Finite Group Databasebeta

← #29647779

Subgroups — #29647779

Order 15616.

990 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459620C211yesmaximal, characteristic
2#21454847C211yesmaximal, characteristic
3#21448760C211yesmaximal, characteristic
4#21444389C212yesmaximal, complemented
5#21444371C211yesmaximal, characteristic, complemented
6#21444370C211yesmaximal, characteristic, complemented
7#21444350C212yesmaximal, complemented
8#21444337C212yesmaximal, complemented
9#21444330C211yesmaximal, characteristic, complemented
10#328×D61C212yesmaximal, complemented
11C61×#1506C211yesmaximal, characteristic, complemented
12#16840473C412yescomplemented
13#16840472—22no—
14#16840472C412yescomplemented
15#16840468—22no—
16Q8×D244C412yescomplemented
17#16840427C412yescomplemented
18#16840390—21no—
19#16840387—21no—
20#16840387—21no—
21#16840319C2211yescharacteristic
22C22⋊Q8×D61C2212yes—
23C22⋊Q8×D61C2212yes—
24#16840236—21no—
25C2×C4×D244C2211yescharacteristic
26#16839835—22no—
27#16839832—22no—
28#16839819C2211yescharacteristic
29#16839724C2212yes—
30C22⋊C8×D61C2212yes—
31#16839653—21no—
32#16839645—21no—
33#16839640—21no—
34#16839630C2211yescharacteristic
35#16839624C2211yescharacteristic
36#16839621C2211yescharacteristic
37C4×#11758198—21no—
38#16839609C2211yescharacteristic
39#95×D61C2211yescharacteristic
40#16839500C2212yes—
41#16839500C2212yes—
42#16839499C2212yes—
43#16839499C2212yes—
44#16839498C2212yes—
45#16839498C2212yes—
46C61×#533C2211yescharacteristic
47C61×#432C2211yescharacteristic
48C61×#376C2211yescharacteristic
49C61×#328C2212yes—
50C61×#328C2212yes—
51C2×Q8×D61C2×C412yes—
52C2×Q8×D61C2×C412yescomplemented
53C22×D244D411yescharacteristic
54C22×C4×D61—21no—
55C22×C4×D61C2311yescharacteristic
56C22×C4×D61C2311yescharacteristic
57C2×#11758189—22no—
58C2×C8×D61—22no—
59#14519777—22no—
60#14519777C2×C411yescharacteristic, complemented
61#14519777C2×C411yescharacteristic, complemented
62#14519776—22no—
63#14519769—21no—
64#14519769—22no—
65#14519768—22no—
66#14519757—22no—
67#14519757—22no—
68#14519757C2×C412yes—
69#14519757C2×C412yescomplemented
70#14519756—21no—
71#14519756C2312yes—
72#14519755—22no—
73#14519755—22no—
74#14519755—22no—
75#14519755—22no—
76#14519755—22no—
77#14519755—22no—
78#14519754—22no—
79#14519754—22no—
80#14519753—22no—
81#14519753—22no—
82#14519753C2×C412yes—
83#14519753C2×C412yescomplemented
84C4×Dic122—21no—
85C4×Dic122C2×C412yescomplemented
86C4×D244—22no—
87C4×D244—22no—
88C4×D244C2×C412yes—
89C4×D244C2×C412yes—
90C4×D244D412yes—
91C4×D244D412yes—
92#14519739—22no—
93#14519739—22no—
94#14519736—21no—
95C2×C4⋊Dic61D411yescharacteristic
96C2×#11758196—21no—
97C4⋊C4×D61—22no—
98C4⋊C4×D61—22no—
99C4⋊C4×D61C2×C412yes—
100C4⋊C4×D61C2×C412yescomplemented
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×#11758198D411yescharacteristic
105C2×#11758198D411yescharacteristic
106C22⋊C4×D61—22no—
107C22⋊C4×D61—22no—
108C2×C4×Dic61—21no—
109C4⋊#92418—21no—
110C22⋊#92418C2312yes—
111#14519689—22no—
112#14519689—22no—
113#14519688—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684C2311yescharacteristic
119#14519684C2311yescharacteristic
120C4⋊Q8×C61C2×C411yescharacteristic, complemented
121C4⋊Q8×C61C2×C411yescharacteristic, complemented
122#125×C61—21no—
123C22⋊Q8×C61—21no—
124C22⋊Q8×C61C2312yes—
125C4×Q8×C61—21no—
126C4×Q8×C61C2×C412yescomplemented
127#117×C61—21no—
128C2×C42×C61—21no—
129C2×C42×C61C2311yescharacteristic
130C4⋊C8×C61—21no—
131C22⋊C8×C61C2312yes—
132#97×C61—21no—
133#95×C61—21no—
134#95×C61C2311yescharacteristic
135#95×C61C2311yescharacteristic
136C23×D61C2×D411yescharacteristic
137C23×D61C2×D411yescharacteristic
138C2×Q8×C61—21no—
139C2×Q8×C61C22×C412yes—
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×Dic61C2×D411yescharacteristic
148C22×Dic61C2×D411yescharacteristic
149Q8×D61—82no—
150Q8×D61—82no—
151C2×D244—22no—
152C2×D244—22no—
153C2×D244C22⋊C412yes—
154C2×D244C22⋊C412yes—
155C2×C4×D61—22no—
156C2×C4×D61—22no—
157C2×C4×D61—22no—
158C2×C4×D61—22no—
159C2×C4×D61—42no—
160C2×C4×D61—42no—
161C2×C4×D61—81no—
162C2×C4×D61—81no—
163C2×C4×D61—81no—
164C2×C4×D61C22×C412yes—
165C2×C4×D61C22×C412yes—
166C2×C4×D61C2×D412yes—
167C2×C4×D61C2×D412yes—
168C2×Dic122—21no—
169C2×Dic122—22no—
170C2×Dic122—22no—
171C2×Dic122C22×C412yes—
172C2×C8×C61—22no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—22no—
177C4⋊C4×C61—22no—
178C4⋊C4×C61C22×C412yes—
179C22⋊C4×C61—22no—
180C42×C61—22no—
181C42×C61—42no—
182C42×C61C22×C411yescharacteristic
183C42×C61C22×C411yescharacteristic
184C42×C61C2×D411yescharacteristic
185C42×C61C2×D411yescharacteristic
186C22⋊Dic61—22no—
187#11758198—22no—
188#11758198—22no—
189#11758198—22no—
190#11758198—22no—
191#11758198—42no—
192#11758198—42no—
193#11758198—81no—
194#11758198C22⋊C412yes—
195#11758198C22⋊C412yes—
196#11758198C22⋊C412yes—
197#11758198C22⋊C412yes—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—22no—
202C4⋊Dic61—22no—
203C4⋊Dic61C22⋊C412yes—
204C4⋊Dic61C22⋊C412yes—
205C4⋊Dic61C22×C412yes—
206#11758196—22no—
207#11758196—22no—
208#11758196—22no—
209#11758196—22no—
210#11758196—22no—
211#11758196—22no—
212#11758196—81no—
213C4×Dic61—22no—
214C4×Dic61—81no—
215C2×#92418—22no—
216#11758189—82no—
217C8×D61—82no—
218C23×C61C22×D411yescharacteristic
219C22×D61—21no—
220C22×D61—21no—
221C22×D61—41no—
222C22×D61—41no—
223C22×D61—41no—
224C22×D61—41no—
225C22×D61C2×C22⋊C412yes—
226C22×D61C2×C22⋊C412yes—
227C22×D61#13712yes—
228C22×D61#13712yes—
229Q8×C61—42no—
230Q8×C61—81no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—22no—
234C2×C4×C61—22no—
235C2×C4×C61—22no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61C2×C22⋊C411yescharacteristic
244C2×C4×C61C2×C22⋊C411yescharacteristic
245C2×C4×C61C2×C22⋊C411yescharacteristic
246C2×C4×C61C2×C22⋊C411yescharacteristic
247C2×C4×C61C23×C411yescharacteristic
248C2×C4×C61C22×D411yescharacteristic
249C2×Dic61—22no—
250C2×Dic61—22no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61C2×C22⋊C412yes—
260C2×Dic61C2×C22⋊C412yes—
261D244—24no—
262D244—24no—
263C4×D61—42no—
264C4×D61—42no—
265C4×D61—42no—
266C4×D61—42no—
267C4×D61—82no—
268C4×D61—82no—
269C4×D61—82no—
270C4×D61—82no—
271C4×D61—84no—
272Dic122—42no—
273Dic122—82no—
274Dic122—82no—
275Dic122—81no—
276C8×C61—42no—
277#92418—42no—
278#17621—611nomaximal, Sylow
279C22×C61—21no—
280C22×C61—21no—
281C22×C61C22×C22⋊C411yescharacteristic
282C22×C61C2×#13711yescharacteristic
283C22×C61C2×#13711yescharacteristic
284C2×D61—22no—
285C2×D61—22no—
286C2×D61—22no—
287C2×D61—22no—
288C2×D61—22no—
289C2×D61—42no—
290C2×D61—42no—
291C2×D61—81no—
292C2×D61—81no—
293C2×D61#41914yes—
294C4×C61—21no—
295C4×C61—21no—
296C4×C61—21no—
297C4×C61—21no—
298C4×C61—21no—
299C4×C61—21no—
300C4×C61—42no—
301C4×C61—42no—
302C4×C61—42no—
303C4×C61—81no—
304Dic61—22no—
305Dic61—22no—
306Dic61—42no—
307Dic61—42no—
308Dic61—81no—
309Dic61—81no—
310#3501—611no—
311#2973—611no—
312#2353—611no—
313#1520—612no—
314#1515—611no—
315#1515—611no—
316#1511—612no—
317#1508—612no—
318#1506—611no—
319#1506D6111yescharacteristic, complemented
320C2×#328—612no—
321C2×C61—21no—
322C2×C61—21no—
323C2×C61#288311yescharacteristic
324C2×C61C2×#41911yescharacteristic
325C2×C61#290111yescharacteristic
326D61—24no—
327D61—42no—
328#554—612no—
329#554—612no—
330#554—1222no—
331#554—1222no—
332D4×Q8—612no—
333D4×Q8—612no—
334#544—1221no—
335#543—1221no—
336#543—1221no—
337#533—611no—
338#533C2×D6111yescharacteristic
339C2×C22⋊Q8—612no—
340C2×C22⋊Q8—612no—
341#518—1221no—
342C2×C4×D4—611no—
343#435—1222no—
344#435—1222no—
345#432—611no—
346#432C2×D6111yescharacteristic
347#407—612no—
348C2×C22⋊C8—612no—
349#388—1221no—
350#387—1221no—
351#386—1221no—
352#383—611no—
353#381—611no—
354#380—611no—
355C4×C22⋊C4—611no—
356C4×C22⋊C4—1221no—
357#376C2×D6111yescharacteristic
358C2×#95—611no—
359#328—612no—
360#328—612no—
361#328—612no—
362#328—612no—
363#328—612no—
364#328—612no—
365#328C2×D6112yes—
366#328C2×D6112yes—
367C61#1762111yescharacteristic, complemented, Sylow
368C22×Q8—612no—
369C22×Q8—612no—
370C22×D4—611no—
371C23×C4—611no—
372C23×C4—611no—
373C23×C4—1221no—
374C2×M16—1222no—
375C22×C8—1222no—
376C4⋊Q8—611no—
377C4⋊Q8—611no—
378C4⋊Q8—1222no—
379C4⋊Q8—1222no—
380C4⋊Q8C4×D6111yescharacteristic, complemented
381C4⋊Q8C4×D6111yescharacteristic, complemented
382#125—21no—
383#125—1222no—
384#125—1222no—
385#125—1221no—
386C22⋊Q8—21no—
387C22⋊Q8—612no—
388C22⋊Q8—612no—
389C22⋊Q8—612no—
390C22⋊Q8—612no—
391C22⋊Q8—612no—
392C22⋊Q8—1222no—
393C22⋊Q8—1222no—
394C22⋊Q8—1222no—
395C22⋊Q8—1222no—
396C22⋊Q8—1222no—
397C22⋊Q8—1222no—
398C22⋊Q8—1222no—
399C22⋊Q8—1222no—
400C22⋊Q8—1222no—
401C22⋊Q8—1222no—
402C22⋊Q8—1222no—
403C22⋊Q8—1222no—
404C22⋊Q8—1221no—
405C22⋊Q8C22×D6112yes—
406C4×Q8—21no—
407C4×Q8—612no—
408C4×Q8—1221no—
409C4×Q8C4×D6112yescomplemented
410C4×D4—612no—
411C4×D4—612no—
412C4×D4—612no—
413C4×D4—612no—
414C4×D4—1222no—
415C4×D4—1222no—
416C4×D4—1222no—
417C4×D4—1222no—
418#117—21no—
419#117—1221no—
420C2×C4⋊C4—611no—
421C2×C4⋊C4—612no—
422C2×C4⋊C4—612no—
423C2×C4⋊C4—1222no—
424C2×C4⋊C4—1222no—
425C2×C4⋊C4—1221no—
426C2×C22⋊C4—611no—
427C2×C22⋊C4—611no—
428C2×C22⋊C4—1222no—
429C2×C22⋊C4—1222no—
430C2×C22⋊C4—1221no—
431C2×C22⋊C4—1221no—
432C2×C22⋊C4—1221no—
433C2×C42—21no—
434C2×C42—1221no—
435C2×C42C22×D6111yescharacteristic
436C4⋊C8—21no—
437C4⋊C8—1221no—
438C22⋊C8—612no—
439C22⋊C8—1222no—
440C22⋊C8—1222no—
441C22⋊C8C22×D6112yes—
442#97—21no—
443#97—1221no—
444#95—21no—
445#95—611no—
446#95—611no—
447#95—1221no—
448#95—1221no—
449#95—1221no—
450#95—1221no—
451#95C22×D6111yescharacteristic
452#95C22×D6111yescharacteristic
453C24—611no—
454C24—611no—
455C2×Q8—21no—
456C2×Q8—612no—
457C2×Q8—1222no—
458C2×Q8—1222no—
459C2×Q8—1221no—
460C2×Q8—4882no—
461C2×Q8—4882no—
462C2×Q8C2×C4×D6112yes—
463C2×D4—612no—
464C2×D4—612no—
465C2×D4—1222no—
466C2×D4—1222no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—611no—
470C22×C4—611no—
471C22×C4—612no—
472C22×C4—612no—
473C22×C4—612no—
474C22×C4—612no—
475C22×C4—1222no—
476C22×C4—1222no—
477C22×C4—1222no—
478C22×C4—1222no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—4881no—
482C22×C4—4881no—
483C22×C4—4881no—
484C22×C4—2442no—
485C22×C4—2442no—
486C22×C4D4×D6111yescharacteristic
487C22×C4D4×D6111yescharacteristic
488C22×C4C23×D6111yescharacteristic
489M16—4882no—
490C2×C8—22no—
491C2×C8—1222no—
492C2×C8—4882no—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—22no—
498C4⋊C4—612no—
499C4⋊C4—612no—
500C4⋊C4—612no—
501C4⋊C4—1222no—
502C4⋊C4—1222no—
503C4⋊C4—1222no—
504C4⋊C4—1222no—
505C4⋊C4—1222no—
506C4⋊C4—1222no—
507C4⋊C4—1222no—
508C4⋊C4—1222no—
509C4⋊C4—1221no—
510C4⋊C4—1221no—
511C4⋊C4—1221no—
512C4⋊C4—4881no—
513C4⋊C4C2×C4×D6112yes—
514C22⋊C4—22no—
515C22⋊C4—612no—
516C22⋊C4—612no—
517C22⋊C4—612no—
518C22⋊C4—612no—
519C22⋊C4—1222no—
520C22⋊C4—1222no—
521C22⋊C4—1222no—
522C22⋊C4—1222no—
523C22⋊C4—1222no—
524C22⋊C4—4881no—
525C22⋊C4—2442no—
526C22⋊C4—2442no—
527C42—22no—
528C42—42no—
529C42—1222no—
530C42—4881no—
531C42C2×C4×D6111yescharacteristic
532C42C2×C4×D6111yescharacteristic
533C42D4×D6111yescharacteristic
534C42D4×D6111yescharacteristic
535C23—612no—
536C23—612no—
537C23—612no—
538C23—612no—
539C23—1221no—
540C23—1221no—
541C23—2441no—
542C23—2441no—
543C23—2441no—
544C23—2441no—
545C23C2×D4×D6111yescharacteristic
546Q8—42no—
547Q8—81no—
548Q8—4881no—
549Q8—4882no—
550Q8—4882no—
551Q8—2442no—
552D4—1224no—
553D4—1224no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—612no—
567C2×C4—612no—
568C2×C4—1222no—
569C2×C4—1222no—
570C2×C4—4884no—
571C2×C4—4882no—
572C2×C4—4882no—
573C2×C4—4882no—
574C2×C4—4882no—
575C2×C4—2442no—
576C2×C4—2442no—
577C2×C4—2442no—
578C2×C4—2442no—
579C2×C4—2441no—
580C2×C4—2441no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4—2441no—
584C2×C4—2441no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4C22⋊C4×D6111yescharacteristic
588C2×C4C22⋊C4×D6111yescharacteristic
589C2×C4C22⋊C4×D6111yescharacteristic
590C2×C4C22⋊C4×D6111yescharacteristic
591C2×C4C22×C4×D6111yescharacteristic
592C2×C4C2×D4×D6111yescharacteristic
593C8—42no—
594C8—2442no—
595C22—21no—
596C22—21no—
597C22—614no—
598C22—1222no—
599C22—1222no—
600C22—1222no—
601C22—1222no—
602C22—1222no—
603C22—4881no—
604C22—4881no—
605C22—2442no—
606C22—2442no—
607C22C2×C22⋊C4×D6111yescharacteristic
608C22#137×D6111yescharacteristic
609C22#137×D6111yescharacteristic
610C4—21no—
611C4—21no—
612C4—21no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—42no—
617C4—42no—
618C4—42no—
619C4—81no—
620C4—1222no—
621C4—1222no—
622C4—4881no—
623C4—4881no—
624C4—2442no—
625C4—2442no—
626C2—21no—
627C2—21no—
628C2—1224no—
629C2—2442no—
630C2#2145427811yescharacteristic
631C2#419×D6111yescharacteristic
632C2#2145436311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1506C2
socleC22×C61C22×C22⋊C4
prime radicalC22×D244D4
cosocleC22×C4×C61C24
hypercenter#1506D61
hypocenterC61#17621
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1506

Complements

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

NH ≅ G/Ntype
4. #21444389C2semidirect
5. #21444371C2semidirect
6. #21444370C2semidirect
7. #21444350C2semidirect
8. #21444337C2semidirect
9. #21444330C2semidirect
10. #328×D61C2semidirect
11. C61×#1506C2semidirect
12. #16840473C4semidirect
14. #16840472C4semidirect
16. Q8×D244C4semidirect
17. #16840427C4semidirect
52. C2×Q8×D61C2×C4semidirect
60. #14519777C2×C4semidirect
61. #14519777C2×C4semidirect
69. #14519757C2×C4semidirect
83. #14519753C2×C4semidirect
85. C4×Dic122C2×C4semidirect
100. C4⋊C4×D61C2×C4semidirect
120. C4⋊Q8×C61C2×C4semidirect
121. C4⋊Q8×C61C2×C4semidirect
126. C4×Q8×C61C2×C4semidirect
319. #1506D61semidirect
367. C61#17621semidirect
380. C4⋊Q8C4×D61semidirect
381. C4⋊Q8C4×D61semidirect
409. C4×Q8C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214596202
#214548472
#214487602
#214443892
#214443712
#214443702
#214443502
#214443372
#214443302
#328×D612
C61×#15062
#1762161