Finite Group Databasebeta

← C2×#20287803 #28265122

Subgroups — C2×#20287803 #28265122

Order 13568.

2066 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811356C211yesmaximal, characteristic, complemented
2C2×#16811355C211yesmaximal, characteristic, complemented
3#20287803C2116yesmaximal, direct product factor
4C2×#16811011C211yesmaximal, characteristic, complemented
5C2×#16811009C211yesmaximal, characteristic, complemented
6C2×#16811005C211yesmaximal, characteristic, complemented
7C2×#16810848C211yesmaximal, characteristic, complemented
8C2×#16810843C211yesmaximal, characteristic, complemented
9C2×#16810839C211yesmaximal, characteristic, complemented
10C2×#16810817C211yesmaximal, characteristic, complemented
11C2×#16810816C211yesmaximal, characteristic, complemented
12C2×#16810750C211yesmaximal, characteristic, complemented
13C2×#16810726C211yesmaximal, characteristic, complemented
14C2×#16810720C211yesmaximal, characteristic, complemented
15C2×C4×#11719922C211yesmaximal, characteristic, complemented
16C2×C53×#463C211yesmaximal, characteristic, complemented
17C22×#11719925C2211yescharacteristic
18C22×#11719913C2211yescharacteristic
19C22×#11719923C2211yescharacteristic
20C22×#11719924C2211yescharacteristic
21C22×D424C2211yescharacteristic
22C22×#11719922C2211yescharacteristic
23C22×#11719922C2211yescharacteristic
24#16811356—24no—
25#16811356C2218yescomplemented
26#16811355—24no—
27#16811355C2218yescomplemented
28C2×#13133213C2211yescharacteristic
29C2×#13133213C2211yescharacteristic
30C2×#13133206C2211yescharacteristic
31C2×#13133205C2211yescharacteristic
32C2×#13133204C2211yescharacteristic
33C2×#13133203—21no—
34C2×#13133203—21no—
35C2×#13133201—21no—
36C2×#13133200—21no—
37C2×#13133199—21no—
38C2×#13133199—21no—
39C2×Q8×Dic53C2211yescharacteristic
40C2×C4×Dic106C2211yescharacteristic
41C2×#13133182C2211yescharacteristic
42C2×C4×D212C2211yescharacteristic
43C2×D4×Dic53C2211yescharacteristic
44C2×#13133179C2211yescharacteristic
45C2×C4×C22⋊D53—21no—
46C2×#13133177—21no—
47#16811011C2218yescomplemented
48#16811009C2218yescomplemented
49#16811005C2218yescomplemented
50#16810848C2218yescomplemented
51#16810843C2218yescomplemented
52#16810839C2218yescomplemented
53#16810817C2218yescomplemented
54#16810816C2218yescomplemented
55#16810750C2218yescomplemented
56#16810726C2218yescomplemented
57#16810720C2218yescomplemented
58C4×#11719922C2218yescomplemented
59C2×#13133150C2211yescharacteristic
60C2×#13133146C2211yescharacteristic
61C2×#13133146C2211yescharacteristic
62C2×#13133142C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133127C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C4×#88322C2211yescharacteristic
69C22×SD16×C53C2211yescharacteristic
70C22×D8×C53C2211yescharacteristic
71C2×#124×C53C2211yescharacteristic
72C2×C4×D4×C53C2211yescharacteristic
73C53×#463C2218yescomplemented
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C22×Dic106D411yescharacteristic
78C22×Dic106C2311yescharacteristic
79C22×D212C2311yescharacteristic
80C22×D212C2311yescharacteristic
81C22×C22⋊D53—21no—
82C22×C22⋊D53—21no—
83C22×C22⋊D53—21no—
84C22×C22⋊D53—21no—
85C23×Dic53—21no—
86C22×C4×D53—21no—
87C22×C4×D53—21no—
88C2×#11719925—42no—
89C2×#11719925C2314yes—
90C2×#11719913—42no—
91C2×#11719913C2314yes—
92C2×#11719923—24no—
93C2×#11719923C2314yes—
94C2×#11719924—24no—
95C2×#11719924C2314yes—
96C2×D424—42no—
97C2×D424C2314yes—
98C2×#11719922—24no—
99C2×#11719922—42no—
100C2×#11719922C2314yes—
101C2×#11719922C2314yes—
102C22×#88322C2311yescharacteristic
103C22×#88322C2311yescharacteristic
104#13133213—22no—
105#13133213—22no—
106#13133213C2314yes—
107#13133213C2314yes—
108#13133206—22no—
109#13133206C2314yes—
110#13133205—22no—
111#13133205C2314yes—
112#13133204—22no—
113#13133204C2314yes—
114#13133203—28no—
115#13133203—28no—
116#13133201—28no—
117#13133200—28no—
118#13133199—28no—
119#13133199—28no—
120Q8×Dic53—22no—
121Q8×Dic53C2314yes—
122C4×Dic106D414yes—
123C4×Dic106C2314yes—
124#13133182—22no—
125#13133182C2314yes—
126C4×D212—22no—
127C4×D212C2314yes—
128D4×Dic53—22no—
129D4×Dic53C2314yes—
130#13133179—22no—
131#13133179C2314yes—
132C4×C22⋊D53—28no—
133#13133177—28no—
134C2×C4⋊Dic53—21no—
135C2×C4⋊Dic53D411yescharacteristic
136C2×C4⋊Dic53C2311yescharacteristic
137C2×#11719919—21no—
138C2×#11719919D411yescharacteristic
139C2×#11719919D411yescharacteristic
140C2×C22⋊Dic53—21no—
141C2×C22⋊Dic53—21no—
142C2×C22⋊Dic53—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×C4×Dic53—21no—
150C2×C4×Dic53—21no—
151C2×C4×Dic53C2311yescharacteristic
152C2×C4×Dic53C2311yescharacteristic
153#13133150C2314yes—
154#13133146C2314yes—
155#13133146C2314yes—
156#13133142C2314yes—
157#13133139C2314yes—
158#13133138C2314yes—
159#13133137C2314yes—
160#13133127C2314yes—
161#13133127C2314yes—
162C4×#88322C2314yes—
163C22×Q8×C53C2311yescharacteristic
164C22×D4×C53C2311yescharacteristic
165C22×D4×C53C2311yescharacteristic
166C23×C4×C53—21no—
167C2×SD16×C53—42no—
168C2×SD16×C53C2314yes—
169C2×D8×C53—42no—
170C2×D8×C53C2314yes—
171C22×C8×C53C2311yescharacteristic
172C22×C8×C53C2311yescharacteristic
173#124×C53—22no—
174#124×C53C2314yes—
175C4×D4×C53—22no—
176C4×D4×C53C2314yes—
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C22⋊C4×C53—21no—
179C2×C22⋊C4×C53—21no—
180C2×C22⋊C4×C53—21no—
181C2×C42×C53C2311yescharacteristic
182C4⋊C8×C53C2314yes—
183#103×C53C2314yes—
184#102×C53C2314yes—
185C24×C53—21no—
186C24×C53—21no—
187C23×D53—21no—
188C23×D53—21no—
189C2×Q8×C53—21no—
190C2×Q8×C53—22no—
191C2×Q8×C53—22no—
192C2×Q8×C53C2412yes—
193C2×D4×C53—21no—
194C2×D4×C53—21no—
195C2×D4×C53—22no—
196C2×D4×C53—22no—
197C2×D4×C53—22no—
198C2×D4×C53—22no—
199C2×D4×C53C2412yes—
200C2×D4×C53C2412yes—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53—24no—
204C22×C4×C53—82no—
205C22×C4×C53C2×D411yescharacteristic
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53C2411yescharacteristic
208C2×C22⋊D53—24no—
209C2×C22⋊D53—24no—
210C2×C22⋊D53—24no—
211C2×C22⋊D53—24no—
212C2×C22⋊D53—44no—
213C2×C22⋊D53—44no—
214C2×C22⋊D53—82no—
215C2×C22⋊D53—82no—
216C22×Dic53—21no—
217C22×Dic53—21no—
218C22×Dic53—24no—
219C22×Dic53—82no—
220C22×Dic53C2×D411yescharacteristic
221C22×Dic53C2×D411yescharacteristic
222C22×Dic53C2×D411yescharacteristic
223C22×Dic53C2×D411yescharacteristic
224C2×D212—22no—
225C2×D212—22no—
226C2×D212—22no—
227C2×D212—22no—
228C2×D212—21no—
229C2×D212—21no—
230C2×D212C2412yes—
231C2×D212C2412yes—
232C2×C4×D53—24no—
233C2×C4×D53—24no—
234C2×C4×D53—82no—
235C2×C4×D53—82no—
236C2×Dic106—22no—
237C2×Dic106—22no—
238C2×Dic106—21no—
239C2×Dic106—42no—
240C2×Dic106C2×D414yes—
241C2×Dic106C2412yes—
242SD16×C53—44no—
243D8×C53—44no—
244C2×C8×C53—22no—
245C2×C8×C53—22no—
246C2×C8×C53C2412yes—
247C2×C8×C53C2412yes—
248C4⋊C4×C53—21no—
249C4⋊C4×C53C2412yes—
250C22⋊C4×C53—24no—
251C22⋊C4×C53—24no—
252C22⋊C4×C53—24no—
253C42×C53C2×D412yes—
254C42×C53C2412yes—
255C22⋊Dic53—24no—
256C22⋊Dic53—24no—
257C22⋊Dic53—24no—
258#11719925—44no—
259#11719924—28no—
260#11719923—28no—
261#11719922—28no—
262#11719922—44no—
263#11719921—24no—
264#11719921—24no—
265#11719921—24no—
266#11719921—24no—
267#11719921—24no—
268#11719921—24no—
269C4⋊Dic53—21no—
270C4⋊Dic53—24no—
271C4⋊Dic53C2×D414yes—
272C4⋊Dic53C2412yes—
273#11719919—24no—
274#11719919C2×D414yes—
275#11719919C2×D414yes—
276C4×Dic53—24no—
277C4×Dic53—24no—
278C4×Dic53C2×D412yes—
279C4×Dic53C2×D412yes—
280C4×Dic53C2412yes—
281C4×Dic53C2412yes—
282C2×#88322—22no—
283C2×#88322#4114yes—
284C2×#88322C2412yes—
285C2×#88322C2412yes—
286D424—44no—
287#11719913—44no—
288C23×C53—22no—
289C23×C53—22no—
290C23×C53—42no—
291C23×C53—42no—
292C23×C53—42no—
293C23×C53—42no—
294C23×C53—42no—
295C23×C53—42no—
296C23×C53C22×D411yescharacteristic
297C22×D53—22no—
298C22×D53—22no—
299C22×D53—42no—
300C22×D53—42no—
301C22×D53—42no—
302C22×D53—42no—
303C22×D53—42no—
304C22×D53—42no—
305Q8×C53—22no—
306Q8×C53—22no—
307Q8×C53—42no—
308D4×C53—22no—
309D4×C53—22no—
310D4×C53—22no—
311D4×C53—22no—
312D4×C53—42no—
313D4×C53—42no—
314C2×C4×C53—22no—
315C2×C4×C53—22no—
316C2×C4×C53—22no—
317C2×C4×C53—22no—
318C2×C4×C53—42no—
319C2×C4×C53—42no—
320C2×C4×C53—84no—
321C2×C4×C53C22×D412yes—
322C2×C4×C53C22×D412yes—
323C2×C4×C53C22×D411yescharacteristic
324C2×C4×C53C2×#4112yes—
325C2×C4×C53H(5,𝔽2)12yes—
326C2×C4×C53C2511yescharacteristic
327C22⋊D53—48no—
328C22⋊D53—48no—
329C22⋊D53—84no—
330C22⋊D53—84no—
331C2×Dic53—22no—
332C2×Dic53—22no—
333C2×Dic53—22no—
334C2×Dic53—22no—
335C2×Dic53—22no—
336C2×Dic53—22no—
337C2×Dic53—42no—
338C2×Dic53—42no—
339C2×Dic53—84no—
340C2×Dic53C22×D412yes—
341C2×Dic53C22×D412yes—
342C2×Dic53C22×D412yes—
343C2×Dic53C22×D412yes—
344D212—22no—
345D212—22no—
346D212—22no—
347D212—22no—
348D212—42no—
349D212—42no—
350C4×D53—84no—
351C4×D53—84no—
352Dic106—22no—
353Dic106—22no—
354Dic106—44no—
355Dic106—42no—
356C8×C53—22no—
357C8×C53—22no—
358#88322—22no—
359#88322C2×#4114yes—
360C2×#3403—531nomaximal, Sylow
361C22×C53—42no—
362C22×C53—42no—
363C22×C53—42no—
364C22×C53—42no—
365C22×C53—42no—
366C22×C53—42no—
367C22×C53—84no—
368C22×C53—84no—
369C22×C53#55012yes—
370C22×C53#57512yes—
371C22×C53#57612yes—
372C22×C53C23×D411yescharacteristic
373C2×D53—42no—
374C2×D53—42no—
375C2×D53—42no—
376C2×D53—42no—
377C2×D53—42no—
378C2×D53—42no—
379C2×D53—84no—
380C2×D53—84no—
381C4×C53—22no—
382C4×C53—22no—
383C4×C53—42no—
384C4×C53—42no—
385C4×C53#55012yes—
386C4×C53C22×#4111yescharacteristic
387C4×C53C2×H(5,𝔽2)11yescharacteristic
388Dic53—22no—
389Dic53—22no—
390Dic53—22no—
391Dic53—22no—
392Dic53—42no—
393Dic53—42no—
394C2×#559—531no—
395C2×#559—531no—
396#3403—5316no—
397C2×#496—531no—
398C2×#496—531no—
399C2×#495—531no—
400C2×#464—531no—
401C2×#464—531no—
402C2×#463—531no—
403C2×#463D5311yescharacteristic, complemented
404C2×#459—531no—
405C2×#459—531no—
406C2×#446—531no—
407C2×#440—531no—
408C2×#440—531no—
409C2×C4×D8—531no—
410C2×C53—82no—
411C2×C53—82no—
412C2×C53#340314yescomplemented
413C2×C53C2×#55011yescharacteristic
414C2×C53C2×#57511yescharacteristic
415C2×C53C2×#57611yescharacteristic
416D53—82no—
417D53—82no—
418C22×Q16—531no—
419C22×SD16—531no—
420C22×SD16—531no—
421C22×SD16—531no—
422C22×SD16C2×D5311yescharacteristic
423C22×D8—531no—
424C22×D8—531no—
425C22×D8—531no—
426C22×D8C2×D5311yescharacteristic
427#559—538no—
428#559—538no—
429#559—1064no—
430#559—1064no—
431C2×#127—531no—
432C2×#127—531no—
433C2×#124—531no—
434C2×#124—531no—
435C2×#124—531no—
436C2×#124—1061no—
437C2×#124—1061no—
438C2×#124C2×D5311yescharacteristic
439C2×#123—1061no—
440C2×#123—1061no—
441C2×#123—1061no—
442C2×#123—1061no—
443C2×C4×Q8—531no—
444C2×C4×Q8—531no—
445C2×C4×Q8—531no—
446C2×C4×D4—531no—
447C2×C4×D4—531no—
448C2×C4×D4—531no—
449C2×C4×D4—1061no—
450C2×C4×D4—1061no—
451C2×C4×D4C2×D5311yescharacteristic
452#496—538no—
453#496—538no—
454#495—538no—
455#464—538no—
456#464—538no—
457#463—538no—
458#463C2×D5318yescomplemented
459#459—538no—
460#459—538no—
461#446—538no—
462#440—538no—
463#440—538no—
464C4×D8—538no—
465C2×#107—531no—
466C2×C4⋊C8—531no—
467C2×C4⋊C8—531no—
468C2×C4⋊C8C2×D5311yescharacteristic
469C2×#103—531no—
470C2×#103C2×D5311yescharacteristic
471C2×#102—531no—
472C2×#102—531no—
473C2×#102—531no—
474C2×#102C2×D5311yescharacteristic
475C2×#97—531no—
476C2×#97—531no—
477C2×C4×C8—531no—
478C53C2×#340311yescharacteristic, complemented, Sylow
479C22×Q8—531no—
480C22×Q8—531no—
481C22×Q8C22×D5311yescharacteristic
482C22×D4—531no—
483C22×D4—531no—
484C22×D4—1061no—
485C22×D4—1061no—
486C22×D4—1061no—
487C22×D4—1061no—
488C22×D4C22×D5311yescharacteristic
489C22×D4C22×D5311yescharacteristic
490C23×C4—21no—
491C23×C4—1061no—
492C23×C4—1061no—
493C23×C4—1061no—
494C2×Q16—534no—
495C2×Q16—2122no—
496C2×SD16—42no—
497C2×SD16—534no—
498C2×SD16—534no—
499C2×SD16—534no—
500C2×SD16—1064no—
501C2×SD16—1064no—
502C2×SD16—2122no—
503C2×SD16C22×D5314yes—
504C2×D8—42no—
505C2×D8—534no—
506C2×D8—534no—
507C2×D8—534no—
508C2×D8—1064no—
509C2×D8—2122no—
510C2×D8—2122no—
511C2×D8C22×D5314yes—
512C22×C8—531no—
513C22×C8—531no—
514C22×C8C22×D5311yescharacteristic
515C22×C8C22×D5311yescharacteristic
516#127—534no—
517#127—534no—
518#127—1062no—
519#127—1062no—
520#124—22no—
521#124—534no—
522#124—534no—
523#124—534no—
524#124—1062no—
525#124—1062no—
526#124—1068no—
527#124—1068no—
528#124—1062no—
529#124C22×D5314yes—
530#123—1068no—
531#123—1068no—
532#123—1068no—
533#123—1068no—
534C4×Q8—534no—
535C4×Q8—534no—
536C4×Q8—534no—
537C4×Q8—534no—
538C4×Q8—1062no—
539C4×Q8—1062no—
540C4×D4—22no—
541C4×D4—534no—
542C4×D4—534no—
543C4×D4—534no—
544C4×D4—1062no—
545C4×D4—1062no—
546C4×D4—1068no—
547C4×D4—1068no—
548C4×D4—1062no—
549C4×D4C22×D5314yes—
550C2×C4⋊C4—531no—
551C2×C4⋊C4—531no—
552C2×C4⋊C4—531no—
553C2×C4⋊C4—531no—
554C2×C4⋊C4—1061no—
555C2×C4⋊C4—1061no—
556C2×C4⋊C4C22×D5311yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—1061no—
561C2×C22⋊C4—1061no—
562C2×C22⋊C4—1061no—
563C2×C22⋊C4—1061no—
564C2×C22⋊C4—1061no—
565C2×C22⋊C4—1061no—
566C2×C22⋊C4—1061no—
567C2×C22⋊C4—1061no—
568C2×C22⋊C4—1061no—
569C2×C42—531no—
570C2×C42—531no—
571C2×C42—1061no—
572C2×C42—1061no—
573C2×C42C22×D5311yescharacteristic
574#107—534no—
575C4⋊C8—534no—
576C4⋊C8—534no—
577C4⋊C8C22×D5314yes—
578#103—534no—
579#103C22×D5314yes—
580#102—534no—
581#102—534no—
582#102—534no—
583#102C22×D5314yes—
584#97—534no—
585#97—534no—
586C4×C8—534no—
587C24—21no—
588C24—21no—
589C24—1061no—
590C24—1061no—
591C2×Q8—21no—
592C2×Q8—22no—
593C2×Q8—22no—
594C2×Q8—534no—
595C2×Q8—532no—
596C2×Q8—1061no—
597C2×Q8—1062no—
598C2×Q8—1062no—
599C2×Q8—2122no—
600C2×Q8C23×D5312yes—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—532no—
608C2×D4—532no—
609C2×D4—1064no—
610C2×D4—1064no—
611C2×D4—1064no—
612C2×D4—1064no—
613C2×D4—1061no—
614C2×D4—1061no—
615C2×D4—1062no—
616C2×D4—1062no—
617C2×D4—1062no—
618C2×D4—1062no—
619C2×D4—4242no—
620C2×D4—4242no—
621C2×D4—2124no—
622C2×D4—2124no—
623C2×D4C23×D5312yes—
624C2×D4C23×D5312yes—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—24no—
628C22×C4—82no—
629C22×C4—531no—
630C22×C4—531no—
631C22×C4—531no—
632C22×C4—531no—
633C22×C4—1064no—
634C22×C4—1064no—
635C22×C4—1061no—
636C22×C4—1061no—
637C22×C4—1064no—
638C22×C4—4242no—
639C22×C4—4242no—
640C22×C4—4242no—
641C22×C4D4×D5311yescharacteristic
642C22×C4D4×D5311yescharacteristic
643C22×C4C23×D5311yescharacteristic
644Q16—2124no—
645SD16—44no—
646SD16—1068no—
647SD16—1068no—
648SD16—2124no—
649D8—44no—
650D8—1068no—
651D8—2124no—
652D8—2124no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—534no—
656C2×C8—532no—
657C2×C8—532no—
658C2×C8—1062no—
659C2×C8C23×D5312yes—
660C2×C8C23×D5312yes—
661C4⋊C4—21no—
662C4⋊C4—534no—
663C4⋊C4—534no—
664C4⋊C4—534no—
665C4⋊C4—532no—
666C4⋊C4—1064no—
667C4⋊C4—1064no—
668C4⋊C4—1061no—
669C4⋊C4C23×D5312yes—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—24no—
673C22⋊C4—1064no—
674C22⋊C4—1064no—
675C22⋊C4—1064no—
676C22⋊C4—1064no—
677C22⋊C4—1064no—
678C22⋊C4—1064no—
679C22⋊C4—1064no—
680C22⋊C4—1064no—
681C22⋊C4—1064no—
682C42—532no—
683C42—532no—
684C42—532no—
685C42—532no—
686C42—1064no—
687C42—1064no—
688C42D4×D5312yes—
689C42C23×D5312yes—
690C23—22no—
691C23—22no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—1062no—
699C23—1062no—
700C23—2122no—
701C23—2122no—
702C23—2122no—
703C23—2122no—
704C23—2122no—
705C23—2122no—
706C23C2×D4×D5311yescharacteristic
707Q8—22no—
708Q8—22no—
709Q8—42no—
710Q8—1062no—
711Q8—1062no—
712Q8—2124no—
713Q8—2122no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—42no—
719D4—42no—
720D4—1062no—
721D4—1062no—
722D4—1062no—
723D4—1062no—
724D4—4244no—
725D4—4244no—
726D4—2128no—
727D4—2128no—
728D4—2122no—
729D4—2122no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—84no—
737C2×C4—532no—
738C2×C4—532no—
739C2×C4—532no—
740C2×C4—532no—
741C2×C4—1062no—
742C2×C4—1062no—
743C2×C4—1062no—
744C2×C4—1062no—
745C2×C4—1062no—
746C2×C4—1062no—
747C2×C4—4244no—
748C2×C4—4244no—
749C2×C4—4244no—
750C2×C4—2122no—
751C2×C4—2122no—
752C2×C4C2×D4×D5312yes—
753C2×C4C2×D4×D5312yes—
754C2×C4C2×D4×D5311yescharacteristic
755C2×C4#41×D5312yes—
756C2×C4#1313326212yes—
757C2×C4C24×D5311yescharacteristic
758C8—22no—
759C8—22no—
760C8—534no—
761C8—1062no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—84no—
769C22—84no—
770C22—4244no—
771C22—4244no—
772C22—2122no—
773C22—2122no—
774C22—2122no—
775C22—2122no—
776C22—2122no—
777C22—2122no—
778C22#1681129112yes—
779C22#1681142012yes—
780C22#1681142712yes—
781C22C22×D4×D5311yescharacteristic
782C4—22no—
783C4—22no—
784C4—42no—
785C4—42no—
786C4—1062no—
787C4—1062no—
788C4—1062no—
789C4—1062no—
790C4—2122no—
791C4—2122no—
792C4#1681129112yes—
793C4C2×#41×D5311yescharacteristic
794C4C2×#1313326211yescharacteristic
795C2—82no—
796C2—82no—
797C2—4242no—
798C2—4242no—
799C2#2028780314yesdirect product factor
800C2C2×#1681129111yescharacteristic
801C2C2×#1681142011yescharacteristic
802C2C2×#1681142711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#463C2
socleC23×C53C22×D4
hypercenterC2×#463D53
hypocenterC53C2×#3403
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#16811356C2semidirect
2. C2×#16811355C2semidirect
3. #20287803C2direct (N × H)
4. C2×#16811011C2semidirect
5. C2×#16811009C2semidirect
6. C2×#16811005C2semidirect
7. C2×#16810848C2semidirect
8. C2×#16810843C2semidirect
9. C2×#16810839C2semidirect
10. C2×#16810817C2semidirect
11. C2×#16810816C2semidirect
12. C2×#16810750C2semidirect
13. C2×#16810726C2semidirect
14. C2×#16810720C2semidirect
15. C2×C4×#11719922C2semidirect
16. C2×C53×#463C2semidirect
25. #16811356C22semidirect
27. #16811355C22semidirect
47. #16811011C22semidirect
48. #16811009C22semidirect
49. #16811005C22semidirect
50. #16810848C22semidirect
51. #16810843C22semidirect
52. #16810839C22semidirect
53. #16810817C22semidirect
54. #16810816C22semidirect
55. #16810750C22semidirect
56. #16810726C22semidirect
57. #16810720C22semidirect
58. C4×#11719922C22semidirect
73. C53×#463C22semidirect
403. C2×#463D53semidirect
412. C2×C53#3403semidirect
458. #463C2×D53semidirect
478. C53C2×#3403semidirect
799. C2#20287803direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113562
C2×#168113552
#202878032
C2×#168110112
C2×#168110092
C2×#168110052
C2×#168108482
C2×#168108432
C2×#168108392
C2×#168108172
C2×#168108162
C2×#168107502
C2×#168107262
C2×#168107202
C2×C4×#117199222
C2×C53×#4632
C2×#340353