Finite Group Databasebeta

← C2×#13124664 #16730475

Subgroups — C2×#13124664 #16730475

Order 3328.

2234 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719394C211yesmaximal, characteristic, complemented
2C2×#11719250C211yesmaximal, characteristic
3#13124664C2116yesmaximal, direct product factor
4C2×#11718552C211yesmaximal, characteristic, complemented
5C2×#11718427C211yesmaximal, characteristic, complemented
6C2×#11718727C211yesmaximal, characteristic, complemented
7C2×#11718669C211yesmaximal, characteristic, complemented
8C2×#11718531C211yesmaximal, characteristic, complemented
9C2×#11718507C211yesmaximal, characteristic, complemented
10C2×#11718420C211yesmaximal, characteristic, complemented
11C2×#11718522C211yesmaximal, characteristic, complemented
12C2×#11718541C211yesmaximal, characteristic, complemented
13C2×#11718500C211yesmaximal, characteristic, complemented
14C2×#11718431C211yesmaximal, characteristic
15C2×D13×#102C211yesmaximal, characteristic
16C2×C13×#478C211yesmaximal, characteristic, complemented
17C22×D4×D13C2211yescharacteristic
18C2×C13×#125C2211yescharacteristic, complemented
19C2×C4×D4×C13C2211yescharacteristic
20C2×D4×Dic13C2211yescharacteristic
21C2×C4×C22⋊D13—21no—
22C22×#6103—21no—
23C22×#6094C2211yescharacteristic
24C22×C8×D13C2211yescharacteristic
25#11719394—24no—
26#11719394C2218yescomplemented
27#11719250—24no—
28#11719250C2218yes—
29C2×#88151—21no—
30C2×#88150—21no—
31C2×#88147C2211yescharacteristic
32C2×#88146C2211yescharacteristic
33C2×#88146C2211yescharacteristic
34C2×C4⋊C4×D13C2211yescharacteristic
35C2×#88144C2211yescharacteristic, complemented
36C2×#88143—21no—
37C2×#88142—21no—
38C2×#88142C2211yescharacteristic, complemented
39C2×#88135—21no—
40C2×C22⋊C4×D13—21no—
41C2×C4×D52C2211yescharacteristic
42C2×#88126C2211yescharacteristic
43C2×#88123C2211yescharacteristic, complemented
44C13×#478C2218yescomplemented
45C2×C13×#107C2211yescharacteristic, complemented
46C2×C13×#106C2211yescharacteristic, complemented
47C2×C13×C4⋊C8C2211yescharacteristic, complemented
48C2×C13×#102C2211yescharacteristic
49C2×C13×#102C2211yescharacteristic
50C2×#88072C2211yescharacteristic
51C2×#88072C2211yescharacteristic
52C2×#88061C2211yescharacteristic
53C2×#88061C2211yescharacteristic
54C2×#88058C2211yescharacteristic, complemented
55C2×#88058C2211yescharacteristic, complemented
56C2×#88054C2211yescharacteristic, complemented
57C2×#88054C2211yescharacteristic, complemented
58#11718727C2218yescomplemented
59#11718669C2218yescomplemented
60C2×#88049C2211yescharacteristic
61C2×#88049C2211yescharacteristic
62C2×#88048C2211yescharacteristic, complemented
63C2×#88048C2211yescharacteristic, complemented
64C2×#88048C2211yescharacteristic, complemented
65C2×#88047C2211yescharacteristic, complemented
66C2×C4⋊#1055C2211yescharacteristic, complemented
67#11718552C2218yescomplemented
68#11718541C2218yescomplemented
69#11718531C2218yescomplemented
70#11718522C2218yescomplemented
71#11718507C2218yescomplemented
72#11718500C2218yescomplemented
73#11718431C2218yes—
74D13×#102C2218yes—
75#11718427C2218yescomplemented
76#11718420C2218yescomplemented
77C24×D13—21no—
78C22×D4×C13C2311yescharacteristic
79C23×C4×C13—21no—
80C22×C22⋊D13—21no—
81C23×Dic13—21no—
82C2×D4×D13—22no—
83C2×D4×D13—24no—
84C2×D4×D13Q818yescomplemented
85C2×D4×D13C2314yes—
86C22×D52C2311yescharacteristic
87C22×C4×D13—21no—
88C22×C4×D13—21no—
89C22×C4×D13—21no—
90C22×C4×D13C2311yescharacteristic
91C22×Dic26—21no—
92C22×Dic26—21no—
93C22×C8×C13C2311yescharacteristic
94C22×C8×C13C2311yescharacteristic
95C13×#125—22no—
96C13×#125C2314yescomplemented
97C4×D4×C13—22no—
98C4×D4×C13C2314yes—
99C2×C13×C4⋊C4—21no—
100C2×C13×C4⋊C4—21no—
101C2×C13×C4⋊C4C2311yescharacteristic
102C2×C13×C4⋊C4C2311yescharacteristic
103C2×C13×C4⋊C4C2311yescharacteristic
104C2×C13×C22⋊C4—21no—
105C2×C42×C13C2311yescharacteristic
106C2×C22⋊Dic13—21no—
107D4×Dic13—22no—
108D4×Dic13C2314yes—
109C4×C22⋊D13—28no—
110C2×#6103—21no—
111C2×#6103—21no—
112C2×#6103—21no—
113C2×#6103—21no—
114C2×#6103—28no—
115C2×#6103D411yescharacteristic
116C2×#6103D411yescharacteristic
117C2×C4⋊Dic13—21no—
118C2×C4⋊Dic13—21no—
119C2×C4⋊Dic13C2311yescharacteristic
120C2×C4⋊Dic13C2311yescharacteristic
121C2×C4⋊Dic13C2311yescharacteristic
122C2×#6101—21no—
123C2×#6101—21no—
124C2×#6101—21no—
125C2×#6101D411yescharacteristic
126C2×#6101D411yescharacteristic
127C2×C4×Dic13—21no—
128C2×C4×Dic13—21no—
129C2×C4×Dic13C2311yescharacteristic
130C22×#1055C2311yescharacteristic
131C22×#1055C2311yescharacteristic
132C2×#6094—24no—
133C2×#6094C2314yes—
134C2×C8×D13—24no—
135C2×C8×D13C2314yes—
136#88151—28no—
137#88150—28no—
138#88147—22no—
139#88147C2314yes—
140#88146—22no—
141#88146—22no—
142#88146C2314yes—
143#88146C2314yes—
144C4⋊C4×D13—22no—
145C4⋊C4×D13C2314yes—
146#88144—22no—
147#88144C2314yescomplemented
148#88143—28no—
149#88142—28no—
150#88142—22no—
151#88142C2314yescomplemented
152#88135—28no—
153C22⋊C4×D13—28no—
154C4×D52—22no—
155C4×D52C2314yes—
156#88126D414yes—
157#88126C2314yes—
158#88123—22no—
159#88123C2314yescomplemented
160C13×#107C2314yescomplemented
161C13×#106C2314yescomplemented
162C13×C4⋊C8C2314yescomplemented
163C13×#102C2314yes—
164C13×#102C2314yes—
165#88072C2314yes—
166#88072C2314yes—
167#88061C2314yes—
168#88061C2314yes—
169#88058C2314yescomplemented
170#88058C2314yescomplemented
171#88054C2314yescomplemented
172#88054C2314yescomplemented
173#88049C2314yes—
174#88049C2314yes—
175#88048C2314yescomplemented
176#88048C2314yescomplemented
177#88048C2314yescomplemented
178#88047C2314yescomplemented
179C4⋊#1055C2314yescomplemented
180C2×#3081—131nomaximal, Sylow
181C24×C13—21no—
182C23×D13—21no—
183C23×D13—28no—
184C23×D13—24no—
185C23×D13—82no—
186C23×D13—82no—
187C23×D13C2×D411yescharacteristic
188C2×D4×C13—21no—
189C2×D4×C13—22no—
190C2×D4×C13C2×Q814yes—
191C2×D4×C13C2412yes—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—24no—
196C22×C4×C13—82no—
197C22×C4×C13C2×D411yescharacteristic
198C22×C4×C13C2×D411yescharacteristic
199C22×C4×C13C2411yescharacteristic
200C2×C22⋊D13—28no—
201C2×C22⋊D13—24no—
202C22×Dic13—21no—
203C22×Dic13—21no—
204C22×Dic13—21no—
205C22×Dic13—24no—
206C22×Dic13—82no—
207C22×Dic13C2×D411yescharacteristic
208C22×Dic13C2×D411yescharacteristic
209C22×Dic13C2×D411yescharacteristic
210D4×D13—216no—
211D4×D13—28no—
212D4×D13C2×Q8116yescomplemented
213C2×D52—21no—
214C2×D52—22no—
215C2×D52C2×Q814yes—
216C2×D52C2412yes—
217C2×C4×D13—24no—
218C2×C4×D13—24no—
219C2×C4×D13—24no—
220C2×C4×D13—82no—
221C2×C4×D13—82no—
222C2×C4×D13—82no—
223C2×C4×D13C2×D412yes—
224C2×C4×D13C2×Q814yes—
225C2×C4×D13#4114yes—
226C2×C4×D13C2412yes—
227C2×Dic26—24no—
228C2×Dic26—24no—
229C2×Dic26—82no—
230C2×Dic26—82no—
231C2×C8×C13—22no—
232C2×C8×C13—22no—
233C2×C8×C13C2412yes—
234C2×C8×C13C2412yes—
235C13×C4⋊C4—21no—
236C13×C4⋊C4—24no—
237C13×C4⋊C4—24no—
238C13×C4⋊C4—21no—
239C13×C4⋊C4—21no—
240C13×C4⋊C4C2412yes—
241C13×C4⋊C4C2412yes—
242C13×C4⋊C4C2412yes—
243C13×C22⋊C4—24no—
244C42×C13C2×D412yes—
245C42×C13C2412yes—
246C22⋊Dic13—24no—
247#6103—24no—
248#6103—24no—
249#6103—24no—
250#6103—24no—
251#6103C2×D414yes—
252#6103C2×D414yes—
253C4⋊Dic13—21no—
254C4⋊Dic13—21no—
255C4⋊Dic13—24no—
256C4⋊Dic13—21no—
257C4⋊Dic13—24no—
258C4⋊Dic13C2412yes—
259C4⋊Dic13C2412yes—
260C4⋊Dic13C2412yes—
261#6101—24no—
262#6101—24no—
263#6101—24no—
264#6101C2×D414yes—
265#6101C2×D414yes—
266C4×Dic13—24no—
267C4×Dic13—24no—
268C4×Dic13C2×D412yes—
269C4×Dic13C2412yes—
270C2×#1055—22no—
271C2×#1055—22no—
272C2×#1055C2412yes—
273C2×#1055C2412yes—
274#6094—28no—
275C8×D13—28no—
276C2×#544—131no—
277C2×#518—131no—
278#3081—1316no—
279C2×#478—131no—
280C2×#478—131no—
281C2×#478—131no—
282C2×#478D1311yescharacteristic, complemented
283C2×#476—131no—
284C2×#476—131no—
285C2×#474—131no—
286C2×#474—131no—
287C2×#428—131no—
288C2×#427—131no—
289C2×#424—131no—
290C2×#418—131no—
291C22×#102—131no—
292C23×C13—24no—
293C23×C13—22no—
294C23×C13—42no—
295C23×C13—42no—
296C23×C13C22×D411yescharacteristic
297C22×D13—22no—
298C22×D13—22no—
299C22×D13—24no—
300C22×D13—22no—
301C22×D13—216no—
302C22×D13—42no—
303C22×D13—42no—
304C22×D13—816no—
305C22×D13—84no—
306C22×D13—84no—
307C22×D13C22⋊Q814yes—
308C22×D13C22×D412yes—
309D4×C13—24no—
310D4×C13—22no—
311D4×C13C22×Q814yes—
312C2×C4×C13—22no—
313C2×C4×C13—22no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—22no—
317C2×C4×C13—42no—
318C2×C4×C13—42no—
319C2×C4×C13—42no—
320C2×C4×C13—84no—
321C2×C4×C13C22×D412yes—
322C2×C4×C13C22×D412yes—
323C2×C4×C13C22×D411yescharacteristic
324C2×C4×C13C22×Q812yes—
325C2×C4×C13C2×#4112yes—
326C2×C4×C13C2511yescharacteristic
327C22⋊D13—216no—
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—22no—
331C2×Dic13—22no—
332C2×Dic13—22no—
333C2×Dic13—42no—
334C2×Dic13—42no—
335C2×Dic13—42no—
336C2×Dic13—84no—
337C2×Dic13C22⋊Q814yes—
338C2×Dic13C22×D412yes—
339C2×Dic13C22×D412yes—
340C2×Dic13C22×D412yes—
341D52—24no—
342D52—22no—
343D52C22×Q814yes—
344C4×D13—84no—
345C4×D13—84no—
346C4×D13—84no—
347C4×D13C22⋊Q818yes—
348C4×D13C22×Q814yes—
349C4×D13C2×#4114yes—
350Dic26—84no—
351Dic26—84no—
352C8×C13—22no—
353C8×C13—22no—
354#1055—22no—
355#1055—22no—
356C23×D4—131no—
357C22×M16—131no—
358C23×C8—131no—
359#544—138no—
360#544—264no—
361C2×C4⋊Q8—131no—
362C2×C4⋊Q8—131no—
363C2×C4⋊Q8—261no—
364C2×#125—131no—
365C2×#125—261no—
366C2×#125C2×D1311yescharacteristic, complemented
367C2×C22⋊Q8—261no—
368C2×C22⋊Q8—261no—
369#518—138no—
370#518—264no—
371C2×C4×D4—131no—
372C2×C4×D4—131no—
373C2×C4×D4—131no—
374C2×C4×D4—261no—
375C2×C4×D4—261no—
376C2×C4×D4C2×D1311yescharacteristic
377C2×#117—131no—
378C2×#117—131no—
379C2×#117—131no—
380C22×C4⋊C4—131no—
381C22×C22⋊C4—261no—
382C22×C22⋊C4—261no—
383#478—138no—
384#478—138no—
385#478—138no—
386#478C2×D1318yescomplemented
387#476—138no—
388#476—138no—
389#474—138no—
390#474—138no—
391#428—138no—
392#427—138no—
393C2×#107—131no—
394C2×#107—131no—
395C2×#107—131no—
396C2×#107C2×D1311yescharacteristic, complemented
397C2×#106—131no—
398C2×#106—131no—
399C2×#106—131no—
400C2×#106C2×D1311yescharacteristic, complemented
401#424—138no—
402C2×C4⋊C8—131no—
403C2×C4⋊C8—131no—
404C2×C4⋊C8—131no—
405C2×C4⋊C8C2×D1311yescharacteristic, complemented
406#418—138no—
407C2×#102—131no—
408C2×#102—131no—
409C2×#102—131no—
410C2×#102—131no—
411C2×#102—131no—
412C2×#102—131no—
413C2×#102—138no—
414C2×#102C2×D1311yescharacteristic
415C2×#102C2×D1311yescharacteristic
416C22×C13—24no—
417C22×C13—48no—
418C22×C13—42no—
419C22×C13—42no—
420C22×C13C2×C22⋊Q812yes—
421C22×C13#57612yes—
422C22×C13#57712yes—
423C22×C13C23×D411yescharacteristic
424C2×D13—28no—
425C2×D13—22no—
426C2×D13—22no—
427C2×D13—24no—
428C2×D13—48no—
429C2×D13—42no—
430C2×D13—42no—
431C2×D13—816no—
432C2×D13C2×C22⋊Q814yes—
433C4×C13—22no—
434C4×C13—22no—
435C4×C13—42no—
436C4×C13—42no—
437C4×C13—42no—
438C4×C13C2×C22⋊Q812yes—
439C4×C13C23×Q811yescharacteristic
440C4×C13C22×#4111yescharacteristic
441Dic13—22no—
442Dic13—22no—
443Dic13—42no—
444Dic13—42no—
445Dic13—42no—
446Dic13C2×C22⋊Q814yes—
447C25—261no—
448C22×Q8—261no—
449C22×Q8—261no—
450C22×D4—138no—
451C22×D4—134no—
452C22×D4—131no—
453C22×D4—262no—
454C22×D4—264no—
455C22×D4—261no—
456C22×D4C22×D1311yescharacteristic
457C23×C4—21no—
458C23×C4—131no—
459C23×C4—261no—
460C23×C4—261no—
461C23×C4—261no—
462C23×C4—261no—
463C2×M16—134no—
464C2×M16—264no—
465C22×C8—131no—
466C22×C8—131no—
467C22×C8—134no—
468C22×C8—264no—
469C22×C8C22×D1311yescharacteristic
470C22×C8C22×D1311yescharacteristic
471C4⋊Q8—134no—
472C4⋊Q8—134no—
473C4⋊Q8—262no—
474C4⋊Q8—268no—
475C4⋊Q8—262no—
476#125—22no—
477#125—134no—
478#125—262no—
479#125—268no—
480#125C22×D1314yescomplemented
481C22⋊Q8—268no—
482C22⋊Q8—268no—
483C4×D4—22no—
484C4×D4—134no—
485C4×D4—134no—
486C4×D4—134no—
487C4×D4—262no—
488C4×D4—262no—
489C4×D4—268no—
490C4×D4—268no—
491C4×D4—262no—
492C4×D4C22×D1314yes—
493#117—134no—
494#117—134no—
495#117—134no—
496#117—134no—
497#117—262no—
498#117—262no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—131no—
502C2×C4⋊C4—131no—
503C2×C4⋊C4—131no—
504C2×C4⋊C4—131no—
505C2×C4⋊C4—131no—
506C2×C4⋊C4—134no—
507C2×C4⋊C4—262no—
508C2×C4⋊C4—261no—
509C2×C4⋊C4—261no—
510C2×C4⋊C4—261no—
511C2×C4⋊C4—261no—
512C2×C4⋊C4—261no—
513C2×C4⋊C4C22×D1311yescharacteristic
514C2×C4⋊C4C22×D1311yescharacteristic
515C2×C4⋊C4C22×D1311yescharacteristic
516C2×C22⋊C4—21no—
517C2×C22⋊C4—131no—
518C2×C22⋊C4—131no—
519C2×C22⋊C4—268no—
520C2×C22⋊C4—268no—
521C2×C22⋊C4—261no—
522C2×C22⋊C4—261no—
523C2×C22⋊C4—261no—
524C2×C22⋊C4—261no—
525C2×C22⋊C4—261no—
526C2×C42—131no—
527C2×C42—261no—
528C2×C42—261no—
529C2×C42C22×D1311yescharacteristic
530#107—134no—
531#107—134no—
532#107—134no—
533#107C22×D1314yescomplemented
534#106—134no—
535#106—134no—
536#106—134no—
537#106C22×D1314yescomplemented
538C4⋊C8—134no—
539C4⋊C8—134no—
540C4⋊C8—134no—
541C4⋊C8C22×D1314yescomplemented
542#102—134no—
543#102—134no—
544#102—134no—
545#102—134no—
546#102—134no—
547#102—134no—
548#102C22×D1314yes—
549#102C22×D1314yes—
550C2×C13—44no—
551C2×C13#308114yescomplemented
552C2×C13C22×C22⋊Q811yescharacteristic
553C2×C13C2×#57611yescharacteristic
554C2×C13C2×#57711yescharacteristic
555D13—24no—
556D13—44no—
557C24—21no—
558C24—131no—
559C24—264no—
560C24—268no—
561C24—261no—
562C24—1042no—
563C24—1042no—
564C2×Q8—264no—
565C2×Q8—264no—
566C2×Q8—1042no—
567C2×Q8—1042no—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4—1316no—
571C2×D4—134no—
572C2×D4—132no—
573C2×D4—2616no—
574C2×D4—268no—
575C2×D4—264no—
576C2×D4—268no—
577C2×D4—261no—
578C2×D4—262no—
579C2×D4Q8×D1314yes—
580C2×D4C23×D1312yes—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—24no—
585C22×C4—82no—
586C22×C4—131no—
587C22×C4—132no—
588C22×C4—134no—
589C22×C4—134no—
590C22×C4—132no—
591C22×C4—131no—
592C22×C4—131no—
593C22×C4—264no—
594C22×C4—264no—
595C22×C4—264no—
596C22×C4—261no—
597C22×C4—261no—
598C22×C4—261no—
599C22×C4—264no—
600C22×C4—1042no—
601C22×C4—1042no—
602C22×C4—1042no—
603C22×C4—1042no—
604C22×C4D4×D1311yescharacteristic
605C22×C4D4×D1311yescharacteristic
606C22×C4C23×D1311yescharacteristic
607M16—268no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—132no—
611C2×C8—132no—
612C2×C8—268no—
613C2×C8—262no—
614C2×C8—262no—
615C2×C8C23×D1312yes—
616C2×C8C23×D1312yes—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—134no—
623C4⋊C4—134no—
624C4⋊C4—132no—
625C4⋊C4—132no—
626C4⋊C4—132no—
627C4⋊C4—264no—
628C4⋊C4—264no—
629C4⋊C4—264no—
630C4⋊C4—264no—
631C4⋊C4—261no—
632C4⋊C4—261no—
633C4⋊C4—261no—
634C4⋊C4—264no—
635C4⋊C4C23×D1312yes—
636C4⋊C4C23×D1312yes—
637C4⋊C4C23×D1312yes—
638C22⋊C4—24no—
639C22⋊C4—134no—
640C22⋊C4—134no—
641C22⋊C4—264no—
642C22⋊C4—264no—
643C22⋊C4—264no—
644C22⋊C4—264no—
645C22⋊C4—264no—
646C42—132no—
647C42—132no—
648C42—264no—
649C42—264no—
650C42D4×D1312yes—
651C42C23×D1312yes—
652C13C2×#308111yescharacteristic, complemented, Sylow
653C23—24no—
654C23—22no—
655C23—42no—
656C23—42no—
657C23—134no—
658C23—132no—
659C23—2616no—
660C23—262no—
661C23—262no—
662C23—264no—
663C23—262no—
664C23—522no—
665C23—522no—
666C23—10416no—
667C23—1044no—
668C23—1044no—
669C23C2×D4×D1311yescharacteristic
670Q8—1044no—
671Q8—1044no—
672D4—24no—
673D4—22no—
674D4—134no—
675D4—2616no—
676D4—264no—
677D4—262no—
678D4C2×Q8×D1314yes—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—84no—
688C2×C4—134no—
689C2×C4—132no—
690C2×C4—138no—
691C2×C4—134no—
692C2×C4—134no—
693C2×C4—132no—
694C2×C4—132no—
695C2×C4—262no—
696C2×C4—262no—
697C2×C4—262no—
698C2×C4—262no—
699C2×C4—262no—
700C2×C4—522no—
701C2×C4—522no—
702C2×C4—522no—
703C2×C4—1044no—
704C2×C4—1044no—
705C2×C4—1044no—
706C2×C4—1044no—
707C2×C4C2×D4×D1312yes—
708C2×C4C2×D4×D1312yes—
709C2×C4C2×D4×D1311yescharacteristic
710C2×C4C2×Q8×D1312yes—
711C2×C4#41×D1312yes—
712C2×C4C24×D1311yescharacteristic
713C8—22no—
714C8—22no—
715C8—262no—
716C8—262no—
717C22—24no—
718C22—48no—
719C22—42no—
720C22—42no—
721C22—134no—
722C22—268no—
723C22—262no—
724C22—262no—
725C22—264no—
726C22—528no—
727C22—522no—
728C22—522no—
729C22—10416no—
730C22D13×C22⋊Q812yes—
731C22#1171947412yes—
732C22#1171948012yes—
733C22C22×D4×D1311yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—134no—
740C4—262no—
741C4—262no—
742C4—522no—
743C4—522no—
744C4—522no—
745C4D13×C22⋊Q812yes—
746C4C22×Q8×D1311yescharacteristic
747C4C2×#41×D1311yescharacteristic
748C2—44no—
749C2—264no—
750C2—524no—
751C2#1312466414yesdirect product factor
752C2C2×D13×C22⋊Q811yescharacteristic
753C2C2×#1171947411yescharacteristic
754C2C2×#1171948011yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#478C2
socleC23×C13C22×D4
prime radicalC22×D4×D13C22
hypercenterC2×#478D13
hypocenterC13C2×#3081
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#11719394C2semidirect
3. #13124664C2direct (N × H)
4. C2×#11718552C2semidirect
5. C2×#11718427C2semidirect
6. C2×#11718727C2semidirect
7. C2×#11718669C2semidirect
8. C2×#11718531C2semidirect
9. C2×#11718507C2semidirect
10. C2×#11718420C2semidirect
11. C2×#11718522C2semidirect
12. C2×#11718541C2semidirect
13. C2×#11718500C2semidirect
16. C2×C13×#478C2semidirect
18. C2×C13×#125C22semidirect
26. #11719394C22semidirect
35. C2×#88144C22semidirect
38. C2×#88142C22semidirect
43. C2×#88123C22semidirect
44. C13×#478C22semidirect
45. C2×C13×#107C22semidirect
46. C2×C13×#106C22semidirect
47. C2×C13×C4⋊C8C22semidirect
54. C2×#88058C22semidirect
55. C2×#88058C22semidirect
56. C2×#88054C22semidirect
57. C2×#88054C22semidirect
58. #11718727C22semidirect
59. #11718669C22semidirect
62. C2×#88048C22semidirect
63. C2×#88048C22semidirect
64. C2×#88048C22semidirect
65. C2×#88047C22semidirect
66. C2×C4⋊#1055C22semidirect
67. #11718552C22semidirect
68. #11718541C22semidirect
69. #11718531C22semidirect
70. #11718522C22semidirect
71. #11718507C22semidirect
72. #11718500C22semidirect
75. #11718427C22semidirect
76. #11718420C22semidirect
84. C2×D4×D13Q8semidirect
96. C13×#125C23semidirect
147. #88144C23semidirect
151. #88142C23semidirect
159. #88123C23semidirect
160. C13×#107C23semidirect
161. C13×#106C23semidirect
162. C13×C4⋊C8C23semidirect
169. #88058C23semidirect
170. #88058C23semidirect
171. #88054C23semidirect
172. #88054C23semidirect
175. #88048C23semidirect
176. #88048C23semidirect
177. #88048C23semidirect
178. #88047C23semidirect
179. C4⋊#1055C23semidirect
212. D4×D13C2×Q8semidirect
282. C2×#478D13semidirect
366. C2×#125C2×D13semidirect
386. #478C2×D13semidirect
396. C2×#107C2×D13semidirect
400. C2×#106C2×D13semidirect
405. C2×C4⋊C8C2×D13semidirect
480. #125C22×D13semidirect
533. #107C22×D13semidirect
537. #106C22×D13semidirect
541. C4⋊C8C22×D13semidirect
551. C2×C13#3081semidirect
652. C13C2×#3081semidirect
751. C2#13124664direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193942
C2×#117192502
#131246642
C2×#117185522
C2×#117184272
C2×#117187272
C2×#117186692
C2×#117185312
C2×#117185072
C2×#117184202
C2×#117185222
C2×#117185412
C2×#117185002
C2×#117184312
C2×D13×#1022
C2×C13×#4782
C2×#308113