Finite Group Databasebeta

← #29648087

Subgroups — #29648087

Order 15616.

984 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840291C211yesmaximal, characteristic
2#21454450C211yesmaximal, characteristic, complemented
3#432×D61C211yesmaximal, characteristic, complemented
4#21444447C214yesmaximal, complemented
5#21444436C214yesmaximal, complemented
6#21444422C211yesmaximal, characteristic, complemented
7#21444420C211yesmaximal, characteristic, complemented
8#21444417C211yesmaximal, characteristic, complemented
9C61×#1527C211yesmaximal, characteristic, complemented
10#16840291—21no—
11#16840291—21no—
12#16840291—21no—
13#16840291—21no—
14#16840291C412yes—
15#16840291C412yes—
16#16840291C2212yes—
17#16840291C2212yes—
18C2×#14519770—21no—
19C2×#14519769C2211yescharacteristic
20C2×#14519759—21no—
21C2×#14519753C411yescharacteristic
22C2×#14519748C411yescharacteristic
23C2×Q8×Dic61C411yescharacteristic
24C2×D4×Dic61C411yescharacteristic
25C2×#14519737—21no—
26C2×#14519733—21no—
27C2×C42×D61C2211yescharacteristic
28#16839819C2211yescharacteristic
29#16839818—21no—
30#16839817C2212yescomplemented
31#16839817C2212yescomplemented
32#16839817C2212yescomplemented
33#16839816—21no—
34#16839813—21no—
35#16839813—21no—
36#16839785—21no—
37C4⋊C8×D61—21no—
38#16839725—21no—
39C22⋊C8×D61—21no—
40C4×#11758194C2211yescharacteristic
41#97×D61C2212yescomplemented
42#16839503C2214yescomplemented
43#16839503C2214yescomplemented
44#16839502C2214yescomplemented
45C2×#124×C61C2211yescharacteristic
46C61×#432C2211yescharacteristic
47C4×M16×C61C2211yescharacteristic
48C61×#329C2214yescomplemented
49C22×C22⋊D61—21no—
50C23×Dic61—21no—
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61D411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C2×#11758194—21no—
55C2×C8×D61—22no—
56#14519770—22no—
57#14519770—22no—
58#14519770—22no—
59#14519770—22no—
60#14519769—21no—
61#14519769—21no—
62#14519769C2×C412yes—
63#14519769C2312yes—
64#14519759—22no—
65#14519759—22no—
66#14519759—22no—
67#14519759—22no—
68#14519753—21no—
69#14519753—21no—
70#14519753C2×C412yes—
71#14519753C2×C412yes—
72#14519748—21no—
73#14519748—21no—
74#14519748C2×C412yes—
75#14519748C2×C412yes—
76Q8×Dic61—21no—
77Q8×Dic61—21no—
78Q8×Dic61C2×C412yes—
79Q8×Dic61C2×C412yes—
80D4×Dic61—21no—
81D4×Dic61—21no—
82D4×Dic61C2×C412yes—
83D4×Dic61C2×C412yes—
84#14519737—22no—
85#14519737—22no—
86#14519737—22no—
87#14519737—22no—
88#14519733—22no—
89#14519733—22no—
90#14519733—22no—
91#14519733—22no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61C2×C411yescharacteristic
94C2×C4⋊Dic61C2×C411yescharacteristic
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×C22⋊Dic61—21no—
99C2×C22⋊Dic61—21no—
100C2×#11758198—21no—
101C2×C4×Dic61—21no—
102C2×C4×Dic61C2×C411yescharacteristic
103C2×C4×Dic61D411yescharacteristic
104C2×C4×Dic61D411yescharacteristic
105C42×D61C2×C411yescharacteristic
106C42×D61C2×C411yescharacteristic
107C42×D61D411yescharacteristic
108C42×D61D411yescharacteristic
109C42×D61D411yescharacteristic
110C42×D61D411yescharacteristic
111C42×D61C2311yescharacteristic
112C42×D61C2311yescharacteristic
113C4⋊#92418—21no—
114#14519706—22no—
115#14519706—22no—
116#14519706—22no—
117C22⋊#92418—21no—
118#14519689—22no—
119#14519689—22no—
120#14519689—22no—
121#14519688C2312yes—
122#14519688C2312yes—
123#14519687—22no—
124C4×#92418—21no—
125C22×Q8×C61C2×C411yescharacteristic
126C22×D4×C61C2×C411yescharacteristic
127C2×M16×C61—21no—
128#124×C61—21no—
129#124×C61—21no—
130#124×C61C2×C412yes—
131#124×C61C2312yes—
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61—21no—
134C2×C42×C61C2311yescharacteristic
135C4⋊C8×C61—21no—
136C22⋊C8×C61—21no—
137#97×C61C2312yes—
138#97×C61C2312yes—
139C4×C8×C61—21no—
140C24×C61—21no—
141C23×D61C22⋊C411yescharacteristic
142C2×Q8×C61—21no—
143C2×Q8×C61—42no—
144C2×Q8×C61C22×C412yes—
145C2×D4×C61—21no—
146C2×D4×C61—42no—
147C2×D4×C61C22×C412yes—
148C22×C4×C61—21no—
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C2×C22⋊D61—22no—
153C2×C22⋊D61—22no—
154C2×C22⋊D61—44no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—22no—
158C22×Dic61—22no—
159C22×Dic61—44no—
160C22×Dic61C22⋊C411yescharacteristic
161C22×Dic61C22⋊C411yescharacteristic
162C22×Dic61C22⋊C411yescharacteristic
163C2×C4×D61—42no—
164C2×C4×D61—42no—
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
178M16×C61—42no—
179C2×C8×C61—22no—
180C2×C8×C61—22no—
181C22⋊C4×C61—22no—
182C22⋊C4×C61—22no—
183C22⋊C4×C61—22no—
184C22⋊C4×C61—22no—
185C42×C61C22×C411yescharacteristic
186C42×C61C2×D411yescharacteristic
187C42×C61C2×D411yescharacteristic
188C42×C61C2411yescharacteristic
189C22⋊Dic61—22no—
190C22⋊Dic61—22no—
191C22⋊Dic61—22no—
192C22⋊Dic61—22no—
193#11758198—22no—
194#11758198—22no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—22no—
198C4⋊Dic61—22no—
199C4⋊Dic61C22×C412yes—
200C4⋊Dic61C22×C412yes—
201#11758196—22no—
202#11758196—22no—
203#11758196—22no—
204#11758196—22no—
205#11758196—22no—
206#11758196—22no—
207C4×Dic61—22no—
208C4×Dic61—22no—
209C4×Dic61C22⋊C411yescharacteristic
210C4×Dic61C22⋊C411yescharacteristic
211C4×Dic61C22⋊C411yescharacteristic
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C22⋊C411yescharacteristic
214C4×Dic61C22⋊C411yescharacteristic
215C4×Dic61C22×C411yescharacteristic
216C4×Dic61C22×C411yescharacteristic
217C4×Dic61C2×D411yescharacteristic
218C4×Dic61C2×D411yescharacteristic
219C4×Dic61C2×D411yescharacteristic
220C4×Dic61C2×D411yescharacteristic
221#11758194—42no—
222C2×#92418—22no—
223C2×#92418—22no—
224C8×D61—44no—
225C23×C61—22no—
226C23×C61—42no—
227C23×C61—42no—
228C23×C61—42no—
229C23×C61C2×C22⋊C411yescharacteristic
230C22×D61—22no—
231C22×D61—22no—
232C22×D61—41no—
233C22×D61C2×C22⋊C411yescharacteristic
234C22×D61C2×C22⋊C411yescharacteristic
235Q8×C61—42no—
236Q8×C61—42no—
237D4×C61—42no—
238D4×C61—42no—
239C2×C4×C61—22no—
240C2×C4×C61—22no—
241C2×C4×C61—22no—
242C2×C4×C61—41no—
243C2×C4×C61—42no—
244C2×C4×C61C2×C22⋊C411yescharacteristic
245C2×C4×C61C2×C22⋊C411yescharacteristic
246C2×C4×C61C2×C22⋊C411yescharacteristic
247C2×C4×C61C23×C411yescharacteristic
248C2×C4×C61C22×D411yescharacteristic
249C2×C4×C61C22×D411yescharacteristic
250C22⋊D61—44no—
251C22⋊D61—44no—
252C2×Dic61—22no—
253C2×Dic61—22no—
254C2×Dic61—22no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61—44no—
258C2×Dic61—44no—
259C2×Dic61—42no—
260C2×Dic61—42no—
261C2×Dic61C2×C22⋊C411yescharacteristic
262C2×Dic61C2×C22⋊C411yescharacteristic
263C2×Dic61C2×C22⋊C411yescharacteristic
264C2×Dic61C2×C22⋊C411yescharacteristic
265C2×Dic61C2×C22⋊C411yescharacteristic
266C2×Dic61C2×C22⋊C411yescharacteristic
267C4×D61—22no—
268C4×D61—22no—
269C4×D61—22no—
270C4×D61—22no—
271C4×D61—41no—
272C4×D61—41no—
273C4×D61—41no—
274C4×D61—41no—
275C4×D61—41no—
276C4×D61—41no—
277C4×D61—41no—
278C4×D61—41no—
279C8×C61—42no—
280C8×C61—42no—
281#92418—42no—
282#92418—42no—
283#17668—611nomaximal, Sylow
284C22×C61—21no—
285C22×C61—21no—
286C22×C61—42no—
287C22×C61—42no—
288C22×C61—42no—
289C22×C61—84no—
290C22×C61#42112yes—
291C22×C61C22×C22⋊C411yescharacteristic
292C2×D61—21no—
293C2×D61—21no—
294C2×D61—21no—
295C2×D61—21no—
296C2×D61—21no—
297C2×D61—44no—
298C2×D61#42112yes—
299C4×C61—21no—
300C4×C61—21no—
301C4×C61—21no—
302C4×C61—21no—
303C4×C61—21no—
304C4×C61—42no—
305C4×C61#41312yes—
306Dic61—21no—
307Dic61—21no—
308Dic61—21no—
309Dic61—21no—
310Dic61—21no—
311Dic61—21no—
312Dic61—42no—
313Dic61—42no—
314C2×#529—611no—
315#2920—611no—
316C2×#432—611no—
317#1535—614no—
318#1532—614no—
319#1528—611no—
320#1528—611no—
321#1527—611no—
322#1527D6111yescharacteristic, complemented
323C2×C61—22no—
324C2×C61—82no—
325C2×C61C2×#41311yescharacteristic
326C2×C61C2×#42111yescharacteristic
327C2×C61C2×#42111yescharacteristic
328D61—22no—
329D61—41no—
330#529—612no—
331#529—612no—
332#529—612no—
333#529—612no—
334#529—1221no—
335#529—1221no—
336#529—1221no—
337#529—1221no—
338C2×#126—1221no—
339C2×#125—611no—
340C2×#124C2×D6111yescharacteristic
341C2×#123—1221no—
342C2×C22⋊Q8—611no—
343C2×#121—611no—
344C2×C4×Q8—611no—
345C2×C4×D4—611no—
346C2×C4×D4—1221no—
347C2×#117—1221no—
348C22×C42—611no—
349#432—611no—
350#432—612no—
351#432—612no—
352#432—612no—
353#432—1221no—
354#432—1221no—
355#432C2×D6111yescharacteristic
356#431—1221no—
357#431—1221no—
358#423—1221no—
359C2×C4⋊C8—1221no—
360#407—1221no—
361C2×C22⋊C8—1221no—
362C4×M16—611no—
363C4×M16C2×D6111yescharacteristic
364C2×#97—612no—
365#330—614no—
366#330—614no—
367#329—614no—
368#329C2×D6114yescomplemented
369C61#1766811yescharacteristic, complemented, Sylow
370C22×Q8C4×D6111yescharacteristic
371C22×D4—1221no—
372C22×D4C4×D6111yescharacteristic
373C23×C4—611no—
374C23×C4—611no—
375C23×C4—611no—
376C23×C4—1221no—
377C2×M16—21no—
378C2×M16—1221no—
379C22×C8—1222no—
380#126—1222no—
381#126—1222no—
382#126—1222no—
383#126—1222no—
384#125—612no—
385#125—612no—
386#125—1221no—
387#125—1221no—
388#124—21no—
389#124—21no—
390#124C4×D6112yes—
391#124C22×D6112yes—
392#123—1222no—
393#123—1222no—
394#123—1222no—
395#123—1222no—
396C22⋊Q8—612no—
397C22⋊Q8—612no—
398C22⋊Q8—1221no—
399C22⋊Q8—1221no—
400#121—612no—
401#121—612no—
402#121—1221no—
403#121—1221no—
404C4×Q8—612no—
405C4×Q8—612no—
406C4×Q8—1221no—
407C4×Q8—1221no—
408C4×D4—612no—
409C4×D4—612no—
410C4×D4—1221no—
411C4×D4—1221no—
412C4×D4—1222no—
413C4×D4—1222no—
414C4×D4—1222no—
415C4×D4—1222no—
416#117—1222no—
417#117—1222no—
418#117—1222no—
419#117—1222no—
420C2×C4⋊C4—611no—
421C2×C4⋊C4—611no—
422C2×C4⋊C4—1221no—
423C2×C4⋊C4—1221no—
424C2×C4⋊C4—1221no—
425C2×C4⋊C4—1221no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—1221no—
429C2×C22⋊C4—1221no—
430C2×C22⋊C4—1221no—
431C2×C42—611no—
432C2×C42—611no—
433C2×C42—611no—
434C2×C42—611no—
435C2×C42—611no—
436C2×C42—611no—
437C2×C42—611no—
438C2×C42—611no—
439C2×C42—611no—
440C2×C42—611no—
441C2×C42—611no—
442C2×C42—1221no—
443C2×C42C22×D6111yescharacteristic
444C4⋊C8—21no—
445C4⋊C8—1222no—
446C4⋊C8—1222no—
447C4⋊C8—1222no—
448C4⋊C8—1221no—
449C22⋊C8—21no—
450C22⋊C8—1222no—
451C22⋊C8—1222no—
452C22⋊C8—1222no—
453C22⋊C8—1221no—
454#97—612no—
455#97—612no—
456#97—1222no—
457#97C22×D6112yes—
458#97C22×D6112yes—
459C4×C8—21no—
460C4×C8—1221no—
461C24—21no—
462C24—611no—
463C2×Q8—21no—
464C2×Q8—42no—
465C2×Q8C2×C4×D6112yes—
466C2×D4—21no—
467C2×D4—42no—
468C2×D4—1222no—
469C2×D4—1222no—
470C2×D4—2444no—
471C2×D4C2×C4×D6112yes—
472C22×C4—21no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—611no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—611no—
488C22×C4—1222no—
489C22×C4—1222no—
490C22×C4—1221no—
491C22×C4—1221no—
492C22×C4—2442no—
493C22×C4—2442no—
494C22×C4—2442no—
495C22×C4—2444no—
496C22×C4C2×C4×D6111yescharacteristic
497C22×C4D4×D6111yescharacteristic
498C22×C4D4×D6111yescharacteristic
499M16—42no—
500M16—2442no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—1222no—
504C2×C8—1222no—
505C2×C8—2444no—
506C4⋊C4—612no—
507C4⋊C4—612no—
508C4⋊C4—1222no—
509C4⋊C4—1222no—
510C4⋊C4—1222no—
511C4⋊C4—1222no—
512C4⋊C4—1222no—
513C4⋊C4—1222no—
514C4⋊C4—1221no—
515C4⋊C4—1221no—
516C4⋊C4—1222no—
517C4⋊C4—1222no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—1222no—
523C22⋊C4—1222no—
524C22⋊C4—1222no—
525C22⋊C4—1222no—
526C22⋊C4—1222no—
527C22⋊C4—1222no—
528C42—611no—
529C42—611no—
530C42—611no—
531C42—611no—
532C42—611no—
533C42—611no—
534C42—611no—
535C42—611no—
536C42—611no—
537C42—611no—
538C42—611no—
539C42—611no—
540C42—1222no—
541C42—1222no—
542C42C2×C4×D6111yescharacteristic
543C42D4×D6111yescharacteristic
544C42D4×D6111yescharacteristic
545C42C23×D6111yescharacteristic
546C23—22no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—611no—
551C23—611no—
552C23—1222no—
553C23—1222no—
554C23—2441no—
555C23C22⋊C4×D6111yescharacteristic
556Q8—42no—
557Q8—42no—
558D4—42no—
559D4—42no—
560D4—2444no—
561D4—2444no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—611no—
568C2×C4—611no—
569C2×C4—611no—
570C2×C4—611no—
571C2×C4—611no—
572C2×C4—611no—
573C2×C4—1222no—
574C2×C4—1222no—
575C2×C4—1222no—
576C2×C4—1222no—
577C2×C4—1222no—
578C2×C4—1222no—
579C2×C4—1222no—
580C2×C4—2441no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4—2441no—
584C2×C4—2441no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4—2441no—
588C2×C4—2441no—
589C2×C4—2441no—
590C2×C4—2444no—
591C2×C4—2444no—
592C2×C4—2442no—
593C2×C4—2442no—
594C2×C4C22⋊C4×D6111yescharacteristic
595C2×C4C22⋊C4×D6111yescharacteristic
596C2×C4C22⋊C4×D6111yescharacteristic
597C2×C4C22×C4×D6111yescharacteristic
598C2×C4C2×D4×D6111yescharacteristic
599C2×C4C2×D4×D6111yescharacteristic
600C8—42no—
601C8—42no—
602C8—2442no—
603C8—2442no—
604C22—21no—
605C22—21no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22—84no—
610C22—612no—
611C22—1221no—
612C22—1221no—
613C22—1221no—
614C22—1221no—
615C22—1221no—
616C22—2444no—
617C22#1683977712yes—
618C22C2×C22⋊C4×D6111yescharacteristic
619C4—21no—
620C4—21no—
621C4—21no—
622C4—21no—
623C4—21no—
624C4—42no—
625C4—1221no—
626C4—1221no—
627C4—1221no—
628C4—1221no—
629C4—1221no—
630C4—1221no—
631C4—2442no—
632C4—2442no—
633C4#1683974312yes—
634C2—22no—
635C2—82no—
636C2—1222no—
637C2—2441no—
638C2C2×#1683974311yescharacteristic
639C2#421×D6111yescharacteristic
640C2C2×#1683977711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1527C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519748C4
cosocleC42×C61C24
hypercenter#1527D61
hypocenterC61#17668
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1527

Complements

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

NH ≅ G/Ntype
2. #21454450C2semidirect
3. #432×D61C2semidirect
4. #21444447C2semidirect
5. #21444436C2semidirect
6. #21444422C2semidirect
7. #21444420C2semidirect
8. #21444417C2semidirect
9. C61×#1527C2semidirect
30. #16839817C22semidirect
31. #16839817C22semidirect
32. #16839817C22semidirect
41. #97×D61C22semidirect
42. #16839503C22semidirect
43. #16839503C22semidirect
44. #16839502C22semidirect
48. C61×#329C22semidirect
322. #1527D61semidirect
368. #329C2×D61semidirect
369. C61#17668semidirect

Maximal subgroups

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

subgroupindex
C2×#168402912
#214544502
#432×D612
#214444472
#214444362
#214444222
#214444202
#214444172
C61×#15272
#1766861