Finite Group Databasebeta

← #30575934

Subgroups — #30575934

Order 15616.

1762 conjugacy classes of subgroups.

The subgroup lattice has 1278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459730C211yesmaximal, characteristic, complemented
2#21458758C212yesmaximal, complemented
3#21458566C212yesmaximal, complemented
4#21458419C212yesmaximal, complemented
5#21458364C212yesmaximal, complemented
6#21458313C212yesmaximal, complemented
7#21458072C212yesmaximal, complemented
8#21458005C212yesmaximal, complemented
9#21457825C212yesmaximal, complemented
10#21457197C211yesmaximal, characteristic, complemented
11#21457181C211yesmaximal, characteristic, complemented
12#21457145C211yesmaximal, characteristic, complemented
13#21457037C211yesmaximal, characteristic, complemented
14#21457013C211yesmaximal, characteristic, complemented
15#21456994C211yesmaximal, characteristic, complemented
16#21455970C211yesmaximal, characteristic, complemented
17#21455941C211yesmaximal, characteristic, complemented
18#21455879C211yesmaximal, characteristic, complemented
19#21455634C211yesmaximal, characteristic, complemented
20#21455624C211yesmaximal, characteristic, complemented
21#21455607C211yesmaximal, characteristic, complemented
22#21454936C211yesmaximal, characteristic, complemented
23C61×#3480C211yesmaximal, characteristic, complemented
24#16840485—21no—
25#16840477C2212yes—
26#16840472C2212yes—
27#16840458C2212yes—
28#16840458C2212yes—
29#16840421—21no—
30#16840421—21no—
31#16840417—21no—
32#16840383—21no—
33#16840383—21no—
34#16840340—21no—
35#16840319C2211yescharacteristic
36#16840319C2211yescharacteristic
37#16840312C2211yescharacteristic
38#16840312C2211yescharacteristic
39#16840312C2211yescharacteristic
40C2×#14519777C2211yescharacteristic
41#16840242—21no—
42#16840172C2212yes—
43#16840168C2212yes—
44#16840161C2212yes—
45#16840126C2212yes—
46#16840121C2212yes—
47#16840116C2212yes—
48#16840100C2212yes—
49#16840090C2212yes—
50#16840086C2212yes—
51#16840086C2212yes—
52#16840083C2212yes—
53#16840083C2212yes—
54#16840083C2212yes—
55#16840075C2212yes—
56#16840073C2212yes—
57#16840069C2212yes—
58#16840069C2212yes—
59#16840069C2212yes—
60#16840062C2212yes—
61#16840059C2212yes—
62#16840059C2212yes—
63#16840057C2211yescharacteristic
64#16840057C2211yescharacteristic
65#16840057C2211yescharacteristic
66#16840057C2211yescharacteristic
67#16840052C2211yescharacteristic
68#16840052C2211yescharacteristic
69#16840052C2211yescharacteristic
70#16840052C2211yescharacteristic
71#16840049C2212yes—
72#16840047C2211yescharacteristic
73#16840047C2211yescharacteristic
74#16840047C2212yes—
75#16840042C2212yes—
76#16840042C2211yescharacteristic
77#16840042C2211yescharacteristic
78#16840013C2212yes—
79#16840013C2212yes—
80#16840013C2212yes—
81#16840010C2212yes—
82#16839996C2212yes—
83#16839993C2212yes—
84#16839974C2212yes—
85#16839974C2212yes—
86#16839962C2211yescharacteristic
87#16839962C2211yescharacteristic
88#16839957C2211yescharacteristic
89#16839957C2211yescharacteristic
90#16839954C2212yes—
91#16839907C2212yes—
92#16839907C2212yes—
93#16839901C2212yes—
94#16839893C2212yes—
95#16839872C2212yes—
96#16839860C2212yes—
97#16839860C2212yes—
98#16839860C2212yes—
99C4×#11758201C2212yes—
100C4×#11758199C2212yes—
101#16839840C2212yes—
102#16839834C2212yes—
103#16839834C2212yes—
104#16839819C2211yescharacteristic
105#16839819C2211yescharacteristic
106#16839815C2211yescharacteristic
107#16839805C2212yes—
108#16839802C2212yes—
109#16839798C2212yes—
110#16839786C2211yescharacteristic
111#16839786C2211yescharacteristic
112C2×C4⋊#92418C2211yescharacteristic
113#16839771C2212yes—
114#16839763C2212yes—
115#16839758C2212yes—
116C61×#559—21no—
117C61×#559C2211yescharacteristic
118C61×#557C2211yescharacteristic
119C61×#556—21no—
120C61×#556C2211yescharacteristic
121C61×#553—21no—
122C61×#553—21no—
123C61×#553C2211yescharacteristic
124C61×#553C2211yescharacteristic
125C61×#550C2211yescharacteristic
126C61×#548C2211yescharacteristic
127C61×#548C2211yescharacteristic
128C61×#532—21no—
129C61×#532C2211yescharacteristic
130C61×#529—21no—
131C61×#529—21no—
132C61×#529C2211yescharacteristic
133C61×#529C2211yescharacteristic
134C4×#41×C61—21no—
135C4×#41×C61C2211yescharacteristic
136C4×#41×C61C2211yescharacteristic
137C4×#41×C61C2211yescharacteristic
138C2×C4×Q8×C61C2211yescharacteristic
139C2×#11758222—21no—
140C2×#11758222—21no—
141C2×#11758222—21no—
142C22×Dic122—21no—
143C2×#11758201C2312yes—
144C2×#11758201C2312yes—
145C2×#11758199C2312yes—
146C2×#11758199C2312yes—
147C2×#11758194C2312yes—
148C2×#11758194C2312yes—
149C22×#92418C2312yes—
150#14519777—21no—
151#14519777—21no—
152#14519777C2312yes—
153#14519777C2311yescharacteristic
154#14519777C2311yescharacteristic
155#14519777C2311yescharacteristic
156#14519774C2311yescharacteristic
157#14519772—22no—
158#14519772—22no—
159#14519769C2312yes—
160#14519769C2312yes—
161#14519765—21no—
162#14519765—21no—
163#14519765—21no—
164#14519763—22no—
165#14519763—22no—
166#14519759—22no—
167#14519759—22no—
168#14519756—21no—
169#14519756—21no—
170#14519756—21no—
171#14519756—21no—
172#14519755—22no—
173#14519755—22no—
174#14519753—22no—
175#14519751—21no—
176#14519751—21no—
177#14519751—21no—
178#14519751C2312yes—
179#14519751C2312yes—
180#14519751C2312yes—
181#14519749—22no—
182#14519749—22no—
183#14519748—22no—
184C4×Dic122—21no—
185C4×Dic122—21no—
186C4×Dic122—21no—
187C4×Dic122—21no—
188C4×D244—21no—
189C4×D244—21no—
190C4×D244—21no—
191C4×D244C2312yes—
192C4×D244C2312yes—
193C4×D244C2312yes—
194#14519737—22no—
195#14519737—22no—
196#14519736C2312yes—
197#14519736C2312yes—
198#14519735—22no—
199C2×C4⋊Dic61—21no—
200C2×C4⋊Dic61C2312yes—
201C4⋊C4×D61—22no—
202#14519710C2312yes—
203#14519710C2312yes—
204#14519710C2312yes—
205#14519710C2312yes—
206#14519710C2312yes—
207#14519710C2312yes—
208#14519708C2312yes—
209#14519708C2312yes—
210#14519708C2312yes—
211#14519708C2312yes—
212#14519708C2312yes—
213#14519708C2312yes—
214C4⋊#92418C2312yes—
215C4⋊#92418C2311yescharacteristic
216C4⋊#92418C2311yescharacteristic
217C4⋊#92418C2311yescharacteristic
218C4⋊#92418C2311yescharacteristic
219C4⋊#92418C2312yes—
220C4⋊#92418C2312yes—
221#14519701C2312yes—
222#14519701C2312yes—
223#14519701C2312yes—
224#14519701C2312yes—
225#14519701C2312yes—
226#14519701C2312yes—
227#14519698C2312yes—
228#14519698C2312yes—
229#14519698C2312yes—
230#14519698C2312yes—
231#14519698C2312yes—
232#14519698C2312yes—
233#14519697C2312yes—
234#14519697C2312yes—
235#14519697C2312yes—
236#14519697C2312yes—
237C22⋊#92418C2312yes—
238C22⋊#92418C2312yes—
239C22⋊#92418C2312yes—
240#14519688C2312yes—
241#14519688C2312yes—
242C4×#92418C2312yes—
243C2×#41×C61—21no—
244C2×#41×C61D411yescharacteristic
245C2×#41×C61C2311yescharacteristic
246C2×#41×C61C2311yescharacteristic
247C22×Q8×C61C2311yescharacteristic
248C4⋊Q8×C61—21no—
249C4⋊Q8×C61C2311yescharacteristic
250#127×C61—21no—
251#127×C61C2311yescharacteristic
252#126×C61—21no—
253#126×C61—21no—
254#126×C61—21no—
255#126×C61—21no—
256#126×C61—21no—
257#126×C61—21no—
258#125×C61—21no—
259#125×C61—21no—
260#125×C61C2311yescharacteristic
261#125×C61C2311yescharacteristic
262#124×C61—21no—
263#124×C61—21no—
264#124×C61—21no—
265#124×C61—21no—
266#124×C61—21no—
267#124×C61C2311yescharacteristic
268#124×C61C2311yescharacteristic
269#123×C61—21no—
270#123×C61—21no—
271#123×C61—21no—
272#123×C61—21no—
273#123×C61—21no—
274#123×C61—21no—
275C22⋊Q8×C61—21no—
276C22⋊Q8×C61—21no—
277C22⋊Q8×C61C2311yescharacteristic
278C22⋊Q8×C61C2311yescharacteristic
279#121×C61—21no—
280#121×C61—21no—
281#121×C61—21no—
282#121×C61—21no—
283#121×C61—21no—
284#121×C61—21no—
285#121×C61—21no—
286#121×C61C2311yescharacteristic
287#121×C61C2311yescharacteristic
288#121×C61C2311yescharacteristic
289#121×C61C2311yescharacteristic
290C4×Q8×C61—21no—
291C4×Q8×C61—21no—
292C4×Q8×C61—21no—
293C4×Q8×C61—21no—
294C4×Q8×C61D411yescharacteristic
295C4×Q8×C61C2311yescharacteristic
296C4×Q8×C61C2311yescharacteristic
297C4×Q8×C61C2311yescharacteristic
298C4×Q8×C61C2311yescharacteristic
299C4×Q8×C61C2311yescharacteristic
300C4×Q8×C61C2311yescharacteristic
301C4×Q8×C61C2311yescharacteristic
302C4×D4×C61—21no—
303C4×D4×C61—21no—
304C4×D4×C61—21no—
305C4×D4×C61—21no—
306C4×D4×C61—21no—
307C4×D4×C61—21no—
308C4×D4×C61—21no—
309C4×D4×C61—21no—
310C4×D4×C61—21no—
311C4×D4×C61—21no—
312C4×D4×C61—21no—
313C4×D4×C61—21no—
314C4×D4×C61—21no—
315C4×D4×C61D411yescharacteristic
316C4×D4×C61D411yescharacteristic
317C4×D4×C61D411yescharacteristic
318C4×D4×C61C2311yescharacteristic
319C4×D4×C61C2311yescharacteristic
320C4×D4×C61C2311yescharacteristic
321C4×D4×C61C2311yescharacteristic
322C4×D4×C61C2311yescharacteristic
323C4×D4×C61C2311yescharacteristic
324C4×D4×C61C2311yescharacteristic
325#117×C61—21no—
326#117×C61—21no—
327#117×C61—21no—
328#117×C61—21no—
329#117×C61D411yescharacteristic
330#117×C61D411yescharacteristic
331#117×C61D411yescharacteristic
332#117×C61C2311yescharacteristic
333#117×C61C2311yescharacteristic
334C2×C4⋊C4×C61—21no—
335C2×C4⋊C4×C61C2311yescharacteristic
336C2×C42×C61—21no—
337C2×C42×C61—21no—
338C2×C42×C61—21no—
339C2×C42×C61C2311yescharacteristic
340C2×C42×C61C2311yescharacteristic
341C2×C42×C61C2311yescharacteristic
342#41×C61—22no—
343#41×C61—22no—
344#41×C61—42no—
345#41×C61—41no—
346#41×C61—41no—
347#41×C61—44no—
348C2×Q8×C61—21no—
349C2×Q8×C61—21no—
350C2×Q8×C61—22no—
351C2×Q8×C61—41no—
352C2×Q8×C61C2×D411yescharacteristic
353C2×Q8×C61C2411yescharacteristic
354C2×Q8×C61C2411yescharacteristic
355C2×D4×C61—21no—
356C2×D4×C61—21no—
357C2×D4×C61—21no—
358C2×D4×C61—21no—
359C2×D4×C61—21no—
360C2×D4×C61—21no—
361C2×D4×C61—21no—
362C2×D4×C61—21no—
363C2×D4×C61C2×D411yescharacteristic
364C2×D4×C61C2×D411yescharacteristic
365C2×D4×C61C2×D411yescharacteristic
366C2×D4×C61C2411yescharacteristic
367C2×D4×C61C2411yescharacteristic
368C22×C4×C61—21no—
369C22×C4×C61—21no—
370C22×C4×C61—21no—
371C22×C4×C61—21no—
372C22×C4×C61—21no—
373C22×C4×C61—21no—
374C22×C4×C61—21no—
375C22×C4×C61—21no—
376C22×C4×C61C2×D411yescharacteristic
377C22×C4×C61C2×D411yescharacteristic
378C22×C4×C61C2×D411yescharacteristic
379C22×C4×C61C2×D411yescharacteristic
380C22×C4×C61C2×D411yescharacteristic
381C22×C4×C61C2×D411yescharacteristic
382C22×C4×C61C2411yescharacteristic
383C22×C4×C61C2411yescharacteristic
384C22×C4×C61C2411yescharacteristic
385C2×C22⋊D61—22no—
386C2×C22⋊D61—22no—
387C2×C22⋊D61—22no—
388C22×Dic61—22no—
389#11758222—44no—
390#11758222—82no—
391#11758222—82no—
392C2×D244—21no—
393C2×D244—21no—
394C2×D244C2412yes—
395C2×C4×D61—22no—
396C2×C4×D61—22no—
397C2×C4×D61—22no—
398C2×Dic122—21no—
399C2×Dic122—21no—
400C2×Dic122—21no—
401C2×Dic122—22no—
402C2×Dic122—82no—
403C4⋊C4×C61—21no—
404C4⋊C4×C61—21no—
405C4⋊C4×C61—21no—
406C4⋊C4×C61—21no—
407C4⋊C4×C61—21no—
408C4⋊C4×C61—21no—
409C4⋊C4×C61—21no—
410C4⋊C4×C61—21no—
411C4⋊C4×C61—21no—
412C4⋊C4×C61—21no—
413C4⋊C4×C61—21no—
414C4⋊C4×C61—21no—
415C4⋊C4×C61—21no—
416C4⋊C4×C61—21no—
417C4⋊C4×C61C2×D411yescharacteristic
418C4⋊C4×C61C2×D411yescharacteristic
419C4⋊C4×C61C2×D411yescharacteristic
420C4⋊C4×C61C2×D411yescharacteristic
421C4⋊C4×C61C2×D411yescharacteristic
422C4⋊C4×C61C2×D411yescharacteristic
423C4⋊C4×C61C2411yescharacteristic
424C4⋊C4×C61C2411yescharacteristic
425C4⋊C4×C61C2411yescharacteristic
426C4⋊C4×C61C2411yescharacteristic
427C22⋊C4×C61—21no—
428C22⋊C4×C61—21no—
429C22⋊C4×C61—21no—
430C22⋊C4×C61—21no—
431C22⋊C4×C61—21no—
432C22⋊C4×C61—21no—
433C22⋊C4×C61—21no—
434C22⋊C4×C61—21no—
435C22⋊C4×C61—21no—
436C22⋊C4×C61—21no—
437C22⋊C4×C61—21no—
438C22⋊C4×C61—21no—
439C22⋊C4×C61—21no—
440C22⋊C4×C61—21no—
441C22⋊C4×C61—21no—
442C22⋊C4×C61—21no—
443C22⋊C4×C61C2×D411yescharacteristic
444C22⋊C4×C61C2×D411yescharacteristic
445C22⋊C4×C61C2×D411yescharacteristic
446C22⋊C4×C61C2×D411yescharacteristic
447C22⋊C4×C61C2×D411yescharacteristic
448C22⋊C4×C61C2×D411yescharacteristic
449C42×C61—21no—
450C42×C61—21no—
451C42×C61—21no—
452C42×C61—21no—
453C42×C61—21no—
454C42×C61—21no—
455C42×C61—21no—
456C42×C61—21no—
457C42×C61C2×D411yescharacteristic
458C42×C61C2×D411yescharacteristic
459C42×C61C2×D411yescharacteristic
460C42×C61C2×D411yescharacteristic
461C42×C61C2×D411yescharacteristic
462C42×C61C2×D411yescharacteristic
463C42×C61C2411yescharacteristic
464C42×C61C2411yescharacteristic
465C42×C61C2411yescharacteristic
466C42×C61C2411yescharacteristic
467C22⋊Dic61—22no—
468C22⋊Dic61—22no—
469#11758201—24no—
470#11758201—42no—
471#11758199—42no—
472#11758199—42no—
473#11758198—22no—
474#11758198—22no—
475#11758198—22no—
476#11758198—22no—
477#11758198—22no—
478#11758198—22no—
479C4⋊Dic61—22no—
480C4⋊Dic61—21no—
481C4⋊Dic61—21no—
482C4⋊Dic61—22no—
483C4⋊Dic61—21no—
484C4⋊Dic61C2412yes—
485C4⋊Dic61C2412yes—
486C4⋊Dic61C2412yes—
487#11758196—22no—
488#11758196—22no—
489#11758196—22no—
490#11758196—22no—
491C4×Dic61—22no—
492C4×Dic61—22no—
493#11758194—42no—
494#11758194—42no—
495C2×#92418—42no—
496C2×#92418C2412yes—
497C2×#92418C2412yes—
498C2×#92418C2412yes—
499C2×#92418C2412yes—
500C23×C61—21no—
501C23×C61—21no—
502C23×C61C22×D411yescharacteristic
503C23×C61C22×D411yescharacteristic
504C23×C61C22×D411yescharacteristic
505C22×D61—22no—
506Q8×C61—21no—
507Q8×C61—21no—
508Q8×C61—21no—
509Q8×C61—41no—
510Q8×C61—42no—
511Q8×C61—42no—
512Q8×C612−1+412yes—
513D4×C61—21no—
514D4×C61—21no—
515D4×C61—21no—
516D4×C61—21no—
517D4×C61—41no—
518D4×C61—41no—
519D4×C61—41no—
520D4×C61—42no—
521D4×C61—42no—
522D4×C61—42no—
523D4×C61—42no—
524D4×C61—42no—
525D4×C61—81no—
526D4×C61—81no—
527D4×C61—81no—
528C2×C4×C61—21no—
529C2×C4×C61—22no—
530C2×C4×C61—22no—
531C2×C4×C61—22no—
532C2×C4×C61—21no—
533C2×C4×C61—21no—
534C2×C4×C61—21no—
535C2×C4×C61—21no—
536C2×C4×C61—21no—
537C2×C4×C61—21no—
538C2×C4×C61—21no—
539C2×C4×C61—21no—
540C2×C4×C61—21no—
541C2×C4×C61—21no—
542C2×C4×C61—21no—
543C2×C4×C61—41no—
544C2×C4×C61—41no—
545C2×C4×C61—41no—
546C2×C4×C61—42no—
547C2×C4×C61—42no—
548C2×C4×C61—42no—
549C2×C4×C61—42no—
550C2×C4×C61—42no—
551C2×C4×C61—81no—
552C2×C4×C61—81no—
553C2×C4×C61—81no—
554C2×C4×C61C22×D411yescharacteristic
555C2×C4×C61C22×D411yescharacteristic
556C2×C4×C61C22×D411yescharacteristic
557C2×C4×C61C22×D411yescharacteristic
558C2×C4×C61C22×D411yescharacteristic
559C2×C4×C61C22×D411yescharacteristic
560C2×C4×C61C22×D411yescharacteristic
561C2×C4×C61C22×D411yescharacteristic
562C2×C4×C61C22×D411yescharacteristic
563C2×C4×C61C22×D411yescharacteristic
564C2×C4×C61C22×D411yescharacteristic
565C2×C4×C61C2511yescharacteristic
566C22⋊D61—44no—
567C22⋊D61—82no—
568C22⋊D61—82no—
569C2×Dic61—22no—
570C2×Dic61—22no—
571C2×Dic61—22no—
572C2×Dic61—82no—
573D244—22no—
574D244—22no—
575D244—42no—
576D244—42no—
577C4×D61—44no—
578C4×D61—82no—
579C4×D61—82no—
580Dic122—42no—
581Dic122—42no—
582Dic122—42no—
583Dic122—82no—
584#92418—22no—
585#92418—22no—
586#92418—22no—
587#92418—22no—
588#62117—611nomaximal, Sylow
589C22×C61—21no—
590C22×C61—21no—
591C22×C61—21no—
592C22×C61—21no—
593C22×C61—21no—
594C22×C61—21no—
595C22×C61—21no—
596C22×C61—21no—
597C22×C61—21no—
598C22×C61—41no—
599C22×C61—41no—
600C22×C61—41no—
601C22×C61—41no—
602C22×C61—41no—
603C22×C61—41no—
604C22×C61C23×D411yescharacteristic
605C2×D61—42no—
606C2×D61—42no—
607C2×D61—42no—
608C4×C61—21no—
609C4×C61—21no—
610C4×C61—21no—
611C4×C61—21no—
612C4×C61—21no—
613C4×C61—21no—
614C4×C61—21no—
615C4×C61—22no—
616C4×C61—21no—
617C4×C61—21no—
618C4×C61—21no—
619C4×C61—41no—
620C4×C61—41no—
621C4×C61—41no—
622C4×C61—41no—
623C4×C61—41no—
624C4×C61#57512yes—
625C4×C61C2×2−1+411yescharacteristic
626C4×C61#58511yescharacteristic
627Dic61—42no—
628Dic61—42no—
629Dic61—42no—
630#3511—611no—
631#3480D6111yescharacteristic, complemented
632#3388—612no—
633#3370—612no—
634#3355—612no—
635#3350—612no—
636#3347—612no—
637#3326—612no—
638#3321—612no—
639#3309—612no—
640#3253—611no—
641#3251—611no—
642#3247—611no—
643#3238—611no—
644#3235—611no—
645#3233—611no—
646#3115—611no—
647#3112—611no—
648#3106—611no—
649#3079—611no—
650#3078—611no—
651#3076—611no—
652#2989—611no—
653C2×C61—41no—
654C2×C61—41no—
655C2×C61—41no—
656C2×C61—81no—
657C2×C61—81no—
658C2×C61#348911yescharacteristic
659C2×C61C2×#57511yescharacteristic
660C2×C61#358511yescharacteristic
661D61—82no—
662#559—21no—
663#559C2×D6111yescharacteristic
664#557C2×D6111yescharacteristic
665#556—21no—
666#556—1221no—
667#556C2×D6111yescharacteristic
668#555—612no—
669#554—612no—
670#553—21no—
671#553—21no—
672#553—612no—
673#553—612no—
674#553C2×D6111yescharacteristic
675#553C2×D6111yescharacteristic
676#550C2×D6111yescharacteristic
677#548—1221no—
678#548—1221no—
679#548C2×D6111yescharacteristic
680#548C2×D6111yescharacteristic
681#547—1221no—
682#542—1221no—
683#542—1221no—
684#537—1221no—
685#533—611no—
686#533—611no—
687#532—21no—
688#532—611no—
689#532—611no—
690#532—611no—
691#532C2×D6111yescharacteristic
692C2×C4⋊Q8—611no—
693#529—21no—
694#529—21no—
695#529C2×D6111yescharacteristic
696#529C2×D6111yescharacteristic
697#520—1221no—
698C4×#41—21no—
699C4×#41C2×D6111yescharacteristic
700C4×#41C2×D6111yescharacteristic
701C4×#41C2×D6111yescharacteristic
702C2×C4×Q8C2×D6111yescharacteristic
703#501—612no—
704#501—612no—
705#499—612no—
706#490—612no—
707#489—612no—
708#488—612no—
709#485—612no—
710#483—612no—
711#482—612no—
712#482—612no—
713#482—612no—
714#482—612no—
715#482—612no—
716#480—612no—
717#480—612no—
718#479—612no—
719#479—612no—
720#479—612no—
721#478—612no—
722#478—612no—
723#478—612no—
724#477—611no—
725#477—611no—
726#477—611no—
727#477—611no—
728#476—612no—
729#476—611no—
730#476—611no—
731#476—611no—
732#476—611no—
733#475—611no—
734#475—611no—
735#475—612no—
736#474—611no—
737#474—612no—
738#474—611no—
739#469—612no—
740#469—612no—
741#469—612no—
742#468—612no—
743#466—612no—
744#465—612no—
745#463—612no—
746#463—612no—
747#460—611no—
748#460—611no—
749#459—612no—
750#459—611no—
751#459—611no—
752#449—612no—
753#449—612no—
754#448—612no—
755#446—612no—
756#442—612no—
757#440—612no—
758#440—612no—
759#440—612no—
760C4×SD16—612no—
761C4×D8—612no—
762#436—612no—
763#435—612no—
764#435—612no—
765#432—611no—
766#432—611no—
767#431—611no—
768#428—612no—
769#428—612no—
770#427—612no—
771#423—611no—
772#423—611no—
773C2×C4⋊C8—611no—
774#419—612no—
775#417—612no—
776#416—612no—
777C61#6211711yescharacteristic, complemented, Sylow
778C2×#41—21no—
779C2×#41—1221no—
780C2×#41—1221no—
781C2×#41—1221no—
782C2×#41C22⋊D6111yescharacteristic
783C2×#41C22×D6111yescharacteristic
784C2×#41C22×D6111yescharacteristic
785C22×Q8—1221no—
786C22×Q8C22×D6111yescharacteristic
787C2×SD16—612no—
788C2×SD16—612no—
789C2×D8—612no—
790C2×D8—612no—
791C2×M16—612no—
792C2×M16—612no—
793C22×C8—612no—
794C4⋊Q8—21no—
795C4⋊Q8—611no—
796C4⋊Q8—611no—
797C4⋊Q8—612no—
798C4⋊Q8—611no—
799C4⋊Q8—1221no—
800C4⋊Q8—1221no—
801C4⋊Q8C22×D6111yescharacteristic
802#127—21no—
803#127—611no—
804#127C22×D6111yescharacteristic
805#126—21no—
806#126—21no—
807#126—21no—
808#126—21no—
809#126—21no—
810#126—21no—
811#126—1222no—
812#126—1222no—
813#125—21no—
814#125—21no—
815#125—612no—
816#125—612no—
817#125C22×D6111yescharacteristic
818#125C22×D6111yescharacteristic
819#124—21no—
820#124—21no—
821#124—21no—
822#124—21no—
823#124—21no—
824#124—1222no—
825#124—1222no—
826#124—1221no—
827#124—1221no—
828#124—1221no—
829#124C22×D6111yescharacteristic
830#124C22×D6111yescharacteristic
831#123—21no—
832#123—21no—
833#123—21no—
834#123—21no—
835#123—21no—
836#123—21no—
837#123—1222no—
838#123—1222no—
839C22⋊Q8—21no—
840C22⋊Q8—21no—
841C22⋊Q8—1222no—
842C22⋊Q8—1221no—
843C22⋊Q8—1221no—
844C22⋊Q8—1221no—
845C22⋊Q8—1221no—
846C22⋊Q8—1222no—
847C22⋊Q8—1222no—
848C22⋊Q8C22×D6111yescharacteristic
849C22⋊Q8C22×D6111yescharacteristic
850#121—21no—
851#121—21no—
852#121—21no—
853#121—21no—
854#121—21no—
855#121—21no—
856#121—21no—
857#121—612no—
858#121—612no—
859#121—612no—
860#121—1222no—
861#121—1222no—
862#121—1222no—
863#121—1221no—
864#121—1221no—
865#121—1221no—
866#121C22×D6111yescharacteristic
867#121C22×D6111yescharacteristic
868#121C22×D6111yescharacteristic
869#121C22×D6111yescharacteristic
870C4×Q8—21no—
871C4×Q8—21no—
872C4×Q8—21no—
873C4×Q8—21no—
874C4×Q8—1221no—
875C4×Q8—1221no—
876C4×Q8—1221no—
877C4×Q8—1221no—
878C4×Q8C22⋊D6111yescharacteristic
879C4×Q8C22×D6111yescharacteristic
880C4×Q8C22×D6111yescharacteristic
881C4×Q8C22×D6111yescharacteristic
882C4×Q8C22×D6111yescharacteristic
883C4×Q8C22×D6111yescharacteristic
884C4×Q8C22×D6111yescharacteristic
885C4×Q8C22×D6111yescharacteristic
886C4×D4—21no—
887C4×D4—21no—
888C4×D4—21no—
889C4×D4—21no—
890C4×D4—21no—
891C4×D4—21no—
892C4×D4—21no—
893C4×D4—21no—
894C4×D4—21no—
895C4×D4—21no—
896C4×D4—21no—
897C4×D4—21no—
898C4×D4—21no—
899C4×D4—612no—
900C4×D4—612no—
901C4×D4—612no—
902C4×D4—1222no—
903C4×D4—1222no—
904C4×D4—1221no—
905C4×D4—1221no—
906C4×D4—1221no—
907C4×D4C22⋊D6111yescharacteristic
908C4×D4C22⋊D6111yescharacteristic
909C4×D4C22⋊D6111yescharacteristic
910C4×D4C22×D6111yescharacteristic
911C4×D4C22×D6111yescharacteristic
912C4×D4C22×D6111yescharacteristic
913C4×D4C22×D6111yescharacteristic
914C4×D4C22×D6111yescharacteristic
915C4×D4C22×D6111yescharacteristic
916C4×D4C22×D6111yescharacteristic
917#117—21no—
918#117—21no—
919#117—21no—
920#117—21no—
921#117—612no—
922#117—612no—
923#117—1222no—
924#117C22⋊D6111yescharacteristic
925#117C22⋊D6111yescharacteristic
926#117C22⋊D6111yescharacteristic
927#117C22×D6111yescharacteristic
928#117C22×D6111yescharacteristic
929C2×C4⋊C4—21no—
930C2×C4⋊C4—612no—
931C2×C4⋊C4—1221no—
932C2×C4⋊C4—1222no—
933C2×C4⋊C4C22×D6111yescharacteristic
934C2×C42—21no—
935C2×C42—21no—
936C2×C42—21no—
937C2×C42C22×D6111yescharacteristic
938C2×C42C22×D6111yescharacteristic
939C2×C42C22×D6111yescharacteristic
940#107—612no—
941#107—612no—
942#107—612no—
943#107—612no—
944#107—612no—
945#107—612no—
946#106—612no—
947#106—612no—
948#106—612no—
949#106—612no—
950#106—612no—
951#106—612no—
952C4⋊C8—611no—
953C4⋊C8—611no—
954C4⋊C8—612no—
955C4⋊C8—611no—
956C4⋊C8—612no—
957C4⋊C8—612no—
958C4⋊C8—611no—
959#103—612no—
960#103—612no—
961#103—612no—
962#103—612no—
963#103—612no—
964#103—612no—
965#102—612no—
966#102—612no—
967#102—612no—
968#102—612no—
969#102—612no—
970#102—612no—
971#102—612no—
972#102—612no—
973#102—612no—
974#102—612no—
975C22⋊C8—612no—
976C22⋊C8—612no—
977C22⋊C8—612no—
978#97—612no—
979#97—612no—
980C4×C8—612no—
981#41—22no—
982#41—22no—
983#41—42no—
984#41—41no—
985#41—41no—
986#41—44no—
987#41—4882no—
988#41—4882no—
989#41—2444no—
990C2×Q8—21no—
991C2×Q8—21no—
992C2×Q8—22no—
993C2×Q8—41no—
994C2×Q8—1222no—
995C2×Q8—1221no—
996C2×Q8—1221no—
997C2×Q8—1221no—
998C2×Q8—4882no—
999C2×Q8C2×C22⋊D6111yescharacteristic
1000C2×Q8C23×D6111yescharacteristic
1001C2×Q8C23×D6111yescharacteristic
1002C2×D4—21no—
1003C2×D4—21no—
1004C2×D4—21no—
1005C2×D4—21no—
1006C2×D4—21no—
1007C2×D4—21no—
1008C2×D4—21no—
1009C2×D4—21no—
1010C2×D4—612no—
1011C2×D4—1222no—
1012C2×D4—1222no—
1013C2×D4—1222no—
1014C2×D4—1221no—
1015C2×D4—1221no—
1016C2×D4C2×C22⋊D6111yescharacteristic
1017C2×D4C2×C22⋊D6111yescharacteristic
1018C2×D4C2×C22⋊D6111yescharacteristic
1019C2×D4C23×D6111yescharacteristic
1020C2×D4C23×D6111yescharacteristic
1021C22×C4—21no—
1022C22×C4—21no—
1023C22×C4—21no—
1024C22×C4—21no—
1025C22×C4—21no—
1026C22×C4—21no—
1027C22×C4—21no—
1028C22×C4—21no—
1029C22×C4—1222no—
1030C22×C4—1222no—
1031C22×C4—1222no—
1032C22×C4—1222no—
1033C22×C4C2×C22⋊D6111yescharacteristic
1034C22×C4C2×C22⋊D6111yescharacteristic
1035C22×C4C2×C22⋊D6111yescharacteristic
1036C22×C4C2×C22⋊D6111yescharacteristic
1037C22×C4C2×C22⋊D6111yescharacteristic
1038C22×C4C2×C22⋊D6111yescharacteristic
1039C22×C4C23×D6111yescharacteristic
1040C22×C4C23×D6111yescharacteristic
1041C22×C4C23×D6111yescharacteristic
1042SD16—1224no—
1043SD16—2442no—
1044D8—2442no—
1045D8—2442no—
1046M16—2442no—
1047M16—2442no—
1048C2×C8—612no—
1049C2×C8—612no—
1050C2×C8—612no—
1051C2×C8—612no—
1052C2×C8—2442no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—21no—
1058C4⋊C4—21no—
1059C4⋊C4—21no—
1060C4⋊C4—21no—
1061C4⋊C4—21no—
1062C4⋊C4—21no—
1063C4⋊C4—21no—
1064C4⋊C4—21no—
1065C4⋊C4—21no—
1066C4⋊C4—21no—
1067C4⋊C4—612no—
1068C4⋊C4—612no—
1069C4⋊C4—612no—
1070C4⋊C4—1222no—
1071C4⋊C4—1222no—
1072C4⋊C4—1222no—
1073C4⋊C4—1222no—
1074C4⋊C4—1221no—
1075C4⋊C4—1221no—
1076C4⋊C4—1222no—
1077C4⋊C4—1222no—
1078C4⋊C4—1221no—
1079C4⋊C4C2×C22⋊D6111yescharacteristic
1080C4⋊C4C2×C22⋊D6111yescharacteristic
1081C4⋊C4C2×C22⋊D6111yescharacteristic
1082C4⋊C4C2×C22⋊D6111yescharacteristic
1083C4⋊C4C2×C22⋊D6111yescharacteristic
1084C4⋊C4C2×C22⋊D6111yescharacteristic
1085C4⋊C4C23×D6111yescharacteristic
1086C4⋊C4C23×D6111yescharacteristic
1087C4⋊C4C23×D6111yescharacteristic
1088C4⋊C4C23×D6111yescharacteristic
1089C22⋊C4—21no—
1090C22⋊C4—21no—
1091C22⋊C4—21no—
1092C22⋊C4—21no—
1093C22⋊C4—21no—
1094C22⋊C4—21no—
1095C22⋊C4—21no—
1096C22⋊C4—21no—
1097C22⋊C4—21no—
1098C22⋊C4—21no—
1099C22⋊C4—21no—
1100C22⋊C4—21no—
1101C22⋊C4—21no—
1102C22⋊C4—21no—
1103C22⋊C4—21no—
1104C22⋊C4—21no—
1105C22⋊C4—1222no—
1106C22⋊C4—1222no—
1107C22⋊C4—1222no—
1108C22⋊C4—1222no—
1109C22⋊C4—1222no—
1110C22⋊C4—1222no—
1111C22⋊C4—1222no—
1112C22⋊C4—1222no—
1113C22⋊C4C2×C22⋊D6111yescharacteristic
1114C22⋊C4C2×C22⋊D6111yescharacteristic
1115C22⋊C4C2×C22⋊D6111yescharacteristic
1116C22⋊C4C2×C22⋊D6111yescharacteristic
1117C22⋊C4C2×C22⋊D6111yescharacteristic
1118C22⋊C4C2×C22⋊D6111yescharacteristic
1119C42—21no—
1120C42—21no—
1121C42—21no—
1122C42—21no—
1123C42—21no—
1124C42—21no—
1125C42—21no—
1126C42—21no—
1127C42—1222no—
1128C42—1222no—
1129C42C2×C22⋊D6111yescharacteristic
1130C42C2×C22⋊D6111yescharacteristic
1131C42C2×C22⋊D6111yescharacteristic
1132C42C2×C22⋊D6111yescharacteristic
1133C42C2×C22⋊D6111yescharacteristic
1134C42C2×C22⋊D6111yescharacteristic
1135C42C23×D6111yescharacteristic
1136C42C23×D6111yescharacteristic
1137C42C23×D6111yescharacteristic
1138C42C23×D6111yescharacteristic
1139C23—21no—
1140C23—21no—
1141C23—1222no—
1142C23C22×C22⋊D6111yescharacteristic
1143C23C22×C22⋊D6111yescharacteristic
1144C23C22×C22⋊D6111yescharacteristic
1145Q8—21no—
1146Q8—21no—
1147Q8—21no—
1148Q8—41no—
1149Q8—42no—
1150Q8—42no—
1151Q8—4882no—
1152Q8—2442no—
1153Q8—2442no—
1154Q8—2442no—
1155Q8#1451982412yes—
1156D4—21no—
1157D4—21no—
1158D4—21no—
1159D4—21no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—42no—
1164D4—42no—
1165D4—42no—
1166D4—42no—
1167D4—42no—
1168D4—81no—
1169D4—81no—
1170D4—81no—
1171D4—1222no—
1172D4—1222no—
1173D4—4882no—
1174D4—4882no—
1175D4—2442no—
1176D4—2444no—
1177D4—2442no—
1178C2×C4—21no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—81no—
1202C2×C4—81no—
1203C2×C4—81no—
1204C2×C4—1222no—
1205C2×C4—1222no—
1206C2×C4—1222no—
1207C2×C4—4882no—
1208C2×C4—4882no—
1209C2×C4—4882no—
1210C2×C4—2444no—
1211C2×C4C22×C22⋊D6111yescharacteristic
1212C2×C4C22×C22⋊D6111yescharacteristic
1213C2×C4C22×C22⋊D6111yescharacteristic
1214C2×C4C22×C22⋊D6111yescharacteristic
1215C2×C4C22×C22⋊D6111yescharacteristic
1216C2×C4C22×C22⋊D6111yescharacteristic
1217C2×C4C22×C22⋊D6111yescharacteristic
1218C2×C4C22×C22⋊D6111yescharacteristic
1219C2×C4C22×C22⋊D6111yescharacteristic
1220C2×C4C22×C22⋊D6111yescharacteristic
1221C2×C4C22×C22⋊D6111yescharacteristic
1222C2×C4C24×D6111yescharacteristic
1223C8—1222no—
1224C8—1222no—
1225C8—1222no—
1226C8—1222no—
1227C22—21no—
1228C22—21no—
1229C22—21no—
1230C22—21no—
1231C22—21no—
1232C22—21no—
1233C22—21no—
1234C22—21no—
1235C22—21no—
1236C22—41no—
1237C22—41no—
1238C22—41no—
1239C22—41no—
1240C22—41no—
1241C22—41no—
1242C22—2442no—
1243C22—2442no—
1244C22—2442no—
1245C22C23×C22⋊D6111yescharacteristic
1246C4—21no—
1247C4—21no—
1248C4—21no—
1249C4—22no—
1250C4—21no—
1251C4—21no—
1252C4—21no—
1253C4—21no—
1254C4—21no—
1255C4—21no—
1256C4—21no—
1257C4—41no—
1258C4—41no—
1259C4—41no—
1260C4—41no—
1261C4—41no—
1262C4—2442no—
1263C4—2442no—
1264C4—2442no—
1265C4#1684056012yes—
1266C4C2×#1451982411yescharacteristic
1267C4#1684059811yescharacteristic
1268C2—41no—
1269C2—41no—
1270C2—41no—
1271C2—81no—
1272C2—81no—
1273C2—4882no—
1274C2#2145949911yescharacteristic
1275C2C2×#1684056011yescharacteristic
1276C2#2146059811yescharacteristic
subgroupG/H
centerC22C23×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3480C2
socleC22×C61C23×D4
hypercenter#3480D61
hypocenterC61#62117
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3480

Complements

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

NH ≅ G/Ntype
1. #21459730C2semidirect
2. #21458758C2semidirect
3. #21458566C2semidirect
4. #21458419C2semidirect
5. #21458364C2semidirect
6. #21458313C2semidirect
7. #21458072C2semidirect
8. #21458005C2semidirect
9. #21457825C2semidirect
10. #21457197C2semidirect
11. #21457181C2semidirect
12. #21457145C2semidirect
13. #21457037C2semidirect
14. #21457013C2semidirect
15. #21456994C2semidirect
16. #21455970C2semidirect
17. #21455941C2semidirect
18. #21455879C2semidirect
19. #21455634C2semidirect
20. #21455624C2semidirect
21. #21455607C2semidirect
22. #21454936C2semidirect
23. C61×#3480C2semidirect
631. #3480D61semidirect
777. C61#62117semidirect

Maximal subgroups

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

subgroupindex
#214597302
#214587582
#214585662
#214584192
#214583642
#214583132
#214580722
#214580052
#214578252
#214571972
#214571812
#214571452
#214570372
#214570132
#214569942
#214559702
#214559412
#214558792
#214556342
#214556242
#214556072
#214549362
C61×#34802
#6211761