Finite Group Databasebeta

← C2×#13128589 #16771351

Subgroups — C2×#13128589 #16771351

Order 3328.

7206 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128589C2132yesmaximal, direct product factor
2C2×#11719238C212yesmaximal, complemented
3C2×#11719216C212yesmaximal, complemented
4C2×#11719246C214yesmaximal, complemented
5C2×#11719234C212yesmaximal, complemented
6C2×#11719218C212yesmaximal, complemented
7C2×#11719261C214yesmaximal, complemented
8C2×#11719205C211yesmaximal, characteristic, complemented
9C2×#11719266C212yesmaximal, complemented
10C2×#11719288C212yesmaximal, complemented
11C2×#11719530C211yesmaximal, characteristic, complemented
12C2×#11719283C212yesmaximal, complemented
13C2×#11719262C212yesmaximal, complemented
14C2×#11719533C211yesmaximal, characteristic
15C22×#88151C211yesmaximal, characteristic, complemented
16C2×#11719221C211yesmaximal, characteristic, complemented
17C2×D13×#117C211yesmaximal, characteristic, complemented
18C2×C13×#520C211yesmaximal, characteristic, complemented
19C22×C13×#41C2211yescharacteristic
20C23×C4×D13C2211yescharacteristic
21C23×Dic26C2211yescharacteristic
22C13×#520C22116yescomplemented
23C2×C4×Q8×C13C2212yescomplemented
24C2×C4×D4×C13C2214yes—
25C2×C4×D4×C13C2212yescomplemented
26C2×C13×#117C2211yescharacteristic
27C2×C13×#117C2212yescomplemented
28C22×C13×C4⋊C4C2211yescharacteristic
29C22×C13×C4⋊C4C2212yescomplemented
30#11719533C22116yes—
31#11719530C22116yescomplemented
32C2×#88200C2211yescharacteristic
33C2×#88200C2211yescharacteristic
34C2×#88198C2212yescomplemented
35C2×#88192C2211yescharacteristic
36C2×#88192C2211yescharacteristic
37C2×#88191C2212yes—
38C2×#88190C2212yescomplemented
39C2×#88189C2212yes—
40C2×#88189C2214yes—
41C2×#88183C2214yes—
42C2×C4×C22⋊D13C2212yes—
43C2×C4×C22⋊D13C2212yes—
44C2×C4×C22⋊D13C2214yes—
45C22×#6103C2212yes—
46C2×#88180C2211yescharacteristic
47C2×#88180C2211yescharacteristic
48C2×#88180C2214yescomplemented
49C22×C4⋊Dic13C2212yes—
50C2×#88178C2214yes—
51C2×#88178C2214yescomplemented
52C2×#88178C2212yescomplemented
53C2×#88178C2212yescomplemented
54#11719288C22132yescomplemented
55#11719283C22132yescomplemented
56#11719266C22132yescomplemented
57#11719262C22132yescomplemented
58#11719261C22164yescomplemented
59#11719246C22164yescomplemented
60#11719238C22132yescomplemented
61#11719234C22132yescomplemented
62D13×#117C22116yescomplemented
63#11719221C22116yescomplemented
64#11719218C22132yescomplemented
65C2×#88152C2214yes—
66#11719216C22132yescomplemented
67C2×#88151C2212yes—
68C2×#88151C2212yes—
69C2×#88151C2212yes—
70C2×#88151C2212yes—
71C2×#88151C22116yescomplemented
72C2×#88150C2214yes—
73C2×#88146C2211yescharacteristic
74C2×#88146C2211yescharacteristic
75C2×C4⋊C4×D13C2211yescharacteristic
76C2×C4⋊C4×D13C2211yescharacteristic
77#11719205C22116yescomplemented
78C2×#88144C2212yescomplemented
79C2×#88144C2212yescomplemented
80C2×#88143C2214yescomplemented
81C2×#88143C2214yescomplemented
82C2×#88142C2212yescomplemented
83C2×#88142C2212yescomplemented
84C2×#88141C2212yescomplemented
85C2×#88141C2212yescomplemented
86C2×#88139C2214yes—
87C2×#88137C2214yes—
88C2×C22⋊C4×D13C2212yes—
89C2×#88133C2214yescomplemented
90C2×#88133C2214yescomplemented
91C2×#88131C2212yes—
92C2×#88131C2214yes—
93C2×#88130C2214yes—
94C2×#88126C2212yes—
95C2×#88126C2214yes—
96C2×C42×D13C2212yes—
97C2×#88124C2214yescomplemented
98C2×C4×Dic26C2212yescomplemented
99C2×C4×Dic26C2212yescomplemented
100C2×C4×Dic26C2214yescomplemented
101C24×D13C2311yescharacteristic
102C2×C13×#41—28no—
103C2×C13×#41C2318yes—
104C22×Q8×C13C2311yescharacteristic
105C22×D4×C13C2312yes—
106C22×D4×C13C2311yescharacteristic
107C23×C4×C13C2312yes—
108C23×C4×C13C2312yes—
109C23×C4×C13C2314yes—
110C23×C4×C13C2311yescharacteristic
111C22×C22⋊D13C2312yes—
112C22×C22⋊D13C2312yes—
113C23×Dic13C2311yescharacteristic
114C23×Dic13C2312yes—
115C22×C4×D13—28no—
116C22×C4×D13C2311yescharacteristic
117C22×C4×D13C2312yes—
118C22×C4×D13C2311yescharacteristic
119C22×C4×D13C2311yescharacteristic
120C22×C4×D13C2311yescharacteristic
121C22×C4×D13C2318yes—
122C22×C4×D13C2312yes—
123C22×Dic26—28no—
124C22×Dic26C2312yes—
125C22×Dic26C2312yes—
126C22×Dic26C2318yes—
127C22×Dic26C2314yes—
128C4×Q8×C13C23116yescomplemented
129C4×D4×C13C23132yes—
130C4×D4×C13C23116yescomplemented
131C13×#117C2318yes—
132C13×#117C23116yescomplemented
133C2×C13×C4⋊C4C2311yescharacteristic
134C2×C13×C4⋊C4C2311yescharacteristic
135C2×C13×C4⋊C4C2312yes—
136C2×C13×C4⋊C4C2312yes—
137C2×C13×C4⋊C4C2314yes—
138C2×C13×C4⋊C4C2318yes—
139C2×C13×C4⋊C4C23116yescomplemented
140C2×C13×C22⋊C4C2312yes—
141C2×C13×C22⋊C4C2314yes—
142C2×C42×C13C2312yes—
143C2×C42×C13C2314yes—
144C2×C22⋊Dic13C2312yes—
145C2×C22⋊Dic13C2312yes—
146C2×C22⋊Dic13C2312yes—
147C2×C22⋊Dic13C2312yes—
148C2×C22⋊Dic13C2314yes—
149C2×C22⋊Dic13C2314yes—
150#88200C2318yes—
151#88200C2318yes—
152#88198C23116yescomplemented
153#88192C2318yes—
154#88192C2318yes—
155#88191C23116yes—
156#88190C23116yescomplemented
157#88189C23116yes—
158#88189C23132yes—
159#88183C23132yes—
160C4×C22⋊D13C23116yes—
161C4×C22⋊D13C23132yes—
162C4×C22⋊D13C23116yes—
163C2×#6103C2312yes—
164C2×#6103C2312yes—
165C2×#6103C2312yes—
166C2×#6103C2314yes—
167C2×#6103C2312yes—
168C2×#6103C2314yes—
169C2×#6103C23116yes—
170#88180C2318yes—
171#88180C2318yes—
172#88180C23132yescomplemented
173C2×C4⋊Dic13C2311yescharacteristic
174C2×C4⋊Dic13C2311yescharacteristic
175C2×C4⋊Dic13C2314yes—
176C2×C4⋊Dic13C2314yes—
177C2×C4⋊Dic13C2314yes—
178C2×C4⋊Dic13C2311yescharacteristic
179C2×C4⋊Dic13C2311yescharacteristic
180C2×C4⋊Dic13C23116yes—
181#88178C23132yes—
182#88178C23116yescomplemented
183#88178C23132yescomplemented
184#88178C23116yescomplemented
185C2×#6101C2312yes—
186C2×#6101C2314yes—
187C2×#6101C2314yes—
188C2×#6101C2314yes—
189C2×#6101C2312yes—
190C2×#6101C2312yes—
191C2×#6101C2314yes—
192C2×#6101C2312yes—
193C2×#6101C2314yes—
194C2×#6101C2314yes—
195C2×C4×Dic13C2312yes—
196C2×C4×Dic13C2314yes—
197C2×C4×Dic13C2314yes—
198C2×C4×Dic13C2312yes—
199C2×C4×Dic13C2312yes—
200C2×C4×Dic13C2312yes—
201#88152C23132yes—
202#88151C23116yes—
203#88151C23116yes—
204#88151C23116yes—
205#88151C23116yes—
206#88150C23132yes—
207#88146C2318yes—
208#88146C2318yes—
209C4⋊C4×D13C2318yes—
210C4⋊C4×D13C2318yes—
211#88144C23116yescomplemented
212#88144C23116yescomplemented
213#88143C23132yescomplemented
214#88143C23132yescomplemented
215#88142C23116yescomplemented
216#88142C23116yescomplemented
217#88141C23116yescomplemented
218#88141C23116yescomplemented
219#88139C23132yes—
220#88137C23132yes—
221C22⋊C4×D13C23116yes—
222#88133C23132yescomplemented
223#88133C23132yescomplemented
224#88131C23132yes—
225#88131C23116yes—
226#88130C23132yes—
227#88126C23116yes—
228#88126C23132yes—
229C42×D13C23116yes—
230#88124C23132yescomplemented
231C4×Dic26C23116yescomplemented
232C4×Dic26C23116yescomplemented
233C4×Dic26C23132yescomplemented
234C2×#3495—131nomaximal, Sylow
235C24×C13C2412yes—
236C24×C13C2411yescharacteristic
237C23×D13—24no—
238C23×D13—24no—
239C23×D13—42no—
240C23×D13C2411yescharacteristic
241C23×D13C2414yes—
242C23×D13C2411yescharacteristic
243C13×#41—232no—
244C2×Q8×C13—24no—
245C2×Q8×C13C2414yes—
246C2×D4×C13—28no—
247C2×D4×C13—24no—
248C2×D4×C13C2418yes—
249C2×D4×C13C2414yes—
250C22×C4×C13—28no—
251C22×C4×C13—44no—
252C22×C4×C13—48no—
253C22×C4×C13#4118yes—
254C22×C4×C13C2412yes—
255C22×C4×C13C2412yes—
256C22×C4×C13C2412yes—
257C22×C4×C13C2414yes—
258C22×C4×C13C2418yes—
259C22×C4×C13C2418yes—
260C22×C4×C13C24116yes—
261C22×C4×C13C2411yescharacteristic
262C22×C4×C13C2411yescharacteristic
263C22×C4×C13C2414yes—
264C2×C22⋊D13—28no—
265C2×C22⋊D13—44no—
266C2×C22⋊D13C2418yes—
267C2×C22⋊D13C2418yes—
268C22×Dic13—28no—
269C22×Dic13—24no—
270C22×Dic13C2414yes—
271C22×Dic13C2418yes—
272C22×Dic13C2411yescharacteristic
273C22×Dic13C2412yes—
274C22×Dic13C2412yes—
275C22×Dic13C2412yes—
276C22×Dic13C2412yes—
277C22×Dic13C2414yes—
278C22×Dic13C2411yescharacteristic
279C2×C4×D13—28no—
280C2×C4×D13—24no—
281C2×C4×D13—24no—
282C2×C4×D13—24no—
283C2×C4×D13—24no—
284C2×C4×D13—232no—
285C2×C4×D13—44no—
286C2×C4×D13C2414yes—
287C2×C4×D13C2418yes—
288C2×C4×D13C2414yes—
289C2×C4×D13C2414yes—
290C2×C4×D13C2414yes—
291C2×C4×D13C2418yes—
292C2×Dic26—28no—
293C2×Dic26—28no—
294C2×Dic26—232no—
295C2×Dic26—48no—
296C2×Dic26C2418yes—
297C2×Dic26C2418yes—
298C2×Dic26C24116yes—
299C13×C4⋊C4C2414yes—
300C13×C4⋊C4C2414yes—
301C13×C4⋊C4C2418yes—
302C13×C4⋊C4C2418yes—
303C13×C4⋊C4C24116yes—
304C13×C22⋊C4C2418yes—
305C13×C22⋊C4C24116yes—
306C42×C13C2418yes—
307C42×C13C24116yes—
308C22⋊Dic13C2418yes—
309C22⋊Dic13C2418yes—
310C22⋊Dic13C2418yes—
311C22⋊Dic13C2418yes—
312C22⋊Dic13C24116yes—
313C22⋊Dic13C24116yes—
314#6103C2418yes—
315#6103C2418yes—
316#6103C2418yes—
317#6103C24116yes—
318#6103C2418yes—
319#6103C24116yes—
320C4⋊Dic13C2414yes—
321C4⋊Dic13C2414yes—
322C4⋊Dic13C24116yes—
323C4⋊Dic13C24116yes—
324C4⋊Dic13C24116yes—
325C4⋊Dic13C2414yes—
326C4⋊Dic13C2414yes—
327#6101C2418yes—
328#6101C24116yes—
329#6101C24116yes—
330#6101C24116yes—
331#6101C2418yes—
332#6101C2418yes—
333#6101C24116yes—
334#6101C2418yes—
335#6101C24116yes—
336#6101C24116yes—
337C4×Dic13C2418yes—
338C4×Dic13C24116yes—
339C4×Dic13C24116yes—
340C4×Dic13C2418yes—
341C4×Dic13C2418yes—
342C4×Dic13C2418yes—
343#3495—1332no—
344C2×#556—132no—
345C2×#554—132no—
346C2×#552—134no—
347C2×#552—132no—
348C2×#552—132no—
349C2×#551—134no—
350C2×#544—131no—
351C2×#542—132no—
352C2×#541—132no—
353C2×#536—131no—
354C2×#533—132no—
355C2×#529—132no—
356C2×#525—131no—
357C22×C22⋊Q8—131no—
358C2×#520D1311yescharacteristic, complemented
359C2×#519—131no—
360C22×#117—131no—
361C23×C13—22no—
362C23×C13—22no—
363C23×C13—24no—
364C23×C13—24no—
365C23×C13—24no—
366C23×C13C2×#4114yes—
367C23×C13C2514yes—
368C23×C13C2512yes—
369C23×C13C2511yescharacteristic
370C22×D13—22no—
371C22×D13—22no—
372C22×D13—28no—
373C22×D13—22no—
374C22×D13—22no—
375C22×D13—22no—
376C22×D13—28no—
377C22×D13—44no—
378C22×D13—416no—
379C22×D132−1+414yes—
380C22×D13C2512yes—
381C22×D13C2512yes—
382Q8×C13—28no—
383D4×C13—216no—
384D4×C13—28no—
385C2×C4×C13—24no—
386C2×C4×C13—24no—
387C2×C4×C13—28no—
388C2×C4×C13—24no—
389C2×C4×C13—216no—
390C2×C4×C13—48no—
391C2×C4×C13—416no—
392C2×C4×C13C2×#4114yes—
393C2×C4×C13C2×#4114yes—
394C2×C4×C13C2×#41116yes—
395C2×C4×C13C2514yes—
396C2×C4×C13C2514yes—
397C2×C4×C13C2514yes—
398C2×C4×C13C2518yes—
399C2×C4×C13C2512yes—
400C2×C4×C13C2512yes—
401C22⋊D13—216no—
402C22⋊D13—48no—
403C2×Dic13—216no—
404C2×Dic13—28no—
405C2×Dic13—28no—
406C2×Dic13—22no—
407C2×Dic13—22no—
408C2×Dic13—24no—
409C2×Dic13—24no—
410C2×Dic13—24no—
411C2×Dic13—24no—
412C2×Dic13C2512yes—
413C2×Dic13C2514yes—
414C2×Dic13C2514yes—
415C2×Dic13C2514yes—
416C2×Dic13C2514yes—
417C2×Dic13C2518yes—
418C2×Dic13C2512yes—
419C4×D13—216no—
420C4×D13—28no—
421C4×D13—28no—
422C4×D13—28no—
423C4×D13—28no—
424C4×D13—48no—
425Dic26—216no—
426Dic26—216no—
427Dic26—416no—
428C22×#41C2×D1311yescharacteristic
429C23×Q8—131no—
430C24×C4—131no—
431#556—1332no—
432#554—1332no—
433#552—1364no—
434#552—1332no—
435#552—1332no—
436#551—1364no—
437#544—1316no—
438#542—1332no—
439#541—1332no—
440#536—1316no—
441#533—1332no—
442C2×C4⋊Q8—132no—
443C2×C4⋊Q8—132no—
444C2×C4⋊Q8—132no—
445#529—1332no—
446C2×#126—134no—
447C2×#126—134no—
448C2×#126—134no—
449C2×#126—134no—
450C2×#125—134no—
451C2×#125—134no—
452C2×#125—132no—
453C2×#125—132no—
454C2×#125—134no—
455C2×#124—132no—
456C2×#124—134no—
457#525—1316no—
458C2×#123—132no—
459C2×#123—134no—
460C2×#123—134no—
461C2×#123—134no—
462C2×C22⋊Q8—131no—
463C2×C22⋊Q8—131no—
464C2×C22⋊Q8—134no—
465C2×C22⋊Q8—132no—
466C2×C22⋊Q8—132no—
467C2×C22⋊Q8—134no—
468C2×C22⋊Q8—134no—
469C2×C22⋊Q8—132no—
470C2×C22⋊Q8—132no—
471C2×C22⋊Q8—132no—
472C2×C22⋊Q8—132no—
473C2×C22⋊Q8—1316no—
474C2×#121—131no—
475C2×#121—131no—
476C2×#120—132no—
477#520C2×D13116yescomplemented
478#519—1316no—
479C2×C4×Q8—132no—
480C2×C4×Q8—132no—
481C2×C4×Q8—132no—
482C2×C4×Q8—132no—
483C2×C4×Q8—134no—
484C2×C4×Q8C2×D1312yescomplemented
485C2×C4×D4—132no—
486C2×C4×D4—132no—
487C2×C4×D4—134no—
488C2×C4×D4C2×D1314yes—
489C2×C4×D4C2×D1312yescomplemented
490C2×#117—131no—
491C2×#117—131no—
492C2×#117—134no—
493C2×#117—1316no—
494C2×#117—131no—
495C2×#117—131no—
496C2×#117—132no—
497C2×#117—134no—
498C2×#117—132no—
499C2×#117—134no—
500C2×#117C2×D1311yescharacteristic
501C2×#117C2×D1312yescomplemented
502C22×C4⋊C4—132no—
503C22×C4⋊C4—131no—
504C22×C4⋊C4—131no—
505C22×C4⋊C4C2×D1311yescharacteristic
506C22×C4⋊C4C2×D1312yescomplemented
507C22×C22⋊C4—132no—
508C22×C22⋊C4—132no—
509C22×C42—132no—
510C22×C13—22no—
511C22×C13—22no—
512C22×C13—28no—
513C22×C13—24no—
514C22×C13—24no—
515C22×C13—24no—
516C22×C13—48no—
517C22×C13C22×#4114yes—
518C22×C13C22×#4112yes—
519C22×C13C2×2−1+412yes—
520C22×C13#58512yes—
521C22×C13C2611yescharacteristic
522C2×D13—22no—
523C2×D13—22no—
524C2×D13—28no—
525C2×D13—22no—
526C2×D13—22no—
527C2×D13—22no—
528C2×D13—416no—
529C2×D13—44no—
530C2×D13C2×2−1+414yes—
531C4×C13—24no—
532C4×C13—24no—
533C4×C13—28no—
534C4×C13—24no—
535C4×C13C22×#4114yes—
536C4×C13C22×#4114yes—
537Dic13—28no—
538Dic13—22no—
539Dic13—22no—
540Dic13—24no—
541Dic13—24no—
542Dic13—24no—
543Dic13—24no—
544C25—131no—
545C2×#41—28no—
546C2×#41C22×D1318yes—
547C22×Q8—132no—
548C22×Q8—132no—
549C22×Q8—138no—
550C22×Q8—134no—
551C22×Q8—268no—
552C22×Q8C22×D1311yescharacteristic
553C22×D4—132no—
554C22×D4—132no—
555C22×D4C22×D1312yes—
556C22×D4C22×D1311yescharacteristic
557C23×C4—132no—
558C23×C4—131no—
559C23×C4—132no—
560C23×C4—131no—
561C23×C4—131no—
562C23×C4—131no—
563C23×C4—138no—
564C23×C4—131no—
565C23×C4—132no—
566C23×C4—268no—
567C23×C4C22×D1312yes—
568C23×C4C22×D1312yes—
569C23×C4C22×D1314yes—
570C23×C4C22×D1311yescharacteristic
571C4⋊Q8—1316no—
572C4⋊Q8—1316no—
573C4⋊Q8—1316no—
574#126—1332no—
575#126—1332no—
576#126—1332no—
577#126—1332no—
578#125—1316no—
579#125—1332no—
580#125—1332no—
581#125—1316no—
582#125—1332no—
583#124—1316no—
584#124—1332no—
585#123—1316no—
586#123—1332no—
587#123—1332no—
588#123—1332no—
589C22⋊Q8—138no—
590C22⋊Q8—138no—
591C22⋊Q8—1316no—
592C22⋊Q8—1316no—
593C22⋊Q8—1332no—
594C22⋊Q8—1332no—
595C22⋊Q8—1316no—
596C22⋊Q8—1316no—
597C22⋊Q8—1316no—
598C22⋊Q8—1316no—
599C22⋊Q8—1332no—
600#121—138no—
601#121—138no—
602#120—1316no—
603C4×Q8—1316no—
604C4×Q8—1316no—
605C4×Q8—1316no—
606C4×Q8—1316no—
607C4×Q8—1332no—
608C4×Q8C22×D13116yescomplemented
609C4×D4—1316no—
610C4×D4—1316no—
611C4×D4—1332no—
612C4×D4C22×D13132yes—
613C4×D4C22×D13116yescomplemented
614#117—138no—
615#117—138no—
616#117—1332no—
617#117—138no—
618#117—138no—
619#117—1316no—
620#117—1332no—
621#117—1316no—
622#117—1332no—
623#117C22×D1318yes—
624#117C22×D13116yescomplemented
625C2×C4⋊C4—132no—
626C2×C4⋊C4—131no—
627C2×C4⋊C4—131no—
628C2×C4⋊C4—132no—
629C2×C4⋊C4—134no—
630C2×C4⋊C4—134no—
631C2×C4⋊C4—1316no—
632C2×C4⋊C4—131no—
633C2×C4⋊C4—131no—
634C2×C4⋊C4—134no—
635C2×C4⋊C4—134no—
636C2×C4⋊C4—134no—
637C2×C4⋊C4—134no—
638C2×C4⋊C4—134no—
639C2×C4⋊C4—132no—
640C2×C4⋊C4—132no—
641C2×C4⋊C4—134no—
642C2×C4⋊C4—134no—
643C2×C4⋊C4—138no—
644C2×C4⋊C4—138no—
645C2×C4⋊C4C22×D1311yescharacteristic
646C2×C4⋊C4C22×D1311yescharacteristic
647C2×C4⋊C4C22×D1312yes—
648C2×C4⋊C4C22×D1312yes—
649C2×C4⋊C4C22×D1318yes—
650C2×C4⋊C4C22×D1314yes—
651C2×C4⋊C4C22×D13116yescomplemented
652C2×C22⋊C4—132no—
653C2×C22⋊C4—132no—
654C2×C22⋊C4—132no—
655C2×C22⋊C4—134no—
656C2×C22⋊C4—132no—
657C2×C22⋊C4—134no—
658C2×C22⋊C4—132no—
659C2×C22⋊C4—132no—
660C2×C22⋊C4—134no—
661C2×C22⋊C4—134no—
662C2×C22⋊C4—1316no—
663C2×C22⋊C4—132no—
664C2×C22⋊C4—132no—
665C2×C22⋊C4—1316no—
666C2×C22⋊C4C22×D1312yes—
667C2×C22⋊C4C22×D1314yes—
668C2×C42—132no—
669C2×C42—134no—
670C2×C42—134no—
671C2×C42—132no—
672C2×C42—132no—
673C2×C42—132no—
674C2×C42—1316no—
675C2×C42C22×D1312yes—
676C2×C42C22×D1314yes—
677C2×C13—24no—
678C2×C13—44no—
679C2×C13#349514yescomplemented
680C2×C13C23×#4111yescharacteristic
681C2×C13C22×2−1+411yescharacteristic
682C2×C13C2×#58511yescharacteristic
683D13—24no—
684D13—42no—
685C24—131no—
686C24—131no—
687C24—134no—
688C24—264no—
689C24—264no—
690C24—522no—
691C24C23×D1312yes—
692C24C23×D1311yescharacteristic
693#41—232no—
694C2×Q8—24no—
695C2×Q8—138no—
696C2×Q8—138no—
697C2×Q8—1316no—
698C2×Q8—268no—
699C2×Q8—268no—
700C2×Q8—2632no—
701C2×Q8—528no—
702C2×Q8C23×D1314yes—
703C2×D4—28no—
704C2×D4—24no—
705C2×D4—138no—
706C2×D4—138no—
707C2×D4—268no—
708C2×D4—524no—
709C2×D4C23×D1318yes—
710C2×D4C23×D1314yes—
711C22×C4—28no—
712C22×C4—48no—
713C22×C4—44no—
714C22×C4—138no—
715C22×C4—134no—
716C22×C4—131no—
717C22×C4—132no—
718C22×C4—132no—
719C22×C4—132no—
720C22×C4—134no—
721C22×C4—132no—
722C22×C4—131no—
723C22×C4—134no—
724C22×C4—138no—
725C22×C4—134no—
726C22×C4—134no—
727C22×C4—134no—
728C22×C4—138no—
729C22×C4—268no—
730C22×C4—264no—
731C22×C4—268no—
732C22×C4—264no—
733C22×C4—264no—
734C22×C4—264no—
735C22×C4—264no—
736C22×C4—2632no—
737C22×C4—524no—
738C22×C4#612718yes—
739C22×C4C23×D1318yes—
740C22×C4C23×D1312yes—
741C22×C4C23×D1312yes—
742C22×C4C23×D1312yes—
743C22×C4C23×D1314yes—
744C22×C4C23×D1318yes—
745C22×C4C23×D13116yes—
746C22×C4C23×D1314yes—
747C22×C4C23×D1311yescharacteristic
748C22×C4C23×D1311yescharacteristic
749C4⋊C4—138no—
750C4⋊C4—134no—
751C4⋊C4—134no—
752C4⋊C4—138no—
753C4⋊C4—1316no—
754C4⋊C4—1316no—
755C4⋊C4—134no—
756C4⋊C4—134no—
757C4⋊C4—1316no—
758C4⋊C4—1316no—
759C4⋊C4—1316no—
760C4⋊C4—1316no—
761C4⋊C4—1316no—
762C4⋊C4—138no—
763C4⋊C4—138no—
764C4⋊C4—1316no—
765C4⋊C4—1316no—
766C4⋊C4C23×D1314yes—
767C4⋊C4C23×D1314yes—
768C4⋊C4C23×D1318yes—
769C4⋊C4C23×D1318yes—
770C4⋊C4C23×D13116yes—
771C22⋊C4—138no—
772C22⋊C4—138no—
773C22⋊C4—138no—
774C22⋊C4—1316no—
775C22⋊C4—138no—
776C22⋊C4—1316no—
777C22⋊C4—138no—
778C22⋊C4—138no—
779C22⋊C4—1316no—
780C22⋊C4—1316no—
781C22⋊C4—138no—
782C22⋊C4—138no—
783C22⋊C4C23×D1318yes—
784C22⋊C4C23×D13116yes—
785C42—138no—
786C42—138no—
787C42—138no—
788C42—1316no—
789C42—1316no—
790C42—138no—
791C42C23×D1318yes—
792C42C23×D13116yes—
793C13C2×#349511yescharacteristic, complemented, Sylow
794C23—22no—
795C23—22no—
796C23—24no—
797C23—24no—
798C23—24no—
799C23—134no—
800C23—132no—
801C23—132no—
802C23—268no—
803C23—262no—
804C23—262no—
805C23—268no—
806C23—262no—
807C23—262no—
808C23—262no—
809C23—524no—
810C23—5216no—
811C23C2×#612714yes—
812C23C24×D1314yes—
813C23C24×D1312yes—
814C23C24×D1311yescharacteristic
815Q8—28no—
816Q8—2616no—
817Q8—2616no—
818Q8—5216no—
819D4—216no—
820D4—28no—
821D4—2616no—
822D4—528no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—28no—
826C2×C4—24no—
827C2×C4—216no—
828C2×C4—416no—
829C2×C4—48no—
830C2×C4—132no—
831C2×C4—134no—
832C2×C4—134no—
833C2×C4—134no—
834C2×C4—138no—
835C2×C4—134no—
836C2×C4—132no—
837C2×C4—2616no—
838C2×C4—268no—
839C2×C4—262no—
840C2×C4—262no—
841C2×C4—2616no—
842C2×C4—268no—
843C2×C4—264no—
844C2×C4—264no—
845C2×C4—264no—
846C2×C4—264no—
847C2×C4—268no—
848C2×C4—268no—
849C2×C4—268no—
850C2×C4—268no—
851C2×C4—528no—
852C2×C4C2×#612714yes—
853C2×C4C2×#612714yes—
854C2×C4C2×#6127116yes—
855C2×C4C24×D1314yes—
856C2×C4C24×D1314yes—
857C2×C4C24×D1314yes—
858C2×C4C24×D1318yes—
859C2×C4C24×D1312yes—
860C2×C4C24×D1312yes—
861C22—28no—
862C22—22no—
863C22—22no—
864C22—24no—
865C22—24no—
866C22—24no—
867C22—48no—
868C22—134no—
869C22—268no—
870C22—262no—
871C22—262no—
872C22—262no—
873C22—262no—
874C22—262no—
875C22—5216no—
876C22—524no—
877C22C22×#612714yes—
878C22C22×#612712yes—
879C22#1171965012yes—
880C22D13×2−1+412yes—
881C22C25×D1311yescharacteristic
882C4—24no—
883C4—24no—
884C4—24no—
885C4—28no—
886C4—262no—
887C4—262no—
888C4—268no—
889C4—264no—
890C4—264no—
891C4—264no—
892C4—264no—
893C4C22×#612714yes—
894C4C22×#612714yes—
895C2—24no—
896C2—44no—
897C2—264no—
898C2—522no—
899C2#1312858914yesdirect product factor
900C2C23×#612711yescharacteristic
901C2C2×D13×2−1+411yescharacteristic
902C2C2×#1171965011yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#520C2
socleC23×C13C25
prime radicalC2×#11719533C2
hypercenterC2×#520D13
hypocenterC13C2×#3495
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #13128589C2direct (N × H)
2. C2×#11719238C2semidirect
3. C2×#11719216C2semidirect
4. C2×#11719246C2semidirect
5. C2×#11719234C2semidirect
6. C2×#11719218C2semidirect
7. C2×#11719261C2semidirect
8. C2×#11719205C2semidirect
9. C2×#11719266C2semidirect
10. C2×#11719288C2semidirect
11. C2×#11719530C2semidirect
12. C2×#11719283C2semidirect
13. C2×#11719262C2semidirect
15. C22×#88151C2semidirect
16. C2×#11719221C2semidirect
17. C2×D13×#117C2semidirect
18. C2×C13×#520C2semidirect
22. C13×#520C22semidirect
23. C2×C4×Q8×C13C22semidirect
25. C2×C4×D4×C13C22semidirect
27. C2×C13×#117C22semidirect
29. C22×C13×C4⋊C4C22semidirect
31. #11719530C22semidirect
34. C2×#88198C22semidirect
38. C2×#88190C22semidirect
48. C2×#88180C22semidirect
51. C2×#88178C22semidirect
52. C2×#88178C22semidirect
53. C2×#88178C22semidirect
54. #11719288C22semidirect
55. #11719283C22semidirect
56. #11719266C22semidirect
57. #11719262C22semidirect
58. #11719261C22semidirect
59. #11719246C22semidirect
60. #11719238C22semidirect
61. #11719234C22semidirect
62. D13×#117C22semidirect
63. #11719221C22semidirect
64. #11719218C22semidirect
66. #11719216C22semidirect
71. C2×#88151C22semidirect
77. #11719205C22semidirect
78. C2×#88144C22semidirect
79. C2×#88144C22semidirect
80. C2×#88143C22semidirect
81. C2×#88143C22semidirect
82. C2×#88142C22semidirect
83. C2×#88142C22semidirect
84. C2×#88141C22semidirect
85. C2×#88141C22semidirect
89. C2×#88133C22semidirect
90. C2×#88133C22semidirect
97. C2×#88124C22semidirect
98. C2×C4×Dic26C22semidirect
99. C2×C4×Dic26C22semidirect
100. C2×C4×Dic26C22semidirect
128. C4×Q8×C13C23semidirect
130. C4×D4×C13C23semidirect
132. C13×#117C23semidirect
139. C2×C13×C4⋊C4C23semidirect
152. #88198C23semidirect
156. #88190C23semidirect
172. #88180C23semidirect
182. #88178C23semidirect
183. #88178C23semidirect
184. #88178C23semidirect
211. #88144C23semidirect
212. #88144C23semidirect
213. #88143C23semidirect
214. #88143C23semidirect
215. #88142C23semidirect
216. #88142C23semidirect
217. #88141C23semidirect
218. #88141C23semidirect
222. #88133C23semidirect
223. #88133C23semidirect
230. #88124C23semidirect
231. C4×Dic26C23semidirect
232. C4×Dic26C23semidirect
233. C4×Dic26C23semidirect
358. C2×#520D13semidirect
477. #520C2×D13semidirect
484. C2×C4×Q8C2×D13semidirect
489. C2×C4×D4C2×D13semidirect
501. C2×#117C2×D13semidirect
506. C22×C4⋊C4C2×D13semidirect
608. C4×Q8C22×D13semidirect
613. C4×D4C22×D13semidirect
624. #117C22×D13semidirect
651. C2×C4⋊C4C22×D13semidirect
679. C2×C13#3495semidirect
793. C13C2×#3495semidirect
899. C2#13128589direct (N × H)

Maximal subgroups

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

subgroupindex
#131285892
C2×#117192382
C2×#117192162
C2×#117192462
C2×#117192342
C2×#117192182
C2×#117192612
C2×#117192052
C2×#117192662
C2×#117192882
C2×#117195302
C2×#117192832
C2×#117192622
C2×#117195332
C22×#881512
C2×#117192212
C2×D13×#1172
C2×C13×#5202
C2×#349513