Finite Group Databasebeta

← C2×#20285910 #28256232

Subgroups — C2×#20285910 #28256232

Order 13568.

2038 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811176C211yesmaximal, characteristic, complemented
2C2×#16811168C211yesmaximal, characteristic
3#20285910C2116yesmaximal, direct product factor
4C2×#16811031C211yesmaximal, characteristic, complemented
5C2×#16811030C211yesmaximal, characteristic, complemented
6C2×#16810986C211yesmaximal, characteristic, complemented
7C2×#16810986C211yesmaximal, characteristic, complemented
8C2×#16810948C211yesmaximal, characteristic, complemented
9C2×#16810947C211yesmaximal, characteristic, complemented
10C2×#16810944C211yesmaximal, characteristic, complemented
11C2×#16810912C211yesmaximal, characteristic, complemented
12C2×#16810911C211yesmaximal, characteristic, complemented
13C2×#16810902C211yesmaximal, characteristic, complemented
14C2×#16810901C211yesmaximal, characteristic, complemented
15C2×#16810677C211yesmaximal, characteristic, complemented
16C2×C53×#482C211yesmaximal, characteristic, complemented
17C22×#11719947—21no—
18#16811176—24no—
19#16811176C2218yescomplemented
20#16811168—24no—
21#16811168C2218yes—
22C2×#13133216C2211yescharacteristic
23C2×#13133216C2211yescharacteristic
24C2×#13133216C2211yescharacteristic
25C2×#13133213C2211yescharacteristic
26C2×#13133208C2211yescharacteristic
27C2×#13133208C2211yescharacteristic
28C2×#13133203—21no—
29C2×#13133194—21no—
30C2×#13133194—21no—
31C2×#13133191C2211yescharacteristic
32C2×#13133189—21no—
33C2×C4×Dic106—21no—
34C2×C4×Dic106—21no—
35C2×D4×Dic53C2211yescharacteristic
36C2×#13133179C2211yescharacteristic
37C2×#13133177—21no—
38C2×#13133176C2211yescharacteristic
39C22×C4×Dic53C2211yescharacteristic
40#16811031C2218yescomplemented
41#16811030C2218yescomplemented
42#16810986C2218yescomplemented
43#16810986C2218yescomplemented
44#16810948C2218yescomplemented
45#16810947C2218yescomplemented
46#16810944C2218yescomplemented
47#16810912C2218yescomplemented
48#16810911C2218yescomplemented
49#16810902C2218yescomplemented
50#16810901C2218yescomplemented
51#16810677C2218yescomplemented
52C2×#13133151C2211yescharacteristic
53C2×#13133150C2211yescharacteristic
54C2×#13133150C2211yescharacteristic
55C2×#13133149C2211yescharacteristic
56C2×#13133148C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×#13133146C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133139C2211yescharacteristic
61C2×#13133139C2211yescharacteristic
62C2×#13133138C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×#13133127C2211yescharacteristic
69C2×#121×C53C2211yescharacteristic
70C2×#117×C53C2211yescharacteristic
71C53×#482C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×#102×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C2×#11719947—28no—
78C2×#11719947—48no—
79C22×Dic106—21no—
80C22×Dic106—21no—
81C22×Dic106—21no—
82C22×D212C2311yescharacteristic
83C22×C22⋊D53—21no—
84C22×C22⋊D53—21no—
85C22×C22⋊D53—21no—
86C23×Dic53—21no—
87C23×Dic53D411yescharacteristic
88C23×Dic53D411yescharacteristic
89C22×C4×D53—21no—
90C22×#88322C2311yescharacteristic
91C22×#88322C2311yescharacteristic
92#13133216—22no—
93#13133216—22no—
94#13133216—22no—
95#13133216C2314yes—
96#13133216C2314yes—
97#13133216C2314yes—
98#13133213—22no—
99#13133213C2314yes—
100#13133208—22no—
101#13133208—22no—
102#13133208C2314yes—
103#13133208C2314yes—
104#13133203—28no—
105#13133194—28no—
106#13133194—28no—
107#13133191—22no—
108#13133191C2314yes—
109#13133189—28no—
110C4×Dic106—28no—
111C4×Dic106—28no—
112D4×Dic53—22no—
113D4×Dic53C2314yes—
114#13133179—22no—
115#13133179C2314yes—
116#13133177—28no—
117#13133176—22no—
118#13133176C2314yes—
119C2×C4⋊Dic53—21no—
120C2×C4⋊Dic53—21no—
121C2×C4⋊Dic53C2311yescharacteristic
122C2×C4⋊Dic53C2311yescharacteristic
123C2×C4⋊Dic53C2311yescharacteristic
124C2×#11719919—21no—
125C2×#11719919—21no—
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×C22⋊Dic53—21no—
130C2×C22⋊Dic53—21no—
131C2×#11719921—21no—
132C2×#11719921—21no—
133C2×C4×Dic53—21no—
134C2×C4×Dic53D411yescharacteristic
135C2×C4×Dic53D411yescharacteristic
136C2×C4×Dic53D414yes—
137C2×C4×Dic53C2311yescharacteristic
138C2×C4×Dic53C2311yescharacteristic
139C2×C4×Dic53C2314yes—
140#13133151C2314yes—
141#13133150C2314yes—
142#13133150C2314yes—
143#13133149C2314yes—
144#13133148C2314yes—
145#13133148C2314yes—
146#13133146C2314yes—
147#13133146C2314yes—
148#13133139C2314yes—
149#13133139C2314yes—
150#13133138C2314yes—
151#13133138C2314yes—
152#13133137C2314yes—
153#13133137C2314yes—
154C22⋊#88322C2314yes—
155#13133127C2314yes—
156#13133127C2314yes—
157C22×D4×C53—21no—
158C22×D4×C53C2311yescharacteristic
159C23×C4×C53C2311yescharacteristic
160C22×C8×C53C2311yescharacteristic
161C22×C8×C53C2311yescharacteristic
162#121×C53—22no—
163#121×C53C2314yes—
164#117×C53—22no—
165#117×C53C2314yes—
166C2×C4⋊C4×C53C2311yescharacteristic
167C2×C4⋊C4×C53C2311yescharacteristic
168C2×C4⋊C4×C53C2311yescharacteristic
169C2×C22⋊C4×C53—21no—
170C2×C22⋊C4×C53—21no—
171C2×C42×C53—21no—
172#107×C53C2314yes—
173#106×C53C2314yes—
174#102×C53C2314yes—
175#102×C53C2314yes—
176C22⋊C8×C53C2314yes—
177C24×C53—21no—
178C24×C53C2×D411yescharacteristic
179C23×D53—21no—
180C2×D4×C53—24no—
181C2×D4×C53—21no—
182C2×D4×C53—22no—
183C2×D4×C53—22no—
184C2×D4×C53—44no—
185C2×D4×C53C2412yes—
186C22×C4×C53—22no—
187C22×C4×C53—22no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53C2×D411yescharacteristic
192C22×C4×C53C2×D412yes—
193C22×C4×C53C2412yes—
194C22×C4×C53C2411yescharacteristic
195C2×C22⋊D53—24no—
196C2×C22⋊D53—24no—
197C2×C22⋊D53—24no—
198C2×C22⋊D53—44no—
199C2×C22⋊D53—44no—
200C2×C22⋊D53—44no—
201C22×Dic53—24no—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—24no—
206C22×Dic53—42no—
207C22×Dic53—44no—
208C22×Dic53C2×D411yescharacteristic
209C22×Dic53C2×D411yescharacteristic
210C22×Dic53C2×D411yescharacteristic
211C22×Dic53C2×D414yes—
212C22×Dic53C2×D414yes—
213C22×Dic53C2×D411yescharacteristic
214#11719947—432no—
215C2×D212—22no—
216C2×D212—22no—
217C2×D212—21no—
218C2×D212C2412yes—
219C2×C4×D53—24no—
220C2×C4×D53—44no—
221C2×Dic106—24no—
222C2×Dic106—24no—
223C2×Dic106—24no—
224C2×Dic106—44no—
225C2×Dic106—44no—
226C2×Dic106—44no—
227C2×C8×C53—22no—
228C2×C8×C53—22no—
229C2×C8×C53C2412yes—
230C2×C8×C53C2412yes—
231C4⋊C4×C53—21no—
232C4⋊C4×C53—21no—
233C4⋊C4×C53—21no—
234C4⋊C4×C53C2412yes—
235C4⋊C4×C53C2412yes—
236C4⋊C4×C53C2412yes—
237C22⋊C4×C53—24no—
238C22⋊C4×C53—24no—
239C42×C53—24no—
240C22⋊Dic53—24no—
241C22⋊Dic53—24no—
242#11719921—24no—
243#11719921—24no—
244C4⋊Dic53—21no—
245C4⋊Dic53—21no—
246C4⋊Dic53—21no—
247C4⋊Dic53—24no—
248C4⋊Dic53—24no—
249C4⋊Dic53C2412yes—
250C4⋊Dic53C2412yes—
251C4⋊Dic53C2412yes—
252#11719919—24no—
253#11719919—24no—
254#11719919—24no—
255#11719919—24no—
256#11719919—24no—
257C4×Dic53—24no—
258C4×Dic53C2×D414yes—
259C4×Dic53C2×D412yes—
260C4×Dic53C2×D414yes—
261C4×Dic53C2×D412yes—
262C4×Dic53C2412yes—
263C4×Dic53C2412yes—
264C2×#88322—22no—
265C2×#88322—22no—
266C2×#88322C2412yes—
267C2×#88322C2412yes—
268C23×C53—22no—
269C23×C53—22no—
270C23×C53—22no—
271C23×C53—22no—
272C23×C53—42no—
273C23×C53—42no—
274C23×C53—42no—
275C23×C53C22×D412yes—
276C23×C53C22×D411yescharacteristic
277C22×D53—22no—
278C22×D53—42no—
279C22×D53—42no—
280C22×D53—42no—
281D4×C53—22no—
282D4×C53—22no—
283D4×C53—48no—
284D4×C53—42no—
285C2×C4×C53—22no—
286C2×C4×C53—24no—
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×D411yescharacteristic
297C2×C4×C532−1+412yes—
298C2×C4×C532−1+412yes—
299C2×C4×C53C2511yescharacteristic
300C22⋊D53—48no—
301C22⋊D53—48no—
302C22⋊D53—48no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—28no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—44no—
311C2×Dic53—42no—
312C2×Dic53—42no—
313C2×Dic53—42no—
314C2×Dic53—48no—
315C2×Dic53AGL(1,ℤ/8)14yes—
316C2×Dic53C22×D412yes—
317C2×Dic53C22×D412yes—
318C2×Dic53C22×D412yes—
319C2×Dic53C22×D412yes—
320D212—22no—
321D212—22no—
322D212—42no—
323C4×D53—48no—
324Dic106—48no—
325Dic106—48no—
326Dic106—48no—
327C8×C53—22no—
328C8×C53—22no—
329#88322—22no—
330#88322—22no—
331C2×#3235—531nomaximal, Sylow
332C22×C53—22no—
333C22×C53—22no—
334C22×C53—22no—
335C22×C53—44no—
336C22×C53—42no—
337C22×C53—42no—
338C22×C53—42no—
339C22×C53—84no—
340C22×C53#53612yes—
341C22×C53C2×AGL(1,ℤ/8)12yes—
342C22×C53#57512yes—
343C22×C53C23×D411yescharacteristic
344C2×D53—42no—
345C2×D53—42no—
346C2×D53—42no—
347C2×D53—84no—
348C4×C53—22no—
349C4×C53—42no—
350C4×C53—42no—
351C4×C53—42no—
352C4×C53#53612yes—
353C4×C53C2×2−1+411yescharacteristic
354C4×C53C2×2−1+411yescharacteristic
355Dic53—22no—
356Dic53—22no—
357Dic53—22no—
358Dic53—42no—
359Dic53—42no—
360Dic53—42no—
361Dic53C2×AGL(1,ℤ/8)14yes—
362C2×#533—531no—
363C2×#532—531no—
364#3235—5316no—
365C2×#501—531no—
366C2×#501—531no—
367C2×#490—531no—
368C2×#490—531no—
369C2×#482—531no—
370C2×#482—531no—
371C2×#482—531no—
372C2×#482D5311yescharacteristic, complemented
373C2×#476—531no—
374C2×#476—531no—
375C2×#474—531no—
376C2×#474—531no—
377C2×#432—531no—
378C2×C53—42no—
379C2×C53—82no—
380C2×C53#323514yescomplemented
381C2×C53C2×#53611yescharacteristic
382C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
383C2×C53C2×#57511yescharacteristic
384D53—82no—
385C22×#41—1061no—
386#533—538no—
387#533—1064no—
388#532—538no—
389#532—1064no—
390C2×C4⋊Q8—531no—
391C2×C4⋊Q8—531no—
392C2×C4⋊Q8—531no—
393C2×#127—531no—
394C2×#125—531no—
395C2×#125—531no—
396C2×#124—1061no—
397C2×C22⋊Q8—1061no—
398C2×C22⋊Q8—1061no—
399C2×#121—531no—
400C2×#121—1061no—
401C2×#121C2×D5311yescharacteristic
402C2×C4×Q8—1061no—
403C2×C4×Q8—1061no—
404C2×C4×D4—531no—
405C2×C4×D4—531no—
406C2×C4×D4—1061no—
407C2×#117—531no—
408C2×#117C2×D5311yescharacteristic
409C22×C42—531no—
410#501—538no—
411#501—538no—
412#490—538no—
413#490—538no—
414#482—538no—
415#482—538no—
416#482—538no—
417#482C2×D5318yescomplemented
418#476—538no—
419#476—538no—
420#474—538no—
421#474—538no—
422#432—538no—
423C2×#107—531no—
424C2×#107—531no—
425C2×#107—531no—
426C2×#107C2×D5311yescharacteristic
427C2×#106—531no—
428C2×#106—531no—
429C2×#106—531no—
430C2×#106C2×D5311yescharacteristic
431C2×C4⋊C8—531no—
432C2×C4⋊C8—531no—
433C2×#102—531no—
434C2×#102—531no—
435C2×#102—531no—
436C2×#102—531no—
437C2×#102—531no—
438C2×#102—531no—
439C2×#102C2×D5311yescharacteristic
440C2×#102C2×D5311yescharacteristic
441C2×C22⋊C8—531no—
442C2×C22⋊C8C2×D5311yescharacteristic
443C2×#97—531no—
444C2×#97—531no—
445C53C2×#323511yescharacteristic, complemented, Sylow
446C2×#41—1068no—
447C2×#41—2128no—
448C22×Q8—1061no—
449C22×Q8—1061no—
450C22×Q8—1061no—
451C22×D4—21no—
452C22×D4—531no—
453C22×D4—1061no—
454C22×D4—1061no—
455C22×D4—1061no—
456C22×D4C22×D5311yescharacteristic
457C23×C4—531no—
458C23×C4—531no—
459C23×C4—1061no—
460C23×C4—1061no—
461C23×C4C22×D5311yescharacteristic
462C22×C8—531no—
463C22×C8—531no—
464C22×C8C22×D5311yescharacteristic
465C22×C8C22×D5311yescharacteristic
466C4⋊Q8—534no—
467C4⋊Q8—534no—
468C4⋊Q8—534no—
469C4⋊Q8—1062no—
470C4⋊Q8—1062no—
471C4⋊Q8—1062no—
472#127—534no—
473#127—1062no—
474#125—534no—
475#125—534no—
476#125—1062no—
477#125—1062no—
478#124—1068no—
479C22⋊Q8—1068no—
480C22⋊Q8—1068no—
481#121—22no—
482#121—534no—
483#121—1068no—
484#121—1062no—
485#121C22×D5314yes—
486C4×Q8—1068no—
487C4×Q8—1068no—
488C4×D4—534no—
489C4×D4—534no—
490C4×D4—1068no—
491C4×D4—1062no—
492C4×D4—1062no—
493#117—22no—
494#117—534no—
495#117—1062no—
496#117C22×D5314yes—
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⋊C4C22×D5311yescharacteristic
508C2×C4⋊C4C22×D5311yescharacteristic
509C2×C4⋊C4C22×D5311yescharacteristic
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—1061no—
513C2×C22⋊C4—1061no—
514C2×C22⋊C4—1061no—
515C2×C22⋊C4—1061no—
516C2×C42—21no—
517C2×C42—531no—
518C2×C42—531no—
519C2×C42—534no—
520C2×C42—531no—
521C2×C42—531no—
522C2×C42—534no—
523C2×C42—1061no—
524#107—534no—
525#107—534no—
526#107—534no—
527#107C22×D5314yes—
528#106—534no—
529#106—534no—
530#106—534no—
531#106C22×D5314yes—
532C4⋊C8—534no—
533C4⋊C8—534no—
534#102—534no—
535#102—534no—
536#102—534no—
537#102—534no—
538#102—534no—
539#102—534no—
540#102C22×D5314yes—
541#102C22×D5314yes—
542C22⋊C8—534no—
543C22⋊C8C22×D5314yes—
544#97—534no—
545#97—534no—
546C24—21no—
547C24—1061no—
548C24D4×D5311yescharacteristic
549#41—21232no—
550C2×Q8—1064no—
551C2×Q8—1064no—
552C2×Q8—1064no—
553C2×Q8—2124no—
554C2×Q8—2124no—
555C2×Q8—2124no—
556C2×D4—24no—
557C2×D4—21no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—44no—
561C2×D4—532no—
562C2×D4—1064no—
563C2×D4—1064no—
564C2×D4—1064no—
565C2×D4—1061no—
566C2×D4—1062no—
567C2×D4—1062no—
568C2×D4—2124no—
569C2×D4—2124no—
570C2×D4—2124no—
571C2×D4C23×D5312yes—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—531no—
578C22×C4—534no—
579C22×C4—531no—
580C22×C4—531no—
581C22×C4—531no—
582C22×C4—534no—
583C22×C4—1064no—
584C22×C4—1064no—
585C22×C4—1064no—
586C22×C4—1061no—
587C22×C4—1061no—
588C22×C4—1061no—
589C22×C4—2124no—
590C22×C4—2124no—
591C22×C4—2122no—
592C22×C4D4×D5312yes—
593C22×C4D4×D5311yescharacteristic
594C22×C4C23×D5312yes—
595C22×C4C23×D5311yescharacteristic
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—532no—
599C2×C8—532no—
600C2×C8—1062no—
601C2×C8—1062no—
602C2×C8C23×D5312yes—
603C2×C8C23×D5312yes—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—532no—
608C4⋊C4—532no—
609C4⋊C4—532no—
610C4⋊C4—1064no—
611C4⋊C4—1064no—
612C4⋊C4—1064no—
613C4⋊C4—1064no—
614C4⋊C4—1064no—
615C4⋊C4—1064no—
616C4⋊C4—1064no—
617C4⋊C4—1061no—
618C4⋊C4—1061no—
619C4⋊C4—1061no—
620C4⋊C4C23×D5312yes—
621C4⋊C4C23×D5312yes—
622C4⋊C4C23×D5312yes—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—1064no—
626C22⋊C4—1064no—
627C22⋊C4—1064no—
628C22⋊C4—1064no—
629C42—24no—
630C42—534no—
631C42—532no—
632C42—534no—
633C42—532no—
634C42—532no—
635C42—532no—
636C42—1064no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—1062no—
645C23—2122no—
646C23—2122no—
647C23—2122no—
648C23C2×D4×D5312yes—
649C23C2×D4×D5311yescharacteristic
650Q8—2128no—
651Q8—2128no—
652Q8—2128no—
653D4—22no—
654D4—22no—
655D4—48no—
656D4—42no—
657D4—1062no—
658D4—1062no—
659D4—2128no—
660D4—2128no—
661D4—2128no—
662D4—2122no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—534no—
674C2×C4—532no—
675C2×C4—532no—
676C2×C4—532no—
677C2×C4—532no—
678C2×C4—1068no—
679C2×C4—1062no—
680C2×C4—1062no—
681C2×C4—1062no—
682C2×C4—1062no—
683C2×C4—1062no—
684C2×C4—1062no—
685C2×C4—2128no—
686C2×C4—2128no—
687C2×C4—2124no—
688C2×C4—2122no—
689C2×C4—2122no—
690C2×C4—2122no—
691C2×C4C2×D4×D5312yes—
692C2×C4C2×D4×D5311yescharacteristic
693C2×C4#1313326412yes—
694C2×C4#1313326412yes—
695C2×C4C24×D5311yescharacteristic
696C8—22no—
697C8—22no—
698C8—1062no—
699C8—1062no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—84no—
708C22—4244no—
709C22—2122no—
710C22—2122no—
711C22—2122no—
712C22#1681119512yes—
713C22AGL(1,ℤ/8)×D5312yes—
714C22#1681142012yes—
715C22C22×D4×D5311yescharacteristic
716C4—22no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—534no—
721C4—1062no—
722C4—1062no—
723C4—1062no—
724C4—2122no—
725C4—2122no—
726C4—2122no—
727C4#1681119512yes—
728C4C2×#1313326411yescharacteristic
729C4C2×#1313326411yescharacteristic
730C2—42no—
731C2—82no—
732C2—4242no—
733C2#2028591014yesdirect product factor
734C2C2×#1681119511yescharacteristic
735C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
736C2C2×#1681142011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#482C2
socleC23×C53C22×D4
prime radicalC2×#16811168C2
hypercenterC2×#482D53
hypocenterC53C2×#3235
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#16811176C2semidirect
3. #20285910C2direct (N × H)
4. C2×#16811031C2semidirect
5. C2×#16811030C2semidirect
6. C2×#16810986C2semidirect
7. C2×#16810986C2semidirect
8. C2×#16810948C2semidirect
9. C2×#16810947C2semidirect
10. C2×#16810944C2semidirect
11. C2×#16810912C2semidirect
12. C2×#16810911C2semidirect
13. C2×#16810902C2semidirect
14. C2×#16810901C2semidirect
15. C2×#16810677C2semidirect
16. C2×C53×#482C2semidirect
19. #16811176C22semidirect
40. #16811031C22semidirect
41. #16811030C22semidirect
42. #16810986C22semidirect
43. #16810986C22semidirect
44. #16810948C22semidirect
45. #16810947C22semidirect
46. #16810944C22semidirect
47. #16810912C22semidirect
48. #16810911C22semidirect
49. #16810902C22semidirect
50. #16810901C22semidirect
51. #16810677C22semidirect
71. C53×#482C22semidirect
372. C2×#482D53semidirect
380. C2×C53#3235semidirect
417. #482C2×D53semidirect
445. C53C2×#3235semidirect
733. C2#20285910direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111762
C2×#168111682
#202859102
C2×#168110312
C2×#168110302
C2×#168109862
C2×#168109482
C2×#168109472
C2×#168109442
C2×#168109122
C2×#168109112
C2×#168109022
C2×#168109012
C2×#168106772
C2×C53×#4822
C2×#323553