Finite Group Databasebeta

← #27406622

Subgroups — #27406622

Order 13568.

864 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20284170C211yesmaximal, characteristic
2C2×#16810743C211yesmaximal, characteristic, complemented
3C2×#16810738C211yesmaximal, characteristic, complemented
4#20283458C211yesmaximal, characteristic, complemented
5#20275546C211yesmaximal, characteristic, complemented
6#20275488C211yesmaximal, characteristic, complemented
7#20275425C211yesmaximal, characteristic, complemented
8#20275418C211yesmaximal, characteristic, complemented
9#20275042C211yesmaximal, characteristic, complemented
10#20275042C211yesmaximal, characteristic, complemented
11#20274989C211yesmaximal, characteristic, complemented
12#20274989C211yesmaximal, characteristic, complemented
13#20274574C211yesmaximal, characteristic, complemented
14#20274525C211yesmaximal, characteristic, complemented
15C53×#2906C211yesmaximal, characteristic, complemented
16C2×#13133237C2211yescharacteristic
17C2×#13133237C2211yescharacteristic
18C2×#13133223C2211yescharacteristic
19C2×#13133223C2211yescharacteristic
20#16811173C2211yescharacteristic
21#16810845C411yescharacteristic, complemented
22#16810845C411yescharacteristic, complemented
23#16810838C411yescharacteristic, complemented
24#16810838C411yescharacteristic, complemented
25#16810833C411yescharacteristic, complemented
26#16810828C411yescharacteristic, complemented
27#16810823C411yescharacteristic, complemented
28#16810818C411yescharacteristic, complemented
29#16810743—24no—
30#16810738—24no—
31#16810700—21no—
32#16810693—21no—
33#16810693—21no—
34#16810688—21no—
35C2×#13133152C2211yescharacteristic
36C2×#13133152C2211yescharacteristic
37C2×C4⋊#88322C2211yescharacteristic
38C2×#13133144C2211yescharacteristic
39C2×#13133144C2211yescharacteristic
40C2×#13133143C2211yescharacteristic
41C2×#13133143C2211yescharacteristic
42C2×#13133143C2211yescharacteristic
43C2×#13133143C2211yescharacteristic
44#16810617C2211yescharacteristic
45#16810617C2211yescharacteristic
46#16810589C2211yescharacteristic
47#16810589C2211yescharacteristic
48C4×#11719917C2211yescharacteristic
49C2×#13133127C2211yescharacteristic
50C2×C8×Dic53C2211yescharacteristic
51#16810469C2211yescharacteristic
52#16810387C2211yescharacteristic
53#16810387C2211yescharacteristic
54#16810382C2211yescharacteristic
55#16810382C2211yescharacteristic
56#16810377C2211yescharacteristic
57#16810377C2211yescharacteristic
58C2×#131×C53C2211yescharacteristic
59C2×#131×C53C2211yescharacteristic
60C4×#41×C53C2211yescharacteristic
61C53×#424—21no—
62C53×#424—21no—
63C53×#424C2211yescharacteristic
64C53×#424C2211yescharacteristic
65C53×#423—21no—
66C53×#423C2211yescharacteristic
67C2×C4⋊C8×C53—21no—
68C2×C4⋊C8×C53C2211yescharacteristic
69C2×#11719945C2311yescharacteristic
70C2×#11719945C2311yescharacteristic
71#13133237—22no—
72#13133237—22no—
73#13133237—22no—
74#13133237—22no—
75C2×#11719925C2×C411yescharacteristic
76C2×#11719925C2×C411yescharacteristic
77C2×#11719923C2×C411yescharacteristic
78C2×#11719923C2×C411yescharacteristic
79C2×#11719924C2×C411yescharacteristic
80C2×#11719924C2×C411yescharacteristic
81C2×#11719922C2×C411yescharacteristic
82C2×#11719922C2×C411yescharacteristic
83#13133223—22no—
84#13133223—22no—
85#13133223—41no—
86#13133223—41no—
87C2×#11719917C2311yescharacteristic
88C2×#11719917C2311yescharacteristic
89C2×#11719912—21no—
90C2×#11719912—21no—
91C22×#88322C2311yescharacteristic
92C22×#88322C2311yescharacteristic
93C2×C8×D53—21no—
94C2×C8×D53—21no—
95#13133217C2×C411yescharacteristic
96#13133214C2×C411yescharacteristic
97#13133205C2×C411yescharacteristic
98#13133205C2×C411yescharacteristic
99#13133191—21no—
100#13133191—21no—
101C4×D212—21no—
102C4×D212—21no—
103C2×C4×Dic53C2311yescharacteristic
104C2×C4×Dic53C2311yescharacteristic
105#13133152—22no—
106#13133152—22no—
107C4⋊#88322C2×C411yescharacteristic
108C4⋊#88322C2×C411yescharacteristic
109C4⋊#88322C2×C411yescharacteristic
110C4⋊#88322C2×C411yescharacteristic
111#13133144—22no—
112#13133144D414yescomplemented
113#13133143—22no—
114#13133143—22no—
115#13133143—41no—
116#13133143—41no—
117#13133140C2×C411yescharacteristic
118#13133140C2×C411yescharacteristic
119#13133140C2×C411yescharacteristic
120#13133140C2×C411yescharacteristic
121#13133137C2×C411yescharacteristic
122#13133137C2×C411yescharacteristic
123#13133137C2×C411yescharacteristic
124#13133137C2×C411yescharacteristic
125#13133129—21no—
126#13133129—21no—
127#13133129—21no—
128#13133129—21no—
129#13133128—21no—
130#13133127—22no—
131C4×#88322—21no—
132C8×Dic53—22no—
133#13133124—21no—
134#13133124—21no—
135C2×#41×C53C2311yescharacteristic
136#131×C53—22no—
137#131×C53—22no—
138#131×C53—41no—
139#131×C53—41no—
140C2×M16×C53—21no—
141C2×M16×C53—21no—
142C2×M16×C53C2311yescharacteristic
143C2×M16×C53C2311yescharacteristic
144C22×C8×C53—21no—
145C22×C8×C53—21no—
146C22×C8×C53C2311yescharacteristic
147C22×C8×C53C2311yescharacteristic
148C4×Q8×C53C2×C411yescharacteristic
149C4×Q8×C53C2×C411yescharacteristic
150C4×D4×C53—21no—
151C4×D4×C53—21no—
152C4×D4×C53C2×C411yescharacteristic
153C4×D4×C53C2×C411yescharacteristic
154#117×C53—21no—
155#117×C53C2311yescharacteristic
156C2×C42×C53—21no—
157C2×C42×C53C2311yescharacteristic
158C4⋊C8×C53—21no—
159C4⋊C8×C53—21no—
160C4⋊C8×C53—21no—
161C4⋊C8×C53—21no—
162C4⋊C8×C53—21no—
163C4⋊C8×C53—21no—
164C4⋊C8×C53D411yescharacteristic
165C4⋊C8×C53D411yescharacteristic
166C4⋊C8×C53D411yescharacteristic
167C4⋊C8×C53D411yescharacteristic
168#41×C53—21no—
169#41×C53—21no—
170#41×C53C2×D412yes—
171#41×C53#4112yes—
172C2×Q8×C53C22×C411yescharacteristic
173C2×D4×C53—21no—
174C2×D4×C53C22×C411yescharacteristic
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53#4111yescharacteristic
179C22×C4×C53#4111yescharacteristic
180C22×C4×C53C2411yescharacteristic
181C2×C22⋊D53—21no—
182C2×C22⋊D53—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—21no—
192#11719945—21no—
193C2×D212—21no—
194C2×D212—21no—
195C2×D212C22×C411yescharacteristic
196C2×D212C22×C411yescharacteristic
197C2×C4×D53—21no—
198C2×C4×D53—21no—
199C2×Dic106C22×C411yescharacteristic
200C2×Dic106C22×C411yescharacteristic
201M16×C53—21no—
202M16×C53—21no—
203M16×C53—21no—
204M16×C53—21no—
205M16×C53—42no—
206M16×C53—42no—
207C2×C8×C53—21no—
208C2×C8×C53—21no—
209C2×C8×C53—21no—
210C2×C8×C53—21no—
211C2×C8×C53—21no—
212C2×C8×C53—21no—
213C2×C8×C53—42no—
214C2×C8×C53—42no—
215C2×C8×C53C2×D411yescharacteristic
216C2×C8×C53C2×D411yescharacteristic
217C2×C8×C53C2×D411yescharacteristic
218C2×C8×C53C2×D411yescharacteristic
219C4⋊C4×C53—21no—
220C4⋊C4×C53—21no—
221C4⋊C4×C53C22×C411yescharacteristic
222C4⋊C4×C53C22×C411yescharacteristic
223C22⋊C4×C53—21no—
224C22⋊C4×C53—21no—
225C22⋊C4×C53—21no—
226C42×C53—21no—
227C42×C53—21no—
228C42×C53—21no—
229C42×C53C22×C411yescharacteristic
230C42×C53C22×C411yescharacteristic
231C42×C53C2×D411yescharacteristic
232C42×C53C2×D411yescharacteristic
233#11719925—22no—
234#11719925—22no—
235#11719924—22no—
236#11719924—22no—
237#11719923—22no—
238#11719923—22no—
239#11719922—22no—
240#11719922—22no—
241#11719921—21no—
242#11719921—21no—
243#11719921—21no—
244#11719921—21no—
245C4⋊Dic53—21no—
246C4⋊Dic53—21no—
247C4×Dic53—21no—
248C4×Dic53—21no—
249C4×Dic53—21no—
250C4×Dic53C2×D412yes—
251#11719917—21no—
252#11719917—21no—
253#11719917—21no—
254#11719917C2×D412yes—
255C2×#88322—21no—
256C2×#88322—21no—
257C2×#88322—21no—
258C2×#88322—21no—
259C2×#88322—21no—
260C2×#88322—21no—
261C2×#88322C22×C411yescharacteristic
262C2×#88322C22×C411yescharacteristic
263C2×#88322C22×C411yescharacteristic
264C2×#88322C22×C411yescharacteristic
265#11719912—42no—
266#11719912—42no—
267C8×D53—42no—
268C8×D53—42no—
269C23×C53—21no—
270C23×C53C2×#4111yescharacteristic
271C22×D53—21no—
272C22×D53—21no—
273Q8×C53—21no—
274Q8×C53C4×D412yes—
275D4×C53—22no—
276D4×C53—22no—
277D4×C53—21no—
278D4×C53C4×D412yes—
279C2×C4×C53—21no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
282C2×C4×C53—21no—
283C2×C4×C53—21no—
284C2×C4×C53—41no—
285C2×C4×C53—41no—
286C2×C4×C53—42no—
287C2×C4×C53—81no—
288C2×C4×C53C4×D411yescharacteristic
289C2×C4×C53C4×D411yescharacteristic
290C2×C4×C53C4×D411yescharacteristic
291C2×C4×C53C4×D411yescharacteristic
292C2×C4×C53C23×C411yescharacteristic
293C2×C4×C53C22×D411yescharacteristic
294C2×C4×C53C22×D411yescharacteristic
295C2×C4×C53C2×#4111yescharacteristic
296C2×C4×C53H(5,𝔽2)11yescharacteristic
297C2×C4×C532−1+411yescharacteristic
298C22⋊D53—41no—
299C22⋊D53—41no—
300C22⋊D53—41no—
301C22⋊D53—41no—
302C2×Dic53—21no—
303C2×Dic53—21no—
304C2×Dic53—22no—
305C2×Dic53—41no—
306C2×Dic53—41no—
307C2×Dic53—41no—
308C2×Dic53—41no—
309C2×Dic53—41no—
310D212—21no—
311D212—21no—
312D212—21no—
313D212—21no—
314D212—42no—
315D212—81no—
316C4×D53—41no—
317C4×D53—41no—
318C4×D53—41no—
319C4×D53—41no—
320Dic106—21no—
321Dic106—21no—
322Dic106—21no—
323Dic106—21no—
324C8×C53—21no—
325C8×C53—21no—
326C8×C53—21no—
327C8×C53—21no—
328C8×C53—41no—
329C8×C53—41no—
330#88322—21no—
331#88322—21no—
332#88322—21no—
333#88322—21no—
334#88322—22no—
335#88322—41no—
336#23017—531nomaximal, Sylow
337C22×C53—21no—
338C22×C53—21no—
339C22×C53—22no—
340C22×C53—41no—
341C22×C53—41no—
342C22×C53C2×C4×D411yescharacteristic
343C22×C53#54711yescharacteristic
344C22×C53#55311yescharacteristic
345C2×D53—41no—
346C2×D53—41no—
347C2×D53—41no—
348C2×D53—41no—
349C2×D53—41no—
350C2×D53—41no—
351C4×C53—22no—
352C4×C53—21no—
353C4×C53—21no—
354C4×C53—21no—
355C4×C53—21no—
356C4×C53—41no—
357C4×C53—41no—
358C4×C53C2×C4×D411yescharacteristic
359C4×C53#52011yescharacteristic
360C4×C53D4211yescharacteristic
361C4×C53#54811yescharacteristic
362Dic53—42no—
363Dic53—41no—
364Dic53—41no—
365Dic53—81no—
366#3035—531no—
367C2×#444—531no—
368C2×#443—531no—
369#2935—531no—
370#2906D5311yescharacteristic, complemented
371#1963—531no—
372#1950—531no—
373#1938—531no—
374#1937—531no—
375#1876—531no—
376#1876—531no—
377#1866—531no—
378#1866—531no—
379#1768—531no—
380#1759—531no—
381C2×C53—21no—
382C2×C53—21no—
383C2×C53—42no—
384C2×C53#236111yescharacteristic
385C2×C53#295511yescharacteristic
386C2×C53#295711yescharacteristic
387D53—81no—
388D53—81no—
389C2×#135—531no—
390C2×#135—531no—
391C2×#131—531no—
392C2×#131—531no—
393C2×#131C2×D5311yescharacteristic
394C2×#131C2×D5311yescharacteristic
395#532—531no—
396C4×#41C2×D5311yescharacteristic
397#464—531no—
398#464—531no—
399#463—531no—
400#463—531no—
401#462—531no—
402#461—531no—
403#460—531no—
404#459—531no—
405#444—1064no—
406#443—1064no—
407#436—1061no—
408#435—1061no—
409#435—1061no—
410C8×D4—1061no—
411C2×#108—531no—
412C2×#108—531no—
413#424—21no—
414#424—21no—
415#424C2×D5311yescharacteristic
416#424C2×D5311yescharacteristic
417#423—21no—
418#423C2×D5311yescharacteristic
419C2×C4⋊C8—21no—
420C2×C4⋊C8—531no—
421C2×C4⋊C8C2×D5311yescharacteristic
422C2×#104—531no—
423C2×#104—531no—
424C2×#104—531no—
425C2×#104—531no—
426C2×#104—531no—
427C2×#104—531no—
428#416—531no—
429#416—531no—
430#408—531no—
431#408—531no—
432C4×M16—531no—
433C2×#97—531no—
434C2×C4×C8—531no—
435#376—531no—
436#341—531no—
437#341—531no—
438#339—531no—
439#339—531no—
440#336—531no—
441#336—531no—
442C53#2301711yescharacteristic, complemented, Sylow
443C2×#41—531no—
444C2×#41—531no—
445C2×#41C22×D5311yescharacteristic
446#135—1062no—
447#135—1062no—
448#135—1062no—
449#135—1062no—
450C2×Q16—531no—
451C2×Q16—531no—
452C2×SD16—531no—
453C2×SD16—531no—
454C2×SD16—531no—
455C2×SD16—531no—
456C2×D8—531no—
457C2×D8—531no—
458#131—22no—
459#131—22no—
460#131—41no—
461#131—41no—
462#131—1062no—
463#131—1062no—
464#131—2121no—
465#131—2121no—
466C2×M16—21no—
467C2×M16—21no—
468C2×M16—531no—
469C2×M16—531no—
470C2×M16—1061no—
471C2×M16—1061no—
472C2×M16C22×D5311yescharacteristic
473C2×M16C22×D5311yescharacteristic
474C22×C8—21no—
475C22×C8—21no—
476C22×C8—531no—
477C22×C8—531no—
478C22×C8—1061no—
479C22×C8—1061no—
480C22×C8C22×D5311yescharacteristic
481C22×C8C22×D5311yescharacteristic
482C4⋊Q8—531no—
483#127—531no—
484#124—531no—
485#124—531no—
486#121—1061no—
487#121—1061no—
488C4×Q8C4×D5311yescharacteristic
489C4×Q8C4×D5311yescharacteristic
490C4×D4—21no—
491C4×D4—21no—
492C4×D4—1061no—
493C4×D4—1061no—
494C4×D4C4×D5311yescharacteristic
495C4×D4C4×D5311yescharacteristic
496#117—21no—
497#117C22×D5311yescharacteristic
498C2×C42—21no—
499C2×C42—531no—
500C2×C42—531no—
501C2×C42C22×D5311yescharacteristic
502#108—1062no—
503#108—1062no—
504C4⋊C8—21no—
505C4⋊C8—21no—
506C4⋊C8—21no—
507C4⋊C8—21no—
508C4⋊C8—21no—
509C4⋊C8—21no—
510C4⋊C8—531no—
511C4⋊C8—531no—
512C4⋊C8—531no—
513C4⋊C8—531no—
514C4⋊C8C22⋊D5311yescharacteristic
515C4⋊C8C22⋊D5311yescharacteristic
516C4⋊C8C22⋊D5311yescharacteristic
517C4⋊C8C22⋊D5311yescharacteristic
518#104—534no—
519#104—1062no—
520#104—1062no—
521#104—1062no—
522#104—2121no—
523#104—2121no—
524#103—531no—
525#103—531no—
526#103—531no—
527#103—531no—
528#102—531no—
529#102—531no—
530#102—531no—
531#102—531no—
532C22⋊C8—1061no—
533C22⋊C8—1061no—
534C22⋊C8—1061no—
535C22⋊C8—1061no—
536#97—1062no—
537#97—1061no—
538C4×C8—1062no—
539C4×C8—1061no—
540#95—1061no—
541#95—1061no—
542#41—21no—
543#41—21no—
544#41—1061no—
545#41—1061no—
546#41—1061no—
547#41—1061no—
548#41—1061no—
549#41—1061no—
550#41—1061no—
551#41—1061no—
552#41D4×D5312yes—
553#41#1171994912yes—
554C2×Q8—531no—
555C2×Q8—531no—
556C2×Q8C2×C4×D5311yescharacteristic
557C2×D4—21no—
558C2×D4—531no—
559C2×D4—531no—
560C2×D4—1061no—
561C2×D4—1061no—
562C2×D4—1061no—
563C2×D4—1061no—
564C2×D4C2×C4×D5311yescharacteristic
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—1061no—
569C22×C4—1061no—
570C22×C4—1061no—
571C22×C4—1061no—
572C22×C4#1171994511yescharacteristic
573C22×C4#1171994511yescharacteristic
574C22×C4C23×D5311yescharacteristic
575Q16—1062no—
576Q16—1062no—
577SD16—1062no—
578SD16—1062no—
579SD16—1062no—
580SD16—1062no—
581D8—1062no—
582D8—1062no—
583M16—21no—
584M16—21no—
585M16—21no—
586M16—21no—
587M16—42no—
588M16—42no—
589M16—532no—
590M16—1061no—
591M16—1061no—
592M16—1061no—
593M16—2122no—
594M16—2122no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—42no—
602C2×C8—42no—
603C2×C8—531no—
604C2×C8—531no—
605C2×C8—531no—
606C2×C8—531no—
607C2×C8—1061no—
608C2×C8—1061no—
609C2×C8—1061no—
610C2×C8—1061no—
611C2×C8—1061no—
612C2×C8—1061no—
613C2×C8—2122no—
614C2×C8—2122no—
615C2×C8C2×C22⋊D5311yescharacteristic
616C2×C8C2×C22⋊D5311yescharacteristic
617C2×C8C2×C22⋊D5311yescharacteristic
618C2×C8C2×C22⋊D5311yescharacteristic
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—1061no—
622C4⋊C4—1061no—
623C4⋊C4C2×C4×D5311yescharacteristic
624C4⋊C4C2×C4×D5311yescharacteristic
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—1061no—
629C22⋊C4—1061no—
630C22⋊C4—1061no—
631C22⋊C4—1061no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—532no—
636C42—1061no—
637C42—1061no—
638C42—1061no—
639C42C2×C4×D5311yescharacteristic
640C42C2×C4×D5311yescharacteristic
641C42C2×C22⋊D5311yescharacteristic
642C42C2×C22⋊D5311yescharacteristic
643C23—21no—
644C23—1061no—
645C23—1061no—
646C23C2×#1171994511yescharacteristic
647Q8—21no—
648Q8—1061no—
649Q8—1061no—
650Q8—1061no—
651Q8—1061no—
652Q8#1313317912yes—
653D4—22no—
654D4—22no—
655D4—21no—
656D4—1061no—
657D4—1061no—
658D4—1061no—
659D4—1061no—
660D4—4241no—
661D4—2122no—
662D4—2121no—
663D4—2121no—
664D4—2121no—
665D4—2121no—
666D4#1313317912yes—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—81no—
676C2×C4—1062no—
677C2×C4—1061no—
678C2×C4—1061no—
679C2×C4—2121no—
680C2×C4—2121no—
681C2×C4—2121no—
682C2×C4—2121no—
683C2×C4—2121no—
684C2×C4—2121no—
685C2×C4—2121no—
686C2×C4—2121no—
687C2×C4—2121no—
688C2×C4C4×C22⋊D5311yescharacteristic
689C2×C4C4×C22⋊D5311yescharacteristic
690C2×C4C4×C22⋊D5311yescharacteristic
691C2×C4C4×C22⋊D5311yescharacteristic
692C2×C4C22×C4×D5311yescharacteristic
693C2×C4C2×D4×D5311yescharacteristic
694C2×C4C22×C22⋊D5311yescharacteristic
695C2×C4C2×#1171994911yescharacteristic
696C2×C4#1313326211yescharacteristic
697C2×C4#1313326511yescharacteristic
698C8—21no—
699C8—21no—
700C8—21no—
701C8—21no—
702C8—41no—
703C8—41no—
704C8—1061no—
705C8—1061no—
706C8—1061no—
707C8—1061no—
708C8—1062no—
709C8—2121no—
710C22—21no—
711C22—21no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—2121no—
716C22—2121no—
717C22—2121no—
718C22—2121no—
719C22—2121no—
720C22—2121no—
721C22C2×C4×C22⋊D5311yescharacteristic
722C22#1681127411yescharacteristic
723C22#1681132111yescharacteristic
724C4—21no—
725C4—21no—
726C4—22no—
727C4—21no—
728C4—21no—
729C4—41no—
730C4—41no—
731C4—4241no—
732C4—2122no—
733C4—2121no—
734C4—2121no—
735C4C2×#1313317911yescharacteristic
736C4#1681110411yescharacteristic
737C4D4×C22⋊D5311yescharacteristic
738C4#1681128411yescharacteristic
739C2—21no—
740C2—21no—
741C2—42no—
742C2—4241no—
743C2—4241no—
744C2#2027773111yescharacteristic
745C2#2028361611yescharacteristic
746C2#2028363011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2906C2
socleC22×C53C2×C4×D4
prime radical#20284170C2
cosocleC22×C4×C53C24
hypercenter#2906D53
hypocenterC53#23017
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #2906

Complements

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

NH ≅ G/Ntype
2. C2×#16810743C2semidirect
3. C2×#16810738C2semidirect
4. #20283458C2semidirect
5. #20275546C2semidirect
6. #20275488C2semidirect
7. #20275425C2semidirect
8. #20275418C2semidirect
9. #20275042C2semidirect
10. #20275042C2semidirect
11. #20274989C2semidirect
12. #20274989C2semidirect
13. #20274574C2semidirect
14. #20274525C2semidirect
15. C53×#2906C2semidirect
21. #16810845C4semidirect
22. #16810845C4semidirect
23. #16810838C4semidirect
24. #16810838C4semidirect
25. #16810833C4semidirect
26. #16810828C4semidirect
27. #16810823C4semidirect
28. #16810818C4semidirect
112. #13133144D4semidirect
370. #2906D53semidirect
442. C53#23017semidirect

Maximal subgroups

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

subgroupindex
#202841702
C2×#168107432
C2×#168107382
#202834582
#202755462
#202754882
#202754252
#202754182
#202750422
#202749892
#202745742
#202745252
C53×#29062
#2301753