Finite Group Databasebeta

← C2×#20286704 #28260664

Subgroups — C2×#20286704 #28260664

Order 13568.

2374 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811279C211yesmaximal, characteristic, complemented
2C2×#16811274C211yesmaximal, characteristic, complemented
3#20286704C2116yesmaximal, direct product factor
4C2×#16810981C211yesmaximal, characteristic, complemented
5C2×#16810960C211yesmaximal, characteristic, complemented
6C2×#16810917C211yesmaximal, characteristic, complemented
7C2×#16810870C211yesmaximal, characteristic, complemented
8C2×#16810857C211yesmaximal, characteristic, complemented
9C2×#16810837C211yesmaximal, characteristic, complemented
10C2×#16810769C211yesmaximal, characteristic, complemented
11C2×#16810764C211yesmaximal, characteristic, complemented
12C2×#16810722C211yesmaximal, characteristic, complemented
13C2×#16810691C211yesmaximal, characteristic, complemented
14C2×#16810621C211yesmaximal, characteristic, complemented
15C22×#13133140C211yesmaximal, characteristic, complemented
16C2×C53×#480C211yesmaximal, characteristic, complemented
17C22×#11719945—21no—
18C22×#11719947C2211yescharacteristic
19C23×Dic106C2211yescharacteristic
20C22×#11719913C2211yescharacteristic
21C22×#11719913C2211yescharacteristic
22C22×#11719922C2211yescharacteristic
23C22×#11719912C2211yescharacteristic
24C23×#88322C2211yescharacteristic
25#16811279—24no—
26#16811279C2218yescomplemented
27#16811274—24no—
28#16811274C2218yescomplemented
29C2×#13133216C2211yescharacteristic
30C2×#13133204C2211yescharacteristic
31C2×#13133203—21no—
32C2×#13133202—21no—
33C2×#13133200—21no—
34C2×#13133197C2211yescharacteristic
35C2×#13133195—21no—
36C2×#13133194—21no—
37C2×#13133192C2211yescharacteristic
38C2×#13133191C2211yescharacteristic
39C2×#13133189—21no—
40C2×#13133182C2211yescharacteristic
41C2×D4×Dic53—21no—
42C2×#13133179C2211yescharacteristic
43C2×C4×C22⋊D53C2211yescharacteristic
44C2×C4⋊C4×D53C2211yescharacteristic
45#16810981C2218yescomplemented
46#16810960C2218yescomplemented
47#16810917C2218yescomplemented
48#16810870C2218yescomplemented
49#16810857C2218yescomplemented
50#16810837C2218yescomplemented
51#16810769C2218yescomplemented
52#16810764C2218yescomplemented
53#16810722C2218yescomplemented
54#16810691C2218yescomplemented
55C2×#13133150C2211yescharacteristic
56C2×#13133146C2211yescharacteristic
57#16810621C2218yescomplemented
58C2×#13133142C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133140C2211yescharacteristic
61C2×#13133140C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133140C2218yescomplemented
65C2×#13133138C2211yescharacteristic
66C2×#13133137C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133127C2211yescharacteristic
69C2×#121×C53C2211yescharacteristic
70C22×C4⋊C4×C53C2211yescharacteristic
71C53×#480C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#107×C53C2211yescharacteristic
74C2×#102×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C2×#11719945—28no—
78C2×#11719945—48no—
79C2×#11719947—22no—
80C2×#11719947—24no—
81C2×#11719947—42no—
82C2×#11719947C2314yes—
83C22×Dic106—24no—
84C22×Dic106—22no—
85C22×Dic106—21no—
86C22×Dic106—21no—
87C22×Dic106—42no—
88C22×Dic106C2311yescharacteristic
89C22×Dic106C2314yes—
90C22×Dic106C2311yescharacteristic
91C22×D212—21no—
92C22×D212C2311yescharacteristic
93C22×C22⋊D53—21no—
94C22×C22⋊D53—21no—
95C22×C22⋊D53D411yescharacteristic
96C23×Dic53—21no—
97C23×Dic53—21no—
98C22×C4×D53—21no—
99C22×C4×D53—21no—
100C22×C4×D53C2311yescharacteristic
101C2×#11719913—24no—
102C2×#11719913—42no—
103C2×#11719913C2314yes—
104C2×#11719913C2314yes—
105C2×#11719922—42no—
106C2×#11719922C2314yes—
107C2×#11719912—42no—
108C2×#11719912C2314yes—
109C22×#88322—42no—
110C22×#88322C2311yescharacteristic
111C22×#88322C2311yescharacteristic
112C22×#88322C2314yes—
113#13133216—22no—
114#13133216C2314yes—
115#13133204—22no—
116#13133204C2314yes—
117#13133203—28no—
118#13133202—28no—
119#13133200—28no—
120#13133197—22no—
121#13133197C2314yes—
122#13133195—28no—
123#13133194—28no—
124#13133192—22no—
125#13133192C2314yes—
126#13133191—22no—
127#13133191C2314yes—
128#13133189—28no—
129#13133182—22no—
130#13133182C2314yes—
131D4×Dic53—28no—
132#13133179—22no—
133#13133179C2314yes—
134C4×C22⋊D53D414yes—
135C4×C22⋊D53C2314yes—
136C2×C4⋊Dic53—21no—
137C2×C4⋊Dic53C2311yescharacteristic
138C2×#11719919—21no—
139C2×#11719919—21no—
140C2×#11719919—21no—
141C2×#11719919D411yescharacteristic
142C4⋊C4×D53—22no—
143C4⋊C4×D53C2314yes—
144C2×C22⋊Dic53—21no—
145C2×C22⋊Dic53—21no—
146C2×C22⋊Dic53D411yescharacteristic
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×#11719921—21no—
150C2×#11719921—21no—
151C2×#11719921D411yescharacteristic
152C2×C4×Dic53—21no—
153C2×C4×Dic53C2311yescharacteristic
154#13133150C2314yes—
155#13133146C2314yes—
156#13133142C2314yes—
157#13133142C2314yes—
158#13133140C2314yes—
159#13133140C2314yes—
160#13133140C2314yes—
161#13133140C2314yes—
162#13133138C2314yes—
163#13133137C2314yes—
164#13133129C2314yes—
165#13133127C2314yes—
166C22×D4×C53—21no—
167C22×D4×C53C2311yescharacteristic
168C23×C4×C53—21no—
169C23×C4×C53C2311yescharacteristic
170C22×C8×C53C2311yescharacteristic
171C22×C8×C53C2311yescharacteristic
172#121×C53—22no—
173#121×C53C2314yes—
174C2×C4⋊C4×C53—22no—
175C2×C4⋊C4×C53—21no—
176C2×C4⋊C4×C53C2314yes—
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C4⋊C4×C53C2311yescharacteristic
179C2×C4⋊C4×C53C2311yescharacteristic
180C2×C22⋊C4×C53—21no—
181#107×C53C2314yes—
182#107×C53C2314yes—
183#102×C53C2314yes—
184#102×C53C2314yes—
185C22⋊C8×C53C2314yes—
186C24×C53—21no—
187C24×C53C2×D411yescharacteristic
188C23×D53—21no—
189C23×D53C2×D411yescharacteristic
190C2×D4×C53—24no—
191C2×D4×C53—21no—
192C2×D4×C53—22no—
193C2×D4×C53—22no—
194C2×D4×C53—44no—
195C2×D4×C53C2412yes—
196C22×C4×C53—22no—
197C22×C4×C53—22no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—24no—
202C22×C4×C53—44no—
203C22×C4×C53C2×D411yescharacteristic
204C22×C4×C53C2×D412yes—
205C22×C4×C53C2412yes—
206C22×C4×C53C2411yescharacteristic
207C2×C22⋊D53—24no—
208C2×C22⋊D53—24no—
209C2×C22⋊D53—24no—
210C2×C22⋊D53—44no—
211C2×C22⋊D53—44no—
212C2×C22⋊D53C2×D414yes—
213C22×Dic53—21no—
214C22×Dic53—21no—
215C22×Dic53—21no—
216C22×Dic53—24no—
217C22×Dic53—24no—
218C22×Dic53—44no—
219C22×Dic53—44no—
220C22×Dic53C2×D411yescharacteristic
221C22×Dic53C2×D411yescharacteristic
222C22×Dic53C2×D411yescharacteristic
223#11719947—28no—
224#11719947—44no—
225#11719947—48no—
226#11719945—432no—
227C2×D212—22no—
228C2×D212—22no—
229C2×D212—24no—
230C2×D212—21no—
231C2×D212—44no—
232C2×D212C2412yes—
233C2×C4×D53—22no—
234C2×C4×D53—22no—
235C2×C4×D53—24no—
236C2×C4×D53—24no—
237C2×C4×D53—44no—
238C2×C4×D53—44no—
239C2×C4×D53C2×D412yes—
240C2×C4×D53C2412yes—
241C2×Dic106—21no—
242C2×Dic106—22no—
243C2×Dic106—22no—
244C2×Dic106—22no—
245C2×Dic106—28no—
246C2×Dic106—24no—
247C2×Dic106—21no—
248C2×Dic106—24no—
249C2×Dic106—44no—
250C2×Dic106—48no—
251C2×Dic106—44no—
252C2×Dic106—44no—
253C2×Dic106#4114yescomplemented
254C2×Dic106C2412yes—
255C2×Dic106C2412yes—
256C2×C8×C53—22no—
257C2×C8×C53—22no—
258C2×C8×C53C2412yes—
259C2×C8×C53C2412yes—
260C4⋊C4×C53—21no—
261C4⋊C4×C53—21no—
262C4⋊C4×C53—24no—
263C4⋊C4×C53—21no—
264C4⋊C4×C53C2412yes—
265C4⋊C4×C53C2412yes—
266C4⋊C4×C53C2412yes—
267C22⋊C4×C53—24no—
268C22⋊Dic53—24no—
269C22⋊Dic53—24no—
270C22⋊Dic53C2×D414yes—
271#11719922—44no—
272#11719921—24no—
273#11719921—24no—
274#11719921—24no—
275#11719921—24no—
276#11719921C2×D414yes—
277C4⋊Dic53—21no—
278C4⋊Dic53—24no—
279C4⋊Dic53C2412yes—
280#11719919—24no—
281#11719919—24no—
282#11719919—24no—
283#11719919C2×D414yes—
284C4×Dic53—24no—
285C4×Dic53C2×D412yes—
286C4×Dic53C2412yes—
287C2×#88322—22no—
288C2×#88322—22no—
289C2×#88322—44no—
290C2×#88322C2412yes—
291C2×#88322C2412yes—
292#11719913—28no—
293#11719913—44no—
294#11719912—44no—
295C23×C53—22no—
296C23×C53—22no—
297C23×C53—22no—
298C23×C53—42no—
299C23×C53—42no—
300C23×C53—42no—
301C23×C53AGL(1,ℤ/8)14yes—
302C23×C53C22×D412yes—
303C23×C53C22×D411yescharacteristic
304C22×D53—22no—
305C22×D53—22no—
306C22×D53—22no—
307C22×D53—22no—
308C22×D53—42no—
309C22×D53—42no—
310C22×D53—42no—
311C22×D53C22×D412yes—
312D4×C53—22no—
313D4×C53—22no—
314D4×C53—48no—
315D4×C53—42no—
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—42no—
324C2×C4×C53—42no—
325C2×C4×C53—48no—
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—28no—
333C22⋊D53—48no—
334C22⋊D53—48no—
335C2×Dic53—24no—
336C2×Dic53—22no—
337C2×Dic53—22no—
338C2×Dic53—22no—
339C2×Dic53—22no—
340C2×Dic53—22no—
341C2×Dic53—22no—
342C2×Dic53—48no—
343C2×Dic53—48no—
344C2×Dic53—42no—
345C2×Dic53—42no—
346C2×Dic53C22×D412yes—
347C2×Dic53C22×D412yes—
348C2×Dic53C22×D412yes—
349D212—22no—
350D212—22no—
351D212—48no—
352D212—42no—
353C4×D53—24no—
354C4×D53—22no—
355C4×D53—22no—
356C4×D53—48no—
357C4×D53—48no—
358Dic106—24no—
359Dic106—22no—
360Dic106—22no—
361Dic106—22no—
362Dic106—48no—
363Dic106—48no—
364Dic106—42no—
365Dic106C2×#4114yescomplemented
366C8×C53—22no—
367C8×C53—22no—
368#88322—22no—
369#88322—22no—
370C2×#3308—531nomaximal, Sylow
371C22×C53—22no—
372C22×C53—28no—
373C22×C53—22no—
374C22×C53—42no—
375C22×C53—42no—
376C22×C53—42no—
377C22×C53—84no—
378C22×C53#54612yes—
379C22×C53C2×AGL(1,ℤ/8)14yes—
380C22×C53C2×AGL(1,ℤ/8)12yes—
381C22×C53#57812yes—
382C22×C53C23×D411yescharacteristic
383C2×D53—22no—
384C2×D53—22no—
385C2×D53—22no—
386C2×D53—44no—
387C2×D53—42no—
388C2×D53—42no—
389C2×D53—42no—
390C2×D53—84no—
391C4×C53—22no—
392C4×C53—42no—
393C4×C53—42no—
394C4×C53—42no—
395C4×C53#54612yes—
396C4×C53C22×#4111yescharacteristic
397C4×C53C2×H(5,𝔽2)11yescharacteristic
398Dic53—24no—
399Dic53—22no—
400Dic53—22no—
401Dic53—22no—
402Dic53—42no—
403Dic53—42no—
404C2×#548—531no—
405C2×#547—531no—
406#3308—5316no—
407C2×#489—531no—
408C2×#484—531no—
409C2×#480D5311yescharacteristic, complemented
410C2×#477—531no—
411C2×#468—531no—
412C2×#466—531no—
413C2×#463—531no—
414C2×#449—531no—
415C2×#448—531no—
416C2×#440—531no—
417C2×#435—531no—
418C2×#417—531no—
419C22×#103—531no—
420C2×C53—24no—
421C2×C53—82no—
422C2×C53#330814yescomplemented
423C2×C53C2×#54611yescharacteristic
424C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
425C2×C53C2×#57811yescharacteristic
426D53—42no—
427D53—82no—
428C22×#41—531no—
429C22×#41—1061no—
430C23×Q8—531no—
431C22×SD16—531no—
432C22×SD16—531no—
433C22×D8—531no—
434C22×M16—531no—
435C23×C8—531no—
436#548—538no—
437#548—1064no—
438#547—538no—
439#547—1064no—
440C2×C4⋊Q8—531no—
441C2×#124—531no—
442C2×#124—1061no—
443C2×#123—1061no—
444C2×#123—1061no—
445C2×C22⋊Q8—531no—
446C2×C22⋊Q8—1061no—
447C2×C22⋊Q8—1061no—
448C2×#121—531no—
449C2×#121—531no—
450C2×#121—1061no—
451C2×#121C2×D5311yescharacteristic
452C2×C4×Q8—531no—
453C2×C4×D4—531no—
454C2×C4×D4—531no—
455C2×C4×D4—1061no—
456C22×C4⋊C4—531no—
457C22×C4⋊C4C2×D5311yescharacteristic
458#489—538no—
459#484—538no—
460#480C2×D5318yescomplemented
461#477—538no—
462#468—538no—
463#466—538no—
464#463—538no—
465#449—538no—
466#448—538no—
467#440—538no—
468#435—538no—
469C2×#107—531no—
470C2×#107C2×D5311yescharacteristic
471C2×#107C2×D5311yescharacteristic
472C2×C4⋊C8—531no—
473#417—538no—
474C2×#103—531no—
475C2×#103—531no—
476C2×#103—531no—
477C2×#103—531no—
478C2×#103—531no—
479C2×#103—531no—
480C2×#103—538no—
481C2×#102—531no—
482C2×#102—531no—
483C2×#102C2×D5311yescharacteristic
484C2×#102C2×D5311yescharacteristic
485C2×C22⋊C8—531no—
486C2×C22⋊C8C2×D5311yescharacteristic
487C2×#97—531no—
488C53C2×#330811yescharacteristic, complemented, Sylow
489C2×#41—534no—
490C2×#41—1068no—
491C2×#41—1062no—
492C2×#41—1064no—
493C2×#41—2128no—
494C2×#41—2122no—
495C22×Q8—531no—
496C22×Q8—531no—
497C22×Q8—534no—
498C22×Q8—1061no—
499C22×Q8—1064no—
500C22×Q8—1061no—
501C22×Q8—1062no—
502C22×Q8—2122no—
503C22×D4—21no—
504C22×D4—531no—
505C22×D4—531no—
506C22×D4—1061no—
507C22×D4—1061no—
508C22×D4—1061no—
509C22×D4C22×D5311yescharacteristic
510C23×C4—21no—
511C23×C4—531no—
512C23×C4—1061no—
513C23×C4—1061no—
514C23×C4—1061no—
515C23×C4—1061no—
516C23×C4C22×D5311yescharacteristic
517C2×SD16—534no—
518C2×SD16—534no—
519C2×SD16—1064no—
520C2×SD16—2122no—
521C2×D8—534no—
522C2×D8—2122no—
523C2×M16—534no—
524C2×M16—2122no—
525C22×C8—531no—
526C22×C8—531no—
527C22×C8—534no—
528C22×C8—2122no—
529C22×C8C22×D5311yescharacteristic
530C22×C8C22×D5311yescharacteristic
531C4⋊Q8—534no—
532C4⋊Q8—1062no—
533#124—534no—
534#124—1062no—
535#124—1068no—
536#123—1068no—
537#123—1068no—
538C22⋊Q8—534no—
539C22⋊Q8—1068no—
540C22⋊Q8—1068no—
541C22⋊Q8—1062no—
542#121—22no—
543#121—534no—
544#121—534no—
545#121—1062no—
546#121—1068no—
547#121—1062no—
548#121C22×D5314yes—
549C4×Q8—534no—
550C4×Q8—1062no—
551C4×D4—534no—
552C4×D4—534no—
553C4×D4—534no—
554C4×D4—1062no—
555C4×D4—1068no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—531no—
559C2×C4⋊C4—531no—
560C2×C4⋊C4—534no—
561C2×C4⋊C4—1062no—
562C2×C4⋊C4—1061no—
563C2×C4⋊C4—1061no—
564C2×C4⋊C4—1061no—
565C2×C4⋊C4—1061no—
566C2×C4⋊C4C22×D5311yescharacteristic
567C2×C4⋊C4C22×D5311yescharacteristic
568C2×C4⋊C4C22×D5314yes—
569C2×C4⋊C4C22×D5311yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—531no—
572C2×C22⋊C4—531no—
573C2×C22⋊C4—1061no—
574C2×C22⋊C4—1061no—
575C2×C22⋊C4—1061no—
576C2×C22⋊C4—1061no—
577C2×C22⋊C4—1061no—
578C2×C22⋊C4—1061no—
579C2×C42—531no—
580C2×C42—1061no—
581#107—534no—
582#107C22×D5314yes—
583#107C22×D5314yes—
584C4⋊C8—534no—
585#103—534no—
586#103—534no—
587#103—534no—
588#103—534no—
589#103—534no—
590#103—534no—
591#102—534no—
592#102—534no—
593#102C22×D5314yes—
594#102C22×D5314yes—
595C22⋊C8—534no—
596C22⋊C8C22×D5314yes—
597#97—534no—
598C24—21no—
599C24—531no—
600C24—1061no—
601C24D4×D5311yescharacteristic
602#41—1068no—
603#41—21232no—
604#41—2124no—
605#41—2128no—
606C2×Q8—534no—
607C2×Q8—532no—
608C2×Q8—532no—
609C2×Q8—1064no—
610C2×Q8—1068no—
611C2×Q8—1061no—
612C2×Q8—1064no—
613C2×Q8—1061no—
614C2×Q8—1062no—
615C2×Q8—1062no—
616C2×Q8—1062no—
617C2×Q8—2124no—
618C2×Q8—2124no—
619C2×Q8—2128no—
620C2×Q8—2124no—
621C2×D4—24no—
622C2×D4—21no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—44no—
626C2×D4—534no—
627C2×D4—532no—
628C2×D4—1064no—
629C2×D4—1064no—
630C2×D4—1064no—
631C2×D4—1064no—
632C2×D4—1061no—
633C2×D4—1062no—
634C2×D4—1062no—
635C2×D4—2124no—
636C2×D4—2124no—
637C2×D4—2124no—
638C2×D4C23×D5312yes—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—24no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—44no—
646C22×C4—531no—
647C22×C4—531no—
648C22×C4—531no—
649C22×C4—532no—
650C22×C4—532no—
651C22×C4—1064no—
652C22×C4—1064no—
653C22×C4—1064no—
654C22×C4—1061no—
655C22×C4—1062no—
656C22×C4—1062no—
657C22×C4—1064no—
658C22×C4—1061no—
659C22×C4—1061no—
660C22×C4—2124no—
661C22×C4—2124no—
662C22×C4—2124no—
663C22×C4—2124no—
664C22×C4D4×D5312yes—
665C22×C4D4×D5311yescharacteristic
666C22×C4C23×D5312yes—
667C22×C4C23×D5311yescharacteristic
668SD16—1068no—
669SD16—2124no—
670D8—2124no—
671M16—2124no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—532no—
675C2×C8—532no—
676C2×C8—1062no—
677C2×C8—1062no—
678C2×C8—2124no—
679C2×C8C23×D5312yes—
680C2×C8C23×D5312yes—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—24no—
684C4⋊C4—21no—
685C4⋊C4—534no—
686C4⋊C4—532no—
687C4⋊C4—1064no—
688C4⋊C4—1064no—
689C4⋊C4—1064no—
690C4⋊C4—1064no—
691C4⋊C4—1061no—
692C4⋊C4C23×D5312yes—
693C4⋊C4C23×D5312yes—
694C4⋊C4C23×D5312yes—
695C22⋊C4—24no—
696C22⋊C4—534no—
697C22⋊C4—534no—
698C22⋊C4—1064no—
699C22⋊C4—1064no—
700C22⋊C4—1064no—
701C22⋊C4—1064no—
702C22⋊C4—1064no—
703C22⋊C4—1064no—
704C42—532no—
705C42—532no—
706C42—1064no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—532no—
714C23—1062no—
715C23—1062no—
716C23—1062no—
717C23—1062no—
718C23—2122no—
719C23—2122no—
720C23—2122no—
721C23#1313324114yes—
722C23C2×D4×D5312yes—
723C23C2×D4×D5311yescharacteristic
724Q8—534no—
725Q8—1064no—
726Q8—1062no—
727Q8—1062no—
728Q8—1062no—
729Q8—2128no—
730Q8—2128no—
731Q8—2122no—
732D4—22no—
733D4—22no—
734D4—48no—
735D4—42no—
736D4—1068no—
737D4—1062no—
738D4—1062no—
739D4—2128no—
740D4—2128no—
741D4—2128no—
742D4—2122no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—48no—
753C2×C4—42no—
754C2×C4—532no—
755C2×C4—532no—
756C2×C4—532no—
757C2×C4—1062no—
758C2×C4—1064no—
759C2×C4—1062no—
760C2×C4—1062no—
761C2×C4—1062no—
762C2×C4—1064no—
763C2×C4—1062no—
764C2×C4—1062no—
765C2×C4—1062no—
766C2×C4—1062no—
767C2×C4—2128no—
768C2×C4—2128no—
769C2×C4—2128no—
770C2×C4—2128no—
771C2×C4—2122no—
772C2×C4—2122no—
773C2×C4C2×D4×D5312yes—
774C2×C4C2×D4×D5311yescharacteristic
775C2×C4#41×D5312yes—
776C2×C4#1313326312yes—
777C2×C4C24×D5311yescharacteristic
778C8—22no—
779C8—22no—
780C8—1062no—
781C8—1062no—
782C22—22no—
783C22—22no—
784C22—28no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—84no—
789C22—1062no—
790C22—1062no—
791C22—1062no—
792C22—4244no—
793C22—2122no—
794C22—2122no—
795C22—2122no—
796C22—2124no—
797C22#1681126512yes—
798C22C2×#1313324114yes—
799C22C2×#1313324112yes—
800C22#1681143912yes—
801C22C22×D4×D5311yescharacteristic
802C4—22no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—1062no—
807C4—1064no—
808C4—1062no—
809C4—1062no—
810C4—2122no—
811C4—2122no—
812C4#1681126512yes—
813C4C2×#41×D5311yescharacteristic
814C4C2×#1313326311yescharacteristic
815C2—24no—
816C2—82no—
817C2—4242no—
818C2—2122no—
819C2#2028670414yesdirect product factor
820C2C2×#1681126511yescharacteristic
821C2C22×#1313324111yescharacteristic
822C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#480C2
socleC23×C53C22×D4
hypercenterC2×#480D53
hypocenterC53C2×#3308
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×#16811279C2semidirect
2. C2×#16811274C2semidirect
3. #20286704C2direct (N × H)
4. C2×#16810981C2semidirect
5. C2×#16810960C2semidirect
6. C2×#16810917C2semidirect
7. C2×#16810870C2semidirect
8. C2×#16810857C2semidirect
9. C2×#16810837C2semidirect
10. C2×#16810769C2semidirect
11. C2×#16810764C2semidirect
12. C2×#16810722C2semidirect
13. C2×#16810691C2semidirect
14. C2×#16810621C2semidirect
15. C22×#13133140C2semidirect
16. C2×C53×#480C2semidirect
26. #16811279C22semidirect
28. #16811274C22semidirect
45. #16810981C22semidirect
46. #16810960C22semidirect
47. #16810917C22semidirect
48. #16810870C22semidirect
49. #16810857C22semidirect
50. #16810837C22semidirect
51. #16810769C22semidirect
52. #16810764C22semidirect
53. #16810722C22semidirect
54. #16810691C22semidirect
57. #16810621C22semidirect
64. C2×#13133140C22semidirect
71. C53×#480C22semidirect
253. C2×Dic106#41semidirect
365. Dic106C2×#41semidirect
409. C2×#480D53semidirect
422. C2×C53#3308semidirect
460. #480C2×D53semidirect
488. C53C2×#3308semidirect
819. C2#20286704direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112792
C2×#168112742
#202867042
C2×#168109812
C2×#168109602
C2×#168109172
C2×#168108702
C2×#168108572
C2×#168108372
C2×#168107692
C2×#168107642
C2×#168107222
C2×#168106912
C2×#168106212
C22×#131331402
C2×C53×#4802
C2×#330853