Finite Group Databasebeta

← #29645996

Subgroups — #29645996

Order 15616.

1020 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840298C211yesmaximal, characteristic
2#21454448C211yesmaximal, characteristic, complemented
3C2×#16839812C211yesmaximal, characteristic, complemented
4#21444187C214yesmaximal, complemented
5#21444183C211yesmaximal, characteristic, complemented
6#21444180C211yesmaximal, characteristic
7#21444178C211yesmaximal, characteristic
8#21444132C214yesmaximal, complemented
9C61×#1472C211yesmaximal, characteristic, complemented
10#16840298—21no—
11#16840298—21no—
12#16840298—21no—
13#16840298—21no—
14#16840298—21no—
15#16840298—21no—
16#16840298—21no—
17#16840298—21no—
18C2×#14519772C2212yes—
19C2×#14519768C411yescharacteristic
20C2×#14519766C411yescharacteristic
21C2×#14519761C412yes—
22C2×#14519751C2211yescharacteristic
23C2×Q8×Dic61C411yescharacteristic
24C2×#14519739C411yescharacteristic
25C2×#14519737C412yes—
26C2×#14519735C2212yes—
27C22×C4×Dic61C2211yescharacteristic
28#16839816—21no—
29#16839816C2212yes—
30#16839812—21no—
31#16839812—21no—
32#16839812—21no—
33#16839812C2212yes—
34#16839812C2212yes—
35#16839812C2212yes—
36#16839785—21no—
37C2×#14519706—21no—
38#16839726C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40M16×Dic61—21no—
41C2×C8×Dic61—21no—
42#16839488C2214yes—
43#16839485C2214yes—
44#16839485C2214yes—
45C2×C22⋊Q8×C61C2211yescharacteristic
46C61×#407C2211yescharacteristic
47C2×C22⋊C8×C61C2211yescharacteristic
48C61×#324C2214yes—
49C22×D244C2×C411yescharacteristic
50C22×C22⋊D61C2×C412yes—
51C23×Dic61C2×C411yescharacteristic
52C23×Dic61C2×C411yescharacteristic
53C22×C4×D61C2×C412yes—
54C2×#11758194—21no—
55C22×#92418—21no—
56#14519772—22no—
57#14519772—22no—
58#14519772—22no—
59#14519772—22no—
60#14519768—21no—
61#14519768—21no—
62#14519768—21no—
63#14519768—21no—
64#14519766—21no—
65#14519766—21no—
66#14519766—21no—
67#14519766—21no—
68#14519761—22no—
69#14519761—22no—
70#14519761—22no—
71#14519761—22no—
72#14519751—21no—
73#14519751—21no—
74#14519751—21no—
75#14519751—21no—
76Q8×Dic61—21no—
77Q8×Dic61—21no—
78Q8×Dic61—21no—
79Q8×Dic61—21no—
80#14519739—21no—
81#14519739—21no—
82#14519739—21no—
83#14519739—21no—
84#14519737—22no—
85#14519737—22no—
86#14519737—22no—
87#14519737—22no—
88#14519735—22no—
89#14519735—22no—
90#14519735—22no—
91#14519735—22no—
92C2×C4⋊Dic61C2×C412yes—
93C2×C4⋊Dic61C2×C411yescharacteristic
94C2×C4⋊Dic61C2×C412yes—
95C2×#11758196C2×C412yes—
96C2×#11758198C2×C412yes—
97C2×#11758198C2×C412yes—
98C2×#11758198C2×C412yes—
99C2×#11758198C2312yes—
100C2×C4×Dic61C2×C412yes—
101C2×C4×Dic61C2×C411yescharacteristic
102C2×C4×Dic61C2×C411yescharacteristic
103C2×C4×Dic61D411yescharacteristic
104C2×C4×Dic61D411yescharacteristic
105C2×C4×Dic61D411yescharacteristic
106C2×C4×Dic61D411yescharacteristic
107C2×C4×Dic61D411yescharacteristic
108C2×C4×Dic61D411yescharacteristic
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61C2311yescharacteristic
112C2×C4×Dic61C2311yescharacteristic
113#14519706—22no—
114#14519706—22no—
115#14519706—22no—
116#14519706—22no—
117C22⋊#92418—21no—
118C22⋊#92418—21no—
119C22⋊#92418C2312yes—
120C22⋊#92418C2312yes—
121#14519687—22no—
122C8×Dic61—22no—
123C8×Dic61—22no—
124C8×Dic61—22no—
125C22×Q8×C61C2×C411yescharacteristic
126C23×C4×C61C2311yescharacteristic
127C2×M16×C61—21no—
128C22×C8×C61—21no—
129C22⋊Q8×C61—21no—
130C22⋊Q8×C61—21no—
131C22⋊Q8×C61—21no—
132C22⋊Q8×C61—21no—
133C2×C4⋊C4×C61C2×C411yescharacteristic
134C2×C4⋊C4×C61C2312yes—
135C2×C22⋊C4×C61C2×C412yes—
136C22⋊C8×C61—21no—
137C22⋊C8×C61—21no—
138C22⋊C8×C61C2312yes—
139C22⋊C8×C61C2312yes—
140C24×C61C22×C411yescharacteristic
141C23×D61C22×C412yes—
142C2×Q8×C61—21no—
143C2×Q8×C61—21no—
144C2×Q8×C61—42no—
145C22×C4×C61—42no—
146C22×C4×C61C22×C412yes—
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C22×C412yes—
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2411yescharacteristic
154C2×C22⋊D61—22no—
155C2×C22⋊D61—22no—
156C2×C22⋊D61—44no—
157C22×Dic61—24no—
158C22×Dic61—42no—
159C22×Dic61C22⋊C411yescharacteristic
160C22×Dic61C22⋊C411yescharacteristic
161C22×Dic61C22⋊C411yescharacteristic
162C22×Dic61C22⋊C411yescharacteristic
163C22×Dic61C22⋊C411yescharacteristic
164C22×Dic61C22⋊C411yescharacteristic
165C22×Dic61C22⋊C411yescharacteristic
166C22×Dic61C22⋊C411yescharacteristic
167C22×Dic61C22×C411yescharacteristic
168C22×Dic61C22×C412yes—
169C22×Dic61C22×C411yescharacteristic
170C22×Dic61C22×C411yescharacteristic
171C22×Dic61C22×C411yescharacteristic
172C2×D244—21no—
173C2×D244—21no—
174C2×D244—42no—
175C2×C4×D61—22no—
176C2×C4×D61—22no—
177C2×C4×D61—28no—
178M16×C61—42no—
179C2×C8×C61—22no—
180C2×C8×C61—22no—
181C2×C8×C61—42no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—22no—
185C4⋊C4×C61—22no—
186C22⋊C4×C61—22no—
187C22⋊C4×C61—22no—
188#11758198—22no—
189#11758198—22no—
190#11758198—22no—
191#11758198—22no—
192#11758198—22no—
193#11758198—22no—
194#11758198—22no—
195#11758198—22no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—22no—
199C4⋊Dic61—22no—
200C4⋊Dic61—22no—
201C4⋊Dic61—22no—
202#11758196—22no—
203#11758196—22no—
204C4×Dic61—22no—
205C4×Dic61—22no—
206C4×Dic61C22⋊C411yescharacteristic
207C4×Dic61C22⋊C411yescharacteristic
208C4×Dic61C22⋊C411yescharacteristic
209C4×Dic61C22⋊C411yescharacteristic
210C4×Dic61C22⋊C411yescharacteristic
211C4×Dic61C22⋊C411yescharacteristic
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C22⋊C411yescharacteristic
214C4×Dic61C2×D411yescharacteristic
215C4×Dic61C2×D411yescharacteristic
216C4×Dic61C2×D411yescharacteristic
217C4×Dic61C2×D411yescharacteristic
218C4×Dic61C2×D411yescharacteristic
219C4×Dic61C2×D411yescharacteristic
220C4×Dic61C2×D411yescharacteristic
221C4×Dic61C2×D411yescharacteristic
222#11758194—42no—
223C2×#92418—22no—
224C2×#92418—22no—
225C2×#92418—42no—
226C23×C61—22no—
227C23×C61—22no—
228C23×C61—41no—
229C23×C61C2×C22⋊C411yescharacteristic
230C23×C61C2×C22⋊C411yescharacteristic
231C23×C61C23×C411yescharacteristic
232C22×D61—22no—
233C22×D61—24no—
234C22×D61—42no—
235C22×D61—42no—
236Q8×C61—42no—
237Q8×C61—42no—
238C2×C4×C61—22no—
239C2×C4×C61—22no—
240C2×C4×C61—22no—
241C2×C4×C61—22no—
242C2×C4×C61—22no—
243C2×C4×C61—24no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—42no—
248C2×C4×C61C2×C22⋊C411yescharacteristic
249C2×C4×C61C2×C22⋊C411yescharacteristic
250C2×C4×C61C22×D411yescharacteristic
251C2×C4×C61C22×D411yescharacteristic
252C22⋊D61—44no—
253C22⋊D61—44no—
254C2×Dic61—22no—
255C2×Dic61—22no—
256C2×Dic61—22no—
257C2×Dic61—22no—
258C2×Dic61—22no—
259C2×Dic61—22no—
260C2×Dic61—22no—
261C2×Dic61—22no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—42no—
267C2×Dic61C2×C22⋊C411yescharacteristic
268C2×Dic61C2×C22⋊C411yescharacteristic
269C2×Dic61C2×C22⋊C411yescharacteristic
270C2×Dic61C2×C22⋊C411yescharacteristic
271C2×Dic61C2×C22⋊C411yescharacteristic
272C2×Dic61C2×C22⋊C411yescharacteristic
273C2×Dic61C2×C22⋊C411yescharacteristic
274C2×Dic61C2×C22⋊C411yescharacteristic
275C2×Dic61#13114yes—
276D244—42no—
277D244—42no—
278C4×D61—44no—
279C4×D61—44no—
280C8×C61—42no—
281C8×C61—42no—
282#92418—42no—
283#92418—42no—
284#17380—611nomaximal, Sylow
285C22×C61—21no—
286C22×C61—21no—
287C22×C61—21no—
288C22×C61—21no—
289C22×C61—21no—
290C22×C61—21no—
291C22×C61—21no—
292C22×C61—44no—
293C22×C61#41312yes—
294C22×C61C22×C22⋊C411yescharacteristic
295C22×C61C2×#13112yes—
296C2×D61—42no—
297C2×D61—42no—
298C2×D61—42no—
299C2×D61—84no—
300C4×C61—21no—
301C4×C61—21no—
302C4×C61—21no—
303C4×C61—42no—
304C4×C61—42no—
305C4×C61#41012yes—
306Dic61—21no—
307Dic61—21no—
308Dic61—21no—
309Dic61—21no—
310Dic61—21no—
311Dic61—21no—
312Dic61—42no—
313Dic61#40812yes—
314Dic61#40812yes—
315C2×#529—611no—
316#2920—611no—
317C2×#431—611no—
318#1473—614no—
319#1472—611no—
320#1472D6111yescharacteristic, complemented
321#1471—611no—
322#1471—611no—
323#1458—614no—
324C2×C61—22no—
325C2×C61—22no—
326C2×C61—41no—
327C2×C61C2×#40811yescharacteristic
328C2×C61C2×#41011yescharacteristic
329C2×C61C2×#41311yescharacteristic
330D61—82no—
331#529—1221no—
332#529—1221no—
333#529—1221no—
334#529—1221no—
335#529—1221no—
336#529—1221no—
337#529—1221no—
338#529—1221no—
339C2×#126—612no—
340C2×#125—611no—
341C2×#124—611no—
342C2×#123—612no—
343C2×C22⋊Q8C2×D6111yescharacteristic
344C2×#121—611no—
345C2×C4×Q8—611no—
346C2×C4×D4—611no—
347C2×C4×D4—612no—
348C2×#117—612no—
349C22×C42—611no—
350#432—612no—
351#432—1221no—
352#431—612no—
353#431—612no—
354#431—612no—
355#431—1221no—
356#431—1221no—
357#431—1221no—
358#423—1221no—
359C2×C4⋊C8—1221no—
360#407—611no—
361#407C2×D6111yescharacteristic
362C2×C22⋊C8—611no—
363C2×C22⋊C8C2×D6111yescharacteristic
364C4×M16—1221no—
365C2×C4×C8—1221no—
366#324—614no—
367#324C2×D6114yes—
368#323—614no—
369#323—614no—
370C61#1738011yescharacteristic, complemented, Sylow
371C22×Q8C4×D6111yescharacteristic
372C22×D4—612no—
373C22×D4—611no—
374C23×C4—611no—
375C23×C4—611no—
376C23×C4—612no—
377C23×C4C22×D6111yescharacteristic
378C2×M16—21no—
379C2×M16—1221no—
380C22×C8—21no—
381C22×C8—1221no—
382#126—1222no—
383#126—1222no—
384#126—1222no—
385#126—1222no—
386#125—1221no—
387#125—1221no—
388#125—1221no—
389#125—1221no—
390#124—1221no—
391#124—1221no—
392#124—1221no—
393#124—1221no—
394#123—1222no—
395#123—1222no—
396#123—1222no—
397#123—1222no—
398C22⋊Q8—21no—
399C22⋊Q8—21no—
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402#121—1221no—
403#121—1221no—
404#121—1221no—
405#121—1221no—
406C4×Q8—1221no—
407C4×Q8—1221no—
408C4×Q8—1221no—
409C4×Q8—1221no—
410C4×D4—1221no—
411C4×D4—1221no—
412C4×D4—1221no—
413C4×D4—1221no—
414C4×D4—1222no—
415C4×D4—1222no—
416C4×D4—1222no—
417C4×D4—1222no—
418#117—1222no—
419#117—1222no—
420#117—1222no—
421#117—1222no—
422C2×C4⋊C4—612no—
423C2×C4⋊C4—612no—
424C2×C4⋊C4—611no—
425C2×C4⋊C4—612no—
426C2×C4⋊C4C4×D6111yescharacteristic
427C2×C4⋊C4C22×D6112yes—
428C2×C22⋊C4—612no—
429C2×C22⋊C4—612no—
430C2×C22⋊C4—612no—
431C2×C22⋊C4—612no—
432C2×C22⋊C4C4×D6112yes—
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—611no—
443C2×C42—611no—
444C2×C42—611no—
445C2×C42—612no—
446C4⋊C8—1222no—
447C4⋊C8—1222no—
448C4⋊C8—1222no—
449C4⋊C8—1222no—
450C22⋊C8—21no—
451C22⋊C8—21no—
452C22⋊C8—612no—
453C22⋊C8—612no—
454C22⋊C8—1221no—
455C22⋊C8—1221no—
456C22⋊C8C22×D6112yes—
457C22⋊C8C22×D6112yes—
458#97—1222no—
459C4×C8—1222no—
460C4×C8—1222no—
461C4×C8—1222no—
462C24—612no—
463C24C2×C4×D6111yescharacteristic
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—42no—
467C2×D4—1222no—
468C2×D4—1222no—
469C2×D4—1221no—
470C2×D4—1221no—
471C2×D4—2442no—
472C2×D4—2444no—
473C22×C4—42no—
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—612no—
487C22×C4—1222no—
488C22×C4—1222no—
489C22×C4—1228no—
490C22×C4—1224no—
491C22×C4—2442no—
492C22×C4C2×C4×D6112yes—
493C22×C4C2×C4×D6111yescharacteristic
494C22×C4C2×C4×D6112yes—
495C22×C4D4×D6111yescharacteristic
496C22×C4D4×D6111yescharacteristic
497C22×C4D4×D6111yescharacteristic
498C22×C4D4×D6111yescharacteristic
499C22×C4C23×D6111yescharacteristic
500M16—42no—
501M16—2442no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—42no—
505C2×C8—1222no—
506C2×C8—1222no—
507C2×C8—2442no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—1222no—
513C4⋊C4—1222no—
514C4⋊C4—1222no—
515C4⋊C4—1222no—
516C4⋊C4—1222no—
517C4⋊C4—1222no—
518C4⋊C4—1221no—
519C4⋊C4—1221no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—1222no—
523C22⋊C4—1222no—
524C22⋊C4—1222no—
525C22⋊C4—1222no—
526C22⋊C4—1222no—
527C22⋊C4—1222no—
528C22⋊C4—1222no—
529C22⋊C4—1222no—
530C42—611no—
531C42—611no—
532C42—611no—
533C42—611no—
534C42—611no—
535C42—611no—
536C42—611no—
537C42—611no—
538C42—611no—
539C42—611no—
540C42—611no—
541C42—611no—
542C42—611no—
543C42—611no—
544C42—611no—
545C42—611no—
546C42—1222no—
547C42—1222no—
548C23—22no—
549C23—22no—
550C23—41no—
551C23—1224no—
552C23—1222no—
553C23—2442no—
554C23—2442no—
555C23C22⋊C4×D6111yescharacteristic
556C23C22⋊C4×D6111yescharacteristic
557C23C22×C4×D6111yescharacteristic
558Q8—42no—
559Q8—42no—
560D4—2442no—
561D4—2444no—
562D4—2444no—
563D4—2442no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—42no—
574C2×C4—611no—
575C2×C4—611no—
576C2×C4—614no—
577C2×C4—611no—
578C2×C4—611no—
579C2×C4—611no—
580C2×C4—611no—
581C2×C4—611no—
582C2×C4—611no—
583C2×C4—1222no—
584C2×C4—1222no—
585C2×C4—1222no—
586C2×C4—1222no—
587C2×C4—1222no—
588C2×C4—1222no—
589C2×C4—1222no—
590C2×C4—1222no—
591C2×C4—2444no—
592C2×C4—2444no—
593C2×C4—2441no—
594C2×C4—2441no—
595C2×C4—2441no—
596C2×C4—2441no—
597C2×C4—2442no—
598C2×C4C22⋊C4×D6111yescharacteristic
599C2×C4C22⋊C4×D6111yescharacteristic
600C2×C4C2×D4×D6111yescharacteristic
601C2×C4C2×D4×D6111yescharacteristic
602C8—42no—
603C8—42no—
604C8—2442no—
605C8—2442no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—44no—
614C22—4884no—
615C22—2442no—
616C22—2442no—
617C22—2442no—
618C22#1683974512yes—
619C22C2×C22⋊C4×D6111yescharacteristic
620C22#131×D6112yes—
621C4—21no—
622C4—21no—
623C4—21no—
624C4—42no—
625C4—42no—
626C4—612no—
627C4—612no—
628C4—1221no—
629C4—1221no—
630C4—1221no—
631C4—1221no—
632C4—1221no—
633C4—1221no—
634C4—2442no—
635C4#1683973412yes—
636C2—22no—
637C2—22no—
638C2—41no—
639C2—4882no—
640C2#408×D6111yescharacteristic
641C2C2×#1683973411yescharacteristic
642C2C2×#1683974511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1472C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519751C22
cosocleC22×C4×C61C24
hypercenter#1472D61
hypocenterC61#17380
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1472

Complements

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

NH ≅ G/Ntype
2. #21454448C2semidirect
3. C2×#16839812C2semidirect
4. #21444187C2semidirect
5. #21444183C2semidirect
8. #21444132C2semidirect
9. C61×#1472C2semidirect
320. #1472D61semidirect
370. C61#17380semidirect

Maximal subgroups

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

subgroupindex
C2×#168402982
#214544482
C2×#168398122
#214441872
#214441832
#214441802
#214441782
#214441322
C61×#14722
#1738061