Finite Group Databasebeta

← C2×#20288581 #28292173

Subgroups — C2×#20288581 #28292173

Order 13568.

7130 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288581C2132yesmaximal, direct product factor
2C2×#16811358C211yesmaximal, characteristic, complemented
3C2×#16811358C211yesmaximal, characteristic, complemented
4C2×#16811348C211yesmaximal, characteristic, complemented
5C2×#16811347C212yesmaximal, complemented
6C2×#16811345C212yesmaximal, complemented
7C2×#16811345C212yesmaximal, complemented
8C2×#16811329C212yesmaximal, complemented
9C2×#16811305C214yesmaximal, complemented
10C2×#16811221C214yesmaximal, complemented
11C2×#16811198C212yesmaximal, complemented
12C2×#16811177C211yesmaximal, characteristic, complemented
13C2×#16811174C211yesmaximal, characteristic
14C2×#16811160C212yesmaximal, complemented
15C2×#16811158C212yesmaximal, complemented
16C2×#16811105C212yesmaximal, complemented
17C2×C4×Q8×D53C211yesmaximal, characteristic, complemented
18C2×C53×#557C211yesmaximal, characteristic, complemented
19C22×#11719949C2212yes—
20C22×Q8×D53C2211yescharacteristic
21#16811358C22116yescomplemented
22#16811358C22116yescomplemented
23#16811348C22116yescomplemented
24#16811347C22132yescomplemented
25#16811345C22132yescomplemented
26#16811345C22132yescomplemented
27#16811329C22132yescomplemented
28#16811305C22164yescomplemented
29#16811221C22164yescomplemented
30#16811198C22132yescomplemented
31#16811177C22116yescomplemented
32#16811174C22116yes—
33C2×#13133216C2211yescharacteristic
34C2×#13133215C2211yescharacteristic
35C2×#13133215C2212yes—
36C2×#13133214C2211yescharacteristic
37#16811160C22132yescomplemented
38#16811158C22132yescomplemented
39C2×#13133212C2214yes—
40C2×#13133212C2214yes—
41C2×#13133212C2214yes—
42C2×#13133211C2214yes—
43C2×#13133208C2212yes—
44C2×#13133207C2212yes—
45C2×#13133207C2214yes—
46C2×#13133206C2212yes—
47C2×#13133206C2212yes—
48C2×#13133206C2212yes—
49C2×#13133205C2212yes—
50C2×#13133205C2212yes—
51C2×#13133202C2214yes—
52C2×#13133202C2214yes—
53C2×#13133202C2214yes—
54C2×#13133202C2214yes—
55C2×#13133197C2211yescharacteristic
56C2×#13133197C2214yes—
57C2×#13133195C2212yes—
58C2×#13133195C2214yes—
59C2×#13133195C2214yes—
60C2×#13133195C2214yes—
61C2×#13133193C2211yescharacteristic
62C2×#13133192C2212yes—
63C2×#13133192C2212yes—
64#16811105C22132yescomplemented
65C2×Q8×Dic53C2211yescharacteristic
66C2×Q8×Dic53C2212yes—
67C2×C4×Dic106C2212yes—
68C2×C4×Dic106C2211yescharacteristic
69C2×C4×Dic106C2212yes—
70C2×C4×Dic106C2211yescharacteristic
71C2×#13133182C2211yescharacteristic
72C2×#13133182C2212yes—
73C2×#13133182C2212yes—
74C4×Q8×D53C22116yescomplemented
75C2×C4×D212C2212yes—
76C2×C4×D212C2212yes—
77C2×C4×D212C2214yes—
78C2×#13133179C2212yes—
79C2×#13133179C2212yes—
80C2×#13133179C2212yes—
81C2×#13133179C2214yes—
82C2×#13133179C2212yes—
83C2×#13133175C2214yes—
84C2×#13133174C2212yes—
85C2×#13133174C2214yes—
86C2×#13133174C2214yes—
87C2×C4⋊C4×D53C2212yes—
88C2×C4⋊C4×D53C2211yescharacteristic
89C2×C4⋊C4×D53C2214yes—
90C2×C42×D53C2211yescharacteristic
91C2×C42×D53C2212yes—
92C53×#557C22116yescomplemented
93C2×C4⋊Q8×C53C2212yes—
94C2×C4⋊Q8×C53C2211yescharacteristic
95C2×#125×C53C2214yes—
96C2×#125×C53C2212yes—
97C2×C4×Q8×C53C2211yescharacteristic
98C2×C4×Q8×C53C2212yes—
99C2×C4×Q8×C53C2212yes—
100C2×C4×Q8×C53C2211yescharacteristic
101C2×#11719949—216no—
102C2×#11719949C23116yes—
103C22×Dic106C2311yescharacteristic
104C22×Dic106C2312yes—
105C22×Dic106C2311yescharacteristic
106C22×Dic106C2312yes—
107C2×Q8×D53—28no—
108C2×Q8×D53C2318yes—
109C22×D212C2312yes—
110C22×D212C2314yes—
111C22×D212C2312yes—
112C22×D212C2312yes—
113C22×C4×D53C2311yescharacteristic
114C22×C4×D53C2312yes—
115C22×C4×D53C2314yes—
116C22×C4×D53C2312yes—
117C22×C4×D53C2311yescharacteristic
118C22×C4×D53C2314yes—
119C22×C4×D53C2314yes—
120C22×C4×D53C2311yescharacteristic
121#13133216C2318yes—
122#13133215C2318yes—
123#13133215C23116yes—
124#13133214C2318yes—
125#13133212C23132yes—
126#13133212C23132yes—
127#13133212C23132yes—
128#13133211C23132yes—
129#13133208C23116yes—
130#13133207C23116yes—
131#13133207C23132yes—
132#13133206C23116yes—
133#13133206C23116yes—
134#13133206C23116yes—
135#13133205C23116yes—
136#13133205C23116yes—
137#13133202C23132yes—
138#13133202C23132yes—
139#13133202C23132yes—
140#13133202C23132yes—
141#13133197C23132yes—
142#13133197C2318yes—
143#13133195C23132yes—
144#13133195C23132yes—
145#13133195C23132yes—
146#13133195C23116yes—
147#13133193C2318yes—
148#13133192C23116yes—
149#13133192C23116yes—
150Q8×Dic53C2318yes—
151Q8×Dic53C23116yes—
152C4×Dic106C23116yes—
153C4×Dic106C2318yes—
154C4×Dic106C23116yes—
155C4×Dic106C2318yes—
156#13133182C23116yes—
157#13133182C2318yes—
158#13133182C23116yes—
159C4×D212C23116yes—
160C4×D212C23116yes—
161C4×D212C23132yes—
162#13133179C23116yes—
163#13133179C23116yes—
164#13133179C23116yes—
165#13133179C23116yes—
166#13133179C23132yes—
167#13133175C23132yes—
168#13133174C23132yes—
169#13133174C23132yes—
170#13133174C23116yes—
171C2×C4⋊Dic53C2311yescharacteristic
172C2×C4⋊Dic53C2314yes—
173C2×C4⋊Dic53C2312yes—
174C2×C4⋊Dic53C2312yes—
175C2×C4⋊Dic53C2311yescharacteristic
176C2×#11719919C2312yes—
177C2×#11719919C2312yes—
178C2×#11719919C2312yes—
179C2×#11719919C2312yes—
180C2×#11719919C2312yes—
181C2×#11719919C2312yes—
182C2×#11719919C2314yes—
183C2×#11719919C2314yes—
184C2×#11719919C2312yes—
185C2×#11719919C2312yes—
186C4⋊C4×D53C23132yes—
187C4⋊C4×D53C2318yes—
188C4⋊C4×D53C23116yes—
189C2×#11719921C2314yes—
190C2×#11719921C2312yes—
191C2×#11719921C2314yes—
192C2×#11719921C2312yes—
193C2×#11719921C2314yes—
194C2×#11719921C2314yes—
195C2×#11719921C2314yes—
196C2×#11719921C2314yes—
197C2×#11719921C2314yes—
198C2×#11719921C2314yes—
199C2×C4×Dic53C2312yes—
200C2×C4×Dic53C2312yes—
201C2×C4×Dic53C2311yescharacteristic
202C2×C4×Dic53C2311yescharacteristic
203C2×C4×Dic53C2312yes—
204C2×C4×Dic53C2311yescharacteristic
205C2×C4×Dic53C2314yes—
206C2×C4×Dic53C2312yes—
207C42×D53C23116yes—
208C42×D53C2318yes—
209C22×Q8×C53C2311yescharacteristic
210C22×Q8×C53C2311yescharacteristic
211C22×Q8×C53C2312yes—
212C4⋊Q8×C53C23116yes—
213C4⋊Q8×C53C2318yes—
214#125×C53C23132yes—
215#125×C53C23116yes—
216C4×Q8×C53C2318yes—
217C4×Q8×C53C23116yes—
218C4×Q8×C53C23116yes—
219C4×Q8×C53C2318yes—
220C2×C4⋊C4×C53C2311yescharacteristic
221C2×C4⋊C4×C53C2314yes—
222C2×C4⋊C4×C53C2312yes—
223C2×C4⋊C4×C53C2311yescharacteristic
224C2×C4⋊C4×C53C2312yes—
225C2×C4⋊C4×C53C2312yes—
226C2×C4⋊C4×C53C2314yes—
227C2×C4⋊C4×C53C2314yes—
228C2×C4⋊C4×C53C2312yes—
229C2×C42×C53C2312yes—
230C2×C42×C53C2314yes—
231C2×C42×C53C2311yescharacteristic
232C2×C42×C53C2312yes—
233C23×D53C2414yes—
234C23×D53C2411yescharacteristic
235C2×Q8×C53—24no—
236C2×Q8×C53—28no—
237C2×Q8×C53—24no—
238C2×Q8×C53C2414yes—
239C2×Q8×C53C2414yes—
240C2×Q8×C53C2418yes—
241C22×C4×C53C2412yes—
242C22×C4×C53C2412yes—
243C22×C4×C53C2411yescharacteristic
244C22×C4×C53C2412yes—
245C22×C4×C53C2412yes—
246C22×C4×C53C2414yes—
247C22×C4×C53C2411yescharacteristic
248C22×C4×C53C2411yescharacteristic
249C22×Dic53C2411yescharacteristic
250C22×Dic53C2412yes—
251C22×Dic53C2412yes—
252C22×Dic53C2412yes—
253C22×Dic53C2411yescharacteristic
254C22×Dic53C2412yes—
255C22×Dic53C2411yescharacteristic
256#11719949—264no—
257Q8×D53—232no—
258C2×D212—216no—
259C2×D212—28no—
260C2×D212—28no—
261C2×D212—44no—
262C2×D212C2418yes—
263C2×D212C24116yes—
264C2×D212C2418yes—
265C2×D212C2418yes—
266C2×C4×D53—28no—
267C2×C4×D53—24no—
268C2×C4×D53—216no—
269C2×C4×D53—42no—
270C2×C4×D53—48no—
271C2×C4×D53—48no—
272C2×C4×D53—44no—
273C2×C4×D53#4118yes—
274C2×C4×D53C2414yes—
275C2×C4×D53C2418yes—
276C2×C4×D53C24116yes—
277C2×C4×D53C2418yes—
278C2×C4×D53C2414yes—
279C2×C4×D53C24116yes—
280C2×C4×D53C24116yes—
281C2×C4×D53C2414yes—
282C2×Dic106—24no—
283C2×Dic106—24no—
284C2×Dic106—28no—
285C2×Dic106—44no—
286C2×Dic106C2414yes—
287C2×Dic106C2418yes—
288C2×Dic106C2414yes—
289C2×Dic106C2418yes—
290C4⋊C4×C53C2414yes—
291C4⋊C4×C53C24116yes—
292C4⋊C4×C53C2418yes—
293C4⋊C4×C53C2414yes—
294C4⋊C4×C53C2418yes—
295C4⋊C4×C53C2418yes—
296C4⋊C4×C53C24116yes—
297C4⋊C4×C53C24116yes—
298C4⋊C4×C53C2418yes—
299C42×C53C2418yes—
300C42×C53C24116yes—
301C42×C53C2414yes—
302C42×C53C2418yes—
303#11719921C24116yes—
304#11719921C2418yes—
305#11719921C24116yes—
306#11719921C2418yes—
307#11719921C24116yes—
308#11719921C24116yes—
309#11719921C24116yes—
310#11719921C24116yes—
311#11719921C24116yes—
312#11719921C24116yes—
313C4⋊Dic53C2414yes—
314C4⋊Dic53C24116yes—
315C4⋊Dic53C2418yes—
316C4⋊Dic53C2418yes—
317C4⋊Dic53C2414yes—
318#11719919C2418yes—
319#11719919C2418yes—
320#11719919C2418yes—
321#11719919C2418yes—
322#11719919C2418yes—
323#11719919C2418yes—
324#11719919C24116yes—
325#11719919C24116yes—
326#11719919C2418yes—
327#11719919C2418yes—
328C4×Dic53C2418yes—
329C4×Dic53C2418yes—
330C4×Dic53C2414yes—
331C4×Dic53C2414yes—
332C4×Dic53C2418yes—
333C4×Dic53C2414yes—
334C4×Dic53C24116yes—
335C4×Dic53C2418yes—
336C23×C53C2511yescharacteristic
337C22×D53—22no—
338C22×D53—22no—
339C22×D53—28no—
340C22×D53—28no—
341C22×D53—28no—
342C22×D53C2×#4114yes—
343C22×D53C2518yes—
344C22×D53C2512yes—
345Q8×C53—28no—
346Q8×C53—216no—
347Q8×C53—28no—
348C2×C4×C53—24no—
349C2×C4×C53—28no—
350C2×C4×C53—24no—
351C2×C4×C53—24no—
352C2×C4×C53—24no—
353C2×C4×C53—22no—
354C2×C4×C53C2×#4114yes—
355C2×C4×C532−1+414yes—
356C2×C4×C53C2514yes—
357C2×C4×C53C2514yes—
358C2×C4×C53C2514yes—
359C2×C4×C53C2512yes—
360C2×C4×C53C2518yes—
361C2×C4×C53C2514yes—
362C2×C4×C53C2512yes—
363C2×C4×C53C2512yes—
364C2×Dic53—24no—
365C2×Dic53—24no—
366C2×Dic53—22no—
367C2×Dic53—22no—
368C2×Dic53—24no—
369C2×Dic53—24no—
370C2×Dic53C2×#4114yes—
371C2×Dic53C2514yes—
372C2×Dic53C2512yes—
373C2×Dic53C2514yes—
374C2×Dic53C2514yes—
375C2×Dic53C2514yes—
376C2×Dic53C2512yes—
377C2×Dic53C2512yes—
378D212—232no—
379D212—216no—
380D212—216no—
381D212—48no—
382C4×D53—216no—
383C4×D53—28no—
384C4×D53—232no—
385C4×D53—44no—
386C4×D53—416no—
387C4×D53—416no—
388C4×D53—48no—
389C4×D53C2×#41116yes—
390Dic106—28no—
391Dic106—28no—
392Dic106—216no—
393Dic106—48no—
394C2×#3507—531nomaximal, Sylow
395C22×C53C22×#4112yes—
396C22×C53C2×2−1+412yes—
397C22×C53#58512yes—
398C22×C53C2611yescharacteristic
399C2×D53—22no—
400C2×D53—22no—
401C2×D53—28no—
402C2×D53—28no—
403C2×D53—28no—
404C2×D53—28no—
405C2×D53—416no—
406C2×D53C22×#4114yes—
407C4×C53—24no—
408C4×C53—28no—
409C4×C53—24no—
410C4×C53—24no—
411C4×C53—24no—
412C4×C53—22no—
413C4×C53C22×#4114yes—
414C4×C53C2×2−1+414yes—
415Dic53—24no—
416Dic53—24no—
417Dic53—22no—
418Dic53—22no—
419Dic53—24no—
420Dic53—24no—
421Dic53C22×#4114yes—
422#3507—5332no—
423C2×#559—531no—
424C2×#559—531no—
425C2×#557—531no—
426C2×#557D5311yescharacteristic, complemented
427C2×#556—532no—
428C2×#556—532no—
429C2×#556—532no—
430C2×#554—532no—
431C2×#552—534no—
432C2×#539—534no—
433C2×#536—532no—
434C2×#533—531no—
435C2×#532—531no—
436C2×#529—532no—
437C2×#529—532no—
438C2×#520—532no—
439C22×C4×Q8—531no—
440C2×C53#350714yescomplemented
441C2×C53C23×#4111yescharacteristic
442C2×C53C22×2−1+411yescharacteristic
443C2×C53C2×#58511yescharacteristic
444D53—24no—
445D53—48no—
446C22×#41—532no—
447C23×Q8—531no—
448#559—5316no—
449#559—5316no—
450#557—5316no—
451#557C2×D53116yescomplemented
452#556—5332no—
453#556—5332no—
454#556—5332no—
455#554—5332no—
456#552—5364no—
457#539—5364no—
458#536—5332no—
459#533—5316no—
460#532—5316no—
461C2×C4⋊Q8—531no—
462C2×C4⋊Q8—532no—
463C2×C4⋊Q8—531no—
464C2×C4⋊Q8C2×D5311yescharacteristic
465C2×C4⋊Q8C2×D5312yes—
466C2×#127—531no—
467#529—5332no—
468#529—5332no—
469C2×#126—534no—
470C2×#126—534no—
471C2×#126—534no—
472C2×#126—534no—
473C2×#125—532no—
474C2×#125—532no—
475C2×#125—534no—
476C2×#125C2×D5312yes—
477C2×#125C2×D5314yes—
478C2×#124—532no—
479C2×#124—532no—
480C2×#124—532no—
481C2×#124—532no—
482C2×#124—532no—
483C2×#123—534no—
484C2×#123—534no—
485C2×#123—534no—
486C2×#123—534no—
487C2×C22⋊Q8—531no—
488C2×C22⋊Q8—531no—
489C2×C22⋊Q8—532no—
490C2×C22⋊Q8—534no—
491C2×C22⋊Q8—534no—
492C2×C22⋊Q8—534no—
493C2×C22⋊Q8—534no—
494C2×#121—532no—
495C2×#121—532no—
496#520—5332no—
497C2×C4×Q8—531no—
498C2×C4×Q8—532no—
499C2×C4×Q8—5316no—
500C2×C4×Q8—532no—
501C2×C4×Q8—531no—
502C2×C4×Q8—532no—
503C2×C4×Q8—532no—
504C2×C4×Q8—531no—
505C2×C4×Q8—532no—
506C2×C4×Q8—531no—
507C2×C4×Q8C2×D5311yescharacteristic
508C2×C4×Q8C2×D5312yes—
509C2×C4×Q8C2×D5312yes—
510C2×C4×Q8C2×D5311yescharacteristic
511C2×C4×D4—534no—
512C2×C4×D4—532no—
513C2×C4×D4—532no—
514C2×C4×D4—532no—
515C2×C4×D4—532no—
516C2×C4×D4—534no—
517C2×C4×D4—532no—
518C2×C4×D4—532no—
519C2×#117—534no—
520C2×#117—532no—
521C2×#117—534no—
522C2×#117—534no—
523C22×C4⋊C4—531no—
524C22×C4⋊C4—532no—
525C22×C4⋊C4—534no—
526C22×C42—532no—
527C22×C42—531no—
528C53C2×#350711yescharacteristic, complemented, Sylow
529C2×#41—5316no—
530C2×#41—10616no—
531C22×Q8—538no—
532C22×Q8—531no—
533C22×Q8—532no—
534C22×Q8—531no—
535C22×Q8—532no—
536C22×Q8—1068no—
537C22×Q8C22×D5311yescharacteristic
538C22×Q8C22×D5312yes—
539C22×Q8C22×D5311yescharacteristic
540C22×D4—532no—
541C22×D4—534no—
542C22×D4—532no—
543C22×D4—532no—
544C23×C4—531no—
545C23×C4—534no—
546C23×C4—532no—
547C23×C4—531no—
548C23×C4—532no—
549C23×C4—531no—
550C23×C4—534no—
551C23×C4—534no—
552C4⋊Q8—538no—
553C4⋊Q8—5316no—
554C4⋊Q8—538no—
555C4⋊Q8C22×D5318yes—
556C4⋊Q8C22×D53116yes—
557#127—538no—
558#126—5332no—
559#126—5332no—
560#126—5332no—
561#126—5332no—
562#125—5316no—
563#125—5316no—
564#125—5332no—
565#125C22×D53116yes—
566#125C22×D53132yes—
567#124—5316no—
568#124—5316no—
569#124—5316no—
570#124—5316no—
571#124—5316no—
572#123—5332no—
573#123—5332no—
574#123—5332no—
575#123—5332no—
576C22⋊Q8—538no—
577C22⋊Q8—538no—
578C22⋊Q8—5316no—
579C22⋊Q8—5332no—
580C22⋊Q8—5332no—
581C22⋊Q8—5332no—
582C22⋊Q8—5332no—
583#121—5316no—
584#121—5316no—
585C4×Q8—538no—
586C4×Q8—5316no—
587C4×Q8—5316no—
588C4×Q8—538no—
589C4×Q8—5316no—
590C4×Q8—5316no—
591C4×Q8—538no—
592C4×Q8—5316no—
593C4×Q8—538no—
594C4×Q8C22×D5318yes—
595C4×Q8C22×D53116yes—
596C4×Q8C22×D53116yes—
597C4×Q8C22×D5318yes—
598C4×D4—5332no—
599C4×D4—5316no—
600C4×D4—5316no—
601C4×D4—5316no—
602C4×D4—5316no—
603C4×D4—5332no—
604C4×D4—5316no—
605C4×D4—5316no—
606#117—5332no—
607#117—5316no—
608#117—5332no—
609#117—5332no—
610C2×C4⋊C4—532no—
611C2×C4⋊C4—532no—
612C2×C4⋊C4—531no—
613C2×C4⋊C4—534no—
614C2×C4⋊C4—532no—
615C2×C4⋊C4—532no—
616C2×C4⋊C4—532no—
617C2×C4⋊C4—532no—
618C2×C4⋊C4—532no—
619C2×C4⋊C4—532no—
620C2×C4⋊C4—534no—
621C2×C4⋊C4—531no—
622C2×C4⋊C4—532no—
623C2×C4⋊C4—534no—
624C2×C4⋊C4—532no—
625C2×C4⋊C4—538no—
626C2×C4⋊C4—5316no—
627C2×C4⋊C4—5332no—
628C2×C4⋊C4C22×D5311yescharacteristic
629C2×C4⋊C4C22×D5314yes—
630C2×C4⋊C4C22×D5312yes—
631C2×C4⋊C4C22×D5314yes—
632C2×C4⋊C4C22×D5311yescharacteristic
633C2×C4⋊C4C22×D5312yes—
634C2×C4⋊C4C22×D5312yes—
635C2×C4⋊C4C22×D5312yes—
636C2×C4⋊C4C22×D5314yes—
637C2×C22⋊C4—534no—
638C2×C22⋊C4—532no—
639C2×C22⋊C4—532no—
640C2×C22⋊C4—534no—
641C2×C22⋊C4—534no—
642C2×C22⋊C4—534no—
643C2×C22⋊C4—534no—
644C2×C22⋊C4—534no—
645C2×C22⋊C4—534no—
646C2×C22⋊C4—534no—
647C2×C42—534no—
648C2×C42—532no—
649C2×C42—532no—
650C2×C42—532no—
651C2×C42—531no—
652C2×C42—531no—
653C2×C42—532no—
654C2×C42—531no—
655C2×C42—5316no—
656C2×C42—538no—
657C2×C42C22×D5314yes—
658C2×C42C22×D5312yes—
659C2×C42C22×D5312yes—
660C2×C42C22×D5311yescharacteristic
661C24—531no—
662C24—534no—
663#41—10664no—
664C2×Q8—24no—
665C2×Q8—28no—
666C2×Q8—24no—
667C2×Q8—534no—
668C2×Q8—538no—
669C2×Q8—534no—
670C2×Q8—538no—
671C2×Q8—1068no—
672C2×Q8—10632no—
673C2×Q8—1064no—
674C2×Q8—1064no—
675C2×Q8—2124no—
676C2×Q8C23×D5314yes—
677C2×Q8C23×D5318yes—
678C2×Q8C23×D5314yes—
679C2×D4—538no—
680C2×D4—5316no—
681C2×D4—538no—
682C2×D4—538no—
683C2×D4—10616no—
684C2×D4—1068no—
685C2×D4—1068no—
686C2×D4—2124no—
687C22×C4—531no—
688C22×C4—538no—
689C22×C4—534no—
690C22×C4—531no—
691C22×C4—532no—
692C22×C4—532no—
693C22×C4—532no—
694C22×C4—531no—
695C22×C4—532no—
696C22×C4—534no—
697C22×C4—538no—
698C22×C4—5316no—
699C22×C4—538no—
700C22×C4—534no—
701C22×C4—5316no—
702C22×C4—5316no—
703C22×C4—10616no—
704C22×C4—1068no—
705C22×C4—1064no—
706C22×C4—2124no—
707C22×C4—2128no—
708C22×C4—2128no—
709C22×C4—2122no—
710C22×C4C23×D5312yes—
711C22×C4C23×D5312yes—
712C22×C4C23×D5314yes—
713C22×C4C23×D5311yescharacteristic
714C22×C4C23×D5312yes—
715C22×C4C23×D5312yes—
716C22×C4C23×D5311yescharacteristic
717C22×C4C23×D5311yescharacteristic
718C4⋊C4—538no—
719C4⋊C4—538no—
720C4⋊C4—534no—
721C4⋊C4—5316no—
722C4⋊C4—538no—
723C4⋊C4—538no—
724C4⋊C4—538no—
725C4⋊C4—538no—
726C4⋊C4—538no—
727C4⋊C4—538no—
728C4⋊C4—5316no—
729C4⋊C4—534no—
730C4⋊C4—538no—
731C4⋊C4—5316no—
732C4⋊C4—538no—
733C4⋊C4C23×D5314yes—
734C4⋊C4C23×D53116yes—
735C4⋊C4C23×D5318yes—
736C4⋊C4C23×D53116yes—
737C4⋊C4C23×D5314yes—
738C4⋊C4C23×D5318yes—
739C4⋊C4C23×D5318yes—
740C4⋊C4C23×D5318yes—
741C4⋊C4C23×D53116yes—
742C22⋊C4—5316no—
743C22⋊C4—538no—
744C22⋊C4—538no—
745C22⋊C4—5316no—
746C22⋊C4—5316no—
747C22⋊C4—5316no—
748C22⋊C4—5316no—
749C22⋊C4—5316no—
750C22⋊C4—5316no—
751C22⋊C4—5316no—
752C42—538no—
753C42—538no—
754C42—534no—
755C42—534no—
756C42—538no—
757C42—534no—
758C42—5316no—
759C42—538no—
760C42C23×D5318yes—
761C42C23×D5314yes—
762C42C23×D53116yes—
763C42C23×D5318yes—
764C23—534no—
765C23—532no—
766C23—538no—
767C23—1062no—
768C23—1062no—
769C23—1068no—
770C23—1068no—
771C23—1068no—
772C23C24×D5311yescharacteristic
773Q8—28no—
774Q8—216no—
775Q8—28no—
776Q8—10616no—
777Q8—1068no—
778Q8—1068no—
779Q8—2128no—
780D4—10632no—
781D4—10616no—
782D4—10616no—
783D4—2128no—
784C2×C4—28no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—534no—
791C2×C4—532no—
792C2×C4—5316no—
793C2×C4—532no—
794C2×C4—534no—
795C2×C4—534no—
796C2×C4—534no—
797C2×C4—532no—
798C2×C4—534no—
799C2×C4—10632no—
800C2×C4—10616no—
801C2×C4—1064no—
802C2×C4—1062no—
803C2×C4—1064no—
804C2×C4—1064no—
805C2×C4—1064no—
806C2×C4—1062no—
807C2×C4—1068no—
808C2×C4—2128no—
809C2×C4—21216no—
810C2×C4—21216no—
811C2×C4—2124no—
812C2×C4#41×D5314yes—
813C2×C4#1313326514yes—
814C2×C4C24×D5314yes—
815C2×C4C24×D5314yes—
816C2×C4C24×D5318yes—
817C2×C4C24×D5312yes—
818C2×C4C24×D5314yes—
819C2×C4C24×D5314yes—
820C2×C4C24×D5312yes—
821C2×C4C24×D5312yes—
822C22—534no—
823C22—1068no—
824C22—1062no—
825C22—1062no—
826C22—1068no—
827C22—1068no—
828C22—1068no—
829C22—21216no—
830C22C2×#41×D5312yes—
831C22C2×#1313326512yes—
832C22#1681146012yes—
833C22C25×D5311yescharacteristic
834C4—28no—
835C4—24no—
836C4—24no—
837C4—24no—
838C4—24no—
839C4—22no—
840C4—534no—
841C4—1064no—
842C4—1062no—
843C4—1064no—
844C4—1064no—
845C4—1064no—
846C4—1062no—
847C4C2×#41×D5314yes—
848C4C2×#1313326514yes—
849C2—1064no—
850C2—2128no—
851C2#2028858114yesdirect product factor
852C2C22×#41×D5311yescharacteristic
853C2C22×#1313326511yescharacteristic
854C2C2×#1681146011yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#557C2
socleC23×C53C25
prime radicalC2×#16811174C2
hypercenterC2×#557D53
hypocenterC53C2×#3507
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #20288581C2direct (N × H)
2. C2×#16811358C2semidirect
3. C2×#16811358C2semidirect
4. C2×#16811348C2semidirect
5. C2×#16811347C2semidirect
6. C2×#16811345C2semidirect
7. C2×#16811345C2semidirect
8. C2×#16811329C2semidirect
9. C2×#16811305C2semidirect
10. C2×#16811221C2semidirect
11. C2×#16811198C2semidirect
12. C2×#16811177C2semidirect
14. C2×#16811160C2semidirect
15. C2×#16811158C2semidirect
16. C2×#16811105C2semidirect
17. C2×C4×Q8×D53C2semidirect
18. C2×C53×#557C2semidirect
21. #16811358C22semidirect
22. #16811358C22semidirect
23. #16811348C22semidirect
24. #16811347C22semidirect
25. #16811345C22semidirect
26. #16811345C22semidirect
27. #16811329C22semidirect
28. #16811305C22semidirect
29. #16811221C22semidirect
30. #16811198C22semidirect
31. #16811177C22semidirect
37. #16811160C22semidirect
38. #16811158C22semidirect
64. #16811105C22semidirect
74. C4×Q8×D53C22semidirect
92. C53×#557C22semidirect
426. C2×#557D53semidirect
440. C2×C53#3507semidirect
451. #557C2×D53semidirect
528. C53C2×#3507semidirect
851. C2#20288581direct (N × H)

Maximal subgroups

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

subgroupindex
#202885812
C2×#168113582
C2×#168113482
C2×#168113472
C2×#168113452
C2×#168113292
C2×#168113052
C2×#168112212
C2×#168111982
C2×#168111772
C2×#168111742
C2×#168111602
C2×#168111582
C2×#168111052
C2×C4×Q8×D532
C2×C53×#5572
C2×#350753