Finite Group Databasebeta

← C2×#20284204 #28250951

Subgroups — C2×#20284204 #28250951

Order 13568.

2918 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133246C211yesmaximal, characteristic, complemented
2C22×#13133241C211yesmaximal, characteristic
3C2×#124×D53C211yesmaximal, characteristic, complemented
4C2×C4×#11719947C211yesmaximal, characteristic, complemented
5#20284204C2116yesmaximal, direct product factor
6C2×#16810848C211yesmaximal, characteristic, complemented
7C2×#16810846C211yesmaximal, characteristic, complemented
8C2×#16810844C211yesmaximal, characteristic, complemented
9C2×#16810842C211yesmaximal, characteristic, complemented
10C2×#16810840C211yesmaximal, characteristic, complemented
11C2×#16810838C211yesmaximal, characteristic, complemented
12C2×#16810836C211yesmaximal, characteristic, complemented
13C2×#16810645C211yesmaximal, characteristic, complemented
14C2×#16810630C211yesmaximal, characteristic, complemented
15C2×#16810626C211yesmaximal, characteristic, complemented
16C2×C53×#463C211yesmaximal, characteristic, complemented
17C22×#11719947C2211yescharacteristic
18C22×Q8×D53C2211yescharacteristic
19C22×D4×D53C2211yescharacteristic
20C2×#13133246—28no—
21C2×#13133246C2218yescomplemented
22C2×#13133241—28no—
23C2×#13133241C2218yes—
24C22×Dic212C2211yescharacteristic, complemented
25C22×#11719925C2211yescharacteristic, complemented
26C22×#11719913C2211yescharacteristic
27C22×#11719923C2211yescharacteristic
28C22×#11719923C2211yescharacteristic, complemented
29C22×#11719922C2211yescharacteristic
30C22×#11719912C2211yescharacteristic
31C22×#11719912C2211yescharacteristic
32C2×#13133206C2211yescharacteristic
33C2×#13133205C2211yescharacteristic
34C2×#13133204C2211yescharacteristic
35C2×#13133203—21no—
36C2×#13133203—21no—
37#124×D53—24no—
38#124×D53C2218yescomplemented
39C4×#11719947—24no—
40C4×#11719947C2218yescomplemented
41C2×C4×Dic106C2211yescharacteristic, complemented
42C2×#13133182C2211yescharacteristic, complemented
43C2×D4×Dic53C2211yescharacteristic, complemented
44C2×C4×C22⋊D53—21no—
45C2×#13133177—21no—
46C2×#13133175C2211yescharacteristic
47C2×#13133173—21no—
48C2×C22⋊C4×D53—21no—
49C2×C22⋊C4×D53—21no—
50C22×C4×Dic53—21no—
51C2×C42×D53C2211yescharacteristic
52#16810848C2218yescomplemented
53#16810846C2218yescomplemented
54#16810844C2218yescomplemented
55#16810842C2218yescomplemented
56#16810840C2218yescomplemented
57#16810838C2218yescomplemented
58#16810836C2218yescomplemented
59#16810645C2218yescomplemented
60C2×C4⋊#88322C2211yescharacteristic, complemented
61C2×#13133146C2211yescharacteristic, complemented
62C2×#13133146C2211yescharacteristic, complemented
63#16810630C2218yescomplemented
64#16810626C2218yescomplemented
65C2×#13133142C2211yescharacteristic, complemented
66C2×#13133141C2211yescharacteristic, complemented
67C2×#13133140C2211yescharacteristic, complemented
68C2×#13133139C2211yescharacteristic
69C2×#13133138C2211yescharacteristic
70C2×#13133137C2211yescharacteristic
71C22×SD16×C53C2211yescharacteristic, complemented
72C22×D8×C53C2211yescharacteristic
73C2×#124×C53C2211yescharacteristic
74C2×C4×D4×C53C2211yescharacteristic, complemented
75C53×#463C2218yescomplemented
76C2×C4⋊C8×C53C2211yescharacteristic, complemented
77C2×#103×C53C2211yescharacteristic, complemented
78C2×#102×C53C2211yescharacteristic
79C24×D53—21no—
80C2×#11719947—22no—
81C2×#11719947—24no—
82C2×#11719947D418yes—
83C2×#11719947C2314yes—
84C22×Dic106—21no—
85C22×Dic106C2311yescharacteristic
86C22×Dic106C2311yescharacteristic
87C2×Q8×D53—22no—
88C2×Q8×D53—24no—
89C2×Q8×D53—24no—
90C2×Q8×D53C2314yes—
91C22×D212C2311yescharacteristic
92C22×C22⋊D53—21no—
93C22×C22⋊D53—21no—
94C2×D4×D53—24no—
95C2×D4×D53—22no—
96C2×D4×D53—24no—
97C2×D4×D53C2314yes—
98C23×Dic53—21no—
99C23×Dic53—21no—
100C22×C4×D53—21no—
101C22×C4×D53D411yescharacteristic
102C22×C4×D53D411yescharacteristic
103C22×C4×D53C2311yescharacteristic
104#13133246—232no—
105#13133241—232no—
106C2×Dic212—24no—
107C2×Dic212C2314yescomplemented
108C2×#11719925—24no—
109C2×#11719925C2314yescomplemented
110C2×#11719913—24no—
111C2×#11719913C2314yes—
112C2×#11719923—24no—
113C2×#11719923—24no—
114C2×#11719923C2314yes—
115C2×#11719923C2314yescomplemented
116C2×#11719922—24no—
117C2×#11719922C2314yes—
118C2×#11719912—24no—
119C2×#11719912—24no—
120C2×#11719912C2314yes—
121C2×#11719912C2314yes—
122C22×#88322C2311yescharacteristic
123C22×#88322C2311yescharacteristic
124#13133206—22no—
125#13133206C2314yes—
126#13133205—22no—
127#13133205C2314yes—
128#13133204—22no—
129#13133204C2314yes—
130#13133203—28no—
131#13133203—28no—
132C4×Dic106—22no—
133C4×Dic106C2314yescomplemented
134#13133182—22no—
135#13133182C2314yescomplemented
136D4×Dic53—22no—
137D4×Dic53C2314yescomplemented
138C4×C22⋊D53—28no—
139#13133177—28no—
140#13133175—22no—
141#13133175C2314yes—
142#13133173—28no—
143C2×C4⋊Dic53C2311yescharacteristic
144C2×#11719919—21no—
145C2×#11719919—21no—
146C2×C22⋊Dic53—21no—
147C2×C22⋊Dic53—21no—
148C2×C22⋊Dic53—21no—
149C2×#11719921—21no—
150C2×#11719921—21no—
151C2×#11719921—21no—
152C2×#11719921—21no—
153C2×#11719921—21no—
154C22⋊C4×D53—28no—
155C22⋊C4×D53—28no—
156C2×C4×Dic53—28no—
157C2×C4×Dic53—21no—
158C2×C4×Dic53—21no—
159C2×C4×Dic53—21no—
160C2×C4×Dic53D411yescharacteristic
161C2×C4×Dic53D411yescharacteristic
162C2×C4×Dic53C2311yescharacteristic
163C42×D53D414yes—
164C42×D53C2314yes—
165C4⋊#88322C2314yescomplemented
166#13133146C2314yescomplemented
167#13133146C2314yescomplemented
168#13133142C2314yescomplemented
169#13133141C2314yescomplemented
170#13133140C2314yescomplemented
171#13133139C2314yes—
172#13133138C2314yes—
173#13133137C2314yes—
174C22×Q8×C53C2311yescharacteristic
175C22×D4×C53C2311yescharacteristic
176C22×D4×C53C2311yescharacteristic
177C23×C4×C53—21no—
178C2×SD16×C53—24no—
179C2×SD16×C53C2314yescomplemented
180C2×D8×C53—24no—
181C2×D8×C53C2314yes—
182C22×C8×C53C2311yescharacteristic
183C22×C8×C53C2311yescharacteristic
184#124×C53—22no—
185#124×C53C2314yes—
186C4×D4×C53—22no—
187C4×D4×C53C2314yescomplemented
188C2×C4⋊C4×C53C2311yescharacteristic
189C2×C22⋊C4×C53—21no—
190C2×C22⋊C4×C53—21no—
191C2×C22⋊C4×C53—21no—
192C2×C42×C53C2311yescharacteristic
193C4⋊C8×C53C2314yescomplemented
194#103×C53C2314yescomplemented
195#102×C53C2314yes—
196C24×C53—21no—
197C24×C53—21no—
198C23×D53—21no—
199C23×D53—24no—
200C23×D53—44no—
201C23×D53—44no—
202C23×D53—44no—
203C23×D53C2×D411yescharacteristic
204C2×Q8×C53—21no—
205C2×Q8×C53—22no—
206C2×Q8×C53—22no—
207C2×Q8×C53C2412yes—
208C2×D4×C53—21no—
209C2×D4×C53—22no—
210C2×D4×C53—21no—
211C2×D4×C53—22no—
212C2×D4×C53—22no—
213C2×D4×C53C2×D414yes—
214C2×D4×C53C2412yes—
215C2×D4×C53C2412yes—
216C22×C4×C53—21no—
217C22×C4×C53—21no—
218C22×C4×C53—24no—
219C22×C4×C53—44no—
220C22×C4×C53C2×D411yescharacteristic
221C22×C4×C53C2×D411yescharacteristic
222C22×C4×C53C2411yescharacteristic
223C2×C22⋊D53—28no—
224C2×C22⋊D53—24no—
225C2×C22⋊D53—24no—
226C2×C22⋊D53—44no—
227C22×Dic53—21no—
228C22×Dic53—28no—
229C22×Dic53—24no—
230C22×Dic53—21no—
231C22×Dic53—21no—
232C22×Dic53—24no—
233C22×Dic53—44no—
234C22×Dic53C2×D411yescharacteristic
235C22×Dic53C2×D411yescharacteristic
236C22×Dic53C2×D411yescharacteristic
237Q8×D53—28no—
238Q8×D53—28no—
239Q8×D53—48no—
240#11719947—216no—
241#11719947—28no—
242#11719947C2×D4116yes—
243D4×D53—28no—
244D4×D53—28no—
245D4×D53—48no—
246C2×D212—22no—
247C2×D212—22no—
248C2×D212—21no—
249C2×D212C2412yes—
250C2×C4×D53—24no—
251C2×C4×D53—42no—
252C2×C4×D53—42no—
253C2×C4×D53—44no—
254C2×C4×D53C2×D414yes—
255C2×C4×D53C2×D414yes—
256C2×C4×D53C2×D412yes—
257C2×C4×D53C2×D414yes—
258C2×C4×D53#4114yes—
259C2×C4×D53C2412yes—
260C2×Dic106—21no—
261C2×Dic106—22no—
262C2×Dic106—22no—
263C2×Dic106—22no—
264C2×Dic106—21no—
265C2×Dic106—24no—
266C2×Dic106—44no—
267C2×Dic106C2×D414yes—
268C2×Dic106C2412yes—
269C2×Dic106C2412yes—
270SD16×C53—28no—
271D8×C53—28no—
272C2×C8×C53—22no—
273C2×C8×C53—22no—
274C2×C8×C53C2412yes—
275C2×C8×C53C2412yes—
276C4⋊C4×C53—21no—
277C4⋊C4×C53C2412yes—
278C22⋊C4×C53—24no—
279C22⋊C4×C53—24no—
280C22⋊C4×C53—24no—
281C42×C53C2×D412yes—
282C42×C53C2412yes—
283C22⋊Dic53—24no—
284C22⋊Dic53—24no—
285C22⋊Dic53—24no—
286#11719925—28no—
287#11719923—28no—
288#11719923—28no—
289#11719922—28no—
290#11719921—24no—
291#11719921—24no—
292#11719921—24no—
293#11719921—24no—
294#11719921—24no—
295C4⋊Dic53—21no—
296C4⋊Dic53C2412yes—
297#11719919—24no—
298#11719919—24no—
299C4×Dic53—24no—
300C4×Dic53—24no—
301C4×Dic53—24no—
302C4×Dic53C2×D412yes—
303C4×Dic53C2×D414yes—
304C4×Dic53C2×D414yes—
305C4×Dic53C2412yes—
306C2×#88322—22no—
307C2×#88322—22no—
308C2×#88322C2412yes—
309C2×#88322C2412yes—
310Dic212—28no—
311#11719913—28no—
312#11719912—28no—
313#11719912—28no—
314C23×C53—24no—
315C23×C53—22no—
316C23×C53—22no—
317C23×C53—42no—
318C23×C53—42no—
319C23×C53—42no—
320C23×C53—42no—
321C23×C53—42no—
322C23×C53C22×D411yescharacteristic
323C22×D53—22no—
324C22×D53—22no—
325C22×D53—22no—
326C22×D53—48no—
327C22×D53—48no—
328C22×D53—42no—
329C22×D53—42no—
330C22×D53—42no—
331C22×D53—48no—
332C22×D53—816no—
333C22×D53#12114yes—
334C22×D53C22×D412yes—
335Q8×C53—22no—
336Q8×C53—22no—
337Q8×C53—42no—
338D4×C53—24no—
339D4×C53—22no—
340D4×C53—22no—
341D4×C53—22no—
342D4×C53—42no—
343D4×C53C22×D414yes—
344C2×C4×C53—22no—
345C2×C4×C53—22no—
346C2×C4×C53—22no—
347C2×C4×C53—22no—
348C2×C4×C53—48no—
349C2×C4×C53—42no—
350C2×C4×C53—42no—
351C2×C4×C53C22×D412yes—
352C2×C4×C53C22×D412yes—
353C2×C4×C53C22×D411yescharacteristic
354C2×C4×C53C22×D412yes—
355C2×C4×C53C2×#4112yes—
356C2×C4×C53C2511yescharacteristic
357C22⋊D53—216no—
358C22⋊D53—48no—
359C2×Dic53—24no—
360C2×Dic53—22no—
361C2×Dic53—22no—
362C2×Dic53—22no—
363C2×Dic53—216no—
364C2×Dic53—22no—
365C2×Dic53—22no—
366C2×Dic53—48no—
367C2×Dic53—42no—
368C2×Dic53—42no—
369C2×Dic53#12114yes—
370C2×Dic53C22×D412yes—
371C2×Dic53C22×D412yes—
372C2×Dic53C22×D412yes—
373D212—22no—
374D212—22no—
375D212—42no—
376C4×D53—44no—
377C4×D53—44no—
378C4×D53—48no—
379C4×D53#12118yes—
380C4×D53C22×D414yes—
381C4×D53C2×#4114yes—
382Dic106—24no—
383Dic106—22no—
384Dic106—22no—
385Dic106—22no—
386Dic106—42no—
387Dic106—48no—
388Dic106C22×D414yes—
389C8×C53—22no—
390C8×C53—22no—
391#88322—22no—
392#88322—22no—
393C2×#3040—531nomaximal, Sylow
394C22×C53—24no—
395C22×C53—48no—
396C22×C53—42no—
397C22×C53—42no—
398C22×C53—42no—
399C22×C53—42no—
400C22×C53—42no—
401C22×C53—84no—
402C22×C53C2×#12112yes—
403C22×C53#57512yes—
404C22×C53#57512yes—
405C22×C53C23×D411yescharacteristic
406C2×D53—28no—
407C2×D53—22no—
408C2×D53—22no—
409C2×D53—42no—
410C2×D53—42no—
411C2×D53—42no—
412C2×D53—816no—
413C2×D53—84no—
414C2×D53C2×#12114yes—
415C4×C53—22no—
416C4×C53—22no—
417C4×C53—42no—
418C4×C53—42no—
419C4×C53C2×#12112yes—
420C4×C53C23×D411yescharacteristic
421C4×C53C22×#4111yescharacteristic
422Dic53—24no—
423Dic53—22no—
424Dic53—22no—
425Dic53—42no—
426Dic53—42no—
427Dic53C2×#12114yes—
428C22×#137—531no—
429C22×AGL(1,ℤ/8)—531no—
430C22×#124—531no—
431C2×C4×#41—531no—
432#3040—5316no—
433C2×#464—531no—
434C2×#464—531no—
435C2×#464—531no—
436C2×#464—531no—
437C2×#463—531no—
438C2×#463—531no—
439C2×#463—531no—
440C2×#463D5311yescharacteristic, complemented
441C2×#423—531no—
442C2×#419—531no—
443C2×#418—531no—
444C2×C53—44no—
445C2×C53—82no—
446C2×C53#304014yescomplemented
447C2×C53C22×#12111yescharacteristic
448C2×C53C2×#57511yescharacteristic
449C2×C53C2×#57511yescharacteristic
450D53—24no—
451D53—82no—
452C22×#41—531no—
453C23×Q8—531no—
454C23×D4—531no—
455C2×#137—538no—
456C2×#137—1068no—
457C2×AGL(1,ℤ/8)—538no—
458C2×AGL(1,ℤ/8)—1068no—
459C22×Q16—531no—
460C22×Q16—531no—
461C22×SD16—531no—
462C22×SD16—531no—
463C22×SD16—531no—
464C22×SD16C2×D5311yescharacteristic, complemented
465C22×D8—531no—
466C22×D8C2×D5311yescharacteristic
467C22×M16—531no—
468C22×M16—531no—
469C2×#124—531no—
470C2×#124—531no—
471C2×#124—538no—
472C2×#124—531no—
473C2×#124—1061no—
474C2×#124—1061no—
475C2×#124—1064no—
476C2×#124C2×D5311yescharacteristic
477C4×#41—538no—
478C4×#41—1064no—
479C2×C4×Q8—531no—
480C2×C4×Q8—531no—
481C2×C4×D4—531no—
482C2×C4×D4—1061no—
483C2×C4×D4—1061no—
484C2×C4×D4C2×D5311yescharacteristic, complemented
485C2×#117—531no—
486C2×#117—1061no—
487C22×C22⋊C4—1061no—
488C22×C22⋊C4—1061no—
489C22×C42—531no—
490C22×C42—1061no—
491#464—538no—
492#464—538no—
493#464—538no—
494#464—538no—
495#463—538no—
496#463—538no—
497#463—538no—
498#463C2×D5318yescomplemented
499#423—538no—
500C2×C4⋊C8—531no—
501C2×C4⋊C8—531no—
502C2×C4⋊C8—531no—
503C2×C4⋊C8C2×D5311yescharacteristic, complemented
504#419—538no—
505#418—538no—
506C2×#103—531no—
507C2×#103—531no—
508C2×#103—531no—
509C2×#103C2×D5311yescharacteristic, complemented
510C2×#102—531no—
511C2×#102—531no—
512C2×#102—531no—
513C2×#102C2×D5311yescharacteristic
514C53C2×#304011yescharacteristic, complemented, Sylow
515C25—1061no—
516C2×#41—538no—
517C2×#41—534no—
518C2×#41—1062no—
519C2×#41—1064no—
520C22×Q8—534no—
521C22×Q8—531no—
522C22×Q8—531no—
523C22×Q8—1061no—
524C22×Q8—1062no—
525C22×Q8—1064no—
526C22×Q8—1064no—
527C22×Q8C22×D5311yescharacteristic
528C22×D4—534no—
529C22×D4—531no—
530C22×D4—1064no—
531C22×D4—1064no—
532C22×D4—1062no—
533C22×D4—1061no—
534C22×D4—1061no—
535C22×D4C22×D5311yescharacteristic
536C22×D4C22×D5311yescharacteristic
537C23×C4—21no—
538C23×C4—531no—
539C23×C4—531no—
540C23×C4—531no—
541C23×C4—1061no—
542C23×C4—1061no—
543C23×C4—1061no—
544#137—10632no—
545AGL(1,ℤ/8)—10632no—
546C2×Q16—534no—
547C2×Q16—534no—
548C2×Q16—1064no—
549C2×Q16—1064no—
550C2×SD16—24no—
551C2×SD16—534no—
552C2×SD16—534no—
553C2×SD16—534no—
554C2×SD16—1064no—
555C2×SD16—1064no—
556C2×SD16—1064no—
557C2×SD16C22×D5314yescomplemented
558C2×D8—24no—
559C2×D8—534no—
560C2×D8—1064no—
561C2×D8C22×D5314yes—
562C2×M16—534no—
563C2×M16—534no—
564C2×M16—1064no—
565C2×M16—1064no—
566C22×C8—531no—
567C22×C8—531no—
568C22×C8C22×D5311yescharacteristic
569C22×C8C22×D5311yescharacteristic
570#124—22no—
571#124—534no—
572#124—534no—
573#124—534no—
574#124—1068no—
575#124—1068no—
576#124—1062no—
577#124—1062no—
578#124—1062no—
579#124C22×D5314yes—
580C4×Q8—534no—
581C4×Q8—534no—
582C4×Q8—1062no—
583C4×Q8—1062no—
584C4×D4—22no—
585C4×D4—534no—
586C4×D4—1062no—
587C4×D4—1068no—
588C4×D4—1068no—
589C4×D4C22×D5314yescomplemented
590#117—534no—
591#117—1068no—
592#117—1062no—
593C2×C4⋊C4—531no—
594C2×C4⋊C4—1061no—
595C2×C4⋊C4—1061no—
596C2×C4⋊C4C22×D5311yescharacteristic
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—1068no—
601C2×C22⋊C4—1068no—
602C2×C22⋊C4—1061no—
603C2×C22⋊C4—1061no—
604C2×C22⋊C4—1061no—
605C2×C22⋊C4—1061no—
606C2×C22⋊C4—1061no—
607C2×C22⋊C4—1061no—
608C2×C22⋊C4—1061no—
609C2×C22⋊C4—1061no—
610C2×C42—531no—
611C2×C42—531no—
612C2×C42—531no—
613C2×C42—534no—
614C2×C42—534no—
615C2×C42—1068no—
616C2×C42—1061no—
617C2×C42—1061no—
618C2×C42—1061no—
619C2×C42C22×D5311yescharacteristic
620C4⋊C8—534no—
621C4⋊C8—534no—
622C4⋊C8—534no—
623C4⋊C8C22×D5314yescomplemented
624#103—534no—
625#103—534no—
626#103—534no—
627#103C22×D5314yescomplemented
628#102—534no—
629#102—534no—
630#102—534no—
631#102C22×D5314yes—
632C24—21no—
633C24—21no—
634C24—531no—
635C24—1064no—
636C24—1061no—
637C24—2124no—
638C24—2124no—
639C24—2124no—
640#41—5316no—
641#41—10616no—
642#41—1068no—
643C2×Q8—21no—
644C2×Q8—22no—
645C2×Q8—22no—
646C2×Q8—534no—
647C2×Q8—532no—
648C2×Q8—532no—
649C2×Q8—1064no—
650C2×Q8—1068no—
651C2×Q8—1068no—
652C2×Q8—1061no—
653C2×Q8—1061no—
654C2×Q8—1062no—
655C2×Q8—1062no—
656C2×Q8—1062no—
657C2×Q8—2124no—
658C2×Q8—2128no—
659C2×Q8C23×D5312yes—
660C2×D4—21no—
661C2×D4—22no—
662C2×D4—21no—
663C2×D4—22no—
664C2×D4—22no—
665C2×D4—532no—
666C2×D4—1068no—
667C2×D4—1068no—
668C2×D4—1064no—
669C2×D4—1064no—
670C2×D4—1068no—
671C2×D4—1062no—
672C2×D4—1061no—
673C2×D4—1062no—
674C2×D4—2128no—
675C2×D4—2124no—
676C2×D4D4×D5314yes—
677C2×D4C23×D5312yes—
678C2×D4C23×D5312yes—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—24no—
682C22×C4—44no—
683C22×C4—531no—
684C22×C4—532no—
685C22×C4—534no—
686C22×C4—534no—
687C22×C4—532no—
688C22×C4—531no—
689C22×C4—531no—
690C22×C4—534no—
691C22×C4—534no—
692C22×C4—1064no—
693C22×C4—1064no—
694C22×C4—1068no—
695C22×C4—1064no—
696C22×C4—1061no—
697C22×C4—1061no—
698C22×C4—1061no—
699C22×C4—2122no—
700C22×C4—2122no—
701C22×C4—2124no—
702C22×C4—2124no—
703C22×C4D4×D5311yescharacteristic
704C22×C4D4×D5311yescharacteristic
705C22×C4C23×D5311yescharacteristic
706Q16—1068no—
707Q16—1068no—
708SD16—28no—
709SD16—1068no—
710SD16—1068no—
711SD16—1068no—
712D8—28no—
713D8—1068no—
714M16—1068no—
715M16—1068no—
716C2×C8—22no—
717C2×C8—22no—
718C2×C8—532no—
719C2×C8—532no—
720C2×C8—1062no—
721C2×C8—1062no—
722C2×C8C23×D5312yes—
723C2×C8C23×D5312yes—
724C4⋊C4—21no—
725C4⋊C4—532no—
726C4⋊C4—1064no—
727C4⋊C4—1061no—
728C4⋊C4—1064no—
729C4⋊C4C23×D5312yes—
730C22⋊C4—24no—
731C22⋊C4—24no—
732C22⋊C4—24no—
733C22⋊C4—1064no—
734C22⋊C4—1064no—
735C22⋊C4—1064no—
736C22⋊C4—1064no—
737C22⋊C4—1064no—
738C22⋊C4—1064no—
739C22⋊C4—1064no—
740C22⋊C4—1064no—
741C42—534no—
742C42—534no—
743C42—532no—
744C42—532no—
745C42—1064no—
746C42—1064no—
747C42—1064no—
748C42D4×D5312yes—
749C42C23×D5312yes—
750C23—24no—
751C23—22no—
752C23—22no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—534no—
759C23—532no—
760C23—1062no—
761C23—1062no—
762C23—1062no—
763C23—42416no—
764C23—2128no—
765C23—2128no—
766C23—2128no—
767C23—2122no—
768C23—2122no—
769C23—2122no—
770C23C2×D4×D5311yescharacteristic
771Q8—22no—
772Q8—22no—
773Q8—42no—
774Q8—534no—
775Q8—1064no—
776Q8—1062no—
777Q8—1062no—
778Q8—1062no—
779Q8—2128no—
780Q8—2122no—
781D4—24no—
782D4—22no—
783D4—22no—
784D4—22no—
785D4—42no—
786D4—10616no—
787D4—1062no—
788D4—1062no—
789D4—2128no—
790D4—2122no—
791D4C2×D4×D5314yes—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—48no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—534no—
800C2×C4—532no—
801C2×C4—538no—
802C2×C4—534no—
803C2×C4—534no—
804C2×C4—532no—
805C2×C4—532no—
806C2×C4—10616no—
807C2×C4—1064no—
808C2×C4—1062no—
809C2×C4—1062no—
810C2×C4—1062no—
811C2×C4—1062no—
812C2×C4—1062no—
813C2×C4—2124no—
814C2×C4—2124no—
815C2×C4—2128no—
816C2×C4—2128no—
817C2×C4—2122no—
818C2×C4—2122no—
819C2×C4C2×D4×D5312yes—
820C2×C4C2×D4×D5312yes—
821C2×C4C2×D4×D5311yescharacteristic
822C2×C4C2×D4×D5312yes—
823C2×C4#41×D5312yes—
824C2×C4C24×D5311yescharacteristic
825C8—22no—
826C8—22no—
827C8—1062no—
828C8—1062no—
829C22—24no—
830C22—48no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—84no—
837C22—534no—
838C22—1068no—
839C22—1062no—
840C22—1062no—
841C22—42416no—
842C22—4244no—
843C22—2122no—
844C22—2122no—
845C22—2122no—
846C22#121×D5312yes—
847C22#1681141912yes—
848C22#1681142012yes—
849C22C22×D4×D5311yescharacteristic
850C4—22no—
851C4—22no—
852C4—42no—
853C4—42no—
854C4—534no—
855C4—1062no—
856C4—1062no—
857C4—1064no—
858C4—2122no—
859C4—2122no—
860C4#121×D5312yes—
861C4C22×D4×D5311yescharacteristic
862C4C2×#41×D5311yescharacteristic
863C2—44no—
864C2—82no—
865C2—1064no—
866C2—4242no—
867C2#2028420414yesdirect product factor
868C2C2×#121×D5311yescharacteristic
869C2C2×#1681141911yescharacteristic
870C2C2×#1681142011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#463C2
socleC23×C53C22×D4
prime radicalC22×#13133241C2
hypercenterC2×#463D53
hypocenterC53C2×#3040
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C22×#13133246C2semidirect
3. C2×#124×D53C2semidirect
4. C2×C4×#11719947C2semidirect
5. #20284204C2direct (N × H)
6. C2×#16810848C2semidirect
7. C2×#16810846C2semidirect
8. C2×#16810844C2semidirect
9. C2×#16810842C2semidirect
10. C2×#16810840C2semidirect
11. C2×#16810838C2semidirect
12. C2×#16810836C2semidirect
13. C2×#16810645C2semidirect
14. C2×#16810630C2semidirect
15. C2×#16810626C2semidirect
16. C2×C53×#463C2semidirect
21. C2×#13133246C22semidirect
24. C22×Dic212C22semidirect
25. C22×#11719925C22semidirect
28. C22×#11719923C22semidirect
38. #124×D53C22semidirect
40. C4×#11719947C22semidirect
41. C2×C4×Dic106C22semidirect
42. C2×#13133182C22semidirect
43. C2×D4×Dic53C22semidirect
52. #16810848C22semidirect
53. #16810846C22semidirect
54. #16810844C22semidirect
55. #16810842C22semidirect
56. #16810840C22semidirect
57. #16810838C22semidirect
58. #16810836C22semidirect
59. #16810645C22semidirect
60. C2×C4⋊#88322C22semidirect
61. C2×#13133146C22semidirect
62. C2×#13133146C22semidirect
63. #16810630C22semidirect
64. #16810626C22semidirect
65. C2×#13133142C22semidirect
66. C2×#13133141C22semidirect
67. C2×#13133140C22semidirect
71. C22×SD16×C53C22semidirect
74. C2×C4×D4×C53C22semidirect
75. C53×#463C22semidirect
76. C2×C4⋊C8×C53C22semidirect
77. C2×#103×C53C22semidirect
107. C2×Dic212C23semidirect
109. C2×#11719925C23semidirect
115. C2×#11719923C23semidirect
133. C4×Dic106C23semidirect
135. #13133182C23semidirect
137. D4×Dic53C23semidirect
165. C4⋊#88322C23semidirect
166. #13133146C23semidirect
167. #13133146C23semidirect
168. #13133142C23semidirect
169. #13133141C23semidirect
170. #13133140C23semidirect
179. C2×SD16×C53C23semidirect
187. C4×D4×C53C23semidirect
193. C4⋊C8×C53C23semidirect
194. #103×C53C23semidirect
440. C2×#463D53semidirect
446. C2×C53#3040semidirect
464. C22×SD16C2×D53semidirect
484. C2×C4×D4C2×D53semidirect
498. #463C2×D53semidirect
503. C2×C4⋊C8C2×D53semidirect
509. C2×#103C2×D53semidirect
514. C53C2×#3040semidirect
557. C2×SD16C22×D53semidirect
589. C4×D4C22×D53semidirect
623. C4⋊C8C22×D53semidirect
627. #103C22×D53semidirect
867. C2#20284204direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332462
C22×#131332412
C2×#124×D532
C2×C4×#117199472
#202842042
C2×#168108482
C2×#168108462
C2×#168108442
C2×#168108422
C2×#168108402
C2×#168108382
C2×#168108362
C2×#168106452
C2×#168106302
C2×#168106262
C2×C53×#4632
C2×#304053