Finite Group Databasebeta

← C2×#13124753 #16730690

Subgroups — C2×#13124753 #16730690

Order 3328.

2378 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719229C211yesmaximal, characteristic
2C2×D13×#117C211yesmaximal, characteristic, complemented
3#13124753C2116yesmaximal, direct product factor
4C2×#11718545C211yesmaximal, characteristic, complemented
5C2×#11718524C211yesmaximal, characteristic, complemented
6C2×#11718528C211yesmaximal, characteristic, complemented
7C2×#11718549C211yesmaximal, characteristic, complemented
8C2×#11718546C211yesmaximal, characteristic, complemented
9C2×#11718527C211yesmaximal, characteristic, complemented
10C2×#11718523C211yesmaximal, characteristic, complemented
11C2×#11718543C211yesmaximal, characteristic, complemented
12C2×#11718659C211yesmaximal, characteristic, complemented
13C2×#11718774C211yesmaximal, characteristic, complemented
14C2×#11718663C211yesmaximal, characteristic, complemented
15C22×#88060C211yesmaximal, characteristic, complemented
16C2×C13×#427C211yesmaximal, characteristic, complemented
17C22×#6127C2211yescharacteristic
18C23×C4×D13C2211yescharacteristic
19C23×C8×C13C2211yescharacteristic
20C2×C13×#117C2211yescharacteristic
21C2×C13×#117C2211yescharacteristic
22C2×#88180C2211yescharacteristic
23C23×#1055C2211yescharacteristic
24#11719229—24no—
25#11719229C2218yes—
26D13×#117—24no—
27D13×#117C2218yescomplemented
28C2×#88151C2211yescharacteristic
29C2×#88151C2211yescharacteristic
30C2×#88149C2211yescharacteristic
31C2×#88149C2211yescharacteristic
32C2×#88146C2211yescharacteristic
33C2×#88146C2211yescharacteristic
34C2×C4⋊C4×D13C2211yescharacteristic
35C2×C4⋊C4×D13C2211yescharacteristic
36C2×#88140—21no—
37C2×#88136—21no—
38C2×C22⋊C4×D13—21no—
39C2×#88131—21no—
40C2×C4×D52—21no—
41C2×C4×D52—21no—
42C2×#88126—21no—
43C2×C42×D13—21no—
44C13×#427C2218yescomplemented
45C2×C13×#107C2211yescharacteristic, complemented
46C2×C13×#107C2211yescharacteristic, complemented
47C2×C13×#106C2211yescharacteristic, complemented
48C2×C13×#106C2211yescharacteristic, complemented
49#11718774C2218yescomplemented
50C2×#88061C2211yescharacteristic, complemented
51C2×#88061C2211yescharacteristic, complemented
52C2×#88060C2211yescharacteristic
53C2×#88060C2211yescharacteristic
54C2×#88060C2211yescharacteristic
55C2×#88060C2211yescharacteristic
56C2×#88060C2218yescomplemented
57C2×#88056C2211yescharacteristic, complemented
58C2×#88056C2211yescharacteristic, complemented
59#11718663C2218yescomplemented
60#11718659C2218yescomplemented
61C2×#88050C2211yescharacteristic, complemented
62C2×#88050C2211yescharacteristic, complemented
63C2×#88049C2211yescharacteristic, complemented
64C2×#88049C2211yescharacteristic, complemented
65C2×#88048C2211yescharacteristic, complemented
66C2×#88048C2211yescharacteristic, complemented
67C2×#88047C2211yescharacteristic, complemented
68C2×#88047C2211yescharacteristic, complemented
69#11718549C2218yescomplemented
70#11718546C2218yescomplemented
71#11718545C2218yescomplemented
72#11718543C2218yescomplemented
73#11718528C2218yescomplemented
74#11718527C2218yescomplemented
75#11718524C2218yescomplemented
76#11718523C2218yescomplemented
77C24×D13D411yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C22×C22⋊D13—21no—
80C23×Dic13D411yescharacteristic
81C2×#6127—22no—
82C2×#6127—24no—
83C2×#6127—24no—
84C2×#6127C2314yes—
85C22×D52—21no—
86C22×D52—21no—
87C22×D52C2311yescharacteristic
88C22×C4×D13—24no—
89C22×C4×D13—24no—
90C22×C4×D13—21no—
91C22×C4×D13—21no—
92C22×C4×D13—21no—
93C22×C4×D13D411yescharacteristic
94C22×C4×D13D411yescharacteristic
95C22×C4×D13D414yes—
96C22×C4×D13C2311yescharacteristic
97C22×C4×D13C2311yescharacteristic
98C22×C4×D13C2314yes—
99C22×Dic26C2311yescharacteristic
100C22×C8×C13—24no—
101C22×C8×C13C2311yescharacteristic
102C22×C8×C13C2311yescharacteristic
103C22×C8×C13C2314yes—
104C13×#117—22no—
105C13×#117—22no—
106C13×#117C2314yes—
107C13×#117C2314yes—
108C2×C13×C4⋊C4C2311yescharacteristic
109C2×C13×C4⋊C4C2311yescharacteristic
110C2×C13×C4⋊C4C2311yescharacteristic
111C2×C13×C4⋊C4C2311yescharacteristic
112C2×C13×C22⋊C4—21no—
113C2×C13×C22⋊C4—21no—
114C2×C42×C13—21no—
115C2×C42×C13—21no—
116C2×C22⋊Dic13—21no—
117C2×#6103—21no—
118C2×#6103—21no—
119C2×#6103—21no—
120C2×#6103—21no—
121C2×#6103—21no—
122C2×#6103—21no—
123#88180—22no—
124#88180C2314yes—
125C2×C4⋊Dic13—21no—
126C2×C4⋊Dic13—21no—
127C2×C4⋊Dic13C2311yescharacteristic
128C2×C4⋊Dic13C2311yescharacteristic
129C2×#6101—21no—
130C2×#6101—21no—
131C2×C4×Dic13—21no—
132C2×C4×Dic13—21no—
133C2×C4×Dic13—21no—
134C22×#1055—24no—
135C22×#1055C2314yes—
136C22×#1055C2311yescharacteristic
137C22×#1055C2311yescharacteristic
138#88151—22no—
139#88151—22no—
140#88151C2314yes—
141#88151C2314yes—
142#88149—22no—
143#88149—22no—
144#88149C2314yes—
145#88149C2314yes—
146#88146—22no—
147#88146—22no—
148#88146C2314yes—
149#88146C2314yes—
150C4⋊C4×D13—22no—
151C4⋊C4×D13—22no—
152C4⋊C4×D13C2314yes—
153C4⋊C4×D13C2314yes—
154#88140—28no—
155#88136—28no—
156C22⋊C4×D13—28no—
157#88131—28no—
158C4×D52—28no—
159C4×D52—28no—
160#88126—28no—
161C42×D13—28no—
162C13×#107C2314yescomplemented
163C13×#107C2314yescomplemented
164C13×#106C2314yescomplemented
165C13×#106C2314yescomplemented
166#88061C2314yescomplemented
167#88061C2314yescomplemented
168#88060C2314yes—
169#88060C2314yes—
170#88060C2314yes—
171#88060C2314yes—
172#88056C2314yescomplemented
173#88056C2314yescomplemented
174#88050C2314yescomplemented
175#88050C2314yescomplemented
176#88049C2314yescomplemented
177#88049C2314yescomplemented
178#88048C2314yescomplemented
179#88048C2314yescomplemented
180#88047C2314yescomplemented
181#88047C2314yescomplemented
182C2×#3091—131nomaximal, Sylow
183C24×C13C2×D411yescharacteristic
184C23×D13—24no—
185C23×D13—24no—
186C23×D13—21no—
187C23×D13—42no—
188C23×D13C2×D411yescharacteristic
189C23×D13C2×D414yes—
190C23×D13C2×D411yescharacteristic
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13C2×D412yes—
196C22×C4×C13C2×D411yescharacteristic
197C22×C4×C13#4114yes—
198C22×C4×C13#4114yes—
199C22×C4×C13C2411yescharacteristic
200C22×C4×C13C2412yes—
201C2×C22⋊D13—24no—
202C2×C22⋊D13—44no—
203C22×Dic13—24no—
204C22×Dic13—21no—
205C22×Dic13—21no—
206C22×Dic13—21no—
207C22×Dic13C2×D414yes—
208C22×Dic13C2×D411yescharacteristic
209C22×Dic13C2×D411yescharacteristic
210#6127—28no—
211#6127—28no—
212#6127—48no—
213C2×D52—22no—
214C2×D52—22no—
215C2×D52—24no—
216C2×D52—24no—
217C2×D52—21no—
218C2×D52—44no—
219C2×D52—44no—
220C2×D52C2412yes—
221C2×C4×D13—24no—
222C2×C4×D13—24no—
223C2×C4×D13—216no—
224C2×C4×D13—22no—
225C2×C4×D13—22no—
226C2×C4×D13—28no—
227C2×C4×D13—22no—
228C2×C4×D13—22no—
229C2×C4×D13—28no—
230C2×C4×D13—24no—
231C2×C4×D13—24no—
232C2×C4×D13—24no—
233C2×C4×D13—44no—
234C2×C4×D13—44no—
235C2×C4×D13—44no—
236C2×C4×D13C2×D414yes—
237C2×C4×D13C2×D414yes—
238C2×C4×D13C2×D412yes—
239C2×C4×D13C2×D412yes—
240C2×C4×D13C2412yes—
241C2×C4×D13C2412yes—
242C2×Dic26—22no—
243C2×Dic26—22no—
244C2×Dic26—21no—
245C2×Dic26C2412yes—
246C2×C8×C13—22no—
247C2×C8×C13—22no—
248C2×C8×C13—28no—
249C2×C8×C13C2412yes—
250C2×C8×C13C2412yes—
251C13×C4⋊C4—21no—
252C13×C4⋊C4—21no—
253C13×C4⋊C4—21no—
254C13×C4⋊C4—21no—
255C13×C4⋊C4C2412yes—
256C13×C4⋊C4C2412yes—
257C13×C4⋊C4C2412yes—
258C13×C4⋊C4C2412yes—
259C13×C22⋊C4—24no—
260C13×C22⋊C4—24no—
261C42×C13—24no—
262C42×C13—24no—
263C22⋊Dic13—24no—
264#6103—24no—
265#6103—24no—
266#6103—24no—
267#6103—24no—
268#6103—24no—
269#6103—24no—
270C4⋊Dic13—21no—
271C4⋊Dic13—21no—
272C4⋊Dic13—24no—
273C4⋊Dic13—24no—
274C4⋊Dic13C2412yes—
275C4⋊Dic13C2412yes—
276#6101—24no—
277#6101—24no—
278C4×Dic13—24no—
279C4×Dic13—24no—
280C4×Dic13—24no—
281C2×#1055—22no—
282C2×#1055—22no—
283C2×#1055—28no—
284C2×#1055C2412yes—
285C2×#1055C2412yes—
286C2×#525—131no—
287C22×#117—131no—
288#3091—1316no—
289C2×#484—131no—
290C2×#481—131no—
291C2×#485—131no—
292C2×#485—131no—
293C2×#482—131no—
294C2×#482—131no—
295C2×#483—131no—
296C2×#480—131no—
297C2×#427—131no—
298C2×#427D1311yescharacteristic, complemented
299C2×#416—131no—
300C2×#416—131no—
301C22×C22⋊C8—131no—
302C23×C13—22no—
303C23×C13—22no—
304C23×C13#12314yes—
305C23×C13C22×D412yes—
306C23×C13C22×D411yescharacteristic
307C22×D13—22no—
308C22×D13—22no—
309C22×D13—28no—
310C22×D13—22no—
311C22×D13—22no—
312C22×D13—22no—
313C22×D13—28no—
314C22×D13—22no—
315C22×D13—44no—
316C22×D13—416no—
317C22×D13—42no—
318C22×D13—42no—
319C22×D13—42no—
320C22×D13#13514yes—
321C22×D13C22×D412yes—
322C22×D13C22×D412yes—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
325C2×C4×C13—22no—
326C2×C4×C13—22no—
327C2×C4×C13—42no—
328C2×C4×C13—42no—
329C2×C4×C13—42no—
330C2×C4×C13—42no—
331C2×C4×C13#12314yes—
332C2×C4×C13#12318yes—
333C2×C4×C13C22×D412yes—
334C2×C4×C13C22×D411yescharacteristic
335C2×C4×C13C2×#4112yes—
336C2×C4×C13C2×#4114yes—
337C2×C4×C13C2×#4112yes—
338C2×C4×C13C2×#4114yes—
339C2×C4×C13C2511yescharacteristic
340C22⋊D13—48no—
341C2×Dic13—28no—
342C2×Dic13—22no—
343C2×Dic13—22no—
344C2×Dic13—22no—
345C2×Dic13—22no—
346C2×Dic13—22no—
347C2×Dic13—42no—
348C2×Dic13—42no—
349C2×Dic13—42no—
350C2×Dic13C22×D412yes—
351C2×Dic13C22×D412yes—
352D52—22no—
353D52—22no—
354D52—48no—
355D52—48no—
356D52—42no—
357C4×D13—24no—
358C4×D13—24no—
359C4×D13—28no—
360C4×D13—28no—
361C4×D13—22no—
362C4×D13—22no—
363C4×D13—22no—
364C4×D13—22no—
365C4×D13—48no—
366C4×D13—48no—
367C4×D13—48no—
368Dic26—22no—
369Dic26—22no—
370Dic26—42no—
371C8×C13—22no—
372C8×C13—22no—
373#1055—22no—
374#1055—22no—
375C22×#41—131no—
376C24×C4—131no—
377C23×C8—131no—
378C23×C8C2×D1311yescharacteristic
379#525—138no—
380#525—264no—
381C2×#123—261no—
382C2×C22⋊Q8—131no—
383C2×C22⋊Q8—131no—
384C2×#121—131no—
385C2×#121—131no—
386C2×#120—261no—
387C2×C4×D4—261no—
388C2×C4×D4—261no—
389C2×#117—131no—
390C2×#117—138no—
391C2×#117—131no—
392C2×#117—131no—
393C2×#117—261no—
394C2×#117—261no—
395C2×#117—264no—
396C2×#117C2×D1311yescharacteristic
397C2×#117C2×D1311yescharacteristic
398C22×C4⋊C4—131no—
399C22×C4⋊C4—131no—
400C22×C22⋊C4—261no—
401C22×C42—261no—
402#485—138no—
403#485—138no—
404#484—138no—
405#483—138no—
406#482—138no—
407#482—138no—
408#481—138no—
409#480—138no—
410#427—138no—
411#427C2×D1318yescomplemented
412C2×#107—131no—
413C2×#107—131no—
414C2×#107C2×D1311yescharacteristic, complemented
415C2×#107C2×D1311yescharacteristic, complemented
416C2×#106—131no—
417C2×#106—131no—
418C2×#106C2×D1311yescharacteristic, complemented
419C2×#106C2×D1311yescharacteristic, complemented
420#416—138no—
421#416—138no—
422C2×#103—131no—
423C2×#103—131no—
424C2×#103—131no—
425C2×#103—131no—
426C2×#102—131no—
427C2×#102—131no—
428C2×#102—131no—
429C2×#102—131no—
430C2×C22⋊C8—131no—
431C2×C22⋊C8—131no—
432C2×C22⋊C8—131no—
433C2×C22⋊C8—131no—
434C2×C22⋊C8—138no—
435C22×C13—28no—
436C22×C13—22no—
437C22×C13—22no—
438C22×C13C2×#12314yes—
439C22×C13C2×#12312yes—
440C22×C13C2×#13512yes—
441C22×C13#57512yes—
442C22×C13C23×D411yescharacteristic
443C2×D13—28no—
444C2×D13—22no—
445C2×D13—22no—
446C2×D13—22no—
447C2×D13—22no—
448C2×D13—22no—
449C2×D13—416no—
450C2×D13—44no—
451C2×D13—42no—
452C2×D13—42no—
453C2×D13—42no—
454C2×D13—84no—
455C2×D13C2×#13514yes—
456C4×C13—42no—
457C4×C13—42no—
458C4×C13—42no—
459C4×C13—42no—
460C4×C13C2×#12312yes—
461C4×C13C2×#12314yes—
462C4×C13C22×#4111yescharacteristic
463C4×C13C22×#4111yescharacteristic
464Dic13—22no—
465Dic13—22no—
466Dic13—42no—
467Dic13—42no—
468Dic13—42no—
469C25—131no—
470C2×#41—134no—
471C2×#41—262no—
472C2×#41—264no—
473C2×#41—264no—
474C22×Q8—131no—
475C22×D4—131no—
476C22×D4—261no—
477C22×D4—261no—
478C22×D4—261no—
479C23×C4—131no—
480C23×C4—134no—
481C23×C4—131no—
482C23×C4—131no—
483C23×C4—131no—
484C23×C4—131no—
485C23×C4—134no—
486C23×C4—261no—
487C23×C4—261no—
488C23×C4—264no—
489C23×C4—264no—
490C23×C4—261no—
491C23×C4C22×D1311yescharacteristic
492C22×C8—24no—
493C22×C8—131no—
494C22×C8—131no—
495C22×C8—134no—
496C22×C8—264no—
497C22×C8C22×D1311yescharacteristic
498C22×C8C22×D1311yescharacteristic
499C22×C8C22×D1314yes—
500#123—268no—
501C22⋊Q8—134no—
502C22⋊Q8—134no—
503C22⋊Q8—262no—
504C22⋊Q8—262no—
505#121—134no—
506#121—134no—
507#121—262no—
508#121—262no—
509#120—268no—
510C4×D4—268no—
511C4×D4—268no—
512#117—22no—
513#117—22no—
514#117—134no—
515#117—134no—
516#117—134no—
517#117—268no—
518#117—268no—
519#117—262no—
520#117—262no—
521#117—262no—
522#117C22×D1314yes—
523#117C22×D1314yes—
524C2×C4⋊C4—131no—
525C2×C4⋊C4—131no—
526C2×C4⋊C4—134no—
527C2×C4⋊C4—134no—
528C2×C4⋊C4—262no—
529C2×C4⋊C4—262no—
530C2×C4⋊C4—261no—
531C2×C4⋊C4—261no—
532C2×C4⋊C4—261no—
533C2×C4⋊C4—261no—
534C2×C4⋊C4C22×D1311yescharacteristic
535C2×C4⋊C4C22×D1311yescharacteristic
536C2×C4⋊C4C22×D1311yescharacteristic
537C2×C4⋊C4C22×D1311yescharacteristic
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—268no—
541C2×C22⋊C4—261no—
542C2×C22⋊C4—261no—
543C2×C22⋊C4—261no—
544C2×C22⋊C4—261no—
545C2×C22⋊C4—261no—
546C2×C22⋊C4—261no—
547C2×C22⋊C4—261no—
548C2×C42—21no—
549C2×C42—21no—
550C2×C42—268no—
551C2×C42—261no—
552C2×C42—261no—
553C2×C42—261no—
554#107—134no—
555#107—134no—
556#107C22×D1314yescomplemented
557#107C22×D1314yescomplemented
558#106—134no—
559#106—134no—
560#106C22×D1314yescomplemented
561#106C22×D1314yescomplemented
562#103—134no—
563#103—134no—
564#103—134no—
565#103—134no—
566#102—134no—
567#102—134no—
568#102—134no—
569#102—134no—
570C22⋊C8—134no—
571C22⋊C8—134no—
572C22⋊C8—134no—
573C22⋊C8—134no—
574C2×C13—24no—
575C2×C13#309114yescomplemented
576C2×C13C22×#12311yescharacteristic
577C2×C13C22×#13511yescharacteristic
578C2×C13C2×#57511yescharacteristic
579D13—24no—
580D13—42no—
581D13—82no—
582C24—131no—
583C24—131no—
584C24—134no—
585C24—264no—
586C24—264no—
587C24—261no—
588C24—522no—
589C24D4×D1311yescharacteristic
590#41—268no—
591#41—268no—
592#41—528no—
593C2×Q8—132no—
594C2×Q8—261no—
595C2×Q8—262no—
596C2×Q8—262no—
597C2×D4—132no—
598C2×D4—264no—
599C2×D4—264no—
600C2×D4—264no—
601C2×D4—262no—
602C2×D4—261no—
603C2×D4—262no—
604C2×D4—524no—
605C2×D4—524no—
606C2×D4—524no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—131no—
612C22×C4—131no—
613C22×C4—134no—
614C22×C4—134no—
615C22×C4—132no—
616C22×C4—134no—
617C22×C4—132no—
618C22×C4—132no—
619C22×C4—132no—
620C22×C4—264no—
621C22×C4—264no—
622C22×C4—264no—
623C22×C4—264no—
624C22×C4—264no—
625C22×C4—2616no—
626C22×C4—262no—
627C22×C4—262no—
628C22×C4—268no—
629C22×C4—262no—
630C22×C4—262no—
631C22×C4—268no—
632C22×C4—261no—
633C22×C4—261no—
634C22×C4—261no—
635C22×C4—264no—
636C22×C4—524no—
637C22×C4—524no—
638C22×C4—524no—
639C22×C4#612714yes—
640C22×C4D4×D1312yes—
641C22×C4D4×D1311yescharacteristic
642C22×C4#613114yes—
643C22×C4C23×D1311yescharacteristic
644C22×C4C23×D1312yes—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—28no—
648C2×C8—132no—
649C2×C8—132no—
650C2×C8—262no—
651C2×C8—262no—
652C2×C8—268no—
653C2×C8C23×D1312yes—
654C2×C8C23×D1312yes—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—132no—
660C4⋊C4—132no—
661C4⋊C4—264no—
662C4⋊C4—264no—
663C4⋊C4—264no—
664C4⋊C4—264no—
665C4⋊C4—261no—
666C4⋊C4—261no—
667C4⋊C4C23×D1312yes—
668C4⋊C4C23×D1312yes—
669C4⋊C4C23×D1312yes—
670C4⋊C4C23×D1312yes—
671C22⋊C4—24no—
672C22⋊C4—24no—
673C22⋊C4—264no—
674C22⋊C4—264no—
675C22⋊C4—264no—
676C22⋊C4—264no—
677C22⋊C4—264no—
678C22⋊C4—264no—
679C22⋊C4—264no—
680C42—24no—
681C42—24no—
682C42—264no—
683C42—264no—
684C42—264no—
685C13C2×#309111yescharacteristic, complemented, Sylow
686C23—22no—
687C23—22no—
688C23—134no—
689C23—132no—
690C23—132no—
691C23—268no—
692C23—262no—
693C23—262no—
694C23—268no—
695C23—262no—
696C23—262no—
697C23—262no—
698C23—262no—
699C23—524no—
700C23—5216no—
701C23—522no—
702C23—522no—
703C23—522no—
704C23#8814814yes—
705C23C2×D4×D1312yes—
706C23C2×D4×D1311yescharacteristic
707Q8—262no—
708Q8—262no—
709Q8—522no—
710D4—262no—
711D4—262no—
712D4—528no—
713D4—528no—
714D4—528no—
715D4—522no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—132no—
725C2×C4—132no—
726C2×C4—268no—
727C2×C4—262no—
728C2×C4—262no—
729C2×C4—268no—
730C2×C4—268no—
731C2×C4—264no—
732C2×C4—264no—
733C2×C4—262no—
734C2×C4—262no—
735C2×C4—262no—
736C2×C4—262no—
737C2×C4—262no—
738C2×C4—262no—
739C2×C4—262no—
740C2×C4—528no—
741C2×C4—528no—
742C2×C4—522no—
743C2×C4—522no—
744C2×C4—522no—
745C2×C4—528no—
746C2×C4#8814814yes—
747C2×C4#8814818yes—
748C2×C4C2×#612712yes—
749C2×C4C2×#612714yes—
750C2×C4C2×D4×D1312yes—
751C2×C4C2×D4×D1311yescharacteristic
752C2×C4C2×#613112yes—
753C2×C4C2×#613114yes—
754C2×C4C24×D1311yescharacteristic
755C8—22no—
756C8—22no—
757C8—262no—
758C8—262no—
759C22—22no—
760C22—22no—
761C22—28no—
762C22—134no—
763C22—262no—
764C22—262no—
765C22—268no—
766C22—262no—
767C22—262no—
768C22—262no—
769C22—5216no—
770C22—524no—
771C22—522no—
772C22—522no—
773C22—522no—
774C22—1044no—
775C22C2×#8814814yes—
776C22C2×#8814812yes—
777C22D13×#13512yes—
778C22#1171947312yes—
779C22C22×D4×D1311yescharacteristic
780C4—42no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—262no—
785C4—262no—
786C4—522no—
787C4—522no—
788C4—522no—
789C4C2×#8814814yes—
790C4C2×#8814812yes—
791C4C22×#612711yescharacteristic
792C4C22×#613111yescharacteristic
793C2—24no—
794C2—264no—
795C2—522no—
796C2—1042no—
797C2#1312475314yesdirect product factor
798C2C22×#8814811yescharacteristic
799C2C2×D13×#13511yescharacteristic
800C2C2×#1171947311yescharacteristic
subgroupG/H
centerC22×C4D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#427C2
socleC23×C13C22×D4
prime radicalC2×#11719229C2
hypercenterC2×#427D13
hypocenterC13C2×#3091
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
2. C2×D13×#117C2semidirect
3. #13124753C2direct (N × H)
4. C2×#11718545C2semidirect
5. C2×#11718524C2semidirect
6. C2×#11718528C2semidirect
7. C2×#11718549C2semidirect
8. C2×#11718546C2semidirect
9. C2×#11718527C2semidirect
10. C2×#11718523C2semidirect
11. C2×#11718543C2semidirect
12. C2×#11718659C2semidirect
13. C2×#11718774C2semidirect
14. C2×#11718663C2semidirect
15. C22×#88060C2semidirect
16. C2×C13×#427C2semidirect
27. D13×#117C22semidirect
44. C13×#427C22semidirect
45. C2×C13×#107C22semidirect
46. C2×C13×#107C22semidirect
47. C2×C13×#106C22semidirect
48. C2×C13×#106C22semidirect
49. #11718774C22semidirect
50. C2×#88061C22semidirect
51. C2×#88061C22semidirect
56. C2×#88060C22semidirect
57. C2×#88056C22semidirect
58. C2×#88056C22semidirect
59. #11718663C22semidirect
60. #11718659C22semidirect
61. C2×#88050C22semidirect
62. C2×#88050C22semidirect
63. C2×#88049C22semidirect
64. C2×#88049C22semidirect
65. C2×#88048C22semidirect
66. C2×#88048C22semidirect
67. C2×#88047C22semidirect
68. C2×#88047C22semidirect
69. #11718549C22semidirect
70. #11718546C22semidirect
71. #11718545C22semidirect
72. #11718543C22semidirect
73. #11718528C22semidirect
74. #11718527C22semidirect
75. #11718524C22semidirect
76. #11718523C22semidirect
162. C13×#107C23semidirect
163. C13×#107C23semidirect
164. C13×#106C23semidirect
165. C13×#106C23semidirect
166. #88061C23semidirect
167. #88061C23semidirect
172. #88056C23semidirect
173. #88056C23semidirect
174. #88050C23semidirect
175. #88050C23semidirect
176. #88049C23semidirect
177. #88049C23semidirect
178. #88048C23semidirect
179. #88048C23semidirect
180. #88047C23semidirect
181. #88047C23semidirect
298. C2×#427D13semidirect
411. #427C2×D13semidirect
414. C2×#107C2×D13semidirect
415. C2×#107C2×D13semidirect
418. C2×#106C2×D13semidirect
419. C2×#106C2×D13semidirect
556. #107C22×D13semidirect
557. #107C22×D13semidirect
560. #106C22×D13semidirect
561. #106C22×D13semidirect
575. C2×C13#3091semidirect
685. C13C2×#3091semidirect
797. C2#13124753direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192292
C2×D13×#1172
#131247532
C2×#117185452
C2×#117185242
C2×#117185282
C2×#117185492
C2×#117185462
C2×#117185272
C2×#117185232
C2×#117185432
C2×#117186592
C2×#117187742
C2×#117186632
C22×#880602
C2×C13×#4272
C2×#309113