Finite Group Databasebeta

← C2×#20286617 #28260515

Subgroups — C2×#20286617 #28260515

Order 13568.

2210 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811319C211yesmaximal, characteristic, complemented
2#20286617C2116yesmaximal, direct product factor
3C2×#16810977C211yesmaximal, characteristic, complemented
4C2×#16810939C211yesmaximal, characteristic, complemented
5C2×#16810961C211yesmaximal, characteristic, complemented
6C2×#16810930C211yesmaximal, characteristic, complemented
7C2×#16810857C211yesmaximal, characteristic, complemented
8C2×#16810854C211yesmaximal, characteristic, complemented
9C2×#16810835C211yesmaximal, characteristic, complemented
10C2×#16810768C211yesmaximal, characteristic, complemented
11C2×#16810762C211yesmaximal, characteristic, complemented
12C2×C4×#11719924C211yesmaximal, characteristic, complemented
13C2×D4×#88322C211yesmaximal, characteristic, complemented
14C2×#16810619C211yesmaximal, characteristic, complemented
15C22×#13133141C211yesmaximal, characteristic, complemented
16C2×C53×#548C211yesmaximal, characteristic, complemented
17C22×#11719924C2211yescharacteristic
18C22×#11719924C2211yescharacteristic
19C22×#11719922C2211yescharacteristic
20C23×#88322C2211yescharacteristic
21C23×#88322C2211yescharacteristic
22#16811319—24no—
23#16811319C2218yescomplemented
24C2×#13133212—21no—
25C2×#13133209C2211yescharacteristic
26C2×#13133199—21no—
27C2×#13133191C2211yescharacteristic
28C2×#13133191C2211yescharacteristic
29C2×#13133189—21no—
30C2×C4×D212C2211yescharacteristic
31C2×#13133177—21no—
32C2×#13133176C2211yescharacteristic
33C22×C4⋊Dic53C2211yescharacteristic
34#16810977C2218yescomplemented
35#16810961C2218yescomplemented
36#16810939C2218yescomplemented
37#16810930C2218yescomplemented
38#16810857C2218yescomplemented
39#16810854C2218yescomplemented
40#16810835C2218yescomplemented
41#16810768C2218yescomplemented
42#16810762C2218yescomplemented
43C4×#11719924C2218yescomplemented
44D4×#88322C2218yescomplemented
45C2×#13133150C2211yescharacteristic
46C2×#13133148C2211yescharacteristic
47C2×#13133148C2211yescharacteristic
48C2×C4⋊#88322C2211yescharacteristic
49#16810619C2218yescomplemented
50C2×#13133141C2211yescharacteristic
51C2×#13133141C2211yescharacteristic
52C2×#13133141C2211yescharacteristic
53C2×#13133141C2211yescharacteristic
54C2×#13133141C2211yescharacteristic
55C2×#13133141C2211yescharacteristic
56C2×#13133141C2218yescomplemented
57C2×#13133138C2211yescharacteristic
58C2×#13133138C2211yescharacteristic
59C2×#13133138C2211yescharacteristic
60C2×#13133137C2211yescharacteristic
61C2×C22⋊#88322C2211yescharacteristic
62C2×C22⋊#88322C2211yescharacteristic
63C2×C4×#88322C2211yescharacteristic
64C22×#41×C53C2211yescharacteristic
65C23×Q8×C53C2211yescharacteristic
66C53×#548—24no—
67C53×#548C2218yescomplemented
68C2×#124×C53—21no—
69C2×#124×C53C2211yescharacteristic
70C2×C22⋊Q8×C53—21no—
71C2×C22⋊Q8×C53C2211yescharacteristic
72C2×#121×C53—21no—
73C2×#121×C53C2211yescharacteristic
74C2×C4×Q8×C53C2211yescharacteristic
75C2×C4×D4×C53—21no—
76C2×C4×D4×C53C2211yescharacteristic
77C22×D212C2311yescharacteristic
78C22×C22⋊D53—21no—
79C22×C22⋊D53—21no—
80C23×Dic53—21no—
81C22×C4×D53—21no—
82C2×#11719924—24no—
83C2×#11719924—42no—
84C2×#11719924C2314yes—
85C2×#11719924C2314yes—
86C2×#11719922—42no—
87C2×#11719922C2314yes—
88C22×#88322—42no—
89C22×#88322—42no—
90C22×#88322C2311yescharacteristic
91C22×#88322C2311yescharacteristic
92C22×#88322C2311yescharacteristic
93C22×#88322C2311yescharacteristic
94C22×#88322C2314yes—
95C22×#88322C2314yes—
96#13133212—28no—
97#13133209—22no—
98#13133209C2314yes—
99#13133199—28no—
100#13133191—22no—
101#13133191—22no—
102#13133191C2314yes—
103#13133191C2314yes—
104#13133189—28no—
105C4×D212—22no—
106C4×D212C2314yes—
107#13133177—28no—
108#13133176—22no—
109#13133176C2314yes—
110C2×C4⋊Dic53—22no—
111C2×C4⋊Dic53—21no—
112C2×C4⋊Dic53C2314yes—
113C2×C4⋊Dic53C2311yescharacteristic
114C2×C4⋊Dic53C2311yescharacteristic
115C2×C4⋊Dic53C2311yescharacteristic
116C2×#11719919—21no—
117C2×#11719919—21no—
118C2×C22⋊Dic53—21no—
119C2×#11719921—21no—
120C2×#11719921—21no—
121C2×#11719921—21no—
122C2×C4×Dic53—21no—
123#13133150C2314yes—
124#13133148C2314yes—
125#13133148C2314yes—
126C4⋊#88322C2314yes—
127#13133141C2314yes—
128#13133141C2314yes—
129#13133141C2314yes—
130#13133141C2314yes—
131#13133141C2314yes—
132#13133141C2314yes—
133#13133138C2314yes—
134#13133138C2314yes—
135#13133138C2314yes—
136#13133137C2314yes—
137C22⋊#88322C2314yes—
138C22⋊#88322C2314yes—
139C4×#88322C2314yes—
140C2×#41×C53—22no—
141C2×#41×C53—24no—
142C2×#41×C53—42no—
143C2×#41×C53C2314yes—
144C22×Q8×C53—21no—
145C22×Q8×C53—22no—
146C22×Q8×C53—24no—
147C22×Q8×C53—42no—
148C22×Q8×C53C2311yescharacteristic
149C22×Q8×C53C2314yes—
150C22×Q8×C53C2311yescharacteristic
151C22×D4×C53—21no—
152C22×D4×C53—21no—
153C22×D4×C53D411yescharacteristic
154C22×D4×C53C2311yescharacteristic
155C23×C4×C53—21no—
156C23×C4×C53—21no—
157C23×C4×C53C2311yescharacteristic
158C23×C4×C53C2311yescharacteristic
159#124×C53—28no—
160#124×C53—22no—
161#124×C53C2314yes—
162C22⋊Q8×C53—28no—
163C22⋊Q8×C53—22no—
164C22⋊Q8×C53C2314yes—
165#121×C53—28no—
166#121×C53—22no—
167#121×C53C2314yes—
168C4×Q8×C53—22no—
169C4×Q8×C53C2314yes—
170C4×D4×C53—28no—
171C4×D4×C53D414yes—
172C4×D4×C53C2314yes—
173C2×C4⋊C4×C53—21no—
174C2×C4⋊C4×C53—21no—
175C2×C4⋊C4×C53D411yescharacteristic
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C22⋊C4×C53—21no—
178C2×C22⋊C4×C53—21no—
179C2×C22⋊C4×C53—21no—
180C2×C22⋊C4×C53—21no—
181C2×C22⋊C4×C53D411yescharacteristic
182C2×C22⋊C4×C53D411yescharacteristic
183C2×C42×C53—21no—
184C2×C42×C53C2311yescharacteristic
185C24×C53—21no—
186C24×C53C2×D411yescharacteristic
187C24×C53C2×D411yescharacteristic
188C23×D53—21no—
189#41×C53—28no—
190#41×C53—44no—
191#41×C53—48no—
192C2×Q8×C53—21no—
193C2×Q8×C53—24no—
194C2×Q8×C53—21no—
195C2×Q8×C53—22no—
196C2×Q8×C53—28no—
197C2×Q8×C53—22no—
198C2×Q8×C53—22no—
199C2×Q8×C53—44no—
200C2×Q8×C53—44no—
201C2×Q8×C53—48no—
202C2×Q8×C53#4114yes—
203C2×Q8×C53C2412yes—
204C2×Q8×C53C2412yes—
205C2×D4×C53—24no—
206C2×D4×C53—24no—
207C2×D4×C53—24no—
208C2×D4×C53—21no—
209C2×D4×C53—22no—
210C2×D4×C53—22no—
211C2×D4×C53—44no—
212C2×D4×C53—44no—
213C2×D4×C53C2×D414yes—
214C2×D4×C53C2412yes—
215C22×C4×C53—21no—
216C22×C4×C53—22no—
217C22×C4×C53—22no—
218C22×C4×C53—22no—
219C22×C4×C53—22no—
220C22×C4×C53—21no—
221C22×C4×C53—21no—
222C22×C4×C53—24no—
223C22×C4×C53—24no—
224C22×C4×C53—44no—
225C22×C4×C53—44no—
226C22×C4×C53C2×D411yescharacteristic
227C22×C4×C53C2×D411yescharacteristic
228C22×C4×C53C2×D411yescharacteristic
229C22×C4×C53C2×D411yescharacteristic
230C22×C4×C53C2×D412yes—
231C22×C4×C53C2×D412yes—
232C22×C4×C53C2412yes—
233C22×C4×C53C2412yes—
234C22×C4×C53C2411yescharacteristic
235C2×C22⋊D53—24no—
236C2×C22⋊D53—24no—
237C2×C22⋊D53—44no—
238C2×C22⋊D53—82no—
239C22×Dic53—21no—
240C22×Dic53—21no—
241C22×Dic53—21no—
242C22×Dic53—24no—
243C22×Dic53—82no—
244C2×D212—22no—
245C2×D212—22no—
246C2×D212—21no—
247C2×D212C2412yes—
248C2×C4×D53—24no—
249C2×C4×D53—82no—
250C4⋊C4×C53—24no—
251C4⋊C4×C53—24no—
252C4⋊C4×C53—21no—
253C4⋊C4×C53C2×D414yes—
254C4⋊C4×C53C2412yes—
255C22⋊C4×C53—24no—
256C22⋊C4×C53—24no—
257C22⋊C4×C53—24no—
258C22⋊C4×C53—24no—
259C22⋊C4×C53C2×D414yes—
260C22⋊C4×C53C2×D414yes—
261C42×C53—24no—
262C42×C53C2×D412yes—
263C42×C53C2412yes—
264C22⋊Dic53—24no—
265#11719924—28no—
266#11719924—44no—
267#11719922—44no—
268#11719921—24no—
269#11719921—24no—
270#11719921—24no—
271C4⋊Dic53—21no—
272C4⋊Dic53—21no—
273C4⋊Dic53—24no—
274C4⋊Dic53—21no—
275C4⋊Dic53C2412yes—
276C4⋊Dic53C2412yes—
277C4⋊Dic53C2412yes—
278#11719919—24no—
279#11719919—24no—
280C4×Dic53—24no—
281C2×#88322—22no—
282C2×#88322—22no—
283C2×#88322—22no—
284C2×#88322—22no—
285C2×#88322—44no—
286C2×#88322—44no—
287C2×#88322C2412yes—
288C2×#88322C2412yes—
289C2×#88322C2412yes—
290C2×#88322C2412yes—
291C23×C53—22no—
292C23×C53—22no—
293C23×C53—22no—
294C23×C53—22no—
295C23×C53—22no—
296C23×C53—22no—
297C23×C53—42no—
298C23×C53—42no—
299C23×C53—42no—
300C23×C53#13514yes—
301C23×C53C22×D412yes—
302C23×C53C22×D412yes—
303C23×C53C22×D411yescharacteristic
304C22×D53—22no—
305C22×D53—42no—
306C22×D53—42no—
307C22×D53—42no—
308Q8×C53—24no—
309Q8×C53—22no—
310Q8×C53—22no—
311Q8×C53—22no—
312Q8×C53—48no—
313Q8×C53—42no—
314Q8×C53C2×#4114yes—
315D4×C53—28no—
316D4×C53—22no—
317D4×C53—22no—
318D4×C53—48no—
319D4×C53—48no—
320D4×C53—42no—
321C2×C4×C53—22no—
322C2×C4×C53—22no—
323C2×C4×C53—24no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53—22no—
327C2×C4×C53—24no—
328C2×C4×C53—24no—
329C2×C4×C53—22no—
330C2×C4×C53—22no—
331C2×C4×C53—22no—
332C2×C4×C53—22no—
333C2×C4×C53—22no—
334C2×C4×C53—22no—
335C2×C4×C53—48no—
336C2×C4×C53—48no—
337C2×C4×C53—42no—
338C2×C4×C53—42no—
339C2×C4×C53C22×D412yes—
340C2×C4×C53C22×D412yes—
341C2×C4×C53C22×D412yes—
342C2×C4×C53C22×D412yes—
343C2×C4×C53C22×D411yescharacteristic
344C2×C4×C53C2×#4112yes—
345C2×C4×C53H(5,𝔽2)12yes—
346C2×C4×C53C2511yescharacteristic
347C22⋊D53—48no—
348C22⋊D53—84no—
349C2×Dic53—22no—
350C2×Dic53—22no—
351C2×Dic53—22no—
352C2×Dic53—42no—
353C2×Dic53—42no—
354C2×Dic53—42no—
355C2×Dic53—84no—
356D212—22no—
357D212—22no—
358D212—42no—
359C4×D53—84no—
360#88322—22no—
361#88322—22no—
362#88322—22no—
363#88322—22no—
364C2×#3301—531nomaximal, Sylow
365C22×C53—22no—
366C22×C53—28no—
367C22×C53—22no—
368C22×C53—22no—
369C22×C53—22no—
370C22×C53—22no—
371C22×C53—44no—
372C22×C53—42no—
373C22×C53—42no—
374C22×C53—42no—
375C22×C53—84no—
376C22×C53#54612yes—
377C22×C53C2×#13514yes—
378C22×C53C2×#13512yes—
379C22×C53#57712yes—
380C22×C53C23×D411yescharacteristic
381C2×D53—42no—
382C2×D53—42no—
383C2×D53—42no—
384C2×D53—84no—
385C4×C53—22no—
386C4×C53—22no—
387C4×C53—24no—
388C4×C53—22no—
389C4×C53—22no—
390C4×C53—42no—
391C4×C53—42no—
392C4×C53#54612yes—
393C4×C53C22×#4111yescharacteristic
394C4×C53C2×H(5,𝔽2)11yescharacteristic
395Dic53—42no—
396Dic53—42no—
397Dic53—42no—
398C2×#553—531no—
399C2×#548D5311yescharacteristic, complemented
400#3301—5316no—
401C2×#488—531no—
402C2×#481—531no—
403C2×#485—531no—
404C2×#479—531no—
405C2×#466—531no—
406C2×#465—531no—
407C2×#463—531no—
408C2×#449—531no—
409C2×#448—531no—
410C2×C4×SD16—531no—
411C2×C8×D4—531no—
412C2×#416—531no—
413C22×#103—531no—
414C2×C53—24no—
415C2×C53—42no—
416C2×C53—82no—
417C2×C53#330114yescomplemented
418C2×C53C2×#54611yescharacteristic
419C2×C53C22×#13511yescharacteristic
420C2×C53C2×#57711yescharacteristic
421D53—82no—
422C22×#41C2×D5311yescharacteristic
423C23×Q8C2×D5311yescharacteristic
424C22×SD16—531no—
425C22×SD16—531no—
426C22×D8—531no—
427C23×C8—531no—
428C23×C8—531no—
429#553—538no—
430#553—1064no—
431#548—24no—
432#548C2×D5318yescomplemented
433C2×#126—1061no—
434C2×#125—531no—
435C2×#124—21no—
436C2×#124C2×D5311yescharacteristic
437C2×#123—1061no—
438C2×C22⋊Q8—21no—
439C2×C22⋊Q8C2×D5311yescharacteristic
440C2×#121—21no—
441C2×#121—531no—
442C2×#121—531no—
443C2×#121—1061no—
444C2×#121C2×D5311yescharacteristic
445C2×C4×Q8C2×D5311yescharacteristic
446C2×C4×D4—21no—
447C2×C4×D4—531no—
448C2×C4×D4—1061no—
449C2×C4×D4C2×D5311yescharacteristic
450C2×#117—531no—
451C22×C4⋊C4—531no—
452#488—538no—
453#485—538no—
454#481—538no—
455#479—538no—
456#466—538no—
457#465—538no—
458#463—538no—
459#449—538no—
460#448—538no—
461C4×SD16—538no—
462C8×D4—538no—
463C2×#107—531no—
464C2×#106—531no—
465C2×#106—531no—
466C2×C4⋊C8—531no—
467#416—538no—
468C2×#103—531no—
469C2×#103—531no—
470C2×#103—531no—
471C2×#103—531no—
472C2×#103—531no—
473C2×#103—531no—
474C2×#103—538no—
475C2×#102—531no—
476C2×#102—531no—
477C2×#102—531no—
478C2×#102—531no—
479C2×C22⋊C8—531no—
480C2×C22⋊C8—531no—
481C2×C4×C8—531no—
482C53C2×#330111yescharacteristic, complemented, Sylow
483C2×#41—22no—
484C2×#41—24no—
485C2×#41—42no—
486C2×#41C22×D5314yes—
487C22×Q8—21no—
488C22×Q8—22no—
489C22×Q8—24no—
490C22×Q8—42no—
491C22×Q8C22×D5311yescharacteristic
492C22×Q8C22×D5314yes—
493C22×Q8C22×D5311yescharacteristic
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—531no—
497C22×D4—1061no—
498C22×D4—1061no—
499C22×D4C22⋊D5311yescharacteristic
500C22×D4C22×D5311yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—1061no—
504C23×C4—1061no—
505C23×C4C22×D5311yescharacteristic
506C23×C4C22×D5311yescharacteristic
507C2×SD16—534no—
508C2×SD16—534no—
509C2×SD16—1064no—
510C2×SD16—2122no—
511C2×D8—534no—
512C2×D8—2122no—
513C22×C8—531no—
514C22×C8—531no—
515C22×C8—531no—
516C22×C8—531no—
517C22×C8—534no—
518C22×C8—534no—
519C22×C8—2122no—
520C22×C8—2122no—
521#126—1068no—
522#125—534no—
523#125—1062no—
524#124—28no—
525#124—22no—
526#124C22×D5314yes—
527#123—1068no—
528C22⋊Q8—22no—
529C22⋊Q8—28no—
530C22⋊Q8C22×D5314yes—
531#121—28no—
532#121—22no—
533#121—534no—
534#121—534no—
535#121—1068no—
536#121—1062no—
537#121—1062no—
538#121C22×D5314yes—
539C4×Q8—22no—
540C4×Q8C22×D5314yes—
541C4×D4—28no—
542C4×D4—534no—
543C4×D4—1068no—
544C4×D4—1062no—
545C4×D4C22⋊D5314yes—
546C4×D4C22×D5314yes—
547#117—534no—
548#117—1062no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—531no—
552C2×C4⋊C4—531no—
553C2×C4⋊C4—534no—
554C2×C4⋊C4—531no—
555C2×C4⋊C4—1061no—
556C2×C4⋊C4—1062no—
557C2×C4⋊C4—1061no—
558C2×C4⋊C4—1061no—
559C2×C4⋊C4C22⋊D5311yescharacteristic
560C2×C4⋊C4C22×D5311yescharacteristic
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—1061no—
566C2×C22⋊C4—1061no—
567C2×C22⋊C4—1061no—
568C2×C22⋊C4—1061no—
569C2×C22⋊C4C22⋊D5311yescharacteristic
570C2×C22⋊C4C22⋊D5311yescharacteristic
571C2×C42—21no—
572C2×C42—1061no—
573C2×C42C22×D5311yescharacteristic
574#107—534no—
575#106—534no—
576#106—534no—
577C4⋊C8—534no—
578#103—534no—
579#103—534no—
580#103—534no—
581#103—534no—
582#103—534no—
583#103—534no—
584#102—534no—
585#102—534no—
586#102—534no—
587#102—534no—
588C22⋊C8—534no—
589C22⋊C8—534no—
590C4×C8—534no—
591C24—21no—
592C24—1061no—
593C24C2×C22⋊D5311yescharacteristic
594C24C2×C22⋊D5311yescharacteristic
595#41—28no—
596#41—44no—
597#41—48no—
598C2×Q8—21no—
599C2×Q8—24no—
600C2×Q8—21no—
601C2×Q8—22no—
602C2×Q8—28no—
603C2×Q8—22no—
604C2×Q8—22no—
605C2×Q8—44no—
606C2×Q8—44no—
607C2×Q8—48no—
608C2×Q8#1171994714yes—
609C2×Q8C23×D5312yes—
610C2×Q8C23×D5312yes—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—24no—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—44no—
618C2×D4—44no—
619C2×D4—532no—
620C2×D4—1064no—
621C2×D4—1064no—
622C2×D4—1061no—
623C2×D4—1062no—
624C2×D4—1062no—
625C2×D4—4242no—
626C2×D4—2124no—
627C2×D4C2×C22⋊D5314yes—
628C2×D4C23×D5312yes—
629C22×C4—21no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—24no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—24no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—1064no—
641C22×C4—1061no—
642C22×C4—1061no—
643C22×C4—1061no—
644C22×C4—1064no—
645C22×C4—4242no—
646C22×C4—4242no—
647C22×C4C2×C22⋊D5312yes—
648C22×C4C2×C22⋊D5312yes—
649C22×C4C2×C22⋊D5311yescharacteristic
650C22×C4C2×C22⋊D5311yescharacteristic
651C22×C4C2×C22⋊D5311yescharacteristic
652C22×C4C2×C22⋊D5311yescharacteristic
653C22×C4C23×D5312yes—
654C22×C4C23×D5312yes—
655C22×C4C23×D5311yescharacteristic
656SD16—1068no—
657SD16—2124no—
658D8—2124no—
659C2×C8—532no—
660C2×C8—532no—
661C2×C8—532no—
662C2×C8—532no—
663C2×C8—1062no—
664C2×C8—1062no—
665C2×C8—1062no—
666C2×C8—1062no—
667C2×C8—2124no—
668C2×C8—2124no—
669C4⋊C4—24no—
670C4⋊C4—24no—
671C4⋊C4—21no—
672C4⋊C4—532no—
673C4⋊C4—532no—
674C4⋊C4—532no—
675C4⋊C4—1061no—
676C4⋊C4—1061no—
677C4⋊C4—1064no—
678C4⋊C4—1061no—
679C4⋊C4—1064no—
680C4⋊C4—1064no—
681C4⋊C4C2×C22⋊D5314yes—
682C4⋊C4C23×D5312yes—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—1064no—
688C22⋊C4—1064no—
689C22⋊C4—1064no—
690C22⋊C4—1064no—
691C22⋊C4C2×C22⋊D5314yes—
692C22⋊C4C2×C22⋊D5314yes—
693C42—24no—
694C42—1064no—
695C42C2×C22⋊D5312yes—
696C42C23×D5312yes—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—1062no—
707C23—2122no—
708C23—2122no—
709C23—2122no—
710C23#1313323714yes—
711C23C22×C22⋊D5312yes—
712C23C22×C22⋊D5312yes—
713C23C22×C22⋊D5311yescharacteristic
714Q8—24no—
715Q8—22no—
716Q8—22no—
717Q8—22no—
718Q8—48no—
719Q8—42no—
720Q8C2×#1171994714yes—
721D4—28no—
722D4—22no—
723D4—22no—
724D4—48no—
725D4—48no—
726D4—42no—
727D4—1062no—
728D4—1062no—
729D4—4244no—
730D4—2128no—
731D4—2122no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—48no—
747C2×C4—48no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—1062no—
751C2×C4—1062no—
752C2×C4—1062no—
753C2×C4—4244no—
754C2×C4—4244no—
755C2×C4—2122no—
756C2×C4—2122no—
757C2×C4—2122no—
758C2×C4C22×C22⋊D5312yes—
759C2×C4C22×C22⋊D5312yes—
760C2×C4C22×C22⋊D5312yes—
761C2×C4C22×C22⋊D5312yes—
762C2×C4C22×C22⋊D5311yescharacteristic
763C2×C4C2×#1171994712yes—
764C2×C4#1313326212yes—
765C2×C4C24×D5311yescharacteristic
766C8—1062no—
767C8—1062no—
768C8—1062no—
769C8—1062no—
770C22—28no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—84no—
781C22—4244no—
782C22—2122no—
783C22—2122no—
784C22—2122no—
785C22#1681126712yes—
786C22C2×#1313323714yes—
787C22C2×#1313323712yes—
788C22#1681143112yes—
789C22C23×C22⋊D5311yescharacteristic
790C4—22no—
791C4—22no—
792C4—22no—
793C4—24no—
794C4—22no—
795C4—42no—
796C4—42no—
797C4—2122no—
798C4—2122no—
799C4—2122no—
800C4#1681126712yes—
801C4C22×#1171994711yescharacteristic
802C4C2×#1313326211yescharacteristic
803C2—24no—
804C2—42no—
805C2—82no—
806C2—4242no—
807C2#2028661714yesdirect product factor
808C2C2×#1681126711yescharacteristic
809C2C22×#1313323711yescharacteristic
810C2C2×#1681143111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#548C2
socleC23×C53C22×D4
hypercenterC2×#548D53
hypocenterC53C2×#3301
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#16811319C2semidirect
2. #20286617C2direct (N × H)
3. C2×#16810977C2semidirect
4. C2×#16810939C2semidirect
5. C2×#16810961C2semidirect
6. C2×#16810930C2semidirect
7. C2×#16810857C2semidirect
8. C2×#16810854C2semidirect
9. C2×#16810835C2semidirect
10. C2×#16810768C2semidirect
11. C2×#16810762C2semidirect
12. C2×C4×#11719924C2semidirect
13. C2×D4×#88322C2semidirect
14. C2×#16810619C2semidirect
15. C22×#13133141C2semidirect
16. C2×C53×#548C2semidirect
23. #16811319C22semidirect
34. #16810977C22semidirect
35. #16810961C22semidirect
36. #16810939C22semidirect
37. #16810930C22semidirect
38. #16810857C22semidirect
39. #16810854C22semidirect
40. #16810835C22semidirect
41. #16810768C22semidirect
42. #16810762C22semidirect
43. C4×#11719924C22semidirect
44. D4×#88322C22semidirect
49. #16810619C22semidirect
56. C2×#13133141C22semidirect
67. C53×#548C22semidirect
399. C2×#548D53semidirect
417. C2×C53#3301semidirect
432. #548C2×D53semidirect
482. C53C2×#3301semidirect
807. C2#20286617direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113192
#202866172
C2×#168109772
C2×#168109392
C2×#168109612
C2×#168109302
C2×#168108572
C2×#168108542
C2×#168108352
C2×#168107682
C2×#168107622
C2×C4×#117199242
C2×D4×#883222
C2×#168106192
C22×#131331412
C2×C53×#5482
C2×#330153