Finite Group Databasebeta

← C2×#13127001 #16739535

Subgroups — C2×#13127001 #16739535

Order 3328.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic26C211yesmaximal, characteristic, complemented
2#13127001C2116yesmaximal, direct product factor
3C2×#11718730C211yesmaximal, characteristic, complemented
4C2×#11718631C211yesmaximal, characteristic, complemented
5C2×#11718657C211yesmaximal, characteristic, complemented
6C2×#11718724C211yesmaximal, characteristic, complemented
7C2×#11718703C211yesmaximal, characteristic, complemented
8C2×#11718702C211yesmaximal, characteristic, complemented
9C2×#11718680C211yesmaximal, characteristic, complemented
10C2×#11718701C211yesmaximal, characteristic, complemented
11C2×#11718701C211yesmaximal, characteristic, complemented
12C2×#11718679C211yesmaximal, characteristic, complemented
13C2×#11718672C211yesmaximal, characteristic, complemented
14C2×#11718665C211yesmaximal, characteristic, complemented
15C22×#88050C211yesmaximal, characteristic, complemented
16C2×C13×#553C211yesmaximal, characteristic
17C23×Dic26C2211yescharacteristic
18C23×Dic26C2211yescharacteristic
19C13×#553—24no—
20C13×#553C2218yes—
21C2×C13×#126—21no—
22C2×C13×#125C2211yescharacteristic
23C2×C13×#123—21no—
24C2×C13×#121—21no—
25C2×C13×#121C2211yescharacteristic
26C2×C13×#121C2211yescharacteristic
27C2×C4×D4×C13—21no—
28C2×C4×D4×C13C2211yescharacteristic
29C2×C4×D4×C13C2211yescharacteristic
30C2×C13×#117C2211yescharacteristic
31C22×C13×C4⋊C4C2211yescharacteristic
32C2×D4×Dic13—21no—
33C22×#6105C2211yescharacteristic
34C22×#6105C2211yescharacteristic
35C22×#6105C2211yescharacteristic
36C2×#88178C2211yescharacteristic
37C2×#88178C2211yescharacteristic
38C22×#6099C2211yescharacteristic
39C23×#1055C2211yescharacteristic
40D4×Dic26—24no—
41D4×Dic26C2218yescomplemented
42C2×#88142—21no—
43C2×#88132—21no—
44C2×#88132—21no—
45C2×#88123C2211yescharacteristic
46C2×C4×Dic26C2211yescharacteristic
47C2×#88072C2211yescharacteristic
48C2×C22⋊#1055C2211yescharacteristic
49C2×C22⋊#1055C2211yescharacteristic
50#11718730C2218yescomplemented
51#11718724C2218yescomplemented
52#11718703C2218yescomplemented
53#11718702C2218yescomplemented
54#11718701C2218yescomplemented
55#11718701C2218yescomplemented
56#11718680C2218yescomplemented
57#11718679C2218yescomplemented
58#11718672C2218yescomplemented
59#11718665C2218yescomplemented
60#11718657C2218yescomplemented
61#11718631C2218yescomplemented
62C2×#88050C2211yescharacteristic
63C2×#88050C2211yescharacteristic
64C2×#88050C2211yescharacteristic
65C2×#88050C2211yescharacteristic
66C2×#88050C2211yescharacteristic
67C2×#88050C2211yescharacteristic
68C2×#88050C2211yescharacteristic
69C2×#88050C2211yescharacteristic
70C2×#88050C2211yescharacteristic
71C2×#88050C2218yescomplemented
72C2×#88048C2211yescharacteristic
73C2×#88047C2211yescharacteristic
74C2×#88047C2211yescharacteristic
75C2×C4⋊#1055C2211yescharacteristic
76C2×#88043C2211yescharacteristic
77C22×D4×C13—21no—
78C22×D4×C13—21no—
79C22×D4×C13D411yescharacteristic
80C22×D4×C13C2311yescharacteristic
81C23×C4×C13—21no—
82C23×C4×C13—21no—
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C23×Dic13—21no—
86C23×Dic13—21no—
87C22×Dic26—24no—
88C22×Dic26—24no—
89C22×Dic26—21no—
90C22×Dic26—21no—
91C22×Dic26—22no—
92C22×Dic26—22no—
93C22×Dic26—42no—
94C22×Dic26—42no—
95C22×Dic26C2311yescharacteristic
96C22×Dic26C2311yescharacteristic
97C22×Dic26C2314yes—
98C22×Dic26C2314yes—
99C22×Dic26C2311yescharacteristic
100C13×#126—28no—
101C13×#125—22no—
102C13×#125C2314yes—
103C13×#123—28no—
104C13×#121—28no—
105C13×#121—22no—
106C13×#121—22no—
107C13×#121C2314yes—
108C13×#121C2314yes—
109C4×D4×C13—28no—
110C4×D4×C13—22no—
111C4×D4×C13D414yes—
112C4×D4×C13C2314yes—
113C4×D4×C13C2314yes—
114C13×#117—22no—
115C13×#117C2314yes—
116C2×C13×C4⋊C4—21no—
117C2×C13×C4⋊C4—22no—
118C2×C13×C4⋊C4—21no—
119C2×C13×C4⋊C4—21no—
120C2×C13×C4⋊C4D411yescharacteristic
121C2×C13×C4⋊C4C2311yescharacteristic
122C2×C13×C4⋊C4C2311yescharacteristic
123C2×C13×C4⋊C4C2314yes—
124C2×C13×C4⋊C4C2311yescharacteristic
125C2×C13×C22⋊C4—21no—
126C2×C13×C22⋊C4—21no—
127C2×C13×C22⋊C4—21no—
128C2×C13×C22⋊C4—21no—
129C2×C13×C22⋊C4D411yescharacteristic
130C2×C13×C22⋊C4D411yescharacteristic
131C2×C42×C13—21no—
132C2×C42×C13C2311yescharacteristic
133C2×C22⋊Dic13—21no—
134C2×C22⋊Dic13—21no—
135D4×Dic13—28no—
136C2×#6105—24no—
137C2×#6105—42no—
138C2×#6105—42no—
139C2×#6105C2314yes—
140C2×#6105C2314yes—
141C2×#6105C2314yes—
142C2×C4⋊Dic13—21no—
143C2×C4⋊Dic13—21no—
144C2×C4⋊Dic13C2311yescharacteristic
145#88178—22no—
146#88178—22no—
147#88178C2314yes—
148#88178C2314yes—
149C2×#6101—21no—
150C2×#6101—21no—
151C2×#6101—21no—
152C2×C4×Dic13—21no—
153C2×#6099—42no—
154C2×#6099C2314yes—
155C22×#1055—42no—
156C22×#1055C2311yescharacteristic
157C22×#1055C2311yescharacteristic
158C22×#1055C2311yescharacteristic
159C22×#1055C2311yescharacteristic
160C22×#1055C2314yes—
161#88142—28no—
162#88132—28no—
163#88132—28no—
164#88123—22no—
165#88123C2314yes—
166C4×Dic26—22no—
167C4×Dic26C2314yes—
168#88072C2314yes—
169C22⋊#1055C2314yes—
170C22⋊#1055C2314yes—
171#88050C2314yes—
172#88050C2314yes—
173#88050C2314yes—
174#88050C2314yes—
175#88050C2314yes—
176#88050C2314yes—
177#88050C2314yes—
178#88050C2314yes—
179#88050C2314yes—
180#88048C2314yes—
181#88047C2314yes—
182#88047C2314yes—
183C4⋊#1055C2314yes—
184#88043C2314yes—
185C2×#3320—131nomaximal, Sylow
186C24×C13—21no—
187C24×C13C2×D411yescharacteristic
188C24×C13C2×D411yescharacteristic
189C2×D4×C13—24no—
190C2×D4×C13—24no—
191C2×D4×C13—24no—
192C2×D4×C13—21no—
193C2×D4×C13—22no—
194C2×D4×C13—22no—
195C2×D4×C13—44no—
196C2×D4×C13—82no—
197C2×D4×C13C2×D414yes—
198C2×D4×C13C2412yes—
199C22×C4×C13—22no—
200C22×C4×C13—22no—
201C22×C4×C13—22no—
202C22×C4×C13—22no—
203C22×C4×C13—21no—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13—24no—
207C22×C4×C13—24no—
208C22×C4×C13—82no—
209C22×C4×C13—82no—
210C22×C4×C13C2×D411yescharacteristic
211C22×C4×C13C2×D411yescharacteristic
212C22×C4×C13C2×D411yescharacteristic
213C22×C4×C13C2×D411yescharacteristic
214C22×C4×C13C2×D412yes—
215C22×C4×C13C2×D412yes—
216C22×C4×C13C2412yes—
217C22×C4×C13C2412yes—
218C22×C4×C13C2411yescharacteristic
219C22×Dic13—21no—
220C22×Dic13—24no—
221C22×Dic13—24no—
222C22×Dic13—21no—
223C22×Dic13—21no—
224C22×Dic13—21no—
225C22×Dic13—44no—
226C22×Dic13—44no—
227C2×Dic26—21no—
228C2×Dic26—22no—
229C2×Dic26—22no—
230C2×Dic26—22no—
231C2×Dic26—22no—
232C2×Dic26—22no—
233C2×Dic26—28no—
234C2×Dic26—28no—
235C2×Dic26—21no—
236C2×Dic26—21no—
237C2×Dic26—24no—
238C2×Dic26—24no—
239C2×Dic26—44no—
240C2×Dic26—44no—
241C2×Dic26—48no—
242C2×Dic26—48no—
243C2×Dic26—44no—
244C2×Dic26—44no—
245C2×Dic26#4114yes—
246C2×Dic26C2412yes—
247C2×Dic26C2412yes—
248C2×Dic26C2412yes—
249C13×C4⋊C4—21no—
250C13×C4⋊C4—21no—
251C13×C4⋊C4—24no—
252C13×C4⋊C4—24no—
253C13×C4⋊C4—24no—
254C13×C4⋊C4—21no—
255C13×C4⋊C4C2×D414yes—
256C13×C4⋊C4C2412yes—
257C13×C4⋊C4C2412yes—
258C13×C4⋊C4C2412yes—
259C13×C22⋊C4—24no—
260C13×C22⋊C4—24no—
261C13×C22⋊C4—24no—
262C13×C22⋊C4—24no—
263C13×C22⋊C4C2×D414yes—
264C13×C22⋊C4C2×D414yes—
265C42×C13—24no—
266C42×C13C2×D412yes—
267C42×C13C2412yes—
268C22⋊Dic13—24no—
269C22⋊Dic13—24no—
270#6105—28no—
271#6105—44no—
272#6105—44no—
273C4⋊Dic13—21no—
274C4⋊Dic13—24no—
275C4⋊Dic13—24no—
276C4⋊Dic13C2412yes—
277#6101—24no—
278#6101—24no—
279#6101—24no—
280C4×Dic13—24no—
281#6099—44no—
282C2×#1055—22no—
283C2×#1055—22no—
284C2×#1055—22no—
285C2×#1055—22no—
286C2×#1055—44no—
287C2×#1055C2412yes—
288C2×#1055C2412yes—
289C2×#1055C2412yes—
290C2×#1055C2412yes—
291C2×#553D1311yescharacteristic
292C2×D4×Q8—131no—
293#3320—1316no—
294C2×#491—131no—
295C2×#484—131no—
296C2×#485—131no—
297C2×#479—131no—
298C2×#468—131no—
299C2×#465—131no—
300C2×#461—131no—
301C2×#448—131no—
302C2×#448—131no—
303C2×#440—131no—
304C2×#435—131no—
305C2×#419—131no—
306C22×#103—131no—
307C23×C13—22no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—42no—
314C23×C13—42no—
315C23×C13—42no—
316C23×C13#13714yes—
317C23×C13C22×D412yes—
318C23×C13C22×D412yes—
319C23×C13C22×D411yescharacteristic
320D4×C13—28no—
321D4×C13—22no—
322D4×C13—22no—
323D4×C13—48no—
324D4×C13—42no—
325D4×C13—84no—
326C2×C4×C13—22no—
327C2×C4×C13—22no—
328C2×C4×C13—22no—
329C2×C4×C13—22no—
330C2×C4×C13—24no—
331C2×C4×C13—24no—
332C2×C4×C13—22no—
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
337C2×C4×C13—22no—
338C2×C4×C13—22no—
339C2×C4×C13—42no—
340C2×C4×C13—42no—
341C2×C4×C13—42no—
342C2×C4×C13—84no—
343C2×C4×C13—84no—
344C2×C4×C13C22×D412yes—
345C2×C4×C13C22×D412yes—
346C2×C4×C13C22×D412yes—
347C2×C4×C13C22×D412yes—
348C2×C4×C13C22×D411yescharacteristic
349C2×C4×C13C2×#4112yes—
350C2×C4×C13H(5,𝔽2)12yes—
351C2×C4×C13C2511yescharacteristic
352C2×Dic13—24no—
353C2×Dic13—22no—
354C2×Dic13—22no—
355C2×Dic13—22no—
356C2×Dic13—22no—
357C2×Dic13—48no—
358C2×Dic13—48no—
359C2×Dic13—42no—
360C2×Dic13—42no—
361C2×Dic13—42no—
362Dic26—24no—
363Dic26—22no—
364Dic26—22no—
365Dic26—22no—
366Dic26—22no—
367Dic26—22no—
368Dic26—48no—
369Dic26—48no—
370Dic26—42no—
371Dic26—42no—
372Dic26C2×#4114yes—
373#1055—22no—
374#1055—22no—
375#1055—22no—
376#1055—22no—
377C23×Q8—131no—
378C23×Q8—131no—
379C22×SD16—131no—
380C22×SD16—131no—
381C22×SD16—131no—
382C22×M16—131no—
383C23×C8—131no—
384#553—24no—
385#553C2×D1318yes—
386D4×Q8—138no—
387D4×Q8—264no—
388C2×C4⋊Q8—131no—
389C2×C4⋊Q8—261no—
390C2×#126—21no—
391C2×#125C2×D1311yescharacteristic
392C2×#123—21no—
393C2×C22⋊Q8—131no—
394C2×C22⋊Q8—131no—
395C2×C22⋊Q8—261no—
396C2×C22⋊Q8—261no—
397C2×#121—21no—
398C2×#121C2×D1311yescharacteristic
399C2×#121C2×D1311yescharacteristic
400C2×C4×Q8—131no—
401C2×C4×D4—21no—
402C2×C4×D4—261no—
403C2×C4×D4C2×D1311yescharacteristic
404C2×C4×D4C2×D1311yescharacteristic
405C2×#117C2×D1311yescharacteristic
406C22×C4⋊C4C2×D1311yescharacteristic
407#491—138no—
408#485—138no—
409#484—138no—
410#479—138no—
411#468—138no—
412#465—138no—
413#461—138no—
414#448—138no—
415#448—138no—
416#440—138no—
417#435—138no—
418C2×#107—131no—
419C2×#107—131no—
420C2×#106—131no—
421C2×C4⋊C8—131no—
422#419—138no—
423C2×#103—131no—
424C2×#103—131no—
425C2×#103—131no—
426C2×#103—131no—
427C2×#103—131no—
428C2×#103—131no—
429C2×#103—131no—
430C2×#103—131no—
431C2×#103—131no—
432C2×#103—138no—
433C2×#102—131no—
434C2×C22⋊C8—131no—
435C2×C22⋊C8—131no—
436C2×#97—131no—
437C22×C13—22no—
438C22×C13—28no—
439C22×C13—22no—
440C22×C13—22no—
441C22×C13—22no—
442C22×C13—22no—
443C22×C13—44no—
444C22×C13—42no—
445C22×C13—42no—
446C22×C13—42no—
447C22×C13—84no—
448C22×C13#54612yes—
449C22×C13C2×#13714yes—
450C22×C13C2×#13712yes—
451C22×C13#57712yes—
452C22×C13C23×D411yescharacteristic
453C4×C13—22no—
454C4×C13—22no—
455C4×C13—22no—
456C4×C13—22no—
457C4×C13—42no—
458C4×C13—42no—
459C4×C13—42no—
460C4×C13#54612yes—
461C4×C13C22×#4111yescharacteristic
462C4×C13C2×H(5,𝔽2)11yescharacteristic
463Dic13—24no—
464Dic13—42no—
465Dic13—42no—
466Dic13—42no—
467C22×Q8—131no—
468C22×Q8—131no—
469C22×Q8—131no—
470C22×Q8—134no—
471C22×Q8—134no—
472C22×Q8—264no—
473C22×Q8—264no—
474C22×Q8—261no—
475C22×Q8—261no—
476C22×Q8—262no—
477C22×Q8—262no—
478C22×Q8—522no—
479C22×Q8—522no—
480C22×D4—21no—
481C22×D4—21no—
482C22×D4C22⋊D1311yescharacteristic
483C22×D4C22×D1311yescharacteristic
484C23×C4—21no—
485C23×C4—21no—
486C23×C4—261no—
487C23×C4—261no—
488C23×C4C22×D1311yescharacteristic
489C23×C4C22×D1311yescharacteristic
490C2×SD16—134no—
491C2×SD16—134no—
492C2×SD16—134no—
493C2×SD16—264no—
494C2×SD16—522no—
495C2×SD16—522no—
496C2×M16—134no—
497C2×M16—522no—
498C22×C8—131no—
499C22×C8—131no—
500C22×C8—131no—
501C22×C8—131no—
502C22×C8—134no—
503C22×C8—522no—
504C4⋊Q8—134no—
505C4⋊Q8—268no—
506C4⋊Q8—262no—
507#126—28no—
508#125—22no—
509#125C22×D1314yes—
510#123—28no—
511C22⋊Q8—134no—
512C22⋊Q8—134no—
513C22⋊Q8—262no—
514C22⋊Q8—262no—
515C22⋊Q8—268no—
516C22⋊Q8—268no—
517#121—28no—
518#121—22no—
519#121—22no—
520#121C22×D1314yes—
521#121C22×D1314yes—
522C4×Q8—134no—
523C4×Q8—262no—
524C4×D4—28no—
525C4×D4—22no—
526C4×D4—268no—
527C4×D4C22⋊D1314yes—
528C4×D4C22×D1314yes—
529C4×D4C22×D1314yes—
530#117—22no—
531#117C22×D1314yes—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—131no—
537C2×C4⋊C4—261no—
538C2×C4⋊C4—261no—
539C2×C4⋊C4—261no—
540C2×C4⋊C4—261no—
541C2×C4⋊C4—261no—
542C2×C4⋊C4C22⋊D1311yescharacteristic
543C2×C4⋊C4C22×D1311yescharacteristic
544C2×C4⋊C4C22×D1311yescharacteristic
545C2×C4⋊C4C22×D1314yes—
546C2×C4⋊C4C22×D1311yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—261no—
552C2×C22⋊C4—261no—
553C2×C22⋊C4C22⋊D1311yescharacteristic
554C2×C22⋊C4C22⋊D1311yescharacteristic
555C2×C42—21no—
556C2×C42—261no—
557C2×C42C22×D1311yescharacteristic
558#107—134no—
559#107—134no—
560#106—134no—
561C4⋊C8—134no—
562#103—134no—
563#103—134no—
564#103—134no—
565#103—134no—
566#103—134no—
567#103—134no—
568#103—134no—
569#103—134no—
570#103—134no—
571#102—134no—
572C22⋊C8—134no—
573C22⋊C8—134no—
574#97—134no—
575C2×C13—24no—
576C2×C13—42no—
577C2×C13—82no—
578C2×C13#332014yescomplemented
579C2×C13C2×#54611yescharacteristic
580C2×C13C22×#13711yescharacteristic
581C2×C13C2×#57711yescharacteristic
582C24—21no—
583C24C2×C22⋊D1311yescharacteristic
584C24C2×C22⋊D1311yescharacteristic
585C2×Q8—134no—
586C2×Q8—132no—
587C2×Q8—132no—
588C2×Q8—132no—
589C2×Q8—268no—
590C2×Q8—268no—
591C2×Q8—262no—
592C2×Q8—261no—
593C2×Q8—264no—
594C2×Q8—264no—
595C2×Q8—261no—
596C2×Q8—261no—
597C2×Q8—262no—
598C2×Q8—262no—
599C2×Q8—262no—
600C2×Q8—262no—
601C2×Q8—524no—
602C2×Q8—524no—
603C2×Q8—524no—
604C2×Q8—524no—
605C2×Q8—528no—
606C2×Q8—528no—
607C2×D4—24no—
608C2×D4—24no—
609C2×D4—24no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—44no—
614C2×D4—82no—
615C2×D4C2×C22⋊D1314yes—
616C2×D4C23×D1312yes—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—24no—
625C22×C4—24no—
626C22×C4—82no—
627C22×C4—82no—
628C22×C4—261no—
629C22×C4—264no—
630C22×C4—264no—
631C22×C4—261no—
632C22×C4—261no—
633C22×C4—261no—
634C22×C4—524no—
635C22×C4—524no—
636C22×C4C2×C22⋊D1312yes—
637C22×C4C2×C22⋊D1312yes—
638C22×C4C2×C22⋊D1311yescharacteristic
639C22×C4C2×C22⋊D1311yescharacteristic
640C22×C4C2×C22⋊D1311yescharacteristic
641C22×C4C2×C22⋊D1311yescharacteristic
642C22×C4C23×D1312yes—
643C22×C4C23×D1312yes—
644C22×C4C23×D1311yescharacteristic
645SD16—268no—
646SD16—524no—
647SD16—524no—
648M16—524no—
649C2×C8—132no—
650C2×C8—132no—
651C2×C8—132no—
652C2×C8—132no—
653C2×C8—262no—
654C2×C8—262no—
655C2×C8—262no—
656C2×C8—262no—
657C2×C8—524no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—24no—
661C4⋊C4—24no—
662C4⋊C4—24no—
663C4⋊C4—21no—
664C4⋊C4—132no—
665C4⋊C4—261no—
666C4⋊C4—264no—
667C4⋊C4—264no—
668C4⋊C4—264no—
669C4⋊C4—264no—
670C4⋊C4—264no—
671C4⋊C4C2×C22⋊D1314yes—
672C4⋊C4C23×D1312yes—
673C4⋊C4C23×D1312yes—
674C4⋊C4C23×D1312yes—
675C22⋊C4—24no—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—24no—
679C22⋊C4—264no—
680C22⋊C4—264no—
681C22⋊C4C2×C22⋊D1314yes—
682C22⋊C4C2×C22⋊D1314yes—
683C42—24no—
684C42—264no—
685C42C2×C22⋊D1312yes—
686C42C23×D1312yes—
687C13C2×#332011yescharacteristic, complemented, Sylow
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23#8820514yes—
698C23C22×C22⋊D1312yes—
699C23C22×C22⋊D1312yes—
700C23C22×C22⋊D1311yescharacteristic
701Q8—134no—
702Q8—264no—
703Q8—262no—
704Q8—262no—
705Q8—262no—
706Q8—262no—
707Q8—262no—
708Q8—528no—
709Q8—528no—
710Q8—522no—
711Q8—522no—
712D4—28no—
713D4—22no—
714D4—22no—
715D4—48no—
716D4—42no—
717D4—84no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—84no—
735C2×C4—84no—
736C2×C4—264no—
737C2×C4—262no—
738C2×C4—262no—
739C2×C4—262no—
740C2×C4—262no—
741C2×C4—528no—
742C2×C4—528no—
743C2×C4—522no—
744C2×C4—522no—
745C2×C4—522no—
746C2×C4#41×D1312yes—
747C2×C4#8825612yes—
748C2×C4C22×C22⋊D1312yes—
749C2×C4C22×C22⋊D1312yes—
750C2×C4C22×C22⋊D1312yes—
751C2×C4C22×C22⋊D1312yes—
752C2×C4C22×C22⋊D1311yescharacteristic
753C2×C4C24×D1311yescharacteristic
754C8—262no—
755C8—262no—
756C8—262no—
757C8—262no—
758C22—22no—
759C22—28no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—44no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—84no—
769C22C2×#8820514yes—
770C22C2×#8820512yes—
771C22#1171953412yes—
772C22#1171954112yes—
773C22C23×C22⋊D1311yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—264no—
782C4—522no—
783C4—522no—
784C4—522no—
785C4#1171953412yes—
786C4C2×#41×D1311yescharacteristic
787C4C2×#8825611yescharacteristic
788C2—24no—
789C2—42no—
790C2—82no—
791C2#1312700114yesdirect product factor
792C2C2×#1171953411yescharacteristic
793C2C22×#8820511yescharacteristic
794C2C2×#1171954111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
Fitting, prime radicalC2×C13×#553C2
socleC23×C13C22×D4
hypercenterC2×#553D13
hypocenterC13C2×#3320
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic26C2semidirect
2. #13127001C2direct (N × H)
3. C2×#11718730C2semidirect
4. C2×#11718631C2semidirect
5. C2×#11718657C2semidirect
6. C2×#11718724C2semidirect
7. C2×#11718703C2semidirect
8. C2×#11718702C2semidirect
9. C2×#11718680C2semidirect
10. C2×#11718701C2semidirect
11. C2×#11718701C2semidirect
12. C2×#11718679C2semidirect
13. C2×#11718672C2semidirect
14. C2×#11718665C2semidirect
15. C22×#88050C2semidirect
41. D4×Dic26C22semidirect
50. #11718730C22semidirect
51. #11718724C22semidirect
52. #11718703C22semidirect
53. #11718702C22semidirect
54. #11718701C22semidirect
55. #11718701C22semidirect
56. #11718680C22semidirect
57. #11718679C22semidirect
58. #11718672C22semidirect
59. #11718665C22semidirect
60. #11718657C22semidirect
61. #11718631C22semidirect
71. C2×#88050C22semidirect
578. C2×C13#3320semidirect
687. C13C2×#3320semidirect
791. C2#13127001direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×Dic262
#131270012
C2×#117187302
C2×#117186312
C2×#117186572
C2×#117187242
C2×#117187032
C2×#117187022
C2×#117186802
C2×#117187012
C2×#117186792
C2×#117186722
C2×#117186652
C22×#880502
C2×C13×#5532
C2×#332013