Finite Group Databasebeta

← C2×#20287401 #28263705

Subgroups — C2×#20287401 #28263705

Order 13568.

1830 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811349C211yesmaximal, characteristic, complemented
2C2×#16811345C211yesmaximal, characteristic
3#20287401C2116yesmaximal, direct product factor
4C2×#16810979C211yesmaximal, characteristic
5C2×#16810978C211yesmaximal, characteristic
6C2×#16810972C211yesmaximal, characteristic, complemented
7C2×#16810930C211yesmaximal, characteristic, complemented
8C2×#16810929C211yesmaximal, characteristic, complemented
9C2×#16810902C211yesmaximal, characteristic
10C2×#16810847C211yesmaximal, characteristic
11C2×#16810845C211yesmaximal, characteristic
12C2×#16810831C211yesmaximal, characteristic, complemented
13C2×C8×Dic106C211yesmaximal, characteristic, complemented
14C2×#16810715C211yesmaximal, characteristic, complemented
15C2×#16810708C211yesmaximal, characteristic
16C2×C4×Q16×C53C211yesmaximal, characteristic, complemented
17C22×#11719925C2211yescharacteristic
18C22×#11719924C2211yescharacteristic
19#16811349—24no—
20#16811349C2218yescomplemented
21#16811345—24no—
22#16811345C2218yes—
23C2×#13133216—21no—
24C2×#13133216C2211yescharacteristic
25C2×#13133215C2211yescharacteristic
26C2×#13133212—21no—
27C2×#13133211—21no—
28C2×#13133209—21no—
29C2×#13133209C2211yescharacteristic
30C2×#13133208—21no—
31C2×#13133208C2211yescharacteristic
32C2×#13133206C2211yescharacteristic
33C2×#13133205C2211yescharacteristic
34C2×#13133195—21no—
35C2×Q8×Dic53C2211yescharacteristic
36C2×Q8×Dic53C2211yescharacteristic
37C2×C4×Dic106—21no—
38C2×C4×Dic106C2211yescharacteristic
39C2×#13133182C2211yescharacteristic
40C2×#13133179C2211yescharacteristic
41C2×#13133174—21no—
42#16810979C2218yes—
43#16810978C2218yes—
44#16810972C2218yescomplemented
45#16810930C2218yescomplemented
46#16810929C2218yescomplemented
47#16810902C2218yes—
48#16810847C2218yes—
49#16810845C2218yes—
50#16810831C2218yescomplemented
51C8×Dic106C2218yescomplemented
52#16810715C2218yescomplemented
53#16810708C2218yes—
54C2×#13133150C2211yescharacteristic
55C2×#13133148C2211yescharacteristic
56C2×C4⋊#88322C2211yescharacteristic
57C2×#13133146C2211yescharacteristic
58C2×#13133146C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133139C2211yescharacteristic
65C2×#13133139C2211yescharacteristic
66C2×#13133137C2211yescharacteristic
67C2×C8×Dic53C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×Q16×C53C2211yescharacteristic
70C2×C4×Q8×C53C2211yescharacteristic
71C2×C4×Q8×C53C2211yescharacteristic
72C4×Q16×C53C2218yescomplemented
73C2×#107×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×C4×C8×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106D411yescharacteristic
79C22×Dic106C2311yescharacteristic
80C22×D212C2311yescharacteristic
81C22×C4×D53—21no—
82C2×#11719925—24no—
83C2×#11719925C2314yes—
84C2×#11719924—24no—
85C2×#11719924C2314yes—
86C22×#88322C2311yescharacteristic
87C22×#88322C2311yescharacteristic
88#13133216—22no—
89#13133216—28no—
90#13133216C2314yes—
91#13133215—22no—
92#13133215C2314yes—
93#13133212—28no—
94#13133211—28no—
95#13133209—22no—
96#13133209—28no—
97#13133209C2314yes—
98#13133208—28no—
99#13133208—22no—
100#13133208C2314yes—
101#13133206—22no—
102#13133206C2314yes—
103#13133205—22no—
104#13133205C2314yes—
105#13133195—28no—
106Q8×Dic53—22no—
107Q8×Dic53—22no—
108Q8×Dic53C2314yes—
109Q8×Dic53C2314yes—
110C4×Dic106—28no—
111C4×Dic106D414yes—
112C4×Dic106C2314yes—
113#13133182—22no—
114#13133182C2314yes—
115#13133179—22no—
116#13133179C2314yes—
117#13133174—28no—
118C2×C4⋊Dic53—21no—
119C2×C4⋊Dic53—21no—
120C2×C4⋊Dic53—21no—
121C2×C4⋊Dic53D411yescharacteristic
122C2×C4⋊Dic53C2311yescharacteristic
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×#11719919D411yescharacteristic
132C2×#11719919D411yescharacteristic
133C2×#11719921—21no—
134C2×#11719921—21no—
135C2×#11719921—21no—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×C4×Dic53—21no—
139C2×C4×Dic53—21no—
140C2×C4×Dic53—21no—
141C2×C4×Dic53C2311yescharacteristic
142C2×C4×Dic53C2311yescharacteristic
143#13133150C2314yes—
144#13133148C2314yes—
145C4⋊#88322C2314yes—
146#13133146C2314yes—
147#13133146C2314yes—
148#13133142C2314yes—
149#13133142C2314yes—
150#13133141C2314yes—
151#13133141C2314yes—
152#13133140C2314yes—
153#13133139C2314yes—
154#13133139C2314yes—
155#13133137C2314yes—
156C8×Dic53C2314yes—
157C8×Dic53C2314yes—
158C22×Q8×C53C2311yescharacteristic
159C22×Q8×C53C2311yescharacteristic
160C2×Q16×C53—24no—
161C2×Q16×C53C2314yes—
162C22×C8×C53C2311yescharacteristic
163C22×C8×C53C2311yescharacteristic
164C4×Q8×C53—22no—
165C4×Q8×C53—22no—
166C4×Q8×C53C2314yes—
167C4×Q8×C53C2314yes—
168C2×C4⋊C4×C53—21no—
169C2×C4⋊C4×C53—21no—
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C42×C53—21no—
173C2×C42×C53—21no—
174C2×C42×C53C2311yescharacteristic
175#107×C53C2314yes—
176#103×C53C2314yes—
177#103×C53C2314yes—
178C4×C8×C53C2314yes—
179C23×D53—21no—
180C2×Q8×C53—21no—
181C2×Q8×C53—21no—
182C2×Q8×C53—22no—
183C2×Q8×C53—22no—
184C2×Q8×C53—22no—
185C2×Q8×C53#4114yes—
186C2×Q8×C53C2412yes—
187C2×Q8×C53C2412yes—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53C2×D411yescharacteristic
193C22×C4×C53C2×D411yescharacteristic
194C22×C4×C53C2411yescharacteristic
195C22×Dic53—21no—
196C22×Dic53—21no—
197C22×Dic53—21no—
198C22×Dic53C2×D411yescharacteristic
199C22×Dic53C2×D411yescharacteristic
200C22×Dic53C2×D411yescharacteristic
201C22×Dic53C2×D411yescharacteristic
202C2×D212—22no—
203C2×D212—22no—
204C2×D212—21no—
205C2×D212C2412yes—
206C2×C4×D53—24no—
207C2×C4×D53—44no—
208C2×Dic106—24no—
209C2×Dic106—22no—
210C2×Dic106—22no—
211C2×Dic106—21no—
212C2×Dic106—24no—
213C2×Dic106—44no—
214C2×Dic106C2×D414yes—
215C2×Dic106C2412yes—
216Q16×C53—28no—
217C2×C8×C53—22no—
218C2×C8×C53—22no—
219C2×C8×C53C2412yes—
220C2×C8×C53C2412yes—
221C4⋊C4×C53—24no—
222C4⋊C4×C53—24no—
223C4⋊C4×C53—21no—
224C4⋊C4×C53—21no—
225C4⋊C4×C53C2412yes—
226C4⋊C4×C53C2412yes—
227C42×C53—24no—
228C42×C53—24no—
229C42×C53C2×D412yes—
230C42×C53C2412yes—
231#11719925—28no—
232#11719924—28no—
233#11719921—24no—
234#11719921—24no—
235#11719921—24no—
236#11719921—24no—
237#11719921—24no—
238C4⋊Dic53—21no—
239C4⋊Dic53—21no—
240C4⋊Dic53—24no—
241C4⋊Dic53—24no—
242C4⋊Dic53—24no—
243C4⋊Dic53C2×D414yes—
244C4⋊Dic53C2412yes—
245C4⋊Dic53C2412yes—
246#11719919—24no—
247#11719919—24no—
248#11719919—24no—
249#11719919—24no—
250#11719919—24no—
251#11719919—24no—
252#11719919—24no—
253#11719919C2×D414yes—
254#11719919C2×D414yes—
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—
266C23×C53C22×D411yescharacteristic
267C22×D53—22no—
268C22×D53—42no—
269C22×D53—42no—
270C22×D53—42no—
271Q8×C53—24no—
272Q8×C53—22no—
273Q8×C53—22no—
274Q8×C53—22no—
275Q8×C53—42no—
276Q8×C53C2×#4114yes—
277C2×C4×C53—24no—
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×C53C22×D412yes—
288C2×C4×C53C22×D412yes—
289C2×C4×C53C22×D411yescharacteristic
290C2×C4×C53C2×#4112yes—
291C2×C4×C532−1+412yes—
292C2×C4×C53C2511yescharacteristic
293C2×Dic53—22no—
294C2×Dic53—22no—
295C2×Dic53—22no—
296C2×Dic53—22no—
297C2×Dic53—22no—
298C2×Dic53—22no—
299C2×Dic53—42no—
300C2×Dic53—42no—
301C2×Dic53—42no—
302C2×Dic53#13514yes—
303C2×Dic53C22×D412yes—
304C2×Dic53C22×D412yes—
305C2×Dic53C22×D412yes—
306C2×Dic53C22×D412yes—
307D212—22no—
308D212—22no—
309D212—42no—
310C4×D53—48no—
311Dic106—28no—
312Dic106—22no—
313Dic106—22no—
314Dic106—42no—
315Dic106—48no—
316C8×C53—22no—
317C8×C53—22no—
318#88322—22no—
319#88322—22no—
320C2×#3364—531nomaximal, Sylow
321C22×C53#54812yes—
322C22×C53C2×#13512yes—
323C22×C53#57812yes—
324C22×C53C23×D411yescharacteristic
325C2×D53—42no—
326C2×D53—42no—
327C2×D53—42no—
328C2×D53—84no—
329C4×C53—24no—
330C4×C53—22no—
331C4×C53—22no—
332C4×C53—42no—
333C4×C53—42no—
334C4×C53—42no—
335C4×C53#54812yes—
336C4×C53C22×#4111yescharacteristic
337C4×C53C2×2−1+411yescharacteristic
338Dic53—22no—
339Dic53—22no—
340Dic53—22no—
341Dic53—42no—
342Dic53—42no—
343Dic53—42no—
344Dic53C2×#13514yes—
345C2×#557—531no—
346C2×#556—531no—
347#3364—5316no—
348C2×#488—531no—
349C2×#488—531no—
350C2×#487—531no—
351C2×#479—531no—
352C2×#479—531no—
353C2×#474—531no—
354C2×#464—531no—
355C2×#464—531no—
356C2×#462—531no—
357C2×C8×Q8—531no—
358C2×C4×Q16—531no—
359C2×C4×Q16D5311yescharacteristic, complemented
360C2×C4×SD16—531no—
361C2×C53#336414yescomplemented
362C2×C53C2×#54811yescharacteristic
363C2×C53C22×#13511yescharacteristic
364C2×C53C2×#57811yescharacteristic
365D53—82no—
366C22×Q16—531no—
367C22×Q16C2×D5311yescharacteristic
368C22×SD16—531no—
369#557—538no—
370#557—1064no—
371#556—538no—
372#556—1064no—
373C2×C4⋊Q8—531no—
374C2×C4⋊Q8—531no—
375C2×C4⋊Q8—1061no—
376C2×#126—1061no—
377C2×#126—1061no—
378C2×#125—531no—
379C2×#125—531no—
380C2×#125—1061no—
381C2×#125—1061no—
382C2×#124—531no—
383C2×#124—531no—
384C2×C22⋊Q8—1061no—
385C2×C4×Q8—531no—
386C2×C4×Q8—531no—
387C2×C4×Q8—531no—
388C2×C4×Q8—531no—
389C2×C4×Q8—1061no—
390C2×C4×Q8C2×D5311yescharacteristic
391C2×C4×Q8C2×D5311yescharacteristic
392C2×C4×D4—531no—
393C2×#117—1061no—
394#488—538no—
395#488—538no—
396#487—538no—
397#479—538no—
398#479—538no—
399#474—538no—
400#464—538no—
401#464—538no—
402#462—538no—
403C8×Q8—538no—
404C4×Q16—538no—
405C4×Q16C2×D5318yescomplemented
406C4×SD16—538no—
407C2×#107—531no—
408C2×#107C2×D5311yescharacteristic
409C2×#106—531no—
410C2×C4⋊C8—531no—
411C2×C4⋊C8—531no—
412C2×C4⋊C8—531no—
413C2×#103—531no—
414C2×#103—531no—
415C2×#103—531no—
416C2×#103—531no—
417C2×#103—531no—
418C2×#103C2×D5311yescharacteristic
419C2×#103C2×D5311yescharacteristic
420C2×#102—531no—
421C2×#102—531no—
422C2×#102—531no—
423C2×C4×C8—531no—
424C2×C4×C8—531no—
425C2×C4×C8C2×D5311yescharacteristic
426C53C2×#336411yescharacteristic, complemented, Sylow
427C22×Q8—531no—
428C22×Q8—531no—
429C22×Q8—1061no—
430C22×Q8C22×D5311yescharacteristic
431C22×Q8C22×D5311yescharacteristic
432C22×D4—531no—
433C23×C4—1061no—
434C2×Q16—24no—
435C2×Q16—534no—
436C2×Q16—1064no—
437C2×Q16C22×D5314yes—
438C2×SD16—534no—
439C2×SD16—1064no—
440C22×C8—531no—
441C22×C8—531no—
442C22×C8C22×D5311yescharacteristic
443C22×C8C22×D5311yescharacteristic
444C4⋊Q8—534no—
445C4⋊Q8—534no—
446C4⋊Q8—1062no—
447C4⋊Q8—1062no—
448C4⋊Q8—1068no—
449#126—1068no—
450#126—1068no—
451#125—534no—
452#125—534no—
453#125—1068no—
454#125—1062no—
455#125—1068no—
456#125—1062no—
457#124—534no—
458#124—534no—
459#124—1062no—
460#124—1062no—
461C22⋊Q8—1068no—
462C4×Q8—22no—
463C4×Q8—22no—
464C4×Q8—534no—
465C4×Q8—534no—
466C4×Q8—534no—
467C4×Q8—534no—
468C4×Q8—534no—
469C4×Q8—1068no—
470C4×Q8—1062no—
471C4×Q8—1062no—
472C4×Q8—1062no—
473C4×Q8C22×D5314yes—
474C4×Q8C22×D5314yes—
475C4×D4—534no—
476C4×D4—1062no—
477#117—1068no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—531no—
481C2×C4⋊C4—531no—
482C2×C4⋊C4—531no—
483C2×C4⋊C4—531no—
484C2×C4⋊C4—531no—
485C2×C4⋊C4—1061no—
486C2×C4⋊C4—1061no—
487C2×C4⋊C4—1061no—
488C2×C4⋊C4—1061no—
489C2×C4⋊C4—1061no—
490C2×C4⋊C4—1061no—
491C2×C4⋊C4—1061no—
492C2×C4⋊C4—1061no—
493C2×C4⋊C4—1061no—
494C2×C4⋊C4—1061no—
495C2×C4⋊C4C22×D5311yescharacteristic
496C2×C4⋊C4C22×D5311yescharacteristic
497C2×C22⋊C4—1061no—
498C2×C22⋊C4—1061no—
499C2×C22⋊C4—1061no—
500C2×C22⋊C4—1061no—
501C2×C22⋊C4—1061no—
502C2×C42—21no—
503C2×C42—21no—
504C2×C42—531no—
505C2×C42—531no—
506C2×C42—1061no—
507C2×C42—1061no—
508C2×C42—1061no—
509C2×C42C22×D5311yescharacteristic
510#107—534no—
511#107C22×D5314yes—
512#106—534no—
513C4⋊C8—534no—
514C4⋊C8—534no—
515C4⋊C8—534no—
516#103—534no—
517#103—534no—
518#103—534no—
519#103—534no—
520#103—534no—
521#103C22×D5314yes—
522#103C22×D5314yes—
523#102—534no—
524#102—534no—
525#102—534no—
526C4×C8—534no—
527C4×C8—534no—
528C4×C8C22×D5314yes—
529C24—1061no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—534no—
536C2×Q8—532no—
537C2×Q8—1064no—
538C2×Q8—1064no—
539C2×Q8—1061no—
540C2×Q8—1062no—
541C2×Q8—1062no—
542C2×Q8—2124no—
543C2×Q8#1171994514yes—
544C2×Q8C23×D5312yes—
545C2×Q8C23×D5312yes—
546C2×D4—532no—
547C2×D4—1061no—
548C2×D4—1062no—
549C2×D4—1062no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—531no—
555C22×C4—531no—
556C22×C4—531no—
557C22×C4—531no—
558C22×C4—1064no—
559C22×C4—1061no—
560C22×C4—1061no—
561C22×C4—1061no—
562C22×C4—2124no—
563C22×C4D4×D5311yescharacteristic
564C22×C4D4×D5311yescharacteristic
565C22×C4C23×D5311yescharacteristic
566Q16—28no—
567Q16—1068no—
568SD16—1068no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—532no—
572C2×C8—532no—
573C2×C8—1062no—
574C2×C8—1062no—
575C2×C8C23×D5312yes—
576C2×C8C23×D5312yes—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—534no—
582C4⋊C4—534no—
583C4⋊C4—534no—
584C4⋊C4—532no—
585C4⋊C4—532no—
586C4⋊C4—1064no—
587C4⋊C4—1064no—
588C4⋊C4—1064no—
589C4⋊C4—1064no—
590C4⋊C4—1064no—
591C4⋊C4—1064no—
592C4⋊C4—1064no—
593C4⋊C4—1064no—
594C4⋊C4—1061no—
595C4⋊C4—1061no—
596C4⋊C4—1064no—
597C4⋊C4—1064no—
598C4⋊C4C23×D5312yes—
599C4⋊C4C23×D5312yes—
600C22⋊C4—1064no—
601C22⋊C4—1064no—
602C22⋊C4—1064no—
603C22⋊C4—1064no—
604C22⋊C4—1064no—
605C42—24no—
606C42—24no—
607C42—532no—
608C42—532no—
609C42—532no—
610C42—532no—
611C42—1064no—
612C42—1064no—
613C42—1064no—
614C42D4×D5312yes—
615C42C23×D5312yes—
616C23—1062no—
617C23—2122no—
618C23—2122no—
619C23—2122no—
620C23C2×D4×D5311yescharacteristic
621Q8—24no—
622Q8—22no—
623Q8—22no—
624Q8—22no—
625Q8—42no—
626Q8—1068no—
627Q8—1062no—
628Q8—1062no—
629Q8—2128no—
630Q8—2122no—
631Q8C2×#1171994514yes—
632D4—1062no—
633D4—1062no—
634D4—2122no—
635C2×C4—24no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—534no—
646C2×C4—532no—
647C2×C4—532no—
648C2×C4—532no—
649C2×C4—532no—
650C2×C4—1062no—
651C2×C4—1062no—
652C2×C4—1062no—
653C2×C4—1062no—
654C2×C4—1062no—
655C2×C4—1062no—
656C2×C4—2128no—
657C2×C4—2122no—
658C2×C4—2122no—
659C2×C4—2122no—
660C2×C4C2×D4×D5312yes—
661C2×C4C2×D4×D5312yes—
662C2×C4C2×D4×D5311yescharacteristic
663C2×C4C2×#1171994512yes—
664C2×C4#1313326412yes—
665C2×C4C24×D5311yescharacteristic
666C8—22no—
667C8—22no—
668C8—1062no—
669C8—1062no—
670C22—4244no—
671C22—2122no—
672C22—2122no—
673C22—2122no—
674C22#1681128212yes—
675C22#135×D5312yes—
676C22#1681143612yes—
677C22C22×D4×D5311yescharacteristic
678C4—22no—
679C4—24no—
680C4—22no—
681C4—42no—
682C4—42no—
683C4—42no—
684C4—534no—
685C4—1062no—
686C4—1062no—
687C4—1062no—
688C4—2122no—
689C4—2122no—
690C4—2122no—
691C4#1681128212yes—
692C4C22×#1171994511yescharacteristic
693C4C2×#1313326411yescharacteristic
694C2—4242no—
695C2#2028740114yesdirect product factor
696C2C2×#1681128211yescharacteristic
697C2C2×#135×D5311yescharacteristic
698C2C2×#1681143611yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C4×Q16×C53C2
socleC23×C53C22×D4
prime radicalC22×D212C23
hypercenterC2×C4×Q16D53
hypocenterC53C2×#3364
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#16811349C2semidirect
3. #20287401C2direct (N × H)
6. C2×#16810972C2semidirect
7. C2×#16810930C2semidirect
8. C2×#16810929C2semidirect
12. C2×#16810831C2semidirect
13. C2×C8×Dic106C2semidirect
14. C2×#16810715C2semidirect
16. C2×C4×Q16×C53C2semidirect
20. #16811349C22semidirect
44. #16810972C22semidirect
45. #16810930C22semidirect
46. #16810929C22semidirect
50. #16810831C22semidirect
51. C8×Dic106C22semidirect
52. #16810715C22semidirect
72. C4×Q16×C53C22semidirect
359. C2×C4×Q16D53semidirect
361. C2×C53#3364semidirect
405. C4×Q16C2×D53semidirect
426. C53C2×#3364semidirect
695. C2#20287401direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113492
C2×#168113452
#202874012
C2×#168109792
C2×#168109782
C2×#168109722
C2×#168109302
C2×#168109292
C2×#168109022
C2×#168108472
C2×#168108452
C2×#168108312
C2×C8×Dic1062
C2×#168107152
C2×#168107082
C2×C4×Q16×C532
C2×#336453