Finite Group Databasebeta

← C2×#20286598 #28260495

Subgroups — C2×#20286598 #28260495

Order 13568.

2146 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811308C211yesmaximal, characteristic, complemented
2C2×#16811284C211yesmaximal, characteristic
3#20286598C2116yesmaximal, direct product factor
4C2×#16810979C211yesmaximal, characteristic, complemented
5C2×#16810962C211yesmaximal, characteristic, complemented
6C2×#16810936C211yesmaximal, characteristic, complemented
7C2×#16810928C211yesmaximal, characteristic, complemented
8C2×#16810863C211yesmaximal, characteristic, complemented
9C2×#16810852C211yesmaximal, characteristic, complemented
10C2×#16810848C211yesmaximal, characteristic, complemented
11C2×#16810788C211yesmaximal, characteristic, complemented
12C2×#16810779C211yesmaximal, characteristic, complemented
13C2×#16810715C211yesmaximal, characteristic, complemented
14C2×C8×C22⋊D53C211yesmaximal, characteristic, complemented
15C2×#16810618C211yesmaximal, characteristic, complemented
16C22×#103×C53C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×#11719925C2211yescharacteristic
19C22×#11719925C2211yescharacteristic
20C22×#11719913C2211yescharacteristic
21C22×C8×D53C2211yescharacteristic
22#16811308—24no—
23#16811308C2218yescomplemented
24#16811284—24no—
25#16811284C2218yes—
26C2×#13133212—21no—
27C2×#13133208C2211yescharacteristic
28C2×#13133207—21no—
29C2×#13133206—21no—
30C2×#13133206C2211yescharacteristic
31C2×#13133200—21no—
32C2×#13133197C2211yescharacteristic
33C2×#13133196C2211yescharacteristic
34C2×#13133193—21no—
35C2×#13133193C2211yescharacteristic
36C2×#13133191—21no—
37C2×#13133191C2211yescharacteristic
38C2×Q8×Dic53C2211yescharacteristic
39C2×#13133182C2211yescharacteristic
40C2×C4×C22⋊D53—21no—
41C2×C4×C22⋊D53C2211yescharacteristic
42C2×#13133176—21no—
43C2×#13133175C2211yescharacteristic
44#16810979C2218yescomplemented
45#16810962C2218yescomplemented
46#16810936C2218yescomplemented
47#16810928C2218yescomplemented
48#16810863C2218yescomplemented
49#16810852C2218yescomplemented
50#16810848C2218yescomplemented
51#16810788C2218yescomplemented
52#16810779C2218yescomplemented
53#16810715C2218yescomplemented
54C8×C22⋊D53C2218yescomplemented
55C2×#13133150C2211yescharacteristic
56C2×#13133150C2211yescharacteristic
57C2×#13133149C2211yescharacteristic
58C2×#13133146C2211yescharacteristic
59#16810618C2218yescomplemented
60C2×#13133142C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C23×Q8×C53C2211yescharacteristic
70C23×C8×C53C2211yescharacteristic
71C22×C4⋊C4×C53C2211yescharacteristic
72C2×#103×C53C2211yescharacteristic
73C2×#103×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#103×C53C2218yescomplemented
77C2×#11719949—22no—
78C2×#11719949—24no—
79C2×#11719949—42no—
80C2×#11719949C2314yes—
81C22×Dic106C2311yescharacteristic
82C22×D212—21no—
83C22×D212C2311yescharacteristic
84C22×C22⋊D53—21no—
85C22×C22⋊D53D411yescharacteristic
86C22×C4×D53—21no—
87C22×C4×D53C2311yescharacteristic
88C2×#11719925—24no—
89C2×#11719925—42no—
90C2×#11719925C2314yes—
91C2×#11719925C2314yes—
92C2×#11719913—42no—
93C2×#11719913C2314yes—
94C22×#88322C2311yescharacteristic
95C22×#88322C2311yescharacteristic
96C2×C8×D53—42no—
97C2×C8×D53C2314yes—
98#13133212—28no—
99#13133208—22no—
100#13133208C2314yes—
101#13133207—28no—
102#13133206—28no—
103#13133206—22no—
104#13133206C2314yes—
105#13133200—28no—
106#13133197—22no—
107#13133197C2314yes—
108#13133196—22no—
109#13133196C2314yes—
110#13133193—28no—
111#13133193—22no—
112#13133193C2314yes—
113#13133191—22no—
114#13133191—28no—
115#13133191C2314yes—
116Q8×Dic53—22no—
117Q8×Dic53C2314yes—
118#13133182—22no—
119#13133182C2314yes—
120C4×C22⋊D53—28no—
121C4×C22⋊D53D414yes—
122C4×C22⋊D53C2314yes—
123#13133176—28no—
124#13133175—22no—
125#13133175C2314yes—
126C2×C4⋊Dic53—21no—
127C2×C4⋊Dic53—21no—
128C2×C4⋊Dic53—21no—
129C2×C4⋊Dic53C2311yescharacteristic
130C2×C4⋊Dic53C2311yescharacteristic
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919D411yescharacteristic
136C2×C22⋊Dic53—21no—
137C2×C22⋊Dic53D411yescharacteristic
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921D411yescharacteristic
145C2×C4×Dic53—21no—
146C2×C4×Dic53—21no—
147C2×C4×Dic53—21no—
148C2×C4×Dic53C2311yescharacteristic
149#13133150C2314yes—
150#13133150C2314yes—
151#13133149C2314yes—
152#13133146C2314yes—
153#13133142C2314yes—
154#13133141C2314yes—
155#13133141C2314yes—
156#13133139C2314yes—
157#13133137C2314yes—
158#13133137C2314yes—
159C22⋊#88322C2314yes—
160#13133129C2314yes—
161C8×Dic53C2314yes—
162C22×Q8×C53—22no—
163C22×Q8×C53—21no—
164C22×Q8×C53—24no—
165C22×Q8×C53—42no—
166C22×Q8×C53C2311yescharacteristic
167C22×Q8×C53C2314yes—
168C22×Q8×C53C2311yescharacteristic
169C23×C4×C53—21no—
170C23×C4×C53—21no—
171C23×C4×C53C2311yescharacteristic
172C22×C8×C53—42no—
173C22×C8×C53C2311yescharacteristic
174C22×C8×C53C2311yescharacteristic
175C22×C8×C53C2314yes—
176C2×C4⋊C4×C53—22no—
177C2×C4⋊C4×C53—21no—
178C2×C4⋊C4×C53C2314yes—
179C2×C4⋊C4×C53C2311yescharacteristic
180C2×C4⋊C4×C53C2311yescharacteristic
181#103×C53C2314yes—
182#103×C53C2314yes—
183#103×C53C2314yes—
184#103×C53C2314yes—
185C24×C53C2×D411yescharacteristic
186C23×D53—21no—
187C23×D53C2×D411yescharacteristic
188C2×Q8×C53—21no—
189C2×Q8×C53—24no—
190C2×Q8×C53—21no—
191C2×Q8×C53—22no—
192C2×Q8×C53—28no—
193C2×Q8×C53—22no—
194C2×Q8×C53—22no—
195C2×Q8×C53—44no—
196C2×Q8×C53—44no—
197C2×Q8×C53—48no—
198C2×Q8×C53#4114yes—
199C2×Q8×C53C2412yes—
200C2×Q8×C53C2412yes—
201C22×C4×C53—21no—
202C22×C4×C53—22no—
203C22×C4×C53—22no—
204C22×C4×C53—21no—
205C22×C4×C53—21no—
206C22×C4×C53—24no—
207C22×C4×C53—21no—
208C22×C4×C53—24no—
209C22×C4×C53—44no—
210C22×C4×C53—44no—
211C22×C4×C53C2×D411yescharacteristic
212C22×C4×C53C2×D412yes—
213C22×C4×C53C2412yes—
214C22×C4×C53C2411yescharacteristic
215C2×C22⋊D53—24no—
216C2×C22⋊D53—24no—
217C2×C22⋊D53—44no—
218C2×C22⋊D53C2×D414yes—
219C22×Dic53—21no—
220C22×Dic53—21no—
221C22×Dic53—21no—
222C22×Dic53C2×D411yescharacteristic
223C22×Dic53C2×D411yescharacteristic
224C22×Dic53C2×D411yescharacteristic
225#11719949—28no—
226#11719949—44no—
227#11719949—48no—
228C2×D212—22no—
229C2×D212—22no—
230C2×D212—24no—
231C2×D212—21no—
232C2×D212—44no—
233C2×D212C2412yes—
234C2×C4×D53—22no—
235C2×C4×D53—22no—
236C2×C4×D53—24no—
237C2×C4×D53—44no—
238C2×C4×D53C2×D412yes—
239C2×C4×D53C2412yes—
240C2×Dic106—22no—
241C2×Dic106—22no—
242C2×Dic106—21no—
243C2×Dic106C2412yes—
244C2×C8×C53—22no—
245C2×C8×C53—22no—
246C2×C8×C53—44no—
247C2×C8×C53C2412yes—
248C2×C8×C53C2412yes—
249C4⋊C4×C53—21no—
250C4⋊C4×C53—21no—
251C4⋊C4×C53—24no—
252C4⋊C4×C53C2412yes—
253C4⋊C4×C53C2412yes—
254C22⋊Dic53—24no—
255C22⋊Dic53C2×D414yes—
256#11719925—28no—
257#11719925—44no—
258#11719921—24no—
259#11719921—24no—
260#11719921—24no—
261#11719921—24no—
262#11719921—24no—
263#11719921—24no—
264#11719921C2×D414yes—
265C4⋊Dic53—21no—
266C4⋊Dic53—21no—
267C4⋊Dic53—24no—
268C4⋊Dic53—24no—
269C4⋊Dic53—24no—
270C4⋊Dic53C2412yes—
271C4⋊Dic53C2412yes—
272#11719919—24no—
273#11719919—24no—
274#11719919—24no—
275#11719919—24no—
276#11719919C2×D414yes—
277C4×Dic53—24no—
278C4×Dic53—24no—
279C4×Dic53—24no—
280C4×Dic53C2×D412yes—
281C4×Dic53C2412yes—
282C2×#88322—22no—
283C2×#88322—22no—
284C2×#88322C2412yes—
285C2×#88322C2412yes—
286#11719913—44no—
287C8×D53—44no—
288C23×C53—22no—
289C23×C53—22no—
290C23×C53#13514yes—
291C23×C53C22×D412yes—
292C23×C53C22×D411yescharacteristic
293C22×D53—22no—
294C22×D53—22no—
295C22×D53—22no—
296C22×D53—22no—
297C22×D53—42no—
298C22×D53—42no—
299C22×D53—42no—
300C22×D53C22×D412yes—
301Q8×C53—24no—
302Q8×C53—22no—
303Q8×C53—22no—
304Q8×C53—22no—
305Q8×C53—48no—
306Q8×C53—42no—
307Q8×C53C2×#4114yes—
308C2×C4×C53—24no—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—24no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—22no—
315C2×C4×C53—22no—
316C2×C4×C53—22no—
317C2×C4×C53—48no—
318C2×C4×C53—42no—
319C2×C4×C53—48no—
320C2×C4×C53—42no—
321C2×C4×C53—42no—
322C2×C4×C53C22×D412yes—
323C2×C4×C53C22×D411yescharacteristic
324C2×C4×C53C2×#4112yes—
325C2×C4×C53H(5,𝔽2)12yes—
326C2×C4×C53C2511yescharacteristic
327C22⋊D53—28no—
328C22⋊D53—48no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—22no—
333C2×Dic53—22no—
334C2×Dic53—22no—
335C2×Dic53—42no—
336C2×Dic53—42no—
337C2×Dic53—42no—
338C2×Dic53C22×D412yes—
339C2×Dic53C22×D412yes—
340C2×Dic53C22×D412yes—
341D212—22no—
342D212—22no—
343D212—48no—
344D212—42no—
345C4×D53—24no—
346C4×D53—22no—
347C4×D53—22no—
348C4×D53—48no—
349Dic106—22no—
350Dic106—22no—
351Dic106—42no—
352C8×C53—22no—
353C8×C53—22no—
354#88322—22no—
355#88322—22no—
356C2×#3300—531nomaximal, Sylow
357C22×C53—22no—
358C22×C53—28no—
359C22×C53—22no—
360C22×C53#54612yes—
361C22×C53C2×#13514yes—
362C22×C53C2×#13512yes—
363C22×C53#57812yes—
364C22×C53C23×D411yescharacteristic
365C2×D53—22no—
366C2×D53—22no—
367C2×D53—22no—
368C2×D53—44no—
369C2×D53—42no—
370C2×D53—42no—
371C2×D53—42no—
372C2×D53—84no—
373C4×C53—24no—
374C4×C53—22no—
375C4×C53—42no—
376C4×C53—42no—
377C4×C53—42no—
378C4×C53#54612yes—
379C4×C53C22×#4111yescharacteristic
380C4×C53C2×H(5,𝔽2)11yescharacteristic
381Dic53—22no—
382Dic53—22no—
383Dic53—22no—
384Dic53—42no—
385Dic53—42no—
386Dic53—42no—
387C2×#552—531no—
388C2×#548—531no—
389#3300—5316no—
390C2×#488—531no—
391C2×#485—531no—
392C2×#480—531no—
393C2×#479—531no—
394C2×#467—531no—
395C2×#465—531no—
396C2×#464—531no—
397C2×#452—531no—
398C2×#451—531no—
399C2×C4×Q16—531no—
400C2×C8×D4—531no—
401C2×#416—531no—
402C22×#103D5311yescharacteristic, complemented
403C2×C53—24no—
404C2×C53#330014yescomplemented
405C2×C53C2×#54611yescharacteristic
406C2×C53C22×#13511yescharacteristic
407C2×C53C2×#57811yescharacteristic
408D53—42no—
409D53—82no—
410C22×#41—531no—
411C23×Q8C2×D5311yescharacteristic
412C22×Q16—531no—
413C22×Q16—531no—
414C22×SD16—531no—
415C23×C8—531no—
416C23×C8C2×D5311yescharacteristic
417#552—538no—
418#552—1064no—
419#548—538no—
420#548—1064no—
421C2×#126—1061no—
422C2×#125—531no—
423C2×#125—1061no—
424C2×#124—531no—
425C2×#124—1061no—
426C2×#123—1061no—
427C2×C22⋊Q8—531no—
428C2×C22⋊Q8—531no—
429C2×C22⋊Q8—531no—
430C2×C22⋊Q8—1061no—
431C2×#121—531no—
432C2×#121—1061no—
433C2×C4×Q8—531no—
434C2×C4×Q8—531no—
435C2×C4×D4—531no—
436C2×C4×D4—1061no—
437C2×#117—531no—
438C2×#117—1061no—
439C22×C4⋊C4C2×D5311yescharacteristic
440#488—538no—
441#485—538no—
442#480—538no—
443#479—538no—
444#467—538no—
445#465—538no—
446#464—538no—
447#452—538no—
448#451—538no—
449C4×Q16—538no—
450C8×D4—538no—
451C2×#107—531no—
452C2×#107—531no—
453C2×#106—531no—
454C2×C4⋊C8—531no—
455#416—538no—
456C2×#103—531no—
457C2×#103—531no—
458C2×#103—531no—
459C2×#103C2×D5311yescharacteristic
460C2×#103C2×D5311yescharacteristic
461C2×#103C2×D5311yescharacteristic
462C2×#103C2×D5311yescharacteristic
463C2×#103C2×D5318yescomplemented
464C2×#102—531no—
465C2×#102—531no—
466C2×#102—531no—
467C2×C22⋊C8—531no—
468C2×C22⋊C8—531no—
469C2×C4×C8—531no—
470C53C2×#330011yescharacteristic, complemented, Sylow
471C2×#41—534no—
472C2×#41—1062no—
473C2×#41—1064no—
474C2×#41—2122no—
475C22×Q8—21no—
476C22×Q8—22no—
477C22×Q8—24no—
478C22×Q8—42no—
479C22×Q8—531no—
480C22×Q8C22×D5311yescharacteristic
481C22×Q8C22×D5314yes—
482C22×Q8C22×D5311yescharacteristic
483C22×D4—531no—
484C22×D4—531no—
485C22×D4—1061no—
486C22×D4—1061no—
487C23×C4—21no—
488C23×C4—21no—
489C23×C4—531no—
490C23×C4—1061no—
491C23×C4C22×D5311yescharacteristic
492C2×Q16—534no—
493C2×Q16—534no—
494C2×Q16—1064no—
495C2×Q16—2122no—
496C2×SD16—534no—
497C2×SD16—2122no—
498C22×C8—42no—
499C22×C8—531no—
500C22×C8—531no—
501C22×C8—534no—
502C22×C8—2122no—
503C22×C8C22×D5311yescharacteristic
504C22×C8C22×D5311yescharacteristic
505C22×C8C22×D5314yes—
506#126—1068no—
507#125—534no—
508#125—1062no—
509#125—1068no—
510#124—534no—
511#124—1062no—
512#124—1068no—
513#123—1068no—
514C22⋊Q8—534no—
515C22⋊Q8—534no—
516C22⋊Q8—534no—
517C22⋊Q8—1062no—
518C22⋊Q8—1068no—
519C22⋊Q8—1062no—
520C22⋊Q8—1062no—
521#121—534no—
522#121—1068no—
523#121—1062no—
524C4×Q8—534no—
525C4×Q8—534no—
526C4×Q8—1062no—
527C4×Q8—1062no—
528C4×D4—534no—
529C4×D4—534no—
530C4×D4—1068no—
531#117—534no—
532#117—1068no—
533#117—1062no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—531no—
537C2×C4⋊C4—531no—
538C2×C4⋊C4—531no—
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⋊C4C22×D5311yescharacteristic
547C2×C4⋊C4C22×D5311yescharacteristic
548C2×C4⋊C4C22×D5314yes—
549C2×C22⋊C4—531no—
550C2×C22⋊C4—531no—
551C2×C22⋊C4—1061no—
552C2×C22⋊C4—1061no—
553C2×C22⋊C4—1061no—
554C2×C22⋊C4—1061no—
555C2×C22⋊C4—1061no—
556C2×C22⋊C4—1061no—
557C2×C22⋊C4—1061no—
558C2×C42—531no—
559C2×C42—1061no—
560C2×C42—1061no—
561C2×C42—1061no—
562#107—534no—
563#107—534no—
564#106—534no—
565C4⋊C8—534no—
566#103—534no—
567#103—534no—
568#103—534no—
569#103C22×D5314yes—
570#103C22×D5314yes—
571#103C22×D5314yes—
572#103C22×D5314yes—
573#102—534no—
574#102—534no—
575#102—534no—
576C22⋊C8—534no—
577C22⋊C8—534no—
578C4×C8—534no—
579C24—531no—
580C24—1061no—
581C24D4×D5311yescharacteristic
582#41—1068no—
583#41—2124no—
584#41—2128no—
585C2×Q8—21no—
586C2×Q8—24no—
587C2×Q8—21no—
588C2×Q8—22no—
589C2×Q8—28no—
590C2×Q8—22no—
591C2×Q8—22no—
592C2×Q8—44no—
593C2×Q8—44no—
594C2×Q8—48no—
595C2×Q8—532no—
596C2×Q8—1061no—
597C2×Q8—1062no—
598C2×Q8—1062no—
599C2×Q8#1171994514yes—
600C2×Q8C23×D5312yes—
601C2×Q8C23×D5312yes—
602C2×D4—534no—
603C2×D4—532no—
604C2×D4—1064no—
605C2×D4—1064no—
606C2×D4—1064no—
607C2×D4—1061no—
608C2×D4—1062no—
609C2×D4—1062no—
610C2×D4—2124no—
611C2×D4—2124no—
612C22×C4—21no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—24no—
616C22×C4—24no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—531no—
623C22×C4—531no—
624C22×C4—531no—
625C22×C4—532no—
626C22×C4—532no—
627C22×C4—1064no—
628C22×C4—1062no—
629C22×C4—1062no—
630C22×C4—1061no—
631C22×C4—1061no—
632C22×C4—1061no—
633C22×C4—2124no—
634C22×C4D4×D5312yes—
635C22×C4D4×D5311yescharacteristic
636C22×C4C23×D5312yes—
637C22×C4C23×D5311yescharacteristic
638Q16—1068no—
639Q16—2124no—
640SD16—2124no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—44no—
644C2×C8—532no—
645C2×C8—532no—
646C2×C8—1062no—
647C2×C8—1062no—
648C2×C8—2124no—
649C2×C8C23×D5312yes—
650C2×C8C23×D5312yes—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—24no—
654C4⋊C4—534no—
655C4⋊C4—532no—
656C4⋊C4—532no—
657C4⋊C4—1064no—
658C4⋊C4—1064no—
659C4⋊C4—1064no—
660C4⋊C4—1064no—
661C4⋊C4—1064no—
662C4⋊C4—1064no—
663C4⋊C4—1061no—
664C4⋊C4—1061no—
665C4⋊C4—1064no—
666C4⋊C4C23×D5312yes—
667C4⋊C4C23×D5312yes—
668C22⋊C4—534no—
669C22⋊C4—534no—
670C22⋊C4—1064no—
671C22⋊C4—1064no—
672C22⋊C4—1064no—
673C22⋊C4—1064no—
674C22⋊C4—1064no—
675C22⋊C4—1064no—
676C22⋊C4—1064no—
677C42—532no—
678C42—532no—
679C42—1064no—
680C42—1064no—
681C42—1064no—
682C23—22no—
683C23—22no—
684C23—532no—
685C23—1062no—
686C23—1062no—
687C23—1062no—
688C23—1062no—
689C23—2122no—
690C23—2122no—
691C23—2122no—
692C23#1313323814yes—
693C23C2×D4×D5312yes—
694C23C2×D4×D5311yescharacteristic
695Q8—22no—
696Q8—24no—
697Q8—22no—
698Q8—22no—
699Q8—48no—
700Q8—42no—
701Q8—1062no—
702Q8—1062no—
703Q8—2122no—
704Q8C2×#1171994514yes—
705D4—1068no—
706D4—1062no—
707D4—1062no—
708D4—2128no—
709D4—2128no—
710D4—2122no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—48no—
721C2×C4—48no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—532no—
726C2×C4—532no—
727C2×C4—532no—
728C2×C4—1062no—
729C2×C4—1062no—
730C2×C4—1062no—
731C2×C4—1062no—
732C2×C4—1062no—
733C2×C4—1064no—
734C2×C4—1062no—
735C2×C4—1062no—
736C2×C4—1062no—
737C2×C4—2128no—
738C2×C4—2122no—
739C2×C4—2122no—
740C2×C4—2122no—
741C2×C4C2×D4×D5312yes—
742C2×C4C2×D4×D5311yescharacteristic
743C2×C4C2×#1171994512yes—
744C2×C4#1313326212yes—
745C2×C4C24×D5311yescharacteristic
746C8—22no—
747C8—22no—
748C8—1062no—
749C8—1062no—
750C22—28no—
751C22—22no—
752C22—22no—
753C22—1062no—
754C22—1062no—
755C22—1062no—
756C22—4244no—
757C22—2122no—
758C22—2122no—
759C22—2122no—
760C22—2124no—
761C22#1681126312yes—
762C22C2×#1313323814yes—
763C22C2×#1313323812yes—
764C22#1681143612yes—
765C22C22×D4×D5311yescharacteristic
766C4—22no—
767C4—24no—
768C4—42no—
769C4—42no—
770C4—42no—
771C4—1062no—
772C4—1062no—
773C4—1062no—
774C4—2122no—
775C4—2122no—
776C4—2122no—
777C4#1681126312yes—
778C4C22×#1171994511yescharacteristic
779C4C2×#1313326211yescharacteristic
780C2—24no—
781C2—4242no—
782C2—2122no—
783C2#2028659814yesdirect product factor
784C2C2×#1681126311yescharacteristic
785C2C22×#1313323811yescharacteristic
786C2C2×#1681143611yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC22×#103×C53C2
socleC23×C53C22×D4
prime radicalC2×#16811284C2
hypercenterC22×#103D53
hypocenterC53C2×#3300
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
1. C2×#16811308C2semidirect
3. #20286598C2direct (N × H)
4. C2×#16810979C2semidirect
5. C2×#16810962C2semidirect
6. C2×#16810936C2semidirect
7. C2×#16810928C2semidirect
8. C2×#16810863C2semidirect
9. C2×#16810852C2semidirect
10. C2×#16810848C2semidirect
11. C2×#16810788C2semidirect
12. C2×#16810779C2semidirect
13. C2×#16810715C2semidirect
14. C2×C8×C22⋊D53C2semidirect
15. C2×#16810618C2semidirect
16. C22×#103×C53C2semidirect
23. #16811308C22semidirect
44. #16810979C22semidirect
45. #16810962C22semidirect
46. #16810936C22semidirect
47. #16810928C22semidirect
48. #16810863C22semidirect
49. #16810852C22semidirect
50. #16810848C22semidirect
51. #16810788C22semidirect
52. #16810779C22semidirect
53. #16810715C22semidirect
54. C8×C22⋊D53C22semidirect
59. #16810618C22semidirect
76. C2×#103×C53C22semidirect
402. C22×#103D53semidirect
404. C2×C53#3300semidirect
463. C2×#103C2×D53semidirect
470. C53C2×#3300semidirect
783. C2#20286598direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113082
C2×#168112842
#202865982
C2×#168109792
C2×#168109622
C2×#168109362
C2×#168109282
C2×#168108632
C2×#168108522
C2×#168108482
C2×#168107882
C2×#168107792
C2×#168107152
C2×C8×C22⋊D532
C2×#168106182
C22×#103×C532
C2×#330053