Finite Group Databasebeta

← #30546509

Subgroups — #30546509

Order 15616.

4726 conjugacy classes of subgroups.

The subgroup lattice has 1354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×2−1+4×D61C211yesmaximal, characteristic, complemented
2C2×#16840561C211yesmaximal, characteristic, complemented
3C22×#14519809C211yesmaximal, characteristic, complemented
4#21459151C211yesmaximal, characteristic, complemented
5#21455138C214yesmaximal, complemented
6#21455135C214yesmaximal, complemented
7#21455113C211yesmaximal, characteristic, complemented
8#21455112C211yesmaximal, characteristic, complemented
9#21455110C211yesmaximal, characteristic, complemented
10#21455108C211yesmaximal, characteristic, complemented
11#21455107C211yesmaximal, characteristic, complemented
12#21455106C211yesmaximal, characteristic, complemented
13#21455105C211yesmaximal, characteristic, complemented
14#21455062C214yesmaximal, complemented
15#21455054C214yesmaximal, complemented
16#21454334C211yesmaximal, characteristic, complemented
17#419×D61C211yesmaximal, characteristic, complemented
18#21454261C211yesmaximal, characteristic, complemented
19C61×#3011C211yesmaximal, characteristic, complemented
20C2×#14519825—21no—
21C2×#14519825C2211yescharacteristic
22C2×#14519825C2212yescomplemented
23C2×#14519824—21no—
24C2×#14519824—22no—
25C2×#14519824C2211yescharacteristic
26C2×#14519824C2211yescharacteristic
27C2×#14519824C2212yescomplemented
282−1+4×D61—28no—
292−1+4×D61—28no—
30C22×#11758226C2211yescharacteristic
31C2×#41×D61—22no—
32C2×#41×D61—21no—
33C2×#41×D61C2211yescharacteristic
34C2×#41×D61C2211yescharacteristic
35C2×#41×D61C2212yescomplemented
36C22×Q8×D61—21no—
37C22×Q8×D61C2211yescharacteristic
38C22×Q8×D61C2212yescomplemented
39#16840561—28no—
40C2×#14519809—28no—
41C2×#14519809C2214yes—
42C2×#14519809C2212yes—
43C2×#14519809C2214yescomplemented
44C2×#14519808C2211yescharacteristic, complemented
45C2×#14519805C2211yescharacteristic, complemented
46C2×#14519804C2212yes—
47C2×#14519802C2211yescharacteristic, complemented
48C2×#14519800C2212yescomplemented
49C2×#14519798C2212yescomplemented
50C22×#11758202C2211yescharacteristic, complemented
51C22×#11758190C2211yescharacteristic, complemented
52C22×#11758201C2211yescharacteristic, complemented
53C22×#11758189C2211yescharacteristic
54C2×M16×D61C2211yescharacteristic
55#16840342C2214yescomplemented
56#16840337—21no—
57#16840336C2211yescharacteristic, complemented
58#16840331C2211yescharacteristic, complemented
59#16840330—21no—
60#16840326C2211yescharacteristic, complemented
61#16840323—22no—
62#16840313—21no—
63#16840311—21no—
64#16840275C2214yes—
65#16840270—22no—
66#117×D61C2211yescharacteristic
67#16839923C2214yescomplemented
68#16839922C2214yescomplemented
69#16839921C2214yescomplemented
70#16839917C2214yescomplemented
71#16839916C2214yescomplemented
72#16839916C2214yescomplemented
73#16839910C2214yescomplemented
74#16839909C2214yescomplemented
75#16839908C2214yescomplemented
76#16839907C2214yescomplemented
77#16839903C2214yescomplemented
78#16839902C2214yescomplemented
79#16839902C2214yescomplemented
80#16839901C2214yescomplemented
81#16839772C2211yescharacteristic, complemented
82#16839771C2211yescharacteristic, complemented
83#16839770C2211yescharacteristic, complemented
84#16839769C2212yescomplemented
85#16839769C2214yescomplemented
86#16839765C2212yescomplemented
87#16839762C2212yescomplemented
88#16839760C2212yescomplemented
89#16839759C2211yescharacteristic, complemented
90#16839758C2211yescharacteristic, complemented
91#16839756C2211yescharacteristic, complemented
92#103×D61C2214yescomplemented
93#16839730C2211yescharacteristic, complemented
94#16839729C2211yescharacteristic, complemented
95#16839728C2211yescharacteristic, complemented
96#16839727C2214yescomplemented
97#16839724C2214yescomplemented
98C2×2−1+4×C61C2211yescharacteristic
99C2×#137×C61C2211yescharacteristic, complemented
100C22×Q16×C61C2211yescharacteristic, complemented
101C61×#536C2211yescharacteristic, complemented
102C61×#452C2214yescomplemented
103C61×#451C2214yescomplemented
104C61×#419C2211yescharacteristic, complemented
105C61×#416C2211yescharacteristic, complemented
106C61×#408C2211yescharacteristic, complemented
107#14519825—216no—
108#14519825—24no—
109#14519825—28no—
110#14519825—28no—
111#14519825—24no—
112#14519824—216no—
113#14519824—232no—
114#14519824—24no—
115#14519824—28no—
116#14519824—28no—
117#14519824—24no—
118#14519824—24no—
119#14519824—24no—
120C2×#11758226—21no—
121C2×#11758226—22no—
122C2×#11758226—21no—
123C2×#11758226—21no—
124C2×#11758226—24no—
125C2×#11758226—24no—
126C2×#11758226D411yescharacteristic
127C2×#11758226C2312yes—
128C2×#11758226C2312yes—
129C2×#11758226C2312yes—
130C2×#11758226C2311yescharacteristic
131C2×#11758222—22no—
132C2×#11758222—22no—
133C2×#11758222—22no—
134C2×#11758222—21no—
135C2×#11758222—22no—
136C2×#11758222—21no—
137C2×#11758222—22no—
138C2×#11758222C2312yes—
139C2×#11758222C2311yescharacteristic
140C2×#11758222C2312yes—
141C2×#11758222C2311yescharacteristic
142C2×#11758224—22no—
143C2×#11758224—21no—
144C2×#11758224—22no—
145C2×#11758224—22no—
146C2×#11758224—22no—
147C2×#11758224—21no—
148C2×#11758224—22no—
149C2×#11758224D412yes—
150C2×#11758224D411yescharacteristic
151C2×#11758224C2312yes—
152C2×#11758224C2311yescharacteristic
153#41×D61—232no—
154#41×D61—216no—
155#41×D61—28no—
156#41×D61—28no—
157#41×D61—24no—
158#41×D61—24no—
159#41×D61—24no—
160#41×D61D418yescomplemented
161C22×Dic122—21no—
162C22×Dic122—22no—
163C22×Dic122—21no—
164C22×Dic122—22no—
165C22×Dic122C2312yes—
166C22×Dic122C2311yescharacteristic
167C2×Q8×D61—216no—
168C2×Q8×D61—21no—
169C2×Q8×D61—28no—
170C2×Q8×D61—28no—
171C2×Q8×D61—21no—
172C2×Q8×D61—22no—
173C2×Q8×D61—24no—
174C2×Q8×D61—21no—
175C2×Q8×D61—22no—
176C2×Q8×D61—21no—
177C2×Q8×D61—22no—
178C2×Q8×D61D411yescharacteristic
179C2×Q8×D61D418yescomplemented
180C2×Q8×D61C2312yes—
181C2×Q8×D61C2312yes—
182C2×Q8×D61C2312yes—
183C2×Q8×D61C2312yes—
184C2×Q8×D61C2311yescharacteristic
185C22×D244—21no—
186C22×D244C2311yescharacteristic
187C2×D4×D61—21no—
188C2×D4×D61—22no—
189C2×D4×D61D412yes—
190C2×D4×D61D411yescharacteristic
191C2×D4×D61C2311yescharacteristic
192C22×C4×D61—21no—
193C22×C4×D61—22no—
194C22×C4×D61—21no—
195C22×C4×D61—22no—
196C22×C4×D61—21no—
197C22×C4×D61C2312yes—
198C22×C4×D61C2311yescharacteristic
199#14519809—216no—
200#14519809—216no—
201#14519809—28no—
202#14519808—24no—
203#14519805—24no—
204#14519804—28no—
205#14519802—24no—
206#14519800—28no—
207#14519798—28no—
208C2×#11758202—24no—
209C2×#11758202C2314yes—
210C2×#11758202C2312yes—
211C2×#11758190—24no—
212C2×#11758190C2314yes—
213C2×#11758190C2312yes—
214C2×#11758201—24no—
215C2×#11758201C2314yes—
216C2×#11758201C2312yes—
217C2×#11758201C2312yes—
218C2×D488C2312yes—
219C2×#11758199C2312yes—
220C2×#11758194C2311yescharacteristic
221C2×#11758189—24no—
222C2×#11758189C2312yes—
223C2×#11758189C2312yes—
224C2×#11758189C2312yes—
225M16×D61—24no—
226C22×#92418C2311yescharacteristic
227C2×C8×D61C2312yes—
228#14519775—21no—
229#14519774—21no—
230#14519773—21no—
231#14519766—21no—
232#14519766—21no—
233#14519765—21no—
234#14519762—24no—
235#14519760—22no—
236#14519755—24no—
237#14519753C2314yes—
238#14519752—24no—
239#14519752C2314yes—
240#14519751C2314yes—
241#14519750—24no—
242#14519750—24no—
243#14519747—24no—
244#14519747—22no—
245#14519745—22no—
246#14519739—24no—
247#14519737—24no—
248#14519736C2311yescharacteristic
249#14519735C2312yes—
250#14519734—21no—
251#14519733—21no—
252C4⋊C4×D61C2312yes—
253C22⋊C4×D61—21no—
254C42×D61—21no—
255#14519702C2314yes—
256#14519702C2312yes—
257#14519701C2314yes—
258#14519701C2312yes—
259#14519700C2314yes—
260#14519700C2312yes—
261#14519699C2312yes—
262#14519698C2312yes—
263#14519697C2312yes—
264C22⋊#92418C2314yes—
265#14519689C2314yes—
266#14519689C2314yes—
2672−1+4×C61—24no—
2682−1+4×C61—24no—
269C2×#41×C61—22no—
270C2×#41×C61—21no—
271C2×#41×C61C2312yes—
272C2×#41×C61C2311yescharacteristic
273C2×#41×C61C2311yescharacteristic
274C22×Q8×C61—21no—
275C22×Q8×C61C2311yescharacteristic
276C22×Q8×C61C2312yes—
277C22×Q8×C61C2311yescharacteristic
278#137×C61—24no—
279C2×Q16×C61—24no—
280C2×Q16×C61C2314yes—
281C2×Q16×C61C2312yes—
282C2×SD16×C61C2312yes—
283C2×M16×C61C2311yescharacteristic
284C22×C8×C61C2311yescharacteristic
285C4⋊Q8×C61—21no—
286#124×C61—21no—
287#123×C61—22no—
288C22⋊Q8×C61C2314yes—
289#117×C61C2311yescharacteristic
290#103×C61C2314yes—
291#103×C61C2312yes—
292#102×C61C2312yes—
293C22⋊C8×C61C2314yes—
294C23×D61—21no—
295C23×D61—21no—
296C23×D61C2×D412yes—
297C23×D61C2×D411yescharacteristic
298#41×C61—216no—
299#41×C61—28no—
300#41×C61—24no—
301#41×C61—24no—
302#41×C61—22no—
303#41×C61—22no—
304#41×C61—22no—
305#41×C61C2×D414yes—
306C2×Q8×C61—28no—
307C2×Q8×C61—24no—
308C2×Q8×C61—24no—
309C2×Q8×C61—22no—
310C2×Q8×C61—21no—
311C2×Q8×C61—22no—
312C2×Q8×C61—21no—
313C2×Q8×C61—22no—
314C2×Q8×C61—22no—
315C2×Q8×C61C2×D414yes—
316C2×Q8×C61C2×D411yescharacteristic
317C2×Q8×C61C2412yes—
318C2×Q8×C61C2411yescharacteristic
319C2×Q8×C61C2412yes—
320C2×D4×C61—22no—
321C2×D4×C61—21no—
322C2×D4×C61C2×D412yes—
323C2×D4×C61C2×D411yescharacteristic
324C2×D4×C61C2411yescharacteristic
325C22×C4×C61—22no—
326C22×C4×C61—21no—
327C22×C4×C61—22no—
328C22×C4×C61—21no—
329C22×C4×C61—21no—
330C22×C4×C61C2412yes—
331C22×C4×C61C2411yescharacteristic
332C2×C22⋊D61—22no—
333C2×C22⋊D61—21no—
334C2×C22⋊D61—22no—
335C2×C22⋊D61—21no—
336C2×C22⋊D61—24no—
337C2×C22⋊D61—21no—
338C2×C22⋊D61C2×D412yes—
339C2×C22⋊D61C2×D412yes—
340C2×C22⋊D61C2×D412yes—
341C22×Dic61—22no—
342C22×Dic61—21no—
343C22×Dic61—22no—
344C22×Dic61—21no—
345C22×Dic61C2×D412yes—
346C22×Dic61C2×D411yescharacteristic
347#11758226—216no—
348#11758226—28no—
349#11758226—24no—
350#11758226—24no—
351#11758226—24no—
352#11758226—22no—
353#11758226—24no—
354#11758226—24no—
355#11758226—24no—
356#11758226—24no—
357#11758226—44no—
358#11758226—44no—
359#11758226C2×D414yes—
360Q8×D61—216no—
361Q8×D61—28no—
362Q8×D61—28no—
363Q8×D61—216no—
364Q8×D61—216no—
365Q8×D61—24no—
366Q8×D61—24no—
367Q8×D61—24no—
368Q8×D61—28no—
369Q8×D61—28no—
370Q8×D61—22no—
371Q8×D61—24no—
372Q8×D61—24no—
373Q8×D61—24no—
374Q8×D61—24no—
375Q8×D61C2×D414yes—
376Q8×D61C2×D418yes—
377Q8×D61C2×D418yes—
378#11758224—216no—
379#11758224—216no—
380#11758224—216no—
381#11758224—28no—
382#11758224—216no—
383#11758224—216no—
384#11758224—24no—
385#11758224—28no—
386#11758224—28no—
387#11758224—24no—
388#11758224—22no—
389#11758224—24no—
390#11758224C2×D414yes—
391D4×D61—216no—
392D4×D61—28no—
393D4×D61—28no—
394D4×D61—24no—
395D4×D61—22no—
396D4×D61C2×D414yes—
397#11758222—216no—
398#11758222—216no—
399#11758222—216no—
400#11758222—28no—
401#11758222—216no—
402#11758222—216no—
403#11758222—22no—
404#11758222—22no—
405#11758222—22no—
406#11758222—24no—
407#11758222—28no—
408#11758222—24no—
409#11758222—24no—
410#11758222—24no—
411#11758222C2×D414yes—
412C2×D244—22no—
413C2×D244—21no—
414C2×D244—22no—
415C2×D244—22no—
416C2×D244—22no—
417C2×D244—22no—
418C2×D244—21no—
419C2×D244—24no—
420C2×D244—44no—
421C2×D244C2×D412yes—
422C2×D244C2×D411yescharacteristic
423C2×D244C2412yes—
424C2×D244C2411yescharacteristic
425C2×C4×D61—216no—
426C2×C4×D61—216no—
427C2×C4×D61—28no—
428C2×C4×D61—22no—
429C2×C4×D61—21no—
430C2×C4×D61—22no—
431C2×C4×D61—22no—
432C2×C4×D61—22no—
433C2×C4×D61—22no—
434C2×C4×D61—21no—
435C2×C4×D61—22no—
436C2×C4×D61—21no—
437C2×C4×D61—28no—
438C2×C4×D61—24no—
439C2×C4×D61—24no—
440C2×C4×D61—22no—
441C2×C4×D61—22no—
442C2×C4×D61—22no—
443C2×C4×D61—44no—
444C2×C4×D61C2×D412yes—
445C2×C4×D61C2×D412yes—
446C2×C4×D61C2×D411yescharacteristic
447C2×C4×D61C2×D411yescharacteristic
448C2×C4×D61C2×D414yes—
449C2×C4×D61C2×D414yes—
450C2×C4×D61C2412yes—
451C2×C4×D61C2411yescharacteristic
452C2×C4×D61C2411yescharacteristic
453C2×Dic122—28no—
454C2×Dic122—216no—
455C2×Dic122—216no—
456C2×Dic122—22no—
457C2×Dic122—21no—
458C2×Dic122—22no—
459C2×Dic122—28no—
460C2×Dic122—22no—
461C2×Dic122—22no—
462C2×Dic122—22no—
463C2×Dic122—21no—
464C2×Dic122—22no—
465C2×Dic122—24no—
466C2×Dic122—24no—
467C2×Dic122C2×D412yes—
468C2×Dic122C2×D411yescharacteristic
469C2×Dic122C2×D414yes—
470C2×Dic122C2411yescharacteristic
471C2×Dic122C2412yes—
472Q16×C61—28no—
473Q16×C61—24no—
474SD16×C61—24no—
475M16×C61—22no—
476C2×C8×C61—22no—
477C2×C8×C61C2412yes—
478C2×C8×C61C2412yes—
479C4⋊C4×C61—24no—
480C4⋊C4×C61C2412yes—
481C22⋊C4×C61—21no—
482C22⋊C4×C61—24no—
483C42×C61—21no—
484C22⋊Dic61—21no—
485#11758202—24no—
486#11758202—28no—
487#11758201—28no—
488#11758201—24no—
489#11758201—24no—
490#11758199—24no—
491#11758198—22no—
492#11758198—24no—
493#11758198—24no—
494#11758198—24no—
495C4⋊Dic61C2412yes—
496#11758196—22no—
497#11758196—24no—
498C4×Dic61—21no—
499C4×Dic61—22no—
500#11758194—22no—
501C2×#92418—22no—
502C2×#92418C2412yes—
503C2×#92418C2412yes—
504D488—24no—
505#11758190—28no—
506#11758190—24no—
507#11758189—24no—
508#11758189—24no—
509#11758189—24no—
510C8×D61—24no—
511C23×C61—21no—
512C23×C61C22×D412yes—
513C23×C61C22×D411yescharacteristic
514C22×D61—21no—
515C22×D61—24no—
516C22×D61—24no—
517C22×D61—22no—
518C22×D61—42no—
519C22×D61—44no—
520C22×D61—44no—
521C22×D61—42no—
522C22×D61—82no—
523C22×D61#12014yes—
524C22×D61C22×D412yes—
525C22×D61C22×D411yescharacteristic
526C22×D61C22×D411yescharacteristic
527Q8×C61—28no—
528Q8×C61—24no—
529Q8×C61—22no—
530Q8×C61—22no—
531Q8×C61—21no—
532Q8×C61—22no—
533Q8×C61—22no—
534Q8×C61—42no—
535Q8×C61C22×D412yes—
536Q8×C61C22×D414yes—
537D4×C61—28no—
538D4×C61—24no—
539D4×C61—24no—
540D4×C61—22no—
541D4×C61—21no—
542D4×C61C22×D412yes—
543C2×C4×C61—28no—
544C2×C4×C61—28no—
545C2×C4×C61—24no—
546C2×C4×C61—21no—
547C2×C4×C61—22no—
548C2×C4×C61—24no—
549C2×C4×C61—22no—
550C2×C4×C61—22no—
551C2×C4×C61—22no—
552C2×C4×C61—22no—
553C2×C4×C61—42no—
554C2×C4×C61C22×D412yes—
555C2×C4×C61C22×D411yescharacteristic
556C2×C4×C61C22×D412yes—
557C2×C4×C61C22×D412yes—
558C2×C4×C61C2511yescharacteristic
559C22⋊D61—28no—
560C22⋊D61—28no—
561C22⋊D61—24no—
562C22⋊D61—24no—
563C22⋊D61—24no—
564C22⋊D61—24no—
565C22⋊D61—24no—
566C22⋊D61—24no—
567C22⋊D61—84no—
568C2×Dic61—28no—
569C2×Dic61—28no—
570C2×Dic61—24no—
571C2×Dic61—21no—
572C2×Dic61—22no—
573C2×Dic61—24no—
574C2×Dic61—24no—
575C2×Dic61—22no—
576C2×Dic61#12014yes—
577C2×Dic61C22×D412yes—
578C2×Dic61C22×D411yescharacteristic
579C2×Dic61C22×D411yescharacteristic
580D244—28no—
581D244—24no—
582D244—24no—
583D244—22no—
584D244—21no—
585D244—22no—
586D244—22no—
587D244—44no—
588D244—44no—
589D244—42no—
590D244—84no—
591D244C22×D412yes—
592C4×D61—28no—
593C4×D61—28no—
594C4×D61—28no—
595C4×D61—28no—
596C4×D61—28no—
597C4×D61—24no—
598C4×D61—24no—
599C4×D61—28no—
600C4×D61—24no—
601C4×D61—22no—
602C4×D61—22no—
603C4×D61—24no—
604C4×D61—24no—
605C4×D61—44no—
606C4×D61—44no—
607C4×D61—82no—
608C4×D61#12014yes—
609C4×D61#12014yes—
610C4×D61C22×D412yes—
611C4×D61C22×D412yes—
612C4×D61C22×D412yes—
613C4×D61C22×D412yes—
614Dic122—28no—
615Dic122—28no—
616Dic122—28no—
617Dic122—22no—
618Dic122—24no—
619Dic122—22no—
620Dic122—21no—
621Dic122—24no—
622Dic122—28no—
623Dic122—28no—
624Dic122—24no—
625Dic122C22×D412yes—
626Dic122C22×D414yes—
627C8×C61—22no—
628C8×C61—22no—
629#92418—22no—
630#92418—22no—
631#60368—611nomaximal, Sylow
632C22×C61—22no—
633C22×C61—24no—
634C22×C61—22no—
635C22×C61—22no—
636C22×C61—42no—
637C22×C61C2×#12012yes—
638C22×C61C23×D411yescharacteristic
639C2×D61—22no—
640C2×D61—22no—
641C2×D61—24no—
642C2×D61—22no—
643C2×D61—22no—
644C2×D61—44no—
645C2×D61—48no—
646C2×D61—48no—
647C2×D61—42no—
648C2×D61—44no—
649C2×D61—42no—
650C2×D61—84no—
651C2×D61C2×#12012yes—
652C2×D61C2×#12012yes—
653C4×C61—22no—
654C4×C61—24no—
655C4×C61—22no—
656C4×C61—42no—
657C4×C61—42no—
658C4×C61C2×#12012yes—
659C4×C61C23×D411yescharacteristic
660C4×C61C23×D411yescharacteristic
661Dic61—22no—
662Dic61—22no—
663Dic61—24no—
664Dic61—42no—
665Dic61C2×#12012yes—
666Dic61C2×#12012yes—
667C22×2−1+4—611no—
668C2×#575—611no—
669C22×#137—611no—
670#3449—611no—
671#3013—614no—
672#3013—614no—
673#3011—611no—
674#3011—611no—
675#3011—611no—
676#3011D6111yescharacteristic, complemented
677#3010—611no—
678#3010—611no—
679#3010—611no—
680#3010—611no—
681#3005—614no—
682#3004—614no—
683#2896—611no—
684C2×#419—611no—
685#2879—611no—
686C2×C61—22no—
687C2×C61—42no—
688C2×C61—42no—
689C2×C61C22×#12011yescharacteristic
690C2×C61#358612yes—
691D61—22no—
692D61—22no—
693D61—42no—
694D61—42no—
695D61—82no—
696C2×2−1+4—611no—
697C2×2−1+4—612no—
698C2×2−1+4—611no—
699C2×2−1+4—611no—
700C2×2−1+4—612no—
701C2×2−1+4—1221no—
702C2×2−1+4—1228no—
703C2×2−1+4—1222no—
704C2×2−1+4—1221no—
705C2×2−1+4—1228no—
706C2×2−1+4C2×D6111yescharacteristic
707C22×#41—611no—
708C22×#41—611no—
709C22×#41—612no—
710C22×#41—611no—
711C22×#41—1222no—
712C22×#41—1221no—
713C23×Q8—611no—
714C23×Q8—612no—
715C23×Q8—1221no—
716#575—1228no—
717C2×#137—611no—
718C2×#137—612no—
719C2×#137—614no—
720C2×#137—614no—
721C2×#137—1228no—
722C2×#137C2×D6111yescharacteristic, complemented
723C2×AGL(1,ℤ/8)—611no—
724C2×AGL(1,ℤ/8)—612no—
725C2×AGL(1,ℤ/8)—611no—
726C2×#135—612no—
727C2×#135—612no—
728C22×Q16—611no—
729C22×Q16C2×D6111yescharacteristic, complemented
730C22×SD16—611no—
731C22×SD16—611no—
732C22×M16—611no—
733C22×M16—611no—
734#537—614no—
735#536—611no—
736#536—1221no—
737#536C2×D6111yescharacteristic, complemented
738#535—611no—
739#535—611no—
740#535—1221no—
741#534—1222no—
742#532—1221no—
743#532—1221no—
744#525—614no—
745#525—1222no—
746C2×#117—611no—
747#452—614no—
748#452—614no—
749#452—614no—
750#452C2×D6114yescomplemented
751#451—614no—
752#451—614no—
753#451—614no—
754#451C2×D6114yescomplemented
755#449—614no—
756#449—614no—
757#449—614no—
758#449—614no—
759#448—614no—
760#448—614no—
761#448—614no—
762#448—614no—
763#419—611no—
764#419—611no—
765#419—611no—
766#419—614no—
767#419—612no—
768#419C2×D6111yescharacteristic, complemented
769#418—612no—
770#417—612no—
771#417—612no—
772#416—611no—
773#416—611no—
774#416—611no—
775#416C2×D6111yescharacteristic, complemented
776C2×#103—614no—
777#408—611no—
778#408—611no—
779#408—611no—
780#408—614no—
781#408C2×D6111yescharacteristic, complemented
782#407—614no—
783C61#6036811yescharacteristic, complemented, Sylow
7842−1+4—24no—
7852−1+4—24no—
7862−1+4—1228no—
7872−1+4—1228no—
7882−1+4—1224no—
7892−1+4—12216no—
7902−1+4—1228no—
7912−1+4—1224no—
7922−1+4—1224no—
7932−1+4—1224no—
7942−1+4—1228no—
7952−1+4—12232no—
7962−1+4—12216no—
7972−1+4—1224no—
7982−1+4—1224no—
799C2×#41—22no—
800C2×#41—21no—
801C2×#41—611no—
802C2×#41—612no—
803C2×#41—611no—
804C2×#41—611no—
805C2×#41—612no—
806C2×#41—618no—
807C2×#41—611no—
808C2×#41—612no—
809C2×#41—612no—
810C2×#41—612no—
811C2×#41—611no—
812C2×#41—612no—
813C2×#41—611no—
814C2×#41—612no—
815C2×#41—1221no—
816C2×#41—1222no—
817C2×#41—1222no—
818C2×#41—1222no—
819C2×#41—1222no—
820C2×#41—1222no—
821C2×#41—1221no—
822C2×#41—1221no—
823C2×#41—1222no—
824C2×#41—1221no—
825C2×#41—1221no—
826C2×#41—1224no—
827C2×#41—1224no—
828C2×#41—1224no—
829C2×#41—1224no—
830C2×#41—1224no—
831C2×#41—1222no—
832C2×#41—1222no—
833C2×#41—1222no—
834C2×#41—1222no—
835C2×#41—1221no—
836C2×#41—1228no—
837C2×#41—1228no—
838C2×#41—12216no—
839C2×#41—12232no—
840C2×#41—1222no—
841C2×#41—1221no—
842C2×#41C22×D6112yes—
843C2×#41C22×D6111yescharacteristic
844C2×#41C22×D6111yescharacteristic
845C22×Q8—21no—
846C22×Q8—611no—
847C22×Q8—618no—
848C22×Q8—612no—
849C22×Q8—611no—
850C22×Q8—612no—
851C22×Q8—612no—
852C22×Q8—612no—
853C22×Q8—611no—
854C22×Q8—612no—
855C22×Q8—1221no—
856C22×Q8—1222no—
857C22×Q8—1222no—
858C22×Q8—1221no—
859C22×Q8—1221no—
860C22×Q8—1222no—
861C22×Q8—1221no—
862C22×Q8—1224no—
863C22×Q8—1222no—
864C22×Q8—1228no—
865C22×Q8—1228no—
866C22×Q8—1222no—
867C22×Q8—1221no—
868C22×Q8—12216no—
869C22×Q8—1221no—
870C22×Q8C22×D6111yescharacteristic
871C22×Q8C22×D6112yes—
872C22×Q8C22×D6111yescharacteristic
873C22×D4—611no—
874C22×D4—612no—
875C22×D4—611no—
876C22×D4—611no—
877C22×D4—1221no—
878C22×D4—1221no—
879C22×D4—1222no—
880C23×C4—611no—
881C23×C4—612no—
882C23×C4—1221no—
883C23×C4—1222no—
884C23×C4—1221no—
885C23×C4—1221no—
886C23×C4—1222no—
887#137—24no—
888#137—12216no—
889#137—12216no—
890#137—1228no—
891#137—1224no—
892AGL(1,ℤ/8)—1224no—
893AGL(1,ℤ/8)—1228no—
894AGL(1,ℤ/8)—1224no—
895#135—1228no—
896#135—1228no—
897C2×Q16—24no—
898C2×Q16—614no—
899C2×Q16—612no—
900C2×Q16—1224no—
901C2×Q16C22×D6114yes—
902C2×Q16C22×D6112yes—
903C2×SD16—614no—
904C2×SD16—612no—
905C2×SD16—612no—
906C2×SD16—614no—
907C2×SD16—612no—
908C2×SD16—1224no—
909C2×SD16—1224no—
910C2×SD16C22×D6112yes—
911C2×D8—612no—
912C2×D8—612no—
913C2×M16—611no—
914C2×M16—612no—
915C2×M16—612no—
916C2×M16—612no—
917C2×M16—1224no—
918C2×M16—1224no—
919C2×M16C22×D6111yescharacteristic
920C22×C8—611no—
921C22×C8—612no—
922C22×C8C22×D6111yescharacteristic
923C4⋊Q8—21no—
924C4⋊Q8—1221no—
925#127—1221no—
926#127—1221no—
927#124—21no—
928#124—1221no—
929#124—1221no—
930#124—1221no—
931#123—22no—
932#123—1224no—
933#123—1222no—
934C22⋊Q8—614no—
935C22⋊Q8—1224no—
936C22⋊Q8C22×D6114yes—
937#121—614no—
938#121—614no—
939#121—1224no—
940#121—1224no—
941#121—1224no—
942#120—1222no—
943#120—1224no—
944#120—1222no—
945C4×D4—1224no—
946C4×D4—1224no—
947#117—611no—
948#117—612no—
949#117—1221no—
950#117—1221no—
951#117C22×D6111yescharacteristic
952C2×C4⋊C4—612no—
953C2×C22⋊C4—1221no—
954C2×C42—1221no—
955#103—614no—
956#103—612no—
957#103—614no—
958#103—612no—
959#103—614no—
960#103—612no—
961#103C22×D6114yes—
962#103C22×D6112yes—
963#102—612no—
964#102—612no—
965#102—612no—
966#102C22×D6112yes—
967C22⋊C8—614no—
968C22⋊C8—614no—
969C22⋊C8—614no—
970C22⋊C8C22×D6114yes—
971C24—611no—
972C24—612no—
973C24—1221no—
974C24—1221no—
975#41—216no—
976#41—28no—
977#41—24no—
978#41—24no—
979#41—22no—
980#41—22no—
981#41—22no—
982#41—614no—
983#41—614no—
984#41—614no—
985#41—1228no—
986#41—1224no—
987#41—1224no—
988#41—1224no—
989#41—1224no—
990#41—12216no—
991#41—12216no—
992#41—12216no—
993#41—12216no—
994#41—12216no—
995#41—1228no—
996#41—1228no—
997#41—1228no—
998#41—1224no—
999#41—1222no—
1000#41—1224no—
1001#41—1222no—
1002#41—1224no—
1003#41—1224no—
1004#41—1224no—
1005#41—1224no—
1006#41—1224no—
1007#41—12216no—
1008#41—12216no—
1009#41—12216no—
1010#41—12216no—
1011#41—12216no—
1012#41—1228no—
1013#41—1224no—
1014#41—12216no—
1015#41—1228no—
1016#41—1224no—
1017#41—1224no—
1018#41—1222no—
1019#41—1222no—
1020#41—1222no—
1021#41—2444no—
1022#41—2444no—
1023#41D4×D6114yes—
1024C2×Q8—28no—
1025C2×Q8—24no—
1026C2×Q8—24no—
1027C2×Q8—22no—
1028C2×Q8—21no—
1029C2×Q8—22no—
1030C2×Q8—21no—
1031C2×Q8—22no—
1032C2×Q8—22no—
1033C2×Q8—612no—
1034C2×Q8—611no—
1035C2×Q8—618no—
1036C2×Q8—618no—
1037C2×Q8—614no—
1038C2×Q8—614no—
1039C2×Q8—612no—
1040C2×Q8—611no—
1041C2×Q8—1222no—
1042C2×Q8—1221no—
1043C2×Q8—1222no—
1044C2×Q8—1222no—
1045C2×Q8—1222no—
1046C2×Q8—1228no—
1047C2×Q8—1224no—
1048C2×Q8—1224no—
1049C2×Q8—12216no—
1050C2×Q8—12216no—
1051C2×Q8—1228no—
1052C2×Q8—1224no—
1053C2×Q8—1228no—
1054C2×Q8—1224no—
1055C2×Q8—1222no—
1056C2×Q8—1228no—
1057C2×Q8—1224no—
1058C2×Q8—1224no—
1059C2×Q8—1224no—
1060C2×Q8—12216no—
1061C2×Q8—12216no—
1062C2×Q8—12216no—
1063C2×Q8—1228no—
1064C2×Q8—1228no—
1065C2×Q8—1224no—
1066C2×Q8—1224no—
1067C2×Q8—1222no—
1068C2×Q8—1221no—
1069C2×Q8—1222no—
1070C2×Q8D4×D6114yes—
1071C2×Q8D4×D6111yescharacteristic
1072C2×Q8C23×D6112yes—
1073C2×Q8C23×D6111yescharacteristic
1074C2×Q8C23×D6112yes—
1075C2×D4—22no—
1076C2×D4—21no—
1077C2×D4—614no—
1078C2×D4—612no—
1079C2×D4—612no—
1080C2×D4—612no—
1081C2×D4—612no—
1082C2×D4—611no—
1083C2×D4—611no—
1084C2×D4—612no—
1085C2×D4—1221no—
1086C2×D4—1222no—
1087C2×D4—1224no—
1088C2×D4—1222no—
1089C2×D4—1222no—
1090C2×D4—1224no—
1091C2×D4—1222no—
1092C2×D4—1221no—
1093C2×D4—1228no—
1094C2×D4—1228no—
1095C2×D4—12216no—
1096C2×D4—1221no—
1097C2×D4—1222no—
1098C2×D4—1222no—
1099C2×D4—1221no—
1100C2×D4—1224no—
1101C2×D4—1222no—
1102C2×D4—1222no—
1103C2×D4—1221no—
1104C2×D4—2444no—
1105C2×D4D4×D6112yes—
1106C2×D4D4×D6111yescharacteristic
1107C2×D4C23×D6111yescharacteristic
1108C22×C4—22no—
1109C22×C4—21no—
1110C22×C4—22no—
1111C22×C4—21no—
1112C22×C4—21no—
1113C22×C4—611no—
1114C22×C4—611no—
1115C22×C4—611no—
1116C22×C4—614no—
1117C22×C4—614no—
1118C22×C4—611no—
1119C22×C4—611no—
1120C22×C4—612no—
1121C22×C4—612no—
1122C22×C4—612no—
1123C22×C4—612no—
1124C22×C4—1224no—
1125C22×C4—1224no—
1126C22×C4—1221no—
1127C22×C4—1222no—
1128C22×C4—1228no—
1129C22×C4—1222no—
1130C22×C4—1222no—
1131C22×C4—1221no—
1132C22×C4—1222no—
1133C22×C4—1228no—
1134C22×C4—1222no—
1135C22×C4—1222no—
1136C22×C4—1222no—
1137C22×C4—12216no—
1138C22×C4—12216no—
1139C22×C4—1222no—
1140C22×C4—1221no—
1141C22×C4—1222no—
1142C22×C4—1222no—
1143C22×C4—1221no—
1144C22×C4—1222no—
1145C22×C4—1221no—
1146C22×C4—2444no—
1147C22×C4C23×D6112yes—
1148C22×C4C23×D6111yescharacteristic
1149Q16—28no—
1150Q16—24no—
1151Q16—1228no—
1152Q16—1224no—
1153SD16—24no—
1154SD16—1228no—
1155SD16—1224no—
1156SD16—1224no—
1157SD16—1228no—
1158SD16—1224no—
1159D8—1224no—
1160D8—1224no—
1161M16—22no—
1162M16—1224no—
1163M16—1224no—
1164M16—1224no—
1165M16—1222no—
1166C2×C8—22no—
1167C2×C8—612no—
1168C2×C8—612no—
1169C2×C8—1224no—
1170C2×C8—1222no—
1171C2×C8C23×D6112yes—
1172C2×C8C23×D6112yes—
1173C4⋊C4—24no—
1174C4⋊C4—612no—
1175C4⋊C4—1222no—
1176C4⋊C4—1224no—
1177C4⋊C4C23×D6112yes—
1178C22⋊C4—21no—
1179C22⋊C4—24no—
1180C22⋊C4—1224no—
1181C22⋊C4—1222no—
1182C22⋊C4—1224no—
1183C22⋊C4—1221no—
1184C22⋊C4—1224no—
1185C42—21no—
1186C42—1222no—
1187C42—1221no—
1188C23—21no—
1189C23—611no—
1190C23—611no—
1191C23—614no—
1192C23—612no—
1193C23—1224no—
1194C23—1224no—
1195C23—1221no—
1196C23—1222no—
1197C23—4882no—
1198C23—2442no—
1199C23—2444no—
1200C23—2444no—
1201C23—2442no—
1202C23C2×D4×D6112yes—
1203C23C2×D4×D6111yescharacteristic
1204Q8—28no—
1205Q8—24no—
1206Q8—22no—
1207Q8—21no—
1208Q8—22no—
1209Q8—22no—
1210Q8—22no—
1211Q8—42no—
1212Q8—614no—
1213Q8—612no—
1214Q8—1228no—
1215Q8—1228no—
1216Q8—1224no—
1217Q8—1224no—
1218Q8—1228no—
1219Q8—1228no—
1220Q8—1228no—
1221Q8—1222no—
1222Q8—1224no—
1223Q8—1221no—
1224Q8—1222no—
1225Q8C2×D4×D6112yes—
1226Q8C2×D4×D6114yes—
1227D4—28no—
1228D4—24no—
1229D4—24no—
1230D4—22no—
1231D4—21no—
1232D4—612no—
1233D4—1224no—
1234D4—1224no—
1235D4—1228no—
1236D4—1224no—
1237D4—1224no—
1238D4—1224no—
1239D4—1224no—
1240D4—1228no—
1241D4—1228no—
1242D4—1224no—
1243D4—1224no—
1244D4—1222no—
1245D4—1221no—
1246D4—1222no—
1247D4—1222no—
1248D4—4884no—
1249D4—4884no—
1250D4—2444no—
1251D4—2444no—
1252D4—2442no—
1253D4C2×D4×D6112yes—
1254C2×C4—28no—
1255C2×C4—28no—
1256C2×C4—24no—
1257C2×C4—22no—
1258C2×C4—21no—
1259C2×C4—24no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—42no—
1265C2×C4—614no—
1266C2×C4—611no—
1267C2×C4—611no—
1268C2×C4—614no—
1269C2×C4—614no—
1270C2×C4—612no—
1271C2×C4—612no—
1272C2×C4—612no—
1273C2×C4—612no—
1274C2×C4—612no—
1275C2×C4—1224no—
1276C2×C4—1224no—
1277C2×C4—1224no—
1278C2×C4—1224no—
1279C2×C4—1228no—
1280C2×C4—1228no—
1281C2×C4—1228no—
1282C2×C4—1228no—
1283C2×C4—1228no—
1284C2×C4—1228no—
1285C2×C4—1224no—
1286C2×C4—1224no—
1287C2×C4—1228no—
1288C2×C4—1228no—
1289C2×C4—1224no—
1290C2×C4—1222no—
1291C2×C4—1221no—
1292C2×C4—1224no—
1293C2×C4—1222no—
1294C2×C4—1222no—
1295C2×C4—1222no—
1296C2×C4—4882no—
1297C2×C4—2444no—
1298C2×C4—2444no—
1299C2×C4C2×D4×D6112yes—
1300C2×C4C2×D4×D6111yescharacteristic
1301C2×C4C2×D4×D6112yes—
1302C2×C4C2×D4×D6112yes—
1303C2×C4C24×D6111yescharacteristic
1304C8—22no—
1305C8—22no—
1306C8—1222no—
1307C8—1222no—
1308C22—22no—
1309C22—22no—
1310C22—22no—
1311C22—24no—
1312C22—42no—
1313C22—612no—
1314C22—612no—
1315C22—1222no—
1316C22—1222no—
1317C22—1222no—
1318C22—1222no—
1319C22—1224no—
1320C22—4884no—
1321C22—2444no—
1322C22—2448no—
1323C22—2448no—
1324C22—2442no—
1325C22—2444no—
1326C22—2442no—
1327C22#120×D6112yes—
1328C22C22×D4×D6111yescharacteristic
1329C4—24no—
1330C4—22no—
1331C4—22no—
1332C4—42no—
1333C4—42no—
1334C4—612no—
1335C4—612no—
1336C4—1222no—
1337C4—1224no—
1338C4—1222no—
1339C4—2442no—
1340C4#120×D6112yes—
1341C4C22×D4×D6111yescharacteristic
1342C4C22×D4×D6111yescharacteristic
1343C2—22no—
1344C2—42no—
1345C2—42no—
1346C2—1222no—
1347C2—1222no—
1348C2—4882no—
1349C2—2442no—
1350C2—2442no—
1351C2C2×#120×D6111yescharacteristic
1352C2#2146060412yes—
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3011C2
socleC22×C61C23×D4
hypercenter#3011D61
hypocenterC61#60368
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3011

Complements

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

NH ≅ G/Ntype
1. C2×2−1+4×D61C2semidirect
2. C2×#16840561C2semidirect
3. C22×#14519809C2semidirect
4. #21459151C2semidirect
5. #21455138C2semidirect
6. #21455135C2semidirect
7. #21455113C2semidirect
8. #21455112C2semidirect
9. #21455110C2semidirect
10. #21455108C2semidirect
11. #21455107C2semidirect
12. #21455106C2semidirect
13. #21455105C2semidirect
14. #21455062C2semidirect
15. #21455054C2semidirect
16. #21454334C2semidirect
17. #419×D61C2semidirect
18. #21454261C2semidirect
19. C61×#3011C2semidirect
22. C2×#14519825C22semidirect
27. C2×#14519824C22semidirect
35. C2×#41×D61C22semidirect
38. C22×Q8×D61C22semidirect
43. C2×#14519809C22semidirect
44. C2×#14519808C22semidirect
45. C2×#14519805C22semidirect
47. C2×#14519802C22semidirect
48. C2×#14519800C22semidirect
49. C2×#14519798C22semidirect
50. C22×#11758202C22semidirect
51. C22×#11758190C22semidirect
52. C22×#11758201C22semidirect
55. #16840342C22semidirect
57. #16840336C22semidirect
58. #16840331C22semidirect
60. #16840326C22semidirect
67. #16839923C22semidirect
68. #16839922C22semidirect
69. #16839921C22semidirect
70. #16839917C22semidirect
71. #16839916C22semidirect
72. #16839916C22semidirect
73. #16839910C22semidirect
74. #16839909C22semidirect
75. #16839908C22semidirect
76. #16839907C22semidirect
77. #16839903C22semidirect
78. #16839902C22semidirect
79. #16839902C22semidirect
80. #16839901C22semidirect
81. #16839772C22semidirect
82. #16839771C22semidirect
83. #16839770C22semidirect
84. #16839769C22semidirect
85. #16839769C22semidirect
86. #16839765C22semidirect
87. #16839762C22semidirect
88. #16839760C22semidirect
89. #16839759C22semidirect
90. #16839758C22semidirect
91. #16839756C22semidirect
92. #103×D61C22semidirect
93. #16839730C22semidirect
94. #16839729C22semidirect
95. #16839728C22semidirect
96. #16839727C22semidirect
97. #16839724C22semidirect
99. C2×#137×C61C22semidirect
100. C22×Q16×C61C22semidirect
101. C61×#536C22semidirect
102. C61×#452C22semidirect
103. C61×#451C22semidirect
104. C61×#419C22semidirect
105. C61×#416C22semidirect
106. C61×#408C22semidirect
160. #41×D61D4semidirect
179. C2×Q8×D61D4semidirect
676. #3011D61semidirect
722. C2×#137C2×D61semidirect
729. C22×Q16C2×D61semidirect
737. #536C2×D61semidirect
750. #452C2×D61semidirect
754. #451C2×D61semidirect
768. #419C2×D61semidirect
775. #416C2×D61semidirect
781. #408C2×D61semidirect
783. C61#60368semidirect

Maximal subgroups

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

subgroupindex
C2×2−1+4×D612
C2×#168405612
C22×#145198092
#214591512
#214551382
#214551352
#214551132
#214551122
#214551102
#214551082
#214551072
#214551062
#214551052
#214550622
#214550542
#214543342
#419×D612
#214542612
C61×#30112
#6036861