Finite Group Databasebeta

← C2×#20287361 #28263661

Subgroups — C2×#20287361 #28263661

Order 13568.

1906 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811342C211yesmaximal, characteristic, complemented
2C2×#16811329C211yesmaximal, characteristic, complemented
3#20287361C2116yesmaximal, direct product factor
4C2×#16810976C211yesmaximal, characteristic, complemented
5C2×#16810972C211yesmaximal, characteristic, complemented
6C2×#16810928C211yesmaximal, characteristic, complemented
7C2×#16810927C211yesmaximal, characteristic, complemented
8C2×#16810911C211yesmaximal, characteristic, complemented
9C2×#16810837C211yesmaximal, characteristic
10C2×#16810835C211yesmaximal, characteristic
11C2×#16810827C211yesmaximal, characteristic, complemented
12C2×C8×Dic106C211yesmaximal, characteristic, complemented
13C2×C4×#11719913C211yesmaximal, characteristic, complemented
14C2×#16810708C211yesmaximal, characteristic, complemented
15C2×#16810703C211yesmaximal, characteristic
16C2×C53×#488C211yesmaximal, characteristic, complemented
17C22×#11719913C2211yescharacteristic
18C22×#11719924C2211yescharacteristic
19C22×#11719922C2211yescharacteristic
20#16811342—24no—
21#16811342C2218yescomplemented
22#16811329—24no—
23#16811329C2218yescomplemented
24C2×#13133216C2211yescharacteristic
25C2×#13133215C2211yescharacteristic
26C2×#13133210—21no—
27C2×#13133210—21no—
28C2×#13133208C2211yescharacteristic
29C2×#13133204C2211yescharacteristic
30C2×#13133197—21no—
31C2×#13133195—21no—
32C2×#13133195—21no—
33C2×#13133194—21no—
34C2×Q8×Dic53C2211yescharacteristic
35C2×C4×Dic106C2211yescharacteristic
36C2×C4×Dic106C2211yescharacteristic
37C2×C4×D212C2211yescharacteristic
38C2×D4×Dic53C2211yescharacteristic
39C2×#13133179C2211yescharacteristic
40C2×#13133179C2211yescharacteristic
41C2×#13133173—21no—
42C2×C4⋊C4×D53—21no—
43#16810976C2218yescomplemented
44#16810972C2218yescomplemented
45#16810928C2218yescomplemented
46#16810927C2218yescomplemented
47#16810911C2218yescomplemented
48#16810837C2218yes—
49#16810835C2218yes—
50#16810827C2218yescomplemented
51C8×Dic106C2218yescomplemented
52C4×#11719913C2218yescomplemented
53#16810708C2218yescomplemented
54#16810703C2218yes—
55C2×#13133150C2211yescharacteristic
56C2×#13133149C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×C4⋊#88322C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133146C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133140C2211yescharacteristic
65C2×#13133139C2211yescharacteristic
66C2×#13133138C2211yescharacteristic
67C2×C8×Dic53C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C2×#125×C53C2211yescharacteristic
70C2×#124×C53C2211yescharacteristic
71C53×#488C2218yescomplemented
72C2×#103×C53C2211yescharacteristic
73C2×#103×C53C2211yescharacteristic
74C2×#102×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×C4×C8×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106D411yescharacteristic
79C22×Dic106C2311yescharacteristic
80C22×D212C2311yescharacteristic
81C23×Dic53—21no—
82C22×C4×D53—21no—
83C22×C4×D53—21no—
84C22×C4×D53—21no—
85C2×#11719913—24no—
86C2×#11719913C2314yes—
87C2×#11719924—24no—
88C2×#11719924C2314yes—
89C2×#11719922—24no—
90C2×#11719922C2314yes—
91C22×#88322C2311yescharacteristic
92C22×#88322C2311yescharacteristic
93#13133216—22no—
94#13133216C2314yes—
95#13133215—22no—
96#13133215C2314yes—
97#13133210—28no—
98#13133210—28no—
99#13133208—22no—
100#13133208C2314yes—
101#13133204—22no—
102#13133204C2314yes—
103#13133197—28no—
104#13133195—28no—
105#13133195—28no—
106#13133194—28no—
107Q8×Dic53—22no—
108Q8×Dic53C2314yes—
109C4×Dic106—22no—
110C4×Dic106D414yes—
111C4×Dic106C2314yes—
112C4×Dic106C2314yes—
113C4×D212—22no—
114C4×D212C2314yes—
115D4×Dic53—22no—
116D4×Dic53C2314yes—
117#13133179—22no—
118#13133179—22no—
119#13133179C2314yes—
120#13133179C2314yes—
121#13133173—28no—
122C2×C4⋊Dic53—21no—
123C2×C4⋊Dic53—21no—
124C2×C4⋊Dic53D411yescharacteristic
125C2×C4⋊Dic53C2311yescharacteristic
126C2×C4⋊Dic53C2311yescharacteristic
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919D411yescharacteristic
133C2×#11719919D411yescharacteristic
134C4⋊C4×D53—28no—
135C2×C22⋊Dic53—21no—
136C2×C22⋊Dic53—21no—
137C2×C22⋊Dic53—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×C4×Dic53—21no—
142C2×C4×Dic53—21no—
143C2×C4×Dic53C2311yescharacteristic
144C2×C4×Dic53C2311yescharacteristic
145#13133150C2314yes—
146#13133149C2314yes—
147#13133148C2314yes—
148C4⋊#88322C2314yes—
149#13133146C2314yes—
150#13133146C2314yes—
151#13133142C2314yes—
152#13133141C2314yes—
153#13133140C2314yes—
154#13133140C2314yes—
155#13133139C2314yes—
156#13133138C2314yes—
157C8×Dic53C2314yes—
158C8×Dic53C2314yes—
159C22×Q8×C53C2311yescharacteristic
160C22×D4×C53C2311yescharacteristic
161C22×C8×C53C2311yescharacteristic
162C22×C8×C53C2311yescharacteristic
163#125×C53—22no—
164#125×C53C2314yes—
165#124×C53—22no—
166#124×C53C2314yes—
167C2×C4⋊C4×C53—21no—
168C2×C4⋊C4×C53—21no—
169C2×C4⋊C4×C53C2311yescharacteristic
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C22⋊C4×C53—21no—
172C2×C22⋊C4×C53—21no—
173C2×C42×C53C2311yescharacteristic
174#103×C53C2314yes—
175#103×C53C2314yes—
176#102×C53C2314yes—
177#102×C53C2314yes—
178C4×C8×C53C2314yes—
179C24×C53—21no—
180C23×D53—21no—
181C2×Q8×C53—21no—
182C2×Q8×C53—22no—
183C2×Q8×C53—22no—
184C2×Q8×C53C2412yes—
185C2×D4×C53—21no—
186C2×D4×C53—22no—
187C2×D4×C53—22no—
188C2×D4×C53C2412yes—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53C2×D411yescharacteristic
193C22×C4×C53C2×D411yescharacteristic
194C22×C4×C53C2411yescharacteristic
195C22×Dic53—21no—
196C22×Dic53—21no—
197C22×Dic53—21no—
198C22×Dic53—24no—
199C22×Dic53—44no—
200C22×Dic53C2×D411yescharacteristic
201C22×Dic53C2×D411yescharacteristic
202C22×Dic53C2×D411yescharacteristic
203C22×Dic53C2×D411yescharacteristic
204C2×D212—21no—
205C2×D212—22no—
206C2×D212#4114yes—
207C2×D212C2412yes—
208C2×C4×D53—24no—
209C2×C4×D53—24no—
210C2×C4×D53—24no—
211C2×C4×D53—44no—
212C2×C4×D53—82no—
213C2×C4×D53—82no—
214C2×Dic106—24no—
215C2×Dic106—22no—
216C2×Dic106—22no—
217C2×Dic106—21no—
218C2×Dic106—24no—
219C2×Dic106—82no—
220C2×Dic106C2×D414yes—
221C2×Dic106C2412yes—
222C2×C8×C53—22no—
223C2×C8×C53—22no—
224C2×C8×C53C2412yes—
225C2×C8×C53C2412yes—
226C4⋊C4×C53—24no—
227C4⋊C4×C53—24no—
228C4⋊C4×C53—21no—
229C4⋊C4×C53—21no—
230C4⋊C4×C53C2412yes—
231C4⋊C4×C53C2412yes—
232C22⋊C4×C53—24no—
233C22⋊C4×C53—24no—
234C42×C53C2×D412yes—
235C42×C53C2412yes—
236C22⋊Dic53—24no—
237C22⋊Dic53—24no—
238C22⋊Dic53—24no—
239#11719924—28no—
240#11719922—28no—
241#11719921—24no—
242#11719921—24no—
243#11719921—24no—
244C4⋊Dic53—21no—
245C4⋊Dic53—21no—
246C4⋊Dic53—24no—
247C4⋊Dic53—24no—
248C4⋊Dic53C2×D414yes—
249C4⋊Dic53C2412yes—
250C4⋊Dic53C2412yes—
251#11719919—24no—
252#11719919—24no—
253#11719919—24no—
254#11719919—24no—
255#11719919—24no—
256#11719919C2×D414yes—
257#11719919C2×D414yes—
258C4×Dic53—24no—
259C4×Dic53—24no—
260C4×Dic53C2×D412yes—
261C4×Dic53C2×D412yes—
262C4×Dic53C2412yes—
263C4×Dic53C2412yes—
264C2×#88322—22no—
265C2×#88322—22no—
266C2×#88322C2412yes—
267C2×#88322C2412yes—
268#11719913—28no—
269C23×C53—22no—
270C23×C53—42no—
271C23×C53—42no—
272C23×C53—42no—
273C23×C53C22×D411yescharacteristic
274C22×D53—24no—
275C22×D53—22no—
276C22×D53—42no—
277C22×D53—42no—
278Q8×C53—22no—
279Q8×C53—22no—
280Q8×C53—42no—
281D4×C53—22no—
282D4×C53—22no—
283D4×C53—42no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—42no—
290C2×C4×C53—42no—
291C2×C4×C53—42no—
292C2×C4×C53C22×D412yes—
293C2×C4×C53C22×D412yes—
294C2×C4×C53C22×D411yescharacteristic
295C2×C4×C53C2×#4112yes—
296C2×C4×C532−1+412yes—
297C2×C4×C53C2511yescharacteristic
298C2×Dic53—22no—
299C2×Dic53—22no—
300C2×Dic53—22no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—42no—
305C2×Dic53—42no—
306C2×Dic53—42no—
307C2×Dic53—48no—
308C2×Dic53#13514yes—
309C2×Dic53C22×D412yes—
310C2×Dic53C22×D412yes—
311C2×Dic53C22×D412yes—
312C2×Dic53C22×D412yes—
313D212—24no—
314D212—22no—
315D212C2×#4114yes—
316C4×D53—48no—
317C4×D53—84no—
318C4×D53—84no—
319Dic106—28no—
320Dic106—22no—
321Dic106—22no—
322Dic106—42no—
323Dic106—84no—
324C8×C53—22no—
325C8×C53—22no—
326#88322—22no—
327#88322—22no—
328C2×#3360—531nomaximal, Sylow
329C22×C53—42no—
330C22×C53—42no—
331C22×C53—42no—
332C22×C53—84no—
333C22×C53#54812yes—
334C22×C53C2×#13512yes—
335C22×C53#57712yes—
336C22×C53C23×D411yescharacteristic
337C2×D53—24no—
338C2×D53—48no—
339C2×D53—42no—
340C2×D53—42no—
341C4×C53—22no—
342C4×C53—22no—
343C4×C53—42no—
344C4×C53—42no—
345C4×C53—42no—
346C4×C53#54812yes—
347C4×C53C22×#4111yescharacteristic
348C4×C53C2×2−1+411yescharacteristic
349Dic53—22no—
350Dic53—22no—
351Dic53—22no—
352Dic53—42no—
353Dic53—42no—
354Dic53—42no—
355Dic53C2×#13514yes—
356C2×#556—531no—
357C2×#554—531no—
358#3360—5316no—
359C2×#488—531no—
360C2×#488D5311yescharacteristic, complemented
361C2×#487—531no—
362C2×#479—531no—
363C2×#479—531no—
364C2×#476—531no—
365C2×#463—531no—
366C2×#463—531no—
367C2×#461—531no—
368C2×C8×Q8—531no—
369C2×C4×SD16—531no—
370C2×C4×SD16—531no—
371C2×C4×D8—531no—
372C2×C53—82no—
373C2×C53#336014yescomplemented
374C2×C53C2×#54811yescharacteristic
375C2×C53C22×#13511yescharacteristic
376C2×C53C2×#57711yescharacteristic
377D53—44no—
378C22×SD16—531no—
379C22×SD16—531no—
380C22×D8—531no—
381#556—538no—
382#556—1064no—
383#554—538no—
384#554—1064no—
385C2×C4⋊Q8—531no—
386C2×C4⋊Q8—531no—
387C2×#126—1061no—
388C2×#126—1061no—
389C2×#125—531no—
390C2×#125C2×D5311yescharacteristic
391C2×#124—531no—
392C2×#124C2×D5311yescharacteristic
393C2×C22⋊Q8—1061no—
394C2×C22⋊Q8—1061no—
395C2×C22⋊Q8—1061no—
396C2×C22⋊Q8—1061no—
397C2×C4×Q8—531no—
398C2×C4×Q8—531no—
399C2×C4×Q8—531no—
400C2×C4×D4—531no—
401C2×C4×D4—531no—
402C2×C4×D4—531no—
403C2×C4×D4—531no—
404C2×#117—1061no—
405C22×C4⋊C4—1061no—
406#488—538no—
407#488C2×D5318yescomplemented
408#487—538no—
409#479—538no—
410#479—538no—
411#476—538no—
412#463—538no—
413#463—538no—
414#461—538no—
415C8×Q8—538no—
416C4×SD16—538no—
417C4×SD16—538no—
418C4×D8—538no—
419C2×#107—531no—
420C2×#106—531no—
421C2×#106—531no—
422C2×C4⋊C8—531no—
423C2×C4⋊C8—531no—
424C2×C4⋊C8—531no—
425C2×#103—531no—
426C2×#103—531no—
427C2×#103—531no—
428C2×#103—531no—
429C2×#103C2×D5311yescharacteristic
430C2×#103C2×D5311yescharacteristic
431C2×#102—531no—
432C2×#102—531no—
433C2×#102C2×D5311yescharacteristic
434C2×#102C2×D5311yescharacteristic
435C2×C4×C8—531no—
436C2×C4×C8—531no—
437C2×C4×C8C2×D5311yescharacteristic
438C53C2×#336011yescharacteristic, complemented, Sylow
439C22×Q8—531no—
440C22×Q8—531no—
441C22×Q8—1061no—
442C22×Q8C22×D5311yescharacteristic
443C22×D4—531no—
444C22×D4C22×D5311yescharacteristic
445C23×C4—1061no—
446C23×C4—1061no—
447C23×C4—1061no—
448C23×C4—1061no—
449C2×SD16—534no—
450C2×SD16—534no—
451C2×SD16—1064no—
452C2×SD16—1064no—
453C2×D8—534no—
454C2×D8—1064no—
455C22×C8—531no—
456C22×C8—531no—
457C22×C8C22×D5311yescharacteristic
458C22×C8C22×D5311yescharacteristic
459C4⋊Q8—534no—
460C4⋊Q8—534no—
461C4⋊Q8—1062no—
462C4⋊Q8—1062no—
463#126—1068no—
464#126—1068no—
465#125—22no—
466#125—534no—
467#125—1062no—
468#125C22×D5314yes—
469#124—22no—
470#124—534no—
471#124—1062no—
472#124C22×D5314yes—
473C22⋊Q8—1068no—
474C22⋊Q8—1068no—
475C22⋊Q8—1068no—
476C22⋊Q8—1068no—
477C4×Q8—534no—
478C4×Q8—534no—
479C4×Q8—534no—
480C4×Q8—534no—
481C4×Q8—1062no—
482C4×Q8—1062no—
483C4×D4—534no—
484C4×D4—534no—
485C4×D4—534no—
486C4×D4—534no—
487C4×D4—1062no—
488C4×D4—1062no—
489C4×D4—1062no—
490C4×D4—1062no—
491#117—1068no—
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—531no—
499C2×C4⋊C4—1068no—
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⋊C4C22×D5311yescharacteristic
508C2×C4⋊C4C22×D5311yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—1061no—
512C2×C22⋊C4—1061no—
513C2×C22⋊C4—1061no—
514C2×C22⋊C4—1061no—
515C2×C22⋊C4—1061no—
516C2×C22⋊C4—1061no—
517C2×C42—531no—
518C2×C42—531no—
519C2×C42—1061no—
520C2×C42—1061no—
521C2×C42C22×D5311yescharacteristic
522#107—534no—
523#106—534no—
524#106—534no—
525C4⋊C8—534no—
526C4⋊C8—534no—
527C4⋊C8—534no—
528#103—534no—
529#103—534no—
530#103—534no—
531#103—534no—
532#103C22×D5314yes—
533#103C22×D5314yes—
534#102—534no—
535#102—534no—
536#102C22×D5314yes—
537#102C22×D5314yes—
538C4×C8—534no—
539C4×C8—534no—
540C4×C8C22×D5314yes—
541C24—21no—
542C24—1061no—
543C2×Q8—21no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—534no—
547C2×Q8—532no—
548C2×Q8—1064no—
549C2×Q8—1064no—
550C2×Q8—1061no—
551C2×Q8—1062no—
552C2×Q8—1062no—
553C2×Q8—4242no—
554C2×Q8C23×D5312yes—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—534no—
559C2×D4—532no—
560C2×D4—1061no—
561C2×D4—1062no—
562C2×D4C23×D5312yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—531no—
567C22×C4—531no—
568C22×C4—531no—
569C22×C4—531no—
570C22×C4—1064no—
571C22×C4—1064no—
572C22×C4—1064no—
573C22×C4—1061no—
574C22×C4—1061no—
575C22×C4—1061no—
576C22×C4—1064no—
577C22×C4—4242no—
578C22×C4—4242no—
579C22×C4—2124no—
580C22×C4—2124no—
581C22×C4D4×D5311yescharacteristic
582C22×C4D4×D5311yescharacteristic
583C22×C4C23×D5311yescharacteristic
584SD16—1068no—
585SD16—1068no—
586D8—1068no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—532no—
590C2×C8—532no—
591C2×C8—1062no—
592C2×C8—1062no—
593C2×C8C23×D5312yes—
594C2×C8C23×D5312yes—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—534no—
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—1061no—
611C4⋊C4—1061no—
612C4⋊C4—1064no—
613C4⋊C4C23×D5312yes—
614C4⋊C4C23×D5312yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—1064no—
618C22⋊C4—1064no—
619C22⋊C4—1064no—
620C22⋊C4—1064no—
621C22⋊C4—1064no—
622C22⋊C4—1064no—
623C42—532no—
624C42—532no—
625C42—532no—
626C42—532no—
627C42—1064no—
628C42—1064no—
629C42D4×D5312yes—
630C42C23×D5312yes—
631C23—22no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—1064no—
636C23—1062no—
637C23—2122no—
638C23—2122no—
639C23C2×D4×D5311yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—42no—
643Q8—1068no—
644Q8—1062no—
645Q8—1062no—
646Q8—4244no—
647Q8—2122no—
648D4—22no—
649D4—22no—
650D4—42no—
651D4—534no—
652D4—1064no—
653D4—1062no—
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—534no—
663C2×C4—532no—
664C2×C4—532no—
665C2×C4—532no—
666C2×C4—532no—
667C2×C4—1062no—
668C2×C4—1062no—
669C2×C4—1062no—
670C2×C4—1062no—
671C2×C4—1062no—
672C2×C4—1062no—
673C2×C4—4244no—
674C2×C4—4244no—
675C2×C4—2128no—
676C2×C4—2128no—
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×C4#1313326412yes—
685C2×C4C24×D5311yescharacteristic
686C8—22no—
687C8—22no—
688C8—1062no—
689C8—1062no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—84no—
694C22—1064no—
695C22—2128no—
696C22—2122no—
697C22—2122no—
698C22#1681128112yes—
699C22#135×D5312yes—
700C22#1681143012yes—
701C22C22×D4×D5311yescharacteristic
702C4—22no—
703C4—22no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—534no—
708C4—1062no—
709C4—1062no—
710C4—1062no—
711C4—2122no—
712C4—2122no—
713C4—2122no—
714C4#1681128112yes—
715C4C2×#41×D5311yescharacteristic
716C4C2×#1313326411yescharacteristic
717C2—82no—
718C2—2124no—
719C2#2028736114yesdirect product factor
720C2C2×#1681128111yescharacteristic
721C2C2×#135×D5311yescharacteristic
722C2C2×#1681143011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#488C2
socleC23×C53C22×D4
prime radicalC22×#11719922C22
hypercenterC2×#488D53
hypocenterC53C2×#3360
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#488

Complements

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

NH ≅ G/Ntype
1. C2×#16811342C2semidirect
2. C2×#16811329C2semidirect
3. #20287361C2direct (N × H)
4. C2×#16810976C2semidirect
5. C2×#16810972C2semidirect
6. C2×#16810928C2semidirect
7. C2×#16810927C2semidirect
8. C2×#16810911C2semidirect
11. C2×#16810827C2semidirect
12. C2×C8×Dic106C2semidirect
13. C2×C4×#11719913C2semidirect
14. C2×#16810708C2semidirect
16. C2×C53×#488C2semidirect
21. #16811342C22semidirect
23. #16811329C22semidirect
43. #16810976C22semidirect
44. #16810972C22semidirect
45. #16810928C22semidirect
46. #16810927C22semidirect
47. #16810911C22semidirect
50. #16810827C22semidirect
51. C8×Dic106C22semidirect
52. C4×#11719913C22semidirect
53. #16810708C22semidirect
71. C53×#488C22semidirect
360. C2×#488D53semidirect
373. C2×C53#3360semidirect
407. #488C2×D53semidirect
438. C53C2×#3360semidirect
719. C2#20287361direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113422
C2×#168113292
#202873612
C2×#168109762
C2×#168109722
C2×#168109282
C2×#168109272
C2×#168109112
C2×#168108372
C2×#168108352
C2×#168108272
C2×C8×Dic1062
C2×C4×#117199132
C2×#168107082
C2×#168107032
C2×C53×#4882
C2×#336053