Finite Group Databasebeta

← #27411598

Subgroups — #27411598

Order 13568.

1650 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×#16810666C211yesmaximal, characteristic, complemented
2C2×#16810624C211yesmaximal, characteristic, complemented
3C2×#16810624C211yesmaximal, characteristic, complemented
4C2×#16810587C211yesmaximal, characteristic, complemented
5C2×#16810483C211yesmaximal, characteristic, complemented
6#20275915C212yesmaximal, complemented
7#20275908C212yesmaximal, complemented
8#20275901C212yesmaximal, complemented
9#20275894C212yesmaximal, complemented
10#20274436C211yesmaximal, characteristic, complemented
11C2×C53×#525C211yesmaximal, characteristic
12C22×#11719917C2211yescharacteristic
13C22×#11719917C2211yescharacteristic
14C22×C4⋊Dic53C2211yescharacteristic
15C22×C4⋊Dic53C2211yescharacteristic
16C22×C22⋊Dic53—21no—
17#16810666—24no—
18C2×#13133150C2212yescomplemented
19C2×#13133148C2212yescomplemented
20#16810624—24no—
21#16810624—24no—
22C2×#13133141C2212yescomplemented
23C2×#13133141C2212yescomplemented
24C2×#13133138C2212yescomplemented
25C2×#13133138C2212yescomplemented
26#16810587—24no—
27C2×C22⋊#88322C2212yes—
28C2×C22⋊#88322C2212yes—
29#16810483—21no—
30#16810483—21no—
31#16810483C2212yes—
32#16810483C2212yes—
33C2×#13133124—21no—
34#16810385C2212yescomplemented
35#16810385C2212yescomplemented
36C22×#41×C53C2211yescharacteristic
37C24×C4×C53C2211yescharacteristic
38C53×#525—24no—
39C53×#525—24no—
40C2×#123×C53—21no—
41C2×C22⋊Q8×C53C2211yescharacteristic
42C2×C22⋊Q8×C53C2211yescharacteristic
43C2×#121×C53C2211yescharacteristic
44C2×#121×C53C2211yescharacteristic
45C2×#120×C53—21no—
46C2×C4×D4×C53—21no—
47C2×C4×D4×C53—21no—
48C2×#117×C53C2211yescharacteristic
49C23×Dic53—21no—
50C23×Dic53—21no—
51C2×#11719917—22no—
52C2×#11719917—22no—
53C2×#11719917—22no—
54C2×#11719917—22no—
55C2×#11719917—22no—
56C2×#11719917D414yescomplemented
57C22×#88322C2312yes—
58C22×#88322C2312yes—
59C2×C4⋊Dic53—21no—
60C2×C4⋊Dic53—21no—
61C2×C4⋊Dic53—22no—
62C2×C4⋊Dic53—22no—
63C2×C4⋊Dic53—22no—
64C2×C4⋊Dic53—22no—
65C2×C4⋊Dic53C2312yes—
66C2×C4⋊Dic53C2312yes—
67C2×C22⋊Dic53—22no—
68C2×C22⋊Dic53—22no—
69C2×C22⋊Dic53—44no—
70#13133150—24no—
71#13133148—24no—
72#13133141—24no—
73#13133141—24no—
74#13133138—24no—
75#13133138—24no—
76C22⋊#88322—24no—
77C22⋊#88322—24no—
78#13133124—22no—
79#13133124—22no—
80C25×C53D411yescharacteristic
81C2×#41×C53—22no—
82C2×#41×C53—22no—
83C2×#41×C53—22no—
84C2×#41×C53—22no—
85C2×#41×C53—22no—
86C2×#41×C53D414yes—
87C22×Q8×C53C2311yescharacteristic
88C22×D4×C53—21no—
89C22×D4×C53—21no—
90C22×D4×C53—21no—
91C22×D4×C53C2311yescharacteristic
92C23×C4×C53—21no—
93C23×C4×C53—22no—
94C23×C4×C53—22no—
95C23×C4×C53—22no—
96C23×C4×C53—22no—
97C23×C4×C53—22no—
98C23×C4×C53—22no—
99C23×C4×C53D411yescharacteristic
100C23×C4×C53D411yescharacteristic
101C23×C4×C53D411yescharacteristic
102C23×C4×C53C2311yescharacteristic
103C23×C4×C53C2311yescharacteristic
104C23×C4×C53C2311yescharacteristic
105#123×C53—28no—
106C22⋊Q8×C53—22no—
107C22⋊Q8×C53—22no—
108C22⋊Q8×C53—22no—
109C22⋊Q8×C53—22no—
110#121×C53—22no—
111#121×C53—22no—
112#121×C53—22no—
113#121×C53—22no—
114#120×C53—28no—
115C4×D4×C53—28no—
116C4×D4×C53—28no—
117#117×C53—22no—
118#117×C53D414yes—
119C2×C4⋊C4×C53—21no—
120C2×C4⋊C4×C53—21no—
121C2×C4⋊C4×C53C2311yescharacteristic
122C2×C4⋊C4×C53C2311yescharacteristic
123C2×C22⋊C4×C53—21no—
124C2×C22⋊C4×C53—21no—
125C2×C22⋊C4×C53—21no—
126C2×C22⋊C4×C53—21no—
127C2×C22⋊C4×C53—21no—
128C2×C42×C53—21no—
129C24×C53—22no—
130C24×C53—22no—
131C24×C53—22no—
132C24×C53—22no—
133C24×C53—22no—
134C24×C53—21no—
135C24×C53—41no—
136C24×C53—41no—
137C24×C53C2×D411yescharacteristic
138C24×C53C2×D411yescharacteristic
139C24×C53C2×D411yescharacteristic
140#41×C53—28no—
141#41×C53—28no—
142#41×C53—44no—
143#41×C53—44no—
144C2×Q8×C53—21no—
145C2×Q8×C53—21no—
146C2×Q8×C53—21no—
147C2×Q8×C53—21no—
148C2×Q8×C53—21no—
149C2×Q8×C53C2×D412yes—
150C2×D4×C53—24no—
151C2×D4×C53—24no—
152C2×D4×C53—24no—
153C2×D4×C53—21no—
154C2×D4×C53—21no—
155C2×D4×C53—21no—
156C2×D4×C53—21no—
157C2×D4×C53—21no—
158C2×D4×C53—42no—
159C2×D4×C53—42no—
160C2×D4×C53—42no—
161C2×D4×C53—42no—
162C2×D4×C53—42no—
163C2×D4×C53—42no—
164C2×D4×C53C2×D412yes—
165C22×C4×C53—22no—
166C22×C4×C53—22no—
167C22×C4×C53—22no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—21no—
171C22×C4×C53—22no—
172C22×C4×C53—22no—
173C22×C4×C53—24no—
174C22×C4×C53—22no—
175C22×C4×C53—22no—
176C22×C4×C53—22no—
177C22×C4×C53—22no—
178C22×C4×C53—21no—
179C22×C4×C53—21no—
180C22×C4×C53—21no—
181C22×C4×C53—21no—
182C22×C4×C53—21no—
183C22×C4×C53—21no—
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—44no—
191C22×C4×C53—44no—
192C22×C4×C53—42no—
193C22×C4×C53—44no—
194C22×C4×C53—42no—
195C22×C4×C53—44no—
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2×D412yes—
200C22×C4×C53C2×D412yes—
201C22×C4×C53C2×D412yes—
202C22×C4×C53#4112yes—
203C22×C4×C53#4112yes—
204C22×C4×C53#4112yes—
205C22×C4×C53C2411yescharacteristic
206C22×Dic53—22no—
207C22×Dic53—22no—
208C22×Dic53—42no—
209C22×Dic53—42no—
210C22×Dic53—42no—
211C22×Dic53—42no—
212C22×Dic53—42no—
213C22×Dic53—42no—
214C4⋊C4×C53—24no—
215C4⋊C4×C53—24no—
216C4⋊C4×C53—21no—
217C4⋊C4×C53—21no—
218C4⋊C4×C53C2×D412yes—
219C4⋊C4×C53C2×D412yes—
220C22⋊C4×C53—24no—
221C22⋊C4×C53—24no—
222C22⋊C4×C53—24no—
223C22⋊C4×C53—24no—
224C22⋊C4×C53—24no—
225C42×C53—24no—
226C22⋊Dic53—44no—
227C22⋊Dic53—44no—
228C4⋊Dic53—22no—
229C4⋊Dic53—22no—
230C4⋊Dic53—22no—
231C4⋊Dic53—22no—
232C4⋊Dic53—42no—
233C4⋊Dic53—42no—
234#11719917—28no—
235#11719917—44no—
236C2×#88322—22no—
237C2×#88322—22no—
238C2×#88322—22no—
239C2×#88322—22no—
240C2×#88322—22no—
241C2×#88322C2×D414yes—
242C23×C53—21no—
243C23×C53—21no—
244C23×C53—21no—
245C23×C53—21no—
246C23×C53—28no—
247C23×C53—21no—
248C23×C53—21no—
249C23×C53—21no—
250C23×C53—21no—
251C23×C53—21no—
252C23×C53—21no—
253C23×C53—21no—
254C23×C53—21no—
255C23×C53—21no—
256C23×C53—21no—
257C23×C53—21no—
258C23×C53—21no—
259C23×C53—22no—
260C23×C53—44no—
261C23×C53—44no—
262C23×C53—44no—
263C23×C53—44no—
264C23×C53—44no—
265C23×C53—44no—
266C23×C53—41no—
267C23×C53—41no—
268C23×C53—41no—
269C23×C53—41no—
270C23×C53—41no—
271C23×C53—41no—
272C23×C53#12012yes—
273C23×C53#12112yes—
274C23×C53#12312yes—
275C23×C53AGL(1,ℤ/8)12yes—
276C23×C53#13712yes—
277C23×C53C22×D411yescharacteristic
278Q8×C53—22no—
279Q8×C53—22no—
280Q8×C53—41no—
281Q8×C53—41no—
282D4×C53—22no—
283D4×C53—22no—
284D4×C53—48no—
285D4×C53—48no—
286D4×C53—48no—
287D4×C53—41no—
288D4×C53—41no—
289C2×C4×C53—21no—
290C2×C4×C53—21no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—21no—
295C2×C4×C53—21no—
296C2×C4×C53—21no—
297C2×C4×C53—21no—
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—44no—
305C2×C4×C53—41no—
306C2×C4×C53—41no—
307C2×C4×C53—41no—
308C2×C4×C53—41no—
309C2×C4×C53—41no—
310C2×C4×C53—41no—
311C2×C4×C53—41no—
312C2×C4×C53—41no—
313C2×C4×C53—44no—
314C2×C4×C53—44no—
315C2×C4×C53—48no—
316C2×C4×C53#12012yes—
317C2×C4×C53#12114yes—
318C2×C4×C53#12114yes—
319C2×C4×C53#12112yes—
320C2×C4×C53#12314yes—
321C2×C4×C53#12312yes—
322C2×C4×C53#12414yes—
323C2×C4×C53C22×D411yescharacteristic
324C2×C4×C53C22×D411yescharacteristic
325C2×C4×C53C22×D411yescharacteristic
326C2×C4×C53C2×#4111yescharacteristic
327C2×C4×C53C2×#4111yescharacteristic
328C2×C4×C53C2×#4111yescharacteristic
329C2×Dic53—42no—
330C2×Dic53—42no—
331C2×Dic53—42no—
332C2×Dic53—42no—
333C2×Dic53—42no—
334C2×Dic53—42no—
335C2×Dic53—84no—
336C2×Dic53—84no—
337#88322—24no—
338#88322—42no—
339#23482—531nomaximal, Sylow
340C22×C53—22no—
341C22×C53—22no—
342C22×C53—22no—
343C22×C53—22no—
344C22×C53—22no—
345C22×C53—22no—
346C22×C53—22no—
347C22×C53—22no—
348C22×C53—22no—
349C22×C53—22no—
350C22×C53—22no—
351C22×C53—22no—
352C22×C53—416no—
353C22×C53—41no—
354C22×C53—41no—
355C22×C53—41no—
356C22×C53—41no—
357C22×C53—41no—
358C22×C53—41no—
359C22×C53—41no—
360C22×C53—41no—
361C22×C53—42no—
362C22×C53—42no—
363C22×C53—42no—
364C22×C53—81no—
365C22×C53—81no—
366C22×C53—81no—
367C22×C53—81no—
368C22×C53#39414yes—
369C22×C53C2×#12011yescharacteristic
370C22×C53C2×#12111yescharacteristic
371C22×C53C2×#12311yescharacteristic
372C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
373C22×C53C2×#13711yescharacteristic
374C22×C53#57511yescharacteristic
375C22×C53#57511yescharacteristic
376C4×C53—41no—
377C4×C53—41no—
378C4×C53—42no—
379C4×C53—42no—
380C4×C53—42no—
381C4×C53#39414yes—
382C4×C53C2×#12111yescharacteristic
383C4×C53C2×#12111yescharacteristic
384C4×C53C2×#12311yescharacteristic
385C4×C53C2×#12411yescharacteristic
386Dic53—82no—
387Dic53—82no—
388C2×#525D5311yescharacteristic
389C2×#428—531no—
390C2×#417—531no—
391C2×#417—531no—
392C2×#407—531no—
393C2×#380—531no—
394#2036—532no—
395#2035—532no—
396#2034—532no—
397#2033—532no—
398#1736—531no—
399C2×C53—24no—
400C2×C53—42no—
401C2×C53—42no—
402C2×C53—82no—
403C2×C53C2×#39411yescharacteristic
404C2×C53#300611yescharacteristic
405C2×C53#300711yescharacteristic
406C2×C53#305511yescharacteristic
407C2×C53#305611yescharacteristic
408C2×C53#309211yescharacteristic
409C2×C53#309311yescharacteristic
410C22×#41C2×D5311yescharacteristic
411C24×C4C2×D5311yescharacteristic
412C22×M16—531no—
413C22×M16—531no—
414#525—24no—
415#525—24no—
416C2×#123—21no—
417C2×C22⋊Q8C2×D5311yescharacteristic
418C2×C22⋊Q8C2×D5311yescharacteristic
419C2×#121C2×D5311yescharacteristic
420C2×#121C2×D5311yescharacteristic
421C2×#120—21no—
422C2×C4×D4—21no—
423C2×C4×D4—21no—
424C2×#117C2×D5311yescharacteristic
425C22×C4⋊C4—531no—
426C22×C4⋊C4—531no—
427C22×C22⋊C4—1061no—
428#428—1064no—
429C2×#107—532no—
430C2×#106—532no—
431#417—1064no—
432#417—1064no—
433C2×#103—532no—
434C2×#103—532no—
435C2×#102—532no—
436C2×#102—532no—
437#407—1064no—
438C2×C22⋊C8—532no—
439C2×C22⋊C8—532no—
440#380—532no—
441#380—532no—
442#380—1061no—
443#380—1061no—
444C2×#95—1061no—
445#340—532no—
446#340—532no—
447C53#2348211yescharacteristic, complemented, Sylow
448C25C22⋊D5311yescharacteristic
449C2×#41—22no—
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41C22⋊D5314yes—
455C22×Q8C22×D5311yescharacteristic
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4C22×D5311yescharacteristic
460C23×C4—22no—
461C23×C4—22no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—21no—
465C23×C4—22no—
466C23×C4—22no—
467C23×C4—1061no—
468C23×C4—1061no—
469C23×C4C22⋊D5311yescharacteristic
470C23×C4C22⋊D5311yescharacteristic
471C23×C4C22⋊D5311yescharacteristic
472C23×C4C22×D5311yescharacteristic
473C23×C4C22×D5311yescharacteristic
474C23×C4C22×D5311yescharacteristic
475C2×M16—534no—
476C2×M16—1062no—
477C2×M16—1062no—
478C2×M16—1062no—
479C2×M16—1062no—
480C2×M16—1062no—
481C22×C8—532no—
482C22×C8—532no—
483#123—28no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488#121—22no—
489#121—22no—
490#121—22no—
491#121—22no—
492#120—28no—
493C4×D4—28no—
494C4×D4—28no—
495#117—22no—
496#117C22⋊D5314yes—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—532no—
500C2×C4⋊C4—532no—
501C2×C4⋊C4—1062no—
502C2×C4⋊C4—1062no—
503C2×C4⋊C4—1062no—
504C2×C4⋊C4—1062no—
505C2×C4⋊C4—1061no—
506C2×C4⋊C4—1061no—
507C2×C4⋊C4C22×D5311yescharacteristic
508C2×C4⋊C4C22×D5311yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—1062no—
515C2×C22⋊C4—1062no—
516C2×C22⋊C4—2124no—
517C2×C42—21no—
518#107—1064no—
519#106—1064no—
520#103—1064no—
521#103—1064no—
522#102—1064no—
523#102—1064no—
524C22⋊C8—1064no—
525C22⋊C8—1064no—
526#95—1062no—
527#95—1062no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—21no—
534C24—41no—
535C24—41no—
536C24C2×C22⋊D5311yescharacteristic
537C24C2×C22⋊D5311yescharacteristic
538C24C2×C22⋊D5311yescharacteristic
539#41—28no—
540#41—28no—
541#41—44no—
542#41—44no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8C2×C22⋊D5312yes—
549C2×D4—24no—
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4C2×C22⋊D5312yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—42no—
592C22×C4—44no—
593C22×C4—42no—
594C22×C4—44no—
595C22×C4—1062no—
596C22×C4—1062no—
597C22×C4—2122no—
598C22×C4—2122no—
599C22×C4—2122no—
600C22×C4—2122no—
601C22×C4—2122no—
602C22×C4—2122no—
603C22×C4D4×D5312yes—
604C22×C4#1171994712yes—
605C22×C4#1171994712yes—
606C22×C4#1171994712yes—
607C22×C4C2×C22⋊D5311yescharacteristic
608C22×C4C2×C22⋊D5311yescharacteristic
609C22×C4C2×C22⋊D5311yescharacteristic
610C22×C4C2×C22⋊D5312yes—
611C22×C4C2×C22⋊D5312yes—
612C22×C4C23×D5311yescharacteristic
613M16—1068no—
614M16—2124no—
615C2×C8—534no—
616C2×C8—1062no—
617C2×C8—1062no—
618C2×C8—1062no—
619C2×C8—1062no—
620C2×C8—1062no—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—1062no—
626C4⋊C4—1062no—
627C4⋊C4—1062no—
628C4⋊C4—1062no—
629C4⋊C4—2122no—
630C4⋊C4—2122no—
631C4⋊C4C2×C22⋊D5312yes—
632C4⋊C4C2×C22⋊D5312yes—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—2124no—
639C22⋊C4—2124no—
640C42—24no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—28no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23#1313318612yes—
672C23#1313318912yes—
673C23#1313319812yes—
674C23#1313324212yes—
675C23#1313324712yes—
676C23C22×C22⋊D5311yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—41no—
680Q8—41no—
681D4—22no—
682D4—22no—
683D4—48no—
684D4—48no—
685D4—48no—
686D4—41no—
687D4—41no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—44no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—48no—
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—4244no—
716C2×C4—4244no—
717C2×C4—2122no—
718C2×C4—2122no—
719C2×C4—2122no—
720C2×C4—2122no—
721C2×C4—2122no—
722C2×C4—2122no—
723C2×C4#1313318612yes—
724C2×C4#1313318814yes—
725C2×C4#1313318912yes—
726C2×C4#1313318914yes—
727C2×C4#1313319812yes—
728C2×C4#1313319814yes—
729C2×C4#1313320414yes—
730C2×C4C2×D4×D5311yescharacteristic
731C2×C4C22×C22⋊D5311yescharacteristic
732C2×C4C22×C22⋊D5311yescharacteristic
733C2×C4C2×#1171994711yescharacteristic
734C2×C4C2×#1171994711yescharacteristic
735C2×C4C2×#1171994711yescharacteristic
736C8—1064no—
737C8—2122no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—416no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22#1681053714yes—
767C22C2×#1313318611yescharacteristic
768C22C2×#1313318911yescharacteristic
769C22C2×#1313319811yescharacteristic
770C22C2×#1313324211yescharacteristic
771C22C2×#1313324711yescharacteristic
772C22#1681142111yescharacteristic
773C22#1681142111yescharacteristic
774C4—42no—
775C4—42no—
776C4—41no—
777C4—41no—
778C4—42no—
779C4—4242no—
780C4—4242no—
781C4#1681053714yes—
782C4C2×#1313318811yescharacteristic
783C4C2×#1313318911yescharacteristic
784C4C2×#1313319811yescharacteristic
785C4C2×#1313320411yescharacteristic
786C2—24no—
787C2—42no—
788C2—42no—
789C2—82no—
790C2C2×#1681053711yescharacteristic
791C2#2028396711yescharacteristic
792C2#2028397511yescharacteristic
793C2#2028433611yescharacteristic
794C2#2028434711yescharacteristic
795C2#2028463511yescharacteristic
796C2#2028464411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
Fitting, prime radicalC2×C53×#525C2
socleC23×C53C22×D4
hypercenterC2×#525D53
hypocenterC53#23482
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#16810666C2semidirect
2. C2×#16810624C2semidirect
3. C2×#16810624C2semidirect
4. C2×#16810587C2semidirect
5. C2×#16810483C2semidirect
6. #20275915C2semidirect
7. #20275908C2semidirect
8. #20275901C2semidirect
9. #20275894C2semidirect
10. #20274436C2semidirect
18. C2×#13133150C22semidirect
19. C2×#13133148C22semidirect
22. C2×#13133141C22semidirect
23. C2×#13133141C22semidirect
24. C2×#13133138C22semidirect
25. C2×#13133138C22semidirect
34. #16810385C22semidirect
35. #16810385C22semidirect
56. C2×#11719917D4semidirect
447. C53#23482semidirect

Maximal subgroups

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

subgroupindex
C2×#168106662
C2×#168106242
C2×#168105872
C2×#168104832
#202759152
#202759082
#202759012
#202758942
#202744362
C2×C53×#5252
#2348253