Finite Group Databasebeta

← C2×#20285970 #28256283

Subgroups — C2×#20285970 #28256283

Order 13568.

1806 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811251C211yesmaximal, characteristic, complemented
2C2×#16811228C211yesmaximal, characteristic
3#20285970C2116yesmaximal, direct product factor
4C2×#16811032C211yesmaximal, characteristic, complemented
5C2×#16811025C211yesmaximal, characteristic, complemented
6C2×#16810988C211yesmaximal, characteristic, complemented
7C2×#16810970C211yesmaximal, characteristic, complemented
8C2×#16810942C211yesmaximal, characteristic, complemented
9C2×#16810948C211yesmaximal, characteristic, complemented
10C2×#16810948C211yesmaximal, characteristic, complemented
11C2×#16810937C211yesmaximal, characteristic, complemented
12C2×#16810924C211yesmaximal, characteristic, complemented
13C2×#16810924C211yesmaximal, characteristic, complemented
14C2×#16810914C211yesmaximal, characteristic, complemented
15C2×#16810904C211yesmaximal, characteristic, complemented
16C2×C53×#433C211yesmaximal, characteristic, complemented
17#16811251—24no—
18#16811251C2218yescomplemented
19#16811228—24no—
20#16811228C2218yes—
21C2×#13133217C2211yescharacteristic
22C2×#13133217C2211yescharacteristic
23C2×#13133216—21no—
24C2×#13133214C2211yescharacteristic
25C2×#13133209C2211yescharacteristic
26C2×#13133209C2211yescharacteristic
27C2×#13133209C2211yescharacteristic
28C2×#13133208—21no—
29C2×#13133202—21no—
30C2×#13133202—21no—
31C2×#13133194—21no—
32C2×#13133194—21no—
33C2×#13133191C2211yescharacteristic
34C2×#13133191C2211yescharacteristic
35C2×#13133190—21no—
36C2×#13133190—21no—
37C2×C4×D212C2211yescharacteristic
38C2×C4×D212C2211yescharacteristic
39C2×#13133176C2211yescharacteristic
40C22×C4⋊Dic53C2211yescharacteristic
41#16811032C2218yescomplemented
42#16811025C2218yescomplemented
43#16810988C2218yescomplemented
44#16810970C2218yescomplemented
45#16810948C2218yescomplemented
46#16810948C2218yescomplemented
47#16810942C2218yescomplemented
48#16810937C2218yescomplemented
49#16810924C2218yescomplemented
50#16810924C2218yescomplemented
51#16810914C2218yescomplemented
52#16810904C2218yescomplemented
53C2×#13133151C2211yescharacteristic
54C2×#13133151C2211yescharacteristic
55C2×#13133151C2211yescharacteristic
56C2×#13133151C2211yescharacteristic
57C2×#13133149C2211yescharacteristic
58C2×#13133149C2211yescharacteristic
59C2×#13133149C2211yescharacteristic
60C2×#13133149C2211yescharacteristic
61C2×#13133139C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133139C2211yescharacteristic
65C2×#13133139C2211yescharacteristic
66C2×#13133139C2211yescharacteristic
67C2×#13133139C2211yescharacteristic
68C2×#13133139C2211yescharacteristic
69C2×#117×C53C2211yescharacteristic
70C53×#433C2218yescomplemented
71C2×C4⋊C8×C53C2211yescharacteristic
72C2×C4⋊C8×C53C2211yescharacteristic
73C2×C22⋊C8×C53C2211yescharacteristic
74C2×C22⋊C8×C53C2211yescharacteristic
75C2×#97×C53C2211yescharacteristic
76C2×C4×C8×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106—21no—
79C22×D212—21no—
80C22×D212—21no—
81C22×D212C2311yescharacteristic
82C22×D212C2311yescharacteristic
83C22×C22⋊D53—21no—
84C22×C22⋊D53—21no—
85C23×Dic53—21no—
86C22×C4×D53—21no—
87C22×C4×D53—21no—
88#13133217—22no—
89#13133217—22no—
90#13133217C2314yes—
91#13133217C2314yes—
92#13133216—28no—
93#13133214—22no—
94#13133214C2314yes—
95#13133209—22no—
96#13133209—22no—
97#13133209—22no—
98#13133209C2314yes—
99#13133209C2314yes—
100#13133209C2314yes—
101#13133208—28no—
102#13133202—28no—
103#13133202—28no—
104#13133194—28no—
105#13133194—28no—
106#13133191—22no—
107#13133191—22no—
108#13133191C2314yes—
109#13133191C2314yes—
110#13133190—28no—
111#13133190—28no—
112C4×D212—22no—
113C4×D212—22no—
114C4×D212C2314yes—
115C4×D212C2314yes—
116#13133176—22no—
117#13133176C2314yes—
118C2×C4⋊Dic53—21no—
119C2×C4⋊Dic53—22no—
120C2×C4⋊Dic53—21no—
121C2×C4⋊Dic53—21no—
122C2×C4⋊Dic53C2311yescharacteristic
123C2×C4⋊Dic53C2311yescharacteristic
124C2×C4⋊Dic53C2314yes—
125C2×C4⋊Dic53C2311yescharacteristic
126C2×C4⋊Dic53C2311yescharacteristic
127C2×C4⋊Dic53C2311yescharacteristic
128C2×C4⋊Dic53C2311yescharacteristic
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×C22⋊Dic53—21no—
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×C4×Dic53—21no—
141#13133151C2314yes—
142#13133151C2314yes—
143#13133151C2314yes—
144#13133151C2314yes—
145#13133149C2314yes—
146#13133149C2314yes—
147#13133149C2314yes—
148#13133149C2314yes—
149#13133139C2314yes—
150#13133139C2314yes—
151#13133139C2314yes—
152#13133139C2314yes—
153#13133139C2314yes—
154#13133139C2314yes—
155#13133139C2314yes—
156#13133139C2314yes—
157C23×C4×C53C2311yescharacteristic
158C22×C8×C53C2311yescharacteristic
159C22×C8×C53C2311yescharacteristic
160C22×C8×C53C2311yescharacteristic
161C22×C8×C53C2311yescharacteristic
162#117×C53D414yes—
163#117×C53C2314yes—
164C2×C4⋊C4×C53D411yescharacteristic
165C2×C4⋊C4×C53D411yescharacteristic
166C2×C22⋊C4×C53D411yescharacteristic
167C2×C22⋊C4×C53D411yescharacteristic
168C2×C42×C53C2311yescharacteristic
169C2×C42×C53C2311yescharacteristic
170C4⋊C8×C53C2314yes—
171C4⋊C8×C53C2314yes—
172C22⋊C8×C53C2314yes—
173C22⋊C8×C53C2314yes—
174#97×C53C2314yes—
175C4×C8×C53C2314yes—
176C24×C53C2×D411yescharacteristic
177C23×D53—21no—
178C23×D53—21no—
179C22×C4×C53—22no—
180C22×C4×C53—22no—
181C22×C4×C53C2×D411yescharacteristic
182C22×C4×C53C2×D411yescharacteristic
183C22×C4×C53C2×D411yescharacteristic
184C22×C4×C53C2×D411yescharacteristic
185C22×C4×C53C2×D411yescharacteristic
186C22×C4×C53C2×D412yes—
187C22×C4×C53C2412yes—
188C22×C4×C53C2411yescharacteristic
189C2×C22⋊D53—24no—
190C2×C22⋊D53—24no—
191C2×C22⋊D53—82no—
192C2×C22⋊D53—82no—
193C22×Dic53—21no—
194C22×Dic53—21no—
195C22×Dic53—21no—
196C22×Dic53—21no—
197C22×Dic53—21no—
198C22×Dic53—21no—
199C22×Dic53—24no—
200C22×Dic53—82no—
201C2×D212—22no—
202C2×D212—22no—
203C2×D212—22no—
204C2×D212—22no—
205C2×D212—21no—
206C2×D212—21no—
207C2×D212—24no—
208C2×D212—24no—
209C2×D212—82no—
210C2×D212—82no—
211C2×D212C2412yes—
212C2×D212C2412yes—
213C2×C4×D53—24no—
214C2×C4×D53—24no—
215C2×C4×D53—82no—
216C2×C4×D53—82no—
217C2×Dic106—24no—
218C2×Dic106—24no—
219C2×Dic106—82no—
220C2×Dic106—82no—
221C2×C8×C53—22no—
222C2×C8×C53—22no—
223C2×C8×C53—22no—
224C2×C8×C53—22no—
225C2×C8×C53C2412yes—
226C2×C8×C53C2412yes—
227C2×C8×C53C2412yes—
228C2×C8×C53C2412yes—
229C4⋊C4×C53C2×D414yes—
230C4⋊C4×C53C2×D414yes—
231C22⋊C4×C53C2×D414yes—
232C22⋊C4×C53C2×D414yes—
233C42×C53C2×D412yes—
234C42×C53C2×D412yes—
235C42×C53C2412yes—
236C42×C53C2412yes—
237C22⋊Dic53—24no—
238#11719921—24no—
239#11719921—24no—
240#11719921—24no—
241#11719921—24no—
242C4⋊Dic53—24no—
243C4⋊Dic53—21no—
244C4⋊Dic53—21no—
245C4⋊Dic53—24no—
246C4⋊Dic53—24no—
247C4⋊Dic53—21no—
248C4⋊Dic53—21no—
249C4⋊Dic53—21no—
250C4⋊Dic53—21no—
251C4⋊Dic53C2412yes—
252C4⋊Dic53C2412yes—
253C4⋊Dic53C2412yes—
254C4⋊Dic53C2412yes—
255C4⋊Dic53C2412yes—
256C4⋊Dic53C2412yes—
257#11719919—24no—
258#11719919—24no—
259#11719919—24no—
260#11719919—24no—
261#11719919—24no—
262#11719919—24no—
263C4×Dic53—24no—
264C23×C53—22no—
265C23×C53—22no—
266C23×C53—22no—
267C23×C53C22×D412yes—
268C23×C53C22×D411yescharacteristic
269C22×D53—22no—
270C22×D53—22no—
271C22×D53—42no—
272C22×D53—42no—
273C22×D53—42no—
274C22×D53—42no—
275C22×D53—42no—
276C22×D53—42no—
277C2×C4×C53—22no—
278C2×C4×C53—22no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
282C2×C4×C53—24no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53C22×D412yes—
286C2×C4×C53C22×D412yes—
287C2×C4×C53C22×D412yes—
288C2×C4×C53C22×D412yes—
289C2×C4×C53C22×D412yes—
290C2×C4×C53C22×D411yescharacteristic
291C2×C4×C532−1+412yes—
292C2×C4×C532−1+412yes—
293C2×C4×C53C2511yescharacteristic
294C22⋊D53—84no—
295C22⋊D53—84no—
296C2×Dic53—22no—
297C2×Dic53—22no—
298C2×Dic53—22no—
299C2×Dic53—22no—
300C2×Dic53—22no—
301C2×Dic53—22no—
302C2×Dic53—42no—
303C2×Dic53—42no—
304C2×Dic53—42no—
305C2×Dic53—42no—
306C2×Dic53—42no—
307C2×Dic53—42no—
308C2×Dic53—84no—
309D212—22no—
310D212—22no—
311D212—22no—
312D212—22no—
313D212—42no—
314D212—42no—
315D212—84no—
316D212—84no—
317C4×D53—84no—
318C4×D53—84no—
319Dic106—84no—
320Dic106—84no—
321C8×C53—22no—
322C8×C53—22no—
323C8×C53—22no—
324C8×C53—22no—
325C2×#3241—531nomaximal, Sylow
326C22×C53—22no—
327C22×C53—22no—
328C22×C53—22no—
329C22×C53—44no—
330C22×C53#53612yes—
331C22×C53#57612yes—
332C22×C53#57712yes—
333C22×C53C23×D411yescharacteristic
334C2×D53—42no—
335C2×D53—42no—
336C2×D53—42no—
337C2×D53—42no—
338C2×D53—42no—
339C2×D53—42no—
340C2×D53—84no—
341C2×D53—84no—
342C4×C53—22no—
343C4×C53—22no—
344C4×C53—22no—
345C4×C53—22no—
346C4×C53—22no—
347C4×C53#53612yes—
348C4×C53C2×2−1+411yescharacteristic
349C4×C53C2×2−1+411yescharacteristic
350Dic53—42no—
351Dic53—42no—
352Dic53—42no—
353Dic53—42no—
354Dic53—42no—
355Dic53—42no—
356C2×#544—531no—
357C2×#540—531no—
358#3241—5316no—
359C2×#501—531no—
360C2×#499—531no—
361C2×#490—531no—
362C2×#486—531no—
363C2×#481—531no—
364C2×#482—531no—
365C2×#482—531no—
366C2×#480—531no—
367C2×#478—531no—
368C2×#478—531no—
369C2×#476—531no—
370C2×#474—531no—
371C2×#433D5311yescharacteristic, complemented
372C2×C53—42no—
373C2×C53#324114yescomplemented
374C2×C53C2×#53611yescharacteristic
375C2×C53C2×#57611yescharacteristic
376C2×C53C2×#57711yescharacteristic
377D53—82no—
378D53—82no—
379#544—538no—
380#544—1064no—
381#540—538no—
382#540—1064no—
383C2×C4⋊Q8—531no—
384C2×C4⋊Q8—531no—
385C2×C4⋊Q8—1061no—
386C2×#127—531no—
387C2×#125—531no—
388C2×#125—531no—
389C2×#125—531no—
390C2×#125—1061no—
391C2×#123—1061no—
392C2×#123—1061no—
393C2×C22⋊Q8—1061no—
394C2×C22⋊Q8—1061no—
395C2×#121—531no—
396C2×#121—531no—
397C2×#121—1061no—
398C2×#121—1061no—
399C2×C4×D4—531no—
400C2×C4×D4—531no—
401C2×#117—531no—
402C2×#117C2×D5311yescharacteristic
403C22×C4⋊C4—531no—
404#501—538no—
405#499—538no—
406#490—538no—
407#486—538no—
408#482—538no—
409#482—538no—
410#481—538no—
411#480—538no—
412#478—538no—
413#478—538no—
414#476—538no—
415#474—538no—
416#433C2×D5318yescomplemented
417C2×#107—531no—
418C2×#107—531no—
419C2×#107—531no—
420C2×#107—531no—
421C2×#106—531no—
422C2×#106—531no—
423C2×#106—531no—
424C2×#106—531no—
425C2×C4⋊C8C2×D5311yescharacteristic
426C2×C4⋊C8C2×D5311yescharacteristic
427C2×#102—531no—
428C2×#102—531no—
429C2×#102—531no—
430C2×#102—531no—
431C2×#102—531no—
432C2×#102—531no—
433C2×#102—531no—
434C2×#102—531no—
435C2×C22⋊C8C2×D5311yescharacteristic
436C2×C22⋊C8C2×D5311yescharacteristic
437C2×#97C2×D5311yescharacteristic
438C2×C4×C8C2×D5311yescharacteristic
439C53C2×#324111yescharacteristic, complemented, Sylow
440C22×Q8—1061no—
441C22×Q8—1061no—
442C22×D4—531no—
443C22×D4—531no—
444C22×D4—1061no—
445C22×D4—1061no—
446C22×D4—1061no—
447C22×D4—1061no—
448C23×C4—1061no—
449C23×C4—1061no—
450C23×C4—1061no—
451C23×C4C22×D5311yescharacteristic
452C22×C8C22×D5311yescharacteristic
453C22×C8C22×D5311yescharacteristic
454C22×C8C22×D5311yescharacteristic
455C22×C8C22×D5311yescharacteristic
456C4⋊Q8—534no—
457C4⋊Q8—534no—
458C4⋊Q8—1068no—
459C4⋊Q8—1062no—
460C4⋊Q8—1062no—
461#127—534no—
462#127—1062no—
463#125—534no—
464#125—534no—
465#125—534no—
466#125—1068no—
467#125—1062no—
468#125—1062no—
469#125—1062no—
470#123—1068no—
471#123—1068no—
472C22⋊Q8—1068no—
473C22⋊Q8—1068no—
474#121—534no—
475#121—534no—
476#121—1062no—
477#121—1062no—
478#121—1068no—
479#121—1068no—
480C4×D4—534no—
481C4×D4—534no—
482C4×D4—1062no—
483C4×D4—1062no—
484#117—534no—
485#117—1062no—
486#117D21214yes—
487#117C22×D5314yes—
488C2×C4⋊C4—531no—
489C2×C4⋊C4—531no—
490C2×C4⋊C4—534no—
491C2×C4⋊C4—531no—
492C2×C4⋊C4—531no—
493C2×C4⋊C4—531no—
494C2×C4⋊C4—531no—
495C2×C4⋊C4—1061no—
496C2×C4⋊C4—1062no—
497C2×C4⋊C4—1061no—
498C2×C4⋊C4—1061no—
499C2×C4⋊C4—1061no—
500C2×C4⋊C4—1061no—
501C2×C4⋊C4—1061no—
502C2×C4⋊C4—1061no—
503C2×C4⋊C4—1061no—
504C2×C4⋊C4—1061no—
505C2×C4⋊C4D21211yescharacteristic
506C2×C4⋊C4D21211yescharacteristic
507C2×C22⋊C4—1061no—
508C2×C22⋊C4—1061no—
509C2×C22⋊C4—1061no—
510C2×C22⋊C4—1061no—
511C2×C22⋊C4—1061no—
512C2×C22⋊C4D21211yescharacteristic
513C2×C22⋊C4D21211yescharacteristic
514C2×C42—1061no—
515C2×C42C22×D5311yescharacteristic
516C2×C42C22×D5311yescharacteristic
517#107—534no—
518#107—534no—
519#107—534no—
520#107—534no—
521#106—534no—
522#106—534no—
523#106—534no—
524#106—534no—
525C4⋊C8C22×D5314yes—
526C4⋊C8C22×D5314yes—
527#102—534no—
528#102—534no—
529#102—534no—
530#102—534no—
531#102—534no—
532#102—534no—
533#102—534no—
534#102—534no—
535C22⋊C8C22×D5314yes—
536C22⋊C8C22×D5314yes—
537#97C22×D5314yes—
538C4×C8C22×D5314yes—
539C24—1061no—
540C24—1061no—
541C24C2×D21211yescharacteristic
542C2×Q8—1064no—
543C2×Q8—1064no—
544C2×Q8—4242no—
545C2×Q8—4242no—
546C2×D4—532no—
547C2×D4—532no—
548C2×D4—1064no—
549C2×D4—1064no—
550C2×D4—1064no—
551C2×D4—1064no—
552C2×D4—1061no—
553C2×D4—1061no—
554C2×D4—1062no—
555C2×D4—1062no—
556C2×D4—1062no—
557C2×D4—1062no—
558C2×D4—4242no—
559C2×D4—4242no—
560C2×D4—4242no—
561C2×D4—4242no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—1064no—
565C22×C4—1061no—
566C22×C4—1061no—
567C22×C4—1061no—
568C22×C4—1061no—
569C22×C4—1061no—
570C22×C4—1061no—
571C22×C4—1064no—
572C22×C4—1064no—
573C22×C4—4242no—
574C22×C4—4242no—
575C22×C4—4242no—
576C22×C4C2×D21212yes—
577C22×C4C2×D21211yescharacteristic
578C22×C4C2×D21211yescharacteristic
579C22×C4C2×D21211yescharacteristic
580C22×C4C2×D21211yescharacteristic
581C22×C4C2×D21211yescharacteristic
582C22×C4C23×D5312yes—
583C22×C4C23×D5311yescharacteristic
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8C23×D5312yes—
589C2×C8C23×D5312yes—
590C2×C8C23×D5312yes—
591C2×C8C23×D5312yes—
592C4⋊C4—532no—
593C4⋊C4—532no—
594C4⋊C4—532no—
595C4⋊C4—532no—
596C4⋊C4—532no—
597C4⋊C4—532no—
598C4⋊C4—1064no—
599C4⋊C4—1061no—
600C4⋊C4—1061no—
601C4⋊C4—1061no—
602C4⋊C4—1061no—
603C4⋊C4—1061no—
604C4⋊C4—1061no—
605C4⋊C4—1064no—
606C4⋊C4—1064no—
607C4⋊C4—1064no—
608C4⋊C4—1064no—
609C4⋊C4—1064no—
610C4⋊C4—1064no—
611C4⋊C4—1064no—
612C4⋊C4—1064no—
613C4⋊C4C2×D21214yes—
614C4⋊C4C2×D21214yes—
615C22⋊C4—1064no—
616C22⋊C4—1064no—
617C22⋊C4—1064no—
618C22⋊C4—1064no—
619C22⋊C4—1064no—
620C22⋊C4C2×D21214yes—
621C22⋊C4C2×D21214yes—
622C42—1064no—
623C42C2×D21212yes—
624C42C2×D21212yes—
625C42C23×D5312yes—
626C42C23×D5312yes—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—1062no—
631C23—1062no—
632C23—2122no—
633C23—2122no—
634C23—2122no—
635C23—2122no—
636C23—2122no—
637C23—2122no—
638C23C22×D21212yes—
639C23C22×D21211yescharacteristic
640Q8—4244no—
641Q8—4244no—
642D4—1062no—
643D4—1062no—
644D4—1062no—
645D4—1062no—
646D4—4244no—
647D4—4244no—
648D4—4244no—
649D4—4244no—
650D4—2122no—
651D4—2122no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—1062no—
661C2×C4—1062no—
662C2×C4—1062no—
663C2×C4—1062no—
664C2×C4—1062no—
665C2×C4—1062no—
666C2×C4—4244no—
667C2×C4—4244no—
668C2×C4—4244no—
669C2×C4—2122no—
670C2×C4—2122no—
671C2×C4—2122no—
672C2×C4—2122no—
673C2×C4—2122no—
674C2×C4—2122no—
675C2×C4C22×D21212yes—
676C2×C4C22×D21212yes—
677C2×C4C22×D21212yes—
678C2×C4C22×D21212yes—
679C2×C4C22×D21212yes—
680C2×C4C22×D21211yescharacteristic
681C2×C4#1313326412yes—
682C2×C4#1313326412yes—
683C2×C4C24×D5311yescharacteristic
684C8—22no—
685C8—22no—
686C8—22no—
687C8—22no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—44no—
692C22—4244no—
693C22—4244no—
694C22—2122no—
695C22—2122no—
696C22—2122no—
697C22—2122no—
698C22—2122no—
699C22—2122no—
700C22#1681119912yes—
701C22#1681142812yes—
702C22#1681143512yes—
703C22C23×D21211yescharacteristic
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—22no—
709C4—2122no—
710C4—2122no—
711C4—2122no—
712C4—2122no—
713C4—2122no—
714C4—2122no—
715C4#1681119912yes—
716C4C2×#1313326411yescharacteristic
717C4C2×#1313326411yescharacteristic
718C2—42no—
719C2—4242no—
720C2—4242no—
721C2#2028597014yesdirect product factor
722C2C2×#1681119911yescharacteristic
723C2C2×#1681142811yescharacteristic
724C2C2×#1681143511yescharacteristic
subgroupG/H
centerC23C22×D212
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#433C2
socleC23×C53C22×D4
prime radicalC2×#16811228C2
hypercenterC2×#433D53
hypocenterC53C2×#3241
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#16811251C2semidirect
3. #20285970C2direct (N × H)
4. C2×#16811032C2semidirect
5. C2×#16811025C2semidirect
6. C2×#16810988C2semidirect
7. C2×#16810970C2semidirect
8. C2×#16810942C2semidirect
9. C2×#16810948C2semidirect
10. C2×#16810948C2semidirect
11. C2×#16810937C2semidirect
12. C2×#16810924C2semidirect
13. C2×#16810924C2semidirect
14. C2×#16810914C2semidirect
15. C2×#16810904C2semidirect
16. C2×C53×#433C2semidirect
18. #16811251C22semidirect
41. #16811032C22semidirect
42. #16811025C22semidirect
43. #16810988C22semidirect
44. #16810970C22semidirect
45. #16810948C22semidirect
46. #16810948C22semidirect
47. #16810942C22semidirect
48. #16810937C22semidirect
49. #16810924C22semidirect
50. #16810924C22semidirect
51. #16810914C22semidirect
52. #16810904C22semidirect
70. C53×#433C22semidirect
371. C2×#433D53semidirect
373. C2×C53#3241semidirect
416. #433C2×D53semidirect
439. C53C2×#3241semidirect
721. C2#20285970direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112512
C2×#168112282
#202859702
C2×#168110322
C2×#168110252
C2×#168109882
C2×#168109702
C2×#168109422
C2×#168109482
C2×#168109372
C2×#168109242
C2×#168109142
C2×#168109042
C2×C53×#4332
C2×#324153