Finite Group Databasebeta

← C2×D13×#547 #16769857

Subgroups — C2×D13×#547 #16769857

Order 3328.

12230 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#41×D13C212yesmaximal, complemented
2C2×#11719256C211yesmaximal, characteristic, complemented
3C2×#11719260C211yesmaximal, characteristic, complemented
4C2×#11719431C211yesmaximal, characteristic, complemented
5C2×#11719336C212yesmaximal, complemented
6C2×#11719212C212yesmaximal, complemented
7C2×#11719316C212yesmaximal, complemented
8C2×#11719529C212yesmaximal, complemented
9C2×#11719360C214yesmaximal, complemented
10D13×#547C2132yesmaximal, direct product factor
11C2×D13×C4⋊Q8C211yesmaximal, characteristic, complemented
12C2×D13×#123C214yesmaximal, complemented
13C2×D13×C22⋊Q8C212yesmaximal, complemented
14C2×D13×#121C212yesmaximal, complemented
15C2×C4×D4×D13C211yesmaximal, characteristic, complemented
16C2×C4×D4×D13C211yesmaximal, characteristic, complemented
17C22×C4⋊C4×D13C212yesmaximal, complemented
18C2×C13×#547C211yesmaximal, characteristic, complemented
19C22×C13×#41C2212yescomplemented
20C2×#41×D13—232no—
21C2×#41×D13C22132yescomplemented
22C22×#6131C2212yescomplemented
23C22×Q8×D13C2212yes—
24C22×#6129C2214yescomplemented
25C22×#6129C2212yescomplemented
26C22×D4×D13C2211yescharacteristic
27C22×D4×D13C2214yes—
28C22×D4×D13C2211yescharacteristic
29C22×#6127C2214yescomplemented
30C22×#6127C2212yescomplemented
31C23×C4×D13C2212yes—
32C23×C4×D13C2214yes—
33C23×C4×D13C2212yes—
34C13×#547C22116yescomplemented
35C2×C13×C4⋊Q8C2211yescharacteristic, complemented
36C2×C13×#123C2214yescomplemented
37C2×C13×C22⋊Q8C2212yescomplemented
38C2×C13×#121C2212yescomplemented
39C2×C4×D4×C13C2211yescharacteristic, complemented
40C2×C4×D4×C13C2211yescharacteristic, complemented
41C22×C13×C4⋊C4C2212yescomplemented
42#11719529C22132yescomplemented
43C2×#88200C2212yescomplemented
44C2×#88198C2212yescomplemented
45C2×#88193C2214yescomplemented
46C2×#88192C2212yescomplemented
47C2×#88189C2214yescomplemented
48C2×D4×Dic13C2211yescharacteristic, complemented
49C2×D4×Dic13C2211yescharacteristic, complemented
50C2×#88184C2212yescomplemented
51C2×#88183C2214yescomplemented
52C2×C4×C22⋊D13C2212yescomplemented
53C2×C4×C22⋊D13C2212yescomplemented
54C22×C4⋊Dic13C2212yescomplemented
55C2×#88178C2212yescomplemented
56C22×#6101C2214yescomplemented
57#11719431C22116yescomplemented
58D13×C4⋊Q8C22116yescomplemented
59#11719360C22164yescomplemented
60D13×#123C22164yescomplemented
61#11719336C22132yescomplemented
62D13×C22⋊Q8C22132yescomplemented
63#11719316C22132yescomplemented
64D13×#121C22132yescomplemented
65#11719260C22116yescomplemented
66#11719256C22116yescomplemented
67C4×D4×D13C22116yescomplemented
68C4×D4×D13C22116yescomplemented
69C2×#88151C2212yescomplemented
70C2×#88150C2214yescomplemented
71#11719212C22132yescomplemented
72C2×#88149C2212yescomplemented
73C2×#88148C2214yescomplemented
74C2×#88148C2214yescomplemented
75C2×#88147C2211yescharacteristic, complemented
76C2×#88147C2211yescharacteristic, complemented
77C2×C4⋊C4×D13C2211yescharacteristic
78C2×C4⋊C4×D13C2212yes—
79C2×C4⋊C4×D13C2214yes—
80C2×C4⋊C4×D13C2211yescharacteristic
81C2×C4⋊C4×D13C2212yes—
82C2×C4⋊C4×D13C22132yescomplemented
83C2×C4⋊C4×D13C2214yescomplemented
84C2×C4⋊C4×D13C2212yescomplemented
85C2×C4⋊C4×D13C2212yescomplemented
86C2×#88142C2212yescomplemented
87C2×#88142C2212yescomplemented
88C2×#88140C2214yescomplemented
89C2×#88138C2214yescomplemented
90C2×#88137C2214yescomplemented
91C2×#88137C2214yescomplemented
92C2×#88135C2212yescomplemented
93C2×#88135C2212yescomplemented
94C2×C22⋊C4×D13C2212yes—
95C2×C22⋊C4×D13C2212yes—
96C2×C22⋊C4×D13C2214yes—
97C2×#88132C2214yescomplemented
98C2×C4×D52C2211yescharacteristic, complemented
99C2×C4×D52C2211yescharacteristic, complemented
100C2×C42×D13C2211yescharacteristic
101C2×#88123C2211yescharacteristic, complemented
102C24×D13C2312yes—
103C24×D13C2312yes—
104C2×C13×#41—216no—
105C2×C13×#41C23116yescomplemented
106C22×Q8×C13C2312yes—
107C22×D4×C13C2311yescharacteristic
108C22×D4×C13C2314yes—
109C22×D4×C13C2311yescharacteristic
110C23×C4×C13C2314yes—
111C23×C4×C13C2312yes—
112C23×C4×C13C2312yes—
113C22×C22⋊D13C2312yes—
114C22×C22⋊D13C2314yes—
115C22×C22⋊D13C2314yes—
116C22×C22⋊D13C2312yes—
117C23×Dic13C2312yes—
118C23×Dic13C2312yes—
119C23×Dic13C2314yes—
120#41×D13—2256no—
121C2×#6131—216no—
122C2×#6131C23116yescomplemented
123C2×Q8×D13—216no—
124C2×Q8×D13C23116yes—
125C2×#6129—216no—
126C2×#6129—232no—
127C2×#6129C23116yescomplemented
128C2×#6129C23132yescomplemented
129C2×D4×D13—232no—
130C2×D4×D13—28no—
131C2×D4×D13D4116yescomplemented
132C2×D4×D13C2318yes—
133C2×D4×D13C23132yes—
134C2×D4×D13C2318yes—
135C2×#6127—232no—
136C2×#6127—216no—
137C2×#6127C23132yescomplemented
138C2×#6127C23116yescomplemented
139C22×D52C2311yescharacteristic
140C22×D52C2314yes—
141C22×D52C2311yescharacteristic
142C22×C4×D13—232no—
143C22×C4×D13—216no—
144C22×C4×D13—216no—
145C22×C4×D13C2311yescharacteristic
146C22×C4×D13C2312yes—
147C22×C4×D13C2312yes—
148C22×C4×D13C2312yes—
149C22×C4×D13C2312yes—
150C22×C4×D13C2314yes—
151C22×C4×D13C2312yes—
152C22×C4×D13C2312yes—
153C22×C4×D13C2314yes—
154C22×C4×D13C2314yes—
155C22×C4×D13C23116yes—
156C22×C4×D13C23132yes—
157C22×C4×D13C23116yes—
158C22×C4×D13C2311yescharacteristic
159C22×C4×D13C2311yescharacteristic
160C22×Dic26C2312yes—
161C22×Dic26C2314yes—
162C13×C4⋊Q8C2318yescomplemented
163C13×#123C23132yescomplemented
164C13×C22⋊Q8C23116yescomplemented
165C13×#121C23116yescomplemented
166C4×D4×C13C2318yescomplemented
167C4×D4×C13C2318yescomplemented
168C2×C13×C4⋊C4C2312yes—
169C2×C13×C4⋊C4C2312yes—
170C2×C13×C4⋊C4C2311yescharacteristic
171C2×C13×C4⋊C4C2314yes—
172C2×C13×C4⋊C4C2311yescharacteristic
173C2×C13×C4⋊C4C23116yescomplemented
174C2×C13×C22⋊C4C2314yes—
175C2×C13×C22⋊C4C2312yes—
176C2×C13×C22⋊C4C2312yes—
177C2×C42×C13C2311yescharacteristic
178C2×C22⋊Dic13C2314yes—
179C2×C22⋊Dic13C2312yes—
180C2×C22⋊Dic13C2312yes—
181#88200C23116yescomplemented
182#88198C23116yescomplemented
183#88193C23132yescomplemented
184#88192C23116yescomplemented
185#88189C23132yescomplemented
186D4×Dic13C2318yescomplemented
187D4×Dic13C2318yescomplemented
188#88184C23116yescomplemented
189#88183C23132yescomplemented
190C4×C22⋊D13C23116yescomplemented
191C4×C22⋊D13C23116yescomplemented
192C2×#6103C2312yes—
193C2×#6103C2312yes—
194C2×#6103C2312yes—
195C2×#6103C2314yes—
196C2×#6103C2312yes—
197C2×#6103C2314yes—
198C2×C4⋊Dic13C2312yes—
199C2×C4⋊Dic13C2312yes—
200C2×C4⋊Dic13C2311yescharacteristic
201C2×C4⋊Dic13C2311yescharacteristic
202C2×C4⋊Dic13C2314yes—
203C2×C4⋊Dic13C23116yescomplemented
204#88178C23116yescomplemented
205C2×#6101C2312yes—
206C2×#6101C2314yes—
207C2×#6101C2312yes—
208C2×#6101C2314yes—
209C2×#6101C2314yes—
210C2×#6101C2314yes—
211C2×#6101C23132yescomplemented
212C2×C4×Dic13C2311yescharacteristic
213C2×C4×Dic13C2311yescharacteristic
214C2×C4×Dic13C2311yescharacteristic
215#88151C23116yescomplemented
216#88150C23132yescomplemented
217#88149C23116yescomplemented
218#88148C23132yescomplemented
219#88148C23132yescomplemented
220#88147C2318yescomplemented
221#88147C2318yescomplemented
222C4⋊C4×D13C23116yes—
223C4⋊C4×D13C23116yes—
224C4⋊C4×D13C2318yes—
225C4⋊C4×D13C23132yes—
226C4⋊C4×D13C2318yes—
227C4⋊C4×D13C23116yescomplemented
228C4⋊C4×D13C23116yescomplemented
229C4⋊C4×D13C23132yescomplemented
230#88142C23116yescomplemented
231#88142C23116yescomplemented
232#88140C23132yescomplemented
233#88138C23132yescomplemented
234#88137C23132yescomplemented
235#88137C23132yescomplemented
236#88135C23116yescomplemented
237#88135C23116yescomplemented
238C22⋊C4×D13C23116yes—
239C22⋊C4×D13C23116yes—
240C22⋊C4×D13C23132yes—
241#88132C23132yescomplemented
242C4×D52C2318yescomplemented
243C4×D52C2318yescomplemented
244C42×D13C2318yes—
245#88123C2318yescomplemented
246C22×#547—131nomaximal, Sylow
247C24×C13C2412yes—
248C24×C13C2412yes—
249C23×D13—28no—
250C23×D13—28no—
251C23×D13—28no—
252C23×D13—28no—
253C23×D13—28no—
254C23×D13C2×D4116yes—
255C23×D13C2418yes—
256C23×D13C2412yes—
257C23×D13C2418yes—
258C23×D13C2412yes—
259C23×D13C2411yescharacteristic
260C13×#41—264no—
261C2×Q8×C13—28no—
262C2×Q8×C13C2418yes—
263C2×D4×C13—216no—
264C2×D4×C13—24no—
265C2×D4×C13C2×D418yescomplemented
266C2×D4×C13C2414yes—
267C2×D4×C13C24116yes—
268C2×D4×C13C2414yes—
269C22×C4×C13—216no—
270C22×C4×C13—28no—
271C22×C4×C13—28no—
272C22×C4×C13C2411yescharacteristic
273C22×C4×C13C2414yes—
274C22×C4×C13C2412yes—
275C22×C4×C13C2412yes—
276C22×C4×C13C24116yes—
277C22×C4×C13C2418yes—
278C22×C4×C13C2418yes—
279C22×C4×C13C2411yescharacteristic
280C22×C4×C13C2411yescharacteristic
281C2×C22⋊D13—216no—
282C2×C22⋊D13—216no—
283C2×C22⋊D13—28no—
284C2×C22⋊D13C2×D4116yescomplemented
285C2×C22⋊D13C2418yes—
286C2×C22⋊D13C24116yes—
287C2×C22⋊D13C24116yes—
288C2×C22⋊D13C2418yes—
289C22×Dic13—216no—
290C22×Dic13—28no—
291C22×Dic13—28no—
292C22×Dic13C2418yes—
293C22×Dic13C2418yes—
294C22×Dic13C24116yes—
295C22×Dic13C2411yescharacteristic
296C22×Dic13C2412yes—
297C22×Dic13C2414yes—
298C22×Dic13C2412yes—
299C22×Dic13C2411yescharacteristic
300C22×Dic13C2411yescharacteristic
301#6131—264no—
302Q8×D13—264no—
303#6129—264no—
304#6129—2128no—
305D4×D13—2128no—
306D4×D13—232no—
307D4×D13C2×D4164yescomplemented
308#6127—2128no—
309#6127—264no—
310C2×D52—216no—
311C2×D52—24no—
312C2×D52C2×D418yescomplemented
313C2×D52C2414yes—
314C2×D52C24116yes—
315C2×D52C2414yes—
316C2×C4×D13—28no—
317C2×C4×D13—216no—
318C2×C4×D13—216no—
319C2×C4×D13—216no—
320C2×C4×D13—2128no—
321C2×C4×D13—28no—
322C2×C4×D13—24no—
323C2×C4×D13—28no—
324C2×C4×D13—28no—
325C2×C4×D13—28no—
326C2×C4×D13—28no—
327C2×C4×D13—264no—
328C2×C4×D13—264no—
329C2×C4×D13C2×D418yes—
330C2×C4×D13#4118yescomplemented
331C2×C4×D13C2414yes—
332C2×C4×D13C2418yes—
333C2×C4×D13C2418yes—
334C2×C4×D13C2418yes—
335C2×C4×D13C2418yes—
336C2×C4×D13C24116yes—
337C2×C4×D13C2418yes—
338C2×C4×D13C2418yes—
339C2×C4×D13C24116yes—
340C2×C4×D13C24116yes—
341C2×C4×D13C2414yes—
342C2×C4×D13C2414yes—
343C2×Dic26—28no—
344C2×Dic26—216no—
345C2×Dic26C2418yes—
346C2×Dic26C24116yes—
347C13×C4⋊C4C2418yes—
348C13×C4⋊C4C2418yes—
349C13×C4⋊C4C2414yes—
350C13×C4⋊C4C24116yes—
351C13×C4⋊C4C2414yes—
352C13×C22⋊C4C24116yes—
353C13×C22⋊C4C2418yes—
354C13×C22⋊C4C2418yes—
355C42×C13C2414yes—
356C22⋊Dic13C24116yes—
357C22⋊Dic13C2418yes—
358C22⋊Dic13C2418yes—
359#6103C2418yes—
360#6103C2418yes—
361#6103C2418yes—
362#6103C24116yes—
363#6103C2418yes—
364#6103C24116yes—
365C4⋊Dic13C2418yes—
366C4⋊Dic13C2418yes—
367C4⋊Dic13C2414yes—
368C4⋊Dic13C2414yes—
369C4⋊Dic13C24116yes—
370#6101C2418yes—
371#6101C24116yes—
372#6101C2418yes—
373#6101C24116yes—
374#6101C24116yes—
375#6101C24116yes—
376C4×Dic13C2414yes—
377C4×Dic13C2414yes—
378C4×Dic13C2414yes—
379C23×#41—132no—
380C2×#547—132no—
381C2×#547—1332no—
382C2×#547—131no—
383C2×#547—134no—
384C2×#547—132no—
385C2×#547—132no—
386C2×#547—131no—
387C2×#547—131no—
388C2×#547—132no—
389C2×#547D1311yescharacteristic, direct product factor
390C22×C4⋊Q8—131no—
391C22×#123—134no—
392C22×C22⋊Q8—132no—
393C22×#121—132no—
394C22×C4×D4—131no—
395C22×C4×D4—131no—
396C23×C4⋊C4—132no—
397C23×C13—24no—
398C23×C13—24no—
399C23×C13—24no—
400C23×C13—24no—
401C23×C13—24no—
402C23×C13C22×D418yes—
403C23×C13C2514yes—
404C23×C13C2514yes—
405C23×C13C2511yescharacteristic
406C22×D13—24no—
407C22×D13—24no—
408C22×D13—264no—
409C22×D13—216no—
410C22×D13—216no—
411C22×D13—24no—
412C22×D13—24no—
413C22×D13—24no—
414C22×D13—216no—
415C22×D13—216no—
416C22×D13—216no—
417C22×D13—432no—
418C22×D13C22×D418yes—
419C22×D13C22×D4132yes—
420C22×D13C22×D414yes—
421C22×D13C2×#4114yes—
422C22×D132−1+414yes—
423C22×D13C2514yes—
424C22×D13C2514yes—
425C22×D13C2512yes—
426Q8×C13—216no—
427D4×C13—232no—
428D4×C13—28no—
429D4×C13C22×D4116yescomplemented
430C2×C4×C13—28no—
431C2×C4×C13—24no—
432C2×C4×C13—232no—
433C2×C4×C13—24no—
434C2×C4×C13—22no—
435C2×C4×C13—216no—
436C2×C4×C13—216no—
437C2×C4×C13C22×D414yes—
438C2×C4×C13C2×#4114yescomplemented
439C2×C4×C13C2512yes—
440C2×C4×C13C2518yes—
441C2×C4×C13C2514yes—
442C2×C4×C13C2514yes—
443C2×C4×C13C2512yes—
444C2×C4×C13C2512yes—
445C22⋊D13—232no—
446C22⋊D13—232no—
447C22⋊D13—216no—
448C22⋊D13C22×D4132yescomplemented
449C2×Dic13—28no—
450C2×Dic13—24no—
451C2×Dic13—232no—
452C2×Dic13—24no—
453C2×Dic13—22no—
454C2×Dic13—216no—
455C2×Dic13—216no—
456C2×Dic13C22×D414yes—
457C2×Dic13C2×#4114yescomplemented
458C2×Dic13C2512yes—
459C2×Dic13C2514yes—
460C2×Dic13C2518yes—
461C2×Dic13C2514yes—
462C2×Dic13C2512yes—
463C2×Dic13C2512yes—
464D52—232no—
465D52—28no—
466D52C22×D4116yescomplemented
467C4×D13—216no—
468C4×D13—232no—
469C4×D13—232no—
470C4×D13—232no—
471C4×D13—216no—
472C4×D13—28no—
473C4×D13—216no—
474C4×D13—216no—
475C4×D13—216no—
476C4×D13—216no—
477C4×D13C22×D4116yes—
478C4×D13C2×#41116yescomplemented
479Dic26—216no—
480Dic26—232no—
481C22×#41—1332no—
482C22×#41—132no—
483C22×#41—132no—
484C22×#41—134no—
485C22×#41—132no—
486C22×#41—134no—
487C22×#41—2632no—
488C22×#41C2×D1312yescomplemented
489C23×Q8—132no—
490C23×D4—131no—
491C23×D4—134no—
492C23×D4—131no—
493C24×C4—134no—
494C24×C4—132no—
495C24×C4—132no—
496#547—1332no—
497#547—1316no—
498#547—1364no—
499#547—1332no—
500#547—1332no—
501#547—1316no—
502#547—1316no—
503#547—1332no—
504#547C2×D13116yesdirect product factor
505C2×C4⋊Q8—132no—
506C2×C4⋊Q8—1316no—
507C2×C4⋊Q8—132no—
508C2×C4⋊Q8—132no—
509C2×C4⋊Q8—131no—
510C2×C4⋊Q8C2×D1311yescharacteristic, complemented
511C2×#123—134no—
512C2×#123—134no—
513C2×#123—1364no—
514C2×#123—134no—
515C2×#123—134no—
516C2×#123—134no—
517C2×#123—134no—
518C2×#123—134no—
519C2×#123C2×D1314yescomplemented
520C2×C22⋊Q8—132no—
521C2×C22⋊Q8—132no—
522C2×C22⋊Q8—1332no—
523C2×C22⋊Q8—134no—
524C2×C22⋊Q8—132no—
525C2×C22⋊Q8—134no—
526C2×C22⋊Q8C2×D1312yescomplemented
527C2×#121—132no—
528C2×#121—134no—
529C2×#121—132no—
530C2×#121—1332no—
531C2×#121—132no—
532C2×#121—134no—
533C2×#121C2×D1312yescomplemented
534C2×C4×D4—131no—
535C2×C4×D4—131no—
536C2×C4×D4—132no—
537C2×C4×D4—132no—
538C2×C4×D4—1316no—
539C2×C4×D4—1316no—
540C2×C4×D4—131no—
541C2×C4×D4—131no—
542C2×C4×D4—132no—
543C2×C4×D4—132no—
544C2×C4×D4—131no—
545C2×C4×D4—131no—
546C2×C4×D4C2×D1311yescharacteristic, complemented
547C2×C4×D4C2×D1311yescharacteristic, complemented
548C22×C4⋊C4—134no—
549C22×C4⋊C4—132no—
550C22×C4⋊C4—131no—
551C22×C4⋊C4—132no—
552C22×C4⋊C4—134no—
553C22×C4⋊C4—131no—
554C22×C4⋊C4—132no—
555C22×C4⋊C4—134no—
556C22×C4⋊C4—132no—
557C22×C4⋊C4—132no—
558C22×C4⋊C4—1332no—
559C22×C4⋊C4C2×D1312yescomplemented
560C22×C22⋊C4—132no—
561C22×C22⋊C4—132no—
562C22×C22⋊C4—134no—
563C22×C42—131no—
564C22×C13—24no—
565C22×C13—24no—
566C22×C13—216no—
567C22×C13—24no—
568C22×C13—24no—
569C22×C13—24no—
570C22×C13—48no—
571C22×C13C23×D418yes—
572C22×C13C23×D412yes—
573C22×C13C22×#4112yes—
574C22×C13C2×2−1+412yes—
575C22×C13C2611yescharacteristic
576C2×D13—24no—
577C2×D13—24no—
578C2×D13—216no—
579C2×D13—264no—
580C2×D13—24no—
581C2×D13—24no—
582C2×D13—24no—
583C2×D13—48no—
584C2×D13—432no—
585C2×D13#547116yesdirect product factor
586C2×D13C23×D418yes—
587C2×D13C23×D414yes—
588C2×D13C22×#4114yes—
589C2×D13C2×2−1+414yes—
590C4×C13—28no—
591C4×C13—24no—
592C4×C13—24no—
593C4×C13—22no—
594C4×C13C23×D414yes—
595C4×C13C22×#4114yescomplemented
596Dic13—28no—
597Dic13—24no—
598Dic13—24no—
599Dic13—22no—
600Dic13C23×D414yes—
601Dic13C22×#4114yescomplemented
602C25—132no—
603C25—132no—
604C2×#41—216no—
605C2×#41—1316no—
606C2×#41—1316no—
607C2×#41—1332no—
608C2×#41—1316no—
609C2×#41—1332no—
610C2×#41—2632no—
611C2×#41—2616no—
612C2×#41—2632no—
613C2×#41—2616no—
614C2×#41—26256no—
615C2×#41—2616no—
616C2×#41C22×D13116yescomplemented
617C22×Q8—1316no—
618C22×Q8—134no—
619C22×Q8—132no—
620C22×Q8—2616no—
621C22×Q8C22×D1312yes—
622C22×D4—132no—
623C22×D4—1316no—
624C22×D4—138no—
625C22×D4—132no—
626C22×D4—134no—
627C22×D4—134no—
628C22×D4—138no—
629C22×D4—1332no—
630C22×D4—131no—
631C22×D4—131no—
632C22×D4—134no—
633C22×D4—268no—
634C22×D4—2632no—
635C22×D4C22×D1311yescharacteristic
636C22×D4C22×D1314yes—
637C22×D4C22×D1311yescharacteristic
638C23×C4—131no—
639C23×C4—131no—
640C23×C4—132no—
641C23×C4—134no—
642C23×C4—132no—
643C23×C4—131no—
644C23×C4—132no—
645C23×C4—132no—
646C23×C4—134no—
647C23×C4—132no—
648C23×C4—1316no—
649C23×C4—132no—
650C23×C4—1332no—
651C23×C4—134no—
652C23×C4—134no—
653C23×C4—132no—
654C23×C4—1316no—
655C23×C4—132no—
656C23×C4—2616no—
657C23×C4—2616no—
658C23×C4—2632no—
659C23×C4C22×D1312yes—
660C23×C4C22×D1314yes—
661C23×C4C22×D1312yes—
662C4⋊Q8—1316no—
663C4⋊Q8—1316no—
664C4⋊Q8—1316no—
665C4⋊Q8—138no—
666C4⋊Q8C22×D1318yescomplemented
667#123—1332no—
668#123—1332no—
669#123—1332no—
670#123—1332no—
671#123—1332no—
672#123—1332no—
673#123—1332no—
674#123C22×D13132yescomplemented
675C22⋊Q8—1316no—
676C22⋊Q8—1316no—
677C22⋊Q8—1332no—
678C22⋊Q8—1316no—
679C22⋊Q8—1332no—
680C22⋊Q8C22×D13116yescomplemented
681#121—1316no—
682#121—1332no—
683#121—1316no—
684#121—1316no—
685#121—1332no—
686#121C22×D13116yescomplemented
687C4×D4—138no—
688C4×D4—138no—
689C4×D4—1316no—
690C4×D4—1316no—
691C4×D4—138no—
692C4×D4—138no—
693C4×D4—1316no—
694C4×D4—1316no—
695C4×D4—138no—
696C4×D4—138no—
697C4×D4C22×D1318yescomplemented
698C4×D4C22×D1318yescomplemented
699C2×C4⋊C4—132no—
700C2×C4⋊C4—131no—
701C2×C4⋊C4—134no—
702C2×C4⋊C4—132no—
703C2×C4⋊C4—134no—
704C2×C4⋊C4—134no—
705C2×C4⋊C4—134no—
706C2×C4⋊C4—1332no—
707C2×C4⋊C4—1316no—
708C2×C4⋊C4—132no—
709C2×C4⋊C4—131no—
710C2×C4⋊C4—134no—
711C2×C4⋊C4—132no—
712C2×C4⋊C4—138no—
713C2×C4⋊C4—1316no—
714C2×C4⋊C4—1332no—
715C2×C4⋊C4—1332no—
716C2×C4⋊C4—1316no—
717C2×C4⋊C4—1316no—
718C2×C4⋊C4—138no—
719C2×C4⋊C4—1316no—
720C2×C4⋊C4C22×D1311yescharacteristic
721C2×C4⋊C4C22×D1312yes—
722C2×C4⋊C4C22×D1314yes—
723C2×C4⋊C4C22×D1311yescharacteristic
724C2×C4⋊C4C22×D1312yes—
725C2×C4⋊C4C22×D13116yescomplemented
726C2×C22⋊C4—132no—
727C2×C22⋊C4—132no—
728C2×C22⋊C4—134no—
729C2×C22⋊C4—132no—
730C2×C22⋊C4—132no—
731C2×C22⋊C4—132no—
732C2×C22⋊C4—132no—
733C2×C22⋊C4—134no—
734C2×C22⋊C4—134no—
735C2×C22⋊C4—1316no—
736C2×C22⋊C4—1316no—
737C2×C22⋊C4—1332no—
738C2×C22⋊C4C22×D1312yes—
739C2×C22⋊C4C22×D1312yes—
740C2×C22⋊C4C22×D1314yes—
741C2×C42—131no—
742C2×C42—131no—
743C2×C42—131no—
744C2×C42—138no—
745C2×C42C22×D1311yescharacteristic
746C2×C13—28no—
747C2×C13—44no—
748C2×C13C2×#54714yescomplemented
749C2×C13C24×D411yescharacteristic
750C2×C13C23×#4111yescharacteristic
751C2×C13C22×2−1+411yescharacteristic
752D13—28no—
753D13—44no—
754D13C2×#54718yesdirect product factor
755C24—131no—
756C24—1316no—
757C24—138no—
758C24—132no—
759C24—138no—
760C24—132no—
761C24—268no—
762C24—268no—
763C24—268no—
764C24—268no—
765C24—268no—
766C24C23×D1312yes—
767C24C23×D1312yes—
768#41—264no—
769#41—26128no—
770#41—2664no—
771#41—26128no—
772#41—2664no—
773#41—2664no—
774C2×Q8—28no—
775C2×Q8—1316no—
776C2×Q8—138no—
777C2×Q8—2616no—
778C2×Q8—2664no—
779C2×Q8—268no—
780C2×Q8C23×D1318yes—
781C2×D4—216no—
782C2×D4—24no—
783C2×D4—1316no—
784C2×D4—138no—
785C2×D4—1364no—
786C2×D4—138no—
787C2×D4—1316no—
788C2×D4—1316no—
789C2×D4—138no—
790C2×D4—134no—
791C2×D4—134no—
792C2×D4—1316no—
793C2×D4—2616no—
794C2×D4—2632no—
795C2×D4—268no—
796C2×D4—26128no—
797C2×D4—2616no—
798C2×D4—2616no—
799C2×D4—264no—
800C2×D4D4×D1318yescomplemented
801C2×D4C23×D1314yes—
802C2×D4C23×D13116yes—
803C2×D4C23×D1314yes—
804C22×C4—216no—
805C22×C4—28no—
806C22×C4—28no—
807C22×C4—131no—
808C22×C4—131no—
809C22×C4—138no—
810C22×C4—138no—
811C22×C4—134no—
812C22×C4—134no—
813C22×C4—138no—
814C22×C4—1316no—
815C22×C4—138no—
816C22×C4—131no—
817C22×C4—132no—
818C22×C4—132no—
819C22×C4—134no—
820C22×C4—134no—
821C22×C4—138no—
822C22×C4—138no—
823C22×C4—1316no—
824C22×C4—138no—
825C22×C4—138no—
826C22×C4—1316no—
827C22×C4—1316no—
828C22×C4—138no—
829C22×C4—138no—
830C22×C4—268no—
831C22×C4—2664no—
832C22×C4—268no—
833C22×C4—2664no—
834C22×C4—268no—
835C22×C4—2616no—
836C22×C4—2616no—
837C22×C4—2616no—
838C22×C4—26128no—
839C22×C4—268no—
840C22×C4—264no—
841C22×C4—268no—
842C22×C4—268no—
843C22×C4—2616no—
844C22×C4—268no—
845C22×C4—268no—
846C22×C4C23×D1318yes—
847C22×C4C23×D13116yes—
848C22×C4C23×D1318yes—
849C22×C4C23×D1311yescharacteristic
850C22×C4C23×D1312yes—
851C22×C4C23×D1312yes—
852C22×C4C23×D1314yes—
853C22×C4C23×D1311yescharacteristic
854C22×C4C23×D1311yescharacteristic
855C4⋊C4—138no—
856C4⋊C4—134no—
857C4⋊C4—1316no—
858C4⋊C4—138no—
859C4⋊C4—1316no—
860C4⋊C4—1316no—
861C4⋊C4—1316no—
862C4⋊C4—138no—
863C4⋊C4—134no—
864C4⋊C4—1316no—
865C4⋊C4—138no—
866C4⋊C4C23×D1314yes—
867C4⋊C4C23×D1318yes—
868C4⋊C4C23×D13116yes—
869C4⋊C4C23×D1314yes—
870C4⋊C4C23×D1318yes—
871C22⋊C4—138no—
872C22⋊C4—138no—
873C22⋊C4—1316no—
874C22⋊C4—138no—
875C22⋊C4—138no—
876C22⋊C4—138no—
877C22⋊C4—138no—
878C22⋊C4—1316no—
879C22⋊C4—1316no—
880C22⋊C4C23×D1318yes—
881C22⋊C4C23×D1318yes—
882C22⋊C4C23×D13116yes—
883C42—134no—
884C42—134no—
885C42—134no—
886C42C23×D1314yes—
887C13C22×#54711yescharacteristic, complemented, Sylow
888C23—24no—
889C23—24no—
890C23—24no—
891C23—24no—
892C23—24no—
893C23—134no—
894C23—134no—
895C23—134no—
896C23—132no—
897C23—1332no—
898C23—138no—
899C23—134no—
900C23—134no—
901C23—2616no—
902C23—2664no—
903C23—2616no—
904C23—2616no—
905C23—2616no—
906C23—2616no—
907C23—264no—
908C23—264no—
909C23—264no—
910C23—264no—
911C23—264no—
912C23—5232no—
913C23C2×D4×D1318yes—
914C23C24×D1314yes—
915C23C24×D1314yes—
916C23C24×D1311yescharacteristic
917Q8—216no—
918Q8—2632no—
919Q8—2616no—
920D4—232no—
921D4—28no—
922D4—1332no—
923D4—1316no—
924D4—2632no—
925D4—2616no—
926D4—2632no—
927D4—2632no—
928D4—268no—
929D4C2×D4×D13116yescomplemented
930C2×C4—24no—
931C2×C4—28no—
932C2×C4—232no—
933C2×C4—24no—
934C2×C4—22no—
935C2×C4—216no—
936C2×C4—216no—
937C2×C4—134no—
938C2×C4—134no—
939C2×C4—132no—
940C2×C4—132no—
941C2×C4—1316no—
942C2×C4—1316no—
943C2×C4—132no—
944C2×C4—134no—
945C2×C4—134no—
946C2×C4—138no—
947C2×C4—2616no—
948C2×C4—2616no—
949C2×C4—268no—
950C2×C4—2616no—
951C2×C4—2616no—
952C2×C4—2632no—
953C2×C4—2632no—
954C2×C4—2632no—
955C2×C4—2616no—
956C2×C4—2616no—
957C2×C4—264no—
958C2×C4—268no—
959C2×C4—2632no—
960C2×C4—264no—
961C2×C4—262no—
962C2×C4—2616no—
963C2×C4—2616no—
964C2×C4C2×D4×D1314yes—
965C2×C4#41×D1314yescomplemented
966C2×C4C24×D1312yes—
967C2×C4C24×D1314yes—
968C2×C4C24×D1314yes—
969C2×C4C24×D1318yes—
970C2×C4C24×D1312yes—
971C2×C4C24×D1312yes—
972C22—216no—
973C22—24no—
974C22—24no—
975C22—24no—
976C22—24no—
977C22—24no—
978C22—48no—
979C22—1316no—
980C22—134no—
981C22—134no—
982C22—134no—
983C22—138no—
984C22—2664no—
985C22—2616no—
986C22—264no—
987C22—264no—
988C22—264no—
989C22—264no—
990C22—264no—
991C22—5232no—
992C22—528no—
993C22C22×D4×D1318yes—
994C22C22×D4×D1312yes—
995C22C2×#41×D1312yes—
996C22D13×2−1+412yes—
997C22C25×D1311yescharacteristic
998C4—24no—
999C4—28no—
1000C4—24no—
1001C4—22no—
1002C4—134no—
1003C4—134no—
1004C4—264no—
1005C4—268no—
1006C4—264no—
1007C4—262no—
1008C4C22×D4×D1314yes—
1009C4C2×#41×D1314yescomplemented
1010C2—28no—
1011C2—44no—
1012C2—138no—
1013C2—268no—
1014C2—524no—
1015C2D13×#54714yesdirect product factor
1016C2C23×D4×D1311yescharacteristic
1017C2C22×#41×D1311yescharacteristic
1018C2C2×D13×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#547C2
socleC23×C13C25
hypercenterC2×#547D13
hypocenterC13C22×#547
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C22×#41×D13C2semidirect
2. C2×#11719256C2semidirect
3. C2×#11719260C2semidirect
4. C2×#11719431C2semidirect
5. C2×#11719336C2semidirect
6. C2×#11719212C2semidirect
7. C2×#11719316C2semidirect
8. C2×#11719529C2semidirect
9. C2×#11719360C2semidirect
10. D13×#547C2direct (N × H)
11. C2×D13×C4⋊Q8C2semidirect
12. C2×D13×#123C2semidirect
13. C2×D13×C22⋊Q8C2semidirect
14. C2×D13×#121C2semidirect
15. C2×C4×D4×D13C2semidirect
16. C2×C4×D4×D13C2semidirect
17. C22×C4⋊C4×D13C2semidirect
18. C2×C13×#547C2semidirect
19. C22×C13×#41C22semidirect
21. C2×#41×D13C22semidirect
22. C22×#6131C22semidirect
24. C22×#6129C22semidirect
25. C22×#6129C22semidirect
29. C22×#6127C22semidirect
30. C22×#6127C22semidirect
34. C13×#547C22semidirect
35. C2×C13×C4⋊Q8C22semidirect
36. C2×C13×#123C22semidirect
37. C2×C13×C22⋊Q8C22semidirect
38. C2×C13×#121C22semidirect
39. C2×C4×D4×C13C22semidirect
40. C2×C4×D4×C13C22semidirect
41. C22×C13×C4⋊C4C22semidirect
42. #11719529C22semidirect
43. C2×#88200C22semidirect
44. C2×#88198C22semidirect
45. C2×#88193C22semidirect
46. C2×#88192C22semidirect
47. C2×#88189C22semidirect
48. C2×D4×Dic13C22semidirect
49. C2×D4×Dic13C22semidirect
50. C2×#88184C22semidirect
51. C2×#88183C22semidirect
52. C2×C4×C22⋊D13C22semidirect
53. C2×C4×C22⋊D13C22semidirect
54. C22×C4⋊Dic13C22semidirect
55. C2×#88178C22semidirect
56. C22×#6101C22semidirect
57. #11719431C22semidirect
58. D13×C4⋊Q8C22semidirect
59. #11719360C22semidirect
60. D13×#123C22semidirect
61. #11719336C22semidirect
62. D13×C22⋊Q8C22semidirect
63. #11719316C22semidirect
64. D13×#121C22semidirect
65. #11719260C22semidirect
66. #11719256C22semidirect
67. C4×D4×D13C22semidirect
68. C4×D4×D13C22semidirect
69. C2×#88151C22semidirect
70. C2×#88150C22semidirect
71. #11719212C22semidirect
72. C2×#88149C22semidirect
73. C2×#88148C22semidirect
74. C2×#88148C22semidirect
75. C2×#88147C22semidirect
76. C2×#88147C22semidirect
82. C2×C4⋊C4×D13C22semidirect
83. C2×C4⋊C4×D13C22semidirect
84. C2×C4⋊C4×D13C22semidirect
85. C2×C4⋊C4×D13C22semidirect
86. C2×#88142C22semidirect
87. C2×#88142C22semidirect
88. C2×#88140C22semidirect
89. C2×#88138C22semidirect
90. C2×#88137C22semidirect
91. C2×#88137C22semidirect
92. C2×#88135C22semidirect
93. C2×#88135C22semidirect
97. C2×#88132C22semidirect
98. C2×C4×D52C22semidirect
99. C2×C4×D52C22semidirect
101. C2×#88123C22semidirect
105. C2×C13×#41C23semidirect
122. C2×#6131C23semidirect
127. C2×#6129C23semidirect
128. C2×#6129C23semidirect
131. C2×D4×D13D4semidirect
137. C2×#6127C23semidirect
138. C2×#6127C23semidirect
162. C13×C4⋊Q8C23semidirect
163. C13×#123C23semidirect
164. C13×C22⋊Q8C23semidirect
165. C13×#121C23semidirect
166. C4×D4×C13C23semidirect
167. C4×D4×C13C23semidirect
173. C2×C13×C4⋊C4C23semidirect
181. #88200C23semidirect
182. #88198C23semidirect
183. #88193C23semidirect
184. #88192C23semidirect
185. #88189C23semidirect
186. D4×Dic13C23semidirect
187. D4×Dic13C23semidirect
188. #88184C23semidirect
189. #88183C23semidirect
190. C4×C22⋊D13C23semidirect
191. C4×C22⋊D13C23semidirect
203. C2×C4⋊Dic13C23semidirect
204. #88178C23semidirect
211. C2×#6101C23semidirect
215. #88151C23semidirect
216. #88150C23semidirect
217. #88149C23semidirect
218. #88148C23semidirect
219. #88148C23semidirect
220. #88147C23semidirect
221. #88147C23semidirect
227. C4⋊C4×D13C23semidirect
228. C4⋊C4×D13C23semidirect
229. C4⋊C4×D13C23semidirect
230. #88142C23semidirect
231. #88142C23semidirect
232. #88140C23semidirect
233. #88138C23semidirect
234. #88137C23semidirect
235. #88137C23semidirect
236. #88135C23semidirect
237. #88135C23semidirect
241. #88132C23semidirect
242. C4×D52C23semidirect
243. C4×D52C23semidirect
245. #88123C23semidirect
265. C2×D4×C13C2×D4semidirect
284. C2×C22⋊D13C2×D4semidirect
307. D4×D13C2×D4semidirect
312. C2×D52C2×D4semidirect
330. C2×C4×D13#41semidirect
389. C2×#547D13direct (N × H)
429. D4×C13C22×D4semidirect
438. C2×C4×C13C2×#41semidirect
448. C22⋊D13C22×D4semidirect
457. C2×Dic13C2×#41semidirect
466. D52C22×D4semidirect
478. C4×D13C2×#41semidirect
488. C22×#41C2×D13semidirect
504. #547C2×D13direct (N × H)
510. C2×C4⋊Q8C2×D13semidirect
519. C2×#123C2×D13semidirect
526. C2×C22⋊Q8C2×D13semidirect
533. C2×#121C2×D13semidirect
546. C2×C4×D4C2×D13semidirect
547. C2×C4×D4C2×D13semidirect
559. C22×C4⋊C4C2×D13semidirect
585. C2×D13#547direct (N × H)
595. C4×C13C22×#41semidirect
601. Dic13C22×#41semidirect
616. C2×#41C22×D13semidirect
666. C4⋊Q8C22×D13semidirect
674. #123C22×D13semidirect
680. C22⋊Q8C22×D13semidirect
686. #121C22×D13semidirect
697. C4×D4C22×D13semidirect
698. C4×D4C22×D13semidirect
725. C2×C4⋊C4C22×D13semidirect
748. C2×C13C2×#547semidirect
754. D13C2×#547direct (N × H)
800. C2×D4D4×D13semidirect
887. C13C22×#547semidirect
929. D4C2×D4×D13semidirect
965. C2×C4#41×D13semidirect
1009. C4C2×#41×D13semidirect
1015. C2D13×#547direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#41×D132
C2×#117192562
C2×#117192602
C2×#117194312
C2×#117193362
C2×#117192122
C2×#117193162
C2×#117195292
C2×#117193602
D13×#5472
C2×D13×C4⋊Q82
C2×D13×#1232
C2×D13×C22⋊Q82
C2×D13×#1212
C2×C4×D4×D132
C22×C4⋊C4×D132
C2×C13×#5472
C22×#54713