Finite Group Databasebeta

← C2×#20288333 #28291186

Subgroups — C2×#20288333 #28291186

Order 13568.

7706 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288333C2132yesmaximal, direct product factor
2C2×#16811348C211yesmaximal, characteristic, complemented
3C2×#16811347C211yesmaximal, characteristic, complemented
4C2×#16811344C212yesmaximal, complemented
5C2×#16811307C212yesmaximal, complemented
6C2×#16811305C214yesmaximal, complemented
7C2×#16811288C211yesmaximal, characteristic, complemented
8C2×#16811283C212yesmaximal, complemented
9C2×#16811276C211yesmaximal, characteristic, complemented
10C2×#16811275C212yesmaximal, complemented
11C2×#16811177C212yesmaximal, complemented
12C2×#16811160C212yesmaximal, complemented
13C2×#16811151C214yesmaximal, complemented
14C2×C4×#11719949C212yesmaximal, complemented
15C2×C4×#11719945C211yesmaximal, characteristic, complemented
16C2×C4×#11719945C211yesmaximal, characteristic, complemented
17C2×C4×Q8×D53C212yesmaximal, complemented
18C2×C53×#533C211yesmaximal, characteristic, complemented
19C22×#11719949C2212yes—
20C22×#11719945C2211yescharacteristic
21C22×#11719945C2211yescharacteristic
22C22×Q8×D53C2212yes—
23#16811348C22116yescomplemented
24#16811347C22116yescomplemented
25#16811344C22132yescomplemented
26#16811307C22132yescomplemented
27#16811305C22164yescomplemented
28#16811288C22116yescomplemented
29#16811283C22132yescomplemented
30#16811276C22116yescomplemented
31#16811275C22132yescomplemented
32#16811177C22132yescomplemented
33C2×#13133216C2212yes—
34C2×#13133215C2212yes—
35#16811160C22132yescomplemented
36#16811151C22164yescomplemented
37C2×#13133212C2214yes—
38C2×#13133212C2214yes—
39C2×#13133210C2214yes—
40C2×#13133208C2212yes—
41C2×#13133207C2214yes—
42C2×#13133207C2214yes—
43C2×#13133206C2212yes—
44C2×#13133203C2214yes—
45C2×#13133202C2214yes—
46C2×#13133202C2214yes—
47C2×#13133199C2214yes—
48C2×#13133197C2212yes—
49C2×#13133195C2214yes—
50C2×#13133195C2214yes—
51C2×#13133193C2212yes—
52C2×#13133193C2212yes—
53C2×#13133192C2212yes—
54C2×#13133190C2214yes—
55C4×#11719949C22132yescomplemented
56C4×#11719945C22116yescomplemented
57C4×#11719945C22116yescomplemented
58C2×Q8×Dic53C2212yes—
59C2×Q8×Dic53C2212yes—
60C2×C4×Dic106C2211yescharacteristic
61C2×C4×Dic106C2214yes—
62C2×C4×Dic106C2211yescharacteristic
63C2×C4×Dic106C2211yescharacteristic
64C2×C4×Dic106C2211yescharacteristic
65C2×#13133182C2214yes—
66C2×#13133182C2212yes—
67C4×Q8×D53C22132yescomplemented
68C2×C4×D212C2211yescharacteristic
69C2×C4×D212C2211yescharacteristic
70C2×C4×D212C2211yescharacteristic
71C2×C4×D212C2211yescharacteristic
72C2×C4×D212C2214yes—
73C2×#13133179C2212yes—
74C2×#13133179C2214yes—
75C2×C4×C22⋊D53C2212yes—
76C2×C4×C22⋊D53C2212yes—
77C2×C4×C22⋊D53C2212yes—
78C2×C4×C22⋊D53C2212yes—
79C2×#13133176C2211yescharacteristic
80C2×#13133176C2211yescharacteristic
81C2×#13133175C2212yes—
82C2×#13133175C2214yes—
83C2×#13133174C2214yes—
84C2×#13133174C2212yes—
85C2×#13133174C2212yes—
86C2×C4⋊C4×D53C2214yes—
87C2×C4⋊C4×D53C2212yes—
88C2×C42×D53C2212yes—
89C2×C42×D53C2212yes—
90C2×C42×D53C2214yes—
91C53×#533C22116yescomplemented
92C2×C4⋊Q8×C53C2211yescharacteristic
93C2×C4⋊Q8×C53C2211yescharacteristic
94C2×#125×C53C2212yes—
95C2×C22⋊Q8×C53C2212yes—
96C2×C22⋊Q8×C53C2212yes—
97C2×C4×Q8×C53C2212yes—
98C2×C4×Q8×C53C2212yes—
99C2×#117×C53C2212yes—
100C22×C42×C53C2211yescharacteristic
101C2×#11719949—216no—
102C2×#11719949C23116yes—
103C2×#11719945—28no—
104C2×#11719945—28no—
105C2×#11719945C2318yes—
106C2×#11719945C2318yes—
107C22×Dic106C2314yes—
108C22×Dic106C2311yescharacteristic
109C22×Dic106C2311yescharacteristic
110C2×Q8×D53—216no—
111C2×Q8×D53C23116yes—
112C22×D212C2314yes—
113C22×D212C2311yescharacteristic
114C22×D212C2311yescharacteristic
115C22×C22⋊D53C2312yes—
116C22×C22⋊D53C2312yes—
117C22×C4×D53C2312yes—
118C22×C4×D53C2312yes—
119C22×C4×D53C2314yes—
120C22×C4×D53C2312yes—
121C22×C4×D53C2314yes—
122C22×C4×D53C2312yes—
123C22×C4×D53C2312yes—
124C22×C4×D53C2312yes—
125#13133216C23116yes—
126#13133215C23116yes—
127#13133212C23132yes—
128#13133212C23132yes—
129#13133210C23132yes—
130#13133208C23116yes—
131#13133207C23132yes—
132#13133207C23132yes—
133#13133206C23116yes—
134#13133203C23132yes—
135#13133202C23132yes—
136#13133202C23132yes—
137#13133199C23132yes—
138#13133197C23116yes—
139#13133195C23132yes—
140#13133195C23132yes—
141#13133193C23116yes—
142#13133193C23116yes—
143#13133192C23116yes—
144#13133190C23132yes—
145Q8×Dic53C23116yes—
146Q8×Dic53C23116yes—
147C4×Dic106C2318yes—
148C4×Dic106C2318yes—
149C4×Dic106C23132yes—
150C4×Dic106C2318yes—
151C4×Dic106C2318yes—
152#13133182C23116yes—
153#13133182C23132yes—
154C4×D212C2318yes—
155C4×D212C2318yes—
156C4×D212C2318yes—
157C4×D212C2318yes—
158C4×D212C23132yes—
159#13133179C23116yes—
160#13133179C23132yes—
161C4×C22⋊D53C23116yes—
162C4×C22⋊D53C23116yes—
163C4×C22⋊D53C23116yes—
164C4×C22⋊D53C23116yes—
165#13133176C2318yes—
166#13133176C2318yes—
167#13133175C23132yes—
168#13133175C23116yes—
169#13133174C23116yes—
170#13133174C23116yes—
171#13133174C23132yes—
172C2×C4⋊Dic53C2311yescharacteristic
173C2×C4⋊Dic53C2314yes—
174C2×C4⋊Dic53C2311yescharacteristic
175C2×C4⋊Dic53C2314yes—
176C2×C4⋊Dic53C2311yescharacteristic
177C2×C4⋊Dic53C2311yescharacteristic
178C2×#11719919C2312yes—
179C2×#11719919C2314yes—
180C2×#11719919C2314yes—
181C2×#11719919C2312yes—
182C2×#11719919C2312yes—
183C2×#11719919C2312yes—
184C2×#11719919C2314yes—
185C2×#11719919C2314yes—
186C4⋊C4×D53C23132yes—
187C4⋊C4×D53C23116yes—
188C2×C22⋊Dic53C2312yes—
189C2×C22⋊Dic53C2312yes—
190C2×#11719921C2312yes—
191C2×#11719921C2312yes—
192C2×#11719921C2312yes—
193C2×#11719921C2312yes—
194C2×#11719921C2314yes—
195C2×#11719921C2314yes—
196C2×#11719921C2314yes—
197C2×#11719921C2314yes—
198C2×C4×Dic53C2312yes—
199C2×C4×Dic53C2312yes—
200C2×C4×Dic53C2312yes—
201C2×C4×Dic53C2312yes—
202C2×C4×Dic53C2314yes—
203C2×C4×Dic53C2312yes—
204C2×C4×Dic53C2312yes—
205C2×C4×Dic53C2314yes—
206C42×D53C23116yes—
207C42×D53C23132yes—
208C42×D53C23116yes—
209C22×Q8×C53C2312yes—
210C22×Q8×C53C2312yes—
211C23×C4×C53C2311yescharacteristic
212C23×C4×C53C2311yescharacteristic
213C23×C4×C53C2311yescharacteristic
214C4⋊Q8×C53C2318yes—
215C4⋊Q8×C53C2318yes—
216#125×C53C23116yes—
217C22⋊Q8×C53C23116yes—
218C22⋊Q8×C53C23116yes—
219C4×Q8×C53C23116yes—
220C4×Q8×C53C23116yes—
221#117×C53C23116yes—
222C2×C4⋊C4×C53C2312yes—
223C2×C4⋊C4×C53C2312yes—
224C2×C4⋊C4×C53C2314yes—
225C2×C4⋊C4×C53C2314yes—
226C2×C4⋊C4×C53C2312yes—
227C2×C4⋊C4×C53C2312yes—
228C2×C22⋊C4×C53C2314yes—
229C2×C42×C53C2311yescharacteristic
230C2×C42×C53C2311yescharacteristic
231C2×C42×C53C2311yescharacteristic
232C2×C42×C53C2311yescharacteristic
233C2×C42×C53C2318yes—
234C2×C42×C53C2314yes—
235C24×C53C2411yescharacteristic
236C23×D53C2412yes—
237C23×D53C2412yes—
238C2×Q8×C53—28no—
239C2×Q8×C53—28no—
240C2×Q8×C53C2418yes—
241C2×Q8×C53C2418yes—
242C22×C4×C53—24no—
243C22×C4×C53—24no—
244C22×C4×C53—24no—
245C22×C4×C53C2411yescharacteristic
246C22×C4×C53C2411yescharacteristic
247C22×C4×C53C2411yescharacteristic
248C22×C4×C53C2414yes—
249C22×C4×C53C2414yes—
250C22×C4×C53C2414yes—
251C22×C4×C53C2414yes—
252C22×C4×C53C2414yes—
253C22×C4×C53C2411yescharacteristic
254C22×C4×C53C2411yescharacteristic
255C22×C4×C53C2411yescharacteristic
256C2×C22⋊D53—28no—
257C2×C22⋊D53—28no—
258C2×C22⋊D53C2418yes—
259C2×C22⋊D53C2418yes—
260C22×Dic53C2412yes—
261C22×Dic53C2412yes—
262C22×Dic53C2412yes—
263C22×Dic53C2412yes—
264C22×Dic53C2412yes—
265C22×Dic53C2412yes—
266#11719949—264no—
267Q8×D53—264no—
268#11719945—232no—
269#11719945—232no—
270C2×D212—216no—
271C2×D212—24no—
272C2×D212#4118yescomplemented
273C2×D212C24116yes—
274C2×D212C2414yes—
275C2×D212C2414yes—
276C2×C4×D53—28no—
277C2×C4×D53—216no—
278C2×C4×D53—28no—
279C2×C4×D53—28no—
280C2×C4×D53—28no—
281C2×C4×D53—28no—
282C2×C4×D53—216no—
283C2×C4×D53—28no—
284C2×C4×D53C2418yes—
285C2×C4×D53C2418yes—
286C2×C4×D53C24116yes—
287C2×C4×D53C2418yes—
288C2×C4×D53C24116yes—
289C2×C4×D53C2418yes—
290C2×C4×D53C2418yes—
291C2×C4×D53C2418yes—
292C2×Dic106—24no—
293C2×Dic106—216no—
294C2×Dic106#4118yescomplemented
295C2×Dic106C24116yes—
296C2×Dic106C2414yes—
297C2×Dic106C2414yes—
298C4⋊C4×C53C2418yes—
299C4⋊C4×C53C2418yes—
300C4⋊C4×C53C24116yes—
301C4⋊C4×C53C24116yes—
302C4⋊C4×C53C2418yes—
303C4⋊C4×C53C2418yes—
304C22⋊C4×C53C24116yes—
305C42×C53C2414yes—
306C42×C53C2414yes—
307C42×C53C2414yes—
308C42×C53C2414yes—
309C42×C53C24116yes—
310C22⋊Dic53C2418yes—
311C22⋊Dic53C2418yes—
312#11719921C2418yes—
313#11719921C2418yes—
314#11719921C2418yes—
315#11719921C2418yes—
316#11719921C24116yes—
317#11719921C24116yes—
318#11719921C24116yes—
319#11719921C24116yes—
320C4⋊Dic53C2414yes—
321C4⋊Dic53C24116yes—
322C4⋊Dic53C2414yes—
323C4⋊Dic53C24116yes—
324C4⋊Dic53C2414yes—
325C4⋊Dic53C2414yes—
326#11719919C2418yes—
327#11719919C24116yes—
328#11719919C24116yes—
329#11719919C2418yes—
330#11719919C2418yes—
331#11719919C2418yes—
332#11719919C24116yes—
333#11719919C24116yes—
334C4×Dic53C2418yes—
335C4×Dic53C2418yes—
336C4×Dic53C2418yes—
337C4×Dic53C2418yes—
338C4×Dic53C24116yes—
339C4×Dic53C2418yes—
340C4×Dic53C2418yes—
341C4×Dic53C24116yes—
342C23×C53—22no—
343C23×C53—22no—
344C23×C53—22no—
345C23×C53C2512yes—
346C23×C53C2511yescharacteristic
347C22×D53—24no—
348C22×D53—24no—
349C22×D53—24no—
350C22×D53—24no—
351C22×D53—24no—
352C22×D53C2×#4118yes—
353C22×D53C2514yes—
354C22×D53C2514yes—
355Q8×C53—216no—
356Q8×C53—216no—
357C2×C4×C53—28no—
358C2×C4×C53—22no—
359C2×C4×C53—22no—
360C2×C4×C53—28no—
361C2×C4×C53—22no—
362C2×C4×C53—28no—
363C2×C4×C53—28no—
364C2×C4×C53—28no—
365C2×C4×C53C2×#4114yes—
366C2×C4×C53C2×#4114yes—
367C2×C4×C532−1+414yes—
368C2×C4×C53C2518yes—
369C2×C4×C53C2512yes—
370C2×C4×C53C2512yes—
371C2×C4×C53C2518yes—
372C2×C4×C53C2512yes—
373C2×C4×C53C2512yes—
374C2×C4×C53C2512yes—
375C2×C4×C53C2512yes—
376C22⋊D53—216no—
377C22⋊D53—216no—
378C2×Dic53—24no—
379C2×Dic53—24no—
380C2×Dic53—24no—
381C2×Dic53—24no—
382C2×Dic53—24no—
383C2×Dic53C2×#4118yes—
384C2×Dic53C2514yes—
385C2×Dic53C2514yes—
386C2×Dic53C2514yes—
387C2×Dic53C2514yes—
388C2×Dic53C2514yes—
389C2×Dic53C2514yes—
390D212—232no—
391D212—28no—
392D212C2×#41116yescomplemented
393C4×D53—216no—
394C4×D53—232no—
395C4×D53—216no—
396C4×D53—216no—
397C4×D53—216no—
398C4×D53—216no—
399C4×D53—216no—
400C4×D53—232no—
401Dic106—28no—
402Dic106—232no—
403Dic106C2×#41116yescomplemented
404C2×#3482—531nomaximal, Sylow
405C22×C53—22no—
406C22×C53—22no—
407C22×C53—22no—
408C22×C53—44no—
409C22×C53C22×#4112yes—
410C22×C53C22×#4112yes—
411C22×C53C2×2−1+412yes—
412C22×C53C2611yescharacteristic
413C2×D53—24no—
414C2×D53—24no—
415C2×D53—216no—
416C2×D53—24no—
417C2×D53—24no—
418C2×D53—24no—
419C2×D53—48no—
420C2×D53C22×#4118yes—
421C4×C53—28no—
422C4×C53—22no—
423C4×C53—22no—
424C4×C53—28no—
425C4×C53—22no—
426C4×C53C22×#4114yes—
427C4×C53C22×#4114yes—
428C4×C53C2×2−1+414yes—
429Dic53—24no—
430Dic53—24no—
431Dic53—24no—
432Dic53—24no—
433Dic53—24no—
434Dic53C22×#4118yes—
435#3482—5332no—
436C2×#557—531no—
437C2×#556—531no—
438C2×#556—532no—
439C2×#552—534no—
440C2×#552—532no—
441C2×D4×Q8—531no—
442C2×#548—532no—
443C2×#547—531no—
444C2×#547—532no—
445C2×#533—532no—
446C2×#533D5311yescharacteristic, complemented
447C2×#529—532no—
448C2×#529—534no—
449C2×C4×#41—531no—
450C2×C4×#41—531no—
451C2×C4×#41—532no—
452C22×C4×Q8—532no—
453C2×C53—42no—
454C2×C53#348214yescomplemented
455C2×C53C23×#4111yescharacteristic
456C2×C53C23×#4111yescharacteristic
457C2×C53C22×2−1+411yescharacteristic
458D53—28no—
459D53—44no—
460C22×#41—532no—
461C22×#41—531no—
462C22×#41—531no—
463C23×Q8—532no—
464#557—5316no—
465#556—5316no—
466#556—5332no—
467#552—5364no—
468#552—5332no—
469D4×Q8—5316no—
470#548—5332no—
471#547—5316no—
472#547—5332no—
473#533—5332no—
474#533C2×D53116yescomplemented
475C2×C4⋊Q8—532no—
476C2×C4⋊Q8—532no—
477C2×C4⋊Q8C2×D5311yescharacteristic
478C2×C4⋊Q8C2×D5311yescharacteristic
479#529—5332no—
480#529—5364no—
481C2×#126—534no—
482C2×#126—534no—
483C2×#126—534no—
484C2×#125—534no—
485C2×#125—532no—
486C2×#125—534no—
487C2×#125C2×D5312yes—
488C2×#124—532no—
489C2×#124—534no—
490C2×#123—534no—
491C2×#123—534no—
492C2×#123—534no—
493C2×C22⋊Q8—532no—
494C2×C22⋊Q8—532no—
495C2×C22⋊Q8—534no—
496C2×C22⋊Q8—534no—
497C2×C22⋊Q8—532no—
498C2×C22⋊Q8C2×D5312yes—
499C2×C22⋊Q8C2×D5312yes—
500C2×#121—532no—
501C2×#121—534no—
502C4×#41—5332no—
503C4×#41—5316no—
504C4×#41—5316no—
505C2×C4×Q8—532no—
506C2×C4×Q8—532no—
507C2×C4×Q8—5332no—
508C2×C4×Q8—532no—
509C2×C4×Q8—534no—
510C2×C4×Q8—531no—
511C2×C4×Q8—534no—
512C2×C4×Q8—531no—
513C2×C4×Q8—531no—
514C2×C4×Q8—531no—
515C2×C4×Q8C2×D5312yes—
516C2×C4×Q8C2×D5312yes—
517C2×C4×D4—532no—
518C2×C4×D4—532no—
519C2×C4×D4—532no—
520C2×C4×D4—532no—
521C2×C4×D4—532no—
522C2×C4×D4—534no—
523C2×C4×D4—531no—
524C2×C4×D4—534no—
525C2×C4×D4—531no—
526C2×C4×D4—531no—
527C2×C4×D4—531no—
528C2×#117—531no—
529C2×#117—531no—
530C2×#117—534no—
531C2×#117—532no—
532C2×#117—532no—
533C2×#117—532no—
534C2×#117—534no—
535C2×#117C2×D5312yes—
536C22×C4⋊C4—534no—
537C22×C4⋊C4—532no—
538C22×C42—532no—
539C22×C42—534no—
540C22×C42—532no—
541C22×C42C2×D5311yescharacteristic
542C53C2×#348211yescharacteristic, complemented, Sylow
543C2×#41—5316no—
544C2×#41—538no—
545C2×#41—538no—
546C2×#41—1068no—
547C2×#41—1068no—
548C2×#41—10616no—
549C22×Q8—5316no—
550C22×Q8—531no—
551C22×Q8—534no—
552C22×Q8—531no—
553C22×Q8—10616no—
554C22×Q8C22×D5312yes—
555C22×Q8C22×D5312yes—
556C22×D4—532no—
557C22×D4—532no—
558C22×D4—531no—
559C22×D4—534no—
560C22×D4—531no—
561C23×C4—534no—
562C23×C4—532no—
563C23×C4—534no—
564C23×C4—532no—
565C23×C4—532no—
566C23×C4—532no—
567C23×C4—532no—
568C23×C4—532no—
569C23×C4C22×D5311yescharacteristic
570C23×C4C22×D5311yescharacteristic
571C23×C4C22×D5311yescharacteristic
572C4⋊Q8—5316no—
573C4⋊Q8—5316no—
574C4⋊Q8C22×D5318yes—
575C4⋊Q8C22×D5318yes—
576#126—5332no—
577#126—5332no—
578#126—5332no—
579#125—5332no—
580#125—5316no—
581#125—5332no—
582#125C22×D53116yes—
583#124—5316no—
584#124—5332no—
585#123—5332no—
586#123—5332no—
587#123—5332no—
588C22⋊Q8—5316no—
589C22⋊Q8—5316no—
590C22⋊Q8—5332no—
591C22⋊Q8—5316no—
592C22⋊Q8—5332no—
593C22⋊Q8C22×D53116yes—
594C22⋊Q8C22×D53116yes—
595#121—5316no—
596#121—5332no—
597C4×Q8—5316no—
598C4×Q8—5316no—
599C4×Q8—5316no—
600C4×Q8—5332no—
601C4×Q8—538no—
602C4×Q8—5332no—
603C4×Q8—538no—
604C4×Q8—538no—
605C4×Q8—538no—
606C4×Q8C22×D53116yes—
607C4×Q8C22×D53116yes—
608C4×D4—5316no—
609C4×D4—5316no—
610C4×D4—5316no—
611C4×D4—5316no—
612C4×D4—5316no—
613C4×D4—5332no—
614C4×D4—538no—
615C4×D4—538no—
616C4×D4—5332no—
617C4×D4—538no—
618C4×D4—538no—
619#117—538no—
620#117—538no—
621#117—5332no—
622#117—5316no—
623#117—5316no—
624#117—5316no—
625#117—5332no—
626#117C22×D53116yes—
627C2×C4⋊C4—532no—
628C2×C4⋊C4—531no—
629C2×C4⋊C4—534no—
630C2×C4⋊C4—534no—
631C2×C4⋊C4—534no—
632C2×C4⋊C4—531no—
633C2×C4⋊C4—532no—
634C2×C4⋊C4—532no—
635C2×C4⋊C4—531no—
636C2×C4⋊C4—531no—
637C2×C4⋊C4—532no—
638C2×C4⋊C4—534no—
639C2×C4⋊C4—534no—
640C2×C4⋊C4—534no—
641C2×C4⋊C4—5332no—
642C2×C4⋊C4—5316no—
643C2×C4⋊C4C22×D5312yes—
644C2×C4⋊C4C22×D5314yes—
645C2×C4⋊C4C22×D5314yes—
646C2×C4⋊C4C22×D5312yes—
647C2×C4⋊C4C22×D5312yes—
648C2×C4⋊C4C22×D5312yes—
649C2×C22⋊C4—532no—
650C2×C22⋊C4—532no—
651C2×C22⋊C4—532no—
652C2×C22⋊C4—534no—
653C2×C22⋊C4—532no—
654C2×C22⋊C4—532no—
655C2×C22⋊C4—532no—
656C2×C22⋊C4—534no—
657C2×C22⋊C4—534no—
658C2×C22⋊C4—534no—
659C2×C22⋊C4C22×D5314yes—
660C2×C42—532no—
661C2×C42—534no—
662C2×C42—532no—
663C2×C42—532no—
664C2×C42—534no—
665C2×C42—532no—
666C2×C42—532no—
667C2×C42—532no—
668C2×C42—5332no—
669C2×C42—5316no—
670C2×C42—5316no—
671C2×C42C22×D5311yescharacteristic
672C2×C42C22×D5311yescharacteristic
673C2×C42C22×D5318yes—
674C2×C42C22×D5314yes—
675C2×C42C22×D5311yescharacteristic
676C2×C42C22×D5311yescharacteristic
677C24—532no—
678C24—532no—
679C24C23×D5311yescharacteristic
680#41—10632no—
681#41—10632no—
682#41—10664no—
683C2×Q8—28no—
684C2×Q8—28no—
685C2×Q8—538no—
686C2×Q8—534no—
687C2×Q8—5316no—
688C2×Q8—534no—
689C2×Q8—10616no—
690C2×Q8—10664no—
691C2×Q8—1064no—
692C2×Q8C23×D5318yes—
693C2×Q8C23×D5318yes—
694C2×D4—538no—
695C2×D4—538no—
696C2×D4—538no—
697C2×D4—534no—
698C2×D4—5316no—
699C2×D4—534no—
700C2×D4—10616no—
701C2×D4—1068no—
702C2×D4—1068no—
703C2×D4—1064no—
704C22×C4—24no—
705C22×C4—24no—
706C22×C4—24no—
707C22×C4—532no—
708C22×C4—532no—
709C22×C4—532no—
710C22×C4—532no—
711C22×C4—532no—
712C22×C4—532no—
713C22×C4—538no—
714C22×C4—5316no—
715C22×C4—538no—
716C22×C4—5316no—
717C22×C4—538no—
718C22×C4—538no—
719C22×C4—538no—
720C22×C4—538no—
721C22×C4—10616no—
722C22×C4—1068no—
723C22×C4—1068no—
724C22×C4—10616no—
725C22×C4—1068no—
726C22×C4—1068no—
727C22×C4—1068no—
728C22×C4—1068no—
729C22×C4C23×D5311yescharacteristic
730C22×C4C23×D5311yescharacteristic
731C22×C4C23×D5314yes—
732C22×C4C23×D5314yes—
733C22×C4C23×D5311yescharacteristic
734C22×C4C23×D5314yes—
735C22×C4C23×D5314yes—
736C22×C4C23×D5314yes—
737C22×C4C23×D5311yescharacteristic
738C22×C4C23×D5311yescharacteristic
739C22×C4C23×D5311yescharacteristic
740C4⋊C4—538no—
741C4⋊C4—534no—
742C4⋊C4—5316no—
743C4⋊C4—5316no—
744C4⋊C4—5316no—
745C4⋊C4—534no—
746C4⋊C4—538no—
747C4⋊C4—538no—
748C4⋊C4—534no—
749C4⋊C4—534no—
750C4⋊C4—538no—
751C4⋊C4—5316no—
752C4⋊C4—5316no—
753C4⋊C4—5316no—
754C4⋊C4C23×D5318yes—
755C4⋊C4C23×D53116yes—
756C4⋊C4C23×D53116yes—
757C4⋊C4C23×D5318yes—
758C4⋊C4C23×D5318yes—
759C4⋊C4C23×D5318yes—
760C22⋊C4—538no—
761C22⋊C4—538no—
762C22⋊C4—538no—
763C22⋊C4—5316no—
764C22⋊C4—538no—
765C22⋊C4—538no—
766C22⋊C4—538no—
767C22⋊C4—5316no—
768C22⋊C4—5316no—
769C22⋊C4—5316no—
770C22⋊C4C23×D53116yes—
771C42—538no—
772C42—538no—
773C42—538no—
774C42—5316no—
775C42—538no—
776C42—538no—
777C42—5316no—
778C42—538no—
779C42C23×D5314yes—
780C42C23×D5314yes—
781C42C23×D53116yes—
782C42C23×D5314yes—
783C42C23×D5314yes—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—538no—
788C23—534no—
789C23—534no—
790C23—1064no—
791C23—1064no—
792C23—1064no—
793C23—1064no—
794C23—1064no—
795C23C24×D5312yes—
796C23C24×D5311yescharacteristic
797Q8—216no—
798Q8—216no—
799Q8—5316no—
800Q8—10632no—
801Q8—1068no—
802D4—5316no—
803D4—10632no—
804D4—10616no—
805D4—10616no—
806D4—1068no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—28no—
810C2×C4—28no—
811C2×C4—22no—
812C2×C4—28no—
813C2×C4—28no—
814C2×C4—28no—
815C2×C4—538no—
816C2×C4—534no—
817C2×C4—534no—
818C2×C4—534no—
819C2×C4—534no—
820C2×C4—534no—
821C2×C4—534no—
822C2×C4—10632no—
823C2×C4—10616no—
824C2×C4—10616no—
825C2×C4—10632no—
826C2×C4—1064no—
827C2×C4—1064no—
828C2×C4—1064no—
829C2×C4—1064no—
830C2×C4—1064no—
831C2×C4—10616no—
832C2×C4—10616no—
833C2×C4—10616no—
834C2×C4—10616no—
835C2×C4#41×D5314yes—
836C2×C4#41×D5314yes—
837C2×C4#1313326514yes—
838C2×C4C24×D5312yes—
839C2×C4C24×D5312yes—
840C2×C4C24×D5318yes—
841C2×C4C24×D5318yes—
842C2×C4C24×D5312yes—
843C2×C4C24×D5312yes—
844C2×C4C24×D5312yes—
845C2×C4C24×D5312yes—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—44no—
850C22—538no—
851C22—10616no—
852C22—1064no—
853C22—1064no—
854C22—1064no—
855C22—1064no—
856C22—1064no—
857C22—2128no—
858C22C2×#41×D5312yes—
859C22C2×#41×D5312yes—
860C22C2×#1313326512yes—
861C22C25×D5311yescharacteristic
862C4—22no—
863C4—22no—
864C4—28no—
865C4—28no—
866C4—22no—
867C4—538no—
868C4—1064no—
869C4—1064no—
870C4—1064no—
871C4—1064no—
872C4—1064no—
873C4C2×#41×D5314yes—
874C4C2×#41×D5314yes—
875C4C2×#1313326514yes—
876C2—42no—
877C2—1068no—
878C2—2124no—
879C2#2028833314yesdirect product factor
880C2C22×#41×D5311yescharacteristic
881C2C22×#41×D5311yescharacteristic
882C2C22×#1313326511yescharacteristic
subgroupG/H
centerC22×C4C23×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#533C2
socleC23×C53C25
hypercenterC2×#533D53
hypocenterC53C2×#3482
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #20288333C2direct (N × H)
2. C2×#16811348C2semidirect
3. C2×#16811347C2semidirect
4. C2×#16811344C2semidirect
5. C2×#16811307C2semidirect
6. C2×#16811305C2semidirect
7. C2×#16811288C2semidirect
8. C2×#16811283C2semidirect
9. C2×#16811276C2semidirect
10. C2×#16811275C2semidirect
11. C2×#16811177C2semidirect
12. C2×#16811160C2semidirect
13. C2×#16811151C2semidirect
14. C2×C4×#11719949C2semidirect
15. C2×C4×#11719945C2semidirect
16. C2×C4×#11719945C2semidirect
17. C2×C4×Q8×D53C2semidirect
18. C2×C53×#533C2semidirect
23. #16811348C22semidirect
24. #16811347C22semidirect
25. #16811344C22semidirect
26. #16811307C22semidirect
27. #16811305C22semidirect
28. #16811288C22semidirect
29. #16811283C22semidirect
30. #16811276C22semidirect
31. #16811275C22semidirect
32. #16811177C22semidirect
35. #16811160C22semidirect
36. #16811151C22semidirect
55. C4×#11719949C22semidirect
56. C4×#11719945C22semidirect
57. C4×#11719945C22semidirect
67. C4×Q8×D53C22semidirect
91. C53×#533C22semidirect
272. C2×D212#41semidirect
294. C2×Dic106#41semidirect
392. D212C2×#41semidirect
403. Dic106C2×#41semidirect
446. C2×#533D53semidirect
454. C2×C53#3482semidirect
474. #533C2×D53semidirect
542. C53C2×#3482semidirect
879. C2#20288333direct (N × H)

Maximal subgroups

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

subgroupindex
#202883332
C2×#168113482
C2×#168113472
C2×#168113442
C2×#168113072
C2×#168113052
C2×#168112882
C2×#168112832
C2×#168112762
C2×#168112752
C2×#168111772
C2×#168111602
C2×#168111512
C2×C4×#117199492
C2×C4×#117199452
C2×C4×Q8×D532
C2×C53×#5332
C2×#348253