Finite Group Databasebeta

← C2×#13129274 #16770521

Subgroups — C2×#13129274 #16770521

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#13129274C2132yesmaximal, direct product factor
2C2×#11719356C214yesmaximal, complemented
3C2×#11719426C211yesmaximal, characteristic, complemented
4C2×#11719247C211yesmaximal, characteristic, complemented
5C2×#11719216C212yesmaximal, complemented
6C2×#11719319C212yesmaximal, complemented
7C2×D4×Dic26C211yesmaximal, characteristic, complemented
8C2×#11719337C212yesmaximal, complemented
9C2×#11719536C212yesmaximal, complemented
10C2×#11719205C212yesmaximal, complemented
11C2×#11719308C212yesmaximal, complemented
12C2×#11719330C212yesmaximal, complemented
13C2×#11719365C214yesmaximal, complemented
14C2×#11719530C212yesmaximal, complemented
15C2×D13×C4⋊Q8C211yesmaximal, characteristic, complemented
16C2×#11719262C211yesmaximal, characteristic, complemented
17C2×#11719262C211yesmaximal, characteristic, complemented
18C2×C13×#547C211yesmaximal, characteristic, complemented
19C22×C13×#41C2212yes—
20C22×Q8×D13C2212yes—
21C23×Dic26C2212yes—
22C13×#547C22116yescomplemented
23C2×C13×C4⋊Q8C2211yescharacteristic
24C2×C13×#123C2214yes—
25C2×C13×C22⋊Q8C2212yes—
26C2×C13×#121C2212yes—
27C2×C4×D4×C13C2211yescharacteristic
28C2×C4×D4×C13C2211yescharacteristic
29C22×C13×C4⋊C4C2212yes—
30#11719536C22132yescomplemented
31#11719530C22132yescomplemented
32C2×Q8×Dic13C2212yes—
33C2×#88198C2212yes—
34C2×#88198C2212yes—
35C2×#88192C2211yescharacteristic
36C2×#88192C2214yes—
37C2×#88192C2211yescharacteristic
38C2×#88190C2214yes—
39C2×#88190C2211yescharacteristic
40C2×#88190C2212yes—
41C2×#88190C2211yescharacteristic
42C2×#88189C2214yes—
43C2×#88189C2214yes—
44C2×D4×Dic13C2212yes—
45C2×C4×C22⋊D13C2212yes—
46C2×C4×C22⋊D13C2214yes—
47C2×C4×C22⋊D13C2212yes—
48C2×#88180C2212yes—
49C2×#88180C2212yes—
50C2×#88180C2212yes—
51C2×#88178C2214yes—
52C2×#88178C2214yes—
53C2×#88178C2212yes—
54C2×#88178C2212yes—
55C2×#88178C2214yes—
56D13×C4⋊Q8C22116yescomplemented
57#11719426C22116yescomplemented
58#11719365C22164yescomplemented
59#11719356C22164yescomplemented
60#11719337C22132yescomplemented
61#11719330C22132yescomplemented
62#11719319C22132yescomplemented
63#11719308C22132yescomplemented
64#11719262C22116yescomplemented
65#11719262C22116yescomplemented
66#11719247C22116yescomplemented
67D4×Dic26C22116yescomplemented
68#11719216C22132yescomplemented
69C2×#88151C2211yescharacteristic
70C2×#88151C2211yescharacteristic
71C2×#88150C2214yes—
72C2×C4⋊C4×D13C2212yes—
73C2×C4⋊C4×D13C2212yes—
74#11719205C22132yescomplemented
75C2×#88144C2211yescharacteristic
76C2×#88144C2214yes—
77C2×#88144C2211yescharacteristic
78C2×#88144C2212yes—
79C2×#88143C2214yes—
80C2×#88143C2214yes—
81C2×#88142C2212yes—
82C2×#88142C2214yes—
83C2×#88142C2212yes—
84C2×#88142C2212yes—
85C2×#88141C2212yes—
86C2×#88141C2212yes—
87C2×#88137C2212yes—
88C2×#88137C2212yes—
89C2×#88135C2214yes—
90C2×#88133C2212yes—
91C2×#88133C2212yes—
92C2×#88133C2214yes—
93C2×#88133C2214yes—
94C2×#88133C2214yes—
95C2×#88132C2214yes—
96C2×#88132C2214yes—
97C2×C42×D13C2211yescharacteristic
98C2×#88123C2211yescharacteristic
99C2×C4×Dic26C2211yescharacteristic
100C2×C4×Dic26C2211yescharacteristic
101C2×C13×#41—48no—
102C2×C13×#41C23116yes—
103C22×Q8×C13C2312yes—
104C22×D4×C13C2311yescharacteristic
105C22×D4×C13C2311yescharacteristic
106C22×D4×C13C2314yes—
107C23×C4×C13C2312yes—
108C23×C4×C13C2312yes—
109C23×C4×C13C2314yes—
110C22×C22⋊D13C2312yes—
111C22×C22⋊D13C2312yes—
112C23×Dic13C2314yes—
113C2×Q8×D13—48no—
114C2×Q8×D13C23116yes—
115C22×C4×D13C2311yescharacteristic
116C22×C4×D13C2311yescharacteristic
117C22×C4×D13C2311yescharacteristic
118C22×C4×D13C2314yes—
119C22×Dic26—48no—
120C22×Dic26C2311yescharacteristic
121C22×Dic26C2311yescharacteristic
122C22×Dic26C2312yes—
123C22×Dic26C2314yes—
124C22×Dic26C2314yes—
125C22×Dic26C23116yes—
126C13×C4⋊Q8C2318yes—
127C13×#123C23132yes—
128C13×C22⋊Q8C23116yes—
129C13×#121C23116yes—
130C4×D4×C13C2318yes—
131C4×D4×C13C2318yes—
132C2×C13×C4⋊C4C2311yescharacteristic
133C2×C13×C4⋊C4C2312yes—
134C2×C13×C4⋊C4C2311yescharacteristic
135C2×C13×C4⋊C4C2312yes—
136C2×C13×C4⋊C4C2314yes—
137C2×C13×C4⋊C4C23116yes—
138C2×C13×C22⋊C4C2312yes—
139C2×C13×C22⋊C4C2314yes—
140C2×C13×C22⋊C4C2312yes—
141C2×C42×C13C2311yescharacteristic
142C2×C22⋊Dic13C2312yes—
143C2×C22⋊Dic13C2314yes—
144C2×C22⋊Dic13C2312yes—
145C2×C22⋊Dic13C2312yes—
146C2×C22⋊Dic13C2314yes—
147C2×C22⋊Dic13C2312yes—
148C2×C22⋊Dic13C2312yes—
149C2×C22⋊Dic13C2314yes—
150C2×C22⋊Dic13C2312yes—
151Q8×Dic13C23116yes—
152#88198C23116yes—
153#88198C23116yes—
154#88192C2318yes—
155#88192C2318yes—
156#88192C23132yes—
157#88190C23116yes—
158#88190C2318yes—
159#88190C2318yes—
160#88190C23132yes—
161#88189C23132yes—
162#88189C23132yes—
163D4×Dic13C23116yes—
164C4×C22⋊D13C23116yes—
165C4×C22⋊D13C23132yes—
166C4×C22⋊D13C23116yes—
167C2×#6103C2312yes—
168C2×#6103C2312yes—
169#88180C23116yes—
170#88180C23116yes—
171#88180C23116yes—
172C2×C4⋊Dic13C2311yescharacteristic
173C2×C4⋊Dic13C2311yescharacteristic
174C2×C4⋊Dic13C2312yes—
175C2×C4⋊Dic13C2312yes—
176C2×C4⋊Dic13C2312yes—
177C2×C4⋊Dic13C2312yes—
178C2×C4⋊Dic13C2312yes—
179C2×C4⋊Dic13C2314yes—
180C2×C4⋊Dic13C2312yes—
181#88178C23132yes—
182#88178C23132yes—
183#88178C23116yes—
184#88178C23132yes—
185#88178C23116yes—
186C2×#6101C2312yes—
187C2×#6101C2312yes—
188C2×#6101C2314yes—
189C2×#6101C2314yes—
190C2×#6101C2314yes—
191C2×#6101C2312yes—
192C2×#6101C2312yes—
193C2×#6101C2314yes—
194C2×#6101C2314yes—
195C2×#6101C2314yes—
196C2×C4×Dic13C2312yes—
197C2×C4×Dic13C2312yes—
198C2×C4×Dic13C2311yescharacteristic
199C2×C4×Dic13C2311yescharacteristic
200C2×C4×Dic13C2311yescharacteristic
201C2×C4×Dic13C2314yes—
202C2×C4×Dic13C2314yes—
203#88151C2318yes—
204#88151C2318yes—
205#88150C23132yes—
206C4⋊C4×D13C23116yes—
207C4⋊C4×D13C23116yes—
208#88144C23116yes—
209#88144C2318yes—
210#88144C23132yes—
211#88144C2318yes—
212#88143C23132yes—
213#88143C23132yes—
214#88142C23116yes—
215#88142C23116yes—
216#88142C23116yes—
217#88142C23132yes—
218#88141C23116yes—
219#88141C23116yes—
220#88137C23116yes—
221#88137C23116yes—
222#88135C23132yes—
223#88133C23132yes—
224#88133C23116yes—
225#88133C23116yes—
226#88133C23132yes—
227#88133C23132yes—
228#88132C23132yes—
229#88132C23132yes—
230C42×D13C2318yes—
231#88123C2318yes—
232C4×Dic26C2318yes—
233C4×Dic26C2318yes—
234C2×#3552—131nomaximal, Sylow
235C24×C13C2412yes—
236C24×C13C2412yes—
237C23×D13C2411yescharacteristic
238C13×#41—432no—
239C2×Q8×C13—28no—
240C2×Q8×C13C2418yes—
241C2×D4×C13—24no—
242C2×D4×C13—24no—
243C2×D4×C13—48no—
244C2×D4×C13C2414yes—
245C2×D4×C13C2414yes—
246C2×D4×C13C24116yes—
247C22×C4×C13—28no—
248C22×C4×C13—28no—
249C22×C4×C13—48no—
250C22×C4×C13C2412yes—
251C22×C4×C13C2411yescharacteristic
252C22×C4×C13C2414yes—
253C22×C4×C13C2412yes—
254C22×C4×C13C2418yes—
255C22×C4×C13C2418yes—
256C22×C4×C13C24116yes—
257C22×C4×C13C2411yescharacteristic
258C22×C4×C13C2411yescharacteristic
259C2×C22⋊D13—28no—
260C2×C22⋊D13—28no—
261C2×C22⋊D13C2418yes—
262C2×C22⋊D13C2418yes—
263C22×Dic13—48no—
264C22×Dic13C2412yes—
265C22×Dic13C2412yes—
266C22×Dic13C2412yes—
267C22×Dic13C2411yescharacteristic
268C22×Dic13C2411yescharacteristic
269C22×Dic13C2411yescharacteristic
270C22×Dic13C2412yes—
271C22×Dic13C2414yes—
272C22×Dic13C24116yes—
273Q8×D13—432no—
274C2×C4×D13—24no—
275C2×C4×D13—24no—
276C2×C4×D13—24no—
277C2×C4×D13—48no—
278C2×C4×D13C2414yes—
279C2×C4×D13C2414yes—
280C2×C4×D13C2414yes—
281C2×C4×D13C24116yes—
282C2×Dic26—24no—
283C2×Dic26—28no—
284C2×Dic26—24no—
285C2×Dic26—432no—
286C2×Dic26—48no—
287C2×Dic26—48no—
288C2×Dic26C2414yes—
289C2×Dic26C2414yes—
290C2×Dic26C2418yes—
291C2×Dic26C24116yes—
292C2×Dic26C24116yes—
293C13×C4⋊C4C2414yes—
294C13×C4⋊C4C2418yes—
295C13×C4⋊C4C2414yes—
296C13×C4⋊C4C2418yes—
297C13×C4⋊C4C24116yes—
298C13×C22⋊C4C2418yes—
299C13×C22⋊C4C24116yes—
300C13×C22⋊C4C2418yes—
301C42×C13C2414yes—
302C22⋊Dic13C2418yes—
303C22⋊Dic13C24116yes—
304C22⋊Dic13C2418yes—
305C22⋊Dic13C2418yes—
306C22⋊Dic13C24116yes—
307C22⋊Dic13C2418yes—
308C22⋊Dic13C2418yes—
309C22⋊Dic13C24116yes—
310C22⋊Dic13C2418yes—
311#6103C2418yes—
312#6103C2418yes—
313C4⋊Dic13C2414yes—
314C4⋊Dic13C2414yes—
315C4⋊Dic13C2418yes—
316C4⋊Dic13C2418yes—
317C4⋊Dic13C2418yes—
318C4⋊Dic13C2418yes—
319C4⋊Dic13C2418yes—
320C4⋊Dic13C24116yes—
321C4⋊Dic13C2418yes—
322#6101C2418yes—
323#6101C2418yes—
324#6101C24116yes—
325#6101C24116yes—
326#6101C24116yes—
327#6101C2418yes—
328#6101C2418yes—
329#6101C24116yes—
330#6101C24116yes—
331#6101C24116yes—
332C4×Dic13C2418yes—
333C4×Dic13C2418yes—
334C4×Dic13C2414yes—
335C4×Dic13C2414yes—
336C4×Dic13C2414yes—
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×#547D1311yescharacteristic, complemented
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×C13—24no—
358C23×C13—24no—
359C23×C13—24no—
360C23×C13—24no—
361C23×C13—24no—
362C23×C13—24no—
363C23×C13C2514yes—
364C23×C13C2514yes—
365C23×C13C2511yescharacteristic
366C22×D13—22no—
367C22×D13—22no—
368C22×D132−1+414yes—
369C22×D13C2512yes—
370Q8×C13—216no—
371D4×C13—28no—
372D4×C13—28no—
373D4×C13—416no—
374C2×C4×C13—24no—
375C2×C4×C13—28no—
376C2×C4×C13—22no—
377C2×C4×C13—24no—
378C2×C4×C13—216no—
379C2×C4×C13—216no—
380C2×C4×C13—416no—
381C2×C4×C13H(5,𝔽2)14yes—
382C2×C4×C132−1+414yes—
383C2×C4×C13C2514yes—
384C2×C4×C13C2512yes—
385C2×C4×C13C2518yes—
386C2×C4×C13C2514yes—
387C2×C4×C13C2512yes—
388C2×C4×C13C2512yes—
389C22⋊D13—216no—
390C22⋊D13—216no—
391C2×Dic13—28no—
392C2×Dic13—24no—
393C2×Dic13—22no—
394C2×Dic13—24no—
395C2×Dic13—22no—
396C2×Dic13—22no—
397C2×Dic13—24no—
398C2×Dic13—24no—
399C2×Dic13—416no—
400C2×Dic13C2514yes—
401C2×Dic13C2514yes—
402C2×Dic13C2514yes—
403C2×Dic13C2512yes—
404C2×Dic13C2512yes—
405C2×Dic13C2512yes—
406C2×Dic13C2514yes—
407C2×Dic13C2518yes—
408C4×D13—28no—
409C4×D13—28no—
410C4×D13—28no—
411C4×D13—416no—
412Dic26—28no—
413Dic26—216no—
414Dic26—28no—
415Dic26—416no—
416Dic26—416no—
417C22×#41C2×D1312yes—
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#547C2×D13116yescomplemented
429#544—1332no—
430#542—1332no—
431#541—1332no—
432#539—1364no—
433#536—1332no—
434C2×C4⋊Q8—132no—
435C2×C4⋊Q8—132no—
436C2×C4⋊Q8—1316no—
437C2×C4⋊Q8—132no—
438C2×C4⋊Q8—132no—
439C2×C4⋊Q8—132no—
440C2×C4⋊Q8—134no—
441C2×C4⋊Q8—131no—
442C2×C4⋊Q8C2×D1311yescharacteristic
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—134no—
452C2×#125—131no—
453C2×#125—131no—
454C2×#125—134no—
455C2×#125—132no—
456C2×#124—131no—
457C2×#124—131no—
458C2×#124—132no—
459C2×#124—134no—
460C2×#123—134no—
461C2×#123—134no—
462C2×#123—132no—
463C2×#123—132no—
464C2×#123C2×D1314yes—
465C2×C22⋊Q8—134no—
466C2×C22⋊Q8—134no—
467C2×C22⋊Q8—132no—
468C2×C22⋊Q8—132no—
469C2×C22⋊Q8—134no—
470C2×C22⋊Q8—134no—
471C2×C22⋊Q8—131no—
472C2×C22⋊Q8—131no—
473C2×C22⋊Q8—134no—
474C2×C22⋊Q8—134no—
475C2×C22⋊Q8C2×D1312yes—
476C2×#121—131no—
477C2×#121—131no—
478C2×#121—134no—
479C2×#121C2×D1312yes—
480C2×C4×Q8—132no—
481C2×C4×Q8—132no—
482C2×C4×Q8—132no—
483C2×C4×Q8—131no—
484C2×C4×Q8—131no—
485C2×C4×D4—132no—
486C2×C4×D4—132no—
487C2×C4×D4—132no—
488C2×C4×D4—134no—
489C2×C4×D4—134no—
490C2×C4×D4C2×D1311yescharacteristic
491C2×C4×D4C2×D1311yescharacteristic
492C2×#117—132no—
493C2×#117—132no—
494C2×#117—132no—
495C22×C4⋊C4—132no—
496C22×C4⋊C4—132no—
497C22×C4⋊C4C2×D1312yes—
498C22×C42—131no—
499C22×C13—24no—
500C22×C13—24no—
501C22×C13—24no—
502C22×C13—24no—
503C22×C13—24no—
504C22×C13—24no—
505C22×C13—48no—
506C22×C13—48no—
507C22×C13C2×H(5,𝔽2)12yes—
508C22×C13C2×2−1+412yes—
509C22×C13C2×2−1+412yes—
510C22×C13C2611yescharacteristic
511C2×D13—22no—
512C2×D13—22no—
513C2×D13—28no—
514C2×D13C2×2−1+414yes—
515C4×C13—24no—
516C4×C13—28no—
517C4×C13—22no—
518C4×C13—24no—
519C4×C13C2×H(5,𝔽2)14yes—
520C4×C13C2×2−1+414yes—
521Dic13—28no—
522Dic13—24no—
523Dic13—22no—
524Dic13—24no—
525Dic13—22no—
526Dic13—22no—
527Dic13—24no—
528Dic13—24no—
529C2×#41—48no—
530C2×#41C22×D13116yes—
531C22×Q8—1316no—
532C22×Q8—131no—
533C22×Q8—132no—
534C22×Q8—131no—
535C22×Q8—134no—
536C22×Q8—134no—
537C22×Q8—1316no—
538C22×Q8—528no—
539C22×Q8—528no—
540C22×Q8C22×D1312yes—
541C22×D4—132no—
542C22×D4—132no—
543C22×D4C22×D1311yescharacteristic
544C22×D4C22×D1311yescharacteristic
545C22×D4C22×D1314yes—
546C23×C4—134no—
547C23×C4—131no—
548C23×C4—131no—
549C23×C4—131no—
550C23×C4—134no—
551C23×C4C22×D1312yes—
552C23×C4C22×D1312yes—
553C23×C4C22×D1314yes—
554C4⋊Q8—1316no—
555C4⋊Q8—1316no—
556C4⋊Q8—1316no—
557C4⋊Q8—1316no—
558C4⋊Q8—1316no—
559C4⋊Q8—1332no—
560C4⋊Q8—138no—
561C4⋊Q8C22×D1318yes—
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#125—1332no—
572#125—1316no—
573#124—138no—
574#124—138no—
575#124—1316no—
576#124—1332no—
577#123—1332no—
578#123—1332no—
579#123—1316no—
580#123—1316no—
581#123C22×D13132yes—
582C22⋊Q8—1332no—
583C22⋊Q8—1332no—
584C22⋊Q8—1316no—
585C22⋊Q8—1316no—
586C22⋊Q8—1332no—
587C22⋊Q8—138no—
588C22⋊Q8—138no—
589C22⋊Q8—1332no—
590C22⋊Q8—1332no—
591C22⋊Q8—1332no—
592C22⋊Q8C22×D13116yes—
593#121—138no—
594#121—138no—
595#121—1332no—
596#121C22×D13116yes—
597C4×Q8—1316no—
598C4×Q8—1316no—
599C4×Q8—1316no—
600C4×Q8—138no—
601C4×Q8—138no—
602C4×D4—1316no—
603C4×D4—1316no—
604C4×D4—1316no—
605C4×D4—1332no—
606C4×D4—1332no—
607C4×D4C22×D1318yes—
608C4×D4C22×D1318yes—
609#117—1316no—
610#117—1316no—
611#117—1316no—
612C2×C4⋊C4—132no—
613C2×C4⋊C4—132no—
614C2×C4⋊C4—134no—
615C2×C4⋊C4—134no—
616C2×C4⋊C4—131no—
617C2×C4⋊C4—132no—
618C2×C4⋊C4—132no—
619C2×C4⋊C4—132no—
620C2×C4⋊C4—132no—
621C2×C4⋊C4—134no—
622C2×C4⋊C4—132no—
623C2×C4⋊C4—134no—
624C2×C4⋊C4—132no—
625C2×C4⋊C4—131no—
626C2×C4⋊C4—134no—
627C2×C4⋊C4—134no—
628C2×C4⋊C4—134no—
629C2×C4⋊C4—132no—
630C2×C4⋊C4—132no—
631C2×C4⋊C4—1316no—
632C2×C4⋊C4—1316no—
633C2×C4⋊C4C22×D1312yes—
634C2×C4⋊C4C22×D1312yes—
635C2×C4⋊C4C22×D1311yescharacteristic
636C2×C4⋊C4C22×D1314yes—
637C2×C4⋊C4C22×D13116yes—
638C2×C4⋊C4C22×D1311yescharacteristic
639C2×C22⋊C4—134no—
640C2×C22⋊C4—132no—
641C2×C22⋊C4—132no—
642C2×C22⋊C4—132no—
643C2×C22⋊C4—132no—
644C2×C22⋊C4—134no—
645C2×C22⋊C4—132no—
646C2×C22⋊C4—134no—
647C2×C22⋊C4—132no—
648C2×C22⋊C4—132no—
649C2×C22⋊C4—132no—
650C2×C22⋊C4C22×D1314yes—
651C2×C22⋊C4C22×D1312yes—
652C2×C22⋊C4C22×D1312yes—
653C2×C42—131no—
654C2×C42—131no—
655C2×C42—132no—
656C2×C42—132no—
657C2×C42—134no—
658C2×C42—134no—
659C2×C42—131no—
660C2×C42—138no—
661C2×C42C22×D1311yescharacteristic
662C2×C13—44no—
663C2×C13—44no—
664C2×C13#355214yescomplemented
665C2×C13C22×H(5,𝔽2)11yescharacteristic
666C2×C13C22×2−1+411yescharacteristic
667C2×C13C22×2−1+411yescharacteristic
668D13—24no—
669C24—131no—
670C24C23×D1312yes—
671C24C23×D1312yes—
672#41—432no—
673C2×Q8—28no—
674C2×Q8—134no—
675C2×Q8—138no—
676C2×Q8—134no—
677C2×Q8—1316no—
678C2×Q8—1316no—
679C2×Q8—264no—
680C2×Q8—268no—
681C2×Q8—264no—
682C2×Q8—528no—
683C2×Q8—528no—
684C2×Q8—5232no—
685C2×Q8—5232no—
686C2×Q8C23×D1318yes—
687C2×D4—24no—
688C2×D4—24no—
689C2×D4—48no—
690C2×D4—138no—
691C2×D4—138no—
692C2×D4—268no—
693C2×D4—268no—
694C2×D4C23×D1314yes—
695C2×D4C23×D1314yes—
696C2×D4C23×D13116yes—
697C22×C4—28no—
698C22×C4—28no—
699C22×C4—48no—
700C22×C4—132no—
701C22×C4—132no—
702C22×C4—132no—
703C22×C4—131no—
704C22×C4—131no—
705C22×C4—131no—
706C22×C4—132no—
707C22×C4—134no—
708C22×C4—1316no—
709C22×C4—134no—
710C22×C4—134no—
711C22×C4—134no—
712C22×C4—1316no—
713C22×C4—264no—
714C22×C4—264no—
715C22×C4—264no—
716C22×C4—528no—
717C22×C4—528no—
718C22×C4C23×D1318yes—
719C22×C4C23×D1318yes—
720C22×C4C23×D1312yes—
721C22×C4C23×D1311yescharacteristic
722C22×C4C23×D1314yes—
723C22×C4C23×D1312yes—
724C22×C4C23×D13116yes—
725C22×C4C23×D1311yescharacteristic
726C22×C4C23×D1311yescharacteristic
727C4⋊C4—138no—
728C4⋊C4—138no—
729C4⋊C4—1316no—
730C4⋊C4—1316no—
731C4⋊C4—134no—
732C4⋊C4—138no—
733C4⋊C4—138no—
734C4⋊C4—138no—
735C4⋊C4—138no—
736C4⋊C4—1316no—
737C4⋊C4—138no—
738C4⋊C4—1316no—
739C4⋊C4—138no—
740C4⋊C4—134no—
741C4⋊C4—1316no—
742C4⋊C4—1316no—
743C4⋊C4—1316no—
744C4⋊C4—138no—
745C4⋊C4—138no—
746C4⋊C4C23×D1318yes—
747C4⋊C4C23×D1318yes—
748C4⋊C4C23×D1314yes—
749C4⋊C4C23×D13116yes—
750C4⋊C4C23×D1314yes—
751C22⋊C4—1316no—
752C22⋊C4—138no—
753C22⋊C4—138no—
754C22⋊C4—138no—
755C22⋊C4—138no—
756C22⋊C4—1316no—
757C22⋊C4—138no—
758C22⋊C4—1316no—
759C22⋊C4—138no—
760C22⋊C4—138no—
761C22⋊C4—138no—
762C22⋊C4C23×D13116yes—
763C22⋊C4C23×D1318yes—
764C22⋊C4C23×D1318yes—
765C42—134no—
766C42—134no—
767C42—134no—
768C42—138no—
769C42—138no—
770C42—1316no—
771C42—1316no—
772C42C23×D1314yes—
773C13C2×#355211yescharacteristic, complemented, Sylow
774C23—24no—
775C23—24no—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—24no—
780C23—134no—
781C23—132no—
782C23—262no—
783C23—262no—
784C23C24×D1314yes—
785C23C24×D1314yes—
786C23C24×D1311yescharacteristic
787Q8—216no—
788Q8—268no—
789Q8—2616no—
790Q8—268no—
791Q8—5216no—
792Q8—5216no—
793D4—28no—
794D4—28no—
795D4—416no—
796D4—2616no—
797D4—2616no—
798C2×C4—24no—
799C2×C4—28no—
800C2×C4—24no—
801C2×C4—22no—
802C2×C4—216no—
803C2×C4—216no—
804C2×C4—416no—
805C2×C4—134no—
806C2×C4—134no—
807C2×C4—134no—
808C2×C4—132no—
809C2×C4—132no—
810C2×C4—132no—
811C2×C4—134no—
812C2×C4—138no—
813C2×C4—268no—
814C2×C4—262no—
815C2×C4—268no—
816C2×C4—264no—
817C2×C4—262no—
818C2×C4—264no—
819C2×C4—262no—
820C2×C4—264no—
821C2×C4—264no—
822C2×C4—268no—
823C2×C4—268no—
824C2×C4—5216no—
825C2×C4—5216no—
826C2×C4#8825114yes—
827C2×C4#8825714yes—
828C2×C4C24×D1314yes—
829C2×C4C24×D1312yes—
830C2×C4C24×D1318yes—
831C2×C4C24×D1314yes—
832C2×C4C24×D1312yes—
833C2×C4C24×D1312yes—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—24no—
838C22—24no—
839C22—24no—
840C22—48no—
841C22—48no—
842C22—134no—
843C22—268no—
844C22—262no—
845C22—262no—
846C22C2×#8825112yes—
847C22C2×#8825712yes—
848C22D13×2−1+412yes—
849C22C25×D1311yescharacteristic
850C4—24no—
851C4—28no—
852C4—22no—
853C4—24no—
854C4—262no—
855C4—268no—
856C4—264no—
857C4—262no—
858C4—264no—
859C4—264no—
860C4—262no—
861C4—264no—
862C4C2×#8825114yes—
863C4C2×#8825714yes—
864C2—44no—
865C2—44no—
866C2—264no—
867C2#1312927414yesdirect product factor
868C2C22×#8825111yescharacteristic
869C2C2×D13×2−1+411yescharacteristic
870C2C22×#8825711yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#547C2
socleC23×C13C25
hypercenterC2×#547D13
hypocenterC13C2×#3552
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. #13129274C2direct (N × H)
2. C2×#11719356C2semidirect
3. C2×#11719426C2semidirect
4. C2×#11719247C2semidirect
5. C2×#11719216C2semidirect
6. C2×#11719319C2semidirect
7. C2×D4×Dic26C2semidirect
8. C2×#11719337C2semidirect
9. C2×#11719536C2semidirect
10. C2×#11719205C2semidirect
11. C2×#11719308C2semidirect
12. C2×#11719330C2semidirect
13. C2×#11719365C2semidirect
14. C2×#11719530C2semidirect
15. C2×D13×C4⋊Q8C2semidirect
16. C2×#11719262C2semidirect
17. C2×#11719262C2semidirect
18. C2×C13×#547C2semidirect
22. C13×#547C22semidirect
30. #11719536C22semidirect
31. #11719530C22semidirect
56. D13×C4⋊Q8C22semidirect
57. #11719426C22semidirect
58. #11719365C22semidirect
59. #11719356C22semidirect
60. #11719337C22semidirect
61. #11719330C22semidirect
62. #11719319C22semidirect
63. #11719308C22semidirect
64. #11719262C22semidirect
65. #11719262C22semidirect
66. #11719247C22semidirect
67. D4×Dic26C22semidirect
68. #11719216C22semidirect
74. #11719205C22semidirect
348. C2×#547D13semidirect
428. #547C2×D13semidirect
664. C2×C13#3552semidirect
773. C13C2×#3552semidirect
867. C2#13129274direct (N × H)

Maximal subgroups

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

subgroupindex
#131292742
C2×#117193562
C2×#117194262
C2×#117192472
C2×#117192162
C2×#117193192
C2×D4×Dic262
C2×#117193372
C2×#117195362
C2×#117192052
C2×#117193082
C2×#117193302
C2×#117193652
C2×#117195302
C2×D13×C4⋊Q82
C2×#117192622
C2×C13×#5472
C2×#355213