Finite Group Databasebeta

← #30610367

Subgroups — #30610367

Order 15616.

1016 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462678C212yesmaximal, complemented
2#21461088C212yesmaximal, complemented
3#21461087C212yesmaximal, complemented
4#21461084C212yesmaximal, complemented
5#21461083C211yesmaximal, characteristic, complemented
6#21461077C211yesmaximal, characteristic, complemented
7#21461074C211yesmaximal, characteristic, complemented
8#21461063C211yesmaximal, characteristic, complemented
9#21461057C211yesmaximal, characteristic, complemented
10#21461054C211yesmaximal, characteristic, complemented
11C2×#16840496C211yesmaximal, 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#16840608C2211yescharacteristic
23#16840608C2211yescharacteristic
24#16840608C2211yescharacteristic
25#16840608C2211yescharacteristic
26#16840608C2212yes—
27#16840608C2212yes—
28#16840606C2212yes—
29#16840606C2212yes—
30#16840605C2212yes—
31#16840605C2212yes—
32#16840496—22no—
33#16840496—22no—
34#16840496—22no—
35#16840496—22no—
36C2×#14519773C411yescharacteristic
37C2×#14519763C411yescharacteristic
38C2×#14519763C411yescharacteristic
39C2×#14519763C411yescharacteristic
40C2×#14519763C2211yescharacteristic
41C2×#14519762C411yescharacteristic
42C2×#14519762C2211yescharacteristic
43C2×#14519758C2211yescharacteristic
44C2×#14519742C411yescharacteristic
45C2×#14519742C2211yescharacteristic
46C2×C4×C22⋊D61C411yescharacteristic
47C2×C4×C22⋊D61C2211yescharacteristic
48C2×#14519737C2211yescharacteristic
49C2×#14519737C2211yescharacteristic
50C2×#123×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×Dic122C2×C411yescharacteristic
68C22×Dic122C2×C411yescharacteristic
69C22×D244C2×C411yescharacteristic
70C22×C22⋊D61C2×C411yescharacteristic
71C22×C22⋊D61C2×C411yescharacteristic
72C22×C22⋊D61C2×C411yescharacteristic
73C22×C22⋊D61C2×C411yescharacteristic
74C23×Dic61C2311yescharacteristic
75C22×C4×D61C2×C411yescharacteristic
76C22×C4×D61C2311yescharacteristic
77#14519773—22no—
78#14519773—22no—
79#14519763—22no—
80#14519763—22no—
81#14519763—22no—
82#14519763—22no—
83#14519763—22no—
84#14519763—22no—
85#14519763—22no—
86#14519763—22no—
87#14519762—22no—
88#14519762—22no—
89#14519762—22no—
90#14519762—22no—
91#14519758—22no—
92#14519758—22no—
93#14519742—21no—
94#14519742—21no—
95#14519742—21no—
96#14519742—21no—
97#14519742—22no—
98#14519742—22no—
99C4×C22⋊D61—22no—
100C4×C22⋊D61—22no—
101C4×C22⋊D61—21no—
102C4×C22⋊D61—21no—
103C4×C22⋊D61—21no—
104C4×C22⋊D61—21no—
105#14519737—22no—
106#14519737—22no—
107#14519737D412yes—
108#14519737D412yes—
109#14519737D412yes—
110#14519737D412yes—
111C2×#11758196C2×C411yescharacteristic
112C2×#11758196C2×C411yescharacteristic
113C2×#11758196C2311yescharacteristic
114C2×#11758196C2311yescharacteristic
115C2×C22⋊Dic61C2×C411yescharacteristic
116C2×C22⋊Dic61C2×C411yescharacteristic
117C2×C22⋊Dic61C2311yescharacteristic
118C2×#11758198C2×C411yescharacteristic
119C2×#11758198C2×C411yescharacteristic
120C2×#11758198C2×C411yescharacteristic
121C2×#11758198C2×C411yescharacteristic
122C2×#11758198C2×C411yescharacteristic
123C2×#11758198C2311yescharacteristic
124C2×C4×Dic61C2×C411yescharacteristic
125C2×C4×Dic61C2×C411yescharacteristic
126C2×C4×Dic61C2×C411yescharacteristic
127C2×C4×Dic61C2×C411yescharacteristic
128C2×C4×Dic61C2311yescharacteristic
129C22×D4×C61C2×C411yescharacteristic
130C23×C4×C61C2×C411yescharacteristic
131#123×C61—22no—
132#123×C61—22no—
133C2×C4⋊C4×C61C2×C411yescharacteristic
134C2×C4⋊C4×C61C2×C411yescharacteristic
135C2×C22⋊C4×C61C2×C411yescharacteristic
136C2×C22⋊C4×C61C2×C411yescharacteristic
137C2×C22⋊C4×C61C2×C411yescharacteristic
138C24×C61C22×C411yescharacteristic
139C24×C61C22×C411yescharacteristic
140C23×D61C22×C411yescharacteristic
141C23×D61C22×C411yescharacteristic
142C2×D4×C61—22no—
143C2×D4×C61—81no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—81no—
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C411yescharacteristic
152C2×C22⋊D61—22no—
153C2×C22⋊D61—22no—
154C2×C22⋊D61—21no—
155C2×C22⋊D61—21no—
156C2×C22⋊D61—22no—
157C2×C22⋊D61—22no—
158C2×C22⋊D61—42no—
159C2×C22⋊D61—41no—
160C2×C22⋊D61—41no—
161C2×C22⋊D61—42no—
162C2×C22⋊D61C22⋊C412yes—
163C2×C22⋊D61C22⋊C412yes—
164C22×Dic61—81no—
165C22×Dic61C22×C411yescharacteristic
166C22×Dic61C22×C411yescharacteristic
167C22×Dic61C22×C411yescharacteristic
168C22×Dic61C22×C411yescharacteristic
169C22×Dic61C22×C411yescharacteristic
170C22×Dic61C2×D412yes—
171C22×Dic61C2×D412yes—
172C22×Dic61C2411yescharacteristic
173C2×D244—22no—
174C2×D244—81no—
175C2×C4×D61—21no—
176C2×C4×D61—21no—
177C2×C4×D61—81no—
178C2×C4×D61—81no—
179C2×C4×D61C2×D412yes—
180C2×C4×D61C2×D412yes—
181C2×Dic122—22no—
182C2×Dic122—21no—
183C2×Dic122—21no—
184C2×Dic122—22no—
185C2×Dic122—41no—
186C2×Dic122—42no—
187#11758217—82no—
188C2×#92420—22no—
189C2×#92420—22no—
190C2×#92420—22no—
191C2×#92420—22no—
192C2×#92420—82no—
193#11758213—82no—
194D61⋊C8—82no—
195C4⋊C4×C61—22no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C22⋊C4×C61—22no—
199C22⋊C4×C61—22no—
200C22⋊C4×C61C22⋊C412yes—
201C22⋊C4×C61C22⋊C412yes—
202C22⋊Dic61—22no—
203C22⋊Dic61—21no—
204C22⋊Dic61—21no—
205C22⋊Dic61—22no—
206#11758198—22no—
207#11758198—22no—
208#11758198—21no—
209#11758198—21no—
210#11758198—22no—
211#11758198—22no—
212#11758198C22⋊C412yes—
213#11758198C22⋊C412yes—
214#11758196—21no—
215#11758196—21no—
216#11758196—22no—
217#11758196—22no—
218#11758196C22⋊C411yescharacteristic
219#11758196C22⋊C411yescharacteristic
220#11758196C22⋊C411yescharacteristic
221#11758196C22⋊C411yescharacteristic
222C4×Dic61—21no—
223C4×Dic61—21no—
224C4×Dic61—21no—
225C4×Dic61—21no—
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—41no—
238C23×C61—41no—
239C23×C61—41no—
240C23×C61—41no—
241C23×C61C2×C22⋊C412yes—
242C23×C61C23×C411yescharacteristic
243C22×D61—21no—
244C22×D61—21no—
245C22×D61—21no—
246C22×D61—21no—
247C22×D61—21no—
248C22×D61—41no—
249C22×D61—41no—
250C22×D61—41no—
251C22×D61—41no—
252C22×D61C2×C22⋊C412yes—
253D4×C61—82no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61—41no—
262C2×C4×C61—41no—
263C2×C4×C61—81no—
264C2×C4×C61—81no—
265C2×C4×C61C2×C22⋊C411yescharacteristic
266C2×C4×C61C2×C22⋊C411yescharacteristic
267C2×C4×C61C2×C22⋊C412yes—
268C22⋊D61—24no—
269C22⋊D61—42no—
270C22⋊D61—44no—
271C22⋊D61—44no—
272C22⋊D61—42no—
273C22⋊D61—42no—
274C2×Dic61—21no—
275C2×Dic61—21no—
276C2×Dic61—22no—
277C2×Dic61—21no—
278C2×Dic61—21no—
279C2×Dic61—21no—
280C2×Dic61—21no—
281C2×Dic61—42no—
282C2×Dic61—42no—
283C2×Dic61—41no—
284C2×Dic61—41no—
285C2×Dic61—41no—
286C2×Dic61C2×C22⋊C411yescharacteristic
287C2×Dic61C2×C22⋊C411yescharacteristic
288C2×Dic61C2×C22⋊C411yescharacteristic
289C2×Dic61C2×C22⋊C411yescharacteristic
290C2×Dic61#13112yes—
291C2×Dic61C22×D412yes—
292D244—82no—
293C4×D61—42no—
294C4×D61—42no—
295C4×D61—81no—
296C4×D61—81no—
297Dic122—44no—
298Dic122—42no—
299Dic122—42no—
300#92420—42no—
301#92420—42no—
302#92420—42no—
303#92420—42no—
304#17429—611nomaximal, Sylow
305C22×C61—21no—
306C22×C61—21no—
307C22×C61—22no—
308C22×C61—22no—
309C22×C61—22no—
310C22×C61—41no—
311C22×C61—41no—
312C22×C61—41no—
313C22×C61—81no—
314C22×C61—81no—
315C22×C61—81no—
316C22×C61—81no—
317C22×C61C22×C22⋊C411yescharacteristic
318C22×C61C2×#13111yescharacteristic
319C22×C61#56811yescharacteristic
320C2×D61—22no—
321C2×D61—22no—
322C2×D61—22no—
323C2×D61—41no—
324C2×D61—41no—
325C2×D61—41no—
326C2×D61—81no—
327C2×D61—81no—
328C2×D61—81no—
329C2×D61—81no—
330C4×C61—22no—
331C4×C61—21no—
332C4×C61—21no—
333C4×C61—41no—
334C4×C61—41no—
335C4×C61—41no—
336Dic61—22no—
337Dic61—22no—
338Dic61—21no—
339Dic61—21no—
340Dic61—21no—
341Dic61—41no—
342Dic61—41no—
343Dic61#41312yes—
344C2×#559—611no—
345#2974—612no—
346#1469—612no—
347#1468—612no—
348#1468—612no—
349#1467—611no—
350#1465—611no—
351#1465—611no—
352#1461—611no—
353#1459—611no—
354#1459—611no—
355C2×C61—21no—
356C2×C61—21no—
357C2×C61—42no—
358C2×C61—81no—
359C2×C61#288011yescharacteristic
360C2×C61#288311yescharacteristic
361C2×C61C2×#41311yescharacteristic
362D61—42no—
363D61—81no—
364#559—1222no—
365#559—1222no—
366#559—1222no—
367#559—1222no—
368C2×#127—611no—
369C2×#124—611no—
370C2×#124—611no—
371C2×#124—611no—
372C2×#124—611no—
373C2×#123—611no—
374C2×#123—611no—
375C2×#123—611no—
376C2×#123#692311yescharacteristic
377C2×C4×Q8—611no—
378C2×C4×Q8—611no—
379C2×C4×D4—611no—
380C2×C4×D4—611no—
381C2×C4×D4—611no—
382C2×C4×D4—611no—
383#436—1222no—
384#435—1222no—
385#435—1222no—
386C8×D4—1222no—
387#432—612no—
388#431—612no—
389#407—612no—
390#407—612no—
391C2×C22⋊C8—612no—
392C2×C22⋊C8—612no—
393#324—611no—
394#324—611no—
395#324—611no—
396#324—611no—
397#324—612no—
398#324—612no—
399#323—612no—
400#323—612no—
401#323—612no—
402#323—612no—
403C61#1742911yescharacteristic, complemented, Sylow
404C22×Q8—611no—
405C22×Q8—611no—
406C22×D4—611no—
407C22×D4—611no—
408C22×D4—611no—
409C22×D4—611no—
410C22×D4—611no—
411C22×D4C2×#692311yescharacteristic
412C23×C4—611no—
413C23×C4—611no—
414C23×C4—611no—
415C23×C4C2×#692311yescharacteristic
416C2×M16—1222no—
417C2×M16—1222no—
418C22×C8—1222no—
419C22×C8—1222no—
420#127—1222no—
421#127—1222no—
422#124—1222no—
423#124—1222no—
424#124—1222no—
425#124—1222no—
426#124—1222no—
427#124—1222no—
428#124—1222no—
429#124—1222no—
430#123—22no—
431#123—22no—
432#123—1222no—
433#123—1222no—
434#123—1222no—
435#123—1222no—
436#123—1222no—
437#123—1222no—
438C4×Q8—1222no—
439C4×Q8—1222no—
440C4×Q8—1221no—
441C4×Q8—1221no—
442C4×Q8—1221no—
443C4×Q8—1221no—
444C4×D4—612no—
445C4×D4—612no—
446C4×D4—612no—
447C4×D4—612no—
448C4×D4—1222no—
449C4×D4—1222no—
450C4×D4—1221no—
451C4×D4—1221no—
452C4×D4—1221no—
453C4×D4—1221no—
454C4×D4—1222no—
455C4×D4—1222no—
456C2×C4⋊C4—611no—
457C2×C4⋊C4—611no—
458C2×C4⋊C4—611no—
459C2×C4⋊C4—611no—
460C2×C4⋊C4C2×#692311yescharacteristic
461C2×C4⋊C4C2×#692311yescharacteristic
462C2×C22⋊C4—611no—
463C2×C22⋊C4—611no—
464C2×C22⋊C4—611no—
465C2×C22⋊C4—611no—
466C2×C22⋊C4—611no—
467C2×C22⋊C4—611no—
468C2×C22⋊C4—611no—
469C2×C22⋊C4—611no—
470C2×C22⋊C4—611no—
471C2×C22⋊C4C2×#692311yescharacteristic
472C2×C22⋊C4C2×#692311yescharacteristic
473C2×C22⋊C4C2×#692311yescharacteristic
474C2×C42—611no—
475C2×C42—611no—
476C2×C42—611no—
477C2×C42—611no—
478C2×C42—611no—
479C4⋊C8—1222no—
480C4⋊C8—1222no—
481C22⋊C8—612no—
482C22⋊C8—612no—
483C22⋊C8—612no—
484C22⋊C8—612no—
485C22⋊C8—1222no—
486C22⋊C8—1222no—
487C22⋊C8—1222no—
488C22⋊C8—1222no—
489#97—1222no—
490C4×C8—1222no—
491C24—611no—
492C24—611no—
493C24C22×#692311yescharacteristic
494C24C22×#692311yescharacteristic
495C2×Q8—1221no—
496C2×Q8—1221no—
497C2×Q8—1222no—
498C2×Q8—1222no—
499C2×Q8—2441no—
500C2×Q8—2442no—
501C2×D4—22no—
502C2×D4—81no—
503C2×D4—612no—
504C2×D4—612no—
505C2×D4—1222no—
506C2×D4—1221no—
507C2×D4—1221no—
508C2×D4—1222no—
509C2×D4—1222no—
510C2×D4—1222no—
511C2×D4—1222no—
512C2×D4—4881no—
513C2×D4—2442no—
514C2×D4—2441no—
515C2×D4—2441no—
516C2×D4—2442no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—81no—
520C22×C4—611no—
521C22×C4—611no—
522C22×C4—612no—
523C22×C4—612no—
524C22×C4—611no—
525C22×C4—611no—
526C22×C4—612no—
527C22×C4—612no—
528C22×C4—611no—
529C22×C4—611no—
530C22×C4—1221no—
531C22×C4—1221no—
532C22×C4—4881no—
533C22×C4—4881no—
534C22×C4—4881no—
535C22×C4C22×#692311yescharacteristic
536C22×C4C22×#692311yescharacteristic
537C22×C4C22×#692311yescharacteristic
538C22×C4C22×#692311yescharacteristic
539C22×C4C22×#692311yescharacteristic
540M16—4882no—
541M16—4882no—
542C2×C8—1222no—
543C2×C8—1222no—
544C2×C8—1222no—
545C2×C8—1222no—
546C2×C8—4882no—
547C2×C8—4882no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—22no—
551C4⋊C4—611no—
552C4⋊C4—611no—
553C4⋊C4—611no—
554C4⋊C4—611no—
555C4⋊C4—1222no—
556C4⋊C4—1221no—
557C4⋊C4—1221no—
558C4⋊C4—1222no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—612no—
562C22⋊C4—612no—
563C22⋊C4—1222no—
564C22⋊C4—1222no—
565C22⋊C4—1222no—
566C22⋊C4—1221no—
567C22⋊C4—1221no—
568C22⋊C4—1222no—
569C22⋊C4—1222no—
570C22⋊C4—1221no—
571C22⋊C4—1221no—
572C22⋊C4—1222no—
573C22⋊C4C22⋊#692312yes—
574C22⋊C4C22⋊#692312yes—
575C42—612no—
576C42—612no—
577C42—1221no—
578C42—1221no—
579C42—1221no—
580C42—1221no—
581C42—1221no—
582C42—1221no—
583C42—1221no—
584C42—1221no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—612no—
595C23—1221no—
596C23—1221no—
597C23—1221no—
598C23—1221no—
599C23—1221no—
600C23—2441no—
601C23—2441no—
602C23—2441no—
603C23—2441no—
604C23C2×C22⋊#692312yes—
605C23C23×#692311yescharacteristic
606Q8—2444no—
607Q8—2442no—
608Q8—2442no—
609D4—82no—
610D4—1224no—
611D4—4882no—
612D4—2442no—
613D4—2442no—
614D4—2444no—
615D4—2444no—
616D4—2442no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—81no—
627C2×C4—81no—
628C2×C4—611no—
629C2×C4—611no—
630C2×C4—611no—
631C2×C4—611no—
632C2×C4—612no—
633C2×C4—612no—
634C2×C4—1222no—
635C2×C4—1221no—
636C2×C4—1221no—
637C2×C4—1221no—
638C2×C4—1221no—
639C2×C4—1221no—
640C2×C4—1221no—
641C2×C4—4881no—
642C2×C4—4881no—
643C2×C4—2442no—
644C2×C4—2442no—
645C2×C4—2442no—
646C2×C4—2442no—
647C2×C4—2441no—
648C2×C4—2441no—
649C2×C4—2441no—
650C2×C4C2×C22⋊#692312yes—
651C2×C4C2×C22⋊#692311yescharacteristic
652C2×C4C2×C22⋊#692311yescharacteristic
653C8—2442no—
654C8—2442no—
655C8—2442no—
656C8—2442no—
657C22—21no—
658C22—21no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22—1222no—
670C22—1222no—
671C22—1222no—
672C22—4881no—
673C22—4881no—
674C22—4881no—
675C22—4881no—
676C22—2441no—
677C22—2441no—
678C22—2441no—
679C22C22×C22⋊#692311yescharacteristic
680C22D61⋊#13111yescharacteristic
681C22#1684084111yescharacteristic
682C4—22no—
683C4—21no—
684C4—21no—
685C4—41no—
686C4—41no—
687C4—41no—
688C4—612no—
689C4—1222no—
690C4—1222no—
691C4—1221no—
692C4—1221no—
693C4—1221no—
694C4—2441no—
695C4—2441no—
696C2—21no—
697C2—21no—
698C2—42no—
699C2—81no—
700C2—4881no—
701C2—2442no—
702C2#2146240911yescharacteristic
703C2#2146241811yescharacteristic
704C2D61⋊#41311yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#123×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519773C4
cosocleC22×Dic61C24
hypercenterC2×#123#6923
hypocenterC61#17429
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. #21462678C2semidirect
2. #21461088C2semidirect
3. #21461087C2semidirect
4. #21461084C2semidirect
5. #21461083C2semidirect
6. #21461077C2semidirect
7. #21461074C2semidirect
8. #21461063C2semidirect
9. #21461057C2semidirect
10. #21461054C2semidirect
403. C61#17429semidirect

Maximal subgroups

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

subgroupindex
#214626782
#214610882
#214610872
#214610842
#214610832
#214610772
#214610742
#214610632
#214610572
#214610542
C2×#168404962
#1742961