Finite Group Databasebeta

← C2×#13124842 #16730921

Subgroups — C2×#13124842 #16730921

Order 3328.

2570 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719283C211yesmaximal, characteristic, complemented
2C2×C4×D4×D13C211yesmaximal, characteristic
3#13124842C2116yesmaximal, direct product factor
4C2×#11718523C211yesmaximal, characteristic, complemented
5C2×#11718466C211yesmaximal, characteristic, complemented
6C2×#11718531C211yesmaximal, characteristic, complemented
7C2×#11718422C211yesmaximal, characteristic, complemented
8C2×#11718479C211yesmaximal, characteristic, complemented
9C2×#11718823C211yesmaximal, characteristic, complemented
10C2×#11718437C211yesmaximal, characteristic
11C2×#11718830C211yesmaximal, characteristic
12C2×C4×#6095C211yesmaximal, characteristic, complemented
13C2×C4×#6106C211yesmaximal, characteristic, complemented
14C2×C4×#6105C211yesmaximal, characteristic, complemented
15C2×#11718346C211yesmaximal, characteristic, complemented
16C2×C4×C13×SD16C211yesmaximal, characteristic, complemented
17C22×D4×D13C2211yescharacteristic
18C23×C4×D13—21no—
19C22×C13×SD16C2211yescharacteristic
20C2×C4×Q8×C13C2211yescharacteristic, complemented
21C2×C4×D4×C13C2211yescharacteristic
22C2×#88200C2211yescharacteristic
23C2×#88198C2211yescharacteristic, complemented
24C22×#6106C2211yescharacteristic
25C2×D4×Dic13C2211yescharacteristic
26C22×#6105C2211yescharacteristic
27C2×C4×C22⋊D13—21no—
28C22×#6095C2211yescharacteristic
29#11719283—24no—
30#11719283C2218yescomplemented
31C4×D4×D13—24no—
32C4×D4×D13C2218yes—
33C2×#88151C2211yescharacteristic
34C2×#88150—21no—
35C2×#88147C2211yescharacteristic
36C2×C4⋊C4×D13C2211yescharacteristic
37C2×#88143—21no—
38C2×#88142C2211yescharacteristic, complemented
39C2×#88135—21no—
40C2×C22⋊C4×D13—21no—
41C2×C4×D52C2211yescharacteristic
42C2×#88126—21no—
43C2×C42×D13C2211yescharacteristic
44C2×C4×Dic26—21no—
45C2×C4×Dic26C2211yescharacteristic, complemented
46C4×C13×SD16C2218yescomplemented
47C2×C13×#106C2211yescharacteristic, complemented
48C2×C13×#103C2211yescharacteristic, complemented
49C2×C13×#102C2211yescharacteristic
50C2×C4×C8×C13C2211yescharacteristic, complemented
51C2×#88075C2211yescharacteristic, complemented
52C2×#88072C2211yescharacteristic
53#11718830C2218yes—
54#11718823C2218yescomplemented
55C2×#88061C2211yescharacteristic
56C2×#88060C2211yescharacteristic
57C2×#88060C2211yescharacteristic
58C2×#88057C2211yescharacteristic, complemented
59C2×#88056C2211yescharacteristic, complemented
60C2×#88054C2211yescharacteristic, complemented
61C2×#88054C2211yescharacteristic, complemented
62C4×#6106C2218yescomplemented
63C4×#6105C2218yescomplemented
64C2×#88050C2211yescharacteristic, complemented
65C2×#88049C2211yescharacteristic
66C2×#88048C2211yescharacteristic, complemented
67C2×#88048C2211yescharacteristic, complemented
68C2×C4×#1055C2211yescharacteristic, complemented
69#11718531C2218yescomplemented
70#11718523C2218yescomplemented
71#11718479C2218yescomplemented
72#11718466C2218yescomplemented
73#11718437C2218yes—
74#11718422C2218yescomplemented
75C4×#6095C2218yescomplemented
76#11718346C2218yescomplemented
77C24×D13—21no—
78C22×Q8×C13C2311yescharacteristic
79C22×D4×C13C2311yescharacteristic
80C23×C4×C13—21no—
81C22×C22⋊D13—21no—
82C23×Dic13—21no—
83C2×D4×D13—24no—
84C2×D4×D13—24no—
85C2×D4×D13—22no—
86C2×D4×D13C2314yes—
87C22×D52C2311yescharacteristic
88C22×C4×D13—21no—
89C22×C4×D13—21no—
90C22×C4×D13—21no—
91C22×C4×D13—28no—
92C22×C4×D13—48no—
93C22×C4×D13D411yescharacteristic
94C22×C4×D13D411yescharacteristic
95C22×C4×D13C2311yescharacteristic
96C22×Dic26—21no—
97C22×Dic26C2311yescharacteristic
98C2×C13×SD16—24no—
99C2×C13×SD16C2314yes—
100C22×C8×C13C2311yescharacteristic
101C22×C8×C13C2311yescharacteristic
102C4×Q8×C13—22no—
103C4×Q8×C13C2314yescomplemented
104C4×D4×C13—22no—
105C4×D4×C13C2314yes—
106C2×C13×C4⋊C4—21no—
107C2×C13×C4⋊C4C2311yescharacteristic
108C2×C13×C4⋊C4C2311yescharacteristic
109C2×C13×C22⋊C4—21no—
110C2×C42×C13—21no—
111C2×C42×C13C2311yescharacteristic
112C2×C22⋊Dic13—21no—
113#88200—22no—
114#88200C2314yes—
115#88198—22no—
116#88198C2314yescomplemented
117C2×#6106—24no—
118C2×#6106C2314yes—
119D4×Dic13—22no—
120D4×Dic13C2314yes—
121C2×#6105—24no—
122C2×#6105C2314yes—
123C4×C22⋊D13—28no—
124C2×#6103—21no—
125C2×#6103—21no—
126C2×#6103—21no—
127C2×#6103—21no—
128C2×C4⋊Dic13—21no—
129C2×C4⋊Dic13C2311yescharacteristic
130C2×C4⋊Dic13C2311yescharacteristic
131C2×#6101—21no—
132C2×#6101—21no—
133C2×#6101—21no—
134C2×#6101—21no—
135C2×#6101—21no—
136C2×#6101—21no—
137C2×C4×Dic13—21no—
138C2×C4×Dic13D411yescharacteristic
139C2×C4×Dic13D411yescharacteristic
140C2×C4×Dic13C2311yescharacteristic
141C22×#1055C2311yescharacteristic
142C22×#1055C2311yescharacteristic
143C2×#6095—24no—
144C2×#6095C2314yes—
145#88151—22no—
146#88151C2314yes—
147#88150—28no—
148#88147—22no—
149#88147C2314yes—
150C4⋊C4×D13—22no—
151C4⋊C4×D13C2314yes—
152#88143—28no—
153#88142—22no—
154#88142C2314yescomplemented
155#88135—28no—
156C22⋊C4×D13—28no—
157C4×D52—22no—
158C4×D52C2314yes—
159#88126—28no—
160C42×D13D414yes—
161C42×D13C2314yes—
162C4×Dic26—22no—
163C4×Dic26—28no—
164C4×Dic26C2314yescomplemented
165C13×#106C2314yescomplemented
166C13×#103C2314yescomplemented
167C13×#102C2314yes—
168C4×C8×C13C2314yescomplemented
169#88075C2314yescomplemented
170#88072C2314yes—
171#88061C2314yes—
172#88060C2314yes—
173#88060C2314yes—
174#88057C2314yescomplemented
175#88056C2314yescomplemented
176#88054C2314yescomplemented
177#88054C2314yescomplemented
178#88050C2314yescomplemented
179#88049C2314yes—
180#88048C2314yescomplemented
181#88048C2314yescomplemented
182C4×#1055C2314yescomplemented
183C2×#3101—131nomaximal, Sylow
184C24×C13—21no—
185C23×D13—28no—
186C23×D13—21no—
187C23×D13—24no—
188C23×D13—44no—
189C23×D13—44no—
190C23×D13C2×D411yescharacteristic
191C2×Q8×C13—21no—
192C2×Q8×C13—22no—
193C2×Q8×C13—22no—
194C2×Q8×C13C2412yes—
195C2×D4×C13—21no—
196C2×D4×C13—22no—
197C2×D4×C13#4114yes—
198C2×D4×C13C2412yes—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—24no—
203C22×C4×C13—44no—
204C22×C4×C13C2×D411yescharacteristic
205C22×C4×C13C2×D411yescharacteristic
206C22×C4×C13C2411yescharacteristic
207C2×C22⋊D13—28no—
208C2×C22⋊D13—24no—
209C22×Dic13—21no—
210C22×Dic13—21no—
211C22×Dic13—21no—
212C22×Dic13—24no—
213C22×Dic13—44no—
214C22×Dic13C2×D411yescharacteristic
215C22×Dic13C2×D411yescharacteristic
216C22×Dic13C2×D411yescharacteristic
217D4×D13—216no—
218D4×D13—28no—
219D4×D13—28no—
220C2×D52—21no—
221C2×D52—22no—
222C2×D52#4114yes—
223C2×D52C2412yes—
224C2×C4×D13—22no—
225C2×C4×D13—22no—
226C2×C4×D13—24no—
227C2×C4×D13—24no—
228C2×C4×D13—24no—
229C2×C4×D13—42no—
230C2×C4×D13—44no—
231C2×C4×D13—44no—
232C2×C4×D13—44no—
233C2×C4×D13—432no—
234C2×C4×D13SD1618yescomplemented
235C2×C4×D13C2×D412yes—
236C2×C4×D13C2×D414yes—
237C2×C4×D13C2×D414yes—
238C2×C4×D13C2412yes—
239C2×Dic26—22no—
240C2×Dic26—22no—
241C2×Dic26—21no—
242C2×Dic26—24no—
243C2×Dic26—44no—
244C2×Dic26C2412yes—
245C13×SD16—28no—
246C2×C8×C13—22no—
247C2×C8×C13—22no—
248C2×C8×C13C2412yes—
249C2×C8×C13C2412yes—
250C13×C4⋊C4—21no—
251C13×C4⋊C4—24no—
252C13×C4⋊C4—21no—
253C13×C4⋊C4C2412yes—
254C13×C4⋊C4C2412yes—
255C13×C22⋊C4—24no—
256C42×C13—24no—
257C42×C13C2×D412yes—
258C42×C13C2412yes—
259C22⋊Dic13—24no—
260#6106—28no—
261#6105—28no—
262#6103—24no—
263#6103—24no—
264#6103—24no—
265#6103—24no—
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#6101—24no—
277C4×Dic13—24no—
278C4×Dic13C2×D414yes—
279C4×Dic13C2×D412yes—
280C4×Dic13C2×D414yes—
281C4×Dic13C2412yes—
282C2×#1055—22no—
283C2×#1055—22no—
284C2×#1055C2412yes—
285C2×#1055C2412yes—
286#6095—28no—
287C2×#533—131no—
288C22×C4×D4—131no—
289#3101—1316no—
290C2×#483—131no—
291C2×#483—131no—
292C2×#476—131no—
293C2×#476—131no—
294C2×#461—131no—
295C2×#461—131no—
296C2×#450—131no—
297C2×#450—131no—
298C2×C4×SD16—131no—
299C2×C4×SD16—131no—
300C2×C4×SD16—131no—
301C2×C4×SD16D1311yescharacteristic, complemented
302C2×#431—131no—
303C23×C13—24no—
304C23×C13—22no—
305C23×C13—42no—
306C23×C13—42no—
307C23×C13C22×D411yescharacteristic
308C22×D13—22no—
309C22×D13—22no—
310C22×D13—216no—
311C22×D13—24no—
312C22×D13—22no—
313C22×D13—432no—
314C22×D13—48no—
315C22×D13—42no—
316C22×D13—42no—
317C22×D13—48no—
318C22×D13C2×SD1614yes—
319C22×D13C22×D412yes—
320Q8×C13—22no—
321Q8×C13—22no—
322Q8×C13—42no—
323D4×C13—24no—
324D4×C13—22no—
325D4×C13C2×#4114yes—
326C2×C4×C13—22no—
327C2×C4×C13—22no—
328C2×C4×C13—22no—
329C2×C4×C13—22no—
330C2×C4×C13—42no—
331C2×C4×C13—42no—
332C2×C4×C13—42no—
333C2×C4×C13—48no—
334C2×C4×C13C2×SD1614yes—
335C2×C4×C13C22×D412yes—
336C2×C4×C13C22×D411yescharacteristic
337C2×C4×C13C22×D412yes—
338C2×C4×C13C2×#4112yes—
339C2×C4×C13C2×#4112yes—
340C2×C4×C13C2511yescharacteristic
341C22⋊D13—216no—
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×Dic13—48no—
351C2×Dic13C2×SD1614yes—
352C2×Dic13C22×D412yes—
353C2×Dic13C22×D412yes—
354C2×Dic13C22×D412yes—
355D52—24no—
356D52—22no—
357D52C2×#4114yes—
358C4×D13—24no—
359C4×D13—22no—
360C4×D13—22no—
361C4×D13—44no—
362C4×D13—48no—
363C4×D13—48no—
364C4×D13—48no—
365C4×D13C2×SD16116yescomplemented
366Dic26—22no—
367Dic26—22no—
368Dic26—48no—
369Dic26—42no—
370C8×C13—22no—
371C8×C13—22no—
372#1055—22no—
373#1055—22no—
374C23×D4—131no—
375C24×C4—261no—
376C22×SD16—131no—
377C22×SD16—131no—
378C22×SD16—131no—
379C22×SD16C2×D1311yescharacteristic
380#533—138no—
381#533—264no—
382C2×C4⋊Q8—131no—
383C2×C4⋊Q8—131no—
384C2×#125—261no—
385C2×C22⋊Q8—131no—
386C2×C22⋊Q8—131no—
387C2×C22⋊Q8—261no—
388C2×C4×Q8—131no—
389C2×C4×Q8—261no—
390C2×C4×Q8C2×D1311yescharacteristic, complemented
391C2×C4×D4—131no—
392C2×C4×D4—138no—
393C2×C4×D4—131no—
394C2×C4×D4—131no—
395C2×C4×D4—261no—
396C2×C4×D4—264no—
397C2×C4×D4—261no—
398C2×C4×D4C2×D1311yescharacteristic
399C2×#117—261no—
400C22×C4⋊C4—131no—
401C22×C22⋊C4—261no—
402C22×C42—131no—
403#483—138no—
404#483—138no—
405#476—138no—
406#476—138no—
407#461—138no—
408#461—138no—
409#450—138no—
410#450—138no—
411C4×SD16—138no—
412C4×SD16—138no—
413C4×SD16—138no—
414C4×SD16C2×D1318yescomplemented
415#431—138no—
416C2×#106—131no—
417C2×#106—131no—
418C2×#106—131no—
419C2×#106C2×D1311yescharacteristic, complemented
420C2×C4⋊C8—131no—
421C2×C4⋊C8—131no—
422C2×#103—131no—
423C2×#103—131no—
424C2×#103—131no—
425C2×#103C2×D1311yescharacteristic, complemented
426C2×#102—131no—
427C2×#102—131no—
428C2×#102—131no—
429C2×#102C2×D1311yescharacteristic
430C2×C22⋊C8—131no—
431C2×C22⋊C8—131no—
432C2×C4×C8—131no—
433C2×C4×C8C2×D1311yescharacteristic, complemented
434C22×C13—24no—
435C22×C13—48no—
436C22×C13—42no—
437C22×C13—42no—
438C22×C13#52512yes—
439C22×C13C22×SD1612yes—
440C22×C13#57512yes—
441C22×C13C23×D411yescharacteristic
442C2×D13—28no—
443C2×D13—22no—
444C2×D13—22no—
445C2×D13—24no—
446C2×D13—432no—
447C2×D13—48no—
448C2×D13—42no—
449C2×D13—42no—
450C2×D13C22×SD1614yes—
451C4×C13—22no—
452C4×C13—42no—
453C4×C13—42no—
454C4×C13—42no—
455C4×C13#52512yes—
456C4×C13C22×SD1614yes—
457C4×C13C22×#4111yescharacteristic
458C4×C13C22×#4111yescharacteristic
459Dic13—22no—
460Dic13—22no—
461Dic13—42no—
462Dic13—42no—
463Dic13—42no—
464Dic13C22×SD1614yes—
465C25—261no—
466C22×Q8—131no—
467C22×Q8—261no—
468C22×Q8C22×D1311yescharacteristic
469C22×D4—134no—
470C22×D4—131no—
471C22×D4—262no—
472C22×D4—261no—
473C22×D4—264no—
474C22×D4—264no—
475C22×D4C22×D1311yescharacteristic
476C23×C4—21no—
477C23×C4—131no—
478C23×C4—131no—
479C23×C4—131no—
480C23×C4—261no—
481C23×C4—268no—
482C23×C4—261no—
483C23×C4—261no—
484C23×C4—261no—
485C23×C4—528no—
486C2×SD16—24no—
487C2×SD16—134no—
488C2×SD16—134no—
489C2×SD16—134no—
490C2×SD16—264no—
491C2×SD16—264no—
492C2×SD16—264no—
493C2×SD16C22×D1314yes—
494C22×C8—131no—
495C22×C8—131no—
496C22×C8C22×D1311yescharacteristic
497C22×C8C22×D1311yescharacteristic
498C4⋊Q8—134no—
499C4⋊Q8—134no—
500C4⋊Q8—262no—
501C4⋊Q8—262no—
502#125—268no—
503C22⋊Q8—134no—
504C22⋊Q8—134no—
505C22⋊Q8—262no—
506C22⋊Q8—268no—
507C22⋊Q8—262no—
508C4×Q8—22no—
509C4×Q8—134no—
510C4×Q8—268no—
511C4×Q8—262no—
512C4×Q8C22×D1314yescomplemented
513C4×D4—22no—
514C4×D4—134no—
515C4×D4—134no—
516C4×D4—134no—
517C4×D4—268no—
518C4×D4—262no—
519C4×D4—268no—
520C4×D4—262no—
521C4×D4—262no—
522C4×D4C22×D1314yes—
523#117—268no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—131no—
526C2×C4⋊C4—131no—
527C2×C4⋊C4—134no—
528C2×C4⋊C4—262no—
529C2×C4⋊C4—261no—
530C2×C4⋊C4—261no—
531C2×C4⋊C4—261no—
532C2×C4⋊C4—261no—
533C2×C4⋊C4—261no—
534C2×C4⋊C4—261no—
535C2×C4⋊C4—261no—
536C2×C4⋊C4C22×D1311yescharacteristic
537C2×C4⋊C4C22×D1311yescharacteristic
538C2×C22⋊C4—21no—
539C2×C22⋊C4—268no—
540C2×C22⋊C4—261no—
541C2×C22⋊C4—261no—
542C2×C22⋊C4—261no—
543C2×C22⋊C4—261no—
544C2×C22⋊C4—261no—
545C2×C42—21no—
546C2×C42—131no—
547C2×C42—131no—
548C2×C42—131no—
549C2×C42—134no—
550C2×C42—134no—
551C2×C42—261no—
552C2×C42C22×D1311yescharacteristic
553#106—134no—
554#106—134no—
555#106—134no—
556#106C22×D1314yescomplemented
557C4⋊C8—134no—
558C4⋊C8—134no—
559#103—134no—
560#103—134no—
561#103—134no—
562#103C22×D1314yescomplemented
563#102—134no—
564#102—134no—
565#102—134no—
566#102C22×D1314yes—
567C22⋊C8—134no—
568C22⋊C8—134no—
569C4×C8—134no—
570C4×C8C22×D1314yescomplemented
571C2×C13—44no—
572C2×C13#310114yescomplemented
573C2×C13C2×#52511yescharacteristic
574C2×C13C23×SD1611yescharacteristic
575C2×C13C2×#57511yescharacteristic
576D13—24no—
577D13—44no—
578C24—21no—
579C24—131no—
580C24—264no—
581C24—268no—
582C24—261no—
583C24—524no—
584C24—524no—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—132no—
589C2×Q8—264no—
590C2×Q8—261no—
591C2×Q8—262no—
592C2×Q8—262no—
593C2×Q8—524no—
594C2×Q8C23×D1312yes—
595C2×D4—21no—
596C2×D4—22no—
597C2×D4—134no—
598C2×D4—132no—
599C2×D4—264no—
600C2×D4—268no—
601C2×D4—2616no—
602C2×D4—268no—
603C2×D4—268no—
604C2×D4—262no—
605C2×D4—261no—
606C2×D4#612714yes—
607C2×D4C23×D1312yes—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—24no—
612C22×C4—44no—
613C22×C4—131no—
614C22×C4—138no—
615C22×C4—134no—
616C22×C4—131no—
617C22×C4—131no—
618C22×C4—132no—
619C22×C4—132no—
620C22×C4—134no—
621C22×C4—264no—
622C22×C4—264no—
623C22×C4—264no—
624C22×C4—262no—
625C22×C4—262no—
626C22×C4—261no—
627C22×C4—261no—
628C22×C4—261no—
629C22×C4—264no—
630C22×C4—522no—
631C22×C4—524no—
632C22×C4—5232no—
633C22×C4—524no—
634C22×C4—524no—
635C22×C4—524no—
636C22×C4D4×D1311yescharacteristic
637C22×C4D4×D1311yescharacteristic
638C22×C4C23×D1311yescharacteristic
639SD16—28no—
640SD16—268no—
641SD16—268no—
642SD16—268no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—132no—
646C2×C8—132no—
647C2×C8—262no—
648C2×C8—262no—
649C2×C8C23×D1312yes—
650C2×C8C23×D1312yes—
651C4⋊C4—24no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—132no—
655C4⋊C4—132no—
656C4⋊C4—264no—
657C4⋊C4—264no—
658C4⋊C4—264no—
659C4⋊C4—264no—
660C4⋊C4—264no—
661C4⋊C4—264no—
662C4⋊C4—261no—
663C4⋊C4—261no—
664C4⋊C4—264no—
665C4⋊C4C23×D1312yes—
666C4⋊C4C23×D1312yes—
667C22⋊C4—24no—
668C22⋊C4—264no—
669C22⋊C4—264no—
670C22⋊C4—264no—
671C22⋊C4—264no—
672C22⋊C4—264no—
673C42—24no—
674C42—134no—
675C42—134no—
676C42—132no—
677C42—132no—
678C42—264no—
679C42D4×D1312yes—
680C42C23×D1312yes—
681C13C2×#310111yescharacteristic, complemented, Sylow
682C23—24no—
683C23—22no—
684C23—42no—
685C23—42no—
686C23—134no—
687C23—132no—
688C23—2616no—
689C23—262no—
690C23—262no—
691C23—264no—
692C23—262no—
693C23—528no—
694C23—528no—
695C23—5232no—
696C23—522no—
697C23—522no—
698C23C2×D4×D1311yescharacteristic
699Q8—22no—
700Q8—22no—
701Q8—42no—
702Q8—262no—
703Q8—262no—
704Q8—528no—
705Q8—522no—
706D4—24no—
707D4—22no—
708D4—134no—
709D4—2616no—
710D4—264no—
711D4—262no—
712D4C2×#612714yes—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—48no—
721C2×C4—134no—
722C2×C4—132no—
723C2×C4—1316no—
724C2×C4—132no—
725C2×C4—132no—
726C2×C4—262no—
727C2×C4—262no—
728C2×C4—264no—
729C2×C4—262no—
730C2×C4—262no—
731C2×C4—262no—
732C2×C4—262no—
733C2×C4—262no—
734C2×C4—524no—
735C2×C4—528no—
736C2×C4—528no—
737C2×C4—528no—
738C2×C4—522no—
739C2×C4—522no—
740C2×C4—522no—
741C2×C4—528no—
742C2×C4SD16×D1314yes—
743C2×C4C2×#612712yes—
744C2×C4C2×D4×D1312yes—
745C2×C4C2×D4×D1312yes—
746C2×C4C2×D4×D1311yescharacteristic
747C2×C4#41×D1312yes—
748C2×C4C24×D1311yescharacteristic
749C8—22no—
750C8—22no—
751C8—262no—
752C8—262no—
753C22—24no—
754C22—42no—
755C22—42no—
756C22—48no—
757C22—134no—
758C22—262no—
759C22—262no—
760C22—268no—
761C22—264no—
762C22—5232no—
763C22—522no—
764C22—522no—
765C22—528no—
766C22#1171925212yes—
767C22C2×SD16×D1312yes—
768C22#1171947312yes—
769C22C22×D4×D1311yescharacteristic
770C4—22no—
771C4—42no—
772C4—42no—
773C4—42no—
774C4—134no—
775C4—262no—
776C4—262no—
777C4—522no—
778C4—522no—
779C4—522no—
780C4#1171925212yes—
781C4C2×SD16×D1314yes—
782C4C22×#612711yescharacteristic
783C4C2×#41×D1311yescharacteristic
784C2—44no—
785C2—264no—
786C2—524no—
787C2#1312484214yesdirect product factor
788C2C2×#1171925211yescharacteristic
789C2C22×SD16×D1311yescharacteristic
790C2C2×#1171947311yescharacteristic
subgroupG/H
centerC22×C4D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C4×C13×SD16C2
socleC23×C13C22×D4
prime radicalC22×D4×D13C22
hypercenterC2×C4×SD16D13
hypocenterC13C2×#3101
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#11719283C2semidirect
3. #13124842C2direct (N × H)
4. C2×#11718523C2semidirect
5. C2×#11718466C2semidirect
6. C2×#11718531C2semidirect
7. C2×#11718422C2semidirect
8. C2×#11718479C2semidirect
9. C2×#11718823C2semidirect
12. C2×C4×#6095C2semidirect
13. C2×C4×#6106C2semidirect
14. C2×C4×#6105C2semidirect
15. C2×#11718346C2semidirect
16. C2×C4×C13×SD16C2semidirect
20. C2×C4×Q8×C13C22semidirect
23. C2×#88198C22semidirect
30. #11719283C22semidirect
38. C2×#88142C22semidirect
45. C2×C4×Dic26C22semidirect
46. C4×C13×SD16C22semidirect
47. C2×C13×#106C22semidirect
48. C2×C13×#103C22semidirect
50. C2×C4×C8×C13C22semidirect
51. C2×#88075C22semidirect
54. #11718823C22semidirect
58. C2×#88057C22semidirect
59. C2×#88056C22semidirect
60. C2×#88054C22semidirect
61. C2×#88054C22semidirect
62. C4×#6106C22semidirect
63. C4×#6105C22semidirect
64. C2×#88050C22semidirect
66. C2×#88048C22semidirect
67. C2×#88048C22semidirect
68. C2×C4×#1055C22semidirect
69. #11718531C22semidirect
70. #11718523C22semidirect
71. #11718479C22semidirect
72. #11718466C22semidirect
74. #11718422C22semidirect
75. C4×#6095C22semidirect
76. #11718346C22semidirect
103. C4×Q8×C13C23semidirect
116. #88198C23semidirect
154. #88142C23semidirect
164. C4×Dic26C23semidirect
165. C13×#106C23semidirect
166. C13×#103C23semidirect
168. C4×C8×C13C23semidirect
169. #88075C23semidirect
174. #88057C23semidirect
175. #88056C23semidirect
176. #88054C23semidirect
177. #88054C23semidirect
178. #88050C23semidirect
180. #88048C23semidirect
181. #88048C23semidirect
182. C4×#1055C23semidirect
234. C2×C4×D13SD16semidirect
301. C2×C4×SD16D13semidirect
365. C4×D13C2×SD16semidirect
390. C2×C4×Q8C2×D13semidirect
414. C4×SD16C2×D13semidirect
419. C2×#106C2×D13semidirect
425. C2×#103C2×D13semidirect
433. C2×C4×C8C2×D13semidirect
512. C4×Q8C22×D13semidirect
556. #106C22×D13semidirect
562. #103C22×D13semidirect
570. C4×C8C22×D13semidirect
572. C2×C13#3101semidirect
681. C13C2×#3101semidirect
787. C2#13124842direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192832
C2×C4×D4×D132
#131248422
C2×#117185232
C2×#117184662
C2×#117185312
C2×#117184222
C2×#117184792
C2×#117188232
C2×#117184372
C2×#117188302
C2×C4×#60952
C2×C4×#61062
C2×C4×#61052
C2×#117183462
C2×C4×C13×SD162
C2×#310113