Finite Group Databasebeta

← C2×#20286366 #28259244

Subgroups — C2×#20286366 #28259244

Order 13568.

2762 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133249C211yesmaximal, characteristic, complemented
2C2×#16811284C211yesmaximal, characteristic, complemented
3C2×#16811280C211yesmaximal, characteristic, complemented
4#20286366C2116yesmaximal, direct product factor
5C2×#16811004C211yesmaximal, characteristic, complemented
6C2×#16810869C211yesmaximal, characteristic, complemented
7C2×#16810866C211yesmaximal, characteristic, complemented
8C2×#16810847C211yesmaximal, characteristic, complemented
9C2×#16810843C211yesmaximal, characteristic, complemented
10C2×#16810768C211yesmaximal, characteristic, complemented
11C2×#16810767C211yesmaximal, characteristic, complemented
12C2×#16810779C211yesmaximal, characteristic, complemented
13C2×#16810777C211yesmaximal, characteristic, complemented
14C2×Q16×Dic53C211yesmaximal, characteristic, complemented
15C2×#16810699C211yesmaximal, characteristic, complemented
16C22×#137×C53C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×Q8×D53C2211yescharacteristic
19C2×#13133249—28no—
20C2×#13133249C2218yescomplemented
21C22×#11719925C2211yescharacteristic
22C22×#11719925C2211yescharacteristic
23C22×#11719913C2211yescharacteristic
24C22×#11719924C2211yescharacteristic
25C22×#11719922C2211yescharacteristic
26C22×#11719912C2211yescharacteristic
27#16811284—24no—
28#16811284C2218yescomplemented
29#16811280—24no—
30#16811280C2218yescomplemented
31C2×#13133206—21no—
32C2×#13133206C2211yescharacteristic
33C2×#13133204—21no—
34C2×#13133204C2211yescharacteristic
35C2×#13133196—21no—
36C2×#13133196C2211yescharacteristic
37C2×#13133193—21no—
38C2×#13133193C2211yescharacteristic
39C2×#13133191—21no—
40C2×#13133191C2211yescharacteristic
41C2×#13133188—21no—
42C2×#13133188C2211yescharacteristic
43C2×Q8×Dic53C2211yescharacteristic
44C2×Q8×Dic53C2211yescharacteristic
45C2×C4×C22⋊D53—21no—
46C2×C4×C22⋊D53—21no—
47C2×C4×C22⋊D53C2211yescharacteristic
48#16811004C2218yescomplemented
49#16810869C2218yescomplemented
50#16810866C2218yescomplemented
51#16810847C2218yescomplemented
52#16810843C2218yescomplemented
53#16810779C2218yescomplemented
54#16810777C2218yescomplemented
55#16810768C2218yescomplemented
56#16810767C2218yescomplemented
57Q16×Dic53C2218yescomplemented
58#16810699C2218yescomplemented
59C2×#13133151C2211yescharacteristic
60C2×#13133146C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133141C2211yescharacteristic
64C2×#13133141C2211yescharacteristic
65C2×#13133139C2211yescharacteristic
66C2×#13133138C2211yescharacteristic
67C2×C22⋊#88322C2211yescharacteristic
68C2×#13133129C2211yescharacteristic
69C2×C8×Dic53C2211yescharacteristic
70C22×#41×C53C2211yescharacteristic
71C23×Q8×C53C2211yescharacteristic
72C2×#137×C53—28no—
73C2×#137×C53C2218yescomplemented
74C22×Q16×C53C2211yescharacteristic
75C22×Q16×C53C2211yescharacteristic
76C22×SD16×C53C2211yescharacteristic
77C22×SD16×C53C2211yescharacteristic
78C22×M16×C53C2211yescharacteristic
79C2×#11719949—22no—
80C2×#11719949—24no—
81C2×#11719949—42no—
82C2×#11719949C2314yes—
83C22×Dic106—21no—
84C22×Dic106C2311yescharacteristic
85C2×Q8×D53—22no—
86C2×Q8×D53—24no—
87C2×Q8×D53—42no—
88C2×Q8×D53C2314yes—
89C22×D212—21no—
90C22×D212C2311yescharacteristic
91C22×C22⋊D53—21no—
92C22×C22⋊D53—21no—
93C22×C22⋊D53D411yescharacteristic
94C22×C4×D53—21no—
95C22×C4×D53—21no—
96C22×C4×D53C2311yescharacteristic
97#13133249—232no—
98C2×#11719925—24no—
99C2×#11719925—42no—
100C2×#11719925C2314yes—
101C2×#11719925C2314yes—
102C2×#11719913—24no—
103C2×#11719913C2314yes—
104C2×#11719924—24no—
105C2×#11719924C2314yes—
106C2×#11719922—42no—
107C2×#11719922C2314yes—
108C2×#11719912—24no—
109C2×#11719912C2314yes—
110C22×#88322C2311yescharacteristic
111C22×#88322C2311yescharacteristic
112#13133206—28no—
113#13133206—22no—
114#13133206C2314yes—
115#13133204—28no—
116#13133204—22no—
117#13133204C2314yes—
118#13133196—28no—
119#13133196—22no—
120#13133196C2314yes—
121#13133193—28no—
122#13133193—22no—
123#13133193C2314yes—
124#13133191—22no—
125#13133191—28no—
126#13133191C2314yes—
127#13133188—28no—
128#13133188—22no—
129#13133188C2314yes—
130Q8×Dic53—22no—
131Q8×Dic53—22no—
132Q8×Dic53C2314yes—
133Q8×Dic53C2314yes—
134C4×C22⋊D53—28no—
135C4×C22⋊D53—28no—
136C4×C22⋊D53D414yes—
137C4×C22⋊D53C2314yes—
138C2×C4⋊Dic53—21no—
139C2×C4⋊Dic53—21no—
140C2×C4⋊Dic53C2311yescharacteristic
141C2×C4⋊Dic53C2311yescharacteristic
142C2×#11719919—21no—
143C2×#11719919—21no—
144C2×#11719919D411yescharacteristic
145C2×C22⋊Dic53—21no—
146C2×C22⋊Dic53—21no—
147C2×C22⋊Dic53—21no—
148C2×C22⋊Dic53—21no—
149C2×C22⋊Dic53D411yescharacteristic
150C2×#11719921—21no—
151C2×#11719921—21no—
152C2×#11719921—21no—
153C2×#11719921—21no—
154C2×#11719921D411yescharacteristic
155C2×C4×Dic53—21no—
156C2×C4×Dic53—21no—
157C2×C4×Dic53C2311yescharacteristic
158#13133151C2314yes—
159#13133146C2314yes—
160#13133142C2314yes—
161#13133141C2314yes—
162#13133141C2314yes—
163#13133141C2314yes—
164#13133139C2314yes—
165#13133138C2314yes—
166C22⋊#88322C2314yes—
167#13133129C2314yes—
168C8×Dic53C2314yes—
169C2×#41×C53—22no—
170C2×#41×C53—24no—
171C2×#41×C53—42no—
172C2×#41×C53C2314yes—
173C22×Q8×C53—22no—
174C22×Q8×C53—21no—
175C22×Q8×C53—24no—
176C22×Q8×C53—42no—
177C22×Q8×C53C2311yescharacteristic
178C22×Q8×C53C2314yes—
179C22×Q8×C53C2311yescharacteristic
180C22×Q8×C53C2311yescharacteristic
181C22×D4×C53—21no—
182C22×D4×C53C2311yescharacteristic
183C23×C4×C53—21no—
184C23×C4×C53—21no—
185C23×C4×C53C2311yescharacteristic
186#137×C53—232no—
187C2×Q16×C53—24no—
188C2×Q16×C53D418yescomplemented
189C2×Q16×C53C2314yes—
190C2×Q16×C53C2314yes—
191C2×SD16×C53—24no—
192C2×SD16×C53—24no—
193C2×SD16×C53C2314yes—
194C2×SD16×C53C2314yes—
195C2×M16×C53—24no—
196C2×M16×C53C2314yes—
197C22×C8×C53C2311yescharacteristic
198C22×C8×C53C2311yescharacteristic
199C24×C53—21no—
200C24×C53C2×D411yescharacteristic
201C23×D53—21no—
202C23×D53C2×D411yescharacteristic
203#41×C53—28no—
204#41×C53—44no—
205#41×C53—48no—
206C2×Q8×C53—21no—
207C2×Q8×C53—21no—
208C2×Q8×C53—24no—
209C2×Q8×C53—21no—
210C2×Q8×C53—22no—
211C2×Q8×C53—22no—
212C2×Q8×C53—28no—
213C2×Q8×C53—22no—
214C2×Q8×C53—22no—
215C2×Q8×C53—44no—
216C2×Q8×C53—44no—
217C2×Q8×C53—48no—
218C2×Q8×C53C2×D414yes—
219C2×Q8×C53C2×D414yes—
220C2×Q8×C53C2412yes—
221C2×Q8×C53C2412yes—
222C2×Q8×C53C2412yes—
223C2×D4×C53—24no—
224C2×D4×C53—22no—
225C2×D4×C53—21no—
226C2×D4×C53—22no—
227C2×D4×C53—44no—
228C2×D4×C53C2412yes—
229C22×C4×C53—21no—
230C22×C4×C53—21no—
231C22×C4×C53—22no—
232C22×C4×C53—22no—
233C22×C4×C53—21no—
234C22×C4×C53—24no—
235C22×C4×C53—24no—
236C22×C4×C53—44no—
237C22×C4×C53—44no—
238C22×C4×C53C2×D411yescharacteristic
239C22×C4×C53C2×D412yes—
240C22×C4×C53C2412yes—
241C22×C4×C53C2411yescharacteristic
242C2×C22⋊D53—24no—
243C2×C22⋊D53—24no—
244C2×C22⋊D53—42no—
245C2×C22⋊D53—44no—
246C2×C22⋊D53—44no—
247C2×C22⋊D53C2×D414yes—
248C22×Dic53—21no—
249C22×Dic53—21no—
250C22×Dic53—21no—
251C22×Dic53C2×D411yescharacteristic
252C22×Dic53C2×D411yescharacteristic
253C22×Dic53C2×D411yescharacteristic
254#11719949—28no—
255#11719949—44no—
256#11719949—48no—
257Q8×D53—28no—
258Q8×D53—44no—
259Q8×D53—48no—
260C2×D212—22no—
261C2×D212—22no—
262C2×D212—24no—
263C2×D212—21no—
264C2×D212—44no—
265C2×D212C2412yes—
266C2×C4×D53—22no—
267C2×C4×D53—22no—
268C2×C4×D53—24no—
269C2×C4×D53—24no—
270C2×C4×D53—44no—
271C2×C4×D53—44no—
272C2×C4×D53C2×D412yes—
273C2×C4×D53C2412yes—
274C2×Dic106—22no—
275C2×Dic106—22no—
276C2×Dic106—21no—
277C2×Dic106—24no—
278C2×Dic106—44no—
279C2×Dic106C2412yes—
280Q16×C53—28no—
281Q16×C53C2×D4116yescomplemented
282SD16×C53—28no—
283SD16×C53—28no—
284M16×C53—28no—
285C2×C8×C53—22no—
286C2×C8×C53C2×D414yes—
287C2×C8×C53C2412yes—
288C2×C8×C53C2412yes—
289C22⋊Dic53—24no—
290C22⋊Dic53—24no—
291C22⋊Dic53—24no—
292C22⋊Dic53—24no—
293C22⋊Dic53C2×D414yes—
294#11719925—28no—
295#11719925—44no—
296#11719924—28no—
297#11719922—44no—
298#11719921—24no—
299#11719921—24no—
300#11719921—24no—
301#11719921—24no—
302#11719921C2×D414yes—
303C4⋊Dic53—21no—
304C4⋊Dic53—21no—
305C4⋊Dic53—24no—
306C4⋊Dic53—24no—
307C4⋊Dic53C2412yes—
308C4⋊Dic53C2412yes—
309#11719919—24no—
310#11719919—24no—
311#11719919C2×D414yes—
312C4×Dic53—24no—
313C4×Dic53—24no—
314C4×Dic53C2×D412yes—
315C4×Dic53C2412yes—
316C2×#88322—22no—
317C2×#88322—22no—
318C2×#88322C2412yes—
319C2×#88322C2412yes—
320#11719913—28no—
321#11719912—28no—
322C23×C53—22no—
323C23×C53—22no—
324C23×C53—22no—
325C23×C53—22no—
326C23×C53—42no—
327C23×C53—42no—
328C23×C53—42no—
329C23×C53C22×D412yes—
330C23×C53C22×D411yescharacteristic
331C22×D53—22no—
332C22×D53—22no—
333C22×D53—22no—
334C22×D53—22no—
335C22×D53—42no—
336C22×D53—42no—
337C22×D53—42no—
338C22×D53C22×D412yes—
339Q8×C53—24no—
340Q8×C53—24no—
341Q8×C53—22no—
342Q8×C53—22no—
343Q8×C53—22no—
344Q8×C53—22no—
345Q8×C53—48no—
346Q8×C53—42no—
347Q8×C53C22×D414yes—
348Q8×C53C22×D414yes—
349D4×C53—22no—
350D4×C53—22no—
351D4×C53—48no—
352D4×C53—42no—
353C2×C4×C53—24no—
354C2×C4×C53—24no—
355C2×C4×C53—22no—
356C2×C4×C53—22no—
357C2×C4×C53—22no—
358C2×C4×C53—24no—
359C2×C4×C53—22no—
360C2×C4×C53—22no—
361C2×C4×C53—22no—
362C2×C4×C53—48no—
363C2×C4×C53—48no—
364C2×C4×C53—42no—
365C2×C4×C53C22×D412yes—
366C2×C4×C53C22×D411yescharacteristic
367C2×C4×C53C22×D412yes—
368C2×C4×C53H(5,𝔽2)12yes—
369C2×C4×C53C2511yescharacteristic
370C22⋊D53—44no—
371C22⋊D53—48no—
372C22⋊D53—48no—
373C2×Dic53—22no—
374C2×Dic53—22no—
375C2×Dic53—22no—
376C2×Dic53—22no—
377C2×Dic53—22no—
378C2×Dic53—22no—
379C2×Dic53—42no—
380C2×Dic53—42no—
381C2×Dic53—42no—
382C2×Dic53C22×D412yes—
383C2×Dic53C22×D412yes—
384C2×Dic53C22×D412yes—
385D212—22no—
386D212—22no—
387D212—48no—
388D212—42no—
389C4×D53—24no—
390C4×D53—22no—
391C4×D53—22no—
392C4×D53—48no—
393C4×D53—48no—
394Dic106—22no—
395Dic106—22no—
396Dic106—48no—
397Dic106—42no—
398C8×C53—22no—
399C8×C53C22×D414yes—
400#88322—22no—
401#88322—22no—
402C2×#3277—531nomaximal, Sylow
403C22×C53—22no—
404C22×C53—22no—
405C22×C53—22no—
406C22×C53—44no—
407C22×C53—42no—
408C22×C53—42no—
409C22×C53—42no—
410C22×C53—84no—
411C22×C53D4212yes—
412C22×C53#57512yes—
413C22×C53#57812yes—
414C22×C53C23×D411yescharacteristic
415C2×D53—22no—
416C2×D53—22no—
417C2×D53—22no—
418C2×D53—44no—
419C2×D53—42no—
420C2×D53—42no—
421C2×D53—42no—
422C2×D53—84no—
423C4×C53—24no—
424C4×C53—24no—
425C4×C53—22no—
426C4×C53—42no—
427C4×C53D4212yes—
428C4×C53C23×D411yescharacteristic
429C4×C53C2×H(5,𝔽2)11yescharacteristic
430Dic53—22no—
431Dic53—22no—
432Dic53—22no—
433Dic53—42no—
434Dic53—42no—
435Dic53—42no—
436C22×#137—531no—
437C22×#137D5311yescharacteristic, complemented
438C2×#548—531no—
439C2×#548—531no—
440#3277—5316no—
441C2×#495—531no—
442C2×#468—531no—
443C2×#468—531no—
444C2×#464—531no—
445C2×#464—531no—
446C2×#449—531no—
447C2×#449—531no—
448C2×#451—531no—
449C2×#451—531no—
450C2×C4×Q16—531no—
451C2×#436—531no—
452C2×C53—42no—
453C2×C53—82no—
454C2×C53#327714yescomplemented
455C2×C53C2×D4211yescharacteristic
456C2×C53C2×#57511yescharacteristic
457C2×C53C2×#57811yescharacteristic
458D53—42no—
459D53—82no—
460C22×#41—531no—
461C22×#41C2×D5311yescharacteristic
462C23×Q8—531no—
463C23×Q8C2×D5311yescharacteristic
464C2×#137—28no—
465C2×#137—538no—
466C2×#137—1068no—
467C2×#137C2×D5318yescomplemented
468C22×Q16—531no—
469C22×Q16—531no—
470C22×Q16C2×D5311yescharacteristic
471C22×Q16C2×D5311yescharacteristic
472C22×SD16—531no—
473C22×SD16—531no—
474C22×SD16C2×D5311yescharacteristic
475C22×SD16C2×D5311yescharacteristic
476C22×D8—531no—
477C22×M16—531no—
478C22×M16C2×D5311yescharacteristic
479#548—538no—
480#548—538no—
481#548—1064no—
482#548—1064no—
483C2×#124—531no—
484C2×#124—531no—
485C2×#124—1061no—
486C2×#124—1061no—
487C2×C22⋊Q8—531no—
488C2×C22⋊Q8—531no—
489C2×C22⋊Q8—1061no—
490C2×C22⋊Q8—1061no—
491C2×#121—531no—
492C2×#121—531no—
493C2×#121—1061no—
494C2×#121—1061no—
495C2×C4×Q8—531no—
496C2×C4×Q8—531no—
497C2×C4×D4—531no—
498C2×C4×D4—1061no—
499C2×C4×D4—1061no—
500#495—538no—
501#468—538no—
502#468—538no—
503#464—538no—
504#464—538no—
505#451—538no—
506#451—538no—
507#449—538no—
508#449—538no—
509C4×Q16—538no—
510#436—538no—
511C2×#107—531no—
512C2×C4⋊C8—531no—
513C2×#103—531no—
514C2×#103—531no—
515C2×#103—531no—
516C2×#103—531no—
517C2×#102—531no—
518C2×#102—531no—
519C2×C22⋊C8—531no—
520C2×C22⋊C8—531no—
521C2×C4×C8—531no—
522C53C2×#327711yescharacteristic, complemented, Sylow
523C2×#41—22no—
524C2×#41—24no—
525C2×#41—42no—
526C2×#41—534no—
527C2×#41—1062no—
528C2×#41—1064no—
529C2×#41—2122no—
530C2×#41C22×D5314yes—
531C22×Q8—21no—
532C22×Q8—22no—
533C22×Q8—24no—
534C22×Q8—42no—
535C22×Q8—534no—
536C22×Q8—531no—
537C22×Q8—1061no—
538C22×Q8—1062no—
539C22×Q8—1064no—
540C22×Q8—2122no—
541C22×Q8C22×D5311yescharacteristic
542C22×Q8C22×D5314yes—
543C22×Q8C22×D5311yescharacteristic
544C22×Q8C22×D5311yescharacteristic
545C22×D4—21no—
546C22×D4—531no—
547C22×D4—531no—
548C22×D4—1061no—
549C22×D4—1061no—
550C22×D4—1061no—
551C22×D4C22×D5311yescharacteristic
552C23×C4—21no—
553C23×C4—21no—
554C23×C4—531no—
555C23×C4—1061no—
556C23×C4—1061no—
557C23×C4C22×D5311yescharacteristic
558#137—232no—
559#137—10632no—
560C2×Q16—24no—
561C2×Q16—534no—
562C2×Q16—534no—
563C2×Q16—1064no—
564C2×Q16—2122no—
565C2×Q16C22⋊D5318yescomplemented
566C2×Q16C22×D5314yes—
567C2×Q16C22×D5314yes—
568C2×SD16—24no—
569C2×SD16—24no—
570C2×SD16—534no—
571C2×SD16—534no—
572C2×SD16—1064no—
573C2×SD16—1064no—
574C2×SD16C22×D5314yes—
575C2×SD16C22×D5314yes—
576C2×D8—534no—
577C2×D8—2122no—
578C2×M16—24no—
579C2×M16—534no—
580C2×M16—1064no—
581C2×M16C22×D5314yes—
582C22×C8—531no—
583C22×C8—531no—
584C22×C8C22×D5311yescharacteristic
585C22×C8C22×D5311yescharacteristic
586#124—534no—
587#124—534no—
588#124—1062no—
589#124—1062no—
590#124—1068no—
591#124—1068no—
592C22⋊Q8—534no—
593C22⋊Q8—534no—
594C22⋊Q8—1068no—
595C22⋊Q8—1068no—
596C22⋊Q8—1062no—
597C22⋊Q8—1062no—
598#121—534no—
599#121—534no—
600#121—1068no—
601#121—1062no—
602#121—1068no—
603#121—1062no—
604C4×Q8—534no—
605C4×Q8—534no—
606C4×Q8—1062no—
607C4×Q8—1062no—
608C4×D4—534no—
609C4×D4—534no—
610C4×D4—1068no—
611C4×D4—1068no—
612C2×C4⋊C4—531no—
613C2×C4⋊C4—531no—
614C2×C4⋊C4—531no—
615C2×C4⋊C4—1061no—
616C2×C4⋊C4—1061no—
617C2×C4⋊C4—1061no—
618C2×C4⋊C4—1061no—
619C2×C22⋊C4—531no—
620C2×C22⋊C4—531no—
621C2×C22⋊C4—1061no—
622C2×C22⋊C4—1061no—
623C2×C22⋊C4—1061no—
624C2×C22⋊C4—1061no—
625C2×C22⋊C4—1061no—
626C2×C22⋊C4—1061no—
627C2×C22⋊C4—1061no—
628C2×C22⋊C4—1061no—
629C2×C42—531no—
630C2×C42—1061no—
631C2×C42—1061no—
632#107—534no—
633C4⋊C8—534no—
634#103—534no—
635#103—534no—
636#103—534no—
637#103—534no—
638#102—534no—
639#102—534no—
640C22⋊C8—534no—
641C22⋊C8—534no—
642C4×C8—534no—
643C24—21no—
644C24—531no—
645C24—1061no—
646C24D4×D5311yescharacteristic
647#41—28no—
648#41—44no—
649#41—48no—
650#41—1068no—
651#41—2124no—
652#41—2128no—
653C2×Q8—21no—
654C2×Q8—21no—
655C2×Q8—24no—
656C2×Q8—21no—
657C2×Q8—22no—
658C2×Q8—22no—
659C2×Q8—28no—
660C2×Q8—22no—
661C2×Q8—22no—
662C2×Q8—44no—
663C2×Q8—44no—
664C2×Q8—48no—
665C2×Q8—532no—
666C2×Q8—1064no—
667C2×Q8—1061no—
668C2×Q8—1068no—
669C2×Q8—1062no—
670C2×Q8—1062no—
671C2×Q8—2124no—
672C2×Q8—2124no—
673C2×Q8—2128no—
674C2×Q8C2×C22⋊D5314yes—
675C2×Q8C2×C22⋊D5314yes—
676C2×Q8C23×D5312yes—
677C2×Q8C23×D5312yes—
678C2×Q8C23×D5312yes—
679C2×D4—24no—
680C2×D4—21no—
681C2×D4—22no—
682C2×D4—22no—
683C2×D4—44no—
684C2×D4—534no—
685C2×D4—532no—
686C2×D4—1064no—
687C2×D4—1064no—
688C2×D4—1064no—
689C2×D4—1061no—
690C2×D4—1062no—
691C2×D4—1062no—
692C2×D4—2124no—
693C2×D4—2122no—
694C2×D4—2124no—
695C2×D4—2124no—
696C2×D4C23×D5312yes—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—24no—
702C22×C4—21no—
703C22×C4—24no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—531no—
707C22×C4—531no—
708C22×C4—531no—
709C22×C4—532no—
710C22×C4—532no—
711C22×C4—1064no—
712C22×C4—1064no—
713C22×C4—1062no—
714C22×C4—1062no—
715C22×C4—1061no—
716C22×C4—1061no—
717C22×C4—1061no—
718C22×C4—2124no—
719C22×C4—2124no—
720C22×C4D4×D5312yes—
721C22×C4D4×D5311yescharacteristic
722C22×C4C23×D5312yes—
723C22×C4C23×D5311yescharacteristic
724Q16—28no—
725Q16—1068no—
726Q16—2124no—
727Q16C2×C22⋊D53116yescomplemented
728SD16—28no—
729SD16—28no—
730SD16—1068no—
731SD16—1068no—
732D8—2124no—
733M16—28no—
734M16—1068no—
735C2×C8—22no—
736C2×C8—532no—
737C2×C8—532no—
738C2×C8—1062no—
739C2×C8—1062no—
740C2×C8C2×C22⋊D5314yes—
741C2×C8C23×D5312yes—
742C2×C8C23×D5312yes—
743C4⋊C4—534no—
744C4⋊C4—532no—
745C4⋊C4—532no—
746C4⋊C4—1064no—
747C4⋊C4—1064no—
748C4⋊C4—1064no—
749C4⋊C4—1061no—
750C4⋊C4—1061no—
751C4⋊C4—1064no—
752C22⋊C4—534no—
753C22⋊C4—534no—
754C22⋊C4—1064no—
755C22⋊C4—1064no—
756C22⋊C4—1064no—
757C22⋊C4—1064no—
758C22⋊C4—1064no—
759C22⋊C4—1064no—
760C22⋊C4—1064no—
761C22⋊C4—1064no—
762C42—532no—
763C42—532no—
764C42—1064no—
765C42—1064no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—532no—
774C23—1062no—
775C23—1062no—
776C23—1062no—
777C23—1062no—
778C23—2122no—
779C23—2122no—
780C23—2122no—
781C23C2×D4×D5312yes—
782C23C2×D4×D5311yescharacteristic
783Q8—22no—
784Q8—22no—
785Q8—24no—
786Q8—24no—
787Q8—22no—
788Q8—22no—
789Q8—48no—
790Q8—42no—
791Q8—1062no—
792Q8—1062no—
793Q8—2128no—
794Q8—2122no—
795Q8C22×C22⋊D5314yes—
796Q8C22×C22⋊D5314yes—
797D4—22no—
798D4—22no—
799D4—48no—
800D4—42no—
801D4—1062no—
802D4—1062no—
803D4—2128no—
804D4—2124no—
805D4—2128no—
806D4—2128no—
807D4—2122no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—24no—
816C2×C4—22no—
817C2×C4—48no—
818C2×C4—48no—
819C2×C4—42no—
820C2×C4—532no—
821C2×C4—532no—
822C2×C4—532no—
823C2×C4—1062no—
824C2×C4—1062no—
825C2×C4—1062no—
826C2×C4—1062no—
827C2×C4—1062no—
828C2×C4—1064no—
829C2×C4—1062no—
830C2×C4—1062no—
831C2×C4—1062no—
832C2×C4—2128no—
833C2×C4—2128no—
834C2×C4—2122no—
835C2×C4—2122no—
836C2×C4—2122no—
837C2×C4C2×D4×D5312yes—
838C2×C4C2×D4×D5311yescharacteristic
839C2×C4C22×C22⋊D5312yes—
840C2×C4#1313326212yes—
841C2×C4C24×D5311yescharacteristic
842C8—22no—
843C8—1062no—
844C8—1062no—
845C8C22×C22⋊D5314yes—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—44no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—84no—
854C22—1062no—
855C22—1062no—
856C22—1062no—
857C22—4244no—
858C22—2122no—
859C22—2122no—
860C22—2122no—
861C22—2124no—
862C22D4×C22⋊D5312yes—
863C22#1681142212yes—
864C22#1681143912yes—
865C22C22×D4×D5311yescharacteristic
866C4—22no—
867C4—24no—
868C4—24no—
869C4—42no—
870C4—1062no—
871C4—1062no—
872C4—1062no—
873C4—2122no—
874C4—2122no—
875C4—2122no—
876C4D4×C22⋊D5312yes—
877C4C23×C22⋊D5311yescharacteristic
878C4C2×#1313326211yescharacteristic
879C2—42no—
880C2—82no—
881C2—4242no—
882C2—2122no—
883C2#2028636614yesdirect product factor
884C2C2×D4×C22⋊D5311yescharacteristic
885C2C2×#1681142211yescharacteristic
886C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC22×#137×C53C2
socleC23×C53C22×D4
hypercenterC22×#137D53
hypocenterC53C2×#3277
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
1. C22×#13133249C2semidirect
2. C2×#16811284C2semidirect
3. C2×#16811280C2semidirect
4. #20286366C2direct (N × H)
5. C2×#16811004C2semidirect
6. C2×#16810869C2semidirect
7. C2×#16810866C2semidirect
8. C2×#16810847C2semidirect
9. C2×#16810843C2semidirect
10. C2×#16810768C2semidirect
11. C2×#16810767C2semidirect
12. C2×#16810779C2semidirect
13. C2×#16810777C2semidirect
14. C2×Q16×Dic53C2semidirect
15. C2×#16810699C2semidirect
16. C22×#137×C53C2semidirect
20. C2×#13133249C22semidirect
28. #16811284C22semidirect
30. #16811280C22semidirect
48. #16811004C22semidirect
49. #16810869C22semidirect
50. #16810866C22semidirect
51. #16810847C22semidirect
52. #16810843C22semidirect
53. #16810779C22semidirect
54. #16810777C22semidirect
55. #16810768C22semidirect
56. #16810767C22semidirect
57. Q16×Dic53C22semidirect
58. #16810699C22semidirect
73. C2×#137×C53C22semidirect
188. C2×Q16×C53D4semidirect
281. Q16×C53C2×D4semidirect
437. C22×#137D53semidirect
454. C2×C53#3277semidirect
467. C2×#137C2×D53semidirect
522. C53C2×#3277semidirect
565. C2×Q16C22⋊D53semidirect
727. Q16C2×C22⋊D53semidirect
883. C2#20286366direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332492
C2×#168112842
C2×#168112802
#202863662
C2×#168110042
C2×#168108692
C2×#168108662
C2×#168108472
C2×#168108432
C2×#168107682
C2×#168107672
C2×#168107792
C2×#168107772
C2×Q16×Dic532
C2×#168106992
C22×#137×C532
C2×#327753