Finite Group Databasebeta

← C2×#20284554 #28251660

Subgroups — C2×#20284554 #28251660

Order 13568.

2018 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811253C211yesmaximal, characteristic
2C2×#16811099C211yesmaximal, characteristic
3#20284554C2116yesmaximal, direct product factor
4C2×#16810933C211yesmaximal, characteristic, complemented
5C2×#16810928C211yesmaximal, characteristic, complemented
6C2×#16810927C211yesmaximal, characteristic, complemented
7C2×#16810918C211yesmaximal, characteristic, complemented
8C2×#16810917C211yesmaximal, characteristic, complemented
9C2×#16810909C211yesmaximal, characteristic, complemented
10C2×#16810906C211yesmaximal, characteristic, complemented
11C2×#16810664C211yesmaximal, characteristic
12C2×#16810658C211yesmaximal, characteristic
13C2×#16810648C211yesmaximal, characteristic
14C2×#16810630C211yesmaximal, characteristic
15C2×#103×D53C211yesmaximal, characteristic
16C2×C53×#479C211yesmaximal, characteristic, complemented
17C22×Q8×D53C2211yescharacteristic
18C22×#11719912C2211yescharacteristic
19C22×C8×D53C2211yescharacteristic
20#16811253—24no—
21#16811253C2218yes—
22C2×#13133217C2211yescharacteristic
23C2×#13133216—21no—
24C2×#13133216C2211yescharacteristic
25C2×#13133208C2211yescharacteristic
26C2×#13133207—21no—
27C2×#13133197—21no—
28C2×#13133195—21no—
29#16811099—24no—
30#16811099C2218yes—
31C2×Q8×Dic53C2211yescharacteristic
32C2×C4×Dic106—21no—
33C2×C4×Dic106C2211yescharacteristic
34C2×#13133182—21no—
35C2×#13133182C2211yescharacteristic
36C2×#13133175—21no—
37C2×#13133175C2211yescharacteristic
38C2×#13133175C2211yescharacteristic
39C2×#13133174—21no—
40C2×#13133174C2211yescharacteristic
41C2×C4⋊C4×D53C2211yescharacteristic
42#16810933C2218yescomplemented
43#16810928C2218yescomplemented
44#16810927C2218yescomplemented
45#16810918C2218yescomplemented
46#16810917C2218yescomplemented
47#16810909C2218yescomplemented
48#16810906C2218yescomplemented
49#16810664C2218yes—
50#16810658C2218yes—
51C2×#13133150C2211yescharacteristic
52C2×#13133150C2211yescharacteristic
53C2×#13133150C2211yescharacteristic
54C2×#13133149C2211yescharacteristic
55C2×#13133149C2211yescharacteristic
56C2×#13133148C2211yescharacteristic
57#16810648C2218yes—
58C2×C4⋊#88322C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133146C2211yescharacteristic
61#16810630C2218yes—
62C2×#13133142C2211yescharacteristic
63C2×#13133142C2211yescharacteristic
64C2×#13133141C2211yescharacteristic
65C2×#13133141C2211yescharacteristic
66C2×#13133140C2211yescharacteristic
67C2×#13133140C2211yescharacteristic
68#103×D53C2218yes—
69C2×#125×C53C2211yescharacteristic
70C2×C4×Q8×C53C2211yescharacteristic
71C53×#479C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#103×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106—21no—
79C22×Dic106—21no—
80C22×Dic106C2311yescharacteristic
81C2×Q8×D53—22no—
82C2×Q8×D53—24no—
83C2×Q8×D53Q818yescomplemented
84C2×Q8×D53C2314yes—
85C22×C4×D53—21no—
86C22×C4×D53—21no—
87C22×C4×D53C2311yescharacteristic
88C2×#11719912—24no—
89C2×#11719912C2314yes—
90C22×#88322C2311yescharacteristic
91C22×#88322C2311yescharacteristic
92C2×C8×D53—24no—
93C2×C8×D53C2314yes—
94#13133217—22no—
95#13133217C2314yes—
96#13133216—28no—
97#13133216—22no—
98#13133216C2314yes—
99#13133208—22no—
100#13133208C2314yes—
101#13133207—28no—
102#13133197—28no—
103#13133195—28no—
104Q8×Dic53—22no—
105Q8×Dic53C2314yes—
106C4×Dic106—22no—
107C4×Dic106—28no—
108C4×Dic106C2314yes—
109#13133182—28no—
110#13133182—22no—
111#13133182C2314yes—
112#13133175—28no—
113#13133175—22no—
114#13133175—22no—
115#13133175C2314yes—
116#13133175C2314yes—
117#13133174—28no—
118#13133174D414yes—
119#13133174C2314yes—
120C2×C4⋊Dic53—21no—
121C2×C4⋊Dic53—21no—
122C2×C4⋊Dic53—21no—
123C2×C4⋊Dic53C2311yescharacteristic
124C2×C4⋊Dic53C2311yescharacteristic
125C2×C4⋊Dic53C2311yescharacteristic
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919D411yescharacteristic
132C2×#11719919D411yescharacteristic
133C4⋊C4×D53—22no—
134C4⋊C4×D53C2314yes—
135C2×#11719921—21no—
136C2×#11719921—21no—
137C2×#11719921D411yescharacteristic
138C2×#11719921D411yescharacteristic
139C2×C4×Dic53—21no—
140C2×C4×Dic53—21no—
141C2×C4×Dic53—21no—
142C2×C4×Dic53—21no—
143C2×C4×Dic53—21no—
144C2×C4×Dic53C2311yescharacteristic
145#13133150C2314yes—
146#13133150C2314yes—
147#13133150C2314yes—
148#13133149C2314yes—
149#13133149C2314yes—
150#13133148C2314yes—
151C4⋊#88322C2314yes—
152#13133146C2314yes—
153#13133146C2314yes—
154#13133142C2314yes—
155#13133142C2314yes—
156#13133141C2314yes—
157#13133141C2314yes—
158#13133140C2314yes—
159#13133140C2314yes—
160C22×Q8×C53C2311yescharacteristic
161C22×C8×C53C2311yescharacteristic
162C22×C8×C53C2311yescharacteristic
163#125×C53—22no—
164#125×C53C2314yes—
165C4×Q8×C53—22no—
166C4×Q8×C53C2314yes—
167C2×C4⋊C4×C53—21no—
168C2×C4⋊C4×C53—21no—
169C2×C4⋊C4×C53—21no—
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C42×C53—21no—
174C2×C42×C53C2311yescharacteristic
175#107×C53C2314yes—
176#106×C53C2314yes—
177C4⋊C8×C53C2314yes—
178#103×C53C2314yes—
179#103×C53C2314yes—
180C23×D53C2×D411yescharacteristic
181C2×Q8×C53—21no—
182C2×Q8×C53—22no—
183C2×Q8×C53C2×Q814yes—
184C2×Q8×C53C2412yes—
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53C2×D411yescharacteristic
190C22×C4×C53C2×D411yescharacteristic
191C22×C4×C53C2411yescharacteristic
192C22×Dic53—21no—
193C22×Dic53—21no—
194C22×Dic53—21no—
195C22×Dic53—21no—
196C22×Dic53C2×D411yescharacteristic
197C22×Dic53C2×D411yescharacteristic
198C22×Dic53C2×D411yescharacteristic
199Q8×D53—216no—
200Q8×D53—28no—
201Q8×D53C2×Q8116yescomplemented
202C2×C4×D53—28no—
203C2×C4×D53—24no—
204C2×C4×D53—24no—
205C2×C4×D53—82no—
206C2×C4×D53C2×D412yes—
207C2×C4×D53C2×Q814yes—
208C2×C4×D53#4114yes—
209C2×C4×D53C2412yes—
210C2×Dic106—21no—
211C2×Dic106—22no—
212C2×Dic106—28no—
213C2×Dic106—24no—
214C2×Dic106—24no—
215C2×Dic106—24no—
216C2×Dic106—82no—
217C2×Dic106—82no—
218C2×Dic106C2×Q814yes—
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—21no—
228C4⋊C4×C53—21no—
229C4⋊C4×C53—21no—
230C4⋊C4×C53C2412yes—
231C4⋊C4×C53C2412yes—
232C4⋊C4×C53C2412yes—
233C42×C53—24no—
234C42×C53C2×D412yes—
235C42×C53C2412yes—
236#11719921—24no—
237#11719921—24no—
238#11719921C2×D414yes—
239#11719921C2×D414yes—
240C4⋊Dic53—21no—
241C4⋊Dic53—24no—
242C4⋊Dic53—21no—
243C4⋊Dic53—21no—
244C4⋊Dic53—24no—
245C4⋊Dic53—24no—
246C4⋊Dic53C2412yes—
247C4⋊Dic53C2412yes—
248C4⋊Dic53C2412yes—
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×Dic53—24no—
260C4×Dic53—24no—
261C4×Dic53C2×D412yes—
262C4×Dic53C2412yes—
263C2×#88322—22no—
264C2×#88322—22no—
265C2×#88322C2412yes—
266C2×#88322C2412yes—
267#11719912—28no—
268C8×D53—28no—
269C23×C53C22×D411yescharacteristic
270C22×D53—22no—
271C22×D53—22no—
272C22×D53C22⋊Q814yes—
273C22×D53C22×D412yes—
274Q8×C53—24no—
275Q8×C53—22no—
276Q8×C53C22×Q814yes—
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×C53C22×Q812yes—
291C2×C4×C53C2×#4112yes—
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—42no—
303C2×Dic53C22⋊Q814yes—
304C2×Dic53C22×D412yes—
305C2×Dic53C22×D412yes—
306C2×Dic53C22×D412yes—
307C4×D53—216no—
308C4×D53—84no—
309C4×D53C22⋊Q818yes—
310C4×D53C22×Q814yes—
311C4×D53C2×#4114yes—
312Dic106—24no—
313Dic106—22no—
314Dic106—216no—
315Dic106—84no—
316Dic106—84no—
317Dic106C22×Q814yes—
318C8×C53—22no—
319C8×C53—22no—
320#88322—22no—
321#88322—22no—
322C2×#3082—531nomaximal, Sylow
323C22×C53C2×C22⋊Q812yes—
324C22×C53#57712yes—
325C22×C53#57812yes—
326C22×C53C23×D411yescharacteristic
327C2×D53—28no—
328C2×D53—22no—
329C2×D53—22no—
330C2×D53C2×C22⋊Q814yes—
331C4×C53—24no—
332C4×C53—22no—
333C4×C53—22no—
334C4×C53—42no—
335C4×C53—42no—
336C4×C53—42no—
337C4×C53C2×C22⋊Q812yes—
338C4×C53C23×Q811yescharacteristic
339C4×C53C22×#4111yescharacteristic
340Dic53—24no—
341Dic53—22no—
342Dic53—22no—
343Dic53—42no—
344Dic53—42no—
345Dic53—42no—
346Dic53C2×C22⋊Q814yes—
347C2×#544—531no—
348C2×#519—531no—
349#3082—5316no—
350C2×#479—531no—
351C2×#479—531no—
352C2×#479—531no—
353C2×#479D5311yescharacteristic, complemented
354C2×#477—531no—
355C2×#477—531no—
356C2×#475—531no—
357C2×#475—531no—
358C2×#428—531no—
359C2×#427—531no—
360C2×#424—531no—
361C2×#419—531no—
362C22×#103—531no—
363C2×C53#308214yescomplemented
364C2×C53C22×C22⋊Q811yescharacteristic
365C2×C53C2×#57711yescharacteristic
366C2×C53C2×#57811yescharacteristic
367D53—24no—
368C23×Q8—531no—
369C22×M16—531no—
370C23×C8—531no—
371#544—538no—
372#544—1064no—
373C2×C4⋊Q8—531no—
374C2×C4⋊Q8—531no—
375C2×C4⋊Q8—1061no—
376C2×#125—531no—
377C2×#125—1061no—
378C2×#125C2×D5311yescharacteristic
379C2×C22⋊Q8—1061no—
380C2×C22⋊Q8—1061no—
381#519—538no—
382#519—1064no—
383C2×C4×Q8—531no—
384C2×C4×Q8—531no—
385C2×C4×Q8—531no—
386C2×C4×Q8—1061no—
387C2×C4×Q8—1061no—
388C2×C4×Q8C2×D5311yescharacteristic
389C2×#117—531no—
390C2×#117—531no—
391C2×#117—531no—
392C2×#117—1061no—
393C2×#117—1061no—
394C22×C4⋊C4—531no—
395#479—538no—
396#479—538no—
397#479—538no—
398#479C2×D5318yescomplemented
399#477—538no—
400#477—538no—
401#475—538no—
402#475—538no—
403#428—538no—
404#427—538no—
405C2×#107—531no—
406C2×#107—531no—
407C2×#107—531no—
408C2×#107C2×D5311yescharacteristic
409C2×#106—531no—
410C2×#106—531no—
411C2×#106—531no—
412C2×#106C2×D5311yescharacteristic
413#424—538no—
414C2×C4⋊C8—531no—
415C2×C4⋊C8—531no—
416C2×C4⋊C8—531no—
417C2×C4⋊C8C2×D5311yescharacteristic
418#419—538no—
419C2×#103—531no—
420C2×#103—531no—
421C2×#103—531no—
422C2×#103—531no—
423C2×#103—531no—
424C2×#103—531no—
425C2×#103—538no—
426C2×#103C2×D5311yescharacteristic
427C2×#103C2×D5311yescharacteristic
428C53C2×#308211yescharacteristic, complemented, Sylow
429C22×Q8—538no—
430C22×Q8—534no—
431C22×Q8—531no—
432C22×Q8—1061no—
433C22×Q8—1061no—
434C22×Q8—1062no—
435C22×Q8—1064no—
436C22×Q8—1061no—
437C22×Q8C22×D5311yescharacteristic
438C23×C4—531no—
439C23×C4—1061no—
440C23×C4—1061no—
441C2×M16—534no—
442C2×M16—1064no—
443C22×C8—531no—
444C22×C8—531no—
445C22×C8—534no—
446C22×C8—1064no—
447C22×C8C22×D5311yescharacteristic
448C22×C8C22×D5311yescharacteristic
449C4⋊Q8—534no—
450C4⋊Q8—534no—
451C4⋊Q8—1062no—
452C4⋊Q8—1068no—
453C4⋊Q8—1062no—
454#125—22no—
455#125—534no—
456#125—1062no—
457#125—1068no—
458#125C22×D5314yes—
459C22⋊Q8—1068no—
460C22⋊Q8—1068no—
461C4×Q8—22no—
462C4×Q8—534no—
463C4×Q8—534no—
464C4×Q8—534no—
465C4×Q8—1068no—
466C4×Q8—1062no—
467C4×Q8—1062no—
468C4×Q8—1068no—
469C4×Q8—1062no—
470C4×Q8C22×D5314yes—
471#117—534no—
472#117—534no—
473#117—534no—
474#117—534no—
475#117—1068no—
476#117—1068no—
477#117—1062no—
478#117—1062no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—531no—
483C2×C4⋊C4—531no—
484C2×C4⋊C4—531no—
485C2×C4⋊C4—531no—
486C2×C4⋊C4—531no—
487C2×C4⋊C4—534no—
488C2×C4⋊C4—1062no—
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⋊C4—1061no—
496C2×C4⋊C4—1061no—
497C2×C4⋊C4C22×D5311yescharacteristic
498C2×C4⋊C4C22×D5311yescharacteristic
499C2×C4⋊C4C22×D5311yescharacteristic
500C2×C22⋊C4—531no—
501C2×C22⋊C4—531no—
502C2×C22⋊C4—1061no—
503C2×C22⋊C4—1061no—
504C2×C42—21no—
505C2×C42—531no—
506C2×C42—1061no—
507C2×C42—1061no—
508C2×C42—1061no—
509C2×C42—1061no—
510C2×C42—1061no—
511C2×C42C22×D5311yescharacteristic
512#107—534no—
513#107—534no—
514#107—534no—
515#107C22×D5314yes—
516#106—534no—
517#106—534no—
518#106—534no—
519#106C22×D5314yes—
520C4⋊C8—534no—
521C4⋊C8—534no—
522C4⋊C8—534no—
523C4⋊C8C22×D5314yes—
524#103—534no—
525#103—534no—
526#103—534no—
527#103—534no—
528#103—534no—
529#103—534no—
530#103C22×D5314yes—
531#103C22×D5314yes—
532C24—531no—
533C2×Q8—21no—
534C2×Q8—22no—
535C2×Q8—5316no—
536C2×Q8—534no—
537C2×Q8—532no—
538C2×Q8—1064no—
539C2×Q8—1068no—
540C2×Q8—1064no—
541C2×Q8—10616no—
542C2×Q8—1068no—
543C2×Q8—1061no—
544C2×Q8—1064no—
545C2×Q8—1062no—
546C2×Q8—4242no—
547C2×Q8—4242no—
548C2×Q8Q8×D5314yes—
549C2×Q8C23×D5312yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—531no—
555C22×C4—532no—
556C22×C4—534no—
557C22×C4—534no—
558C22×C4—532no—
559C22×C4—531no—
560C22×C4—531no—
561C22×C4—1064no—
562C22×C4—1068no—
563C22×C4—1064no—
564C22×C4—1061no—
565C22×C4—1061no—
566C22×C4—1061no—
567C22×C4—1061no—
568C22×C4—4242no—
569C22×C4D4×D5311yescharacteristic
570C22×C4D4×D5311yescharacteristic
571C22×C4C23×D5311yescharacteristic
572M16—1068no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—532no—
576C2×C8—532no—
577C2×C8—1068no—
578C2×C8—1062no—
579C2×C8—1062no—
580C2×C8C23×D5312yes—
581C2×C8C23×D5312yes—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—534no—
589C4⋊C4—534no—
590C4⋊C4—532no—
591C4⋊C4—532no—
592C4⋊C4—532no—
593C4⋊C4—1064no—
594C4⋊C4—1064no—
595C4⋊C4—1064no—
596C4⋊C4—1064no—
597C4⋊C4—1064no—
598C4⋊C4—1064no—
599C4⋊C4—1061no—
600C4⋊C4—1061no—
601C4⋊C4—1061no—
602C4⋊C4—1064no—
603C4⋊C4—1064no—
604C4⋊C4C23×D5312yes—
605C4⋊C4C23×D5312yes—
606C4⋊C4C23×D5312yes—
607C22⋊C4—534no—
608C22⋊C4—534no—
609C22⋊C4—1064no—
610C22⋊C4—1064no—
611C42—24no—
612C42—532no—
613C42—532no—
614C42—1064no—
615C42—1064no—
616C42—1064no—
617C42—1064no—
618C42—1064no—
619C42D4×D5312yes—
620C42C23×D5312yes—
621C23—534no—
622C23—532no—
623C23—1062no—
624C23—1062no—
625C23C2×D4×D5311yescharacteristic
626Q8—24no—
627Q8—22no—
628Q8—534no—
629Q8—10616no—
630Q8—1064no—
631Q8—1062no—
632Q8—4244no—
633Q8—4244no—
634Q8C2×Q8×D5314yes—
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—538no—
648C2×C4—534no—
649C2×C4—534no—
650C2×C4—532no—
651C2×C4—532no—
652C2×C4—10616no—
653C2×C4—1064no—
654C2×C4—1062no—
655C2×C4—1062no—
656C2×C4—1062no—
657C2×C4—1062no—
658C2×C4—1062no—
659C2×C4—1062no—
660C2×C4—4244no—
661C2×C4—2122no—
662C2×C4—2122no—
663C2×C4—2122no—
664C2×C4C2×D4×D5312yes—
665C2×C4C2×D4×D5312yes—
666C2×C4C2×D4×D5311yescharacteristic
667C2×C4C2×Q8×D5312yes—
668C2×C4#41×D5312yes—
669C2×C4C24×D5311yescharacteristic
670C8—22no—
671C8—22no—
672C8—1062no—
673C8—1062no—
674C22—534no—
675C22—1068no—
676C22—1062no—
677C22—1062no—
678C22C22⋊Q8×D5312yes—
679C22#1681143012yes—
680C22#1681143912yes—
681C22C22×D4×D5311yescharacteristic
682C4—22no—
683C4—24no—
684C4—22no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—534no—
689C4—1062no—
690C4—1064no—
691C4—1062no—
692C4—2122no—
693C4—2122no—
694C4—2122no—
695C4C22⋊Q8×D5312yes—
696C4C22×Q8×D5311yescharacteristic
697C4C2×#41×D5311yescharacteristic
698C2—1064no—
699C2#2028455414yesdirect product factor
700C2C2×C22⋊Q8×D5311yescharacteristic
701C2C2×#1681143011yescharacteristic
702C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#479C2
socleC23×C53C22×D4
prime radicalC23×D53C2×D4
hypercenterC2×#479D53
hypocenterC53C2×#3082
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
3. #20284554C2direct (N × H)
4. C2×#16810933C2semidirect
5. C2×#16810928C2semidirect
6. C2×#16810927C2semidirect
7. C2×#16810918C2semidirect
8. C2×#16810917C2semidirect
9. C2×#16810909C2semidirect
10. C2×#16810906C2semidirect
16. C2×C53×#479C2semidirect
42. #16810933C22semidirect
43. #16810928C22semidirect
44. #16810927C22semidirect
45. #16810918C22semidirect
46. #16810917C22semidirect
47. #16810909C22semidirect
48. #16810906C22semidirect
71. C53×#479C22semidirect
83. C2×Q8×D53Q8semidirect
201. Q8×D53C2×Q8semidirect
353. C2×#479D53semidirect
363. C2×C53#3082semidirect
398. #479C2×D53semidirect
428. C53C2×#3082semidirect
699. C2#20284554direct (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×#168110992
#202845542
C2×#168109332
C2×#168109282
C2×#168109272
C2×#168109182
C2×#168109172
C2×#168109092
C2×#168109062
C2×#168106642
C2×#168106582
C2×#168106482
C2×#168106302
C2×#103×D532
C2×C53×#4792
C2×#308253