Finite Group Databasebeta

← C2×#20286062 #28256909

Subgroups — C2×#20286062 #28256909

Order 13568.

1962 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811157C211yesmaximal, characteristic, complemented
2#20286062C2116yesmaximal, direct product factor
3C2×#16810930C211yesmaximal, characteristic, complemented
4C2×#16810927C211yesmaximal, characteristic, complemented
5C2×#16810923C211yesmaximal, characteristic, complemented
6C2×#16810920C211yesmaximal, characteristic, complemented
7C2×#16810862C211yesmaximal, characteristic, complemented
8C2×#16810857C211yesmaximal, characteristic
9C2×#16810854C211yesmaximal, characteristic, complemented
10C2×#16810850C211yesmaximal, characteristic, complemented
11C2×#16810845C211yesmaximal, characteristic, complemented
12C2×#16810842C211yesmaximal, characteristic, complemented
13C2×#16810838C211yesmaximal, characteristic, complemented
14C2×#16810835C211yesmaximal, characteristic, complemented
15C22×C4⋊#88322C211yesmaximal, characteristic, complemented
16C2×C53×#529C211yesmaximal, characteristic, complemented
17C22×#11719925C2211yescharacteristic
18C22×#11719923C2211yescharacteristic
19C22×#11719924C2211yescharacteristic
20C22×#11719922C2211yescharacteristic
21C23×#88322C2211yescharacteristic
22C23×#88322C2211yescharacteristic
23#16811157—24no—
24#16811157C2218yescomplemented
25C2×#13133211—21no—
26C2×#13133209C2211yescharacteristic
27C2×#13133205C2211yescharacteristic
28C2×#13133200—21no—
29C2×#13133196C2211yescharacteristic
30C2×#13133191C2211yescharacteristic
31C2×C4×Dic106C2211yescharacteristic
32C2×C4×D212C2211yescharacteristic
33C2×C4×C22⋊D53—21no—
34C2×#13133174—21no—
35#16810930C2218yescomplemented
36#16810927C2218yescomplemented
37#16810923C2218yescomplemented
38#16810920C2218yescomplemented
39#16810862C2218yescomplemented
40#16810857C2218yes—
41#16810854C2218yescomplemented
42#16810850C2218yescomplemented
43#16810845C2218yescomplemented
44#16810842C2218yescomplemented
45#16810838C2218yescomplemented
46#16810835C2218yescomplemented
47C2×#13133150C2211yescharacteristic
48C2×#13133150C2211yescharacteristic
49C2×#13133148C2211yescharacteristic
50C2×#13133148C2211yescharacteristic
51C2×C4⋊#88322C2211yescharacteristic
52C2×C4⋊#88322C2211yescharacteristic
53C2×C4⋊#88322C2211yescharacteristic
54C2×C4⋊#88322C2211yescharacteristic
55C2×C4⋊#88322C2218yescomplemented
56C2×#13133141C2211yescharacteristic
57C2×#13133141C2211yescharacteristic
58C2×#13133140C2211yescharacteristic
59C2×#13133140C2211yescharacteristic
60C2×#13133138C2211yescharacteristic
61C2×#13133138C2211yescharacteristic
62C2×#13133137C2211yescharacteristic
63C2×#13133137C2211yescharacteristic
64C53×#529—24no—
65C53×#529C2218yescomplemented
66C2×#126×C53—21no—
67C2×#125×C53C2211yescharacteristic
68C2×#124×C53C2211yescharacteristic
69C2×#123×C53—21no—
70C2×C22⋊Q8×C53C2211yescharacteristic
71C2×#121×C53C2211yescharacteristic
72C2×C4×Q8×C53C2211yescharacteristic
73C2×C4×D4×C53—21no—
74C2×C4×D4×C53C2211yescharacteristic
75C2×#117×C53—21no—
76C22×C42×C53C2211yescharacteristic
77C22×Dic106C2311yescharacteristic
78C22×D212C2311yescharacteristic
79C22×C22⋊D53—21no—
80C22×C4×D53—21no—
81C2×#11719925—42no—
82C2×#11719925C2314yes—
83C2×#11719923—42no—
84C2×#11719923C2314yes—
85C2×#11719924—42no—
86C2×#11719924C2314yes—
87C2×#11719922—42no—
88C2×#11719922C2314yes—
89C22×#88322—42no—
90C22×#88322—42no—
91C22×#88322C2311yescharacteristic
92C22×#88322C2311yescharacteristic
93C22×#88322C2311yescharacteristic
94C22×#88322C2311yescharacteristic
95C22×#88322C2314yes—
96C22×#88322C2314yes—
97#13133211—28no—
98#13133209—22no—
99#13133209C2314yes—
100#13133205—22no—
101#13133205C2314yes—
102#13133200—28no—
103#13133196—22no—
104#13133196C2314yes—
105#13133191—22no—
106#13133191C2314yes—
107C4×Dic106—22no—
108C4×Dic106C2314yes—
109C4×D212—22no—
110C4×D212C2314yes—
111C4×C22⋊D53—28no—
112#13133174—28no—
113C2×C4⋊Dic53C2311yescharacteristic
114C2×C4⋊Dic53C2311yescharacteristic
115C2×#11719919—21no—
116C2×#11719919—21no—
117C2×#11719919—21no—
118C2×#11719919—21no—
119C2×C22⋊Dic53—21no—
120C2×#11719921—21no—
121C2×#11719921—21no—
122C2×#11719921—21no—
123C2×#11719921—21no—
124C2×C4×Dic53—21no—
125#13133150C2314yes—
126#13133150C2314yes—
127#13133148C2314yes—
128#13133148C2314yes—
129C4⋊#88322C2314yes—
130C4⋊#88322C2314yes—
131C4⋊#88322C2314yes—
132C4⋊#88322C2314yes—
133#13133141C2314yes—
134#13133141C2314yes—
135#13133140C2314yes—
136#13133140C2314yes—
137#13133138C2314yes—
138#13133138C2314yes—
139#13133137C2314yes—
140#13133137C2314yes—
141C22×Q8×C53C2311yescharacteristic
142C22×D4×C53—21no—
143C22×D4×C53C2311yescharacteristic
144C23×C4×C53—21no—
145C23×C4×C53D411yescharacteristic
146C23×C4×C53D411yescharacteristic
147C23×C4×C53C2311yescharacteristic
148#126×C53—28no—
149#125×C53—22no—
150#125×C53C2314yes—
151#124×C53—22no—
152#124×C53C2314yes—
153#123×C53—28no—
154C22⋊Q8×C53—22no—
155C22⋊Q8×C53C2314yes—
156#121×C53—22no—
157#121×C53C2314yes—
158C4×Q8×C53—22no—
159C4×Q8×C53C2314yes—
160C4×D4×C53—22no—
161C4×D4×C53—28no—
162C4×D4×C53C2314yes—
163#117×C53—28no—
164C2×C4⋊C4×C53—21no—
165C2×C4⋊C4×C53—21no—
166C2×C4⋊C4×C53—21no—
167C2×C4⋊C4×C53—21no—
168C2×C4⋊C4×C53C2311yescharacteristic
169C2×C4⋊C4×C53C2311yescharacteristic
170C2×C22⋊C4×C53—21no—
171C2×C22⋊C4×C53—21no—
172C2×C22⋊C4×C53—21no—
173C2×C22⋊C4×C53—21no—
174C2×C22⋊C4×C53—21no—
175C2×C42×C53—21no—
176C2×C42×C53D411yescharacteristic
177C2×C42×C53D411yescharacteristic
178C2×C42×C53D414yes—
179C2×C42×C53C2311yescharacteristic
180C2×C42×C53C2311yescharacteristic
181C2×C42×C53C2314yes—
182C24×C53—21no—
183C24×C53C2×D411yescharacteristic
184C23×D53—21no—
185C2×Q8×C53—21no—
186C2×Q8×C53—22no—
187C2×Q8×C53—22no—
188C2×Q8×C53C2412yes—
189C2×D4×C53—24no—
190C2×D4×C53—21no—
191C2×D4×C53—22no—
192C2×D4×C53—22no—
193C2×D4×C53—44no—
194C2×D4×C53C2412yes—
195C22×C4×C53—24no—
196C22×C4×C53—22no—
197C22×C4×C53—22no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—24no—
202C22×C4×C53—42no—
203C22×C4×C53—44no—
204C22×C4×C53C2×D411yescharacteristic
205C22×C4×C53C2×D411yescharacteristic
206C22×C4×C53C2×D412yes—
207C22×C4×C53C2×D411yescharacteristic
208C22×C4×C53C2×D411yescharacteristic
209C22×C4×C53C2×D411yescharacteristic
210C22×C4×C53C2×D414yes—
211C22×C4×C53C2×D414yes—
212C22×C4×C53C2412yes—
213C22×C4×C53C2411yescharacteristic
214C2×C22⋊D53—24no—
215C2×C22⋊D53—44no—
216C22×Dic53—21no—
217C22×Dic53—21no—
218C22×Dic53—21no—
219C2×D212—22no—
220C2×D212—22no—
221C2×D212—21no—
222C2×D212C2412yes—
223C2×C4×D53—24no—
224C2×C4×D53—44no—
225C2×Dic106—22no—
226C2×Dic106—22no—
227C2×Dic106—21no—
228C2×Dic106C2412yes—
229C4⋊C4×C53—24no—
230C4⋊C4×C53—24no—
231C4⋊C4×C53—24no—
232C4⋊C4×C53—24no—
233C4⋊C4×C53—21no—
234C4⋊C4×C53—21no—
235C4⋊C4×C53C2412yes—
236C4⋊C4×C53C2412yes—
237C22⋊C4×C53—24no—
238C22⋊C4×C53—24no—
239C22⋊C4×C53—24no—
240C22⋊C4×C53—24no—
241C22⋊C4×C53—24no—
242C42×C53—24no—
243C42×C53C2×D414yes—
244C42×C53C2×D412yes—
245C42×C53C2×D412yes—
246C42×C53C2×D414yes—
247C42×C53C2412yes—
248C42×C53C2412yes—
249C22⋊Dic53—24no—
250#11719925—44no—
251#11719924—44no—
252#11719923—44no—
253#11719922—44no—
254#11719921—24no—
255#11719921—24no—
256#11719921—24no—
257#11719921—24no—
258C4⋊Dic53—21no—
259C4⋊Dic53—21no—
260C4⋊Dic53C2412yes—
261C4⋊Dic53C2412yes—
262#11719919—24no—
263#11719919—24no—
264#11719919—24no—
265#11719919—24no—
266C4×Dic53—24no—
267C2×#88322—22no—
268C2×#88322—22no—
269C2×#88322—22no—
270C2×#88322—22no—
271C2×#88322—44no—
272C2×#88322—44no—
273C2×#88322C2412yes—
274C2×#88322C2412yes—
275C2×#88322C2412yes—
276C2×#88322C2412yes—
277C23×C53—22no—
278C23×C53—22no—
279C23×C53—22no—
280C23×C53—42no—
281C23×C53—42no—
282C23×C53—42no—
283C23×C53#13514yes—
284C23×C53C22×D412yes—
285C23×C53C22×D411yescharacteristic
286C22×D53—22no—
287C22×D53—42no—
288C22×D53—42no—
289C22×D53—42no—
290Q8×C53—22no—
291Q8×C53—22no—
292Q8×C53—42no—
293D4×C53—22no—
294D4×C53—22no—
295D4×C53—48no—
296D4×C53—42no—
297C2×C4×C53—22no—
298C2×C4×C53—28no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—24no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—44no—
310C2×C4×C53—48no—
311C2×C4×C53—42no—
312C2×C4×C53—42no—
313C2×C4×C53—42no—
314C2×C4×C53C22×D412yes—
315C2×C4×C53C22×D412yes—
316C2×C4×C53C22×D412yes—
317C2×C4×C53C22×D412yes—
318C2×C4×C53C22×D412yes—
319C2×C4×C53C22×D411yescharacteristic
320C2×C4×C53H(5,𝔽2)12yes—
321C2×C4×C532−1+412yes—
322C2×C4×C53C2511yescharacteristic
323C22⋊D53—48no—
324C2×Dic53—22no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—42no—
328C2×Dic53—42no—
329C2×Dic53—42no—
330D212—22no—
331D212—22no—
332D212—42no—
333C4×D53—48no—
334Dic106—22no—
335Dic106—22no—
336Dic106—42no—
337#88322—22no—
338#88322—22no—
339#88322—22no—
340#88322—22no—
341C2×#3250—531nomaximal, Sylow
342C22×C53—22no—
343C22×C53—28no—
344C22×C53—22no—
345C22×C53—42no—
346C22×C53—42no—
347C22×C53—42no—
348C22×C53—84no—
349C22×C53#53712yes—
350C22×C53C2×#13514yes—
351C22×C53C2×#13512yes—
352C22×C53#57512yes—
353C22×C53C23×D411yescharacteristic
354C2×D53—42no—
355C2×D53—42no—
356C2×D53—42no—
357C2×D53—84no—
358C4×C53—22no—
359C4×C53—22no—
360C4×C53—22no—
361C4×C53—22no—
362C4×C53—22no—
363C4×C53—42no—
364C4×C53—42no—
365C4×C53—42no—
366C4×C53#53712yes—
367C4×C53C2×H(5,𝔽2)11yescharacteristic
368C4×C53C2×2−1+411yescharacteristic
369Dic53—42no—
370Dic53—42no—
371Dic53—42no—
372C2×#529—531no—
373C2×#529D5311yescharacteristic, complemented
374#3250—5316no—
375C2×#479—531no—
376C2×#479—531no—
377C2×#478—531no—
378C2×#478—531no—
379C2×#467—531no—
380C2×#466—531no—
381C2×#465—531no—
382C2×#465—531no—
383C2×#464—531no—
384C2×#464—531no—
385C2×#463—531no—
386C2×#463—531no—
387C22×C4⋊C8—531no—
388C2×C53—24no—
389C2×C53—82no—
390C2×C53#325014yescomplemented
391C2×C53C2×#53711yescharacteristic
392C2×C53C22×#13511yescharacteristic
393C2×C53C2×#57511yescharacteristic
394D53—82no—
395C22×Q16—531no—
396C22×SD16—531no—
397C22×SD16—531no—
398C22×D8—531no—
399C23×C8—531no—
400C23×C8—531no—
401#529—24no—
402#529—538no—
403#529—1064no—
404#529C2×D5318yescomplemented
405C2×#126—21no—
406C2×#126—1061no—
407C2×#125—531no—
408C2×#125C2×D5311yescharacteristic
409C2×#124—531no—
410C2×#124C2×D5311yescharacteristic
411C2×#123—21no—
412C2×#123—1061no—
413C2×C22⋊Q8—531no—
414C2×C22⋊Q8C2×D5311yescharacteristic
415C2×#121—531no—
416C2×#121C2×D5311yescharacteristic
417C2×C4×Q8—531no—
418C2×C4×Q8C2×D5311yescharacteristic
419C2×C4×D4—21no—
420C2×C4×D4—531no—
421C2×C4×D4—1061no—
422C2×C4×D4C2×D5311yescharacteristic
423C2×#117—21no—
424C2×#117—1061no—
425C22×C42C2×D5311yescharacteristic
426#479—538no—
427#479—538no—
428#478—538no—
429#478—538no—
430#467—538no—
431#466—538no—
432#465—538no—
433#465—538no—
434#464—538no—
435#464—538no—
436#463—538no—
437#463—538no—
438C2×#107—531no—
439C2×#107—531no—
440C2×#106—531no—
441C2×#106—531no—
442C2×C4⋊C8—531no—
443C2×C4⋊C8—531no—
444C2×C4⋊C8—531no—
445C2×C4⋊C8—531no—
446C2×C4⋊C8—538no—
447C2×#103—531no—
448C2×#103—531no—
449C2×#103—531no—
450C2×#103—531no—
451C2×#102—531no—
452C2×#102—531no—
453C2×#102—531no—
454C2×#102—531no—
455C53C2×#325011yescharacteristic, complemented, Sylow
456C22×Q8—531no—
457C22×Q8C22×D5311yescharacteristic
458C22×D4—21no—
459C22×D4—531no—
460C22×D4—1061no—
461C22×D4C22×D5311yescharacteristic
462C23×C4—21no—
463C23×C4—1061no—
464C23×C4C22⋊D5311yescharacteristic
465C23×C4C22⋊D5311yescharacteristic
466C23×C4C22×D5311yescharacteristic
467C2×Q16—534no—
468C2×Q16—2122no—
469C2×SD16—534no—
470C2×SD16—534no—
471C2×SD16—2122no—
472C2×SD16—2122no—
473C2×D8—534no—
474C2×D8—2122no—
475C22×C8—531no—
476C22×C8—531no—
477C22×C8—531no—
478C22×C8—531no—
479C22×C8—534no—
480C22×C8—534no—
481C22×C8—2122no—
482C22×C8—2122no—
483#126—28no—
484#126—1068no—
485#125—22no—
486#125—534no—
487#125—1062no—
488#125C22×D5314yes—
489#124—22no—
490#124—534no—
491#124—1062no—
492#124C22×D5314yes—
493#123—28no—
494#123—1068no—
495C22⋊Q8—22no—
496C22⋊Q8—534no—
497C22⋊Q8—1062no—
498C22⋊Q8C22×D5314yes—
499#121—22no—
500#121—534no—
501#121—1062no—
502#121C22×D5314yes—
503C4×Q8—22no—
504C4×Q8—534no—
505C4×Q8—1062no—
506C4×Q8C22×D5314yes—
507C4×D4—28no—
508C4×D4—22no—
509C4×D4—534no—
510C4×D4—1068no—
511C4×D4—1062no—
512C4×D4C22×D5314yes—
513#117—28no—
514#117—1068no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—531no—
520C2×C4⋊C4—531no—
521C2×C4⋊C4—1061no—
522C2×C4⋊C4—1061no—
523C2×C4⋊C4—1061no—
524C2×C4⋊C4—1061no—
525C2×C4⋊C4C22×D5311yescharacteristic
526C2×C4⋊C4C22×D5311yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—1061no—
533C2×C22⋊C4—1061no—
534C2×C22⋊C4—1061no—
535C2×C22⋊C4—1061no—
536C2×C22⋊C4—1061no—
537C2×C42—21no—
538C2×C42—1061no—
539C2×C42C22⋊D5311yescharacteristic
540C2×C42C22⋊D5311yescharacteristic
541C2×C42C22⋊D5314yes—
542C2×C42C22×D5311yescharacteristic
543C2×C42C22×D5311yescharacteristic
544C2×C42C22×D5314yes—
545#107—534no—
546#107—534no—
547#106—534no—
548#106—534no—
549C4⋊C8—534no—
550C4⋊C8—534no—
551C4⋊C8—534no—
552C4⋊C8—534no—
553#103—534no—
554#103—534no—
555#103—534no—
556#103—534no—
557#102—534no—
558#102—534no—
559#102—534no—
560#102—534no—
561C24—21no—
562C24—1061no—
563C24C2×C22⋊D5311yescharacteristic
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—532no—
568C2×Q8—1061no—
569C2×Q8—1062no—
570C2×Q8—1062no—
571C2×Q8C23×D5312yes—
572C2×D4—24no—
573C2×D4—21no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—44no—
577C2×D4—532no—
578C2×D4—1064no—
579C2×D4—1061no—
580C2×D4—1062no—
581C2×D4—1062no—
582C2×D4—2124no—
583C2×D4C23×D5312yes—
584C22×C4—24no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—24no—
591C22×C4—42no—
592C22×C4—44no—
593C22×C4—1061no—
594C22×C4—1061no—
595C22×C4—1061no—
596C22×C4—1064no—
597C22×C4—2124no—
598C22×C4C2×C22⋊D5312yes—
599C22×C4C2×C22⋊D5314yes—
600C22×C4C2×C22⋊D5311yescharacteristic
601C22×C4C2×C22⋊D5311yescharacteristic
602C22×C4C2×C22⋊D5311yescharacteristic
603C22×C4C2×C22⋊D5311yescharacteristic
604C22×C4C2×C22⋊D5311yescharacteristic
605C22×C4C2×C22⋊D5314yes—
606C22×C4C23×D5312yes—
607C22×C4C23×D5311yescharacteristic
608Q16—2124no—
609SD16—2124no—
610SD16—2124no—
611D8—2124no—
612C2×C8—532no—
613C2×C8—532no—
614C2×C8—532no—
615C2×C8—532no—
616C2×C8—1062no—
617C2×C8—1062no—
618C2×C8—1062no—
619C2×C8—1062no—
620C2×C8—2124no—
621C2×C8—2124no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—532no—
629C4⋊C4—532no—
630C4⋊C4—1061no—
631C4⋊C4—1061no—
632C4⋊C4—1064no—
633C4⋊C4—1064no—
634C4⋊C4—1064no—
635C4⋊C4—1064no—
636C4⋊C4C23×D5312yes—
637C4⋊C4C23×D5312yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—1064no—
644C22⋊C4—1064no—
645C22⋊C4—1064no—
646C22⋊C4—1064no—
647C22⋊C4—1064no—
648C42—24no—
649C42—1064no—
650C42C2×C22⋊D5314yes—
651C42C2×C22⋊D5314yes—
652C42C2×C22⋊D5312yes—
653C42C2×C22⋊D5312yes—
654C42C23×D5312yes—
655C42C23×D5312yes—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—1062no—
663C23—2122no—
664C23—2122no—
665C23—2122no—
666C23#1313323714yes—
667C23C22×C22⋊D5312yes—
668C23C22×C22⋊D5311yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—1062no—
673Q8—1062no—
674Q8—2122no—
675D4—22no—
676D4—22no—
677D4—48no—
678D4—42no—
679D4—1062no—
680D4—1062no—
681D4—2128no—
682D4—2122no—
683C2×C4—28no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—44no—
696C2×C4—48no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—1062no—
701C2×C4—1062no—
702C2×C4—1062no—
703C2×C4—2128no—
704C2×C4—2122no—
705C2×C4—2122no—
706C2×C4—2122no—
707C2×C4C22×C22⋊D5312yes—
708C2×C4C22×C22⋊D5312yes—
709C2×C4C22×C22⋊D5312yes—
710C2×C4C22×C22⋊D5312yes—
711C2×C4C22×C22⋊D5312yes—
712C2×C4C22×C22⋊D5311yescharacteristic
713C2×C4#1313326312yes—
714C2×C4#1313326412yes—
715C2×C4C24×D5311yescharacteristic
716C8—1062no—
717C8—1062no—
718C8—1062no—
719C8—1062no—
720C22—22no—
721C22—28no—
722C22—22no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—84no—
727C22—4244no—
728C22—2122no—
729C22—2122no—
730C22—2122no—
731C22#1681120112yes—
732C22C2×#1313323714yes—
733C22C2×#1313323712yes—
734C22#1681142112yes—
735C22C23×C22⋊D5311yescharacteristic
736C4—22no—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—22no—
741C4—42no—
742C4—42no—
743C4—42no—
744C4—2122no—
745C4—2122no—
746C4—2122no—
747C4#1681120112yes—
748C4C2×#1313326311yescharacteristic
749C4C2×#1313326411yescharacteristic
750C2—24no—
751C2—82no—
752C2—4242no—
753C2#2028606214yesdirect product factor
754C2C2×#1681120111yescharacteristic
755C2C22×#1313323711yescharacteristic
756C2C2×#1681142111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#529C2
socleC23×C53C22×D4
prime radicalC2×#16810857C2
hypercenterC2×#529D53
hypocenterC53C2×#3250
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×#16811157C2semidirect
2. #20286062C2direct (N × H)
3. C2×#16810930C2semidirect
4. C2×#16810927C2semidirect
5. C2×#16810923C2semidirect
6. C2×#16810920C2semidirect
7. C2×#16810862C2semidirect
9. C2×#16810854C2semidirect
10. C2×#16810850C2semidirect
11. C2×#16810845C2semidirect
12. C2×#16810842C2semidirect
13. C2×#16810838C2semidirect
14. C2×#16810835C2semidirect
15. C22×C4⋊#88322C2semidirect
16. C2×C53×#529C2semidirect
24. #16811157C22semidirect
35. #16810930C22semidirect
36. #16810927C22semidirect
37. #16810923C22semidirect
38. #16810920C22semidirect
39. #16810862C22semidirect
41. #16810854C22semidirect
42. #16810850C22semidirect
43. #16810845C22semidirect
44. #16810842C22semidirect
45. #16810838C22semidirect
46. #16810835C22semidirect
55. C2×C4⋊#88322C22semidirect
65. C53×#529C22semidirect
373. C2×#529D53semidirect
390. C2×C53#3250semidirect
404. #529C2×D53semidirect
455. C53C2×#3250semidirect
753. C2#20286062direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111572
#202860622
C2×#168109302
C2×#168109272
C2×#168109232
C2×#168109202
C2×#168108622
C2×#168108572
C2×#168108542
C2×#168108502
C2×#168108452
C2×#168108422
C2×#168108382
C2×#168108352
C22×C4⋊#883222
C2×C53×#5292
C2×#325053