Finite Group Databasebeta

← C2×#20291345 #28329285

Subgroups — C2×#20291345 #28329285

Order 13568.

4946 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811702C211yesmaximal, characteristic, complemented
2C2×#41×#6157C211yesmaximal, characteristic, complemented
3#20291345C2116yesmaximal, direct product factor
4C2×#16811620C213yesmaximal, complemented
5C2×#16811621C213yesmaximal, complemented
6C2×D53⋊#104C213yesmaximal, complemented
7C22×#13133281C213yesmaximal, complemented
8C2×#16811458C211yesmaximal, characteristic
9#16811702—24no—
10#16811702C2218yescomplemented
11C2×#13133305—21no—
12C2×#13133304—23no—
13C22×#11719936C2213yescomplemented
14C2×D53⋊M16C2213yescomplemented
15#41×#6157—24no—
16#41×#6157C2218yescomplemented
17C2×Q8×#6157—21no—
18C2×D4×#6157—23no—
19C2×#13133296C2213yescomplemented
20C22×C4×#6157C2213yescomplemented
21#16811621C22124yescomplemented
22#16811620C22124yescomplemented
23C2×#13133282C2211yescharacteristic, complemented
24C2×#13133282C2213yescomplemented
25D53⋊#104C22124yescomplemented
26C2×#13133281C2213yescomplemented
27C2×#13133281C2216yescomplemented
28C2×#13133281C2213yescomplemented
29C2×#13133281C22124yescomplemented
30#16811458—24no—
31#16811458—24no—
32#16811458C418yescomplemented
33#16811458C2218yes—
34C2×#13133264—21no—
35C2×#13133264C411yescharacteristic, complemented
36C2×#13133264C413yescomplemented
37C2×#13133262—23no—
38C2×#13133262C413yescomplemented
39C22×#11719947—23no—
40C22×#11719947C2213yes—
41C2×#41×D53—21no—
42C2×#41×D53C2211yescharacteristic
43C2×#41×D53C2213yes—
44C2×H(5,𝔽2)×C53C411yescharacteristic, complemented
45C23×#6157—23no—
46#13133305—28no—
47#13133304—224no—
48C2×#11719936—23no—
49C2×#11719936—26no—
50C2×#11719936C2311yescharacteristic
51C2×#11719936C2313yes—
52C2×#11719936C23112yescomplemented
53D53⋊M16—26no—
54D53⋊M16C23112yescomplemented
55C2×#11719940—23no—
56C2×D53⋊C8—23no—
57C22×#88324—23no—
58Q8×#6157—28no—
59D4×#6157—224no—
60#13133296—26no—
61#13133296C23112yescomplemented
62C2×C4⋊#6157—23no—
63C2×C22⋊#6157—23no—
64C2×C4×#6157—23no—
65C2×C4×#6157—26no—
66C2×C4×#6157C2311yescharacteristic
67C2×C4×#6157C2313yes—
68C2×C4×#6157C23112yescomplemented
69#13133282C2314yescomplemented
70#13133282C23112yescomplemented
71#13133281C23112yescomplemented
72#13133281C23124yescomplemented
73#13133281C23112yescomplemented
74#13133264—24no—
75#13133264—28no—
76#13133264—28no—
77#13133264—212no—
78#13133264C2×C4124yescomplemented
79#13133264C2×C418yescomplemented
80#13133262—224no—
81#13133262—224no—
82#13133262—212no—
83#13133262C2×C4124yescomplemented
84C2×#11719949D411yescharacteristic
85C2×#11719949C2311yescharacteristic
86C2×#11719945—23no—
87C2×#11719945—23no—
88C2×#11719945C2×C413yes—
89C2×#11719945C2×C413yescomplemented
90C2×#11719947—23no—
91C2×#11719947—26no—
92C2×#11719947—23no—
93C2×#11719947—224no—
94C2×#11719947—224no—
95C2×#11719947—23no—
96C2×#11719947—23no—
97C2×#11719947—26no—
98C2×#11719947—26no—
99C2×#11719947—23no—
100C2×#11719947C2×C416yescomplemented
101C2×#11719947C2×C4112yescomplemented
102C2×#11719947D413yes—
103C2×#11719947C2313yes—
104C2×#11719947C23112yes—
105#41×D53—28no—
106#41×D53—28no—
107#41×D53—26no—
108#41×D53—26no—
109#41×D53C2×C414yes—
110#41×D53C2×C4112yescomplemented
111#41×D53D414yes—
112#41×D53D414yes—
113#41×D53C23112yes—
114#41×D53C2314yes—
115C22×Dic106—23no—
116C22×Dic106C2×C413yescomplemented
117C2×Q8×D53—21no—
118C2×Q8×D53C2×C413yescomplemented
119C2×Q8×D53D411yescharacteristic
120C22×C22⋊D53—23no—
121C22×C22⋊D53—26no—
122C2×D4×D53—23no—
123C2×D4×D53—23no—
124C2×D4×D53C2×C413yescomplemented
125C2×D4×D53D413yes—
126C23×Dic53—23no—
127C22×C4×D53—23no—
128C22×C4×D53C2313yes—
129H(5,𝔽2)×C53—24no—
130H(5,𝔽2)×C53C2×C418yescomplemented
131C2×#41×C53—21no—
132C2×#41×C53C2×C411yescharacteristic
133C2×#41×C53C2×C413yescomplemented
134C22×D4×C53—23no—
135C22×D4×C53C2×C413yescomplemented
136C24×C53—23no—
137C23×D53—23no—
138C23×D53C2×D413yes—
139C22×#6157—21no—
140C22×#6157—23no—
141C22×#6157—212no—
142C22×#6157—412no—
143#41×C53—28no—
144#41×C53—26no—
145#41×C53C22⋊C414yes—
146#41×C53C22×C414yes—
147#41×C53C22×C4112yescomplemented
148C2×Q8×C53C22⋊C411yescharacteristic
149C2×Q8×C53C22×C411yescharacteristic
150C2×D4×C53—23no—
151C2×D4×C53—224no—
152C2×D4×C53—23no—
153C2×D4×C53—26no—
154C2×D4×C53C22⋊C413yes—
155C2×D4×C53C22×C413yes—
156C2×D4×C53C22×C4112yescomplemented
157C22×C4×C53—23no—
158C22×C4×C53C22×C413yes—
159C2×C22⋊D53—23no—
160C2×C22⋊D53—26no—
161C2×C22⋊D53—212no—
162C2×C22⋊D53—23no—
163C2×C22⋊D53—212no—
164C2×C22⋊D53—248no—
165C2×C22⋊D53—23no—
166C2×C22⋊D53C22⋊C416yes—
167C22×Dic53—23no—
168C22×Dic53—26no—
169C22×Dic53—212no—
170C22×Dic53—23no—
171C22×Dic53—212no—
172C22×Dic53C2×D413yes—
173#11719949—21no—
174#11719949—21no—
175#11719949C22⋊C414yes—
176#11719949C22×C412yes—
177#11719949C2×D414yes—
178#11719949C2412yes—
179Q8×D53—28no—
180Q8×D53—26no—
181Q8×D53C22⋊C414yes—
182Q8×D53C22×C4112yescomplemented
183Q8×D53C2×D414yes—
184#11719947—224no—
185#11719947—248no—
186#11719947—212no—
187#11719947—212no—
188#11719947—212no—
189#11719947—212no—
190#11719947—212no—
191#11719947—23no—
192#11719947—23no—
193#11719947—212no—
194#11719947—212no—
195#11719947—224no—
196#11719947C22⋊C4112yes—
197#11719947C22×C416yes—
198#11719947C22×C4124yescomplemented
199#11719947C2×D4112yes—
200#11719947C2416yes—
201D4×D53—212no—
202D4×D53—212no—
203D4×D53—224no—
204D4×D53—26no—
205D4×D53C22⋊C4112yes—
206D4×D53C22×C4112yescomplemented
207D4×D53C2×D4112yes—
208#11719945—26no—
209#11719945—224no—
210#11719945—212no—
211#11719945—212no—
212#11719945C22⋊C4112yes—
213#11719945C22×C4112yes—
214#11719945C22×C4112yescomplemented
215C2×D212—21no—
216C2×D212C22⋊C413yes—
217C2×D212C22×C411yescharacteristic
218C2×C4×D53—23no—
219C2×C4×D53—23no—
220C2×C4×D53—21no—
221C2×C4×D53—212no—
222C2×C4×D53—212no—
223C2×C4×D53C22×C413yes—
224C2×C4×D53C22×C416yes—
225C2×C4×D53C2×D413yes—
226C2×C4×D53C2×D416yes—
227C2×C4×D53C2×D413yes—
228C2×C4×D53C2×D416yes—
229C2×C4×D53C2411yescharacteristic
230C2×C4×D53C2416yes—
231C2×Dic106—23no—
232C2×Dic106—26no—
233C2×Dic106—23no—
234C2×Dic106—224no—
235C2×Dic106C22⋊C413yes—
236C2×Dic106C22×C413yes—
237C2×Dic106C22×C4112yescomplemented
238C22⋊#6157—212no—
239#11719940—212no—
240C2×#88324—23no—
241C2×#88324—212no—
242C2×#88324—21no—
243C4⋊#6157—212no—
244C4×#6157—21no—
245C4×#6157—23no—
246C4×#6157—212no—
247C4×#6157C2412yes—
248C4×#6157C2416yes—
249#11719936—21no—
250#11719936—23no—
251#11719936—212no—
252#11719936C2412yes—
253#11719936C2416yes—
254D53⋊C8—212no—
255C23×C53—23no—
256C23×C53—212no—
257C23×C53—86no—
258C23×C53C2×C22⋊C413yes—
259C22×D53—21no—
260C22×D53—212no—
261C22×D53—46no—
262C22×D53—86no—
263C22×D53C2×C22⋊C413yes—
264C22×D53C2×C22⋊C416yes—
265C22×D53C22×D411yescharacteristic
266C22×D53C22×D416yes—
267C2×#6157—24no—
268C2×#6157—22no—
269C2×#6157—26no—
270C2×#6157—424no—
271C2×#6157—46no—
272Q8×C53—21no—
273Q8×C53C2×C22⋊C414yes—
274Q8×C53C23×C412yes—
275D4×C53—212no—
276D4×C53—23no—
277D4×C53—212no—
278D4×C53C2×C22⋊C4112yes—
279D4×C53C23×C416yes—
280C2×C4×C53—21no—
281C2×C4×C53—212no—
282C2×C4×C53C2×C22⋊C413yes—
283C2×C4×C53C2×C22⋊C416yes—
284C2×C4×C53C23×C411yescharacteristic
285C2×C4×C53C23×C416yes—
286C22⋊D53—212no—
287C22⋊D53—26no—
288C22⋊D53—224no—
289C22⋊D53—26no—
290C22⋊D53—212no—
291C22⋊D53C2×C22⋊C4124yes—
292C2×Dic53—23no—
293C2×Dic53—212no—
294C2×Dic53—224no—
295C2×Dic53—26no—
296C2×Dic53—26no—
297C2×Dic53C2×C22⋊C413yes—
298C2×Dic53C2×C22⋊C416yes—
299C2×Dic53C22×D411yescharacteristic
300C2×Dic53C22×D416yes—
301D212—22no—
302D212—22no—
303D212—21no—
304D212C2×C22⋊C4112yes—
305D212C23×C412yes—
306C4×D53—212no—
307C4×D53—212no—
308C4×D53—22no—
309C4×D53—22no—
310C4×D53C2×C22⋊C416yes—
311C4×D53C2×C22⋊C416yes—
312C4×D53C2×C22⋊C416yes—
313C4×D53C23×C411yescharacteristic
314C4×D53C23×C416yes—
315C4×D53C22×D411yescharacteristic
316C4×D53C22×D416yes—
317C4×D53C22×D411yescharacteristic
318C4×D53C22×D416yes—
319C4×D53C2511yescharacteristic
320Dic106—23no—
321Dic106—212no—
322Dic106—212no—
323Dic106C2×C22⋊C4112yes—
324Dic106C23×C416yes—
325#88324—26no—
326#88324—22no—
327C2×#2901—531nomaximal, Sylow
328C22×C53—26no—
329C22×C53—26no—
330C22×C53—46no—
331C22×C53—812no—
332C22×C53C22×C22⋊C416yes—
333C22×C53C22×C22⋊C411yescharacteristic
334C2×D53—22no—
335C2×D53—26no—
336C2×D53—22no—
337C2×D53—46no—
338C2×D53—46no—
339C2×D53—42no—
340C2×D53—812no—
341C2×D53C22×C22⋊C416yes—
342C2×D53C22×C22⋊C411yescharacteristic
343C2×D53C23×D411yescharacteristic
344#6157—24no—
345#6157—46no—
346C4×C53—22no—
347C4×C53C22×C22⋊C411yescharacteristic
348C4×C53C22×C22⋊C416yes—
349C4×C53C24×C411yescharacteristic
350Dic53—26no—
351Dic53C22×C22⋊C416yes—
352Dic53C22×C22⋊C411yescharacteristic
353Dic53C23×D411yescharacteristic
354C2×#585—531no—
355C2×#568—531no—
356C2×C4×#41—531no—
357#2901—5316no—
358C2×#421—533no—
359C2×#421—533no—
360C22×#104—533no—
361C22×#104—533no—
362C2×C53—26no—
363C2×C53—46no—
364C2×C53#290112yescomplemented
365C2×C53C23×C22⋊C411yescharacteristic
366D53—21no—
367D53—21no—
368D53—26no—
369D53—42no—
370#585—538no—
371#585—538no—
372#585—1064no—
373#585—1064no—
374C2×2−1+4—531no—
375C2×2−1+4—533no—
376C2×2−1+4—1061no—
377C2×H(5,𝔽2)—533no—
378C2×H(5,𝔽2)—1063no—
379C2×H(5,𝔽2)#615711yescharacteristic, complemented
380C22×#41—531no—
381C22×#41—533no—
382C22×#41—533no—
383C22×#41—1063no—
384C22×#41—1061no—
385#568—538no—
386#568—1064no—
387C2×#131—1063no—
388C2×#131—1061no—
389C22×M16—533no—
390C22×M16—533no—
391C4×#41—538no—
392C4×#41—1064no—
393C2×C4×Q8—1061no—
394C2×C4×D4—1063no—
395C2×#117—533no—
396C22×C42—533no—
397#421—5324no—
398#421—5324no—
399C2×#104—533no—
400C2×#104—531no—
401C2×#104—536no—
402C2×#104—533no—
403C2×#104—533no—
404C2×#104—5324no—
405C2×#104—5324no—
406C53C2×#290111yescharacteristic, complemented, Sylow
4072−1+4—538no—
4082−1+4—5324no—
4092−1+4—1068no—
4102−1+4—1068no—
4112−1+4—10612no—
4122−1+4—1064no—
413H(5,𝔽2)—24no—
414H(5,𝔽2)—5324no—
415H(5,𝔽2)—10624no—
416H(5,𝔽2)—10624no—
417H(5,𝔽2)—10612no—
418H(5,𝔽2)C2×#615718yescomplemented
419C2×#41—21no—
420C2×#41—534no—
421C2×#41—534no—
422C2×#41—534no—
423C2×#41—534no—
424C2×#41—531no—
425C2×#41—533no—
426C2×#41—533no—
427C2×#41—5312no—
428C2×#41—5312no—
429C2×#41—531no—
430C2×#41—533no—
431C2×#41—536no—
432C2×#41—5312no—
433C2×#41—5312no—
434C2×#41—533no—
435C2×#41—1063no—
436C2×#41—1063no—
437C2×#41—1063no—
438C2×#41—1063no—
439C2×#41—1063no—
440C2×#41—1066no—
441C2×#41—1066no—
442C2×#41—1066no—
443C2×#41—1066no—
444C2×#41—1066no—
445C2×#41—1063no—
446C2×#41—10624no—
447C2×#41—10624no—
448C2×#41—1068no—
449C2×#41—1068no—
450C2×#41—1063no—
451C2×#41C2×#615711yescharacteristic
452C2×#41C2×#615713yescomplemented
453C22×Q8—531no—
454C22×Q8—533no—
455C22×Q8—533no—
456C22×Q8—1063no—
457C22×Q8—1061no—
458C22×D4—23no—
459C22×D4—533no—
460C22×D4—533no—
461C22×D4—1063no—
462C22×D4—1063no—
463C22×D4—1066no—
464C22×D4—1063no—
465C22×D4C2×#615713yescomplemented
466C23×C4—533no—
467C23×C4—1063no—
468C23×C4—1063no—
469C23×C4—1063no—
470#131—10624no—
471#131—1068no—
472C2×M16—531no—
473C2×M16—533no—
474C2×M16—5312no—
475C2×M16—5312no—
476C2×M16—1063no—
477C2×M16—1063no—
478C2×M16—1066no—
479C2×M16—1066no—
480C22×C8—1063no—
481C22×C8—1063no—
482C4×Q8—1068no—
483C4×D4—10624no—
484#117—5312no—
485#117—1066no—
486C2×C4⋊C4—1063no—
487C2×C22⋊C4—1063no—
488C2×C42—533no—
489C2×C42—5312no—
490C2×C42—531no—
491C2×C42—1063no—
492C2×C42—1066no—
493#104—5312no—
494#104—534no—
495#104—5324no—
496#104—5312no—
497#104—5312no—
498C24—23no—
499C24—533no—
500C24—1063no—
501#41—28no—
502#41—26no—
503#41—534no—
504#41—534no—
505#41—5312no—
506#41—5312no—
507#41—5312no—
508#41—5312no—
509#41—532no—
510#41—532no—
511#41—536no—
512#41—5324no—
513#41—536no—
514#41—5312no—
515#41—10612no—
516#41—10612no—
517#41—10624no—
518#41—10612no—
519#41—10612no—
520#41—10612no—
521#41—1063no—
522#41—10612no—
523#41—1063no—
524#41—10612no—
525#41—10612no—
526#41—10612no—
527#41—1061no—
528#41—1061no—
529#41—10648no—
530#41—10624no—
531#41—10624no—
532#41—1066no—
533#41C22⋊#615714yes—
534#41C22×#615714yes—
535#41C22×#6157112yescomplemented
536C2×Q8—534no—
537C2×Q8—534no—
538C2×Q8—533no—
539C2×Q8—5312no—
540C2×Q8—533no—
541C2×Q8—5312no—
542C2×Q8—1063no—
543C2×Q8—10624no—
544C2×Q8—1066no—
545C2×Q8—1068no—
546C2×Q8—1063no—
547C2×Q8—1066no—
548C2×Q8C22⋊#615711yescharacteristic
549C2×Q8C22×#615711yescharacteristic
550C2×D4—23no—
551C2×D4—224no—
552C2×D4—23no—
553C2×D4—26no—
554C2×D4—536no—
555C2×D4—5312no—
556C2×D4—5312no—
557C2×D4—5312no—
558C2×D4—533no—
559C2×D4—531no—
560C2×D4—1061no—
561C2×D4—1066no—
562C2×D4—1063no—
563C2×D4—10624no—
564C2×D4—10612no—
565C2×D4—10612no—
566C2×D4—10648no—
567C2×D4—1066no—
568C2×D4—1063no—
569C2×D4—10612no—
570C2×D4—10612no—
571C2×D4—1063no—
572C2×D4C22⋊#615713yes—
573C2×D4C22×#615713yes—
574C2×D4C22×#6157112yescomplemented
575C22×C4—23no—
576C22×C4—533no—
577C22×C4—533no—
578C22×C4—536no—
579C22×C4—533no—
580C22×C4—536no—
581C22×C4—533no—
582C22×C4—536no—
583C22×C4—531no—
584C22×C4—536no—
585C22×C4—1061no—
586C22×C4—10612no—
587C22×C4—10612no—
588C22×C4—1063no—
589C22×C4—1063no—
590C22×C4—1066no—
591C22×C4—10612no—
592C22×C4—10612no—
593C22×C4—1061no—
594C22×C4—1063no—
595C22×C4—1063no—
596C22×C4—1063no—
597C22×C4—10612no—
598C22×C4—21212no—
599C22×C4C22×#615713yes—
600M16—532no—
601M16—536no—
602M16—1061no—
603M16—1063no—
604M16—10612no—
605M16—10612no—
606C2×C8—1063no—
607C2×C8—1061no—
608C2×C8—10612no—
609C2×C8—10612no—
610C4⋊C4—10612no—
611C22⋊C4—10612no—
612C42—532no—
613C42—536no—
614C42—1061no—
615C42—1063no—
616C42—10612no—
617C23—23no—
618C23—212no—
619C23—86no—
620C23—533no—
621C23—531no—
622C23—536no—
623C23—536no—
624C23—10612no—
625C23—1061no—
626C23—4246no—
627C23—2126no—
628C23C2×C22⋊#615713yes—
629Q8—21no—
630Q8—5312no—
631Q8—536no—
632Q8—10612no—
633Q8—10612no—
634Q8—1063no—
635Q8C2×C22⋊#615714yes—
636Q8C23×#615712yes—
637D4—212no—
638D4—23no—
639D4—212no—
640D4—5324no—
641D4—5312no—
642D4—532no—
643D4—1062no—
644D4—1062no—
645D4—10612no—
646D4—1066no—
647D4—1066no—
648D4—10624no—
649D4—10612no—
650D4—1061no—
651D4C2×C22⋊#6157112yes—
652D4C23×#615716yes—
653C2×C4—21no—
654C2×C4—212no—
655C2×C4—536no—
656C2×C4—536no—
657C2×C4—533no—
658C2×C4—531no—
659C2×C4—536no—
660C2×C4—536no—
661C2×C4—536no—
662C2×C4—531no—
663C2×C4—536no—
664C2×C4—536no—
665C2×C4—531no—
666C2×C4—531no—
667C2×C4—536no—
668C2×C4—531no—
669C2×C4—1062no—
670C2×C4—1062no—
671C2×C4—10612no—
672C2×C4—1066no—
673C2×C4—1066no—
674C2×C4—10624no—
675C2×C4—1062no—
676C2×C4—1064no—
677C2×C4—10612no—
678C2×C4—1063no—
679C2×C4—10612no—
680C2×C4—1066no—
681C2×C4—21224no—
682C2×C4—2126no—
683C2×C4C2×C22⋊#615716yes—
684C2×C4C2×C22⋊#615713yes—
685C2×C4C23×#615716yes—
686C2×C4C23×#615711yescharacteristic
687C8—1066no—
688C8—1062no—
689C22—26no—
690C22—26no—
691C22—46no—
692C22—812no—
693C22—531no—
694C22—531no—
695C22—536no—
696C22—1062no—
697C22—1066no—
698C22—1062no—
699C22—42412no—
700C22—2126no—
701C22—2126no—
702C22—2122no—
703C22C22×C22⋊#615716yes—
704C22C22×C22⋊#615711yescharacteristic
705C4—22no—
706C4—531no—
707C4—531no—
708C4—536no—
709C4—1064no—
710C4—1066no—
711C4—2126no—
712C4C22×C22⋊#615716yes—
713C4C22×C22⋊#615711yescharacteristic
714C4C24×#615711yescharacteristic
715C2—26no—
716C2—46no—
717C2—1061no—
718C2—1066no—
719C2—1061no—
720C2—2122no—
721C2#2029134512yesdirect product factor
722C2C23×C22⋊#615711yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6157
commutatorC4×C53C24×C4
FrattiniC4C24×#6157
FittingC2×H(5,𝔽2)×C53C4
socleC22×C53C22×C22⋊C4
prime radicalC2×#16811458C2
cosocleC4×D53C25
hypercenterC2×H(5,𝔽2)#6157
hypocenterC53C2×#2901
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. C2×#16811702C2semidirect
2. C2×#41×#6157C2semidirect
3. #20291345C2direct (N × H)
4. C2×#16811620C2semidirect
5. C2×#16811621C2semidirect
6. C2×D53⋊#104C2semidirect
7. C22×#13133281C2semidirect
10. #16811702C22semidirect
13. C22×#11719936C22semidirect
14. C2×D53⋊M16C22semidirect
16. #41×#6157C22semidirect
19. C2×#13133296C22semidirect
20. C22×C4×#6157C22semidirect
21. #16811621C22semidirect
22. #16811620C22semidirect
23. C2×#13133282C22semidirect
24. C2×#13133282C22semidirect
25. D53⋊#104C22semidirect
26. C2×#13133281C22semidirect
27. C2×#13133281C22semidirect
28. C2×#13133281C22semidirect
29. C2×#13133281C22semidirect
32. #16811458C4semidirect
35. C2×#13133264C4semidirect
36. C2×#13133264C4semidirect
38. C2×#13133262C4semidirect
44. C2×H(5,𝔽2)×C53C4semidirect
52. C2×#11719936C23semidirect
54. D53⋊M16C23semidirect
61. #13133296C23semidirect
68. C2×C4×#6157C23semidirect
69. #13133282C23semidirect
70. #13133282C23semidirect
71. #13133281C23semidirect
72. #13133281C23semidirect
73. #13133281C23semidirect
78. #13133264C2×C4semidirect
79. #13133264C2×C4semidirect
83. #13133262C2×C4semidirect
89. C2×#11719945C2×C4semidirect
100. C2×#11719947C2×C4semidirect
101. C2×#11719947C2×C4semidirect
110. #41×D53C2×C4semidirect
116. C22×Dic106C2×C4semidirect
118. C2×Q8×D53C2×C4semidirect
124. C2×D4×D53C2×C4semidirect
130. H(5,𝔽2)×C53C2×C4semidirect
133. C2×#41×C53C2×C4semidirect
135. C22×D4×C53C2×C4semidirect
147. #41×C53C22×C4semidirect
156. C2×D4×C53C22×C4semidirect
182. Q8×D53C22×C4semidirect
198. #11719947C22×C4semidirect
206. D4×D53C22×C4semidirect
214. #11719945C22×C4semidirect
237. C2×Dic106C22×C4semidirect
364. C2×C53#2901semidirect
379. C2×H(5,𝔽2)#6157semidirect
406. C53C2×#2901semidirect
418. H(5,𝔽2)C2×#6157semidirect
452. C2×#41C2×#6157semidirect
465. C22×D4C2×#6157semidirect
535. #41C22×#6157semidirect
574. C2×D4C22×#6157semidirect
721. C2#20291345direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168117022
C2×#41×#61572
#202913452
C2×#168116202
C2×#168116212
C2×D53⋊#1042
C22×#131332812
C2×#168114582
C2×#290153