Finite Group Databasebeta

← C2×#20285420 #28254011

Subgroups — C2×#20285420 #28254011

Order 13568.

1998 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811177C211yesmaximal, characteristic, complemented
2C2×#16811155C211yesmaximal, characteristic
3#20285420C2116yesmaximal, direct product factor
4C2×#16811031C211yesmaximal, characteristic, complemented
5C2×#16811014C211yesmaximal, characteristic, complemented
6C2×#16810990C211yesmaximal, characteristic, complemented
7C2×#16810981C211yesmaximal, characteristic, complemented
8C2×#16810865C211yesmaximal, characteristic, complemented
9C2×#16810863C211yesmaximal, characteristic, complemented
10C2×#16810851C211yesmaximal, characteristic
11C2×#16810849C211yesmaximal, characteristic
12C2×#16810731C211yesmaximal, characteristic, complemented
13C2×#16810728C211yesmaximal, characteristic, complemented
14C2×#16810723C211yesmaximal, characteristic, complemented
15C2×#97×D53C211yesmaximal, characteristic, complemented
16C2×C53×#440C211yesmaximal, characteristic, complemented
17C22×Dic212C2211yescharacteristic
18C22×#11719925C2211yescharacteristic
19C22×#11719923C2211yescharacteristic
20C22×C8×D53C2211yescharacteristic
21C22×C8×D53C2211yescharacteristic
22#16811177—24no—
23#16811177C2218yescomplemented
24C2×#13133216C2211yescharacteristic
25C2×#13133215C2211yescharacteristic
26#16811155—24no—
27#16811155C2218yes—
28C2×#13133210—21no—
29C2×#13133208C2211yescharacteristic
30C2×#13133207—21no—
31C2×#13133204C2211yescharacteristic
32C2×#13133199—21no—
33C2×#13133197C2211yescharacteristic
34C2×#13133197C2211yescharacteristic
35C2×#13133195—21no—
36C2×#13133193C2211yescharacteristic
37C2×#13133188C2211yescharacteristic
38C2×C4×Dic106—21no—
39C2×C4×Dic106C2211yescharacteristic
40C2×C4×Dic106C2211yescharacteristic
41C2×C4×C22⋊D53—21no—
42C2×#13133176—21no—
43C2×#13133174—21no—
44C2×C42×D53C2211yescharacteristic
45#16811031C2218yescomplemented
46#16811014C2218yescomplemented
47#16810990C2218yescomplemented
48#16810981C2218yescomplemented
49#16810865C2218yescomplemented
50#16810863C2218yescomplemented
51#16810851C2218yes—
52#16810849C2218yes—
53#16810731C2218yescomplemented
54#16810728C2218yescomplemented
55#16810723C2218yescomplemented
56C2×#13133150C2211yescharacteristic
57C2×#13133149C2211yescharacteristic
58C2×#13133148C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133128C2211yescharacteristic
66C2×#13133127C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68#97×D53C2218yescomplemented
69C22×SD16×C53C2211yescharacteristic
70C2×C4×Q8×C53C2211yescharacteristic
71C2×C4×D4×C53C2211yescharacteristic
72C53×#440C2218yescomplemented
73C2×#107×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106C2311yescharacteristic
79C22×Dic106C2311yescharacteristic
80C22×C22⋊D53—21no—
81C22×C4×D53D411yescharacteristic
82C22×C4×D53D411yescharacteristic
83C22×C4×D53C2311yescharacteristic
84C2×Dic212—24no—
85C2×Dic212C2314yes—
86C2×#11719925—24no—
87C2×#11719925C2314yes—
88C2×#11719923—24no—
89C2×#11719923C2314yes—
90C22×#88322C2311yescharacteristic
91C22×#88322C2311yescharacteristic
92C2×C8×D53—24no—
93C2×C8×D53—24no—
94C2×C8×D53C2314yes—
95C2×C8×D53C2314yes—
96#13133216—22no—
97#13133216C2314yes—
98#13133215—22no—
99#13133215C2314yes—
100#13133210—28no—
101#13133208—22no—
102#13133208C2314yes—
103#13133207—28no—
104#13133204—22no—
105#13133204C2314yes—
106#13133199—28no—
107#13133197—22no—
108#13133197—22no—
109#13133197C2314yes—
110#13133197C2314yes—
111#13133195—28no—
112#13133193—22no—
113#13133193C2314yes—
114#13133188—22no—
115#13133188C2314yes—
116C4×Dic106—22no—
117C4×Dic106—22no—
118C4×Dic106—28no—
119C4×Dic106C2314yes—
120C4×Dic106C2314yes—
121C4×C22⋊D53—28no—
122#13133176—28no—
123#13133174—28no—
124C2×C4⋊Dic53—21no—
125C2×C4⋊Dic53—21no—
126C2×C4⋊Dic53—21no—
127C2×C4⋊Dic53C2311yescharacteristic
128C2×C4⋊Dic53C2311yescharacteristic
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×C22⋊Dic53—21no—
137C2×C22⋊Dic53—21no—
138C2×C22⋊Dic53—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×C4×Dic53—21no—
143C2×C4×Dic53—21no—
144C2×C4×Dic53D411yescharacteristic
145C2×C4×Dic53D411yescharacteristic
146C2×C4×Dic53C2311yescharacteristic
147C42×D53D414yes—
148C42×D53C2314yes—
149#13133150C2314yes—
150#13133149C2314yes—
151#13133148C2314yes—
152#13133142C2314yes—
153#13133142C2314yes—
154#13133141C2314yes—
155#13133140C2314yes—
156#13133140C2314yes—
157#13133138C2314yes—
158#13133128C2314yes—
159#13133127C2314yes—
160#13133127C2314yes—
161C22×Q8×C53C2311yescharacteristic
162C22×D4×C53C2311yescharacteristic
163C23×C4×C53—21no—
164C2×SD16×C53—24no—
165C2×SD16×C53C2314yes—
166C22×C8×C53C2311yescharacteristic
167C22×C8×C53C2311yescharacteristic
168C4×Q8×C53—22no—
169C4×Q8×C53C2314yes—
170C4×D4×C53—22no—
171C4×D4×C53C2314yes—
172C2×C4⋊C4×C53—21no—
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C22⋊C4×C53—21no—
176C2×C42×C53—21no—
177C2×C42×C53C2311yescharacteristic
178#107×C53C2314yes—
179#103×C53C2314yes—
180#102×C53C2314yes—
181#97×C53C2314yes—
182C24×C53—21no—
183C23×D53C2×D411yescharacteristic
184C2×Q8×C53—21no—
185C2×Q8×C53—22no—
186C2×Q8×C53—22no—
187C2×Q8×C53C2412yes—
188C2×D4×C53—21no—
189C2×D4×C53—22no—
190C2×D4×C53—22no—
191C2×D4×C53C2412yes—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—24no—
196C22×C4×C53—44no—
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2411yescharacteristic
200C2×C22⋊D53—24no—
201C2×C22⋊D53—44no—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53C2×D411yescharacteristic
207C22×Dic53C2×D411yescharacteristic
208C22×Dic53C2×D411yescharacteristic
209C2×C4×D53—24no—
210C2×C4×D53—22no—
211C2×C4×D53—22no—
212C2×C4×D53—42no—
213C2×C4×D53C2×D412yes—
214C2×C4×D53C2×D414yes—
215C2×C4×D53C2×D414yes—
216C2×C4×D53C2412yes—
217C2×Dic106—22no—
218C2×Dic106—22no—
219C2×Dic106—22no—
220C2×Dic106—22no—
221C2×Dic106—21no—
222C2×Dic106—21no—
223C2×Dic106—24no—
224C2×Dic106—44no—
225C2×Dic106C2412yes—
226C2×Dic106C2412yes—
227SD16×C53—28no—
228C2×C8×C53—22no—
229C2×C8×C53#4114yes—
230C2×C8×C53C2412yes—
231C2×C8×C53C2412yes—
232C4⋊C4×C53—24no—
233C4⋊C4×C53—21no—
234C4⋊C4×C53—21no—
235C4⋊C4×C53C2412yes—
236C4⋊C4×C53C2412yes—
237C22⋊C4×C53—24no—
238C42×C53—24no—
239C42×C53C2×D412yes—
240C42×C53C2412yes—
241C22⋊Dic53—24no—
242C22⋊Dic53—24no—
243C22⋊Dic53—24no—
244#11719925—28no—
245#11719923—28no—
246#11719921—24no—
247#11719921—24no—
248#11719921—24no—
249C4⋊Dic53—21no—
250C4⋊Dic53—21no—
251C4⋊Dic53—24no—
252C4⋊Dic53—24no—
253C4⋊Dic53—24no—
254C4⋊Dic53C2412yes—
255C4⋊Dic53C2412yes—
256#11719919—24no—
257#11719919—24no—
258#11719919—24no—
259#11719919—24no—
260#11719919—24no—
261#11719919—24no—
262#11719919—24no—
263C4×Dic53—24no—
264C4×Dic53—24no—
265C4×Dic53C2×D412yes—
266C4×Dic53C2×D414yes—
267C4×Dic53C2×D414yes—
268C4×Dic53C2412yes—
269C2×#88322—22no—
270C2×#88322#4114yes—
271C2×#88322C2412yes—
272C2×#88322C2412yes—
273Dic212—28no—
274C8×D53—28no—
275C8×D53—28no—
276C23×C53—22no—
277C23×C53—42no—
278C23×C53—42no—
279C23×C53—42no—
280C23×C53C22×D411yescharacteristic
281C22×D53—22no—
282C22×D53—22no—
283C22×D53#13714yes—
284C22×D53C22×D412yes—
285Q8×C53—22no—
286Q8×C53—22no—
287Q8×C53—42no—
288D4×C53—22no—
289D4×C53—22no—
290D4×C53—42no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—48no—
297C2×C4×C53—42no—
298C2×C4×C53—42no—
299C2×C4×C53—42no—
300C2×C4×C53C22×D412yes—
301C2×C4×C53C22×D412yes—
302C2×C4×C53C22×D411yescharacteristic
303C2×C4×C53C2×#4112yes—
304C2×C4×C53C2×#4112yes—
305C2×C4×C53C2511yescharacteristic
306C22⋊D53—48no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—42no—
315C2×Dic53—42no—
316C2×Dic53—42no—
317C2×Dic53—42no—
318C2×Dic53C22×D412yes—
319C2×Dic53C22×D412yes—
320C2×Dic53C22×D412yes—
321C4×D53—28no—
322C4×D53—24no—
323C4×D53—22no—
324C4×D53—22no—
325C4×D53—44no—
326Dic106—22no—
327Dic106—22no—
328Dic106—22no—
329Dic106—22no—
330Dic106—48no—
331Dic106—42no—
332Dic106—42no—
333C8×C53—22no—
334C8×C53C2×#4114yes—
335#88322—22no—
336#88322C2×#4114yes—
337C2×#3181—531nomaximal, Sylow
338C22×C53—42no—
339C22×C53—42no—
340C22×C53—42no—
341C22×C53—84no—
342C22×C53#53212yes—
343C22×C53C2×#13712yes—
344C22×C53#57512yes—
345C22×C53C23×D411yescharacteristic
346C2×D53—28no—
347C2×D53—22no—
348C2×D53—22no—
349C2×D53C2×#13714yes—
350C4×C53—22no—
351C4×C53—22no—
352C4×C53—42no—
353C4×C53—42no—
354C4×C53—42no—
355C4×C53#53212yes—
356C4×C53C22×#4111yescharacteristic
357C4×C53C22×#4111yescharacteristic
358Dic53—22no—
359Dic53—22no—
360Dic53—22no—
361Dic53—42no—
362Dic53—42no—
363Dic53—42no—
364Dic53—42no—
365C2×#533—531no—
366C2×#529—531no—
367#3181—5316no—
368C2×#501—531no—
369C2×#497—531no—
370C2×#491—531no—
371C2×#489—531no—
372C2×#467—531no—
373C2×#467—531no—
374C2×#465—531no—
375C2×#465—531no—
376C2×#441—531no—
377C2×#441—531no—
378C2×#440—531no—
379C2×#440D5311yescharacteristic, complemented
380C22×#97—531no—
381C2×C53—82no—
382C2×C53#318114yescomplemented
383C2×C53C2×#53211yescharacteristic
384C2×C53C22×#13711yescharacteristic
385C2×C53C2×#57511yescharacteristic
386D53—24no—
387C22×Q16—531no—
388C22×Q16—531no—
389C22×SD16—531no—
390C22×SD16C2×D5311yescharacteristic
391C23×C8—531no—
392C23×C8—531no—
393#533—538no—
394#533—1064no—
395C2×C4⋊Q8—531no—
396C2×C4⋊Q8—531no—
397#529—538no—
398#529—1064no—
399C2×#126—1061no—
400C2×#125—531no—
401C2×#125—1061no—
402C2×#124—531no—
403C2×#123—1061no—
404C2×C22⋊Q8—531no—
405C2×C22⋊Q8—531no—
406C2×C22⋊Q8—531no—
407C2×C22⋊Q8—1061no—
408C2×#121—531no—
409C2×C4×Q8—531no—
410C2×C4×Q8—531no—
411C2×C4×Q8—1061no—
412C2×C4×Q8C2×D5311yescharacteristic
413C2×C4×D4—1061no—
414C2×C4×D4C2×D5311yescharacteristic
415C2×#117—1061no—
416C2×#117—1061no—
417C22×C42—531no—
418#501—538no—
419#497—538no—
420#491—538no—
421#489—538no—
422#467—538no—
423#467—538no—
424#465—538no—
425#465—538no—
426#441—538no—
427#441—538no—
428#440—538no—
429#440C2×D5318yescomplemented
430C2×#107—531no—
431C2×#107C2×D5311yescharacteristic
432C2×#106—531no—
433C2×#106—531no—
434C2×#103—531no—
435C2×#103—531no—
436C2×#103—531no—
437C2×#103—531no—
438C2×#103—531no—
439C2×#103C2×D5311yescharacteristic
440C2×#102—531no—
441C2×#102C2×D5311yescharacteristic
442C2×#97—531no—
443C2×#97—531no—
444C2×#97—531no—
445C2×#97—538no—
446C2×#97C2×D5311yescharacteristic
447C53C2×#318111yescharacteristic, complemented, Sylow
448C22×Q8—531no—
449C22×Q8—531no—
450C22×Q8—1061no—
451C22×Q8C22×D5311yescharacteristic
452C22×D4—1061no—
453C22×D4C22×D5311yescharacteristic
454C23×C4—21no—
455C23×C4—531no—
456C23×C4—531no—
457C23×C4—531no—
458C2×Q16—534no—
459C2×Q16—534no—
460C2×Q16—1064no—
461C2×Q16—1064no—
462C2×SD16—24no—
463C2×SD16—534no—
464C2×SD16—1064no—
465C2×SD16C22×D5314yes—
466C22×C8—531no—
467C22×C8—531no—
468C22×C8—534no—
469C22×C8—534no—
470C22×C8—1064no—
471C22×C8—1064no—
472C22×C8C22×D5311yescharacteristic
473C22×C8C22×D5311yescharacteristic
474C4⋊Q8—534no—
475C4⋊Q8—534no—
476C4⋊Q8—1062no—
477C4⋊Q8—1062no—
478#126—1068no—
479#125—534no—
480#125—1062no—
481#125—1068no—
482#124—534no—
483#124—1062no—
484#123—1068no—
485C22⋊Q8—534no—
486C22⋊Q8—534no—
487C22⋊Q8—534no—
488C22⋊Q8—1062no—
489C22⋊Q8—1062no—
490C22⋊Q8—1068no—
491C22⋊Q8—1062no—
492#121—534no—
493#121—1062no—
494C4×Q8—22no—
495C4×Q8—534no—
496C4×Q8—534no—
497C4×Q8—1068no—
498C4×Q8—1062no—
499C4×Q8—1062no—
500C4×Q8C22×D5314yes—
501C4×D4—22no—
502C4×D4—1068no—
503C4×D4C22×D5314yes—
504#117—1068no—
505#117—1068no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—531no—
508C2×C4⋊C4—531no—
509C2×C4⋊C4—1061no—
510C2×C4⋊C4—1061no—
511C2×C4⋊C4—1061no—
512C2×C4⋊C4—1061no—
513C2×C4⋊C4—1061no—
514C2×C4⋊C4—1061no—
515C2×C4⋊C4—1061no—
516C2×C4⋊C4—1061no—
517C2×C4⋊C4—1061no—
518C2×C4⋊C4—1061no—
519C2×C4⋊C4C22×D5311yescharacteristic
520C2×C4⋊C4C22×D5311yescharacteristic
521C2×C22⋊C4—21no—
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—531no—
530C2×C42—531no—
531C2×C42—531no—
532C2×C42—534no—
533C2×C42—534no—
534C2×C42—1061no—
535C2×C42—1061no—
536C2×C42C22×D5311yescharacteristic
537#107—534no—
538#107C22×D5314yes—
539#106—534no—
540#106—534no—
541#103—534no—
542#103—534no—
543#103—534no—
544#103—534no—
545#103—534no—
546#103C22×D5314yes—
547#102—534no—
548#102C22×D5314yes—
549#97—534no—
550#97—534no—
551#97—534no—
552#97C22×D5314yes—
553C24—21no—
554C24—531no—
555C2×Q8—21no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—532no—
559C2×Q8—532no—
560C2×Q8—1064no—
561C2×Q8—1061no—
562C2×Q8—1061no—
563C2×Q8—1062no—
564C2×Q8—1062no—
565C2×Q8—1062no—
566C2×Q8—1062no—
567C2×Q8—2124no—
568C2×Q8C23×D5312yes—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—1064no—
573C2×D4—2124no—
574C2×D4C23×D5312yes—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—44no—
580C22×C4—531no—
581C22×C4—531no—
582C22×C4—531no—
583C22×C4—534no—
584C22×C4—532no—
585C22×C4—532no—
586C22×C4—534no—
587C22×C4—1064no—
588C22×C4—1062no—
589C22×C4—1062no—
590C22×C4—1061no—
591C22×C4—1061no—
592C22×C4—1061no—
593C22×C4—1061no—
594C22×C4—2122no—
595C22×C4D4×D5311yescharacteristic
596C22×C4D4×D5311yescharacteristic
597C22×C4C23×D5311yescharacteristic
598Q16—1068no—
599Q16—1068no—
600SD16—28no—
601SD16—1068no—
602C2×C8—22no—
603C2×C8—534no—
604C2×C8—532no—
605C2×C8—532no—
606C2×C8—1068no—
607C2×C8—1062no—
608C2×C8—1068no—
609C2×C8#1171994514yes—
610C2×C8C23×D5312yes—
611C2×C8C23×D5312yes—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—532no—
616C4⋊C4—532no—
617C4⋊C4—1064no—
618C4⋊C4—1064no—
619C4⋊C4—1064no—
620C4⋊C4—1064no—
621C4⋊C4—1064no—
622C4⋊C4—1064no—
623C4⋊C4—1064no—
624C4⋊C4—1064no—
625C4⋊C4—1061no—
626C4⋊C4—1061no—
627C4⋊C4—1064no—
628C4⋊C4—1064no—
629C4⋊C4C23×D5312yes—
630C4⋊C4C23×D5312yes—
631C22⋊C4—24no—
632C22⋊C4—1064no—
633C22⋊C4—1064no—
634C22⋊C4—1064no—
635C22⋊C4—1064no—
636C22⋊C4—1064no—
637C22⋊C4—1064no—
638C42—24no—
639C42—534no—
640C42—534no—
641C42—532no—
642C42—532no—
643C42—1064no—
644C42—1064no—
645C42D4×D5312yes—
646C42C23×D5312yes—
647C23—22no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—534no—
652C23—532no—
653C23—1062no—
654C23—1062no—
655C23C2×D4×D5311yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—1062no—
660Q8—1062no—
661Q8—1062no—
662Q8—1062no—
663Q8—2128no—
664Q8—2122no—
665Q8—2122no—
666D4—22no—
667D4—22no—
668D4—42no—
669D4—2128no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—48no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—532no—
680C2×C4—532no—
681C2×C4—532no—
682C2×C4—1068no—
683C2×C4—1062no—
684C2×C4—1062no—
685C2×C4—1062no—
686C2×C4—1064no—
687C2×C4—1062no—
688C2×C4—1062no—
689C2×C4—1062no—
690C2×C4—1062no—
691C2×C4—1062no—
692C2×C4—1062no—
693C2×C4—2124no—
694C2×C4—2122no—
695C2×C4—2122no—
696C2×C4—2122no—
697C2×C4—2122no—
698C2×C4C2×D4×D5312yes—
699C2×C4C2×D4×D5312yes—
700C2×C4C2×D4×D5311yescharacteristic
701C2×C4#41×D5312yes—
702C2×C4C2×#1171994512yes—
703C2×C4C24×D5311yescharacteristic
704C8—22no—
705C8—534no—
706C8—1062no—
707C8C2×#1171994514yes—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—84no—
712C22—534no—
713C22—1062no—
714C22—1068no—
715C22—1062no—
716C22#1681117012yes—
717C22#137×D5312yes—
718C22#1681141912yes—
719C22C22×D4×D5311yescharacteristic
720C4—22no—
721C4—22no—
722C4—42no—
723C4—42no—
724C4—42no—
725C4—1062no—
726C4—1062no—
727C4—1062no—
728C4—2122no—
729C4—2122no—
730C4—2122no—
731C4—2122no—
732C4#1681117012yes—
733C4C2×#41×D5311yescharacteristic
734C4C22×#1171994511yescharacteristic
735C2—82no—
736C2—1064no—
737C2#2028542014yesdirect product factor
738C2C2×#1681117011yescharacteristic
739C2C2×#137×D5311yescharacteristic
740C2C2×#1681141911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#440C2
socleC23×C53C22×D4
prime radicalC2×#13133188C22
hypercenterC2×#440D53
hypocenterC53C2×#3181
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×#16811177C2semidirect
3. #20285420C2direct (N × H)
4. C2×#16811031C2semidirect
5. C2×#16811014C2semidirect
6. C2×#16810990C2semidirect
7. C2×#16810981C2semidirect
8. C2×#16810865C2semidirect
9. C2×#16810863C2semidirect
12. C2×#16810731C2semidirect
13. C2×#16810728C2semidirect
14. C2×#16810723C2semidirect
15. C2×#97×D53C2semidirect
16. C2×C53×#440C2semidirect
23. #16811177C22semidirect
45. #16811031C22semidirect
46. #16811014C22semidirect
47. #16810990C22semidirect
48. #16810981C22semidirect
49. #16810865C22semidirect
50. #16810863C22semidirect
53. #16810731C22semidirect
54. #16810728C22semidirect
55. #16810723C22semidirect
68. #97×D53C22semidirect
72. C53×#440C22semidirect
379. C2×#440D53semidirect
382. C2×C53#3181semidirect
429. #440C2×D53semidirect
447. C53C2×#3181semidirect
737. C2#20285420direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111772
C2×#168111552
#202854202
C2×#168110312
C2×#168110142
C2×#168109902
C2×#168109812
C2×#168108652
C2×#168108632
C2×#168108512
C2×#168108492
C2×#168107312
C2×#168107282
C2×#168107232
C2×#97×D532
C2×C53×#4402
C2×#318153