Finite Group Databasebeta

← C2×#20285969 #28256282

Subgroups — C2×#20285969 #28256282

Order 13568.

1806 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811250C211yesmaximal, characteristic, complemented
2C2×#16811229C211yesmaximal, characteristic
3#20285969C2116yesmaximal, direct product factor
4C2×#16811022C211yesmaximal, characteristic, complemented
5C2×#16810988C211yesmaximal, characteristic, complemented
6C2×#16810971C211yesmaximal, characteristic, complemented
7C2×#16810943C211yesmaximal, characteristic, complemented
8C2×#16810950C211yesmaximal, characteristic, complemented
9C2×#16810949C211yesmaximal, characteristic, complemented
10C2×#16810938C211yesmaximal, characteristic, complemented
11C2×#16810926C211yesmaximal, characteristic, complemented
12C2×#16810922C211yesmaximal, characteristic, complemented
13C2×#16810912C211yesmaximal, characteristic, complemented
14C2×#16810902C211yesmaximal, characteristic, complemented
15C2×#16810685C211yesmaximal, characteristic, complemented
16C2×C53×#501C211yesmaximal, characteristic, complemented
17#16811250—24no—
18#16811250C2218yescomplemented
19#16811229—24no—
20#16811229C2218yes—
21C2×#13133216C2211yescharacteristic
22C2×#13133215—21no—
23C2×#13133214C2211yescharacteristic
24C2×#13133209C2211yescharacteristic
25C2×#13133208C2211yescharacteristic
26C2×#13133207—21no—
27C2×#13133202—21no—
28C2×#13133202—21no—
29C2×#13133195—21no—
30C2×#13133193—21no—
31C2×#13133192—21no—
32C2×#13133192—21no—
33C2×#13133192C2211yescharacteristic
34C2×#13133192C2211yescharacteristic
35C2×#13133179C2211yescharacteristic
36C2×#13133179C2211yescharacteristic
37C2×#13133175C2211yescharacteristic
38C2×#13133174C2211yescharacteristic
39C2×C4⋊C4×D53C2211yescharacteristic
40#16811022C2218yescomplemented
41#16810988C2218yescomplemented
42#16810971C2218yescomplemented
43#16810950C2218yescomplemented
44#16810949C2218yescomplemented
45#16810943C2218yescomplemented
46#16810938C2218yescomplemented
47#16810926C2218yescomplemented
48#16810922C2218yescomplemented
49#16810912C2218yescomplemented
50#16810902C2218yescomplemented
51#16810685C2218yescomplemented
52C2×#13133150C2211yescharacteristic
53C2×#13133150C2211yescharacteristic
54C2×#13133148C2211yescharacteristic
55C2×#13133148C2211yescharacteristic
56C2×#13133146C2211yescharacteristic
57C2×#13133146C2211yescharacteristic
58C2×#13133139C2211yescharacteristic
59C2×#13133139C2211yescharacteristic
60C2×#13133139C2211yescharacteristic
61C2×#13133139C2211yescharacteristic
62C2×#13133137C2211yescharacteristic
63C2×#13133137C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C4×#88322C2211yescharacteristic
69C2×C4⋊Q8×C53C2211yescharacteristic
70C2×#125×C53C2211yescharacteristic
71C53×#501C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#107×C53C2211yescharacteristic
74C2×#106×C53C2211yescharacteristic
75C2×#106×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×D212—21no—
79C22×D212—21no—
80C22×D212—21no—
81C22×D212—21no—
82C22×D212C2311yescharacteristic
83C22×D212C2311yescharacteristic
84C22×C4×D53—21no—
85C22×C4×D53—21no—
86C22×C4×D53—21no—
87C22×C4×D53C2311yescharacteristic
88C22×#88322C2311yescharacteristic
89C22×#88322C2311yescharacteristic
90#13133216—22no—
91#13133216C2314yes—
92#13133215—28no—
93#13133214—22no—
94#13133214C2314yes—
95#13133209—22no—
96#13133209C2314yes—
97#13133208—22no—
98#13133208C2314yes—
99#13133207—28no—
100#13133202—28no—
101#13133202—28no—
102#13133195—28no—
103#13133193—28no—
104#13133192—28no—
105#13133192—28no—
106#13133192—22no—
107#13133192—22no—
108#13133192C2314yes—
109#13133192C2314yes—
110#13133179—22no—
111#13133179—22no—
112#13133179C2314yes—
113#13133179C2314yes—
114#13133175—22no—
115#13133175C2314yes—
116#13133174D414yes—
117#13133174C2314yes—
118C2×C4⋊Dic53—21no—
119C2×C4⋊Dic53C2311yescharacteristic
120C2×C4⋊Dic53C2311yescharacteristic
121C2×#11719919—21no—
122C2×#11719919—21no—
123C2×#11719919—21no—
124C2×#11719919—21no—
125C2×#11719919—21no—
126C2×#11719919D411yescharacteristic
127C2×#11719919D411yescharacteristic
128C4⋊C4×D53—22no—
129C4⋊C4×D53C2314yes—
130C2×#11719921—21no—
131C2×#11719921—21no—
132C2×#11719921—21no—
133C2×#11719921—21no—
134C2×#11719921—21no—
135C2×#11719921D411yescharacteristic
136C2×#11719921D411yescharacteristic
137C2×C4×Dic53—21no—
138C2×C4×Dic53C2311yescharacteristic
139#13133150C2314yes—
140#13133150C2314yes—
141#13133148C2314yes—
142#13133148C2314yes—
143#13133146C2314yes—
144#13133146C2314yes—
145#13133139C2314yes—
146#13133139C2314yes—
147#13133139C2314yes—
148#13133139C2314yes—
149#13133137C2314yes—
150#13133137C2314yes—
151#13133137C2314yes—
152#13133137C2314yes—
153#13133129C2314yes—
154#13133129C2314yes—
155C4×#88322C2314yes—
156C22×Q8×C53—21no—
157C22×C8×C53C2311yescharacteristic
158C22×C8×C53C2311yescharacteristic
159C4⋊Q8×C53—22no—
160C4⋊Q8×C53C2314yes—
161#125×C53—22no—
162#125×C53C2314yes—
163C2×C4⋊C4×C53—21no—
164C2×C4⋊C4×C53—21no—
165C2×C4⋊C4×C53—21no—
166C2×C4⋊C4×C53C2311yescharacteristic
167C2×C4⋊C4×C53C2311yescharacteristic
168C2×C4⋊C4×C53C2311yescharacteristic
169C2×C4⋊C4×C53C2311yescharacteristic
170C2×C42×C53C2311yescharacteristic
171#107×C53C2314yes—
172#107×C53C2314yes—
173#106×C53C2314yes—
174#106×C53C2314yes—
175#97×C53C2314yes—
176C23×D53—21no—
177C23×D53—21no—
178C23×D53C2×D411yescharacteristic
179C2×Q8×C53—24no—
180C2×Q8×C53—82no—
181C22×C4×C53—21no—
182C22×C4×C53—21no—
183C22×C4×C53—21no—
184C22×C4×C53—21no—
185C22×C4×C53C2×D411yescharacteristic
186C22×C4×C53C2×D411yescharacteristic
187C22×C4×C53C2411yescharacteristic
188C22×Dic53—21no—
189C22×Dic53—21no—
190C22×Dic53C2×D411yescharacteristic
191C22×Dic53C2×D411yescharacteristic
192C22×Dic53C2×D411yescharacteristic
193C2×D212—22no—
194C2×D212—22no—
195C2×D212—22no—
196C2×D212—22no—
197C2×D212—21no—
198C2×D212—21no—
199C2×D212—24no—
200C2×D212—24no—
201C2×D212—24no—
202C2×D212—24no—
203C2×D212—82no—
204C2×D212—82no—
205C2×D212—82no—
206C2×D212—82no—
207C2×D212C2412yes—
208C2×D212C2412yes—
209C2×C4×D53—22no—
210C2×C4×D53—22no—
211C2×C4×D53—24no—
212C2×C4×D53—24no—
213C2×C4×D53—24no—
214C2×C4×D53—82no—
215C2×C4×D53—82no—
216C2×C4×D53—82no—
217C2×C4×D53C2×D412yes—
218C2×C4×D53C2412yes—
219C2×Dic106—24no—
220C2×Dic106—82no—
221C2×C8×C53—22no—
222C2×C8×C53—22no—
223C2×C8×C53C2412yes—
224C2×C8×C53C2412yes—
225C4⋊C4×C53—24no—
226C4⋊C4×C53—24no—
227C4⋊C4×C53—24no—
228C4⋊C4×C53—21no—
229C4⋊C4×C53—21no—
230C4⋊C4×C53—21no—
231C4⋊C4×C53—21no—
232C4⋊C4×C53C2412yes—
233C4⋊C4×C53C2412yes—
234C4⋊C4×C53C2412yes—
235C4⋊C4×C53C2412yes—
236C42×C53C2×D412yes—
237C42×C53C2412yes—
238#11719921—24no—
239#11719921—24no—
240#11719921—24no—
241#11719921—24no—
242#11719921—24no—
243#11719921C2×D414yes—
244#11719921C2×D414yes—
245C4⋊Dic53—21no—
246C4⋊Dic53—21no—
247C4⋊Dic53—24no—
248C4⋊Dic53C2412yes—
249C4⋊Dic53C2412yes—
250#11719919—24no—
251#11719919—24no—
252#11719919—24no—
253#11719919—24no—
254#11719919—24no—
255#11719919C2×D414yes—
256#11719919C2×D414yes—
257C4×Dic53—24no—
258C4×Dic53C2×D412yes—
259C4×Dic53C2412yes—
260C2×#88322—22no—
261C2×#88322—22no—
262C2×#88322C2412yes—
263C2×#88322C2412yes—
264C23×C53C22×D411yescharacteristic
265C22×D53—22no—
266C22×D53—22no—
267C22×D53—22no—
268C22×D53—22no—
269C22×D53—22no—
270C22×D53—42no—
271C22×D53—42no—
272C22×D53—42no—
273C22×D53—42no—
274C22×D53—42no—
275C22×D53—42no—
276C22×D53C22×D412yes—
277Q8×C53—84no—
278C2×C4×C53—22no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—42no—
285C2×C4×C53—42no—
286C2×C4×C53—42no—
287C2×C4×C53—42no—
288C2×C4×C53C22×D412yes—
289C2×C4×C53C22×D412yes—
290C2×C4×C53C22×D411yescharacteristic
291C2×C4×C532−1+412yes—
292C2×C4×C532−1+412yes—
293C2×C4×C53C2511yescharacteristic
294C2×Dic53—22no—
295C2×Dic53—22no—
296C2×Dic53—22no—
297C2×Dic53—22no—
298C2×Dic53—22no—
299C2×Dic53—42no—
300C2×Dic53—42no—
301C2×Dic53C22×D412yes—
302C2×Dic53C22×D412yes—
303C2×Dic53C22×D412yes—
304D212—22no—
305D212—22no—
306D212—22no—
307D212—22no—
308D212—42no—
309D212—42no—
310D212—84no—
311D212—84no—
312D212—84no—
313D212—84no—
314C4×D53—24no—
315C4×D53—22no—
316C4×D53—22no—
317C4×D53—84no—
318C4×D53—84no—
319C4×D53—84no—
320Dic106—84no—
321C8×C53—22no—
322C8×C53—22no—
323#88322—22no—
324#88322—22no—
325C2×#3241—531nomaximal, Sylow
326C22×C53#53612yes—
327C22×C53#57612yes—
328C22×C53#57712yes—
329C22×C53C23×D411yescharacteristic
330C2×D53—22no—
331C2×D53—22no—
332C2×D53—22no—
333C2×D53—44no—
334C2×D53—42no—
335C2×D53—42no—
336C2×D53—42no—
337C2×D53—42no—
338C2×D53—42no—
339C2×D53—42no—
340C2×D53—84no—
341C2×D53—84no—
342C4×C53—22no—
343C4×C53—22no—
344C4×C53—42no—
345C4×C53—42no—
346C4×C53—42no—
347C4×C53—42no—
348C4×C53#53612yes—
349C4×C53C2×2−1+411yescharacteristic
350C4×C53C2×2−1+411yescharacteristic
351Dic53—22no—
352Dic53—22no—
353Dic53—22no—
354Dic53—42no—
355Dic53—42no—
356C2×#544—531no—
357C2×#540—531no—
358#3241—5316no—
359C2×#501D5311yescharacteristic, complemented
360C2×#499—531no—
361C2×#490—531no—
362C2×#486—531no—
363C2×#481—531no—
364C2×#482—531no—
365C2×#482—531no—
366C2×#480—531no—
367C2×#478—531no—
368C2×#478—531no—
369C2×#476—531no—
370C2×#474—531no—
371C2×#433—531no—
372C2×C53#324114yescomplemented
373C2×C53C2×#53611yescharacteristic
374C2×C53C2×#57611yescharacteristic
375C2×C53C2×#57711yescharacteristic
376D53—42no—
377D53—82no—
378D53—82no—
379#544—538no—
380#544—1064no—
381#540—538no—
382#540—1064no—
383C2×C4⋊Q8—531no—
384C2×C4⋊Q8—1061no—
385C2×C4⋊Q8C2×D5311yescharacteristic
386C2×#127—531no—
387C2×#125—531no—
388C2×#125—531no—
389C2×#125—1061no—
390C2×#125C2×D5311yescharacteristic
391C2×#123—1061no—
392C2×#123—1061no—
393C2×C22⋊Q8—1061no—
394C2×C22⋊Q8—1061no—
395C2×#121—531no—
396C2×#121—531no—
397C2×#121—1061no—
398C2×#121—1061no—
399C2×C4×D4—531no—
400C2×C4×D4—531no—
401C2×#117—531no—
402C2×#117—531no—
403C22×C4⋊C4—531no—
404#501C2×D5318yescomplemented
405#499—538no—
406#490—538no—
407#486—538no—
408#482—538no—
409#482—538no—
410#481—538no—
411#480—538no—
412#478—538no—
413#478—538no—
414#476—538no—
415#474—538no—
416#433—538no—
417C2×#107—531no—
418C2×#107—531no—
419C2×#107C2×D5311yescharacteristic
420C2×#107C2×D5311yescharacteristic
421C2×#106—531no—
422C2×#106—531no—
423C2×#106C2×D5311yescharacteristic
424C2×#106C2×D5311yescharacteristic
425C2×C4⋊C8—531no—
426C2×C4⋊C8—531no—
427C2×#102—531no—
428C2×#102—531no—
429C2×#102—531no—
430C2×#102—531no—
431C2×#102—531no—
432C2×#102—531no—
433C2×#102—531no—
434C2×#102—531no—
435C2×C22⋊C8—531no—
436C2×C22⋊C8—531no—
437C2×#97C2×D5311yescharacteristic
438C2×C4×C8—531no—
439C53C2×#324111yescharacteristic, complemented, Sylow
440C22×Q8—21no—
441C22×Q8—1061no—
442C22×D4—531no—
443C22×D4—531no—
444C22×D4—1061no—
445C22×D4—1061no—
446C22×D4—1061no—
447C22×D4—1061no—
448C23×C4—531no—
449C23×C4—1061no—
450C23×C4—1061no—
451C23×C4—1061no—
452C22×C8—531no—
453C22×C8—531no—
454C22×C8C22×D5311yescharacteristic
455C22×C8C22×D5311yescharacteristic
456C4⋊Q8—22no—
457C4⋊Q8—534no—
458C4⋊Q8—1062no—
459C4⋊Q8—1068no—
460C4⋊Q8C22×D5314yes—
461#127—534no—
462#127—1062no—
463#125—22no—
464#125—534no—
465#125—534no—
466#125—1062no—
467#125—1068no—
468#125—1062no—
469#125C22×D5314yes—
470#123—1068no—
471#123—1068no—
472C22⋊Q8—1068no—
473C22⋊Q8—1068no—
474#121—534no—
475#121—534no—
476#121—1068no—
477#121—1068no—
478#121—1062no—
479#121—1062no—
480C4×D4—534no—
481C4×D4—534no—
482C4×D4—1062no—
483C4×D4—1062no—
484#117—534no—
485#117—534no—
486#117—534no—
487#117—1062no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—531no—
492C2×C4⋊C4—531no—
493C2×C4⋊C4—531no—
494C2×C4⋊C4—531no—
495C2×C4⋊C4—534no—
496C2×C4⋊C4—1062no—
497C2×C4⋊C4—1061no—
498C2×C4⋊C4—1061no—
499C2×C4⋊C4—1061no—
500C2×C4⋊C4—1061no—
501C2×C4⋊C4—1061no—
502C2×C4⋊C4—1061no—
503C2×C4⋊C4C22×D5311yescharacteristic
504C2×C4⋊C4C22×D5311yescharacteristic
505C2×C4⋊C4C22×D5311yescharacteristic
506C2×C4⋊C4C22×D5311yescharacteristic
507C2×C22⋊C4—531no—
508C2×C22⋊C4—531no—
509C2×C22⋊C4—1061no—
510C2×C22⋊C4—1061no—
511C2×C22⋊C4—1061no—
512C2×C22⋊C4—1061no—
513C2×C22⋊C4—1061no—
514C2×C42—531no—
515C2×C42—1061no—
516C2×C42C22×D5311yescharacteristic
517#107—534no—
518#107—534no—
519#107C22×D5314yes—
520#107C22×D5314yes—
521#106—534no—
522#106—534no—
523#106C22×D5314yes—
524#106C22×D5314yes—
525C4⋊C8—534no—
526C4⋊C8—534no—
527#102—534no—
528#102—534no—
529#102—534no—
530#102—534no—
531#102—534no—
532#102—534no—
533#102—534no—
534#102—534no—
535C22⋊C8—534no—
536C22⋊C8—534no—
537#97C22×D5314yes—
538C4×C8—534no—
539C24—531no—
540C24—1061no—
541C24—1061no—
542C2×Q8—24no—
543C2×Q8—82no—
544C2×Q8—1064no—
545C2×Q8—4242no—
546C2×D4—532no—
547C2×D4—532no—
548C2×D4—1064no—
549C2×D4—1064no—
550C2×D4—1064no—
551C2×D4—1064no—
552C2×D4—1061no—
553C2×D4—1061no—
554C2×D4—1062no—
555C2×D4—1062no—
556C2×D4—1062no—
557C2×D4—1062no—
558C2×D4—4242no—
559C2×D4—4242no—
560C2×D4—4242no—
561C2×D4—4242no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—531no—
567C22×C4—531no—
568C22×C4—531no—
569C22×C4—532no—
570C22×C4—532no—
571C22×C4—1064no—
572C22×C4—1064no—
573C22×C4—1064no—
574C22×C4—1062no—
575C22×C4—1062no—
576C22×C4—1061no—
577C22×C4—1061no—
578C22×C4—4242no—
579C22×C4—4242no—
580C22×C4—4242no—
581C22×C4D4×D5311yescharacteristic
582C22×C4D4×D5311yescharacteristic
583C22×C4C23×D5311yescharacteristic
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—532no—
587C2×C8—532no—
588C2×C8—1062no—
589C2×C8—1062no—
590C2×C8C23×D5312yes—
591C2×C8C23×D5312yes—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—24no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—534no—
600C4⋊C4—534no—
601C4⋊C4—532no—
602C4⋊C4—532no—
603C4⋊C4—1064no—
604C4⋊C4—1064no—
605C4⋊C4—1064no—
606C4⋊C4—1064no—
607C4⋊C4—1061no—
608C4⋊C4—1061no—
609C4⋊C4—1064no—
610C4⋊C4—1064no—
611C4⋊C4C23×D5312yes—
612C4⋊C4C23×D5312yes—
613C4⋊C4C23×D5312yes—
614C4⋊C4C23×D5312yes—
615C22⋊C4—534no—
616C22⋊C4—534no—
617C22⋊C4—1064no—
618C22⋊C4—1064no—
619C22⋊C4—1064no—
620C22⋊C4—1064no—
621C22⋊C4—1064no—
622C42—532no—
623C42—532no—
624C42—1064no—
625C42D4×D5312yes—
626C42C23×D5312yes—
627C23—532no—
628C23—1062no—
629C23—1062no—
630C23—1062no—
631C23—1062no—
632C23—1062no—
633C23—2122no—
634C23—2122no—
635C23—2122no—
636C23—2122no—
637C23—2122no—
638C23—2122no—
639C23C2×D4×D5311yescharacteristic
640Q8—84no—
641Q8—4244no—
642D4—1062no—
643D4—1062no—
644D4—1062no—
645D4—1062no—
646D4—4244no—
647D4—4244no—
648D4—4244no—
649D4—4244no—
650D4—2122no—
651D4—2122no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—532no—
663C2×C4—532no—
664C2×C4—532no—
665C2×C4—1062no—
666C2×C4—1062no—
667C2×C4—1062no—
668C2×C4—1064no—
669C2×C4—1062no—
670C2×C4—1062no—
671C2×C4—1062no—
672C2×C4—1062no—
673C2×C4—4244no—
674C2×C4—4244no—
675C2×C4—4244no—
676C2×C4—2122no—
677C2×C4—2122no—
678C2×C4C2×D4×D5312yes—
679C2×C4C2×D4×D5312yes—
680C2×C4C2×D4×D5311yescharacteristic
681C2×C4#1313326512yes—
682C2×C4#1313326512yes—
683C2×C4C24×D5311yescharacteristic
684C8—22no—
685C8—22no—
686C8—1062no—
687C8—1062no—
688C22—1062no—
689C22—1062no—
690C22—1062no—
691C22—4244no—
692C22—4244no—
693C22—2122no—
694C22—2122no—
695C22—2122no—
696C22—2122no—
697C22—2122no—
698C22—2122no—
699C22—2124no—
700C22#1681119812yes—
701C22#1681142712yes—
702C22#1681143212yes—
703C22C22×D4×D5311yescharacteristic
704C4—22no—
705C4—22no—
706C4—42no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—1062no—
711C4—1062no—
712C4—1062no—
713C4—2122no—
714C4—2122no—
715C4#1681119812yes—
716C4C2×#1313326511yescharacteristic
717C4C2×#1313326511yescharacteristic
718C2—4242no—
719C2—4242no—
720C2—2122no—
721C2#2028596914yesdirect product factor
722C2C2×#1681119811yescharacteristic
723C2C2×#1681142711yescharacteristic
724C2C2×#1681143211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#501C2
socleC23×C53C22×D4
prime radicalC2×#16811229C2
hypercenterC2×#501D53
hypocenterC53C2×#3241
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
1. C2×#16811250C2semidirect
3. #20285969C2direct (N × H)
4. C2×#16811022C2semidirect
5. C2×#16810988C2semidirect
6. C2×#16810971C2semidirect
7. C2×#16810943C2semidirect
8. C2×#16810950C2semidirect
9. C2×#16810949C2semidirect
10. C2×#16810938C2semidirect
11. C2×#16810926C2semidirect
12. C2×#16810922C2semidirect
13. C2×#16810912C2semidirect
14. C2×#16810902C2semidirect
15. C2×#16810685C2semidirect
16. C2×C53×#501C2semidirect
18. #16811250C22semidirect
40. #16811022C22semidirect
41. #16810988C22semidirect
42. #16810971C22semidirect
43. #16810950C22semidirect
44. #16810949C22semidirect
45. #16810943C22semidirect
46. #16810938C22semidirect
47. #16810926C22semidirect
48. #16810922C22semidirect
49. #16810912C22semidirect
50. #16810902C22semidirect
51. #16810685C22semidirect
71. C53×#501C22semidirect
359. C2×#501D53semidirect
372. C2×C53#3241semidirect
404. #501C2×D53semidirect
439. C53C2×#3241semidirect
721. C2#20285969direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112502
C2×#168112292
#202859692
C2×#168110222
C2×#168109882
C2×#168109712
C2×#168109432
C2×#168109502
C2×#168109492
C2×#168109382
C2×#168109262
C2×#168109222
C2×#168109122
C2×#168109022
C2×#168106852
C2×C53×#5012
C2×#324153