Finite Group Databasebeta

← C2×#13128539 #16770855

Subgroups — C2×#13128539 #16770855

Order 3328.

7910 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128539C2132yesmaximal, direct product factor
2C2×#11719284C212yesmaximal, complemented
3C2×#11719216C212yesmaximal, complemented
4C2×#11719263C212yesmaximal, complemented
5C2×#11719235C212yesmaximal, complemented
6C2×#11719286C212yesmaximal, complemented
7C2×#11719234C212yesmaximal, complemented
8C2×#11719256C212yesmaximal, complemented
9C2×#11719212C212yesmaximal, complemented
10C2×#11719224C211yesmaximal, characteristic, complemented
11C2×#11719269C214yesmaximal, complemented
12C2×#11719538C211yesmaximal, characteristic, complemented
13C2×#11719229C211yesmaximal, characteristic, complemented
14C2×#11719252C214yesmaximal, complemented
15C2×#11719533C211yesmaximal, characteristic, complemented
16C2×#11719209C211yesmaximal, characteristic, complemented
17C22×C4⋊C4×D13C211yesmaximal, characteristic, complemented
18C2×C13×#520C211yesmaximal, characteristic, complemented
19C22×C13×#41C2211yescharacteristic
20C22×#6127C2211yescharacteristic
21C22×#6127C2214yes—
22C23×C4×D13C2211yescharacteristic
23C23×C4×D13C2212yes—
24C13×#520C22116yescomplemented
25C2×C4×Q8×C13C2212yescomplemented
26C2×C4×D4×C13C2214yes—
27C2×C4×D4×C13C2212yescomplemented
28C2×C13×#117C2211yescharacteristic
29C2×C13×#117C2212yescomplemented
30C22×C13×C4⋊C4C2211yescharacteristic
31C22×C13×C4⋊C4C2212yescomplemented
32#11719538C22116yescomplemented
33#11719533C22116yescomplemented
34C2×#88200C2211yescharacteristic
35C2×#88200C2211yescharacteristic
36C2×#88200C2212yescomplemented
37C2×#88193C2214yes—
38C2×#88192C2211yescharacteristic
39C2×#88192C2211yescharacteristic
40C2×#88192C2212yescomplemented
41C2×#88191C2212yes—
42C2×#88189C2212yes—
43C2×#88184C2212yescomplemented
44C2×#88183C2214yescomplemented
45C2×C4×C22⋊D13C2214yes—
46C2×C4×C22⋊D13C2212yes—
47C2×C4×C22⋊D13C2212yes—
48C2×C4×C22⋊D13C2214yes—
49C2×#88180C2211yescharacteristic
50C22×C4⋊Dic13C2211yescharacteristic
51C2×#88178C2214yescomplemented
52C2×#88178C2212yescomplemented
53C22×#6101C2212yes—
54#11719286C22132yescomplemented
55#11719284C22132yescomplemented
56#11719269C22164yescomplemented
57#11719263C22132yescomplemented
58#11719256C22132yescomplemented
59#11719252C22164yescomplemented
60#11719235C22132yescomplemented
61#11719234C22132yescomplemented
62#11719229C22116yescomplemented
63#11719224C22116yescomplemented
64#11719216C22132yescomplemented
65C2×#88151C2211yescharacteristic
66C2×#88151C2211yescharacteristic
67C2×#88150C2214yes—
68C2×#88150C2214yescomplemented
69#11719212C22132yescomplemented
70C2×#88149C2211yescharacteristic
71C2×#88149C2211yescharacteristic
72C2×#88148C2214yes—
73#11719209C22116yescomplemented
74C2×#88147C2212yescomplemented
75C2×#88146C2212yescomplemented
76C2×C4⋊C4×D13C2212yes—
77C2×C4⋊C4×D13C2212yes—
78C2×C4⋊C4×D13C2212yes—
79C2×C4⋊C4×D13C2212yes—
80C2×C4⋊C4×D13C22116yescomplemented
81C2×C4⋊C4×D13C2212yescomplemented
82C2×#88144C2212yescomplemented
83C2×#88143C2214yescomplemented
84C2×#88142C2212yescomplemented
85C2×#88141C2212yescomplemented
86C2×#88140C2212yes—
87C2×#88138C2214yes—
88C2×#88137C2214yes—
89C2×#88137C2214yescomplemented
90C2×#88136C2212yes—
91C2×#88133C2214yescomplemented
92C2×#88132C2214yes—
93C2×#88130C2214yescomplemented
94C2×C4×D52C2212yes—
95C2×C4×D52C2214yes—
96C2×C4×D52C2212yes—
97C2×#88126C2214yes—
98C2×#88124C2212yescomplemented
99C2×#88124C2214yescomplemented
100C2×#88123C2212yescomplemented
101C24×D13C2311yescharacteristic
102C2×C13×#41—28no—
103C2×C13×#41C2318yes—
104C22×Q8×C13C2311yescharacteristic
105C22×D4×C13C2312yes—
106C22×D4×C13C2311yescharacteristic
107C23×C4×C13C2312yes—
108C23×C4×C13C2312yes—
109C23×C4×C13C2314yes—
110C23×C4×C13C2311yescharacteristic
111C22×C22⋊D13C2312yes—
112C22×C22⋊D13C2312yes—
113C22×C22⋊D13C2312yes—
114C22×C22⋊D13C2314yes—
115C23×Dic13C2311yescharacteristic
116C23×Dic13C2312yes—
117C2×#6127—28no—
118C2×#6127—416no—
119C2×#6127C2318yes—
120C2×#6127C23132yes—
121C22×D52C2312yes—
122C22×D52C2312yes—
123C22×D52C2311yescharacteristic
124C22×C4×D13—28no—
125C22×C4×D13—48no—
126C22×C4×D13C2314yes—
127C22×C4×D13C2311yescharacteristic
128C22×C4×D13C2311yescharacteristic
129C22×C4×D13C2312yes—
130C22×C4×D13C2311yescharacteristic
131C22×C4×D13C2311yescharacteristic
132C22×C4×D13C2318yes—
133C22×C4×D13C2314yes—
134C22×C4×D13C2314yes—
135C22×C4×D13C23116yes—
136C22×Dic26C2311yescharacteristic
137C22×Dic26C2314yes—
138C4×Q8×C13C23116yescomplemented
139C4×D4×C13C23132yes—
140C4×D4×C13C23116yescomplemented
141C13×#117C2318yes—
142C13×#117C23116yescomplemented
143C2×C13×C4⋊C4C2312yes—
144C2×C13×C4⋊C4C2311yescharacteristic
145C2×C13×C4⋊C4C2314yes—
146C2×C13×C4⋊C4C2311yescharacteristic
147C2×C13×C4⋊C4C2312yes—
148C2×C13×C4⋊C4C2318yes—
149C2×C13×C4⋊C4C23116yescomplemented
150C2×C13×C22⋊C4C2312yes—
151C2×C13×C22⋊C4C2314yes—
152C2×C42×C13C2312yes—
153C2×C42×C13C2314yes—
154C2×C22⋊Dic13C2312yes—
155C2×C22⋊Dic13C2312yes—
156C2×C22⋊Dic13C2314yes—
157C2×C22⋊Dic13C2312yes—
158#88200C2318yes—
159#88200C2318yes—
160#88200C23116yescomplemented
161#88193C23132yes—
162#88192C2318yes—
163#88192C2318yes—
164#88192C23116yescomplemented
165#88191C23116yes—
166#88189C23116yes—
167#88184C23116yescomplemented
168#88183C23132yescomplemented
169C4×C22⋊D13C23132yes—
170C4×C22⋊D13C23116yes—
171C4×C22⋊D13C23116yes—
172C4×C22⋊D13C23132yes—
173C2×#6103C2312yes—
174C2×#6103C2312yes—
175C2×#6103C2312yes—
176C2×#6103C2312yes—
177C2×#6103C2314yes—
178C2×#6103C2312yes—
179C2×#6103C2312yes—
180C2×#6103C2314yes—
181#88180C2318yes—
182C2×C4⋊Dic13C2311yescharacteristic
183C2×C4⋊Dic13C2314yes—
184C2×C4⋊Dic13C2312yes—
185C2×C4⋊Dic13C2312yes—
186C2×C4⋊Dic13C2311yescharacteristic
187C2×C4⋊Dic13C2312yes—
188C2×C4⋊Dic13C2312yes—
189C2×C4⋊Dic13C2318yes—
190#88178C23116yescomplemented
191#88178C23132yescomplemented
192C2×#6101C2312yes—
193C2×#6101C2314yes—
194C2×#6101C2314yes—
195C2×#6101C2314yes—
196C2×#6101C2314yes—
197C2×#6101C2314yes—
198C2×#6101C2312yes—
199C2×#6101C2314yes—
200C2×#6101C23116yes—
201C2×C4×Dic13C2314yes—
202C2×C4×Dic13C2312yes—
203#88151C2318yes—
204#88151C2318yes—
205#88150C23132yes—
206#88150C23132yescomplemented
207#88149C2318yes—
208#88149C2318yes—
209#88148C23132yes—
210#88147C23116yescomplemented
211#88146C23116yescomplemented
212C4⋊C4×D13C23116yes—
213C4⋊C4×D13C23116yes—
214C4⋊C4×D13C23116yes—
215C4⋊C4×D13C23116yes—
216C4⋊C4×D13C23116yescomplemented
217#88144C23116yescomplemented
218#88143C23132yescomplemented
219#88142C23116yescomplemented
220#88141C23116yescomplemented
221#88140C23116yes—
222#88138C23132yes—
223#88137C23132yes—
224#88137C23132yescomplemented
225#88136C23116yes—
226#88133C23132yescomplemented
227#88132C23132yes—
228#88130C23132yescomplemented
229C4×D52C23116yes—
230C4×D52C23116yes—
231C4×D52C23132yes—
232#88126C23132yes—
233#88124C23116yescomplemented
234#88124C23132yescomplemented
235#88123C23116yescomplemented
236C2×#3492—131nomaximal, Sylow
237C24×C13C2412yes—
238C24×C13C2411yescharacteristic
239C23×D13—24no—
240C23×D13—24no—
241C23×D13—24no—
242C23×D13C2414yes—
243C23×D13C2412yes—
244C23×D13C2411yescharacteristic
245C23×D13C2411yescharacteristic
246C13×#41—232no—
247C2×Q8×C13—24no—
248C2×Q8×C13C2414yes—
249C2×D4×C13—28no—
250C2×D4×C13—24no—
251C2×D4×C13C2418yes—
252C2×D4×C13C2414yes—
253C22×C4×C13—28no—
254C22×C4×C13—44no—
255C22×C4×C13—48no—
256C22×C4×C13#4118yescomplemented
257C22×C4×C13C2414yes—
258C22×C4×C13C2412yes—
259C22×C4×C13C2412yes—
260C22×C4×C13C2412yes—
261C22×C4×C13C2418yes—
262C22×C4×C13C2418yes—
263C22×C4×C13C24116yes—
264C22×C4×C13C2411yescharacteristic
265C22×C4×C13C2411yescharacteristic
266C22×C4×C13C2414yes—
267C2×C22⋊D13—28no—
268C2×C22⋊D13—28no—
269C2×C22⋊D13—28no—
270C2×C22⋊D13—48no—
271C2×C22⋊D13C2418yes—
272C2×C22⋊D13C2418yes—
273C2×C22⋊D13C2418yes—
274C2×C22⋊D13C24116yes—
275C22×Dic13—24no—
276C22×Dic13—44no—
277C22×Dic13C2414yes—
278C22×Dic13C2412yes—
279C22×Dic13C2412yes—
280C22×Dic13C2412yes—
281C22×Dic13C2411yescharacteristic
282C22×Dic13C2411yescharacteristic
283C22×Dic13C2414yes—
284C22×Dic13C2418yes—
285#6127—232no—
286#6127—464no—
287C2×D52—28no—
288C2×D52—28no—
289C2×D52—24no—
290C2×D52C2418yes—
291C2×D52C2418yes—
292C2×D52C2414yes—
293C2×C4×D13—216no—
294C2×C4×D13—24no—
295C2×C4×D13—24no—
296C2×C4×D13—24no—
297C2×C4×D13—24no—
298C2×C4×D13—28no—
299C2×C4×D13—232no—
300C2×C4×D13—432no—
301C2×C4×D13—48no—
302C2×C4×D13—48no—
303C2×C4×D13C24116yes—
304C2×C4×D13C2414yes—
305C2×C4×D13C2414yes—
306C2×C4×D13C2418yes—
307C2×C4×D13C2414yes—
308C2×C4×D13C2414yes—
309C2×C4×D13C24116yes—
310C2×C4×D13C24116yes—
311C2×Dic26—24no—
312C2×Dic26—48no—
313C2×Dic26C2414yes—
314C2×Dic26C24116yes—
315C13×C4⋊C4C2418yes—
316C13×C4⋊C4C2414yes—
317C13×C4⋊C4C24116yes—
318C13×C4⋊C4C2414yes—
319C13×C4⋊C4C2418yes—
320C13×C22⋊C4C2418yes—
321C13×C22⋊C4C24116yes—
322C42×C13C2418yes—
323C42×C13C24116yes—
324C22⋊Dic13C2418yes—
325C22⋊Dic13C2418yes—
326C22⋊Dic13C24116yes—
327C22⋊Dic13C2418yes—
328#6103C2418yes—
329#6103C2418yes—
330#6103C2418yes—
331#6103C2418yes—
332#6103C24116yes—
333#6103C2418yes—
334#6103C2418yes—
335#6103C24116yes—
336C4⋊Dic13C2414yes—
337C4⋊Dic13C24116yes—
338C4⋊Dic13C2418yes—
339C4⋊Dic13C2418yes—
340C4⋊Dic13C2414yes—
341C4⋊Dic13C2418yes—
342C4⋊Dic13C2418yes—
343#6101C2418yes—
344#6101C24116yes—
345#6101C24116yes—
346#6101C24116yes—
347#6101C24116yes—
348#6101C24116yes—
349#6101C2418yes—
350#6101C24116yes—
351C4×Dic13C24116yes—
352C4×Dic13C2418yes—
353#3492—1332no—
354C2×#554—132no—
355C2×#554—132no—
356C2×#553—132no—
357C2×#553—132no—
358C2×#552—132no—
359C2×#552—132no—
360C2×#547—132no—
361C2×#547—132no—
362C2×#544—131no—
363C2×#539—134no—
364C2×#537—131no—
365C2×#525—131no—
366C2×#525—134no—
367C2×#525—131no—
368C2×#520—131no—
369C2×#520D1311yescharacteristic, complemented
370C23×C4⋊C4—131no—
371C23×C13—22no—
372C23×C13—22no—
373C23×C13—24no—
374C23×C13—24no—
375C23×C13—24no—
376C23×C13C2×#4114yes—
377C23×C13C2514yes—
378C23×C13C2512yes—
379C23×C13C2511yescharacteristic
380C22×D13—232no—
381C22×D13—28no—
382C22×D13—22no—
383C22×D13—22no—
384C22×D13—22no—
385C22×D13—22no—
386C22×D13—28no—
387C22×D13—28no—
388C22×D13—24no—
389C22×D13—24no—
390C22×D13—24no—
391C22×D13H(5,𝔽2)14yes—
392C22×D132−1+414yes—
393C22×D13C2514yes—
394C22×D13C2512yes—
395C22×D13C2512yes—
396Q8×C13—28no—
397D4×C13—216no—
398D4×C13—28no—
399C2×C4×C13—24no—
400C2×C4×C13—24no—
401C2×C4×C13—28no—
402C2×C4×C13—24no—
403C2×C4×C13—216no—
404C2×C4×C13—48no—
405C2×C4×C13—416no—
406C2×C4×C13C2×#4114yes—
407C2×C4×C13C2×#4114yes—
408C2×C4×C13C2×#41116yescomplemented
409C2×C4×C13C2518yes—
410C2×C4×C13C2514yes—
411C2×C4×C13C2514yes—
412C2×C4×C13C2514yes—
413C2×C4×C13C2512yes—
414C2×C4×C13C2512yes—
415C22⋊D13—216no—
416C22⋊D13—216no—
417C22⋊D13—216no—
418C22⋊D13—416no—
419C2×Dic13—24no—
420C2×Dic13—28no—
421C2×Dic13—22no—
422C2×Dic13—22no—
423C2×Dic13—24no—
424C2×Dic13—28no—
425C2×Dic13—24no—
426C2×Dic13—48no—
427C2×Dic13C2514yes—
428C2×Dic13C2514yes—
429C2×Dic13C2514yes—
430C2×Dic13C2512yes—
431C2×Dic13C2512yes—
432C2×Dic13C2518yes—
433D52—216no—
434D52—216no—
435D52—28no—
436C4×D13—232no—
437C4×D13—28no—
438C4×D13—28no—
439C4×D13—28no—
440C4×D13—28no—
441C4×D13—216no—
442C4×D13—416no—
443C4×D13—416no—
444Dic26—28no—
445Dic26—416no—
446C22×#41—131no—
447C22×#41—134no—
448C22×#41C2×D1311yescharacteristic
449C24×C4—131no—
450C24×C4—132no—
451#554—1332no—
452#554—1332no—
453#553—1332no—
454#553—1332no—
455#552—1332no—
456#552—1332no—
457#547—1332no—
458#547—1332no—
459#544—1316no—
460#539—1364no—
461#537—1316no—
462C2×C4⋊Q8—132no—
463C2×C4⋊Q8—132no—
464C2×#126—134no—
465C2×#126—134no—
466C2×#125—134no—
467C2×#125—132no—
468C2×#125—134no—
469C2×#125—132no—
470#525—1316no—
471#525—1364no—
472#525—1316no—
473C2×#123—132no—
474C2×#123—134no—
475C2×#123—134no—
476C2×#123—134no—
477C2×#123—134no—
478C2×#123—132no—
479C2×C22⋊Q8—131no—
480C2×C22⋊Q8—131no—
481C2×C22⋊Q8—132no—
482C2×C22⋊Q8—132no—
483C2×C22⋊Q8—134no—
484C2×C22⋊Q8—134no—
485C2×C22⋊Q8—134no—
486C2×C22⋊Q8—131no—
487C2×C22⋊Q8—131no—
488C2×C22⋊Q8—134no—
489C2×#121—131no—
490C2×#121—131no—
491C2×#121—132no—
492C2×#121—134no—
493C2×#121—132no—
494C2×#121—131no—
495C2×#121—131no—
496C2×#121—134no—
497C2×#120—132no—
498C2×#120—132no—
499#520—1316no—
500#520C2×D13116yescomplemented
501C2×C4×Q8—132no—
502C2×C4×Q8C2×D1312yescomplemented
503C2×C4×D4—134no—
504C2×C4×D4—132no—
505C2×C4×D4—134no—
506C2×C4×D4—132no—
507C2×C4×D4—132no—
508C2×C4×D4—132no—
509C2×C4×D4—134no—
510C2×C4×D4—132no—
511C2×C4×D4C2×D1314yes—
512C2×C4×D4C2×D1312yescomplemented
513C2×#117—131no—
514C2×#117—132no—
515C2×#117—134no—
516C2×#117C2×D1311yescharacteristic
517C2×#117C2×D1312yescomplemented
518C22×C4⋊C4—132no—
519C22×C4⋊C4—131no—
520C22×C4⋊C4—132no—
521C22×C4⋊C4—132no—
522C22×C4⋊C4—132no—
523C22×C4⋊C4—132no—
524C22×C4⋊C4—1316no—
525C22×C4⋊C4—132no—
526C22×C4⋊C4C2×D1311yescharacteristic
527C22×C4⋊C4C2×D1312yescomplemented
528C22×C13—22no—
529C22×C13—22no—
530C22×C13—28no—
531C22×C13—24no—
532C22×C13—24no—
533C22×C13—24no—
534C22×C13—48no—
535C22×C13C22×#4114yes—
536C22×C13C22×#4112yes—
537C22×C13C2×H(5,𝔽2)12yes—
538C22×C13C2×2−1+412yes—
539C22×C13C2611yescharacteristic
540C2×D13—232no—
541C2×D13—22no—
542C2×D13—22no—
543C2×D13—22no—
544C2×D13—22no—
545C2×D13—28no—
546C2×D13—28no—
547C2×D13—24no—
548C2×D13—24no—
549C2×D13—24no—
550C2×D13—48no—
551C2×D13C2×H(5,𝔽2)14yes—
552C2×D13C2×2−1+414yes—
553C4×C13—24no—
554C4×C13—24no—
555C4×C13—28no—
556C4×C13—24no—
557C4×C13C22×#4114yes—
558C4×C13C22×#4114yes—
559Dic13—24no—
560Dic13—22no—
561Dic13—22no—
562Dic13—24no—
563Dic13—28no—
564Dic13—24no—
565C25—131no—
566C2×#41—28no—
567C2×#41—138no—
568C2×#41—1332no—
569C2×#41—268no—
570C2×#41—5216no—
571C2×#41C22×D1318yes—
572C22×Q8—131no—
573C22×Q8—134no—
574C22×Q8C22×D1311yescharacteristic
575C22×D4—132no—
576C22×D4—132no—
577C22×D4—132no—
578C22×D4—134no—
579C22×D4—132no—
580C22×D4—131no—
581C22×D4—132no—
582C22×D4C22×D1312yes—
583C22×D4C22×D1311yescharacteristic
584C23×C4—131no—
585C23×C4—132no—
586C23×C4—134no—
587C23×C4—131no—
588C23×C4—131no—
589C23×C4—131no—
590C23×C4—131no—
591C23×C4—138no—
592C23×C4—132no—
593C23×C4—134no—
594C23×C4—1316no—
595C23×C4—134no—
596C23×C4—268no—
597C23×C4—528no—
598C23×C4C22×D1312yes—
599C23×C4C22×D1312yes—
600C23×C4C22×D1314yes—
601C23×C4C22×D1311yescharacteristic
602C4⋊Q8—1316no—
603C4⋊Q8—1316no—
604#126—1332no—
605#126—1332no—
606#125—1332no—
607#125—1316no—
608#125—1332no—
609#125—1316no—
610#123—1316no—
611#123—1332no—
612#123—1332no—
613#123—1316no—
614#123—1332no—
615#123—1332no—
616C22⋊Q8—138no—
617C22⋊Q8—138no—
618C22⋊Q8—1316no—
619C22⋊Q8—1316no—
620C22⋊Q8—1332no—
621C22⋊Q8—138no—
622C22⋊Q8—1332no—
623C22⋊Q8—138no—
624C22⋊Q8—1332no—
625C22⋊Q8—1332no—
626#121—1332no—
627#121—138no—
628#121—138no—
629#121—1316no—
630#121—1316no—
631#121—138no—
632#121—138no—
633#121—1332no—
634#120—1316no—
635#120—1316no—
636C4×Q8—1316no—
637C4×Q8C22×D13116yescomplemented
638C4×D4—1332no—
639C4×D4—1316no—
640C4×D4—1332no—
641C4×D4—1316no—
642C4×D4—1316no—
643C4×D4—1316no—
644C4×D4—1332no—
645C4×D4—1316no—
646C4×D4C22×D13132yes—
647C4×D4C22×D13116yescomplemented
648#117—138no—
649#117—1316no—
650#117—1332no—
651#117C22×D1318yes—
652#117C22×D13116yescomplemented
653C2×C4⋊C4—132no—
654C2×C4⋊C4—132no—
655C2×C4⋊C4—134no—
656C2×C4⋊C4—134no—
657C2×C4⋊C4—138no—
658C2×C4⋊C4—1316no—
659C2×C4⋊C4—131no—
660C2×C4⋊C4—134no—
661C2×C4⋊C4—131no—
662C2×C4⋊C4—134no—
663C2×C4⋊C4—134no—
664C2×C4⋊C4—132no—
665C2×C4⋊C4—132no—
666C2×C4⋊C4—134no—
667C2×C4⋊C4—134no—
668C2×C4⋊C4—132no—
669C2×C4⋊C4—132no—
670C2×C4⋊C4—1316no—
671C2×C4⋊C4—1316no—
672C2×C4⋊C4—1316no—
673C2×C4⋊C4—1316no—
674C2×C4⋊C4—1316no—
675C2×C4⋊C4C22×D1312yes—
676C2×C4⋊C4C22×D1312yes—
677C2×C4⋊C4C22×D1318yes—
678C2×C4⋊C4C22×D1311yescharacteristic
679C2×C4⋊C4C22×D1314yes—
680C2×C4⋊C4C22×D1311yescharacteristic
681C2×C4⋊C4C22×D13116yescomplemented
682C2×C22⋊C4—132no—
683C2×C22⋊C4—134no—
684C2×C22⋊C4—132no—
685C2×C22⋊C4—132no—
686C2×C22⋊C4—132no—
687C2×C22⋊C4—132no—
688C2×C22⋊C4—134no—
689C2×C22⋊C4—132no—
690C2×C22⋊C4—132no—
691C2×C22⋊C4—134no—
692C2×C22⋊C4—132no—
693C2×C22⋊C4—132no—
694C2×C22⋊C4C22×D1312yes—
695C2×C22⋊C4C22×D1314yes—
696C2×C42—134no—
697C2×C42—132no—
698C2×C42C22×D1314yes—
699C2×C42C22×D1312yes—
700C2×C13—24no—
701C2×C13—44no—
702C2×C13#349214yescomplemented
703C2×C13C23×#4111yescharacteristic
704C2×C13C22×H(5,𝔽2)11yescharacteristic
705C2×C13C22×2−1+411yescharacteristic
706D13—24no—
707D13—24no—
708D13—44no—
709C24—131no—
710C24—131no—
711C24—134no—
712C24—132no—
713C24—264no—
714C24—264no—
715C24—264no—
716C24C23×D1312yes—
717C24C23×D1311yescharacteristic
718#41—232no—
719#41—2632no—
720#41—5264no—
721C2×Q8—24no—
722C2×Q8—134no—
723C2×Q8—1316no—
724C2×Q8—264no—
725C2×Q8—528no—
726C2×Q8C23×D1314yes—
727C2×D4—28no—
728C2×D4—24no—
729C2×D4—138no—
730C2×D4—138no—
731C2×D4—138no—
732C2×D4—1316no—
733C2×D4—138no—
734C2×D4—134no—
735C2×D4—138no—
736C2×D4—268no—
737C2×D4—268no—
738C2×D4—268no—
739C2×D4—268no—
740C2×D4—268no—
741C2×D4—264no—
742C2×D4—528no—
743C2×D4C23×D1318yes—
744C2×D4C23×D1314yes—
745C22×C4—28no—
746C22×C4—44no—
747C22×C4—48no—
748C22×C4—134no—
749C22×C4—132no—
750C22×C4—132no—
751C22×C4—132no—
752C22×C4—131no—
753C22×C4—131no—
754C22×C4—134no—
755C22×C4—138no—
756C22×C4—1316no—
757C22×C4—134no—
758C22×C4—134no—
759C22×C4—134no—
760C22×C4—134no—
761C22×C4—138no—
762C22×C4—1316no—
763C22×C4—1316no—
764C22×C4—2616no—
765C22×C4—264no—
766C22×C4—264no—
767C22×C4—264no—
768C22×C4—264no—
769C22×C4—264no—
770C22×C4—268no—
771C22×C4—2632no—
772C22×C4—528no—
773C22×C4—528no—
774C22×C4—5232no—
775C22×C4—524no—
776C22×C4#612718yescomplemented
777C22×C4C23×D1318yes—
778C22×C4C23×D1314yes—
779C22×C4C23×D1312yes—
780C22×C4C23×D1312yes—
781C22×C4C23×D1312yes—
782C22×C4C23×D1318yes—
783C22×C4C23×D13116yes—
784C22×C4C23×D1311yescharacteristic
785C22×C4C23×D1311yescharacteristic
786C22×C4C23×D1314yes—
787C4⋊C4—138no—
788C4⋊C4—138no—
789C4⋊C4—1316no—
790C4⋊C4—1316no—
791C4⋊C4—134no—
792C4⋊C4—1316no—
793C4⋊C4—134no—
794C4⋊C4—1316no—
795C4⋊C4—1316no—
796C4⋊C4—138no—
797C4⋊C4—138no—
798C4⋊C4—1316no—
799C4⋊C4—1316no—
800C4⋊C4—138no—
801C4⋊C4—138no—
802C4⋊C4C23×D1318yes—
803C4⋊C4C23×D1318yes—
804C4⋊C4C23×D1314yes—
805C4⋊C4C23×D13116yes—
806C4⋊C4C23×D1314yes—
807C22⋊C4—138no—
808C22⋊C4—1316no—
809C22⋊C4—138no—
810C22⋊C4—138no—
811C22⋊C4—138no—
812C22⋊C4—138no—
813C22⋊C4—1316no—
814C22⋊C4—138no—
815C22⋊C4—138no—
816C22⋊C4—1316no—
817C22⋊C4—138no—
818C22⋊C4—138no—
819C22⋊C4C23×D1318yes—
820C22⋊C4C23×D13116yes—
821C42—1316no—
822C42—138no—
823C42C23×D13116yes—
824C42C23×D1318yes—
825C13C2×#349211yescharacteristic, complemented, Sylow
826C23—22no—
827C23—22no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—134no—
832C23—134no—
833C23—132no—
834C23—132no—
835C23—134no—
836C23—268no—
837C23—268no—
838C23—2632no—
839C23—268no—
840C23—262no—
841C23—262no—
842C23—262no—
843C23—262no—
844C23—264no—
845C23—264no—
846C23—264no—
847C23C2×#612714yes—
848C23C24×D1314yes—
849C23C24×D1312yes—
850C23C24×D1311yescharacteristic
851Q8—28no—
852Q8—268no—
853Q8—5216no—
854D4—216no—
855D4—28no—
856D4—2616no—
857D4—2616no—
858D4—2616no—
859D4—2616no—
860D4—2616no—
861D4—268no—
862D4—5216no—
863C2×C4—24no—
864C2×C4—28no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—216no—
868C2×C4—48no—
869C2×C4—416no—
870C2×C4—134no—
871C2×C4—134no—
872C2×C4—134no—
873C2×C4—132no—
874C2×C4—132no—
875C2×C4—138no—
876C2×C4—2632no—
877C2×C4—268no—
878C2×C4—262no—
879C2×C4—262no—
880C2×C4—264no—
881C2×C4—268no—
882C2×C4—264no—
883C2×C4—264no—
884C2×C4—268no—
885C2×C4—268no—
886C2×C4—268no—
887C2×C4—268no—
888C2×C4—2616no—
889C2×C4—5216no—
890C2×C4—5216no—
891C2×C4—528no—
892C2×C4C2×#612714yes—
893C2×C4C2×#612714yes—
894C2×C4C2×#6127116yescomplemented
895C2×C4C24×D1318yes—
896C2×C4C24×D1314yes—
897C2×C4C24×D1314yes—
898C2×C4C24×D1314yes—
899C2×C4C24×D1312yes—
900C2×C4C24×D1312yes—
901C22—28no—
902C22—22no—
903C22—22no—
904C22—24no—
905C22—24no—
906C22—24no—
907C22—48no—
908C22—134no—
909C22—134no—
910C22—2632no—
911C22—268no—
912C22—268no—
913C22—262no—
914C22—262no—
915C22—262no—
916C22—262no—
917C22—264no—
918C22—264no—
919C22—264no—
920C22—528no—
921C22C22×#612714yes—
922C22C22×#612712yes—
923C22D13×H(5,𝔽2)12yes—
924C22D13×2−1+412yes—
925C22C25×D1311yescharacteristic
926C4—24no—
927C4—28no—
928C4—24no—
929C4—24no—
930C4—262no—
931C4—262no—
932C4—264no—
933C4—268no—
934C4—264no—
935C4—264no—
936C4C22×#612714yes—
937C4C22×#612714yes—
938C2—24no—
939C2—44no—
940C2—264no—
941C2—264no—
942C2—524no—
943C2#1312853914yesdirect product factor
944C2C23×#612711yescharacteristic
945C2C2×D13×H(5,𝔽2)11yescharacteristic
946C2C2×D13×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#520C2
socleC23×C13C25
hypercenterC2×#520D13
hypocenterC13C2×#3492
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #13128539C2direct (N × H)
2. C2×#11719284C2semidirect
3. C2×#11719216C2semidirect
4. C2×#11719263C2semidirect
5. C2×#11719235C2semidirect
6. C2×#11719286C2semidirect
7. C2×#11719234C2semidirect
8. C2×#11719256C2semidirect
9. C2×#11719212C2semidirect
10. C2×#11719224C2semidirect
11. C2×#11719269C2semidirect
12. C2×#11719538C2semidirect
13. C2×#11719229C2semidirect
14. C2×#11719252C2semidirect
15. C2×#11719533C2semidirect
16. C2×#11719209C2semidirect
17. C22×C4⋊C4×D13C2semidirect
18. C2×C13×#520C2semidirect
24. C13×#520C22semidirect
25. C2×C4×Q8×C13C22semidirect
27. C2×C4×D4×C13C22semidirect
29. C2×C13×#117C22semidirect
31. C22×C13×C4⋊C4C22semidirect
32. #11719538C22semidirect
33. #11719533C22semidirect
36. C2×#88200C22semidirect
40. C2×#88192C22semidirect
43. C2×#88184C22semidirect
44. C2×#88183C22semidirect
51. C2×#88178C22semidirect
52. C2×#88178C22semidirect
54. #11719286C22semidirect
55. #11719284C22semidirect
56. #11719269C22semidirect
57. #11719263C22semidirect
58. #11719256C22semidirect
59. #11719252C22semidirect
60. #11719235C22semidirect
61. #11719234C22semidirect
62. #11719229C22semidirect
63. #11719224C22semidirect
64. #11719216C22semidirect
68. C2×#88150C22semidirect
69. #11719212C22semidirect
73. #11719209C22semidirect
74. C2×#88147C22semidirect
75. C2×#88146C22semidirect
80. C2×C4⋊C4×D13C22semidirect
81. C2×C4⋊C4×D13C22semidirect
82. C2×#88144C22semidirect
83. C2×#88143C22semidirect
84. C2×#88142C22semidirect
85. C2×#88141C22semidirect
89. C2×#88137C22semidirect
91. C2×#88133C22semidirect
93. C2×#88130C22semidirect
98. C2×#88124C22semidirect
99. C2×#88124C22semidirect
100. C2×#88123C22semidirect
138. C4×Q8×C13C23semidirect
140. C4×D4×C13C23semidirect
142. C13×#117C23semidirect
149. C2×C13×C4⋊C4C23semidirect
160. #88200C23semidirect
164. #88192C23semidirect
167. #88184C23semidirect
168. #88183C23semidirect
190. #88178C23semidirect
191. #88178C23semidirect
206. #88150C23semidirect
210. #88147C23semidirect
211. #88146C23semidirect
216. C4⋊C4×D13C23semidirect
217. #88144C23semidirect
218. #88143C23semidirect
219. #88142C23semidirect
220. #88141C23semidirect
224. #88137C23semidirect
226. #88133C23semidirect
228. #88130C23semidirect
233. #88124C23semidirect
234. #88124C23semidirect
235. #88123C23semidirect
256. C22×C4×C13#41semidirect
369. C2×#520D13semidirect
408. C2×C4×C13C2×#41semidirect
500. #520C2×D13semidirect
502. C2×C4×Q8C2×D13semidirect
512. C2×C4×D4C2×D13semidirect
517. C2×#117C2×D13semidirect
527. C22×C4⋊C4C2×D13semidirect
637. C4×Q8C22×D13semidirect
647. C4×D4C22×D13semidirect
652. #117C22×D13semidirect
681. C2×C4⋊C4C22×D13semidirect
702. C2×C13#3492semidirect
776. C22×C4#6127semidirect
825. C13C2×#3492semidirect
894. C2×C4C2×#6127semidirect
943. C2#13128539direct (N × H)

Maximal subgroups

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

subgroupindex
#131285392
C2×#117192842
C2×#117192162
C2×#117192632
C2×#117192352
C2×#117192862
C2×#117192342
C2×#117192562
C2×#117192122
C2×#117192242
C2×#117192692
C2×#117195382
C2×#117192292
C2×#117192522
C2×#117195332
C2×#117192092
C22×C4⋊C4×D132
C2×C13×#5202
C2×#349213