Finite Group Databasebeta

← #29585387

Subgroups — #29585387

Order 15616.

1254 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840528C211yesmaximal, characteristic
2C2×#16839735C211yesmaximal, characteristic
3#21448309C211yesmaximal, characteristic
4#21445530C211yesmaximal, characteristic, complemented
5#21445529C211yesmaximal, characteristic, complemented
6C2×#16839522C211yesmaximal, characteristic, complemented
7C2×C61×#339C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9#16840528—22no—
10#16840528—22no—
11#16840528—22no—
12#16840528C414yescomplemented
13C2×#14519785—22no—
14C2×#14519783—22no—
15C22×#11758194C2211yescharacteristic
16C2×M16×D61—22no—
17C2×#14519736C2211yescharacteristic
18C2×#14519736C2211yescharacteristic
19#16839735—22no—
20#16839735C414yescomplemented
21C2×#14519691—22no—
22#16839668C412yescomplemented
23#16839664C412yescomplemented
24#16839641—22no—
25C4×#11758198—22no—
26#16839523—22no—
27#16839522—22no—
28#16839522—22no—
29C22×M16×C61C2211yescharacteristic
30C2×#117×C61C2211yescharacteristic
31C22×C42×C61C2211yescharacteristic
32C61×#339—22no—
33C2×#11758222—21no—
34C2×#11758222—21no—
35C2×#11758222—21no—
36C2×#11758222—21no—
37C2×#11758222—21no—
38C2×#11758222—21no—
39C2×#11758222—21no—
40C2×#11758222—21no—
41C2×#11758222C2×C412yes—
42C2×#11758222C2×C412yes—
43C2×#11758222D412yes—
44C2×#11758222Q812yes—
45C22×Dic122C2×C411yescharacteristic
46C22×D244C2×C411yescharacteristic
47C22×C22⋊D61D412yes—
48C22×C4×D61D412yes—
49#14519785—28no—
50#14519785—28no—
51#14519783—28no—
52#14519783—28no—
53C2×#11758194—21no—
54C2×#11758194—21no—
55C2×#11758194—21no—
56C2×#11758194C2×C412yes—
57C2×#11758194D412yes—
58C2×#11758194D412yes—
59C2×#11758189—24no—
60M16×D61—28no—
61M16×D61—28no—
62C22×#92418—21no—
63C2×C8×D61—24no—
64#14519736—21no—
65#14519736—21no—
66#14519736—21no—
67#14519736—21no—
68#14519736—21no—
69#14519736—21no—
70#14519736—21no—
71#14519736C2×C412yes—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61C2×C412yes—
74C2×C22⋊Dic61—21no—
75C2×C22⋊Dic61—21no—
76C2×#11758198—24no—
77C2×C4×Dic61—21no—
78C2×C4×Dic61—21no—
79#14519691—28no—
80#14519684—24no—
81C23×C4×C61—21no—
82C23×C4×C61C2311yescharacteristic
83C2×M16×C61—21no—
84C2×M16×C61—21no—
85C2×M16×C61—21no—
86C2×M16×C61C2×C412yes—
87C2×M16×C61D412yes—
88C2×M16×C61D412yes—
89C22×C8×C61—21no—
90#117×C61—21no—
91#117×C61—21no—
92#117×C61—21no—
93#117×C61C2×C412yes—
94C2×C4⋊C4×C61—21no—
95C2×C22⋊C4×C61—21no—
96C2×C42×C61—21no—
97C2×C42×C61—21no—
98C2×C42×C61—21no—
99C2×C42×C61—21no—
100C2×C42×C61—21no—
101C2×C42×C61—21no—
102C2×C42×C61C2×C412yes—
103C24×C61C2×D411yescharacteristic
104C23×D61C22⋊C412yes—
105C22×C4×C61—22no—
106C22×C4×C61—44no—
107C22×C4×C61—41no—
108C22×C4×C61—41no—
109C22×C4×C61—41no—
110C22×C4×C61C22×C411yescharacteristic
111C22×C4×C61C22×C411yescharacteristic
112C22×C4×C61C22×C411yescharacteristic
113C22×C4×C61C2×D411yescharacteristic
114C22×C4×C61C2×D411yescharacteristic
115C22×C4×C61C2×D411yescharacteristic
116C22×C4×C61C2×D411yescharacteristic
117C22×C4×C61C2×D411yescharacteristic
118C22×C4×C61C2×D411yescharacteristic
119C22×C4×C61C2×Q811yescharacteristic
120C22×C4×C61#4111yescharacteristic
121C22×C4×C61#4111yescharacteristic
122C22×C4×C61#4111yescharacteristic
123C22×C4×C61#4111yescharacteristic
124C2×C22⋊D61—22no—
125C2×C22⋊D61—22no—
126C2×C22⋊D61—22no—
127C2×C22⋊D61—22no—
128C2×C22⋊D61C22⋊C414yes—
129C2×C22⋊D61C4⋊C414yes—
130C22×Dic61—22no—
131C22×Dic61—41no—
132C22×Dic61C22⋊C412yes—
133#11758222—22no—
134#11758222—22no—
135#11758222—22no—
136#11758222—22no—
137#11758222—22no—
138#11758222—22no—
139#11758222—22no—
140#11758222—22no—
141#11758222—22no—
142#11758222—22no—
143#11758222—22no—
144#11758222—22no—
145#11758222—22no—
146#11758222—22no—
147#11758222—22no—
148#11758222—22no—
149C2×D244—21no—
150C2×D244—21no—
151C2×D244—21no—
152C2×D244—21no—
153C2×D244C4212yes—
154C2×D244C4⋊C412yes—
155C2×C4×D61—22no—
156C2×C4×D61—22no—
157C2×C4×D61—22no—
158C2×C4×D61—22no—
159C2×C4×D61C22⋊C414yes—
160C2×C4×D61C4⋊C414yes—
161C2×Dic122—21no—
162C2×Dic122—21no—
163C2×Dic122—21no—
164C2×Dic122—21no—
165C2×Dic122C4212yes—
166C2×Dic122C4⋊C412yes—
167M16×C61—22no—
168M16×C61—22no—
169M16×C61—22no—
170M16×C61C22⋊C414yescomplemented
171C2×C8×C61—22no—
172C2×C8×C61—22no—
173C2×C8×C61—22no—
174C4⋊C4×C61—22no—
175C4⋊C4×C61—41no—
176C22⋊C4×C61—22no—
177C22⋊C4×C61—41no—
178C42×C61—22no—
179C42×C61—22no—
180C42×C61—22no—
181C42×C61—41no—
182C42×C61—41no—
183C42×C61—41no—
184C22⋊Dic61—22no—
185C22⋊Dic61—41no—
186C22⋊Dic61—41no—
187C22⋊Dic61—41no—
188#11758198—48no—
189C4⋊Dic61—22no—
190C4⋊Dic61—22no—
191C4⋊Dic61—22no—
192C4⋊Dic61—41no—
193C4×Dic61—22no—
194C4×Dic61—41no—
195C4×Dic61—41no—
196C4×Dic61—41no—
197#11758194—22no—
198#11758194—22no—
199#11758194—22no—
200#11758194C22⋊C414yescomplemented
201C2×#92418—22no—
202C2×#92418—22no—
203C2×#92418—22no—
204#11758189—216no—
205C8×D61—216no—
206C23×C61—42no—
207C23×C61C2×C22⋊C411yescharacteristic
208C23×C61C2×C22⋊C411yescharacteristic
209C23×C61C2×C4⋊C411yescharacteristic
210C23×C61#12111yescharacteristic
211C23×C61#12111yescharacteristic
212C23×C61#12111yescharacteristic
213C23×C61#12111yescharacteristic
214C22×D61—22no—
215C22×D61—22no—
216C22×D61—44no—
217C22×D61#9514yes—
218C2×C4×C61—24no—
219C2×C4×C61—42no—
220C2×C4×C61—44no—
221C2×C4×C61—44no—
222C2×C4×C61—42no—
223C2×C4×C61—42no—
224C2×C4×C61—82no—
225C2×C4×C61C2×C4211yescharacteristic
226C2×C4×C61C2×C22⋊C411yescharacteristic
227C2×C4×C61C2×C22⋊C411yescharacteristic
228C2×C4×C61C2×C22⋊C411yescharacteristic
229C2×C4×C61C2×C4⋊C411yescharacteristic
230C2×C4×C61C2×C4⋊C411yescharacteristic
231C2×C4×C61#11711yescharacteristic
232C2×C4×C61#11711yescharacteristic
233C2×C4×C61C4×D411yescharacteristic
234C2×C4×C61C4×D411yescharacteristic
235C2×C4×C61C4×D411yescharacteristic
236C2×C4×C61C4×D411yescharacteristic
237C2×C4×C61C4×D411yescharacteristic
238C2×C4×C61C4×D411yescharacteristic
239C2×C4×C61C4×D411yescharacteristic
240C2×C4×C61C4×D411yescharacteristic
241C2×C4×C61#12011yescharacteristic
242C2×C4×C61#12011yescharacteristic
243C2×C4×C61#12011yescharacteristic
244C2×C4×C61#12011yescharacteristic
245C2×C4×C61C22⋊Q811yescharacteristic
246C2×C4×C61C22⋊Q811yescharacteristic
247C2×C4×C61C22⋊Q811yescharacteristic
248C2×C4×C61C22⋊Q811yescharacteristic
249C2×C4×C61#12311yescharacteristic
250C2×C4×C61#12311yescharacteristic
251C2×C4×C61#12311yescharacteristic
252C2×C4×C61#12311yescharacteristic
253C22⋊D61—24no—
254C22⋊D61—24no—
255C22⋊D61—24no—
256C22⋊D61—24no—
257C2×Dic61—22no—
258C2×Dic61—22no—
259C2×Dic61—44no—
260C2×Dic61—42no—
261C2×Dic61—42no—
262C2×Dic61—82no—
263C2×Dic61#9514yes—
264D244—22no—
265D244—22no—
266D244—22no—
267D244—22no—
268C4×D61—24no—
269C4×D61—24no—
270C4×D61—24no—
271C4×D61—24no—
272Dic122—22no—
273Dic122—22no—
274Dic122—22no—
275Dic122—22no—
276C8×C61—24no—
277#92418—24no—
278#10751—611nomaximal, Sylow
279C22×C61—22no—
280C22×C61—22no—
281C22×C61—22no—
282C22×C61—41no—
283C22×C61—41no—
284C22×C61—41no—
285C22×C61—41no—
286C22×C61C2×#9511yescharacteristic
287C22×C61#38011yescharacteristic
288C22×C61#38011yescharacteristic
289C22×C61#38611yescharacteristic
290C22×C61#38611yescharacteristic
291C22×C61#38611yescharacteristic
292C22×C61#38611yescharacteristic
293C2×D61—24no—
294C2×D61—44no—
295C2×D61—44no—
296C2×D61—82no—
297C4×C61—44no—
298C4×C61—82no—
299C4×C61C4×C22⋊C411yescharacteristic
300C4×C61C4×C22⋊C411yescharacteristic
301C4×C61#37911yescharacteristic
302C4×C61#38111yescharacteristic
303C4×C61#38511yescharacteristic
304C4×C61#38511yescharacteristic
305C4×C61#38511yescharacteristic
306C4×C61#38511yescharacteristic
307Dic61—24no—
308Dic61—82no—
309Dic61—82no—
310C2×#568—611no—
311C2×#410—611no—
312#2297—611no—
313#1733—611no—
314#1733—611no—
315C2×#339—611no—
316C2×#339D6111yescharacteristic, complemented
317C2×C61—21no—
318C2×C61—21no—
319C2×C61—21no—
320C2×C61—21no—
321C2×C61—21no—
322C2×C61—21no—
323C2×C61C22⋊#9511yescharacteristic
324C2×C61#188412yes—
325D61—44no—
326C22×#41—611no—
327#568—614no—
328#568—1222no—
329#568—1222no—
330#568—1222no—
331C2×#131—1222no—
332C2×#131—1222no—
333C22×M16—611no—
334C22×M16—1222no—
335C22×M16C2×D6111yescharacteristic
336C2×#117—611no—
337C2×#117—611no—
338C2×#117C2×D6111yescharacteristic
339C22×C42C2×D6111yescharacteristic
340#410—614no—
341#410—1222no—
342C2×#99—1222no—
343#391—612no—
344#390—612no—
345#386—1222no—
346C4×C22⋊C4—1222no—
347#339—22no—
348#339—1222no—
349#339—1222no—
350#339—1222no—
351C61#1075111yescharacteristic, complemented, Sylow
352C2×#41—612no—
353C2×#41—612no—
354C2×#41—612no—
355C2×#41—612no—
356C2×#41—1221no—
357C2×#41—1221no—
358C2×#41—1221no—
359C2×#41—1221no—
360C2×#41—1221no—
361C2×#41—1221no—
362C2×#41—1221no—
363C2×#41—1221no—
364C22×Q8—611no—
365C22×D4—612no—
366C22×D4—611no—
367C23×C4—21no—
368C23×C4—612no—
369C23×C4C22×D6111yescharacteristic
370#131—1228no—
371#131—1228no—
372#131—1228no—
373#131—1228no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16—612no—
378C2×M16—612no—
379C2×M16—612no—
380C2×M16—1224no—
381C2×M16—1228no—
382C2×M16—1228no—
383C2×M16—1221no—
384C2×M16—1221no—
385C2×M16—1221no—
386C2×M16C4×D6112yes—
387C2×M16D24412yes—
388C2×M16C22⋊D6112yes—
389C22×C8—21no—
390C22×C8—1224no—
391C22×C8—1221no—
392#117—21no—
393#117—21no—
394#117—21no—
395#117—612no—
396#117—1221no—
397#117—1221no—
398#117—1221no—
399#117—1221no—
400#117—1221no—
401#117—1221no—
402#117—1221no—
403#117C4×D6112yes—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—612no—
406C2×C4⋊C4—1221no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—1221no—
409C2×C22⋊C4—1224no—
410C2×C22⋊C4—1221no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42—21no—
414C2×C42—21no—
415C2×C42—21no—
416C2×C42—21no—
417C2×C42—1221no—
418C2×C42—1221no—
419C2×C42C4×D6112yes—
420#99—1228no—
421#95—1224no—
422C24—612no—
423C24D4×D6111yescharacteristic
424#41—1222no—
425#41—1222no—
426#41—1222no—
427#41—1222no—
428#41—1222no—
429#41—1222no—
430#41—1222no—
431#41—1222no—
432#41—1222no—
433#41—1222no—
434#41—1222no—
435#41—1222no—
436#41—1222no—
437#41—1222no—
438#41—1222no—
439#41—1222no—
440C2×Q8—612no—
441C2×Q8—612no—
442C2×Q8—1221no—
443C2×Q8—1221no—
444C2×Q8—1221no—
445C2×Q8—1221no—
446C2×D4—614no—
447C2×D4—614no—
448C2×D4—612no—
449C2×D4—612no—
450C2×D4—1222no—
451C2×D4—1222no—
452C2×D4—1222no—
453C2×D4—1222no—
454C2×D4—1221no—
455C2×D4—1221no—
456C2×D4—1221no—
457C2×D4—1221no—
458C22×C4—22no—
459C22×C4—44no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—612no—
464C22×C4—614no—
465C22×C4—614no—
466C22×C4—1222no—
467C22×C4—1222no—
468C22×C4—1222no—
469C22×C4—1222no—
470C22×C4—1222no—
471C22×C4—2441no—
472C22×C4C2×C4×D6111yescharacteristic
473C22×C4C2×C4×D6111yescharacteristic
474C22×C4C2×C4×D6111yescharacteristic
475C22×C4C2×D24411yescharacteristic
476C22×C4#1175822211yescharacteristic
477C22×C4#1175822211yescharacteristic
478C22×C4D4×D6111yescharacteristic
479C22×C4D4×D6111yescharacteristic
480C22×C4D4×D6111yescharacteristic
481C22×C4D4×D6111yescharacteristic
482C22×C4#1175822411yescharacteristic
483C22×C4Q8×D6111yescharacteristic
484C22×C4#1175822611yescharacteristic
485C22×C4C2×C22⋊D6111yescharacteristic
486M16—22no—
487M16—22no—
488M16—22no—
489M16—614no—
490M16—12216no—
491M16—1222no—
492M16—1222no—
493M16—1222no—
494M16#1175819814yescomplemented
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—12216no—
499C2×C8—1222no—
500C2×C8—1222no—
501C2×C8—1222no—
502C4⋊C4—22no—
503C4⋊C4—41no—
504C4⋊C4—1222no—
505C4⋊C4—1222no—
506C4⋊C4—1222no—
507C4⋊C4—2441no—
508C22⋊C4—22no—
509C22⋊C4—41no—
510C22⋊C4—1222no—
511C22⋊C4—2448no—
512C22⋊C4—2441no—
513C22⋊C4—2441no—
514C22⋊C4—2441no—
515C42—22no—
516C42—22no—
517C42—22no—
518C42—41no—
519C42—41no—
520C42—41no—
521C42—1222no—
522C42—2441no—
523C42—2441no—
524C42—2441no—
525C23—42no—
526C23—614no—
527C23—1222no—
528C23—1222no—
529C23—2444no—
530C23C22⋊C4×D6111yescharacteristic
531C23C22⋊C4×D6111yescharacteristic
532C23C4⋊C4×D6111yescharacteristic
533C23#1451974811yescharacteristic
534C23#1451975011yescharacteristic
535C23#1451975011yescharacteristic
536C23#1451975211yescharacteristic
537Q8—1222no—
538Q8—1222no—
539Q8—1222no—
540Q8—1222no—
541D4—1224no—
542D4—1224no—
543D4—1224no—
544D4—1224no—
545D4—1222no—
546D4—1222no—
547D4—1222no—
548D4—1222no—
549C2×C4—24no—
550C2×C4—42no—
551C2×C4—44no—
552C2×C4—44no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—82no—
556C2×C4—614no—
557C2×C4—1222no—
558C2×C4—1222no—
559C2×C4—1224no—
560C2×C4—1224no—
561C2×C4—1224no—
562C2×C4—1224no—
563C2×C4—4882no—
564C2×C4—2444no—
565C2×C4—2442no—
566C2×C4—2442no—
567C2×C4C42×D6111yescharacteristic
568C2×C4C22⋊C4×D6111yescharacteristic
569C2×C4C22⋊C4×D6111yescharacteristic
570C2×C4C2×#1175819811yescharacteristic
571C2×C4C4⋊C4×D6111yescharacteristic
572C2×C4C4⋊C4×D6111yescharacteristic
573C2×C4#1451973411yescharacteristic
574C2×C4#1451973511yescharacteristic
575C2×C4#1451973711yescharacteristic
576C2×C4#1451973711yescharacteristic
577C2×C4C4×C22⋊D6111yescharacteristic
578C2×C4C4×C22⋊D6111yescharacteristic
579C2×C4#1451973911yescharacteristic
580C2×C4#1451973911yescharacteristic
581C2×C4C4×D24411yescharacteristic
582C2×C4C4×D24411yescharacteristic
583C2×C4#1451974511yescharacteristic
584C2×C4#1451974511yescharacteristic
585C2×C4#1451974711yescharacteristic
586C2×C4#1451974711yescharacteristic
587C2×C4#1451975311yescharacteristic
588C2×C4#1451975511yescharacteristic
589C2×C4#1451975511yescharacteristic
590C2×C4#1451975711yescharacteristic
591C2×C4#1451975911yescharacteristic
592C2×C4#1451975911yescharacteristic
593C2×C4#1451976211yescharacteristic
594C2×C4#1451976211yescharacteristic
595C8—24no—
596C8—1224no—
597C22—22no—
598C22—22no—
599C22—22no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—1224no—
605C22—4882no—
606C22—2444no—
607C22—2444no—
608C22#95×D6111yescharacteristic
609C22#1683961911yescharacteristic
610C22#1683962111yescharacteristic
611C22#1683963811yescharacteristic
612C22#1683963811yescharacteristic
613C22#1683964011yescharacteristic
614C22#1683964011yescharacteristic
615C4—44no—
616C4—82no—
617C4—1224no—
618C4—4882no—
619C4—4882no—
620C4#1683960911yescharacteristic
621C4C4×#1175819811yescharacteristic
622C4#1683961711yescharacteristic
623C4#1683962411yescharacteristic
624C4#1683963311yescharacteristic
625C4#1683963311yescharacteristic
626C4#1683963611yescharacteristic
627C4#1683963611yescharacteristic
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—21no—
633C2—21no—
634C2—2444no—
635C2#2144404011yescharacteristic
636C2#2144620112yes—
subgroupG/H
centerC2×C4#14519747
commutatorC2×C4×C61C2×C42
FrattiniC23×C4C22×D61
FittingC2×C61×#339C2
socleC22×C61#386
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenterC2×#339D61
hypocenterC61#10751
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
4. #21445530C2semidirect
5. #21445529C2semidirect
6. C2×#16839522C2semidirect
7. C2×C61×#339C2semidirect
12. #16840528C4semidirect
20. #16839735C4semidirect
22. #16839668C4semidirect
23. #16839664C4semidirect
170. M16×C61C22⋊C4semidirect
200. #11758194C22⋊C4semidirect
316. C2×#339D61semidirect
351. C61#10751semidirect
494. M16#11758198semidirect

Maximal subgroups

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

subgroupindex
C2×#168405282
C2×#168397352
#214483092
#214455302
#214455292
C2×#168395222
C2×C61×#3392
#1075161