Finite Group Databasebeta

← #15789366

Subgroups — #15789366

Order 3328.

1262 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718646C211yesmaximal, characteristic
2C2×#11718593C211yesmaximal, characteristic
3#13113104C212yesmaximal
4#13113098C212yesmaximal
5#13113093C212yesmaximal
6#13113089C212yesmaximal
7#13113066C211yesmaximal, characteristic
8#13113065C211yesmaximal, characteristic
9#13113065C211yesmaximal, characteristic
10#13113065C211yesmaximal, characteristic
11C2×C13×#389C211yesmaximal, characteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2212yes—
15C22×C42×C13C2211yescharacteristic
16C22×C4⋊Dic13C2211yescharacteristic
17C22×C4⋊Dic13C2211yescharacteristic
18C22×C4⋊Dic13C2212yes—
19C22×C4×Dic13C2211yescharacteristic
20C22×C4×Dic13C2211yescharacteristic
21C13×#389C418yescomplemented
22C2×C13×#95C2212yes—
23C2×#88071C2211yescharacteristic
24C2×#88071C2211yescharacteristic
25C2×#88071C2211yescharacteristic
26C2×#88071C2212yes—
27C2×#88071C2211yescharacteristic
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36#11718646—24no—
37#11718593—24no—
38C23×C4×C13C2312yes—
39C23×C4×C13C2311yescharacteristic
40C23×C4×C13C2311yescharacteristic
41C23×C4×C13C2312yes—
42C23×C4×C13C2311yescharacteristic
43C23×Dic13C2312yes—
44C23×Dic13C2312yes—
45C23×Dic13C2311yescharacteristic
46C23×Dic13C2311yescharacteristic
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2311yescharacteristic
49C2×C13×C4⋊C4—22no—
50C2×C13×C4⋊C4—22no—
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4—22no—
53C2×C13×C4⋊C4—42no—
54C2×C13×C4⋊C4—42no—
55C2×C13×C4⋊C4C2×C414yes—
56C2×C13×C4⋊C4C2×C414yes—
57C2×C13×C4⋊C4C2×C418yes—
58C2×C42×C13—22no—
59C2×C42×C13—22no—
60C2×C42×C13C2×C414yes—
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—24no—
68C2×C4⋊Dic13—42no—
69C2×C4⋊Dic13—42no—
70C2×C4×Dic13—22no—
71C2×C4×Dic13—22no—
72C2×C4×Dic13—22no—
73C2×C4×Dic13—22no—
74C2×C4×Dic13D414yes—
75C2×C4×Dic13Q814yes—
76C13×#95C2×C418yes—
77#88071—22no—
78#88071—22no—
79#88071—22no—
80#88071—22no—
81#88071—24no—
82#88071—42no—
83#88071—42no—
84#88071—42no—
85#88071—42no—
86#88071—42no—
87#88071—42no—
88#88071—42no—
89#88071—42no—
90#14266—131nomaximal, Sylow
91C24×C13C2411yescharacteristic
92C22×C4×C13—21no—
93C22×C4×C13—21no—
94C22×C4×C13—22no—
95C22×C4×C13—21no—
96C22×C4×C13—21no—
97C22×C4×C13—22no—
98C22×C4×C13—22no—
99C22×C4×C13—22no—
100C22×C4×C13—21no—
101C22×C4×C13—21no—
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—21no—
109C22×C4×C13—21no—
110C22×C4×C13—21no—
111C22×C4×C13—21no—
112C22×C4×C13—21no—
113C22×C4×C13—22no—
114C22×C4×C13—21no—
115C22×C4×C13—22no—
116C22×C4×C13C22×C412yes—
117C22×C4×C13C22×C414yes—
118C22×C4×C13C22×C414yes—
119C22×C4×C13C22×C412yes—
120C22×C4×C13C22×C412yes—
121C22×C4×C13C2×D412yes—
122C22×C4×C13C2×Q812yes—
123C22×C4×C13#4112yes—
124C22×C4×C13#4112yes—
125C22×C4×C13#4112yes—
126C22×C4×C13#4112yes—
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—21no—
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
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×Dic13—22no—
160C22×Dic13—22no—
161C22×Dic13—22no—
162C22×Dic13—22no—
163C22×Dic13—22no—
164C22×Dic13—22no—
165C22×Dic13C2×D412yes—
166C22×Dic13C2×D412yes—
167C22×Dic13C2×Q812yes—
168C22×Dic13C2×Q812yes—
169C13×C4⋊C4—28no—
170C13×C4⋊C4—28no—
171C13×C4⋊C4—48no—
172C42×C13—28no—
173C4⋊Dic13—48no—
174C4⋊Dic13—44no—
175C4⋊Dic13—44no—
176C4×Dic13—28no—
177C4×Dic13—28no—
178C2×#389—131no—
179C2×#389D1311yescharacteristic
180C2×#376—131no—
181#1445—132no—
182#1443—132no—
183#1442—132no—
184#1441—132no—
185C4⋊#95—131no—
186C4⋊#95—131no—
187C4⋊#95—131no—
188C4⋊#95—131no—
189C23×C13C23×C411yescharacteristic
190C23×C13C22×D411yescharacteristic
191C23×C13C22×Q811yescharacteristic
192C23×C13C2×#4111yescharacteristic
193C23×C13C2×#4111yescharacteristic
194C23×C13C2×#4111yescharacteristic
195C23×C13C2×#4111yescharacteristic
196C23×C13H(5,𝔽2)11yescharacteristic
197C23×C13H(5,𝔽2)11yescharacteristic
198C23×C13H(5,𝔽2)11yescharacteristic
199C23×C13H(5,𝔽2)11yescharacteristic
200C23×C132−1+411yescharacteristic
201C23×C132−1+411yescharacteristic
202C23×C132−1+411yescharacteristic
203C23×C132−1+411yescharacteristic
204C2×C4×C13—24no—
205C2×C4×C13—22no—
206C2×C4×C13—22no—
207C2×C4×C13—24no—
208C2×C4×C13—22no—
209C2×C4×C13—24no—
210C2×C4×C13—24no—
211C2×C4×C13—22no—
212C2×C4×C13—24no—
213C2×C4×C13—22no—
214C2×C4×C13—22no—
215C2×C4×C13—24no—
216C2×C4×C13—42no—
217C2×C4×C13—41no—
218C2×C4×C13—41no—
219C2×C4×C13—41no—
220C2×C4×C13—41no—
221C2×C4×C13—42no—
222C2×C4×C13—42no—
223C2×C4×C13—42no—
224C2×C4×C13—41no—
225C2×C4×C13—42no—
226C2×C4×C13—41no—
227C2×C4×C13—42no—
228C2×C4×C13—42no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—42no—
232C2×C4×C13#11714yes—
233C2×C4×C13C4×D414yes—
234C2×C4×C13C4×Q814yes—
235C2×C4×C13C22⋊Q814yes—
236C2×C4×C13#12314yes—
237C2×C4×C13#12514yes—
238C2×C4×C13#12614yes—
239C2×Dic13—22no—
240C2×Dic13—22no—
241C2×Dic13—22no—
242C2×Dic13—22no—
243C2×Dic13—22no—
244C2×Dic13—22no—
245C2×Dic13—22no—
246C2×Dic13—22no—
247C2×Dic13—22no—
248C2×Dic13—22no—
249C2×Dic13—22no—
250C2×Dic13—22no—
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—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—42no—
268C2×Dic13—42no—
269C2×Dic13—42no—
270C2×Dic13—42no—
271C2×Dic13—42no—
272C2×Dic13—42no—
273C2×Dic13—42no—
274C2×Dic13—42no—
275C2×Dic13—42no—
276C2×Dic13—42no—
277C2×Dic13—42no—
278C2×Dic13—42no—
279C2×Dic13—42no—
280C2×Dic13—42no—
281C22×C4⋊C4—131no—
282C22×C4⋊C4—131no—
283C22×C4⋊C4—132no—
284C22×C4⋊C4C2×D1311yescharacteristic
285C22×C4⋊C4C2×D1311yescharacteristic
286C22×C4⋊C4C2×D1312yes—
287C22×C42—131no—
288C22×C42—131no—
289C22×C42C2×D1311yescharacteristic
290#389—264no—
291#389Dic1318yescomplemented
292#376—264no—
293C2×#95—131no—
294C2×#95—131no—
295C2×#95—131no—
296C2×#95—132no—
297C2×#95—131no—
298C2×#95—132no—
299C2×#95—132no—
300C2×#95—132no—
301C2×#95—132no—
302C2×#95—132no—
303C2×#95—132no—
304C2×#95—132no—
305C2×#95—132no—
306C2×#95C2×D1312yes—
307C22×C13C2×#11711yescharacteristic
308C22×C13C2×C4×D411yescharacteristic
309C22×C13C2×C4×Q811yescharacteristic
310C22×C13#51811yescharacteristic
311C22×C13#51911yescharacteristic
312C22×C13#52011yescharacteristic
313C22×C13#52011yescharacteristic
314C22×C13C2×C22⋊Q811yescharacteristic
315C22×C13C2×#12311yescharacteristic
316C22×C13C2×#12511yescharacteristic
317C22×C13C2×#12611yescharacteristic
318C22×C13#53511yescharacteristic
319C22×C13#53611yescharacteristic
320C22×C13#53711yescharacteristic
321C22×C13#53711yescharacteristic
322C22×C13#54011yescharacteristic
323C22×C13#54011yescharacteristic
324C22×C13#54011yescharacteristic
325C22×C13#54011yescharacteristic
326C22×C13#54111yescharacteristic
327C22×C13#54111yescharacteristic
328C22×C13#54111yescharacteristic
329C22×C13#54111yescharacteristic
330C22×C13#54211yescharacteristic
331C22×C13#54211yescharacteristic
332C22×C13#54211yescharacteristic
333C22×C13#54211yescharacteristic
334C22×C13#54211yescharacteristic
335C22×C13#54211yescharacteristic
336C22×C13#54211yescharacteristic
337C22×C13#54211yescharacteristic
338C22×C13#54411yescharacteristic
339C22×C13#54411yescharacteristic
340C22×C13#54411yescharacteristic
341C22×C13#54411yescharacteristic
342C4×C13—44no—
343C4×C13—42no—
344C4×C13—42no—
345C4×C13—44no—
346C4×C13#38718yes—
347Dic13—42no—
348Dic13—42no—
349Dic13—42no—
350Dic13—42no—
351Dic13—82no—
352Dic13—82no—
353C23×C4—131no—
354C23×C4—131no—
355C23×C4—131no—
356C23×C4—131no—
357C23×C4—132no—
358C23×C4—132no—
359C23×C4C22×D1312yes—
360C23×C4C22×D1312yes—
361C23×C4C22×D1311yescharacteristic
362C23×C4C22×D1311yescharacteristic
363C23×C4C22×D1311yescharacteristic
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—264no—
371C2×C4⋊C4—262no—
372C2×C4⋊C4—262no—
373C2×C4⋊C4—262no—
374C2×C4⋊C4—262no—
375C2×C4⋊C4—262no—
376C2×C4⋊C4—262no—
377C2×C4⋊C4—522no—
378C2×C4⋊C4—522no—
379C2×C4⋊C4C2×Dic1314yes—
380C2×C4⋊C4C2×Dic1314yes—
381C2×C4⋊C4C2×Dic1318yes—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—134no—
385C2×C42—134no—
386C2×C42—262no—
387C2×C42—262no—
388C2×C42—262no—
389C2×C42—262no—
390C2×C42C2×Dic1314yes—
391#95—262no—
392#95—262no—
393#95—262no—
394#95—262no—
395#95—264no—
396#95—522no—
397#95—522no—
398#95—522no—
399#95—522no—
400#95—522no—
401#95—522no—
402#95—522no—
403#95—522no—
404#95C2×Dic1318yes—
405C2×C13C2×#38711yescharacteristic
406C2×C13#231911yescharacteristic
407C2×C13#232011yescharacteristic
408C2×C13#232311yescharacteristic
409C2×C13#232411yescharacteristic
410C2×C13#233011yescharacteristic
411C2×C13#233111yescharacteristic
412C2×C13#262411yescharacteristic
413C2×C13#262511yescharacteristic
414C2×C13#262811yescharacteristic
415C2×C13#262911yescharacteristic
416C2×C13#264411yescharacteristic
417C2×C13#264511yescharacteristic
418C2×C13#264711yescharacteristic
419C2×C13#264711yescharacteristic
420C24C23×D1311yescharacteristic
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—132no—
446C22×C4—132no—
447C22×C4—132no—
448C22×C4—132no—
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—261no—
462C22×C4—261no—
463C22×C4—261no—
464C22×C4—261no—
465C22×C4—261no—
466C22×C4—261no—
467C22×C4—261no—
468C22×C4—261no—
469C22×C4—261no—
470C22×C4—261no—
471C22×C4—261no—
472C22×C4—261no—
473C22×C4—262no—
474C22×C4—262no—
475C22×C4—262no—
476C22×C4—262no—
477C22×C4—262no—
478C22×C4—262no—
479C22×C4—262no—
480C22×C4—262no—
481C22×C4—262no—
482C22×C4—262no—
483C22×C4—262no—
484C22×C4—262no—
485C22×C4—262no—
486C22×C4—262no—
487C22×C4#612712yes—
488C22×C4#612712yes—
489C22×C4D4×D1312yes—
490C22×C4#612912yes—
491C22×C4Q8×D1312yes—
492C22×C4#613112yes—
493C22×C4C22×Dic1312yes—
494C22×C4C22×Dic1314yes—
495C22×C4C22×Dic1314yes—
496C22×C4C22×Dic1312yes—
497C22×C4C22×Dic1312yes—
498C4⋊C4—28no—
499C4⋊C4—28no—
500C4⋊C4—48no—
501C4⋊C4—528no—
502C4⋊C4—524no—
503C4⋊C4—524no—
504C42—28no—
505C42—268no—
506C42—268no—
507C13#1426611yescharacteristic, complemented, Sylow
508C23C2×#612711yescharacteristic
509C23C2×#612711yescharacteristic
510C23C2×D4×D1311yescharacteristic
511C23C2×#612911yescharacteristic
512C23#8825111yescharacteristic
513C23#8825111yescharacteristic
514C23C2×Q8×D1311yescharacteristic
515C23C2×#613111yescharacteristic
516C23#8825411yescharacteristic
517C23#8825411yescharacteristic
518C23#8825611yescharacteristic
519C23#8825611yescharacteristic
520C23#8825711yescharacteristic
521C23#8825711yescharacteristic
522C23C23×Dic1311yescharacteristic
523C2×C4—24no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—262no—
552C2×C4—262no—
553C2×C4—262no—
554C2×C4—262no—
555C2×C4—262no—
556C2×C4—262no—
557C2×C4—262no—
558C2×C4—262no—
559C2×C4—262no—
560C2×C4—262no—
561C2×C4—262no—
562C2×C4—262no—
563C2×C4—521no—
564C2×C4—521no—
565C2×C4—521no—
566C2×C4—521no—
567C2×C4—521no—
568C2×C4—521no—
569C2×C4—521no—
570C2×C4—521no—
571C2×C4—521no—
572C2×C4—521no—
573C2×C4—521no—
574C2×C4—521no—
575C2×C4—521no—
576C2×C4—521no—
577C2×C4—521no—
578C2×C4—521no—
579C2×C4—522no—
580C2×C4—522no—
581C2×C4—522no—
582C2×C4—522no—
583C2×C4—522no—
584C2×C4—522no—
585C2×C4—522no—
586C2×C4—522no—
587C2×C4—522no—
588C2×C4—522no—
589C2×C4—522no—
590C2×C4—522no—
591C2×C4—522no—
592C2×C4—522no—
593C2×C4#8814314yes—
594C2×C4#8814814yes—
595C2×C4#8815014yes—
596C2×C4#8815214yes—
597C2×C4#8818014yes—
598C2×C4D4×Dic1314yes—
599C2×C4Q8×Dic1314yes—
600C22C2×#8814311yescharacteristic
601C22C2×#8814811yescharacteristic
602C22C2×#8815011yescharacteristic
603C22C2×#8815211yescharacteristic
604C22#1171926611yescharacteristic
605C22#1171926611yescharacteristic
606C22#1171926711yescharacteristic
607C22#1171926711yescharacteristic
608C22#1171928711yescharacteristic
609C22#1171928711yescharacteristic
610C22#1171928811yescharacteristic
611C22#1171928811yescharacteristic
612C22#1171930811yescharacteristic
613C22#1171931211yescharacteristic
614C22#1171931311yescharacteristic
615C22#1171932411yescharacteristic
616C22#1171933011yescharacteristic
617C22#1171933311yescharacteristic
618C22#1171933411yescharacteristic
619C22#1171934811yescharacteristic
620C22#1171939411yescharacteristic
621C22#1171939411yescharacteristic
622C22#1171940211yescharacteristic
623C22#1171940311yescharacteristic
624C22#1171943411yescharacteristic
625C22#1171943411yescharacteristic
626C22#1171943811yescharacteristic
627C22#1171943811yescharacteristic
628C22C2×#8818011yescharacteristic
629C22C2×D4×Dic1311yescharacteristic
630C22#1171950311yescharacteristic
631C22C2×Q8×Dic1311yescharacteristic
632C22#1171951711yescharacteristic
633C22#1171953211yescharacteristic
634C22#1171953211yescharacteristic
635C4—44no—
636C4—42no—
637C4—42no—
638C4—44no—
639C4—522no—
640C4—522no—
641C4—522no—
642C4—522no—
643C4—1042no—
644C4—1042no—
645C4#1171864218yes—
646C2C2×#1171864211yescharacteristic
647C2#1311747911yescharacteristic
648C2#1311748711yescharacteristic
649C2#1311752011yescharacteristic
650C2#1311753111yescharacteristic
651C2#1311757811yescharacteristic
652C2#1311758511yescharacteristic
653C2#1312063011yescharacteristic
654C2#1312063811yescharacteristic
655C2#1312066311yescharacteristic
656C2#1312067111yescharacteristic
657C2#1312079911yescharacteristic
658C2#1312080411yescharacteristic
659C2#1312081211yescharacteristic
660C2#1312081311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#389C2
socle, prime radical, cosocleC24×C13C24
hypercenterC2×#389D13
hypocenterC13#14266
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
21. C13×#389C4semidirect
291. #389Dic13semidirect
507. C13#14266semidirect

Maximal subgroups

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

subgroupindex
C2×#117186462
C2×#117185932
#131131042
#131130982
#131130932
#131130892
#131130662
#131130652
C2×C13×#3892
#1426613