Finite Group Databasebeta

← C2×#13129243 #16770725

Subgroups — C2×#13129243 #16770725

Order 3328.

7074 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13129243C2132yesmaximal, direct product factor
2C2×#11719351C214yesmaximal, complemented
3C2×#11719264C212yesmaximal, complemented
4C2×#11719427C212yesmaximal, complemented
5C2×#11719289C211yesmaximal, characteristic, complemented
6C2×#11719346C212yesmaximal, complemented
7C2×#11719247C211yesmaximal, characteristic, complemented
8C2×#11719432C211yesmaximal, characteristic, complemented
9C2×Q8×C22⋊D13C212yesmaximal, complemented
10C2×#11719438C212yesmaximal, complemented
11C2×#11719345C214yesmaximal, complemented
12C2×#11719266C212yesmaximal, complemented
13C2×#11719521C212yesmaximal, complemented
14C2×#11719333C212yesmaximal, complemented
15C2×#11719433C211yesmaximal, characteristic, complemented
16C2×#11719283C211yesmaximal, characteristic, complemented
17C2×#11719253C211yesmaximal, characteristic
18C2×D4×Q8×C13C211yesmaximal, characteristic, complemented
19C23×Q8×C13C2212yes—
20C22×Q8×D13C2212yes—
21C22×#6127C2212yes—
22D4×Q8×C13C22116yescomplemented
23C2×C13×C4⋊Q8C2212yes—
24C2×C13×C4⋊Q8C2211yescharacteristic
25C2×C13×C22⋊Q8C2214yes—
26C2×C13×C22⋊Q8C2212yes—
27C2×C4×Q8×C13C2211yescharacteristic
28C2×C4×D4×C13C2212yes—
29C2×C4×D4×C13C2211yescharacteristic
30#11719521C22132yescomplemented
31Q8×C22⋊D13C22132yescomplemented
32C2×#88201C2214yes—
33C2×#88200C2214yes—
34C2×#88200C2212yes—
35C2×#88200C2212yes—
36C2×#88200C2211yescharacteristic
37C2×#88200C2212yes—
38C2×Q8×Dic13C2212yes—
39C2×#88198C2214yes—
40C2×#88198C2214yes—
41C2×#88198C2211yescharacteristic
42C2×#88194C2211yescharacteristic
43C2×#88192C2211yescharacteristic
44C2×#88190C2212yes—
45C2×#88183C2214yes—
46C2×#88183C2214yes—
47C2×C4×C22⋊D13C2214yes—
48C2×C4×C22⋊D13C2212yes—
49C2×#88180C2212yes—
50C2×#88178C2214yes—
51C2×#88178C2212yes—
52#11719438C22132yescomplemented
53#11719433C22116yescomplemented
54#11719432C22116yescomplemented
55#11719427C22132yescomplemented
56#11719351C22164yescomplemented
57#11719346C22132yescomplemented
58#11719345C22164yescomplemented
59#11719333C22132yescomplemented
60#11719289C22116yescomplemented
61#11719283C22116yescomplemented
62#11719266C22132yescomplemented
63#11719264C22132yescomplemented
64#11719253C22116yes—
65#11719247C22116yescomplemented
66C2×#88152C2214yes—
67C2×#88152C2214yes—
68C2×#88151C2212yes—
69C2×#88151C2211yescharacteristic
70C2×#88150C2214yes—
71C2×#88150C2212yes—
72C2×#88149C2211yescharacteristic
73C2×#88148C2214yes—
74C2×#88147C2212yes—
75C2×#88146C2212yes—
76C2×#88146C2212yes—
77C2×#88144C2212yes—
78C2×#88143C2212yes—
79C2×#88142C2214yes—
80C2×#88142C2212yes—
81C2×#88142C2211yescharacteristic
82C2×#88142C2211yescharacteristic
83C2×#88141C2214yes—
84C2×#88141C2212yes—
85C2×#88141C2212yes—
86C2×#88139C2212yes—
87C2×#88139C2214yes—
88C2×#88139C2214yes—
89C2×#88138C2212yes—
90C2×#88137C2214yes—
91C2×#88133C2214yes—
92C2×#88133C2214yes—
93C2×#88129C2212yes—
94C2×C4×D52C2211yescharacteristic
95C2×#88126C2212yes—
96C2×C42×D13C2211yescharacteristic
97C2×#88123C2211yescharacteristic
98C2×C4×Dic26C2212yes—
99C2×C4×Dic26C2211yescharacteristic
100C2×C4×Dic26C2212yes—
101C22×Q8×C13—48no—
102C22×Q8×C13C2311yescharacteristic
103C22×Q8×C13C2312yes—
104C22×Q8×C13C2314yes—
105C22×Q8×C13C23116yes—
106C22×D4×C13C2311yescharacteristic
107C23×C4×C13C2312yes—
108C23×C4×C13C2314yes—
109C22×C22⋊D13C2312yes—
110C22×C22⋊D13C2312yes—
111C22×C22⋊D13C2312yes—
112C2×Q8×D13—48no—
113C2×Q8×D13C23116yes—
114C2×#6127—48no—
115C2×#6127C23116yes—
116C22×D52C2311yescharacteristic
117C22×D52C2312yes—
118C22×C4×D13C2311yescharacteristic
119C22×C4×D13C2311yescharacteristic
120C22×C4×D13C2311yescharacteristic
121C22×C4×D13C2312yes—
122C22×C4×D13C2314yes—
123C22×Dic26C2312yes—
124C22×Dic26C2312yes—
125C22×Dic26C2311yescharacteristic
126C22×Dic26C2312yes—
127C22×Dic26C2314yes—
128C13×C4⋊Q8C23116yes—
129C13×C4⋊Q8C2318yes—
130C13×C22⋊Q8C23116yes—
131C13×C22⋊Q8C23132yes—
132C4×Q8×C13C2318yes—
133C4×D4×C13C2318yes—
134C4×D4×C13C23116yes—
135C2×C13×C4⋊C4C2311yescharacteristic
136C2×C13×C4⋊C4C2312yes—
137C2×C13×C4⋊C4C2314yes—
138C2×C13×C4⋊C4C2311yescharacteristic
139C2×C13×C4⋊C4C2312yes—
140C2×C13×C4⋊C4C2312yes—
141C2×C13×C22⋊C4C2312yes—
142C2×C13×C22⋊C4C2314yes—
143C2×C42×C13C2312yes—
144C2×C42×C13C2311yescharacteristic
145C2×C22⋊Dic13C2312yes—
146C2×C22⋊Dic13C2314yes—
147C2×C22⋊Dic13C2314yes—
148#88201C23132yes—
149#88200C23116yes—
150#88200C23116yes—
151#88200C23132yes—
152#88200C23116yes—
153#88200C2318yes—
154Q8×Dic13C23116yes—
155#88198C23132yes—
156#88198C23132yes—
157#88198C2318yes—
158#88194C2318yes—
159#88192C2318yes—
160#88190C23116yes—
161#88183C23132yes—
162#88183C23132yes—
163C4×C22⋊D13C23116yes—
164C4×C22⋊D13C23132yes—
165C2×#6103C2312yes—
166C2×#6103C2312yes—
167C2×#6103C2312yes—
168C2×#6103C2314yes—
169C2×#6103C2314yes—
170C2×#6103C2314yes—
171C2×#6103C2314yes—
172C2×#6103C2312yes—
173#88180C23116yes—
174C2×C4⋊Dic13C2311yescharacteristic
175C2×C4⋊Dic13C2312yes—
176C2×C4⋊Dic13C2311yescharacteristic
177C2×C4⋊Dic13C2312yes—
178C2×C4⋊Dic13C2312yes—
179C2×C4⋊Dic13C2314yes—
180#88178C23116yes—
181#88178C23132yes—
182C2×#6101C2312yes—
183C2×#6101C2312yes—
184C2×#6101C2312yes—
185C2×#6101C2314yes—
186C2×#6101C2312yes—
187C2×#6101C2312yes—
188C2×#6101C2314yes—
189C2×#6101C2314yes—
190C2×#6101C2314yes—
191C2×#6101C2312yes—
192C2×C4×Dic13C2311yescharacteristic
193C2×C4×Dic13C2312yes—
194C2×C4×Dic13C2314yes—
195C2×C4×Dic13C2311yescharacteristic
196C2×C4×Dic13C2311yescharacteristic
197C2×C4×Dic13C2314yes—
198C2×C4×Dic13C2314yes—
199#88152C23132yes—
200#88152C23132yes—
201#88151C23116yes—
202#88151C2318yes—
203#88150C23132yes—
204#88150C23116yes—
205#88149C2318yes—
206#88148C23132yes—
207#88147C23116yes—
208#88146C23116yes—
209#88146C23116yes—
210#88144C23116yes—
211#88143C23116yes—
212#88142C2318yes—
213#88142C23116yes—
214#88142C23132yes—
215#88142C2318yes—
216#88141C23116yes—
217#88141C23116yes—
218#88141C23132yes—
219#88139C23116yes—
220#88139C23132yes—
221#88139C23132yes—
222#88138C23116yes—
223#88137C23132yes—
224#88133C23132yes—
225#88133C23132yes—
226#88129C23116yes—
227C4×D52C2318yes—
228#88126C23116yes—
229C42×D13C2318yes—
230#88123C2318yes—
231C4×Dic26C23116yes—
232C4×Dic26C23116yes—
233C4×Dic26C2318yes—
234C2×#3550—131nomaximal, Sylow
235C24×C13C2412yes—
236C23×D13C2412yes—
237C23×D13C2411yescharacteristic
238C2×Q8×C13—28no—
239C2×Q8×C13—24no—
240C2×Q8×C13—48no—
241C2×Q8×C13—432no—
242C2×Q8×C13C2414yes—
243C2×Q8×C13C2418yes—
244C2×Q8×C13C24116yes—
245C2×D4×C13—24no—
246C2×D4×C13C2414yes—
247C22×C4×C13—28no—
248C22×C4×C13—48no—
249C22×C4×C13C2412yes—
250C22×C4×C13C2412yes—
251C22×C4×C13C2411yescharacteristic
252C22×C4×C13C2414yes—
253C22×C4×C13C2412yes—
254C22×C4×C13C2418yes—
255C22×C4×C13C24116yes—
256C22×C4×C13C2411yescharacteristic
257C22×C4×C13C2411yescharacteristic
258C2×C22⋊D13—28no—
259C2×C22⋊D13—44no—
260C2×C22⋊D13—44no—
261C2×C22⋊D13C2418yes—
262C2×C22⋊D13C2418yes—
263C2×C22⋊D13C2418yes—
264C22×Dic13C2412yes—
265C22×Dic13C2414yes—
266C22×Dic13C2411yescharacteristic
267C22×Dic13C2412yes—
268C22×Dic13C2411yescharacteristic
269C22×Dic13C2412yes—
270C22×Dic13C2411yescharacteristic
271Q8×D13—432no—
272#6127—432no—
273C2×D52—24no—
274C2×D52—44no—
275C2×D52C2414yes—
276C2×D52C2418yes—
277C2×C4×D13—24no—
278C2×C4×D13—28no—
279C2×C4×D13—24no—
280C2×C4×D13—24no—
281C2×C4×D13—48no—
282C2×C4×D13C2414yes—
283C2×C4×D13C2414yes—
284C2×C4×D13C2414yes—
285C2×C4×D13C2418yes—
286C2×C4×D13C24116yes—
287C2×Dic26—24no—
288C2×Dic26—28no—
289C2×Dic26—28no—
290C2×Dic26—44no—
291C2×Dic26—48no—
292C2×Dic26C2418yes—
293C2×Dic26C2418yes—
294C2×Dic26C2414yes—
295C2×Dic26C2418yes—
296C2×Dic26C24116yes—
297C13×C4⋊C4C2414yes—
298C13×C4⋊C4C2418yes—
299C13×C4⋊C4C24116yes—
300C13×C4⋊C4C2414yes—
301C13×C4⋊C4C2418yes—
302C13×C4⋊C4C2418yes—
303C13×C22⋊C4C2418yes—
304C13×C22⋊C4C24116yes—
305C42×C13C2418yes—
306C42×C13C2414yes—
307C22⋊Dic13C2418yes—
308C22⋊Dic13C24116yes—
309C22⋊Dic13C24116yes—
310#6103C2418yes—
311#6103C2418yes—
312#6103C2418yes—
313#6103C24116yes—
314#6103C24116yes—
315#6103C24116yes—
316#6103C24116yes—
317#6103C2418yes—
318C4⋊Dic13C2414yes—
319C4⋊Dic13C2418yes—
320C4⋊Dic13C2414yes—
321C4⋊Dic13C2418yes—
322C4⋊Dic13C2418yes—
323C4⋊Dic13C24116yes—
324#6101C2418yes—
325#6101C2418yes—
326#6101C2418yes—
327#6101C24116yes—
328#6101C2418yes—
329#6101C2418yes—
330#6101C24116yes—
331#6101C24116yes—
332#6101C24116yes—
333#6101C2418yes—
334C4×Dic13C2414yes—
335C4×Dic13C2418yes—
336C4×Dic13C24116yes—
337C4×Dic13C2414yes—
338C4×Dic13C2414yes—
339C4×Dic13C24116yes—
340C4×Dic13C24116yes—
341#3550—1332no—
342C2×#563—134no—
343C2×#559—132no—
344C2×Q82—132no—
345C2×#556—132no—
346C2×#556—131no—
347C2×#556—131no—
348C2×D4×Q8—132no—
349C2×D4×Q8—131no—
350C2×D4×Q8D1311yescharacteristic, complemented
351C2×#542—132no—
352C2×#542—134no—
353C2×#542—132no—
354C2×#536—132no—
355C2×#536—132no—
356C2×#533—131no—
357C2×#533—131no—
358C2×#532—131no—
359C23×C13—24no—
360C23×C13—24no—
361C23×C13—24no—
362C23×C13C2514yes—
363C23×C13C2511yescharacteristic
364C22×D13—24no—
365C22×D13—22no—
366C22×D13—22no—
367C22×D13—22no—
368C22×D13—24no—
369C22×D13—24no—
370C22×D13C2514yes—
371C22×D13C2512yes—
372Q8×C13—216no—
373Q8×C13—28no—
374Q8×C13—416no—
375D4×C13—28no—
376C2×C4×C13—28no—
377C2×C4×C13—24no—
378C2×C4×C13—24no—
379C2×C4×C13—24no—
380C2×C4×C13—22no—
381C2×C4×C13—216no—
382C2×C4×C13—416no—
383C2×C4×C13H(5,𝔽2)14yes—
384C2×C4×C132−1+414yes—
385C2×C4×C13C2514yes—
386C2×C4×C13C2514yes—
387C2×C4×C13C2512yes—
388C2×C4×C13C2518yes—
389C2×C4×C13C2514yes—
390C2×C4×C13C2512yes—
391C2×C4×C13C2512yes—
392C22⋊D13—216no—
393C22⋊D13—48no—
394C22⋊D13—48no—
395C2×Dic13—24no—
396C2×Dic13—24no—
397C2×Dic13—22no—
398C2×Dic13—28no—
399C2×Dic13—24no—
400C2×Dic13—22no—
401C2×Dic132−1+414yes—
402C2×Dic13C2514yes—
403C2×Dic13C2518yes—
404C2×Dic13C2512yes—
405C2×Dic13C2514yes—
406C2×Dic13C2512yes—
407C2×Dic13C2514yes—
408C2×Dic13C2512yes—
409D52—28no—
410D52—48no—
411C4×D13—28no—
412C4×D13—216no—
413C4×D13—28no—
414C4×D13—28no—
415C4×D13—416no—
416Dic26—28no—
417Dic26—216no—
418Dic26—216no—
419Dic26—48no—
420Dic26—416no—
421C22×#41—132no—
422C23×Q8—132no—
423C23×Q8C2×D1312yes—
424#563—1364no—
425#559—1332no—
426Q82—1332no—
427#556—1332no—
428#556—1316no—
429#556—1316no—
430D4×Q8—1332no—
431D4×Q8—1316no—
432D4×Q8C2×D13116yescomplemented
433#542—1332no—
434#542—1364no—
435#542—1332no—
436#536—1332no—
437#536—1332no—
438#533—1316no—
439#533—1316no—
440#532—1316no—
441C2×C4⋊Q8—131no—
442C2×C4⋊Q8—134no—
443C2×C4⋊Q8—134no—
444C2×C4⋊Q8—131no—
445C2×C4⋊Q8—131no—
446C2×C4⋊Q8—134no—
447C2×C4⋊Q8—132no—
448C2×C4⋊Q8—131no—
449C2×C4⋊Q8C2×D1311yescharacteristic
450C2×C4⋊Q8C2×D1312yes—
451C2×#127—131no—
452C2×#126—134no—
453C2×#126—134no—
454C2×#126—134no—
455C2×#126—134no—
456C2×#125—132no—
457C2×#125—132no—
458C2×#124—134no—
459C2×#124—132no—
460C2×#124—132no—
461C2×#124—134no—
462C2×#124—134no—
463C2×#124—132no—
464C2×#123—134no—
465C2×#123—134no—
466C2×#123—134no—
467C2×#123—134no—
468C2×C22⋊Q8—132no—
469C2×C22⋊Q8—131no—
470C2×C22⋊Q8—132no—
471C2×C22⋊Q8—132no—
472C2×C22⋊Q8—134no—
473C2×C22⋊Q8—132no—
474C2×C22⋊Q8—134no—
475C2×C22⋊Q8—132no—
476C2×C22⋊Q8—134no—
477C2×C22⋊Q8—131no—
478C2×C22⋊Q8—132no—
479C2×C22⋊Q8C2×D1312yes—
480C2×C22⋊Q8C2×D1314yes—
481C2×#121—131no—
482C2×#121—131no—
483C2×#121—132no—
484C2×C4×Q8—132no—
485C2×C4×Q8—132no—
486C2×C4×Q8—134no—
487C2×C4×Q8—132no—
488C2×C4×Q8—131no—
489C2×C4×Q8—132no—
490C2×C4×Q8—132no—
491C2×C4×Q8C2×D1311yescharacteristic
492C2×C4×D4—132no—
493C2×C4×D4—134no—
494C2×C4×D4—132no—
495C2×C4×D4—131no—
496C2×C4×D4C2×D1311yescharacteristic
497C2×C4×D4C2×D1312yes—
498C2×#117—132no—
499C2×#117—132no—
500C2×#117—132no—
501C2×#117—132no—
502C22×C42—131no—
503C22×C13—24no—
504C22×C13—24no—
505C22×C13—24no—
506C22×C13—48no—
507C22×C13C2×H(5,𝔽2)12yes—
508C22×C13C2×2−1+412yes—
509C22×C13C2×2−1+412yes—
510C22×C13C2611yescharacteristic
511C2×D13—24no—
512C2×D13—22no—
513C2×D13—22no—
514C2×D13—22no—
515C2×D13—24no—
516C2×D13—24no—
517C2×D13—48no—
518C2×D13—44no—
519C4×C13—28no—
520C4×C13—24no—
521C4×C13—24no—
522C4×C13—24no—
523C4×C13—22no—
524C4×C13C2×H(5,𝔽2)14yes—
525C4×C13C2×2−1+414yes—
526Dic13—24no—
527Dic13—24no—
528Dic13—22no—
529Dic13—24no—
530Dic13—28no—
531Dic13—22no—
532Dic13C2×2−1+414yes—
533C2×#41—1316no—
534C2×#41—528no—
535C22×Q8—48no—
536C22×Q8—1316no—
537C22×Q8—132no—
538C22×Q8—132no—
539C22×Q8—131no—
540C22×Q8—134no—
541C22×Q8—132no—
542C22×Q8—528no—
543C22×Q8C22×D1312yes—
544C22×Q8C22×D1311yescharacteristic
545C22×Q8C22×D1314yes—
546C22×Q8C22×D13116yes—
547C22×D4—132no—
548C22×D4—132no—
549C22×D4—132no—
550C22×D4—131no—
551C22×D4—132no—
552C22×D4C22×D1311yescharacteristic
553C23×C4—131no—
554C23×C4—131no—
555C23×C4—132no—
556C23×C4—131no—
557C23×C4—134no—
558C23×C4C22×D1312yes—
559C23×C4C22×D1314yes—
560C4⋊Q8—138no—
561C4⋊Q8—1332no—
562C4⋊Q8—1332no—
563C4⋊Q8—138no—
564C4⋊Q8—138no—
565C4⋊Q8—1332no—
566C4⋊Q8—1316no—
567C4⋊Q8—138no—
568C4⋊Q8C22×D1318yes—
569C4⋊Q8C22×D13116yes—
570#127—138no—
571#126—1332no—
572#126—1332no—
573#126—1332no—
574#126—1332no—
575#125—1316no—
576#125—1316no—
577#124—1332no—
578#124—1316no—
579#124—1316no—
580#124—1332no—
581#124—1332no—
582#124—1316no—
583#123—1332no—
584#123—1332no—
585#123—1332no—
586#123—1332no—
587C22⋊Q8—1316no—
588C22⋊Q8—138no—
589C22⋊Q8—1316no—
590C22⋊Q8—1316no—
591C22⋊Q8—1332no—
592C22⋊Q8—1316no—
593C22⋊Q8—1332no—
594C22⋊Q8—138no—
595C22⋊Q8—1316no—
596C22⋊Q8—1316no—
597C22⋊Q8—1332no—
598C22⋊Q8C22×D13116yes—
599C22⋊Q8C22×D13132yes—
600#121—138no—
601#121—138no—
602#121—1316no—
603C4×Q8—1316no—
604C4×Q8—1316no—
605C4×Q8—1332no—
606C4×Q8—1316no—
607C4×Q8—138no—
608C4×Q8—1316no—
609C4×Q8—1316no—
610C4×Q8C22×D1318yes—
611C4×D4—1316no—
612C4×D4—1332no—
613C4×D4—1316no—
614C4×D4—138no—
615C4×D4C22×D1318yes—
616C4×D4C22×D13116yes—
617#117—1316no—
618#117—1316no—
619#117—1316no—
620#117—1316no—
621C2×C4⋊C4—131no—
622C2×C4⋊C4—132no—
623C2×C4⋊C4—132no—
624C2×C4⋊C4—132no—
625C2×C4⋊C4—132no—
626C2×C4⋊C4—132no—
627C2×C4⋊C4—132no—
628C2×C4⋊C4—131no—
629C2×C4⋊C4—132no—
630C2×C4⋊C4—134no—
631C2×C4⋊C4—134no—
632C2×C4⋊C4—134no—
633C2×C4⋊C4—134no—
634C2×C4⋊C4—134no—
635C2×C4⋊C4—132no—
636C2×C4⋊C4—132no—
637C2×C4⋊C4C22×D1311yescharacteristic
638C2×C4⋊C4C22×D1312yes—
639C2×C4⋊C4C22×D1312yes—
640C2×C4⋊C4C22×D1311yescharacteristic
641C2×C4⋊C4C22×D1314yes—
642C2×C4⋊C4C22×D1312yes—
643C2×C22⋊C4—134no—
644C2×C22⋊C4—132no—
645C2×C22⋊C4—134no—
646C2×C22⋊C4—134no—
647C2×C22⋊C4—132no—
648C2×C22⋊C4—132no—
649C2×C22⋊C4—134no—
650C2×C22⋊C4—132no—
651C2×C22⋊C4—132no—
652C2×C22⋊C4—134no—
653C2×C22⋊C4—134no—
654C2×C22⋊C4C22×D1312yes—
655C2×C22⋊C4C22×D1314yes—
656C2×C42—134no—
657C2×C42—132no—
658C2×C42—134no—
659C2×C42—134no—
660C2×C42—131no—
661C2×C42—131no—
662C2×C42—131no—
663C2×C42—138no—
664C2×C42C22×D1312yes—
665C2×C42C22×D1311yescharacteristic
666C2×C13—44no—
667C2×C13#355014yescomplemented
668C2×C13C22×H(5,𝔽2)11yescharacteristic
669C2×C13C22×2−1+411yescharacteristic
670C2×C13C22×2−1+411yescharacteristic
671D13—44no—
672D13—42no—
673C24—132no—
674C24—131no—
675C24C23×D1312yes—
676#41—5232no—
677C2×Q8—24no—
678C2×Q8—28no—
679C2×Q8—48no—
680C2×Q8—432no—
681C2×Q8—138no—
682C2×Q8—138no—
683C2×Q8—134no—
684C2×Q8—1316no—
685C2×Q8—138no—
686C2×Q8—268no—
687C2×Q8—264no—
688C2×Q8—268no—
689C2×Q8—528no—
690C2×Q8—524no—
691C2×Q8—5232no—
692C2×Q8C23×D1318yes—
693C2×Q8C23×D1314yes—
694C2×Q8C23×D13116yes—
695C2×D4—24no—
696C2×D4—138no—
697C2×D4—138no—
698C2×D4—138no—
699C2×D4—134no—
700C2×D4—138no—
701C2×D4—268no—
702C2×D4—264no—
703C2×D4—524no—
704C2×D4—524no—
705C2×D4—524no—
706C2×D4C23×D1314yes—
707C22×C4—28no—
708C22×C4—48no—
709C22×C4—131no—
710C22×C4—134no—
711C22×C4—132no—
712C22×C4—131no—
713C22×C4—132no—
714C22×C4—131no—
715C22×C4—132no—
716C22×C4—134no—
717C22×C4—134no—
718C22×C4—134no—
719C22×C4—138no—
720C22×C4—1316no—
721C22×C4—264no—
722C22×C4—268no—
723C22×C4—264no—
724C22×C4—264no—
725C22×C4—528no—
726C22×C4C23×D1318yes—
727C22×C4C23×D1312yes—
728C22×C4C23×D1312yes—
729C22×C4C23×D1311yescharacteristic
730C22×C4C23×D1314yes—
731C22×C4C23×D1312yes—
732C22×C4C23×D13116yes—
733C22×C4C23×D1311yescharacteristic
734C22×C4C23×D1311yescharacteristic
735C4⋊C4—134no—
736C4⋊C4—138no—
737C4⋊C4—138no—
738C4⋊C4—138no—
739C4⋊C4—138no—
740C4⋊C4—138no—
741C4⋊C4—138no—
742C4⋊C4—134no—
743C4⋊C4—138no—
744C4⋊C4—1316no—
745C4⋊C4—1316no—
746C4⋊C4—1316no—
747C4⋊C4—1316no—
748C4⋊C4—1316no—
749C4⋊C4—138no—
750C4⋊C4—138no—
751C4⋊C4C23×D1314yes—
752C4⋊C4C23×D1318yes—
753C4⋊C4C23×D1318yes—
754C4⋊C4C23×D1314yes—
755C4⋊C4C23×D13116yes—
756C4⋊C4C23×D1318yes—
757C22⋊C4—1316no—
758C22⋊C4—138no—
759C22⋊C4—1316no—
760C22⋊C4—1316no—
761C22⋊C4—138no—
762C22⋊C4—138no—
763C22⋊C4—1316no—
764C22⋊C4—138no—
765C22⋊C4—138no—
766C22⋊C4—1316no—
767C22⋊C4—1316no—
768C22⋊C4C23×D1318yes—
769C22⋊C4C23×D13116yes—
770C42—134no—
771C42—134no—
772C42—134no—
773C42—1316no—
774C42—138no—
775C42—1316no—
776C42—1316no—
777C42C23×D1314yes—
778C42C23×D1318yes—
779C13C2×#355011yescharacteristic, complemented, Sylow
780C23—24no—
781C23—24no—
782C23—24no—
783C23—134no—
784C23—132no—
785C23—264no—
786C23—262no—
787C23—262no—
788C23—264no—
789C23—262no—
790C23—264no—
791C23C24×D1314yes—
792C23C24×D1311yescharacteristic
793Q8—28no—
794Q8—216no—
795Q8—416no—
796Q8—2616no—
797Q8—268no—
798Q8—2616no—
799Q8—5216no—
800Q8—528no—
801D4—28no—
802D4—2616no—
803D4—268no—
804D4—528no—
805D4—528no—
806D4—528no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—28no—
810C2×C4—22no—
811C2×C4—24no—
812C2×C4—216no—
813C2×C4—416no—
814C2×C4—134no—
815C2×C4—132no—
816C2×C4—134no—
817C2×C4—138no—
818C2×C4—132no—
819C2×C4—134no—
820C2×C4—132no—
821C2×C4—134no—
822C2×C4—268no—
823C2×C4—262no—
824C2×C4—264no—
825C2×C4—264no—
826C2×C4—262no—
827C2×C4—268no—
828C2×C4—264no—
829C2×C4—2616no—
830C2×C4—268no—
831C2×C4—268no—
832C2×C4—5216no—
833C2×C4#8825114yes—
834C2×C4#8825414yes—
835C2×C4C24×D1314yes—
836C2×C4C24×D1314yes—
837C2×C4C24×D1312yes—
838C2×C4C24×D1318yes—
839C2×C4C24×D1314yes—
840C2×C4C24×D1312yes—
841C2×C4C24×D1312yes—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—48no—
846C22—264no—
847C22—262no—
848C22—262no—
849C22—264no—
850C22—262no—
851C22—264no—
852C22—528no—
853C22—524no—
854C22C2×#8825112yes—
855C22C2×#8825412yes—
856C22D13×2−1+412yes—
857C22C25×D1311yescharacteristic
858C4—24no—
859C4—24no—
860C4—28no—
861C4—22no—
862C4—24no—
863C4—134no—
864C4—262no—
865C4—264no—
866C4—264no—
867C4—264no—
868C4—262no—
869C4—268no—
870C4C2×#8825114yes—
871C4C2×#8825414yes—
872C2—44no—
873C2—524no—
874C2—522no—
875C2#1312924314yesdirect product factor
876C2C22×#8825111yescharacteristic
877C2C2×D13×2−1+411yescharacteristic
878C2C22×#8825411yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×D4×Q8×C13C2
socleC23×C13C25
prime radicalC2×#11719253C2
hypercenterC2×D4×Q8D13
hypocenterC13C2×#3550
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. #13129243C2direct (N × H)
2. C2×#11719351C2semidirect
3. C2×#11719264C2semidirect
4. C2×#11719427C2semidirect
5. C2×#11719289C2semidirect
6. C2×#11719346C2semidirect
7. C2×#11719247C2semidirect
8. C2×#11719432C2semidirect
9. C2×Q8×C22⋊D13C2semidirect
10. C2×#11719438C2semidirect
11. C2×#11719345C2semidirect
12. C2×#11719266C2semidirect
13. C2×#11719521C2semidirect
14. C2×#11719333C2semidirect
15. C2×#11719433C2semidirect
16. C2×#11719283C2semidirect
18. C2×D4×Q8×C13C2semidirect
22. D4×Q8×C13C22semidirect
30. #11719521C22semidirect
31. Q8×C22⋊D13C22semidirect
52. #11719438C22semidirect
53. #11719433C22semidirect
54. #11719432C22semidirect
55. #11719427C22semidirect
56. #11719351C22semidirect
57. #11719346C22semidirect
58. #11719345C22semidirect
59. #11719333C22semidirect
60. #11719289C22semidirect
61. #11719283C22semidirect
62. #11719266C22semidirect
63. #11719264C22semidirect
65. #11719247C22semidirect
350. C2×D4×Q8D13semidirect
432. D4×Q8C2×D13semidirect
667. C2×C13#3550semidirect
779. C13C2×#3550semidirect
875. C2#13129243direct (N × H)

Maximal subgroups

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

subgroupindex
#131292432
C2×#117193512
C2×#117192642
C2×#117194272
C2×#117192892
C2×#117193462
C2×#117192472
C2×#117194322
C2×Q8×C22⋊D132
C2×#117194382
C2×#117193452
C2×#117192662
C2×#117195212
C2×#117193332
C2×#117194332
C2×#117192832
C2×#117192532
C2×D4×Q8×C132
C2×#355013