Finite Group Databasebeta

← C2×#20287732 #28265045

Subgroups — C2×#20287732 #28265045

Order 13568.

2250 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×#16811342C211yesmaximal, characteristic, complemented
2C2×#16811293C211yesmaximal, characteristic, complemented
3#20287732C2116yesmaximal, direct product factor
4C2×#16811011C211yesmaximal, characteristic, complemented
5C2×#16810994C211yesmaximal, characteristic, complemented
6C2×#16810821C211yesmaximal, characteristic, complemented
7C2×#16810820C211yesmaximal, characteristic, complemented
8C2×#16810836C211yesmaximal, characteristic, complemented
9C2×#16810835C211yesmaximal, characteristic, complemented
10C2×#16810826C211yesmaximal, characteristic, complemented
11C2×#16810816C211yesmaximal, characteristic, complemented
12C2×#16810751C211yesmaximal, characteristic, complemented
13C2×#16810725C211yesmaximal, characteristic, complemented
14C2×#16810724C211yesmaximal, characteristic, complemented
15C2×D8×Dic53C211yesmaximal, characteristic, complemented
16C2×C53×#496C211yesmaximal, characteristic, complemented
17C22×#11719947—21no—
18C22×#11719913C2211yescharacteristic
19C22×#11719923C2211yescharacteristic
20C22×#11719923C2211yescharacteristic
21C22×#11719924C2211yescharacteristic
22C22×#11719922C2211yescharacteristic
23#16811342—24no—
24#16811342C2218yescomplemented
25#16811293—24no—
26#16811293C2218yescomplemented
27C2×#13133215C2211yescharacteristic
28C2×#13133213C2211yescharacteristic
29C2×#13133213C2211yescharacteristic
30C2×#13133210—21no—
31C2×#13133210—21no—
32C2×#13133204C2211yescharacteristic
33C2×#13133194—21no—
34C2×#13133189—21no—
35C2×#13133189—21no—
36C2×#13133188—21no—
37C2×Q8×Dic53C2211yescharacteristic
38C2×C4×Dic106C2211yescharacteristic
39C2×C4×Dic106C2211yescharacteristic
40C2×C4×D212C2211yescharacteristic
41C2×D4×Dic53C2211yescharacteristic
42C2×D4×Dic53C2211yescharacteristic
43C2×D4×Dic53C2211yescharacteristic
44C2×#13133173—21no—
45#16811011C2218yescomplemented
46#16810994C2218yescomplemented
47#16810836C2218yescomplemented
48#16810835C2218yescomplemented
49#16810826C2218yescomplemented
50#16810821C2218yescomplemented
51#16810820C2218yescomplemented
52#16810816C2218yescomplemented
53#16810751C2218yescomplemented
54#16810725C2218yescomplemented
55#16810724C2218yescomplemented
56D8×Dic53C2218yescomplemented
57C2×#13133151C2211yescharacteristic
58C2×C4⋊#88322C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133146C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×#13133138C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×SD16×C53C2211yescharacteristic
70C22×SD16×C53C2211yescharacteristic
71C22×D8×C53C2211yescharacteristic
72C22×D8×C53C2211yescharacteristic
73C2×#127×C53C2211yescharacteristic
74C2×#124×C53C2211yescharacteristic
75C53×#496C2218yescomplemented
76C2×#97×C53C2211yescharacteristic
77C2×#11719947—28no—
78C2×#11719947—48no—
79C22×Dic106D411yescharacteristic
80C22×Dic106C2311yescharacteristic
81C22×D212C2311yescharacteristic
82C22×C22⋊D53—21no—
83C22×C22⋊D53—21no—
84C22×C22⋊D53—21no—
85C22×C22⋊D53—21no—
86C23×Dic53—21no—
87C23×Dic53—21no—
88C23×Dic53—21no—
89C22×C4×D53—21no—
90C2×#11719913—24no—
91C2×#11719913C2314yes—
92C2×#11719923—42no—
93C2×#11719923—42no—
94C2×#11719923C2314yes—
95C2×#11719923C2314yes—
96C2×#11719924—42no—
97C2×#11719924C2314yes—
98C2×#11719922—42no—
99C2×#11719922C2314yes—
100C22×#88322C2311yescharacteristic
101C22×#88322C2311yescharacteristic
102#13133215—22no—
103#13133215C2314yes—
104#13133213—22no—
105#13133213—22no—
106#13133213C2314yes—
107#13133213C2314yes—
108#13133210—28no—
109#13133210—28no—
110#13133204—22no—
111#13133204C2314yes—
112#13133194—28no—
113#13133189—28no—
114#13133189—28no—
115#13133188—28no—
116Q8×Dic53—22no—
117Q8×Dic53C2314yes—
118C4×Dic106—22no—
119C4×Dic106D414yes—
120C4×Dic106C2314yes—
121C4×Dic106C2314yes—
122C4×D212—22no—
123C4×D212C2314yes—
124D4×Dic53—22no—
125D4×Dic53—22no—
126D4×Dic53—22no—
127D4×Dic53C2314yes—
128D4×Dic53C2314yes—
129D4×Dic53C2314yes—
130#13133173—28no—
131C2×C4⋊Dic53—21no—
132C2×C4⋊Dic53D411yescharacteristic
133C2×C4⋊Dic53C2311yescharacteristic
134C2×C4⋊Dic53C2311yescharacteristic
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×#11719919D411yescharacteristic
139C2×#11719919D411yescharacteristic
140C2×C22⋊Dic53—21no—
141C2×C22⋊Dic53—21no—
142C2×C22⋊Dic53—21no—
143C2×C22⋊Dic53—21no—
144C2×C22⋊Dic53—21no—
145C2×#11719921—21no—
146C2×C4×Dic53—21no—
147C2×C4×Dic53—21no—
148C2×C4×Dic53C2311yescharacteristic
149C2×C4×Dic53C2311yescharacteristic
150#13133151C2314yes—
151C4⋊#88322C2314yes—
152#13133146C2314yes—
153#13133146C2314yes—
154#13133142C2314yes—
155#13133141C2314yes—
156#13133139C2314yes—
157#13133138C2314yes—
158#13133138C2314yes—
159#13133138C2314yes—
160#13133127C2314yes—
161C8×Dic53C2314yes—
162C22×Q8×C53C2311yescharacteristic
163C22×D4×C53—21no—
164C22×D4×C53—21no—
165C22×D4×C53C2311yescharacteristic
166C22×D4×C53C2311yescharacteristic
167C22×D4×C53C2311yescharacteristic
168C2×SD16×C53—24no—
169C2×SD16×C53—42no—
170C2×SD16×C53C2314yes—
171C2×SD16×C53C2314yes—
172C2×D8×C53—24no—
173C2×D8×C53—42no—
174C2×D8×C53C2314yes—
175C2×D8×C53C2314yes—
176C22×C8×C53C2311yescharacteristic
177C22×C8×C53C2311yescharacteristic
178#127×C53—22no—
179#127×C53C2314yes—
180#124×C53—22no—
181#124×C53C2314yes—
182C2×C22⋊C4×C53—21no—
183C2×C22⋊C4×C53—21no—
184C2×C42×C53C2311yescharacteristic
185#97×C53C2314yes—
186C24×C53—21no—
187C24×C53—21no—
188C24×C53—21no—
189C23×D53—21no—
190C2×Q8×C53—21no—
191C2×Q8×C53—22no—
192C2×Q8×C53—22no—
193C2×Q8×C53C2412yes—
194C2×D4×C53—21no—
195C2×D4×C53—21no—
196C2×D4×C53—21no—
197C2×D4×C53—24no—
198C2×D4×C53—24no—
199C2×D4×C53—22no—
200C2×D4×C53—22no—
201C2×D4×C53—22no—
202C2×D4×C53—22no—
203C2×D4×C53—22no—
204C2×D4×C53—22no—
205C2×D4×C53—44no—
206C2×D4×C53—82no—
207C2×D4×C53C2412yes—
208C2×D4×C53C2412yes—
209C2×D4×C53C2412yes—
210C22×C4×C53—21no—
211C22×C4×C53C2×D411yescharacteristic
212C22×C4×C53C2×D411yescharacteristic
213C22×C4×C53C2411yescharacteristic
214C2×C22⋊D53—24no—
215C2×C22⋊D53—24no—
216C2×C22⋊D53—24no—
217C2×C22⋊D53—24no—
218C2×C22⋊D53—44no—
219C2×C22⋊D53—44no—
220C2×C22⋊D53—82no—
221C2×C22⋊D53—82no—
222C22×Dic53—21no—
223C22×Dic53—21no—
224C22×Dic53—21no—
225C22×Dic53—24no—
226C22×Dic53—24no—
227C22×Dic53—24no—
228C22×Dic53—44no—
229C22×Dic53—44no—
230C22×Dic53—44no—
231C22×Dic53C2×D411yescharacteristic
232C22×Dic53C2×D411yescharacteristic
233C22×Dic53C2×D411yescharacteristic
234C22×Dic53C2×D411yescharacteristic
235#11719947—432no—
236C2×D212—22no—
237C2×D212—22no—
238C2×D212—21no—
239C2×D212C2412yes—
240C2×C4×D53—24no—
241C2×C4×D53—44no—
242C2×Dic106—24no—
243C2×Dic106—22no—
244C2×Dic106—22no—
245C2×Dic106—21no—
246C2×Dic106C2×D414yes—
247C2×Dic106C2412yes—
248SD16×C53—28no—
249SD16×C53—44no—
250D8×C53—28no—
251D8×C53—44no—
252C2×C8×C53—22no—
253C2×C8×C53#4114yescomplemented
254C2×C8×C53C2412yes—
255C2×C8×C53C2412yes—
256C22⋊C4×C53—24no—
257C22⋊C4×C53—24no—
258C42×C53C2×D412yes—
259C42×C53C2412yes—
260C22⋊Dic53—24no—
261C22⋊Dic53—24no—
262C22⋊Dic53—24no—
263C22⋊Dic53—24no—
264C22⋊Dic53—24no—
265#11719924—44no—
266#11719923—44no—
267#11719923—44no—
268#11719922—44no—
269#11719921—24no—
270C4⋊Dic53—21no—
271C4⋊Dic53—21no—
272C4⋊Dic53—24no—
273C4⋊Dic53C2×D414yes—
274C4⋊Dic53C2412yes—
275C4⋊Dic53C2412yes—
276#11719919—24no—
277#11719919—24no—
278#11719919—24no—
279#11719919C2×D414yes—
280#11719919C2×D414yes—
281C4×Dic53—24no—
282C4×Dic53—24no—
283C4×Dic53C2×D412yes—
284C4×Dic53C2×D412yes—
285C4×Dic53C2412yes—
286C4×Dic53C2412yes—
287C2×#88322—22no—
288C2×#88322—22no—
289C2×#88322C2412yes—
290C2×#88322C2412yes—
291#11719913—28no—
292C23×C53—22no—
293C23×C53—22no—
294C23×C53—22no—
295C23×C53—42no—
296C23×C53—42no—
297C23×C53—42no—
298C23×C53—42no—
299C23×C53—42no—
300C23×C53—42no—
301C23×C53—42no—
302C23×C53—42no—
303C23×C53—42no—
304C23×C53C22×D411yescharacteristic
305C22×D53—22no—
306C22×D53—42no—
307C22×D53—42no—
308C22×D53—42no—
309Q8×C53—22no—
310Q8×C53—22no—
311Q8×C53—42no—
312D4×C53—22no—
313D4×C53—22no—
314D4×C53—22no—
315D4×C53—22no—
316D4×C53—22no—
317D4×C53—22no—
318D4×C53—48no—
319D4×C53—42no—
320D4×C53—42no—
321D4×C53—42no—
322D4×C53—84no—
323C2×C4×C53—22no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53—42no—
327C2×C4×C53C22×D412yes—
328C2×C4×C53C22×D412yes—
329C2×C4×C53C22×D411yescharacteristic
330C2×C4×C53C2×#4112yes—
331C2×C4×C53H(5,𝔽2)12yes—
332C2×C4×C53C2511yescharacteristic
333C22⋊D53—48no—
334C22⋊D53—48no—
335C22⋊D53—84no—
336C22⋊D53—84no—
337C2×Dic53—22no—
338C2×Dic53—22no—
339C2×Dic53—22no—
340C2×Dic53—22no—
341C2×Dic53—22no—
342C2×Dic53—22no—
343C2×Dic53—48no—
344C2×Dic53—42no—
345C2×Dic53—42no—
346C2×Dic53—42no—
347C2×Dic53—48no—
348C2×Dic53—48no—
349C2×Dic53AGL(1,ℤ/8)14yes—
350C2×Dic53C22×D412yes—
351C2×Dic53C22×D412yes—
352C2×Dic53C22×D412yes—
353C2×Dic53C22×D412yes—
354D212—22no—
355D212—22no—
356D212—42no—
357C4×D53—48no—
358Dic106—28no—
359Dic106—22no—
360Dic106—22no—
361Dic106—42no—
362C8×C53—22no—
363C8×C53C2×#4114yescomplemented
364#88322—22no—
365#88322—22no—
366C2×#3397—531nomaximal, Sylow
367C22×C53—42no—
368C22×C53—42no—
369C22×C53—42no—
370C22×C53—42no—
371C22×C53—42no—
372C22×C53—42no—
373C22×C53—42no—
374C22×C53—42no—
375C22×C53—42no—
376C22×C53—84no—
377C22×C53—84no—
378C22×C53—84no—
379C22×C53#55012yes—
380C22×C53C2×AGL(1,ℤ/8)12yes—
381C22×C53#57712yes—
382C22×C53C23×D411yescharacteristic
383C2×D53—42no—
384C2×D53—42no—
385C2×D53—42no—
386C2×D53—84no—
387C4×C53—22no—
388C4×C53—22no—
389C4×C53—42no—
390C4×C53#55012yes—
391C4×C53C22×#4111yescharacteristic
392C4×C53C2×H(5,𝔽2)11yescharacteristic
393Dic53—22no—
394Dic53—22no—
395Dic53—22no—
396Dic53—42no—
397Dic53—42no—
398Dic53—42no—
399Dic53C2×AGL(1,ℤ/8)14yes—
400C2×#556—531no—
401C2×#550—531no—
402#3397—5316no—
403C2×#496—531no—
404C2×#496D5311yescharacteristic, complemented
405C2×#492—531no—
406C2×#460—531no—
407C2×#460—531no—
408C2×#463—531no—
409C2×#463—531no—
410C2×#461—531no—
411C2×#459—531no—
412C2×#446—531no—
413C2×#440—531no—
414C2×#440—531no—
415C2×C4×D8—531no—
416C2×C53—82no—
417C2×C53—82no—
418C2×C53—82no—
419C2×C53#339714yescomplemented
420C2×C53C2×#55011yescharacteristic
421C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
422C2×C53C2×#57711yescharacteristic
423D53—82no—
424C22×#41—1061no—
425C22×SD16—531no—
426C22×SD16—531no—
427C22×SD16—531no—
428C22×SD16—531no—
429C22×SD16C2×D5311yescharacteristic
430C22×SD16C2×D5311yescharacteristic
431C22×D8—531no—
432C22×D8C2×D5311yescharacteristic
433C22×D8C2×D5311yescharacteristic
434#556—538no—
435#556—1064no—
436#550—538no—
437#550—1064no—
438C2×C4⋊Q8—531no—
439C2×#127—531no—
440C2×#127—531no—
441C2×#127C2×D5311yescharacteristic
442C2×#126—1061no—
443C2×#126—1061no—
444C2×#124—531no—
445C2×#124C2×D5311yescharacteristic
446C2×C22⋊Q8—1061no—
447C2×#121—1061no—
448C2×#121—1061no—
449C2×#121—1061no—
450C2×C4×Q8—531no—
451C2×C4×Q8—531no—
452C2×C4×Q8—531no—
453C2×C4×D4—531no—
454C2×C4×D4—531no—
455C2×C4×D4—531no—
456C2×C4×D4—531no—
457C2×#117—1061no—
458#496—538no—
459#496C2×D5318yescomplemented
460#492—538no—
461#463—538no—
462#463—538no—
463#461—538no—
464#460—538no—
465#460—538no—
466#459—538no—
467#446—538no—
468#440—538no—
469#440—538no—
470C4×D8—538no—
471C2×#107—531no—
472C2×C4⋊C8—531no—
473C2×C4⋊C8—531no—
474C2×C4⋊C8—531no—
475C2×#103—531no—
476C2×#103—531no—
477C2×#102—531no—
478C2×#102—531no—
479C2×#102—531no—
480C2×#102—531no—
481C2×#97—531no—
482C2×#97C2×D5311yescharacteristic
483C2×C4×C8—531no—
484C53C2×#339711yescharacteristic, complemented, Sylow
485C2×#41—1068no—
486C2×#41—2128no—
487C22×Q8—531no—
488C22×Q8—531no—
489C22×Q8C22×D5311yescharacteristic
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—531no—
493C22×D4—1061no—
494C22×D4—1061no—
495C22×D4—1061no—
496C22×D4—1061no—
497C22×D4C22×D5311yescharacteristic
498C22×D4C22×D5311yescharacteristic
499C22×D4C22×D5311yescharacteristic
500C23×C4—1061no—
501C23×C4—1061no—
502C23×C4—1061no—
503C23×C4—1061no—
504C2×SD16—24no—
505C2×SD16—42no—
506C2×SD16—534no—
507C2×SD16—534no—
508C2×SD16—534no—
509C2×SD16—534no—
510C2×SD16—1064no—
511C2×SD16—2122no—
512C2×SD16—2122no—
513C2×SD16—2122no—
514C2×SD16C22×D5314yes—
515C2×SD16C22×D5314yes—
516C2×D8—24no—
517C2×D8—42no—
518C2×D8—534no—
519C2×D8—2122no—
520C2×D8C22×D5314yes—
521C2×D8C22×D5314yes—
522C22×C8—531no—
523C22×C8—531no—
524C22×C8C22×D5311yescharacteristic
525C22×C8C22×D5311yescharacteristic
526C4⋊Q8—534no—
527C4⋊Q8—1062no—
528#127—22no—
529#127—534no—
530#127—534no—
531#127—1062no—
532#127—1062no—
533#127C22×D5314yes—
534#126—1068no—
535#126—1068no—
536#124—22no—
537#124—534no—
538#124—1062no—
539#124C22×D5314yes—
540C22⋊Q8—1068no—
541#121—1068no—
542#121—1068no—
543#121—1068no—
544C4×Q8—534no—
545C4×Q8—534no—
546C4×Q8—534no—
547C4×Q8—534no—
548C4×Q8—1062no—
549C4×Q8—1062no—
550C4×D4—534no—
551C4×D4—534no—
552C4×D4—534no—
553C4×D4—534no—
554C4×D4—1062no—
555C4×D4—1062no—
556C4×D4—1062no—
557C4×D4—1062no—
558#117—1068no—
559C2×C4⋊C4—531no—
560C2×C4⋊C4—531no—
561C2×C4⋊C4—531no—
562C2×C4⋊C4—531no—
563C2×C4⋊C4—531no—
564C2×C4⋊C4—1061no—
565C2×C4⋊C4—1061no—
566C2×C4⋊C4—1061no—
567C2×C4⋊C4—1061no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—1061no—
571C2×C22⋊C4—1061no—
572C2×C22⋊C4—1061no—
573C2×C22⋊C4—1061no—
574C2×C22⋊C4—1061no—
575C2×C22⋊C4—1061no—
576C2×C42—531no—
577C2×C42—531no—
578C2×C42—1061no—
579C2×C42—1061no—
580C2×C42C22×D5311yescharacteristic
581#107—534no—
582C4⋊C8—534no—
583C4⋊C8—534no—
584C4⋊C8—534no—
585#103—534no—
586#103—534no—
587#102—534no—
588#102—534no—
589#102—534no—
590#102—534no—
591#97—534no—
592#97C22×D5314yes—
593C4×C8—534no—
594C24—21no—
595C24—21no—
596C24—21no—
597C24—1061no—
598#41—21232no—
599C2×Q8—21no—
600C2×Q8—22no—
601C2×Q8—22no—
602C2×Q8—534no—
603C2×Q8—532no—
604C2×Q8—1064no—
605C2×Q8—1061no—
606C2×Q8—1062no—
607C2×Q8—1062no—
608C2×Q8C23×D5312yes—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—24no—
613C2×D4—24no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—22no—
620C2×D4—44no—
621C2×D4—82no—
622C2×D4—532no—
623C2×D4—1064no—
624C2×D4—1064no—
625C2×D4—1064no—
626C2×D4—1064no—
627C2×D4—1061no—
628C2×D4—1062no—
629C2×D4—1062no—
630C2×D4—4242no—
631C2×D4—4242no—
632C2×D4—2124no—
633C2×D4—2124no—
634C2×D4C23×D5312yes—
635C2×D4C23×D5312yes—
636C2×D4C23×D5312yes—
637C22×C4—21no—
638C22×C4—531no—
639C22×C4—531no—
640C22×C4—531no—
641C22×C4—531no—
642C22×C4—1064no—
643C22×C4—1064no—
644C22×C4—1064no—
645C22×C4—1061no—
646C22×C4—1061no—
647C22×C4—1061no—
648C22×C4—1064no—
649C22×C4—2124no—
650C22×C4—2124no—
651C22×C4—2124no—
652C22×C4—2124no—
653C22×C4D4×D5311yescharacteristic
654C22×C4D4×D5311yescharacteristic
655C22×C4C23×D5311yescharacteristic
656SD16—28no—
657SD16—44no—
658SD16—1068no—
659SD16—2124no—
660SD16—2124no—
661SD16—2124no—
662D8—28no—
663D8—44no—
664D8—2124no—
665C2×C8—22no—
666C2×C8—532no—
667C2×C8—532no—
668C2×C8—1062no—
669C2×C8—1062no—
670C2×C8#1171994714yescomplemented
671C2×C8C23×D5312yes—
672C2×C8C23×D5312yes—
673C4⋊C4—534no—
674C4⋊C4—534no—
675C4⋊C4—534no—
676C4⋊C4—532no—
677C4⋊C4—532no—
678C4⋊C4—1064no—
679C4⋊C4—1064no—
680C4⋊C4—1064no—
681C4⋊C4—1061no—
682C4⋊C4—1061no—
683C4⋊C4—1064no—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—1064no—
687C22⋊C4—1064no—
688C22⋊C4—1064no—
689C22⋊C4—1064no—
690C22⋊C4—1064no—
691C22⋊C4—1064no—
692C42—532no—
693C42—532no—
694C42—532no—
695C42—532no—
696C42—1064no—
697C42—1064no—
698C42D4×D5312yes—
699C42C23×D5312yes—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—1062no—
713C23—2122no—
714C23—2122no—
715C23—2122no—
716C23C2×D4×D5311yescharacteristic
717Q8—22no—
718Q8—22no—
719Q8—42no—
720Q8—1068no—
721Q8—1062no—
722Q8—1062no—
723Q8—2122no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—22no—
728D4—22no—
729D4—22no—
730D4—48no—
731D4—42no—
732D4—42no—
733D4—42no—
734D4—84no—
735D4—1062no—
736D4—1062no—
737D4—4244no—
738D4—4244no—
739D4—2128no—
740D4—2128no—
741D4—2122no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—42no—
746C2×C4—534no—
747C2×C4—532no—
748C2×C4—532no—
749C2×C4—532no—
750C2×C4—532no—
751C2×C4—1062no—
752C2×C4—1062no—
753C2×C4—1062no—
754C2×C4—1062no—
755C2×C4—1062no—
756C2×C4—1062no—
757C2×C4—2128no—
758C2×C4—2128no—
759C2×C4—2128no—
760C2×C4—2128no—
761C2×C4—2122no—
762C2×C4—2122no—
763C2×C4—2122no—
764C2×C4C2×D4×D5312yes—
765C2×C4C2×D4×D5312yes—
766C2×C4C2×D4×D5311yescharacteristic
767C2×C4C2×#1171994712yes—
768C2×C4#1313326212yes—
769C2×C4C24×D5311yescharacteristic
770C8—22no—
771C8—1062no—
772C8—1062no—
773C8C2×#1171994714yescomplemented
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—84no—
784C22—84no—
785C22—84no—
786C22—4244no—
787C22—2122no—
788C22—2122no—
789C22—2122no—
790C22#1681129312yes—
791C22AGL(1,ℤ/8)×D5312yes—
792C22#1681143312yes—
793C22C22×D4×D5311yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—534no—
798C4—1062no—
799C4—1062no—
800C4—1062no—
801C4—2122no—
802C4—2122no—
803C4—2122no—
804C4#1681129312yes—
805C4C22×#1171994711yescharacteristic
806C4C2×#1313326211yescharacteristic
807C2—82no—
808C2—82no—
809C2—82no—
810C2—4242no—
811C2#2028773214yesdirect product factor
812C2C2×#1681129311yescharacteristic
813C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
814C2C2×#1681143311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#496C2
socleC23×C53C22×D4
hypercenterC2×#496D53
hypocenterC53C2×#3397
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×#16811342C2semidirect
2. C2×#16811293C2semidirect
3. #20287732C2direct (N × H)
4. C2×#16811011C2semidirect
5. C2×#16810994C2semidirect
6. C2×#16810821C2semidirect
7. C2×#16810820C2semidirect
8. C2×#16810836C2semidirect
9. C2×#16810835C2semidirect
10. C2×#16810826C2semidirect
11. C2×#16810816C2semidirect
12. C2×#16810751C2semidirect
13. C2×#16810725C2semidirect
14. C2×#16810724C2semidirect
15. C2×D8×Dic53C2semidirect
16. C2×C53×#496C2semidirect
24. #16811342C22semidirect
26. #16811293C22semidirect
45. #16811011C22semidirect
46. #16810994C22semidirect
47. #16810836C22semidirect
48. #16810835C22semidirect
49. #16810826C22semidirect
50. #16810821C22semidirect
51. #16810820C22semidirect
52. #16810816C22semidirect
53. #16810751C22semidirect
54. #16810725C22semidirect
55. #16810724C22semidirect
56. D8×Dic53C22semidirect
75. C53×#496C22semidirect
253. C2×C8×C53#41semidirect
363. C8×C53C2×#41semidirect
404. C2×#496D53semidirect
419. C2×C53#3397semidirect
459. #496C2×D53semidirect
484. C53C2×#3397semidirect
670. C2×C8#11719947semidirect
773. C8C2×#11719947semidirect
811. C2#20287732direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113422
C2×#168112932
#202877322
C2×#168110112
C2×#168109942
C2×#168108212
C2×#168108202
C2×#168108362
C2×#168108352
C2×#168108262
C2×#168108162
C2×#168107512
C2×#168107252
C2×#168107242
C2×D8×Dic532
C2×C53×#4962
C2×#339753