Finite Group Databasebeta

← C2×#20287038 #28261021

Subgroups — C2×#20287038 #28261021

Order 13568.

2426 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811292C211yesmaximal, characteristic, complemented
2C2×#16811274C211yesmaximal, characteristic, complemented
3#20287038C2116yesmaximal, direct product factor
4C2×#16810968C211yesmaximal, characteristic, complemented
5C2×#16810941C211yesmaximal, characteristic, complemented
6C2×#16810940C211yesmaximal, characteristic, complemented
7C2×#16810906C211yesmaximal, characteristic, complemented
8C2×#16810876C211yesmaximal, characteristic, complemented
9C2×#16810875C211yesmaximal, characteristic, complemented
10C2×#16810817C211yesmaximal, characteristic, complemented
11C2×#16810771C211yesmaximal, characteristic, complemented
12C2×#16810768C211yesmaximal, characteristic, complemented
13C2×#16810708C211yesmaximal, characteristic, complemented
14C2×#16810699C211yesmaximal, characteristic, complemented
15C2×#16810623C211yesmaximal, characteristic, complemented
16C2×C53×#417C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×#11719945—21no—
19C22×#11719924C2211yescharacteristic
20C22×D424C2211yescharacteristic
21C22×#11719922C2211yescharacteristic
22C22×#11719912C2211yescharacteristic
23#16811292—24no—
24#16811292C2218yescomplemented
25#16811274—24no—
26#16811274C2218yescomplemented
27C2×#13133216C2211yescharacteristic
28C2×#13133213—21no—
29C2×#13133213C2211yescharacteristic
30C2×#13133202—21no—
31C2×#13133200—21no—
32C2×#13133195—21no—
33C2×#13133192C2211yescharacteristic
34C2×#13133191—21no—
35C2×#13133191C2211yescharacteristic
36C2×#13133191C2211yescharacteristic
37C2×#13133188—21no—
38C2×#13133188C2211yescharacteristic
39C2×Q8×Dic53C2211yescharacteristic
40C2×#13133179C2211yescharacteristic
41C2×C4×C22⋊D53—21no—
42C2×C4×C22⋊D53C2211yescharacteristic
43C2×C4⋊C4×D53C2211yescharacteristic
44#16810968C2218yescomplemented
45#16810941C2218yescomplemented
46#16810940C2218yescomplemented
47#16810906C2218yescomplemented
48#16810876C2218yescomplemented
49#16810875C2218yescomplemented
50#16810817C2218yescomplemented
51#16810771C2218yescomplemented
52#16810768C2218yescomplemented
53#16810708C2218yescomplemented
54#16810699C2218yescomplemented
55C2×#13133149C2211yescharacteristic
56C2×#13133148C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×#13133146C2211yescharacteristic
59#16810623C2218yescomplemented
60C2×#13133141C2211yescharacteristic
61C2×#13133139C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×#41×C53C2211yescharacteristic
70C22×M16×C53C2211yescharacteristic
71C22×C4⋊C4×C53C2211yescharacteristic
72C53×#417C2218yescomplemented
73C2×#103×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C2×#11719949—22no—
78C2×#11719949—24no—
79C2×#11719949—42no—
80C2×#11719949C2314yes—
81C2×#11719945—28no—
82C2×#11719945—48no—
83C22×Dic106—21no—
84C22×D212—21no—
85C22×D212—21no—
86C22×D212C2311yescharacteristic
87C22×D212C2311yescharacteristic
88C22×C22⋊D53—21no—
89C22×C22⋊D53—21no—
90C22×C22⋊D53—21no—
91C22×C22⋊D53—21no—
92C22×C22⋊D53—21no—
93C22×C22⋊D53D411yescharacteristic
94C22×C4×D53—21no—
95C22×C4×D53—21no—
96C22×C4×D53—21no—
97C22×C4×D53C2311yescharacteristic
98C2×#11719924—24no—
99C2×#11719924C2314yes—
100C2×D424—42no—
101C2×D424C2314yes—
102C2×#11719922—42no—
103C2×#11719922C2314yes—
104C2×#11719912—42no—
105C2×#11719912C2314yes—
106C22×#88322C2311yescharacteristic
107C22×#88322C2311yescharacteristic
108#13133216—22no—
109#13133216C2314yes—
110#13133213—22no—
111#13133213—28no—
112#13133213C2314yes—
113#13133202—28no—
114#13133200—28no—
115#13133195—28no—
116#13133192—22no—
117#13133192C2314yes—
118#13133191—28no—
119#13133191—22no—
120#13133191—22no—
121#13133191C2314yes—
122#13133191C2314yes—
123#13133188—28no—
124#13133188—22no—
125#13133188C2314yes—
126Q8×Dic53—22no—
127Q8×Dic53C2314yes—
128#13133179—22no—
129#13133179C2314yes—
130C4×C22⋊D53—28no—
131C4×C22⋊D53D414yes—
132C4×C22⋊D53C2314yes—
133C2×C4⋊Dic53—21no—
134C2×C4⋊Dic53C2311yescharacteristic
135C2×C4⋊Dic53C2311yescharacteristic
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×#11719919D411yescharacteristic
139C4⋊C4×D53—22no—
140C4⋊C4×D53C2314yes—
141C2×C22⋊Dic53—21no—
142C2×C22⋊Dic53D411yescharacteristic
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921D411yescharacteristic
148C2×C4×Dic53—21no—
149C2×C4×Dic53C2311yescharacteristic
150#13133149C2314yes—
151#13133148C2314yes—
152#13133148C2314yes—
153#13133146C2314yes—
154#13133141C2314yes—
155#13133139C2314yes—
156#13133139C2314yes—
157#13133138C2314yes—
158#13133137C2314yes—
159#13133137C2314yes—
160C22⋊#88322C2314yes—
161#13133129C2314yes—
162C8×Dic53C2314yes—
163C2×#41×C53—22no—
164C2×#41×C53—24no—
165C2×#41×C53—42no—
166C2×#41×C53C2314yes—
167C22×Q8×C53C2311yescharacteristic
168C22×D4×C53—21no—
169C22×D4×C53C2311yescharacteristic
170C23×C4×C53—21no—
171C23×C4×C53—21no—
172C23×C4×C53C2311yescharacteristic
173C2×M16×C53—42no—
174C2×M16×C53C2314yes—
175C22×C8×C53C2311yescharacteristic
176C22×C8×C53C2311yescharacteristic
177C2×C4⋊C4×C53—22no—
178C2×C4⋊C4×C53—21no—
179C2×C4⋊C4×C53C2314yes—
180C2×C4⋊C4×C53C2311yescharacteristic
181C2×C4⋊C4×C53C2311yescharacteristic
182#103×C53C2314yes—
183#103×C53C2314yes—
184#102×C53C2314yes—
185#102×C53C2314yes—
186C24×C53—21no—
187C24×C53C2×D411yescharacteristic
188C23×D53—21no—
189C23×D53—21no—
190C23×D53C2×D411yescharacteristic
191#41×C53—28no—
192#41×C53—44no—
193#41×C53—48no—
194C2×Q8×C53—21no—
195C2×Q8×C53—22no—
196C2×Q8×C53#4114yescomplemented
197C2×Q8×C53C2412yes—
198C2×D4×C53—24no—
199C2×D4×C53—21no—
200C2×D4×C53—22no—
201C2×D4×C53—22no—
202C2×D4×C53—44no—
203C2×D4×C53C2412yes—
204C22×C4×C53—21no—
205C22×C4×C53—22no—
206C22×C4×C53—22no—
207C22×C4×C53—21no—
208C22×C4×C53—21no—
209C22×C4×C53—24no—
210C22×C4×C53—24no—
211C22×C4×C53—44no—
212C22×C4×C53—44no—
213C22×C4×C53C2×D411yescharacteristic
214C22×C4×C53C2×D412yes—
215C22×C4×C53C2412yes—
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—44no—
225C2×C22⋊D53—82no—
226C2×C22⋊D53—82no—
227C2×C22⋊D53—82no—
228C2×C22⋊D53C2×D414yes—
229C22×Dic53—21no—
230C22×Dic53—21no—
231C22×Dic53C2×D411yescharacteristic
232C22×Dic53C2×D411yescharacteristic
233C22×Dic53C2×D411yescharacteristic
234#11719949—28no—
235#11719949—44no—
236#11719949—48no—
237#11719945—432no—
238C2×D212—22no—
239C2×D212—22no—
240C2×D212—22no—
241C2×D212—22no—
242C2×D212—24no—
243C2×D212—24no—
244C2×D212—21no—
245C2×D212—21no—
246C2×D212—44no—
247C2×D212—44no—
248C2×D212C2412yes—
249C2×D212C2412yes—
250C2×C4×D53—22no—
251C2×C4×D53—22no—
252C2×C4×D53—24no—
253C2×C4×D53—24no—
254C2×C4×D53—24no—
255C2×C4×D53—44no—
256C2×C4×D53—44no—
257C2×C4×D53—44no—
258C2×C4×D53C2×D412yes—
259C2×C4×D53C2412yes—
260C2×Dic106—24no—
261C2×Dic106—44no—
262M16×C53—44no—
263C2×C8×C53—22no—
264C2×C8×C53—22no—
265C2×C8×C53C2412yes—
266C2×C8×C53C2412yes—
267C4⋊C4×C53—21no—
268C4⋊C4×C53—21no—
269C4⋊C4×C53—24no—
270C4⋊C4×C53C2412yes—
271C4⋊C4×C53C2412yes—
272C22⋊Dic53—24no—
273C22⋊Dic53C2×D414yes—
274#11719924—28no—
275#11719922—44no—
276#11719921—24no—
277#11719921—24no—
278#11719921—24no—
279#11719921—24no—
280#11719921C2×D414yes—
281C4⋊Dic53—21no—
282C4⋊Dic53—21no—
283C4⋊Dic53—24no—
284C4⋊Dic53C2412yes—
285C4⋊Dic53C2412yes—
286#11719919—24no—
287#11719919—24no—
288#11719919C2×D414yes—
289C4×Dic53—24no—
290C4×Dic53C2×D412yes—
291C4×Dic53C2412yes—
292C2×#88322—22no—
293C2×#88322—22no—
294C2×#88322C2412yes—
295C2×#88322C2412yes—
296D424—44no—
297#11719912—44no—
298C23×C53—22no—
299C23×C53—22no—
300C23×C53—22no—
301C23×C53—22no—
302C23×C53—42no—
303C23×C53—42no—
304C23×C53—42no—
305C23×C53C22×D412yes—
306C23×C53C22×D411yescharacteristic
307C22×D53—22no—
308C22×D53—22no—
309C22×D53—22no—
310C22×D53—22no—
311C22×D53—22no—
312C22×D53—42no—
313C22×D53—42no—
314C22×D53—42no—
315C22×D53—42no—
316C22×D53—42no—
317C22×D53—42no—
318C22×D53C22×D412yes—
319Q8×C53—24no—
320Q8×C53—22no—
321Q8×C53C2×#4114yescomplemented
322D4×C53—22no—
323D4×C53—22no—
324D4×C53—48no—
325D4×C53—42no—
326C2×C4×C53—24no—
327C2×C4×C53—22no—
328C2×C4×C53—22no—
329C2×C4×C53—24no—
330C2×C4×C53—22no—
331C2×C4×C53—22no—
332C2×C4×C53—22no—
333C2×C4×C53—22no—
334C2×C4×C53—48no—
335C2×C4×C53—48no—
336C2×C4×C53—42no—
337C2×C4×C53—42no—
338C2×C4×C53C22×D412yes—
339C2×C4×C53C22×D411yescharacteristic
340C2×C4×C53C2×#4112yes—
341C2×C4×C53H(5,𝔽2)12yes—
342C2×C4×C53C2511yescharacteristic
343C22⋊D53—28no—
344C22⋊D53—48no—
345C22⋊D53—48no—
346C22⋊D53—84no—
347C22⋊D53—84no—
348C22⋊D53—84no—
349C2×Dic53—22no—
350C2×Dic53—22no—
351C2×Dic53—22no—
352C2×Dic53—22no—
353C2×Dic53—42no—
354C2×Dic53—42no—
355C2×Dic53AGL(1,ℤ/8)14yes—
356C2×Dic53C22×D412yes—
357C2×Dic53C22×D412yes—
358C2×Dic53C22×D412yes—
359D212—22no—
360D212—22no—
361D212—22no—
362D212—22no—
363D212—48no—
364D212—48no—
365D212—42no—
366D212—42no—
367C4×D53—24no—
368C4×D53—22no—
369C4×D53—22no—
370C4×D53—48no—
371C4×D53—48no—
372C4×D53—48no—
373Dic106—48no—
374C8×C53—22no—
375C8×C53—22no—
376#88322—22no—
377#88322—22no—
378C2×#3332—531nomaximal, Sylow
379C22×C53—22no—
380C22×C53—22no—
381C22×C53—22no—
382C22×C53—44no—
383C22×C53—42no—
384C22×C53—42no—
385C22×C53—42no—
386C22×C53—84no—
387C22×C53#54612yes—
388C22×C53C2×AGL(1,ℤ/8)12yes—
389C22×C53#57712yes—
390C22×C53C23×D411yescharacteristic
391C2×D53—22no—
392C2×D53—22no—
393C2×D53—22no—
394C2×D53—44no—
395C2×D53—42no—
396C2×D53—42no—
397C2×D53—42no—
398C2×D53—42no—
399C2×D53—42no—
400C2×D53—42no—
401C2×D53—84no—
402C2×D53—84no—
403C4×C53—24no—
404C4×C53—22no—
405C4×C53—42no—
406C4×C53—42no—
407C4×C53#54612yes—
408C4×C53C22×#4111yescharacteristic
409C4×C53C2×H(5,𝔽2)11yescharacteristic
410Dic53—22no—
411Dic53—22no—
412Dic53—42no—
413Dic53—42no—
414Dic53C2×AGL(1,ℤ/8)14yes—
415C2×#550—531no—
416C2×#547—531no—
417#3332—5316no—
418C2×#486—531no—
419C2×#481—531no—
420C2×#481—531no—
421C2×#475—531no—
422C2×#469—531no—
423C2×#469—531no—
424C2×#459—531no—
425C2×#449—531no—
426C2×#449—531no—
427C2×C4×SD16—531no—
428C2×#436—531no—
429C2×#417—531no—
430C2×#417D5311yescharacteristic, complemented
431C2×C53—42no—
432C2×C53—82no—
433C2×C53#333214yescomplemented
434C2×C53C2×#54611yescharacteristic
435C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
436C2×C53C2×#57711yescharacteristic
437D53—42no—
438D53—82no—
439D53—82no—
440C22×#41—531no—
441C22×#41—1061no—
442C22×#41C2×D5311yescharacteristic
443C22×SD16—531no—
444C22×D8—531no—
445C22×D8—531no—
446C22×M16—531no—
447C22×M16C2×D5311yescharacteristic
448#550—538no—
449#550—1064no—
450#547—538no—
451#547—1064no—
452C2×C4⋊Q8—531no—
453C2×#127—531no—
454C2×#127—1061no—
455C2×#123—1061no—
456C2×#123—1061no—
457C2×C22⋊Q8—1061no—
458C2×#121—531no—
459C2×#121—531no—
460C2×#121—531no—
461C2×#121—531no—
462C2×#121—1061no—
463C2×#121—1061no—
464C2×C4×Q8—531no—
465C2×C4×D4—531no—
466C2×C4×D4—531no—
467C2×C4×D4—1061no—
468C22×C4⋊C4—531no—
469C22×C4⋊C4C2×D5311yescharacteristic
470#486—538no—
471#481—538no—
472#481—538no—
473#475—538no—
474#469—538no—
475#469—538no—
476#459—538no—
477#449—538no—
478#449—538no—
479C4×SD16—538no—
480#436—538no—
481C2×#106—531no—
482C2×#106—531no—
483C2×#106—531no—
484C2×C4⋊C8—531no—
485#417—538no—
486#417C2×D5318yescomplemented
487C2×#103—531no—
488C2×#103C2×D5311yescharacteristic
489C2×#103C2×D5311yescharacteristic
490C2×#102—531no—
491C2×#102—531no—
492C2×#102—531no—
493C2×#102—531no—
494C2×#102—531no—
495C2×#102C2×D5311yescharacteristic
496C2×#102C2×D5311yescharacteristic
497C2×C22⋊C8—531no—
498C2×C22⋊C8—531no—
499C2×C4×C8—531no—
500C53C2×#333211yescharacteristic, complemented, Sylow
501C2×#41—22no—
502C2×#41—24no—
503C2×#41—42no—
504C2×#41—534no—
505C2×#41—1068no—
506C2×#41—1062no—
507C2×#41—1064no—
508C2×#41—2128no—
509C2×#41—2122no—
510C2×#41C22×D5314yes—
511C22×Q8—1061no—
512C22×Q8C22×D5311yescharacteristic
513C22×D4—21no—
514C22×D4—531no—
515C22×D4—531no—
516C22×D4—531no—
517C22×D4—1061no—
518C22×D4—1061no—
519C22×D4—1061no—
520C22×D4—1061no—
521C22×D4—1061no—
522C22×D4—1061no—
523C22×D4—1061no—
524C22×D4C22×D5311yescharacteristic
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—531no—
528C23×C4—1061no—
529C23×C4—1061no—
530C23×C4—1061no—
531C23×C4C22×D5311yescharacteristic
532C2×SD16—534no—
533C2×SD16—1064no—
534C2×D8—534no—
535C2×D8—534no—
536C2×D8—2122no—
537C2×D8—2122no—
538C2×M16—42no—
539C2×M16—534no—
540C2×M16—2122no—
541C2×M16C22×D5314yes—
542C22×C8—531no—
543C22×C8—531no—
544C22×C8C22×D5311yescharacteristic
545C22×C8C22×D5311yescharacteristic
546C4⋊Q8—534no—
547C4⋊Q8—1062no—
548#127—534no—
549#127—1062no—
550#127—1068no—
551#123—1068no—
552#123—1068no—
553C22⋊Q8—1068no—
554#121—534no—
555#121—534no—
556#121—534no—
557#121—534no—
558#121—1068no—
559#121—1068no—
560#121—1062no—
561#121—1062no—
562#121—1062no—
563#121—1062no—
564C4×Q8—534no—
565C4×Q8—1062no—
566C4×D4—534no—
567C4×D4—534no—
568C4×D4—534no—
569C4×D4—1062no—
570C4×D4—1068no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—22no—
573C2×C4⋊C4—531no—
574C2×C4⋊C4—531no—
575C2×C4⋊C4—531no—
576C2×C4⋊C4—534no—
577C2×C4⋊C4—1062no—
578C2×C4⋊C4—1061no—
579C2×C4⋊C4—1061no—
580C2×C4⋊C4—1061no—
581C2×C4⋊C4C22×D5311yescharacteristic
582C2×C4⋊C4C22×D5311yescharacteristic
583C2×C4⋊C4C22×D5314yes—
584C2×C22⋊C4—531no—
585C2×C22⋊C4—531no—
586C2×C22⋊C4—1061no—
587C2×C22⋊C4—1061no—
588C2×C22⋊C4—1061no—
589C2×C22⋊C4—1061no—
590C2×C22⋊C4—1061no—
591C2×C42—531no—
592C2×C42—1061no—
593#106—534no—
594#106—534no—
595#106—534no—
596C4⋊C8—534no—
597#103—534no—
598#103C22×D5314yes—
599#103C22×D5314yes—
600#102—534no—
601#102—534no—
602#102—534no—
603#102—534no—
604#102—534no—
605#102C22×D5314yes—
606#102C22×D5314yes—
607C22⋊C8—534no—
608C22⋊C8—534no—
609C4×C8—534no—
610C24—21no—
611C24—531no—
612C24—1061no—
613C24—1061no—
614C24D4×D5311yescharacteristic
615#41—28no—
616#41—44no—
617#41—48no—
618#41—1068no—
619#41—21232no—
620#41—2124no—
621#41—2128no—
622C2×Q8—21no—
623C2×Q8—22no—
624C2×Q8—1064no—
625C2×Q8—2124no—
626C2×Q8#1171994514yescomplemented
627C2×Q8C23×D5312yes—
628C2×D4—24no—
629C2×D4—21no—
630C2×D4—22no—
631C2×D4—22no—
632C2×D4—44no—
633C2×D4—534no—
634C2×D4—532no—
635C2×D4—532no—
636C2×D4—1064no—
637C2×D4—1064no—
638C2×D4—1064no—
639C2×D4—1064no—
640C2×D4—1064no—
641C2×D4—1064no—
642C2×D4—1064no—
643C2×D4—1064no—
644C2×D4—1061no—
645C2×D4—1061no—
646C2×D4—1062no—
647C2×D4—1062no—
648C2×D4—1062no—
649C2×D4—1062no—
650C2×D4—4242no—
651C2×D4—4242no—
652C2×D4—4242no—
653C2×D4—2124no—
654C2×D4—2124no—
655C2×D4—2124no—
656C2×D4—2124no—
657C2×D4C23×D5312yes—
658C22×C4—21no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—24no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—24no—
665C22×C4—44no—
666C22×C4—44no—
667C22×C4—531no—
668C22×C4—531no—
669C22×C4—531no—
670C22×C4—532no—
671C22×C4—532no—
672C22×C4—1064no—
673C22×C4—1064no—
674C22×C4—1064no—
675C22×C4—1062no—
676C22×C4—1062no—
677C22×C4—1061no—
678C22×C4—1061no—
679C22×C4—2124no—
680C22×C4—2124no—
681C22×C4—2124no—
682C22×C4D4×D5312yes—
683C22×C4D4×D5311yescharacteristic
684C22×C4C23×D5312yes—
685C22×C4C23×D5311yescharacteristic
686SD16—1068no—
687D8—2124no—
688D8—2124no—
689M16—44no—
690M16—2124no—
691C2×C8—22no—
692C2×C8—22no—
693C2×C8—532no—
694C2×C8—532no—
695C2×C8—1062no—
696C2×C8—1062no—
697C2×C8C23×D5312yes—
698C2×C8C23×D5312yes—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—24no—
702C4⋊C4—534no—
703C4⋊C4—532no—
704C4⋊C4—532no—
705C4⋊C4—1064no—
706C4⋊C4—1064no—
707C4⋊C4—1064no—
708C4⋊C4—1061no—
709C4⋊C4—1061no—
710C4⋊C4C23×D5312yes—
711C4⋊C4C23×D5312yes—
712C22⋊C4—534no—
713C22⋊C4—534no—
714C22⋊C4—1064no—
715C22⋊C4—1064no—
716C22⋊C4—1064no—
717C22⋊C4—1064no—
718C22⋊C4—1064no—
719C42—532no—
720C42—532no—
721C42—1064no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—532no—
730C23—1062no—
731C23—1062no—
732C23—1062no—
733C23—1062no—
734C23—1062no—
735C23—2122no—
736C23—2122no—
737C23—2122no—
738C23—2122no—
739C23—2122no—
740C23—2122no—
741C23C2×D4×D5312yes—
742C23C2×D4×D5311yescharacteristic
743Q8—22no—
744Q8—24no—
745Q8—2128no—
746Q8C2×#1171994514yescomplemented
747D4—22no—
748D4—22no—
749D4—48no—
750D4—42no—
751D4—1068no—
752D4—1062no—
753D4—1062no—
754D4—1062no—
755D4—1062no—
756D4—4244no—
757D4—4244no—
758D4—4244no—
759D4—2128no—
760D4—2128no—
761D4—2128no—
762D4—2128no—
763D4—2122no—
764D4—2122no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—24no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—48no—
774C2×C4—48no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—534no—
778C2×C4—532no—
779C2×C4—532no—
780C2×C4—532no—
781C2×C4—1062no—
782C2×C4—1062no—
783C2×C4—1062no—
784C2×C4—1062no—
785C2×C4—1064no—
786C2×C4—1062no—
787C2×C4—1062no—
788C2×C4—2128no—
789C2×C4—2128no—
790C2×C4—2128no—
791C2×C4—2122no—
792C2×C4—2122no—
793C2×C4C2×D4×D5312yes—
794C2×C4C2×D4×D5311yescharacteristic
795C2×C4C2×#1171994512yes—
796C2×C4#1313326212yes—
797C2×C4C24×D5311yescharacteristic
798C8—22no—
799C8—22no—
800C8—1062no—
801C8—1062no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—44no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—84no—
810C22—1062no—
811C22—1062no—
812C22—1062no—
813C22—4244no—
814C22—4244no—
815C22—2122no—
816C22—2122no—
817C22—2122no—
818C22—2122no—
819C22—2122no—
820C22—2122no—
821C22—2124no—
822C22#1681126312yes—
823C22AGL(1,ℤ/8)×D5312yes—
824C22#1681143212yes—
825C22C22×D4×D5311yescharacteristic
826C4—22no—
827C4—24no—
828C4—42no—
829C4—42no—
830C4—534no—
831C4—1062no—
832C4—1062no—
833C4—2122no—
834C4—2122no—
835C4#1681126312yes—
836C4C22×#1171994511yescharacteristic
837C4C2×#1313326211yescharacteristic
838C2—42no—
839C2—82no—
840C2—4242no—
841C2—4242no—
842C2—2122no—
843C2#2028703814yesdirect product factor
844C2C2×#1681126311yescharacteristic
845C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
846C2C2×#1681143211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#417C2
socleC23×C53C22×D4
hypercenterC2×#417D53
hypocenterC53C2×#3332
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#16811292C2semidirect
2. C2×#16811274C2semidirect
3. #20287038C2direct (N × H)
4. C2×#16810968C2semidirect
5. C2×#16810941C2semidirect
6. C2×#16810940C2semidirect
7. C2×#16810906C2semidirect
8. C2×#16810876C2semidirect
9. C2×#16810875C2semidirect
10. C2×#16810817C2semidirect
11. C2×#16810771C2semidirect
12. C2×#16810768C2semidirect
13. C2×#16810708C2semidirect
14. C2×#16810699C2semidirect
15. C2×#16810623C2semidirect
16. C2×C53×#417C2semidirect
24. #16811292C22semidirect
26. #16811274C22semidirect
44. #16810968C22semidirect
45. #16810941C22semidirect
46. #16810940C22semidirect
47. #16810906C22semidirect
48. #16810876C22semidirect
49. #16810875C22semidirect
50. #16810817C22semidirect
51. #16810771C22semidirect
52. #16810768C22semidirect
53. #16810708C22semidirect
54. #16810699C22semidirect
59. #16810623C22semidirect
72. C53×#417C22semidirect
196. C2×Q8×C53#41semidirect
321. Q8×C53C2×#41semidirect
430. C2×#417D53semidirect
433. C2×C53#3332semidirect
486. #417C2×D53semidirect
500. C53C2×#3332semidirect
626. C2×Q8#11719945semidirect
746. Q8C2×#11719945semidirect
843. C2#20287038direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112922
C2×#168112742
#202870382
C2×#168109682
C2×#168109412
C2×#168109402
C2×#168109062
C2×#168108762
C2×#168108752
C2×#168108172
C2×#168107712
C2×#168107682
C2×#168107082
C2×#168106992
C2×#168106232
C2×C53×#4172
C2×#333253