Finite Group Databasebeta

← C2×#20288810 #28292308

Subgroups — C2×#20288810 #28292308

Order 13568.

7022 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288810C2132yesmaximal, direct product factor
2C2×#16811351C211yesmaximal, characteristic, complemented
3C2×#16811349C212yesmaximal, complemented
4C2×#16811348C211yesmaximal, characteristic, complemented
5C2×#16811342C212yesmaximal, complemented
6C2×#16811312C212yesmaximal, complemented
7C2×#16811309C214yesmaximal, complemented
8C2×D4×Dic106C211yesmaximal, characteristic, complemented
9C2×#16811286C212yesmaximal, complemented
10C2×#16811233C212yesmaximal, complemented
11C2×#16811230C214yesmaximal, complemented
12C2×#16811178C211yesmaximal, characteristic, complemented
13C2×#16811177C212yesmaximal, complemented
14C2×#16811155C211yesmaximal, characteristic
15C2×#16811152C212yesmaximal
16C2×#16811100C212yesmaximal, complemented
17C2×C4×Q8×D53C211yesmaximal, characteristic, complemented
18C2×C53×#556C211yesmaximal, characteristic, complemented
19C23×Dic106C2212yes—
20C22×Q8×D53C2211yescharacteristic
21#16811351C22116yescomplemented
22#16811349C22132yescomplemented
23#16811348C22116yescomplemented
24#16811342C22132yescomplemented
25#16811312C22132yescomplemented
26#16811309C22164yescomplemented
27D4×Dic106C22116yescomplemented
28#16811286C22132yescomplemented
29#16811233C22132yescomplemented
30#16811230C22164yescomplemented
31#16811178C22116yescomplemented
32#16811177C22132yescomplemented
33C2×#13133217C2211yescharacteristic
34C2×#13133216C2212yes—
35C2×#13133216C2214yes—
36C2×#13133215C2212yes—
37C2×#13133215C2212yes—
38#16811155C22116yes—
39#16811152C22132yes—
40C2×#13133210C2214yes—
41C2×#13133210C2214yes—
42C2×#13133210C2212yes—
43C2×#13133210C2214yes—
44C2×#13133209C2212yes—
45C2×#13133209C2214yes—
46C2×#13133208C2212yes—
47C2×#13133208C2212yes—
48C2×#13133208C2211yescharacteristic
49C2×#13133208C2214yes—
50C2×#13133207C2214yes—
51C2×#13133207C2214yes—
52C2×#13133207C2214yes—
53C2×#13133204C2211yescharacteristic
54C2×#13133199C2212yes—
55C2×#13133199C2214yes—
56C2×#13133197C2211yescharacteristic
57C2×#13133197C2212yes—
58C2×#13133196C2212yes—
59C2×#13133195C2214yes—
60C2×#13133194C2214yes—
61C2×#13133194C2214yes—
62C2×#13133193C2212yes—
63C2×#13133188C2211yescharacteristic
64#16811100C22132yescomplemented
65C2×Q8×Dic53C2212yes—
66C2×Q8×Dic53C2212yes—
67C2×Q8×Dic53C2211yescharacteristic
68C2×C4×Dic106C2212yes—
69C2×C4×Dic106C2214yes—
70C2×C4×Dic106C2212yes—
71C2×C4×Dic106C2211yescharacteristic
72C2×C4×Dic106C2211yescharacteristic
73C2×C4×Dic106C2214yes—
74C2×#13133182C2212yes—
75C2×#13133182C2212yes—
76C2×#13133182C2212yes—
77C2×#13133182C2212yes—
78C2×#13133182C2211yescharacteristic
79C4×Q8×D53C22116yescomplemented
80C2×D4×Dic53C2212yes—
81C2×C4×C22⋊D53C2212yes—
82C2×#13133177C2214yes—
83C2×#13133176C2212yes—
84C2×#13133175C2212yes—
85C2×#13133174C2214yes—
86C2×#13133173C2214yes—
87C2×#13133173C2214yes—
88C2×C4⋊C4×D53C2212yes—
89C2×C4⋊C4×D53C2211yescharacteristic
90C2×C42×D53C2212yes—
91C2×C42×D53C2211yescharacteristic
92C53×#556C22116yescomplemented
93C2×C4⋊Q8×C53C2211yescharacteristic
94C2×#126×C53C2214yes—
95C2×#124×C53C2212yes—
96C2×C22⋊Q8×C53C2212yes—
97C2×C4×Q8×C53C2212yes—
98C2×C4×Q8×C53C2211yescharacteristic
99C2×C4×D4×C53C2211yescharacteristic
100C2×#117×C53C2212yes—
101C22×Dic106—216no—
102C22×Dic106C23116yes—
103C22×Dic106C2312yes—
104C22×Dic106C2312yes—
105C22×Dic106C2311yescharacteristic
106C22×Dic106C2314yes—
107C22×Dic106C2311yescharacteristic
108C2×Q8×D53—28no—
109C2×Q8×D53C2318yes—
110C22×C22⋊D53C2312yes—
111C23×Dic53C2314yes—
112C22×C4×D53C2311yescharacteristic
113C22×C4×D53C2312yes—
114C22×C4×D53C2311yescharacteristic
115C22×C4×D53C2312yes—
116C22×C4×D53C2311yescharacteristic
117#13133217C2318yes—
118#13133216C23132yes—
119#13133216C23116yes—
120#13133215C23116yes—
121#13133215C23116yes—
122#13133210C23132yes—
123#13133210C23132yes—
124#13133210C23132yes—
125#13133210C23116yes—
126#13133209C23132yes—
127#13133209C23116yes—
128#13133208C23132yes—
129#13133208C23116yes—
130#13133208C2318yes—
131#13133208C23116yes—
132#13133207C23132yes—
133#13133207C23132yes—
134#13133207C23132yes—
135#13133204C2318yes—
136#13133199C23116yes—
137#13133199C23132yes—
138#13133197C23116yes—
139#13133197C2318yes—
140#13133196C23116yes—
141#13133195C23132yes—
142#13133194C23132yes—
143#13133194C23132yes—
144#13133193C23116yes—
145#13133188C2318yes—
146Q8×Dic53C2318yes—
147Q8×Dic53C23116yes—
148Q8×Dic53C23116yes—
149C4×Dic106C2318yes—
150C4×Dic106C23132yes—
151C4×Dic106C23116yes—
152C4×Dic106C23116yes—
153C4×Dic106C2318yes—
154C4×Dic106C23132yes—
155#13133182C23116yes—
156#13133182C23116yes—
157#13133182C2318yes—
158#13133182C23116yes—
159#13133182C23116yes—
160D4×Dic53C23116yes—
161C4×C22⋊D53C23116yes—
162#13133177C23132yes—
163#13133176C23116yes—
164#13133175C23116yes—
165#13133174C23132yes—
166#13133173C23132yes—
167#13133173C23132yes—
168C2×C4⋊Dic53C2311yescharacteristic
169C2×C4⋊Dic53C2312yes—
170C2×C4⋊Dic53C2312yes—
171C2×C4⋊Dic53C2312yes—
172C2×C4⋊Dic53C2312yes—
173C2×C4⋊Dic53C2312yes—
174C2×C4⋊Dic53C2311yescharacteristic
175C2×C4⋊Dic53C2314yes—
176C2×C4⋊Dic53C2314yes—
177C2×#11719919C2312yes—
178C2×#11719919C2312yes—
179C2×#11719919C2312yes—
180C2×#11719919C2314yes—
181C2×#11719919C2314yes—
182C2×#11719919C2314yes—
183C2×#11719919C2314yes—
184C2×#11719919C2314yes—
185C2×#11719919C2314yes—
186C2×#11719919C2312yes—
187C2×#11719919C2314yes—
188C2×#11719919C2312yes—
189C4⋊C4×D53C23116yes—
190C4⋊C4×D53C2318yes—
191C2×C22⋊Dic53C2312yes—
192C2×C22⋊Dic53C2312yes—
193C2×C22⋊Dic53C2312yes—
194C2×C22⋊Dic53C2314yes—
195C2×#11719921C2312yes—
196C2×#11719921C2314yes—
197C2×C4×Dic53C2312yes—
198C2×C4×Dic53C2311yescharacteristic
199C2×C4×Dic53C2312yes—
200C2×C4×Dic53C2311yescharacteristic
201C2×C4×Dic53C2312yes—
202C2×C4×Dic53C2311yescharacteristic
203C2×C4×Dic53C2314yes—
204C2×C4×Dic53C2314yes—
205C2×C4×Dic53C2314yes—
206C2×C4×Dic53C2312yes—
207C42×D53C23116yes—
208C42×D53C2318yes—
209C22×Q8×C53C2311yescharacteristic
210C22×Q8×C53C2312yes—
211C22×D4×C53C2311yescharacteristic
212C23×C4×C53C2312yes—
213C4⋊Q8×C53C2318yes—
214#126×C53C23132yes—
215#124×C53C23116yes—
216C22⋊Q8×C53C23116yes—
217C4×Q8×C53C2318yes—
218C4×Q8×C53C23116yes—
219C4×D4×C53C2318yes—
220#117×C53C23116yes—
221C2×C4⋊C4×C53C2311yescharacteristic
222C2×C4⋊C4×C53C2312yes—
223C2×C4⋊C4×C53C2311yescharacteristic
224C2×C4⋊C4×C53C2314yes—
225C2×C4⋊C4×C53C2312yes—
226C2×C4⋊C4×C53C2312yes—
227C2×C22⋊C4×C53C2314yes—
228C2×C22⋊C4×C53C2312yes—
229C2×C22⋊C4×C53C2314yes—
230C2×C42×C53C2314yes—
231C2×C42×C53C2311yescharacteristic
232C2×C42×C53C2312yes—
233C24×C53C2412yes—
234C23×D53C2411yescharacteristic
235C2×Q8×C53—24no—
236C2×Q8×C53—28no—
237C2×Q8×C53C2414yes—
238C2×Q8×C53C2418yes—
239C2×D4×C53—24no—
240C2×D4×C53C2414yes—
241C22×C4×C53—28no—
242C22×C4×C53C2412yes—
243C22×C4×C53C2412yes—
244C22×C4×C53C2411yescharacteristic
245C22×C4×C53C2414yes—
246C22×C4×C53C2412yes—
247C22×C4×C53C2418yes—
248C22×C4×C53C2411yescharacteristic
249C22×C4×C53C2411yescharacteristic
250C2×C22⋊D53—28no—
251C2×C22⋊D53C2418yes—
252C22×Dic53—216no—
253C22×Dic53C2411yescharacteristic
254C22×Dic53C2411yescharacteristic
255C22×Dic53C2412yes—
256C22×Dic53C2412yes—
257C22×Dic53C2414yes—
258C22×Dic53C2412yes—
259C22×Dic53C2411yescharacteristic
260C22×Dic53C24116yes—
261C22×Dic53C2412yes—
262Q8×D53—232no—
263C2×C4×D53—28no—
264C2×C4×D53—24no—
265C2×C4×D53—24no—
266C2×C4×D53—24no—
267C2×C4×D53—28no—
268C2×C4×D53C2414yes—
269C2×C4×D53C2418yes—
270C2×C4×D53C2414yes—
271C2×C4×D53C2418yes—
272C2×C4×D53C2414yes—
273C2×Dic106—28no—
274C2×Dic106—24no—
275C2×Dic106—28no—
276C2×Dic106—216no—
277C2×Dic106—264no—
278C2×Dic106#4118yes—
279C2×Dic106C2418yes—
280C2×Dic106C2418yes—
281C2×Dic106C2414yes—
282C2×Dic106C24116yes—
283C2×Dic106C2414yes—
284C4⋊C4×C53C2414yes—
285C4⋊C4×C53C2418yes—
286C4⋊C4×C53C2414yes—
287C4⋊C4×C53C24116yes—
288C4⋊C4×C53C2418yes—
289C4⋊C4×C53C2418yes—
290C22⋊C4×C53C24116yes—
291C22⋊C4×C53C2418yes—
292C22⋊C4×C53C24116yes—
293C42×C53C24116yes—
294C42×C53C2414yes—
295C42×C53C2418yes—
296C22⋊Dic53C2418yes—
297C22⋊Dic53C2418yes—
298C22⋊Dic53C2418yes—
299C22⋊Dic53C24116yes—
300#11719921C2418yes—
301#11719921C24116yes—
302C4⋊Dic53C2414yes—
303C4⋊Dic53C2418yes—
304C4⋊Dic53C2418yes—
305C4⋊Dic53C2418yes—
306C4⋊Dic53C2418yes—
307C4⋊Dic53C2418yes—
308C4⋊Dic53C2414yes—
309C4⋊Dic53C24116yes—
310C4⋊Dic53C24116yes—
311#11719919C2418yes—
312#11719919C2418yes—
313#11719919C2418yes—
314#11719919C24116yes—
315#11719919C24116yes—
316#11719919C24116yes—
317#11719919C24116yes—
318#11719919C24116yes—
319#11719919C24116yes—
320#11719919C2418yes—
321#11719919C24116yes—
322#11719919C2418yes—
323C4×Dic53C2418yes—
324C4×Dic53C2414yes—
325C4×Dic53C2418yes—
326C4×Dic53C2414yes—
327C4×Dic53C2418yes—
328C4×Dic53C2414yes—
329C4×Dic53C24116yes—
330C4×Dic53C24116yes—
331C4×Dic53C24116yes—
332C4×Dic53C2418yes—
333C23×C53—24no—
334C23×C53—24no—
335C23×C53—24no—
336C23×C53C2514yes—
337C23×C53C2511yescharacteristic
338C22×D53—22no—
339C22×D53—22no—
340C22×D532−1+414yes—
341C22×D53C2512yes—
342Q8×C53—28no—
343Q8×C53—216no—
344D4×C53—28no—
345C2×C4×C53—24no—
346C2×C4×C53—24no—
347C2×C4×C53—24no—
348C2×C4×C53—22no—
349C2×C4×C53—28no—
350C2×C4×C53—216no—
351C2×C4×C53C2×#4114yes—
352C2×C4×C532−1+414yes—
353C2×C4×C53C2514yes—
354C2×C4×C53C2514yes—
355C2×C4×C53C2514yes—
356C2×C4×C53C2512yes—
357C2×C4×C53C2518yes—
358C2×C4×C53C2512yes—
359C2×C4×C53C2512yes—
360C22⋊D53—216no—
361C2×Dic53—22no—
362C2×Dic53—28no—
363C2×Dic53—24no—
364C2×Dic53—22no—
365C2×Dic53—24no—
366C2×Dic53—22no—
367C2×Dic53—24no—
368C2×Dic53—232no—
369C2×Dic53C2×#4118yes—
370C2×Dic53C2512yes—
371C2×Dic53C2518yes—
372C2×Dic53C2514yes—
373C2×Dic53C2512yes—
374C2×Dic53C2512yes—
375C2×Dic53C2514yes—
376C2×Dic53C2514yes—
377C2×Dic53C2514yes—
378C4×D53—216no—
379C4×D53—28no—
380C4×D53—28no—
381C4×D53—28no—
382C4×D53—216no—
383Dic106—216no—
384Dic106—28no—
385Dic106—232no—
386Dic106—216no—
387Dic106C2×#41116yes—
388C2×#3523—531nomaximal, Sylow
389C22×C53—24no—
390C22×C53—24no—
391C22×C53—24no—
392C22×C53—48no—
393C22×C53C22×#4112yes—
394C22×C53C2×2−1+412yes—
395C22×C53C2×2−1+412yes—
396C22×C53C2611yescharacteristic
397C2×D53—22no—
398C2×D53—22no—
399C2×D53—28no—
400C2×D53C2×2−1+414yes—
401C4×C53—24no—
402C4×C53—24no—
403C4×C53—24no—
404C4×C53—22no—
405C4×C53—28no—
406C4×C53C22×#4114yes—
407C4×C53C2×2−1+414yes—
408Dic53—22no—
409Dic53—28no—
410Dic53—24no—
411Dic53—22no—
412Dic53—24no—
413Dic53—22no—
414Dic53—24no—
415Dic53C22×#4118yes—
416#3523—5332no—
417C2×#557—531no—
418C2×#557—532no—
419C2×#557—531no—
420C2×#556—532no—
421C2×#556D5311yescharacteristic, complemented
422C2×#552—534no—
423C2×#552—532no—
424C2×D4×Q8—532no—
425C2×D4×Q8—531no—
426C2×#541—534no—
427C2×#541—532no—
428C2×#533—531no—
429C2×#533—532no—
430C2×#529—532no—
431C2×#529—531no—
432C2×#519—532no—
433C22×C4×Q8—531no—
434C2×C53—44no—
435C2×C53#352314yescomplemented
436C2×C53C23×#4111yescharacteristic
437C2×C53C22×2−1+411yescharacteristic
438C2×C53C22×2−1+411yescharacteristic
439D53—24no—
440C23×Q8—531no—
441C23×Q8—532no—
442#557—5316no—
443#557—5332no—
444#557—5316no—
445#556—5332no—
446#556C2×D53116yescomplemented
447#552—5364no—
448#552—5332no—
449D4×Q8—5332no—
450D4×Q8—5316no—
451#541—5364no—
452#541—5332no—
453#533—5316no—
454#533—5332no—
455C2×C4⋊Q8—532no—
456C2×C4⋊Q8—532no—
457C2×C4⋊Q8—532no—
458C2×C4⋊Q8—534no—
459C2×C4⋊Q8—531no—
460C2×C4⋊Q8C2×D5311yescharacteristic
461#529—5332no—
462#529—5316no—
463C2×#126—534no—
464C2×#126—532no—
465C2×#126—534no—
466C2×#126—534no—
467C2×#126C2×D5314yes—
468C2×#125—531no—
469C2×#125—534no—
470C2×#125—532no—
471C2×#125—534no—
472C2×#125—534no—
473C2×#125—534no—
474C2×#125—532no—
475C2×#125—532no—
476C2×#125—534no—
477C2×#124—531no—
478C2×#124C2×D5312yes—
479C2×#123—532no—
480C2×#123—534no—
481C2×C22⋊Q8—532no—
482C2×C22⋊Q8—532no—
483C2×C22⋊Q8—531no—
484C2×C22⋊Q8—534no—
485C2×C22⋊Q8—532no—
486C2×C22⋊Q8—534no—
487C2×C22⋊Q8—534no—
488C2×C22⋊Q8C2×D5312yes—
489C2×#121—531no—
490#519—5332no—
491C2×C4×Q8—531no—
492C2×C4×Q8—532no—
493C2×C4×Q8—532no—
494C2×C4×Q8—5316no—
495C2×C4×Q8—531no—
496C2×C4×Q8—532no—
497C2×C4×Q8—532no—
498C2×C4×Q8—532no—
499C2×C4×Q8—532no—
500C2×C4×Q8—531no—
501C2×C4×Q8—532no—
502C2×C4×Q8—534no—
503C2×C4×Q8—534no—
504C2×C4×Q8—531no—
505C2×C4×Q8—532no—
506C2×C4×Q8C2×D5311yescharacteristic
507C2×C4×Q8C2×D5312yes—
508C2×C4×D4—532no—
509C2×C4×D4—532no—
510C2×C4×D4—534no—
511C2×C4×D4C2×D5311yescharacteristic
512C2×#117—532no—
513C2×#117—532no—
514C2×#117—534no—
515C2×#117—534no—
516C2×#117—534no—
517C2×#117C2×D5312yes—
518C22×C4⋊C4—532no—
519C22×C4⋊C4—531no—
520C22×C42—532no—
521C22×C42—531no—
522C53C2×#352311yescharacteristic, complemented, Sylow
523C22×Q8—538no—
524C22×Q8—531no—
525C22×Q8—531no—
526C22×Q8—532no—
527C22×Q8—534no—
528C22×Q8—532no—
529C22×Q8—5316no—
530C22×Q8—10616no—
531C22×Q8—1068no—
532C22×Q8C22×D5312yes—
533C22×Q8C22×D5311yescharacteristic
534C22×D4—532no—
535C22×D4C22×D5311yescharacteristic
536C23×C4—534no—
537C23×C4—531no—
538C23×C4—532no—
539C23×C4—532no—
540C23×C4—531no—
541C23×C4—531no—
542C23×C4C22×D5312yes—
543C4⋊Q8—5316no—
544C4⋊Q8—5316no—
545C4⋊Q8—5316no—
546C4⋊Q8—5332no—
547C4⋊Q8—538no—
548C4⋊Q8C22×D5318yes—
549#126—5332no—
550#126—5316no—
551#126—5332no—
552#126—5332no—
553#126C22×D53132yes—
554#125—538no—
555#125—5332no—
556#125—5316no—
557#125—5332no—
558#125—5332no—
559#125—5332no—
560#125—5316no—
561#125—5316no—
562#125—5332no—
563#124—538no—
564#124C22×D53116yes—
565#123—5316no—
566#123—5332no—
567C22⋊Q8—5316no—
568C22⋊Q8—5316no—
569C22⋊Q8—538no—
570C22⋊Q8—5332no—
571C22⋊Q8—5316no—
572C22⋊Q8—5332no—
573C22⋊Q8—5332no—
574C22⋊Q8C22×D53116yes—
575#121—538no—
576C4×Q8—538no—
577C4×Q8—5316no—
578C4×Q8—5316no—
579C4×Q8—538no—
580C4×Q8—5316no—
581C4×Q8—5316no—
582C4×Q8—5316no—
583C4×Q8—5316no—
584C4×Q8—538no—
585C4×Q8—5316no—
586C4×Q8—5332no—
587C4×Q8—5332no—
588C4×Q8—538no—
589C4×Q8—5316no—
590C4×Q8C22×D5318yes—
591C4×Q8C22×D53116yes—
592C4×D4—5316no—
593C4×D4—5316no—
594C4×D4—5332no—
595C4×D4C22×D5318yes—
596#117—5316no—
597#117—5316no—
598#117—5332no—
599#117—5332no—
600#117—5332no—
601#117C22×D53116yes—
602C2×C4⋊C4—532no—
603C2×C4⋊C4—532no—
604C2×C4⋊C4—531no—
605C2×C4⋊C4—532no—
606C2×C4⋊C4—532no—
607C2×C4⋊C4—534no—
608C2×C4⋊C4—534no—
609C2×C4⋊C4—532no—
610C2×C4⋊C4—534no—
611C2×C4⋊C4—532no—
612C2×C4⋊C4—534no—
613C2×C4⋊C4—532no—
614C2×C4⋊C4—534no—
615C2×C4⋊C4—532no—
616C2×C4⋊C4—534no—
617C2×C4⋊C4—532no—
618C2×C4⋊C4—531no—
619C2×C4⋊C4—534no—
620C2×C4⋊C4—534no—
621C2×C4⋊C4—532no—
622C2×C4⋊C4—534no—
623C2×C4⋊C4—5316no—
624C2×C4⋊C4—538no—
625C2×C4⋊C4C22×D5311yescharacteristic
626C2×C4⋊C4C22×D5312yes—
627C2×C4⋊C4C22×D5312yes—
628C2×C4⋊C4C22×D5312yes—
629C2×C4⋊C4C22×D5311yescharacteristic
630C2×C4⋊C4C22×D5314yes—
631C2×C22⋊C4—532no—
632C2×C22⋊C4—532no—
633C2×C22⋊C4—534no—
634C2×C22⋊C4—532no—
635C2×C22⋊C4—532no—
636C2×C22⋊C4—534no—
637C2×C22⋊C4C22×D5314yes—
638C2×C22⋊C4C22×D5314yes—
639C2×C22⋊C4C22×D5312yes—
640C2×C42—532no—
641C2×C42—531no—
642C2×C42—534no—
643C2×C42—534no—
644C2×C42—534no—
645C2×C42—532no—
646C2×C42—532no—
647C2×C42—531no—
648C2×C42—532no—
649C2×C42—531no—
650C2×C42—5316no—
651C2×C42—538no—
652C2×C42C22×D5314yes—
653C2×C42C22×D5311yescharacteristic
654C2×C42C22×D5312yes—
655C24—531no—
656C24C23×D5312yes—
657C2×Q8—24no—
658C2×Q8—28no—
659C2×Q8—538no—
660C2×Q8—534no—
661C2×Q8—534no—
662C2×Q8—538no—
663C2×Q8—5316no—
664C2×Q8—538no—
665C2×Q8—10616no—
666C2×Q8—1068no—
667C2×Q8—10664no—
668C2×Q8—10632no—
669C2×Q8—1068no—
670C2×Q8—1064no—
671C2×Q8C23×D5318yes—
672C2×Q8C23×D5314yes—
673C2×D4—24no—
674C2×D4—538no—
675C2×D4—1068no—
676C2×D4C23×D5314yes—
677C22×C4—28no—
678C22×C4—532no—
679C22×C4—5316no—
680C22×C4—531no—
681C22×C4—531no—
682C22×C4—532no—
683C22×C4—532no—
684C22×C4—532no—
685C22×C4—534no—
686C22×C4—531no—
687C22×C4—534no—
688C22×C4—534no—
689C22×C4—538no—
690C22×C4—538no—
691C22×C4—534no—
692C22×C4—1068no—
693C22×C4—1068no—
694C22×C4—1064no—
695C22×C4—10616no—
696C22×C4—1064no—
697C22×C4—1064no—
698C22×C4C23×D5318yes—
699C22×C4C23×D5312yes—
700C22×C4C23×D5314yes—
701C22×C4C23×D5311yescharacteristic
702C22×C4C23×D5312yes—
703C22×C4C23×D5312yes—
704C22×C4C23×D5311yescharacteristic
705C22×C4C23×D5311yescharacteristic
706C4⋊C4—538no—
707C4⋊C4—538no—
708C4⋊C4—534no—
709C4⋊C4—538no—
710C4⋊C4—538no—
711C4⋊C4—5316no—
712C4⋊C4—5316no—
713C4⋊C4—538no—
714C4⋊C4—5316no—
715C4⋊C4—538no—
716C4⋊C4—5316no—
717C4⋊C4—538no—
718C4⋊C4—5316no—
719C4⋊C4—538no—
720C4⋊C4—5316no—
721C4⋊C4—538no—
722C4⋊C4—534no—
723C4⋊C4—5316no—
724C4⋊C4—5316no—
725C4⋊C4—538no—
726C4⋊C4—5316no—
727C4⋊C4C23×D5314yes—
728C4⋊C4C23×D5318yes—
729C4⋊C4C23×D5318yes—
730C4⋊C4C23×D5318yes—
731C4⋊C4C23×D5314yes—
732C4⋊C4C23×D53116yes—
733C22⋊C4—538no—
734C22⋊C4—538no—
735C22⋊C4—5316no—
736C22⋊C4—538no—
737C22⋊C4—538no—
738C22⋊C4—5316no—
739C22⋊C4C23×D53116yes—
740C22⋊C4C23×D53116yes—
741C22⋊C4C23×D5318yes—
742C42—538no—
743C42—534no—
744C42—538no—
745C42—534no—
746C42—538no—
747C42—534no—
748C42—5316no—
749C42—5316no—
750C42—5316no—
751C42—538no—
752C42C23×D5314yes—
753C42C23×D5318yes—
754C42C23×D53116yes—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—534no—
759C23—532no—
760C23—1062no—
761C23—1062no—
762C23C24×D5314yes—
763C23C24×D5311yescharacteristic
764Q8—28no—
765Q8—216no—
766Q8—5316no—
767Q8—10632no—
768Q8—10616no—
769Q8—10616no—
770Q8—1068no—
771D4—28no—
772D4—10616no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—28no—
778C2×C4—216no—
779C2×C4—538no—
780C2×C4—534no—
781C2×C4—532no—
782C2×C4—532no—
783C2×C4—534no—
784C2×C4—534no—
785C2×C4—534no—
786C2×C4—532no—
787C2×C4—538no—
788C2×C4—10616no—
789C2×C4—10616no—
790C2×C4—1068no—
791C2×C4—10632no—
792C2×C4—1062no—
793C2×C4—1068no—
794C2×C4—1062no—
795C2×C4—1064no—
796C2×C4—1064no—
797C2×C4—1062no—
798C2×C4—1064no—
799C2×C4—1068no—
800C2×C4—1068no—
801C2×C4#41×D5314yes—
802C2×C4#1313326414yes—
803C2×C4C24×D5314yes—
804C2×C4C24×D5318yes—
805C2×C4C24×D5312yes—
806C2×C4C24×D5314yes—
807C2×C4C24×D5314yes—
808C2×C4C24×D5312yes—
809C2×C4C24×D5312yes—
810C22—24no—
811C22—24no—
812C22—24no—
813C22—48no—
814C22—534no—
815C22—1068no—
816C22—1062no—
817C22—1062no—
818C22C2×#41×D5312yes—
819C222−1+4×D5312yes—
820C22C2×#1313326412yes—
821C22C25×D5311yescharacteristic
822C4—24no—
823C4—24no—
824C4—24no—
825C4—22no—
826C4—28no—
827C4—538no—
828C4—1068no—
829C4—1062no—
830C4—1062no—
831C4—1064no—
832C4—1064no—
833C4—1062no—
834C4—1064no—
835C4C2×#41×D5314yes—
836C4C2×#1313326414yes—
837C2—44no—
838C2—1064no—
839C2#2028881014yesdirect product factor
840C2C22×#41×D5311yescharacteristic
841C2C2×2−1+4×D5311yescharacteristic
842C2C22×#1313326411yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#556C2
socleC23×C53C25
prime radicalC2×#13133188C22
hypercenterC2×#556D53
hypocenterC53C2×#3523
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #20288810C2direct (N × H)
2. C2×#16811351C2semidirect
3. C2×#16811349C2semidirect
4. C2×#16811348C2semidirect
5. C2×#16811342C2semidirect
6. C2×#16811312C2semidirect
7. C2×#16811309C2semidirect
8. C2×D4×Dic106C2semidirect
9. C2×#16811286C2semidirect
10. C2×#16811233C2semidirect
11. C2×#16811230C2semidirect
12. C2×#16811178C2semidirect
13. C2×#16811177C2semidirect
16. C2×#16811100C2semidirect
17. C2×C4×Q8×D53C2semidirect
18. C2×C53×#556C2semidirect
21. #16811351C22semidirect
22. #16811349C22semidirect
23. #16811348C22semidirect
24. #16811342C22semidirect
25. #16811312C22semidirect
26. #16811309C22semidirect
27. D4×Dic106C22semidirect
28. #16811286C22semidirect
29. #16811233C22semidirect
30. #16811230C22semidirect
31. #16811178C22semidirect
32. #16811177C22semidirect
64. #16811100C22semidirect
79. C4×Q8×D53C22semidirect
92. C53×#556C22semidirect
421. C2×#556D53semidirect
435. C2×C53#3523semidirect
446. #556C2×D53semidirect
522. C53C2×#3523semidirect
839. C2#20288810direct (N × H)

Maximal subgroups

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

subgroupindex
#202888102
C2×#168113512
C2×#168113492
C2×#168113482
C2×#168113422
C2×#168113122
C2×#168113092
C2×D4×Dic1062
C2×#168112862
C2×#168112332
C2×#168112302
C2×#168111782
C2×#168111772
C2×#168111552
C2×#168111522
C2×#168111002
C2×C4×Q8×D532
C2×C53×#5562
C2×#352353