Finite Group Databasebeta

← C2×#20275213 #27385996

Subgroups — C2×#20275213 #27385996

Order 13568.

1798 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
1C2×#16811421C211yesmaximal, characteristic
2C2×#16811091C211yesmaximal, characteristic, complemented
3C2×#16810641C211yesmaximal, characteristic, complemented
4C22×#13133144C211yesmaximal, characteristic, complemented
5#20275213C218yesmaximal, direct product factor
6C2×#16810393C211yesmaximal, characteristic, complemented
7C2×#16810382C211yesmaximal, characteristic, complemented
8C2×C53×#410C211yesmaximal, characteristic, complemented
9C22×#11719945C2211yescharacteristic
10#16811421—22no—
11#16811421—22no—
12#16811421C414yescomplemented
13#16811421C2214yes—
14C2×#13133248C412yescomplemented
15C2×#13133247—21no—
16C2×#13133243C412yescomplemented
17C2×#13133242—21no—
18C2×#13133237—22no—
19C22×#11719917C2211yescharacteristic
20C22×#11719917C2211yescharacteristic
21#16811091—22no—
22#16811091—22no—
23#16811091—22no—
24#16811091C2214yescomplemented
25C2×#13133182—21no—
26C2×#13133179—21no—
27C2×#13133177—22no—
28C2×#13133174—21no—
29C22×C4×Dic53C2211yescharacteristic
30C2×C42×D53—21no—
31#16810641—22no—
32#16810641C2214yescomplemented
33C2×#13133145—22no—
34C2×#13133144—21no—
35C2×#13133144—21no—
36C2×#13133144—22no—
37C2×#13133144C2214yescomplemented
38#16810393C2214yescomplemented
39#16810382C2214yescomplemented
40C22×#41×C53C2211yescharacteristic
41C2×#117×C53C2211yescharacteristic
42C2×#117×C53C2211yescharacteristic
43C53×#410—22no—
44C53×#410C2214yescomplemented
45C2×#99×C53—22no—
46C2×#11719945—21no—
47C2×#11719945—21no—
48C2×#11719945—21no—
49C2×#11719945—21no—
50C2×#11719945—21no—
51C2×#11719945—21no—
52C2×#11719945C2×C412yes—
53C2×#11719945C2×C412yes—
54C2×#11719945D412yes—
55C2×#11719945D412yes—
56C2×#11719945D412yes—
57C2×#11719945C2312yes—
58C22×Dic106D411yescharacteristic
59C22×D212D411yescharacteristic
60C22×C22⋊D53—21no—
61C23×Dic53—21no—
62C22×C4×D53—21no—
63C22×C4×D53—22no—
64#13133248—24no—
65#13133248C2×C418yescomplemented
66#13133247—24no—
67#13133247—24no—
68#13133243—24no—
69#13133243C2×C418yescomplemented
70#13133242—24no—
71#13133242—24no—
72#13133237—28no—
73#13133237—28no—
74C2×#11719925—22no—
75C2×#11719923—22no—
76C2×#11719924—22no—
77C2×#11719922—22no—
78C2×#11719917—21no—
79C2×#11719917—21no—
80C2×#11719917—21no—
81C2×#11719917—21no—
82C2×#11719917—21no—
83C2×#11719917—21no—
84C2×#11719917—21no—
85C2×#11719917—21no—
86C2×#11719917C2×C412yescomplemented
87C2×#11719917C2×C412yescomplemented
88C2×#11719917C2312yes—
89C2×#11719917C2312yes—
90C22×#88322—21no—
91C22×#88322—21no—
92#13133182—24no—
93#13133182—24no—
94#13133179—24no—
95#13133179—24no—
96#13133177—28no—
97#13133177—28no—
98#13133174—24no—
99#13133174—24no—
100C2×#11719919—22no—
101C2×#11719921—22no—
102C2×C4×Dic53—22no—
103C2×C4×Dic53—21no—
104C2×C4×Dic53—21no—
105C2×C4×Dic53—21no—
106C2×C4×Dic53D411yescharacteristic
107C2×C4×Dic53D411yescharacteristic
108C2×C4×Dic53D412yes—
109C2×C4×Dic53C2312yes—
110C42×D53—24no—
111C42×D53—24no—
112#13133145—28no—
113#13133144—24no—
114#13133144—24no—
115C2×#41×C53—21no—
116C2×#41×C53—21no—
117C2×#41×C53—21no—
118C2×#41×C53—21no—
119C2×#41×C53—21no—
120C2×#41×C53—21no—
121C2×#41×C53—21no—
122C2×#41×C53—21no—
123C2×#41×C53—21no—
124C2×#41×C53—21no—
125C2×#41×C53C2×C412yescomplemented
126C2×#41×C53C2312yes—
127C22×Q8×C53C2×C411yescharacteristic, complemented
128C22×D4×C53—21no—
129C22×D4×C53C2×C411yescharacteristic, complemented
130C23×C4×C53—21no—
131C23×C4×C53C2311yescharacteristic
132#117×C53—21no—
133#117×C53—21no—
134#117×C53—21no—
135#117×C53—21no—
136#117×C53—21no—
137#117×C53D412yes—
138#117×C53C2312yes—
139#117×C53C2312yes—
140C2×C4⋊C4×C53—21no—
141C2×C4⋊C4×C53—21no—
142C2×C22⋊C4×C53—21no—
143C2×C22⋊C4×C53D412yes—
144C2×C42×C53—21no—
145C2×C42×C53—21no—
146#99×C53—28no—
147C24×C53—21no—
148C24×C53C2×D411yescharacteristic
149C23×D53—21no—
150#41×C53—22no—
151#41×C53—22no—
152#41×C53—22no—
153#41×C53—22no—
154#41×C53—22no—
155#41×C53—22no—
156#41×C53—22no—
157#41×C53—22no—
158#41×C53—41no—
159#41×C53—41no—
160#41×C53—41no—
161#41×C53—41no—
162#41×C53—41no—
163#41×C53—41no—
164#41×C53—41no—
165#41×C53—41no—
166C2×Q8×C53—21no—
167C2×Q8×C53—21no—
168C2×Q8×C53—21no—
169C2×Q8×C53—21no—
170C2×Q8×C53—21no—
171C2×Q8×C53C22×C412yescomplemented
172C2×D4×C53—22no—
173C2×D4×C53—22no—
174C2×D4×C53—21no—
175C2×D4×C53—21no—
176C2×D4×C53—21no—
177C2×D4×C53—21no—
178C2×D4×C53—21no—
179C2×D4×C53—41no—
180C2×D4×C53—41no—
181C2×D4×C53—41no—
182C2×D4×C53—41no—
183C2×D4×C53C22×C412yescomplemented
184C22×C4×C53—21no—
185C22×C4×C53—22no—
186C22×C4×C53—22no—
187C22×C4×C53—22no—
188C22×C4×C53—41no—
189C22×C4×C53—41no—
190C22×C4×C53—41no—
191C22×C4×C53—41no—
192C22×C4×C53—41no—
193C22×C4×C53C22×C411yescharacteristic
194C22×C4×C53C22×C411yescharacteristic
195C22×C4×C53C2×D411yescharacteristic
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53#4111yescharacteristic
203C22×C4×C53#4111yescharacteristic
204C22×C4×C53#4111yescharacteristic
205C22×C4×C53#4111yescharacteristic
206C22×C4×C53C2411yescharacteristic
207C2×C22⋊D53—22no—
208C2×C22⋊D53—22no—
209C2×C22⋊D53—22no—
210C2×C22⋊D53—22no—
211C2×C22⋊D53—22no—
212C2×C22⋊D53—22no—
213C22×Dic53—21no—
214C22×Dic53—21no—
215C22×Dic53—21no—
216C22×Dic53—22no—
217C22×Dic53—22no—
218C22×Dic53—44no—
219#11719945—22no—
220#11719945—22no—
221#11719945—22no—
222#11719945—22no—
223#11719945—22no—
224#11719945—22no—
225#11719945—22no—
226#11719945—22no—
227#11719945—22no—
228#11719945—22no—
229#11719945—22no—
230#11719945—22no—
231#11719945C22⋊C414yes—
232#11719945C22⋊C414yes—
233#11719945C22×C414yes—
234#11719945C2×D414yes—
235C2×D212—21no—
236C2×D212—21no—
237C2×D212—21no—
238C2×D212C22⋊C412yes—
239C2×D212C22⋊C412yes—
240C2×D212C2×D412yes—
241C2×C4×D53—22no—
242C2×C4×D53—22no—
243C2×C4×D53—22no—
244C2×C4×D53—22no—
245C2×C4×D53—22no—
246C2×C4×D53—22no—
247C2×C4×D53—28no—
248C2×C4×D53—48no—
249C2×Dic106—21no—
250C2×Dic106—21no—
251C2×Dic106—21no—
252C2×Dic106C22⋊C412yes—
253C2×Dic106C22⋊C412yes—
254C2×Dic106C2×D412yes—
255C4⋊C4×C53—22no—
256C4⋊C4×C53—22no—
257C4⋊C4×C53—22no—
258C4⋊C4×C53—41no—
259C22⋊C4×C53—22no—
260C22⋊C4×C53—22no—
261C22⋊C4×C53—41no—
262C22⋊C4×C53C2×D414yes—
263C42×C53—22no—
264C42×C53—22no—
265C42×C53—22no—
266C42×C53—41no—
267#11719925—28no—
268#11719924—28no—
269#11719923—28no—
270#11719922—28no—
271#11719921—28no—
272#11719919—28no—
273C4×Dic53—28no—
274C4×Dic53—21no—
275C4×Dic53—21no—
276C4×Dic53—22no—
277C4×Dic53—22no—
278C4×Dic53C2×D412yes—
279C4×Dic53C2×D412yes—
280#11719917—22no—
281#11719917—22no—
282#11719917—22no—
283#11719917—22no—
284#11719917—22no—
285#11719917—41no—
286#11719917—41no—
287#11719917C22×C414yescomplemented
288C2×#88322—22no—
289C2×#88322—22no—
290C2×#88322—22no—
291C2×#88322—22no—
292C2×#88322—41no—
293C2×#88322—41no—
294C23×C53—22no—
295C23×C53—42no—
296C23×C53—41no—
297C23×C53—41no—
298C23×C53—82no—
299C23×C53C4×D411yescharacteristic
300C23×C53C4×D411yescharacteristic
301C23×C53#12011yescharacteristic
302C23×C53#12011yescharacteristic
303C23×C53#12111yescharacteristic
304C23×C53#12111yescharacteristic
305C23×C53C22×D411yescharacteristic
306C22×D53—22no—
307C22×D53—22no—
308C22×D53—22no—
309C22×D53—44no—
310Q8×C53—22no—
311Q8×C53—22no—
312Q8×C53—41no—
313Q8×C53—41no—
314D4×C53—22no—
315D4×C53—22no—
316D4×C53—42no—
317D4×C53—42no—
318D4×C53—42no—
319D4×C53—42no—
320D4×C53—41no—
321D4×C53—41no—
322C2×C4×C53—22no—
323C2×C4×C53—24no—
324C2×C4×C53—44no—
325C2×C4×C53—41no—
326C2×C4×C53—41no—
327C2×C4×C53—42no—
328C2×C4×C53—42no—
329C2×C4×C53—42no—
330C2×C4×C53—42no—
331C2×C4×C53—42no—
332C2×C4×C53—82no—
333C2×C4×C53C2×C22⋊C411yescharacteristic
334C2×C4×C53C2×C22⋊C411yescharacteristic
335C2×C4×C53C2×C22⋊C411yescharacteristic
336C2×C4×C53C2×C22⋊C411yescharacteristic
337C2×C4×C53C4×D411yescharacteristic
338C2×C4×C53C4×D411yescharacteristic
339C2×C4×C53C4×D411yescharacteristic
340C2×C4×C53C4×D411yescharacteristic
341C2×C4×C53C4×D411yescharacteristic
342C2×C4×C53C4×D411yescharacteristic
343C2×C4×C53#12011yescharacteristic
344C2×C4×C53#12011yescharacteristic
345C2×C4×C53#12111yescharacteristic
346C2×C4×C53#12111yescharacteristic
347C2×C4×C53#12111yescharacteristic
348C2×C4×C53#12111yescharacteristic
349C2×C4×C53#12111yescharacteristic
350C2×C4×C53#12111yescharacteristic
351C2×C4×C53#12311yescharacteristic
352C2×C4×C53#12311yescharacteristic
353C2×C4×C53#12311yescharacteristic
354C2×C4×C53#12311yescharacteristic
355C2×C4×C53C23×C411yescharacteristic
356C2×C4×C53C22×D411yescharacteristic
357C2×C4×C53C22×D411yescharacteristic
358C2×C4×C53C22×D411yescharacteristic
359C2×C4×C53C2×#4111yescharacteristic
360C2×C4×C53C2×#4111yescharacteristic
361C22⋊D53—24no—
362C22⋊D53—24no—
363C22⋊D53—24no—
364C22⋊D53—24no—
365C2×Dic53—24no—
366C2×Dic53—22no—
367C2×Dic53—22no—
368C2×Dic53—22no—
369C2×Dic53—22no—
370C2×Dic53—22no—
371C2×Dic53—44no—
372C2×Dic53—44no—
373C2×Dic53—42no—
374D212—22no—
375D212—22no—
376D212—22no—
377D212C2×C22⋊C414yes—
378C4×D53—24no—
379C4×D53—24no—
380C4×D53—24no—
381C4×D53—24no—
382C4×D53—416no—
383Dic106—22no—
384Dic106—22no—
385Dic106—22no—
386Dic106C2×C22⋊C414yes—
387#88322—24no—
388#88322—42no—
389C2×#1906—531nomaximal, Sylow
390C22×C53—22no—
391C22×C53—22no—
392C22×C53—22no—
393C22×C53—41no—
394C22×C53—41no—
395C22×C53—41no—
396C22×C53—41no—
397C22×C53—42no—
398C22×C53—82no—
399C22×C53—82no—
400C22×C53—82no—
401C22×C53#38611yescharacteristic
402C22×C53#38611yescharacteristic
403C22×C53#38611yescharacteristic
404C22×C53#38611yescharacteristic
405C22×C53C2×C4×D411yescharacteristic
406C22×C53C2×#12011yescharacteristic
407C22×C53C2×#12111yescharacteristic
408C2×D53—24no—
409C2×D53—44no—
410C2×D53—44no—
411C2×D53—44no—
412C4×C53—44no—
413C4×C53—42no—
414C4×C53—82no—
415C4×C53#38611yescharacteristic
416C4×C53#38611yescharacteristic
417C4×C53#38611yescharacteristic
418C4×C53#38611yescharacteristic
419C4×C53C22×C22⋊C411yescharacteristic
420C4×C53C2×C4×D411yescharacteristic
421C4×C53C2×#12111yescharacteristic
422C4×C53C2×#12311yescharacteristic
423Dic53—24no—
424Dic53—24no—
425Dic53—42no—
426C2×#575—531no—
427C2×C4×#41—531no—
428C2×#421—531no—
429C22×#104—531no—
430C2×#410D5311yescharacteristic, complemented
431#1906—538no—
432C2×#344—531no—
433C2×#339—531no—
434C2×C53—21no—
435C2×C53—21no—
436C2×C53—21no—
437C2×C53—21no—
438C2×C53—21no—
439C2×C53—21no—
440C2×C53—82no—
441C2×C53#190612yescomplemented
442C2×C53C2×#38611yescharacteristic
443D53—44no—
444C22×#41—531no—
445C22×#41C2×D5311yescharacteristic
446#575—534no—
447#575—534no—
448#575—1062no—
449#575—1062no—
450C2×#137—532no—
451C2×#137—1061no—
452C2×AGL(1,ℤ/8)—532no—
453C2×AGL(1,ℤ/8)—1061no—
454C2×#135—1062no—
455C22×M16—531no—
456C22×M16—531no—
457C4×#41—534no—
458C4×#41—1062no—
459C4×#41—1062no—
460C4×#41—1062no—
461C2×C4×Q8—1061no—
462C2×C4×D4—1061no—
463C2×C4×D4—1062no—
464C2×#117—1061no—
465C2×#117C2×D5311yescharacteristic
466C2×#117C2×D5311yescharacteristic
467C22×C42—531no—
468C22×C42—1061no—
469#421—534no—
470#421—1062no—
471C2×#104—534no—
472C2×#104—1062no—
473C2×#104—1061no—
474C2×#104—1062no—
475C2×#104—1061no—
476#410—22no—
477#410C2×D5314yescomplemented
478C2×#99—22no—
479#344—534no—
480#339—534no—
481C53C2×#190611yescharacteristic, complemented, Sylow
482C2×#41—21no—
483C2×#41—21no—
484C2×#41—21no—
485C2×#41—21no—
486C2×#41—21no—
487C2×#41—21no—
488C2×#41—21no—
489C2×#41—21no—
490C2×#41—21no—
491C2×#41—21no—
492C2×#41—532no—
493C2×#41—532no—
494C2×#41—532no—
495C2×#41—532no—
496C2×#41—532no—
497C2×#41—532no—
498C2×#41—1061no—
499C2×#41—1061no—
500C2×#41—1061no—
501C2×#41—1061no—
502C2×#41—1061no—
503C2×#41—1061no—
504C2×#41C4×D5312yescomplemented
505C2×#41C22×D5312yes—
506C22×Q8—531no—
507C22×Q8C4×D5311yescharacteristic, complemented
508C22×D4—21no—
509C22×D4—531no—
510C22×D4—1061no—
511C22×D4C4×D5311yescharacteristic, complemented
512C23×C4—21no—
513C23×C4—1062no—
514C23×C4—1061no—
515C23×C4—1061no—
516C23×C4C22×D5311yescharacteristic
517#137—538no—
518#137—1064no—
519#137—1064no—
520#137—1064no—
521AGL(1,ℤ/8)—538no—
522AGL(1,ℤ/8)—1064no—
523AGL(1,ℤ/8)—1064no—
524AGL(1,ℤ/8)—1064no—
525#135—1068no—
526#135—1068no—
527C2×Q16—1062no—
528C2×SD16—1062no—
529C2×SD16—1062no—
530C2×D8—1062no—
531C2×M16—532no—
532C2×M16—532no—
533C2×M16—532no—
534C2×M16—532no—
535C2×M16—1061no—
536C2×M16—1061no—
537C2×M16—1061no—
538C2×M16—1061no—
539C2×M16—1061no—
540C2×M16—1061no—
541C2×M16—1061no—
542C2×M16—1061no—
543C22×C8—1061no—
544C22×C8—1061no—
545C4×Q8—1064no—
546C4×Q8—1064no—
547C4×D4—1068no—
548C4×D4—1064no—
549C4×D4—1064no—
550C4×D4—1068no—
551#117—21no—
552#117—21no—
553#117—21no—
554#117—21no—
555#117—21no—
556#117—1064no—
557#117—1064no—
558#117C22⋊D5312yes—
559#117C22×D5312yes—
560#117C22×D5312yes—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—1062no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—1062no—
566C2×C22⋊C4C22⋊D5312yes—
567C2×C42—21no—
568C2×C42—21no—
569C2×C42—531no—
570C2×C42—532no—
571C2×C42—531no—
572C2×C42—532no—
573C2×C42—1064no—
574C2×C42—1064no—
575C2×C42—1062no—
576C2×C42—1061no—
577C2×C42—1061no—
578C2×C42—1061no—
579#104—1068no—
580#104—1064no—
581#104—1064no—
582#99—28no—
583C24—21no—
584C24—1061no—
585C24C2×C22⋊D5311yescharacteristic
586#41—22no—
587#41—22no—
588#41—22no—
589#41—22no—
590#41—22no—
591#41—22no—
592#41—22no—
593#41—22no—
594#41—41no—
595#41—41no—
596#41—41no—
597#41—41no—
598#41—41no—
599#41—41no—
600#41—41no—
601#41—41no—
602#41—534no—
603#41—534no—
604#41—534no—
605#41—534no—
606#41—1062no—
607#41—1062no—
608#41—1062no—
609#41—1062no—
610#41—1062no—
611#41—1062no—
612#41—1062no—
613#41—1062no—
614#41—1062no—
615#41—1062no—
616#41—1062no—
617#41—1062no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—532no—
624C2×Q8—532no—
625C2×Q8—532no—
626C2×Q8—1061no—
627C2×Q8—1061no—
628C2×Q8—1061no—
629C2×Q8C2×C4×D5312yescomplemented
630C2×D4—22no—
631C2×D4—22no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—41no—
638C2×D4—41no—
639C2×D4—41no—
640C2×D4—41no—
641C2×D4—532no—
642C2×D4—532no—
643C2×D4—532no—
644C2×D4—1062no—
645C2×D4—1062no—
646C2×D4—1062no—
647C2×D4—1062no—
648C2×D4—1062no—
649C2×D4—1062no—
650C2×D4—1061no—
651C2×D4—1061no—
652C2×D4—1061no—
653C2×D4C2×C4×D5312yescomplemented
654C22×C4—21no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—41no—
661C22×C4—41no—
662C22×C4—41no—
663C22×C4—1068no—
664C22×C4—1061no—
665C22×C4—1061no—
666C22×C4—1062no—
667C22×C4—1062no—
668C22×C4—1062no—
669C22×C4—1062no—
670C22×C4—1062no—
671C22×C4—1062no—
672C22×C4—1061no—
673C22×C4—1062no—
674C22×C4—1062no—
675C22×C4—2128no—
676C22×C4—2124no—
677C22×C4C2×C4×D5311yescharacteristic
678C22×C4C2×C4×D5311yescharacteristic
679C22×C4#1171994511yescharacteristic
680C22×C4#1171994511yescharacteristic
681C22×C4D4×D5311yescharacteristic
682C22×C4D4×D5311yescharacteristic
683C22×C4D4×D5311yescharacteristic
684C22×C4D4×D5311yescharacteristic
685C22×C4D4×D5311yescharacteristic
686C22×C4D4×D5311yescharacteristic
687C22×C4#1171994711yescharacteristic
688C22×C4#1171994711yescharacteristic
689C22×C4C2×C22⋊D5311yescharacteristic
690C22×C4C23×D5311yescharacteristic
691Q16—1068no—
692SD16—1068no—
693SD16—1068no—
694D8—1068no—
695M16—534no—
696M16—1062no—
697M16—1062no—
698M16—1062no—
699M16—1062no—
700M16—1062no—
701M16—2121no—
702M16—2121no—
703C2×C8—1062no—
704C2×C8—1062no—
705C2×C8—1062no—
706C2×C8—1062no—
707C2×C8—2121no—
708C2×C8—2121no—
709C4⋊C4—22no—
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—41no—
713C4⋊C4—1068no—
714C22⋊C4—22no—
715C22⋊C4—22no—
716C22⋊C4—41no—
717C22⋊C4—1068no—
718C22⋊C4C2×C22⋊D5314yes—
719C42—22no—
720C42—22no—
721C42—22no—
722C42—41no—
723C42—532no—
724C42—532no—
725C42—1068no—
726C42—1061no—
727C42—1061no—
728C42—1062no—
729C42—1062no—
730C23—22no—
731C23—42no—
732C23—41no—
733C23—41no—
734C23—82no—
735C23—1062no—
736C23—1062no—
737C23—1062no—
738C23—2124no—
739C23C4×C22⋊D5311yescharacteristic
740C23C4×C22⋊D5311yescharacteristic
741C23#1313318511yescharacteristic
742C23#1313318511yescharacteristic
743C23#1313318811yescharacteristic
744C23#1313318811yescharacteristic
745C23C22×C22⋊D5311yescharacteristic
746Q8—22no—
747Q8—22no—
748Q8—41no—
749Q8—41no—
750Q8—534no—
751Q8—1062no—
752Q8—1062no—
753Q8—1062no—
754D4—22no—
755D4—22no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—42no—
760D4—41no—
761D4—41no—
762D4—534no—
763D4—1064no—
764D4—1064no—
765D4—1064no—
766D4—1064no—
767D4—1062no—
768D4—1062no—
769D4—1062no—
770C2×C4—22no—
771C2×C4—24no—
772C2×C4—44no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—82no—
781C2×C4—1064no—
782C2×C4—1062no—
783C2×C4—1062no—
784C2×C4—1062no—
785C2×C4—1062no—
786C2×C4—1064no—
787C2×C4—1064no—
788C2×C4—1064no—
789C2×C4—1064no—
790C2×C4—1062no—
791C2×C4—21216no—
792C2×C4—2124no—
793C2×C4—2124no—
794C2×C4—2122no—
795C2×C4C22⋊C4×D5311yescharacteristic
796C2×C4C22⋊C4×D5311yescharacteristic
797C2×C4C22⋊C4×D5311yescharacteristic
798C2×C4C22⋊C4×D5311yescharacteristic
799C2×C4#1313317711yescharacteristic
800C2×C4#1313317711yescharacteristic
801C2×C4#1313317711yescharacteristic
802C2×C4#1313317711yescharacteristic
803C2×C4C4×C22⋊D5311yescharacteristic
804C2×C4C4×C22⋊D5311yescharacteristic
805C2×C4#1313318511yescharacteristic
806C2×C4#1313318511yescharacteristic
807C2×C4#1313318811yescharacteristic
808C2×C4#1313318811yescharacteristic
809C2×C4#1313319011yescharacteristic
810C2×C4#1313319011yescharacteristic
811C2×C4#1313319011yescharacteristic
812C2×C4#1313319011yescharacteristic
813C2×C4#1313319911yescharacteristic
814C2×C4#1313319911yescharacteristic
815C2×C4#1313319911yescharacteristic
816C2×C4#1313319911yescharacteristic
817C2×C4C22×C4×D5311yescharacteristic
818C2×C4C2×D4×D5311yescharacteristic
819C2×C4C2×D4×D5311yescharacteristic
820C2×C4C2×D4×D5311yescharacteristic
821C2×C4C2×#1171994711yescharacteristic
822C2×C4C2×#1171994511yescharacteristic
823C8—1064no—
824C8—2122no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—42no—
833C22—82no—
834C22—82no—
835C22—82no—
836C22—1064no—
837C22—2124no—
838C22—2124no—
839C22—2124no—
840C22#1681049911yescharacteristic
841C22#1681049911yescharacteristic
842C22#1681049911yescharacteristic
843C22#1681049911yescharacteristic
844C22C2×C4×C22⋊D5311yescharacteristic
845C22C2×#1313318511yescharacteristic
846C22C2×#1313318811yescharacteristic
847C4—44no—
848C4—42no—
849C4—82no—
850C4—1064no—
851C4—1064no—
852C4—2122no—
853C4#1681049911yescharacteristic
854C4#1681049911yescharacteristic
855C4#1681049911yescharacteristic
856C4#1681049911yescharacteristic
857C4C2×C22⋊C4×D5311yescharacteristic
858C4C2×#1313317711yescharacteristic
859C4C2×#1313319011yescharacteristic
860C4C2×#1313319911yescharacteristic
861C2—21no—
862C2—21no—
863C2—21no—
864C2—21no—
865C2—21no—
866C2—21no—
867C2—82no—
868C2—2124no—
869C2#2027521312yesdirect product factor
870C2C2×#1681049911yescharacteristic
subgroupG/H
centerC2×C4#13133190
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#410C2
socleC22×C53#386
prime radicalC2×#16811421C2
cosocleC22×C4×C53C24
hypercenterC2×#410D53
hypocenterC53C2×#1906
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
2. C2×#16811091C2semidirect
3. C2×#16810641C2semidirect
4. C22×#13133144C2semidirect
5. #20275213C2direct (N × H)
6. C2×#16810393C2semidirect
7. C2×#16810382C2semidirect
8. C2×C53×#410C2semidirect
12. #16811421C4semidirect
14. C2×#13133248C4semidirect
16. C2×#13133243C4semidirect
24. #16811091C22semidirect
32. #16810641C22semidirect
37. C2×#13133144C22semidirect
38. #16810393C22semidirect
39. #16810382C22semidirect
44. C53×#410C22semidirect
65. #13133248C2×C4semidirect
69. #13133243C2×C4semidirect
86. C2×#11719917C2×C4semidirect
87. C2×#11719917C2×C4semidirect
125. C2×#41×C53C2×C4semidirect
127. C22×Q8×C53C2×C4semidirect
129. C22×D4×C53C2×C4semidirect
171. C2×Q8×C53C22×C4semidirect
183. C2×D4×C53C22×C4semidirect
287. #11719917C22×C4semidirect
430. C2×#410D53semidirect
441. C2×C53#1906semidirect
477. #410C2×D53semidirect
481. C53C2×#1906semidirect
504. C2×#41C4×D53semidirect
507. C22×Q8C4×D53semidirect
511. C22×D4C4×D53semidirect
629. C2×Q8C2×C4×D53semidirect
653. C2×D4C2×C4×D53semidirect
869. C2#20275213direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168114212
C2×#168110912
C2×#168106412
C22×#131331442
#202752132
C2×#168103932
C2×#168103822
C2×C53×#4102
C2×#190653