Finite Group Databasebeta

← C2×#20284950 #28252377

Subgroups — C2×#20284950 #28252377

Order 13568.

2058 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811245C211yesmaximal, characteristic
2C2×#16811099C211yesmaximal, characteristic, complemented
3#20284950C2116yesmaximal, direct product factor
4C2×#16810962C211yesmaximal, characteristic, complemented
5C2×#16810950C211yesmaximal, characteristic
6C2×#16810917C211yesmaximal, characteristic, complemented
7C2×#16810906C211yesmaximal, characteristic, complemented
8C2×#16810848C211yesmaximal, characteristic, complemented
9C2×#16810847C211yesmaximal, characteristic, complemented
10C2×#16810777C211yesmaximal, characteristic, complemented
11C2×#16810763C211yesmaximal, characteristic
12C2×#16810728C211yesmaximal, characteristic, complemented
13C2×#16810721C211yesmaximal, characteristic, complemented
14C2×C4×#11719913C211yesmaximal, characteristic, complemented
15C2×#16810682C211yesmaximal, characteristic, complemented
16C2×C4×Q16×C53C211yesmaximal, characteristic, complemented
17C22×Q8×D53C2211yescharacteristic
18C22×#11719925C2211yescharacteristic
19C22×#11719913C2211yescharacteristic
20C22×#11719924C2211yescharacteristic
21#16811245—24no—
22#16811245C2218yes—
23C2×#13133216C2211yescharacteristic
24C2×#13133211—21no—
25C2×#13133206C2211yescharacteristic
26C2×#13133205—21no—
27C2×#13133202—21no—
28C2×#13133195—21no—
29C2×#13133193C2211yescharacteristic
30C2×#13133192C2211yescharacteristic
31#16811099—24no—
32#16811099C2218yescomplemented
33C2×Q8×Dic53C2211yescharacteristic
34C2×C4×Dic106—21no—
35C2×C4×Dic106C2211yescharacteristic
36C2×#13133182—21no—
37C2×#13133182C2211yescharacteristic
38C2×C4×D212C2211yescharacteristic
39C2×#13133175—21no—
40C2×#13133175C2211yescharacteristic
41C2×#13133174—21no—
42C2×#13133174C2211yescharacteristic
43#16810962C2218yescomplemented
44#16810950C2218yes—
45#16810917C2218yescomplemented
46#16810906C2218yescomplemented
47#16810848C2218yescomplemented
48#16810847C2218yescomplemented
49#16810777C2218yescomplemented
50#16810763C2218yes—
51#16810728C2218yescomplemented
52#16810721C2218yescomplemented
53C4×#11719913C2218yescomplemented
54#16810682C2218yescomplemented
55C2×#13133150C2211yescharacteristic
56C2×#13133149C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×#13133146C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133139C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133128C2211yescharacteristic
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×Dic106—21no—
79C22×Dic106C2311yescharacteristic
80C2×Q8×D53—24no—
81C2×Q8×D53—22no—
82C2×Q8×D53—24no—
83C2×Q8×D53C2314yes—
84C22×D212—21no—
85C22×D212C2311yescharacteristic
86C22×C4×D53—21no—
87C22×C4×D53—21no—
88C22×C4×D53C2311yescharacteristic
89C2×#11719925—24no—
90C2×#11719925C2314yes—
91C2×#11719913—24no—
92C2×#11719913C2314yes—
93C2×#11719924—24no—
94C2×#11719924C2314yes—
95C22×#88322C2311yescharacteristic
96C22×#88322C2311yescharacteristic
97#13133216—22no—
98#13133216C2314yes—
99#13133211—28no—
100#13133206—22no—
101#13133206C2314yes—
102#13133205—28no—
103#13133202—28no—
104#13133195—28no—
105#13133193—22no—
106#13133193C2314yes—
107#13133192—22no—
108#13133192C2314yes—
109Q8×Dic53—22no—
110Q8×Dic53C2314yes—
111C4×Dic106—22no—
112C4×Dic106—28no—
113C4×Dic106C2314yes—
114#13133182—28no—
115#13133182—22no—
116#13133182C2314yes—
117C4×D212—22no—
118C4×D212C2314yes—
119#13133175—28no—
120#13133175—22no—
121#13133175C2314yes—
122#13133174—28no—
123#13133174D414yes—
124#13133174C2314yes—
125C2×C4⋊Dic53—21no—
126C2×C4⋊Dic53C2311yescharacteristic
127C2×C4⋊Dic53C2311yescharacteristic
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919D411yescharacteristic
133C2×#11719919D411yescharacteristic
134C2×#11719921—21no—
135C2×#11719921—21no—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921D411yescharacteristic
141C2×#11719921D411yescharacteristic
142C2×C4×Dic53—21no—
143C2×C4×Dic53—21no—
144C2×C4×Dic53—21no—
145C2×C4×Dic53—21no—
146C2×C4×Dic53C2311yescharacteristic
147#13133150C2314yes—
148#13133149C2314yes—
149#13133148C2314yes—
150#13133146C2314yes—
151#13133146C2314yes—
152#13133142C2314yes—
153#13133141C2314yes—
154#13133141C2314yes—
155#13133140C2314yes—
156#13133139C2314yes—
157#13133137C2314yes—
158#13133129C2314yes—
159#13133129C2314yes—
160#13133128C2314yes—
161C22×Q8×C53C2311yescharacteristic
162C22×Q8×C53C2311yescharacteristic
163C2×Q16×C53—24no—
164C2×Q16×C53C2314yes—
165C22×C8×C53C2311yescharacteristic
166C22×C8×C53C2311yescharacteristic
167C4×Q8×C53—22no—
168C4×Q8×C53—22no—
169C4×Q8×C53C2314yes—
170C4×Q8×C53C2314yes—
171C2×C4⋊C4×C53—21no—
172C2×C4⋊C4×C53—21no—
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C42×C53—21no—
176C2×C42×C53—21no—
177C2×C42×C53C2311yescharacteristic
178#107×C53C2314yes—
179#103×C53C2314yes—
180#103×C53C2314yes—
181C4×C8×C53C2314yes—
182C23×D53—21no—
183C23×D53C2×D411yescharacteristic
184C2×Q8×C53—21no—
185C2×Q8×C53—21no—
186C2×Q8×C53—22no—
187C2×Q8×C53—22no—
188C2×Q8×C53—22no—
189C2×Q8×C53#4114yes—
190C2×Q8×C53C2412yes—
191C2×Q8×C53C2412yes—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2411yescharacteristic
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53—21no—
202C22×Dic53C2×D411yescharacteristic
203C22×Dic53C2×D411yescharacteristic
204C22×Dic53C2×D411yescharacteristic
205Q8×D53—216no—
206Q8×D53—28no—
207Q8×D53—28no—
208C2×D212—22no—
209C2×D212—22no—
210C2×D212—21no—
211C2×D212—24no—
212C2×D212—82no—
213C2×D212C2412yes—
214C2×C4×D53—28no—
215C2×C4×D53—24no—
216C2×C4×D53—22no—
217C2×C4×D53—22no—
218C2×C4×D53—24no—
219C2×C4×D53—82no—
220C2×C4×D53C2×D412yes—
221C2×C4×D53C2412yes—
222C2×Dic106—28no—
223C2×Dic106—21no—
224C2×Dic106—22no—
225C2×Dic106—24no—
226C2×Dic106—24no—
227C2×Dic106—82no—
228C2×Dic106#4114yes—
229C2×Dic106C2412yes—
230Q16×C53—28no—
231C2×C8×C53—22no—
232C2×C8×C53—22no—
233C2×C8×C53C2412yes—
234C2×C8×C53C2412yes—
235C4⋊C4×C53—24no—
236C4⋊C4×C53—24no—
237C4⋊C4×C53—21no—
238C4⋊C4×C53—21no—
239C4⋊C4×C53C2412yes—
240C4⋊C4×C53C2412yes—
241C42×C53—24no—
242C42×C53—24no—
243C42×C53C2×D412yes—
244C42×C53C2412yes—
245#11719925—28no—
246#11719924—28no—
247#11719921—24no—
248#11719921—24no—
249#11719921—24no—
250#11719921—24no—
251#11719921—24no—
252#11719921—24no—
253#11719921C2×D414yes—
254#11719921C2×D414yes—
255C4⋊Dic53—21no—
256C4⋊Dic53—21no—
257C4⋊Dic53—24no—
258C4⋊Dic53C2412yes—
259C4⋊Dic53C2412yes—
260#11719919—24no—
261#11719919—24no—
262#11719919—24no—
263#11719919—24no—
264#11719919C2×D414yes—
265#11719919C2×D414yes—
266C4×Dic53—24no—
267C4×Dic53—24no—
268C4×Dic53—24no—
269C4×Dic53—24no—
270C4×Dic53C2×D412yes—
271C4×Dic53C2412yes—
272C2×#88322—22no—
273C2×#88322—22no—
274C2×#88322C2412yes—
275C2×#88322C2412yes—
276#11719913—28no—
277C23×C53C22×D411yescharacteristic
278C22×D53—22no—
279C22×D53—22no—
280C22×D53—22no—
281C22×D53—22no—
282C22×D53—42no—
283C22×D53—42no—
284C22×D53—42no—
285C22×D53C22×D412yes—
286Q8×C53—24no—
287Q8×C53—22no—
288Q8×C53—22no—
289Q8×C53—22no—
290Q8×C53—42no—
291Q8×C53C2×#4114yes—
292C2×C4×C53—24no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—42no—
300C2×C4×C53—42no—
301C2×C4×C53—42no—
302C2×C4×C53C22×D412yes—
303C2×C4×C53C22×D412yes—
304C2×C4×C53C22×D411yescharacteristic
305C2×C4×C53C2×#4112yes—
306C2×C4×C53C2×#4112yes—
307C2×C4×C53C2511yescharacteristic
308C2×Dic53—22no—
309C2×Dic53—24no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—42no—
316C2×Dic53—42no—
317C2×Dic53C22×D412yes—
318C2×Dic53C22×D412yes—
319C2×Dic53C22×D412yes—
320D212—22no—
321D212—22no—
322D212—42no—
323D212—84no—
324C4×D53—216no—
325C4×D53—24no—
326C4×D53—22no—
327C4×D53—22no—
328C4×D53—84no—
329Dic106—216no—
330Dic106—24no—
331Dic106—22no—
332Dic106—84no—
333Dic106C2×#4114yes—
334C8×C53—22no—
335C8×C53—22no—
336#88322—22no—
337#88322—22no—
338C2×#3121—531nomaximal, Sylow
339C22×C53#52512yes—
340C22×C53#57712yes—
341C22×C53#57812yes—
342C22×C53C23×D411yescharacteristic
343C2×D53—22no—
344C2×D53—22no—
345C2×D53—22no—
346C2×D53—44no—
347C2×D53—42no—
348C2×D53—42no—
349C2×D53—42no—
350C2×D53—84no—
351C4×C53—24no—
352C4×C53—22no—
353C4×C53—22no—
354C4×C53—42no—
355C4×C53—42no—
356C4×C53—42no—
357C4×C53#52512yes—
358C4×C53C22×#4111yescharacteristic
359C4×C53C22×#4111yescharacteristic
360Dic53—22no—
361Dic53—24no—
362Dic53—22no—
363Dic53—22no—
364Dic53—42no—
365Dic53—42no—
366C2×#542—531no—
367C2×#519—531no—
368#3121—5316no—
369C2×#485—531no—
370C2×#482—531no—
371C2×#477—531no—
372C2×#475—531no—
373C2×#464—531no—
374C2×#464—531no—
375C2×#451—531no—
376C2×#448—531no—
377C2×#441—531no—
378C2×#440—531no—
379C2×C4×Q16D5311yescharacteristic, complemented
380C2×C4×SD16—531no—
381C2×#433—531no—
382C2×C53#312114yescomplemented
383C2×C53C2×#52511yescharacteristic
384C2×C53C2×#57711yescharacteristic
385C2×C53C2×#57811yescharacteristic
386D53—42no—
387D53—82no—
388C23×Q8—531no—
389C22×Q16—531no—
390C22×Q16C2×D5311yescharacteristic
391C22×SD16—531no—
392C22×SD16—531no—
393#542—538no—
394#542—1064no—
395C2×C4⋊Q8—531no—
396C2×#126—1061no—
397C2×#124—531no—
398C2×#124—1061no—
399C2×#123—1061no—
400C2×C22⋊Q8—531no—
401C2×C22⋊Q8—1061no—
402C2×#121—531no—
403#519—538no—
404#519—1064no—
405C2×C4×Q8—531no—
406C2×C4×Q8—531no—
407C2×C4×Q8—531no—
408C2×C4×Q8—1061no—
409C2×C4×Q8—1061no—
410C2×C4×Q8C2×D5311yescharacteristic
411C2×C4×Q8C2×D5311yescharacteristic
412C2×C4×D4—531no—
413C2×#117—531no—
414C2×#117—531no—
415C2×#117—1061no—
416C2×#117—1061no—
417#485—538no—
418#482—538no—
419#477—538no—
420#475—538no—
421#464—538no—
422#464—538no—
423#451—538no—
424#448—538no—
425#441—538no—
426#440—538no—
427C4×Q16C2×D5318yescomplemented
428C4×SD16—538no—
429#433—538no—
430C2×#107—531no—
431C2×#107C2×D5311yescharacteristic
432C2×#106—531no—
433C2×#106—531no—
434C2×C4⋊C8—531no—
435C2×C4⋊C8—531no—
436C2×#103—531no—
437C2×#103—531no—
438C2×#103—531no—
439C2×#103—531no—
440C2×#103C2×D5311yescharacteristic
441C2×#103C2×D5311yescharacteristic
442C2×#102—531no—
443C2×#102—531no—
444C2×C22⋊C8—531no—
445C2×C22⋊C8—531no—
446C2×#97—531no—
447C2×C4×C8C2×D5311yescharacteristic
448C53C2×#312111yescharacteristic, complemented, Sylow
449C22×Q8—534no—
450C22×Q8—531no—
451C22×Q8—1061no—
452C22×Q8—1061no—
453C22×Q8—1062no—
454C22×Q8—1064no—
455C22×Q8—1064no—
456C22×Q8C22×D5311yescharacteristic
457C22×Q8C22×D5311yescharacteristic
458C22×D4—531no—
459C22×D4—1061no—
460C23×C4—531no—
461C23×C4—1061no—
462C23×C4—1061no—
463C2×Q16—24no—
464C2×Q16—534no—
465C2×Q16—1064no—
466C2×Q16C22×D5314yes—
467C2×SD16—534no—
468C2×SD16—534no—
469C2×SD16—1064no—
470C2×SD16—1064no—
471C22×C8—531no—
472C22×C8—531no—
473C22×C8C22×D5311yescharacteristic
474C22×C8C22×D5311yescharacteristic
475C4⋊Q8—534no—
476C4⋊Q8—1062no—
477#126—1068no—
478#124—534no—
479#124—1068no—
480#124—1062no—
481#123—1068no—
482C22⋊Q8—534no—
483C22⋊Q8—1068no—
484C22⋊Q8—1062no—
485#121—534no—
486#121—1062no—
487C4×Q8—22no—
488C4×Q8—22no—
489C4×Q8—534no—
490C4×Q8—534no—
491C4×Q8—534no—
492C4×Q8—1068no—
493C4×Q8—1062no—
494C4×Q8—1062no—
495C4×Q8—1068no—
496C4×Q8—1062no—
497C4×Q8C22×D5314yes—
498C4×Q8C22×D5314yes—
499C4×D4—534no—
500C4×D4—1062no—
501#117—534no—
502#117—534no—
503#117—534no—
504#117—1068no—
505#117—1068no—
506#117—1062no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—531no—
510C2×C4⋊C4—531no—
511C2×C4⋊C4—531no—
512C2×C4⋊C4—531no—
513C2×C4⋊C4—1061no—
514C2×C4⋊C4—1061no—
515C2×C4⋊C4—1061no—
516C2×C4⋊C4—1061no—
517C2×C4⋊C4—1061no—
518C2×C4⋊C4C22×D5311yescharacteristic
519C2×C4⋊C4C22×D5311yescharacteristic
520C2×C22⋊C4—531no—
521C2×C22⋊C4—531no—
522C2×C22⋊C4—1061no—
523C2×C22⋊C4—1061no—
524C2×C22⋊C4—1061no—
525C2×C22⋊C4—1061no—
526C2×C22⋊C4—1061no—
527C2×C22⋊C4—1061no—
528C2×C42—21no—
529C2×C42—21no—
530C2×C42—531no—
531C2×C42—1061no—
532C2×C42—1061no—
533C2×C42—1061no—
534C2×C42—1061no—
535C2×C42C22×D5311yescharacteristic
536#107—534no—
537#107C22×D5314yes—
538#106—534no—
539#106—534no—
540C4⋊C8—534no—
541C4⋊C8—534no—
542#103—534no—
543#103—534no—
544#103—534no—
545#103—534no—
546#103C22×D5314yes—
547#103C22×D5314yes—
548#102—534no—
549#102—534no—
550C22⋊C8—534no—
551C22⋊C8—534no—
552#97—534no—
553C4×C8C22×D5314yes—
554C24—531no—
555C24—1061no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—534no—
562C2×Q8—532no—
563C2×Q8—1064no—
564C2×Q8—1064no—
565C2×Q8—1068no—
566C2×Q8—1068no—
567C2×Q8—10616no—
568C2×Q8—1068no—
569C2×Q8—1061no—
570C2×Q8—1062no—
571C2×Q8—4242no—
572C2×Q8#1171994514yes—
573C2×Q8C23×D5312yes—
574C2×Q8C23×D5312yes—
575C2×D4—532no—
576C2×D4—1064no—
577C2×D4—1061no—
578C2×D4—1062no—
579C2×D4—1062no—
580C2×D4—4242no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—531no—
586C22×C4—531no—
587C22×C4—531no—
588C22×C4—532no—
589C22×C4—532no—
590C22×C4—1064no—
591C22×C4—1068no—
592C22×C4—1061no—
593C22×C4—1062no—
594C22×C4—1062no—
595C22×C4—1061no—
596C22×C4—1061no—
597C22×C4—1064no—
598C22×C4—4242no—
599C22×C4D4×D5311yescharacteristic
600C22×C4D4×D5311yescharacteristic
601C22×C4C23×D5311yescharacteristic
602Q16—28no—
603Q16—1068no—
604SD16—1068no—
605SD16—1068no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—532no—
609C2×C8—532no—
610C2×C8—1062no—
611C2×C8—1062no—
612C2×C8C23×D5312yes—
613C2×C8C23×D5312yes—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—534no—
619C4⋊C4—534no—
620C4⋊C4—532no—
621C4⋊C4—532no—
622C4⋊C4—1064no—
623C4⋊C4—1064no—
624C4⋊C4—1064no—
625C4⋊C4—1064no—
626C4⋊C4—1061no—
627C4⋊C4—1061no—
628C4⋊C4—1064no—
629C4⋊C4C23×D5312yes—
630C4⋊C4C23×D5312yes—
631C22⋊C4—534no—
632C22⋊C4—534no—
633C22⋊C4—1064no—
634C22⋊C4—1064no—
635C22⋊C4—1064no—
636C22⋊C4—1064no—
637C22⋊C4—1064no—
638C22⋊C4—1064no—
639C42—24no—
640C42—24no—
641C42—532no—
642C42—532no—
643C42—1064no—
644C42—1064no—
645C42—1064no—
646C42—1064no—
647C42D4×D5312yes—
648C42C23×D5312yes—
649C23—532no—
650C23—1062no—
651C23—1062no—
652C23—1062no—
653C23—1062no—
654C23—2122no—
655C23—2122no—
656C23—2122no—
657C23C2×D4×D5311yescharacteristic
658Q8—24no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—534no—
664Q8—10616no—
665Q8—1064no—
666Q8—1062no—
667Q8—4244no—
668Q8C2×#1171994514yes—
669D4—1062no—
670D4—1062no—
671D4—4244no—
672D4—2122no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—532no—
684C2×C4—532no—
685C2×C4—532no—
686C2×C4—10616no—
687C2×C4—1062no—
688C2×C4—1064no—
689C2×C4—1062no—
690C2×C4—1062no—
691C2×C4—1062no—
692C2×C4—1064no—
693C2×C4—1062no—
694C2×C4—1062no—
695C2×C4—1062no—
696C2×C4—1062no—
697C2×C4—4244no—
698C2×C4—2122no—
699C2×C4—2122no—
700C2×C4C2×D4×D5312yes—
701C2×C4C2×D4×D5312yes—
702C2×C4C2×D4×D5311yescharacteristic
703C2×C4#41×D5312yes—
704C2×C4C2×#1171994512yes—
705C2×C4C24×D5311yescharacteristic
706C8—22no—
707C8—22no—
708C8—1062no—
709C8—1062no—
710C22—1062no—
711C22—1062no—
712C22—1062no—
713C22—4244no—
714C22—2122no—
715C22—2122no—
716C22—2122no—
717C22—2124no—
718C22#1681113212yes—
719C22#1681143012yes—
720C22#1681143612yes—
721C22C22×D4×D5311yescharacteristic
722C4—22no—
723C4—22no—
724C4—24no—
725C4—42no—
726C4—42no—
727C4—42no—
728C4—1062no—
729C4—1062no—
730C4—1062no—
731C4—1064no—
732C4—2122no—
733C4—2122no—
734C4#1681113212yes—
735C4C2×#41×D5311yescharacteristic
736C4C22×#1171994511yescharacteristic
737C2—4242no—
738C2—2122no—
739C2#2028495014yesdirect product factor
740C2C2×#1681113211yescharacteristic
741C2C2×#1681143011yescharacteristic
742C2C2×#1681143611yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C4×Q16×C53C2
socleC23×C53C22×D4
prime radicalC2×#13133192C22
hypercenterC2×C4×Q16D53
hypocenterC53C2×#3121
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
2. C2×#16811099C2semidirect
3. #20284950C2direct (N × H)
4. C2×#16810962C2semidirect
6. C2×#16810917C2semidirect
7. C2×#16810906C2semidirect
8. C2×#16810848C2semidirect
9. C2×#16810847C2semidirect
10. C2×#16810777C2semidirect
12. C2×#16810728C2semidirect
13. C2×#16810721C2semidirect
14. C2×C4×#11719913C2semidirect
15. C2×#16810682C2semidirect
16. C2×C4×Q16×C53C2semidirect
32. #16811099C22semidirect
43. #16810962C22semidirect
45. #16810917C22semidirect
46. #16810906C22semidirect
47. #16810848C22semidirect
48. #16810847C22semidirect
49. #16810777C22semidirect
51. #16810728C22semidirect
52. #16810721C22semidirect
53. C4×#11719913C22semidirect
54. #16810682C22semidirect
72. C4×Q16×C53C22semidirect
379. C2×C4×Q16D53semidirect
382. C2×C53#3121semidirect
427. C4×Q16C2×D53semidirect
448. C53C2×#3121semidirect
739. C2#20284950direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112452
C2×#168110992
#202849502
C2×#168109622
C2×#168109502
C2×#168109172
C2×#168109062
C2×#168108482
C2×#168108472
C2×#168107772
C2×#168107632
C2×#168107282
C2×#168107212
C2×C4×#117199132
C2×#168106822
C2×C4×Q16×C532
C2×#312153