Finite Group Databasebeta

← C2×#13125187 #16732152

Subgroups — C2×#13125187 #16732152

Order 3328.

2262 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719434C211yesmaximal, characteristic, complemented
2C2×#11719379C211yesmaximal, characteristic
3#13125187C2116yesmaximal, direct product factor
4C2×#11718374C211yesmaximal, characteristic, complemented
5C2×#11718425C211yesmaximal, characteristic, complemented
6C2×#11718456C211yesmaximal, characteristic, complemented
7C2×#11718461C211yesmaximal, characteristic, complemented
8C2×#11718717C211yesmaximal, characteristic, complemented
9C2×#11718749C211yesmaximal, characteristic, complemented
10C2×#11718421C211yesmaximal, characteristic, complemented
11C2×#11718464C211yesmaximal, characteristic, complemented
12C2×#11718431C211yesmaximal, characteristic, complemented
13C2×#11718465C211yesmaximal, characteristic, complemented
14C2×D13×#102C211yesmaximal, characteristic, complemented
15C2×#11718369C211yesmaximal, characteristic, complemented
16C2×C13×#489C211yesmaximal, characteristic, complemented
17C22×#6131C2211yescharacteristic
18C22×D4×D13C2211yescharacteristic
19C2×C13×C4⋊Q8C2211yescharacteristic, complemented
20C2×C13×#124C2211yescharacteristic
21C2×#88201C2211yescharacteristic
22C2×#88200—21no—
23C2×#88198—21no—
24C2×#88194C2211yescharacteristic
25C22×#6094C2211yescharacteristic
26C22×C8×D13C2211yescharacteristic
27#11719434—24no—
28#11719434C2218yescomplemented
29#11719379—24no—
30#11719379C2218yes—
31C2×#88150—21no—
32C2×#88146C2211yescharacteristic
33C2×C4⋊C4×D13C2211yescharacteristic
34C2×#88144C2211yescharacteristic, complemented
35C2×#88143—21no—
36C2×#88142C2211yescharacteristic, complemented
37C2×#88138—21no—
38C2×#88138—21no—
39C2×#88136—21no—
40C2×#88136—21no—
41C2×#88128C2211yescharacteristic
42C2×#88126C2211yescharacteristic
43C2×#88124C2211yescharacteristic, complemented
44C13×#489C2218yescomplemented
45C2×C13×#103C2211yescharacteristic, complemented
46C2×C13×#103C2211yescharacteristic, complemented
47C2×C13×#102C2211yescharacteristic
48C2×C13×#102C2211yescharacteristic
49C2×C13×#97C2211yescharacteristic, complemented
50C2×#88075C2211yescharacteristic, complemented
51C2×#88075C2211yescharacteristic, complemented
52C2×#88072C2211yescharacteristic
53C2×#88072C2211yescharacteristic
54C2×#88061C2211yescharacteristic
55C2×#88061C2211yescharacteristic
56C2×#88061C2211yescharacteristic, complemented
57C2×#88061C2211yescharacteristic, complemented
58C2×#88055C2211yescharacteristic, complemented
59C2×C8×Dic13C2211yescharacteristic, complemented
60#11718749C2218yescomplemented
61#11718717C2218yescomplemented
62C2×#88049C2211yescharacteristic
63C2×#88049C2211yescharacteristic
64C2×#88049C2211yescharacteristic, complemented
65C2×#88049C2211yescharacteristic, complemented
66C2×C4×#1055C2211yescharacteristic, complemented
67#11718465C2218yescomplemented
68#11718464C2218yescomplemented
69#11718461C2218yescomplemented
70#11718456C2218yescomplemented
71#11718431C2218yescomplemented
72D13×#102C2218yescomplemented
73#11718425C2218yescomplemented
74#11718421C2218yescomplemented
75#11718374C2218yescomplemented
76#11718369C2218yescomplemented
77C24×D13—21no—
78C22×Q8×C13—21no—
79C22×Q8×C13C2311yescharacteristic
80C22×D4×C13C2311yescharacteristic
81C22×C22⋊D13—21no—
82C22×C22⋊D13—21no—
83C22×C22⋊D13—21no—
84C2×#6131—22no—
85C2×#6131—24no—
86C2×#6131—24no—
87C2×#6131C2314yes—
88C2×D4×D13—22no—
89C2×D4×D13—24no—
90C2×D4×D13—24no—
91C2×D4×D13C2314yes—
92C22×D52—21no—
93C22×D52—21no—
94C22×D52—21no—
95C22×D52C2311yescharacteristic
96C22×D52C2311yescharacteristic
97C22×C4×D13—21no—
98C22×C4×D13—21no—
99C22×C4×D13C2311yescharacteristic
100C22×Dic26—21no—
101C22×C8×C13C2311yescharacteristic
102C22×C8×C13C2311yescharacteristic
103C13×C4⋊Q8—22no—
104C13×C4⋊Q8C2314yescomplemented
105C13×#124—22no—
106C13×#124C2314yes—
107C2×C13×C4⋊C4—21no—
108C2×C13×C4⋊C4C2311yescharacteristic
109C2×C13×C4⋊C4C2311yescharacteristic
110C2×C13×C22⋊C4—21no—
111C2×C13×C22⋊C4—21no—
112C2×C42×C13C2311yescharacteristic
113#88201—22no—
114#88201C2314yes—
115#88200—28no—
116#88198—28no—
117#88194—22no—
118#88194C2314yes—
119C2×#6103—21no—
120C2×#6103—21no—
121C2×#6103—21no—
122C2×#6103D411yescharacteristic
123C2×#6103D411yescharacteristic
124C2×C4⋊Dic13—21no—
125C2×C4⋊Dic13C2311yescharacteristic
126C2×C4⋊Dic13C2311yescharacteristic
127C2×#6101—21no—
128C2×#6101—21no—
129C2×#6101—21no—
130C2×#6101—21no—
131C2×#6101—21no—
132C2×#6101D411yescharacteristic
133C2×#6101D411yescharacteristic
134C2×C4×Dic13—21no—
135C2×C4×Dic13C2311yescharacteristic
136C22×#1055C2311yescharacteristic
137C22×#1055C2311yescharacteristic
138C2×#6094—24no—
139C2×#6094C2314yes—
140C2×C8×D13—24no—
141C2×C8×D13C2314yes—
142#88150—28no—
143#88146—22no—
144#88146C2314yes—
145C4⋊C4×D13—22no—
146C4⋊C4×D13C2314yes—
147#88144—22no—
148#88144C2314yescomplemented
149#88143—28no—
150#88142—22no—
151#88142C2314yescomplemented
152#88138—28no—
153#88138—28no—
154#88136—28no—
155#88136—28no—
156#88128—22no—
157#88128C2314yes—
158#88126D414yes—
159#88126C2314yes—
160#88124—22no—
161#88124C2314yescomplemented
162C13×#103C2314yescomplemented
163C13×#103C2314yescomplemented
164C13×#102C2314yes—
165C13×#102C2314yes—
166C13×#97C2314yescomplemented
167#88075C2314yescomplemented
168#88075C2314yescomplemented
169#88072C2314yes—
170#88072C2314yes—
171#88061C2314yes—
172#88061C2314yes—
173#88061C2314yescomplemented
174#88061C2314yescomplemented
175#88055C2314yescomplemented
176C8×Dic13C2314yescomplemented
177#88049C2314yes—
178#88049C2314yes—
179#88049C2314yescomplemented
180#88049C2314yescomplemented
181C4×#1055C2314yescomplemented
182C2×#3136—131nomaximal, Sylow
183C24×C13—21no—
184C23×D13—21no—
185C23×D13—21no—
186C23×D13—24no—
187C23×D13—44no—
188C23×D13—82no—
189C23×D13—82no—
190C23×D13C2×D411yescharacteristic
191C2×Q8×C13—21no—
192C2×Q8×C13—24no—
193C2×Q8×C13—22no—
194C2×Q8×C13—22no—
195C2×Q8×C13—82no—
196C2×Q8×C13C2412yes—
197C2×D4×C13—21no—
198C2×D4×C13—22no—
199C2×D4×C13—22no—
200C2×D4×C13C2412yes—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13C2×D411yescharacteristic
205C22×C4×C13C2×D411yescharacteristic
206C22×C4×C13C2411yescharacteristic
207C2×C22⋊D13—24no—
208C2×C22⋊D13—24no—
209C2×C22⋊D13—24no—
210C2×C22⋊D13—44no—
211C2×C22⋊D13—82no—
212C2×C22⋊D13—82no—
213C22×Dic13—21no—
214C22×Dic13—21no—
215C22×Dic13C2×D411yescharacteristic
216C22×Dic13C2×D411yescharacteristic
217C22×Dic13C2×D411yescharacteristic
218#6131—28no—
219#6131—28no—
220#6131—48no—
221D4×D13—28no—
222D4×D13—28no—
223D4×D13—48no—
224C2×D52—22no—
225C2×D52—22no—
226C2×D52—22no—
227C2×D52—22no—
228C2×D52—24no—
229C2×D52—21no—
230C2×D52—21no—
231C2×D52—24no—
232C2×D52—24no—
233C2×D52—44no—
234C2×D52—82no—
235C2×D52—82no—
236C2×D52C2412yes—
237C2×D52C2412yes—
238C2×C4×D13—24no—
239C2×C4×D13—24no—
240C2×C4×D13—44no—
241C2×C4×D13—82no—
242C2×C4×D13C2×D412yes—
243C2×C4×D13#4114yes—
244C2×C4×D13#4114yes—
245C2×C4×D13C2412yes—
246C2×Dic26—24no—
247C2×Dic26—82no—
248C2×C8×C13—22no—
249C2×C8×C13—22no—
250C2×C8×C13C2412yes—
251C2×C8×C13C2412yes—
252C13×C4⋊C4—21no—
253C13×C4⋊C4—24no—
254C13×C4⋊C4—21no—
255C13×C4⋊C4C2412yes—
256C13×C4⋊C4C2412yes—
257C13×C22⋊C4—24no—
258C13×C22⋊C4—24no—
259C42×C13C2×D412yes—
260C42×C13C2412yes—
261#6103—24no—
262#6103—24no—
263#6103—24no—
264#6103C2×D414yes—
265#6103C2×D414yes—
266C4⋊Dic13—21no—
267C4⋊Dic13—21no—
268C4⋊Dic13—24no—
269C4⋊Dic13C2412yes—
270C4⋊Dic13C2412yes—
271#6101—24no—
272#6101—24no—
273#6101—24no—
274#6101—24no—
275#6101—24no—
276#6101C2×D414yes—
277#6101C2×D414yes—
278C4×Dic13—24no—
279C4×Dic13C2×D412yes—
280C4×Dic13C2412yes—
281C2×#1055—22no—
282C2×#1055—22no—
283C2×#1055C2412yes—
284C2×#1055C2412yes—
285#6094—28no—
286C8×D13—28no—
287C2×#544—131no—
288C2×#535—131no—
289#3136—1316no—
290C2×#490—131no—
291C2×#490—131no—
292C2×#489—131no—
293C2×#489D1311yescharacteristic, complemented
294C2×#488—131no—
295C2×#488—131no—
296C2×#486—131no—
297C2×#486—131no—
298C2×#417—131no—
299C2×#418—131no—
300C2×#416—131no—
301C22×#102—131no—
302C2×#405—131no—
303C23×C13—22no—
304C23×C13—42no—
305C23×C13—42no—
306C23×C13—42no—
307C23×C13C22×D411yescharacteristic
308C22×D13—22no—
309C22×D13—22no—
310C22×D13—22no—
311C22×D13—22no—
312C22×D13—42no—
313C22×D13—42no—
314C22×D13—42no—
315C22×D13—42no—
316C22×D13—42no—
317C22×D13—42no—
318C22×D13—48no—
319C22×D13—84no—
320C22×D13—84no—
321C22×D13—816no—
322C22×D13#12414yes—
323C22×D13C22×D412yes—
324Q8×C13—22no—
325Q8×C13—22no—
326Q8×C13—42no—
327Q8×C13—84no—
328D4×C13—22no—
329D4×C13—22no—
330D4×C13—42no—
331C2×C4×C13—22no—
332C2×C4×C13—22no—
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—42no—
337C2×C4×C13—42no—
338C2×C4×C13—42no—
339C2×C4×C13C22×D412yes—
340C2×C4×C13C22×D412yes—
341C2×C4×C13C22×D411yescharacteristic
342C2×C4×C13C2×#4112yes—
343C2×C4×C13C2×#4112yes—
344C2×C4×C13C2511yescharacteristic
345C22⋊D13—48no—
346C22⋊D13—84no—
347C22⋊D13—84no—
348C2×Dic13—22no—
349C2×Dic13—22no—
350C2×Dic13—22no—
351C2×Dic13—22no—
352C2×Dic13—42no—
353C2×Dic13—42no—
354C2×Dic13#12414yes—
355C2×Dic13C22×D412yes—
356C2×Dic13C22×D412yes—
357C2×Dic13C22×D412yes—
358D52—22no—
359D52—22no—
360D52—22no—
361D52—22no—
362D52—48no—
363D52—42no—
364D52—42no—
365D52—84no—
366D52—84no—
367C4×D13—48no—
368C4×D13—84no—
369C4×D13#12418yes—
370C4×D13C2×#4114yes—
371C4×D13C2×#4114yes—
372Dic26—84no—
373C8×C13—22no—
374C8×C13—22no—
375#1055—22no—
376#1055—22no—
377C22×#41—131no—
378C23×D4—131no—
379C22×M16—131no—
380C23×C8—131no—
381#544—138no—
382#544—264no—
383#535—138no—
384#535—264no—
385C2×C4⋊Q8—131no—
386C2×C4⋊Q8—261no—
387C2×C4⋊Q8C2×D1311yescharacteristic, complemented
388C2×#127—131no—
389C2×#127—131no—
390C2×#125—131no—
391C2×#125—131no—
392C2×#125—261no—
393C2×#124—131no—
394C2×#124C2×D1311yescharacteristic
395C2×C22⋊Q8—261no—
396C2×C22⋊Q8—261no—
397C2×#121—261no—
398C2×#121—261no—
399C2×#120—261no—
400C2×#120—261no—
401C2×#117—131no—
402C2×#117—131no—
403C22×C4⋊C4—131no—
404#490—138no—
405#490—138no—
406#489—138no—
407#489C2×D1318yescomplemented
408#488—138no—
409#488—138no—
410#486—138no—
411#486—138no—
412#418—138no—
413#417—138no—
414#416—138no—
415C2×#103—131no—
416C2×#103—131no—
417C2×#103C2×D1311yescharacteristic, complemented
418C2×#103C2×D1311yescharacteristic, complemented
419C2×#102—131no—
420C2×#102—131no—
421C2×#102—131no—
422C2×#102—131no—
423C2×#102—131no—
424C2×#102—131no—
425C2×#102—131no—
426C2×#102—131no—
427C2×#102—131no—
428C2×#102—131no—
429C2×#102—138no—
430C2×#102C2×D1311yescharacteristic
431C2×#102C2×D1311yescharacteristic
432#405—138no—
433C2×#97—131no—
434C2×#97C2×D1311yescharacteristic, complemented
435C2×C4×C8—131no—
436C2×C4×C8—131no—
437C22×C13—42no—
438C22×C13—42no—
439C22×C13—42no—
440C22×C13—84no—
441C22×C13C2×#12412yes—
442C22×C13#57612yes—
443C22×C13#57712yes—
444C22×C13C23×D411yescharacteristic
445C2×D13—28no—
446C2×D13—22no—
447C2×D13—22no—
448C2×D13—42no—
449C2×D13—42no—
450C2×D13—42no—
451C2×D13—42no—
452C2×D13—42no—
453C2×D13—42no—
454C2×D13—816no—
455C2×D13—84no—
456C2×D13—84no—
457C2×D13C2×#12414yes—
458C4×C13—22no—
459C4×C13—22no—
460C4×C13—42no—
461C4×C13—42no—
462C4×C13—42no—
463C4×C13C2×#12412yes—
464C4×C13C22×#4111yescharacteristic
465C4×C13C22×#4111yescharacteristic
466Dic13—22no—
467Dic13—22no—
468Dic13—42no—
469Dic13—42no—
470Dic13C2×#12414yes—
471C25—261no—
472C2×#41—134no—
473C2×#41—262no—
474C2×#41—264no—
475C2×#41—264no—
476C22×Q8—21no—
477C22×Q8—261no—
478C22×Q8C22×D1311yescharacteristic
479C22×D4—134no—
480C22×D4—131no—
481C22×D4—131no—
482C22×D4—261no—
483C22×D4—264no—
484C22×D4—264no—
485C22×D4—262no—
486C22×D4—261no—
487C22×D4—261no—
488C22×D4—261no—
489C22×D4—261no—
490C22×D4—261no—
491C22×D4C22×D1311yescharacteristic
492C23×C4—131no—
493C23×C4—261no—
494C23×C4—261no—
495C2×M16—134no—
496C2×M16—264no—
497C22×C8—131no—
498C22×C8—131no—
499C22×C8—134no—
500C22×C8—264no—
501C22×C8C22×D1311yescharacteristic
502C22×C8C22×D1311yescharacteristic
503C4⋊Q8—22no—
504C4⋊Q8—134no—
505C4⋊Q8—262no—
506C4⋊Q8—268no—
507C4⋊Q8C22×D1314yescomplemented
508#127—134no—
509#127—134no—
510#127—262no—
511#127—262no—
512#125—134no—
513#125—134no—
514#125—262no—
515#125—268no—
516#125—262no—
517#124—22no—
518#124—134no—
519#124—262no—
520#124C22×D1314yes—
521C22⋊Q8—268no—
522C22⋊Q8—268no—
523#121—268no—
524#121—268no—
525#120—268no—
526#120—268no—
527#117—134no—
528#117—134no—
529#117—134no—
530#117—262no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—131no—
533C2×C4⋊C4—131no—
534C2×C4⋊C4—131no—
535C2×C4⋊C4—131no—
536C2×C4⋊C4—134no—
537C2×C4⋊C4—262no—
538C2×C4⋊C4—261no—
539C2×C4⋊C4—261no—
540C2×C4⋊C4—261no—
541C2×C4⋊C4—261no—
542C2×C4⋊C4—261no—
543C2×C4⋊C4—261no—
544C2×C4⋊C4C22×D1311yescharacteristic
545C2×C4⋊C4C22×D1311yescharacteristic
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—131no—
549C2×C22⋊C4—131no—
550C2×C22⋊C4—261no—
551C2×C22⋊C4—261no—
552C2×C22⋊C4—261no—
553C2×C42—131no—
554C2×C42—261no—
555C2×C42C22×D1311yescharacteristic
556#103—134no—
557#103—134no—
558#103C22×D1314yescomplemented
559#103C22×D1314yescomplemented
560#102—134no—
561#102—134no—
562#102—134no—
563#102—134no—
564#102—134no—
565#102—134no—
566#102—134no—
567#102—134no—
568#102—134no—
569#102—134no—
570#102C22×D1314yes—
571#102C22×D1314yes—
572#97—134no—
573#97C22×D1314yescomplemented
574C4×C8—134no—
575C4×C8—134no—
576C2×C13—82no—
577C2×C13#313614yescomplemented
578C2×C13C22×#12411yescharacteristic
579C2×C13C2×#57611yescharacteristic
580C2×C13C2×#57711yescharacteristic
581D13—24no—
582D13—82no—
583D13—82no—
584C24—21no—
585C24—131no—
586C24—264no—
587C24—261no—
588C24—261no—
589C24—524no—
590C24—1042no—
591C24—1042no—
592#41—268no—
593#41—268no—
594#41—528no—
595C2×Q8—21no—
596C2×Q8—24no—
597C2×Q8—22no—
598C2×Q8—22no—
599C2×Q8—82no—
600C2×Q8—264no—
601C2×Q8—1042no—
602C2×Q8C23×D1312yes—
603C2×D4—21no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—132no—
607C2×D4—132no—
608C2×D4—264no—
609C2×D4—268no—
610C2×D4—268no—
611C2×D4—264no—
612C2×D4—264no—
613C2×D4—264no—
614C2×D4—261no—
615C2×D4—261no—
616C2×D4—264no—
617C2×D4—264no—
618C2×D4—262no—
619C2×D4—262no—
620C2×D4—262no—
621C2×D4—262no—
622C2×D4—524no—
623C2×D4—528no—
624C2×D4—524no—
625C2×D4—1042no—
626C2×D4—1042no—
627C2×D4—1042no—
628C2×D4—1042no—
629C2×D4C23×D1312yes—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—131no—
634C22×C4—132no—
635C22×C4—134no—
636C22×C4—134no—
637C22×C4—132no—
638C22×C4—131no—
639C22×C4—131no—
640C22×C4—264no—
641C22×C4—264no—
642C22×C4—261no—
643C22×C4—261no—
644C22×C4—524no—
645C22×C4—1042no—
646C22×C4D4×D1311yescharacteristic
647C22×C4D4×D1311yescharacteristic
648C22×C4C23×D1311yescharacteristic
649M16—268no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—132no—
653C2×C8—132no—
654C2×C8—268no—
655C2×C8—262no—
656C2×C8—262no—
657C2×C8C23×D1312yes—
658C2×C8C23×D1312yes—
659C4⋊C4—24no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—134no—
663C4⋊C4—134no—
664C4⋊C4—132no—
665C4⋊C4—132no—
666C4⋊C4—264no—
667C4⋊C4—264no—
668C4⋊C4—264no—
669C4⋊C4—264no—
670C4⋊C4—261no—
671C4⋊C4—261no—
672C4⋊C4—264no—
673C4⋊C4—264no—
674C4⋊C4C23×D1312yes—
675C4⋊C4C23×D1312yes—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—134no—
679C22⋊C4—134no—
680C22⋊C4—264no—
681C22⋊C4—264no—
682C22⋊C4—264no—
683C42—132no—
684C42—132no—
685C42—264no—
686C42D4×D1312yes—
687C42C23×D1312yes—
688C13C2×#313611yescharacteristic, complemented, Sylow
689C23—22no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—134no—
694C23—132no—
695C23—262no—
696C23—262no—
697C23—262no—
698C23—262no—
699C23—528no—
700C23—522no—
701C23—522no—
702C23—522no—
703C23—522no—
704C23—522no—
705C23—522no—
706C23—1044no—
707C23—1044no—
708C23—10416no—
709C23C2×D4×D1311yescharacteristic
710Q8—22no—
711Q8—22no—
712Q8—42no—
713Q8—84no—
714Q8—1044no—
715D4—22no—
716D4—22no—
717D4—42no—
718D4—262no—
719D4—262no—
720D4—262no—
721D4—262no—
722D4—528no—
723D4—528no—
724D4—522no—
725D4—522no—
726D4—1044no—
727D4—1044no—
728D4—1044no—
729D4—1044no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—134no—
739C2×C4—132no—
740C2×C4—138no—
741C2×C4—134no—
742C2×C4—134no—
743C2×C4—132no—
744C2×C4—132no—
745C2×C4—262no—
746C2×C4—262no—
747C2×C4—262no—
748C2×C4—262no—
749C2×C4—528no—
750C2×C4—522no—
751C2×C4—522no—
752C2×C4—1044no—
753C2×C4C2×D4×D1312yes—
754C2×C4C2×D4×D1312yes—
755C2×C4C2×D4×D1311yescharacteristic
756C2×C4#41×D1312yes—
757C2×C4#41×D1312yes—
758C2×C4C24×D1311yescharacteristic
759C8—22no—
760C8—22no—
761C8—262no—
762C8—262no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—84no—
767C22—134no—
768C22—268no—
769C22—262no—
770C22—262no—
771C22—522no—
772C22—522no—
773C22—522no—
774C22—522no—
775C22—522no—
776C22—522no—
777C22—10416no—
778C22—1044no—
779C22—1044no—
780C22D13×#12412yes—
781C22#1171947912yes—
782C22#1171948312yes—
783C22C22×D4×D1311yescharacteristic
784C4—22no—
785C4—22no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—134no—
790C4—262no—
791C4—262no—
792C4—522no—
793C4—522no—
794C4D13×#12412yes—
795C4C2×#41×D1311yescharacteristic
796C4C2×#41×D1311yescharacteristic
797C2—82no—
798C2—264no—
799C2—1042no—
800C2—1042no—
801C2#1312518714yesdirect product factor
802C2C2×D13×#12411yescharacteristic
803C2C2×#1171947911yescharacteristic
804C2C2×#1171948311yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#489C2
socleC23×C13C22×D4
prime radicalC2×#11719379C2
hypercenterC2×#489D13
hypocenterC13C2×#3136
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#11719434C2semidirect
3. #13125187C2direct (N × H)
4. C2×#11718374C2semidirect
5. C2×#11718425C2semidirect
6. C2×#11718456C2semidirect
7. C2×#11718461C2semidirect
8. C2×#11718717C2semidirect
9. C2×#11718749C2semidirect
10. C2×#11718421C2semidirect
11. C2×#11718464C2semidirect
12. C2×#11718431C2semidirect
13. C2×#11718465C2semidirect
14. C2×D13×#102C2semidirect
15. C2×#11718369C2semidirect
16. C2×C13×#489C2semidirect
19. C2×C13×C4⋊Q8C22semidirect
28. #11719434C22semidirect
34. C2×#88144C22semidirect
36. C2×#88142C22semidirect
43. C2×#88124C22semidirect
44. C13×#489C22semidirect
45. C2×C13×#103C22semidirect
46. C2×C13×#103C22semidirect
49. C2×C13×#97C22semidirect
50. C2×#88075C22semidirect
51. C2×#88075C22semidirect
56. C2×#88061C22semidirect
57. C2×#88061C22semidirect
58. C2×#88055C22semidirect
59. C2×C8×Dic13C22semidirect
60. #11718749C22semidirect
61. #11718717C22semidirect
64. C2×#88049C22semidirect
65. C2×#88049C22semidirect
66. C2×C4×#1055C22semidirect
67. #11718465C22semidirect
68. #11718464C22semidirect
69. #11718461C22semidirect
70. #11718456C22semidirect
71. #11718431C22semidirect
72. D13×#102C22semidirect
73. #11718425C22semidirect
74. #11718421C22semidirect
75. #11718374C22semidirect
76. #11718369C22semidirect
104. C13×C4⋊Q8C23semidirect
148. #88144C23semidirect
151. #88142C23semidirect
161. #88124C23semidirect
162. C13×#103C23semidirect
163. C13×#103C23semidirect
166. C13×#97C23semidirect
167. #88075C23semidirect
168. #88075C23semidirect
173. #88061C23semidirect
174. #88061C23semidirect
175. #88055C23semidirect
176. C8×Dic13C23semidirect
179. #88049C23semidirect
180. #88049C23semidirect
181. C4×#1055C23semidirect
293. C2×#489D13semidirect
387. C2×C4⋊Q8C2×D13semidirect
407. #489C2×D13semidirect
417. C2×#103C2×D13semidirect
418. C2×#103C2×D13semidirect
434. C2×#97C2×D13semidirect
507. C4⋊Q8C22×D13semidirect
558. #103C22×D13semidirect
559. #103C22×D13semidirect
573. #97C22×D13semidirect
577. C2×C13#3136semidirect
688. C13C2×#3136semidirect
801. C2#13125187direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117194342
C2×#117193792
#131251872
C2×#117183742
C2×#117184252
C2×#117184562
C2×#117184612
C2×#117187172
C2×#117187492
C2×#117184212
C2×#117184642
C2×#117184312
C2×#117184652
C2×D13×#1022
C2×#117183692
C2×C13×#4892
C2×#313613