Finite Group Databasebeta

← C2×#20289128 #28291903

Subgroups — C2×#20289128 #28291903

Order 13568.

7074 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#20289128C2132yesmaximal, direct product factor
2C2×#16811375C214yesmaximal, complemented
3C2×#16811355C212yesmaximal, complemented
4C2×Q8×Dic106C212yesmaximal, complemented
5C2×#16811347C211yesmaximal, characteristic, complemented
6C2×#16811341C212yesmaximal, complemented
7C2×Q8×D212C211yesmaximal, characteristic, complemented
8C2×D4×Dic106C211yesmaximal, characteristic, complemented
9C2×#16811286C212yesmaximal, complemented
10C2×#16811245C212yesmaximal, complemented
11C2×#16811242C212yesmaximal, complemented
12C2×#16811239C214yesmaximal, complemented
13C2×#16811199C212yesmaximal, complemented
14C2×#16811196C212yesmaximal, complemented
15C2×#16811178C211yesmaximal, characteristic, complemented
16C2×#16811177C211yesmaximal, characteristic, complemented
17C2×#16811170C211yesmaximal, characteristic
18C2×C53×#556C211yesmaximal, characteristic, complemented
19C22×#11719945C2212yes—
20C23×Dic106C2212yes—
21C22×Q8×D53C2212yes—
22#16811375C22164yescomplemented
23#16811355C22132yescomplemented
24Q8×Dic106C22132yescomplemented
25#16811347C22116yescomplemented
26#16811341C22132yescomplemented
27Q8×D212C22116yescomplemented
28D4×Dic106C22116yescomplemented
29#16811286C22132yescomplemented
30#16811245C22132yescomplemented
31#16811242C22132yescomplemented
32#16811239C22164yescomplemented
33#16811199C22132yescomplemented
34#16811196C22132yescomplemented
35#16811178C22116yescomplemented
36#16811177C22116yescomplemented
37#16811170C22116yes—
38C2×#13133217C2211yescharacteristic
39C2×#13133217C2214yes—
40C2×#13133217C2212yes—
41C2×#13133216C2211yescharacteristic
42C2×#13133216C2214yes—
43C2×#13133216C2211yescharacteristic
44C2×#13133216C2214yes—
45C2×#13133216C2212yes—
46C2×#13133215C2211yescharacteristic
47C2×#13133213C2211yescharacteristic
48C2×#13133212C2214yes—
49C2×#13133211C2214yes—
50C2×#13133210C2214yes—
51C2×#13133208C2212yes—
52C2×#13133207C2212yes—
53C2×#13133206C2212yes—
54C2×#13133205C2214yes—
55C2×#13133203C2214yes—
56C2×#13133203C2214yes—
57C2×#13133203C2212yes—
58C2×#13133202C2214yes—
59C2×#13133201C2214yes—
60C2×#13133201C2214yes—
61C2×#13133199C2214yes—
62C2×#13133197C2211yescharacteristic
63C2×#13133197C2212yes—
64C2×#13133197C2212yes—
65C2×#13133197C2212yes—
66C2×#13133197C2214yes—
67C2×#13133196C2212yes—
68C2×#13133195C2212yes—
69C2×#13133195C2214yes—
70C2×#13133194C2214yes—
71C2×#13133194C2214yes—
72C2×#13133193C2211yescharacteristic
73C2×#13133193C2212yes—
74C2×#13133192C2211yescharacteristic
75C2×#13133190C2212yes—
76C2×#13133188C2211yescharacteristic
77C2×Q8×Dic53C2212yes—
78C2×Q8×Dic53C2212yes—
79C2×C4×Dic106C2211yescharacteristic
80C2×C4×Dic106C2212yes—
81C2×C4×Dic106C2214yes—
82C2×#13133182C2212yes—
83C2×C4×D212C2211yescharacteristic
84C2×C4×D212C2212yes—
85C2×D4×Dic53C2212yes—
86C2×C4×C22⋊D53C2212yes—
87C2×#13133177C2214yes—
88C2×#13133175C2212yes—
89C2×#13133175C2212yes—
90C2×#13133174C2212yes—
91C2×C42×D53C2211yescharacteristic
92C53×#556C22116yescomplemented
93C2×C4⋊Q8×C53C2211yescharacteristic
94C2×#126×C53C2214yes—
95C2×#124×C53C2212yes—
96C2×C22⋊Q8×C53C2212yes—
97C2×C4×Q8×C53C2211yescharacteristic
98C2×C4×Q8×C53C2212yes—
99C2×C4×D4×C53C2211yescharacteristic
100C2×#117×C53C2212yes—
101C2×#11719945—48no—
102C2×#11719945C23116yes—
103C22×Dic106—48no—
104C22×Dic106C2312yes—
105C22×Dic106C2312yes—
106C22×Dic106C2311yescharacteristic
107C22×Dic106C23116yes—
108C22×Dic106C2314yes—
109C22×Dic106C2314yes—
110C22×Dic106C2312yes—
111C2×Q8×D53—48no—
112C2×Q8×D53C23116yes—
113C22×D212C2311yescharacteristic
114C22×D212C2312yes—
115C22×C22⋊D53C2312yes—
116C22×C22⋊D53C2312yes—
117C22×C22⋊D53C2312yes—
118C23×Dic53C2314yes—
119C22×C4×D53C2311yescharacteristic
120C22×C4×D53C2311yescharacteristic
121C22×C4×D53C2311yescharacteristic
122C22×C4×D53C2312yes—
123C22×C4×D53C2314yes—
124#13133217C2318yes—
125#13133217C23116yes—
126#13133217C23132yes—
127#13133216C23132yes—
128#13133216C23116yes—
129#13133216C2318yes—
130#13133216C2318yes—
131#13133216C23132yes—
132#13133215C2318yes—
133#13133213C2318yes—
134#13133212C23132yes—
135#13133211C23132yes—
136#13133210C23132yes—
137#13133208C23116yes—
138#13133207C23116yes—
139#13133206C23116yes—
140#13133205C23132yes—
141#13133203C23132yes—
142#13133203C23116yes—
143#13133203C23132yes—
144#13133202C23132yes—
145#13133201C23132yes—
146#13133201C23132yes—
147#13133199C23132yes—
148#13133197C23116yes—
149#13133197C23116yes—
150#13133197C23132yes—
151#13133197C2318yes—
152#13133197C23116yes—
153#13133196C23116yes—
154#13133195C23132yes—
155#13133195C23116yes—
156#13133194C23132yes—
157#13133194C23132yes—
158#13133193C2318yes—
159#13133193C23116yes—
160#13133192C2318yes—
161#13133190C23116yes—
162#13133188C2318yes—
163Q8×Dic53C23116yes—
164Q8×Dic53C23116yes—
165C4×Dic106C2318yes—
166C4×Dic106C23132yes—
167C4×Dic106C23116yes—
168#13133182C23116yes—
169C4×D212C2318yes—
170C4×D212C23116yes—
171D4×Dic53C23116yes—
172C4×C22⋊D53C23116yes—
173#13133177C23132yes—
174#13133175C23116yes—
175#13133175C23116yes—
176#13133174C23116yes—
177C2×C4⋊Dic53C2311yescharacteristic
178C2×C4⋊Dic53C2312yes—
179C2×C4⋊Dic53C2312yes—
180C2×C4⋊Dic53C2311yescharacteristic
181C2×C4⋊Dic53C2314yes—
182C2×C4⋊Dic53C2312yes—
183C2×C4⋊Dic53C2314yes—
184C2×C4⋊Dic53C2314yes—
185C2×#11719919C2312yes—
186C2×#11719919C2312yes—
187C2×#11719919C2312yes—
188C2×#11719919C2312yes—
189C2×#11719919C2314yes—
190C2×#11719919C2312yes—
191C2×#11719919C2312yes—
192C2×#11719919C2314yes—
193C2×C22⋊Dic53C2312yes—
194C2×C22⋊Dic53C2314yes—
195C2×#11719921C2312yes—
196C2×#11719921C2312yes—
197C2×#11719921C2314yes—
198C2×#11719921C2314yes—
199C2×#11719921C2314yes—
200C2×#11719921C2312yes—
201C2×#11719921C2312yes—
202C2×#11719921C2314yes—
203C2×C4×Dic53C2311yescharacteristic
204C2×C4×Dic53C2311yescharacteristic
205C2×C4×Dic53C2311yescharacteristic
206C2×C4×Dic53C2312yes—
207C2×C4×Dic53C2314yes—
208C2×C4×Dic53C2314yes—
209C42×D53C2318yes—
210C22×Q8×C53C2311yescharacteristic
211C22×Q8×C53C2312yes—
212C22×D4×C53C2311yescharacteristic
213C23×C4×C53C2312yes—
214C4⋊Q8×C53C2318yes—
215#126×C53C23132yes—
216#124×C53C23116yes—
217C22⋊Q8×C53C23116yes—
218C4×Q8×C53C2318yes—
219C4×Q8×C53C23116yes—
220C4×D4×C53C2318yes—
221#117×C53C23116yes—
222C2×C4⋊C4×C53C2311yescharacteristic
223C2×C4⋊C4×C53C2312yes—
224C2×C4⋊C4×C53C2311yescharacteristic
225C2×C4⋊C4×C53C2314yes—
226C2×C4⋊C4×C53C2312yes—
227C2×C4⋊C4×C53C2312yes—
228C2×C22⋊C4×C53C2314yes—
229C2×C22⋊C4×C53C2312yes—
230C2×C22⋊C4×C53C2314yes—
231C2×C42×C53C2314yes—
232C2×C42×C53C2311yescharacteristic
233C2×C42×C53C2312yes—
234C24×C53C2412yes—
235C23×D53C2412yes—
236C23×D53C2411yescharacteristic
237C2×Q8×C53—24no—
238C2×Q8×C53—28no—
239C2×Q8×C53C2414yes—
240C2×Q8×C53C2418yes—
241C2×D4×C53—24no—
242C2×D4×C53C2414yes—
243C22×C4×C53—28no—
244C22×C4×C53C2412yes—
245C22×C4×C53C2412yes—
246C22×C4×C53C2411yescharacteristic
247C22×C4×C53C2414yes—
248C22×C4×C53C2412yes—
249C22×C4×C53C2418yes—
250C22×C4×C53C2411yescharacteristic
251C22×C4×C53C2411yescharacteristic
252C2×C22⋊D53—28no—
253C2×C22⋊D53—44no—
254C2×C22⋊D53—44no—
255C2×C22⋊D53C2418yes—
256C2×C22⋊D53C2418yes—
257C2×C22⋊D53C2418yes—
258C22×Dic53—48no—
259C22×Dic53C2412yes—
260C22×Dic53C2411yescharacteristic
261C22×Dic53C2412yes—
262C22×Dic53C2411yescharacteristic
263C22×Dic53C2412yes—
264C22×Dic53C2414yes—
265C22×Dic53C24116yes—
266C22×Dic53C2411yescharacteristic
267Q8×D53—432no—
268#11719945—432no—
269C2×D212—24no—
270C2×D212—44no—
271C2×D212C2414yes—
272C2×D212C2418yes—
273C2×C4×D53—28no—
274C2×C4×D53—24no—
275C2×C4×D53—24no—
276C2×C4×D53—24no—
277C2×C4×D53—48no—
278C2×C4×D53C2414yes—
279C2×C4×D53C2414yes—
280C2×C4×D53C2414yes—
281C2×C4×D53C2418yes—
282C2×C4×D53C24116yes—
283C2×Dic106—28no—
284C2×Dic106—24no—
285C2×Dic106—28no—
286C2×Dic106—432no—
287C2×Dic106—48no—
288C2×Dic106—48no—
289C2×Dic106—44no—
290C2×Dic106C2418yes—
291C2×Dic106C2418yes—
292C2×Dic106C2414yes—
293C2×Dic106C24116yes—
294C2×Dic106C24116yes—
295C2×Dic106C2418yes—
296C4⋊C4×C53C2414yes—
297C4⋊C4×C53C2418yes—
298C4⋊C4×C53C2414yes—
299C4⋊C4×C53C24116yes—
300C4⋊C4×C53C2418yes—
301C4⋊C4×C53C2418yes—
302C22⋊C4×C53C24116yes—
303C22⋊C4×C53C2418yes—
304C22⋊C4×C53C24116yes—
305C42×C53C24116yes—
306C42×C53C2414yes—
307C42×C53C2418yes—
308C22⋊Dic53C2418yes—
309C22⋊Dic53C24116yes—
310#11719921C2418yes—
311#11719921C2418yes—
312#11719921C24116yes—
313#11719921C24116yes—
314#11719921C24116yes—
315#11719921C2418yes—
316#11719921C2418yes—
317#11719921C24116yes—
318C4⋊Dic53C2414yes—
319C4⋊Dic53C2418yes—
320C4⋊Dic53C2418yes—
321C4⋊Dic53C2414yes—
322C4⋊Dic53C24116yes—
323C4⋊Dic53C2418yes—
324C4⋊Dic53C24116yes—
325C4⋊Dic53C24116yes—
326#11719919C2418yes—
327#11719919C2418yes—
328#11719919C2418yes—
329#11719919C2418yes—
330#11719919C24116yes—
331#11719919C2418yes—
332#11719919C2418yes—
333#11719919C24116yes—
334C4×Dic53C2414yes—
335C4×Dic53C2414yes—
336C4×Dic53C2414yes—
337C4×Dic53C2418yes—
338C4×Dic53C24116yes—
339C4×Dic53C24116yes—
340C23×C53—24no—
341C23×C53—24no—
342C23×C53—24no—
343C23×C53C2514yes—
344C23×C53C2511yescharacteristic
345C22×D53—24no—
346C22×D53—22no—
347C22×D53—22no—
348C22×D53—22no—
349C22×D53—24no—
350C22×D53—24no—
351C22×D53C2514yes—
352C22×D53C2512yes—
353Q8×C53—28no—
354Q8×C53—216no—
355D4×C53—28no—
356C2×C4×C53—24no—
357C2×C4×C53—24no—
358C2×C4×C53—24no—
359C2×C4×C53—22no—
360C2×C4×C53—28no—
361C2×C4×C53—216no—
362C2×C4×C53H(5,𝔽2)14yes—
363C2×C4×C532−1+414yes—
364C2×C4×C53C2514yes—
365C2×C4×C53C2514yes—
366C2×C4×C53C2514yes—
367C2×C4×C53C2512yes—
368C2×C4×C53C2518yes—
369C2×C4×C53C2512yes—
370C2×C4×C53C2512yes—
371C22⋊D53—216no—
372C22⋊D53—48no—
373C22⋊D53—48no—
374C2×Dic53—28no—
375C2×Dic53—24no—
376C2×Dic53—24no—
377C2×Dic53—22no—
378C2×Dic53—24no—
379C2×Dic53—22no—
380C2×Dic53—416no—
381C2×Dic532−1+414yes—
382C2×Dic53C2518yes—
383C2×Dic53C2514yes—
384C2×Dic53C2514yes—
385C2×Dic53C2512yes—
386C2×Dic53C2514yes—
387C2×Dic53C2512yes—
388C2×Dic53C2512yes—
389D212—28no—
390D212—48no—
391C4×D53—28no—
392C4×D53—216no—
393C4×D53—28no—
394C4×D53—28no—
395C4×D53—416no—
396Dic106—28no—
397Dic106—216no—
398Dic106—216no—
399Dic106—416no—
400Dic106—48no—
401Dic106—416no—
402C2×#3550—531nomaximal, Sylow
403C22×C53—24no—
404C22×C53—24no—
405C22×C53—24no—
406C22×C53—48no—
407C22×C53C2×H(5,𝔽2)12yes—
408C22×C53C2×2−1+412yes—
409C22×C53C2×2−1+412yes—
410C22×C53C2611yescharacteristic
411C2×D53—24no—
412C2×D53—22no—
413C2×D53—22no—
414C2×D53—22no—
415C2×D53—24no—
416C2×D53—24no—
417C2×D53—48no—
418C2×D53—44no—
419C4×C53—24no—
420C4×C53—24no—
421C4×C53—24no—
422C4×C53—22no—
423C4×C53—28no—
424C4×C53C2×H(5,𝔽2)14yes—
425C4×C53C2×2−1+414yes—
426Dic53—28no—
427Dic53—24no—
428Dic53—24no—
429Dic53—22no—
430Dic53—24no—
431Dic53—22no—
432Dic53C2×2−1+414yes—
433#3550—5332no—
434C2×#563—534no—
435C2×#559—532no—
436C2×Q82—532no—
437C2×#556—531no—
438C2×#556—532no—
439C2×#556D5311yescharacteristic, complemented
440C2×D4×Q8—532no—
441C2×D4×Q8—531no—
442C2×D4×Q8—531no—
443C2×#542—534no—
444C2×#542—532no—
445C2×#542—532no—
446C2×#536—532no—
447C2×#536—532no—
448C2×#533—531no—
449C2×#533—531no—
450C2×#532—531no—
451C2×C53—44no—
452C2×C53#355014yescomplemented
453C2×C53C22×H(5,𝔽2)11yescharacteristic
454C2×C53C22×2−1+411yescharacteristic
455C2×C53C22×2−1+411yescharacteristic
456D53—44no—
457D53—42no—
458C22×#41—532no—
459C23×Q8—532no—
460C23×Q8—532no—
461#563—5364no—
462#559—5332no—
463Q82—5332no—
464#556—5316no—
465#556—5332no—
466#556C2×D53116yescomplemented
467D4×Q8—5332no—
468D4×Q8—5316no—
469D4×Q8—5316no—
470#542—5364no—
471#542—5332no—
472#542—5332no—
473#536—5332no—
474#536—5332no—
475#533—5316no—
476#533—5316no—
477#532—5316no—
478C2×C4⋊Q8—531no—
479C2×C4⋊Q8—531no—
480C2×C4⋊Q8—531no—
481C2×C4⋊Q8—534no—
482C2×C4⋊Q8—534no—
483C2×C4⋊Q8—532no—
484C2×C4⋊Q8—531no—
485C2×C4⋊Q8—534no—
486C2×C4⋊Q8—532no—
487C2×C4⋊Q8C2×D5311yescharacteristic
488C2×#127—531no—
489C2×#126—534no—
490C2×#126—534no—
491C2×#126—534no—
492C2×#126C2×D5314yes—
493C2×#125—532no—
494C2×#125—532no—
495C2×#124—532no—
496C2×#124—532no—
497C2×#124—534no—
498C2×#124—534no—
499C2×#124—534no—
500C2×#124C2×D5312yes—
501C2×#123—534no—
502C2×#123—534no—
503C2×#123—534no—
504C2×#123—534no—
505C2×C22⋊Q8—531no—
506C2×C22⋊Q8—532no—
507C2×C22⋊Q8—532no—
508C2×C22⋊Q8—532no—
509C2×C22⋊Q8—534no—
510C2×C22⋊Q8—532no—
511C2×C22⋊Q8—531no—
512C2×C22⋊Q8—532no—
513C2×C22⋊Q8—532no—
514C2×C22⋊Q8—534no—
515C2×C22⋊Q8—534no—
516C2×C22⋊Q8—534no—
517C2×C22⋊Q8C2×D5312yes—
518C2×#121—531no—
519C2×#121—531no—
520C2×#121—532no—
521C2×C4×Q8—532no—
522C2×C4×Q8—532no—
523C2×C4×Q8—532no—
524C2×C4×Q8—531no—
525C2×C4×Q8—532no—
526C2×C4×Q8—534no—
527C2×C4×Q8C2×D5311yescharacteristic
528C2×C4×Q8C2×D5312yes—
529C2×C4×D4—532no—
530C2×C4×D4—532no—
531C2×C4×D4—534no—
532C2×C4×D4—531no—
533C2×C4×D4—532no—
534C2×C4×D4C2×D5311yescharacteristic
535C2×#117—532no—
536C2×#117—532no—
537C2×#117—532no—
538C2×#117C2×D5312yes—
539C22×C42—531no—
540C53C2×#355011yescharacteristic, complemented, Sylow
541C2×#41—5316no—
542C2×#41—2128no—
543C22×Q8—5316no—
544C22×Q8—532no—
545C22×Q8—532no—
546C22×Q8—531no—
547C22×Q8—534no—
548C22×Q8—534no—
549C22×Q8—532no—
550C22×Q8—5316no—
551C22×Q8—2128no—
552C22×Q8—2128no—
553C22×Q8C22×D5312yes—
554C22×Q8C22×D5311yescharacteristic
555C22×D4—532no—
556C22×D4—532no—
557C22×D4—532no—
558C22×D4—531no—
559C22×D4—532no—
560C22×D4C22×D5311yescharacteristic
561C23×C4—534no—
562C23×C4—531no—
563C23×C4—531no—
564C23×C4—532no—
565C23×C4—531no—
566C23×C4—534no—
567C23×C4C22×D5312yes—
568C4⋊Q8—538no—
569C4⋊Q8—538no—
570C4⋊Q8—538no—
571C4⋊Q8—5332no—
572C4⋊Q8—5332no—
573C4⋊Q8—5316no—
574C4⋊Q8—538no—
575C4⋊Q8—5332no—
576C4⋊Q8—5316no—
577C4⋊Q8C22×D5318yes—
578#127—538no—
579#126—5332no—
580#126—5332no—
581#126—5332no—
582#126C22×D53132yes—
583#125—5316no—
584#125—5316no—
585#124—5316no—
586#124—5316no—
587#124—5332no—
588#124—5332no—
589#124—5332no—
590#124C22×D53116yes—
591#123—5332no—
592#123—5332no—
593#123—5332no—
594#123—5332no—
595C22⋊Q8—538no—
596C22⋊Q8—5316no—
597C22⋊Q8—5316no—
598C22⋊Q8—5316no—
599C22⋊Q8—538no—
600C22⋊Q8—5316no—
601C22⋊Q8—5316no—
602C22⋊Q8—5316no—
603C22⋊Q8—5332no—
604C22⋊Q8—5332no—
605C22⋊Q8—5332no—
606C22⋊Q8—5332no—
607C22⋊Q8C22×D53116yes—
608#121—538no—
609#121—538no—
610#121—5316no—
611C4×Q8—5316no—
612C4×Q8—5316no—
613C4×Q8—5316no—
614C4×Q8—538no—
615C4×Q8—5316no—
616C4×Q8—5332no—
617C4×Q8C22×D5318yes—
618C4×Q8C22×D53116yes—
619C4×D4—5316no—
620C4×D4—5316no—
621C4×D4—5332no—
622C4×D4—538no—
623C4×D4—5316no—
624C4×D4C22×D5318yes—
625#117—5316no—
626#117—5316no—
627#117—5316no—
628#117C22×D53116yes—
629C2×C4⋊C4—531no—
630C2×C4⋊C4—532no—
631C2×C4⋊C4—532no—
632C2×C4⋊C4—532no—
633C2×C4⋊C4—532no—
634C2×C4⋊C4—532no—
635C2×C4⋊C4—532no—
636C2×C4⋊C4—531no—
637C2×C4⋊C4—532no—
638C2×C4⋊C4—534no—
639C2×C4⋊C4—534no—
640C2×C4⋊C4—534no—
641C2×C4⋊C4—534no—
642C2×C4⋊C4—532no—
643C2×C4⋊C4—534no—
644C2×C4⋊C4—532no—
645C2×C4⋊C4C22×D5312yes—
646C2×C4⋊C4C22×D5312yes—
647C2×C4⋊C4C22×D5311yescharacteristic
648C2×C4⋊C4C22×D5311yescharacteristic
649C2×C4⋊C4C22×D5312yes—
650C2×C4⋊C4C22×D5314yes—
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—532no—
658C2×C22⋊C4—532no—
659C2×C22⋊C4—534no—
660C2×C22⋊C4—534no—
661C2×C22⋊C4C22×D5314yes—
662C2×C22⋊C4C22×D5314yes—
663C2×C22⋊C4C22×D5312yes—
664C2×C42—534no—
665C2×C42—532no—
666C2×C42—534no—
667C2×C42—531no—
668C2×C42—531no—
669C2×C42—531no—
670C2×C42—538no—
671C2×C42C22×D5312yes—
672C2×C42C22×D5314yes—
673C2×C42C22×D5311yescharacteristic
674C24—532no—
675C24—531no—
676C24C23×D5312yes—
677#41—21232no—
678C2×Q8—24no—
679C2×Q8—28no—
680C2×Q8—538no—
681C2×Q8—538no—
682C2×Q8—534no—
683C2×Q8—5316no—
684C2×Q8—5316no—
685C2×Q8—538no—
686C2×Q8—1068no—
687C2×Q8—1068no—
688C2×Q8—1064no—
689C2×Q8—2128no—
690C2×Q8—2128no—
691C2×Q8—2124no—
692C2×Q8—21232no—
693C2×Q8—21232no—
694C2×Q8C23×D5318yes—
695C2×Q8C23×D5314yes—
696C2×D4—24no—
697C2×D4—538no—
698C2×D4—538no—
699C2×D4—538no—
700C2×D4—534no—
701C2×D4—538no—
702C2×D4—1068no—
703C2×D4—1064no—
704C2×D4—2124no—
705C2×D4—2124no—
706C2×D4—2124no—
707C2×D4C23×D5314yes—
708C22×C4—28no—
709C22×C4—531no—
710C22×C4—532no—
711C22×C4—531no—
712C22×C4—532no—
713C22×C4—531no—
714C22×C4—532no—
715C22×C4—534no—
716C22×C4—5316no—
717C22×C4—534no—
718C22×C4—534no—
719C22×C4—534no—
720C22×C4—538no—
721C22×C4—5316no—
722C22×C4—1064no—
723C22×C4—1068no—
724C22×C4—1064no—
725C22×C4—1064no—
726C22×C4—2128no—
727C22×C4—2128no—
728C22×C4C23×D5318yes—
729C22×C4C23×D5314yes—
730C22×C4C23×D5311yescharacteristic
731C22×C4C23×D5312yes—
732C22×C4C23×D5312yes—
733C22×C4C23×D5312yes—
734C22×C4C23×D5311yescharacteristic
735C22×C4C23×D5311yescharacteristic
736C4⋊C4—534no—
737C4⋊C4—538no—
738C4⋊C4—538no—
739C4⋊C4—538no—
740C4⋊C4—538no—
741C4⋊C4—538no—
742C4⋊C4—538no—
743C4⋊C4—534no—
744C4⋊C4—538no—
745C4⋊C4—5316no—
746C4⋊C4—5316no—
747C4⋊C4—5316no—
748C4⋊C4—5316no—
749C4⋊C4—538no—
750C4⋊C4—5316no—
751C4⋊C4—538no—
752C4⋊C4C23×D5318yes—
753C4⋊C4C23×D5318yes—
754C4⋊C4C23×D5314yes—
755C4⋊C4C23×D5314yes—
756C4⋊C4C23×D5318yes—
757C4⋊C4C23×D53116yes—
758C22⋊C4—538no—
759C22⋊C4—5316no—
760C22⋊C4—538no—
761C22⋊C4—5316no—
762C22⋊C4—538no—
763C22⋊C4—5316no—
764C22⋊C4—538no—
765C22⋊C4—538no—
766C22⋊C4—5316no—
767C22⋊C4—5316no—
768C22⋊C4C23×D53116yes—
769C22⋊C4C23×D53116yes—
770C22⋊C4C23×D5318yes—
771C42—534no—
772C42—534no—
773C42—534no—
774C42—5316no—
775C42—538no—
776C42—5316no—
777C42C23×D5314yes—
778C42C23×D5318yes—
779C42C23×D53116yes—
780C23—24no—
781C23—24no—
782C23—24no—
783C23—534no—
784C23—532no—
785C23—1064no—
786C23—1062no—
787C23—1062no—
788C23—1064no—
789C23—1062no—
790C23—1064no—
791C23C24×D5314yes—
792C23C24×D5311yescharacteristic
793Q8—28no—
794Q8—216no—
795Q8—10616no—
796Q8—1068no—
797Q8—10616no—
798Q8—21216no—
799Q8—21216no—
800Q8—2128no—
801D4—28no—
802D4—10616no—
803D4—1068no—
804D4—2128no—
805D4—2128no—
806D4—2128no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—22no—
810C2×C4—24no—
811C2×C4—28no—
812C2×C4—216no—
813C2×C4—534no—
814C2×C4—532no—
815C2×C4—534no—
816C2×C4—532no—
817C2×C4—534no—
818C2×C4—532no—
819C2×C4—538no—
820C2×C4—534no—
821C2×C4—1068no—
822C2×C4—1062no—
823C2×C4—1064no—
824C2×C4—1068no—
825C2×C4—1064no—
826C2×C4—1064no—
827C2×C4—1062no—
828C2×C4—10616no—
829C2×C4—1068no—
830C2×C4—1068no—
831C2×C4—21216no—
832C2×C4—21216no—
833C2×C4#1313326314yes—
834C2×C4#1313326414yes—
835C2×C4C24×D5318yes—
836C2×C4C24×D5312yes—
837C2×C4C24×D5314yes—
838C2×C4C24×D5314yes—
839C2×C4C24×D5314yes—
840C2×C4C24×D5312yes—
841C2×C4C24×D5312yes—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—48no—
846C22—1064no—
847C22—1062no—
848C22—1062no—
849C22—1064no—
850C22—1062no—
851C22—1064no—
852C22—2128no—
853C22—2124no—
854C22C2×#1313326312yes—
855C222−1+4×D5312yes—
856C22C2×#1313326412yes—
857C22C25×D5311yescharacteristic
858C4—24no—
859C4—24no—
860C4—22no—
861C4—24no—
862C4—28no—
863C4—534no—
864C4—1062no—
865C4—1064no—
866C4—1068no—
867C4—1064no—
868C4—1064no—
869C4—1062no—
870C4C2×#1313326314yes—
871C4C2×#1313326414yes—
872C2—44no—
873C2—2124no—
874C2—2122no—
875C2#2028912814yesdirect product factor
876C2C22×#1313326311yescharacteristic
877C2C2×2−1+4×D5311yescharacteristic
878C2C22×#1313326411yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#556C2
socleC23×C53C25
prime radicalC2×#16811170C2
hypercenterC2×#556D53
hypocenterC53C2×#3550
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #20289128C2direct (N × H)
2. C2×#16811375C2semidirect
3. C2×#16811355C2semidirect
4. C2×Q8×Dic106C2semidirect
5. C2×#16811347C2semidirect
6. C2×#16811341C2semidirect
7. C2×Q8×D212C2semidirect
8. C2×D4×Dic106C2semidirect
9. C2×#16811286C2semidirect
10. C2×#16811245C2semidirect
11. C2×#16811242C2semidirect
12. C2×#16811239C2semidirect
13. C2×#16811199C2semidirect
14. C2×#16811196C2semidirect
15. C2×#16811178C2semidirect
16. C2×#16811177C2semidirect
18. C2×C53×#556C2semidirect
22. #16811375C22semidirect
23. #16811355C22semidirect
24. Q8×Dic106C22semidirect
25. #16811347C22semidirect
26. #16811341C22semidirect
27. Q8×D212C22semidirect
28. D4×Dic106C22semidirect
29. #16811286C22semidirect
30. #16811245C22semidirect
31. #16811242C22semidirect
32. #16811239C22semidirect
33. #16811199C22semidirect
34. #16811196C22semidirect
35. #16811178C22semidirect
36. #16811177C22semidirect
92. C53×#556C22semidirect
439. C2×#556D53semidirect
452. C2×C53#3550semidirect
466. #556C2×D53semidirect
540. C53C2×#3550semidirect
875. C2#20289128direct (N × H)

Maximal subgroups

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

subgroupindex
#202891282
C2×#168113752
C2×#168113552
C2×Q8×Dic1062
C2×#168113472
C2×#168113412
C2×Q8×D2122
C2×D4×Dic1062
C2×#168112862
C2×#168112452
C2×#168112422
C2×#168112392
C2×#168111992
C2×#168111962
C2×#168111782
C2×#168111772
C2×#168111702
C2×C53×#5562
C2×#355053