C412yes—
166C2×C4×D61—22no—
167C2×C4×D61—22no—
168C2×C4×D61—42no—
169C2×C4×D61—81no—
170C2×C4×D61—81no—
171C2×C4×D61—81no—
172C2×C4×D61C2×D412yes—
173C2×C4×D61C2×D412yes—
174C2×C4×D61C2×D412yes—
175C2×C4×D61C2×D412yes—
176C2×Dic122—22no—
177C2×Dic122—81no—
178C2×C8×C61—22no—
179C2×C8×C61—22no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—21no—
186C22⋊C4×C61—21no—
187C22⋊C4×C61—21no—
188C22⋊C4×C61—21no—
189C22⋊C4×C61—21no—
190C22⋊C4×C61—21no—
191C22⋊C4×C61—21no—
192C42×C61C2×D411yescharacteristic
193C42×C61C2×D411yescharacteristic
194C42×C61C2×D411yescharacteristic
195C42×C61C2×D411yescharacteristic
196C22⋊Dic61—22no—
197#11758198—22no—
198#11758198—22no—
199#11758198—22no—
200#11758198—22no—
201#11758198C22⋊C412yes—
202#11758198C22⋊C412yes—
203#11758198C22⋊C412yes—
204#11758198C22⋊C412yes—
205C4⋊Dic61—21no—
206C4⋊Dic61—21no—
207C4⋊Dic61—21no—
208C4⋊Dic61—21no—
209C4⋊Dic61—22no—
210C4⋊Dic61—22no—
211C4⋊Dic61C22⋊C412yes—
212C4⋊Dic61C22⋊C412yes—
213#11758196—21no—
214#11758196—21no—
215#11758196—21no—
216#11758196—21no—
217#11758196—21no—
218#11758196—21no—
219#11758196—21no—
220#11758196—21no—
221#11758196—22no—
222#11758196—22no—
223C4×Dic61—22no—
224C2×#92418—22no—
225C2×#92418—22no—
226#11758189—82no—
227#11758189—82no—
228#11758189—82no—
229C8×D61—82no—
230C23×C61—21no—
231C23×C61—22no—
232C23×C61—41no—
233C23×C61—41no—
234C23×C61C23×C411yescharacteristic
235C22×D61—22no—
236C22×D61—22no—
237C22×D61—41no—
238C22×D61—41no—
239C22×D61—41no—
240C22×D61—41no—
241C22×D61C2×C22⋊C412yes—
242C22×D61C2×C22⋊C412yes—
243C2×C4×C61—22no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—22no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61C2×C22⋊C411yescharacteristic
253C2×C4×C61C2×C22⋊C411yescharacteristic
254C2×C4×C61C2×C22⋊C411yescharacteristic
255C2×C4×C61C2×C22⋊C411yescharacteristic
256C2×C4×C61C22×D411yescharacteristic
257C2×C4×C61C22×D411yescharacteristic
258C22⋊D61—44no—
259C22⋊D61—82no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—21no—
263C2×Dic61—21no—
264C2×Dic61—22no—
265C2×Dic61—22no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270C2×Dic61—82no—
271C2×Dic61C2×C22⋊C412yes—
272C2×Dic61C2×C22⋊C412yes—
273D244—42no—
274D244—42no—
275C4×D61—42no—
276C4×D61—42no—
277C4×D61—42no—
278C4×D61—42no—
279C4×D61—44no—
280C4×D61—82no—
281Dic122—82no—
282C8×C61—42no—
283C8×C61—42no—
284#92418—42no—
285#92418—42no—
286#17406—611nomaximal, Sylow
287C22×C61—21no—
288C22×C61—21no—
289C22×C61—41no—
290C22×C61—41no—
291C22×C61—41no—
292C22×C61—82no—
293C22×C61C22×C22⋊C411yescharacteristic
294C22×C61#56812yes—
295C2×D61—22no—
296C2×D61—22no—
297C2×D61—22no—
298C2×D61—22no—
299C2×D61—22no—
300C2×D61—22no—
301C2×D61—44no—
302C2×D61—82no—
303C4×C61—21no—
304C4×C61—21no—
305C4×C61—21no—
306C4×C61—21no—
307C4×C61—21no—
308C4×C61—21no—
309C4×C61—41no—
310C4×C61—41no—
311C4×C61—41no—
312Dic61—22no—
313Dic61—22no—
314Dic61—41no—
315Dic61—41no—
316Dic61—41no—
317Dic61—41no—
318C2×#539—611no—
319#2975—611no—
320#2973—611no—
321#1473—611no—
322#1473D6111yescharacteristic, complemented
323#1472—612no—
324#1470—611no—
325#1470—611no—
326#1468—612no—
327#1465—612no—
328#1463—612no—
329C2×C61—22no—
330C2×C61—81no—
331C2×C61#287911yescharacteristic
332C2×C61#288311yescharacteristic
333C2×C61#288911yescharacteristic
334D61—42no—
335D61—42no—
336#539—1222no—
337#539—1222no—
338#539—1222no—
339#539—1222no—
340C2×#126—611no—
341C2×#126C2×D6111yescharacteristic
342C2×#125—611no—
343C2×#125—611no—
344C2×#123—611no—
345C2×#123—611no—
346C2×#123—611no—
347C2×#123—611no—
348C2×C22⋊Q8—611no—
349C2×C22⋊Q8—611no—
350C2×C22⋊Q8—611no—
351C2×#121—611no—
352C2×C4×D4—611no—
353C2×C4×D4—611no—
354C22×C4⋊C4—611no—
355#436—1222no—
356#436—1222no—
357#435—1222no—
358#435—1222no—
359#432—611no—
360#432C2×D6111yescharacteristic
361#431—611no—
362#431C2×D6111yescharacteristic
363#407—612no—
364#407—612no—
365#407—612no—
366C2×C22⋊C8—612no—
367#324—612no—
368#324—612no—
369#324—612no—
370#324—612no—
371#324—612no—
372#324C2×D6112yes—
373#323—612no—
374#323C2×D6112yes—
375C61#1740611yescharacteristic, complemented, Sylow
376C22×Q8—611no—
377C22×D4—611no—
378C22×D4—611no—
379C22×D4—611no—
380C23×C4—611no—
381C23×C4—611no—
382C23×C4—611no—
383C23×C4—611no—
384C23×C4—611no—
385C2×M16—1222no—
386C2×M16—1222no—
387C2×M16—1222no—
388C22×C8—1222no—
389#126—21no—
390#126—21no—
391#126—21no—
392#126—21no—
393#126—1222no—
394#126—1222no—
395#125—1222no—
396#125—1222no—
397#125—1221no—
398#125—1221no—
399#125—1221no—
400#125—1221no—
401#123—1222no—
402#123—1222no—
403#123—1222no—
404#123—1222no—
405#123—1222no—
406#123—1222no—
407#123—1222no—
408#123—1222no—
409C22⋊Q8—1222no—
410C22⋊Q8—1222no—
411C22⋊Q8—1222no—
412C22⋊Q8—1222no—
413C22⋊Q8—1222no—
414C22⋊Q8—1222no—
415#121—1222no—
416#121—1222no—
417C4×D4—612no—
418C4×D4—612no—
419C4×D4—612no—
420C4×D4—612no—
421C4×D4—1222no—
422C4×D4—1222no—
423C2×C4⋊C4—611no—
424C2×C4⋊C4—611no—
425C2×C4⋊C4—611no—
426C2×C4⋊C4—611no—
427C2×C4⋊C4—611no—
428C2×C4⋊C4—611no—
429C2×C4⋊C4—611no—
430C2×C4⋊C4—611no—
431C2×C4⋊C4—611no—
432C2×C4⋊C4—611no—
433C2×C4⋊C4—611no—
434C2×C4⋊C4—1222no—
435C2×C4⋊C4—1222no—
436C2×C4⋊C4C4×D6111yescharacteristic
437C2×C4⋊C4C4×D6111yescharacteristic
438C2×C4⋊C4C22×D6111yescharacteristic
439C2×C22⋊C4—611no—
440C2×C22⋊C4—611no—
441C2×C22⋊C4—611no—
442C2×C22⋊C4—611no—
443C2×C22⋊C4—611no—
444C2×C22⋊C4—611no—
445C2×C22⋊C4—611no—
446C2×C22⋊C4C4×D6111yescharacteristic
447C2×C22⋊C4C4×D6111yescharacteristic
448C2×C22⋊C4C22×D6111yescharacteristic
449C2×C42—611no—
450C2×C42C22×D6111yescharacteristic
451C4⋊C8—21no—
452C4⋊C8—21no—
453C4⋊C8—1221no—
454C4⋊C8—1221no—
455C22⋊C8—612no—
456C22⋊C8—612no—
457C22⋊C8—1222no—
458C22⋊C8—1222no—
459C22⋊C8—1222no—
460C22⋊C8—1222no—
461C22⋊C8C22×D6112yes—
462C22⋊C8C22×D6112yes—
463#97—21no—
464#97—1221no—
465C4×C8—21no—
466C4×C8—1221no—
467C24—611no—
468C24—611no—
469C24C2×C4×D6111yescharacteristic
470C2×Q8—1222no—
471C2×Q8—4881no—
472C2×D4—612no—
473C2×D4—612no—
474C2×D4—1222no—
475C2×D4—1222no—
476C2×D4—4881no—
477C2×D4—2442no—
478C2×D4—2442no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—612no—
482C22×C4—612no—
483C22×C4—612no—
484C22×C4—612no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—611no—
488C22×C4—611no—
489C22×C4—1222no—
490C22×C4—1222no—
491C22×C4—1222no—
492C22×C4—4881no—
493C22×C4—4881no—
494C22×C4—4881no—
495C22×C4—4881no—
496C22×C4—2442no—
497C22×C4C2×C4×D6111yescharacteristic
498C22×C4C2×C4×D6111yescharacteristic
499C22×C4C2×C4×D6111yescharacteristic
500C22×C4C2×C4×D6111yescharacteristic
501C22×C4C2×C4×D6111yescharacteristic
502C22×C4C23×D6111yescharacteristic
503M16—4882no—
504M16—4882no—
505M16—4882no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—1222no—
509C2×C8—1222no—
510C2×C8—4882no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—612no—
518C4⋊C4—612no—
519C4⋊C4—1222no—
520C4⋊C4—1222no—
521C4⋊C4—1222no—
522C4⋊C4—1222no—
523C4⋊C4—1221no—
524C4⋊C4—1221no—
525C4⋊C4—1221no—
526C4⋊C4—1221no—
527C4⋊C4—1221no—
528C4⋊C4—1221no—
529C4⋊C4—1221no—
530C4⋊C4—1221no—
531C4⋊C4—1221no—
532C4⋊C4—1221no—
533C4⋊C4—1221no—
534C4⋊C4—1221no—
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—21no—
540C22⋊C4—21no—
541C22⋊C4—612no—
542C22⋊C4—612no—
543C22⋊C4—612no—
544C22⋊C4—612no—
545C22⋊C4—1222no—
546C22⋊C4—1222no—
547C22⋊C4—1222no—
548C22⋊C4—1222no—
549C22⋊C4—1222no—
550C42—1222no—
551C42D4×D6111yescharacteristic
552C42D4×D6111yescharacteristic
553C42D4×D6111yescharacteristic
554C42D4×D6111yescharacteristic
555C23—21no—
556C23—22no—
557C23—41no—
558C23—41no—
559C23—612no—
560C23—612no—
561C23—1222no—
562C23—1222no—
563C23—2441no—
564C23—2441no—
565C23—2441no—
566C23—2441no—
567C23C22×C4×D6111yescharacteristic
568Q8—4882no—
569D4—4882no—
570D4—2442no—
571D4—2442no—
572D4—2444no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—612no—
583C2×C4—612no—
584C2×C4—1221no—
585C2×C4—1221no—
586C2×C4—1221no—
587C2×C4—1221no—
588C2×C4—1222no—
589C2×C4—1222no—
590C2×C4—4882no—
591C2×C4—4882no—
592C2×C4—2442no—
593C2×C4—2442no—
594C2×C4—2442no—
595C2×C4—2442no—
596C2×C4—2444no—
597C2×C4—2441no—
598C2×C4—2441no—
599C2×C4—2441no—
600C2×C4—2441no—
601C2×C4C22⋊C4×D6111yescharacteristic
602C2×C4C22⋊C4×D6111yescharacteristic
603C2×C4C22⋊C4×D6111yescharacteristic
604C2×C4C22⋊C4×D6111yescharacteristic
605C2×C4C2×D4×D6111yescharacteristic
606C2×C4C2×D4×D6111yescharacteristic
607C8—42no—
608C8—42no—
609C8—2442no—
610C8—2442no—
611C22—21no—
612C22—21no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—82no—
617C22—1222no—
618C22—1222no—
619C22—1222no—
620C22—1222no—
621C22—1222no—
622C22—1222no—
623C22—4882no—
624C22—2444no—
625C22C2×C22⋊C4×D6111yescharacteristic
626C22#1684052712yes—
627C4—21no—
628C4—21no—
629C4—21no—
630C4—21no—
631C4—21no—
632C4—21no—
633C4—41no—
634C4—41no—
635C4—41no—
636C4—1222no—
637C4—1222no—
638C4—2441no—
639C4—2441no—
640C4—2441no—
641C4—2441no—
642C2—22no—
643C2—81no—
644C2—2442no—
645C2—2442no—
646C2#2145426111yescharacteristic
647C2#2145427811yescharacteristic
648C2#2145430011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1473C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519750C4
cosocleC22×C4×C61C24
hypercenter#1473D61
hypocenterC61#17406
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1473

Complements

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

NH ≅ G/Ntype
2. #21454859C2semidirect
3. #21454847C2semidirect
4. #21444188C2semidirect
5. #21444181C2semidirect
6. #21444176C2semidirect
7. #21444174C2semidirect
8. #21444164C2semidirect
9. #21444154C2semidirect
10. #21444147C2semidirect
11. C61×#1473C2semidirect
322. #1473D61semidirect
375. C61#17406semidirect

Maximal subgroups

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

subgroupindex
C2×#168403532
#214548592
#214548472
#214441882
#214441812
#214441762
#214441742
#214441642
#214441542
#214441472
C61×#14732
#1740661