Finite Group Databasebeta

← C2×#20284266 #28251030

Subgroups — C2×#20284266 #28251030

Order 13568.

2742 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133246C211yesmaximal, characteristic, complemented
2C22×#13133236C211yesmaximal, characteristic
3C2×#16811193C211yesmaximal, characteristic, complemented
4C2×#16811102C211yesmaximal, characteristic, complemented
5#20284266C2116yesmaximal, direct product factor
6C2×#16810844C211yesmaximal, characteristic, complemented
7C2×#16810842C211yesmaximal, characteristic, complemented
8C2×#16810834C211yesmaximal, characteristic, complemented
9C2×#16810832C211yesmaximal, characteristic, complemented
10C2×#16810836C211yesmaximal, characteristic, complemented
11C2×#16810828C211yesmaximal, characteristic, complemented
12C2×#16810826C211yesmaximal, characteristic, complemented
13C2×#16810648C211yesmaximal, characteristic, complemented
14C2×#16810621C211yesmaximal, characteristic, complemented
15C2×#103×D53C211yesmaximal, characteristic, complemented
16C2×C53×#463C211yesmaximal, characteristic, complemented
17C22×#11719947C2211yescharacteristic
18C22×#11719947C2211yescharacteristic
19C22×Q8×D53C2211yescharacteristic
20C2×#13133246—28no—
21C2×#13133246C2218yescomplemented
22C2×#13133236—28no—
23C2×#13133236C2218yes—
24C22×Dic212C2211yescharacteristic
25C22×Dic212C2211yescharacteristic
26C22×#11719925C2211yescharacteristic
27C22×#11719923C2211yescharacteristic
28C22×#11719923C2211yescharacteristic
29C22×#11719923C2211yescharacteristic
30C22×#11719912C2211yescharacteristic
31C22×C8×D53C2211yescharacteristic
32#16811193—24no—
33#16811193C2218yescomplemented
34C2×#13133217C2211yescharacteristic
35C2×#13133215C2211yescharacteristic
36C2×#13133204C2211yescharacteristic
37C2×#13133199—21no—
38C2×#13133199—21no—
39C2×#13133194—21no—
40C2×#13133194—21no—
41#16811102—24no—
42#16811102C2218yescomplemented
43C2×C4×Dic106C2211yescharacteristic
44C2×#13133182C2211yescharacteristic
45C2×D4×Dic53C2211yescharacteristic
46C2×C4×C22⋊D53—21no—
47C2×#13133177—21no—
48C2×#13133174C2211yescharacteristic
49C2×#13133173—21no—
50C22×#11719919—21no—
51C2×C4⋊C4×D53C2211yescharacteristic
52#16810844C2218yescomplemented
53#16810842C2218yescomplemented
54#16810836C2218yescomplemented
55#16810834C2218yescomplemented
56#16810832C2218yescomplemented
57#16810828C2218yescomplemented
58#16810826C2218yescomplemented
59#16810648C2218yescomplemented
60C2×C4⋊#88322C2211yescharacteristic
61C2×#13133146C2211yescharacteristic
62C2×#13133146C2211yescharacteristic
63#16810621C2218yescomplemented
64C2×#13133142C2211yescharacteristic
65C2×#13133142C2211yescharacteristic
66C2×#13133141C2211yescharacteristic
67C2×#13133140C2211yescharacteristic
68C2×#13133140C2211yescharacteristic
69#103×D53C2218yescomplemented
70C2×#13133138C2211yescharacteristic
71C22×SD16×C53C2211yescharacteristic
72C22×D8×C53C2211yescharacteristic
73C2×#124×C53C2211yescharacteristic
74C2×C4×D4×C53C2211yescharacteristic
75C53×#463C2218yescomplemented
76C2×C4⋊C8×C53C2211yescharacteristic
77C2×#103×C53C2211yescharacteristic
78C2×#102×C53C2211yescharacteristic
79C2×#11719947—22no—
80C2×#11719947—24no—
81C2×#11719947—22no—
82C2×#11719947—24no—
83C2×#11719947—24no—
84C2×#11719947D418yes—
85C2×#11719947C2314yes—
86C2×#11719947C2314yes—
87C22×Dic106—21no—
88C22×Dic106C2311yescharacteristic
89C22×Dic106C2311yescharacteristic
90C22×Dic106C2311yescharacteristic
91C2×Q8×D53—22no—
92C2×Q8×D53—24no—
93C2×Q8×D53—24no—
94C2×Q8×D53C2314yes—
95C22×C22⋊D53—21no—
96C22×C22⋊D53—21no—
97C23×Dic53—21no—
98C23×Dic53—21no—
99C23×Dic53—21no—
100C22×C4×D53—21no—
101C22×C4×D53—21no—
102C22×C4×D53C2311yescharacteristic
103#13133246—232no—
104#13133236—232no—
105C2×Dic212—24no—
106C2×Dic212—24no—
107C2×Dic212C2314yes—
108C2×Dic212C2314yes—
109C2×#11719925—24no—
110C2×#11719925C2314yes—
111C2×#11719923—24no—
112C2×#11719923—24no—
113C2×#11719923—24no—
114C2×#11719923C2314yes—
115C2×#11719923C2314yes—
116C2×#11719923C2314yes—
117C2×#11719912—24no—
118C2×#11719912C2314yes—
119C22×#88322C2311yescharacteristic
120C22×#88322C2311yescharacteristic
121C2×C8×D53—24no—
122C2×C8×D53C2314yes—
123#13133217—22no—
124#13133217C2314yes—
125#13133215—22no—
126#13133215C2314yes—
127#13133204—22no—
128#13133204C2314yes—
129#13133199—28no—
130#13133199—28no—
131#13133194—28no—
132#13133194—28no—
133C4×Dic106—22no—
134C4×Dic106C2314yes—
135#13133182—22no—
136#13133182C2314yes—
137D4×Dic53—22no—
138D4×Dic53C2314yes—
139C4×C22⋊D53—28no—
140#13133177—28no—
141#13133174D414yes—
142#13133174C2314yes—
143#13133173—28no—
144C2×C4⋊Dic53—21no—
145C2×C4⋊Dic53—21no—
146C2×C4⋊Dic53C2311yescharacteristic
147C2×#11719919—28no—
148C2×#11719919—21no—
149C2×#11719919—21no—
150C2×#11719919—21no—
151C2×#11719919—21no—
152C2×#11719919—21no—
153C2×#11719919D411yescharacteristic
154C2×#11719919D411yescharacteristic
155C4⋊C4×D53—22no—
156C4⋊C4×D53C2314yes—
157C2×C22⋊Dic53—21no—
158C2×C22⋊Dic53—21no—
159C2×C22⋊Dic53—21no—
160C2×#11719921D411yescharacteristic
161C2×#11719921D411yescharacteristic
162C2×C4×Dic53—21no—
163C2×C4×Dic53—21no—
164C2×C4×Dic53C2311yescharacteristic
165C4⋊#88322C2314yes—
166#13133146C2314yes—
167#13133146C2314yes—
168#13133142C2314yes—
169#13133142C2314yes—
170#13133141C2314yes—
171#13133140C2314yes—
172#13133140C2314yes—
173#13133138C2314yes—
174C22×Q8×C53C2311yescharacteristic
175C22×D4×C53C2311yescharacteristic
176C22×D4×C53C2311yescharacteristic
177C23×C4×C53—21no—
178C2×SD16×C53—24no—
179C2×SD16×C53C2314yes—
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×C53C2314yes—
188C2×C4⋊C4×C53C2311yescharacteristic
189C2×C22⋊C4×C53—21no—
190C2×C22⋊C4×C53—21no—
191C2×C22⋊C4×C53—21no—
192C2×C42×C53C2311yescharacteristic
193C4⋊C8×C53C2314yes—
194#103×C53C2314yes—
195#102×C53C2314yes—
196C24×C53—21no—
197C24×C53—21no—
198C23×D53C2×D411yescharacteristic
199C2×Q8×C53—21no—
200C2×Q8×C53—22no—
201C2×Q8×C53—22no—
202C2×Q8×C53C2412yes—
203C2×D4×C53—21no—
204C2×D4×C53—22no—
205C2×D4×C53—21no—
206C2×D4×C53—22no—
207C2×D4×C53—22no—
208C2×D4×C53C2×D414yes—
209C2×D4×C53C2412yes—
210C2×D4×C53C2412yes—
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53—24no—
214C22×C4×C53—82no—
215C22×C4×C53C2×D411yescharacteristic
216C22×C4×C53C2×D411yescharacteristic
217C22×C4×C53C2411yescharacteristic
218C2×C22⋊D53—28no—
219C2×C22⋊D53—24no—
220C2×C22⋊D53—24no—
221C2×C22⋊D53—44no—
222C22×Dic53—21no—
223C22×Dic53—28no—
224C22×Dic53—24no—
225C22×Dic53—21no—
226C22×Dic53—21no—
227C22×Dic53—21no—
228C22×Dic53—24no—
229C22×Dic53—24no—
230C22×Dic53—44no—
231C22×Dic53—82no—
232C22×Dic53C2×D411yescharacteristic
233C22×Dic53C2×D411yescharacteristic
234C22×Dic53C2×D411yescharacteristic
235Q8×D53—28no—
236Q8×D53—28no—
237Q8×D53—48no—
238#11719947—216no—
239#11719947—28no—
240#11719947—28no—
241#11719947—28no—
242#11719947—48no—
243#11719947C2×D4116yes—
244C2×C4×D53—24no—
245C2×C4×D53—24no—
246C2×C4×D53—44no—
247C2×C4×D53—82no—
248C2×C4×D53C2×D412yes—
249C2×C4×D53C2×D414yes—
250C2×C4×D53#4114yes—
251C2×C4×D53C2412yes—
252C2×Dic106—21no—
253C2×Dic106—22no—
254C2×Dic106—22no—
255C2×Dic106—22no—
256C2×Dic106—22no—
257C2×Dic106—22no—
258C2×Dic106—21no—
259C2×Dic106—21no—
260C2×Dic106—24no—
261C2×Dic106—44no—
262C2×Dic106C2×D414yes—
263C2×Dic106C2412yes—
264C2×Dic106C2412yes—
265C2×Dic106C2412yes—
266SD16×C53—28no—
267D8×C53—28no—
268C2×C8×C53—22no—
269C2×C8×C53—22no—
270C2×C8×C53C2412yes—
271C2×C8×C53C2412yes—
272C4⋊C4×C53—21no—
273C4⋊C4×C53C2412yes—
274C22⋊C4×C53—24no—
275C22⋊C4×C53—24no—
276C22⋊C4×C53—24no—
277C42×C53C2×D412yes—
278C42×C53C2412yes—
279C22⋊Dic53—24no—
280C22⋊Dic53—24no—
281C22⋊Dic53—24no—
282#11719925—28no—
283#11719923—28no—
284#11719923—28no—
285#11719923—28no—
286#11719921C2×D414yes—
287#11719921C2×D414yes—
288C4⋊Dic53—21no—
289C4⋊Dic53—24no—
290C4⋊Dic53—24no—
291C4⋊Dic53C2412yes—
292#11719919—24no—
293#11719919—24no—
294#11719919—24no—
295#11719919—24no—
296#11719919—24no—
297#11719919C2×D414yes—
298#11719919C2×D414yes—
299C4×Dic53—24no—
300C4×Dic53—24no—
301C4×Dic53C2×D412yes—
302C4×Dic53C2412yes—
303C2×#88322—22no—
304C2×#88322—22no—
305C2×#88322C2412yes—
306C2×#88322C2412yes—
307Dic212—28no—
308Dic212—28no—
309#11719912—28no—
310C8×D53—28no—
311C23×C53—24no—
312C23×C53—22no—
313C23×C53—22no—
314C23×C53—42no—
315C23×C53—42no—
316C23×C53—42no—
317C23×C53—42no—
318C23×C53—42no—
319C23×C53C22×D411yescharacteristic
320C22×D53—22no—
321C22×D53—22no—
322C22×D53#12114yes—
323C22×D53C22×D412yes—
324Q8×C53—22no—
325Q8×C53—22no—
326Q8×C53—42no—
327D4×C53—24no—
328D4×C53—22no—
329D4×C53—22no—
330D4×C53—22no—
331D4×C53—42no—
332D4×C53C22×D414yes—
333C2×C4×C53—22no—
334C2×C4×C53—22no—
335C2×C4×C53—22no—
336C2×C4×C53—22no—
337C2×C4×C53—42no—
338C2×C4×C53—42no—
339C2×C4×C53—84no—
340C2×C4×C53C22×D412yes—
341C2×C4×C53C22×D412yes—
342C2×C4×C53C22×D411yescharacteristic
343C2×C4×C53C22×D412yes—
344C2×C4×C53C2×#4112yes—
345C2×C4×C53C2511yescharacteristic
346C22⋊D53—216no—
347C22⋊D53—48no—
348C2×Dic53—24no—
349C2×Dic53—22no—
350C2×Dic53—22no—
351C2×Dic53—22no—
352C2×Dic53—216no—
353C2×Dic53—22no—
354C2×Dic53—22no—
355C2×Dic53—22no—
356C2×Dic53—42no—
357C2×Dic53—42no—
358C2×Dic53—42no—
359C2×Dic53—48no—
360C2×Dic53—84no—
361C2×Dic53#12114yes—
362C2×Dic53C22×D412yes—
363C2×Dic53C22×D412yes—
364C2×Dic53C22×D412yes—
365C4×D53—48no—
366C4×D53—84no—
367C4×D53#12118yes—
368C4×D53C22×D414yes—
369C4×D53C2×#4114yes—
370Dic106—24no—
371Dic106—22no—
372Dic106—22no—
373Dic106—22no—
374Dic106—22no—
375Dic106—22no—
376Dic106—42no—
377Dic106—42no—
378Dic106—48no—
379Dic106C22×D414yes—
380C8×C53—22no—
381C8×C53—22no—
382#88322—22no—
383#88322—22no—
384C2×#3046—531nomaximal, Sylow
385C22×C53—24no—
386C22×C53—48no—
387C22×C53—42no—
388C22×C53—42no—
389C22×C53—42no—
390C22×C53—42no—
391C22×C53—42no—
392C22×C53—84no—
393C22×C53C2×#12112yes—
394C22×C53#57712yes—
395C22×C53#57812yes—
396C22×C53C23×D411yescharacteristic
397C2×D53—28no—
398C2×D53—22no—
399C2×D53—22no—
400C2×D53C2×#12114yes—
401C4×C53—22no—
402C4×C53—22no—
403C4×C53—42no—
404C4×C53—42no—
405C4×C53C2×#12112yes—
406C4×C53C23×D411yescharacteristic
407C4×C53C22×#4111yescharacteristic
408Dic53—24no—
409Dic53—22no—
410Dic53—22no—
411Dic53—42no—
412Dic53—42no—
413Dic53—42no—
414Dic53C2×#12114yes—
415C22×#137—531no—
416C22×#135—531no—
417C2×#536—531no—
418C2×#520—531no—
419#3046—5316no—
420C2×#464—531no—
421C2×#464—531no—
422C2×#462—531no—
423C2×#462—531no—
424C2×#463—531no—
425C2×#463D5311yescharacteristic, complemented
426C2×#461—531no—
427C2×#461—531no—
428C2×#424—531no—
429C2×#417—531no—
430C22×#103—531no—
431C2×C53—44no—
432C2×C53—82no—
433C2×C53#304614yescomplemented
434C2×C53C22×#12111yescharacteristic
435C2×C53C2×#57711yescharacteristic
436C2×C53C2×#57811yescharacteristic
437D53—24no—
438C22×#41—531no—
439C22×#41—531no—
440C23×Q8—531no—
441C2×#137—538no—
442C2×#137—1068no—
443C2×#135—538no—
444C2×#135—1068no—
445C22×Q16—531no—
446C22×Q16—531no—
447C22×Q16—531no—
448C22×SD16—531no—
449C22×SD16—531no—
450C22×SD16—531no—
451C22×SD16C2×D5311yescharacteristic
452C22×D8C2×D5311yescharacteristic
453C22×M16—531no—
454C23×C8—531no—
455#536—538no—
456#536—1064no—
457C2×C4⋊Q8—531no—
458C2×C4⋊Q8—531no—
459C2×#124—531no—
460C2×#124C2×D5311yescharacteristic
461C2×#123—1061no—
462C2×#123—1061no—
463C2×C22⋊Q8—1061no—
464C2×C22⋊Q8—1061no—
465#520—538no—
466#520—1064no—
467C2×C4×Q8—531no—
468C2×C4×Q8—531no—
469C2×C4×D4—531no—
470C2×C4×D4—1061no—
471C2×C4×D4—1061no—
472C2×C4×D4C2×D5311yescharacteristic
473C2×#117—531no—
474C2×#117—1061no—
475C22×C4⋊C4—531no—
476C22×C4⋊C4—1061no—
477#464—538no—
478#464—538no—
479#463—538no—
480#463C2×D5318yescomplemented
481#462—538no—
482#462—538no—
483#461—538no—
484#461—538no—
485#424—538no—
486C2×C4⋊C8—531no—
487C2×C4⋊C8—531no—
488C2×C4⋊C8—531no—
489C2×C4⋊C8C2×D5311yescharacteristic
490#417—538no—
491C2×#103—531no—
492C2×#103—531no—
493C2×#103—531no—
494C2×#103—531no—
495C2×#103—531no—
496C2×#103—538no—
497C2×#103C2×D5311yescharacteristic
498C2×#102—531no—
499C2×#102C2×D5311yescharacteristic
500C53C2×#304611yescharacteristic, complemented, Sylow
501C2×#41—538no—
502C2×#41—534no—
503C2×#41—534no—
504C2×#41—1062no—
505C2×#41—1064no—
506C2×#41—1062no—
507C2×#41—1064no—
508C2×#41—1064no—
509C22×Q8—534no—
510C22×Q8—531no—
511C22×Q8—531no—
512C22×Q8—531no—
513C22×Q8—1061no—
514C22×Q8—1062no—
515C22×Q8—1064no—
516C22×Q8—1064no—
517C22×Q8C22×D5311yescharacteristic
518C22×D4—1061no—
519C22×D4—1061no—
520C22×D4C22×D5311yescharacteristic
521C22×D4C22×D5311yescharacteristic
522C23×C4—21no—
523C23×C4—531no—
524C23×C4—1061no—
525C23×C4—1061no—
526C23×C4—1061no—
527C23×C4—1061no—
528C23×C4—1061no—
529#137—10632no—
530#135—10632no—
531C2×Q16—534no—
532C2×Q16—534no—
533C2×Q16—534no—
534C2×Q16—1064no—
535C2×Q16—1064no—
536C2×Q16—1064no—
537C2×SD16—24no—
538C2×SD16—534no—
539C2×SD16—534no—
540C2×SD16—534no—
541C2×SD16—1064no—
542C2×SD16—1064no—
543C2×SD16—1064no—
544C2×SD16C22×D5314yes—
545C2×D8—24no—
546C2×D8C22×D5314yes—
547C2×M16—534no—
548C2×M16—1064no—
549C22×C8—531no—
550C22×C8—531no—
551C22×C8—534no—
552C22×C8—1064no—
553C22×C8C22×D5311yescharacteristic
554C22×C8C22×D5311yescharacteristic
555C4⋊Q8—534no—
556C4⋊Q8—534no—
557C4⋊Q8—1062no—
558C4⋊Q8—1062no—
559#124—22no—
560#124—534no—
561#124—1062no—
562#124C22×D5314yes—
563#123—1068no—
564#123—1068no—
565C22⋊Q8—1068no—
566C22⋊Q8—1068no—
567C4×Q8—534no—
568C4×Q8—534no—
569C4×Q8—1062no—
570C4×Q8—1062no—
571C4×D4—22no—
572C4×D4—534no—
573C4×D4—1062no—
574C4×D4—1068no—
575C4×D4—1068no—
576C4×D4C22×D5314yes—
577#117—534no—
578#117—534no—
579#117—1068no—
580C2×C4⋊C4—531no—
581C2×C4⋊C4—531no—
582C2×C4⋊C4—531no—
583C2×C4⋊C4—534no—
584C2×C4⋊C4—1062no—
585C2×C4⋊C4—1068no—
586C2×C4⋊C4—1061no—
587C2×C4⋊C4—1061no—
588C2×C4⋊C4—1061no—
589C2×C4⋊C4—1061no—
590C2×C4⋊C4—1061no—
591C2×C4⋊C4—1061no—
592C2×C4⋊C4—1061no—
593C2×C4⋊C4C22×D5311yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—531no—
598C2×C22⋊C4—531no—
599C2×C22⋊C4—1061no—
600C2×C22⋊C4—1061no—
601C2×C22⋊C4—1061no—
602C2×C42—531no—
603C2×C42—1061no—
604C2×C42—1061no—
605C2×C42C22×D5311yescharacteristic
606C4⋊C8—534no—
607C4⋊C8—534no—
608C4⋊C8—534no—
609C4⋊C8C22×D5314yes—
610#103—534no—
611#103—534no—
612#103—534no—
613#103—534no—
614#103—534no—
615#103C22×D5314yes—
616#102—534no—
617#102C22×D5314yes—
618C24—21no—
619C24—21no—
620C24—531no—
621#41—5316no—
622#41—10616no—
623#41—1068no—
624#41—1068no—
625#41—1068no—
626#41—2128no—
627C2×Q8—21no—
628C2×Q8—22no—
629C2×Q8—22no—
630C2×Q8—534no—
631C2×Q8—532no—
632C2×Q8—532no—
633C2×Q8—532no—
634C2×Q8—1064no—
635C2×Q8—1068no—
636C2×Q8—1068no—
637C2×Q8—1061no—
638C2×Q8—1061no—
639C2×Q8—1061no—
640C2×Q8—1062no—
641C2×Q8—1062no—
642C2×Q8—1062no—
643C2×Q8—1062no—
644C2×Q8—1062no—
645C2×Q8—2124no—
646C2×Q8—2128no—
647C2×Q8C23×D5312yes—
648C2×D4—21no—
649C2×D4—22no—
650C2×D4—21no—
651C2×D4—22no—
652C2×D4—22no—
653C2×D4—1064no—
654C2×D4—1068no—
655C2×D4—1064no—
656C2×D4—2124no—
657C2×D4D4×D5314yes—
658C2×D4C23×D5312yes—
659C2×D4C23×D5312yes—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—24no—
663C22×C4—82no—
664C22×C4—531no—
665C22×C4—532no—
666C22×C4—534no—
667C22×C4—534no—
668C22×C4—532no—
669C22×C4—531no—
670C22×C4—531no—
671C22×C4—1064no—
672C22×C4—1064no—
673C22×C4—1064no—
674C22×C4—1068no—
675C22×C4—1064no—
676C22×C4—1064no—
677C22×C4—1061no—
678C22×C4—1061no—
679C22×C4—1061no—
680C22×C4—1061no—
681C22×C4—4242no—
682C22×C4—4242no—
683C22×C4—2124no—
684C22×C4—2124no—
685C22×C4D4×D5311yescharacteristic
686C22×C4D4×D5311yescharacteristic
687C22×C4C23×D5311yescharacteristic
688Q16—1068no—
689Q16—1068no—
690Q16—1068no—
691SD16—28no—
692SD16—1068no—
693SD16—1068no—
694SD16—1068no—
695D8—28no—
696M16—1068no—
697C2×C8—22no—
698C2×C8—22no—
699C2×C8—532no—
700C2×C8—532no—
701C2×C8—1068no—
702C2×C8—1062no—
703C2×C8—1062no—
704C2×C8C23×D5312yes—
705C2×C8C23×D5312yes—
706C4⋊C4—21no—
707C4⋊C4—534no—
708C4⋊C4—534no—
709C4⋊C4—532no—
710C4⋊C4—1064no—
711C4⋊C4—1064no—
712C4⋊C4—1064no—
713C4⋊C4—1064no—
714C4⋊C4—1061no—
715C4⋊C4—1064no—
716C4⋊C4—1064no—
717C4⋊C4—1064no—
718C4⋊C4C23×D5312yes—
719C22⋊C4—24no—
720C22⋊C4—24no—
721C22⋊C4—24no—
722C22⋊C4—534no—
723C22⋊C4—534no—
724C22⋊C4—1064no—
725C22⋊C4—1064no—
726C22⋊C4—1064no—
727C42—532no—
728C42—532no—
729C42—1064no—
730C42—1064no—
731C42D4×D5312yes—
732C42C23×D5312yes—
733C23—24no—
734C23—22no—
735C23—22no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—534no—
742C23—532no—
743C23—1062no—
744C23—1062no—
745C23C2×D4×D5311yescharacteristic
746Q8—22no—
747Q8—22no—
748Q8—42no—
749Q8—534no—
750Q8—1064no—
751Q8—1062no—
752Q8—1062no—
753Q8—1062no—
754Q8—1062no—
755Q8—1062no—
756Q8—2128no—
757Q8—2122no—
758Q8—2122no—
759D4—24no—
760D4—22no—
761D4—22no—
762D4—22no—
763D4—42no—
764D4—10616no—
765D4—2128no—
766D4C2×D4×D5314yes—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—84no—
774C2×C4—534no—
775C2×C4—532no—
776C2×C4—538no—
777C2×C4—534no—
778C2×C4—534no—
779C2×C4—532no—
780C2×C4—532no—
781C2×C4—10616no—
782C2×C4—1064no—
783C2×C4—1062no—
784C2×C4—1062no—
785C2×C4—1062no—
786C2×C4—1062no—
787C2×C4—1062no—
788C2×C4—1062no—
789C2×C4—4244no—
790C2×C4—4244no—
791C2×C4—2128no—
792C2×C4—2128no—
793C2×C4—2122no—
794C2×C4—2122no—
795C2×C4—2122no—
796C2×C4C2×D4×D5312yes—
797C2×C4C2×D4×D5312yes—
798C2×C4C2×D4×D5311yescharacteristic
799C2×C4C2×D4×D5312yes—
800C2×C4#41×D5312yes—
801C2×C4C24×D5311yescharacteristic
802C8—22no—
803C8—22no—
804C8—1062no—
805C8—1062no—
806C22—24no—
807C22—48no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—84no—
814C22—534no—
815C22—1068no—
816C22—1062no—
817C22—1062no—
818C22#121×D5312yes—
819C22#1681143312yes—
820C22#1681143712yes—
821C22C22×D4×D5311yescharacteristic
822C4—22no—
823C4—22no—
824C4—42no—
825C4—42no—
826C4—534no—
827C4—1064no—
828C4—1062no—
829C4—1062no—
830C4—2122no—
831C4—2122no—
832C4—2122no—
833C4#121×D5312yes—
834C4C22×D4×D5311yescharacteristic
835C4C2×#41×D5311yescharacteristic
836C2—44no—
837C2—82no—
838C2—1064no—
839C2#2028426614yesdirect product factor
840C2C2×#121×D5311yescharacteristic
841C2C2×#1681143311yescharacteristic
842C2C2×#1681143711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#463C2
socleC23×C53C22×D4
prime radicalC22×#13133236C2
hypercenterC2×#463D53
hypocenterC53C2×#3046
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×#16811193C2semidirect
4. C2×#16811102C2semidirect
5. #20284266C2direct (N × H)
6. C2×#16810844C2semidirect
7. C2×#16810842C2semidirect
8. C2×#16810834C2semidirect
9. C2×#16810832C2semidirect
10. C2×#16810836C2semidirect
11. C2×#16810828C2semidirect
12. C2×#16810826C2semidirect
13. C2×#16810648C2semidirect
14. C2×#16810621C2semidirect
15. C2×#103×D53C2semidirect
16. C2×C53×#463C2semidirect
21. C2×#13133246C22semidirect
33. #16811193C22semidirect
42. #16811102C22semidirect
52. #16810844C22semidirect
53. #16810842C22semidirect
54. #16810836C22semidirect
55. #16810834C22semidirect
56. #16810832C22semidirect
57. #16810828C22semidirect
58. #16810826C22semidirect
59. #16810648C22semidirect
63. #16810621C22semidirect
69. #103×D53C22semidirect
75. C53×#463C22semidirect
425. C2×#463D53semidirect
433. C2×C53#3046semidirect
480. #463C2×D53semidirect
500. C53C2×#3046semidirect
839. C2#20284266direct (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×#131332362
C2×#168111932
C2×#168111022
#202842662
C2×#168108442
C2×#168108422
C2×#168108342
C2×#168108322
C2×#168108362
C2×#168108282
C2×#168108262
C2×#168106482
C2×#168106212
C2×#103×D532
C2×C53×#4632
C2×#304653