Finite Group Databasebeta

← #28293279

Subgroups — #28293279

Order 13568.

7310 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288827C214yesmaximal, complemented
2#20288748C2112yesmaximal, complemented
3#20288722C214yesmaximal, complemented
4#20288658C2112yesmaximal, complemented
5#20288639C213yesmaximal, complemented
6#20288592C213yesmaximal, complemented
7#20288493C211yesmaximal, characteristic, complemented
8#20288453C216yesmaximal, complemented
9#20288385C212yesmaximal, complemented
10#20288138C216yesmaximal, complemented
11#20288107C213yesmaximal, complemented
12C2×#16811229C213yesmaximal, complemented
13#20287921C212yesmaximal, complemented
14#20287914C211yesmaximal, characteristic, complemented
15C53×#3504C211yesmaximal, characteristic, complemented
16C2×#13133263C2212yes—
17C2×#41×D53C2211yescharacteristic
18#16811358C22112yescomplemented
19#16811339C22112yescomplemented
20#16811326C22112yescomplemented
21#16811326C22112yescomplemented
22#16811326C22112yescomplemented
23#16811321C22124yescomplemented
24#16811311C22112yescomplemented
25#16811300C22124yescomplemented
26#16811295C2214yescomplemented
27#16811295C22112yescomplemented
28#16811295C2214yescomplemented
29#16811285C2214yescomplemented
30#16811276C22112yescomplemented
31#16811268C22112yescomplemented
32#16811264C22124yescomplemented
33#16811264C22124yescomplemented
34D4×D212C22112yescomplemented
35D4×D212C22112yescomplemented
36#16811247C22112yescomplemented
37#16811247C2216yescomplemented
38#16811247C2216yescomplemented
39#16811236C2211yescharacteristic, complemented
40#16811236C2213yescomplemented
41#16811229C22112yescomplemented
42#16811229C2213yescomplemented
43#16811229C2216yescomplemented
44#16811229C2216yescomplemented
45#16811229C22112yescomplemented
46#16811229C2216yescomplemented
47#16811229C2213yescomplemented
48#16811229C22112yescomplemented
49#16811222C22112yescomplemented
50#16811213C22112yescomplemented
51#16811213C22124yescomplemented
52#16811204C2216yescomplemented
53#16811192C2216yescomplemented
54#16811192C2216yescomplemented
55#16811174C22112yescomplemented
56#16811174C22112yescomplemented
57#16811173C2213yescomplemented
58C2×#13133214C2213yescomplemented
59#16811160C22112yescomplemented
60#16811160C22112yescomplemented
61#16811158C22112yescomplemented
62#16811158C22112yescomplemented
63#16811136C22124yescomplemented
64#16811135C2216yescomplemented
65C2×#13133202C22112yescomplemented
66C2×#13133192C2216yescomplemented
67C2×#13133192C22112yescomplemented
68#16811105C2214yescomplemented
69#16811105C2212yescomplemented
70#16811104C2216yescomplemented
71#16811102C2216yescomplemented
72#16811099C2212yescomplemented
73#16811097C2216yescomplemented
74#16811095C22112yescomplemented
75#16811095C2216yescomplemented
76#41×Dic53C2211yescharacteristic
77C4×#11719949C2214yescomplemented
78C4×#11719945C2213yescomplemented
79#16811091C2216yescomplemented
80#16811091C2213yescomplemented
81C2×#13133179C2216yescomplemented
82C4×D4×D53C22112yescomplemented
83C2×#13133174C2213yescomplemented
84#117×D53C2213yescomplemented
85C53×#557C2214yescomplemented
86C53×#554C22112yescomplemented
87C53×#544C2216yescomplemented
88C53×#533C2213yescomplemented
89C2×#125×C53C2213yescomplemented
90C53×#520C2212yes—
91C4×#41×C53C2211yescharacteristic
92#13133263—216no—
93C2×#11719949C2314yes—
94C2×#11719949C2311yescharacteristic
95C2×#11719949C23124yes—
96C2×#11719945C2313yes—
97C2×#11719945C2316yes—
98C2×#11719947C2313yes—
99#41×D53—28no—
100C2×Q8×D53C2311yescharacteristic
101C22×D212C2316yes—
102C22×D212C23112yes—
103C22×D212C23112yes—
104C2×D4×D53C23112yes—
105C2×D4×D53C2313yes—
106C22×C4×D53C2313yes—
107C22×C4×D53C23112yes—
108#13133217C2311yescharacteristic
109#13133214C23112yes—
110#13133214C23112yes—
111#13133214C2313yes—
112#13133214C2316yes—
113#13133212C23112yes—
114#13133212C23124yes—
115#13133212C23112yes—
116#13133212C23112yes—
117#13133212C2314yes—
118#13133208C23112yes—
119#13133208C2314yes—
120#13133206C23112yes—
121#13133206C23124yes—
122#13133206C23112yes—
123#13133205C23112yes—
124#13133205C2316yes—
125#13133202C23112yes—
126#13133202C23112yes—
127#13133202C23124yes—
128#13133202C23124yes—
129#13133202C23124yes—
130#13133202C23112yes—
131#13133202C23124yes—
132#13133202C23112yes—
133#13133201C23112yes—
134#13133197C23112yes—
135#13133197C2312yes—
136#13133197C2316yes—
137#13133193C23112yes—
138#13133193C23112yes—
139#13133192C23112yes—
140#13133192C23124yes—
141#13133192C23124yes—
142#13133192C23124yes—
143#13133192C23112yes—
144#13133192C23112yes—
145#13133192C23112yes—
146#13133192C23112yes—
147#13133192C23112yes—
148#13133192C2316yes—
149#13133192C23112yes—
150#13133192C23124yes—
151#13133192C23112yes—
152#13133192C2316yes—
153#13133191C23124yes—
154#13133191C23112yes—
155#13133187C23124yes—
156#13133187C23112yes—
157#13133187C23124yes—
158Q8×Dic53C2312yes—
159C4×Dic106C2316yes—
160#13133182C2312yes—
161#13133182C2316yes—
162#13133182C2316yes—
163C4×D212C23112yes—
164C4×D212C23112yes—
165C4×D212C23112yes—
166C4×D212C2316yes—
167C4×D212C23112yes—
168C4×D212C23112yes—
169D4×Dic53C2316yes—
170#13133179C23124yes—
171#13133179C23124yes—
172#13133179C23112yes—
173#13133179C2316yes—
174#13133179C23112yes—
175#13133179C23112yes—
176#13133179C2316yes—
177#13133179C2316yes—
178C4×C22⋊D53C23112yes—
179C4×C22⋊D53C23124yes—
180#13133177C23112yes—
181#13133177C23112yes—
182#13133177C23112yes—
183#13133176C2313yes—
184#13133175C23124yes—
185#13133175C23112yes—
186#13133175C2316yes—
187#13133174C2313yes—
188#13133174C2311yescharacteristic
189#13133174C2313yes—
190#13133174C2313yes—
191#13133174C2316yes—
192#13133174C2316yes—
193#13133174C23112yes—
194#13133173C2316yes—
195C2×#11719919C2316yes—
196C4⋊C4×D53C2316yes—
197C4⋊C4×D53C23112yes—
198C2×#11719921C23112yes—
199C2×#11719921C2316yes—
200C2×#11719921C23112yes—
201C22⋊C4×D53C2316yes—
202C22⋊C4×D53C23124yes—
203C2×C4×Dic53C2313yes—
204C42×D53C2316yes—
205C42×D53C23112yes—
206C2×#41×C53C2311yescharacteristic
207C4⋊Q8×C53C23112yes—
208C4⋊Q8×C53C2316yes—
209#125×C53C2313yes—
210#125×C53C23112yes—
211#125×C53C2316yes—
212#125×C53C2311yescharacteristic
213#125×C53C23112yes—
214C22⋊Q8×C53C23112yes—
215C22⋊Q8×C53C23124yes—
216C4×Q8×C53C2314yes—
217C4×Q8×C53C2312yes—
218C4×Q8×C53C23112yes—
219C4×D4×C53C23112yes—
220C4×D4×C53C2316yes—
221#117×C53C2313yes—
222#117×C53C2316yes—
223C2×C4⋊C4×C53C2316yes—
224C2×C4⋊C4×C53C23112yes—
225C2×C42×C53C2313yes—
226C23×D53C2413yes—
227C23×D53C24112yes—
228#41×C53#4118yescomplemented
229C2×Q8×C53C24112yes—
230C2×Q8×C53C2411yescharacteristic
231C2×D4×C53C2413yes—
232C22×C4×C53C2416yes—
233C22×C4×C53C24112yes—
234C22×C4×C53C2413yes—
235C2×C22⋊D53C2416yes—
236C2×C22⋊D53C24112yes—
237C22×Dic53C2413yes—
238C22×Dic53C2416yes—
239#11719949—24no—
240#11719949—216no—
241#11719949—824no—
242Q8×D53—24no—
243#11719947—212no—
244D4×D53—212no—
245D4×D53—248no—
246#11719945—212no—
247#11719945—224no—
248C2×D212—224no—
249C2×D212—812no—
250C2×D212—812no—
251C2×D212C2416yes—
252C2×D212C24112yes—
253C2×D212C2413yes—
254C2×D212C24124yes—
255C2×D212C24124yes—
256C2×D212C24112yes—
257C2×D212C24112yes—
258C2×D212C24112yes—
259C2×C4×D53—212no—
260C2×C4×D53—812no—
261C2×C4×D53C2413yes—
262C2×C4×D53C24112yes—
263C2×C4×D53C2413yes—
264C2×C4×D53C2411yescharacteristic
265C2×C4×D53C2413yes—
266C2×C4×D53C24112yes—
267C2×C4×D53C24112yes—
268C2×C4×D53C24112yes—
269C2×C4×D53C24124yes—
270C2×Dic106C2412yes—
271C2×Dic106C2413yes—
272C4⋊C4×C53C2416yes—
273C4⋊C4×C53C24112yes—
274C4⋊C4×C53C24112yes—
275C4⋊C4×C53C24124yes—
276C4⋊C4×C53C2412yes—
277C4⋊C4×C53C2416yes—
278C4⋊C4×C53C2414yes—
279C4⋊C4×C53C24112yes—
280C22⋊C4×C53C24112yes—
281C22⋊C4×C53C2416yes—
282C42×C53C2411yescharacteristic
283C42×C53C2413yes—
284C42×C53C2416yes—
285C42×C53C24112yes—
286C22⋊Dic53C2416yes—
287#11719921C2416yes—
288#11719921C24112yes—
289#11719921C24124yes—
290#11719921C2412yes—
291#11719921C24112yes—
292#11719921C24112yes—
293#11719921C2416yes—
294#11719921C2416yes—
295#11719921C24124yes—
296#11719921C24112yes—
297#11719921C24112yes—
298#11719921C24112yes—
299#11719921C24112yes—
300#11719921C2414yes—
301C4⋊Dic53C2416yes—
302C4⋊Dic53C24112yes—
303C4⋊Dic53C2414yes—
304C4⋊Dic53C2414yes—
305#11719919C2416yes—
306#11719919C24112yes—
307#11719919C2412yes—
308#11719919C2416yes—
309#11719919C2416yes—
310#11719919C2414yes—
311C4×Dic53C2414yes—
312C4×Dic53C2416yes—
313C4×Dic53C2413yes—
314C4×Dic53C24112yes—
315C4×Dic53C24112yes—
316C4×Dic53C2411yescharacteristic
317C23×C53C2513yes—
318C22×D53—26no—
319C22×D53—224no—
320C22×D53—412no—
321C22×D53—46no—
322C22×D53—412no—
323C22×D53C2513yes—
324C22×D53C25112yes—
325C22×D53C2511yescharacteristic
326Q8×C53—412no—
327Q8×C53C2×#4114yes—
328D4×C53C2×#41112yes—
329C2×C4×C53—412no—
330C2×C4×C53—46no—
331C2×C4×C53C2×#41112yes—
332C2×C4×C53C25112yes—
333C2×C4×C53C2514yes—
334C2×C4×C53C2516yes—
335C2×C4×C53C2512yes—
336C2×C4×C53C2511yescharacteristic
337C2×C4×C53C2513yes—
338C22⋊D53—224no—
339C22⋊D53—212no—
340C2×Dic53—26no—
341C2×Dic53—46no—
342C2×Dic53C2513yes—
343C2×Dic53C2514yes—
344C2×Dic53C2516yes—
345C2×Dic53C2512yes—
346C2×Dic53C2511yescharacteristic
347D212—212no—
348D212—224no—
349D212—26no—
350D212—412no—
351D212—412no—
352D212—424no—
353D212—424no—
354D212—412no—
355C4×D53—22no—
356C4×D53—26no—
357C4×D53—26no—
358C4×D53—26no—
359C4×D53—224no—
360C4×D53—412no—
361C4×D53—424no—
362C4×D53—412no—
363C4×D53—412no—
364Dic106—24no—
365Dic106—26no—
366#62858—531nomaximal, Sylow
367C22×C53—26no—
368C22×C53C22×#4116yes—
369C22×C53C2611yescharacteristic
370C2×D53—21no—
371C2×D53—23no—
372C2×D53—212no—
373C2×D53—212no—
374C2×D53—26no—
375C2×D53—212no—
376C2×D53—22no—
377C2×D53—86no—
378C2×D53—824no—
379C4×C53—212no—
380C4×C53—24no—
381C4×C53—26no—
382C4×C53—22no—
383C4×C53C22×#4112yes—
384C4×C53C22×#4116yes—
385Dic53—23no—
386Dic53—24no—
387Dic53—21no—
388Dic53—26no—
389Dic53—22no—
390#3524—534no—
391#3519—5312no—
392#3517—534no—
393#3513—5312no—
394#3512—533no—
395#3508—533no—
396#3504D5311yescharacteristic, complemented
397#3498—531no—
398#3494—536no—
399#3488—532no—
400#3460—536no—
401#3455—533no—
402C2×#540—533no—
403C4×H(5,𝔽2)—532no—
404#3428—531no—
405C2×C53—26no—
406C2×C53C23×#4111yescharacteristic
407C2×C53H(7,𝔽2)12yes—
408D53—43no—
409D53—412no—
410D53—41no—
411C2×H(5,𝔽2)—532no—
412C22×#41—531no—
413#559—5312no—
414#557C2×D5314yescomplemented
415#555—5312no—
416#554C2×D53112yescomplemented
417#553—5312no—
418#553—5312no—
419#553—5312no—
420#553—5324no—
421#552—5312no—
422#551—5324no—
423#550—534no—
424#550—534no—
425#550—5312no—
426#548—534no—
427#547—5312no—
428#546—5324no—
429#546—5324no—
430#546—5312no—
431D42—5312no—
432D42—5312no—
433#544C2×D5316yescomplemented
434#542—536no—
435#542—536no—
436#542—5312no—
437#541—531no—
438#541—533no—
439#540—533no—
440#540—536no—
441#540—536no—
442#540—536no—
443#540—5312no—
444#540—5312no—
445#540—533no—
446#540—5312no—
447#539—5312no—
448#538—5312no—
449#538—5324no—
450#537—536no—
451#535—536no—
452#535—536no—
453#533C2×D5313yescomplemented
454#532—5312no—
455#532—5312no—
456#532—533no—
457C2×#127—533no—
458#529—5312no—
459#529—5312no—
460#529—5312no—
461#529—5312no—
462C2×#125C2×D5313yescomplemented
463#525—5324no—
464#525—536no—
465C2×#123—5312no—
466C2×#121—536no—
467C2×#121—5312no—
468#520—532no—
469#520—534no—
470#520—536no—
471#520—536no—
472#520C2×D5312yes—
473#519—532no—
474#518—536no—
475#518—5312no—
476#518—536no—
477C4×#41—531no—
478C4×#41—534no—
479C4×#41—533no—
480C4×#41—536no—
481C4×#41—533no—
482C4×#41C2×D5311yescharacteristic
483C2×C4×D4—5312no—
484C2×C4×D4—536no—
485C2×#117—533no—
486C2×#117—533no—
487C53#6285811yescharacteristic, complemented, Sylow
488H(5,𝔽2)—10616no—
489C2×#41—534no—
490C2×#41—531no—
491C2×#41—5324no—
492C2×#41—533no—
493C2×#41—533no—
494C2×#41—536no—
495C2×#41—1068no—
496C2×#41C22×D5311yescharacteristic
497C22×Q8—531no—
498C22×D4—5312no—
499C22×D4—533no—
500C22×D4—536no—
501C22×D4—5312no—
502C22×D4—5312no—
503C23×C4—533no—
504C23×C4—5312no—
505C4⋊Q8—531no—
506C4⋊Q8C22×D5316yes—
507C4⋊Q8C22×D53112yes—
508#127—533no—
509#127—536no—
510#127—5312no—
511#127—5312no—
512#126—534no—
513#126—5312no—
514#126—5312no—
515#126—5324no—
516#126—5312no—
517#125—534no—
518#125—5312no—
519#125C22×D5313yes—
520#125C22×D5316yes—
521#125C22×D53112yes—
522#125C22×D53112yes—
523#125C22×D5311yescharacteristic
524#124—5312no—
525#124—5312no—
526#124—5324no—
527#124—536no—
528#124—5312no—
529#123—5312no—
530#123—5324no—
531#123—5324no—
532#123—5324no—
533#123—5312no—
534#123—5324no—
535#123—5312no—
536#123—5312no—
537#123—5312no—
538C22⋊Q8—5312no—
539C22⋊Q8—5312no—
540C22⋊Q8—532no—
541C22⋊Q8—536no—
542C22⋊Q8—5312no—
543C22⋊Q8C22×D53124yes—
544C22⋊Q8C22×D53112yes—
545#121—5324no—
546#121—5312no—
547#121—536no—
548#121—5312no—
549#121—5324no—
550#121—5312no—
551#121—5312no—
552#121—5324no—
553#121—5312no—
554#121—5324no—
555#121—536no—
556#121—5312no—
557#121—5312no—
558#121—5312no—
559#121—5312no—
560#121—5324no—
561#120—5324no—
562#120—5324no—
563#120—5312no—
564C4×Q8—532no—
565C4×Q8—532no—
566C4×Q8—536no—
567C4×Q8—536no—
568C4×Q8—536no—
569C4×Q8C22×D5314yes—
570C4×Q8C22×D5312yes—
571C4×Q8C22×D53112yes—
572C4×D4—536no—
573C4×D4—5324no—
574C4×D4—5312no—
575C4×D4—5312no—
576C4×D4—536no—
577C4×D4—5312no—
578C4×D4—5312no—
579C4×D4—536no—
580C4×D4—536no—
581C4×D4—5324no—
582C4×D4—5324no—
583C4×D4—5312no—
584C4×D4—5312no—
585C4×D4—5312no—
586C4×D4—5312no—
587C4×D4—5312no—
588C4×D4—536no—
589C4×D4—5312no—
590C4×D4—5312no—
591C4×D4—5312no—
592C4×D4C22×D53112yes—
593C4×D4C22×D5316yes—
594#117—533no—
595#117—536no—
596#117—5312no—
597#117—5324no—
598#117—536no—
599#117—531no—
600#117—533no—
601#117—533no—
602#117—533no—
603#117—536no—
604#117—536no—
605#117—5312no—
606#117C22×D5313yes—
607#117C22×D5316yes—
608C2×C4⋊C4—536no—
609C2×C4⋊C4—536no—
610C2×C4⋊C4—5312no—
611C2×C4⋊C4C22×D5316yes—
612C2×C4⋊C4C22×D53112yes—
613C2×C22⋊C4—536no—
614C2×C22⋊C4—5312no—
615C2×C22⋊C4—5312no—
616C2×C22⋊C4—536no—
617C2×C22⋊C4—5324no—
618C2×C42—533no—
619C2×C42—536no—
620C2×C42—5312no—
621C2×C42C22×D5313yes—
622C24—533no—
623C24—5312no—
624#41—1064no—
625#41—10616no—
626#41—10612no—
627#41—10612no—
628#41—10624no—
629#41—42424no—
630#41#1171994918yescomplemented
631C2×Q8—533no—
632C2×Q8—532no—
633C2×Q8—1064no—
634C2×Q8C23×D53112yes—
635C2×Q8C23×D5311yescharacteristic
636C2×D4—536no—
637C2×D4—5312no—
638C2×D4—536no—
639C2×D4—5312no—
640C2×D4—533no—
641C2×D4—5312no—
642C2×D4—5324no—
643C2×D4—5312no—
644C2×D4—5324no—
645C2×D4—5312no—
646C2×D4—10612no—
647C2×D4—10648no—
648C2×D4—10624no—
649C2×D4—42412no—
650C2×D4—42412no—
651C2×D4C23×D5313yes—
652C22×C4—533no—
653C22×C4—536no—
654C22×C4—533no—
655C22×C4—5312no—
656C22×C4—533no—
657C22×C4—533no—
658C22×C4—531no—
659C22×C4—5312no—
660C22×C4—5312no—
661C22×C4—5312no—
662C22×C4—5324no—
663C22×C4—10612no—
664C22×C4—42412no—
665C22×C4C23×D5316yes—
666C22×C4C23×D53112yes—
667C22×C4C23×D5313yes—
668C4⋊C4—536no—
669C4⋊C4—536no—
670C4⋊C4—532no—
671C4⋊C4—5312no—
672C4⋊C4—536no—
673C4⋊C4—536no—
674C4⋊C4—534no—
675C4⋊C4—5312no—
676C4⋊C4—534no—
677C4⋊C4—534no—
678C4⋊C4C23×D53112yes—
679C4⋊C4C23×D5316yes—
680C4⋊C4C23×D5316yes—
681C4⋊C4C23×D53112yes—
682C4⋊C4C23×D53124yes—
683C4⋊C4C23×D5312yes—
684C4⋊C4C23×D53112yes—
685C4⋊C4C23×D5314yes—
686C22⋊C4—536no—
687C22⋊C4—532no—
688C22⋊C4—536no—
689C22⋊C4—5312no—
690C22⋊C4—5324no—
691C22⋊C4—5312no—
692C22⋊C4—5312no—
693C22⋊C4—536no—
694C22⋊C4—536no—
695C22⋊C4—5324no—
696C22⋊C4—5312no—
697C22⋊C4—534no—
698C22⋊C4—5312no—
699C22⋊C4—5312no—
700C22⋊C4—5312no—
701C22⋊C4C23×D53112yes—
702C22⋊C4C23×D5316yes—
703C42—531no—
704C42—533no—
705C42—536no—
706C42—534no—
707C42—5312no—
708C42—5312no—
709C42C23×D5313yes—
710C42C23×D53112yes—
711C42C23×D5311yescharacteristic
712C42C23×D5316yes—
713C23—531no—
714C23—5312no—
715C23—533no—
716C23—1066no—
717C23—10624no—
718C23—21212no—
719C23—2126no—
720C23—21212no—
721C23C24×D5313yes—
722Q8—412no—
723Q8—1066no—
724Q8—1064no—
725Q8C2×#1171994914yes—
726D4—10624no—
727D4—10612no—
728D4—10624no—
729D4—10612no—
730D4—1066no—
731D4—21212no—
732D4—21212no—
733D4—21224no—
734D4—21224no—
735D4—21212no—
736D4C2×#11719949112yes—
737C2×C4—412no—
738C2×C4—46no—
739C2×C4—536no—
740C2×C4—532no—
741C2×C4—533no—
742C2×C4—534no—
743C2×C4—531no—
744C2×C4—1066no—
745C2×C4—1062no—
746C2×C4—1066no—
747C2×C4—1066no—
748C2×C4—1066no—
749C2×C4—10624no—
750C2×C4—21212no—
751C2×C4—21224no—
752C2×C4—21212no—
753C2×C4—21212no—
754C2×C4—2126no—
755C2×C4C2×#11719949112yes—
756C2×C4C24×D5316yes—
757C2×C4C24×D5314yes—
758C2×C4C24×D53112yes—
759C2×C4C24×D5312yes—
760C2×C4C24×D5311yescharacteristic
761C2×C4C24×D5313yes—
762C22—26no—
763C22—1061no—
764C22—1063no—
765C22—10612no—
766C22—10612no—
767C22—1066no—
768C22—10612no—
769C22—1062no—
770C22—4246no—
771C22—42424no—
772C22C22×#1171994916yes—
773C22C25×D5311yescharacteristic
774C4—22no—
775C4—212no—
776C4—26no—
777C4—24no—
778C4—1061no—
779C4—1064no—
780C4—1063no—
781C4—1062no—
782C4—1066no—
783C4C22×#1171994916yes—
784C4C22×#1171994912yes—
785C2—26no—
786C2—2121no—
787C2—21212no—
788C2—2123no—
789C2C23×#1171994911yescharacteristic
790C2#2028952612yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3504C2
hypercenter#3504D53
hypocenterC53#62858
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3504

Complements

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

NH ≅ G/Ntype
1. #20288827C2semidirect
2. #20288748C2semidirect
3. #20288722C2semidirect
4. #20288658C2semidirect
5. #20288639C2semidirect
6. #20288592C2semidirect
7. #20288493C2semidirect
8. #20288453C2semidirect
9. #20288385C2semidirect
10. #20288138C2semidirect
11. #20288107C2semidirect
12. C2×#16811229C2semidirect
13. #20287921C2semidirect
14. #20287914C2semidirect
15. C53×#3504C2semidirect
18. #16811358C22semidirect
19. #16811339C22semidirect
20. #16811326C22semidirect
21. #16811326C22semidirect
22. #16811326C22semidirect
23. #16811321C22semidirect
24. #16811311C22semidirect
25. #16811300C22semidirect
26. #16811295C22semidirect
27. #16811295C22semidirect
28. #16811295C22semidirect
29. #16811285C22semidirect
30. #16811276C22semidirect
31. #16811268C22semidirect
32. #16811264C22semidirect
33. #16811264C22semidirect
34. D4×D212C22semidirect
35. D4×D212C22semidirect
36. #16811247C22semidirect
37. #16811247C22semidirect
38. #16811247C22semidirect
39. #16811236C22semidirect
40. #16811236C22semidirect
41. #16811229C22semidirect
42. #16811229C22semidirect
43. #16811229C22semidirect
44. #16811229C22semidirect
45. #16811229C22semidirect
46. #16811229C22semidirect
47. #16811229C22semidirect
48. #16811229C22semidirect
49. #16811222C22semidirect
50. #16811213C22semidirect
51. #16811213C22semidirect
52. #16811204C22semidirect
53. #16811192C22semidirect
54. #16811192C22semidirect
55. #16811174C22semidirect
56. #16811174C22semidirect
57. #16811173C22semidirect
58. C2×#13133214C22semidirect
59. #16811160C22semidirect
60. #16811160C22semidirect
61. #16811158C22semidirect
62. #16811158C22semidirect
63. #16811136C22semidirect
64. #16811135C22semidirect
65. C2×#13133202C22semidirect
66. C2×#13133192C22semidirect
67. C2×#13133192C22semidirect
68. #16811105C22semidirect
69. #16811105C22semidirect
70. #16811104C22semidirect
71. #16811102C22semidirect
72. #16811099C22semidirect
73. #16811097C22semidirect
74. #16811095C22semidirect
75. #16811095C22semidirect
77. C4×#11719949C22semidirect
78. C4×#11719945C22semidirect
79. #16811091C22semidirect
80. #16811091C22semidirect
81. C2×#13133179C22semidirect
82. C4×D4×D53C22semidirect
83. C2×#13133174C22semidirect
84. #117×D53C22semidirect
85. C53×#557C22semidirect
86. C53×#554C22semidirect
87. C53×#544C22semidirect
88. C53×#533C22semidirect
89. C2×#125×C53C22semidirect
228. #41×C53#41semidirect
396. #3504D53semidirect
414. #557C2×D53semidirect
416. #554C2×D53semidirect
433. #544C2×D53semidirect
453. #533C2×D53semidirect
462. C2×#125C2×D53semidirect
487. C53#62858semidirect
630. #41#11719949semidirect

Maximal subgroups

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

subgroupindex
#202888272
#202887482
#202887222
#202886582
#202886392
#202885922
#202884932
#202884532
#202883852
#202881382
#202881072
C2×#168112292
#202879212
#202879142
C53×#35042
#6285853