Finite Group Databasebeta

← C2×#20285998 #28256313

Subgroups — C2×#20285998 #28256313

Order 13568.

1742 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811244C211yesmaximal, characteristic
2#20285998C2116yesmaximal, direct product factor
3C2×#16811033C211yesmaximal, characteristic, complemented
4C2×#16811026C211yesmaximal, characteristic, complemented
5C2×#16810985C211yesmaximal, characteristic, complemented
6C2×#16810980C211yesmaximal, characteristic, complemented
7C2×#16810958C211yesmaximal, characteristic, complemented
8C2×#16810964C211yesmaximal, characteristic, complemented
9C2×#16810947C211yesmaximal, characteristic
10C2×#16810936C211yesmaximal, characteristic
11C2×#16810927C211yesmaximal, characteristic, complemented
12C2×#16810915C211yesmaximal, characteristic, complemented
13C2×#16810920C211yesmaximal, characteristic, complemented
14C2×#16810900C211yesmaximal, characteristic, complemented
15C2×#16810684C211yesmaximal, characteristic, complemented
16C2×C53×#544C211yesmaximal, characteristic, complemented
17#16811244—24no—
18#16811244C2218yes—
19C2×#13133217C2211yescharacteristic
20C2×#13133212—21no—
21C2×#13133205C2211yescharacteristic
22C2×#13133203—21no—
23C2×#13133199—21no—
24C2×#13133196C2211yescharacteristic
25C2×#13133195—21no—
26C2×#13133191C2211yescharacteristic
27C2×C4×Dic106C2211yescharacteristic
28C2×C4×D212C2211yescharacteristic
29#16811033C2218yescomplemented
30#16811026C2218yescomplemented
31#16810985C2218yescomplemented
32#16810980C2218yescomplemented
33#16810964C2218yescomplemented
34#16810958C2218yescomplemented
35#16810947C2218yes—
36#16810936C2218yes—
37#16810927C2218yescomplemented
38#16810920C2218yescomplemented
39#16810915C2218yescomplemented
40#16810900C2218yescomplemented
41#16810684C2218yescomplemented
42C2×#13133150C2211yescharacteristic
43C2×#13133150C2211yescharacteristic
44C2×#13133150C2211yescharacteristic
45C2×#13133150C2211yescharacteristic
46C2×#13133150C2211yescharacteristic
47C2×#13133150C2211yescharacteristic
48C2×#13133148C2211yescharacteristic
49C2×#13133148C2211yescharacteristic
50C2×C4⋊#88322C2211yescharacteristic
51C2×C4⋊#88322C2211yescharacteristic
52C2×#13133140C2211yescharacteristic
53C2×#13133140C2211yescharacteristic
54C2×#13133140C2211yescharacteristic
55C2×#13133140C2211yescharacteristic
56C2×#13133137C2211yescharacteristic
57C2×#13133137C2211yescharacteristic
58C2×#13133137C2211yescharacteristic
59C2×#13133137C2211yescharacteristic
60C2×C22⋊#88322C2211yescharacteristic
61C2×C22⋊#88322C2211yescharacteristic
62C2×#13133128C2211yescharacteristic
63C2×C4×#88322C2211yescharacteristic
64C53×#544—24no—
65C53×#544C2218yescomplemented
66C2×C4⋊Q8×C53—21no—
67C2×C4⋊Q8×C53C2211yescharacteristic
68C2×C4⋊Q8×C53C2211yescharacteristic
69C2×#125×C53—21no—
70C2×#125×C53C2211yescharacteristic
71C2×#125×C53C2211yescharacteristic
72C2×C22⋊Q8×C53—21no—
73C2×C22⋊Q8×C53—21no—
74C2×#117×C53C2211yescharacteristic
75C2×#117×C53C2211yescharacteristic
76C22×C4⋊C4×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106C2311yescharacteristic
79C22×D212C2311yescharacteristic
80C22×C22⋊D53—21no—
81C22×C4×D53—21no—
82C22×#88322C2311yescharacteristic
83C22×#88322C2311yescharacteristic
84C22×#88322C2311yescharacteristic
85C22×#88322C2311yescharacteristic
86#13133217—22no—
87#13133217C2314yes—
88#13133212—28no—
89#13133205—22no—
90#13133205C2314yes—
91#13133203—28no—
92#13133199—28no—
93#13133196—22no—
94#13133196C2314yes—
95#13133195—28no—
96#13133191—22no—
97#13133191C2314yes—
98C4×Dic106—22no—
99C4×Dic106C2314yes—
100C4×D212—22no—
101C4×D212C2314yes—
102C2×C4⋊Dic53—21no—
103C2×C4⋊Dic53C2311yescharacteristic
104C2×C4⋊Dic53C2311yescharacteristic
105C2×#11719919—21no—
106C2×#11719919—21no—
107C2×C22⋊Dic53—21no—
108C2×#11719921—21no—
109C2×#11719921—21no—
110C2×#11719921—21no—
111C2×#11719921—21no—
112C2×C4×Dic53—21no—
113#13133150C2314yes—
114#13133150C2314yes—
115#13133150C2314yes—
116#13133150C2314yes—
117#13133150C2314yes—
118#13133150C2314yes—
119#13133148C2314yes—
120#13133148C2314yes—
121C4⋊#88322C2314yes—
122C4⋊#88322C2314yes—
123#13133140C2314yes—
124#13133140C2314yes—
125#13133140C2314yes—
126#13133140C2314yes—
127#13133137C2314yes—
128#13133137C2314yes—
129#13133137C2314yes—
130#13133137C2314yes—
131C22⋊#88322C2314yes—
132C22⋊#88322C2314yes—
133#13133128C2314yes—
134C4×#88322C2314yes—
135C22×Q8×C53—21no—
136C22×Q8×C53—21no—
137C23×C4×C53—21no—
138C23×C4×C53C2311yescharacteristic
139C4⋊Q8×C53—28no—
140C4⋊Q8×C53—22no—
141C4⋊Q8×C53—22no—
142C4⋊Q8×C53C2314yes—
143C4⋊Q8×C53C2314yes—
144#125×C53—28no—
145#125×C53—22no—
146#125×C53—22no—
147#125×C53C2314yes—
148#125×C53C2314yes—
149C22⋊Q8×C53—28no—
150C22⋊Q8×C53—28no—
151#117×C53—22no—
152#117×C53D414yes—
153#117×C53C2314yes—
154#117×C53C2314yes—
155C2×C4⋊C4×C53—21no—
156C2×C4⋊C4×C53—22no—
157C2×C4⋊C4×C53—21no—
158C2×C4⋊C4×C53—21no—
159C2×C4⋊C4×C53—21no—
160C2×C4⋊C4×C53—21no—
161C2×C4⋊C4×C53—21no—
162C2×C4⋊C4×C53—21no—
163C2×C4⋊C4×C53D411yescharacteristic
164C2×C4⋊C4×C53D411yescharacteristic
165C2×C4⋊C4×C53C2311yescharacteristic
166C2×C4⋊C4×C53C2311yescharacteristic
167C2×C4⋊C4×C53C2314yes—
168C2×C4⋊C4×C53C2311yescharacteristic
169C2×C4⋊C4×C53C2311yescharacteristic
170C2×C22⋊C4×C53—21no—
171C2×C22⋊C4×C53D411yescharacteristic
172C2×C22⋊C4×C53D411yescharacteristic
173C2×C42×C53—21no—
174C2×C42×C53C2311yescharacteristic
175C2×C42×C53C2311yescharacteristic
176C24×C53C2×D411yescharacteristic
177C23×D53—21no—
178C2×Q8×C53—24no—
179C2×Q8×C53—24no—
180C2×Q8×C53—82no—
181C2×Q8×C53—82no—
182C22×C4×C53—22no—
183C22×C4×C53—22no—
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—24no—
189C22×C4×C53—82no—
190C22×C4×C53C2×D411yescharacteristic
191C22×C4×C53C2×D411yescharacteristic
192C22×C4×C53C2×D411yescharacteristic
193C22×C4×C53C2×D411yescharacteristic
194C22×C4×C53C2×D411yescharacteristic
195C22×C4×C53C2×D412yes—
196C22×C4×C53C2412yes—
197C22×C4×C53C2411yescharacteristic
198C2×C22⋊D53—24no—
199C2×C22⋊D53—82no—
200C22×Dic53—21no—
201C22×Dic53—21no—
202C22×Dic53—21no—
203C2×D212—22no—
204C2×D212—22no—
205C2×D212—21no—
206C2×D212C2412yes—
207C2×C4×D53—24no—
208C2×C4×D53—82no—
209C2×Dic106—22no—
210C2×Dic106—22no—
211C2×Dic106—21no—
212C2×Dic106—24no—
213C2×Dic106—82no—
214C2×Dic106C2412yes—
215C4⋊C4×C53—24no—
216C4⋊C4×C53—21no—
217C4⋊C4×C53—21no—
218C4⋊C4×C53—24no—
219C4⋊C4×C53—24no—
220C4⋊C4×C53—24no—
221C4⋊C4×C53—24no—
222C4⋊C4×C53—24no—
223C4⋊C4×C53—24no—
224C4⋊C4×C53—21no—
225C4⋊C4×C53—21no—
226C4⋊C4×C53C2×D414yes—
227C4⋊C4×C53C2×D414yes—
228C4⋊C4×C53C2412yes—
229C4⋊C4×C53C2412yes—
230C4⋊C4×C53C2412yes—
231C4⋊C4×C53C2412yes—
232C22⋊C4×C53—24no—
233C22⋊C4×C53C2×D414yes—
234C22⋊C4×C53C2×D414yes—
235C42×C53—24no—
236C42×C53C2×D412yes—
237C42×C53C2×D412yes—
238C42×C53C2412yes—
239C42×C53C2412yes—
240C22⋊Dic53—24no—
241#11719921—24no—
242#11719921—24no—
243#11719921—24no—
244#11719921—24no—
245C4⋊Dic53—24no—
246C4⋊Dic53—21no—
247C4⋊Dic53—21no—
248C4⋊Dic53C2412yes—
249C4⋊Dic53C2412yes—
250#11719919—24no—
251#11719919—24no—
252C4×Dic53—24no—
253C2×#88322—22no—
254C2×#88322—22no—
255C2×#88322—22no—
256C2×#88322—22no—
257C2×#88322C2412yes—
258C2×#88322C2412yes—
259C2×#88322C2412yes—
260C2×#88322C2412yes—
261C23×C53—22no—
262C23×C53—22no—
263C23×C53—22no—
264C23×C53C22×D412yes—
265C23×C53C22×D411yescharacteristic
266C22×D53—22no—
267C22×D53—42no—
268C22×D53—42no—
269C22×D53—42no—
270Q8×C53—84no—
271Q8×C53—84no—
272C2×C4×C53—22no—
273C2×C4×C53—22no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—22no—
277C2×C4×C53—24no—
278C2×C4×C53—22no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—42no—
285C2×C4×C53—42no—
286C2×C4×C53—42no—
287C2×C4×C53—42no—
288C2×C4×C53—84no—
289C2×C4×C53C22×D412yes—
290C2×C4×C53C22×D412yes—
291C2×C4×C53C22×D412yes—
292C2×C4×C53C22×D412yes—
293C2×C4×C53C22×D412yes—
294C2×C4×C53C22×D411yescharacteristic
295C2×C4×C532−1+412yes—
296C2×C4×C532−1+412yes—
297C2×C4×C53C2511yescharacteristic
298C22⋊D53—84no—
299C2×Dic53—22no—
300C2×Dic53—22no—
301C2×Dic53—22no—
302C2×Dic53—42no—
303C2×Dic53—42no—
304C2×Dic53—42no—
305D212—22no—
306D212—22no—
307D212—42no—
308C4×D53—84no—
309Dic106—22no—
310Dic106—22no—
311Dic106—42no—
312Dic106—84no—
313#88322—22no—
314#88322—22no—
315#88322—22no—
316#88322—22no—
317C2×#3243—531nomaximal, Sylow
318C22×C53—22no—
319C22×C53—22no—
320C22×C53—22no—
321C22×C53—44no—
322C22×C53#53612yes—
323C22×C53#57612yes—
324C22×C53#57812yes—
325C22×C53C23×D411yescharacteristic
326C2×D53—42no—
327C2×D53—42no—
328C2×D53—42no—
329C2×D53—84no—
330C4×C53—22no—
331C4×C53—22no—
332C4×C53—22no—
333C4×C53—22no—
334C4×C53—22no—
335C4×C53—42no—
336C4×C53—42no—
337C4×C53—42no—
338C4×C53—42no—
339C4×C53#53612yes—
340C4×C53C2×2−1+411yescharacteristic
341C4×C53C2×2−1+411yescharacteristic
342Dic53—42no—
343Dic53—42no—
344Dic53—42no—
345C2×#544D5311yescharacteristic, complemented
346C2×#542—531no—
347#3243—5316no—
348C2×#501—531no—
349C2×#500—531no—
350C2×#489—531no—
351C2×#488—531no—
352C2×#484—531no—
353C2×#485—531no—
354C2×#482—531no—
355C2×#480—531no—
356C2×#479—531no—
357C2×#477—531no—
358C2×#478—531no—
359C2×#474—531no—
360C2×#433—531no—
361C2×C53—42no—
362C2×C53#324314yescomplemented
363C2×C53C2×#53611yescharacteristic
364C2×C53C2×#57611yescharacteristic
365C2×C53C2×#57811yescharacteristic
366D53—82no—
367#544—24no—
368#544C2×D5318yescomplemented
369#542—538no—
370#542—1064no—
371C2×C4⋊Q8—21no—
372C2×C4⋊Q8—531no—
373C2×C4⋊Q8C2×D5311yescharacteristic
374C2×C4⋊Q8C2×D5311yescharacteristic
375C2×#126—1061no—
376C2×#125—21no—
377C2×#125C2×D5311yescharacteristic
378C2×#125C2×D5311yescharacteristic
379C2×#124—531no—
380C2×#124—1061no—
381C2×#123—1061no—
382C2×C22⋊Q8—21no—
383C2×C22⋊Q8—21no—
384C2×C22⋊Q8—531no—
385C2×C22⋊Q8—1061no—
386C2×#121—531no—
387C2×C4×Q8—531no—
388C2×C4×D4—531no—
389C2×#117C2×D5311yescharacteristic
390C2×#117C2×D5311yescharacteristic
391C22×C4⋊C4C2×D5311yescharacteristic
392#501—538no—
393#500—538no—
394#489—538no—
395#488—538no—
396#485—538no—
397#484—538no—
398#482—538no—
399#480—538no—
400#479—538no—
401#478—538no—
402#477—538no—
403#474—538no—
404#433—538no—
405C2×#107—531no—
406C2×#107—531no—
407C2×#107—531no—
408C2×#107—531no—
409C2×#107—531no—
410C2×#107—531no—
411C2×#106—531no—
412C2×#106—531no—
413C2×C4⋊C8—531no—
414C2×C4⋊C8—531no—
415C2×#103—531no—
416C2×#103—531no—
417C2×#103—531no—
418C2×#103—531no—
419C2×#102—531no—
420C2×#102—531no—
421C2×#102—531no—
422C2×#102—531no—
423C2×C22⋊C8—531no—
424C2×C22⋊C8—531no—
425C2×#97—531no—
426C2×C4×C8—531no—
427C53C2×#324311yescharacteristic, complemented, Sylow
428C22×Q8—21no—
429C22×Q8—21no—
430C22×Q8—531no—
431C22×Q8—1061no—
432C22×D4—531no—
433C22×D4—1061no—
434C23×C4—21no—
435C23×C4—1061no—
436C23×C4C22×D5311yescharacteristic
437C22×C8—531no—
438C22×C8—531no—
439C22×C8—531no—
440C22×C8—531no—
441C4⋊Q8—28no—
442C4⋊Q8—22no—
443C4⋊Q8—22no—
444C4⋊Q8—534no—
445C4⋊Q8—1062no—
446C4⋊Q8C22×D5314yes—
447C4⋊Q8C22×D5314yes—
448#126—1068no—
449#125—28no—
450#125—22no—
451#125—22no—
452#125C22×D5314yes—
453#125C22×D5314yes—
454#124—534no—
455#124—1068no—
456#124—1062no—
457#123—1068no—
458C22⋊Q8—28no—
459C22⋊Q8—28no—
460C22⋊Q8—534no—
461C22⋊Q8—1062no—
462C22⋊Q8—1068no—
463#121—534no—
464#121—1062no—
465C4×Q8—534no—
466C4×Q8—1062no—
467C4×D4—534no—
468C4×D4—1062no—
469#117—22no—
470#117C22⋊D5314yes—
471#117C22×D5314yes—
472#117C22×D5314yes—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—531no—
482C2×C4⋊C4—531no—
483C2×C4⋊C4—1061no—
484C2×C4⋊C4—1061no—
485C2×C4⋊C4—1061no—
486C2×C4⋊C4C22⋊D5311yescharacteristic
487C2×C4⋊C4C22⋊D5311yescharacteristic
488C2×C4⋊C4C22×D5311yescharacteristic
489C2×C4⋊C4C22×D5311yescharacteristic
490C2×C4⋊C4C22×D5314yes—
491C2×C4⋊C4C22×D5311yescharacteristic
492C2×C4⋊C4C22×D5311yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—1061no—
495C2×C22⋊C4—1061no—
496C2×C22⋊C4—1061no—
497C2×C22⋊C4—1061no—
498C2×C22⋊C4—1061no—
499C2×C22⋊C4C22⋊D5311yescharacteristic
500C2×C22⋊C4C22⋊D5311yescharacteristic
501C2×C42—21no—
502C2×C42—1061no—
503C2×C42C22×D5311yescharacteristic
504C2×C42C22×D5311yescharacteristic
505#107—534no—
506#107—534no—
507#107—534no—
508#107—534no—
509#107—534no—
510#107—534no—
511#106—534no—
512#106—534no—
513C4⋊C8—534no—
514C4⋊C8—534no—
515#103—534no—
516#103—534no—
517#103—534no—
518#103—534no—
519#102—534no—
520#102—534no—
521#102—534no—
522#102—534no—
523C22⋊C8—534no—
524C22⋊C8—534no—
525#97—534no—
526C4×C8—534no—
527C24—1061no—
528C24C2×C22⋊D5311yescharacteristic
529C2×Q8—24no—
530C2×Q8—24no—
531C2×Q8—82no—
532C2×Q8—82no—
533C2×Q8—532no—
534C2×Q8—1064no—
535C2×Q8—1061no—
536C2×Q8—1062no—
537C2×Q8—1062no—
538C2×Q8—4242no—
539C2×D4—532no—
540C2×D4—1064no—
541C2×D4—1061no—
542C2×D4—1062no—
543C2×D4—1062no—
544C2×D4—4242no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—24no—
552C22×C4—82no—
553C22×C4—1061no—
554C22×C4—1061no—
555C22×C4—1061no—
556C22×C4—1064no—
557C22×C4—4242no—
558C22×C4C2×C22⋊D5312yes—
559C22×C4C2×C22⋊D5311yescharacteristic
560C22×C4C2×C22⋊D5311yescharacteristic
561C22×C4C2×C22⋊D5311yescharacteristic
562C22×C4C2×C22⋊D5311yescharacteristic
563C22×C4C2×C22⋊D5311yescharacteristic
564C22×C4C23×D5312yes—
565C22×C4C23×D5311yescharacteristic
566C2×C8—532no—
567C2×C8—532no—
568C2×C8—532no—
569C2×C8—532no—
570C2×C8—1062no—
571C2×C8—1062no—
572C2×C8—1062no—
573C2×C8—1062no—
574C4⋊C4—24no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—532no—
586C4⋊C4—532no—
587C4⋊C4—1061no—
588C4⋊C4—1061no—
589C4⋊C4—1064no—
590C4⋊C4—1064no—
591C4⋊C4—1064no—
592C4⋊C4C2×C22⋊D5314yes—
593C4⋊C4C2×C22⋊D5314yes—
594C4⋊C4C23×D5312yes—
595C4⋊C4C23×D5312yes—
596C4⋊C4C23×D5312yes—
597C4⋊C4C23×D5312yes—
598C22⋊C4—24no—
599C22⋊C4—1064no—
600C22⋊C4—1064no—
601C22⋊C4—1064no—
602C22⋊C4—1064no—
603C22⋊C4—1064no—
604C22⋊C4C2×C22⋊D5314yes—
605C22⋊C4C2×C22⋊D5314yes—
606C42—24no—
607C42—1064no—
608C42C2×C22⋊D5312yes—
609C42C2×C22⋊D5312yes—
610C42C23×D5312yes—
611C42C23×D5312yes—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—1062no—
616C23—2122no—
617C23—2122no—
618C23—2122no—
619C23C22×C22⋊D5312yes—
620C23C22×C22⋊D5311yescharacteristic
621Q8—84no—
622Q8—84no—
623Q8—1062no—
624Q8—1062no—
625Q8—4244no—
626Q8—2122no—
627D4—1062no—
628D4—1062no—
629D4—4244no—
630D4—2122no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—24no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—84no—
648C2×C4—1062no—
649C2×C4—1062no—
650C2×C4—1062no—
651C2×C4—4244no—
652C2×C4—2122no—
653C2×C4—2122no—
654C2×C4—2122no—
655C2×C4C22×C22⋊D5312yes—
656C2×C4C22×C22⋊D5312yes—
657C2×C4C22×C22⋊D5312yes—
658C2×C4C22×C22⋊D5312yes—
659C2×C4C22×C22⋊D5312yes—
660C2×C4C22×C22⋊D5311yescharacteristic
661C2×C4#1313326512yes—
662C2×C4#1313326512yes—
663C2×C4C24×D5311yescharacteristic
664C8—1062no—
665C8—1062no—
666C8—1062no—
667C8—1062no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—44no—
672C22—4244no—
673C22—2122no—
674C22—2122no—
675C22—2122no—
676C22#1681119712yes—
677C22#1681142612yes—
678C22#1681143812yes—
679C22C23×C22⋊D5311yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—22no—
684C4—22no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—42no—
689C4—2122no—
690C4—2122no—
691C4—2122no—
692C4#1681119712yes—
693C4C2×#1313326511yescharacteristic
694C4C2×#1313326511yescharacteristic
695C2—42no—
696C2—4242no—
697C2#2028599814yesdirect product factor
698C2C2×#1681119711yescharacteristic
699C2C2×#1681142611yescharacteristic
700C2C2×#1681143811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#544C2
socleC23×C53C22×D4
prime radicalC2×#13133191C22
hypercenterC2×#544D53
hypocenterC53C2×#3243
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
2. #20285998C2direct (N × H)
3. C2×#16811033C2semidirect
4. C2×#16811026C2semidirect
5. C2×#16810985C2semidirect
6. C2×#16810980C2semidirect
7. C2×#16810958C2semidirect
8. C2×#16810964C2semidirect
11. C2×#16810927C2semidirect
12. C2×#16810915C2semidirect
13. C2×#16810920C2semidirect
14. C2×#16810900C2semidirect
15. C2×#16810684C2semidirect
16. C2×C53×#544C2semidirect
29. #16811033C22semidirect
30. #16811026C22semidirect
31. #16810985C22semidirect
32. #16810980C22semidirect
33. #16810964C22semidirect
34. #16810958C22semidirect
37. #16810927C22semidirect
38. #16810920C22semidirect
39. #16810915C22semidirect
40. #16810900C22semidirect
41. #16810684C22semidirect
65. C53×#544C22semidirect
345. C2×#544D53semidirect
362. C2×C53#3243semidirect
368. #544C2×D53semidirect
427. C53C2×#3243semidirect
697. C2#20285998direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112442
#202859982
C2×#168110332
C2×#168110262
C2×#168109852
C2×#168109802
C2×#168109582
C2×#168109642
C2×#168109472
C2×#168109362
C2×#168109272
C2×#168109152
C2×#168109202
C2×#168109002
C2×#168106842
C2×C53×#5442
C2×#324353