Finite Group Databasebeta

← #30610683

Subgroups — #30610683

Order 15616.

1036 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462495C211yesmaximal, characteristic, complemented
2C2×#16840765C211yesmaximal, characteristic, complemented
3#21461174C214yesmaximal, complemented
4#21461149C212yesmaximal, complemented
5#21461144C212yesmaximal, complemented
6#21461134C214yesmaximal, complemented
7C2×#16840293C211yesmaximal, characteristic
8C22×#11758217—21no—
9#16840783—21no—
10#16840782—21no—
11#16840779C2212yes—
12#16840778C2212yescomplemented
13#16840765—21no—
14#16840765—21no—
15#16840765—21no—
16#16840765C2212yes—
17#16840765C2212yescomplemented
18C2×#14519844—21no—
19C2×C4⋊#92420C2212yescomplemented
20#16840732—21no—
21C4×#11758217C2212yescomplemented
22#16840612C2218yescomplemented
23D4⋊#92420C2218yescomplemented
24#16840293—21no—
25#16840293—21no—
26#16840293—21no—
27#16840293—21no—
28#16840293C412yes—
29#16840293C412yes—
30#16840293C2212yes—
31#16840293C2212yes—
32C2×#14519770—21no—
33C2×#14519768C411yescharacteristic
34C2×#14519764C411yescharacteristic
35C2×#14519758—21no—
36C2×#14519756C411yescharacteristic
37C2×#14519742C2211yescharacteristic
38C2×D4×Dic61—21no—
39C2×D4×Dic61C2211yescharacteristic
40C2×#14519733—21no—
41C22×C4×Dic61C2211yescharacteristic
42C2×#121×C61C411yescharacteristic
43C2×#11758217—22no—
44C2×#11758217—22no—
45C2×#11758217—22no—
46C2×#11758217—44no—
47C22×#92420—22no—
48#14519844—22no—
49#14519844—22no—
50#14519844—22no—
51C4⋊#92420—22no—
52C4⋊#92420—22no—
53C4⋊#92420C2314yes—
54C22⋊#92420—22no—
55C22⋊#92420—22no—
56#14519832—22no—
57C4×#92420C2314yes—
58C22×Dic122C2×C411yescharacteristic
59C23×Dic61—21no—
60C23×Dic61D411yescharacteristic
61C23×Dic61D411yescharacteristic
62#14519770—22no—
63#14519770—22no—
64#14519770—22no—
65#14519770—22no—
66#14519768—21no—
67#14519768—21no—
68#14519768C2×C412yes—
69#14519768C2×C412yes—
70#14519764—21no—
71#14519764—21no—
72#14519764C2×C412yes—
73#14519764C2×C412yes—
74#14519758—22no—
75#14519758—22no—
76#14519758—22no—
77#14519758—22no—
78#14519756—21no—
79#14519756—21no—
80#14519756C2×C412yes—
81#14519756C2×C412yes—
82#14519742—21no—
83#14519742—21no—
84#14519742C2×C412yes—
85#14519742C2312yes—
86D4×Dic61—22no—
87D4×Dic61—22no—
88D4×Dic61—22no—
89D4×Dic61—22no—
90D4×Dic61—21no—
91D4×Dic61—21no—
92D4×Dic61C2×C412yes—
93D4×Dic61C2312yes—
94#14519733—22no—
95#14519733—22no—
96#14519733—22no—
97#14519733—22no—
98C2×C4⋊Dic61—21no—
99C2×C4⋊Dic61C2×C411yescharacteristic
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×#11758196—21no—
103C2×C22⋊Dic61—21no—
104C2×C22⋊Dic61—21no—
105C2×C22⋊Dic61—21no—
106C2×C22⋊Dic61—21no—
107C2×C4×Dic61—21no—
108C2×C4×Dic61C2×C411yescharacteristic
109C2×C4×Dic61C2×C411yescharacteristic
110C2×C4×Dic61C2×C411yescharacteristic
111C2×C4×Dic61D411yescharacteristic
112C2×C4×Dic61D411yescharacteristic
113C2×C4×Dic61D411yescharacteristic
114C2×C4×Dic61D411yescharacteristic
115C2×C4×Dic61D411yescharacteristic
116C2×C4×Dic61D411yescharacteristic
117C2×C4×Dic61C2311yescharacteristic
118C2×C4×Dic61C2311yescharacteristic
119C2×C4×Dic61C2311yescharacteristic
120C22×D4×C61—21no—
121C22×D4×C61C2×C411yescharacteristic
122C23×C4×C61C2×C411yescharacteristic
123#121×C61—21no—
124#121×C61—21no—
125#121×C61C2×C412yes—
126#121×C61C2×C412yes—
127C2×C4⋊C4×C61C2×C411yescharacteristic
128C2×C22⋊C4×C61—21no—
129C24×C61—21no—
130C24×C61C22⋊C411yescharacteristic
131C2×D4×C61—22no—
132C2×D4×C61—22no—
133C2×D4×C61—21no—
134C2×D4×C61—42no—
135C2×D4×C61—44no—
136C2×D4×C61C22×C412yes—
137C22×C4×C61—21no—
138C22×C4×C61—42no—
139C22×C4×C61C22⋊C411yescharacteristic
140C22×C4×C61C22⋊C411yescharacteristic
141C22×C4×C61C22⋊C411yescharacteristic
142C22×C4×C61C22×C411yescharacteristic
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C22×C411yescharacteristic
145C22×Dic61—22no—
146C22×Dic61—22no—
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—22no—
150C22×Dic61—22no—
151C22×Dic61—42no—
152C22×Dic61—42no—
153C22×Dic61—42no—
154C22×Dic61C22⋊C411yescharacteristic
155C22×Dic61C22⋊C411yescharacteristic
156C22×Dic61C22⋊C411yescharacteristic
157C22×Dic61C22⋊C411yescharacteristic
158C22×Dic61C22⋊C411yescharacteristic
159C22×Dic61C22⋊C411yescharacteristic
160C22×Dic61C2×D411yescharacteristic
161C22×Dic61C2×D411yescharacteristic
162C22×Dic61C2×D411yescharacteristic
163C22×Dic61C2×D411yescharacteristic
164C22×Dic61C2×D411yescharacteristic
165C22×Dic61C2×D411yescharacteristic
166C2×Dic122—21no—
167C2×Dic122—42no—
168C2×Dic122C22×C412yes—
169#11758217—44no—
170#11758217—44no—
171#11758217—44no—
172C2×#92420—24no—
173C2×#92420—24no—
174C2×#92420—44no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61C22×C412yes—
177C22⋊C4×C61—22no—
178C22⋊C4×C61—22no—
179C22⋊Dic61—22no—
180C22⋊Dic61—22no—
181C22⋊Dic61—22no—
182C22⋊Dic61—22no—
183C22⋊Dic61—22no—
184C22⋊Dic61—22no—
185C22⋊Dic61—22no—
186C22⋊Dic61—22no—
187C4⋊Dic61—21no—
188C4⋊Dic61—22no—
189C4⋊Dic61—22no—
190C4⋊Dic61C22×C412yes—
191#11758196—22no—
192#11758196—22no—
193#11758196—22no—
194#11758196—22no—
195#11758196—22no—
196#11758196—22no—
197C4×Dic61—22no—
198C4×Dic61—22no—
199C4×Dic61C22⋊C411yescharacteristic
200C4×Dic61C22⋊C411yescharacteristic
201C4×Dic61C22⋊C411yescharacteristic
202C4×Dic61C22⋊C411yescharacteristic
203C4×Dic61C22⋊C411yescharacteristic
204C4×Dic61C22⋊C411yescharacteristic
205C4×Dic61C22×C411yescharacteristic
206C4×Dic61C22×C411yescharacteristic
207C4×Dic61C22×C411yescharacteristic
208C4×Dic61C2×D411yescharacteristic
209C4×Dic61C2×D411yescharacteristic
210C4×Dic61C2×D411yescharacteristic
211C4×Dic61C2×D411yescharacteristic
212C4×Dic61C2×D411yescharacteristic
213C4×Dic61C2×D411yescharacteristic
214C4×Dic61C2411yescharacteristic
215C23×C61—22no—
216C23×C61—22no—
217C23×C61—22no—
218C23×C61—41no—
219C23×C61—42no—
220C23×C61—42no—
221C23×C61—42no—
222C23×C61C2×C22⋊C411yescharacteristic
223C23×C61C2×C22⋊C411yescharacteristic
224C23×C61C2×C22⋊C411yescharacteristic
225D4×C61—24no—
226D4×C61—42no—
227D4×C61—44no—
228D4×C61—44no—
229C2×C4×C61—22no—
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—42no—
237C2×C4×C61C2×C22⋊C411yescharacteristic
238C2×C4×C61C2×C22⋊C411yescharacteristic
239C2×C4×C61C2×C22⋊C411yescharacteristic
240C2×C4×C61C23×C411yescharacteristic
241C2×Dic61—22no—
242C2×Dic61—22no—
243C2×Dic61—22no—
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—22no—
249C2×Dic61—22no—
250C2×Dic61—22no—
251C2×Dic61—22no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—42no—
257C2×Dic61—42no—
258C2×Dic61—42no—
259C2×Dic61—42no—
260C2×Dic61—44no—
261C2×Dic61C2×C22⋊C411yescharacteristic
262C2×Dic61C2×C22⋊C411yescharacteristic
263C2×Dic61C2×C22⋊C411yescharacteristic
264C2×Dic61C2×C22⋊C411yescharacteristic
265C2×Dic61C2×C22⋊C411yescharacteristic
266C2×Dic61C2×C22⋊C411yescharacteristic
267C2×Dic61AGL(1,ℤ/8)12yes—
268C2×Dic61#13712yes—
269C2×Dic61C22×D411yescharacteristic
270C2×Dic61C22×D411yescharacteristic
271Dic122—24no—
272Dic122—42no—
273#92420—44no—
274#92420—44no—
275#17492—611nomaximal, Sylow
276C22×C61—21no—
277C22×C61—21no—
278C22×C61—21no—
279C22×C61—21no—
280C22×C61—21no—
281C22×C61—21no—
282C22×C61—21no—
283C22×C61—44no—
284C22×C61—42no—
285C22×C61—42no—
286C22×C61—42no—
287C22×C61—84no—
288C22×C61#41712yes—
289C22×C61#42112yes—
290C22×C61C22×C22⋊C411yescharacteristic
291C4×C61—21no—
292C4×C61—21no—
293C4×C61—21no—
294C4×C61—42no—
295C4×C61#56812yes—
296Dic61—21no—
297Dic61—21no—
298Dic61—21no—
299Dic61—21no—
300Dic61—21no—
301Dic61—21no—
302Dic61—42no—
303Dic61—42no—
304Dic61#41712yes—
305Dic61C2×AGL(1,ℤ/8)11yescharacteristic
306Dic61C2×#13711yescharacteristic
307C2×#529—611no—
308#2920—611no—
309C2×#423—611no—
310#1495—614no—
311#1487—612no—
312#1486—612no—
313#1483—614no—
314C2×C61—22no—
315C2×C61—22no—
316C2×C61—41no—
317C2×C61—82no—
318C2×C61#287911yescharacteristic
319C2×C61C2×#41711yescharacteristic
320C2×C61C2×#42111yescharacteristic
321C22×M16—1221no—
322#529—612no—
323#529—612no—
324#529—612no—
325#529—612no—
326#529—1221no—
327#529—1221no—
328#529—1221no—
329#529—1221no—
330C2×#126—1221no—
331C2×#125—611no—
332C2×#124—611no—
333C2×#123—1221no—
334C2×C22⋊Q8—611no—
335C2×#121#692311yescharacteristic
336C2×C4×Q8—611no—
337C2×C4×D4—611no—
338C2×C4×D4—1221no—
339C2×#117—1221no—
340C22×C42—611no—
341#432—1221no—
342#432—1221no—
343#431—612no—
344#431—612no—
345#423—612no—
346#423—612no—
347#423—1221no—
348#423—1221no—
349#423—1221no—
350C2×C4⋊C8—612no—
351C2×C4⋊C8—1221no—
352#407—1221no—
353C4×M16—612no—
354Q8⋊C8—618no—
355D4⋊C8—618no—
356C61#1749211yescharacteristic, complemented, Sylow
357C22×Q8—611no—
358C22×D4—21no—
359C22×D4C2×#692311yescharacteristic
360C23×C4—611no—
361C23×C4—611no—
362C23×C4—1221no—
363C23×C4C2×#692311yescharacteristic
364C2×M16—1222no—
365C2×M16—1222no—
366C2×M16—1222no—
367C2×M16—2444no—
368C22×C8—1222no—
369#126—1222no—
370#126—1222no—
371#126—1222no—
372#126—1222no—
373#125—612no—
374#125—612no—
375#125—1221no—
376#125—1221no—
377#124—612no—
378#124—612no—
379#124—1221no—
380#124—1221no—
381#123—1222no—
382#123—1222no—
383#123—1222no—
384#123—1222no—
385C22⋊Q8—612no—
386C22⋊Q8—612no—
387C22⋊Q8—1221no—
388C22⋊Q8—1221no—
389#121—21no—
390#121—21no—
391#121C2×#692312yes—
392#121C2×#692312yes—
393C4×Q8—612no—
394C4×Q8—612no—
395C4×Q8—1221no—
396C4×Q8—1221no—
397C4×D4—612no—
398C4×D4—612no—
399C4×D4—1221no—
400C4×D4—1221no—
401C4×D4—1222no—
402C4×D4—1222no—
403C4×D4—1222no—
404C4×D4—1222no—
405#117—1222no—
406#117—1222no—
407#117—1222no—
408#117—1222no—
409C2×C4⋊C4—611no—
410C2×C4⋊C4—1221no—
411C2×C4⋊C4—1221no—
412C2×C4⋊C4—1221no—
413C2×C4⋊C4—1221no—
414C2×C4⋊C4C2×#692311yescharacteristic
415C2×C22⋊C4—21no—
416C2×C22⋊C4—1221no—
417C2×C22⋊C4—1221no—
418C2×C22⋊C4—1221no—
419C2×C22⋊C4—1221no—
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×C42—611no—
432C2×C42—1221no—
433C4⋊C8—614no—
434C4⋊C8—1222no—
435C4⋊C8—1222no—
436C4⋊C8—1222no—
437C4⋊C8—1222no—
438C4⋊C8—1222no—
439C22⋊C8—1222no—
440C22⋊C8—1222no—
441#97—1222no—
442C4×C8—614no—
443C24—21no—
444C24C22⋊#692311yescharacteristic
445C2×Q8—612no—
446C2×Q8—1221no—
447C2×Q8—2442no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—21no—
451C2×D4—42no—
452C2×D4—44no—
453C2×D4C22×#692312yes—
454C22×C4—21no—
455C22×C4—42no—
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—611no—
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—2442no—
477C22×C4C22⋊#692311yescharacteristic
478C22×C4C22⋊#692311yescharacteristic
479C22×C4C22⋊#692311yescharacteristic
480C22×C4C22×#692311yescharacteristic
481C22×C4C22×#692311yescharacteristic
482C22×C4C22×#692311yescharacteristic
483M16—2444no—
484M16—2444no—
485M16—2444no—
486C2×C8—1224no—
487C2×C8—1224no—
488C2×C8—2444no—
489C4⋊C4—21no—
490C4⋊C4—612no—
491C4⋊C4—1222no—
492C4⋊C4—1222no—
493C4⋊C4—1222no—
494C4⋊C4—1222no—
495C4⋊C4—1222no—
496C4⋊C4—1222no—
497C4⋊C4—1221no—
498C4⋊C4—1222no—
499C4⋊C4—1222no—
500C4⋊C4C22×#692312yes—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—1222no—
504C22⋊C4—1222no—
505C22⋊C4—1222no—
506C22⋊C4—1222no—
507C22⋊C4—1222no—
508C22⋊C4—1222no—
509C22⋊C4—1222no—
510C22⋊C4—1222no—
511C42—611no—
512C42—611no—
513C42—611no—
514C42—611no—
515C42—611no—
516C42—611no—
517C42—611no—
518C42—611no—
519C42—611no—
520C42—611no—
521C42—611no—
522C42—611no—
523C42—611no—
524C42—611no—
525C42—611no—
526C42—611no—
527C42—1222no—
528C42—1222no—
529C23—22no—
530C23—22no—
531C23—22no—
532C23—41no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23C2×C22⋊#692311yescharacteristic
537C23C2×C22⋊#692311yescharacteristic
538C23C2×C22⋊#692311yescharacteristic
539Q8—1224no—
540Q8—2442no—
541D4—24no—
542D4—42no—
543D4—44no—
544D4—44no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—42no—
553C2×C4—612no—
554C2×C4—612no—
555C2×C4—611no—
556C2×C4—611no—
557C2×C4—611no—
558C2×C4—611no—
559C2×C4—611no—
560C2×C4—611no—
561C2×C4—611no—
562C2×C4—611no—
563C2×C4—1221no—
564C2×C4—1221no—
565C2×C4—1221no—
566C2×C4—1221no—
567C2×C4—1222no—
568C2×C4—1222no—
569C2×C4—1222no—
570C2×C4—1222no—
571C2×C4—1222no—
572C2×C4—1222no—
573C2×C4—1222no—
574C2×C4—2442no—
575C2×C4—2442no—
576C2×C4—2444no—
577C2×C4—2441no—
578C2×C4—2441no—
579C2×C4—2441no—
580C2×C4—2441no—
581C2×C4—2442no—
582C2×C4—2442no—
583C2×C4C2×C22⋊#692311yescharacteristic
584C2×C4C2×C22⋊#692311yescharacteristic
585C2×C4C2×C22⋊#692311yescharacteristic
586C2×C4C23×#692311yescharacteristic
587C8—2444no—
588C8—2444no—
589C22—21no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—44no—
597C22—42no—
598C22—42no—
599C22—42no—
600C22—84no—
601C22#1684075312yes—
602C22#1684076012yes—
603C22C22×C22⋊#692311yescharacteristic
604C4—21no—
605C4—21no—
606C4—21no—
607C4—42no—
608C4—611no—
609C4—611no—
610C4—612no—
611C4—1221no—
612C4—1221no—
613C4—1221no—
614C4—1221no—
615C4—1221no—
616C4—1221no—
617C4—2442no—
618C4—2442no—
619C4#1684084012yes—
620C2—22no—
621C2—22no—
622C2—41no—
623C2—82no—
624C2#2146240311yescharacteristic
625C2C2×#1684075311yescharacteristic
626C2C2×#1684076011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
Fitting, prime radicalC2×#121×C61C4
socleC22×C61C22×C22⋊C4
cosocleC4×Dic61C24
hypercenterC2×#121#6923
hypocenterC61#17492
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #21462495C2semidirect
2. C2×#16840765C2semidirect
3. #21461174C2semidirect
4. #21461149C2semidirect
5. #21461144C2semidirect
6. #21461134C2semidirect
12. #16840778C22semidirect
17. #16840765C22semidirect
19. C2×C4⋊#92420C22semidirect
21. C4×#11758217C22semidirect
22. #16840612C22semidirect
23. D4⋊#92420C22semidirect
356. C61#17492semidirect

Maximal subgroups

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

subgroupindex
#214624952
C2×#168407652
#214611742
#214611492
#214611442
#214611342
C2×#168402932
#1749261