Finite Group Databasebeta

← C2×#20285012 #28252445

Subgroups — C2×#20285012 #28252445

Order 13568.

1994 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811231C211yesmaximal, characteristic
2C2×#16811099C211yesmaximal, characteristic
3#20285012C2116yesmaximal, direct product factor
4C2×#16810966C211yesmaximal, characteristic
5C2×#16810963C211yesmaximal, characteristic
6C2×#16810932C211yesmaximal, characteristic, complemented
7C2×#16810929C211yesmaximal, characteristic, complemented
8C2×#16810832C211yesmaximal, characteristic, complemented
9C2×#16810831C211yesmaximal, characteristic, complemented
10C2×#16810780C211yesmaximal, characteristic
11C2×#16810777C211yesmaximal, characteristic
12C2×#16810728C211yesmaximal, characteristic, complemented
13C2×#16810728C211yesmaximal, characteristic, complemented
14C2×C4×Dic212C211yesmaximal, characteristic, complemented
15C2×#16810682C211yesmaximal, characteristic
16C2×C4×Q16×C53C211yesmaximal, characteristic, complemented
17C22×Q8×D53C2211yescharacteristic
18C22×Dic212C2211yescharacteristic
19C22×#11719925C2211yescharacteristic
20C22×#11719925C2211yescharacteristic
21#16811231—24no—
22#16811231C2218yes—
23C2×#13133215C2211yescharacteristic
24C2×#13133212—21no—
25C2×#13133211—21no—
26C2×#13133209—21no—
27C2×#13133208C2211yescharacteristic
28C2×#13133207—21no—
29C2×#13133197C2211yescharacteristic
30C2×#13133193C2211yescharacteristic
31#16811099—24no—
32#16811099C2218yes—
33C2×Q8×Dic53C2211yescharacteristic
34C2×C4×Dic106—21no—
35C2×C4×Dic106C2211yescharacteristic
36C2×C4×Dic106C2211yescharacteristic
37C2×#13133182—21no—
38C2×#13133182C2211yescharacteristic
39C2×#13133175—21no—
40C2×#13133175C2211yescharacteristic
41C2×#13133174—21no—
42C2×#13133174C2211yescharacteristic
43#16810966C2218yes—
44#16810963C2218yes—
45#16810932C2218yescomplemented
46#16810929C2218yescomplemented
47#16810832C2218yescomplemented
48#16810831C2218yescomplemented
49#16810780C2218yes—
50#16810777C2218yes—
51#16810728C2218yescomplemented
52#16810728C2218yescomplemented
53C4×Dic212C2218yescomplemented
54#16810682C2218yes—
55C2×#13133151C2211yescharacteristic
56C2×#13133148C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×#13133146C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133141C2211yescharacteristic
64C2×#13133140C2211yescharacteristic
65C2×#13133140C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133128C2211yescharacteristic
69C22×Q16×C53C2211yescharacteristic
70C2×C4×Q8×C53C2211yescharacteristic
71C2×C4×Q8×C53C2211yescharacteristic
72C4×Q16×C53C2218yescomplemented
73C2×#107×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×C4×C8×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106C2311yescharacteristic
79C22×Dic106C2311yescharacteristic
80C2×Q8×D53—24no—
81C2×Q8×D53—22no—
82C2×Q8×D53—24no—
83C2×Q8×D53C2314yes—
84C22×C4×D53—21no—
85C22×C4×D53C2311yescharacteristic
86C2×Dic212—24no—
87C2×Dic212C2314yes—
88C2×#11719925—24no—
89C2×#11719925—24no—
90C2×#11719925C2314yes—
91C2×#11719925C2314yes—
92C22×#88322C2311yescharacteristic
93C22×#88322C2311yescharacteristic
94#13133215—22no—
95#13133215C2314yes—
96#13133212—28no—
97#13133211—28no—
98#13133209—28no—
99#13133208—22no—
100#13133208C2314yes—
101#13133207—28no—
102#13133197—22no—
103#13133197C2314yes—
104#13133193—22no—
105#13133193C2314yes—
106Q8×Dic53—22no—
107Q8×Dic53C2314yes—
108C4×Dic106—22no—
109C4×Dic106—22no—
110C4×Dic106—28no—
111C4×Dic106C2314yes—
112C4×Dic106C2314yes—
113#13133182—28no—
114#13133182—22no—
115#13133182C2314yes—
116#13133175—28no—
117#13133175—22no—
118#13133175C2314yes—
119#13133174—28no—
120#13133174D414yes—
121#13133174C2314yes—
122C2×C4⋊Dic53—21no—
123C2×C4⋊Dic53—21no—
124C2×C4⋊Dic53—21no—
125C2×C4⋊Dic53C2311yescharacteristic
126C2×C4⋊Dic53C2311yescharacteristic
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919D411yescharacteristic
135C2×#11719919D411yescharacteristic
136C2×#11719921—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921D411yescharacteristic
140C2×#11719921D411yescharacteristic
141C2×C4×Dic53—21no—
142C2×C4×Dic53—21no—
143C2×C4×Dic53—21no—
144C2×C4×Dic53—21no—
145C2×C4×Dic53—21no—
146C2×C4×Dic53C2311yescharacteristic
147#13133151C2314yes—
148#13133148C2314yes—
149#13133148C2314yes—
150#13133146C2314yes—
151#13133146C2314yes—
152#13133142C2314yes—
153#13133142C2314yes—
154#13133141C2314yes—
155#13133141C2314yes—
156#13133140C2314yes—
157#13133140C2314yes—
158#13133129C2314yes—
159#13133129C2314yes—
160#13133128C2314yes—
161C22×Q8×C53C2311yescharacteristic
162C22×Q8×C53C2311yescharacteristic
163C2×Q16×C53—24no—
164C2×Q16×C53C2314yes—
165C22×C8×C53C2311yescharacteristic
166C22×C8×C53C2311yescharacteristic
167C4×Q8×C53—22no—
168C4×Q8×C53—22no—
169C4×Q8×C53C2314yes—
170C4×Q8×C53C2314yes—
171C2×C4⋊C4×C53—21no—
172C2×C4⋊C4×C53—21no—
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C42×C53—21no—
176C2×C42×C53—21no—
177C2×C42×C53C2311yescharacteristic
178#107×C53C2314yes—
179#103×C53C2314yes—
180#103×C53C2314yes—
181C4×C8×C53C2314yes—
182C23×D53C2×D411yescharacteristic
183C2×Q8×C53—21no—
184C2×Q8×C53—21no—
185C2×Q8×C53—22no—
186C2×Q8×C53—22no—
187C2×Q8×C53—22no—
188C2×Q8×C53#4114yes—
189C2×Q8×C53C2412yes—
190C2×Q8×C53C2412yes—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53C2×D411yescharacteristic
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2411yescharacteristic
198C22×Dic53—21no—
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53—21no—
202C22×Dic53C2×D411yescharacteristic
203C22×Dic53C2×D411yescharacteristic
204C22×Dic53C2×D411yescharacteristic
205Q8×D53—216no—
206Q8×D53—28no—
207Q8×D53—28no—
208C2×C4×D53—28no—
209C2×C4×D53—24no—
210C2×C4×D53—22no—
211C2×C4×D53—22no—
212C2×C4×D53C2×D412yes—
213C2×C4×D53C2412yes—
214C2×Dic106—28no—
215C2×Dic106—21no—
216C2×Dic106—22no—
217C2×Dic106—24no—
218C2×Dic106—22no—
219C2×Dic106—22no—
220C2×Dic106—21no—
221C2×Dic106#4114yes—
222C2×Dic106C2412yes—
223C2×Dic106C2412yes—
224Q16×C53—28no—
225C2×C8×C53—22no—
226C2×C8×C53—22no—
227C2×C8×C53C2412yes—
228C2×C8×C53C2412yes—
229C4⋊C4×C53—24no—
230C4⋊C4×C53—24no—
231C4⋊C4×C53—21no—
232C4⋊C4×C53—21no—
233C4⋊C4×C53C2412yes—
234C4⋊C4×C53C2412yes—
235C42×C53—24no—
236C42×C53—24no—
237C42×C53C2×D412yes—
238C42×C53C2412yes—
239#11719925—28no—
240#11719925—28no—
241#11719921—24no—
242#11719921—24no—
243#11719921—24no—
244#11719921C2×D414yes—
245#11719921C2×D414yes—
246C4⋊Dic53—21no—
247C4⋊Dic53—21no—
248C4⋊Dic53—24no—
249C4⋊Dic53—24no—
250C4⋊Dic53—24no—
251C4⋊Dic53C2412yes—
252C4⋊Dic53C2412yes—
253#11719919—24no—
254#11719919—24no—
255#11719919—24no—
256#11719919—24no—
257#11719919—24no—
258#11719919—24no—
259#11719919—24no—
260#11719919C2×D414yes—
261#11719919C2×D414yes—
262C4×Dic53—24no—
263C4×Dic53—24no—
264C4×Dic53—24no—
265C4×Dic53—24no—
266C4×Dic53—24no—
267C4×Dic53C2×D412yes—
268C4×Dic53C2412yes—
269C2×#88322—22no—
270C2×#88322—22no—
271C2×#88322C2412yes—
272C2×#88322C2412yes—
273Dic212—28no—
274C23×C53C22×D411yescharacteristic
275C22×D53—22no—
276C22×D53—22no—
277C22×D53—22no—
278C22×D53C22×D412yes—
279Q8×C53—24no—
280Q8×C53—22no—
281Q8×C53—22no—
282Q8×C53—22no—
283Q8×C53—42no—
284Q8×C53C2×#4114yes—
285C2×C4×C53—24no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—42no—
293C2×C4×C53—42no—
294C2×C4×C53—42no—
295C2×C4×C53C22×D412yes—
296C2×C4×C53C22×D412yes—
297C2×C4×C53C22×D411yescharacteristic
298C2×C4×C53C2×#4112yes—
299C2×C4×C53C2×#4112yes—
300C2×C4×C53C2511yescharacteristic
301C2×Dic53—22no—
302C2×Dic53—24no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—42no—
310C2×Dic53—42no—
311C2×Dic53—42no—
312C2×Dic53C22×D412yes—
313C2×Dic53C22×D412yes—
314C2×Dic53C22×D412yes—
315C4×D53—216no—
316C4×D53—24no—
317C4×D53—22no—
318C4×D53—22no—
319Dic106—216no—
320Dic106—24no—
321Dic106—22no—
322Dic106—22no—
323Dic106—22no—
324Dic106—42no—
325Dic106C2×#4114yes—
326C8×C53—22no—
327C8×C53—22no—
328#88322—22no—
329#88322—22no—
330C2×#3127—531nomaximal, Sylow
331C22×C53#52512yes—
332C22×C53#57812yes—
333C22×C53#57812yes—
334C22×C53C23×D411yescharacteristic
335C2×D53—22no—
336C2×D53—22no—
337C2×D53—22no—
338C2×D53—44no—
339C4×C53—24no—
340C4×C53—22no—
341C4×C53—22no—
342C4×C53—42no—
343C4×C53—42no—
344C4×C53—42no—
345C4×C53#52512yes—
346C4×C53C22×#4111yescharacteristic
347C4×C53C22×#4111yescharacteristic
348Dic53—22no—
349Dic53—24no—
350Dic53—22no—
351Dic53—22no—
352Dic53—42no—
353Dic53—42no—
354Dic53—42no—
355C2×#541—531no—
356C2×#519—531no—
357#3127—5316no—
358C2×#485—531no—
359C2×#485—531no—
360C2×#479—531no—
361C2×#479—531no—
362C2×#462—531no—
363C2×#462—531no—
364C2×#451—531no—
365C2×#451—531no—
366C2×#441—531no—
367C2×#441—531no—
368C2×C4×Q16—531no—
369C2×C4×Q16D5311yescharacteristic, complemented
370C2×#433—531no—
371C2×C53#312714yescomplemented
372C2×C53C2×#52511yescharacteristic
373C2×C53C2×#57811yescharacteristic
374C2×C53C2×#57811yescharacteristic
375D53—42no—
376C23×Q8—531no—
377C22×Q16—531no—
378C22×Q16—531no—
379C22×Q16—531no—
380C22×Q16C2×D5311yescharacteristic
381#541—538no—
382#541—1064no—
383C2×C4⋊Q8—531no—
384C2×#126—1061no—
385C2×#126—1061no—
386C2×#125—531no—
387C2×#125—1061no—
388C2×#125—1061no—
389C2×C22⋊Q8—531no—
390C2×C22⋊Q8—531no—
391#519—538no—
392#519—1064no—
393C2×C4×Q8—531no—
394C2×C4×Q8—531no—
395C2×C4×Q8—531no—
396C2×C4×Q8—531no—
397C2×C4×Q8—1061no—
398C2×C4×Q8—1061no—
399C2×C4×Q8C2×D5311yescharacteristic
400C2×C4×Q8C2×D5311yescharacteristic
401C2×#117—531no—
402C2×#117—531no—
403C2×#117—1061no—
404C2×#117—1061no—
405#485—538no—
406#485—538no—
407#479—538no—
408#479—538no—
409#462—538no—
410#462—538no—
411#451—538no—
412#451—538no—
413#441—538no—
414#441—538no—
415C4×Q16—538no—
416C4×Q16C2×D5318yescomplemented
417#433—538no—
418C2×#107—531no—
419C2×#107C2×D5311yescharacteristic
420C2×#106—531no—
421C2×#106—531no—
422C2×C4⋊C8—531no—
423C2×C4⋊C8—531no—
424C2×#103—531no—
425C2×#103—531no—
426C2×#103—531no—
427C2×#103—531no—
428C2×#103—531no—
429C2×#103—531no—
430C2×#103C2×D5311yescharacteristic
431C2×#103C2×D5311yescharacteristic
432C2×C22⋊C8—531no—
433C2×C22⋊C8—531no—
434C2×#97—531no—
435C2×C4×C8C2×D5311yescharacteristic
436C53C2×#312711yescharacteristic, complemented, Sylow
437C22×Q8—534no—
438C22×Q8—531no—
439C22×Q8—531no—
440C22×Q8—1061no—
441C22×Q8—1062no—
442C22×Q8—1064no—
443C22×Q8—1064no—
444C22×Q8C22×D5311yescharacteristic
445C22×Q8C22×D5311yescharacteristic
446C23×C4—531no—
447C23×C4—1061no—
448C2×Q16—24no—
449C2×Q16—534no—
450C2×Q16—534no—
451C2×Q16—534no—
452C2×Q16—1064no—
453C2×Q16—1064no—
454C2×Q16—1064no—
455C2×Q16C22×D5314yes—
456C22×C8—531no—
457C22×C8—531no—
458C22×C8C22×D5311yescharacteristic
459C22×C8C22×D5311yescharacteristic
460C4⋊Q8—534no—
461C4⋊Q8—1062no—
462#126—1068no—
463#126—1068no—
464#125—534no—
465#125—1068no—
466#125—1062no—
467#125—1068no—
468C22⋊Q8—534no—
469C22⋊Q8—534no—
470C22⋊Q8—1062no—
471C22⋊Q8—1062no—
472C4×Q8—22no—
473C4×Q8—22no—
474C4×Q8—534no—
475C4×Q8—534no—
476C4×Q8—534no—
477C4×Q8—534no—
478C4×Q8—1068no—
479C4×Q8—1062no—
480C4×Q8—1062no—
481C4×Q8—1068no—
482C4×Q8—1062no—
483C4×Q8—1062no—
484C4×Q8C22×D5314yes—
485C4×Q8C22×D5314yes—
486#117—534no—
487#117—534no—
488#117—534no—
489#117—1068no—
490#117—1068no—
491#117—1062no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—531no—
495C2×C4⋊C4—531no—
496C2×C4⋊C4—531no—
497C2×C4⋊C4—531no—
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⋊C4—1061no—
506C2×C4⋊C4—1061no—
507C2×C4⋊C4—1061no—
508C2×C4⋊C4C22×D5311yescharacteristic
509C2×C4⋊C4C22×D5311yescharacteristic
510C2×C22⋊C4—531no—
511C2×C22⋊C4—531no—
512C2×C22⋊C4—1061no—
513C2×C22⋊C4—1061no—
514C2×C22⋊C4—1061no—
515C2×C42—21no—
516C2×C42—21no—
517C2×C42—531no—
518C2×C42—1061no—
519C2×C42—1061no—
520C2×C42—1061no—
521C2×C42—1061no—
522C2×C42—1061no—
523C2×C42C22×D5311yescharacteristic
524#107—534no—
525#107C22×D5314yes—
526#106—534no—
527#106—534no—
528C4⋊C8—534no—
529C4⋊C8—534no—
530#103—534no—
531#103—534no—
532#103—534no—
533#103—534no—
534#103—534no—
535#103—534no—
536#103C22×D5314yes—
537#103C22×D5314yes—
538C22⋊C8—534no—
539C22⋊C8—534no—
540#97—534no—
541C4×C8C22×D5314yes—
542C24—531no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—534no—
549C2×Q8—532no—
550C2×Q8—532no—
551C2×Q8—1064no—
552C2×Q8—1068no—
553C2×Q8—1068no—
554C2×Q8—10616no—
555C2×Q8—1068no—
556C2×Q8—1061no—
557C2×Q8—1061no—
558C2×Q8—1062no—
559C2×Q8—1062no—
560C2×Q8—1062no—
561C2×Q8#1171994514yes—
562C2×Q8C23×D5312yes—
563C2×Q8C23×D5312yes—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—531no—
569C22×C4—531no—
570C22×C4—531no—
571C22×C4—532no—
572C22×C4—532no—
573C22×C4—1064no—
574C22×C4—1068no—
575C22×C4—1061no—
576C22×C4—1062no—
577C22×C4—1062no—
578C22×C4—1061no—
579C22×C4—1061no—
580C22×C4—1061no—
581C22×C4D4×D5311yescharacteristic
582C22×C4D4×D5311yescharacteristic
583C22×C4C23×D5311yescharacteristic
584Q16—28no—
585Q16—1068no—
586Q16—1068no—
587Q16—1068no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—532no—
591C2×C8—532no—
592C2×C8—1062no—
593C2×C8—1062no—
594C2×C8C23×D5312yes—
595C2×C8C23×D5312yes—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—534no—
601C4⋊C4—534no—
602C4⋊C4—532no—
603C4⋊C4—532no—
604C4⋊C4—1064no—
605C4⋊C4—1064no—
606C4⋊C4—1064no—
607C4⋊C4—1064no—
608C4⋊C4—1064no—
609C4⋊C4—1064no—
610C4⋊C4—1064no—
611C4⋊C4—1064no—
612C4⋊C4—1061no—
613C4⋊C4—1061no—
614C4⋊C4—1064no—
615C4⋊C4—1064no—
616C4⋊C4C23×D5312yes—
617C4⋊C4C23×D5312yes—
618C22⋊C4—534no—
619C22⋊C4—534no—
620C22⋊C4—1064no—
621C22⋊C4—1064no—
622C22⋊C4—1064no—
623C42—24no—
624C42—24no—
625C42—532no—
626C42—532no—
627C42—1064no—
628C42—1064no—
629C42—1064no—
630C42—1064no—
631C42—1064no—
632C42D4×D5312yes—
633C42C23×D5312yes—
634C23—532no—
635C23—1062no—
636C23—1062no—
637C23—1062no—
638C23C2×D4×D5311yescharacteristic
639Q8—24no—
640Q8—22no—
641Q8—22no—
642Q8—22no—
643Q8—42no—
644Q8—534no—
645Q8—10616no—
646Q8—1064no—
647Q8—1062no—
648Q8—1062no—
649Q8—1062no—
650Q8—2122no—
651Q8C2×#1171994514yes—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—532no—
663C2×C4—532no—
664C2×C4—532no—
665C2×C4—10616no—
666C2×C4—1062no—
667C2×C4—1064no—
668C2×C4—1062no—
669C2×C4—1062no—
670C2×C4—1062no—
671C2×C4—1064no—
672C2×C4—1062no—
673C2×C4—1062no—
674C2×C4—1062no—
675C2×C4—1062no—
676C2×C4—1062no—
677C2×C4—2122no—
678C2×C4—2122no—
679C2×C4—2122no—
680C2×C4C2×D4×D5312yes—
681C2×C4C2×D4×D5312yes—
682C2×C4C2×D4×D5311yescharacteristic
683C2×C4#41×D5312yes—
684C2×C4C2×#1171994512yes—
685C2×C4C24×D5311yescharacteristic
686C8—22no—
687C8—22no—
688C8—1062no—
689C8—1062no—
690C22—1062no—
691C22—1062no—
692C22—1062no—
693C22—2124no—
694C22#1681113212yes—
695C22#1681143612yes—
696C22#1681143712yes—
697C22C22×D4×D5311yescharacteristic
698C4—22no—
699C4—22no—
700C4—24no—
701C4—42no—
702C4—42no—
703C4—42no—
704C4—1062no—
705C4—1062no—
706C4—1062no—
707C4—1064no—
708C4—2122no—
709C4—2122no—
710C4—2122no—
711C4#1681113212yes—
712C4C2×#41×D5311yescharacteristic
713C4C22×#1171994511yescharacteristic
714C2—2122no—
715C2#2028501214yesdirect product factor
716C2C2×#1681113211yescharacteristic
717C2C2×#1681143611yescharacteristic
718C2C2×#1681143711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C4×Q16×C53C2
socleC23×C53C22×D4
prime radicalC23×D53C2×D4
hypercenterC2×C4×Q16D53
hypocenterC53C2×#3127
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
3. #20285012C2direct (N × H)
6. C2×#16810932C2semidirect
7. C2×#16810929C2semidirect
8. C2×#16810832C2semidirect
9. C2×#16810831C2semidirect
12. C2×#16810728C2semidirect
13. C2×#16810728C2semidirect
14. C2×C4×Dic212C2semidirect
16. C2×C4×Q16×C53C2semidirect
45. #16810932C22semidirect
46. #16810929C22semidirect
47. #16810832C22semidirect
48. #16810831C22semidirect
51. #16810728C22semidirect
52. #16810728C22semidirect
53. C4×Dic212C22semidirect
72. C4×Q16×C53C22semidirect
369. C2×C4×Q16D53semidirect
371. C2×C53#3127semidirect
416. C4×Q16C2×D53semidirect
436. C53C2×#3127semidirect
715. C2#20285012direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112312
C2×#168110992
#202850122
C2×#168109662
C2×#168109632
C2×#168109322
C2×#168109292
C2×#168108322
C2×#168108312
C2×#168107802
C2×#168107772
C2×#168107282
C2×C4×Dic2122
C2×#168106822
C2×C4×Q16×C532
C2×#312753