Finite Group Databasebeta

← C2×#20285716 #28255346

Subgroups — C2×#20285716 #28255346

Order 13568.

2242 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811177C211yesmaximal, characteristic, complemented
2C2×#124×D53C211yesmaximal, characteristic
3#20285716C2116yesmaximal, direct product factor
4C2×#16811016C211yesmaximal, characteristic, complemented
5C2×#16811014C211yesmaximal, characteristic, complemented
6C2×#16810984C211yesmaximal, characteristic, complemented
7C2×#16810981C211yesmaximal, characteristic, complemented
8C2×#16810846C211yesmaximal, characteristic, complemented
9C2×#16810845C211yesmaximal, characteristic, complemented
10C2×#16810842C211yesmaximal, characteristic, complemented
11C2×#16810780C211yesmaximal, characteristic, complemented
12C2×#16810777C211yesmaximal, characteristic, complemented
13C2×#16810775C211yesmaximal, characteristic
14C2×#16810772C211yesmaximal, characteristic
15C2×#16810679C211yesmaximal, characteristic, complemented
16C2×C53×#464C211yesmaximal, characteristic, complemented
17C22×Q8×D53C2211yescharacteristic
18C22×D4×D53C2211yescharacteristic
19C22×Dic212C2211yescharacteristic, complemented
20C22×#11719925C2211yescharacteristic, complemented
21C22×#11719925C2211yescharacteristic, complemented
22C22×#11719913C2211yescharacteristic
23C22×#11719923C2211yescharacteristic
24C22×#11719924C2211yescharacteristic
25#16811177—24no—
26#16811177C2218yescomplemented
27C2×#13133216C2211yescharacteristic, complemented
28C2×#13133215C2211yescharacteristic, complemented
29C2×#13133207—21no—
30C2×#13133206C2211yescharacteristic
31C2×#13133205C2211yescharacteristic
32C2×#13133204C2211yescharacteristic
33C2×#13133203—21no—
34C2×#13133203—21no—
35#124×D53—24no—
36#124×D53C2218yes—
37C2×#13133197C2211yescharacteristic
38C2×#13133195—21no—
39C2×#13133193C2211yescharacteristic
40C2×C4×Dic106—21no—
41C2×C4×Dic106C2211yescharacteristic, complemented
42C2×#13133174—21no—
43C2×C22⋊C4×D53—21no—
44C2×C22⋊C4×D53—21no—
45C2×C42×D53C2211yescharacteristic
46#16811016C2218yescomplemented
47#16811014C2218yescomplemented
48#16810984C2218yescomplemented
49#16810981C2218yescomplemented
50#16810846C2218yescomplemented
51#16810845C2218yescomplemented
52#16810842C2218yescomplemented
53#16810780C2218yescomplemented
54#16810777C2218yescomplemented
55#16810775C2218yes—
56#16810772C2218yes—
57#16810679C2218yescomplemented
58C2×C4⋊#88322C2211yescharacteristic, complemented
59C2×#13133142C2211yescharacteristic, complemented
60C2×#13133141C2211yescharacteristic, complemented
61C2×#13133140C2211yescharacteristic, complemented
62C2×#13133139C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65C2×#13133129C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133127C2211yescharacteristic, complemented
68C2×#13133127C2211yescharacteristic, complemented
69C22×Q16×C53C2211yescharacteristic, complemented
70C22×SD16×C53C2211yescharacteristic
71C2×#124×C53C2211yescharacteristic
72C2×C4×Q8×C53C2211yescharacteristic, complemented
73C53×#464C2218yescomplemented
74C2×C4⋊C8×C53C2211yescharacteristic, complemented
75C2×#103×C53C2211yescharacteristic, complemented
76C2×#102×C53C2211yescharacteristic
77C24×D53—21no—
78C22×Dic106—21no—
79C22×Dic106—21no—
80C22×Dic106C2311yescharacteristic
81C22×Dic106C2311yescharacteristic
82C2×Q8×D53—22no—
83C2×Q8×D53—42no—
84C2×Q8×D53—42no—
85C2×Q8×D53C2314yes—
86C22×D212C2311yescharacteristic
87C22×C22⋊D53—21no—
88C2×D4×D53—22no—
89C2×D4×D53—42no—
90C2×D4×D53—42no—
91C2×D4×D53C2314yes—
92C22×C4×D53—21no—
93C22×C4×D53D411yescharacteristic
94C22×C4×D53D411yescharacteristic
95C22×C4×D53C2311yescharacteristic
96C2×Dic212—42no—
97C2×Dic212C2314yescomplemented
98C2×#11719925—42no—
99C2×#11719925—42no—
100C2×#11719925C2314yescomplemented
101C2×#11719925C2314yescomplemented
102C2×#11719913—42no—
103C2×#11719913C2314yes—
104C2×#11719923—42no—
105C2×#11719923C2314yes—
106C2×#11719924—42no—
107C2×#11719924C2314yes—
108C22×#88322C2311yescharacteristic
109C22×#88322C2311yescharacteristic
110#13133216—22no—
111#13133216C2314yescomplemented
112#13133215—22no—
113#13133215C2314yescomplemented
114#13133207—28no—
115#13133206—22no—
116#13133206C2314yes—
117#13133205—22no—
118#13133205C2314yes—
119#13133204—22no—
120#13133204C2314yes—
121#13133203—28no—
122#13133203—28no—
123#13133197—22no—
124#13133197C2314yes—
125#13133195—28no—
126#13133193—22no—
127#13133193C2314yes—
128C4×Dic106—22no—
129C4×Dic106—28no—
130C4×Dic106C2314yescomplemented
131#13133174—28no—
132C2×C4⋊Dic53—21no—
133C2×C4⋊Dic53C2311yescharacteristic
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×#11719919—21no—
139C2×C22⋊Dic53—21no—
140C2×C22⋊Dic53—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C22⋊C4×D53—28no—
148C22⋊C4×D53—28no—
149C2×C4×Dic53—21no—
150C2×C4×Dic53D411yescharacteristic
151C2×C4×Dic53D411yescharacteristic
152C2×C4×Dic53C2311yescharacteristic
153C42×D53D414yes—
154C42×D53C2314yes—
155C4⋊#88322C2314yescomplemented
156#13133142C2314yescomplemented
157#13133141C2314yescomplemented
158#13133140C2314yescomplemented
159#13133139C2314yes—
160#13133138C2314yes—
161#13133137C2314yes—
162#13133129C2314yes—
163#13133129C2314yes—
164#13133127C2314yescomplemented
165#13133127C2314yescomplemented
166C22×Q8×C53C2311yescharacteristic
167C22×Q8×C53C2311yescharacteristic
168C22×D4×C53C2311yescharacteristic
169C2×Q16×C53—42no—
170C2×Q16×C53C2314yescomplemented
171C2×SD16×C53—42no—
172C2×SD16×C53C2314yes—
173C22×C8×C53C2311yescharacteristic
174C22×C8×C53C2311yescharacteristic
175#124×C53—22no—
176#124×C53C2314yes—
177C4×Q8×C53—22no—
178C4×Q8×C53C2314yescomplemented
179C2×C4⋊C4×C53—21no—
180C2×C4⋊C4×C53C2311yescharacteristic
181C2×C22⋊C4×C53—21no—
182C2×C22⋊C4×C53—21no—
183C2×C42×C53—21no—
184C2×C42×C53C2311yescharacteristic
185C4⋊C8×C53C2314yescomplemented
186#103×C53C2314yescomplemented
187#102×C53C2314yes—
188C24×C53—21no—
189C23×D53—21no—
190C23×D53—24no—
191C23×D53—44no—
192C23×D53—44no—
193C23×D53—44no—
194C23×D53C2×D411yescharacteristic
195C2×Q8×C53—21no—
196C2×Q8×C53—21no—
197C2×Q8×C53—22no—
198C2×Q8×C53—22no—
199C2×Q8×C53—22no—
200C2×Q8×C53—22no—
201C2×Q8×C53C2412yes—
202C2×Q8×C53C2412yes—
203C2×D4×C53—21no—
204C2×D4×C53—22no—
205C2×D4×C53—22no—
206C2×D4×C53C2412yes—
207C22×C4×C53—21no—
208C22×C4×C53—21no—
209C22×C4×C53—21no—
210C22×C4×C53C2×D411yescharacteristic
211C22×C4×C53C2×D411yescharacteristic
212C22×C4×C53C2411yescharacteristic
213C2×C22⋊D53—24no—
214C2×C22⋊D53—44no—
215C22×Dic53—21no—
216C22×Dic53—21no—
217C22×Dic53—21no—
218C22×Dic53C2×D411yescharacteristic
219C22×Dic53C2×D411yescharacteristic
220C22×Dic53C2×D411yescharacteristic
221Q8×D53—44no—
222Q8×D53—44no—
223Q8×D53—48no—
224D4×D53—44no—
225D4×D53—44no—
226D4×D53—48no—
227C2×D212—22no—
228C2×D212—22no—
229C2×D212—21no—
230C2×D212C2412yes—
231C2×C4×D53—24no—
232C2×C4×D53—22no—
233C2×C4×D53—22no—
234C2×C4×D53—24no—
235C2×C4×D53—42no—
236C2×C4×D53—44no—
237C2×C4×D53C2×D412yes—
238C2×C4×D53C2×D414yes—
239C2×C4×D53C2×D414yes—
240C2×C4×D53C2412yes—
241C2×Dic106—22no—
242C2×Dic106—22no—
243C2×Dic106—22no—
244C2×Dic106—22no—
245C2×Dic106—21no—
246C2×Dic106—21no—
247C2×Dic106—24no—
248C2×Dic106—24no—
249C2×Dic106—44no—
250C2×Dic106—44no—
251C2×Dic106C2412yes—
252C2×Dic106C2412yes—
253Q16×C53—44no—
254SD16×C53—44no—
255C2×C8×C53—22no—
256C2×C8×C53—22no—
257C2×C8×C53C2412yes—
258C2×C8×C53C2412yes—
259C4⋊C4×C53—24no—
260C4⋊C4×C53—21no—
261C4⋊C4×C53C2412yes—
262C22⋊C4×C53—24no—
263C22⋊C4×C53—24no—
264C42×C53—24no—
265C42×C53C2×D412yes—
266C42×C53C2412yes—
267C22⋊Dic53—24no—
268C22⋊Dic53—24no—
269#11719925—44no—
270#11719925—44no—
271#11719924—44no—
272#11719923—44no—
273#11719921—24no—
274#11719921—24no—
275#11719921—24no—
276#11719921—24no—
277#11719921—24no—
278#11719921—24no—
279C4⋊Dic53—21no—
280C4⋊Dic53—24no—
281C4⋊Dic53C2412yes—
282#11719919—24no—
283#11719919—24no—
284#11719919—24no—
285#11719919—24no—
286#11719919—24no—
287C4×Dic53—24no—
288C4×Dic53C2×D412yes—
289C4×Dic53C2×D414yes—
290C4×Dic53C2×D414yes—
291C4×Dic53C2412yes—
292C2×#88322—22no—
293C2×#88322—22no—
294C2×#88322C2412yes—
295C2×#88322C2412yes—
296Dic212—44no—
297#11719913—44no—
298C23×C53—22no—
299C23×C53—42no—
300C23×C53—42no—
301C23×C53—42no—
302C23×C53C22×D411yescharacteristic
303C22×D53—22no—
304C22×D53—22no—
305C22×D53—22no—
306C22×D53—48no—
307C22×D53—48no—
308C22×D53—42no—
309C22×D53—42no—
310C22×D53—42no—
311C22×D53—48no—
312C22×D53—816no—
313C22×D53#13714yes—
314C22×D53C22×D412yes—
315Q8×C53—22no—
316Q8×C53—22no—
317Q8×C53—22no—
318Q8×C53—22no—
319Q8×C53—42no—
320Q8×C53—42no—
321D4×C53—22no—
322D4×C53—22no—
323D4×C53—42no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53—22no—
327C2×C4×C53—22no—
328C2×C4×C53—22no—
329C2×C4×C53—42no—
330C2×C4×C53—42no—
331C2×C4×C53—42no—
332C2×C4×C53C22×D412yes—
333C2×C4×C53C22×D412yes—
334C2×C4×C53C22×D411yescharacteristic
335C2×C4×C53H(5,𝔽2)12yes—
336C2×C4×C53H(5,𝔽2)12yes—
337C2×C4×C53C2511yescharacteristic
338C22⋊D53—48no—
339C2×Dic53—22no—
340C2×Dic53—22no—
341C2×Dic53—22no—
342C2×Dic53—22no—
343C2×Dic53—22no—
344C2×Dic53—22no—
345C2×Dic53—42no—
346C2×Dic53—42no—
347C2×Dic53—42no—
348C2×Dic53C22×D412yes—
349C2×Dic53C22×D412yes—
350C2×Dic53C22×D412yes—
351D212—22no—
352D212—22no—
353D212—42no—
354C4×D53—28no—
355C4×D53—24no—
356C4×D53—22no—
357C4×D53—22no—
358C4×D53—44no—
359C4×D53—48no—
360Dic106—22no—
361Dic106—22no—
362Dic106—22no—
363Dic106—22no—
364Dic106—48no—
365Dic106—48no—
366Dic106—42no—
367Dic106—42no—
368C8×C53—22no—
369C8×C53—22no—
370#88322—22no—
371#88322—22no—
372C2×#3215—531nomaximal, Sylow
373C22×C53—42no—
374C22×C53—42no—
375C22×C53—42no—
376C22×C53—84no—
377C22×C53#53512yes—
378C22×C53C2×#13712yes—
379C22×C53#57512yes—
380C22×C53C23×D411yescharacteristic
381C2×D53—22no—
382C2×D53—28no—
383C2×D53—22no—
384C2×D53—42no—
385C2×D53—42no—
386C2×D53—42no—
387C2×D53—816no—
388C2×D53—84no—
389C2×D53C2×#13714yes—
390C4×C53—22no—
391C4×C53—22no—
392C4×C53—42no—
393C4×C53—42no—
394C4×C53—42no—
395C4×C53#53512yes—
396C4×C53C2×H(5,𝔽2)11yescharacteristic
397C4×C53C2×H(5,𝔽2)11yescharacteristic
398Dic53—22no—
399Dic53—22no—
400Dic53—22no—
401Dic53—42no—
402Dic53—42no—
403Dic53—42no—
404C2×#533—531no—
405C22×#124—531no—
406#3215—5316no—
407C2×#497—531no—
408C2×#497—531no—
409C2×#489—531no—
410C2×#489—531no—
411C2×#464—531no—
412C2×#464—531no—
413C2×#464—531no—
414C2×#464D5311yescharacteristic, complemented
415C2×#451—531no—
416C2×#451—531no—
417C2×#450—531no—
418C2×#450—531no—
419C2×#432—531no—
420C2×C53—82no—
421C2×C53#321514yescomplemented
422C2×C53C2×#53511yescharacteristic
423C2×C53C22×#13711yescharacteristic
424C2×C53C2×#57511yescharacteristic
425D53—24no—
426D53—82no—
427C23×Q8—531no—
428C23×D4—531no—
429C22×Q16—531no—
430C22×Q16—531no—
431C22×Q16—531no—
432C22×Q16C2×D5311yescharacteristic, complemented
433C22×SD16—531no—
434C22×SD16—531no—
435C22×SD16—531no—
436C22×SD16C2×D5311yescharacteristic
437#533—538no—
438#533—1064no—
439C2×C4⋊Q8—531no—
440C2×C4⋊Q8—531no—
441C2×#125—1061no—
442C2×#124—531no—
443C2×#124—531no—
444C2×#124—538no—
445C2×#124—531no—
446C2×#124—1061no—
447C2×#124—1061no—
448C2×#124—1064no—
449C2×#124C2×D5311yescharacteristic
450C2×C22⋊Q8—531no—
451C2×C22⋊Q8—531no—
452C2×C22⋊Q8—1061no—
453C2×C4×Q8—531no—
454C2×C4×Q8—1061no—
455C2×C4×Q8C2×D5311yescharacteristic, complemented
456C2×#117—1061no—
457C22×C22⋊C4—1061no—
458C22×C22⋊C4—1061no—
459C22×C42—531no—
460#497—538no—
461#497—538no—
462#489—538no—
463#489—538no—
464#464—538no—
465#464—538no—
466#464—538no—
467#464C2×D5318yescomplemented
468#451—538no—
469#451—538no—
470#450—538no—
471#450—538no—
472#432—538no—
473C2×C4⋊C8—531no—
474C2×C4⋊C8C2×D5311yescharacteristic, complemented
475C2×#103—531no—
476C2×#103—531no—
477C2×#103—531no—
478C2×#103C2×D5311yescharacteristic, complemented
479C2×#102—531no—
480C2×#102—531no—
481C2×#102—531no—
482C2×#102C2×D5311yescharacteristic
483C2×C22⋊C8—531no—
484C2×C22⋊C8—531no—
485C2×#97—531no—
486C2×#97—531no—
487C53C2×#321511yescharacteristic, complemented, Sylow
488C25—1061no—
489C22×Q8—534no—
490C22×Q8—531no—
491C22×Q8—531no—
492C22×Q8—1061no—
493C22×Q8—1061no—
494C22×Q8—1062no—
495C22×Q8—2122no—
496C22×Q8—2122no—
497C22×Q8C22×D5311yescharacteristic
498C22×Q8C22×D5311yescharacteristic
499C22×D4—534no—
500C22×D4—531no—
501C22×D4—1062no—
502C22×D4—1061no—
503C22×D4—2122no—
504C22×D4—2122no—
505C22×D4C22×D5311yescharacteristic
506C23×C4—531no—
507C23×C4—531no—
508C23×C4—531no—
509C23×C4—1061no—
510C2×Q16—42no—
511C2×Q16—534no—
512C2×Q16—534no—
513C2×Q16—534no—
514C2×Q16—2122no—
515C2×Q16—2122no—
516C2×Q16—2122no—
517C2×Q16C22×D5314yescomplemented
518C2×SD16—42no—
519C2×SD16—534no—
520C2×SD16—534no—
521C2×SD16—534no—
522C2×SD16—2122no—
523C2×SD16—2122no—
524C2×SD16—2122no—
525C2×SD16C22×D5314yes—
526C22×C8—531no—
527C22×C8—531no—
528C22×C8C22×D5311yescharacteristic
529C22×C8C22×D5311yescharacteristic
530C4⋊Q8—534no—
531C4⋊Q8—534no—
532C4⋊Q8—1062no—
533C4⋊Q8—1062no—
534#125—1068no—
535#124—22no—
536#124—534no—
537#124—534no—
538#124—534no—
539#124—1068no—
540#124—1068no—
541#124—1062no—
542#124—1062no—
543#124—1062no—
544#124C22×D5314yes—
545C22⋊Q8—534no—
546C22⋊Q8—534no—
547C22⋊Q8—1062no—
548C22⋊Q8—1068no—
549C22⋊Q8—1062no—
550C4×Q8—22no—
551C4×Q8—534no—
552C4×Q8—1068no—
553C4×Q8—1062no—
554C4×Q8C22×D5314yescomplemented
555#117—1068no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—531no—
558C2×C4⋊C4—1061no—
559C2×C4⋊C4—1061no—
560C2×C4⋊C4—1061no—
561C2×C4⋊C4—1061no—
562C2×C4⋊C4—1061no—
563C2×C4⋊C4—1061no—
564C2×C4⋊C4C22×D5311yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—1068no—
568C2×C22⋊C4—1068no—
569C2×C22⋊C4—1061no—
570C2×C22⋊C4—1061no—
571C2×C22⋊C4—1061no—
572C2×C22⋊C4—1061no—
573C2×C22⋊C4—1061no—
574C2×C22⋊C4—1061no—
575C2×C22⋊C4—1061no—
576C2×C22⋊C4—1061no—
577C2×C42—21no—
578C2×C42—531no—
579C2×C42—531no—
580C2×C42—531no—
581C2×C42—534no—
582C2×C42—534no—
583C2×C42—1061no—
584C2×C42C22×D5311yescharacteristic
585C4⋊C8—534no—
586C4⋊C8C22×D5314yescomplemented
587#103—534no—
588#103—534no—
589#103—534no—
590#103C22×D5314yescomplemented
591#102—534no—
592#102—534no—
593#102—534no—
594#102C22×D5314yes—
595C22⋊C8—534no—
596C22⋊C8—534no—
597#97—534no—
598#97—534no—
599C24—21no—
600C24—531no—
601C24—1064no—
602C24—1061no—
603C24—2124no—
604C24—2124no—
605C24—2124no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—22no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—22no—
612C2×Q8—532no—
613C2×Q8—532no—
614C2×Q8—1064no—
615C2×Q8—1064no—
616C2×Q8—1061no—
617C2×Q8—1061no—
618C2×Q8—1062no—
619C2×Q8—1062no—
620C2×Q8—1062no—
621C2×Q8—1062no—
622C2×Q8—2124no—
623C2×Q8—2124no—
624C2×Q8—2124no—
625C2×Q8—2124no—
626C2×Q8—2128no—
627C2×Q8C23×D5312yes—
628C2×Q8C23×D5312yes—
629C2×D4—21no—
630C2×D4—22no—
631C2×D4—22no—
632C2×D4—532no—
633C2×D4—1064no—
634C2×D4—1061no—
635C2×D4—1062no—
636C2×D4—1062no—
637C2×D4—2124no—
638C2×D4—2124no—
639C2×D4—2128no—
640C2×D4—2124no—
641C2×D4C23×D5312yes—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—531no—
646C22×C4—531no—
647C22×C4—531no—
648C22×C4—534no—
649C22×C4—532no—
650C22×C4—532no—
651C22×C4—534no—
652C22×C4—1064no—
653C22×C4—1064no—
654C22×C4—1062no—
655C22×C4—1062no—
656C22×C4—1061no—
657C22×C4—1061no—
658C22×C4—1061no—
659C22×C4—2122no—
660C22×C4—2124no—
661C22×C4D4×D5311yescharacteristic
662C22×C4D4×D5311yescharacteristic
663C22×C4C23×D5311yescharacteristic
664Q16—44no—
665Q16—2124no—
666Q16—2124no—
667Q16—2124no—
668SD16—44no—
669SD16—2124no—
670SD16—2124no—
671SD16—2124no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—532no—
675C2×C8—532no—
676C2×C8—1062no—
677C2×C8—1062no—
678C2×C8C23×D5312yes—
679C2×C8C23×D5312yes—
680C4⋊C4—24no—
681C4⋊C4—21no—
682C4⋊C4—532no—
683C4⋊C4—1064no—
684C4⋊C4—1064no—
685C4⋊C4—1064no—
686C4⋊C4—1064no—
687C4⋊C4—1064no—
688C4⋊C4—1061no—
689C4⋊C4—1064no—
690C4⋊C4C23×D5312yes—
691C22⋊C4—24no—
692C22⋊C4—24no—
693C22⋊C4—1064no—
694C22⋊C4—1064no—
695C22⋊C4—1064no—
696C22⋊C4—1064no—
697C22⋊C4—1064no—
698C22⋊C4—1064no—
699C22⋊C4—1064no—
700C22⋊C4—1064no—
701C42—24no—
702C42—534no—
703C42—534no—
704C42—532no—
705C42—532no—
706C42—1064no—
707C42D4×D5312yes—
708C42C23×D5312yes—
709C23—22no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—534no—
714C23—532no—
715C23—1062no—
716C23—1062no—
717C23—1062no—
718C23—42416no—
719C23—2128no—
720C23—2128no—
721C23—2128no—
722C23—2122no—
723C23—2122no—
724C23—2122no—
725C23C2×D4×D5311yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—22no—
729Q8—22no—
730Q8—42no—
731Q8—42no—
732Q8—1062no—
733Q8—1062no—
734Q8—1062no—
735Q8—1062no—
736Q8—2128no—
737Q8—2128no—
738Q8—2122no—
739Q8—2122no—
740D4—22no—
741D4—22no—
742D4—42no—
743D4—1062no—
744D4—1062no—
745D4—2128no—
746D4—2122no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—532no—
756C2×C4—532no—
757C2×C4—532no—
758C2×C4—1068no—
759C2×C4—1062no—
760C2×C4—1062no—
761C2×C4—1062no—
762C2×C4—1064no—
763C2×C4—1062no—
764C2×C4—1062no—
765C2×C4—1062no—
766C2×C4—1062no—
767C2×C4—1062no—
768C2×C4—2124no—
769C2×C4—2128no—
770C2×C4—2122no—
771C2×C4—2122no—
772C2×C4—2122no—
773C2×C4C2×D4×D5312yes—
774C2×C4C2×D4×D5312yes—
775C2×C4C2×D4×D5311yescharacteristic
776C2×C4#1313326212yes—
777C2×C4#1313326312yes—
778C2×C4C24×D5311yescharacteristic
779C8—22no—
780C8—22no—
781C8—1062no—
782C8—1062no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—84no—
787C22—534no—
788C22—1068no—
789C22—1062no—
790C22—1062no—
791C22—42416no—
792C22—4244no—
793C22—2122no—
794C22—2122no—
795C22—2122no—
796C22#1681118912yes—
797C22#137×D5312yes—
798C22#1681142012yes—
799C22C22×D4×D5311yescharacteristic
800C4—22no—
801C4—22no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—1062no—
806C4—1062no—
807C4—1062no—
808C4—2122no—
809C4—2122no—
810C4—2122no—
811C4#1681118912yes—
812C4C2×#1313326211yescharacteristic
813C4C2×#1313326311yescharacteristic
814C2—82no—
815C2—1064no—
816C2—4242no—
817C2#2028571614yesdirect product factor
818C2C2×#1681118911yescharacteristic
819C2C2×#137×D5311yescharacteristic
820C2C2×#1681142011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#464C2
socleC23×C53C22×D4
prime radicalC22×D4×D53C22
hypercenterC2×#464D53
hypocenterC53C2×#3215
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×#16811177C2semidirect
3. #20285716C2direct (N × H)
4. C2×#16811016C2semidirect
5. C2×#16811014C2semidirect
6. C2×#16810984C2semidirect
7. C2×#16810981C2semidirect
8. C2×#16810846C2semidirect
9. C2×#16810845C2semidirect
10. C2×#16810842C2semidirect
11. C2×#16810780C2semidirect
12. C2×#16810777C2semidirect
15. C2×#16810679C2semidirect
16. C2×C53×#464C2semidirect
19. C22×Dic212C22semidirect
20. C22×#11719925C22semidirect
21. C22×#11719925C22semidirect
26. #16811177C22semidirect
27. C2×#13133216C22semidirect
28. C2×#13133215C22semidirect
41. C2×C4×Dic106C22semidirect
46. #16811016C22semidirect
47. #16811014C22semidirect
48. #16810984C22semidirect
49. #16810981C22semidirect
50. #16810846C22semidirect
51. #16810845C22semidirect
52. #16810842C22semidirect
53. #16810780C22semidirect
54. #16810777C22semidirect
57. #16810679C22semidirect
58. C2×C4⋊#88322C22semidirect
59. C2×#13133142C22semidirect
60. C2×#13133141C22semidirect
61. C2×#13133140C22semidirect
67. C2×#13133127C22semidirect
68. C2×#13133127C22semidirect
69. C22×Q16×C53C22semidirect
72. C2×C4×Q8×C53C22semidirect
73. C53×#464C22semidirect
74. C2×C4⋊C8×C53C22semidirect
75. C2×#103×C53C22semidirect
97. C2×Dic212C23semidirect
100. C2×#11719925C23semidirect
101. C2×#11719925C23semidirect
111. #13133216C23semidirect
113. #13133215C23semidirect
130. C4×Dic106C23semidirect
155. C4⋊#88322C23semidirect
156. #13133142C23semidirect
157. #13133141C23semidirect
158. #13133140C23semidirect
164. #13133127C23semidirect
165. #13133127C23semidirect
170. C2×Q16×C53C23semidirect
178. C4×Q8×C53C23semidirect
185. C4⋊C8×C53C23semidirect
186. #103×C53C23semidirect
414. C2×#464D53semidirect
421. C2×C53#3215semidirect
432. C22×Q16C2×D53semidirect
455. C2×C4×Q8C2×D53semidirect
467. #464C2×D53semidirect
474. C2×C4⋊C8C2×D53semidirect
478. C2×#103C2×D53semidirect
487. C53C2×#3215semidirect
517. C2×Q16C22×D53semidirect
554. C4×Q8C22×D53semidirect
586. C4⋊C8C22×D53semidirect
590. #103C22×D53semidirect
817. C2#20285716direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111772
C2×#124×D532
#202857162
C2×#168110162
C2×#168110142
C2×#168109842
C2×#168109812
C2×#168108462
C2×#168108452
C2×#168108422
C2×#168107802
C2×#168107772
C2×#168107752
C2×#168107722
C2×#168106792
C2×C53×#4642
C2×#321553