Finite Group Databasebeta

← C2×#20288578 #28292169

Subgroups — C2×#20288578 #28292169

Order 13568.

7130 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288578C2132yesmaximal, direct product factor
2C2×#16811356C212yesmaximal, complemented
3C2×#16811350C212yesmaximal, complemented
4C2×#16811346C211yesmaximal, characteristic, complemented
5C2×#16811344C214yesmaximal, complemented
6C2×#16811343C211yesmaximal, characteristic, complemented
7C2×#16811334C211yesmaximal, characteristic, complemented
8C2×#16811308C212yesmaximal, complemented
9C2×#16811307C212yesmaximal, complemented
10C2×#16811219C214yesmaximal, complemented
11C2×#16811196C212yesmaximal, complemented
12C2×#16811178C211yesmaximal, characteristic, complemented
13C2×#16811170C211yesmaximal, characteristic
14C2×#16811158C212yesmaximal, complemented
15C2×#16811155C212yesmaximal, complemented
16C2×#16811104C212yesmaximal, complemented
17C2×C4×Q8×D53C211yesmaximal, characteristic, complemented
18C2×C53×#554C211yesmaximal, characteristic, complemented
19C22×#11719945C2212yes—
20C22×Q8×D53C2211yescharacteristic
21#16811356C22132yescomplemented
22#16811350C22132yescomplemented
23#16811346C22116yescomplemented
24#16811344C22164yescomplemented
25#16811343C22116yescomplemented
26#16811334C22116yescomplemented
27#16811308C22132yescomplemented
28#16811307C22132yescomplemented
29#16811219C22164yescomplemented
30#16811196C22132yescomplemented
31#16811178C22116yescomplemented
32#16811170C22116yes—
33C2×#13133217C2211yescharacteristic
34C2×#13133216C2214yes—
35C2×#13133216C2211yescharacteristic
36C2×#13133213C2211yescharacteristic
37#16811158C22132yescomplemented
38#16811155C22132yescomplemented
39C2×#13133212C2214yes—
40C2×#13133212C2214yes—
41C2×#13133210C2214yes—
42C2×#13133210C2214yes—
43C2×#13133208C2212yes—
44C2×#13133208C2212yes—
45C2×#13133207C2214yes—
46C2×#13133207C2214yes—
47C2×#13133205C2212yes—
48C2×#13133204C2212yes—
49C2×#13133203C2212yes—
50C2×#13133203C2214yes—
51C2×#13133202C2214yes—
52C2×#13133200C2214yes—
53C2×#13133199C2214yes—
54C2×#13133199C2214yes—
55C2×#13133197C2212yes—
56C2×#13133197C2212yes—
57C2×#13133196C2212yes—
58C2×#13133193C2212yes—
59C2×#13133193C2214yes—
60C2×#13133193C2212yes—
61C2×#13133192C2211yescharacteristic
62C2×#13133190C2212yes—
63C2×#13133188C2211yescharacteristic
64#16811104C22132yescomplemented
65C2×Q8×Dic53C2212yes—
66C2×Q8×Dic53C2211yescharacteristic
67C2×C4×Dic106C2211yescharacteristic
68C2×C4×Dic106C2212yes—
69C2×C4×Dic106C2212yes—
70C2×#13133182C2212yes—
71C2×#13133182C2212yes—
72C2×#13133182C2212yes—
73C2×#13133182C2214yes—
74C2×#13133182C2211yescharacteristic
75C4×Q8×D53C22116yescomplemented
76C2×C4×D212C2211yescharacteristic
77C2×#13133179C2212yes—
78C2×#13133179C2214yes—
79C2×C4×C22⋊D53C2214yes—
80C2×C4×C22⋊D53C2214yes—
81C2×C4×C22⋊D53C2212yes—
82C2×#13133176C2212yes—
83C2×#13133176C2214yes—
84C2×#13133175C2212yes—
85C2×#13133175C2214yes—
86C2×#13133175C2212yes—
87C2×C4⋊C4×D53C2212yes—
88C2×C4⋊C4×D53C2211yescharacteristic
89C2×C4⋊C4×D53C2212yes—
90C2×C42×D53C2211yescharacteristic
91C2×C42×D53C2212yes—
92C53×#554C22116yescomplemented
93C2×C4⋊Q8×C53C2211yescharacteristic
94C2×#125×C53C2212yes—
95C2×C22⋊Q8×C53C2214yes—
96C2×C22⋊Q8×C53C2212yes—
97C2×C4×Q8×C53C2211yescharacteristic
98C2×C4×D4×C53C2211yescharacteristic
99C2×C4×D4×C53C2212yes—
100C22×C4⋊C4×C53C2212yes—
101C2×#11719945—216no—
102C2×#11719945C23116yes—
103C22×Dic106C2312yes—
104C22×Dic106C2312yes—
105C22×Dic106C2311yescharacteristic
106C22×Dic106C2312yes—
107C2×Q8×D53—28no—
108C2×Q8×D53C2318yes—
109C22×D212C2311yescharacteristic
110C22×D212C2312yes—
111C22×C22⋊D53C2312yes—
112C22×C22⋊D53C2312yes—
113C22×C22⋊D53C2312yes—
114C22×C4×D53C2311yescharacteristic
115C22×C4×D53C2312yes—
116C22×C4×D53C2312yes—
117C22×C4×D53C2312yes—
118C22×C4×D53C2311yescharacteristic
119C22×C4×D53C2314yes—
120C22×C4×D53C2311yescharacteristic
121#13133217C2318yes—
122#13133216C23132yes—
123#13133216C2318yes—
124#13133213C2318yes—
125#13133212C23132yes—
126#13133212C23132yes—
127#13133210C23132yes—
128#13133210C23132yes—
129#13133208C23116yes—
130#13133208C23116yes—
131#13133207C23132yes—
132#13133207C23132yes—
133#13133205C23116yes—
134#13133204C23116yes—
135#13133203C23116yes—
136#13133203C23132yes—
137#13133202C23132yes—
138#13133200C23132yes—
139#13133199C23132yes—
140#13133199C23132yes—
141#13133197C23116yes—
142#13133197C23116yes—
143#13133196C23116yes—
144#13133193C23116yes—
145#13133193C23132yes—
146#13133193C23116yes—
147#13133192C2318yes—
148#13133190C23116yes—
149#13133188C2318yes—
150Q8×Dic53C2318yes—
151Q8×Dic53C23116yes—
152C4×Dic106C2318yes—
153C4×Dic106C23116yes—
154C4×Dic106C23116yes—
155#13133182C2318yes—
156#13133182C23116yes—
157#13133182C23116yes—
158#13133182C23132yes—
159#13133182C23116yes—
160C4×D212C2318yes—
161#13133179C23116yes—
162#13133179C23132yes—
163C4×C22⋊D53C23116yes—
164C4×C22⋊D53C23132yes—
165C4×C22⋊D53C23132yes—
166#13133176C23116yes—
167#13133176C23132yes—
168#13133175C23132yes—
169#13133175C23116yes—
170#13133175C23116yes—
171C2×C4⋊Dic53C2311yescharacteristic
172C2×C4⋊Dic53C2312yes—
173C2×C4⋊Dic53C2312yes—
174C2×C4⋊Dic53C2314yes—
175C2×C4⋊Dic53C2314yes—
176C2×C4⋊Dic53C2311yescharacteristic
177C2×C4⋊Dic53C2312yes—
178C2×#11719919C2312yes—
179C2×#11719919C2314yes—
180C2×#11719919C2312yes—
181C2×#11719919C2312yes—
182C2×#11719919C2312yes—
183C2×#11719919C2314yes—
184C2×#11719919C2314yes—
185C2×#11719919C2314yes—
186C4⋊C4×D53C23116yes—
187C4⋊C4×D53C2318yes—
188C4⋊C4×D53C23116yes—
189C2×C22⋊Dic53C2312yes—
190C2×C22⋊Dic53C2314yes—
191C2×C22⋊Dic53C2314yes—
192C2×#11719921C2312yes—
193C2×#11719921C2314yes—
194C2×#11719921C2314yes—
195C2×#11719921C2314yes—
196C2×#11719921C2314yes—
197C2×#11719921C2312yes—
198C2×C4×Dic53C2312yes—
199C2×C4×Dic53C2312yes—
200C2×C4×Dic53C2311yescharacteristic
201C2×C4×Dic53C2312yes—
202C2×C4×Dic53C2311yescharacteristic
203C2×C4×Dic53C2311yescharacteristic
204C2×C4×Dic53C2314yes—
205C2×C4×Dic53C2314yes—
206C2×C4×Dic53C2314yes—
207C42×D53C23116yes—
208C42×D53C2318yes—
209C22×Q8×C53C2311yescharacteristic
210C22×Q8×C53C2312yes—
211C22×D4×C53C2311yescharacteristic
212C23×C4×C53C2312yes—
213C23×C4×C53C2314yes—
214C4⋊Q8×C53C2318yes—
215#125×C53C23116yes—
216C22⋊Q8×C53C23116yes—
217C22⋊Q8×C53C23132yes—
218C4×Q8×C53C2318yes—
219C4×D4×C53C2318yes—
220C4×D4×C53C23116yes—
221C2×C4⋊C4×C53C2311yescharacteristic
222C2×C4⋊C4×C53C2314yes—
223C2×C4⋊C4×C53C2312yes—
224C2×C4⋊C4×C53C23116yes—
225C2×C4⋊C4×C53C2311yescharacteristic
226C2×C4⋊C4×C53C2312yes—
227C2×C4⋊C4×C53C2312yes—
228C2×C4⋊C4×C53C2314yes—
229C2×C22⋊C4×C53C2312yes—
230C2×C22⋊C4×C53C2314yes—
231C2×C42×C53C2312yes—
232C2×C42×C53C2311yescharacteristic
233C24×C53C2412yes—
234C23×D53C2412yes—
235C23×D53C2411yescharacteristic
236C2×Q8×C53—24no—
237C2×Q8×C53—44no—
238C2×Q8×C53C2414yes—
239C2×Q8×C53C2418yes—
240C2×D4×C53—24no—
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⋊D53—28no—
254C2×C22⋊D53—28no—
255C2×C22⋊D53—44no—
256C2×C22⋊D53C2418yes—
257C2×C22⋊D53C2418yes—
258C2×C22⋊D53C2418yes—
259C22×Dic53C2411yescharacteristic
260C22×Dic53C2412yes—
261C22×Dic53C2414yes—
262C22×Dic53C2412yes—
263C22×Dic53C2412yes—
264C22×Dic53C2411yescharacteristic
265C22×Dic53C2411yescharacteristic
266Q8×D53—232no—
267#11719945—264no—
268C2×D212—28no—
269C2×D212—24no—
270C2×D212C2414yes—
271C2×D212C2418yes—
272C2×C4×D53—28no—
273C2×C4×D53—28no—
274C2×C4×D53—24no—
275C2×C4×D53—44no—
276C2×C4×D53—48no—
277C2×C4×D53—42no—
278C2×C4×D53#4118yes—
279C2×C4×D53C2414yes—
280C2×C4×D53C2418yes—
281C2×C4×D53C2418yes—
282C2×C4×D53C2418yes—
283C2×C4×D53C2414yes—
284C2×C4×D53C24116yes—
285C2×C4×D53C2414yes—
286C2×Dic106—24no—
287C2×Dic106—28no—
288C2×Dic106—28no—
289C2×Dic106—28no—
290C2×Dic106C2418yes—
291C2×Dic106C2418yes—
292C2×Dic106C2414yes—
293C2×Dic106C2418yes—
294C4⋊C4×C53C2414yes—
295C4⋊C4×C53C24116yes—
296C4⋊C4×C53C2418yes—
297C4⋊C4×C53C2414yes—
298C4⋊C4×C53C2418yes—
299C4⋊C4×C53C2418yes—
300C4⋊C4×C53C24116yes—
301C22⋊C4×C53C2418yes—
302C22⋊C4×C53C24116yes—
303C42×C53C2418yes—
304C42×C53C2414yes—
305C22⋊Dic53C2418yes—
306C22⋊Dic53C24116yes—
307C22⋊Dic53C24116yes—
308#11719921C2418yes—
309#11719921C24116yes—
310#11719921C24116yes—
311#11719921C24116yes—
312#11719921C24116yes—
313#11719921C2418yes—
314C4⋊Dic53C2414yes—
315C4⋊Dic53C2418yes—
316C4⋊Dic53C2418yes—
317C4⋊Dic53C24116yes—
318C4⋊Dic53C24116yes—
319C4⋊Dic53C2414yes—
320C4⋊Dic53C2418yes—
321#11719919C2418yes—
322#11719919C24116yes—
323#11719919C2418yes—
324#11719919C2418yes—
325#11719919C2418yes—
326#11719919C24116yes—
327#11719919C24116yes—
328#11719919C24116yes—
329C4×Dic53C2418yes—
330C4×Dic53C2418yes—
331C4×Dic53C2414yes—
332C4×Dic53C2418yes—
333C4×Dic53C2414yes—
334C4×Dic53C2414yes—
335C4×Dic53C24116yes—
336C4×Dic53C24116yes—
337C4×Dic53C24116yes—
338C23×C53—24no—
339C23×C53—24no—
340C23×C53—24no—
341C23×C53C2514yes—
342C23×C53C2511yescharacteristic
343C22×D53—22no—
344C22×D53—22no—
345C22×D53—24no—
346C22×D53—24no—
347C22×D53—24no—
348C22×D53C2×#4114yes—
349C22×D53C2514yes—
350C22×D53C2512yes—
351Q8×C53—28no—
352Q8×C53—48no—
353D4×C53—28no—
354C2×C4×C53—24no—
355C2×C4×C53—24no—
356C2×C4×C53—24no—
357C2×C4×C53—28no—
358C2×C4×C53—22no—
359C2×C4×C53—216no—
360C2×C4×C53—416no—
361C2×C4×C53C2×#4114yes—
362C2×C4×C532−1+414yes—
363C2×C4×C53C2514yes—
364C2×C4×C53C2514yes—
365C2×C4×C53C2514yes—
366C2×C4×C53C2518yes—
367C2×C4×C53C2512yes—
368C2×C4×C53C2512yes—
369C2×C4×C53C2512yes—
370C22⋊D53—216no—
371C22⋊D53—216no—
372C22⋊D53—48no—
373C2×Dic53—24no—
374C2×Dic53—24no—
375C2×Dic53—28no—
376C2×Dic53—22no—
377C2×Dic53—24no—
378C2×Dic53—22no—
379C2×Dic53C2×#4114yes—
380C2×Dic53C2514yes—
381C2×Dic53C2514yes—
382C2×Dic53C2518yes—
383C2×Dic53C2514yes—
384C2×Dic53C2512yes—
385C2×Dic53C2512yes—
386C2×Dic53C2512yes—
387D212—216no—
388D212—28no—
389C4×D53—216no—
390C4×D53—216no—
391C4×D53—28no—
392C4×D53—48no—
393C4×D53—416no—
394C4×D53—44no—
395C4×D53C2×#41116yes—
396Dic106—28no—
397Dic106—216no—
398Dic106—216no—
399Dic106—216no—
400C2×#3507—531nomaximal, Sylow
401C22×C53—24no—
402C22×C53—24no—
403C22×C53—24no—
404C22×C53—48no—
405C22×C53C22×#4112yes—
406C22×C53C2×2−1+412yes—
407C22×C53#58512yes—
408C22×C53C2611yescharacteristic
409C2×D53—22no—
410C2×D53—22no—
411C2×D53—28no—
412C2×D53—24no—
413C2×D53—24no—
414C2×D53—24no—
415C2×D53—48no—
416C2×D53C22×#4114yes—
417C4×C53—24no—
418C4×C53—24no—
419C4×C53—24no—
420C4×C53—28no—
421C4×C53—22no—
422C4×C53C22×#4114yes—
423C4×C53C2×2−1+414yes—
424Dic53—24no—
425Dic53—24no—
426Dic53—28no—
427Dic53—22no—
428Dic53—24no—
429Dic53—22no—
430Dic53C22×#4114yes—
431#3507—5332no—
432C2×#559—532no—
433C2×#557—532no—
434C2×#556—534no—
435C2×#556—531no—
436C2×#556—531no—
437C2×#554—531no—
438C2×#554D5311yescharacteristic, complemented
439C2×#552—532no—
440C2×#552—532no—
441C2×#539—534no—
442C2×#536—532no—
443C2×#533—531no—
444C2×#532—531no—
445C2×#529—532no—
446C2×#529—532no—
447C2×#520—532no—
448C22×C4×Q8—531no—
449C2×C53—44no—
450C2×C53#350714yescomplemented
451C2×C53C23×#4111yescharacteristic
452C2×C53C22×2−1+411yescharacteristic
453C2×C53C2×#58511yescharacteristic
454D53—24no—
455D53—44no—
456C22×#41—532no—
457C23×Q8—531no—
458#559—5332no—
459#557—5332no—
460#556—5364no—
461#556—5316no—
462#556—5316no—
463#554—5316no—
464#554C2×D53116yescomplemented
465#552—5332no—
466#552—5332no—
467#539—5364no—
468#536—5332no—
469#533—5316no—
470#532—5316no—
471C2×C4⋊Q8—531no—
472C2×C4⋊Q8—534no—
473C2×C4⋊Q8—531no—
474C2×C4⋊Q8C2×D5311yescharacteristic
475C2×#127—531no—
476#529—5332no—
477#529—5332no—
478C2×#126—534no—
479C2×#126—534no—
480C2×#126—534no—
481C2×#126—534no—
482C2×#125—532no—
483C2×#125—532no—
484C2×#125—534no—
485C2×#125—534no—
486C2×#125C2×D5312yes—
487C2×#124—532no—
488C2×#124—532no—
489C2×#124—534no—
490C2×#124—532no—
491C2×#123—534no—
492C2×#123—534no—
493C2×#123—534no—
494C2×#123—534no—
495C2×C22⋊Q8—532no—
496C2×C22⋊Q8—532no—
497C2×C22⋊Q8—534no—
498C2×C22⋊Q8—532no—
499C2×C22⋊Q8—532no—
500C2×C22⋊Q8—532no—
501C2×C22⋊Q8C2×D5312yes—
502C2×C22⋊Q8C2×D5314yes—
503C2×#121—531no—
504C2×#121—531no—
505C2×#121—532no—
506#520—5332no—
507C2×C4×Q8—531no—
508C2×C4×Q8—532no—
509C2×C4×Q8—5316no—
510C2×C4×Q8—531no—
511C2×C4×Q8—532no—
512C2×C4×Q8—534no—
513C2×C4×Q8—532no—
514C2×C4×Q8—532no—
515C2×C4×Q8—531no—
516C2×C4×Q8—532no—
517C2×C4×Q8—532no—
518C2×C4×Q8C2×D5311yescharacteristic
519C2×C4×D4—534no—
520C2×C4×D4—534no—
521C2×C4×D4—532no—
522C2×C4×D4—534no—
523C2×C4×D4—532no—
524C2×C4×D4—531no—
525C2×C4×D4C2×D5312yes—
526C2×C4×D4C2×D5311yescharacteristic
527C2×#117—532no—
528C2×#117—534no—
529C2×#117—532no—
530C2×#117—532no—
531C2×#117—534no—
532C22×C4⋊C4—531no—
533C22×C4⋊C4—532no—
534C22×C4⋊C4—532no—
535C22×C4⋊C4C2×D5312yes—
536C22×C42—532no—
537C22×C42—531no—
538C53C2×#350711yescharacteristic, complemented, Sylow
539C2×#41—5316no—
540C2×#41—10616no—
541C22×Q8—538no—
542C22×Q8—532no—
543C22×Q8—531no—
544C22×Q8—532no—
545C22×Q8—532no—
546C22×Q8—1068no—
547C22×Q8C22×D5311yescharacteristic
548C22×Q8C22×D5312yes—
549C22×D4—532no—
550C22×D4—532no—
551C22×D4—532no—
552C22×D4—531no—
553C22×D4—532no—
554C22×D4C22×D5311yescharacteristic
555C23×C4—531no—
556C23×C4—532no—
557C23×C4—532no—
558C23×C4—531no—
559C23×C4—532no—
560C23×C4—531no—
561C23×C4—534no—
562C23×C4C22×D5312yes—
563C23×C4C22×D5314yes—
564C4⋊Q8—538no—
565C4⋊Q8—5332no—
566C4⋊Q8—538no—
567C4⋊Q8C22×D5318yes—
568#127—538no—
569#126—5332no—
570#126—5332no—
571#126—5332no—
572#126—5332no—
573#125—5316no—
574#125—5316no—
575#125—5332no—
576#125—5332no—
577#125C22×D53116yes—
578#124—5316no—
579#124—5316no—
580#124—5332no—
581#124—5316no—
582#123—5332no—
583#123—5332no—
584#123—5332no—
585#123—5332no—
586C22⋊Q8—5316no—
587C22⋊Q8—5316no—
588C22⋊Q8—5332no—
589C22⋊Q8—5316no—
590C22⋊Q8—5316no—
591C22⋊Q8—5316no—
592C22⋊Q8C22×D53116yes—
593C22⋊Q8C22×D53132yes—
594#121—538no—
595#121—538no—
596#121—5316no—
597C4×Q8—538no—
598C4×Q8—5316no—
599C4×Q8—538no—
600C4×Q8—5316no—
601C4×Q8—5332no—
602C4×Q8—5316no—
603C4×Q8—5316no—
604C4×Q8—538no—
605C4×Q8—5316no—
606C4×Q8—5316no—
607C4×Q8C22×D5318yes—
608C4×D4—5332no—
609C4×D4—5332no—
610C4×D4—5316no—
611C4×D4—5332no—
612C4×D4—5316no—
613C4×D4—538no—
614C4×D4C22×D53116yes—
615C4×D4C22×D5318yes—
616#117—5316no—
617#117—5332no—
618#117—5316no—
619#117—5316no—
620#117—5332no—
621C2×C4⋊C4—531no—
622C2×C4⋊C4—532no—
623C2×C4⋊C4—534no—
624C2×C4⋊C4—532no—
625C2×C4⋊C4—532no—
626C2×C4⋊C4—532no—
627C2×C4⋊C4—532no—
628C2×C4⋊C4—534no—
629C2×C4⋊C4—534no—
630C2×C4⋊C4—531no—
631C2×C4⋊C4—532no—
632C2×C4⋊C4—534no—
633C2×C4⋊C4—534no—
634C2×C4⋊C4—534no—
635C2×C4⋊C4—532no—
636C2×C4⋊C4—538no—
637C2×C4⋊C4—5316no—
638C2×C4⋊C4—5316no—
639C2×C4⋊C4C22×D5311yescharacteristic
640C2×C4⋊C4C22×D5312yes—
641C2×C4⋊C4C22×D5312yes—
642C2×C4⋊C4C22×D5314yes—
643C2×C4⋊C4C22×D53116yes—
644C2×C4⋊C4C22×D5314yes—
645C2×C4⋊C4C22×D5312yes—
646C2×C4⋊C4C22×D5311yescharacteristic
647C2×C22⋊C4—532no—
648C2×C22⋊C4—534no—
649C2×C22⋊C4—534no—
650C2×C22⋊C4—532no—
651C2×C22⋊C4—534no—
652C2×C22⋊C4—534no—
653C2×C22⋊C4—534no—
654C2×C22⋊C4—532no—
655C2×C22⋊C4—534no—
656C2×C22⋊C4C22×D5312yes—
657C2×C22⋊C4C22×D5314yes—
658C2×C42—534no—
659C2×C42—534no—
660C2×C42—532no—
661C2×C42—532no—
662C2×C42—534no—
663C2×C42—531no—
664C2×C42—532no—
665C2×C42—531no—
666C2×C42—531no—
667C2×C42—5316no—
668C2×C42—538no—
669C2×C42C22×D5311yescharacteristic
670C2×C42C22×D5312yes—
671C24—531no—
672C24—532no—
673C24C23×D5312yes—
674#41—10664no—
675C2×Q8—24no—
676C2×Q8—44no—
677C2×Q8—538no—
678C2×Q8—534no—
679C2×Q8—538no—
680C2×Q8—538no—
681C2×Q8—1068no—
682C2×Q8—1068no—
683C2×Q8—10632no—
684C2×Q8—1064no—
685C2×Q8—1068no—
686C2×Q8C23×D5314yes—
687C2×Q8C23×D5318yes—
688C2×D4—24no—
689C2×D4—538no—
690C2×D4—538no—
691C2×D4—538no—
692C2×D4—534no—
693C2×D4—538no—
694C2×D4—1068no—
695C2×D4—1068no—
696C2×D4—1068no—
697C2×D4—1064no—
698C2×D4—2124no—
699C2×D4C23×D5314yes—
700C22×C4—28no—
701C22×C4—48no—
702C22×C4—531no—
703C22×C4—538no—
704C22×C4—534no—
705C22×C4—531no—
706C22×C4—532no—
707C22×C4—534no—
708C22×C4—532no—
709C22×C4—532no—
710C22×C4—531no—
711C22×C4—534no—
712C22×C4—538no—
713C22×C4—538no—
714C22×C4—538no—
715C22×C4—534no—
716C22×C4—5316no—
717C22×C4—1068no—
718C22×C4—1068no—
719C22×C4—1064no—
720C22×C4—2124no—
721C22×C4—2128no—
722C22×C4—2122no—
723C22×C4C23×D5318yes—
724C22×C4C23×D5312yes—
725C22×C4C23×D5312yes—
726C22×C4C23×D5311yescharacteristic
727C22×C4C23×D5312yes—
728C22×C4C23×D5314yes—
729C22×C4C23×D53116yes—
730C22×C4C23×D5311yescharacteristic
731C22×C4C23×D5311yescharacteristic
732C4⋊C4—534no—
733C4⋊C4—538no—
734C4⋊C4—5316no—
735C4⋊C4—538no—
736C4⋊C4—538no—
737C4⋊C4—538no—
738C4⋊C4—538no—
739C4⋊C4—5316no—
740C4⋊C4—5316no—
741C4⋊C4—534no—
742C4⋊C4—538no—
743C4⋊C4—5316no—
744C4⋊C4—5316no—
745C4⋊C4—5316no—
746C4⋊C4—538no—
747C4⋊C4C23×D5314yes—
748C4⋊C4C23×D5318yes—
749C4⋊C4C23×D5318yes—
750C4⋊C4C23×D53116yes—
751C4⋊C4C23×D53116yes—
752C4⋊C4C23×D5318yes—
753C4⋊C4C23×D5314yes—
754C22⋊C4—538no—
755C22⋊C4—5316no—
756C22⋊C4—5316no—
757C22⋊C4—538no—
758C22⋊C4—5316no—
759C22⋊C4—5316no—
760C22⋊C4—5316no—
761C22⋊C4—538no—
762C22⋊C4—5316no—
763C22⋊C4C23×D5318yes—
764C22⋊C4C23×D53116yes—
765C42—538no—
766C42—538no—
767C42—534no—
768C42—538no—
769C42—534no—
770C42—534no—
771C42—5316no—
772C42—5316no—
773C42—5316no—
774C42C23×D5314yes—
775C42C23×D5318yes—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—534no—
780C23—532no—
781C23—534no—
782C23—1062no—
783C23—1062no—
784C23—1064no—
785C23—1064no—
786C23—1064no—
787C23C24×D5314yes—
788C23C24×D5311yescharacteristic
789Q8—28no—
790Q8—48no—
791Q8—10616no—
792Q8—10616no—
793Q8—1068no—
794Q8—10616no—
795D4—28no—
796D4—10616no—
797D4—10616no—
798D4—10616no—
799D4—1068no—
800D4—2128no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—28no—
805C2×C4—22no—
806C2×C4—216no—
807C2×C4—416no—
808C2×C4—534no—
809C2×C4—532no—
810C2×C4—5316no—
811C2×C4—532no—
812C2×C4—534no—
813C2×C4—538no—
814C2×C4—534no—
815C2×C4—534no—
816C2×C4—532no—
817C2×C4—10616no—
818C2×C4—1064no—
819C2×C4—1064no—
820C2×C4—1062no—
821C2×C4—1068no—
822C2×C4—1064no—
823C2×C4—1062no—
824C2×C4—10616no—
825C2×C4—1068no—
826C2×C4—2128no—
827C2×C4—21216no—
828C2×C4—2124no—
829C2×C4#41×D5314yes—
830C2×C4#1313326514yes—
831C2×C4C24×D5314yes—
832C2×C4C24×D5314yes—
833C2×C4C24×D5312yes—
834C2×C4C24×D5314yes—
835C2×C4C24×D5318yes—
836C2×C4C24×D5312yes—
837C2×C4C24×D5312yes—
838C22—24no—
839C22—24no—
840C22—24no—
841C22—48no—
842C22—534no—
843C22—1068no—
844C22—1062no—
845C22—1062no—
846C22—1064no—
847C22—1064no—
848C22—1064no—
849C22—2128no—
850C22C2×#41×D5312yes—
851C22C2×#1313326512yes—
852C22#1681145812yes—
853C22C25×D5311yescharacteristic
854C4—24no—
855C4—24no—
856C4—24no—
857C4—28no—
858C4—22no—
859C4—534no—
860C4—1064no—
861C4—1064no—
862C4—1062no—
863C4—1068no—
864C4—1064no—
865C4—1062no—
866C4C2×#41×D5314yes—
867C4C2×#1313326514yes—
868C2—44no—
869C2—1064no—
870C2—2124no—
871C2#2028857814yesdirect product factor
872C2C22×#41×D5311yescharacteristic
873C2C22×#1313326511yescharacteristic
874C2C2×#1681145811yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#554C2
socleC23×C53C25
prime radicalC2×#16811170C2
hypercenterC2×#554D53
hypocenterC53C2×#3507
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #20288578C2direct (N × H)
2. C2×#16811356C2semidirect
3. C2×#16811350C2semidirect
4. C2×#16811346C2semidirect
5. C2×#16811344C2semidirect
6. C2×#16811343C2semidirect
7. C2×#16811334C2semidirect
8. C2×#16811308C2semidirect
9. C2×#16811307C2semidirect
10. C2×#16811219C2semidirect
11. C2×#16811196C2semidirect
12. C2×#16811178C2semidirect
14. C2×#16811158C2semidirect
15. C2×#16811155C2semidirect
16. C2×#16811104C2semidirect
17. C2×C4×Q8×D53C2semidirect
18. C2×C53×#554C2semidirect
21. #16811356C22semidirect
22. #16811350C22semidirect
23. #16811346C22semidirect
24. #16811344C22semidirect
25. #16811343C22semidirect
26. #16811334C22semidirect
27. #16811308C22semidirect
28. #16811307C22semidirect
29. #16811219C22semidirect
30. #16811196C22semidirect
31. #16811178C22semidirect
37. #16811158C22semidirect
38. #16811155C22semidirect
64. #16811104C22semidirect
75. C4×Q8×D53C22semidirect
92. C53×#554C22semidirect
438. C2×#554D53semidirect
450. C2×C53#3507semidirect
464. #554C2×D53semidirect
538. C53C2×#3507semidirect
871. C2#20288578direct (N × H)

Maximal subgroups

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

subgroupindex
#202885782
C2×#168113562
C2×#168113502
C2×#168113462
C2×#168113442
C2×#168113432
C2×#168113342
C2×#168113082
C2×#168113072
C2×#168112192
C2×#168111962
C2×#168111782
C2×#168111702
C2×#168111582
C2×#168111552
C2×#168111042
C2×C4×Q8×D532
C2×C53×#5542
C2×#350753