Finite Group Databasebeta

← C2×#13129273 #16770530

Subgroups — C2×#13129273 #16770530

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#13129273C2132yesmaximal, direct product factor
2C2×#11719417C214yesmaximal, complemented
3C2×#11719272C211yesmaximal, characteristic, complemented
4C2×#11719247C211yesmaximal, characteristic, complemented
5C2×#11719248C212yesmaximal, complemented
6C2×#11719270C212yesmaximal, complemented
7C2×Q8×D52C211yesmaximal, characteristic, complemented
8C2×#11719337C212yesmaximal, complemented
9C2×#11719303C212yesmaximal, complemented
10C2×#11719260C211yesmaximal, characteristic, complemented
11C2×#11719224C212yesmaximal, complemented
12C2×#11719239C212yesmaximal, complemented
13C2×#11719402C212yesmaximal, complemented
14C2×#11719370C214yesmaximal, complemented
15C2×#11719380C212yesmaximal, complemented
16C22×#88123C211yesmaximal, characteristic, complemented
17C2×#11719184C211yesmaximal, characteristic, complemented
18C2×C13×#529C211yesmaximal, characteristic, complemented
19C22×Q8×D13C2212yes—
20C22×#6129C2212yes—
21C23×Dic26C2212yes—
22C13×#529C22116yescomplemented
23C2×C13×#126C2212yes—
24C2×C13×#125C2211yescharacteristic
25C2×C13×#124C2211yescharacteristic
26C2×C13×#123C2212yes—
27C2×C13×C22⋊Q8C2211yescharacteristic
28C2×C13×#121C2211yescharacteristic
29C2×C4×Q8×C13C2211yescharacteristic
30C2×C4×D4×C13C2211yescharacteristic
31C2×C4×D4×C13C2212yes—
32C2×C13×#117C2212yes—
33C22×C42×C13C2211yescharacteristic
34C2×#88198C2212yes—
35C2×#88193C2214yes—
36C2×#88190C2212yes—
37C2×D4×Dic13C2214yes—
38C2×#88184C2212yes—
39C2×#88184C2211yescharacteristic
40C2×#88183C2212yes—
41C2×C4×C22⋊D13C2212yes—
42C2×#88180C2212yes—
43C22×C4⋊Dic13C2212yes—
44C22×C4⋊Dic13C2212yes—
45C22×C4⋊Dic13C2212yes—
46C2×#88178C2212yes—
47C2×#88178C2211yescharacteristic
48#11719417C22164yescomplemented
49#11719402C22132yescomplemented
50#11719380C22132yescomplemented
51#11719370C22164yescomplemented
52#11719337C22132yescomplemented
53#11719303C22132yescomplemented
54Q8×D52C22116yescomplemented
55#11719272C22116yescomplemented
56#11719270C22132yescomplemented
57#11719260C22116yescomplemented
58#11719248C22132yescomplemented
59#11719247C22116yescomplemented
60#11719239C22132yescomplemented
61#11719224C22132yescomplemented
62C2×#88152C2214yes—
63C2×#88152C2214yes—
64C2×#88151C2214yes—
65C2×#88151C2212yes—
66C2×#88151C2212yes—
67C2×#88150C2214yes—
68C2×#88144C2214yes—
69C2×#88144C2214yes—
70C2×#88143C2214yes—
71C2×#88142C2214yes—
72C2×#88141C2212yes—
73C2×#88141C2212yes—
74C2×#88140C2214yes—
75C2×#88139C2214yes—
76C2×#88137C2214yes—
77C2×#88137C2214yes—
78C2×#88135C2214yes—
79C2×#88133C2214yes—
80C2×#88132C2214yes—
81C2×#88132C2214yes—
82C2×#88132C2214yes—
83C2×#88132C2214yes—
84#11719184C22116yescomplemented
85C2×#88130C2212yes—
86C2×#88129C2211yescharacteristic
87C2×C4×D52C2212yes—
88C2×C4×D52C2211yescharacteristic
89C2×#88126C2212yes—
90C2×#88124C2211yescharacteristic
91C2×#88124C2212yes—
92C2×#88123C2212yes—
93C2×#88123C2212yes—
94C2×#88123C2212yes—
95C2×#88123C2212yes—
96C2×#88123C2211yescharacteristic
97C2×#88123C2211yescharacteristic
98C2×#88123C22116yescomplemented
99C2×C4×Dic26C2212yes—
100C2×C4×Dic26C2211yescharacteristic
101C22×Q8×C13C2311yescharacteristic
102C22×D4×C13C2312yes—
103C22×D4×C13C2311yescharacteristic
104C23×C4×C13C2311yescharacteristic
105C23×C4×C13C2312yes—
106C23×C4×C13C2311yescharacteristic
107C23×C4×C13C2311yescharacteristic
108C22×C22⋊D13C2312yes—
109C22×C22⋊D13C2314yes—
110C23×Dic13C2314yes—
111C23×Dic13C2314yes—
112C2×Q8×D13—48no—
113C2×Q8×D13C23116yes—
114C2×#6129—48no—
115C2×#6129C23116yes—
116C22×D52C2311yescharacteristic
117C22×C4×D13C2312yes—
118C22×C4×D13C2314yes—
119C22×Dic26—48no—
120C22×Dic26C2311yescharacteristic
121C22×Dic26C2312yes—
122C22×Dic26C2312yes—
123C22×Dic26C2314yes—
124C22×Dic26C2314yes—
125C22×Dic26C23116yes—
126C13×#126C23116yes—
127C13×#125C2318yes—
128C13×#124C2318yes—
129C13×#123C23116yes—
130C13×C22⋊Q8C2318yes—
131C13×#121C2318yes—
132C4×Q8×C13C2318yes—
133C4×D4×C13C2318yes—
134C4×D4×C13C23116yes—
135C13×#117C23116yes—
136C2×C13×C4⋊C4C2311yescharacteristic
137C2×C13×C4⋊C4C2311yescharacteristic
138C2×C13×C4⋊C4C2312yes—
139C2×C13×C4⋊C4C2312yes—
140C2×C13×C4⋊C4C2312yes—
141C2×C13×C4⋊C4C2312yes—
142C2×C13×C22⋊C4C2312yes—
143C2×C13×C22⋊C4C2312yes—
144C2×C13×C22⋊C4C2312yes—
145C2×C13×C22⋊C4C2312yes—
146C2×C13×C22⋊C4C2312yes—
147C2×C42×C13C2311yescharacteristic
148C2×C42×C13C2312yes—
149C2×C42×C13C2311yescharacteristic
150C2×C42×C13C2311yescharacteristic
151C2×C42×C13C2311yescharacteristic
152C2×C42×C13C2318yes—
153C2×C22⋊Dic13C2314yes—
154C2×C22⋊Dic13C2312yes—
155C2×C22⋊Dic13C2314yes—
156#88198C23116yes—
157#88193C23132yes—
158#88190C23116yes—
159D4×Dic13C23132yes—
160#88184C2318yes—
161#88184C23116yes—
162#88183C23116yes—
163C4×C22⋊D13C23116yes—
164C2×#6103C2312yes—
165C2×#6103C2312yes—
166C2×#6103C2312yes—
167C2×#6103C2314yes—
168C2×#6103C2312yes—
169C2×#6103C2314yes—
170#88180C23116yes—
171C2×C4⋊Dic13C2312yes—
172C2×C4⋊Dic13C2311yescharacteristic
173C2×C4⋊Dic13C2312yes—
174C2×C4⋊Dic13C2311yescharacteristic
175C2×C4⋊Dic13C2314yes—
176C2×C4⋊Dic13C2314yes—
177C2×C4⋊Dic13C2312yes—
178C2×C4⋊Dic13C2312yes—
179C2×C4⋊Dic13C2314yes—
180C2×C4⋊Dic13C23116yes—
181C2×C4⋊Dic13C23116yes—
182C2×C4⋊Dic13C2314yes—
183C2×C4⋊Dic13C23116yes—
184#88178C2318yes—
185#88178C23116yes—
186C2×#6101C2312yes—
187C2×#6101C2314yes—
188C2×#6101C2312yes—
189C2×#6101C2312yes—
190C2×#6101C2314yes—
191C2×#6101C2314yes—
192C2×#6101C2312yes—
193C2×#6101C2314yes—
194C2×C4×Dic13C2312yes—
195C2×C4×Dic13C2314yes—
196C2×C4×Dic13C2314yes—
197#88152C23132yes—
198#88152C23132yes—
199#88151C23116yes—
200#88151C23116yes—
201#88151C23132yes—
202#88150C23132yes—
203#88144C23132yes—
204#88144C23132yes—
205#88143C23132yes—
206#88142C23132yes—
207#88141C23116yes—
208#88141C23116yes—
209#88140C23132yes—
210#88139C23132yes—
211#88137C23132yes—
212#88137C23132yes—
213#88135C23132yes—
214#88133C23132yes—
215#88132C23132yes—
216#88132C23132yes—
217#88132C23132yes—
218#88132C23132yes—
219#88130C23116yes—
220#88129C2318yes—
221C4×D52C2318yes—
222C4×D52C23116yes—
223#88126C23116yes—
224#88124C2318yes—
225#88124C23116yes—
226#88123C23116yes—
227#88123C2318yes—
228#88123C2318yes—
229#88123C23116yes—
230#88123C23116yes—
231#88123C23116yes—
232C4×Dic26C2318yes—
233C4×Dic26C23116yes—
234C2×#3552—131nomaximal, Sylow
235C24×C13C2412yes—
236C24×C13C2411yescharacteristic
237C23×D13C2412yes—
238C2×Q8×C13—24no—
239C2×Q8×C13C2414yes—
240C2×D4×C13—28no—
241C2×D4×C13—24no—
242C2×D4×C13C2418yes—
243C2×D4×C13C2414yes—
244C22×C4×C13—24no—
245C22×C4×C13—24no—
246C22×C4×C13—24no—
247C22×C4×C13—28no—
248C22×C4×C13C2412yes—
249C22×C4×C13C2412yes—
250C22×C4×C13C2412yes—
251C22×C4×C13C2411yescharacteristic
252C22×C4×C13C2411yescharacteristic
253C22×C4×C13C2411yescharacteristic
254C22×C4×C13C2411yescharacteristic
255C22×C4×C13C2414yes—
256C22×C4×C13C2418yes—
257C22×C4×C13C2414yes—
258C22×C4×C13C2414yes—
259C22×C4×C13C2411yescharacteristic
260C22×C4×C13C2411yescharacteristic
261C2×C22⋊D13—28no—
262C2×C22⋊D13—48no—
263C2×C22⋊D13C2418yes—
264C2×C22⋊D13C24116yes—
265C22×Dic13—48no—
266C22×Dic13—48no—
267C22×Dic13C2412yes—
268C22×Dic13C2412yes—
269C22×Dic13C2414yes—
270C22×Dic13C2414yes—
271C22×Dic13C2412yes—
272C22×Dic13C24116yes—
273C22×Dic13C24116yes—
274Q8×D13—432no—
275#6129—432no—
276C2×D52—24no—
277C2×D52C2414yes—
278C2×C4×D13—28no—
279C2×C4×D13—48no—
280C2×C4×D13C2418yes—
281C2×C4×D13C24116yes—
282C2×Dic26—28no—
283C2×Dic26—28no—
284C2×Dic26—24no—
285C2×Dic26—432no—
286C2×Dic26—48no—
287C2×Dic26—48no—
288C2×Dic26C2414yes—
289C2×Dic26C2418yes—
290C2×Dic26C2418yes—
291C2×Dic26C24116yes—
292C2×Dic26C24116yes—
293C13×C4⋊C4C2414yes—
294C13×C4⋊C4C2414yes—
295C13×C4⋊C4C2418yes—
296C13×C4⋊C4C2418yes—
297C13×C4⋊C4C2418yes—
298C13×C4⋊C4C2418yes—
299C13×C22⋊C4C2418yes—
300C13×C22⋊C4C2418yes—
301C13×C22⋊C4C2418yes—
302C13×C22⋊C4C2418yes—
303C13×C22⋊C4C2418yes—
304C42×C13C2414yes—
305C42×C13C2418yes—
306C42×C13C2414yes—
307C42×C13C2414yes—
308C42×C13C2414yes—
309C22⋊Dic13C24116yes—
310C22⋊Dic13C2418yes—
311C22⋊Dic13C24116yes—
312#6103C2418yes—
313#6103C2418yes—
314#6103C2418yes—
315#6103C24116yes—
316#6103C2418yes—
317#6103C24116yes—
318C4⋊Dic13C2418yes—
319C4⋊Dic13C2414yes—
320C4⋊Dic13C2418yes—
321C4⋊Dic13C2414yes—
322C4⋊Dic13C24116yes—
323C4⋊Dic13C24116yes—
324C4⋊Dic13C2418yes—
325C4⋊Dic13C2418yes—
326C4⋊Dic13C24116yes—
327C4⋊Dic13C24116yes—
328#6101C2418yes—
329#6101C24116yes—
330#6101C2418yes—
331#6101C2418yes—
332#6101C24116yes—
333#6101C24116yes—
334#6101C2418yes—
335#6101C24116yes—
336C4×Dic13C2418yes—
337C4×Dic13C24116yes—
338C4×Dic13C24116yes—
339#3552—1332no—
340C2×#563—134no—
341C2×#557—131no—
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×#529D1311yescharacteristic, complemented
357C23×C13—22no—
358C23×C13—22no—
359C23×C13—24no—
360C23×C13—24no—
361C23×C13—24no—
362C23×C132−1+414yes—
363C23×C13C2514yes—
364C23×C13C2512yes—
365C23×C13C2511yescharacteristic
366C22×D13—24no—
367C22×D13—24no—
368C22×D13—24no—
369C22×D13C2514yes—
370Q8×C13—28no—
371D4×C13—216no—
372D4×C13—28no—
373C2×C4×C13—22no—
374C2×C4×C13—24no—
375C2×C4×C13—28no—
376C2×C4×C13—22no—
377C2×C4×C13—22no—
378C2×C4×C13—24no—
379C2×C4×C13—22no—
380C2×C4×C13—24no—
381C2×C4×C13—28no—
382C2×C4×C13—28no—
383C2×C4×C13—216no—
384C2×C4×C13H(5,𝔽2)14yes—
385C2×C4×C132−1+414yes—
386C2×C4×C13C2514yes—
387C2×C4×C13C2514yes—
388C2×C4×C13C2514yes—
389C2×C4×C13C2512yes—
390C2×C4×C13C2512yes—
391C2×C4×C13C2512yes—
392C2×C4×C13C2512yes—
393C2×C4×C13C2512yes—
394C2×C4×C13C2512yes—
395C22⋊D13—216no—
396C22⋊D13—416no—
397C2×Dic13—28no—
398C2×Dic13—28no—
399C2×Dic13—24no—
400C2×Dic13—24no—
401C2×Dic13—24no—
402C2×Dic13—416no—
403C2×Dic13—416no—
404C2×Dic13C2514yes—
405C2×Dic13C2514yes—
406C2×Dic13C2518yes—
407C2×Dic13C2518yes—
408C2×Dic13C2514yes—
409D52—28no—
410C4×D13—216no—
411C4×D13—416no—
412Dic26—216no—
413Dic26—216no—
414Dic26—28no—
415Dic26—416no—
416Dic26—416no—
417C22×#41—132no—
418C23×Q8—132no—
419C23×Q8—132no—
420#563—1364no—
421#557—1316no—
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—134no—
436C2×C4⋊Q8—132no—
437C2×C4⋊Q8—132no—
438C2×C4⋊Q8—131no—
439C2×C4⋊Q8—131no—
440C2×C4⋊Q8—132no—
441C2×C4⋊Q8—132no—
442C2×C4⋊Q8—1316no—
443#529—1316no—
444#529C2×D13116yescomplemented
445C2×#126—134no—
446C2×#126—134no—
447C2×#126—134no—
448C2×#126—132no—
449C2×#126C2×D1312yes—
450C2×#125—134no—
451C2×#125—134no—
452C2×#125—134no—
453C2×#125—131no—
454C2×#125—132no—
455C2×#125C2×D1311yescharacteristic
456C2×#124—132no—
457C2×#124—134no—
458C2×#124—131no—
459C2×#124C2×D1311yescharacteristic
460C2×#123—132no—
461C2×#123—134no—
462C2×#123—134no—
463C2×#123—134no—
464C2×#123C2×D1312yes—
465C2×C22⋊Q8—131no—
466C2×C22⋊Q8—132no—
467C2×C22⋊Q8—134no—
468C2×C22⋊Q8—134no—
469C2×C22⋊Q8—132no—
470C2×C22⋊Q8—132no—
471C2×C22⋊Q8—134no—
472C2×C22⋊Q8—134no—
473C2×C22⋊Q8—134no—
474C2×C22⋊Q8—134no—
475C2×C22⋊Q8C2×D1311yescharacteristic
476C2×#121—134no—
477C2×#121—131no—
478C2×#121—132no—
479C2×#121C2×D1311yescharacteristic
480C2×C4×Q8—132no—
481C2×C4×Q8—132no—
482C2×C4×Q8—131no—
483C2×C4×Q8—132no—
484C2×C4×Q8C2×D1311yescharacteristic
485C2×C4×D4—134no—
486C2×C4×D4—132no—
487C2×C4×D4—134no—
488C2×C4×D4—131no—
489C2×C4×D4—132no—
490C2×C4×D4C2×D1311yescharacteristic
491C2×C4×D4C2×D1312yes—
492C2×#117—132no—
493C2×#117—132no—
494C2×#117C2×D1312yes—
495C22×C4⋊C4—132no—
496C22×C4⋊C4—132no—
497C22×C4⋊C4—132no—
498C22×C42C2×D1311yescharacteristic
499C22×C13—22no—
500C22×C13—22no—
501C22×C13—28no—
502C22×C13—24no—
503C22×C13—24no—
504C22×C13—24no—
505C22×C13—48no—
506C22×C13C2×H(5,𝔽2)12yes—
507C22×C13C2×2−1+414yes—
508C22×C13C2×2−1+412yes—
509C22×C13C2×2−1+412yes—
510C22×C13C2611yescharacteristic
511C2×D13—24no—
512C2×D13—24no—
513C2×D13—24no—
514C2×D13—48no—
515C4×C13—22no—
516C4×C13—24no—
517C4×C13—22no—
518C4×C13—22no—
519C4×C13—24no—
520C4×C13—22no—
521C4×C13—24no—
522C4×C13C2×H(5,𝔽2)14yes—
523C4×C13C2×2−1+414yes—
524Dic13—28no—
525Dic13—28no—
526Dic13—24no—
527Dic13—24no—
528Dic13—24no—
529C2×#41—1316no—
530C2×#41—528no—
531C22×Q8—1316no—
532C22×Q8—131no—
533C22×Q8—132no—
534C22×Q8—132no—
535C22×Q8—134no—
536C22×Q8—134no—
537C22×Q8—1316no—
538C22×Q8—528no—
539C22×Q8—528no—
540C22×Q8C22×D1311yescharacteristic
541C22×D4—132no—
542C22×D4—134no—
543C22×D4—131no—
544C22×D4C22×D1312yes—
545C22×D4C22×D1311yescharacteristic
546C23×C4—134no—
547C23×C4—134no—
548C23×C4—132no—
549C23×C4—134no—
550C23×C4C22×D1311yescharacteristic
551C23×C4C22×D1311yescharacteristic
552C23×C4C22×D1312yes—
553C23×C4C22×D1311yescharacteristic
554C4⋊Q8—1316no—
555C4⋊Q8—1332no—
556C4⋊Q8—1316no—
557C4⋊Q8—1316no—
558C4⋊Q8—138no—
559C4⋊Q8—138no—
560C4⋊Q8—1316no—
561C4⋊Q8—1316no—
562#126—1332no—
563#126—1332no—
564#126—1332no—
565#126—1316no—
566#126C22×D13116yes—
567#125—1332no—
568#125—1332no—
569#125—1332no—
570#125—138no—
571#125—1316no—
572#125C22×D1318yes—
573#124—1316no—
574#124—1332no—
575#124—138no—
576#124C22×D1318yes—
577#123—1316no—
578#123—1332no—
579#123—1332no—
580#123—1332no—
581#123C22×D13116yes—
582C22⋊Q8—138no—
583C22⋊Q8—1316no—
584C22⋊Q8—1332no—
585C22⋊Q8—1316no—
586C22⋊Q8—1316no—
587C22⋊Q8—1332no—
588C22⋊Q8—1332no—
589C22⋊Q8—1332no—
590C22⋊Q8—1332no—
591C22⋊Q8—1332no—
592C22⋊Q8C22×D1318yes—
593#121—1332no—
594#121—138no—
595#121—1316no—
596#121C22×D1318yes—
597C4×Q8—1316no—
598C4×Q8—1316no—
599C4×Q8—138no—
600C4×Q8—1316no—
601C4×Q8C22×D1318yes—
602C4×D4—1332no—
603C4×D4—1316no—
604C4×D4—1332no—
605C4×D4—138no—
606C4×D4—1316no—
607C4×D4C22×D1318yes—
608C4×D4C22×D13116yes—
609#117—1316no—
610#117—1316no—
611#117C22×D13116yes—
612C2×C4⋊C4—131no—
613C2×C4⋊C4—132no—
614C2×C4⋊C4—132no—
615C2×C4⋊C4—134no—
616C2×C4⋊C4—132no—
617C2×C4⋊C4—134no—
618C2×C4⋊C4—134no—
619C2×C4⋊C4—132no—
620C2×C4⋊C4—1316no—
621C2×C4⋊C4—1316no—
622C2×C4⋊C4—1316no—
623C2×C4⋊C4—131no—
624C2×C4⋊C4—132no—
625C2×C4⋊C4—132no—
626C2×C4⋊C4—134no—
627C2×C4⋊C4—132no—
628C2×C4⋊C4—134no—
629C2×C4⋊C4—134no—
630C2×C4⋊C4—134no—
631C2×C4⋊C4—134no—
632C2×C4⋊C4—132no—
633C2×C4⋊C4C22×D1312yes—
634C2×C4⋊C4C22×D1312yes—
635C2×C4⋊C4C22×D1311yescharacteristic
636C2×C4⋊C4C22×D1312yes—
637C2×C4⋊C4C22×D1311yescharacteristic
638C2×C4⋊C4C22×D1312yes—
639C2×C22⋊C4—134no—
640C2×C22⋊C4—132no—
641C2×C22⋊C4—134no—
642C2×C22⋊C4—132no—
643C2×C22⋊C4—132no—
644C2×C22⋊C4—134no—
645C2×C22⋊C4—134no—
646C2×C22⋊C4—132no—
647C2×C22⋊C4—132no—
648C2×C22⋊C4C22×D1312yes—
649C2×C22⋊C4C22×D1312yes—
650C2×C22⋊C4C22×D1312yes—
651C2×C22⋊C4C22×D1312yes—
652C2×C22⋊C4C22×D1312yes—
653C2×C42—132no—
654C2×C42—134no—
655C2×C42—134no—
656C2×C42C22×D1311yescharacteristic
657C2×C42C22×D1311yescharacteristic
658C2×C42C22×D1312yes—
659C2×C42C22×D1311yescharacteristic
660C2×C42C22×D1311yescharacteristic
661C2×C42C22×D1318yes—
662C2×C13—24no—
663C2×C13—44no—
664C2×C13#355214yescomplemented
665C2×C13C22×H(5,𝔽2)11yescharacteristic
666C2×C13C22×2−1+411yescharacteristic
667C2×C13C22×2−1+411yescharacteristic
668D13—44no—
669C24—132no—
670C24C23×D1312yes—
671C24C23×D1311yescharacteristic
672#41—5232no—
673C2×Q8—24no—
674C2×Q8—134no—
675C2×Q8—138no—
676C2×Q8—138no—
677C2×Q8—1316no—
678C2×Q8—1316no—
679C2×Q8—268no—
680C2×Q8—268no—
681C2×Q8—264no—
682C2×Q8—528no—
683C2×Q8—528no—
684C2×Q8—5232no—
685C2×Q8—5232no—
686C2×Q8C23×D1314yes—
687C2×D4—28no—
688C2×D4—24no—
689C2×D4—138no—
690C2×D4—1316no—
691C2×D4—134no—
692C2×D4—268no—
693C2×D4—264no—
694C2×D4—528no—
695C2×D4C23×D1318yes—
696C2×D4C23×D1314yes—
697C22×C4—24no—
698C22×C4—24no—
699C22×C4—24no—
700C22×C4—28no—
701C22×C4—132no—
702C22×C4—132no—
703C22×C4—134no—
704C22×C4—134no—
705C22×C4—132no—
706C22×C4—1316no—
707C22×C4—1316no—
708C22×C4—138no—
709C22×C4—1316no—
710C22×C4—268no—
711C22×C4—528no—
712C22×C4—528no—
713C22×C4—528no—
714C22×C4C23×D1314yes—
715C22×C4C23×D1314yes—
716C22×C4C23×D1314yes—
717C22×C4C23×D1318yes—
718C22×C4C23×D1312yes—
719C22×C4C23×D1312yes—
720C22×C4C23×D1311yescharacteristic
721C22×C4C23×D1311yescharacteristic
722C22×C4C23×D1311yescharacteristic
723C22×C4C23×D1311yescharacteristic
724C22×C4C23×D1312yes—
725C22×C4C23×D1311yescharacteristic
726C22×C4C23×D1311yescharacteristic
727C4⋊C4—134no—
728C4⋊C4—138no—
729C4⋊C4—138no—
730C4⋊C4—1316no—
731C4⋊C4—138no—
732C4⋊C4—1316no—
733C4⋊C4—1316no—
734C4⋊C4—138no—
735C4⋊C4—134no—
736C4⋊C4—138no—
737C4⋊C4—138no—
738C4⋊C4—1316no—
739C4⋊C4—138no—
740C4⋊C4—1316no—
741C4⋊C4—1316no—
742C4⋊C4—1316no—
743C4⋊C4—1316no—
744C4⋊C4—138no—
745C4⋊C4C23×D1318yes—
746C4⋊C4C23×D1318yes—
747C4⋊C4C23×D1314yes—
748C4⋊C4C23×D1318yes—
749C4⋊C4C23×D1314yes—
750C4⋊C4C23×D1318yes—
751C22⋊C4—1316no—
752C22⋊C4—138no—
753C22⋊C4—1316no—
754C22⋊C4—138no—
755C22⋊C4—138no—
756C22⋊C4—1316no—
757C22⋊C4—1316no—
758C22⋊C4—138no—
759C22⋊C4—138no—
760C22⋊C4C23×D1318yes—
761C22⋊C4C23×D1318yes—
762C22⋊C4C23×D1318yes—
763C22⋊C4C23×D1318yes—
764C22⋊C4C23×D1318yes—
765C42—138no—
766C42—1316no—
767C42—1316no—
768C42C23×D1314yes—
769C42C23×D1314yes—
770C42C23×D1314yes—
771C42C23×D1314yes—
772C42C23×D1318yes—
773C13C2×#355211yescharacteristic, complemented, Sylow
774C23—22no—
775C23—22no—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—134no—
780C23—264no—
781C23—264no—
782C23—264no—
783C23#8825714yes—
784C23C24×D1314yes—
785C23C24×D1312yes—
786C23C24×D1311yescharacteristic
787Q8—28no—
788Q8—2616no—
789Q8—2616no—
790Q8—268no—
791Q8—5216no—
792Q8—5216no—
793D4—216no—
794D4—28no—
795D4—2616no—
796D4—268no—
797D4—5216no—
798C2×C4—22no—
799C2×C4—24no—
800C2×C4—28no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—24no—
804C2×C4—22no—
805C2×C4—24no—
806C2×C4—28no—
807C2×C4—28no—
808C2×C4—216no—
809C2×C4—134no—
810C2×C4—134no—
811C2×C4—138no—
812C2×C4—138no—
813C2×C4—134no—
814C2×C4—264no—
815C2×C4—268no—
816C2×C4—268no—
817C2×C4—264no—
818C2×C4—264no—
819C2×C4—2616no—
820C2×C4—5216no—
821C2×C4—5216no—
822C2×C4—5216no—
823C2×C4#8825614yes—
824C2×C4#8825714yes—
825C2×C4C24×D1314yes—
826C2×C4C24×D1314yes—
827C2×C4C24×D1312yes—
828C2×C4C24×D1312yes—
829C2×C4C24×D1312yes—
830C2×C4C24×D1312yes—
831C2×C4C24×D1314yes—
832C2×C4C24×D1312yes—
833C2×C4C24×D1312yes—
834C22—28no—
835C22—22no—
836C22—22no—
837C22—24no—
838C22—24no—
839C22—24no—
840C22—48no—
841C22—264no—
842C22—264no—
843C22—264no—
844C22—528no—
845C22C2×#8825612yes—
846C22C2×#8825714yes—
847C22C2×#8825712yes—
848C22C2×#8825712yes—
849C22C25×D1311yescharacteristic
850C4—22no—
851C4—24no—
852C4—22no—
853C4—22no—
854C4—24no—
855C4—22no—
856C4—24no—
857C4—264no—
858C4—268no—
859C4—268no—
860C4—264no—
861C4—264no—
862C4C2×#8825614yes—
863C4C2×#8825714yes—
864C2—24no—
865C2—44no—
866C2—524no—
867C2#1312927314yesdirect product factor
868C2C22×#8825611yescharacteristic
869C2C22×#8825711yescharacteristic
870C2C22×#8825711yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#529C2
socleC23×C13C25
hypercenterC2×#529D13
hypocenterC13C2×#3552
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #13129273C2direct (N × H)
2. C2×#11719417C2semidirect
3. C2×#11719272C2semidirect
4. C2×#11719247C2semidirect
5. C2×#11719248C2semidirect
6. C2×#11719270C2semidirect
7. C2×Q8×D52C2semidirect
8. C2×#11719337C2semidirect
9. C2×#11719303C2semidirect
10. C2×#11719260C2semidirect
11. C2×#11719224C2semidirect
12. C2×#11719239C2semidirect
13. C2×#11719402C2semidirect
14. C2×#11719370C2semidirect
15. C2×#11719380C2semidirect
16. C22×#88123C2semidirect
17. C2×#11719184C2semidirect
18. C2×C13×#529C2semidirect
22. C13×#529C22semidirect
48. #11719417C22semidirect
49. #11719402C22semidirect
50. #11719380C22semidirect
51. #11719370C22semidirect
52. #11719337C22semidirect
53. #11719303C22semidirect
54. Q8×D52C22semidirect
55. #11719272C22semidirect
56. #11719270C22semidirect
57. #11719260C22semidirect
58. #11719248C22semidirect
59. #11719247C22semidirect
60. #11719239C22semidirect
61. #11719224C22semidirect
84. #11719184C22semidirect
98. C2×#88123C22semidirect
356. C2×#529D13semidirect
444. #529C2×D13semidirect
664. C2×C13#3552semidirect
773. C13C2×#3552semidirect
867. C2#13129273direct (N × H)

Maximal subgroups

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

subgroupindex
#131292732
C2×#117194172
C2×#117192722
C2×#117192472
C2×#117192482
C2×#117192702
C2×Q8×D522
C2×#117193372
C2×#117193032
C2×#117192602
C2×#117192242
C2×#117192392
C2×#117194022
C2×#117193702
C2×#117193802
C22×#881232
C2×#117191842
C2×C13×#5292
C2×#355213