Finite Group Databasebeta

← C2×#20285242 #28253712

Subgroups — C2×#20285242 #28253712

Order 13568.

1854 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811253C211yesmaximal, characteristic
2C2×#16811250C211yesmaximal, characteristic
3#20285242C2116yesmaximal, direct product factor
4C2×#16811032C211yesmaximal, characteristic, complemented
5C2×#16811031C211yesmaximal, characteristic, complemented
6C2×#16811030C211yesmaximal, characteristic, complemented
7C2×#16811024C211yesmaximal, characteristic, complemented
8C2×#16811022C211yesmaximal, characteristic, complemented
9C2×#16811020C211yesmaximal, characteristic, complemented
10C2×#16811019C211yesmaximal, characteristic, complemented
11C2×#16810664C211yesmaximal, characteristic
12C2×#16810662C211yesmaximal, characteristic
13C2×#16810660C211yesmaximal, characteristic
14C2×#106×D53C211yesmaximal, characteristic
15C2×#16810580C211yesmaximal, characteristic
16C2×C53×#501C211yesmaximal, characteristic, complemented
17C22×#11719912C2211yescharacteristic
18C22×C8×D53C2211yescharacteristic
19#16811253—24no—
20#16811253C2218yes—
21#16811250—24no—
22#16811250C2218yes—
23C2×#13133217C2211yescharacteristic
24C2×#13133216—21no—
25C2×#13133216C2211yescharacteristic
26C2×#13133216C2211yescharacteristic
27C2×#13133215—21no—
28C2×#13133209C2211yescharacteristic
29C2×#13133208C2211yescharacteristic
30C2×#13133208C2211yescharacteristic
31C2×#13133207—21no—
32C2×#13133207—21no—
33C2×#13133197—21no—
34C2×#13133195—21no—
35C2×#13133195—21no—
36C2×#13133193—21no—
37C2×#13133175C2211yescharacteristic
38C2×#13133175C2211yescharacteristic
39C2×#13133174C2211yescharacteristic
40C2×C4⋊C4×D53C2211yescharacteristic
41C2×C4⋊C4×D53C2211yescharacteristic
42#16811032C2218yescomplemented
43#16811031C2218yescomplemented
44#16811030C2218yescomplemented
45#16811024C2218yescomplemented
46#16811022C2218yescomplemented
47#16811020C2218yescomplemented
48#16811019C2218yescomplemented
49#16810664C2218yes—
50#16810662C2218yes—
51#16810660C2218yes—
52C2×#13133151C2211yescharacteristic
53C2×#13133151C2211yescharacteristic
54C2×#13133150C2211yescharacteristic
55C2×#13133150C2211yescharacteristic
56C2×#13133149C2211yescharacteristic
57C2×#13133149C2211yescharacteristic
58C2×#13133148C2211yescharacteristic
59C2×#13133148C2211yescharacteristic
60C2×#13133148C2211yescharacteristic
61C2×#13133148C2211yescharacteristic
62C2×#13133148C2211yescharacteristic
63C2×#13133148C2211yescharacteristic
64#106×D53C2218yes—
65#16810580C2218yes—
66C2×#13133127C2211yescharacteristic
67C2×C4×#88322C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
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×Dic106—21no—
79C22×Dic106—21no—
80C22×C4×D53—21no—
81C22×C4×D53—21no—
82C22×C4×D53C2311yescharacteristic
83C2×#11719912Q818yescomplemented
84C2×#11719912C2314yes—
85C22×#88322C2311yescharacteristic
86C22×#88322C2311yescharacteristic
87C2×C8×D53Q818yescomplemented
88C2×C8×D53C2314yes—
89#13133217—22no—
90#13133217C2314yes—
91#13133216—28no—
92#13133216—22no—
93#13133216—22no—
94#13133216C2314yes—
95#13133216C2314yes—
96#13133215—28no—
97#13133209—22no—
98#13133209C2314yes—
99#13133208—22no—
100#13133208—22no—
101#13133208C2314yes—
102#13133208C2314yes—
103#13133207—28no—
104#13133207—28no—
105#13133197—28no—
106#13133195—28no—
107#13133195—28no—
108#13133193—28no—
109#13133175—22no—
110#13133175—22no—
111#13133175C2314yes—
112#13133175C2314yes—
113#13133174D414yes—
114#13133174C2314yes—
115C2×C4⋊Dic53—21no—
116C2×C4⋊Dic53—21no—
117C2×C4⋊Dic53—21no—
118C2×C4⋊Dic53C2311yescharacteristic
119C2×C4⋊Dic53C2311yescharacteristic
120C2×C4⋊Dic53C2311yescharacteristic
121C2×C4⋊Dic53C2311yescharacteristic
122C2×#11719919—21no—
123C2×#11719919—21no—
124C2×#11719919—21no—
125C2×#11719919—21no—
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919D411yescharacteristic
131C2×#11719919D411yescharacteristic
132C4⋊C4×D53—22no—
133C4⋊C4×D53—22no—
134C4⋊C4×D53C2314yes—
135C4⋊C4×D53C2314yes—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921D411yescharacteristic
139C2×#11719921D411yescharacteristic
140C2×C4×Dic53—21no—
141C2×C4×Dic53—21no—
142C2×C4×Dic53C2311yescharacteristic
143#13133151C2314yes—
144#13133151C2314yes—
145#13133150C2314yes—
146#13133150C2314yes—
147#13133149C2314yes—
148#13133149C2314yes—
149#13133148C2314yes—
150#13133148C2314yes—
151#13133148C2314yes—
152#13133148C2314yes—
153#13133148C2314yes—
154#13133148C2314yes—
155#13133127C2314yes—
156C4×#88322C2314yes—
157C8×Dic53C2314yes—
158C22×Q8×C53—21no—
159C22×C8×C53C2311yescharacteristic
160C22×C8×C53C2311yescharacteristic
161C4⋊Q8×C53—22no—
162C4⋊Q8×C53C2314yes—
163#125×C53—22no—
164#125×C53C2314yes—
165C2×C4⋊C4×C53—21no—
166C2×C4⋊C4×C53—21no—
167C2×C4⋊C4×C53—21no—
168C2×C4⋊C4×C53C2311yescharacteristic
169C2×C4⋊C4×C53C2311yescharacteristic
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C42×C53C2311yescharacteristic
173#107×C53C2314yes—
174#107×C53C2314yes—
175#106×C53C2314yes—
176#106×C53C2314yes—
177#97×C53C2314yes—
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×Dic53—21no—
191C22×Dic53—21no—
192C22×Dic53C2×D411yescharacteristic
193C22×Dic53C2×D411yescharacteristic
194C22×Dic53C2×D411yescharacteristic
195C2×C4×D53—24no—
196C2×C4×D53—24no—
197C2×C4×D53—82no—
198C2×C4×D53—82no—
199C2×C4×D53C2×D412yes—
200C2×C4×D53C2×Q814yes—
201C2×C4×D53C2×Q814yes—
202C2×C4×D53C2412yes—
203C2×Dic106—24no—
204C2×Dic106—24no—
205C2×Dic106—24no—
206C2×Dic106—82no—
207C2×Dic106—82no—
208C2×Dic106—82no—
209C2×C8×C53C2×Q814yes—
210C2×C8×C53C2×Q814yes—
211C2×C8×C53C2412yes—
212C2×C8×C53C2412yes—
213C4⋊C4×C53—24no—
214C4⋊C4×C53—24no—
215C4⋊C4×C53—24no—
216C4⋊C4×C53—21no—
217C4⋊C4×C53—21no—
218C4⋊C4×C53—21no—
219C4⋊C4×C53—21no—
220C4⋊C4×C53C2412yes—
221C4⋊C4×C53C2412yes—
222C4⋊C4×C53C2412yes—
223C4⋊C4×C53C2412yes—
224C42×C53C2×D412yes—
225C42×C53C2412yes—
226#11719921—24no—
227#11719921—24no—
228#11719921C2×D414yes—
229#11719921C2×D414yes—
230C4⋊Dic53—21no—
231C4⋊Dic53—21no—
232C4⋊Dic53—24no—
233C4⋊Dic53—21no—
234C4⋊Dic53—21no—
235C4⋊Dic53—24no—
236C4⋊Dic53—24no—
237C4⋊Dic53C2412yes—
238C4⋊Dic53C2412yes—
239C4⋊Dic53C2412yes—
240C4⋊Dic53C2412yes—
241#11719919—24no—
242#11719919—24no—
243#11719919—24no—
244#11719919—24no—
245#11719919—24no—
246#11719919—24no—
247#11719919—24no—
248#11719919—24no—
249#11719919C2×D414yes—
250#11719919C2×D414yes—
251C4×Dic53—24no—
252C4×Dic53—24no—
253C4×Dic53C2×D412yes—
254C4×Dic53C2412yes—
255C2×#88322C2×Q814yes—
256C2×#88322C2×Q814yes—
257C2×#88322C2412yes—
258C2×#88322C2412yes—
259#11719912C2×Q8116yescomplemented
260C8×D53C2×Q8116yescomplemented
261C23×C53C22×D411yescharacteristic
262C22×D53—22no—
263C22×D53—22no—
264C22×D53C4⋊Q814yes—
265C22×D53C22×D412yes—
266Q8×C53—84no—
267C2×C4×C53—22no—
268C2×C4×C53—22no—
269C2×C4×C53—22no—
270C2×C4×C53—22no—
271C2×C4×C53—22no—
272C2×C4×C53—22no—
273C2×C4×C53—42no—
274C2×C4×C53—42no—
275C2×C4×C53—42no—
276C2×C4×C53—42no—
277C2×C4×C53C22×D412yes—
278C2×C4×C53C22×D412yes—
279C2×C4×C53C22×D411yescharacteristic
280C2×C4×C53C22×Q812yes—
281C2×C4×C53C22×Q812yes—
282C2×C4×C53C2511yescharacteristic
283C2×Dic53—22no—
284C2×Dic53—22no—
285C2×Dic53—22no—
286C2×Dic53—22no—
287C2×Dic53—22no—
288C2×Dic53—22no—
289C2×Dic53—42no—
290C2×Dic53—42no—
291C2×Dic53—42no—
292C2×Dic53—42no—
293C2×Dic53C4⋊Q814yes—
294C2×Dic53C22×D412yes—
295C2×Dic53C22×D412yes—
296C2×Dic53C22×D412yes—
297C4×D53—84no—
298C4×D53—84no—
299C4×D53C4⋊Q818yes—
300C4×D53C22×Q814yes—
301C4×D53C22×Q814yes—
302Dic106—84no—
303Dic106—84no—
304Dic106—84no—
305C8×C53C22×Q814yes—
306C8×C53C22×Q814yes—
307#88322C22×Q814yes—
308#88322C22×Q814yes—
309C2×#3163—531nomaximal, Sylow
310C22×C53C2×C4⋊Q812yes—
311C22×C53#57712yes—
312C22×C53#57712yes—
313C22×C53C23×D411yescharacteristic
314C2×D53—28no—
315C2×D53—22no—
316C2×D53—22no—
317C2×D53C2×C4⋊Q814yes—
318C4×C53—22no—
319C4×C53—22no—
320C4×C53—42no—
321C4×C53—42no—
322C4×C53—42no—
323C4×C53—42no—
324C4×C53C2×C4⋊Q812yes—
325C4×C53C23×Q811yescharacteristic
326C4×C53C23×Q811yescharacteristic
327Dic53—22no—
328Dic53—22no—
329Dic53—42no—
330Dic53—42no—
331Dic53—42no—
332Dic53—42no—
333Dic53C2×C4⋊Q814yes—
334C2×#544—531no—
335C2×#544—531no—
336#3163—5316no—
337C2×#501—531no—
338C2×#501—531no—
339C2×#501—531no—
340C2×#501D5311yescharacteristic, complemented
341C2×#499—531no—
342C2×#499—531no—
343C2×#498—531no—
344C2×#498—531no—
345C2×#428—531no—
346C2×#428—531no—
347C2×#427—531no—
348C22×#106—531no—
349C2×#405—531no—
350C2×C53#316314yescomplemented
351C2×C53C22×C4⋊Q811yescharacteristic
352C2×C53C2×#57711yescharacteristic
353C2×C53C2×#57711yescharacteristic
354D53—24no—
355C22×M16—531no—
356C23×C8—531no—
357#544—538no—
358#544—538no—
359#544—1064no—
360#544—1064no—
361C2×C4⋊Q8—531no—
362C2×C4⋊Q8—531no—
363C2×C4⋊Q8—531no—
364C2×C4⋊Q8—1061no—
365C2×C4⋊Q8—1061no—
366C2×C4⋊Q8C2×D5311yescharacteristic
367C2×#125—531no—
368C2×#125—531no—
369C2×#125—531no—
370C2×#125—1061no—
371C2×#125—1061no—
372C2×#125C2×D5311yescharacteristic
373C2×C22⋊Q8—1061no—
374C2×C22⋊Q8—1061no—
375C2×C22⋊Q8—1061no—
376C2×C22⋊Q8—1061no—
377C2×#117—531no—
378C2×#117—531no—
379C2×#117—531no—
380C22×C4⋊C4—531no—
381C22×C4⋊C4—531no—
382#501—538no—
383#501—538no—
384#501—538no—
385#501C2×D5318yescomplemented
386#499—538no—
387#499—538no—
388#498—538no—
389#498—538no—
390#428—538no—
391#428—538no—
392#427—538no—
393C2×#107—531no—
394C2×#107—531no—
395C2×#107—531no—
396C2×#107—531no—
397C2×#107C2×D5311yescharacteristic
398C2×#107C2×D5311yescharacteristic
399C2×#106—531no—
400C2×#106—531no—
401C2×#106—531no—
402C2×#106—531no—
403C2×#106—531no—
404C2×#106—531no—
405C2×#106—531no—
406C2×#106—531no—
407C2×#106—538no—
408C2×#106C2×D5311yescharacteristic
409C2×#106C2×D5311yescharacteristic
410#405—538no—
411C2×#97—531no—
412C2×#97C2×D5311yescharacteristic
413C2×C4×C8—531no—
414C2×C4×C8—531no—
415C53C2×#316311yescharacteristic, complemented, Sylow
416C22×Q8—21no—
417C22×Q8—1061no—
418C22×Q8—1061no—
419C22×Q8—1061no—
420C23×C4—531no—
421C23×C4—1061no—
422C23×C4—1061no—
423C2×M16—538no—
424C2×M16—534no—
425C22×C8—531no—
426C22×C8—531no—
427C22×C8—538no—
428C22×C8—534no—
429C22×C8C22×D5311yescharacteristic
430C22×C8C22×D5311yescharacteristic
431C4⋊Q8—22no—
432C4⋊Q8—534no—
433C4⋊Q8—534no—
434C4⋊Q8—534no—
435C4⋊Q8—1062no—
436C4⋊Q8—1062no—
437C4⋊Q8—1068no—
438C4⋊Q8—1068no—
439C4⋊Q8—1062no—
440C4⋊Q8C22×D5314yes—
441#125—22no—
442#125—534no—
443#125—534no—
444#125—534no—
445#125—1062no—
446#125—1062no—
447#125—1068no—
448#125—1068no—
449#125—1062no—
450#125C22×D5314yes—
451C22⋊Q8—1068no—
452C22⋊Q8—1068no—
453C22⋊Q8—1068no—
454C22⋊Q8—1068no—
455#117—534no—
456#117—534no—
457#117—534no—
458#117—534no—
459#117—1062no—
460#117—1062no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—531no—
465C2×C4⋊C4—531no—
466C2×C4⋊C4—531no—
467C2×C4⋊C4—531no—
468C2×C4⋊C4—531no—
469C2×C4⋊C4—531no—
470C2×C4⋊C4—534no—
471C2×C4⋊C4—534no—
472C2×C4⋊C4—1062no—
473C2×C4⋊C4—1062no—
474C2×C4⋊C4—1061no—
475C2×C4⋊C4—1061no—
476C2×C4⋊C4—1061no—
477C2×C4⋊C4—1061no—
478C2×C4⋊C4—1061no—
479C2×C4⋊C4—1061no—
480C2×C4⋊C4—1061no—
481C2×C4⋊C4—1061no—
482C2×C4⋊C4—1061no—
483C2×C4⋊C4—1061no—
484C2×C4⋊C4—1061no—
485C2×C4⋊C4C22×D5311yescharacteristic
486C2×C4⋊C4C22×D5311yescharacteristic
487C2×C4⋊C4C22×D5311yescharacteristic
488C2×C4⋊C4C22×D5311yescharacteristic
489C2×C22⋊C4—531no—
490C2×C22⋊C4—531no—
491C2×C22⋊C4—1061no—
492C2×C22⋊C4—1061no—
493C2×C42—531no—
494C2×C42—1061no—
495C2×C42—1061no—
496C2×C42C22×D5311yescharacteristic
497#107—534no—
498#107—534no—
499#107—534no—
500#107—534no—
501#107C22×D5314yes—
502#107C22×D5314yes—
503#106—534no—
504#106—534no—
505#106—534no—
506#106—534no—
507#106—534no—
508#106—534no—
509#106—534no—
510#106—534no—
511#106C22×D5314yes—
512#106C22×D5314yes—
513#97—534no—
514#97C22×D5314yes—
515C4×C8—534no—
516C4×C8—534no—
517C24—531no—
518C2×Q8—24no—
519C2×Q8—82no—
520C2×Q8—1064no—
521C2×Q8—1064no—
522C2×Q8—1064no—
523C2×Q8—4242no—
524C2×Q8—4242no—
525C2×Q8—4242no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—531no—
531C22×C4—532no—
532C22×C4—534no—
533C22×C4—534no—
534C22×C4—532no—
535C22×C4—531no—
536C22×C4—531no—
537C22×C4—1064no—
538C22×C4—1064no—
539C22×C4—1061no—
540C22×C4—1061no—
541C22×C4—1061no—
542C22×C4—1061no—
543C22×C4—4242no—
544C22×C4—4242no—
545C22×C4D4×D5311yescharacteristic
546C22×C4D4×D5311yescharacteristic
547C22×C4C23×D5311yescharacteristic
548M16—5316no—
549C2×C8—534no—
550C2×C8—534no—
551C2×C8—532no—
552C2×C8—532no—
553C2×C8—5316no—
554C2×C8Q8×D5314yes—
555C2×C8Q8×D5314yes—
556C2×C8C23×D5312yes—
557C2×C8C23×D5312yes—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—534no—
566C4⋊C4—534no—
567C4⋊C4—532no—
568C4⋊C4—532no—
569C4⋊C4—532no—
570C4⋊C4—532no—
571C4⋊C4—1064no—
572C4⋊C4—1064no—
573C4⋊C4—1064no—
574C4⋊C4—1064no—
575C4⋊C4—1064no—
576C4⋊C4—1064no—
577C4⋊C4—1064no—
578C4⋊C4—1064no—
579C4⋊C4—1061no—
580C4⋊C4—1061no—
581C4⋊C4—1061no—
582C4⋊C4—1061no—
583C4⋊C4—1064no—
584C4⋊C4—1064no—
585C4⋊C4—1064no—
586C4⋊C4C23×D5312yes—
587C4⋊C4C23×D5312yes—
588C4⋊C4C23×D5312yes—
589C4⋊C4C23×D5312yes—
590C22⋊C4—534no—
591C22⋊C4—534no—
592C22⋊C4—1064no—
593C22⋊C4—1064no—
594C42—532no—
595C42—532no—
596C42—1064no—
597C42—1064no—
598C42D4×D5312yes—
599C42C23×D5312yes—
600C23—534no—
601C23—532no—
602C23—1062no—
603C23—1062no—
604C23C2×D4×D5311yescharacteristic
605Q8—84no—
606Q8—4244no—
607Q8—4244no—
608Q8—4244no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—534no—
620C2×C4—532no—
621C2×C4—538no—
622C2×C4—534no—
623C2×C4—534no—
624C2×C4—532no—
625C2×C4—532no—
626C2×C4—1062no—
627C2×C4—1062no—
628C2×C4—1062no—
629C2×C4—1062no—
630C2×C4—1062no—
631C2×C4—1062no—
632C2×C4—4244no—
633C2×C4—4244no—
634C2×C4—2122no—
635C2×C4—2122no—
636C2×C4—2122no—
637C2×C4—2122no—
638C2×C4C2×D4×D5312yes—
639C2×C4C2×D4×D5312yes—
640C2×C4C2×D4×D5311yescharacteristic
641C2×C4C2×Q8×D5312yes—
642C2×C4C2×Q8×D5312yes—
643C2×C4C24×D5311yescharacteristic
644C8—534no—
645C8—534no—
646C8C2×Q8×D5314yes—
647C8C2×Q8×D5314yes—
648C22—534no—
649C22—1068no—
650C22—1062no—
651C22—1062no—
652C22C4⋊Q8×D5312yes—
653C22#1681143212yes—
654C22#1681143312yes—
655C22C22×D4×D5311yescharacteristic
656C4—22no—
657C4—22no—
658C4—42no—
659C4—42no—
660C4—42no—
661C4—42no—
662C4—534no—
663C4—1062no—
664C4—1062no—
665C4—2122no—
666C4—2122no—
667C4—2122no—
668C4—2122no—
669C4C4⋊Q8×D5312yes—
670C4C22×Q8×D5311yescharacteristic
671C4C22×Q8×D5311yescharacteristic
672C2—1064no—
673C2#2028524214yesdirect product factor
674C2C2×C4⋊Q8×D5311yescharacteristic
675C2C2×#1681143211yescharacteristic
676C2C2×#1681143311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#501C2
socleC23×C53C22×D4
prime radicalC23×D53C2×D4
hypercenterC2×#501D53
hypocenterC53C2×#3163
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
3. #20285242C2direct (N × H)
4. C2×#16811032C2semidirect
5. C2×#16811031C2semidirect
6. C2×#16811030C2semidirect
7. C2×#16811024C2semidirect
8. C2×#16811022C2semidirect
9. C2×#16811020C2semidirect
10. C2×#16811019C2semidirect
16. C2×C53×#501C2semidirect
42. #16811032C22semidirect
43. #16811031C22semidirect
44. #16811030C22semidirect
45. #16811024C22semidirect
46. #16811022C22semidirect
47. #16811020C22semidirect
48. #16811019C22semidirect
71. C53×#501C22semidirect
83. C2×#11719912Q8semidirect
87. C2×C8×D53Q8semidirect
259. #11719912C2×Q8semidirect
260. C8×D53C2×Q8semidirect
340. C2×#501D53semidirect
350. C2×C53#3163semidirect
385. #501C2×D53semidirect
415. C53C2×#3163semidirect
673. C2#20285242direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112532
C2×#168112502
#202852422
C2×#168110322
C2×#168110312
C2×#168110302
C2×#168110242
C2×#168110222
C2×#168110202
C2×#168110192
C2×#168106642
C2×#168106622
C2×#168106602
C2×#106×D532
C2×#168105802
C2×C53×#5012
C2×#316353