Finite Group Databasebeta

← #29679680

Subgroups — #29679680

Order 15616.

1308 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840528C211yesmaximal, characteristic
2C2×#16839810C211yesmaximal, characteristic, complemented
3#21454408C211yesmaximal, characteristic, complemented
4C2×#16839780C211yesmaximal, characteristic
5C2×#16839778C211yesmaximal, characteristic
6#21445872C218yesmaximal, complemented
7C2×#16839534C211yesmaximal, characteristic, complemented
8C2×C61×#344C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10#16840528—22no—
11#16840528—22no—
12#16840528C414yescomplemented
13#16840528C414yescomplemented
14C2×#14519785C2214yes—
15C2×#14519783—22no—
16C22×#11758194C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C2×M16×D61—22no—
19C2×#14519736C2211yescharacteristic
20#16839810—22no—
21#16839810—22no—
22C2×#14519712C2214yescomplemented
23#16839805—22no—
24#16839802—22no—
25#16839798C2214yescomplemented
26#16839780—22no—
27#16839780C2214yes—
28#16839778—22no—
29#16839778C2214yes—
30C2×#14519705—22no—
31C2×#14519703—22no—
32#16839534C2214yescomplemented
33C22×M16×C61C2211yescharacteristic
34C22×M16×C61C2211yescharacteristic
35C2×#117×C61C2211yescharacteristic
36C61×#344C2214yescomplemented
37C2×#11758222—21no—
38C2×#11758222—21no—
39C2×#11758222—21no—
40C2×#11758222—21no—
41C2×#11758222—21no—
42C2×#11758222—21no—
43C2×#11758222C2×C412yes—
44C2×#11758222C2×C412yes—
45C2×#11758222D412yes—
46C2×#11758222D412yes—
47C2×#11758222Q812yes—
48C2×#11758222C2312yes—
49C22×Dic122Q811yescharacteristic
50C22×D244Q811yescharacteristic
51C22×C22⋊D61—21no—
52C22×C4×D61—21no—
53#14519785—28no—
54#14519785C2×C4116yescomplemented
55#14519783—28no—
56#14519783—28no—
57C2×#11758194—21no—
58C2×#11758194—21no—
59C2×#11758194—21no—
60C2×#11758194—21no—
61C2×#11758194—21no—
62C2×#11758194C2×C412yes—
63C2×#11758194C2×C412yes—
64C2×#11758194D412yes—
65C2×#11758194D412yes—
66C2×#11758194D412yes—
67C2×#11758194D412yes—
68C2×#11758194C2312yes—
69C2×#11758189—24no—
70M16×D61—28no—
71M16×D61—28no—
72C22×#92418—21no—
73C22×#92418C2312yes—
74C2×C8×D61—24no—
75#14519736—21no—
76#14519736—21no—
77#14519736—21no—
78#14519736C2312yes—
79C2×C4⋊Dic61—21no—
80C2×C22⋊Dic61—21no—
81C2×C4×Dic61—21no—
82#14519712—28no—
83#14519710—24no—
84#14519708—24no—
85#14519705—28no—
86#14519703—28no—
87C23×C4×C61C2311yescharacteristic
88C2×M16×C61—21no—
89C2×M16×C61—21no—
90C2×M16×C61—21no—
91C2×M16×C61—21no—
92C2×M16×C61—21no—
93C2×M16×C61—21no—
94C2×M16×C61—21no—
95C2×M16×C61—21no—
96C2×M16×C61C2×C412yes—
97C2×M16×C61C2×C412yes—
98C2×M16×C61C2312yes—
99C2×M16×C61C2312yes—
100C22×C8×C61—21no—
101C22×C8×C61—21no—
102#117×C61—21no—
103#117×C61—21no—
104#117×C61—21no—
105#117×C61C2312yes—
106C2×C4⋊C4×C61—21no—
107C2×C22⋊C4×C61—21no—
108C2×C42×C61—21no—
109C24×C61#4111yescharacteristic
110C23×D61—21no—
111C22×C4×C61—41no—
112C22×C4×C61C22×C411yescharacteristic
113C22×C4×C61C22×C411yescharacteristic
114C22×C4×C61C2×D411yescharacteristic
115C22×C4×C61C2×D411yescharacteristic
116C22×C4×C61C2×D411yescharacteristic
117C22×C4×C61C2×D411yescharacteristic
118C22×C4×C61C2×D411yescharacteristic
119C22×C4×C61C2×D411yescharacteristic
120C22×C4×C61C2×Q811yescharacteristic
121C22×C4×C61C2×Q811yescharacteristic
122C22×C4×C61#4111yescharacteristic
123C22×C4×C61#4111yescharacteristic
124C22×C4×C61#4111yescharacteristic
125C22×C4×C61C2411yescharacteristic
126C2×C22⋊D61—22no—
127C2×C22⋊D61—22no—
128C2×C22⋊D61—22no—
129C2×C22⋊D61—22no—
130C2×C22⋊D61—22no—
131C2×C22⋊D61—22no—
132C22×Dic61—21no—
133C22×Dic61—41no—
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#11758222C4⋊C414yes—
147#11758222C4⋊C414yes—
148#11758222C22×C414yes—
149#11758222C2×D414yes—
150C2×D244—21no—
151C2×D244—21no—
152C2×D244—21no—
153C2×D244C4⋊C412yes—
154C2×D244C4⋊C412yes—
155C2×D244C2×Q812yes—
156C2×C4×D61—22no—
157C2×C4×D61—22no—
158C2×C4×D61—22no—
159C2×C4×D61—22no—
160C2×C4×D61—22no—
161C2×C4×D61—22no—
162C2×Dic122—21no—
163C2×Dic122—21no—
164C2×Dic122—21no—
165C2×Dic122C4⋊C412yes—
166C2×Dic122C4⋊C412yes—
167C2×Dic122C2×Q812yes—
168M16×C61—22no—
169M16×C61—22no—
170M16×C61—22no—
171M16×C61—22no—
172M16×C61—22no—
173M16×C61—41no—
174M16×C61—41no—
175M16×C61C22×C414yes—
176C2×C8×C61—22no—
177C2×C8×C61—22no—
178C2×C8×C61—22no—
179C2×C8×C61—22no—
180C2×C8×C61—41no—
181C2×C8×C61—41no—
182C4⋊C4×C61—22no—
183C4⋊C4×C61—41no—
184C22⋊C4×C61—22no—
185C22⋊C4×C61—41no—
186C42×C61—22no—
187C42×C61—41no—
188C22⋊Dic61—22no—
189C22⋊Dic61—41no—
190C4⋊Dic61—22no—
191C4⋊Dic61—41no—
192C4×Dic61—22no—
193C4×Dic61—41no—
194#11758194—22no—
195#11758194—22no—
196#11758194—41no—
197#11758194—41no—
198#11758194C22⋊C414yes—
199#11758194C22⋊C414yes—
200#11758194C22⋊C414yes—
201#11758194C22⋊C414yes—
202C2×#92418—22no—
203C2×#92418—41no—
204C2×#92418—41no—
205C2×#92418C22×C414yes—
206C2×#92418C2×D414yes—
207C2×#92418C2×D414yes—
208#11758189—216no—
209C8×D61—216no—
210C23×C61—81no—
211C23×C61#11711yescharacteristic
212C23×C61#11711yescharacteristic
213C23×C61#12111yescharacteristic
214C23×C61#12111yescharacteristic
215C23×C61C22⋊Q811yescharacteristic
216C23×C61C22⋊Q811yescharacteristic
217C23×C61C2×#4111yescharacteristic
218C22×D61—22no—
219C22×D61—22no—
220C22×D61—22no—
221C22×D61—82no—
222C2×C4×C61—42no—
223C2×C4×C61—82no—
224C2×C4×C61C2×C22⋊C411yescharacteristic
225C2×C4×C61C2×C22⋊C411yescharacteristic
226C2×C4×C61C2×C22⋊C411yescharacteristic
227C2×C4×C61C2×C22⋊C411yescharacteristic
228C2×C4×C61C2×C4⋊C411yescharacteristic
229C2×C4×C61C2×C4⋊C411yescharacteristic
230C2×C4×C61C2×C4⋊C411yescharacteristic
231C2×C4×C61C2×C4⋊C411yescharacteristic
232C2×C4×C61#11711yescharacteristic
233C2×C4×C61#11711yescharacteristic
234C2×C4×C61#12111yescharacteristic
235C2×C4×C61#12111yescharacteristic
236C2×C4×C61#12111yescharacteristic
237C2×C4×C61#12111yescharacteristic
238C2×C4×C61#12111yescharacteristic
239C2×C4×C61#12111yescharacteristic
240C2×C4×C61C22⋊Q811yescharacteristic
241C2×C4×C61C22⋊Q811yescharacteristic
242C2×C4×C61C22⋊Q811yescharacteristic
243C2×C4×C61C22⋊Q811yescharacteristic
244C2×C4×C61C22⋊Q811yescharacteristic
245C2×C4×C61C22⋊Q811yescharacteristic
246C2×C4×C61C23×C411yescharacteristic
247C2×C4×C61C22×D411yescharacteristic
248C2×C4×C61C22×D411yescharacteristic
249C2×C4×C61C22×D411yescharacteristic
250C2×C4×C61C22×Q811yescharacteristic
251C2×C4×C61C2×#4111yescharacteristic
252C22⋊D61—24no—
253C22⋊D61—24no—
254C22⋊D61—24no—
255C22⋊D61—24no—
256C2×Dic61—22no—
257C2×Dic61—22no—
258C2×Dic61—22no—
259C2×Dic61—42no—
260C2×Dic61—82no—
261D244—22no—
262D244—22no—
263D244—22no—
264D244C2×C4⋊C414yes—
265C4×D61—24no—
266C4×D61—24no—
267C4×D61—24no—
268C4×D61—24no—
269Dic122—22no—
270Dic122—22no—
271Dic122—22no—
272Dic122C2×C4⋊C414yes—
273C8×C61—24no—
274C8×C61—42no—
275#92418—42no—
276#92418C2×C22⋊C418yes—
277#20675—611nomaximal, Sylow
278C22×C61—41no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61—41no—
282C22×C61—41no—
283C22×C61—41no—
284C22×C61—41no—
285C22×C61#38011yescharacteristic
286C22×C61#38011yescharacteristic
287C22×C61#38011yescharacteristic
288C22×C61#38011yescharacteristic
289C22×C61C2×#11711yescharacteristic
290C22×C61C2×#12111yescharacteristic
291C22×C61C2×C22⋊Q811yescharacteristic
292C2×D61—24no—
293C2×D61—44no—
294C2×D61—82no—
295C2×D61—82no—
296C4×C61—82no—
297C4×C61#38011yescharacteristic
298C4×C61#38011yescharacteristic
299C4×C61#38011yescharacteristic
300C4×C61#38011yescharacteristic
301C4×C61C22×C22⋊C411yescharacteristic
302C4×C61C22×C4⋊C411yescharacteristic
303C4×C61C2×#12111yescharacteristic
304C4×C61C2×C22⋊Q811yescharacteristic
305Dic61—24no—
306Dic61—82no—
307C2×#568—611no—
308C2×#430—611no—
309#2911—611no—
310C2×#421—611no—
311C2×#421—611no—
312#1814—618no—
313C2×#344—611no—
314C2×#344D6111yescharacteristic, complemented
315C2×C61—21no—
316C2×C61—21no—
317C2×C61—21no—
318C2×C61—21no—
319C2×C61—21no—
320C2×C61—21no—
321C2×C61—21no—
322C2×C61C2×#38011yescharacteristic
323D61—44no—
324C22×#41—611no—
325#568—614no—
326#568—614no—
327#568—1222no—
328#568—1222no—
329C2×#131—614no—
330C2×#131—1222no—
331C22×M16—611no—
332C22×M16—611no—
333C22×M16—1222no—
334C22×M16C2×D6111yescharacteristic
335C22×M16C2×D6111yescharacteristic
336C2×#117—611no—
337C2×#117C2×D6111yescharacteristic
338#430—1222no—
339#430—1222no—
340C2×#108—614no—
341#428—1222no—
342#428—1222no—
343#427—614no—
344#421—614no—
345#421—614no—
346#421—1222no—
347#421—1222no—
348C2×#104—1222no—
349C2×#104—1222no—
350#344—614no—
351#344C2×D6114yescomplemented
352C61#2067511yescharacteristic, complemented, Sylow
353C2×#41—612no—
354C2×#41—612no—
355C2×#41—612no—
356C2×#41—612no—
357C2×#41—612no—
358C2×#41—612no—
359C2×#41—1221no—
360C2×#41—1221no—
361C2×#41—1221no—
362C2×#41—1221no—
363C2×#41—1221no—
364C2×#41—1221no—
365C22×Q8—611no—
366C22×D4—611no—
367C22×D4—1221no—
368C23×C4—1221no—
369C23×C4C22×D6111yescharacteristic
370#131—6116no—
371#131—1228no—
372#131—1228no—
373#131—1228no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16—21no—
379C2×M16—21no—
380C2×M16—21no—
381C2×M16—21no—
382C2×M16—612no—
383C2×M16—612no—
384C2×M16—612no—
385C2×M16—612no—
386C2×M16—612no—
387C2×M16—612no—
388C2×M16—612no—
389C2×M16—1224no—
390C2×M16—1228no—
391C2×M16—1228no—
392C2×M16—1221no—
393C2×M16—1221no—
394C2×M16—1221no—
395C2×M16—1221no—
396C2×M16—1221no—
397C2×M16C4×D6112yes—
398C2×M16C4×D6112yes—
399C2×M16C22×D6112yes—
400C2×M16C22×D6112yes—
401C22×C8—21no—
402C22×C8—21no—
403C22×C8—612no—
404C22×C8—1224no—
405C22×C8—1221no—
406#117—21no—
407#117—21no—
408#117—21no—
409#117—612no—
410#117—1221no—
411#117—1221no—
412#117—1221no—
413#117C22×D6112yes—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—1221no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—1221no—
418C2×C42—21no—
419C2×C42—1221no—
420#108—1228no—
421#107—1224no—
422#106—1224no—
423#104—1228no—
424#104—1228no—
425C24—1221no—
426C24#1175822211yescharacteristic
427#41—614no—
428#41—614no—
429#41—614no—
430#41—614no—
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—
440#41—1222no—
441#41—1222no—
442#41—1222no—
443C2×Q8—612no—
444C2×Q8—612no—
445C2×Q8—612no—
446C2×Q8—1221no—
447C2×Q8—1221no—
448C2×Q8—1221no—
449C2×D4—612no—
450C2×D4—612no—
451C2×D4—612no—
452C2×D4—1222no—
453C2×D4—1222no—
454C2×D4—1222no—
455C2×D4—1222no—
456C2×D4—1222no—
457C2×D4—1222no—
458C2×D4—1221no—
459C2×D4—1221no—
460C2×D4—1221no—
461C22×C4—41no—
462C22×C4—1221no—
463C22×C4—1222no—
464C22×C4—1222no—
465C22×C4—1222no—
466C22×C4—1222no—
467C22×C4—1222no—
468C22×C4—1222no—
469C22×C4—2441no—
470C22×C4C2×C4×D6111yescharacteristic
471C22×C4C2×C4×D6111yescharacteristic
472C22×C4#1175822211yescharacteristic
473C22×C4#1175822211yescharacteristic
474C22×C4#1175822211yescharacteristic
475C22×C4D4×D6111yescharacteristic
476C22×C4D4×D6111yescharacteristic
477C22×C4D4×D6111yescharacteristic
478C22×C4D4×D6111yescharacteristic
479C22×C4D4×D6111yescharacteristic
480C22×C4D4×D6111yescharacteristic
481C22×C4Q8×D6111yescharacteristic
482C22×C4Q8×D6111yescharacteristic
483C22×C4C23×D6111yescharacteristic
484M16—22no—
485M16—22no—
486M16—22no—
487M16—22no—
488M16—22no—
489M16—41no—
490M16—41no—
491M16—614no—
492M16—614no—
493M16—614no—
494M16—614no—
495M16—12216no—
496M16—1222no—
497M16—1222no—
498M16—2441no—
499M16—2441no—
500M16C2×C4×D6114yes—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—41no—
506C2×C8—41no—
507C2×C8—614no—
508C2×C8—614no—
509C2×C8—614no—
510C2×C8—12216no—
511C2×C8—1222no—
512C2×C8—2441no—
513C2×C8—2441no—
514C4⋊C4—22no—
515C4⋊C4—41no—
516C4⋊C4—1222no—
517C4⋊C4—2441no—
518C22⋊C4—22no—
519C22⋊C4—41no—
520C22⋊C4—1222no—
521C22⋊C4—2441no—
522C42—22no—
523C42—41no—
524C42—1222no—
525C42—2441no—
526C23—81no—
527C23—1222no—
528C23—1222no—
529C23—1222no—
530C23—4882no—
531C23#1451973411yescharacteristic
532C23#1451973411yescharacteristic
533C23#1451975011yescharacteristic
534C23#1451975011yescharacteristic
535C23#1451975511yescharacteristic
536C23#1451975511yescharacteristic
537C23C2×#1175822211yescharacteristic
538Q8—614no—
539Q8—1222no—
540Q8—1222no—
541Q8—1222no—
542D4—614no—
543D4—1224no—
544D4—1224no—
545D4—1224no—
546D4—1224no—
547D4—1222no—
548D4—1222no—
549D4—1222no—
550C2×C4—42no—
551C2×C4—82no—
552C2×C4—1222no—
553C2×C4—1222no—
554C2×C4—1222no—
555C2×C4—1224no—
556C2×C4—1224no—
557C2×C4—1224no—
558C2×C4—1224no—
559C2×C4—4882no—
560C2×C4—2442no—
561C2×C4C22⋊C4×D6111yescharacteristic
562C2×C4C22⋊C4×D6111yescharacteristic
563C2×C4C22⋊C4×D6111yescharacteristic
564C2×C4C22⋊C4×D6111yescharacteristic
565C2×C4C4⋊C4×D6111yescharacteristic
566C2×C4C4⋊C4×D6111yescharacteristic
567C2×C4C4⋊C4×D6111yescharacteristic
568C2×C4C4⋊C4×D6111yescharacteristic
569C2×C4#1451973411yescharacteristic
570C2×C4#1451973411yescharacteristic
571C2×C4#1451975011yescharacteristic
572C2×C4#1451975011yescharacteristic
573C2×C4#1451975011yescharacteristic
574C2×C4#1451975011yescharacteristic
575C2×C4#1451975011yescharacteristic
576C2×C4#1451975011yescharacteristic
577C2×C4#1451975511yescharacteristic
578C2×C4#1451975511yescharacteristic
579C2×C4#1451975511yescharacteristic
580C2×C4#1451975511yescharacteristic
581C2×C4#1451975511yescharacteristic
582C2×C4#1451975511yescharacteristic
583C2×C4C22×C4×D6111yescharacteristic
584C2×C4C2×D4×D6111yescharacteristic
585C2×C4C2×D4×D6111yescharacteristic
586C2×C4C2×D4×D6111yescharacteristic
587C2×C4C2×Q8×D6111yescharacteristic
588C2×C4C2×#1175822211yescharacteristic
589C8—24no—
590C8—42no—
591C8—618no—
592C8—2442no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—1224no—
601C22—4882no—
602C22—4882no—
603C22—2444no—
604C22#1683962111yescharacteristic
605C22#1683962111yescharacteristic
606C22#1683962111yescharacteristic
607C22#1683962111yescharacteristic
608C22C2×#1451973411yescharacteristic
609C22C2×#1451975011yescharacteristic
610C22C2×#1451975511yescharacteristic
611C4—82no—
612C4—1224no—
613C4—4882no—
614C4#1683962111yescharacteristic
615C4#1683962111yescharacteristic
616C4#1683962111yescharacteristic
617C4#1683962111yescharacteristic
618C4C2×C22⋊C4×D6111yescharacteristic
619C4C2×C4⋊C4×D6111yescharacteristic
620C4C2×#1451975011yescharacteristic
621C4C2×#1451975511yescharacteristic
622C2—21no—
623C2—21no—
624C2—21no—
625C2—21no—
626C2—21no—
627C2—21no—
628C2—21no—
629C2—2444no—
630C2C2×#1683962111yescharacteristic
subgroupG/H
centerC4C2×#14519750
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#344C2
socleC2×C61C2×#380
prime radicalC22×#11758222C22
cosocleC22×C4×C61C24
hypercenterC2×#344D61
hypocenterC61#20675
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
2. C2×#16839810C2semidirect
3. #21454408C2semidirect
6. #21445872C2semidirect
7. C2×#16839534C2semidirect
8. C2×C61×#344C2semidirect
12. #16840528C4semidirect
13. #16840528C4semidirect
22. C2×#14519712C22semidirect
25. #16839798C22semidirect
32. #16839534C22semidirect
36. C61×#344C22semidirect
54. #14519785C2×C4semidirect
314. C2×#344D61semidirect
351. #344C2×D61semidirect
352. C61#20675semidirect

Maximal subgroups

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

subgroupindex
C2×#168405282
C2×#168398102
#214544082
C2×#168397802
C2×#168397782
#214458722
C2×#168395342
C2×C61×#3442
#2067561