Finite Group Databasebeta

← #15799714

Subgroups — #15799714

Order 3328.

1106 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13⋊#401C212yesmaximal
2#13113097C212yesmaximal
3#13113097C212yesmaximal
4#13113096C212yesmaximal
5#13113066C211yesmaximal, characteristic
6#13113065C211yesmaximal, characteristic
7#13113065C211yesmaximal, characteristic
8#13113065C211yesmaximal, characteristic
9#13113065C211yesmaximal, characteristic
10C4×#88071C211yesmaximal, characteristic
11C13×C4⋊#95C211yesmaximal, characteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C42×C13C2211yescharacteristic
15C22×C4⋊Dic13C2211yescharacteristic
16C22×C4⋊Dic13C2211yescharacteristic
17C22×C4×Dic13C2211yescharacteristic
18C22×C4×Dic13C2211yescharacteristic
19C2×C13×#95C2212yes—
20C2×C13×#95C2212yes—
21C2×#88071C2211yescharacteristic
22C2×#88071C2212yes—
23C2×#88071C2212yes—
24C2×#88071C2212yes—
25C2×#88071C2212yes—
26C2×#88071C2211yescharacteristic
27C2×#88071C2211yescharacteristic
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2211yescharacteristic
35C13⋊#401—28no—
36C23×C4×C13C2312yes—
37C23×C4×C13C2312yes—
38C23×C4×C13C2311yescharacteristic
39C23×C4×C13C2311yescharacteristic
40C23×C4×C13C2311yescharacteristic
41C23×Dic13C2312yes—
42C23×Dic13C2312yes—
43C23×Dic13C2311yescharacteristic
44C23×Dic13C2311yescharacteristic
45C23×Dic13C2311yescharacteristic
46C23×Dic13C2311yescharacteristic
47C2×C13×C4⋊C4—22no—
48C2×C13×C4⋊C4—22no—
49C2×C13×C4⋊C4—22no—
50C2×C13×C4⋊C4—22no—
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4—22no—
53C2×C42×C13—22no—
54C2×C42×C13—22no—
55C2×C42×C13—22no—
56C2×C4⋊Dic13—22no—
57C2×C4⋊Dic13—22no—
58C2×C4⋊Dic13—22no—
59C2×C4⋊Dic13—22no—
60C2×C4⋊Dic13—22no—
61C2×C4⋊Dic13—22no—
62C2×C4×Dic13—22no—
63C2×C4×Dic13—22no—
64C2×C4×Dic13—22no—
65C2×C4×Dic13—22no—
66C2×C4×Dic13—22no—
67C2×C4×Dic13—22no—
68C13×#95—24no—
69C13×#95—42no—
70#88071—24no—
71#88071—22no—
72#88071—24no—
73#88071—24no—
74#88071—24no—
75#88071—24no—
76#88071—24no—
77#88071—22no—
78#88071—22no—
79#88071—24no—
80#88071—24no—
81#88071—42no—
82#88071—42no—
83#88071D414yes—
84C4⋊#401—131nomaximal, Sylow
85C24×C13C2411yescharacteristic
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13—21no—
93C22×C4×C13—21no—
94C22×C4×C13—21no—
95C22×C4×C13—21no—
96C22×C4×C13—21no—
97C22×C4×C13—21no—
98C22×C4×C13—22no—
99C22×C4×C13—22no—
100C22×C4×C13—22no—
101C22×C4×C13—22no—
102C22×C4×C13—22no—
103C22×C4×C13—22no—
104C22×C4×C13—22no—
105C22×C4×C13—22no—
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13C2×D412yes—
113C22×C4×C13#4112yes—
114C22×C4×C13#4112yes—
115C22×C4×C13#4112yes—
116C22×C4×C13#4112yes—
117C22×C4×C13#4112yes—
118C22×C4×C13#4112yes—
119C22×C4×C13#4112yes—
120C22×C4×C13#4112yes—
121C22×Dic13—21no—
122C22×Dic13—21no—
123C22×Dic13—21no—
124C22×Dic13—21no—
125C22×Dic13—21no—
126C22×Dic13—21no—
127C22×Dic13—21no—
128C22×Dic13—21no—
129C22×Dic13—21no—
130C22×Dic13—21no—
131C22×Dic13—21no—
132C22×Dic13—21no—
133C22×Dic13—21no—
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—21no—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—22no—
148C22×Dic13—22no—
149C22×Dic13—22no—
150C22×Dic13—22no—
151C22×Dic13—22no—
152C22×Dic13—22no—
153C22×Dic13—22no—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13—22no—
157C22×Dic13—22no—
158C22×Dic13—22no—
159C22×Dic13C2×D412yes—
160C22×Dic13C2×D412yes—
161C22×Dic13#4112yes—
162C22×Dic13#4112yes—
163C13×C4⋊C4—44no—
164C13×C4⋊C4—44no—
165C42×C13—44no—
166C4⋊Dic13—44no—
167C4⋊Dic13—44no—
168C4×Dic13—44no—
169C4×Dic13—44no—
170C2×#401—132no—
171#1443—132no—
172#1443—132no—
173#1443—132no—
174C4⋊#95—131no—
175C4⋊#95—131no—
176C4⋊#95—131no—
177C4⋊#95—131no—
178C4⋊#95—131no—
179C4⋊#95D1311yescharacteristic
180C4×#95—131no—
181C23×C13C22×D411yescharacteristic
182C23×C13C2×#4111yescharacteristic
183C23×C13C2×#4111yescharacteristic
184C23×C13C2×#4111yescharacteristic
185C23×C13C2×#4111yescharacteristic
186C23×C13C2×#4111yescharacteristic
187C23×C13C2×#4111yescharacteristic
188C23×C13C2×#4111yescharacteristic
189C23×C13C2×#4111yescharacteristic
190C23×C13C2×#4111yescharacteristic
191C23×C13C2×#4111yescharacteristic
192C23×C13H(5,𝔽2)11yescharacteristic
193C23×C132−1+411yescharacteristic
194C23×C132−1+411yescharacteristic
195C23×C132−1+411yescharacteristic
196C2×C4×C13—22no—
197C2×C4×C13—22no—
198C2×C4×C13—22no—
199C2×C4×C13—22no—
200C2×C4×C13—22no—
201C2×C4×C13—22no—
202C2×C4×C13—41no—
203C2×C4×C13—41no—
204C2×C4×C13—41no—
205C2×C4×C13—41no—
206C2×C4×C13—41no—
207C2×C4×C13—41no—
208C2×C4×C13—41no—
209C2×C4×C13—41no—
210C2×C4×C13—42no—
211C2×C4×C13—42no—
212C2×C4×C13—42no—
213C2×C4×C13—42no—
214C2×C4×C13—42no—
215C2×C4×C13—42no—
216C2×C4×C13—42no—
217C2×C4×C13—42no—
218C2×C4×C13—42no—
219C2×C4×C13—42no—
220C2×C4×C13—42no—
221C2×C4×C13—42no—
222C2×C4×C13—42no—
223C2×C4×C13—42no—
224C2×C4×C13#12614yes—
225C2×C4×C13#12614yes—
226C2×C4×C13#12614yes—
227C2×C4×C13#12614yes—
228C2×C4×C13#12614yes—
229C2×C4×C13#12614yes—
230C2×C4×C13#12614yes—
231C2×Dic13—22no—
232C2×Dic13—22no—
233C2×Dic13—22no—
234C2×Dic13—22no—
235C2×Dic13—22no—
236C2×Dic13—22no—
237C2×Dic13—22no—
238C2×Dic13—22no—
239C2×Dic13—22no—
240C2×Dic13—22no—
241C2×Dic13—22no—
242C2×Dic13—22no—
243C2×Dic13—41no—
244C2×Dic13—41no—
245C2×Dic13—41no—
246C2×Dic13—41no—
247C2×Dic13—41no—
248C2×Dic13—41no—
249C2×Dic13—41no—
250C2×Dic13—41no—
251C2×Dic13—41no—
252C2×Dic13—41no—
253C2×Dic13—41no—
254C2×Dic13—41no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—42no—
260C2×Dic13—42no—
261C2×Dic13—42no—
262C2×Dic13—42no—
263C2×Dic13—42no—
264C2×Dic13—42no—
265C2×Dic13—42no—
266C2×Dic13—42no—
267C2×Dic13—42no—
268C2×Dic13—42no—
269C2×Dic13—42no—
270C2×Dic13—42no—
271C2×Dic13—42no—
272C2×Dic13—42no—
273C22×C4⋊C4—131no—
274C22×C4⋊C4—131no—
275C22×C4⋊C4C2×D1311yescharacteristic
276C22×C4⋊C4C2×D1311yescharacteristic
277C22×C42—131no—
278C22×C42—131no—
279C22×C42C2×D1311yescharacteristic
280#401—268no—
281C2×#95—131no—
282C2×#95—132no—
283C2×#95—132no—
284C2×#95—132no—
285C2×#95—132no—
286C2×#95—132no—
287C2×#95—131no—
288C2×#95—131no—
289C2×#95—131no—
290C2×#95—132no—
291C2×#95—132no—
292C2×#95—132no—
293C2×#95—132no—
294C2×#95—132no—
295C2×#95C2×D1312yes—
296C2×#95C2×D1312yes—
297C22×C13C2×#12611yescharacteristic
298C22×C13C2×#12611yescharacteristic
299C22×C13C2×#12611yescharacteristic
300C22×C13C2×#12611yescharacteristic
301C22×C13C2×#12611yescharacteristic
302C22×C13C2×#12611yescharacteristic
303C22×C13C2×#12611yescharacteristic
304C22×C13#52911yescharacteristic
305C22×C13#52911yescharacteristic
306C22×C13#52911yescharacteristic
307C22×C13#53211yescharacteristic
308C22×C13#53211yescharacteristic
309C22×C13#53211yescharacteristic
310C22×C13#54111yescharacteristic
311C22×C13#54111yescharacteristic
312C22×C13#54111yescharacteristic
313C22×C13#54211yescharacteristic
314C22×C13#54211yescharacteristic
315C22×C13#54211yescharacteristic
316C22×C13#54711yescharacteristic
317C22×C13#54711yescharacteristic
318C22×C13#54711yescharacteristic
319C22×C13#55011yescharacteristic
320C22×C13#55211yescharacteristic
321C22×C13#55211yescharacteristic
322C22×C13#55211yescharacteristic
323C22×C13#55311yescharacteristic
324C22×C13#55311yescharacteristic
325C22×C13#55311yescharacteristic
326C22×C13#55611yescharacteristic
327C22×C13#55611yescharacteristic
328C22×C13#55611yescharacteristic
329C22×C13#55611yescharacteristic
330C22×C13#55611yescharacteristic
331C22×C13#55611yescharacteristic
332C4×C13—42no—
333C4×C13—42no—
334C4×C13—82no—
335C4×C13—82no—
336C4×C13#40118yescomplemented
337Dic13—42no—
338Dic13—42no—
339Dic13—42no—
340Dic13—42no—
341Dic13—82no—
342Dic13—82no—
343C23×C4—131no—
344C23×C4—131no—
345C23×C4—131no—
346C23×C4—131no—
347C23×C4—132no—
348C23×C4—132no—
349C23×C4C22×D1312yes—
350C23×C4C22×D1312yes—
351C23×C4C22×D1311yescharacteristic
352C23×C4C22×D1311yescharacteristic
353C23×C4C22×D1311yescharacteristic
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—262no—
361C2×C4⋊C4—262no—
362C2×C4⋊C4—262no—
363C2×C4⋊C4—262no—
364C2×C4⋊C4—262no—
365C2×C4⋊C4—262no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—262no—
370C2×C42—262no—
371C2×C42—262no—
372C2×C42—262no—
373C2×C42—262no—
374C2×C42—262no—
375#95—24no—
376#95—42no—
377#95—134no—
378#95—262no—
379#95—262no—
380#95—264no—
381#95—264no—
382#95—264no—
383#95—264no—
384#95—264no—
385#95—264no—
386#95—264no—
387#95—262no—
388#95—264no—
389#95—522no—
390#95—522no—
391C2×C13C2×#40111yescharacteristic
392C2×C13#249411yescharacteristic
393C2×C13#249411yescharacteristic
394C2×C13#249411yescharacteristic
395C2×C13#249611yescharacteristic
396C2×C13#249611yescharacteristic
397C2×C13#249611yescharacteristic
398C2×C13#251211yescharacteristic
399C2×C13#251211yescharacteristic
400C2×C13#251211yescharacteristic
401C2×C13#251411yescharacteristic
402C2×C13#251411yescharacteristic
403C2×C13#251411yescharacteristic
404C2×C13#264511yescharacteristic
405C2×C13#286011yescharacteristic
406C24C23×D1311yescharacteristic
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—132no—
434C22×C4—132no—
435C22×C4—132no—
436C22×C4—132no—
437C22×C4—261no—
438C22×C4—261no—
439C22×C4—261no—
440C22×C4—261no—
441C22×C4—261no—
442C22×C4—261no—
443C22×C4—261no—
444C22×C4—261no—
445C22×C4—261no—
446C22×C4—261no—
447C22×C4—261no—
448C22×C4—261no—
449C22×C4—261no—
450C22×C4—261no—
451C22×C4—261no—
452C22×C4—261no—
453C22×C4—261no—
454C22×C4—261no—
455C22×C4—261no—
456C22×C4—261no—
457C22×C4—261no—
458C22×C4—261no—
459C22×C4—261no—
460C22×C4—261no—
461C22×C4—262no—
462C22×C4—262no—
463C22×C4—262no—
464C22×C4—262no—
465C22×C4—262no—
466C22×C4—262no—
467C22×C4—262no—
468C22×C4—262no—
469C22×C4—262no—
470C22×C4—262no—
471C22×C4—262no—
472C22×C4—262no—
473C22×C4—262no—
474C22×C4—262no—
475C22×C4#612712yes—
476C22×C4#612712yes—
477C22×C4#612712yes—
478C22×C4D4×D1312yes—
479C22×C4#612912yes—
480C22×C4#612912yes—
481C22×C4#612912yes—
482C22×C4#613112yes—
483C22×C4#613112yes—
484C4⋊C4—44no—
485C4⋊C4—44no—
486C4⋊C4—524no—
487C4⋊C4—524no—
488C42—44no—
489C42—524no—
490C42—524no—
491C13C4⋊#40111yescharacteristic, complemented, Sylow
492C23C2×#612711yescharacteristic
493C23C2×#612711yescharacteristic
494C23C2×#612711yescharacteristic
495C23C2×D4×D1311yescharacteristic
496C23C2×#612911yescharacteristic
497C23C2×#612911yescharacteristic
498C23C2×#612911yescharacteristic
499C23#8825111yescharacteristic
500C23C2×#613111yescharacteristic
501C23C2×#613111yescharacteristic
502C23#8825411yescharacteristic
503C23#41×D1311yescharacteristic
504C23#41×D1311yescharacteristic
505C23#8825711yescharacteristic
506C23#8825711yescharacteristic
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—262no—
536C2×C4—262no—
537C2×C4—262no—
538C2×C4—262no—
539C2×C4—262no—
540C2×C4—262no—
541C2×C4—262no—
542C2×C4—262no—
543C2×C4—262no—
544C2×C4—262no—
545C2×C4—262no—
546C2×C4—262no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—521no—
552C2×C4—521no—
553C2×C4—521no—
554C2×C4—521no—
555C2×C4—521no—
556C2×C4—521no—
557C2×C4—521no—
558C2×C4—521no—
559C2×C4—521no—
560C2×C4—521no—
561C2×C4—521no—
562C2×C4—521no—
563C2×C4—522no—
564C2×C4—522no—
565C2×C4—522no—
566C2×C4—522no—
567C2×C4—522no—
568C2×C4—522no—
569C2×C4—522no—
570C2×C4—522no—
571C2×C4—522no—
572C2×C4—522no—
573C2×C4—522no—
574C2×C4—522no—
575C2×C4—522no—
576C2×C4—522no—
577C2×C4#8813014yes—
578C2×C4#8813314yes—
579C2×C4#8813314yes—
580C2×C4#8813314yes—
581C2×C4#8815214yes—
582C2×C4#8815214yes—
583C2×C4#8815214yes—
584C22C2×#8813011yescharacteristic
585C22C2×#8813311yescharacteristic
586C22C2×#8813311yescharacteristic
587C22C2×#8813311yescharacteristic
588C22#1171921211yescharacteristic
589C22C2×#8815211yescharacteristic
590C22C2×#8815211yescharacteristic
591C22C2×#8815211yescharacteristic
592C22#1171921911yescharacteristic
593C22#1171923411yescharacteristic
594C22#1171923811yescharacteristic
595C22#1171925311yescharacteristic
596C22#1171925611yescharacteristic
597C22#1171926311yescharacteristic
598C22#1171926611yescharacteristic
599C22#1171928511yescharacteristic
600C22#1171928611yescharacteristic
601C22#1171928811yescharacteristic
602C22#1171928911yescharacteristic
603C22#1171930111yescharacteristic
604C22#1171930811yescharacteristic
605C22#1171931611yescharacteristic
606C22#1171931911yescharacteristic
607C22#1171932911yescharacteristic
608C22#1171933011yescharacteristic
609C22#1171934611yescharacteristic
610C22#1171934711yescharacteristic
611C22#1171937611yescharacteristic
612C22#1171937611yescharacteristic
613C22#1171939611yescharacteristic
614C22#1171940211yescharacteristic
615C22#1171942311yescharacteristic
616C22#1171943011yescharacteristic
617C22#1171943711yescharacteristic
618C22#1171943811yescharacteristic
619C4—42no—
620C4—42no—
621C4—82no—
622C4—82no—
623C4—522no—
624C4—522no—
625C4—522no—
626C4—522no—
627C4—1042no—
628C4—1042no—
629C4C13⋊#40118yescomplemented
630C2C2×C13⋊#40111yescharacteristic
631C2#1311923011yescharacteristic
632C2#1311923411yescharacteristic
633C2#1311923811yescharacteristic
634C2#1311925211yescharacteristic
635C2#1311925611yescharacteristic
636C2#1311926011yescharacteristic
637C2#1311941811yescharacteristic
638C2#1311942011yescharacteristic
639C2#1311942311yescharacteristic
640C2#1311944011yescharacteristic
641C2#1311944211yescharacteristic
642C2#1311944511yescharacteristic
643C2#1312080411yescharacteristic
644C2#1312320411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutator, socle, prime radical, cosocleC24×C13C24
FittingC13×C4⋊#95C2
hypercenterC4⋊#95D13
hypocenterC13C4⋊#401
LCSG ▷ C24×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
336. C4×C13#401semidirect
491. C13C4⋊#401semidirect
629. C4C13⋊#401semidirect

Maximal subgroups

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

subgroupindex
C2×C13⋊#4012
#131130972
#131130962
#131130662
#131130652
C4×#880712
C13×C4⋊#952
C4⋊#40113