Finite Group Databasebeta

← C2×#20287220 #28262692

Subgroups — C2×#20287220 #28262692

Order 13568.

1962 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811338C211yesmaximal, characteristic, complemented
2C2×#16811323C211yesmaximal, characteristic, complemented
3#20287220C2116yesmaximal, direct product factor
4C2×#16811032C211yesmaximal, characteristic, complemented
5C2×#16810946C211yesmaximal, characteristic, complemented
6C2×#16810946C211yesmaximal, characteristic, complemented
7C2×#16810945C211yesmaximal, characteristic, complemented
8C2×#16810935C211yesmaximal, characteristic, complemented
9C2×#16810923C211yesmaximal, characteristic, complemented
10C2×#16810903C211yesmaximal, characteristic, complemented
11C2×#16810873C211yesmaximal, characteristic, complemented
12C2×#16810856C211yesmaximal, characteristic, complemented
13C2×#16810696C211yesmaximal, characteristic, complemented
14C2×#16810662C211yesmaximal, characteristic, complemented
15C2×#16810658C211yesmaximal, characteristic, complemented
16C2×C53×#442C211yesmaximal, characteristic, complemented
17C22×#11719912C2211yescharacteristic
18C22×C8×D53C2211yescharacteristic
19#16811338—24no—
20#16811338C2218yescomplemented
21#16811323—24no—
22#16811323C2218yescomplemented
23C2×#13133217C2211yescharacteristic
24C2×#13133210—21no—
25C2×#13133209C2211yescharacteristic
26C2×#13133203—21no—
27C2×#13133203—21no—
28C2×#13133200—21no—
29C2×#13133191—21no—
30C2×#13133190—21no—
31C2×#13133188C2211yescharacteristic
32C2×#13133188C2211yescharacteristic
33C2×#13133188C2211yescharacteristic
34C2×#13133188C2211yescharacteristic
35C2×C4×D212C2211yescharacteristic
36C2×C4×C22⋊D53—21no—
37C2×#13133176—21no—
38C2×#13133175C2211yescharacteristic
39C2×#13133175C2211yescharacteristic
40C2×#13133175C2211yescharacteristic
41C2×C4⋊C4×D53C2211yescharacteristic
42#16811032C2218yescomplemented
43#16810946C2218yescomplemented
44#16810946C2218yescomplemented
45#16810945C2218yescomplemented
46#16810935C2218yescomplemented
47#16810923C2218yescomplemented
48#16810903C2218yescomplemented
49#16810873C2218yescomplemented
50#16810856C2218yescomplemented
51#16810696C2218yescomplemented
52#16810662C2218yescomplemented
53#16810658C2218yescomplemented
54C2×#13133151C2211yescharacteristic
55C2×#13133151C2211yescharacteristic
56C2×#13133150C2211yescharacteristic
57C2×#13133150C2211yescharacteristic
58C2×#13133150C2211yescharacteristic
59C2×#13133149C2211yescharacteristic
60C2×#13133149C2211yescharacteristic
61C2×#13133148C2211yescharacteristic
62C2×C4⋊#88322C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×#13133138C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133129C2211yescharacteristic
69C22×D8×C53C2211yescharacteristic
70C2×C4×D4×C53C2211yescharacteristic
71C2×C4×D4×C53C2211yescharacteristic
72C53×#442C2218yescomplemented
73C2×#106×C53C2211yescharacteristic
74C2×#102×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×D212D411yescharacteristic
79C22×C22⋊D53—21no—
80C22×C22⋊D53—21no—
81C22×C22⋊D53—21no—
82C22×C22⋊D53—21no—
83C22×C4×D53—21no—
84C22×C4×D53C2311yescharacteristic
85C22×C4×D53C2311yescharacteristic
86C2×#11719912—24no—
87C2×#11719912C2314yes—
88C22×#88322C2311yescharacteristic
89C22×#88322C2311yescharacteristic
90C2×C8×D53—24no—
91C2×C8×D53C2314yes—
92#13133217—22no—
93#13133217C2314yes—
94#13133210—28no—
95#13133209—22no—
96#13133209C2314yes—
97#13133203—28no—
98#13133203—28no—
99#13133200—28no—
100#13133191—28no—
101#13133190—28no—
102#13133188—22no—
103#13133188—22no—
104#13133188—22no—
105#13133188—22no—
106#13133188C2314yes—
107#13133188C2314yes—
108#13133188C2314yes—
109#13133188C2314yes—
110C4×D212D414yes—
111C4×D212C2314yes—
112C4×C22⋊D53—28no—
113#13133176—28no—
114#13133175—22no—
115#13133175—22no—
116#13133175—22no—
117#13133175C2314yes—
118#13133175C2314yes—
119#13133175C2314yes—
120C2×C4⋊Dic53—21no—
121C2×C4⋊Dic53D411yescharacteristic
122C2×C4⋊Dic53C2311yescharacteristic
123C2×C4⋊Dic53C2311yescharacteristic
124C2×C4⋊Dic53C2311yescharacteristic
125C2×C4⋊Dic53C2311yescharacteristic
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919—21no—
129C4⋊C4×D53—22no—
130C4⋊C4×D53C2314yes—
131C2×C22⋊Dic53—21no—
132C2×C22⋊Dic53—21no—
133C2×C22⋊Dic53—21no—
134C2×C22⋊Dic53—21no—
135C2×#11719921—21no—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921D411yescharacteristic
139C2×#11719921D411yescharacteristic
140C2×C4×Dic53—21no—
141C2×C4×Dic53—21no—
142C2×C4×Dic53—21no—
143#13133151C2314yes—
144#13133151C2314yes—
145#13133150C2314yes—
146#13133150C2314yes—
147#13133150C2314yes—
148#13133149C2314yes—
149#13133149C2314yes—
150#13133148C2314yes—
151C4⋊#88322C2314yes—
152#13133138C2314yes—
153#13133138C2314yes—
154#13133138C2314yes—
155#13133138C2314yes—
156#13133129C2314yes—
157#13133129C2314yes—
158C22×D4×C53C2311yescharacteristic
159C22×D4×C53C2311yescharacteristic
160C23×C4×C53—21no—
161C23×C4×C53—21no—
162C2×D8×C53—24no—
163C2×D8×C53C2314yes—
164C22×C8×C53C2311yescharacteristic
165C22×C8×C53C2311yescharacteristic
166C4×D4×C53—22no—
167C4×D4×C53—22no—
168C4×D4×C53C2314yes—
169C4×D4×C53C2314yes—
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C22⋊C4×C53—21no—
173C2×C22⋊C4×C53—21no—
174C2×C42×C53C2311yescharacteristic
175#106×C53C2314yes—
176#102×C53C2314yes—
177#102×C53C2314yes—
178#97×C53C2314yes—
179C24×C53—21no—
180C24×C53—21no—
181C23×D53C2×D411yescharacteristic
182C23×D53C2×D411yescharacteristic
183C2×D4×C53—21no—
184C2×D4×C53—21no—
185C2×D4×C53—22no—
186C2×D4×C53—22no—
187C2×D4×C53—22no—
188C2×D4×C53—22no—
189C2×D4×C53C2412yes—
190C2×D4×C53C2412yes—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—24no—
194C22×C4×C53—24no—
195C22×C4×C53—44no—
196C22×C4×C53—82no—
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2411yescharacteristic
200C2×C22⋊D53—24no—
201C2×C22⋊D53—24no—
202C2×C22⋊D53—24no—
203C2×C22⋊D53—24no—
204C2×C22⋊D53—44no—
205C2×C22⋊D53—82no—
206C2×C22⋊D53—82no—
207C2×C22⋊D53—82no—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53—21no—
211C22×Dic53—21no—
212C22×Dic53C2×D411yescharacteristic
213C22×Dic53C2×D411yescharacteristic
214C2×D212—42no—
215C2×D212C2×D414yes—
216C2×C4×D53—22no—
217C2×C4×D53—22no—
218C2×C4×D53—22no—
219C2×C4×D53—22no—
220C2×C4×D53—24no—
221C2×C4×D53—82no—
222C2×C4×D53C2×D412yes—
223C2×C4×D53C2×D412yes—
224C2×C4×D53C2412yes—
225C2×C4×D53C2412yes—
226C2×Dic106—24no—
227C2×Dic106—82no—
228D8×C53—28no—
229C2×C8×C53—22no—
230C2×C8×C53#4114yes—
231C2×C8×C53C2412yes—
232C2×C8×C53C2412yes—
233C4⋊C4×C53—21no—
234C4⋊C4×C53—21no—
235C4⋊C4×C53C2412yes—
236C4⋊C4×C53C2412yes—
237C22⋊C4×C53—24no—
238C22⋊C4×C53—24no—
239C42×C53C2×D412yes—
240C42×C53C2412yes—
241C22⋊Dic53—24no—
242C22⋊Dic53—24no—
243C22⋊Dic53—24no—
244C22⋊Dic53—24no—
245#11719921—24no—
246#11719921—24no—
247#11719921—24no—
248#11719921C2×D414yes—
249#11719921C2×D414yes—
250C4⋊Dic53—21no—
251C4⋊Dic53—24no—
252C4⋊Dic53—21no—
253C4⋊Dic53—21no—
254C4⋊Dic53—21no—
255C4⋊Dic53C2×D414yes—
256C4⋊Dic53C2412yes—
257C4⋊Dic53C2412yes—
258C4⋊Dic53C2412yes—
259C4⋊Dic53C2412yes—
260#11719919—24no—
261#11719919—24no—
262#11719919—24no—
263C4×Dic53—24no—
264C4×Dic53—24no—
265C4×Dic53—24no—
266C2×#88322—22no—
267C2×#88322—22no—
268C2×#88322C2412yes—
269C2×#88322C2412yes—
270#11719912—28no—
271C8×D53—28no—
272C23×C53—22no—
273C23×C53—22no—
274C23×C53—42no—
275C23×C53—42no—
276C23×C53—42no—
277C23×C53—42no—
278C23×C53—42no—
279C23×C53—42no—
280C23×C53C22×D411yescharacteristic
281C22×D53—22no—
282C22×D53—22no—
283C22×D53—22no—
284C22×D53—22no—
285C22×D53—22no—
286C22×D53—22no—
287C22×D53C22×D412yes—
288C22×D53C22×D412yes—
289D4×C53—22no—
290D4×C53—22no—
291D4×C53—22no—
292D4×C53—22no—
293D4×C53—42no—
294D4×C53—42no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—48no—
300C2×C4×C53—42no—
301C2×C4×C53—42no—
302C2×C4×C53—84no—
303C2×C4×C53C22×D412yes—
304C2×C4×C53C22×D412yes—
305C2×C4×C53C22×D411yescharacteristic
306C2×C4×C53C2×#4112yes—
307C2×C4×C532−1+412yes—
308C2×C4×C53C2511yescharacteristic
309C22⋊D53—48no—
310C22⋊D53—84no—
311C22⋊D53—84no—
312C22⋊D53—84no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—42no—
320C2×Dic53—42no—
321C2×Dic53—42no—
322C2×Dic53—42no—
323C2×Dic53C22×D412yes—
324C2×Dic53C22×D412yes—
325D212—44no—
326C4×D53—24no—
327C4×D53—24no—
328C4×D53—22no—
329C4×D53—22no—
330C4×D53—22no—
331C4×D53—22no—
332C4×D53—84no—
333Dic106—84no—
334C8×C53—22no—
335C8×C53C2×#4114yes—
336#88322—22no—
337#88322—22no—
338C2×#3347—531nomaximal, Sylow
339C22×C53—42no—
340C22×C53—42no—
341C22×C53—42no—
342C22×C53—42no—
343C22×C53—42no—
344C22×C53—42no—
345C22×C53—84no—
346C22×C53—84no—
347C22×C53#54712yes—
348C22×C53#57512yes—
349C22×C53#57612yes—
350C22×C53C23×D411yescharacteristic
351C2×D53—22no—
352C2×D53—22no—
353C2×D53—22no—
354C2×D53—22no—
355C2×D53—22no—
356C2×D53—22no—
357C2×D53—44no—
358C2×D53—44no—
359C4×C53—22no—
360C4×C53—22no—
361C4×C53—42no—
362C4×C53—42no—
363C4×C53#54712yes—
364C4×C53C22×#4111yescharacteristic
365C4×C53C2×2−1+411yescharacteristic
366Dic53—22no—
367Dic53—22no—
368Dic53—42no—
369Dic53—42no—
370Dic53—42no—
371Dic53—42no—
372C2×#555—531no—
373C2×#553—531no—
374#3347—5316no—
375C2×#501—531no—
376C2×#482—531no—
377C2×#482—531no—
378C2×#482—531no—
379C2×#480—531no—
380C2×#478—531no—
381C2×#474—531no—
382C2×#469—531no—
383C2×#466—531no—
384C2×#442D5311yescharacteristic, complemented
385C2×#435—531no—
386C2×#428—531no—
387C2×#427—531no—
388C2×C53—82no—
389C2×C53—82no—
390C2×C53#334714yescomplemented
391C2×C53C2×#54711yescharacteristic
392C2×C53C2×#57511yescharacteristic
393C2×C53C2×#57611yescharacteristic
394D53—42no—
395D53—42no—
396C22×D8C2×D5311yescharacteristic
397C22×M16—531no—
398C23×C8—531no—
399#555—538no—
400#555—1064no—
401#553—538no—
402#553—1064no—
403C2×C4⋊Q8—531no—
404C2×#126—1061no—
405C2×#125—531no—
406C2×#124—1061no—
407C2×#124—1061no—
408C2×#123—1061no—
409C2×#121—531no—
410C2×#121—531no—
411C2×#121—531no—
412C2×#121—531no—
413C2×#121—1061no—
414C2×#121—1061no—
415C2×C4×D4—531no—
416C2×C4×D4—1061no—
417C2×C4×D4C2×D5311yescharacteristic
418C2×C4×D4C2×D5311yescharacteristic
419C2×#117—531no—
420C2×#117—531no—
421C2×#117—531no—
422C2×#117—1061no—
423C22×C4⋊C4—531no—
424#501—538no—
425#482—538no—
426#482—538no—
427#482—538no—
428#480—538no—
429#478—538no—
430#474—538no—
431#469—538no—
432#466—538no—
433#442C2×D5318yescomplemented
434#435—538no—
435#428—538no—
436#427—538no—
437C2×#107—531no—
438C2×#107—531no—
439C2×#107—531no—
440C2×#107—531no—
441C2×#107—531no—
442C2×#106—531no—
443C2×#106—531no—
444C2×#106—531no—
445C2×#106C2×D5311yescharacteristic
446C2×C4⋊C8—531no—
447C2×#102—531no—
448C2×#102—531no—
449C2×#102—531no—
450C2×#102—531no—
451C2×#102C2×D5311yescharacteristic
452C2×#102C2×D5311yescharacteristic
453C2×C22⋊C8—531no—
454C2×C22⋊C8—531no—
455C2×#97C2×D5311yescharacteristic
456C53C2×#334711yescharacteristic, complemented, Sylow
457C22×Q8—1061no—
458C22×D4—531no—
459C22×D4—1061no—
460C22×D4—1061no—
461C22×D4—1061no—
462C22×D4—1061no—
463C22×D4C22×D5311yescharacteristic
464C22×D4C22×D5311yescharacteristic
465C23×C4—21no—
466C23×C4—21no—
467C23×C4—531no—
468C23×C4—531no—
469C23×C4—1061no—
470C2×D8—24no—
471C2×D8C22×D5314yes—
472C2×M16—534no—
473C2×M16—1064no—
474C22×C8—531no—
475C22×C8—531no—
476C22×C8—534no—
477C22×C8—1064no—
478C22×C8C22×D5311yescharacteristic
479C22×C8C22×D5311yescharacteristic
480C4⋊Q8—534no—
481C4⋊Q8—1062no—
482#126—1068no—
483#125—534no—
484#125—1062no—
485#124—1068no—
486#124—1068no—
487#123—1068no—
488#121—534no—
489#121—534no—
490#121—534no—
491#121—534no—
492#121—1068no—
493#121—1068no—
494#121—1062no—
495#121—1062no—
496#121—1062no—
497#121—1062no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—534no—
501C4×D4—534no—
502C4×D4—1068no—
503C4×D4C22×D5314yes—
504C4×D4C22×D5314yes—
505#117—534no—
506#117—534no—
507#117—534no—
508#117—1062no—
509#117—1062no—
510#117—1062no—
511#117—1068no—
512C2×C4⋊C4—531no—
513C2×C4⋊C4—531no—
514C2×C4⋊C4—531no—
515C2×C4⋊C4—531no—
516C2×C4⋊C4—531no—
517C2×C4⋊C4—534no—
518C2×C4⋊C4—1062no—
519C2×C4⋊C4—1061no—
520C2×C4⋊C4—1061no—
521C2×C4⋊C4—1061no—
522C2×C4⋊C4—1061no—
523C2×C4⋊C4C22×D5311yescharacteristic
524C2×C4⋊C4C22×D5311yescharacteristic
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—531no—
528C2×C22⋊C4—531no—
529C2×C22⋊C4—1061no—
530C2×C22⋊C4—1061no—
531C2×C22⋊C4—1061no—
532C2×C22⋊C4—1061no—
533C2×C22⋊C4—1061no—
534C2×C22⋊C4—1061no—
535C2×C22⋊C4—1061no—
536C2×C42—1061no—
537C2×C42—1061no—
538C2×C42—1061no—
539C2×C42C22×D5311yescharacteristic
540#107—534no—
541#107—534no—
542#107—534no—
543#107—534no—
544#107—534no—
545#106—534no—
546#106—534no—
547#106—534no—
548#106C22×D5314yes—
549C4⋊C8—534no—
550#102—534no—
551#102—534no—
552#102—534no—
553#102—534no—
554#102C22×D5314yes—
555#102C22×D5314yes—
556C22⋊C8—534no—
557C22⋊C8—534no—
558#97C22×D5314yes—
559C24—21no—
560C24—21no—
561C24—531no—
562C24—531no—
563C2×Q8—1064no—
564C2×Q8—4242no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—534no—
572C2×D4—1064no—
573C2×D4—1064no—
574C2×D4—1064no—
575C2×D4—1064no—
576C2×D4—4242no—
577C2×D4—4242no—
578C2×D4—4242no—
579C2×D4—2122no—
580C2×D4—2124no—
581C2×D4C23×D5312yes—
582C2×D4C23×D5312yes—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—44no—
588C22×C4—82no—
589C22×C4—531no—
590C22×C4—531no—
591C22×C4—532no—
592C22×C4—532no—
593C22×C4—532no—
594C22×C4—532no—
595C22×C4—1064no—
596C22×C4—1062no—
597C22×C4—1062no—
598C22×C4—1062no—
599C22×C4—1062no—
600C22×C4—1061no—
601C22×C4—1061no—
602C22×C4—1061no—
603C22×C4—1061no—
604C22×C4—4242no—
605C22×C4D4×D5311yescharacteristic
606C22×C4D4×D5311yescharacteristic
607C22×C4C23×D5311yescharacteristic
608D8—28no—
609M16—1068no—
610C2×C8—22no—
611C2×C8—532no—
612C2×C8—532no—
613C2×C8—1062no—
614C2×C8—1062no—
615C2×C8—1068no—
616C2×C8#1171994514yes—
617C2×C8C23×D5312yes—
618C2×C8C23×D5312yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—534no—
622C4⋊C4—532no—
623C4⋊C4—532no—
624C4⋊C4—532no—
625C4⋊C4—532no—
626C4⋊C4—1064no—
627C4⋊C4—1061no—
628C4⋊C4—1061no—
629C4⋊C4—1061no—
630C4⋊C4—1061no—
631C4⋊C4—1064no—
632C4⋊C4—1064no—
633C4⋊C4—1064no—
634C4⋊C4C23×D5312yes—
635C4⋊C4C23×D5312yes—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—534no—
639C22⋊C4—534no—
640C22⋊C4—1064no—
641C22⋊C4—1064no—
642C22⋊C4—1064no—
643C22⋊C4—1064no—
644C22⋊C4—1064no—
645C22⋊C4—1064no—
646C22⋊C4—1064no—
647C42—1064no—
648C42—1064no—
649C42—1064no—
650C42D4×D5312yes—
651C42C23×D5312yes—
652C23—22no—
653C23—22no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—532no—
661C23—532no—
662C23—1062no—
663C23—1062no—
664C23—1062no—
665C23—1062no—
666C23—1062no—
667C23—1062no—
668C23C2×D4×D5311yescharacteristic
669Q8—4244no—
670D4—22no—
671D4—22no—
672D4—22no—
673D4—22no—
674D4—42no—
675D4—42no—
676D4—4244no—
677D4—4244no—
678D4—4244no—
679D4—2124no—
680D4—2128no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—48no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—84no—
689C2×C4—532no—
690C2×C4—532no—
691C2×C4—1062no—
692C2×C4—1062no—
693C2×C4—1064no—
694C2×C4—1064no—
695C2×C4—1062no—
696C2×C4—1062no—
697C2×C4—1062no—
698C2×C4—1062no—
699C2×C4—1062no—
700C2×C4—1062no—
701C2×C4—1062no—
702C2×C4—1062no—
703C2×C4—4244no—
704C2×C4—2122no—
705C2×C4—2122no—
706C2×C4—2122no—
707C2×C4—2122no—
708C2×C4C2×D4×D5312yes—
709C2×C4C2×D4×D5312yes—
710C2×C4C2×D4×D5311yescharacteristic
711C2×C4C2×#1171994512yes—
712C2×C4#1313326412yes—
713C2×C4C24×D5311yescharacteristic
714C8—22no—
715C8—1062no—
716C8—1062no—
717C8C2×#1171994514yes—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—84no—
725C22—84no—
726C22—1062no—
727C22—1062no—
728C22—1062no—
729C22—1062no—
730C22—1062no—
731C22—1062no—
732C22—2124no—
733C22—2124no—
734C22#1681127812yes—
735C22#1681141912yes—
736C22#1681142712yes—
737C22C22×D4×D5311yescharacteristic
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—1062no—
743C4—1062no—
744C4—2122no—
745C4—2122no—
746C4—2122no—
747C4—2122no—
748C4#1681127812yes—
749C4C22×#1171994511yescharacteristic
750C4C2×#1313326411yescharacteristic
751C2—82no—
752C2—82no—
753C2—2122no—
754C2—2122no—
755C2#2028722014yesdirect product factor
756C2C2×#1681127811yescharacteristic
757C2C2×#1681141911yescharacteristic
758C2C2×#1681142711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#442C2
socleC23×C53C22×D4
hypercenterC2×#442D53
hypocenterC53C2×#3347
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#16811338C2semidirect
2. C2×#16811323C2semidirect
3. #20287220C2direct (N × H)
4. C2×#16811032C2semidirect
5. C2×#16810946C2semidirect
6. C2×#16810946C2semidirect
7. C2×#16810945C2semidirect
8. C2×#16810935C2semidirect
9. C2×#16810923C2semidirect
10. C2×#16810903C2semidirect
11. C2×#16810873C2semidirect
12. C2×#16810856C2semidirect
13. C2×#16810696C2semidirect
14. C2×#16810662C2semidirect
15. C2×#16810658C2semidirect
16. C2×C53×#442C2semidirect
20. #16811338C22semidirect
22. #16811323C22semidirect
42. #16811032C22semidirect
43. #16810946C22semidirect
44. #16810946C22semidirect
45. #16810945C22semidirect
46. #16810935C22semidirect
47. #16810923C22semidirect
48. #16810903C22semidirect
49. #16810873C22semidirect
50. #16810856C22semidirect
51. #16810696C22semidirect
52. #16810662C22semidirect
53. #16810658C22semidirect
72. C53×#442C22semidirect
384. C2×#442D53semidirect
390. C2×C53#3347semidirect
433. #442C2×D53semidirect
456. C53C2×#3347semidirect
755. C2#20287220direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113382
C2×#168113232
#202872202
C2×#168110322
C2×#168109462
C2×#168109452
C2×#168109352
C2×#168109232
C2×#168109032
C2×#168108732
C2×#168108562
C2×#168106962
C2×#168106622
C2×#168106582
C2×C53×#4422
C2×#334753