Finite Group Databasebeta

← #29647861

Subgroups — #29647861

Order 15616.

1010 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459668C211yesmaximal, characteristic
2#21454847C211yesmaximal, characteristic, complemented
3#21448752C211yesmaximal, characteristic, complemented
4#21444372C212yesmaximal, complemented
5#21444369C211yesmaximal, characteristic, complemented
6#21444359C212yesmaximal, complemented
7#21444332C211yesmaximal, characteristic, complemented
8#21444327C211yesmaximal, characteristic, complemented
9#21444320C212yesmaximal, complemented
10#21444307C212yesmaximal, complemented
11C61×#1514C211yesmaximal, characteristic, complemented
12#16840494—22no—
13#16840486C412yescomplemented
14#16840477C412yescomplemented
15#16840458—22no—
16#16840432C412yescomplemented
17#16840416C412yescomplemented
18#16840349—21no—
19#16840349—21no—
20#16840326—21no—
21#16840319C2211yescharacteristic
22#16840272C2212yes—
23#16840272C2212yes—
24#16840245—21no—
25C2×C4×D244C2211yescharacteristic
26#16839835—22no—
27#16839832—22no—
28#16839819C2211yescharacteristic
29#16839724C2212yes—
30C22⋊C8×D61C2212yes—
31#16839651—21no—
32#16839647—21no—
33#16839640—21no—
34#16839624C2211yescharacteristic
35#16839621C2211yescharacteristic
36#16839609—21no—
37#16839609C2211yescharacteristic
38#16839608C2211yescharacteristic
39#95×D61C2211yescharacteristic
40#16839500C2212yes—
41#16839500C2212yes—
42#16839498C2212yes—
43#16839498C2212yes—
44#16839496C2212yes—
45#16839496C2212yes—
46C61×#532C2211yescharacteristic
47C61×#432C2211yescharacteristic
48C61×#383C2211yescharacteristic
49C61×#327C2212yes—
50C61×#327C2212yes—
51C2×#11758224C2×C412yes—
52C2×#11758224C2×C412yescomplemented
53C22×D244D411yescharacteristic
54C22×C4×D61—21no—
55C22×C4×D61C2311yescharacteristic
56C22×C4×D61C2311yescharacteristic
57C2×#11758189—22no—
58C2×C8×D61—22no—
59#14519777C2×C411yescharacteristic, complemented
60#14519777C2×C411yescharacteristic, complemented
61#14519773—22no—
62#14519772—22no—
63#14519772—22no—
64#14519769—21no—
65#14519766—22no—
66#14519763—22no—
67#14519763—22no—
68#14519761—22no—
69#14519761—22no—
70#14519759—22no—
71#14519759—22no—
72#14519757C2×C412yes—
73#14519757C2×C412yescomplemented
74#14519756—21no—
75#14519756C2312yes—
76#14519751—22no—
77#14519751—22no—
78#14519749—22no—
79#14519749—22no—
80#14519748C2×C412yes—
81#14519748C2×C412yescomplemented
82#14519745—22no—
83#14519745—22no—
84Q8×Dic61—22no—
85C4×Dic122—21no—
86C4×Dic122C2×C412yescomplemented
87C4×D244C2×C412yes—
88C4×D244C2×C412yes—
89C4×D244D412yes—
90C4×D244D412yes—
91D4×Dic61—22no—
92D4×Dic61—22no—
93D4×Dic61—22no—
94#14519737—22no—
95#14519737—22no—
96#14519736—21no—
97#14519736—22no—
98#14519735C2×C412yes—
99#14519735C2×C412yescomplemented
100C2×C4⋊Dic61—22no—
101C2×C4⋊Dic61D411yescharacteristic
102C2×#11758196—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198D411yescharacteristic
107C2×#11758198D411yescharacteristic
108C2×C4×Dic61—21no—
109C2×C4×Dic61—21no—
110C4⋊#92418—21no—
111C22⋊#92418C2312yes—
112#14519689—22no—
113#14519689—22no—
114#14519688—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684C2311yescharacteristic
119#14519684C2311yescharacteristic
120C2×#41×C61—21no—
121C4⋊Q8×C61C2×C411yescharacteristic, complemented
122#127×C61C2×C411yescharacteristic, complemented
123#124×C61—21no—
124#121×C61—21no—
125#121×C61C2312yes—
126C4×D4×C61—21no—
127C4×D4×C61C2×C412yescomplemented
128C2×C42×C61C2311yescharacteristic
129C4⋊C8×C61—21no—
130C22⋊C8×C61C2312yes—
131#97×C61—21no—
132#95×C61—21no—
133#95×C61—21no—
134#95×C61C2311yescharacteristic
135#95×C61C2311yescharacteristic
136C23×D61C2×D411yescharacteristic
137C23×D61C2×D411yescharacteristic
138#41×C61—42no—
139#41×C61—42no—
140C2×Q8×C61—21no—
141C2×D4×C61—22no—
142C2×D4×C61—21no—
143C2×D4×C61—21no—
144C2×D4×C61C22×C412yes—
145C22×C4×C61—22no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2411yescharacteristic
151C2×C22⋊D61—22no—
152C2×C22⋊D61—22no—
153C2×C22⋊D61—22no—
154C2×C22⋊D61—22no—
155C22×Dic61—21no—
156C22×Dic61—22no—
157C22×Dic61—22no—
158C22×Dic61—21no—
159C22×Dic61C2×D411yescharacteristic
160C22×Dic61C2×D411yescharacteristic
161#11758224—82no—
162#11758224—82no—
163C2×D244—41no—
164C2×D244—41no—
165C2×D244C22⋊C412yes—
166C2×D244C22⋊C412yes—
167C2×C4×D61—42no—
168C2×C4×D61—42no—
169C2×C4×D61—81no—
170C2×C4×D61—81no—
171C2×C4×D61—81no—
172C2×C4×D61C22×C412yes—
173C2×C4×D61C22×C412yes—
174C2×C4×D61C2×D412yes—
175C2×C4×D61C2×D412yes—
176C2×Dic122—21no—
177C2×Dic122C22×C412yes—
178C2×C8×C61—22no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61C22×C412yes—
181C22⋊C4×C61—22no—
182C22⋊C4×C61—22no—
183C42×C61C22×C411yescharacteristic
184C42×C61C22×C411yescharacteristic
185C42×C61C2×D411yescharacteristic
186C42×C61C2×D411yescharacteristic
187C22⋊Dic61—22no—
188C22⋊Dic61—22no—
189C22⋊Dic61—22no—
190#11758198—22no—
191#11758198—22no—
192#11758198—22no—
193#11758198—22no—
194#11758198—42no—
195#11758198—42no—
196#11758198—81no—
197#11758198C22⋊C412yes—
198#11758198C22⋊C412yes—
199#11758198C22⋊C412yes—
200#11758198C22⋊C412yes—
201C4⋊Dic61—21no—
202C4⋊Dic61—21no—
203C4⋊Dic61—21no—
204C4⋊Dic61—22no—
205C4⋊Dic61—22no—
206C4⋊Dic61C22⋊C412yes—
207C4⋊Dic61C22⋊C412yes—
208C4⋊Dic61C22×C412yes—
209#11758196—22no—
210#11758196—22no—
211#11758196—81no—
212C4×Dic61—22no—
213C4×Dic61—22no—
214C4×Dic61—22no—
215C4×Dic61—42no—
216C4×Dic61—81no—
217C2×#92418—22no—
218#11758189—82no—
219C8×D61—82no—
220C23×C61—22no—
221C23×C61C22×D411yescharacteristic
222C22×D61—21no—
223C22×D61—21no—
224C22×D61—21no—
225C22×D61—21no—
226C22×D61—41no—
227C22×D61—41no—
228C22×D61—41no—
229C22×D61—41no—
230C22×D61C2×C22⋊C412yes—
231C22×D61C2×C22⋊C412yes—
232Q8×C61—42no—
233D4×C61—42no—
234D4×C61—42no—
235D4×C61—42no—
236D4×C61—42no—
237D4×C61—81no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—22no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—44no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61C2×C22⋊C411yescharacteristic
251C2×C4×C61C2×C22⋊C411yescharacteristic
252C2×C4×C61C2×C22⋊C411yescharacteristic
253C2×C4×C61C2×C22⋊C411yescharacteristic
254C2×C4×C61C23×C411yescharacteristic
255C2×C4×C61C22×D411yescharacteristic
256C22⋊D61—82no—
257C22⋊D61—82no—
258C22⋊D61—82no—
259C22⋊D61—82no—
260C2×Dic61—22no—
261C2×Dic61—22no—
262C2×Dic61—22no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270C2×Dic61—82no—
271C2×Dic61—82no—
272C2×Dic61C2×C22⋊C412yes—
273C2×Dic61C2×C22⋊C412yes—
274D244—42no—
275D244—42no—
276C4×D61—42no—
277C4×D61—42no—
278C4×D61—42no—
279C4×D61—42no—
280C4×D61—84no—
281Dic122—42no—
282Dic122—81no—
283C8×C61—42no—
284#92418—42no—
285#17629—611nomaximal, Sylow
286C22×C61—21no—
287C22×C61—21no—
288C22×C61—42no—
289C22×C61—42no—
290C22×C61—42no—
291C22×C61C22×C22⋊C411yescharacteristic
292C22×C61#57511yescharacteristic
293C22×C61#57511yescharacteristic
294C2×D61—22no—
295C2×D61—22no—
296C2×D61—22no—
297C2×D61—22no—
298C2×D61—22no—
299C2×D61—22no—
300C2×D61—42no—
301C2×D61—42no—
302C2×D61—81no—
303C2×D61—81no—
304C4×C61—21no—
305C4×C61—21no—
306C4×C61—21no—
307C4×C61—21no—
308C4×C61—21no—
309C4×C61—21no—
310C4×C61—42no—
311C4×C61—81no—
312C4×C61—81no—
313Dic61—22no—
314Dic61—22no—
315Dic61—42no—
316Dic61—42no—
317Dic61—42no—
318Dic61—81no—
319#3506—611no—
320#2973—611no—
321#2353—611no—
322#1516—612no—
323#1515—611no—
324#1514D6111yescharacteristic, complemented
325#1513—612no—
326#1506—611no—
327#1505—611no—
328#1504—612no—
329#1501—612no—
330C2×C61—21no—
331C2×C61—21no—
332C2×C61—82no—
333C2×C61#288311yescharacteristic
334C2×C61#289611yescharacteristic
335C2×C61#290111yescharacteristic
336D61—42no—
337D61—42no—
338#559—1222no—
339#556—612no—
340#555—612no—
341#553—1222no—
342#550—612no—
343#547—612no—
344#538—1221no—
345#538—1221no—
346#535—1221no—
347#533—611no—
348#532C2×D6111yescharacteristic
349#525—612no—
350#525—612no—
351#520—1221no—
352C2×C4×D4—611no—
353#435—1222no—
354#435—1222no—
355#432—611no—
356#432C2×D6111yescharacteristic
357#407—612no—
358C2×C22⋊C8—612no—
359#388—1221no—
360#387—1221no—
361#386—1221no—
362#383C2×D6111yescharacteristic
363#381—611no—
364#380—611no—
365C4×C22⋊C4—611no—
366C4×C22⋊C4—1221no—
367#376—611no—
368C2×#95—611no—
369#328—612no—
370#328—612no—
371#328—612no—
372#328—612no—
373#327—612no—
374#327—612no—
375#327C2×D6112yes—
376#327C2×D6112yes—
377C61#1762911yescharacteristic, complemented, Sylow
378C2×#41—21no—
379C2×#41—612no—
380C2×#41—612no—
381C22×D4—611no—
382C23×C4—611no—
383C23×C4—611no—
384C23×C4—1221no—
385C2×M16—1222no—
386C22×C8—1222no—
387C4⋊Q8—611no—
388C4⋊Q8—611no—
389C4⋊Q8C4×D6111yescharacteristic, complemented
390#127—1222no—
391#127C4×D6111yescharacteristic, complemented
392#126—1222no—
393#126—1222no—
394#125—1221no—
395#124—21no—
396#124—1222no—
397#124—1222no—
398#124—1222no—
399#123—1222no—
400#123—1222no—
401#123—1222no—
402#123—1222no—
403C22⋊Q8—612no—
404C22⋊Q8—612no—
405C22⋊Q8—612no—
406C22⋊Q8—1221no—
407#121—21no—
408#121—612no—
409#121—612no—
410#121—1222no—
411#121—1222no—
412#121—1222no—
413#121—1222no—
414#121C22×D6112yes—
415#120—1222no—
416#120—1222no—
417C4×Q8—612no—
418C4×Q8—1222no—
419C4×Q8—1221no—
420C4×D4—21no—
421C4×D4—612no—
422C4×D4—612no—
423C4×D4—612no—
424C4×D4—612no—
425C4×D4—1222no—
426C4×D4—1222no—
427C4×D4—1222no—
428C4×D4—1222no—
429C4×D4—1222no—
430C4×D4C4×D6112yescomplemented
431#117—612no—
432#117—612no—
433#117—1222no—
434#117—1221no—
435C2×C4⋊C4—611no—
436C2×C4⋊C4—1222no—
437C2×C4⋊C4—1221no—
438C2×C22⋊C4—611no—
439C2×C22⋊C4—611no—
440C2×C22⋊C4—1221no—
441C2×C22⋊C4—1221no—
442C2×C22⋊C4—1221no—
443C2×C42—1221no—
444C2×C42—1221no—
445C2×C42C22×D6111yescharacteristic
446C4⋊C8—21no—
447C4⋊C8—1221no—
448C22⋊C8—612no—
449C22⋊C8—1222no—
450C22⋊C8—1222no—
451C22⋊C8C22×D6112yes—
452#97—21no—
453#97—1221no—
454#95—21no—
455#95—21no—
456#95—611no—
457#95—611no—
458#95—1221no—
459#95—1221no—
460#95—1221no—
461#95C22×D6111yescharacteristic
462#95C22×D6111yescharacteristic
463C24—611no—
464C24—611no—
465#41—42no—
466#41—42no—
467#41—4882no—
468#41—4882no—
469C2×Q8—21no—
470C2×Q8—612no—
471C2×Q8—1221no—
472C2×D4—22no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—612no—
476C2×D4—612no—
477C2×D4—1222no—
478C2×D4—1222no—
479C2×D4—1222no—
480C2×D4—1222no—
481C2×D4—2441no—
482C2×D4—2441no—
483C2×D4C2×C4×D6112yes—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—611no—
488C22×C4—611no—
489C22×C4—612no—
490C22×C4—612no—
491C22×C4—612no—
492C22×C4—612no—
493C22×C4—1222no—
494C22×C4—1222no—
495C22×C4—1221no—
496C22×C4—1221no—
497C22×C4—4881no—
498C22×C4—4881no—
499C22×C4—4881no—
500C22×C4—2442no—
501C22×C4—2442no—
502C22×C4D4×D6111yescharacteristic
503C22×C4D4×D6111yescharacteristic
504C22×C4C23×D6111yescharacteristic
505M16—4882no—
506C2×C8—22no—
507C2×C8—1222no—
508C2×C8—4882no—
509C4⋊C4—21no—
510C4⋊C4—612no—
511C4⋊C4—612no—
512C4⋊C4—612no—
513C4⋊C4—1222no—
514C4⋊C4—1222no—
515C4⋊C4—1222no—
516C4⋊C4—1221no—
517C4⋊C4—1222no—
518C4⋊C4—1221no—
519C4⋊C4—1221no—
520C4⋊C4—4881no—
521C4⋊C4C2×C4×D6112yes—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—612no—
525C22⋊C4—612no—
526C22⋊C4—612no—
527C22⋊C4—612no—
528C22⋊C4—1222no—
529C22⋊C4—1222no—
530C22⋊C4—1222no—
531C22⋊C4—1222no—
532C22⋊C4—1222no—
533C22⋊C4—1222no—
534C22⋊C4—1222no—
535C22⋊C4—4881no—
536C22⋊C4—2442no—
537C22⋊C4—2442no—
538C42—1222no—
539C42—1222no—
540C42—1222no—
541C42—4881no—
542C42—2442no—
543C42C2×C4×D6111yescharacteristic
544C42C2×C4×D6111yescharacteristic
545C42D4×D6111yescharacteristic
546C42D4×D6111yescharacteristic
547C23—22no—
548C23—612no—
549C23—612no—
550C23—1221no—
551C23—1221no—
552C23—1221no—
553C23—1221no—
554C23—2441no—
555C23—2441no—
556C23—2441no—
557C23—2441no—
558C23C2×D4×D6111yescharacteristic
559Q8—42no—
560Q8—4881no—
561Q8—2442no—
562D4—42no—
563D4—42no—
564D4—42no—
565D4—42no—
566D4—81no—
567D4—4882no—
568D4—4882no—
569D4—4882no—
570D4—4882no—
571D4—2442no—
572D4—2442no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—44no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—612no—
586C2×C4—612no—
587C2×C4—1222no—
588C2×C4—1222no—
589C2×C4—1222no—
590C2×C4—4884no—
591C2×C4—4882no—
592C2×C4—4882no—
593C2×C4—2442no—
594C2×C4—2442no—
595C2×C4—2442no—
596C2×C4—2442no—
597C2×C4—2441no—
598C2×C4—2441no—
599C2×C4—2441no—
600C2×C4—2441no—
601C2×C4—2441no—
602C2×C4—2441no—
603C2×C4—2441no—
604C2×C4C22⋊C4×D6111yescharacteristic
605C2×C4C22⋊C4×D6111yescharacteristic
606C2×C4C22⋊C4×D6111yescharacteristic
607C2×C4C22⋊C4×D6111yescharacteristic
608C2×C4C22×C4×D6111yescharacteristic
609C2×C4C2×D4×D6111yescharacteristic
610C8—42no—
611C8—2442no—
612C22—21no—
613C22—21no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—1222no—
618C22—1222no—
619C22—1222no—
620C22—1222no—
621C22—1222no—
622C22—1222no—
623C22—4881no—
624C22—4881no—
625C22—2442no—
626C22—2442no—
627C22C2×C22⋊C4×D6111yescharacteristic
628C22#1684055811yescharacteristic
629C22#1684055811yescharacteristic
630C4—21no—
631C4—21no—
632C4—21no—
633C4—21no—
634C4—21no—
635C4—21no—
636C4—42no—
637C4—81no—
638C4—81no—
639C4—1222no—
640C4—1222no—
641C4—4881no—
642C4—2442no—
643C4—2442no—
644C4—2442no—
645C2—21no—
646C2—21no—
647C2—82no—
648C2—2442no—
649C2—2442no—
650C2#2145427811yescharacteristic
651C2#2145433311yescharacteristic
652C2#2145436511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1514C2
socleC22×C61C22×C22⋊C4
prime radical#21459668C2
cosocleC22×C4×C61C24
hypercenter#1514D61
hypocenterC61#17629
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1514

Complements

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

NH ≅ G/Ntype
2. #21454847C2semidirect
3. #21448752C2semidirect
4. #21444372C2semidirect
5. #21444369C2semidirect
6. #21444359C2semidirect
7. #21444332C2semidirect
8. #21444327C2semidirect
9. #21444320C2semidirect
10. #21444307C2semidirect
11. C61×#1514C2semidirect
13. #16840486C4semidirect
14. #16840477C4semidirect
16. #16840432C4semidirect
17. #16840416C4semidirect
52. C2×#11758224C2×C4semidirect
59. #14519777C2×C4semidirect
60. #14519777C2×C4semidirect
73. #14519757C2×C4semidirect
81. #14519748C2×C4semidirect
86. C4×Dic122C2×C4semidirect
99. #14519735C2×C4semidirect
121. C4⋊Q8×C61C2×C4semidirect
122. #127×C61C2×C4semidirect
127. C4×D4×C61C2×C4semidirect
324. #1514D61semidirect
377. C61#17629semidirect
389. C4⋊Q8C4×D61semidirect
391. #127C4×D61semidirect
430. C4×D4C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214596682
#214548472
#214487522
#214443722
#214443692
#214443592
#214443322
#214443272
#214443202
#214443072
C61×#15142
#1762961