Finite Group Databasebeta

← #30610350

Subgroups — #30610350

Order 15616.

1022 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462678C212yesmaximal, complemented
2#21461101C212yesmaximal, complemented
3#21461094C212yesmaximal, complemented
4#21461084C212yesmaximal, complemented
5#21461075C211yesmaximal, characteristic, complemented
6#21461070C211yesmaximal, characteristic, complemented
7#21461068C211yesmaximal, characteristic, complemented
8#21461055C211yesmaximal, characteristic, complemented
9#21461050C211yesmaximal, characteristic, complemented
10D61⋊#324C211yesmaximal, characteristic, complemented
11C2×#16840459C211yesmaximal, characteristic
12#16840795—22no—
13#16840794—22no—
14#16840791—22no—
15#16840789—22no—
16#16840782C2212yes—
17#16840778C2212yes—
18#16840733C2212yes—
19#16840732C2212yes—
20D61⋊(C22⋊C8)C2212yes—
21C2×C22⋊#92420C2212yes—
22#16840608C2212yes—
23#16840608C2212yes—
24#16840607C2211yescharacteristic
25#16840607C2211yescharacteristic
26#16840607C2211yescharacteristic
27#16840607C2211yescharacteristic
28#16840605C2212yes—
29#16840605C2212yes—
30#16840605C2212yes—
31#16840605C2212yes—
32#16840459—22no—
33#16840459—22no—
34#16840459—22no—
35#16840459—22no—
36C2×#14519770C411yescharacteristic
37C2×#14519770C2211yescharacteristic
38C2×#14519768C411yescharacteristic
39C2×#14519758C411yescharacteristic
40C2×#14519758C2211yescharacteristic
41C2×#14519748C411yescharacteristic
42C2×#14519748C411yescharacteristic
43C2×#14519748C2211yescharacteristic
44C2×D4×Dic61C2211yescharacteristic
45C2×C4×C22⋊D61C411yescharacteristic
46C2×#14519737C411yescharacteristic
47C2×#14519737C2211yescharacteristic
48C2×#14519736C2211yescharacteristic
49C2×C4⋊C4×D61C2211yescharacteristic
50C2×#121×C61C411yescharacteristic
51C2×#11758213—22no—
52C2×#11758217—22no—
53C2×D61⋊C8—22no—
54C22×#92420—22no—
55#14519844—22no—
56C4⋊#92420—22no—
57#14519834—22no—
58#14519834—22no—
59C22⋊#92420—22no—
60C22⋊#92420—22no—
61C22⋊#92420C2312yes—
62C22⋊#92420C2312yes—
63C22⋊#92420C2312yes—
64C22⋊#92420C2312yes—
65#14519832—22no—
66C4×#92420—22no—
67C22×C22⋊D61C2×C411yescharacteristic
68C22×C22⋊D61C2×C411yescharacteristic
69C22×C22⋊D61C2×C411yescharacteristic
70C23×Dic61C2×C411yescharacteristic
71C23×Dic61C2311yescharacteristic
72C22×C4×D61C2×C411yescharacteristic
73C22×C4×D61C2×C411yescharacteristic
74C22×C4×D61C2311yescharacteristic
75#14519770—22no—
76#14519770—22no—
77#14519770—22no—
78#14519770—22no—
79#14519768—22no—
80#14519768—22no—
81#14519758—22no—
82#14519758—22no—
83#14519758—22no—
84#14519758—22no—
85#14519748—22no—
86#14519748—22no—
87#14519748—22no—
88#14519748—22no—
89#14519748—22no—
90#14519748—22no—
91D4×Dic61—22no—
92D4×Dic61—22no—
93C4×C22⋊D61—21no—
94C4×C22⋊D61—21no—
95C4×C22⋊D61—21no—
96C4×C22⋊D61—21no—
97#14519737—21no—
98#14519737—21no—
99#14519737—21no—
100#14519737—21no—
101#14519737D412yes—
102#14519737D412yes—
103#14519737D412yes—
104#14519737D412yes—
105#14519736—22no—
106#14519736—22no—
107C2×C4⋊Dic61C2×C411yescharacteristic
108C2×C4⋊Dic61C2×C411yescharacteristic
109C2×C4⋊Dic61C2×C411yescharacteristic
110C2×C4⋊Dic61C2311yescharacteristic
111C2×#11758196C2×C411yescharacteristic
112C2×#11758196C2×C411yescharacteristic
113C2×#11758196C2×C411yescharacteristic
114C2×#11758196C2×C411yescharacteristic
115C2×#11758196C2311yescharacteristic
116C4⋊C4×D61—22no—
117C4⋊C4×D61—22no—
118C2×C22⋊Dic61C2×C411yescharacteristic
119C2×C22⋊Dic61C2×C411yescharacteristic
120C2×C22⋊Dic61C2×C411yescharacteristic
121C2×C22⋊Dic61C2×C411yescharacteristic
122C2×C22⋊Dic61C2×C411yescharacteristic
123C2×C22⋊Dic61C2311yescharacteristic
124C2×C22⋊Dic61C2311yescharacteristic
125C2×#11758198C2×C411yescharacteristic
126C2×C4×Dic61C2×C411yescharacteristic
127C2×C4×Dic61C2×C411yescharacteristic
128C2×C4×Dic61C2311yescharacteristic
129C22×D4×C61C2×C411yescharacteristic
130C22×D4×C61C2×C411yescharacteristic
131C22×D4×C61C2×C411yescharacteristic
132C23×C4×C61C2×C411yescharacteristic
133#121×C61—22no—
134#121×C61—22no—
135C2×C4⋊C4×C61C2×C411yescharacteristic
136C2×C22⋊C4×C61C2×C411yescharacteristic
137C2×C22⋊C4×C61C2×C411yescharacteristic
138C24×C61C22×C411yescharacteristic
139C24×C61C22×C411yescharacteristic
140C24×C61C22×C411yescharacteristic
141C23×D61C22×C411yescharacteristic
142C2×D4×C61—22no—
143C2×D4×C61—22no—
144C2×D4×C61—22no—
145C2×D4×C61—22no—
146C2×D4×C61—41no—
147C2×D4×C61—81no—
148C2×D4×C61—81no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—22no—
152C22×C4×C61—41no—
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C22×C411yescharacteristic
157C2×C22⋊D61—21no—
158C2×C22⋊D61—21no—
159C2×C22⋊D61—21no—
160C2×C22⋊D61—21no—
161C2×C22⋊D61—42no—
162C2×C22⋊D61—42no—
163C2×C22⋊D61—42no—
164C2×C22⋊D61C22⋊C412yes—
165C2×C22⋊D61C22⋊C412yes—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—81no—
169C22×Dic61—81no—
170C22×Dic61C22×C411yescharacteristic
171C22×Dic61C22×C411yescharacteristic
172C22×Dic61C22×C411yescharacteristic
173C22×Dic61C22×C411yescharacteristic
174C22×Dic61C22×C411yescharacteristic
175C22×Dic61C22×C411yescharacteristic
176C22×Dic61C2×D412yes—
177C22×Dic61C2×D412yes—
178C22×Dic61C2411yescharacteristic
179C2×C4×D61—21no—
180C2×C4×D61—21no—
181C2×C4×D61—22no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—41no—
185C2×C4×D61—81no—
186C2×C4×D61—81no—
187C2×C4×D61C2×D412yes—
188C2×C4×D61C2×D412yes—
189#11758217—82no—
190C2×#92420—22no—
191C2×#92420—22no—
192C2×#92420—22no—
193C2×#92420—22no—
194C2×#92420—82no—
195#11758213—82no—
196D61⋊C8—82no—
197C4⋊C4×C61—22no—
198C22⋊C4×C61—21no—
199C22⋊C4×C61—21no—
200C22⋊C4×C61C22⋊C412yes—
201C22⋊C4×C61C22⋊C412yes—
202C22⋊Dic61—22no—
203C22⋊Dic61—22no—
204C22⋊Dic61—22no—
205C22⋊Dic61—21no—
206C22⋊Dic61—21no—
207C22⋊Dic61—22no—
208C22⋊Dic61—22no—
209C22⋊Dic61—22no—
210#11758198C22⋊C411yescharacteristic
211#11758198C22⋊C411yescharacteristic
212#11758198C22⋊C411yescharacteristic
213#11758198C22⋊C411yescharacteristic
214C4⋊Dic61—22no—
215C4⋊Dic61—22no—
216C4⋊Dic61—22no—
217C4⋊Dic61—22no—
218#11758196—22no—
219#11758196—21no—
220#11758196—21no—
221#11758196—21no—
222#11758196—21no—
223#11758196—22no—
224#11758196C22⋊C412yes—
225#11758196C22⋊C412yes—
226C4×Dic61—21no—
227C4×Dic61—21no—
228C4×Dic61—21no—
229C4×Dic61—21no—
230C4×Dic61C2×D412yes—
231C4×Dic61C2×D412yes—
232C23×C61—21no—
233C23×C61—21no—
234C23×C61—21no—
235C23×C61—21no—
236C23×C61—21no—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61C2×C22⋊C412yes—
247C23×C61C23×C411yescharacteristic
248C22×D61—21no—
249C22×D61—21no—
250C22×D61—22no—
251C22×D61—41no—
252C22×D61C2×C22⋊C411yescharacteristic
253C22×D61C2×C22⋊C411yescharacteristic
254D4×C61—44no—
255D4×C61—82no—
256D4×C61—82no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—41no—
263C2×C4×C61—42no—
264C2×C4×C61—42no—
265C2×C4×C61—41no—
266C2×C4×C61C2×C22⋊C411yescharacteristic
267C2×C4×C61C2×C22⋊C411yescharacteristic
268C2×C4×C61C2×C22⋊C412yes—
269C2×C4×C61#13112yes—
270C22⋊D61—24no—
271C22⋊D61—42no—
272C22⋊D61—42no—
273C22⋊D61—42no—
274C22⋊D61—42no—
275C22⋊D61—42no—
276C2×Dic61—21no—
277C2×Dic61—21no—
278C2×Dic61—21no—
279C2×Dic61—21no—
280C2×Dic61—21no—
281C2×Dic61—21no—
282C2×Dic61—42no—
283C2×Dic61—42no—
284C2×Dic61—41no—
285C2×Dic61—41no—
286C2×Dic61—41no—
287C2×Dic61—41no—
288C2×Dic61—41no—
289C2×Dic61—41no—
290C2×Dic61—81no—
291C2×Dic61—81no—
292C2×Dic61C2×C22⋊C411yescharacteristic
293C2×Dic61C2×C22⋊C411yescharacteristic
294C2×Dic61C2×C22⋊C412yes—
295C2×Dic61C22×D412yes—
296C4×D61—42no—
297C4×D61—42no—
298C4×D61—42no—
299C4×D61—42no—
300C4×D61—81no—
301C4×D61—81no—
302#92420—42no—
303#92420—42no—
304#92420—42no—
305#92420—42no—
306#17427—611nomaximal, Sylow
307C22×C61—21no—
308C22×C61—21no—
309C22×C61—22no—
310C22×C61—22no—
311C22×C61—22no—
312C22×C61—41no—
313C22×C61—41no—
314C22×C61—41no—
315C22×C61—41no—
316C22×C61—41no—
317C22×C61—41no—
318C22×C61—81no—
319C22×C61—81no—
320C22×C61—81no—
321C22×C61—81no—
322C22×C61—81no—
323C22×C61—81no—
324C22×C61C22×C22⋊C411yescharacteristic
325C22×C61C2×#13111yescharacteristic
326C22×C61#56811yescharacteristic
327C2×D61—21no—
328C2×D61—21no—
329C2×D61—21no—
330C2×D61—21no—
331C2×D61—21no—
332C2×D61—42no—
333C2×D61—42no—
334C2×D61#41312yes—
335C4×C61—22no—
336C4×C61—21no—
337C4×C61—21no—
338C4×C61—22no—
339C4×C61—41no—
340Dic61—22no—
341Dic61—21no—
342Dic61—21no—
343Dic61—22no—
344Dic61—41no—
345Dic61—41no—
346Dic61—41no—
347Dic61—41no—
348C2×#553—611no—
349#2974—612no—
350#1473—612no—
351#1471—612no—
352#1468—612no—
353#1465—611no—
354#1464—611no—
355#1463—611no—
356#1459—611no—
357#1458—611no—
358C2×#324—611no—
359C2×C61—21no—
360C2×C61—21no—
361C2×C61—42no—
362C2×C61—81no—
363C2×C61—81no—
364C2×C61#288011yescharacteristic
365C2×C61#288311yescharacteristic
366C2×C61C2×#41311yescharacteristic
367D61—22no—
368D61—41no—
369#553—1222no—
370#553—1222no—
371#553—1222no—
372#553—1222no—
373C2×#126—611no—
374C2×#126—611no—
375C2×#125—611no—
376C2×#123—611no—
377C2×#123—611no—
378C2×#121—611no—
379C2×#121—611no—
380C2×#121—611no—
381C2×#121#692311yescharacteristic
382C2×C4×D4—611no—
383C2×C4×D4—611no—
384C2×C4×D4—611no—
385C2×C4×D4—611no—
386C2×#117—611no—
387C22×C4⋊C4—611no—
388#436—1222no—
389#435—1222no—
390#435—1222no—
391C8×D4—1222no—
392#432—612no—
393#431—612no—
394#407—612no—
395#407—612no—
396C2×C22⋊C8—612no—
397C2×C22⋊C8—612no—
398#324—611no—
399#324—611no—
400#324—611no—
401#324—611no—
402#324—612no—
403#324—612no—
404#323—612no—
405#323—612no—
406#323—612no—
407#323—612no—
408C61#1742711yescharacteristic, complemented, Sylow
409C22×D4—611no—
410C22×D4—611no—
411C22×D4—611no—
412C22×D4C2×#692311yescharacteristic
413C22×D4C2×#692311yescharacteristic
414C22×D4C2×#692311yescharacteristic
415C23×C4—611no—
416C23×C4—611no—
417C23×C4—611no—
418C23×C4—611no—
419C23×C4—611no—
420C23×C4C2×#692311yescharacteristic
421C2×M16—1222no—
422C2×M16—1222no—
423C22×C8—1222no—
424C22×C8—1222no—
425#126—1222no—
426#126—1222no—
427#126—1222no—
428#126—1222no—
429#125—1222no—
430#125—1222no—
431#123—1222no—
432#123—1222no—
433#123—1222no—
434#123—1222no—
435#121—22no—
436#121—22no—
437#121—1222no—
438#121—1222no—
439#121—1222no—
440#121—1222no—
441#121—1222no—
442#121—1222no—
443C4×D4—612no—
444C4×D4—612no—
445C4×D4—612no—
446C4×D4—612no—
447C4×D4—1221no—
448C4×D4—1221no—
449C4×D4—1221no—
450C4×D4—1221no—
451C4×D4—1221no—
452C4×D4—1221no—
453C4×D4—1221no—
454C4×D4—1221no—
455C4×D4—1222no—
456C4×D4—1222no—
457#117—1222no—
458#117—1222no—
459C2×C4⋊C4—611no—
460C2×C4⋊C4—611no—
461C2×C4⋊C4—611no—
462C2×C4⋊C4—611no—
463C2×C4⋊C4—611no—
464C2×C4⋊C4—611no—
465C2×C4⋊C4—611no—
466C2×C4⋊C4—611no—
467C2×C4⋊C4—611no—
468C2×C4⋊C4—1222no—
469C2×C4⋊C4—1222no—
470C2×C4⋊C4C2×#692311yescharacteristic
471C2×C22⋊C4—611no—
472C2×C22⋊C4—611no—
473C2×C22⋊C4—611no—
474C2×C22⋊C4—611no—
475C2×C22⋊C4—611no—
476C2×C22⋊C4—611no—
477C2×C22⋊C4—611no—
478C2×C22⋊C4—611no—
479C2×C22⋊C4C2×#692311yescharacteristic
480C2×C22⋊C4C2×#692311yescharacteristic
481C2×C42—611no—
482C2×C42—611no—
483C2×C42—611no—
484C4⋊C8—1222no—
485C4⋊C8—1222no—
486C22⋊C8—612no—
487C22⋊C8—612no—
488C22⋊C8—612no—
489C22⋊C8—612no—
490C22⋊C8—1222no—
491C22⋊C8—1222no—
492C22⋊C8—1222no—
493C22⋊C8—1222no—
494#97—1222no—
495C4×C8—1222no—
496C24—611no—
497C24C22×#692311yescharacteristic
498C24C22×#692311yescharacteristic
499C24C22×#692311yescharacteristic
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—41no—
505C2×D4—81no—
506C2×D4—81no—
507C2×D4—612no—
508C2×D4—612no—
509C2×D4—1221no—
510C2×D4—1221no—
511C2×D4—1221no—
512C2×D4—1221no—
513C2×D4—2442no—
514C2×D4—2442no—
515C2×D4—2442no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—41no—
520C22×C4—612no—
521C22×C4—612no—
522C22×C4—611no—
523C22×C4—611no—
524C22×C4—611no—
525C22×C4—612no—
526C22×C4—612no—
527C22×C4—611no—
528C22×C4—611no—
529C22×C4—611no—
530C22×C4—611no—
531C22×C4—1221no—
532C22×C4—1221no—
533C22×C4—1221no—
534C22×C4—1221no—
535C22×C4—1221no—
536C22×C4—1221no—
537C22×C4—1222no—
538C22×C4—4881no—
539C22×C4—4881no—
540C22×C4—4881no—
541C22×C4—4881no—
542C22×C4—2441no—
543C22×C4C22×#692311yescharacteristic
544C22×C4C22×#692311yescharacteristic
545C22×C4C22×#692311yescharacteristic
546C22×C4C22×#692311yescharacteristic
547M16—4882no—
548M16—4882no—
549C2×C8—1222no—
550C2×C8—1222no—
551C2×C8—1222no—
552C2×C8—1222no—
553C2×C8—4882no—
554C2×C8—4882no—
555C4⋊C4—22no—
556C4⋊C4—612no—
557C4⋊C4—612no—
558C4⋊C4—1222no—
559C4⋊C4—1222no—
560C4⋊C4—1221no—
561C4⋊C4—1221no—
562C4⋊C4—1222no—
563C4⋊C4—1222no—
564C4⋊C4—1222no—
565C4⋊C4—1221no—
566C4⋊C4—1221no—
567C4⋊C4—1222no—
568C22⋊C4—21no—
569C22⋊C4—21no—
570C22⋊C4—611no—
571C22⋊C4—611no—
572C22⋊C4—611no—
573C22⋊C4—611no—
574C22⋊C4—1222no—
575C22⋊C4—1222no—
576C22⋊C4—1222no—
577C22⋊C4—1221no—
578C22⋊C4—1221no—
579C22⋊C4—1222no—
580C22⋊C4—1222no—
581C22⋊C4—1222no—
582C22⋊C4C22⋊#692312yes—
583C22⋊C4C22⋊#692312yes—
584C42—612no—
585C42—612no—
586C42—1221no—
587C42—1221no—
588C42—1221no—
589C42—1221no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—611no—
605C23—611no—
606C23—1222no—
607C23—1221no—
608C23—1221no—
609C23—2441no—
610C23C2×C22⋊#692312yes—
611C23C23×#692311yescharacteristic
612D4—44no—
613D4—82no—
614D4—82no—
615D4—1224no—
616D4—2442no—
617D4—2442no—
618D4—2442no—
619D4—2442no—
620D4—2442no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—41no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—41no—
630C2×C4—612no—
631C2×C4—611no—
632C2×C4—611no—
633C2×C4—612no—
634C2×C4—1221no—
635C2×C4—1221no—
636C2×C4—1221no—
637C2×C4—1221no—
638C2×C4—1221no—
639C2×C4—1221no—
640C2×C4—4881no—
641C2×C4—4881no—
642C2×C4—4881no—
643C2×C4—4881no—
644C2×C4—2442no—
645C2×C4—2442no—
646C2×C4—2442no—
647C2×C4—2442no—
648C2×C4—2442no—
649C2×C4—2442no—
650C2×C4—2441no—
651C2×C4—2441no—
652C2×C4—2441no—
653C2×C4—2441no—
654C2×C4—2441no—
655C2×C4—2441no—
656C2×C4C2×C22⋊#692311yescharacteristic
657C2×C4C2×C22⋊#692311yescharacteristic
658C2×C4C2×C22⋊#692312yes—
659C2×C4#1451986412yes—
660C8—2442no—
661C8—2442no—
662C8—2442no—
663C8—2442no—
664C22—21no—
665C22—21no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—612no—
682C22—1221no—
683C22—1221no—
684C22—1221no—
685C22—1221no—
686C22—1221no—
687C22—2442no—
688C22—2442no—
689C22C22×C22⋊#692311yescharacteristic
690C22C2×#1451986411yescharacteristic
691C22#1684084011yescharacteristic
692C4—22no—
693C4—21no—
694C4—21no—
695C4—22no—
696C4—41no—
697C4—1222no—
698C4—1221no—
699C4—1221no—
700C4—1222no—
701C4—2441no—
702C4—2441no—
703C4—2441no—
704C4—2441no—
705C2—21no—
706C2—21no—
707C2—42no—
708C2—81no—
709C2—81no—
710C2—1222no—
711C2—2441no—
712C2#2146240711yescharacteristic
713C2#2146241811yescharacteristic
714C2D61⋊#41311yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#121×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840459C2
cosocleC22×Dic61C24
hypercenterC2×#121#6923
hypocenterC61#17427
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #21462678C2semidirect
2. #21461101C2semidirect
3. #21461094C2semidirect
4. #21461084C2semidirect
5. #21461075C2semidirect
6. #21461070C2semidirect
7. #21461068C2semidirect
8. #21461055C2semidirect
9. #21461050C2semidirect
10. D61⋊#324C2semidirect
408. C61#17427semidirect

Maximal subgroups

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

subgroupindex
#214626782
#214611012
#214610942
#214610842
#214610752
#214610702
#214610682
#214610552
#214610502
D61⋊#3242
C2×#168404592
#1742761