Finite Group Databasebeta

← C2×#20286586 #28260482

Subgroups — C2×#20286586 #28260482

Order 13568.

2158 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811331C211yesmaximal, characteristic
2C2×#16811286C211yesmaximal, characteristic
3#20286586C2116yesmaximal, direct product factor
4C2×#16810972C211yesmaximal, characteristic, complemented
5C2×#16810960C211yesmaximal, characteristic, complemented
6C2×#16810956C211yesmaximal, characteristic, complemented
7C2×#16810917C211yesmaximal, characteristic, complemented
8C2×#16810863C211yesmaximal, characteristic, complemented
9C2×#16810831C211yesmaximal, characteristic, complemented
10C2×#16810778C211yesmaximal, characteristic, complemented
11C2×#16810777C211yesmaximal, characteristic, complemented
12C2×#16810715C211yesmaximal, characteristic, complemented
13C2×C8×C22⋊D53C211yesmaximal, characteristic
14C22×#13133142C211yesmaximal, characteristic, complemented
15C2×#103×D53C211yesmaximal, characteristic, complemented
16C2×C53×#467C211yesmaximal, characteristic, complemented
17C23×Dic106C2211yescharacteristic
18C22×Q8×D53C2211yescharacteristic
19C22×#11719925C2211yescharacteristic
20C22×#11719925C2211yescharacteristic
21C22×C8×D53C2211yescharacteristic
22#16811331—24no—
23#16811331C2218yes—
24#16811286—24no—
25#16811286C2218yes—
26C2×#13133216—21no—
27C2×#13133216C2211yescharacteristic
28C2×#13133215C2211yescharacteristic
29C2×#13133207—21no—
30C2×#13133197—21no—
31C2×#13133197C2211yescharacteristic
32C2×#13133195—21no—
33C2×#13133194—21no—
34C2×#13133194—21no—
35C2×#13133193C2211yescharacteristic
36C2×Q8×Dic53C2211yescharacteristic
37C2×#13133182C2211yescharacteristic
38C2×C4×C22⋊D53C2211yescharacteristic
39C2×#13133177—21no—
40C2×#13133177—21no—
41C22×C4⋊Dic53C2211yescharacteristic
42C2×C4⋊C4×D53C2211yescharacteristic
43#16810972C2218yescomplemented
44#16810960C2218yescomplemented
45#16810956C2218yescomplemented
46#16810917C2218yescomplemented
47#16810863C2218yescomplemented
48#16810831C2218yescomplemented
49#16810778C2218yescomplemented
50#16810777C2218yescomplemented
51#16810715C2218yescomplemented
52C8×C22⋊D53C2218yes—
53C2×#13133150C2211yescharacteristic
54C2×#13133150C2211yescharacteristic
55C2×#13133146C2211yescharacteristic
56C2×#13133142C2211yescharacteristic
57C2×#13133142C2211yescharacteristic
58C2×#13133142C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133142C2218yescomplemented
61C2×#13133141C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133140C2211yescharacteristic
65#103×D53C2218yescomplemented
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×Q16×C53C2211yescharacteristic
70C23×C8×C53C2211yescharacteristic
71C2×C22⋊Q8×C53C2211yescharacteristic
72C2×C22⋊Q8×C53C2211yescharacteristic
73C53×#467C2218yescomplemented
74C2×#107×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#103×C53C2211yescharacteristic
77C22×Dic106—24no—
78C22×Dic106—22no—
79C22×Dic106—21no—
80C22×Dic106—21no—
81C22×Dic106—21no—
82C22×Dic106—42no—
83C22×Dic106C2311yescharacteristic
84C22×Dic106C2314yes—
85C22×Dic106C2311yescharacteristic
86C2×Q8×D53—22no—
87C2×Q8×D53—24no—
88C2×Q8×D53—42no—
89C2×Q8×D53C2314yes—
90C22×C22⋊D53D411yescharacteristic
91C23×Dic53—21no—
92C23×Dic53—21no—
93C22×C4×D53—21no—
94C22×C4×D53—21no—
95C22×C4×D53C2311yescharacteristic
96C2×#11719925—24no—
97C2×#11719925—42no—
98C2×#11719925C2314yes—
99C2×#11719925C2314yes—
100C22×#88322C2311yescharacteristic
101C22×#88322C2311yescharacteristic
102C2×C8×D53—42no—
103C2×C8×D53C2314yes—
104#13133216—28no—
105#13133216—22no—
106#13133216C2314yes—
107#13133215—22no—
108#13133215C2314yes—
109#13133207—28no—
110#13133197—28no—
111#13133197—22no—
112#13133197C2314yes—
113#13133195—28no—
114#13133194—28no—
115#13133194—28no—
116#13133193—22no—
117#13133193C2314yes—
118Q8×Dic53—22no—
119Q8×Dic53C2314yes—
120#13133182—22no—
121#13133182C2314yes—
122C4×C22⋊D53D414yes—
123C4×C22⋊D53C2314yes—
124#13133177—28no—
125#13133177—28no—
126C2×C4⋊Dic53—22no—
127C2×C4⋊Dic53—21no—
128C2×C4⋊Dic53—21no—
129C2×C4⋊Dic53—21no—
130C2×C4⋊Dic53C2311yescharacteristic
131C2×C4⋊Dic53C2314yes—
132C2×C4⋊Dic53C2311yescharacteristic
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×#11719919—21no—
139C2×#11719919D411yescharacteristic
140C4⋊C4×D53—22no—
141C4⋊C4×D53C2314yes—
142C2×C22⋊Dic53D411yescharacteristic
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921D411yescharacteristic
146C2×C4×Dic53—21no—
147C2×C4×Dic53—21no—
148C2×C4×Dic53C2311yescharacteristic
149#13133150C2314yes—
150#13133150C2314yes—
151#13133146C2314yes—
152#13133142C2314yes—
153#13133142C2314yes—
154#13133142C2314yes—
155#13133142C2314yes—
156#13133141C2314yes—
157#13133141C2314yes—
158#13133140C2314yes—
159#13133140C2314yes—
160C22⋊#88322C2314yes—
161#13133129C2314yes—
162C8×Dic53C2314yes—
163C22×Q8×C53C2311yescharacteristic
164C22×Q8×C53C2311yescharacteristic
165C23×C4×C53C2311yescharacteristic
166C2×Q16×C53—42no—
167C2×Q16×C53C2314yes—
168C22×C8×C53—42no—
169C22×C8×C53C2311yescharacteristic
170C22×C8×C53C2311yescharacteristic
171C22×C8×C53C2314yes—
172C22⋊Q8×C53—22no—
173C22⋊Q8×C53—22no—
174C22⋊Q8×C53C2314yes—
175C22⋊Q8×C53C2314yes—
176C2×C4⋊C4×C53—21no—
177C2×C4⋊C4×C53—21no—
178C2×C4⋊C4×C53C2311yescharacteristic
179C2×C4⋊C4×C53C2311yescharacteristic
180C2×C22⋊C4×C53—21no—
181C2×C22⋊C4×C53—21no—
182#107×C53C2314yes—
183#103×C53C2314yes—
184#103×C53C2314yes—
185C24×C53C2×D411yescharacteristic
186C23×D53C2×D411yescharacteristic
187C2×Q8×C53—21no—
188C2×Q8×C53—21no—
189C2×Q8×C53—22no—
190C2×Q8×C53—22no—
191C2×Q8×C53—22no—
192C2×Q8×C53—22no—
193C2×Q8×C53C2412yes—
194C2×Q8×C53C2412yes—
195C22×C4×C53—22no—
196C22×C4×C53—22no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53C2×D412yes—
203C22×C4×C53C2412yes—
204C22×C4×C53C2411yescharacteristic
205C2×C22⋊D53Q1618yescomplemented
206C2×C22⋊D53C2×D414yes—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53—21no—
211C22×Dic53—24no—
212C22×Dic53—24no—
213C22×Dic53—44no—
214C22×Dic53—82no—
215C22×Dic53C2×D411yescharacteristic
216C22×Dic53C2×D411yescharacteristic
217C22×Dic53C2×D411yescharacteristic
218Q8×D53—28no—
219Q8×D53—44no—
220Q8×D53—48no—
221C2×C4×D53—22no—
222C2×C4×D53—22no—
223C2×C4×D53—24no—
224C2×C4×D53—24no—
225C2×C4×D53—44no—
226C2×C4×D53—82no—
227C2×C4×D53C2×D412yes—
228C2×C4×D53C2412yes—
229C2×Dic106—21no—
230C2×Dic106—22no—
231C2×Dic106—22no—
232C2×Dic106—22no—
233C2×Dic106—28no—
234C2×Dic106—24no—
235C2×Dic106—21no—
236C2×Dic106—24no—
237C2×Dic106—24no—
238C2×Dic106—44no—
239C2×Dic106—48no—
240C2×Dic106—44no—
241C2×Dic106—44no—
242C2×Dic106—82no—
243C2×Dic106#4114yes—
244C2×Dic106C2412yes—
245C2×Dic106C2412yes—
246Q16×C53—44no—
247C2×C8×C53—22no—
248C2×C8×C53—22no—
249C2×C8×C53—44no—
250C2×C8×C53C2412yes—
251C2×C8×C53C2412yes—
252C4⋊C4×C53—24no—
253C4⋊C4×C53—24no—
254C4⋊C4×C53—21no—
255C4⋊C4×C53—21no—
256C4⋊C4×C53C2412yes—
257C4⋊C4×C53C2412yes—
258C22⋊C4×C53—24no—
259C22⋊C4×C53—24no—
260C22⋊Dic53C2×D414yes—
261#11719925—28no—
262#11719925—44no—
263#11719921—24no—
264#11719921—24no—
265#11719921C2×D414yes—
266C4⋊Dic53—21no—
267C4⋊Dic53—21no—
268C4⋊Dic53—24no—
269C4⋊Dic53—24no—
270C4⋊Dic53—24no—
271C4⋊Dic53C2412yes—
272C4⋊Dic53C2412yes—
273#11719919—24no—
274#11719919—24no—
275#11719919—24no—
276#11719919—24no—
277#11719919—24no—
278#11719919—24no—
279#11719919C2×D414yes—
280C4×Dic53—24no—
281C4×Dic53—24no—
282C4×Dic53C2×D412yes—
283C4×Dic53C2412yes—
284C2×#88322—22no—
285C2×#88322—22no—
286C2×#88322C2412yes—
287C2×#88322C2412yes—
288C8×D53—44no—
289C23×C53—22no—
290C23×C53—22no—
291C23×C53C2×Q1614yes—
292C23×C53C22×D412yes—
293C23×C53C22×D411yescharacteristic
294C22×D53—22no—
295C22×D53—22no—
296C22×D53C2×Q1614yes—
297C22×D53C22×D412yes—
298Q8×C53—22no—
299Q8×C53—22no—
300Q8×C53—22no—
301Q8×C53—22no—
302Q8×C53—42no—
303Q8×C53—42no—
304C2×C4×C53—22no—
305C2×C4×C53—24no—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—42no—
313C2×C4×C53—42no—
314C2×C4×C53—42no—
315C2×C4×C53—42no—
316C2×C4×C53C22×D412yes—
317C2×C4×C53C22×D411yescharacteristic
318C2×C4×C53C2×#4112yes—
319C2×C4×C53H(5,𝔽2)12yes—
320C2×C4×C53C2511yescharacteristic
321C22⋊D53C2×Q16116yescomplemented
322C2×Dic53—24no—
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—48no—
330C2×Dic53—42no—
331C2×Dic53—42no—
332C2×Dic53—42no—
333C2×Dic53—84no—
334C2×Dic53C2×Q1614yes—
335C2×Dic53C22×D412yes—
336C2×Dic53C22×D412yes—
337C2×Dic53C22×D412yes—
338C4×D53—24no—
339C4×D53—22no—
340C4×D53—22no—
341C4×D53—48no—
342C4×D53—84no—
343Dic106—24no—
344Dic106—22no—
345Dic106—22no—
346Dic106—22no—
347Dic106—48no—
348Dic106—48no—
349Dic106—42no—
350Dic106—84no—
351Dic106C2×#4114yes—
352C8×C53—22no—
353C8×C53—22no—
354#88322—22no—
355#88322—22no—
356C2×#3299—531nomaximal, Sylow
357C22×C53—22no—
358C22×C53—28no—
359C22×C53—22no—
360C22×C53#54612yes—
361C22×C53C22×Q1614yes—
362C22×C53C22×Q1612yes—
363C22×C53#57712yes—
364C22×C53C23×D411yescharacteristic
365C2×D53—22no—
366C2×D53—28no—
367C2×D53—22no—
368C2×D53C22×Q1614yes—
369C4×C53—22no—
370C4×C53—42no—
371C4×C53—42no—
372C4×C53—42no—
373C4×C53—42no—
374C4×C53#54612yes—
375C4×C53C22×#4111yescharacteristic
376C4×C53C2×H(5,𝔽2)11yescharacteristic
377Dic53—24no—
378Dic53—22no—
379Dic53—22no—
380Dic53—42no—
381Dic53—42no—
382Dic53—42no—
383Dic53C22×Q1614yes—
384C2×#554—531no—
385C2×D4×Q8—531no—
386#3299—5316no—
387C2×#487—531no—
388C2×#484—531no—
389C2×#484—531no—
390C2×#477—531no—
391C2×#467—531no—
392C2×#467D5311yescharacteristic, complemented
393C2×#462—531no—
394C2×#451—531no—
395C2×#451—531no—
396C2×C4×Q16—531no—
397C2×C8×D4—531no—
398C22×#103—531no—
399C22×#103—531no—
400C2×C53—24no—
401C2×C53#329914yescomplemented
402C2×C53C2×#54611yescharacteristic
403C2×C53C23×Q1611yescharacteristic
404C2×C53C2×#57711yescharacteristic
405D53—24no—
406C23×Q8—531no—
407C23×Q8—531no—
408C22×Q16—531no—
409C22×Q16—531no—
410C22×Q16C2×D5311yescharacteristic
411C23×C8—531no—
412C23×C8C2×D5311yescharacteristic
413#554—538no—
414#554—1064no—
415D4×Q8—538no—
416D4×Q8—1064no—
417C2×C4⋊Q8—531no—
418C2×C4⋊Q8—531no—
419C2×C4⋊Q8—1061no—
420C2×#125—1061no—
421C2×C22⋊Q8—531no—
422C2×C22⋊Q8—531no—
423C2×C22⋊Q8—1061no—
424C2×C22⋊Q8—1061no—
425C2×C22⋊Q8—1061no—
426C2×C22⋊Q8—1061no—
427C2×C22⋊Q8C2×D5311yescharacteristic
428C2×C22⋊Q8C2×D5311yescharacteristic
429C2×C4×Q8—531no—
430C2×C4×Q8—531no—
431C2×C4×D4—531no—
432C2×C4×D4—1061no—
433C2×C4×D4—1061no—
434C22×C4⋊C4—531no—
435C22×C4⋊C4—531no—
436#487—538no—
437#484—538no—
438#484—538no—
439#477—538no—
440#467—538no—
441#467C2×D5318yescomplemented
442#462—538no—
443#451—538no—
444#451—538no—
445C4×Q16—538no—
446C8×D4—538no—
447C2×#107—531no—
448C2×#107—531no—
449C2×#107C2×D5311yescharacteristic
450C2×C4⋊C8—531no—
451C2×#103—531no—
452C2×#103—531no—
453C2×#103—531no—
454C2×#103—531no—
455C2×#103—531no—
456C2×#103—531no—
457C2×#103—538no—
458C2×#103—531no—
459C2×#103—531no—
460C2×#103—538no—
461C2×#103C2×D5311yescharacteristic
462C2×#103C2×D5311yescharacteristic
463C2×C22⋊C8—531no—
464C2×C22⋊C8—531no—
465C2×C4×C8—531no—
466C53C2×#329911yescharacteristic, complemented, Sylow
467C22×Q8—534no—
468C22×Q8—531no—
469C22×Q8—531no—
470C22×Q8—534no—
471C22×Q8—1061no—
472C22×Q8—1061no—
473C22×Q8—1064no—
474C22×Q8—1062no—
475C22×Q8—1061no—
476C22×Q8—1062no—
477C22×Q8—1064no—
478C22×Q8—2122no—
479C22×Q8—2122no—
480C22×Q8C22×D5311yescharacteristic
481C22×Q8C22×D5311yescharacteristic
482C22×D4—531no—
483C23×C4—531no—
484C23×C4—1061no—
485C23×C4—1061no—
486C23×C4—1061no—
487C23×C4—1061no—
488C23×C4C22×D5311yescharacteristic
489C2×Q16—42no—
490C2×Q16—534no—
491C2×Q16—534no—
492C2×Q16—1064no—
493C2×Q16—2122no—
494C2×Q16C22×D5314yes—
495C22×C8—42no—
496C22×C8—531no—
497C22×C8—531no—
498C22×C8—534no—
499C22×C8—2122no—
500C22×C8C22×D5311yescharacteristic
501C22×C8C22×D5311yescharacteristic
502C22×C8C22×D5314yes—
503C4⋊Q8—534no—
504C4⋊Q8—534no—
505C4⋊Q8—1062no—
506C4⋊Q8—1062no—
507C4⋊Q8—1068no—
508#125—1068no—
509C22⋊Q8—22no—
510C22⋊Q8—22no—
511C22⋊Q8—534no—
512C22⋊Q8—534no—
513C22⋊Q8—1068no—
514C22⋊Q8—1068no—
515C22⋊Q8—1068no—
516C22⋊Q8—1068no—
517C22⋊Q8—1062no—
518C22⋊Q8—1062no—
519C22⋊Q8C22×D5314yes—
520C22⋊Q8C22×D5314yes—
521C4×Q8—534no—
522C4×Q8—534no—
523C4×Q8—1062no—
524C4×Q8—1062no—
525C4×D4—534no—
526C4×D4—534no—
527C4×D4—1068no—
528C4×D4—1068no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—531no—
532C2×C4⋊C4—531no—
533C2×C4⋊C4—531no—
534C2×C4⋊C4—534no—
535C2×C4⋊C4—534no—
536C2×C4⋊C4—1062no—
537C2×C4⋊C4—1061no—
538C2×C4⋊C4—1061no—
539C2×C4⋊C4—1061no—
540C2×C4⋊C4—1061no—
541C2×C4⋊C4—1061no—
542C2×C4⋊C4—1061no—
543C2×C4⋊C4—1061no—
544C2×C4⋊C4—1061no—
545C2×C4⋊C4—1061no—
546C2×C4⋊C4—1062no—
547C2×C4⋊C4C22×D5311yescharacteristic
548C2×C4⋊C4C22×D5311yescharacteristic
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—531no—
552C2×C22⋊C4—531no—
553C2×C22⋊C4—1061no—
554C2×C22⋊C4—1061no—
555C2×C42—531no—
556C2×C42—1061no—
557C2×C42—1061no—
558#107—534no—
559#107—534no—
560#107C22×D5314yes—
561C4⋊C8—534no—
562#103—534no—
563#103—534no—
564#103—534no—
565#103—534no—
566#103—534no—
567#103—534no—
568#103—534no—
569#103—534no—
570#103C22×D5314yes—
571#103C22×D5314yes—
572C22⋊C8—534no—
573C22⋊C8—534no—
574C4×C8—534no—
575C24—531no—
576C24D4×D5311yescharacteristic
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—22no—
582C2×Q8—22no—
583C2×Q8—534no—
584C2×Q8—532no—
585C2×Q8—532no—
586C2×Q8—1064no—
587C2×Q8—1064no—
588C2×Q8—1068no—
589C2×Q8—1061no—
590C2×Q8—1064no—
591C2×Q8—1061no—
592C2×Q8—1062no—
593C2×Q8—1068no—
594C2×Q8—1062no—
595C2×Q8—1062no—
596C2×Q8—4242no—
597C2×Q8—2124no—
598C2×Q8—2124no—
599C2×Q8—2128no—
600C2×Q8—2124no—
601C2×Q8—2124no—
602C2×Q8—2128no—
603C2×Q8C23×D5312yes—
604C2×Q8C23×D5312yes—
605C2×D4—538no—
606C2×D4—534no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—531no—
614C22×C4—531no—
615C22×C4—531no—
616C22×C4—532no—
617C22×C4—532no—
618C22×C4—1064no—
619C22×C4—1064no—
620C22×C4—1061no—
621C22×C4—1062no—
622C22×C4—1062no—
623C22×C4—1064no—
624C22×C4—1064no—
625C22×C4—1061no—
626C22×C4—1061no—
627C22×C4—1061no—
628C22×C4—4242no—
629C22×C4—4242no—
630C22×C4—2124no—
631C22×C4—2124no—
632C22×C4D4×D5312yes—
633C22×C4D4×D5311yescharacteristic
634C22×C4C23×D5312yes—
635C22×C4C23×D5311yescharacteristic
636Q16—44no—
637Q16—1068no—
638Q16—2124no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—44no—
642C2×C8—532no—
643C2×C8—532no—
644C2×C8—1062no—
645C2×C8—1062no—
646C2×C8—2124no—
647C2×C8C23×D5312yes—
648C2×C8C23×D5312yes—
649C4⋊C4—24no—
650C4⋊C4—24no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—534no—
654C4⋊C4—532no—
655C4⋊C4—532no—
656C4⋊C4—1064no—
657C4⋊C4—1064no—
658C4⋊C4—1064no—
659C4⋊C4—1064no—
660C4⋊C4—1064no—
661C4⋊C4—1064no—
662C4⋊C4—1064no—
663C4⋊C4—1064no—
664C4⋊C4—1061no—
665C4⋊C4—1064no—
666C4⋊C4—1061no—
667C4⋊C4C23×D5312yes—
668C4⋊C4C23×D5312yes—
669C22⋊C4—24no—
670C22⋊C4—24no—
671C22⋊C4—534no—
672C22⋊C4—534no—
673C22⋊C4—1064no—
674C22⋊C4—1064no—
675C42—532no—
676C42—532no—
677C42—1064no—
678C42—1064no—
679C23—22no—
680C23—22no—
681C23—534no—
682C23—532no—
683C23—1062no—
684C23—1062no—
685C23Q16×D5314yes—
686C23C2×D4×D5312yes—
687C23C2×D4×D5311yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—22no—
691Q8—22no—
692Q8—42no—
693Q8—42no—
694Q8—534no—
695Q8—1062no—
696Q8—1064no—
697Q8—1062no—
698Q8—1062no—
699Q8—4244no—
700Q8—2128no—
701Q8—2128no—
702Q8—2122no—
703D4—5316no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—534no—
717C2×C4—532no—
718C2×C4—532no—
719C2×C4—532no—
720C2×C4—1062no—
721C2×C4—1062no—
722C2×C4—1062no—
723C2×C4—1064no—
724C2×C4—1062no—
725C2×C4—1062no—
726C2×C4—1064no—
727C2×C4—1062no—
728C2×C4—1062no—
729C2×C4—1062no—
730C2×C4—4244no—
731C2×C4—4244no—
732C2×C4—2128no—
733C2×C4—2128no—
734C2×C4—2122no—
735C2×C4—2122no—
736C2×C4—2122no—
737C2×C4C2×D4×D5312yes—
738C2×C4C2×D4×D5311yescharacteristic
739C2×C4#41×D5312yes—
740C2×C4#1313326212yes—
741C2×C4C24×D5311yescharacteristic
742C8—22no—
743C8—22no—
744C8—1062no—
745C8—1062no—
746C22—28no—
747C22—22no—
748C22—22no—
749C22—534no—
750C22—1068no—
751C22—1062no—
752C22—1062no—
753C22#1681126212yes—
754C22C2×Q16×D5314yes—
755C22C2×Q16×D5312yes—
756C22#1681143012yes—
757C22C22×D4×D5311yescharacteristic
758C4—22no—
759C4—42no—
760C4—42no—
761C4—42no—
762C4—42no—
763C4—534no—
764C4—1062no—
765C4—1064no—
766C4—1062no—
767C4—2122no—
768C4—2122no—
769C4—2122no—
770C4#1681126212yes—
771C4C2×#41×D5311yescharacteristic
772C4C2×#1313326211yescharacteristic
773C2—24no—
774C2—1064no—
775C2#2028658614yesdirect product factor
776C2C2×#1681126211yescharacteristic
777C2C22×Q16×D5311yescharacteristic
778C2C2×#1681143011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#467C2
socleC23×C53C22×D4
prime radicalC22×C22⋊D53D4
hypercenterC2×#467D53
hypocenterC53C2×#3299
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
3. #20286586C2direct (N × H)
4. C2×#16810972C2semidirect
5. C2×#16810960C2semidirect
6. C2×#16810956C2semidirect
7. C2×#16810917C2semidirect
8. C2×#16810863C2semidirect
9. C2×#16810831C2semidirect
10. C2×#16810778C2semidirect
11. C2×#16810777C2semidirect
12. C2×#16810715C2semidirect
14. C22×#13133142C2semidirect
15. C2×#103×D53C2semidirect
16. C2×C53×#467C2semidirect
43. #16810972C22semidirect
44. #16810960C22semidirect
45. #16810956C22semidirect
46. #16810917C22semidirect
47. #16810863C22semidirect
48. #16810831C22semidirect
49. #16810778C22semidirect
50. #16810777C22semidirect
51. #16810715C22semidirect
60. C2×#13133142C22semidirect
65. #103×D53C22semidirect
73. C53×#467C22semidirect
205. C2×C22⋊D53Q16semidirect
321. C22⋊D53C2×Q16semidirect
392. C2×#467D53semidirect
401. C2×C53#3299semidirect
441. #467C2×D53semidirect
466. C53C2×#3299semidirect
775. C2#20286586direct (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×#168112862
#202865862
C2×#168109722
C2×#168109602
C2×#168109562
C2×#168109172
C2×#168108632
C2×#168108312
C2×#168107782
C2×#168107772
C2×#168107152
C2×C8×C22⋊D532
C22×#131331422
C2×#103×D532
C2×C53×#4672
C2×#329953