Finite Group Databasebeta

← C2×#20287458 #28263818

Subgroups — C2×#20287458 #28263818

Order 13568.

1842 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811353C211yesmaximal, characteristic, complemented
2C2×#16811345C211yesmaximal, characteristic
3#20287458C2116yesmaximal, direct product factor
4C2×#16810985C211yesmaximal, characteristic
5C2×#16810984C211yesmaximal, characteristic
6C2×#16810972C211yesmaximal, characteristic, complemented
7C2×#16810907C211yesmaximal, characteristic, complemented
8C2×#16810912C211yesmaximal, characteristic
9C2×#16810848C211yesmaximal, characteristic
10C2×#16810846C211yesmaximal, characteristic
11C2×#16810832C211yesmaximal, characteristic, complemented
12C2×#16810752C211yesmaximal, characteristic, complemented
13C2×#16810729C211yesmaximal, characteristic, complemented
14C2×#16810728C211yesmaximal, characteristic, complemented
15C2×#16810710C211yesmaximal, characteristic
16C2×C53×#475C211yesmaximal, characteristic, complemented
17C22×Dic212C2211yescharacteristic
18C22×#11719925C2211yescharacteristic
19C22×#11719913C2211yescharacteristic
20#16811353—24no—
21#16811353C2218yescomplemented
22#16811345—24no—
23#16811345C2218yes—
24C2×#13133216—21no—
25C2×#13133216C2211yescharacteristic
26C2×#13133216C2211yescharacteristic
27C2×#13133215—21no—
28C2×#13133215—21no—
29C2×#13133215C2211yescharacteristic
30C2×#13133212—21no—
31C2×#13133211—21no—
32C2×#13133206C2211yescharacteristic
33C2×#13133205C2211yescharacteristic
34C2×#13133195—21no—
35C2×C4×Dic106C2211yescharacteristic
36C2×C4×Dic106C2211yescharacteristic
37C2×#13133182—21no—
38C2×#13133182C2211yescharacteristic
39C2×#13133182C2211yescharacteristic
40C2×#13133182C2211yescharacteristic
41C2×#13133179C2211yescharacteristic
42C2×#13133174—21no—
43#16810985C2218yes—
44#16810984C2218yes—
45#16810972C2218yescomplemented
46#16810912C2218yes—
47#16810907C2218yescomplemented
48#16810848C2218yes—
49#16810846C2218yes—
50#16810832C2218yescomplemented
51#16810752C2218yescomplemented
52#16810729C2218yescomplemented
53#16810728C2218yescomplemented
54#16810710C2218yes—
55C2×#13133148C2211yescharacteristic
56C2×#13133146C2211yescharacteristic
57C2×#13133146C2211yescharacteristic
58C2×#13133142C2211yescharacteristic
59C2×#13133141C2211yescharacteristic
60C2×#13133140C2211yescharacteristic
61C2×#13133140C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133128C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C2×C4⋊Q8×C53C2211yescharacteristic
70C2×C4×Q8×C53C2211yescharacteristic
71C53×#475C2218yescomplemented
72C2×#106×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#103×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106—21no—
79C22×Dic106D411yescharacteristic
80C22×Dic106C2311yescharacteristic
81C22×Dic106C2311yescharacteristic
82C22×D212C2311yescharacteristic
83C22×C4×D53—21no—
84C2×Dic212—24no—
85C2×Dic212C2314yes—
86C2×#11719925—24no—
87C2×#11719925C2314yes—
88C2×#11719913—24no—
89C2×#11719913C2314yes—
90C22×#88322C2311yescharacteristic
91C22×#88322C2311yescharacteristic
92#13133216—28no—
93#13133216—22no—
94#13133216—22no—
95#13133216C2314yes—
96#13133216C2314yes—
97#13133215—28no—
98#13133215—28no—
99#13133215—22no—
100#13133215C2314yes—
101#13133212—28no—
102#13133211—28no—
103#13133206—22no—
104#13133206C2314yes—
105#13133205—22no—
106#13133205C2314yes—
107#13133195—28no—
108C4×Dic106—22no—
109C4×Dic106D414yes—
110C4×Dic106C2314yes—
111C4×Dic106C2314yes—
112#13133182—22no—
113#13133182—22no—
114#13133182—22no—
115#13133182—28no—
116#13133182C2314yes—
117#13133182C2314yes—
118#13133182C2314yes—
119#13133179—22no—
120#13133179C2314yes—
121#13133174—28no—
122C2×C4⋊Dic53D411yescharacteristic
123C2×C4⋊Dic53C2311yescharacteristic
124C2×#11719919—21no—
125C2×#11719919—21no—
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919D411yescharacteristic
133C2×#11719919D411yescharacteristic
134C2×#11719921—21no—
135C2×#11719921—21no—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×C4×Dic53—21no—
140C2×C4×Dic53—21no—
141C2×C4×Dic53—21no—
142C2×C4×Dic53—21no—
143C2×C4×Dic53C2311yescharacteristic
144C2×C4×Dic53C2311yescharacteristic
145#13133148C2314yes—
146#13133146C2314yes—
147#13133146C2314yes—
148#13133142C2314yes—
149#13133141C2314yes—
150#13133140C2314yes—
151#13133140C2314yes—
152#13133140C2314yes—
153#13133139C2314yes—
154#13133137C2314yes—
155#13133137C2314yes—
156#13133128C2314yes—
157#13133127C2314yes—
158C8×Dic53C2314yes—
159C22×Q8×C53—21no—
160C22×Q8×C53C2311yescharacteristic
161C22×C8×C53C2311yescharacteristic
162C22×C8×C53C2311yescharacteristic
163C4⋊Q8×C53—22no—
164C4⋊Q8×C53C2314yes—
165C4×Q8×C53—22no—
166C4×Q8×C53C2314yes—
167C2×C4⋊C4×C53—21no—
168C2×C4⋊C4×C53—21no—
169C2×C4⋊C4×C53C2311yescharacteristic
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C42×C53—21no—
173C2×C42×C53C2311yescharacteristic
174#106×C53C2314yes—
175#106×C53C2314yes—
176C4⋊C8×C53C2314yes—
177#103×C53C2314yes—
178#103×C53C2314yes—
179C23×D53—21no—
180C2×Q8×C53—21no—
181C2×Q8×C53—24no—
182C2×Q8×C53—22no—
183C2×Q8×C53—22no—
184C2×Q8×C53—82no—
185C2×Q8×C53C2412yes—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53C2×D411yescharacteristic
191C22×C4×C53C2×D411yescharacteristic
192C22×C4×C53C2411yescharacteristic
193C22×Dic53—21no—
194C22×Dic53—21no—
195C22×Dic53—21no—
196C22×Dic53C2×D411yescharacteristic
197C22×Dic53C2×D411yescharacteristic
198C22×Dic53C2×D411yescharacteristic
199C22×Dic53C2×D411yescharacteristic
200C2×D212—22no—
201C2×D212—22no—
202C2×D212—21no—
203C2×D212C2412yes—
204C2×C4×D53—24no—
205C2×C4×D53—44no—
206C2×Dic106—21no—
207C2×Dic106—22no—
208C2×Dic106—24no—
209C2×Dic106—22no—
210C2×Dic106—22no—
211C2×Dic106—21no—
212C2×Dic106—24no—
213C2×Dic106—24no—
214C2×Dic106—82no—
215C2×Dic106—82no—
216C2×Dic106C2×D414yes—
217C2×Dic106#4114yes—
218C2×Dic106C2412yes—
219C2×Dic106C2412yes—
220C2×C8×C53—22no—
221C2×C8×C53—22no—
222C2×C8×C53C2412yes—
223C2×C8×C53C2412yes—
224C4⋊C4×C53—24no—
225C4⋊C4×C53—24no—
226C4⋊C4×C53—21no—
227C4⋊C4×C53—21no—
228C4⋊C4×C53—21no—
229C4⋊C4×C53C2412yes—
230C4⋊C4×C53C2412yes—
231C4⋊C4×C53C2412yes—
232C42×C53—24no—
233C42×C53C2×D412yes—
234C42×C53C2412yes—
235#11719925—28no—
236#11719921—24no—
237#11719921—24no—
238#11719921—24no—
239#11719921—24no—
240#11719921—24no—
241C4⋊Dic53—21no—
242C4⋊Dic53C2×D414yes—
243C4⋊Dic53C2412yes—
244#11719919—24no—
245#11719919—24no—
246#11719919—24no—
247#11719919—24no—
248#11719919—24no—
249#11719919—24no—
250#11719919—24no—
251#11719919—24no—
252#11719919C2×D414yes—
253#11719919C2×D414yes—
254C4×Dic53—24no—
255C4×Dic53—24no—
256C4×Dic53—24no—
257C4×Dic53—24no—
258C4×Dic53C2×D412yes—
259C4×Dic53C2×D412yes—
260C4×Dic53C2412yes—
261C4×Dic53C2412yes—
262C2×#88322—22no—
263C2×#88322—22no—
264C2×#88322C2412yes—
265C2×#88322C2412yes—
266Dic212—28no—
267#11719913—28no—
268C23×C53C22×D411yescharacteristic
269C22×D53—22no—
270C22×D53—42no—
271C22×D53—42no—
272C22×D53—42no—
273Q8×C53—22no—
274Q8×C53—22no—
275Q8×C53—42no—
276Q8×C53—84no—
277C2×C4×C53—22no—
278C2×C4×C53—22no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
282C2×C4×C53—22no—
283C2×C4×C53—42no—
284C2×C4×C53—42no—
285C2×C4×C53—42no—
286C2×C4×C53—42no—
287C2×C4×C53C22×D412yes—
288C2×C4×C53C22×D412yes—
289C2×C4×C53C22×D411yescharacteristic
290C2×C4×C53C2×#4112yes—
291C2×C4×C532−1+412yes—
292C2×C4×C53C2511yescharacteristic
293C2×Dic53—24no—
294C2×Dic53—22no—
295C2×Dic53—22no—
296C2×Dic53—22no—
297C2×Dic53—22no—
298C2×Dic53—22no—
299C2×Dic53—22no—
300C2×Dic53—42no—
301C2×Dic53—42no—
302C2×Dic53#13714yes—
303C2×Dic53C22×D412yes—
304C2×Dic53C22×D412yes—
305C2×Dic53C22×D412yes—
306C2×Dic53C22×D412yes—
307D212—22no—
308D212—22no—
309D212—42no—
310C4×D53—48no—
311Dic106—24no—
312Dic106—22no—
313Dic106—28no—
314Dic106—22no—
315Dic106—22no—
316Dic106—42no—
317Dic106—84no—
318Dic106—84no—
319Dic106C2×#4114yes—
320C8×C53—22no—
321C8×C53—22no—
322#88322—22no—
323#88322—22no—
324C2×#3369—531nomaximal, Sylow
325C22×C53#54812yes—
326C22×C53C2×#13712yes—
327C22×C53#57712yes—
328C22×C53C23×D411yescharacteristic
329C2×D53—42no—
330C2×D53—42no—
331C2×D53—42no—
332C2×D53—84no—
333C4×C53—22no—
334C4×C53—22no—
335C4×C53—42no—
336C4×C53—42no—
337C4×C53—42no—
338C4×C53—42no—
339C4×C53#54812yes—
340C4×C53C22×#4111yescharacteristic
341C4×C53C2×2−1+411yescharacteristic
342Dic53—24no—
343Dic53—22no—
344Dic53—22no—
345Dic53—22no—
346Dic53—42no—
347Dic53—42no—
348Dic53C2×#13714yes—
349C2×Q82—531no—
350C2×#556—531no—
351#3369—5316no—
352C2×#489—531no—
353C2×#489—531no—
354C2×#487—531no—
355C2×#475—531no—
356C2×#475D5311yescharacteristic, complemented
357C2×#476—531no—
358C2×#464—531no—
359C2×#464—531no—
360C2×#462—531no—
361C2×#446—531no—
362C2×#441—531no—
363C2×#441—531no—
364C2×C4×SD16—531no—
365C2×C53#336914yescomplemented
366C2×C53C2×#54811yescharacteristic
367C2×C53C22×#13711yescharacteristic
368C2×C53C2×#57711yescharacteristic
369D53—82no—
370C22×Q16—531no—
371C22×Q16—531no—
372C22×SD16—531no—
373Q82—538no—
374Q82—1064no—
375#556—538no—
376#556—1064no—
377C2×C4⋊Q8—531no—
378C2×C4⋊Q8—531no—
379C2×C4⋊Q8—531no—
380C2×C4⋊Q8—1061no—
381C2×C4⋊Q8—1061no—
382C2×C4⋊Q8—1061no—
383C2×C4⋊Q8C2×D5311yescharacteristic
384C2×#126—1061no—
385C2×#126—1061no—
386C2×#124—531no—
387C2×#124—531no—
388C2×C22⋊Q8—1061no—
389C2×C4×Q8—531no—
390C2×C4×Q8—531no—
391C2×C4×Q8—531no—
392C2×C4×Q8—531no—
393C2×C4×Q8—531no—
394C2×C4×Q8—1061no—
395C2×C4×Q8C2×D5311yescharacteristic
396C2×C4×D4—531no—
397C2×#117—1061no—
398#489—538no—
399#489—538no—
400#487—538no—
401#476—538no—
402#475—538no—
403#475C2×D5318yescomplemented
404#464—538no—
405#464—538no—
406#462—538no—
407#446—538no—
408#441—538no—
409#441—538no—
410C4×SD16—538no—
411C2×#106—531no—
412C2×#106C2×D5311yescharacteristic
413C2×#106C2×D5311yescharacteristic
414C2×C4⋊C8—531no—
415C2×C4⋊C8—531no—
416C2×C4⋊C8C2×D5311yescharacteristic
417C2×#103—531no—
418C2×#103—531no—
419C2×#103—531no—
420C2×#103—531no—
421C2×#103—531no—
422C2×#103C2×D5311yescharacteristic
423C2×#103C2×D5311yescharacteristic
424C2×#102—531no—
425C2×#102—531no—
426C2×#102—531no—
427C2×#97—531no—
428C2×#97—531no—
429C2×C4×C8—531no—
430C53C2×#336911yescharacteristic, complemented, Sylow
431C22×Q8—21no—
432C22×Q8—531no—
433C22×Q8—531no—
434C22×Q8—531no—
435C22×Q8—1061no—
436C22×Q8—1061no—
437C22×Q8C22×D5311yescharacteristic
438C22×D4—531no—
439C23×C4—1061no—
440C2×Q16—534no—
441C2×Q16—534no—
442C2×Q16—1064no—
443C2×Q16—1064no—
444C2×SD16—534no—
445C2×SD16—1064no—
446C22×C8—531no—
447C22×C8—531no—
448C22×C8C22×D5311yescharacteristic
449C22×C8C22×D5311yescharacteristic
450C4⋊Q8—22no—
451C4⋊Q8—534no—
452C4⋊Q8—534no—
453C4⋊Q8—534no—
454C4⋊Q8—1062no—
455C4⋊Q8—1062no—
456C4⋊Q8—1062no—
457C4⋊Q8—1068no—
458C4⋊Q8—1068no—
459C4⋊Q8—1068no—
460C4⋊Q8C22×D5314yes—
461#126—1068no—
462#126—1068no—
463#124—534no—
464#124—534no—
465#124—1062no—
466#124—1062no—
467C22⋊Q8—1068no—
468C4×Q8—22no—
469C4×Q8—534no—
470C4×Q8—534no—
471C4×Q8—534no—
472C4×Q8—534no—
473C4×Q8—534no—
474C4×Q8—534no—
475C4×Q8—1062no—
476C4×Q8—1062no—
477C4×Q8—1062no—
478C4×Q8—1068no—
479C4×Q8—1062no—
480C4×Q8C22×D5314yes—
481C4×D4—534no—
482C4×D4—1062no—
483#117—1068no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—531no—
487C2×C4⋊C4—531no—
488C2×C4⋊C4—531no—
489C2×C4⋊C4—531no—
490C2×C4⋊C4—1061no—
491C2×C4⋊C4—1061no—
492C2×C4⋊C4—1061no—
493C2×C4⋊C4—1061no—
494C2×C4⋊C4—1061no—
495C2×C4⋊C4—1061no—
496C2×C4⋊C4—1061no—
497C2×C4⋊C4—1061no—
498C2×C4⋊C4C22×D5311yescharacteristic
499C2×C4⋊C4C22×D5311yescharacteristic
500C2×C4⋊C4C22×D5311yescharacteristic
501C2×C22⋊C4—1061no—
502C2×C22⋊C4—1061no—
503C2×C22⋊C4—1061no—
504C2×C22⋊C4—1061no—
505C2×C22⋊C4—1061no—
506C2×C42—21no—
507C2×C42—531no—
508C2×C42—531no—
509C2×C42—1061no—
510C2×C42—1061no—
511C2×C42—1061no—
512C2×C42—1061no—
513C2×C42C22×D5311yescharacteristic
514#106—534no—
515#106C22×D5314yes—
516#106C22×D5314yes—
517C4⋊C8—534no—
518C4⋊C8—534no—
519C4⋊C8C22×D5314yes—
520#103—534no—
521#103—534no—
522#103—534no—
523#103—534no—
524#103—534no—
525#103C22×D5314yes—
526#103C22×D5314yes—
527#102—534no—
528#102—534no—
529#102—534no—
530#97—534no—
531#97—534no—
532C4×C8—534no—
533C24—1061no—
534C2×Q8—21no—
535C2×Q8—24no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—82no—
539C2×Q8—534no—
540C2×Q8—534no—
541C2×Q8—532no—
542C2×Q8—532no—
543C2×Q8—1064no—
544C2×Q8—1064no—
545C2×Q8—1064no—
546C2×Q8—1061no—
547C2×Q8—1061no—
548C2×Q8—1062no—
549C2×Q8—1062no—
550C2×Q8—1062no—
551C2×Q8—4242no—
552C2×Q8—4242no—
553C2×Q8C23×D5312yes—
554C2×D4—532no—
555C2×D4—1061no—
556C2×D4—1062no—
557C2×D4—1062no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—531no—
563C22×C4—531no—
564C22×C4—531no—
565C22×C4—531no—
566C22×C4—1064no—
567C22×C4—1061no—
568C22×C4—1061no—
569C22×C4—1061no—
570C22×C4—2124no—
571C22×C4D4×D5311yescharacteristic
572C22×C4D4×D5311yescharacteristic
573C22×C4C23×D5311yescharacteristic
574Q16—1068no—
575Q16—1068no—
576SD16—1068no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—532no—
580C2×C8—532no—
581C2×C8—1062no—
582C2×C8—1062no—
583C2×C8C23×D5312yes—
584C2×C8C23×D5312yes—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—534no—
591C4⋊C4—534no—
592C4⋊C4—534no—
593C4⋊C4—532no—
594C4⋊C4—1064no—
595C4⋊C4—1064no—
596C4⋊C4—1064no—
597C4⋊C4—1064no—
598C4⋊C4—1064no—
599C4⋊C4—1064no—
600C4⋊C4—1064no—
601C4⋊C4—1061no—
602C4⋊C4—1064no—
603C4⋊C4C23×D5312yes—
604C4⋊C4C23×D5312yes—
605C4⋊C4C23×D5312yes—
606C22⋊C4—1064no—
607C22⋊C4—1064no—
608C22⋊C4—1064no—
609C22⋊C4—1064no—
610C22⋊C4—1064no—
611C42—24no—
612C42—532no—
613C42—532no—
614C42—532no—
615C42—532no—
616C42—1064no—
617C42—1064no—
618C42—1064no—
619C42—1064no—
620C42D4×D5312yes—
621C42C23×D5312yes—
622C23—1062no—
623C23—2122no—
624C23—2122no—
625C23—2122no—
626C23C2×D4×D5311yescharacteristic
627Q8—22no—
628Q8—22no—
629Q8—42no—
630Q8—84no—
631Q8—534no—
632Q8—1068no—
633Q8—1064no—
634Q8—1062no—
635Q8—1062no—
636Q8—1062no—
637Q8—4244no—
638Q8—4244no—
639Q8—2122no—
640D4—1062no—
641D4—1062no—
642D4—2122no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—534no—
654C2×C4—532no—
655C2×C4—532no—
656C2×C4—532no—
657C2×C4—532no—
658C2×C4—1064no—
659C2×C4—1062no—
660C2×C4—1062no—
661C2×C4—1062no—
662C2×C4—1062no—
663C2×C4—1062no—
664C2×C4—1062no—
665C2×C4—2128no—
666C2×C4—2122no—
667C2×C4—2122no—
668C2×C4C2×D4×D5312yes—
669C2×C4C2×D4×D5312yes—
670C2×C4C2×D4×D5311yescharacteristic
671C2×C4#41×D5312yes—
672C2×C4#1313326512yes—
673C2×C4C24×D5311yescharacteristic
674C8—22no—
675C8—22no—
676C8—1062no—
677C8—1062no—
678C22—4244no—
679C22—2122no—
680C22—2122no—
681C22—2122no—
682C22#1681128312yes—
683C22#137×D5312yes—
684C22#1681142912yes—
685C22C22×D4×D5311yescharacteristic
686C4—22no—
687C4—22no—
688C4—42no—
689C4—42no—
690C4—42no—
691C4—42no—
692C4—534no—
693C4—1062no—
694C4—1064no—
695C4—1062no—
696C4—1062no—
697C4—2122no—
698C4—2122no—
699C4#1681128312yes—
700C4C2×#41×D5311yescharacteristic
701C4C2×#1313326511yescharacteristic
702C2—4242no—
703C2#2028745814yesdirect product factor
704C2C2×#1681128311yescharacteristic
705C2C2×#137×D5311yescharacteristic
706C2C2×#1681142911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#475C2
socleC23×C53C22×D4
prime radicalC22×D212C23
hypercenterC2×#475D53
hypocenterC53C2×#3369
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
1. C2×#16811353C2semidirect
3. #20287458C2direct (N × H)
6. C2×#16810972C2semidirect
7. C2×#16810907C2semidirect
11. C2×#16810832C2semidirect
12. C2×#16810752C2semidirect
13. C2×#16810729C2semidirect
14. C2×#16810728C2semidirect
16. C2×C53×#475C2semidirect
21. #16811353C22semidirect
45. #16810972C22semidirect
47. #16810907C22semidirect
50. #16810832C22semidirect
51. #16810752C22semidirect
52. #16810729C22semidirect
53. #16810728C22semidirect
71. C53×#475C22semidirect
356. C2×#475D53semidirect
365. C2×C53#3369semidirect
403. #475C2×D53semidirect
430. C53C2×#3369semidirect
703. C2#20287458direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113532
C2×#168113452
#202874582
C2×#168109852
C2×#168109842
C2×#168109722
C2×#168109072
C2×#168109122
C2×#168108482
C2×#168108462
C2×#168108322
C2×#168107522
C2×#168107292
C2×#168107282
C2×#168107102
C2×C53×#4752
C2×#336953