Finite Group Databasebeta

← #30610355

Subgroups — #30610355

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#21462675C212yesmaximal, complemented
2#21461102C212yesmaximal, complemented
3#21461095C212yesmaximal, complemented
4#21461084C212yesmaximal, complemented
5#21461077C211yesmaximal, characteristic, complemented
6#21461071C211yesmaximal, characteristic, complemented
7#21461069C211yesmaximal, characteristic, complemented
8#21461057C211yesmaximal, characteristic, complemented
9#21461051C211yesmaximal, characteristic, complemented
10C2×#16840608C211yesmaximal, characteristic, complemented
11C2×#16840455C211yesmaximal, characteristic
12#16840797—22no—
13#16840793—22no—
14#16840793—22no—
15D4×#92420—22no—
16#16840783C2212yes—
17#16840779C2212yes—
18#16840732C2212yes—
19#16840732C2212yes—
20C2×C22⋊#92420C2212yes—
21C2×C22⋊#92420C2212yes—
22#16840608C2211yescharacteristic
23#16840608C2211yescharacteristic
24#16840608C2212yes—
25#16840608C2211yescharacteristic
26#16840608C2211yescharacteristic
27#16840608C2212yes—
28#16840606C2212yes—
29#16840606C2212yes—
30#16840605C2212yes—
31#16840605C2212yes—
32#16840455—22no—
33#16840455—22no—
34#16840455—22no—
35#16840455—22no—
36C2×#14519772C2211yescharacteristic
37C2×#14519770C411yescharacteristic
38C2×#14519767C411yescharacteristic
39C2×#14519759C411yescharacteristic
40C2×#14519758C2211yescharacteristic
41C2×#14519749C411yescharacteristic
42C2×#14519749C411yescharacteristic
43C2×#14519749C2211yescharacteristic
44C2×D4×Dic61C411yescharacteristic
45C2×D4×Dic61C2211yescharacteristic
46C2×C4×C22⋊D61C411yescharacteristic
47C2×#14519737C2211yescharacteristic
48C2×#14519733C2211yescharacteristic
49C22×#11758196C2211yescharacteristic
50C2×#121×C61C411yescharacteristic
51C2×#11758217—22no—
52C2×#11758217—22no—
53C22×#92420—22no—
54C22×#92420—22no—
55#14519844—22no—
56C4⋊#92420—22no—
57C22⋊#92420—22no—
58C22⋊#92420—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×Dic61C2×C411yescharacteristic
72C23×Dic61C2311yescharacteristic
73C23×Dic61C2311yescharacteristic
74C22×C4×D61C2×C411yescharacteristic
75#14519772—22no—
76#14519772—22no—
77#14519770—22no—
78#14519770—22no—
79#14519767—22no—
80#14519767—22no—
81#14519759—22no—
82#14519759—22no—
83#14519758—22no—
84#14519758—22no—
85#14519749—22no—
86#14519749—22no—
87#14519749—22no—
88#14519749—22no—
89#14519749—22no—
90#14519749—22no—
91D4×Dic61—21no—
92D4×Dic61—21no—
93D4×Dic61—21no—
94D4×Dic61—21no—
95D4×Dic61D412yes—
96D4×Dic61D412yes—
97D4×Dic61D412yes—
98D4×Dic61D412yes—
99C4×C22⋊D61—21no—
100C4×C22⋊D61—21no—
101C4×C22⋊D61—21no—
102C4×C22⋊D61—21no—
103#14519737—22no—
104#14519737—22no—
105#14519733—22no—
106#14519733—22no—
107C2×C4⋊Dic61C2×C411yescharacteristic
108C2×C4⋊Dic61C2×C411yescharacteristic
109C2×#11758196—22no—
110C2×#11758196—22no—
111C2×#11758196C2×C411yescharacteristic
112C2×#11758196C2×C411yescharacteristic
113C2×#11758196C2×C411yescharacteristic
114C2×#11758196C2×C411yescharacteristic
115C2×#11758196C2×C411yescharacteristic
116C2×#11758196C2311yescharacteristic
117C2×#11758196C2311yescharacteristic
118C2×C22⋊Dic61C2×C411yescharacteristic
119C2×C22⋊Dic61C2×C411yescharacteristic
120C2×C22⋊Dic61C2×C411yescharacteristic
121C2×C22⋊Dic61C2×C411yescharacteristic
122C2×C22⋊Dic61C2311yescharacteristic
123C2×#11758198C2×C411yescharacteristic
124C2×#11758198C2×C411yescharacteristic
125C2×#11758198C2311yescharacteristic
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—21no—
143C2×D4×C61—21no—
144C2×D4×C61—22no—
145C2×D4×C61—42no—
146C2×D4×C61—42no—
147C2×D4×C61—81no—
148C2×D4×C61C22⋊C412yes—
149C2×D4×C61C22⋊C412yes—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—81no—
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C22×C411yescharacteristic
157C2×C22⋊D61—22no—
158C2×C22⋊D61—21no—
159C2×C22⋊D61—21no—
160C2×C22⋊D61—22no—
161C2×C22⋊D61—22no—
162C2×C22⋊D61—41no—
163C2×C22⋊D61—42no—
164C2×C22⋊D61—81no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—22no—
170C22×Dic61—22no—
171C22×Dic61—41no—
172C22×Dic61—41no—
173C22×Dic61—81no—
174C22×Dic61—81no—
175C22×Dic61C22×C411yescharacteristic
176C22×Dic61C22×C411yescharacteristic
177C22×Dic61C22×C411yescharacteristic
178C22×Dic61C22×C411yescharacteristic
179C22×Dic61C22×C411yescharacteristic
180C22×Dic61C22×C411yescharacteristic
181C22×Dic61C2×D412yes—
182C22×Dic61C2×D412yes—
183C22×Dic61C2×D412yes—
184C22×Dic61C2×D412yes—
185C22×Dic61C2411yescharacteristic
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61—81no—
189#11758217—82no—
190#11758217—82no—
191C2×#92420—22no—
192C2×#92420—22no—
193C2×#92420—22no—
194C2×#92420—22no—
195C2×#92420—82no—
196C2×#92420—82no—
197C4⋊C4×C61—22no—
198C22⋊C4×C61—22no—
199C22⋊C4×C61—22no—
200C22⋊Dic61—22no—
201C22⋊Dic61—21no—
202C22⋊Dic61—21no—
203C22⋊Dic61—22no—
204C22⋊Dic61C22⋊C411yescharacteristic
205C22⋊Dic61C22⋊C411yescharacteristic
206C22⋊Dic61C22⋊C411yescharacteristic
207C22⋊Dic61C22⋊C411yescharacteristic
208C22⋊Dic61C22⋊C412yes—
209C22⋊Dic61C22⋊C412yes—
210#11758198—22no—
211#11758198—21no—
212#11758198—21no—
213#11758198—22no—
214C4⋊Dic61—21no—
215C4⋊Dic61—21no—
216C4⋊Dic61C22⋊C412yes—
217C4⋊Dic61C22⋊C412yes—
218#11758196—22no—
219#11758196—22no—
220#11758196—22no—
221#11758196—21no—
222#11758196—21no—
223#11758196—22no—
224#11758196—22no—
225#11758196—22no—
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—22no—
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×C61C2×C22⋊C412yes—
246C23×C61C2×C22⋊C411yescharacteristic
247C23×C61C2×C22⋊C411yescharacteristic
248C23×C61C23×C411yescharacteristic
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—41no—
253C22×D61—41no—
254D4×C61—24no—
255D4×C61—42no—
256D4×C61—42no—
257D4×C61—42no—
258D4×C61—82no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—41no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
266C2×C4×C61—81no—
267C2×C4×C61—81no—
268C2×C4×C61C2×C22⋊C412yes—
269C22⋊D61—44no—
270C22⋊D61—42no—
271C22⋊D61—42no—
272C22⋊D61—82no—
273C2×Dic61—21no—
274C2×Dic61—21no—
275C2×Dic61—21no—
276C2×Dic61—21no—
277C2×Dic61—21no—
278C2×Dic61—21no—
279C2×Dic61—21no—
280C2×Dic61—21no—
281C2×Dic61—42no—
282C2×Dic61—42no—
283C2×Dic61—42no—
284C2×Dic61—42no—
285C2×Dic61—41no—
286C2×Dic61—41no—
287C2×Dic61—41no—
288C2×Dic61—42no—
289C2×Dic61—42no—
290C2×Dic61—42no—
291C2×Dic61—42no—
292C2×Dic61—41no—
293C2×Dic61C2×C22⋊C411yescharacteristic
294C2×Dic61C2×C22⋊C411yescharacteristic
295C2×Dic61C2×C22⋊C411yescharacteristic
296C2×Dic61C2×C22⋊C411yescharacteristic
297C2×Dic61C2×C22⋊C412yes—
298C2×Dic61#13112yes—
299C2×Dic61C22×D412yes—
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—21no—
310C22×C61—21no—
311C22×C61—21no—
312C22×C61—22no—
313C22×C61—21no—
314C22×C61—22no—
315C22×C61—21no—
316C22×C61—22no—
317C22×C61—42no—
318C22×C61—42no—
319C22×C61—41no—
320C22×C61—41no—
321C22×C61—41no—
322C22×C61—81no—
323C22×C61—81no—
324C22×C61—81no—
325C22×C61—81no—
326C22×C61#41312yes—
327C22×C61C22×C22⋊C411yescharacteristic
328C22×C61C2×#13111yescharacteristic
329C22×C61#56811yescharacteristic
330C2×D61—41no—
331C2×D61—41no—
332C2×D61—41no—
333C2×D61—81no—
334C2×D61—81no—
335C4×C61—22no—
336C4×C61—41no—
337C4×C61—41no—
338C4×C61—41no—
339Dic61—22no—
340Dic61—21no—
341Dic61—21no—
342Dic61—22no—
343Dic61—21no—
344Dic61—21no—
345Dic61—22no—
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—22no—
362C2×C61—41no—
363C2×C61—42no—
364C2×C61—81no—
365C2×C61#288011yescharacteristic
366C2×C61#288311yescharacteristic
367C2×C61C2×#41311yescharacteristic
368D61—81no—
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—612no—
401#324—611no—
402#324—611no—
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—1222no—
448C4×D4—1222no—
449C4×D4—1221no—
450C4×D4—1221no—
451C4×D4—1221no—
452C4×D4—1221no—
453C4×D4—1221no—
454C4×D4—1221no—
455C4×D4—1221no—
456C4×D4—1221no—
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—21no—
501C2×D4—21no—
502C2×D4—22no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—81no—
506C2×D4—1222no—
507C2×D4—1222no—
508C2×D4—1222no—
509C2×D4—1221no—
510C2×D4—1221no—
511C2×D4—4881no—
512C2×D4—2441no—
513C2×D4—2442no—
514C2×D4C22⋊#692312yes—
515C2×D4C22⋊#692312yes—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—81no—
519C22×C4—611no—
520C22×C4—611no—
521C22×C4—612no—
522C22×C4—612no—
523C22×C4—612no—
524C22×C4—612no—
525C22×C4—611no—
526C22×C4—611no—
527C22×C4—611no—
528C22×C4—611no—
529C22×C4—611no—
530C22×C4—1221no—
531C22×C4—1221no—
532C22×C4—1221no—
533C22×C4—1221no—
534C22×C4—1222no—
535C22×C4—1222no—
536C22×C4—1221no—
537C22×C4—1221no—
538C22×C4—4881no—
539C22×C4—4881no—
540C22×C4—4881no—
541C22×C4—2441no—
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—1222no—
561C4⋊C4—1222no—
562C4⋊C4—1221no—
563C4⋊C4—1221no—
564C4⋊C4—1222no—
565C4⋊C4—1221no—
566C4⋊C4—1221no—
567C4⋊C4—1222no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—611no—
571C22⋊C4—611no—
572C22⋊C4—611no—
573C22⋊C4—611no—
574C22⋊C4—612no—
575C22⋊C4—612no—
576C22⋊C4—1222no—
577C22⋊C4—1221no—
578C22⋊C4—1221no—
579C22⋊C4—1222no—
580C22⋊C4—1221no—
581C22⋊C4—1221no—
582C22⋊C4—1222no—
583C22⋊C4—1222no—
584C42—612no—
585C42—612no—
586C42—1221no—
587C42—1221no—
588C42—1221no—
589C42—1221no—
590C23—22no—
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—1221no—
604C23—1221no—
605C23—1221no—
606C23—2441no—
607C23—2441no—
608C23C2×C22⋊#692312yes—
609C23C2×C22⋊#692311yescharacteristic
610C23C2×C22⋊#692311yescharacteristic
611C23C23×#692311yescharacteristic
612D4—24no—
613D4—42no—
614D4—42no—
615D4—42no—
616D4—82no—
617D4—4882no—
618D4—2444no—
619D4—2442no—
620D4—2442no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—81no—
629C2×C4—81no—
630C2×C4—611no—
631C2×C4—611no—
632C2×C4—611no—
633C2×C4—611no—
634C2×C4—612no—
635C2×C4—612no—
636C2×C4—612no—
637C2×C4—1221no—
638C2×C4—1221no—
639C2×C4—1221no—
640C2×C4—1221no—
641C2×C4—1221no—
642C2×C4—1221no—
643C2×C4—1221no—
644C2×C4—1221no—
645C2×C4—4881no—
646C2×C4—4881no—
647C2×C4—2442no—
648C2×C4—2442no—
649C2×C4—2442no—
650C2×C4—2442no—
651C2×C4—2441no—
652C2×C4—2441no—
653C2×C4—2441no—
654C2×C4—2442no—
655C2×C4—2442no—
656C2×C4—2442no—
657C2×C4—2442no—
658C2×C4—2441no—
659C2×C4C2×C22⋊#692312yes—
660C8—2442no—
661C8—2442no—
662C8—2442no—
663C8—2442no—
664C22—21no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—21no—
669C22—22no—
670C22—21no—
671C22—22no—
672C22—22no—
673C22—21no—
674C22—42no—
675C22—42no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22—4881no—
684C22—4881no—
685C22—2441no—
686C22—2441no—
687C22—2441no—
688C22#1684074912yes—
689C22C22×C22⋊#692311yescharacteristic
690C22D61⋊#13111yescharacteristic
691C22#1684084111yescharacteristic
692C4—22no—
693C4—41no—
694C4—41no—
695C4—41no—
696C4—1221no—
697C4—1221no—
698C4—1222no—
699C4—1222no—
700C4—1221no—
701C4—1221no—
702C4—1222no—
703C4—2441no—
704C4—2441no—
705C2—21no—
706C2—21no—
707C2—22no—
708C2—41no—
709C2—42no—
710C2—81no—
711C2—4881no—
712C2#2146240911yescharacteristic
713C2#2146241811yescharacteristic
714C2C2×#1684074911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#121×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840455C2
cosocleC22×Dic61C24
hypercenterC2×#121#6923
hypocenterC61#17427
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×D4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #21462675C2semidirect
2. #21461102C2semidirect
3. #21461095C2semidirect
4. #21461084C2semidirect
5. #21461077C2semidirect
6. #21461071C2semidirect
7. #21461069C2semidirect
8. #21461057C2semidirect
9. #21461051C2semidirect
10. C2×#16840608C2semidirect
408. C61#17427semidirect

Maximal subgroups

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

subgroupindex
#214626752
#214611022
#214610952
#214610842
#214610772
#214610712
#214610692
#214610572
#214610512
C2×#168406082
C2×#168404552
#1742761