Finite Group Databasebeta

← #27351550

Subgroups — #27351550

Order 13568.

1466 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811134C211yesmaximal, characteristic
2C2×#16810486C211yesmaximal, characteristic, complemented
3#20273272C214yesmaximal, complemented
4#20273249C212yesmaximal, complemented
5#20273245C212yesmaximal, complemented
6#20273220C214yesmaximal, 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×#13133176C411yescharacteristic, complemented
26C22×C22⋊Dic53—21no—
27#16810486—21no—
28#16810486—21no—
29#16810486C2212yes—
30#16810486C2212yescomplemented
31C2×#13133124—21no—
32C2×#13133124C2212yescomplemented
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×C412yescomplemented
48C22×Dic106C2×C411yescharacteristic, complemented
49C22×D212C2×C411yescharacteristic, complemented
50C22×C22⋊D53—21no—
51C22×C22⋊D53—21no—
52C22×C22⋊D53—21no—
53C23×Dic53—22no—
54C22×C4×D53—21no—
55#13133200—22no—
56#13133200—22no—
57#13133200—22no—
58#13133200—22no—
59#13133196—21no—
60#13133196—21no—
61#13133196—21no—
62#13133196—21no—
63#13133196C2×C412yes—
64#13133196C2×C412yescomplemented
65#13133196C2×C412yescomplemented
66#13133196C2312yes—
67#13133191—21no—
68#13133191—21no—
69#13133191—21no—
70#13133191—21no—
71#13133191C2×C412yes—
72#13133191C2×C412yescomplemented
73#13133191C2×C412yescomplemented
74#13133191C2312yes—
75#13133186—22no—
76#13133186—22no—
77#13133186—22no—
78#13133186—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—
86C4×C22⋊D53—22no—
87#13133176—21no—
88#13133176—21no—
89#13133176C2×C412yes—
90#13133176C2×C412yescomplemented
91C2×C4⋊Dic53C2×C411yescharacteristic, complemented
92C2×C4⋊Dic53C2×C411yescharacteristic, complemented
93C2×#11719919—21no—
94C2×#11719919—21no—
95C2×C22⋊Dic53—21no—
96C2×C22⋊Dic53—21no—
97C2×C22⋊Dic53—21no—
98C2×C22⋊Dic53—22no—
99C2×C22⋊Dic53—22no—
100C2×C22⋊Dic53—44no—
101C2×#11719921—21no—
102C2×#11719921—21no—
103C2×C4×Dic53—21no—
104#13133124—22no—
105#13133124—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—24no—
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—42no—
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—
198C22×Dic53—44no—
199C22×Dic53—44no—
200C22×Dic53—44no—
201#11719945—44no—
202#11719945—44no—
203#11719945—44no—
204#11719945—44no—
205C2×D212—21no—
206C2×D212—42no—
207C2×D212C22×C412yes—
208C2×C4×D53—22no—
209C2×C4×D53—22no—
210C2×C4×D53—44no—
211C2×Dic106—21no—
212C2×Dic106—42no—
213C2×Dic106C22×C412yes—
214M16×C53—44no—
215M16×C53—44no—
216C2×C8×C53—24no—
217C2×C8×C53—44no—
218C22⋊Dic53—22no—
219C22⋊Dic53—22no—
220C22⋊Dic53—22no—
221C22⋊Dic53—22no—
222C22⋊Dic53—22no—
223C22⋊Dic53—22no—
224C22⋊Dic53—44no—
225C22⋊Dic53—44no—
226#11719921—22no—
227#11719921—22no—
228#11719921—22no—
229#11719921—22no—
230C4⋊Dic53—21no—
231C4⋊Dic53—21no—
232C4⋊Dic53C22×C412yes—
233C4⋊Dic53C22×C412yes—
234#11719919—22no—
235#11719919—22no—
236#11719919—22no—
237#11719919—22no—
238C4×Dic53—22no—
239C4×Dic53—22no—
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—22no—
250C23×C53—22no—
251C23×C53—22no—
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—416no—
261C23×C53#9914yes—
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—41no—
286C2×C4×C53—41no—
287C2×C4×C53—41no—
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—41no—
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—
324C2×Dic53—88no—
325D212—42no—
326D212—42no—
327C4×D53—44no—
328C4×D53—44no—
329Dic106—42no—
330Dic106—42no—
331C8×C53—44no—
332#17587—531nomaximal, Sylow
333C22×C53—28no—
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×C53C2×#9912yes—
357C22×C53C2×#9912yes—
358C22×C53C2×#9912yes—
359C22×C53#42112yes—
360C22×C53C22×C22⋊C411yescharacteristic
361C22×C53#57512yes—
362C2×D53—42no—
363C2×D53—42no—
364C2×D53—42no—
365C2×D53—84no—
366C4×C53—21no—
367C4×C53—21no—
368C4×C53—21no—
369C4×C53—21no—
370C4×C53—21no—
371C4×C53—21no—
372C4×C53—21no—
373C4×C53—21no—
374Dic53—42no—
375Dic53—42no—
376Dic53—42no—
377Dic53—84no—
378C2×#525—531no—
379C2×#407D5311yescharacteristic, complemented
380C2×#381—531no—
381#1516—534no—
382#1511—532no—
383#1510—532no—
384#1504—534no—
385C2×C53—22no—
386C2×C53—22no—
387C2×C53—22no—
388C2×C53—22no—
389C2×C53—22no—
390C2×C53—41no—
391C2×C53—41no—
392C2×C53C22×#9911yescharacteristic
393C2×C53#289611yescharacteristic
394C2×C53C2×#42111yescharacteristic
395D53—82no—
396C22×#41—531no—
397C24×C4C2×D5311yescharacteristic
398C22×M16—21no—
399#525—532no—
400#525—532no—
401#525—532no—
402#525—532no—
403#525—1061no—
404#525—1061no—
405#525—1061no—
406#525—1061no—
407C2×#123—1061no—
408C2×C22⋊Q8—531no—
409C2×C22⋊Q8—531no—
410C2×#121—531no—
411C2×#121—531no—
412C2×#120—1061no—
413C2×C4×D4—1061no—
414C2×C4×D4—1061no—
415C2×#117—531no—
416C22×C22⋊C4—1061no—
417#407—21no—
418#407—21no—
419#407C2×D5312yes—
420#407C2×D5312yescomplemented
421C2×C22⋊C8—21no—
422C2×C22⋊C8C2×D5312yescomplemented
423#381—532no—
424#381—532no—
425#381—1061no—
426#381—1061no—
427C2×#95—532no—
428C2×#95—1061no—
429#328—538no—
430#327—538no—
431C53#1758711yescharacteristic, complemented, Sylow
432C25D21211yescharacteristic
433C2×#41—532no—
434C2×#41—532no—
435C2×#41—1061no—
436C2×#41—1061no—
437C2×#41—2124no—
438C22×Q8—531no—
439C22×D4—531no—
440C22×D4—1061no—
441C22×D4—1061no—
442C22×D4—1061no—
443C23×C4—44no—
444C23×C4—1061no—
445C23×C4—1062no—
446C23×C4C4×D5311yescharacteristic
447C23×C4C4×D5311yescharacteristic
448C23×C4C4×D5311yescharacteristic
449C23×C4C4×D5311yescharacteristic
450C23×C4D21211yescharacteristic
451C23×C4D21211yescharacteristic
452C23×C4D21211yescharacteristic
453C23×C4C22⋊D5311yescharacteristic
454C23×C4C22⋊D5311yescharacteristic
455C23×C4C22⋊D5311yescharacteristic
456C23×C4C22⋊D5311yescharacteristic
457C23×C4C22×D5311yescharacteristic
458C23×C4C22×D5311yescharacteristic
459C23×C4C22×D5311yescharacteristic
460C2×M16—22no—
461C2×M16—22no—
462C2×M16—44no—
463C22×C8—22no—
464#123—1062no—
465#123—1062no—
466#123—1062no—
467#123—1062no—
468C22⋊Q8—532no—
469C22⋊Q8—532no—
470C22⋊Q8—532no—
471C22⋊Q8—532no—
472C22⋊Q8—1061no—
473C22⋊Q8—1061no—
474C22⋊Q8—1061no—
475C22⋊Q8—1061no—
476#121—532no—
477#121—532no—
478#121—532no—
479#121—532no—
480#121—1061no—
481#121—1061no—
482#121—1061no—
483#121—1061no—
484#120—1062no—
485#120—1062no—
486#120—1062no—
487#120—1062no—
488C4×D4—1062no—
489C4×D4—1062no—
490C4×D4—1062no—
491C4×D4—1062no—
492C4×D4—1062no—
493C4×D4—1062no—
494C4×D4—1062no—
495C4×D4—1062no—
496#117—532no—
497#117—532no—
498#117—1061no—
499#117—1061no—
500C2×C4⋊C4—531no—
501C2×C4⋊C4—531no—
502C2×C4⋊C4—1061no—
503C2×C4⋊C4—1061no—
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—2124no—
512C2×C42—1061no—
513C22⋊C8—22no—
514C22⋊C8—22no—
515C22⋊C8—22no—
516C22⋊C8C22×D5314yes—
517#95—534no—
518#95—1062no—
519#95—1062no—
520#95—1062no—
521C24—24no—
522C24—42no—
523C24—42no—
524C24—1061no—
525C24#1171992111yescharacteristic
526C24#1171992111yescharacteristic
527C24#1171992111yescharacteristic
528C24#1171992111yescharacteristic
529C24C2×D21211yescharacteristic
530C24C2×D21211yescharacteristic
531C24C2×D21211yescharacteristic
532#41—2124no—
533#41—2124no—
534#41—2124no—
535#41—2124no—
536C2×Q8—532no—
537C2×Q8—1061no—
538C2×Q8—2122no—
539C2×D4—532no—
540C2×D4—1062no—
541C2×D4—1062no—
542C2×D4—1062no—
543C2×D4—1062no—
544C2×D4—1062no—
545C2×D4—1062no—
546C2×D4—1061no—
547C2×D4—2122no—
548C2×D4—2124no—
549C2×D4—2124no—
550C2×D4—2124no—
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—42no—
565C22×C4—1061no—
566C22×C4—1061no—
567C22×C4—1061no—
568C22×C4—1062no—
569C22×C4—1062no—
570C22×C4—1064no—
571C22×C4—2124no—
572C22×C4—2124no—
573C22×C4—2124no—
574C22×C4—2124no—
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×C4#1171992111yescharacteristic
584C22×C4#1171992111yescharacteristic
585C22×C4#1171992111yescharacteristic
586C22×C4#1171992111yescharacteristic
587C22×C4C2×C4×D5311yescharacteristic
588C22×C4C2×C4×D5311yescharacteristic
589C22×C4C2×C4×D5311yescharacteristic
590C22×C4C2×C4×D5311yescharacteristic
591C22×C4C2×C4×D5311yescharacteristic
592C22×C4C2×C4×D5311yescharacteristic
593C22×C4C2×D21211yescharacteristic
594C22×C4C2×D21211yescharacteristic
595C22×C4C2×D21211yescharacteristic
596C22×C4C2×C22⋊D5311yescharacteristic
597C22×C4C2×C22⋊D5311yescharacteristic
598C22×C4C2×C22⋊D5311yescharacteristic
599C22×C4C2×C22⋊D5311yescharacteristic
600C22×C4C2×C22⋊D5311yescharacteristic
601C22×C4C2×C22⋊D5311yescharacteristic
602C22×C4C23×D5311yescharacteristic
603M16—44no—
604M16—44no—
605C2×C8—24no—
606C2×C8—44no—
607C4⋊C4—532no—
608C4⋊C4—532no—
609C4⋊C4—1061no—
610C4⋊C4—1061no—
611C4⋊C4—1062no—
612C4⋊C4—1062no—
613C4⋊C4—1062no—
614C4⋊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—1062no—
623C22⋊C4—1062no—
624C22⋊C4—1062no—
625C22⋊C4—2124no—
626C22⋊C4—2124no—
627C42—1062no—
628C42—1062no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
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—
654C23#1313313114yes—
655C23C2×#1171992111yescharacteristic
656C23C2×#1171992111yescharacteristic
657C23C2×#1171992111yescharacteristic
658C23C2×#1171992111yescharacteristic
659C23C2×#1171992111yescharacteristic
660C23C2×#1171992111yescharacteristic
661C23C22×D21211yescharacteristic
662Q8—2122no—
663Q8—2122no—
664D4—2122no—
665D4—2122no—
666D4—2124no—
667D4—2124no—
668D4—2124no—
669D4—2124no—
670D4—2124no—
671D4—2124no—
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—41no—
685C2×C4—41no—
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—41no—
699C2×C4—41no—
700C2×C4—1062no—
701C2×C4—1062no—
702C2×C4—1062no—
703C2×C4—4248no—
704C2×C4—2124no—
705C2×C4—2124no—
706C2×C4—2124no—
707C2×C4—2124no—
708C2×C4—2124no—
709C2×C4—2122no—
710C2×C4—2122no—
711C2×C4—2122no—
712C2×C4C2×#1171992111yescharacteristic
713C2×C4C2×#1171992111yescharacteristic
714C2×C4C2×#1171992111yescharacteristic
715C2×C4C2×#1171992111yescharacteristic
716C2×C4C2×#1171992111yescharacteristic
717C2×C4C2×#1171992111yescharacteristic
718C2×C4C22×C4×D5311yescharacteristic
719C2×C4C22×C22⋊D5311yescharacteristic
720C8—44no—
721C22—28no—
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—21no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—4244no—
745C22—2122no—
746C22—2122no—
747C22—2122no—
748C22C2×#1313313112yes—
749C22C2×#1313313112yes—
750C22C2×#1313313112yes—
751C22#1681063912yes—
752C22C22×#1171992111yescharacteristic
753C22#1681142312yes—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—21no—
760C4—21no—
761C4—21no—
762C4—4244no—
763C4—2122no—
764C4—2122no—
765C4—2122no—
766C2—22no—
767C2—22no—
768C2—22no—
769C2—22no—
770C2—22no—
771C2—41no—
772C2—41no—
773C2—4242no—
774C2C22×#1313313111yescharacteristic
775C2#2028323511yescharacteristic
776C2C2×#1681063911yescharacteristic
subgroupG/H
centerC22C22×#11719921
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#407C2
socleC22×C53C22×C22⋊C4
prime radicalC2×#16811134C2
cosocleC22×C4×C53C24
hypercenterC2×#407D53
hypocenterC53#17587
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×#16810486C2semidirect
3. #20273272C2semidirect
4. #20273249C2semidirect
5. #20273245C2semidirect
6. #20273220C2semidirect
7. C2×C53×#407C2semidirect
8. C22×#11719945C4semidirect
13. #16811134C4semidirect
14. #16811134C4semidirect
18. C2×#13133196C4semidirect
20. C2×#13133191C4semidirect
25. C2×#13133176C4semidirect
30. #16810486C22semidirect
32. C2×#13133124C22semidirect
33. #16810361C22semidirect
34. #16810358C22semidirect
40. C53×#407C22semidirect
42. C2×C22⋊C8×C53C22semidirect
47. C2×#11719945C2×C4semidirect
48. C22×Dic106C2×C4semidirect
49. C22×D212C2×C4semidirect
64. #13133196C2×C4semidirect
65. #13133196C2×C4semidirect
72. #13133191C2×C4semidirect
73. #13133191C2×C4semidirect
90. #13133176C2×C4semidirect
91. C2×C4⋊Dic53C2×C4semidirect
92. C2×C4⋊Dic53C2×C4semidirect
379. C2×#407D53semidirect
420. #407C2×D53semidirect
422. C2×C22⋊C8C2×D53semidirect
431. C53#17587semidirect

Maximal subgroups

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

subgroupindex
C2×#168111342
C2×#168104862
#202732722
#202732492
#202732452
#202732202
C2×C53×#4072
#1758753