Finite Group Databasebeta

← C2×#20285555 #28254721

Subgroups — C2×#20285555 #28254721

Order 13568.

2362 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811135C211yesmaximal, characteristic, complemented
2C2×#16811133C211yesmaximal, characteristic, complemented
3#20285555C2116yesmaximal, direct product factor
4C2×#16810966C211yesmaximal, characteristic, complemented
5C2×#16810964C211yesmaximal, characteristic, complemented
6C2×#16810949C211yesmaximal, characteristic, complemented
7C2×#16810882C211yesmaximal, characteristic, complemented
8C2×#16810875C211yesmaximal, characteristic, complemented
9C2×#16810870C211yesmaximal, characteristic, complemented
10C2×#16810868C211yesmaximal, characteristic, complemented
11C2×#16810787C211yesmaximal, characteristic, complemented
12C2×#16810786C211yesmaximal, characteristic, complemented
13C2×#16810769C211yesmaximal, characteristic, complemented
14C2×#16810766C211yesmaximal, characteristic, complemented
15C2×#16810585C211yesmaximal, characteristic, complemented
16C2×C53×#482C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×#11719947C2211yescharacteristic
19C23×C4×D53C2211yescharacteristic
20C22×Dic212C2211yescharacteristic, complemented
21C22×#11719913C2211yescharacteristic, complemented
22C22×#11719923C2211yescharacteristic, complemented
23C22×#11719922C2211yescharacteristic, complemented
24C22×#11719912C2211yescharacteristic
25C22×#11719912C2211yescharacteristic
26#16811135—24no—
27#16811135C2218yescomplemented
28#16811133—24no—
29#16811133C2218yescomplemented
30C2×#13133201—21no—
31C2×#13133199—21no—
32C2×#13133197C2211yescharacteristic
33C2×#13133197C2211yescharacteristic
34C2×#13133197C2211yescharacteristic
35C2×#13133196C2211yescharacteristic
36C2×#13133192C2211yescharacteristic
37C2×#13133192C2211yescharacteristic
38C2×#13133188C2211yescharacteristic
39C2×#13133187—21no—
40C2×#13133185—21no—
41C2×C4×D212—21no—
42C2×C4×D212—21no—
43C2×D4×Dic53—21no—
44C2×#13133177—21no—
45C2×#13133175C2211yescharacteristic
46#16810966C2218yescomplemented
47#16810964C2218yescomplemented
48#16810949C2218yescomplemented
49#16810882C2218yescomplemented
50#16810875C2218yescomplemented
51#16810870C2218yescomplemented
52#16810868C2218yescomplemented
53#16810787C2218yescomplemented
54#16810786C2218yescomplemented
55#16810769C2218yescomplemented
56#16810766C2218yescomplemented
57C2×#13133150C2211yescharacteristic, complemented
58C2×#13133148C2211yescharacteristic, complemented
59C2×#13133142C2211yescharacteristic, complemented
60C2×#13133140C2211yescharacteristic, complemented
61C2×#13133140C2211yescharacteristic, complemented
62C2×#13133140C2211yescharacteristic, complemented
63C2×#13133139C2211yescharacteristic, complemented
64C2×#13133137C2211yescharacteristic, complemented
65#16810585C2218yescomplemented
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133129C2211yescharacteristic
69C2×#121×C53C2211yescharacteristic
70C2×#117×C53C2211yescharacteristic
71C53×#482C2218yescomplemented
72C2×#107×C53C2211yescharacteristic, complemented
73C2×#106×C53C2211yescharacteristic, complemented
74C2×#102×C53C2211yescharacteristic, complemented
75C2×#102×C53C2211yescharacteristic, complemented
76C2×C22⋊C8×C53C2211yescharacteristic
77C24×D53D411yescharacteristic
78C2×#11719945—22no—
79C2×#11719945—42no—
80C2×#11719945—42no—
81C2×#11719945C2314yes—
82C2×#11719947—22no—
83C2×#11719947—42no—
84C2×#11719947—42no—
85C2×#11719947C2314yes—
86C22×Dic106C2311yescharacteristic
87C22×Dic106C2311yescharacteristic
88C22×D212—21no—
89C22×D212—21no—
90C22×D212C2311yescharacteristic
91C22×C22⋊D53—21no—
92C22×C22⋊D53—21no—
93C22×C22⋊D53—21no—
94C23×Dic53—21no—
95C23×Dic53D411yescharacteristic
96C22×C4×D53—21no—
97C22×C4×D53—42no—
98C22×C4×D53—42no—
99C22×C4×D53D411yescharacteristic
100C22×C4×D53D411yescharacteristic
101C22×C4×D53D414yes—
102C22×C4×D53C2311yescharacteristic
103C22×C4×D53C2311yescharacteristic
104C22×C4×D53C2314yes—
105C2×Dic212—42no—
106C2×Dic212C2314yescomplemented
107C2×#11719913—42no—
108C2×#11719913C2314yescomplemented
109C2×#11719923—42no—
110C2×#11719923C2314yescomplemented
111C2×#11719922—42no—
112C2×#11719922C2314yescomplemented
113C2×#11719912—42no—
114C2×#11719912—42no—
115C2×#11719912C2314yes—
116C2×#11719912C2314yes—
117C22×#88322C2311yescharacteristic
118C22×#88322C2311yescharacteristic
119#13133201—28no—
120#13133199—28no—
121#13133197—22no—
122#13133197—22no—
123#13133197—22no—
124#13133197C2314yes—
125#13133197C2314yes—
126#13133197C2314yes—
127#13133196—22no—
128#13133196C2314yes—
129#13133192—22no—
130#13133192—22no—
131#13133192C2314yes—
132#13133192C2314yes—
133#13133188—22no—
134#13133188C2314yes—
135#13133187—28no—
136#13133185—28no—
137C4×D212—28no—
138C4×D212—28no—
139D4×Dic53—28no—
140#13133177—28no—
141#13133175—22no—
142#13133175C2314yes—
143C2×C4⋊Dic53—21no—
144C2×C4⋊Dic53—21no—
145C2×C4⋊Dic53—21no—
146C2×C4⋊Dic53C2311yescharacteristic
147C2×#11719919—21no—
148C2×C22⋊Dic53—21no—
149C2×C22⋊Dic53—21no—
150C2×#11719921—21no—
151C2×#11719921—21no—
152C2×#11719921—21no—
153C2×#11719921—21no—
154C2×#11719921—21no—
155C2×#11719921—21no—
156C2×C4×Dic53—21no—
157#13133150C2314yescomplemented
158#13133148C2314yescomplemented
159#13133142C2314yescomplemented
160#13133140C2314yescomplemented
161#13133140C2314yescomplemented
162#13133140C2314yescomplemented
163#13133139C2314yescomplemented
164#13133137C2314yescomplemented
165C22⋊#88322C2314yes—
166#13133129C2314yes—
167#13133129C2314yes—
168C22×D4×C53—21no—
169C22×D4×C53C2311yescharacteristic
170C23×C4×C53C2311yescharacteristic
171C22×C8×C53C2311yescharacteristic
172C22×C8×C53C2311yescharacteristic
173#121×C53—22no—
174#121×C53C2314yes—
175#117×C53—22no—
176#117×C53C2314yes—
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C4⋊C4×C53C2311yescharacteristic
179C2×C4⋊C4×C53C2311yescharacteristic
180C2×C22⋊C4×C53—21no—
181C2×C22⋊C4×C53—21no—
182C2×C42×C53—21no—
183#107×C53C2314yescomplemented
184#106×C53C2314yescomplemented
185#102×C53C2314yescomplemented
186#102×C53C2314yescomplemented
187C22⋊C8×C53C2314yes—
188C24×C53—21no—
189C24×C53C2×D411yescharacteristic
190C23×D53—21no—
191C23×D53—42no—
192C23×D53—42no—
193C23×D53—42no—
194C23×D53C2×D411yescharacteristic
195C23×D53C2×D411yescharacteristic
196C23×D53C2×D414yes—
197C2×D4×C53—24no—
198C2×D4×C53—21no—
199C2×D4×C53—22no—
200C2×D4×C53—22no—
201C2×D4×C53—44no—
202C2×D4×C53C2412yes—
203C22×C4×C53—22no—
204C22×C4×C53—22no—
205C22×C4×C53—21no—
206C22×C4×C53—21no—
207C22×C4×C53—21no—
208C22×C4×C53C2×D411yescharacteristic
209C22×C4×C53C2×D412yes—
210C22×C4×C53C2412yes—
211C22×C4×C53C2411yescharacteristic
212C2×C22⋊D53—24no—
213C2×C22⋊D53—24no—
214C2×C22⋊D53—24no—
215C2×C22⋊D53—44no—
216C2×C22⋊D53—44no—
217C2×C22⋊D53—44no—
218C22×Dic53—21no—
219C22×Dic53—21no—
220C22×Dic53—21no—
221C22×Dic53—24no—
222C22×Dic53—42no—
223C22×Dic53—44no—
224C22×Dic53C2×D411yescharacteristic
225C22×Dic53C2×D411yescharacteristic
226C22×Dic53C2×D414yes—
227#11719947—44no—
228#11719947—44no—
229#11719947—48no—
230#11719945—44no—
231#11719945—44no—
232#11719945—48no—
233C2×D212—22no—
234C2×D212—22no—
235C2×D212—24no—
236C2×D212—24no—
237C2×D212—21no—
238C2×D212—44no—
239C2×D212—44no—
240C2×D212C2412yes—
241C2×C4×D53—22no—
242C2×C4×D53—22no—
243C2×C4×D53—22no—
244C2×C4×D53—22no—
245C2×C4×D53—24no—
246C2×C4×D53—48no—
247C2×C4×D53—44no—
248C2×C4×D53—44no—
249C2×C4×D53—42no—
250C2×C4×D53—42no—
251C2×C4×D53—44no—
252C2×C4×D53C2×D412yes—
253C2×C4×D53C2×D412yes—
254C2×C4×D53C2×D414yes—
255C2×C4×D53C2×D414yes—
256C2×C4×D53C2412yes—
257C2×C4×D53C2412yes—
258C2×Dic106—22no—
259C2×Dic106—22no—
260C2×Dic106—22no—
261C2×Dic106—22no—
262C2×Dic106—21no—
263C2×Dic106—21no—
264C2×Dic106C2412yes—
265C2×Dic106C2412yes—
266C2×C8×C53—22no—
267C2×C8×C53—22no—
268C2×C8×C53C2412yes—
269C2×C8×C53C2412yes—
270C4⋊C4×C53—21no—
271C4⋊C4×C53—21no—
272C4⋊C4×C53—21no—
273C4⋊C4×C53C2412yes—
274C4⋊C4×C53C2412yes—
275C4⋊C4×C53C2412yes—
276C22⋊C4×C53—24no—
277C22⋊C4×C53—24no—
278C42×C53—24no—
279C22⋊Dic53—24no—
280C22⋊Dic53—24no—
281#11719923—44no—
282#11719922—44no—
283#11719921—24no—
284#11719921—24no—
285#11719921—24no—
286#11719921—24no—
287#11719921—24no—
288#11719921—24no—
289C4⋊Dic53—21no—
290C4⋊Dic53—24no—
291C4⋊Dic53—24no—
292C4⋊Dic53—24no—
293C4⋊Dic53C2412yes—
294#11719919—24no—
295C4×Dic53—24no—
296C2×#88322—22no—
297C2×#88322—22no—
298C2×#88322C2412yes—
299C2×#88322C2412yes—
300Dic212—44no—
301#11719913—44no—
302#11719912—44no—
303#11719912—44no—
304C23×C53—22no—
305C23×C53—22no—
306C23×C53—22no—
307C23×C53—22no—
308C23×C53—42no—
309C23×C53—42no—
310C23×C53—42no—
311C23×C53C22×D412yes—
312C23×C53C22×D411yescharacteristic
313C22×D53—22no—
314C22×D53—22no—
315C22×D53—22no—
316C22×D53—22no—
317C22×D53—22no—
318C22×D53—22no—
319C22×D53—22no—
320C22×D53—44no—
321C22×D53—44no—
322C22×D53—44no—
323C22×D53—416no—
324C22×D53—42no—
325C22×D53—42no—
326C22×D53—42no—
327C22×D53C22×D412yes—
328C22×D53C22×D412yes—
329D4×C53—22no—
330D4×C53—22no—
331D4×C53—48no—
332D4×C53—42no—
333C2×C4×C53—22no—
334C2×C4×C53—24no—
335C2×C4×C53—22no—
336C2×C4×C53—22no—
337C2×C4×C53—22no—
338C2×C4×C53—22no—
339C2×C4×C53—22no—
340C2×C4×C53—42no—
341C2×C4×C53—42no—
342C2×C4×C53—42no—
343C2×C4×C53C22×D412yes—
344C2×C4×C53C22×D411yescharacteristic
345C2×C4×C53H(5,𝔽2)12yes—
346C2×C4×C53H(5,𝔽2)12yes—
347C2×C4×C53C2511yescharacteristic
348C22⋊D53—48no—
349C22⋊D53—48no—
350C22⋊D53—48no—
351C2×Dic53—22no—
352C2×Dic53—22no—
353C2×Dic53—22no—
354C2×Dic53—22no—
355C2×Dic53—22no—
356C2×Dic53—44no—
357C2×Dic53—48no—
358C2×Dic53—42no—
359C2×Dic53—42no—
360C2×Dic53—42no—
361C2×Dic53C22×D412yes—
362C2×Dic53C22×D412yes—
363D212—22no—
364D212—22no—
365D212—48no—
366D212—48no—
367D212—42no—
368C4×D53—24no—
369C4×D53—24no—
370C4×D53—22no—
371C4×D53—22no—
372C4×D53—22no—
373C4×D53—22no—
374C4×D53—44no—
375C4×D53—44no—
376C4×D53—48no—
377Dic106—22no—
378Dic106—22no—
379Dic106—22no—
380Dic106—22no—
381Dic106—42no—
382Dic106—42no—
383C8×C53—22no—
384C8×C53—22no—
385#88322—22no—
386#88322—22no—
387C2×#3197—531nomaximal, Sylow
388C22×C53—22no—
389C22×C53—22no—
390C22×C53—22no—
391C22×C53—44no—
392C22×C53—42no—
393C22×C53—42no—
394C22×C53—42no—
395C22×C53—84no—
396C22×C53#53412yes—
397C22×C53#57512yes—
398C22×C53#57512yes—
399C22×C53C23×D411yescharacteristic
400C2×D53—22no—
401C2×D53—22no—
402C2×D53—22no—
403C2×D53—22no—
404C2×D53—22no—
405C2×D53—22no—
406C2×D53—416no—
407C2×D53—44no—
408C2×D53—44no—
409C2×D53—42no—
410C2×D53—42no—
411C2×D53—42no—
412C2×D53—84no—
413C4×C53—22no—
414C4×C53—42no—
415C4×C53—42no—
416C4×C53—42no—
417C4×C53#53412yes—
418C4×C53C2×H(5,𝔽2)11yescharacteristic
419C4×C53C2×H(5,𝔽2)11yescharacteristic
420Dic53—22no—
421Dic53—22no—
422Dic53—42no—
423Dic53—42no—
424Dic53—42no—
425C2×#525—531no—
426C2×#525—531no—
427#3197—5316no—
428C2×#485—531no—
429C2×#485—531no—
430C2×#482—531no—
431C2×#482D5311yescharacteristic, complemented
432C2×#470—531no—
433C2×#469—531no—
434C2×#468—531no—
435C2×#468—531no—
436C2×#452—531no—
437C2×#452—531no—
438C2×#449—531no—
439C2×#449—531no—
440C2×#407—531no—
441C2×C53—42no—
442C2×C53—82no—
443C2×C53#319714yescomplemented
444C2×C53C2×#53411yescharacteristic
445C2×C53C2×#57511yescharacteristic
446C2×C53C2×#57511yescharacteristic
447D53—42no—
448D53—42no—
449D53—82no—
450C22×#41—531no—
451C22×#41—531no—
452C24×C4—531no—
453C22×Q16—531no—
454C22×SD16—531no—
455C22×SD16—531no—
456C22×D8—531no—
457C22×M16—531no—
458C22×M16—531no—
459#525—538no—
460#525—538no—
461#525—1064no—
462#525—1064no—
463C2×#123—1061no—
464C2×#123—1061no—
465C2×C22⋊Q8—531no—
466C2×C22⋊Q8—531no—
467C2×C22⋊Q8—531no—
468C2×C22⋊Q8—531no—
469C2×#121—531no—
470C2×#121—531no—
471C2×#121—531no—
472C2×#121C2×D5311yescharacteristic
473C2×#120—1061no—
474C2×#120—1061no—
475C2×C4×D4—1061no—
476C2×C4×D4—1061no—
477C2×C4×D4—1061no—
478C2×C4×D4—1061no—
479C2×#117—531no—
480C2×#117C2×D5311yescharacteristic
481#485—538no—
482#485—538no—
483#482—538no—
484#482C2×D5318yescomplemented
485#470—538no—
486#469—538no—
487#468—538no—
488#468—538no—
489#452—538no—
490#452—538no—
491#449—538no—
492#449—538no—
493C2×#107—531no—
494C2×#107C2×D5311yescharacteristic, complemented
495C2×#106—531no—
496C2×#106C2×D5311yescharacteristic, complemented
497C2×#103—531no—
498C2×#103—531no—
499C2×#103—531no—
500C2×#103—531no—
501C2×#102—531no—
502C2×#102—531no—
503C2×#102C2×D5311yescharacteristic, complemented
504C2×#102C2×D5311yescharacteristic, complemented
505#407—538no—
506C2×C22⋊C8—531no—
507C2×C22⋊C8—531no—
508C2×C22⋊C8—531no—
509C2×C22⋊C8C2×D5311yescharacteristic
510C53C2×#319711yescharacteristic, complemented, Sylow
511C25—531no—
512C2×#41—534no—
513C2×#41—534no—
514C2×#41—1062no—
515C2×#41—1062no—
516C2×#41—2122no—
517C2×#41—2122no—
518C2×#41—2122no—
519C2×#41—2122no—
520C22×Q8—531no—
521C22×Q8—531no—
522C22×D4—21no—
523C22×D4—531no—
524C22×D4—1061no—
525C22×D4—1061no—
526C22×D4—1061no—
527C22×D4—1061no—
528C22×D4—1061no—
529C22×D4C22×D5311yescharacteristic
530C23×C4—531no—
531C23×C4—531no—
532C23×C4—531no—
533C23×C4—531no—
534C23×C4—531no—
535C23×C4—534no—
536C23×C4—534no—
537C23×C4—1061no—
538C23×C4—1061no—
539C23×C4—2122no—
540C23×C4—2122no—
541C23×C4C22×D5311yescharacteristic
542C2×Q16—534no—
543C2×Q16—2122no—
544C2×SD16—534no—
545C2×SD16—534no—
546C2×SD16—2122no—
547C2×SD16—2122no—
548C2×D8—534no—
549C2×D8—2122no—
550C2×M16—534no—
551C2×M16—534no—
552C2×M16—2122no—
553C2×M16—2122no—
554C22×C8—531no—
555C22×C8—531no—
556C22×C8C22×D5311yescharacteristic
557C22×C8C22×D5311yescharacteristic
558#123—1068no—
559#123—1068no—
560C22⋊Q8—534no—
561C22⋊Q8—534no—
562C22⋊Q8—534no—
563C22⋊Q8—534no—
564C22⋊Q8—1062no—
565C22⋊Q8—1062no—
566C22⋊Q8—1062no—
567C22⋊Q8—1062no—
568#121—22no—
569#121—534no—
570#121—534no—
571#121—534no—
572#121—1062no—
573#121—1062no—
574#121—1062no—
575#121C22×D5314yes—
576#120—1068no—
577#120—1068no—
578C4×D4—1068no—
579C4×D4—1068no—
580C4×D4—1068no—
581C4×D4—1068no—
582#117—22no—
583#117—534no—
584#117—1062no—
585#117C22×D5314yes—
586C2×C4⋊C4—531no—
587C2×C4⋊C4—1061no—
588C2×C4⋊C4—1061no—
589C2×C4⋊C4—1061no—
590C2×C4⋊C4—1061no—
591C2×C4⋊C4C22×D5311yescharacteristic
592C2×C4⋊C4C22×D5311yescharacteristic
593C2×C4⋊C4C22×D5311yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—1061no—
597C2×C22⋊C4—1061no—
598C2×C22⋊C4—1061no—
599C2×C22⋊C4—1061no—
600C2×C22⋊C4—1061no—
601C2×C22⋊C4—1061no—
602C2×C22⋊C4—1061no—
603C2×C22⋊C4—1061no—
604C2×C42—21no—
605C2×C42—1061no—
606#107—534no—
607#107C22×D5314yescomplemented
608#106—534no—
609#106C22×D5314yescomplemented
610#103—534no—
611#103—534no—
612#103—534no—
613#103—534no—
614#102—534no—
615#102—534no—
616#102C22×D5314yescomplemented
617#102C22×D5314yescomplemented
618C22⋊C8—534no—
619C22⋊C8—534no—
620C22⋊C8—534no—
621C22⋊C8C22×D5314yes—
622C24—21no—
623C24—531no—
624C24—531no—
625C24—534no—
626C24—1061no—
627C24—2122no—
628C24—2122no—
629C24—2122no—
630C24D4×D5311yescharacteristic
631#41—2124no—
632#41—2124no—
633#41—2128no—
634#41—2124no—
635#41—2124no—
636#41—2128no—
637C2×Q8—532no—
638C2×Q8—532no—
639C2×Q8—1061no—
640C2×Q8—1061no—
641C2×Q8—1062no—
642C2×Q8—1062no—
643C2×Q8—1062no—
644C2×Q8—1062no—
645C2×D4—24no—
646C2×D4—21no—
647C2×D4—22no—
648C2×D4—22no—
649C2×D4—44no—
650C2×D4—532no—
651C2×D4—1064no—
652C2×D4—1064no—
653C2×D4—1064no—
654C2×D4—1064no—
655C2×D4—1064no—
656C2×D4—1061no—
657C2×D4—1062no—
658C2×D4—1062no—
659C2×D4—2124no—
660C2×D4—2124no—
661C2×D4—2124no—
662C2×D4—2124no—
663C2×D4—2124no—
664C2×D4C23×D5312yes—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—531no—
671C22×C4—531no—
672C22×C4—534no—
673C22×C4—532no—
674C22×C4—532no—
675C22×C4—532no—
676C22×C4—532no—
677C22×C4—534no—
678C22×C4—534no—
679C22×C4—1064no—
680C22×C4—1062no—
681C22×C4—1062no—
682C22×C4—1062no—
683C22×C4—1062no—
684C22×C4—1061no—
685C22×C4—1061no—
686C22×C4—1061no—
687C22×C4—1064no—
688C22×C4—2128no—
689C22×C4—2124no—
690C22×C4—2124no—
691C22×C4—2122no—
692C22×C4—2122no—
693C22×C4—2124no—
694C22×C4—2122no—
695C22×C4—2124no—
696C22×C4D4×D5312yes—
697C22×C4D4×D5311yescharacteristic
698C22×C4C23×D5312yes—
699C22×C4C23×D5311yescharacteristic
700Q16—2124no—
701SD16—2124no—
702SD16—2124no—
703D8—2124no—
704M16—2124no—
705M16—2124no—
706C2×C8—22no—
707C2×C8—22no—
708C2×C8—532no—
709C2×C8—532no—
710C2×C8—1062no—
711C2×C8—1062no—
712C2×C8C23×D5312yes—
713C2×C8C23×D5312yes—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—532no—
718C4⋊C4—1064no—
719C4⋊C4—1064no—
720C4⋊C4—1064no—
721C4⋊C4—1061no—
722C4⋊C4—1064no—
723C4⋊C4C23×D5312yes—
724C4⋊C4C23×D5312yes—
725C4⋊C4C23×D5312yes—
726C22⋊C4—24no—
727C22⋊C4—24no—
728C22⋊C4—1064no—
729C22⋊C4—1064no—
730C22⋊C4—1064no—
731C22⋊C4—1064no—
732C22⋊C4—1064no—
733C22⋊C4—1064no—
734C22⋊C4—1064no—
735C22⋊C4—1064no—
736C42—24no—
737C42—1064no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—532no—
746C23—532no—
747C23—1062no—
748C23—1062no—
749C23—1062no—
750C23—1062no—
751C23—1062no—
752C23—1062no—
753C23—1062no—
754C23—2124no—
755C23—2124no—
756C23—2124no—
757C23—21216no—
758C23—2122no—
759C23—2122no—
760C23—2122no—
761C23C2×D4×D5312yes—
762C23C2×D4×D5311yescharacteristic
763Q8—1062no—
764Q8—1062no—
765Q8—1062no—
766Q8—1062no—
767Q8—2122no—
768Q8—2122no—
769D4—22no—
770D4—22no—
771D4—48no—
772D4—42no—
773D4—1062no—
774D4—1062no—
775D4—2128no—
776D4—2128no—
777D4—2128no—
778D4—2128no—
779D4—2128no—
780D4—2122no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—532no—
792C2×C4—532no—
793C2×C4—1062no—
794C2×C4—1062no—
795C2×C4—1064no—
796C2×C4—1064no—
797C2×C4—1062no—
798C2×C4—1062no—
799C2×C4—1062no—
800C2×C4—1062no—
801C2×C4—1062no—
802C2×C4—1062no—
803C2×C4—1062no—
804C2×C4—2124no—
805C2×C4—2124no—
806C2×C4—2128no—
807C2×C4—2124no—
808C2×C4—2128no—
809C2×C4—2122no—
810C2×C4—2122no—
811C2×C4—2122no—
812C2×C4C2×D4×D5312yes—
813C2×C4C2×D4×D5311yescharacteristic
814C2×C4#1313326312yes—
815C2×C4#1313326312yes—
816C2×C4C24×D5311yescharacteristic
817C8—22no—
818C8—22no—
819C8—1062no—
820C8—1062no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—44no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—84no—
829C22—1062no—
830C22—1062no—
831C22—1062no—
832C22—1062no—
833C22—1062no—
834C22—1062no—
835C22—4244no—
836C22—21216no—
837C22—2122no—
838C22—2122no—
839C22—2122no—
840C22—2124no—
841C22—2124no—
842C22#1681118412yes—
843C22#1681141912yes—
844C22#1681142012yes—
845C22C22×D4×D5311yescharacteristic
846C4—22no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—1062no—
851C4—1062no—
852C4—2122no—
853C4—2122no—
854C4—2122no—
855C4#1681118412yes—
856C4C2×#1313326311yescharacteristic
857C4C2×#1313326311yescharacteristic
858C2—42no—
859C2—82no—
860C2—4242no—
861C2—2122no—
862C2—2122no—
863C2#2028555514yesdirect product factor
864C2C2×#1681118411yescharacteristic
865C2C2×#1681141911yescharacteristic
866C2C2×#1681142011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#482C2
socleC23×C53C22×D4
hypercenterC2×#482D53
hypocenterC53C2×#3197
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#16811135C2semidirect
2. C2×#16811133C2semidirect
3. #20285555C2direct (N × H)
4. C2×#16810966C2semidirect
5. C2×#16810964C2semidirect
6. C2×#16810949C2semidirect
7. C2×#16810882C2semidirect
8. C2×#16810875C2semidirect
9. C2×#16810870C2semidirect
10. C2×#16810868C2semidirect
11. C2×#16810787C2semidirect
12. C2×#16810786C2semidirect
13. C2×#16810769C2semidirect
14. C2×#16810766C2semidirect
15. C2×#16810585C2semidirect
16. C2×C53×#482C2semidirect
20. C22×Dic212C22semidirect
21. C22×#11719913C22semidirect
22. C22×#11719923C22semidirect
23. C22×#11719922C22semidirect
27. #16811135C22semidirect
29. #16811133C22semidirect
46. #16810966C22semidirect
47. #16810964C22semidirect
48. #16810949C22semidirect
49. #16810882C22semidirect
50. #16810875C22semidirect
51. #16810870C22semidirect
52. #16810868C22semidirect
53. #16810787C22semidirect
54. #16810786C22semidirect
55. #16810769C22semidirect
56. #16810766C22semidirect
57. C2×#13133150C22semidirect
58. C2×#13133148C22semidirect
59. C2×#13133142C22semidirect
60. C2×#13133140C22semidirect
61. C2×#13133140C22semidirect
62. C2×#13133140C22semidirect
63. C2×#13133139C22semidirect
64. C2×#13133137C22semidirect
65. #16810585C22semidirect
71. C53×#482C22semidirect
72. C2×#107×C53C22semidirect
73. C2×#106×C53C22semidirect
74. C2×#102×C53C22semidirect
75. C2×#102×C53C22semidirect
106. C2×Dic212C23semidirect
108. C2×#11719913C23semidirect
110. C2×#11719923C23semidirect
112. C2×#11719922C23semidirect
157. #13133150C23semidirect
158. #13133148C23semidirect
159. #13133142C23semidirect
160. #13133140C23semidirect
161. #13133140C23semidirect
162. #13133140C23semidirect
163. #13133139C23semidirect
164. #13133137C23semidirect
183. #107×C53C23semidirect
184. #106×C53C23semidirect
185. #102×C53C23semidirect
186. #102×C53C23semidirect
431. C2×#482D53semidirect
443. C2×C53#3197semidirect
484. #482C2×D53semidirect
494. C2×#107C2×D53semidirect
496. C2×#106C2×D53semidirect
503. C2×#102C2×D53semidirect
504. C2×#102C2×D53semidirect
510. C53C2×#3197semidirect
607. #107C22×D53semidirect
609. #106C22×D53semidirect
616. #102C22×D53semidirect
617. #102C22×D53semidirect
863. C2#20285555direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111352
C2×#168111332
#202855552
C2×#168109662
C2×#168109642
C2×#168109492
C2×#168108822
C2×#168108752
C2×#168108702
C2×#168108682
C2×#168107872
C2×#168107862
C2×#168107692
C2×#168107662
C2×#168105852
C2×C53×#4822
C2×#319753