Finite Group Databasebeta

← C2×#20285566 #28254744

Subgroups — C2×#20285566 #28254744

Order 13568.

2378 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811201C211yesmaximal, characteristic, complemented
2C2×#16811189C211yesmaximal, characteristic, complemented
3#20285566C2116yesmaximal, direct product factor
4C2×#16810942C211yesmaximal, characteristic, complemented
5C2×#16810962C211yesmaximal, characteristic, complemented
6C2×#16810946C211yesmaximal, characteristic, complemented
7C2×#16810934C211yesmaximal, characteristic, complemented
8C2×#16810873C211yesmaximal, characteristic, complemented
9C2×#16810872C211yesmaximal, characteristic, complemented
10C2×#16810858C211yesmaximal, characteristic, complemented
11C2×#16810849C211yesmaximal, characteristic, complemented
12C2×#16810768C211yesmaximal, characteristic, complemented
13C2×#16810772C211yesmaximal, characteristic, complemented
14C2×#16810755C211yesmaximal, characteristic, complemented
15C2×#16810588C211yesmaximal, characteristic, complemented
16C2×C53×#449C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×D4×D53C2211yescharacteristic
19C22×#11719924C2211yescharacteristic
20C22×#11719922C2211yescharacteristic
21C22×#11719912C2211yescharacteristic, complemented
22C22×C8×D53C2211yescharacteristic, complemented
23#16811201—24no—
24#16811201C2218yescomplemented
25#16811189—24no—
26#16811189C2218yescomplemented
27C2×#13133213—21no—
28C2×#13133203—21no—
29C2×#13133196—21no—
30C2×#13133193C2211yescharacteristic
31C2×#13133193C2211yescharacteristic, complemented
32C2×#13133192C2211yescharacteristic
33C2×#13133191—21no—
34C2×#13133191C2211yescharacteristic
35C2×#13133189—21no—
36C2×#13133189—21no—
37C2×#13133188C2211yescharacteristic
38C2×#13133188C2211yescharacteristic
39C2×#13133188C2211yescharacteristic, complemented
40C2×#13133187—21no—
41C2×#13133185—21no—
42C2×#13133175C2211yescharacteristic
43C22×C4⋊Dic53C2211yescharacteristic, complemented
44#16810962C2218yescomplemented
45#16810946C2218yescomplemented
46#16810942C2218yescomplemented
47#16810934C2218yescomplemented
48#16810873C2218yescomplemented
49#16810872C2218yescomplemented
50#16810858C2218yescomplemented
51#16810849C2218yescomplemented
52#16810772C2218yescomplemented
53#16810768C2218yescomplemented
54#16810755C2218yescomplemented
55C2×#13133150C2211yescharacteristic, complemented
56C2×#13133150C2211yescharacteristic, complemented
57C2×#13133149C2211yescharacteristic, complemented
58C2×#13133149C2211yescharacteristic, complemented
59C2×#13133141C2211yescharacteristic, complemented
60C2×#13133139C2211yescharacteristic
61C2×#13133139C2211yescharacteristic
62C2×#13133138C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C2×#13133138C2211yescharacteristic, complemented
65#16810588C2218yescomplemented
66C2×C22⋊#88322C2211yescharacteristic, complemented
67C2×#13133129C2211yescharacteristic
68C2×#13133129C2211yescharacteristic
69C22×#41×C53C2211yescharacteristic, complemented
70C22×SD16×C53C2211yescharacteristic
71C22×D8×C53C2211yescharacteristic
72C2×#121×C53C2211yescharacteristic
73C53×#449C2218yescomplemented
74C2×#103×C53C2211yescharacteristic, complemented
75C2×#102×C53C2211yescharacteristic, complemented
76C2×C22⋊C8×C53C2211yescharacteristic, complemented
77C24×D53—21no—
78C2×#11719945—42no—
79C2×#11719945—42no—
80C2×#11719945D414yes—
81C2×#11719945C2314yes—
82C22×Dic106D411yescharacteristic
83C22×D212—21no—
84C22×D212D411yescharacteristic
85C22×D212C2311yescharacteristic
86C22×C22⋊D53—21no—
87C22×C22⋊D53—21no—
88C22×C22⋊D53—21no—
89C22×C22⋊D53—21no—
90C22×C22⋊D53—21no—
91C22×C22⋊D53D411yescharacteristic
92C22×C22⋊D53D411yescharacteristic
93C2×D4×D53—22no—
94C2×D4×D53—42no—
95C2×D4×D53—42no—
96C2×D4×D53C2314yes—
97C23×Dic53—21no—
98C22×C4×D53C2311yescharacteristic
99C22×C4×D53C2311yescharacteristic
100C2×#11719924—42no—
101C2×#11719924C2314yes—
102C2×#11719922—42no—
103C2×#11719922C2314yes—
104C2×#11719912—42no—
105C2×#11719912C2314yescomplemented
106C22×#88322C2311yescharacteristic
107C22×#88322C2311yescharacteristic
108C2×C8×D53—42no—
109C2×C8×D53C2314yescomplemented
110#13133213—28no—
111#13133203—28no—
112#13133196—28no—
113#13133193—22no—
114#13133193—22no—
115#13133193C2314yes—
116#13133193C2314yescomplemented
117#13133192—22no—
118#13133192C2314yes—
119#13133191—22no—
120#13133191—28no—
121#13133191C2314yes—
122#13133189—28no—
123#13133189—28no—
124#13133188—22no—
125#13133188—22no—
126#13133188—22no—
127#13133188C2314yes—
128#13133188C2314yes—
129#13133188C2314yescomplemented
130#13133187—28no—
131#13133185—28no—
132#13133175—22no—
133#13133175C2314yes—
134C2×C4⋊Dic53—21no—
135C2×C4⋊Dic53—22no—
136C2×C4⋊Dic53C2311yescharacteristic
137C2×C4⋊Dic53C2311yescharacteristic
138C2×C4⋊Dic53C2311yescharacteristic
139C2×C4⋊Dic53C2314yescomplemented
140C2×#11719919—21no—
141C2×#11719919—21no—
142C2×C22⋊Dic53—21no—
143C2×C22⋊Dic53—21no—
144C2×C22⋊Dic53—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×#11719921—21no—
150C2×C4×Dic53—21no—
151#13133150C2314yescomplemented
152#13133150C2314yescomplemented
153#13133149C2314yescomplemented
154#13133149C2314yescomplemented
155#13133141C2314yescomplemented
156#13133139C2314yes—
157#13133139C2314yes—
158#13133138C2314yes—
159#13133138C2314yes—
160#13133138C2314yescomplemented
161C22⋊#88322C2314yescomplemented
162#13133129C2314yes—
163#13133129C2314yes—
164C2×#41×C53—22no—
165C2×#41×C53—42no—
166C2×#41×C53—42no—
167C2×#41×C53C2314yescomplemented
168C22×Q8×C53C2311yescharacteristic
169C22×D4×C53—21no—
170C22×D4×C53—21no—
171C22×D4×C53C2311yescharacteristic
172C22×D4×C53C2311yescharacteristic
173C23×C4×C53—21no—
174C23×C4×C53C2311yescharacteristic
175C2×SD16×C53—42no—
176C2×SD16×C53C2314yes—
177C2×D8×C53—42no—
178C2×D8×C53C2314yes—
179C22×C8×C53C2311yescharacteristic
180C22×C8×C53C2311yescharacteristic
181#121×C53—22no—
182#121×C53C2314yes—
183C2×C4⋊C4×C53C2311yescharacteristic
184C2×C22⋊C4×C53—21no—
185#103×C53C2314yescomplemented
186#102×C53C2314yescomplemented
187C22⋊C8×C53C2314yescomplemented
188C24×C53—21no—
189C24×C53—21no—
190C24×C53C2×D411yescharacteristic
191C23×D53—21no—
192C23×D53—24no—
193C23×D53—44no—
194C23×D53—82no—
195C23×D53—82no—
196C23×D53C2×D411yescharacteristic
197C23×D53C2×D411yescharacteristic
198#41×C53—44no—
199#41×C53—44no—
200#41×C53—48no—
201C2×Q8×C53—21no—
202C2×Q8×C53—22no—
203C2×Q8×C53—22no—
204C2×Q8×C53C2412yes—
205C2×D4×C53—24no—
206C2×D4×C53—24no—
207C2×D4×C53—21no—
208C2×D4×C53—21no—
209C2×D4×C53—22no—
210C2×D4×C53—22no—
211C2×D4×C53—22no—
212C2×D4×C53—22no—
213C2×D4×C53—44no—
214C2×D4×C53—82no—
215C2×D4×C53C2412yes—
216C2×D4×C53C2412yes—
217C22×C4×C53—22no—
218C22×C4×C53—22no—
219C22×C4×C53—21no—
220C22×C4×C53—21no—
221C22×C4×C53—24no—
222C22×C4×C53—44no—
223C22×C4×C53C2×D411yescharacteristic
224C22×C4×C53C2×D412yes—
225C22×C4×C53C2412yes—
226C22×C4×C53C2411yescharacteristic
227C2×C22⋊D53—24no—
228C2×C22⋊D53—24no—
229C2×C22⋊D53—24no—
230C2×C22⋊D53—24no—
231C2×C22⋊D53—24no—
232C2×C22⋊D53—42no—
233C2×C22⋊D53—42no—
234C2×C22⋊D53—44no—
235C2×C22⋊D53—82no—
236C2×C22⋊D53—82no—
237C2×C22⋊D53—82no—
238C2×C22⋊D53—82no—
239C2×C22⋊D53C2×D414yes—
240C2×C22⋊D53C2×D414yes—
241C22×Dic53—21no—
242C22×Dic53—21no—
243C22×Dic53—21no—
244C22×Dic53—24no—
245C22×Dic53—82no—
246C22×Dic53C2×D411yescharacteristic
247C22×Dic53C2×D411yescharacteristic
248D4×D53—44no—
249D4×D53—44no—
250D4×D53—48no—
251#11719945—48no—
252#11719945—44no—
253#11719945—44no—
254C2×D212—22no—
255C2×D212—22no—
256C2×D212—21no—
257C2×D212—24no—
258C2×D212—42no—
259C2×D212—82no—
260C2×D212C2×D414yes—
261C2×D212C2412yes—
262C2×C4×D53—22no—
263C2×C4×D53—22no—
264C2×C4×D53—22no—
265C2×C4×D53—22no—
266C2×C4×D53C2×D412yes—
267C2×C4×D53C2×D412yes—
268C2×C4×D53C2412yes—
269C2×C4×D53C2412yes—
270C2×Dic106—42no—
271C2×Dic106C2×D414yes—
272SD16×C53—44no—
273D8×C53—44no—
274C2×C8×C53—22no—
275C2×C8×C53—22no—
276C2×C8×C53C2412yes—
277C2×C8×C53C2412yes—
278C4⋊C4×C53—21no—
279C4⋊C4×C53C2412yes—
280C22⋊C4×C53—24no—
281C22⋊Dic53—24no—
282C22⋊Dic53—24no—
283C22⋊Dic53—24no—
284#11719924—44no—
285#11719922—44no—
286#11719921—24no—
287#11719921—24no—
288#11719921—24no—
289#11719921—24no—
290#11719921—24no—
291C4⋊Dic53—21no—
292C4⋊Dic53—21no—
293C4⋊Dic53—24no—
294C4⋊Dic53—21no—
295C4⋊Dic53C2412yes—
296C4⋊Dic53C2412yes—
297C4⋊Dic53C2412yes—
298#11719919—24no—
299#11719919—24no—
300C4×Dic53—24no—
301C2×#88322—22no—
302C2×#88322—22no—
303C2×#88322C2412yes—
304C2×#88322C2412yes—
305#11719912—44no—
306C8×D53—44no—
307C23×C53—22no—
308C23×C53—22no—
309C23×C53—22no—
310C23×C53—22no—
311C23×C53—22no—
312C23×C53—42no—
313C23×C53—42no—
314C23×C53—42no—
315C23×C53—42no—
316C23×C53—42no—
317C23×C53—42no—
318C23×C53C22×D412yes—
319C23×C53C22×D411yescharacteristic
320C22×D53—22no—
321C22×D53—22no—
322C22×D53—22no—
323C22×D53—22no—
324C22×D53—22no—
325C22×D53—22no—
326C22×D53—22no—
327C22×D53—48no—
328C22×D53—42no—
329C22×D53—42no—
330C22×D53—42no—
331C22×D53—84no—
332C22×D53—84no—
333C22×D53—816no—
334C22×D53C22×D412yes—
335C22×D53C22×D412yes—
336Q8×C53—22no—
337Q8×C53—22no—
338Q8×C53—42no—
339D4×C53—22no—
340D4×C53—22no—
341D4×C53—22no—
342D4×C53—22no—
343D4×C53—48no—
344D4×C53—42no—
345D4×C53—42no—
346D4×C53—84no—
347C2×C4×C53—22no—
348C2×C4×C53—24no—
349C2×C4×C53—22no—
350C2×C4×C53—22no—
351C2×C4×C53—22no—
352C2×C4×C53—22no—
353C2×C4×C53—48no—
354C2×C4×C53—42no—
355C2×C4×C53—42no—
356C2×C4×C53C22×D412yes—
357C2×C4×C53C22×D411yescharacteristic
358C2×C4×C53H(5,𝔽2)12yes—
359C2×C4×C53H(5,𝔽2)12yes—
360C2×C4×C53C2511yescharacteristic
361C22⋊D53—44no—
362C22⋊D53—44no—
363C22⋊D53—48no—
364C22⋊D53—84no—
365C22⋊D53—84no—
366C22⋊D53—84no—
367C22⋊D53—84no—
368C2×Dic53—22no—
369C2×Dic53—22no—
370C2×Dic53—22no—
371C2×Dic53—22no—
372C2×Dic53—22no—
373C2×Dic53—42no—
374C2×Dic53—42no—
375C2×Dic53—42no—
376C2×Dic53—84no—
377C2×Dic53C22×D412yes—
378C2×Dic53C22×D412yes—
379D212—22no—
380D212—22no—
381D212—44no—
382D212—42no—
383D212—84no—
384C4×D53—24no—
385C4×D53—24no—
386C4×D53—22no—
387C4×D53—22no—
388C4×D53—22no—
389C4×D53—22no—
390Dic106—44no—
391C8×C53—22no—
392C8×C53—22no—
393#88322—22no—
394#88322—22no—
395C2×#3198—531nomaximal, Sylow
396C22×C53—22no—
397C22×C53—22no—
398C22×C53—22no—
399C22×C53—44no—
400C22×C53—42no—
401C22×C53—42no—
402C22×C53—42no—
403C22×C53—42no—
404C22×C53—42no—
405C22×C53—42no—
406C22×C53—84no—
407C22×C53—84no—
408C22×C53#53412yes—
409C22×C53#57612yes—
410C22×C53#57712yes—
411C22×C53C23×D411yescharacteristic
412C2×D53—22no—
413C2×D53—22no—
414C2×D53—22no—
415C2×D53—22no—
416C2×D53—22no—
417C2×D53—22no—
418C2×D53—44no—
419C2×D53—44no—
420C2×D53—42no—
421C2×D53—42no—
422C2×D53—42no—
423C2×D53—816no—
424C2×D53—84no—
425C4×C53—22no—
426C4×C53—42no—
427C4×C53—42no—
428C4×C53#53412yes—
429C4×C53C2×H(5,𝔽2)11yescharacteristic
430C4×C53C2×H(5,𝔽2)11yescharacteristic
431Dic53—22no—
432Dic53—22no—
433Dic53—42no—
434Dic53—42no—
435Dic53—42no—
436C2×#537—531no—
437C2×#535—531no—
438#3198—5316no—
439C2×#481—531no—
440C2×#485—531no—
441C2×#482—531no—
442C2×#480—531no—
443C2×#469—531no—
444C2×#468—531no—
445C2×#466—531no—
446C2×#465—531no—
447C2×#449—531no—
448C2×#449D5311yescharacteristic, complemented
449C2×#450—531no—
450C2×#447—531no—
451C2×#408—531no—
452C2×C53—42no—
453C2×C53—82no—
454C2×C53—82no—
455C2×C53#319814yescomplemented
456C2×C53C2×#53411yescharacteristic
457C2×C53C2×#57611yescharacteristic
458C2×C53C2×#57711yescharacteristic
459D53—42no—
460D53—42no—
461D53—82no—
462C22×#41—531no—
463C22×#41C2×D5311yescharacteristic, complemented
464C23×D4—531no—
465C22×SD16—531no—
466C22×SD16C2×D5311yescharacteristic
467C22×D8—531no—
468C22×D8C2×D5311yescharacteristic
469C22×M16—531no—
470C23×C8—531no—
471#537—538no—
472#537—1064no—
473#535—538no—
474#535—1064no—
475C2×#127—1061no—
476C2×#124—1061no—
477C2×C22⋊Q8—531no—
478C2×C22⋊Q8—531no—
479C2×C22⋊Q8—1061no—
480C2×#121—531no—
481C2×#121—531no—
482C2×#121—531no—
483C2×#121—531no—
484C2×#121—531no—
485C2×#121—1061no—
486C2×#121—1061no—
487C2×#121—1061no—
488C2×#121C2×D5311yescharacteristic
489C2×#120—1061no—
490C2×#120—1061no—
491C2×#117—531no—
492C22×C4⋊C4—531no—
493#485—538no—
494#482—538no—
495#481—538no—
496#480—538no—
497#469—538no—
498#468—538no—
499#466—538no—
500#465—538no—
501#450—538no—
502#449—538no—
503#449C2×D5318yescomplemented
504#447—538no—
505C2×#107—531no—
506C2×#107—531no—
507C2×#106—531no—
508C2×#106—531no—
509C2×#103—531no—
510C2×#103C2×D5311yescharacteristic, complemented
511C2×#102—531no—
512C2×#102—531no—
513C2×#102—531no—
514C2×#102—531no—
515C2×#102—531no—
516C2×#102C2×D5311yescharacteristic, complemented
517#408—538no—
518C2×C22⋊C8—531no—
519C2×C22⋊C8—531no—
520C2×C22⋊C8—531no—
521C2×C22⋊C8C2×D5311yescharacteristic, complemented
522C53C2×#319811yescharacteristic, complemented, Sylow
523C25—1061no—
524C2×#41—22no—
525C2×#41—42no—
526C2×#41—42no—
527C2×#41—534no—
528C2×#41—534no—
529C2×#41—2122no—
530C2×#41—2122no—
531C2×#41C22×D5314yescomplemented
532C22×Q8—531no—
533C22×Q8C22×D5311yescharacteristic
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—531no—
537C22×D4—531no—
538C22×D4—534no—
539C22×D4—531no—
540C22×D4—531no—
541C22×D4—1061no—
542C22×D4—1062no—
543C22×D4—1061no—
544C22×D4—1061no—
545C22×D4—1061no—
546C22×D4—1061no—
547C22×D4—1061no—
548C22×D4—2122no—
549C22×D4—2122no—
550C22×D4C22×D5311yescharacteristic
551C22×D4C22×D5311yescharacteristic
552C23×C4—21no—
553C23×C4—531no—
554C23×C4—531no—
555C23×C4—1061no—
556C23×C4C22×D5311yescharacteristic
557C2×SD16—42no—
558C2×SD16—534no—
559C2×SD16—2122no—
560C2×SD16C22×D5314yes—
561C2×D8—42no—
562C2×D8—534no—
563C2×D8—2122no—
564C2×D8C22×D5314yes—
565C2×M16—534no—
566C2×M16—2122no—
567C22×C8—531no—
568C22×C8—531no—
569C22×C8—534no—
570C22×C8—2122no—
571C22×C8C22×D5311yescharacteristic
572C22×C8C22×D5311yescharacteristic
573#127—1068no—
574#124—1068no—
575C22⋊Q8—534no—
576C22⋊Q8—534no—
577C22⋊Q8—1068no—
578C22⋊Q8—1062no—
579C22⋊Q8—1062no—
580#121—22no—
581#121—534no—
582#121—534no—
583#121—534no—
584#121—534no—
585#121—534no—
586#121—1062no—
587#121—1068no—
588#121—1062no—
589#121—1062no—
590#121—1062no—
591#121—1068no—
592#121—1068no—
593#121—1062no—
594#121C22×D5314yes—
595#120—1068no—
596#120—1068no—
597#117—534no—
598#117—1062no—
599C2×C4⋊C4—531no—
600C2×C4⋊C4—531no—
601C2×C4⋊C4—534no—
602C2×C4⋊C4—531no—
603C2×C4⋊C4—1061no—
604C2×C4⋊C4—1061no—
605C2×C4⋊C4—1061no—
606C2×C4⋊C4—1062no—
607C2×C4⋊C4C22×D5311yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—1061no—
610C2×C22⋊C4—1061no—
611C2×C22⋊C4—1061no—
612C2×C22⋊C4—1061no—
613C2×C22⋊C4—1061no—
614C2×C22⋊C4—1061no—
615C2×C22⋊C4—1061no—
616C2×C22⋊C4—1061no—
617C2×C42—1061no—
618#107—534no—
619#107—534no—
620#106—534no—
621#106—534no—
622#103—534no—
623#103C22×D5314yescomplemented
624#102—534no—
625#102—534no—
626#102—534no—
627#102—534no—
628#102—534no—
629#102C22×D5314yescomplemented
630C22⋊C8—534no—
631C22⋊C8—534no—
632C22⋊C8—534no—
633C22⋊C8C22×D5314yescomplemented
634C24—21no—
635C24—21no—
636C24—531no—
637C24—531no—
638C24—1064no—
639C24—1061no—
640C24—4242no—
641C24—4242no—
642C24—2124no—
643C24D4×D5311yescharacteristic
644#41—44no—
645#41—44no—
646#41—48no—
647#41—2128no—
648#41—2124no—
649#41—2124no—
650C2×Q8—21no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—534no—
654C2×Q8—2122no—
655C2×Q8C23×D5312yes—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—22no—
663C2×D4—22no—
664C2×D4—44no—
665C2×D4—82no—
666C2×D4—534no—
667C2×D4—534no—
668C2×D4—534no—
669C2×D4—532no—
670C2×D4—1064no—
671C2×D4—1064no—
672C2×D4—1064no—
673C2×D4—1064no—
674C2×D4—1064no—
675C2×D4—1064no—
676C2×D4—1061no—
677C2×D4—1062no—
678C2×D4—1062no—
679C2×D4—4242no—
680C2×D4—4242no—
681C2×D4—4242no—
682C2×D4—4242no—
683C2×D4—4242no—
684C2×D4—2122no—
685C2×D4—2124no—
686C2×D4—2124no—
687C2×D4—2128no—
688C2×D4—2122no—
689C2×D4—2122no—
690C2×D4—2124no—
691C2×D4C23×D5312yes—
692C2×D4C23×D5312yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—24no—
698C22×C4—44no—
699C22×C4—531no—
700C22×C4—531no—
701C22×C4—532no—
702C22×C4—532no—
703C22×C4—532no—
704C22×C4—532no—
705C22×C4—1062no—
706C22×C4—1062no—
707C22×C4—1062no—
708C22×C4—1062no—
709C22×C4—1064no—
710C22×C4—1061no—
711C22×C4—1061no—
712C22×C4—1061no—
713C22×C4—4242no—
714C22×C4D4×D5312yes—
715C22×C4D4×D5311yescharacteristic
716C22×C4C23×D5312yes—
717C22×C4C23×D5311yescharacteristic
718SD16—44no—
719SD16—2124no—
720D8—44no—
721D8—2124no—
722M16—2124no—
723C2×C8—22no—
724C2×C8—22no—
725C2×C8—532no—
726C2×C8—532no—
727C2×C8—1062no—
728C2×C8—1062no—
729C2×C8—2124no—
730C2×C8C23×D5312yes—
731C2×C8C23×D5312yes—
732C4⋊C4—21no—
733C4⋊C4—532no—
734C4⋊C4—532no—
735C4⋊C4—532no—
736C4⋊C4—1064no—
737C4⋊C4—1064no—
738C4⋊C4—1064no—
739C4⋊C4—1061no—
740C4⋊C4—1061no—
741C4⋊C4—1061no—
742C4⋊C4C23×D5312yes—
743C22⋊C4—24no—
744C22⋊C4—1064no—
745C22⋊C4—1064no—
746C22⋊C4—1064no—
747C22⋊C4—1064no—
748C22⋊C4—1064no—
749C22⋊C4—1064no—
750C22⋊C4—1064no—
751C22⋊C4—1064no—
752C42—1064no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—532no—
765C23—532no—
766C23—1062no—
767C23—1062no—
768C23—1062no—
769C23—1062no—
770C23—1062no—
771C23—1062no—
772C23—1062no—
773C23—4244no—
774C23—4244no—
775C23—42416no—
776C23—2128no—
777C23—2122no—
778C23—2122no—
779C23—2122no—
780C23C2×D4×D5312yes—
781C23C2×D4×D5311yescharacteristic
782Q8—22no—
783Q8—22no—
784Q8—42no—
785Q8—2124no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—48no—
791D4—42no—
792D4—42no—
793D4—84no—
794D4—1062no—
795D4—1062no—
796D4—4244no—
797D4—4244no—
798D4—4244no—
799D4—4244no—
800D4—4244no—
801D4—2124no—
802D4—2124no—
803D4—2124no—
804D4—2128no—
805D4—2122no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—48no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—532no—
816C2×C4—532no—
817C2×C4—1062no—
818C2×C4—1062no—
819C2×C4—1064no—
820C2×C4—1064no—
821C2×C4—1062no—
822C2×C4—1062no—
823C2×C4—1062no—
824C2×C4—1062no—
825C2×C4—1062no—
826C2×C4—1062no—
827C2×C4—1062no—
828C2×C4—4244no—
829C2×C4—2122no—
830C2×C4—2122no—
831C2×C4—2122no—
832C2×C4C2×D4×D5312yes—
833C2×C4C2×D4×D5311yescharacteristic
834C2×C4#1313326212yes—
835C2×C4#1313326212yes—
836C2×C4C24×D5311yescharacteristic
837C8—22no—
838C8—22no—
839C8—1062no—
840C8—1062no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—44no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—84no—
852C22—84no—
853C22—1062no—
854C22—1062no—
855C22—1062no—
856C22—1062no—
857C22—1062no—
858C22—1062no—
859C22—42416no—
860C22—4244no—
861C22—2122no—
862C22—2122no—
863C22—2122no—
864C22—2124no—
865C22—2124no—
866C22#1681118312yes—
867C22#1681142712yes—
868C22#1681143012yes—
869C22C22×D4×D5311yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—1062no—
874C4—1062no—
875C4—2122no—
876C4—2122no—
877C4—2122no—
878C4#1681118312yes—
879C4C2×#1313326211yescharacteristic
880C4C2×#1313326211yescharacteristic
881C2—42no—
882C2—82no—
883C2—82no—
884C2—4242no—
885C2—2122no—
886C2—2122no—
887C2#2028556614yesdirect product factor
888C2C2×#1681118311yescharacteristic
889C2C2×#1681142711yescharacteristic
890C2C2×#1681143011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#449C2
socleC23×C53C22×D4
hypercenterC2×#449D53
hypocenterC53C2×#3198
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#16811201C2semidirect
2. C2×#16811189C2semidirect
3. #20285566C2direct (N × H)
4. C2×#16810942C2semidirect
5. C2×#16810962C2semidirect
6. C2×#16810946C2semidirect
7. C2×#16810934C2semidirect
8. C2×#16810873C2semidirect
9. C2×#16810872C2semidirect
10. C2×#16810858C2semidirect
11. C2×#16810849C2semidirect
12. C2×#16810768C2semidirect
13. C2×#16810772C2semidirect
14. C2×#16810755C2semidirect
15. C2×#16810588C2semidirect
16. C2×C53×#449C2semidirect
21. C22×#11719912C22semidirect
22. C22×C8×D53C22semidirect
24. #16811201C22semidirect
26. #16811189C22semidirect
31. C2×#13133193C22semidirect
39. C2×#13133188C22semidirect
43. C22×C4⋊Dic53C22semidirect
44. #16810962C22semidirect
45. #16810946C22semidirect
46. #16810942C22semidirect
47. #16810934C22semidirect
48. #16810873C22semidirect
49. #16810872C22semidirect
50. #16810858C22semidirect
51. #16810849C22semidirect
52. #16810772C22semidirect
53. #16810768C22semidirect
54. #16810755C22semidirect
55. C2×#13133150C22semidirect
56. C2×#13133150C22semidirect
57. C2×#13133149C22semidirect
58. C2×#13133149C22semidirect
59. C2×#13133141C22semidirect
64. C2×#13133138C22semidirect
65. #16810588C22semidirect
66. C2×C22⋊#88322C22semidirect
69. C22×#41×C53C22semidirect
73. C53×#449C22semidirect
74. C2×#103×C53C22semidirect
75. C2×#102×C53C22semidirect
76. C2×C22⋊C8×C53C22semidirect
105. C2×#11719912C23semidirect
109. C2×C8×D53C23semidirect
116. #13133193C23semidirect
129. #13133188C23semidirect
139. C2×C4⋊Dic53C23semidirect
151. #13133150C23semidirect
152. #13133150C23semidirect
153. #13133149C23semidirect
154. #13133149C23semidirect
155. #13133141C23semidirect
160. #13133138C23semidirect
161. C22⋊#88322C23semidirect
167. C2×#41×C53C23semidirect
185. #103×C53C23semidirect
186. #102×C53C23semidirect
187. C22⋊C8×C53C23semidirect
448. C2×#449D53semidirect
455. C2×C53#3198semidirect
463. C22×#41C2×D53semidirect
503. #449C2×D53semidirect
510. C2×#103C2×D53semidirect
516. C2×#102C2×D53semidirect
521. C2×C22⋊C8C2×D53semidirect
522. C53C2×#3198semidirect
531. C2×#41C22×D53semidirect
623. #103C22×D53semidirect
629. #102C22×D53semidirect
633. C22⋊C8C22×D53semidirect
887. C2#20285566direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112012
C2×#168111892
#202855662
C2×#168109422
C2×#168109622
C2×#168109462
C2×#168109342
C2×#168108732
C2×#168108722
C2×#168108582
C2×#168108492
C2×#168107682
C2×#168107722
C2×#168107552
C2×#168105882
C2×C53×#4492
C2×#319853