Finite Group Databasebeta

← C13×#15384 #15701723

Subgroups — C13×#15384 #15701723

Order 3328.

2118 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×#123C211yesmaximal, characteristic
2C2×C13×#399C211yesmaximal, characteristic, complemented
3C2×C13×#397C211yesmaximal, characteristic, complemented
4C2×C13×#394C212yesmaximal
5C2×C13×#385C212yesmaximal, complemented
6C2×C13×#384C211yesmaximal, characteristic, complemented
7C13×#1445C211yesmaximal, characteristic, complemented
8C13×#1444C212yesmaximal, complemented
9C13×#1439C212yesmaximal, complemented
10C13×#1437C211yesmaximal, characteristic, complemented
11C13×#1437C211yesmaximal, characteristic, complemented
12C23×D4×C13C2211yescharacteristic
13C24×C4×C13C2211yescharacteristic
14C2×C13×#123—24no—
15C2×C13×#123—24no—
16C2×C13×#123—24no—
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2212yes—
20C22×C13×C4⋊C4C2212yes—
21C22×C13×C4⋊C4C2212yes—
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2212yes—
24C22×C13×C22⋊C4C2212yes—
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2212yes—
27C22×C13×C22⋊C4C2212yes—
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C13×C22⋊C4C2211yescharacteristic
30C22×C42×C13C2211yescharacteristic
31C13×#399—24no—
32C13×#397—24no—
33C13×#394—28no—
34C13×#385—28no—
35C13×#384—24no—
36C2×C13×#95C2212yes—
37C2×C13×#95C2212yes—
38C2×C13×#95C2212yes—
39C2×C13×#95C2211yescharacteristic
40C2×C13×#95C2212yes—
41C2×C13×#95C2211yescharacteristic
42C2×C13×#95C2212yes—
43C25×C13C2311yescharacteristic
44C25×C13C2311yescharacteristic
45C22×D4×C13—22no—
46C22×D4×C13—22no—
47C22×D4×C13—24no—
48C22×D4×C13—22no—
49C22×D4×C13—42no—
50C23×C4×C13—22no—
51C23×C4×C13—22no—
52C23×C4×C13—22no—
53C23×C4×C13—24no—
54C23×C4×C13—42no—
55C23×C4×C13C2312yes—
56C23×C4×C13C2312yes—
57C23×C4×C13C2312yes—
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2312yes—
64C13×#123—232no—
65C2×C13×C4⋊C4—22no—
66C2×C13×C4⋊C4—22no—
67C2×C13×C4⋊C4—22no—
68C2×C13×C4⋊C4—22no—
69C2×C13×C4⋊C4—22no—
70C2×C13×C4⋊C4—24no—
71C2×C13×C4⋊C4—24no—
72C2×C13×C4⋊C4—22no—
73C2×C13×C4⋊C4—24no—
74C2×C13×C4⋊C4—24no—
75C2×C13×C4⋊C4—24no—
76C2×C13×C4⋊C4—22no—
77C2×C13×C4⋊C4—24no—
78C2×C13×C4⋊C4—22no—
79C2×C13×C4⋊C4—42no—
80C2×C13×C4⋊C4—42no—
81C2×C13×C4⋊C4—42no—
82C2×C13×C4⋊C4D414yes—
83C2×C13×C22⋊C4—22no—
84C2×C13×C22⋊C4—22no—
85C2×C13×C22⋊C4—22no—
86C2×C13×C22⋊C4—22no—
87C2×C13×C22⋊C4—22no—
88C2×C13×C22⋊C4—22no—
89C2×C13×C22⋊C4—22no—
90C2×C13×C22⋊C4—24no—
91C2×C13×C22⋊C4—24no—
92C2×C13×C22⋊C4—24no—
93C2×C13×C22⋊C4—24no—
94C2×C13×C22⋊C4—24no—
95C2×C13×C22⋊C4—24no—
96C2×C13×C22⋊C4—24no—
97C2×C13×C22⋊C4—24no—
98C2×C13×C22⋊C4—24no—
99C2×C13×C22⋊C4—24no—
100C2×C13×C22⋊C4—42no—
101C2×C13×C22⋊C4D418yes—
102C2×C13×C22⋊C4D414yes—
103C2×C13×C22⋊C4D414yes—
104C2×C42×C13—22no—
105C2×C42×C13—24no—
106C13×#95—24no—
107C13×#95—24no—
108C13×#95—24no—
109C13×#95—22no—
110C13×#95—24no—
111C13×#95—22no—
112C13×#95—24no—
113#15384C1311yesmaximal, characteristic, direct product factor, Sylow
114C24×C13—21no—
115C24×C13—21no—
116C24×C13—22no—
117C24×C13—22no—
118C24×C13—22no—
119C24×C13—22no—
120C24×C13—22no—
121C24×C13—21no—
122C24×C13—21no—
123C24×C13—22no—
124C24×C13—22no—
125C24×C13—22no—
126C24×C13—22no—
127C24×C13—22no—
128C24×C13—22no—
129C24×C13C2×D412yes—
130C24×C13C2×D412yes—
131C24×C13C2×D414yes—
132C24×C13C2411yescharacteristic
133C2×D4×C13—28no—
134C2×D4×C13—48no—
135C2×D4×C13—48no—
136C2×D4×C13—44no—
137C2×D4×C13—44no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—22no—
141C22×C4×C13—22no—
142C22×C4×C13—22no—
143C22×C4×C13—22no—
144C22×C4×C13—28no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—22no—
158C22×C4×C13—22no—
159C22×C4×C13—22no—
160C22×C4×C13—22no—
161C22×C4×C13—22no—
162C22×C4×C13—22no—
163C22×C4×C13—22no—
164C22×C4×C13—22no—
165C22×C4×C13—22no—
166C22×C4×C13—22no—
167C22×C4×C13—22no—
168C22×C4×C13—22no—
169C22×C4×C13—22no—
170C22×C4×C13—22no—
171C22×C4×C13—22no—
172C22×C4×C13—22no—
173C22×C4×C13—22no—
174C22×C4×C13—22no—
175C22×C4×C13—22no—
176C22×C4×C13—22no—
177C22×C4×C13—22no—
178C22×C4×C13—22no—
179C22×C4×C13—22no—
180C22×C4×C13—22no—
181C22×C4×C13—48no—
182C22×C4×C13—48no—
183C22×C4×C13—44no—
184C22×C4×C13—44no—
185C22×C4×C13C2×D412yes—
186C22×C4×C13C2×D414yes—
187C22×C4×C13C2×D412yes—
188C22×C4×C13C2×D412yes—
189C22×C4×C13C2×D412yes—
190C22×C4×C13C2×D412yes—
191C22×C4×C13C2×D412yes—
192C22×C4×C13C2×D412yes—
193C22×C4×C13C2×D414yes—
194C22×C4×C13#4114yes—
195C22×C4×C13#4114yes—
196C13×C4⋊C4—28no—
197C13×C4⋊C4—28no—
198C13×C4⋊C4—48no—
199C13×C4⋊C4—48no—
200C13×C4⋊C4—48no—
201C13×C4⋊C4—44no—
202C13×C22⋊C4—28no—
203C13×C22⋊C4—28no—
204C13×C22⋊C4—28no—
205C13×C22⋊C4—216no—
206C13×C22⋊C4—48no—
207C13×C22⋊C4—48no—
208C13×C22⋊C4—48no—
209C42×C13—28no—
210C22×#123C2×C1311yescharacteristic
211C2×#399C2×C1311yescharacteristic, complemented
212C2×#397C2×C1311yescharacteristic, complemented
213C2×#394C2×C1312yes—
214C2×#385C2×C1312yescomplemented
215C2×#384C2×C1311yescharacteristic, complemented
216#1445C2×C1311yescharacteristic, complemented
217#1444C2×C1312yescomplemented
218#1439C2×C1312yescomplemented
219#1437C2×C1311yescharacteristic, complemented
220#1437C2×C1311yescharacteristic, complemented
221C23×C13—22no—
222C23×C13—24no—
223C23×C13—22no—
224C23×C13—24no—
225C23×C13—24no—
226C23×C13—24no—
227C23×C13—24no—
228C23×C13—24no—
229C23×C13—24no—
230C23×C13—24no—
231C23×C13—22no—
232C23×C13—22no—
233C23×C13—22no—
234C23×C13—24no—
235C23×C13—24no—
236C23×C13—41no—
237C23×C13—41no—
238C23×C13—41no—
239C23×C13—41no—
240C23×C13—42no—
241C23×C13—42no—
242C23×C13—42no—
243C23×C13—42no—
244C23×C13—42no—
245C23×C13—42no—
246C23×C13—42no—
247C23×C13—41no—
248C23×C13—41no—
249C23×C13—41no—
250C23×C13—41no—
251C23×C13—42no—
252C23×C13—42no—
253C23×C13—42no—
254C23×C13—42no—
255C23×C13—42no—
256C23×C13—42no—
257C23×C13—42no—
258C23×C13—42no—
259C23×C13—42no—
260C23×C13—42no—
261C23×C13—42no—
262C23×C13#12714yes—
263C23×C13C22×D411yescharacteristic
264C23×C13C22×D411yescharacteristic
265C23×C13C22×D411yescharacteristic
266C23×C13C22×D412yes—
267C23×C13C2×#4112yes—
268C23×C13C2×#4112yes—
269C23×C13H(5,𝔽2)12yes—
270C23×C132−1+412yes—
271C23×C132−1+412yes—
272D4×C13—416no—
273C2×C4×C13—22no—
274C2×C4×C13—24no—
275C2×C4×C13—22no—
276C2×C4×C13—24no—
277C2×C4×C13—24no—
278C2×C4×C13—24no—
279C2×C4×C13—24no—
280C2×C4×C13—24no—
281C2×C4×C13—24no—
282C2×C4×C13—24no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—22no—
287C2×C4×C13—24no—
288C2×C4×C13—24no—
289C2×C4×C13—24no—
290C2×C4×C13—24no—
291C2×C4×C13—24no—
292C2×C4×C13—24no—
293C2×C4×C13—24no—
294C2×C4×C13—416no—
295C2×C4×C13—41no—
296C2×C4×C13—41no—
297C2×C4×C13—41no—
298C2×C4×C13—42no—
299C2×C4×C13—41no—
300C2×C4×C13—41no—
301C2×C4×C13—41no—
302C2×C4×C13—41no—
303C2×C4×C13—41no—
304C2×C4×C13—42no—
305C2×C4×C13—42no—
306C2×C4×C13—42no—
307C2×C4×C13—42no—
308C2×C4×C13—42no—
309C2×C4×C13—42no—
310C2×C4×C13—42no—
311C2×C4×C13—42no—
312C2×C4×C13—42no—
313C2×C4×C13—42no—
314C2×C4×C13—42no—
315C2×C4×C13—42no—
316C2×C4×C13—42no—
317C2×C4×C13—42no—
318C2×C4×C13—42no—
319C2×C4×C13—42no—
320C2×C4×C13—42no—
321C2×C4×C13—42no—
322C2×C4×C13—42no—
323C2×C4×C13—42no—
324C2×C4×C13—42no—
325C2×C4×C13#12014yes—
326C2×C4×C13#12318yescomplemented
327C23×D4C22×C1311yescharacteristic
328C24×C4C22×C1311yescharacteristic
329C2×#123—24no—
330C2×#123—24no—
331C2×#123—24no—
332C22×C4⋊C4C22×C1311yescharacteristic
333C22×C4⋊C4C22×C1311yescharacteristic
334C22×C4⋊C4C22×C1312yes—
335C22×C4⋊C4C22×C1312yes—
336C22×C4⋊C4C22×C1312yes—
337C22×C4⋊C4C22×C1311yescharacteristic
338C22×C22⋊C4C22×C1312yes—
339C22×C22⋊C4C22×C1312yes—
340C22×C22⋊C4C22×C1311yescharacteristic
341C22×C22⋊C4C22×C1312yes—
342C22×C22⋊C4C22×C1312yes—
343C22×C22⋊C4C22×C1311yescharacteristic
344C22×C22⋊C4C22×C1311yescharacteristic
345C22×C42C22×C1311yescharacteristic
346#399—24no—
347#397—24no—
348#394—28no—
349#385—28no—
350#384—24no—
351C2×#95C22×C1312yes—
352C2×#95C22×C1311yescharacteristic
353C2×#95C22×C1312yes—
354C2×#95C22×C1311yescharacteristic
355C2×#95C22×C1312yes—
356C2×#95C22×C1312yes—
357C2×#95C22×C1312yes—
358C22×C13—24no—
359C22×C13—28no—
360C22×C13—42no—
361C22×C13—44no—
362C22×C13—44no—
363C22×C13—44no—
364C22×C13—42no—
365C22×C13—44no—
366C22×C13—44no—
367C22×C13—42no—
368C22×C13—44no—
369C22×C13—44no—
370C22×C13—42no—
371C22×C13—42no—
372C22×C13—82no—
373C22×C13—82no—
374C22×C13—82no—
375C22×C13—82no—
376C22×C13C2×#12011yescharacteristic
377C22×C13C2×#12312yes—
378C22×C13#52511yescharacteristic
379C22×C13C2×#12711yescharacteristic
380C22×C13#53211yescharacteristic
381C22×C13#53511yescharacteristic
382C22×C13#53611yescharacteristic
383C22×C13#53612yes—
384C22×C13#53611yescharacteristic
385C22×C13#53912yes—
386C22×C13#54212yes—
387C22×C13D4212yes—
388C22×C13D4212yes—
389C22×C13#54712yes—
390C22×C13#54712yes—
391C22×C13#54712yes—
392C22×C13#54712yes—
393C22×C13#54712yes—
394C22×C13#54812yes—
395C22×C13#55312yes—
396C22×C13#56312yes—
397C4×C13—24no—
398C4×C13—28no—
399C4×C13—44no—
400C4×C13—42no—
401C4×C13—42no—
402C4×C13—42no—
403C4×C13—42no—
404C4×C13—82no—
405C4×C13—82no—
406C25C23×C1311yescharacteristic
407C25C23×C1311yescharacteristic
408C22×D4—22no—
409C22×D4—22no—
410C22×D4—24no—
411C22×D4—22no—
412C22×D4—42no—
413C23×C4—22no—
414C23×C4—22no—
415C23×C4—22no—
416C23×C4—24no—
417C23×C4—42no—
418C23×C4C23×C1312yes—
419C23×C4C23×C1312yes—
420C23×C4C23×C1312yes—
421C23×C4C23×C1311yescharacteristic
422C23×C4C23×C1311yescharacteristic
423C23×C4C23×C1311yescharacteristic
424C23×C4C23×C1311yescharacteristic
425C23×C4C23×C1311yescharacteristic
426C23×C4C23×C1312yes—
427#123—232no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—24no—
434C2×C4⋊C4—24no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—42no—
443C2×C4⋊C4—42no—
444C2×C4⋊C4—42no—
445C2×C4⋊C4D4×C1314yes—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—42no—
464C2×C22⋊C4D4×C1314yes—
465C2×C22⋊C4D4×C1314yes—
466C2×C22⋊C4D4×C1318yes—
467C2×C42—22no—
468C2×C42—24no—
469#95—24no—
470#95—24no—
471#95—24no—
472#95—22no—
473#95—24no—
474#95—22no—
475#95—24no—
476C2×C13—44no—
477C2×C13—82no—
478C2×C13#240611yescharacteristic
479C2×C13#242212yes—
480C2×C13#243211yescharacteristic
481C2×C13#243311yescharacteristic
482C2×C13#244312yes—
483C2×C13#250112yes—
484C2×C13#267412yes—
485C2×C13#268012yes—
486C2×C13#271812yes—
487C24—21no—
488C24—21no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—21no—
495C24—21no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24C2×D4×C1312yes—
503C24C2×D4×C1312yes—
504C24C2×D4×C1314yes—
505C24C24×C1311yescharacteristic
506C2×D4—28no—
507C2×D4—48no—
508C2×D4—48no—
509C2×D4—44no—
510C2×D4—44no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—28no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4C2×D4×C1312yes—
559C22×C4C2×D4×C1314yes—
560C22×C4C2×D4×C1312yes—
561C22×C4C2×D4×C1312yes—
562C22×C4C2×D4×C1312yes—
563C22×C4C2×D4×C1312yes—
564C22×C4C2×D4×C1312yes—
565C22×C4C2×D4×C1312yes—
566C22×C4C2×D4×C1314yes—
567C22×C4C13×#4114yes—
568C22×C4C13×#4114yes—
569C4⋊C4—28no—
570C4⋊C4—28no—
571C4⋊C4—48no—
572C4⋊C4—48no—
573C4⋊C4—48no—
574C4⋊C4—44no—
575C22⋊C4—28no—
576C22⋊C4—28no—
577C22⋊C4—28no—
578C22⋊C4—216no—
579C22⋊C4—48no—
580C22⋊C4—48no—
581C22⋊C4—48no—
582C42—28no—
583C13#1538411yescharacteristic, direct product factor, Sylow
584C23—22no—
585C23—24no—
586C23—22no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—24no—
598C23—24no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23C13×#12714yes—
626C23C22×D4×C1311yescharacteristic
627C23C22×D4×C1311yescharacteristic
628C23C22×D4×C1311yescharacteristic
629C23C22×D4×C1312yes—
630C23C2×C13×#4112yes—
631C23C2×C13×#4112yes—
632C23C13×H(5,𝔽2)12yes—
633C23C13×2−1+412yes—
634C23C13×2−1+412yes—
635D4—416no—
636C2×C4—22no—
637C2×C4—24no—
638C2×C4—22no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—416no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—42no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4C13×#12014yes—
689C2×C4C13×#12318yescomplemented
690C22—28no—
691C22—24no—
692C22—42no—
693C22—44no—
694C22—44no—
695C22—44no—
696C22—42no—
697C22—44no—
698C22—44no—
699C22—42no—
700C22—44no—
701C22—44no—
702C22—42no—
703C22—42no—
704C22—82no—
705C22—82no—
706C22—82no—
707C22—82no—
708C22C2×C13×#12011yescharacteristic
709C22C2×C13×#12312yes—
710C22C13×#52511yescharacteristic
711C22C2×C13×#12711yescharacteristic
712C22C13×#53211yescharacteristic
713C22C13×#53511yescharacteristic
714C22C13×#53612yes—
715C22C13×#53611yescharacteristic
716C22C13×#53611yescharacteristic
717C22C13×#53912yes—
718C22C13×#54212yes—
719C22D42×C1312yes—
720C22D42×C1312yes—
721C22C13×#54712yes—
722C22C13×#54712yes—
723C22C13×#54712yes—
724C22C13×#54712yes—
725C22C13×#54712yes—
726C22C13×#54812yes—
727C22C13×#55312yes—
728C22C13×#56312yes—
729C4—24no—
730C4—28no—
731C4—44no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—42no—
736C4—82no—
737C4—82no—
738C2—44no—
739C2—82no—
740C2C13×#240611yescharacteristic
741C2C13×#242212yes—
742C2C13×#243211yescharacteristic
743C2C13×#243311yescharacteristic
744C2C13×#244312yes—
745C2C13×#250112yes—
746C2C13×#267412yes—
747C2C13×#268012yes—
748C2C13×#271812yes—
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC24C24×C13
prime radicalC23×D4×C13C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#399C2semidirect
3. C2×C13×#397C2semidirect
5. C2×C13×#385C2semidirect
6. C2×C13×#384C2semidirect
7. C13×#1445C2semidirect
8. C13×#1444C2semidirect
9. C13×#1439C2semidirect
10. C13×#1437C2semidirect
11. C13×#1437C2semidirect
113. #15384C13direct (N × H)
211. C2×#399C2×C13semidirect
212. C2×#397C2×C13semidirect
214. C2×#385C2×C13semidirect
215. C2×#384C2×C13semidirect
216. #1445C2×C13semidirect
217. #1444C2×C13semidirect
218. #1439C2×C13semidirect
219. #1437C2×C13semidirect
220. #1437C2×C13semidirect
326. C2×C4×C13#123semidirect
583. C13#15384direct (N × H)
689. C2×C4C13×#123semidirect

Maximal subgroups

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

subgroupindex
C22×C13×#1232
C2×C13×#3992
C2×C13×#3972
C2×C13×#3942
C2×C13×#3852
C2×C13×#3842
C13×#14452
C13×#14442
C13×#14392
C13×#14372
#1538413