Finite Group Databasebeta

← #27430929

Subgroups — #27430929

Order 13568.

1318 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810850C211yesmaximal, characteristic, complemented
2C2×#16810774C211yesmaximal, characteristic, complemented
3C2×D4×#88322C211yesmaximal, characteristic, complemented
4C22×#13133138C211yesmaximal, characteristic, complemented
5#20278166C211yesmaximal, characteristic, complemented
6#20276089C211yesmaximal, characteristic, complemented
7#20276032C211yesmaximal, characteristic, complemented
8#20275901C211yesmaximal, characteristic, complemented
9#20275718C211yesmaximal, characteristic, complemented
10#20275568C211yesmaximal, characteristic, complemented
11#20275401C211yesmaximal, characteristic, complemented
12#20275144C211yesmaximal, characteristic, complemented
13#20275136C211yesmaximal, characteristic, complemented
14#20274907C211yesmaximal, characteristic, complemented
15C53×#2408C211yesmaximal, characteristic
16C22×#11719923C2211yescharacteristic
17C22×#11719923C2211yescharacteristic
18C23×#88322C2211yescharacteristic
19C23×#88322C2211yescharacteristic, complemented
20C2×#13133196C2211yescharacteristic
21C2×#13133196C2211yescharacteristic, complemented
22C22×C4⋊Dic53C2211yescharacteristic
23#16810850—24no—
24#16810774—24no—
25D4×#88322—24no—
26C2×#13133148C2211yescharacteristic, complemented
27C2×#13133148C2211yescharacteristic, complemented
28C2×C4⋊#88322C2211yescharacteristic, complemented
29C2×#13133140C2211yescharacteristic, complemented
30C2×#13133140C2211yescharacteristic, complemented
31C2×#13133138—24no—
32C2×#13133138C2211yescharacteristic
33C2×#13133138C2211yescharacteristic
34C2×#13133138C2211yescharacteristic
35C2×#13133138C2211yescharacteristic
36C2×#13133138C2211yescharacteristic
37C2×#13133138C2211yescharacteristic
38C2×C22⋊#88322C2211yescharacteristic
39C2×C22⋊#88322C2211yescharacteristic, complemented
40C2×C4×#88322C2211yescharacteristic, complemented
41#16810556—21no—
42#16810546—21no—
43#16810529C2211yescharacteristic, complemented
44#16810521C2211yescharacteristic, complemented
45#16810503—21no—
46#16810483C2211yescharacteristic, complemented
47#16810481—21no—
48#16810385C2211yescharacteristic, complemented
49#16810385C2211yescharacteristic, complemented
50#16810385C2211yescharacteristic, complemented
51#16810385C2211yescharacteristic, complemented
52C23×D4×C53C2211yescharacteristic
53C2×#121×C53C2211yescharacteristic
54C2×#121×C53C2211yescharacteristic
55C2×#120×C53—21no—
56C2×C4×D4×C53C2211yescharacteristic
57C53×#394—21no—
58C53×#392—21no—
59C53×#390C2211yescharacteristic
60C53×#390C2211yescharacteristic
61C53×#380C2211yescharacteristic
62C53×#379—21no—
63C22×Dic106C2311yescharacteristic
64C23×Dic53—21no—
65C2×#11719923—22no—
66C2×#11719923—22no—
67C2×#11719923—22no—
68C2×#11719923—22no—
69C2×#11719923—41no—
70C2×#11719923—41no—
71C22×#88322—22no—
72C22×#88322—22no—
73C22×#88322—22no—
74C22×#88322—22no—
75C22×#88322—41no—
76C22×#88322—41no—
77C22×#88322C2311yescharacteristic
78C22×#88322C2311yescharacteristic
79C22×#88322C2311yescharacteristic
80C22×#88322C2311yescharacteristic
81#13133196—22no—
82#13133196—22no—
83#13133196—22no—
84#13133196—41no—
85C2×C4⋊Dic53—21no—
86C2×C4⋊Dic53—22no—
87C2×C4⋊Dic53—41no—
88C2×C4⋊Dic53C2311yescharacteristic
89C2×C4⋊Dic53C2311yescharacteristic
90C2×C4⋊Dic53C2311yescharacteristic
91C2×#11719919—21no—
92C2×#11719919—21no—
93C2×#11719919—21no—
94C2×C22⋊Dic53—21no—
95C2×C22⋊Dic53—21no—
96C2×C22⋊Dic53—21no—
97#13133148—22no—
98#13133148—41no—
99C4⋊#88322—22no—
100#13133140—22no—
101#13133140—41no—
102#13133138—22no—
103#13133138—22no—
104#13133138—22no—
105#13133138—22no—
106#13133138—22no—
107#13133138D414yescomplemented
108C22⋊#88322—22no—
109C22⋊#88322D414yescomplemented
110C4×#88322—22no—
111#13133124—21no—
112#13133124—21no—
113#13133124—21no—
114#13133124—21no—
115C25×C53—21no—
116C22×D4×C53—22no—
117C22×D4×C53—22no—
118C22×D4×C53—21no—
119C22×D4×C53—21no—
120C22×D4×C53—22no—
121C22×D4×C53—21no—
122C22×D4×C53—22no—
123C22×D4×C53—41no—
124C22×D4×C53—41no—
125C22×D4×C53D411yescharacteristic
126C22×D4×C53C2311yescharacteristic
127C22×D4×C53C2311yescharacteristic
128C23×C4×C53C2311yescharacteristic
129C23×C4×C53C2311yescharacteristic
130#121×C53—22no—
131#121×C53—22no—
132#121×C53—41no—
133#121×C53—41no—
134#120×C53—44no—
135C4×D4×C53—22no—
136C4×D4×C53—22no—
137C2×C4⋊C4×C53D411yescharacteristic
138C2×C4⋊C4×C53C2311yescharacteristic
139C2×C4⋊C4×C53C2311yescharacteristic
140C2×C22⋊C4×C53—21no—
141C2×C22⋊C4×C53—21no—
142C2×C22⋊C4×C53—21no—
143C2×C22⋊C4×C53—21no—
144C2×C22⋊C4×C53—21no—
145C2×C22⋊C4×C53—21no—
146C2×C22⋊C4×C53—21no—
147C2×C22⋊C4×C53D411yescharacteristic
148C2×C22⋊C4×C53D411yescharacteristic
149C2×C42×C53C2311yescharacteristic
150#95×C53—21no—
151C24×C53—21no—
152C24×C53—21no—
153C24×C53—42no—
154C24×C53—42no—
155C24×C53—42no—
156C24×C53—42no—
157C24×C53—42no—
158C24×C53—81no—
159C24×C53—81no—
160C24×C53C2×D411yescharacteristic
161C24×C53C2×D411yescharacteristic
162C2×D4×C53—22no—
163C2×D4×C53—22no—
164C2×D4×C53—28no—
165C2×D4×C53—21no—
166C2×D4×C53—21no—
167C2×D4×C53—21no—
168C2×D4×C53—21no—
169C2×D4×C53—21no—
170C2×D4×C53—21no—
171C2×D4×C53—21no—
172C2×D4×C53—21no—
173C2×D4×C53—21no—
174C2×D4×C53—21no—
175C2×D4×C53—44no—
176C2×D4×C53—44no—
177C2×D4×C53—42no—
178C2×D4×C53—42no—
179C2×D4×C53—44no—
180C2×D4×C53—42no—
181C2×D4×C53—42no—
182C2×D4×C53—42no—
183C2×D4×C53—42no—
184C2×D4×C53—42no—
185C2×D4×C53—81no—
186C2×D4×C53—81no—
187C2×D4×C53SD1614yescomplemented
188C2×D4×C53C2×D412yes—
189C2×D4×C53#4112yes—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53C2×D411yescharacteristic
203C22×C4×C53C2×D411yescharacteristic
204C22×C4×C53C2×D411yescharacteristic
205C22×C4×C53C2×D412yes—
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53#4112yes—
208C22×C4×C53C2411yescharacteristic
209C22×Dic53—21no—
210C22×Dic53—21no—
211C22×Dic53—21no—
212C22×Dic53—21no—
213C22×Dic53—42no—
214C22×Dic53—42no—
215C22×Dic53—81no—
216C2×Dic106—21no—
217C2×Dic106—21no—
218C2×Dic106—21no—
219C2×Dic106—21no—
220C2×Dic106—21no—
221C2×Dic106—21no—
222C4⋊C4×C53—22no—
223C4⋊C4×C53—21no—
224C4⋊C4×C53—21no—
225C4⋊C4×C53—21no—
226C4⋊C4×C53—21no—
227C22⋊C4×C53—22no—
228C22⋊C4×C53—22no—
229C22⋊C4×C53—42no—
230C22⋊C4×C53—42no—
231C22⋊C4×C53—42no—
232C22⋊C4×C53—42no—
233C22⋊C4×C53—42no—
234C22⋊C4×C53—81no—
235C22⋊C4×C53—81no—
236C42×C53—21no—
237C42×C53—21no—
238C22⋊Dic53—42no—
239C22⋊Dic53—42no—
240C22⋊Dic53—81no—
241#11719923—44no—
242#11719923—44no—
243C4⋊Dic53—21no—
244C4⋊Dic53—21no—
245C4⋊Dic53—21no—
246C4⋊Dic53—21no—
247C4⋊Dic53—21no—
248C4⋊Dic53—42no—
249C4⋊Dic53C2×D412yes—
250#11719919—42no—
251#11719919—42no—
252#11719919—81no—
253C2×#88322—21no—
254C2×#88322—21no—
255C2×#88322—21no—
256C2×#88322—21no—
257C2×#88322—21no—
258C2×#88322—21no—
259C2×#88322—21no—
260C2×#88322—21no—
261C2×#88322—21no—
262C2×#88322—44no—
263C2×#88322—44no—
264C2×#88322C2×D412yes—
265C2×#88322C2×D412yes—
266C2×#88322C2×D412yes—
267C23×C53—21no—
268C23×C53—21no—
269C23×C53—21no—
270C23×C53—21no—
271C23×C53—21no—
272C23×C53—21no—
273C23×C53—21no—
274C23×C53—21no—
275C23×C53—21no—
276C23×C53—21no—
277C23×C53—22no—
278C23×C53—22no—
279C23×C53—48no—
280C23×C53—41no—
281C23×C53—41no—
282C23×C53—41no—
283C23×C53—41no—
284C23×C53—41no—
285C23×C53—41no—
286C23×C53—41no—
287C23×C53—41no—
288C23×C53—41no—
289C23×C53—41no—
290C23×C53—41no—
291C23×C53—41no—
292C23×C53—84no—
293C23×C53—84no—
294C23×C53—84no—
295C23×C53—84no—
296C23×C53—84no—
297C23×C53—84no—
298C23×C53#12112yes—
299C23×C53C2×SD1612yes—
300C23×C53C2×SD1612yes—
301C23×C53#13512yes—
302C23×C53C22×D411yescharacteristic
303D4×C53—28no—
304D4×C53—22no—
305D4×C53—22no—
306D4×C53—22no—
307D4×C53—22no—
308D4×C53—48no—
309D4×C53—41no—
310D4×C53—41no—
311D4×C53—41no—
312D4×C53—41no—
313D4×C53—84no—
314D4×C53—84no—
315C2×C4×C53—21no—
316C2×C4×C53—21no—
317C2×C4×C53—21no—
318C2×C4×C53—21no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—22no—
322C2×C4×C53—22no—
323C2×C4×C53—21no—
324C2×C4×C53—21no—
325C2×C4×C53—21no—
326C2×C4×C53—21no—
327C2×C4×C53—21no—
328C2×C4×C53—21no—
329C2×C4×C53—41no—
330C2×C4×C53—41no—
331C2×C4×C53—41no—
332C2×C4×C53—41no—
333C2×C4×C53—41no—
334C2×C4×C53—41no—
335C2×C4×C53—41no—
336C2×C4×C53—41no—
337C2×C4×C53—41no—
338C2×C4×C53—41no—
339C2×C4×C53#12112yes—
340C2×C4×C53C2×SD1612yes—
341C2×C4×C53C22×D411yescharacteristic
342C2×C4×C53C22×D411yescharacteristic
343C2×C4×C53C2×#4111yescharacteristic
344C2×C4×C53C2×#4111yescharacteristic
345C2×C4×C53H(5,𝔽2)11yescharacteristic
346C2×C4×C53H(5,𝔽2)11yescharacteristic
347C2×Dic53—22no—
348C2×Dic53—41no—
349C2×Dic53—41no—
350C2×Dic53—41no—
351C2×Dic53—41no—
352C2×Dic53—41no—
353C2×Dic53—41no—
354C2×Dic53—41no—
355C2×Dic53—41no—
356C2×Dic53—41no—
357C2×Dic53—41no—
358C2×Dic53—41no—
359C2×Dic53—84no—
360Dic106—41no—
361Dic106—41no—
362Dic106—41no—
363Dic106—41no—
364#88322—22no—
365#88322—22no—
366#88322—22no—
367#88322—41no—
368#25112—531nomaximal, Sylow
369C22×C53—22no—
370C22×C53—22no—
371C22×C53—22no—
372C22×C53—22no—
373C22×C53—22no—
374C22×C53—22no—
375C22×C53—22no—
376C22×C53—22no—
377C22×C53—22no—
378C22×C53—41no—
379C22×C53—41no—
380C22×C53—41no—
381C22×C53—41no—
382C22×C53—42no—
383C22×C53—42no—
384C22×C53—42no—
385C22×C53—42no—
386C22×C53—42no—
387C22×C53—42no—
388C22×C53—816no—
389C22×C53—81no—
390C22×C53—81no—
391C22×C53—81no—
392C22×C53—81no—
393C22×C53—81no—
394C22×C53—81no—
395C22×C53—81no—
396C22×C53—81no—
397C22×C53#46514yescomplemented
398C22×C53C2×#12111yescharacteristic
399C22×C53D4211yescharacteristic
400C22×C53#54611yescharacteristic
401C22×C53C22×SD1611yescharacteristic
402C22×C53C2×#13511yescharacteristic
403C22×C53#57611yescharacteristic
404C22×C53#57711yescharacteristic
405C4×C53—22no—
406C4×C53—22no—
407C4×C53—41no—
408C4×C53—41no—
409C4×C53—81no—
410C4×C53—81no—
411C4×C53#52511yescharacteristic
412C4×C53#53811yescharacteristic
413C4×C53D4211yescharacteristic
414C4×C53#54611yescharacteristic
415Dic53—42no—
416Dic53—81no—
417Dic53—81no—
418Dic53—81no—
419C2×#465—531no—
420C2×#450—531no—
421C2×C8×D4—531no—
422C22×#102—531no—
423#2417—531no—
424#2408D5311yescharacteristic
425#2065—531no—
426#2055—531no—
427#2034—531no—
428#2000—531no—
429#1968—531no—
430#1934—531no—
431#1893—531no—
432#1892—531no—
433#1853—531no—
434C2×C53—24no—
435C2×C53—42no—
436C2×C53—82no—
437C2×C53—82no—
438C2×C53#242411yescharacteristic
439C2×C53C2×#46511yescharacteristic
440C2×C53#306211yescharacteristic
441C2×C53#328011yescharacteristic
442C2×C53D4×SD1611yescharacteristic
443C2×C53#329511yescharacteristic
444C2×C53#329611yescharacteristic
445C23×D4C2×D5311yescharacteristic
446C22×SD16—531no—
447C22×SD16—531no—
448C23×C8—531no—
449C23×C8—531no—
450C2×C22⋊Q8—531no—
451C2×C22⋊Q8—531no—
452C2×#121C2×D5311yescharacteristic
453C2×#121C2×D5311yescharacteristic
454C2×#120—21no—
455C2×C4×D4C2×D5311yescharacteristic
456C22×C4⋊C4—531no—
457#465—1064no—
458#450—1064no—
459C8×D4—1064no—
460C2×#106—531no—
461C2×#106—531no—
462C2×C4⋊C8—531no—
463C2×#103—531no—
464C2×#103—531no—
465C2×#102—531no—
466C2×#102—531no—
467C2×#102—531no—
468C2×#102—531no—
469C2×#102—531no—
470C2×#102—531no—
471C2×#102—1064no—
472C2×C22⋊C8—531no—
473C2×C22⋊C8—531no—
474C2×C4×C8—531no—
475#398—1061no—
476#396—1061no—
477#394—21no—
478#392—21no—
479#391—531no—
480#390C2×D5311yescharacteristic
481#390C2×D5311yescharacteristic
482#389—531no—
483#386—1061no—
484#380—531no—
485#380—1061no—
486#380C2×D5311yescharacteristic
487#379—21no—
488#340—531no—
489#340—531no—
490#340—531no—
491#340—531no—
492C53#2511211yescharacteristic, complemented, Sylow
493C25—21no—
494C22×Q8—531no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—22no—
500C22×D4—22no—
501C22×D4—21no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4C22⋊D5311yescharacteristic
505C22×D4C22×D5311yescharacteristic
506C22×D4C22×D5311yescharacteristic
507C23×C4—1061no—
508C23×C4C22×D5311yescharacteristic
509C23×C4C22×D5311yescharacteristic
510C2×SD16—1062no—
511C2×SD16—1062no—
512C2×SD16—1062no—
513C2×SD16—1062no—
514C2×SD16—2121no—
515C2×SD16—2121no—
516C22×C8—531no—
517C22×C8—531no—
518C22×C8—531no—
519C22×C8—531no—
520C22×C8—1062no—
521C22×C8—1062no—
522C22×C8—1062no—
523C22×C8—1062no—
524C22×C8—2121no—
525C22×C8—2121no—
526C22⋊Q8—1062no—
527C22⋊Q8—1062no—
528C22⋊Q8—1062no—
529C22⋊Q8—2121no—
530#121—22no—
531#121—22no—
532#121—41no—
533#121—41no—
534#120—44no—
535C4×D4—22no—
536C4×D4—22no—
537C2×C4⋊C4—531no—
538C2×C4⋊C4—531no—
539C2×C4⋊C4—531no—
540C2×C4⋊C4—1062no—
541C2×C4⋊C4—1061no—
542C2×C4⋊C4—1061no—
543C2×C4⋊C4—1061no—
544C2×C4⋊C4—1061no—
545C2×C4⋊C4—2121no—
546C2×C4⋊C4C22⋊D5311yescharacteristic
547C2×C4⋊C4C22×D5311yescharacteristic
548C2×C4⋊C4C22×D5311yescharacteristic
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—1061no—
557C2×C22⋊C4—1061no—
558C2×C22⋊C4—1061no—
559C2×C22⋊C4C22⋊D5311yescharacteristic
560C2×C22⋊C4C22⋊D5311yescharacteristic
561C2×C42C22×D5311yescharacteristic
562#106—1062no—
563#106—2121no—
564C4⋊C8—1062no—
565#103—1062no—
566#103—2121no—
567#102—534no—
568#102—1062no—
569#102—1062no—
570#102—1062no—
571#102—1062no—
572#102—1062no—
573C22⋊C8—534no—
574C22⋊C8—1062no—
575C4×C8—1062no—
576#95—21no—
577#95—1061no—
578#95—1061no—
579#95—1061no—
580#95—1061no—
581C24—21no—
582C24—21no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—42no—
588C24—81no—
589C24—81no—
590C24C2×C22⋊D5311yescharacteristic
591C24C2×C22⋊D5311yescharacteristic
592C2×Q8—1061no—
593C2×Q8—1061no—
594C2×Q8—1061no—
595C2×Q8—1061no—
596C2×Q8—1061no—
597C2×Q8—1061no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—28no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—44no—
612C2×D4—44no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—44no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4—81no—
622C2×D4—81no—
623C2×D4#1171992314yescomplemented
624C2×D4D4×D5312yes—
625C2×D4#1171994712yes—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—1061no—
639C22×C4—1061no—
640C22×C4—1061no—
641C22×C4—1061no—
642C22×C4—4241no—
643C22×C4—2122no—
644C22×C4—2122no—
645C22×C4D4×D5312yes—
646C22×C4#1171994712yes—
647C22×C4C2×C22⋊D5311yescharacteristic
648C22×C4C2×C22⋊D5311yescharacteristic
649C22×C4C2×C22⋊D5311yescharacteristic
650C22×C4C2×C22⋊D5311yescharacteristic
651C22×C4C23×D5311yescharacteristic
652SD16—2124no—
653SD16—2124no—
654C2×C8—532no—
655C2×C8—532no—
656C2×C8—532no—
657C2×C8—1061no—
658C2×C8—1061no—
659C2×C8—1061no—
660C2×C8—1061no—
661C2×C8—1061no—
662C2×C8—1061no—
663C2×C8—1061no—
664C2×C8—1061no—
665C2×C8—1061no—
666C2×C8—2124no—
667C2×C8—2124no—
668C4⋊C4—22no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—532no—
674C4⋊C4—1061no—
675C4⋊C4—1061no—
676C4⋊C4—1061no—
677C4⋊C4—1061no—
678C4⋊C4—1061no—
679C4⋊C4—4241no—
680C4⋊C4—2122no—
681C4⋊C4—2122no—
682C4⋊C4—2122no—
683C22⋊C4—22no—
684C22⋊C4—22no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—42no—
690C22⋊C4—81no—
691C22⋊C4—81no—
692C22⋊C4—4241no—
693C22⋊C4—2122no—
694C22⋊C4—2122no—
695C42—21no—
696C42—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—22no—
708C23—22no—
709C23—48no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—84no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23#1313318912yes—
729C23C2×#1171992312yes—
730C23C2×#1171992312yes—
731C23#1313323712yes—
732C23C22×C22⋊D5311yescharacteristic
733Q8—2121no—
734Q8—2121no—
735Q8—2121no—
736Q8—2121no—
737D4—28no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—48no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—84no—
748D4—84no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—1062no—
774C2×C4—4244no—
775C2×C4—2121no—
776C2×C4—2121no—
777C2×C4—2121no—
778C2×C4—2121no—
779C2×C4—2121no—
780C2×C4—2121no—
781C2×C4—2121no—
782C2×C4—2121no—
783C2×C4—2121no—
784C2×C4—2121no—
785C2×C4—2121no—
786C2×C4#1313318912yes—
787C2×C4C2×#1171992312yes—
788C2×C4C2×D4×D5311yescharacteristic
789C2×C4C2×D4×D5311yescharacteristic
790C2×C4C2×#1171994711yescharacteristic
791C2×C4C2×#1171994711yescharacteristic
792C2×C4#1313326211yescharacteristic
793C2×C4#1313326211yescharacteristic
794C8—1062no—
795C8—1062no—
796C8—1062no—
797C8—2121no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—816no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22#1681085014yescomplemented
827C22C2×#1313318911yescharacteristic
828C22D4×C22⋊D5311yescharacteristic
829C22#1681126711yescharacteristic
830C22C22×#1171992311yescharacteristic
831C22C2×#1313323711yescharacteristic
832C22#1681142611yescharacteristic
833C22#1681143411yescharacteristic
834C4—22no—
835C4—22no—
836C4—41no—
837C4—41no—
838C4—81no—
839C4—81no—
840C4—4241no—
841C4—4241no—
842C4—4241no—
843C4—2122no—
844C4#1681112911yescharacteristic
845C4#1681120811yescharacteristic
846C4#1681125511yescharacteristic
847C4#1681126011yescharacteristic
848C2—24no—
849C2—42no—
850C2—82no—
851C2—82no—
852C2#2027825511yescharacteristic
853C2C2×#1681085011yescharacteristic
854C2#2028439111yescharacteristic
855C2#2028639611yescharacteristic
856C2D4×#1171992311yescharacteristic
857C2#2028653911yescharacteristic
858C2#2028655011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
Fitting, prime radicalC53×#2408C2
socleC23×C53C22×D4
hypercenter#2408D53
hypocenterC53#25112
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2408

Complements

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

NH ≅ G/Ntype
1. C2×#16810850C2semidirect
2. C2×#16810774C2semidirect
3. C2×D4×#88322C2semidirect
4. C22×#13133138C2semidirect
5. #20278166C2semidirect
6. #20276089C2semidirect
7. #20276032C2semidirect
8. #20275901C2semidirect
9. #20275718C2semidirect
10. #20275568C2semidirect
11. #20275401C2semidirect
12. #20275144C2semidirect
13. #20275136C2semidirect
14. #20274907C2semidirect
19. C23×#88322C22semidirect
21. C2×#13133196C22semidirect
26. C2×#13133148C22semidirect
27. C2×#13133148C22semidirect
28. C2×C4⋊#88322C22semidirect
29. C2×#13133140C22semidirect
30. C2×#13133140C22semidirect
39. C2×C22⋊#88322C22semidirect
40. C2×C4×#88322C22semidirect
43. #16810529C22semidirect
44. #16810521C22semidirect
46. #16810483C22semidirect
48. #16810385C22semidirect
49. #16810385C22semidirect
50. #16810385C22semidirect
51. #16810385C22semidirect
107. #13133138D4semidirect
109. C22⋊#88322D4semidirect
187. C2×D4×C53SD16semidirect
397. C22×C53#465semidirect
492. C53#25112semidirect
623. C2×D4#11719923semidirect
826. C22#16810850semidirect

Maximal subgroups

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

subgroupindex
C2×#168108502
C2×#168107742
C2×D4×#883222
C22×#131331382
#202781662
#202760892
#202760322
#202759012
#202757182
#202755682
#202754012
#202751442
#202751362
#202749072
C53×#24082
#2511253