Finite Group Databasebeta

← #15785191

Subgroups — #15785191

Order 3328.

1774 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718308C212yesmaximal
2C2×#11718633C212yesmaximal
3C2×#11718637C212yesmaximal
4C2×#11718637C211yesmaximal, characteristic
5C2×#11718310C211yesmaximal, characteristic
6C2×#11718310C211yesmaximal, characteristic
7#13113101C211yesmaximal, characteristic
8#13113100C211yesmaximal, characteristic
9#13113099C211yesmaximal, characteristic
10#13113064C212yesmaximal
11C13×#1444C211yesmaximal, characteristic
12C22×C13×C4⋊C4C2212yes—
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C4⋊Dic13C2212yes—
15C22×C4⋊Dic13C2211yescharacteristic
16C22×#6101C2212yes—
17C22×#6101C2212yes—
18C22×#6101C2212yes—
19C22×#6101C2212yes—
20C22×#6101C2211yescharacteristic
21C22×#6101C2211yescharacteristic
22C22×#6101C2212yes—
23C22×C4×Dic13C2211yescharacteristic
24C22×C4×Dic13C2211yescharacteristic
25C22×C4×Dic13C2212yes—
26C22×C4×Dic13C2211yescharacteristic
27C2×C13×#95C2211yescharacteristic
28C2×C13×#95C2212yes—
29C2×C13×#95C2211yescharacteristic
30C2×#88071C2211yescharacteristic
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2211yescharacteristic
35#11718637—28no—
36#11718637—24no—
37#11718633—28no—
38#11718310—24no—
39#11718310C418yescomplemented
40#11718308—28no—
41C23×C4×C13C2312yes—
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2312yes—
45C23×C4×C13C2311yescharacteristic
46C23×Dic13C2312yes—
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2312yes—
50C23×Dic13C2311yescharacteristic
51C23×Dic13C2311yescharacteristic
52C2×C13×C4⋊C4—24no—
53C2×C13×C4⋊C4—24no—
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4—42no—
56C2×C13×C4⋊C4—42no—
57C2×C4⋊Dic13—24no—
58C2×C4⋊Dic13—22no—
59C2×C4⋊Dic13—24no—
60C2×C4⋊Dic13—42no—
61C2×C4⋊Dic13—42no—
62C2×#6101—22no—
63C2×#6101—22no—
64C2×#6101—22no—
65C2×#6101—22no—
66C2×#6101—24no—
67C2×#6101—24no—
68C2×#6101—24no—
69C2×#6101—24no—
70C2×#6101—24no—
71C2×#6101—24no—
72C2×#6101—24no—
73C2×#6101—24no—
74C2×#6101—24no—
75C2×#6101—24no—
76C2×#6101—42no—
77C2×#6101—42no—
78C2×#6101C2×C418yes—
79C2×#6101D414yes—
80C2×#6101D418yes—
81C2×#6101Q814yes—
82C2×#6101Q818yes—
83C2×C4×Dic13—24no—
84C2×C4×Dic13—24no—
85C2×C4×Dic13—24no—
86C2×C4×Dic13—22no—
87C2×C4×Dic13—22no—
88C2×C4×Dic13—24no—
89C2×C4×Dic13C2×C418yes—
90C2×C4×Dic13C2×C414yes—
91C2×C4×Dic13D414yes—
92C2×C4×Dic13Q814yes—
93C13×#95—24no—
94C13×#95—22no—
95C13×#95C2×C414yes—
96#88071—22no—
97#88071—24no—
98#88071—24no—
99#88071—24no—
100#88071C2×C414yes—
101#13910—131nomaximal, Sylow
102C24×C13C2411yescharacteristic
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—21no—
111C22×C4×C13—21no—
112C22×C4×C13—22no—
113C22×C4×C13—21no—
114C22×C4×C13—21no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13C22×C412yes—
125C22×C4×C13C22×C414yes—
126C22×C4×C13C2×D412yes—
127C22×C4×C13C2×D412yes—
128C22×C4×C13C2×D414yes—
129C22×C4×C13C2×Q812yes—
130C22×C4×C13C2×Q812yes—
131C22×C4×C13C2×Q814yes—
132C22×Dic13—22no—
133C22×Dic13—22no—
134C22×Dic13—22no—
135C22×Dic13—22no—
136C22×Dic13—22no—
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13—22no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—22no—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—22no—
148C22×Dic13—22no—
149C22×Dic13—22no—
150C22×Dic13—22no—
151C22×Dic13C22×C414yes—
152C22×Dic13C22×C412yes—
153C22×Dic13C22×C412yes—
154C22×Dic13C2×D412yes—
155C22×Dic13C2×D414yes—
156C22×Dic13C2×D412yes—
157C22×Dic13C2×D412yes—
158C22×Dic13C2×D414yes—
159C22×Dic13C2×D412yes—
160C22×Dic13C2×Q812yes—
161C22×Dic13C2×Q814yes—
162C22×Dic13C2×Q812yes—
163C22×Dic13C2×Q812yes—
164C22×Dic13C2×Q814yes—
165C22×Dic13C2×Q812yes—
166C22×Dic13#4112yes—
167C22×Dic13#4112yes—
168C13×C4⋊C4—48no—
169C13×C4⋊C4—44no—
170C4⋊Dic13—48no—
171C4⋊Dic13—44no—
172#6101—28no—
173#6101—28no—
174#6101—48no—
175#6101—48no—
176#6101—48no—
177#6101—48no—
178#6101C4⋊C4132yescomplemented
179C4×Dic13—216no—
180C4×Dic13—44no—
181C4×Dic13—44no—
182C4×Dic13C4⋊C4116yescomplemented
183C2×#389—132no—
184C2×#389—132no—
185C2×#384—132no—
186C2×#384—131no—
187C2×C4×C4⋊C4—131no—
188C2×C4×C4⋊C4—131no—
189#1444—131no—
190#1444—131no—
191#1444—131no—
192#1444D1311yescharacteristic
193C4⋊#95—132no—
194C23×C13C23×C411yescharacteristic
195C23×C13C22×D411yescharacteristic
196C23×C13C22×D412yes—
197C23×C13C22×D411yescharacteristic
198C23×C13C22×Q811yescharacteristic
199C23×C13C22×Q812yes—
200C23×C13C22×Q811yescharacteristic
201C23×C13C2×#4111yescharacteristic
202C23×C13C2×#4111yescharacteristic
203C23×C13H(5,𝔽2)12yes—
204C23×C132−1+412yes—
205C2×C4×C13—24no—
206C2×C4×C13—24no—
207C2×C4×C13—24no—
208C2×C4×C13—22no—
209C2×C4×C13—22no—
210C2×C4×C13—24no—
211C2×C4×C13—24no—
212C2×C4×C13—24no—
213C2×C4×C13—24no—
214C2×C4×C13—24no—
215C2×C4×C13—22no—
216C2×C4×C13—22no—
217C2×C4×C13—24no—
218C2×C4×C13—24no—
219C2×C4×C13—41no—
220C2×C4×C13—41no—
221C2×C4×C13—41no—
222C2×C4×C13—41no—
223C2×C4×C13—42no—
224C2×C4×C13—42no—
225C2×C4×C13—42no—
226C2×C4×C13—42no—
227C2×C4×C13—42no—
228C2×C4×C13—42no—
229C2×C4×C13—42no—
230C2×C4×C13—42no—
231C2×C4×C13—42no—
232C2×C4×C13C2×C4⋊C414yes—
233C2×C4×C13C2×C4⋊C418yes—
234C2×Dic13—24no—
235C2×Dic13—24no—
236C2×Dic13—24no—
237C2×Dic13—24no—
238C2×Dic13—24no—
239C2×Dic13—24no—
240C2×Dic13—22no—
241C2×Dic13—22no—
242C2×Dic13—24no—
243C2×Dic13—24no—
244C2×Dic13—41no—
245C2×Dic13—41no—
246C2×Dic13—41no—
247C2×Dic13—41no—
248C2×Dic13—42no—
249C2×Dic13—42no—
250C2×Dic13—42no—
251C2×Dic13—42no—
252C2×Dic13—42no—
253C2×Dic13—42no—
254C2×Dic13—42no—
255C2×Dic13—42no—
256C2×Dic13—42no—
257C2×Dic13C2×C4⋊C418yes—
258C2×Dic13C2×C4⋊C414yes—
259C2×Dic13C2×C4⋊C418yes—
260C2×Dic13C2×C4⋊C414yes—
261C2×Dic13C4×D414yes—
262C2×Dic13C4×Q814yes—
263C2×Dic13#12114yes—
264C2×Dic13C22⋊Q814yes—
265C2×Dic13#12514yes—
266C2×Dic13#12714yes—
267C2×Dic13C4⋊Q814yes—
268C2×Dic13C4⋊Q818yes—
269C2×Dic13C4⋊Q814yes—
270C22×C4⋊C4—132no—
271C22×C4⋊C4—131no—
272C22×C4⋊C4—131no—
273C22×C4⋊C4—132no—
274C22×C4⋊C4—132no—
275C22×C4⋊C4—132no—
276C22×C4⋊C4—132no—
277C22×C4⋊C4—132no—
278C22×C4⋊C4—131no—
279C22×C4⋊C4C2×D1312yes—
280C22×C4⋊C4C2×D1311yescharacteristic
281C22×C42—131no—
282C22×C42—132no—
283C22×C42—131no—
284C22×C42—131no—
285#389—268no—
286#389—268no—
287#384—264no—
288#384—268no—
289C4×C4⋊C4—138no—
290C4×C4⋊C4—264no—
291C2×#95—131no—
292C2×#95—132no—
293C2×#95—132no—
294C2×#95—132no—
295C2×#95—131no—
296C2×#95C2×D1312yes—
297C2×#95C2×D1311yescharacteristic
298C2×#95C2×D1311yescharacteristic
299C22×C13C22×C4⋊C411yescharacteristic
300C22×C13C22×C4⋊C412yes—
301C22×C13C2×C4×D411yescharacteristic
302C22×C13C2×C4×Q811yescharacteristic
303C22×C13#52012yes—
304C22×C13C2×#12111yescharacteristic
305C22×C13C2×C22⋊Q811yescharacteristic
306C22×C13C2×#12511yescharacteristic
307C22×C13C2×#12711yescharacteristic
308C22×C13C2×C4⋊Q811yescharacteristic
309C22×C13C2×C4⋊Q812yes—
310C22×C13C2×C4⋊Q811yescharacteristic
311C22×C13#53511yescharacteristic
312C22×C13#53611yescharacteristic
313C22×C13#54412yes—
314C22×C13D4212yes—
315C22×C13#54712yes—
316C22×C13D4×Q812yes—
317C22×C13D4×Q812yes—
318C22×C13#55012yes—
319C22×C13#55412yes—
320C22×C13#55712yes—
321C22×C13Q8212yes—
322C4×C13—24no—
323C4×C13—28no—
324C4×C13—42no—
325C4×C13—42no—
326C4×C13—82no—
327Dic13—28no—
328Dic13—42no—
329Dic13—42no—
330Dic13—82no—
331Dic13#38418yescomplemented
332Dic13#38918yescomplemented
333C23×C4—131no—
334C23×C4—131no—
335C23×C4—132no—
336C23×C4—131no—
337C23×C4—131no—
338C23×C4—132no—
339C23×C4C22×D1312yes—
340C23×C4C22×D1311yescharacteristic
341C23×C4C22×D1311yescharacteristic
342C23×C4C22×D1312yes—
343C23×C4C22×D1311yescharacteristic
344C2×C4⋊C4—24no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—138no—
350C2×C4⋊C4—138no—
351C2×C4⋊C4—138no—
352C2×C4⋊C4—134no—
353C2×C4⋊C4—134no—
354C2×C4⋊C4—262no—
355C2×C4⋊C4—262no—
356C2×C4⋊C4—262no—
357C2×C4⋊C4—262no—
358C2×C4⋊C4—264no—
359C2×C4⋊C4—264no—
360C2×C4⋊C4—264no—
361C2×C4⋊C4—264no—
362C2×C4⋊C4—264no—
363C2×C4⋊C4—264no—
364C2×C4⋊C4—264no—
365C2×C4⋊C4—264no—
366C2×C4⋊C4—264no—
367C2×C4⋊C4—264no—
368C2×C4⋊C4—264no—
369C2×C4⋊C4—262no—
370C2×C4⋊C4—264no—
371C2×C4⋊C4—522no—
372C2×C4⋊C4—522no—
373C2×C4⋊C4—522no—
374C2×C4⋊C4—522no—
375C2×C42—134no—
376C2×C42—134no—
377C2×C42—134no—
378C2×C42—138no—
379C2×C42—264no—
380C2×C42—264no—
381C2×C42—262no—
382C2×C42—262no—
383C2×C42—264no—
384C2×C42—264no—
385#95—22no—
386#95—24no—
387#95—134no—
388#95—264no—
389#95—264no—
390#95—262no—
391#95—264no—
392#95C4×D1314yes—
393C2×C13C2×#38411yescharacteristic
394C2×C13C2×#38911yescharacteristic
395C2×C13#231711yescharacteristic
396C2×C13D4×C4⋊C412yes—
397C2×C13Q8×C4⋊C412yes—
398C2×C13#254111yescharacteristic
399C2×C13#254211yescharacteristic
400C2×C13#254611yescharacteristic
401C2×C13#255112yes—
402C2×C13#255212yes—
403C2×C13#256711yescharacteristic
404C24C23×D1311yescharacteristic
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—132no—
427C22×C4—132no—
428C22×C4—132no—
429C22×C4—132no—
430C22×C4—134no—
431C22×C4—132no—
432C22×C4—132no—
433C22×C4—132no—
434C22×C4—134no—
435C22×C4—132no—
436C22×C4—132no—
437C22×C4—132no—
438C22×C4—134no—
439C22×C4—134no—
440C22×C4—134no—
441C22×C4—132no—
442C22×C4—132no—
443C22×C4—262no—
444C22×C4—262no—
445C22×C4—262no—
446C22×C4—262no—
447C22×C4—262no—
448C22×C4—261no—
449C22×C4—261no—
450C22×C4—262no—
451C22×C4—262no—
452C22×C4—261no—
453C22×C4—261no—
454C22×C4—262no—
455C22×C4—262no—
456C22×C4—262no—
457C22×C4—262no—
458C22×C4—262no—
459C22×C4—262no—
460C22×C4—262no—
461C22×C4—262no—
462C22×C4C2×C4×D1312yes—
463C22×C4C2×C4×D1314yes—
464C22×C4D4×D1312yes—
465C22×C4D4×D1312yes—
466C22×C4D4×D1314yes—
467C22×C4Q8×D1312yes—
468C22×C4Q8×D1312yes—
469C22×C4Q8×D1314yes—
470C4⋊C4—48no—
471C4⋊C4—44no—
472C4⋊C4—1332no—
473C4⋊C4—268no—
474C4⋊C4—268no—
475C4⋊C4—528no—
476C4⋊C4—528no—
477C4⋊C4—524no—
478C4⋊C4—528no—
479C4⋊C4—528no—
480C4⋊C4—528no—
481C42—1316no—
482C42—2616no—
483C42—524no—
484C42—524no—
485C13#1391011yescharacteristic, complemented, Sylow
486C23C22×C4×D1311yescharacteristic
487C23C2×D4×D1312yes—
488C23C2×D4×D1311yescharacteristic
489C23C2×D4×D1311yescharacteristic
490C23#8825112yes—
491C23C2×Q8×D1311yescharacteristic
492C23C2×Q8×D1312yes—
493C23C2×Q8×D1311yescharacteristic
494C23#41×D1311yescharacteristic
495C23#41×D1311yescharacteristic
496C23#8825712yes—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—22no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—134no—
525C2×C4—138no—
526C2×C4—134no—
527C2×C4—134no—
528C2×C4—134no—
529C2×C4—138no—
530C2×C4—134no—
531C2×C4—134no—
532C2×C4—134no—
533C2×C4—134no—
534C2×C4—134no—
535C2×C4—134no—
536C2×C4—138no—
537C2×C4—264no—
538C2×C4—264no—
539C2×C4—264no—
540C2×C4—264no—
541C2×C4—264no—
542C2×C4—264no—
543C2×C4—264no—
544C2×C4—262no—
545C2×C4—262no—
546C2×C4—264no—
547C2×C4—521no—
548C2×C4—522no—
549C2×C4—521no—
550C2×C4—522no—
551C2×C4—521no—
552C2×C4—521no—
553C2×C4—522no—
554C2×C4—522no—
555C2×C4—522no—
556C2×C4—522no—
557C2×C4—522no—
558C2×C4—522no—
559C2×C4—522no—
560C2×C4C4⋊C4×D1314yes—
561C2×C4C4⋊C4×D1318yes—
562C22C2×C4⋊C4×D1311yescharacteristic
563C22C2×C4⋊C4×D1312yes—
564C22C4×D4×D1311yescharacteristic
565C22#1171925112yes—
566C22C4×Q8×D1311yescharacteristic
567C22#1171929512yes—
568C22#1171929711yescharacteristic
569C22#1171930412yes—
570C22D13×#12111yescharacteristic
571C22#1171932812yes—
572C22D13×C22⋊Q811yescharacteristic
573C22#1171933712yes—
574C22#1171933712yes—
575C22#1171934112yes—
576C22#1171935311yescharacteristic
577C22#1171936012yes—
578C22#1171939012yes—
579C22D13×#12511yescharacteristic
580C22D13×#12711yescharacteristic
581C22#1171942712yes—
582C22D13×C4⋊Q811yescharacteristic
583C22D13×C4⋊Q812yes—
584C22D13×C4⋊Q811yescharacteristic
585C4—24no—
586C4—28no—
587C4—42no—
588C4—42no—
589C4—82no—
590C4—138no—
591C4—138no—
592C4—268no—
593C4—522no—
594C4—522no—
595C4—1042no—
596C2D13×#38411yescharacteristic
597C2D13×#38911yescharacteristic
598C2#1311745511yescharacteristic
599C2#1311773412yes—
600C2#1311775012yes—
601C2#1311977711yescharacteristic
602C2#1311978411yescharacteristic
603C2#1311982011yescharacteristic
604C2#1311986112yes—
605C2#1311986612yes—
606C2#1312004011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1444C2
socle, prime radical, cosocleC24×C13C24
hypercenter#1444D13
hypocenterC13#13910
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
39. #11718310C4semidirect
178. #6101C4⋊C4semidirect
182. C4×Dic13C4⋊C4semidirect
331. Dic13#384semidirect
332. Dic13#389semidirect
485. C13#13910semidirect

Maximal subgroups

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

subgroupindex
C2×#117183082
C2×#117186332
C2×#117186372
C2×#117183102
#131131012
#131131002
#131130992
#131130642
C13×#14442
#1391013