Finite Group Databasebeta

← #30555931

Subgroups — #30555931

Order 15616.

2810 conjugacy classes of subgroups.

The subgroup lattice has 1110 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840572C211yesmaximal, characteristic, complemented
2C2×#16840565C211yesmaximal, characteristic, complemented
3#21459607C211yesmaximal, characteristic, complemented
4#21459594C211yesmaximal, characteristic, complemented
5#21457397C214yesmaximal, complemented
6#21457357C214yesmaximal, complemented
7#21457317C214yesmaximal, complemented
8#21457292C214yesmaximal, complemented
9C2×#16840150C211yesmaximal, characteristic, complemented
10#21455466C211yesmaximal, characteristic, complemented
11#21455455C211yesmaximal, characteristic, complemented
12#21455312C211yesmaximal, characteristic, complemented
13#21455297C211yesmaximal, characteristic, complemented
14#21455108C211yesmaximal, characteristic, complemented
15#21455098C211yesmaximal, characteristic, complemented
16#21455083C211yesmaximal, characteristic, complemented
17#21454615C211yesmaximal, characteristic, complemented
18#21454534C211yesmaximal, characteristic, complemented
19C61×#3008C211yesmaximal, characteristic, complemented
20C2×#14519824C2211yescharacteristic, complemented
21C2×#14519823C2211yescharacteristic
22C2×#14519822C2211yescharacteristic, complemented
23#16840572—28no—
24#16840565—28no—
25C2×#14519810C2211yescharacteristic, complemented
26C2×#14519806C2212yescomplemented
27C2×#14519803C2211yescharacteristic
28C2×#14519803C2212yescomplemented
29C2×#14519802C2211yescharacteristic, complemented
30C2×#14519802C2212yescomplemented
31C2×#14519801C2212yescomplemented
32C2×#14519797C2211yescharacteristic
33C2×#14519797C2212yescomplemented
34C2×#14519796C2212yescomplemented
35C22×#11758190C2211yescharacteristic, complemented
36C22×#11758200C2211yescharacteristic, complemented
37C2×SD16×D61C2212yescomplemented
38C22×#11758199C2211yescharacteristic, complemented
39C22×#11758199C2212yescomplemented
40C2×#14519785C2211yescharacteristic, complemented
41C2×#14519784C2211yescharacteristic, complemented
42#16840430C2214yescomplemented
43#16840419C2214yescomplemented
44#16840406—24no—
45#16840406C2214yescomplemented
46#16840396C2214yescomplemented
47#16840394—24no—
48#16840333—21no—
49#16840333C2211yescharacteristic, complemented
50#16840331C2211yescharacteristic, complemented
51#16840330—21no—
52#16840329—21no—
53#16840329C2211yescharacteristic, complemented
54#16840325—21no—
55#16840311—21no—
56#16840308—21no—
57#16840308C2211yescharacteristic
58C2×#14519773C2211yescharacteristic, complemented
59#127×D61—21no—
60C2×#14519764—21no—
61C2×#14519764C2211yescharacteristic, complemented
62#41×Dic61C2211yescharacteristic, complemented
63#16840230C2211yescharacteristic, complemented
64#16840150C2214yescomplemented
65#16840150C2214yescomplemented
66#16840014C2214yescomplemented
67#16840006C2214yescomplemented
68#16839997C2214yescomplemented
69#16839989C2214yescomplemented
70#16839983C2214yescomplemented
71#16839976C2214yescomplemented
72#16839960C2214yescomplemented
73#16839955C2214yescomplemented
74#16839926C2214yescomplemented
75#16839915C2214yescomplemented
76#16839908C2214yescomplemented
77#16839904C2214yescomplemented
78#16839902C2214yescomplemented
79#16839894C2214yescomplemented
80#16839871C2212yescomplemented
81#16839866C2212yescomplemented
82#16839865C2212yescomplemented
83#16839859C2212yescomplemented
84#16839836C2214yescomplemented
85#16839830C2214yescomplemented
86#16839798C2211yescharacteristic, complemented
87#16839785C2211yescharacteristic, complemented
88#16839770C2211yescharacteristic, complemented
89#16839768C2211yescharacteristic, complemented
90#16839767C2211yescharacteristic, complemented
91#16839759C2211yescharacteristic, complemented
92#16839728C2211yescharacteristic, complemented
93C2×#14519687C2211yescharacteristic, complemented
94C2×H(5,𝔽2)×C61C2211yescharacteristic, complemented
95C2×AGL(1,ℤ/8)×C61C2211yescharacteristic, complemented
96C22×D8×C61C2211yescharacteristic, complemented
97C61×#535C2211yescharacteristic
98C61×#449C2214yescomplemented
99C61×#447C2214yescomplemented
100C61×#418C2211yescharacteristic, complemented
101C61×#416C2211yescharacteristic, complemented
102C61×#408C2211yescharacteristic, complemented
103#14519824—24no—
104#14519824—42no—
105#14519823—24no—
106#14519823—42no—
107#14519822—24no—
108#14519822—42no—
109C2×#11758226—21no—
110C2×#11758222—21no—
111C2×#11758222C2311yescharacteristic
112C2×#11758222C2312yes—
113C2×#11758222C2311yescharacteristic
114C2×#11758224—22no—
115C2×#11758224—21no—
116C2×#11758224C2312yes—
117C2×#11758224C2312yes—
118C22×Dic122—21no—
119C22×Dic122C2311yescharacteristic
120C2×Q8×D61C2312yes—
121C22×D244C2311yescharacteristic
122C22×D244C2312yes—
123C22×C22⋊D61—22no—
124C22×C22⋊D61—22no—
125C2×D4×D61—21no—
126C2×D4×D61—22no—
127C2×D4×D61—24no—
128C2×D4×D61—21no—
129C2×D4×D61C2312yes—
130#14519810—24no—
131#14519806—28no—
132#14519803—24no—
133#14519803—28no—
134#14519802—24no—
135#14519802—28no—
136#14519801—28no—
137#14519797—28no—
138#14519797D418yescomplemented
139#14519796—28no—
140C2×Dic244C2312yes—
141C2×#11758202C2311yescharacteristic
142C2×#11758190—42no—
143C2×#11758190C2312yes—
144C2×#11758190C2314yes—
145C2×#11758200—24no—
146C2×#11758200C2312yes—
147C2×#11758200C2312yes—
148C2×#11758200C2312yes—
149C2×#11758200C2311yescharacteristic
150C2×#11758201C2312yes—
151C2×#11758201C2311yescharacteristic
152SD16×D61—28no—
153C2×#11758199—28no—
154C2×#11758199—24no—
155C2×#11758199C2312yes—
156C2×#11758199C2312yes—
157C2×#11758199C2312yes—
158C2×#11758199C2312yes—
159C2×#11758199C2311yescharacteristic
160#14519785—24no—
161#14519784—24no—
162C2×#11758194C2311yescharacteristic
163C2×#11758194C2312yes—
164C2×#11758189C2312yes—
165C22×#92418C2312yes—
166C22×#92418C2311yescharacteristic
167C2×C8×D61C2312yes—
168#14519775—21no—
169#14519775D411yescharacteristic
170#14519774—21no—
171#14519773—24no—
172#14519773—21no—
173#14519773—21no—
174#14519773—21no—
175#14519773D411yescharacteristic
176#14519773C2314yes—
177#14519766D411yescharacteristic
178#14519765—21no—
179#14519764—21no—
180#14519764—21no—
181#14519764—24no—
182#14519764—21no—
183#14519764—21no—
184#14519764D411yescharacteristic
185#14519764C2314yes—
186#14519758—22no—
187#14519758—24no—
188#14519756—24no—
189#14519756C2314yes—
190#14519752C2314yes—
191#14519750—24no—
192#14519750—24no—
193#14519749—24no—
194#14519749—24no—
195#14519749D414yes—
196#14519748—24no—
197#14519748C2314yes—
198#14519747—22no—
199#14519747—24no—
200#14519746—24no—
201#14519746—22no—
202#14519745—24no—
203Q8×Dic61C2312yes—
204#14519742C2312yes—
205D4×Dic61—22no—
206D4×Dic61C2312yes—
207#14519739C2312yes—
208C4×C22⋊D61—24no—
209C4×C22⋊D61C2314yes—
210#14519737—22no—
211#14519737—24no—
212#14519736—21no—
213#14519736C2311yescharacteristic
214#14519734—21no—
215C2×C22⋊Dic61—22no—
216C2×C22⋊Dic61—24no—
217C2×C4×Dic61—21no—
218C2×C4×Dic61C2311yescharacteristic
219C42×D61—21no—
220#14519710C2312yes—
221#14519708C2312yes—
222#14519706C2314yes—
223#14519702C2312yes—
224#14519700C2314yes—
225#14519699C2314yes—
226#14519699C2312yes—
227#14519698C2314yes—
228#14519689C2314yes—
229#14519687C2312yes—
230#14519687C2312yes—
231H(5,𝔽2)×C61—24no—
232H(5,𝔽2)×C61—42no—
233C2×#41×C61—21no—
234C2×#41×C61C2312yes—
235C2×#41×C61C2311yescharacteristic
236C2×#41×C61C2311yescharacteristic
237C22×D4×C61—21no—
238C22×D4×C61—22no—
239C22×D4×C61C2311yescharacteristic
240C22×D4×C61C2311yescharacteristic
241C22×D4×C61C2312yes—
242AGL(1,ℤ/8)×C61—24no—
243C2×SD16×C61C2312yes—
244C2×D8×C61—42no—
245C2×D8×C61C2312yes—
246C2×D8×C61C2314yes—
247C2×M16×C61C2311yescharacteristic
248C22×C8×C61C2311yescharacteristic
249#127×C61—21no—
250#124×C61—21no—
251#121×C61C2314yes—
252#120×C61—22no—
253#117×C61C2311yescharacteristic
254#103×C61C2312yes—
255#102×C61C2314yes—
256#102×C61C2312yes—
257C22⋊C8×C61C2314yes—
258C24×C61—21no—
259C24×C61—22no—
260C24×C61—21no—
261C23×D61—22no—
262C23×D61—21no—
263C23×D61—22no—
264#41×C61—22no—
265#41×C61—22no—
266#41×C61—22no—
267#41×C61—24no—
268#41×C61—42no—
269#41×C61—44no—
270#41×C61C2×D414yescomplemented
271C2×Q8×C61C2×D411yescharacteristic
272C2×Q8×C61C2411yescharacteristic
273C2×D4×C61—21no—
274C2×D4×C61—24no—
275C2×D4×C61—22no—
276C2×D4×C61—24no—
277C2×D4×C61—22no—
278C2×D4×C61—22no—
279C2×D4×C61—21no—
280C2×D4×C61—22no—
281C2×D4×C61—21no—
282C2×D4×C61—22no—
283C2×D4×C61—22no—
284C2×D4×C61—42no—
285C2×D4×C61—44no—
286C2×D4×C61—48no—
287C2×D4×C61C2×D412yes—
288C2×D4×C61C2×D411yescharacteristic
289C2×D4×C61C2412yes—
290C2×D4×C61C2412yes—
291C2×D4×C61C2411yescharacteristic
292C22×C4×C61—21no—
293C22×C4×C61—22no—
294C22×C4×C61C2412yes—
295C22×C4×C61C2411yescharacteristic
296C2×C22⋊D61—21no—
297C2×C22⋊D61—22no—
298C2×C22⋊D61—22no—
299C2×C22⋊D61—22no—
300C2×C22⋊D61—24no—
301C2×C22⋊D61—24no—
302C2×C22⋊D61—22no—
303C2×C22⋊D61—24no—
304C2×C22⋊D61—48no—
305C2×C22⋊D61—84no—
306C2×C22⋊D61C2×D412yes—
307C2×C22⋊D61C2×D414yes—
308C22×Dic61—21no—
309C22×Dic61—22no—
310C22×Dic61—22no—
311C22×Dic61—22no—
312C22×Dic61C2×D412yes—
313#11758226—44no—
314Q8×D61—24no—
315Q8×D61—42no—
316#11758224—24no—
317#11758224—24no—
318#11758224—42no—
319#11758224—42no—
320#11758224—44no—
321#11758224—48no—
322D4×D61—24no—
323D4×D61—42no—
324D4×D61—44no—
325D4×D61—44no—
326D4×D61—48no—
327D4×D61—88no—
328#11758222—22no—
329#11758222—22no—
330#11758222—22no—
331#11758222—24no—
332#11758222—42no—
333#11758222—44no—
334#11758222C2×D414yes—
335C2×D244—22no—
336C2×D244—22no—
337C2×D244—24no—
338C2×D244—22no—
339C2×D244—21no—
340C2×D244—24no—
341C2×D244—42no—
342C2×D244C2×D411yescharacteristic
343C2×D244C2412yes—
344C2×D244C2411yescharacteristic
345C2×C4×D61—21no—
346C2×C4×D61—22no—
347C2×C4×D61—22no—
348C2×C4×D61—22no—
349C2×C4×D61C2412yes—
350C2×Dic122—22no—
351C2×Dic122—22no—
352C2×Dic122—21no—
353C2×Dic122—22no—
354C2×Dic122—44no—
355C2×Dic122C2×D411yescharacteristic
356C2×Dic122C2412yes—
357C2×Dic122C2411yescharacteristic
358SD16×C61—24no—
359D8×C61—24no—
360D8×C61—44no—
361M16×C61—22no—
362C2×C8×C61—22no—
363C2×C8×C61C2412yes—
364C2×C8×C61C2412yes—
365C4⋊C4×C61C2412yes—
366C22⋊C4×C61—21no—
367C22⋊C4×C61—24no—
368C42×C61—21no—
369C22⋊Dic61—24no—
370C22⋊Dic61—21no—
371C22⋊Dic61—24no—
372C22⋊Dic61—24no—
373C22⋊Dic61—24no—
374C22⋊Dic61—22no—
375C22⋊Dic61C2×D414yes—
376#11758202C2×D414yescomplemented
377#11758201—24no—
378#11758201C2×D414yescomplemented
379#11758200—24no—
380#11758200—24no—
381#11758200—24no—
382#11758200C2×D414yescomplemented
383#11758199—24no—
384#11758199—24no—
385#11758199—24no—
386#11758199—24no—
387#11758199C2×D414yescomplemented
388#11758198—22no—
389#11758198—24no—
390#11758198C2×D414yes—
391C4⋊Dic61—22no—
392C4⋊Dic61C2412yes—
393#11758196—24no—
394#11758196—22no—
395#11758196C2×D414yes—
396C4×Dic61—21no—
397C4×Dic61—22no—
398C4×Dic61—22no—
399C4×Dic61C2×D411yescharacteristic
400C4×Dic61C2×D411yescharacteristic
401C4×Dic61C2412yes—
402#11758194—22no—
403#11758194—24no—
404C2×#92418—24no—
405C2×#92418C2×D414yescomplemented
406C2×#92418C2412yes—
407C2×#92418C2411yescharacteristic
408C2×#92418C2411yescharacteristic
409Dic244—24no—
410#11758190—24no—
411#11758190—44no—
412#11758189—24no—
413C8×D61—24no—
414C23×C61—21no—
415C23×C61—22no—
416C23×C61—22no—
417C23×C61—44no—
418C23×C61—42no—
419C23×C61—42no—
420C23×C61—82no—
421C23×C61—82no—
422C23×C61—84no—
423C23×C61C22×D412yes—
424C23×C61C22×D411yescharacteristic
425C22×D61—21no—
426C22×D61—22no—
427C22×D61—44no—
428C22×D61—44no—
429C22×D61—42no—
430C22×D61—84no—
431C22×D61—84no—
432C22×D61—82no—
433C22×D61C22×D412yes—
434Q8×C61—22no—
435Q8×C61—21no—
436Q8×C61C22×D412yes—
437D4×C61—24no—
438D4×C61—24no—
439D4×C61—22no—
440D4×C61—22no—
441D4×C61—22no—
442D4×C61—21no—
443D4×C61—22no—
444D4×C61—22no—
445D4×C61—44no—
446D4×C61—44no—
447D4×C61—42no—
448D4×C61—42no—
449D4×C61—84no—
450D4×C61C22×D412yes—
451C2×C4×C61—21no—
452C2×C4×C61—24no—
453C2×C4×C61—22no—
454C2×C4×C61—22no—
455C2×C4×C61—22no—
456C2×C4×C61—44no—
457C2×C4×C61C22×D412yes—
458C2×C4×C61C22×D411yescharacteristic
459C2×C4×C61C22×D412yes—
460C2×C4×C61H(5,𝔽2)12yes—
461C2×C4×C61C2511yescharacteristic
462C22⋊D61—24no—
463C22⋊D61—24no—
464C22⋊D61—44no—
465C22⋊D61—44no—
466C22⋊D61—44no—
467C22⋊D61—44no—
468C22⋊D61—48no—
469C22⋊D61—44no—
470C22⋊D61—84no—
471C22⋊D61—84no—
472C2×Dic61—21no—
473C2×Dic61—22no—
474C2×Dic61—22no—
475C2×Dic61—42no—
476C2×Dic61—44no—
477C2×Dic61—44no—
478C2×Dic61—42no—
479C2×Dic61—82no—
480C2×Dic61C22×D412yes—
481C2×Dic61C22×D412yes—
482C2×Dic61C22×D412yes—
483D244—22no—
484D244—22no—
485D244—21no—
486D244—22no—
487D244—44no—
488D244—42no—
489D244—84no—
490D244C22×D412yes—
491C4×D61—24no—
492C4×D61—22no—
493C4×D61—22no—
494C4×D61—44no—
495C4×D61—44no—
496C4×D61—44no—
497Dic122—22no—
498Dic122—21no—
499Dic122—22no—
500Dic122—22no—
501Dic122—44no—
502Dic122—42no—
503Dic122C22×D412yes—
504C8×C61—22no—
505C8×C61—22no—
506#92418—22no—
507#92418C22×D412yes—
508#92418C22×D412yes—
509#61082—611nomaximal, Sylow
510C22×C61—22no—
511C22×C61—24no—
512C22×C61—22no—
513C22×C61—22no—
514C22×C61—42no—
515C22×C61—44no—
516C22×C61—44no—
517C22×C61—42no—
518C22×C61—42no—
519C22×C61—162no—
520C22×C61—162no—
521C22×C61—164no—
522C22×C61D4212yes—
523C22×C61C23×D411yescharacteristic
524C2×D61—24no—
525C2×D61—22no—
526C2×D61—22no—
527C2×D61—42no—
528C2×D61—44no—
529C2×D61—42no—
530C2×D61—164no—
531C2×D61—164no—
532C2×D61—162no—
533C4×C61—22no—
534C4×C61—22no—
535C4×C61—42no—
536C4×C61D4212yes—
537C4×C61C23×D411yescharacteristic
538C4×C61C2×H(5,𝔽2)11yescharacteristic
539Dic61—22no—
540Dic61—22no—
541Dic61—22no—
542Dic61—22no—
543Dic61—42no—
544Dic61—42no—
545C2×#577—611no—
546C2×#576—611no—
547#3500—611no—
548#3498—611no—
549#3271—614no—
550#3268—614no—
551#3265—614no—
552#3264—614no—
553C2×#496—611no—
554#3058—611no—
555#3057—611no—
556#3040—611no—
557#3038—611no—
558#3010—611no—
559#3009—611no—
560#3008—611no—
561#3008D6111yescharacteristic, complemented
562#2943—611no—
563#2932—611no—
564C2×C61—22no—
565C2×C61—42no—
566C2×C61—42no—
567C2×C61—82no—
568C2×C61—82no—
569C2×C61C2×D4211yescharacteristic
570C2×C61#358512yes—
571D61—42no—
572D61—42no—
573D61—82no—
574C2×2−1+4—611no—
575C2×H(5,𝔽2)—611no—
576C2×H(5,𝔽2)—611no—
577C2×H(5,𝔽2)C2×D6111yescharacteristic, complemented
578#577—1228no—
579#576—1228no—
580C2×#137—612no—
581C2×#137—611no—
582C2×AGL(1,ℤ/8)—612no—
583C2×AGL(1,ℤ/8)—611no—
584C2×AGL(1,ℤ/8)—611no—
585C2×AGL(1,ℤ/8)—612no—
586C2×AGL(1,ℤ/8)—612no—
587C2×AGL(1,ℤ/8)C2×D6111yescharacteristic, complemented
588C2×#135—611no—
589C2×#135—612no—
590C2×#135—612no—
591C22×SD16—611no—
592C22×SD16—612no—
593C22×SD16—611no—
594C22×D8—611no—
595C22×D8—612no—
596C22×D8C2×D6111yescharacteristic, complemented
597C2×#131—611no—
598C2×#131—611no—
599#550—614no—
600#548—614no—
601#546—614no—
602#546—1224no—
603D42—614no—
604D42—1224no—
605#536—611no—
606#536—1221no—
607#535—611no—
608#535—611no—
609#535—1221no—
610#535—1221no—
611#535—1221no—
612#535C2×D6111yescharacteristic
613#532—611no—
614#532—1221no—
615#532—1221no—
616C2×#127—611no—
617C2×#127—1221no—
618C2×#124—611no—
619C2×#124—1221no—
620C4×#41—611no—
621C4×#41—611no—
622#496—614no—
623#496—614no—
624#469—614no—
625#468—614no—
626#466—614no—
627#465—614no—
628#464—614no—
629#463—614no—
630#460—614no—
631#459—614no—
632#452—614no—
633#450—614no—
634#449—614no—
635#449—614no—
636#449C2×D6114yescomplemented
637#448—614no—
638#447—614no—
639#447C2×D6114yescomplemented
640#442—612no—
641#441—612no—
642#440—612no—
643#440—612no—
644#435—614no—
645#435—614no—
646#427—611no—
647#423—611no—
648#419—611no—
649#418—611no—
650#418—611no—
651#418C2×D6111yescharacteristic, complemented
652#416—611no—
653#416C2×D6111yescharacteristic, complemented
654#408—611no—
655#408C2×D6111yescharacteristic, complemented
656C2×#97—611no—
657C61#6108211yescharacteristic, complemented, Sylow
6582−1+4—1224no—
6592−1+4—2442no—
660H(5,𝔽2)—24no—
661H(5,𝔽2)—42no—
662H(5,𝔽2)—1224no—
663H(5,𝔽2)—1224no—
664H(5,𝔽2)—2442no—
665H(5,𝔽2)—2442no—
666C2×#41—21no—
667C2×#41—611no—
668C2×#41—612no—
669C2×#41—612no—
670C2×#41—611no—
671C2×#41—612no—
672C2×#41—1221no—
673C2×#41—1222no—
674C2×#41—1221no—
675C2×#41—1221no—
676C2×#41C22×D6112yes—
677C2×#41C22×D6111yescharacteristic
678C2×#41C22×D6111yescharacteristic
679C22×Q8—612no—
680C22×Q8—611no—
681C22×Q8—1221no—
682C22×D4—21no—
683C22×D4—22no—
684C22×D4—612no—
685C22×D4—611no—
686C22×D4—612no—
687C22×D4—1222no—
688C22×D4—1224no—
689C22×D4—1221no—
690C22×D4—1222no—
691C22×D4—1221no—
692C22×D4—1222no—
693C22×D4C22×D6111yescharacteristic
694C22×D4C22×D6111yescharacteristic
695C22×D4C22×D6112yes—
696#137—1224no—
697#137—1228no—
698AGL(1,ℤ/8)—24no—
699AGL(1,ℤ/8)—1228no—
700AGL(1,ℤ/8)—1228no—
701AGL(1,ℤ/8)—1228no—
702AGL(1,ℤ/8)—1224no—
703AGL(1,ℤ/8)—1224no—
704#135—618no—
705#135—1228no—
706#135—1228no—
707C2×Q16—611no—
708C2×Q16—612no—
709C2×SD16—611no—
710C2×SD16—611no—
711C2×SD16—612no—
712C2×SD16—612no—
713C2×SD16—612no—
714C2×SD16—612no—
715C2×SD16—612no—
716C2×SD16—614no—
717C2×SD16—1224no—
718C2×SD16—1228no—
719C2×SD16—2442no—
720C2×SD16C22×D6112yes—
721C2×D8—42no—
722C2×D8—611no—
723C2×D8—612no—
724C2×D8—612no—
725C2×D8—612no—
726C2×D8—612no—
727C2×D8—1224no—
728C2×D8—1228no—
729C2×D8C22×D6112yes—
730C2×D8C22×D6114yes—
731#131—1224no—
732#131—1224no—
733C2×M16—611no—
734C2×M16—612no—
735C2×M16—612no—
736C2×M16C22×D6111yescharacteristic
737C22×C8—611no—
738C22×C8—612no—
739C22×C8—612no—
740C22×C8C22×D6111yescharacteristic
741C4⋊Q8—611no—
742C4⋊Q8—1221no—
743#127—21no—
744#127—611no—
745#127—614no—
746#127—1221no—
747#127—1221no—
748#127—1221no—
749#127—1224no—
750#127—1221no—
751#124—21no—
752#124—611no—
753#124—611no—
754#124—614no—
755#124—1221no—
756#124—1221no—
757#124—1221no—
758#124—1224no—
759#124—1221no—
760#124—1221no—
761#123—1224no—
762#123—1222no—
763C22⋊Q8—614no—
764C22⋊Q8—1224no—
765#121—614no—
766#121—614no—
767#121—614no—
768#121—1224no—
769#121—1224no—
770#121—1224no—
771#121—1224no—
772#121—1224no—
773#121C22×D6114yes—
774#120—22no—
775#120—1224no—
776#120—1222no—
777#120—1224no—
778#120—1222no—
779#120—1224no—
780C4×Q8—612no—
781C4×Q8—612no—
782C4×D4—614no—
783C4×D4—612no—
784C4×D4—612no—
785C4×D4—1224no—
786C4×D4—1222no—
787C4×D4—1224no—
788C4×D4—1222no—
789#117—611no—
790#117—1221no—
791#117—1221no—
792#117C22×D6111yescharacteristic
793C2×C22⋊C4—1224no—
794C2×C22⋊C4—1222no—
795C2×C42—611no—
796C2×C42—1221no—
797C2×C42—1221no—
798#107—612no—
799#106—612no—
800C4⋊C8—614no—
801#103—612no—
802#103—614no—
803#103C22×D6112yes—
804#102—614no—
805#102—612no—
806#102—614no—
807#102C22×D6112yes—
808#102C22×D6114yes—
809C22⋊C8—614no—
810C22⋊C8C22×D6114yes—
811#97—612no—
812#97—612no—
813C24—22no—
814C24—21no—
815C24—21no—
816C24—1222no—
817C24—1222no—
818C24—1221no—
819#41—22no—
820#41—22no—
821#41—22no—
822#41—24no—
823#41—42no—
824#41—44no—
825#41—614no—
826#41—1224no—
827#41—1222no—
828#41—1222no—
829#41—1222no—
830#41—1224no—
831#41—1224no—
832#41—2442no—
833#41—2444no—
834#41—2442no—
835#41—2442no—
836#41—2444no—
837#41—2444no—
838#41—2448no—
839#41D4×D6114yescomplemented
840C2×Q8—611no—
841C2×Q8—611no—
842C2×Q8—612no—
843C2×Q8—1222no—
844C2×Q8—1221no—
845C2×Q8—1224no—
846C2×Q8—1222no—
847C2×Q8—1222no—
848C2×Q8—2444no—
849C2×Q8—2442no—
850C2×Q8D4×D6111yescharacteristic
851C2×Q8C23×D6111yescharacteristic
852C2×D4—21no—
853C2×D4—24no—
854C2×D4—22no—
855C2×D4—24no—
856C2×D4—22no—
857C2×D4—22no—
858C2×D4—22no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—22no—
862C2×D4—22no—
863C2×D4—42no—
864C2×D4—44no—
865C2×D4—48no—
866C2×D4—612no—
867C2×D4—614no—
868C2×D4—611no—
869C2×D4—611no—
870C2×D4—612no—
871C2×D4—1224no—
872C2×D4—1224no—
873C2×D4—1224no—
874C2×D4—1224no—
875C2×D4—1222no—
876C2×D4—1224no—
877C2×D4—1221no—
878C2×D4—1224no—
879C2×D4—1222no—
880C2×D4—1222no—
881C2×D4—1222no—
882C2×D4—1222no—
883C2×D4—1222no—
884C2×D4—1221no—
885C2×D4—1222no—
886C2×D4—4888no—
887C2×D4—4884no—
888C2×D4—2442no—
889C2×D4—2442no—
890C2×D4—2444no—
891C2×D4—2444no—
892C2×D4—2448no—
893C2×D4—2448no—
894C2×D4D4×D6112yes—
895C2×D4D4×D6111yescharacteristic
896C2×D4C23×D6112yes—
897C2×D4C23×D6112yes—
898C2×D4C23×D6111yescharacteristic
899C22×C4—21no—
900C22×C4—22no—
901C22×C4—612no—
902C22×C4—612no—
903C22×C4—1222no—
904C22×C4—1222no—
905C22×C4—1222no—
906C22×C4—1222no—
907C22×C4—1222no—
908C22×C4—1221no—
909C22×C4—1221no—
910C22×C4—1222no—
911C22×C4C23×D6112yes—
912C22×C4C23×D6111yescharacteristic
913Q16—614no—
914Q16—1224no—
915SD16—24no—
916SD16—614no—
917SD16—614no—
918SD16—1224no—
919SD16—1224no—
920SD16—1224no—
921SD16—1224no—
922SD16—1224no—
923SD16—2444no—
924D8—24no—
925D8—44no—
926D8—614no—
927D8—1224no—
928D8—1224no—
929D8—1224no—
930D8—1224no—
931M16—22no—
932M16—1224no—
933M16—1224no—
934M16—1222no—
935C2×C8—22no—
936C2×C8—614no—
937C2×C8—611no—
938C2×C8—611no—
939C2×C8—612no—
940C2×C8—1224no—
941C2×C8—1224no—
942C2×C8C23×D6112yes—
943C2×C8C23×D6112yes—
944C4⋊C4—614no—
945C4⋊C4—612no—
946C4⋊C4—1222no—
947C4⋊C4—1222no—
948C4⋊C4—1224no—
949C4⋊C4C23×D6112yes—
950C22⋊C4—21no—
951C22⋊C4—24no—
952C22⋊C4—614no—
953C22⋊C4—614no—
954C22⋊C4—1222no—
955C22⋊C4—1224no—
956C22⋊C4—1224no—
957C22⋊C4—1224no—
958C22⋊C4—1224no—
959C22⋊C4—1222no—
960C22⋊C4—1224no—
961C22⋊C4—1221no—
962C42—21no—
963C42—611no—
964C42—611no—
965C42—612no—
966C42—1222no—
967C42—1222no—
968C42—1221no—
969C23—21no—
970C23—22no—
971C23—22no—
972C23—44no—
973C23—42no—
974C23—42no—
975C23—82no—
976C23—82no—
977C23—84no—
978C23—612no—
979C23—1221no—
980C23—1222no—
981C23—4882no—
982C23—4884no—
983C23—4884no—
984C23—2444no—
985C23—2444no—
986C23—2442no—
987C23C2×D4×D6112yes—
988C23C2×D4×D6111yescharacteristic
989Q8—21no—
990Q8—22no—
991Q8—612no—
992Q8—1221no—
993Q8—1222no—
994Q8—1222no—
995Q8—1222no—
996Q8—2444no—
997Q8—2442no—
998Q8C2×D4×D6112yes—
999D4—24no—
1000D4—24no—
1001D4—22no—
1002D4—22no—
1003D4—21no—
1004D4—22no—
1005D4—22no—
1006D4—22no—
1007D4—44no—
1008D4—44no—
1009D4—42no—
1010D4—42no—
1011D4—84no—
1012D4—612no—
1013D4—1224no—
1014D4—1224no—
1015D4—1222no—
1016D4—1221no—
1017D4—1222no—
1018D4—1222no—
1019D4—4884no—
1020D4—4884no—
1021D4—4884no—
1022D4—2444no—
1023D4—2444no—
1024D4—2444no—
1025D4—2444no—
1026D4—2444no—
1027D4—2448no—
1028D4—2444no—
1029D4—2442no—
1030D4C2×D4×D6112yes—
1031C2×C4—21no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—24no—
1035C2×C4—22no—
1036C2×C4—44no—
1037C2×C4—612no—
1038C2×C4—612no—
1039C2×C4—612no—
1040C2×C4—1221no—
1041C2×C4—1222no—
1042C2×C4—1222no—
1043C2×C4—1224no—
1044C2×C4—1222no—
1045C2×C4—1222no—
1046C2×C4—4882no—
1047C2×C4—2444no—
1048C2×C4—2444no—
1049C2×C4—2444no—
1050C2×C4—2442no—
1051C2×C4—2444no—
1052C2×C4—2444no—
1053C2×C4—2442no—
1054C2×C4C2×D4×D6112yes—
1055C2×C4C2×D4×D6112yes—
1056C2×C4C2×D4×D6111yescharacteristic
1057C2×C4#1451982212yes—
1058C2×C4C24×D6111yescharacteristic
1059C8—22no—
1060C8—22no—
1061C8—612no—
1062C8—612no—
1063C8—1222no—
1064C22—22no—
1065C22—22no—
1066C22—22no—
1067C22—24no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—44no—
1072C22—44no—
1073C22—162no—
1074C22—162no—
1075C22—164no—
1076C22—1222no—
1077C22—1222no—
1078C22—1224no—
1079C22—9762no—
1080C22—9764no—
1081C22—9764no—
1082C22—2442no—
1083C22—2444no—
1084C22—2442no—
1085C22#1684039412yes—
1086C22C22×D4×D6111yescharacteristic
1087C4—22no—
1088C4—22no—
1089C4—42no—
1090C4—1222no—
1091C4—1222no—
1092C4—1222no—
1093C4—1222no—
1094C4—2442no—
1095C4—2442no—
1096C4#1684039412yes—
1097C4C22×D4×D6111yescharacteristic
1098C4C2×#1451982211yescharacteristic
1099C2—22no—
1100C2—42no—
1101C2—42no—
1102C2—82no—
1103C2—82no—
1104C2—4882no—
1105C2—2442no—
1106C2—2442no—
1107C2C2×#1684039411yescharacteristic
1108C2#2146059412yes—
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3008C2
socleC22×C61C23×D4
hypercenter#3008D61
hypocenterC61#61082
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3008

Complements

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

NH ≅ G/Ntype
1. C2×#16840572C2semidirect
2. C2×#16840565C2semidirect
3. #21459607C2semidirect
4. #21459594C2semidirect
5. #21457397C2semidirect
6. #21457357C2semidirect
7. #21457317C2semidirect
8. #21457292C2semidirect
9. C2×#16840150C2semidirect
10. #21455466C2semidirect
11. #21455455C2semidirect
12. #21455312C2semidirect
13. #21455297C2semidirect
14. #21455108C2semidirect
15. #21455098C2semidirect
16. #21455083C2semidirect
17. #21454615C2semidirect
18. #21454534C2semidirect
19. C61×#3008C2semidirect
20. C2×#14519824C22semidirect
22. C2×#14519822C22semidirect
25. C2×#14519810C22semidirect
26. C2×#14519806C22semidirect
28. C2×#14519803C22semidirect
29. C2×#14519802C22semidirect
30. C2×#14519802C22semidirect
31. C2×#14519801C22semidirect
33. C2×#14519797C22semidirect
34. C2×#14519796C22semidirect
35. C22×#11758190C22semidirect
36. C22×#11758200C22semidirect
37. C2×SD16×D61C22semidirect
38. C22×#11758199C22semidirect
39. C22×#11758199C22semidirect
40. C2×#14519785C22semidirect
41. C2×#14519784C22semidirect
42. #16840430C22semidirect
43. #16840419C22semidirect
45. #16840406C22semidirect
46. #16840396C22semidirect
49. #16840333C22semidirect
50. #16840331C22semidirect
53. #16840329C22semidirect
58. C2×#14519773C22semidirect
61. C2×#14519764C22semidirect
62. #41×Dic61C22semidirect
63. #16840230C22semidirect
64. #16840150C22semidirect
65. #16840150C22semidirect
66. #16840014C22semidirect
67. #16840006C22semidirect
68. #16839997C22semidirect
69. #16839989C22semidirect
70. #16839983C22semidirect
71. #16839976C22semidirect
72. #16839960C22semidirect
73. #16839955C22semidirect
74. #16839926C22semidirect
75. #16839915C22semidirect
76. #16839908C22semidirect
77. #16839904C22semidirect
78. #16839902C22semidirect
79. #16839894C22semidirect
80. #16839871C22semidirect
81. #16839866C22semidirect
82. #16839865C22semidirect
83. #16839859C22semidirect
84. #16839836C22semidirect
85. #16839830C22semidirect
86. #16839798C22semidirect
87. #16839785C22semidirect
88. #16839770C22semidirect
89. #16839768C22semidirect
90. #16839767C22semidirect
91. #16839759C22semidirect
92. #16839728C22semidirect
93. C2×#14519687C22semidirect
94. C2×H(5,𝔽2)×C61C22semidirect
95. C2×AGL(1,ℤ/8)×C61C22semidirect
96. C22×D8×C61C22semidirect
98. C61×#449C22semidirect
99. C61×#447C22semidirect
100. C61×#418C22semidirect
101. C61×#416C22semidirect
102. C61×#408C22semidirect
138. #14519797D4semidirect
270. #41×C61C2×D4semidirect
376. #11758202C2×D4semidirect
378. #11758201C2×D4semidirect
382. #11758200C2×D4semidirect
387. #11758199C2×D4semidirect
405. C2×#92418C2×D4semidirect
561. #3008D61semidirect
577. C2×H(5,𝔽2)C2×D61semidirect
587. C2×AGL(1,ℤ/8)C2×D61semidirect
596. C22×D8C2×D61semidirect
636. #449C2×D61semidirect
639. #447C2×D61semidirect
651. #418C2×D61semidirect
653. #416C2×D61semidirect
655. #408C2×D61semidirect
657. C61#61082semidirect
839. #41D4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168405722
C2×#168405652
#214596072
#214595942
#214573972
#214573572
#214573172
#214572922
C2×#168401502
#214554662
#214554552
#214553122
#214552972
#214551082
#214550982
#214550832
#214546152
#214545342
C61×#30082
#6108261