Finite Group Databasebeta

← C2×#20288692 #28292209

Subgroups — C2×#20288692 #28292209

Order 13568.

7142 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288692C2132yesmaximal, direct product factor
2C2×#16811333C211yesmaximal, characteristic, complemented
3C2×#16811333C211yesmaximal, characteristic, complemented
4C2×#16811326C212yesmaximal, complemented
5C2×#16811314C212yesmaximal, complemented
6C2×#16811314C212yesmaximal, complemented
7C2×#16811305C214yesmaximal, complemented
8C2×#16811276C211yesmaximal, characteristic, complemented
9C2×#16811276C212yesmaximal, complemented
10C2×#16811234C212yesmaximal, complemented
11C2×#16811221C214yesmaximal, complemented
12C2×#16811178C211yesmaximal, characteristic, complemented
13C2×#16811160C212yesmaximal, complemented
14C2×#16811160C211yesmaximal, characteristic, complemented
15C2×#125×D53C212yesmaximal, complemented
16C2×#16811105C212yesmaximal, complemented
17C2×C4×#11719949C211yesmaximal, characteristic, complemented
18C2×C53×#557C211yesmaximal, characteristic, complemented
19C22×#11719949C2211yescharacteristic
20C22×#11719949C2212yes—
21#16811333C22116yescomplemented
22#16811333C22116yescomplemented
23#16811326C22132yescomplemented
24#16811314C22132yescomplemented
25#16811314C22132yescomplemented
26#16811305C22164yescomplemented
27#16811276C22116yescomplemented
28#16811276C22132yescomplemented
29#16811234C22132yescomplemented
30#16811221C22164yescomplemented
31#16811178C22116yescomplemented
32C2×#13133217C2211yescharacteristic
33#16811160C22132yescomplemented
34#16811160C22116yescomplemented
35C2×#13133212C2214yes—
36C2×#13133212C2214yes—
37C2×#13133212C2212yes—
38C2×#13133211C2214yes—
39C2×#13133209C2212yes—
40C2×#13133209C2212yes—
41C2×#13133208C2212yes—
42C2×#13133208C2211yescharacteristic
43C2×#13133207C2214yes—
44C2×#13133207C2214yes—
45C2×#13133207C2214yes—
46#125×D53C22132yescomplemented
47C2×#13133206C2211yescharacteristic
48C2×#13133202C2212yes—
49C2×#13133202C2214yes—
50C2×#13133202C2214yes—
51C2×#13133202C2214yes—
52C2×#13133202C2214yes—
53C2×#13133197C2212yes—
54C2×#13133195C2214yes—
55C2×#13133195C2214yes—
56C2×#13133193C2212yes—
57C2×#13133193C2212yes—
58C2×#13133193C2212yes—
59C2×#13133193C2211yescharacteristic
60C2×#13133193C2212yes—
61C2×#13133192C2214yes—
62C2×#13133192C2212yes—
63C2×#13133192C2211yescharacteristic
64#16811105C22132yescomplemented
65C4×#11719949C22116yescomplemented
66C2×Q8×Dic53C2212yes—
67C2×Q8×Dic53C2211yescharacteristic
68C2×#13133182C2212yes—
69C2×C4×D212C2214yes—
70C2×C4×D212C2211yescharacteristic
71C2×C4×D212C2212yes—
72C2×C4×D212C2212yes—
73C2×C4×D212C2212yes—
74C2×C4×D212C2211yescharacteristic
75C2×C4×D212C2212yes—
76C2×#13133179C2212yes—
77C2×#13133179C2211yescharacteristic
78C2×#13133179C2214yes—
79C2×#13133175C2212yes—
80C2×#13133175C2212yes—
81C2×#13133175C2211yescharacteristic
82C2×#13133174C2212yes—
83C2×#13133174C2214yes—
84C2×#13133174C2214yes—
85C2×C4⋊C4×D53C2214yes—
86C2×C4⋊C4×D53C2212yes—
87C2×C4⋊C4×D53C2214yes—
88C2×C4⋊C4×D53C2212yes—
89C2×C4⋊C4×D53C2212yes—
90C2×C42×D53C2211yescharacteristic
91C2×C42×D53C2212yes—
92C53×#557C22116yescomplemented
93C2×C4⋊Q8×C53C2211yescharacteristic
94C2×C4⋊Q8×C53C2212yes—
95C2×#125×C53C2214yes—
96C2×#125×C53C2212yes—
97C2×C4×Q8×C53C2211yescharacteristic
98C2×C4×Q8×C53C2212yes—
99C2×C4×Q8×C53C2212yes—
100C2×C4×Q8×C53C2211yescharacteristic
101C2×#11719949—28no—
102C2×#11719949—216no—
103C2×#11719949C2318yes—
104C2×#11719949C23116yes—
105C22×Dic106C2312yes—
106C22×D212C2312yes—
107C22×D212C2314yes—
108C22×D212C2311yescharacteristic
109C22×D212C2312yes—
110C22×D212C2311yescharacteristic
111C22×C4×D53C2312yes—
112C22×C4×D53C2312yes—
113C22×C4×D53C2311yescharacteristic
114C22×C4×D53C2311yescharacteristic
115C22×C4×D53C2314yes—
116C22×C4×D53C2312yes—
117C22×C4×D53C2312yes—
118C22×C4×D53C2311yescharacteristic
119C22×C4×D53C2314yes—
120C22×C4×D53C2314yes—
121#13133217C2318yes—
122#13133212C23116yes—
123#13133212C23132yes—
124#13133212C23132yes—
125#13133211C23132yes—
126#13133209C23116yes—
127#13133209C23116yes—
128#13133208C2318yes—
129#13133208C23116yes—
130#13133207C23132yes—
131#13133207C23132yes—
132#13133207C23132yes—
133#13133206C2318yes—
134#13133202C23132yes—
135#13133202C23132yes—
136#13133202C23132yes—
137#13133202C23132yes—
138#13133202C23116yes—
139#13133197C23116yes—
140#13133195C23132yes—
141#13133195C23132yes—
142#13133193C23116yes—
143#13133193C23116yes—
144#13133193C23116yes—
145#13133193C2318yes—
146#13133193C23116yes—
147#13133192C23116yes—
148#13133192C23132yes—
149#13133192C2318yes—
150Q8×Dic53C2318yes—
151Q8×Dic53C23116yes—
152#13133182C23116yes—
153C4×D212C23116yes—
154C4×D212C2318yes—
155C4×D212C23116yes—
156C4×D212C2318yes—
157C4×D212C23116yes—
158C4×D212C23116yes—
159C4×D212C23132yes—
160#13133179C23132yes—
161#13133179C2318yes—
162#13133179C23116yes—
163#13133175C23116yes—
164#13133175C2318yes—
165#13133175C23116yes—
166#13133174C23132yes—
167#13133174C23132yes—
168#13133174C23116yes—
169C2×C4⋊Dic53C2311yescharacteristic
170C2×C4⋊Dic53C2312yes—
171C2×C4⋊Dic53C2312yes—
172C2×C4⋊Dic53C2312yes—
173C2×C4⋊Dic53C2314yes—
174C2×C4⋊Dic53C2311yescharacteristic
175C2×C4⋊Dic53C2312yes—
176C2×#11719919C2314yes—
177C2×#11719919C2312yes—
178C2×#11719919C2314yes—
179C2×#11719919C2314yes—
180C2×#11719919C2314yes—
181C2×#11719919C2314yes—
182C2×#11719919C2312yes—
183C2×#11719919C2314yes—
184C4⋊C4×D53C23132yes—
185C4⋊C4×D53C23116yes—
186C4⋊C4×D53C23116yes—
187C4⋊C4×D53C23116yes—
188C4⋊C4×D53C23132yes—
189C2×#11719921C2312yes—
190C2×#11719921C2312yes—
191C2×#11719921C2312yes—
192C2×#11719921C2314yes—
193C2×#11719921C2312yes—
194C2×#11719921C2314yes—
195C2×#11719921C2312yes—
196C2×#11719921C2312yes—
197C2×#11719921C2314yes—
198C2×#11719921C2314yes—
199C2×#11719921C2312yes—
200C2×#11719921C2312yes—
201C2×C4×Dic53C2311yescharacteristic
202C2×C4×Dic53C2312yes—
203C2×C4×Dic53C2311yescharacteristic
204C2×C4×Dic53C2311yescharacteristic
205C2×C4×Dic53C2312yes—
206C2×C4×Dic53C2314yes—
207C42×D53C23116yes—
208C42×D53C2318yes—
209C22×Q8×C53C2311yescharacteristic
210C22×Q8×C53C2311yescharacteristic
211C22×Q8×C53C2312yes—
212C4⋊Q8×C53C2318yes—
213C4⋊Q8×C53C23116yes—
214#125×C53C23132yes—
215#125×C53C23116yes—
216C4×Q8×C53C23116yes—
217C4×Q8×C53C23116yes—
218C4×Q8×C53C2318yes—
219C4×Q8×C53C2318yes—
220C2×C4⋊C4×C53C2311yescharacteristic
221C2×C4⋊C4×C53C2311yescharacteristic
222C2×C4⋊C4×C53C2314yes—
223C2×C4⋊C4×C53C2312yes—
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×D53C2411yescharacteristic
234C23×D53C2412yes—
235C23×D53C2412yes—
236C2×Q8×C53—24no—
237C2×Q8×C53—28no—
238C2×Q8×C53—24no—
239C2×Q8×C53C2414yes—
240C2×Q8×C53C2418yes—
241C2×Q8×C53C2414yes—
242C22×C4×C53C2412yes—
243C22×C4×C53C2412yes—
244C22×C4×C53C2411yescharacteristic
245C22×C4×C53C2412yes—
246C22×C4×C53C2412yes—
247C22×C4×C53C2414yes—
248C22×C4×C53C2411yescharacteristic
249C22×C4×C53C2411yescharacteristic
250C22×Dic53C2411yescharacteristic
251C22×Dic53C2411yescharacteristic
252C22×Dic53C2411yescharacteristic
253C22×Dic53C2412yes—
254C22×Dic53C2414yes—
255C22×Dic53C2412yes—
256#11719949—232no—
257#11719949—264no—
258C2×D212—28no—
259C2×D212—216no—
260C2×D212—24no—
261C2×D212—44no—
262C2×D212#4118yes—
263C2×D212C24116yes—
264C2×D212C2418yes—
265C2×D212C2414yes—
266C2×D212C2418yes—
267C2×D212C2414yes—
268C2×C4×D53—28no—
269C2×C4×D53—216no—
270C2×C4×D53—24no—
271C2×C4×D53—28no—
272C2×C4×D53—28no—
273C2×C4×D53—24no—
274C2×C4×D53—48no—
275C2×C4×D53—48no—
276C2×C4×D53—42no—
277C2×C4×D53—44no—
278C2×C4×D53C2418yes—
279C2×C4×D53C2418yes—
280C2×C4×D53C2414yes—
281C2×C4×D53C2414yes—
282C2×C4×D53C24116yes—
283C2×C4×D53C2418yes—
284C2×C4×D53C2418yes—
285C2×C4×D53C2414yes—
286C2×C4×D53C24116yes—
287C2×C4×D53C24116yes—
288C2×Dic106—44no—
289C2×Dic106C2418yes—
290C4⋊C4×C53C2414yes—
291C4⋊C4×C53C2414yes—
292C4⋊C4×C53C24116yes—
293C4⋊C4×C53C2418yes—
294C4⋊C4×C53C2418yes—
295C4⋊C4×C53C2418yes—
296C4⋊C4×C53C24116yes—
297C4⋊C4×C53C24116yes—
298C4⋊C4×C53C2418yes—
299C42×C53C2418yes—
300C42×C53C24116yes—
301C42×C53C2414yes—
302C42×C53C2418yes—
303#11719921C2418yes—
304#11719921C2418yes—
305#11719921C2418yes—
306#11719921C24116yes—
307#11719921C2418yes—
308#11719921C24116yes—
309#11719921C2418yes—
310#11719921C2418yes—
311#11719921C24116yes—
312#11719921C24116yes—
313#11719921C2418yes—
314#11719921C2418yes—
315C4⋊Dic53C2414yes—
316C4⋊Dic53C2418yes—
317C4⋊Dic53C2418yes—
318C4⋊Dic53C2418yes—
319C4⋊Dic53C24116yes—
320C4⋊Dic53C2414yes—
321C4⋊Dic53C2418yes—
322#11719919C24116yes—
323#11719919C2418yes—
324#11719919C24116yes—
325#11719919C24116yes—
326#11719919C24116yes—
327#11719919C24116yes—
328#11719919C2418yes—
329#11719919C24116yes—
330C4×Dic53C2414yes—
331C4×Dic53C2418yes—
332C4×Dic53C2414yes—
333C4×Dic53C2414yes—
334C4×Dic53C2418yes—
335C4×Dic53C24116yes—
336C23×C53C2511yescharacteristic
337C22×D53—24no—
338C22×D53—24no—
339C22×D53—22no—
340C22×D53—24no—
341C22×D53—22no—
342C22×D53—24no—
343C22×D53—24no—
344C22×D53—22no—
345C22×D53C2×#4118yes—
346C22×D53C2512yes—
347C22×D53C2514yes—
348C22×D53C2514yes—
349Q8×C53—28no—
350Q8×C53—216no—
351Q8×C53—28no—
352C2×C4×C53—24no—
353C2×C4×C53—28no—
354C2×C4×C53—24no—
355C2×C4×C53—22no—
356C2×C4×C53—24no—
357C2×C4×C53—24no—
358C2×C4×C53C2×#4114yes—
359C2×C4×C532−1+414yes—
360C2×C4×C53C2512yes—
361C2×C4×C53C2514yes—
362C2×C4×C53C2514yes—
363C2×C4×C53C2514yes—
364C2×C4×C53C2518yes—
365C2×C4×C53C2514yes—
366C2×C4×C53C2512yes—
367C2×C4×C53C2512yes—
368C2×Dic53—22no—
369C2×Dic53—24no—
370C2×Dic53—22no—
371C2×Dic53—24no—
372C2×Dic53—28no—
373C2×Dic53—22no—
374C2×Dic53C2518yes—
375C2×Dic53C2512yes—
376C2×Dic53C2512yes—
377C2×Dic53C2514yes—
378C2×Dic53C2512yes—
379C2×Dic53C2514yes—
380D212—232no—
381D212—216no—
382D212—28no—
383D212—48no—
384D212C2×#41116yes—
385C4×D53—216no—
386C4×D53—232no—
387C4×D53—28no—
388C4×D53—216no—
389C4×D53—216no—
390C4×D53—28no—
391C4×D53—416no—
392C4×D53—416no—
393C4×D53—44no—
394C4×D53—48no—
395Dic106—48no—
396C2×#3515—531nomaximal, Sylow
397C22×C53C22×#4112yes—
398C22×C53C2×2−1+412yes—
399C22×C53#58512yes—
400C22×C53C2611yescharacteristic
401C2×D53—24no—
402C2×D53—24no—
403C2×D53—216no—
404C2×D53—22no—
405C2×D53—24no—
406C2×D53—22no—
407C2×D53—24no—
408C2×D53—24no—
409C2×D53—22no—
410C2×D53—44no—
411C2×D53—48no—
412C2×D53C22×#4118yes—
413C4×C53—24no—
414C4×C53—28no—
415C4×C53—24no—
416C4×C53—22no—
417C4×C53—24no—
418C4×C53—24no—
419C4×C53C22×#4114yes—
420C4×C53C2×2−1+414yes—
421Dic53—22no—
422Dic53—24no—
423Dic53—22no—
424Dic53—24no—
425Dic53—28no—
426Dic53—22no—
427#3515—5332no—
428C2×#557D5311yescharacteristic, complemented
429C2×#554—531no—
430C2×#554—531no—
431C2×#553—532no—
432C2×#552—534no—
433C2×#552—532no—
434C2×#552—532no—
435C2×#547—531no—
436C2×#547—532no—
437C2×#541—532no—
438C2×#539—534no—
439C2×#533—531no—
440C2×#529—531no—
441C2×#529—532no—
442C22×#125—532no—
443C2×#520—532no—
444C2×C4×#41—531no—
445C2×C53#351514yescomplemented
446C2×C53C23×#4111yescharacteristic
447C2×C53C22×2−1+411yescharacteristic
448C2×C53C2×#58511yescharacteristic
449D53—28no—
450D53—42no—
451D53—44no—
452C22×#41—531no—
453C22×#41—532no—
454#557C2×D53116yescomplemented
455#554—5316no—
456#554—5316no—
457#553—5332no—
458#552—5364no—
459#552—5332no—
460#552—5332no—
461#547—5316no—
462#547—5332no—
463#541—5332no—
464#539—5364no—
465#533—5316no—
466C2×C4⋊Q8—531no—
467C2×C4⋊Q8C2×D5311yescharacteristic
468C2×C4⋊Q8C2×D5312yes—
469#529—5332no—
470#529—5316no—
471C2×#126—534no—
472C2×#126—532no—
473C2×#126—534no—
474C2×#126—534no—
475C2×#125—5332no—
476C2×#125—531no—
477C2×#125—532no—
478C2×#125—534no—
479C2×#125—534no—
480C2×#125—534no—
481C2×#125—532no—
482C2×#125—532no—
483C2×#125C2×D5312yes—
484C2×#125C2×D5314yes—
485C2×#124—531no—
486C2×#123—532no—
487C2×#123—534no—
488C2×#123—534no—
489C2×#123—534no—
490C2×#123—534no—
491C2×C22⋊Q8—531no—
492C2×C22⋊Q8—532no—
493C2×C22⋊Q8—532no—
494C2×C22⋊Q8—532no—
495C2×C22⋊Q8—532no—
496C2×C22⋊Q8—534no—
497C2×C22⋊Q8—534no—
498C2×C22⋊Q8—532no—
499C2×#121—532no—
500C2×#121—531no—
501C2×#121—534no—
502#520—5332no—
503C4×#41—5316no—
504C2×C4×Q8—531no—
505C2×C4×Q8—532no—
506C2×C4×Q8—532no—
507C2×C4×Q8C2×D5311yescharacteristic
508C2×C4×Q8C2×D5312yes—
509C2×C4×Q8C2×D5312yes—
510C2×C4×Q8C2×D5311yescharacteristic
511C2×C4×D4—531no—
512C2×C4×D4—532no—
513C2×C4×D4—534no—
514C2×C4×D4—531no—
515C2×C4×D4—532no—
516C2×C4×D4—534no—
517C2×C4×D4—532no—
518C2×C4×D4—532no—
519C2×C4×D4—531no—
520C2×C4×D4—532no—
521C2×#117—531no—
522C2×#117—532no—
523C2×#117—532no—
524C2×#117—532no—
525C2×#117—534no—
526C2×#117—534no—
527C22×C4⋊C4—534no—
528C22×C4⋊C4—532no—
529C22×C4⋊C4—532no—
530C22×C4⋊C4—534no—
531C22×C4⋊C4—532no—
532C22×C42—532no—
533C22×C42—531no—
534C53C2×#351511yescharacteristic, complemented, Sylow
535C2×#41—538no—
536C2×#41—5316no—
537C2×#41—1068no—
538C2×#41—10616no—
539C22×Q8—532no—
540C22×Q8C22×D5311yescharacteristic
541C22×Q8C22×D5312yes—
542C22×Q8C22×D5311yescharacteristic
543C22×D4—531no—
544C22×D4—531no—
545C22×D4—532no—
546C22×D4—534no—
547C22×D4—532no—
548C23×C4—534no—
549C23×C4—532no—
550C23×C4—532no—
551C23×C4—532no—
552C23×C4—531no—
553C23×C4—531no—
554C23×C4—534no—
555C23×C4—532no—
556C23×C4—534no—
557C23×C4—531no—
558C4⋊Q8—538no—
559C4⋊Q8C22×D5318yes—
560C4⋊Q8C22×D53116yes—
561#126—5332no—
562#126—5316no—
563#126—5332no—
564#126—5332no—
565#125—538no—
566#125—5316no—
567#125—5332no—
568#125—5332no—
569#125—5332no—
570#125—5316no—
571#125—5316no—
572#125C22×D53116yes—
573#125C22×D53132yes—
574#124—538no—
575#123—5316no—
576#123—5332no—
577#123—5332no—
578#123—5332no—
579#123—5332no—
580C22⋊Q8—538no—
581C22⋊Q8—5316no—
582C22⋊Q8—5316no—
583C22⋊Q8—5316no—
584C22⋊Q8—5316no—
585C22⋊Q8—5316no—
586C22⋊Q8—5332no—
587C22⋊Q8—5332no—
588#121—5316no—
589#121—538no—
590#121—5332no—
591C4×Q8—538no—
592C4×Q8—5316no—
593C4×Q8—5316no—
594C4×Q8C22×D5318yes—
595C4×Q8C22×D53116yes—
596C4×Q8C22×D53116yes—
597C4×Q8C22×D5318yes—
598C4×D4—538no—
599C4×D4—5316no—
600C4×D4—5332no—
601C4×D4—538no—
602C4×D4—5316no—
603C4×D4—5332no—
604C4×D4—5316no—
605C4×D4—5316no—
606C4×D4—538no—
607C4×D4—5316no—
608#117—538no—
609#117—5316no—
610#117—5316no—
611#117—5316no—
612#117—5332no—
613#117—5332no—
614C2×C4⋊C4—534no—
615C2×C4⋊C4—532no—
616C2×C4⋊C4—531no—
617C2×C4⋊C4—532no—
618C2×C4⋊C4—532no—
619C2×C4⋊C4—534no—
620C2×C4⋊C4—532no—
621C2×C4⋊C4—534no—
622C2×C4⋊C4—534no—
623C2×C4⋊C4—534no—
624C2×C4⋊C4—534no—
625C2×C4⋊C4—532no—
626C2×C4⋊C4—531no—
627C2×C4⋊C4—532no—
628C2×C4⋊C4—534no—
629C2×C4⋊C4—5332no—
630C2×C4⋊C4—5316no—
631C2×C4⋊C4—5316no—
632C2×C4⋊C4—5332no—
633C2×C4⋊C4—5316no—
634C2×C4⋊C4C22×D5311yescharacteristic
635C2×C4⋊C4C22×D5311yescharacteristic
636C2×C4⋊C4C22×D5312yes—
637C2×C4⋊C4C22×D5314yes—
638C2×C4⋊C4C22×D5314yes—
639C2×C4⋊C4C22×D5312yes—
640C2×C4⋊C4C22×D5312yes—
641C2×C4⋊C4C22×D5312yes—
642C2×C4⋊C4C22×D5314yes—
643C2×C22⋊C4—532no—
644C2×C22⋊C4—532no—
645C2×C22⋊C4—532no—
646C2×C22⋊C4—532no—
647C2×C22⋊C4—534no—
648C2×C22⋊C4—532no—
649C2×C22⋊C4—532no—
650C2×C22⋊C4—534no—
651C2×C22⋊C4—534no—
652C2×C22⋊C4—534no—
653C2×C22⋊C4—532no—
654C2×C22⋊C4—532no—
655C2×C42—532no—
656C2×C42—531no—
657C2×C42—534no—
658C2×C42—531no—
659C2×C42—532no—
660C2×C42—531no—
661C2×C42—5316no—
662C2×C42—538no—
663C2×C42C22×D5314yes—
664C2×C42C22×D5312yes—
665C2×C42C22×D5312yes—
666C2×C42C22×D5311yescharacteristic
667C24—532no—
668C24—531no—
669C24—532no—
670#41—10632no—
671#41—10664no—
672C2×Q8—24no—
673C2×Q8—28no—
674C2×Q8—24no—
675C2×Q8—538no—
676C2×Q8—2124no—
677C2×Q8C23×D5314yes—
678C2×Q8C23×D5318yes—
679C2×Q8C23×D5314yes—
680C2×D4—538no—
681C2×D4—534no—
682C2×D4—534no—
683C2×D4—538no—
684C2×D4—5316no—
685C2×D4—538no—
686C2×D4—1068no—
687C2×D4—10616no—
688C2×D4—1064no—
689C2×D4—2124no—
690C22×C4—531no—
691C22×C4—531no—
692C22×C4—531no—
693C22×C4—532no—
694C22×C4—534no—
695C22×C4—532no—
696C22×C4—538no—
697C22×C4—538no—
698C22×C4—534no—
699C22×C4—534no—
700C22×C4—5316no—
701C22×C4—538no—
702C22×C4—538no—
703C22×C4—534no—
704C22×C4—5316no—
705C22×C4—5316no—
706C22×C4—10616no—
707C22×C4—1068no—
708C22×C4—1068no—
709C22×C4—1064no—
710C22×C4—1068no—
711C22×C4—1064no—
712C22×C4—2124no—
713C22×C4—2128no—
714C22×C4—2128no—
715C22×C4—2122no—
716C22×C4C23×D5312yes—
717C22×C4C23×D5311yescharacteristic
718C22×C4C23×D5314yes—
719C22×C4C23×D5312yes—
720C22×C4C23×D5312yes—
721C22×C4C23×D5312yes—
722C22×C4C23×D5311yescharacteristic
723C22×C4C23×D5311yescharacteristic
724C4⋊C4—5316no—
725C4⋊C4—538no—
726C4⋊C4—534no—
727C4⋊C4—538no—
728C4⋊C4—538no—
729C4⋊C4—5316no—
730C4⋊C4—538no—
731C4⋊C4—5316no—
732C4⋊C4—5316no—
733C4⋊C4—5316no—
734C4⋊C4—5316no—
735C4⋊C4—538no—
736C4⋊C4—534no—
737C4⋊C4—538no—
738C4⋊C4—5316no—
739C4⋊C4C23×D5314yes—
740C4⋊C4C23×D5314yes—
741C4⋊C4C23×D5318yes—
742C4⋊C4C23×D53116yes—
743C4⋊C4C23×D53116yes—
744C4⋊C4C23×D5318yes—
745C4⋊C4C23×D5318yes—
746C4⋊C4C23×D5318yes—
747C4⋊C4C23×D53116yes—
748C22⋊C4—538no—
749C22⋊C4—538no—
750C22⋊C4—538no—
751C22⋊C4—538no—
752C22⋊C4—5316no—
753C22⋊C4—538no—
754C22⋊C4—538no—
755C22⋊C4—5316no—
756C22⋊C4—5316no—
757C22⋊C4—5316no—
758C22⋊C4—538no—
759C22⋊C4—538no—
760C42—534no—
761C42—538no—
762C42—534no—
763C42—534no—
764C42—538no—
765C42—5316no—
766C42C23×D5318yes—
767C42C23×D5314yes—
768C42C23×D53116yes—
769C42C23×D5318yes—
770C23—538no—
771C23—534no—
772C23—532no—
773C23—534no—
774C23—1064no—
775C23—1064no—
776C23—1062no—
777C23—1064no—
778C23—1062no—
779C23—1064no—
780C23—1064no—
781C23—1062no—
782C23C24×D5311yescharacteristic
783Q8—28no—
784Q8—216no—
785Q8—28no—
786Q8—2128no—
787D4—5316no—
788D4—10616no—
789D4—10632no—
790D4—1068no—
791D4—2128no—
792C2×C4—28no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—532no—
799C2×C4—532no—
800C2×C4—532no—
801C2×C4—534no—
802C2×C4—538no—
803C2×C4—534no—
804C2×C4—10616no—
805C2×C4—10632no—
806C2×C4—1062no—
807C2×C4—1064no—
808C2×C4—1062no—
809C2×C4—1064no—
810C2×C4—1062no—
811C2×C4—1068no—
812C2×C4—1068no—
813C2×C4—10616no—
814C2×C4—10616no—
815C2×C4—1068no—
816C2×C4—2128no—
817C2×C4—21216no—
818C2×C4—21216no—
819C2×C4—2124no—
820C2×C4#41×D5314yes—
821C2×C4#1313326514yes—
822C2×C4C24×D5314yes—
823C2×C4C24×D5312yes—
824C2×C4C24×D5314yes—
825C2×C4C24×D5318yes—
826C2×C4C24×D5314yes—
827C2×C4C24×D5314yes—
828C2×C4C24×D5312yes—
829C2×C4C24×D5312yes—
830C22—538no—
831C22—10616no—
832C22—1064no—
833C22—1064no—
834C22—1062no—
835C22—1064no—
836C22—1062no—
837C22—1064no—
838C22—1064no—
839C22—1062no—
840C22—2124no—
841C22—2128no—
842C22C2×#41×D5312yes—
843C22C2×#1313326512yes—
844C22#1681146012yes—
845C22C25×D5311yescharacteristic
846C4—24no—
847C4—28no—
848C4—24no—
849C4—24no—
850C4—24no—
851C4—22no—
852C4—1062no—
853C4—1064no—
854C4—1062no—
855C4—1064no—
856C4—1062no—
857C4—1068no—
858C4C2×#41×D5314yes—
859C4C2×#1313326514yes—
860C2—1068no—
861C2—2122no—
862C2—2124no—
863C2#2028869214yesdirect product factor
864C2C22×#41×D5311yescharacteristic
865C2C22×#1313326511yescharacteristic
866C2C2×#1681146011yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#557C2
socleC23×C53C25
hypercenterC2×#557D53
hypocenterC53C2×#3515
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #20288692C2direct (N × H)
2. C2×#16811333C2semidirect
3. C2×#16811333C2semidirect
4. C2×#16811326C2semidirect
5. C2×#16811314C2semidirect
6. C2×#16811314C2semidirect
7. C2×#16811305C2semidirect
8. C2×#16811276C2semidirect
9. C2×#16811276C2semidirect
10. C2×#16811234C2semidirect
11. C2×#16811221C2semidirect
12. C2×#16811178C2semidirect
13. C2×#16811160C2semidirect
14. C2×#16811160C2semidirect
15. C2×#125×D53C2semidirect
16. C2×#16811105C2semidirect
17. C2×C4×#11719949C2semidirect
18. C2×C53×#557C2semidirect
21. #16811333C22semidirect
22. #16811333C22semidirect
23. #16811326C22semidirect
24. #16811314C22semidirect
25. #16811314C22semidirect
26. #16811305C22semidirect
27. #16811276C22semidirect
28. #16811276C22semidirect
29. #16811234C22semidirect
30. #16811221C22semidirect
31. #16811178C22semidirect
33. #16811160C22semidirect
34. #16811160C22semidirect
46. #125×D53C22semidirect
64. #16811105C22semidirect
65. C4×#11719949C22semidirect
92. C53×#557C22semidirect
428. C2×#557D53semidirect
445. C2×C53#3515semidirect
454. #557C2×D53semidirect
534. C53C2×#3515semidirect
863. C2#20288692direct (N × H)

Maximal subgroups

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

subgroupindex
#202886922
C2×#168113332
C2×#168113262
C2×#168113142
C2×#168113052
C2×#168112762
C2×#168112342
C2×#168112212
C2×#168111782
C2×#168111602
C2×#125×D532
C2×#168111052
C2×C4×#117199492
C2×C53×#5572
C2×#351553