Finite Group Databasebeta

← #27351372

Subgroups — #27351372

Order 13568.

1438 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811134C211yesmaximal, characteristic
2#20277098C211yesmaximal, characteristic, complemented
3#20273259C214yesmaximal, complemented
4#20273249C212yesmaximal, complemented
5#20273245C212yesmaximal, complemented
6#20273207C214yesmaximal, complemented
7C2×C53×#407C211yesmaximal, characteristic, complemented
8C22×#11719945C411yescharacteristic, complemented
9#16811134—21no—
10#16811134—21no—
11#16811134—21no—
12#16811134—21no—
13#16811134C412yescomplemented
14#16811134C412yescomplemented
15#16811134C2212yes—
16#16811134C2212yes—
17C2×#13133200—21no—
18C2×#13133196C411yescharacteristic, complemented
19C2×#13133196C2211yescharacteristic
20C2×#13133191C411yescharacteristic, complemented
21C2×#13133191C2211yescharacteristic
22C2×#13133186—21no—
23C2×C4×C22⋊D53—21no—
24C2×C4×C22⋊D53—21no—
25C2×#13133176—21no—
26C2×#13133176C411yescharacteristic, complemented
27#16810486C2212yes—
28#16810483—21no—
29#16810483C2212yescomplemented
30#16810479—21no—
31C4×C22⋊Dic53—21no—
32C4×C22⋊Dic53C2212yescomplemented
33#16810361C2218yescomplemented
34#16810358C2218yescomplemented
35C24×C4×C53C2211yescharacteristic
36C22×M16×C53—21no—
37C53×#407—21no—
38C53×#407—21no—
39C53×#407C2212yes—
40C53×#407C2212yescomplemented
41C2×C22⋊C8×C53—21no—
42C2×C22⋊C8×C53C2212yescomplemented
43C2×#11719945—21no—
44C2×#11719945—21no—
45C2×#11719945—44no—
46C2×#11719945C2×C412yes—
47C2×#11719945C2×C412yes—
48C22×Dic106C2×C411yescharacteristic
49C22×D212C2×C411yescharacteristic
50C22×C22⋊D53—21no—
51C22×C22⋊D53—21no—
52C22×C22⋊D53—21no—
53C22×C4×D53—21no—
54#13133200—22no—
55#13133200—22no—
56#13133200—22no—
57#13133200—22no—
58#13133196—21no—
59#13133196—21no—
60#13133196—21no—
61#13133196—21no—
62#13133196C2×C412yes—
63#13133196C2×C412yes—
64#13133196C2×C412yes—
65#13133196C2312yes—
66#13133191—21no—
67#13133191—21no—
68#13133191—21no—
69#13133191—21no—
70#13133191C2×C412yes—
71#13133191C2×C412yes—
72#13133191C2×C412yes—
73#13133191C2312yes—
74#13133186—22no—
75#13133186—22no—
76#13133186—22no—
77#13133186—22no—
78C4×C22⋊D53—22no—
79C4×C22⋊D53—22no—
80C4×C22⋊D53—22no—
81C4×C22⋊D53—22no—
82C4×C22⋊D53—22no—
83C4×C22⋊D53—22no—
84C4×C22⋊D53—22no—
85C4×C22⋊D53—22no—
86#13133176—21no—
87#13133176—21no—
88#13133176—44no—
89#13133176C2×C412yes—
90#13133176C2×C412yes—
91C2×C4⋊Dic53—22no—
92C2×C4⋊Dic53C2×C411yescharacteristic
93C2×C4⋊Dic53C2×C411yescharacteristic
94C2×#11719919—21no—
95C2×#11719919—21no—
96C2×C22⋊Dic53—21no—
97C2×C22⋊Dic53—21no—
98C2×C22⋊Dic53—21no—
99C2×C22⋊Dic53—22no—
100C2×C22⋊Dic53—22no—
101C2×C22⋊Dic53—22no—
102C2×#11719921—21no—
103C2×#11719921—21no—
104C2×C4×Dic53—21no—
105C2×C4×Dic53—22no—
106#13133124—22no—
107#13133124C2314yes—
108C25×C53D411yescharacteristic
109C23×C4×C53—44no—
110C23×C4×C53C2×C411yescharacteristic
111C23×C4×C53C2×C411yescharacteristic
112C23×C4×C53C2×C411yescharacteristic
113C23×C4×C53C2×C411yescharacteristic
114C23×C4×C53D411yescharacteristic
115C23×C4×C53D411yescharacteristic
116C23×C4×C53D411yescharacteristic
117C23×C4×C53D411yescharacteristic
118C23×C4×C53D411yescharacteristic
119C23×C4×C53D411yescharacteristic
120C23×C4×C53D411yescharacteristic
121C23×C4×C53C2311yescharacteristic
122C23×C4×C53C2311yescharacteristic
123C23×C4×C53C2311yescharacteristic
124C2×M16×C53—22no—
125C2×M16×C53—22no—
126C2×M16×C53—44no—
127C22×C8×C53—22no—
128C22⋊C8×C53—22no—
129C22⋊C8×C53—22no—
130C22⋊C8×C53—22no—
131C22⋊C8×C53C2314yes—
132C24×C53—42no—
133C24×C53—42no—
134C24×C53—42no—
135C24×C53C22⋊C411yescharacteristic
136C24×C53C22⋊C411yescharacteristic
137C24×C53C22⋊C411yescharacteristic
138C24×C53C22⋊C411yescharacteristic
139C24×C53C2×D411yescharacteristic
140C24×C53C2×D411yescharacteristic
141C24×C53C2×D411yescharacteristic
142C23×D53—21no—
143C22×C4×C53—24no—
144C22×C4×C53—24no—
145C22×C4×C53—24no—
146C22×C4×C53—42no—
147C22×C4×C53—42no—
148C22×C4×C53—42no—
149C22×C4×C53—42no—
150C22×C4×C53—42no—
151C22×C4×C53—42no—
152C22×C4×C53—42no—
153C22×C4×C53—42no—
154C22×C4×C53—42no—
155C22×C4×C53—42no—
156C22×C4×C53—42no—
157C22×C4×C53C22⋊C411yescharacteristic
158C22×C4×C53C22⋊C411yescharacteristic
159C22×C4×C53C22⋊C411yescharacteristic
160C22×C4×C53C22⋊C411yescharacteristic
161C22×C4×C53C22⋊C411yescharacteristic
162C22×C4×C53C22⋊C411yescharacteristic
163C22×C4×C53C22⋊C411yescharacteristic
164C22×C4×C53C22⋊C411yescharacteristic
165C22×C4×C53C22⋊C411yescharacteristic
166C22×C4×C53C22⋊C411yescharacteristic
167C22×C4×C53C22⋊C411yescharacteristic
168C22×C4×C53C22⋊C411yescharacteristic
169C22×C4×C53C22×C411yescharacteristic
170C22×C4×C53C22×C411yescharacteristic
171C22×C4×C53C22×C411yescharacteristic
172C22×C4×C53C22×C411yescharacteristic
173C22×C4×C53C22×C411yescharacteristic
174C22×C4×C53C22×C411yescharacteristic
175C22×C4×C53C2×D411yescharacteristic
176C22×C4×C53C2×D411yescharacteristic
177C22×C4×C53C2×D411yescharacteristic
178C22×C4×C53C2×D411yescharacteristic
179C22×C4×C53C2×D411yescharacteristic
180C22×C4×C53C2×D411yescharacteristic
181C22×C4×C53C2×D411yescharacteristic
182C22×C4×C53C2×D411yescharacteristic
183C22×C4×C53C2×D411yescharacteristic
184C22×C4×C53C2411yescharacteristic
185C2×C22⋊D53—22no—
186C2×C22⋊D53—22no—
187C2×C22⋊D53—22no—
188C2×C22⋊D53—22no—
189C2×C22⋊D53—22no—
190C2×C22⋊D53—22no—
191C2×C22⋊D53—44no—
192C2×C22⋊D53—44no—
193C2×C22⋊D53—44no—
194C22×Dic53—21no—
195C22×Dic53—21no—
196C22×Dic53—21no—
197C22×Dic53—24no—
198#11719945—44no—
199#11719945—44no—
200#11719945—44no—
201#11719945—44no—
202C2×D212—21no—
203C2×D212—42no—
204C2×D212C22×C412yes—
205C2×C4×D53—22no—
206C2×C4×D53—22no—
207C2×C4×D53—44no—
208C2×Dic106—21no—
209C2×Dic106—42no—
210C2×Dic106C22×C412yes—
211M16×C53—44no—
212M16×C53—44no—
213C2×C8×C53—24no—
214C2×C8×C53—44no—
215C22⋊Dic53—22no—
216C22⋊Dic53—22no—
217C22⋊Dic53—22no—
218C22⋊Dic53—22no—
219C22⋊Dic53—22no—
220C22⋊Dic53—22no—
221C22⋊Dic53—44no—
222C22⋊Dic53—44no—
223C22⋊Dic53—44no—
224#11719921—22no—
225#11719921—22no—
226#11719921—22no—
227#11719921—22no—
228C4⋊Dic53—21no—
229C4⋊Dic53—21no—
230C4⋊Dic53—44no—
231C4⋊Dic53C22×C412yes—
232C4⋊Dic53C22×C412yes—
233#11719919—22no—
234#11719919—22no—
235#11719919—22no—
236#11719919—22no—
237C4×Dic53—22no—
238C4×Dic53—22no—
239C4×Dic53—44no—
240C23×C53—22no—
241C23×C53—22no—
242C23×C53—22no—
243C23×C53—22no—
244C23×C53—22no—
245C23×C53—22no—
246C23×C53—22no—
247C23×C53—22no—
248C23×C53—22no—
249C23×C53—41no—
250C23×C53—41no—
251C23×C53—41no—
252C23×C53—41no—
253C23×C53—41no—
254C23×C53—41no—
255C23×C53—41no—
256C23×C53—41no—
257C23×C53—41no—
258C23×C53—41no—
259C23×C53—41no—
260C23×C53—41no—
261C23×C53—416no—
262C23×C53C2×C22⋊C411yescharacteristic
263C23×C53C2×C22⋊C411yescharacteristic
264C23×C53C2×C22⋊C411yescharacteristic
265C23×C53C2×C22⋊C411yescharacteristic
266C23×C53C2×C22⋊C411yescharacteristic
267C23×C53C2×C22⋊C411yescharacteristic
268C23×C53C22×D411yescharacteristic
269C22×D53—22no—
270C22×D53—42no—
271C22×D53—42no—
272C22×D53—42no—
273C2×C4×C53—22no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—22no—
277C2×C4×C53—22no—
278C2×C4×C53—22no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—41no—
289C2×C4×C53—41no—
290C2×C4×C53—41no—
291C2×C4×C53—41no—
292C2×C4×C53—41no—
293C2×C4×C53—41no—
294C2×C4×C53—41no—
295C2×C4×C53—41no—
296C2×C4×C53—41no—
297C2×C4×C53—41no—
298C2×C4×C53—41no—
299C2×C4×C53—41no—
300C2×C4×C53#9914yes—
301C2×C4×C53C2×C22⋊C411yescharacteristic
302C2×C4×C53C2×C22⋊C411yescharacteristic
303C2×C4×C53C2×C22⋊C411yescharacteristic
304C2×C4×C53C2×C22⋊C411yescharacteristic
305C2×C4×C53C2×C22⋊C411yescharacteristic
306C2×C4×C53C2×C22⋊C411yescharacteristic
307C2×C4×C53C23×C411yescharacteristic
308C2×C4×C53C22×D411yescharacteristic
309C22⋊D53—44no—
310C22⋊D53—44no—
311C22⋊D53—44no—
312C22⋊D53—44no—
313C22⋊D53—44no—
314C22⋊D53—44no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—42no—
319C2×Dic53—42no—
320C2×Dic53—42no—
321C2×Dic53—44no—
322C2×Dic53—44no—
323C2×Dic53—44no—
324D212—42no—
325D212—42no—
326C4×D53—44no—
327C4×D53—44no—
328Dic106—42no—
329Dic106—42no—
330C8×C53—44no—
331#17559—531nomaximal, Sylow
332C22×C53—21no—
333C22×C53—21no—
334C22×C53—21no—
335C22×C53—21no—
336C22×C53—21no—
337C22×C53—21no—
338C22×C53—21no—
339C22×C53—21no—
340C22×C53—21no—
341C22×C53—21no—
342C22×C53—21no—
343C22×C53—21no—
344C22×C53—21no—
345C22×C53—21no—
346C22×C53—21no—
347C22×C53—21no—
348C22×C53—21no—
349C22×C53—21no—
350C22×C53—44no—
351C22×C53—44no—
352C22×C53—44no—
353C22×C53—44no—
354C22×C53—44no—
355C22×C53—44no—
356C22×C53—44no—
357C22×C53C2×#9912yes—
358C22×C53#42112yes—
359C22×C53C22×C22⋊C411yescharacteristic
360C22×C53#57512yes—
361C2×D53—42no—
362C2×D53—42no—
363C2×D53—42no—
364C2×D53—84no—
365C4×C53—21no—
366C4×C53—21no—
367C4×C53—21no—
368C4×C53—21no—
369C4×C53—21no—
370C4×C53—21no—
371C4×C53C2×#9912yes—
372C4×C53C2×#9912yes—
373Dic53—42no—
374Dic53—42no—
375Dic53—42no—
376Dic53—84no—
377C2×#525—531no—
378C2×#407D5311yescharacteristic, complemented
379#2280—531no—
380#1513—534no—
381#1511—532no—
382#1510—532no—
383#1501—534no—
384C2×C53—22no—
385C2×C53—22no—
386C2×C53—22no—
387C2×C53—41no—
388C2×C53—41no—
389C2×C53—41no—
390C2×C53—41no—
391C2×C53C22×#9911yescharacteristic
392C2×C53#289611yescharacteristic
393C2×C53C2×#42111yescharacteristic
394D53—82no—
395C22×#41—531no—
396C24×C4C2×D5311yescharacteristic
397C22×M16—21no—
398#525—532no—
399#525—532no—
400#525—532no—
401#525—532no—
402#525—1061no—
403#525—1061no—
404#525—1061no—
405#525—1061no—
406C2×#123—1061no—
407C2×C22⋊Q8—531no—
408C2×C22⋊Q8—531no—
409C2×#121—531no—
410C2×#121—531no—
411C2×#120—1061no—
412C2×C4×D4—1061no—
413C2×C4×D4—1061no—
414C2×#117—531no—
415C2×#117—1061no—
416#407—21no—
417#407—21no—
418#407C2×D5312yes—
419#407C2×D5312yescomplemented
420C2×C22⋊C8—21no—
421C2×C22⋊C8C2×D5312yescomplemented
422#381—532no—
423#380—532no—
424#380—1061no—
425#379—1061no—
426C4×C22⋊C4—532no—
427C4×C22⋊C4—1061no—
428#328—538no—
429#327—538no—
430C53#1755911yescharacteristic, complemented, Sylow
431C25D21211yescharacteristic
432C2×#41—532no—
433C2×#41—532no—
434C2×#41—1061no—
435C2×#41—1061no—
436C2×#41—2124no—
437C22×Q8—531no—
438C22×D4—531no—
439C22×D4—1061no—
440C22×D4—1061no—
441C22×D4—1061no—
442C23×C4—44no—
443C23×C4—1061no—
444C23×C4C4×D5311yescharacteristic
445C23×C4C4×D5311yescharacteristic
446C23×C4C4×D5311yescharacteristic
447C23×C4C4×D5311yescharacteristic
448C23×C4D21211yescharacteristic
449C23×C4D21211yescharacteristic
450C23×C4D21211yescharacteristic
451C23×C4C22⋊D5311yescharacteristic
452C23×C4C22⋊D5311yescharacteristic
453C23×C4C22⋊D5311yescharacteristic
454C23×C4C22⋊D5311yescharacteristic
455C23×C4C22×D5311yescharacteristic
456C23×C4C22×D5311yescharacteristic
457C23×C4C22×D5311yescharacteristic
458C2×M16—22no—
459C2×M16—22no—
460C2×M16—44no—
461C22×C8—22no—
462#123—1062no—
463#123—1062no—
464#123—1062no—
465#123—1062no—
466C22⋊Q8—532no—
467C22⋊Q8—532no—
468C22⋊Q8—532no—
469C22⋊Q8—532no—
470C22⋊Q8—1061no—
471C22⋊Q8—1061no—
472C22⋊Q8—1061no—
473C22⋊Q8—1061no—
474#121—532no—
475#121—532no—
476#121—532no—
477#121—532no—
478#121—1061no—
479#121—1061no—
480#121—1061no—
481#121—1061no—
482#120—1062no—
483#120—1062no—
484#120—1062no—
485#120—1062no—
486C4×D4—1062no—
487C4×D4—1062no—
488C4×D4—1062no—
489C4×D4—1062no—
490C4×D4—1062no—
491C4×D4—1062no—
492C4×D4—1062no—
493C4×D4—1062no—
494#117—532no—
495#117—532no—
496#117—1061no—
497#117—1061no—
498#117—2124no—
499C2×C4⋊C4—531no—
500C2×C4⋊C4—531no—
501C2×C4⋊C4—1061no—
502C2×C4⋊C4—1061no—
503C2×C4⋊C4—1062no—
504C2×C22⋊C4—1061no—
505C2×C22⋊C4—1061no—
506C2×C22⋊C4—1061no—
507C2×C22⋊C4—1061no—
508C2×C22⋊C4—1061no—
509C2×C22⋊C4—1062no—
510C2×C22⋊C4—1062no—
511C2×C22⋊C4—1062no—
512C2×C42—1061no—
513C2×C42—1062no—
514C22⋊C8—22no—
515C22⋊C8—22no—
516C22⋊C8—22no—
517C22⋊C8C22×D5314yes—
518#95—534no—
519#95—1062no—
520C24—42no—
521C24—42no—
522C24—42no—
523C24—1061no—
524C24#1171992111yescharacteristic
525C24#1171992111yescharacteristic
526C24#1171992111yescharacteristic
527C24#1171992111yescharacteristic
528C24C2×D21211yescharacteristic
529C24C2×D21211yescharacteristic
530C24C2×D21211yescharacteristic
531#41—2124no—
532#41—2124no—
533#41—2124no—
534#41—2124no—
535C2×Q8—532no—
536C2×Q8—1061no—
537C2×Q8—2122no—
538C2×D4—532no—
539C2×D4—1062no—
540C2×D4—1062no—
541C2×D4—1062no—
542C2×D4—1062no—
543C2×D4—1062no—
544C2×D4—1062no—
545C2×D4—1061no—
546C2×D4—2122no—
547C2×D4—2124no—
548C2×D4—2124no—
549C2×D4—2124no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—1061no—
565C22×C4—1061no—
566C22×C4—1061no—
567C22×C4—1062no—
568C22×C4—1062no—
569C22×C4—1064no—
570C22×C4—2124no—
571C22×C4#1171992111yescharacteristic
572C22×C4#1171992111yescharacteristic
573C22×C4#1171992111yescharacteristic
574C22×C4#1171992111yescharacteristic
575C22×C4#1171992111yescharacteristic
576C22×C4#1171992111yescharacteristic
577C22×C4#1171992111yescharacteristic
578C22×C4#1171992111yescharacteristic
579C22×C4#1171992111yescharacteristic
580C22×C4#1171992111yescharacteristic
581C22×C4#1171992111yescharacteristic
582C22×C4#1171992111yescharacteristic
583C22×C4C2×C4×D5311yescharacteristic
584C22×C4C2×C4×D5311yescharacteristic
585C22×C4C2×C4×D5311yescharacteristic
586C22×C4C2×C4×D5311yescharacteristic
587C22×C4C2×C4×D5311yescharacteristic
588C22×C4C2×C4×D5311yescharacteristic
589C22×C4C2×D21211yescharacteristic
590C22×C4C2×D21211yescharacteristic
591C22×C4C2×D21211yescharacteristic
592C22×C4C2×C22⋊D5311yescharacteristic
593C22×C4C2×C22⋊D5311yescharacteristic
594C22×C4C2×C22⋊D5311yescharacteristic
595C22×C4C2×C22⋊D5311yescharacteristic
596C22×C4C2×C22⋊D5311yescharacteristic
597C22×C4C2×C22⋊D5311yescharacteristic
598C22×C4C23×D5311yescharacteristic
599M16—44no—
600M16—44no—
601C2×C8—24no—
602C2×C8—44no—
603C4⋊C4—532no—
604C4⋊C4—532no—
605C4⋊C4—1061no—
606C4⋊C4—1061no—
607C4⋊C4—1062no—
608C4⋊C4—1062no—
609C4⋊C4—1062no—
610C4⋊C4—1062no—
611C4⋊C4—2124no—
612C22⋊C4—1062no—
613C22⋊C4—1062no—
614C22⋊C4—1062no—
615C22⋊C4—1062no—
616C22⋊C4—1062no—
617C22⋊C4—1062no—
618C22⋊C4—1062no—
619C22⋊C4—1062no—
620C22⋊C4—1062no—
621C22⋊C4—1062no—
622C22⋊C4—2124no—
623C22⋊C4—2124no—
624C22⋊C4—2124no—
625C42—1062no—
626C42—1062no—
627C42—2124no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—416no—
650C23—1062no—
651C23—2122no—
652C23—2122no—
653C23—2122no—
654C23C2×#1171992111yescharacteristic
655C23C2×#1171992111yescharacteristic
656C23C2×#1171992111yescharacteristic
657C23C2×#1171992111yescharacteristic
658C23C2×#1171992111yescharacteristic
659C23C2×#1171992111yescharacteristic
660C23C22×D21211yescharacteristic
661Q8—2122no—
662Q8—2122no—
663D4—2122no—
664D4—2122no—
665D4—2124no—
666D4—2124no—
667D4—2124no—
668D4—2124no—
669D4—2124no—
670D4—2124no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—1062no—
699C2×C4—1062no—
700C2×C4—1062no—
701C2×C4—2124no—
702C2×C4—2124no—
703C2×C4—2124no—
704C2×C4—2122no—
705C2×C4—2122no—
706C2×C4—2122no—
707C2×C4—2124no—
708C2×C4—2124no—
709C2×C4#1313313114yes—
710C2×C4C2×#1171992111yescharacteristic
711C2×C4C2×#1171992111yescharacteristic
712C2×C4C2×#1171992111yescharacteristic
713C2×C4C2×#1171992111yescharacteristic
714C2×C4C2×#1171992111yescharacteristic
715C2×C4C2×#1171992111yescharacteristic
716C2×C4C22×C4×D5311yescharacteristic
717C2×C4C22×C22⋊D5311yescharacteristic
718C8—44no—
719C22—21no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—44no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—4244no—
745C22—2122no—
746C22—2122no—
747C22—2122no—
748C22C2×#1313313112yes—
749C22#1681063912yes—
750C22C22×#1171992111yescharacteristic
751C22#1681142312yes—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—4244no—
759C4—2122no—
760C4—2122no—
761C4—2122no—
762C4C2×#1313313112yes—
763C4C2×#1313313112yes—
764C2—22no—
765C2—22no—
766C2—22no—
767C2—41no—
768C2—41no—
769C2—41no—
770C2—41no—
771C2—4242no—
772C2C22×#1313313111yescharacteristic
773C2#2028323511yescharacteristic
774C2C2×#1681063911yescharacteristic
subgroupG/H
centerC2×C4C2×#11719921
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#407C2
socleC22×C53C22×C22⋊C4
prime radicalC2×#16811134C2
cosocleC22×C4×C53C24
hypercenterC2×#407D53
hypocenterC53#17559
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. #20277098C2semidirect
3. #20273259C2semidirect
4. #20273249C2semidirect
5. #20273245C2semidirect
6. #20273207C2semidirect
7. C2×C53×#407C2semidirect
8. C22×#11719945C4semidirect
13. #16811134C4semidirect
14. #16811134C4semidirect
18. C2×#13133196C4semidirect
20. C2×#13133191C4semidirect
26. C2×#13133176C4semidirect
29. #16810483C22semidirect
32. C4×C22⋊Dic53C22semidirect
33. #16810361C22semidirect
34. #16810358C22semidirect
40. C53×#407C22semidirect
42. C2×C22⋊C8×C53C22semidirect
378. C2×#407D53semidirect
419. #407C2×D53semidirect
421. C2×C22⋊C8C2×D53semidirect
430. C53#17559semidirect

Maximal subgroups

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

subgroupindex
C2×#168111342
#202770982
#202732592
#202732492
#202732452
#202732072
C2×C53×#4072
#1755953