Finite Group Databasebeta

← #27389433

Subgroups — #27389433

Order 13568.

1678 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811134C211yesmaximal, characteristic
2C2×C4×C22⋊Dic53C211yesmaximal, characteristic, complemented
3#20275699C212yesmaximal, complemented
4#20275550C212yesmaximal, complemented
5#20275166C214yesmaximal, complemented
6C4×#13133131C214yesmaximal, complemented
7C53×#2280C211yesmaximal, characteristic, complemented
8C22×#11719945C411yescharacteristic, complemented
9#16811134—21no—
10#16811134—21no—
11#16811134—21no—
12#16811134—21no—
13#16811134—21no—
14#16811134—21no—
15#16811134—21no—
16#16811134—21no—
17C2×#13133200C412yescomplemented
18C2×#13133196C411yescharacteristic, complemented
19C2×#13133196C2211yescharacteristic
20C2×#13133191C411yescharacteristic, complemented
21C2×#13133191C2211yescharacteristic
22C2×#13133186C2212yes—
23C2×C4×C22⋊D53C412yescomplemented
24C2×C4×C22⋊D53C2212yes—
25C2×#13133176C411yescharacteristic, complemented
26C22×C22⋊Dic53C2212yes—
27C22×C4×Dic53—21no—
28C2×#13133131C2218yes—
29C4×C22⋊Dic53—21no—
30C4×C22⋊Dic53—21no—
31C4×C22⋊Dic53C2212yes—
32C4×C22⋊Dic53C2212yes—
33C2×#13133124—21no—
34#16810389C2218yes—
35C24×C4×C53C2211yescharacteristic
36C2×#117×C53—21no—
37C53×#381—21no—
38C53×#380—21no—
39C53×#380C2212yes—
40C53×#379C2212yes—
41C4×C22⋊C4×C53—21no—
42C4×C22⋊C4×C53C2212yes—
43C2×#11719945—21no—
44C2×#11719945—21no—
45C2×#11719945—21no—
46C2×#11719945—21no—
47C2×#11719945—44no—
48C22×Dic106C2×C411yescharacteristic, complemented
49C22×D212C2×C411yescharacteristic, complemented
50C22×C22⋊D53C2×C412yes—
51C22×C22⋊D53C2×C412yes—
52C22×C22⋊D53C2312yes—
53C23×Dic53—22no—
54C22×C4×D53C2×C412yescomplemented
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#13133196—21no—
64#13133196—21no—
65#13133196—21no—
66#13133196—21no—
67#13133191—21no—
68#13133191—21no—
69#13133191—21no—
70#13133191—21no—
71#13133191—21no—
72#13133191—21no—
73#13133191—21no—
74#13133191—21no—
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#13133176—21no—
90#13133176—21no—
91C2×C4⋊Dic53C2×C411yescharacteristic, complemented
92C2×C4⋊Dic53C2×C411yescharacteristic, complemented
93C2×#11719919C2×C412yescomplemented
94C2×#11719919C2×C412yescomplemented
95C2×C22⋊Dic53—28no—
96C2×C22⋊Dic53—22no—
97C2×C22⋊Dic53C2×C412yes—
98C2×C22⋊Dic53C2×C412yes—
99C2×C22⋊Dic53C2314yes—
100C2×C22⋊Dic53C2312yes—
101C2×#11719921C2×C412yescomplemented
102C2×#11719921C2×C412yescomplemented
103C2×C4×Dic53—22no—
104C2×C4×Dic53—22no—
105C2×C4×Dic53—44no—
106C2×C4×Dic53C2×C412yescomplemented
107#13133131—216no—
108#13133124—22no—
109#13133124—22no—
110C25×C53C2311yescharacteristic
111C23×C4×C53—44no—
112C23×C4×C53C2×C411yescharacteristic
113C23×C4×C53C2×C411yescharacteristic
114C23×C4×C53C2×C411yescharacteristic
115C23×C4×C53C2×C411yescharacteristic
116C23×C4×C53D411yescharacteristic
117C23×C4×C53D411yescharacteristic
118C23×C4×C53D411yescharacteristic
119C23×C4×C53D411yescharacteristic
120C23×C4×C53D411yescharacteristic
121C23×C4×C53D411yescharacteristic
122C23×C4×C53D411yescharacteristic
123C23×C4×C53D411yescharacteristic
124C23×C4×C53C2311yescharacteristic
125C23×C4×C53C2311yescharacteristic
126#117×C53—44no—
127C2×C4⋊C4×C53—22no—
128C2×C22⋊C4×C53—22no—
129C2×C22⋊C4×C53—22no—
130C2×C22⋊C4×C53C2314yes—
131C2×C42×C53—22no—
132#95×C53—22no—
133#95×C53—22no—
134C24×C53—24no—
135C24×C53—42no—
136C24×C53—42no—
137C24×C53C22×C411yescharacteristic
138C24×C53C22×C411yescharacteristic
139C24×C53C2×D411yescharacteristic
140C24×C53C2×D411yescharacteristic
141C24×C53C2×D411yescharacteristic
142C24×C53C2×D411yescharacteristic
143C24×C53C2411yescharacteristic
144C23×D53C22×C412yes—
145C22×C4×C53—24no—
146C22×C4×C53—24no—
147C22×C4×C53—24no—
148C22×C4×C53—24no—
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×C53—42no—
158C22×C4×C53—42no—
159C22×C4×C53—42no—
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×C53C22⋊C411yescharacteristic
176C22×C4×C53C22×C411yescharacteristic
177C22×C4×C53C22×C411yescharacteristic
178C22×C4×C53C22×C411yescharacteristic
179C22×C4×C53C22×C411yescharacteristic
180C22×C4×C53C2×D411yescharacteristic
181C22×C4×C53C2×D411yescharacteristic
182C22×C4×C53C2×D411yescharacteristic
183C22×C4×C53C2×D411yescharacteristic
184C22×C4×C53C2×D411yescharacteristic
185C22×C4×C53C2×D411yescharacteristic
186C22×C4×C53C2×D411yescharacteristic
187C22×C4×C53C2×D411yescharacteristic
188C2×C22⋊D53—22no—
189C2×C22⋊D53—22no—
190C2×C22⋊D53—22no—
191C2×C22⋊D53—22no—
192C2×C22⋊D53—22no—
193C2×C22⋊D53—22no—
194C2×C22⋊D53—28no—
195C2×C22⋊D53—44no—
196C2×C22⋊D53—44no—
197C22×Dic53—28no—
198C22×Dic53—24no—
199C22×Dic53—44no—
200C22×Dic53—44no—
201C22×Dic53C22×C412yes—
202C22×Dic53C22×C412yes—
203C22×Dic53C22×C412yes—
204#11719945—44no—
205#11719945—44no—
206#11719945—44no—
207#11719945—44no—
208C2×D212—21no—
209C2×D212—21no—
210C2×D212—42no—
211C2×C4×D53—22no—
212C2×C4×D53—22no—
213C2×C4×D53—44no—
214C2×Dic106—21no—
215C2×Dic106—21no—
216C2×Dic106—42no—
217C4⋊C4×C53—44no—
218C22⋊C4×C53—28no—
219C22⋊C4×C53—44no—
220C22⋊C4×C53—44no—
221C42×C53—44no—
222C22⋊Dic53—28no—
223C22⋊Dic53—22no—
224C22⋊Dic53—22no—
225C22⋊Dic53—22no—
226C22⋊Dic53—22no—
227C22⋊Dic53—22no—
228C22⋊Dic53—22no—
229C22⋊Dic53—24no—
230C22⋊Dic53#4118yescomplemented
231#11719921—22no—
232#11719921—22no—
233#11719921—22no—
234#11719921—22no—
235C4⋊Dic53—21no—
236C4⋊Dic53—21no—
237C4⋊Dic53—21no—
238C4⋊Dic53—21no—
239#11719919—22no—
240#11719919—22no—
241#11719919—22no—
242#11719919—22no—
243C4×Dic53—22no—
244C4×Dic53—22no—
245C4×Dic53—44no—
246C4×Dic53—44no—
247C23×C53—22no—
248C23×C53—22no—
249C23×C53—22no—
250C23×C53—22no—
251C23×C53—22no—
252C23×C53—22no—
253C23×C53—22no—
254C23×C53—22no—
255C23×C53—22no—
256C23×C53—22no—
257C23×C53—22no—
258C23×C53—22no—
259C23×C53—41no—
260C23×C53—41no—
261C23×C53—41no—
262C23×C53—41no—
263C23×C53—41no—
264C23×C53—41no—
265C23×C53—41no—
266C23×C53—41no—
267C23×C53—416no—
268C23×C53C2×C22⋊C411yescharacteristic
269C23×C53C2×C22⋊C411yescharacteristic
270C23×C53C2×C22⋊C411yescharacteristic
271C23×C53C2×C22⋊C411yescharacteristic
272C23×C53C23×C411yescharacteristic
273C23×C53C22×D411yescharacteristic
274C23×C53C22×D411yescharacteristic
275C23×C53C2×#4114yes—
276C22×D53—22no—
277C22×D53—24no—
278C22×D53—42no—
279C22×D53—42no—
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—22no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
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×C53—41no—
302C2×C4×C53—41no—
303C2×C4×C53—41no—
304C2×C4×C53—41no—
305C2×C4×C53—41no—
306C2×C4×C53—41no—
307C2×C4×C53—44no—
308C2×C4×C53—44no—
309C2×C4×C53—44no—
310C2×C4×C53#9914yescomplemented
311C2×C4×C53C2×C22⋊C411yescharacteristic
312C2×C4×C53C2×C22⋊C411yescharacteristic
313C2×C4×C53C2×C22⋊C411yescharacteristic
314C2×C4×C53C2×C22⋊C411yescharacteristic
315C2×C4×C53C2×C22⋊C411yescharacteristic
316C2×C4×C53C2×C22⋊C411yescharacteristic
317C2×C4×C53C2×C22⋊C411yescharacteristic
318C2×C4×C53C2×C22⋊C411yescharacteristic
319C22⋊D53—44no—
320C22⋊D53—44no—
321C22⋊D53—44no—
322C22⋊D53—44no—
323C22⋊D53—44no—
324C22⋊D53—44no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—24no—
329C2×Dic53—28no—
330C2×Dic53—416no—
331C2×Dic53—44no—
332C2×Dic53—44no—
333C2×Dic53—42no—
334C2×Dic53—42no—
335D212—42no—
336D212—42no—
337C4×D53—44no—
338C4×D53—44no—
339Dic106—42no—
340Dic106—42no—
341#21420—531nomaximal, Sylow
342C22×C53—28no—
343C22×C53—21no—
344C22×C53—21no—
345C22×C53—21no—
346C22×C53—21no—
347C22×C53—21no—
348C22×C53—21no—
349C22×C53—21no—
350C22×C53—21no—
351C22×C53—21no—
352C22×C53—21no—
353C22×C53—21no—
354C22×C53—21no—
355C22×C53—21no—
356C22×C53—21no—
357C22×C53—21no—
358C22×C53—21no—
359C22×C53—44no—
360C22×C53—44no—
361C22×C53—44no—
362C22×C53—44no—
363C22×C53—44no—
364C22×C53—44no—
365C22×C53C2×#9912yes—
366C22×C53#41012yes—
367C22×C53C22×C22⋊C411yescharacteristic
368C22×C53C4×#4112yes—
369C22×C53#52512yes—
370C22×C53#53212yes—
371C2×D53—42no—
372C2×D53—42no—
373C2×D53—42no—
374C2×D53—84no—
375C4×C53—21no—
376C4×C53—21no—
377C4×C53—21no—
378C4×C53—21no—
379C4×C53—21no—
380C4×C53—21no—
381C4×C53—84no—
382C4×C53C2×#9912yes—
383C4×C53C2×#9912yes—
384Dic53—48no—
385Dic53—42no—
386Dic53—42no—
387Dic53—42no—
388C2×#525—531no—
389#2280D5311yescharacteristic, complemented
390C2×C4×C22⋊C4—531no—
391#1996—532no—
392#1964—532no—
393#1898—534no—
394C4×#99—534no—
395C2×C53—22no—
396C2×C53—22no—
397C2×C53—22no—
398C2×C53—22no—
399C2×C53—22no—
400C2×C53—41no—
401C2×C53—41no—
402C2×C53#229711yescharacteristic
403C2×C53C22×#9911yescharacteristic
404C2×C53C2×#41011yescharacteristic
405D53—82no—
406C22×#41—531no—
407C24×C4C2×D5311yescharacteristic
408#525—1061no—
409#525—1061no—
410#525—1061no—
411#525—1061no—
412#525—1061no—
413#525—1061no—
414#525—1061no—
415#525—1061no—
416C2×#123—532no—
417C2×C22⋊Q8—531no—
418C2×C22⋊Q8—531no—
419C2×#121—531no—
420C2×#121—531no—
421C2×#120—532no—
422C2×C4×D4—532no—
423C2×C4×D4—532no—
424C2×#117—21no—
425C2×#117—531no—
426C22×C22⋊C4—532no—
427C22×C42—1061no—
428C2×#99—538no—
429#381—21no—
430#380—21no—
431#380C2×D5312yes—
432#379C2×D5312yes—
433C4×C22⋊C4—21no—
434C4×C22⋊C4—532no—
435C4×C22⋊C4—532no—
436C4×C22⋊C4—1061no—
437C4×C22⋊C4—1061no—
438C4×C22⋊C4C2×D5312yes—
439C2×#95—1061no—
440#342—538no—
441C53#2142011yescharacteristic, complemented, Sylow
442C25C22×D5311yescharacteristic
443C2×#41—1061no—
444C2×#41—1061no—
445C2×#41—1061no—
446C2×#41—1061no—
447C2×#41—2124no—
448C22×Q8—531no—
449C22×D4—532no—
450C22×D4—532no—
451C22×D4—532no—
452C22×D4—531no—
453C23×C4—44no—
454C23×C4—532no—
455C23×C4—1062no—
456C23×C4C4×D5311yescharacteristic
457C23×C4C4×D5311yescharacteristic
458C23×C4C4×D5311yescharacteristic
459C23×C4C4×D5311yescharacteristic
460C23×C4D21211yescharacteristic
461C23×C4D21211yescharacteristic
462C23×C4D21211yescharacteristic
463C23×C4D21211yescharacteristic
464C23×C4C22⋊D5311yescharacteristic
465C23×C4C22⋊D5311yescharacteristic
466C23×C4C22⋊D5311yescharacteristic
467C23×C4C22⋊D5311yescharacteristic
468C23×C4C22×D5311yescharacteristic
469C23×C4C22×D5311yescharacteristic
470#123—1062no—
471#123—1062no—
472#123—1062no—
473#123—1062no—
474C22⋊Q8—1061no—
475C22⋊Q8—1061no—
476C22⋊Q8—1061no—
477C22⋊Q8—1061no—
478C22⋊Q8—1061no—
479C22⋊Q8—1061no—
480C22⋊Q8—1061no—
481C22⋊Q8—1061no—
482#121—1061no—
483#121—1061no—
484#121—1061no—
485#121—1061no—
486#121—1061no—
487#121—1061no—
488#121—1061no—
489#121—1061no—
490#120—1062no—
491#120—1062no—
492#120—1062no—
493#120—1062no—
494C4×D4—1062no—
495C4×D4—1062no—
496C4×D4—1062no—
497C4×D4—1062no—
498C4×D4—1062no—
499C4×D4—1062no—
500C4×D4—1062no—
501C4×D4—1062no—
502#117—44no—
503#117—1061no—
504#117—1061no—
505#117—1061no—
506#117—1061no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—531no—
509C2×C4⋊C4—531no—
510C2×C4⋊C4—532no—
511C2×C4⋊C4—532no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—534no—
515C2×C22⋊C4—532no—
516C2×C22⋊C4—532no—
517C2×C22⋊C4—532no—
518C2×C22⋊C4—532no—
519C2×C22⋊C4—532no—
520C2×C22⋊C4—1068no—
521C2×C22⋊C4—1062no—
522C2×C22⋊C4C22×D5314yes—
523C2×C42—22no—
524C2×C42—532no—
525C2×C42—1062no—
526C2×C42—1062no—
527C2×C42—2124no—
528#99—10616no—
529#95—22no—
530#95—22no—
531#95—1062no—
532#95—1062no—
533C24—24no—
534C24—42no—
535C24—42no—
536C24—532no—
537C24C2×C4×D5311yescharacteristic
538C24C2×C4×D5311yescharacteristic
539C24C2×D21211yescharacteristic
540C24C2×D21211yescharacteristic
541C24C2×C22⋊D5311yescharacteristic
542C24C2×C22⋊D5311yescharacteristic
543C24C23×D5311yescharacteristic
544#41—2124no—
545#41—2124no—
546#41—2124no—
547#41—2124no—
548C2×Q8—1061no—
549C2×Q8—1061no—
550C2×Q8—2122no—
551C2×D4—1062no—
552C2×D4—1062no—
553C2×D4—1062no—
554C2×D4—1062no—
555C2×D4—1062no—
556C2×D4—1062no—
557C2×D4—1068no—
558C2×D4—1061no—
559C2×D4—1061no—
560C2×D4—2122no—
561C2×D4—2124no—
562C2×D4—2124no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—532no—
579C22×C4—532no—
580C22×C4—532no—
581C22×C4—1068no—
582C22×C4—1064no—
583C22×C4—1062no—
584C22×C4—1062no—
585C22×C4—2124no—
586C22×C4—2124no—
587C22×C4—2124no—
588C22×C4#1171992111yescharacteristic
589C22×C4#1171992111yescharacteristic
590C22×C4#1171992111yescharacteristic
591C22×C4#1171992111yescharacteristic
592C22×C4#1171992111yescharacteristic
593C22×C4#1171992111yescharacteristic
594C22×C4#1171992111yescharacteristic
595C22×C4#1171992111yescharacteristic
596C22×C4#1171992111yescharacteristic
597C22×C4#1171992111yescharacteristic
598C22×C4#1171992111yescharacteristic
599C22×C4#1171992111yescharacteristic
600C22×C4#1171992111yescharacteristic
601C22×C4#1171992111yescharacteristic
602C22×C4#1171992111yescharacteristic
603C22×C4#1171992111yescharacteristic
604C22×C4C2×C4×D5311yescharacteristic
605C22×C4C2×C4×D5311yescharacteristic
606C22×C4C2×C4×D5311yescharacteristic
607C22×C4C2×C4×D5311yescharacteristic
608C22×C4C2×D21211yescharacteristic
609C22×C4C2×D21211yescharacteristic
610C22×C4C2×D21211yescharacteristic
611C22×C4C2×D21211yescharacteristic
612C22×C4C2×C22⋊D5311yescharacteristic
613C22×C4C2×C22⋊D5311yescharacteristic
614C22×C4C2×C22⋊D5311yescharacteristic
615C22×C4C2×C22⋊D5311yescharacteristic
616C4⋊C4—44no—
617C4⋊C4—1061no—
618C4⋊C4—1061no—
619C4⋊C4—1061no—
620C4⋊C4—1061no—
621C4⋊C4—1062no—
622C4⋊C4—1062no—
623C4⋊C4—1062no—
624C4⋊C4—1062no—
625C22⋊C4—28no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—538no—
629C22⋊C4—1068no—
630C22⋊C4—1062no—
631C22⋊C4—1062no—
632C22⋊C4—1062no—
633C22⋊C4—1062no—
634C22⋊C4—1062no—
635C22⋊C4—1062no—
636C22⋊C4—1064no—
637C22⋊C4—1062no—
638C22⋊C4—1062no—
639C22⋊C4—1062no—
640C22⋊C4—1062no—
641C42—44no—
642C42—1062no—
643C42—1062no—
644C42—2124no—
645C42—2124no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—416no—
667C23—1064no—
668C23—1062no—
669C23—2122no—
670C23—2122no—
671C23C2×#1171992111yescharacteristic
672C23C2×#1171992111yescharacteristic
673C23C2×#1171992111yescharacteristic
674C23C2×#1171992111yescharacteristic
675C23C22×C4×D5311yescharacteristic
676C23C22×C22⋊D5311yescharacteristic
677C23C22×D21211yescharacteristic
678C23#41×D5314yes—
679Q8—2122no—
680Q8—2122no—
681D4—2122no—
682D4—2124no—
683D4—2124no—
684D4—2124no—
685D4—2124no—
686D4—2124no—
687D4—2124no—
688D4—2122no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—1062no—
720C2×C4—1062no—
721C2×C4—1062no—
722C2×C4—1064no—
723C2×C4—1068no—
724C2×C4—2124no—
725C2×C4—2124no—
726C2×C4—21216no—
727C2×C4—2124no—
728C2×C4—2124no—
729C2×C4—2122no—
730C2×C4—2122no—
731C2×C4#1313313114yescomplemented
732C2×C4C2×#1171992111yescharacteristic
733C2×C4C2×#1171992111yescharacteristic
734C2×C4C2×#1171992111yescharacteristic
735C2×C4C2×#1171992111yescharacteristic
736C2×C4C2×#1171992111yescharacteristic
737C2×C4C2×#1171992111yescharacteristic
738C2×C4C2×#1171992111yescharacteristic
739C2×C4C2×#1171992111yescharacteristic
740C22—28no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—21no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—4244no—
764C22—2122no—
765C22—2122no—
766C22—2122no—
767C22C2×#1313313112yes—
768C22#1681059612yes—
769C22C22×#1171992111yescharacteristic
770C22#1681109112yes—
771C22#1681113512yes—
772C22#1681116912yes—
773C4—21no—
774C4—21no—
775C4—21no—
776C4—21no—
777C4—21no—
778C4—21no—
779C4—84no—
780C4—2128no—
781C4—2122no—
782C4—2122no—
783C4—2122no—
784C4C2×#1313313112yes—
785C4C2×#1313313112yes—
786C2—22no—
787C2—22no—
788C2—22no—
789C2—22no—
790C2—22no—
791C2—41no—
792C2—41no—
793C2—4242no—
794C2#2027720311yescharacteristic
795C2C22×#1313313111yescharacteristic
796C2C2×#1681059611yescharacteristic
subgroupG/H
centerC2×C4C2×#11719921
commutatorC23×C53C23×C4
FrattiniC24C23×D53
FittingC53×#2280C2
socleC22×C53C22×C22⋊C4
prime radicalC2×#16811134C2
cosocleC24×C53C24
hypercenter#2280D53
hypocenterC53#21420
LCSG ▷ C23×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊Dic53C2semidirect
3. #20275699C2semidirect
4. #20275550C2semidirect
5. #20275166C2semidirect
6. C4×#13133131C2semidirect
7. C53×#2280C2semidirect
8. C22×#11719945C4semidirect
17. C2×#13133200C4semidirect
18. C2×#13133196C4semidirect
20. C2×#13133191C4semidirect
23. C2×C4×C22⋊D53C4semidirect
25. C2×#13133176C4semidirect
48. C22×Dic106C2×C4semidirect
49. C22×D212C2×C4semidirect
54. C22×C4×D53C2×C4semidirect
91. C2×C4⋊Dic53C2×C4semidirect
92. C2×C4⋊Dic53C2×C4semidirect
93. C2×#11719919C2×C4semidirect
94. C2×#11719919C2×C4semidirect
101. C2×#11719921C2×C4semidirect
102. C2×#11719921C2×C4semidirect
106. C2×C4×Dic53C2×C4semidirect
230. C22⋊Dic53#41semidirect
310. C2×C4×C53#99semidirect
389. #2280D53semidirect
441. C53#21420semidirect
731. C2×C4#13133131semidirect

Maximal subgroups

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

subgroupindex
C2×#168111342
C2×C4×C22⋊Dic532
#202756992
#202755502
#202751662
C4×#131331312
C53×#22802
#2142053