Finite Group Databasebeta

← C2×#20287217 #28262689

Subgroups — C2×#20287217 #28262689

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×#16811319C211yesmaximal, characteristic, complemented
3#20287217C2116yesmaximal, direct product factor
4C2×#16811032C211yesmaximal, characteristic, complemented
5C2×#16810948C211yesmaximal, characteristic, complemented
6C2×#16810948C211yesmaximal, characteristic, complemented
7C2×#16810948C211yesmaximal, characteristic, complemented
8C2×#16810937C211yesmaximal, characteristic, complemented
9C2×#16810924C211yesmaximal, characteristic, complemented
10C2×#16810904C211yesmaximal, characteristic, complemented
11C2×#16810876C211yesmaximal, characteristic, complemented
12C2×#16810859C211yesmaximal, characteristic, complemented
13C2×#16810736C211yesmaximal, characteristic, complemented
14C2×#16810665C211yesmaximal, characteristic, complemented
15C2×#16810661C211yesmaximal, characteristic, complemented
16C2×C53×#435C211yesmaximal, characteristic, complemented
17C22×D424C2211yescharacteristic
18#16811338—24no—
19#16811338C2218yescomplemented
20#16811319—24no—
21#16811319C2218yescomplemented
22C2×#13133217C2211yescharacteristic
23C2×#13133212—21no—
24C2×#13133209C2211yescharacteristic
25C2×#13133203—21no—
26C2×#13133203—21no—
27C2×#13133199—21no—
28C2×#13133191C2211yescharacteristic
29C2×#13133191C2211yescharacteristic
30C2×#13133191C2211yescharacteristic
31C2×#13133191C2211yescharacteristic
32C2×#13133189—21no—
33C2×#13133188—21no—
34C2×C4×D212C2211yescharacteristic
35C2×C4×D212C2211yescharacteristic
36C2×#13133177—21no—
37C2×#13133176C2211yescharacteristic
38C2×#13133176C2211yescharacteristic
39C2×#13133176C2211yescharacteristic
40C2×#13133175—21no—
41C22×C4⋊Dic53C2211yescharacteristic
42#16811032C2218yescomplemented
43#16810948C2218yescomplemented
44#16810948C2218yescomplemented
45#16810948C2218yescomplemented
46#16810937C2218yescomplemented
47#16810924C2218yescomplemented
48#16810904C2218yescomplemented
49#16810876C2218yescomplemented
50#16810859C2218yescomplemented
51#16810736C2218yescomplemented
52#16810665C2218yescomplemented
53#16810661C2218yescomplemented
54C2×#13133151C2211yescharacteristic
55C2×#13133151C2211yescharacteristic
56C2×#13133151C2211yescharacteristic
57C2×#13133151C2211yescharacteristic
58C2×#13133151C2211yescharacteristic
59C2×#13133149C2211yescharacteristic
60C2×#13133149C2211yescharacteristic
61C2×#13133149C2211yescharacteristic
62C2×#13133149C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133139C2211yescharacteristic
65C2×#13133139C2211yescharacteristic
66C2×#13133139C2211yescharacteristic
67C2×#13133139C2211yescharacteristic
68C2×#13133139C2211yescharacteristic
69C22×M16×C53C2211yescharacteristic
70C23×C8×C53C2211yescharacteristic
71C2×C4×D4×C53C2211yescharacteristic
72C53×#435C2218yescomplemented
73C2×C4⋊C8×C53C2211yescharacteristic
74C2×C22⋊C8×C53C2211yescharacteristic
75C2×C22⋊C8×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×D212C2311yescharacteristic
79C22×D212C2311yescharacteristic
80C22×C22⋊D53—21no—
81C22×C22⋊D53—21no—
82C22×C22⋊D53—21no—
83C22×C22⋊D53—21no—
84C23×Dic53—21no—
85C22×C4×D53—21no—
86C22×C4×D53—21no—
87C2×D424—24no—
88C2×D424C2314yes—
89#13133217—22no—
90#13133217C2314yes—
91#13133212—28no—
92#13133209—22no—
93#13133209C2314yes—
94#13133203—28no—
95#13133203—28no—
96#13133199—28no—
97#13133191—22no—
98#13133191—22no—
99#13133191—22no—
100#13133191—22no—
101#13133191C2314yes—
102#13133191C2314yes—
103#13133191C2314yes—
104#13133191C2314yes—
105#13133189—28no—
106#13133188—28no—
107C4×D212—22no—
108C4×D212—22no—
109C4×D212C2314yes—
110C4×D212C2314yes—
111#13133177—28no—
112#13133176—22no—
113#13133176—22no—
114#13133176—22no—
115#13133176C2314yes—
116#13133176C2314yes—
117#13133176C2314yes—
118#13133175—28no—
119C2×C4⋊Dic53—22no—
120C2×C4⋊Dic53—21no—
121C2×C4⋊Dic53—21no—
122C2×C4⋊Dic53C2314yes—
123C2×C4⋊Dic53C2311yescharacteristic
124C2×C4⋊Dic53C2311yescharacteristic
125C2×C4⋊Dic53C2311yescharacteristic
126C2×C4⋊Dic53C2311yescharacteristic
127C2×C4⋊Dic53C2311yescharacteristic
128C2×C4⋊Dic53C2311yescharacteristic
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×C22⋊Dic53—21no—
132C2×C22⋊Dic53—21no—
133C2×C22⋊Dic53—21no—
134C2×#11719921—21no—
135C2×#11719921—21no—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×C4×Dic53—21no—
141C2×C4×Dic53—21no—
142C2×C4×Dic53—21no—
143#13133151C2314yes—
144#13133151C2314yes—
145#13133151C2314yes—
146#13133151C2314yes—
147#13133151C2314yes—
148#13133149C2314yes—
149#13133149C2314yes—
150#13133149C2314yes—
151#13133149C2314yes—
152#13133139C2314yes—
153#13133139C2314yes—
154#13133139C2314yes—
155#13133139C2314yes—
156#13133139C2314yes—
157#13133139C2314yes—
158C22×D4×C53D411yescharacteristic
159C23×C4×C53C2311yescharacteristic
160C23×C4×C53C2311yescharacteristic
161C2×M16×C53—24no—
162C2×M16×C53C2314yes—
163C22×C8×C53—24no—
164C22×C8×C53C2314yes—
165C22×C8×C53C2311yescharacteristic
166C22×C8×C53C2311yescharacteristic
167C22×C8×C53C2311yescharacteristic
168C22×C8×C53C2311yescharacteristic
169C4×D4×C53D414yes—
170C4×D4×C53C2314yes—
171C2×C4⋊C4×C53D411yescharacteristic
172C2×C22⋊C4×C53D411yescharacteristic
173C2×C22⋊C4×C53D411yescharacteristic
174C2×C42×C53C2311yescharacteristic
175C4⋊C8×C53C2314yes—
176C22⋊C8×C53C2314yes—
177C22⋊C8×C53C2314yes—
178#97×C53C2314yes—
179C24×C53C2×D411yescharacteristic
180C24×C53C2×D411yescharacteristic
181C23×D53—21no—
182C23×D53—21no—
183C2×D4×C53—42no—
184C2×D4×C53C2×D414yes—
185C22×C4×C53—22no—
186C22×C4×C53—22no—
187C22×C4×C53—22no—
188C22×C4×C53—22no—
189C22×C4×C53C2×D411yescharacteristic
190C22×C4×C53C2×D411yescharacteristic
191C22×C4×C53C2×D411yescharacteristic
192C22×C4×C53C2×D411yescharacteristic
193C22×C4×C53C2×D412yes—
194C22×C4×C53C2×D412yes—
195C22×C4×C53C2412yes—
196C22×C4×C53C2412yes—
197C22×C4×C53C2411yescharacteristic
198C2×C22⋊D53—24no—
199C2×C22⋊D53—24no—
200C2×C22⋊D53—24no—
201C2×C22⋊D53—24no—
202C2×C22⋊D53—44no—
203C2×C22⋊D53—82no—
204C2×C22⋊D53—82no—
205C2×C22⋊D53—82no—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53—21no—
211C22×Dic53—21no—
212C22×Dic53—24no—
213C22×Dic53—82no—
214C2×D212—22no—
215C2×D212—22no—
216C2×D212—22no—
217C2×D212—22no—
218C2×D212—21no—
219C2×D212—21no—
220C2×D212C2412yes—
221C2×D212C2412yes—
222C2×C4×D53—24no—
223C2×C4×D53—24no—
224C2×C4×D53—44no—
225C2×C4×D53—82no—
226C2×Dic106—24no—
227C2×Dic106—82no—
228M16×C53—28no—
229C2×C8×C53—22no—
230C2×C8×C53—22no—
231C2×C8×C53—22no—
232C2×C8×C53—28no—
233C2×C8×C53#4114yes—
234C2×C8×C53C2412yes—
235C2×C8×C53C2412yes—
236C2×C8×C53C2412yes—
237C2×C8×C53C2412yes—
238C4⋊C4×C53C2×D414yes—
239C22⋊C4×C53C2×D414yes—
240C22⋊C4×C53C2×D414yes—
241C42×C53C2×D412yes—
242C42×C53C2412yes—
243C22⋊Dic53—24no—
244C22⋊Dic53—24no—
245C22⋊Dic53—24no—
246#11719921—24no—
247#11719921—24no—
248#11719921—24no—
249#11719921—24no—
250#11719921—24no—
251#11719921—24no—
252C4⋊Dic53—21no—
253C4⋊Dic53—21no—
254C4⋊Dic53—24no—
255C4⋊Dic53—24no—
256C4⋊Dic53—21no—
257C4⋊Dic53—21no—
258C4⋊Dic53—21no—
259C4⋊Dic53—21no—
260C4⋊Dic53C2412yes—
261C4⋊Dic53C2412yes—
262C4⋊Dic53C2412yes—
263C4⋊Dic53C2412yes—
264C4⋊Dic53C2412yes—
265C4⋊Dic53C2412yes—
266#11719919—24no—
267#11719919—24no—
268C4×Dic53—24no—
269C4×Dic53—24no—
270C4×Dic53—24no—
271D424—28no—
272C23×C53—22no—
273C23×C53—22no—
274C23×C53—22no—
275C23×C53—22no—
276C23×C53—22no—
277C23×C53—22no—
278C23×C53C22×D412yes—
279C23×C53C22×D412yes—
280C23×C53C22×D411yescharacteristic
281C22×D53—22no—
282C22×D53—22no—
283C22×D53—42no—
284C22×D53—42no—
285C22×D53—42no—
286C22×D53—42no—
287C22×D53—42no—
288C22×D53—42no—
289D4×C53—44no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—24no—
295C2×C4×C53—24no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53C22×D412yes—
301C2×C4×C53C22×D412yes—
302C2×C4×C53C22×D412yes—
303C2×C4×C53C22×D412yes—
304C2×C4×C53C22×D411yescharacteristic
305C2×C4×C53C2×#4112yes—
306C2×C4×C532−1+412yes—
307C2×C4×C53C2511yescharacteristic
308C22⋊D53—48no—
309C22⋊D53—84no—
310C22⋊D53—84no—
311C22⋊D53—84no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—42no—
319C2×Dic53—42no—
320C2×Dic53—42no—
321C2×Dic53—42no—
322C2×Dic53—42no—
323C2×Dic53—42no—
324C2×Dic53—84no—
325D212—22no—
326D212—22no—
327D212—22no—
328D212—22no—
329D212—42no—
330D212—42no—
331C4×D53—48no—
332C4×D53—84no—
333Dic106—84no—
334C8×C53—22no—
335C8×C53—22no—
336C8×C53—22no—
337C8×C53C2×#4114yes—
338C2×#3347—531nomaximal, Sylow
339C22×C53—22no—
340C22×C53—22no—
341C22×C53—22no—
342C22×C53—22no—
343C22×C53—22no—
344C22×C53—22no—
345C22×C53—44no—
346C22×C53—44no—
347C22×C53#54712yes—
348C22×C53#57512yes—
349C22×C53#57612yes—
350C22×C53C23×D411yescharacteristic
351C2×D53—42no—
352C2×D53—42no—
353C2×D53—42no—
354C2×D53—42no—
355C2×D53—42no—
356C2×D53—42no—
357C2×D53—84no—
358C2×D53—84no—
359C4×C53—22no—
360C4×C53—22no—
361C4×C53—22no—
362C4×C53—22no—
363C4×C53#54712yes—
364C4×C53C22×#4111yescharacteristic
365C4×C53C2×2−1+411yescharacteristic
366Dic53—42no—
367Dic53—42no—
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×#442—531no—
385C2×#435D5311yescharacteristic, complemented
386C2×#428—531no—
387C2×#427—531no—
388C2×C53—42no—
389C2×C53—42no—
390C2×C53#334714yescomplemented
391C2×C53C2×#54711yescharacteristic
392C2×C53C2×#57511yescharacteristic
393C2×C53C2×#57611yescharacteristic
394D53—82no—
395D53—82no—
396C22×D8—531no—
397C22×M16C2×D5311yescharacteristic
398C23×C8C2×D5311yescharacteristic
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—531no—
417C2×C4×D4—1061no—
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#442—538no—
434#435C2×D5318yescomplemented
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×#106—531no—
446C2×C4⋊C8C2×D5311yescharacteristic
447C2×#102—531no—
448C2×#102—531no—
449C2×#102—531no—
450C2×#102—531no—
451C2×#102—531no—
452C2×#102—531no—
453C2×C22⋊C8C2×D5311yescharacteristic
454C2×C22⋊C8C2×D5311yescharacteristic
455C2×#97C2×D5311yescharacteristic
456C53C2×#334711yescharacteristic, complemented, Sylow
457C22×Q8—1061no—
458C22×D4—531no—
459C22×D4—531no—
460C22×D4—1061no—
461C22×D4—1061no—
462C22×D4—1061no—
463C22×D4—1061no—
464C22×D4D21211yescharacteristic
465C23×C4—1061no—
466C23×C4—1061no—
467C23×C4—1061no—
468C23×C4C22×D5311yescharacteristic
469C23×C4C22×D5311yescharacteristic
470C2×D8—534no—
471C2×D8—1064no—
472C2×M16—24no—
473C2×M16C22×D5314yes—
474C22×C8—24no—
475C22×C8C22×D5311yescharacteristic
476C22×C8C22×D5314yes—
477C22×C8C22×D5311yescharacteristic
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—534no—
499C4×D4—534no—
500C4×D4—1068no—
501C4×D4—1062no—
502C4×D4—1062no—
503C4×D4D21214yes—
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—534no—
515C2×C4⋊C4—531no—
516C2×C4⋊C4—531no—
517C2×C4⋊C4—531no—
518C2×C4⋊C4—531no—
519C2×C4⋊C4—1061no—
520C2×C4⋊C4—1062no—
521C2×C4⋊C4—1061no—
522C2×C4⋊C4—1061no—
523C2×C4⋊C4—1061no—
524C2×C4⋊C4D21211yescharacteristic
525C2×C22⋊C4—1061no—
526C2×C22⋊C4—1061no—
527C2×C22⋊C4—1061no—
528C2×C22⋊C4—1061no—
529C2×C22⋊C4—1061no—
530C2×C22⋊C4—1061no—
531C2×C22⋊C4—1061no—
532C2×C22⋊C4—1061no—
533C2×C22⋊C4—1061no—
534C2×C22⋊C4D21211yescharacteristic
535C2×C22⋊C4D21211yescharacteristic
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#106—534no—
549C4⋊C8C22×D5314yes—
550#102—534no—
551#102—534no—
552#102—534no—
553#102—534no—
554#102—534no—
555#102—534no—
556C22⋊C8C22×D5314yes—
557C22⋊C8C22×D5314yes—
558#97C22×D5314yes—
559C24—1061no—
560C24—1061no—
561C24C2×D21211yescharacteristic
562C24C2×D21211yescharacteristic
563C2×Q8—1064no—
564C2×Q8—4242no—
565C2×D4—42no—
566C2×D4—532no—
567C2×D4—532no—
568C2×D4—1064no—
569C2×D4—1064no—
570C2×D4—1064no—
571C2×D4—1064no—
572C2×D4—1061no—
573C2×D4—1061no—
574C2×D4—1062no—
575C2×D4—1062no—
576C2×D4—1062no—
577C2×D4—1062no—
578C2×D4—4242no—
579C2×D4—4242no—
580C2×D4—4242no—
581C2×D4—2124no—
582C2×D4C2×D21214yes—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—1064no—
588C22×C4—1061no—
589C22×C4—1061no—
590C22×C4—1061no—
591C22×C4—1061no—
592C22×C4—1061no—
593C22×C4—1061no—
594C22×C4—1064no—
595C22×C4—1064no—
596C22×C4—4242no—
597C22×C4—4242no—
598C22×C4—2124no—
599C22×C4C2×D21212yes—
600C22×C4C2×D21212yes—
601C22×C4C2×D21211yescharacteristic
602C22×C4C2×D21211yescharacteristic
603C22×C4C2×D21211yescharacteristic
604C22×C4C2×D21211yescharacteristic
605C22×C4C23×D5312yes—
606C22×C4C23×D5312yes—
607C22×C4C23×D5311yescharacteristic
608D8—1068no—
609M16—28no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—28no—
614C2×C8#1171994714yes—
615C2×C8C23×D5312yes—
616C2×C8C23×D5312yes—
617C2×C8C23×D5312yes—
618C2×C8C23×D5312yes—
619C4⋊C4—532no—
620C4⋊C4—532no—
621C4⋊C4—532no—
622C4⋊C4—532no—
623C4⋊C4—532no—
624C4⋊C4—532no—
625C4⋊C4—1061no—
626C4⋊C4—1061no—
627C4⋊C4—1064no—
628C4⋊C4—1061no—
629C4⋊C4—1061no—
630C4⋊C4—1061no—
631C4⋊C4—1061no—
632C4⋊C4—1064no—
633C4⋊C4—1064no—
634C4⋊C4—1064no—
635C4⋊C4C2×D21214yes—
636C22⋊C4—1064no—
637C22⋊C4—1064no—
638C22⋊C4—1064no—
639C22⋊C4—1064no—
640C22⋊C4—1064no—
641C22⋊C4—1064no—
642C22⋊C4—1064no—
643C22⋊C4—1064no—
644C22⋊C4—1064no—
645C22⋊C4C2×D21214yes—
646C22⋊C4C2×D21214yes—
647C42—1064no—
648C42—1064no—
649C42—1064no—
650C42C2×D21212yes—
651C42C23×D5312yes—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—1062no—
659C23—1062no—
660C23—2122no—
661C23—2122no—
662C23—2122no—
663C23—2122no—
664C23—2122no—
665C23—2122no—
666C23C22×D21212yes—
667C23C22×D21212yes—
668C23C22×D21211yescharacteristic
669Q8—4244no—
670D4—44no—
671D4—1062no—
672D4—1062no—
673D4—1062no—
674D4—1062no—
675D4—4244no—
676D4—4244no—
677D4—4244no—
678D4—2128no—
679D4—2122no—
680D4—2122no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—1062no—
692C2×C4—1062no—
693C2×C4—1062no—
694C2×C4—1062no—
695C2×C4—1062no—
696C2×C4—1062no—
697C2×C4—4244no—
698C2×C4—4244no—
699C2×C4—2128no—
700C2×C4—2122no—
701C2×C4—2122no—
702C2×C4—2122no—
703C2×C4—2122no—
704C2×C4—2122no—
705C2×C4—2122no—
706C2×C4C22×D21212yes—
707C2×C4C22×D21212yes—
708C2×C4C22×D21212yes—
709C2×C4C22×D21212yes—
710C2×C4C22×D21211yescharacteristic
711C2×C4C2×#1171994712yes—
712C2×C4#1313326412yes—
713C2×C4C24×D5311yescharacteristic
714C8—22no—
715C8—22no—
716C8—22no—
717C8C2×#1171994714yes—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—44no—
725C22—44no—
726C22—4244no—
727C22—4244no—
728C22—2122no—
729C22—2122no—
730C22—2122no—
731C22—2122no—
732C22—2122no—
733C22—2122no—
734C22#1681127712yes—
735C22#1681142312yes—
736C22#1681142812yes—
737C22C23×D21211yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—2122no—
743C4—2122no—
744C4—2122no—
745C4—2122no—
746C4—2122no—
747C4—2122no—
748C4#1681127712yes—
749C4C22×#1171994711yescharacteristic
750C4C2×#1313326411yescharacteristic
751C2—42no—
752C2—42no—
753C2—4242no—
754C2—4242no—
755C2#2028721714yesdirect product factor
756C2C2×#1681127711yescharacteristic
757C2C2×#1681142311yescharacteristic
758C2C2×#1681142811yescharacteristic
subgroupG/H
centerC23C22×D212
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#435C2
socleC23×C53C22×D4
hypercenterC2×#435D53
hypocenterC53C2×#3347
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#16811338C2semidirect
2. C2×#16811319C2semidirect
3. #20287217C2direct (N × H)
4. C2×#16811032C2semidirect
5. C2×#16810948C2semidirect
6. C2×#16810948C2semidirect
7. C2×#16810948C2semidirect
8. C2×#16810937C2semidirect
9. C2×#16810924C2semidirect
10. C2×#16810904C2semidirect
11. C2×#16810876C2semidirect
12. C2×#16810859C2semidirect
13. C2×#16810736C2semidirect
14. C2×#16810665C2semidirect
15. C2×#16810661C2semidirect
16. C2×C53×#435C2semidirect
19. #16811338C22semidirect
21. #16811319C22semidirect
42. #16811032C22semidirect
43. #16810948C22semidirect
44. #16810948C22semidirect
45. #16810948C22semidirect
46. #16810937C22semidirect
47. #16810924C22semidirect
48. #16810904C22semidirect
49. #16810876C22semidirect
50. #16810859C22semidirect
51. #16810736C22semidirect
52. #16810665C22semidirect
53. #16810661C22semidirect
72. C53×#435C22semidirect
385. C2×#435D53semidirect
390. C2×C53#3347semidirect
434. #435C2×D53semidirect
456. C53C2×#3347semidirect
755. C2#20287217direct (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×#168113192
#202872172
C2×#168110322
C2×#168109482
C2×#168109372
C2×#168109242
C2×#168109042
C2×#168108762
C2×#168108592
C2×#168107362
C2×#168106652
C2×#168106612
C2×C53×#4352
C2×#334753