Finite Group Databasebeta

← #27401456

Subgroups — #27401456

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#20283373C211yesmaximal, characteristic, complemented
2#20283232C211yesmaximal, characteristic
3#20283165C211yesmaximal, characteristic
4#20275427C211yesmaximal, characteristic, complemented
5#20275420C211yesmaximal, characteristic, complemented
6#20275361C211yesmaximal, characteristic, complemented
7#20275361C211yesmaximal, characteristic, complemented
8#20274991C211yesmaximal, characteristic, complemented
9#20274991C211yesmaximal, characteristic, complemented
10#20274755C211yesmaximal, characteristic, complemented
11#20274660C211yesmaximal, characteristic
12#20274556C211yesmaximal, characteristic, complemented
13#20274549C211yesmaximal, characteristic, complemented
14#20274499C211yesmaximal, characteristic, complemented
15C53×#1826C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C2×#13133225C2211yescharacteristic
18C2×#13133225C2211yescharacteristic
19C22×#11719917C2211yescharacteristic
20#16810684—21no—
21#16810684—21no—
22#16810680—21no—
23#16810676—21no—
24C2×#13133152C2211yescharacteristic, complemented
25C2×#13133152C2211yescharacteristic, complemented
26#16810650C2211yescharacteristic, complemented
27#16810650C2211yescharacteristic, complemented
28C2×#13133145C2211yescharacteristic
29C2×#13133145C2211yescharacteristic
30C2×#13133145C2211yescharacteristic
31C2×#13133145C2211yescharacteristic
32#16810631C411yescharacteristic, complemented
33#16810631C411yescharacteristic, complemented
34#16810627C411yescharacteristic, complemented
35#16810627C411yescharacteristic, complemented
36#16810622C411yescharacteristic, complemented
37#16810622C411yescharacteristic, complemented
38#16810622C411yescharacteristic, complemented
39#16810622C411yescharacteristic, complemented
40#16810617C2211yescharacteristic
41#16810617C2211yescharacteristic
42#16810617C2211yescharacteristic
43#16810617C2211yescharacteristic
44#16810591C2211yescharacteristic
45#16810591C2211yescharacteristic
46#16810588—21no—
47#16810588—21no—
48#16810587C2211yescharacteristic
49#16810585—21no—
50C2×C22⋊#88322C2211yescharacteristic
51C22⋊C8×D53—21no—
52#16810579C2211yescharacteristic, complemented
53#16810579C2211yescharacteristic, complemented
54C2×#13133128C2211yescharacteristic, complemented
55C2×C4×#88322C2211yescharacteristic, complemented
56#16810387C2211yescharacteristic, complemented
57#16810387C2211yescharacteristic, complemented
58#16810378C2211yescharacteristic, complemented
59#16810378C2211yescharacteristic, complemented
60C2×#117×C53C2211yescharacteristic
61C53×#407C2211yescharacteristic
62C4×C22⋊C4×C53C2211yescharacteristic
63C53×#339C2211yescharacteristic, complemented
64C53×#339C2211yescharacteristic, complemented
65C53×#339C2211yescharacteristic, complemented
66C53×#339C2211yescharacteristic, 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×#11719917—41no—
86C2×#11719917—41no—
87C2×#11719917C2×C411yescharacteristic
88C2×#11719917C2×C411yescharacteristic
89C2×#11719917C2×C411yescharacteristic
90C2×#11719917C2×C411yescharacteristic
91C2×#11719917C2311yescharacteristic
92C2×#11719917C2311yescharacteristic
93C2×#11719912—21no—
94C2×#11719912—21no—
95C22×#88322C2311yescharacteristic
96C22×#88322C2311yescharacteristic
97C22×#88322C2311yescharacteristic
98C22×#88322C2311yescharacteristic
99C2×C8×D53—21no—
100C2×C8×D53—21no—
101#13133152—41no—
102#13133152—41no—
103C4⋊#88322—21no—
104C4⋊#88322—21no—
105C4⋊#88322—21no—
106C4⋊#88322—21no—
107#13133145—22no—
108#13133145—22no—
109#13133145—41no—
110#13133145—41no—
111#13133140C2×C411yescharacteristic
112#13133140C2×C411yescharacteristic
113#13133140C2×C411yescharacteristic
114#13133140C2×C411yescharacteristic
115#13133140C2×C411yescharacteristic
116#13133140C2×C411yescharacteristic
117#13133140C2×C411yescharacteristic
118#13133140C2×C411yescharacteristic
119#13133137C2×C411yescharacteristic
120#13133137C2×C411yescharacteristic
121#13133137C2×C411yescharacteristic
122#13133137C2×C411yescharacteristic
123#13133137C2×C411yescharacteristic
124#13133137C2×C411yescharacteristic
125#13133137C2×C411yescharacteristic
126#13133137C2×C411yescharacteristic
127C22⋊#88322—21no—
128C22⋊#88322—21no—
129C22⋊#88322D411yescharacteristic
130C22⋊#88322D411yescharacteristic
131C22⋊#88322D411yescharacteristic
132C22⋊#88322D411yescharacteristic
133#13133129—21no—
134#13133129—21no—
135#13133129—21no—
136#13133129—21no—
137#13133128—21no—
138#13133128—21no—
139#13133128—41no—
140C4×#88322—21no—
141C4×#88322—21no—
142C4×#88322—41no—
143C23×C4×C53C2311yescharacteristic
144C2×M16×C53C2311yescharacteristic
145C2×M16×C53C2311yescharacteristic
146#117×C53—21no—
147#117×C53—21no—
148#117×C53C2×C411yescharacteristic
149#117×C53C2×C411yescharacteristic
150#117×C53C2311yescharacteristic
151#117×C53C2311yescharacteristic
152C2×C4⋊C4×C53C2×C411yescharacteristic
153C2×C4⋊C4×C53C2×C411yescharacteristic
154C2×C22⋊C4×C53—21no—
155C2×C22⋊C4×C53—21no—
156C2×C42×C53—21no—
157C2×C42×C53C2311yescharacteristic
158C2×C42×C53C2311yescharacteristic
159C22⋊C8×C53—21no—
160C22⋊C8×C53—21no—
161#95×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×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—21no—
171C22×C4×C53—21no—
172C22×C4×C53C22×C411yescharacteristic
173C22×C4×C53C22×C411yescharacteristic
174C22×C4×C53C2×D411yescharacteristic
175C22×C4×C53C2×D411yescharacteristic
176C22×C4×C53#4111yescharacteristic
177C22×C4×C53C2411yescharacteristic
178C2×C22⋊D53—21no—
179C2×C22⋊D53—21no—
180C2×C22⋊D53—21no—
181C2×C22⋊D53—21no—
182C2×C22⋊D53—42no—
183C2×C22⋊D53—42no—
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—
221C2×C8×C53—21no—
222C2×C8×C53—21no—
223C4⋊C4×C53—21no—
224C4⋊C4×C53—21no—
225C4⋊C4×C53C22×C411yescharacteristic
226C4⋊C4×C53C22×C411yescharacteristic
227C4⋊C4×C53C22×C411yescharacteristic
228C4⋊C4×C53C22×C411yescharacteristic
229C22⋊C4×C53—21no—
230C22⋊C4×C53—21no—
231C22⋊C4×C53—21no—
232C22⋊C4×C53—21no—
233C22⋊C4×C53—42no—
234C42×C53—21no—
235C42×C53—21no—
236C42×C53—21no—
237C42×C53—21no—
238C42×C53—21no—
239C42×C53—21no—
240C42×C53—21no—
241C42×C53—21no—
242#11719917—21no—
243#11719917—21no—
244#11719917—21no—
245#11719917—21no—
246#11719917—41no—
247#11719917—41no—
248#11719917—41no—
249#11719917—41no—
250C2×#88322—21no—
251C2×#88322—21no—
252C2×#88322—21no—
253C2×#88322—21no—
254C2×#88322—21no—
255C2×#88322—21no—
256C2×#88322—21no—
257C2×#88322—21no—
258C2×#88322—21no—
259C2×#88322—21no—
260C2×#88322C22×C411yescharacteristic
261C2×#88322C22×C411yescharacteristic
262C2×#88322C22×C411yescharacteristic
263C2×#88322C22×C411yescharacteristic
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×C53—22no—
295C2×C4×C53—21no—
296C2×C4×C53—21no—
297C2×C4×C53—21no—
298C2×C4×C53—21no—
299C2×C4×C53—41no—
300C2×C4×C53—42no—
301C2×C4×C53—41no—
302C2×C4×C53—41no—
303C2×C4×C53—41no—
304C2×C4×C53—41no—
305C2×C4×C53—81no—
306C2×C4×C53C4×D411yescharacteristic
307C2×C4×C53C4×D411yescharacteristic
308C2×C4×C53C23×C411yescharacteristic
309C2×C4×C53C22×D411yescharacteristic
310C2×C4×C53C2×#4111yescharacteristic
311C2×C4×C53C2×#4111yescharacteristic
312C2×C4×C53H(5,𝔽2)11yescharacteristic
313C2×C4×C53H(5,𝔽2)11yescharacteristic
314C22⋊D53—22no—
315C22⋊D53—22no—
316C22⋊D53—42no—
317C22⋊D53—42no—
318C22⋊D53—41no—
319C22⋊D53—41no—
320C2×Dic53—21no—
321C2×Dic53—21no—
322C2×Dic53—42no—
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—41no—
340C8×C53—41no—
341#88322—21no—
342#88322—21no—
343#88322—21no—
344#88322—21no—
345#88322—21no—
346#88322—21no—
347#88322—21no—
348#88322—21no—
349#88322—41no—
350#88322—41no—
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×C53—42no—
375C4×C53—41no—
376C4×C53—41no—
377C4×C53—41no—
378C4×C53—41no—
379C4×C53—81no—
380C4×C53C2×#11711yescharacteristic
381C4×C53#51811yescharacteristic
382C4×C53#54611yescharacteristic
383C4×C53#54611yescharacteristic
384Dic53—22no—
385Dic53—41no—
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#1826D5311yescharacteristic, complemented
396#1811—531no—
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×M16—531no—
414C2×#117C2×D5311yescharacteristic
415#433—1061no—
416#433—1061no—
417#432—1061no—
418#431—1061no—
419C2×#108—531no—
420C2×#108—531no—
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—531no—
444#407—1061no—
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⋊C4C2×D5311yescharacteristic
453#341—531no—
454#341—531no—
455#339C2×D5311yescharacteristic, complemented
456#339C2×D5311yescharacteristic, complemented
457#339C2×D5311yescharacteristic, complemented
458#339C2×D5311yescharacteristic, complemented
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—531no—
482C2×M16—531no—
483C2×M16—531no—
484C2×M16—531no—
485C2×M16—531no—
486C2×M16—531no—
487C2×M16—1061no—
488C2×M16—1061no—
489C2×M16—2121no—
490C2×M16—2121no—
491C2×M16C22×D5311yescharacteristic
492C2×M16C22×D5311yescharacteristic
493C22×C8—531no—
494C22×C8—531no—
495C22×C8—531no—
496C22×C8—531no—
497C22×C8—1061no—
498C22×C8—1061no—
499#117—21no—
500#117—21no—
501#117C4×D5311yescharacteristic
502#117C4×D5311yescharacteristic
503#117C22×D5311yescharacteristic
504#117C22×D5311yescharacteristic
505C2×C4⋊C4C4×D5311yescharacteristic
506C2×C4⋊C4C4×D5311yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C42—21no—
510C2×C42C22×D5311yescharacteristic
511C2×C42C22×D5311yescharacteristic
512#108—2121no—
513#108—2121no—
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—531no—
541C22⋊C8—531no—
542C22⋊C8—531no—
543C22⋊C8—531no—
544C22⋊C8—1061no—
545C22⋊C8—1061no—
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—21no—
557C24—1061no—
558C24#1171994711yescharacteristic
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—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
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#1171994711yescharacteristic
611C22×C4C23×D5311yescharacteristic
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—1061no—
617M16—1061no—
618M16—1061no—
619M16—1061no—
620M16—2122no—
621M16—2122no—
622M16—2121no—
623M16—2121no—
624M16—2121no—
625M16—2121no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—531no—
629C2×C8—531no—
630C2×C8—531no—
631C2×C8—531no—
632C2×C8—531no—
633C2×C8—531no—
634C2×C8—531no—
635C2×C8—531no—
636C2×C8—1061no—
637C2×C8—1061no—
638C2×C8—1061no—
639C2×C8—1061no—
640C2×C8—1061no—
641C2×C8—1061no—
642C2×C8—1061no—
643C2×C8—1061no—
644C2×C8—1061no—
645C2×C8—1061no—
646C2×C8—2122no—
647C2×C8—2122no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4C2×C4×D5311yescharacteristic
651C4⋊C4C2×C4×D5311yescharacteristic
652C4⋊C4C2×C4×D5311yescharacteristic
653C4⋊C4C2×C4×D5311yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—42no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C23—21no—
668C23—21no—
669C23—41no—
670C23—41no—
671C23—1061no—
672C23—1061no—
673C23—4241no—
674C23—2122no—
675C23—2122no—
676C23#1313317711yescharacteristic
677C23#1313317711yescharacteristic
678C23C2×#1171994711yescharacteristic
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—22no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—81no—
717C2×C4—1061no—
718C2×C4—1062no—
719C2×C4—1062no—
720C2×C4—1061no—
721C2×C4—2122no—
722C2×C4—2122no—
723C2×C4—2122no—
724C2×C4—2121no—
725C2×C4—2121no—
726C2×C4#1313317711yescharacteristic
727C2×C4#1313317711yescharacteristic
728C2×C4C22×C4×D5311yescharacteristic
729C2×C4C2×D4×D5311yescharacteristic
730C2×C4#41×D5311yescharacteristic
731C2×C4#41×D5311yescharacteristic
732C2×C4#1313326311yescharacteristic
733C2×C4#1313326311yescharacteristic
734C8—41no—
735C8—41no—
736C8—1061no—
737C8—1061no—
738C8—1061no—
739C8—1061no—
740C8—1061no—
741C8—1061no—
742C8—1061no—
743C8—1061no—
744C8—2121no—
745C8—2121no—
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×#1313317711yescharacteristic
764C22#1681129611yescharacteristic
765C22#1681129611yescharacteristic
766C4—21no—
767C4—21no—
768C4—42no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—81no—
774C4—1062no—
775C4—2121no—
776C4#117×D5311yescharacteristic
777C4#1681109711yescharacteristic
778C4#1681126511yescharacteristic
779C4#1681126511yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—4241no—
785C2—2122no—
786C2#2027755711yescharacteristic
787C2#2028361411yescharacteristic
788C2#2028362111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1826C2
socleC22×C53C2×C4×D4
prime radicalC22×#11719945C22
cosocleC22×C4×C53C24
hypercenter#1826D53
hypocenterC53#22588
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
1. #20283373C2semidirect
4. #20275427C2semidirect
5. #20275420C2semidirect
6. #20275361C2semidirect
7. #20275361C2semidirect
8. #20274991C2semidirect
9. #20274991C2semidirect
10. #20274755C2semidirect
12. #20274556C2semidirect
13. #20274549C2semidirect
14. #20274499C2semidirect
15. C53×#1826C2semidirect
24. C2×#13133152C22semidirect
25. C2×#13133152C22semidirect
26. #16810650C22semidirect
27. #16810650C22semidirect
32. #16810631C4semidirect
33. #16810631C4semidirect
34. #16810627C4semidirect
35. #16810627C4semidirect
36. #16810622C4semidirect
37. #16810622C4semidirect
38. #16810622C4semidirect
39. #16810622C4semidirect
52. #16810579C22semidirect
53. #16810579C22semidirect
54. C2×#13133128C22semidirect
55. C2×C4×#88322C22semidirect
56. #16810387C22semidirect
57. #16810387C22semidirect
58. #16810378C22semidirect
59. #16810378C22semidirect
63. C53×#339C22semidirect
64. C53×#339C22semidirect
65. C53×#339C22semidirect
66. C53×#339C22semidirect
395. #1826D53semidirect
455. #339C2×D53semidirect
456. #339C2×D53semidirect
457. #339C2×D53semidirect
458. #339C2×D53semidirect
461. C53#22588semidirect

Maximal subgroups

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

subgroupindex
#202833732
#202832322
#202831652
#202754272
#202754202
#202753612
#202749912
#202747552
#202746602
#202745562
#202745492
#202744992
C53×#18262
#2258853