Finite Group Databasebeta

← C2×#13128549 #16770980

Subgroups — C2×#13128549 #16770980

Order 3328.

7302 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128549C2132yesmaximal, direct product factor
2C2×#11719289C212yesmaximal, complemented
3C2×#11719238C212yesmaximal, complemented
4C2×#11719268C212yesmaximal, complemented
5C2×#11719237C212yesmaximal, complemented
6C2×#11719263C212yesmaximal, complemented
7C2×#11719219C212yesmaximal, complemented
8C2×#11719286C212yesmaximal, complemented
9C2×#11719218C212yesmaximal, complemented
10C2×#11719224C211yesmaximal, characteristic, complemented
11C2×#11719265C214yesmaximal, complemented
12C2×#11719538C211yesmaximal, characteristic, complemented
13C2×#11719243C214yesmaximal, complemented
14C2×#11719229C211yesmaximal, characteristic, complemented
15C2×#11719533C211yesmaximal, characteristic, complemented
16C2×#11719209C211yesmaximal, characteristic, complemented
17C22×#88146C211yesmaximal, characteristic, complemented
18C2×C13×#520C211yesmaximal, characteristic, complemented
19C22×C13×#41C2211yescharacteristic
20C22×#6127C2211yescharacteristic
21C23×C4×D13C2211yescharacteristic
22C13×#520C22116yescomplemented
23C2×C4×Q8×C13C2212yescomplemented
24C2×C4×D4×C13C2214yes—
25C2×C4×D4×C13C2212yescomplemented
26C2×C13×#117C2211yescharacteristic
27C2×C13×#117C2212yescomplemented
28C22×C13×C4⋊C4C2211yescharacteristic
29C22×C13×C4⋊C4C2212yescomplemented
30#11719538C22116yescomplemented
31#11719533C22116yescomplemented
32C2×#88200C2211yescharacteristic
33C2×#88200C2211yescharacteristic
34C2×#88200C2212yescomplemented
35C2×#88193C2214yes—
36C2×#88192C2211yescharacteristic
37C2×#88192C2211yescharacteristic
38C2×#88192C2212yescomplemented
39C2×#88191C2212yes—
40C2×#88189C2212yes—
41C2×#88184C2214yes—
42C2×#88184C2212yescomplemented
43C2×#88183C2214yes—
44C2×C4×C22⋊D13C2214yes—
45C2×C4×C22⋊D13C2212yes—
46C2×C4×C22⋊D13C2212yes—
47C2×C4×C22⋊D13C2214yescomplemented
48C22×#6103C2212yes—
49C2×#88180C2211yescharacteristic
50C2×#88180C2214yescomplemented
51C22×C4⋊Dic13C2211yescharacteristic
52C2×#88178C2212yescomplemented
53C22×C4×Dic13C2212yes—
54#11719289C22132yescomplemented
55#11719286C22132yescomplemented
56#11719268C22132yescomplemented
57#11719265C22164yescomplemented
58#11719263C22132yescomplemented
59#11719243C22164yescomplemented
60#11719238C22132yescomplemented
61#11719237C22132yescomplemented
62#11719229C22116yescomplemented
63#11719224C22116yescomplemented
64#11719219C22132yescomplemented
65#11719218C22132yescomplemented
66C2×#88152C2214yes—
67C2×#88152C2214yescomplemented
68C2×#88151C2211yescharacteristic
69C2×#88151C2211yescharacteristic
70C2×#88149C2211yescharacteristic
71C2×#88149C2211yescharacteristic
72C2×#88148C2214yes—
73#11719209C22116yescomplemented
74C2×#88147C2212yescomplemented
75C2×#88146C2212yes—
76C2×#88146C2212yes—
77C2×#88146C2212yes—
78C2×#88146C2212yes—
79C2×#88146C22116yescomplemented
80C2×#88146C2212yescomplemented
81C2×C4⋊C4×D13C2212yescomplemented
82C2×#88144C2212yescomplemented
83C2×#88143C2214yescomplemented
84C2×#88142C2212yescomplemented
85C2×#88141C2212yescomplemented
86C2×#88140C2212yes—
87C2×#88139C2214yes—
88C2×#88139C2214yescomplemented
89C2×#88138C2214yes—
90C2×#88136C2212yes—
91C2×#88133C2214yescomplemented
92C2×#88132C2214yes—
93C2×#88130C2214yes—
94C2×#88129C2214yes—
95C2×C4×D52C2212yes—
96C2×C4×D52C2212yes—
97C2×#88126C2214yescomplemented
98C2×#88124C2212yescomplemented
99C2×#88123C2212yescomplemented
100C2×C4×Dic26C2214yescomplemented
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⋊D13C2314yes—
114C22×C22⋊D13C2312yes—
115C23×Dic13C2311yescharacteristic
116C23×Dic13C2312yes—
117C2×#6127—28no—
118C2×#6127C2318yes—
119C22×D52C2311yescharacteristic
120C22×D52C2312yes—
121C22×D52C2312yes—
122C22×C4×D13—28no—
123C22×C4×D13C2312yes—
124C22×C4×D13C2311yescharacteristic
125C22×C4×D13C2311yescharacteristic
126C22×C4×D13C2311yescharacteristic
127C22×C4×D13C2311yescharacteristic
128C22×C4×D13C2318yes—
129C22×C4×D13C2314yes—
130C22×Dic26C2311yescharacteristic
131C22×Dic26C2314yes—
132C4×Q8×C13C23116yescomplemented
133C4×D4×C13C23132yes—
134C4×D4×C13C23116yescomplemented
135C13×#117C2318yes—
136C13×#117C23116yescomplemented
137C2×C13×C4⋊C4C2312yes—
138C2×C13×C4⋊C4C2311yescharacteristic
139C2×C13×C4⋊C4C2314yes—
140C2×C13×C4⋊C4C2311yescharacteristic
141C2×C13×C4⋊C4C2312yes—
142C2×C13×C4⋊C4C2318yes—
143C2×C13×C4⋊C4C23116yescomplemented
144C2×C13×C22⋊C4C2312yes—
145C2×C13×C22⋊C4C2314yes—
146C2×C42×C13C2314yes—
147C2×C42×C13C2312yes—
148C2×C22⋊Dic13C2312yes—
149C2×C22⋊Dic13C2312yes—
150C2×C22⋊Dic13C2314yes—
151C2×C22⋊Dic13C2312yes—
152#88200C2318yes—
153#88200C2318yes—
154#88200C23116yescomplemented
155#88193C23132yes—
156#88192C2318yes—
157#88192C2318yes—
158#88192C23116yescomplemented
159#88191C23116yes—
160#88189C23116yes—
161#88184C23132yes—
162#88184C23116yescomplemented
163#88183C23132yes—
164C4×C22⋊D13C23132yes—
165C4×C22⋊D13C23116yes—
166C4×C22⋊D13C23116yes—
167C4×C22⋊D13C23132yescomplemented
168C2×#6103C2312yes—
169C2×#6103C2314yes—
170C2×#6103C2312yes—
171C2×#6103C2312yes—
172C2×#6103C2312yes—
173C2×#6103C2312yes—
174C2×#6103C2314yes—
175C2×#6103C2314yes—
176C2×#6103C2312yes—
177C2×#6103C2314yes—
178C2×#6103C23116yes—
179#88180C2318yes—
180#88180C23132yescomplemented
181C2×C4⋊Dic13C2312yes—
182C2×C4⋊Dic13C2311yescharacteristic
183C2×C4⋊Dic13C2312yes—
184C2×C4⋊Dic13C2314yes—
185C2×C4⋊Dic13C2311yescharacteristic
186C2×C4⋊Dic13C2312yes—
187C2×C4⋊Dic13C2312yes—
188C2×C4⋊Dic13C2318yes—
189#88178C23116yescomplemented
190C2×#6101C2312yes—
191C2×#6101C2314yes—
192C2×#6101C2314yes—
193C2×#6101C2314yes—
194C2×#6101C2312yes—
195C2×#6101C2314yes—
196C2×C4×Dic13C2314yes—
197C2×C4×Dic13C2314yes—
198C2×C4×Dic13C2314yes—
199C2×C4×Dic13C2312yes—
200C2×C4×Dic13C23116yes—
201#88152C23132yes—
202#88152C23132yescomplemented
203#88151C2318yes—
204#88151C2318yes—
205#88149C2318yes—
206#88149C2318yes—
207#88148C23132yes—
208#88147C23116yescomplemented
209#88146C23116yes—
210#88146C23116yes—
211#88146C23116yes—
212#88146C23116yes—
213#88146C23116yescomplemented
214C4⋊C4×D13C23116yescomplemented
215#88144C23116yescomplemented
216#88143C23132yescomplemented
217#88142C23116yescomplemented
218#88141C23116yescomplemented
219#88140C23116yes—
220#88139C23132yes—
221#88139C23132yescomplemented
222#88138C23132yes—
223#88136C23116yes—
224#88133C23132yescomplemented
225#88132C23132yes—
226#88130C23132yes—
227#88129C23132yes—
228C4×D52C23116yes—
229C4×D52C23116yes—
230#88126C23132yescomplemented
231#88124C23116yescomplemented
232#88123C23116yescomplemented
233C4×Dic26C23132yescomplemented
234C2×#3493—131nomaximal, Sylow
235C24×C13C2412yes—
236C24×C13C2411yescharacteristic
237C23×D13—24no—
238C23×D13—42no—
239C23×D13—42no—
240C23×D13C2411yescharacteristic
241C23×D13C2411yescharacteristic
242C23×D13C2412yes—
243C23×D13C2414yes—
244C13×#41—232no—
245C2×Q8×C13—24no—
246C2×Q8×C13C2414yes—
247C2×D4×C13—28no—
248C2×D4×C13—24no—
249C2×D4×C13C2418yes—
250C2×D4×C13C2414yes—
251C22×C4×C13—28no—
252C22×C4×C13—44no—
253C22×C4×C13—48no—
254C22×C4×C13#4118yes—
255C22×C4×C13C2414yes—
256C22×C4×C13C2412yes—
257C22×C4×C13C2412yes—
258C22×C4×C13C2412yes—
259C22×C4×C13C2418yes—
260C22×C4×C13C2418yes—
261C22×C4×C13C24116yes—
262C22×C4×C13C2411yescharacteristic
263C22×C4×C13C2411yescharacteristic
264C22×C4×C13C2414yes—
265C2×C22⋊D13—28no—
266C2×C22⋊D13—44no—
267C2×C22⋊D13—48no—
268C2×C22⋊D13—44no—
269C2×C22⋊D13C2418yes—
270C2×C22⋊D13C2418yes—
271C2×C22⋊D13C24116yes—
272C2×C22⋊D13C2418yes—
273C22×Dic13—24no—
274C22×Dic13—44no—
275C22×Dic13C2414yes—
276C22×Dic13C2411yescharacteristic
277C22×Dic13C2411yescharacteristic
278C22×Dic13C2412yes—
279C22×Dic13C2412yes—
280C22×Dic13C2414yes—
281C22×Dic13C2412yes—
282C22×Dic13C2418yes—
283#6127—232no—
284C2×D52—24no—
285C2×D52—44no—
286C2×D52—44no—
287C2×D52C2414yes—
288C2×D52C2418yes—
289C2×D52C2418yes—
290C2×C4×D13—24no—
291C2×C4×D13—24no—
292C2×C4×D13—24no—
293C2×C4×D13—24no—
294C2×C4×D13—232no—
295C2×C4×D13—28no—
296C2×C4×D13—48no—
297C2×C4×D13C2418yes—
298C2×C4×D13C2414yes—
299C2×C4×D13C2414yes—
300C2×C4×D13C2414yes—
301C2×C4×D13C2414yes—
302C2×C4×D13C24116yes—
303C2×Dic26—24no—
304C2×Dic26—48no—
305C2×Dic26C2414yes—
306C2×Dic26C24116yes—
307C13×C4⋊C4C2418yes—
308C13×C4⋊C4C2414yes—
309C13×C4⋊C4C24116yes—
310C13×C4⋊C4C2414yes—
311C13×C4⋊C4C2418yes—
312C13×C22⋊C4C2418yes—
313C13×C22⋊C4C24116yes—
314C42×C13C24116yes—
315C42×C13C2418yes—
316C22⋊Dic13C2418yes—
317C22⋊Dic13C2418yes—
318C22⋊Dic13C24116yes—
319C22⋊Dic13C2418yes—
320#6103C2418yes—
321#6103C24116yes—
322#6103C2418yes—
323#6103C2418yes—
324#6103C2418yes—
325#6103C2418yes—
326#6103C24116yes—
327#6103C24116yes—
328#6103C2418yes—
329#6103C24116yes—
330C4⋊Dic13C2418yes—
331C4⋊Dic13C2414yes—
332C4⋊Dic13C2418yes—
333C4⋊Dic13C24116yes—
334C4⋊Dic13C2414yes—
335C4⋊Dic13C2418yes—
336C4⋊Dic13C2418yes—
337#6101C2418yes—
338#6101C24116yes—
339#6101C24116yes—
340#6101C24116yes—
341#6101C2418yes—
342#6101C24116yes—
343C4×Dic13C24116yes—
344C4×Dic13C24116yes—
345C4×Dic13C24116yes—
346C4×Dic13C2418yes—
347#3493—1332no—
348C2×#556—132no—
349C2×#556—132no—
350C2×#555—132no—
351C2×#555—132no—
352C2×#553—132no—
353C2×#553—132no—
354C2×#552—132no—
355C2×#552—132no—
356C2×#544—131no—
357C2×#538—134no—
358C2×#537—131no—
359C2×#529—134no—
360C2×#525—131no—
361C2×#525—131no—
362C2×#520—131no—
363C2×#520D1311yescharacteristic, complemented
364C22×#117—131no—
365C23×C13—22no—
366C23×C13—22no—
367C23×C13—24no—
368C23×C13—24no—
369C23×C13—24no—
370C23×C13C2×#4114yes—
371C23×C13C2514yes—
372C23×C13C2512yes—
373C23×C13C2511yescharacteristic
374C22×D13—28no—
375C22×D13—22no—
376C22×D13—22no—
377C22×D13—24no—
378C22×D13—24no—
379C22×D13—22no—
380C22×D13—22no—
381C22×D13—24no—
382C22×D13—22no—
383C22×D13—22no—
384C22×D13—44no—
385C22×D13—44no—
386C22×D13—416no—
387C22×D13C2512yes—
388C22×D13C2512yes—
389C22×D13C2514yes—
390Q8×C13—28no—
391D4×C13—216no—
392D4×C13—28no—
393C2×C4×C13—24no—
394C2×C4×C13—24no—
395C2×C4×C13—28no—
396C2×C4×C13—24no—
397C2×C4×C13—216no—
398C2×C4×C13—48no—
399C2×C4×C13—416no—
400C2×C4×C13C2×#4114yes—
401C2×C4×C13C2×#4114yes—
402C2×C4×C13C2×#41116yes—
403C2×C4×C13C2518yes—
404C2×C4×C13C2514yes—
405C2×C4×C13C2514yes—
406C2×C4×C13C2514yes—
407C2×C4×C13C2512yes—
408C2×C4×C13C2512yes—
409C22⋊D13—216no—
410C22⋊D13—48no—
411C22⋊D13—416no—
412C22⋊D13—48no—
413C2×Dic13—24no—
414C2×Dic13—28no—
415C2×Dic13—22no—
416C2×Dic13—22no—
417C2×Dic13—24no—
418C2×Dic13—28no—
419C2×Dic13—24no—
420C2×Dic13—48no—
421C2×Dic13C2512yes—
422C2×Dic13C2512yes—
423C2×Dic13C2514yes—
424C2×Dic13C2514yes—
425C2×Dic13C2518yes—
426C2×Dic13C2514yes—
427D52—28no—
428D52—48no—
429D52—48no—
430C4×D13—28no—
431C4×D13—28no—
432C4×D13—28no—
433C4×D13—28no—
434C4×D13—216no—
435C4×D13—416no—
436Dic26—28no—
437Dic26—416no—
438C22×#41—131no—
439C22×#41C2×D1311yescharacteristic
440C24×C4—131no—
441#556—1332no—
442#556—1332no—
443#555—1332no—
444#555—1332no—
445#553—1332no—
446#553—1332no—
447#552—1332no—
448#552—1332no—
449#544—1316no—
450#538—1364no—
451#537—1316no—
452C2×C4⋊Q8—132no—
453C2×C4⋊Q8—132no—
454#529—1364no—
455C2×#126—134no—
456C2×#126—134no—
457C2×#126—134no—
458C2×#126—134no—
459C2×#125—134no—
460C2×#125—132no—
461C2×#125—132no—
462C2×#124—134no—
463C2×#124—134no—
464C2×#124—134no—
465#525—1316no—
466#525—1316no—
467C2×#123—132no—
468C2×#123—134no—
469C2×#123—134no—
470C2×#123—132no—
471C2×C22⋊Q8—131no—
472C2×C22⋊Q8—131no—
473C2×C22⋊Q8—132no—
474C2×C22⋊Q8—132no—
475C2×C22⋊Q8—131no—
476C2×C22⋊Q8—131no—
477C2×C22⋊Q8—134no—
478C2×#121—131no—
479C2×#121—131no—
480C2×#121—132no—
481C2×#121—134no—
482C2×#121—134no—
483C2×#121—132no—
484C2×#121—131no—
485C2×#121—131no—
486C2×#121—134no—
487C2×#120—132no—
488C2×#120—132no—
489#520—1316no—
490#520C2×D13116yescomplemented
491C2×C4×Q8—132no—
492C2×C4×Q8—134no—
493C2×C4×Q8C2×D1312yescomplemented
494C2×C4×D4—134no—
495C2×C4×D4—132no—
496C2×C4×D4—132no—
497C2×C4×D4—134no—
498C2×C4×D4—132no—
499C2×C4×D4—132no—
500C2×C4×D4—132no—
501C2×C4×D4C2×D1314yes—
502C2×C4×D4C2×D1312yescomplemented
503C2×#117—131no—
504C2×#117—134no—
505C2×#117—132no—
506C2×#117—132no—
507C2×#117—132no—
508C2×#117—132no—
509C2×#117—1316no—
510C2×#117—132no—
511C2×#117—134no—
512C2×#117C2×D1311yescharacteristic
513C2×#117C2×D1312yescomplemented
514C22×C4⋊C4—131no—
515C22×C4⋊C4—132no—
516C22×C4⋊C4C2×D1311yescharacteristic
517C22×C4⋊C4C2×D1312yescomplemented
518C22×C22⋊C4—132no—
519C22×C42—132no—
520C22×C13—22no—
521C22×C13—22no—
522C22×C13—28no—
523C22×C13—24no—
524C22×C13—24no—
525C22×C13—24no—
526C22×C13—48no—
527C22×C13C22×#4114yes—
528C22×C13C22×#4112yes—
529C22×C13#58512yes—
530C22×C13#58512yes—
531C22×C13C2611yescharacteristic
532C2×D13—22no—
533C2×D13—22no—
534C2×D13—24no—
535C2×D13—24no—
536C2×D13—22no—
537C2×D13—22no—
538C2×D13—24no—
539C2×D13—22no—
540C2×D13—22no—
541C2×D13—416no—
542C2×D13—48no—
543C2×D13—44no—
544C2×D13—44no—
545C4×C13—24no—
546C4×C13—24no—
547C4×C13—28no—
548C4×C13—24no—
549C4×C13C22×#4114yes—
550C4×C13C22×#4114yes—
551Dic13—24no—
552Dic13—22no—
553Dic13—22no—
554Dic13—24no—
555Dic13—28no—
556Dic13—24no—
557C25—131no—
558C2×#41—28no—
559C2×#41—138no—
560C2×#41—268no—
561C2×#41C22×D1318yes—
562C22×Q8—131no—
563C22×Q8—134no—
564C22×Q8C22×D1311yescharacteristic
565C22×D4—132no—
566C22×D4—132no—
567C22×D4—132no—
568C22×D4—134no—
569C22×D4—131no—
570C22×D4—132no—
571C22×D4—132no—
572C22×D4C22×D1312yes—
573C22×D4C22×D1311yescharacteristic
574C23×C4—131no—
575C23×C4—132no—
576C23×C4—132no—
577C23×C4—131no—
578C23×C4—131no—
579C23×C4—131no—
580C23×C4—131no—
581C23×C4—138no—
582C23×C4—134no—
583C23×C4—268no—
584C23×C4C22×D1312yes—
585C23×C4C22×D1312yes—
586C23×C4C22×D1314yes—
587C23×C4C22×D1311yescharacteristic
588C4⋊Q8—1316no—
589C4⋊Q8—1316no—
590#126—1332no—
591#126—1332no—
592#126—1332no—
593#126—1332no—
594#125—1332no—
595#125—1316no—
596#125—1316no—
597#124—1332no—
598#124—1332no—
599#124—1332no—
600#123—1316no—
601#123—1332no—
602#123—1332no—
603#123—1316no—
604C22⋊Q8—138no—
605C22⋊Q8—138no—
606C22⋊Q8—1316no—
607C22⋊Q8—1316no—
608C22⋊Q8—138no—
609C22⋊Q8—138no—
610C22⋊Q8—1332no—
611#121—138no—
612#121—138no—
613#121—1332no—
614#121—1316no—
615#121—1316no—
616#121—1332no—
617#121—138no—
618#121—138no—
619#121—1332no—
620#120—1316no—
621#120—1316no—
622C4×Q8—1316no—
623C4×Q8—1332no—
624C4×Q8C22×D13116yescomplemented
625C4×D4—1332no—
626C4×D4—1316no—
627C4×D4—1316no—
628C4×D4—1332no—
629C4×D4—1316no—
630C4×D4—1316no—
631C4×D4—1316no—
632C4×D4C22×D13132yes—
633C4×D4C22×D13116yescomplemented
634#117—138no—
635#117—1332no—
636#117—1316no—
637#117—1316no—
638#117—1316no—
639#117—1316no—
640#117—1316no—
641#117—1332no—
642#117C22×D1318yes—
643#117C22×D13116yescomplemented
644C2×C4⋊C4—131no—
645C2×C4⋊C4—132no—
646C2×C4⋊C4—132no—
647C2×C4⋊C4—138no—
648C2×C4⋊C4—134no—
649C2×C4⋊C4—131no—
650C2×C4⋊C4—132no—
651C2×C4⋊C4—132no—
652C2×C4⋊C4—134no—
653C2×C4⋊C4—134no—
654C2×C4⋊C4—132no—
655C2×C4⋊C4—132no—
656C2×C4⋊C4—134no—
657C2×C4⋊C4—134no—
658C2×C4⋊C4—1316no—
659C2×C4⋊C4C22×D1312yes—
660C2×C4⋊C4C22×D1312yes—
661C2×C4⋊C4C22×D1318yes—
662C2×C4⋊C4C22×D1311yescharacteristic
663C2×C4⋊C4C22×D1314yes—
664C2×C4⋊C4C22×D1311yescharacteristic
665C2×C4⋊C4C22×D13116yescomplemented
666C2×C22⋊C4—132no—
667C2×C22⋊C4—132no—
668C2×C22⋊C4—134no—
669C2×C22⋊C4—132no—
670C2×C22⋊C4—134no—
671C2×C22⋊C4—134no—
672C2×C22⋊C4—1316no—
673C2×C22⋊C4—132no—
674C2×C22⋊C4—134no—
675C2×C22⋊C4—134no—
676C2×C22⋊C4—132no—
677C2×C22⋊C4—132no—
678C2×C22⋊C4—132no—
679C2×C22⋊C4—132no—
680C2×C22⋊C4—132no—
681C2×C22⋊C4C22×D1312yes—
682C2×C22⋊C4C22×D1314yes—
683C2×C42—134no—
684C2×C42—134no—
685C2×C42—134no—
686C2×C42—1316no—
687C2×C42—132no—
688C2×C42C22×D1314yes—
689C2×C42C22×D1312yes—
690C2×C13—24no—
691C2×C13—44no—
692C2×C13#349314yescomplemented
693C2×C13C23×#4111yescharacteristic
694C2×C13C2×#58511yescharacteristic
695C2×C13C2×#58511yescharacteristic
696D13—44no—
697D13—42no—
698D13—42no—
699C24—131no—
700C24—131no—
701C24—132no—
702C24—134no—
703C24—264no—
704C24—522no—
705C24—522no—
706C24C23×D1312yes—
707C24C23×D1311yescharacteristic
708#41—232no—
709#41—2632no—
710C2×Q8—24no—
711C2×Q8—134no—
712C2×Q8—1316no—
713C2×Q8—264no—
714C2×Q8—528no—
715C2×Q8C23×D1314yes—
716C2×D4—28no—
717C2×D4—24no—
718C2×D4—138no—
719C2×D4—138no—
720C2×D4—138no—
721C2×D4—1316no—
722C2×D4—134no—
723C2×D4—138no—
724C2×D4—138no—
725C2×D4—268no—
726C2×D4—264no—
727C2×D4—524no—
728C2×D4—524no—
729C2×D4—524no—
730C2×D4—528no—
731C2×D4—524no—
732C2×D4C23×D1318yes—
733C2×D4C23×D1314yes—
734C22×C4—28no—
735C22×C4—44no—
736C22×C4—48no—
737C22×C4—134no—
738C22×C4—131no—
739C22×C4—131no—
740C22×C4—132no—
741C22×C4—132no—
742C22×C4—134no—
743C22×C4—132no—
744C22×C4—138no—
745C22×C4—138no—
746C22×C4—134no—
747C22×C4—134no—
748C22×C4—134no—
749C22×C4—134no—
750C22×C4—1316no—
751C22×C4—264no—
752C22×C4—264no—
753C22×C4—264no—
754C22×C4—264no—
755C22×C4—264no—
756C22×C4—2632no—
757C22×C4—268no—
758C22×C4—528no—
759C22×C4—524no—
760C22×C4#612718yes—
761C22×C4C23×D1318yes—
762C22×C4C23×D1314yes—
763C22×C4C23×D1312yes—
764C22×C4C23×D1312yes—
765C22×C4C23×D1312yes—
766C22×C4C23×D1318yes—
767C22×C4C23×D13116yes—
768C22×C4C23×D1314yes—
769C22×C4C23×D1311yescharacteristic
770C22×C4C23×D1311yescharacteristic
771C4⋊C4—134no—
772C4⋊C4—138no—
773C4⋊C4—138no—
774C4⋊C4—1316no—
775C4⋊C4—134no—
776C4⋊C4—138no—
777C4⋊C4—138no—
778C4⋊C4—1316no—
779C4⋊C4—1316no—
780C4⋊C4—138no—
781C4⋊C4—138no—
782C4⋊C4—1316no—
783C4⋊C4—1316no—
784C4⋊C4C23×D1318yes—
785C4⋊C4C23×D1318yes—
786C4⋊C4C23×D1314yes—
787C4⋊C4C23×D13116yes—
788C4⋊C4C23×D1314yes—
789C22⋊C4—138no—
790C22⋊C4—138no—
791C22⋊C4—1316no—
792C22⋊C4—138no—
793C22⋊C4—1316no—
794C22⋊C4—1316no—
795C22⋊C4—138no—
796C22⋊C4—1316no—
797C22⋊C4—1316no—
798C22⋊C4—138no—
799C22⋊C4—138no—
800C22⋊C4—138no—
801C22⋊C4—138no—
802C22⋊C4—138no—
803C22⋊C4C23×D1318yes—
804C22⋊C4C23×D13116yes—
805C42—1316no—
806C42—1316no—
807C42—1316no—
808C42—138no—
809C42C23×D13116yes—
810C42C23×D1318yes—
811C13C2×#349311yescharacteristic, complemented, Sylow
812C23—22no—
813C23—22no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—132no—
818C23—132no—
819C23—134no—
820C23—268no—
821C23—262no—
822C23—262no—
823C23—264no—
824C23—264no—
825C23—262no—
826C23—262no—
827C23—264no—
828C23—262no—
829C23—262no—
830C23—524no—
831C23—524no—
832C23—5216no—
833C23C2×#612714yes—
834C23C24×D1314yes—
835C23C24×D1312yes—
836C23C24×D1311yescharacteristic
837Q8—28no—
838Q8—268no—
839Q8—5216no—
840D4—216no—
841D4—28no—
842D4—2616no—
843D4—268no—
844D4—528no—
845D4—528no—
846D4—528no—
847D4—5216no—
848D4—528no—
849C2×C4—24no—
850C2×C4—28no—
851C2×C4—24no—
852C2×C4—24no—
853C2×C4—216no—
854C2×C4—48no—
855C2×C4—416no—
856C2×C4—132no—
857C2×C4—132no—
858C2×C4—134no—
859C2×C4—134no—
860C2×C4—138no—
861C2×C4—134no—
862C2×C4—268no—
863C2×C4—262no—
864C2×C4—262no—
865C2×C4—264no—
866C2×C4—264no—
867C2×C4—268no—
868C2×C4—264no—
869C2×C4—268no—
870C2×C4—268no—
871C2×C4—268no—
872C2×C4—268no—
873C2×C4—2616no—
874C2×C4—5216no—
875C2×C4—528no—
876C2×C4C2×#612714yes—
877C2×C4C2×#612714yes—
878C2×C4C2×#6127116yes—
879C2×C4C24×D1318yes—
880C2×C4C24×D1314yes—
881C2×C4C24×D1314yes—
882C2×C4C24×D1314yes—
883C2×C4C24×D1312yes—
884C2×C4C24×D1312yes—
885C22—28no—
886C22—22no—
887C22—22no—
888C22—24no—
889C22—24no—
890C22—24no—
891C22—48no—
892C22—262no—
893C22—262no—
894C22—264no—
895C22—264no—
896C22—262no—
897C22—262no—
898C22—264no—
899C22—262no—
900C22—262no—
901C22—5216no—
902C22—528no—
903C22—524no—
904C22—524no—
905C22C22×#612714yes—
906C22C22×#612712yes—
907C22#1171965012yes—
908C22#1171965212yes—
909C22C25×D1311yescharacteristic
910C4—24no—
911C4—28no—
912C4—24no—
913C4—24no—
914C4—262no—
915C4—262no—
916C4—264no—
917C4—264no—
918C4—268no—
919C4—264no—
920C4C22×#612714yes—
921C4C22×#612714yes—
922C2—24no—
923C2—44no—
924C2—522no—
925C2—522no—
926C2—524no—
927C2#1312854914yesdirect product factor
928C2C23×#612711yescharacteristic
929C2C2×#1171965011yescharacteristic
930C2C2×#1171965211yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#520C2
socleC23×C13C25
hypercenterC2×#520D13
hypocenterC13C2×#3493
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #13128549C2direct (N × H)
2. C2×#11719289C2semidirect
3. C2×#11719238C2semidirect
4. C2×#11719268C2semidirect
5. C2×#11719237C2semidirect
6. C2×#11719263C2semidirect
7. C2×#11719219C2semidirect
8. C2×#11719286C2semidirect
9. C2×#11719218C2semidirect
10. C2×#11719224C2semidirect
11. C2×#11719265C2semidirect
12. C2×#11719538C2semidirect
13. C2×#11719243C2semidirect
14. C2×#11719229C2semidirect
15. C2×#11719533C2semidirect
16. C2×#11719209C2semidirect
17. C22×#88146C2semidirect
18. C2×C13×#520C2semidirect
22. C13×#520C22semidirect
23. C2×C4×Q8×C13C22semidirect
25. C2×C4×D4×C13C22semidirect
27. C2×C13×#117C22semidirect
29. C22×C13×C4⋊C4C22semidirect
30. #11719538C22semidirect
31. #11719533C22semidirect
34. C2×#88200C22semidirect
38. C2×#88192C22semidirect
42. C2×#88184C22semidirect
47. C2×C4×C22⋊D13C22semidirect
50. C2×#88180C22semidirect
52. C2×#88178C22semidirect
54. #11719289C22semidirect
55. #11719286C22semidirect
56. #11719268C22semidirect
57. #11719265C22semidirect
58. #11719263C22semidirect
59. #11719243C22semidirect
60. #11719238C22semidirect
61. #11719237C22semidirect
62. #11719229C22semidirect
63. #11719224C22semidirect
64. #11719219C22semidirect
65. #11719218C22semidirect
67. C2×#88152C22semidirect
73. #11719209C22semidirect
74. C2×#88147C22semidirect
79. C2×#88146C22semidirect
80. C2×#88146C22semidirect
81. C2×C4⋊C4×D13C22semidirect
82. C2×#88144C22semidirect
83. C2×#88143C22semidirect
84. C2×#88142C22semidirect
85. C2×#88141C22semidirect
88. C2×#88139C22semidirect
91. C2×#88133C22semidirect
97. C2×#88126C22semidirect
98. C2×#88124C22semidirect
99. C2×#88123C22semidirect
100. C2×C4×Dic26C22semidirect
132. C4×Q8×C13C23semidirect
134. C4×D4×C13C23semidirect
136. C13×#117C23semidirect
143. C2×C13×C4⋊C4C23semidirect
154. #88200C23semidirect
158. #88192C23semidirect
162. #88184C23semidirect
167. C4×C22⋊D13C23semidirect
180. #88180C23semidirect
189. #88178C23semidirect
202. #88152C23semidirect
208. #88147C23semidirect
213. #88146C23semidirect
214. C4⋊C4×D13C23semidirect
215. #88144C23semidirect
216. #88143C23semidirect
217. #88142C23semidirect
218. #88141C23semidirect
221. #88139C23semidirect
224. #88133C23semidirect
230. #88126C23semidirect
231. #88124C23semidirect
232. #88123C23semidirect
233. C4×Dic26C23semidirect
363. C2×#520D13semidirect
490. #520C2×D13semidirect
493. C2×C4×Q8C2×D13semidirect
502. C2×C4×D4C2×D13semidirect
513. C2×#117C2×D13semidirect
517. C22×C4⋊C4C2×D13semidirect
624. C4×Q8C22×D13semidirect
633. C4×D4C22×D13semidirect
643. #117C22×D13semidirect
665. C2×C4⋊C4C22×D13semidirect
692. C2×C13#3493semidirect
811. C13C2×#3493semidirect
927. C2#13128549direct (N × H)

Maximal subgroups

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

subgroupindex
#131285492
C2×#117192892
C2×#117192382
C2×#117192682
C2×#117192372
C2×#117192632
C2×#117192192
C2×#117192862
C2×#117192182
C2×#117192242
C2×#117192652
C2×#117195382
C2×#117192432
C2×#117192292
C2×#117195332
C2×#117192092
C22×#881462
C2×C13×#5202
C2×#349313