Finite Group Databasebeta

← C2×#20287799 #28265118

Subgroups — C2×#20287799 #28265118

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×#16811358C211yesmaximal, characteristic, complemented
2#20287799C2116yesmaximal, direct product factor
3C2×#16811013C211yesmaximal, characteristic, complemented
4C2×#16811010C211yesmaximal, characteristic, complemented
5C2×#16811005C211yesmaximal, characteristic, complemented
6C2×#16810845C211yesmaximal, characteristic, complemented
7C2×#16810842C211yesmaximal, characteristic, complemented
8C2×#16810838C211yesmaximal, characteristic, complemented
9C2×#16810835C211yesmaximal, characteristic, complemented
10C2×#16810818C211yesmaximal, characteristic, complemented
11C2×#16810815C211yesmaximal, characteristic, complemented
12C2×#16810754C211yesmaximal, characteristic, complemented
13C2×#16810723C211yesmaximal, characteristic, complemented
14C2×#16810721C211yesmaximal, characteristic, complemented
15C2×C4×#11719922C211yesmaximal, characteristic, complemented
16C2×C53×#559C211yesmaximal, characteristic, complemented
17C22×#11719925C2211yescharacteristic
18C22×#11719923C2211yescharacteristic
19C22×#11719923C2211yescharacteristic
20C22×#11719924C2211yescharacteristic
21C22×#11719924C2211yescharacteristic
22C22×#11719922C2211yescharacteristic
23C22×#11719922C2211yescharacteristic
24C22×#11719922C2211yescharacteristic
25C22×#11719922C2211yescharacteristic
26#16811358—24no—
27#16811358C2218yescomplemented
28C2×#13133214C2211yescharacteristic
29C2×#13133206—21no—
30C2×#13133205C2211yescharacteristic
31C2×#13133205C2211yescharacteristic
32C2×#13133202—21no—
33C2×#13133202—21no—
34C2×C4×Dic106C2211yescharacteristic
35C2×C4×D212C2211yescharacteristic
36C2×C4×D212C2211yescharacteristic
37C2×#13133179—21no—
38#16811013C2218yescomplemented
39#16811010C2218yescomplemented
40#16811005C2218yescomplemented
41#16810845C2218yescomplemented
42#16810842C2218yescomplemented
43#16810838C2218yescomplemented
44#16810835C2218yescomplemented
45#16810818C2218yescomplemented
46#16810815C2218yescomplemented
47#16810754C2218yescomplemented
48#16810723C2218yescomplemented
49#16810721C2218yescomplemented
50C4×#11719922C2218yescomplemented
51C2×#13133150C2211yescharacteristic
52C2×C4⋊#88322C2211yescharacteristic
53C2×C4⋊#88322C2211yescharacteristic
54C2×C4⋊#88322C2211yescharacteristic
55C2×#13133141C2211yescharacteristic
56C2×#13133140C2211yescharacteristic
57C2×#13133138C2211yescharacteristic
58C2×#13133138C2211yescharacteristic
59C2×#13133137C2211yescharacteristic
60C2×#13133137C2211yescharacteristic
61C2×#13133128C2211yescharacteristic
62C2×#13133128C2211yescharacteristic
63C2×C4×#88322C2211yescharacteristic
64C53×#559—24no—
65C53×#559C2218yescomplemented
66C2×#127×C53C2211yescharacteristic
67C2×#124×C53—21no—
68C2×#124×C53C2211yescharacteristic
69C2×#124×C53C2211yescharacteristic
70C2×#123×C53—21no—
71C2×#123×C53—21no—
72C2×C4×Q8×C53C2211yescharacteristic
73C2×C4×Q8×C53C2211yescharacteristic
74C2×C4×D4×C53—21no—
75C2×C4×D4×C53C2211yescharacteristic
76C2×C4×D4×C53C2211yescharacteristic
77C22×Dic106C2311yescharacteristic
78C22×D212—21no—
79C22×D212—21no—
80C22×D212C2311yescharacteristic
81C22×D212C2311yescharacteristic
82C22×C4×D53—21no—
83C22×C4×D53—21no—
84C2×#11719925—42no—
85C2×#11719925C2314yes—
86C2×#11719923—24no—
87C2×#11719923—42no—
88C2×#11719923C2314yes—
89C2×#11719923C2314yes—
90C2×#11719924—24no—
91C2×#11719924—42no—
92C2×#11719924C2314yes—
93C2×#11719924C2314yes—
94C2×#11719922—24no—
95C2×#11719922—42no—
96C2×#11719922—42no—
97C2×#11719922—42no—
98C2×#11719922C2314yes—
99C2×#11719922C2314yes—
100C2×#11719922C2314yes—
101C2×#11719922C2314yes—
102C22×#88322C2311yescharacteristic
103C22×#88322C2311yescharacteristic
104C22×#88322C2311yescharacteristic
105C22×#88322C2311yescharacteristic
106#13133214—22no—
107#13133214C2314yes—
108#13133206—28no—
109#13133205—22no—
110#13133205—22no—
111#13133205C2314yes—
112#13133205C2314yes—
113#13133202—28no—
114#13133202—28no—
115C4×Dic106—22no—
116C4×Dic106C2314yes—
117C4×D212—22no—
118C4×D212—22no—
119C4×D212C2314yes—
120C4×D212C2314yes—
121#13133179—28no—
122C2×C4⋊Dic53C2311yescharacteristic
123C2×#11719919—21no—
124C2×#11719921—21no—
125C2×#11719921—21no—
126C2×#11719921—21no—
127C2×#11719921—21no—
128C2×#11719921—21no—
129C2×#11719921—21no—
130C2×C4×Dic53—21no—
131#13133150C2314yes—
132C4⋊#88322C2314yes—
133C4⋊#88322C2314yes—
134C4⋊#88322C2314yes—
135#13133141C2314yes—
136#13133140C2314yes—
137#13133138C2314yes—
138#13133138C2314yes—
139#13133137C2314yes—
140#13133137C2314yes—
141#13133128C2314yes—
142#13133128C2314yes—
143C4×#88322C2314yes—
144C22×Q8×C53D411yescharacteristic
145C22×Q8×C53C2311yescharacteristic
146C22×D4×C53—21no—
147C22×D4×C53—21no—
148C22×D4×C53C2311yescharacteristic
149C22×D4×C53C2311yescharacteristic
150C23×C4×C53—21no—
151C23×C4×C53—21no—
152#127×C53—22no—
153#127×C53C2314yes—
154#124×C53—22no—
155#124×C53—22no—
156#124×C53—28no—
157#124×C53C2314yes—
158#124×C53C2314yes—
159#123×C53—28no—
160#123×C53—28no—
161C4×Q8×C53—22no—
162C4×Q8×C53D414yes—
163C4×Q8×C53C2314yes—
164C4×Q8×C53C2314yes—
165C4×D4×C53—28no—
166C4×D4×C53—22no—
167C4×D4×C53—22no—
168C4×D4×C53C2314yes—
169C4×D4×C53C2314yes—
170C2×C4⋊C4×C53—21no—
171C2×C4⋊C4×C53D411yescharacteristic
172C2×C4⋊C4×C53D411yescharacteristic
173C2×C4⋊C4×C53D411yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C22⋊C4×C53—21no—
176C2×C22⋊C4×C53—21no—
177C2×C22⋊C4×C53—21no—
178C2×C22⋊C4×C53—21no—
179C2×C22⋊C4×C53—21no—
180C2×C22⋊C4×C53—21no—
181C2×C42×C53—21no—
182C2×C42×C53C2311yescharacteristic
183C2×C42×C53C2311yescharacteristic
184C2×C42×C53C2311yescharacteristic
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×C53—42no—
193C2×Q8×C53C2×D414yes—
194C2×Q8×C53C2412yes—
195C2×D4×C53—21no—
196C2×D4×C53—21no—
197C2×D4×C53—24no—
198C2×D4×C53—24no—
199C2×D4×C53—22no—
200C2×D4×C53—22no—
201C2×D4×C53—22no—
202C2×D4×C53—22no—
203C2×D4×C53—44no—
204C2×D4×C53—82no—
205C2×D4×C53C2412yes—
206C2×D4×C53C2412yes—
207C22×C4×C53—21no—
208C22×C4×C53—21no—
209C22×C4×C53—24no—
210C22×C4×C53—24no—
211C22×C4×C53—82no—
212C22×C4×C53—82no—
213C22×C4×C53C2×D411yescharacteristic
214C22×C4×C53C2×D411yescharacteristic
215C22×C4×C53C2×D411yescharacteristic
216C22×C4×C53C2×D411yescharacteristic
217C22×C4×C53C2×D411yescharacteristic
218C22×C4×C53C2×D411yescharacteristic
219C22×C4×C53C2411yescharacteristic
220C22×Dic53—21no—
221C22×Dic53—21no—
222C2×D212—22no—
223C2×D212—22no—
224C2×D212—22no—
225C2×D212—22no—
226C2×D212—24no—
227C2×D212—21no—
228C2×D212—21no—
229C2×D212—24no—
230C2×D212—44no—
231C2×D212—82no—
232C2×D212C2412yes—
233C2×D212C2412yes—
234C2×C4×D53—24no—
235C2×C4×D53—24no—
236C2×C4×D53—82no—
237C2×C4×D53—82no—
238C2×Dic106—22no—
239C2×Dic106—22no—
240C2×Dic106—21no—
241C2×Dic106C2412yes—
242C4⋊C4×C53—24no—
243C4⋊C4×C53—21no—
244C4⋊C4×C53C2×D414yes—
245C4⋊C4×C53C2×D414yes—
246C4⋊C4×C53C2×D414yes—
247C4⋊C4×C53C2412yes—
248C22⋊C4×C53—24no—
249C22⋊C4×C53—24no—
250C22⋊C4×C53—24no—
251C22⋊C4×C53—24no—
252C22⋊C4×C53—24no—
253C22⋊C4×C53—24no—
254C42×C53—24no—
255C42×C53C2×D412yes—
256C42×C53C2×D412yes—
257C42×C53C2×D412yes—
258C42×C53C2412yes—
259C42×C53C2412yes—
260C42×C53C2412yes—
261#11719925—44no—
262#11719924—28no—
263#11719924—44no—
264#11719923—28no—
265#11719923—44no—
266#11719922—28no—
267#11719922—44no—
268#11719922—44no—
269#11719922—44no—
270#11719921—24no—
271#11719921—24no—
272#11719921—24no—
273#11719921—24no—
274#11719921—24no—
275#11719921—24no—
276C4⋊Dic53—21no—
277C4⋊Dic53C2412yes—
278#11719919—24no—
279C4×Dic53—24no—
280C2×#88322—22no—
281C2×#88322—22no—
282C2×#88322—22no—
283C2×#88322#4114yes—
284C2×#88322C2412yes—
285C2×#88322C2412yes—
286C2×#88322C2412yes—
287C2×#88322C2412yes—
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—44no—
308Q8×C53—42no—
309D4×C53—22no—
310D4×C53—22no—
311D4×C53—22no—
312D4×C53—22no—
313D4×C53—48no—
314D4×C53—42no—
315D4×C53—42no—
316D4×C53—84no—
317C2×C4×C53—22no—
318C2×C4×C53—22no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—22no—
322C2×C4×C53—22no—
323C2×C4×C53—22no—
324C2×C4×C53—22no—
325C2×C4×C53—42no—
326C2×C4×C53—42no—
327C2×C4×C53—84no—
328C2×C4×C53—84no—
329C2×C4×C53C22×D412yes—
330C2×C4×C53C22×D412yes—
331C2×C4×C53C22×D412yes—
332C2×C4×C53C22×D412yes—
333C2×C4×C53C22×D412yes—
334C2×C4×C53C22×D412yes—
335C2×C4×C53C22×D411yescharacteristic
336C2×C4×C53C2×#4112yes—
337C2×C4×C53H(5,𝔽2)12yes—
338C2×C4×C53C2511yescharacteristic
339C2×Dic53—22no—
340C2×Dic53—22no—
341C2×Dic53—42no—
342C2×Dic53—42no—
343D212—22no—
344D212—22no—
345D212—22no—
346D212—22no—
347D212—48no—
348D212—42no—
349D212—42no—
350D212—84no—
351C4×D53—84no—
352C4×D53—84no—
353Dic106—22no—
354Dic106—22no—
355Dic106—42no—
356#88322—22no—
357#88322—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—22no—
384C4×C53—22no—
385C4×C53—22no—
386C4×C53—22no—
387C4×C53—42no—
388C4×C53—42no—
389C4×C53#55012yes—
390C4×C53C22×#4111yescharacteristic
391C4×C53C2×H(5,𝔽2)11yescharacteristic
392Dic53—42no—
393Dic53—42no—
394C2×#559—531no—
395C2×#559D5311yescharacteristic, complemented
396#3403—5316no—
397C2×#496—531no—
398C2×#496—531no—
399C2×#495—531no—
400C2×#464—531no—
401C2×#464—531no—
402C2×#463—531no—
403C2×#463—531no—
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×SD16—531no—
423C22×D8—531no—
424C22×D8—531no—
425C22×D8—531no—
426C22×D8—531no—
427#559—24no—
428#559—538no—
429#559—1064no—
430#559C2×D5318yescomplemented
431C2×#127—531no—
432C2×#127C2×D5311yescharacteristic
433C2×#124—21no—
434C2×#124—531no—
435C2×#124—531no—
436C2×#124—1061no—
437C2×#124C2×D5311yescharacteristic
438C2×#124C2×D5311yescharacteristic
439C2×#123—21no—
440C2×#123—21no—
441C2×#123—1061no—
442C2×#123—1061no—
443C2×C4×Q8—531no—
444C2×C4×Q8C2×D5311yescharacteristic
445C2×C4×Q8C2×D5311yescharacteristic
446C2×C4×D4—21no—
447C2×C4×D4—531no—
448C2×C4×D4—531no—
449C2×C4×D4—1061no—
450C2×C4×D4C2×D5311yescharacteristic
451C2×C4×D4C2×D5311yescharacteristic
452#496—538no—
453#496—538no—
454#495—538no—
455#464—538no—
456#464—538no—
457#463—538no—
458#463—538no—
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⋊C8—531no—
469C2×#103—531no—
470C2×#103—531no—
471C2×#102—531no—
472C2×#102—531no—
473C2×#102—531no—
474C2×#102—531no—
475C2×#97—531no—
476C2×#97—531no—
477C2×C4×C8—531no—
478C53C2×#340311yescharacteristic, complemented, Sylow
479C22×Q8—531no—
480C22×Q8C22⋊D5311yescharacteristic
481C22×Q8C22×D5311yescharacteristic
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—531no—
485C22×D4—531no—
486C22×D4—1061no—
487C22×D4—1061no—
488C22×D4C22×D5311yescharacteristic
489C22×D4C22×D5311yescharacteristic
490C23×C4—21no—
491C23×C4—21no—
492C23×C4—1061no—
493C23×C4—1061no—
494C2×Q16—534no—
495C2×Q16—2122no—
496C2×SD16—534no—
497C2×SD16—534no—
498C2×SD16—534no—
499C2×SD16—534no—
500C2×SD16—1064no—
501C2×SD16—1064no—
502C2×SD16—2122no—
503C2×SD16—2122no—
504C2×D8—534no—
505C2×D8—534no—
506C2×D8—534no—
507C2×D8—534no—
508C2×D8—1064no—
509C2×D8—2122no—
510C2×D8—2122no—
511C2×D8—2122no—
512C22×C8—531no—
513C22×C8—531no—
514C22×C8—531no—
515C22×C8—531no—
516#127—22no—
517#127—534no—
518#127—1062no—
519#127C22×D5314yes—
520#124—28no—
521#124—22no—
522#124—22no—
523#124—534no—
524#124—534no—
525#124—1068no—
526#124—1062no—
527#124—1062no—
528#124C22×D5314yes—
529#124C22×D5314yes—
530#123—28no—
531#123—28no—
532#123—1068no—
533#123—1068no—
534C4×Q8—22no—
535C4×Q8—534no—
536C4×Q8—1062no—
537C4×Q8C22⋊D5314yes—
538C4×Q8C22×D5314yes—
539C4×Q8C22×D5314yes—
540C4×D4—28no—
541C4×D4—22no—
542C4×D4—22no—
543C4×D4—534no—
544C4×D4—534no—
545C4×D4—1068no—
546C4×D4—1062no—
547C4×D4—1062no—
548C4×D4C22×D5314yes—
549C4×D4C22×D5314yes—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—531no—
552C2×C4⋊C4—1061no—
553C2×C4⋊C4C22⋊D5311yescharacteristic
554C2×C4⋊C4C22⋊D5311yescharacteristic
555C2×C4⋊C4C22⋊D5311yescharacteristic
556C2×C4⋊C4C22×D5311yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
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—21no—
570C2×C42—1061no—
571C2×C42C22×D5311yescharacteristic
572C2×C42C22×D5311yescharacteristic
573C2×C42C22×D5311yescharacteristic
574#107—534no—
575C4⋊C8—534no—
576C4⋊C8—534no—
577C4⋊C8—534no—
578#103—534no—
579#103—534no—
580#102—534no—
581#102—534no—
582#102—534no—
583#102—534no—
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—42no—
595C2×Q8—532no—
596C2×Q8—1061no—
597C2×Q8—1062no—
598C2×Q8—1062no—
599C2×Q8C2×C22⋊D5314yes—
600C2×Q8C23×D5312yes—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—24no—
604C2×D4—24no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—44no—
610C2×D4—82no—
611C2×D4—532no—
612C2×D4—532no—
613C2×D4—1064no—
614C2×D4—1064no—
615C2×D4—1061no—
616C2×D4—1061no—
617C2×D4—1062no—
618C2×D4—1062no—
619C2×D4—1062no—
620C2×D4—1062no—
621C2×D4—4242no—
622C2×D4—2124no—
623C2×D4C23×D5312yes—
624C2×D4C23×D5312yes—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—24no—
628C22×C4—24no—
629C22×C4—82no—
630C22×C4—82no—
631C22×C4—1061no—
632C22×C4—1061no—
633C22×C4—1064no—
634C22×C4—1064no—
635C22×C4—4242no—
636C22×C4—4242no—
637C22×C4C2×C22⋊D5311yescharacteristic
638C22×C4C2×C22⋊D5311yescharacteristic
639C22×C4C2×C22⋊D5311yescharacteristic
640C22×C4C2×C22⋊D5311yescharacteristic
641C22×C4C2×C22⋊D5311yescharacteristic
642C22×C4C2×C22⋊D5311yescharacteristic
643C22×C4C23×D5311yescharacteristic
644Q16—2124no—
645SD16—1068no—
646SD16—1068no—
647SD16—2124no—
648SD16—2124no—
649D8—1068no—
650D8—2124no—
651D8—2124no—
652D8—2124no—
653C2×C8—534no—
654C2×C8—532no—
655C2×C8—532no—
656C2×C8—532no—
657C2×C8—532no—
658C2×C8—1062no—
659C2×C8—1062no—
660C2×C8—1062no—
661C4⋊C4—24no—
662C4⋊C4—21no—
663C4⋊C4—532no—
664C4⋊C4—1061no—
665C4⋊C4—1064no—
666C4⋊C4C2×C22⋊D5314yes—
667C4⋊C4C2×C22⋊D5314yes—
668C4⋊C4C2×C22⋊D5314yes—
669C4⋊C4C23×D5312yes—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—1064no—
677C22⋊C4—1064no—
678C22⋊C4—1064no—
679C22⋊C4—1064no—
680C22⋊C4—1064no—
681C22⋊C4—1064no—
682C42—24no—
683C42—1064no—
684C42C2×C22⋊D5312yes—
685C42C2×C22⋊D5312yes—
686C42C2×C22⋊D5312yes—
687C42C23×D5312yes—
688C42C23×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—
706C23C22×C22⋊D5311yescharacteristic
707Q8—22no—
708Q8—22no—
709Q8—44no—
710Q8—42no—
711Q8—1062no—
712Q8—1062no—
713Q8—2122no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—48no—
719D4—42no—
720D4—42no—
721D4—84no—
722D4—1062no—
723D4—1062no—
724D4—1062no—
725D4—1062no—
726D4—4244no—
727D4—2128no—
728D4—2122no—
729D4—2122no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—84no—
741C2×C4—84no—
742C2×C4—1062no—
743C2×C4—1062no—
744C2×C4—4244no—
745C2×C4—4244no—
746C2×C4—2122no—
747C2×C4—2122no—
748C2×C4C22×C22⋊D5312yes—
749C2×C4C22×C22⋊D5312yes—
750C2×C4C22×C22⋊D5312yes—
751C2×C4C22×C22⋊D5312yes—
752C2×C4C22×C22⋊D5312yes—
753C2×C4C22×C22⋊D5312yes—
754C2×C4C22×C22⋊D5311yescharacteristic
755C2×C4#41×D5312yes—
756C2×C4#1313326312yes—
757C2×C4C24×D5311yescharacteristic
758C8—534no—
759C8—1062no—
760C8—1062no—
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#1681129212yes—
779C22#1681142112yes—
780C22#1681142612yes—
781C22C23×C22⋊D5311yescharacteristic
782C4—22no—
783C4—22no—
784C4—22no—
785C4—22no—
786C4—22no—
787C4—22no—
788C4—42no—
789C4—42no—
790C4—2122no—
791C4—2122no—
792C4#1681129212yes—
793C4C2×#41×D5311yescharacteristic
794C4C2×#1313326311yescharacteristic
795C2—82no—
796C2—82no—
797C2—4242no—
798C2—4242no—
799C2#2028779914yesdirect product factor
800C2C2×#1681129211yescharacteristic
801C2C2×#1681142111yescharacteristic
802C2C2×#1681142611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#559C2
socleC23×C53C22×D4
hypercenterC2×#559D53
hypocenterC53C2×#3403
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×#16811358C2semidirect
2. #20287799C2direct (N × H)
3. C2×#16811013C2semidirect
4. C2×#16811010C2semidirect
5. C2×#16811005C2semidirect
6. C2×#16810845C2semidirect
7. C2×#16810842C2semidirect
8. C2×#16810838C2semidirect
9. C2×#16810835C2semidirect
10. C2×#16810818C2semidirect
11. C2×#16810815C2semidirect
12. C2×#16810754C2semidirect
13. C2×#16810723C2semidirect
14. C2×#16810721C2semidirect
15. C2×C4×#11719922C2semidirect
16. C2×C53×#559C2semidirect
27. #16811358C22semidirect
38. #16811013C22semidirect
39. #16811010C22semidirect
40. #16811005C22semidirect
41. #16810845C22semidirect
42. #16810842C22semidirect
43. #16810838C22semidirect
44. #16810835C22semidirect
45. #16810818C22semidirect
46. #16810815C22semidirect
47. #16810754C22semidirect
48. #16810723C22semidirect
49. #16810721C22semidirect
50. C4×#11719922C22semidirect
65. C53×#559C22semidirect
395. C2×#559D53semidirect
412. C2×C53#3403semidirect
430. #559C2×D53semidirect
478. C53C2×#3403semidirect
799. C2#20287799direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113582
#202877992
C2×#168110132
C2×#168110102
C2×#168110052
C2×#168108452
C2×#168108422
C2×#168108382
C2×#168108352
C2×#168108182
C2×#168108152
C2×#168107542
C2×#168107232
C2×#168107212
C2×C4×#117199222
C2×C53×#5592
C2×#340353