Finite Group Databasebeta

← C2×#20286552 #28260445

Subgroups — C2×#20286552 #28260445

Order 13568.

2286 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811313C211yesmaximal, characteristic, complemented
2C2×#16811269C211yesmaximal, characteristic
3#20286552C2116yesmaximal, direct product factor
4C2×#16810978C211yesmaximal, characteristic, complemented
5C2×#16810948C211yesmaximal, characteristic, complemented
6C2×#16810954C211yesmaximal, characteristic, complemented
7C2×#16810924C211yesmaximal, characteristic, complemented
8C2×#16810864C211yesmaximal, characteristic, complemented
9C2×#16810852C211yesmaximal, characteristic, complemented
10C2×#16810846C211yesmaximal, characteristic, complemented
11C2×#16810787C211yesmaximal, characteristic, complemented
12C2×#16810776C211yesmaximal, characteristic, complemented
13C2×C4×#11719913C211yesmaximal, characteristic, complemented
14C2×#16810620C211yesmaximal, characteristic, complemented
15C22×#13133139C211yesmaximal, characteristic, complemented
16C2×C8×D4×C53C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C23×D212C2211yescharacteristic
19C22×Dic212C2211yescharacteristic, complemented
20C22×#11719913C2211yescharacteristic
21C22×#11719913C2211yescharacteristic
22#16811313—24no—
23#16811313C2218yescomplemented
24#16811269—24no—
25#16811269C2218yes—
26C2×#13133210—21no—
27C2×#13133209C2211yescharacteristic, complemented
28C2×#13133207—21no—
29C2×#13133205C2211yescharacteristic
30C2×#13133202—21no—
31C2×#13133198—21no—
32C2×#13133196C2211yescharacteristic
33C2×#13133196C2211yescharacteristic
34C2×#13133196C2211yescharacteristic, complemented
35C2×#13133191C2211yescharacteristic
36C2×#13133190—21no—
37C2×#13133185—21no—
38C2×C4×Dic106C2211yescharacteristic, complemented
39C2×C4×D212C2211yescharacteristic
40C2×#13133176C2211yescharacteristic, complemented
41C2×#13133173—21no—
42C22×C4⋊Dic53C2211yescharacteristic
43C2×C22⋊C4×D53—21no—
44#16810978C2218yescomplemented
45#16810954C2218yescomplemented
46#16810948C2218yescomplemented
47#16810924C2218yescomplemented
48#16810864C2218yescomplemented
49#16810852C2218yescomplemented
50#16810846C2218yescomplemented
51#16810787C2218yescomplemented
52#16810776C2218yescomplemented
53C4×#11719913C2218yescomplemented
54C2×#13133151C2211yescharacteristic, complemented
55C2×#13133149C2211yescharacteristic, complemented
56C2×#13133149C2211yescharacteristic, complemented
57#16810620C2218yescomplemented
58C2×#13133142C2211yescharacteristic, complemented
59C2×#13133142C2211yescharacteristic, complemented
60C2×#13133142C2211yescharacteristic, complemented
61C2×#13133142C2211yescharacteristic, complemented
62C2×#13133139C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133139C2211yescharacteristic
65C2×#13133139C2211yescharacteristic
66C2×#13133139C2211yescharacteristic
67C2×#13133139C2211yescharacteristic
68C2×#13133139C2218yescomplemented
69C23×C8×C53C2211yescharacteristic
70C23×C8×C53C2211yescharacteristic, complemented
71C2×C4×D4×C53C2211yescharacteristic
72C8×D4×C53C2218yescomplemented
73C2×C4⋊C8×C53C2211yescharacteristic, complemented
74C2×C22⋊C8×C53C2211yescharacteristic
75C2×C22⋊C8×C53C2211yescharacteristic, complemented
76C2×C4×C8×C53C2211yescharacteristic, complemented
77C24×D53—21no—
78C2×#11719945—22no—
79C2×#11719945—24no—
80C2×#11719945—42no—
81C2×#11719945C2314yes—
82C22×Dic106C2311yescharacteristic
83C22×Dic106C2311yescharacteristic
84C22×D212—24no—
85C22×D212—22no—
86C22×D212—21no—
87C22×D212—42no—
88C22×D212C2311yescharacteristic
89C22×D212C2314yes—
90C22×D212C2311yescharacteristic
91C22×C22⋊D53—21no—
92C22×C22⋊D53—21no—
93C23×Dic53—21no—
94C22×C4×D53—21no—
95C22×C4×D53—21no—
96C2×Dic212—42no—
97C2×Dic212C2314yescomplemented
98C2×#11719913—24no—
99C2×#11719913—42no—
100C2×#11719913C2314yes—
101C2×#11719913C2314yes—
102#13133210—28no—
103#13133209—22no—
104#13133209C2314yescomplemented
105#13133207—28no—
106#13133205—22no—
107#13133205C2314yes—
108#13133202—28no—
109#13133198—28no—
110#13133196—22no—
111#13133196—22no—
112#13133196—22no—
113#13133196C2314yes—
114#13133196C2314yes—
115#13133196C2314yescomplemented
116#13133191—22no—
117#13133191C2314yes—
118#13133190—28no—
119#13133185—28no—
120C4×Dic106—22no—
121C4×Dic106C2314yescomplemented
122C4×D212—22no—
123C4×D212C2314yes—
124#13133176—22no—
125#13133176C2314yescomplemented
126#13133173—28no—
127C2×C4⋊Dic53—22no—
128C2×C4⋊Dic53—21no—
129C2×C4⋊Dic53C2314yes—
130C2×C4⋊Dic53C2311yescharacteristic
131C2×C4⋊Dic53C2311yescharacteristic
132C2×C4⋊Dic53C2311yescharacteristic
133C2×C4⋊Dic53C2311yescharacteristic
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×#11719919—21no—
139C2×#11719919—21no—
140C2×C22⋊Dic53—21no—
141C2×C22⋊Dic53—21no—
142C2×C22⋊Dic53—21no—
143C2×C22⋊Dic53—21no—
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C22⋊C4×D53—28no—
149C2×C4×Dic53—21no—
150C2×C4×Dic53—21no—
151#13133151C2314yescomplemented
152#13133149C2314yescomplemented
153#13133149C2314yescomplemented
154#13133142C2314yescomplemented
155#13133142C2314yescomplemented
156#13133142C2314yescomplemented
157#13133142C2314yescomplemented
158#13133139C2314yes—
159#13133139C2314yes—
160#13133139C2314yes—
161#13133139C2314yes—
162#13133139C2314yes—
163#13133139C2314yes—
164C22×D4×C53D411yescharacteristic
165C23×C4×C53C2311yescharacteristic
166C23×C4×C53C2311yescharacteristic
167C22×C8×C53—42no—
168C22×C8×C53—42no—
169C22×C8×C53C2311yescharacteristic
170C22×C8×C53C2311yescharacteristic
171C22×C8×C53C2311yescharacteristic
172C22×C8×C53C2311yescharacteristic
173C22×C8×C53C2314yes—
174C22×C8×C53C2314yescomplemented
175C4×D4×C53D414yes—
176C4×D4×C53C2314yes—
177C2×C4⋊C4×C53D411yescharacteristic
178C2×C22⋊C4×C53D411yescharacteristic
179C2×C22⋊C4×C53D411yescharacteristic
180C2×C42×C53C2311yescharacteristic
181C4⋊C8×C53C2314yescomplemented
182C22⋊C8×C53C2314yes—
183C22⋊C8×C53C2314yescomplemented
184C4×C8×C53C2314yescomplemented
185C24×C53C2×D411yescharacteristic
186C24×C53C2×D411yescharacteristic
187C23×D53—21no—
188C23×D53—21no—
189C23×D53—24no—
190C23×D53—44no—
191C23×D53—44no—
192C23×D53—82no—
193C2×D4×C53—24no—
194C2×D4×C53C2×D414yes—
195C22×C4×C53—22no—
196C22×C4×C53—22no—
197C22×C4×C53—22no—
198C22×C4×C53—22no—
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53C2×D411yescharacteristic
203C22×C4×C53C2×D412yes—
204C22×C4×C53C2×D412yes—
205C22×C4×C53C2412yes—
206C22×C4×C53C2412yes—
207C22×C4×C53C2411yescharacteristic
208C2×C22⋊D53—24no—
209C2×C22⋊D53—24no—
210C2×C22⋊D53—44no—
211C2×C22⋊D53—82no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—21no—
215C22×Dic53—21no—
216C22×Dic53—21no—
217C22×Dic53—21no—
218C22×Dic53—24no—
219C22×Dic53—44no—
220#11719945—28no—
221#11719945—44no—
222#11719945—48no—
223C2×D212—21no—
224C2×D212—22no—
225C2×D212—22no—
226C2×D212—22no—
227C2×D212—28no—
228C2×D212—24no—
229C2×D212—21no—
230C2×D212—44no—
231C2×D212—48no—
232C2×D212—44no—
233C2×D212#4114yes—
234C2×D212C2412yes—
235C2×D212C2412yes—
236C2×C4×D53—24no—
237C2×C4×D53—24no—
238C2×C4×D53—44no—
239C2×C4×D53—82no—
240C2×Dic106—22no—
241C2×Dic106—22no—
242C2×Dic106—22no—
243C2×Dic106—22no—
244C2×Dic106—21no—
245C2×Dic106—21no—
246C2×Dic106C2412yes—
247C2×Dic106C2412yes—
248C2×C8×C53—22no—
249C2×C8×C53—22no—
250C2×C8×C53—22no—
251C2×C8×C53—22no—
252C2×C8×C53—44no—
253C2×C8×C53—44no—
254C2×C8×C53C2412yes—
255C2×C8×C53C2412yes—
256C2×C8×C53C2412yes—
257C2×C8×C53C2412yes—
258C4⋊C4×C53C2×D414yes—
259C22⋊C4×C53C2×D414yes—
260C22⋊C4×C53C2×D414yes—
261C42×C53C2×D412yes—
262C42×C53C2412yes—
263C22⋊Dic53—24no—
264C22⋊Dic53—24no—
265C22⋊Dic53—24no—
266C22⋊Dic53—24no—
267#11719921—24no—
268#11719921—24no—
269#11719921—24no—
270#11719921—24no—
271C4⋊Dic53—21no—
272C4⋊Dic53—21no—
273C4⋊Dic53—24no—
274C4⋊Dic53—21no—
275C4⋊Dic53—21no—
276C4⋊Dic53C2412yes—
277C4⋊Dic53C2412yes—
278C4⋊Dic53C2412yes—
279C4⋊Dic53C2412yes—
280#11719919—24no—
281#11719919—24no—
282#11719919—24no—
283#11719919—24no—
284#11719919—24no—
285#11719919—24no—
286C4×Dic53—24no—
287C4×Dic53—24no—
288Dic212—44no—
289#11719913—28no—
290#11719913—44no—
291C23×C53—22no—
292C23×C53—22no—
293C23×C53—22no—
294C23×C53—22no—
295C23×C53—22no—
296C23×C53#13514yes—
297C23×C53C22×D412yes—
298C23×C53C22×D412yes—
299C23×C53C22×D411yescharacteristic
300C22×D53—24no—
301C22×D53—22no—
302C22×D53—22no—
303C22×D53—48no—
304C22×D53—42no—
305C22×D53—42no—
306C22×D53—42no—
307C22×D53—48no—
308C22×D53—42no—
309C22×D53—42no—
310C22×D53—84no—
311C22×D53—816no—
312D4×C53—28no—
313C2×C4×C53—22no—
314C2×C4×C53—22no—
315C2×C4×C53—22no—
316C2×C4×C53—22no—
317C2×C4×C53—24no—
318C2×C4×C53—24no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—22no—
322C2×C4×C53—22no—
323C2×C4×C53C22×D412yes—
324C2×C4×C53C22×D412yes—
325C2×C4×C53C22×D412yes—
326C2×C4×C53C22×D412yes—
327C2×C4×C53C22×D411yescharacteristic
328C2×C4×C53C2×#4112yes—
329C2×C4×C53H(5,𝔽2)12yes—
330C2×C4×C53C2511yescharacteristic
331C22⋊D53—48no—
332C22⋊D53—84no—
333C2×Dic53—22no—
334C2×Dic53—22no—
335C2×Dic53—22no—
336C2×Dic53—22no—
337C2×Dic53—22no—
338C2×Dic53—22no—
339C2×Dic53—42no—
340C2×Dic53—42no—
341C2×Dic53—48no—
342C2×Dic53—42no—
343C2×Dic53—42no—
344C2×Dic53—42no—
345C2×Dic53—42no—
346D212—24no—
347D212—22no—
348D212—22no—
349D212—22no—
350D212—48no—
351D212—42no—
352D212C2×#4114yes—
353C4×D53—48no—
354C4×D53—84no—
355Dic106—22no—
356Dic106—22no—
357Dic106—22no—
358Dic106—22no—
359Dic106—42no—
360Dic106—42no—
361C8×C53—22no—
362C8×C53—22no—
363C8×C53—22no—
364C8×C53—22no—
365C2×#3296—531nomaximal, Sylow
366C22×C53—22no—
367C22×C53—28no—
368C22×C53—22no—
369C22×C53—22no—
370C22×C53—22no—
371C22×C53—22no—
372C22×C53—44no—
373C22×C53#54612yes—
374C22×C53C2×#13514yes—
375C22×C53C2×#13512yes—
376C22×C53#57712yes—
377C22×C53C23×D411yescharacteristic
378C2×D53—24no—
379C2×D53—48no—
380C2×D53—42no—
381C2×D53—42no—
382C2×D53—42no—
383C2×D53—42no—
384C2×D53—42no—
385C2×D53—816no—
386C2×D53—84no—
387C4×C53—22no—
388C4×C53—22no—
389C4×C53—22no—
390C4×C53—22no—
391C4×C53#54612yes—
392C4×C53C22×#4111yescharacteristic
393C4×C53C2×H(5,𝔽2)11yescharacteristic
394Dic53—42no—
395Dic53—42no—
396Dic53—42no—
397Dic53—42no—
398Dic53—42no—
399Dic53—42no—
400C2×#552—531no—
401C2×#546—531no—
402#3296—5316no—
403C2×#488—531no—
404C2×#482—531no—
405C2×#483—531no—
406C2×#478—531no—
407C2×#467—531no—
408C2×#465—531no—
409C2×#464—531no—
410C2×#452—531no—
411C2×#450—531no—
412C2×C4×SD16—531no—
413C2×C8×D4D5311yescharacteristic, complemented
414C2×#416—531no—
415C22×#102—531no—
416C2×C53—24no—
417C2×C53—42no—
418C2×C53#329614yescomplemented
419C2×C53C2×#54611yescharacteristic
420C2×C53C22×#13511yescharacteristic
421C2×C53C2×#57711yescharacteristic
422D53—44no—
423D53—82no—
424C22×#41—531no—
425C23×D4—531no—
426C22×Q16—531no—
427C22×SD16—531no—
428C22×SD16—531no—
429C23×C8C2×D5311yescharacteristic
430C23×C8C2×D5311yescharacteristic, complemented
431#552—538no—
432#552—1064no—
433#546—538no—
434#546—1064no—
435C2×#126—1061no—
436C2×#125—531no—
437C2×#125—1061no—
438C2×#124—531no—
439C2×#123—1061no—
440C2×#123—1061no—
441C2×C22⋊Q8—531no—
442C2×C22⋊Q8—531no—
443C2×C22⋊Q8—531no—
444C2×#121—531no—
445C2×#121—1061no—
446C2×#120—1061no—
447C2×C4×Q8—531no—
448C2×C4×D4—531no—
449C2×C4×D4C2×D5311yescharacteristic
450C2×#117—531no—
451C2×#117—1061no—
452C22×C4⋊C4—531no—
453C22×C22⋊C4—1061no—
454#488—538no—
455#483—538no—
456#482—538no—
457#478—538no—
458#467—538no—
459#465—538no—
460#464—538no—
461#452—538no—
462#450—538no—
463C4×SD16—538no—
464C8×D4C2×D5318yescomplemented
465C2×#107—531no—
466C2×#106—531no—
467C2×#106—531no—
468C2×C4⋊C8C2×D5311yescharacteristic, complemented
469#416—538no—
470C2×#103—531no—
471C2×#103—531no—
472C2×#103—531no—
473C2×#103—531no—
474C2×#102—531no—
475C2×#102—531no—
476C2×#102—531no—
477C2×#102—531no—
478C2×#102—531no—
479C2×#102—531no—
480C2×#102—538no—
481C2×C22⋊C8C2×D5311yescharacteristic
482C2×C22⋊C8C2×D5311yescharacteristic, complemented
483C2×C4×C8C2×D5311yescharacteristic, complemented
484C53C2×#329611yescharacteristic, complemented, Sylow
485C25—1061no—
486C2×#41—534no—
487C2×#41—1064no—
488C2×#41—1062no—
489C2×#41—2122no—
490C22×Q8—531no—
491C22×Q8—531no—
492C22×D4—531no—
493C22×D4—531no—
494C22×D4—534no—
495C22×D4—1064no—
496C22×D4—1061no—
497C22×D4—1061no—
498C22×D4—1061no—
499C22×D4—1062no—
500C22×D4—2122no—
501C22×D4D21211yescharacteristic
502C23×C4—1061no—
503C23×C4—1061no—
504C23×C4—1061no—
505C23×C4C22×D5311yescharacteristic
506C23×C4C22×D5311yescharacteristic
507C2×Q16—534no—
508C2×Q16—2122no—
509C2×SD16—534no—
510C2×SD16—534no—
511C2×SD16—1064no—
512C2×SD16—2122no—
513C22×C8—42no—
514C22×C8—42no—
515C22×C8C22×D5311yescharacteristic
516C22×C8C22×D5311yescharacteristic
517C22×C8C22×D5311yescharacteristic
518C22×C8C22×D5311yescharacteristic
519C22×C8C22×D5314yes—
520C22×C8C22×D5314yescomplemented
521#126—1068no—
522#125—534no—
523#125—1068no—
524#125—1062no—
525#124—534no—
526#124—1062no—
527#123—1068no—
528#123—1068no—
529C22⋊Q8—534no—
530C22⋊Q8—534no—
531C22⋊Q8—534no—
532C22⋊Q8—1062no—
533C22⋊Q8—1062no—
534C22⋊Q8—1062no—
535#121—534no—
536#121—1062no—
537#121—1068no—
538#120—1068no—
539C4×Q8—534no—
540C4×Q8—1062no—
541C4×D4—534no—
542C4×D4—1062no—
543C4×D4D21214yes—
544C4×D4C22×D5314yes—
545#117—534no—
546#117—1062no—
547#117—1068no—
548C2×C4⋊C4—531no—
549C2×C4⋊C4—531no—
550C2×C4⋊C4—534no—
551C2×C4⋊C4—531no—
552C2×C4⋊C4—531no—
553C2×C4⋊C4—1061no—
554C2×C4⋊C4—1062no—
555C2×C4⋊C4—1061no—
556C2×C4⋊C4—1061no—
557C2×C4⋊C4—1061no—
558C2×C4⋊C4—1061no—
559C2×C4⋊C4—1061no—
560C2×C4⋊C4—1061no—
561C2×C4⋊C4D21211yescharacteristic
562C2×C22⋊C4—1061no—
563C2×C22⋊C4—1061no—
564C2×C22⋊C4—1061no—
565C2×C22⋊C4—1061no—
566C2×C22⋊C4—1061no—
567C2×C22⋊C4—1061no—
568C2×C22⋊C4—1061no—
569C2×C22⋊C4—1061no—
570C2×C22⋊C4—1068no—
571C2×C22⋊C4D21211yescharacteristic
572C2×C22⋊C4D21211yescharacteristic
573C2×C42—1061no—
574C2×C42—1061no—
575C2×C42C22×D5311yescharacteristic
576#107—534no—
577#106—534no—
578#106—534no—
579C4⋊C8C22×D5314yescomplemented
580#103—534no—
581#103—534no—
582#103—534no—
583#103—534no—
584#102—534no—
585#102—534no—
586#102—534no—
587#102—534no—
588#102—534no—
589#102—534no—
590C22⋊C8C22×D5314yes—
591C22⋊C8C22×D5314yescomplemented
592C4×C8C22×D5314yescomplemented
593C24—1061no—
594C24—1064no—
595C24—1061no—
596C24—4242no—
597C24—2124no—
598C24—2124no—
599C24C2×D21211yescharacteristic
600C24C2×D21211yescharacteristic
601#41—1068no—
602#41—2124no—
603#41—2128no—
604C2×Q8—532no—
605C2×Q8—532no—
606C2×Q8—1061no—
607C2×Q8—1061no—
608C2×Q8—1062no—
609C2×Q8—1062no—
610C2×Q8—1062no—
611C2×Q8—1062no—
612C2×D4—24no—
613C2×D4—534no—
614C2×D4—532no—
615C2×D4—532no—
616C2×D4—1068no—
617C2×D4—1064no—
618C2×D4—1064no—
619C2×D4—1061no—
620C2×D4—1064no—
621C2×D4—1061no—
622C2×D4—1062no—
623C2×D4—1062no—
624C2×D4—1062no—
625C2×D4—4242no—
626C2×D4—2124no—
627C2×D4—2128no—
628C2×D4—2124no—
629C2×D4—2124no—
630C2×D4C2×D21214yes—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—1064no—
636C22×C4—1061no—
637C22×C4—1061no—
638C22×C4—1061no—
639C22×C4—1061no—
640C22×C4—1061no—
641C22×C4—1061no—
642C22×C4—1064no—
643C22×C4—1064no—
644C22×C4—4242no—
645C22×C4—2124no—
646C22×C4—2124no—
647C22×C4C2×D21212yes—
648C22×C4C2×D21212yes—
649C22×C4C2×D21211yescharacteristic
650C22×C4C2×D21211yescharacteristic
651C22×C4C2×D21211yescharacteristic
652C22×C4C2×D21211yescharacteristic
653C22×C4C23×D5312yes—
654C22×C4C23×D5312yes—
655C22×C4C23×D5311yescharacteristic
656Q16—2124no—
657SD16—1068no—
658SD16—2124no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—44no—
664C2×C8—44no—
665C2×C8C23×D5312yes—
666C2×C8C23×D5312yes—
667C2×C8C23×D5312yes—
668C2×C8C23×D5312yes—
669C4⋊C4—532no—
670C4⋊C4—532no—
671C4⋊C4—532no—
672C4⋊C4—532no—
673C4⋊C4—1061no—
674C4⋊C4—1061no—
675C4⋊C4—1064no—
676C4⋊C4—1061no—
677C4⋊C4—1061no—
678C4⋊C4—1064no—
679C4⋊C4—1064no—
680C4⋊C4—1064no—
681C4⋊C4—1064no—
682C4⋊C4—1064no—
683C4⋊C4—1064no—
684C4⋊C4C2×D21214yes—
685C22⋊C4—1064no—
686C22⋊C4—1064no—
687C22⋊C4—1064no—
688C22⋊C4—1064no—
689C22⋊C4—1064no—
690C22⋊C4—1064no—
691C22⋊C4—1064no—
692C22⋊C4—1064no—
693C22⋊C4C2×D21214yes—
694C22⋊C4C2×D21214yes—
695C42—1064no—
696C42—1064no—
697C42C2×D21212yes—
698C42C23×D5312yes—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—1064no—
705C23—1062no—
706C23—1062no—
707C23—42416no—
708C23—4244no—
709C23—2128no—
710C23—2122no—
711C23—2128no—
712C23—2122no—
713C23—2122no—
714C23—2122no—
715C23—2122no—
716C23#1313323914yes—
717C23C22×D21212yes—
718C23C22×D21212yes—
719C23C22×D21211yescharacteristic
720Q8—1062no—
721Q8—1062no—
722Q8—1062no—
723Q8—1062no—
724Q8—2122no—
725Q8—2122no—
726D4—28no—
727D4—534no—
728D4—1064no—
729D4—1062no—
730D4—1062no—
731D4—1062no—
732D4—4244no—
733D4—2128no—
734D4—2128no—
735D4—2122no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—1062no—
747C2×C4—1062no—
748C2×C4—1062no—
749C2×C4—1062no—
750C2×C4—1062no—
751C2×C4—1062no—
752C2×C4—4244no—
753C2×C4—2128no—
754C2×C4—2122no—
755C2×C4—2122no—
756C2×C4—2128no—
757C2×C4—2122no—
758C2×C4—2122no—
759C2×C4—2122no—
760C2×C4—2122no—
761C2×C4C22×D21212yes—
762C2×C4C22×D21212yes—
763C2×C4C22×D21212yes—
764C2×C4C22×D21212yes—
765C2×C4C22×D21211yescharacteristic
766C2×C4#41×D5312yes—
767C2×C4#1313326212yes—
768C2×C4C24×D5311yescharacteristic
769C8—22no—
770C8—22no—
771C8—22no—
772C8—22no—
773C22—28no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—44no—
780C22—1064no—
781C22—42416no—
782C22—4244no—
783C22—2122no—
784C22—2122no—
785C22—2122no—
786C22—2128no—
787C22—2122no—
788C22—2122no—
789C22#1681126812yes—
790C22C2×#1313323914yes—
791C22C2×#1313323912yes—
792C22#1681143512yes—
793C22C23×D21211yescharacteristic
794C4—22no—
795C4—22no—
796C4—22no—
797C4—22no—
798C4—2122no—
799C4—2122no—
800C4—2122no—
801C4—2122no—
802C4—2122no—
803C4—2122no—
804C4#1681126812yes—
805C4C2×#41×D5311yescharacteristic
806C4C2×#1313326211yescharacteristic
807C2—24no—
808C2—42no—
809C2—4242no—
810C2—2124no—
811C2#2028655214yesdirect product factor
812C2C2×#1681126811yescharacteristic
813C2C22×#1313323911yescharacteristic
814C2C2×#1681143511yescharacteristic
subgroupG/H
centerC23C22×D212
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C8×D4×C53C2
socleC23×C53C22×D4
prime radicalC2×#16811269C2
hypercenterC2×C8×D4D53
hypocenterC53C2×#3296
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
1. C2×#16811313C2semidirect
3. #20286552C2direct (N × H)
4. C2×#16810978C2semidirect
5. C2×#16810948C2semidirect
6. C2×#16810954C2semidirect
7. C2×#16810924C2semidirect
8. C2×#16810864C2semidirect
9. C2×#16810852C2semidirect
10. C2×#16810846C2semidirect
11. C2×#16810787C2semidirect
12. C2×#16810776C2semidirect
13. C2×C4×#11719913C2semidirect
14. C2×#16810620C2semidirect
15. C22×#13133139C2semidirect
16. C2×C8×D4×C53C2semidirect
19. C22×Dic212C22semidirect
23. #16811313C22semidirect
27. C2×#13133209C22semidirect
34. C2×#13133196C22semidirect
38. C2×C4×Dic106C22semidirect
40. C2×#13133176C22semidirect
44. #16810978C22semidirect
45. #16810954C22semidirect
46. #16810948C22semidirect
47. #16810924C22semidirect
48. #16810864C22semidirect
49. #16810852C22semidirect
50. #16810846C22semidirect
51. #16810787C22semidirect
52. #16810776C22semidirect
53. C4×#11719913C22semidirect
54. C2×#13133151C22semidirect
55. C2×#13133149C22semidirect
56. C2×#13133149C22semidirect
57. #16810620C22semidirect
58. C2×#13133142C22semidirect
59. C2×#13133142C22semidirect
60. C2×#13133142C22semidirect
61. C2×#13133142C22semidirect
68. C2×#13133139C22semidirect
70. C23×C8×C53C22semidirect
72. C8×D4×C53C22semidirect
73. C2×C4⋊C8×C53C22semidirect
75. C2×C22⋊C8×C53C22semidirect
76. C2×C4×C8×C53C22semidirect
97. C2×Dic212C23semidirect
104. #13133209C23semidirect
115. #13133196C23semidirect
121. C4×Dic106C23semidirect
125. #13133176C23semidirect
151. #13133151C23semidirect
152. #13133149C23semidirect
153. #13133149C23semidirect
154. #13133142C23semidirect
155. #13133142C23semidirect
156. #13133142C23semidirect
157. #13133142C23semidirect
174. C22×C8×C53C23semidirect
181. C4⋊C8×C53C23semidirect
183. C22⋊C8×C53C23semidirect
184. C4×C8×C53C23semidirect
413. C2×C8×D4D53semidirect
418. C2×C53#3296semidirect
430. C23×C8C2×D53semidirect
464. C8×D4C2×D53semidirect
468. C2×C4⋊C8C2×D53semidirect
482. C2×C22⋊C8C2×D53semidirect
483. C2×C4×C8C2×D53semidirect
484. C53C2×#3296semidirect
520. C22×C8C22×D53semidirect
579. C4⋊C8C22×D53semidirect
591. C22⋊C8C22×D53semidirect
592. C4×C8C22×D53semidirect
811. C2#20286552direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113132
C2×#168112692
#202865522
C2×#168109782
C2×#168109482
C2×#168109542
C2×#168109242
C2×#168108642
C2×#168108522
C2×#168108462
C2×#168107872
C2×#168107762
C2×C4×#117199132
C2×#168106202
C22×#131331392
C2×C8×D4×C532
C2×#329653