Finite Group Databasebeta

← C2×#20285762 #28255420

Subgroups — C2×#20285762 #28255420

Order 13568.

2342 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811224C211yesmaximal, characteristic, complemented
2C2×#16811191C211yesmaximal, characteristic, complemented
3#20285762C2116yesmaximal, direct product factor
4C2×#16811009C211yesmaximal, characteristic, complemented
5C2×#16810998C211yesmaximal, characteristic, complemented
6C2×#16810986C211yesmaximal, characteristic, complemented
7C2×#16810979C211yesmaximal, characteristic, complemented
8C2×#16810835C211yesmaximal, characteristic, complemented
9C2×#16810819C211yesmaximal, characteristic, complemented
10C2×#16810818C211yesmaximal, characteristic, complemented
11C2×#16810771C211yesmaximal, characteristic, complemented
12C2×#16810767C211yesmaximal, characteristic, complemented
13C2×#16810758C211yesmaximal, characteristic, complemented
14C2×#16810755C211yesmaximal, characteristic, complemented
15C2×#16810683C211yesmaximal, characteristic, complemented
16C2×C53×#463C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×D4×D53C2211yescharacteristic
19C22×#11719924C2211yescharacteristic, complemented
20C22×D424C2211yescharacteristic
21C22×D424C2211yescharacteristic, complemented
22C22×#11719922C2211yescharacteristic
23C22×#11719922C2211yescharacteristic
24C22×#11719922C2211yescharacteristic, complemented
25#16811224—24no—
26#16811224C2218yescomplemented
27#16811191—24no—
28#16811191C2218yescomplemented
29C2×#13133214C2211yescharacteristic
30C2×#13133213C2211yescharacteristic
31C2×#13133213C2211yescharacteristic, complemented
32C2×#13133208C2211yescharacteristic, complemented
33C2×#13133206C2211yescharacteristic
34C2×#13133200—21no—
35C2×#13133199—21no—
36C2×#13133192C2211yescharacteristic
37C2×#13133191—21no—
38C2×#13133190—21no—
39C2×#13133190—21no—
40C2×#13133190—21no—
41C2×#13133188C2211yescharacteristic
42C2×#13133187—21no—
43C2×#13133187—21no—
44C2×C4×D212C2211yescharacteristic, complemented
45C2×#13133174C2211yescharacteristic
46#16811009C2218yescomplemented
47#16810998C2218yescomplemented
48#16810986C2218yescomplemented
49#16810979C2218yescomplemented
50#16810835C2218yescomplemented
51#16810819C2218yescomplemented
52#16810818C2218yescomplemented
53#16810771C2218yescomplemented
54#16810767C2218yescomplemented
55#16810758C2218yescomplemented
56#16810755C2218yescomplemented
57#16810683C2218yescomplemented
58C2×C4⋊#88322C2211yescharacteristic, complemented
59C2×#13133141C2211yescharacteristic, complemented
60C2×#13133139C2211yescharacteristic
61C2×#13133139C2211yescharacteristic, complemented
62C2×#13133138C2211yescharacteristic
63C2×#13133137C2211yescharacteristic
64C2×#13133137C2211yescharacteristic, complemented
65C2×#13133129C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133127C2211yescharacteristic, complemented
68C2×C8×Dic53C2211yescharacteristic, complemented
69C22×SD16×C53C2211yescharacteristic, complemented
70C22×D8×C53C2211yescharacteristic
71C2×#124×C53C2211yescharacteristic
72C2×C4×D4×C53C2211yescharacteristic, complemented
73C53×#463C2218yescomplemented
74C2×C4⋊C8×C53C2211yescharacteristic, complemented
75C2×#103×C53C2211yescharacteristic, complemented
76C2×#102×C53C2211yescharacteristic
77C24×D53—21no—
78C2×#11719949—22no—
79C2×#11719949—42no—
80C2×#11719949—42no—
81C2×#11719949C2314yes—
82C22×D212—21no—
83C22×D212—21no—
84C22×D212—21no—
85C22×D212—21no—
86C22×D212C2311yescharacteristic
87C22×D212C2311yescharacteristic
88C22×D212C2311yescharacteristic
89C22×C22⋊D53—21no—
90C22×C22⋊D53—21no—
91C22×C22⋊D53—21no—
92C22×C22⋊D53—21no—
93C22×C22⋊D53—21no—
94C22×C22⋊D53—21no—
95C2×D4×D53—22no—
96C2×D4×D53—42no—
97C2×D4×D53—42no—
98C2×D4×D53C2314yes—
99C22×C4×D53—21no—
100C22×C4×D53—21no—
101C22×C4×D53C2311yescharacteristic
102C2×#11719924—42no—
103C2×#11719924C2314yescomplemented
104C2×D424—42no—
105C2×D424—42no—
106C2×D424C2314yes—
107C2×D424C2314yescomplemented
108C2×#11719922—42no—
109C2×#11719922—42no—
110C2×#11719922—42no—
111C2×#11719922C2314yes—
112C2×#11719922C2314yes—
113C2×#11719922C2314yescomplemented
114C22×#88322C2311yescharacteristic
115C22×#88322C2311yescharacteristic
116#13133214—22no—
117#13133214C2314yes—
118#13133213—22no—
119#13133213—22no—
120#13133213C2314yes—
121#13133213C2314yescomplemented
122#13133208—22no—
123#13133208C2314yescomplemented
124#13133206—22no—
125#13133206C2314yes—
126#13133200—28no—
127#13133199—28no—
128#13133192—22no—
129#13133192C2314yes—
130#13133191—28no—
131#13133190—28no—
132#13133190—28no—
133#13133190—28no—
134#13133188—22no—
135#13133188C2314yes—
136#13133187—28no—
137#13133187—28no—
138C4×D212—22no—
139C4×D212C2314yescomplemented
140#13133174D414yes—
141#13133174C2314yes—
142C2×C4⋊Dic53—21no—
143C2×C4⋊Dic53C2311yescharacteristic
144C2×#11719919—21no—
145C2×#11719919D411yescharacteristic
146C2×#11719919D411yescharacteristic
147C2×C22⋊Dic53—21no—
148C2×#11719921—21no—
149C2×#11719921—21no—
150C2×#11719921—21no—
151C2×#11719921—21no—
152C2×#11719921D411yescharacteristic
153C2×#11719921D411yescharacteristic
154C2×C4×Dic53C2311yescharacteristic
155C4⋊#88322C2314yescomplemented
156#13133141C2314yescomplemented
157#13133139C2314yes—
158#13133139C2314yescomplemented
159#13133138C2314yes—
160#13133137C2314yes—
161#13133137C2314yescomplemented
162#13133129C2314yes—
163#13133129C2314yes—
164#13133127C2314yescomplemented
165C8×Dic53C2314yescomplemented
166C22×Q8×C53C2311yescharacteristic
167C22×D4×C53C2311yescharacteristic
168C22×D4×C53C2311yescharacteristic
169C23×C4×C53—21no—
170C2×SD16×C53—42no—
171C2×SD16×C53C2314yescomplemented
172C2×D8×C53—42no—
173C2×D8×C53C2314yes—
174C22×C8×C53C2311yescharacteristic
175C22×C8×C53C2311yescharacteristic
176#124×C53—22no—
177#124×C53C2314yes—
178C4×D4×C53—22no—
179C4×D4×C53C2314yescomplemented
180C2×C4⋊C4×C53C2311yescharacteristic
181C2×C22⋊C4×C53—21no—
182C2×C22⋊C4×C53—21no—
183C2×C22⋊C4×C53—21no—
184C2×C42×C53C2311yescharacteristic
185C4⋊C8×C53C2314yescomplemented
186#103×C53C2314yescomplemented
187#102×C53C2314yes—
188C24×C53—21no—
189C24×C53—21no—
190C23×D53—21no—
191C23×D53—21no—
192C23×D53—21no—
193C23×D53—24no—
194C23×D53—44no—
195C23×D53—82no—
196C23×D53—82no—
197C23×D53C2×D411yescharacteristic
198C2×Q8×C53—21no—
199C2×Q8×C53—22no—
200C2×Q8×C53—22no—
201C2×Q8×C53C2412yes—
202C2×D4×C53—21no—
203C2×D4×C53—21no—
204C2×D4×C53—22no—
205C2×D4×C53—22no—
206C2×D4×C53—22no—
207C2×D4×C53—22no—
208C2×D4×C53C2412yes—
209C2×D4×C53C2412yes—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—24no—
213C22×C4×C53—82no—
214C22×C4×C53C2×D411yescharacteristic
215C22×C4×C53C2×D411yescharacteristic
216C22×C4×C53C2411yescharacteristic
217C2×C22⋊D53—24no—
218C2×C22⋊D53—24no—
219C2×C22⋊D53—24no—
220C2×C22⋊D53—24no—
221C2×C22⋊D53—24no—
222C2×C22⋊D53—24no—
223C2×C22⋊D53—44no—
224C2×C22⋊D53—82no—
225C2×C22⋊D53—82no—
226C2×C22⋊D53—82no—
227C2×C22⋊D53—82no—
228C2×C22⋊D53—82no—
229C22×Dic53—21no—
230C22×Dic53C2×D411yescharacteristic
231C22×Dic53C2×D411yescharacteristic
232C22×Dic53C2×D411yescharacteristic
233#11719949—44no—
234#11719949—44no—
235#11719949—48no—
236D4×D53—44no—
237D4×D53—44no—
238D4×D53—48no—
239C2×D212—22no—
240C2×D212—22no—
241C2×D212—22no—
242C2×D212—22no—
243C2×D212—22no—
244C2×D212—22no—
245C2×D212—24no—
246C2×D212—21no—
247C2×D212—21no—
248C2×D212—21no—
249C2×D212—24no—
250C2×D212—24no—
251C2×D212—24no—
252C2×D212—44no—
253C2×D212—82no—
254C2×D212—82no—
255C2×D212—82no—
256C2×D212C2412yes—
257C2×D212C2412yes—
258C2×D212C2412yes—
259C2×C4×D53—22no—
260C2×C4×D53—22no—
261C2×C4×D53—24no—
262C2×C4×D53—24no—
263C2×C4×D53—44no—
264C2×C4×D53—82no—
265C2×C4×D53C2×D412yes—
266C2×C4×D53C2412yes—
267SD16×C53—44no—
268D8×C53—44no—
269C2×C8×C53—22no—
270C2×C8×C53—22no—
271C2×C8×C53C2412yes—
272C2×C8×C53C2412yes—
273C4⋊C4×C53—21no—
274C4⋊C4×C53C2412yes—
275C22⋊C4×C53—24no—
276C22⋊C4×C53—24no—
277C22⋊C4×C53—24no—
278C42×C53C2×D412yes—
279C42×C53C2412yes—
280C22⋊Dic53—24no—
281#11719924—44no—
282#11719922—44no—
283#11719922—44no—
284#11719922—44no—
285#11719921—24no—
286#11719921—24no—
287#11719921—24no—
288#11719921—24no—
289#11719921C2×D414yes—
290#11719921C2×D414yes—
291C4⋊Dic53—21no—
292C4⋊Dic53—24no—
293C4⋊Dic53C2412yes—
294#11719919—24no—
295#11719919C2×D414yes—
296#11719919C2×D414yes—
297C4×Dic53C2×D412yes—
298C4×Dic53C2412yes—
299C2×#88322—22no—
300C2×#88322—22no—
301C2×#88322C2412yes—
302C2×#88322C2412yes—
303D424—44no—
304D424—44no—
305C23×C53—22no—
306C23×C53—22no—
307C23×C53—42no—
308C23×C53—42no—
309C23×C53—42no—
310C23×C53—42no—
311C23×C53—42no—
312C23×C53—42no—
313C23×C53C22×D411yescharacteristic
314C22×D53—22no—
315C22×D53—22no—
316C22×D53—22no—
317C22×D53—22no—
318C22×D53—22no—
319C22×D53—22no—
320C22×D53—48no—
321C22×D53—42no—
322C22×D53—42no—
323C22×D53—42no—
324C22×D53—42no—
325C22×D53—42no—
326C22×D53—42no—
327C22×D53—42no—
328C22×D53—42no—
329C22×D53—42no—
330C22×D53—84no—
331C22×D53—84no—
332C22×D53—816no—
333C22×D53C22×D412yes—
334Q8×C53—22no—
335Q8×C53—22no—
336Q8×C53—42no—
337D4×C53—22no—
338D4×C53—22no—
339D4×C53—22no—
340D4×C53—22no—
341D4×C53—42no—
342D4×C53—42no—
343C2×C4×C53—22no—
344C2×C4×C53—22no—
345C2×C4×C53—22no—
346C2×C4×C53—22no—
347C2×C4×C53—42no—
348C2×C4×C53—42no—
349C2×C4×C53—84no—
350C2×C4×C53C22×D412yes—
351C2×C4×C53C22×D412yes—
352C2×C4×C53C22×D411yescharacteristic
353C2×C4×C53H(5,𝔽2)12yes—
354C2×C4×C53H(5,𝔽2)12yes—
355C2×C4×C53C2511yescharacteristic
356C22⋊D53—48no—
357C22⋊D53—84no—
358C22⋊D53—84no—
359C22⋊D53—84no—
360C22⋊D53—84no—
361C22⋊D53—84no—
362C2×Dic53—22no—
363C2×Dic53—22no—
364C2×Dic53—22no—
365C2×Dic53—22no—
366C2×Dic53—42no—
367C2×Dic53C22×D412yes—
368C2×Dic53C22×D412yes—
369C2×Dic53C22×D412yes—
370D212—22no—
371D212—22no—
372D212—22no—
373D212—22no—
374D212—22no—
375D212—22no—
376D212—48no—
377D212—42no—
378D212—42no—
379D212—42no—
380D212—84no—
381D212—84no—
382D212—84no—
383C4×D53—24no—
384C4×D53—22no—
385C4×D53—22no—
386C4×D53—48no—
387C4×D53—84no—
388C8×C53—22no—
389C8×C53—22no—
390#88322—22no—
391#88322—22no—
392C2×#3220—531nomaximal, Sylow
393C22×C53—42no—
394C22×C53—42no—
395C22×C53—42no—
396C22×C53—42no—
397C22×C53—42no—
398C22×C53—42no—
399C22×C53—84no—
400C22×C53—84no—
401C22×C53#53512yes—
402C22×C53#57612yes—
403C22×C53#57612yes—
404C22×C53C23×D411yescharacteristic
405C2×D53—22no—
406C2×D53—22no—
407C2×D53—22no—
408C2×D53—44no—
409C2×D53—42no—
410C2×D53—42no—
411C2×D53—42no—
412C2×D53—42no—
413C2×D53—42no—
414C2×D53—42no—
415C2×D53—42no—
416C2×D53—42no—
417C2×D53—42no—
418C2×D53—816no—
419C2×D53—84no—
420C2×D53—84no—
421C2×D53—84no—
422C4×C53—22no—
423C4×C53—22no—
424C4×C53—42no—
425C4×C53—42no—
426C4×C53#53512yes—
427C4×C53C2×H(5,𝔽2)11yescharacteristic
428C4×C53C2×H(5,𝔽2)11yescharacteristic
429Dic53—22no—
430Dic53—22no—
431Dic53—22no—
432Dic53—42no—
433C2×#540—531no—
434C2×#535—531no—
435#3220—5316no—
436C2×#496—531no—
437C2×#493—531no—
438C2×#490—531no—
439C2×#488—531no—
440C2×#463—531no—
441C2×#463D5311yescharacteristic, complemented
442C2×#459—531no—
443C2×#459—531no—
444C2×#449—531no—
445C2×#449—531no—
446C2×#447—531no—
447C2×#447—531no—
448C2×#433—531no—
449C2×C53—82no—
450C2×C53—82no—
451C2×C53#322014yescomplemented
452C2×C53C2×#53511yescharacteristic
453C2×C53C2×#57611yescharacteristic
454C2×C53C2×#57611yescharacteristic
455D53—42no—
456D53—82no—
457D53—82no—
458D53—82no—
459C22×#41—531no—
460C23×D4—531no—
461C22×SD16—531no—
462C22×SD16C2×D5311yescharacteristic, complemented
463C22×D8—531no—
464C22×D8—531no—
465C22×D8—531no—
466C22×D8—531no—
467C22×D8—531no—
468C22×D8C2×D5311yescharacteristic
469#540—538no—
470#540—1064no—
471#535—538no—
472#535—1064no—
473C2×#127—531no—
474C2×#127—531no—
475C2×#127—531no—
476C2×#125—531no—
477C2×#124—531no—
478C2×#124C2×D5311yescharacteristic
479C2×#123—1061no—
480C2×#123—1061no—
481C2×#121—531no—
482C2×#121—531no—
483C2×#121—1061no—
484C2×#121—1061no—
485C2×#121—1061no—
486C2×#121—1061no—
487C2×#120—1061no—
488C2×#120—1061no—
489C2×C4×D4—531no—
490C2×C4×D4C2×D5311yescharacteristic, complemented
491C2×#117—531no—
492#496—538no—
493#493—538no—
494#490—538no—
495#488—538no—
496#463—538no—
497#463C2×D5318yescomplemented
498#459—538no—
499#459—538no—
500#449—538no—
501#449—538no—
502#447—538no—
503#447—538no—
504#433—538no—
505C2×C4⋊C8—531no—
506C2×C4⋊C8C2×D5311yescharacteristic, complemented
507C2×#103—531no—
508C2×#103C2×D5311yescharacteristic, complemented
509C2×#102—531no—
510C2×#102—531no—
511C2×#102—531no—
512C2×#102—531no—
513C2×#102—531no—
514C2×#102C2×D5311yescharacteristic
515C2×C22⋊C8—531no—
516C2×C22⋊C8—531no—
517C2×#97—531no—
518C2×C4×C8—531no—
519C53C2×#322011yescharacteristic, complemented, Sylow
520C25—1061no—
521C2×#41—534no—
522C2×#41—1062no—
523C2×#41—2122no—
524C2×#41—2122no—
525C22×Q8C22×D5311yescharacteristic
526C22×D4—534no—
527C22×D4—531no—
528C22×D4—531no—
529C22×D4—531no—
530C22×D4—1061no—
531C22×D4—1061no—
532C22×D4—1062no—
533C22×D4—1061no—
534C22×D4—1061no—
535C22×D4—1061no—
536C22×D4—1061no—
537C22×D4—1061no—
538C22×D4—1061no—
539C22×D4—1061no—
540C22×D4—1061no—
541C22×D4—2122no—
542C22×D4—2122no—
543C22×D4C22×D5311yescharacteristic
544C22×D4C22×D5311yescharacteristic
545C23×C4—21no—
546C23×C4—531no—
547C23×C4—1061no—
548C23×C4—1061no—
549C2×SD16—42no—
550C2×SD16—534no—
551C2×SD16—2122no—
552C2×SD16C22×D5314yescomplemented
553C2×D8—42no—
554C2×D8—534no—
555C2×D8—534no—
556C2×D8—534no—
557C2×D8—534no—
558C2×D8—534no—
559C2×D8—2122no—
560C2×D8—2122no—
561C2×D8—2122no—
562C2×D8—2122no—
563C2×D8—2122no—
564C2×D8C22×D5314yes—
565C22×C8—531no—
566C22×C8—531no—
567C22×C8C22×D5311yescharacteristic
568C22×C8C22×D5311yescharacteristic
569#127—534no—
570#127—534no—
571#127—534no—
572#127—1062no—
573#127—1062no—
574#127—1062no—
575#125—534no—
576#125—1062no—
577#124—22no—
578#124—534no—
579#124—1062no—
580#124C22×D5314yes—
581#123—1068no—
582#123—1068no—
583#121—534no—
584#121—534no—
585#121—1068no—
586#121—1068no—
587#121—1068no—
588#121—1068no—
589#121—1062no—
590#121—1062no—
591#120—1068no—
592#120—1068no—
593C4×D4—22no—
594C4×D4—534no—
595C4×D4—1062no—
596C4×D4C22×D5314yescomplemented
597#117—534no—
598#117—534no—
599C2×C4⋊C4—531no—
600C2×C4⋊C4—531no—
601C2×C4⋊C4—531no—
602C2×C4⋊C4—1061no—
603C2×C4⋊C4—1061no—
604C2×C4⋊C4C22×D5311yescharacteristic
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—531no—
609C2×C22⋊C4—531no—
610C2×C22⋊C4—1061no—
611C2×C22⋊C4—1061no—
612C2×C22⋊C4—1061no—
613C2×C22⋊C4—1061no—
614C2×C22⋊C4—1061no—
615C2×C42—531no—
616C2×C42C22×D5311yescharacteristic
617C4⋊C8—534no—
618C4⋊C8C22×D5314yescomplemented
619#103—534no—
620#103C22×D5314yescomplemented
621#102—534no—
622#102—534no—
623#102—534no—
624#102—534no—
625#102—534no—
626#102C22×D5314yes—
627C22⋊C8—534no—
628C22⋊C8—534no—
629#97—534no—
630C4×C8—534no—
631C24—21no—
632C24—21no—
633C24—531no—
634C24—1064no—
635C24—1061no—
636C24—1061no—
637C24—1061no—
638C24—4242no—
639C24—4242no—
640C24—2124no—
641#41—2124no—
642#41—2124no—
643#41—2128no—
644C2×Q8—21no—
645C2×Q8—22no—
646C2×Q8—22no—
647C2×Q8C23×D5312yes—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—22no—
651C2×D4—22no—
652C2×D4—22no—
653C2×D4—22no—
654C2×D4—532no—
655C2×D4—532no—
656C2×D4—532no—
657C2×D4—1064no—
658C2×D4—1064no—
659C2×D4—1064no—
660C2×D4—1064no—
661C2×D4—1064no—
662C2×D4—1064no—
663C2×D4—1064no—
664C2×D4—1064no—
665C2×D4—1064no—
666C2×D4—1064no—
667C2×D4—1061no—
668C2×D4—1061no—
669C2×D4—1061no—
670C2×D4—1062no—
671C2×D4—1062no—
672C2×D4—1062no—
673C2×D4—1062no—
674C2×D4—1062no—
675C2×D4—1062no—
676C2×D4—4242no—
677C2×D4—4242no—
678C2×D4—4242no—
679C2×D4—4242no—
680C2×D4—4242no—
681C2×D4—4242no—
682C2×D4—4242no—
683C2×D4—4242no—
684C2×D4—2124no—
685C2×D4—2124no—
686C2×D4—2124no—
687C2×D4—2128no—
688C2×D4—2124no—
689C2×D4C23×D5312yes—
690C2×D4C23×D5312yes—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—24no—
694C22×C4—82no—
695C22×C4—531no—
696C22×C4—531no—
697C22×C4—531no—
698C22×C4—532no—
699C22×C4—532no—
700C22×C4—1064no—
701C22×C4—1062no—
702C22×C4—1062no—
703C22×C4—1061no—
704C22×C4—1064no—
705C22×C4—4242no—
706C22×C4—2124no—
707C22×C4D4×D5311yescharacteristic
708C22×C4D4×D5311yescharacteristic
709C22×C4C23×D5311yescharacteristic
710SD16—44no—
711SD16—2124no—
712D8—44no—
713D8—2124no—
714D8—2124no—
715D8—2124no—
716D8—2124no—
717D8—2124no—
718C2×C8—22no—
719C2×C8—22no—
720C2×C8—532no—
721C2×C8—532no—
722C2×C8—1062no—
723C2×C8—1062no—
724C2×C8C23×D5312yes—
725C2×C8C23×D5312yes—
726C4⋊C4—21no—
727C4⋊C4—534no—
728C4⋊C4—534no—
729C4⋊C4—532no—
730C4⋊C4—1064no—
731C4⋊C4—1064no—
732C4⋊C4—1061no—
733C4⋊C4C23×D5312yes—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4—24no—
737C22⋊C4—534no—
738C22⋊C4—534no—
739C22⋊C4—1064no—
740C22⋊C4—1064no—
741C22⋊C4—1064no—
742C22⋊C4—1064no—
743C22⋊C4—1064no—
744C42—532no—
745C42—532no—
746C42D4×D5312yes—
747C42C23×D5312yes—
748C23—22no—
749C23—22no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—532no—
757C23—1062no—
758C23—1062no—
759C23—1062no—
760C23—1062no—
761C23—1062no—
762C23—1062no—
763C23—4244no—
764C23—4244no—
765C23—42416no—
766C23—2128no—
767C23—2122no—
768C23—2122no—
769C23—2122no—
770C23—2122no—
771C23—2122no—
772C23—2122no—
773C23—2122no—
774C23—2122no—
775C23—2122no—
776C23C2×D4×D5311yescharacteristic
777Q8—22no—
778Q8—22no—
779Q8—42no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—22no—
784D4—42no—
785D4—42no—
786D4—1062no—
787D4—1062no—
788D4—1062no—
789D4—1062no—
790D4—1062no—
791D4—1062no—
792D4—4244no—
793D4—4244no—
794D4—4244no—
795D4—4244no—
796D4—4244no—
797D4—4244no—
798D4—4244no—
799D4—4244no—
800D4—2128no—
801D4—2128no—
802D4—2122no—
803D4—2122no—
804D4—2122no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—84no—
812C2×C4—532no—
813C2×C4—532no—
814C2×C4—532no—
815C2×C4—1062no—
816C2×C4—1062no—
817C2×C4—1062no—
818C2×C4—1064no—
819C2×C4—1062no—
820C2×C4—1062no—
821C2×C4—1062no—
822C2×C4—4244no—
823C2×C4—2128no—
824C2×C4—2122no—
825C2×C4C2×D4×D5312yes—
826C2×C4C2×D4×D5312yes—
827C2×C4C2×D4×D5311yescharacteristic
828C2×C4#1313326212yes—
829C2×C4#1313326312yes—
830C2×C4C24×D5311yescharacteristic
831C8—22no—
832C8—22no—
833C8—1062no—
834C8—1062no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—84no—
842C22—84no—
843C22—1062no—
844C22—1062no—
845C22—1062no—
846C22—42416no—
847C22—4244no—
848C22—4244no—
849C22—4244no—
850C22—2122no—
851C22—2122no—
852C22—2122no—
853C22—2122no—
854C22—2122no—
855C22—2122no—
856C22—2122no—
857C22—2122no—
858C22—2122no—
859C22—2124no—
860C22#1681118912yes—
861C22#1681142512yes—
862C22#1681142712yes—
863C22C22×D4×D5311yescharacteristic
864C4—22no—
865C4—22no—
866C4—42no—
867C4—42no—
868C4—1062no—
869C4—1062no—
870C4—1062no—
871C4—2122no—
872C4#1681118912yes—
873C4C2×#1313326211yescharacteristic
874C4C2×#1313326311yescharacteristic
875C2—82no—
876C2—82no—
877C2—4242no—
878C2—4242no—
879C2—4242no—
880C2—2122no—
881C2#2028576214yesdirect product factor
882C2C2×#1681118911yescharacteristic
883C2C2×#1681142511yescharacteristic
884C2C2×#1681142711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#463C2
socleC23×C53C22×D4
hypercenterC2×#463D53
hypocenterC53C2×#3220
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#16811224C2semidirect
2. C2×#16811191C2semidirect
3. #20285762C2direct (N × H)
4. C2×#16811009C2semidirect
5. C2×#16810998C2semidirect
6. C2×#16810986C2semidirect
7. C2×#16810979C2semidirect
8. C2×#16810835C2semidirect
9. C2×#16810819C2semidirect
10. C2×#16810818C2semidirect
11. C2×#16810771C2semidirect
12. C2×#16810767C2semidirect
13. C2×#16810758C2semidirect
14. C2×#16810755C2semidirect
15. C2×#16810683C2semidirect
16. C2×C53×#463C2semidirect
19. C22×#11719924C22semidirect
21. C22×D424C22semidirect
24. C22×#11719922C22semidirect
26. #16811224C22semidirect
28. #16811191C22semidirect
31. C2×#13133213C22semidirect
32. C2×#13133208C22semidirect
44. C2×C4×D212C22semidirect
46. #16811009C22semidirect
47. #16810998C22semidirect
48. #16810986C22semidirect
49. #16810979C22semidirect
50. #16810835C22semidirect
51. #16810819C22semidirect
52. #16810818C22semidirect
53. #16810771C22semidirect
54. #16810767C22semidirect
55. #16810758C22semidirect
56. #16810755C22semidirect
57. #16810683C22semidirect
58. C2×C4⋊#88322C22semidirect
59. C2×#13133141C22semidirect
61. C2×#13133139C22semidirect
64. C2×#13133137C22semidirect
67. C2×#13133127C22semidirect
68. C2×C8×Dic53C22semidirect
69. C22×SD16×C53C22semidirect
72. C2×C4×D4×C53C22semidirect
73. C53×#463C22semidirect
74. C2×C4⋊C8×C53C22semidirect
75. C2×#103×C53C22semidirect
103. C2×#11719924C23semidirect
107. C2×D424C23semidirect
113. C2×#11719922C23semidirect
121. #13133213C23semidirect
123. #13133208C23semidirect
139. C4×D212C23semidirect
155. C4⋊#88322C23semidirect
156. #13133141C23semidirect
158. #13133139C23semidirect
161. #13133137C23semidirect
164. #13133127C23semidirect
165. C8×Dic53C23semidirect
171. C2×SD16×C53C23semidirect
179. C4×D4×C53C23semidirect
185. C4⋊C8×C53C23semidirect
186. #103×C53C23semidirect
441. C2×#463D53semidirect
451. C2×C53#3220semidirect
462. C22×SD16C2×D53semidirect
490. C2×C4×D4C2×D53semidirect
497. #463C2×D53semidirect
506. C2×C4⋊C8C2×D53semidirect
508. C2×#103C2×D53semidirect
519. C53C2×#3220semidirect
552. C2×SD16C22×D53semidirect
596. C4×D4C22×D53semidirect
618. C4⋊C8C22×D53semidirect
620. #103C22×D53semidirect
881. C2#20285762direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112242
C2×#168111912
#202857622
C2×#168110092
C2×#168109982
C2×#168109862
C2×#168109792
C2×#168108352
C2×#168108192
C2×#168108182
C2×#168107712
C2×#168107672
C2×#168107582
C2×#168107552
C2×#168106832
C2×C53×#4632
C2×#322053