Finite Group Databasebeta

← #27401460

Subgroups — #27401460

Order 13568.

888 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20283375C211yesmaximal, characteristic, complemented
2#20283235C211yesmaximal, characteristic
3#20283165C211yesmaximal, characteristic
4#20275424C211yesmaximal, characteristic, complemented
5#20275417C211yesmaximal, characteristic, complemented
6#20275362C211yesmaximal, characteristic, complemented
7#20275362C211yesmaximal, characteristic, complemented
8#20274987C211yesmaximal, characteristic, complemented
9#20274987C211yesmaximal, characteristic, complemented
10#20274812C211yesmaximal, characteristic, complemented
11#20274658C211yesmaximal, characteristic
12#20274558C211yesmaximal, characteristic, complemented
13#20274551C211yesmaximal, characteristic, complemented
14#20274496C211yesmaximal, characteristic, complemented
15C53×#1811C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C2×#13133225C2211yescharacteristic
18C2×#13133225C2211yescharacteristic
19C2×#13133176C2211yescharacteristic
20#16810681—21no—
21#16810681—21no—
22#16810677—21no—
23#16810673—21no—
24#16810651C2211yescharacteristic, complemented
25#16810651C2211yescharacteristic, complemented
26C2×#13133143C2211yescharacteristic
27C2×#13133143C2211yescharacteristic
28C2×#13133143C2211yescharacteristic
29C2×#13133143C2211yescharacteristic
30#16810633C411yescharacteristic, complemented
31#16810633C411yescharacteristic, complemented
32#16810629C411yescharacteristic, complemented
33#16810629C411yescharacteristic, complemented
34#16810625C411yescharacteristic, complemented
35#16810625C411yescharacteristic, complemented
36#16810625C411yescharacteristic, complemented
37#16810625C411yescharacteristic, complemented
38#16810620C2211yescharacteristic
39#16810620C2211yescharacteristic
40#16810620C2211yescharacteristic
41#16810620C2211yescharacteristic
42#16810591C2211yescharacteristic
43#16810591C2211yescharacteristic
44#16810588—21no—
45#16810588—21no—
46#16810585—21no—
47C2×C22⋊#88322C2211yescharacteristic
48C22⋊C8×D53—21no—
49#16810581C2211yescharacteristic, complemented
50#16810581C2211yescharacteristic, complemented
51C2×#13133127C2211yescharacteristic, complemented
52C2×C8×Dic53C2211yescharacteristic, complemented
53C4×C22⋊Dic53C2211yescharacteristic
54#16810384C2211yescharacteristic, complemented
55#16810384C2211yescharacteristic, complemented
56#16810384C2211yescharacteristic, complemented
57#16810384C2211yescharacteristic, complemented
58#16810377C2211yescharacteristic, complemented
59#16810377C2211yescharacteristic, complemented
60C22×M16×C53C2211yescharacteristic
61C2×#108×C53C2211yescharacteristic, complemented
62C2×#108×C53C2211yescharacteristic, complemented
63C53×#407C2211yescharacteristic
64C53×#407C2211yescharacteristic
65C53×#341C2211yescharacteristic, complemented
66C53×#341C2211yescharacteristic, complemented
67C2×#11719945—21no—
68C2×#11719945—21no—
69C2×#11719945—22no—
70C2×#11719945—22no—
71C2×#11719945—41no—
72C2×#11719945—41no—
73C2×#11719945C2×C411yescharacteristic
74C2×#11719945C2×C411yescharacteristic
75C2×#11719945C2311yescharacteristic
76C2×#11719945C2311yescharacteristic
77C22×Dic106C2×C411yescharacteristic
78C22×D212C2×C411yescharacteristic
79C22×C22⋊D53—21no—
80C22×C4×D53—21no—
81#13133225—22no—
82#13133225—22no—
83#13133225—41no—
84#13133225—41no—
85C2×#11719912—21no—
86C2×#11719912—21no—
87C22×#88322C2311yescharacteristic
88C22×#88322C2311yescharacteristic
89C2×C8×D53—21no—
90C2×C8×D53—21no—
91#13133176—21no—
92#13133176—21no—
93#13133176C2×C411yescharacteristic
94#13133176C2×C411yescharacteristic
95#13133176C2311yescharacteristic
96#13133176C2311yescharacteristic
97C2×C4⋊Dic53C2×C411yescharacteristic
98C2×C4⋊Dic53C2×C411yescharacteristic
99C2×C22⋊Dic53—21no—
100C2×C22⋊Dic53—21no—
101C2×C4×Dic53—21no—
102C2×C4×Dic53C2311yescharacteristic
103C2×C4×Dic53C2311yescharacteristic
104#13133146—21no—
105#13133146—21no—
106#13133146—21no—
107#13133146—21no—
108#13133143—22no—
109#13133143—22no—
110#13133143—41no—
111#13133143—41no—
112#13133142C2×C411yescharacteristic
113#13133142C2×C411yescharacteristic
114#13133142C2×C411yescharacteristic
115#13133142C2×C411yescharacteristic
116#13133142C2×C411yescharacteristic
117#13133142C2×C411yescharacteristic
118#13133142C2×C411yescharacteristic
119#13133142C2×C411yescharacteristic
120#13133139C2×C411yescharacteristic
121#13133139C2×C411yescharacteristic
122#13133139C2×C411yescharacteristic
123#13133139C2×C411yescharacteristic
124#13133139C2×C411yescharacteristic
125#13133139C2×C411yescharacteristic
126#13133139C2×C411yescharacteristic
127#13133139C2×C411yescharacteristic
128C22⋊#88322D411yescharacteristic
129C22⋊#88322D411yescharacteristic
130C22⋊#88322D411yescharacteristic
131C22⋊#88322D411yescharacteristic
132#13133129—21no—
133#13133129—21no—
134#13133129—21no—
135#13133129—21no—
136#13133127—21no—
137#13133127—21no—
138#13133127—41no—
139C8×Dic53—21no—
140C8×Dic53—21no—
141C8×Dic53—41no—
142#13133124—21no—
143C23×C4×C53C2311yescharacteristic
144C2×M16×C53—41no—
145C2×M16×C53—41no—
146C2×M16×C53C2×C411yescharacteristic
147C2×M16×C53C2×C411yescharacteristic
148C2×M16×C53C2×C411yescharacteristic
149C2×M16×C53C2×C411yescharacteristic
150C2×M16×C53C2311yescharacteristic
151C2×M16×C53C2311yescharacteristic
152C2×M16×C53C2311yescharacteristic
153C2×M16×C53C2311yescharacteristic
154C22×C8×C53C2311yescharacteristic
155C22×C8×C53C2311yescharacteristic
156#108×C53—41no—
157#108×C53—41no—
158C22⋊C8×C53—21no—
159C22⋊C8×C53—21no—
160C22⋊C8×C53—21no—
161C22⋊C8×C53—21no—
162C24×C53#4111yescharacteristic
163C23×D53—21no—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53C22×C411yescharacteristic
169C22×C4×C53C22×C411yescharacteristic
170C22×C4×C53C2×D411yescharacteristic
171C22×C4×C53C2×D411yescharacteristic
172C22×C4×C53#4111yescharacteristic
173C22×C4×C53C2411yescharacteristic
174C2×C22⋊D53—21no—
175C2×C22⋊D53—21no—
176C2×C22⋊D53—21no—
177C2×C22⋊D53—21no—
178C2×C22⋊D53—42no—
179C2×C22⋊D53—42no—
180C22×Dic53—21no—
181C22×Dic53—21no—
182C22×Dic53—21no—
183C22×Dic53—21no—
184C22×Dic53—21no—
185#11719945—21no—
186#11719945—21no—
187#11719945—21no—
188#11719945—21no—
189#11719945—21no—
190#11719945—21no—
191#11719945—22no—
192#11719945—22no—
193#11719945—41no—
194#11719945—41no—
195#11719945—42no—
196#11719945—42no—
197#11719945—42no—
198#11719945—42no—
199#11719945#4112yes—
200#11719945#4112yes—
201C2×D212—22no—
202C2×D212—21no—
203C2×D212—41no—
204C2×D212C22×C411yescharacteristic
205C2×D212C22×C411yescharacteristic
206C2×C4×D53—21no—
207C2×C4×D53—21no—
208C2×C4×D53—21no—
209C2×C4×D53—21no—
210C2×C4×D53—42no—
211C2×C4×D53—42no—
212C2×Dic106—22no—
213C2×Dic106—21no—
214C2×Dic106—41no—
215C2×Dic106C22×C411yescharacteristic
216C2×Dic106C22×C411yescharacteristic
217M16×C53—21no—
218M16×C53—21no—
219M16×C53—21no—
220M16×C53—21no—
221M16×C53—21no—
222M16×C53—21no—
223M16×C53—21no—
224M16×C53—21no—
225M16×C53—41no—
226M16×C53—41no—
227M16×C53—41no—
228M16×C53—41no—
229C2×C8×C53—21no—
230C2×C8×C53—21no—
231C2×C8×C53—21no—
232C2×C8×C53—21no—
233C2×C8×C53—21no—
234C2×C8×C53—21no—
235C2×C8×C53—21no—
236C2×C8×C53—21no—
237C2×C8×C53C22×C411yescharacteristic
238C2×C8×C53C22×C411yescharacteristic
239C2×C8×C53C22×C411yescharacteristic
240C2×C8×C53C22×C411yescharacteristic
241C22⋊Dic53—21no—
242C22⋊Dic53—21no—
243C22⋊Dic53—21no—
244C22⋊Dic53—21no—
245C22⋊Dic53—42no—
246C4⋊Dic53—21no—
247C4⋊Dic53—21no—
248C4⋊Dic53C22×C411yescharacteristic
249C4⋊Dic53C22×C411yescharacteristic
250C4⋊Dic53C22×C411yescharacteristic
251C4⋊Dic53C22×C411yescharacteristic
252C4×Dic53—21no—
253C4×Dic53—21no—
254C4×Dic53—21no—
255C4×Dic53—21no—
256C4×Dic53—21no—
257C4×Dic53—21no—
258C4×Dic53—21no—
259C4×Dic53—21no—
260C2×#88322—21no—
261C2×#88322—21no—
262C2×#88322—21no—
263C2×#88322—21no—
264C2×#88322C2×D411yescharacteristic
265C2×#88322C2×D411yescharacteristic
266C2×#88322C2×D411yescharacteristic
267C2×#88322C2×D411yescharacteristic
268#11719912—42no—
269#11719912—42no—
270C8×D53—42no—
271C8×D53—42no—
272C23×C53—21no—
273C23×C53—21no—
274C23×C53—41no—
275C23×C53—41no—
276C23×C53C4×D411yescharacteristic
277C23×C53C4×D411yescharacteristic
278C23×C53C2×#4111yescharacteristic
279C22×D53—21no—
280C22×D53—21no—
281C22×D53—42no—
282C22×D53—42no—
283C22×D53—81no—
284C2×C4×C53—21no—
285C2×C4×C53—21no—
286C2×C4×C53—21no—
287C2×C4×C53—21no—
288C2×C4×C53—21no—
289C2×C4×C53—21no—
290C2×C4×C53—21no—
291C2×C4×C53—21no—
292C2×C4×C53—21no—
293C2×C4×C53—21no—
294C2×C4×C53C4×D411yescharacteristic
295C2×C4×C53C4×D411yescharacteristic
296C2×C4×C53C23×C411yescharacteristic
297C2×C4×C53C22×D411yescharacteristic
298C2×C4×C53C2×#4111yescharacteristic
299C2×C4×C53C2×#4111yescharacteristic
300C2×C4×C53H(5,𝔽2)11yescharacteristic
301C2×C4×C53H(5,𝔽2)11yescharacteristic
302C22⋊D53—22no—
303C22⋊D53—22no—
304C22⋊D53—42no—
305C22⋊D53—42no—
306C22⋊D53—41no—
307C22⋊D53—41no—
308C2×Dic53—21no—
309C2×Dic53—22no—
310C2×Dic53—21no—
311C2×Dic53—21no—
312C2×Dic53—21no—
313C2×Dic53—21no—
314C2×Dic53—21no—
315C2×Dic53—42no—
316C2×Dic53—41no—
317C2×Dic53—42no—
318C2×Dic53—41no—
319C2×Dic53—41no—
320C2×Dic53—41no—
321C2×Dic53—41no—
322C2×Dic53—81no—
323D212—21no—
324D212—21no—
325D212—21no—
326D212—42no—
327D212#11712yes—
328C4×D53—22no—
329C4×D53—22no—
330C4×D53—42no—
331C4×D53—42no—
332C4×D53—41no—
333C4×D53—41no—
334Dic106—21no—
335Dic106—21no—
336Dic106—21no—
337Dic106—42no—
338Dic106#11712yes—
339C8×C53—21no—
340C8×C53—21no—
341C8×C53—21no—
342C8×C53—21no—
343C8×C53—41no—
344C8×C53—41no—
345C8×C53—41no—
346C8×C53—41no—
347#88322—21no—
348#88322—21no—
349#88322—21no—
350#88322—21no—
351#22588—531nomaximal, Sylow
352C22×C53—21no—
353C22×C53—21no—
354C22×C53—21no—
355C22×C53—21no—
356C22×C53—21no—
357C22×C53—21no—
358C22×C53—21no—
359C22×C53—21no—
360C22×C53—81no—
361C22×C53—81no—
362C22×C53C2×C4×D411yescharacteristic
363C22×C53#55111yescharacteristic
364C22×C53#55111yescharacteristic
365C2×D53—22no—
366C2×D53—41no—
367C2×D53—41no—
368C2×D53—41no—
369C2×D53—41no—
370C2×D53—41no—
371C2×D53—84no—
372C4×C53—21no—
373C4×C53—21no—
374C4×C53C2×#11711yescharacteristic
375C4×C53#51811yescharacteristic
376C4×C53#54611yescharacteristic
377C4×C53#54611yescharacteristic
378Dic53—22no—
379Dic53—42no—
380Dic53—41no—
381Dic53—41no—
382Dic53—41no—
383Dic53—41no—
384Dic53—41no—
385Dic53—81no—
386#2924—531no—
387#2896—531no—
388#2880—531no—
389#1938—531no—
390#1937—531no—
391#1929—531no—
392#1929—531no—
393#1866—531no—
394#1866—531no—
395#1826—531no—
396#1811D5311yescharacteristic, complemented
397#1789—531no—
398#1765—531no—
399#1764—531no—
400#1753—531no—
401C2×C53—21no—
402C2×C53—21no—
403C2×C53—41no—
404C2×C53—41no—
405C2×C53#234211yescharacteristic
406C2×C53#295511yescharacteristic
407C2×C53#295611yescharacteristic
408D53—42no—
409D53—81no—
410C22×#41—531no—
411C2×#131—531no—
412C2×#131—531no—
413C22×M16C2×D5311yescharacteristic
414C2×#117—531no—
415#433—1061no—
416#433—1061no—
417#432—1061no—
418#431—1061no—
419C2×#108C2×D5311yescharacteristic, complemented
420C2×#108C2×D5311yescharacteristic, complemented
421#424—531no—
422#424—531no—
423C2×#104—531no—
424C2×#104—531no—
425C2×#104—531no—
426C2×#104—531no—
427#419—531no—
428#419—531no—
429#418—531no—
430#418—531no—
431#417—531no—
432#417—531no—
433#417—531no—
434#417—531no—
435#416—531no—
436#416—531no—
437#416—531no—
438#416—531no—
439#408—531no—
440#408—531no—
441#408—1061no—
442#408—1061no—
443#407—1061no—
444#407C2×D5311yescharacteristic
445#407C2×D5311yescharacteristic
446C2×C22⋊C8—531no—
447C2×C22⋊C8—1061no—
448#405—531no—
449#405—531no—
450C2×#97—531no—
451C2×C4×C8—531no—
452C4×C22⋊C4—531no—
453#341C2×D5311yescharacteristic, complemented
454#341C2×D5311yescharacteristic, complemented
455#339—531no—
456#339—531no—
457#339—531no—
458#339—531no—
459#336—531no—
460#336—531no—
461C53#2258811yescharacteristic, complemented, Sylow
462C2×#41—531no—
463C2×#41—531no—
464C2×#41—531no—
465C2×#41—531no—
466C2×#41—1062no—
467C2×#41—1062no—
468C2×#41—1061no—
469C2×#41—1061no—
470C2×#41—2121no—
471C2×#41—2121no—
472C22×Q8—531no—
473C22×D4—531no—
474C22×D4—1061no—
475C23×C4—1061no—
476C23×C4C22×D5311yescharacteristic
477#131—1062no—
478#131—1062no—
479#131—2121no—
480#131—2121no—
481C2×M16—41no—
482C2×M16—41no—
483C2×M16—1061no—
484C2×M16—1061no—
485C2×M16C4×D5311yescharacteristic
486C2×M16C4×D5311yescharacteristic
487C2×M16C4×D5311yescharacteristic
488C2×M16C4×D5311yescharacteristic
489C2×M16C22×D5311yescharacteristic
490C2×M16C22×D5311yescharacteristic
491C2×M16C22×D5311yescharacteristic
492C2×M16C22×D5311yescharacteristic
493C22×C8—531no—
494C22×C8—531no—
495C22×C8—1061no—
496C22×C8—1061no—
497C22×C8C22×D5311yescharacteristic
498C22×C8C22×D5311yescharacteristic
499#117—531no—
500#117—531no—
501#117—531no—
502#117—531no—
503#117—1061no—
504#117—1061no—
505C2×C4⋊C4—531no—
506C2×C4⋊C4—531no—
507C2×C22⋊C4—1061no—
508C2×C22⋊C4—1061no—
509C2×C42—531no—
510C2×C42—531no—
511C2×C42—1061no—
512#108—41no—
513#108—41no—
514C4⋊C8—1061no—
515C4⋊C8—1061no—
516C4⋊C8—1061no—
517C4⋊C8—1061no—
518#104—1062no—
519#104—1062no—
520#104—2121no—
521#104—2121no—
522#103—531no—
523#103—531no—
524#103—531no—
525#103—531no—
526#103—531no—
527#103—531no—
528#103—531no—
529#103—531no—
530#102—531no—
531#102—531no—
532#102—531no—
533#102—531no—
534#102—531no—
535#102—531no—
536#102—531no—
537#102—531no—
538C22⋊C8—21no—
539C22⋊C8—21no—
540C22⋊C8—21no—
541C22⋊C8—21no—
542C22⋊C8—531no—
543C22⋊C8—531no—
544C22⋊C8—531no—
545C22⋊C8—531no—
546C22⋊C8—1061no—
547C22⋊C8—1061no—
548C22⋊C8—1061no—
549C22⋊C8—1061no—
550#97—1061no—
551#97—1061no—
552#97—2121no—
553C4×C8—1061no—
554C4×C8—1061no—
555C4×C8—2121no—
556#95—1061no—
557C24—1061no—
558C24#1171994911yescharacteristic
559#41—532no—
560#41—532no—
561#41—1062no—
562#41—1062no—
563#41—1061no—
564#41—1061no—
565#41—1061no—
566#41—1061no—
567#41—1061no—
568#41—1061no—
569#41—2122no—
570#41—2122no—
571#41—2121no—
572#41—2121no—
573#41—2122no—
574#41—2122no—
575C2×Q8—531no—
576C2×Q8—531no—
577C2×Q8—1062no—
578C2×Q8—1061no—
579C2×Q8—2121no—
580C2×D4—531no—
581C2×D4—531no—
582C2×D4—1062no—
583C2×D4—1061no—
584C2×D4—1061no—
585C2×D4—1061no—
586C2×D4—1061no—
587C2×D4—1061no—
588C2×D4—2121no—
589C2×D4—2122no—
590C2×D4—2122no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—1061no—
596C22×C4—1061no—
597C22×C4—1061no—
598C22×C4—1061no—
599C22×C4—1061no—
600C22×C4—1061no—
601C22×C4—1061no—
602C22×C4—1061no—
603C22×C4—1061no—
604C22×C4—2122no—
605C22×C4—2122no—
606C22×C4C2×C4×D5311yescharacteristic
607C22×C4C2×C4×D5311yescharacteristic
608C22×C4D4×D5311yescharacteristic
609C22×C4D4×D5311yescharacteristic
610C22×C4#1171994911yescharacteristic
611C22×C4C23×D5311yescharacteristic
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—21no—
617M16—21no—
618M16—21no—
619M16—21no—
620M16—41no—
621M16—41no—
622M16—41no—
623M16—41no—
624M16—2122no—
625M16—2122no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—531no—
635C2×C8—531no—
636C2×C8—531no—
637C2×C8—531no—
638C2×C8—1061no—
639C2×C8—1061no—
640C2×C8—1061no—
641C2×C8—1061no—
642C2×C8—2122no—
643C2×C8—2122no—
644C2×C8C2×C4×D5311yescharacteristic
645C2×C8C2×C4×D5311yescharacteristic
646C2×C8C2×C4×D5311yescharacteristic
647C2×C8C2×C4×D5311yescharacteristic
648C4⋊C4—531no—
649C4⋊C4—531no—
650C4⋊C4—531no—
651C4⋊C4—531no—
652C4⋊C4—1061no—
653C4⋊C4—1061no—
654C22⋊C4—1061no—
655C22⋊C4—1061no—
656C22⋊C4—1061no—
657C22⋊C4—1061no—
658C22⋊C4—2122no—
659C42—1061no—
660C42—1061no—
661C42—1061no—
662C42—1061no—
663C42—1061no—
664C42—1061no—
665C42—1061no—
666C42—1061no—
667C23—21no—
668C23—21no—
669C23—41no—
670C23—41no—
671C23—1061no—
672C23—1061no—
673C23—4241no—
674C23—2122no—
675C23—2122no—
676C23#1313317911yescharacteristic
677C23#1313317911yescharacteristic
678C23C2×#1171994911yescharacteristic
679Q8—532no—
680Q8—1061no—
681Q8—1061no—
682Q8—1061no—
683Q8—2122no—
684D4—532no—
685D4—1062no—
686D4—1062no—
687D4—1061no—
688D4—1061no—
689D4—1061no—
690D4—2122no—
691D4—2122no—
692D4—2122no—
693D4—2121no—
694D4—2121no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—1061no—
706C2×C4—1062no—
707C2×C4—1062no—
708C2×C4—1062no—
709C2×C4—1061no—
710C2×C4—1061no—
711C2×C4—1061no—
712C2×C4—1061no—
713C2×C4—1061no—
714C2×C4—4241no—
715C2×C4—2122no—
716C2×C4—2122no—
717C2×C4—2122no—
718C2×C4—2121no—
719C2×C4—2121no—
720C2×C4—2121no—
721C2×C4—2121no—
722C2×C4—2122no—
723C2×C4—2121no—
724C2×C4—2121no—
725C2×C4—2121no—
726C2×C4#1313317911yescharacteristic
727C2×C4#1313317911yescharacteristic
728C2×C4C22×C4×D5311yescharacteristic
729C2×C4C2×D4×D5311yescharacteristic
730C2×C4#41×D5311yescharacteristic
731C2×C4#41×D5311yescharacteristic
732C2×C4#1313326211yescharacteristic
733C2×C4#1313326211yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—41no—
739C8—41no—
740C8—41no—
741C8—41no—
742C8—1061no—
743C8—1061no—
744C8—1061no—
745C8—1061no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—81no—
755C22—81no—
756C22—1062no—
757C22—4244no—
758C22—2121no—
759C22—2121no—
760C22—2121no—
761C22—2121no—
762C22—2121no—
763C22C2×#1313317911yescharacteristic
764C22#1681130011yescharacteristic
765C22#1681130011yescharacteristic
766C4—21no—
767C4—21no—
768C4—1062no—
769C4—4241no—
770C4—2122no—
771C4—2121no—
772C4—2121no—
773C4—2121no—
774C4—2121no—
775C4—2121no—
776C4#117×D5311yescharacteristic
777C4#1681109611yescharacteristic
778C4#1681126211yescharacteristic
779C4#1681126211yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—4241no—
785C2—2122no—
786C2#2027756111yescharacteristic
787C2#2028361711yescharacteristic
788C2#2028362411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1811C2
socleC22×C53C2×C4×D4
prime radicalC22×#11719945C22
cosocleC22×C4×C53C24
hypercenter#1811D53
hypocenterC53#22588
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1811

Complements

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

NH ≅ G/Ntype
1. #20283375C2semidirect
4. #20275424C2semidirect
5. #20275417C2semidirect
6. #20275362C2semidirect
7. #20275362C2semidirect
8. #20274987C2semidirect
9. #20274987C2semidirect
10. #20274812C2semidirect
12. #20274558C2semidirect
13. #20274551C2semidirect
14. #20274496C2semidirect
15. C53×#1811C2semidirect
24. #16810651C22semidirect
25. #16810651C22semidirect
30. #16810633C4semidirect
31. #16810633C4semidirect
32. #16810629C4semidirect
33. #16810629C4semidirect
34. #16810625C4semidirect
35. #16810625C4semidirect
36. #16810625C4semidirect
37. #16810625C4semidirect
49. #16810581C22semidirect
50. #16810581C22semidirect
51. C2×#13133127C22semidirect
52. C2×C8×Dic53C22semidirect
54. #16810384C22semidirect
55. #16810384C22semidirect
56. #16810384C22semidirect
57. #16810384C22semidirect
58. #16810377C22semidirect
59. #16810377C22semidirect
61. C2×#108×C53C22semidirect
62. C2×#108×C53C22semidirect
65. C53×#341C22semidirect
66. C53×#341C22semidirect
396. #1811D53semidirect
419. C2×#108C2×D53semidirect
420. C2×#108C2×D53semidirect
453. #341C2×D53semidirect
454. #341C2×D53semidirect
461. C53#22588semidirect

Maximal subgroups

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

subgroupindex
#202833752
#202832352
#202831652
#202754242
#202754172
#202753622
#202749872
#202748122
#202746582
#202745582
#202745512
#202744962
C53×#18112
#2258853