Finite Group Databasebeta

← C2×#20275246 #27386083

Subgroups — C2×#20275246 #27386083

Order 13568.

1974 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811192C211yesmaximal, characteristic
2C2×#16811097C211yesmaximal, characteristic, complemented
3C2×#16810641C211yesmaximal, characteristic, complemented
4C2×#16810639C211yesmaximal, characteristic, complemented
5C22×#13133133C211yesmaximal, characteristic, complemented
6#20275246C218yesmaximal, direct product factor
7C2×#16810379C211yesmaximal, characteristic, complemented
8C2×C53×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
9C22×#11719945C2211yescharacteristic
10C23×D212C2211yescharacteristic
11C22×#11719917C2211yescharacteristic
12#16811192—22no—
13#16811192—22no—
14#16811192C414yescomplemented
15#16811192C2214yes—
16C2×#13133214C412yescomplemented
17C2×#13133205C412yescomplemented
18C2×#13133192—22no—
19C2×#13133187—22no—
20#16811097—22no—
21#16811097—22no—
22#16811097—22no—
23#16811097C2214yescomplemented
24C2×C4×D212—22no—
25C2×#13133179—22no—
26C2×#13133176C2211yescharacteristic
27C2×C22⋊C4×D53—22no—
28#16810641—22no—
29#16810641C2214yescomplemented
30#16810639—22no—
31#16810639C2214yescomplemented
32C2×#13133145—22no—
33C2×#13133143—22no—
34C2×#13133133—22no—
35C2×#13133133—22no—
36C2×#13133133C2214yescomplemented
37#16810379C2214yescomplemented
38C22×M16×C53C2211yescharacteristic
39C2×#117×C53C2211yescharacteristic
40C2×#117×C53C2211yescharacteristic
41C53×H(3,ℤ/4)C2214yescomplemented
42C24×D53D412yes—
43C2×#11719945—21no—
44C2×#11719945—21no—
45C2×#11719945—21no—
46C2×#11719945—21no—
47C2×#11719945—21no—
48C2×#11719945—21no—
49C2×#11719945—21no—
50C2×#11719945—21no—
51C2×#11719945—21no—
52C2×#11719945—21no—
53C2×#11719945C2×C412yescomplemented
54C2×#11719945C2312yes—
55C22×Dic106C2×C411yescharacteristic, complemented
56C22×D212—21no—
57C22×D212—21no—
58C22×D212—21no—
59C22×D212—21no—
60C22×D212—21no—
61C22×D212—21no—
62C22×D212—21no—
63C22×D212—21no—
64C22×D212—24no—
65C22×D212C2×C412yes—
66C22×D212C2×C412yes—
67C22×D212C2×C411yescharacteristic, complemented
68C22×D212D412yes—
69C22×D212D412yes—
70C22×D212D412yes—
71C22×D212C2312yes—
72C22×C22⋊D53—21no—
73C22×C4×D53—21no—
74C22×C4×D53—24no—
75C2×#11719917—21no—
76C2×#11719917—21no—
77C2×#11719917—21no—
78C2×#11719917—21no—
79C2×#11719917—21no—
80C2×#11719917C2312yes—
81C22×#88322—21no—
82#13133214—24no—
83#13133214C2×C418yescomplemented
84#13133205—24no—
85#13133205C2×C418yescomplemented
86#13133192—28no—
87#13133192—28no—
88#13133187—28no—
89#13133187—28no—
90C4×D212—28no—
91C4×D212—28no—
92#13133179—28no—
93#13133179—28no—
94#13133176—21no—
95#13133176—21no—
96#13133176D412yescomplemented
97#13133176C2312yes—
98C2×C4⋊Dic53—21no—
99C2×C22⋊Dic53—21no—
100C2×#11719921—24no—
101C2×#11719921—24no—
102C22⋊C4×D53—28no—
103C22⋊C4×D53—28no—
104C2×C4×Dic53D412yescomplemented
105#13133145—28no—
106#13133143—28no—
107#13133133—28no—
108C23×C4×C53C2311yescharacteristic
109C2×M16×C53—21no—
110C2×M16×C53—21no—
111C2×M16×C53—21no—
112C2×M16×C53—21no—
113C2×M16×C53—21no—
114C2×M16×C53C2312yes—
115C22×C8×C53—21no—
116#117×C53—21no—
117#117×C53—21no—
118#117×C53—21no—
119#117×C53—21no—
120#117×C53C2×C412yescomplemented
121#117×C53D412yescomplemented
122#117×C53C2312yes—
123#117×C53C2312yes—
124C2×C4⋊C4×C53—21no—
125C2×C4⋊C4×C53—21no—
126C2×C22⋊C4×C53—21no—
127C2×C22⋊C4×C53—21no—
128C2×C42×C53C2×C412yescomplemented
129C2×C42×C53D412yescomplemented
130C24×C53C2×D411yescharacteristic
131C23×D53—22no—
132C23×D53—22no—
133C23×D53—22no—
134C23×D53—22no—
135C23×D53—21no—
136C23×D53—84no—
137C23×D53C22⋊C414yes—
138C23×D53C22⋊C414yes—
139C23×D53C2×D414yes—
140C22×C4×C53—22no—
141C22×C4×C53—22no—
142C22×C4×C53C22×C411yescharacteristic
143C22×C4×C53C22×C411yescharacteristic
144C22×C4×C53C2×D411yescharacteristic
145C22×C4×C53C2×D411yescharacteristic
146C22×C4×C53C2×D411yescharacteristic
147C22×C4×C53C2×D411yescharacteristic
148C22×C4×C53C2×D411yescharacteristic
149C22×C4×C53C2×D411yescharacteristic
150C22×C4×C53C2×D411yescharacteristic
151C22×C4×C53#4111yescharacteristic
152C22×C4×C53#4111yescharacteristic
153C22×C4×C53#4111yescharacteristic
154C22×C4×C53#4111yescharacteristic
155C22×C4×C53C2411yescharacteristic
156C2×C22⋊D53—22no—
157C2×C22⋊D53—22no—
158C2×C22⋊D53—41no—
159C2×C22⋊D53—41no—
160C2×C22⋊D53—41no—
161C2×C22⋊D53—41no—
162C22×Dic53—21no—
163C22×Dic53—22no—
164#11719945—22no—
165#11719945—22no—
166#11719945—22no—
167#11719945—22no—
168#11719945—22no—
169#11719945—22no—
170#11719945—22no—
171#11719945—22no—
172#11719945—41no—
173#11719945—41no—
174#11719945—41no—
175#11719945—41no—
176#11719945—41no—
177#11719945—41no—
178#11719945—41no—
179#11719945—41no—
180C2×D212—22no—
181C2×D212—22no—
182C2×D212—22no—
183C2×D212—22no—
184C2×D212—22no—
185C2×D212—22no—
186C2×D212—22no—
187C2×D212—22no—
188C2×D212—22no—
189C2×D212—22no—
190C2×D212—22no—
191C2×D212—22no—
192C2×D212—22no—
193C2×D212—22no—
194C2×D212—22no—
195C2×D212—22no—
196C2×D212—22no—
197C2×D212—22no—
198C2×D212—22no—
199C2×D212—22no—
200C2×D212—22no—
201C2×D212—22no—
202C2×D212—22no—
203C2×D212—22no—
204C2×D212—21no—
205C2×D212—21no—
206C2×D212—21no—
207C2×D212—21no—
208C2×D212—21no—
209C2×D212—216no—
210C2×D212—88no—
211C2×D212C22⋊C414yes—
212C2×D212C22⋊C414yes—
213C2×D212C22×C414yes—
214C2×D212C22×C412yescomplemented
215C2×D212C2×D414yes—
216C2×C4×D53—22no—
217C2×C4×D53—22no—
218C2×C4×D53—216no—
219C2×C4×D53—41no—
220C2×C4×D53—41no—
221C2×C4×D53—41no—
222C2×C4×D53—41no—
223C2×C4×D53—88no—
224C2×Dic106—21no—
225C2×Dic106—21no—
226C2×Dic106—21no—
227C2×Dic106—21no—
228C2×Dic106—21no—
229C2×Dic106C22×C412yescomplemented
230M16×C53—22no—
231M16×C53—22no—
232M16×C53—41no—
233M16×C53—41no—
234C2×C8×C53—22no—
235C2×C8×C53—41no—
236C2×C8×C53—41no—
237C4⋊C4×C53—22no—
238C4⋊C4×C53—22no—
239C4⋊C4×C53—22no—
240C4⋊C4×C53—22no—
241C22⋊C4×C53—22no—
242C22⋊C4×C53—22no—
243C22⋊C4×C53—22no—
244C22⋊C4×C53—22no—
245C42×C53—22no—
246C42×C53—22no—
247C42×C53C22×C414yescomplemented
248C42×C53C2×D414yescomplemented
249C22⋊Dic53—22no—
250C22⋊Dic53—22no—
251#11719921—216no—
252#11719921—216no—
253C4⋊Dic53—22no—
254C4⋊Dic53—22no—
255C4×Dic53—22no—
256C4×Dic53C2×D414yescomplemented
257#11719917—22no—
258#11719917—22no—
259#11719917—41no—
260#11719917—41no—
261C2×#88322—22no—
262C2×#88322—41no—
263C2×#88322—41no—
264C23×C53—42no—
265C23×C53C2×C22⋊C411yescharacteristic
266C23×C53C2×C22⋊C411yescharacteristic
267C23×C53#12011yescharacteristic
268C23×C53#12011yescharacteristic
269C23×C53#12311yescharacteristic
270C23×C53#12311yescharacteristic
271C23×C53C22×D411yescharacteristic
272C22×D53—24no—
273C22×D53—24no—
274C22×D53—24no—
275C22×D53—24no—
276C22×D53—24no—
277C22×D53—24no—
278C22×D53—22no—
279C22×D53—48no—
280C22×D53—48no—
281C22×D53—44no—
282C22×D53—41no—
283C22×D53—41no—
284C22×D53—84no—
285C22×D53—84no—
286C22×D53—84no—
287C22×D53—84no—
288C22×D53—84no—
289C22×D53C2×C22⋊C418yes—
290C2×C4×C53—24no—
291C2×C4×C53—24no—
292C2×C4×C53—44no—
293C2×C4×C53—44no—
294C2×C4×C53C2×C22⋊C411yescharacteristic
295C2×C4×C53C2×C22⋊C411yescharacteristic
296C2×C4×C53C4×D411yescharacteristic
297C2×C4×C53C4×D411yescharacteristic
298C2×C4×C53C4×D411yescharacteristic
299C2×C4×C53C4×D411yescharacteristic
300C2×C4×C53C4×D411yescharacteristic
301C2×C4×C53C4×D411yescharacteristic
302C2×C4×C53C4×D411yescharacteristic
303C2×C4×C53C4×D411yescharacteristic
304C2×C4×C53#12011yescharacteristic
305C2×C4×C53#12011yescharacteristic
306C2×C4×C53#12111yescharacteristic
307C2×C4×C53#12111yescharacteristic
308C2×C4×C53#12111yescharacteristic
309C2×C4×C53#12111yescharacteristic
310C2×C4×C53#12111yescharacteristic
311C2×C4×C53#12111yescharacteristic
312C2×C4×C53#12111yescharacteristic
313C2×C4×C53#12111yescharacteristic
314C2×C4×C53#12311yescharacteristic
315C2×C4×C53#12311yescharacteristic
316C2×C4×C53C23×C411yescharacteristic
317C2×C4×C53C22×D411yescharacteristic
318C2×C4×C53C22×D411yescharacteristic
319C2×C4×C53C22×D411yescharacteristic
320C2×C4×C53C2×#4111yescharacteristic
321C2×C4×C53C2×#4111yescharacteristic
322C22⋊D53—42no—
323C22⋊D53—42no—
324C22⋊D53—42no—
325C22⋊D53—42no—
326C2×Dic53—22no—
327C2×Dic53—24no—
328C2×Dic53—44no—
329C2×Dic53—41no—
330C2×Dic53—41no—
331D212—24no—
332D212—24no—
333D212—22no—
334D212—22no—
335D212—24no—
336D212—24no—
337D212—24no—
338D212—24no—
339D212—24no—
340D212—24no—
341D212—41no—
342D212—41no—
343D212—816no—
344C4×D53—42no—
345C4×D53—42no—
346C4×D53—42no—
347C4×D53—42no—
348C4×D53—816no—
349Dic106—22no—
350Dic106—22no—
351Dic106—41no—
352Dic106—41no—
353C8×C53—42no—
354#88322—42no—
355C2×#1911—531nomaximal, Sylow
356C22×C53—22no—
357C22×C53—22no—
358C22×C53—22no—
359C22×C53—41no—
360C22×C53—41no—
361C22×C53—41no—
362C22×C53—41no—
363C22×C53#38611yescharacteristic
364C22×C53#38611yescharacteristic
365C22×C53#38611yescharacteristic
366C22×C53#38611yescharacteristic
367C22×C53C22×C22⋊C411yescharacteristic
368C22×C53C2×#12011yescharacteristic
369C22×C53C2×#12311yescharacteristic
370C2×D53—28no—
371C2×D53—48no—
372C2×D53—48no—
373C2×D53—48no—
374C2×D53—48no—
375C2×D53—44no—
376C2×D53—42no—
377C2×D53—84no—
378C2×D53—84no—
379C2×D53—84no—
380C2×D53—82no—
381C2×D53—82no—
382C4×C53—44no—
383C4×C53—44no—
384C4×C53#38611yescharacteristic
385C4×C53#38611yescharacteristic
386C4×C53#38611yescharacteristic
387C4×C53#38611yescharacteristic
388C4×C53C2×C4×D411yescharacteristic
389C4×C53C2×C4×D411yescharacteristic
390C4×C53C2×#12111yescharacteristic
391C4×C53C2×#12111yescharacteristic
392Dic53—44no—
393Dic53—42no—
394C2×#535—531no—
395C2×#518—531no—
396C2×#421—531no—
397C2×#421—531no—
398C22×#100—531no—
399#1911—538no—
400C2×H(3,ℤ/4)—531no—
401C2×H(3,ℤ/4)D5311yescharacteristic, complemented
402C2×C53—21no—
403C2×C53—21no—
404C2×C53—21no—
405C2×C53—21no—
406C2×C53—21no—
407C2×C53—21no—
408C2×C53#191112yescomplemented
409C2×C53C2×#38611yescharacteristic
410D53—48no—
411D53—82no—
412C22×#41—531no—
413C23×D4—531no—
414C22×M16—531no—
415C22×M16C2×D5311yescharacteristic
416#535—534no—
417#535—534no—
418#535—1062no—
419#535—1062no—
420C2×#127—532no—
421C2×#124—532no—
422C2×#121—1062no—
423C2×#120—1062no—
424#518—534no—
425#518—1062no—
426#518—1062no—
427#518—1062no—
428C2×C4×D4—1062no—
429C2×C4×D4—1062no—
430C2×#117—531no—
431C2×#117C2×D5311yescharacteristic
432C2×#117C2×D5311yescharacteristic
433C22×C22⋊C4—1062no—
434#421—534no—
435#421—534no—
436#421—1062no—
437#421—1062no—
438C2×#104—1062no—
439C2×#104—1062no—
440C2×#100—534no—
441C2×#100—1062no—
442C2×#100—1062no—
443H(3,ℤ/4)—534no—
444H(3,ℤ/4)C2×D5314yescomplemented
445C53C2×#191111yescharacteristic, complemented, Sylow
446C25—532no—
447C2×#41—532no—
448C2×#41—532no—
449C2×#41—1061no—
450C2×#41—1061no—
451C2×#41—1061no—
452C2×#41—1061no—
453C2×#41—1061no—
454C2×#41—1061no—
455C2×#41—1061no—
456C2×#41—1061no—
457C2×#41—1061no—
458C2×#41—1061no—
459C22×Q8—531no—
460C22×D4—532no—
461C22×D4—532no—
462C22×D4—531no—
463C22×D4—532no—
464C22×D4—532no—
465C22×D4—532no—
466C22×D4—532no—
467C22×D4—1064no—
468C22×D4—1061no—
469C22×D4—1061no—
470C22×D4—1061no—
471C22×D4—1061no—
472C22×D4—1061no—
473C22×D4—1061no—
474C22×D4—1061no—
475C22×D4—1061no—
476C22×D4—1061no—
477C23×C4—1064no—
478C23×C4—1061no—
479C23×C4C22×D5311yescharacteristic
480C2×M16—21no—
481C2×M16—21no—
482C2×M16—21no—
483C2×M16—21no—
484C2×M16—21no—
485C2×M16—532no—
486C2×M16—1061no—
487C2×M16—1061no—
488C2×M16—1061no—
489C2×M16—1061no—
490C2×M16—1061no—
491C2×M16C22×D5312yes—
492C22×C8—21no—
493C22×C8—1061no—
494#127—538no—
495#127—1064no—
496#124—538no—
497#124—1064no—
498#121—1068no—
499#121—1068no—
500#120—1068no—
501#120—1068no—
502C4×D4—1068no—
503C4×D4—1068no—
504C4×D4—1068no—
505C4×D4—1068no—
506#117—21no—
507#117—21no—
508#117—21no—
509#117—21no—
510#117—532no—
511#117—532no—
512#117—1061no—
513#117—1061no—
514#117C4×D5312yescomplemented
515#117D21212yescomplemented
516#117C22×D5312yes—
517#117C22×D5312yes—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—1061no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—1068no—
524C2×C22⋊C4—1068no—
525C2×C22⋊C4—1064no—
526C2×C22⋊C4—1064no—
527C2×C22⋊C4—1061no—
528C2×C42—532no—
529C2×C42C4×D5312yescomplemented
530C2×C42D21212yescomplemented
531#104—1068no—
532#104—1068no—
533#100—1068no—
534C24—534no—
535C24—534no—
536C24—534no—
537C24—1062no—
538C24—1062no—
539C24—1062no—
540C24—1062no—
541C24—1061no—
542C24—4244no—
543C24D4×D5311yescharacteristic
544#41—1062no—
545#41—1062no—
546#41—1062no—
547#41—1062no—
548#41—1062no—
549#41—1062no—
550#41—1062no—
551#41—1062no—
552#41—2121no—
553#41—2121no—
554#41—2121no—
555#41—2121no—
556#41—2121no—
557#41—2121no—
558#41—2121no—
559#41—2121no—
560C2×Q8—532no—
561C2×Q8—1061no—
562C2×Q8—1061no—
563C2×Q8—1061no—
564C2×Q8—1061no—
565C2×Q8—1061no—
566C2×D4—534no—
567C2×D4—534no—
568C2×D4—534no—
569C2×D4—532no—
570C2×D4—534no—
571C2×D4—10616no—
572C2×D4—1062no—
573C2×D4—1062no—
574C2×D4—1061no—
575C2×D4—1062no—
576C2×D4—1062no—
577C2×D4—1062no—
578C2×D4—1062no—
579C2×D4—1061no—
580C2×D4—1061no—
581C2×D4—1062no—
582C2×D4—1062no—
583C2×D4—1062no—
584C2×D4—1062no—
585C2×D4—1061no—
586C2×D4—1061no—
587C2×D4—1062no—
588C2×D4—1062no—
589C2×D4—1062no—
590C2×D4—1062no—
591C2×D4—1062no—
592C2×D4—1062no—
593C2×D4—1062no—
594C2×D4—1062no—
595C2×D4—1062no—
596C2×D4—1062no—
597C2×D4—1062no—
598C2×D4—1062no—
599C2×D4—1062no—
600C2×D4—1062no—
601C2×D4—1062no—
602C2×D4—1062no—
603C2×D4—4248no—
604C2×D4—2121no—
605C2×D4—2121no—
606C2×D4—2121no—
607C2×D4—2121no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—10616no—
611C22×C4—1061no—
612C22×C4—1062no—
613C22×C4—1062no—
614C22×C4—1062no—
615C22×C4—4248no—
616C22×C4—2121no—
617C22×C4—2121no—
618C22×C4—2121no—
619C22×C4—2121no—
620C22×C4C2×C4×D5311yescharacteristic
621C22×C4C2×C4×D5311yescharacteristic
622C22×C4C2×D21211yescharacteristic
623C22×C4C2×D21211yescharacteristic
624C22×C4#1171994511yescharacteristic
625C22×C4#1171994511yescharacteristic
626C22×C4D4×D5311yescharacteristic
627C22×C4D4×D5311yescharacteristic
628C22×C4D4×D5311yescharacteristic
629C22×C4D4×D5311yescharacteristic
630C22×C4D4×D5311yescharacteristic
631C22×C4#1171994911yescharacteristic
632C22×C4#1171994911yescharacteristic
633C22×C4C23×D5311yescharacteristic
634M16—22no—
635M16—22no—
636M16—41no—
637M16—41no—
638M16—1062no—
639M16—1062no—
640M16—2121no—
641M16—2121no—
642C2×C8—22no—
643C2×C8—41no—
644C2×C8—41no—
645C2×C8—1062no—
646C2×C8—2121no—
647C2×C8—2121no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—1062no—
653C4⋊C4—1062no—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—10616no—
659C22⋊C4—10616no—
660C22⋊C4—1062no—
661C22⋊C4—1062no—
662C42—22no—
663C42—22no—
664C42—534no—
665C42—1062no—
666C42C2×C4×D5314yescomplemented
667C42C2×D21214yescomplemented
668C23—42no—
669C23—538no—
670C23—1064no—
671C23—1064no—
672C23—1064no—
673C23—1064no—
674C23—1064no—
675C23—1064no—
676C23—1062no—
677C23—4244no—
678C23—4244no—
679C23—4244no—
680C23—4244no—
681C23—4244no—
682C23—2124no—
683C23—2128no—
684C23—2128no—
685C23—2121no—
686C23—2121no—
687C23C22⋊C4×D5311yescharacteristic
688C23C22⋊C4×D5311yescharacteristic
689C23#1313318711yescharacteristic
690C23#1313318711yescharacteristic
691C23#1313320211yescharacteristic
692C23#1313320211yescharacteristic
693C23C2×D4×D5311yescharacteristic
694Q8—1062no—
695Q8—1062no—
696Q8—2121no—
697Q8—2121no—
698D4—1064no—
699D4—1064no—
700D4—1064no—
701D4—1064no—
702D4—1064no—
703D4—1062no—
704D4—1064no—
705D4—1062no—
706D4—1064no—
707D4—1064no—
708D4—42416no—
709D4—2122no—
710D4—2122no—
711D4—2122no—
712D4—2122no—
713D4—2121no—
714D4—2121no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—1062no—
720C2×C4—1064no—
721C2×C4—42416no—
722C2×C4—2124no—
723C2×C4—2121no—
724C2×C4—2121no—
725C2×C4—2122no—
726C2×C4—2122no—
727C2×C4—2122no—
728C2×C4—2122no—
729C2×C4C22⋊C4×D5311yescharacteristic
730C2×C4C22⋊C4×D5311yescharacteristic
731C2×C4#1313317911yescharacteristic
732C2×C4#1313317911yescharacteristic
733C2×C4#1313317911yescharacteristic
734C2×C4#1313317911yescharacteristic
735C2×C4C4×D21211yescharacteristic
736C2×C4C4×D21211yescharacteristic
737C2×C4C4×D21211yescharacteristic
738C2×C4C4×D21211yescharacteristic
739C2×C4#1313318711yescharacteristic
740C2×C4#1313318711yescharacteristic
741C2×C4#1313319011yescharacteristic
742C2×C4#1313319011yescharacteristic
743C2×C4#1313319011yescharacteristic
744C2×C4#1313319011yescharacteristic
745C2×C4#1313319211yescharacteristic
746C2×C4#1313319211yescharacteristic
747C2×C4#1313319211yescharacteristic
748C2×C4#1313319211yescharacteristic
749C2×C4#1313320211yescharacteristic
750C2×C4#1313320211yescharacteristic
751C2×C4C22×C4×D5311yescharacteristic
752C2×C4C2×D4×D5311yescharacteristic
753C2×C4C2×D4×D5311yescharacteristic
754C2×C4C22×D21211yescharacteristic
755C2×C4C2×#1171994511yescharacteristic
756C2×C4C2×#1171994911yescharacteristic
757C8—42no—
758C8—2122no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—1068no—
767C22—4242no—
768C22—4244no—
769C22—4244no—
770C22—4244no—
771C22—4242no—
772C22—2124no—
773C22—2128no—
774C22—2128no—
775C22—2128no—
776C22—2122no—
777C22—2128no—
778C22#1681050111yescharacteristic
779C22#1681050111yescharacteristic
780C22#1681050111yescharacteristic
781C22#1681050111yescharacteristic
782C22C2×C22⋊C4×D5311yescharacteristic
783C22C2×#1313318711yescharacteristic
784C22C2×#1313320211yescharacteristic
785C4—44no—
786C4—44no—
787C4—2124no—
788C4—2122no—
789C4#1681050111yescharacteristic
790C4#1681050111yescharacteristic
791C4#1681050111yescharacteristic
792C4#1681050111yescharacteristic
793C4C2×#1313317911yescharacteristic
794C4C2×C4×D21211yescharacteristic
795C4C2×#1313319011yescharacteristic
796C4C2×#1313319211yescharacteristic
797C2—21no—
798C2—21no—
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—4242no—
804C2—2128no—
805C2#2027524612yesdirect product factor
806C2C2×#1681050111yescharacteristic
subgroupG/H
centerC22#16810501
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×H(3,ℤ/4)C2
socleC22×C53#386
prime radicalC2×#16811192C2
cosocleC22×C4×C53C24
hypercenterC2×H(3,ℤ/4)D53
hypocenterC53C2×#1911
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
2. C2×#16811097C2semidirect
3. C2×#16810641C2semidirect
4. C2×#16810639C2semidirect
5. C22×#13133133C2semidirect
6. #20275246C2direct (N × H)
7. C2×#16810379C2semidirect
8. C2×C53×H(3,ℤ/4)C2semidirect
14. #16811192C4semidirect
16. C2×#13133214C4semidirect
17. C2×#13133205C4semidirect
23. #16811097C22semidirect
29. #16810641C22semidirect
31. #16810639C22semidirect
36. C2×#13133133C22semidirect
37. #16810379C22semidirect
41. C53×H(3,ℤ/4)C22semidirect
53. C2×#11719945C2×C4semidirect
55. C22×Dic106C2×C4semidirect
67. C22×D212C2×C4semidirect
83. #13133214C2×C4semidirect
85. #13133205C2×C4semidirect
96. #13133176D4semidirect
104. C2×C4×Dic53D4semidirect
120. #117×C53C2×C4semidirect
121. #117×C53D4semidirect
128. C2×C42×C53C2×C4semidirect
129. C2×C42×C53D4semidirect
214. C2×D212C22×C4semidirect
229. C2×Dic106C22×C4semidirect
247. C42×C53C22×C4semidirect
248. C42×C53C2×D4semidirect
256. C4×Dic53C2×D4semidirect
401. C2×H(3,ℤ/4)D53semidirect
408. C2×C53#1911semidirect
444. H(3,ℤ/4)C2×D53semidirect
445. C53C2×#1911semidirect
514. #117C4×D53semidirect
515. #117D212semidirect
529. C2×C42C4×D53semidirect
530. C2×C42D212semidirect
666. C42C2×C4×D53semidirect
667. C42C2×D212semidirect
805. C2#20275246direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111922
C2×#168110972
C2×#168106412
C2×#168106392
C22×#131331332
#202752462
C2×#168103792
C2×C53×H(3,ℤ/4)2
C2×#191153