Finite Group Databasebeta

← C2×#20288529 #28292421

Subgroups — C2×#20288529 #28292421

Order 13568.

7478 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288529C2132yesmaximal, direct product factor
2C2×Q8×Dic106C211yesmaximal, characteristic, complemented
3C2×#16811353C211yesmaximal, characteristic, complemented
4C2×#16811350C212yesmaximal, complemented
5C2×#16811331C212yesmaximal, complemented
6C2×#16811330C211yesmaximal, characteristic, complemented
7C2×#16811328C212yesmaximal, complemented
8C2×D4×Dic106C212yesmaximal, complemented
9C2×#16811286C214yesmaximal, complemented
10C2×#16811253C212yesmaximal, complemented
11C2×#16811252C214yesmaximal, complemented
12C2×#16811177C211yesmaximal, characteristic, complemented
13C2×#16811175C212yesmaximal, complemented
14C22×#13133216C212yesmaximal, complemented
15C2×C4⋊Q8×D53C211yesmaximal, characteristic, complemented
16C2×#16811102C212yesmaximal
17C2×C4×#11719947C211yesmaximal, characteristic
18C2×C53×#554C211yesmaximal, characteristic, complemented
19C22×#11719947C2211yescharacteristic
20C23×Dic106C2214yes—
21C22×Q8×D53C2212yes—
22Q8×Dic106C22116yescomplemented
23#16811353C22116yescomplemented
24#16811350C22132yescomplemented
25#16811331C22132yescomplemented
26#16811330C22116yescomplemented
27#16811328C22132yescomplemented
28D4×Dic106C22132yescomplemented
29#16811286C22164yescomplemented
30#16811253C22132yescomplemented
31#16811252C22164yescomplemented
32#16811177C22116yescomplemented
33#16811175C22132yescomplemented
34C2×#13133217C2212yes—
35C2×#13133217C2211yescharacteristic
36C2×#13133216C2212yes—
37C2×#13133216C2211yescharacteristic
38C2×#13133216C2214yes—
39C2×#13133216C2212yes—
40C2×#13133216C2212yes—
41C2×#13133216C2212yes—
42C2×#13133216C2214yes—
43C2×#13133216C2212yes—
44C2×#13133216C2214yes—
45C2×#13133216C22132yescomplemented
46C2×#13133215C2211yescharacteristic
47C2×#13133215C2214yes—
48C2×#13133215C2212yes—
49C4⋊Q8×D53C22116yescomplemented
50C2×#13133208C2212yes—
51C2×#13133207C2214yes—
52C2×#13133207C2212yes—
53C2×#13133207C2214yes—
54C2×#13133207C2214yes—
55C2×#13133197C2211yescharacteristic
56C2×#13133197C2214yes—
57C2×#13133196C2212yes—
58C2×#13133196C2214yes—
59C2×#13133195C2212yes—
60C2×#13133195C2214yes—
61C2×#13133194C2214yes—
62C2×#13133194C2214yes—
63C2×#13133194C2214yes—
64C2×#13133193C2211yescharacteristic
65#16811102C22132yes—
66C4×#11719947C22116yes—
67C2×Q8×Dic53C2212yes—
68C2×C4×Dic106C2212yes—
69C2×C4×Dic106C2211yescharacteristic
70C2×C4×Dic106C2212yes—
71C2×C4×Dic106C2211yescharacteristic
72C2×#13133182C2214yes—
73C2×#13133182C2212yes—
74C2×#13133182C2211yescharacteristic
75C2×#13133182C2212yes—
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×C4⋊Dic53C2212yes—
87C22×#11719919C2214yes—
88C2×C4⋊C4×D53C2212yes—
89C2×C4⋊C4×D53C2212yes—
90C22×C4×Dic53C2212yes—
91C2×C42×D53C2211yescharacteristic
92C53×#554C22116yescomplemented
93C2×C4⋊Q8×C53C2211yescharacteristic
94C2×#125×C53C2212yes—
95C2×C22⋊Q8×C53C2212yes—
96C2×C22⋊Q8×C53C2214yes—
97C2×C4×Q8×C53C2211yescharacteristic
98C2×C4×D4×C53C2211yescharacteristic
99C2×C4×D4×C53C2212yes—
100C22×C4⋊C4×C53C2212yes—
101C2×#11719947Q8116yescomplemented
102C2×#11719947C2318yes—
103C22×Dic106—416no—
104C22×Dic106C2311yescharacteristic
105C22×Dic106C2314yes—
106C22×Dic106C2312yes—
107C22×Dic106C23132yes—
108C22×Dic106C2312yes—
109C22×Dic106C2314yes—
110C22×Dic106C2314yes—
111C22×Dic106C2311yescharacteristic
112C2×Q8×D53—48no—
113C2×Q8×D53C23116yes—
114C22×C22⋊D53C2312yes—
115C23×Dic53C2312yes—
116C23×Dic53C2314yes—
117C23×Dic53C2312yes—
118C22×C4×D53C2311yescharacteristic
119C22×C4×D53C2311yescharacteristic
120C22×C4×D53C2314yes—
121C22×C4×D53C2311yescharacteristic
122#13133217C23116yes—
123#13133217C2318yes—
124#13133216C23132yes—
125#13133216C23132yes—
126#13133216C23116yes—
127#13133216C23116yes—
128#13133216C23116yes—
129#13133216C23116yes—
130#13133216C23116yes—
131#13133216C2318yes—
132#13133216C23132yes—
133#13133215C23132yes—
134#13133215C23116yes—
135#13133215C2318yes—
136#13133208C23116yes—
137#13133207C23132yes—
138#13133207C23132yes—
139#13133207C23132yes—
140#13133207C23116yes—
141#13133197C23132yes—
142#13133197C2318yes—
143#13133196C23132yes—
144#13133196C23116yes—
145#13133195C23116yes—
146#13133195C23132yes—
147#13133194C23132yes—
148#13133194C23132yes—
149#13133194C23132yes—
150#13133193C2318yes—
151Q8×Dic53C23116yes—
152C4×Dic106C23116yes—
153C4×Dic106C2318yes—
154C4×Dic106C2318yes—
155C4×Dic106C23116yes—
156#13133182C23132yes—
157#13133182C23116yes—
158#13133182C2318yes—
159#13133182C23116yes—
160D4×Dic53C2318yes—
161D4×Dic53C23116yes—
162C4×C22⋊D53C23132yes—
163C4×C22⋊D53C23116yes—
164#13133177C23116yes—
165#13133177C23132yes—
166#13133175C2318yes—
167#13133174C23116yes—
168#13133173C23116yes—
169#13133173C23132yes—
170C2×C4⋊Dic53C2312yes—
171C2×C4⋊Dic53C2312yes—
172C2×C4⋊Dic53C2311yescharacteristic
173C2×C4⋊Dic53C23116yes—
174C2×C4⋊Dic53C2314yes—
175C2×C4⋊Dic53C2311yescharacteristic
176C2×C4⋊Dic53C2312yes—
177C2×C4⋊Dic53C2314yes—
178C2×#11719919C2314yes—
179C2×#11719919C2314yes—
180C2×#11719919C2312yes—
181C2×#11719919C2314yes—
182C2×#11719919C2314yes—
183C2×#11719919C23132yes—
184C2×#11719919C2312yes—
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×C53C2311yescharacteristic
211C22×Q8×C53C2312yes—
212C22×D4×C53C2311yescharacteristic
213C23×C4×C53C2312yes—
214C23×C4×C53C2314yes—
215C4⋊Q8×C53C2318yes—
216#125×C53C23116yes—
217C22⋊Q8×C53C23132yes—
218C22⋊Q8×C53C23116yes—
219C4×Q8×C53C2318yes—
220C4×D4×C53C23116yes—
221C4×D4×C53C2318yes—
222C2×C4⋊C4×C53C2311yescharacteristic
223C2×C4⋊C4×C53C2314yes—
224C2×C4⋊C4×C53C2312yes—
225C2×C4⋊C4×C53C23116yes—
226C2×C4⋊C4×C53C2311yescharacteristic
227C2×C4⋊C4×C53C2312yes—
228C2×C4⋊C4×C53C2312yes—
229C2×C4⋊C4×C53C2314yes—
230C2×C22⋊C4×C53C2314yes—
231C2×C22⋊C4×C53C2312yes—
232C2×C42×C53C2312yes—
233C2×C42×C53C2311yescharacteristic
234C24×C53C2412yes—
235C23×D53C2411yescharacteristic
236C2×Q8×C53—24no—
237C2×Q8×C53—44no—
238C2×Q8×C53C2414yes—
239C2×Q8×C53C2418yes—
240C2×D4×C53C2×Q818yescomplemented
241C2×D4×C53C2414yes—
242C22×C4×C53—28no—
243C22×C4×C53—48no—
244C22×C4×C53C2412yes—
245C22×C4×C53C2411yescharacteristic
246C22×C4×C53C2412yes—
247C22×C4×C53C2412yes—
248C22×C4×C53C2414yes—
249C22×C4×C53C2418yes—
250C22×C4×C53C24116yes—
251C22×C4×C53C2411yescharacteristic
252C22×C4×C53C2411yescharacteristic
253C2×C22⋊D53C2×Q8116yescomplemented
254C2×C22⋊D53C2418yes—
255C22×Dic53—28no—
256C22×Dic53—48no—
257C22×Dic53C2×Q8116yescomplemented
258C22×Dic53C2412yes—
259C22×Dic53C2412yes—
260C22×Dic53C2411yescharacteristic
261C22×Dic53C2418yes—
262C22×Dic53C2412yes—
263C22×Dic53C2414yes—
264C22×Dic53C24116yes—
265C22×Dic53C2412yes—
266C22×Dic53C2411yescharacteristic
267C22×Dic53C2418yes—
268C22×Dic53C2411yescharacteristic
269Q8×D53—432no—
270#11719947C2×Q8164yescomplemented
271C2×C4×D53—24no—
272C2×C4×D53—24no—
273C2×C4×D53—48no—
274C2×C4×D53C2×Q818yescomplemented
275C2×C4×D53C2414yes—
276C2×C4×D53C2414yes—
277C2×C4×D53C24116yes—
278C2×C4×D53C2414yes—
279C2×Dic106—24no—
280C2×Dic106—216no—
281C2×Dic106—28no—
282C2×Dic106—464no—
283C2×Dic106—44no—
284C2×Dic106—48no—
285C2×Dic106—48no—
286C2×Dic106C2×Q818yescomplemented
287C2×Dic106C2414yes—
288C2×Dic106C24116yes—
289C2×Dic106C2418yes—
290C2×Dic106C2418yes—
291C2×Dic106C24116yes—
292C2×Dic106C24116yes—
293C2×Dic106C2414yes—
294C4⋊C4×C53C2414yes—
295C4⋊C4×C53C24116yes—
296C4⋊C4×C53C2418yes—
297C4⋊C4×C53C2414yes—
298C4⋊C4×C53C2418yes—
299C4⋊C4×C53C2418yes—
300C4⋊C4×C53C24116yes—
301C22⋊C4×C53C24116yes—
302C22⋊C4×C53C2418yes—
303C42×C53C2418yes—
304C42×C53C2414yes—
305C22⋊Dic53C2418yes—
306C22⋊Dic53C24116yes—
307#11719921C2418yes—
308#11719921C2418yes—
309#11719921C2418yes—
310C4⋊Dic53C2418yes—
311C4⋊Dic53C2418yes—
312C4⋊Dic53C2414yes—
313C4⋊Dic53C24116yes—
314C4⋊Dic53C2414yes—
315C4⋊Dic53C2418yes—
316C4⋊Dic53C24116yes—
317#11719919C24116yes—
318#11719919C24116yes—
319#11719919C2418yes—
320#11719919C24116yes—
321#11719919C24116yes—
322#11719919C2418yes—
323#11719919C2418yes—
324#11719919C2418yes—
325#11719919C2418yes—
326#11719919C24116yes—
327#11719919C24116yes—
328#11719919C2418yes—
329#11719919C2418yes—
330C4×Dic53C2414yes—
331C4×Dic53C2414yes—
332C4×Dic53C2414yes—
333C4×Dic53C2418yes—
334C4×Dic53C2418yes—
335C4×Dic53C2418yes—
336C4×Dic53C24116yes—
337C4×Dic53C24116yes—
338C4×Dic53C2418yes—
339C23×C53—24no—
340C23×C53—24no—
341C23×C53C22×Q818yes—
342C23×C53C2514yes—
343C23×C53C2511yescharacteristic
344C22×D53—22no—
345C22×D53—22no—
346C22×D53C22×Q814yes—
347C22×D53C2512yes—
348Q8×C53—28no—
349Q8×C53—48no—
350D4×C53C22×Q8116yescomplemented
351C2×C4×C53—24no—
352C2×C4×C53—28no—
353C2×C4×C53—22no—
354C2×C4×C53—24no—
355C2×C4×C53—24no—
356C2×C4×C53—216no—
357C2×C4×C53—416no—
358C2×C4×C53C22×Q814yes—
359C2×C4×C532−1+414yes—
360C2×C4×C53C2514yes—
361C2×C4×C53C2518yes—
362C2×C4×C53C2512yes—
363C2×C4×C53C2514yes—
364C2×C4×C53C2514yes—
365C2×C4×C53C2512yes—
366C2×C4×C53C2512yes—
367C22⋊D53C22×Q8132yescomplemented
368C2×Dic53—28no—
369C2×Dic53—24no—
370C2×Dic53—24no—
371C2×Dic53—24no—
372C2×Dic53—22no—
373C2×Dic53—216no—
374C2×Dic53—416no—
375C2×Dic53C22×Q818yes—
376C2×Dic53C22×Q814yes—
377C2×Dic53C22×Q8132yescomplemented
378C2×Dic53H(5,𝔽2)14yes—
379C2×Dic53C2514yes—
380C2×Dic53C2518yes—
381C2×Dic53C2514yes—
382C2×Dic53C2514yes—
383C2×Dic53C2512yes—
384C2×Dic53C2514yes—
385C2×Dic53C2512yes—
386C2×Dic53C2512yes—
387C4×D53—28no—
388C4×D53—28no—
389C4×D53—416no—
390C4×D53C22×Q8116yescomplemented
391Dic106—28no—
392Dic106—216no—
393Dic106—232no—
394Dic106—416no—
395Dic106—416no—
396Dic106—48no—
397Dic106C22×Q8116yescomplemented
398C2×#3503—531nomaximal, Sylow
399C22×C53—24no—
400C22×C53—24no—
401C22×C53—216no—
402C22×C53C23×Q818yes—
403C22×C53C23×Q812yes—
404C22×C53C2×H(5,𝔽2)12yes—
405C22×C53C2×2−1+412yes—
406C22×C53C2611yescharacteristic
407C2×D53—22no—
408C2×D53—22no—
409C2×D53—28no—
410C2×D53C23×Q814yes—
411C4×C53—24no—
412C4×C53—28no—
413C4×C53—22no—
414C4×C53—24no—
415C4×C53—24no—
416C4×C53C23×Q814yes—
417C4×C53C2×2−1+414yes—
418Dic53—28no—
419Dic53—24no—
420Dic53—24no—
421Dic53—24no—
422Dic53—22no—
423Dic53C23×Q818yes—
424Dic53C23×Q814yes—
425Dic53C2×H(5,𝔽2)14yes—
426#3503—5332no—
427C2×Q82—531no—
428C2×Q82—531no—
429C2×#557—532no—
430C2×#554—532no—
431C2×#554—531no—
432C2×#554—532no—
433C2×#554D5311yescharacteristic, complemented
434C2×D4×Q8—534no—
435C2×D4×Q8—532no—
436C2×#544—532no—
437C2×#544—534no—
438C2×#533—532no—
439C2×#533—531no—
440C22×C4⋊Q8—531no—
441C22×C4⋊Q8—532no—
442C2×#520—532no—
443C2×C4×#41—531no—
444C2×C53—28no—
445C2×C53#350314yescomplemented
446C2×C53C24×Q811yescharacteristic
447C2×C53C22×H(5,𝔽2)11yescharacteristic
448C2×C53C22×2−1+411yescharacteristic
449D53—24no—
450C22×#41—531no—
451C23×Q8—532no—
452C23×Q8—534no—
453Q82—5316no—
454Q82—5316no—
455#557—5332no—
456#554—5332no—
457#554—5316no—
458#554—5332no—
459#554C2×D53116yescomplemented
460D4×Q8—5364no—
461D4×Q8—5332no—
462#544—5332no—
463#544—5364no—
464#533—5332no—
465#533—5316no—
466C2×C4⋊Q8—532no—
467C2×C4⋊Q8—531no—
468C2×C4⋊Q8—534no—
469C2×C4⋊Q8—5316no—
470C2×C4⋊Q8—532no—
471C2×C4⋊Q8—531no—
472C2×C4⋊Q8—534no—
473C2×C4⋊Q8—534no—
474C2×C4⋊Q8—532no—
475C2×C4⋊Q8—532no—
476C2×C4⋊Q8—532no—
477C2×C4⋊Q8—5332no—
478C2×C4⋊Q8—534no—
479C2×C4⋊Q8—532no—
480C2×C4⋊Q8—531no—
481C2×C4⋊Q8—532no—
482C2×C4⋊Q8C2×D5311yescharacteristic
483C2×#125—532no—
484C2×#125—534no—
485C2×#125—534no—
486C2×#125—534no—
487C2×#125—532no—
488C2×#125C2×D5312yes—
489C2×C22⋊Q8—531no—
490C2×C22⋊Q8—532no—
491C2×C22⋊Q8—534no—
492C2×C22⋊Q8—532no—
493C2×C22⋊Q8—534no—
494C2×C22⋊Q8—531no—
495C2×C22⋊Q8—534no—
496C2×C22⋊Q8—534no—
497C2×C22⋊Q8—534no—
498C2×C22⋊Q8—534no—
499C2×C22⋊Q8C2×D5312yes—
500C2×C22⋊Q8C2×D5314yes—
501#520—5332no—
502C4×#41—5316no—
503C2×C4×Q8—532no—
504C2×C4×Q8—531no—
505C2×C4×Q8—532no—
506C2×C4×Q8—534no—
507C2×C4×Q8—532no—
508C2×C4×Q8—531no—
509C2×C4×Q8—532no—
510C2×C4×Q8—532no—
511C2×C4×Q8—531no—
512C2×C4×Q8C2×D5311yescharacteristic
513C2×C4×D4—531no—
514C2×C4×D4—532no—
515C2×C4×D4—532no—
516C2×C4×D4—534no—
517C2×C4×D4—532no—
518C2×C4×D4—534no—
519C2×C4×D4C2×D5311yescharacteristic
520C2×C4×D4C2×D5312yes—
521C2×#117—531no—
522C2×#117—532no—
523C2×#117—534no—
524C2×#117—532no—
525C22×C4⋊C4—534no—
526C22×C4⋊C4—532no—
527C22×C4⋊C4—532no—
528C22×C4⋊C4—532no—
529C22×C4⋊C4C2×D5312yes—
530C22×C42—532no—
531C22×C42—531no—
532C53C2×#350311yescharacteristic, complemented, Sylow
533C2×#41—5316no—
534C2×#41—538no—
535C22×Q8—5316no—
536C22×Q8—531no—
537C22×Q8—531no—
538C22×Q8—534no—
539C22×Q8—532no—
540C22×Q8—534no—
541C22×Q8—534no—
542C22×Q8—532no—
543C22×Q8—5332no—
544C22×Q8—21216no—
545C22×Q8—2128no—
546C22×Q8C22×D5311yescharacteristic
547C22×Q8C22×D5312yes—
548C22×D4—532no—
549C22×D4C22×D5311yescharacteristic
550C23×C4—532no—
551C23×C4—531no—
552C23×C4—532no—
553C23×C4—534no—
554C23×C4—531no—
555C23×C4—531no—
556C23×C4—534no—
557C23×C4C22×D5312yes—
558C23×C4C22×D5314yes—
559C4⋊Q8—5316no—
560C4⋊Q8—538no—
561C4⋊Q8—5332no—
562C4⋊Q8—5316no—
563C4⋊Q8—538no—
564C4⋊Q8—5332no—
565C4⋊Q8—5332no—
566C4⋊Q8—5316no—
567C4⋊Q8—5316no—
568C4⋊Q8—5316no—
569C4⋊Q8—5332no—
570C4⋊Q8—5316no—
571C4⋊Q8—538no—
572C4⋊Q8—5316no—
573C4⋊Q8C22×D5318yes—
574#125—5316no—
575#125—5332no—
576#125—5332no—
577#125—5332no—
578#125—5316no—
579#125C22×D53116yes—
580C22⋊Q8—538no—
581C22⋊Q8—5316no—
582C22⋊Q8—5332no—
583C22⋊Q8—5316no—
584C22⋊Q8—538no—
585C22⋊Q8—5332no—
586C22⋊Q8—5332no—
587C22⋊Q8—5332no—
588C22⋊Q8—5332no—
589C22⋊Q8—5332no—
590C22⋊Q8C22×D53116yes—
591C22⋊Q8C22×D53132yes—
592C4×Q8—5316no—
593C4×Q8—538no—
594C4×Q8—5316no—
595C4×Q8—5332no—
596C4×Q8—5316no—
597C4×Q8—538no—
598C4×Q8—5316no—
599C4×Q8—5316no—
600C4×Q8—538no—
601C4×Q8C22×D5318yes—
602C4×D4—538no—
603C4×D4—5316no—
604C4×D4—5316no—
605C4×D4—5332no—
606C4×D4—5316no—
607C4×D4—5332no—
608C4×D4C22×D5318yes—
609C4×D4C22×D53116yes—
610#117—538no—
611#117—5316no—
612#117—5332no—
613#117—5316no—
614C2×C4⋊C4—534no—
615C2×C4⋊C4—532no—
616C2×C4⋊C4—531no—
617C2×C4⋊C4—532no—
618C2×C4⋊C4—534no—
619C2×C4⋊C4—534no—
620C2×C4⋊C4—532no—
621C2×C4⋊C4—5332no—
622C2×C4⋊C4—534no—
623C2×C4⋊C4—534no—
624C2×C4⋊C4—5316no—
625C2×C4⋊C4—532no—
626C2×C4⋊C4—532no—
627C2×C4⋊C4—532no—
628C2×C4⋊C4—531no—
629C2×C4⋊C4—532no—
630C2×C4⋊C4—534no—
631C2×C4⋊C4—532no—
632C2×C4⋊C4—532no—
633C2×C4⋊C4—534no—
634C2×C4⋊C4—532no—
635C2×C4⋊C4—534no—
636C2×C4⋊C4—5316no—
637C2×C4⋊C4—5316no—
638C2×C4⋊C4C22×D5312yes—
639C2×C4⋊C4C22×D5312yes—
640C2×C4⋊C4C22×D5311yescharacteristic
641C2×C4⋊C4C22×D5314yes—
642C2×C4⋊C4C22×D53116yes—
643C2×C4⋊C4C22×D5311yescharacteristic
644C2×C4⋊C4C22×D5314yes—
645C2×C4⋊C4C22×D5312yes—
646C2×C22⋊C4—534no—
647C2×C22⋊C4—532no—
648C2×C22⋊C4—532no—
649C2×C22⋊C4—532no—
650C2×C22⋊C4—532no—
651C2×C22⋊C4C22×D5314yes—
652C2×C22⋊C4C22×D5312yes—
653C2×C42—531no—
654C2×C42—532no—
655C2×C42—534no—
656C2×C42—534no—
657C2×C42—532no—
658C2×C42—532no—
659C2×C42—532no—
660C2×C42—531no—
661C2×C42—5316no—
662C2×C42—531no—
663C2×C42—538no—
664C2×C42C22×D5312yes—
665C2×C42C22×D5311yescharacteristic
666C24—531no—
667C24C23×D5312yes—
668#41—5364no—
669C2×Q8—24no—
670C2×Q8—44no—
671C2×Q8—538no—
672C2×Q8—534no—
673C2×Q8—534no—
674C2×Q8—5316no—
675C2×Q8—538no—
676C2×Q8—5316no—
677C2×Q8—5316no—
678C2×Q8—538no—
679C2×Q8—1068no—
680C2×Q8—10616no—
681C2×Q8—1064no—
682C2×Q8—2128no—
683C2×Q8—2128no—
684C2×Q8—2124no—
685C2×Q8—21264no—
686C2×Q8—21232no—
687C2×Q8C23×D5314yes—
688C2×Q8C23×D5318yes—
689C2×D4—5316no—
690C2×D4—538no—
691C2×D4Q8×D5318yescomplemented
692C2×D4C23×D5314yes—
693C22×C4—28no—
694C22×C4—48no—
695C22×C4—5316no—
696C22×C4—538no—
697C22×C4—532no—
698C22×C4—531no—
699C22×C4—531no—
700C22×C4—538no—
701C22×C4—534no—
702C22×C4—538no—
703C22×C4—532no—
704C22×C4—531no—
705C22×C4—532no—
706C22×C4—532no—
707C22×C4—534no—
708C22×C4—5316no—
709C22×C4—534no—
710C22×C4—534no—
711C22×C4—5316no—
712C22×C4—1064no—
713C22×C4—1068no—
714C22×C4—1064no—
715C22×C4—2128no—
716C22×C4—2128no—
717C22×C4C23×D5318yes—
718C22×C4C23×D5312yes—
719C22×C4C23×D5312yes—
720C22×C4C23×D5311yescharacteristic
721C22×C4C23×D5314yes—
722C22×C4C23×D5312yes—
723C22×C4C23×D53116yes—
724C22×C4C23×D5311yescharacteristic
725C22×C4C23×D5311yescharacteristic
726C4⋊C4—5316no—
727C4⋊C4—538no—
728C4⋊C4—534no—
729C4⋊C4—538no—
730C4⋊C4—5316no—
731C4⋊C4—5316no—
732C4⋊C4—538no—
733C4⋊C4—5316no—
734C4⋊C4—5316no—
735C4⋊C4—538no—
736C4⋊C4—538no—
737C4⋊C4—538no—
738C4⋊C4—534no—
739C4⋊C4—538no—
740C4⋊C4—5316no—
741C4⋊C4—538no—
742C4⋊C4—538no—
743C4⋊C4—5316no—
744C4⋊C4—538no—
745C4⋊C4—5316no—
746C4⋊C4C23×D5318yes—
747C4⋊C4C23×D5318yes—
748C4⋊C4C23×D5314yes—
749C4⋊C4C23×D53116yes—
750C4⋊C4C23×D5314yes—
751C4⋊C4C23×D53116yes—
752C4⋊C4C23×D5318yes—
753C22⋊C4—5316no—
754C22⋊C4—538no—
755C22⋊C4—538no—
756C22⋊C4—538no—
757C22⋊C4—538no—
758C22⋊C4C23×D53116yes—
759C22⋊C4C23×D5318yes—
760C42—534no—
761C42—534no—
762C42—538no—
763C42—538no—
764C42—538no—
765C42—534no—
766C42—5316no—
767C42—5316no—
768C42—538no—
769C42C23×D5314yes—
770C42C23×D5318yes—
771C23—24no—
772C23—24no—
773C23—534no—
774C23—532no—
775C23—1062no—
776C23—1062no—
777C23C2×Q8×D5318yes—
778C23C24×D5314yes—
779C23C24×D5311yescharacteristic
780Q8—28no—
781Q8—48no—
782Q8—5316no—
783Q8—10616no—
784Q8—10632no—
785Q8—1068no—
786Q8—21216no—
787Q8—21216no—
788Q8—2128no—
789D4—5332no—
790D4C2×Q8×D53116yescomplemented
791C2×C4—24no—
792C2×C4—28no—
793C2×C4—22no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—216no—
797C2×C4—416no—
798C2×C4—534no—
799C2×C4—538no—
800C2×C4—5332no—
801C2×C4—534no—
802C2×C4—534no—
803C2×C4—532no—
804C2×C4—532no—
805C2×C4—5316no—
806C2×C4—534no—
807C2×C4—532no—
808C2×C4—534no—
809C2×C4—538no—
810C2×C4—534no—
811C2×C4—1068no—
812C2×C4—10616no—
813C2×C4—1064no—
814C2×C4—1068no—
815C2×C4—1064no—
816C2×C4—1062no—
817C2×C4—1064no—
818C2×C4—1068no—
819C2×C4—21216no—
820C2×C4—21216no—
821C2×C4C2×Q8×D5314yes—
822C2×C4#1313326414yes—
823C2×C4C24×D5314yes—
824C2×C4C24×D5314yes—
825C2×C4C24×D5312yes—
826C2×C4C24×D5318yes—
827C2×C4C24×D5314yes—
828C2×C4C24×D5312yes—
829C2×C4C24×D5312yes—
830C22—216no—
831C22—24no—
832C22—24no—
833C22—534no—
834C22—1068no—
835C22—1062no—
836C22—1062no—
837C22C22×Q8×D5318yes—
838C22C22×Q8×D5312yes—
839C22H(5,𝔽2)×D5312yes—
840C22C2×#1313326412yes—
841C22C25×D5311yescharacteristic
842C4—24no—
843C4—28no—
844C4—22no—
845C4—24no—
846C4—24no—
847C4—534no—
848C4—538no—
849C4—534no—
850C4—1064no—
851C4—1068no—
852C4—1064no—
853C4—1062no—
854C4—1064no—
855C4C22×Q8×D5314yes—
856C4C2×#1313326414yes—
857C2—28no—
858C2—1064no—
859C2#2028852914yesdirect product factor
860C2C23×Q8×D5311yescharacteristic
861C2C2×H(5,𝔽2)×D5311yescharacteristic
862C2C22×#1313326411yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#554C2
socleC23×C53C25
prime radicalC22×#11719947C22
hypercenterC2×#554D53
hypocenterC53C2×#3503
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #20288529C2direct (N × H)
2. C2×Q8×Dic106C2semidirect
3. C2×#16811353C2semidirect
4. C2×#16811350C2semidirect
5. C2×#16811331C2semidirect
6. C2×#16811330C2semidirect
7. C2×#16811328C2semidirect
8. C2×D4×Dic106C2semidirect
9. C2×#16811286C2semidirect
10. C2×#16811253C2semidirect
11. C2×#16811252C2semidirect
12. C2×#16811177C2semidirect
13. C2×#16811175C2semidirect
14. C22×#13133216C2semidirect
15. C2×C4⋊Q8×D53C2semidirect
18. C2×C53×#554C2semidirect
22. Q8×Dic106C22semidirect
23. #16811353C22semidirect
24. #16811350C22semidirect
25. #16811331C22semidirect
26. #16811330C22semidirect
27. #16811328C22semidirect
28. D4×Dic106C22semidirect
29. #16811286C22semidirect
30. #16811253C22semidirect
31. #16811252C22semidirect
32. #16811177C22semidirect
33. #16811175C22semidirect
45. C2×#13133216C22semidirect
49. C4⋊Q8×D53C22semidirect
92. C53×#554C22semidirect
101. C2×#11719947Q8semidirect
240. C2×D4×C53C2×Q8semidirect
253. C2×C22⋊D53C2×Q8semidirect
257. C22×Dic53C2×Q8semidirect
270. #11719947C2×Q8semidirect
274. C2×C4×D53C2×Q8semidirect
286. C2×Dic106C2×Q8semidirect
350. D4×C53C22×Q8semidirect
367. C22⋊D53C22×Q8semidirect
377. C2×Dic53C22×Q8semidirect
390. C4×D53C22×Q8semidirect
397. Dic106C22×Q8semidirect
433. C2×#554D53semidirect
445. C2×C53#3503semidirect
459. #554C2×D53semidirect
532. C53C2×#3503semidirect
691. C2×D4Q8×D53semidirect
790. D4C2×Q8×D53semidirect
859. C2#20288529direct (N × H)

Maximal subgroups

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

subgroupindex
#202885292
C2×Q8×Dic1062
C2×#168113532
C2×#168113502
C2×#168113312
C2×#168113302
C2×#168113282
C2×D4×Dic1062
C2×#168112862
C2×#168112532
C2×#168112522
C2×#168111772
C2×#168111752
C22×#131332162
C2×C4⋊Q8×D532
C2×#168111022
C2×C4×#117199472
C2×C53×#5542
C2×#350353