Finite Group Databasebeta

← C2×#20286694 #28260733

Subgroups — C2×#20286694 #28260733

Order 13568.

2190 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×#16811321C211yesmaximal, characteristic, complemented
2C2×#16811275C211yesmaximal, characteristic, complemented
3#20286694C2116yesmaximal, direct product factor
4C2×#16810990C211yesmaximal, characteristic, complemented
5C2×#16810967C211yesmaximal, characteristic, complemented
6C2×#16810922C211yesmaximal, characteristic, complemented
7C2×#16810871C211yesmaximal, characteristic, complemented
8C2×#16810853C211yesmaximal, characteristic, complemented
9C2×#16810827C211yesmaximal, characteristic, complemented
10C2×#16810771C211yesmaximal, characteristic, complemented
11C2×#16810770C211yesmaximal, characteristic, complemented
12C2×#16810734C211yesmaximal, characteristic, complemented
13C2×#16810697C211yesmaximal, characteristic, complemented
14C2×#16810622C211yesmaximal, characteristic, complemented
15C2×#16810618C211yesmaximal, characteristic, complemented
16C2×C53×#483C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×#11719945C2211yescharacteristic
19C22×#11719913C2211yescharacteristic
20C22×#11719924C2211yescharacteristic
21C22×D424C2211yescharacteristic
22C22×#11719917C2211yescharacteristic
23C22×C8×D53C2211yescharacteristic
24#16811321—24no—
25#16811321C2218yescomplemented
26#16811275—24no—
27#16811275C2218yescomplemented
28C2×#13133215C2211yescharacteristic
29C2×#13133212—21no—
30C2×#13133208C2211yescharacteristic
31C2×#13133202—21no—
32C2×#13133202—21no—
33C2×#13133199—21no—
34C2×#13133197C2211yescharacteristic
35C2×#13133192C2211yescharacteristic
36C2×#13133191—21no—
37C2×#13133191C2211yescharacteristic
38C2×#13133190—21no—
39C2×#13133179C2211yescharacteristic
40C2×#13133179C2211yescharacteristic
41C2×C4×C22⋊D53—21no—
42C2×C4×C22⋊D53C2211yescharacteristic
43C2×#13133175C2211yescharacteristic
44C2×C4⋊C4×D53—21no—
45#16810990C2218yescomplemented
46#16810967C2218yescomplemented
47#16810922C2218yescomplemented
48#16810871C2218yescomplemented
49#16810853C2218yescomplemented
50#16810827C2218yescomplemented
51#16810771C2218yescomplemented
52#16810770C2218yescomplemented
53#16810734C2218yescomplemented
54#16810697C2218yescomplemented
55C2×#13133150C2211yescharacteristic
56C2×#13133146C2211yescharacteristic
57#16810622C2218yescomplemented
58#16810618C2218yescomplemented
59C2×#13133142C2211yescharacteristic
60C2×#13133141C2211yescharacteristic
61C2×#13133140C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133137C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133127C2211yescharacteristic
69C2×C22⋊Q8×C53C2211yescharacteristic
70C22×C4⋊C4×C53C2211yescharacteristic
71C53×#483C2218yescomplemented
72C2×#106×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C2×#11719949—22no—
78C2×#11719949—24no—
79C2×#11719949—42no—
80C2×#11719949C2314yes—
81C2×#11719945—22no—
82C2×#11719945—24no—
83C2×#11719945—42no—
84C2×#11719945C2314yes—
85C22×Dic106C2311yescharacteristic
86C22×D212—21no—
87C22×D212—21no—
88C22×D212C2311yescharacteristic
89C22×D212C2311yescharacteristic
90C22×C22⋊D53—21no—
91C22×C22⋊D53—21no—
92C22×C22⋊D53D411yescharacteristic
93C22×C4×D53—21no—
94C22×C4×D53—21no—
95C22×C4×D53—21no—
96C22×C4×D53—21no—
97C22×C4×D53C2311yescharacteristic
98C2×#11719913—42no—
99C2×#11719913C2314yes—
100C2×#11719924—42no—
101C2×#11719924C2314yes—
102C2×D424—24no—
103C2×D424C2314yes—
104C2×#11719917—42no—
105C2×#11719917C2314yes—
106C22×#88322C2311yescharacteristic
107C22×#88322C2311yescharacteristic
108C2×C8×D53—42no—
109C2×C8×D53C2314yes—
110#13133215—22no—
111#13133215C2314yes—
112#13133212—28no—
113#13133208—22no—
114#13133208C2314yes—
115#13133202—28no—
116#13133202—28no—
117#13133199—28no—
118#13133197—22no—
119#13133197C2314yes—
120#13133192—22no—
121#13133192C2314yes—
122#13133191—22no—
123#13133191—28no—
124#13133191C2314yes—
125#13133190—28no—
126#13133179—22no—
127#13133179—22no—
128#13133179C2314yes—
129#13133179C2314yes—
130C4×C22⋊D53—28no—
131C4×C22⋊D53D414yes—
132C4×C22⋊D53C2314yes—
133#13133175—22no—
134#13133175C2314yes—
135C2×C4⋊Dic53—21no—
136C2×C4⋊Dic53—21no—
137C2×C4⋊Dic53C2311yescharacteristic
138C2×#11719919—21no—
139C2×#11719919—21no—
140C2×#11719919—21no—
141C2×#11719919D411yescharacteristic
142C4⋊C4×D53—28no—
143C2×C22⋊Dic53D411yescharacteristic
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×#11719921—21no—
150C2×#11719921D411yescharacteristic
151C2×C4×Dic53—21no—
152C2×C4×Dic53C2311yescharacteristic
153#13133150C2314yes—
154#13133146C2314yes—
155#13133142C2314yes—
156#13133141C2314yes—
157#13133140C2314yes—
158#13133140C2314yes—
159#13133139C2314yes—
160#13133137C2314yes—
161#13133137C2314yes—
162#13133137C2314yes—
163#13133129C2314yes—
164#13133127C2314yes—
165C22×Q8×C53C2311yescharacteristic
166C23×C4×C53—21no—
167C23×C4×C53C2311yescharacteristic
168C22×C8×C53C2311yescharacteristic
169C22×C8×C53C2311yescharacteristic
170C22⋊Q8×C53—22no—
171C22⋊Q8×C53C2314yes—
172C2×C4⋊C4×C53—22no—
173C2×C4⋊C4×C53—21no—
174C2×C4⋊C4×C53—21no—
175C2×C4⋊C4×C53C2314yes—
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C4⋊C4×C53C2311yescharacteristic
179C2×C22⋊C4×C53—21no—
180#106×C53C2314yes—
181#106×C53C2314yes—
182#103×C53C2314yes—
183#103×C53C2314yes—
184C22⋊C8×C53C2314yes—
185C24×C53C2×D411yescharacteristic
186C23×D53—21no—
187C23×D53—21no—
188C23×D53C2×D411yescharacteristic
189C2×Q8×C53—21no—
190C2×Q8×C53—22no—
191C2×Q8×C53—22no—
192C2×Q8×C53C2412yes—
193C22×C4×C53—22no—
194C22×C4×C53—22no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—24no—
200C22×C4×C53—82no—
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53C2×D412yes—
203C22×C4×C53C2412yes—
204C22×C4×C53C2411yescharacteristic
205C2×C22⋊D53—24no—
206C2×C22⋊D53—24no—
207C2×C22⋊D53—42no—
208C2×C22⋊D53—44no—
209C2×C22⋊D53—44no—
210C2×C22⋊D53C2×D414yes—
211C22×Dic53—21no—
212C22×Dic53—21no—
213C22×Dic53C2×D411yescharacteristic
214C22×Dic53C2×D411yescharacteristic
215C22×Dic53C2×D411yescharacteristic
216#11719949—28no—
217#11719949—44no—
218#11719949—48no—
219#11719945—28no—
220#11719945—44no—
221#11719945—48no—
222C2×D212—21no—
223C2×D212—22no—
224C2×D212—22no—
225C2×D212—22no—
226C2×D212—24no—
227C2×D212—21no—
228C2×D212—24no—
229C2×D212—44no—
230C2×D212—82no—
231C2×D212#4114yes—
232C2×D212C2412yes—
233C2×D212C2412yes—
234C2×C4×D53—22no—
235C2×C4×D53—22no—
236C2×C4×D53—24no—
237C2×C4×D53—24no—
238C2×C4×D53—24no—
239C2×C4×D53—24no—
240C2×C4×D53—44no—
241C2×C4×D53—44no—
242C2×C4×D53—44no—
243C2×C4×D53—82no—
244C2×C4×D53C2×D412yes—
245C2×C4×D53C2412yes—
246C2×Dic106—22no—
247C2×Dic106—22no—
248C2×Dic106—21no—
249C2×Dic106C2412yes—
250C2×C8×C53—22no—
251C2×C8×C53—22no—
252C2×C8×C53C2412yes—
253C2×C8×C53C2412yes—
254C4⋊C4×C53—21no—
255C4⋊C4×C53—21no—
256C4⋊C4×C53—24no—
257C4⋊C4×C53—24no—
258C4⋊C4×C53—21no—
259C4⋊C4×C53C2412yes—
260C4⋊C4×C53C2412yes—
261C4⋊C4×C53C2412yes—
262C22⋊C4×C53—24no—
263C22⋊Dic53C2×D414yes—
264#11719924—44no—
265#11719921—24no—
266#11719921—24no—
267#11719921—24no—
268#11719921—24no—
269#11719921—24no—
270#11719921—24no—
271#11719921C2×D414yes—
272C4⋊Dic53—21no—
273C4⋊Dic53—24no—
274C4⋊Dic53—24no—
275C4⋊Dic53C2412yes—
276#11719919—24no—
277#11719919—24no—
278#11719919—24no—
279#11719919C2×D414yes—
280C4×Dic53—24no—
281C4×Dic53C2×D412yes—
282C4×Dic53C2412yes—
283#11719917—44no—
284C2×#88322—22no—
285C2×#88322—22no—
286C2×#88322C2412yes—
287C2×#88322C2412yes—
288D424—28no—
289#11719913—44no—
290C8×D53—44no—
291C23×C53—22no—
292C23×C53—22no—
293C23×C53—22no—
294C23×C53C22×D412yes—
295C23×C53C22×D411yescharacteristic
296C22×D53—22no—
297C22×D53—24no—
298C22×D53—22no—
299C22×D53—22no—
300C22×D53—22no—
301C22×D53—22no—
302C22×D53—42no—
303C22×D53—42no—
304C22×D53—42no—
305C22×D53—42no—
306C22×D53—42no—
307C22×D53C22×D412yes—
308Q8×C53—22no—
309Q8×C53—22no—
310Q8×C53—42no—
311C2×C4×C53—22no—
312C2×C4×C53—24no—
313C2×C4×C53—22no—
314C2×C4×C53—22no—
315C2×C4×C53—22no—
316C2×C4×C53—22no—
317C2×C4×C53—22no—
318C2×C4×C53—22no—
319C2×C4×C53—42no—
320C2×C4×C53—42no—
321C2×C4×C53—42no—
322C2×C4×C53—42no—
323C2×C4×C53—84no—
324C2×C4×C53C22×D412yes—
325C2×C4×C53C22×D411yescharacteristic
326C2×C4×C53C2×#4112yes—
327C2×C4×C53H(5,𝔽2)12yes—
328C2×C4×C53C2511yescharacteristic
329C22⋊D53—44no—
330C22⋊D53—48no—
331C22⋊D53—48no—
332C2×Dic53—22no—
333C2×Dic53—22no—
334C2×Dic53—22no—
335C2×Dic53—22no—
336C2×Dic53—22no—
337C2×Dic53—42no—
338C2×Dic53—42no—
339C2×Dic53C22×D412yes—
340C2×Dic53C22×D412yes—
341C2×Dic53C22×D412yes—
342D212—24no—
343D212—22no—
344D212—22no—
345D212—22no—
346D212—48no—
347D212—42no—
348D212—84no—
349D212C2×#4114yes—
350C4×D53—24no—
351C4×D53—22no—
352C4×D53—22no—
353C4×D53—48no—
354C4×D53—48no—
355C4×D53—48no—
356C4×D53—84no—
357Dic106—22no—
358Dic106—22no—
359Dic106—42no—
360C8×C53—22no—
361C8×C53—22no—
362#88322—22no—
363#88322—22no—
364C2×#3307—531nomaximal, Sylow
365C22×C53—22no—
366C22×C53—22no—
367C22×C53—22no—
368C22×C53—44no—
369C22×C53#54612yes—
370C22×C53#57512yes—
371C22×C53#57712yes—
372C22×C53C23×D411yescharacteristic
373C2×D53—22no—
374C2×D53—24no—
375C2×D53—22no—
376C2×D53—22no—
377C2×D53—44no—
378C2×D53—48no—
379C2×D53—42no—
380C2×D53—42no—
381C2×D53—42no—
382C2×D53—42no—
383C2×D53—42no—
384C2×D53—84no—
385C4×C53—22no—
386C4×C53—42no—
387C4×C53—42no—
388C4×C53—42no—
389C4×C53—42no—
390C4×C53#54612yes—
391C4×C53C22×#4111yescharacteristic
392C4×C53C2×H(5,𝔽2)11yescharacteristic
393Dic53—22no—
394Dic53—22no—
395Dic53—22no—
396Dic53—42no—
397Dic53—42no—
398C2×#553—531no—
399C2×#547—531no—
400#3307—5316no—
401C2×#491—531no—
402C2×#485—531no—
403C2×#483D5311yescharacteristic, complemented
404C2×#478—531no—
405C2×#468—531no—
406C2×#465—531no—
407C2×#461—531no—
408C2×#449—531no—
409C2×#449—531no—
410C2×#442—531no—
411C2×#435—531no—
412C2×#417—531no—
413C2×#416—531no—
414C2×C53—42no—
415C2×C53#330714yescomplemented
416C2×C53C2×#54611yescharacteristic
417C2×C53C2×#57511yescharacteristic
418C2×C53C2×#57711yescharacteristic
419D53—42no—
420D53—44no—
421D53—82no—
422C22×#41—531no—
423C22×#41—531no—
424C22×SD16—531no—
425C22×SD16—531no—
426C22×D8—531no—
427C22×M16—531no—
428C23×C8—531no—
429#553—538no—
430#553—1064no—
431#547—538no—
432#547—1064no—
433C2×C4⋊Q8—531no—
434C2×#126—1061no—
435C2×#125—531no—
436C2×#123—1061no—
437C2×#123—1061no—
438C2×#123—1061no—
439C2×C22⋊Q8—531no—
440C2×C22⋊Q8C2×D5311yescharacteristic
441C2×#121—531no—
442C2×#121—531no—
443C2×#121—1061no—
444C2×#121—1061no—
445C2×C4×D4—531no—
446C2×C4×D4—531no—
447C2×C4×D4—531no—
448C2×C4×D4—1061no—
449C2×#117—531no—
450C22×C4⋊C4—1061no—
451C22×C4⋊C4C2×D5311yescharacteristic
452#491—538no—
453#485—538no—
454#483C2×D5318yescomplemented
455#478—538no—
456#468—538no—
457#465—538no—
458#461—538no—
459#449—538no—
460#449—538no—
461#442—538no—
462#435—538no—
463C2×#107—531no—
464C2×#106C2×D5311yescharacteristic
465C2×#106C2×D5311yescharacteristic
466C2×C4⋊C8—531no—
467#417—538no—
468#416—538no—
469C2×#103—531no—
470C2×#103—531no—
471C2×#103—531no—
472C2×#103—531no—
473C2×#103C2×D5311yescharacteristic
474C2×#103C2×D5311yescharacteristic
475C2×#102—531no—
476C2×#102—531no—
477C2×#102—531no—
478C2×#102—531no—
479C2×C22⋊C8—531no—
480C2×C22⋊C8C2×D5311yescharacteristic
481C2×#97—531no—
482C53C2×#330711yescharacteristic, complemented, Sylow
483C2×#41—534no—
484C2×#41—534no—
485C2×#41—1064no—
486C2×#41—1062no—
487C2×#41—1062no—
488C2×#41—1064no—
489C2×#41—2122no—
490C2×#41—2122no—
491C22×Q8—531no—
492C22×Q8C22×D5311yescharacteristic
493C22×D4—531no—
494C22×D4—531no—
495C22×D4—531no—
496C22×D4—1061no—
497C22×D4—1061no—
498C22×D4—1061no—
499C22×D4—1061no—
500C23×C4—21no—
501C23×C4—531no—
502C23×C4—1061no—
503C23×C4—1061no—
504C23×C4—1061no—
505C23×C4—1061no—
506C23×C4C22×D5311yescharacteristic
507C2×SD16—534no—
508C2×SD16—534no—
509C2×SD16—2122no—
510C2×SD16—2122no—
511C2×D8—534no—
512C2×D8—1064no—
513C2×M16—534no—
514C2×M16—2122no—
515C22×C8—531no—
516C22×C8—531no—
517C22×C8—534no—
518C22×C8—2122no—
519C22×C8C22×D5311yescharacteristic
520C22×C8C22×D5311yescharacteristic
521C4⋊Q8—534no—
522C4⋊Q8—1062no—
523#126—1068no—
524#125—534no—
525#125—1062no—
526#123—1068no—
527#123—1068no—
528#123—1068no—
529C22⋊Q8—22no—
530C22⋊Q8—534no—
531C22⋊Q8—1062no—
532C22⋊Q8C22×D5314yes—
533#121—534no—
534#121—534no—
535#121—1068no—
536#121—1062no—
537#121—1068no—
538#121—1062no—
539C4×D4—534no—
540C4×D4—534no—
541C4×D4—534no—
542C4×D4—534no—
543C4×D4—1062no—
544C4×D4—1062no—
545C4×D4—1068no—
546#117—534no—
547#117—1062no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—531no—
552C2×C4⋊C4—531no—
553C2×C4⋊C4—1068no—
554C2×C4⋊C4—1061no—
555C2×C4⋊C4—1061no—
556C2×C4⋊C4—1061no—
557C2×C4⋊C4—1061no—
558C2×C4⋊C4—1061no—
559C2×C4⋊C4C22×D5311yescharacteristic
560C2×C4⋊C4C22×D5311yescharacteristic
561C2×C4⋊C4C22×D5314yes—
562C2×C4⋊C4C22×D5311yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—531no—
565C2×C22⋊C4—531no—
566C2×C22⋊C4—1061no—
567C2×C22⋊C4—1061no—
568C2×C22⋊C4—1061no—
569C2×C22⋊C4—1061no—
570C2×C22⋊C4—1061no—
571C2×C22⋊C4—1061no—
572C2×C42—531no—
573C2×C42—1061no—
574#107—534no—
575#106C22×D5314yes—
576#106C22×D5314yes—
577C4⋊C8—534no—
578#103—534no—
579#103—534no—
580#103—534no—
581#103—534no—
582#103C22×D5314yes—
583#103C22×D5314yes—
584#102—534no—
585#102—534no—
586#102—534no—
587#102—534no—
588C22⋊C8—534no—
589C22⋊C8C22×D5314yes—
590#97—534no—
591C24—531no—
592C24—1061no—
593C24—1061no—
594C24D4×D5311yescharacteristic
595#41—1068no—
596#41—1068no—
597#41—2124no—
598#41—2128no—
599#41—2124no—
600#41—2128no—
601C2×Q8—21no—
602C2×Q8—22no—
603C2×Q8—22no—
604C2×Q8—532no—
605C2×Q8—1061no—
606C2×Q8—1062no—
607C2×Q8—1062no—
608C2×Q8C23×D5312yes—
609C2×D4—534no—
610C2×D4—534no—
611C2×D4—532no—
612C2×D4—532no—
613C2×D4—1064no—
614C2×D4—1064no—
615C2×D4—1064no—
616C2×D4—1064no—
617C2×D4—1061no—
618C2×D4—1061no—
619C2×D4—1062no—
620C2×D4—1062no—
621C2×D4—1062no—
622C2×D4—4242no—
623C2×D4—2124no—
624C2×D4—2122no—
625C2×D4—2124no—
626C2×D4—2124no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—24no—
634C22×C4—82no—
635C22×C4—531no—
636C22×C4—531no—
637C22×C4—531no—
638C22×C4—532no—
639C22×C4—532no—
640C22×C4—1064no—
641C22×C4—1064no—
642C22×C4—1064no—
643C22×C4—1062no—
644C22×C4—1062no—
645C22×C4—1061no—
646C22×C4—1061no—
647C22×C4—1064no—
648C22×C4—4242no—
649C22×C4—2124no—
650C22×C4—2124no—
651C22×C4—2124no—
652C22×C4D4×D5312yes—
653C22×C4D4×D5311yescharacteristic
654C22×C4C23×D5312yes—
655C22×C4C23×D5311yescharacteristic
656SD16—2124no—
657SD16—2124no—
658D8—1068no—
659M16—2124no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—532no—
663C2×C8—532no—
664C2×C8—1062no—
665C2×C8—1062no—
666C2×C8—2124no—
667C2×C8C23×D5312yes—
668C2×C8C23×D5312yes—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—21no—
674C4⋊C4—534no—
675C4⋊C4—532no—
676C4⋊C4—1064no—
677C4⋊C4—1064no—
678C4⋊C4—1064no—
679C4⋊C4—1064no—
680C4⋊C4—1064no—
681C4⋊C4—1061no—
682C4⋊C4C23×D5312yes—
683C4⋊C4C23×D5312yes—
684C4⋊C4C23×D5312yes—
685C22⋊C4—24no—
686C22⋊C4—534no—
687C22⋊C4—534no—
688C22⋊C4—1064no—
689C22⋊C4—1064no—
690C22⋊C4—1064no—
691C22⋊C4—1064no—
692C22⋊C4—1064no—
693C22⋊C4—1064no—
694C42—532no—
695C42—532no—
696C42—1064no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—532no—
701C23—1062no—
702C23—1064no—
703C23—1062no—
704C23—1062no—
705C23—1062no—
706C23—1062no—
707C23—2122no—
708C23—2122no—
709C23—2122no—
710C23—2122no—
711C23—2122no—
712C23C2×D4×D5312yes—
713C23C2×D4×D5311yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—1062no—
718Q8—1062no—
719Q8—2122no—
720D4—534no—
721D4—1064no—
722D4—1062no—
723D4—1062no—
724D4—1062no—
725D4—4244no—
726D4—2128no—
727D4—2124no—
728D4—2128no—
729D4—2128no—
730D4—2122no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—84no—
744C2×C4—532no—
745C2×C4—532no—
746C2×C4—532no—
747C2×C4—1062no—
748C2×C4—1062no—
749C2×C4—1062no—
750C2×C4—1064no—
751C2×C4—1062no—
752C2×C4—1062no—
753C2×C4—1062no—
754C2×C4—1062no—
755C2×C4—4244no—
756C2×C4—2128no—
757C2×C4—2128no—
758C2×C4—2128no—
759C2×C4—2122no—
760C2×C4—2122no—
761C2×C4C2×D4×D5312yes—
762C2×C4C2×D4×D5311yescharacteristic
763C2×C4#41×D5312yes—
764C2×C4#1313326312yes—
765C2×C4C24×D5311yescharacteristic
766C8—22no—
767C8—22no—
768C8—1062no—
769C8—1062no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—44no—
774C22—1062no—
775C22—1064no—
776C22—1062no—
777C22—1062no—
778C22—4244no—
779C22—2122no—
780C22—2122no—
781C22—2122no—
782C22—2122no—
783C22—2122no—
784C22—2124no—
785C22—2128no—
786C22#1681126512yes—
787C22#1681142212yes—
788C22#1681142912yes—
789C22C22×D4×D5311yescharacteristic
790C4—22no—
791C4—42no—
792C4—42no—
793C4—42no—
794C4—42no—
795C4—1062no—
796C4—1062no—
797C4—1062no—
798C4—2122no—
799C4—2122no—
800C4#1681126512yes—
801C4C2×#41×D5311yescharacteristic
802C4C2×#1313326311yescharacteristic
803C2—42no—
804C2—4242no—
805C2—2122no—
806C2—2124no—
807C2#2028669414yesdirect product factor
808C2C2×#1681126511yescharacteristic
809C2C2×#1681142211yescharacteristic
810C2C2×#1681142911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#483C2
socleC23×C53C22×D4
hypercenterC2×#483D53
hypocenterC53C2×#3307
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
1. C2×#16811321C2semidirect
2. C2×#16811275C2semidirect
3. #20286694C2direct (N × H)
4. C2×#16810990C2semidirect
5. C2×#16810967C2semidirect
6. C2×#16810922C2semidirect
7. C2×#16810871C2semidirect
8. C2×#16810853C2semidirect
9. C2×#16810827C2semidirect
10. C2×#16810771C2semidirect
11. C2×#16810770C2semidirect
12. C2×#16810734C2semidirect
13. C2×#16810697C2semidirect
14. C2×#16810622C2semidirect
15. C2×#16810618C2semidirect
16. C2×C53×#483C2semidirect
25. #16811321C22semidirect
27. #16811275C22semidirect
45. #16810990C22semidirect
46. #16810967C22semidirect
47. #16810922C22semidirect
48. #16810871C22semidirect
49. #16810853C22semidirect
50. #16810827C22semidirect
51. #16810771C22semidirect
52. #16810770C22semidirect
53. #16810734C22semidirect
54. #16810697C22semidirect
57. #16810622C22semidirect
58. #16810618C22semidirect
71. C53×#483C22semidirect
403. C2×#483D53semidirect
415. C2×C53#3307semidirect
454. #483C2×D53semidirect
482. C53C2×#3307semidirect
807. C2#20286694direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113212
C2×#168112752
#202866942
C2×#168109902
C2×#168109672
C2×#168109222
C2×#168108712
C2×#168108532
C2×#168108272
C2×#168107712
C2×#168107702
C2×#168107342
C2×#168106972
C2×#168106222
C2×#168106182
C2×C53×#4832
C2×#330753