Finite Group Databasebeta

← C2×#20289157 #28291698

Subgroups — C2×#20289157 #28291698

Order 13568.

7086 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289157C2132yesmaximal, direct product factor
2C2×#16811374C214yesmaximal, complemented
3C2×#16811351C211yesmaximal, characteristic, complemented
4C2×#16811347C211yesmaximal, characteristic, complemented
5C2×#16811334C212yesmaximal, complemented
6C2×#16811323C212yesmaximal, complemented
7C2×Q8×C22⋊D53C212yesmaximal, complemented
8C2×#16811283C212yesmaximal, complemented
9C2×#16811278C211yesmaximal, characteristic, complemented
10C2×#16811250C212yesmaximal, complemented
11C2×#16811238C212yesmaximal, complemented
12C2×#16811233C212yesmaximal, complemented
13C2×#16811219C214yesmaximal, complemented
14C2×#16811197C212yesmaximal, complemented
15C2×C4⋊Q8×D53C211yesmaximal, characteristic, complemented
16C2×#16811160C211yesmaximal, characteristic, complemented
17C2×#16811155C211yesmaximal, characteristic, complemented
18C2×D4×Q8×C53C211yesmaximal, characteristic, complemented
19C22×#11719945C2212yes—
20C22×Q8×D53C2212yes—
21#16811374C22164yescomplemented
22#16811351C22116yescomplemented
23#16811347C22116yescomplemented
24#16811334C22132yescomplemented
25#16811323C22132yescomplemented
26Q8×C22⋊D53C22132yescomplemented
27#16811283C22132yescomplemented
28#16811278C22116yescomplemented
29#16811250C22132yescomplemented
30#16811238C22132yescomplemented
31#16811233C22132yescomplemented
32#16811219C22164yescomplemented
33#16811197C22132yescomplemented
34C2×#13133217C2211yescharacteristic
35C2×#13133216C2212yes—
36C2×#13133216C2212yes—
37C2×#13133215C2212yes—
38C2×#13133215C2212yes—
39C2×#13133215C2214yes—
40C4⋊Q8×D53C22116yescomplemented
41#16811160C22116yescomplemented
42#16811155C22116yescomplemented
43C2×#13133212C2214yes—
44C2×#13133212C2212yes—
45C2×#13133210C2214yes—
46C2×#13133210C2212yes—
47C2×#13133210C2214yes—
48C2×#13133209C2212yes—
49C2×#13133208C2214yes—
50C2×#13133208C2211yescharacteristic
51C2×#13133208C2211yescharacteristic
52C2×#13133207C2214yes—
53C2×#13133207C2214yes—
54C2×#13133206C2212yes—
55C2×#13133206C2211yescharacteristic
56C2×#13133204C2211yescharacteristic
57C2×#13133203C2214yes—
58C2×#13133202C2212yes—
59C2×#13133200C2214yes—
60C2×#13133200C2214yes—
61C2×#13133199C2212yes—
62C2×#13133199C2214yes—
63C2×#13133197C2212yes—
64C2×#13133197C2211yescharacteristic
65C2×#13133196C2214yes—
66C2×#13133196C2212yes—
67C2×#13133195C2214yes—
68C2×#13133193C2214yes—
69C2×#13133193C2214yes—
70C2×#13133193C2214yes—
71C2×#13133193C2211yescharacteristic
72C2×#13133192C2211yescharacteristic
73C2×#13133190C2214yes—
74C2×#13133188C2212yes—
75C2×#13133188C2211yescharacteristic
76C2×Q8×Dic53C2212yes—
77C2×C4×Dic106C2211yescharacteristic
78C2×C4×Dic106C2212yes—
79C2×#13133182C2212yes—
80C2×C4×D212C2211yescharacteristic
81C2×C4×D212C2212yes—
82C2×#13133179C2214yes—
83C2×C4×C22⋊D53C2214yes—
84C2×C4×C22⋊D53C2212yes—
85C2×#13133176C2212yes—
86C2×#13133175C2212yes—
87C2×#13133174C2212yes—
88C2×C4⋊C4×D53C2212yes—
89C2×C4⋊C4×D53C2212yes—
90C2×C4⋊C4×D53C2212yes—
91C2×C42×D53C2211yescharacteristic
92C23×Q8×C53C2212yes—
93D4×Q8×C53C22116yescomplemented
94C2×C4⋊Q8×C53C2211yescharacteristic
95C2×C4⋊Q8×C53C2212yes—
96C2×C22⋊Q8×C53C2214yes—
97C2×C22⋊Q8×C53C2212yes—
98C2×C4×Q8×C53C2211yescharacteristic
99C2×C4×D4×C53C2212yes—
100C2×C4×D4×C53C2211yescharacteristic
101C2×#11719945—48no—
102C2×#11719945C23116yes—
103C22×Dic106C2312yes—
104C22×Dic106C2311yescharacteristic
105C22×Dic106C2314yes—
106C2×Q8×D53—48no—
107C2×Q8×D53C23116yes—
108C22×D212C2312yes—
109C22×D212C2311yescharacteristic
110C22×C22⋊D53C2312yes—
111C22×C22⋊D53C2314yes—
112C22×C4×D53C2311yescharacteristic
113C22×C4×D53C2311yescharacteristic
114C22×C4×D53C2311yescharacteristic
115C22×C4×D53C2312yes—
116C22×C4×D53C2314yes—
117C22×C4×D53C2314yes—
118#13133217C2318yes—
119#13133216C23116yes—
120#13133216C23116yes—
121#13133215C23116yes—
122#13133215C23132yes—
123#13133215C23116yes—
124#13133212C23132yes—
125#13133212C23116yes—
126#13133210C23132yes—
127#13133210C23116yes—
128#13133210C23132yes—
129#13133209C23116yes—
130#13133208C23132yes—
131#13133208C2318yes—
132#13133208C2318yes—
133#13133207C23132yes—
134#13133207C23132yes—
135#13133206C23116yes—
136#13133206C2318yes—
137#13133204C2318yes—
138#13133203C23132yes—
139#13133202C23116yes—
140#13133200C23132yes—
141#13133200C23132yes—
142#13133199C23132yes—
143#13133199C23116yes—
144#13133197C2318yes—
145#13133197C23116yes—
146#13133196C23116yes—
147#13133196C23132yes—
148#13133195C23132yes—
149#13133193C2318yes—
150#13133193C23132yes—
151#13133193C23132yes—
152#13133193C23132yes—
153#13133192C2318yes—
154#13133190C23132yes—
155#13133188C23116yes—
156#13133188C2318yes—
157Q8×Dic53C23116yes—
158C4×Dic106C23116yes—
159C4×Dic106C2318yes—
160#13133182C23116yes—
161C4×D212C2318yes—
162C4×D212C23116yes—
163#13133179C23132yes—
164C4×C22⋊D53C23116yes—
165C4×C22⋊D53C23132yes—
166#13133176C23116yes—
167#13133175C23116yes—
168#13133174C23116yes—
169C2×C4⋊Dic53C2312yes—
170C2×C4⋊Dic53C2312yes—
171C2×C4⋊Dic53C2311yescharacteristic
172C2×C4⋊Dic53C2312yes—
173C2×C4⋊Dic53C2312yes—
174C2×C4⋊Dic53C2311yescharacteristic
175C2×C4⋊Dic53C2312yes—
176C2×C4⋊Dic53C2314yes—
177C2×#11719919C2314yes—
178C2×#11719919C2314yes—
179C2×#11719919C2314yes—
180C2×#11719919C2312yes—
181C2×#11719919C2312yes—
182C2×#11719919C2314yes—
183C2×#11719919C2312yes—
184C2×#11719919C2314yes—
185C2×#11719919C2314yes—
186C2×#11719919C2312yes—
187C4⋊C4×D53C23116yes—
188C4⋊C4×D53C23116yes—
189C4⋊C4×D53C23116yes—
190C2×C22⋊Dic53C2312yes—
191C2×C22⋊Dic53C2312yes—
192C2×C22⋊Dic53C2314yes—
193C2×C22⋊Dic53C2312yes—
194C2×#11719921C2312yes—
195C2×#11719921C2312yes—
196C2×#11719921C2314yes—
197C2×#11719921C2312yes—
198C2×#11719921C2312yes—
199C2×#11719921C2314yes—
200C2×#11719921C2312yes—
201C2×#11719921C2312yes—
202C2×C4×Dic53C2311yescharacteristic
203C2×C4×Dic53C2311yescharacteristic
204C2×C4×Dic53C2311yescharacteristic
205C2×C4×Dic53C2314yes—
206C2×C4×Dic53C2312yes—
207C2×C4×Dic53C2314yes—
208C42×D53C2318yes—
209C22×Q8×C53—48no—
210C22×Q8×C53C2311yescharacteristic
211C22×Q8×C53C2312yes—
212C22×Q8×C53C23116yes—
213C22×Q8×C53C2314yes—
214C22×D4×C53C2311yescharacteristic
215C23×C4×C53C2312yes—
216C23×C4×C53C2314yes—
217C4⋊Q8×C53C23116yes—
218C4⋊Q8×C53C2318yes—
219C22⋊Q8×C53C23116yes—
220C22⋊Q8×C53C23132yes—
221C4×Q8×C53C2318yes—
222C4×D4×C53C2318yes—
223C4×D4×C53C23116yes—
224C2×C4⋊C4×C53C2311yescharacteristic
225C2×C4⋊C4×C53C2312yes—
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×C53C2311yescharacteristic
233C2×C42×C53C2312yes—
234C24×C53C2412yes—
235C23×D53C2412yes—
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×C53—24no—
245C2×D4×C53C2414yes—
246C22×C4×C53—28no—
247C22×C4×C53—48no—
248C22×C4×C53C2412yes—
249C22×C4×C53C2411yescharacteristic
250C22×C4×C53C2412yes—
251C22×C4×C53C2414yes—
252C22×C4×C53C2412yes—
253C22×C4×C53C2418yes—
254C22×C4×C53C24116yes—
255C22×C4×C53C2411yescharacteristic
256C22×C4×C53C2411yescharacteristic
257C2×C22⋊D53—28no—
258C2×C22⋊D53—48no—
259C2×C22⋊D53C2418yes—
260C2×C22⋊D53C24116yes—
261C22×Dic53C2412yes—
262C22×Dic53C2412yes—
263C22×Dic53C2411yescharacteristic
264C22×Dic53C2411yescharacteristic
265C22×Dic53C2412yes—
266C22×Dic53C2411yescharacteristic
267C22×Dic53C2414yes—
268Q8×D53—432no—
269#11719945—432no—
270C2×D212—28no—
271C2×D212—24no—
272C2×D212C2418yes—
273C2×D212C2414yes—
274C2×C4×D53—24no—
275C2×C4×D53—24no—
276C2×C4×D53—24no—
277C2×C4×D53—28no—
278C2×C4×D53—48no—
279C2×C4×D53—48no—
280C2×C4×D53C2414yes—
281C2×C4×D53C2414yes—
282C2×C4×D53C2414yes—
283C2×C4×D53C2418yes—
284C2×C4×D53C24116yes—
285C2×C4×D53C24116yes—
286C2×Dic106—28no—
287C2×Dic106—24no—
288C2×Dic106—48no—
289C2×Dic106C2418yes—
290C2×Dic106C2414yes—
291C2×Dic106C24116yes—
292C4⋊C4×C53C2414yes—
293C4⋊C4×C53C2418yes—
294C4⋊C4×C53C2414yes—
295C4⋊C4×C53C2418yes—
296C4⋊C4×C53C2418yes—
297C4⋊C4×C53C24116yes—
298C22⋊C4×C53C24116yes—
299C22⋊C4×C53C2418yes—
300C42×C53C2414yes—
301C42×C53C2418yes—
302C22⋊Dic53C2418yes—
303C22⋊Dic53C2418yes—
304C22⋊Dic53C24116yes—
305C22⋊Dic53C2418yes—
306#11719921C2418yes—
307#11719921C2418yes—
308#11719921C24116yes—
309#11719921C2418yes—
310#11719921C2418yes—
311#11719921C24116yes—
312#11719921C2418yes—
313#11719921C2418yes—
314C4⋊Dic53C2418yes—
315C4⋊Dic53C2418yes—
316C4⋊Dic53C2414yes—
317C4⋊Dic53C2418yes—
318C4⋊Dic53C2418yes—
319C4⋊Dic53C2414yes—
320C4⋊Dic53C2418yes—
321C4⋊Dic53C24116yes—
322#11719919C24116yes—
323#11719919C24116yes—
324#11719919C24116yes—
325#11719919C2418yes—
326#11719919C2418yes—
327#11719919C24116yes—
328#11719919C2418yes—
329#11719919C24116yes—
330#11719919C24116yes—
331#11719919C2418yes—
332C4×Dic53C2414yes—
333C4×Dic53C2414yes—
334C4×Dic53C2414yes—
335C4×Dic53C24116yes—
336C4×Dic53C2418yes—
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×D532−1+414yes—
349C22×D53C2514yes—
350C22×D53C2512yes—
351Q8×C53—216no—
352Q8×C53—28no—
353Q8×C53—416no—
354D4×C53—28no—
355C2×C4×C53—28no—
356C2×C4×C53—24no—
357C2×C4×C53—24no—
358C2×C4×C53—22no—
359C2×C4×C53—24no—
360C2×C4×C53—216no—
361C2×C4×C53—416no—
362C2×C4×C53H(5,𝔽2)14yes—
363C2×C4×C532−1+414yes—
364C2×C4×C53C2518yes—
365C2×C4×C53C2514yes—
366C2×C4×C53C2512yes—
367C2×C4×C53C2514yes—
368C2×C4×C53C2514yes—
369C2×C4×C53C2512yes—
370C2×C4×C53C2512yes—
371C22⋊D53—216no—
372C22⋊D53—416no—
373C2×Dic53—28no—
374C2×Dic53—22no—
375C2×Dic53—24no—
376C2×Dic53—22no—
377C2×Dic53—22no—
378C2×Dic53—24no—
379C2×Dic53—24no—
380C2×Dic53C2512yes—
381C2×Dic53C2518yes—
382C2×Dic53C2514yes—
383C2×Dic53C2512yes—
384C2×Dic53C2512yes—
385C2×Dic53C2514yes—
386C2×Dic53C2514yes—
387D212—216no—
388D212—28no—
389C4×D53—28no—
390C4×D53—28no—
391C4×D53—28no—
392C4×D53—216no—
393C4×D53—416no—
394C4×D53—416no—
395Dic106—216no—
396Dic106—28no—
397Dic106—416no—
398C2×#3552—531nomaximal, Sylow
399C22×C53—24no—
400C22×C53—24no—
401C22×C53—24no—
402C22×C53—48no—
403C22×C53C2×H(5,𝔽2)12yes—
404C22×C53C2×2−1+412yes—
405C22×C53C2×2−1+412yes—
406C22×C53C2611yescharacteristic
407C2×D53—22no—
408C2×D53—22no—
409C2×D53—28no—
410C2×D53—24no—
411C2×D53—24no—
412C2×D53—24no—
413C2×D53—48no—
414C2×D53C2×2−1+414yes—
415C4×C53—28no—
416C4×C53—24no—
417C4×C53—24no—
418C4×C53—22no—
419C4×C53—24no—
420C4×C53C2×H(5,𝔽2)14yes—
421C4×C53C2×2−1+414yes—
422Dic53—28no—
423Dic53—22no—
424Dic53—24no—
425Dic53—22no—
426Dic53—22no—
427Dic53—24no—
428Dic53—24no—
429#3552—5332no—
430C2×#563—534no—
431C2×#557—531no—
432C2×#556—531no—
433C2×#554—532no—
434C2×#553—532no—
435C2×D4×Q8—532no—
436C2×D4×Q8D5311yescharacteristic, complemented
437C2×#548—532no—
438C2×#547—531no—
439C2×#544—532no—
440C2×#542—532no—
441C2×#541—532no—
442C2×#539—534no—
443C2×#536—532no—
444C22×C4⋊Q8—531no—
445C2×#529—531no—
446C2×#529—531no—
447C2×C53—44no—
448C2×C53#355214yescomplemented
449C2×C53C22×H(5,𝔽2)11yescharacteristic
450C2×C53C22×2−1+411yescharacteristic
451C2×C53C22×2−1+411yescharacteristic
452D53—24no—
453D53—44no—
454C22×#41—532no—
455C23×Q8—532no—
456C23×Q8C2×D5312yes—
457#563—5364no—
458#557—5316no—
459#556—5316no—
460#554—5332no—
461#553—5332no—
462D4×Q8—5332no—
463D4×Q8C2×D53116yescomplemented
464#548—5332no—
465#547—5316no—
466#544—5332no—
467#542—5332no—
468#541—5332no—
469#539—5364no—
470#536—5332no—
471C2×C4⋊Q8—532no—
472C2×C4⋊Q8—532no—
473C2×C4⋊Q8—534no—
474C2×C4⋊Q8—5316no—
475C2×C4⋊Q8—532no—
476C2×C4⋊Q8—532no—
477C2×C4⋊Q8—531no—
478C2×C4⋊Q8C2×D5311yescharacteristic
479C2×C4⋊Q8C2×D5312yes—
480#529—5316no—
481#529—5316no—
482C2×#126—532no—
483C2×#126—534no—
484C2×#126—532no—
485C2×#126—534no—
486C2×#126—534no—
487C2×#125—531no—
488C2×#125—531no—
489C2×#125—534no—
490C2×#125—534no—
491C2×#125—534no—
492C2×#125—532no—
493C2×#124—531no—
494C2×#124—532no—
495C2×#124—531no—
496C2×#124—534no—
497C2×#123—534no—
498C2×#123—534no—
499C2×#123—532no—
500C2×#123—532no—
501C2×#123—534no—
502C2×C22⋊Q8—531no—
503C2×C22⋊Q8—534no—
504C2×C22⋊Q8—534no—
505C2×C22⋊Q8—534no—
506C2×C22⋊Q8—532no—
507C2×C22⋊Q8—534no—
508C2×C22⋊Q8—531no—
509C2×C22⋊Q8—534no—
510C2×C22⋊Q8—532no—
511C2×C22⋊Q8C2×D5314yes—
512C2×C22⋊Q8C2×D5312yes—
513C2×#121—531no—
514C2×#121—532no—
515C2×#121—531no—
516C2×#121—534no—
517C2×C4×Q8—532no—
518C2×C4×Q8—532no—
519C2×C4×Q8—531no—
520C2×C4×Q8—532no—
521C2×C4×Q8C2×D5311yescharacteristic
522C2×C4×D4—532no—
523C2×C4×D4—534no—
524C2×C4×D4—534no—
525C2×C4×D4—531no—
526C2×C4×D4—532no—
527C2×C4×D4C2×D5311yescharacteristic
528C2×C4×D4C2×D5312yes—
529C2×#117—532no—
530C2×#117—532no—
531C2×#117—532no—
532C22×C4⋊C4—532no—
533C22×C4⋊C4—532no—
534C22×C4⋊C4—532no—
535C22×C42—531no—
536C53C2×#355211yescharacteristic, complemented, Sylow
537C2×#41—5316no—
538C2×#41—2128no—
539C22×Q8—48no—
540C22×Q8—5316no—
541C22×Q8—531no—
542C22×Q8—532no—
543C22×Q8—534no—
544C22×Q8—2128no—
545C22×Q8C22×D5312yes—
546C22×Q8C22×D5311yescharacteristic
547C22×Q8C22×D5314yes—
548C22×Q8C22×D53116yes—
549C22×D4—532no—
550C22×D4—534no—
551C22×D4—532no—
552C22×D4—531no—
553C22×D4C22×D5311yescharacteristic
554C23×C4—531no—
555C23×C4—531no—
556C23×C4—532no—
557C23×C4—531no—
558C23×C4—534no—
559C23×C4—534no—
560C23×C4C22×D5312yes—
561C23×C4C22×D5314yes—
562C4⋊Q8—5316no—
563C4⋊Q8—5316no—
564C4⋊Q8—5332no—
565C4⋊Q8—5316no—
566C4⋊Q8—5316no—
567C4⋊Q8—538no—
568C4⋊Q8C22×D5318yes—
569C4⋊Q8C22×D53116yes—
570#126—5316no—
571#126—5332no—
572#126—5316no—
573#126—5332no—
574#126—5332no—
575#125—538no—
576#125—538no—
577#125—5332no—
578#125—5332no—
579#125—5332no—
580#125—5316no—
581#124—538no—
582#124—5316no—
583#124—538no—
584#124—5332no—
585#123—5332no—
586#123—5332no—
587#123—5316no—
588#123—5316no—
589#123—5332no—
590C22⋊Q8—538no—
591C22⋊Q8—5332no—
592C22⋊Q8—5332no—
593C22⋊Q8—5332no—
594C22⋊Q8—5316no—
595C22⋊Q8—5332no—
596C22⋊Q8—538no—
597C22⋊Q8—5316no—
598C22⋊Q8—5332no—
599C22⋊Q8C22×D53132yes—
600C22⋊Q8C22×D53116yes—
601#121—538no—
602#121—5316no—
603#121—538no—
604#121—5332no—
605C4×Q8—5316no—
606C4×Q8—5316no—
607C4×Q8—538no—
608C4×Q8—5316no—
609C4×Q8C22×D5318yes—
610C4×D4—5316no—
611C4×D4—5332no—
612C4×D4—5332no—
613C4×D4—538no—
614C4×D4—5316no—
615C4×D4C22×D5318yes—
616C4×D4C22×D53116yes—
617#117—5316no—
618#117—5316no—
619#117—5316no—
620C2×C4⋊C4—532no—
621C2×C4⋊C4—534no—
622C2×C4⋊C4—534no—
623C2×C4⋊C4—534no—
624C2×C4⋊C4—532no—
625C2×C4⋊C4—531no—
626C2×C4⋊C4—532no—
627C2×C4⋊C4—532no—
628C2×C4⋊C4—532no—
629C2×C4⋊C4—532no—
630C2×C4⋊C4—531no—
631C2×C4⋊C4—532no—
632C2×C4⋊C4—534no—
633C2×C4⋊C4—532no—
634C2×C4⋊C4—534no—
635C2×C4⋊C4—534no—
636C2×C4⋊C4—534no—
637C2×C4⋊C4—532no—
638C2×C4⋊C4—5316no—
639C2×C4⋊C4—5316no—
640C2×C4⋊C4—5316no—
641C2×C4⋊C4C22×D5311yescharacteristic
642C2×C4⋊C4C22×D5312yes—
643C2×C4⋊C4C22×D5312yes—
644C2×C4⋊C4C22×D5314yes—
645C2×C4⋊C4C22×D5311yescharacteristic
646C2×C4⋊C4C22×D5312yes—
647C2×C22⋊C4—532no—
648C2×C22⋊C4—532no—
649C2×C22⋊C4—534no—
650C2×C22⋊C4—532no—
651C2×C22⋊C4—534no—
652C2×C22⋊C4—532no—
653C2×C22⋊C4—532no—
654C2×C22⋊C4—532no—
655C2×C22⋊C4—532no—
656C2×C22⋊C4—532no—
657C2×C22⋊C4—534no—
658C2×C22⋊C4—532no—
659C2×C22⋊C4C22×D5314yes—
660C2×C22⋊C4C22×D5312yes—
661C2×C42—531no—
662C2×C42—531no—
663C2×C42—532no—
664C2×C42—534no—
665C2×C42—534no—
666C2×C42—531no—
667C2×C42—538no—
668C2×C42C22×D5312yes—
669C2×C42C22×D5311yescharacteristic
670C24—531no—
671C24—532no—
672C24C23×D5312yes—
673#41—21232no—
674C2×Q8—24no—
675C2×Q8—28no—
676C2×Q8—48no—
677C2×Q8—432no—
678C2×Q8—534no—
679C2×Q8—538no—
680C2×Q8—5316no—
681C2×Q8—1068no—
682C2×Q8—1064no—
683C2×Q8—2128no—
684C2×Q8—21232no—
685C2×Q8C23×D5318yes—
686C2×Q8C23×D5314yes—
687C2×Q8C23×D53116yes—
688C2×D4—24no—
689C2×D4—538no—
690C2×D4—5316no—
691C2×D4—538no—
692C2×D4—534no—
693C2×D4—1068no—
694C2×D4—1068no—
695C2×D4—1064no—
696C2×D4—2128no—
697C2×D4C23×D5314yes—
698C22×C4—28no—
699C22×C4—48no—
700C22×C4—532no—
701C22×C4—532no—
702C22×C4—531no—
703C22×C4—531no—
704C22×C4—532no—
705C22×C4—531no—
706C22×C4—534no—
707C22×C4—534no—
708C22×C4—534no—
709C22×C4—534no—
710C22×C4—538no—
711C22×C4—5316no—
712C22×C4—5316no—
713C22×C4—1064no—
714C22×C4—1064no—
715C22×C4—1064no—
716C22×C4—1068no—
717C22×C4—2128no—
718C22×C4—2128no—
719C22×C4C23×D5318yes—
720C22×C4C23×D5312yes—
721C22×C4C23×D5311yescharacteristic
722C22×C4C23×D5314yes—
723C22×C4C23×D5312yes—
724C22×C4C23×D5312yes—
725C22×C4C23×D53116yes—
726C22×C4C23×D5311yescharacteristic
727C22×C4C23×D5311yescharacteristic
728C4⋊C4—538no—
729C4⋊C4—5316no—
730C4⋊C4—5316no—
731C4⋊C4—5316no—
732C4⋊C4—538no—
733C4⋊C4—534no—
734C4⋊C4—538no—
735C4⋊C4—538no—
736C4⋊C4—538no—
737C4⋊C4—538no—
738C4⋊C4—534no—
739C4⋊C4—538no—
740C4⋊C4—5316no—
741C4⋊C4—538no—
742C4⋊C4—5316no—
743C4⋊C4—5316no—
744C4⋊C4—5316no—
745C4⋊C4—538no—
746C4⋊C4C23×D5314yes—
747C4⋊C4C23×D5318yes—
748C4⋊C4C23×D5318yes—
749C4⋊C4C23×D53116yes—
750C4⋊C4C23×D5314yes—
751C4⋊C4C23×D5318yes—
752C22⋊C4—538no—
753C22⋊C4—538no—
754C22⋊C4—5316no—
755C22⋊C4—538no—
756C22⋊C4—5316no—
757C22⋊C4—538no—
758C22⋊C4—538no—
759C22⋊C4—538no—
760C22⋊C4—538no—
761C22⋊C4—538no—
762C22⋊C4—5316no—
763C22⋊C4—538no—
764C22⋊C4C23×D53116yes—
765C22⋊C4C23×D5318yes—
766C42—534no—
767C42—534no—
768C42—534no—
769C42—538no—
770C42—5316no—
771C42—5316no—
772C42C23×D5314yes—
773C42C23×D5318yes—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—534no—
778C23—532no—
779C23—534no—
780C23—1062no—
781C23—1062no—
782C23—1064no—
783C23—1064no—
784C23—1064no—
785C23C24×D5314yes—
786C23C24×D5311yescharacteristic
787Q8—28no—
788Q8—216no—
789Q8—416no—
790Q8—10616no—
791Q8—1068no—
792Q8—21216no—
793D4—28no—
794D4—10616no—
795D4—10616no—
796D4—1068no—
797D4—21216no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—28no—
801C2×C4—22no—
802C2×C4—24no—
803C2×C4—216no—
804C2×C4—416no—
805C2×C4—534no—
806C2×C4—534no—
807C2×C4—532no—
808C2×C4—532no—
809C2×C4—534no—
810C2×C4—532no—
811C2×C4—538no—
812C2×C4—1068no—
813C2×C4—1062no—
814C2×C4—1068no—
815C2×C4—1062no—
816C2×C4—1064no—
817C2×C4—1062no—
818C2×C4—1064no—
819C2×C4—1064no—
820C2×C4—1068no—
821C2×C4—1068no—
822C2×C4—10616no—
823C2×C4—21216no—
824C2×C4—21216no—
825C2×C4#1313326214yes—
826C2×C4#1313326514yes—
827C2×C4C24×D5314yes—
828C2×C4C24×D5312yes—
829C2×C4C24×D5318yes—
830C2×C4C24×D5314yes—
831C2×C4C24×D5314yes—
832C2×C4C24×D5312yes—
833C2×C4C24×D5312yes—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—48no—
838C22—534no—
839C22—1068no—
840C22—1062no—
841C22—1062no—
842C22—1064no—
843C22—1064no—
844C22—1064no—
845C22—2128no—
846C22C2×#1313326212yes—
847C222−1+4×D5312yes—
848C22C2×#1313326512yes—
849C22C25×D5311yescharacteristic
850C4—24no—
851C4—24no—
852C4—28no—
853C4—22no—
854C4—24no—
855C4—1062no—
856C4—1068no—
857C4—1062no—
858C4—1064no—
859C4—1062no—
860C4—1064no—
861C4—1064no—
862C4C2×#1313326214yes—
863C4C2×#1313326514yes—
864C2—44no—
865C2—1064no—
866C2—2124no—
867C2#2028915714yesdirect product factor
868C2C22×#1313326211yescharacteristic
869C2C2×2−1+4×D5311yescharacteristic
870C2C22×#1313326511yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×D4×Q8×C53C2
socleC23×C53C25
hypercenterC2×D4×Q8D53
hypocenterC53C2×#3552
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. #20289157C2direct (N × H)
2. C2×#16811374C2semidirect
3. C2×#16811351C2semidirect
4. C2×#16811347C2semidirect
5. C2×#16811334C2semidirect
6. C2×#16811323C2semidirect
7. C2×Q8×C22⋊D53C2semidirect
8. C2×#16811283C2semidirect
9. C2×#16811278C2semidirect
10. C2×#16811250C2semidirect
11. C2×#16811238C2semidirect
12. C2×#16811233C2semidirect
13. C2×#16811219C2semidirect
14. C2×#16811197C2semidirect
15. C2×C4⋊Q8×D53C2semidirect
16. C2×#16811160C2semidirect
17. C2×#16811155C2semidirect
18. C2×D4×Q8×C53C2semidirect
21. #16811374C22semidirect
22. #16811351C22semidirect
23. #16811347C22semidirect
24. #16811334C22semidirect
25. #16811323C22semidirect
26. Q8×C22⋊D53C22semidirect
27. #16811283C22semidirect
28. #16811278C22semidirect
29. #16811250C22semidirect
30. #16811238C22semidirect
31. #16811233C22semidirect
32. #16811219C22semidirect
33. #16811197C22semidirect
40. C4⋊Q8×D53C22semidirect
41. #16811160C22semidirect
42. #16811155C22semidirect
93. D4×Q8×C53C22semidirect
436. C2×D4×Q8D53semidirect
448. C2×C53#3552semidirect
463. D4×Q8C2×D53semidirect
536. C53C2×#3552semidirect
867. C2#20289157direct (N × H)

Maximal subgroups

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

subgroupindex
#202891572
C2×#168113742
C2×#168113512
C2×#168113472
C2×#168113342
C2×#168113232
C2×Q8×C22⋊D532
C2×#168112832
C2×#168112782
C2×#168112502
C2×#168112382
C2×#168112332
C2×#168112192
C2×#168111972
C2×C4⋊Q8×D532
C2×#168111602
C2×#168111552
C2×D4×Q8×C532
C2×#355253