Finite Group Databasebeta

← #29586389

Subgroups — #29586389

Order 15616.

994 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
1C22×#14519705C211yesmaximal, characteristic
2#21454339C211yesmaximal, characteristic
3C2×#16839735C211yesmaximal, characteristic
4C4×#14519736C211yesmaximal, characteristic, complemented
5C2×#16839534C211yesmaximal, characteristic, complemented
6#21445529C211yesmaximal, characteristic, complemented
7C2×C61×#339C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C2×#14519736C2211yescharacteristic
11C2×#14519736C2211yescharacteristic
12C2×#14519705—21no—
13C2×#14519705—21no—
14C2×#14519705—22no—
15C2×#14519705C414yescomplemented
16#16839772C412yescomplemented
17#16839768C412yescomplemented
18#16839764—22no—
19#16839759—22no—
20#16839735—22no—
21#16839735C414yescomplemented
22C2×#14519691—22no—
23C4×C4⋊Dic61—22no—
24C4×C22⋊Dic61—22no—
25#16839608—21no—
26C42×Dic61—21no—
27#16839534—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×#11758222—21no—
42C2×#11758222—21no—
43C2×#11758222C2×C412yes—
44C2×#11758222C2×C412yes—
45C22×Dic122C2×C411yescharacteristic
46C22×D244C2×C411yescharacteristic
47C22×C22⋊D61—21no—
48C22×C4×D61—21no—
49C2×#11758194—21no—
50C2×#11758194—21no—
51C2×#11758194—21no—
52C2×#11758194—21no—
53C2×#11758194—21no—
54C2×#11758194C2×C412yes—
55C22×#92418—21no—
56#14519736—21no—
57#14519736—21no—
58#14519736—21no—
59#14519736—21no—
60#14519736C2×C412yes—
61#14519736C2×C412yes—
62#14519736D412yes—
63#14519736D412yes—
64C2×C4⋊Dic61—21no—
65C2×C4⋊Dic61D412yes—
66C2×C22⋊Dic61—21no—
67C2×C22⋊Dic61D412yes—
68C2×C4×Dic61—21no—
69C2×C4×Dic61—21no—
70C2×C4×Dic61—24no—
71#14519705—24no—
72#14519705—24no—
73#14519702—24no—
74#14519699—24no—
75#14519691—28no—
76#14519684—24no—
77C23×C4×C61—21no—
78C23×C4×C61C2311yescharacteristic
79C2×M16×C61—21no—
80C2×M16×C61—21no—
81C2×M16×C61—21no—
82C2×M16×C61—21no—
83C2×M16×C61—21no—
84C2×M16×C61C2×C412yes—
85C22×C8×C61—21no—
86#117×C61—21no—
87#117×C61—21no—
88#117×C61—21no—
89#117×C61C2×C412yes—
90C2×C4⋊C4×C61—21no—
91C2×C22⋊C4×C61—21no—
92C2×C42×C61—21no—
93C2×C42×C61—21no—
94C2×C42×C61—21no—
95C2×C42×C61—21no—
96C2×C42×C61C2×C412yes—
97C2×C42×C61D411yescharacteristic
98C2×C42×C61D411yescharacteristic
99C2×C42×C61D412yes—
100C24×C61C2×D411yescharacteristic
101C23×D61—21no—
102C22×C4×C61—21no—
103C22×C4×C61—22no—
104C22×C4×C61—21no—
105C22×C4×C61—22no—
106C22×C4×C61—44no—
107C22×C4×C61—41no—
108C22×C4×C61C22×C411yescharacteristic
109C22×C4×C61C22×C411yescharacteristic
110C22×C4×C61C22×C411yescharacteristic
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61C2×D411yescharacteristic
114C22×C4×C61C2×D411yescharacteristic
115C22×C4×C61C2×D411yescharacteristic
116C22×C4×C61#4111yescharacteristic
117C22×C4×C61#4111yescharacteristic
118C22×C4×C61#4111yescharacteristic
119C22×C4×C61#4111yescharacteristic
120C22×C4×C61#4111yescharacteristic
121C22×C4×C61#4111yescharacteristic
122C2×C22⋊D61—22no—
123C2×C22⋊D61—22no—
124C2×C22⋊D61—41no—
125C2×C22⋊D61—41no—
126C2×C22⋊D61—41no—
127C2×C22⋊D61—41no—
128C22×Dic61—21no—
129C22×Dic61—22no—
130C22×Dic61—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—41no—
140#11758222—41no—
141#11758222—41no—
142#11758222—41no—
143#11758222—41no—
144#11758222—41no—
145#11758222—41no—
146#11758222—41no—
147C2×D244—21no—
148C2×D244—21no—
149C2×D244—21no—
150C2×D244—21no—
151C2×D244—21no—
152C2×D244C4212yescomplemented
153C2×C4×D61—22no—
154C2×C4×D61—22no—
155C2×C4×D61—41no—
156C2×C4×D61—41no—
157C2×C4×D61—41no—
158C2×C4×D61—41no—
159C2×Dic122—21no—
160C2×Dic122—21no—
161C2×Dic122—21no—
162C2×Dic122—21no—
163C2×Dic122—21no—
164C2×Dic122C4212yescomplemented
165M16×C61—22no—
166M16×C61—22no—
167M16×C61—41no—
168M16×C61—41no—
169C2×C8×C61—22no—
170C2×C8×C61—41no—
171C2×C8×C61—41no—
172C4⋊C4×C61—22no—
173C4⋊C4×C61—41no—
174C22⋊C4×C61—22no—
175C22⋊C4×C61—41no—
176C42×C61—22no—
177C42×C61—22no—
178C42×C61—21no—
179C42×C61—21no—
180C42×C61—22no—
181C42×C61—41no—
182C42×C61C22⋊C412yes—
183C42×C61C22⋊C412yes—
184C22⋊Dic61—22no—
185C22⋊Dic61—22no—
186C22⋊Dic61—22no—
187C22⋊Dic61C22⋊C414yes—
188C4⋊Dic61—22no—
189C4⋊Dic61—22no—
190C4⋊Dic61—22no—
191C4⋊Dic61C22⋊C414yes—
192C4×Dic61—22no—
193C4×Dic61—22no—
194C4×Dic61—22no—
195C4×Dic61—22no—
196C4×Dic61—48no—
197#11758194—22no—
198#11758194—22no—
199#11758194—41no—
200#11758194—41no—
201C2×#92418—22no—
202C2×#92418—41no—
203C2×#92418—41no—
204C23×C61—42no—
205C23×C61C2×C22⋊C411yescharacteristic
206C23×C61C4×D411yescharacteristic
207C23×C61C4×D411yescharacteristic
208C23×C61#12011yescharacteristic
209C23×C61#12111yescharacteristic
210C23×C61#12111yescharacteristic
211C23×C61#12311yescharacteristic
212C22×D61—22no—
213C22×D61—41no—
214C22×D61—41no—
215C22×D61—82no—
216C2×C4×C61—24no—
217C2×C4×C61—22no—
218C2×C4×C61—22no—
219C2×C4×C61—44no—
220C2×C4×C61—44no—
221C2×C4×C61—42no—
222C2×C4×C61—42no—
223C2×C4×C61—82no—
224C2×C4×C61C2×C4211yescharacteristic
225C2×C4×C61C2×C22⋊C411yescharacteristic
226C2×C4×C61C2×C22⋊C411yescharacteristic
227C2×C4×C61#11711yescharacteristic
228C2×C4×C61#11711yescharacteristic
229C2×C4×C61#11711yescharacteristic
230C2×C4×C61C4×D411yescharacteristic
231C2×C4×C61C4×D411yescharacteristic
232C2×C4×C61C4×D411yescharacteristic
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×C61#12111yescharacteristic
241C2×C4×C61#12111yescharacteristic
242C2×C4×C61#12111yescharacteristic
243C2×C4×C61#12111yescharacteristic
244C2×C4×C61#12311yescharacteristic
245C2×C4×C61#12311yescharacteristic
246C2×C4×C61#12411yescharacteristic
247C2×C4×C61#12411yescharacteristic
248C2×C4×C61#12411yescharacteristic
249C2×C4×C61#12611yescharacteristic
250C2×C4×C61#12611yescharacteristic
251C2×C4×C61#12711yescharacteristic
252C22⋊D61—42no—
253C22⋊D61—42no—
254C22⋊D61—42no—
255C22⋊D61—42no—
256C2×Dic61—22no—
257C2×Dic61—24no—
258C2×Dic61—24no—
259C2×Dic61—44no—
260C2×Dic61—44no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263D244—22no—
264D244—22no—
265D244—41no—
266D244—41no—
267C4×D61—42no—
268C4×D61—42no—
269C4×D61—42no—
270C4×D61—42no—
271Dic122—22no—
272Dic122—22no—
273Dic122—41no—
274Dic122—41no—
275C8×C61—42no—
276#92418—42no—
277#10945—611nomaximal, Sylow
278C22×C61—22no—
279C22×C61—22no—
280C22×C61—22no—
281C22×C61—41no—
282C22×C61—41no—
283C22×C61—41no—
284C22×C61—41no—
285C22×C61C4×C22⋊C411yescharacteristic
286C22×C61#38611yescharacteristic
287C22×C61#38611yescharacteristic
288C22×C61#38611yescharacteristic
289C22×C61#38811yescharacteristic
290C22×C61#38811yescharacteristic
291C22×C61#39011yescharacteristic
292C2×D61—42no—
293C2×D61—82no—
294C2×D61—82no—
295C2×D61—82no—
296C4×C61—24no—
297C4×C61—42no—
298C4×C61—82no—
299C4×C61C4×C22⋊C411yescharacteristic
300C4×C61C4×C22⋊C411yescharacteristic
301C4×C61#38811yescharacteristic
302C4×C61#38811yescharacteristic
303C4×C61#38811yescharacteristic
304C4×C61#38811yescharacteristic
305C4×C61#39011yescharacteristic
306C4×C61#39011yescharacteristic
307Dic61—44no—
308Dic61—44no—
309Dic61—42no—
310C22×#104—611no—
311#2896—611no—
312C2×#410—611no—
313C4×#117—611no—
314C2×#344—611no—
315#1733—611no—
316C2×#339D6111yescharacteristic, complemented
317C2×C61—21no—
318C2×C61—21no—
319C2×C61—21no—
320C2×C61—21no—
321C2×C61—21no—
322C2×C61—21no—
323C2×C61#143711yescharacteristic
324C2×C61#190612yes—
325D61—82no—
326C22×#41—611no—
327C22×M16—611no—
328C22×M16C2×D6111yescharacteristic
329C2×#117—611no—
330C2×#117—611no—
331C2×#117C2×D6111yescharacteristic
332C22×C42C2×D6111yescharacteristic
333C2×#104—614no—
334C2×#104—1221no—
335C2×#104—1221no—
336C2×#104—1222no—
337#419—612no—
338#418—612no—
339#417—1222no—
340#416—1222no—
341#410—614no—
342#410—1222no—
343C2×#99—1222no—
344C4×C4⋊C4—1222no—
345C4×C22⋊C4—1222no—
346#376—1221no—
347C43—1221no—
348#344—1222no—
349#339—22no—
350#339—1222no—
351C61#1094511yescharacteristic, complemented, Sylow
352C2×#41—612no—
353C2×#41—612no—
354C2×#41—1221no—
355C2×#41—1221no—
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—611no—
366C22×D4—1221no—
367C23×C4—21no—
368C23×C4—1221no—
369C23×C4C22×D6111yescharacteristic
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—612no—
376C2×M16—1221no—
377C2×M16—1221no—
378C2×M16—1221no—
379C2×M16—1221no—
380C2×M16—1221no—
381C2×M16C4×D6112yes—
382C22×C8—21no—
383C22×C8—1221no—
384#117—21no—
385#117—21no—
386#117—21no—
387#117—612no—
388#117—612no—
389#117—612no—
390#117—612no—
391#117—1221no—
392#117—1221no—
393#117—1221no—
394#117—1221no—
395#117C4×D6112yes—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—612no—
398C2×C4⋊C4—1221no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—612no—
401C2×C22⋊C4—1221no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—1221no—
407C2×C42—1221no—
408C2×C42—1224no—
409C2×C42C4×D6112yes—
410C2×C42D24411yescharacteristic
411C2×C42D24411yescharacteristic
412C2×C42C22⋊D6112yes—
413#104—1224no—
414#104—1224no—
415#103—1224no—
416#102—1224no—
417#99—1228no—
418#95—1224no—
419C24—1221no—
420C24D4×D6111yescharacteristic
421#41—1222no—
422#41—1222no—
423#41—1222no—
424#41—1222no—
425#41—1222no—
426#41—1222no—
427#41—1222no—
428#41—1222no—
429#41—2441no—
430#41—2441no—
431#41—2441no—
432#41—2441no—
433#41—2441no—
434#41—2441no—
435#41—2441no—
436#41—2441no—
437C2×Q8—612no—
438C2×Q8—1221no—
439C2×Q8—1221no—
440C2×Q8—1221no—
441C2×Q8—1221no—
442C2×Q8—1221no—
443C2×D4—612no—
444C2×D4—1222no—
445C2×D4—1222no—
446C2×D4—1221no—
447C2×D4—1221no—
448C2×D4—1221no—
449C2×D4—1221no—
450C2×D4—1221no—
451C2×D4—2441no—
452C2×D4—2441no—
453C2×D4—2441no—
454C2×D4—2441no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—44no—
460C22×C4—41no—
461C22×C4—1221no—
462C22×C4—1222no—
463C22×C4—1222no—
464C22×C4—1222no—
465C22×C4—1222no—
466C22×C4—2441no—
467C22×C4—2441no—
468C22×C4—2441no—
469C22×C4—2441no—
470C22×C4C2×C4×D6111yescharacteristic
471C22×C4C2×C4×D6111yescharacteristic
472C22×C4C2×C4×D6111yescharacteristic
473C22×C4C2×D24411yescharacteristic
474C22×C4#1175822211yescharacteristic
475C22×C4#1175822211yescharacteristic
476C22×C4D4×D6111yescharacteristic
477C22×C4D4×D6111yescharacteristic
478C22×C4D4×D6111yescharacteristic
479C22×C4#1175822411yescharacteristic
480C22×C4#1175822411yescharacteristic
481C22×C4#1175822611yescharacteristic
482C22×C4#1175822611yescharacteristic
483C22×C4C2×C22⋊D6111yescharacteristic
484M16—22no—
485M16—22no—
486M16—41no—
487M16—41no—
488M16—1222no—
489M16—1222no—
490M16—2441no—
491M16—2441no—
492C2×C8—22no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—1222no—
496C2×C8—2441no—
497C2×C8—2441no—
498C4⋊C4—22no—
499C4⋊C4—41no—
500C4⋊C4—614no—
501C4⋊C4—1222no—
502C4⋊C4—1222no—
503C4⋊C4—1222no—
504C22⋊C4—22no—
505C22⋊C4—41no—
506C22⋊C4—614no—
507C22⋊C4—1222no—
508C22⋊C4—1222no—
509C22⋊C4—1222no—
510C42—22no—
511C42—22no—
512C42—21no—
513C42—21no—
514C42—22no—
515C42—41no—
516C42—1222no—
517C42—1222no—
518C42—1222no—
519C42—1222no—
520C42—2448no—
521C42#1175819812yes—
522C42#1175819812yes—
523C23—42no—
524C23—1222no—
525C23—4882no—
526C23—2441no—
527C23—2441no—
528C23C22⋊C4×D6111yescharacteristic
529C23#1451973711yescharacteristic
530C23#1451973911yescharacteristic
531C23#1451974711yescharacteristic
532C23#1451974911yescharacteristic
533C23#1451975011yescharacteristic
534C23#1451976211yescharacteristic
535Q8—1222no—
536Q8—1222no—
537Q8—2441no—
538Q8—2441no—
539D4—1222no—
540D4—1222no—
541D4—2442no—
542D4—2442no—
543D4—2442no—
544D4—2442no—
545D4—2441no—
546D4—2441no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—44no—
551C2×C4—44no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—82no—
555C2×C4—1222no—
556C2×C4—1224no—
557C2×C4—1224no—
558C2×C4—2444no—
559C2×C4—2444no—
560C2×C4—2441no—
561C2×C4—2441no—
562C2×C4—2442no—
563C2×C4—2442no—
564C2×C4—2442no—
565C2×C4—2442no—
566C2×C4C42×D6111yescharacteristic
567C2×C4C22⋊C4×D6111yescharacteristic
568C2×C4C2×#1175819811yescharacteristic
569C2×C4#1451973411yescharacteristic
570C2×C4#1451973511yescharacteristic
571C2×C4#1451973511yescharacteristic
572C2×C4#1451973711yescharacteristic
573C2×C4#1451973711yescharacteristic
574C2×C4#1451973711yescharacteristic
575C2×C4C4×C22⋊D6111yescharacteristic
576C2×C4C4×C22⋊D6111yescharacteristic
577C2×C4#1451973911yescharacteristic
578C2×C4#1451973911yescharacteristic
579C2×C4#1451973911yescharacteristic
580C2×C4C4×D24411yescharacteristic
581C2×C4C4×D24411yescharacteristic
582C2×C4#1451974911yescharacteristic
583C2×C4#1451975011yescharacteristic
584C2×C4#1451975211yescharacteristic
585C2×C4#1451975211yescharacteristic
586C2×C4#1451976111yescharacteristic
587C2×C4#1451976211yescharacteristic
588C2×C4#1451976311yescharacteristic
589C2×C4#1451976311yescharacteristic
590C2×C4#1451976611yescharacteristic
591C2×C4#1451977211yescharacteristic
592C2×C4#1451977211yescharacteristic
593C2×C4#1451977311yescharacteristic
594C8—42no—
595C8—2442no—
596C22—22no—
597C22—22no—
598C22—22no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—4882no—
604C22—4882no—
605C22—4882no—
606C22—2442no—
607C22#1683960911yescharacteristic
608C22#1683963911yescharacteristic
609C22#1683964011yescharacteristic
610C22#1683964011yescharacteristic
611C22#1683965111yescharacteristic
612C22#1683965211yescharacteristic
613C22#1683966211yescharacteristic
614C4—24no—
615C4—42no—
616C4—82no—
617C4—2444no—
618C4—2444no—
619C4—2442no—
620C4#1683960911yescharacteristic
621C4C4×#1175819811yescharacteristic
622C4#1683965111yescharacteristic
623C4#1683965211yescharacteristic
624C4#1683965411yescharacteristic
625C4#1683965411yescharacteristic
626C4#1683966211yescharacteristic
627C4#1683966311yescharacteristic
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—21no—
633C2—21no—
634C2—4882no—
635C2#2144405511yescharacteristic
636C2#2144631912yes—
subgroupG/H
centerC2×C4#14519752
commutatorC2×C4×C61C2×C42
FrattiniC23×C4C22×D61
FittingC2×C61×#339C2
socleC22×C61#386
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenterC2×#339D61
hypocenterC61#10945
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. C4×#14519736C2semidirect
5. C2×#16839534C2semidirect
6. #21445529C2semidirect
7. C2×C61×#339C2semidirect
15. C2×#14519705C4semidirect
16. #16839772C4semidirect
17. #16839768C4semidirect
21. #16839735C4semidirect
152. C2×D244C42semidirect
164. C2×Dic122C42semidirect
316. C2×#339D61semidirect
351. C61#10945semidirect

Maximal subgroups

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

subgroupindex
C22×#145197052
#214543392
C2×#168397352
C4×#145197362
C2×#168395342
#214455292
C2×C61×#3392
#1094561