Finite Group Databasebeta

← C2×#20287493 #28263752

Subgroups — C2×#20287493 #28263752

Order 13568.

1854 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×#16811348C211yesmaximal, characteristic, complemented
2C2×#16811329C211yesmaximal, characteristic
3#20287493C2116yesmaximal, direct product factor
4C2×#16810990C211yesmaximal, characteristic, complemented
5C2×#16810972C211yesmaximal, characteristic, complemented
6C2×#16810932C211yesmaximal, characteristic, complemented
7C2×#16810927C211yesmaximal, characteristic, complemented
8C2×#16810916C211yesmaximal, characteristic, complemented
9C2×#16810827C211yesmaximal, characteristic
10C2×#16810827C211yesmaximal, characteristic
11C2×#16810825C211yesmaximal, characteristic
12C2×#16810751C211yesmaximal, characteristic, complemented
13C2×#16810726C211yesmaximal, characteristic
14C2×#16810725C211yesmaximal, characteristic
15C2×#16810708C211yesmaximal, characteristic
16C2×C53×#491C211yesmaximal, characteristic, complemented
17C22×#11719913C2211yescharacteristic
18C22×#11719924C2211yescharacteristic
19C22×#11719924C2211yescharacteristic
20#16811348—24no—
21#16811348C2218yescomplemented
22#16811329—24no—
23#16811329C2218yes—
24C2×#13133216C2211yescharacteristic
25C2×#13133215C2211yescharacteristic
26C2×#13133215C2211yescharacteristic
27C2×#13133208—21no—
28C2×#13133208C2211yescharacteristic
29C2×#13133207—21no—
30C2×#13133207—21no—
31C2×#13133197—21no—
32C2×#13133195—21no—
33C2×#13133195—21no—
34C2×Q8×Dic53C2211yescharacteristic
35C2×Q8×Dic53C2211yescharacteristic
36C2×C4×Dic106C2211yescharacteristic
37C2×C4×Dic106C2211yescharacteristic
38C2×#13133182—21no—
39C2×C4×D212C2211yescharacteristic
40C2×#13133179C2211yescharacteristic
41C2×#13133179C2211yescharacteristic
42C2×C4⋊C4×D53—21no—
43#16810990C2218yescomplemented
44#16810972C2218yescomplemented
45#16810932C2218yescomplemented
46#16810927C2218yescomplemented
47#16810916C2218yescomplemented
48#16810827C2218yes—
49#16810827C2218yes—
50#16810825C2218yes—
51#16810751C2218yescomplemented
52#16810726C2218yes—
53#16810725C2218yes—
54#16810708C2218yes—
55C2×#13133151C2211yescharacteristic
56C2×#13133150C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×C4⋊#88322C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133146C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133141C2211yescharacteristic
64C2×#13133140C2211yescharacteristic
65C2×#13133140C2211yescharacteristic
66C2×#13133139C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C2×C4⋊Q8×C53C2211yescharacteristic
70C2×#125×C53C2211yescharacteristic
71C53×#491C2218yescomplemented
72C2×#103×C53C2211yescharacteristic
73C2×#103×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106D411yescharacteristic
79C22×Dic106C2311yescharacteristic
80C22×D212C2311yescharacteristic
81C22×C4×D53—21no—
82C22×C4×D53—21no—
83C22×C4×D53—21no—
84C2×#11719913—24no—
85C2×#11719913C2314yes—
86C2×#11719924—24no—
87C2×#11719924—24no—
88C2×#11719924C2314yes—
89C2×#11719924C2314yes—
90C22×#88322C2311yescharacteristic
91C22×#88322C2311yescharacteristic
92#13133216—22no—
93#13133216C2314yes—
94#13133215—22no—
95#13133215—22no—
96#13133215C2314yes—
97#13133215C2314yes—
98#13133208—28no—
99#13133208—22no—
100#13133208C2314yes—
101#13133207—28no—
102#13133207—28no—
103#13133197—28no—
104#13133195—28no—
105#13133195—28no—
106Q8×Dic53—22no—
107Q8×Dic53—22no—
108Q8×Dic53C2314yes—
109Q8×Dic53C2314yes—
110C4×Dic106—22no—
111C4×Dic106D414yes—
112C4×Dic106C2314yes—
113C4×Dic106C2314yes—
114#13133182—28no—
115C4×D212—22no—
116C4×D212C2314yes—
117#13133179—22no—
118#13133179—22no—
119#13133179C2314yes—
120#13133179C2314yes—
121C2×C4⋊Dic53—21no—
122C2×C4⋊Dic53—21no—
123C2×C4⋊Dic53—21no—
124C2×C4⋊Dic53D411yescharacteristic
125C2×C4⋊Dic53C2311yescharacteristic
126C2×C4⋊Dic53C2311yescharacteristic
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919D411yescharacteristic
135C2×#11719919D411yescharacteristic
136C4⋊C4×D53—28no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×C4×Dic53—21no—
141C2×C4×Dic53—21no—
142C2×C4×Dic53—21no—
143C2×C4×Dic53C2311yescharacteristic
144C2×C4×Dic53C2311yescharacteristic
145#13133151C2314yes—
146#13133150C2314yes—
147#13133148C2314yes—
148C4⋊#88322C2314yes—
149#13133146C2314yes—
150#13133146C2314yes—
151#13133142C2314yes—
152#13133141C2314yes—
153#13133141C2314yes—
154#13133140C2314yes—
155#13133140C2314yes—
156#13133139C2314yes—
157#13133127C2314yes—
158C8×Dic53C2314yes—
159C22×Q8×C53C2311yescharacteristic
160C22×Q8×C53C2311yescharacteristic
161C22×C8×C53C2311yescharacteristic
162C22×C8×C53C2311yescharacteristic
163C4⋊Q8×C53—22no—
164C4⋊Q8×C53C2314yes—
165#125×C53—22no—
166#125×C53C2314yes—
167C2×C4⋊C4×C53—21no—
168C2×C4⋊C4×C53—21no—
169C2×C4⋊C4×C53—21no—
170C2×C4⋊C4×C53—21no—
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C42×C53C2311yescharacteristic
174#103×C53C2314yes—
175#103×C53C2314yes—
176#103×C53C2314yes—
177#103×C53C2314yes—
178#97×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—22no—
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—21no—
203C2×D212—22no—
204C2×D212#4114yes—
205C2×D212C2412yes—
206C2×C4×D53—24no—
207C2×C4×D53—24no—
208C2×C4×D53—24no—
209C2×C4×D53—44no—
210C2×C4×D53—82no—
211C2×C4×D53—82no—
212C2×Dic106—24no—
213C2×Dic106—22no—
214C2×Dic106—22no—
215C2×Dic106—21no—
216C2×Dic106—24no—
217C2×Dic106—82no—
218C2×Dic106C2×D414yes—
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—24no—
227C4⋊C4×C53—24no—
228C4⋊C4×C53—21no—
229C4⋊C4×C53—21no—
230C4⋊C4×C53C2412yes—
231C4⋊C4×C53C2412yes—
232C42×C53C2×D412yes—
233C42×C53C2412yes—
234#11719924—28no—
235#11719924—28no—
236#11719921—24no—
237#11719921—24no—
238#11719921—24no—
239C4⋊Dic53—21no—
240C4⋊Dic53—21no—
241C4⋊Dic53—24no—
242C4⋊Dic53—24no—
243C4⋊Dic53—24no—
244C4⋊Dic53C2×D414yes—
245C4⋊Dic53C2412yes—
246C4⋊Dic53C2412yes—
247#11719919—24no—
248#11719919—24no—
249#11719919—24no—
250#11719919—24no—
251#11719919—24no—
252#11719919—24no—
253#11719919—24no—
254#11719919C2×D414yes—
255#11719919C2×D414yes—
256C4×Dic53—24no—
257C4×Dic53—24no—
258C4×Dic53—24no—
259C4×Dic53C2×D412yes—
260C4×Dic53C2×D412yes—
261C4×Dic53C2412yes—
262C4×Dic53C2412yes—
263C2×#88322—22no—
264C2×#88322—22no—
265C2×#88322C2412yes—
266C2×#88322C2412yes—
267#11719913—28no—
268C23×C53C22×D411yescharacteristic
269C22×D53—24no—
270C22×D53—22no—
271C22×D53—42no—
272C22×D53—42no—
273Q8×C53—22no—
274Q8×C53—22no—
275Q8×C53—22no—
276Q8×C53—22no—
277Q8×C53—42no—
278Q8×C53—42no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—42no—
286C2×C4×C53—42no—
287C2×C4×C53—42no—
288C2×C4×C53—42no—
289C2×C4×C53C22×D412yes—
290C2×C4×C53C22×D412yes—
291C2×C4×C53C22×D411yescharacteristic
292C2×C4×C53C2×#4112yes—
293C2×C4×C532−1+412yes—
294C2×C4×C53C2511yescharacteristic
295C2×Dic53—22no—
296C2×Dic53—22no—
297C2×Dic53—22no—
298C2×Dic53—22no—
299C2×Dic53—22no—
300C2×Dic53—22no—
301C2×Dic53—42no—
302C2×Dic53—42no—
303C2×Dic53—42no—
304C2×Dic53#13714yes—
305C2×Dic53C22×D412yes—
306C2×Dic53C22×D412yes—
307C2×Dic53C22×D412yes—
308C2×Dic53C22×D412yes—
309D212—24no—
310D212—22no—
311D212C2×#4114yes—
312C4×D53—48no—
313C4×D53—84no—
314C4×D53—84no—
315Dic106—28no—
316Dic106—22no—
317Dic106—22no—
318Dic106—42no—
319Dic106—84no—
320C8×C53—22no—
321C8×C53—22no—
322#88322—22no—
323#88322—22no—
324C2×#3372—531nomaximal, Sylow
325C22×C53#54812yes—
326C22×C53C2×#13712yes—
327C22×C53#57712yes—
328C22×C53C23×D411yescharacteristic
329C2×D53—24no—
330C2×D53—48no—
331C2×D53—42no—
332C2×D53—42no—
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—22no—
343Dic53—22no—
344Dic53—22no—
345Dic53—42no—
346Dic53—42no—
347Dic53—42no—
348Dic53C2×#13714yes—
349C2×#557—531no—
350C2×#554—531no—
351#3372—5316no—
352C2×#491—531no—
353C2×#491D5311yescharacteristic, complemented
354C2×#487—531no—
355C2×#479—531no—
356C2×#479—531no—
357C2×#477—531no—
358C2×#461—531no—
359C2×#461—531no—
360C2×#461—531no—
361C2×#446—531no—
362C2×#440—531no—
363C2×#440—531no—
364C2×C4×SD16—531no—
365C2×C53#337214yescomplemented
366C2×C53C2×#54811yescharacteristic
367C2×C53C22×#13711yescharacteristic
368C2×C53C2×#57711yescharacteristic
369D53—44no—
370C22×SD16—531no—
371C22×SD16—531no—
372C22×SD16—531no—
373#557—538no—
374#557—1064no—
375#554—538no—
376#554—1064no—
377C2×C4⋊Q8—531no—
378C2×C4⋊Q8—531no—
379C2×C4⋊Q8—531no—
380C2×C4⋊Q8C2×D5311yescharacteristic
381C2×#125—531no—
382C2×#125—1061no—
383C2×#125—1061no—
384C2×#125—1061no—
385C2×#125C2×D5311yescharacteristic
386C2×C22⋊Q8—1061no—
387C2×C22⋊Q8—1061no—
388C2×C22⋊Q8—1061no—
389C2×C4×Q8—531no—
390C2×C4×Q8—531no—
391C2×C4×Q8—531no—
392C2×C4×Q8—531no—
393C2×C4×Q8—1061no—
394C2×C4×D4—531no—
395C2×C4×D4—531no—
396C2×C4×D4—531no—
397C22×C4⋊C4—1061no—
398#491—538no—
399#491C2×D5318yescomplemented
400#487—538no—
401#479—538no—
402#479—538no—
403#477—538no—
404#461—538no—
405#461—538no—
406#461—538no—
407#446—538no—
408#440—538no—
409#440—538no—
410C4×SD16—538no—
411C2×#107—531no—
412C2×#107—531no—
413C2×#106—531no—
414C2×C4⋊C8—531no—
415C2×C4⋊C8—531no—
416C2×C4⋊C8—531no—
417C2×#103—531no—
418C2×#103—531no—
419C2×#103—531no—
420C2×#103—531no—
421C2×#103—531no—
422C2×#103C2×D5311yescharacteristic
423C2×#103C2×D5311yescharacteristic
424C2×#103C2×D5311yescharacteristic
425C2×#103C2×D5311yescharacteristic
426C2×#102—531no—
427C2×#97—531no—
428C2×#97C2×D5311yescharacteristic
429C2×C4×C8—531no—
430C53C2×#337211yescharacteristic, complemented, Sylow
431C22×Q8—531no—
432C22×Q8—531no—
433C22×Q8—1061no—
434C22×Q8C22×D5311yescharacteristic
435C22×Q8C22×D5311yescharacteristic
436C22×D4—531no—
437C23×C4—1061no—
438C23×C4—1061no—
439C23×C4—1061no—
440C2×SD16—534no—
441C2×SD16—534no—
442C2×SD16—534no—
443C2×SD16—1064no—
444C2×SD16—1064no—
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⋊Q8C22×D5314yes—
458#125—22no—
459#125—534no—
460#125—1062no—
461#125—1068no—
462#125—1068no—
463#125—1068no—
464#125C22×D5314yes—
465C22⋊Q8—1068no—
466C22⋊Q8—1068no—
467C22⋊Q8—1068no—
468C4×Q8—534no—
469C4×Q8—534no—
470C4×Q8—534no—
471C4×Q8—534no—
472C4×Q8—534no—
473C4×Q8—1062no—
474C4×Q8—1062no—
475C4×Q8—1068no—
476C4×Q8—1062no—
477C4×D4—534no—
478C4×D4—534no—
479C4×D4—534no—
480C4×D4—1062no—
481C4×D4—1062no—
482C4×D4—1062no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—531no—
488C2×C4⋊C4—531no—
489C2×C4⋊C4—531no—
490C2×C4⋊C4—531no—
491C2×C4⋊C4—531no—
492C2×C4⋊C4—1068no—
493C2×C4⋊C4—1061no—
494C2×C4⋊C4—1061no—
495C2×C4⋊C4—1061no—
496C2×C4⋊C4—1061no—
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×C22⋊C4—1061no—
506C2×C22⋊C4—1061no—
507C2×C22⋊C4—1061no—
508C2×C42—531no—
509C2×C42—531no—
510C2×C42—1061no—
511C2×C42—1061no—
512C2×C42—1061no—
513C2×C42C22×D5311yescharacteristic
514#107—534no—
515#107—534no—
516#106—534no—
517C4⋊C8—534no—
518C4⋊C8—534no—
519C4⋊C8—534no—
520#103—534no—
521#103—534no—
522#103—534no—
523#103—534no—
524#103—534no—
525#103C22×D5314yes—
526#103C22×D5314yes—
527#103C22×D5314yes—
528#103C22×D5314yes—
529#102—534no—
530#97—534no—
531#97C22×D5314yes—
532C4×C8—534no—
533C24—1061no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—534no—
541C2×Q8—532no—
542C2×Q8—1064no—
543C2×Q8—1064no—
544C2×Q8—1061no—
545C2×Q8—1062no—
546C2×Q8—1062no—
547C2×Q8—4242no—
548C2×Q8C23×D5312yes—
549C2×Q8C23×D5312yes—
550C2×D4—534no—
551C2×D4—532no—
552C2×D4—1061no—
553C2×D4—1062no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—531no—
559C22×C4—531no—
560C22×C4—531no—
561C22×C4—531no—
562C22×C4—1064no—
563C22×C4—1064no—
564C22×C4—1061no—
565C22×C4—1061no—
566C22×C4—1061no—
567C22×C4—1064no—
568C22×C4—4242no—
569C22×C4—4242no—
570C22×C4—2124no—
571C22×C4D4×D5311yescharacteristic
572C22×C4D4×D5311yescharacteristic
573C22×C4C23×D5311yescharacteristic
574SD16—1068no—
575SD16—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—24no—
588C4⋊C4—24no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—534no—
592C4⋊C4—534no—
593C4⋊C4—534no—
594C4⋊C4—532no—
595C4⋊C4—532no—
596C4⋊C4—1064no—
597C4⋊C4—1064no—
598C4⋊C4—1064no—
599C4⋊C4—1064no—
600C4⋊C4—1064no—
601C4⋊C4—1064no—
602C4⋊C4—1064no—
603C4⋊C4—1064no—
604C4⋊C4—1064no—
605C4⋊C4—1061no—
606C4⋊C4—1061no—
607C4⋊C4—1064no—
608C4⋊C4C23×D5312yes—
609C4⋊C4C23×D5312yes—
610C22⋊C4—1064no—
611C22⋊C4—1064no—
612C22⋊C4—1064no—
613C42—532no—
614C42—532no—
615C42—532no—
616C42—532no—
617C42—1064no—
618C42—1064no—
619C42—1064no—
620C42D4×D5312yes—
621C42C23×D5312yes—
622C23—1064no—
623C23—1062no—
624C23—2122no—
625C23—2122no—
626C23C2×D4×D5311yescharacteristic
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—22no—
631Q8—42no—
632Q8—42no—
633Q8—1068no—
634Q8—1062no—
635Q8—1062no—
636Q8—4244no—
637Q8—2122no—
638D4—534no—
639D4—1064no—
640D4—1062no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—534no—
652C2×C4—532no—
653C2×C4—532no—
654C2×C4—532no—
655C2×C4—532no—
656C2×C4—1062no—
657C2×C4—1062no—
658C2×C4—1062no—
659C2×C4—1062no—
660C2×C4—1062no—
661C2×C4—1062no—
662C2×C4—4244no—
663C2×C4—4244no—
664C2×C4—2128no—
665C2×C4—2122no—
666C2×C4—2122no—
667C2×C4—2122no—
668C2×C4C2×D4×D5312yes—
669C2×C4C2×D4×D5312yes—
670C2×C4C2×D4×D5311yescharacteristic
671C2×C4#41×D5312yes—
672C2×C4#1313326412yes—
673C2×C4C24×D5311yescharacteristic
674C8—22no—
675C8—22no—
676C8—1062no—
677C8—1062no—
678C22—1064no—
679C22—2128no—
680C22—2122no—
681C22—2122no—
682C22#1681128112yes—
683C22#137×D5312yes—
684C22#1681143212yes—
685C22C22×D4×D5311yescharacteristic
686C4—22no—
687C4—22no—
688C4—42no—
689C4—42no—
690C4—42no—
691C4—42no—
692C4—534no—
693C4—1062no—
694C4—1062no—
695C4—1062no—
696C4—2122no—
697C4—2122no—
698C4—2122no—
699C4#1681128112yes—
700C4C2×#41×D5311yescharacteristic
701C4C2×#1313326411yescharacteristic
702C2—2124no—
703C2#2028749314yesdirect product factor
704C2C2×#1681128111yescharacteristic
705C2C2×#137×D5311yescharacteristic
706C2C2×#1681143211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#491C2
socleC23×C53C22×D4
prime radicalC22×D212C23
hypercenterC2×#491D53
hypocenterC53C2×#3372
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#491

Complements

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

NH ≅ G/Ntype
1. C2×#16811348C2semidirect
3. #20287493C2direct (N × H)
4. C2×#16810990C2semidirect
5. C2×#16810972C2semidirect
6. C2×#16810932C2semidirect
7. C2×#16810927C2semidirect
8. C2×#16810916C2semidirect
12. C2×#16810751C2semidirect
16. C2×C53×#491C2semidirect
21. #16811348C22semidirect
43. #16810990C22semidirect
44. #16810972C22semidirect
45. #16810932C22semidirect
46. #16810927C22semidirect
47. #16810916C22semidirect
51. #16810751C22semidirect
71. C53×#491C22semidirect
353. C2×#491D53semidirect
365. C2×C53#3372semidirect
399. #491C2×D53semidirect
430. C53C2×#3372semidirect
703. C2#20287493direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113482
C2×#168113292
#202874932
C2×#168109902
C2×#168109722
C2×#168109322
C2×#168109272
C2×#168109162
C2×#168108272
C2×#168108252
C2×#168107512
C2×#168107262
C2×#168107252
C2×#168107082
C2×C53×#4912
C2×#337253