Finite Group Databasebeta

← #29585362

Subgroups — #29585362

Order 15616.

1246 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×#16839744C211yesmaximal, characteristic
3#21448309C211yesmaximal, characteristic
4C2×#16839534C211yesmaximal, characteristic, complemented
5C2×#16839533C211yesmaximal, characteristic, complemented
6#21445513C211yesmaximal, characteristic, complemented
7C61×#1728C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9#16840528—22no—
10#16840528—22no—
11#16840528—22no—
12#16840528C414yescomplemented
13C2×#14519785—22no—
14C2×#14519783—22no—
15C22×#11758194C2211yescharacteristic
16C22×#11758194C2211yescharacteristic
17C2×M16×D61—22no—
18C2×#14519736C2211yescharacteristic
19#16839744—22no—
20#16839744C414yescomplemented
21C2×#14519695—21no—
22C2×#14519693—21no—
23#16839668—21no—
24#16839664—21no—
25#16839641C414yes—
26C4×#11758198—22no—
27#16839534—22no—
28#16839533—22no—
29#16839517—22no—
30C22×M16×C61C2211yescharacteristic
31C22×M16×C61C2211yescharacteristic
32C22×C42×C61C2211yescharacteristic
33C61×#336—22no—
34C2×#11758222—21no—
35C2×#11758222—21no—
36C2×#11758222—21no—
37C2×#11758222—21no—
38C2×#11758222—21no—
39C2×#11758222—21no—
40C2×#11758222—21no—
41C2×#11758222—21no—
42C2×#11758222C2×C412yes—
43C2×#11758222C2×C412yes—
44C2×#11758222D412yes—
45C2×#11758222Q812yes—
46C22×Dic122D411yescharacteristic
47C22×D244D411yescharacteristic
48C22×C22⋊D61C2×C412yes—
49C22×C4×D61D412yes—
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×#11758194—21no—
59C2×#11758194—21no—
60C2×#11758194—21no—
61C2×#11758194—21no—
62C2×#11758194—21no—
63C2×#11758194C2×C412yes—
64C2×#11758194C2×C412yes—
65C2×#11758194D412yes—
66C2×#11758189—24no—
67M16×D61—28no—
68M16×D61—28no—
69C22×#92418—21no—
70C22×#92418D412yes—
71C2×C8×D61—24no—
72#14519736—21no—
73#14519736—21no—
74#14519736—21no—
75#14519736—21no—
76C2×C4⋊Dic61—21no—
77C2×C22⋊Dic61C2×C412yes—
78C2×#11758198—24no—
79C2×C4×Dic61—21no—
80#14519695—24no—
81#14519693—24no—
82#14519684—24no—
83C23×C4×C61C2×C412yes—
84C23×C4×C61C2311yescharacteristic
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×C61—21no—
93C2×M16×C61—21no—
94C2×M16×C61C2×C412yes—
95C2×M16×C61C2×C412yes—
96C2×M16×C61D412yes—
97C22×C8×C61—21no—
98C22×C8×C61D412yes—
99C2×C42×C61—21no—
100C2×C42×C61—21no—
101C2×C42×C61—21no—
102C2×C42×C61—21no—
103C2×C42×C61—21no—
104C2×C42×C61—21no—
105C24×C61C22×C411yescharacteristic
106C23×D61C22⋊C412yes—
107C22×C4×C61—22no—
108C22×C4×C61—22no—
109C22×C4×C61—22no—
110C22×C4×C61—44no—
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×D411yescharacteristic
120C22×C4×C61C2×Q811yescharacteristic
121C22×C4×C61#4111yescharacteristic
122C22×C4×C61#4111yescharacteristic
123C22×C4×C61#4111yescharacteristic
124C22×C4×C61#4111yescharacteristic
125C2×C22⋊D61—22no—
126C2×C22⋊D61—22no—
127C2×C22⋊D61—22no—
128C2×C22⋊D61—22no—
129C2×C22⋊D61C4214yes—
130C2×C22⋊D61C4⋊C414yes—
131C22×Dic61—22no—
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×D244C22⋊C412yes—
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×Dic122C22⋊C412yes—
166C2×Dic122C4⋊C412yes—
167M16×C61—22no—
168M16×C61—22no—
169M16×C61—22no—
170M16×C61—22no—
171M16×C61—22no—
172M16×C61—22no—
173M16×C61—41no—
174M16×C61—41no—
175C2×C8×C61—22no—
176C2×C8×C61—22no—
177C2×C8×C61—22no—
178C2×C8×C61—41no—
179C2×C8×C61—41no—
180C2×C8×C61C22⋊C414yescomplemented
181C42×C61—41no—
182C42×C61—41no—
183C42×C61—41no—
184C42×C61—41no—
185C22⋊Dic61—22no—
186C22⋊Dic61—22no—
187#11758198—48no—
188C4⋊Dic61—41no—
189C4⋊Dic61—41no—
190C4×Dic61—41no—
191C4×Dic61—41no—
192#11758194—22no—
193#11758194—22no—
194#11758194—22no—
195#11758194—22no—
196#11758194—22no—
197#11758194—22no—
198#11758194—41no—
199#11758194—41no—
200C2×#92418—22no—
201C2×#92418—22no—
202C2×#92418—22no—
203C2×#92418—41no—
204C2×#92418—41no—
205C2×#92418C22⋊C414yescomplemented
206#11758189—216no—
207C8×D61—216no—
208C23×C61—42no—
209C23×C61C2×C4211yescharacteristic
210C23×C61C2×C22⋊C411yescharacteristic
211C23×C61C2×C4⋊C411yescharacteristic
212C23×C61C4×D411yescharacteristic
213C23×C61C4×D411yescharacteristic
214C23×C61C4×D411yescharacteristic
215C23×C61C4×D411yescharacteristic
216C22×D61—22no—
217C22×D61—22no—
218C22×D61—44no—
219C22×D61#9514yes—
220C2×C4×C61—24no—
221C2×C4×C61—24no—
222C2×C4×C61—24no—
223C2×C4×C61—42no—
224C2×C4×C61—42no—
225C2×C4×C61—42no—
226C2×C4×C61—42no—
227C2×C4×C61C2×C22⋊C411yescharacteristic
228C2×C4×C61C2×C22⋊C411yescharacteristic
229C2×C4×C61C2×C22⋊C411yescharacteristic
230C2×C4×C61C2×C22⋊C411yescharacteristic
231C2×C4×C61C2×C4⋊C411yescharacteristic
232C2×C4×C61C2×C4⋊C411yescharacteristic
233C2×C4×C61#11711yescharacteristic
234C2×C4×C61#11711yescharacteristic
235C2×C4×C61C4×D411yescharacteristic
236C2×C4×C61C4×D411yescharacteristic
237C2×C4×C61C4×D411yescharacteristic
238C2×C4×C61C4×D411yescharacteristic
239C2×C4×C61#12011yescharacteristic
240C2×C4×C61#12011yescharacteristic
241C2×C4×C61#12011yescharacteristic
242C2×C4×C61#12011yescharacteristic
243C2×C4×C61#12111yescharacteristic
244C2×C4×C61#12111yescharacteristic
245C2×C4×C61#12111yescharacteristic
246C2×C4×C61#12111yescharacteristic
247C2×C4×C61C22⋊Q811yescharacteristic
248C2×C4×C61C22⋊Q811yescharacteristic
249C2×C4×C61C22⋊Q811yescharacteristic
250C2×C4×C61C22⋊Q811yescharacteristic
251C2×C4×C61#12311yescharacteristic
252C2×C4×C61#12311yescharacteristic
253C2×C4×C61#12311yescharacteristic
254C2×C4×C61#12311yescharacteristic
255C22⋊D61—24no—
256C22⋊D61—24no—
257C22⋊D61—24no—
258C22⋊D61—24no—
259C2×Dic61—22no—
260C2×Dic61—22no—
261C2×Dic61—44no—
262C2×Dic61—42no—
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—
277C8×C61—42no—
278#92418—24no—
279#92418—42no—
280#10746—611nomaximal, Sylow
281C22×C61—22no—
282C22×C61—22no—
283C22×C61—22no—
284C22×C61—41no—
285C22×C61—41no—
286C22×C61—41no—
287C22×C61—41no—
288C22×C61C2×#9511yescharacteristic
289C22×C61C4×C22⋊C411yescharacteristic
290C22×C61C4×C22⋊C411yescharacteristic
291C22×C61#38511yescharacteristic
292C22×C61#38511yescharacteristic
293C22×C61#38611yescharacteristic
294C22×C61#38611yescharacteristic
295C2×D61—24no—
296C2×D61—44no—
297C2×D61—44no—
298C2×D61—82no—
299C4×C61—44no—
300C4×C61#37911yescharacteristic
301C4×C61#38011yescharacteristic
302C4×C61#38011yescharacteristic
303C4×C61#38111yescharacteristic
304C4×C61#38511yescharacteristic
305C4×C61#38511yescharacteristic
306C4×C61#38611yescharacteristic
307C4×C61#38611yescharacteristic
308Dic61—24no—
309Dic61—82no—
310C2×#568—611no—
311C2×#413—611no—
312#2297—611no—
313C2×#344—611no—
314C2×#344—611no—
315#1728—611no—
316#1728D6111yescharacteristic, complemented
317C2×C61—21no—
318C2×C61—21no—
319C2×C61—21no—
320C2×C61—21no—
321C2×C61—21no—
322C2×C61—21no—
323C2×C61C22⋊#9511yescharacteristic
324C2×C61#189112yes—
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—611no—
335C22×M16—1222no—
336C22×M16C2×D6111yescharacteristic
337C22×M16C2×D6111yescharacteristic
338C2×#117—611no—
339C22×C42C2×D6111yescharacteristic
340#413—614no—
341#413—1222no—
342C2×#101—1221no—
343C2×#100—1221no—
344#391—1221no—
345#390—1221no—
346#386—614no—
347C4×C22⋊C4—1222no—
348#344—1222no—
349#344—1222no—
350#336—22no—
351#336—1222no—
352C61#1074611yescharacteristic, complemented, Sylow
353C2×#41—612no—
354C2×#41—612no—
355C2×#41—612no—
356C2×#41—612no—
357C2×#41—1221no—
358C2×#41—1221no—
359C2×#41—1221no—
360C2×#41—1221no—
361C2×#41—1221no—
362C2×#41—1221no—
363C2×#41—1221no—
364C2×#41—1221no—
365C22×Q8—611no—
366C22×D4—612no—
367C22×D4—611no—
368C23×C4—612no—
369C23×C4C4×D6112yes—
370C23×C4C22×D6111yescharacteristic
371#131—1228no—
372#131—1228no—
373#131—1228no—
374#131—1228no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16—21no—
379C2×M16—21no—
380C2×M16—21no—
381C2×M16—21no—
382C2×M16—21no—
383C2×M16—21no—
384C2×M16—612no—
385C2×M16—612no—
386C2×M16—612no—
387C2×M16—1224no—
388C2×M16—1228no—
389C2×M16—1228no—
390C2×M16—1221no—
391C2×M16—1221no—
392C2×M16—1221no—
393C2×M16—1221no—
394C2×M16—1221no—
395C2×M16—1221no—
396C2×M16—1221no—
397C2×M16—1221no—
398C2×M16—1221no—
399C2×M16C4×D6112yes—
400C2×M16C4×D6112yes—
401C2×M16D24412yes—
402C22×C8—21no—
403C22×C8—612no—
404C22×C8—1224no—
405C22×C8—1221no—
406C22×C8C22⋊D6112yes—
407#117—1221no—
408#117—1221no—
409#117—1221no—
410#117—1221no—
411C2×C4⋊C4—1221no—
412C2×C22⋊C4—612no—
413C2×C22⋊C4—1224no—
414C2×C42—21no—
415C2×C42—21no—
416C2×C42—21no—
417C2×C42—21no—
418C2×C42—21no—
419C2×C42—21no—
420C2×C42—1221no—
421#101—1224no—
422#100—1224no—
423#95—1224no—
424C24—612no—
425C24C2×C4×D6111yescharacteristic
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—
440#41—1222no—
441#41—1222no—
442C2×Q8—612no—
443C2×Q8—612no—
444C2×Q8—1221no—
445C2×Q8—1221no—
446C2×Q8—1221no—
447C2×Q8—1221no—
448C2×D4—614no—
449C2×D4—614no—
450C2×D4—612no—
451C2×D4—612no—
452C2×D4—1222no—
453C2×D4—1222no—
454C2×D4—1222no—
455C2×D4—1222no—
456C2×D4—1221no—
457C2×D4—1221no—
458C2×D4—1221no—
459C2×D4—1221no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—44no—
464C22×C4—612no—
465C22×C4—614no—
466C22×C4—614no—
467C22×C4—1222no—
468C22×C4—1222no—
469C22×C4—1222no—
470C22×C4—1222no—
471C22×C4—1222no—
472C22×C4C2×C4×D6111yescharacteristic
473C22×C4C2×C4×D6111yescharacteristic
474C22×C4C2×D24411yescharacteristic
475C22×C4#1175822211yescharacteristic
476C22×C4#1175822211yescharacteristic
477C22×C4D4×D6111yescharacteristic
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—22no—
490M16—22no—
491M16—22no—
492M16—41no—
493M16—41no—
494M16—12216no—
495M16—1222no—
496M16—1222no—
497M16—1222no—
498M16—1222no—
499M16—1222no—
500M16—1222no—
501M16—2441no—
502M16—2441no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—41no—
507C2×C8—41no—
508C2×C8—614no—
509C2×C8—12216no—
510C2×C8—1222no—
511C2×C8—1222no—
512C2×C8—1222no—
513C2×C8—2441no—
514C2×C8—2441no—
515C2×C8#1175819814yescomplemented
516C4⋊C4—2441no—
517C4⋊C4—2441no—
518C22⋊C4—1222no—
519C22⋊C4—1222no—
520C22⋊C4—2448no—
521C42—41no—
522C42—41no—
523C42—41no—
524C42—41no—
525C42—2441no—
526C42—2441no—
527C23—42no—
528C23—614no—
529C23—1222no—
530C23—1222no—
531C23—2444no—
532C23C42×D6111yescharacteristic
533C23C22⋊C4×D6111yescharacteristic
534C23C4⋊C4×D6111yescharacteristic
535C23#1451973711yescharacteristic
536C23C4×C22⋊D6111yescharacteristic
537C23#1451973911yescharacteristic
538C23C4×D24411yescharacteristic
539Q8—1222no—
540Q8—1222no—
541Q8—1222no—
542Q8—1222no—
543D4—1224no—
544D4—1224no—
545D4—1224no—
546D4—1224no—
547D4—1222no—
548D4—1222no—
549D4—1222no—
550D4—1222no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—614no—
559C2×C4—1222no—
560C2×C4—1222no—
561C2×C4—1224no—
562C2×C4—1224no—
563C2×C4—1224no—
564C2×C4—1224no—
565C2×C4—2444no—
566C2×C4—2442no—
567C2×C4C22⋊C4×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×C4C4×C22⋊D6111yescharacteristic
577C2×C4#1451973911yescharacteristic
578C2×C4C4×D24411yescharacteristic
579C2×C4#1451974511yescharacteristic
580C2×C4#1451974511yescharacteristic
581C2×C4#1451974711yescharacteristic
582C2×C4#1451974711yescharacteristic
583C2×C4#1451974811yescharacteristic
584C2×C4#1451975011yescharacteristic
585C2×C4#1451975011yescharacteristic
586C2×C4#1451975211yescharacteristic
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—42no—
597C8—1224no—
598C8—2442no—
599C22—22no—
600C22—22no—
601C22—22no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—1224no—
607C22—4882no—
608C22—2444no—
609C22—2444no—
610C22#95×D6111yescharacteristic
611C22#1683960911yescharacteristic
612C22C4×#1175819811yescharacteristic
613C22#1683963311yescharacteristic
614C22#1683963611yescharacteristic
615C22#1683963811yescharacteristic
616C22#1683964011yescharacteristic
617C4—44no—
618C4—1224no—
619C4—4882no—
620C4#1683961711yescharacteristic
621C4#1683961911yescharacteristic
622C4#1683962111yescharacteristic
623C4#1683962411yescharacteristic
624C4#1683963311yescharacteristic
625C4#1683963611yescharacteristic
626C4#1683963811yescharacteristic
627C4#1683964011yescharacteristic
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—21no—
633C2—21no—
634C2—2444no—
635C2#2144404011yescharacteristic
636C2#2144623412yes—
subgroupG/H
centerC2×C4#14519745
commutatorC23×C61C2×C42
FrattiniC23×C4C22×D61
FittingC61×#1728C2
socleC22×C61#386
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenter#1728D61
hypocenterC61#10746
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1728

Complements

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

NH ≅ G/Ntype
4. C2×#16839534C2semidirect
5. C2×#16839533C2semidirect
6. #21445513C2semidirect
7. C61×#1728C2semidirect
12. #16840528C4semidirect
20. #16839744C4semidirect
180. C2×C8×C61C22⋊C4semidirect
205. C2×#92418C22⋊C4semidirect
316. #1728D61semidirect
352. C61#10746semidirect
515. C2×C8#11758198semidirect

Maximal subgroups

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

subgroupindex
C2×#168405282
C2×#168397442
#214483092
C2×#168395342
C2×#168395332
#214455132
C61×#17282
#1074661