Finite Group Databasebeta

← C2×#20285804 #28255442

Subgroups — C2×#20285804 #28255442

Order 13568.

2278 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811242C211yesmaximal, characteristic, complemented
2C2×#16811186C211yesmaximal, characteristic, complemented
3#20285804C2116yesmaximal, direct product factor
4C2×#16811005C211yesmaximal, characteristic, complemented
5C2×#16810983C211yesmaximal, characteristic, complemented
6C2×#16810969C211yesmaximal, characteristic, complemented
7C2×#16810843C211yesmaximal, characteristic, complemented
8C2×#16810821C211yesmaximal, characteristic, complemented
9C2×#16810836C211yesmaximal, characteristic, complemented
10C2×#16810816C211yesmaximal, characteristic, complemented
11C2×#16810782C211yesmaximal, characteristic, complemented
12C2×#16810765C211yesmaximal, characteristic, complemented
13C2×#16810772C211yesmaximal, characteristic, complemented
14C2×#16810755C211yesmaximal, characteristic, complemented
15C2×#16810685C211yesmaximal, characteristic, complemented
16C2×C53×#496C211yesmaximal, characteristic, complemented
17C22×#11719947C2211yescharacteristic
18C22×D4×D53C2211yescharacteristic
19C22×#11719925C2211yescharacteristic, complemented
20C22×#11719923C2211yescharacteristic, complemented
21C22×#11719924C2211yescharacteristic
22C22×#11719922C2211yescharacteristic
23#16811242—24no—
24#16811242C2218yescomplemented
25#16811186—24no—
26#16811186C2218yescomplemented
27C2×#13133217C2211yescharacteristic, complemented
28C2×#13133213C2211yescharacteristic
29C2×#13133210—21no—
30C2×#13133205C2211yescharacteristic
31C2×#13133204C2211yescharacteristic
32C2×#13133203—21no—
33C2×#13133201—21no—
34C2×#13133194—21no—
35C2×#13133193C2211yescharacteristic
36C2×#13133189—21no—
37C2×#13133189—21no—
38C2×#13133188C2211yescharacteristic
39C2×#13133185—21no—
40C2×#13133185—21no—
41C2×Q8×Dic53C2211yescharacteristic, complemented
42C2×D4×Dic53C2211yescharacteristic, complemented
43C2×#13133174C2211yescharacteristic
44#16811005C2218yescomplemented
45#16810983C2218yescomplemented
46#16810969C2218yescomplemented
47#16810843C2218yescomplemented
48#16810836C2218yescomplemented
49#16810821C2218yescomplemented
50#16810816C2218yescomplemented
51#16810782C2218yescomplemented
52#16810772C2218yescomplemented
53#16810765C2218yescomplemented
54#16810755C2218yescomplemented
55#16810685C2218yescomplemented
56C2×#13133146C2211yescharacteristic, complemented
57C2×#13133146C2211yescharacteristic, complemented
58C2×#13133142C2211yescharacteristic, complemented
59C2×#13133142C2211yescharacteristic, complemented
60C2×#13133139C2211yescharacteristic
61C2×#13133139C2211yescharacteristic
62C2×#13133138C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C2×#13133138C2211yescharacteristic, complemented
65C2×#13133138C2211yescharacteristic, complemented
66C2×#13133129C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C4×#88322C2211yescharacteristic, complemented
69C22×SD16×C53C2211yescharacteristic
70C22×SD16×C53C2211yescharacteristic, complemented
71C22×D8×C53C2211yescharacteristic
72C22×D8×C53C2211yescharacteristic, complemented
73C2×#127×C53C2211yescharacteristic
74C2×#124×C53C2211yescharacteristic, complemented
75C53×#496C2218yescomplemented
76C2×#97×C53C2211yescharacteristic, complemented
77C24×D53—21no—
78C2×#11719947—22no—
79C2×#11719947—42no—
80C2×#11719947—42no—
81C2×#11719947C2314yes—
82C22×Dic106—21no—
83C22×Dic106C2311yescharacteristic
84C22×D212C2311yescharacteristic
85C22×C22⋊D53—21no—
86C22×C22⋊D53—21no—
87C22×C22⋊D53—21no—
88C22×C22⋊D53—21no—
89C22×C22⋊D53—21no—
90C2×D4×D53—22no—
91C2×D4×D53—42no—
92C2×D4×D53—42no—
93C2×D4×D53C2314yes—
94C23×Dic53—21no—
95C23×Dic53—21no—
96C22×C4×D53C2311yescharacteristic
97C2×#11719925—42no—
98C2×#11719925C2314yescomplemented
99C2×#11719923—42no—
100C2×#11719923C2314yescomplemented
101C2×#11719924—42no—
102C2×#11719924C2314yes—
103C2×#11719922—42no—
104C2×#11719922C2314yes—
105C22×#88322C2311yescharacteristic
106C22×#88322C2311yescharacteristic
107#13133217—22no—
108#13133217C2314yescomplemented
109#13133213—22no—
110#13133213C2314yes—
111#13133210—28no—
112#13133205—22no—
113#13133205C2314yes—
114#13133204—22no—
115#13133204C2314yes—
116#13133203—28no—
117#13133201—28no—
118#13133194—28no—
119#13133193—22no—
120#13133193C2314yes—
121#13133189—28no—
122#13133189—28no—
123#13133188—22no—
124#13133188C2314yes—
125#13133185—28no—
126#13133185—28no—
127Q8×Dic53—22no—
128Q8×Dic53C2314yescomplemented
129D4×Dic53—22no—
130D4×Dic53C2314yescomplemented
131#13133174D414yes—
132#13133174C2314yes—
133C2×C4⋊Dic53—21no—
134C2×C4⋊Dic53—21no—
135C2×C4⋊Dic53C2311yescharacteristic
136C2×C4⋊Dic53C2311yescharacteristic
137C2×#11719919—21no—
138C2×#11719919D411yescharacteristic
139C2×#11719919D411yescharacteristic
140C2×C22⋊Dic53—21no—
141C2×C22⋊Dic53—21no—
142C2×C22⋊Dic53—21no—
143C2×C22⋊Dic53—21no—
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921D411yescharacteristic
148C2×#11719921D411yescharacteristic
149C2×C4×Dic53—21no—
150C2×C4×Dic53C2311yescharacteristic
151#13133146C2314yescomplemented
152#13133146C2314yescomplemented
153#13133142C2314yescomplemented
154#13133142C2314yescomplemented
155#13133139C2314yes—
156#13133139C2314yes—
157#13133138C2314yes—
158#13133138C2314yes—
159#13133138C2314yescomplemented
160#13133138C2314yescomplemented
161#13133129C2314yes—
162#13133129C2314yes—
163C4×#88322C2314yescomplemented
164C22×Q8×C53C2311yescharacteristic
165C22×D4×C53—21no—
166C22×D4×C53—21no—
167C22×D4×C53C2311yescharacteristic
168C22×D4×C53C2311yescharacteristic
169C22×D4×C53C2311yescharacteristic
170C2×SD16×C53—42no—
171C2×SD16×C53—42no—
172C2×SD16×C53C2314yes—
173C2×SD16×C53C2314yescomplemented
174C2×D8×C53—42no—
175C2×D8×C53—42no—
176C2×D8×C53C2314yes—
177C2×D8×C53C2314yescomplemented
178C22×C8×C53C2311yescharacteristic
179C22×C8×C53C2311yescharacteristic
180#127×C53—22no—
181#127×C53C2314yes—
182#124×C53—22no—
183#124×C53C2314yescomplemented
184C2×C22⋊C4×C53—21no—
185C2×C22⋊C4×C53—21no—
186C2×C42×C53C2311yescharacteristic
187#97×C53C2314yescomplemented
188C24×C53—21no—
189C24×C53—21no—
190C24×C53—21no—
191C23×D53—21no—
192C23×D53—24no—
193C23×D53—44no—
194C23×D53—82no—
195C23×D53—82no—
196C23×D53C2×D411yescharacteristic
197C2×Q8×C53—21no—
198C2×Q8×C53—22no—
199C2×Q8×C53—22no—
200C2×Q8×C53C2412yes—
201C2×D4×C53—21no—
202C2×D4×C53—21no—
203C2×D4×C53—21no—
204C2×D4×C53—24no—
205C2×D4×C53—24no—
206C2×D4×C53—22no—
207C2×D4×C53—22no—
208C2×D4×C53—22no—
209C2×D4×C53—22no—
210C2×D4×C53—22no—
211C2×D4×C53—22no—
212C2×D4×C53—82no—
213C2×D4×C53—82no—
214C2×D4×C53C2412yes—
215C2×D4×C53C2412yes—
216C2×D4×C53C2412yes—
217C22×C4×C53—21no—
218C22×C4×C53C2×D411yescharacteristic
219C22×C4×C53C2×D411yescharacteristic
220C22×C4×C53C2411yescharacteristic
221C2×C22⋊D53—24no—
222C2×C22⋊D53—24no—
223C2×C22⋊D53—24no—
224C2×C22⋊D53—24no—
225C2×C22⋊D53—24no—
226C2×C22⋊D53—44no—
227C2×C22⋊D53—44no—
228C2×C22⋊D53—82no—
229C2×C22⋊D53—82no—
230C2×C22⋊D53—82no—
231C22×Dic53—21no—
232C22×Dic53—21no—
233C22×Dic53—21no—
234C22×Dic53—24no—
235C22×Dic53—24no—
236C22×Dic53—44no—
237C22×Dic53—82no—
238C22×Dic53C2×D411yescharacteristic
239C22×Dic53C2×D411yescharacteristic
240C22×Dic53C2×D411yescharacteristic
241#11719947—44no—
242#11719947—44no—
243#11719947—48no—
244D4×D53—44no—
245D4×D53—44no—
246D4×D53—48no—
247C2×D212—22no—
248C2×D212—22no—
249C2×D212—21no—
250C2×D212C2412yes—
251C2×C4×D53—22no—
252C2×C4×D53—22no—
253C2×C4×D53C2×D412yes—
254C2×C4×D53C2412yes—
255C2×Dic106—22no—
256C2×Dic106—22no—
257C2×Dic106—21no—
258C2×Dic106—24no—
259C2×Dic106—82no—
260C2×Dic106C2412yes—
261SD16×C53—44no—
262SD16×C53—44no—
263D8×C53—44no—
264D8×C53—44no—
265C2×C8×C53—22no—
266C2×C8×C53—22no—
267C2×C8×C53C2412yes—
268C2×C8×C53C2412yes—
269C22⋊C4×C53—24no—
270C22⋊C4×C53—24no—
271C42×C53C2×D412yes—
272C42×C53C2412yes—
273C22⋊Dic53—24no—
274C22⋊Dic53—24no—
275C22⋊Dic53—24no—
276C22⋊Dic53—24no—
277#11719925—44no—
278#11719924—44no—
279#11719923—44no—
280#11719922—44no—
281#11719921—24no—
282#11719921—24no—
283#11719921—24no—
284#11719921C2×D414yes—
285#11719921C2×D414yes—
286C4⋊Dic53—24no—
287C4⋊Dic53—21no—
288C4⋊Dic53—21no—
289C4⋊Dic53—24no—
290C4⋊Dic53C2412yes—
291C4⋊Dic53C2412yes—
292#11719919—24no—
293#11719919C2×D414yes—
294#11719919C2×D414yes—
295C4×Dic53—24no—
296C4×Dic53C2×D412yes—
297C4×Dic53C2412yes—
298C2×#88322—22no—
299C2×#88322—22no—
300C2×#88322C2412yes—
301C2×#88322C2412yes—
302C23×C53—22no—
303C23×C53—22no—
304C23×C53—22no—
305C23×C53—42no—
306C23×C53—42no—
307C23×C53—42no—
308C23×C53—42no—
309C23×C53—42no—
310C23×C53—42no—
311C23×C53—42no—
312C23×C53—42no—
313C23×C53—42no—
314C23×C53C22×D411yescharacteristic
315C22×D53—22no—
316C22×D53—22no—
317C22×D53—22no—
318C22×D53—22no—
319C22×D53—48no—
320C22×D53—42no—
321C22×D53—42no—
322C22×D53—42no—
323C22×D53—84no—
324C22×D53—84no—
325C22×D53—816no—
326C22×D53C22×D412yes—
327Q8×C53—22no—
328Q8×C53—22no—
329Q8×C53—42no—
330D4×C53—22no—
331D4×C53—22no—
332D4×C53—22no—
333D4×C53—22no—
334D4×C53—22no—
335D4×C53—22no—
336D4×C53—42no—
337D4×C53—42no—
338D4×C53—42no—
339D4×C53—84no—
340D4×C53—84no—
341C2×C4×C53—22no—
342C2×C4×C53—22no—
343C2×C4×C53—22no—
344C2×C4×C53—42no—
345C2×C4×C53C22×D412yes—
346C2×C4×C53C22×D412yes—
347C2×C4×C53C22×D411yescharacteristic
348C2×C4×C53H(5,𝔽2)12yes—
349C2×C4×C53H(5,𝔽2)12yes—
350C2×C4×C53C2511yescharacteristic
351C22⋊D53—48no—
352C22⋊D53—48no—
353C22⋊D53—84no—
354C22⋊D53—84no—
355C22⋊D53—84no—
356C2×Dic53—22no—
357C2×Dic53—22no—
358C2×Dic53—22no—
359C2×Dic53—22no—
360C2×Dic53—22no—
361C2×Dic53—22no—
362C2×Dic53—48no—
363C2×Dic53—42no—
364C2×Dic53—42no—
365C2×Dic53—42no—
366C2×Dic53—84no—
367C2×Dic53C22×D412yes—
368C2×Dic53C22×D412yes—
369C2×Dic53C22×D412yes—
370D212—22no—
371D212—22no—
372D212—42no—
373C4×D53—24no—
374C4×D53—22no—
375C4×D53—22no—
376Dic106—22no—
377Dic106—22no—
378Dic106—42no—
379Dic106—84no—
380C8×C53—22no—
381C8×C53—22no—
382#88322—22no—
383#88322—22no—
384C2×#3224—531nomaximal, Sylow
385C22×C53—42no—
386C22×C53—42no—
387C22×C53—42no—
388C22×C53—42no—
389C22×C53—42no—
390C22×C53—42no—
391C22×C53—42no—
392C22×C53—42no—
393C22×C53—42no—
394C22×C53—84no—
395C22×C53—84no—
396C22×C53—84no—
397C22×C53#53512yes—
398C22×C53#57612yes—
399C22×C53#57712yes—
400C22×C53C23×D411yescharacteristic
401C2×D53—22no—
402C2×D53—22no—
403C2×D53—22no—
404C2×D53—44no—
405C2×D53—42no—
406C2×D53—42no—
407C2×D53—42no—
408C2×D53—816no—
409C2×D53—84no—
410C4×C53—22no—
411C4×C53—22no—
412C4×C53—42no—
413C4×C53#53512yes—
414C4×C53C2×H(5,𝔽2)11yescharacteristic
415C4×C53C2×H(5,𝔽2)11yescharacteristic
416Dic53—22no—
417Dic53—22no—
418Dic53—22no—
419Dic53—42no—
420Dic53—42no—
421Dic53—42no—
422C2×#542—531no—
423C2×#535—531no—
424#3224—5316no—
425C2×#496D5311yescharacteristic, complemented
426C2×#495—531no—
427C2×#489—531no—
428C2×#486—531no—
429C2×#464—531no—
430C2×#460—531no—
431C2×#463—531no—
432C2×#459—531no—
433C2×#452—531no—
434C2×#449—531no—
435C2×#450—531no—
436C2×#447—531no—
437C2×#433—531no—
438C2×C53—82no—
439C2×C53—82no—
440C2×C53—82no—
441C2×C53#322414yescomplemented
442C2×C53C2×#53511yescharacteristic
443C2×C53C2×#57611yescharacteristic
444C2×C53C2×#57711yescharacteristic
445D53—42no—
446D53—82no—
447C22×#41—531no—
448C23×D4—531no—
449C22×Q16—531no—
450C22×SD16—531no—
451C22×SD16—531no—
452C22×SD16C2×D5311yescharacteristic
453C22×SD16C2×D5311yescharacteristic, complemented
454C22×D8—531no—
455C22×D8C2×D5311yescharacteristic
456C22×D8C2×D5311yescharacteristic, complemented
457#542—538no—
458#542—1064no—
459#535—538no—
460#535—1064no—
461C2×C4⋊Q8—531no—
462C2×#127—531no—
463C2×#127C2×D5311yescharacteristic
464C2×#126—1061no—
465C2×#124—531no—
466C2×#124—531no—
467C2×#124—1061no—
468C2×#124C2×D5311yescharacteristic, complemented
469C2×#123—1061no—
470C2×C22⋊Q8—531no—
471C2×C22⋊Q8—1061no—
472C2×#121—531no—
473C2×#121—1061no—
474C2×#121—1061no—
475C2×#120—1061no—
476C2×#120—1061no—
477C2×C4×Q8—531no—
478C2×C4×D4—531no—
479C2×#117—531no—
480#496C2×D5318yescomplemented
481#495—538no—
482#489—538no—
483#486—538no—
484#464—538no—
485#463—538no—
486#460—538no—
487#459—538no—
488#452—538no—
489#450—538no—
490#449—538no—
491#447—538no—
492#433—538no—
493C2×C4⋊C8—531no—
494C2×C4⋊C8—531no—
495C2×#103—531no—
496C2×#103—531no—
497C2×#102—531no—
498C2×#102—531no—
499C2×#102—531no—
500C2×#102—531no—
501C2×#102—531no—
502C2×#102—531no—
503C2×C22⋊C8—531no—
504C2×C22⋊C8—531no—
505C2×#97C2×D5311yescharacteristic, complemented
506C2×C4×C8—531no—
507C53C2×#322411yescharacteristic, complemented, Sylow
508C25—1061no—
509C2×#41—534no—
510C2×#41—1062no—
511C2×#41—2122no—
512C2×#41—2122no—
513C22×Q8—531no—
514C22×Q8—1061no—
515C22×Q8C22×D5311yescharacteristic
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—534no—
519C22×D4—531no—
520C22×D4—1062no—
521C22×D4—1061no—
522C22×D4—1061no—
523C22×D4—1061no—
524C22×D4—1061no—
525C22×D4—1061no—
526C22×D4—2122no—
527C22×D4—2122no—
528C22×D4C22×D5311yescharacteristic
529C22×D4C22×D5311yescharacteristic
530C22×D4C22×D5311yescharacteristic
531C23×C4—531no—
532C23×C4—1061no—
533C23×C4—1061no—
534C2×Q16—534no—
535C2×Q16—2122no—
536C2×SD16—42no—
537C2×SD16—42no—
538C2×SD16—534no—
539C2×SD16—534no—
540C2×SD16—2122no—
541C2×SD16—2122no—
542C2×SD16C22×D5314yes—
543C2×SD16C22×D5314yescomplemented
544C2×D8—42no—
545C2×D8—42no—
546C2×D8—534no—
547C2×D8—2122no—
548C2×D8C22×D5314yes—
549C2×D8C22×D5314yescomplemented
550C22×C8—531no—
551C22×C8—531no—
552C22×C8C22×D5311yescharacteristic
553C22×C8C22×D5311yescharacteristic
554C4⋊Q8—534no—
555C4⋊Q8—1062no—
556#127—22no—
557#127—534no—
558#127—1062no—
559#127C22×D5314yes—
560#126—1068no—
561#124—22no—
562#124—534no—
563#124—534no—
564#124—1062no—
565#124—1068no—
566#124—1062no—
567#124C22×D5314yescomplemented
568#123—1068no—
569C22⋊Q8—534no—
570C22⋊Q8—1068no—
571C22⋊Q8—1062no—
572#121—534no—
573#121—1068no—
574#121—1068no—
575#121—1062no—
576#120—1068no—
577#120—1068no—
578C4×Q8—534no—
579C4×Q8—1062no—
580C4×D4—534no—
581C4×D4—1062no—
582#117—534no—
583#117—534no—
584C2×C4⋊C4—531no—
585C2×C4⋊C4—531no—
586C2×C4⋊C4—531no—
587C2×C4⋊C4—531no—
588C2×C4⋊C4—1061no—
589C2×C4⋊C4—1061no—
590C2×C4⋊C4—1061no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—531no—
594C2×C22⋊C4—531no—
595C2×C22⋊C4—1061no—
596C2×C22⋊C4—1061no—
597C2×C22⋊C4—1061no—
598C2×C22⋊C4—1061no—
599C2×C22⋊C4—1061no—
600C2×C22⋊C4—1061no—
601C2×C22⋊C4—1061no—
602C2×C42—531no—
603C2×C42—1061no—
604C2×C42C22×D5311yescharacteristic
605C4⋊C8—534no—
606C4⋊C8—534no—
607#103—534no—
608#103—534no—
609#102—534no—
610#102—534no—
611#102—534no—
612#102—534no—
613#102—534no—
614#102—534no—
615C22⋊C8—534no—
616C22⋊C8—534no—
617#97C22×D5314yescomplemented
618C4×C8—534no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—531no—
623C24—1064no—
624C24—1061no—
625C24—4242no—
626C24—4242no—
627C24—2124no—
628#41—2124no—
629#41—2124no—
630#41—2128no—
631C2×Q8—21no—
632C2×Q8—22no—
633C2×Q8—22no—
634C2×Q8—532no—
635C2×Q8—1064no—
636C2×Q8—1061no—
637C2×Q8—1062no—
638C2×Q8—1062no—
639C2×Q8—4242no—
640C2×Q8C23×D5312yes—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—24no—
645C2×D4—24no—
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—22no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—22no—
652C2×D4—82no—
653C2×D4—82no—
654C2×D4—532no—
655C2×D4—1064no—
656C2×D4—1064no—
657C2×D4—1064no—
658C2×D4—1064no—
659C2×D4—1064no—
660C2×D4—1061no—
661C2×D4—1062no—
662C2×D4—1062no—
663C2×D4—4242no—
664C2×D4—4242no—
665C2×D4—4242no—
666C2×D4—2124no—
667C2×D4—2124no—
668C2×D4—2128no—
669C2×D4—2124no—
670C2×D4—2124no—
671C2×D4C23×D5312yes—
672C2×D4C23×D5312yes—
673C2×D4C23×D5312yes—
674C22×C4—21no—
675C22×C4—531no—
676C22×C4—531no—
677C22×C4—531no—
678C22×C4—532no—
679C22×C4—532no—
680C22×C4—1064no—
681C22×C4—1064no—
682C22×C4—1062no—
683C22×C4—1062no—
684C22×C4—1061no—
685C22×C4—1061no—
686C22×C4—1061no—
687C22×C4—4242no—
688C22×C4—2124no—
689C22×C4D4×D5311yescharacteristic
690C22×C4D4×D5311yescharacteristic
691C22×C4C23×D5311yescharacteristic
692Q16—2124no—
693SD16—44no—
694SD16—44no—
695SD16—2124no—
696SD16—2124no—
697D8—44no—
698D8—44no—
699D8—2124no—
700C2×C8—22no—
701C2×C8—22no—
702C2×C8—532no—
703C2×C8—532no—
704C2×C8—1062no—
705C2×C8—1062no—
706C2×C8C23×D5312yes—
707C2×C8C23×D5312yes—
708C4⋊C4—534no—
709C4⋊C4—534no—
710C4⋊C4—532no—
711C4⋊C4—532no—
712C4⋊C4—1064no—
713C4⋊C4—1064no—
714C4⋊C4—1061no—
715C4⋊C4—1061no—
716C4⋊C4—1064no—
717C22⋊C4—24no—
718C22⋊C4—24no—
719C22⋊C4—534no—
720C22⋊C4—534no—
721C22⋊C4—1064no—
722C22⋊C4—1064no—
723C22⋊C4—1064no—
724C22⋊C4—1064no—
725C22⋊C4—1064no—
726C22⋊C4—1064no—
727C22⋊C4—1064no—
728C42—532no—
729C42—532no—
730C42—1064no—
731C42D4×D5312yes—
732C42C23×D5312yes—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—532no—
746C23—1062no—
747C23—1062no—
748C23—1062no—
749C23—1062no—
750C23—4244no—
751C23—4244no—
752C23—42416no—
753C23—2128no—
754C23—2122no—
755C23—2122no—
756C23—2122no—
757C23C2×D4×D5311yescharacteristic
758Q8—22no—
759Q8—22no—
760Q8—42no—
761Q8—1062no—
762Q8—1062no—
763Q8—4244no—
764Q8—2122no—
765D4—22no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—42no—
772D4—42no—
773D4—42no—
774D4—84no—
775D4—84no—
776D4—1062no—
777D4—1062no—
778D4—4244no—
779D4—4244no—
780D4—4244no—
781D4—2128no—
782D4—2128no—
783D4—2122no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—42no—
788C2×C4—532no—
789C2×C4—532no—
790C2×C4—532no—
791C2×C4—1062no—
792C2×C4—1062no—
793C2×C4—1062no—
794C2×C4—1064no—
795C2×C4—1062no—
796C2×C4—1062no—
797C2×C4—1062no—
798C2×C4—1062no—
799C2×C4—1062no—
800C2×C4—4244no—
801C2×C4—2128no—
802C2×C4—2122no—
803C2×C4—2122no—
804C2×C4—2122no—
805C2×C4C2×D4×D5312yes—
806C2×C4C2×D4×D5312yes—
807C2×C4C2×D4×D5311yescharacteristic
808C2×C4#1313326212yes—
809C2×C4#1313326212yes—
810C2×C4C24×D5311yescharacteristic
811C8—22no—
812C8—22no—
813C8—1062no—
814C8—1062no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—84no—
825C22—84no—
826C22—84no—
827C22—1062no—
828C22—1062no—
829C22—1062no—
830C22—42416no—
831C22—4244no—
832C22—2122no—
833C22—2122no—
834C22—2122no—
835C22—2124no—
836C22#1681118612yes—
837C22#1681142712yes—
838C22#1681143312yes—
839C22C22×D4×D5311yescharacteristic
840C4—22no—
841C4—22no—
842C4—42no—
843C4—1062no—
844C4—1062no—
845C4—1062no—
846C4—2122no—
847C4—2122no—
848C4—2122no—
849C4#1681118612yes—
850C4C2×#1313326211yescharacteristic
851C4C2×#1313326211yescharacteristic
852C2—82no—
853C2—82no—
854C2—82no—
855C2—4242no—
856C2—2122no—
857C2#2028580414yesdirect product factor
858C2C2×#1681118611yescharacteristic
859C2C2×#1681142711yescharacteristic
860C2C2×#1681143311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#496C2
socleC23×C53C22×D4
hypercenterC2×#496D53
hypocenterC53C2×#3224
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#496

Complements

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

NH ≅ G/Ntype
1. C2×#16811242C2semidirect
2. C2×#16811186C2semidirect
3. #20285804C2direct (N × H)
4. C2×#16811005C2semidirect
5. C2×#16810983C2semidirect
6. C2×#16810969C2semidirect
7. C2×#16810843C2semidirect
8. C2×#16810821C2semidirect
9. C2×#16810836C2semidirect
10. C2×#16810816C2semidirect
11. C2×#16810782C2semidirect
12. C2×#16810765C2semidirect
13. C2×#16810772C2semidirect
14. C2×#16810755C2semidirect
15. C2×#16810685C2semidirect
16. C2×C53×#496C2semidirect
19. C22×#11719925C22semidirect
20. C22×#11719923C22semidirect
24. #16811242C22semidirect
26. #16811186C22semidirect
27. C2×#13133217C22semidirect
41. C2×Q8×Dic53C22semidirect
42. C2×D4×Dic53C22semidirect
44. #16811005C22semidirect
45. #16810983C22semidirect
46. #16810969C22semidirect
47. #16810843C22semidirect
48. #16810836C22semidirect
49. #16810821C22semidirect
50. #16810816C22semidirect
51. #16810782C22semidirect
52. #16810772C22semidirect
53. #16810765C22semidirect
54. #16810755C22semidirect
55. #16810685C22semidirect
56. C2×#13133146C22semidirect
57. C2×#13133146C22semidirect
58. C2×#13133142C22semidirect
59. C2×#13133142C22semidirect
64. C2×#13133138C22semidirect
65. C2×#13133138C22semidirect
68. C2×C4×#88322C22semidirect
70. C22×SD16×C53C22semidirect
72. C22×D8×C53C22semidirect
74. C2×#124×C53C22semidirect
75. C53×#496C22semidirect
76. C2×#97×C53C22semidirect
98. C2×#11719925C23semidirect
100. C2×#11719923C23semidirect
108. #13133217C23semidirect
128. Q8×Dic53C23semidirect
130. D4×Dic53C23semidirect
151. #13133146C23semidirect
152. #13133146C23semidirect
153. #13133142C23semidirect
154. #13133142C23semidirect
159. #13133138C23semidirect
160. #13133138C23semidirect
163. C4×#88322C23semidirect
173. C2×SD16×C53C23semidirect
177. C2×D8×C53C23semidirect
183. #124×C53C23semidirect
187. #97×C53C23semidirect
425. C2×#496D53semidirect
441. C2×C53#3224semidirect
453. C22×SD16C2×D53semidirect
456. C22×D8C2×D53semidirect
468. C2×#124C2×D53semidirect
480. #496C2×D53semidirect
505. C2×#97C2×D53semidirect
507. C53C2×#3224semidirect
543. C2×SD16C22×D53semidirect
549. C2×D8C22×D53semidirect
567. #124C22×D53semidirect
617. #97C22×D53semidirect
857. C2#20285804direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112422
C2×#168111862
#202858042
C2×#168110052
C2×#168109832
C2×#168109692
C2×#168108432
C2×#168108212
C2×#168108362
C2×#168108162
C2×#168107822
C2×#168107652
C2×#168107722
C2×#168107552
C2×#168106852
C2×C53×#4962
C2×#322453