Finite Group Databasebeta

← C2×#20285803 #28255441

Subgroups — C2×#20285803 #28255441

Order 13568.

2278 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811192C211yesmaximal, characteristic, complemented
2#20285803C2116yesmaximal, direct product factor
3C2×#16811013C211yesmaximal, characteristic, complemented
4C2×#16811005C211yesmaximal, characteristic, complemented
5C2×#16810985C211yesmaximal, characteristic, complemented
6C2×#16810971C211yesmaximal, characteristic, complemented
7C2×#16810845C211yesmaximal, characteristic, complemented
8C2×#16810823C211yesmaximal, characteristic, complemented
9C2×#16810838C211yesmaximal, characteristic, complemented
10C2×#16810818C211yesmaximal, characteristic, complemented
11C2×#16810783C211yesmaximal, characteristic, complemented
12C2×#16810766C211yesmaximal, characteristic, complemented
13C2×#16810773C211yesmaximal, characteristic, complemented
14C2×#16810756C211yesmaximal, characteristic, complemented
15C2×#16810684C211yesmaximal, characteristic, complemented
16C2×C53×#542C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C23×D212C2211yescharacteristic
19C22×#11719925C2211yescharacteristic, complemented
20C22×#11719923C2211yescharacteristic, complemented
21C22×#11719924C2211yescharacteristic
22C22×#11719924C2211yescharacteristic
23C22×#11719924C2211yescharacteristic, complemented
24C22×#11719922C2211yescharacteristic
25C22×#11719922C2211yescharacteristic
26C22×#11719922C2211yescharacteristic, complemented
27#16811192—24no—
28#16811192C2218yescomplemented
29C2×#13133214C2211yescharacteristic
30C2×#13133214C2211yescharacteristic
31C2×#13133205C2211yescharacteristic
32C2×#13133205C2211yescharacteristic
33C2×#13133192—21no—
34C2×#13133192—21no—
35C2×#13133187—21no—
36C2×#13133187—21no—
37#16811013C2218yescomplemented
38#16811005C2218yescomplemented
39#16810985C2218yescomplemented
40#16810971C2218yescomplemented
41#16810845C2218yescomplemented
42#16810838C2218yescomplemented
43#16810823C2218yescomplemented
44#16810818C2218yescomplemented
45#16810783C2218yescomplemented
46#16810773C2218yescomplemented
47#16810766C2218yescomplemented
48#16810756C2218yescomplemented
49#16810684C2218yescomplemented
50C2×C4⋊#88322C2211yescharacteristic, complemented
51C2×C4⋊#88322C2211yescharacteristic, complemented
52C2×#13133140C2211yescharacteristic, complemented
53C2×#13133140C2211yescharacteristic, complemented
54C2×#13133137C2211yescharacteristic
55C2×#13133137C2211yescharacteristic
56C2×#13133137C2211yescharacteristic
57C2×#13133137C2211yescharacteristic
58C2×#13133137C2211yescharacteristic, complemented
59C2×#13133137C2211yescharacteristic, complemented
60C2×C22⋊#88322C2211yescharacteristic
61C2×C22⋊#88322C2211yescharacteristic
62C2×#13133128C2211yescharacteristic, complemented
63C2×C4×#88322C2211yescharacteristic, complemented
64C53×#542—24no—
65C53×#542C2218yescomplemented
66C2×C4⋊Q8×C53C2211yescharacteristic, complemented
67C2×#126×C53—21no—
68C2×#124×C53—21no—
69C2×#124×C53C2211yescharacteristic, complemented
70C2×#123×C53—21no—
71C2×C22⋊Q8×C53—21no—
72C2×C22⋊Q8×C53C2211yescharacteristic
73C2×#121×C53C2211yescharacteristic
74C2×C4×Q8×C53C2211yescharacteristic, complemented
75C2×C4×D4×C53C2211yescharacteristic, complemented
76C2×#117×C53C2211yescharacteristic
77C24×D53—21no—
78C2×#11719945—22no—
79C2×#11719945—42no—
80C2×#11719945—42no—
81C2×#11719945C2314yes—
82C22×Dic106C2311yescharacteristic
83C22×D212—21no—
84C22×D212—22no—
85C22×D212—21no—
86C22×D212—21no—
87C22×D212—21no—
88C22×D212—21no—
89C22×D212—42no—
90C22×D212—42no—
91C22×D212C2311yescharacteristic
92C22×D212C2311yescharacteristic
93C22×D212C2311yescharacteristic
94C22×D212C2314yes—
95C22×C22⋊D53—21no—
96C22×C4×D53—21no—
97C2×#11719925—42no—
98C2×#11719925C2314yescomplemented
99C2×#11719923—42no—
100C2×#11719923C2314yescomplemented
101C2×#11719924—42no—
102C2×#11719924—42no—
103C2×#11719924—42no—
104C2×#11719924C2314yes—
105C2×#11719924C2314yes—
106C2×#11719924C2314yescomplemented
107C2×#11719922—42no—
108C2×#11719922—42no—
109C2×#11719922—42no—
110C2×#11719922C2314yes—
111C2×#11719922C2314yes—
112C2×#11719922C2314yescomplemented
113C22×#88322C2311yescharacteristic
114C22×#88322C2311yescharacteristic
115C22×#88322C2311yescharacteristic
116C22×#88322C2311yescharacteristic
117#13133214—22no—
118#13133214—22no—
119#13133214C2314yes—
120#13133214C2314yes—
121#13133205—22no—
122#13133205—22no—
123#13133205C2314yes—
124#13133205C2314yes—
125#13133192—28no—
126#13133192—28no—
127#13133187—28no—
128#13133187—28no—
129C2×#11719921—21no—
130C2×#11719921—21no—
131C2×#11719921—21no—
132C2×#11719921—21no—
133C4⋊#88322C2314yescomplemented
134C4⋊#88322C2314yescomplemented
135#13133140C2314yescomplemented
136#13133140C2314yescomplemented
137#13133137C2314yes—
138#13133137C2314yes—
139#13133137C2314yes—
140#13133137C2314yes—
141#13133137C2314yescomplemented
142#13133137C2314yescomplemented
143C22⋊#88322C2314yes—
144C22⋊#88322C2314yes—
145#13133128C2314yescomplemented
146C4×#88322C2314yescomplemented
147C22×Q8×C53—21no—
148C22×Q8×C53C2311yescharacteristic
149C22×D4×C53—21no—
150C22×D4×C53C2311yescharacteristic
151C23×C4×C53—21no—
152C23×C4×C53C2311yescharacteristic
153C4⋊Q8×C53—22no—
154C4⋊Q8×C53C2314yescomplemented
155#126×C53—28no—
156#124×C53—28no—
157#124×C53—22no—
158#124×C53C2314yescomplemented
159#123×C53—28no—
160C22⋊Q8×C53—28no—
161C22⋊Q8×C53—22no—
162C22⋊Q8×C53C2314yes—
163#121×C53—22no—
164#121×C53C2314yes—
165C4×Q8×C53—22no—
166C4×Q8×C53C2314yescomplemented
167C4×D4×C53—22no—
168C4×D4×C53C2314yescomplemented
169#117×C53D414yes—
170#117×C53C2314yes—
171C2×C4⋊C4×C53—21no—
172C2×C4⋊C4×C53—21no—
173C2×C4⋊C4×C53—21no—
174C2×C4⋊C4×C53D411yescharacteristic
175C2×C4⋊C4×C53D411yescharacteristic
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C22⋊C4×C53—21no—
179C2×C22⋊C4×C53—21no—
180C2×C22⋊C4×C53—21no—
181C2×C22⋊C4×C53—21no—
182C2×C22⋊C4×C53—21no—
183C2×C22⋊C4×C53D411yescharacteristic
184C2×C22⋊C4×C53D411yescharacteristic
185C2×C42×C53—21no—
186C2×C42×C53C2311yescharacteristic
187C2×C42×C53C2311yescharacteristic
188C24×C53—21no—
189C24×C53C2×D411yescharacteristic
190C23×D53—21no—
191C23×D53—21no—
192C23×D53—21no—
193C23×D53—24no—
194C23×D53—44no—
195C23×D53—82no—
196C23×D53—82no—
197C2×Q8×C53—21no—
198C2×Q8×C53—24no—
199C2×Q8×C53—22no—
200C2×Q8×C53—22no—
201C2×Q8×C53—82no—
202C2×Q8×C53C2412yes—
203C2×D4×C53—24no—
204C2×D4×C53—21no—
205C2×D4×C53—22no—
206C2×D4×C53—22no—
207C2×D4×C53—82no—
208C2×D4×C53C2412yes—
209C22×C4×C53—22no—
210C22×C4×C53—22no—
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53—21no—
214C22×C4×C53—24no—
215C22×C4×C53—82no—
216C22×C4×C53C2×D411yescharacteristic
217C22×C4×C53C2×D411yescharacteristic
218C22×C4×C53C2×D411yescharacteristic
219C22×C4×C53C2×D411yescharacteristic
220C22×C4×C53C2×D411yescharacteristic
221C22×C4×C53C2×D412yes—
222C22×C4×C53C2412yes—
223C22×C4×C53C2411yescharacteristic
224C2×C22⋊D53—24no—
225C2×C22⋊D53—44no—
226C22×Dic53—21no—
227#11719945—44no—
228#11719945—44no—
229#11719945—48no—
230C2×D212—22no—
231C2×D212—22no—
232C2×D212—22no—
233C2×D212—22no—
234C2×D212—22no—
235C2×D212—22no—
236C2×D212—24no—
237C2×D212—21no—
238C2×D212—21no—
239C2×D212—21no—
240C2×D212—24no—
241C2×D212—24no—
242C2×D212—24no—
243C2×D212—24no—
244C2×D212—44no—
245C2×D212—44no—
246C2×D212—44no—
247C2×D212—48no—
248C2×D212—82no—
249C2×D212—82no—
250C2×D212—82no—
251C2×D212—82no—
252C2×D212C2412yes—
253C2×D212C2412yes—
254C2×D212C2412yes—
255C2×C4×D53—24no—
256C2×C4×D53—44no—
257C2×Dic106—22no—
258C2×Dic106—22no—
259C2×Dic106—21no—
260C2×Dic106C2412yes—
261C4⋊C4×C53—24no—
262C4⋊C4×C53—24no—
263C4⋊C4×C53—24no—
264C4⋊C4×C53—21no—
265C4⋊C4×C53—21no—
266C4⋊C4×C53C2×D414yes—
267C4⋊C4×C53C2×D414yes—
268C4⋊C4×C53C2412yes—
269C4⋊C4×C53C2412yes—
270C22⋊C4×C53—24no—
271C22⋊C4×C53—24no—
272C22⋊C4×C53—24no—
273C22⋊C4×C53—24no—
274C22⋊C4×C53—24no—
275C22⋊C4×C53C2×D414yes—
276C22⋊C4×C53C2×D414yes—
277C42×C53—24no—
278C42×C53C2×D412yes—
279C42×C53C2×D412yes—
280C42×C53C2412yes—
281C42×C53C2412yes—
282#11719925—44no—
283#11719924—44no—
284#11719924—44no—
285#11719924—44no—
286#11719923—44no—
287#11719922—44no—
288#11719922—44no—
289#11719922—44no—
290#11719921—24no—
291#11719921—24no—
292#11719921—24no—
293#11719921—24no—
294C2×#88322—22no—
295C2×#88322—22no—
296C2×#88322—22no—
297C2×#88322—22no—
298C2×#88322C2412yes—
299C2×#88322C2412yes—
300C2×#88322C2412yes—
301C2×#88322C2412yes—
302C23×C53—22no—
303C23×C53—22no—
304C23×C53—22no—
305C23×C53—22no—
306C23×C53—42no—
307C23×C53—42no—
308C23×C53—42no—
309C23×C53C22×D412yes—
310C23×C53C22×D411yescharacteristic
311C22×D53—22no—
312C22×D53—22no—
313C22×D53—22no—
314C22×D53—48no—
315C22×D53—42no—
316C22×D53—42no—
317C22×D53—42no—
318C22×D53—42no—
319C22×D53—42no—
320C22×D53—42no—
321C22×D53—42no—
322C22×D53—42no—
323C22×D53—42no—
324C22×D53—84no—
325C22×D53—84no—
326C22×D53—816no—
327Q8×C53—22no—
328Q8×C53—22no—
329Q8×C53—42no—
330Q8×C53—84no—
331D4×C53—22no—
332D4×C53—22no—
333D4×C53—42no—
334D4×C53—84no—
335C2×C4×C53—22no—
336C2×C4×C53—22no—
337C2×C4×C53—22no—
338C2×C4×C53—22no—
339C2×C4×C53—22no—
340C2×C4×C53—24no—
341C2×C4×C53—22no—
342C2×C4×C53—22no—
343C2×C4×C53—22no—
344C2×C4×C53—22no—
345C2×C4×C53—22no—
346C2×C4×C53—42no—
347C2×C4×C53—42no—
348C2×C4×C53—42no—
349C2×C4×C53—84no—
350C2×C4×C53C22×D412yes—
351C2×C4×C53C22×D412yes—
352C2×C4×C53C22×D412yes—
353C2×C4×C53C22×D412yes—
354C2×C4×C53C22×D412yes—
355C2×C4×C53C22×D411yescharacteristic
356C2×C4×C53H(5,𝔽2)12yes—
357C2×C4×C53H(5,𝔽2)12yes—
358C2×C4×C53C2511yescharacteristic
359C22⋊D53—48no—
360C2×Dic53—22no—
361C2×Dic53—42no—
362D212—22no—
363D212—22no—
364D212—22no—
365D212—22no—
366D212—22no—
367D212—22no—
368D212—48no—
369D212—42no—
370D212—42no—
371D212—42no—
372D212—84no—
373D212—84no—
374D212—84no—
375D212—84no—
376C4×D53—48no—
377Dic106—22no—
378Dic106—22no—
379Dic106—42no—
380#88322—22no—
381#88322—22no—
382#88322—22no—
383#88322—22no—
384C2×#3224—531nomaximal, Sylow
385C22×C53—22no—
386C22×C53—22no—
387C22×C53—22no—
388C22×C53—44no—
389C22×C53—42no—
390C22×C53—42no—
391C22×C53—42no—
392C22×C53—84no—
393C22×C53#53512yes—
394C22×C53#57612yes—
395C22×C53#57712yes—
396C22×C53C23×D411yescharacteristic
397C2×D53—42no—
398C2×D53—42no—
399C2×D53—42no—
400C2×D53—42no—
401C2×D53—42no—
402C2×D53—42no—
403C2×D53—42no—
404C2×D53—42no—
405C2×D53—42no—
406C2×D53—816no—
407C2×D53—84no—
408C2×D53—84no—
409C2×D53—84no—
410C4×C53—22no—
411C4×C53—22no—
412C4×C53—22no—
413C4×C53—22no—
414C4×C53—22no—
415C4×C53—42no—
416C4×C53—42no—
417C4×C53—42no—
418C4×C53#53512yes—
419C4×C53C2×H(5,𝔽2)11yescharacteristic
420C4×C53C2×H(5,𝔽2)11yescharacteristic
421Dic53—42no—
422C2×#542D5311yescharacteristic, complemented
423C2×#535—531no—
424#3224—5316no—
425C2×#496—531no—
426C2×#495—531no—
427C2×#489—531no—
428C2×#486—531no—
429C2×#464—531no—
430C2×#460—531no—
431C2×#463—531no—
432C2×#459—531no—
433C2×#452—531no—
434C2×#449—531no—
435C2×#450—531no—
436C2×#447—531no—
437C2×#433—531no—
438C2×C53—42no—
439C2×C53—82no—
440C2×C53#322414yescomplemented
441C2×C53C2×#53511yescharacteristic
442C2×C53C2×#57611yescharacteristic
443C2×C53C2×#57711yescharacteristic
444D53—82no—
445D53—82no—
446D53—82no—
447C22×#41—531no—
448C23×D4—531no—
449C22×Q16—531no—
450C22×SD16—531no—
451C22×SD16—531no—
452C22×SD16—531no—
453C22×SD16—531no—
454C22×D8—531no—
455C22×D8—531no—
456C22×D8—531no—
457#542—24no—
458#542C2×D5318yescomplemented
459#535—538no—
460#535—1064no—
461C2×C4⋊Q8C2×D5311yescharacteristic, complemented
462C2×#127—531no—
463C2×#127—531no—
464C2×#126—21no—
465C2×#124—21no—
466C2×#124—531no—
467C2×#124—531no—
468C2×#124C2×D5311yescharacteristic, complemented
469C2×#123—21no—
470C2×C22⋊Q8—21no—
471C2×C22⋊Q8C2×D5311yescharacteristic
472C2×#121—1061no—
473C2×#121—1061no—
474C2×#121C2×D5311yescharacteristic
475C2×#120—1061no—
476C2×#120—1061no—
477C2×C4×Q8C2×D5311yescharacteristic, complemented
478C2×C4×D4C2×D5311yescharacteristic, complemented
479C2×#117C2×D5311yescharacteristic
480#496—538no—
481#495—538no—
482#489—538no—
483#486—538no—
484#464—538no—
485#463—538no—
486#460—538no—
487#459—538no—
488#452—538no—
489#450—538no—
490#449—538no—
491#447—538no—
492#433—538no—
493C2×C4⋊C8—531no—
494C2×C4⋊C8—531no—
495C2×#103—531no—
496C2×#103—531no—
497C2×#102—531no—
498C2×#102—531no—
499C2×#102—531no—
500C2×#102—531no—
501C2×#102—531no—
502C2×#102—531no—
503C2×C22⋊C8—531no—
504C2×C22⋊C8—531no—
505C2×#97—531no—
506C2×C4×C8—531no—
507C53C2×#322411yescharacteristic, complemented, Sylow
508C25—1061no—
509C2×#41—534no—
510C2×#41—1062no—
511C2×#41—2122no—
512C2×#41—2122no—
513C22×Q8—21no—
514C22×Q8—531no—
515C22×Q8C22×D5311yescharacteristic
516C22×D4—21no—
517C22×D4—531no—
518C22×D4—531no—
519C22×D4—531no—
520C22×D4—534no—
521C22×D4—1061no—
522C22×D4—1061no—
523C22×D4—1061no—
524C22×D4—1061no—
525C22×D4—1061no—
526C22×D4—1061no—
527C22×D4—1062no—
528C22×D4—2122no—
529C22×D4—2122no—
530C22×D4C22×D5311yescharacteristic
531C23×C4—21no—
532C23×C4—1061no—
533C23×C4C22×D5311yescharacteristic
534C2×Q16—534no—
535C2×Q16—2122no—
536C2×SD16—534no—
537C2×SD16—534no—
538C2×SD16—534no—
539C2×SD16—534no—
540C2×SD16—2122no—
541C2×SD16—2122no—
542C2×SD16—2122no—
543C2×SD16—2122no—
544C2×D8—534no—
545C2×D8—534no—
546C2×D8—534no—
547C2×D8—2122no—
548C2×D8—2122no—
549C2×D8—2122no—
550C22×C8—531no—
551C22×C8—531no—
552C22×C8—531no—
553C22×C8—531no—
554C4⋊Q8—22no—
555C4⋊Q8C22×D5314yescomplemented
556#127—534no—
557#127—534no—
558#127—1062no—
559#127—1062no—
560#126—28no—
561#124—28no—
562#124—22no—
563#124—534no—
564#124—534no—
565#124—1062no—
566#124—1062no—
567#124C22×D5314yescomplemented
568#123—28no—
569C22⋊Q8—22no—
570C22⋊Q8—28no—
571C22⋊Q8C22×D5314yes—
572#121—22no—
573#121—1068no—
574#121—1068no—
575#121C22×D5314yes—
576#120—1068no—
577#120—1068no—
578C4×Q8—22no—
579C4×Q8C22×D5314yescomplemented
580C4×D4—22no—
581C4×D4C22×D5314yescomplemented
582#117C22⋊D5314yes—
583#117C22×D5314yes—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4C22⋊D5311yescharacteristic
588C2×C4⋊C4C22⋊D5311yescharacteristic
589C2×C4⋊C4C22×D5311yescharacteristic
590C2×C4⋊C4C22×D5311yescharacteristic
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
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⋊C4C22⋊D5311yescharacteristic
601C2×C22⋊C4C22⋊D5311yescharacteristic
602C2×C42—21no—
603C2×C42C22×D5311yescharacteristic
604C2×C42C22×D5311yescharacteristic
605C4⋊C8—534no—
606C4⋊C8—534no—
607#103—534no—
608#103—534no—
609#102—534no—
610#102—534no—
611#102—534no—
612#102—534no—
613#102—534no—
614#102—534no—
615C22⋊C8—534no—
616C22⋊C8—534no—
617#97—534no—
618C4×C8—534no—
619C24—21no—
620C24—1064no—
621C24—1061no—
622C24—1061no—
623C24—1061no—
624C24—4242no—
625C24—4242no—
626C24—2124no—
627C24C2×C22⋊D5311yescharacteristic
628#41—2124no—
629#41—2124no—
630#41—2128no—
631C2×Q8—21no—
632C2×Q8—24no—
633C2×Q8—22no—
634C2×Q8—22no—
635C2×Q8—82no—
636C2×Q8—532no—
637C2×Q8—1061no—
638C2×Q8—1062no—
639C2×Q8—1062no—
640C2×Q8C23×D5312yes—
641C2×D4—24no—
642C2×D4—21no—
643C2×D4—22no—
644C2×D4—22no—
645C2×D4—82no—
646C2×D4—532no—
647C2×D4—532no—
648C2×D4—532no—
649C2×D4—1064no—
650C2×D4—1064no—
651C2×D4—1064no—
652C2×D4—1064no—
653C2×D4—1064no—
654C2×D4—1064no—
655C2×D4—1061no—
656C2×D4—1061no—
657C2×D4—1061no—
658C2×D4—1062no—
659C2×D4—1062no—
660C2×D4—1062no—
661C2×D4—1062no—
662C2×D4—1062no—
663C2×D4—1062no—
664C2×D4—4242no—
665C2×D4—4242no—
666C2×D4—4242no—
667C2×D4—4242no—
668C2×D4—2124no—
669C2×D4—2124no—
670C2×D4—2124no—
671C2×D4—2128no—
672C2×D4—2124no—
673C2×D4C23×D5312yes—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—24no—
680C22×C4—82no—
681C22×C4—1061no—
682C22×C4—1064no—
683C22×C4—2124no—
684C22×C4C2×C22⋊D5312yes—
685C22×C4C2×C22⋊D5311yescharacteristic
686C22×C4C2×C22⋊D5311yescharacteristic
687C22×C4C2×C22⋊D5311yescharacteristic
688C22×C4C2×C22⋊D5311yescharacteristic
689C22×C4C2×C22⋊D5311yescharacteristic
690C22×C4C23×D5312yes—
691C22×C4C23×D5311yescharacteristic
692Q16—2124no—
693SD16—2124no—
694SD16—2124no—
695SD16—2124no—
696SD16—2124no—
697D8—2124no—
698D8—2124no—
699D8—2124no—
700C2×C8—532no—
701C2×C8—532no—
702C2×C8—532no—
703C2×C8—532no—
704C2×C8—1062no—
705C2×C8—1062no—
706C2×C8—1062no—
707C2×C8—1062no—
708C4⋊C4—24no—
709C4⋊C4—24no—
710C4⋊C4—24no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4C2×C22⋊D5314yes—
714C4⋊C4C2×C22⋊D5314yes—
715C4⋊C4C23×D5312yes—
716C4⋊C4C23×D5312yes—
717C22⋊C4—24no—
718C22⋊C4—24no—
719C22⋊C4—24no—
720C22⋊C4—24no—
721C22⋊C4—24no—
722C22⋊C4—1064no—
723C22⋊C4—1064no—
724C22⋊C4—1064no—
725C22⋊C4—1064no—
726C22⋊C4C2×C22⋊D5314yes—
727C22⋊C4C2×C22⋊D5314yes—
728C42—24no—
729C42C2×C22⋊D5312yes—
730C42C2×C22⋊D5312yes—
731C42C23×D5312yes—
732C42C23×D5312yes—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—1062no—
741C23—1062no—
742C23—1062no—
743C23—4244no—
744C23—4244no—
745C23—42416no—
746C23—2128no—
747C23—2122no—
748C23—2122no—
749C23—2122no—
750C23—2122no—
751C23—2122no—
752C23—2122no—
753C23—2122no—
754C23—2122no—
755C23—2122no—
756C23C22×C22⋊D5312yes—
757C23C22×C22⋊D5311yescharacteristic
758Q8—22no—
759Q8—22no—
760Q8—42no—
761Q8—84no—
762Q8—1062no—
763Q8—1062no—
764Q8—2122no—
765D4—22no—
766D4—22no—
767D4—42no—
768D4—84no—
769D4—1062no—
770D4—1062no—
771D4—1062no—
772D4—1062no—
773D4—1062no—
774D4—1062no—
775D4—4244no—
776D4—4244no—
777D4—4244no—
778D4—4244no—
779D4—2128no—
780D4—2128no—
781D4—2122no—
782D4—2122no—
783D4—2122no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—84no—
799C2×C4—1062no—
800C2×C4—2128no—
801C2×C4—2122no—
802C2×C4C22×C22⋊D5312yes—
803C2×C4C22×C22⋊D5312yes—
804C2×C4C22×C22⋊D5312yes—
805C2×C4C22×C22⋊D5312yes—
806C2×C4C22×C22⋊D5312yes—
807C2×C4C22×C22⋊D5311yescharacteristic
808C2×C4#1313326312yes—
809C2×C4#1313326312yes—
810C2×C4C24×D5311yescharacteristic
811C8—1062no—
812C8—1062no—
813C8—1062no—
814C8—1062no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—44no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—84no—
823C22—42416no—
824C22—4244no—
825C22—4244no—
826C22—4244no—
827C22—2122no—
828C22—2122no—
829C22—2122no—
830C22—2122no—
831C22—2122no—
832C22—2122no—
833C22—2122no—
834C22—2122no—
835C22—2122no—
836C22#1681118712yes—
837C22#1681142612yes—
838C22#1681143112yes—
839C22C23×C22⋊D5311yescharacteristic
840C4—22no—
841C4—22no—
842C4—22no—
843C4—22no—
844C4—22no—
845C4—42no—
846C4—42no—
847C4—42no—
848C4—2122no—
849C4#1681118712yes—
850C4C2×#1313326311yescharacteristic
851C4C2×#1313326311yescharacteristic
852C2—42no—
853C2—82no—
854C2—4242no—
855C2—4242no—
856C2—4242no—
857C2#2028580314yesdirect product factor
858C2C2×#1681118711yescharacteristic
859C2C2×#1681142611yescharacteristic
860C2C2×#1681143111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#542C2
socleC23×C53C22×D4
hypercenterC2×#542D53
hypocenterC53C2×#3224
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#16811192C2semidirect
2. #20285803C2direct (N × H)
3. C2×#16811013C2semidirect
4. C2×#16811005C2semidirect
5. C2×#16810985C2semidirect
6. C2×#16810971C2semidirect
7. C2×#16810845C2semidirect
8. C2×#16810823C2semidirect
9. C2×#16810838C2semidirect
10. C2×#16810818C2semidirect
11. C2×#16810783C2semidirect
12. C2×#16810766C2semidirect
13. C2×#16810773C2semidirect
14. C2×#16810756C2semidirect
15. C2×#16810684C2semidirect
16. C2×C53×#542C2semidirect
19. C22×#11719925C22semidirect
20. C22×#11719923C22semidirect
23. C22×#11719924C22semidirect
26. C22×#11719922C22semidirect
28. #16811192C22semidirect
37. #16811013C22semidirect
38. #16811005C22semidirect
39. #16810985C22semidirect
40. #16810971C22semidirect
41. #16810845C22semidirect
42. #16810838C22semidirect
43. #16810823C22semidirect
44. #16810818C22semidirect
45. #16810783C22semidirect
46. #16810773C22semidirect
47. #16810766C22semidirect
48. #16810756C22semidirect
49. #16810684C22semidirect
50. C2×C4⋊#88322C22semidirect
51. C2×C4⋊#88322C22semidirect
52. C2×#13133140C22semidirect
53. C2×#13133140C22semidirect
58. C2×#13133137C22semidirect
59. C2×#13133137C22semidirect
62. C2×#13133128C22semidirect
63. C2×C4×#88322C22semidirect
65. C53×#542C22semidirect
66. C2×C4⋊Q8×C53C22semidirect
69. C2×#124×C53C22semidirect
74. C2×C4×Q8×C53C22semidirect
75. C2×C4×D4×C53C22semidirect
98. C2×#11719925C23semidirect
100. C2×#11719923C23semidirect
106. C2×#11719924C23semidirect
112. C2×#11719922C23semidirect
133. C4⋊#88322C23semidirect
134. C4⋊#88322C23semidirect
135. #13133140C23semidirect
136. #13133140C23semidirect
141. #13133137C23semidirect
142. #13133137C23semidirect
145. #13133128C23semidirect
146. C4×#88322C23semidirect
154. C4⋊Q8×C53C23semidirect
158. #124×C53C23semidirect
166. C4×Q8×C53C23semidirect
168. C4×D4×C53C23semidirect
422. C2×#542D53semidirect
440. C2×C53#3224semidirect
458. #542C2×D53semidirect
461. C2×C4⋊Q8C2×D53semidirect
468. C2×#124C2×D53semidirect
477. C2×C4×Q8C2×D53semidirect
478. C2×C4×D4C2×D53semidirect
507. C53C2×#3224semidirect
555. C4⋊Q8C22×D53semidirect
567. #124C22×D53semidirect
579. C4×Q8C22×D53semidirect
581. C4×D4C22×D53semidirect
857. C2#20285803direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111922
#202858032
C2×#168110132
C2×#168110052
C2×#168109852
C2×#168109712
C2×#168108452
C2×#168108232
C2×#168108382
C2×#168108182
C2×#168107832
C2×#168107662
C2×#168107732
C2×#168107562
C2×#168106842
C2×C53×#5422
C2×#322453