Finite Group Databasebeta

← C2×#20286322 #28259196

Subgroups — C2×#20286322 #28259196

Order 13568.

3042 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133243C211yesmaximal, characteristic, complemented
2C22×#13133242C211yesmaximal, characteristic, complemented
3C2×#16811269C211yesmaximal, characteristic, complemented
4#20286322C2116yesmaximal, direct product factor
5C2×#16811005C211yesmaximal, characteristic, complemented
6C2×#16810871C211yesmaximal, characteristic, complemented
7C2×#16810867C211yesmaximal, characteristic, complemented
8C2×#16810838C211yesmaximal, characteristic, complemented
9C2×#16810835C211yesmaximal, characteristic, complemented
10C2×#16810785C211yesmaximal, characteristic, complemented
11C2×#16810783C211yesmaximal, characteristic, complemented
12C2×#16810757C211yesmaximal, characteristic, complemented
13C2×#16810756C211yesmaximal, characteristic, complemented
14C2×C4×#11719922C211yesmaximal, characteristic, complemented
15C2×#16810701C211yesmaximal, characteristic, complemented
16C2×C53×#546C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C23×D212C2211yescharacteristic, complemented
19C2×#13133243—28no—
20C2×#13133243C2218yescomplemented
21C2×#13133242—28no—
22C2×#13133242C2218yescomplemented
23C22×#11719925C2211yescharacteristic, complemented
24C22×#11719923C2211yescharacteristic, complemented
25C22×#11719923C2211yescharacteristic, complemented
26C22×#11719924C2211yescharacteristic, complemented
27C22×#11719924C2211yescharacteristic, complemented
28C22×#11719922C2211yescharacteristic
29C22×#11719922C2211yescharacteristic
30C22×#11719922C2211yescharacteristic
31C22×#11719922C2211yescharacteristic
32C22×#11719917C2211yescharacteristic, complemented
33C22×#11719917C2211yescharacteristic, complemented
34#16811269—24no—
35#16811269C2218yescomplemented
36C2×#13133205C2211yescharacteristic, complemented
37C2×#13133202—21no—
38C2×#13133196C2211yescharacteristic, complemented
39C2×#13133191C2211yescharacteristic
40C2×#13133190—21no—
41C2×#13133185—21no—
42C2×C4×D212C2211yescharacteristic, complemented
43C2×C22⋊C4×D53—21no—
44#16811005C2218yescomplemented
45#16810871C2218yescomplemented
46#16810867C2218yescomplemented
47#16810838C2218yescomplemented
48#16810835C2218yescomplemented
49#16810785C2218yescomplemented
50#16810783C2218yescomplemented
51#16810757C2218yescomplemented
52#16810756C2218yescomplemented
53C4×#11719922C2218yescomplemented
54#16810701C2218yescomplemented
55C2×#13133150C2211yescharacteristic, complemented
56C2×C4⋊#88322C2211yescharacteristic, complemented
57C2×#13133141C2211yescharacteristic, complemented
58C2×#13133140C2211yescharacteristic, complemented
59C2×#13133138C2211yescharacteristic, complemented
60C2×#13133138C2211yescharacteristic, complemented
61C2×#13133137C2211yescharacteristic, complemented
62C2×#13133137C2211yescharacteristic, complemented
63C2×C22⋊#88322C2211yescharacteristic, complemented
64C2×C22⋊#88322C2211yescharacteristic, complemented
65C2×C4×#88322C2211yescharacteristic, complemented
66C22×#41×C53C2211yescharacteristic
67C23×D4×C53C2211yescharacteristic, complemented
68C53×#546—24no—
69C53×#546C2218yescomplemented
70C2×#124×C53C2211yescharacteristic, complemented
71C2×#123×C53—21no—
72C2×C22⋊Q8×C53C2211yescharacteristic, complemented
73C2×#121×C53—21no—
74C2×#121×C53C2211yescharacteristic
75C2×#120×C53—21no—
76C2×C4×D4×C53C2211yescharacteristic
77C2×C4×D4×C53C2211yescharacteristic, complemented
78C22×C22⋊C4×C53—21no—
79C24×D53—21no—
80C2×#11719945—22no—
81C2×#11719945—24no—
82C2×#11719945—42no—
83C2×#11719945C2314yes—
84C22×Dic106C2311yescharacteristic
85C22×D212—24no—
86C22×D212—22no—
87C22×D212—21no—
88C22×D212—42no—
89C22×D212C2311yescharacteristic
90C22×D212C2311yescharacteristic
91C22×D212C2314yescomplemented
92C22×C22⋊D53—21no—
93C22×C22⋊D53—21no—
94C22×C4×D53—21no—
95C22×C4×D53—21no—
96#13133243—232no—
97#13133242—232no—
98C2×#11719925—42no—
99C2×#11719925C2314yescomplemented
100C2×#11719923—24no—
101C2×#11719923—24no—
102C2×#11719923C2314yescomplemented
103C2×#11719923C2314yescomplemented
104C2×#11719924—24no—
105C2×#11719924—24no—
106C2×#11719924C2314yescomplemented
107C2×#11719924C2314yescomplemented
108C2×#11719922—24no—
109C2×#11719922—24no—
110C2×#11719922—42no—
111C2×#11719922D418yescomplemented
112C2×#11719922C2314yes—
113C2×#11719922C2314yes—
114C2×#11719922C2314yes—
115C2×#11719922C2314yes—
116C2×#11719917—24no—
117C2×#11719917—24no—
118C2×#11719917C2314yescomplemented
119C2×#11719917C2314yescomplemented
120C22×#88322C2311yescharacteristic
121C22×#88322C2311yescharacteristic
122C22×#88322C2311yescharacteristic
123C22×#88322C2311yescharacteristic
124#13133205—22no—
125#13133205C2314yescomplemented
126#13133202—28no—
127#13133196—22no—
128#13133196C2314yescomplemented
129#13133191—22no—
130#13133191C2314yes—
131#13133190—28no—
132#13133185—28no—
133C4×D212—22no—
134C4×D212C2314yescomplemented
135C2×C4⋊Dic53C2311yescharacteristic
136C2×#11719919—21no—
137C2×C22⋊Dic53—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C22⋊C4×D53—28no—
143#13133150C2314yescomplemented
144C4⋊#88322C2314yescomplemented
145#13133141C2314yescomplemented
146#13133140C2314yescomplemented
147#13133138C2314yescomplemented
148#13133138C2314yescomplemented
149#13133137C2314yescomplemented
150#13133137C2314yescomplemented
151C22⋊#88322C2314yescomplemented
152C22⋊#88322C2314yescomplemented
153C4×#88322C2314yescomplemented
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×C53C2311yescharacteristic
169C22×D4×C53C2314yescomplemented
170C23×C4×C53—21no—
171C23×C4×C53—21no—
172C23×C4×C53C2311yescharacteristic
173C23×C4×C53C2311yescharacteristic
174#124×C53—22no—
175#124×C53C2314yescomplemented
176#123×C53—28no—
177C22⋊Q8×C53—22no—
178C22⋊Q8×C53C2314yescomplemented
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×C53C2314yescomplemented
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—
209C23×D53—24no—
210C23×D53—44no—
211C23×D53—44no—
212C23×D53—82no—
213#41×C53—28no—
214#41×C53—44no—
215#41×C53—48no—
216C2×Q8×C53—21no—
217C2×Q8×C53—22no—
218C2×Q8×C53—22no—
219C2×Q8×C53C2412yes—
220C2×D4×C53—28no—
221C2×D4×C53—24no—
222C2×D4×C53—24no—
223C2×D4×C53—21no—
224C2×D4×C53—22no—
225C2×D4×C53—24no—
226C2×D4×C53—21no—
227C2×D4×C53—22no—
228C2×D4×C53—22no—
229C2×D4×C53—44no—
230C2×D4×C53—48no—
231C2×D4×C53—42no—
232C2×D4×C53—44no—
233C2×D4×C53—44no—
234C2×D4×C53—82no—
235C2×D4×C53C2×D414yes—
236C2×D4×C53C2×D414yes—
237C2×D4×C53C2412yes—
238C2×D4×C53C2412yes—
239C22×C4×C53—22no—
240C22×C4×C53—22no—
241C22×C4×C53—22no—
242C22×C4×C53—22no—
243C22×C4×C53—21no—
244C22×C4×C53—21no—
245C22×C4×C53—24no—
246C22×C4×C53—24no—
247C22×C4×C53—44no—
248C22×C4×C53—82no—
249C22×C4×C53C2×D411yescharacteristic
250C22×C4×C53C2×D411yescharacteristic
251C22×C4×C53C2×D411yescharacteristic
252C22×C4×C53C2×D411yescharacteristic
253C22×C4×C53C2×D412yes—
254C22×C4×C53C2×D412yes—
255C22×C4×C53C2412yes—
256C22×C4×C53C2412yes—
257C22×C4×C53C2411yescharacteristic
258C2×C22⋊D53—24no—
259C2×C22⋊D53—24no—
260C2×C22⋊D53—44no—
261C2×C22⋊D53—82no—
262C22×Dic53—21no—
263C22×Dic53—21no—
264#11719945—28no—
265#11719945—44no—
266#11719945—48no—
267C2×D212—21no—
268C2×D212—22no—
269C2×D212—22no—
270C2×D212—22no—
271C2×D212—28no—
272C2×D212—24no—
273C2×D212—21no—
274C2×D212—44no—
275C2×D212—48no—
276C2×D212—44no—
277C2×D212C2×D414yes—
278C2×D212C2412yes—
279C2×D212C2412yes—
280C2×C4×D53—24no—
281C2×C4×D53—24no—
282C2×C4×D53—44no—
283C2×C4×D53—82no—
284C2×Dic106—22no—
285C2×Dic106—22no—
286C2×Dic106—21no—
287C2×Dic106C2412yes—
288C4⋊C4×C53—24no—
289C4⋊C4×C53—21no—
290C4⋊C4×C53C2×D414yes—
291C4⋊C4×C53C2412yes—
292C22⋊C4×C53—24no—
293C22⋊C4×C53—24no—
294C22⋊C4×C53—24no—
295C22⋊C4×C53—24no—
296C22⋊C4×C53—24no—
297C22⋊C4×C53C2×D414yes—
298C22⋊C4×C53C2×D414yes—
299C42×C53C2×D412yes—
300C42×C53C2412yes—
301C22⋊Dic53—24no—
302#11719925—44no—
303#11719924—28no—
304#11719924—28no—
305#11719923—28no—
306#11719923—28no—
307#11719922—28no—
308#11719922—28no—
309#11719922—44no—
310#11719922C2×D4116yescomplemented
311#11719921—24no—
312#11719921—24no—
313#11719921—24no—
314#11719921—24no—
315C4⋊Dic53—21no—
316C4⋊Dic53C2412yes—
317#11719919—24no—
318#11719917—28no—
319#11719917—28no—
320C2×#88322—22no—
321C2×#88322—22no—
322C2×#88322—22no—
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—24no—
350C22×D53—22no—
351C22×D53—22no—
352C22×D53—48no—
353C22×D53—42no—
354C22×D53—42no—
355C22×D53—48no—
356C22×D53—42no—
357C22×D53—42no—
358C22×D53—42no—
359C22×D53—84no—
360C22×D53—816no—
361Q8×C53—22no—
362Q8×C53—22no—
363Q8×C53—42no—
364D4×C53—24no—
365D4×C53—22no—
366D4×C53—22no—
367D4×C53—22no—
368D4×C53—44no—
369D4×C53—48no—
370D4×C53—48no—
371D4×C53—42no—
372D4×C53—84no—
373D4×C53C22×D414yes—
374C2×C4×C53—22no—
375C2×C4×C53—22no—
376C2×C4×C53—22no—
377C2×C4×C53—22no—
378C2×C4×C53—24no—
379C2×C4×C53—24no—
380C2×C4×C53—22no—
381C2×C4×C53—22no—
382C2×C4×C53—22no—
383C2×C4×C53—22no—
384C2×C4×C53—22no—
385C2×C4×C53—22no—
386C2×C4×C53—48no—
387C2×C4×C53—42no—
388C2×C4×C53—42no—
389C2×C4×C53—84no—
390C2×C4×C53C22×D412yes—
391C2×C4×C53C22×D412yes—
392C2×C4×C53C22×D412yes—
393C2×C4×C53C22×D412yes—
394C2×C4×C53C22×D412yes—
395C2×C4×C53C22×D411yescharacteristic
396C2×C4×C53H(5,𝔽2)12yes—
397C2×C4×C53C2511yescharacteristic
398C22⋊D53—48no—
399C22⋊D53—84no—
400C2×Dic53—22no—
401C2×Dic53—22no—
402C2×Dic53—42no—
403C2×Dic53—42no—
404D212—24no—
405D212—22no—
406D212—22no—
407D212—22no—
408D212—48no—
409D212—42no—
410D212C22×D414yes—
411C4×D53—48no—
412C4×D53—84no—
413Dic106—22no—
414Dic106—22no—
415Dic106—42no—
416#88322—22no—
417#88322—22no—
418#88322—22no—
419#88322C22×D414yes—
420C2×#3273—531nomaximal, Sylow
421C22×C53—22no—
422C22×C53—22no—
423C22×C53—24no—
424C22×C53—22no—
425C22×C53—22no—
426C22×C53—22no—
427C22×C53—22no—
428C22×C53—44no—
429C22×C53—44no—
430C22×C53—48no—
431C22×C53—42no—
432C22×C53—42no—
433C22×C53—42no—
434C22×C53—42no—
435C22×C53—42no—
436C22×C53—816no—
437C22×C53—84no—
438C22×C53D4212yes—
439C22×C53#57512yes—
440C22×C53#57612yes—
441C22×C53C23×D411yescharacteristic
442C2×D53—24no—
443C2×D53—48no—
444C2×D53—42no—
445C2×D53—42no—
446C2×D53—42no—
447C2×D53—42no—
448C2×D53—42no—
449C2×D53—816no—
450C2×D53—84no—
451C4×C53—22no—
452C4×C53—22no—
453C4×C53—22no—
454C4×C53—22no—
455C4×C53—42no—
456C4×C53—42no—
457C4×C53D4212yes—
458C4×C53C23×D411yescharacteristic
459C4×C53C2×H(5,𝔽2)11yescharacteristic
460Dic53—42no—
461Dic53—42no—
462C22×AGL(1,ℤ/8)—531no—
463C22×AGL(1,ℤ/8)—531no—
464C2×#546—531no—
465C2×#546D5311yescharacteristic, complemented
466#3273—5316no—
467C2×#495—531no—
468C2×#468—531no—
469C2×#468—531no—
470C2×#463—531no—
471C2×#463—531no—
472C2×#452—531no—
473C2×#452—531no—
474C2×#447—531no—
475C2×#447—531no—
476C2×C4×D8—531no—
477C2×#436—531no—
478C2×C53—42no—
479C2×C53—42no—
480C2×C53—44no—
481C2×C53—82no—
482C2×C53#327314yescomplemented
483C2×C53C2×D4211yescharacteristic
484C2×C53C2×#57511yescharacteristic
485C2×C53C2×#57611yescharacteristic
486D53—44no—
487D53—82no—
488C22×#41—531no—
489C22×#41C2×D5311yescharacteristic
490C23×D4—531no—
491C23×D4C2×D5311yescharacteristic, complemented
492C2×AGL(1,ℤ/8)—538no—
493C2×AGL(1,ℤ/8)—538no—
494C2×AGL(1,ℤ/8)—1068no—
495C2×AGL(1,ℤ/8)—1068no—
496C22×Q16—531no—
497C22×SD16—531no—
498C22×SD16—531no—
499C22×SD16—531no—
500C22×SD16—531no—
501C22×D8—531no—
502C22×D8—531no—
503C22×D8—531no—
504C22×D8—531no—
505C22×M16—531no—
506C22×M16—531no—
507#546—24no—
508#546—538no—
509#546—1064no—
510#546C2×D5318yescomplemented
511C2×#124—531no—
512C2×#124C2×D5311yescharacteristic, complemented
513C2×#123—21no—
514C2×#123—1061no—
515C2×C22⋊Q8—531no—
516C2×C22⋊Q8C2×D5311yescharacteristic, complemented
517C2×#121—21no—
518C2×#121—531no—
519C2×#121—1061no—
520C2×#121C2×D5311yescharacteristic
521C2×#120—21no—
522C2×#120—1061no—
523C2×C4×D4—531no—
524C2×C4×D4C2×D5311yescharacteristic
525C2×C4×D4C2×D5311yescharacteristic, complemented
526C22×C22⋊C4—21no—
527C22×C22⋊C4—1061no—
528#495—538no—
529#468—538no—
530#468—538no—
531#463—538no—
532#463—538no—
533#452—538no—
534#452—538no—
535#447—538no—
536#447—538no—
537C4×D8—538no—
538#436—538no—
539C2×#107—531no—
540C2×C4⋊C8—531no—
541C2×#103—531no—
542C2×#103—531no—
543C2×#102—531no—
544C2×#102—531no—
545C2×#102—531no—
546C2×#102—531no—
547C2×C22⋊C8—531no—
548C2×C22⋊C8—531no—
549C2×C4×C8—531no—
550C53C2×#327311yescharacteristic, complemented, Sylow
551C25—21no—
552C25—1061no—
553C2×#41—22no—
554C2×#41—24no—
555C2×#41—42no—
556C2×#41—534no—
557C2×#41—1064no—
558C2×#41—1062no—
559C2×#41—2122no—
560C2×#41C22×D5314yes—
561C22×Q8—531no—
562C22×Q8C22×D5311yescharacteristic
563C22×D4—24no—
564C22×D4—21no—
565C22×D4—21no—
566C22×D4—21no—
567C22×D4—22no—
568C22×D4—42no—
569C22×D4—531no—
570C22×D4—531no—
571C22×D4—534no—
572C22×D4—1064no—
573C22×D4—1061no—
574C22×D4—1061no—
575C22×D4—1061no—
576C22×D4—1062no—
577C22×D4—2122no—
578C22×D4C22⋊D5311yescharacteristic
579C22×D4C22×D5311yescharacteristic
580C22×D4C22×D5311yescharacteristic
581C22×D4C22×D5314yescomplemented
582C23×C4—21no—
583C23×C4—21no—
584C23×C4—1061no—
585C23×C4—1061no—
586C23×C4C22×D5311yescharacteristic
587C23×C4C22×D5311yescharacteristic
588AGL(1,ℤ/8)—10632no—
589AGL(1,ℤ/8)—10632no—
590C2×Q16—534no—
591C2×Q16—2122no—
592C2×SD16—534no—
593C2×SD16—534no—
594C2×SD16—534no—
595C2×SD16—534no—
596C2×SD16—1064no—
597C2×SD16—1064no—
598C2×SD16—1064no—
599C2×SD16—1064no—
600C2×D8—538no—
601C2×D8—534no—
602C2×D8—534no—
603C2×D8—534no—
604C2×D8—534no—
605C2×D8—1064no—
606C2×D8—1064no—
607C2×D8—2122no—
608C2×M16—534no—
609C2×M16—534no—
610C2×M16—1064no—
611C2×M16—1064no—
612C22×C8—531no—
613C22×C8—531no—
614C22×C8—531no—
615C22×C8—531no—
616#124—22no—
617#124—534no—
618#124—1062no—
619#124C22×D5314yescomplemented
620#123—28no—
621#123—1068no—
622C22⋊Q8—22no—
623C22⋊Q8—534no—
624C22⋊Q8—1062no—
625C22⋊Q8C22×D5314yescomplemented
626#121—22no—
627#121—28no—
628#121—534no—
629#121—1062no—
630#121—1068no—
631#121C22×D5314yes—
632#120—28no—
633#120—1068no—
634C4×D4—22no—
635C4×D4—534no—
636C4×D4—1062no—
637C4×D4C22⋊D5314yes—
638C4×D4C22×D5314yes—
639C4×D4C22×D5314yescomplemented
640C2×C4⋊C4—21no—
641C2×C4⋊C4—531no—
642C2×C4⋊C4—1061no—
643C2×C4⋊C4C22⋊D5311yescharacteristic
644C2×C4⋊C4C22×D5311yescharacteristic
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—28no—
651C2×C22⋊C4—1061no—
652C2×C22⋊C4—1061no—
653C2×C22⋊C4—1061no—
654C2×C22⋊C4—1061no—
655C2×C22⋊C4—1061no—
656C2×C22⋊C4—1068no—
657C2×C22⋊C4C22⋊D5311yescharacteristic
658C2×C22⋊C4C22⋊D5311yescharacteristic
659C2×C42C22×D5311yescharacteristic
660#107—534no—
661C4⋊C8—534no—
662#103—534no—
663#103—534no—
664#102—534no—
665#102—534no—
666#102—534no—
667#102—534no—
668C22⋊C8—534no—
669C22⋊C8—534no—
670C4×C8—534no—
671C24—21no—
672C24—21no—
673C24—24no—
674C24—44no—
675C24—44no—
676C24—82no—
677C24—1061no—
678C24—1064no—
679C24—1061no—
680C24—4242no—
681C24—2124no—
682C24—2124no—
683C24C2×C22⋊D5311yescharacteristic
684C24C2×C22⋊D5311yescharacteristic
685#41—28no—
686#41—44no—
687#41—48no—
688#41—1068no—
689#41—2124no—
690#41—2128no—
691C2×Q8—21no—
692C2×Q8—22no—
693C2×Q8—22no—
694C2×Q8—532no—
695C2×Q8—1061no—
696C2×Q8—1062no—
697C2×Q8—1062no—
698C2×Q8C23×D5312yes—
699C2×D4—28no—
700C2×D4—24no—
701C2×D4—24no—
702C2×D4—22no—
703C2×D4—21no—
704C2×D4—24no—
705C2×D4—21no—
706C2×D4—22no—
707C2×D4—22no—
708C2×D4—44no—
709C2×D4—48no—
710C2×D4—42no—
711C2×D4—44no—
712C2×D4—44no—
713C2×D4—82no—
714C2×D4—534no—
715C2×D4—532no—
716C2×D4—532no—
717C2×D4—1068no—
718C2×D4—1064no—
719C2×D4—1064no—
720C2×D4—1062no—
721C2×D4—1061no—
722C2×D4—1064no—
723C2×D4—1061no—
724C2×D4—1062no—
725C2×D4—1062no—
726C2×D4—4242no—
727C2×D4—2124no—
728C2×D4—2128no—
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—4242no—
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—2124no—
761SD16—1068no—
762SD16—1068no—
763SD16—1068no—
764SD16—1068no—
765D8—5316no—
766D8—1068no—
767D8—1068no—
768D8—2124no—
769M16—1068no—
770M16—1068no—
771C2×C8—534no—
772C2×C8—532no—
773C2×C8—532no—
774C2×C8—532no—
775C2×C8—532no—
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⋊C4—1064no—
794C22⋊C4—1064no—
795C22⋊C4—1064no—
796C22⋊C4C2×C22⋊D5314yes—
797C22⋊C4C2×C22⋊D5314yes—
798C42C2×C22⋊D5312yes—
799C42C23×D5312yes—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—24no—
808C23—22no—
809C23—48no—
810C23—48no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—84no—
817C23—816no—
818C23—1062no—
819C23—1064no—
820C23—1062no—
821C23—4244no—
822C23—42416no—
823C23—2128no—
824C23—2128no—
825C23—2122no—
826C23—2122no—
827C23—2122no—
828C23—2122no—
829C23—2122no—
830C23C22×C22⋊D5312yes—
831C23C22×C22⋊D5312yes—
832C23C22×C22⋊D5311yescharacteristic
833Q8—22no—
834Q8—22no—
835Q8—42no—
836Q8—1062no—
837Q8—1062no—
838Q8—2122no—
839D4—22no—
840D4—22no—
841D4—22no—
842D4—24no—
843D4—44no—
844D4—48no—
845D4—48no—
846D4—42no—
847D4—84no—
848D4—534no—
849D4—1062no—
850D4—1062no—
851D4—1062no—
852D4—1064no—
853D4—4244no—
854D4—2128no—
855D4—2128no—
856D4—2122no—
857D4C2×D4×D5314yes—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—48no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—84no—
874C2×C4—1062no—
875C2×C4—1062no—
876C2×C4—4244no—
877C2×C4—2128no—
878C2×C4—2122no—
879C2×C4—2122no—
880C2×C4C2×D4×D5312yes—
881C2×C4C22×C22⋊D5312yes—
882C2×C4C22×C22⋊D5312yes—
883C2×C4C22×C22⋊D5312yes—
884C2×C4C22×C22⋊D5312yes—
885C2×C4C22×C22⋊D5311yescharacteristic
886C2×C4#1313326212yes—
887C2×C4C24×D5311yescharacteristic
888C8—534no—
889C8—1062no—
890C8—1062no—
891C8—1062no—
892C22—22no—
893C22—22no—
894C22—24no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—44no—
900C22—44no—
901C22—48no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—816no—
908C22—84no—
909C22—1064no—
910C22—42416no—
911C22—4244no—
912C22—2122no—
913C22—2122no—
914C22—2122no—
915C22—2128no—
916C22—2122no—
917C22—2122no—
918C22D4×C22⋊D5312yes—
919C22#1681142112yes—
920C22#1681142612yes—
921C22C23×C22⋊D5311yescharacteristic
922C4—22no—
923C4—22no—
924C4—22no—
925C4—22no—
926C4—42no—
927C4—42no—
928C4—2122no—
929C4—2122no—
930C4D4×C22⋊D5312yes—
931C4C22×D4×D5311yescharacteristic
932C4C2×#1313326211yescharacteristic
933C2—42no—
934C2—42no—
935C2—44no—
936C2—82no—
937C2—4242no—
938C2—2124no—
939C2#2028632214yesdirect product factor
940C2C2×D4×C22⋊D5311yescharacteristic
941C2C2×#1681142111yescharacteristic
942C2C2×#1681142611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#546C2
socleC23×C53C22×D4
hypercenterC2×#546D53
hypocenterC53C2×#3273
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×#13133242C2semidirect
3. C2×#16811269C2semidirect
4. #20286322C2direct (N × H)
5. C2×#16811005C2semidirect
6. C2×#16810871C2semidirect
7. C2×#16810867C2semidirect
8. C2×#16810838C2semidirect
9. C2×#16810835C2semidirect
10. C2×#16810785C2semidirect
11. C2×#16810783C2semidirect
12. C2×#16810757C2semidirect
13. C2×#16810756C2semidirect
14. C2×C4×#11719922C2semidirect
15. C2×#16810701C2semidirect
16. C2×C53×#546C2semidirect
18. C23×D212C22semidirect
20. C2×#13133243C22semidirect
22. C2×#13133242C22semidirect
23. C22×#11719925C22semidirect
24. C22×#11719923C22semidirect
25. C22×#11719923C22semidirect
26. C22×#11719924C22semidirect
27. C22×#11719924C22semidirect
32. C22×#11719917C22semidirect
33. C22×#11719917C22semidirect
35. #16811269C22semidirect
36. C2×#13133205C22semidirect
38. C2×#13133196C22semidirect
42. C2×C4×D212C22semidirect
44. #16811005C22semidirect
45. #16810871C22semidirect
46. #16810867C22semidirect
47. #16810838C22semidirect
48. #16810835C22semidirect
49. #16810785C22semidirect
50. #16810783C22semidirect
51. #16810757C22semidirect
52. #16810756C22semidirect
53. C4×#11719922C22semidirect
54. #16810701C22semidirect
55. C2×#13133150C22semidirect
56. C2×C4⋊#88322C22semidirect
57. C2×#13133141C22semidirect
58. C2×#13133140C22semidirect
59. C2×#13133138C22semidirect
60. C2×#13133138C22semidirect
61. C2×#13133137C22semidirect
62. C2×#13133137C22semidirect
63. C2×C22⋊#88322C22semidirect
64. C2×C22⋊#88322C22semidirect
65. C2×C4×#88322C22semidirect
67. C23×D4×C53C22semidirect
69. C53×#546C22semidirect
70. C2×#124×C53C22semidirect
72. C2×C22⋊Q8×C53C22semidirect
77. C2×C4×D4×C53C22semidirect
91. C22×D212C23semidirect
99. C2×#11719925C23semidirect
102. C2×#11719923C23semidirect
103. C2×#11719923C23semidirect
106. C2×#11719924C23semidirect
107. C2×#11719924C23semidirect
111. C2×#11719922D4semidirect
118. C2×#11719917C23semidirect
119. C2×#11719917C23semidirect
125. #13133205C23semidirect
128. #13133196C23semidirect
134. C4×D212C23semidirect
143. #13133150C23semidirect
144. C4⋊#88322C23semidirect
145. #13133141C23semidirect
146. #13133140C23semidirect
147. #13133138C23semidirect
148. #13133138C23semidirect
149. #13133137C23semidirect
150. #13133137C23semidirect
151. C22⋊#88322C23semidirect
152. C22⋊#88322C23semidirect
153. C4×#88322C23semidirect
169. C22×D4×C53C23semidirect
175. #124×C53C23semidirect
178. C22⋊Q8×C53C23semidirect
186. C4×D4×C53C23semidirect
310. #11719922C2×D4semidirect
465. C2×#546D53semidirect
482. C2×C53#3273semidirect
491. C23×D4C2×D53semidirect
510. #546C2×D53semidirect
512. C2×#124C2×D53semidirect
516. C2×C22⋊Q8C2×D53semidirect
525. C2×C4×D4C2×D53semidirect
550. C53C2×#3273semidirect
581. C22×D4C22×D53semidirect
619. #124C22×D53semidirect
625. C22⋊Q8C22×D53semidirect
639. C4×D4C22×D53semidirect
939. C2#20286322direct (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×#131332422
C2×#168112692
#202863222
C2×#168110052
C2×#168108712
C2×#168108672
C2×#168108382
C2×#168108352
C2×#168107852
C2×#168107832
C2×#168107572
C2×#168107562
C2×C4×#117199222
C2×#168107012
C2×C53×#5462
C2×#327353