Finite Group Databasebeta

← C2×#20286794 #28260616

Subgroups — C2×#20286794 #28260616

Order 13568.

2298 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811328C211yesmaximal, characteristic, complemented
2C2×#16811264C211yesmaximal, characteristic
3#20286794C2116yesmaximal, direct product factor
4C2×#16810984C211yesmaximal, characteristic, complemented
5C2×#16810938C211yesmaximal, characteristic, complemented
6C2×#16810902C211yesmaximal, characteristic, complemented
7C2×#16810870C211yesmaximal, characteristic, complemented
8C2×#16810862C211yesmaximal, characteristic, complemented
9C2×#16810848C211yesmaximal, characteristic, complemented
10C2×#16810788C211yesmaximal, characteristic, complemented
11C2×#16810776C211yesmaximal, characteristic, complemented
12C2×#16810722C211yesmaximal, characteristic, complemented
13C2×#16810691C211yesmaximal, characteristic, complemented
14C2×#16810623C211yesmaximal, characteristic, complemented
15C22×#13133137C211yesmaximal, characteristic, complemented
16C2×C53×#484C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C23×D212C2211yescharacteristic
19C22×#11719925C2211yescharacteristic, complemented
20C22×#11719913C2211yescharacteristic
21C22×#11719913C2211yescharacteristic
22C22×#11719912C2211yescharacteristic, complemented
23C23×#88322C2211yescharacteristic
24#16811328—24no—
25#16811328C2218yescomplemented
26#16811264—24no—
27#16811264C2218yes—
28C2×#13133216C2211yescharacteristic, complemented
29C2×#13133207—21no—
30C2×#13133206C2211yescharacteristic
31C2×#13133202—21no—
32C2×#13133197C2211yescharacteristic, complemented
33C2×#13133196—21no—
34C2×#13133196C2211yescharacteristic
35C2×#13133195—21no—
36C2×#13133192—21no—
37C2×#13133192C2211yescharacteristic
38C2×#13133187—21no—
39C2×#13133182C2211yescharacteristic, complemented
40C2×#13133179C2211yescharacteristic
41C2×C4×C22⋊D53—21no—
42C2×C4×C22⋊D53C2211yescharacteristic
43C2×C4⋊C4×D53C2211yescharacteristic, complemented
44C2×C22⋊C4×D53—21no—
45#16810984C2218yescomplemented
46#16810938C2218yescomplemented
47#16810902C2218yescomplemented
48#16810870C2218yescomplemented
49#16810862C2218yescomplemented
50#16810848C2218yescomplemented
51#16810788C2218yescomplemented
52#16810776C2218yescomplemented
53#16810722C2218yescomplemented
54#16810691C2218yescomplemented
55C2×#13133150C2211yescharacteristic, complemented
56C2×#13133146C2211yescharacteristic, complemented
57#16810623C2218yescomplemented
58C2×#13133141C2211yescharacteristic, complemented
59C2×#13133140C2211yescharacteristic, complemented
60C2×#13133139C2211yescharacteristic
61C2×#13133139C2211yescharacteristic
62C2×#13133137C2211yescharacteristic
63C2×#13133137C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×#13133137C2218yescomplemented
67C2×#13133129C2211yescharacteristic, complemented
68C2×#13133127C2211yescharacteristic, complemented
69C2×C22⋊Q8×C53C2211yescharacteristic
70C22×C4⋊C4×C53C2211yescharacteristic
71C53×#484C2218yescomplemented
72C2×#107×C53C2211yescharacteristic, complemented
73C2×#107×C53C2211yescharacteristic, complemented
74C2×#103×C53C2211yescharacteristic, complemented
75C2×#103×C53C2211yescharacteristic, complemented
76C2×C22⋊C8×C53C2211yescharacteristic
77C24×D53—21no—
78C2×#11719949—22no—
79C2×#11719949—24no—
80C2×#11719949—42no—
81C2×#11719949C2314yes—
82C22×Dic106—21no—
83C22×Dic106C2311yescharacteristic
84C22×D212—24no—
85C22×D212—21no—
86C22×D212—22no—
87C22×D212—21no—
88C22×D212—21no—
89C22×D212—42no—
90C22×D212C2311yescharacteristic
91C22×D212C2314yes—
92C22×D212C2311yescharacteristic
93C22×C22⋊D53D411yescharacteristic
94C22×C4×D53—21no—
95C22×C4×D53—21no—
96C22×C4×D53—21no—
97C22×C4×D53C2311yescharacteristic
98C2×#11719925—42no—
99C2×#11719925C2314yescomplemented
100C2×#11719913—24no—
101C2×#11719913—42no—
102C2×#11719913C2314yes—
103C2×#11719913C2314yes—
104C2×#11719912—42no—
105C2×#11719912C2314yescomplemented
106C22×#88322—42no—
107C22×#88322C2311yescharacteristic
108C22×#88322C2311yescharacteristic
109C22×#88322C2314yes—
110#13133216—22no—
111#13133216C2314yescomplemented
112#13133207—28no—
113#13133206—22no—
114#13133206C2314yes—
115#13133202—28no—
116#13133197—22no—
117#13133197C2314yescomplemented
118#13133196—28no—
119#13133196—22no—
120#13133196C2314yes—
121#13133195—28no—
122#13133192—28no—
123#13133192—22no—
124#13133192C2314yes—
125#13133187—28no—
126#13133182—22no—
127#13133182C2314yescomplemented
128#13133179—22no—
129#13133179C2314yes—
130C4×C22⋊D53—28no—
131C4×C22⋊D53D414yes—
132C4×C22⋊D53C2314yes—
133C2×C4⋊Dic53—21no—
134C2×C4⋊Dic53C2311yescharacteristic
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×#11719919—21no—
139C2×#11719919D411yescharacteristic
140C4⋊C4×D53—22no—
141C4⋊C4×D53C2314yescomplemented
142C2×C22⋊Dic53—21no—
143C2×C22⋊Dic53D411yescharacteristic
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×#11719921D411yescharacteristic
150C22⋊C4×D53—28no—
151C2×C4×Dic53—21no—
152C2×C4×Dic53C2311yescharacteristic
153#13133150C2314yescomplemented
154#13133146C2314yescomplemented
155#13133141C2314yescomplemented
156#13133140C2314yescomplemented
157#13133139C2314yes—
158#13133139C2314yes—
159#13133137C2314yes—
160#13133137C2314yes—
161#13133137C2314yes—
162#13133137C2314yes—
163#13133129C2314yescomplemented
164#13133127C2314yescomplemented
165C22×Q8×C53C2311yescharacteristic
166C23×C4×C53—21no—
167C23×C4×C53C2311yescharacteristic
168C22×C8×C53C2311yescharacteristic
169C22×C8×C53C2311yescharacteristic
170C22⋊Q8×C53—22no—
171C22⋊Q8×C53C2314yes—
172C2×C4⋊C4×C53—22no—
173C2×C4⋊C4×C53—21no—
174C2×C4⋊C4×C53—21no—
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C4⋊C4×C53C2314yes—
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C4⋊C4×C53C2311yescharacteristic
179C2×C22⋊C4×C53—21no—
180#107×C53C2314yescomplemented
181#107×C53C2314yescomplemented
182#103×C53C2314yescomplemented
183#103×C53C2314yescomplemented
184C22⋊C8×C53C2314yes—
185C24×C53C2×D411yescharacteristic
186C23×D53—21no—
187C23×D53—21no—
188C23×D53—24no—
189C23×D53—44no—
190C23×D53—44no—
191C23×D53—82no—
192C23×D53C2×D411yescharacteristic
193C2×Q8×C53—21no—
194C2×Q8×C53—22no—
195C2×Q8×C53—22no—
196C2×Q8×C53C2412yes—
197C22×C4×C53—22no—
198C22×C4×C53—22no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53—24no—
204C22×C4×C53—82no—
205C22×C4×C53C2×D411yescharacteristic
206C22×C4×C53C2×D412yes—
207C22×C4×C53C2412yes—
208C22×C4×C53C2411yescharacteristic
209C2×C22⋊D53—24no—
210C2×C22⋊D53C2×D414yes—
211C22×Dic53—21no—
212C22×Dic53—21no—
213C22×Dic53C2×D411yescharacteristic
214C22×Dic53C2×D411yescharacteristic
215C22×Dic53C2×D411yescharacteristic
216#11719949—28no—
217#11719949—44no—
218#11719949—48no—
219C2×D212—21no—
220C2×D212—22no—
221C2×D212—22no—
222C2×D212—22no—
223C2×D212—28no—
224C2×D212—24no—
225C2×D212—24no—
226C2×D212—21no—
227C2×D212—24no—
228C2×D212—44no—
229C2×D212—48no—
230C2×D212—44no—
231C2×D212—44no—
232C2×D212—82no—
233C2×D212#4114yes—
234C2×D212C2412yes—
235C2×D212C2412yes—
236C2×C4×D53—22no—
237C2×C4×D53—22no—
238C2×C4×D53—24no—
239C2×C4×D53—24no—
240C2×C4×D53—24no—
241C2×C4×D53—44no—
242C2×C4×D53—82no—
243C2×C4×D53—82no—
244C2×C4×D53C2×D412yes—
245C2×C4×D53C2412yes—
246C2×Dic106—22no—
247C2×Dic106—22no—
248C2×Dic106—21no—
249C2×Dic106—24no—
250C2×Dic106—82no—
251C2×Dic106C2412yes—
252C2×C8×C53—22no—
253C2×C8×C53—22no—
254C2×C8×C53C2412yes—
255C2×C8×C53C2412yes—
256C4⋊C4×C53—21no—
257C4⋊C4×C53—24no—
258C4⋊C4×C53—21no—
259C4⋊C4×C53—24no—
260C4⋊C4×C53—21no—
261C4⋊C4×C53C2412yes—
262C4⋊C4×C53C2412yes—
263C4⋊C4×C53C2412yes—
264C22⋊C4×C53—24no—
265C22⋊Dic53—24no—
266C22⋊Dic53C2×D414yes—
267#11719925—44no—
268#11719921—24no—
269#11719921—24no—
270#11719921—24no—
271#11719921—24no—
272#11719921—24no—
273#11719921C2×D414yes—
274C4⋊Dic53—21no—
275C4⋊Dic53—24no—
276C4⋊Dic53C2412yes—
277#11719919—24no—
278#11719919—24no—
279#11719919—24no—
280#11719919—24no—
281#11719919C2×D414yes—
282C4×Dic53—24no—
283C4×Dic53C2×D412yes—
284C4×Dic53C2412yes—
285C2×#88322—22no—
286C2×#88322—22no—
287C2×#88322—44no—
288C2×#88322C2412yes—
289C2×#88322C2412yes—
290#11719913—28no—
291#11719913—44no—
292#11719912—44no—
293C23×C53—22no—
294C23×C53—22no—
295C23×C53#13714yes—
296C23×C53C22×D412yes—
297C23×C53C22×D411yescharacteristic
298C22×D53—22no—
299C22×D53—24no—
300C22×D53—22no—
301C22×D53—22no—
302C22×D53—22no—
303C22×D53—22no—
304C22×D53—48no—
305C22×D53—42no—
306C22×D53—42no—
307C22×D53—42no—
308C22×D53—48no—
309C22×D53—42no—
310C22×D53—42no—
311C22×D53—84no—
312C22×D53—816no—
313C22×D53C22×D412yes—
314Q8×C53—22no—
315Q8×C53—22no—
316Q8×C53—42no—
317C2×C4×C53—22no—
318C2×C4×C53—24no—
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—42no—
328C2×C4×C53—42no—
329C2×C4×C53—84no—
330C2×C4×C53C22×D412yes—
331C2×C4×C53C22×D411yescharacteristic
332C2×C4×C53C2×#4112yes—
333C2×C4×C53H(5,𝔽2)12yes—
334C2×C4×C53C2511yescharacteristic
335C22⋊D53—28no—
336C2×Dic53—22no—
337C2×Dic53—22no—
338C2×Dic53—22no—
339C2×Dic53—22no—
340C2×Dic53—22no—
341C2×Dic53—42no—
342C2×Dic53—42no—
343C2×Dic53C22×D412yes—
344C2×Dic53C22×D412yes—
345C2×Dic53C22×D412yes—
346D212—24no—
347D212—22no—
348D212—22no—
349D212—22no—
350D212—48no—
351D212—48no—
352D212—42no—
353D212—84no—
354D212C2×#4114yes—
355C4×D53—24no—
356C4×D53—22no—
357C4×D53—22no—
358C4×D53—48no—
359C4×D53—84no—
360C4×D53—84no—
361Dic106—22no—
362Dic106—22no—
363Dic106—42no—
364Dic106—84no—
365C8×C53—22no—
366C8×C53—22no—
367#88322—22no—
368#88322—22no—
369C2×#3314—531nomaximal, Sylow
370C22×C53—22no—
371C22×C53—28no—
372C22×C53—22no—
373C22×C53#54612yes—
374C22×C53C2×#13714yes—
375C22×C53C2×#13712yes—
376C22×C53#57612yes—
377C22×C53C23×D411yescharacteristic
378C2×D53—22no—
379C2×D53—24no—
380C2×D53—22no—
381C2×D53—22no—
382C2×D53—44no—
383C2×D53—48no—
384C2×D53—42no—
385C2×D53—42no—
386C2×D53—42no—
387C2×D53—42no—
388C2×D53—42no—
389C2×D53—816no—
390C2×D53—84no—
391C4×C53—22no—
392C4×C53—42no—
393C4×C53—42no—
394C4×C53—42no—
395C4×C53—42no—
396C4×C53#54612yes—
397C4×C53C22×#4111yescharacteristic
398C4×C53C2×H(5,𝔽2)11yescharacteristic
399Dic53—22no—
400Dic53—22no—
401Dic53—22no—
402Dic53—42no—
403Dic53—42no—
404C2×#554—531no—
405C2×#546—531no—
406#3314—5316no—
407C2×#489—531no—
408C2×#484D5311yescharacteristic, complemented
409C2×#480—531no—
410C2×#474—531no—
411C2×#468—531no—
412C2×#467—531no—
413C2×#464—531no—
414C2×#452—531no—
415C2×#450—531no—
416C2×#440—531no—
417C2×#435—531no—
418C2×#417—531no—
419C22×#102—531no—
420C2×C53—24no—
421C2×C53#331414yescomplemented
422C2×C53C2×#54611yescharacteristic
423C2×C53C22×#13711yescharacteristic
424C2×C53C2×#57611yescharacteristic
425D53—42no—
426D53—44no—
427D53—82no—
428C22×#41—531no—
429C23×D4—531no—
430C22×Q16—531no—
431C22×SD16—531no—
432C22×SD16—531no—
433C22×M16—531no—
434C23×C8—531no—
435#554—538no—
436#554—1064no—
437#546—538no—
438#546—1064no—
439C2×C4⋊Q8—531no—
440C2×#125—1061no—
441C2×#124—531no—
442C2×#123—1061no—
443C2×C22⋊Q8—531no—
444C2×C22⋊Q8—531no—
445C2×C22⋊Q8—1061no—
446C2×C22⋊Q8—1061no—
447C2×C22⋊Q8C2×D5311yescharacteristic
448C2×#121—531no—
449C2×#121—1061no—
450C2×#120—1061no—
451C2×C4×Q8—531no—
452C2×C4×D4—531no—
453C2×C4×D4—531no—
454C2×C4×D4—1061no—
455C22×C4⋊C4—531no—
456C22×C4⋊C4C2×D5311yescharacteristic
457C22×C22⋊C4—1061no—
458#489—538no—
459#484C2×D5318yescomplemented
460#480—538no—
461#474—538no—
462#468—538no—
463#467—538no—
464#464—538no—
465#452—538no—
466#450—538no—
467#440—538no—
468#435—538no—
469C2×#107—531no—
470C2×#107C2×D5311yescharacteristic, complemented
471C2×#107C2×D5311yescharacteristic, complemented
472C2×C4⋊C8—531no—
473#417—538no—
474C2×#103—531no—
475C2×#103—531no—
476C2×#103C2×D5311yescharacteristic, complemented
477C2×#103C2×D5311yescharacteristic, complemented
478C2×#102—531no—
479C2×#102—531no—
480C2×#102—531no—
481C2×#102—531no—
482C2×#102—531no—
483C2×#102—531no—
484C2×#102—538no—
485C2×C22⋊C8—531no—
486C2×C22⋊C8C2×D5311yescharacteristic
487C2×#97—531no—
488C53C2×#331411yescharacteristic, complemented, Sylow
489C25—1061no—
490C2×#41—534no—
491C2×#41—1062no—
492C2×#41—1064no—
493C2×#41—2122no—
494C22×Q8—531no—
495C22×Q8—1061no—
496C22×Q8C22×D5311yescharacteristic
497C22×D4—531no—
498C22×D4—531no—
499C22×D4—531no—
500C22×D4—534no—
501C22×D4—1064no—
502C22×D4—1061no—
503C22×D4—1061no—
504C22×D4—1061no—
505C22×D4—1062no—
506C22×D4—2122no—
507C23×C4—21no—
508C23×C4—531no—
509C23×C4—1061no—
510C23×C4—1061no—
511C23×C4—1061no—
512C23×C4C22×D5311yescharacteristic
513C2×Q16—534no—
514C2×Q16—2122no—
515C2×SD16—534no—
516C2×SD16—534no—
517C2×SD16—1064no—
518C2×SD16—2122no—
519C2×M16—534no—
520C2×M16—2122no—
521C22×C8—531no—
522C22×C8—531no—
523C22×C8—534no—
524C22×C8—2122no—
525C22×C8C22×D5311yescharacteristic
526C22×C8C22×D5311yescharacteristic
527C4⋊Q8—534no—
528C4⋊Q8—1062no—
529#125—1068no—
530#124—534no—
531#124—1062no—
532#123—1068no—
533C22⋊Q8—22no—
534C22⋊Q8—534no—
535C22⋊Q8—534no—
536C22⋊Q8—1068no—
537C22⋊Q8—1068no—
538C22⋊Q8—1062no—
539C22⋊Q8—1062no—
540C22⋊Q8C22×D5314yes—
541#121—534no—
542#121—1068no—
543#121—1062no—
544#120—1068no—
545C4×Q8—534no—
546C4×Q8—1062no—
547C4×D4—534no—
548C4×D4—534no—
549C4×D4—534no—
550C4×D4—1062no—
551C4×D4—1068no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—22no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—531no—
556C2×C4⋊C4—531no—
557C2×C4⋊C4—534no—
558C2×C4⋊C4—1062no—
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×C4⋊C4C22×D5311yescharacteristic
566C2×C4⋊C4C22×D5314yes—
567C2×C4⋊C4C22×D5311yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—531no—
570C2×C22⋊C4—531no—
571C2×C22⋊C4—1068no—
572C2×C22⋊C4—1061no—
573C2×C22⋊C4—1061no—
574C2×C22⋊C4—1061no—
575C2×C22⋊C4—1061no—
576C2×C22⋊C4—1061no—
577C2×C22⋊C4—1061no—
578C2×C42—531no—
579C2×C42—1061no—
580#107—534no—
581#107C22×D5314yescomplemented
582#107C22×D5314yescomplemented
583C4⋊C8—534no—
584#103—534no—
585#103—534no—
586#103C22×D5314yescomplemented
587#103C22×D5314yescomplemented
588#102—534no—
589#102—534no—
590#102—534no—
591#102—534no—
592#102—534no—
593#102—534no—
594C22⋊C8—534no—
595C22⋊C8C22×D5314yes—
596#97—534no—
597C24—531no—
598C24—1061no—
599C24—1064no—
600C24—1061no—
601C24—4242no—
602C24—2124no—
603C24—2124no—
604C24D4×D5311yescharacteristic
605#41—1068no—
606#41—2124no—
607#41—2128no—
608C2×Q8—21no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—532no—
612C2×Q8—1064no—
613C2×Q8—1061no—
614C2×Q8—1062no—
615C2×Q8—1062no—
616C2×Q8—4242no—
617C2×Q8C23×D5312yes—
618C2×D4—534no—
619C2×D4—534no—
620C2×D4—532no—
621C2×D4—532no—
622C2×D4—1068no—
623C2×D4—1064no—
624C2×D4—1064no—
625C2×D4—1064no—
626C2×D4—1061no—
627C2×D4—1064no—
628C2×D4—1061no—
629C2×D4—1062no—
630C2×D4—1062no—
631C2×D4—1062no—
632C2×D4—4242no—
633C2×D4—2124no—
634C2×D4—2128no—
635C2×D4—2124no—
636C2×D4—2124no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—24no—
644C22×C4—82no—
645C22×C4—531no—
646C22×C4—531no—
647C22×C4—531no—
648C22×C4—532no—
649C22×C4—532no—
650C22×C4—1064no—
651C22×C4—1064no—
652C22×C4—1064no—
653C22×C4—1062no—
654C22×C4—1062no—
655C22×C4—1061no—
656C22×C4—1061no—
657C22×C4—4242no—
658C22×C4—4242no—
659C22×C4—2124no—
660C22×C4D4×D5312yes—
661C22×C4D4×D5311yescharacteristic
662C22×C4C23×D5312yes—
663C22×C4C23×D5311yescharacteristic
664Q16—2124no—
665SD16—1068no—
666SD16—2124no—
667M16—2124no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—532no—
671C2×C8—532no—
672C2×C8—1062no—
673C2×C8—1062no—
674C2×C8—2124no—
675C2×C8C23×D5312yes—
676C2×C8C23×D5312yes—
677C4⋊C4—21no—
678C4⋊C4—24no—
679C4⋊C4—21no—
680C4⋊C4—24no—
681C4⋊C4—21no—
682C4⋊C4—534no—
683C4⋊C4—532no—
684C4⋊C4—1064no—
685C4⋊C4—1064no—
686C4⋊C4—1064no—
687C4⋊C4—1064no—
688C4⋊C4—1061no—
689C4⋊C4—1064no—
690C4⋊C4C23×D5312yes—
691C4⋊C4C23×D5312yes—
692C4⋊C4C23×D5312yes—
693C22⋊C4—24no—
694C22⋊C4—534no—
695C22⋊C4—534no—
696C22⋊C4—1064no—
697C22⋊C4—1064no—
698C22⋊C4—1064no—
699C22⋊C4—1064no—
700C22⋊C4—1064no—
701C22⋊C4—1064no—
702C42—532no—
703C42—532no—
704C42—1064no—
705C23—22no—
706C23—22no—
707C23—532no—
708C23—1062no—
709C23—1064no—
710C23—1062no—
711C23—1062no—
712C23—1062no—
713C23—1062no—
714C23—42416no—
715C23—4244no—
716C23—2128no—
717C23—2122no—
718C23—2128no—
719C23—2122no—
720C23—2122no—
721C23—2122no—
722C23—2122no—
723C23#1313324914yes—
724C23C2×D4×D5312yes—
725C23C2×D4×D5311yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—42no—
729Q8—1062no—
730Q8—1062no—
731Q8—4244no—
732Q8—2122no—
733D4—534no—
734D4—1068no—
735D4—1064no—
736D4—1062no—
737D4—1062no—
738D4—1062no—
739D4—4244no—
740D4—2128no—
741D4—2128no—
742D4—2122no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—84no—
756C2×C4—532no—
757C2×C4—532no—
758C2×C4—532no—
759C2×C4—1062no—
760C2×C4—1062no—
761C2×C4—1062no—
762C2×C4—1064no—
763C2×C4—1062no—
764C2×C4—1062no—
765C2×C4—1062no—
766C2×C4—1062no—
767C2×C4—4244no—
768C2×C4—4244no—
769C2×C4—2128no—
770C2×C4—2122no—
771C2×C4—2122no—
772C2×C4C2×D4×D5312yes—
773C2×C4C2×D4×D5311yescharacteristic
774C2×C4#41×D5312yes—
775C2×C4#1313326312yes—
776C2×C4C24×D5311yescharacteristic
777C8—22no—
778C8—22no—
779C8—1062no—
780C8—1062no—
781C22—28no—
782C22—22no—
783C22—22no—
784C22—1062no—
785C22—1064no—
786C22—1062no—
787C22—1062no—
788C22—42416no—
789C22—4244no—
790C22—2122no—
791C22—2122no—
792C22—2122no—
793C22—2124no—
794C22—2128no—
795C22—2122no—
796C22—2122no—
797C22#1681126512yes—
798C22C2×#1313324914yes—
799C22C2×#1313324912yes—
800C22#1681142712yes—
801C22C22×D4×D5311yescharacteristic
802C4—22no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—1062no—
808C4—1062no—
809C4—1062no—
810C4—2122no—
811C4—2122no—
812C4#1681126512yes—
813C4C2×#41×D5311yescharacteristic
814C4C2×#1313326311yescharacteristic
815C2—24no—
816C2—4242no—
817C2—2122no—
818C2—2124no—
819C2#2028679414yesdirect product factor
820C2C2×#1681126511yescharacteristic
821C2C22×#1313324911yescharacteristic
822C2C2×#1681142711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#484C2
socleC23×C53C22×D4
prime radicalC2×#16811264C2
hypercenterC2×#484D53
hypocenterC53C2×#3314
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
1. C2×#16811328C2semidirect
3. #20286794C2direct (N × H)
4. C2×#16810984C2semidirect
5. C2×#16810938C2semidirect
6. C2×#16810902C2semidirect
7. C2×#16810870C2semidirect
8. C2×#16810862C2semidirect
9. C2×#16810848C2semidirect
10. C2×#16810788C2semidirect
11. C2×#16810776C2semidirect
12. C2×#16810722C2semidirect
13. C2×#16810691C2semidirect
14. C2×#16810623C2semidirect
15. C22×#13133137C2semidirect
16. C2×C53×#484C2semidirect
19. C22×#11719925C22semidirect
22. C22×#11719912C22semidirect
25. #16811328C22semidirect
28. C2×#13133216C22semidirect
32. C2×#13133197C22semidirect
39. C2×#13133182C22semidirect
43. C2×C4⋊C4×D53C22semidirect
45. #16810984C22semidirect
46. #16810938C22semidirect
47. #16810902C22semidirect
48. #16810870C22semidirect
49. #16810862C22semidirect
50. #16810848C22semidirect
51. #16810788C22semidirect
52. #16810776C22semidirect
53. #16810722C22semidirect
54. #16810691C22semidirect
55. C2×#13133150C22semidirect
56. C2×#13133146C22semidirect
57. #16810623C22semidirect
58. C2×#13133141C22semidirect
59. C2×#13133140C22semidirect
66. C2×#13133137C22semidirect
67. C2×#13133129C22semidirect
68. C2×#13133127C22semidirect
71. C53×#484C22semidirect
72. C2×#107×C53C22semidirect
73. C2×#107×C53C22semidirect
74. C2×#103×C53C22semidirect
75. C2×#103×C53C22semidirect
99. C2×#11719925C23semidirect
105. C2×#11719912C23semidirect
111. #13133216C23semidirect
117. #13133197C23semidirect
127. #13133182C23semidirect
141. C4⋊C4×D53C23semidirect
153. #13133150C23semidirect
154. #13133146C23semidirect
155. #13133141C23semidirect
156. #13133140C23semidirect
163. #13133129C23semidirect
164. #13133127C23semidirect
180. #107×C53C23semidirect
181. #107×C53C23semidirect
182. #103×C53C23semidirect
183. #103×C53C23semidirect
408. C2×#484D53semidirect
421. C2×C53#3314semidirect
459. #484C2×D53semidirect
470. C2×#107C2×D53semidirect
471. C2×#107C2×D53semidirect
476. C2×#103C2×D53semidirect
477. C2×#103C2×D53semidirect
488. C53C2×#3314semidirect
581. #107C22×D53semidirect
582. #107C22×D53semidirect
586. #103C22×D53semidirect
587. #103C22×D53semidirect
819. C2#20286794direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113282
C2×#168112642
#202867942
C2×#168109842
C2×#168109382
C2×#168109022
C2×#168108702
C2×#168108622
C2×#168108482
C2×#168107882
C2×#168107762
C2×#168107222
C2×#168106912
C2×#168106232
C22×#131331372
C2×C53×#4842
C2×#331453