Finite Group Databasebeta

← C2×#20285561 #28254739

Subgroups — C2×#20285561 #28254739

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×#16811187C211yesmaximal, characteristic, complemented
2#20285561C2116yesmaximal, direct product factor
3C2×#16810941C211yesmaximal, characteristic, complemented
4C2×#16810961C211yesmaximal, characteristic, complemented
5C2×#16810944C211yesmaximal, characteristic, complemented
6C2×#16810936C211yesmaximal, characteristic, complemented
7C2×#16810874C211yesmaximal, characteristic, complemented
8C2×#16810871C211yesmaximal, characteristic, complemented
9C2×#16810857C211yesmaximal, characteristic, complemented
10C2×#16810854C211yesmaximal, characteristic, complemented
11C2×#16810768C211yesmaximal, characteristic, complemented
12C2×#16810768C211yesmaximal, characteristic, complemented
13C2×#16810773C211yesmaximal, characteristic, complemented
14C2×#16810756C211yesmaximal, characteristic, complemented
15C2×#16810590C211yesmaximal, characteristic, complemented
16C2×C53×#537C211yesmaximal, characteristic, complemented
17C23×D212C2211yescharacteristic
18C22×#11719924C2211yescharacteristic
19C22×#11719924C2211yescharacteristic
20C22×#11719922C2211yescharacteristic
21C22×#11719922C2211yescharacteristic
22C22×#11719917C2211yescharacteristic, complemented
23C23×#88322C2211yescharacteristic, complemented
24#16811187—24no—
25#16811187C2218yescomplemented
26C2×#13133213—21no—
27C2×#13133206—21no—
28C2×#13133191C2211yescharacteristic
29C2×#13133191C2211yescharacteristic
30C2×#13133191C2211yescharacteristic
31C2×#13133191C2211yescharacteristic
32C2×#13133185—21no—
33C2×#13133185—21no—
34C2×#13133176C2211yescharacteristic
35#16810961C2218yescomplemented
36#16810944C2218yescomplemented
37#16810941C2218yescomplemented
38#16810936C2218yescomplemented
39#16810874C2218yescomplemented
40#16810871C2218yescomplemented
41#16810857C2218yescomplemented
42#16810854C2218yescomplemented
43#16810773C2218yescomplemented
44#16810768C2218yescomplemented
45#16810768C2218yescomplemented
46#16810756C2218yescomplemented
47C2×#13133150C2211yescharacteristic, complemented
48C2×#13133150C2211yescharacteristic, complemented
49C2×#13133148C2211yescharacteristic, complemented
50C2×#13133148C2211yescharacteristic, complemented
51C2×#13133141C2211yescharacteristic, complemented
52C2×#13133141C2211yescharacteristic, complemented
53C2×#13133138C2211yescharacteristic, complemented
54C2×#13133138C2211yescharacteristic, complemented
55C2×#13133137C2211yescharacteristic
56C2×#13133137C2211yescharacteristic
57C2×#13133137C2211yescharacteristic
58C2×#13133137C2211yescharacteristic
59#16810590C2218yescomplemented
60C2×C22⋊#88322C2211yescharacteristic
61C2×C22⋊#88322C2211yescharacteristic
62C2×C22⋊#88322C2211yescharacteristic, complemented
63C2×C22⋊#88322C2211yescharacteristic, complemented
64C22×#41×C53C2211yescharacteristic
65C22×#41×C53C2211yescharacteristic, complemented
66C53×#537—24no—
67C53×#537C2218yescomplemented
68C2×C22⋊Q8×C53—21no—
69C2×C22⋊Q8×C53C2211yescharacteristic
70C2×C22⋊Q8×C53C2211yescharacteristic, complemented
71C2×#121×C53—21no—
72C2×#121×C53—21no—
73C2×#121×C53—21no—
74C2×#121×C53C2211yescharacteristic
75C2×#121×C53C2211yescharacteristic, complemented
76C22×C4⋊C4×C53C2211yescharacteristic, complemented
77C24×D53—21no—
78C22×D212—21no—
79C22×D212—22no—
80C22×D212—42no—
81C22×D212—42no—
82C22×D212C2311yescharacteristic
83C22×D212C2311yescharacteristic
84C22×D212C2314yes—
85C22×C22⋊D53—21no—
86C22×C22⋊D53—21no—
87C22×C22⋊D53—21no—
88C22×C22⋊D53—21no—
89C2×#11719924—42no—
90C2×#11719924—42no—
91C2×#11719924C2314yes—
92C2×#11719924C2314yes—
93C2×#11719922—42no—
94C2×#11719922—42no—
95C2×#11719922C2314yes—
96C2×#11719922C2314yes—
97C2×#11719917—42no—
98C2×#11719917C2314yescomplemented
99C22×#88322—42no—
100C22×#88322C2311yescharacteristic
101C22×#88322C2311yescharacteristic
102C22×#88322C2311yescharacteristic
103C22×#88322C2311yescharacteristic
104C22×#88322C2314yescomplemented
105#13133213—28no—
106#13133206—28no—
107#13133191—22no—
108#13133191—22no—
109#13133191—22no—
110#13133191—22no—
111#13133191C2314yes—
112#13133191C2314yes—
113#13133191C2314yes—
114#13133191C2314yes—
115#13133185—28no—
116#13133185—28no—
117#13133176—22no—
118#13133176C2314yes—
119C2×C4⋊Dic53C2311yescharacteristic
120C2×C4⋊Dic53C2311yescharacteristic
121C2×C22⋊Dic53—21no—
122C2×#11719921—21no—
123C2×#11719921—21no—
124C2×#11719921—21no—
125C2×#11719921—21no—
126C2×C4×Dic53—21no—
127#13133150C2314yescomplemented
128#13133150C2314yescomplemented
129#13133148C2314yescomplemented
130#13133148C2314yescomplemented
131#13133141C2314yescomplemented
132#13133141C2314yescomplemented
133#13133138C2314yescomplemented
134#13133138C2314yescomplemented
135#13133137C2314yes—
136#13133137C2314yes—
137#13133137C2314yes—
138#13133137C2314yes—
139C22⋊#88322C2314yes—
140C22⋊#88322C2314yes—
141C22⋊#88322C2314yescomplemented
142C22⋊#88322C2314yescomplemented
143C2×#41×C53—22no—
144C2×#41×C53—42no—
145C2×#41×C53—42no—
146C2×#41×C53—42no—
147C2×#41×C53—42no—
148C2×#41×C53D414yes—
149C2×#41×C53C2314yes—
150C2×#41×C53C2314yescomplemented
151C22×Q8×C53D411yescharacteristic
152C22×Q8×C53C2311yescharacteristic
153C22×D4×C53—21no—
154C22×D4×C53—21no—
155C22×D4×C53—21no—
156C22×D4×C53D411yescharacteristic
157C22×D4×C53D411yescharacteristic
158C22×D4×C53D411yescharacteristic
159C22×D4×C53C2311yescharacteristic
160C23×C4×C53—21no—
161C23×C4×C53—21no—
162C23×C4×C53C2311yescharacteristic
163C23×C4×C53C2311yescharacteristic
164C23×C4×C53C2311yescharacteristic
165C22⋊Q8×C53—28no—
166C22⋊Q8×C53—22no—
167C22⋊Q8×C53—22no—
168C22⋊Q8×C53C2314yes—
169C22⋊Q8×C53C2314yescomplemented
170#121×C53—28no—
171#121×C53—28no—
172#121×C53—28no—
173#121×C53—22no—
174#121×C53—22no—
175#121×C53C2314yes—
176#121×C53C2314yescomplemented
177C2×C4⋊C4×C53—21no—
178C2×C4⋊C4×C53—22no—
179C2×C4⋊C4×C53—21no—
180C2×C4⋊C4×C53—21no—
181C2×C4⋊C4×C53C2311yescharacteristic
182C2×C4⋊C4×C53C2311yescharacteristic
183C2×C4⋊C4×C53C2314yescomplemented
184C2×C22⋊C4×C53—21no—
185C2×C22⋊C4×C53—21no—
186C2×C22⋊C4×C53—21no—
187C2×C22⋊C4×C53—21no—
188C24×C53—21no—
189C24×C53C2×D411yescharacteristic
190C24×C53C2×D411yescharacteristic
191C24×C53C2×D411yescharacteristic
192C23×D53—21no—
193C23×D53—21no—
194C23×D53—24no—
195C23×D53—44no—
196C23×D53—82no—
197C23×D53—82no—
198#41×C53—48no—
199#41×C53—44no—
200#41×C53—44no—
201#41×C53—44no—
202#41×C53—44no—
203#41×C53—48no—
204C2×Q8×C53—21no—
205C2×Q8×C53—22no—
206C2×Q8×C53—22no—
207C2×Q8×C53—42no—
208C2×Q8×C53C2×D414yes—
209C2×Q8×C53C2412yes—
210C2×D4×C53—24no—
211C2×D4×C53—24no—
212C2×D4×C53—24no—
213C2×D4×C53—21no—
214C2×D4×C53—22no—
215C2×D4×C53—22no—
216C2×D4×C53—42no—
217C2×D4×C53—42no—
218C2×D4×C53—42no—
219C2×D4×C53—44no—
220C2×D4×C53—82no—
221C2×D4×C53—82no—
222C2×D4×C53C2×D414yes—
223C2×D4×C53C2×D414yes—
224C2×D4×C53C2×D414yes—
225C2×D4×C53C2412yes—
226C22×C4×C53—22no—
227C22×C4×C53—22no—
228C22×C4×C53—22no—
229C22×C4×C53—22no—
230C22×C4×C53—22no—
231C22×C4×C53—22no—
232C22×C4×C53—21no—
233C22×C4×C53—21no—
234C22×C4×C53—21no—
235C22×C4×C53—24no—
236C22×C4×C53—24no—
237C22×C4×C53—44no—
238C22×C4×C53—82no—
239C22×C4×C53C2×D411yescharacteristic
240C22×C4×C53C2×D411yescharacteristic
241C22×C4×C53C2×D411yescharacteristic
242C22×C4×C53C2×D412yes—
243C22×C4×C53C2×D412yes—
244C22×C4×C53C2×D412yes—
245C22×C4×C53C2412yes—
246C22×C4×C53C2412yes—
247C22×C4×C53C2412yes—
248C22×C4×C53C2411yescharacteristic
249C2×C22⋊D53—24no—
250C2×C22⋊D53—24no—
251C2×C22⋊D53—24no—
252C2×C22⋊D53—24no—
253C2×C22⋊D53—82no—
254C2×C22⋊D53—82no—
255C2×C22⋊D53—82no—
256C2×C22⋊D53—82no—
257C22×Dic53—21no—
258C22×Dic53—21no—
259C2×D212—22no—
260C2×D212—22no—
261C2×D212—22no—
262C2×D212—22no—
263C2×D212—21no—
264C2×D212—21no—
265C2×D212—24no—
266C2×D212—44no—
267C2×D212—44no—
268C2×D212—44no—
269C2×D212—48no—
270C2×D212C2412yes—
271C2×D212C2412yes—
272C4⋊C4×C53—21no—
273C4⋊C4×C53—21no—
274C4⋊C4×C53—24no—
275C4⋊C4×C53—24no—
276C4⋊C4×C53—24no—
277C4⋊C4×C53C2412yes—
278C4⋊C4×C53C2412yes—
279C22⋊C4×C53—24no—
280C22⋊C4×C53—24no—
281C22⋊C4×C53—24no—
282C22⋊C4×C53—24no—
283C22⋊Dic53—24no—
284#11719924—44no—
285#11719924—44no—
286#11719922—44no—
287#11719922—44no—
288#11719921—24no—
289#11719921—24no—
290#11719921—24no—
291#11719921—24no—
292C4⋊Dic53—21no—
293C4⋊Dic53—21no—
294C4⋊Dic53C2412yes—
295C4⋊Dic53C2412yes—
296C4×Dic53—24no—
297#11719917—44no—
298C2×#88322—22no—
299C2×#88322—22no—
300C2×#88322—22no—
301C2×#88322—22no—
302C2×#88322—44no—
303C2×#88322C2412yes—
304C2×#88322C2412yes—
305C2×#88322C2412yes—
306C2×#88322C2412yes—
307C23×C53—22no—
308C23×C53—22no—
309C23×C53—22no—
310C23×C53—22no—
311C23×C53—22no—
312C23×C53—22no—
313C23×C53—22no—
314C23×C53—22no—
315C23×C53—22no—
316C23×C53—22no—
317C23×C53—42no—
318C23×C53—42no—
319C23×C53—42no—
320C23×C53C22×D412yes—
321C23×C53C22×D412yes—
322C23×C53C22×D412yes—
323C23×C53C22×D411yescharacteristic
324C22×D53—22no—
325C22×D53—22no—
326C22×D53—48no—
327C22×D53—42no—
328C22×D53—42no—
329C22×D53—42no—
330C22×D53—42no—
331C22×D53—42no—
332C22×D53—42no—
333C22×D53—84no—
334C22×D53—84no—
335C22×D53—816no—
336Q8×C53—22no—
337Q8×C53—22no—
338Q8×C53—44no—
339Q8×C53—42no—
340D4×C53—22no—
341D4×C53—22no—
342D4×C53—44no—
343D4×C53—44no—
344D4×C53—44no—
345D4×C53—48no—
346D4×C53—42no—
347D4×C53—84no—
348D4×C53—84no—
349C2×C4×C53—22no—
350C2×C4×C53—22no—
351C2×C4×C53—22no—
352C2×C4×C53—24no—
353C2×C4×C53—24no—
354C2×C4×C53—24no—
355C2×C4×C53—22no—
356C2×C4×C53—22no—
357C2×C4×C53—22no—
358C2×C4×C53—22no—
359C2×C4×C53—22no—
360C2×C4×C53—22no—
361C2×C4×C53—22no—
362C2×C4×C53—22no—
363C2×C4×C53—22no—
364C2×C4×C53—48no—
365C2×C4×C53—42no—
366C2×C4×C53—42no—
367C2×C4×C53—42no—
368C2×C4×C53—84no—
369C2×C4×C53C22×D412yes—
370C2×C4×C53C22×D412yes—
371C2×C4×C53C22×D412yes—
372C2×C4×C53C22×D411yescharacteristic
373C2×C4×C53H(5,𝔽2)12yes—
374C2×C4×C53H(5,𝔽2)12yes—
375C2×C4×C53C2511yescharacteristic
376C22⋊D53—84no—
377C22⋊D53—84no—
378C22⋊D53—84no—
379C22⋊D53—84no—
380C2×Dic53—22no—
381C2×Dic53—22no—
382C2×Dic53—42no—
383C2×Dic53—42no—
384D212—22no—
385D212—22no—
386D212—22no—
387D212—22no—
388D212—48no—
389D212—42no—
390D212—42no—
391#88322—22no—
392#88322—22no—
393#88322—22no—
394#88322—22no—
395C2×#3198—531nomaximal, Sylow
396C22×C53—22no—
397C22×C53—22no—
398C22×C53—22no—
399C22×C53—22no—
400C22×C53—22no—
401C22×C53—22no—
402C22×C53—22no—
403C22×C53—22no—
404C22×C53—22no—
405C22×C53—44no—
406C22×C53—44no—
407C22×C53—44no—
408C22×C53—42no—
409C22×C53—42no—
410C22×C53—42no—
411C22×C53—84no—
412C22×C53#53412yes—
413C22×C53#57612yes—
414C22×C53#57712yes—
415C22×C53C23×D411yescharacteristic
416C2×D53—42no—
417C2×D53—42no—
418C2×D53—42no—
419C2×D53—42no—
420C2×D53—42no—
421C2×D53—42no—
422C2×D53—816no—
423C2×D53—84no—
424C2×D53—84no—
425C4×C53—22no—
426C4×C53—22no—
427C4×C53—22no—
428C4×C53—42no—
429C4×C53—42no—
430C4×C53—42no—
431C4×C53#53412yes—
432C4×C53C2×H(5,𝔽2)11yescharacteristic
433C4×C53C2×H(5,𝔽2)11yescharacteristic
434Dic53—42no—
435Dic53—42no—
436C2×#537D5311yescharacteristic, complemented
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×#449—531no—
449C2×#450—531no—
450C2×#447—531no—
451C2×#408—531no—
452C2×C53—42no—
453C2×C53—42no—
454C2×C53—42no—
455C2×C53—82no—
456C2×C53#319814yescomplemented
457C2×C53C2×#53411yescharacteristic
458C2×C53C2×#57611yescharacteristic
459C2×C53C2×#57711yescharacteristic
460D53—82no—
461D53—82no—
462C22×#41C2×D5311yescharacteristic
463C22×#41C2×D5311yescharacteristic, complemented
464C23×D4—531no—
465C22×SD16—531no—
466C22×SD16—531no—
467C22×D8—531no—
468C22×D8—531no—
469C22×M16—531no—
470C23×C8—531no—
471#537—24no—
472#537C2×D5318yescomplemented
473#535—538no—
474#535—1064no—
475C2×#127—1061no—
476C2×#124—1061no—
477C2×C22⋊Q8—21no—
478C2×C22⋊Q8C2×D5311yescharacteristic
479C2×C22⋊Q8C2×D5311yescharacteristic, complemented
480C2×#121—21no—
481C2×#121—21no—
482C2×#121—21no—
483C2×#121—531no—
484C2×#121—531no—
485C2×#121—531no—
486C2×#121—531no—
487C2×#121C2×D5311yescharacteristic
488C2×#121C2×D5311yescharacteristic, complemented
489C2×#120—1061no—
490C2×#120—1061no—
491C2×#117—531no—
492C22×C4⋊C4C2×D5311yescharacteristic, complemented
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#449—538no—
504#447—538no—
505C2×#107—531no—
506C2×#107—531no—
507C2×#106—531no—
508C2×#106—531no—
509C2×#103—531no—
510C2×#103—531no—
511C2×#102—531no—
512C2×#102—531no—
513C2×#102—531no—
514C2×#102—531no—
515C2×#102—531no—
516C2×#102—531no—
517#408—538no—
518C2×C22⋊C8—531no—
519C2×C22⋊C8—531no—
520C2×C22⋊C8—531no—
521C2×C22⋊C8—531no—
522C53C2×#319811yescharacteristic, complemented, Sylow
523C25—1061no—
524C2×#41—22no—
525C2×#41—42no—
526C2×#41—42no—
527C2×#41—42no—
528C2×#41—42no—
529C2×#41C22⋊D5314yes—
530C2×#41C22×D5314yes—
531C2×#41C22×D5314yescomplemented
532C22×Q8C22⋊D5311yescharacteristic
533C22×Q8C22×D5311yescharacteristic
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—531no—
538C22×D4—531no—
539C22×D4—534no—
540C22×D4—1061no—
541C22×D4—1061no—
542C22×D4—1061no—
543C22×D4—1061no—
544C22×D4—1061no—
545C22×D4—1062no—
546C22×D4—2122no—
547C22×D4—2122no—
548C22×D4C22⋊D5311yescharacteristic
549C22×D4C22⋊D5311yescharacteristic
550C22×D4C22⋊D5311yescharacteristic
551C22×D4C22×D5311yescharacteristic
552C23×C4—21no—
553C23×C4—21no—
554C23×C4C22×D5311yescharacteristic
555C23×C4C22×D5311yescharacteristic
556C23×C4C22×D5311yescharacteristic
557C2×SD16—534no—
558C2×SD16—534no—
559C2×SD16—2122no—
560C2×SD16—2122no—
561C2×D8—534no—
562C2×D8—534no—
563C2×D8—2122no—
564C2×D8—2122no—
565C2×M16—534no—
566C2×M16—2122no—
567C22×C8—531no—
568C22×C8—531no—
569C22×C8—531no—
570C22×C8—531no—
571C22×C8—534no—
572C22×C8—2122no—
573#127—1068no—
574#124—1068no—
575C22⋊Q8—28no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8C22×D5314yes—
579C22⋊Q8C22×D5314yescomplemented
580#121—28no—
581#121—28no—
582#121—28no—
583#121—22no—
584#121—22no—
585#121—534no—
586#121—534no—
587#121—534no—
588#121—534no—
589#121—1062no—
590#121—1062no—
591#121—1062no—
592#121—1062no—
593#121C22×D5314yes—
594#121C22×D5314yescomplemented
595#120—1068no—
596#120—1068no—
597#117—534no—
598#117—1062no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—531no—
604C2×C4⋊C4—531no—
605C2×C4⋊C4C22×D5311yescharacteristic
606C2×C4⋊C4C22×D5311yescharacteristic
607C2×C4⋊C4C22×D5314yescomplemented
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
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#103—534no—
624#102—534no—
625#102—534no—
626#102—534no—
627#102—534no—
628#102—534no—
629#102—534no—
630C22⋊C8—534no—
631C22⋊C8—534no—
632C22⋊C8—534no—
633C22⋊C8—534no—
634C24—21no—
635C24—1064no—
636C24—1061no—
637C24—1061no—
638C24—4242no—
639C24—4242no—
640C24—2124no—
641C24C2×C22⋊D5311yescharacteristic
642C24C2×C22⋊D5311yescharacteristic
643C24C2×C22⋊D5311yescharacteristic
644#41—48no—
645#41—44no—
646#41—44no—
647#41—44no—
648#41—44no—
649#41—48no—
650C2×Q8—21no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—42no—
654C2×Q8C2×C22⋊D5314yes—
655C2×Q8C23×D5312yes—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—21no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—44no—
666C2×D4—82no—
667C2×D4—82no—
668C2×D4—532no—
669C2×D4—532no—
670C2×D4—1064no—
671C2×D4—1064no—
672C2×D4—1064no—
673C2×D4—1064no—
674C2×D4—1061no—
675C2×D4—1061no—
676C2×D4—1064no—
677C2×D4—1062no—
678C2×D4—1062no—
679C2×D4—1062no—
680C2×D4—1062no—
681C2×D4—4242no—
682C2×D4—4242no—
683C2×D4—4242no—
684C2×D4—4242no—
685C2×D4—2124no—
686C2×D4—2124no—
687C2×D4—2124no—
688C2×D4—2128no—
689C2×D4C2×C22⋊D5314yes—
690C2×D4C2×C22⋊D5314yes—
691C2×D4C2×C22⋊D5314yes—
692C2×D4C23×D5312yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—24no—
703C22×C4—24no—
704C22×C4—44no—
705C22×C4—82no—
706C22×C4—1061no—
707C22×C4—1061no—
708C22×C4C2×C22⋊D5312yes—
709C22×C4C2×C22⋊D5312yes—
710C22×C4C2×C22⋊D5312yes—
711C22×C4C2×C22⋊D5311yescharacteristic
712C22×C4C2×C22⋊D5311yescharacteristic
713C22×C4C2×C22⋊D5311yescharacteristic
714C22×C4C23×D5312yes—
715C22×C4C23×D5312yes—
716C22×C4C23×D5312yes—
717C22×C4C23×D5311yescharacteristic
718SD16—2124no—
719SD16—2124no—
720D8—2124no—
721D8—2124no—
722M16—2124no—
723C2×C8—532no—
724C2×C8—532no—
725C2×C8—532no—
726C2×C8—532no—
727C2×C8—1062no—
728C2×C8—1062no—
729C2×C8—1062no—
730C2×C8—1062no—
731C2×C8—2124no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—24no—
737C4⋊C4—532no—
738C4⋊C4—532no—
739C4⋊C4—1061no—
740C4⋊C4—1061no—
741C4⋊C4C23×D5312yes—
742C4⋊C4C23×D5312yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—24no—
746C22⋊C4—24no—
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—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—1062no—
767C23—1062no—
768C23—4244no—
769C23—4244no—
770C23—42416no—
771C23—2128no—
772C23—2122no—
773C23—2122no—
774C23—2122no—
775C23—2122no—
776C23—2122no—
777C23—2122no—
778C23C22×C22⋊D5312yes—
779C23C22×C22⋊D5312yes—
780C23C22×C22⋊D5312yes—
781C23C22×C22⋊D5311yescharacteristic
782Q8—22no—
783Q8—22no—
784Q8—44no—
785Q8—42no—
786D4—22no—
787D4—22no—
788D4—44no—
789D4—44no—
790D4—44no—
791D4—48no—
792D4—42no—
793D4—84no—
794D4—84no—
795D4—1062no—
796D4—1062no—
797D4—1062no—
798D4—1062no—
799D4—4244no—
800D4—4244no—
801D4—4244no—
802D4—4244no—
803D4—2128no—
804D4—2122no—
805D4—2122no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—48no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—84no—
826C2×C4—1062no—
827C2×C4—1062no—
828C2×C4—2122no—
829C2×C4—2122no—
830C2×C4C22×C22⋊D5312yes—
831C2×C4C22×C22⋊D5312yes—
832C2×C4C22×C22⋊D5312yes—
833C2×C4C22×C22⋊D5311yescharacteristic
834C2×C4#1313326212yes—
835C2×C4#1313326212yes—
836C2×C4C24×D5311yescharacteristic
837C8—1062no—
838C8—1062no—
839C8—1062no—
840C8—1062no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—84no—
857C22—42416no—
858C22—4244no—
859C22—4244no—
860C22—2122no—
861C22—2122no—
862C22—2122no—
863C22—2122no—
864C22—2122no—
865C22—2122no—
866C22#1681118212yes—
867C22#1681142612yes—
868C22#1681143112yes—
869C22C23×C22⋊D5311yescharacteristic
870C4—22no—
871C4—22no—
872C4—22no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—2122no—
877C4—2122no—
878C4#1681118212yes—
879C4C2×#1313326211yescharacteristic
880C4C2×#1313326211yescharacteristic
881C2—42no—
882C2—42no—
883C2—42no—
884C2—82no—
885C2—4242no—
886C2—4242no—
887C2#2028556114yesdirect product factor
888C2C2×#1681118211yescharacteristic
889C2C2×#1681142611yescharacteristic
890C2C2×#1681143111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#537C2
socleC23×C53C22×D4
hypercenterC2×#537D53
hypocenterC53C2×#3198
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×#16811187C2semidirect
2. #20285561C2direct (N × H)
3. C2×#16810941C2semidirect
4. C2×#16810961C2semidirect
5. C2×#16810944C2semidirect
6. C2×#16810936C2semidirect
7. C2×#16810874C2semidirect
8. C2×#16810871C2semidirect
9. C2×#16810857C2semidirect
10. C2×#16810854C2semidirect
11. C2×#16810768C2semidirect
12. C2×#16810768C2semidirect
13. C2×#16810773C2semidirect
14. C2×#16810756C2semidirect
15. C2×#16810590C2semidirect
16. C2×C53×#537C2semidirect
22. C22×#11719917C22semidirect
23. C23×#88322C22semidirect
25. #16811187C22semidirect
35. #16810961C22semidirect
36. #16810944C22semidirect
37. #16810941C22semidirect
38. #16810936C22semidirect
39. #16810874C22semidirect
40. #16810871C22semidirect
41. #16810857C22semidirect
42. #16810854C22semidirect
43. #16810773C22semidirect
44. #16810768C22semidirect
45. #16810768C22semidirect
46. #16810756C22semidirect
47. C2×#13133150C22semidirect
48. C2×#13133150C22semidirect
49. C2×#13133148C22semidirect
50. C2×#13133148C22semidirect
51. C2×#13133141C22semidirect
52. C2×#13133141C22semidirect
53. C2×#13133138C22semidirect
54. C2×#13133138C22semidirect
59. #16810590C22semidirect
62. C2×C22⋊#88322C22semidirect
63. C2×C22⋊#88322C22semidirect
65. C22×#41×C53C22semidirect
67. C53×#537C22semidirect
70. C2×C22⋊Q8×C53C22semidirect
75. C2×#121×C53C22semidirect
76. C22×C4⋊C4×C53C22semidirect
98. C2×#11719917C23semidirect
104. C22×#88322C23semidirect
127. #13133150C23semidirect
128. #13133150C23semidirect
129. #13133148C23semidirect
130. #13133148C23semidirect
131. #13133141C23semidirect
132. #13133141C23semidirect
133. #13133138C23semidirect
134. #13133138C23semidirect
141. C22⋊#88322C23semidirect
142. C22⋊#88322C23semidirect
150. C2×#41×C53C23semidirect
169. C22⋊Q8×C53C23semidirect
176. #121×C53C23semidirect
183. C2×C4⋊C4×C53C23semidirect
436. C2×#537D53semidirect
456. C2×C53#3198semidirect
463. C22×#41C2×D53semidirect
472. #537C2×D53semidirect
479. C2×C22⋊Q8C2×D53semidirect
488. C2×#121C2×D53semidirect
492. C22×C4⋊C4C2×D53semidirect
522. C53C2×#3198semidirect
531. C2×#41C22×D53semidirect
579. C22⋊Q8C22×D53semidirect
594. #121C22×D53semidirect
607. C2×C4⋊C4C22×D53semidirect
887. C2#20285561direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111872
#202855612
C2×#168109412
C2×#168109612
C2×#168109442
C2×#168109362
C2×#168108742
C2×#168108712
C2×#168108572
C2×#168108542
C2×#168107682
C2×#168107732
C2×#168107562
C2×#168105902
C2×C53×#5372
C2×#319853