Finite Group Databasebeta

← #29585534

Subgroups — #29585534

Order 15616.

1178 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840528C211yesmaximal, characteristic
2#21454339C211yesmaximal, characteristic
3C2×#16839759C211yesmaximal, characteristic
4C2×#16839534C211yesmaximal, characteristic, complemented
5#21445530C211yesmaximal, characteristic, complemented
6#21445515C211yesmaximal, characteristic, complemented
7C2×C61×#341C211yesmaximal, 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#16839772—21no—
20#16839768—21no—
21#16839764C414yescomplemented
22#16839759—22no—
23#16839759—22no—
24#16839759C414yescomplemented
25C2×#14519702—21no—
26C2×#14519699—21no—
27#16839534—22no—
28#16839523—22no—
29#16839516—22no—
30C22×M16×C61C2211yescharacteristic
31C22×M16×C61C2211yescharacteristic
32C23×C8×C61C2211yescharacteristic
33C61×#341—22no—
34C2×#11758222—21no—
35C2×#11758222—21no—
36C2×#11758222—21no—
37C2×#11758222—21no—
38C2×#11758222—21no—
39C2×#11758222—21no—
40C2×#11758222C2×C412yes—
41C2×#11758222C2×C412yes—
42C2×#11758222C2×C412yes—
43C2×#11758222D412yes—
44C2×#11758222D412yes—
45C2×#11758222Q812yes—
46C22×Dic122D411yescharacteristic
47C22×D244D411yescharacteristic
48C22×C22⋊D61—21no—
49C22×C4×D61—21no—
50#14519785—28no—
51#14519785—28no—
52#14519783—28no—
53#14519783—28no—
54C2×#11758194—21no—
55C2×#11758194—21no—
56C2×#11758194—21no—
57C2×#11758194—21no—
58C2×#11758194C2×C412yes—
59C2×#11758194D412yes—
60C2×#11758189—24no—
61M16×D61—28no—
62M16×D61—28no—
63C22×#92418D412yes—
64C2×C8×D61—24no—
65#14519736—21no—
66#14519736—21no—
67#14519736—21no—
68#14519736—21no—
69#14519736—21no—
70#14519736—21no—
71#14519736—21no—
72#14519736C2×C412yes—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61C2×C412yes—
75C2×C22⋊Dic61—21no—
76C2×C22⋊Dic61—21no—
77C2×C4×Dic61—21no—
78C2×C4×Dic61—21no—
79#14519702—24no—
80#14519702—24no—
81#14519699—24no—
82#14519699—24no—
83C23×C4×C61C2311yescharacteristic
84C2×M16×C61—21no—
85C2×M16×C61—21no—
86C2×M16×C61—21no—
87C2×M16×C61—21no—
88C2×M16×C61—21no—
89C2×M16×C61—21no—
90C2×M16×C61—21no—
91C2×M16×C61—21no—
92C2×M16×C61C2×C412yes—
93C2×M16×C61C2×C412yes—
94C2×M16×C61D412yes—
95C2×M16×C61D412yes—
96C22×C8×C61—21no—
97C22×C8×C61—21no—
98C22×C8×C61—21no—
99C22×C8×C61—21no—
100C22×C8×C61—21no—
101C22×C8×C61—21no—
102C22×C8×C61—21no—
103C22×C8×C61—21no—
104C22×C8×C61C2×C412yes—
105C24×C61#4111yescharacteristic
106C23×D61—21no—
107C22×C4×C61C22×C411yescharacteristic
108C22×C4×C61C22×C411yescharacteristic
109C22×C4×C61C22×C411yescharacteristic
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61C2×D411yescharacteristic
114C22×C4×C61C2×D411yescharacteristic
115C22×C4×C61C2×D411yescharacteristic
116C22×C4×C61C2×D411yescharacteristic
117C22×C4×C61C2×Q811yescharacteristic
118C22×C4×C61#4111yescharacteristic
119C22×C4×C61#4111yescharacteristic
120C22×C4×C61#4111yescharacteristic
121C2×C22⋊D61—22no—
122C2×C22⋊D61—22no—
123C2×C22⋊D61—22no—
124C2×C22⋊D61—22no—
125C2×C22⋊D61—22no—
126C2×C22⋊D61—22no—
127C22×Dic61—21no—
128C22×Dic61—22no—
129C22×Dic61—41no—
130#11758222—22no—
131#11758222—22no—
132#11758222—22no—
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#11758222C4214yes—
143#11758222C22⋊C414yes—
144#11758222C4⋊C414yes—
145#11758222C4⋊C414yes—
146C2×D244—21no—
147C2×D244—21no—
148C2×D244—21no—
149C2×D244C22⋊C412yes—
150C2×D244C22⋊C412yes—
151C2×D244C4⋊C412yes—
152C2×C4×D61—22no—
153C2×C4×D61—22no—
154C2×C4×D61—22no—
155C2×C4×D61—22no—
156C2×C4×D61—22no—
157C2×C4×D61—22no—
158C2×Dic122—21no—
159C2×Dic122—21no—
160C2×Dic122—21no—
161C2×Dic122C22⋊C412yes—
162C2×Dic122C22⋊C412yes—
163C2×Dic122C4⋊C412yes—
164M16×C61—22no—
165M16×C61—22no—
166M16×C61—22no—
167M16×C61—22no—
168M16×C61—22no—
169M16×C61—41no—
170M16×C61—41no—
171M16×C61C22⋊C414yes—
172C2×C8×C61—22no—
173C2×C8×C61—22no—
174C2×C8×C61—22no—
175C2×C8×C61—22no—
176C2×C8×C61—22no—
177C2×C8×C61—22no—
178C2×C8×C61—22no—
179C2×C8×C61—41no—
180C2×C8×C61—41no—
181C2×C8×C61—41no—
182C2×C8×C61—41no—
183C2×C8×C61—41no—
184C2×C8×C61—41no—
185C22⋊Dic61—22no—
186C22⋊Dic61—41no—
187C22⋊Dic61—41no—
188C22⋊Dic61—41no—
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#11758194—22no—
201C2×#92418—22no—
202C2×#92418—22no—
203C2×#92418C22⋊C414yes—
204#11758189—216no—
205C8×D61—216no—
206C23×C61—42no—
207C23×C61#11711yescharacteristic
208C23×C61C4×D411yescharacteristic
209C23×C61C4×D411yescharacteristic
210C23×C61#12111yescharacteristic
211C23×C61C22⋊Q811yescharacteristic
212C23×C61#12311yescharacteristic
213C23×C61#12311yescharacteristic
214C22×D61—22no—
215C22×D61—22no—
216C22×D61—22no—
217C22×D61—82no—
218C2×C4×C61C2×C4211yescharacteristic
219C2×C4×C61C2×C22⋊C411yescharacteristic
220C2×C4×C61C2×C22⋊C411yescharacteristic
221C2×C4×C61C2×C22⋊C411yescharacteristic
222C2×C4×C61C2×C22⋊C411yescharacteristic
223C2×C4×C61C2×C22⋊C411yescharacteristic
224C2×C4×C61C2×C4⋊C411yescharacteristic
225C2×C4×C61C2×C4⋊C411yescharacteristic
226C2×C4×C61C2×C4⋊C411yescharacteristic
227C2×C4×C61#11711yescharacteristic
228C2×C4×C61C4×D411yescharacteristic
229C2×C4×C61C4×D411yescharacteristic
230C2×C4×C61C4×D411yescharacteristic
231C2×C4×C61C4×D411yescharacteristic
232C2×C4×C61C4×D411yescharacteristic
233C2×C4×C61C4×D411yescharacteristic
234C2×C4×C61#12011yescharacteristic
235C2×C4×C61#12011yescharacteristic
236C2×C4×C61#12011yescharacteristic
237C2×C4×C61#12011yescharacteristic
238C2×C4×C61#12111yescharacteristic
239C2×C4×C61#12111yescharacteristic
240C2×C4×C61#12111yescharacteristic
241C2×C4×C61C22⋊Q811yescharacteristic
242C2×C4×C61C22⋊Q811yescharacteristic
243C2×C4×C61C22⋊Q811yescharacteristic
244C2×C4×C61#12311yescharacteristic
245C2×C4×C61#12311yescharacteristic
246C22⋊D61—24no—
247C22⋊D61—24no—
248C22⋊D61—24no—
249C22⋊D61—24no—
250C2×Dic61—22no—
251C2×Dic61—22no—
252C2×Dic61—22no—
253C2×Dic61—44no—
254C2×Dic61—42no—
255C2×Dic61—42no—
256C2×Dic61—82no—
257D244—22no—
258D244—22no—
259D244—22no—
260D244#9514yes—
261C4×D61—24no—
262C4×D61—24no—
263C4×D61—24no—
264C4×D61—24no—
265Dic122—22no—
266Dic122—22no—
267Dic122—22no—
268Dic122#9514yes—
269C8×C61—24no—
270C8×C61—42no—
271C8×C61—42no—
272#92418—24no—
273#10782—611nomaximal, Sylow
274C22×C61—22no—
275C22×C61—22no—
276C22×C61—22no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61C4×C22⋊C411yescharacteristic
282C22×C61#38011yescharacteristic
283C22×C61#38111yescharacteristic
284C22×C61#38511yescharacteristic
285C22×C61#38511yescharacteristic
286C22×C61#38611yescharacteristic
287C22×C61#38611yescharacteristic
288C2×D61—24no—
289C2×D61—44no—
290C2×D61—82no—
291C2×D61—82no—
292C4×C61C2×#9511yescharacteristic
293C4×C61C4×C22⋊C411yescharacteristic
294C4×C61#37911yescharacteristic
295C4×C61#38011yescharacteristic
296C4×C61#38511yescharacteristic
297C4×C61#38511yescharacteristic
298C4×C61#38611yescharacteristic
299C4×C61#38611yescharacteristic
300Dic61—24no—
301Dic61—82no—
302Dic61—82no—
303C2×#568—611no—
304#2896—611no—
305C2×#416—611no—
306C2×#344—611no—
307C2×#341D6111yescharacteristic, complemented
308#1733—611no—
309#1729—611no—
310C2×C61—21no—
311C2×C61—21no—
312C2×C61—21no—
313C2×C61—21no—
314C2×C61—21no—
315C2×C61—21no—
316C2×C61C22⋊#9511yescharacteristic
317C2×C61#188112yes—
318D61—44no—
319C22×#41—611no—
320#568—614no—
321#568—1222no—
322#568—1222no—
323#568—1222no—
324C2×#131—1222no—
325C2×#131—1222no—
326C22×M16—611no—
327C22×M16—1222no—
328C22×M16C2×D6111yescharacteristic
329C22×M16C2×D6111yescharacteristic
330C23×C8C2×D6111yescharacteristic
331C2×#117—611no—
332C2×#117—611no—
333#419—1221no—
334#418—1221no—
335#417—614no—
336#416—614no—
337#416—1222no—
338#416—1222no—
339C2×#103—1221no—
340C2×#102—1221no—
341#344—1222no—
342#341—22no—
343#339—1222no—
344#336—1222no—
345C61#1078211yescharacteristic, complemented, Sylow
346C2×#41—612no—
347C2×#41—612no—
348C2×#41—612no—
349C2×#41—612no—
350C2×#41—612no—
351C2×#41—612no—
352C2×#41—1221no—
353C2×#41—1221no—
354C2×#41—1221no—
355C2×#41—1221no—
356C2×#41—1221no—
357C2×#41—1221no—
358C22×Q8—611no—
359C22×D4—611no—
360C22×D4—1221no—
361C23×C4—1221no—
362C23×C4C22×D6111yescharacteristic
363#131—1228no—
364#131—1228no—
365#131—1228no—
366#131—1228no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—612no—
376C2×M16—612no—
377C2×M16—1224no—
378C2×M16—1228no—
379C2×M16—1221no—
380C2×M16—1221no—
381C2×M16—1221no—
382C2×M16—1221no—
383C2×M16—1228no—
384C2×M16C4×D6112yes—
385C2×M16C4×D6112yes—
386C2×M16D24412yes—
387C2×M16C22⋊D6112yes—
388C22×C8—21no—
389C22×C8—21no—
390C22×C8—21no—
391C22×C8—21no—
392C22×C8—21no—
393C22×C8—21no—
394C22×C8—21no—
395C22×C8—21no—
396C22×C8—612no—
397C22×C8—1224no—
398C22×C8C4×D6112yes—
399#117—612no—
400#117—1221no—
401#117—1221no—
402#117—1221no—
403#117—1221no—
404#117—1221no—
405#117—1221no—
406#117—1221no—
407C2×C4⋊C4—612no—
408C2×C4⋊C4—1221no—
409C2×C22⋊C4—1221no—
410C2×C22⋊C4—1221no—
411C2×C42—1221no—
412C2×C42—1221no—
413#103—1224no—
414#103—1224no—
415#102—1224no—
416#102—1224no—
417C24—1221no—
418C24#1175822611yescharacteristic
419#41—614no—
420#41—614no—
421#41—614no—
422#41—614no—
423#41—1222no—
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—
435C2×Q8—612no—
436C2×Q8—612no—
437C2×Q8—612no—
438C2×Q8—1221no—
439C2×Q8—1221no—
440C2×Q8—1221no—
441C2×D4—612no—
442C2×D4—612no—
443C2×D4—612no—
444C2×D4—1222no—
445C2×D4—1222no—
446C2×D4—1222no—
447C2×D4—1222no—
448C2×D4—1222no—
449C2×D4—1222no—
450C2×D4—1221no—
451C2×D4—1221no—
452C2×D4—1221no—
453C22×C4—1221no—
454C22×C4—1222no—
455C22×C4—1222no—
456C22×C4—1222no—
457C22×C4—1222no—
458C22×C4—1222no—
459C22×C4—1222no—
460C22×C4—1222no—
461C22×C4—2441no—
462C22×C4C2×C4×D6111yescharacteristic
463C22×C4C2×C4×D6111yescharacteristic
464C22×C4C2×C4×D6111yescharacteristic
465C22×C4C2×D24411yescharacteristic
466C22×C4#1175822211yescharacteristic
467C22×C4#1175822211yescharacteristic
468C22×C4D4×D6111yescharacteristic
469C22×C4D4×D6111yescharacteristic
470C22×C4D4×D6111yescharacteristic
471C22×C4D4×D6111yescharacteristic
472C22×C4D4×D6111yescharacteristic
473C22×C4#1175822411yescharacteristic
474C22×C4Q8×D6111yescharacteristic
475C22×C4C2×C22⋊D6111yescharacteristic
476M16—22no—
477M16—22no—
478M16—22no—
479M16—22no—
480M16—22no—
481M16—41no—
482M16—41no—
483M16—12216no—
484M16—1222no—
485M16—1222no—
486M16—1222no—
487M16—1222no—
488M16#1175819814yes—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8—41no—
500C2×C8—41no—
501C2×C8—41no—
502C2×C8—614no—
503C2×C8—12216no—
504C2×C8—1222no—
505C2×C8—1222no—
506C4⋊C4—1222no—
507C4⋊C4—1222no—
508C4⋊C4—1222no—
509C4⋊C4—2441no—
510C22⋊C4—1222no—
511C22⋊C4—2441no—
512C22⋊C4—2441no—
513C22⋊C4—2441no—
514C42—1222no—
515C42—2441no—
516C42—2441no—
517C42—2441no—
518C23—42no—
519C23—1222no—
520C23—1222no—
521C23—1222no—
522C23—4882no—
523C23#1451973511yescharacteristic
524C23#1451973911yescharacteristic
525C23#1451973911yescharacteristic
526C23#1451975211yescharacteristic
527C23#1451975311yescharacteristic
528C23#1451976211yescharacteristic
529C23#1451976211yescharacteristic
530Q8—614no—
531Q8—1222no—
532Q8—1222no—
533Q8—1222no—
534D4—614no—
535D4—1224no—
536D4—1224no—
537D4—1224no—
538D4—1224no—
539D4—1222no—
540D4—1222no—
541D4—1222no—
542C2×C4—1222no—
543C2×C4—1222no—
544C2×C4—1222no—
545C2×C4—1224no—
546C2×C4—1224no—
547C2×C4—1224no—
548C2×C4—1224no—
549C2×C4—4882no—
550C2×C4—2444no—
551C2×C4—2442no—
552C2×C4—2442no—
553C2×C4C42×D6111yescharacteristic
554C2×C4C22⋊C4×D6111yescharacteristic
555C2×C4C22⋊C4×D6111yescharacteristic
556C2×C4C22⋊C4×D6111yescharacteristic
557C2×C4C22⋊C4×D6111yescharacteristic
558C2×C4C2×#1175819811yescharacteristic
559C2×C4C4⋊C4×D6111yescharacteristic
560C2×C4C4⋊C4×D6111yescharacteristic
561C2×C4C4⋊C4×D6111yescharacteristic
562C2×C4#1451973411yescharacteristic
563C2×C4#1451973711yescharacteristic
564C2×C4#1451973711yescharacteristic
565C2×C4C4×C22⋊D6111yescharacteristic
566C2×C4C4×C22⋊D6111yescharacteristic
567C2×C4C4×D24411yescharacteristic
568C2×C4C4×D24411yescharacteristic
569C2×C4#1451974511yescharacteristic
570C2×C4#1451974511yescharacteristic
571C2×C4#1451974711yescharacteristic
572C2×C4#1451974711yescharacteristic
573C2×C4#1451974811yescharacteristic
574C2×C4#1451975011yescharacteristic
575C2×C4#1451975011yescharacteristic
576C2×C4#1451975511yescharacteristic
577C2×C4#1451975511yescharacteristic
578C2×C4#1451975711yescharacteristic
579C2×C4#1451975911yescharacteristic
580C2×C4#1451975911yescharacteristic
581C8—24no—
582C8—42no—
583C8—42no—
584C8—1224no—
585C22—22no—
586C22—22no—
587C22—22no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—1224no—
593C22—4882no—
594C22—4882no—
595C22—2444no—
596C22#1683960911yescharacteristic
597C22#1683961911yescharacteristic
598C22#1683962411yescharacteristic
599C22#1683963311yescharacteristic
600C22#1683963311yescharacteristic
601C22#1683964011yescharacteristic
602C22#1683964011yescharacteristic
603C4—1224no—
604C4—4882no—
605C4—4882no—
606C4#95×D6111yescharacteristic
607C4C4×#1175819811yescharacteristic
608C4#1683961711yescharacteristic
609C4#1683962111yescharacteristic
610C4#1683963611yescharacteristic
611C4#1683963611yescharacteristic
612C4#1683963811yescharacteristic
613C4#1683963811yescharacteristic
614C2—21no—
615C2—21no—
616C2—21no—
617C2—21no—
618C2—21no—
619C2—21no—
620C2—2444no—
621C2#2144404011yescharacteristic
622C2#2144618212yes—
subgroupG/H
centerC2×C4#14519747
commutatorC2×C4×C61C2×C42
FrattiniC23×C4C22×D61
FittingC2×C61×#341C2
socleC22×C61#386
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenterC2×#341D61
hypocenterC61#10782
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#341

Complements

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

NH ≅ G/Ntype
4. C2×#16839534C2semidirect
5. #21445530C2semidirect
6. #21445515C2semidirect
7. C2×C61×#341C2semidirect
12. #16840528C4semidirect
21. #16839764C4semidirect
24. #16839759C4semidirect
307. C2×#341D61semidirect
345. C61#10782semidirect

Maximal subgroups

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

subgroupindex
C2×#168405282
#214543392
C2×#168397592
C2×#168395342
#214455302
#214455152
C2×C61×#3412
#1078261