Finite Group Databasebeta

← #27404346

Subgroups — #27404346

Order 13568.

1302 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810773C211yesmaximal, characteristic
2C2×#16810726C211yesmaximal, characteristic, complemented
3C22×#13133139C211yesmaximal, characteristic
4#20277724C211yesmaximal, characteristic, complemented
5#20277535C211yesmaximal, characteristic
6#20275593C211yesmaximal, characteristic, complemented
7#20275413C211yesmaximal, characteristic, complemented
8#20275333C211yesmaximal, characteristic, complemented
9#20275068C211yesmaximal, characteristic, complemented
10#20275046C211yesmaximal, characteristic, complemented
11#20274963C211yesmaximal, characteristic, complemented
12#20274902C211yesmaximal, characteristic, complemented
13#20274539C211yesmaximal, characteristic, complemented
14#20274491C211yesmaximal, characteristic, complemented
15C53×#1892C211yesmaximal, characteristic, complemented
16C23×D212C2211yescharacteristic
17C22×#11719924C2211yescharacteristic
18C22×#11719924C2211yescharacteristic
19C2×Q8×Dic53C2211yescharacteristic, complemented
20C2×#13133179C2211yescharacteristic
21C2×#13133179C2211yescharacteristic
22C22×C4⋊Dic53C2211yescharacteristic
23C2×C22⋊C4×D53—21no—
24#16810773C418yescomplemented
25#16810726—24no—
26C2×#13133150C2211yescharacteristic, complemented
27C2×#13133150C2211yescharacteristic, complemented
28C2×#13133139—24no—
29C2×#13133139C2211yescharacteristic
30C2×#13133139C2211yescharacteristic
31C2×#13133139C2211yescharacteristic
32C2×#13133139C2211yescharacteristic
33C2×#13133137C2211yescharacteristic
34C2×#13133137C2211yescharacteristic
35C2×C22⋊#88322C2211yescharacteristic
36C2×#13133127C2211yescharacteristic, complemented
37C2×#13133127C2211yescharacteristic, complemented
38#16810530C2211yescharacteristic, complemented
39#16810524C2211yescharacteristic
40#16810524C2211yescharacteristic
41#16810522—21no—
42#16810522C2211yescharacteristic, complemented
43#16810509—21no—
44#16810501—21no—
45#16810501—21no—
46#16810498—21no—
47#16810478—21no—
48C4⋊C4×Dic53C2211yescharacteristic, complemented
49C22⋊C4×Dic53—21no—
50C4×C22⋊Dic53C2211yescharacteristic
51#16810385C2211yescharacteristic, complemented
52#16810385C2211yescharacteristic, complemented
53#16810377C2211yescharacteristic, complemented
54#16810377C2211yescharacteristic, complemented
55C23×C8×C53C2211yescharacteristic
56C2×C22⋊Q8×C53C2211yescharacteristic
57C2×#103×C53C2211yescharacteristic, complemented
58C2×#103×C53C2211yescharacteristic, complemented
59C53×#380C2211yescharacteristic
60C53×#340C2211yescharacteristic, complemented
61C53×#340C2211yescharacteristic, complemented
62C24×D53—21no—
63C22×D212—22no—
64C22×D212—22no—
65C22×D212—21no—
66C22×D212—22no—
67C22×D212—41no—
68C22×D212—41no—
69C22×D212C2×C414yes—
70C22×D212C2311yescharacteristic
71C22×D212C2311yescharacteristic
72C23×Dic53—21no—
73C22×C4×D53—21no—
74C22×C4×D53—21no—
75C2×#11719924—22no—
76C2×#11719924—22no—
77C2×#11719924—41no—
78C2×#11719924—41no—
79C2×#11719924C2×C414yescomplemented
80C2×#11719924C2×C414yescomplemented
81C22×#88322C2311yescharacteristic
82C22×#88322C2311yescharacteristic
83Q8×Dic53—22no—
84Q8×Dic53—41no—
85#13133179—22no—
86#13133179—22no—
87#13133179—41no—
88#13133179—41no—
89C2×C4⋊Dic53—21no—
90C2×C4⋊Dic53—21no—
91C2×C4⋊Dic53—21no—
92C2×C4⋊Dic53—22no—
93C2×C4⋊Dic53—41no—
94C2×C4⋊Dic53C2311yescharacteristic
95C2×C4⋊Dic53C2311yescharacteristic
96C2×C22⋊Dic53D411yescharacteristic
97C2×C22⋊Dic53D411yescharacteristic
98C2×#11719921—21no—
99C2×#11719921—21no—
100C2×#11719921—21no—
101C2×#11719921—21no—
102C2×#11719921—21no—
103C2×#11719921—21no—
104C22⋊C4×D53—44no—
105C2×C4×Dic53—21no—
106C2×C4×Dic53—21no—
107C2×C4×Dic53C2311yescharacteristic
108C2×C4×Dic53C2311yescharacteristic
109#13133150—22no—
110#13133150—41no—
111#13133139—22no—
112#13133139—22no—
113#13133139—22no—
114#13133139D414yes—
115#13133137C2×C414yescomplemented
116#13133137C2×C414yescomplemented
117C22⋊#88322C2×C414yescomplemented
118#13133127—22no—
119#13133127—41no—
120#13133124—21no—
121#13133124—21no—
122#13133124—21no—
123#13133124—21no—
124#13133124D411yescharacteristic
125#13133124D411yescharacteristic
126C22×Q8×C53C2311yescharacteristic
127C23×C4×C53C2311yescharacteristic
128C22×C8×C53—22no—
129C22×C8×C53—22no—
130C22×C8×C53—41no—
131C22×C8×C53C2311yescharacteristic
132C22×C8×C53C2311yescharacteristic
133C22⋊Q8×C53—22no—
134C22⋊Q8×C53C2×C414yescomplemented
135C2×C4⋊C4×C53—21no—
136C2×C4⋊C4×C53C2311yescharacteristic
137C2×C4⋊C4×C53C2311yescharacteristic
138C2×C4⋊C4×C53C2311yescharacteristic
139C2×C22⋊C4×C53—21no—
140C2×C22⋊C4×C53—21no—
141#103×C53—22no—
142#103×C53—41no—
143#95×C53—21no—
144C24×C53C2×D411yescharacteristic
145C23×D53—21no—
146C23×D53—21no—
147C23×D53—24no—
148C23×D53—42no—
149C23×D53—42no—
150C23×D53—42no—
151C23×D53—42no—
152C23×D53—81no—
153C23×D53—81no—
154C2×Q8×C53—21no—
155C2×Q8×C53—21no—
156C2×Q8×C53—21no—
157C2×Q8×C53—21no—
158C2×Q8×C53—21no—
159C2×Q8×C53C22×C412yes—
160C22×C4×C53—21no—
161C22×C4×C53—21no—
162C22×C4×C53—21no—
163C22×C4×C53—21no—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53C22×C412yes—
169C22×C4×C53C2×D411yescharacteristic
170C22×C4×C53#4112yes—
171C22×C4×C53C2411yescharacteristic
172C22×Dic53—21no—
173C22×Dic53—21no—
174C22×Dic53—42no—
175C22×Dic53—42no—
176C22×Dic53—81no—
177C22×Dic53C2×D411yescharacteristic
178C22×Dic53C2×D411yescharacteristic
179C22×Dic53C2×D411yescharacteristic
180C22×Dic53C2×D411yescharacteristic
181C2×D212—21no—
182C2×D212—21no—
183C2×D212—21no—
184C2×D212—21no—
185C2×D212—21no—
186C2×D212—21no—
187C2×D212—21no—
188C2×D212—28no—
189C2×D212—24no—
190C2×D212—21no—
191C2×D212—44no—
192C2×D212—44no—
193C2×D212—44no—
194C2×D212—42no—
195C2×D212—42no—
196C2×D212C22×C412yes—
197C2×D212C22×C412yes—
198C2×D212C2×D412yes—
199C2×D212#4112yes—
200C2×C4×D53—42no—
201C2×C4×D53—42no—
202C2×C4×D53—42no—
203C2×C4×D53—42no—
204C2×C4×D53—81no—
205C2×C4×D53—81no—
206C2×C8×C53—21no—
207C2×C8×C53—21no—
208C2×C8×C53—21no—
209C2×C8×C53—21no—
210C2×C8×C53—21no—
211C2×C8×C53—44no—
212C2×C8×C53C2×D412yes—
213C4⋊C4×C53—24no—
214C4⋊C4×C53—21no—
215C4⋊C4×C53—21no—
216C4⋊C4×C53—21no—
217C4⋊C4×C53—21no—
218C4⋊C4×C53—21no—
219C4⋊C4×C53C22×C412yes—
220C22⋊C4×C53—24no—
221C22⋊C4×C53—42no—
222C22⋊Dic53—22no—
223C22⋊Dic53—22no—
224#11719924—28no—
225#11719924—44no—
226#11719921—42no—
227#11719921—42no—
228#11719921—42no—
229#11719921—42no—
230#11719921—81no—
231#11719921—81no—
232C4⋊Dic53—21no—
233C4⋊Dic53—21no—
234C4⋊Dic53—21no—
235C4⋊Dic53—42no—
236C4⋊Dic53—42no—
237C4⋊Dic53—81no—
238C4⋊Dic53C2×D412yes—
239C4×Dic53—21no—
240C4×Dic53—21no—
241C4×Dic53—21no—
242C4×Dic53—21no—
243C4×Dic53—42no—
244C4×Dic53—81no—
245C2×#88322—21no—
246C2×#88322—21no—
247C2×#88322—21no—
248C2×#88322—21no—
249C2×#88322C22×C412yes—
250C2×#88322C22×C412yes—
251C23×C53—21no—
252C23×C53—21no—
253C23×C53—21no—
254C23×C53—21no—
255C23×C53C4×D412yes—
256C23×C53AGL(1,ℤ/8)12yes—
257C23×C53#13712yes—
258C23×C53C22×D411yescharacteristic
259C22×D53—22no—
260C22×D53—22no—
261C22×D53—22no—
262C22×D53—22no—
263C22×D53—48no—
264C22×D53—41no—
265C22×D53—41no—
266C22×D53—41no—
267C22×D53—41no—
268C22×D53—41no—
269C22×D53—41no—
270C22×D53—41no—
271C22×D53—41no—
272C22×D53—41no—
273C22×D53—41no—
274C22×D53—48no—
275C22×D53—84no—
276C22×D53—84no—
277C22×D53—84no—
278C22×D53—84no—
279C22×D53—84no—
280Q8×C53—22no—
281Q8×C53—22no—
282Q8×C53—41no—
283Q8×C53—41no—
284C2×C4×C53—21no—
285C2×C4×C53—21no—
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—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×C53—41no—
302C2×C4×C53C4×D412yes—
303C2×C4×C53C23×C411yescharacteristic
304C2×C4×C53C22×D411yescharacteristic
305C2×C4×C53C2×#4111yescharacteristic
306C2×C4×C53C2×#4111yescharacteristic
307C2×C4×C53H(5,𝔽2)11yescharacteristic
308C2×C4×C53H(5,𝔽2)11yescharacteristic
309C2×Dic53—21no—
310C2×Dic53—22no—
311C2×Dic53—21no—
312C2×Dic53—21no—
313C2×Dic53—21no—
314C2×Dic53—21no—
315C2×Dic53—21no—
316C2×Dic53—21no—
317C2×Dic53—21no—
318C2×Dic53—21no—
319C2×Dic53—21no—
320C2×Dic53—21no—
321C2×Dic53—21no—
322C2×Dic53—41no—
323C2×Dic53—41no—
324C2×Dic53—41no—
325C2×Dic53—41no—
326C2×Dic53—41no—
327C2×Dic53—84no—
328D212—22no—
329D212—22no—
330D212—22no—
331D212—22no—
332D212—22no—
333D212—48no—
334D212—41no—
335D212—41no—
336D212C4×D414yes—
337C4×D53—84no—
338C4×D53—84no—
339C8×C53—22no—
340C8×C53—41no—
341#88322—22no—
342#88322—22no—
343#22854—531nomaximal, Sylow
344C22×C53—22no—
345C22×C53—22no—
346C22×C53—22no—
347C22×C53—22no—
348C22×C53—22no—
349C22×C53—22no—
350C22×C53#44014yescomplemented
351C22×C53C2×C4×D411yescharacteristic
352C22×C53D4211yescharacteristic
353C22×C53#54611yescharacteristic
354C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
355C22×C53C2×#13711yescharacteristic
356C22×C53#57611yescharacteristic
357C22×C53#57711yescharacteristic
358C2×D53—24no—
359C2×D53—42no—
360C2×D53—42no—
361C2×D53—42no—
362C2×D53—42no—
363C2×D53—42no—
364C2×D53—42no—
365C2×D53—42no—
366C2×D53—42no—
367C2×D53—42no—
368C2×D53—816no—
369C2×D53—81no—
370C2×D53—81no—
371C2×D53—81no—
372C2×D53—81no—
373C4×C53—22no—
374C4×C53—42no—
375C4×C53—42no—
376C4×C53—81no—
377C4×C53—81no—
378C4×C53C2×C4×D411yescharacteristic
379C4×C53#51811yescharacteristic
380C4×C53#54611yescharacteristic
381C4×C53#55111yescharacteristic
382Dic53—41no—
383Dic53—42no—
384Dic53—41no—
385Dic53—41no—
386Dic53—41no—
387Dic53—81no—
388C2×#450—531no—
389C2×#440—531no—
390C22×#102—531no—
391#2360—531no—
392D4×C22⋊C4—531no—
393#1973—531no—
394#1936—531no—
395#1925—531no—
396#1892D5311yescharacteristic, complemented
397#1880—531no—
398#1877—531no—
399#1862—531no—
400#1852—531no—
401#1762—531no—
402#1752—531no—
403C2×C53—24no—
404C2×C53#235811yescharacteristic
405C2×C53C2×#44011yescharacteristic
406C2×C53#294611yescharacteristic
407C2×C53#326411yescharacteristic
408C2×C53#326611yescharacteristic
409C2×C53#331011yescharacteristic
410C2×C53#331411yescharacteristic
411D53—44no—
412D53—82no—
413C23×D4—531no—
414C22×SD16—531no—
415C22×SD16—531no—
416C23×C8C2×D5311yescharacteristic
417C2×C22⋊Q8C2×D5311yescharacteristic
418C2×C4×Q8—531no—
419C2×C4×D4—531no—
420C2×C4×D4—531no—
421C22×C4⋊C4—531no—
422C22×C22⋊C4—1061no—
423#450—538no—
424#440—1064no—
425C2×#107—531no—
426C2×#107—531no—
427C2×#103C2×D5311yescharacteristic, complemented
428C2×#103C2×D5311yescharacteristic, complemented
429C2×#102—531no—
430C2×#102—531no—
431C2×#102—531no—
432C2×#102—531no—
433C2×#102—531no—
434C2×#102—531no—
435C2×#102—1064no—
436C2×C22⋊C8—531no—
437C2×#97—531no—
438C2×#97—531no—
439#391—531no—
440#390—531no—
441#390—531no—
442#389—531no—
443#389—1061no—
444#387—1061no—
445#386—1061no—
446#386—1061no—
447#385—1061no—
448#380C2×D5311yescharacteristic
449#379—1061no—
450C4×C4⋊C4—531no—
451C4×C22⋊C4—531no—
452C4×C22⋊C4—1061no—
453#340—531no—
454#340—531no—
455#340C2×D5311yescharacteristic, complemented
456#340C2×D5311yescharacteristic, complemented
457#336—531no—
458#336—531no—
459C53#2285411yescharacteristic, complemented, Sylow
460C25—1061no—
461C22×Q8C22×D5311yescharacteristic
462C22×D4—534no—
463C22×D4—531no—
464C22×D4—531no—
465C22×D4—1062no—
466C22×D4—1062no—
467C22×D4—1061no—
468C22×D4—1062no—
469C22×D4—2121no—
470C22×D4—2121no—
471C23×C4—1061no—
472C23×C4—1061no—
473C23×C4—1061no—
474C23×C4C22×D5311yescharacteristic
475C2×SD16—534no—
476C2×SD16—534no—
477C2×SD16—1062no—
478C2×SD16—1062no—
479C2×SD16—2121no—
480C2×SD16—2121no—
481C22×C8—22no—
482C22×C8—22no—
483C22×C8—41no—
484C22×C8—531no—
485C22×C8—531no—
486C22×C8C22×D5311yescharacteristic
487C22×C8C22×D5311yescharacteristic
488C22⋊Q8—22no—
489C22⋊Q8C4×D5314yescomplemented
490C4×Q8—1062no—
491C4×Q8—2121no—
492C4×D4—1062no—
493C4×D4—1062no—
494C4×D4—2121no—
495C4×D4—2121no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—531no—
498C2×C4⋊C4—531no—
499C2×C4⋊C4—1062no—
500C2×C4⋊C4—1061no—
501C2×C4⋊C4—1061no—
502C2×C4⋊C4—1061no—
503C2×C4⋊C4—2121no—
504C2×C4⋊C4C22×D5311yescharacteristic
505C2×C4⋊C4C22×D5311yescharacteristic
506C2×C4⋊C4C22×D5311yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—531no—
510C2×C22⋊C4—531no—
511C2×C22⋊C4—1061no—
512C2×C22⋊C4—1061no—
513C2×C22⋊C4—1061no—
514C2×C22⋊C4—1061no—
515C2×C22⋊C4—1061no—
516C2×C22⋊C4—1061no—
517C2×C22⋊C4—2124no—
518C2×C42—531no—
519C2×C42—531no—
520C2×C42—1061no—
521C2×C42—1061no—
522#107—1062no—
523#107—2121no—
524#103—22no—
525#103—41no—
526#102—534no—
527#102—534no—
528#102—534no—
529#102—1062no—
530#102—1062no—
531#102—1062no—
532C22⋊C8—534no—
533#97—1062no—
534#97—2121no—
535#95—21no—
536#95—531no—
537#95—531no—
538#95—1061no—
539#95—1061no—
540#95—1061no—
541#95—1061no—
542C24—1061no—
543C24—1064no—
544C24—1061no—
545C24—4241no—
546C24—4241no—
547C24—2122no—
548C24—2122no—
549C24—2122no—
550C24—2122no—
551C24D4×D5311yescharacteristic
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8C2×C4×D5312yes—
558C2×D4—532no—
559C2×D4—532no—
560C2×D4—532no—
561C2×D4—532no—
562C2×D4—1068no—
563C2×D4—1064no—
564C2×D4—1061no—
565C2×D4—1061no—
566C2×D4—1061no—
567C2×D4—1061no—
568C2×D4—1061no—
569C2×D4—1061no—
570C2×D4—1061no—
571C2×D4—1061no—
572C2×D4—2124no—
573C2×D4—2124no—
574C2×D4—2124no—
575C2×D4—2122no—
576C2×D4—2122no—
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—531no—
586C22×C4—531no—
587C22×C4—531no—
588C22×C4—531no—
589C22×C4—1061no—
590C22×C4—1061no—
591C22×C4—4241no—
592C22×C4—4241no—
593C22×C4—4241no—
594C22×C4—2122no—
595C22×C4—2122no—
596C22×C4—2122no—
597C22×C4—2122no—
598C22×C4—2122no—
599C22×C4—2122no—
600C22×C4C2×C4×D5312yes—
601C22×C4D4×D5311yescharacteristic
602C22×C4#1171994712yes—
603C22×C4C23×D5311yescharacteristic
604SD16—1068no—
605SD16—2124no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—44no—
612C2×C8—532no—
613C2×C8—532no—
614C2×C8—1061no—
615C2×C8—1061no—
616C2×C8—1061no—
617C2×C8—1061no—
618C2×C8D4×D5312yes—
619C4⋊C4—24no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—532no—
626C4⋊C4—1061no—
627C4⋊C4—1061no—
628C4⋊C4—1061no—
629C4⋊C4—4241no—
630C4⋊C4—2122no—
631C4⋊C4—2122no—
632C4⋊C4C2×C4×D5312yes—
633C22⋊C4—24no—
634C22⋊C4—42no—
635C22⋊C4—1062no—
636C22⋊C4—1062no—
637C22⋊C4—4241no—
638C22⋊C4—4241no—
639C22⋊C4—2122no—
640C22⋊C4—2122no—
641C22⋊C4—2122no—
642C22⋊C4—2122no—
643C42—1061no—
644C42—1061no—
645C42—1061no—
646C42—1061no—
647C42—4241no—
648C42—2122no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—1062no—
654C23—1062no—
655C23—1062no—
656C23—1062no—
657C23—4244no—
658C23—4244no—
659C23—4244no—
660C23—4244no—
661C23—4244no—
662C23—2128no—
663C23—2121no—
664C23—2121no—
665C23—2121no—
666C23—2121no—
667C23—2128no—
668C23—2121no—
669C23—2121no—
670C23—2121no—
671C23—2121no—
672C23—2121no—
673C23—2121no—
674C23#1313317712yes—
675C23#1313324412yes—
676C23#1313324912yes—
677C23C2×D4×D5311yescharacteristic
678Q8—22no—
679Q8—22no—
680Q8—41no—
681Q8—41no—
682D4—534no—
683D4—1062no—
684D4—1062no—
685D4—1062no—
686D4—1062no—
687D4—1062no—
688D4—2128no—
689D4—2121no—
690D4—2121no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—1061no—
710C2×C4—1061no—
711C2×C4—1061no—
712C2×C4—1061no—
713C2×C4—1061no—
714C2×C4—1061no—
715C2×C4—1061no—
716C2×C4—1061no—
717C2×C4—1061no—
718C2×C4—1061no—
719C2×C4—1062no—
720C2×C4—1061no—
721C2×C4—1061no—
722C2×C4—4244no—
723C2×C4—4244no—
724C2×C4—4244no—
725C2×C4—2121no—
726C2×C4—2121no—
727C2×C4—2121no—
728C2×C4—2121no—
729C2×C4—2121no—
730C2×C4#1313317712yes—
731C2×C4C22×C4×D5311yescharacteristic
732C2×C4C2×D4×D5311yescharacteristic
733C2×C4#41×D5311yescharacteristic
734C2×C4C2×#1171994711yescharacteristic
735C2×C4#1313326211yescharacteristic
736C2×C4#1313326311yescharacteristic
737C8—22no—
738C8—41no—
739C8—1062no—
740C8—1062no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—1064no—
748C22—42416no—
749C22—4241no—
750C22—4241no—
751C22—4241no—
752C22—4241no—
753C22—2122no—
754C22—2122no—
755C22—2122no—
756C22—2122no—
757C22—2122no—
758C22—2122no—
759C22—2122no—
760C22—2122no—
761C22—2122no—
762C22#1681072614yescomplemented
763C22C2×#1313317711yescharacteristic
764C22#1681125711yescharacteristic
765C22#1681126211yescharacteristic
766C22C2×#1313324411yescharacteristic
767C22C2×#1313324911yescharacteristic
768C22#1681142511yescharacteristic
769C22#1681143011yescharacteristic
770C4—22no—
771C4—42no—
772C4—42no—
773C4—81no—
774C4—81no—
775C4—4241no—
776C4—2121no—
777C4—2121no—
778C4—2121no—
779C4—2121no—
780C4—2122no—
781C4C4×D4×D5311yescharacteristic
782C4#1681109511yescharacteristic
783C4#1681126011yescharacteristic
784C4#1681129611yescharacteristic
785C2—24no—
786C2—4242no—
787C2—2124no—
788C2#2027769511yescharacteristic
789C2C2×#1681072611yescharacteristic
790C2#2028355011yescharacteristic
791C2#2028619211yescharacteristic
792C2#2028622211yescharacteristic
793C2#2028674211yescharacteristic
794C2#2028680211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1892C2
socleC23×C53C22×D4
prime radicalC23×D212C22
cosocleC22×C4×C53C24
hypercenter#1892D53
hypocenterC53#22854
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1892

Complements

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

NH ≅ G/Ntype
2. C2×#16810726C2semidirect
4. #20277724C2semidirect
6. #20275593C2semidirect
7. #20275413C2semidirect
8. #20275333C2semidirect
9. #20275068C2semidirect
10. #20275046C2semidirect
11. #20274963C2semidirect
12. #20274902C2semidirect
13. #20274539C2semidirect
14. #20274491C2semidirect
15. C53×#1892C2semidirect
19. C2×Q8×Dic53C22semidirect
24. #16810773C4semidirect
26. C2×#13133150C22semidirect
27. C2×#13133150C22semidirect
36. C2×#13133127C22semidirect
37. C2×#13133127C22semidirect
38. #16810530C22semidirect
42. #16810522C22semidirect
48. C4⋊C4×Dic53C22semidirect
51. #16810385C22semidirect
52. #16810385C22semidirect
53. #16810377C22semidirect
54. #16810377C22semidirect
57. C2×#103×C53C22semidirect
58. C2×#103×C53C22semidirect
60. C53×#340C22semidirect
61. C53×#340C22semidirect
79. C2×#11719924C2×C4semidirect
80. C2×#11719924C2×C4semidirect
115. #13133137C2×C4semidirect
116. #13133137C2×C4semidirect
117. C22⋊#88322C2×C4semidirect
134. C22⋊Q8×C53C2×C4semidirect
350. C22×C53#440semidirect
396. #1892D53semidirect
427. C2×#103C2×D53semidirect
428. C2×#103C2×D53semidirect
455. #340C2×D53semidirect
456. #340C2×D53semidirect
459. C53#22854semidirect
489. C22⋊Q8C4×D53semidirect
762. C22#16810726semidirect

Maximal subgroups

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

subgroupindex
C2×#168107732
C2×#168107262
C22×#131331392
#202777242
#202775352
#202755932
#202754132
#202753332
#202750682
#202750462
#202749632
#202749022
#202745392
#202744912
C53×#18922
#2285453