Finite Group Databasebeta

← C4×#16811426 #28248309

Subgroups — C4×#16811426 #28248309

Order 13568.

2826 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811426C211yesmaximal, characteristic
2C4×#13133263C211yesmaximal, characteristic, complemented
3#20283588C213yesmaximal, complemented
4#20283565C213yesmaximal, complemented
5#20283547C213yesmaximal, complemented
6#20283543C213yesmaximal, complemented
7C4×#13133243C213yesmaximal, complemented
8C4×#13133242C213yesmaximal, complemented
9C4×#13133237C213yesmaximal, complemented
10C2×C4×#11719922C213yesmaximal, complemented
11#20283313C211yesmaximal, characteristic, complemented
12#20283241C211yesmaximal, characteristic, complemented
13#20283238C211yesmaximal, characteristic, complemented
14C4×#13133224C211yesmaximal, characteristic, complemented
15C4×H(5,𝔽2)×C53C211yesmaximal, characteristic, complemented
16C2×#13133263C2211yescharacteristic
17#16811426C4116yesdirect product factor
18C2×#13133243C2213yes—
19C2×#13133242C2213yes—
20C2×#13133237C2213yes—
21C22×#11719922C2213yes—
22C2×#13133224C2211yescharacteristic
23C2×#13133224C2211yescharacteristic
24#16811106C2211yescharacteristic
25#16811105—21no—
26#16811103C2213yescomplemented
27#16811097C2213yescomplemented
28#16811095—23no—
29C4×#11719949—21no—
30C4×#11719945C2213yescomplemented
31C2×C4×D212C2213yescomplemented
32C4×D4×D53—23no—
33#16810733C2216yescomplemented
34#16810733C2216yescomplemented
35#16810723C2216yescomplemented
36#16810721C2216yescomplemented
37C4×#11719925C2211yescharacteristic, complemented
38C4×#11719925C2213yescomplemented
39C4×#11719924C2213yescomplemented
40C4×#11719924C2213yescomplemented
41C4×#11719923C2213yescomplemented
42C4×#11719923C2213yescomplemented
43C4×#11719922C2213yescomplemented
44C4×#11719922C2216yescomplemented
45C4×#11719922C2216yescomplemented
46C4×#11719922C2216yescomplemented
47C4×#11719922C2213yescomplemented
48#16810666C2213yescomplemented
49#16810663C2213yescomplemented
50#16810659C2213yescomplemented
51C2×#13133150C2213yescomplemented
52#16810628C2213yescomplemented
53#16810627C2213yescomplemented
54#16810624C2213yescomplemented
55#16810622C2213yescomplemented
56#16810619C2213yescomplemented
57#16810617C2213yescomplemented
58C2×#13133138C2213yescomplemented
59C2×#13133137C2213yescomplemented
60#16810579C2213yescomplemented
61#16810579C2213yescomplemented
62C4×#11719917C2213yescomplemented
63C2×C4×#88322C2213yescomplemented
64C2×H(5,𝔽2)×C53C2211yescharacteristic
65C53×#520—21no—
66C53×#520C2211yescharacteristic
67C53×#520C2213yescomplemented
68C53×#518—23no—
69C53×#518C2213yescomplemented
70C4×#41×C53—21no—
71C4×#41×C53C2211yescharacteristic
72C4×#41×C53C2213yescomplemented
73C2×C4×D4×C53—23no—
74C2×C4×D4×C53C2213yescomplemented
75#13133263—24no—
76#13133263C2×C418yescomplemented
77C2×#11719949—21no—
78C2×#11719945C2313yes—
79C22×D212C2313yes—
80C2×D4×D53—23no—
81C22×C4×D53—23no—
82#13133243C2×C4124yescomplemented
83#13133242C2×C4124yescomplemented
84#13133237C2×C4124yescomplemented
85C2×#11719925C2311yescharacteristic
86C2×#11719923C2313yes—
87C2×#11719924C2313yes—
88C2×#11719922C2×C4124yescomplemented
89C2×#11719922C2313yes—
90C2×#11719922C2316yes—
91#13133224—24no—
92#13133224C2×C418yescomplemented
93C2×#11719917C2313yes—
94C2×#11719917C2313yes—
95C22×#88322C2313yes—
96C22×#88322C2313yes—
97Q8×Dic53—21no—
98C4×Dic106C2311yescharacteristic
99C4×Dic106C2313yes—
100C4×D212—23no—
101C4×D212—23no—
102C4×D212C2313yes—
103C4×D212C2316yes—
104C4×D212C2313yes—
105D4×Dic53—23no—
106#13133179—23no—
107#13133179—23no—
108C4×C22⋊D53—23no—
109C4×C22⋊D53—23no—
110#13133177—26no—
111#13133176C2313yes—
112#13133175—23no—
113#13133174—23no—
114C2×C4⋊Dic53C2313yes—
115C4⋊C4×D53—23no—
116C2×#11719921—23no—
117C22⋊C4×D53—26no—
118C42×D53—23no—
119#13133150C2313yes—
120#13133150C2316yes—
121#13133150C2311yescharacteristic
122#13133148C2313yes—
123#13133148C2313yes—
124#13133141C2311yescharacteristic
125#13133141C2313yes—
126#13133140C2311yescharacteristic
127#13133140C2313yes—
128#13133138C2313yes—
129#13133138C2316yes—
130#13133138C2313yes—
131#13133137C2313yes—
132#13133137C2316yes—
133#13133137C2313yes—
134#13133128C2316yes—
135C4×#88322C2311yescharacteristic
136C4×#88322C2313yes—
137C4×#88322C2313yes—
138C4×#88322C2313yes—
139H(5,𝔽2)×C53—24no—
140H(5,𝔽2)×C53C2×C418yescomplemented
141C2×#41×C53—21no—
142C2×#41×C53C2313yes—
143C2×#41×C53C2311yescharacteristic
144C22×D4×C53—23no—
145C22×D4×C53C2313yes—
146C23×C4×C53—23no—
147C4×Q8×C53—21no—
148C4×Q8×C53D411yescharacteristic
149C4×Q8×C53D411yescharacteristic
150C4×Q8×C53C2311yescharacteristic
151C4×Q8×C53C2313yes—
152C4×D4×C53—23no—
153C4×D4×C53—23no—
154C4×D4×C53—26no—
155C4×D4×C53—23no—
156C4×D4×C53—23no—
157C4×D4×C53—23no—
158C4×D4×C53—23no—
159C4×D4×C53—23no—
160C4×D4×C53D413yes—
161C4×D4×C53D413yes—
162C4×D4×C53C2313yes—
163C4×D4×C53C2316yes—
164C4×D4×C53C2313yes—
165#117×C53—23no—
166#117×C53—23no—
167#117×C53C2313yes—
168#117×C53C2313yes—
169C2×C4⋊C4×C53—23no—
170C2×C4⋊C4×C53C2313yes—
171C2×C22⋊C4×C53—26no—
172C2×C22⋊C4×C53—23no—
173C2×C42×C53—23no—
174C2×C42×C53C2313yes—
175C24×C53—23no—
176C23×D53—23no—
177#41×C53—28no—
178#41×C53—26no—
179#41×C53C22×C414yes—
180#41×C53C22×C4112yescomplemented
181#41×C53#4114yes—
182C2×Q8×C53C2×D411yescharacteristic
183C2×Q8×C53C2411yescharacteristic
184C2×D4×C53—23no—
185C2×D4×C53—224no—
186C2×D4×C53—23no—
187C2×D4×C53—26no—
188C2×D4×C53C22×C4112yescomplemented
189C2×D4×C53C2×D413yes—
190C2×D4×C53C2413yes—
191C22×C4×C53—23no—
192C22×C4×C53—23no—
193C22×C4×C53—23no—
194C22×C4×C53—23no—
195C22×C4×C53—26no—
196C22×C4×C53—86no—
197C22×C4×C53C2×D413yes—
198C22×C4×C53C2×D413yes—
199C22×C4×C53C2413yes—
200C2×C22⋊D53—23no—
201C22×Dic53—23no—
202#11719949—28no—
203D4×D53—224no—
204#11719945—26no—
205#11719945C22×C4112yescomplemented
206C2×D212—23no—
207C2×D212—26no—
208C2×D212C22×C4112yescomplemented
209C2×D212C2413yes—
210C2×C4×D53—23no—
211C2×C4×D53—23no—
212C2×C4×D53—23no—
213C2×C4×D53—26no—
214C2×C4×D53—86no—
215C2×Dic106C2411yescharacteristic
216C4⋊C4×C53—23no—
217C4⋊C4×C53—23no—
218C4⋊C4×C53—21no—
219C4⋊C4×C53C2×D413yes—
220C4⋊C4×C53C2×D413yes—
221C4⋊C4×C53C2413yes—
222C4⋊C4×C53C2411yescharacteristic
223C22⋊C4×C53—23no—
224C22⋊C4×C53—26no—
225C22⋊C4×C53—23no—
226C22⋊C4×C53—23no—
227C22⋊C4×C53C2×D416yes—
228C42×C53—21no—
229C42×C53—23no—
230C42×C53—23no—
231C42×C53C2×D413yes—
232C42×C53C2×D413yes—
233C42×C53C2411yescharacteristic
234C42×C53C2413yes—
235C22⋊Dic53—23no—
236#11719925C22×C414yescomplemented
237#11719924C22×C4112yescomplemented
238#11719923C22×C4112yescomplemented
239#11719922C22×C4112yescomplemented
240#11719922C22×C4124yescomplemented
241#11719921—23no—
242#11719921—26no—
243#11719921—23no—
244C4⋊Dic53—23no—
245C4⋊Dic53C2411yescharacteristic
246C4⋊Dic53C2413yes—
247#11719919—23no—
248#11719919—21no—
249C4×Dic53—21no—
250C4×Dic53—23no—
251C4×Dic53—23no—
252#11719917—26no—
253#11719917C22×C4112yescomplemented
254C2×#88322—26no—
255C2×#88322C22×C4112yescomplemented
256C2×#88322C2411yescharacteristic
257C2×#88322C2413yes—
258C2×#88322C2411yescharacteristic
259C2×#88322C2413yes—
260C23×C53—23no—
261C23×C53—212no—
262C23×C53—83no—
263C23×C53—83no—
264C23×C53C22×D413yes—
265C22×D53—23no—
266C22×D53—212no—
267C22×D53—83no—
268C22×D53—83no—
269Q8×C53—21no—
270Q8×C53C4×D414yes—
271Q8×C53C23×C412yes—
272D4×C53—212no—
273D4×C53—212no—
274D4×C53—23no—
275D4×C53C4×D4112yes—
276D4×C53C23×C416yes—
277C2×C4×C53—21no—
278C2×C4×C53—212no—
279C2×C4×C53—26no—
280C2×C4×C53—23no—
281C2×C4×C53—21no—
282C2×C4×C53—43no—
283C2×C4×C53—46no—
284C2×C4×C53—83no—
285C2×C4×C53—86no—
286C2×C4×C53—83no—
287C2×C4×C53C23×C416yes—
288C2×C4×C53C22×D413yes—
289C2×C4×C53C22×D413yes—
290C2×C4×C53C22×D411yescharacteristic
291C2×C4×C53C22×D413yes—
292C2×C4×C53C22×D411yescharacteristic
293C2×C4×C53C2×#4116yes—
294C2×C4×C53C2511yescharacteristic
295C22⋊D53—212no—
296C2×Dic53—21no—
297C2×Dic53—23no—
298C2×Dic53—21no—
299C2×Dic53—83no—
300D212—212no—
301D212—23no—
302D212C23×C416yes—
303C4×D53—212no—
304C4×D53—46no—
305C4×D53—83no—
306C4×D53—86no—
307Dic106—21no—
308Dic106C23×C412yes—
309#88322—21no—
310#88322—23no—
311#88322C23×C412yes—
312#88322C23×C416yes—
313C4×#576—531nomaximal, Sylow
314C22×C53—23no—
315C22×C53—23no—
316C22×C53—26no—
317C22×C53—43no—
318C22×C53—43no—
319C22×C53—812no—
320C22×C53C2×C4×D416yes—
321C22×C53C23×D411yescharacteristic
322C2×D53—26no—
323C2×D53—43no—
324C2×D53—43no—
325C2×D53—812no—
326C4×C53—23no—
327C4×C53—21no—
328C4×C53—22no—
329C4×C53—23no—
330C4×C53—41no—
331C4×C53—43no—
332C4×C53C2×C4×D416yes—
333C4×C53#57612yescomplemented
334C4×C53C24×C411yescharacteristic
335C4×C53C22×#4111yescharacteristic
336Dic53—22no—
337Dic53—41no—
338Dic53—43no—
339C2×#576—531no—
340C4×H(5,𝔽2)—531no—
341C4×H(5,𝔽2)D5311yescharacteristic, complemented
342#2951—533no—
343#2948—533no—
344#2946—533no—
345#2946—533no—
346C4×AGL(1,ℤ/8)—533no—
347C4×AGL(1,ℤ/8)—533no—
348C4×#135—533no—
349C2×C4×D8—533no—
350#2913—531no—
351#2897—531no—
352#2897—531no—
353C4×#131—531no—
354C2×C53—26no—
355C2×C53—46no—
356C2×C53C22×C4×D411yescharacteristic
357C2×C53C2×#57611yescharacteristic
358C2×C53#358411yescharacteristic
359D53—46no—
360C2×H(5,𝔽2)—531no—
361C2×H(5,𝔽2)C2×D5311yescharacteristic
362#576—5316no—
363C2×AGL(1,ℤ/8)—533no—
364C2×AGL(1,ℤ/8)—533no—
365C2×#135—533no—
366C22×D8—533no—
367C2×#131—531no—
368C2×#131—531no—
369#520—21no—
370#520—531no—
371#520—533no—
372#520—1061no—
373#520C2×D5311yescharacteristic
374#520C2×D5313yescomplemented
375#518—23no—
376#518—533no—
377#518—1063no—
378#518C2×D5313yescomplemented
379C4×#41—21no—
380C4×#41—533no—
381C4×#41—1061no—
382C4×#41C2×D5311yescharacteristic
383C4×#41C2×D5313yescomplemented
384C2×C4×D4—23no—
385C2×C4×D4—533no—
386C2×C4×D4—1063no—
387C2×C4×D4C2×D5313yescomplemented
388#442—536no—
389#442—536no—
390#440—536no—
391#440—536no—
392C4×Q16—531no—
393C4×Q16—533no—
394C4×SD16—533no—
395C4×SD16—533no—
396C4×SD16—533no—
397C4×SD16—533no—
398C4×D8—533no—
399C4×D8—536no—
400C4×D8—536no—
401C4×D8—536no—
402C4×D8—533no—
403#428—533no—
404#428—533no—
405#427—533no—
406C2×#107—533no—
407#418—533no—
408#418—533no—
409#417—533no—
410#417—533no—
411#416—533no—
412#416—533no—
413C2×#102—533no—
414C2×#102—533no—
415#405—533no—
416#405—533no—
417C4×M16—533no—
418C2×C4×C8—533no—
419C53C4×#57611yescharacteristic, complemented, Sylow
420H(5,𝔽2)—24no—
421H(5,𝔽2)—538no—
422H(5,𝔽2)—1064no—
423H(5,𝔽2)C4×D5318yescomplemented
424C2×#41—21no—
425C2×#41—533no—
426C2×#41—1061no—
427C2×#41C22×D5313yes—
428C2×#41C22×D5311yescharacteristic
429C22×D4—23no—
430C22×D4—533no—
431C22×D4—1063no—
432C22×D4C22×D5313yes—
433C23×C4—23no—
434C23×C4—1063no—
435AGL(1,ℤ/8)—5324no—
436AGL(1,ℤ/8)—5324no—
437#135—5324no—
438C2×Q16—531no—
439C2×SD16—533no—
440C2×SD16—533no—
441C2×D8—5324no—
442C2×D8—533no—
443C2×D8—536no—
444#131—538no—
445#131—1064no—
446C2×M16—533no—
447C2×M16—533no—
448C22×C8—533no—
449C22×C8—533no—
450C4×Q8—21no—
451C4×Q8—531no—
452C4×Q8—533no—
453C4×Q8—1061no—
454C4×Q8C22⋊D5311yescharacteristic
455C4×Q8C22⋊D5311yescharacteristic
456C4×Q8C22×D5311yescharacteristic
457C4×Q8C22×D5313yes—
458C4×D4—23no—
459C4×D4—23no—
460C4×D4—23no—
461C4×D4—23no—
462C4×D4—23no—
463C4×D4—26no—
464C4×D4—23no—
465C4×D4—23no—
466C4×D4—533no—
467C4×D4—536no—
468C4×D4—533no—
469C4×D4—1063no—
470C4×D4—1063no—
471C4×D4—1063no—
472C4×D4—1063no—
473C4×D4—1063no—
474C4×D4—1066no—
475C4×D4—1063no—
476C4×D4—1063no—
477C4×D4C22⋊D5313yes—
478C4×D4C22⋊D5313yes—
479C4×D4C22×D5313yes—
480C4×D4C22×D5316yes—
481C4×D4C22×D5313yes—
482#117—23no—
483#117—23no—
484#117—533no—
485#117—1063no—
486#117—1063no—
487#117C22×D5313yes—
488#117C22×D5313yes—
489C2×C4⋊C4—23no—
490C2×C4⋊C4—533no—
491C2×C4⋊C4—1063no—
492C2×C4⋊C4C22×D5313yes—
493C2×C22⋊C4—23no—
494C2×C22⋊C4—26no—
495C2×C22⋊C4—1063no—
496C2×C22⋊C4—1066no—
497C2×C42—23no—
498C2×C42—1063no—
499C2×C42C22×D5313yes—
500#107—533no—
501#107—536no—
502#107—531no—
503#106—533no—
504#106—533no—
505#103—531no—
506#103—533no—
507#103—531no—
508#103—533no—
509#102—533no—
510#102—536no—
511#102—533no—
512#102—533no—
513#102—536no—
514#102—533no—
515#97—536no—
516C4×C8—531no—
517C4×C8—533no—
518C4×C8—533no—
519C4×C8—533no—
520C24—23no—
521C24—1063no—
522#41—28no—
523#41—26no—
524#41—5312no—
525#41—1068no—
526#41—1066no—
527#41C2×C4×D5314yes—
528#41C2×C4×D53112yescomplemented
529#41#1171994514yes—
530C2×Q8—531no—
531C2×Q8C2×C22⋊D5311yescharacteristic
532C2×Q8C23×D5311yescharacteristic
533C2×D4—23no—
534C2×D4—224no—
535C2×D4—23no—
536C2×D4—26no—
537C2×D4—5312no—
538C2×D4—533no—
539C2×D4—1063no—
540C2×D4—10624no—
541C2×D4—1063no—
542C2×D4—1066no—
543C2×D4C2×C4×D53112yescomplemented
544C2×D4C2×C22⋊D5313yes—
545C2×D4C23×D5313yes—
546C22×C4—23no—
547C22×C4—23no—
548C22×C4—23no—
549C22×C4—23no—
550C22×C4—26no—
551C22×C4—86no—
552C22×C4—1063no—
553C22×C4—1063no—
554C22×C4—1063no—
555C22×C4—1066no—
556C22×C4—1063no—
557C22×C4—4246no—
558C22×C4C2×C22⋊D5313yes—
559C22×C4C2×C22⋊D5313yes—
560C22×C4C23×D5313yes—
561Q16—534no—
562SD16—5312no—
563SD16—5312no—
564D8—5312no—
565D8—5324no—
566M16—5312no—
567M16—1066no—
568C2×C8—5312no—
569C2×C8—531no—
570C2×C8—533no—
571C2×C8—531no—
572C2×C8—533no—
573C2×C8—1066no—
574C4⋊C4—23no—
575C4⋊C4—23no—
576C4⋊C4—21no—
577C4⋊C4—531no—
578C4⋊C4—533no—
579C4⋊C4—1063no—
580C4⋊C4—1063no—
581C4⋊C4—1061no—
582C4⋊C4C2×C22⋊D5313yes—
583C4⋊C4C2×C22⋊D5313yes—
584C4⋊C4C23×D5311yescharacteristic
585C4⋊C4C23×D5313yes—
586C22⋊C4—23no—
587C22⋊C4—23no—
588C22⋊C4—26no—
589C22⋊C4—23no—
590C22⋊C4—1063no—
591C22⋊C4—1063no—
592C22⋊C4—1066no—
593C22⋊C4—1063no—
594C22⋊C4C2×C22⋊D5316yes—
595C42—23no—
596C42—23no—
597C42—21no—
598C42—1063no—
599C42—1063no—
600C42—1061no—
601C42C2×C22⋊D5313yes—
602C42C2×C22⋊D5313yes—
603C42C23×D5313yes—
604C42C23×D5311yescharacteristic
605C23—23no—
606C23—212no—
607C23—83no—
608C23—83no—
609C23—10612no—
610C23—1063no—
611C23—4243no—
612C23—4243no—
613C23C22×C22⋊D5313yes—
614Q8—21no—
615Q8—532no—
616Q8—1061no—
617Q8C4×C22⋊D5314yes—
618Q8C22×C4×D5312yes—
619D4—212no—
620D4—212no—
621D4—23no—
622D4—536no—
623D4—10612no—
624D4—10612no—
625D4—1063no—
626D4C4×C22⋊D53112yes—
627D4C22×C4×D5316yes—
628C2×C4—21no—
629C2×C4—212no—
630C2×C4—26no—
631C2×C4—21no—
632C2×C4—23no—
633C2×C4—43no—
634C2×C4—46no—
635C2×C4—83no—
636C2×C4—86no—
637C2×C4—83no—
638C2×C4—1061no—
639C2×C4—10612no—
640C2×C4—1061no—
641C2×C4—1063no—
642C2×C4—4243no—
643C2×C4—4246no—
644C2×C4—4243no—
645C2×C4—2126no—
646C2×C4C22×C4×D5316yes—
647C2×C4C22×C22⋊D5313yes—
648C2×C4C22×C22⋊D5311yescharacteristic
649C2×C4C22×C22⋊D5313yes—
650C2×C4C22×C22⋊D5313yes—
651C2×C4C22×C22⋊D5311yescharacteristic
652C2×C4C2×#1171994516yes—
653C2×C4C24×D5311yescharacteristic
654C8—532no—
655C8—536no—
656C8—1061no—
657C8—1063no—
658C22—23no—
659C22—23no—
660C22—26no—
661C22—43no—
662C22—43no—
663C22—812no—
664C22—1066no—
665C22—42412no—
666C22—2123no—
667C22—2123no—
668C22C2×C4×C22⋊D5316yes—
669C22C23×C22⋊D5311yescharacteristic
670C4—22no—
671C4—23no—
672C4—21no—
673C4—23no—
674C4—43no—
675C4—41no—
676C4—1062no—
677C4—2123no—
678C4—2121no—
679C4C2×C4×C22⋊D5316yes—
680C4#1681142612yesdirect product factor
681C4C23×C4×D5311yescharacteristic
682C4C22×#1171994511yescharacteristic
683C2—26no—
684C2—46no—
685C2—2126no—
686C2C22×C4×C22⋊D5311yescharacteristic
687C2C2×#1681142611yescharacteristic
688C2#2028948611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D53
commutatorC4×C53C24×C4
FrattiniC2×C4C24×D53
FittingC4×H(5,𝔽2)×C53C2
socleC22×C53C23×D4
prime radicalC2×#16811426C2
cosocleC2×C4×C53C25
hypercenterC4×H(5,𝔽2)D53
hypocenterC53C4×#576
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ C4×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
2. C4×#13133263C2semidirect
3. #20283588C2semidirect
4. #20283565C2semidirect
5. #20283547C2semidirect
6. #20283543C2semidirect
7. C4×#13133243C2semidirect
8. C4×#13133242C2semidirect
9. C4×#13133237C2semidirect
10. C2×C4×#11719922C2semidirect
11. #20283313C2semidirect
12. #20283241C2semidirect
13. #20283238C2semidirect
14. C4×#13133224C2semidirect
15. C4×H(5,𝔽2)×C53C2semidirect
17. #16811426C4direct (N × H)
26. #16811103C22semidirect
27. #16811097C22semidirect
30. C4×#11719945C22semidirect
31. C2×C4×D212C22semidirect
33. #16810733C22semidirect
34. #16810733C22semidirect
35. #16810723C22semidirect
36. #16810721C22semidirect
37. C4×#11719925C22semidirect
38. C4×#11719925C22semidirect
39. C4×#11719924C22semidirect
40. C4×#11719924C22semidirect
41. C4×#11719923C22semidirect
42. C4×#11719923C22semidirect
43. C4×#11719922C22semidirect
44. C4×#11719922C22semidirect
45. C4×#11719922C22semidirect
46. C4×#11719922C22semidirect
47. C4×#11719922C22semidirect
48. #16810666C22semidirect
49. #16810663C22semidirect
50. #16810659C22semidirect
51. C2×#13133150C22semidirect
52. #16810628C22semidirect
53. #16810627C22semidirect
54. #16810624C22semidirect
55. #16810622C22semidirect
56. #16810619C22semidirect
57. #16810617C22semidirect
58. C2×#13133138C22semidirect
59. C2×#13133137C22semidirect
60. #16810579C22semidirect
61. #16810579C22semidirect
62. C4×#11719917C22semidirect
63. C2×C4×#88322C22semidirect
67. C53×#520C22semidirect
69. C53×#518C22semidirect
72. C4×#41×C53C22semidirect
74. C2×C4×D4×C53C22semidirect
76. #13133263C2×C4semidirect
82. #13133243C2×C4semidirect
83. #13133242C2×C4semidirect
84. #13133237C2×C4semidirect
88. C2×#11719922C2×C4semidirect
92. #13133224C2×C4semidirect
140. H(5,𝔽2)×C53C2×C4semidirect
180. #41×C53C22×C4semidirect
188. C2×D4×C53C22×C4semidirect
205. #11719945C22×C4semidirect
208. C2×D212C22×C4semidirect
236. #11719925C22×C4semidirect
237. #11719924C22×C4semidirect
238. #11719923C22×C4semidirect
239. #11719922C22×C4semidirect
240. #11719922C22×C4semidirect
253. #11719917C22×C4semidirect
255. C2×#88322C22×C4semidirect
333. C4×C53#576semidirect
341. C4×H(5,𝔽2)D53semidirect
374. #520C2×D53semidirect
378. #518C2×D53semidirect
383. C4×#41C2×D53semidirect
387. C2×C4×D4C2×D53semidirect
419. C53C4×#576semidirect
423. H(5,𝔽2)C4×D53semidirect
528. #41C2×C4×D53semidirect
543. C2×D4C2×C4×D53semidirect
680. C4#16811426direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168114262
C4×#131332632
#202835882
#202835652
#202835472
#202835432
C4×#131332432
C4×#131332422
C4×#131332372
C2×C4×#117199222
#202833132
#202832412
#202832382
C4×#131332242
C4×H(5,𝔽2)×C532
C4×#57653