Finite Group Databasebeta

← #30576214

Subgroups — #30576214

Order 15616.

1758 conjugacy classes of subgroups.

The subgroup lattice has 1262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459730C211yesmaximal, characteristic, complemented
2#21458758C212yesmaximal, complemented
3#21458640C212yesmaximal, complemented
4#21458328C212yesmaximal, complemented
5#21458289C212yesmaximal, complemented
6#21458198C212yesmaximal, complemented
7#21458005C212yesmaximal, complemented
8#21457990C212yesmaximal, complemented
9#21457721C212yesmaximal, complemented
10#21457181C211yesmaximal, characteristic, complemented
11#21457145C211yesmaximal, characteristic, complemented
12#21457131C211yesmaximal, characteristic, complemented
13#21457046C211yesmaximal, characteristic, complemented
14#21457029C211yesmaximal, characteristic, complemented
15#21456994C211yesmaximal, characteristic, complemented
16#21455970C211yesmaximal, characteristic, complemented
17#21455941C211yesmaximal, characteristic, complemented
18#21455850C211yesmaximal, characteristic, complemented
19#21455624C211yesmaximal, characteristic, complemented
20#21455607C211yesmaximal, characteristic, complemented
21C2×#16840047C211yesmaximal, characteristic, complemented
22#21454944C211yesmaximal, characteristic, complemented
23C61×#3482C211yesmaximal, 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#16840130C2212yes—
46#16840121C2212yes—
47#16840116C2212yes—
48#16840100C2212yes—
49#16840100C2212yes—
50#16840100C2212yes—
51#16840095C2212yes—
52#16840086C2212yes—
53#16840083C2212yes—
54#16840080C2212yes—
55#16840078C2212yes—
56#16840075C2212yes—
57#16840069C2212yes—
58#16840069C2212yes—
59#16840069C2212yes—
60#16840062C2212yes—
61#16840059C2212yes—
62#16840059C2212yes—
63#16840057C2211yescharacteristic
64#16840057C2211yescharacteristic
65#16840057C2211yescharacteristic
66#16840052C2211yescharacteristic
67#16840049C2212yes—
68#16840047C2211yescharacteristic
69#16840047C2211yescharacteristic
70#16840047C2211yescharacteristic
71#16840047C2212yes—
72#16840047C2211yescharacteristic
73#16840047C2211yescharacteristic
74#16840047C2212yes—
75#16840047C2211yescharacteristic
76#16840042C2211yescharacteristic
77#16840042C2211yescharacteristic
78#16840013C2212yes—
79#16840010C2212yes—
80#16839996C2212yes—
81#16839993C2212yes—
82#16839993C2212yes—
83#16839993C2212yes—
84#16839974C2212yes—
85#16839974C2212yes—
86#16839964C2212yes—
87#16839962C2211yescharacteristic
88#16839962C2211yescharacteristic
89#16839962C2211yescharacteristic
90#16839957C2211yescharacteristic
91#16839907C2212yes—
92#16839901C2212yes—
93#16839901C2212yes—
94#16839893C2212yes—
95#16839872C2212yes—
96#16839860C2212yes—
97#16839860C2212yes—
98#16839860C2212yes—
99C4×#11758201C2212yes—
100C4×#11758201C2212yes—
101#16839834C2212yes—
102#16839834C2212yes—
103D4×#92418C2212yes—
104#16839819C2211yescharacteristic
105#16839819C2211yescharacteristic
106#16839815C2211yescharacteristic
107#16839802C2212yes—
108#16839798C2212yes—
109C2×#14519708C2212yes—
110#16839786C2211yescharacteristic
111C2×C4⋊#92418C2211yescharacteristic
112C2×C4⋊#92418C2211yescharacteristic
113#16839771C2212yes—
114#16839758C2212yes—
115C2×#14519701C2212yes—
116C61×#557C2211yescharacteristic
117C61×#556—21no—
118C61×#556C2211yescharacteristic
119C61×#552—21no—
120C61×#552—21no—
121C61×#552C2211yescharacteristic
122C61×#552C2211yescharacteristic
123D4×Q8×C61C2211yescharacteristic
124C61×#548C2211yescharacteristic
125C61×#548C2211yescharacteristic
126C61×#547—21no—
127C61×#547C2211yescharacteristic
128C61×#533—21no—
129C61×#533C2211yescharacteristic
130C61×#529—21no—
131C61×#529—21no—
132C61×#529C2211yescharacteristic
133C61×#529C2211yescharacteristic
134C4×#41×C61—21no—
135C4×#41×C61C2211yescharacteristic
136C4×#41×C61C2211yescharacteristic
137C2×C4×Q8×C61C2211yescharacteristic
138C2×C4×Q8×C61C2211yescharacteristic
139C2×#11758222—21no—
140C2×#11758222—21no—
141C2×#11758222—21no—
142C22×Dic122—21no—
143C2×#11758201C2312yes—
144C2×#11758201C2312yes—
145C2×#11758201C2312yes—
146C2×#11758199C2312yes—
147C2×#11758194C2312yes—
148C22×#92418C2312yes—
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#14519708C2312yes—
208#14519708C2312yes—
209#14519708C2312yes—
210#14519708C2312yes—
211#14519708C2312yes—
212#14519708C2312yes—
213#14519708C2312yes—
214C4⋊#92418C2311yescharacteristic
215C4⋊#92418C2311yescharacteristic
216C4⋊#92418C2311yescharacteristic
217C4⋊#92418C2311yescharacteristic
218C4⋊#92418C2312yes—
219C4⋊#92418C2312yes—
220C4⋊#92418C2312yes—
221#14519701C2312yes—
222#14519701C2312yes—
223#14519701C2312yes—
224#14519701C2312yes—
225#14519701C2312yes—
226#14519701C2312yes—
227#14519701C2312yes—
228#14519701C2312yes—
229#14519701C2312yes—
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
246C22×Q8×C61C2311yescharacteristic
247C22×Q8×C61C2311yescharacteristic
248C4⋊Q8×C61—21no—
249C4⋊Q8×C61—21no—
250C4⋊Q8×C61C2311yescharacteristic
251C4⋊Q8×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×C61—21no—
261#125×C61—21no—
262#125×C61—21no—
263#125×C61C2311yescharacteristic
264#125×C61C2311yescharacteristic
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×C61—21no—
278C22⋊Q8×C61—21no—
279C22⋊Q8×C61—21no—
280C22⋊Q8×C61—21no—
281C22⋊Q8×C61—21no—
282C22⋊Q8×C61C2311yescharacteristic
283C22⋊Q8×C61C2311yescharacteristic
284C22⋊Q8×C61C2311yescharacteristic
285C22⋊Q8×C61C2311yescharacteristic
286#121×C61—21no—
287#121×C61—21no—
288#121×C61C2311yescharacteristic
289#121×C61C2311yescharacteristic
290C4×Q8×C61—21no—
291C4×Q8×C61—21no—
292C4×Q8×C61—21no—
293C4×Q8×C61—21no—
294C4×Q8×C61—21no—
295C4×Q8×C61—21no—
296C4×Q8×C61D411yescharacteristic
297C4×Q8×C61C2311yescharacteristic
298C4×Q8×C61C2311yescharacteristic
299C4×Q8×C61C2311yescharacteristic
300C4×Q8×C61C2311yescharacteristic
301C4×Q8×C61C2311yescharacteristic
302C4×Q8×C61C2311yescharacteristic
303C4×Q8×C61C2311yescharacteristic
304C4×Q8×C61C2311yescharacteristic
305C4×Q8×C61C2311yescharacteristic
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×C61D411yescharacteristic
314C4×D4×C61D411yescharacteristic
315C4×D4×C61D411yescharacteristic
316C4×D4×C61C2311yescharacteristic
317C4×D4×C61C2311yescharacteristic
318C4×D4×C61C2311yescharacteristic
319C4×D4×C61C2311yescharacteristic
320C4×D4×C61C2311yescharacteristic
321#117×C61—21no—
322#117×C61—21no—
323#117×C61—21no—
324#117×C61—21no—
325#117×C61—21no—
326#117×C61—21no—
327#117×C61—21no—
328#117×C61D411yescharacteristic
329#117×C61D411yescharacteristic
330#117×C61D411yescharacteristic
331#117×C61C2311yescharacteristic
332C2×C4⋊C4×C61—21no—
333C2×C4⋊C4×C61—21no—
334C2×C4⋊C4×C61C2311yescharacteristic
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—42no—
344#41×C61—41no—
345#41×C61—44no—
346C2×Q8×C61—21no—
347C2×Q8×C61—21no—
348C2×Q8×C61—21no—
349C2×Q8×C61—22no—
350C2×Q8×C61—22no—
351C2×Q8×C61—41no—
352C2×Q8×C61—41no—
353C2×Q8×C61C2×D411yescharacteristic
354C2×Q8×C61C2411yescharacteristic
355C2×Q8×C61C2411yescharacteristic
356C2×Q8×C61C2411yescharacteristic
357C2×D4×C61—21no—
358C2×D4×C61—21no—
359C2×D4×C61—21no—
360C2×D4×C61C2×D411yescharacteristic
361C2×D4×C61C2×D411yescharacteristic
362C2×D4×C61C2×D411yescharacteristic
363C2×D4×C61C2411yescharacteristic
364C22×C4×C61—21no—
365C22×C4×C61—21no—
366C22×C4×C61—21no—
367C22×C4×C61—21no—
368C22×C4×C61—21no—
369C22×C4×C61—21no—
370C22×C4×C61—21no—
371C22×C4×C61C2×D411yescharacteristic
372C22×C4×C61C2×D411yescharacteristic
373C22×C4×C61C2×D411yescharacteristic
374C22×C4×C61C2×D411yescharacteristic
375C22×C4×C61C2×D411yescharacteristic
376C22×C4×C61C2×D411yescharacteristic
377C22×C4×C61C2411yescharacteristic
378C22×C4×C61C2411yescharacteristic
379C22×C4×C61C2411yescharacteristic
380C2×C22⋊D61—22no—
381C2×C22⋊D61—22no—
382C2×C22⋊D61—22no—
383C22×Dic61—22no—
384#11758222—44no—
385#11758222—82no—
386#11758222—82no—
387C2×D244—21no—
388C2×D244—21no—
389C2×D244C2412yes—
390C2×C4×D61—22no—
391C2×C4×D61—22no—
392C2×C4×D61—22no—
393C2×Dic122—21no—
394C2×Dic122—21no—
395C2×Dic122—21no—
396C2×Dic122—22no—
397C2×Dic122—82no—
398C4⋊C4×C61—21no—
399C4⋊C4×C61—21no—
400C4⋊C4×C61—21no—
401C4⋊C4×C61—21no—
402C4⋊C4×C61—21no—
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×C61—21no—
418C4⋊C4×C61—21no—
419C4⋊C4×C61C2×D411yescharacteristic
420C4⋊C4×C61C2×D411yescharacteristic
421C4⋊C4×C61C2×D411yescharacteristic
422C4⋊C4×C61C2×D411yescharacteristic
423C4⋊C4×C61C2×D411yescharacteristic
424C4⋊C4×C61C2×D411yescharacteristic
425C4⋊C4×C61C2411yescharacteristic
426C4⋊C4×C61C2411yescharacteristic
427C4⋊C4×C61C2411yescharacteristic
428C4⋊C4×C61C2411yescharacteristic
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×C61C2×D411yescharacteristic
443C22⋊C4×C61C2×D411yescharacteristic
444C22⋊C4×C61C2×D411yescharacteristic
445C22⋊C4×C61C2×D411yescharacteristic
446C22⋊C4×C61C2×D411yescharacteristic
447C22⋊C4×C61C2×D411yescharacteristic
448C42×C61—21no—
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#11758201—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—
494C2×#92418—42no—
495C2×#92418—42no—
496C2×#92418C2412yes—
497C2×#92418C2412yes—
498C2×#92418C2412yes—
499C2×#92418C2412yes—
500C23×C61—21no—
501C23×C61C22×D411yescharacteristic
502C23×C61C22×D411yescharacteristic
503C23×C61C22×D411yescharacteristic
504C22×D61—22no—
505Q8×C61—21no—
506Q8×C61—21no—
507Q8×C61—21no—
508Q8×C61—21no—
509Q8×C61—21no—
510Q8×C61—41no—
511Q8×C61—42no—
512Q8×C61—42no—
513Q8×C61—42no—
514Q8×C612−1+412yes—
515D4×C61—22no—
516D4×C61—22no—
517D4×C61—21no—
518D4×C61—21no—
519D4×C61—41no—
520D4×C61—42no—
521D4×C61—42no—
522D4×C61—42no—
523C2×C4×C61—22no—
524C2×C4×C61—21no—
525C2×C4×C61—22no—
526C2×C4×C61—22no—
527C2×C4×C61—22no—
528C2×C4×C61—21no—
529C2×C4×C61—21no—
530C2×C4×C61—21no—
531C2×C4×C61—21no—
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—41no—
541C2×C4×C61—41no—
542C2×C4×C61—42no—
543C2×C4×C61—42no—
544C2×C4×C61—42no—
545C2×C4×C61—42no—
546C2×C4×C61—42no—
547C2×C4×C61—42no—
548C2×C4×C61—42no—
549C2×C4×C61C22×D411yescharacteristic
550C2×C4×C61C22×D411yescharacteristic
551C2×C4×C61C22×D411yescharacteristic
552C2×C4×C61C22×D411yescharacteristic
553C2×C4×C61C22×D411yescharacteristic
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×C61C2511yescharacteristic
561C22⋊D61—44no—
562C22⋊D61—82no—
563C22⋊D61—82no—
564C2×Dic61—22no—
565C2×Dic61—22no—
566C2×Dic61—22no—
567C2×Dic61—82no—
568D244—22no—
569D244—22no—
570D244—42no—
571D244—42no—
572C4×D61—44no—
573C4×D61—82no—
574C4×D61—82no—
575Dic122—42no—
576Dic122—42no—
577Dic122—42no—
578Dic122—82no—
579#92418—22no—
580#92418—22no—
581#92418—22no—
582#92418—22no—
583#62129—611nomaximal, Sylow
584C22×C61—21no—
585C22×C61—21no—
586C22×C61—21no—
587C22×C61—21no—
588C22×C61—21no—
589C22×C61—21no—
590C22×C61—21no—
591C22×C61—21no—
592C22×C61—41no—
593C22×C61—41no—
594C22×C61—41no—
595C22×C61#57512yes—
596C22×C61C23×D411yescharacteristic
597C2×D61—42no—
598C2×D61—42no—
599C2×D61—42no—
600C4×C61—21no—
601C4×C61—21no—
602C4×C61—21no—
603C4×C61—22no—
604C4×C61—21no—
605C4×C61—21no—
606C4×C61—21no—
607C4×C61—21no—
608C4×C61—21no—
609C4×C61—21no—
610C4×C61—21no—
611C4×C61—41no—
612C4×C61—41no—
613C4×C61—41no—
614C4×C61—41no—
615C4×C61—41no—
616C4×C61—41no—
617C4×C61#57712yes—
618C4×C61C2×2−1+411yescharacteristic
619C4×C61#58511yescharacteristic
620Dic61—42no—
621Dic61—42no—
622Dic61—42no—
623#3511—611no—
624#3482D6111yescharacteristic, complemented
625#3388—612no—
626#3376—612no—
627#3348—612no—
628#3345—612no—
629#3337—612no—
630#3321—612no—
631#3320—612no—
632#3301—612no—
633#3251—611no—
634#3247—611no—
635#3246—611no—
636#3239—611no—
637#3237—611no—
638#3233—611no—
639#3115—611no—
640#3112—611no—
641#3103—611no—
642#3078—611no—
643#3076—611no—
644C2×#475—611no—
645#2990—611no—
646C2×C61—22no—
647C2×C61—41no—
648C2×C61—41no—
649C2×C61—81no—
650C2×C61#348911yescharacteristic
651C2×C61C2×#57511yescharacteristic
652C2×C61C2×#57711yescharacteristic
653D61—82no—
654#557C2×D6111yescharacteristic
655#556—21no—
656#556—1221no—
657#556C2×D6111yescharacteristic
658#555—612no—
659#554—612no—
660#553—612no—
661#553—612no—
662#552—21no—
663#552—21no—
664#552C2×D6111yescharacteristic
665#552C2×D6111yescharacteristic
666D4×Q8C2×D6111yescharacteristic
667#548—1221no—
668#548—1221no—
669#548C2×D6111yescharacteristic
670#548C2×D6111yescharacteristic
671#547—21no—
672#547—1221no—
673#547C2×D6111yescharacteristic
674#542—1221no—
675#542—1221no—
676#537—1221no—
677#533—21no—
678#533—611no—
679#533—611no—
680#533C2×D6111yescharacteristic
681#532—611no—
682#532—611no—
683#532—611no—
684C2×C4⋊Q8—611no—
685#529—21no—
686#529—21no—
687#529C2×D6111yescharacteristic
688#529C2×D6111yescharacteristic
689#520—1221no—
690C4×#41—21no—
691C4×#41C2×D6111yescharacteristic
692C4×#41C2×D6111yescharacteristic
693C2×C4×Q8C2×D6111yescharacteristic
694C2×C4×Q8C2×D6111yescharacteristic
695#501—612no—
696#501—612no—
697#499—612no—
698#491—612no—
699#489—612no—
700#488—612no—
701#485—612no—
702#485—612no—
703#485—612no—
704#484—612no—
705#482—612no—
706#482—612no—
707#481—612no—
708#481—612no—
709#480—612no—
710#479—612no—
711#479—612no—
712#479—612no—
713#478—612no—
714#478—612no—
715#478—612no—
716#477—611no—
717#477—611no—
718#477—611no—
719#476—612no—
720#476—611no—
721#475—611no—
722#475—611no—
723#475—612no—
724#475—612no—
725#475—611no—
726#475—611no—
727#475—611no—
728#475—611no—
729#474—611no—
730#474—611no—
731#469—612no—
732#468—612no—
733#466—612no—
734#465—612no—
735#465—612no—
736#465—612no—
737#463—612no—
738#463—612no—
739#461—612no—
740#460—611no—
741#460—611no—
742#460—611no—
743#459—611no—
744#449—612no—
745#448—612no—
746#448—612no—
747#446—612no—
748#442—612no—
749#440—612no—
750#440—612no—
751#440—612no—
752C4×SD16—612no—
753C4×SD16—612no—
754#435—612no—
755#435—612no—
756C8×D4—612no—
757#432—611no—
758#432—611no—
759#431—611no—
760#428—612no—
761#427—612no—
762C2×#106—612no—
763#423—611no—
764C2×C4⋊C8—611no—
765C2×C4⋊C8—611no—
766#419—612no—
767#416—612no—
768C2×#103—612no—
769C61#6212911yescharacteristic, complemented, Sylow
770C2×#41—21no—
771C2×#41—1221no—
772C2×#41—1221no—
773C2×#41—1221no—
774C2×#41C22⋊D6111yescharacteristic
775C2×#41C22×D6111yescharacteristic
776C22×Q8—1221no—
777C22×Q8C22×D6111yescharacteristic
778C22×Q8C22×D6111yescharacteristic
779C2×SD16—612no—
780C2×SD16—612no—
781C2×SD16—612no—
782C2×D8—612no—
783C2×M16—612no—
784C22×C8—612no—
785C22×C8—612no—
786C4⋊Q8—21no—
787C4⋊Q8—21no—
788C4⋊Q8—611no—
789C4⋊Q8—611no—
790C4⋊Q8—612no—
791C4⋊Q8—611no—
792C4⋊Q8—1221no—
793C4⋊Q8—1221no—
794C4⋊Q8C22×D6111yescharacteristic
795C4⋊Q8C22×D6111yescharacteristic
796#127—611no—
797#126—21no—
798#126—21no—
799#126—21no—
800#126—21no—
801#126—21no—
802#126—21no—
803#126—1222no—
804#126—1222no—
805#125—21no—
806#125—21no—
807#125—21no—
808#125—21no—
809#125—21no—
810#125—612no—
811#125—612no—
812#125C22×D6111yescharacteristic
813#125C22×D6111yescharacteristic
814#124—21no—
815#124—21no—
816#124—1222no—
817#124—1222no—
818#124—1221no—
819#124—1221no—
820#124—1221no—
821#124C22×D6111yescharacteristic
822#124C22×D6111yescharacteristic
823#123—21no—
824#123—21no—
825#123—21no—
826#123—21no—
827#123—21no—
828#123—21no—
829#123—1222no—
830#123—1222no—
831C22⋊Q8—21no—
832C22⋊Q8—21no—
833C22⋊Q8—21no—
834C22⋊Q8—21no—
835C22⋊Q8—21no—
836C22⋊Q8—21no—
837C22⋊Q8—21no—
838C22⋊Q8—1222no—
839C22⋊Q8—1221no—
840C22⋊Q8—1221no—
841C22⋊Q8—1221no—
842C22⋊Q8—1221no—
843C22⋊Q8—1222no—
844C22⋊Q8—1222no—
845C22⋊Q8C22×D6111yescharacteristic
846C22⋊Q8C22×D6111yescharacteristic
847C22⋊Q8C22×D6111yescharacteristic
848C22⋊Q8C22×D6111yescharacteristic
849#121—21no—
850#121—21no—
851#121—612no—
852#121—612no—
853#121—612no—
854#121—1222no—
855#121—1222no—
856#121—1222no—
857#121—1221no—
858#121—1221no—
859#121—1221no—
860#121C22×D6111yescharacteristic
861#121C22×D6111yescharacteristic
862C4×Q8—21no—
863C4×Q8—21no—
864C4×Q8—21no—
865C4×Q8—21no—
866C4×Q8—21no—
867C4×Q8—21no—
868C4×Q8—1221no—
869C4×Q8—1221no—
870C4×Q8—1221no—
871C4×Q8—1221no—
872C4×Q8C22⋊D6111yescharacteristic
873C4×Q8C22×D6111yescharacteristic
874C4×Q8C22×D6111yescharacteristic
875C4×Q8C22×D6111yescharacteristic
876C4×Q8C22×D6111yescharacteristic
877C4×Q8C22×D6111yescharacteristic
878C4×Q8C22×D6111yescharacteristic
879C4×Q8C22×D6111yescharacteristic
880C4×Q8C22×D6111yescharacteristic
881C4×Q8C22×D6111yescharacteristic
882C4×D4—21no—
883C4×D4—21no—
884C4×D4—21no—
885C4×D4—21no—
886C4×D4—21no—
887C4×D4—21no—
888C4×D4—21no—
889C4×D4—612no—
890C4×D4—612no—
891C4×D4—612no—
892C4×D4—1222no—
893C4×D4—1222no—
894C4×D4—1221no—
895C4×D4—1221no—
896C4×D4—1221no—
897C4×D4C22⋊D6111yescharacteristic
898C4×D4C22⋊D6111yescharacteristic
899C4×D4C22⋊D6111yescharacteristic
900C4×D4C22×D6111yescharacteristic
901C4×D4C22×D6111yescharacteristic
902C4×D4C22×D6111yescharacteristic
903C4×D4C22×D6111yescharacteristic
904C4×D4C22×D6111yescharacteristic
905#117—21no—
906#117—21no—
907#117—21no—
908#117—21no—
909#117—21no—
910#117—21no—
911#117—21no—
912#117—612no—
913#117—612no—
914#117—1222no—
915#117C22⋊D6111yescharacteristic
916#117C22⋊D6111yescharacteristic
917#117C22⋊D6111yescharacteristic
918#117C22×D6111yescharacteristic
919C2×C4⋊C4—21no—
920C2×C4⋊C4—21no—
921C2×C4⋊C4—612no—
922C2×C4⋊C4—1221no—
923C2×C4⋊C4—1222no—
924C2×C4⋊C4C22×D6111yescharacteristic
925C2×C4⋊C4C22×D6111yescharacteristic
926C2×C42—21no—
927C2×C42—21no—
928C2×C42—21no—
929C2×C42C22×D6111yescharacteristic
930C2×C42C22×D6111yescharacteristic
931C2×C42C22×D6111yescharacteristic
932#107—612no—
933#107—612no—
934#107—612no—
935#107—612no—
936#107—612no—
937#106—612no—
938#106—612no—
939#106—612no—
940#106—612no—
941#106—612no—
942#106—612no—
943#106—612no—
944C4⋊C8—611no—
945C4⋊C8—611no—
946C4⋊C8—611no—
947C4⋊C8—612no—
948C4⋊C8—612no—
949C4⋊C8—612no—
950C4⋊C8—611no—
951#103—612no—
952#103—612no—
953#103—612no—
954#103—612no—
955#103—612no—
956#103—612no—
957#103—612no—
958#103—612no—
959#103—612no—
960#102—612no—
961#102—612no—
962#102—612no—
963#102—612no—
964#102—612no—
965#102—612no—
966#102—612no—
967C22⋊C8—612no—
968C22⋊C8—612no—
969C22⋊C8—612no—
970#97—612no—
971#97—612no—
972C4×C8—612no—
973#41—22no—
974#41—42no—
975#41—41no—
976#41—44no—
977#41—4882no—
978#41—4882no—
979#41—2444no—
980C2×Q8—21no—
981C2×Q8—21no—
982C2×Q8—21no—
983C2×Q8—22no—
984C2×Q8—22no—
985C2×Q8—41no—
986C2×Q8—41no—
987C2×Q8—1222no—
988C2×Q8—1221no—
989C2×Q8—1221no—
990C2×Q8—1221no—
991C2×Q8—4882no—
992C2×Q8C2×C22⋊D6111yescharacteristic
993C2×Q8C23×D6111yescharacteristic
994C2×Q8C23×D6111yescharacteristic
995C2×Q8C23×D6111yescharacteristic
996C2×D4—21no—
997C2×D4—21no—
998C2×D4—21no—
999C2×D4—612no—
1000C2×D4—1222no—
1001C2×D4—1222no—
1002C2×D4—1222no—
1003C2×D4—1221no—
1004C2×D4—1221no—
1005C2×D4C2×C22⋊D6111yescharacteristic
1006C2×D4C2×C22⋊D6111yescharacteristic
1007C2×D4C2×C22⋊D6111yescharacteristic
1008C2×D4C23×D6111yescharacteristic
1009C22×C4—21no—
1010C22×C4—21no—
1011C22×C4—21no—
1012C22×C4—21no—
1013C22×C4—21no—
1014C22×C4—21no—
1015C22×C4—21no—
1016C22×C4—1222no—
1017C22×C4—1222no—
1018C22×C4—1222no—
1019C22×C4—1222no—
1020C22×C4C2×C22⋊D6111yescharacteristic
1021C22×C4C2×C22⋊D6111yescharacteristic
1022C22×C4C2×C22⋊D6111yescharacteristic
1023C22×C4C2×C22⋊D6111yescharacteristic
1024C22×C4C2×C22⋊D6111yescharacteristic
1025C22×C4C2×C22⋊D6111yescharacteristic
1026C22×C4C23×D6111yescharacteristic
1027C22×C4C23×D6111yescharacteristic
1028C22×C4C23×D6111yescharacteristic
1029SD16—1224no—
1030SD16—2442no—
1031SD16—2442no—
1032D8—2442no—
1033M16—2442no—
1034C2×C8—612no—
1035C2×C8—612no—
1036C2×C8—612no—
1037C2×C8—612no—
1038C2×C8—2442no—
1039C2×C8—2442no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
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—612no—
1062C4⋊C4—612no—
1063C4⋊C4—612no—
1064C4⋊C4—1222no—
1065C4⋊C4—1222no—
1066C4⋊C4—1222no—
1067C4⋊C4—1222no—
1068C4⋊C4—1221no—
1069C4⋊C4—1221no—
1070C4⋊C4—1222no—
1071C4⋊C4—1222no—
1072C4⋊C4—1221no—
1073C4⋊C4C2×C22⋊D6111yescharacteristic
1074C4⋊C4C2×C22⋊D6111yescharacteristic
1075C4⋊C4C2×C22⋊D6111yescharacteristic
1076C4⋊C4C2×C22⋊D6111yescharacteristic
1077C4⋊C4C2×C22⋊D6111yescharacteristic
1078C4⋊C4C2×C22⋊D6111yescharacteristic
1079C4⋊C4C23×D6111yescharacteristic
1080C4⋊C4C23×D6111yescharacteristic
1081C4⋊C4C23×D6111yescharacteristic
1082C4⋊C4C23×D6111yescharacteristic
1083C22⋊C4—21no—
1084C22⋊C4—21no—
1085C22⋊C4—21no—
1086C22⋊C4—21no—
1087C22⋊C4—21no—
1088C22⋊C4—21no—
1089C22⋊C4—21no—
1090C22⋊C4—21no—
1091C22⋊C4—21no—
1092C22⋊C4—21no—
1093C22⋊C4—21no—
1094C22⋊C4—21no—
1095C22⋊C4—21no—
1096C22⋊C4—1222no—
1097C22⋊C4—1222no—
1098C22⋊C4—1222no—
1099C22⋊C4—1222no—
1100C22⋊C4—1222no—
1101C22⋊C4—1222no—
1102C22⋊C4—1222no—
1103C22⋊C4—1222no—
1104C22⋊C4C2×C22⋊D6111yescharacteristic
1105C22⋊C4C2×C22⋊D6111yescharacteristic
1106C22⋊C4C2×C22⋊D6111yescharacteristic
1107C22⋊C4C2×C22⋊D6111yescharacteristic
1108C22⋊C4C2×C22⋊D6111yescharacteristic
1109C22⋊C4C2×C22⋊D6111yescharacteristic
1110C42—21no—
1111C42—21no—
1112C42—21no—
1113C42—21no—
1114C42—21no—
1115C42—21no—
1116C42—21no—
1117C42—21no—
1118C42—21no—
1119C42—1222no—
1120C42—1222no—
1121C42C2×C22⋊D6111yescharacteristic
1122C42C2×C22⋊D6111yescharacteristic
1123C42C2×C22⋊D6111yescharacteristic
1124C42C2×C22⋊D6111yescharacteristic
1125C42C2×C22⋊D6111yescharacteristic
1126C42C2×C22⋊D6111yescharacteristic
1127C42C23×D6111yescharacteristic
1128C42C23×D6111yescharacteristic
1129C42C23×D6111yescharacteristic
1130C42C23×D6111yescharacteristic
1131C23—21no—
1132C23—1222no—
1133C23C22×C22⋊D6111yescharacteristic
1134C23C22×C22⋊D6111yescharacteristic
1135C23C22×C22⋊D6111yescharacteristic
1136Q8—21no—
1137Q8—21no—
1138Q8—21no—
1139Q8—21no—
1140Q8—21no—
1141Q8—41no—
1142Q8—42no—
1143Q8—42no—
1144Q8—42no—
1145Q8—4882no—
1146Q8—2442no—
1147Q8—2442no—
1148Q8—2442no—
1149Q8#1451982412yes—
1150D4—22no—
1151D4—22no—
1152D4—21no—
1153D4—21no—
1154D4—41no—
1155D4—42no—
1156D4—42no—
1157D4—42no—
1158D4—1222no—
1159D4—1222no—
1160D4—4882no—
1161D4—4882no—
1162D4—2442no—
1163D4—2444no—
1164D4—2442no—
1165C2×C4—22no—
1166C2×C4—21no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—1222no—
1192C2×C4—1222no—
1193C2×C4—1222no—
1194C2×C4—4882no—
1195C2×C4—4882no—
1196C2×C4—4882no—
1197C2×C4—2444no—
1198C2×C4C22×C22⋊D6111yescharacteristic
1199C2×C4C22×C22⋊D6111yescharacteristic
1200C2×C4C22×C22⋊D6111yescharacteristic
1201C2×C4C22×C22⋊D6111yescharacteristic
1202C2×C4C22×C22⋊D6111yescharacteristic
1203C2×C4C22×C22⋊D6111yescharacteristic
1204C2×C4C22×C22⋊D6111yescharacteristic
1205C2×C4C22×C22⋊D6111yescharacteristic
1206C2×C4C22×C22⋊D6111yescharacteristic
1207C2×C4C22×C22⋊D6111yescharacteristic
1208C2×C4C22×C22⋊D6111yescharacteristic
1209C2×C4C24×D6111yescharacteristic
1210C8—1222no—
1211C8—1222no—
1212C8—1222no—
1213C8—1222no—
1214C22—21no—
1215C22—21no—
1216C22—21no—
1217C22—21no—
1218C22—21no—
1219C22—21no—
1220C22—21no—
1221C22—21no—
1222C22—41no—
1223C22—41no—
1224C22—41no—
1225C22—2442no—
1226C22—2442no—
1227C22—2442no—
1228C22#1684056012yes—
1229C22C23×C22⋊D6111yescharacteristic
1230C4—21no—
1231C4—21no—
1232C4—21no—
1233C4—22no—
1234C4—21no—
1235C4—21no—
1236C4—21no—
1237C4—21no—
1238C4—21no—
1239C4—21no—
1240C4—21no—
1241C4—41no—
1242C4—41no—
1243C4—41no—
1244C4—41no—
1245C4—41no—
1246C4—41no—
1247C4—2442no—
1248C4—2442no—
1249C4—2442no—
1250C4#1684057012yes—
1251C4C2×#1451982411yescharacteristic
1252C4#1684059811yescharacteristic
1253C2—22no—
1254C2—41no—
1255C2—41no—
1256C2—81no—
1257C2—4882no—
1258C2#2145949911yescharacteristic
1259C2C2×#1684056011yescharacteristic
1260C2C2×#1684057011yescharacteristic
subgroupG/H
centerC22C23×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3482C2
socleC22×C61C23×D4
hypercenter#3482D61
hypocenterC61#62129
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3482

Complements

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

NH ≅ G/Ntype
1. #21459730C2semidirect
2. #21458758C2semidirect
3. #21458640C2semidirect
4. #21458328C2semidirect
5. #21458289C2semidirect
6. #21458198C2semidirect
7. #21458005C2semidirect
8. #21457990C2semidirect
9. #21457721C2semidirect
10. #21457181C2semidirect
11. #21457145C2semidirect
12. #21457131C2semidirect
13. #21457046C2semidirect
14. #21457029C2semidirect
15. #21456994C2semidirect
16. #21455970C2semidirect
17. #21455941C2semidirect
18. #21455850C2semidirect
19. #21455624C2semidirect
20. #21455607C2semidirect
21. C2×#16840047C2semidirect
22. #21454944C2semidirect
23. C61×#3482C2semidirect
624. #3482D61semidirect
769. C61#62129semidirect

Maximal subgroups

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

subgroupindex
#214597302
#214587582
#214586402
#214583282
#214582892
#214581982
#214580052
#214579902
#214577212
#214571812
#214571452
#214571312
#214570462
#214570292
#214569942
#214559702
#214559412
#214558502
#214556242
#214556072
C2×#168400472
#214549442
C61×#34822
#6212961