Finite Group Databasebeta

← C2×#20285968 #28256281

Subgroups — C2×#20285968 #28256281

Order 13568.

1806 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811228C211yesmaximal, characteristic
2#20285968C2116yesmaximal, direct product factor
3C2×#16811029C211yesmaximal, characteristic, complemented
4C2×#16811022C211yesmaximal, characteristic, complemented
5C2×#16810989C211yesmaximal, characteristic, complemented
6C2×#16810971C211yesmaximal, characteristic, complemented
7C2×#16810941C211yesmaximal, characteristic, complemented
8C2×#16810947C211yesmaximal, characteristic, complemented
9C2×#16810947C211yesmaximal, characteristic, complemented
10C2×#16810936C211yesmaximal, characteristic, complemented
11C2×#16810920C211yesmaximal, characteristic, complemented
12C2×#16810920C211yesmaximal, characteristic, complemented
13C2×#16810910C211yesmaximal, characteristic, complemented
14C2×#16810900C211yesmaximal, characteristic, complemented
15C2×#16810684C211yesmaximal, characteristic, complemented
16C2×C53×#544C211yesmaximal, characteristic, complemented
17#16811228—24no—
18#16811228C2218yes—
19C2×#13133214C2211yescharacteristic
20C2×#13133209C2211yescharacteristic
21C2×#13133202—21no—
22C2×#13133202—21no—
23C2×#13133191C2211yescharacteristic
24C2×#13133191C2211yescharacteristic
25C2×#13133190—21no—
26C2×#13133190—21no—
27C2×C4×D212C2211yescharacteristic
28C2×C4×D212C2211yescharacteristic
29#16811029C2218yescomplemented
30#16811022C2218yescomplemented
31#16810989C2218yescomplemented
32#16810971C2218yescomplemented
33#16810947C2218yescomplemented
34#16810947C2218yescomplemented
35#16810941C2218yescomplemented
36#16810936C2218yescomplemented
37#16810920C2218yescomplemented
38#16810920C2218yescomplemented
39#16810910C2218yescomplemented
40#16810900C2218yescomplemented
41#16810684C2218yescomplemented
42C2×#13133150C2211yescharacteristic
43C2×#13133150C2211yescharacteristic
44C2×#13133150C2211yescharacteristic
45C2×#13133150C2211yescharacteristic
46C2×#13133148C2211yescharacteristic
47C2×#13133148C2211yescharacteristic
48C2×#13133148C2211yescharacteristic
49C2×#13133148C2211yescharacteristic
50C2×C4⋊#88322C2211yescharacteristic
51C2×C4⋊#88322C2211yescharacteristic
52C2×#13133137C2211yescharacteristic
53C2×#13133137C2211yescharacteristic
54C2×#13133137C2211yescharacteristic
55C2×#13133137C2211yescharacteristic
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×D212—21no—
78C22×D212—21no—
79C22×D212C2311yescharacteristic
80C22×D212C2311yescharacteristic
81C22×C22⋊D53—21no—
82C22×C22⋊D53—21no—
83C22×C4×D53—21no—
84C22×C4×D53—21no—
85C22×#88322C2311yescharacteristic
86C22×#88322C2311yescharacteristic
87C22×#88322C2311yescharacteristic
88C22×#88322C2311yescharacteristic
89#13133214—22no—
90#13133214C2314yes—
91#13133209—22no—
92#13133209C2314yes—
93#13133202—28no—
94#13133202—28no—
95#13133191—22no—
96#13133191—22no—
97#13133191C2314yes—
98#13133191C2314yes—
99#13133190—28no—
100#13133190—28no—
101C4×D212—22no—
102C4×D212—22no—
103C4×D212C2314yes—
104C4×D212C2314yes—
105C2×C4⋊Dic53C2311yescharacteristic
106C2×C4⋊Dic53C2311yescharacteristic
107C2×#11719919—21no—
108C2×#11719919—21no—
109C2×#11719921—21no—
110C2×#11719921—21no—
111C2×#11719921—21no—
112C2×#11719921—21no—
113#13133150C2314yes—
114#13133150C2314yes—
115#13133150C2314yes—
116#13133150C2314yes—
117#13133148C2314yes—
118#13133148C2314yes—
119#13133148C2314yes—
120#13133148C2314yes—
121C4⋊#88322C2314yes—
122C4⋊#88322C2314yes—
123#13133137C2314yes—
124#13133137C2314yes—
125#13133137C2314yes—
126#13133137C2314yes—
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—
178C23×D53—21no—
179C2×Q8×C53—24no—
180C2×Q8×C53—24no—
181C2×Q8×C53—82no—
182C2×Q8×C53—82no—
183C22×C4×C53—22no—
184C22×C4×C53—22no—
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—24no—
190C22×C4×C53—82no—
191C22×C4×C53C2×D411yescharacteristic
192C22×C4×C53C2×D411yescharacteristic
193C22×C4×C53C2×D411yescharacteristic
194C22×C4×C53C2×D411yescharacteristic
195C22×C4×C53C2×D411yescharacteristic
196C22×C4×C53C2×D412yes—
197C22×C4×C53C2412yes—
198C22×C4×C53C2411yescharacteristic
199C2×C22⋊D53—24no—
200C2×C22⋊D53—24no—
201C2×C22⋊D53—82no—
202C2×C22⋊D53—82no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C2×D212—22no—
206C2×D212—22no—
207C2×D212—22no—
208C2×D212—22no—
209C2×D212—21no—
210C2×D212—21no—
211C2×D212—24no—
212C2×D212—24no—
213C2×D212—82no—
214C2×D212—82no—
215C2×D212C2412yes—
216C2×D212C2412yes—
217C2×C4×D53—24no—
218C2×C4×D53—24no—
219C2×C4×D53—82no—
220C2×C4×D53—82no—
221C4⋊C4×C53—24no—
222C4⋊C4×C53—21no—
223C4⋊C4×C53—21no—
224C4⋊C4×C53—24no—
225C4⋊C4×C53—24no—
226C4⋊C4×C53—24no—
227C4⋊C4×C53—24no—
228C4⋊C4×C53—24no—
229C4⋊C4×C53—24no—
230C4⋊C4×C53—21no—
231C4⋊C4×C53—21no—
232C4⋊C4×C53C2×D414yes—
233C4⋊C4×C53C2×D414yes—
234C4⋊C4×C53C2412yes—
235C4⋊C4×C53C2412yes—
236C4⋊C4×C53C2412yes—
237C4⋊C4×C53C2412yes—
238C22⋊C4×C53—24no—
239C22⋊C4×C53C2×D414yes—
240C22⋊C4×C53C2×D414yes—
241C42×C53—24no—
242C42×C53C2×D412yes—
243C42×C53C2×D412yes—
244C42×C53C2412yes—
245C42×C53C2412yes—
246#11719921—24no—
247#11719921—24no—
248#11719921—24no—
249#11719921—24no—
250C4⋊Dic53—21no—
251C4⋊Dic53—21no—
252C4⋊Dic53C2412yes—
253C4⋊Dic53C2412yes—
254#11719919—24no—
255#11719919—24no—
256C2×#88322—22no—
257C2×#88322—22no—
258C2×#88322—22no—
259C2×#88322—22no—
260C2×#88322C2412yes—
261C2×#88322C2412yes—
262C2×#88322C2412yes—
263C2×#88322C2412yes—
264C23×C53—22no—
265C23×C53—22no—
266C23×C53—22no—
267C23×C53C22×D412yes—
268C23×C53C22×D411yescharacteristic
269C22×D53—22no—
270C22×D53—22no—
271C22×D53—42no—
272C22×D53—42no—
273C22×D53—42no—
274C22×D53—42no—
275C22×D53—42no—
276C22×D53—42no—
277Q8×C53—84no—
278Q8×C53—84no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—24no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—42no—
292C2×C4×C53—42no—
293C2×C4×C53—42no—
294C2×C4×C53—42no—
295C2×C4×C53—84no—
296C2×C4×C53C22×D412yes—
297C2×C4×C53C22×D412yes—
298C2×C4×C53C22×D412yes—
299C2×C4×C53C22×D412yes—
300C2×C4×C53C22×D412yes—
301C2×C4×C53C22×D411yescharacteristic
302C2×C4×C532−1+412yes—
303C2×C4×C532−1+412yes—
304C2×C4×C53C2511yescharacteristic
305C22⋊D53—84no—
306C22⋊D53—84no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—42no—
310C2×Dic53—42no—
311D212—22no—
312D212—22no—
313D212—22no—
314D212—22no—
315D212—42no—
316D212—42no—
317D212—84no—
318D212—84no—
319C4×D53—84no—
320C4×D53—84no—
321#88322—22no—
322#88322—22no—
323#88322—22no—
324#88322—22no—
325C2×#3241—531nomaximal, Sylow
326C22×C53—22no—
327C22×C53—22no—
328C22×C53—22no—
329C22×C53—44no—
330C22×C53#53612yes—
331C22×C53#57612yes—
332C22×C53#57712yes—
333C22×C53C23×D411yescharacteristic
334C2×D53—42no—
335C2×D53—42no—
336C2×D53—42no—
337C2×D53—42no—
338C2×D53—42no—
339C2×D53—42no—
340C2×D53—84no—
341C2×D53—84no—
342C4×C53—22no—
343C4×C53—22no—
344C4×C53—22no—
345C4×C53—22no—
346C4×C53—22no—
347C4×C53—42no—
348C4×C53—42no—
349C4×C53—42no—
350C4×C53—42no—
351C4×C53#53612yes—
352C4×C53C2×2−1+411yescharacteristic
353C4×C53C2×2−1+411yescharacteristic
354Dic53—42no—
355Dic53—42no—
356C2×#544D5311yescharacteristic, complemented
357C2×#540—531no—
358#3241—5316no—
359C2×#501—531no—
360C2×#499—531no—
361C2×#490—531no—
362C2×#486—531no—
363C2×#481—531no—
364C2×#482—531no—
365C2×#482—531no—
366C2×#480—531no—
367C2×#478—531no—
368C2×#478—531no—
369C2×#476—531no—
370C2×#474—531no—
371C2×#433—531no—
372C2×C53—42no—
373C2×C53#324114yescomplemented
374C2×C53C2×#53611yescharacteristic
375C2×C53C2×#57611yescharacteristic
376C2×C53C2×#57711yescharacteristic
377D53—82no—
378D53—82no—
379#544—24no—
380#544C2×D5318yescomplemented
381#540—538no—
382#540—1064no—
383C2×C4⋊Q8—21no—
384C2×C4⋊Q8C2×D5311yescharacteristic
385C2×C4⋊Q8C2×D5311yescharacteristic
386C2×#127—531no—
387C2×#125—21no—
388C2×#125—531no—
389C2×#125C2×D5311yescharacteristic
390C2×#125C2×D5311yescharacteristic
391C2×#123—1061no—
392C2×#123—1061no—
393C2×C22⋊Q8—21no—
394C2×C22⋊Q8—21no—
395C2×#121—531no—
396C2×#121—531no—
397C2×#121—1061no—
398C2×#121—1061no—
399C2×C4×D4—531no—
400C2×C4×D4—531no—
401C2×#117C2×D5311yescharacteristic
402C2×#117C2×D5311yescharacteristic
403C22×C4⋊C4C2×D5311yescharacteristic
404#501—538no—
405#499—538no—
406#490—538no—
407#486—538no—
408#482—538no—
409#482—538no—
410#481—538no—
411#480—538no—
412#478—538no—
413#478—538no—
414#476—538no—
415#474—538no—
416#433—538no—
417C2×#107—531no—
418C2×#107—531no—
419C2×#107—531no—
420C2×#107—531no—
421C2×#106—531no—
422C2×#106—531no—
423C2×#106—531no—
424C2×#106—531no—
425C2×C4⋊C8—531no—
426C2×C4⋊C8—531no—
427C2×#102—531no—
428C2×#102—531no—
429C2×#102—531no—
430C2×#102—531no—
431C2×#102—531no—
432C2×#102—531no—
433C2×#102—531no—
434C2×#102—531no—
435C2×C22⋊C8—531no—
436C2×C22⋊C8—531no—
437C2×#97—531no—
438C2×C4×C8—531no—
439C53C2×#324111yescharacteristic, complemented, Sylow
440C22×Q8—21no—
441C22×Q8—21no—
442C22×D4—531no—
443C22×D4—531no—
444C22×D4—1061no—
445C22×D4—1061no—
446C22×D4—1061no—
447C22×D4—1061no—
448C23×C4—21no—
449C23×C4—1061no—
450C23×C4—1061no—
451C23×C4C22×D5311yescharacteristic
452C22×C8—531no—
453C22×C8—531no—
454C22×C8—531no—
455C22×C8—531no—
456C4⋊Q8—28no—
457C4⋊Q8—22no—
458C4⋊Q8—22no—
459C4⋊Q8C22×D5314yes—
460C4⋊Q8C22×D5314yes—
461#127—534no—
462#127—1062no—
463#125—28no—
464#125—22no—
465#125—22no—
466#125—534no—
467#125—1062no—
468#125C22×D5314yes—
469#125C22×D5314yes—
470#123—1068no—
471#123—1068no—
472C22⋊Q8—28no—
473C22⋊Q8—28no—
474#121—534no—
475#121—534no—
476#121—1062no—
477#121—1062no—
478#121—1068no—
479#121—1068no—
480C4×D4—534no—
481C4×D4—534no—
482C4×D4—1062no—
483C4×D4—1062no—
484#117—22no—
485#117C22⋊D5314yes—
486#117C22×D5314yes—
487#117C22×D5314yes—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—531no—
497C2×C4⋊C4—531no—
498C2×C4⋊C4—1061no—
499C2×C4⋊C4—1061no—
500C2×C4⋊C4C22⋊D5311yescharacteristic
501C2×C4⋊C4C22⋊D5311yescharacteristic
502C2×C4⋊C4C22×D5311yescharacteristic
503C2×C4⋊C4C22×D5311yescharacteristic
504C2×C4⋊C4C22×D5314yes—
505C2×C4⋊C4C22×D5311yescharacteristic
506C2×C4⋊C4C22×D5311yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—1061no—
509C2×C22⋊C4—1061no—
510C2×C22⋊C4—1061no—
511C2×C22⋊C4—1061no—
512C2×C22⋊C4C22⋊D5311yescharacteristic
513C2×C22⋊C4C22⋊D5311yescharacteristic
514C2×C42—21no—
515C2×C42C22×D5311yescharacteristic
516C2×C42C22×D5311yescharacteristic
517#107—534no—
518#107—534no—
519#107—534no—
520#107—534no—
521#106—534no—
522#106—534no—
523#106—534no—
524#106—534no—
525C4⋊C8—534no—
526C4⋊C8—534no—
527#102—534no—
528#102—534no—
529#102—534no—
530#102—534no—
531#102—534no—
532#102—534no—
533#102—534no—
534#102—534no—
535C22⋊C8—534no—
536C22⋊C8—534no—
537#97—534no—
538C4×C8—534no—
539C24—1061no—
540C24—1061no—
541C24C2×C22⋊D5311yescharacteristic
542C2×Q8—24no—
543C2×Q8—24no—
544C2×Q8—82no—
545C2×Q8—82no—
546C2×D4—532no—
547C2×D4—532no—
548C2×D4—1064no—
549C2×D4—1064no—
550C2×D4—1064no—
551C2×D4—1064no—
552C2×D4—1061no—
553C2×D4—1061no—
554C2×D4—1062no—
555C2×D4—1062no—
556C2×D4—1062no—
557C2×D4—1062no—
558C2×D4—4242no—
559C2×D4—4242no—
560C2×D4—4242no—
561C2×D4—4242no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—24no—
569C22×C4—82no—
570C22×C4—1061no—
571C22×C4—1061no—
572C22×C4—1064no—
573C22×C4—1064no—
574C22×C4—4242no—
575C22×C4—4242no—
576C22×C4C2×C22⋊D5312yes—
577C22×C4C2×C22⋊D5311yescharacteristic
578C22×C4C2×C22⋊D5311yescharacteristic
579C22×C4C2×C22⋊D5311yescharacteristic
580C22×C4C2×C22⋊D5311yescharacteristic
581C22×C4C2×C22⋊D5311yescharacteristic
582C22×C4C23×D5312yes—
583C22×C4C23×D5311yescharacteristic
584C2×C8—532no—
585C2×C8—532no—
586C2×C8—532no—
587C2×C8—532no—
588C2×C8—1062no—
589C2×C8—1062no—
590C2×C8—1062no—
591C2×C8—1062no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—24no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—532no—
604C4⋊C4—532no—
605C4⋊C4—1061no—
606C4⋊C4—1061no—
607C4⋊C4—1064no—
608C4⋊C4—1064no—
609C4⋊C4C2×C22⋊D5314yes—
610C4⋊C4C2×C22⋊D5314yes—
611C4⋊C4C23×D5312yes—
612C4⋊C4C23×D5312yes—
613C4⋊C4C23×D5312yes—
614C4⋊C4C23×D5312yes—
615C22⋊C4—24no—
616C22⋊C4—1064no—
617C22⋊C4—1064no—
618C22⋊C4—1064no—
619C22⋊C4—1064no—
620C22⋊C4C2×C22⋊D5314yes—
621C22⋊C4C2×C22⋊D5314yes—
622C42—24no—
623C42C2×C22⋊D5312yes—
624C42C2×C22⋊D5312yes—
625C42C23×D5312yes—
626C42C23×D5312yes—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—1062no—
631C23—1062no—
632C23—2122no—
633C23—2122no—
634C23—2122no—
635C23—2122no—
636C23—2122no—
637C23—2122no—
638C23C22×C22⋊D5312yes—
639C23C22×C22⋊D5311yescharacteristic
640Q8—84no—
641Q8—84no—
642D4—1062no—
643D4—1062no—
644D4—1062no—
645D4—1062no—
646D4—4244no—
647D4—4244no—
648D4—4244no—
649D4—4244no—
650D4—2122no—
651D4—2122no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—84no—
669C2×C4—1062no—
670C2×C4—1062no—
671C2×C4—4244no—
672C2×C4—4244no—
673C2×C4—2122no—
674C2×C4—2122no—
675C2×C4C22×C22⋊D5312yes—
676C2×C4C22×C22⋊D5312yes—
677C2×C4C22×C22⋊D5312yes—
678C2×C4C22×C22⋊D5312yes—
679C2×C4C22×C22⋊D5312yes—
680C2×C4C22×C22⋊D5311yescharacteristic
681C2×C4#1313326512yes—
682C2×C4#1313326512yes—
683C2×C4C24×D5311yescharacteristic
684C8—1062no—
685C8—1062no—
686C8—1062no—
687C8—1062no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—44no—
692C22—4244no—
693C22—4244no—
694C22—2122no—
695C22—2122no—
696C22—2122no—
697C22—2122no—
698C22—2122no—
699C22—2122no—
700C22#1681119712yes—
701C22#1681142612yes—
702C22#1681143112yes—
703C22C23×C22⋊D5311yescharacteristic
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—22no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—42no—
713C4—2122no—
714C4—2122no—
715C4#1681119712yes—
716C4C2×#1313326511yescharacteristic
717C4C2×#1313326511yescharacteristic
718C2—42no—
719C2—4242no—
720C2—4242no—
721C2#2028596814yesdirect product factor
722C2C2×#1681119711yescharacteristic
723C2C2×#1681142611yescharacteristic
724C2C2×#1681143111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#544C2
socleC23×C53C22×D4
prime radicalC2×#16811228C2
hypercenterC2×#544D53
hypocenterC53C2×#3241
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. #20285968C2direct (N × H)
3. C2×#16811029C2semidirect
4. C2×#16811022C2semidirect
5. C2×#16810989C2semidirect
6. C2×#16810971C2semidirect
7. C2×#16810941C2semidirect
8. C2×#16810947C2semidirect
9. C2×#16810947C2semidirect
10. C2×#16810936C2semidirect
11. C2×#16810920C2semidirect
12. C2×#16810920C2semidirect
13. C2×#16810910C2semidirect
14. C2×#16810900C2semidirect
15. C2×#16810684C2semidirect
16. C2×C53×#544C2semidirect
29. #16811029C22semidirect
30. #16811022C22semidirect
31. #16810989C22semidirect
32. #16810971C22semidirect
33. #16810947C22semidirect
34. #16810947C22semidirect
35. #16810941C22semidirect
36. #16810936C22semidirect
37. #16810920C22semidirect
38. #16810920C22semidirect
39. #16810910C22semidirect
40. #16810900C22semidirect
41. #16810684C22semidirect
65. C53×#544C22semidirect
356. C2×#544D53semidirect
373. C2×C53#3241semidirect
380. #544C2×D53semidirect
439. C53C2×#3241semidirect
721. C2#20285968direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112282
#202859682
C2×#168110292
C2×#168110222
C2×#168109892
C2×#168109712
C2×#168109412
C2×#168109472
C2×#168109362
C2×#168109202
C2×#168109102
C2×#168109002
C2×#168106842
C2×C53×#5442
C2×#324153