Finite Group Databasebeta

← #29646338

Subgroups — #29646338

Order 15616.

916 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×#16840480C211yesmaximal, characteristic
2#21454909C212yesmaximal, complemented
3#21444189C212yesmaximal, complemented
4#21444185C212yesmaximal, complemented
5#21444169C212yesmaximal
6#21444161C211yesmaximal, characteristic, complemented
7#21444152C211yesmaximal, characteristic, complemented
8#21444141C211yesmaximal, characteristic, complemented
9#21444133C211yesmaximal, characteristic, complemented
10#21444132C211yesmaximal, characteristic, complemented
11C61×#1464C211yesmaximal, characteristic, complemented
12#16840480—22no—
13#16840480—22no—
14#16840480—22no—
15#16840480—22no—
16C2×#14519776C411yescharacteristic
17C2×#14519771C411yescharacteristic
18C2×#14519771C2211yescharacteristic
19C2×#14519770C411yescharacteristic
20C2×#14519770C2211yescharacteristic
21C2×#14519763C411yescharacteristic
22C2×#14519763C2211yescharacteristic
23C2×#14519757C411yescharacteristic
24C2×#14519756C411yescharacteristic
25C2×C4×Dic122C411yescharacteristic
26C2×C4×Dic122C2211yescharacteristic
27C2×#14519742C2211yescharacteristic
28C2×C4×C22⋊D61C411yescharacteristic
29C2×#14519735C2211yescharacteristic
30#16839890—22no—
31#16839890—22no—
32#16839889—22no—
33#16839886—22no—
34#16839816C2212yes—
35#16839816C2212yes—
36#16839815C2212yes—
37#16839812C2212yes—
38#16839812C2212yes—
39#16839488C2211yescharacteristic
40#16839488C2211yescharacteristic
41#16839487C2212yes—
42#16839487C2212yes—
43#16839486C2212yes—
44#16839485C2212yes—
45#16839485C2212yes—
46C2×#117×C61C2211yescharacteristic
47C61×#432C2212yes—
48C61×#324C2211yescharacteristic
49C61×#324C2211yescharacteristic
50C61×#323C2212yes—
51C22×Dic122C2×C411yescharacteristic
52C22×Dic122C2×C411yescharacteristic
53C22×Dic122C2×C411yescharacteristic
54C22×C22⋊D61C2×C411yescharacteristic
55C22×C4×D61C2×C411yescharacteristic
56#14519776—22no—
57#14519776—22no—
58#14519771—22no—
59#14519771—22no—
60#14519771—22no—
61#14519771—22no—
62#14519770—22no—
63#14519770—22no—
64#14519770—22no—
65#14519770—22no—
66#14519763—22no—
67#14519763—22no—
68#14519763—22no—
69#14519763—22no—
70#14519757—22no—
71#14519757—22no—
72#14519756—22no—
73#14519756—22no—
74C4×Dic122—21no—
75C4×Dic122—21no—
76C4×Dic122—21no—
77C4×Dic122—21no—
78C4×Dic122D412yes—
79C4×Dic122D412yes—
80C4×Dic122D412yes—
81C4×Dic122D412yes—
82#14519742—22no—
83#14519742—22no—
84C4×C22⋊D61—21no—
85C4×C22⋊D61—21no—
86C4×C22⋊D61—21no—
87C4×C22⋊D61—21no—
88#14519735—22no—
89#14519735—22no—
90C2×C4⋊Dic61C2×C411yescharacteristic
91C2×C4⋊Dic61C2×C411yescharacteristic
92C2×C4⋊Dic61C2×C411yescharacteristic
93C2×#11758196C2×C411yescharacteristic
94C2×#11758196C2×C411yescharacteristic
95C2×#11758196C2×C411yescharacteristic
96C2×#11758196C2×C411yescharacteristic
97C2×#11758196C2×C411yescharacteristic
98C2×#11758196C2×C411yescharacteristic
99C2×#11758196C2311yescharacteristic
100C2×C22⋊Dic61C2×C411yescharacteristic
101C2×C22⋊Dic61C2×C411yescharacteristic
102C2×C22⋊Dic61C2×C411yescharacteristic
103C2×#11758198C2×C411yescharacteristic
104C2×#11758198C2×C411yescharacteristic
105C2×#11758198C2×C411yescharacteristic
106C2×#11758198C2×C411yescharacteristic
107C2×#11758198C2311yescharacteristic
108C2×C4×Dic61C2×C411yescharacteristic
109C2×C4×Dic61C2×C411yescharacteristic
110C2×C4×Dic61C2×C411yescharacteristic
111C2×C4×Dic61C2311yescharacteristic
112C2×C4×Dic61C2311yescharacteristic
113C4⋊#92418—22no—
114#14519706—22no—
115#14519706—22no—
116#14519706—22no—
117#14519706—22no—
118C22⋊#92418C2312yes—
119C22⋊#92418C2312yes—
120#14519687—22no—
121#14519687—22no—
122C4×#92418—22no—
123C8×Dic61—22no—
124C8×Dic61—22no—
125C23×C4×C61C2×C411yescharacteristic
126#117×C61—22no—
127#117×C61—22no—
128C2×C4⋊C4×C61C2×C411yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C22⋊C4×C61C2×C411yescharacteristic
131C2×C22⋊C4×C61C2311yescharacteristic
132C2×C42×C61C2×C411yescharacteristic
133C2×C42×C61C2311yescharacteristic
134C4⋊C8×C61—22no—
135C22⋊C8×C61C2312yes—
136C22⋊C8×C61C2312yes—
137#97×C61—22no—
138C24×C61C22×C411yescharacteristic
139C23×D61C22×C411yescharacteristic
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—22no—
143C22×C4×C61—41no—
144C22×C4×C61C22×C411yescharacteristic
145C22×C4×C61C22×C411yescharacteristic
146C22×C4×C61C22×C411yescharacteristic
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C2411yescharacteristic
150C2×C22⋊D61—21no—
151C2×C22⋊D61—21no—
152C2×C22⋊D61—42no—
153C22×Dic61C22×C411yescharacteristic
154C22×Dic61C22×C411yescharacteristic
155C22×Dic61C22×C411yescharacteristic
156C22×Dic61C22×C411yescharacteristic
157C22×Dic61C22×C411yescharacteristic
158C22×Dic61C22×C411yescharacteristic
159C22×Dic61C22×C411yescharacteristic
160C2×C4×D61—22no—
161C2×C4×D61—21no—
162C2×C4×D61—21no—
163C2×C4×D61—41no—
164C2×Dic122—22no—
165C2×Dic122—22no—
166C2×Dic122—21no—
167C2×Dic122—21no—
168C2×Dic122—42no—
169C2×Dic122—41no—
170C2×Dic122—42no—
171C2×Dic122C22⋊C412yes—
172C2×Dic122C22⋊C412yes—
173C2×C8×C61—22no—
174C2×C8×C61—22no—
175C4⋊C4×C61—22no—
176C4⋊C4×C61—22no—
177C22⋊C4×C61—22no—
178C22⋊C4×C61—22no—
179C42×C61—21no—
180C42×C61—21no—
181C42×C61C2×D412yes—
182C42×C61C2×D412yes—
183C22⋊Dic61—21no—
184C22⋊Dic61—21no—
185C22⋊Dic61—22no—
186C22⋊Dic61—22no—
187#11758198—21no—
188#11758198—21no—
189#11758198—22no—
190#11758198—22no—
191#11758198—22no—
192#11758198—22no—
193C4⋊Dic61—22no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61C22⋊C412yes—
197C4⋊Dic61C22⋊C412yes—
198#11758196—21no—
199#11758196—21no—
200#11758196—22no—
201#11758196—22no—
202#11758196—22no—
203#11758196—22no—
204#11758196C22⋊C411yescharacteristic
205#11758196C22⋊C411yescharacteristic
206#11758196C22⋊C411yescharacteristic
207#11758196C22⋊C411yescharacteristic
208#11758196C22⋊C412yes—
209#11758196C22⋊C412yes—
210C4×Dic61—21no—
211C4×Dic61—21no—
212C4×Dic61—21no—
213C4×Dic61—21no—
214C4×Dic61—21no—
215C4×Dic61—21no—
216C4×Dic61C2×D412yes—
217C4×Dic61C2×D412yes—
218C4×Dic61C2×D412yes—
219C4×Dic61C2×D412yes—
220C2×#92418—22no—
221C2×#92418—22no—
222C23×C61—21no—
223C23×C61—21no—
224C23×C61—21no—
225C23×C61—41no—
226C23×C61—41no—
227C23×C61C23×C411yescharacteristic
228C22×D61—21no—
229C22×D61—21no—
230C22×D61—21no—
231C22×D61—41no—
232C22×D61—41no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—42no—
242C2×C4×C61—42no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61C2×C22⋊C411yescharacteristic
246C2×C4×C61C2×C22⋊C411yescharacteristic
247C2×C4×C61C2×C22⋊C412yes—
248C2×C4×C61#13112yes—
249C2×C4×C61C22×D412yes—
250C22⋊D61—42no—
251C22⋊D61—42no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—22no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61C2×C22⋊C411yescharacteristic
266C2×Dic61C2×C22⋊C411yescharacteristic
267C2×Dic61C2×C22⋊C411yescharacteristic
268C2×Dic61C2×C22⋊C412yes—
269C2×Dic61C2×C22⋊C412yes—
270C2×Dic61C2×C22⋊C411yescharacteristic
271C4×D61—42no—
272C4×D61—42no—
273Dic122—24no—
274Dic122—42no—
275Dic122—44no—
276Dic122—42no—
277Dic122—42no—
278C8×C61—42no—
279C8×C61—42no—
280#92418—42no—
281#92418—42no—
282#17428—611nomaximal, Sylow
283C22×C61—21no—
284C22×C61—21no—
285C22×C61—41no—
286C22×C61—41no—
287C22×C61—41no—
288C22×C61—81no—
289C22×C61—81no—
290C22×C61C22×C22⋊C411yescharacteristic
291C22×C61C2×#13111yescharacteristic
292C22×C61#56811yescharacteristic
293C2×D61—41no—
294C2×D61—41no—
295C2×D61—41no—
296C2×D61—81no—
297C2×D61—81no—
298C4×C61—22no—
299C4×C61—21no—
300C4×C61—21no—
301C4×C61—22no—
302C4×C61—22no—
303C4×C61—41no—
304C4×C61—41no—
305Dic61—22no—
306Dic61—21no—
307Dic61—21no—
308Dic61—22no—
309Dic61—21no—
310Dic61—41no—
311Dic61—41no—
312Dic61—41no—
313Dic61#41312yes—
314C2×#556—611no—
315#2984—612no—
316#1473—612no—
317#1473—612no—
318#1469—612no—
319#1467—611no—
320#1464—611no—
321#1464D6111yescharacteristic, complemented
322#1461—611no—
323#1458—611no—
324#1458—611no—
325C2×C61—21no—
326C2×C61—21no—
327C2×C61—81no—
328C2×C61#288011yescharacteristic
329C2×C61#288411yescharacteristic
330C2×C61C2×#41311yescharacteristic
331D61—81no—
332#556—1222no—
333#556—1222no—
334#556—1222no—
335#556—1222no—
336C2×C4⋊Q8—611no—
337C2×#126—611no—
338C2×#126—611no—
339C2×#126—611no—
340C2×#126—611no—
341C2×#124—611no—
342C2×#124—611no—
343C2×C22⋊Q8—611no—
344C2×C22⋊Q8—611no—
345C2×C4×Q8—611no—
346C2×C4×Q8—611no—
347C2×C4×Q8—611no—
348C2×C4×D4—611no—
349C2×#117—611no—
350C2×#117C2×D6111yescharacteristic
351#446—1222no—
352#446—1222no—
353#446—1222no—
354C8×Q8—1222no—
355#432—612no—
356#432—612no—
357#432C2×D6112yes—
358#431—612no—
359#431—612no—
360#431—612no—
361#324—611no—
362#324—611no—
363#324—612no—
364#324—612no—
365#324C2×D6111yescharacteristic
366#324C2×D6111yescharacteristic
367#323—612no—
368#323—612no—
369#323—612no—
370#323C2×D6112yes—
371C61#1742811yescharacteristic, complemented, Sylow
372C22×Q8—611no—
373C22×Q8—611no—
374C22×Q8—611no—
375C22×D4—611no—
376C23×C4—611no—
377C23×C4C4×D6111yescharacteristic
378C4⋊Q8—1222no—
379C4⋊Q8—1222no—
380#126—1222no—
381#126—1222no—
382#126—1222no—
383#126—1222no—
384#126—1222no—
385#126—1222no—
386#126—1222no—
387#126—1222no—
388#124—1222no—
389#124—1222no—
390#124—1222no—
391#124—1222no—
392C22⋊Q8—1222no—
393C22⋊Q8—1222no—
394C22⋊Q8—1222no—
395C22⋊Q8—1222no—
396C4×Q8—612no—
397C4×Q8—612no—
398C4×Q8—612no—
399C4×Q8—612no—
400C4×Q8—1221no—
401C4×Q8—1221no—
402C4×Q8—1221no—
403C4×Q8—1221no—
404C4×Q8—1222no—
405C4×Q8—1222no—
406C4×D4—1221no—
407C4×D4—1221no—
408C4×D4—1221no—
409C4×D4—1221no—
410#117—22no—
411#117—22no—
412#117—1222no—
413#117—1222no—
414C2×C4⋊C4—611no—
415C2×C4⋊C4—611no—
416C2×C4⋊C4—611no—
417C2×C4⋊C4—611no—
418C2×C4⋊C4—611no—
419C2×C4⋊C4—611no—
420C2×C4⋊C4—611no—
421C2×C4⋊C4—611no—
422C2×C4⋊C4—611no—
423C2×C4⋊C4—611no—
424C2×C4⋊C4C4×D6111yescharacteristic
425C2×C4⋊C4C22×D6111yescharacteristic
426C2×C22⋊C4—611no—
427C2×C22⋊C4—611no—
428C2×C22⋊C4—611no—
429C2×C22⋊C4—611no—
430C2×C22⋊C4—611no—
431C2×C22⋊C4—611no—
432C2×C22⋊C4—611no—
433C2×C22⋊C4—611no—
434C2×C22⋊C4C4×D6111yescharacteristic
435C2×C22⋊C4C22×D6111yescharacteristic
436C2×C42—611no—
437C2×C42—611no—
438C2×C42—611no—
439C2×C42—611no—
440C2×C42—611no—
441C2×C42C4×D6111yescharacteristic
442C2×C42C22×D6111yescharacteristic
443C4⋊C8—22no—
444C4⋊C8—1222no—
445C4⋊C8—1222no—
446C4⋊C8—1222no—
447C4⋊C8—1222no—
448C4⋊C8—1222no—
449C22⋊C8—612no—
450C22⋊C8—612no—
451C22⋊C8C22×D6112yes—
452C22⋊C8C22×D6112yes—
453#97—22no—
454#97—1222no—
455#97—1222no—
456C4×C8—1222no—
457C4×C8—1222no—
458C4×C8—1222no—
459C24—611no—
460C24C2×C4×D6111yescharacteristic
461C2×Q8—612no—
462C2×Q8—612no—
463C2×Q8—1222no—
464C2×Q8—1221no—
465C2×Q8—1221no—
466C2×Q8—1222no—
467C2×Q8—2441no—
468C2×Q8—2442no—
469C2×Q8—2442no—
470C2×D4—1221no—
471C2×D4—1221no—
472C2×D4—2442no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—41no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—611no—
483C22×C4—611no—
484C22×C4—1221no—
485C22×C4—1221no—
486C22×C4—1222no—
487C22×C4—2441no—
488C22×C4C2×C4×D6111yescharacteristic
489C22×C4C2×C4×D6111yescharacteristic
490C22×C4C2×C4×D6111yescharacteristic
491C22×C4C2×C4×D6111yescharacteristic
492C22×C4C2×C4×D6111yescharacteristic
493C22×C4C23×D6111yescharacteristic
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—1222no—
497C2×C8—1222no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—611no—
501C4⋊C4—611no—
502C4⋊C4—611no—
503C4⋊C4—611no—
504C4⋊C4—612no—
505C4⋊C4—612no—
506C4⋊C4—612no—
507C4⋊C4—612no—
508C4⋊C4—1222no—
509C4⋊C4—1222no—
510C4⋊C4—1222no—
511C4⋊C4—1221no—
512C4⋊C4—1221no—
513C4⋊C4—1222no—
514C4⋊C4—1221no—
515C4⋊C4—1221no—
516C4⋊C4—1222no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—1222no—
520C22⋊C4—1222no—
521C22⋊C4—1221no—
522C22⋊C4—1221no—
523C22⋊C4—1222no—
524C22⋊C4—1222no—
525C22⋊C4—1222no—
526C22⋊C4—1221no—
527C22⋊C4—1221no—
528C22⋊C4—1222no—
529C42—21no—
530C42—21no—
531C42—612no—
532C42—612no—
533C42—612no—
534C42—612no—
535C42—1221no—
536C42—1221no—
537C42—1221no—
538C42—1221no—
539C42—1221no—
540C42—1221no—
541C42D4×D6112yes—
542C42D4×D6112yes—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—41no—
547C23—41no—
548C23—1221no—
549C23—1221no—
550C23—1221no—
551C23—2441no—
552C23—2441no—
553C23C22×C4×D6111yescharacteristic
554Q8—1224no—
555Q8—2442no—
556Q8—2444no—
557Q8—2442no—
558Q8—2442no—
559D4—2442no—
560D4—2442no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—611no—
574C2×C4—611no—
575C2×C4—611no—
576C2×C4—611no—
577C2×C4—612no—
578C2×C4—612no—
579C2×C4—1222no—
580C2×C4—1221no—
581C2×C4—1221no—
582C2×C4—1221no—
583C2×C4—1221no—
584C2×C4—1221no—
585C2×C4—1221no—
586C2×C4—1221no—
587C2×C4—1221no—
588C2×C4—1221no—
589C2×C4—2442no—
590C2×C4—2442no—
591C2×C4—2441no—
592C2×C4—2441no—
593C2×C4—2441no—
594C2×C4C22⋊C4×D6111yescharacteristic
595C2×C4C22⋊C4×D6111yescharacteristic
596C2×C4C22⋊C4×D6112yes—
597C2×C4#1451978512yes—
598C2×C4C2×D4×D6112yes—
599C8—42no—
600C8—42no—
601C8—2442no—
602C8—2442no—
603C22—21no—
604C22—21no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—81no—
609C22—81no—
610C22—4881no—
611C22—4881no—
612C22—2441no—
613C22—2441no—
614C22—2441no—
615C22C2×C22⋊C4×D6111yescharacteristic
616C22C2×#1451978511yescharacteristic
617C22#1684052811yescharacteristic
618C4—22no—
619C4—21no—
620C4—21no—
621C4—22no—
622C4—22no—
623C4—41no—
624C4—41no—
625C4—612no—
626C4—1221no—
627C4—1221no—
628C4—1222no—
629C4—1221no—
630C4—1222no—
631C4—2441no—
632C4—2441no—
633C4—2441no—
634C2—21no—
635C2—21no—
636C2—81no—
637C2—4881no—
638C2#2145426911yescharacteristic
639C2#2145428111yescharacteristic
640C2#413×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1464C2
socleC22×C61C22×C22⋊C4
prime radicalC22×C22⋊D61C2×C4
cosocleC22×C4×C61C24
hypercenter#1464D61
hypocenterC61#17428
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1464

Complements

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

NH ≅ G/Ntype
2. #21454909C2semidirect
3. #21444189C2semidirect
4. #21444185C2semidirect
6. #21444161C2semidirect
7. #21444152C2semidirect
8. #21444141C2semidirect
9. #21444133C2semidirect
10. #21444132C2semidirect
11. C61×#1464C2semidirect
321. #1464D61semidirect
371. C61#17428semidirect

Maximal subgroups

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

subgroupindex
C2×#168404802
#214549092
#214441892
#214441852
#214441692
#214441612
#214441522
#214441412
#214441332
#214441322
C61×#14642
#1742861