Finite Group Databasebeta

← C2×#13128591 #16771352

Subgroups — C2×#13128591 #16771352

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#13128591C2132yesmaximal, direct product factor
2C2×#11719437C212yesmaximal, complemented
3C2×#11719435C212yesmaximal, complemented
4C2×#11719347C214yesmaximal, complemented
5C2×#11719399C212yesmaximal, complemented
6C2×#11719399C212yesmaximal, complemented
7C2×#11719342C214yesmaximal, complemented
8C2×#11719438C212yesmaximal, complemented
9C2×#11719402C212yesmaximal, complemented
10C2×#11719231C211yesmaximal, characteristic, complemented
11C2×#11719433C212yesmaximal, complemented
12C2×#11719396C212yesmaximal, complemented
13C2×#11719229C211yesmaximal, characteristic
14C22×#88151C211yesmaximal, characteristic, complemented
15C2×#11719209C211yesmaximal, characteristic, complemented
16C2×#11719221C211yesmaximal, characteristic, complemented
17C2×D13×#117C211yesmaximal, characteristic, complemented
18C2×C13×#544C211yesmaximal, characteristic, complemented
19C22×#6127C2211yescharacteristic
20C23×C4×D13C2211yescharacteristic
21C23×Dic26C2211yescharacteristic
22C13×#544C22116yescomplemented
23C2×C13×C4⋊Q8C2212yescomplemented
24C2×C13×C4⋊Q8C2212yescomplemented
25C2×C13×#125C2212yescomplemented
26C2×C13×#125C2212yescomplemented
27C2×C13×C22⋊Q8C2214yes—
28C2×C13×#117C2211yescharacteristic
29C2×C13×#117C2211yescharacteristic
30C22×C13×C4⋊C4C2211yescharacteristic
31C2×#88201C2214yes—
32C2×#88200C2214yes—
33C2×#88200C2214yescomplemented
34C2×Q8×Dic13C2214yescomplemented
35C2×C4×C22⋊D13C2214yes—
36C22×#6103C2212yes—
37C2×#88180C2211yescharacteristic
38C22×C4⋊Dic13C2212yes—
39#11719438C22132yescomplemented
40#11719437C22132yescomplemented
41#11719435C22132yescomplemented
42#11719433C22132yescomplemented
43#11719402C22132yescomplemented
44#11719399C22132yescomplemented
45#11719399C22132yescomplemented
46#11719396C22132yescomplemented
47#11719347C22164yescomplemented
48#11719342C22164yescomplemented
49#11719231C22116yescomplemented
50#11719229C22116yes—
51D13×#117C22116yescomplemented
52#11719221C22116yescomplemented
53C2×#88152C2214yes—
54C2×#88152C2214yes—
55C2×#88152C2214yescomplemented
56C2×#88152C2214yescomplemented
57C2×#88151C2211yescharacteristic
58C2×#88151C2212yes—
59C2×#88151C2212yes—
60C2×#88151C2212yes—
61C2×#88151C2212yes—
62C2×#88151C2211yescharacteristic
63C2×#88151C22116yescomplemented
64C2×#88151C2212yescomplemented
65C2×#88151C2212yescomplemented
66C2×#88149C2211yescharacteristic
67C2×#88149C2211yescharacteristic
68C2×#88148C2214yes—
69C2×#88148C2214yes—
70#11719209C22116yescomplemented
71C2×#88147C2214yes—
72C2×#88147C2212yescomplemented
73C2×#88146C2211yescharacteristic
74C2×#88146C2211yescharacteristic
75C2×#88146C2214yes—
76C2×#88146C2212yescomplemented
77C2×#88146C2214yescomplemented
78C2×C4⋊C4×D13C2211yescharacteristic
79C2×C4⋊C4×D13C2211yescharacteristic
80C2×C4⋊C4×D13C2212yescomplemented
81C2×#88144C2214yescomplemented
82C2×#88144C2214yescomplemented
83C2×#88144C2214yescomplemented
84C2×#88141C2212yescomplemented
85C2×#88141C2212yescomplemented
86C2×#88141C2212yescomplemented
87C2×#88140C2214yes—
88C2×#88140C2212yes—
89C2×#88136C2212yes—
90C2×C22⋊C4×D13C2212yes—
91C2×#88131C2212yes—
92C2×#88131C2214yes—
93C2×#88129C2212yescomplemented
94C2×C4×D52C2212yes—
95C2×C4×D52C2212yes—
96C2×#88126C2212yes—
97C2×C42×D13C2212yes—
98C2×#88123C2212yescomplemented
99C2×C4×Dic26C2212yescomplemented
100C2×C4×Dic26C2212yescomplemented
101C24×D13C2311yescharacteristic
102C22×Q8×C13C2314yes—
103C23×C4×C13C2312yes—
104C23×C4×C13C2311yescharacteristic
105C22×C22⋊D13C2312yes—
106C23×Dic13C2311yescharacteristic
107C23×Dic13C2312yes—
108C2×#6127—28no—
109C2×#6127C2318yes—
110C22×D52C2312yes—
111C22×D52C2311yescharacteristic
112C22×D52C2312yes—
113C22×C4×D13—28no—
114C22×C4×D13C2311yescharacteristic
115C22×C4×D13C2312yes—
116C22×C4×D13C2311yescharacteristic
117C22×C4×D13C2311yescharacteristic
118C22×C4×D13C2312yes—
119C22×C4×D13C2311yescharacteristic
120C22×C4×D13C2318yes—
121C22×C4×D13C2312yes—
122C22×C4×D13C2314yes—
123C22×Dic26—28no—
124C22×Dic26C2312yes—
125C22×Dic26C2311yescharacteristic
126C22×Dic26C2312yes—
127C22×Dic26C2318yes—
128C13×C4⋊Q8C23116yescomplemented
129C13×C4⋊Q8C23116yescomplemented
130C13×#125C23116yescomplemented
131C13×#125C23116yescomplemented
132C13×C22⋊Q8C23132yes—
133C13×#117C2318yes—
134C13×#117C2318yes—
135C2×C13×C4⋊C4C2311yescharacteristic
136C2×C13×C4⋊C4C2311yescharacteristic
137C2×C13×C4⋊C4C2312yes—
138C2×C13×C4⋊C4C2314yes—
139C2×C13×C4⋊C4C2314yes—
140C2×C13×C4⋊C4C2314yes—
141C2×C13×C4⋊C4C2311yescharacteristic
142C2×C13×C4⋊C4C2311yescharacteristic
143C2×C13×C4⋊C4C2312yes—
144C2×C13×C4⋊C4C2318yes—
145C2×C13×C22⋊C4C2312yes—
146C2×C13×C22⋊C4C2312yes—
147C2×C42×C13C2312yes—
148C2×C42×C13C2312yes—
149C2×C22⋊Dic13C2312yes—
150#88201C23132yes—
151#88200C23132yes—
152#88200C23132yescomplemented
153Q8×Dic13C23132yescomplemented
154C4×C22⋊D13C23132yes—
155C2×#6103C2312yes—
156C2×#6103C2312yes—
157C2×#6103C2312yes—
158C2×#6103C2312yes—
159C2×#6103C2312yes—
160C2×#6103C2312yes—
161C2×#6103C2314yes—
162C2×#6103C2314yes—
163C2×#6103C2314yes—
164C2×#6103C2314yes—
165C2×#6103C2314yes—
166C2×#6103C23116yes—
167#88180C2318yes—
168C2×C4⋊Dic13C2311yescharacteristic
169C2×C4⋊Dic13C2311yescharacteristic
170C2×C4⋊Dic13C2314yes—
171C2×C4⋊Dic13C2314yes—
172C2×C4⋊Dic13C2312yes—
173C2×C4⋊Dic13C2312yes—
174C2×C4⋊Dic13C2314yes—
175C2×C4⋊Dic13C2314yes—
176C2×C4⋊Dic13C23116yes—
177C2×#6101C2314yes—
178C2×#6101C2314yes—
179C2×#6101C2312yes—
180C2×#6101C2312yes—
181C2×#6101C2314yes—
182C2×C4×Dic13C2314yes—
183C2×C4×Dic13C2314yes—
184C2×C4×Dic13C2312yes—
185C2×C4×Dic13C2312yes—
186C2×C4×Dic13C2312yes—
187C2×C4×Dic13C2314yes—
188#88152C23132yes—
189#88152C23132yes—
190#88152C23132yescomplemented
191#88152C23132yescomplemented
192#88151C2318yes—
193#88151C23116yes—
194#88151C23116yes—
195#88151C23116yes—
196#88151C23116yes—
197#88151C2318yes—
198#88151C23116yescomplemented
199#88151C23116yescomplemented
200#88149C2318yes—
201#88149C2318yes—
202#88148C23132yes—
203#88148C23132yes—
204#88147C23132yes—
205#88147C23116yescomplemented
206#88146C23132yes—
207#88146C2318yes—
208#88146C2318yes—
209#88146C23116yescomplemented
210#88146C23132yescomplemented
211C4⋊C4×D13C2318yes—
212C4⋊C4×D13C2318yes—
213C4⋊C4×D13C23116yescomplemented
214#88144C23132yescomplemented
215#88144C23132yescomplemented
216#88144C23132yescomplemented
217#88141C23116yescomplemented
218#88141C23116yescomplemented
219#88141C23116yescomplemented
220#88140C23116yes—
221#88140C23132yes—
222#88136C23116yes—
223C22⋊C4×D13C23116yes—
224#88131C23132yes—
225#88131C23116yes—
226#88129C23116yescomplemented
227C4×D52C23116yes—
228C4×D52C23116yes—
229#88126C23116yes—
230C42×D13C23116yes—
231#88123C23116yescomplemented
232C4×Dic26C23116yescomplemented
233C4×Dic26C23116yescomplemented
234C2×#3495—131nomaximal, Sylow
235C24×C13C2411yescharacteristic
236C23×D13—24no—
237C23×D13—24no—
238C23×D13—42no—
239C23×D13C2411yescharacteristic
240C23×D13C2412yes—
241C23×D13C2414yes—
242C23×D13C2411yescharacteristic
243C2×Q8×C13—48no—
244C2×Q8×C13C24116yes—
245C22×C4×C13—44no—
246C22×C4×C13#4118yes—
247C22×C4×C13C2412yes—
248C22×C4×C13C2412yes—
249C22×C4×C13C2412yes—
250C22×C4×C13C2412yes—
251C22×C4×C13C2414yes—
252C22×C4×C13C2418yes—
253C22×C4×C13C2411yescharacteristic
254C22×C4×C13C2411yescharacteristic
255C22×C4×C13C2414yes—
256C2×C22⋊D13—28no—
257C2×C22⋊D13C2418yes—
258C22×Dic13—28no—
259C22×Dic13—24no—
260C22×Dic13C2414yes—
261C22×Dic13C2418yes—
262C22×Dic13C2412yes—
263C22×Dic13C2412yes—
264C22×Dic13C2411yescharacteristic
265C22×Dic13C2412yes—
266C22×Dic13C2414yes—
267C22×Dic13C2411yescharacteristic
268#6127—232no—
269C2×D52—28no—
270C2×D52—24no—
271C2×D52—44no—
272C2×D52C2418yes—
273C2×D52C2414yes—
274C2×D52C2418yes—
275C2×C4×D13—28no—
276C2×C4×D13—24no—
277C2×C4×D13—24no—
278C2×C4×D13—24no—
279C2×C4×D13—24no—
280C2×C4×D13—232no—
281C2×C4×D13—28no—
282C2×C4×D13—48no—
283C2×C4×D13—44no—
284C2×C4×D13C2414yes—
285C2×C4×D13C2418yes—
286C2×C4×D13C2414yes—
287C2×C4×D13C2414yes—
288C2×C4×D13C2418yes—
289C2×C4×D13C2414yes—
290C2×C4×D13C2418yes—
291C2×C4×D13C24116yes—
292C2×Dic26—28no—
293C2×Dic26—28no—
294C2×Dic26—232no—
295C2×Dic26—24no—
296C2×Dic26C2418yes—
297C2×Dic26C2414yes—
298C2×Dic26C2418yes—
299C13×C4⋊C4C2414yes—
300C13×C4⋊C4C2414yes—
301C13×C4⋊C4C2418yes—
302C13×C4⋊C4C24116yes—
303C13×C4⋊C4C24116yes—
304C13×C4⋊C4C24116yes—
305C13×C4⋊C4C2414yes—
306C13×C4⋊C4C2414yes—
307C13×C4⋊C4C2418yes—
308C13×C22⋊C4C2418yes—
309C13×C22⋊C4C2418yes—
310C42×C13C2418yes—
311C42×C13C2418yes—
312C22⋊Dic13C2418yes—
313#6103C2418yes—
314#6103C2418yes—
315#6103C2418yes—
316#6103C2418yes—
317#6103C2418yes—
318#6103C2418yes—
319#6103C24116yes—
320#6103C24116yes—
321#6103C24116yes—
322#6103C24116yes—
323#6103C24116yes—
324C4⋊Dic13C2414yes—
325C4⋊Dic13C2414yes—
326C4⋊Dic13C24116yes—
327C4⋊Dic13C24116yes—
328C4⋊Dic13C2418yes—
329C4⋊Dic13C2418yes—
330C4⋊Dic13C24116yes—
331C4⋊Dic13C24116yes—
332#6101C24116yes—
333#6101C24116yes—
334#6101C2418yes—
335#6101C2418yes—
336#6101C24116yes—
337C4×Dic13C24116yes—
338C4×Dic13C24116yes—
339C4×Dic13C2418yes—
340C4×Dic13C2418yes—
341C4×Dic13C2418yes—
342C4×Dic13C24116yes—
343#3495—1332no—
344C2×#556—132no—
345C2×#554—132no—
346C2×#552—132no—
347C2×#552—132no—
348C2×#552—134no—
349C2×#551—134no—
350C2×#544D1311yescharacteristic, complemented
351C2×#542—132no—
352C2×#541—132no—
353C2×#536—131no—
354C2×#533—132no—
355C2×#529—132no—
356C2×#525—131no—
357C22×C22⋊Q8—131no—
358C2×#520—131no—
359C2×#519—131no—
360C22×#117—131no—
361C23×C13—22no—
362C23×C13—22no—
363C23×C13C2×#4114yes—
364C23×C13C2512yes—
365C23×C13C2511yescharacteristic
366C22×D13—22no—
367C22×D13—22no—
368C22×D13—28no—
369C22×D13—22no—
370C22×D13—24no—
371C22×D13—24no—
372C22×D13—22no—
373C22×D13—24no—
374C22×D13—22no—
375C22×D13—28no—
376C22×D13—44no—
377C22×D13—416no—
378C22×D132−1+414yes—
379C22×D13C2512yes—
380C22×D13C2514yes—
381C22×D13C2512yes—
382Q8×C13—416no—
383C2×C4×C13—24no—
384C2×C4×C13—24no—
385C2×C4×C13—28no—
386C2×C4×C13—24no—
387C2×C4×C13—24no—
388C2×C4×C13—48no—
389C2×C4×C13C2×#4114yes—
390C2×C4×C13C2×#4114yes—
391C2×C4×C13C2×#41116yes—
392C2×C4×C13C2514yes—
393C2×C4×C13C2514yes—
394C2×C4×C13C2514yes—
395C2×C4×C13C2514yes—
396C2×C4×C13C2518yes—
397C2×C4×C13C2512yes—
398C2×C4×C13C2512yes—
399C22⋊D13—216no—
400C2×Dic13—216no—
401C2×Dic13—28no—
402C2×Dic13—24no—
403C2×Dic13—28no—
404C2×Dic13—22no—
405C2×Dic13—22no—
406C2×Dic13—24no—
407C2×Dic13—24no—
408C2×Dic13C2514yes—
409C2×Dic13C2514yes—
410C2×Dic13C2512yes—
411C2×Dic13C2514yes—
412C2×Dic13C2518yes—
413C2×Dic13C2512yes—
414D52—216no—
415D52—28no—
416D52—48no—
417C4×D13—216no—
418C4×D13—28no—
419C4×D13—28no—
420C4×D13—28no—
421C4×D13—28no—
422C4×D13—216no—
423C4×D13—416no—
424C4×D13—48no—
425Dic26—216no—
426Dic26—216no—
427Dic26—28no—
428C22×#41—131no—
429C23×Q8—131no—
430C24×C4—131no—
431#556—1332no—
432#554—1332no—
433#552—1332no—
434#552—1332no—
435#552—1364no—
436#551—1364no—
437#544C2×D13116yescomplemented
438#542—1332no—
439#541—1332no—
440#536—1316no—
441#533—1332no—
442C2×C4⋊Q8—132no—
443C2×C4⋊Q8C2×D1312yescomplemented
444C2×C4⋊Q8C2×D1312yescomplemented
445#529—1332no—
446C2×#126—134no—
447C2×#126—134no—
448C2×#126—134no—
449C2×#126—134no—
450C2×#125—134no—
451C2×#125—134no—
452C2×#125—134no—
453C2×#125C2×D1312yescomplemented
454C2×#125C2×D1312yescomplemented
455C2×#124—134no—
456C2×#124—132no—
457#525—1316no—
458C2×#123—134no—
459C2×#123—134no—
460C2×#123—132no—
461C2×#123—134no—
462C2×C22⋊Q8—134no—
463C2×C22⋊Q8—134no—
464C2×C22⋊Q8—132no—
465C2×C22⋊Q8—132no—
466C2×C22⋊Q8—132no—
467C2×C22⋊Q8—132no—
468C2×C22⋊Q8—131no—
469C2×C22⋊Q8—131no—
470C2×C22⋊Q8—1316no—
471C2×C22⋊Q8—132no—
472C2×C22⋊Q8—132no—
473C2×C22⋊Q8C2×D1314yes—
474C2×#121—131no—
475C2×#121—131no—
476C2×#120—132no—
477#520—1316no—
478#519—1316no—
479C2×C4×Q8—134no—
480C2×C4×Q8—132no—
481C2×C4×Q8—132no—
482C2×C4×Q8—132no—
483C2×C4×Q8—132no—
484C2×C4×Q8—132no—
485C2×C4×D4—134no—
486C2×C4×D4—134no—
487C2×C4×D4—132no—
488C2×C4×D4—132no—
489C2×C4×D4—132no—
490C2×#117—131no—
491C2×#117—1316no—
492C2×#117—131no—
493C2×#117—131no—
494C2×#117—134no—
495C2×#117—132no—
496C2×#117—134no—
497C2×#117—132no—
498C2×#117—134no—
499C2×#117—132no—
500C2×#117C2×D1311yescharacteristic
501C2×#117C2×D1311yescharacteristic
502C22×C4⋊C4—132no—
503C22×C4⋊C4—131no—
504C22×C4⋊C4—131no—
505C22×C4⋊C4—132no—
506C22×C4⋊C4C2×D1311yescharacteristic
507C22×C22⋊C4—132no—
508C22×C22⋊C4—132no—
509C22×C42—132no—
510C22×C13—22no—
511C22×C13—22no—
512C22×C13—28no—
513C22×C13C22×#4114yes—
514C22×C13C22×#4112yes—
515C22×C13C2×2−1+412yes—
516C22×C13#58512yes—
517C22×C13C2611yescharacteristic
518C2×D13—22no—
519C2×D13—22no—
520C2×D13—28no—
521C2×D13—22no—
522C2×D13—24no—
523C2×D13—24no—
524C2×D13—22no—
525C2×D13—24no—
526C2×D13—22no—
527C2×D13—416no—
528C2×D13—48no—
529C2×D13—44no—
530C2×D13C2×2−1+414yes—
531C4×C13—24no—
532C4×C13—24no—
533C4×C13—28no—
534C4×C13—24no—
535C4×C13—24no—
536C4×C13C22×#4114yes—
537C4×C13C22×#4114yes—
538Dic13—28no—
539Dic13—24no—
540Dic13—22no—
541Dic13—22no—
542Dic13—24no—
543Dic13—24no—
544C25—131no—
545C2×#41—138no—
546C2×#41—268no—
547C22×Q8—132no—
548C22×Q8—132no—
549C22×Q8—131no—
550C22×Q8—138no—
551C22×Q8—268no—
552C22×Q8C22×D1314yes—
553C22×D4—132no—
554C22×D4—132no—
555C22×D4—131no—
556C22×D4—132no—
557C23×C4—132no—
558C23×C4—131no—
559C23×C4—132no—
560C23×C4—131no—
561C23×C4—132no—
562C23×C4—131no—
563C23×C4—131no—
564C23×C4—138no—
565C23×C4—131no—
566C23×C4—132no—
567C23×C4—134no—
568C23×C4—268no—
569C23×C4C22×D1312yes—
570C23×C4C22×D1311yescharacteristic
571C4⋊Q8—1316no—
572C4⋊Q8C22×D13116yescomplemented
573C4⋊Q8C22×D13116yescomplemented
574#126—1332no—
575#126—1332no—
576#126—1332no—
577#126—1332no—
578#125—1332no—
579#125—1332no—
580#125—1332no—
581#125C22×D13116yescomplemented
582#125C22×D13116yescomplemented
583#124—1332no—
584#124—1316no—
585#123—1332no—
586#123—1332no—
587#123—1316no—
588#123—1332no—
589C22⋊Q8—1332no—
590C22⋊Q8—1332no—
591C22⋊Q8—1316no—
592C22⋊Q8—1316no—
593C22⋊Q8—1316no—
594C22⋊Q8—1316no—
595C22⋊Q8—138no—
596C22⋊Q8—138no—
597C22⋊Q8—1316no—
598C22⋊Q8—1316no—
599C22⋊Q8C22×D13132yes—
600#121—138no—
601#121—138no—
602#120—1316no—
603C4×Q8—1332no—
604C4×Q8—1316no—
605C4×Q8—1316no—
606C4×Q8—1316no—
607C4×Q8—1316no—
608C4×Q8—1316no—
609C4×D4—1332no—
610C4×D4—1316no—
611C4×D4—1332no—
612C4×D4—1316no—
613C4×D4—1316no—
614#117—138no—
615#117—138no—
616#117—138no—
617#117—1316no—
618#117—1332no—
619#117—1332no—
620#117—1316no—
621#117—1332no—
622#117—1316no—
623#117C22×D1318yes—
624#117C22×D1318yes—
625C2×C4⋊C4—131no—
626C2×C4⋊C4—131no—
627C2×C4⋊C4—132no—
628C2×C4⋊C4—132no—
629C2×C4⋊C4—134no—
630C2×C4⋊C4—134no—
631C2×C4⋊C4—134no—
632C2×C4⋊C4—1316no—
633C2×C4⋊C4—134no—
634C2×C4⋊C4—134no—
635C2×C4⋊C4—134no—
636C2×C4⋊C4—132no—
637C2×C4⋊C4—132no—
638C2×C4⋊C4—134no—
639C2×C4⋊C4—138no—
640C2×C4⋊C4—138no—
641C2×C4⋊C4—1316no—
642C2×C4⋊C4C22×D1312yes—
643C2×C4⋊C4C22×D1311yescharacteristic
644C2×C4⋊C4C22×D1311yescharacteristic
645C2×C4⋊C4C22×D1312yes—
646C2×C4⋊C4C22×D1318yes—
647C2×C4⋊C4C22×D1314yes—
648C2×C4⋊C4C22×D1314yes—
649C2×C4⋊C4C22×D1311yescharacteristic
650C2×C4⋊C4C22×D1311yescharacteristic
651C2×C4⋊C4C22×D1314yes—
652C2×C22⋊C4—132no—
653C2×C22⋊C4—132no—
654C2×C22⋊C4—132no—
655C2×C22⋊C4—134no—
656C2×C22⋊C4—134no—
657C2×C22⋊C4—1316no—
658C2×C22⋊C4—132no—
659C2×C22⋊C4—132no—
660C2×C22⋊C4—134no—
661C2×C22⋊C4—134no—
662C2×C22⋊C4—132no—
663C2×C22⋊C4—132no—
664C2×C22⋊C4—134no—
665C2×C22⋊C4—1316no—
666C2×C22⋊C4C22×D1312yes—
667C2×C22⋊C4C22×D1312yes—
668C2×C42—132no—
669C2×C42—132no—
670C2×C42—134no—
671C2×C42—134no—
672C2×C42—134no—
673C2×C42—132no—
674C2×C42—1316no—
675C2×C42C22×D1312yes—
676C2×C42C22×D1312yes—
677C2×C13—24no—
678C2×C13#349514yescomplemented
679C2×C13C23×#4111yescharacteristic
680C2×C13C22×2−1+411yescharacteristic
681C2×C13C2×#58511yescharacteristic
682D13—24no—
683D13—44no—
684D13—42no—
685C24—131no—
686C24—131no—
687C24—132no—
688C24—134no—
689C24—264no—
690C24—264no—
691C24—522no—
692C24C23×D1311yescharacteristic
693#41—2632no—
694C2×Q8—48no—
695C2×Q8—138no—
696C2×Q8—138no—
697C2×Q8—134no—
698C2×Q8—268no—
699C2×Q8—268no—
700C2×Q8—2632no—
701C2×Q8—264no—
702C2×Q8C23×D13116yes—
703C2×D4—138no—
704C2×D4—138no—
705C2×D4—134no—
706C2×D4—138no—
707C2×D4—268no—
708C2×D4—268no—
709C2×D4—264no—
710C2×D4—524no—
711C22×C4—44no—
712C22×C4—138no—
713C22×C4—134no—
714C22×C4—132no—
715C22×C4—131no—
716C22×C4—132no—
717C22×C4—134no—
718C22×C4—132no—
719C22×C4—131no—
720C22×C4—134no—
721C22×C4—138no—
722C22×C4—134no—
723C22×C4—138no—
724C22×C4—134no—
725C22×C4—134no—
726C22×C4—138no—
727C22×C4—1316no—
728C22×C4—268no—
729C22×C4—264no—
730C22×C4—268no—
731C22×C4—264no—
732C22×C4—264no—
733C22×C4—264no—
734C22×C4—264no—
735C22×C4—2632no—
736C22×C4—268no—
737C22×C4—528no—
738C22×C4—524no—
739C22×C4#613118yes—
740C22×C4C23×D1312yes—
741C22×C4C23×D1312yes—
742C22×C4C23×D1312yes—
743C22×C4C23×D1312yes—
744C22×C4C23×D1314yes—
745C22×C4C23×D1318yes—
746C22×C4C23×D1314yes—
747C22×C4C23×D1311yescharacteristic
748C22×C4C23×D1311yescharacteristic
749C4⋊C4—134no—
750C4⋊C4—134no—
751C4⋊C4—138no—
752C4⋊C4—138no—
753C4⋊C4—1316no—
754C4⋊C4—1316no—
755C4⋊C4—1316no—
756C4⋊C4—1316no—
757C4⋊C4—1316no—
758C4⋊C4—1316no—
759C4⋊C4—138no—
760C4⋊C4—138no—
761C4⋊C4—1316no—
762C4⋊C4C23×D1318yes—
763C4⋊C4C23×D1314yes—
764C4⋊C4C23×D1314yes—
765C4⋊C4C23×D1318yes—
766C4⋊C4C23×D13116yes—
767C4⋊C4C23×D13116yes—
768C4⋊C4C23×D1314yes—
769C4⋊C4C23×D1314yes—
770C4⋊C4C23×D13116yes—
771C22⋊C4—138no—
772C22⋊C4—138no—
773C22⋊C4—138no—
774C22⋊C4—1316no—
775C22⋊C4—1316no—
776C22⋊C4—138no—
777C22⋊C4—138no—
778C22⋊C4—1316no—
779C22⋊C4—1316no—
780C22⋊C4—138no—
781C22⋊C4—138no—
782C22⋊C4—1316no—
783C22⋊C4C23×D1318yes—
784C22⋊C4C23×D1318yes—
785C42—138no—
786C42—138no—
787C42—138no—
788C42—1316no—
789C42—1316no—
790C42—1316no—
791C42C23×D1318yes—
792C42C23×D1318yes—
793C13C2×#349511yescharacteristic, complemented, Sylow
794C23—22no—
795C23—22no—
796C23—134no—
797C23—132no—
798C23—132no—
799C23—134no—
800C23—268no—
801C23—262no—
802C23—262no—
803C23—268no—
804C23—262no—
805C23—264no—
806C23—264no—
807C23—262no—
808C23—264no—
809C23—262no—
810C23—524no—
811C23—5216no—
812C23C2×#613114yes—
813C23C24×D1312yes—
814C23C24×D1311yescharacteristic
815Q8—416no—
816Q8—2616no—
817Q8—2616no—
818Q8—268no—
819D4—2616no—
820D4—2616no—
821D4—268no—
822D4—528no—
823C2×C4—28no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—48no—
829C2×C4—134no—
830C2×C4—132no—
831C2×C4—134no—
832C2×C4—138no—
833C2×C4—134no—
834C2×C4—132no—
835C2×C4—2616no—
836C2×C4—268no—
837C2×C4—262no—
838C2×C4—262no—
839C2×C4—264no—
840C2×C4—2616no—
841C2×C4—268no—
842C2×C4—264no—
843C2×C4—264no—
844C2×C4—268no—
845C2×C4—268no—
846C2×C4—268no—
847C2×C4—268no—
848C2×C4—2616no—
849C2×C4—5216no—
850C2×C4—528no—
851C2×C4C2×#613114yes—
852C2×C4C2×#613114yes—
853C2×C4C2×#6131116yes—
854C2×C4C24×D1314yes—
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—134no—
865C22—268no—
866C22—262no—
867C22—262no—
868C22—262no—
869C22—264no—
870C22—264no—
871C22—262no—
872C22—264no—
873C22—262no—
874C22—5216no—
875C22—528no—
876C22—524no—
877C22C22×#613114yes—
878C22C22×#613112yes—
879C22#1171965012yes—
880C22D13×2−1+412yes—
881C22C25×D1311yescharacteristic
882C4—24no—
883C4—24no—
884C4—28no—
885C4—24no—
886C4—24no—
887C4—262no—
888C4—262no—
889C4—264no—
890C4—268no—
891C4—264no—
892C4—264no—
893C4C22×#613114yes—
894C4C22×#613114yes—
895C2—24no—
896C2—264no—
897C2—522no—
898C2—524no—
899C2#1312859114yesdirect product factor
900C2C23×#613111yescharacteristic
901C2C2×D13×2−1+411yescharacteristic
902C2C2×#1171965011yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#544C2
socleC23×C13C25
prime radicalC2×#11719229C2
hypercenterC2×#544D13
hypocenterC13C2×#3495
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. #13128591C2direct (N × H)
2. C2×#11719437C2semidirect
3. C2×#11719435C2semidirect
4. C2×#11719347C2semidirect
5. C2×#11719399C2semidirect
6. C2×#11719399C2semidirect
7. C2×#11719342C2semidirect
8. C2×#11719438C2semidirect
9. C2×#11719402C2semidirect
10. C2×#11719231C2semidirect
11. C2×#11719433C2semidirect
12. C2×#11719396C2semidirect
14. C22×#88151C2semidirect
15. C2×#11719209C2semidirect
16. C2×#11719221C2semidirect
17. C2×D13×#117C2semidirect
18. C2×C13×#544C2semidirect
22. C13×#544C22semidirect
23. C2×C13×C4⋊Q8C22semidirect
24. C2×C13×C4⋊Q8C22semidirect
25. C2×C13×#125C22semidirect
26. C2×C13×#125C22semidirect
33. C2×#88200C22semidirect
34. C2×Q8×Dic13C22semidirect
39. #11719438C22semidirect
40. #11719437C22semidirect
41. #11719435C22semidirect
42. #11719433C22semidirect
43. #11719402C22semidirect
44. #11719399C22semidirect
45. #11719399C22semidirect
46. #11719396C22semidirect
47. #11719347C22semidirect
48. #11719342C22semidirect
49. #11719231C22semidirect
51. D13×#117C22semidirect
52. #11719221C22semidirect
55. C2×#88152C22semidirect
56. C2×#88152C22semidirect
63. C2×#88151C22semidirect
64. C2×#88151C22semidirect
65. C2×#88151C22semidirect
70. #11719209C22semidirect
72. C2×#88147C22semidirect
76. C2×#88146C22semidirect
77. C2×#88146C22semidirect
80. C2×C4⋊C4×D13C22semidirect
81. C2×#88144C22semidirect
82. C2×#88144C22semidirect
83. C2×#88144C22semidirect
84. C2×#88141C22semidirect
85. C2×#88141C22semidirect
86. C2×#88141C22semidirect
93. C2×#88129C22semidirect
98. C2×#88123C22semidirect
99. C2×C4×Dic26C22semidirect
100. C2×C4×Dic26C22semidirect
128. C13×C4⋊Q8C23semidirect
129. C13×C4⋊Q8C23semidirect
130. C13×#125C23semidirect
131. C13×#125C23semidirect
152. #88200C23semidirect
153. Q8×Dic13C23semidirect
190. #88152C23semidirect
191. #88152C23semidirect
198. #88151C23semidirect
199. #88151C23semidirect
205. #88147C23semidirect
209. #88146C23semidirect
210. #88146C23semidirect
213. C4⋊C4×D13C23semidirect
214. #88144C23semidirect
215. #88144C23semidirect
216. #88144C23semidirect
217. #88141C23semidirect
218. #88141C23semidirect
219. #88141C23semidirect
226. #88129C23semidirect
231. #88123C23semidirect
232. C4×Dic26C23semidirect
233. C4×Dic26C23semidirect
350. C2×#544D13semidirect
437. #544C2×D13semidirect
443. C2×C4⋊Q8C2×D13semidirect
444. C2×C4⋊Q8C2×D13semidirect
453. C2×#125C2×D13semidirect
454. C2×#125C2×D13semidirect
572. C4⋊Q8C22×D13semidirect
573. C4⋊Q8C22×D13semidirect
581. #125C22×D13semidirect
582. #125C22×D13semidirect
678. C2×C13#3495semidirect
793. C13C2×#3495semidirect
899. C2#13128591direct (N × H)

Maximal subgroups

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

subgroupindex
#131285912
C2×#117194372
C2×#117194352
C2×#117193472
C2×#117193992
C2×#117193422
C2×#117194382
C2×#117194022
C2×#117192312
C2×#117194332
C2×#117193962
C2×#117192292
C22×#881512
C2×#117192092
C2×#117192212
C2×D13×#1172
C2×C13×#5442
C2×#349513