Finite Group Databasebeta

← C2×#20284965 #28252394

Subgroups — C2×#20284965 #28252394

Order 13568.

2210 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811234C211yesmaximal, characteristic, complemented
2C2×#16811095C211yesmaximal, characteristic
3#20284965C2116yesmaximal, direct product factor
4C2×#16810963C211yesmaximal, characteristic, complemented
5C2×#16810962C211yesmaximal, characteristic, complemented
6C2×#16810924C211yesmaximal, characteristic, complemented
7C2×#16810923C211yesmaximal, characteristic, complemented
8C2×#16810825C211yesmaximal, characteristic, complemented
9C2×#16810772C211yesmaximal, characteristic
10C2×#16810772C211yesmaximal, characteristic
11C2×#16810726C211yesmaximal, characteristic, complemented
12C2×#16810724C211yesmaximal, characteristic, complemented
13C2×SD16×Dic53C211yesmaximal, characteristic, complemented
14C2×#16810708C211yesmaximal, characteristic, complemented
15C2×#16810683C211yesmaximal, characteristic, complemented
16C2×C53×#461C211yesmaximal, characteristic, complemented
17C22×D4×D53C2211yescharacteristic
18C22×#11719924C2211yescharacteristic
19C22×#11719924C2211yescharacteristic
20#16811234—24no—
21#16811234C2218yescomplemented
22C2×#13133212—21no—
23C2×#13133212—21no—
24C2×#13133209C2211yescharacteristic, complemented
25C2×#13133207—21no—
26C2×#13133207—21no—
27C2×#13133193C2211yescharacteristic
28C2×#13133193C2211yescharacteristic
29#16811095—24no—
30#16811095C2218yes—
31C2×Q8×Dic53C2211yescharacteristic, complemented
32C2×Q8×Dic53C2211yescharacteristic, complemented
33C2×C4×D212C2211yescharacteristic
34C2×D4×Dic53C2211yescharacteristic
35C2×#13133179C2211yescharacteristic
36C2×C4×C22⋊D53—21no—
37C2×#13133177—21no—
38C2×#13133175C2211yescharacteristic
39C2×#13133174C2211yescharacteristic
40C22×#11719921—21no—
41C2×C22⋊C4×D53—21no—
42#16810963C2218yescomplemented
43#16810962C2218yescomplemented
44#16810924C2218yescomplemented
45#16810923C2218yescomplemented
46#16810825C2218yescomplemented
47#16810772C2218yes—
48#16810772C2218yes—
49#16810726C2218yescomplemented
50#16810724C2218yescomplemented
51SD16×Dic53C2218yescomplemented
52#16810708C2218yescomplemented
53#16810683C2218yescomplemented
54C2×#13133151C2211yescharacteristic, complemented
55C2×#13133150C2211yescharacteristic, complemented
56C2×#13133149C2211yescharacteristic, complemented
57C2×#13133148C2211yescharacteristic, complemented
58C2×C4⋊#88322C2211yescharacteristic, complemented
59C2×#13133141C2211yescharacteristic, complemented
60C2×#13133141C2211yescharacteristic, complemented
61C2×#13133139C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133129C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133127C2211yescharacteristic, complemented
68C2×C8×Dic53C2211yescharacteristic, complemented
69C22×SD16×C53C2211yescharacteristic
70C22×SD16×C53C2211yescharacteristic
71C2×C4⋊Q8×C53C2211yescharacteristic, complemented
72C2×C4×D4×C53C2211yescharacteristic
73C53×#461C2218yescomplemented
74C2×C4⋊C8×C53C2211yescharacteristic, complemented
75C2×#103×C53C2211yescharacteristic, complemented
76C2×#103×C53C2211yescharacteristic, complemented
77C24×D53—21no—
78C22×D212C2311yescharacteristic
79C22×C22⋊D53—21no—
80C2×D4×D53—24no—
81C2×D4×D53—24no—
82C2×D4×D53—22no—
83C2×D4×D53C2314yes—
84C23×Dic53—21no—
85C22×C4×D53—21no—
86C22×C4×D53—21no—
87C22×C4×D53C2311yescharacteristic
88C2×#11719924—24no—
89C2×#11719924—24no—
90C2×#11719924C2314yes—
91C2×#11719924C2314yes—
92C22×#88322C2311yescharacteristic
93C22×#88322C2311yescharacteristic
94#13133212—28no—
95#13133212—28no—
96#13133209—22no—
97#13133209C2314yescomplemented
98#13133207—28no—
99#13133207—28no—
100#13133193—22no—
101#13133193—22no—
102#13133193C2314yes—
103#13133193C2314yes—
104Q8×Dic53—22no—
105Q8×Dic53—22no—
106Q8×Dic53C2314yescomplemented
107Q8×Dic53C2314yescomplemented
108C4×D212—22no—
109C4×D212C2314yes—
110D4×Dic53—22no—
111D4×Dic53C2314yes—
112#13133179—22no—
113#13133179C2314yes—
114C4×C22⋊D53—28no—
115#13133177—28no—
116#13133175—22no—
117#13133175C2314yes—
118#13133174D414yes—
119#13133174C2314yes—
120C2×C4⋊Dic53—21no—
121C2×C4⋊Dic53—21no—
122C2×C4⋊Dic53C2311yescharacteristic
123C2×C4⋊Dic53C2311yescharacteristic
124C2×C4⋊Dic53C2311yescharacteristic
125C2×#11719919—21no—
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919D411yescharacteristic
130C2×#11719919D411yescharacteristic
131C2×C22⋊Dic53—21no—
132C2×#11719921—28no—
133C2×#11719921—21no—
134C2×#11719921—21no—
135C2×#11719921—21no—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921D411yescharacteristic
139C2×#11719921D411yescharacteristic
140C22⋊C4×D53—28no—
141C2×C4×Dic53—21no—
142C2×C4×Dic53—21no—
143C2×C4×Dic53—21no—
144C2×C4×Dic53C2311yescharacteristic
145#13133151C2314yescomplemented
146#13133150C2314yescomplemented
147#13133149C2314yescomplemented
148#13133148C2314yescomplemented
149C4⋊#88322C2314yescomplemented
150#13133141C2314yescomplemented
151#13133141C2314yescomplemented
152#13133139C2314yes—
153#13133139C2314yes—
154#13133138C2314yes—
155#13133138C2314yes—
156#13133129C2314yes—
157#13133129C2314yes—
158#13133127C2314yescomplemented
159C8×Dic53C2314yescomplemented
160C22×Q8×C53C2311yescharacteristic
161C22×Q8×C53C2311yescharacteristic
162C22×D4×C53C2311yescharacteristic
163C23×C4×C53—21no—
164C2×SD16×C53—24no—
165C2×SD16×C53—24no—
166C2×SD16×C53C2314yes—
167C2×SD16×C53C2314yes—
168C22×C8×C53C2311yescharacteristic
169C22×C8×C53C2311yescharacteristic
170C4⋊Q8×C53—22no—
171C4⋊Q8×C53C2314yescomplemented
172C4×D4×C53—22no—
173C4×D4×C53C2314yes—
174C2×C4⋊C4×C53—21no—
175C2×C4⋊C4×C53—21no—
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C22⋊C4×C53—21no—
178C2×C42×C53C2311yescharacteristic
179C4⋊C8×C53C2314yescomplemented
180#103×C53C2314yescomplemented
181#103×C53C2314yescomplemented
182C24×C53—21no—
183C23×D53—21no—
184C23×D53—28no—
185C23×D53—24no—
186C23×D53—82no—
187C23×D53—82no—
188C23×D53C2×D411yescharacteristic
189C2×Q8×C53—21no—
190C2×Q8×C53—21no—
191C2×Q8×C53—22no—
192C2×Q8×C53—22no—
193C2×Q8×C53—22no—
194C2×Q8×C53—22no—
195C2×Q8×C53C2412yes—
196C2×Q8×C53C2412yes—
197C2×D4×C53—21no—
198C2×D4×C53—22no—
199C2×D4×C53#4114yes—
200C2×D4×C53C2412yes—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53—21no—
204C22×C4×C53—24no—
205C22×C4×C53—82no—
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53C2×D411yescharacteristic
208C22×C4×C53C2411yescharacteristic
209C2×C22⋊D53—28no—
210C2×C22⋊D53—24no—
211C22×Dic53—21no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—24no—
215C22×Dic53—82no—
216C22×Dic53C2×D411yescharacteristic
217C22×Dic53C2×D411yescharacteristic
218C22×Dic53C2×D411yescharacteristic
219D4×D53—216no—
220D4×D53—28no—
221D4×D53—28no—
222C2×D212—21no—
223C2×D212—22no—
224C2×D212#4114yes—
225C2×D212C2412yes—
226C2×C4×D53—22no—
227C2×C4×D53—22no—
228C2×C4×D53—24no—
229C2×C4×D53—24no—
230C2×C4×D53—82no—
231C2×C4×D53—82no—
232C2×C4×D53C2×D412yes—
233C2×C4×D53C2412yes—
234SD16×C53—28no—
235SD16×C53—28no—
236C2×C8×C53—22no—
237C2×C8×C53—22no—
238C2×C8×C53C2412yes—
239C2×C8×C53C2412yes—
240C4⋊C4×C53—24no—
241C4⋊C4×C53—24no—
242C4⋊C4×C53—21no—
243C4⋊C4×C53C2412yes—
244C22⋊C4×C53—24no—
245C42×C53C2×D412yes—
246C42×C53C2412yes—
247C22⋊Dic53—24no—
248#11719924—28no—
249#11719924—28no—
250#11719921—24no—
251#11719921—24no—
252#11719921—24no—
253#11719921—24no—
254#11719921—24no—
255#11719921C2×D414yes—
256#11719921C2×D414yes—
257C4⋊Dic53—21no—
258C4⋊Dic53—21no—
259C4⋊Dic53—21no—
260C4⋊Dic53—24no—
261C4⋊Dic53—24no—
262C4⋊Dic53C2412yes—
263C4⋊Dic53C2412yes—
264C4⋊Dic53C2412yes—
265#11719919—24no—
266#11719919—24no—
267#11719919—24no—
268#11719919—24no—
269#11719919C2×D414yes—
270#11719919C2×D414yes—
271C4×Dic53—24no—
272C4×Dic53—24no—
273C4×Dic53—24no—
274C4×Dic53C2×D412yes—
275C4×Dic53C2412yes—
276C2×#88322—22no—
277C2×#88322—22no—
278C2×#88322C2412yes—
279C2×#88322C2412yes—
280C23×C53—24no—
281C23×C53—22no—
282C23×C53—42no—
283C23×C53—42no—
284C23×C53C22×D411yescharacteristic
285C22×D53—22no—
286C22×D53—24no—
287C22×D53—22no—
288C22×D53—22no—
289C22×D53—22no—
290C22×D53—216no—
291C22×D53—42no—
292C22×D53—42no—
293C22×D53—84no—
294C22×D53—84no—
295C22×D53—816no—
296C22×D53C22×D412yes—
297Q8×C53—22no—
298Q8×C53—22no—
299Q8×C53—22no—
300Q8×C53—22no—
301Q8×C53—42no—
302Q8×C53—42no—
303D4×C53—24no—
304D4×C53—22no—
305D4×C53C2×#4114yes—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—42no—
312C2×C4×C53—42no—
313C2×C4×C53—42no—
314C2×C4×C53—84no—
315C2×C4×C53C22×D412yes—
316C2×C4×C53C22×D412yes—
317C2×C4×C53C22×D411yescharacteristic
318C2×C4×C53C2×#4112yes—
319C2×C4×C53C2×#4112yes—
320C2×C4×C53C2511yescharacteristic
321C22⋊D53—216no—
322C2×Dic53—22no—
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—42no—
329C2×Dic53—42no—
330C2×Dic53—42no—
331C2×Dic53—84no—
332C2×Dic53C22×D412yes—
333C2×Dic53C22×D412yes—
334C2×Dic53C22×D412yes—
335D212—24no—
336D212—22no—
337D212C2×#4114yes—
338C4×D53—24no—
339C4×D53—22no—
340C4×D53—22no—
341C4×D53—84no—
342C4×D53—84no—
343C8×C53—22no—
344C8×C53—22no—
345#88322—22no—
346#88322—22no—
347C2×#3123—531nomaximal, Sylow
348C22×C53—24no—
349C22×C53—48no—
350C22×C53—42no—
351C22×C53—42no—
352C22×C53#52512yes—
353C22×C53#57712yes—
354C22×C53#57712yes—
355C22×C53C23×D411yescharacteristic
356C2×D53—22no—
357C2×D53—24no—
358C2×D53—22no—
359C2×D53—22no—
360C2×D53—44no—
361C2×D53—48no—
362C2×D53—42no—
363C2×D53—42no—
364C2×D53—816no—
365C4×C53—22no—
366C4×C53—22no—
367C4×C53—42no—
368C4×C53—42no—
369C4×C53—42no—
370C4×C53#52512yes—
371C4×C53C22×#4111yescharacteristic
372C4×C53C22×#4111yescharacteristic
373Dic53—22no—
374Dic53—22no—
375Dic53—22no—
376Dic53—42no—
377Dic53—42no—
378Dic53—42no—
379C2×#541—531no—
380C2×#518—531no—
381#3123—5316no—
382C2×#485—531no—
383C2×#485—531no—
384C2×#478—531no—
385C2×#478—531no—
386C2×#461—531no—
387C2×#461D5311yescharacteristic, complemented
388C2×#450—531no—
389C2×#450—531no—
390C2×#440—531no—
391C2×#440—531no—
392C2×C4×SD16—531no—
393C2×C4×SD16—531no—
394C2×#433—531no—
395C2×C53—44no—
396C2×C53#312314yescomplemented
397C2×C53C2×#52511yescharacteristic
398C2×C53C2×#57711yescharacteristic
399C2×C53C2×#57711yescharacteristic
400D53—42no—
401D53—44no—
402C23×D4—531no—
403C22×SD16—531no—
404C22×SD16—531no—
405C22×SD16C2×D5311yescharacteristic
406C22×SD16C2×D5311yescharacteristic
407#541—538no—
408#541—1064no—
409C2×C4⋊Q8C2×D5311yescharacteristic, complemented
410C2×#126—1061no—
411C2×#126—1061no—
412C2×#125—531no—
413C2×#125—1061no—
414C2×#125—1061no—
415C2×C22⋊Q8—531no—
416C2×C22⋊Q8—531no—
417#518—538no—
418#518—1064no—
419C2×C4×Q8—531no—
420C2×C4×Q8—531no—
421C2×C4×D4—531no—
422C2×C4×D4—531no—
423C2×C4×D4—531no—
424C2×C4×D4—1061no—
425C2×C4×D4—1061no—
426C2×C4×D4C2×D5311yescharacteristic
427C2×#117—531no—
428C2×#117—531no—
429C22×C22⋊C4—1061no—
430C22×C22⋊C4—1061no—
431#485—538no—
432#485—538no—
433#478—538no—
434#478—538no—
435#461—538no—
436#461C2×D5318yescomplemented
437#450—538no—
438#450—538no—
439#440—538no—
440#440—538no—
441C4×SD16—538no—
442C4×SD16—538no—
443#433—538no—
444C2×#107—531no—
445C2×#107—531no—
446C2×#106—531no—
447C2×#106—531no—
448C2×C4⋊C8—531no—
449C2×C4⋊C8C2×D5311yescharacteristic, complemented
450C2×#103—531no—
451C2×#103—531no—
452C2×#103C2×D5311yescharacteristic, complemented
453C2×#103C2×D5311yescharacteristic, complemented
454C2×#102—531no—
455C2×#102—531no—
456C2×#102—531no—
457C2×#102—531no—
458C2×C22⋊C8—531no—
459C2×C22⋊C8—531no—
460C2×#97—531no—
461C2×C4×C8—531no—
462C53C2×#312311yescharacteristic, complemented, Sylow
463C25—1061no—
464C22×Q8C22×D5311yescharacteristic
465C22×Q8C22×D5311yescharacteristic
466C22×D4—534no—
467C22×D4—531no—
468C22×D4—1062no—
469C22×D4—1061no—
470C22×D4—1064no—
471C22×D4—1064no—
472C22×D4C22×D5311yescharacteristic
473C23×C4—21no—
474C23×C4—531no—
475C23×C4—1061no—
476C23×C4—1061no—
477C23×C4—1061no—
478C2×SD16—24no—
479C2×SD16—24no—
480C2×SD16—534no—
481C2×SD16—534no—
482C2×SD16—1064no—
483C2×SD16—1064no—
484C2×SD16C22×D5314yes—
485C2×SD16C22×D5314yes—
486C22×C8—531no—
487C22×C8—531no—
488C22×C8C22×D5311yescharacteristic
489C22×C8C22×D5311yescharacteristic
490C4⋊Q8—22no—
491C4⋊Q8C22×D5314yescomplemented
492#126—1068no—
493#126—1068no—
494#125—534no—
495#125—1068no—
496#125—1068no—
497#125—1062no—
498C22⋊Q8—534no—
499C22⋊Q8—534no—
500C22⋊Q8—1062no—
501C22⋊Q8—1062no—
502C4×Q8—534no—
503C4×Q8—534no—
504C4×Q8—1062no—
505C4×Q8—1062no—
506C4×D4—22no—
507C4×D4—534no—
508C4×D4—534no—
509C4×D4—534no—
510C4×D4—1062no—
511C4×D4—1062no—
512C4×D4—1068no—
513C4×D4—1068no—
514C4×D4—1062no—
515C4×D4C22×D5314yes—
516#117—534no—
517#117—534no—
518#117—534no—
519#117—1062no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—531no—
523C2×C4⋊C4—531no—
524C2×C4⋊C4—531no—
525C2×C4⋊C4—531no—
526C2×C4⋊C4—531no—
527C2×C4⋊C4—1061no—
528C2×C4⋊C4—1061no—
529C2×C4⋊C4—1061no—
530C2×C4⋊C4—1061no—
531C2×C4⋊C4—1061no—
532C2×C4⋊C4—1061no—
533C2×C4⋊C4C22×D5311yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—531no—
536C2×C22⋊C4—531no—
537C2×C22⋊C4—1068no—
538C2×C22⋊C4—1068no—
539C2×C22⋊C4—1061no—
540C2×C22⋊C4—1061no—
541C2×C22⋊C4—1061no—
542C2×C22⋊C4—1061no—
543C2×C22⋊C4—1061no—
544C2×C22⋊C4—1061no—
545C2×C42—531no—
546C2×C42—1061no—
547C2×C42—1061no—
548C2×C42—1061no—
549C2×C42C22×D5311yescharacteristic
550#107—534no—
551#107—534no—
552#106—534no—
553#106—534no—
554C4⋊C8—534no—
555C4⋊C8C22×D5314yescomplemented
556#103—534no—
557#103—534no—
558#103C22×D5314yescomplemented
559#103C22×D5314yescomplemented
560#102—534no—
561#102—534no—
562#102—534no—
563#102—534no—
564C22⋊C8—534no—
565C22⋊C8—534no—
566#97—534no—
567C4×C8—534no—
568C24—21no—
569C24—531no—
570C24—1064no—
571C24—1068no—
572C24—1061no—
573C24—4242no—
574C24—4242no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—22no—
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8C23×D5312yes—
582C2×Q8C23×D5312yes—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—534no—
586C2×D4—532no—
587C2×D4—1064no—
588C2×D4—1068no—
589C2×D4—10616no—
590C2×D4—1068no—
591C2×D4—1068no—
592C2×D4—1061no—
593C2×D4—1062no—
594C2×D4#1171994714yes—
595C2×D4C23×D5312yes—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—82no—
601C22×C4—531no—
602C22×C4—531no—
603C22×C4—531no—
604C22×C4—532no—
605C22×C4—532no—
606C22×C4—1064no—
607C22×C4—1064no—
608C22×C4—1062no—
609C22×C4—1062no—
610C22×C4—1061no—
611C22×C4—1061no—
612C22×C4—1061no—
613C22×C4—1064no—
614C22×C4—4242no—
615C22×C4—4242no—
616C22×C4—4242no—
617C22×C4D4×D5311yescharacteristic
618C22×C4D4×D5311yescharacteristic
619C22×C4C23×D5311yescharacteristic
620SD16—28no—
621SD16—28no—
622SD16—1068no—
623SD16—1068no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—532no—
627C2×C8—532no—
628C2×C8—1062no—
629C2×C8—1062no—
630C2×C8C23×D5312yes—
631C2×C8C23×D5312yes—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—21no—
635C4⋊C4—534no—
636C4⋊C4—534no—
637C4⋊C4—532no—
638C4⋊C4—532no—
639C4⋊C4—532no—
640C4⋊C4—1064no—
641C4⋊C4—1064no—
642C4⋊C4—1064no—
643C4⋊C4—1064no—
644C4⋊C4—1061no—
645C4⋊C4—1061no—
646C4⋊C4—1061no—
647C4⋊C4—1064no—
648C4⋊C4—1064no—
649C4⋊C4C23×D5312yes—
650C22⋊C4—24no—
651C22⋊C4—534no—
652C22⋊C4—534no—
653C22⋊C4—1064no—
654C22⋊C4—1064no—
655C22⋊C4—1064no—
656C22⋊C4—1064no—
657C22⋊C4—1064no—
658C22⋊C4—1064no—
659C42—532no—
660C42—532no—
661C42—1064no—
662C42—1064no—
663C42—1064no—
664C42D4×D5312yes—
665C42C23×D5312yes—
666C23—24no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—532no—
671C23—10616no—
672C23—1062no—
673C23—1064no—
674C23—1062no—
675C23—1062no—
676C23—1062no—
677C23—4244no—
678C23—4244no—
679C23—42416no—
680C23—2122no—
681C23—2122no—
682C23C2×D4×D5311yescharacteristic
683Q8—22no—
684Q8—22no—
685Q8—22no—
686Q8—22no—
687Q8—42no—
688Q8—42no—
689D4—24no—
690D4—22no—
691D4—534no—
692D4—10616no—
693D4—1064no—
694D4—1062no—
695D4C2×#1171994714yes—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—84no—
705C2×C4—532no—
706C2×C4—532no—
707C2×C4—532no—
708C2×C4—1062no—
709C2×C4—1062no—
710C2×C4—1062no—
711C2×C4—1064no—
712C2×C4—1062no—
713C2×C4—1062no—
714C2×C4—1062no—
715C2×C4—1062no—
716C2×C4—1062no—
717C2×C4—4244no—
718C2×C4—4244no—
719C2×C4—4244no—
720C2×C4—2122no—
721C2×C4—2122no—
722C2×C4—2122no—
723C2×C4C2×D4×D5312yes—
724C2×C4C2×D4×D5312yes—
725C2×C4C2×D4×D5311yescharacteristic
726C2×C4#41×D5312yes—
727C2×C4C2×#1171994712yes—
728C2×C4C24×D5311yescharacteristic
729C8—22no—
730C8—22no—
731C8—1062no—
732C8—1062no—
733C22—24no—
734C22—48no—
735C22—42no—
736C22—42no—
737C22—1062no—
738C22—1062no—
739C22—1062no—
740C22—1064no—
741C22—42416no—
742C22—2124no—
743C22—2128no—
744C22—2122no—
745C22—2122no—
746C22#1681113312yes—
747C22#1681142912yes—
748C22#1681143212yes—
749C22C22×D4×D5311yescharacteristic
750C4—22no—
751C4—22no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—1062no—
756C4—1062no—
757C4—1062no—
758C4—2122no—
759C4—2122no—
760C4—2122no—
761C4#1681113312yes—
762C4C2×#41×D5311yescharacteristic
763C4C22×#1171994711yescharacteristic
764C2—44no—
765C2—2122no—
766C2—2124no—
767C2#2028496514yesdirect product factor
768C2C2×#1681113311yescharacteristic
769C2C2×#1681142911yescharacteristic
770C2C2×#1681143211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#461C2
socleC23×C53C22×D4
prime radicalC22×D4×D53C22
hypercenterC2×#461D53
hypocenterC53C2×#3123
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#16811234C2semidirect
3. #20284965C2direct (N × H)
4. C2×#16810963C2semidirect
5. C2×#16810962C2semidirect
6. C2×#16810924C2semidirect
7. C2×#16810923C2semidirect
8. C2×#16810825C2semidirect
11. C2×#16810726C2semidirect
12. C2×#16810724C2semidirect
13. C2×SD16×Dic53C2semidirect
14. C2×#16810708C2semidirect
15. C2×#16810683C2semidirect
16. C2×C53×#461C2semidirect
21. #16811234C22semidirect
24. C2×#13133209C22semidirect
31. C2×Q8×Dic53C22semidirect
32. C2×Q8×Dic53C22semidirect
42. #16810963C22semidirect
43. #16810962C22semidirect
44. #16810924C22semidirect
45. #16810923C22semidirect
46. #16810825C22semidirect
49. #16810726C22semidirect
50. #16810724C22semidirect
51. SD16×Dic53C22semidirect
52. #16810708C22semidirect
53. #16810683C22semidirect
54. C2×#13133151C22semidirect
55. C2×#13133150C22semidirect
56. C2×#13133149C22semidirect
57. C2×#13133148C22semidirect
58. C2×C4⋊#88322C22semidirect
59. C2×#13133141C22semidirect
60. C2×#13133141C22semidirect
67. C2×#13133127C22semidirect
68. C2×C8×Dic53C22semidirect
71. C2×C4⋊Q8×C53C22semidirect
73. C53×#461C22semidirect
74. C2×C4⋊C8×C53C22semidirect
75. C2×#103×C53C22semidirect
76. C2×#103×C53C22semidirect
97. #13133209C23semidirect
106. Q8×Dic53C23semidirect
107. Q8×Dic53C23semidirect
145. #13133151C23semidirect
146. #13133150C23semidirect
147. #13133149C23semidirect
148. #13133148C23semidirect
149. C4⋊#88322C23semidirect
150. #13133141C23semidirect
151. #13133141C23semidirect
158. #13133127C23semidirect
159. C8×Dic53C23semidirect
171. C4⋊Q8×C53C23semidirect
179. C4⋊C8×C53C23semidirect
180. #103×C53C23semidirect
181. #103×C53C23semidirect
387. C2×#461D53semidirect
396. C2×C53#3123semidirect
409. C2×C4⋊Q8C2×D53semidirect
436. #461C2×D53semidirect
449. C2×C4⋊C8C2×D53semidirect
452. C2×#103C2×D53semidirect
453. C2×#103C2×D53semidirect
462. C53C2×#3123semidirect
491. C4⋊Q8C22×D53semidirect
555. C4⋊C8C22×D53semidirect
558. #103C22×D53semidirect
559. #103C22×D53semidirect
767. C2#20284965direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112342
C2×#168110952
#202849652
C2×#168109632
C2×#168109622
C2×#168109242
C2×#168109232
C2×#168108252
C2×#168107722
C2×#168107262
C2×#168107242
C2×SD16×Dic532
C2×#168107082
C2×#168106832
C2×C53×#4612
C2×#312353