Finite Group Databasebeta

← C2×#20285828 #28255493

Subgroups — C2×#20285828 #28255493

Order 13568.

2086 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811246C211yesmaximal, characteristic, complemented
2C2×#16811194C211yesmaximal, characteristic, complemented
3#20285828C2116yesmaximal, direct product factor
4C2×#16811016C211yesmaximal, characteristic, complemented
5C2×#16811004C211yesmaximal, characteristic, complemented
6C2×#16810981C211yesmaximal, characteristic, complemented
7C2×#16810972C211yesmaximal, characteristic, complemented
8C2×#16810843C211yesmaximal, characteristic, complemented
9C2×#16810831C211yesmaximal, characteristic, complemented
10C2×#16810837C211yesmaximal, characteristic, complemented
11C2×#16810827C211yesmaximal, characteristic, complemented
12C2×#16810768C211yesmaximal, characteristic
13C2×#16810778C211yesmaximal, characteristic, complemented
14C2×#16810764C211yesmaximal, characteristic, complemented
15C2×#16810681C211yesmaximal, characteristic, complemented
16C2×C53×#452C211yesmaximal, characteristic, complemented
17C23×Dic106C2211yescharacteristic
18C22×#11719925C2211yescharacteristic
19C22×#11719925C2211yescharacteristic
20C22×#11719913C2211yescharacteristic
21C22×#11719913C2211yescharacteristic
22C22×#11719924C2211yescharacteristic
23C22×#11719922C2211yescharacteristic
24#16811246—24no—
25#16811246C2218yescomplemented
26#16811194—24no—
27#16811194C2218yescomplemented
28C2×#13133216C2211yescharacteristic
29C2×#13133215C2211yescharacteristic
30C2×#13133215C2211yescharacteristic
31C2×#13133212—21no—
32C2×#13133206C2211yescharacteristic
33C2×#13133204C2211yescharacteristic
34C2×#13133204C2211yescharacteristic
35C2×#13133203—21no—
36C2×#13133199—21no—
37C2×#13133198—21no—
38C2×#13133198—21no—
39C2×#13133197—21no—
40C2×#13133196—21no—
41C2×#13133196—21no—
42C2×#13133191C2211yescharacteristic
43C2×Q8×Dic53C2211yescharacteristic
44C2×#13133179C2211yescharacteristic
45C2×#13133176C2211yescharacteristic
46#16811016C2218yescomplemented
47#16811004C2218yescomplemented
48#16810981C2218yescomplemented
49#16810972C2218yescomplemented
50#16810843C2218yescomplemented
51#16810837C2218yescomplemented
52#16810831C2218yescomplemented
53#16810827C2218yescomplemented
54#16810778C2218yescomplemented
55#16810768C2218yes—
56#16810764C2218yescomplemented
57#16810681C2218yescomplemented
58C2×#13133146C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133140C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×#41×C53C2211yescharacteristic
70C22×Q16×C53C2211yescharacteristic
71C22×SD16×C53C2211yescharacteristic
72C2×C22⋊Q8×C53C2211yescharacteristic
73C53×#452C2218yescomplemented
74C2×#103×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106—22no—
79C22×Dic106—21no—
80C22×Dic106—42no—
81C22×Dic106—42no—
82C22×Dic106C2311yescharacteristic
83C22×Dic106C2311yescharacteristic
84C22×Dic106C2314yes—
85C22×D212C2311yescharacteristic
86C22×C22⋊D53—21no—
87C23×Dic53—21no—
88C22×C4×D53—21no—
89C2×#11719925—42no—
90C2×#11719925—42no—
91C2×#11719925C2314yes—
92C2×#11719925C2314yes—
93C2×#11719913—42no—
94C2×#11719913—42no—
95C2×#11719913C2314yes—
96C2×#11719913C2314yes—
97C2×#11719924—42no—
98C2×#11719924C2314yes—
99C2×#11719922—42no—
100C2×#11719922C2314yes—
101C22×#88322C2311yescharacteristic
102C22×#88322C2311yescharacteristic
103#13133216—22no—
104#13133216C2314yes—
105#13133215—22no—
106#13133215—22no—
107#13133215C2314yes—
108#13133215C2314yes—
109#13133212—28no—
110#13133206—22no—
111#13133206C2314yes—
112#13133204—22no—
113#13133204—22no—
114#13133204C2314yes—
115#13133204C2314yes—
116#13133203—28no—
117#13133199—28no—
118#13133198—28no—
119#13133198—28no—
120#13133197—28no—
121#13133196—28no—
122#13133196—28no—
123#13133191—22no—
124#13133191C2314yes—
125Q8×Dic53—22no—
126Q8×Dic53C2314yes—
127#13133179—22no—
128#13133179C2314yes—
129#13133176D414yes—
130#13133176C2314yes—
131C2×C4⋊Dic53—21no—
132C2×C4⋊Dic53D411yescharacteristic
133C2×C4⋊Dic53D411yescharacteristic
134C2×C4⋊Dic53C2311yescharacteristic
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×#11719919—21no—
139C2×#11719919—21no—
140C2×C22⋊Dic53—21no—
141C2×C22⋊Dic53—21no—
142C2×C22⋊Dic53—21no—
143C2×C22⋊Dic53—21no—
144C2×C22⋊Dic53D411yescharacteristic
145C2×C22⋊Dic53D411yescharacteristic
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×#11719921—21no—
150C2×C4×Dic53—21no—
151C2×C4×Dic53C2311yescharacteristic
152C2×C4×Dic53C2311yescharacteristic
153#13133146C2314yes—
154#13133146C2314yes—
155#13133142C2314yes—
156#13133142C2314yes—
157#13133141C2314yes—
158#13133140C2314yes—
159#13133140C2314yes—
160#13133138C2314yes—
161C22⋊#88322C2314yes—
162#13133127C2314yes—
163C8×Dic53C2314yes—
164C2×#41×C53—22no—
165C2×#41×C53—42no—
166C2×#41×C53—42no—
167C2×#41×C53C2314yes—
168C22×Q8×C53C2311yescharacteristic
169C22×Q8×C53C2311yescharacteristic
170C22×D4×C53—21no—
171C22×D4×C53C2311yescharacteristic
172C23×C4×C53—21no—
173C23×C4×C53C2311yescharacteristic
174C2×Q16×C53—42no—
175C2×Q16×C53C2314yes—
176C2×SD16×C53—42no—
177C2×SD16×C53C2314yes—
178C22×C8×C53C2311yescharacteristic
179C22×C8×C53C2311yescharacteristic
180C22⋊Q8×C53—22no—
181C22⋊Q8×C53C2314yes—
182C2×C4⋊C4×C53—21no—
183C2×C4⋊C4×C53C2311yescharacteristic
184C2×C22⋊C4×C53—21no—
185#103×C53C2314yes—
186#102×C53C2314yes—
187C22⋊C8×C53C2314yes—
188C24×C53—21no—
189C24×C53C2×D411yescharacteristic
190C23×D53—21no—
191#41×C53—44no—
192#41×C53—44no—
193#41×C53—48no—
194C2×Q8×C53—21no—
195C2×Q8×C53—21no—
196C2×Q8×C53—22no—
197C2×Q8×C53—22no—
198C2×Q8×C53—22no—
199C2×Q8×C53—22no—
200C2×Q8×C53C2412yes—
201C2×Q8×C53C2412yes—
202C2×D4×C53—24no—
203C2×D4×C53—21no—
204C2×D4×C53—22no—
205C2×D4×C53—22no—
206C2×D4×C53—44no—
207C2×D4×C53C2412yes—
208C22×C4×C53—22no—
209C22×C4×C53—22no—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53—24no—
214C22×C4×C53—44no—
215C22×C4×C53C2×D411yescharacteristic
216C22×C4×C53C2×D412yes—
217C22×C4×C53C2412yes—
218C22×C4×C53C2411yescharacteristic
219C2×C22⋊D53—24no—
220C2×C22⋊D53—82no—
221C22×Dic53—21no—
222C22×Dic53—21no—
223C22×Dic53—21no—
224C22×Dic53—24no—
225C22×Dic53—44no—
226C22×Dic53C2×D411yescharacteristic
227C22×Dic53C2×D411yescharacteristic
228C22×Dic53C2×D411yescharacteristic
229C22×Dic53C2×D411yescharacteristic
230C2×D212—22no—
231C2×D212—22no—
232C2×D212—21no—
233C2×D212C2412yes—
234C2×C4×D53—24no—
235C2×C4×D53—82no—
236C2×Dic106—22no—
237C2×Dic106—22no—
238C2×Dic106—22no—
239C2×Dic106—22no—
240C2×Dic106—24no—
241C2×Dic106—21no—
242C2×Dic106—21no—
243C2×Dic106—24no—
244C2×Dic106—44no—
245C2×Dic106—44no—
246C2×Dic106—44no—
247C2×Dic106—48no—
248C2×Dic106—82no—
249C2×Dic106C2412yes—
250C2×Dic106C2412yes—
251Q16×C53—44no—
252SD16×C53—44no—
253C2×C8×C53—22no—
254C2×C8×C53—22no—
255C2×C8×C53C2412yes—
256C2×C8×C53C2412yes—
257C4⋊C4×C53—24no—
258C4⋊C4×C53—21no—
259C4⋊C4×C53C2412yes—
260C22⋊C4×C53—24no—
261C22⋊Dic53—24no—
262C22⋊Dic53—24no—
263C22⋊Dic53—24no—
264C22⋊Dic53—24no—
265C22⋊Dic53C2×D414yes—
266C22⋊Dic53C2×D414yes—
267#11719925—44no—
268#11719925—44no—
269#11719924—44no—
270#11719922—44no—
271#11719921—24no—
272#11719921—24no—
273#11719921—24no—
274#11719921—24no—
275C4⋊Dic53—21no—
276C4⋊Dic53—24no—
277C4⋊Dic53C2×D414yes—
278C4⋊Dic53C2×D414yes—
279C4⋊Dic53C2412yes—
280#11719919—24no—
281#11719919—24no—
282#11719919—24no—
283#11719919—24no—
284#11719919—24no—
285C4×Dic53—24no—
286C4×Dic53C2×D412yes—
287C4×Dic53C2×D412yes—
288C4×Dic53C2412yes—
289C4×Dic53C2412yes—
290C2×#88322—22no—
291C2×#88322—22no—
292C2×#88322C2412yes—
293C2×#88322C2412yes—
294#11719913—44no—
295#11719913—44no—
296C23×C53—22no—
297C23×C53—22no—
298C23×C53—22no—
299C23×C53—22no—
300C23×C53—42no—
301C23×C53—42no—
302C23×C53—42no—
303C23×C53C22×D412yes—
304C23×C53C22×D411yescharacteristic
305C22×D53—22no—
306C22×D53—42no—
307C22×D53—42no—
308C22×D53—42no—
309Q8×C53—22no—
310Q8×C53—22no—
311Q8×C53—22no—
312Q8×C53—22no—
313Q8×C53—42no—
314Q8×C53—42no—
315D4×C53—22no—
316D4×C53—22no—
317D4×C53—48no—
318D4×C53—42no—
319C2×C4×C53—22no—
320C2×C4×C53—24no—
321C2×C4×C53—22no—
322C2×C4×C53—22no—
323C2×C4×C53—22no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53—48no—
327C2×C4×C53—42no—
328C2×C4×C53—42no—
329C2×C4×C53—42no—
330C2×C4×C53C22×D412yes—
331C2×C4×C53C22×D411yescharacteristic
332C2×C4×C53H(5,𝔽2)12yes—
333C2×C4×C53H(5,𝔽2)12yes—
334C2×C4×C53C2511yescharacteristic
335C22⋊D53—84no—
336C2×Dic53—22no—
337C2×Dic53—22no—
338C2×Dic53—22no—
339C2×Dic53—22no—
340C2×Dic53—22no—
341C2×Dic53—22no—
342C2×Dic53—22no—
343C2×Dic53—48no—
344C2×Dic53—42no—
345C2×Dic53—42no—
346C2×Dic53—42no—
347C2×Dic53C22×D412yes—
348C2×Dic53C22×D412yes—
349C2×Dic53C22×D412yes—
350C2×Dic53C22×D412yes—
351D212—22no—
352D212—22no—
353D212—42no—
354C4×D53—84no—
355Dic106—22no—
356Dic106—22no—
357Dic106—22no—
358Dic106—22no—
359Dic106—48no—
360Dic106—42no—
361Dic106—42no—
362Dic106—84no—
363C8×C53—22no—
364C8×C53—22no—
365#88322—22no—
366#88322—22no—
367C2×#3225—531nomaximal, Sylow
368C22×C53—22no—
369C22×C53—22no—
370C22×C53—22no—
371C22×C53—44no—
372C22×C53—42no—
373C22×C53—42no—
374C22×C53—42no—
375C22×C53—84no—
376C22×C53#53512yes—
377C22×C53#57712yes—
378C22×C53#57812yes—
379C22×C53C23×D411yescharacteristic
380C2×D53—42no—
381C2×D53—42no—
382C2×D53—42no—
383C2×D53—84no—
384C4×C53—22no—
385C4×C53—42no—
386C4×C53—42no—
387C4×C53—42no—
388C4×C53#53512yes—
389C4×C53C2×H(5,𝔽2)11yescharacteristic
390C4×C53C2×H(5,𝔽2)11yescharacteristic
391Dic53—22no—
392Dic53—22no—
393Dic53—22no—
394Dic53—22no—
395Dic53—42no—
396Dic53—42no—
397Dic53—42no—
398C2×#542—531no—
399C2×#536—531no—
400#3225—5316no—
401C2×#497—531no—
402C2×#495—531no—
403C2×#489—531no—
404C2×#487—531no—
405C2×#464—531no—
406C2×#462—531no—
407C2×#463—531no—
408C2×#461—531no—
409C2×#452D5311yescharacteristic, complemented
410C2×#449—531no—
411C2×#451—531no—
412C2×#448—531no—
413C2×#433—531no—
414C2×C53—42no—
415C2×C53—82no—
416C2×C53#322514yescomplemented
417C2×C53C2×#53511yescharacteristic
418C2×C53C2×#57711yescharacteristic
419C2×C53C2×#57811yescharacteristic
420D53—82no—
421C22×#41C2×D5311yescharacteristic
422C23×Q8—531no—
423C22×Q16—531no—
424C22×Q16—531no—
425C22×Q16C2×D5311yescharacteristic
426C22×SD16—531no—
427C22×SD16—531no—
428C22×SD16—531no—
429C22×SD16C2×D5311yescharacteristic
430C22×D8—531no—
431#542—538no—
432#542—1064no—
433#536—538no—
434#536—1064no—
435C2×C4⋊Q8—531no—
436C2×C4⋊Q8—531no—
437C2×C4⋊Q8—531no—
438C2×#126—1061no—
439C2×#124—531no—
440C2×#124—531no—
441C2×#124—531no—
442C2×#124—1061no—
443C2×#123—1061no—
444C2×#123—1061no—
445C2×#123—1061no—
446C2×C22⋊Q8—1061no—
447C2×C22⋊Q8—1061no—
448C2×C22⋊Q8—1061no—
449C2×C22⋊Q8C2×D5311yescharacteristic
450C2×#121—531no—
451C2×C4×Q8—531no—
452C2×C4×D4—531no—
453C2×#117—531no—
454#497—538no—
455#495—538no—
456#489—538no—
457#487—538no—
458#464—538no—
459#463—538no—
460#462—538no—
461#461—538no—
462#452C2×D5318yescomplemented
463#451—538no—
464#449—538no—
465#448—538no—
466#433—538no—
467C2×C4⋊C8—531no—
468C2×C4⋊C8—531no—
469C2×#103—531no—
470C2×#103—531no—
471C2×#103—531no—
472C2×#103—531no—
473C2×#103—531no—
474C2×#103C2×D5311yescharacteristic
475C2×#102—531no—
476C2×#102C2×D5311yescharacteristic
477C2×C22⋊C8—531no—
478C2×C22⋊C8C2×D5311yescharacteristic
479C2×#97—531no—
480C2×C4×C8—531no—
481C53C2×#322511yescharacteristic, complemented, Sylow
482C2×#41—22no—
483C2×#41—42no—
484C2×#41—42no—
485C2×#41C22×D5314yes—
486C22×Q8—531no—
487C22×Q8—531no—
488C22×Q8—534no—
489C22×Q8—1061no—
490C22×Q8—1061no—
491C22×Q8—1062no—
492C22×Q8—2122no—
493C22×Q8—2122no—
494C22×Q8C22×D5311yescharacteristic
495C22×Q8C22×D5311yescharacteristic
496C22×D4—21no—
497C22×D4—531no—
498C22×D4—1061no—
499C22×D4C22×D5311yescharacteristic
500C23×C4—21no—
501C23×C4—1061no—
502C23×C4—1061no—
503C23×C4C22×D5311yescharacteristic
504C2×Q16—42no—
505C2×Q16—534no—
506C2×Q16—534no—
507C2×Q16—2122no—
508C2×Q16—2122no—
509C2×Q16C22×D5314yes—
510C2×SD16—42no—
511C2×SD16—534no—
512C2×SD16—534no—
513C2×SD16—534no—
514C2×SD16—2122no—
515C2×SD16—2122no—
516C2×SD16—2122no—
517C2×SD16C22×D5314yes—
518C2×D8—534no—
519C2×D8—2122no—
520C22×C8—531no—
521C22×C8—531no—
522C22×C8C22×D5311yescharacteristic
523C22×C8C22×D5311yescharacteristic
524C4⋊Q8—534no—
525C4⋊Q8—534no—
526C4⋊Q8—534no—
527C4⋊Q8—1062no—
528C4⋊Q8—1062no—
529C4⋊Q8—1062no—
530#126—1068no—
531#124—534no—
532#124—534no—
533#124—534no—
534#124—1062no—
535#124—1062no—
536#124—1062no—
537#124—1068no—
538#123—1068no—
539#123—1068no—
540#123—1068no—
541C22⋊Q8—22no—
542C22⋊Q8—1068no—
543C22⋊Q8—1068no—
544C22⋊Q8—1068no—
545C22⋊Q8C22×D5314yes—
546#121—534no—
547#121—1062no—
548C4×Q8—534no—
549C4×Q8—1062no—
550C4×D4—534no—
551C4×D4—1062no—
552#117—534no—
553#117—534no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—531no—
556C2×C4⋊C4—531no—
557C2×C4⋊C4—531no—
558C2×C4⋊C4—1061no—
559C2×C4⋊C4—1061no—
560C2×C4⋊C4—1061no—
561C2×C4⋊C4—1061no—
562C2×C4⋊C4—1061no—
563C2×C4⋊C4—1061no—
564C2×C4⋊C4C22×D5311yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—531no—
567C2×C22⋊C4—531no—
568C2×C22⋊C4—1061no—
569C2×C22⋊C4—1061no—
570C2×C22⋊C4—1061no—
571C2×C22⋊C4—1061no—
572C2×C22⋊C4—1061no—
573C2×C22⋊C4—1061no—
574C2×C22⋊C4—1061no—
575C2×C22⋊C4—1061no—
576C2×C42—531no—
577C2×C42—531no—
578C2×C42—1061no—
579C4⋊C8—534no—
580C4⋊C8—534no—
581#103—534no—
582#103—534no—
583#103—534no—
584#103—534no—
585#103—534no—
586#103C22×D5314yes—
587#102—534no—
588#102C22×D5314yes—
589C22⋊C8—534no—
590C22⋊C8C22×D5314yes—
591#97—534no—
592C4×C8—534no—
593C24—21no—
594C24—1061no—
595C24D4×D5311yescharacteristic
596#41—44no—
597#41—44no—
598#41—48no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—22no—
602C2×Q8—22no—
603C2×Q8—22no—
604C2×Q8—22no—
605C2×Q8—532no—
606C2×Q8—532no—
607C2×Q8—1064no—
608C2×Q8—1064no—
609C2×Q8—1061no—
610C2×Q8—1061no—
611C2×Q8—1062no—
612C2×Q8—1062no—
613C2×Q8—1062no—
614C2×Q8—1062no—
615C2×Q8—4242no—
616C2×Q8—2124no—
617C2×Q8—2124no—
618C2×Q8—2124no—
619C2×Q8—2128no—
620C2×Q8C23×D5312yes—
621C2×Q8C23×D5312yes—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—44no—
627C2×D4—532no—
628C2×D4—1064no—
629C2×D4—1061no—
630C2×D4—1062no—
631C2×D4—1062no—
632C2×D4—4242no—
633C2×D4C23×D5312yes—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—24no—
640C22×C4—44no—
641C22×C4—531no—
642C22×C4—531no—
643C22×C4—531no—
644C22×C4—531no—
645C22×C4—1064no—
646C22×C4—1064no—
647C22×C4—1061no—
648C22×C4—1061no—
649C22×C4—1061no—
650C22×C4—4242no—
651C22×C4—2124no—
652C22×C4D4×D5312yes—
653C22×C4D4×D5311yescharacteristic
654C22×C4C23×D5312yes—
655C22×C4C23×D5311yescharacteristic
656Q16—44no—
657Q16—2124no—
658Q16—2124no—
659SD16—44no—
660SD16—2124no—
661SD16—2124no—
662SD16—2124no—
663D8—2124no—
664C2×C8—22no—
665C2×C8—22no—
666C2×C8—532no—
667C2×C8—532no—
668C2×C8—1062no—
669C2×C8—1062no—
670C2×C8C23×D5312yes—
671C2×C8C23×D5312yes—
672C4⋊C4—24no—
673C4⋊C4—21no—
674C4⋊C4—534no—
675C4⋊C4—534no—
676C4⋊C4—532no—
677C4⋊C4—1064no—
678C4⋊C4—1064no—
679C4⋊C4—1064no—
680C4⋊C4—1064no—
681C4⋊C4—1064no—
682C4⋊C4—1064no—
683C4⋊C4—1061no—
684C4⋊C4C23×D5312yes—
685C22⋊C4—24no—
686C22⋊C4—534no—
687C22⋊C4—534no—
688C22⋊C4—1064no—
689C22⋊C4—1064no—
690C22⋊C4—1064no—
691C22⋊C4—1064no—
692C22⋊C4—1064no—
693C22⋊C4—1064no—
694C22⋊C4—1064no—
695C22⋊C4—1064no—
696C42—532no—
697C42—532no—
698C42—532no—
699C42—532no—
700C42—1064no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—1062no—
709C23—2122no—
710C23—2122no—
711C23—2122no—
712C23C2×D4×D5312yes—
713C23C2×D4×D5311yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—22no—
717Q8—22no—
718Q8—42no—
719Q8—42no—
720Q8—1062no—
721Q8—1062no—
722Q8—1062no—
723Q8—1062no—
724Q8—4244no—
725Q8—2128no—
726Q8—2122no—
727Q8—2122no—
728D4—22no—
729D4—22no—
730D4—48no—
731D4—42no—
732D4—1062no—
733D4—1062no—
734D4—4244no—
735D4—2122no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—48no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—532no—
748C2×C4—532no—
749C2×C4—532no—
750C2×C4—532no—
751C2×C4—1062no—
752C2×C4—1062no—
753C2×C4—1062no—
754C2×C4—1062no—
755C2×C4—1062no—
756C2×C4—1062no—
757C2×C4—1062no—
758C2×C4—4244no—
759C2×C4—2128no—
760C2×C4—2122no—
761C2×C4—2122no—
762C2×C4—2122no—
763C2×C4C2×D4×D5312yes—
764C2×C4C2×D4×D5311yescharacteristic
765C2×C4#1313326212yes—
766C2×C4#1313326212yes—
767C2×C4C24×D5311yescharacteristic
768C8—22no—
769C8—22no—
770C8—1062no—
771C8—1062no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—44no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—84no—
780C22—4244no—
781C22—2122no—
782C22—2122no—
783C22—2122no—
784C22#1681118812yes—
785C22#1681143012yes—
786C22#1681143912yes—
787C22C22×D4×D5311yescharacteristic
788C4—22no—
789C4—42no—
790C4—42no—
791C4—42no—
792C4—1062no—
793C4—1062no—
794C4—1062no—
795C4—1062no—
796C4—2122no—
797C4—2122no—
798C4—2122no—
799C4#1681118812yes—
800C4C2×#1313326211yescharacteristic
801C4C2×#1313326211yescharacteristic
802C2—42no—
803C2—82no—
804C2—4242no—
805C2#2028582814yesdirect product factor
806C2C2×#1681118811yescharacteristic
807C2C2×#1681143011yescharacteristic
808C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#452C2
socleC23×C53C22×D4
prime radicalC2×#16810768C2
hypercenterC2×#452D53
hypocenterC53C2×#3225
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#16811246C2semidirect
2. C2×#16811194C2semidirect
3. #20285828C2direct (N × H)
4. C2×#16811016C2semidirect
5. C2×#16811004C2semidirect
6. C2×#16810981C2semidirect
7. C2×#16810972C2semidirect
8. C2×#16810843C2semidirect
9. C2×#16810831C2semidirect
10. C2×#16810837C2semidirect
11. C2×#16810827C2semidirect
13. C2×#16810778C2semidirect
14. C2×#16810764C2semidirect
15. C2×#16810681C2semidirect
16. C2×C53×#452C2semidirect
25. #16811246C22semidirect
27. #16811194C22semidirect
46. #16811016C22semidirect
47. #16811004C22semidirect
48. #16810981C22semidirect
49. #16810972C22semidirect
50. #16810843C22semidirect
51. #16810837C22semidirect
52. #16810831C22semidirect
53. #16810827C22semidirect
54. #16810778C22semidirect
56. #16810764C22semidirect
57. #16810681C22semidirect
73. C53×#452C22semidirect
409. C2×#452D53semidirect
416. C2×C53#3225semidirect
462. #452C2×D53semidirect
481. C53C2×#3225semidirect
805. C2#20285828direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112462
C2×#168111942
#202858282
C2×#168110162
C2×#168110042
C2×#168109812
C2×#168109722
C2×#168108432
C2×#168108312
C2×#168108372
C2×#168108272
C2×#168107682
C2×#168107782
C2×#168107642
C2×#168106812
C2×C53×#4522
C2×#322553