Finite Group Databasebeta

← C2×#20288573 #28292165

Subgroups — C2×#20288573 #28292165

Order 13568.

7130 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288573C2132yesmaximal, direct product factor
2C2×#16811356C212yesmaximal, complemented
3C2×#16811351C212yesmaximal, complemented
4C2×#16811345C212yesmaximal, complemented
5C2×#16811343C212yesmaximal, complemented
6C2×#16811341C212yesmaximal, complemented
7C2×#16811328C212yesmaximal, complemented
8C2×#16811312C212yesmaximal, complemented
9C2×#16811308C212yesmaximal, complemented
10C2×#16811215C214yesmaximal, complemented
11C2×#16811199C211yesmaximal, characteristic, complemented
12C2×#16811194C211yesmaximal, characteristic, complemented
13C2×#16811176C211yesmaximal, characteristic, complemented
14C2×#16811169C211yesmaximal, characteristic
15C2×#16811153C214yesmaximal, complemented
16C2×#16811104C211yesmaximal, characteristic, complemented
17C22×#13133182C211yesmaximal, characteristic, complemented
18C2×C53×#520C211yesmaximal, characteristic, complemented
19C22×#11719945C2211yescharacteristic
20C23×Dic106C2211yescharacteristic
21#16811356C22132yescomplemented
22#16811351C22132yescomplemented
23#16811345C22132yescomplemented
24#16811343C22132yescomplemented
25#16811341C22132yescomplemented
26#16811328C22132yescomplemented
27#16811312C22132yescomplemented
28#16811308C22132yescomplemented
29#16811215C22164yescomplemented
30#16811199C22116yescomplemented
31#16811194C22116yescomplemented
32#16811176C22116yescomplemented
33#16811169C22116yes—
34C2×#13133217C2212yes—
35C2×#13133216C2211yescharacteristic
36C2×#13133216C2211yescharacteristic
37C2×#13133215C2212yes—
38C2×#13133215C2211yescharacteristic
39C2×#13133213C2211yescharacteristic
40#16811153C22164yescomplemented
41C2×#13133212C2214yes—
42C2×#13133211C2214yes—
43C2×#13133210C2214yes—
44C2×#13133210C2214yes—
45C2×#13133209C2214yes—
46C2×#13133208C2211yescharacteristic
47C2×#13133208C2211yescharacteristic
48C2×#13133207C2214yes—
49C2×#13133207C2214yes—
50C2×#13133206C2211yescharacteristic
51C2×#13133205C2212yes—
52C2×#13133204C2211yescharacteristic
53C2×#13133204C2212yes—
54C2×#13133203C2214yes—
55C2×#13133201C2214yes—
56C2×#13133200C2214yes—
57C2×#13133199C2214yes—
58C2×#13133198C2214yes—
59C2×#13133197C2212yes—
60C2×#13133197C2212yes—
61C2×#13133196C2212yes—
62C2×#13133196C2214yes—
63C2×#13133196C2212yes—
64C2×#13133195C2214yes—
65C2×#13133194C2212yes—
66C2×#13133194C2212yes—
67C2×#13133189C2212yes—
68C2×#13133189C2212yes—
69#16811104C22116yescomplemented
70C2×C4×Dic106C2212yes—
71C2×C4×Dic106C2212yes—
72C2×C4×Dic106C2214yes—
73C2×#13133182C2212yes—
74C2×#13133182C2212yes—
75C2×#13133182C2212yes—
76C2×#13133182C2212yes—
77C2×#13133182C2212yes—
78C2×#13133182C22116yescomplemented
79C2×#13133179C2212yes—
80C2×C4×C22⋊D53C2212yes—
81C2×C4×C22⋊D53C2214yes—
82C2×C4×C22⋊D53C2214yes—
83C2×C4×C22⋊D53C2212yes—
84C2×#13133176C2211yescharacteristic
85C2×#13133176C2214yes—
86C2×#13133175C2212yes—
87C2×#13133174C2214yes—
88C22×#11719919C2212yes—
89C2×C4⋊C4×D53C2212yes—
90C22×C4×Dic53C2211yescharacteristic
91C22×C4×Dic53C2212yes—
92C22×#41×C53C2211yescharacteristic
93C53×#520C22116yescomplemented
94C2×C4×Q8×C53C2212yes—
95C2×C4×D4×C53C2212yes—
96C2×C4×D4×C53C2214yes—
97C2×#117×C53C2211yescharacteristic
98C2×#117×C53C2212yes—
99C22×C4⋊C4×C53C2211yescharacteristic
100C22×C4⋊C4×C53C2212yes—
101C2×#11719945—28no—
102C2×#11719945C2318yes—
103C22×Dic106—28no—
104C22×Dic106C2312yes—
105C22×Dic106C2312yes—
106C22×Dic106C2311yescharacteristic
107C22×Dic106C2318yes—
108C22×Dic106C2312yes—
109C22×Dic106C2312yes—
110C22×D212C2311yescharacteristic
111C22×C22⋊D53C2312yes—
112C22×C22⋊D53C2312yes—
113C22×C22⋊D53C2312yes—
114C23×Dic53C2311yescharacteristic
115C23×Dic53C2312yes—
116C23×Dic53C2311yescharacteristic
117C22×C4×D53C2312yes—
118C22×C4×D53C2314yes—
119#13133217C23116yes—
120#13133216C2318yes—
121#13133216C2318yes—
122#13133215C23116yes—
123#13133215C2318yes—
124#13133213C2318yes—
125#13133212C23132yes—
126#13133211C23132yes—
127#13133210C23132yes—
128#13133210C23132yes—
129#13133209C23132yes—
130#13133208C2318yes—
131#13133208C2318yes—
132#13133207C23132yes—
133#13133207C23132yes—
134#13133206C2318yes—
135#13133205C23116yes—
136#13133204C2318yes—
137#13133204C23116yes—
138#13133203C23132yes—
139#13133201C23132yes—
140#13133200C23132yes—
141#13133199C23132yes—
142#13133198C23132yes—
143#13133197C23116yes—
144#13133197C23116yes—
145#13133196C23116yes—
146#13133196C23116yes—
147#13133196C23132yes—
148#13133195C23132yes—
149#13133194C23116yes—
150#13133194C23116yes—
151#13133189C23116yes—
152#13133189C23116yes—
153C4×Dic106C23132yes—
154C4×Dic106C23116yes—
155C4×Dic106C23116yes—
156#13133182C23116yes—
157#13133182C23116yes—
158#13133182C23116yes—
159#13133182C23116yes—
160#13133182C23116yes—
161#13133179C23116yes—
162C4×C22⋊D53C23116yes—
163C4×C22⋊D53C23116yes—
164C4×C22⋊D53C23132yes—
165C4×C22⋊D53C23132yes—
166#13133176C23132yes—
167#13133176C2318yes—
168#13133175C23116yes—
169#13133174C23132yes—
170C2×C4⋊Dic53C2311yescharacteristic
171C2×C4⋊Dic53C2311yescharacteristic
172C2×C4⋊Dic53C2312yes—
173C2×C4⋊Dic53C2314yes—
174C2×C4⋊Dic53C2312yes—
175C2×C4⋊Dic53C2314yes—
176C2×#11719919C2314yes—
177C2×#11719919C2314yes—
178C2×#11719919C2314yes—
179C2×#11719919C23116yes—
180C2×#11719919C2312yes—
181C2×#11719919C2314yes—
182C2×#11719919C2312yes—
183C2×#11719919C2312yes—
184C2×#11719919C2312yes—
185C2×#11719919C2312yes—
186C2×#11719919C2312yes—
187C2×#11719919C2314yes—
188C4⋊C4×D53C23116yes—
189C2×C22⋊Dic53C2312yes—
190C2×C22⋊Dic53C2312yes—
191C2×C22⋊Dic53C2314yes—
192C2×C22⋊Dic53C2312yes—
193C2×C22⋊Dic53C2314yes—
194C2×#11719921C2312yes—
195C2×#11719921C2314yes—
196C2×#11719921C2314yes—
197C2×#11719921C2312yes—
198C2×#11719921C2314yes—
199C2×C4×Dic53C2314yes—
200C2×C4×Dic53C2311yescharacteristic
201C2×C4×Dic53C2311yescharacteristic
202C2×C4×Dic53C2314yes—
203C2×C4×Dic53C2311yescharacteristic
204C2×C4×Dic53C2311yescharacteristic
205C2×C4×Dic53C23116yes—
206C2×C4×Dic53C2318yes—
207C2×C4×Dic53C2314yes—
208C2×C4×Dic53C2312yes—
209C2×#41×C53—28no—
210C2×#41×C53C2318yes—
211C22×Q8×C53C2311yescharacteristic
212C22×D4×C53C2312yes—
213C22×D4×C53C2311yescharacteristic
214C23×C4×C53C2312yes—
215C23×C4×C53C2312yes—
216C23×C4×C53C2314yes—
217C23×C4×C53C2311yescharacteristic
218C4×Q8×C53C23116yes—
219C4×D4×C53C23116yes—
220C4×D4×C53C23132yes—
221#117×C53C23116yes—
222#117×C53C2318yes—
223C2×C4⋊C4×C53C2312yes—
224C2×C4⋊C4×C53C2311yescharacteristic
225C2×C4⋊C4×C53C2312yes—
226C2×C4⋊C4×C53C2314yes—
227C2×C4⋊C4×C53C23116yes—
228C2×C4⋊C4×C53C2318yes—
229C2×C4⋊C4×C53C2311yescharacteristic
230C2×C22⋊C4×C53C2312yes—
231C2×C22⋊C4×C53C2314yes—
232C2×C42×C53C2314yes—
233C2×C42×C53C2312yes—
234C24×C53C2412yes—
235C24×C53C2411yescharacteristic
236C23×D53C2412yes—
237#41×C53—232no—
238C2×Q8×C53—24no—
239C2×Q8×C53C2414yes—
240C2×D4×C53—28no—
241C2×D4×C53—24no—
242C2×D4×C53C2418yes—
243C2×D4×C53C2414yes—
244C22×C4×C53—28no—
245C22×C4×C53—48no—
246C22×C4×C53—44no—
247C22×C4×C53#4118yes—
248C22×C4×C53C2412yes—
249C22×C4×C53C2412yes—
250C22×C4×C53C2414yes—
251C22×C4×C53C2412yes—
252C22×C4×C53C2418yes—
253C22×C4×C53C2418yes—
254C22×C4×C53C24116yes—
255C22×C4×C53C2411yescharacteristic
256C22×C4×C53C2411yescharacteristic
257C22×C4×C53C2414yes—
258C2×C22⋊D53—28no—
259C2×C22⋊D53—28no—
260C2×C22⋊D53—44no—
261C2×C22⋊D53C2418yes—
262C2×C22⋊D53C2418yes—
263C2×C22⋊D53C2418yes—
264C22×Dic53—28no—
265C22×Dic53—24no—
266C22×Dic53—42no—
267C22×Dic53C2411yescharacteristic
268C22×Dic53C2414yes—
269C22×Dic53C2412yes—
270C22×Dic53C2411yescharacteristic
271C22×Dic53C2414yes—
272C22×Dic53C2412yes—
273C22×Dic53C2411yescharacteristic
274C22×Dic53C2418yes—
275C22×Dic53C2412yes—
276C22×Dic53C2414yes—
277C22×Dic53C2411yescharacteristic
278#11719945—232no—
279C2×D212—24no—
280C2×D212C2414yes—
281C2×C4×D53—28no—
282C2×C4×D53—48no—
283C2×C4×D53C2418yes—
284C2×C4×D53C24116yes—
285C2×Dic106—28no—
286C2×Dic106—28no—
287C2×Dic106—232no—
288C2×Dic106—24no—
289C2×Dic106—28no—
290C2×Dic106—44no—
291C2×Dic106C2418yes—
292C2×Dic106C2418yes—
293C2×Dic106C2414yes—
294C2×Dic106C2418yes—
295C2×Dic106C2418yes—
296C4⋊C4×C53C2418yes—
297C4⋊C4×C53C2414yes—
298C4⋊C4×C53C2418yes—
299C4⋊C4×C53C24116yes—
300C4⋊C4×C53C2414yes—
301C22⋊C4×C53C2418yes—
302C22⋊C4×C53C24116yes—
303C42×C53C24116yes—
304C42×C53C2418yes—
305C22⋊Dic53C2418yes—
306C22⋊Dic53C2418yes—
307C22⋊Dic53C24116yes—
308C22⋊Dic53C2418yes—
309C22⋊Dic53C24116yes—
310#11719921C2418yes—
311#11719921C24116yes—
312#11719921C24116yes—
313#11719921C2418yes—
314#11719921C24116yes—
315C4⋊Dic53C2414yes—
316C4⋊Dic53C2414yes—
317C4⋊Dic53C2418yes—
318C4⋊Dic53C24116yes—
319C4⋊Dic53C2418yes—
320C4⋊Dic53C24116yes—
321#11719919C24116yes—
322#11719919C24116yes—
323#11719919C24116yes—
324#11719919C2418yes—
325#11719919C24116yes—
326#11719919C2418yes—
327#11719919C2418yes—
328#11719919C2418yes—
329#11719919C2418yes—
330#11719919C2418yes—
331#11719919C24116yes—
332C4×Dic53C24116yes—
333C4×Dic53C2414yes—
334C4×Dic53C2414yes—
335C4×Dic53C24116yes—
336C4×Dic53C2414yes—
337C4×Dic53C2414yes—
338C4×Dic53C24116yes—
339C4×Dic53C2418yes—
340C23×C53—22no—
341C23×C53—22no—
342C23×C53—24no—
343C23×C53—24no—
344C23×C53—24no—
345C23×C53C2×#4114yes—
346C23×C53C2514yes—
347C23×C53C2512yes—
348C23×C53C2511yescharacteristic
349C22×D53—24no—
350C22×D53—24no—
351C22×D53—24no—
352C22×D53C2514yes—
353Q8×C53—28no—
354D4×C53—216no—
355D4×C53—28no—
356C2×C4×C53—24no—
357C2×C4×C53—24no—
358C2×C4×C53—24no—
359C2×C4×C53—28no—
360C2×C4×C53—216no—
361C2×C4×C53—416no—
362C2×C4×C53—48no—
363C2×C4×C53C2×#4114yes—
364C2×C4×C53C2×#4114yes—
365C2×C4×C53C2×#41116yes—
366C2×C4×C53C2514yes—
367C2×C4×C53C2514yes—
368C2×C4×C53C2518yes—
369C2×C4×C53C2514yes—
370C2×C4×C53C2512yes—
371C2×C4×C53C2512yes—
372C22⋊D53—216no—
373C22⋊D53—216no—
374C22⋊D53—48no—
375C2×Dic53—216no—
376C2×Dic53—28no—
377C2×Dic53—24no—
378C2×Dic53—24no—
379C2×Dic53—22no—
380C2×Dic53—22no—
381C2×Dic53—24no—
382C2×Dic53—22no—
383C2×Dic53—28no—
384C2×Dic53—44no—
385C2×Dic532−1+414yes—
386C2×Dic53C2512yes—
387C2×Dic53C2518yes—
388C2×Dic53C2514yes—
389C2×Dic53C2514yes—
390C2×Dic53C2514yes—
391C2×Dic53C2512yes—
392C2×Dic53C2512yes—
393C2×Dic53C2512yes—
394D212—28no—
395C4×D53—216no—
396C4×D53—416no—
397Dic106—216no—
398Dic106—216no—
399Dic106—28no—
400Dic106—216no—
401Dic106—48no—
402C2×#3507—531nomaximal, Sylow
403C22×C53—22no—
404C22×C53—22no—
405C22×C53—28no—
406C22×C53—24no—
407C22×C53—24no—
408C22×C53—24no—
409C22×C53—48no—
410C22×C53C22×#4114yes—
411C22×C53C22×#4112yes—
412C22×C53C2×2−1+412yes—
413C22×C53#58512yes—
414C22×C53C2611yescharacteristic
415C2×D53—24no—
416C2×D53—24no—
417C2×D53—24no—
418C2×D53—48no—
419C4×C53—24no—
420C4×C53—24no—
421C4×C53—24no—
422C4×C53—28no—
423C4×C53C22×#4114yes—
424C4×C53C22×#4114yes—
425Dic53—28no—
426Dic53—24no—
427Dic53—24no—
428Dic53—22no—
429Dic53—22no—
430Dic53—24no—
431Dic53—22no—
432Dic53C2×2−1+414yes—
433#3507—5332no—
434C2×#559—532no—
435C2×#557—532no—
436C2×#556—532no—
437C2×#556—532no—
438C2×#556—532no—
439C2×#554—532no—
440C2×#552—532no—
441C2×#552—532no—
442C2×#539—534no—
443C2×#536—531no—
444C2×#536—531no—
445C2×#533—531no—
446C2×#532—531no—
447C2×#529—534no—
448C2×#520—531no—
449C2×#520D5311yescharacteristic, complemented
450C22×C4×Q8—531no—
451C2×C53—24no—
452C2×C53—44no—
453C2×C53#350714yescomplemented
454C2×C53C23×#4111yescharacteristic
455C2×C53C22×2−1+411yescharacteristic
456C2×C53C2×#58511yescharacteristic
457D53—44no—
458C22×#41—531no—
459C22×#41C2×D5311yescharacteristic
460C23×Q8—531no—
461#559—5332no—
462#557—5332no—
463#556—5332no—
464#556—5332no—
465#556—5332no—
466#554—5332no—
467#552—5332no—
468#552—5332no—
469#539—5364no—
470#536—5316no—
471#536—5316no—
472#533—5316no—
473#532—5316no—
474C2×C4⋊Q8—531no—
475C2×C4⋊Q8—532no—
476C2×C4⋊Q8—531no—
477C2×C4⋊Q8—531no—
478C2×C4⋊Q8—532no—
479C2×#127—531no—
480#529—5364no—
481C2×#126—534no—
482C2×#126—534no—
483C2×#126—534no—
484C2×#126—534no—
485C2×#125—534no—
486C2×#125—531no—
487C2×#125—531no—
488C2×#125—534no—
489C2×#125—534no—
490C2×#124—531no—
491C2×#124—531no—
492C2×#124—532no—
493C2×#124—534no—
494C2×#124—532no—
495C2×#123—534no—
496C2×#123—534no—
497C2×#123—534no—
498C2×#123—534no—
499C2×C22⋊Q8—532no—
500C2×C22⋊Q8—532no—
501C2×C22⋊Q8—534no—
502C2×C22⋊Q8—534no—
503C2×C22⋊Q8—532no—
504C2×C22⋊Q8—532no—
505C2×C22⋊Q8—532no—
506C2×C22⋊Q8—532no—
507C2×#121—532no—
508C2×#121—532no—
509#520—5316no—
510#520C2×D53116yescomplemented
511C2×C4×Q8—532no—
512C2×C4×Q8—532no—
513C2×C4×Q8—532no—
514C2×C4×Q8—532no—
515C2×C4×Q8—532no—
516C2×C4×Q8—5316no—
517C2×C4×Q8—534no—
518C2×C4×Q8—532no—
519C2×C4×Q8—532no—
520C2×C4×Q8C2×D5312yes—
521C2×C4×D4—534no—
522C2×C4×D4—534no—
523C2×C4×D4—532no—
524C2×C4×D4—532no—
525C2×C4×D4—532no—
526C2×C4×D4C2×D5314yes—
527C2×C4×D4C2×D5312yes—
528C2×#117—531no—
529C2×#117—534no—
530C2×#117—532no—
531C2×#117—534no—
532C2×#117C2×D5311yescharacteristic
533C2×#117C2×D5312yes—
534C22×C4⋊C4—532no—
535C22×C4⋊C4—532no—
536C22×C4⋊C4C2×D5311yescharacteristic
537C22×C4⋊C4C2×D5312yes—
538C22×C42—532no—
539C22×C42—531no—
540C53C2×#350711yescharacteristic, complemented, Sylow
541C2×#41—28no—
542C2×#41—538no—
543C2×#41—1068no—
544C2×#41C22×D5318yes—
545C22×Q8—532no—
546C22×Q8—532no—
547C22×Q8—532no—
548C22×Q8—531no—
549C22×Q8—538no—
550C22×Q8—532no—
551C22×Q8—1068no—
552C22×Q8C22×D5311yescharacteristic
553C22×D4—532no—
554C22×D4—532no—
555C22×D4—532no—
556C22×D4—531no—
557C22×D4C22×D5312yes—
558C22×D4C22×D5311yescharacteristic
559C23×C4—532no—
560C23×C4—531no—
561C23×C4—531no—
562C23×C4—532no—
563C23×C4—534no—
564C23×C4C22×D5312yes—
565C23×C4C22×D5312yes—
566C23×C4C22×D5314yes—
567C23×C4C22×D5311yescharacteristic
568C4⋊Q8—538no—
569C4⋊Q8—5316no—
570C4⋊Q8—538no—
571C4⋊Q8—538no—
572C4⋊Q8—5316no—
573#127—538no—
574#126—5332no—
575#126—5332no—
576#126—5332no—
577#126—5332no—
578#125—5332no—
579#125—538no—
580#125—538no—
581#125—5332no—
582#125—5332no—
583#124—538no—
584#124—538no—
585#124—5316no—
586#124—5332no—
587#124—5316no—
588#123—5332no—
589#123—5332no—
590#123—5332no—
591#123—5332no—
592C22⋊Q8—5316no—
593C22⋊Q8—5316no—
594C22⋊Q8—5332no—
595C22⋊Q8—5316no—
596C22⋊Q8—5316no—
597C22⋊Q8—5332no—
598C22⋊Q8—5316no—
599C22⋊Q8—5316no—
600#121—5316no—
601#121—5316no—
602C4×Q8—5316no—
603C4×Q8—5316no—
604C4×Q8—5316no—
605C4×Q8—5316no—
606C4×Q8—5316no—
607C4×Q8—5332no—
608C4×Q8—5316no—
609C4×Q8—5316no—
610C4×Q8C22×D53116yes—
611C4×D4—5332no—
612C4×D4—5332no—
613C4×D4—5316no—
614C4×D4—5316no—
615C4×D4—5316no—
616C4×D4C22×D53132yes—
617C4×D4C22×D53116yes—
618#117—538no—
619#117—5332no—
620#117—5316no—
621#117—5332no—
622#117C22×D5318yes—
623#117C22×D53116yes—
624C2×C4⋊C4—531no—
625C2×C4⋊C4—534no—
626C2×C4⋊C4—534no—
627C2×C4⋊C4—534no—
628C2×C4⋊C4—5316no—
629C2×C4⋊C4—531no—
630C2×C4⋊C4—532no—
631C2×C4⋊C4—532no—
632C2×C4⋊C4—534no—
633C2×C4⋊C4—534no—
634C2×C4⋊C4—532no—
635C2×C4⋊C4—532no—
636C2×C4⋊C4—532no—
637C2×C4⋊C4—532no—
638C2×C4⋊C4—532no—
639C2×C4⋊C4—534no—
640C2×C4⋊C4—534no—
641C2×C4⋊C4—532no—
642C2×C4⋊C4—5316no—
643C2×C4⋊C4C22×D5312yes—
644C2×C4⋊C4C22×D5311yescharacteristic
645C2×C4⋊C4C22×D5312yes—
646C2×C4⋊C4C22×D5314yes—
647C2×C4⋊C4C22×D5318yes—
648C2×C4⋊C4C22×D53116yes—
649C2×C4⋊C4C22×D5311yescharacteristic
650C2×C22⋊C4—532no—
651C2×C22⋊C4—532no—
652C2×C22⋊C4—534no—
653C2×C22⋊C4—532no—
654C2×C22⋊C4—534no—
655C2×C22⋊C4—532no—
656C2×C22⋊C4—534no—
657C2×C22⋊C4—534no—
658C2×C22⋊C4—532no—
659C2×C22⋊C4—534no—
660C2×C22⋊C4C22×D5312yes—
661C2×C22⋊C4C22×D5314yes—
662C2×C42—534no—
663C2×C42—534no—
664C2×C42—532no—
665C2×C42—531no—
666C2×C42—531no—
667C2×C42—534no—
668C2×C42—531no—
669C2×C42—531no—
670C2×C42—5316no—
671C2×C42—538no—
672C2×C42C22×D5314yes—
673C2×C42C22×D5312yes—
674C24—532no—
675C24C23×D5312yes—
676C24C23×D5311yescharacteristic
677#41—232no—
678#41—10632no—
679C2×Q8—24no—
680C2×Q8—538no—
681C2×Q8—538no—
682C2×Q8—538no—
683C2×Q8—534no—
684C2×Q8—538no—
685C2×Q8—1068no—
686C2×Q8—1068no—
687C2×Q8—1068no—
688C2×Q8—10632no—
689C2×Q8—1064no—
690C2×Q8—2124no—
691C2×Q8C23×D5314yes—
692C2×D4—28no—
693C2×D4—24no—
694C2×D4—538no—
695C2×D4—538no—
696C2×D4—538no—
697C2×D4—534no—
698C2×D4—1068no—
699C2×D4—1068no—
700C2×D4—1064no—
701C2×D4—2124no—
702C2×D4C23×D5318yes—
703C2×D4C23×D5314yes—
704C22×C4—28no—
705C22×C4—44no—
706C22×C4—48no—
707C22×C4—531no—
708C22×C4—534no—
709C22×C4—538no—
710C22×C4—531no—
711C22×C4—532no—
712C22×C4—534no—
713C22×C4—531no—
714C22×C4—532no—
715C22×C4—531no—
716C22×C4—532no—
717C22×C4—534no—
718C22×C4—538no—
719C22×C4—5316no—
720C22×C4—1064no—
721C22×C4—1068no—
722C22×C4—1068no—
723C22×C4—2128no—
724C22×C4—2122no—
725C22×C4#1171994518yes—
726C22×C4C23×D5318yes—
727C22×C4C23×D5314yes—
728C22×C4C23×D5312yes—
729C22×C4C23×D5312yes—
730C22×C4C23×D5312yes—
731C22×C4C23×D5318yes—
732C22×C4C23×D53116yes—
733C22×C4C23×D5314yes—
734C22×C4C23×D5311yescharacteristic
735C22×C4C23×D5311yescharacteristic
736C4⋊C4—534no—
737C4⋊C4—5316no—
738C4⋊C4—5316no—
739C4⋊C4—5316no—
740C4⋊C4—534no—
741C4⋊C4—538no—
742C4⋊C4—538no—
743C4⋊C4—5316no—
744C4⋊C4—5316no—
745C4⋊C4—538no—
746C4⋊C4—538no—
747C4⋊C4—538no—
748C4⋊C4—538no—
749C4⋊C4—538no—
750C4⋊C4—5316no—
751C4⋊C4—5316no—
752C4⋊C4—538no—
753C4⋊C4C23×D5318yes—
754C4⋊C4C23×D5314yes—
755C4⋊C4C23×D5318yes—
756C4⋊C4C23×D53116yes—
757C4⋊C4C23×D5314yes—
758C22⋊C4—538no—
759C22⋊C4—538no—
760C22⋊C4—5316no—
761C22⋊C4—538no—
762C22⋊C4—5316no—
763C22⋊C4—538no—
764C22⋊C4—5316no—
765C22⋊C4—5316no—
766C22⋊C4—538no—
767C22⋊C4—5316no—
768C22⋊C4C23×D5318yes—
769C22⋊C4C23×D53116yes—
770C42—5316no—
771C42—534no—
772C42—534no—
773C42—5316no—
774C42—534no—
775C42—534no—
776C42—5316no—
777C42—538no—
778C42C23×D53116yes—
779C42C23×D5318yes—
780C23—22no—
781C23—22no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—534no—
786C23—1064no—
787C23—1064no—
788C23—1064no—
789C23C2×#1171994514yes—
790C23C24×D5314yes—
791C23C24×D5312yes—
792C23C24×D5311yescharacteristic
793Q8—28no—
794Q8—10616no—
795Q8—10616no—
796Q8—10616no—
797Q8—1068no—
798Q8—2128no—
799D4—216no—
800D4—28no—
801D4—10616no—
802D4—10616no—
803D4—1068no—
804D4—2128no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—28no—
808C2×C4—24no—
809C2×C4—216no—
810C2×C4—48no—
811C2×C4—416no—
812C2×C4—534no—
813C2×C4—532no—
814C2×C4—532no—
815C2×C4—534no—
816C2×C4—538no—
817C2×C4—532no—
818C2×C4—534no—
819C2×C4—532no—
820C2×C4—534no—
821C2×C4—1068no—
822C2×C4—1064no—
823C2×C4—10616no—
824C2×C4—1068no—
825C2×C4—1062no—
826C2×C4—1064no—
827C2×C4—1064no—
828C2×C4—1062no—
829C2×C4—1062no—
830C2×C4—10616no—
831C2×C4—21216no—
832C2×C4—2124no—
833C2×C4C2×#1171994514yes—
834C2×C4C2×#1171994514yes—
835C2×C4C2×#11719945116yes—
836C2×C4C24×D5318yes—
837C2×C4C24×D5314yes—
838C2×C4C24×D5314yes—
839C2×C4C24×D5314yes—
840C2×C4C24×D5312yes—
841C2×C4C24×D5312yes—
842C22—28no—
843C22—22no—
844C22—22no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—48no—
849C22—1064no—
850C22—1064no—
851C22—1064no—
852C22—2128no—
853C22C22×#1171994514yes—
854C22C22×#1171994512yes—
855C222−1+4×D5312yes—
856C22#1681145812yes—
857C22C25×D5311yescharacteristic
858C4—24no—
859C4—24no—
860C4—28no—
861C4—24no—
862C4—534no—
863C4—1064no—
864C4—1068no—
865C4—1062no—
866C4—1064no—
867C4—1064no—
868C4—1062no—
869C4—1062no—
870C4C22×#1171994514yes—
871C4C22×#1171994514yes—
872C2—24no—
873C2—44no—
874C2—2124no—
875C2#2028857314yesdirect product factor
876C2C23×#1171994511yescharacteristic
877C2C2×2−1+4×D5311yescharacteristic
878C2C2×#1681145811yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#520C2
socleC23×C53C25
prime radicalC2×#16811169C2
hypercenterC2×#520D53
hypocenterC53C2×#3507
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #20288573C2direct (N × H)
2. C2×#16811356C2semidirect
3. C2×#16811351C2semidirect
4. C2×#16811345C2semidirect
5. C2×#16811343C2semidirect
6. C2×#16811341C2semidirect
7. C2×#16811328C2semidirect
8. C2×#16811312C2semidirect
9. C2×#16811308C2semidirect
10. C2×#16811215C2semidirect
11. C2×#16811199C2semidirect
12. C2×#16811194C2semidirect
13. C2×#16811176C2semidirect
15. C2×#16811153C2semidirect
16. C2×#16811104C2semidirect
17. C22×#13133182C2semidirect
18. C2×C53×#520C2semidirect
21. #16811356C22semidirect
22. #16811351C22semidirect
23. #16811345C22semidirect
24. #16811343C22semidirect
25. #16811341C22semidirect
26. #16811328C22semidirect
27. #16811312C22semidirect
28. #16811308C22semidirect
29. #16811215C22semidirect
30. #16811199C22semidirect
31. #16811194C22semidirect
32. #16811176C22semidirect
40. #16811153C22semidirect
69. #16811104C22semidirect
78. C2×#13133182C22semidirect
93. C53×#520C22semidirect
449. C2×#520D53semidirect
453. C2×C53#3507semidirect
510. #520C2×D53semidirect
540. C53C2×#3507semidirect
875. C2#20288573direct (N × H)

Maximal subgroups

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

subgroupindex
#202885732
C2×#168113562
C2×#168113512
C2×#168113452
C2×#168113432
C2×#168113412
C2×#168113282
C2×#168113122
C2×#168113082
C2×#168112152
C2×#168111992
C2×#168111942
C2×#168111762
C2×#168111692
C2×#168111532
C2×#168111042
C22×#131331822
C2×C53×#5202
C2×#350753