Finite Group Databasebeta

← C2×#20287204 #28262675

Subgroups — C2×#20287204 #28262675

Order 13568.

1942 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×#16811331C211yesmaximal, characteristic, complemented
2C2×#16811321C211yesmaximal, characteristic
3#20287204C2116yesmaximal, direct product factor
4C2×#16811031C211yesmaximal, characteristic, complemented
5C2×#16810942C211yesmaximal, characteristic, complemented
6C2×#16810962C211yesmaximal, characteristic, complemented
7C2×#16810938C211yesmaximal, characteristic, complemented
8C2×#16810928C211yesmaximal, characteristic, complemented
9C2×#16810902C211yesmaximal, characteristic, complemented
10C2×#16810872C211yesmaximal, characteristic, complemented
11C2×#16810854C211yesmaximal, characteristic, complemented
12C2×#16810726C211yesmaximal, characteristic, complemented
13C2×#16810691C211yesmaximal, characteristic, complemented
14C2×#16810664C211yesmaximal, characteristic, complemented
15C22×#13133150C211yesmaximal, characteristic, complemented
16C2×C53×#484C211yesmaximal, characteristic, complemented
17C22×#11719924C2211yescharacteristic
18C22×#11719912C2211yescharacteristic
19C23×#88322C2211yescharacteristic
20#16811331—24no—
21#16811331C2218yescomplemented
22#16811321—24no—
23#16811321C2218yes—
24C2×#13133216C2211yescharacteristic
25C2×#13133212—21no—
26C2×#13133208C2211yescharacteristic
27C2×#13133207—21no—
28C2×#13133202—21no—
29C2×#13133197—21no—
30C2×#13133194—21no—
31C2×#13133193C2211yescharacteristic
32C2×#13133192C2211yescharacteristic
33C2×#13133191—21no—
34C2×#13133191C2211yescharacteristic
35C2×Q8×Dic53C2211yescharacteristic
36C2×#13133179C2211yescharacteristic
37C2×C4×C22⋊D53—21no—
38C2×C4×C22⋊D53C2211yescharacteristic
39C2×#13133177—21no—
40C2×#13133175C2211yescharacteristic
41C22×C4⋊Dic53C2211yescharacteristic
42C2×C4⋊C4×D53C2211yescharacteristic
43#16811031C2218yescomplemented
44#16810962C2218yescomplemented
45#16810942C2218yescomplemented
46#16810938C2218yescomplemented
47#16810928C2218yescomplemented
48#16810902C2218yescomplemented
49#16810872C2218yescomplemented
50#16810854C2218yescomplemented
51#16810726C2218yescomplemented
52#16810691C2218yescomplemented
53#16810664C2218yescomplemented
54C2×#13133150C2211yescharacteristic
55C2×#13133150C2211yescharacteristic
56C2×#13133150C2211yescharacteristic
57C2×#13133150C2211yescharacteristic
58C2×#13133150C2218yescomplemented
59C2×#13133149C2211yescharacteristic
60C2×#13133149C2211yescharacteristic
61C2×#13133148C2211yescharacteristic
62C2×#13133146C2211yescharacteristic
63C2×#13133141C2211yescharacteristic
64C2×#13133139C2211yescharacteristic
65C2×#13133139C2211yescharacteristic
66C2×#13133137C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133127C2211yescharacteristic
69C2×C22⋊Q8×C53C2211yescharacteristic
70C22×C4⋊C4×C53C2211yescharacteristic
71C53×#484C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#107×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×D212—21no—
79C22×D212C2311yescharacteristic
80C22×C22⋊D53—21no—
81C22×C22⋊D53D411yescharacteristic
82C23×Dic53—21no—
83C22×C4×D53—21no—
84C22×C4×D53—21no—
85C22×C4×D53C2311yescharacteristic
86C2×#11719924—24no—
87C2×#11719924C2314yes—
88C2×#11719912—24no—
89C2×#11719912C2314yes—
90C22×#88322—24no—
91C22×#88322C2311yescharacteristic
92C22×#88322C2314yes—
93C22×#88322C2311yescharacteristic
94#13133216—22no—
95#13133216C2314yes—
96#13133212—28no—
97#13133208—22no—
98#13133208C2314yes—
99#13133207—28no—
100#13133202—28no—
101#13133197—28no—
102#13133194—28no—
103#13133193—22no—
104#13133193C2314yes—
105#13133192—22no—
106#13133192C2314yes—
107#13133191—22no—
108#13133191—28no—
109#13133191C2314yes—
110Q8×Dic53—22no—
111Q8×Dic53C2314yes—
112#13133179—22no—
113#13133179C2314yes—
114C4×C22⋊D53—28no—
115C4×C22⋊D53D414yes—
116C4×C22⋊D53C2314yes—
117#13133177—28no—
118#13133175—22no—
119#13133175C2314yes—
120C2×C4⋊Dic53—22no—
121C2×C4⋊Dic53—21no—
122C2×C4⋊Dic53—21no—
123C2×C4⋊Dic53—21no—
124C2×C4⋊Dic53C2311yescharacteristic
125C2×C4⋊Dic53C2314yes—
126C2×C4⋊Dic53C2311yescharacteristic
127C2×C4⋊Dic53C2311yescharacteristic
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919D411yescharacteristic
133C4⋊C4×D53—22no—
134C4⋊C4×D53C2314yes—
135C2×C22⋊Dic53D411yescharacteristic
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921D411yescharacteristic
142C2×C4×Dic53—21no—
143C2×C4×Dic53—21no—
144C2×C4×Dic53C2311yescharacteristic
145#13133150C2314yes—
146#13133150C2314yes—
147#13133150C2314yes—
148#13133150C2314yes—
149#13133149C2314yes—
150#13133149C2314yes—
151#13133148C2314yes—
152#13133146C2314yes—
153#13133141C2314yes—
154#13133139C2314yes—
155#13133139C2314yes—
156#13133137C2314yes—
157#13133129C2314yes—
158#13133127C2314yes—
159C22×Q8×C53C2311yescharacteristic
160C23×C4×C53—21no—
161C23×C4×C53C2311yescharacteristic
162C22×C8×C53C2311yescharacteristic
163C22×C8×C53C2311yescharacteristic
164C22⋊Q8×C53—22no—
165C22⋊Q8×C53C2314yes—
166C2×C4⋊C4×C53—22no—
167C2×C4⋊C4×C53—21no—
168C2×C4⋊C4×C53—21no—
169C2×C4⋊C4×C53C2314yes—
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C22⋊C4×C53—21no—
174#107×C53C2314yes—
175#107×C53C2314yes—
176#103×C53C2314yes—
177#103×C53C2314yes—
178C22⋊C8×C53C2314yes—
179C24×C53C2×D411yescharacteristic
180C23×D53—21no—
181C23×D53C2×D411yescharacteristic
182C2×Q8×C53—21no—
183C2×Q8×C53—22no—
184C2×Q8×C53—22no—
185C2×Q8×C53C2412yes—
186C22×C4×C53—22no—
187C22×C4×C53—22no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—24no—
193C22×C4×C53—82no—
194C22×C4×C53C2×D411yescharacteristic
195C22×C4×C53C2×D412yes—
196C22×C4×C53C2412yes—
197C22×C4×C53C2411yescharacteristic
198C2×C22⋊D53—24no—
199C2×C22⋊D53—24no—
200C2×C22⋊D53—44no—
201C2×C22⋊D53C2×D414yes—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—24no—
206C22×Dic53—82no—
207C22×Dic53C2×D411yescharacteristic
208C22×Dic53C2×D411yescharacteristic
209C22×Dic53C2×D411yescharacteristic
210C2×D212—22no—
211C2×D212—22no—
212C2×D212—21no—
213C2×D212—24no—
214C2×D212—82no—
215C2×D212C2412yes—
216C2×C4×D53—22no—
217C2×C4×D53—22no—
218C2×C4×D53—24no—
219C2×C4×D53—24no—
220C2×C4×D53—82no—
221C2×C4×D53—82no—
222C2×C4×D53C2×D412yes—
223C2×C4×D53C2412yes—
224C2×Dic106—24no—
225C2×Dic106—82no—
226C2×C8×C53—22no—
227C2×C8×C53—22no—
228C2×C8×C53C2412yes—
229C2×C8×C53C2412yes—
230C4⋊C4×C53—21no—
231C4⋊C4×C53—21no—
232C4⋊C4×C53—24no—
233C4⋊C4×C53—24no—
234C4⋊C4×C53—21no—
235C4⋊C4×C53C2412yes—
236C4⋊C4×C53C2412yes—
237C4⋊C4×C53C2412yes—
238C22⋊C4×C53—24no—
239C22⋊Dic53C2×D414yes—
240#11719924—28no—
241#11719921—24no—
242#11719921—24no—
243#11719921—24no—
244#11719921—24no—
245#11719921—24no—
246#11719921C2×D414yes—
247C4⋊Dic53—21no—
248C4⋊Dic53—21no—
249C4⋊Dic53—24no—
250C4⋊Dic53—21no—
251C4⋊Dic53—24no—
252C4⋊Dic53—24no—
253C4⋊Dic53C2412yes—
254C4⋊Dic53C2412yes—
255C4⋊Dic53C2412yes—
256#11719919—24no—
257#11719919—24no—
258#11719919—24no—
259#11719919—24no—
260#11719919C2×D414yes—
261C4×Dic53—24no—
262C4×Dic53—24no—
263C4×Dic53C2×D412yes—
264C4×Dic53C2412yes—
265C2×#88322—22no—
266C2×#88322—28no—
267C2×#88322#4114yes—
268C2×#88322C2412yes—
269C2×#88322C2412yes—
270#11719912—28no—
271C23×C53—22no—
272C23×C53—22no—
273C23×C53#13714yes—
274C23×C53C22×D412yes—
275C23×C53C22×D411yescharacteristic
276C22×D53—22no—
277C22×D53—22no—
278C22×D53—22no—
279C22×D53—22no—
280C22×D53—42no—
281C22×D53—42no—
282C22×D53—42no—
283C22×D53C22×D412yes—
284Q8×C53—22no—
285Q8×C53—22no—
286Q8×C53—42no—
287C2×C4×C53—22no—
288C2×C4×C53—24no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—42no—
296C2×C4×C53—42no—
297C2×C4×C53—42no—
298C2×C4×C53—42no—
299C2×C4×C53—84no—
300C2×C4×C53C22×D412yes—
301C2×C4×C53C22×D411yescharacteristic
302C2×C4×C53C2×#4112yes—
303C2×C4×C532−1+412yes—
304C2×C4×C53C2511yescharacteristic
305C22⋊D53—28no—
306C22⋊D53—48no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—42no—
314C2×Dic53—42no—
315C2×Dic53—42no—
316C2×Dic53—84no—
317C2×Dic53C22×D412yes—
318C2×Dic53C22×D412yes—
319C2×Dic53C22×D412yes—
320D212—22no—
321D212—22no—
322D212—42no—
323D212—84no—
324C4×D53—24no—
325C4×D53—22no—
326C4×D53—22no—
327C4×D53—84no—
328C4×D53—84no—
329Dic106—84no—
330C8×C53—22no—
331C8×C53—22no—
332#88322—22no—
333#88322C2×#4114yes—
334C2×#3346—531nomaximal, Sylow
335C22×C53—28no—
336C22×C53—22no—
337C22×C53—22no—
338C22×C53#54712yes—
339C22×C53C2×#13714yes—
340C22×C53C2×#13712yes—
341C22×C53#57612yes—
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—22no—
352C4×C53—42no—
353C4×C53—42no—
354C4×C53—42no—
355C4×C53—42no—
356C4×C53#54712yes—
357C4×C53C22×#4111yescharacteristic
358C4×C53C2×2−1+411yescharacteristic
359Dic53—22no—
360Dic53—22no—
361Dic53—22no—
362Dic53—42no—
363Dic53—42no—
364Dic53—42no—
365C2×#554—531no—
366C2×#553—531no—
367#3346—5316no—
368C2×#501—531no—
369C2×#484D5311yescharacteristic, complemented
370C2×#481—531no—
371C2×#485—531no—
372C2×#480—531no—
373C2×#479—531no—
374C2×#474—531no—
375C2×#468—531no—
376C2×#465—531no—
377C2×#440—531no—
378C2×#435—531no—
379C2×#428—531no—
380C22×#107—531no—
381C2×C53—24no—
382C2×C53#334614yescomplemented
383C2×C53C2×#54711yescharacteristic
384C2×C53C22×#13711yescharacteristic
385C2×C53C2×#57611yescharacteristic
386D53—42no—
387D53—82no—
388C22×SD16—531no—
389C22×M16—531no—
390C23×C8—531no—
391#554—538no—
392#554—1064no—
393#553—538no—
394#553—1064no—
395C2×C4⋊Q8—531no—
396C2×#126—1061no—
397C2×#125—531no—
398C2×#125—1061no—
399C2×#123—1061no—
400C2×C22⋊Q8—531no—
401C2×C22⋊Q8—1061no—
402C2×C22⋊Q8—1061no—
403C2×C22⋊Q8C2×D5311yescharacteristic
404C2×#121—531no—
405C2×#121—531no—
406C2×#121—1061no—
407C2×C4×Q8—531no—
408C2×C4×D4—531no—
409C2×C4×D4—531no—
410C2×C4×D4—1061no—
411C2×C4×D4—1061no—
412C2×#117—531no—
413C22×C4⋊C4—531no—
414C22×C4⋊C4—531no—
415C22×C4⋊C4C2×D5311yescharacteristic
416#501—538no—
417#485—538no—
418#484C2×D5318yescomplemented
419#481—538no—
420#480—538no—
421#479—538no—
422#474—538no—
423#468—538no—
424#465—538no—
425#440—538no—
426#435—538no—
427#428—538no—
428C2×#107—531no—
429C2×#107—531no—
430C2×#107—538no—
431C2×#107—531no—
432C2×#107—531no—
433C2×#107C2×D5311yescharacteristic
434C2×#107C2×D5311yescharacteristic
435C2×#106—531no—
436C2×#106—531no—
437C2×#106—531no—
438C2×C4⋊C8—531no—
439C2×#103—531no—
440C2×#103C2×D5311yescharacteristic
441C2×#103C2×D5311yescharacteristic
442C2×#102—531no—
443C2×#102—531no—
444C2×#102—531no—
445C2×C22⋊C8—531no—
446C2×C22⋊C8C2×D5311yescharacteristic
447C2×#97—531no—
448C53C2×#334611yescharacteristic, complemented, Sylow
449C22×Q8—1061no—
450C22×Q8C22×D5311yescharacteristic
451C22×D4—531no—
452C22×D4—531no—
453C22×D4—1061no—
454C22×D4—1061no—
455C23×C4—21no—
456C23×C4—531no—
457C23×C4—1061no—
458C23×C4—1061no—
459C23×C4—1061no—
460C23×C4C22×D5311yescharacteristic
461C2×SD16—534no—
462C2×SD16—1064no—
463C2×M16—534no—
464C2×M16—1064no—
465C22×C8—531no—
466C22×C8—531no—
467C22×C8—534no—
468C22×C8—1064no—
469C22×C8C22×D5311yescharacteristic
470C22×C8C22×D5311yescharacteristic
471C4⋊Q8—534no—
472C4⋊Q8—1062no—
473#126—1068no—
474#125—534no—
475#125—1062no—
476#125—1068no—
477#123—1068no—
478C22⋊Q8—22no—
479C22⋊Q8—534no—
480C22⋊Q8—1068no—
481C22⋊Q8—1068no—
482C22⋊Q8—1062no—
483C22⋊Q8C22×D5314yes—
484#121—534no—
485#121—534no—
486#121—1062no—
487#121—1068no—
488#121—1062no—
489C4×Q8—534no—
490C4×Q8—1062no—
491C4×D4—534no—
492C4×D4—534no—
493C4×D4—534no—
494C4×D4—1062no—
495C4×D4—1068no—
496C4×D4—1068no—
497#117—534no—
498#117—1062no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—531no—
503C2×C4⋊C4—531no—
504C2×C4⋊C4—531no—
505C2×C4⋊C4—534no—
506C2×C4⋊C4—531no—
507C2×C4⋊C4—534no—
508C2×C4⋊C4—1062no—
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—1062no—
517C2×C4⋊C4C22×D5311yescharacteristic
518C2×C4⋊C4C22×D5311yescharacteristic
519C2×C4⋊C4C22×D5311yescharacteristic
520C2×C4⋊C4C22×D5314yes—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—531no—
523C2×C22⋊C4—531no—
524C2×C22⋊C4—1061no—
525C2×C22⋊C4—1061no—
526C2×C22⋊C4—1061no—
527C2×C22⋊C4—1061no—
528C2×C22⋊C4—1061no—
529C2×C42—531no—
530C2×C42—1061no—
531C2×C42—1061no—
532#107—534no—
533#107—534no—
534#107—534no—
535#107—534no—
536#107C22×D5314yes—
537#107C22×D5314yes—
538#106—534no—
539#106—534no—
540#106—534no—
541C4⋊C8—534no—
542#103—534no—
543#103C22×D5314yes—
544#103C22×D5314yes—
545#102—534no—
546#102—534no—
547#102—534no—
548C22⋊C8—534no—
549C22⋊C8C22×D5314yes—
550#97—534no—
551C24—531no—
552C24—1061no—
553C24D4×D5311yescharacteristic
554C2×Q8—21no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—1064no—
558C2×Q8—4242no—
559C2×Q8C23×D5312yes—
560C2×D4—534no—
561C2×D4—532no—
562C2×D4—1064no—
563C2×D4—1064no—
564C2×D4—1064no—
565C2×D4—1061no—
566C2×D4—1062no—
567C2×D4—1062no—
568C2×D4—4242no—
569C2×D4—2124no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—24no—
577C22×C4—82no—
578C22×C4—531no—
579C22×C4—531no—
580C22×C4—531no—
581C22×C4—532no—
582C22×C4—532no—
583C22×C4—1064no—
584C22×C4—1064no—
585C22×C4—1062no—
586C22×C4—1062no—
587C22×C4—1064no—
588C22×C4—1061no—
589C22×C4—1061no—
590C22×C4—1061no—
591C22×C4—4242no—
592C22×C4—4242no—
593C22×C4—4242no—
594C22×C4D4×D5312yes—
595C22×C4D4×D5311yescharacteristic
596C22×C4C23×D5312yes—
597C22×C4C23×D5311yescharacteristic
598SD16—1068no—
599M16—1068no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—534no—
603C2×C8—532no—
604C2×C8—532no—
605C2×C8—1068no—
606C2×C8—1062no—
607C2×C8C23×D5312yes—
608C2×C8C23×D5312yes—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—534no—
615C4⋊C4—532no—
616C4⋊C4—532no—
617C4⋊C4—532no—
618C4⋊C4—1064no—
619C4⋊C4—1064no—
620C4⋊C4—1064no—
621C4⋊C4—1064no—
622C4⋊C4—1064no—
623C4⋊C4—1064no—
624C4⋊C4—1061no—
625C4⋊C4—1064no—
626C4⋊C4—1061no—
627C4⋊C4—1061no—
628C4⋊C4C23×D5312yes—
629C4⋊C4C23×D5312yes—
630C4⋊C4C23×D5312yes—
631C22⋊C4—24no—
632C22⋊C4—534no—
633C22⋊C4—534no—
634C22⋊C4—1064no—
635C22⋊C4—1064no—
636C22⋊C4—1064no—
637C22⋊C4—1064no—
638C22⋊C4—1064no—
639C42—532no—
640C42—532no—
641C42—1064no—
642C42—1064no—
643C23—22no—
644C23—22no—
645C23—532no—
646C23—1062no—
647C23—1062no—
648C23—1062no—
649C23—1062no—
650C23—2122no—
651C23—2122no—
652C23—2122no—
653C23#1313324914yes—
654C23C2×D4×D5312yes—
655C23C2×D4×D5311yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—4244no—
660D4—1068no—
661D4—1062no—
662D4—1062no—
663D4—4244no—
664D4—2128no—
665D4—2122no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—84no—
679C2×C4—532no—
680C2×C4—532no—
681C2×C4—532no—
682C2×C4—1062no—
683C2×C4—1062no—
684C2×C4—1062no—
685C2×C4—1064no—
686C2×C4—1062no—
687C2×C4—1062no—
688C2×C4—1062no—
689C2×C4—1062no—
690C2×C4—1062no—
691C2×C4—4244no—
692C2×C4—4244no—
693C2×C4—4244no—
694C2×C4—2122no—
695C2×C4—2122no—
696C2×C4—2122no—
697C2×C4C2×D4×D5312yes—
698C2×C4C2×D4×D5311yescharacteristic
699C2×C4#41×D5312yes—
700C2×C4#1313326412yes—
701C2×C4C24×D5311yescharacteristic
702C8—22no—
703C8—22no—
704C8—534no—
705C8—1062no—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—1062no—
710C22—1062no—
711C22—1062no—
712C22—4244no—
713C22—2122no—
714C22—2122no—
715C22—2122no—
716C22—2124no—
717C22#1681127112yes—
718C22C2×#1313324914yes—
719C22C2×#1313324912yes—
720C22#1681142712yes—
721C22C22×D4×D5311yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—1062no—
728C4—1062no—
729C4—1062no—
730C4—2122no—
731C4—2122no—
732C4—2122no—
733C4#1681127112yes—
734C4C2×#41×D5311yescharacteristic
735C4C2×#1313326411yescharacteristic
736C2—24no—
737C2—4242no—
738C2—2122no—
739C2#2028720414yesdirect product factor
740C2C2×#1681127111yescharacteristic
741C2C22×#1313324911yescharacteristic
742C2C2×#1681142711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#484C2
socleC23×C53C22×D4
prime radicalC2×#16811321C2
hypercenterC2×#484D53
hypocenterC53C2×#3346
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
1. C2×#16811331C2semidirect
3. #20287204C2direct (N × H)
4. C2×#16811031C2semidirect
5. C2×#16810942C2semidirect
6. C2×#16810962C2semidirect
7. C2×#16810938C2semidirect
8. C2×#16810928C2semidirect
9. C2×#16810902C2semidirect
10. C2×#16810872C2semidirect
11. C2×#16810854C2semidirect
12. C2×#16810726C2semidirect
13. C2×#16810691C2semidirect
14. C2×#16810664C2semidirect
15. C22×#13133150C2semidirect
16. C2×C53×#484C2semidirect
21. #16811331C22semidirect
43. #16811031C22semidirect
44. #16810962C22semidirect
45. #16810942C22semidirect
46. #16810938C22semidirect
47. #16810928C22semidirect
48. #16810902C22semidirect
49. #16810872C22semidirect
50. #16810854C22semidirect
51. #16810726C22semidirect
52. #16810691C22semidirect
53. #16810664C22semidirect
58. C2×#13133150C22semidirect
71. C53×#484C22semidirect
369. C2×#484D53semidirect
382. C2×C53#3346semidirect
418. #484C2×D53semidirect
448. C53C2×#3346semidirect
739. C2#20287204direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113312
C2×#168113212
#202872042
C2×#168110312
C2×#168109422
C2×#168109622
C2×#168109382
C2×#168109282
C2×#168109022
C2×#168108722
C2×#168108542
C2×#168107262
C2×#168106912
C2×#168106642
C22×#131331502
C2×C53×#4842
C2×#334653