Finite Group Databasebeta

← C2×#20288526 #28292416

Subgroups — C2×#20288526 #28292416

Order 13568.

7478 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288526C2132yesmaximal, direct product factor
2C2×#16811353C212yesmaximal, complemented
3C2×#16811351C211yesmaximal, characteristic, complemented
4C2×#16811348C211yesmaximal, characteristic, complemented
5C2×#16811332C212yesmaximal, complemented
6C2×#16811327C214yesmaximal, complemented
7C2×D4×Dic106C211yesmaximal, characteristic, complemented
8C2×Q8×C22⋊D53C212yesmaximal, complemented
9C2×#16811286C212yesmaximal, complemented
10C2×#16811252C214yesmaximal, complemented
11C2×#16811250C212yesmaximal, complemented
12C2×#16811177C211yesmaximal, characteristic, complemented
13C2×#16811175C212yesmaximal, complemented
14C22×#13133215C212yesmaximal, complemented
15C2×C4⋊Q8×D53C211yesmaximal, characteristic, complemented
16C2×#16811102C212yesmaximal
17C2×C4×#11719947C211yesmaximal, characteristic
18C2×D4×Q8×C53C211yesmaximal, characteristic, complemented
19C22×#11719947C2211yescharacteristic
20C23×Dic106C2212yes—
21C22×Q8×D53C2212yes—
22#16811353C22132yescomplemented
23#16811351C22116yescomplemented
24#16811348C22116yescomplemented
25#16811332C22132yescomplemented
26#16811327C22164yescomplemented
27D4×Dic106C22116yescomplemented
28Q8×C22⋊D53C22132yescomplemented
29#16811286C22132yescomplemented
30#16811252C22164yescomplemented
31#16811250C22132yescomplemented
32#16811177C22116yescomplemented
33#16811175C22132yescomplemented
34C2×#13133217C2211yescharacteristic
35C2×#13133216C2211yescharacteristic
36C2×#13133216C2212yes—
37C2×#13133216C2214yes—
38C2×#13133216C2212yes—
39C2×#13133216C2212yes—
40C2×#13133215C2212yes—
41C2×#13133215C2211yescharacteristic
42C2×#13133215C2212yes—
43C2×#13133215C2212yes—
44C2×#13133215C2214yes—
45C2×#13133215C2214yes—
46C2×#13133215C2214yes—
47C2×#13133215C22132yescomplemented
48C4⋊Q8×D53C22116yescomplemented
49C2×#13133209C2212yes—
50C2×#13133208C2212yes—
51C2×#13133207C2214yes—
52C2×#13133207C2212yes—
53C2×#13133207C2214yes—
54C2×#13133207C2214yes—
55C2×#13133197C2211yescharacteristic
56C2×#13133196C2212yes—
57C2×#13133196C2214yes—
58C2×#13133195C2212yes—
59C2×#13133195C2214yes—
60C2×#13133194C2214yes—
61C2×#13133194C2214yes—
62C2×#13133194C2214yes—
63C2×#13133193C2211yescharacteristic
64C2×#13133193C2214yes—
65#16811102C22132yes—
66C4×#11719947C22116yes—
67C2×Q8×Dic53C2212yes—
68C2×C4×Dic106C2211yescharacteristic
69C2×C4×Dic106C2212yes—
70C2×C4×Dic106C2211yescharacteristic
71C2×C4×Dic106C2212yes—
72C2×#13133182C2212yes—
73C2×#13133182C2214yes—
74C2×#13133182C2212yes—
75C2×#13133182C2211yescharacteristic
76C2×D4×Dic53C2211yescharacteristic
77C2×D4×Dic53C2212yes—
78C2×C4×C22⋊D53C2212yes—
79C2×C4×C22⋊D53C2214yes—
80C2×#13133177C2212yes—
81C2×#13133177C2214yes—
82C2×#13133175C2211yescharacteristic
83C2×#13133174C2212yes—
84C2×#13133173C2214yes—
85C2×#13133173C2212yes—
86C22×#11719919C2214yes—
87C22×#11719919C2214yes—
88C2×C4⋊C4×D53C2212yes—
89C2×C4⋊C4×D53C2212yes—
90C22×C4×Dic53C2212yes—
91C2×C42×D53C2211yescharacteristic
92C23×Q8×C53C2212yes—
93D4×Q8×C53C22116yescomplemented
94C2×C4⋊Q8×C53C2211yescharacteristic
95C2×C4⋊Q8×C53C2212yes—
96C2×C22⋊Q8×C53C2212yes—
97C2×C22⋊Q8×C53C2214yes—
98C2×C4×Q8×C53C2211yescharacteristic
99C2×C4×D4×C53C2211yescharacteristic
100C2×C4×D4×C53C2212yes—
101C2×#11719947Q8116yescomplemented
102C2×#11719947C2318yes—
103C22×Dic106—48no—
104C22×Dic106C2312yes—
105C22×Dic106C2312yes—
106C22×Dic106C2311yescharacteristic
107C22×Dic106C23116yes—
108C22×Dic106C2314yes—
109C22×Dic106C2314yes—
110C22×Dic106C2311yescharacteristic
111C2×Q8×D53—48no—
112C2×Q8×D53C23116yes—
113C22×C22⋊D53C2312yes—
114C23×Dic53C2312yes—
115C23×Dic53C2314yes—
116C23×Dic53C2312yes—
117C22×C4×D53C2311yescharacteristic
118C22×C4×D53C2311yescharacteristic
119C22×C4×D53C2314yes—
120C22×C4×D53C2311yescharacteristic
121#13133217C2318yes—
122#13133216C23132yes—
123#13133216C23116yes—
124#13133216C23116yes—
125#13133216C23116yes—
126#13133216C2318yes—
127#13133215C23116yes—
128#13133215C23116yes—
129#13133215C23132yes—
130#13133215C23132yes—
131#13133215C23116yes—
132#13133215C2318yes—
133#13133215C23132yes—
134#13133209C23116yes—
135#13133208C23116yes—
136#13133207C23132yes—
137#13133207C23132yes—
138#13133207C23132yes—
139#13133207C23116yes—
140#13133197C2318yes—
141#13133196C23116yes—
142#13133196C23132yes—
143#13133195C23132yes—
144#13133195C23116yes—
145#13133194C23132yes—
146#13133194C23132yes—
147#13133194C23132yes—
148#13133193C2318yes—
149#13133193C23132yes—
150Q8×Dic53C23116yes—
151C4×Dic106C2318yes—
152C4×Dic106C23116yes—
153C4×Dic106C2318yes—
154C4×Dic106C23116yes—
155#13133182C23116yes—
156#13133182C23132yes—
157#13133182C2318yes—
158#13133182C23116yes—
159D4×Dic53C23116yes—
160D4×Dic53C2318yes—
161C4×C22⋊D53C23116yes—
162C4×C22⋊D53C23132yes—
163#13133177C23132yes—
164#13133177C23116yes—
165#13133175C2318yes—
166#13133174C23116yes—
167#13133173C23116yes—
168#13133173C23132yes—
169C2×C4⋊Dic53C2312yes—
170C2×C4⋊Dic53C2312yes—
171C2×C4⋊Dic53C2311yescharacteristic
172C2×C4⋊Dic53C2311yescharacteristic
173C2×C4⋊Dic53C2312yes—
174C2×C4⋊Dic53C2314yes—
175C2×#11719919C23132yes—
176C2×#11719919C2314yes—
177C2×#11719919C2314yes—
178C2×#11719919C2312yes—
179C2×#11719919C2312yes—
180C2×#11719919C2314yes—
181C2×#11719919C2314yes—
182C2×#11719919C23132yes—
183C2×#11719919C2314yes—
184C2×#11719919C2314yes—
185C2×#11719919C2312yes—
186C2×#11719919C2312yes—
187C2×#11719919C2312yes—
188C2×#11719919C2314yes—
189C2×#11719919C2314yes—
190C2×#11719919C2312yes—
191C2×#11719919C2312yes—
192C4⋊C4×D53C23116yes—
193C4⋊C4×D53C23116yes—
194C2×C22⋊Dic53C2314yes—
195C2×C22⋊Dic53C2312yes—
196C2×#11719921C2312yes—
197C2×#11719921C2312yes—
198C2×#11719921C2312yes—
199C2×C4×Dic53C2311yescharacteristic
200C2×C4×Dic53C2311yescharacteristic
201C2×C4×Dic53C2311yescharacteristic
202C2×C4×Dic53C2312yes—
203C2×C4×Dic53C2312yes—
204C2×C4×Dic53C2312yes—
205C2×C4×Dic53C23116yes—
206C2×C4×Dic53C2314yes—
207C2×C4×Dic53C2314yes—
208C2×C4×Dic53C2312yes—
209C42×D53C2318yes—
210C22×Q8×C53—48no—
211C22×Q8×C53C2311yescharacteristic
212C22×Q8×C53C2312yes—
213C22×Q8×C53C23116yes—
214C22×Q8×C53C2314yes—
215C22×D4×C53C2311yescharacteristic
216C23×C4×C53C2312yes—
217C23×C4×C53C2314yes—
218C4⋊Q8×C53C2318yes—
219C4⋊Q8×C53C23116yes—
220C22⋊Q8×C53C23116yes—
221C22⋊Q8×C53C23132yes—
222C4×Q8×C53C2318yes—
223C4×D4×C53C2318yes—
224C4×D4×C53C23116yes—
225C2×C4⋊C4×C53C2312yes—
226C2×C4⋊C4×C53C2311yescharacteristic
227C2×C4⋊C4×C53C2311yescharacteristic
228C2×C4⋊C4×C53C2312yes—
229C2×C4⋊C4×C53C2312yes—
230C2×C4⋊C4×C53C2314yes—
231C2×C22⋊C4×C53C2314yes—
232C2×C22⋊C4×C53C2312yes—
233C2×C42×C53C2311yescharacteristic
234C2×C42×C53C2312yes—
235C24×C53C2412yes—
236C23×D53C2411yescharacteristic
237C2×Q8×C53—24no—
238C2×Q8×C53—28no—
239C2×Q8×C53—48no—
240C2×Q8×C53—432no—
241C2×Q8×C53C2414yes—
242C2×Q8×C53C2418yes—
243C2×Q8×C53C24116yes—
244C2×D4×C53C2×Q818yescomplemented
245C2×D4×C53C2414yes—
246C22×C4×C53—28no—
247C22×C4×C53—48no—
248C22×C4×C53C2412yes—
249C22×C4×C53C2411yescharacteristic
250C22×C4×C53C2412yes—
251C22×C4×C53C2412yes—
252C22×C4×C53C2414yes—
253C22×C4×C53C2418yes—
254C22×C4×C53C24116yes—
255C22×C4×C53C2411yescharacteristic
256C22×C4×C53C2411yescharacteristic
257C2×C22⋊D53C2×Q8116yescomplemented
258C2×C22⋊D53C2418yes—
259C22×Dic53—28no—
260C22×Dic53—48no—
261C22×Dic53C2×Q8116yescomplemented
262C22×Dic53C2412yes—
263C22×Dic53C2412yes—
264C22×Dic53C2411yescharacteristic
265C22×Dic53C2418yes—
266C22×Dic53C2412yes—
267C22×Dic53C2414yes—
268C22×Dic53C24116yes—
269C22×Dic53C2412yes—
270C22×Dic53C2411yescharacteristic
271C22×Dic53C2418yes—
272C22×Dic53C2411yescharacteristic
273Q8×D53—432no—
274#11719947C2×Q8164yescomplemented
275C2×C4×D53—24no—
276C2×C4×D53—24no—
277C2×C4×D53—48no—
278C2×C4×D53C2×Q818yescomplemented
279C2×C4×D53C2414yes—
280C2×C4×D53C2414yes—
281C2×C4×D53C24116yes—
282C2×C4×D53C2414yes—
283C2×Dic106—28no—
284C2×Dic106—24no—
285C2×Dic106—28no—
286C2×Dic106—432no—
287C2×Dic106—48no—
288C2×Dic106—48no—
289C2×Dic106C2×Q818yescomplemented
290C2×Dic106C2418yes—
291C2×Dic106C2418yes—
292C2×Dic106C2414yes—
293C2×Dic106C24116yes—
294C2×Dic106C24116yes—
295C2×Dic106C2414yes—
296C4⋊C4×C53C2418yes—
297C4⋊C4×C53C2414yes—
298C4⋊C4×C53C2414yes—
299C4⋊C4×C53C2418yes—
300C4⋊C4×C53C2418yes—
301C4⋊C4×C53C24116yes—
302C22⋊C4×C53C2418yes—
303C22⋊C4×C53C24116yes—
304C42×C53C2414yes—
305C42×C53C2418yes—
306C22⋊Dic53C2418yes—
307C22⋊Dic53C24116yes—
308#11719921C2418yes—
309#11719921C2418yes—
310#11719921C2418yes—
311C4⋊Dic53C2418yes—
312C4⋊Dic53C2418yes—
313C4⋊Dic53C2414yes—
314C4⋊Dic53C2414yes—
315C4⋊Dic53C2418yes—
316C4⋊Dic53C24116yes—
317#11719919C24116yes—
318#11719919C24116yes—
319#11719919C2418yes—
320#11719919C2418yes—
321#11719919C24116yes—
322#11719919C24116yes—
323#11719919C24116yes—
324#11719919C24116yes—
325#11719919C2418yes—
326#11719919C2418yes—
327#11719919C2418yes—
328#11719919C24116yes—
329#11719919C24116yes—
330#11719919C2418yes—
331#11719919C2418yes—
332C4×Dic53C2414yes—
333C4×Dic53C2414yes—
334C4×Dic53C2414yes—
335C4×Dic53C2418yes—
336C4×Dic53C2418yes—
337C4×Dic53C2418yes—
338C4×Dic53C24116yes—
339C4×Dic53C24116yes—
340C4×Dic53C2418yes—
341C23×C53—24no—
342C23×C53—24no—
343C23×C53C22×Q818yes—
344C23×C53C2514yes—
345C23×C53C2511yescharacteristic
346C22×D53—22no—
347C22×D53—22no—
348C22×D53C22×Q814yes—
349C22×D53C2512yes—
350Q8×C53—216no—
351Q8×C53—28no—
352Q8×C53—416no—
353D4×C53C22×Q8116yescomplemented
354C2×C4×C53—24no—
355C2×C4×C53—28no—
356C2×C4×C53—24no—
357C2×C4×C53—24no—
358C2×C4×C53—22no—
359C2×C4×C53—216no—
360C2×C4×C53—416no—
361C2×C4×C53C22×Q814yes—
362C2×C4×C53H(5,𝔽2)14yes—
363C2×C4×C53C2514yes—
364C2×C4×C53C2518yes—
365C2×C4×C53C2514yes—
366C2×C4×C53C2512yes—
367C2×C4×C53C2514yes—
368C2×C4×C53C2512yes—
369C2×C4×C53C2512yes—
370C22⋊D53C22×Q8132yescomplemented
371C2×Dic53—28no—
372C2×Dic53—24no—
373C2×Dic53—22no—
374C2×Dic53—24no—
375C2×Dic53—24no—
376C2×Dic53—216no—
377C2×Dic53—416no—
378C2×Dic53C22×Q818yes—
379C2×Dic53C22×Q814yes—
380C2×Dic53C22×Q8132yescomplemented
381C2×Dic532−1+414yes—
382C2×Dic53C2512yes—
383C2×Dic53C2518yes—
384C2×Dic53C2514yes—
385C2×Dic53C2514yes—
386C2×Dic53C2514yes—
387C2×Dic53C2514yes—
388C2×Dic53C2512yes—
389C2×Dic53C2512yes—
390C4×D53—28no—
391C4×D53—28no—
392C4×D53—416no—
393C4×D53C22×Q8116yescomplemented
394Dic106—28no—
395Dic106—216no—
396Dic106—216no—
397Dic106—416no—
398Dic106—416no—
399Dic106C22×Q8116yescomplemented
400C2×#3503—531nomaximal, Sylow
401C22×C53—24no—
402C22×C53—24no—
403C22×C53—216no—
404C22×C53C23×Q818yes—
405C22×C53C23×Q812yes—
406C22×C53C2×H(5,𝔽2)12yes—
407C22×C53C2×2−1+412yes—
408C22×C53C2611yescharacteristic
409C2×D53—22no—
410C2×D53—22no—
411C2×D53—28no—
412C2×D53C23×Q814yes—
413C4×C53—24no—
414C4×C53—28no—
415C4×C53—24no—
416C4×C53—24no—
417C4×C53—22no—
418C4×C53C23×Q814yes—
419C4×C53C2×H(5,𝔽2)14yes—
420Dic53—28no—
421Dic53—24no—
422Dic53—22no—
423Dic53—24no—
424Dic53—24no—
425Dic53C23×Q818yes—
426Dic53C23×Q814yes—
427Dic53C2×2−1+414yes—
428#3503—5332no—
429C2×Q82—532no—
430C2×#557—531no—
431C2×#557—531no—
432C2×#554—534no—
433C2×#554—532no—
434C2×D4×Q8—532no—
435C2×D4×Q8—532no—
436C2×D4×Q8—531no—
437C2×D4×Q8D5311yescharacteristic, complemented
438C2×#544—532no—
439C2×#544—534no—
440C2×#533—532no—
441C2×#533—531no—
442C22×C4⋊Q8—532no—
443C22×C4⋊Q8—531no—
444C2×#520—532no—
445C2×C4×#41—531no—
446C2×C53—28no—
447C2×C53#350314yescomplemented
448C2×C53C24×Q811yescharacteristic
449C2×C53C22×H(5,𝔽2)11yescharacteristic
450C2×C53C22×2−1+411yescharacteristic
451D53—24no—
452C22×#41—531no—
453C23×Q8—532no—
454C23×Q8—532no—
455C23×Q8C2×D5312yes—
456Q82—5332no—
457#557—5316no—
458#557—5316no—
459#554—5364no—
460#554—5332no—
461D4×Q8—5332no—
462D4×Q8—5332no—
463D4×Q8—5316no—
464D4×Q8C2×D53116yescomplemented
465#544—5332no—
466#544—5364no—
467#533—5332no—
468#533—5316no—
469C2×C4⋊Q8—532no—
470C2×C4⋊Q8—531no—
471C2×C4⋊Q8—534no—
472C2×C4⋊Q8—532no—
473C2×C4⋊Q8—532no—
474C2×C4⋊Q8—534no—
475C2×C4⋊Q8—5332no—
476C2×C4⋊Q8—534no—
477C2×C4⋊Q8—5316no—
478C2×C4⋊Q8—532no—
479C2×C4⋊Q8—532no—
480C2×C4⋊Q8—531no—
481C2×C4⋊Q8—534no—
482C2×C4⋊Q8—532no—
483C2×C4⋊Q8—531no—
484C2×C4⋊Q8C2×D5311yescharacteristic
485C2×C4⋊Q8C2×D5312yes—
486C2×#125—534no—
487C2×#125—532no—
488C2×#125—534no—
489C2×#125—534no—
490C2×#125—532no—
491C2×#125—532no—
492C2×C22⋊Q8—531no—
493C2×C22⋊Q8—534no—
494C2×C22⋊Q8—532no—
495C2×C22⋊Q8—534no—
496C2×C22⋊Q8—532no—
497C2×C22⋊Q8—534no—
498C2×C22⋊Q8—531no—
499C2×C22⋊Q8—534no—
500C2×C22⋊Q8—534no—
501C2×C22⋊Q8—534no—
502C2×C22⋊Q8C2×D5312yes—
503C2×C22⋊Q8C2×D5314yes—
504#520—5332no—
505C4×#41—5316no—
506C2×C4×Q8—532no—
507C2×C4×Q8—531no—
508C2×C4×Q8—532no—
509C2×C4×Q8—532no—
510C2×C4×Q8—534no—
511C2×C4×Q8—531no—
512C2×C4×Q8—532no—
513C2×C4×Q8—531no—
514C2×C4×Q8—532no—
515C2×C4×Q8C2×D5311yescharacteristic
516C2×C4×D4—531no—
517C2×C4×D4—532no—
518C2×C4×D4—532no—
519C2×C4×D4—534no—
520C2×C4×D4—532no—
521C2×C4×D4—534no—
522C2×C4×D4C2×D5311yescharacteristic
523C2×C4×D4C2×D5312yes—
524C2×#117—531no—
525C2×#117—532no—
526C2×#117—534no—
527C2×#117—532no—
528C22×C4⋊C4—534no—
529C22×C4⋊C4—534no—
530C22×C4⋊C4—532no—
531C22×C4⋊C4—532no—
532C22×C42—532no—
533C22×C42—531no—
534C53C2×#350311yescharacteristic, complemented, Sylow
535C2×#41—5316no—
536C2×#41—538no—
537C22×Q8—48no—
538C22×Q8—5316no—
539C22×Q8—531no—
540C22×Q8—532no—
541C22×Q8—532no—
542C22×Q8—531no—
543C22×Q8—534no—
544C22×Q8—534no—
545C22×Q8—5316no—
546C22×Q8—2128no—
547C22×Q8—2128no—
548C22×Q8C22×D5312yes—
549C22×Q8C22×D5311yescharacteristic
550C22×Q8C22×D5314yes—
551C22×Q8C22×D53116yes—
552C22×D4—532no—
553C22×D4C22×D5311yescharacteristic
554C23×C4—532no—
555C23×C4—531no—
556C23×C4—532no—
557C23×C4—534no—
558C23×C4—531no—
559C23×C4—531no—
560C23×C4—534no—
561C23×C4C22×D5312yes—
562C23×C4C22×D5314yes—
563C4⋊Q8—5316no—
564C4⋊Q8—538no—
565C4⋊Q8—5332no—
566C4⋊Q8—5316no—
567C4⋊Q8—5316no—
568C4⋊Q8—5332no—
569C4⋊Q8—5332no—
570C4⋊Q8—5316no—
571C4⋊Q8—5316no—
572C4⋊Q8—538no—
573C4⋊Q8—5332no—
574C4⋊Q8—5316no—
575C4⋊Q8—538no—
576C4⋊Q8C22×D5318yes—
577C4⋊Q8C22×D53116yes—
578#125—5332no—
579#125—5316no—
580#125—5332no—
581#125—5332no—
582#125—5316no—
583#125—5316no—
584C22⋊Q8—538no—
585C22⋊Q8—5332no—
586C22⋊Q8—5316no—
587C22⋊Q8—5332no—
588C22⋊Q8—538no—
589C22⋊Q8—5316no—
590C22⋊Q8—5332no—
591C22⋊Q8—5332no—
592C22⋊Q8—5332no—
593C22⋊Q8—5332no—
594C22⋊Q8C22×D53116yes—
595C22⋊Q8C22×D53132yes—
596C4×Q8—5316no—
597C4×Q8—538no—
598C4×Q8—5316no—
599C4×Q8—5316no—
600C4×Q8—5332no—
601C4×Q8—538no—
602C4×Q8—5316no—
603C4×Q8—538no—
604C4×Q8—5316no—
605C4×Q8C22×D5318yes—
606C4×D4—538no—
607C4×D4—5316no—
608C4×D4—5316no—
609C4×D4—5332no—
610C4×D4—5316no—
611C4×D4—5332no—
612C4×D4C22×D5318yes—
613C4×D4C22×D53116yes—
614#117—538no—
615#117—5316no—
616#117—5332no—
617#117—5316no—
618C2×C4⋊C4—534no—
619C2×C4⋊C4—532no—
620C2×C4⋊C4—534no—
621C2×C4⋊C4—532no—
622C2×C4⋊C4—534no—
623C2×C4⋊C4—534no—
624C2×C4⋊C4—532no—
625C2×C4⋊C4—5332no—
626C2×C4⋊C4—534no—
627C2×C4⋊C4—534no—
628C2×C4⋊C4—532no—
629C2×C4⋊C4—5332no—
630C2×C4⋊C4—532no—
631C2×C4⋊C4—532no—
632C2×C4⋊C4—531no—
633C2×C4⋊C4—532no—
634C2×C4⋊C4—531no—
635C2×C4⋊C4—532no—
636C2×C4⋊C4—534no—
637C2×C4⋊C4—534no—
638C2×C4⋊C4—532no—
639C2×C4⋊C4—534no—
640C2×C4⋊C4—532no—
641C2×C4⋊C4—5316no—
642C2×C4⋊C4—5316no—
643C2×C4⋊C4C22×D5312yes—
644C2×C4⋊C4C22×D5312yes—
645C2×C4⋊C4C22×D5311yescharacteristic
646C2×C4⋊C4C22×D5311yescharacteristic
647C2×C4⋊C4C22×D5314yes—
648C2×C4⋊C4C22×D5312yes—
649C2×C22⋊C4—534no—
650C2×C22⋊C4—532no—
651C2×C22⋊C4—532no—
652C2×C22⋊C4—532no—
653C2×C22⋊C4—532no—
654C2×C22⋊C4C22×D5314yes—
655C2×C22⋊C4C22×D5312yes—
656C2×C42—532no—
657C2×C42—531no—
658C2×C42—534no—
659C2×C42—534no—
660C2×C42—532no—
661C2×C42—532no—
662C2×C42—532no—
663C2×C42—531no—
664C2×C42—5316no—
665C2×C42—531no—
666C2×C42—538no—
667C2×C42C22×D5312yes—
668C2×C42C22×D5311yescharacteristic
669C24—531no—
670C24C23×D5312yes—
671#41—5364no—
672C2×Q8—24no—
673C2×Q8—28no—
674C2×Q8—48no—
675C2×Q8—432no—
676C2×Q8—538no—
677C2×Q8—534no—
678C2×Q8—538no—
679C2×Q8—538no—
680C2×Q8—534no—
681C2×Q8—5316no—
682C2×Q8—5316no—
683C2×Q8—1068no—
684C2×Q8—1068no—
685C2×Q8—1064no—
686C2×Q8—2128no—
687C2×Q8—2128no—
688C2×Q8—21232no—
689C2×Q8—21232no—
690C2×Q8C23×D5318yes—
691C2×Q8C23×D5314yes—
692C2×Q8C23×D53116yes—
693C2×D4—5316no—
694C2×D4—538no—
695C2×D4Q8×D5318yescomplemented
696C2×D4C23×D5314yes—
697C22×C4—28no—
698C22×C4—48no—
699C22×C4—5316no—
700C22×C4—538no—
701C22×C4—532no—
702C22×C4—531no—
703C22×C4—531no—
704C22×C4—538no—
705C22×C4—534no—
706C22×C4—538no—
707C22×C4—532no—
708C22×C4—532no—
709C22×C4—531no—
710C22×C4—532no—
711C22×C4—534no—
712C22×C4—5316no—
713C22×C4—534no—
714C22×C4—534no—
715C22×C4—5316no—
716C22×C4—1064no—
717C22×C4—1068no—
718C22×C4—1064no—
719C22×C4—2128no—
720C22×C4—2128no—
721C22×C4C23×D5318yes—
722C22×C4C23×D5312yes—
723C22×C4C23×D5312yes—
724C22×C4C23×D5311yescharacteristic
725C22×C4C23×D5314yes—
726C22×C4C23×D5312yes—
727C22×C4C23×D53116yes—
728C22×C4C23×D5311yescharacteristic
729C22×C4C23×D5311yescharacteristic
730C4⋊C4—5316no—
731C4⋊C4—538no—
732C4⋊C4—5316no—
733C4⋊C4—538no—
734C4⋊C4—5316no—
735C4⋊C4—5316no—
736C4⋊C4—538no—
737C4⋊C4—5316no—
738C4⋊C4—5316no—
739C4⋊C4—538no—
740C4⋊C4—538no—
741C4⋊C4—538no—
742C4⋊C4—534no—
743C4⋊C4—538no—
744C4⋊C4—534no—
745C4⋊C4—538no—
746C4⋊C4—5316no—
747C4⋊C4—5316no—
748C4⋊C4—538no—
749C4⋊C4—5316no—
750C4⋊C4—538no—
751C4⋊C4C23×D5318yes—
752C4⋊C4C23×D5318yes—
753C4⋊C4C23×D5314yes—
754C4⋊C4C23×D5314yes—
755C4⋊C4C23×D53116yes—
756C4⋊C4C23×D5318yes—
757C22⋊C4—5316no—
758C22⋊C4—538no—
759C22⋊C4—538no—
760C22⋊C4—538no—
761C22⋊C4—538no—
762C22⋊C4C23×D53116yes—
763C22⋊C4C23×D5318yes—
764C42—534no—
765C42—538no—
766C42—534no—
767C42—538no—
768C42—538no—
769C42—534no—
770C42—5316no—
771C42—5316no—
772C42—538no—
773C42C23×D5314yes—
774C42C23×D5318yes—
775C23—24no—
776C23—24no—
777C23—534no—
778C23—532no—
779C23—1062no—
780C23—1062no—
781C23C2×Q8×D5318yes—
782C23C24×D5314yes—
783C23C24×D5311yescharacteristic
784Q8—28no—
785Q8—216no—
786Q8—416no—
787Q8—5316no—
788Q8—10616no—
789Q8—1068no—
790Q8—10616no—
791Q8—21216no—
792Q8—21216no—
793D4—5332no—
794D4C2×Q8×D53116yescomplemented
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—28no—
798C2×C4—22no—
799C2×C4—24no—
800C2×C4—216no—
801C2×C4—416no—
802C2×C4—534no—
803C2×C4—538no—
804C2×C4—5332no—
805C2×C4—534no—
806C2×C4—534no—
807C2×C4—532no—
808C2×C4—532no—
809C2×C4—5316no—
810C2×C4—534no—
811C2×C4—534no—
812C2×C4—532no—
813C2×C4—538no—
814C2×C4—534no—
815C2×C4—1068no—
816C2×C4—10616no—
817C2×C4—1062no—
818C2×C4—1068no—
819C2×C4—1064no—
820C2×C4—1064no—
821C2×C4—1064no—
822C2×C4—1068no—
823C2×C4—21216no—
824C2×C4—21216no—
825C2×C4C2×Q8×D5314yes—
826C2×C4#1313326214yes—
827C2×C4C24×D5314yes—
828C2×C4C24×D5314yes—
829C2×C4C24×D5312yes—
830C2×C4C24×D5318yes—
831C2×C4C24×D5314yes—
832C2×C4C24×D5312yes—
833C2×C4C24×D5312yes—
834C22—216no—
835C22—24no—
836C22—24no—
837C22—534no—
838C22—1068no—
839C22—1062no—
840C22—1062no—
841C22C22×Q8×D5318yes—
842C22C22×Q8×D5312yes—
843C22C2×#1313326212yes—
844C222−1+4×D5312yes—
845C22C25×D5311yescharacteristic
846C4—24no—
847C4—24no—
848C4—28no—
849C4—22no—
850C4—24no—
851C4—534no—
852C4—538no—
853C4—534no—
854C4—1062no—
855C4—1068no—
856C4—1064no—
857C4—1064no—
858C4—1064no—
859C4C22×Q8×D5314yes—
860C4C2×#1313326214yes—
861C2—28no—
862C2—1064no—
863C2#2028852614yesdirect product factor
864C2C23×Q8×D5311yescharacteristic
865C2C22×#1313326211yescharacteristic
866C2C2×2−1+4×D5311yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×D4×Q8×C53C2
socleC23×C53C25
prime radicalC22×#11719947C22
hypercenterC2×D4×Q8D53
hypocenterC53C2×#3503
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. #20288526C2direct (N × H)
2. C2×#16811353C2semidirect
3. C2×#16811351C2semidirect
4. C2×#16811348C2semidirect
5. C2×#16811332C2semidirect
6. C2×#16811327C2semidirect
7. C2×D4×Dic106C2semidirect
8. C2×Q8×C22⋊D53C2semidirect
9. C2×#16811286C2semidirect
10. C2×#16811252C2semidirect
11. C2×#16811250C2semidirect
12. C2×#16811177C2semidirect
13. C2×#16811175C2semidirect
14. C22×#13133215C2semidirect
15. C2×C4⋊Q8×D53C2semidirect
18. C2×D4×Q8×C53C2semidirect
22. #16811353C22semidirect
23. #16811351C22semidirect
24. #16811348C22semidirect
25. #16811332C22semidirect
26. #16811327C22semidirect
27. D4×Dic106C22semidirect
28. Q8×C22⋊D53C22semidirect
29. #16811286C22semidirect
30. #16811252C22semidirect
31. #16811250C22semidirect
32. #16811177C22semidirect
33. #16811175C22semidirect
47. C2×#13133215C22semidirect
48. C4⋊Q8×D53C22semidirect
93. D4×Q8×C53C22semidirect
101. C2×#11719947Q8semidirect
244. C2×D4×C53C2×Q8semidirect
257. C2×C22⋊D53C2×Q8semidirect
261. C22×Dic53C2×Q8semidirect
274. #11719947C2×Q8semidirect
278. C2×C4×D53C2×Q8semidirect
289. C2×Dic106C2×Q8semidirect
353. D4×C53C22×Q8semidirect
370. C22⋊D53C22×Q8semidirect
380. C2×Dic53C22×Q8semidirect
393. C4×D53C22×Q8semidirect
399. Dic106C22×Q8semidirect
437. C2×D4×Q8D53semidirect
447. C2×C53#3503semidirect
464. D4×Q8C2×D53semidirect
534. C53C2×#3503semidirect
695. C2×D4Q8×D53semidirect
794. D4C2×Q8×D53semidirect
863. C2#20288526direct (N × H)

Maximal subgroups

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

subgroupindex
#202885262
C2×#168113532
C2×#168113512
C2×#168113482
C2×#168113322
C2×#168113272
C2×D4×Dic1062
C2×Q8×C22⋊D532
C2×#168112862
C2×#168112522
C2×#168112502
C2×#168111772
C2×#168111752
C22×#131332152
C2×C4⋊Q8×D532
C2×#168111022
C2×C4×#117199472
C2×D4×Q8×C532
C2×#350353