Finite Group Databasebeta

← C2×#20286251 #28259101

Subgroups — C2×#20286251 #28259101

Order 13568.

2966 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133243C211yesmaximal, characteristic, complemented
2C22×#13133237C211yesmaximal, characteristic, complemented
3C2×#16811294C211yesmaximal, characteristic, complemented
4#20286251C2116yesmaximal, direct product factor
5C2×#16811013C211yesmaximal, characteristic, complemented
6C2×#16810871C211yesmaximal, characteristic, complemented
7C2×#16810857C211yesmaximal, characteristic, complemented
8C2×#16810842C211yesmaximal, characteristic, complemented
9C2×#16810818C211yesmaximal, characteristic, complemented
10C2×#16810783C211yesmaximal, characteristic, complemented
11C2×#16810768C211yesmaximal, characteristic, complemented
12C2×#16810766C211yesmaximal, characteristic, complemented
13C2×#16810757C211yesmaximal, characteristic, complemented
14C2×#16810723C211yesmaximal, characteristic, complemented
15C2×#16810695C211yesmaximal, characteristic, complemented
16C2×C53×#546C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×#11719945C2211yescharacteristic, complemented
19C2×#13133243—28no—
20C2×#13133243C2218yescomplemented
21C2×#13133237—28no—
22C2×#13133237C2218yescomplemented
23C22×#11719925C2211yescharacteristic, complemented
24C22×#11719923C2211yescharacteristic
25C22×#11719923C2211yescharacteristic
26C22×#11719924C2211yescharacteristic, complemented
27C22×#11719924C2211yescharacteristic, complemented
28C22×#11719922C2211yescharacteristic
29C22×#11719922C2211yescharacteristic
30C22×#11719922C2211yescharacteristic
31C22×#11719922C2211yescharacteristic
32C22×#11719917C2211yescharacteristic
33C23×#88322C2211yescharacteristic, complemented
34#16811294—24no—
35#16811294C2218yescomplemented
36C2×#13133214C2211yescharacteristic, complemented
37C2×#13133213—21no—
38C2×#13133191C2211yescharacteristic
39C2×#13133191C2211yescharacteristic, complemented
40C2×#13133190—21no—
41C2×#13133190—21no—
42C2×C4×Dic106C2211yescharacteristic, complemented
43C2×#13133179—21no—
44#16811013C2218yescomplemented
45#16810871C2218yescomplemented
46#16810857C2218yescomplemented
47#16810842C2218yescomplemented
48#16810818C2218yescomplemented
49#16810783C2218yescomplemented
50#16810768C2218yescomplemented
51#16810766C2218yescomplemented
52#16810757C2218yescomplemented
53#16810723C2218yescomplemented
54#16810695C2218yescomplemented
55C2×#13133150C2211yescharacteristic, complemented
56C2×C4⋊#88322C2211yescharacteristic, complemented
57C2×#13133141C2211yescharacteristic, complemented
58C2×#13133140C2211yescharacteristic, complemented
59C2×#13133138C2211yescharacteristic
60C2×#13133138C2211yescharacteristic
61C2×#13133137C2211yescharacteristic, complemented
62C2×#13133137C2211yescharacteristic, complemented
63C2×C22⋊#88322C2211yescharacteristic
64C2×C22⋊#88322C2211yescharacteristic, complemented
65C2×#13133128C2211yescharacteristic, complemented
66C22×#41×C53C2211yescharacteristic
67C23×D4×C53C2211yescharacteristic
68C53×#546—24no—
69C53×#546C2218yescomplemented
70C2×#124×C53C2211yescharacteristic
71C2×#123×C53—21no—
72C2×C22⋊Q8×C53C2211yescharacteristic
73C2×#121×C53—21no—
74C2×#121×C53C2211yescharacteristic
75C2×#120×C53—21no—
76C2×C4×D4×C53C2211yescharacteristic
77C2×C4×D4×C53C2211yescharacteristic
78C22×C22⋊C4×C53—21no—
79C2×#11719945—22no—
80C2×#11719945—22no—
81C2×#11719945—24no—
82C2×#11719945—24no—
83C2×#11719945—42no—
84C2×#11719945—42no—
85C2×#11719945C2314yes—
86C2×#11719945C2314yescomplemented
87C22×Dic106C2311yescharacteristic
88C22×D212—21no—
89C22×D212—21no—
90C22×D212C2311yescharacteristic
91C22×D212C2311yescharacteristic
92C22×C22⋊D53—21no—
93C22×C22⋊D53—21no—
94C22×C22⋊D53—21no—
95C22×C22⋊D53—21no—
96C22×C4×D53—21no—
97C22×C4×D53—21no—
98#13133243—232no—
99#13133237—232no—
100C2×#11719925—24no—
101C2×#11719925C2314yescomplemented
102C2×#11719923—24no—
103C2×#11719923D418yescomplemented
104C2×#11719923C2314yes—
105C2×#11719923C2314yes—
106C2×#11719924—24no—
107C2×#11719924—42no—
108C2×#11719924C2314yescomplemented
109C2×#11719924C2314yescomplemented
110C2×#11719922—24no—
111C2×#11719922—24no—
112C2×#11719922—24no—
113C2×#11719922—42no—
114C2×#11719922C2314yes—
115C2×#11719922C2314yes—
116C2×#11719922C2314yes—
117C2×#11719922C2314yes—
118C2×#11719917—24no—
119C2×#11719917C2314yes—
120C22×#88322—24no—
121C22×#88322C2311yescharacteristic
122C22×#88322C2311yescharacteristic
123C22×#88322C2311yescharacteristic
124C22×#88322C2311yescharacteristic
125C22×#88322C2314yescomplemented
126#13133214—22no—
127#13133214C2314yescomplemented
128#13133213—28no—
129#13133191—22no—
130#13133191—22no—
131#13133191C2314yes—
132#13133191C2314yescomplemented
133#13133190—28no—
134#13133190—28no—
135C4×Dic106—22no—
136C4×Dic106C2314yescomplemented
137#13133179—28no—
138C2×C4⋊Dic53C2311yescharacteristic
139C2×#11719919—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×C4×Dic53—21no—
143#13133150C2314yescomplemented
144C4⋊#88322C2314yescomplemented
145#13133141C2314yescomplemented
146#13133140C2314yescomplemented
147#13133138C2314yes—
148#13133138C2314yes—
149#13133137C2314yescomplemented
150#13133137C2314yescomplemented
151C22⋊#88322C2314yes—
152C22⋊#88322C2314yescomplemented
153#13133128C2314yescomplemented
154C25×C53—21no—
155C2×#41×C53—22no—
156C2×#41×C53—24no—
157C2×#41×C53—42no—
158C2×#41×C53C2314yes—
159C22×Q8×C53C2311yescharacteristic
160C22×D4×C53—24no—
161C22×D4×C53—21no—
162C22×D4×C53—21no—
163C22×D4×C53—21no—
164C22×D4×C53—22no—
165C22×D4×C53—42no—
166C22×D4×C53D411yescharacteristic
167C22×D4×C53C2311yescharacteristic
168C22×D4×C53C2314yes—
169C22×D4×C53C2311yescharacteristic
170C23×C4×C53—21no—
171C23×C4×C53—21no—
172C23×C4×C53C2311yescharacteristic
173C23×C4×C53C2311yescharacteristic
174#124×C53—22no—
175#124×C53C2314yes—
176#123×C53—28no—
177C22⋊Q8×C53—22no—
178C22⋊Q8×C53C2314yes—
179#121×C53—28no—
180#121×C53—22no—
181#121×C53C2314yes—
182#120×C53—28no—
183C4×D4×C53—22no—
184C4×D4×C53D414yes—
185C4×D4×C53C2314yes—
186C4×D4×C53C2314yes—
187C2×C4⋊C4×C53—21no—
188C2×C4⋊C4×C53D411yescharacteristic
189C2×C4⋊C4×C53C2311yescharacteristic
190C2×C22⋊C4×C53—28no—
191C2×C22⋊C4×C53—21no—
192C2×C22⋊C4×C53—21no—
193C2×C22⋊C4×C53—21no—
194C2×C22⋊C4×C53—21no—
195C2×C22⋊C4×C53—21no—
196C2×C22⋊C4×C53D411yescharacteristic
197C2×C22⋊C4×C53D411yescharacteristic
198C2×C42×C53C2311yescharacteristic
199C24×C53—21no—
200C24×C53—21no—
201C24×C53—24no—
202C24×C53—44no—
203C24×C53—44no—
204C24×C53—82no—
205C24×C53C2×D411yescharacteristic
206C24×C53C2×D411yescharacteristic
207C23×D53—21no—
208C23×D53—21no—
209#41×C53—28no—
210#41×C53—44no—
211#41×C53—48no—
212C2×Q8×C53—21no—
213C2×Q8×C53—22no—
214C2×Q8×C53—22no—
215C2×Q8×C53C2412yes—
216C2×D4×C53—28no—
217C2×D4×C53—24no—
218C2×D4×C53—24no—
219C2×D4×C53—21no—
220C2×D4×C53—22no—
221C2×D4×C53—24no—
222C2×D4×C53—21no—
223C2×D4×C53—22no—
224C2×D4×C53—22no—
225C2×D4×C53—44no—
226C2×D4×C53—48no—
227C2×D4×C53—42no—
228C2×D4×C53—44no—
229C2×D4×C53—44no—
230C2×D4×C53—82no—
231C2×D4×C53C2×D414yes—
232C2×D4×C53C2×D414yes—
233C2×D4×C53C2412yes—
234C2×D4×C53C2412yes—
235C22×C4×C53—22no—
236C22×C4×C53—22no—
237C22×C4×C53—22no—
238C22×C4×C53—22no—
239C22×C4×C53—21no—
240C22×C4×C53—21no—
241C22×C4×C53—24no—
242C22×C4×C53—24no—
243C22×C4×C53—44no—
244C22×C4×C53—82no—
245C22×C4×C53C2×D411yescharacteristic
246C22×C4×C53C2×D411yescharacteristic
247C22×C4×C53C2×D411yescharacteristic
248C22×C4×C53C2×D411yescharacteristic
249C22×C4×C53C2×D412yes—
250C22×C4×C53C2×D412yes—
251C22×C4×C53C2412yes—
252C22×C4×C53C2412yes—
253C22×C4×C53C2411yescharacteristic
254C2×C22⋊D53—24no—
255C2×C22⋊D53—24no—
256C2×C22⋊D53—24no—
257C2×C22⋊D53—24no—
258C2×C22⋊D53—44no—
259C2×C22⋊D53—44no—
260C2×C22⋊D53—82no—
261C2×C22⋊D53—82no—
262C22×Dic53—21no—
263C22×Dic53—21no—
264#11719945—28no—
265#11719945—28no—
266#11719945—44no—
267#11719945—44no—
268#11719945—48no—
269#11719945—48no—
270C2×D212—22no—
271C2×D212—22no—
272C2×D212—22no—
273C2×D212—22no—
274C2×D212—24no—
275C2×D212—21no—
276C2×D212—21no—
277C2×D212—24no—
278C2×D212—44no—
279C2×D212—82no—
280C2×D212C2412yes—
281C2×D212C2412yes—
282C2×C4×D53—24no—
283C2×C4×D53—24no—
284C2×C4×D53—44no—
285C2×C4×D53—44no—
286C2×Dic106—21no—
287C2×Dic106—22no—
288C2×Dic106C2×D414yes—
289C2×Dic106C2412yes—
290C4⋊C4×C53—24no—
291C4⋊C4×C53—21no—
292C4⋊C4×C53C2×D414yes—
293C4⋊C4×C53C2412yes—
294C22⋊C4×C53—24no—
295C22⋊C4×C53—24no—
296C22⋊C4×C53—24no—
297C22⋊C4×C53—24no—
298C22⋊C4×C53—24no—
299C22⋊C4×C53C2×D414yes—
300C22⋊C4×C53C2×D414yes—
301C42×C53C2×D412yes—
302C42×C53C2412yes—
303#11719925—28no—
304#11719924—28no—
305#11719924—44no—
306#11719923—28no—
307#11719923C2×D4116yescomplemented
308#11719922—28no—
309#11719922—28no—
310#11719922—28no—
311#11719922—44no—
312#11719921—24no—
313#11719921—24no—
314C4⋊Dic53—21no—
315C4⋊Dic53C2412yes—
316#11719919—24no—
317C4×Dic53—24no—
318#11719917—28no—
319C2×#88322—22no—
320C2×#88322—22no—
321C2×#88322—22no—
322C2×#88322—28no—
323C2×#88322C2×D414yes—
324C2×#88322C2412yes—
325C2×#88322C2412yes—
326C2×#88322C2412yes—
327C2×#88322C2412yes—
328C23×C53—22no—
329C23×C53—22no—
330C23×C53—24no—
331C23×C53—22no—
332C23×C53—22no—
333C23×C53—22no—
334C23×C53—22no—
335C23×C53—22no—
336C23×C53—22no—
337C23×C53—48no—
338C23×C53—48no—
339C23×C53—42no—
340C23×C53—42no—
341C23×C53—42no—
342C23×C53—42no—
343C23×C53—42no—
344C23×C53—84no—
345C23×C53—816no—
346C23×C53C22×D412yes—
347C23×C53C22×D412yes—
348C23×C53C22×D411yescharacteristic
349C22×D53—22no—
350C22×D53—22no—
351C22×D53—42no—
352C22×D53—42no—
353C22×D53—42no—
354C22×D53—42no—
355C22×D53—42no—
356C22×D53—42no—
357Q8×C53—22no—
358Q8×C53—22no—
359Q8×C53—42no—
360D4×C53—24no—
361D4×C53—22no—
362D4×C53—22no—
363D4×C53—22no—
364D4×C53—44no—
365D4×C53—48no—
366D4×C53—48no—
367D4×C53—42no—
368D4×C53—84no—
369D4×C53C22×D414yes—
370C2×C4×C53—22no—
371C2×C4×C53—22no—
372C2×C4×C53—22no—
373C2×C4×C53—22no—
374C2×C4×C53—24no—
375C2×C4×C53—24no—
376C2×C4×C53—22no—
377C2×C4×C53—22no—
378C2×C4×C53—22no—
379C2×C4×C53—22no—
380C2×C4×C53—22no—
381C2×C4×C53—22no—
382C2×C4×C53—48no—
383C2×C4×C53—42no—
384C2×C4×C53—42no—
385C2×C4×C53—84no—
386C2×C4×C53C22×D412yes—
387C2×C4×C53C22×D412yes—
388C2×C4×C53C22×D412yes—
389C2×C4×C53C22×D412yes—
390C2×C4×C53C22×D412yes—
391C2×C4×C53C22×D411yescharacteristic
392C2×C4×C53H(5,𝔽2)12yes—
393C2×C4×C53C2511yescharacteristic
394C22⋊D53—48no—
395C22⋊D53—48no—
396C22⋊D53—84no—
397C22⋊D53—84no—
398C2×Dic53—24no—
399C2×Dic53—22no—
400C2×Dic53—22no—
401C2×Dic53—42no—
402D212—22no—
403D212—22no—
404D212—22no—
405D212—22no—
406D212—48no—
407D212—42no—
408D212—42no—
409D212—84no—
410C4×D53—48no—
411C4×D53—48no—
412Dic106—24no—
413Dic106—22no—
414Dic106C22×D414yes—
415#88322—22no—
416#88322—22no—
417#88322—22no—
418#88322C22×D414yes—
419C2×#3268—531nomaximal, Sylow
420C22×C53—22no—
421C22×C53—22no—
422C22×C53—24no—
423C22×C53—22no—
424C22×C53—22no—
425C22×C53—22no—
426C22×C53—22no—
427C22×C53—44no—
428C22×C53—44no—
429C22×C53—48no—
430C22×C53—42no—
431C22×C53—42no—
432C22×C53—42no—
433C22×C53—42no—
434C22×C53—42no—
435C22×C53—816no—
436C22×C53—84no—
437C22×C53D4212yes—
438C22×C53#57512yes—
439C22×C53#57612yes—
440C22×C53C23×D411yescharacteristic
441C2×D53—42no—
442C2×D53—42no—
443C2×D53—42no—
444C2×D53—42no—
445C2×D53—42no—
446C2×D53—42no—
447C2×D53—84no—
448C2×D53—84no—
449C4×C53—22no—
450C4×C53—22no—
451C4×C53—22no—
452C4×C53—22no—
453C4×C53—42no—
454C4×C53—42no—
455C4×C53D4212yes—
456C4×C53C23×D411yescharacteristic
457C4×C53C2×H(5,𝔽2)11yescharacteristic
458Dic53—24no—
459Dic53—42no—
460C22×AGL(1,ℤ/8)—531no—
461C22×#135—531no—
462C2×#550—531no—
463C2×#546D5311yescharacteristic, complemented
464#3268—5316no—
465C2×#496—531no—
466C2×#468—531no—
467C2×#466—531no—
468C2×#464—531no—
469C2×#459—531no—
470C2×#452—531no—
471C2×#449—531no—
472C2×#449—531no—
473C2×#447—531no—
474C2×#440—531no—
475C2×#435—531no—
476C2×C53—42no—
477C2×C53—42no—
478C2×C53—44no—
479C2×C53—82no—
480C2×C53#326814yescomplemented
481C2×C53C2×D4211yescharacteristic
482C2×C53C2×#57511yescharacteristic
483C2×C53C2×#57611yescharacteristic
484D53—82no—
485D53—82no—
486C22×#41—531no—
487C22×#41—531no—
488C22×#41C2×D5311yescharacteristic
489C23×D4C2×D5311yescharacteristic
490C2×AGL(1,ℤ/8)—538no—
491C2×AGL(1,ℤ/8)—1068no—
492C2×#135—538no—
493C2×#135—1068no—
494C22×Q16—531no—
495C22×SD16—531no—
496C22×SD16—531no—
497C22×SD16—531no—
498C22×SD16—531no—
499C22×D8—531no—
500C22×D8—531no—
501C22×D8—531no—
502C22×D8—531no—
503C22×M16—531no—
504C23×C8—531no—
505#550—538no—
506#550—1064no—
507#546—24no—
508#546C2×D5318yescomplemented
509C2×#127—531no—
510C2×#127—1061no—
511C2×#124C2×D5311yescharacteristic
512C2×#123—21no—
513C2×C22⋊Q8C2×D5311yescharacteristic
514C2×#121—21no—
515C2×#121—531no—
516C2×#121—531no—
517C2×#121—1061no—
518C2×#121—1061no—
519C2×#121C2×D5311yescharacteristic
520C2×#120—21no—
521C2×C4×Q8—531no—
522C2×C4×D4—1061no—
523C2×C4×D4C2×D5311yescharacteristic
524C2×C4×D4C2×D5311yescharacteristic
525C22×C22⋊C4—21no—
526#496—538no—
527#468—538no—
528#466—538no—
529#464—538no—
530#459—538no—
531#452—538no—
532#449—538no—
533#449—538no—
534#447—538no—
535#440—538no—
536#435—538no—
537C2×#107—531no—
538C2×C4⋊C8—531no—
539C2×#103—531no—
540C2×#103—531no—
541C2×#102—531no—
542C2×#102—531no—
543C2×#102—531no—
544C2×#102—531no—
545C2×C22⋊C8—531no—
546C2×C22⋊C8—531no—
547C2×#97—531no—
548C53C2×#326811yescharacteristic, complemented, Sylow
549C25—21no—
550C2×#41—22no—
551C2×#41—24no—
552C2×#41—42no—
553C2×#41—534no—
554C2×#41—534no—
555C2×#41—1064no—
556C2×#41—1064no—
557C2×#41—1062no—
558C2×#41—1062no—
559C2×#41—2122no—
560C2×#41—2122no—
561C2×#41C22×D5314yes—
562C22×Q8—531no—
563C22×Q8C22×D5311yescharacteristic
564C22×D4—24no—
565C22×D4—21no—
566C22×D4—21no—
567C22×D4—21no—
568C22×D4—22no—
569C22×D4—42no—
570C22×D4—531no—
571C22×D4—531no—
572C22×D4—1061no—
573C22×D4—1061no—
574C22×D4—1061no—
575C22×D4—1061no—
576C22×D4—1061no—
577C22×D4—1061no—
578C22×D4C22⋊D5311yescharacteristic
579C22×D4C22×D5311yescharacteristic
580C22×D4C22×D5314yes—
581C22×D4C22×D5311yescharacteristic
582C23×C4—21no—
583C23×C4—21no—
584C23×C4—1061no—
585C23×C4—1061no—
586C23×C4C22×D5311yescharacteristic
587C23×C4C22×D5311yescharacteristic
588AGL(1,ℤ/8)—10632no—
589#135—10632no—
590C2×Q16—534no—
591C2×Q16—1064no—
592C2×SD16—538no—
593C2×SD16—534no—
594C2×SD16—534no—
595C2×SD16—534no—
596C2×SD16—534no—
597C2×SD16—1064no—
598C2×SD16—1064no—
599C2×SD16—2122no—
600C2×D8—534no—
601C2×D8—534no—
602C2×D8—534no—
603C2×D8—534no—
604C2×D8—1064no—
605C2×D8—1064no—
606C2×D8—1064no—
607C2×D8—2122no—
608C2×M16—534no—
609C2×M16—1064no—
610C22×C8—531no—
611C22×C8—531no—
612C22×C8—534no—
613C22×C8—531no—
614C22×C8—531no—
615C22×C8—1064no—
616#127—534no—
617#127—1068no—
618#127—1062no—
619#124—22no—
620#124C22×D5314yes—
621#123—28no—
622C22⋊Q8—22no—
623C22⋊Q8C22×D5314yes—
624#121—22no—
625#121—28no—
626#121—534no—
627#121—534no—
628#121—1062no—
629#121—1062no—
630#121—1068no—
631#121—1068no—
632#121C22×D5314yes—
633#120—28no—
634C4×Q8—534no—
635C4×Q8—1062no—
636C4×D4—22no—
637C4×D4—1068no—
638C4×D4C22⋊D5314yes—
639C4×D4C22×D5314yes—
640C4×D4C22×D5314yes—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—531no—
643C2×C4⋊C4—1061no—
644C2×C4⋊C4C22⋊D5311yescharacteristic
645C2×C4⋊C4C22×D5311yescharacteristic
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—28no—
652C2×C22⋊C4—1061no—
653C2×C22⋊C4—1061no—
654C2×C22⋊C4C22⋊D5311yescharacteristic
655C2×C22⋊C4C22⋊D5311yescharacteristic
656C2×C42—1061no—
657C2×C42C22×D5311yescharacteristic
658#107—534no—
659C4⋊C8—534no—
660#103—534no—
661#103—534no—
662#102—534no—
663#102—534no—
664#102—534no—
665#102—534no—
666C22⋊C8—534no—
667C22⋊C8—534no—
668#97—534no—
669C24—21no—
670C24—21no—
671C24—24no—
672C24—44no—
673C24—44no—
674C24—82no—
675C24—1061no—
676C24—1061no—
677C24C2×C22⋊D5311yescharacteristic
678C24C2×C22⋊D5311yescharacteristic
679#41—28no—
680#41—44no—
681#41—48no—
682#41—1068no—
683#41—1068no—
684#41—2124no—
685#41—2124no—
686#41—2128no—
687#41—2128no—
688C2×Q8—21no—
689C2×Q8—22no—
690C2×Q8—22no—
691C2×Q8—534no—
692C2×Q8—532no—
693C2×Q8—1061no—
694C2×Q8—1062no—
695C2×Q8C23×D5312yes—
696C2×D4—28no—
697C2×D4—24no—
698C2×D4—24no—
699C2×D4—22no—
700C2×D4—21no—
701C2×D4—24no—
702C2×D4—21no—
703C2×D4—22no—
704C2×D4—22no—
705C2×D4—44no—
706C2×D4—48no—
707C2×D4—42no—
708C2×D4—44no—
709C2×D4—44no—
710C2×D4—82no—
711C2×D4—532no—
712C2×D4—532no—
713C2×D4—1064no—
714C2×D4—1064no—
715C2×D4—1064no—
716C2×D4—1064no—
717C2×D4—1062no—
718C2×D4—1062no—
719C2×D4—1064no—
720C2×D4—1064no—
721C2×D4—1061no—
722C2×D4—1061no—
723C2×D4—1062no—
724C2×D4—1062no—
725C2×D4—4242no—
726C2×D4—4242no—
727C2×D4—4242no—
728C2×D4—2124no—
729C2×D4—2124no—
730C2×D4—2124no—
731C2×D4D4×D5314yes—
732C2×D4C2×C22⋊D5314yes—
733C2×D4C23×D5312yes—
734C2×D4C23×D5312yes—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—24no—
742C22×C4—24no—
743C22×C4—44no—
744C22×C4—82no—
745C22×C4—1061no—
746C22×C4—1061no—
747C22×C4—1064no—
748C22×C4—1064no—
749C22×C4—2124no—
750C22×C4—2124no—
751C22×C4C2×C22⋊D5312yes—
752C22×C4C2×C22⋊D5312yes—
753C22×C4C2×C22⋊D5311yescharacteristic
754C22×C4C2×C22⋊D5311yescharacteristic
755C22×C4C2×C22⋊D5311yescharacteristic
756C22×C4C2×C22⋊D5311yescharacteristic
757C22×C4C23×D5312yes—
758C22×C4C23×D5312yes—
759C22×C4C23×D5311yescharacteristic
760Q16—1068no—
761SD16—5316no—
762SD16—1068no—
763SD16—1068no—
764SD16—2124no—
765D8—1068no—
766D8—1068no—
767D8—1068no—
768D8—2124no—
769M16—1068no—
770C2×C8—534no—
771C2×C8—532no—
772C2×C8—532no—
773C2×C8—532no—
774C2×C8—532no—
775C2×C8—1068no—
776C2×C8—1062no—
777C2×C8—1062no—
778C2×C8—1062no—
779C4⋊C4—24no—
780C4⋊C4—21no—
781C4⋊C4—532no—
782C4⋊C4—1061no—
783C4⋊C4—1064no—
784C4⋊C4C2×C22⋊D5314yes—
785C4⋊C4C23×D5312yes—
786C22⋊C4—24no—
787C22⋊C4—24no—
788C22⋊C4—24no—
789C22⋊C4—24no—
790C22⋊C4—24no—
791C22⋊C4—1064no—
792C22⋊C4—1064no—
793C22⋊C4C2×C22⋊D5314yes—
794C22⋊C4C2×C22⋊D5314yes—
795C42—1064no—
796C42C2×C22⋊D5312yes—
797C42C23×D5312yes—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—24no—
806C23—22no—
807C23—48no—
808C23—48no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—84no—
815C23—816no—
816C23—1062no—
817C23—1062no—
818C23—2122no—
819C23—2122no—
820C23—2122no—
821C23—2122no—
822C23—2122no—
823C23—2122no—
824C23C22×C22⋊D5312yes—
825C23C22×C22⋊D5312yes—
826C23C22×C22⋊D5311yescharacteristic
827Q8—22no—
828Q8—22no—
829Q8—42no—
830Q8—534no—
831Q8—1062no—
832Q8—1064no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—24no—
837D4—44no—
838D4—48no—
839D4—48no—
840D4—42no—
841D4—84no—
842D4—1062no—
843D4—1062no—
844D4—1062no—
845D4—1062no—
846D4—4244no—
847D4—4244no—
848D4—4244no—
849D4—2128no—
850D4—2128no—
851D4—2128no—
852D4—2122no—
853D4—2122no—
854D4C2×D4×D5314yes—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—48no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—84no—
871C2×C4—1062no—
872C2×C4—1064no—
873C2×C4—1062no—
874C2×C4—2128no—
875C2×C4—2128no—
876C2×C4—2122no—
877C2×C4C2×D4×D5312yes—
878C2×C4C22×C22⋊D5312yes—
879C2×C4C22×C22⋊D5312yes—
880C2×C4C22×C22⋊D5312yes—
881C2×C4C22×C22⋊D5312yes—
882C2×C4C22×C22⋊D5311yescharacteristic
883C2×C4#1313326212yes—
884C2×C4C24×D5311yescharacteristic
885C8—534no—
886C8—1062no—
887C8—1062no—
888C8—1062no—
889C22—22no—
890C22—22no—
891C22—24no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—44no—
897C22—44no—
898C22—48no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—816no—
905C22—84no—
906C22—4244no—
907C22—4244no—
908C22—2122no—
909C22—2122no—
910C22—2122no—
911C22—2122no—
912C22—2122no—
913C22—2122no—
914C22D4×C22⋊D5312yes—
915C22#1681142112yes—
916C22#1681142612yes—
917C22C23×C22⋊D5311yescharacteristic
918C4—22no—
919C4—22no—
920C4—22no—
921C4—22no—
922C4—42no—
923C4—42no—
924C4—1064no—
925C4—2122no—
926C4D4×C22⋊D5312yes—
927C4C22×D4×D5311yescharacteristic
928C4C2×#1313326211yescharacteristic
929C2—42no—
930C2—42no—
931C2—44no—
932C2—82no—
933C2—4242no—
934C2—4242no—
935C2#2028625114yesdirect product factor
936C2C2×D4×C22⋊D5311yescharacteristic
937C2C2×#1681142111yescharacteristic
938C2C2×#1681142611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#546C2
socleC23×C53C22×D4
hypercenterC2×#546D53
hypocenterC53C2×#3268
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C22×#13133243C2semidirect
2. C22×#13133237C2semidirect
3. C2×#16811294C2semidirect
4. #20286251C2direct (N × H)
5. C2×#16811013C2semidirect
6. C2×#16810871C2semidirect
7. C2×#16810857C2semidirect
8. C2×#16810842C2semidirect
9. C2×#16810818C2semidirect
10. C2×#16810783C2semidirect
11. C2×#16810768C2semidirect
12. C2×#16810766C2semidirect
13. C2×#16810757C2semidirect
14. C2×#16810723C2semidirect
15. C2×#16810695C2semidirect
16. C2×C53×#546C2semidirect
18. C22×#11719945C22semidirect
20. C2×#13133243C22semidirect
22. C2×#13133237C22semidirect
23. C22×#11719925C22semidirect
26. C22×#11719924C22semidirect
27. C22×#11719924C22semidirect
33. C23×#88322C22semidirect
35. #16811294C22semidirect
36. C2×#13133214C22semidirect
39. C2×#13133191C22semidirect
42. C2×C4×Dic106C22semidirect
44. #16811013C22semidirect
45. #16810871C22semidirect
46. #16810857C22semidirect
47. #16810842C22semidirect
48. #16810818C22semidirect
49. #16810783C22semidirect
50. #16810768C22semidirect
51. #16810766C22semidirect
52. #16810757C22semidirect
53. #16810723C22semidirect
54. #16810695C22semidirect
55. C2×#13133150C22semidirect
56. C2×C4⋊#88322C22semidirect
57. C2×#13133141C22semidirect
58. C2×#13133140C22semidirect
61. C2×#13133137C22semidirect
62. C2×#13133137C22semidirect
64. C2×C22⋊#88322C22semidirect
65. C2×#13133128C22semidirect
69. C53×#546C22semidirect
86. C2×#11719945C23semidirect
101. C2×#11719925C23semidirect
103. C2×#11719923D4semidirect
108. C2×#11719924C23semidirect
109. C2×#11719924C23semidirect
125. C22×#88322C23semidirect
127. #13133214C23semidirect
132. #13133191C23semidirect
136. C4×Dic106C23semidirect
143. #13133150C23semidirect
144. C4⋊#88322C23semidirect
145. #13133141C23semidirect
146. #13133140C23semidirect
149. #13133137C23semidirect
150. #13133137C23semidirect
152. C22⋊#88322C23semidirect
153. #13133128C23semidirect
307. #11719923C2×D4semidirect
463. C2×#546D53semidirect
480. C2×C53#3268semidirect
508. #546C2×D53semidirect
548. C53C2×#3268semidirect
935. C2#20286251direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332432
C22×#131332372
C2×#168112942
#202862512
C2×#168110132
C2×#168108712
C2×#168108572
C2×#168108422
C2×#168108182
C2×#168107832
C2×#168107682
C2×#168107662
C2×#168107572
C2×#168107232
C2×#168106952
C2×C53×#5462
C2×#326853