Finite Group Databasebeta

← C2×#13129282 #16770529

Subgroups — C2×#13129282 #16770529

Order 3328.

7086 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13129282C2132yesmaximal, direct product factor
2C2×#11719404C214yesmaximal, complemented
3C2×#11719289C211yesmaximal, characteristic, complemented
4C2×#11719284C212yesmaximal, complemented
5C2×#11719400C212yesmaximal, complemented
6C2×Q8×D52C211yesmaximal, characteristic, complemented
7C2×#11719432C212yesmaximal, complemented
8C2×#11719281C212yesmaximal, complemented
9C2×#11719431C211yesmaximal, characteristic, complemented
10C2×#11719394C212yesmaximal, complemented
11C2×#11719287C212yesmaximal, complemented
12C2×#11719288C212yesmaximal, complemented
13C2×#11719397C214yesmaximal, complemented
14C2×#11719429C212yesmaximal, complemented
15C2×D13×C4⋊Q8C211yesmaximal, characteristic, complemented
16C2×#11719285C211yesmaximal, characteristic, complemented
17C2×#11719285C211yesmaximal, characteristic, complemented
18C2×C13×#557C211yesmaximal, characteristic, complemented
19C22×#6131C2212yes—
20C22×Q8×D13C2212yes—
21C22×Q8×D13C2212yes—
22C13×#557C22116yescomplemented
23C2×C13×C4⋊Q8C2211yescharacteristic
24C2×C13×C4⋊Q8C2212yes—
25C2×C13×#125C2214yes—
26C2×C13×#125C2212yes—
27C2×C4×Q8×C13C2212yes—
28C2×C4×Q8×C13C2212yes—
29C2×C4×Q8×C13C2211yescharacteristic
30C2×C4×Q8×C13C2211yescharacteristic
31C2×#88201C2211yescharacteristic
32C2×#88201C2211yescharacteristic
33C2×#88200C2212yes—
34C2×#88200C2212yes—
35C2×#88200C2211yescharacteristic
36C2×#88200C2211yescharacteristic
37C2×#88198C2212yes—
38#11719432C22132yescomplemented
39#11719431C22116yescomplemented
40#11719429C22132yescomplemented
41D13×C4⋊Q8C22116yescomplemented
42#11719404C22164yescomplemented
43#11719400C22132yescomplemented
44#11719397C22164yescomplemented
45#11719394C22132yescomplemented
46#11719289C22116yescomplemented
47#11719288C22132yescomplemented
48#11719287C22132yescomplemented
49#11719285C22116yescomplemented
50#11719285C22116yescomplemented
51#11719284C22132yescomplemented
52#11719281C22132yescomplemented
53Q8×D52C22116yescomplemented
54C2×#88152C2214yes—
55C2×#88152C2212yes—
56C2×#88152C2212yes—
57C2×#88152C2214yes—
58C2×#88151C2212yes—
59C2×#88151C2214yes—
60C2×#88151C2214yes—
61C2×#88150C2214yes—
62C2×#88150C2214yes—
63C2×#88150C2214yes—
64C2×#88150C2214yes—
65C2×#88149C2212yes—
66C2×#88149C2211yescharacteristic
67C2×#88149C2214yes—
68C2×#88149C2211yescharacteristic
69C2×#88148C2214yes—
70C2×#88148C2214yes—
71C2×#88148C2214yes—
72C2×#88148C2212yes—
73C2×#88148C2212yes—
74C2×#88147C2214yes—
75C2×#88146C2212yes—
76C2×C4⋊C4×D13C2212yes—
77C2×C4⋊C4×D13C2212yes—
78C2×C4⋊C4×D13C2212yes—
79C2×#88144C2211yescharacteristic
80C2×#88144C2211yescharacteristic
81C2×#88143C2214yes—
82C2×#88142C2212yes—
83C2×#88142C2214yes—
84C2×#88142C2212yes—
85C2×#88130C2214yes—
86C2×#88129C2214yes—
87C2×#88129C2212yes—
88C2×C4×D52C2212yes—
89C2×C4×D52C2211yescharacteristic
90C2×C4×D52C2211yescharacteristic
91C2×C4×D52C2212yes—
92C2×C4×D52C2214yes—
93C2×C4×D52C2212yes—
94C2×#88126C2212yes—
95C2×#88126C2212yes—
96C2×C42×D13C2211yescharacteristic
97C2×#88124C2214yes—
98C2×#88123C2212yes—
99C2×#88123C2211yescharacteristic
100C2×C4×Dic26C2212yes—
101C22×Q8×C13C2312yes—
102C22×Q8×C13C2311yescharacteristic
103C22×Q8×C13C2311yescharacteristic
104C2×#6131—48no—
105C2×#6131C23116yes—
106C2×Q8×D13—48no—
107C2×Q8×D13—48no—
108C2×Q8×D13C23116yes—
109C2×Q8×D13C23116yes—
110C22×D52C2312yes—
111C22×D52C2311yescharacteristic
112C22×D52C2311yescharacteristic
113C22×D52C2312yes—
114C22×D52C2314yes—
115C22×C4×D13C2311yescharacteristic
116C22×C4×D13C2311yescharacteristic
117C22×C4×D13C2311yescharacteristic
118C22×C4×D13C2312yes—
119C22×C4×D13C2312yes—
120C22×C4×D13C2314yes—
121C22×C4×D13C2314yes—
122C22×C4×D13C2314yes—
123C22×Dic26C2312yes—
124C22×Dic26C2314yes—
125C22×Dic26C2314yes—
126C13×C4⋊Q8C2318yes—
127C13×C4⋊Q8C23116yes—
128C13×#125C23116yes—
129C13×#125C23132yes—
130C4×Q8×C13C2318yes—
131C4×Q8×C13C23116yes—
132C4×Q8×C13C23116yes—
133C4×Q8×C13C2318yes—
134C2×C13×C4⋊C4C2312yes—
135C2×C13×C4⋊C4C2312yes—
136C2×C13×C4⋊C4C2314yes—
137C2×C13×C4⋊C4C2314yes—
138C2×C13×C4⋊C4C2311yescharacteristic
139C2×C13×C4⋊C4C2311yescharacteristic
140C2×C13×C4⋊C4C2314yes—
141C2×C13×C4⋊C4C2312yes—
142C2×C13×C4⋊C4C2312yes—
143C2×C42×C13C2312yes—
144C2×C42×C13C2311yescharacteristic
145C2×C42×C13C2312yes—
146C2×C42×C13C2314yes—
147#88201C2318yes—
148#88201C2318yes—
149#88200C23116yes—
150#88200C2318yes—
151#88200C2318yes—
152#88200C23116yes—
153#88198C23116yes—
154C2×#6103C2312yes—
155C2×#6103C2312yes—
156C2×#6103C2312yes—
157C2×#6103C2312yes—
158C2×#6103C2312yes—
159C2×#6103C2314yes—
160C2×#6103C2312yes—
161C2×#6103C2314yes—
162C2×#6103C2312yes—
163C2×#6103C2312yes—
164C2×#6103C2312yes—
165C2×#6103C2312yes—
166C2×#6103C2314yes—
167C2×#6103C2314yes—
168C2×C4⋊Dic13C2311yescharacteristic
169C2×C4⋊Dic13C2312yes—
170C2×C4⋊Dic13C2311yescharacteristic
171C2×C4⋊Dic13C2314yes—
172C2×C4⋊Dic13C2312yes—
173C2×C4⋊Dic13C2312yes—
174C2×C4⋊Dic13C2312yes—
175C2×#6101C2314yes—
176C2×#6101C2312yes—
177C2×#6101C2314yes—
178C2×#6101C2314yes—
179C2×#6101C2312yes—
180C2×#6101C2312yes—
181C2×#6101C2312yes—
182C2×#6101C2314yes—
183C2×C4×Dic13C2314yes—
184C2×C4×Dic13C2311yescharacteristic
185C2×C4×Dic13C2311yescharacteristic
186C2×C4×Dic13C2311yescharacteristic
187#88152C23116yes—
188#88152C23116yes—
189#88152C23132yes—
190#88152C23132yes—
191#88151C23116yes—
192#88151C23132yes—
193#88151C23132yes—
194#88150C23132yes—
195#88150C23132yes—
196#88150C23132yes—
197#88150C23132yes—
198#88149C23116yes—
199#88149C2318yes—
200#88149C23132yes—
201#88149C2318yes—
202#88148C23132yes—
203#88148C23132yes—
204#88148C23132yes—
205#88148C23116yes—
206#88148C23116yes—
207#88147C23132yes—
208#88146C23116yes—
209C4⋊C4×D13C23116yes—
210C4⋊C4×D13C23116yes—
211C4⋊C4×D13C23116yes—
212#88144C2318yes—
213#88144C2318yes—
214#88143C23132yes—
215#88142C23116yes—
216#88142C23116yes—
217#88142C23132yes—
218#88130C23132yes—
219#88129C23116yes—
220#88129C23132yes—
221C4×D52C2318yes—
222C4×D52C2318yes—
223C4×D52C23116yes—
224C4×D52C23116yes—
225C4×D52C23132yes—
226C4×D52C23116yes—
227#88126C23116yes—
228#88126C23116yes—
229C42×D13C2318yes—
230#88124C23132yes—
231#88123C2318yes—
232#88123C23116yes—
233C4×Dic26C23116yes—
234C2×#3552—131nomaximal, Sylow
235C23×D13C2412yes—
236C23×D13C2412yes—
237C23×D13C2411yescharacteristic
238C2×Q8×C13—24no—
239C2×Q8×C13—28no—
240C2×Q8×C13—24no—
241C2×Q8×C13C2418yes—
242C2×Q8×C13C2414yes—
243C2×Q8×C13C2414yes—
244C22×C4×C13C2412yes—
245C22×C4×C13C2411yescharacteristic
246C22×C4×C13C2412yes—
247C22×C4×C13C2414yes—
248C22×C4×C13C2412yes—
249C22×C4×C13C2412yes—
250C22×C4×C13C2411yescharacteristic
251C22×C4×C13C2411yescharacteristic
252C22×Dic13C2411yescharacteristic
253C22×Dic13C2412yes—
254C22×Dic13C2411yescharacteristic
255C22×Dic13C2411yescharacteristic
256C22×Dic13C2414yes—
257C22×Dic13C2412yes—
258#6131—432no—
259Q8×D13—432no—
260Q8×D13—432no—
261C2×D52—28no—
262C2×D52—28no—
263C2×D52—24no—
264C2×D52—24no—
265C2×D52—48no—
266C2×D52C2418yes—
267C2×D52C2414yes—
268C2×D52C2414yes—
269C2×D52C2418yes—
270C2×D52C24116yes—
271C2×C4×D13—24no—
272C2×C4×D13—24no—
273C2×C4×D13—28no—
274C2×C4×D13—24no—
275C2×C4×D13—28no—
276C2×C4×D13—48no—
277C2×C4×D13—48no—
278C2×C4×D13—48no—
279C2×C4×D13C2414yes—
280C2×C4×D13C2414yes—
281C2×C4×D13C2414yes—
282C2×C4×D13C2418yes—
283C2×C4×D13C2418yes—
284C2×C4×D13C24116yes—
285C2×C4×D13C24116yes—
286C2×C4×D13C24116yes—
287C2×Dic26—28no—
288C2×Dic26—48no—
289C2×Dic26—48no—
290C2×Dic26C2418yes—
291C2×Dic26C24116yes—
292C2×Dic26C24116yes—
293C13×C4⋊C4C2418yes—
294C13×C4⋊C4C2418yes—
295C13×C4⋊C4C24116yes—
296C13×C4⋊C4C24116yes—
297C13×C4⋊C4C2414yes—
298C13×C4⋊C4C2414yes—
299C13×C4⋊C4C24116yes—
300C13×C4⋊C4C2418yes—
301C13×C4⋊C4C2418yes—
302C42×C13C2418yes—
303C42×C13C2414yes—
304C42×C13C2418yes—
305C42×C13C24116yes—
306#6103C2418yes—
307#6103C2418yes—
308#6103C2418yes—
309#6103C2418yes—
310#6103C2418yes—
311#6103C24116yes—
312#6103C2418yes—
313#6103C24116yes—
314#6103C2418yes—
315#6103C2418yes—
316#6103C2418yes—
317#6103C2418yes—
318#6103C24116yes—
319#6103C24116yes—
320C4⋊Dic13C2414yes—
321C4⋊Dic13C2418yes—
322C4⋊Dic13C2414yes—
323C4⋊Dic13C24116yes—
324C4⋊Dic13C2418yes—
325C4⋊Dic13C2418yes—
326C4⋊Dic13C2418yes—
327#6101C24116yes—
328#6101C2418yes—
329#6101C24116yes—
330#6101C24116yes—
331#6101C2418yes—
332#6101C2418yes—
333#6101C2418yes—
334#6101C24116yes—
335C4×Dic13C24116yes—
336C4×Dic13C2414yes—
337C4×Dic13C2414yes—
338C4×Dic13C2414yes—
339#3552—1332no—
340C2×#563—134no—
341C2×#557D1311yescharacteristic, complemented
342C2×#556—131no—
343C2×#554—132no—
344C2×#553—132no—
345C2×D4×Q8—132no—
346C2×D4×Q8—131no—
347C2×#548—132no—
348C2×#547—131no—
349C2×#544—132no—
350C2×#542—132no—
351C2×#541—132no—
352C2×#539—134no—
353C2×#536—132no—
354C22×C4⋊Q8—131no—
355C2×#529—131no—
356C2×#529—131no—
357C23×C13C2511yescharacteristic
358C22×D13—22no—
359C22×D13—22no—
360C22×D13—24no—
361C22×D13—24no—
362C22×D13—24no—
363C22×D13—24no—
364C22×D13—24no—
365C22×D13—24no—
366C22×D132−1+414yes—
367C22×D13C2514yes—
368C22×D13C2514yes—
369C22×D13C2512yes—
370Q8×C13—28no—
371Q8×C13—216no—
372Q8×C13—28no—
373C2×C4×C13—24no—
374C2×C4×C13—28no—
375C2×C4×C13—22no—
376C2×C4×C13—24no—
377C2×C4×C13—24no—
378C2×C4×C13—24no—
379C2×C4×C13H(5,𝔽2)14yes—
380C2×C4×C132−1+414yes—
381C2×C4×C13C2514yes—
382C2×C4×C13C2512yes—
383C2×C4×C13C2514yes—
384C2×C4×C13C2518yes—
385C2×C4×C13C2514yes—
386C2×C4×C13C2514yes—
387C2×C4×C13C2512yes—
388C2×C4×C13C2512yes—
389C2×Dic13—28no—
390C2×Dic13—22no—
391C2×Dic13—24no—
392C2×Dic13—22no—
393C2×Dic13—24no—
394C2×Dic13—22no—
395C2×Dic13C2512yes—
396C2×Dic13C2514yes—
397C2×Dic13C2512yes—
398C2×Dic13C2512yes—
399C2×Dic13C2518yes—
400C2×Dic13C2514yes—
401D52—216no—
402D52—216no—
403D52—28no—
404D52—28no—
405D52—416no—
406C4×D13—28no—
407C4×D13—28no—
408C4×D13—216no—
409C4×D13—28no—
410C4×D13—216no—
411C4×D13—416no—
412C4×D13—416no—
413C4×D13—416no—
414Dic26—216no—
415Dic26—416no—
416Dic26—416no—
417C22×#41—132no—
418C23×Q8—132no—
419C23×Q8—132no—
420#563—1364no—
421#557C2×D13116yescomplemented
422#556—1316no—
423#554—1332no—
424#553—1332no—
425D4×Q8—1332no—
426D4×Q8—1316no—
427#548—1332no—
428#547—1316no—
429#544—1332no—
430#542—1332no—
431#541—1332no—
432#539—1364no—
433#536—1332no—
434C2×C4⋊Q8—132no—
435C2×C4⋊Q8—1316no—
436C2×C4⋊Q8—132no—
437C2×C4⋊Q8—132no—
438C2×C4⋊Q8—134no—
439C2×C4⋊Q8—131no—
440C2×C4⋊Q8—132no—
441C2×C4⋊Q8C2×D1311yescharacteristic
442C2×C4⋊Q8C2×D1312yes—
443#529—1316no—
444#529—1316no—
445C2×#126—132no—
446C2×#126—132no—
447C2×#126—134no—
448C2×#126—134no—
449C2×#126—134no—
450C2×#125—134no—
451C2×#125—131no—
452C2×#125—131no—
453C2×#125—134no—
454C2×#125C2×D1314yes—
455C2×#125C2×D1312yes—
456C2×#124—131no—
457C2×#124—131no—
458C2×#124—132no—
459C2×#124—134no—
460C2×#123—132no—
461C2×#123—132no—
462C2×#123—134no—
463C2×#123—134no—
464C2×#123—134no—
465C2×C22⋊Q8—131no—
466C2×C22⋊Q8—131no—
467C2×C22⋊Q8—132no—
468C2×C22⋊Q8—132no—
469C2×C22⋊Q8—134no—
470C2×C22⋊Q8—134no—
471C2×C22⋊Q8—134no—
472C2×C22⋊Q8—134no—
473C2×C22⋊Q8—134no—
474C2×C22⋊Q8—132no—
475C2×C22⋊Q8—134no—
476C2×#121—131no—
477C2×#121—131no—
478C2×#121—134no—
479C2×#121—132no—
480C2×C4×Q8—132no—
481C2×C4×Q8C2×D1311yescharacteristic
482C2×C4×Q8C2×D1311yescharacteristic
483C2×C4×Q8C2×D1312yes—
484C2×C4×Q8C2×D1312yes—
485C2×C4×D4—134no—
486C2×C4×D4—131no—
487C2×C4×D4—131no—
488C2×C4×D4—132no—
489C2×C4×D4—132no—
490C2×C4×D4—134no—
491C2×C4×D4—132no—
492C2×#117—132no—
493C2×#117—132no—
494C2×#117—132no—
495C22×C4⋊C4—132no—
496C22×C4⋊C4—132no—
497C22×C4⋊C4—132no—
498C22×C42—131no—
499C22×C13C2×H(5,𝔽2)12yes—
500C22×C13C2×2−1+412yes—
501C22×C13C2×2−1+412yes—
502C22×C13C2611yescharacteristic
503C2×D13—22no—
504C2×D13—22no—
505C2×D13—28no—
506C2×D13—24no—
507C2×D13—24no—
508C2×D13—24no—
509C2×D13—24no—
510C2×D13—24no—
511C2×D13—24no—
512C2×D13—48no—
513C2×D13—48no—
514C2×D13C2×2−1+414yes—
515C4×C13—24no—
516C4×C13—28no—
517C4×C13—22no—
518C4×C13—24no—
519C4×C13—24no—
520C4×C13—24no—
521C4×C13C2×H(5,𝔽2)14yes—
522C4×C13C2×2−1+414yes—
523Dic13—28no—
524Dic13—22no—
525Dic13—24no—
526Dic13—22no—
527Dic13—22no—
528Dic13—24no—
529C2×#41—1316no—
530C2×#41—528no—
531C22×Q8—1316no—
532C22×Q8—1316no—
533C22×Q8—132no—
534C22×Q8—134no—
535C22×Q8—134no—
536C22×Q8—528no—
537C22×Q8—528no—
538C22×Q8C22×D1311yescharacteristic
539C22×Q8C22×D1311yescharacteristic
540C22×Q8C22×D1312yes—
541C22×D4—132no—
542C22×D4—132no—
543C22×D4—131no—
544C22×D4—131no—
545C22×D4—134no—
546C23×C4—131no—
547C23×C4—131no—
548C23×C4—132no—
549C23×C4—132no—
550C23×C4—131no—
551C23×C4—134no—
552C23×C4—134no—
553C23×C4—134no—
554C4⋊Q8—1316no—
555C4⋊Q8—1316no—
556C4⋊Q8—1316no—
557C4⋊Q8—1332no—
558C4⋊Q8—138no—
559C4⋊Q8—1316no—
560C4⋊Q8C22×D1318yes—
561C4⋊Q8C22×D13116yes—
562#126—1316no—
563#126—1316no—
564#126—1332no—
565#126—1332no—
566#126—1332no—
567#125—138no—
568#125—138no—
569#125—1332no—
570#125—1332no—
571#125C22×D13132yes—
572#125C22×D13116yes—
573#124—138no—
574#124—138no—
575#124—1316no—
576#124—1332no—
577#123—1316no—
578#123—1316no—
579#123—1332no—
580#123—1332no—
581#123—1332no—
582C22⋊Q8—138no—
583C22⋊Q8—138no—
584C22⋊Q8—1316no—
585C22⋊Q8—1316no—
586C22⋊Q8—1332no—
587C22⋊Q8—1332no—
588C22⋊Q8—1332no—
589C22⋊Q8—1332no—
590C22⋊Q8—1316no—
591C22⋊Q8—1332no—
592C22⋊Q8—1332no—
593#121—138no—
594#121—138no—
595#121—1332no—
596#121—1316no—
597C4×Q8—1316no—
598C4×Q8C22×D1318yes—
599C4×Q8C22×D1318yes—
600C4×Q8C22×D13116yes—
601C4×Q8C22×D13116yes—
602C4×D4—1332no—
603C4×D4—138no—
604C4×D4—138no—
605C4×D4—1316no—
606C4×D4—1316no—
607C4×D4—1332no—
608C4×D4—1316no—
609#117—1316no—
610#117—1316no—
611#117—1316no—
612C2×C4⋊C4—131no—
613C2×C4⋊C4—132no—
614C2×C4⋊C4—134no—
615C2×C4⋊C4—132no—
616C2×C4⋊C4—134no—
617C2×C4⋊C4—134no—
618C2×C4⋊C4—132no—
619C2×C4⋊C4—132no—
620C2×C4⋊C4—132no—
621C2×C4⋊C4—132no—
622C2×C4⋊C4—131no—
623C2×C4⋊C4—134no—
624C2×C4⋊C4—132no—
625C2×C4⋊C4—132no—
626C2×C4⋊C4—134no—
627C2×C4⋊C4—1316no—
628C2×C4⋊C4—1316no—
629C2×C4⋊C4—1316no—
630C2×C4⋊C4C22×D1312yes—
631C2×C4⋊C4C22×D1312yes—
632C2×C4⋊C4C22×D1311yescharacteristic
633C2×C4⋊C4C22×D1314yes—
634C2×C4⋊C4C22×D1311yescharacteristic
635C2×C4⋊C4C22×D1314yes—
636C2×C4⋊C4C22×D1314yes—
637C2×C4⋊C4C22×D1312yes—
638C2×C4⋊C4C22×D1312yes—
639C2×C22⋊C4—134no—
640C2×C22⋊C4—132no—
641C2×C22⋊C4—132no—
642C2×C22⋊C4—132no—
643C2×C22⋊C4—132no—
644C2×C22⋊C4—132no—
645C2×C22⋊C4—132no—
646C2×C22⋊C4—134no—
647C2×C22⋊C4—134no—
648C2×C22⋊C4—132no—
649C2×C22⋊C4—132no—
650C2×C22⋊C4—134no—
651C2×C22⋊C4—132no—
652C2×C22⋊C4—132no—
653C2×C42—131no—
654C2×C42—131no—
655C2×C42—134no—
656C2×C42—131no—
657C2×C42—138no—
658C2×C42C22×D1312yes—
659C2×C42C22×D1312yes—
660C2×C42C22×D1311yescharacteristic
661C2×C42C22×D1314yes—
662C2×C13#355214yescomplemented
663C2×C13C22×H(5,𝔽2)11yescharacteristic
664C2×C13C22×2−1+411yescharacteristic
665C2×C13C22×2−1+411yescharacteristic
666D13—24no—
667D13—44no—
668D13—44no—
669C24—131no—
670C24—132no—
671C24—132no—
672#41—5232no—
673C2×Q8—24no—
674C2×Q8—24no—
675C2×Q8—28no—
676C2×Q8—138no—
677C2×Q8—1316no—
678C2×Q8—1316no—
679C2×Q8—268no—
680C2×Q8—528no—
681C2×Q8—528no—
682C2×Q8—5232no—
683C2×Q8—5232no—
684C2×Q8C23×D1314yes—
685C2×Q8C23×D1314yes—
686C2×Q8C23×D1318yes—
687C2×D4—138no—
688C2×D4—138no—
689C2×D4—134no—
690C2×D4—134no—
691C2×D4—1316no—
692C2×D4—268no—
693C2×D4—268no—
694C2×D4—264no—
695C2×D4—264no—
696C2×D4—528no—
697C22×C4—131no—
698C22×C4—132no—
699C22×C4—131no—
700C22×C4—131no—
701C22×C4—134no—
702C22×C4—132no—
703C22×C4—134no—
704C22×C4—134no—
705C22×C4—134no—
706C22×C4—138no—
707C22×C4—138no—
708C22×C4—1316no—
709C22×C4—1316no—
710C22×C4—1316no—
711C22×C4—264no—
712C22×C4—264no—
713C22×C4—268no—
714C22×C4—264no—
715C22×C4—268no—
716C22×C4—528no—
717C22×C4—528no—
718C22×C4—528no—
719C22×C4C23×D1312yes—
720C22×C4C23×D1311yescharacteristic
721C22×C4C23×D1312yes—
722C22×C4C23×D1312yes—
723C22×C4C23×D1312yes—
724C22×C4C23×D1314yes—
725C22×C4C23×D1311yescharacteristic
726C22×C4C23×D1311yescharacteristic
727C4⋊C4—134no—
728C4⋊C4—138no—
729C4⋊C4—1316no—
730C4⋊C4—138no—
731C4⋊C4—1316no—
732C4⋊C4—1316no—
733C4⋊C4—138no—
734C4⋊C4—138no—
735C4⋊C4—138no—
736C4⋊C4—138no—
737C4⋊C4—134no—
738C4⋊C4—1316no—
739C4⋊C4—138no—
740C4⋊C4—138no—
741C4⋊C4—1316no—
742C4⋊C4C23×D1318yes—
743C4⋊C4C23×D1318yes—
744C4⋊C4C23×D1314yes—
745C4⋊C4C23×D13116yes—
746C4⋊C4C23×D1314yes—
747C4⋊C4C23×D13116yes—
748C4⋊C4C23×D13116yes—
749C4⋊C4C23×D1318yes—
750C4⋊C4C23×D1318yes—
751C22⋊C4—1316no—
752C22⋊C4—138no—
753C22⋊C4—138no—
754C22⋊C4—138no—
755C22⋊C4—138no—
756C22⋊C4—138no—
757C22⋊C4—138no—
758C22⋊C4—1316no—
759C22⋊C4—1316no—
760C22⋊C4—138no—
761C22⋊C4—138no—
762C22⋊C4—1316no—
763C22⋊C4—138no—
764C22⋊C4—138no—
765C42—134no—
766C42—134no—
767C42—134no—
768C42—1316no—
769C42C23×D1314yes—
770C42C23×D1318yes—
771C42C23×D1318yes—
772C42C23×D13116yes—
773C13C2×#355211yescharacteristic, complemented, Sylow
774C23—134no—
775C23—132no—
776C23—134no—
777C23—134no—
778C23—262no—
779C23—262no—
780C23—264no—
781C23—264no—
782C23—264no—
783C23—264no—
784C23—264no—
785C23—264no—
786C23C24×D1311yescharacteristic
787Q8—28no—
788Q8—28no—
789Q8—216no—
790Q8—2616no—
791Q8—5216no—
792Q8—5216no—
793D4—2616no—
794D4—2616no—
795D4—268no—
796D4—268no—
797D4—5216no—
798C2×C4—24no—
799C2×C4—28no—
800C2×C4—24no—
801C2×C4—22no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—132no—
805C2×C4—132no—
806C2×C4—134no—
807C2×C4—132no—
808C2×C4—138no—
809C2×C4—134no—
810C2×C4—268no—
811C2×C4—262no—
812C2×C4—264no—
813C2×C4—264no—
814C2×C4—262no—
815C2×C4—268no—
816C2×C4—262no—
817C2×C4—268no—
818C2×C4—2616no—
819C2×C4—268no—
820C2×C4—2616no—
821C2×C4—5216no—
822C2×C4—5216no—
823C2×C4—5216no—
824C2×C4#8825414yes—
825C2×C4#8825614yes—
826C2×C4C24×D1314yes—
827C2×C4C24×D1312yes—
828C2×C4C24×D1314yes—
829C2×C4C24×D1314yes—
830C2×C4C24×D1314yes—
831C2×C4C24×D1318yes—
832C2×C4C24×D1312yes—
833C2×C4C24×D1312yes—
834C22—134no—
835C22—268no—
836C22—262no—
837C22—262no—
838C22—264no—
839C22—264no—
840C22—264no—
841C22—264no—
842C22—264no—
843C22—264no—
844C22—528no—
845C22—528no—
846C22C2×#8825412yes—
847C22C2×#8825612yes—
848C22D13×2−1+412yes—
849C22C25×D1311yescharacteristic
850C4—28no—
851C4—24no—
852C4—22no—
853C4—24no—
854C4—24no—
855C4—24no—
856C4—264no—
857C4—262no—
858C4—268no—
859C4—262no—
860C4—262no—
861C4—264no—
862C4C2×#8825414yes—
863C4C2×#8825614yes—
864C2—264no—
865C2—524no—
866C2—524no—
867C2#1312928214yesdirect product factor
868C2C22×#8825611yescharacteristic
869C2C2×D13×2−1+411yescharacteristic
870C2C22×#8825411yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#557C2
socleC23×C13C25
hypercenterC2×#557D13
hypocenterC13C2×#3552
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #13129282C2direct (N × H)
2. C2×#11719404C2semidirect
3. C2×#11719289C2semidirect
4. C2×#11719284C2semidirect
5. C2×#11719400C2semidirect
6. C2×Q8×D52C2semidirect
7. C2×#11719432C2semidirect
8. C2×#11719281C2semidirect
9. C2×#11719431C2semidirect
10. C2×#11719394C2semidirect
11. C2×#11719287C2semidirect
12. C2×#11719288C2semidirect
13. C2×#11719397C2semidirect
14. C2×#11719429C2semidirect
15. C2×D13×C4⋊Q8C2semidirect
16. C2×#11719285C2semidirect
17. C2×#11719285C2semidirect
18. C2×C13×#557C2semidirect
22. C13×#557C22semidirect
38. #11719432C22semidirect
39. #11719431C22semidirect
40. #11719429C22semidirect
41. D13×C4⋊Q8C22semidirect
42. #11719404C22semidirect
43. #11719400C22semidirect
44. #11719397C22semidirect
45. #11719394C22semidirect
46. #11719289C22semidirect
47. #11719288C22semidirect
48. #11719287C22semidirect
49. #11719285C22semidirect
50. #11719285C22semidirect
51. #11719284C22semidirect
52. #11719281C22semidirect
53. Q8×D52C22semidirect
341. C2×#557D13semidirect
421. #557C2×D13semidirect
662. C2×C13#3552semidirect
773. C13C2×#3552semidirect
867. C2#13129282direct (N × H)

Maximal subgroups

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

subgroupindex
#131292822
C2×#117194042
C2×#117192892
C2×#117192842
C2×#117194002
C2×Q8×D522
C2×#117194322
C2×#117192812
C2×#117194312
C2×#117193942
C2×#117192872
C2×#117192882
C2×#117193972
C2×#117194292
C2×D13×C4⋊Q82
C2×#117192852
C2×C13×#5572
C2×#355213