Finite Group Databasebeta

← C2×#20285013 #28252446

Subgroups — C2×#20285013 #28252446

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×#16811234C211yesmaximal, characteristic
2C2×#16811099C211yesmaximal, characteristic
3#20285013C2116yesmaximal, direct product factor
4C2×#16810963C211yesmaximal, characteristic
5C2×#16810962C211yesmaximal, characteristic
6C2×#16810931C211yesmaximal, characteristic, complemented
7C2×#16810930C211yesmaximal, characteristic, complemented
8C2×#16810830C211yesmaximal, characteristic, complemented
9C2×#16810777C211yesmaximal, characteristic
10C2×#16810777C211yesmaximal, characteristic
11C2×#16810730C211yesmaximal, characteristic, complemented
12C2×#16810727C211yesmaximal, characteristic, complemented
13C2×Q16×Dic53C211yesmaximal, characteristic, complemented
14C2×#16810715C211yesmaximal, characteristic, complemented
15C2×#16810683C211yesmaximal, characteristic
16C2×C53×#462C211yesmaximal, characteristic, complemented
17C22×Q8×D53C2211yescharacteristic
18C22×#11719925C2211yescharacteristic
19C22×#11719925C2211yescharacteristic
20#16811234—24no—
21#16811234C2218yes—
22C2×#13133212—21no—
23C2×#13133212—21no—
24C2×#13133209C2211yescharacteristic
25C2×#13133207—21no—
26C2×#13133207—21no—
27C2×#13133193C2211yescharacteristic
28C2×#13133193C2211yescharacteristic
29#16811099—24no—
30#16811099C2218yes—
31C2×Q8×Dic53C2211yescharacteristic
32C2×Q8×Dic53C2211yescharacteristic
33C2×Q8×Dic53C2211yescharacteristic
34C2×C4×Dic106—21no—
35C2×C4×Dic106C2211yescharacteristic
36C2×#13133182—21no—
37C2×#13133182C2211yescharacteristic
38C2×#13133175—21no—
39C2×#13133175C2211yescharacteristic
40C2×#13133174—21no—
41C2×#13133174C2211yescharacteristic
42#16810963C2218yes—
43#16810962C2218yes—
44#16810931C2218yescomplemented
45#16810930C2218yescomplemented
46#16810830C2218yescomplemented
47#16810777C2218yes—
48#16810777C2218yes—
49#16810730C2218yescomplemented
50#16810727C2218yescomplemented
51Q16×Dic53C2218yescomplemented
52#16810715C2218yescomplemented
53#16810683C2218yes—
54C2×#13133151C2211yescharacteristic
55C2×#13133150C2211yescharacteristic
56C2×#13133149C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×C4⋊#88322C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133141C2211yescharacteristic
64C2×#13133141C2211yescharacteristic
65C2×#13133129C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×Q16×C53C2211yescharacteristic
70C22×Q16×C53C2211yescharacteristic
71C2×C4⋊Q8×C53C2211yescharacteristic
72C2×C4×Q8×C53C2211yescharacteristic
73C53×#462C2218yescomplemented
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#103×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106C2311yescharacteristic
79C2×Q8×D53—24no—
80C2×Q8×D53—22no—
81C2×Q8×D53—24no—
82C2×Q8×D53C2314yes—
83C22×C4×D53—21no—
84C22×C4×D53C2311yescharacteristic
85C2×#11719925—24no—
86C2×#11719925—24no—
87C2×#11719925C2314yes—
88C2×#11719925C2314yes—
89C22×#88322C2311yescharacteristic
90C22×#88322C2311yescharacteristic
91#13133212—28no—
92#13133212—28no—
93#13133209—22no—
94#13133209C2314yes—
95#13133207—28no—
96#13133207—28no—
97#13133193—22no—
98#13133193—22no—
99#13133193C2314yes—
100#13133193C2314yes—
101Q8×Dic53—22no—
102Q8×Dic53—22no—
103Q8×Dic53—22no—
104Q8×Dic53C2314yes—
105Q8×Dic53C2314yes—
106Q8×Dic53C2314yes—
107C4×Dic106—22no—
108C4×Dic106—28no—
109C4×Dic106C2314yes—
110#13133182—28no—
111#13133182—22no—
112#13133182C2314yes—
113#13133175—28no—
114#13133175—22no—
115#13133175C2314yes—
116#13133174—28no—
117#13133174D414yes—
118#13133174C2314yes—
119C2×C4⋊Dic53—21no—
120C2×C4⋊Dic53—21no—
121C2×C4⋊Dic53—21no—
122C2×C4⋊Dic53C2311yescharacteristic
123C2×C4⋊Dic53C2311yescharacteristic
124C2×C4⋊Dic53C2311yescharacteristic
125C2×#11719919—21no—
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919D411yescharacteristic
132C2×#11719919D411yescharacteristic
133C2×#11719921—21no—
134C2×#11719921—21no—
135C2×#11719921—21no—
136C2×#11719921D411yescharacteristic
137C2×#11719921D411yescharacteristic
138C2×C4×Dic53—21no—
139C2×C4×Dic53—21no—
140C2×C4×Dic53—21no—
141C2×C4×Dic53—21no—
142C2×C4×Dic53—21no—
143C2×C4×Dic53—21no—
144C2×C4×Dic53C2311yescharacteristic
145#13133151C2314yes—
146#13133150C2314yes—
147#13133149C2314yes—
148#13133148C2314yes—
149C4⋊#88322C2314yes—
150#13133142C2314yes—
151#13133142C2314yes—
152#13133141C2314yes—
153#13133141C2314yes—
154#13133141C2314yes—
155#13133141C2314yes—
156#13133129C2314yes—
157#13133129C2314yes—
158#13133127C2314yes—
159C8×Dic53C2314yes—
160C22×Q8×C53C2311yescharacteristic
161C22×Q8×C53C2311yescharacteristic
162C22×Q8×C53C2311yescharacteristic
163C2×Q16×C53—24no—
164C2×Q16×C53—24no—
165C2×Q16×C53C2314yes—
166C2×Q16×C53C2314yes—
167C22×C8×C53C2311yescharacteristic
168C22×C8×C53C2311yescharacteristic
169C4⋊Q8×C53—22no—
170C4⋊Q8×C53C2314yes—
171C4×Q8×C53—22no—
172C4×Q8×C53C2314yes—
173C2×C4⋊C4×C53—21no—
174C2×C4⋊C4×C53—21no—
175C2×C4⋊C4×C53—21no—
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C42×C53—21no—
178C2×C42×C53C2311yescharacteristic
179C4⋊C8×C53C2314yes—
180#103×C53C2314yes—
181#103×C53C2314yes—
182C23×D53C2×D411yescharacteristic
183C2×Q8×C53—21no—
184C2×Q8×C53—21no—
185C2×Q8×C53—21no—
186C2×Q8×C53—22no—
187C2×Q8×C53—22no—
188C2×Q8×C53—22no—
189C2×Q8×C53—22no—
190C2×Q8×C53—22no—
191C2×Q8×C53#4114yes—
192C2×Q8×C53C2412yes—
193C2×Q8×C53C2412yes—
194C2×Q8×C53C2412yes—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2411yescharacteristic
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53C2×D411yescharacteristic
207C22×Dic53C2×D411yescharacteristic
208C22×Dic53C2×D411yescharacteristic
209Q8×D53—216no—
210Q8×D53—28no—
211Q8×D53—28no—
212C2×C4×D53—28no—
213C2×C4×D53—24no—
214C2×C4×D53—22no—
215C2×C4×D53—22no—
216C2×C4×D53C2×D412yes—
217C2×C4×D53C2412yes—
218C2×Dic106—28no—
219C2×Dic106—21no—
220C2×Dic106—22no—
221C2×Dic106—24no—
222C2×Dic106#4114yes—
223C2×Dic106C2412yes—
224Q16×C53—28no—
225Q16×C53—28no—
226C2×C8×C53—22no—
227C2×C8×C53—22no—
228C2×C8×C53C2412yes—
229C2×C8×C53C2412yes—
230C4⋊C4×C53—24no—
231C4⋊C4×C53—24no—
232C4⋊C4×C53—24no—
233C4⋊C4×C53—21no—
234C4⋊C4×C53C2412yes—
235C42×C53—24no—
236C42×C53C2×D412yes—
237C42×C53C2412yes—
238#11719925—28no—
239#11719925—28no—
240#11719921—24no—
241#11719921—24no—
242#11719921—24no—
243#11719921C2×D414yes—
244#11719921C2×D414yes—
245C4⋊Dic53—21no—
246C4⋊Dic53—21no—
247C4⋊Dic53—21no—
248C4⋊Dic53—24no—
249C4⋊Dic53—24no—
250C4⋊Dic53—24no—
251C4⋊Dic53C2412yes—
252C4⋊Dic53C2412yes—
253C4⋊Dic53C2412yes—
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×Dic53—24no—
268C4×Dic53C2×D412yes—
269C4×Dic53C2412yes—
270C2×#88322—22no—
271C2×#88322—22no—
272C2×#88322C2412yes—
273C2×#88322C2412yes—
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—22no—
284Q8×C53—22no—
285Q8×C53—42no—
286Q8×C53—42no—
287Q8×C53C2×#4114yes—
288C2×C4×C53—24no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—42no—
296C2×C4×C53—42no—
297C2×C4×C53—42no—
298C2×C4×C53C22×D412yes—
299C2×C4×C53C22×D412yes—
300C2×C4×C53C22×D411yescharacteristic
301C2×C4×C53C2×#4112yes—
302C2×C4×C53C2×#4112yes—
303C2×C4×C53C2511yescharacteristic
304C2×Dic53—22no—
305C2×Dic53—24no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—42no—
313C2×Dic53—42no—
314C2×Dic53—42no—
315C2×Dic53C22×D412yes—
316C2×Dic53C22×D412yes—
317C2×Dic53C22×D412yes—
318C4×D53—216no—
319C4×D53—24no—
320C4×D53—22no—
321C4×D53—22no—
322Dic106—216no—
323Dic106—24no—
324Dic106—22no—
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×#462D5311yescharacteristic, complemented
364C2×#451—531no—
365C2×#451—531no—
366C2×#441—531no—
367C2×#441—531no—
368C2×C4×Q16—531no—
369C2×C4×Q16—531no—
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×Q16C2×D5311yescharacteristic
380C22×Q16C2×D5311yescharacteristic
381#541—538no—
382#541—1064no—
383C2×C4⋊Q8C2×D5311yescharacteristic
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—531no—
398C2×C4×Q8—1061no—
399C2×C4×Q8—1061no—
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#462C2×D5318yescomplemented
411#451—538no—
412#451—538no—
413#441—538no—
414#441—538no—
415C4×Q16—538no—
416C4×Q16—538no—
417#433—538no—
418C2×#107—531no—
419C2×#107—531no—
420C2×#106—531no—
421C2×#106—531no—
422C2×C4⋊C8—531no—
423C2×C4⋊C8C2×D5311yescharacteristic
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×C8—531no—
436C53C2×#312711yescharacteristic, complemented, Sylow
437C22×Q8—534no—
438C22×Q8—531no—
439C22×Q8—1061no—
440C22×Q8—1062no—
441C22×Q8—1064no—
442C22×Q8—1064no—
443C22×Q8C22×D5311yescharacteristic
444C22×Q8C22×D5311yescharacteristic
445C22×Q8C22×D5311yescharacteristic
446C23×C4—531no—
447C23×C4—1061no—
448C2×Q16—24no—
449C2×Q16—24no—
450C2×Q16—534no—
451C2×Q16—534no—
452C2×Q16—1064no—
453C2×Q16—1064no—
454C2×Q16C22×D5314yes—
455C2×Q16C22×D5314yes—
456C22×C8—531no—
457C22×C8—531no—
458C22×C8C22×D5311yescharacteristic
459C22×C8C22×D5311yescharacteristic
460C4⋊Q8—22no—
461C4⋊Q8C22×D5314yes—
462#126—1068no—
463#126—1068no—
464#125—534no—
465#125—1068no—
466#125—1068no—
467#125—1062no—
468C22⋊Q8—534no—
469C22⋊Q8—534no—
470C22⋊Q8—1062no—
471C22⋊Q8—1062no—
472C4×Q8—22no—
473C4×Q8—534no—
474C4×Q8—534no—
475C4×Q8—534no—
476C4×Q8—534no—
477C4×Q8—534no—
478C4×Q8—1068no—
479C4×Q8—1062no—
480C4×Q8—1062no—
481C4×Q8—1062no—
482C4×Q8—1062no—
483C4×Q8—1068no—
484C4×Q8—1062no—
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—21no—
495C2×C4⋊C4—531no—
496C2×C4⋊C4—531no—
497C2×C4⋊C4—531no—
498C2×C4⋊C4—531no—
499C2×C4⋊C4—531no—
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⋊C4—1061no—
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—531no—
517C2×C42—1061no—
518C2×C42—1061no—
519C2×C42—1061no—
520C2×C42—1061no—
521C2×C42—1061no—
522C2×C42—1061no—
523C2×C42C22×D5311yescharacteristic
524#107—534no—
525#107—534no—
526#106—534no—
527#106—534no—
528C4⋊C8—534no—
529C4⋊C8C22×D5314yes—
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×C8—534no—
542C24—531no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—534no—
552C2×Q8—532no—
553C2×Q8—1064no—
554C2×Q8—1068no—
555C2×Q8—1068no—
556C2×Q8—10616no—
557C2×Q8—1068no—
558C2×Q8—1061no—
559C2×Q8—1062no—
560C2×Q8#1171994714yes—
561C2×Q8C23×D5312yes—
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—28no—
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—24no—
599C4⋊C4—21no—
600C4⋊C4—534no—
601C4⋊C4—534no—
602C4⋊C4—532no—
603C4⋊C4—532no—
604C4⋊C4—532no—
605C4⋊C4—1064no—
606C4⋊C4—1064no—
607C4⋊C4—1064no—
608C4⋊C4—1064no—
609C4⋊C4—1064no—
610C4⋊C4—1064no—
611C4⋊C4—1061no—
612C4⋊C4—1061no—
613C4⋊C4—1061no—
614C4⋊C4—1064no—
615C4⋊C4—1064no—
616C4⋊C4—1064no—
617C4⋊C4C23×D5312yes—
618C22⋊C4—534no—
619C22⋊C4—534no—
620C22⋊C4—1064no—
621C22⋊C4—1064no—
622C22⋊C4—1064no—
623C42—24no—
624C42—532no—
625C42—532no—
626C42—1064no—
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—22no—
644Q8—22no—
645Q8—42no—
646Q8—42no—
647Q8—534no—
648Q8—10616no—
649Q8—1064no—
650Q8—1062no—
651Q8C2×#1171994714yes—
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×#1171994712yes—
685C2×C4C24×D5311yescharacteristic
686C8—22no—
687C8—22no—
688C8—1062no—
689C8—1062no—
690C22—1062no—
691C22—1062no—
692C22—1062no—
693C22—2124no—
694C22#1681113312yes—
695C22#1681143612yes—
696C22#1681143912yes—
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#1681113312yes—
712C4C2×#41×D5311yescharacteristic
713C4C22×#1171994711yescharacteristic
714C2—2122no—
715C2#2028501314yesdirect product factor
716C2C2×#1681113311yescharacteristic
717C2C2×#1681143611yescharacteristic
718C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#462C2
socleC23×C53C22×D4
prime radicalC23×D53C2×D4
hypercenterC2×#462D53
hypocenterC53C2×#3127
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
3. #20285013C2direct (N × H)
6. C2×#16810931C2semidirect
7. C2×#16810930C2semidirect
8. C2×#16810830C2semidirect
11. C2×#16810730C2semidirect
12. C2×#16810727C2semidirect
13. C2×Q16×Dic53C2semidirect
14. C2×#16810715C2semidirect
16. C2×C53×#462C2semidirect
44. #16810931C22semidirect
45. #16810930C22semidirect
46. #16810830C22semidirect
49. #16810730C22semidirect
50. #16810727C22semidirect
51. Q16×Dic53C22semidirect
52. #16810715C22semidirect
73. C53×#462C22semidirect
363. C2×#462D53semidirect
371. C2×C53#3127semidirect
410. #462C2×D53semidirect
436. C53C2×#3127semidirect
715. C2#20285013direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112342
C2×#168110992
#202850132
C2×#168109632
C2×#168109622
C2×#168109312
C2×#168109302
C2×#168108302
C2×#168107772
C2×#168107302
C2×#168107272
C2×Q16×Dic532
C2×#168107152
C2×#168106832
C2×C53×#4622
C2×#312753