Finite Group Databasebeta

← #30555937

Subgroups — #30555937

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×#16840568C211yesmaximal, characteristic, complemented
2C2×#16840567C211yesmaximal, characteristic, complemented
3#21459608C211yesmaximal, characteristic, complemented
4#21459594C211yesmaximal, characteristic, complemented
5#21457401C214yesmaximal, complemented
6#21457366C214yesmaximal, complemented
7#21457321C214yesmaximal, complemented
8#21457296C214yesmaximal, complemented
9C2×#16840148C211yesmaximal, characteristic, complemented
10#21455468C211yesmaximal, characteristic, complemented
11#21455316C211yesmaximal, characteristic, complemented
12#21455298C211yesmaximal, characteristic, complemented
13#21455106C211yesmaximal, characteristic, complemented
14#21455094C211yesmaximal, characteristic, complemented
15#21455088C211yesmaximal, characteristic, complemented
16#21455085C211yesmaximal, characteristic, complemented
17#21454619C211yesmaximal, characteristic, complemented
18#21454535C211yesmaximal, characteristic, complemented
19C61×#3057C211yesmaximal, characteristic, complemented
20C2×#14519825C2211yescharacteristic, complemented
21C2×#14519823C2211yescharacteristic
22C2×#14519823C2211yescharacteristic, complemented
23C2×#14519822C2211yescharacteristic, complemented
24#16840568—28no—
25#16840567—28no—
26C2×#14519808C2211yescharacteristic, complemented
27C2×#14519806C2212yescomplemented
28C2×#14519805C2211yescharacteristic
29C2×#14519805C2211yescharacteristic, complemented
30C2×#14519805C2212yescomplemented
31C2×#14519805C2212yescomplemented
32C2×#14519804C2212yescomplemented
33C2×#14519803C2211yescharacteristic, complemented
34C2×#14519799C2211yescharacteristic
35C2×#14519799C2212yescomplemented
36C2×#14519798C2212yescomplemented
37C22×#11758201C2211yescharacteristic, complemented
38C2×SD16×D61C2212yescomplemented
39C22×D488C2211yescharacteristic, complemented
40C22×D488C2212yescomplemented
41C22×#11758199C2211yescharacteristic, complemented
42C2×#14519783C2211yescharacteristic, complemented
43#16840430C2214yescomplemented
44#16840422C2214yescomplemented
45#16840404—24no—
46#16840403C2214yescomplemented
47#16840396C2214yescomplemented
48#16840394—24no—
49#16840337—21no—
50#16840331C2211yescharacteristic, complemented
51#16840331C2211yescharacteristic, complemented
52#16840330—21no—
53#16840330—21no—
54#16840325—21no—
55#16840313—21no—
56#16840311—21no—
57#16840308C2211yescharacteristic
58C2×#14519773C2211yescharacteristic, complemented
59#127×D61—21no—
60C2×#14519766C2211yescharacteristic, complemented
61#124×D61—21no—
62#16840230C2211yescharacteristic, complemented
63#16840230C2211yescharacteristic, complemented
64#16840148C2214yescomplemented
65#16840148C2214yescomplemented
66#16840016C2214yescomplemented
67#16839999C2214yescomplemented
68#16839987C2214yescomplemented
69#16839980C2214yescomplemented
70#16839961C2214yescomplemented
71#16839956C2214yescomplemented
72#16839922C2214yescomplemented
73#16839912C2214yescomplemented
74#16839910C2214yescomplemented
75#16839908C2214yescomplemented
76#16839905C2214yescomplemented
77#16839902C2214yescomplemented
78#16839897C2214yescomplemented
79#16839895C2214yescomplemented
80#16839873C2212yescomplemented
81#16839868C2212yescomplemented
82#16839861C2212yescomplemented
83#16839861C2212yescomplemented
84#16839833C2214yescomplemented
85#16839831C2214yescomplemented
86#16839785C2211yescharacteristic, complemented
87#16839766C2211yescharacteristic, complemented
88#16839766C2211yescharacteristic, complemented
89#16839756C2211yescharacteristic, complemented
90#16839756C2211yescharacteristic, complemented
91#16839730C2211yescharacteristic, complemented
92#16839729C2211yescharacteristic, complemented
93C2×#14519687C2211yescharacteristic, complemented
94C22×SD16×C61C2211yescharacteristic, complemented
95C2×#131×C61C2211yescharacteristic, complemented
96C61×#536C2211yescharacteristic, complemented
97C61×#535C2211yescharacteristic
98C61×#468C2214yescomplemented
99C61×#465C2214yescomplemented
100C61×#427C2211yescharacteristic, complemented
101C61×#419C2211yescharacteristic, complemented
102C61×#418C2211yescharacteristic, complemented
103#14519825—24no—
104#14519825—42no—
105#14519823—24no—
106#14519823—24no—
107#14519823—42no—
108#14519823—42no—
109#14519822—24no—
110#14519822—42no—
111C2×#11758226—21no—
112C2×#11758226—21no—
113C2×#11758226—21no—
114C2×#11758226C2312yes—
115C2×#11758222—22no—
116C2×#11758222C2311yescharacteristic
117C2×#11758222C2312yes—
118C2×#11758222C2312yes—
119C2×#11758222C2311yescharacteristic
120C2×#11758222C2311yescharacteristic
121C2×#11758224—21no—
122C2×#11758224C2312yes—
123C2×Q8×D61—21no—
124C2×Q8×D61C2312yes—
125C22×D244C2311yescharacteristic
126C22×D244C2311yescharacteristic
127C22×D244C2312yes—
128C22×D244C2312yes—
129C22×C22⋊D61—22no—
130C22×C22⋊D61—22no—
131C2×D4×D61—21no—
132C2×D4×D61—21no—
133C2×D4×D61—22no—
134C2×D4×D61—22no—
135C2×D4×D61—24no—
136C2×D4×D61—21no—
137C2×D4×D61C2312yes—
138#14519808—24no—
139#14519806—28no—
140#14519805—24no—
141#14519805—24no—
142#14519805—28no—
143#14519805—28no—
144#14519804—28no—
145#14519803—24no—
146#14519799—28no—
147#14519799D418yescomplemented
148#14519798—28no—
149C2×Dic244C2311yescharacteristic
150C2×#11758202C2312yes—
151C2×#11758190C2312yes—
152C2×#11758190C2312yes—
153C2×#11758190C2311yescharacteristic
154C2×#11758190C2311yescharacteristic
155C2×#11758200C2312yes—
156C2×#11758201—42no—
157C2×#11758201C2312yes—
158C2×#11758201C2314yes—
159SD16×D61—28no—
160C2×D488—24no—
161C2×D488—28no—
162C2×D488C2312yes—
163C2×D488C2312yes—
164C2×D488C2312yes—
165C2×D488C2312yes—
166C2×D488C2311yescharacteristic
167C2×#11758199—42no—
168C2×#11758199C2312yes—
169C2×#11758199C2314yes—
170#14519783—24no—
171C2×#11758194C2311yescharacteristic
172C2×#11758189C2312yes—
173C22×#92418C2311yescharacteristic
174C2×C8×D61C2312yes—
175#14519775D411yescharacteristic
176#14519774—21no—
177#14519774—21no—
178#14519773—24no—
179#14519773—21no—
180#14519773—21no—
181#14519773D411yescharacteristic
182#14519773C2314yes—
183#14519766—21no—
184#14519766—21no—
185#14519766D411yescharacteristic
186#14519766C2314yes—
187#14519765—21no—
188#14519765—21no—
189#14519764D411yescharacteristic
190#14519763—24no—
191#14519762—24no—
192#14519755—24no—
193#14519752—24no—
194#14519752C2314yes—
195#14519752C2314yes—
196#14519750—24no—
197#14519750—24no—
198#14519750—24no—
199#14519749—24no—
200#14519749D414yes—
201#14519747—24no—
202#14519747—22no—
203#14519747—22no—
204#14519747—24no—
205#14519745—24no—
206#14519742C2312yes—
207#14519742C2312yes—
208#14519739—24no—
209#14519739C2312yes—
210#14519739C2312yes—
211C4×C22⋊D61C2314yes—
212#14519737—22no—
213#14519737—22no—
214#14519737—24no—
215#14519734—21no—
216#14519734—21no—
217C2×#11758198—22no—
218C22⋊C4×D61—24no—
219C2×C4×Dic61C2311yescharacteristic
220C42×D61—21no—
221C42×D61—21no—
222#14519706C2314yes—
223#14519700C2312yes—
224#14519700C2312yes—
225#14519697C2314yes—
226#14519697C2314yes—
227#14519697C2312yes—
228#14519697C2312yes—
229C22⋊#92418C2314yes—
230#14519689C2314yes—
231#14519687C2312yes—
232#14519687C2312yes—
233C2×#41×C61C2311yescharacteristic
234C22×Q8×C61C2311yescharacteristic
235C22×D4×C61C2311yescharacteristic
236C2×SD16×C61—24no—
237C2×SD16×C61C2312yes—
238C2×SD16×C61C2312yes—
239#131×C61—24no—
240C2×M16×C61C2311yescharacteristic
241C2×M16×C61C2312yes—
242C22×C8×C61C2312yes—
243C22×C8×C61C2311yescharacteristic
244C4⋊Q8×C61—21no—
245#127×C61—21no—
246#124×C61—21no—
247#124×C61—21no—
248#123×C61—22no—
249C22⋊Q8×C61C2314yes—
250#121×C61C2314yes—
251#120×C61—22no—
252#117×C61C2311yescharacteristic
253#117×C61C2311yescharacteristic
254#107×C61C2312yes—
255#106×C61C2312yes—
256#103×C61C2314yes—
257#102×C61C2314yes—
258C24×C61—21no—
259C23×D61—22no—
260C23×D61—21no—
261C23×D61—22no—
262C23×D61—21no—
263C23×D61—22no—
264#41×C61—22no—
265#41×C61—22no—
266C2×Q8×C61—21no—
267C2×Q8×C61—22no—
268C2×Q8×C61—22no—
269C2×Q8×C61C2×D411yescharacteristic
270C2×Q8×C61C2412yes—
271C2×D4×C61—24no—
272C2×D4×C61—22no—
273C2×D4×C61—21no—
274C2×D4×C61—22no—
275C2×D4×C61C2×D412yes—
276C2×D4×C61C2×D411yescharacteristic
277C2×D4×C61C2412yes—
278C22×C4×C61—21no—
279C22×C4×C61C2412yes—
280C22×C4×C61C2411yescharacteristic
281C2×C22⋊D61—21no—
282C2×C22⋊D61—21no—
283C2×C22⋊D61—22no—
284C2×C22⋊D61—22no—
285C2×C22⋊D61—22no—
286C2×C22⋊D61—24no—
287C2×C22⋊D61—22no—
288C2×C22⋊D61—24no—
289C2×C22⋊D61—48no—
290C2×C22⋊D61—84no—
291C2×C22⋊D61C2×D412yes—
292C2×C22⋊D61C2×D414yes—
293C22×Dic61—22no—
294C22×Dic61C2×D412yes—
295#11758226—24no—
296#11758226—42no—
297#11758226—44no—
298#11758226—44no—
299#11758226—44no—
300Q8×D61—24no—
301Q8×D61—42no—
302Q8×D61—44no—
303#11758224—24no—
304#11758224—42no—
305#11758224—44no—
306D4×D61—24no—
307D4×D61—42no—
308D4×D61—44no—
309D4×D61—44no—
310D4×D61—44no—
311D4×D61—48no—
312D4×D61—48no—
313D4×D61—88no—
314#11758222—22no—
315#11758222—22no—
316#11758222—22no—
317#11758222—22no—
318#11758222—24no—
319#11758222—24no—
320#11758222—42no—
321#11758222—42no—
322#11758222—48no—
323#11758222C2×D414yes—
324#11758222C2×D414yescomplemented
325C2×D244—22no—
326C2×D244—22no—
327C2×D244—22no—
328C2×D244—22no—
329C2×D244—24no—
330C2×D244—24no—
331C2×D244—22no—
332C2×D244—22no—
333C2×D244—22no—
334C2×D244—21no—
335C2×D244—21no—
336C2×D244—24no—
337C2×D244—24no—
338C2×D244—42no—
339C2×D244—42no—
340C2×D244C2×D411yescharacteristic
341C2×D244C2412yes—
342C2×D244C2412yes—
343C2×D244C2411yescharacteristic
344C2×D244C2411yescharacteristic
345C2×C4×D61—21no—
346C2×C4×D61—21no—
347C2×C4×D61—22no—
348C2×C4×D61—22no—
349C2×C4×D61—22no—
350C2×C4×D61—22no—
351C2×C4×D61—22no—
352C2×C4×D61—22no—
353C2×C4×D61C2412yes—
354C2×Dic122—22no—
355C2×Dic122C2×D411yescharacteristic
356C2×Dic122C2411yescharacteristic
357C2×Dic122C2411yescharacteristic
358SD16×C61—24no—
359SD16×C61—24no—
360M16×C61—22no—
361M16×C61—24no—
362C2×C8×C61—24no—
363C2×C8×C61C2×D414yescomplemented
364C2×C8×C61C2412yes—
365C2×C8×C61C2411yescharacteristic
366C2×C8×C61C2411yescharacteristic
367C4⋊C4×C61—24no—
368C4⋊C4×C61C2412yes—
369C4⋊C4×C61C2412yes—
370C22⋊C4×C61—21no—
371C22⋊C4×C61—21no—
372C22⋊C4×C61—24no—
373C22⋊C4×C61—24no—
374C42×C61—21no—
375C42×C61—21no—
376C22⋊Dic61C2×D414yes—
377#11758202—24no—
378#11758201—24no—
379#11758201—44no—
380#11758200—24no—
381#11758199—24no—
382#11758199—44no—
383#11758198—24no—
384#11758198—24no—
385#11758198—24no—
386#11758198—22no—
387#11758198—22no—
388#11758198—24no—
389#11758198C2×D414yes—
390#11758196—22no—
391#11758196—22no—
392#11758196C2×D414yes—
393C4×Dic61—22no—
394C4×Dic61—22no—
395C4×Dic61C2×D411yescharacteristic
396C4×Dic61C2×D411yescharacteristic
397C4×Dic61C2412yes—
398#11758194—22no—
399C2×#92418—22no—
400C2×#92418C2412yes—
401C2×#92418C2412yes—
402Dic244C2×D414yescomplemented
403D488—24no—
404D488—24no—
405D488—24no—
406D488—24no—
407D488C2×D414yescomplemented
408#11758190—24no—
409#11758190—24no—
410#11758190C2×D414yescomplemented
411#11758190C2×D414yescomplemented
412#11758189—24no—
413C8×D61—24no—
414C23×C61—22no—
415C23×C61—42no—
416C23×C61—82no—
417C23×C61C22×D412yes—
418C23×C61C22×D411yescharacteristic
419C22×D61—21no—
420C22×D61—21no—
421C22×D61—22no—
422C22×D61—22no—
423C22×D61—44no—
424C22×D61—44no—
425C22×D61—44no—
426C22×D61—42no—
427C22×D61—42no—
428C22×D61—84no—
429C22×D61—84no—
430C22×D61—82no—
431C22×D61—84no—
432C22×D61—82no—
433C22×D61C22×D412yes—
434Q8×C61—22no—
435Q8×C61—22no—
436Q8×C61—22no—
437Q8×C61—42no—
438D4×C61—24no—
439D4×C61—22no—
440D4×C61—22no—
441D4×C61—22no—
442D4×C61—42no—
443D4×C61—84no—
444C2×C4×C61—22no—
445C2×C4×C61—22no—
446C2×C4×C61—22no—
447C2×C4×C61—22no—
448C2×C4×C61—22no—
449C2×C4×C61—42no—
450C2×C4×C61C22×D412yes—
451C2×C4×C61C22×D411yescharacteristic
452C2×C4×C61C22×D412yes—
453C2×C4×C61H(5,𝔽2)12yes—
454C2×C4×C61C2511yescharacteristic
455C22⋊D61—24no—
456C22⋊D61—24no—
457C22⋊D61—24no—
458C22⋊D61—44no—
459C22⋊D61—44no—
460C22⋊D61—44no—
461C22⋊D61—44no—
462C22⋊D61—44no—
463C22⋊D61—48no—
464C22⋊D61—84no—
465C2×Dic61—21no—
466C2×Dic61—21no—
467C2×Dic61—42no—
468C2×Dic61—44no—
469C2×Dic61C22×D412yes—
470C2×Dic61C22×D412yes—
471C2×Dic61C22×D412yes—
472D244—22no—
473D244—22no—
474D244—22no—
475D244—21no—
476D244—21no—
477D244—22no—
478D244—22no—
479D244—44no—
480D244—44no—
481D244—44no—
482D244—42no—
483D244—42no—
484D244—84no—
485D244—84no—
486D244C22×D412yes—
487D244C22×D412yes—
488C4×D61—24no—
489C4×D61—24no—
490C4×D61—22no—
491C4×D61—22no—
492C4×D61—44no—
493C4×D61—44no—
494C4×D61—44no—
495C4×D61—44no—
496C4×D61—44no—
497C4×D61—82no—
498Dic122—22no—
499Dic122—21no—
500Dic122—21no—
501Dic122—44no—
502Dic122C22×D412yes—
503Dic122C22×D412yes—
504C8×C61—22no—
505C8×C61C22×D412yes—
506C8×C61C22×D412yes—
507#92418—22no—
508#92418—22no—
509#61082—611nomaximal, Sylow
510C22×C61—22no—
511C22×C61—24no—
512C22×C61—22no—
513C22×C61—44no—
514C22×C61—42no—
515C22×C61—162no—
516C22×C61D4212yes—
517C22×C61C23×D411yescharacteristic
518C2×D61—24no—
519C2×D61—22no—
520C2×D61—22no—
521C2×D61—22no—
522C2×D61—42no—
523C2×D61—42no—
524C2×D61—44no—
525C2×D61—44no—
526C2×D61—42no—
527C2×D61—42no—
528C2×D61—164no—
529C2×D61—164no—
530C2×D61—164no—
531C2×D61—162no—
532C2×D61—162no—
533C4×C61—22no—
534C4×C61—42no—
535C4×C61—42no—
536C4×C61—42no—
537C4×C61D4212yes—
538C4×C61C23×D411yescharacteristic
539C4×C61C2×H(5,𝔽2)11yescharacteristic
540Dic61—22no—
541Dic61—22no—
542Dic61—22no—
543Dic61—22no—
544Dic61—22no—
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#3057D6111yescharacteristic, complemented
556#3040—611no—
557#3038—611no—
558#3010—611no—
559#3009—611no—
560#3008—611no—
561#3008—611no—
562#2943—611no—
563#2932—611no—
564C2×C61—22no—
565C2×C61—42no—
566C2×C61—82no—
567C2×C61C2×D4211yescharacteristic
568C2×C61#358512yes—
569D61—42no—
570D61—42no—
571D61—42no—
572D61—82no—
573D61—82no—
574C2×2−1+4—611no—
575C2×H(5,𝔽2)—611no—
576C2×H(5,𝔽2)—611no—
577C2×H(5,𝔽2)—611no—
578#577—1228no—
579#576—1228no—
580C2×#137—611no—
581C2×#137—612no—
582C2×AGL(1,ℤ/8)—611no—
583C2×AGL(1,ℤ/8)—612no—
584C2×AGL(1,ℤ/8)—611no—
585C2×AGL(1,ℤ/8)—612no—
586C2×AGL(1,ℤ/8)—611no—
587C2×AGL(1,ℤ/8)—612no—
588C2×#135—612no—
589C2×#135—611no—
590C2×#135—612no—
591C22×SD16—611no—
592C22×SD16—612no—
593C22×SD16C2×D6111yescharacteristic, complemented
594C22×D8—611no—
595C22×D8—611no—
596C22×D8—612no—
597C2×#131—611no—
598C2×#131C2×D6111yescharacteristic, complemented
599#550—614no—
600#548—614no—
601#546—614no—
602#546—1224no—
603D42—614no—
604D42—1224no—
605#536—1221no—
606#536C2×D6111yescharacteristic, complemented
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#468C2×D6114yescomplemented
626#466—614no—
627#465C2×D6114yescomplemented
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#449—614no—
637#448—614no—
638#447—614no—
639#447—614no—
640#442—612no—
641#441—612no—
642#440—612no—
643#440—612no—
644#435—614no—
645#435—614no—
646#427C2×D6111yescharacteristic, complemented
647#423—611no—
648#419C2×D6111yescharacteristic, complemented
649#418—611no—
650#418—611no—
651#418C2×D6111yescharacteristic, complemented
652#416—611no—
653#416—611no—
654#408—611no—
655#408—611no—
656C2×#97—611no—
657C61#6108211yescharacteristic, complemented, Sylow
6582−1+4—1224no—
6592−1+4—2442no—
660H(5,𝔽2)—1224no—
661H(5,𝔽2)—1224no—
662H(5,𝔽2)—1224no—
663H(5,𝔽2)—2442no—
664H(5,𝔽2)—2442no—
665H(5,𝔽2)—2442no—
666C2×#41—611no—
667C2×#41—612no—
668C2×#41—612no—
669C2×#41—611no—
670C2×#41—611no—
671C2×#41—612no—
672C2×#41—612no—
673C2×#41—1222no—
674C2×#41—1221no—
675C2×#41—1221no—
676C2×#41—1221no—
677C2×#41—1221no—
678C2×#41C22×D6111yescharacteristic
679C22×Q8—612no—
680C22×Q8—1221no—
681C22×Q8C22×D6111yescharacteristic
682C22×D4—612no—
683C22×D4—611no—
684C22×D4—611no—
685C22×D4—612no—
686C22×D4—612no—
687C22×D4—1222no—
688C22×D4—1224no—
689C22×D4—1221no—
690C22×D4—1222no—
691C22×D4—1221no—
692C22×D4—1221no—
693C22×D4—1222no—
694C22×D4—1222no—
695C22×D4C22×D6111yescharacteristic
696#137—1228no—
697#137—1224no—
698AGL(1,ℤ/8)—1228no—
699AGL(1,ℤ/8)—1228no—
700AGL(1,ℤ/8)—1224no—
701AGL(1,ℤ/8)—1224no—
702AGL(1,ℤ/8)—1228no—
703AGL(1,ℤ/8)—1224no—
704#135—618no—
705#135—1228no—
706#135—1228no—
707C2×Q16—612no—
708C2×Q16—611no—
709C2×SD16—24no—
710C2×SD16—612no—
711C2×SD16—612no—
712C2×SD16—614no—
713C2×SD16—611no—
714C2×SD16—611no—
715C2×SD16—612no—
716C2×SD16—612no—
717C2×SD16—1228no—
718C2×SD16—2442no—
719C2×SD16C22×D6112yes—
720C2×SD16C22×D6112yes—
721C2×D8—612no—
722C2×D8—614no—
723C2×D8—611no—
724C2×D8—612no—
725C2×D8—612no—
726C2×D8—612no—
727C2×D8—612no—
728C2×D8—1228no—
729C2×D8—1224no—
730C2×D8—2442no—
731#131—24no—
732#131—1224no—
733C2×M16—611no—
734C2×M16—612no—
735C2×M16C22×D6111yescharacteristic
736C2×M16C22×D6112yes—
737C22×C8—611no—
738C22×C8—612no—
739C22×C8C22×D6112yes—
740C22×C8C22×D6111yescharacteristic
741C4⋊Q8—21no—
742C4⋊Q8—611no—
743#127—21no—
744#127—611no—
745#127—614no—
746#127—1221no—
747#127—1221no—
748#127—1221no—
749#127—1221no—
750#127—1224no—
751#124—21no—
752#124—21no—
753#124—611no—
754#124—611no—
755#124—614no—
756#124—1221no—
757#124—1221no—
758#124—1221no—
759#124—1221no—
760#124—1224no—
761#123—22no—
762#123—1224no—
763C22⋊Q8—1224no—
764C22⋊Q8C22×D6114yes—
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—1222no—
778#120—1224no—
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—1222no—
788C4×D4—1224no—
789#117—1221no—
790#117—1221no—
791#117C22×D6111yescharacteristic
792#117C22×D6111yescharacteristic
793C2×C22⋊C4—1224no—
794C2×C22⋊C4—1222no—
795C2×C42—611no—
796C2×C42—1221no—
797C2×C42—1221no—
798#107C22×D6112yes—
799#106C22×D6112yes—
800C4⋊C8—614no—
801#103—612no—
802#103—612no—
803#103C22×D6114yes—
804#102—612no—
805#102—612no—
806#102—614no—
807#102—614no—
808#102C22×D6114yes—
809C22⋊C8—614no—
810C22⋊C8—614no—
811#97—612no—
812#97—612no—
813C24—21no—
814C24—1222no—
815C24—1222no—
816C24—1221no—
817C24—1222no—
818C24—1221no—
819#41—22no—
820#41—22no—
821#41—614no—
822#41—614no—
823#41—1224no—
824#41—1224no—
825#41—1222no—
826#41—1222no—
827#41—1222no—
828#41—1222no—
829#41—1224no—
830#41—1224no—
831#41—2442no—
832#41—2442no—
833#41—2448no—
834#41—2442no—
835#41—2444no—
836#41—2442no—
837#41—2444no—
838#41—2444no—
839#41—2444no—
840C2×Q8—21no—
841C2×Q8—22no—
842C2×Q8—22no—
843C2×Q8—611no—
844C2×Q8—611no—
845C2×Q8—611no—
846C2×Q8—1222no—
847C2×Q8—1224no—
848C2×Q8—2442no—
849C2×Q8—2444no—
850C2×Q8D4×D6111yescharacteristic
851C2×Q8C23×D6112yes—
852C2×D4—24no—
853C2×D4—22no—
854C2×D4—21no—
855C2×D4—22no—
856C2×D4—612no—
857C2×D4—614no—
858C2×D4—611no—
859C2×D4—611no—
860C2×D4—611no—
861C2×D4—612no—
862C2×D4—612no—
863C2×D4—1224no—
864C2×D4—1224no—
865C2×D4—1224no—
866C2×D4—1224no—
867C2×D4—1222no—
868C2×D4—1224no—
869C2×D4—1224no—
870C2×D4—1222no—
871C2×D4—1224no—
872C2×D4—1221no—
873C2×D4—1221no—
874C2×D4—1222no—
875C2×D4—1222no—
876C2×D4—1222no—
877C2×D4—1222no—
878C2×D4—1222no—
879C2×D4—1222no—
880C2×D4—1222no—
881C2×D4—1221no—
882C2×D4—1221no—
883C2×D4—1222no—
884C2×D4—1222no—
885C2×D4—4888no—
886C2×D4—4884no—
887C2×D4—2442no—
888C2×D4—2442no—
889C2×D4—2442no—
890C2×D4—2444no—
891C2×D4—2444no—
892C2×D4—2444no—
893C2×D4—2448no—
894C2×D4—2448no—
895C2×D4—2448no—
896C2×D4D4×D6112yes—
897C2×D4D4×D6111yescharacteristic
898C2×D4C23×D6112yes—
899C22×C4—21no—
900C22×C4—612no—
901C22×C4—612no—
902C22×C4—1222no—
903C22×C4—1222no—
904C22×C4—1222no—
905C22×C4—1222no—
906C22×C4—1222no—
907C22×C4—1221no—
908C22×C4—1221no—
909C22×C4—1222no—
910C22×C4—1222no—
911C22×C4C23×D6112yes—
912C22×C4C23×D6111yescharacteristic
913Q16—614no—
914Q16—1224no—
915SD16—24no—
916SD16—24no—
917SD16—614no—
918SD16—614no—
919SD16—1224no—
920SD16—1224no—
921SD16—1224no—
922SD16—1224no—
923SD16—2444no—
924D8—614no—
925D8—1224no—
926D8—1224no—
927D8—1224no—
928D8—1224no—
929D8—1224no—
930D8—2444no—
931M16—22no—
932M16—24no—
933M16—1222no—
934M16—1224no—
935C2×C8—24no—
936C2×C8—612no—
937C2×C8—612no—
938C2×C8—1222no—
939C2×C8—1224no—
940C2×C8D4×D6114yescomplemented
941C2×C8C23×D6112yes—
942C2×C8C23×D6111yescharacteristic
943C2×C8C23×D6111yescharacteristic
944C4⋊C4—24no—
945C4⋊C4—614no—
946C4⋊C4—1222no—
947C4⋊C4—1222no—
948C4⋊C4C23×D6112yes—
949C4⋊C4C23×D6112yes—
950C22⋊C4—24no—
951C22⋊C4—21no—
952C22⋊C4—21no—
953C22⋊C4—24no—
954C22⋊C4—614no—
955C22⋊C4—614no—
956C22⋊C4—1224no—
957C22⋊C4—1224no—
958C22⋊C4—1224no—
959C22⋊C4—1222no—
960C22⋊C4—1222no—
961C22⋊C4—1224no—
962C42—21no—
963C42—21no—
964C42—611no—
965C42—611no—
966C42—612no—
967C42—1222no—
968C42—1222no—
969C23—22no—
970C23—42no—
971C23—82no—
972C23—612no—
973C23—1221no—
974C23—1221no—
975C23—1222no—
976C23—1222no—
977C23—4882no—
978C23—4884no—
979C23—4882no—
980C23—4884no—
981C23—4884no—
982C23—2444no—
983C23—2444no—
984C23—2444no—
985C23—2442no—
986C23—2442no—
987C23C2×D4×D6112yes—
988C23C2×D4×D6111yescharacteristic
989Q8—22no—
990Q8—22no—
991Q8—22no—
992Q8—42no—
993Q8—612no—
994Q8—612no—
995Q8—1221no—
996Q8—1221no—
997Q8—1222no—
998Q8—2444no—
999D4—24no—
1000D4—22no—
1001D4—22no—
1002D4—22no—
1003D4—42no—
1004D4—84no—
1005D4—612no—
1006D4—612no—
1007D4—1224no—
1008D4—1224no—
1009D4—1224no—
1010D4—1222no—
1011D4—1222no—
1012D4—1221no—
1013D4—1221no—
1014D4—1222no—
1015D4—1222no—
1016D4—1222no—
1017D4—4884no—
1018D4—4884no—
1019D4—4884no—
1020D4—2444no—
1021D4—2444no—
1022D4—2444no—
1023D4—2444no—
1024D4—2444no—
1025D4—2444no—
1026D4—2444no—
1027D4—2444no—
1028D4—2448no—
1029D4—2442no—
1030D4—2442no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—42no—
1037C2×C4—612no—
1038C2×C4—612no—
1039C2×C4—612no—
1040C2×C4—1221no—
1041C2×C4—1221no—
1042C2×C4—1222no—
1043C2×C4—1222no—
1044C2×C4—1224no—
1045C2×C4—1224no—
1046C2×C4—4882no—
1047C2×C4—2444no—
1048C2×C4—2444no—
1049C2×C4—2444no—
1050C2×C4—2444no—
1051C2×C4—2444no—
1052C2×C4—2442no—
1053C2×C4—2444no—
1054C2×C4C2×D4×D6112yes—
1055C2×C4C2×D4×D6112yes—
1056C2×C4C2×D4×D6111yescharacteristic
1057C2×C4#1451982312yes—
1058C2×C4C24×D6111yescharacteristic
1059C8—22no—
1060C8—1222no—
1061C8—1222no—
1062C8C2×D4×D6112yes—
1063C8C2×D4×D6112yes—
1064C22—22no—
1065C22—22no—
1066C22—24no—
1067C22—42no—
1068C22—44no—
1069C22—162no—
1070C22—1222no—
1071C22—1222no—
1072C22—1222no—
1073C22—1224no—
1074C22—9762no—
1075C22—9762no—
1076C22—9764no—
1077C22—9764no—
1078C22—9764no—
1079C22—2442no—
1080C22—2442no—
1081C22—2444no—
1082C22—2444no—
1083C22—2442no—
1084C22—2442no—
1085C22#1684039612yes—
1086C22C22×D4×D6111yescharacteristic
1087C4—22no—
1088C4—42no—
1089C4—42no—
1090C4—42no—
1091C4—1222no—
1092C4—1222no—
1093C4—1222no—
1094C4—1222no—
1095C4—1222no—
1096C4#1684039612yes—
1097C4C22×D4×D6111yescharacteristic
1098C4C2×#1451982311yescharacteristic
1099C2—22no—
1100C2—42no—
1101C2—82no—
1102C2—4882no—
1103C2—4882no—
1104C2—2442no—
1105C2—2442no—
1106C2—2442no—
1107C2C2×#1684039611yescharacteristic
1108C2#2146059712yes—
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3057C2
socleC22×C61C23×D4
hypercenter#3057D61
hypocenterC61#61082
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3057

Complements

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

NH ≅ G/Ntype
1. C2×#16840568C2semidirect
2. C2×#16840567C2semidirect
3. #21459608C2semidirect
4. #21459594C2semidirect
5. #21457401C2semidirect
6. #21457366C2semidirect
7. #21457321C2semidirect
8. #21457296C2semidirect
9. C2×#16840148C2semidirect
10. #21455468C2semidirect
11. #21455316C2semidirect
12. #21455298C2semidirect
13. #21455106C2semidirect
14. #21455094C2semidirect
15. #21455088C2semidirect
16. #21455085C2semidirect
17. #21454619C2semidirect
18. #21454535C2semidirect
19. C61×#3057C2semidirect
20. C2×#14519825C22semidirect
22. C2×#14519823C22semidirect
23. C2×#14519822C22semidirect
26. C2×#14519808C22semidirect
27. C2×#14519806C22semidirect
29. C2×#14519805C22semidirect
30. C2×#14519805C22semidirect
31. C2×#14519805C22semidirect
32. C2×#14519804C22semidirect
33. C2×#14519803C22semidirect
35. C2×#14519799C22semidirect
36. C2×#14519798C22semidirect
37. C22×#11758201C22semidirect
38. C2×SD16×D61C22semidirect
39. C22×D488C22semidirect
40. C22×D488C22semidirect
41. C22×#11758199C22semidirect
42. C2×#14519783C22semidirect
43. #16840430C22semidirect
44. #16840422C22semidirect
46. #16840403C22semidirect
47. #16840396C22semidirect
50. #16840331C22semidirect
51. #16840331C22semidirect
58. C2×#14519773C22semidirect
60. C2×#14519766C22semidirect
62. #16840230C22semidirect
63. #16840230C22semidirect
64. #16840148C22semidirect
65. #16840148C22semidirect
66. #16840016C22semidirect
67. #16839999C22semidirect
68. #16839987C22semidirect
69. #16839980C22semidirect
70. #16839961C22semidirect
71. #16839956C22semidirect
72. #16839922C22semidirect
73. #16839912C22semidirect
74. #16839910C22semidirect
75. #16839908C22semidirect
76. #16839905C22semidirect
77. #16839902C22semidirect
78. #16839897C22semidirect
79. #16839895C22semidirect
80. #16839873C22semidirect
81. #16839868C22semidirect
82. #16839861C22semidirect
83. #16839861C22semidirect
84. #16839833C22semidirect
85. #16839831C22semidirect
86. #16839785C22semidirect
87. #16839766C22semidirect
88. #16839766C22semidirect
89. #16839756C22semidirect
90. #16839756C22semidirect
91. #16839730C22semidirect
92. #16839729C22semidirect
93. C2×#14519687C22semidirect
94. C22×SD16×C61C22semidirect
95. C2×#131×C61C22semidirect
96. C61×#536C22semidirect
98. C61×#468C22semidirect
99. C61×#465C22semidirect
100. C61×#427C22semidirect
101. C61×#419C22semidirect
102. C61×#418C22semidirect
147. #14519799D4semidirect
324. #11758222C2×D4semidirect
363. C2×C8×C61C2×D4semidirect
402. Dic244C2×D4semidirect
407. D488C2×D4semidirect
410. #11758190C2×D4semidirect
411. #11758190C2×D4semidirect
555. #3057D61semidirect
593. C22×SD16C2×D61semidirect
598. C2×#131C2×D61semidirect
606. #536C2×D61semidirect
625. #468C2×D61semidirect
627. #465C2×D61semidirect
646. #427C2×D61semidirect
648. #419C2×D61semidirect
651. #418C2×D61semidirect
657. C61#61082semidirect
940. C2×C8D4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168405682
C2×#168405672
#214596082
#214595942
#214574012
#214573662
#214573212
#214572962
C2×#168401482
#214554682
#214553162
#214552982
#214551062
#214550942
#214550882
#214550852
#214546192
#214545352
C61×#30572
#6108261