Finite Group Databasebeta

← C2×#20286934 #28260908

Subgroups — C2×#20286934 #28260908

Order 13568.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811308C211yesmaximal, characteristic, complemented
2C2×#16811270C211yesmaximal, characteristic
3#20286934C2116yesmaximal, direct product factor
4C2×#16810976C211yesmaximal, characteristic, complemented
5C2×#16810967C211yesmaximal, characteristic, complemented
6C2×#16810922C211yesmaximal, characteristic, complemented
7C2×#16810882C211yesmaximal, characteristic, complemented
8C2×#16810867C211yesmaximal, characteristic, complemented
9C2×#16810844C211yesmaximal, characteristic, complemented
10C2×#16810787C211yesmaximal, characteristic, complemented
11C2×#16810775C211yesmaximal, characteristic, complemented
12C2×#16810710C211yesmaximal, characteristic, complemented
13C2×#16810698C211yesmaximal, characteristic, complemented
14C2×#16810622C211yesmaximal, characteristic, complemented
15C2×#16810626C211yesmaximal, characteristic, complemented
16C2×C53×#481C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×D4×D53C2211yescharacteristic
19C22×Dic212C2211yescharacteristic, complemented
20C22×#11719913C2211yescharacteristic
21C22×#11719923C2211yescharacteristic
22C22×#11719917C2211yescharacteristic, complemented
23C22×#11719912C2211yescharacteristic
24#16811308—24no—
25#16811308C2218yescomplemented
26#16811270—24no—
27#16811270C2218yes—
28C2×#13133212—21no—
29C2×#13133208C2211yescharacteristic, complemented
30C2×#13133207—21no—
31C2×#13133204C2211yescharacteristic
32C2×#13133200—21no—
33C2×#13133199—21no—
34C2×#13133197C2211yescharacteristic
35C2×#13133197C2211yescharacteristic
36C2×#13133196C2211yescharacteristic, complemented
37C2×#13133188—21no—
38C2×#13133185—21no—
39C2×#13133182C2211yescharacteristic, complemented
40C2×#13133179C2211yescharacteristic
41C2×C4×C22⋊D53C2211yescharacteristic
42C2×#13133176—21no—
43C2×#13133175C2211yescharacteristic
44C2×C22⋊C4×D53—21no—
45#16810976C2218yescomplemented
46#16810967C2218yescomplemented
47#16810922C2218yescomplemented
48#16810882C2218yescomplemented
49#16810867C2218yescomplemented
50#16810844C2218yescomplemented
51#16810787C2218yescomplemented
52#16810775C2218yescomplemented
53#16810710C2218yescomplemented
54#16810698C2218yescomplemented
55C2×#13133150C2211yescharacteristic, complemented
56C2×#13133146C2211yescharacteristic, complemented
57#16810626C2218yescomplemented
58#16810622C2218yescomplemented
59C2×#13133142C2211yescharacteristic, complemented
60C2×#13133140C2211yescharacteristic, complemented
61C2×#13133140C2211yescharacteristic, complemented
62C2×#13133140C2211yescharacteristic, complemented
63C2×#13133139C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133137C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic, complemented
69C2×#121×C53C2211yescharacteristic
70C22×C4⋊C4×C53C2211yescharacteristic, complemented
71C53×#481C2218yescomplemented
72C2×#106×C53C2211yescharacteristic, complemented
73C2×#106×C53C2211yescharacteristic, complemented
74C2×#102×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic, complemented
77C24×D53—21no—
78C2×#11719945—22no—
79C2×#11719945—24no—
80C2×#11719945—42no—
81C2×#11719945C2314yes—
82C22×Dic106C2311yescharacteristic
83C22×Dic106C2311yescharacteristic
84C22×D212C2311yescharacteristic
85C22×C22⋊D53—21no—
86C22×C22⋊D53—21no—
87C22×C22⋊D53D411yescharacteristic
88C2×D4×D53—24no—
89C2×D4×D53—22no—
90C2×D4×D53—42no—
91C2×D4×D53C2314yes—
92C22×C4×D53—21no—
93C22×C4×D53—21no—
94C22×C4×D53C2311yescharacteristic
95C2×Dic212—42no—
96C2×Dic212C2314yescomplemented
97C2×#11719913—24no—
98C2×#11719913C2314yes—
99C2×#11719923—42no—
100C2×#11719923C2314yes—
101C2×#11719917—42no—
102C2×#11719917C2314yescomplemented
103C2×#11719912—42no—
104C2×#11719912C2314yes—
105C22×#88322C2311yescharacteristic
106C22×#88322C2311yescharacteristic
107#13133212—28no—
108#13133208—22no—
109#13133208C2314yescomplemented
110#13133207—28no—
111#13133204—22no—
112#13133204C2314yes—
113#13133200—28no—
114#13133199—28no—
115#13133197—22no—
116#13133197—22no—
117#13133197C2314yes—
118#13133197C2314yes—
119#13133196—22no—
120#13133196C2314yescomplemented
121#13133188—28no—
122#13133185—28no—
123#13133182—22no—
124#13133182C2314yescomplemented
125#13133179—22no—
126#13133179C2314yes—
127C4×C22⋊D53D414yes—
128C4×C22⋊D53C2314yes—
129#13133176—28no—
130#13133175—22no—
131#13133175C2314yes—
132C2×C4⋊Dic53—21no—
133C2×C4⋊Dic53—21no—
134C2×C4⋊Dic53—21no—
135C2×C4⋊Dic53C2311yescharacteristic
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×#11719919—21no—
139C2×#11719919D411yescharacteristic
140C2×C22⋊Dic53—21no—
141C2×C22⋊Dic53—21no—
142C2×C22⋊Dic53—21no—
143C2×C22⋊Dic53D411yescharacteristic
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921D411yescharacteristic
149C22⋊C4×D53—28no—
150C2×C4×Dic53—21no—
151C2×C4×Dic53—21no—
152C2×C4×Dic53C2311yescharacteristic
153#13133150C2314yescomplemented
154#13133146C2314yescomplemented
155#13133142C2314yescomplemented
156#13133140C2314yescomplemented
157#13133140C2314yescomplemented
158#13133140C2314yescomplemented
159#13133139C2314yes—
160#13133138C2314yes—
161#13133137C2314yes—
162#13133137C2314yes—
163#13133129C2314yes—
164C8×Dic53C2314yescomplemented
165C22×D4×C53—21no—
166C22×D4×C53C2311yescharacteristic
167C23×C4×C53—21no—
168C23×C4×C53C2311yescharacteristic
169C22×C8×C53C2311yescharacteristic
170C22×C8×C53C2311yescharacteristic
171#121×C53—22no—
172#121×C53C2314yes—
173C2×C4⋊C4×C53—22no—
174C2×C4⋊C4×C53—21no—
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C4⋊C4×C53C2314yescomplemented
179C2×C22⋊C4×C53—21no—
180#106×C53C2314yescomplemented
181#106×C53C2314yescomplemented
182#102×C53C2314yes—
183#102×C53C2314yes—
184C22⋊C8×C53C2314yescomplemented
185C24×C53—21no—
186C24×C53C2×D411yescharacteristic
187C23×D53—21no—
188C23×D53—24no—
189C23×D53—44no—
190C23×D53—44no—
191C23×D53—82no—
192C23×D53C2×D411yescharacteristic
193C2×D4×C53—24no—
194C2×D4×C53—21no—
195C2×D4×C53—22no—
196C2×D4×C53—22no—
197C2×D4×C53—82no—
198C2×D4×C53C2412yes—
199C22×C4×C53—22no—
200C22×C4×C53—22no—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53—21no—
204C22×C4×C53—24no—
205C22×C4×C53—44no—
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53C2×D412yes—
208C22×C4×C53C2412yes—
209C22×C4×C53C2411yescharacteristic
210C2×C22⋊D53—24no—
211C2×C22⋊D53—24no—
212C2×C22⋊D53—42no—
213C2×C22⋊D53—44no—
214C2×C22⋊D53—44no—
215C2×C22⋊D53C2×D414yes—
216C22×Dic53—21no—
217C22×Dic53—21no—
218C22×Dic53—21no—
219C22×Dic53C2×D411yescharacteristic
220C22×Dic53C2×D411yescharacteristic
221C22×Dic53C2×D411yescharacteristic
222D4×D53—28no—
223D4×D53—44no—
224D4×D53—48no—
225#11719945—28no—
226#11719945—44no—
227#11719945—48no—
228C2×D212—21no—
229C2×D212—22no—
230C2×D212#4114yes—
231C2×D212C2412yes—
232C2×C4×D53—22no—
233C2×C4×D53—22no—
234C2×C4×D53—24no—
235C2×C4×D53—24no—
236C2×C4×D53—44no—
237C2×C4×D53—82no—
238C2×C4×D53C2×D412yes—
239C2×C4×D53C2412yes—
240C2×Dic106—22no—
241C2×Dic106—22no—
242C2×Dic106—22no—
243C2×Dic106—22no—
244C2×Dic106—21no—
245C2×Dic106—21no—
246C2×Dic106C2412yes—
247C2×Dic106C2412yes—
248C2×C8×C53—22no—
249C2×C8×C53—22no—
250C2×C8×C53C2412yes—
251C2×C8×C53C2412yes—
252C4⋊C4×C53—21no—
253C4⋊C4×C53—21no—
254C4⋊C4×C53—24no—
255C4⋊C4×C53—21no—
256C4⋊C4×C53C2412yes—
257C4⋊C4×C53C2412yes—
258C4⋊C4×C53C2412yes—
259C22⋊C4×C53—24no—
260C22⋊Dic53—24no—
261C22⋊Dic53—24no—
262C22⋊Dic53—24no—
263C22⋊Dic53C2×D414yes—
264#11719923—44no—
265#11719921—24no—
266#11719921—24no—
267#11719921—24no—
268#11719921—24no—
269#11719921C2×D414yes—
270C4⋊Dic53—21no—
271C4⋊Dic53—24no—
272C4⋊Dic53—24no—
273C4⋊Dic53—24no—
274C4⋊Dic53C2412yes—
275#11719919—24no—
276#11719919—24no—
277#11719919—24no—
278#11719919C2×D414yes—
279C4×Dic53—24no—
280C4×Dic53—24no—
281C4×Dic53C2×D412yes—
282C4×Dic53C2412yes—
283#11719917—44no—
284C2×#88322—22no—
285C2×#88322—22no—
286C2×#88322C2412yes—
287C2×#88322C2412yes—
288Dic212—44no—
289#11719913—28no—
290#11719912—44no—
291C23×C53—22no—
292C23×C53—22no—
293C23×C53—22no—
294C23×C53—22no—
295C23×C53—42no—
296C23×C53—42no—
297C23×C53—42no—
298C23×C53C22×D412yes—
299C23×C53C22×D411yescharacteristic
300C22×D53—22no—
301C22×D53—24no—
302C22×D53—22no—
303C22×D53—22no—
304C22×D53—22no—
305C22×D53—48no—
306C22×D53—48no—
307C22×D53—42no—
308C22×D53—42no—
309C22×D53—84no—
310C22×D53—816no—
311C22×D53C22×D412yes—
312D4×C53—22no—
313D4×C53—22no—
314D4×C53—42no—
315D4×C53—84no—
316C2×C4×C53—22no—
317C2×C4×C53—24no—
318C2×C4×C53—22no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—22no—
322C2×C4×C53—22no—
323C2×C4×C53—48no—
324C2×C4×C53—42no—
325C2×C4×C53—42no—
326C2×C4×C53—42no—
327C2×C4×C53C22×D412yes—
328C2×C4×C53C22×D411yescharacteristic
329C2×C4×C53C2×#4112yes—
330C2×C4×C53H(5,𝔽2)12yes—
331C2×C4×C53C2511yescharacteristic
332C22⋊D53—44no—
333C22⋊D53—48no—
334C22⋊D53—48no—
335C2×Dic53—22no—
336C2×Dic53—22no—
337C2×Dic53—22no—
338C2×Dic53—22no—
339C2×Dic53—22no—
340C2×Dic53—22no—
341C2×Dic53—42no—
342C2×Dic53—42no—
343C2×Dic53—42no—
344C2×Dic53C22×D412yes—
345C2×Dic53C22×D412yes—
346C2×Dic53C22×D412yes—
347D212—24no—
348D212—22no—
349D212C2×#4114yes—
350C4×D53—24no—
351C4×D53—22no—
352C4×D53—22no—
353C4×D53—48no—
354C4×D53—84no—
355Dic106—22no—
356Dic106—22no—
357Dic106—22no—
358Dic106—22no—
359Dic106—42no—
360Dic106—42no—
361C8×C53—22no—
362C8×C53—22no—
363#88322—22no—
364#88322—22no—
365C2×#3323—531nomaximal, Sylow
366C22×C53—22no—
367C22×C53—22no—
368C22×C53—22no—
369C22×C53—44no—
370C22×C53—42no—
371C22×C53—42no—
372C22×C53—42no—
373C22×C53—84no—
374C22×C53#54612yes—
375C22×C53#57512yes—
376C22×C53#57712yes—
377C22×C53C23×D411yescharacteristic
378C2×D53—22no—
379C2×D53—24no—
380C2×D53—22no—
381C2×D53—22no—
382C2×D53—44no—
383C2×D53—48no—
384C2×D53—42no—
385C2×D53—42no—
386C2×D53—816no—
387C4×C53—22no—
388C4×C53—42no—
389C4×C53—42no—
390C4×C53—42no—
391C4×C53#54612yes—
392C4×C53C22×#4111yescharacteristic
393C4×C53C2×H(5,𝔽2)11yescharacteristic
394Dic53—22no—
395Dic53—22no—
396Dic53—22no—
397Dic53—42no—
398Dic53—42no—
399Dic53—42no—
400C2×#552—531no—
401C2×#546—531no—
402#3323—5316no—
403C2×#488—531no—
404C2×#481D5311yescharacteristic, complemented
405C2×#485—531no—
406C2×#478—531no—
407C2×#470—531no—
408C2×#468—531no—
409C2×#464—531no—
410C2×#452—531no—
411C2×#450—531no—
412C2×C4×SD16—531no—
413C2×#436—531no—
414C2×#417—531no—
415C2×#418—531no—
416C2×C53—42no—
417C2×C53—82no—
418C2×C53#332314yescomplemented
419C2×C53C2×#54611yescharacteristic
420C2×C53C2×#57511yescharacteristic
421C2×C53C2×#57711yescharacteristic
422D53—42no—
423D53—44no—
424C22×#41—531no—
425C23×D4—531no—
426C22×Q16—531no—
427C22×SD16—531no—
428C22×SD16—531no—
429C22×M16—531no—
430C22×M16—531no—
431#552—538no—
432#552—1064no—
433#546—538no—
434#546—1064no—
435C2×#126—1061no—
436C2×#125—531no—
437C2×#125—1061no—
438C2×#124—531no—
439C2×#123—1061no—
440C2×#123—1061no—
441C2×C22⋊Q8—531no—
442C2×C22⋊Q8—531no—
443C2×C22⋊Q8—531no—
444C2×#121—1061no—
445C2×#121C2×D5311yescharacteristic
446C2×#120—1061no—
447C2×C4×Q8—531no—
448C2×C4×D4—531no—
449C2×C4×D4—531no—
450C2×#117—531no—
451C2×#117—1061no—
452C22×C4⋊C4C2×D5311yescharacteristic, complemented
453C22×C22⋊C4—1061no—
454#488—538no—
455#485—538no—
456#481C2×D5318yescomplemented
457#478—538no—
458#470—538no—
459#468—538no—
460#464—538no—
461#452—538no—
462#450—538no—
463C4×SD16—538no—
464#436—538no—
465C2×#107—531no—
466C2×#106C2×D5311yescharacteristic, complemented
467C2×#106C2×D5311yescharacteristic, complemented
468C2×C4⋊C8—531no—
469#418—538no—
470#417—538no—
471C2×#103—531no—
472C2×#103—531no—
473C2×#103—531no—
474C2×#103—531no—
475C2×#102—531no—
476C2×#102—531no—
477C2×#102—531no—
478C2×#102—531no—
479C2×#102C2×D5311yescharacteristic
480C2×#102C2×D5311yescharacteristic
481C2×C22⋊C8—531no—
482C2×C22⋊C8C2×D5311yescharacteristic, complemented
483C2×C4×C8—531no—
484C53C2×#332311yescharacteristic, complemented, Sylow
485C25—1061no—
486C2×#41—534no—
487C2×#41—1064no—
488C2×#41—1062no—
489C2×#41—2122no—
490C22×Q8—531no—
491C22×Q8—531no—
492C22×D4—21no—
493C22×D4—531no—
494C22×D4—534no—
495C22×D4—531no—
496C22×D4—1062no—
497C22×D4—1061no—
498C22×D4—1064no—
499C22×D4—1061no—
500C22×D4—2122no—
501C22×D4C22×D5311yescharacteristic
502C23×C4—21no—
503C23×C4—531no—
504C23×C4—1061no—
505C23×C4—1061no—
506C23×C4C22×D5311yescharacteristic
507C2×Q16—534no—
508C2×Q16—2122no—
509C2×SD16—534no—
510C2×SD16—534no—
511C2×SD16—1064no—
512C2×SD16—2122no—
513C2×M16—534no—
514C2×M16—534no—
515C2×M16—2122no—
516C2×M16—2122no—
517C22×C8—531no—
518C22×C8—531no—
519C22×C8C22×D5311yescharacteristic
520C22×C8C22×D5311yescharacteristic
521#126—1068no—
522#125—534no—
523#125—1062no—
524#125—1068no—
525#124—534no—
526#124—1062no—
527#123—1068no—
528#123—1068no—
529C22⋊Q8—534no—
530C22⋊Q8—534no—
531C22⋊Q8—534no—
532C22⋊Q8—1062no—
533C22⋊Q8—1062no—
534C22⋊Q8—1062no—
535#121—22no—
536#121—1068no—
537#121C22×D5314yes—
538#120—1068no—
539C4×Q8—534no—
540C4×Q8—1062no—
541C4×D4—534no—
542C4×D4—534no—
543C4×D4—534no—
544C4×D4—1062no—
545#117—534no—
546#117—1068no—
547#117—1062no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—22no—
550C2×C4⋊C4—531no—
551C2×C4⋊C4—531no—
552C2×C4⋊C4—1061no—
553C2×C4⋊C4—1061no—
554C2×C4⋊C4—1061no—
555C2×C4⋊C4—1061no—
556C2×C4⋊C4—1061no—
557C2×C4⋊C4—1061no—
558C2×C4⋊C4C22×D5311yescharacteristic
559C2×C4⋊C4C22×D5311yescharacteristic
560C2×C4⋊C4C22×D5311yescharacteristic
561C2×C4⋊C4C22×D5314yescomplemented
562C2×C22⋊C4—21no—
563C2×C22⋊C4—531no—
564C2×C22⋊C4—531no—
565C2×C22⋊C4—1068no—
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×C22⋊C4—1061no—
573C2×C42—531no—
574C2×C42—1061no—
575C2×C42—1061no—
576#107—534no—
577#106C22×D5314yescomplemented
578#106C22×D5314yescomplemented
579C4⋊C8—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—
588#102C22×D5314yes—
589#102C22×D5314yes—
590C22⋊C8—534no—
591C22⋊C8C22×D5314yescomplemented
592C4×C8—534no—
593C24—21no—
594C24—531no—
595C24—1064no—
596C24—1061no—
597C24—4242no—
598C24—2124no—
599C24—2124no—
600C24D4×D5311yescharacteristic
601#41—1068no—
602#41—2124no—
603#41—2128no—
604C2×Q8—532no—
605C2×Q8—532no—
606C2×Q8—1061no—
607C2×Q8—1061no—
608C2×Q8—1062no—
609C2×Q8—1062no—
610C2×Q8—1062no—
611C2×Q8—1062no—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—82no—
617C2×D4—534no—
618C2×D4—534no—
619C2×D4—532no—
620C2×D4—1064no—
621C2×D4—1068no—
622C2×D4—1064no—
623C2×D4—1061no—
624C2×D4—1062no—
625C2×D4—2124no—
626C2×D4—2128no—
627C2×D4—2122no—
628C2×D4—2124no—
629C2×D4—2124no—
630C2×D4C23×D5312yes—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—24no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—44no—
638C22×C4—531no—
639C22×C4—531no—
640C22×C4—531no—
641C22×C4—532no—
642C22×C4—532no—
643C22×C4—1064no—
644C22×C4—1062no—
645C22×C4—1062no—
646C22×C4—1061no—
647C22×C4—1061no—
648C22×C4—1061no—
649C22×C4—1064no—
650C22×C4—4242no—
651C22×C4—2124no—
652C22×C4D4×D5312yes—
653C22×C4D4×D5311yescharacteristic
654C22×C4C23×D5312yes—
655C22×C4C23×D5311yescharacteristic
656Q16—2124no—
657SD16—1068no—
658SD16—2124no—
659M16—2124no—
660M16—2124no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—532no—
664C2×C8—532no—
665C2×C8—1062no—
666C2×C8—1062no—
667C2×C8C23×D5312yes—
668C2×C8C23×D5312yes—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—24no—
672C4⋊C4—21no—
673C4⋊C4—534no—
674C4⋊C4—532no—
675C4⋊C4—1064no—
676C4⋊C4—1064no—
677C4⋊C4—1064no—
678C4⋊C4—1064no—
679C4⋊C4—1064no—
680C4⋊C4—1061no—
681C4⋊C4—1064no—
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—
694C22⋊C4—1064no—
695C42—532no—
696C42—532no—
697C42—1064no—
698C42—1064no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—532no—
707C23—1062no—
708C23—1064no—
709C23—1062no—
710C23—1062no—
711C23—1062no—
712C23—4244no—
713C23—42416no—
714C23—2128no—
715C23—2128no—
716C23—2122no—
717C23—2122no—
718C23C2×D4×D5312yes—
719C23C2×D4×D5311yescharacteristic
720Q8—1062no—
721Q8—1062no—
722Q8—1062no—
723Q8—1062no—
724Q8—2122no—
725Q8—2122no—
726D4—22no—
727D4—22no—
728D4—42no—
729D4—84no—
730D4—534no—
731D4—1064no—
732D4—1062no—
733D4—2124no—
734D4—2128no—
735D4—2128no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—48no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—532no—
748C2×C4—532no—
749C2×C4—532no—
750C2×C4—1062no—
751C2×C4—1062no—
752C2×C4—1062no—
753C2×C4—1064no—
754C2×C4—1062no—
755C2×C4—1062no—
756C2×C4—1062no—
757C2×C4—1062no—
758C2×C4—1062no—
759C2×C4—4244no—
760C2×C4—2128no—
761C2×C4—2122no—
762C2×C4—2122no—
763C2×C4—2122no—
764C2×C4C2×D4×D5312yes—
765C2×C4C2×D4×D5311yescharacteristic
766C2×C4#41×D5312yes—
767C2×C4#1313326312yes—
768C2×C4C24×D5311yescharacteristic
769C8—22no—
770C8—22no—
771C8—1062no—
772C8—1062no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—84no—
781C22—1062no—
782C22—1064no—
783C22—1062no—
784C22—1062no—
785C22—42416no—
786C22—2122no—
787C22—2122no—
788C22—2124no—
789C22—2128no—
790C22#1681126512yes—
791C22#1681141912yes—
792C22#1681142912yes—
793C22C22×D4×D5311yescharacteristic
794C4—22no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—1062no—
799C4—1062no—
800C4—1062no—
801C4—2122no—
802C4—2122no—
803C4—2122no—
804C4#1681126512yes—
805C4C2×#41×D5311yescharacteristic
806C4C2×#1313326311yescharacteristic
807C2—42no—
808C2—82no—
809C2—2122no—
810C2—2124no—
811C2#2028693414yesdirect product factor
812C2C2×#1681126511yescharacteristic
813C2C2×#1681141911yescharacteristic
814C2C2×#1681142911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#481C2
socleC23×C53C22×D4
prime radicalC2×#16811270C2
hypercenterC2×#481D53
hypocenterC53C2×#3323
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
1. C2×#16811308C2semidirect
3. #20286934C2direct (N × H)
4. C2×#16810976C2semidirect
5. C2×#16810967C2semidirect
6. C2×#16810922C2semidirect
7. C2×#16810882C2semidirect
8. C2×#16810867C2semidirect
9. C2×#16810844C2semidirect
10. C2×#16810787C2semidirect
11. C2×#16810775C2semidirect
12. C2×#16810710C2semidirect
13. C2×#16810698C2semidirect
14. C2×#16810622C2semidirect
15. C2×#16810626C2semidirect
16. C2×C53×#481C2semidirect
19. C22×Dic212C22semidirect
22. C22×#11719917C22semidirect
25. #16811308C22semidirect
29. C2×#13133208C22semidirect
36. C2×#13133196C22semidirect
39. C2×#13133182C22semidirect
45. #16810976C22semidirect
46. #16810967C22semidirect
47. #16810922C22semidirect
48. #16810882C22semidirect
49. #16810867C22semidirect
50. #16810844C22semidirect
51. #16810787C22semidirect
52. #16810775C22semidirect
53. #16810710C22semidirect
54. #16810698C22semidirect
55. C2×#13133150C22semidirect
56. C2×#13133146C22semidirect
57. #16810626C22semidirect
58. #16810622C22semidirect
59. C2×#13133142C22semidirect
60. C2×#13133140C22semidirect
61. C2×#13133140C22semidirect
62. C2×#13133140C22semidirect
68. C2×C8×Dic53C22semidirect
70. C22×C4⋊C4×C53C22semidirect
71. C53×#481C22semidirect
72. C2×#106×C53C22semidirect
73. C2×#106×C53C22semidirect
76. C2×C22⋊C8×C53C22semidirect
96. C2×Dic212C23semidirect
102. C2×#11719917C23semidirect
109. #13133208C23semidirect
120. #13133196C23semidirect
124. #13133182C23semidirect
153. #13133150C23semidirect
154. #13133146C23semidirect
155. #13133142C23semidirect
156. #13133140C23semidirect
157. #13133140C23semidirect
158. #13133140C23semidirect
164. C8×Dic53C23semidirect
178. C2×C4⋊C4×C53C23semidirect
180. #106×C53C23semidirect
181. #106×C53C23semidirect
184. C22⋊C8×C53C23semidirect
404. C2×#481D53semidirect
418. C2×C53#3323semidirect
452. C22×C4⋊C4C2×D53semidirect
456. #481C2×D53semidirect
466. C2×#106C2×D53semidirect
467. C2×#106C2×D53semidirect
482. C2×C22⋊C8C2×D53semidirect
484. C53C2×#3323semidirect
561. C2×C4⋊C4C22×D53semidirect
577. #106C22×D53semidirect
578. #106C22×D53semidirect
591. C22⋊C8C22×D53semidirect
811. C2#20286934direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113082
C2×#168112702
#202869342
C2×#168109762
C2×#168109672
C2×#168109222
C2×#168108822
C2×#168108672
C2×#168108442
C2×#168107872
C2×#168107752
C2×#168107102
C2×#168106982
C2×#168106222
C2×#168106262
C2×C53×#4812
C2×#332353