Finite Group Databasebeta

← #27404823

Subgroups — #27404823

Order 13568.

1058 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20283929C211yesmaximal, characteristic
2#20283437C211yesmaximal, characteristic, complemented
3C2×#104×D53C211yesmaximal, characteristic, complemented
4#20283162C211yesmaximal, characteristic, complemented
5#20275605C211yesmaximal, characteristic, complemented
6#20275426C211yesmaximal, characteristic, complemented
7#20275362C211yesmaximal, characteristic, complemented
8#20275155C211yesmaximal, characteristic, complemented
9#20275044C211yesmaximal, characteristic, complemented
10#20275042C211yesmaximal, characteristic, complemented
11#20274990C211yesmaximal, characteristic, complemented
12#20274918C211yesmaximal, characteristic, complemented
13#20274560C211yesmaximal, characteristic, complemented
14#20274478C211yesmaximal, characteristic, complemented
15C2×C53×#444C211yesmaximal, characteristic, complemented
16C2×#41×D53C2211yescharacteristic
17C2×#13133237C2211yescharacteristic
18C2×#13133224C2211yescharacteristic
19C2×M16×D53C2211yescharacteristic
20#16811130C2211yescharacteristic
21C2×C42×D53C2211yescharacteristic
22#16810784C411yescharacteristic, complemented
23#16810782C411yescharacteristic, complemented
24#16810777C411yescharacteristic, complemented
25#16810772C411yescharacteristic, complemented
26#16810767C411yescharacteristic, complemented
27#16810765C411yescharacteristic, complemented
28#16810760C411yescharacteristic, complemented
29#16810755C411yescharacteristic, complemented
30#16810699—21no—
31#16810694—21no—
32#16810692—21no—
33C8×C22⋊D53—21no—
34C2×#13133152C2211yescharacteristic, complemented
35#16810649C2211yescharacteristic, complemented
36C2×#13133145C2211yescharacteristic
37C2×#13133144C2211yescharacteristic
38C2×#13133144C2211yescharacteristic, complemented
39C2×#13133143C2211yescharacteristic
40#104×D53—24no—
41#16810620C2211yescharacteristic
42#16810619C2211yescharacteristic
43#16810591—21no—
44#16810591C2211yescharacteristic
45#16810590C2211yescharacteristic, complemented
46#16810589—21no—
47#16810589C2211yescharacteristic
48#16810586—21no—
49#16810586C2211yescharacteristic
50C2×#13133129—21no—
51C2×#13133129C2211yescharacteristic
52C2×#13133129C2211yescharacteristic
53#16810581C2211yescharacteristic, complemented
54C2×#13133128C2211yescharacteristic, complemented
55#16810388C2211yescharacteristic, complemented
56#16810387C2211yescharacteristic, complemented
57#16810384C2211yescharacteristic, complemented
58#16810383C2211yescharacteristic, complemented
59#16810377C2211yescharacteristic, complemented
60#16810377C2211yescharacteristic, complemented
61C2×#135×C53C2211yescharacteristic
62C2×#131×C53C2211yescharacteristic
63C2×#131×C53C2211yescharacteristic, complemented
64C53×#444—24no—
65C2×#108×C53C2211yescharacteristic, complemented
66C2×#104×C53C2211yescharacteristic
67C2×#104×C53C2211yescharacteristic, complemented
68C2×#97×C53C2211yescharacteristic, complemented
69C2×#11719949C2×C411yescharacteristic
70C2×#11719945—21no—
71C2×#11719945C2311yescharacteristic
72C2×#11719947—21no—
73C2×#11719947C2×C411yescharacteristic
74#41×D53—22no—
75#41×D53—22no—
76#41×D53—41no—
77#41×D53—41no—
78C2×Q8×D53C2×C411yescharacteristic
79C2×D4×D53—21no—
80C2×D4×D53C2×C411yescharacteristic
81C22×C4×D53—21no—
82C22×C4×D53—21no—
83C22×C4×D53C2311yescharacteristic
84#13133237—41no—
85#13133237—41no—
86C2×#11719925C2×C411yescharacteristic, complemented
87C2×#11719923C2×C411yescharacteristic, complemented
88C2×#11719924C2×C411yescharacteristic, complemented
89C2×#11719922C2×C411yescharacteristic, complemented
90#13133224—22no—
91#13133224—41no—
92C2×#11719917—21no—
93C2×#11719917C2311yescharacteristic
94C2×#11719917C2311yescharacteristic
95C2×#11719912—21no—
96M16×D53—22no—
97M16×D53—41no—
98C22×#88322—21no—
99C22×#88322C2311yescharacteristic
100C22×#88322C2311yescharacteristic
101C2×C8×D53—21no—
102#13133198—21no—
103#13133193C2×C411yescharacteristic
104#13133193C2×C411yescharacteristic
105#13133188C2×C411yescharacteristic
106#13133188C2×C411yescharacteristic
107#13133185—21no—
108C4×C22⋊D53—21no—
109C4×C22⋊D53—21no—
110#13133176C2311yescharacteristic
111C2×C4×Dic53—21no—
112C2×C4×Dic53C2311yescharacteristic
113C42×D53—22no—
114C42×D53—41no—
115#13133152—41no—
116#13133146—21no—
117#13133146—21no—
118#13133145—22no—
119#13133144—22no—
120#13133144—41no—
121#13133143—22no—
122#13133142C2×C411yescharacteristic, complemented
123#13133142C2×C411yescharacteristic, complemented
124#13133141C2×C411yescharacteristic, complemented
125#13133141C2×C411yescharacteristic, complemented
126#13133139C2×C411yescharacteristic, complemented
127#13133139C2×C411yescharacteristic, complemented
128#13133138C2×C411yescharacteristic, complemented
129#13133138C2×C411yescharacteristic, complemented
130C22⋊#88322—21no—
131C22⋊#88322—21no—
132#13133129—21no—
133#13133129—21no—
134#13133129—21no—
135#13133129—21no—
136#13133129—21no—
137#13133129—21no—
138#13133129C2×C411yescharacteristic
139#13133129C2×C411yescharacteristic
140#13133129C2×C411yescharacteristic
141#13133129C2×C411yescharacteristic
142#13133129D411yescharacteristic
143#13133129D411yescharacteristic
144#13133129D411yescharacteristic
145#13133129D411yescharacteristic
146#13133128—41no—
147#13133127—21no—
148C8×Dic53—21no—
149C2×#41×C53C2311yescharacteristic
150C2×#41×C53C2311yescharacteristic
151#135×C53—22no—
152#135×C53—22no—
153C2×Q16×C53C2×C411yescharacteristic, complemented
154C2×SD16×C53C2×C411yescharacteristic, complemented
155C2×SD16×C53C2×C411yescharacteristic, complemented
156C2×D8×C53C2×C411yescharacteristic, complemented
157#131×C53—22no—
158#131×C53—22no—
159#131×C53—41no—
160#131×C53—41no—
161C2×M16×C53—21no—
162C2×M16×C53—21no—
163C2×M16×C53C2311yescharacteristic
164C2×M16×C53C2311yescharacteristic
165C22×C8×C53—21no—
166C22×C8×C53—21no—
167C22×C8×C53C2311yescharacteristic
168C22×C8×C53C2311yescharacteristic
169C2×C42×C53C2311yescharacteristic
170#108×C53—22no—
171#104×C53—22no—
172#104×C53D414yescomplemented
173#97×C53—22no—
174C23×D53—21no—
175C23×D53#4111yescharacteristic
176#41×C53—21no—
177#41×C53—21no—
178#41×C53—21no—
179#41×C53—21no—
180#41×C53—21no—
181#41×C53—21no—
182#41×C53C2×D412yes—
183#41×C53#4112yes—
184C2×Q8×C53C22×C411yescharacteristic
185C2×Q8×C53C22×C411yescharacteristic
186C2×D4×C53—21no—
187C2×D4×C53—21no—
188C2×D4×C53C22×C411yescharacteristic
189C2×D4×C53C22×C411yescharacteristic
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53C2411yescharacteristic
194C2×C22⋊D53—21no—
195C2×C22⋊D53—21no—
196C2×C22⋊D53—21no—
197C2×C22⋊D53—21no—
198C2×C22⋊D53—21no—
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53#4111yescharacteristic
202#11719949—22no—
203#11719949—41no—
204Q8×D53—22no—
205Q8×D53—41no—
206#11719947—22no—
207#11719947—41no—
208#11719947—42no—
209#11719947—42no—
210D4×D53—22no—
211D4×D53—41no—
212D4×D53—42no—
213D4×D53—42no—
214#11719945—21no—
215#11719945—21no—
216#11719945—21no—
217#11719945—21no—
218#11719945—42no—
219#11719945—42no—
220C2×D212—21no—
221C2×D212C22×C411yescharacteristic
222C2×C4×D53—21no—
223C2×C4×D53—21no—
224C2×C4×D53—21no—
225C2×C4×D53—21no—
226C2×C4×D53—21no—
227C2×C4×D53—21no—
228C2×C4×D53—21no—
229C2×C4×D53—42no—
230C2×C4×D53—42no—
231C2×C4×D53—42no—
232C2×C4×D53—42no—
233C2×C4×D53—42no—
234C2×C4×D53C22×C411yescharacteristic
235C2×C4×D53C22×C411yescharacteristic
236C2×C4×D53C2×D411yescharacteristic
237C2×C4×D53C2×D411yescharacteristic
238C2×Dic106—21no—
239C2×Dic106C22×C411yescharacteristic
240Q16×C53—22no—
241SD16×C53—22no—
242SD16×C53—22no—
243D8×C53—22no—
244M16×C53—21no—
245M16×C53—21no—
246M16×C53—21no—
247M16×C53—42no—
248M16×C53—42no—
249M16×C53C2×D412yes—
250C2×C8×C53—21no—
251C2×C8×C53—21no—
252C2×C8×C53—21no—
253C2×C8×C53—21no—
254C2×C8×C53—21no—
255C2×C8×C53—21no—
256C2×C8×C53—42no—
257C2×C8×C53—42no—
258C2×C8×C53C22×C411yescharacteristic
259C2×C8×C53C22×C411yescharacteristic
260C2×C8×C53C2×D411yescharacteristic
261C2×C8×C53C2×D411yescharacteristic
262C42×C53—21no—
263C42×C53C2×D412yes—
264C22⋊Dic53—21no—
265C22⋊Dic53—21no—
266C22⋊Dic53—21no—
267#11719925—41no—
268#11719924—41no—
269#11719923—41no—
270#11719922—41no—
271#11719921—21no—
272#11719921—21no—
273C4⋊Dic53C22×C411yescharacteristic
274C4⋊Dic53C22×C411yescharacteristic
275#11719919—21no—
276#11719919—21no—
277C4×Dic53—21no—
278C4×Dic53—21no—
279C4×Dic53—21no—
280C4×Dic53—42no—
281#11719917—21no—
282#11719917—21no—
283#11719917—21no—
284#11719917—21no—
285#11719917—42no—
286C2×#88322—21no—
287C2×#88322—21no—
288C2×#88322—21no—
289C2×#88322—21no—
290C2×#88322—21no—
291C2×#88322—21no—
292C2×#88322—42no—
293C2×#88322C22×C411yescharacteristic
294C2×#88322C22×C411yescharacteristic
295C2×#88322C2×D411yescharacteristic
296C2×#88322C2×D411yescharacteristic
297#11719912—42no—
298C8×D53—42no—
299C23×C53—21no—
300C23×C53—21no—
301C23×C53C2×#4111yescharacteristic
302C22×D53—21no—
303C22×D53—21no—
304C22×D53—22no—
305C22×D53—21no—
306C22×D53—41no—
307C22×D53—42no—
308C22×D53—42no—
309C22×D53—81no—
310C22×D53C4×D411yescharacteristic
311C22×D53C4×D411yescharacteristic
312Q8×C53—21no—
313Q8×C53—21no—
314Q8×C53—21no—
315Q8×C53C4×D412yes—
316D4×C53—22no—
317D4×C53—22no—
318D4×C53—21no—
319D4×C53—21no—
320D4×C53—21no—
321D4×C53—41no—
322D4×C53—41no—
323D4×C53C4×D412yes—
324C2×C4×C53—21no—
325C2×C4×C53—22no—
326C2×C4×C53—22no—
327C2×C4×C53—21no—
328C2×C4×C53—22no—
329C2×C4×C53—41no—
330C2×C4×C53—41no—
331C2×C4×C53—41no—
332C2×C4×C53—41no—
333C2×C4×C53C23×C411yescharacteristic
334C2×C4×C53C22×D411yescharacteristic
335C2×C4×C53C22×D411yescharacteristic
336C2×C4×C53C2×#4111yescharacteristic
337C2×C4×C53H(5,𝔽2)11yescharacteristic
338C2×C4×C53H(5,𝔽2)11yescharacteristic
339C22⋊D53—42no—
340C22⋊D53—42no—
341C22⋊D53—41no—
342C22⋊D53—41no—
343C22⋊D53—42no—
344C22⋊D53—81no—
345C2×Dic53—21no—
346C2×Dic53—21no—
347C2×Dic53—22no—
348C2×Dic53—21no—
349C2×Dic53—21no—
350C2×Dic53—21no—
351C2×Dic53—42no—
352C2×Dic53—41no—
353C2×Dic53—41no—
354C2×Dic53C4×D411yescharacteristic
355C2×Dic53C4×D411yescharacteristic
356D212—21no—
357D212—21no—
358D212—42no—
359C4×D53—21no—
360C4×D53—21no—
361C4×D53—21no—
362C4×D53—21no—
363C4×D53—21no—
364C4×D53—21no—
365C4×D53—21no—
366C4×D53—21no—
367C4×D53—42no—
368C4×D53—42no—
369C4×D53—48no—
370C4×D53—41no—
371C4×D53—41no—
372Dic106—21no—
373Dic106—21no—
374Dic106—42no—
375C8×C53—21no—
376C8×C53—21no—
377C8×C53—22no—
378C8×C53—21no—
379C8×C53—21no—
380C8×C53—41no—
381#88322—21no—
382#88322—21no—
383#88322—21no—
384#88322—21no—
385#88322—41no—
386#88322—41no—
387#22886—531nomaximal, Sylow
388C22×C53—21no—
389C22×C53—21no—
390C22×C53—22no—
391C22×C53—41no—
392C22×C53—41no—
393C22×C53—41no—
394C22×C53—41no—
395C22×C53—41no—
396C22×C53C2×C4×D411yescharacteristic
397C22×C53#54611yescharacteristic
398C22×C53#55111yescharacteristic
399C2×D53—21no—
400C2×D53—21no—
401C2×D53—21no—
402C2×D53—21no—
403C2×D53—21no—
404C2×D53—42no—
405C2×D53—42no—
406C2×D53—41no—
407C2×D53—41no—
408C2×D53—41no—
409C2×D53—84no—
410C2×D53#44412yescomplemented
411C4×C53—22no—
412C4×C53—42no—
413C4×C53—41no—
414C4×C53C2×C4×D411yescharacteristic
415C4×C53#51811yescharacteristic
416C4×C53D4211yescharacteristic
417C4×C53#54611yescharacteristic
418Dic53—21no—
419Dic53—21no—
420Dic53—42no—
421Dic53—41no—
422Dic53—41no—
423Dic53—41no—
424#3002—531no—
425C2×#444D5311yescharacteristic, complemented
426#2933—531no—
427C22×#104—531no—
428#2880—531no—
429#1975—531no—
430#1938—531no—
431#1929—531no—
432#1896—531no—
433#1876—531no—
434#1876—531no—
435#1866—531no—
436#1855—531no—
437#1765—531no—
438#1749—531no—
439C2×C53—21no—
440C2×C53—21no—
441C2×C53—42no—
442C2×C53—81no—
443C2×C53#235811yescharacteristic
444C2×C53C2×#44411yescharacteristic
445C2×C53#295611yescharacteristic
446D53—22no—
447D53—41no—
448D53—81no—
449C22×#41—531no—
450C2×#135—531no—
451C2×#135C2×D5311yescharacteristic
452C2×#131—531no—
453C2×#131C2×D5311yescharacteristic
454C2×#131C2×D5311yescharacteristic, complemented
455C22×M16—531no—
456#525—531no—
457C22×C42—531no—
458#452—531no—
459#452—531no—
460#451—531no—
461#450—531no—
462#449—531no—
463#449—531no—
464#448—531no—
465#447—531no—
466#444—24no—
467#436—1061no—
468#435—1061no—
469#435—1061no—
470C8×D4—1061no—
471C2×#108—531no—
472C2×#108C2×D5311yescharacteristic, complemented
473#424—531no—
474C2×#104—531no—
475C2×#104—531no—
476C2×#104—531no—
477C2×#104—531no—
478C2×#104—1064no—
479C2×#104C2×D5311yescharacteristic
480C2×#104C2×D5311yescharacteristic, complemented
481#416—531no—
482#416—531no—
483#408—531no—
484#408—531no—
485#408—531no—
486#408—1061no—
487#408—1061no—
488#407—531no—
489#407—1061no—
490C2×C22⋊C8—531no—
491C2×C22⋊C8—531no—
492C2×C22⋊C8—1061no—
493#405—531no—
494C2×#97—531no—
495C2×#97C2×D5311yescharacteristic, complemented
496#341—531no—
497#341—531no—
498#339—531no—
499#339—531no—
500#336—531no—
501#336—531no—
502C53#2288611yescharacteristic, complemented, Sylow
503C2×#41—531no—
504C2×#41—531no—
505C2×#41—531no—
506C2×#41—1061no—
507C2×#41—1061no—
508C2×#41—1062no—
509C2×#41—1062no—
510C2×#41—2121no—
511C2×#41—2121no—
512C2×#41C22×D5311yescharacteristic
513C2×#41C22×D5311yescharacteristic
514C22×Q8—531no—
515C22×D4—531no—
516C22×D4—1061no—
517C23×C4—531no—
518C23×C4—1061no—
519C23×C4—1061no—
520#135—22no—
521#135—22no—
522#135—2121no—
523#135—2121no—
524C2×Q16—531no—
525C2×Q16C4×D5311yescharacteristic, complemented
526C2×SD16—531no—
527C2×SD16—531no—
528C2×SD16C4×D5311yescharacteristic, complemented
529C2×SD16C4×D5311yescharacteristic, complemented
530C2×D8—531no—
531C2×D8C4×D5311yescharacteristic, complemented
532#131—22no—
533#131—22no—
534#131—41no—
535#131—41no—
536#131—1062no—
537#131—2121no—
538C2×M16—21no—
539C2×M16—21no—
540C2×M16—531no—
541C2×M16—531no—
542C2×M16—1061no—
543C2×M16—1061no—
544C2×M16—1062no—
545C2×M16—2121no—
546C2×M16C22×D5311yescharacteristic
547C2×M16C22×D5311yescharacteristic
548C22×C8—21no—
549C22×C8—21no—
550C22×C8—531no—
551C22×C8—531no—
552C22×C8—1061no—
553C22×C8—1061no—
554C22×C8C22×D5311yescharacteristic
555C22×C8C22×D5311yescharacteristic
556#123—1061no—
557C22⋊Q8—531no—
558C22⋊Q8—531no—
559#121—531no—
560#121—531no—
561#120—1061no—
562C4×D4—1061no—
563C4×D4—1061no—
564#117—531no—
565C2×C42—531no—
566C2×C42—1062no—
567C2×C42—1061no—
568C2×C42—2121no—
569C2×C42C22×D5311yescharacteristic
570#108—22no—
571#108—2121no—
572C4⋊C8—1061no—
573C4⋊C8—1061no—
574#104—22no—
575#104—1062no—
576#104—1062no—
577#104—1062no—
578#104—2121no—
579#104C22⋊D5314yescomplemented
580#103—531no—
581#103—531no—
582#103—531no—
583#103—531no—
584#102—531no—
585#102—531no—
586#102—531no—
587#102—531no—
588C22⋊C8—531no—
589C22⋊C8—531no—
590C22⋊C8—531no—
591C22⋊C8—531no—
592C22⋊C8—531no—
593C22⋊C8—531no—
594C22⋊C8—531no—
595C22⋊C8—531no—
596C22⋊C8—1061no—
597C22⋊C8—1061no—
598C22⋊C8—1061no—
599C22⋊C8—1061no—
600C22⋊C8—1061no—
601C22⋊C8—1061no—
602C22⋊C8—1061no—
603C22⋊C8—1061no—
604#97—22no—
605#97—1061no—
606#97—2121no—
607C4×C8—1061no—
608C24—531no—
609C24—1061no—
610#41—21no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—1062no—
617#41—1062no—
618#41—1061no—
619#41—1061no—
620#41—1061no—
621#41—1061no—
622#41—2122no—
623#41—2122no—
624#41—2121no—
625#41—2122no—
626#41—2122no—
627#41—2121no—
628#41#1171994512yes—
629#41C2×C22⋊D5312yes—
630C2×Q8—531no—
631C2×Q8—1061no—
632C2×Q8—1062no—
633C2×Q8—2121no—
634C2×Q8C2×C4×D5311yescharacteristic
635C2×Q8C2×C4×D5311yescharacteristic
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—531no—
639C2×D4—1061no—
640C2×D4—1061no—
641C2×D4—1062no—
642C2×D4—1061no—
643C2×D4—1061no—
644C2×D4—1061no—
645C2×D4—1061no—
646C2×D4—2121no—
647C2×D4—2122no—
648C2×D4—2122no—
649C2×D4C2×C4×D5311yescharacteristic
650C2×D4C2×C4×D5311yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—531no—
655C22×C4—531no—
656C22×C4—531no—
657C22×C4—531no—
658C22×C4—531no—
659C22×C4—1061no—
660C22×C4—1061no—
661C22×C4—1061no—
662C22×C4—1061no—
663C22×C4—1061no—
664C22×C4—1061no—
665C22×C4—1061no—
666C22×C4—1061no—
667C22×C4—1061no—
668C22×C4—2122no—
669C22×C4—2122no—
670C22×C4—2122no—
671C22×C4—2122no—
672C22×C4—2122no—
673C22×C4C23×D5311yescharacteristic
674Q16—22no—
675Q16—2121no—
676SD16—22no—
677SD16—22no—
678SD16—2121no—
679SD16—2121no—
680D8—22no—
681D8—2121no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—42no—
686M16—42no—
687M16—1061no—
688M16—1061no—
689M16—1061no—
690M16—1061no—
691M16—2122no—
692M16—2122no—
693M16C2×C22⋊D5312yes—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—42no—
701C2×C8—42no—
702C2×C8—531no—
703C2×C8—531no—
704C2×C8—531no—
705C2×C8—531no—
706C2×C8—1061no—
707C2×C8—1061no—
708C2×C8—1061no—
709C2×C8—1061no—
710C2×C8—1061no—
711C2×C8—1061no—
712C2×C8—2122no—
713C2×C8—2122no—
714C2×C8C2×C4×D5311yescharacteristic
715C2×C8C2×C4×D5311yescharacteristic
716C2×C8D4×D5311yescharacteristic
717C2×C8D4×D5311yescharacteristic
718C4⋊C4—531no—
719C4⋊C4—531no—
720C4⋊C4—1061no—
721C4⋊C4—1061no—
722C22⋊C4—1061no—
723C22⋊C4—1061no—
724C22⋊C4—1061no—
725C22⋊C4—1061no—
726C22⋊C4—1061no—
727C42—21no—
728C42—1061no—
729C42—1061no—
730C42—1061no—
731C42—2122no—
732C42C2×C22⋊D5312yes—
733C23—21no—
734C23—21no—
735C23—531no—
736C23—531no—
737C23—1062no—
738C23—1061no—
739C23—1061no—
740C23—1061no—
741C23—4241no—
742C23—2121no—
743C23—2122no—
744C23—2122no—
745C23#41×D5311yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—21no—
749Q8—1061no—
750Q8—1061no—
751Q8—2122no—
752Q8C4×C22⋊D5312yes—
753D4—22no—
754D4—22no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—41no—
759D4—41no—
760D4—1061no—
761D4—1061no—
762D4—4241no—
763D4—2122no—
764D4—2122no—
765D4—2122no—
766D4—2122no—
767D4—2121no—
768D4—2121no—
769D4C4×C22⋊D5312yes—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—531no—
780C2×C4—531no—
781C2×C4—1061no—
782C2×C4—1061no—
783C2×C4—1061no—
784C2×C4—1061no—
785C2×C4—1061no—
786C2×C4—1061no—
787C2×C4—1061no—
788C2×C4—1061no—
789C2×C4—1061no—
790C2×C4—1061no—
791C2×C4—1062no—
792C2×C4—1061no—
793C2×C4—1061no—
794C2×C4—1061no—
795C2×C4—2122no—
796C2×C4—2122no—
797C2×C4—2128no—
798C2×C4—2122no—
799C2×C4—2121no—
800C2×C4—2121no—
801C2×C4—2121no—
802C2×C4—2121no—
803C2×C4C22×C4×D5311yescharacteristic
804C2×C4C2×D4×D5311yescharacteristic
805C2×C4C22×C22⋊D5311yescharacteristic
806C2×C4C2×#1171994511yescharacteristic
807C2×C4#1313326211yescharacteristic
808C2×C4#1313326311yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—22no—
814C8—41no—
815C8—1061no—
816C8—1061no—
817C8—1061no—
818C8—1061no—
819C8—2121no—
820C8—2121no—
821C22—21no—
822C22—21no—
823C22—22no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—532no—
830C22—1061no—
831C22—1061no—
832C22—1061no—
833C22—1061no—
834C22—1061no—
835C22—4244no—
836C22—2122no—
837C22—2122no—
838C22—2121no—
839C22—2121no—
840C22—2121no—
841C22C4×D4×D5311yescharacteristic
842C22#1681126111yescharacteristic
843C22#1681130211yescharacteristic
844C4—22no—
845C4—42no—
846C4—41no—
847C4—1061no—
848C4—1061no—
849C4—2122no—
850C4—2121no—
851C4—2121no—
852C4—2121no—
853C4C2×C4×C22⋊D5311yescharacteristic
854C4#1681109511yescharacteristic
855C4D4×C22⋊D5311yescharacteristic
856C4#1681126911yescharacteristic
857C2—21no—
858C2—21no—
859C2—42no—
860C2—81no—
861C2—1062no—
862C2—4241no—
863C2—2121no—
864C2#2027769211yescharacteristic
865C2#444×D5311yescharacteristic
866C2#2028362311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#444C2
socleC22×C53C2×C4×D4
prime radical#20283929C2
cosocleC22×C4×C53C24
hypercenterC2×#444D53
hypocenterC53#22886
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#444

Complements

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

NH ≅ G/Ntype
2. #20283437C2semidirect
3. C2×#104×D53C2semidirect
4. #20283162C2semidirect
5. #20275605C2semidirect
6. #20275426C2semidirect
7. #20275362C2semidirect
8. #20275155C2semidirect
9. #20275044C2semidirect
10. #20275042C2semidirect
11. #20274990C2semidirect
12. #20274918C2semidirect
13. #20274560C2semidirect
14. #20274478C2semidirect
15. C2×C53×#444C2semidirect
22. #16810784C4semidirect
23. #16810782C4semidirect
24. #16810777C4semidirect
25. #16810772C4semidirect
26. #16810767C4semidirect
27. #16810765C4semidirect
28. #16810760C4semidirect
29. #16810755C4semidirect
34. C2×#13133152C22semidirect
35. #16810649C22semidirect
38. C2×#13133144C22semidirect
45. #16810590C22semidirect
53. #16810581C22semidirect
54. C2×#13133128C22semidirect
55. #16810388C22semidirect
56. #16810387C22semidirect
57. #16810384C22semidirect
58. #16810383C22semidirect
59. #16810377C22semidirect
60. #16810377C22semidirect
63. C2×#131×C53C22semidirect
65. C2×#108×C53C22semidirect
67. C2×#104×C53C22semidirect
68. C2×#97×C53C22semidirect
86. C2×#11719925C2×C4semidirect
87. C2×#11719923C2×C4semidirect
88. C2×#11719924C2×C4semidirect
89. C2×#11719922C2×C4semidirect
122. #13133142C2×C4semidirect
123. #13133142C2×C4semidirect
124. #13133141C2×C4semidirect
125. #13133141C2×C4semidirect
126. #13133139C2×C4semidirect
127. #13133139C2×C4semidirect
128. #13133138C2×C4semidirect
129. #13133138C2×C4semidirect
153. C2×Q16×C53C2×C4semidirect
154. C2×SD16×C53C2×C4semidirect
155. C2×SD16×C53C2×C4semidirect
156. C2×D8×C53C2×C4semidirect
172. #104×C53D4semidirect
410. C2×D53#444semidirect
425. C2×#444D53semidirect
454. C2×#131C2×D53semidirect
472. C2×#108C2×D53semidirect
480. C2×#104C2×D53semidirect
495. C2×#97C2×D53semidirect
502. C53#22886semidirect
525. C2×Q16C4×D53semidirect
528. C2×SD16C4×D53semidirect
529. C2×SD16C4×D53semidirect
531. C2×D8C4×D53semidirect
579. #104C22⋊D53semidirect

Maximal subgroups

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

subgroupindex
#202839292
#202834372
C2×#104×D532
#202831622
#202756052
#202754262
#202753622
#202751552
#202750442
#202750422
#202749902
#202749182
#202745602
#202744782
C2×C53×#4442
#2288653