Finite Group Databasebeta

← C2×#20287558 #28263890

Subgroups — C2×#20287558 #28263890

Order 13568.

1810 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×#16811343C211yesmaximal, characteristic
3#20287558C2116yesmaximal, direct product factor
4C2×#16810992C211yesmaximal, characteristic, complemented
5C2×#16810981C211yesmaximal, characteristic
6C2×#16810976C211yesmaximal, characteristic
7C2×#16810929C211yesmaximal, characteristic, complemented
8C2×#16810917C211yesmaximal, characteristic, complemented
9C2×#16810923C211yesmaximal, characteristic
10C2×#16810843C211yesmaximal, characteristic
11C2×#16810843C211yesmaximal, characteristic
12C2×#16810833C211yesmaximal, characteristic, complemented
13C2×#16810751C211yesmaximal, characteristic, complemented
14C2×#16810727C211yesmaximal, characteristic, complemented
15C2×#16810715C211yesmaximal, characteristic, complemented
16C2×C53×#440C211yesmaximal, characteristic
17C22×#11719925C2211yescharacteristic
18C22×#11719925C2211yescharacteristic
19#16811349—24no—
20#16811349C2218yescomplemented
21#16811343—24no—
22#16811343C2218yes—
23C2×#13133217C2211yescharacteristic
24C2×#13133216—21no—
25C2×#13133216C2211yescharacteristic
26C2×#13133210—21no—
27C2×#13133210—21no—
28C2×#13133209—21no—
29C2×#13133209C2211yescharacteristic
30C2×#13133208—21no—
31C2×#13133208C2211yescharacteristic
32C2×#13133204C2211yescharacteristic
33C2×#13133204C2211yescharacteristic
34C2×#13133196—21no—
35C2×Q8×Dic53C2211yescharacteristic
36C2×Q8×Dic53C2211yescharacteristic
37C2×C4×Dic106—21no—
38C2×C4×Dic106C2211yescharacteristic
39C2×#13133182C2211yescharacteristic
40C2×#13133182C2211yescharacteristic
41C2×#13133176—21no—
42#16810992C2218yescomplemented
43#16810981C2218yes—
44#16810976C2218yes—
45#16810929C2218yescomplemented
46#16810923C2218yes—
47#16810917C2218yescomplemented
48#16810843C2218yes—
49#16810843C2218yes—
50#16810833C2218yescomplemented
51#16810751C2218yescomplemented
52#16810727C2218yescomplemented
53#16810715C2218yescomplemented
54C2×#13133150C2211yescharacteristic
55C2×#13133148C2211yescharacteristic
56C2×C4⋊#88322C2211yescharacteristic
57C2×#13133146C2211yescharacteristic
58C2×#13133146C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133142C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133140C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×#13133138C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×SD16×C53C2211yescharacteristic
70C2×C4×Q8×C53C2211yescharacteristic
71C2×C4×D4×C53C2211yescharacteristic
72C53×#440C2218yes—
73C2×#107×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106D411yescharacteristic
79C22×Dic106C2311yescharacteristic
80C22×Dic106C2311yescharacteristic
81C2×#11719925—24no—
82C2×#11719925—24no—
83C2×#11719925C2314yes—
84C2×#11719925C2314yes—
85C22×#88322C2311yescharacteristic
86C22×#88322C2311yescharacteristic
87#13133217—22no—
88#13133217C2314yes—
89#13133216—22no—
90#13133216—28no—
91#13133216C2314yes—
92#13133210—28no—
93#13133210—28no—
94#13133209—22no—
95#13133209—28no—
96#13133209C2314yes—
97#13133208—28no—
98#13133208—22no—
99#13133208C2314yes—
100#13133204—22no—
101#13133204—22no—
102#13133204C2314yes—
103#13133204C2314yes—
104#13133196—28no—
105Q8×Dic53—22no—
106Q8×Dic53—22no—
107Q8×Dic53C2314yes—
108Q8×Dic53C2314yes—
109C4×Dic106—28no—
110C4×Dic106D414yes—
111C4×Dic106C2314yes—
112#13133182—22no—
113#13133182—22no—
114#13133182C2314yes—
115#13133182C2314yes—
116#13133176—28no—
117C2×C4⋊Dic53—21no—
118C2×C4⋊Dic53—21no—
119C2×C4⋊Dic53—21no—
120C2×C4⋊Dic53—21no—
121C2×C4⋊Dic53—21no—
122C2×C4⋊Dic53D411yescharacteristic
123C2×C4⋊Dic53C2311yescharacteristic
124C2×C4⋊Dic53C2311yescharacteristic
125C2×#11719919—21no—
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919D411yescharacteristic
132C2×#11719919D411yescharacteristic
133C2×C22⋊Dic53—21no—
134C2×C22⋊Dic53—21no—
135C2×C22⋊Dic53—21no—
136C2×C22⋊Dic53—21no—
137C2×C4×Dic53—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#13133142C2314yes—
151#13133142C2314yes—
152#13133140C2314yes—
153#13133140C2314yes—
154#13133138C2314yes—
155#13133138C2314yes—
156#13133127C2314yes—
157C8×Dic53C2314yes—
158C22×Q8×C53C2311yescharacteristic
159C22×D4×C53C2311yescharacteristic
160C23×C4×C53—21no—
161C2×SD16×C53—24no—
162C2×SD16×C53C2314yes—
163C22×C8×C53C2311yescharacteristic
164C22×C8×C53C2311yescharacteristic
165C4×Q8×C53—22no—
166C4×Q8×C53C2314yes—
167C4×D4×C53—22no—
168C4×D4×C53C2314yes—
169C2×C4⋊C4×C53—21no—
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C22⋊C4×C53—21no—
173C2×C42×C53—21no—
174C2×C42×C53C2311yescharacteristic
175#107×C53C2314yes—
176#103×C53C2314yes—
177#102×C53C2314yes—
178#97×C53C2314yes—
179C24×C53—21no—
180C2×Q8×C53—21no—
181C2×Q8×C53—22no—
182C2×Q8×C53#4114yes—
183C2×Q8×C53C2412yes—
184C2×D4×C53—21no—
185C2×D4×C53—22no—
186C2×D4×C53—22no—
187C2×D4×C53C2412yes—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—24no—
192C22×C4×C53—44no—
193C22×C4×C53C2×D411yescharacteristic
194C22×C4×C53C2×D411yescharacteristic
195C22×C4×C53C2411yescharacteristic
196C22×Dic53—21no—
197C22×Dic53—21no—
198C22×Dic53—21no—
199C22×Dic53—21no—
200C22×Dic53C2×D411yescharacteristic
201C22×Dic53C2×D411yescharacteristic
202C22×Dic53C2×D411yescharacteristic
203C22×Dic53C2×D411yescharacteristic
204C2×Dic106—22no—
205C2×Dic106—22no—
206C2×Dic106—22no—
207C2×Dic106—22no—
208C2×Dic106—21no—
209C2×Dic106—21no—
210C2×Dic106—24no—
211C2×Dic106—42no—
212C2×Dic106—44no—
213C2×Dic106C2×D414yes—
214C2×Dic106C2412yes—
215C2×Dic106C2412yes—
216SD16×C53—28no—
217C2×C8×C53—22no—
218C2×C8×C53—22no—
219C2×C8×C53C2412yes—
220C2×C8×C53C2412yes—
221C4⋊C4×C53—24no—
222C4⋊C4×C53—21no—
223C4⋊C4×C53—21no—
224C4⋊C4×C53C2412yes—
225C4⋊C4×C53C2412yes—
226C22⋊C4×C53—24no—
227C42×C53—24no—
228C42×C53C2×D412yes—
229C42×C53C2412yes—
230C22⋊Dic53—24no—
231C22⋊Dic53—24no—
232C22⋊Dic53—24no—
233C22⋊Dic53—24no—
234#11719925—28no—
235#11719925—28no—
236C4⋊Dic53—24no—
237C4⋊Dic53—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#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—
266C23×C53—22no—
267C23×C53—42no—
268C23×C53—42no—
269C23×C53—42no—
270C23×C53C22×D411yescharacteristic
271Q8×C53—24no—
272Q8×C53—22no—
273Q8×C53C2×#4114yes—
274D4×C53—22no—
275D4×C53—22no—
276D4×C53—42no—
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—48no—
284C2×C4×C53—42no—
285C2×C4×C53—42no—
286C2×C4×C53C22×D412yes—
287C2×C4×C53C22×D412yes—
288C2×C4×C53C22×D411yescharacteristic
289C2×C4×C53C2×#4112yes—
290C2×C4×C532−1+412yes—
291C2×C4×C53C2511yescharacteristic
292C2×Dic53—22no—
293C2×Dic53—22no—
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—42no—
303C2×Dic53—42no—
304C2×Dic53C22×D412yes—
305C2×Dic53C22×D412yes—
306C2×Dic53C22×D412yes—
307C2×Dic53C22×D412yes—
308Dic106—22no—
309Dic106—22no—
310Dic106—22no—
311Dic106—22no—
312Dic106—44no—
313Dic106—48no—
314Dic106—42no—
315Dic106—42no—
316C8×C53—22no—
317C8×C53—22no—
318#88322—22no—
319#88322—22no—
320C2×#3377—531nomaximal, Sylow
321C22×C53—42no—
322C22×C53—42no—
323C22×C53—42no—
324C22×C53—84no—
325C22×C53#54812yes—
326C22×C53#57512yes—
327C22×C53#57812yes—
328C22×C53C23×D411yescharacteristic
329C4×C53—24no—
330C4×C53—22no—
331C4×C53—22no—
332C4×C53—42no—
333C4×C53—42no—
334C4×C53#54812yes—
335C4×C53C22×#4111yescharacteristic
336C4×C53C2×2−1+411yescharacteristic
337Dic53—22no—
338Dic53—22no—
339Dic53—22no—
340Dic53—22no—
341Dic53—42no—
342Dic53—42no—
343Dic53—42no—
344Dic53—42no—
345C2×#557—531no—
346C2×#556—531no—
347#3377—5316no—
348C2×#491—531no—
349C2×#489—531no—
350C2×#488—531no—
351C2×#479—531no—
352C2×#477—531no—
353C2×#478—531no—
354C2×#464—531no—
355C2×#464—531no—
356C2×#462—531no—
357C2×#446—531no—
358C2×#441—531no—
359C2×#440D5311yescharacteristic
360C2×C4×Q16—531no—
361C2×C53—82no—
362C2×C53#337714yescomplemented
363C2×C53C2×#54811yescharacteristic
364C2×C53C2×#57511yescharacteristic
365C2×C53C2×#57811yescharacteristic
366C22×Q16—531no—
367C22×Q16—531no—
368C22×SD16C2×D5311yescharacteristic
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—531no—
390C2×C4×Q8—1061no—
391C2×C4×Q8C2×D5311yescharacteristic
392C2×C4×D4C2×D5311yescharacteristic
393C2×#117—1061no—
394#491—538no—
395#489—538no—
396#488—538no—
397#479—538no—
398#478—538no—
399#477—538no—
400#464—538no—
401#464—538no—
402#462—538no—
403#446—538no—
404#441—538no—
405#440C2×D5318yes—
406C4×Q16—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×#103—531no—
419C2×#103C2×D5311yescharacteristic
420C2×#102—531no—
421C2×#102—531no—
422C2×#102C2×D5311yescharacteristic
423C2×#97—531no—
424C2×#97C2×D5311yescharacteristic
425C2×C4×C8—531no—
426C53C2×#337711yescharacteristic, complemented, Sylow
427C22×Q8—531no—
428C22×Q8—531no—
429C22×Q8—531no—
430C22×Q8—1061no—
431C22×Q8C22×D5311yescharacteristic
432C22×D4C22×D5311yescharacteristic
433C23×C4—21no—
434C2×Q16—534no—
435C2×Q16—534no—
436C2×Q16—1064no—
437C2×Q16—1064no—
438C2×SD16—24no—
439C2×SD16C22×D5314yes—
440C22×C8—531no—
441C22×C8—531no—
442C22×C8C22×D5311yescharacteristic
443C22×C8C22×D5311yescharacteristic
444C4⋊Q8—534no—
445C4⋊Q8—534no—
446C4⋊Q8—1062no—
447C4⋊Q8—1068no—
448C4⋊Q8—1062no—
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—534no—
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×Q8—1062no—
474C4×Q8C22×D5314yes—
475C4×D4—22no—
476C4×D4C22×D5314yes—
477#117—1068no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—531no—
480C2×C4⋊C4—531no—
481C2×C4⋊C4—531no—
482C2×C4⋊C4—531no—
483C2×C4⋊C4—531no—
484C2×C4⋊C4—1061no—
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—21no—
498C2×C22⋊C4—1061no—
499C2×C22⋊C4—1061no—
500C2×C22⋊C4—1061no—
501C2×C22⋊C4—1061no—
502C2×C42—21no—
503C2×C42—531no—
504C2×C42—531no—
505C2×C42—1061no—
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#103—534no—
522#103C22×D5314yes—
523#102—534no—
524#102—534no—
525#102C22×D5314yes—
526#97—534no—
527#97C22×D5314yes—
528C4×C8—534no—
529C24—21no—
530C2×Q8—21no—
531C2×Q8—22no—
532C2×Q8—534no—
533C2×Q8—532no—
534C2×Q8—532no—
535C2×Q8—1064no—
536C2×Q8—1061no—
537C2×Q8—1061no—
538C2×Q8—1062no—
539C2×Q8—1062no—
540C2×Q8—1062no—
541C2×Q8—1062no—
542C2×Q8—2122no—
543C2×Q8—2124no—
544C2×Q8#1171994514yes—
545C2×Q8C23×D5312yes—
546C2×D4—21no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4C23×D5312yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—24no—
554C22×C4—44no—
555C22×C4—531no—
556C22×C4—531no—
557C22×C4—531no—
558C22×C4—531no—
559C22×C4—1061no—
560C22×C4—1061no—
561C22×C4—1061no—
562C22×C4—1061no—
563C22×C4D4×D5311yescharacteristic
564C22×C4D4×D5311yescharacteristic
565C22×C4C23×D5311yescharacteristic
566Q16—1068no—
567Q16—1068no—
568SD16—28no—
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—21no—
579C4⋊C4—21no—
580C4⋊C4—534no—
581C4⋊C4—534no—
582C4⋊C4—534no—
583C4⋊C4—532no—
584C4⋊C4—532no—
585C4⋊C4—1064no—
586C4⋊C4—1064no—
587C4⋊C4—1064no—
588C4⋊C4—1064no—
589C4⋊C4—1064no—
590C4⋊C4—1064no—
591C4⋊C4—1064no—
592C4⋊C4—1061no—
593C4⋊C4—1061no—
594C4⋊C4—1064no—
595C4⋊C4—1064no—
596C4⋊C4—1064no—
597C4⋊C4—1064no—
598C4⋊C4C23×D5312yes—
599C4⋊C4C23×D5312yes—
600C22⋊C4—24no—
601C22⋊C4—1064no—
602C22⋊C4—1064no—
603C22⋊C4—1064no—
604C22⋊C4—1064no—
605C42—24no—
606C42—532no—
607C42—532no—
608C42—532no—
609C42—532no—
610C42—1064no—
611C42—1064no—
612C42—1064no—
613C42—1064no—
614C42D4×D5312yes—
615C42C23×D5312yes—
616C23—22no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23C2×D4×D5311yescharacteristic
621Q8—24no—
622Q8—22no—
623Q8—1062no—
624Q8—1062no—
625Q8—1062no—
626Q8—1062no—
627Q8—2124no—
628Q8—2128no—
629Q8—2122no—
630Q8—2122no—
631Q8C2×#1171994514yes—
632D4—22no—
633D4—22no—
634D4—42no—
635C2×C4—24no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—48no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—532no—
645C2×C4—532no—
646C2×C4—532no—
647C2×C4—532no—
648C2×C4—1062no—
649C2×C4—1062no—
650C2×C4—1062no—
651C2×C4—1062no—
652C2×C4—1062no—
653C2×C4—1062no—
654C2×C4—1062no—
655C2×C4—1062no—
656C2×C4—2122no—
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—42no—
671C22—42no—
672C22—42no—
673C22—84no—
674C22#1681128212yes—
675C22#1681141912yes—
676C22#1681143912yes—
677C22C22×D4×D5311yescharacteristic
678C4—22no—
679C4—24no—
680C4—22no—
681C4—42no—
682C4—42no—
683C4—1062no—
684C4—1062no—
685C4—1062no—
686C4—1062no—
687C4—2122no—
688C4—2122no—
689C4—2122no—
690C4—2122no—
691C4#1681128212yes—
692C4C22×#1171994511yescharacteristic
693C4C2×#1313326411yescharacteristic
694C2—82no—
695C2#2028755814yesdirect product factor
696C2C2×#1681128211yescharacteristic
697C2C2×#1681141911yescharacteristic
698C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#440C2
socleC23×C53C22×D4
prime radicalC22×D4×C53C23
hypercenterC2×#440D53
hypocenterC53C2×#3377
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#16811349C2semidirect
3. #20287558C2direct (N × H)
4. C2×#16810992C2semidirect
7. C2×#16810929C2semidirect
8. C2×#16810917C2semidirect
12. C2×#16810833C2semidirect
13. C2×#16810751C2semidirect
14. C2×#16810727C2semidirect
15. C2×#16810715C2semidirect
20. #16811349C22semidirect
42. #16810992C22semidirect
45. #16810929C22semidirect
47. #16810917C22semidirect
50. #16810833C22semidirect
51. #16810751C22semidirect
52. #16810727C22semidirect
53. #16810715C22semidirect
362. C2×C53#3377semidirect
426. C53C2×#3377semidirect
695. C2#20287558direct (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×#168113432
#202875582
C2×#168109922
C2×#168109812
C2×#168109762
C2×#168109292
C2×#168109172
C2×#168109232
C2×#168108432
C2×#168108332
C2×#168107512
C2×#168107272
C2×#168107152
C2×C53×#4402
C2×#337753