Finite Group Databasebeta

← #28292639

Subgroups — #28292639

Order 13568.

11346 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811460C212yesmaximal, complemented
2#20288506C218yesmaximal, complemented
3#20288499C214yesmaximal, complemented
4#20288492C214yesmaximal, complemented
5#20288486C211yesmaximal, characteristic, complemented
6#20288482C212yesmaximal, complemented
7#20288478C216yesmaximal, complemented
8#20288477C216yesmaximal, complemented
9D4×#11719949C214yesmaximal, complemented
10#20288205C214yesmaximal, complemented
11#20288204C218yesmaximal, complemented
12#20288043C216yesmaximal, complemented
13#532×D53C216yesmaximal, complemented
14C2×C4×#11719949C211yesmaximal, characteristic, complemented
15C53×#3497C211yesmaximal, characteristic, complemented
16#16811460—232no—
17C2×#13133265C2212yescomplemented
18C2×#13133265C2218yescomplemented
19C2×#13133263C22112yescomplemented
20C2×#13133263C2218yescomplemented
21C22×#11719949C2211yescharacteristic
22C22×#11719949C2218yescomplemented
23C2×#41×D53C22112yescomplemented
24C2×#41×D53C2218yescomplemented
25#16811295C2214yescomplemented
26#16811292C2218yescomplemented
27Q8×D212C2214yescomplemented
28Q8×C22⋊D53C2218yescomplemented
29#16811285C2218yescomplemented
30#16811284C2218yescomplemented
31#16811280C2218yescomplemented
32#16811278C22112yescomplemented
33#16811276C22112yescomplemented
34#16811275C22124yescomplemented
35#16811270C22124yescomplemented
36#16811269C22124yescomplemented
37#16811266C22124yescomplemented
38#16811264C22124yescomplemented
39D4×D212C22112yescomplemented
40#16811258C22112yescomplemented
41#16811257C22124yescomplemented
42#16811204C2216yescomplemented
43#16811201C22112yescomplemented
44#16811196C22124yescomplemented
45#16811189C22124yescomplemented
46#16811181C22124yescomplemented
47#16811174C2216yescomplemented
48#16811173C2216yescomplemented
49#16811172C22112yescomplemented
50#16811171C2216yescomplemented
51#16811170C22112yescomplemented
52#16811170C22112yescomplemented
53#16811169C22112yescomplemented
54#16811168C22112yescomplemented
55#16811168C2214yescomplemented
56C4⋊Q8×D53C2216yescomplemented
57#127×D53C2216yescomplemented
58#124×D53C22112yescomplemented
59#16811136C22124yescomplemented
60#16811133C22124yescomplemented
61#121×D53C22112yescomplemented
62#121×D53C22112yescomplemented
63C4×#11719949C2214yescomplemented
64C4×#11719949C2214yescomplemented
65C4×#11719949C2214yescomplemented
66C4×#11719949C2214yescomplemented
67C2×Q8×Dic53C2211yescharacteristic, complemented
68C2×C4×D212C2213yescomplemented
69C2×#13133179C2213yescomplemented
70C4×D4×D53C22112yescomplemented
71C4×D4×D53C22112yescomplemented
72C2×#13133175C2213yescomplemented
73C2×C42×D53C2213yescomplemented
74C2×2−1+4×C53C2212yescomplemented
75C53×#550C2214yescomplemented
76D4×Q8×C53C2214yescomplemented
77C53×#548C2218yescomplemented
78C53×#537C2216yescomplemented
79C53×#532C2216yescomplemented
80C2×C4×Q8×C53C2211yescharacteristic, complemented
81#13133265—216no—
82#13133265—264no—
83#13133263—264no—
84#13133263—296no—
85C2×#11719949—264no—
86C2×#11719949D4116yescomplemented
87C2×#11719949C23124yes—
88C2×#11719949C2318yes—
89C2×#11719949C23112yes—
90C2×#11719949C2314yes—
91C2×#11719949C2314yes—
92C2×#11719945C23124yes—
93C2×#11719945C23112yes—
94C2×#11719945C23124yes—
95C2×#11719947C23112yes—
96C2×#11719947C2318yes—
97#41×D53—264no—
98#41×D53—296no—
99C2×Q8×D53C2318yes—
100C2×Q8×D53C23112yes—
101C22×D212C23124yes—
102C22×D212C2313yes—
103C2×D4×D53C23124yes—
104C2×D4×D53C23124yes—
105C2×D4×D53C23112yes—
106C2×D4×D53C23112yes—
107C2×D4×D53C23112yes—
108C22×C4×D53C23124yes—
109C22×C4×D53C2313yes—
110C22×C4×D53C2313yes—
111C22×C4×D53C2313yes—
112#13133217C2316yes—
113#13133216C2314yes—
114#13133216C23112yes—
115#13133215C23112yes—
116#13133214C2316yes—
117#13133213C23112yes—
118#13133213C2314yes—
119#13133213C23112yes—
120#13133206C23112yes—
121#13133205C23112yes—
122#13133204C23112yes—
123#13133203C2318yes—
124#13133203C23124yes—
125#13133202C23148yes—
126#13133199C23148yes—
127#13133197C23124yes—
128#13133196C23124yes—
129#13133193C23124yes—
130#13133192C23112yes—
131#13133192C23124yes—
132#13133192C23112yes—
133#13133191C23124yes—
134#13133191C2314yes—
135#13133191C23112yes—
136#13133190C23124yes—
137#13133190C23124yes—
138#13133189C2318yes—
139#13133189C23124yes—
140#13133188C23124yes—
141#13133188C23112yes—
142#13133188C23112yes—
143#13133187C23148yes—
144#13133185C23148yes—
145Q8×Dic53C2314yes—
146Q8×Dic53C2314yes—
147C4×D212C23112yes—
148C4×D212C23112yes—
149C4×D212C23112yes—
150C4×D212C23112yes—
151D4×Dic53C2314yes—
152D4×Dic53C23112yes—
153#13133179C23112yes—
154#13133179C23112yes—
155#13133179C2314yes—
156#13133179C23112yes—
157C4×C22⋊D53C23124yes—
158C4×C22⋊D53C23124yes—
159#13133177C2318yes—
160#13133177C23124yes—
161#13133175C23112yes—
162#13133175C23112yes—
163C2×C4⋊Dic53C2313yes—
164C4⋊C4×D53C23112yes—
165C4⋊C4×D53C23112yes—
166C2×#11719921C2316yes—
167C22⋊C4×D53C23124yes—
168C22⋊C4×D53C23124yes—
169C2×C4×Dic53C2311yescharacteristic
170C2×C4×Dic53C2313yes—
171C2×C4×Dic53C2313yes—
172C42×D53C2316yes—
173C42×D53C2316yes—
174C42×D53C2316yes—
175C42×D53C2316yes—
1762−1+4×C53—216no—
177C2×#41×C53C2318yes—
178C2×#41×C53C23112yes—
179C22×Q8×C53C2318yes—
180C22×Q8×C53C2311yescharacteristic
181C4⋊Q8×C53C2316yes—
182#127×C53C2316yes—
183#124×C53C23112yes—
184C22⋊Q8×C53C23124yes—
185#121×C53C23124yes—
186#121×C53C2314yes—
187#121×C53C23112yes—
188C4×Q8×C53C2314yes—
189C4×Q8×C53C2314yes—
190C4×D4×C53C23112yes—
191C4×D4×C53C23112yes—
192C2×C4⋊C4×C53C2313yes—
193C2×C42×C53C2313yes—
194C23×D53C24124yes—
195C23×D53C2413yes—
196#41×C53—232no—
197#41×C53—248no—
198C2×Q8×C53—232no—
199C2×Q8×C53C2×D418yescomplemented
200C2×Q8×C53C24112yes—
201C2×Q8×C53C2414yes—
202C2×D4×C53C2414yes—
203C2×D4×C53C2418yes—
204C2×D4×C53C24112yes—
205C2×D4×C53C24112yes—
206C22×C4×C53C2411yescharacteristic
207C22×C4×C53C24124yes—
208C22×C4×C53C2413yes—
209C22×C4×C53C2413yes—
210C2×C22⋊D53C2418yes—
211C2×C22⋊D53C24124yes—
212C2×C22⋊D53C2418yes—
213C2×C22⋊D53C2418yes—
214C2×C22⋊D53C24124yes—
215C22×Dic53C2411yescharacteristic
216C22×Dic53C2418yes—
217C22×Dic53C2413yes—
218C22×Dic53C2411yescharacteristic
219#11719949—232no—
220#11719949—296no—
221#11719949—248no—
222#11719949C2×D4132yescomplemented
223#11719949C2×D4132yescomplemented
224Q8×D53—232no—
225Q8×D53—248no—
226#11719947—232no—
227#11719947—248no—
228D4×D53—296no—
229D4×D53—296no—
230D4×D53—248no—
231D4×D53—424no—
232D4×D53—424no—
233#11719945—248no—
234#11719945—296no—
235#11719945—296no—
236C2×D212—296no—
237C2×D212C2×D4124yescomplemented
238C2×D212C2414yes—
239C2×D212C24124yes—
240C2×D212C24112yes—
241C2×D212C24112yes—
242C2×D212C24112yes—
243C2×C4×D53—296no—
244C2×C4×D53—46no—
245C2×C4×D53—46no—
246C2×C4×D53C2×D4124yescomplemented
247C2×C4×D53C2416yes—
248C2×C4×D53C2416yes—
249C2×C4×D53C24124yes—
250C2×C4×D53C2418yes—
251C2×C4×D53C24124yes—
252C2×C4×D53C2416yes—
253C2×C4×D53C2416yes—
254C2×C4×D53C2416yes—
255C2×C4×D53C2416yes—
256C2×Dic106C24112yes—
257C2×Dic106C2418yes—
258C4⋊C4×C53C24112yes—
259C4⋊C4×C53C2414yes—
260C4⋊C4×C53C24112yes—
261C22⋊C4×C53C2418yes—
262C22⋊C4×C53C24124yes—
263C42×C53C2416yes—
264C42×C53C2416yes—
265C22⋊Dic53C2418yes—
266C22⋊Dic53C24124yes—
267#11719921C2418yes—
268#11719921C2418yes—
269#11719921C24124yes—
270#11719921C24124yes—
271#11719921C24124yes—
272C4⋊Dic53C2414yes—
273C4⋊Dic53C24112yes—
274C4⋊Dic53C24112yes—
275#11719919C2418yes—
276#11719919C24124yes—
277C4×Dic53C2411yescharacteristic
278C4×Dic53C2411yescharacteristic
279C4×Dic53C2411yescharacteristic
280C4×Dic53C2411yescharacteristic
281C4×Dic53C2416yes—
282C4×Dic53C2416yes—
283C4×Dic53C2416yes—
284C4×Dic53C2416yes—
285C23×C53C2518yes—
286C23×C53C2511yescharacteristic
287C22×D53—248no—
288C22×D53—43no—
289C22×D53—43no—
290C22×D53—424no—
291C22×D53—424no—
292C22×D53C22×D4112yes—
293C22×D53C2518yes—
294C22×D53C2516yes—
295Q8×C53—224no—
296Q8×C53C22×D4116yes—
297D4×C53—216no—
298D4×C53—224no—
299D4×C53—28no—
300D4×C53—412no—
301C2×C4×C53—248no—
302C2×C4×C53—22no—
303C2×C4×C53—43no—
304C2×C4×C53C22×D4112yes—
305C2×C4×C53C2518yes—
306C2×C4×C53C2511yescharacteristic
307C2×C4×C53C2516yes—
308C2×C4×C53C2516yes—
309C2×C4×C53C2511yescharacteristic
310C22⋊D53—216no—
311C22⋊D53—248no—
312C22⋊D53—216no—
313C22⋊D53—216no—
314C22⋊D53—424no—
315C2×Dic53—216no—
316C2×Dic53—22no—
317C2×Dic53—43no—
318C2×Dic53C22×D414yes—
319C2×Dic53C2518yes—
320C2×Dic53C2511yescharacteristic
321C2×Dic53C2516yes—
322C2×Dic53C2511yescharacteristic
323C2×Dic53C2511yescharacteristic
324C2×Dic53C2511yescharacteristic
325D212—248no—
326D212—224no—
327D212—28no—
328D212—412no—
329D212C22×D4148yes—
330C4×D53—248no—
331C4×D53—248no—
332C4×D53—212no—
333C4×D53—216no—
334C4×D53—212no—
335C4×D53—46no—
336C4×D53—46no—
337C4×D53C22×D4124yes—
338C4×D53C22×D4124yes—
339Dic106—224no—
340Dic106—216no—
341#62812—531nomaximal, Sylow
342C22×C53—21no—
343C22×C53—21no—
344C22×C53—28no—
345C22×C53—28no—
346C22×C53—28no—
347C22×C53C23×D412yes—
348C22×C53C2611yescharacteristic
349C2×D53—26no—
350C2×D53—26no—
351C2×D53—28no—
352C2×D53—28no—
353C2×D53—28no—
354C2×D53—412no—
355C2×D53—848no—
356C2×D53C23×D4112yes—
357C4×C53—28no—
358C4×C53—26no—
359C4×C53—21no—
360C4×C53C23×D4112yes—
361C4×C53#58512yescomplemented
362Dic53—28no—
363Dic53—26no—
364Dic53—21no—
365Dic53C23×D412yes—
366Dic53C23×D412yes—
367Dic53#58512yescomplemented
368C2×#585—532no—
369#3500—538no—
370#3499—534no—
371#3498—534no—
372#3497—532no—
373#3497—531no—
374#3497D5311yescharacteristic, complemented
375#3496—536no—
376#3496—536no—
377D4×#41—534no—
378D4×#41—534no—
379D4×#41—538no—
380#3449—536no—
381C2×#532—536no—
382C2×C4×#41—531no—
383C2×C53—22no—
384C2×C53—48no—
385C2×C53C24×D411yescharacteristic
386C2×C53C2×#58511yescharacteristic
387C2×C53C2×#58511yescharacteristic
388D53—212no—
389D53—48no—
390#585—10632no—
391C2×2−1+4—532no—
392C2×2−1+4—538no—
393C2×2−1+4C2×D5312yescomplemented
394C2×H(5,𝔽2)—5312no—
395C2×H(5,𝔽2)—538no—
396C22×#41—5312no—
397C22×#41—538no—
398C22×#41—531no—
399C22×#41—538no—
400#550—538no—
401#550—534no—
402#550C2×D5314yescomplemented
403D4×Q8—538no—
404D4×Q8—534no—
405D4×Q8C2×D5314yescomplemented
406#548—538no—
407#548—538no—
408#548—538no—
409#548C2×D5318yescomplemented
410#547—5312no—
411#547—5324no—
412#547—5312no—
413#546—5324no—
414#546—5324no—
415#546—5324no—
416#546—5324no—
417D42—5312no—
418D42—5324no—
419D42—5312no—
420#537—5312no—
421#537—536no—
422#537C2×D5316yescomplemented
423#536—5324no—
424#535—5324no—
425#534—5324no—
426#532—5312no—
427#532—536no—
428#532—536no—
429#532—5312no—
430#532—534no—
431#532—5312no—
432#532—5312no—
433#532—5312no—
434#532—536no—
435#532C2×D5316yescomplemented
436C2×C4⋊Q8—536no—
437C2×#127—536no—
438C2×#124—5312no—
439#525—5324no—
440#525—5324no—
441C2×#121—5312no—
442C2×#121—5312no—
443C4×#41—534no—
444C4×#41—534no—
445C4×#41—534no—
446C4×#41—534no—
447C2×C4×Q8—531no—
448C2×C4×Q8C2×D5311yescharacteristic, complemented
449C2×C4×D4—5312no—
450C2×C4×D4—5312no—
451C2×C4×D4—533no—
452C2×C4×D4—533no—
453C2×#117—533no—
454C22×C42—533no—
455C53#6281211yescharacteristic, complemented, Sylow
4562−1+4—216no—
4572−1+4—10664no—
4582−1+4—10616no—
459H(5,𝔽2)—10696no—
460H(5,𝔽2)—10664no—
461C2×#41—5316no—
462C2×#41—534no—
463C2×#41—534no—
464C2×#41—5312no—
465C2×#41—5324no—
466C2×#41—538no—
467C2×#41—5312no—
468C2×#41—538no—
469C2×#41—5324no—
470C2×#41—5312no—
471C2×#41—5324no—
472C2×#41—10696no—
473C2×#41—10664no—
474C2×#41—10664no—
475C2×#41C22×D53112yes—
476C2×#41C22×D5318yes—
477C22×Q8—5312no—
478C22×Q8—538no—
479C22×Q8C22×D5318yes—
480C22×Q8C22×D5311yescharacteristic
481C22×D4—5324no—
482C22×D4—5312no—
483C22×D4—5324no—
484C22×D4—5312no—
485C22×D4—5312no—
486C22×D4—533no—
487C22×D4—5324no—
488C23×C4—533no—
489C23×C4—5324no—
490C23×C4—533no—
491C23×C4—533no—
492C4⋊Q8—5312no—
493C4⋊Q8—534no—
494C4⋊Q8—5312no—
495C4⋊Q8—536no—
496C4⋊Q8C22×D5316yes—
497#127—534no—
498#127—5312no—
499#127—5312no—
500#127—536no—
501#127C22×D5316yes—
502#124—5312no—
503#124—5312no—
504#124—538no—
505#124—5324no—
506#124—5312no—
507#124C22×D53112yes—
508#123—5348no—
509#123—5348no—
510C22⋊Q8—5324no—
511C22⋊Q8—5324no—
512C22⋊Q8—5324no—
513C22⋊Q8C22×D53124yes—
514#121—538no—
515#121—5324no—
516#121—5312no—
517#121—5312no—
518#121—5324no—
519#121—534no—
520#121—5312no—
521#121—5324no—
522#121—5312no—
523#121—5312no—
524#121—5324no—
525#121—5324no—
526#121—5324no—
527#121C22×D5314yes—
528#121C22×D53112yes—
529#121C22×D53124yes—
530#120—5348no—
531#120—5348no—
532C4×Q8—534no—
533C4×Q8—534no—
534C4×Q8C22×D5314yes—
535C4×Q8C22×D5314yes—
536C4×D4—534no—
537C4×D4—5312no—
538C4×D4—5324no—
539C4×D4—5324no—
540C4×D4—534no—
541C4×D4—5312no—
542C4×D4—5312no—
543C4×D4—5312no—
544C4×D4—538no—
545C4×D4—5324no—
546C4×D4—5312no—
547C4×D4—5312no—
548C4×D4—5312no—
549C4×D4—5312no—
550C4×D4C22×D53112yes—
551C4×D4C22×D53112yes—
552#117—5312no—
553#117—5312no—
554C2×C4⋊C4—533no—
555C2×C4⋊C4—5312no—
556C2×C4⋊C4—5312no—
557C2×C4⋊C4C22×D5313yes—
558C2×C22⋊C4—536no—
559C2×C22⋊C4—5324no—
560C2×C22⋊C4—5324no—
561C2×C42—533no—
562C2×C42—533no—
563C2×C42—531no—
564C2×C42—536no—
565C2×C42—536no—
566C2×C42—536no—
567C2×C42—536no—
568C2×C42C22×D5313yes—
569C24—533no—
570C24—5324no—
571#41—232no—
572#41—248no—
573#41—5332no—
574#41—5332no—
575#41—10696no—
576#41—10696no—
577#41—10632no—
578#41—10648no—
579#41—10648no—
580#41—10696no—
581#41—10632no—
582#41—10648no—
583C2×Q8—232no—
584C2×Q8—5312no—
585C2×Q8—538no—
586C2×Q8—10648no—
587C2×Q8—10632no—
588C2×Q8D4×D5318yescomplemented
589C2×Q8C23×D53112yes—
590C2×Q8C23×D5314yes—
591C2×D4—538no—
592C2×D4—5324no—
593C2×D4—538no—
594C2×D4—538no—
595C2×D4—5324no—
596C2×D4—5324no—
597C2×D4—5312no—
598C2×D4—534no—
599C2×D4—5324no—
600C2×D4—5312no—
601C2×D4—5312no—
602C2×D4—10696no—
603C2×D4—10648no—
604C2×D4—10696no—
605C2×D4—10696no—
606C2×D4—21224no—
607C2×D4—21224no—
608C2×D4C23×D5314yes—
609C2×D4C23×D5318yes—
610C2×D4C23×D53112yes—
611C2×D4C23×D53112yes—
612C22×C4—531no—
613C22×C4—5324no—
614C22×C4—536no—
615C22×C4—536no—
616C22×C4—531no—
617C22×C4—538no—
618C22×C4—533no—
619C22×C4—536no—
620C22×C4—536no—
621C22×C4—5324no—
622C22×C4—538no—
623C22×C4—5324no—
624C22×C4—536no—
625C22×C4—536no—
626C22×C4—10696no—
627C22×C4—2126no—
628C22×C4—2126no—
629C22×C4C23×D5311yescharacteristic
630C22×C4C23×D53124yes—
631C22×C4C23×D5313yes—
632C22×C4C23×D5313yes—
633C4⋊C4—538no—
634C4⋊C4—534no—
635C4⋊C4—5312no—
636C4⋊C4—5324no—
637C4⋊C4—5312no—
638C4⋊C4C23×D5314yes—
639C4⋊C4C23×D53112yes—
640C4⋊C4C23×D53112yes—
641C22⋊C4—538no—
642C22⋊C4—5324no—
643C22⋊C4—538no—
644C22⋊C4—538no—
645C22⋊C4—5324no—
646C22⋊C4—5324no—
647C22⋊C4—5324no—
648C22⋊C4C23×D5318yes—
649C22⋊C4C23×D53124yes—
650C42—531no—
651C42—531no—
652C42—531no—
653C42—531no—
654C42—536no—
655C42—536no—
656C42—536no—
657C42—536no—
658C42C23×D5316yes—
659C42C23×D5316yes—
660C23—536no—
661C23—5312no—
662C23—538no—
663C23—10648no—
664C23—21224no—
665C23—21224no—
666C23—2123no—
667C23—2123no—
668C23C24×D5318yes—
669C23C24×D5311yescharacteristic
670Q8—224no—
671Q8—10616no—
672Q8—10624no—
673Q8C2×D4×D53116yes—
674D4—216no—
675D4—224no—
676D4—28no—
677D4—412no—
678D4—5348no—
679D4—10648no—
680D4—10616no—
681D4—10616no—
682D4—10648no—
683D4—10616no—
684D4—10624no—
685D4—1068no—
686D4—21212no—
687D4—21224no—
688C2×C4—248no—
689C2×C4—22no—
690C2×C4—43no—
691C2×C4—534no—
692C2×C4—531no—
693C2×C4—531no—
694C2×C4—531no—
695C2×C4—5324no—
696C2×C4—5324no—
697C2×C4—531no—
698C2×C4—536no—
699C2×C4—538no—
700C2×C4—10616no—
701C2×C4—10612no—
702C2×C4—10648no—
703C2×C4—10616no—
704C2×C4—1062no—
705C2×C4—10648no—
706C2×C4—10612no—
707C2×C4—2126no—
708C2×C4—2126no—
709C2×C4—2123no—
710C2×C4C2×D4×D53112yes—
711C2×C4C24×D5311yescharacteristic
712C2×C4C24×D5316yes—
713C2×C4C24×D5318yes—
714C2×C4C24×D5316yes—
715C2×C4C24×D5311yescharacteristic
716C22—21no—
717C22—21no—
718C22—28no—
719C22—28no—
720C22—28no—
721C22—5312no—
722C22—1066no—
723C22—1066no—
724C22—1068no—
725C22—1068no—
726C22—1068no—
727C22—42448no—
728C22—21212no—
729C22C22×D4×D5312yes—
730C22C25×D5311yescharacteristic
731C4—28no—
732C4—26no—
733C4—21no—
734C4—532no—
735C4—532no—
736C4—532no—
737C4—1068no—
738C4—1061no—
739C4—1066no—
740C4C22×D4×D53112yes—
741C4#1681146012yescomplemented
742C2—22no—
743C2—48no—
744C2—10612no—
745C2—2128no—
746C2C23×D4×D5311yescharacteristic
747C2#585×D5311yescharacteristic
748C2C2×#1681146011yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3497C2
hypercenter#3497D53
hypocenterC53#62812
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3497

Complements

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

NH ≅ G/Ntype
1. C2×#16811460C2semidirect
2. #20288506C2semidirect
3. #20288499C2semidirect
4. #20288492C2semidirect
5. #20288486C2semidirect
6. #20288482C2semidirect
7. #20288478C2semidirect
8. #20288477C2semidirect
9. D4×#11719949C2semidirect
10. #20288205C2semidirect
11. #20288204C2semidirect
12. #20288043C2semidirect
13. #532×D53C2semidirect
14. C2×C4×#11719949C2semidirect
15. C53×#3497C2semidirect
17. C2×#13133265C22semidirect
18. C2×#13133265C22semidirect
19. C2×#13133263C22semidirect
20. C2×#13133263C22semidirect
22. C22×#11719949C22semidirect
23. C2×#41×D53C22semidirect
24. C2×#41×D53C22semidirect
25. #16811295C22semidirect
26. #16811292C22semidirect
27. Q8×D212C22semidirect
28. Q8×C22⋊D53C22semidirect
29. #16811285C22semidirect
30. #16811284C22semidirect
31. #16811280C22semidirect
32. #16811278C22semidirect
33. #16811276C22semidirect
34. #16811275C22semidirect
35. #16811270C22semidirect
36. #16811269C22semidirect
37. #16811266C22semidirect
38. #16811264C22semidirect
39. D4×D212C22semidirect
40. #16811258C22semidirect
41. #16811257C22semidirect
42. #16811204C22semidirect
43. #16811201C22semidirect
44. #16811196C22semidirect
45. #16811189C22semidirect
46. #16811181C22semidirect
47. #16811174C22semidirect
48. #16811173C22semidirect
49. #16811172C22semidirect
50. #16811171C22semidirect
51. #16811170C22semidirect
52. #16811170C22semidirect
53. #16811169C22semidirect
54. #16811168C22semidirect
55. #16811168C22semidirect
56. C4⋊Q8×D53C22semidirect
57. #127×D53C22semidirect
58. #124×D53C22semidirect
59. #16811136C22semidirect
60. #16811133C22semidirect
61. #121×D53C22semidirect
62. #121×D53C22semidirect
63. C4×#11719949C22semidirect
64. C4×#11719949C22semidirect
65. C4×#11719949C22semidirect
66. C4×#11719949C22semidirect
67. C2×Q8×Dic53C22semidirect
68. C2×C4×D212C22semidirect
69. C2×#13133179C22semidirect
70. C4×D4×D53C22semidirect
71. C4×D4×D53C22semidirect
72. C2×#13133175C22semidirect
73. C2×C42×D53C22semidirect
74. C2×2−1+4×C53C22semidirect
75. C53×#550C22semidirect
76. D4×Q8×C53C22semidirect
77. C53×#548C22semidirect
78. C53×#537C22semidirect
79. C53×#532C22semidirect
80. C2×C4×Q8×C53C22semidirect
86. C2×#11719949D4semidirect
199. C2×Q8×C53C2×D4semidirect
222. #11719949C2×D4semidirect
223. #11719949C2×D4semidirect
237. C2×D212C2×D4semidirect
246. C2×C4×D53C2×D4semidirect
361. C4×C53#585semidirect
367. Dic53#585semidirect
374. #3497D53semidirect
393. C2×2−1+4C2×D53semidirect
402. #550C2×D53semidirect
405. D4×Q8C2×D53semidirect
409. #548C2×D53semidirect
422. #537C2×D53semidirect
435. #532C2×D53semidirect
448. C2×C4×Q8C2×D53semidirect
455. C53#62812semidirect
588. C2×Q8D4×D53semidirect
741. C4#16811460semidirect

Maximal subgroups

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

subgroupindex
C2×#168114602
#202885062
#202884992
#202884922
#202884862
#202884822
#202884782
#202884772
D4×#117199492
#202882052
#202882042
#202880432
#532×D532
C2×C4×#117199492
C53×#34972
#6281253