Finite Group Databasebeta

← #29709219

Subgroups — #29709219

Order 15616.

880 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839856C211yesmaximal, characteristic, complemented
2C2×#16839853C211yesmaximal, characteristic
3#21448366C211yesmaximal, characteristic
4#21448290C211yesmaximal, characteristic, complemented
5#21447303C211yesmaximal, characteristic, complemented
6#21447241C211yesmaximal, characteristic, complemented
7#21447197C211yesmaximal, characteristic, complemented
8#21447142C211yesmaximal, characteristic, complemented
9#21447136C211yesmaximal, characteristic
10#21447059C211yesmaximal, characteristic
11#21446915C211yesmaximal, characteristic
12C4⋊C8×Dic61C211yesmaximal, characteristic, complemented
13#21445638C211yesmaximal, characteristic, complemented
14#102×Dic61C211yesmaximal, characteristic
15C61×#2067C211yesmaximal, characteristic
16C22×Dic244C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C2×#14519764C2211yescharacteristic
19C2×#14519742C2211yescharacteristic
20C2×#14519742C2211yescharacteristic
21C2×D4×Dic61C2211yescharacteristic
22#16839856—24no—
23#16839853—24no—
24C2×#14519708C2211yescharacteristic
25C2×C4⋊#92418C2211yescharacteristic
26C2×#14519702C2211yescharacteristic
27C2×#14519702C2211yescharacteristic
28C2×#14519700C2211yescharacteristic
29C2×#14519700C2211yescharacteristic
30C2×#14519700C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×C8×Dic61C2211yescharacteristic
33C2×C8×Dic61C2211yescharacteristic
34#16839668C2211yescharacteristic
35#16839668C2211yescharacteristic
36#16839667C2211yescharacteristic
37#16839661C2211yescharacteristic
38#16839650—21no—
39#16839650—21no—
40#16839649—21no—
41#16839643—21no—
42#16839627C2211yescharacteristic
43C4⋊C4×Dic61—21no—
44C4⋊C4×Dic61C2211yescharacteristic
45C22⋊C4×Dic61—21no—
46C22⋊C4×Dic61—21no—
47#16839607—21no—
48C42×Dic61C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C2×#107×C61C2211yescharacteristic
55C2×C4⋊C8×C61C2211yescharacteristic
56C2×#102×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C61×#390C2211yescharacteristic
59C61×#389C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C22×Dic122C2311yescharacteristic
62C22×Dic122C2311yescharacteristic
63C23×Dic61—21no—
64C2×Dic244—22no—
65C2×Dic244—22no—
66C2×Dic244—22no—
67C2×#11758200—22no—
68C2×#11758200—22no—
69C2×#11758200—22no—
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72#14519764—22no—
73#14519764—22no—
74#14519742—22no—
75#14519742—22no—
76#14519742—22no—
77#14519742D414yes—
78D4×Dic61—22no—
79D4×Dic61—22no—
80C2×C4⋊Dic61—21no—
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×#11758196—21no—
84C2×#11758196—21no—
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×C4×Dic61—21no—
89C2×C4×Dic61—21no—
90C2×C4×Dic61—21no—
91C2×C4×Dic61D411yescharacteristic
92C2×C4×Dic61D411yescharacteristic
93C2×C4×Dic61D411yescharacteristic
94C2×C4×Dic61D411yescharacteristic
95C2×C4×Dic61C2311yescharacteristic
96C2×C4×Dic61C2311yescharacteristic
97#14519708—22no—
98C4⋊#92418—22no—
99#14519702—22no—
100#14519702—22no—
101#14519700—22no—
102#14519700—22no—
103#14519700—22no—
104#14519698—22no—
105C8×Dic61—22no—
106C8×Dic61—22no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117C22×D4×C61C2311yescharacteristic
118C22×C8×C61C2311yescharacteristic
119C22×C8×C61C2311yescharacteristic
120C2×C4⋊C4×C61—21no—
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61—21no—
126C2×C42×C61C2311yescharacteristic
127#107×C61—22no—
128C4⋊C8×C61—22no—
129#102×C61—22no—
130#102×C61—22no—
131#95×C61—21no—
132C24×C61—21no—
133C2×D4×C61—21no—
134C2×D4×C61—21no—
135C2×D4×C61—21no—
136C2×D4×C61—21no—
137C2×D4×C61—21no—
138C2×D4×C61#4112yes—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2411yescharacteristic
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—42no—
150C22×Dic61—42no—
151C22×Dic61—42no—
152C22×Dic61C2×D411yescharacteristic
153C22×Dic61C2×D411yescharacteristic
154C22×Dic61C2×D411yescharacteristic
155C22×Dic61C2×D411yescharacteristic
156C2×Dic122—21no—
157C2×Dic122—21no—
158C2×Dic122—21no—
159C2×Dic122—21no—
160C2×Dic122—21no—
161C2×Dic122—21no—
162C2×Dic122—21no—
163C2×Dic122—21no—
164C2×Dic122—21no—
165C2×Dic122—21no—
166C2×Dic122C2×D412yes—
167C2×Dic122#4112yes—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61—21no—
172C2×C8×C61—21no—
173C2×C8×C61#4112yes—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—42no—
180C4⋊C4×C61C2×D412yes—
181C22⋊C4×C61—42no—
182C22⋊C4×C61—42no—
183C42×C61—21no—
184C42×C61—21no—
185C22⋊Dic61—24no—
186C22⋊Dic61—24no—
187C22⋊Dic61—42no—
188#11758200—28no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—42no—
194#11758196—24no—
195#11758196—42no—
196C4×Dic61—22no—
197C4×Dic61—21no—
198C4×Dic61—21no—
199C4×Dic61—24no—
200C4×Dic61—22no—
201C4×Dic61—22no—
202C4×Dic61—41no—
203C4×Dic61—42no—
204C4×Dic61—42no—
205C4×Dic61C2×D412yes—
206C4×Dic61#4112yes—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418#4112yes—
213Dic244—28no—
214C23×C61—22no—
215C23×C61—41no—
216C23×C61—41no—
217C23×C61—41no—
218C23×C61—41no—
219C23×C61—41no—
220C23×C61—41no—
221C23×C61C22×D411yescharacteristic
222D4×C61—22no—
223D4×C61—22no—
224D4×C61—41no—
225D4×C61—41no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—22no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61#13512yes—
241C2×C4×C61C22×D411yescharacteristic
242C2×C4×C61C2×#4111yescharacteristic
243C2×C4×C61C2×#4111yescharacteristic
244C2×C4×C61C2×#4111yescharacteristic
245C2×C4×C61C2×#4111yescharacteristic
246C2×C4×C61C2×#4111yescharacteristic
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—22no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—22no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—84no—
268C2×Dic61#12112yes—
269C2×Dic61#12112yes—
270C2×Dic61#13512yes—
271C2×Dic61#13712yes—
272Dic122—22no—
273Dic122—22no—
274Dic122—22no—
275Dic122—22no—
276Dic122—41no—
277Dic122—41no—
278Dic122—41no—
279Dic122—41no—
280C8×C61—22no—
281C8×C61—41no—
282#92418—22no—
283#92418—41no—
284#23681—611nomaximal, Sylow
285C22×C61—42no—
286C22×C61—42no—
287C22×C61—42no—
288C22×C61—81no—
289C22×C61—81no—
290C22×C61—81no—
291C22×C61—81no—
292C22×C61C2×#12111yescharacteristic
293C22×C61#52511yescharacteristic
294C22×C61#53211yescharacteristic
295C22×C61C2×#13511yescharacteristic
296C22×C61C2×#13511yescharacteristic
297C22×C61C2×#13711yescharacteristic
298C22×C61#57511yescharacteristic
299C4×C61—22no—
300C4×C61—41no—
301C4×C61—42no—
302C4×C61—81no—
303C4×C61—81no—
304C4×C61#52511yescharacteristic
305C4×C61#52511yescharacteristic
306C4×C61#52911yescharacteristic
307C4×C61#52911yescharacteristic
308Dic61—22no—
309Dic61—41no—
310Dic61—41no—
311Dic61—42no—
312Dic61—42no—
313Dic61—81no—
314Dic61—81no—
315Dic61#46414yes—
316C2×C4×Q16—611no—
317C2×C4×SD16—611no—
318C4×#124—611no—
319#2295—611no—
320#2085—611no—
321#2074—611no—
322#2067D6111yescharacteristic
323#2066—611no—
324#2056—611no—
325#2055—611no—
326#2042—611no—
327#2015—611no—
328C4×C4⋊C8—611no—
329C4×#103—611no—
330C4×#102—611no—
331C2×C61—82no—
332C2×C61#239211yescharacteristic
333C2×C61C2×#46411yescharacteristic
334C2×C61#303511yescharacteristic
335C2×C61#310211yescharacteristic
336C2×C61#310711yescharacteristic
337C2×C61#316811yescharacteristic
338C2×C61#317211yescharacteristic
339C22×Q16—611no—
340C22×SD16—611no—
341C2×#124—611no—
342C2×C4×Q8—611no—
343C2×C4×Q8—611no—
344C2×C4×D4—611no—
345C4×Q16—1224no—
346C4×SD16—1224no—
347C2×#107C2×D6111yescharacteristic
348C2×#106—611no—
349C2×C4⋊C8—611no—
350C2×C4⋊C8C2×D6111yescharacteristic
351C2×#103—611no—
352C2×#103—611no—
353C2×#103—611no—
354C2×#103—611no—
355C2×#103—611no—
356C2×#102—611no—
357C2×#102C2×D6111yescharacteristic
358C2×#102C2×D6111yescharacteristic
359C2×C4×C8—611no—
360C2×C4×C8—611no—
361#391—611no—
362#391—611no—
363#391—611no—
364#390C2×D6111yescharacteristic
365#389—611no—
366#389C2×D6111yescharacteristic
367#388—1221no—
368#388—1221no—
369#387—1221no—
370#387—1221no—
371#382—611no—
372C4×C4⋊C4—611no—
373C4×C4⋊C4—1221no—
374C4×C22⋊C4—1221no—
375C4×C22⋊C4—1221no—
376#376—1221no—
377C43—611no—
378#340—611no—
379#340—611no—
380#340—611no—
381#340C2×D6111yescharacteristic
382#336—611no—
383#336—611no—
384C61#2368111yescharacteristic, complemented, Sylow
385C22×Q8—611no—
386C22×Q8—611no—
387C22×D4C22×D6111yescharacteristic
388C23×C4—1221no—
389C2×Q16—1222no—
390C2×Q16—1222no—
391C2×Q16—1222no—
392C2×SD16—1222no—
393C2×SD16—1222no—
394C2×SD16—1222no—
395C22×C8—611no—
396C22×C8—611no—
397C22×C8C22×D6111yescharacteristic
398C22×C8C22×D6111yescharacteristic
399#124—1222no—
400#124—1222no—
401C4×Q8—614no—
402C4×Q8—1222no—
403C4×Q8—1222no—
404C4×Q8—1222no—
405C4×D4—1222no—
406C4×D4—1222no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—611no—
409C2×C4⋊C4—611no—
410C2×C4⋊C4—1221no—
411C2×C4⋊C4—1221no—
412C2×C4⋊C4—1221no—
413C2×C4⋊C4C22×D6111yescharacteristic
414C2×C4⋊C4C22×D6111yescharacteristic
415C2×C4⋊C4C22×D6111yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—1221no—
419C2×C22⋊C4—1221no—
420C2×C22⋊C4—1221no—
421C2×C42—611no—
422C2×C42—611no—
423C2×C42—611no—
424C2×C42—611no—
425C2×C42—611no—
426C2×C42—611no—
427C2×C42—1221no—
428C2×C42—1221no—
429C2×C42—1221no—
430C2×C42C22×D6111yescharacteristic
431#107—22no—
432#106—1222no—
433C4⋊C8—22no—
434C4⋊C8—1222no—
435#103—1222no—
436#103—1222no—
437#103—1222no—
438#103—1222no—
439#103—1222no—
440#102—22no—
441#102—22no—
442#102—1222no—
443C4×C8—1222no—
444C4×C8—1222no—
445#95—21no—
446#95—1221no—
447#95—1221no—
448#95—1221no—
449#95—1221no—
450#95—1221no—
451#95—1221no—
452#95—1221no—
453#95—1221no—
454#95—1221no—
455#95—1221no—
456C24—21no—
457C2×Q8—612no—
458C2×Q8—612no—
459C2×Q8—1221no—
460C2×Q8—1221no—
461C2×Q8—1221no—
462C2×Q8—1221no—
463C2×Q8—1221no—
464C2×Q8—1221no—
465C2×Q8—1221no—
466C2×Q8—1221no—
467C2×Q8—1221no—
468C2×Q8—1221no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4#1175822612yes—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—1221no—
483C22×C4—1221no—
484C22×C4—1221no—
485C22×C4—1221no—
486C22×C4—2442no—
487C22×C4—2442no—
488C22×C4—2442no—
489C22×C4D4×D6111yescharacteristic
490C22×C4D4×D6111yescharacteristic
491C22×C4C23×D6111yescharacteristic
492Q16—1228no—
493SD16—1228no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—612no—
500C2×C8—1221no—
501C2×C8—1221no—
502C2×C8—1221no—
503C2×C8—1221no—
504C2×C8—1221no—
505C2×C8#1175822412yes—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—42no—
512C4⋊C4—1224no—
513C4⋊C4—1221no—
514C4⋊C4—1221no—
515C4⋊C4—1221no—
516C4⋊C4—1221no—
517C4⋊C4—2442no—
518C4⋊C4—2442no—
519C4⋊C4D4×D6112yes—
520C22⋊C4—42no—
521C22⋊C4—42no—
522C22⋊C4—1224no—
523C22⋊C4—1224no—
524C22⋊C4—2442no—
525C42—21no—
526C42—21no—
527C42—612no—
528C42—612no—
529C42—1222no—
530C42—1222no—
531C42—1224no—
532C42—1221no—
533C42—1221no—
534C42—1222no—
535C42—2441no—
536C42—2442no—
537C42—2442no—
538C23—22no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23C2×D4×D6111yescharacteristic
546Q8—1222no—
547Q8—1222no—
548Q8—1222no—
549Q8—1222no—
550Q8—2441no—
551Q8—2441no—
552Q8—2441no—
553Q8—2441no—
554D4—22no—
555D4—22no—
556D4—41no—
557D4—41no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—612no—
573C2×C4—612no—
574C2×C4—612no—
575C2×C4—612no—
576C2×C4—1221no—
577C2×C4—1221no—
578C2×C4—1222no—
579C2×C4—1221no—
580C2×C4—1221no—
581C2×C4—1222no—
582C2×C4—1221no—
583C2×C4—1221no—
584C2×C4—1221no—
585C2×C4—1221no—
586C2×C4—4884no—
587C2×C4—2441no—
588C2×C4—2441no—
589C2×C4—2441no—
590C2×C4—2441no—
591C2×C4—2441no—
592C2×C4—2441no—
593C2×C4—2441no—
594C2×C4—2441no—
595C2×C4—2441no—
596C2×C4—2441no—
597C2×C4#1451979612yes—
598C2×C4C2×D4×D6111yescharacteristic
599C2×C4#41×D6111yescharacteristic
600C2×C4#41×D6111yescharacteristic
601C2×C4#41×D6111yescharacteristic
602C2×C4C2×#1175822411yescharacteristic
603C2×C4C2×#1175822611yescharacteristic
604C8—22no—
605C8—41no—
606C8—1222no—
607C8—2441no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22#121×D6111yescharacteristic
616C22#1684027511yescharacteristic
617C22#1684030711yescharacteristic
618C22#135×D6111yescharacteristic
619C22C2×#1451979611yescharacteristic
620C22#137×D6111yescharacteristic
621C22#1684055811yescharacteristic
622C4—22no—
623C4—41no—
624C4—42no—
625C4—81no—
626C4—81no—
627C4—614no—
628C4—1222no—
629C4—4881no—
630C4—4881no—
631C4—2441no—
632C4—2442no—
633C4—2442no—
634C4—2441no—
635C4#1684027211yescharacteristic
636C4#1684027511yescharacteristic
637C4#1684029511yescharacteristic
638C4#1684029811yescharacteristic
639C2—82no—
640C2#2144906411yescharacteristic
641C2#464×D6111yescharacteristic
642C2#2145526711yescharacteristic
643C2#2145584211yescharacteristic
644C2#2145589211yescharacteristic
645C2#2145638411yescharacteristic
646C2#2145641811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2067C2
socleC23×C61C22×D4
prime radicalC22×D4×C61C23
hypercenter#2067D61
hypocenterC61#23681
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2067

Complements

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

NH ≅ G/Ntype
1. C2×#16839856C2semidirect
4. #21448290C2semidirect
5. #21447303C2semidirect
6. #21447241C2semidirect
7. #21447197C2semidirect
8. #21447142C2semidirect
12. C4⋊C8×Dic61C2semidirect
13. #21445638C2semidirect
384. C61#23681semidirect

Maximal subgroups

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

subgroupindex
C2×#168398562
C2×#168398532
#214483662
#214482902
#214473032
#214472412
#214471972
#214471422
#214471362
#214470592
#214469152
C4⋊C8×Dic612
#214456382
#102×Dic612
C61×#20672
#2368161