Finite Group Databasebeta

← #29646671

Subgroups — #29646671

Order 15616.

1056 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459114C211yesmaximal, characteristic
2C2×#16839813C211yesmaximal, characteristic, complemented
3#423×D61C211yesmaximal, characteristic, complemented
4#21444281C214yesmaximal, complemented
5#21444275C211yesmaximal, characteristic, complemented
6#21444273C211yesmaximal, characteristic, complemented
7#21444270C211yesmaximal, characteristic, complemented
8#21444203C214yesmaximal, complemented
9C61×#1492C211yesmaximal, characteristic, complemented
10C2×M16×D61—21no—
11#16840319C2211yescharacteristic
12#16840317C411yescharacteristic
13#16840317C411yescharacteristic
14#16840310C411yescharacteristic
15#16840310C411yescharacteristic
16#16840294—21no—
17#16840294C2212yes—
18#16840293—21no—
19#16840293C412yes—
20#16840291—21no—
21#16840291—21no—
22#16840272—21no—
23#16840272C412yes—
24#16840269—21no—
25#41×Dic61—21no—
26C4×#11758224—21no—
27C4×#11758224C2212yes—
28C2×C42×D61C2211yescharacteristic
29#16839813—21no—
30#16839813—21no—
31#16839813C2212yes—
32#16839813C2212yes—
33#16839786C2211yescharacteristic
34#16839785—21no—
35#16839784—21no—
36#16839784C2212yes—
37C2×#14519706—21no—
38C4⋊C8×D61—21no—
39C4⋊C8×D61C2212yes—
40C2×#14519689—21no—
41C2×C4×#92418C2211yescharacteristic
42#16839494C2214yescomplemented
43#16839492C2214yescomplemented
44D4⋊#92418C2214yescomplemented
45C61×#532C2211yescharacteristic
46C61×#423C2211yescharacteristic
47C2×C4×C8×C61C2211yescharacteristic
48C61×D4⋊C8C2214yescomplemented
49C2×#11758224—21no—
50C2×#11758224C2×C412yes—
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61D411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C2×#11758194—21no—
55C2×#11758189—22no—
56M16×D61—44no—
57C22×#92418—21no—
58C2×C8×D61—22no—
59#14519777C2×C411yescharacteristic
60#14519777C2×C411yescharacteristic
61#14519770—22no—
62#14519770—22no—
63#14519769—21no—
64#14519768—21no—
65#14519768C2×C412yes—
66#14519764—21no—
67#14519764C2×C412yes—
68#14519759—22no—
69#14519759—22no—
70#14519758—22no—
71#14519757—21no—
72#14519757C2×C412yes—
73#14519756—21no—
74#14519756C2×C412yes—
75#14519753—21no—
76#14519753—21no—
77#14519748—21no—
78#14519748—21no—
79#14519748—21no—
80#14519748C2×C412yes—
81#14519745—22no—
82Q8×Dic61—21no—
83Q8×Dic61—21no—
84C4×Dic122—21no—
85C4×Dic122C2312yes—
86#14519742—21no—
87#14519742C2×C412yes—
88D4×Dic61—22no—
89D4×Dic61—22no—
90D4×Dic61—21no—
91D4×Dic61—21no—
92D4×Dic61—21no—
93D4×Dic61C2×C412yes—
94C4×C22⋊D61—22no—
95C4×C22⋊D61—22no—
96#14519737—22no—
97#14519737—22no—
98#14519736—21no—
99#14519736—22no—
100#14519735—21no—
101#14519735C2×C412yes—
102#14519733—22no—
103#14519733—22no—
104C2×C4×Dic61—22no—
105C2×C4×Dic61C2×C411yescharacteristic
106C2×C4×Dic61D411yescharacteristic
107C2×C4×Dic61D411yescharacteristic
108C42×D61C2×C411yescharacteristic
109C42×D61C2×C411yescharacteristic
110C42×D61D411yescharacteristic
111C42×D61D411yescharacteristic
112C42×D61D411yescharacteristic
113C42×D61D411yescharacteristic
114C42×D61C2311yescharacteristic
115C42×D61C2311yescharacteristic
116C4⋊#92418—21no—
117C4⋊#92418C2312yes—
118#14519706—22no—
119#14519706—22no—
120#14519706—22no—
121#14519706—22no—
122#14519689—22no—
123#14519689—22no—
124C4×#92418—21no—
125C4×#92418C2312yes—
126C2×#41×C61—21no—
127C2×M16×C61—21no—
128C22×C8×C61—21no—
129C4⋊Q8×C61C2×C411yescharacteristic
130#127×C61C2×C411yescharacteristic
131#124×C61—21no—
132#121×C61—21no—
133#121×C61C2×C412yes—
134C4×D4×C61—21no—
135C4×D4×C61C2312yes—
136C2×C42×C61C2311yescharacteristic
137C4⋊C8×C61—21no—
138C4⋊C8×C61C2312yes—
139C4×C8×C61—21no—
140C4×C8×C61C2312yes—
141C23×D61C22⋊C411yescharacteristic
142#41×C61—42no—
143#41×C61—42no—
144C2×Q8×C61—21no—
145C2×D4×C61—22no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61C22×C412yes—
149C22×C4×C61—22no—
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C2×C22⋊D61—22no—
154C2×C22⋊D61—22no—
155C22×Dic61—22no—
156C22×Dic61—22no—
157C22×Dic61C22⋊C411yescharacteristic
158C22×Dic61C22⋊C411yescharacteristic
159C22×Dic61C22⋊C411yescharacteristic
160#11758224—28no—
161#11758224—44no—
162C2×C4×D61—22no—
163C2×C4×D61—22no—
164C2×C4×D61—24no—
165C2×C4×D61—42no—
166C2×C4×D61C22⋊C411yescharacteristic
167C2×C4×D61C22⋊C411yescharacteristic
168C2×C4×D61C22⋊C411yescharacteristic
169C2×C4×D61C22⋊C411yescharacteristic
170C2×C4×D61C22⋊C411yescharacteristic
171C2×C4×D61C22⋊C411yescharacteristic
172C2×C4×D61C22×C411yescharacteristic
173C2×C4×D61C22×C411yescharacteristic
174C2×C4×D61C2×D411yescharacteristic
175C2×C4×D61C2×D411yescharacteristic
176C2×C4×D61C2×D411yescharacteristic
177C2×C4×D61C2×D411yescharacteristic
178C2×Dic122—21no—
179C2×Dic122C22×C412yes—
180M16×C61—42no—
181C2×C8×C61—22no—
182C2×C8×C61—22no—
183C2×C8×C61—42no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61C22×C412yes—
186C22⋊C4×C61—22no—
187C22⋊C4×C61—22no—
188C42×C61C22×C411yescharacteristic
189C42×C61C2×D411yescharacteristic
190C42×C61C2×D411yescharacteristic
191C42×C61C2411yescharacteristic
192C22⋊Dic61—22no—
193C22⋊Dic61—22no—
194C22⋊Dic61—22no—
195C22⋊Dic61—22no—
196C22⋊Dic61—22no—
197#11758198—22no—
198#11758198—22no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—21no—
202C4⋊Dic61—22no—
203C4⋊Dic61—22no—
204C4⋊Dic61C22×C412yes—
205#11758196—22no—
206#11758196—22no—
207#11758196—22no—
208#11758196—22no—
209C4×Dic61—22no—
210C4×Dic61—22no—
211C4×Dic61—22no—
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C22⋊C411yescharacteristic
214C4×Dic61C22⋊C411yescharacteristic
215C4×Dic61C22⋊C411yescharacteristic
216C4×Dic61C22⋊C411yescharacteristic
217C4×Dic61C22⋊C411yescharacteristic
218C4×Dic61C22×C411yescharacteristic
219C4×Dic61C22×C411yescharacteristic
220C4×Dic61C2×D411yescharacteristic
221C4×Dic61C2×D411yescharacteristic
222C4×Dic61C2×D411yescharacteristic
223C4×Dic61C2×D411yescharacteristic
224#11758194—42no—
225C2×#92418—22no—
226C2×#92418—22no—
227C2×#92418—42no—
228#11758189—44no—
229C8×D61—44no—
230C23×C61—22no—
231C23×C61C2×C22⋊C411yescharacteristic
232C22×D61—22no—
233C22×D61—22no—
234C22×D61—41no—
235C22×D61C2×C22⋊C411yescharacteristic
236C22×D61C2×C22⋊C411yescharacteristic
237Q8×C61—42no—
238D4×C61—24no—
239D4×C61—44no—
240D4×C61—42no—
241D4×C61—42no—
242C2×C4×C61—22no—
243C2×C4×C61—22no—
244C2×C4×C61—22no—
245C2×C4×C61—42no—
246C2×C4×C61—42no—
247C2×C4×C61C2×C22⋊C411yescharacteristic
248C2×C4×C61C2×C22⋊C411yescharacteristic
249C2×C4×C61C2×C22⋊C411yescharacteristic
250C2×C4×C61AGL(1,ℤ/8)12yes—
251C2×C4×C61#13712yes—
252C2×C4×C61C23×C411yescharacteristic
253C2×C4×C61C22×D411yescharacteristic
254C2×C4×C61C22×D411yescharacteristic
255C22⋊D61—44no—
256C22⋊D61—44no—
257C2×Dic61—22no—
258C2×Dic61—22no—
259C2×Dic61—22no—
260C2×Dic61—22no—
261C2×Dic61—41no—
262C2×Dic61—44no—
263C2×Dic61—44no—
264C2×Dic61C2×C22⋊C411yescharacteristic
265C2×Dic61C2×C22⋊C411yescharacteristic
266C2×Dic61C2×C22⋊C411yescharacteristic
267C2×Dic61C2×C22⋊C411yescharacteristic
268C2×Dic61C2×C22⋊C411yescharacteristic
269C2×Dic61C2×C22⋊C411yescharacteristic
270C4×D61—22no—
271C4×D61—22no—
272C4×D61—21no—
273C4×D61—21no—
274C4×D61—21no—
275C4×D61—21no—
276C4×D61—22no—
277C4×D61—22no—
278C4×D61—22no—
279C4×D61—22no—
280C4×D61—22no—
281C4×D61—41no—
282C4×D61—41no—
283C4×D61#13114yes—
284Dic122—24no—
285Dic122—42no—
286C8×C61—42no—
287C8×C61—42no—
288#92418—42no—
289#92418—42no—
290#17481—611nomaximal, Sylow
291C22×C61—21no—
292C22×C61—21no—
293C22×C61—42no—
294C22×C61—42no—
295C22×C61—42no—
296C22×C61#41712yes—
297C22×C61C22×C22⋊C411yescharacteristic
298C2×D61—21no—
299C2×D61—21no—
300C2×D61—21no—
301C2×D61—21no—
302C2×D61—21no—
303C2×D61—44no—
304C2×D61#40812yes—
305C4×C61—21no—
306C4×C61—21no—
307C4×C61—42no—
308C4×C61#41712yes—
309C4×C61#42112yes—
310C4×C61C2×#13112yes—
311C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
312C4×C61C2×#13711yescharacteristic
313Dic61—21no—
314Dic61—21no—
315Dic61—21no—
316Dic61—21no—
317Dic61—21no—
318Dic61—42no—
319Dic61—42no—
320Dic61#40812yes—
321#3444—611no—
322C2×#431—611no—
323C2×#423—611no—
324#1495—614no—
325#1493—611no—
326#1493—611no—
327#1492—611no—
328#1492D6111yescharacteristic, complemented
329#1477—614no—
330C2×C61—22no—
331C2×C61—82no—
332C2×C61C2×#40811yescharacteristic
333C2×C61C2×#41711yescharacteristic
334C2×C61C2×#42111yescharacteristic
335D61—22no—
336D61—41no—
337C22×M16—1221no—
338#533—611no—
339#533—611no—
340#533—611no—
341#532—611no—
342#532—611no—
343#532C2×D6111yescharacteristic
344#529—612no—
345#529—612no—
346#529—1221no—
347#529—1221no—
348#529—1221no—
349#529—1221no—
350#525—612no—
351#525—1221no—
352#525—1221no—
353C4×#41—612no—
354C4×#41—1221no—
355C4×#41—1221no—
356C22×C42—611no—
357#431—612no—
358#431—612no—
359#431—1221no—
360#431—1221no—
361#423—611no—
362#423—612no—
363#423—1221no—
364#423—1221no—
365#423C2×D6111yescharacteristic
366C2×C4⋊C8—612no—
367C2×C4⋊C8—1221no—
368C2×C4⋊C8—1221no—
369C2×C22⋊C8—1221no—
370C2×C4×C8—611no—
371C2×C4×C8C2×D6111yescharacteristic
372Q8⋊C8—614no—
373Q8⋊C8—614no—
374D4⋊C8—614no—
375D4⋊C8C2×D6114yescomplemented
376C61#1748111yescharacteristic, complemented, Sylow
377C2×#41—21no—
378C2×#41—612no—
379C2×#41—1221no—
380C23×C4—611no—
381C23×C4—611no—
382C23×C4—611no—
383C2×M16—21no—
384C2×M16—1222no—
385C2×M16—1221no—
386C2×M16—2444no—
387C22×C8—21no—
388C22×C8—1222no—
389C22×C8—1221no—
390C4⋊Q8—611no—
391C4⋊Q8—611no—
392C4⋊Q8C4×D6111yescharacteristic
393#127C4×D6111yescharacteristic
394#126—1222no—
395#126—1222no—
396#125—612no—
397#125—1221no—
398#125—1221no—
399#124—21no—
400#124—612no—
401#124—1221no—
402#123—1222no—
403#123—1222no—
404#123—1222no—
405C22⋊Q8—612no—
406C22⋊Q8—612no—
407C22⋊Q8—1221no—
408C22⋊Q8—1221no—
409C22⋊Q8—1221no—
410C22⋊Q8—1221no—
411#121—21no—
412#121—612no—
413#121—1221no—
414#121—1221no—
415#121—1221no—
416#121C4×D6112yes—
417#120—1222no—
418C4×Q8—612no—
419C4×Q8—612no—
420C4×Q8—1221no—
421C4×Q8—1221no—
422C4×Q8—1221no—
423C4×Q8—1221no—
424C4×D4—21no—
425C4×D4—612no—
426C4×D4—1221no—
427C4×D4—1221no—
428C4×D4—1221no—
429C4×D4—1222no—
430C4×D4—1222no—
431C4×D4—1222no—
432C4×D4—1222no—
433C4×D4—1222no—
434C4×D4—1222no—
435C4×D4C22×D6112yes—
436#117—612no—
437#117—1222no—
438#117—1222no—
439#117—1222no—
440#117—1221no—
441#117—1221no—
442C2×C42—611no—
443C2×C42—611no—
444C2×C42—611no—
445C2×C42—611no—
446C2×C42—611no—
447C2×C42—611no—
448C2×C42—611no—
449C2×C42—611no—
450C2×C42—611no—
451C2×C42—611no—
452C2×C42—611no—
453C2×C42—1222no—
454C2×C42C22×D6111yescharacteristic
455C4⋊C8—21no—
456C4⋊C8—612no—
457C4⋊C8—1222no—
458C4⋊C8—1222no—
459C4⋊C8—1222no—
460C4⋊C8—1222no—
461C4⋊C8—1221no—
462C4⋊C8C22×D6112yes—
463C22⋊C8—1222no—
464C22⋊C8—1222no—
465C4×C8—21no—
466C4×C8—612no—
467C4×C8—1221no—
468C4×C8C22×D6112yes—
469C24—611no—
470#41—42no—
471#41—42no—
472#41—1228no—
473#41—2444no—
474C2×Q8—21no—
475C2×Q8—612no—
476C2×Q8—1221no—
477C2×D4—22no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—1222no—
481C2×D4—1222no—
482C2×D4C2×C4×D6112yes—
483C22×C4—22no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—611no—
488C22×C4—611no—
489C22×C4—611no—
490C22×C4—611no—
491C22×C4—611no—
492C22×C4—611no—
493C22×C4—611no—
494C22×C4—611no—
495C22×C4—611no—
496C22×C4—611no—
497C22×C4—611no—
498C22×C4—611no—
499C22×C4—1224no—
500C22×C4—1222no—
501C22×C4—1222no—
502C22×C4—1222no—
503C22×C4—1222no—
504C22×C4—2442no—
505C22×C4C2×C4×D6111yescharacteristic
506C22×C4D4×D6111yescharacteristic
507C22×C4D4×D6111yescharacteristic
508M16—42no—
509M16—2444no—
510M16—2442no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8—42no—
514C2×C8—1222no—
515C2×C8—1222no—
516C2×C8—2444no—
517C2×C8—2442no—
518C4⋊C4—21no—
519C4⋊C4—612no—
520C4⋊C4—1222no—
521C4⋊C4—1222no—
522C4⋊C4—1222no—
523C4⋊C4—1222no—
524C4⋊C4—1222no—
525C4⋊C4—1222no—
526C4⋊C4—1221no—
527C4⋊C4—1221no—
528C4⋊C4—1221no—
529C4⋊C4C2×C4×D6112yes—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—1222no—
533C22⋊C4—1222no—
534C22⋊C4—1222no—
535C22⋊C4—1222no—
536C22⋊C4—1222no—
537C22⋊C4—1222no—
538C22⋊C4—1222no—
539C42—611no—
540C42—611no—
541C42—611no—
542C42—611no—
543C42—611no—
544C42—611no—
545C42—611no—
546C42—611no—
547C42—611no—
548C42—611no—
549C42—611no—
550C42—611no—
551C42—1222no—
552C42—1222no—
553C42—1222no—
554C42C2×C4×D6111yescharacteristic
555C42D4×D6111yescharacteristic
556C42D4×D6111yescharacteristic
557C42C23×D6111yescharacteristic
558C23—22no—
559C23—611no—
560C23—611no—
561C23—1222no—
562C23—1222no—
563C23—2441no—
564C23C22⋊C4×D6111yescharacteristic
565Q8—42no—
566Q8—1224no—
567Q8—2442no—
568D4—24no—
569D4—44no—
570D4—42no—
571D4—42no—
572D4—2444no—
573D4—2444no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—611no—
580C2×C4—614no—
581C2×C4—611no—
582C2×C4—611no—
583C2×C4—611no—
584C2×C4—611no—
585C2×C4—611no—
586C2×C4—1222no—
587C2×C4—1222no—
588C2×C4—1222no—
589C2×C4—1222no—
590C2×C4—1222no—
591C2×C4—1222no—
592C2×C4—1222no—
593C2×C4—1222no—
594C2×C4—1222no—
595C2×C4—1221no—
596C2×C4—1221no—
597C2×C4—1221no—
598C2×C4—1221no—
599C2×C4—1222no—
600C2×C4—1222no—
601C2×C4—2441no—
602C2×C4—2441no—
603C2×C4—2444no—
604C2×C4—2441no—
605C2×C4—2444no—
606C2×C4C22⋊C4×D6111yescharacteristic
607C2×C4C22⋊C4×D6111yescharacteristic
608C2×C4C22⋊C4×D6111yescharacteristic
609C2×C4#1451980112yes—
610C2×C4#1451980612yes—
611C2×C4C22×C4×D6111yescharacteristic
612C2×C4C2×D4×D6111yescharacteristic
613C2×C4C2×D4×D6111yescharacteristic
614C8—42no—
615C8—42no—
616C8—2442no—
617C8—2442no—
618C22—21no—
619C22—21no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22—612no—
624C22—1221no—
625C22—1221no—
626C22—1221no—
627C22—1221no—
628C22—1221no—
629C22—2444no—
630C22#1683976012yes—
631C22C2×C22⋊C4×D6111yescharacteristic
632C4—21no—
633C4—21no—
634C4—42no—
635C4—612no—
636C4—1221no—
637C4—1221no—
638C4—1221no—
639C4—1221no—
640C4—1221no—
641C4—2442no—
642C4—2442no—
643C4#1683976012yes—
644C4#1683977712yes—
645C4#131×D6112yes—
646C4C2×#1451980111yescharacteristic
647C4C2×#1451980611yescharacteristic
648C2—22no—
649C2—82no—
650C2—1222no—
651C2—2441no—
652C2#408×D6111yescharacteristic
653C2C2×#1683976011yescharacteristic
654C2C2×#1683977711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1492C2
socleC22×C61C22×C22⋊C4
prime radical#21459114C2
cosocleC42×C61C24
hypercenter#1492D61
hypocenterC61#17481
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1492

Complements

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

NH ≅ G/Ntype
2. C2×#16839813C2semidirect
3. #423×D61C2semidirect
4. #21444281C2semidirect
5. #21444275C2semidirect
6. #21444273C2semidirect
7. #21444270C2semidirect
8. #21444203C2semidirect
9. C61×#1492C2semidirect
42. #16839494C22semidirect
43. #16839492C22semidirect
44. D4⋊#92418C22semidirect
48. C61×D4⋊C8C22semidirect
328. #1492D61semidirect
375. D4⋊C8C2×D61semidirect
376. C61#17481semidirect

Maximal subgroups

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

subgroupindex
#214591142
C2×#168398132
#423×D612
#214442812
#214442752
#214442732
#214442702
#214442032
C61×#14922
#1748161