Finite Group Databasebeta

← #29646693

Subgroups — #29646693

Order 15616.

984 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459241C211yesmaximal, characteristic
2#21454932C211yesmaximal, characteristic, complemented
3#21454775C211yesmaximal, characteristic, complemented
4#21444286C212yesmaximal, complemented
5#21444281C212yesmaximal, complemented
6#21444276C212yesmaximal, complemented
7#21444268C212yesmaximal, complemented
8#21444207C211yesmaximal, characteristic, complemented
9#21444199C211yesmaximal, characteristic, complemented
10C2×D4⋊#92418C211yesmaximal, characteristic, complemented
11C61×#1478C211yesmaximal, characteristic, complemented
12#16840393C411yescharacteristic
13#16840377—21no—
14#16840377C412yes—
15#16840363—21no—
16#16840363C412yes—
17#16840350—22no—
18#16840343C411yescharacteristic
19#16840329C411yescharacteristic
20#16840329C411yescharacteristic
21#16840309—21no—
22#16840309C2212yes—
23#16840294—21no—
24#16840294C2212yes—
25#16840273—22no—
26C4×#11758222C2211yescharacteristic
27C4×#11758222C2211yescharacteristic
28#16839892—21no—
29#16839886—21no—
30#16839841—21no—
31#16839830—22no—
32#16839827—21no—
33#16839825—22no—
34#16839818C2212yescomplemented
35#16839813C2212yescomplemented
36#16839784C2212yescomplemented
37C2×C4⋊#92418C2211yescharacteristic
38C2×C4×#92418C2211yescharacteristic
39C4×C8×D61C2212yescomplemented
40#16839494C2212yescomplemented
41#16839492C2211yescharacteristic, complemented
42#16839492C2211yescharacteristic, complemented
43#16839491C2212yescomplemented
44D4⋊#92418C2212yes—
45D4⋊#92418C2212yes—
46#16839489C2211yescharacteristic, complemented
47#16839489C2211yescharacteristic, complemented
48C2×C4×D4×C61C2211yescharacteristic
49C61×#431C2211yescharacteristic
50C61×#431C2211yescharacteristic
51C61×D4⋊C8C2212yes—
52C61×D4⋊C8C2212yes—
53C2×#11758222—22no—
54C2×#11758222C2×C411yescharacteristic
55C2×#11758222C2×C411yescharacteristic
56C2×#11758189—22no—
57C22×#92418—21no—
58C22×#92418—21no—
59C2×C8×D61—22no—
60#14519776—21no—
61#14519776C2×C412yes—
62#14519773—21no—
63#14519773C2×C412yes—
64#14519770—22no—
65#14519770—22no—
66#14519768—21no—
67#14519768C2×C412yes—
68#14519764—21no—
69#14519764C2×C412yes—
70#14519763—22no—
71#14519763—22no—
72#14519760—22no—
73#14519760—22no—
74#14519759—22no—
75#14519759—22no—
76#14519757—21no—
77#14519757C2×C412yes—
78#14519756—22no—
79#14519756—22no—
80#14519752—21no—
81#14519752C2×C412yes—
82#14519751—22no—
83#14519751—22no—
84#14519750—22no—
85#14519750—22no—
86#14519748—21no—
87#14519748—21no—
88#14519748C2×C412yes—
89#14519748C2×C412yes—
90#14519746—22no—
91#14519746—22no—
92C4×Dic122C2×C411yescharacteristic
93C4×Dic122D411yescharacteristic
94C4×Dic122D411yescharacteristic
95C4×Dic122C2311yescharacteristic
96C4×D244C2×C411yescharacteristic
97C4×D244D411yescharacteristic
98C4×D244D411yescharacteristic
99C4×D244C2311yescharacteristic
100C4×C22⋊D61—21no—
101C4×C22⋊D61—21no—
102C4×C22⋊D61—22no—
103C4×C22⋊D61—22no—
104C4×C22⋊D61D412yes—
105C4×C22⋊D61D412yes—
106#14519736—22no—
107#14519736C2×C411yescharacteristic
108#14519736C2×C411yescharacteristic
109#14519734—21no—
110#14519734C2×C412yes—
111C42×D61—21no—
112C42×D61C2312yes—
113C4⋊#92418—21no—
114C4⋊#92418C2312yes—
115#14519706—22no—
116#14519706—22no—
117#14519689—22no—
118#14519689—22no—
119#14519687—22no—
120C4×#92418—21no—
121C4×#92418C2311yescharacteristic
122C4×#92418C2311yescharacteristic
123C8×Dic61—22no—
124C22×D4×C61C2×C411yescharacteristic
125C23×C4×C61—21no—
126C4×D4×C61—21no—
127C4×D4×C61—21no—
128C4×D4×C61C2×C412yes—
129C4×D4×C61C2312yes—
130C2×C4⋊C4×C61C2×C411yescharacteristic
131C2×C22⋊C4×C61—21no—
132C2×C42×C61C2311yescharacteristic
133C4⋊C8×C61—21no—
134C4⋊C8×C61C2311yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136C22⋊C8×C61—21no—
137C22⋊C8×C61—21no—
138C4×C8×C61—21no—
139C4×C8×C61C2312yes—
140C24×C61—21no—
141C2×D4×C61—21no—
142C2×D4×C61—22no—
143C2×D4×C61—22no—
144C2×D4×C61C22×C412yes—
145C22×C4×C61—21no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—81no—
149C22×C4×C61—81no—
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C2×C22⋊D61—21no—
154C2×C22⋊D61—22no—
155C2×C22⋊D61—22no—
156C2×C22⋊D61—22no—
157C2×C22⋊D61—22no—
158C2×C22⋊D61C22⋊C412yes—
159#11758222—22no—
160#11758222—22no—
161#11758222—22no—
162#11758222—22no—
163#11758222—82no—
164#11758222—82no—
165C2×D244—22no—
166C2×D244C22⋊C411yescharacteristic
167C2×D244C22×C411yescharacteristic
168C2×C4×D61—21no—
169C2×C4×D61—21no—
170C2×C4×D61—21no—
171C2×C4×D61C22×C412yes—
172C2×C4×D61C2×D412yes—
173C2×C4×D61C2×D412yes—
174C2×Dic122—22no—
175C2×Dic122C22⋊C411yescharacteristic
176C2×Dic122C22×C411yescharacteristic
177C2×C8×C61—21no—
178C2×C8×C61—21no—
179C2×C8×C61—22no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61C22×C412yes—
182C22⋊C4×C61—22no—
183C22⋊C4×C61—22no—
184C42×C61C22×C411yescharacteristic
185C42×C61C2×D411yescharacteristic
186C42×C61C2×D411yescharacteristic
187C42×C61C2411yescharacteristic
188C22⋊Dic61—21no—
189C22⋊Dic61—22no—
190C22⋊Dic61—22no—
191C22⋊Dic61—22no—
192C22⋊Dic61—22no—
193C22⋊Dic61C22⋊C412yes—
194#11758198—22no—
195#11758198—21no—
196#11758198—21no—
197#11758198—22no—
198#11758198C22⋊C412yes—
199#11758198C22⋊C412yes—
200C4⋊Dic61—22no—
201C4⋊Dic61—22no—
202C4⋊Dic61C22⋊C411yescharacteristic
203C4⋊Dic61C22⋊C411yescharacteristic
204C4⋊Dic61C22×C411yescharacteristic
205C4⋊Dic61C22×C411yescharacteristic
206#11758196—21no—
207#11758196—21no—
208#11758196—22no—
209#11758196—22no—
210#11758196C22⋊C412yes—
211#11758196C22⋊C412yes—
212C4×Dic61—21no—
213C4×Dic61—21no—
214C4×Dic61—21no—
215C4×Dic61C22×C412yes—
216C4×Dic61C2×D412yes—
217C4×Dic61C2×D412yes—
218C2×#92418—21no—
219C2×#92418—21no—
220C2×#92418—22no—
221C2×#92418—42no—
222C2×#92418—81no—
223#11758189—82no—
224C8×D61—44no—
225C23×C61—22no—
226C23×C61—42no—
227C23×C61—81no—
228C23×C61—81no—
229C23×C61C2×C22⋊C411yescharacteristic
230C22×D61—21no—
231C22×D61C2×C22⋊C412yes—
232D4×C61—22no—
233D4×C61—22no—
234D4×C61—42no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—22no—
238C2×C4×C61—41no—
239C2×C4×C61—42no—
240C2×C4×C61—42no—
241C2×C4×C61—82no—
242C2×C4×C61—81no—
243C2×C4×C61C2×C22⋊C411yescharacteristic
244C2×C4×C61C2×C22⋊C411yescharacteristic
245C2×C4×C61C2×C22⋊C411yescharacteristic
246C2×C4×C61#13112yes—
247C2×C4×C61#13112yes—
248C2×C4×C61C23×C411yescharacteristic
249C2×C4×C61C22×D411yescharacteristic
250C2×C4×C61C22×D411yescharacteristic
251C22⋊D61—24no—
252C22⋊D61—42no—
253C22⋊D61—82no—
254C22⋊D61—82no—
255C22⋊D61—82no—
256C22⋊D61—82no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61C2×C22⋊C412yes—
261C2×Dic61C2×C22⋊C412yes—
262C2×Dic61C2×C22⋊C412yes—
263D244—21no—
264D244—21no—
265D244—22no—
266D244—82no—
267C4×D61—22no—
268C4×D61—22no—
269C4×D61—22no—
270C4×D61—22no—
271C4×D61—42no—
272C4×D61—41no—
273C4×D61—41no—
274C4×D61—42no—
275C4×D61—81no—
276Dic122—22no—
277Dic122—21no—
278Dic122—21no—
279Dic122—82no—
280C8×C61—42no—
281C8×C61—41no—
282C8×C61—41no—
283#92418—22no—
284#92418—41no—
285#92418—42no—
286#17483—611nomaximal, Sylow
287C22×C61—21no—
288C22×C61—21no—
289C22×C61—42no—
290C22×C61—42no—
291C22×C61—42no—
292C22×C61—84no—
293C22×C61#40812yes—
294C22×C61C22×C22⋊C411yescharacteristic
295C2×D61—22no—
296C2×D61—22no—
297C2×D61—22no—
298C2×D61—41no—
299C2×D61—41no—
300C2×D61—41no—
301C4×C61—21no—
302C4×C61—21no—
303C4×C61—21no—
304C4×C61—42no—
305C4×C61#40812yes—
306C4×C61C2×#13111yescharacteristic
307C4×C61C2×#13111yescharacteristic
308C4×C61#57611yescharacteristic
309C4×C61#57711yescharacteristic
310Dic61—22no—
311Dic61—22no—
312Dic61—22no—
313Dic61—41no—
314Dic61—41no—
315Dic61—41no—
316#3460—611no—
317#2989—611no—
318C8×#41—611no—
319#1496—612no—
320#1495—612no—
321#1494—612no—
322#1492—612no—
323#1478D6111yescharacteristic, complemented
324#1477—611no—
325#1476—611no—
326C2×D4⋊C8—611no—
327C2×C61—22no—
328C2×C61—82no—
329C2×C61C2×#40811yescharacteristic
330C2×C61#289711yescharacteristic
331C2×C61#290111yescharacteristic
332D61—42no—
333D61—81no—
334#544—611no—
335#542—612no—
336#542—1221no—
337#540—612no—
338#540—1221no—
339#538—1222no—
340#537—611no—
341#535—611no—
342#535—611no—
343#532—612no—
344#532—1221no—
345#529—612no—
346#529—1221no—
347#525—1222no—
348C4×#41—611no—
349C4×#41—611no—
350C2×C4×D4C2×D6111yescharacteristic
351#446—1221no—
352C8×Q8—1221no—
353#436—1221no—
354#435—1222no—
355C8×D4—1222no—
356C8×D4—1221no—
357#432—612no—
358#431—612no—
359#431C2×D6111yescharacteristic
360#431C2×D6111yescharacteristic
361#423—612no—
362C2×C4⋊C8—611no—
363C2×C4×C8—611no—
364C2×C4×C8—612no—
365Q8⋊C8—611no—
366Q8⋊C8—611no—
367Q8⋊C8—612no—
368D4⋊C8—612no—
369D4⋊C8—612no—
370D4⋊C8—611no—
371D4⋊C8—611no—
372D4⋊C8—612no—
373D4⋊C8C2×D6112yes—
374D4⋊C8C2×D6112yes—
375C61#1748311yescharacteristic, complemented, Sylow
376C2×#41—611no—
377C2×#41—611no—
378C2×#41—1222no—
379C22×D4C4×D6111yescharacteristic
380C23×C4—21no—
381C2×M16—1222no—
382C22×C8—1222no—
383C22×C8—1221no—
384C22×C8—1221no—
385C4⋊Q8—612no—
386C4⋊Q8—1221no—
387#127—612no—
388#127—1221no—
389#126—1222no—
390#126—1222no—
391#125—612no—
392#125—1221no—
393#124—612no—
394#124—1222no—
395#124—1222no—
396#124—1221no—
397#123—1222no—
398#123—1222no—
399#123—1222no—
400#123—1222no—
401C22⋊Q8—612no—
402C22⋊Q8—1222no—
403C22⋊Q8—1221no—
404C22⋊Q8—1222no—
405#121—612no—
406#121—612no—
407#121—612no—
408#121—1222no—
409#121—1222no—
410#121—1222no—
411#121—1221no—
412#121—1221no—
413#121—1221no—
414#121—1222no—
415#120—1222no—
416#120—1222no—
417C4×Q8—611no—
418C4×Q8—611no—
419C4×Q8—611no—
420C4×Q8—611no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—612no—
424C4×D4—612no—
425C4×D4—611no—
426C4×D4—611no—
427C4×D4—611no—
428C4×D4—611no—
429C4×D4—1222no—
430C4×D4—1222no—
431C4×D4—1221no—
432C4×D4—1221no—
433C4×D4C4×D6112yes—
434C4×D4C22×D6112yes—
435#117—611no—
436#117—612no—
437#117—611no—
438#117—1222no—
439#117—1221no—
440C2×C4⋊C4C4×D6111yescharacteristic
441C2×C22⋊C4—21no—
442C2×C42—612no—
443C2×C42—1221no—
444C2×C42C22×D6111yescharacteristic
445C4⋊C8—21no—
446C4⋊C8—612no—
447C4⋊C8—1222no—
448C4⋊C8—1222no—
449C4⋊C8—1221no—
450C4⋊C8C22×D6111yescharacteristic
451C4⋊C8C22×D6111yescharacteristic
452C22⋊C8—21no—
453C22⋊C8—21no—
454C22⋊C8—1222no—
455C22⋊C8—1222no—
456#97—1222no—
457C4×C8—21no—
458C4×C8—611no—
459C4×C8—611no—
460C4×C8—1222no—
461C4×C8—1221no—
462C4×C8C22×D6112yes—
463C24—21no—
464#41—1222no—
465#41—1222no—
466#41—1222no—
467#41—1222no—
468#41—4882no—
469#41—4882no—
470C2×Q8—611no—
471C2×Q8—611no—
472C2×Q8—1222no—
473C2×D4—21no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—612no—
477C2×D4—611no—
478C2×D4—611no—
479C2×D4—1222no—
480C2×D4—1222no—
481C2×D4—1222no—
482C2×D4—1222no—
483C2×D4—1222no—
484C2×D4—1221no—
485C2×D4C2×C4×D6112yes—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—81no—
490C22×C4—81no—
491C22×C4—612no—
492C22×C4—612no—
493C22×C4—612no—
494C22×C4—1221no—
495C22×C4—1221no—
496C22×C4—1221no—
497C22×C4C2×C4×D6111yescharacteristic
498C22×C4D4×D6111yescharacteristic
499C22×C4D4×D6111yescharacteristic
500M16—4882no—
501C2×C8—22no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—1221no—
505C2×C8—1221no—
506C2×C8—1222no—
507C2×C8—4881no—
508C2×C8—2444no—
509C2×C8—2442no—
510C4⋊C4—21no—
511C4⋊C4—612no—
512C4⋊C4—612no—
513C4⋊C4—611no—
514C4⋊C4—611no—
515C4⋊C4—611no—
516C4⋊C4—611no—
517C4⋊C4—1222no—
518C4⋊C4—1222no—
519C4⋊C4—1222no—
520C4⋊C4—1222no—
521C4⋊C4—1221no—
522C4⋊C4—1221no—
523C4⋊C4C2×C4×D6112yes—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—612no—
527C22⋊C4—612no—
528C22⋊C4—612no—
529C22⋊C4—1222no—
530C22⋊C4—1222no—
531C22⋊C4—1222no—
532C22⋊C4—1222no—
533C22⋊C4—1222no—
534C22⋊C4—1222no—
535C22⋊C4—1221no—
536C22⋊C4—1221no—
537C22⋊C4—1221no—
538C42—612no—
539C42—612no—
540C42—612no—
541C42—1221no—
542C42—1221no—
543C42—1221no—
544C42C2×C4×D6111yescharacteristic
545C42D4×D6111yescharacteristic
546C42D4×D6111yescharacteristic
547C42C23×D6111yescharacteristic
548C23—22no—
549C23—42no—
550C23—81no—
551C23—81no—
552C23—612no—
553C23—1221no—
554C23C22⋊C4×D6111yescharacteristic
555Q8—1222no—
556Q8—1221no—
557Q8—1221no—
558Q8—4882no—
559D4—22no—
560D4—22no—
561D4—42no—
562D4—1224no—
563D4—1222no—
564D4—1221no—
565D4—1221no—
566D4—4882no—
567D4—4882no—
568D4—4882no—
569D4—4882no—
570D4—4882no—
571D4—2442no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—82no—
579C2×C4—81no—
580C2×C4—612no—
581C2×C4—612no—
582C2×C4—612no—
583C2×C4—1222no—
584C2×C4—1222no—
585C2×C4—1222no—
586C2×C4—1222no—
587C2×C4—1221no—
588C2×C4—1221no—
589C2×C4—1221no—
590C2×C4—4881no—
591C2×C4—2442no—
592C2×C4—2442no—
593C2×C4—2441no—
594C2×C4—2441no—
595C2×C4C22⋊C4×D6111yescharacteristic
596C2×C4C22⋊C4×D6111yescharacteristic
597C2×C4C22⋊C4×D6111yescharacteristic
598C2×C4#1451978312yes—
599C2×C4#1451978512yes—
600C2×C4C22×C4×D6111yescharacteristic
601C2×C4C2×D4×D6111yescharacteristic
602C2×C4C2×D4×D6111yescharacteristic
603C8—42no—
604C8—41no—
605C8—41no—
606C8—1222no—
607C8—2441no—
608C8—2442no—
609C22—21no—
610C22—21no—
611C22—42no—
612C22—42no—
613C22—42no—
614C22—84no—
615C22—1222no—
616C22—1222no—
617C22—1222no—
618C22—2441no—
619C22—2441no—
620C22—2441no—
621C22#1683972712yes—
622C22C2×C22⋊C4×D6111yescharacteristic
623C4—21no—
624C4—21no—
625C4—21no—
626C4—42no—
627C4—1222no—
628C4—1222no—
629C4—1222no—
630C4—2441no—
631C4—2441no—
632C4—2441no—
633C4#1683972712yes—
634C4C2×#1451978311yescharacteristic
635C4C2×#1451978511yescharacteristic
636C4#1684056611yescharacteristic
637C4#1684057211yescharacteristic
638C2—22no—
639C2—82no—
640C2—4881no—
641C2—2442no—
642C2C2×#1683972711yescharacteristic
643C2#2145434411yescharacteristic
644C2#2145436511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1478C2
socleC22×C61C22×C22⋊C4
prime radical#21459241C2
cosocleC42×C61C24
hypercenter#1478D61
hypocenterC61#17483
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
2. #21454932C2semidirect
3. #21454775C2semidirect
4. #21444286C2semidirect
5. #21444281C2semidirect
6. #21444276C2semidirect
7. #21444268C2semidirect
8. #21444207C2semidirect
9. #21444199C2semidirect
10. C2×D4⋊#92418C2semidirect
11. C61×#1478C2semidirect
34. #16839818C22semidirect
35. #16839813C22semidirect
36. #16839784C22semidirect
39. C4×C8×D61C22semidirect
40. #16839494C22semidirect
41. #16839492C22semidirect
42. #16839492C22semidirect
43. #16839491C22semidirect
46. #16839489C22semidirect
47. #16839489C22semidirect
323. #1478D61semidirect
375. C61#17483semidirect

Maximal subgroups

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

subgroupindex
#214592412
#214549322
#214547752
#214442862
#214442812
#214442762
#214442682
#214442072
#214441992
C2×D4⋊#924182
C61×#14782
#1748361