Finite Group Databasebeta

← #27404840

Subgroups — #27404840

Order 13568.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20283933C211yesmaximal, characteristic
2C2×#16810743C211yesmaximal, characteristic, complemented
3#20283436C211yesmaximal, characteristic, complemented
4C2×#16810640C211yesmaximal, characteristic, complemented
5#20275602C211yesmaximal, characteristic, complemented
6#20275429C211yesmaximal, characteristic, complemented
7#20275360C211yesmaximal, characteristic, complemented
8#20275161C211yesmaximal, characteristic, complemented
9#20275045C211yesmaximal, characteristic, complemented
10#20275042C211yesmaximal, characteristic, complemented
11#20274990C211yesmaximal, characteristic, complemented
12#20274919C211yesmaximal, characteristic, complemented
13#20274550C211yesmaximal, characteristic, complemented
14#20274483C211yesmaximal, characteristic, complemented
15C53×#2880C211yesmaximal, characteristic, complemented
16C2×#13133237C2211yescharacteristic
17C2×#13133237C2211yescharacteristic
18C2×#13133223C2211yescharacteristic, complemented
19C22×#11719917C2211yescharacteristic
20#16811134C2211yescharacteristic
21C2×#13133176C2211yescharacteristic
22#16810785C411yescharacteristic, complemented
23#16810785C411yescharacteristic, complemented
24#16810779C411yescharacteristic, complemented
25#16810774C411yescharacteristic, complemented
26#16810768C411yescharacteristic, complemented
27#16810768C411yescharacteristic, complemented
28#16810762C411yescharacteristic, complemented
29#16810757C411yescharacteristic, complemented
30#16810743—24no—
31#16810698—21no—
32#16810697—21no—
33#16810691—21no—
34#16810686—21no—
35C2×#13133152C2211yescharacteristic, complemented
36C2×#13133152C2211yescharacteristic, complemented
37#16810649C2211yescharacteristic, complemented
38#16810640—24no—
39C2×#13133144C2211yescharacteristic
40C2×#13133144C2211yescharacteristic
41C2×#13133144C2211yescharacteristic
42C2×#13133144C2211yescharacteristic
43C2×#13133143C2211yescharacteristic, complemented
44C2×#13133143C2211yescharacteristic, complemented
45#16810619C2211yescharacteristic
46#16810619C2211yescharacteristic
47#16810589C2211yescharacteristic, complemented
48C2×C22⋊#88322C2211yescharacteristic
49#16810578C2211yescharacteristic, complemented
50C2×#13133127C2211yescharacteristic, complemented
51C2×C8×Dic53C2211yescharacteristic, complemented
52#16810387C2211yescharacteristic, complemented
53#16810387C2211yescharacteristic, complemented
54#16810384C2211yescharacteristic, complemented
55#16810384C2211yescharacteristic, complemented
56#16810377C2211yescharacteristic, complemented
57#16810377C2211yescharacteristic, complemented
58C22×#41×C53C2211yescharacteristic
59C2×#131×C53C2211yescharacteristic
60C2×#131×C53C2211yescharacteristic
61C53×#408—21no—
62C53×#408—21no—
63C53×#408C2211yescharacteristic
64C53×#408C2211yescharacteristic
65C53×#407—21no—
66C53×#407C2211yescharacteristic
67C2×C22⋊C8×C53—21no—
68C2×C22⋊C8×C53C2211yescharacteristic
69C2×#11719945C2311yescharacteristic
70#13133237—22no—
71#13133237—22no—
72#13133237—41no—
73#13133237—41no—
74C2×#11719925C2×C411yescharacteristic
75C2×#11719925C2×C411yescharacteristic
76C2×#11719923C2×C411yescharacteristic
77C2×#11719923C2×C411yescharacteristic
78C2×#11719924C2×C411yescharacteristic
79C2×#11719924C2×C411yescharacteristic
80C2×#11719922C2×C411yescharacteristic
81C2×#11719922C2×C411yescharacteristic
82#13133223—22no—
83#13133223—41no—
84C2×#11719917—22no—
85C2×#11719917—21no—
86C2×#11719917—41no—
87C2×#11719917C2311yescharacteristic
88C2×#11719917C2311yescharacteristic
89C2×#11719912—21no—
90C22×#88322—21no—
91C22×#88322C2311yescharacteristic
92C22×#88322C2311yescharacteristic
93C2×C8×D53—21no—
94#13133200—21no—
95#13133196C2×C411yescharacteristic
96#13133196C2×C411yescharacteristic
97#13133191C2×C411yescharacteristic
98#13133191C2×C411yescharacteristic
99#13133186—21no—
100C4×C22⋊D53—21no—
101C4×C22⋊D53—21no—
102#13133176—22no—
103#13133176—41no—
104#13133176C2311yescharacteristic
105C2×C4⋊Dic53—21no—
106C2×C22⋊Dic53—21no—
107C2×C4×Dic53C2311yescharacteristic
108C2×C4×Dic53C2311yescharacteristic
109#13133152—22no—
110#13133152—41no—
111#13133146—21no—
112#13133146—21no—
113#13133144—22no—
114#13133144—22no—
115#13133144—22no—
116#13133144D414yescomplemented
117#13133143—22no—
118#13133143—41no—
119#13133141C2×C411yescharacteristic
120#13133141C2×C411yescharacteristic
121#13133141C2×C411yescharacteristic
122#13133141C2×C411yescharacteristic
123#13133138C2×C411yescharacteristic
124#13133138C2×C411yescharacteristic
125#13133138C2×C411yescharacteristic
126#13133138C2×C411yescharacteristic
127C22⋊#88322C2×C411yescharacteristic
128C22⋊#88322C2×C411yescharacteristic
129C22⋊#88322C2×C411yescharacteristic
130C22⋊#88322C2×C411yescharacteristic
131#13133129—21no—
132#13133129—21no—
133#13133127—21no—
134#13133127—22no—
135C8×Dic53—21no—
136C8×Dic53—41no—
137C2×#41×C53—21no—
138C2×#41×C53—21no—
139C2×#41×C53—22no—
140C2×#41×C53—22no—
141C2×#41×C53—41no—
142C2×#41×C53—41no—
143C2×#41×C53C2×C411yescharacteristic
144C2×#41×C53C2×C411yescharacteristic
145C2×#41×C53C2311yescharacteristic
146C2×#41×C53C2311yescharacteristic
147C22×Q8×C53C2×C411yescharacteristic
148C22×D4×C53—21no—
149C22×D4×C53C2×C411yescharacteristic
150C23×C4×C53—21no—
151C23×C4×C53C2311yescharacteristic
152#131×C53—22no—
153#131×C53—22no—
154#131×C53—41no—
155#131×C53—41no—
156C2×M16×C53—21no—
157C2×M16×C53—21no—
158C2×M16×C53C2311yescharacteristic
159C2×M16×C53C2311yescharacteristic
160C22×C8×C53—21no—
161C22×C8×C53—21no—
162C22×C8×C53C2311yescharacteristic
163C22×C8×C53C2311yescharacteristic
164C22⋊C8×C53—21no—
165C22⋊C8×C53—21no—
166C22⋊C8×C53—21no—
167C22⋊C8×C53—21no—
168C22⋊C8×C53—21no—
169C22⋊C8×C53—21no—
170C22⋊C8×C53D411yescharacteristic
171C22⋊C8×C53D411yescharacteristic
172C22⋊C8×C53D411yescharacteristic
173C22⋊C8×C53D411yescharacteristic
174C24×C53—21no—
175C24×C53#4111yescharacteristic
176#41×C53—21no—
177#41×C53—21no—
178#41×C53—22no—
179#41×C53—22no—
180#41×C53—21no—
181#41×C53—21no—
182#41×C53—21no—
183#41×C53—21no—
184#41×C53—42no—
185#41×C53—42no—
186#41×C53—41no—
187#41×C53—41no—
188#41×C53—42no—
189#41×C53—42no—
190#41×C53C2×D412yes—
191#41×C53#4112yes—
192C2×Q8×C53—21no—
193C2×Q8×C53—22no—
194C2×Q8×C53—41no—
195C2×Q8×C53C22×C411yescharacteristic
196C2×Q8×C53C22×C411yescharacteristic
197C2×D4×C53—21no—
198C2×D4×C53—22no—
199C2×D4×C53—21no—
200C2×D4×C53—21no—
201C2×D4×C53—21no—
202C2×D4×C53—21no—
203C2×D4×C53—41no—
204C2×D4×C53—42no—
205C2×D4×C53—42no—
206C2×D4×C53C22×C411yescharacteristic
207C2×D4×C53C22×C411yescharacteristic
208C22×C4×C53—21no—
209C22×C4×C53—21no—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53—21no—
214C22×C4×C53—21no—
215C22×C4×C53—21no—
216C22×C4×C53—21no—
217C22×C4×C53—42no—
218C22×C4×C53—42no—
219C22×C4×C53C22×C411yescharacteristic
220C22×C4×C53C22×C411yescharacteristic
221C22×C4×C53C2×D411yescharacteristic
222C22×C4×C53C2×D411yescharacteristic
223C22×C4×C53#4111yescharacteristic
224C22×C4×C53C2411yescharacteristic
225C2×C22⋊D53—21no—
226C2×C22⋊D53—21no—
227C2×C22⋊D53—21no—
228C22×Dic53—21no—
229C22×Dic53—21no—
230#11719945—21no—
231#11719945—21no—
232#11719945—21no—
233#11719945—21no—
234C2×D212C22×C411yescharacteristic
235C2×C4×D53—21no—
236C2×Dic106C22×C411yescharacteristic
237M16×C53—21no—
238M16×C53—21no—
239M16×C53—21no—
240M16×C53—21no—
241M16×C53—42no—
242M16×C53—42no—
243C2×C8×C53—21no—
244C2×C8×C53—21no—
245C2×C8×C53—21no—
246C2×C8×C53—21no—
247C2×C8×C53—21no—
248C2×C8×C53—21no—
249C2×C8×C53—42no—
250C2×C8×C53—42no—
251C2×C8×C53C2×D411yescharacteristic
252C2×C8×C53C2×D411yescharacteristic
253C2×C8×C53C2×D411yescharacteristic
254C2×C8×C53C2×D411yescharacteristic
255C22⋊Dic53—21no—
256C22⋊Dic53—21no—
257C22⋊Dic53—21no—
258C22⋊Dic53—42no—
259#11719925—22no—
260#11719925—41no—
261#11719924—22no—
262#11719924—41no—
263#11719923—22no—
264#11719923—41no—
265#11719922—22no—
266#11719922—41no—
267#11719921—21no—
268#11719921—21no—
269C4⋊Dic53—42no—
270C4⋊Dic53C22×C411yescharacteristic
271C4⋊Dic53C22×C411yescharacteristic
272#11719919—21no—
273#11719919—21no—
274C4×Dic53—21no—
275C4×Dic53—21no—
276C4×Dic53—21no—
277C4×Dic53—21no—
278C4×Dic53C2×D412yes—
279#11719917—21no—
280#11719917—21no—
281#11719917—21no—
282#11719917—42no—
283#11719917C2×D412yes—
284C2×#88322—21no—
285C2×#88322—21no—
286C2×#88322—21no—
287C2×#88322—21no—
288C2×#88322—21no—
289C2×#88322—21no—
290C2×#88322—42no—
291C2×#88322C22×C411yescharacteristic
292C2×#88322C22×C411yescharacteristic
293C2×#88322C22×C411yescharacteristic
294C2×#88322C22×C411yescharacteristic
295#11719912—42no—
296C8×D53—42no—
297C23×C53—21no—
298C23×C53—21no—
299C23×C53—21no—
300C23×C53—21no—
301C23×C53—41no—
302C23×C53—41no—
303C23×C53—42no—
304C23×C53—42no—
305C23×C53—81no—
306C23×C53C4×D411yescharacteristic
307C23×C53C4×D411yescharacteristic
308C23×C53C2×#4111yescharacteristic
309C22×D53—21no—
310Q8×C53—21no—
311Q8×C53—21no—
312Q8×C53—21no—
313Q8×C53—42no—
314Q8×C53C4×D412yes—
315D4×C53—22no—
316D4×C53—22no—
317D4×C53—21no—
318D4×C53—21no—
319D4×C53—21no—
320D4×C53—42no—
321D4×C53—42no—
322D4×C53—42no—
323D4×C53—41no—
324D4×C53—41no—
325D4×C53C4×D412yes—
326C2×C4×C53—21no—
327C2×C4×C53—21no—
328C2×C4×C53—21no—
329C2×C4×C53—21no—
330C2×C4×C53—21no—
331C2×C4×C53—21no—
332C2×C4×C53—21no—
333C2×C4×C53—21no—
334C2×C4×C53—21no—
335C2×C4×C53—22no—
336C2×C4×C53—21no—
337C2×C4×C53—21no—
338C2×C4×C53—22no—
339C2×C4×C53—21no—
340C2×C4×C53—42no—
341C2×C4×C53—42no—
342C2×C4×C53—42no—
343C2×C4×C53—41no—
344C2×C4×C53—41no—
345C2×C4×C53C4×D411yescharacteristic
346C2×C4×C53C4×D411yescharacteristic
347C2×C4×C53C23×C411yescharacteristic
348C2×C4×C53C22×D411yescharacteristic
349C2×C4×C53C22×D411yescharacteristic
350C2×C4×C53C2×#4111yescharacteristic
351C2×C4×C53H(5,𝔽2)11yescharacteristic
352C2×C4×C53H(5,𝔽2)11yescharacteristic
353C22⋊D53—42no—
354C22⋊D53—41no—
355C22⋊D53—41no—
356C22⋊D53—81no—
357C2×Dic53—21no—
358C2×Dic53—21no—
359C2×Dic53—21no—
360C2×Dic53—22no—
361C2×Dic53—41no—
362C2×Dic53—41no—
363C2×Dic53—41no—
364C2×Dic53—41no—
365C2×Dic53—41no—
366D212—21no—
367D212—21no—
368C4×D53—41no—
369C4×D53—41no—
370Dic106—21no—
371Dic106—21no—
372C8×C53—21no—
373C8×C53—21no—
374C8×C53—21no—
375C8×C53—21no—
376C8×C53—41no—
377C8×C53—41no—
378#88322—21no—
379#88322—21no—
380#88322—21no—
381#88322—21no—
382#88322—22no—
383#88322—41no—
384#22887—531nomaximal, Sylow
385C22×C53—21no—
386C22×C53—21no—
387C22×C53—21no—
388C22×C53—21no—
389C22×C53—22no—
390C22×C53—21no—
391C22×C53—21no—
392C22×C53—21no—
393C22×C53—21no—
394C22×C53—41no—
395C22×C53—41no—
396C22×C53—41no—
397C22×C53—41no—
398C22×C53—41no—
399C22×C53—81no—
400C22×C53—81no—
401C22×C53—84no—
402C22×C53C2×C4×D411yescharacteristic
403C22×C53#54611yescharacteristic
404C22×C53#55111yescharacteristic
405C2×D53—41no—
406C2×D53—41no—
407C2×D53—41no—
408C4×C53—21no—
409C4×C53—21no—
410C4×C53—22no—
411C4×C53—41no—
412C4×C53C2×C4×D411yescharacteristic
413C4×C53#51811yescharacteristic
414C4×C53D4211yescharacteristic
415C4×C53#54611yescharacteristic
416Dic53—42no—
417Dic53—41no—
418Dic53—41no—
419Dic53—41no—
420Dic53—81no—
421#3002—531no—
422C2×#444—531no—
423#2933—531no—
424C2×#421—531no—
425#2880D5311yescharacteristic, complemented
426#1974—531no—
427#1938—531no—
428#1929—531no—
429#1897—531no—
430#1876—531no—
431#1876—531no—
432#1866—531no—
433#1855—531no—
434#1764—531no—
435#1750—531no—
436C2×C53—21no—
437C2×C53—21no—
438C2×C53—41no—
439C2×C53—41no—
440C2×C53—42no—
441C2×C53—81no—
442C2×C53#235811yescharacteristic
443C2×C53#295511yescharacteristic
444C2×C53#295711yescharacteristic
445D53—81no—
446C22×#41C2×D5311yescharacteristic
447C2×#135—531no—
448C2×#135—531no—
449C2×#131—531no—
450C2×#131C2×D5311yescharacteristic
451C2×#131C2×D5311yescharacteristic
452C22×M16—531no—
453#525—531no—
454C2×#117—531no—
455#452—531no—
456#452—531no—
457#451—531no—
458#450—531no—
459#449—531no—
460#449—531no—
461#448—531no—
462#447—531no—
463#444—1064no—
464#436—1061no—
465#435—1061no—
466#435—1061no—
467C8×D4—1061no—
468C2×#108—531no—
469C2×#108—531no—
470#424—531no—
471#421—1064no—
472C2×#104—531no—
473C2×#104—531no—
474C2×#104—531no—
475C2×#104—531no—
476C2×#104—531no—
477C2×#104—531no—
478#416—531no—
479#416—531no—
480#408—21no—
481#408—21no—
482#408—531no—
483#408C2×D5311yescharacteristic
484#408C2×D5311yescharacteristic
485#407—21no—
486#407C2×D5311yescharacteristic
487C2×C22⋊C8—21no—
488C2×C22⋊C8—531no—
489C2×C22⋊C8C2×D5311yescharacteristic
490#405—531no—
491C2×#97—531no—
492C2×C4×C8—531no—
493#341—531no—
494#341—531no—
495#339—531no—
496#339—531no—
497#336—531no—
498#336—531no—
499C53#2288711yescharacteristic, complemented, Sylow
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—531no—
507C2×#41C4×D5311yescharacteristic
508C2×#41C4×D5311yescharacteristic
509C2×#41C22×D5311yescharacteristic
510C2×#41C22×D5311yescharacteristic
511C22×Q8C4×D5311yescharacteristic
512C22×D4—21no—
513C22×D4C4×D5311yescharacteristic
514C23×C4—21no—
515C23×C4C22×D5311yescharacteristic
516#135—1062no—
517#135—1062no—
518#135—2121no—
519#135—2121no—
520C2×Q16—531no—
521C2×Q16—531no—
522C2×SD16—531no—
523C2×SD16—531no—
524C2×SD16—531no—
525C2×SD16—531no—
526C2×D8—531no—
527C2×D8—531no—
528#131—22no—
529#131—22no—
530#131—41no—
531#131—41no—
532#131—1062no—
533#131—2121no—
534C2×M16—21no—
535C2×M16—21no—
536C2×M16—531no—
537C2×M16—531no—
538C2×M16—1061no—
539C2×M16—1061no—
540C2×M16—1062no—
541C2×M16—2121no—
542C2×M16C22×D5311yescharacteristic
543C2×M16C22×D5311yescharacteristic
544C22×C8—21no—
545C22×C8—21no—
546C22×C8—531no—
547C22×C8—531no—
548C22×C8—1061no—
549C22×C8—1061no—
550C22×C8C22×D5311yescharacteristic
551C22×C8C22×D5311yescharacteristic
552#123—1061no—
553C22⋊Q8—531no—
554C22⋊Q8—531no—
555#121—531no—
556#121—531no—
557#120—1061no—
558C4×D4—1061no—
559C4×D4—1061no—
560#117—531no—
561#117—1062no—
562#117—2121no—
563C2×C4⋊C4—1061no—
564C2×C22⋊C4—1061no—
565C2×C42—531no—
566C2×C42—531no—
567#108—1062no—
568#108—2121no—
569C4⋊C8—1061no—
570C4⋊C8—1061no—
571#104—534no—
572#104—1062no—
573#104—1062no—
574#104—1062no—
575#104—1062no—
576#104—2121no—
577#103—531no—
578#103—531no—
579#103—531no—
580#103—531no—
581#102—531no—
582#102—531no—
583#102—531no—
584#102—531no—
585C22⋊C8—21no—
586C22⋊C8—21no—
587C22⋊C8—21no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—21no—
591C22⋊C8—531no—
592C22⋊C8—531no—
593C22⋊C8—531no—
594C22⋊C8—531no—
595C22⋊C8—1061no—
596C22⋊C8—1061no—
597C22⋊C8C22⋊D5311yescharacteristic
598C22⋊C8C22⋊D5311yescharacteristic
599C22⋊C8C22⋊D5311yescharacteristic
600C22⋊C8C22⋊D5311yescharacteristic
601#97—1062no—
602#97—1061no—
603C4×C8—1061no—
604C4×C8—2121no—
605C24—21no—
606C24#1171994511yescharacteristic
607#41—21no—
608#41—21no—
609#41—22no—
610#41—22no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—42no—
616#41—42no—
617#41—41no—
618#41—41no—
619#41—42no—
620#41—42no—
621#41—1061no—
622#41—1061no—
623#41—1061no—
624#41—1061no—
625#41D4×D5312yes—
626#41#1171994712yes—
627C2×Q8—21no—
628C2×Q8—22no—
629C2×Q8—41no—
630C2×Q8—531no—
631C2×Q8C2×C4×D5311yescharacteristic
632C2×Q8C2×C4×D5311yescharacteristic
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—41no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—531no—
643C2×D4—1061no—
644C2×D4—1061no—
645C2×D4—1061no—
646C2×D4C2×C4×D5311yescharacteristic
647C2×D4C2×C4×D5311yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—1061no—
660C22×C4—1061no—
661C22×C4—1061no—
662C22×C4C2×C4×D5311yescharacteristic
663C22×C4C2×C4×D5311yescharacteristic
664C22×C4#1171994511yescharacteristic
665C22×C4C2×C22⋊D5311yescharacteristic
666C22×C4C2×C22⋊D5311yescharacteristic
667C22×C4C23×D5311yescharacteristic
668Q16—1062no—
669Q16—2121no—
670SD16—1062no—
671SD16—1062no—
672SD16—2121no—
673SD16—2121no—
674D8—1062no—
675D8—2121no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—21no—
680M16—42no—
681M16—42no—
682M16—532no—
683M16—1061no—
684M16—1061no—
685M16—1061no—
686M16—2122no—
687M16—2122no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—42no—
695C2×C8—42no—
696C2×C8—531no—
697C2×C8—531no—
698C2×C8—531no—
699C2×C8—531no—
700C2×C8—1061no—
701C2×C8—1061no—
702C2×C8—1061no—
703C2×C8—1061no—
704C2×C8—1061no—
705C2×C8—1061no—
706C2×C8—2122no—
707C2×C8—2122no—
708C2×C8C2×C22⋊D5311yescharacteristic
709C2×C8C2×C22⋊D5311yescharacteristic
710C2×C8C2×C22⋊D5311yescharacteristic
711C2×C8C2×C22⋊D5311yescharacteristic
712C4⋊C4—531no—
713C4⋊C4—531no—
714C4⋊C4—1061no—
715C4⋊C4—1061no—
716C4⋊C4—2122no—
717C22⋊C4—1061no—
718C22⋊C4—1061no—
719C22⋊C4—1061no—
720C22⋊C4—1061no—
721C22⋊C4—1061no—
722C22⋊C4—2122no—
723C42—532no—
724C42—1061no—
725C42—1061no—
726C42—1061no—
727C42—1061no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—41no—
733C23—41no—
734C23—42no—
735C23—42no—
736C23—81no—
737C23—1061no—
738C23C4×C22⋊D5311yescharacteristic
739C23C4×C22⋊D5311yescharacteristic
740C23C2×#1171994511yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—42no—
745Q8—1061no—
746Q8—1061no—
747Q8#1313317712yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—42no—
754D4—42no—
755D4—42no—
756D4—41no—
757D4—41no—
758D4—1061no—
759D4—1061no—
760D4—4241no—
761D4—2122no—
762D4—2121no—
763D4—2121no—
764D4#1313317712yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—1061no—
785C2×C4—1061no—
786C2×C4—1061no—
787C2×C4—1062no—
788C2×C4—2121no—
789C2×C4—2121no—
790C2×C4—2121no—
791C2×C4—2121no—
792C2×C4—2121no—
793C2×C4—2121no—
794C2×C4—2121no—
795C2×C4C4×C22⋊D5311yescharacteristic
796C2×C4C4×C22⋊D5311yescharacteristic
797C2×C4C22×C4×D5311yescharacteristic
798C2×C4C2×D4×D5311yescharacteristic
799C2×C4C22×C22⋊D5311yescharacteristic
800C2×C4C2×#1171994711yescharacteristic
801C2×C4#1313326211yescharacteristic
802C2×C4#1313326211yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—41no—
808C8—41no—
809C8—1061no—
810C8—1061no—
811C8—1061no—
812C8—1061no—
813C8—1062no—
814C8—2121no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—81no—
830C22—81no—
831C22—84no—
832C22—2121no—
833C22—2121no—
834C22—2121no—
835C22C2×C4×C22⋊D5311yescharacteristic
836C22#1681126311yescharacteristic
837C22#1681129911yescharacteristic
838C4—21no—
839C4—21no—
840C4—22no—
841C4—41no—
842C4—4241no—
843C4—2122no—
844C4—2121no—
845C4—2121no—
846C4—2121no—
847C4C2×#1313317711yescharacteristic
848C4#1681109611yescharacteristic
849C4D4×C22⋊D5311yescharacteristic
850C4#1681126711yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—4241no—
858C2#2027769411yescharacteristic
859C2#2028361611yescharacteristic
860C2#2028363011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2880C2
socleC22×C53C2×C4×D4
prime radical#20283933C2
cosocleC22×C4×C53C24
hypercenter#2880D53
hypocenterC53#22887
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2880

Complements

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

NH ≅ G/Ntype
2. C2×#16810743C2semidirect
3. #20283436C2semidirect
4. C2×#16810640C2semidirect
5. #20275602C2semidirect
6. #20275429C2semidirect
7. #20275360C2semidirect
8. #20275161C2semidirect
9. #20275045C2semidirect
10. #20275042C2semidirect
11. #20274990C2semidirect
12. #20274919C2semidirect
13. #20274550C2semidirect
14. #20274483C2semidirect
15. C53×#2880C2semidirect
18. C2×#13133223C22semidirect
22. #16810785C4semidirect
23. #16810785C4semidirect
24. #16810779C4semidirect
25. #16810774C4semidirect
26. #16810768C4semidirect
27. #16810768C4semidirect
28. #16810762C4semidirect
29. #16810757C4semidirect
35. C2×#13133152C22semidirect
36. C2×#13133152C22semidirect
37. #16810649C22semidirect
43. C2×#13133143C22semidirect
44. C2×#13133143C22semidirect
47. #16810589C22semidirect
49. #16810578C22semidirect
50. C2×#13133127C22semidirect
51. C2×C8×Dic53C22semidirect
52. #16810387C22semidirect
53. #16810387C22semidirect
54. #16810384C22semidirect
55. #16810384C22semidirect
56. #16810377C22semidirect
57. #16810377C22semidirect
116. #13133144D4semidirect
425. #2880D53semidirect
499. C53#22887semidirect

Maximal subgroups

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

subgroupindex
#202839332
C2×#168107432
#202834362
C2×#168106402
#202756022
#202754292
#202753602
#202751612
#202750452
#202750422
#202749902
#202749192
#202745502
#202744832
C53×#28802
#2288753