Finite Group Databasebeta

← C2×#13129310 #16770549

Subgroups — C2×#13129310 #16770549

Order 3328.

7182 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#13129310C2132yesmaximal, direct product factor
2C2×#11719405C214yesmaximal, complemented
3C2×#11719290C211yesmaximal, characteristic, complemented
4C2×#11719290C212yesmaximal, complemented
5C2×#11719395C212yesmaximal, complemented
6C2×#11719282C211yesmaximal, characteristic, complemented
7C2×#11719432C211yesmaximal, characteristic, complemented
8C2×#11719281C212yesmaximal, complemented
9C2×#11719431C212yesmaximal, complemented
10C2×#11719287C212yesmaximal, complemented
11C2×#11719287C212yesmaximal, complemented
12C2×#11719403C212yesmaximal, complemented
13C2×#11719397C214yesmaximal, complemented
14C2×#11719429C212yesmaximal, complemented
15C2×#11719283C211yesmaximal, characteristic, complemented
16C2×#11719430C211yesmaximal, characteristic, complemented
17C2×#11719285C211yesmaximal, characteristic, complemented
18C2×C13×#557C211yesmaximal, characteristic, complemented
19C22×#6131C2212yes—
20C22×#6131C2212yes—
21C22×Q8×D13C2212yes—
22C13×#557C22116yescomplemented
23C2×C13×C4⋊Q8C2212yes—
24C2×C13×C4⋊Q8C2211yescharacteristic
25C2×C13×#125C2214yes—
26C2×C13×#125C2212yes—
27C2×C4×Q8×C13C2212yes—
28C2×C4×Q8×C13C2212yes—
29C2×C4×Q8×C13C2211yescharacteristic
30C2×C4×Q8×C13C2211yescharacteristic
31C2×#88201C2212yes—
32C2×#88201C2212yes—
33C2×#88201C2211yescharacteristic
34C2×#88200C2211yescharacteristic
35C2×#88200C2212yes—
36C2×#88200C2211yescharacteristic
37C2×#88198C2211yescharacteristic
38#11719432C22116yescomplemented
39#11719431C22132yescomplemented
40#11719430C22116yescomplemented
41#11719429C22132yescomplemented
42#11719405C22164yescomplemented
43#11719403C22132yescomplemented
44#11719397C22164yescomplemented
45#11719395C22132yescomplemented
46#11719290C22116yescomplemented
47#11719290C22132yescomplemented
48#11719287C22132yescomplemented
49#11719287C22132yescomplemented
50#11719285C22116yescomplemented
51#11719283C22116yescomplemented
52#11719282C22116yescomplemented
53#11719281C22132yescomplemented
54C2×#88152C2212yes—
55C2×#88151C2211yescharacteristic
56C2×#88151C2214yes—
57C2×#88150C2212yes—
58C2×#88150C2214yes—
59C2×#88150C2214yes—
60C2×#88150C2214yes—
61C2×#88150C2214yes—
62C2×#88149C2212yes—
63C2×#88149C2214yes—
64C2×#88149C2214yes—
65C2×#88149C2214yes—
66C2×#88149C2211yescharacteristic
67C2×#88149C2212yes—
68C2×#88149C2212yes—
69C2×#88148C2212yes—
70C2×#88148C2214yes—
71C2×#88148C2214yes—
72C2×#88148C2214yes—
73C2×#88148C2214yes—
74C2×#88148C2214yes—
75C2×#88148C2214yes—
76C2×#88147C2212yes—
77C2×#88147C2212yes—
78C2×#88147C2212yes—
79C2×#88147C2212yes—
80C2×C4⋊C4×D13C2214yes—
81C2×#88144C2211yescharacteristic
82C2×#88143C2212yes—
83C2×#88142C2211yescharacteristic
84C2×#88142C2212yes—
85C2×#88130C2214yes—
86C2×#88129C2214yes—
87C2×#88129C2214yes—
88C2×#88129C2212yes—
89C2×#88128C2212yes—
90C2×#88128C2211yescharacteristic
91C2×C4×D52C2212yes—
92C2×C4×D52C2212yes—
93C2×C4×D52C2212yes—
94C2×C4×D52C2214yes—
95C2×C4×D52C2211yescharacteristic
96C2×#88126C2212yes—
97C2×#88126C2212yes—
98C2×C42×D13C2211yescharacteristic
99C2×C4×Dic26C2211yescharacteristic
100C2×C4×Dic26C2212yes—
101C22×Q8×C13C2311yescharacteristic
102C22×Q8×C13C2311yescharacteristic
103C22×Q8×C13C2312yes—
104C2×#6131—48no—
105C2×#6131—48no—
106C2×#6131C23116yes—
107C2×#6131C23116yes—
108C2×Q8×D13—48no—
109C2×Q8×D13C23116yes—
110C22×D52C2312yes—
111C22×D52C2311yescharacteristic
112C22×D52C2312yes—
113C22×D52C2314yes—
114C22×D52C2312yes—
115C22×D52C2312yes—
116C22×D52C2314yes—
117C22×D52C2314yes—
118C22×C4×D13C2311yescharacteristic
119C22×C4×D13C2311yescharacteristic
120C22×C4×D13C2312yes—
121C22×C4×D13C2311yescharacteristic
122C22×C4×D13C2314yes—
123C22×C4×D13C2314yes—
124C22×C4×D13C2314yes—
125C22×C4×D13C2314yes—
126C22×Dic26C2311yescharacteristic
127C22×Dic26C2312yes—
128C22×Dic26C2314yes—
129C13×C4⋊Q8C23116yes—
130C13×C4⋊Q8C2318yes—
131C13×#125C23116yes—
132C13×#125C23132yes—
133C4×Q8×C13C23116yes—
134C4×Q8×C13C2318yes—
135C4×Q8×C13C2318yes—
136C4×Q8×C13C23116yes—
137C2×C13×C4⋊C4C2312yes—
138C2×C13×C4⋊C4C2311yescharacteristic
139C2×C13×C4⋊C4C2312yes—
140C2×C13×C4⋊C4C2311yescharacteristic
141C2×C13×C4⋊C4C2314yes—
142C2×C13×C4⋊C4C2312yes—
143C2×C13×C4⋊C4C2314yes—
144C2×C13×C4⋊C4C2312yes—
145C2×C13×C4⋊C4C2314yes—
146C2×C42×C13C2311yescharacteristic
147C2×C42×C13C2312yes—
148C2×C42×C13C2312yes—
149C2×C42×C13C2314yes—
150#88201C23116yes—
151#88201C2318yes—
152#88201C23116yes—
153#88200C2318yes—
154#88200C23116yes—
155#88200C2318yes—
156#88198C2318yes—
157C2×#6103C2312yes—
158C2×#6103C2312yes—
159C2×#6103C2312yes—
160C2×#6103C2312yes—
161C2×#6103C2312yes—
162C2×#6103C2312yes—
163C2×#6103C2314yes—
164C2×#6103C2314yes—
165C2×#6103C2314yes—
166C2×#6103C2312yes—
167C2×#6103C2314yes—
168C2×#6103C2314yes—
169C2×#6103C2314yes—
170C2×#6103C2314yes—
171C2×C4⋊Dic13C2311yescharacteristic
172C2×C4⋊Dic13C2312yes—
173C2×C4⋊Dic13C2311yescharacteristic
174C2×C4⋊Dic13C2312yes—
175C2×#6101C2312yes—
176C2×#6101C2312yes—
177C2×#6101C2312yes—
178C2×#6101C2312yes—
179C2×#6101C2312yes—
180C2×#6101C2312yes—
181C2×#6101C2312yes—
182C2×#6101C2314yes—
183C2×C4×Dic13C2311yescharacteristic
184C2×C4×Dic13C2312yes—
185C2×C4×Dic13C2311yescharacteristic
186C2×C4×Dic13C2311yescharacteristic
187#88152C23116yes—
188#88151C2318yes—
189#88151C23132yes—
190#88150C23132yes—
191#88150C23132yes—
192#88150C23132yes—
193#88150C23116yes—
194#88150C23132yes—
195#88149C23116yes—
196#88149C23116yes—
197#88149C23132yes—
198#88149C23116yes—
199#88149C23132yes—
200#88149C23132yes—
201#88149C2318yes—
202#88148C23132yes—
203#88148C23132yes—
204#88148C23132yes—
205#88148C23132yes—
206#88148C23116yes—
207#88148C23132yes—
208#88148C23132yes—
209#88147C23116yes—
210#88147C23116yes—
211#88147C23116yes—
212#88147C23116yes—
213C4⋊C4×D13C23132yes—
214#88144C2318yes—
215#88143C23116yes—
216#88142C23116yes—
217#88142C2318yes—
218#88130C23132yes—
219#88129C23116yes—
220#88129C23132yes—
221#88129C23132yes—
222#88128C2318yes—
223#88128C23116yes—
224C4×D52C23116yes—
225C4×D52C23116yes—
226C4×D52C2318yes—
227C4×D52C23132yes—
228C4×D52C23116yes—
229#88126C23116yes—
230#88126C23116yes—
231C42×D13C2318yes—
232C4×Dic26C2318yes—
233C4×Dic26C23116yes—
234C2×#3554—131nomaximal, Sylow
235C23×D13C2412yes—
236C23×D13C2411yescharacteristic
237C23×D13C2414yes—
238C2×Q8×C13—28no—
239C2×Q8×C13—24no—
240C2×Q8×C13—24no—
241C2×Q8×C13C2414yes—
242C2×Q8×C13C2414yes—
243C2×Q8×C13C2418yes—
244C22×C4×C13C2411yescharacteristic
245C22×C4×C13C2412yes—
246C22×C4×C13C2412yes—
247C22×C4×C13C2412yes—
248C22×C4×C13C2412yes—
249C22×C4×C13C2414yes—
250C22×C4×C13C2411yescharacteristic
251C22×C4×C13C2411yescharacteristic
252C22×Dic13C2411yescharacteristic
253C22×Dic13C2411yescharacteristic
254C22×Dic13C2411yescharacteristic
255C22×Dic13C2412yes—
256C22×Dic13C2412yes—
257C22×Dic13C2412yes—
258#6131—432no—
259#6131—432no—
260Q8×D13—432no—
261C2×D52—28no—
262C2×D52—28no—
263C2×D52—24no—
264C2×D52—48no—
265C2×D52—44no—
266C2×D52—44no—
267C2×D52—48no—
268C2×D52—48no—
269C2×D52C2414yes—
270C2×D52C2418yes—
271C2×D52C2418yes—
272C2×D52C24116yes—
273C2×D52C2418yes—
274C2×D52C2418yes—
275C2×D52C24116yes—
276C2×D52C24116yes—
277C2×C4×D13—28no—
278C2×C4×D13—24no—
279C2×C4×D13—24no—
280C2×C4×D13—42no—
281C2×C4×D13—48no—
282C2×C4×D13—48no—
283C2×C4×D13—48no—
284C2×C4×D13—48no—
285C2×C4×D13C2414yes—
286C2×C4×D13C2414yes—
287C2×C4×D13C2418yes—
288C2×C4×D13C2414yes—
289C2×C4×D13C24116yes—
290C2×C4×D13C24116yes—
291C2×C4×D13C24116yes—
292C2×C4×D13C24116yes—
293C2×Dic26—24no—
294C2×Dic26—44no—
295C2×Dic26—48no—
296C2×Dic26C2414yes—
297C2×Dic26C2418yes—
298C2×Dic26C24116yes—
299C13×C4⋊C4C2418yes—
300C13×C4⋊C4C2414yes—
301C13×C4⋊C4C2418yes—
302C13×C4⋊C4C2414yes—
303C13×C4⋊C4C24116yes—
304C13×C4⋊C4C2418yes—
305C13×C4⋊C4C24116yes—
306C13×C4⋊C4C2418yes—
307C13×C4⋊C4C24116yes—
308C42×C13C2414yes—
309C42×C13C2418yes—
310C42×C13C2418yes—
311C42×C13C24116yes—
312#6103C2418yes—
313#6103C2418yes—
314#6103C2418yes—
315#6103C2418yes—
316#6103C2418yes—
317#6103C2418yes—
318#6103C24116yes—
319#6103C24116yes—
320#6103C24116yes—
321#6103C2418yes—
322#6103C24116yes—
323#6103C24116yes—
324#6103C24116yes—
325#6103C24116yes—
326C4⋊Dic13C2414yes—
327C4⋊Dic13C2418yes—
328C4⋊Dic13C2414yes—
329C4⋊Dic13C2418yes—
330#6101C2418yes—
331#6101C2418yes—
332#6101C2418yes—
333#6101C2418yes—
334#6101C2418yes—
335#6101C2418yes—
336#6101C2418yes—
337#6101C24116yes—
338C4×Dic13C2414yes—
339C4×Dic13C2418yes—
340C4×Dic13C2414yes—
341C4×Dic13C2414yes—
342#3554—1332no—
343C2×#562—134no—
344C2×#559—132no—
345C2×#559—131no—
346C2×#557D1311yescharacteristic, complemented
347C2×#554—132no—
348C2×#550—131no—
349C2×D4×Q8—131no—
350C2×#548—132no—
351C2×#547—132no—
352C2×#542—132no—
353C2×#542—132no—
354C2×#540—132no—
355C2×#539—134no—
356C2×#536—132no—
357C2×#533—131no—
358C2×#532—131no—
359C2×#529—131no—
360C23×C13C2511yescharacteristic
361C22×D13—24no—
362C22×D13—22no—
363C22×D13—28no—
364C22×D13—22no—
365C22×D13—24no—
366C22×D13—28no—
367C22×D13—22no—
368C22×D13—28no—
369C22×D13—24no—
370C22×D13C2514yes—
371C22×D13C2512yes—
372C22×D13C2518yes—
373Q8×C13—216no—
374Q8×C13—28no—
375Q8×C13—28no—
376C2×C4×C13—28no—
377C2×C4×C13—24no—
378C2×C4×C13—24no—
379C2×C4×C13—24no—
380C2×C4×C13—24no—
381C2×C4×C13—22no—
382C2×C4×C13H(5,𝔽2)14yes—
383C2×C4×C132−1+414yes—
384C2×C4×C13C2512yes—
385C2×C4×C13C2514yes—
386C2×C4×C13C2514yes—
387C2×C4×C13C2514yes—
388C2×C4×C13C2514yes—
389C2×C4×C13C2518yes—
390C2×C4×C13C2512yes—
391C2×C4×C13C2512yes—
392C2×Dic13—24no—
393C2×Dic13—24no—
394C2×Dic13—22no—
395C2×Dic13—22no—
396C2×Dic13—22no—
397C2×Dic13—24no—
398C2×Dic13C2512yes—
399C2×Dic13C2512yes—
400C2×Dic13C2512yes—
401C2×Dic13C2514yes—
402C2×Dic13C2514yes—
403C2×Dic13C2514yes—
404D52—216no—
405D52—28no—
406D52—216no—
407D52—416no—
408D52—48no—
409D52—48no—
410D52—416no—
411D52—416no—
412C4×D13—216no—
413C4×D13—28no—
414C4×D13—28no—
415C4×D13—44no—
416C4×D13—416no—
417C4×D13—416no—
418C4×D13—416no—
419C4×D13—416no—
420Dic26—28no—
421Dic26—48no—
422Dic26—416no—
423C22×#41—132no—
424C22×#41—132no—
425C23×Q8—132no—
426#562—1364no—
427#559—1332no—
428#559—1316no—
429#557C2×D13116yescomplemented
430#554—1332no—
431#550—1316no—
432D4×Q8—1316no—
433#548—1332no—
434#547—1332no—
435#542—1332no—
436#542—1332no—
437#540—1332no—
438#539—1364no—
439#536—1332no—
440#533—1316no—
441#532—1316no—
442C2×C4⋊Q8—131no—
443C2×C4⋊Q8—131no—
444C2×C4⋊Q8—132no—
445C2×C4⋊Q8C2×D1311yescharacteristic
446C2×C4⋊Q8C2×D1312yes—
447C2×#127—131no—
448C2×#127—132no—
449#529—1316no—
450C2×#126—132no—
451C2×#126—134no—
452C2×#125—132no—
453C2×#125—131no—
454C2×#125C2×D1314yes—
455C2×#125C2×D1312yes—
456C2×#124—131no—
457C2×#124—132no—
458C2×#124—132no—
459C2×#124—132no—
460C2×#124—134no—
461C2×#124—134no—
462C2×#123—132no—
463C2×#123—134no—
464C2×#123—134no—
465C2×#123—134no—
466C2×#123—134no—
467C2×#123—134no—
468C2×#123—134no—
469C2×C22⋊Q8—131no—
470C2×C22⋊Q8—131no—
471C2×C22⋊Q8—132no—
472C2×C22⋊Q8—132no—
473C2×C22⋊Q8—134no—
474C2×C22⋊Q8—134no—
475C2×C22⋊Q8—134no—
476C2×C22⋊Q8—134no—
477C2×C22⋊Q8—131no—
478C2×C22⋊Q8—134no—
479C2×#121—131no—
480C2×#121—132no—
481C2×#121—132no—
482C2×#121—134no—
483C2×#121—134no—
484C2×#121—134no—
485C2×#121—132no—
486C2×C4×Q8—131no—
487C2×C4×Q8—132no—
488C2×C4×Q8C2×D1311yescharacteristic
489C2×C4×Q8C2×D1311yescharacteristic
490C2×C4×Q8C2×D1312yes—
491C2×C4×Q8C2×D1312yes—
492C2×C4×D4—132no—
493C2×C4×D4—132no—
494C2×C4×D4—132no—
495C2×C4×D4—132no—
496C2×C4×D4—132no—
497C2×C4×D4—131no—
498C2×C4×D4—134no—
499C2×C4×D4—132no—
500C2×C4×D4—132no—
501C2×#117—132no—
502C2×#117—132no—
503C22×C4⋊C4—134no—
504C22×C42—131no—
505C22×C13C2×H(5,𝔽2)12yes—
506C22×C13C2×2−1+412yes—
507C22×C13#58512yes—
508C22×C13C2611yescharacteristic
509C2×D13—24no—
510C2×D13—22no—
511C2×D13—28no—
512C2×D13—22no—
513C2×D13—24no—
514C2×D13—28no—
515C2×D13—22no—
516C2×D13—28no—
517C2×D13—24no—
518C2×D13—48no—
519C2×D13—44no—
520C2×D13—416no—
521C4×C13—28no—
522C4×C13—24no—
523C4×C13—24no—
524C4×C13—24no—
525C4×C13—24no—
526C4×C13—22no—
527C4×C13C2×H(5,𝔽2)14yes—
528C4×C13C2×2−1+414yes—
529Dic13—24no—
530Dic13—24no—
531Dic13—22no—
532Dic13—22no—
533Dic13—22no—
534Dic13—24no—
535C2×#41—1316no—
536C2×#41—1316no—
537C2×#41—528no—
538C2×#41—528no—
539C22×Q8—1316no—
540C22×Q8—131no—
541C22×Q8—132no—
542C22×Q8—134no—
543C22×Q8—528no—
544C22×Q8C22×D1311yescharacteristic
545C22×Q8C22×D1312yes—
546C22×Q8C22×D1311yescharacteristic
547C22×D4—132no—
548C22×D4—131no—
549C22×D4—132no—
550C22×D4—132no—
551C22×D4—132no—
552C22×D4—134no—
553C22×D4—134no—
554C22×D4—134no—
555C23×C4—131no—
556C23×C4—132no—
557C23×C4—131no—
558C23×C4—134no—
559C23×C4—134no—
560C23×C4—134no—
561C23×C4—134no—
562C23×C4—131no—
563C4⋊Q8—138no—
564C4⋊Q8—138no—
565C4⋊Q8—1316no—
566C4⋊Q8C22×D1318yes—
567C4⋊Q8C22×D13116yes—
568#127—138no—
569#127—1316no—
570#126—1316no—
571#126—1332no—
572#125—138no—
573#125—1316no—
574#125C22×D13132yes—
575#125C22×D13116yes—
576#124—138no—
577#124—1316no—
578#124—1316no—
579#124—1316no—
580#124—1332no—
581#124—1332no—
582#123—1316no—
583#123—1332no—
584#123—1332no—
585#123—1332no—
586#123—1332no—
587#123—1332no—
588#123—1332no—
589C22⋊Q8—138no—
590C22⋊Q8—138no—
591C22⋊Q8—1316no—
592C22⋊Q8—138no—
593C22⋊Q8—1316no—
594C22⋊Q8—1332no—
595C22⋊Q8—1332no—
596C22⋊Q8—1332no—
597C22⋊Q8—1332no—
598C22⋊Q8—1332no—
599#121—138no—
600#121—1316no—
601#121—1316no—
602#121—1332no—
603#121—1332no—
604#121—1332no—
605#121—1316no—
606C4×Q8—138no—
607C4×Q8—1316no—
608C4×Q8C22×D1318yes—
609C4×Q8C22×D1318yes—
610C4×Q8C22×D13116yes—
611C4×Q8C22×D13116yes—
612C4×D4—1316no—
613C4×D4—1316no—
614C4×D4—1316no—
615C4×D4—1316no—
616C4×D4—1316no—
617C4×D4—138no—
618C4×D4—1332no—
619C4×D4—1316no—
620C4×D4—1316no—
621#117—1316no—
622#117—1316no—
623C2×C4⋊C4—132no—
624C2×C4⋊C4—132no—
625C2×C4⋊C4—134no—
626C2×C4⋊C4—132no—
627C2×C4⋊C4—132no—
628C2×C4⋊C4—132no—
629C2×C4⋊C4—132no—
630C2×C4⋊C4—131no—
631C2×C4⋊C4—132no—
632C2×C4⋊C4—131no—
633C2×C4⋊C4—132no—
634C2×C4⋊C4—132no—
635C2×C4⋊C4—1332no—
636C2×C4⋊C4C22×D1314yes—
637C2×C4⋊C4C22×D1311yescharacteristic
638C2×C4⋊C4C22×D1312yes—
639C2×C4⋊C4C22×D1312yes—
640C2×C4⋊C4C22×D1311yescharacteristic
641C2×C4⋊C4C22×D1312yes—
642C2×C4⋊C4C22×D1314yes—
643C2×C4⋊C4C22×D1314yes—
644C2×C4⋊C4C22×D1312yes—
645C2×C22⋊C4—132no—
646C2×C22⋊C4—132no—
647C2×C22⋊C4—132no—
648C2×C22⋊C4—132no—
649C2×C22⋊C4—132no—
650C2×C22⋊C4—132no—
651C2×C22⋊C4—134no—
652C2×C22⋊C4—134no—
653C2×C22⋊C4—134no—
654C2×C22⋊C4—134no—
655C2×C22⋊C4—134no—
656C2×C22⋊C4—132no—
657C2×C22⋊C4—134no—
658C2×C22⋊C4—134no—
659C2×C42—131no—
660C2×C42—132no—
661C2×C42—131no—
662C2×C42—131no—
663C2×C42—138no—
664C2×C42C22×D1312yes—
665C2×C42C22×D1312yes—
666C2×C42C22×D1311yescharacteristic
667C2×C42C22×D1314yes—
668C2×C13#355414yescomplemented
669C2×C13C22×H(5,𝔽2)11yescharacteristic
670C2×C13C22×2−1+411yescharacteristic
671C2×C13C2×#58511yescharacteristic
672D13—44no—
673D13—42no—
674D13—48no—
675C24—131no—
676C24—132no—
677C24—134no—
678#41—5232no—
679#41—5232no—
680C2×Q8—24no—
681C2×Q8—28no—
682C2×Q8—24no—
683C2×Q8—134no—
684C2×Q8—138no—
685C2×Q8—1316no—
686C2×Q8—264no—
687C2×Q8—528no—
688C2×Q8—524no—
689C2×Q8—5232no—
690C2×Q8C23×D1314yes—
691C2×Q8C23×D1318yes—
692C2×Q8C23×D1314yes—
693C2×D4—138no—
694C2×D4—134no—
695C2×D4—138no—
696C2×D4—138no—
697C2×D4—138no—
698C2×D4—1316no—
699C2×D4—1316no—
700C2×D4—1316no—
701C2×D4—268no—
702C2×D4—264no—
703C2×D4—268no—
704C2×D4—528no—
705C2×D4—528no—
706C2×D4—524no—
707C2×D4—524no—
708C2×D4—528no—
709C22×C4—131no—
710C22×C4—131no—
711C22×C4—131no—
712C22×C4—132no—
713C22×C4—132no—
714C22×C4—132no—
715C22×C4—134no—
716C22×C4—134no—
717C22×C4—138no—
718C22×C4—134no—
719C22×C4—1316no—
720C22×C4—1316no—
721C22×C4—1316no—
722C22×C4—1316no—
723C22×C4—264no—
724C22×C4—268no—
725C22×C4—264no—
726C22×C4—528no—
727C22×C4—528no—
728C22×C4—528no—
729C22×C4—528no—
730C22×C4—522no—
731C22×C4C23×D1311yescharacteristic
732C22×C4C23×D1312yes—
733C22×C4C23×D1312yes—
734C22×C4C23×D1312yes—
735C22×C4C23×D1314yes—
736C22×C4C23×D1312yes—
737C22×C4C23×D1311yescharacteristic
738C22×C4C23×D1311yescharacteristic
739C4⋊C4—138no—
740C4⋊C4—138no—
741C4⋊C4—1316no—
742C4⋊C4—138no—
743C4⋊C4—138no—
744C4⋊C4—138no—
745C4⋊C4—138no—
746C4⋊C4—134no—
747C4⋊C4—138no—
748C4⋊C4—134no—
749C4⋊C4—138no—
750C4⋊C4—138no—
751C4⋊C4C23×D13116yes—
752C4⋊C4C23×D1314yes—
753C4⋊C4C23×D1318yes—
754C4⋊C4C23×D1318yes—
755C4⋊C4C23×D1314yes—
756C4⋊C4C23×D1318yes—
757C4⋊C4C23×D13116yes—
758C4⋊C4C23×D13116yes—
759C4⋊C4C23×D1318yes—
760C22⋊C4—138no—
761C22⋊C4—138no—
762C22⋊C4—138no—
763C22⋊C4—138no—
764C22⋊C4—138no—
765C22⋊C4—138no—
766C22⋊C4—1316no—
767C22⋊C4—1316no—
768C22⋊C4—1316no—
769C22⋊C4—1316no—
770C22⋊C4—1316no—
771C22⋊C4—138no—
772C22⋊C4—1316no—
773C22⋊C4—1316no—
774C42—134no—
775C42—134no—
776C42—134no—
777C42—138no—
778C42C23×D1314yes—
779C42C23×D1318yes—
780C42C23×D1318yes—
781C42C23×D13116yes—
782C13C2×#355411yescharacteristic, complemented, Sylow
783C23—134no—
784C23—132no—
785C23—138no—
786C23—262no—
787C23—264no—
788C23—268no—
789C23—264no—
790C23—262no—
791C23—268no—
792C23—262no—
793C23—268no—
794C23—264no—
795C23C24×D1311yescharacteristic
796Q8—28no—
797Q8—216no—
798Q8—28no—
799Q8—268no—
800Q8—528no—
801Q8—5216no—
802D4—2616no—
803D4—268no—
804D4—2616no—
805D4—528no—
806D4—528no—
807D4—5216no—
808D4—5216no—
809D4—5216no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—28no—
813C2×C4—24no—
814C2×C4—22no—
815C2×C4—24no—
816C2×C4—132no—
817C2×C4—132no—
818C2×C4—132no—
819C2×C4—134no—
820C2×C4—134no—
821C2×C4—134no—
822C2×C4—262no—
823C2×C4—262no—
824C2×C4—264no—
825C2×C4—264no—
826C2×C4—264no—
827C2×C4—262no—
828C2×C4—268no—
829C2×C4—2616no—
830C2×C4—268no—
831C2×C4—5216no—
832C2×C4—524no—
833C2×C4—5216no—
834C2×C4—5216no—
835C2×C4—5216no—
836C2×C4#8825414yes—
837C2×C4#8825614yes—
838C2×C4C24×D1312yes—
839C2×C4C24×D1314yes—
840C2×C4C24×D1314yes—
841C2×C4C24×D1314yes—
842C2×C4C24×D1318yes—
843C2×C4C24×D1314yes—
844C2×C4C24×D1312yes—
845C2×C4C24×D1312yes—
846C22—264no—
847C22—262no—
848C22—268no—
849C22—262no—
850C22—264no—
851C22—268no—
852C22—262no—
853C22—268no—
854C22—264no—
855C22—524no—
856C22—528no—
857C22—5216no—
858C22C2×#8825412yes—
859C22C2×#8825612yes—
860C22#1171965212yes—
861C22C25×D1311yescharacteristic
862C4—24no—
863C4—28no—
864C4—24no—
865C4—24no—
866C4—22no—
867C4—24no—
868C4—262no—
869C4—264no—
870C4—264no—
871C4—262no—
872C4—264no—
873C4—262no—
874C4C2×#8825414yes—
875C4C2×#8825614yes—
876C2—524no—
877C2—522no—
878C2—528no—
879C2#1312931014yesdirect product factor
880C2C22×#8825611yescharacteristic
881C2C22×#8825411yescharacteristic
882C2C2×#1171965211yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#557C2
socleC23×C13C25
hypercenterC2×#557D13
hypocenterC13C2×#3554
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #13129310C2direct (N × H)
2. C2×#11719405C2semidirect
3. C2×#11719290C2semidirect
4. C2×#11719290C2semidirect
5. C2×#11719395C2semidirect
6. C2×#11719282C2semidirect
7. C2×#11719432C2semidirect
8. C2×#11719281C2semidirect
9. C2×#11719431C2semidirect
10. C2×#11719287C2semidirect
11. C2×#11719287C2semidirect
12. C2×#11719403C2semidirect
13. C2×#11719397C2semidirect
14. C2×#11719429C2semidirect
15. C2×#11719283C2semidirect
16. C2×#11719430C2semidirect
17. C2×#11719285C2semidirect
18. C2×C13×#557C2semidirect
22. C13×#557C22semidirect
38. #11719432C22semidirect
39. #11719431C22semidirect
40. #11719430C22semidirect
41. #11719429C22semidirect
42. #11719405C22semidirect
43. #11719403C22semidirect
44. #11719397C22semidirect
45. #11719395C22semidirect
46. #11719290C22semidirect
47. #11719290C22semidirect
48. #11719287C22semidirect
49. #11719287C22semidirect
50. #11719285C22semidirect
51. #11719283C22semidirect
52. #11719282C22semidirect
53. #11719281C22semidirect
346. C2×#557D13semidirect
429. #557C2×D13semidirect
668. C2×C13#3554semidirect
782. C13C2×#3554semidirect
879. C2#13129310direct (N × H)

Maximal subgroups

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

subgroupindex
#131293102
C2×#117194052
C2×#117192902
C2×#117193952
C2×#117192822
C2×#117194322
C2×#117192812
C2×#117194312
C2×#117192872
C2×#117194032
C2×#117193972
C2×#117194292
C2×#117192832
C2×#117194302
C2×#117192852
C2×C13×#5572
C2×#355413