Finite Group Databasebeta

← #28247656

Subgroups — #28247656

Order 13568.

4874 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811459C211yesmaximal, characteristic
2C22×#13133225C211yesmaximal, characteristic, complemented
3#20287916C211yesmaximal, characteristic, complemented
4#20283247C214yesmaximal, complemented
5#20283246C214yesmaximal, complemented
6#20283240C214yesmaximal, complemented
7#20283239C214yesmaximal, complemented
8#20283235C211yesmaximal, characteristic, complemented
9#20283230C214yesmaximal, complemented
10C2×#16810619C211yesmaximal, characteristic, complemented
11C2×#16810617C211yesmaximal, characteristic, complemented
12#416×D53C214yesmaximal, complemented
13C53×#2896C211yesmaximal, characteristic, complemented
14#16811459—28no—
15#16811459C4116yescomplemented
16C2×#13133265C2212yes—
17C2×#13133264—21no—
18C2×#13133264C2212yes—
19C2×#13133263—21no—
20C2×#13133263C2212yes—
21C2×#13133262—22no—
22C2×#13133262C2212yes—
23C22×#11719945—22no—
24C22×#11719945C2211yescharacteristic
25C22×#11719945C2211yescharacteristic
26C2×#41×D53—22no—
27C2×#41×D53C2214yes—
28C2×#13133225—28no—
29C2×#13133225C2214yescomplemented
30C2×#13133225C2214yescomplemented
31C22×#11719912C2212yescomplemented
32C23×#88322C2211yescharacteristic, complemented
33C22×C8×D53C2212yescomplemented
34#16811104C2214yescomplemented
35#16811103C2214yescomplemented
36#16811100—21no—
37#16811097—21no—
38#16811096—22no—
39C4×#11719945—22no—
40#16811091—22no—
41C2×#13133176C2211yescharacteristic, complemented
42#117×D53C2214yescomplemented
43#16810633C2212yescomplemented
44#16810630C2218yescomplemented
45#16810629C2212yescomplemented
46#16810626C2218yescomplemented
47#16810625C2214yescomplemented
48#16810623C2218yescomplemented
49#16810621C2218yescomplemented
50#16810620C2214yescomplemented
51#16810619C2212yescomplemented
52#16810619C2212yescomplemented
53#16810619C2214yescomplemented
54#16810618C2218yescomplemented
55#16810617C2212yescomplemented
56#16810617C2212yescomplemented
57#16810617C2214yescomplemented
58#16810616C2218yescomplemented
59C2×#13133141C2212yescomplemented
60C2×#13133140C2212yescomplemented
61#103×D53C2218yescomplemented
62C2×#13133138C2212yescomplemented
63C2×#13133137C2212yescomplemented
64#102×D53C2218yescomplemented
65C22×#41×C53C2211yescharacteristic
66C22×M16×C53C2211yescharacteristic, complemented
67C2×#117×C53C2211yescharacteristic, complemented
68C53×#419C2212yescomplemented
69C53×#418C2212yescomplemented
70C53×#417C2214yescomplemented
71C53×#416C2214yescomplemented
72#13133265—28no—
73#13133265C2×C4116yescomplemented
74#13133264—28no—
75#13133264—216no—
76#13133264C2×C4116yescomplemented
77#13133263—28no—
78#13133263—216no—
79#13133263C2×C4116yescomplemented
80#13133262—232no—
81#13133262—28no—
82#13133262C2×C4116yescomplemented
83C2×#11719949—22no—
84C2×#11719949C2314yes—
85C2×#11719945—21no—
86C2×#11719945—21no—
87C2×#11719945—24no—
88C2×#11719945—24no—
89C2×#11719945—232no—
90C2×#11719945—22no—
91C2×#11719945—24no—
92C2×#11719945—22no—
93C2×#11719945C2×C418yes—
94C2×#11719945C2×C418yescomplemented
95C2×#11719945D418yes—
96C2×#11719945D412yes—
97C2×#11719945D412yes—
98C2×#11719945C2312yes—
99C2×#11719945C2312yes—
100C2×#11719945C2312yes—
101C2×#11719945C2312yes—
102C2×#11719947—24no—
103C2×#11719947—24no—
104C2×#11719947—22no—
105C2×#11719947C2314yes—
106#41×D53—232no—
107#41×D53—216no—
108#41×D53C2×C4132yescomplemented
109C22×Dic106—22no—
110C22×Dic106D411yescharacteristic
111C22×Dic106C2311yescharacteristic
112C2×Q8×D53—22no—
113C2×Q8×D53C2314yes—
114C22×D212—22no—
115C22×D212D411yescharacteristic
116C22×D212C2311yescharacteristic
117C22×C22⋊D53—21no—
118C22×C22⋊D53—24no—
119C22×C22⋊D53D412yes—
120C2×D4×D53—24no—
121C2×D4×D53—24no—
122C2×D4×D53—22no—
123C2×D4×D53C2314yes—
124C22×C4×D53—21no—
125C22×C4×D53—24no—
126C22×C4×D53C2312yes—
127#13133225—216no—
128#13133225—216no—
129C2×#11719912—28no—
130C2×#11719912C2318yes—
131C22×#88322—24no—
132C22×#88322C2312yes—
133C22×#88322C2312yes—
134C22×#88322C2311yescharacteristic
135C22×#88322C2311yescharacteristic
136C2×C8×D53—28no—
137C2×C8×D53C2318yes—
138C4×Dic106—24no—
139#13133182—24no—
140C4×D212—24no—
141#13133179—24no—
142C4×C22⋊D53—28no—
143#13133177—28no—
144#13133176—21no—
145#13133176—21no—
146#13133176C2312yes—
147#13133176C2312yes—
148#13133175C2318yes—
149#13133174—24no—
150#13133173—24no—
151C2×C4⋊Dic53C2312yes—
152C4⋊C4×D53C2318yes—
153C2×C22⋊Dic53—21no—
154C22⋊C4×D53—24no—
155C2×C4×Dic53—21no—
156C42×D53—24no—
157#13133142C2318yes—
158#13133141C2314yes—
159#13133141C2314yes—
160#13133140C2314yes—
161#13133140C2314yes—
162#13133139C2318yes—
163#13133138C2314yes—
164#13133138C2314yes—
165#13133137C2314yes—
166#13133137C2314yes—
167C2×#41×C53—21no—
168C2×#41×C53—21no—
169C2×#41×C53—24no—
170C2×#41×C53C2×C418yescomplemented
171C2×#41×C53C2312yes—
172C2×#41×C53C2312yes—
173C22×Q8×C53C2311yescharacteristic
174C22×D4×C53—21no—
175C22×D4×C53C2311yescharacteristic
176C23×C4×C53—21no—
177C23×C4×C53C2311yescharacteristic
178C2×M16×C53—24no—
179C2×M16×C53C2312yes—
180C2×M16×C53C2312yes—
181C22×C8×C53C2312yes—
182#117×C53—21no—
183#117×C53—21no—
184#117×C53C2312yes—
185#117×C53C2312yes—
186C2×C4⋊C4×C53C2312yes—
187C2×C22⋊C4×C53—21no—
188C2×C42×C53—21no—
189#103×C53C2318yes—
190#102×C53C2318yes—
191C24×C53—21no—
192C24×C53C2×D411yescharacteristic
193C23×D53—21no—
194C23×D53—24no—
195C23×D53C2×D412yes—
196#41×C53—28no—
197#41×C53—28no—
198#41×C53—24no—
199#41×C53—24no—
200#41×C53C22×C418yes—
201#41×C53C22×C418yes—
202C2×Q8×C53—21no—
203C2×Q8×C53—22no—
204C2×Q8×C53C22×C414yes—
205C2×Q8×C53C2412yes—
206C2×D4×C53—28no—
207C2×D4×C53—22no—
208C2×D4×C53—22no—
209C2×D4×C53—21no—
210C2×D4×C53—22no—
211C2×D4×C53C22×C414yes—
212C2×D4×C53C2412yes—
213C22×C4×C53—21no—
214C22×C4×C53—28no—
215C22×C4×C53—22no—
216C22×C4×C53—22no—
217C22×C4×C53—22no—
218C22×C4×C53C22×C414yes—
219C22×C4×C53C2×D411yescharacteristic
220C22×C4×C53C2×D411yescharacteristic
221C22×C4×C53C2×D411yescharacteristic
222C22×C4×C53C2×D414yes—
223C22×C4×C53C2411yescharacteristic
224C22×C4×C53C2411yescharacteristic
225C22×C4×C53C2411yescharacteristic
226C2×C22⋊D53—28no—
227C2×C22⋊D53—22no—
228C2×C22⋊D53—22no—
229C2×C22⋊D53—24no—
230C2×C22⋊D53—232no—
231C2×C22⋊D53—24no—
232C2×C22⋊D53C22⋊C4116yes—
233C2×C22⋊D53C2×D414yes—
234C2×C22⋊D53C2×D414yes—
235C22×Dic53—21no—
236C22×Dic53—24no—
237C22×Dic53—22no—
238C22×Dic53C2×D412yes—
239#11719949—216no—
240#11719949—28no—
241#11719949C22×C4116yes—
242Q8×D53—28no—
243Q8×D53—216no—
244Q8×D53C22×C4116yes—
245#11719947—232no—
246#11719947—232no—
247#11719947—28no—
248#11719947—216no—
249#11719947C22×C4116yes—
250D4×D53—232no—
251D4×D53—232no—
252D4×D53—216no—
253D4×D53—28no—
254D4×D53C22×C4116yes—
255#11719945—28no—
256#11719945—28no—
257#11719945—24no—
258#11719945—24no—
259#11719945—232no—
260#11719945—216no—
261#11719945—232no—
262#11719945—216no—
263#11719945C22⋊C4116yes—
264#11719945C22⋊C4116yes—
265#11719945C22×C418yes—
266#11719945C22×C418yes—
267#11719945C22×C418yes—
268#11719945C22×C418yes—
269#11719945C2×D418yes—
270#11719945C2×D418yes—
271C2×D212—24no—
272C2×D212—21no—
273C2×D212—22no—
274C2×D212—216no—
275C2×D212C22⋊C418yes—
276C2×D212C22×C414yes—
277C2×D212C2×D412yes—
278C2×D212C2×D412yes—
279C2×D212C2412yes—
280C2×C4×D53—24no—
281C2×C4×D53—28no—
282C2×C4×D53—22no—
283C2×C4×D53—22no—
284C2×C4×D53—24no—
285C2×C4×D53—232no—
286C2×C4×D53—28no—
287C2×C4×D53C22×C418yes—
288C2×C4×D53C2×D414yes—
289C2×C4×D53C2×D418yes—
290C2×C4×D53C2414yes—
291C2×Dic106—21no—
292C2×Dic106—22no—
293C2×Dic106—24no—
294C2×Dic106—216no—
295C2×Dic106C22⋊C418yes—
296C2×Dic106C22×C414yes—
297C2×Dic106C2×D412yes—
298C2×Dic106C2×D412yes—
299C2×Dic106C2412yes—
300M16×C53—24no—
301M16×C53—24no—
302C2×C8×C53—24no—
303C2×C8×C53C2414yes—
304C4⋊C4×C53—22no—
305C4⋊C4×C53C2414yes—
306C22⋊C4×C53—22no—
307C22⋊C4×C53—22no—
308C42×C53—22no—
309C42×C53—22no—
310C22⋊Dic53—22no—
311C22⋊Dic53—22no—
312#11719921—28no—
313C4⋊Dic53—22no—
314C4⋊Dic53C2414yes—
315#11719919—28no—
316C4×Dic53—22no—
317C4×Dic53—22no—
318C4×Dic53—28no—
319C2×#88322—22no—
320C2×#88322—22no—
321C2×#88322—24no—
322C2×#88322—24no—
323C2×#88322C2412yes—
324C2×#88322C2412yes—
325#11719912—216no—
326C8×D53—216no—
327C23×C53—22no—
328C23×C53—24no—
329C23×C53—42no—
330C23×C53—82no—
331C23×C53C2×C22⋊C414yes—
332C23×C53C22×D411yescharacteristic
333C23×C53C22×D411yescharacteristic
334C23×C53C22×D411yescharacteristic
335C22×D53—22no—
336C22×D53—24no—
337C22×D53—216no—
338C22×D53—44no—
339C22×D53—88no—
340C22×D53—82no—
341C22×D53C2×C22⋊C418yes—
342C22×D53C22×D414yes—
343Q8×C53—24no—
344Q8×C53—22no—
345Q8×C53C23×C414yes—
346D4×C53—28no—
347D4×C53—28no—
348D4×C53—24no—
349D4×C53—22no—
350D4×C53C23×C414yes—
351C2×C4×C53—24no—
352C2×C4×C53—22no—
353C2×C4×C53—28no—
354C2×C4×C53—28no—
355C2×C4×C53—24no—
356C2×C4×C53—82no—
357C2×C4×C53C2×C22⋊C414yes—
358C2×C4×C53C2×C22⋊C414yes—
359C2×C4×C53C2×C22⋊C414yes—
360C2×C4×C53C23×C412yes—
361C2×C4×C53C23×C412yes—
362C2×C4×C53C23×C412yes—
363C2×C4×C53C22×D411yescharacteristic
364C2×C4×C53C22×D411yescharacteristic
365C2×C4×C53C22×D412yes—
366C2×C4×C53C22×D412yes—
367C2×C4×C53C22×D412yes—
368C2×C4×C53C22×D411yescharacteristic
369C2×C4×C53C2511yescharacteristic
370C22⋊D53—28no—
371C22⋊D53—28no—
372C22⋊D53—216no—
373C22⋊D53—216no—
374C22⋊D53C2×C22⋊C4116yes—
375C22⋊D53C2×C22⋊C4116yes—
376C2×Dic53—24no—
377C2×Dic53—22no—
378C2×Dic53—216no—
379C2×Dic53—24no—
380C2×Dic53—82no—
381C2×Dic53C2×C22⋊C418yes—
382C2×Dic53C22×D414yes—
383D212—216no—
384D212—24no—
385D212—22no—
386D212C2×C22⋊C418yes—
387D212C2×C22⋊C418yes—
388D212C23×C414yes—
389C4×D53—216no—
390C4×D53—28no—
391C4×D53—28no—
392C4×D53—216no—
393C4×D53—88no—
394C4×D53C2×C22⋊C4116yes—
395C4×D53C23×C418yes—
396C4×D53C22×D418yes—
397Dic106—24no—
398Dic106—22no—
399Dic106—216no—
400Dic106C2×C22⋊C418yes—
401Dic106C2×C22⋊C418yes—
402Dic106C23×C414yes—
403C8×C53—24no—
404#88322—22no—
405#88322—22no—
406#60086—531nomaximal, Sylow
407C22×C53—22no—
408C22×C53—22no—
409C22×C53—22no—
410C22×C53—24no—
411C22×C53—44no—
412C22×C53—44no—
413C22×C53—84no—
414C22×C53C22×C22⋊C412yes—
415C22×C53C22×C22⋊C412yes—
416C22×C53C22×C22⋊C412yes—
417C22×C53C23×D411yescharacteristic
418C2×D53—28no—
419C2×D53—24no—
420C2×D53—48no—
421C2×D53—44no—
422C2×D53—816no—
423C2×D53—84no—
424C2×D53C22×C22⋊C418yes—
425C4×C53—24no—
426C4×C53—44no—
427C4×C53C22×C22⋊C412yes—
428C4×C53C22×C22⋊C412yes—
429C4×C53C22×C22⋊C412yes—
430C4×C53C24×C411yescharacteristic
431C4×C53C23×D411yescharacteristic
432Dic53—24no—
433Dic53—44no—
434Dic53C22×C22⋊C418yes—
435C2×#585—531no—
436C22×#131—531no—
437#3428—531no—
438#2898—534no—
439#2898—534no—
440#2897—534no—
441#2897—534no—
442#2896—534no—
443#2896—531no—
444#2896D5311yescharacteristic, complemented
445C2×#416—534no—
446C2×#416—531no—
447C2×#416—531no—
448C2×C53—22no—
449C2×C53—22no—
450C2×C53—22no—
451C2×C53—44no—
452C2×C53C23×C22⋊C411yescharacteristic
453C2×C53#358412yes—
454D53—28no—
455D53—44no—
456#585—5316no—
457#585—1068no—
458C2×2−1+4—532no—
459C2×2−1+4—532no—
460C2×2−1+4—1061no—
461C2×H(5,𝔽2)—532no—
462C2×H(5,𝔽2)—532no—
463C2×H(5,𝔽2)—1062no—
464C2×H(5,𝔽2)—1061no—
465C22×#41—531no—
466C22×#41—534no—
467C22×#41—531no—
468C22×#41—1062no—
469C22×#41—1062no—
470C22×#41C2×D5311yescharacteristic
471C2×#131—534no—
472C2×#131—534no—
473C2×#131—1068no—
474C22×M16—532no—
475C22×M16C2×D5311yescharacteristic, complemented
476C23×C8—531no—
477C23×C8—532no—
478#520—534no—
479#520—534no—
480#519—1061no—
481#518—1062no—
482#518—1061no—
483C4×#41—1062no—
484C4×#41—1062no—
485C2×#117—531no—
486C2×#117—534no—
487C2×#117C2×D5311yescharacteristic, complemented
488#419—532no—
489#419—538no—
490#419C2×D5312yescomplemented
491#418—532no—
492#418—538no—
493#418C2×D5312yescomplemented
494#417—534no—
495#417—538no—
496#417—538no—
497#417C2×D5314yescomplemented
498#416—532no—
499#416—532no—
500#416—534no—
501#416—534no—
502#416—532no—
503#416—532no—
504#416—534no—
505#416—538no—
506#416—538no—
507#416C2×D5314yescomplemented
508C2×#103—532no—
509C2×#103—532no—
510C2×#103—538no—
511C2×#102—532no—
512C2×#102—532no—
513C2×#102—538no—
514C53#6008611yescharacteristic, complemented, Sylow
5152−1+4—5316no—
5162−1+4—5316no—
5172−1+4—1068no—
5182−1+4—10616no—
5192−1+4—1068no—
520H(5,𝔽2)—5316no—
521H(5,𝔽2)—5316no—
522H(5,𝔽2)—10632no—
523H(5,𝔽2)—1068no—
524H(5,𝔽2)—10616no—
525H(5,𝔽2)—1068no—
526C2×#41—21no—
527C2×#41—21no—
528C2×#41—24no—
529C2×#41—538no—
530C2×#41—532no—
531C2×#41—532no—
532C2×#41—538no—
533C2×#41—532no—
534C2×#41—532no—
535C2×#41—5332no—
536C2×#41—534no—
537C2×#41—534no—
538C2×#41—538no—
539C2×#41—532no—
540C2×#41—532no—
541C2×#41—1064no—
542C2×#41—1064no—
543C2×#41—1062no—
544C2×#41—1062no—
545C2×#41—10632no—
546C2×#41—1064no—
547C2×#41—10616no—
548C2×#41—1064no—
549C2×#41—1062no—
550C2×#41—1062no—
551C2×#41—10632no—
552C2×#41—1061no—
553C2×#41—1061no—
554C2×#41—1064no—
555C2×#41C4×D5318yescomplemented
556C2×#41C22×D5312yes—
557C2×#41C22×D5312yes—
558C22×Q8—531no—
559C22×Q8—534no—
560C22×Q8—531no—
561C22×Q8—1062no—
562C22×Q8—1062no—
563C22×Q8C22×D5311yescharacteristic
564C22×D4—21no—
565C22×D4—532no—
566C22×D4—534no—
567C22×D4—531no—
568C22×D4—531no—
569C22×D4—1062no—
570C22×D4—1064no—
571C22×D4—1062no—
572C22×D4—1064no—
573C22×D4—1064no—
574C22×D4—1061no—
575C22×D4C22×D5311yescharacteristic
576C23×C4—21no—
577C23×C4—532no—
578C23×C4—1064no—
579C23×C4—1061no—
580C23×C4C22×D5311yescharacteristic
581#131—10616no—
582#131—10616no—
583C2×M16—24no—
584C2×M16—538no—
585C2×M16—1068no—
586C2×M16C22×D5312yes—
587C2×M16C22×D5312yes—
588C22×C8—531no—
589C22×C8—531no—
590C22×C8—532no—
591C22×C8—532no—
592C22×C8—538no—
593C22×C8—1068no—
594C22×C8—1064no—
595C22×C8C22×D5312yes—
596C4×Q8—1064no—
597C4×Q8—1064no—
598C4×D4—1064no—
599C4×D4—1068no—
600C4×D4—1064no—
601C4×D4—1068no—
602#117—21no—
603#117—21no—
604#117—532no—
605#117—532no—
606#117—538no—
607#117—1064no—
608#117—1064no—
609#117—1061no—
610#117—1061no—
611#117C22×D5312yes—
612#117C22×D5312yes—
613C2×C4⋊C4—532no—
614C2×C4⋊C4—538no—
615C2×C4⋊C4C22×D5312yes—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—1064no—
618C2×C22⋊C4—1061no—
619C2×C42—21no—
620C2×C42—1064no—
621C2×C42—1061no—
622#103—534no—
623#103—534no—
624#103—538no—
625#103—534no—
626#103—534no—
627#103C22×D5318yes—
628#102—534no—
629#102—534no—
630#102—538no—
631#102—534no—
632#102—534no—
633#102C22×D5318yes—
634C24—21no—
635C24—532no—
636C24—1064no—
637C24—1061no—
638C24D4×D5311yescharacteristic
639#41—28no—
640#41—28no—
641#41—24no—
642#41—24no—
643#41—5316no—
644#41—5316no—
645#41—538no—
646#41—538no—
647#41—538no—
648#41—538no—
649#41—5316no—
650#41—5316no—
651#41—538no—
652#41—538no—
653#41—10632no—
654#41—10632no—
655#41—10616no—
656#41—10616no—
657#41—10632no—
658#41—1068no—
659#41—1068no—
660#41—10632no—
661#41—10616no—
662#41—10616no—
663#41—1068no—
664#41—1068no—
665#41—1064no—
666#41—1064no—
667#41C2×C4×D5318yes—
668#41C2×C4×D5318yes—
669C2×Q8—21no—
670C2×Q8—22no—
671C2×Q8—538no—
672C2×Q8—532no—
673C2×Q8—532no—
674C2×Q8—5316no—
675C2×Q8—534no—
676C2×Q8—532no—
677C2×Q8—1064no—
678C2×Q8—10616no—
679C2×Q8—1068no—
680C2×Q8—10616no—
681C2×Q8—1061no—
682C2×Q8—1062no—
683C2×Q8C2×C4×D5314yes—
684C2×Q8C23×D5312yes—
685C2×D4—28no—
686C2×D4—22no—
687C2×D4—22no—
688C2×D4—21no—
689C2×D4—22no—
690C2×D4—5316no—
691C2×D4—534no—
692C2×D4—534no—
693C2×D4—5316no—
694C2×D4—538no—
695C2×D4—534no—
696C2×D4—532no—
697C2×D4—532no—
698C2×D4—532no—
699C2×D4—10616no—
700C2×D4—1064no—
701C2×D4—1068no—
702C2×D4—1064no—
703C2×D4—10632no—
704C2×D4—10616no—
705C2×D4—10632no—
706C2×D4—10632no—
707C2×D4—1064no—
708C2×D4—1068no—
709C2×D4—1062no—
710C2×D4—1062no—
711C2×D4—1061no—
712C2×D4—1062no—
713C2×D4C2×C4×D5314yes—
714C2×D4C23×D5312yes—
715C22×C4—21no—
716C22×C4—28no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—532no—
721C22×C4—538no—
722C22×C4—538no—
723C22×C4—534no—
724C22×C4—534no—
725C22×C4—1064no—
726C22×C4—10632no—
727C22×C4—1064no—
728C22×C4—1068no—
729C22×C4—1064no—
730C22×C4—1061no—
731C22×C4—1068no—
732C22×C4—1062no—
733C22×C4—1062no—
734C22×C4—1062no—
735C22×C4C2×C4×D5314yes—
736C22×C4D4×D5311yescharacteristic
737C22×C4D4×D5311yescharacteristic
738C22×C4D4×D5311yescharacteristic
739C22×C4D4×D5314yes—
740C22×C4C23×D5311yescharacteristic
741C22×C4C23×D5311yescharacteristic
742C22×C4C23×D5311yescharacteristic
743M16—24no—
744M16—24no—
745M16—10616no—
746C2×C8—24no—
747C2×C8—532no—
748C2×C8—532no—
749C2×C8—10616no—
750C2×C8—1062no—
751C2×C8—1062no—
752C2×C8—1064no—
753C2×C8—1064no—
754C2×C8C23×D5314yes—
755C4⋊C4—22no—
756C4⋊C4—534no—
757C4⋊C4—1068no—
758C4⋊C4—1062no—
759C4⋊C4C23×D5314yes—
760C22⋊C4—22no—
761C22⋊C4—22no—
762C22⋊C4—1068no—
763C22⋊C4—1062no—
764C22⋊C4—1062no—
765C42—22no—
766C42—22no—
767C42—1068no—
768C42—1062no—
769C42—1062no—
770C23—22no—
771C23—24no—
772C23—42no—
773C23—82no—
774C23—534no—
775C23—538no—
776C23—10616no—
777C23—1064no—
778C23—1062no—
779C23—4242no—
780C23—4248no—
781C23—2124no—
782C23C22⋊C4×D5314yes—
783C23C2×D4×D5311yescharacteristic
784C23C2×D4×D5311yescharacteristic
785C23C2×D4×D5311yescharacteristic
786Q8—24no—
787Q8—22no—
788Q8—538no—
789Q8—538no—
790Q8—534no—
791Q8—10616no—
792Q8—1064no—
793Q8—1062no—
794Q8C22×C4×D5314yes—
795D4—28no—
796D4—28no—
797D4—24no—
798D4—22no—
799D4—5316no—
800D4—5316no—
801D4—538no—
802D4—538no—
803D4—534no—
804D4—10616no—
805D4—10616no—
806D4—10616no—
807D4—1068no—
808D4—1068no—
809D4—1064no—
810D4—1062no—
811D4C22×C4×D5314yes—
812C2×C4—24no—
813C2×C4—22no—
814C2×C4—28no—
815C2×C4—28no—
816C2×C4—24no—
817C2×C4—82no—
818C2×C4—538no—
819C2×C4—534no—
820C2×C4—5316no—
821C2×C4—538no—
822C2×C4—538no—
823C2×C4—10616no—
824C2×C4—10616no—
825C2×C4—10616no—
826C2×C4—1064no—
827C2×C4—1062no—
828C2×C4—1068no—
829C2×C4—1068no—
830C2×C4—1064no—
831C2×C4—4248no—
832C2×C4—4242no—
833C2×C4C22⋊C4×D5314yes—
834C2×C4C22⋊C4×D5314yes—
835C2×C4C22⋊C4×D5314yes—
836C2×C4C22×C4×D5312yes—
837C2×C4C22×C4×D5312yes—
838C2×C4C22×C4×D5312yes—
839C2×C4C2×D4×D5311yescharacteristic
840C2×C4C2×D4×D5311yescharacteristic
841C2×C4C2×D4×D5312yes—
842C2×C4C2×D4×D5312yes—
843C2×C4C2×D4×D5312yes—
844C2×C4C2×D4×D5311yescharacteristic
845C2×C4C24×D5311yescharacteristic
846C8—24no—
847C8—1062no—
848C8—1062no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—24no—
853C22—44no—
854C22—44no—
855C22—84no—
856C22—538no—
857C22—1068no—
858C22—1064no—
859C22—4244no—
860C22—42416no—
861C22—2128no—
862C22—2124no—
863C22C2×C22⋊C4×D5312yes—
864C22C2×C22⋊C4×D5312yes—
865C22C2×C22⋊C4×D5312yes—
866C22C22×D4×D5311yescharacteristic
867C4—24no—
868C4—44no—
869C4—538no—
870C4—1064no—
871C4—2124no—
872C4C2×C22⋊C4×D5312yes—
873C4C2×C22⋊C4×D5312yes—
874C4C2×C22⋊C4×D5312yes—
875C4C23×C4×D5311yescharacteristic
876C4C22×D4×D5311yescharacteristic
877C2—22no—
878C2—22no—
879C2—22no—
880C2—44no—
881C2—1068no—
882C2—2124no—
883C2C22×C22⋊C4×D5311yescharacteristic
884C2#2028948812yes—
subgroupG/H
centerC2×C4C2×D4×D53
commutatorC4×C53C24×C4
FrattiniC2×C4C24×D53
FittingC53×#2896C2
socleC22×C53C23×D4
prime radicalC2×#16811459C2
cosocleC2×C4×C53C25
hypercenter#2896D53
hypocenterC53#60086
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2896

Complements

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

NH ≅ G/Ntype
2. C22×#13133225C2semidirect
3. #20287916C2semidirect
4. #20283247C2semidirect
5. #20283246C2semidirect
6. #20283240C2semidirect
7. #20283239C2semidirect
8. #20283235C2semidirect
9. #20283230C2semidirect
10. C2×#16810619C2semidirect
11. C2×#16810617C2semidirect
12. #416×D53C2semidirect
13. C53×#2896C2semidirect
15. #16811459C4semidirect
29. C2×#13133225C22semidirect
30. C2×#13133225C22semidirect
31. C22×#11719912C22semidirect
32. C23×#88322C22semidirect
33. C22×C8×D53C22semidirect
34. #16811104C22semidirect
35. #16811103C22semidirect
41. C2×#13133176C22semidirect
42. #117×D53C22semidirect
43. #16810633C22semidirect
44. #16810630C22semidirect
45. #16810629C22semidirect
46. #16810626C22semidirect
47. #16810625C22semidirect
48. #16810623C22semidirect
49. #16810621C22semidirect
50. #16810620C22semidirect
51. #16810619C22semidirect
52. #16810619C22semidirect
53. #16810619C22semidirect
54. #16810618C22semidirect
55. #16810617C22semidirect
56. #16810617C22semidirect
57. #16810617C22semidirect
58. #16810616C22semidirect
59. C2×#13133141C22semidirect
60. C2×#13133140C22semidirect
61. #103×D53C22semidirect
62. C2×#13133138C22semidirect
63. C2×#13133137C22semidirect
64. #102×D53C22semidirect
66. C22×M16×C53C22semidirect
67. C2×#117×C53C22semidirect
68. C53×#419C22semidirect
69. C53×#418C22semidirect
70. C53×#417C22semidirect
71. C53×#416C22semidirect
73. #13133265C2×C4semidirect
76. #13133264C2×C4semidirect
79. #13133263C2×C4semidirect
82. #13133262C2×C4semidirect
94. C2×#11719945C2×C4semidirect
108. #41×D53C2×C4semidirect
170. C2×#41×C53C2×C4semidirect
444. #2896D53semidirect
475. C22×M16C2×D53semidirect
487. C2×#117C2×D53semidirect
490. #419C2×D53semidirect
493. #418C2×D53semidirect
497. #417C2×D53semidirect
507. #416C2×D53semidirect
514. C53#60086semidirect
555. C2×#41C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168114592
C22×#131332252
#202879162
#202832472
#202832462
#202832402
#202832392
#202832352
#202832302
C2×#168106192
C2×#168106172
#416×D532
C53×#28962
#6008653