Finite Group Databasebeta

← #15784393

Subgroups — #15784393

Order 3328.

2154 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#6103C211yesmaximal, characteristic
2C2×#11718327C212yesmaximal
3C2×#11718309C211yesmaximal, characteristic, complemented
4C2×D13×#95C211yesmaximal, characteristic
5#13113062C212yesmaximal, complemented
6#13113061C212yesmaximal, complemented
7#13113060C211yesmaximal, characteristic, complemented
8#13113057C211yesmaximal, characteristic
9#13113057C212yesmaximal
10C4×#88071C211yesmaximal, characteristic, complemented
11C13×#1434C211yesmaximal, characteristic, complemented
12C23×C4×D13C2212yes—
13C23×C4×D13C2211yescharacteristic
14C22×C42×C13C2211yescharacteristic
15C22×#6103C2212yes—
16C22×#6103C2211yescharacteristic
17C22×#6103C2211yescharacteristic
18C22×C4×Dic13C2211yescharacteristic
19C22×C4×Dic13C2212yes—
20C22×C4×Dic13C2212yes—
21C2×C13×#95C2211yescharacteristic
22C2×C13×#95C2211yescharacteristic
23C2×C13×#95C2212yes—
24C2×C13×#95C2212yes—
25C2×#88071C2211yescharacteristic
26C2×#88071C2212yes—
27C2×#88071C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2211yescharacteristic
33C2×#88071C2211yescharacteristic
34C2×#88071C2211yescharacteristic
35C4×#6103C418yescomplemented
36#11718327C4116yescomplemented
37D13×#95—24no—
38#11718309—24no—
39C24×D13C2311yescharacteristic
40C23×C4×C13C2312yes—
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2312yes—
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2311yescharacteristic
45C23×Dic13C2311yescharacteristic
46C23×Dic13C2312yes—
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2312yes—
50C22×C4×D13—24no—
51C22×C4×D13—24no—
52C22×C4×D13—24no—
53C22×C4×D13—22no—
54C22×C4×D13—22no—
55C22×C4×D13—24no—
56C22×C4×D13—24no—
57C22×C4×D13—42no—
58C22×C4×D13—42no—
59C22×C4×D13—42no—
60C22×C4×D13C2×C418yes—
61C22×C4×D13C2×C414yes—
62C2×C42×C13—42no—
63C2×C42×C13C2×C414yescomplemented
64C2×#6103—24no—
65C2×#6103—22no—
66C2×#6103—24no—
67C2×#6103—22no—
68C2×#6103C2×C418yes—
69C2×#6103C2×C414yes—
70C2×#6103C2×C418yes—
71C2×#6103C2×C414yes—
72C2×C4×Dic13—22no—
73C2×C4×Dic13—22no—
74C2×C4×Dic13—24no—
75C2×C4×Dic13—24no—
76C2×C4×Dic13—42no—
77C2×C4×Dic13—42no—
78C2×C4×Dic13C2×C418yescomplemented
79C2×C4×Dic13C2×C414yescomplemented
80C2×C4×Dic13C2×C418yescomplemented
81C13×#95—22no—
82C13×#95—22no—
83C13×#95—42no—
84C13×#95C2×C418yescomplemented
85#88071—22no—
86#88071—24no—
87#88071—24no—
88#88071—24no—
89#88071—42no—
90#88071—42no—
91#88071C2×C418yescomplemented
92#88071C2×C414yescomplemented
93#88071C2×C414yescomplemented
94#88071D414yes—
95#13809—131nomaximal, Sylow
96C24×C13C2411yescharacteristic
97C23×D13—21no—
98C23×D13—21no—
99C23×D13—22no—
100C23×D13—22no—
101C23×D13—21no—
102C23×D13—21no—
103C23×D13C22×C414yes—
104C23×D13C22×C412yes—
105C23×D13#4112yes—
106C23×D13#4114yes—
107C23×D13#4112yes—
108C22×C4×C13—22no—
109C22×C4×C13—21no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—21no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—21no—
120C22×C4×C13—21no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13C22×C414yes—
130C22×C4×C13C22×C412yes—
131C22×C4×C13C22×C414yes—
132C22×C4×C13C22×C412yes—
133C22×C4×C13C22×C414yes—
134C22×C4×C13C22×C412yes—
135C22×C4×C13C2×D412yes—
136C22×C4×C13#4112yes—
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13—22no—
140C22×Dic13—22no—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—21no—
145C22×Dic13—21no—
146C22×Dic13—22no—
147C22×Dic13—22no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—22no—
152C22×Dic13—22no—
153C22×Dic13—22no—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—22no—
157C22×Dic13—22no—
158C22×Dic13—22no—
159C22×Dic13—21no—
160C22×Dic13C22×C412yes—
161C22×Dic13C22×C412yes—
162C22×Dic13C22×C414yes—
163C22×Dic13C22×C414yes—
164C22×Dic13C22×C412yes—
165C22×Dic13C22×C414yes—
166C22×Dic13C2×D414yes—
167C22×Dic13#4114yes—
168C2×C4×D13—216no—
169C2×C4×D13—28no—
170C2×C4×D13—28no—
171C2×C4×D13—216no—
172C2×C4×D13—48no—
173C2×C4×D13—44no—
174C2×C4×D13—48no—
175C2×C4×D13—48no—
176C2×C4×D13—48no—
177C2×C4×D13—48no—
178C2×C4×D13—48no—
179C2×C4×D13—48no—
180C42×C13—44no—
181#6103—216no—
182#6103—28no—
183#6103C42116yes—
184C4×Dic13—28no—
185C4×Dic13—216no—
186C4×Dic13—48no—
187C2×C4×C22⋊C4—131no—
188C2×C4×C22⋊C4—132no—
189C2×#376—131no—
190C22×#95—131no—
191#1434—131no—
192#1434—132no—
193#1434—132no—
194#1434D1311yescharacteristic, complemented
195C22⋊#95—132no—
196C22⋊#95—131no—
197C4×#95—131no—
198C23×C13C23×C411yescharacteristic
199C23×C13C23×C412yes—
200C23×C13C22×D411yescharacteristic
201C23×C13C2×#4112yes—
202C23×C13C2×#4111yescharacteristic
203C23×C13C2×#4111yescharacteristic
204C23×C13C2×#4111yescharacteristic
205C23×C13C2×#4112yes—
206C23×C13H(5,𝔽2)12yes—
207C23×C13H(5,𝔽2)11yescharacteristic
208C23×C132−1+411yescharacteristic
209C22×D13—22no—
210C22×D13—24no—
211C22×D13—22no—
212C22×D13—24no—
213C22×D13—22no—
214C22×D13—24no—
215C22×D13—22no—
216C22×D13—24no—
217C22×D13—24no—
218C22×D13—22no—
219C22×D13—22no—
220C22×D13—24no—
221C22×D13—24no—
222C22×D13—24no—
223C22×D13—22no—
224C22×D13—24no—
225C22×D13—24no—
226C22×D13—22no—
227C22×D13C2×C4214yes—
228C22×D13#11714yes—
229C22×D13#11718yes—
230C22×D13#11714yes—
231C22×D13#11718yes—
232C2×C4×C13—22no—
233C2×C4×C13—24no—
234C2×C4×C13—22no—
235C2×C4×C13—22no—
236C2×C4×C13—22no—
237C2×C4×C13—24no—
238C2×C4×C13—24no—
239C2×C4×C13—24no—
240C2×C4×C13—24no—
241C2×C4×C13—22no—
242C2×C4×C13—24no—
243C2×C4×C13—24no—
244C2×C4×C13—24no—
245C2×C4×C13—22no—
246C2×C4×C13—22no—
247C2×C4×C13—24no—
248C2×C4×C13—24no—
249C2×C4×C13—42no—
250C2×C4×C13—42no—
251C2×C4×C13—42no—
252C2×C4×C13—42no—
253C2×C4×C13—42no—
254C2×C4×C13—42no—
255C2×C4×C13—42no—
256C2×C4×C13—42no—
257C2×C4×C13—42no—
258C2×C4×C13—42no—
259C2×C4×C13C2×C4214yes—
260C2×C4×C13C4×D414yes—
261C2×Dic13—24no—
262C2×Dic13—22no—
263C2×Dic13—24no—
264C2×Dic13—22no—
265C2×Dic13—24no—
266C2×Dic13—24no—
267C2×Dic13—24no—
268C2×Dic13—24no—
269C2×Dic13—24no—
270C2×Dic13—24no—
271C2×Dic13—22no—
272C2×Dic13—24no—
273C2×Dic13—22no—
274C2×Dic13—22no—
275C2×Dic13—22no—
276C2×Dic13—24no—
277C2×Dic13—24no—
278C2×Dic13—22no—
279C2×Dic13—22no—
280C2×Dic13—42no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—42no—
284C2×Dic13—42no—
285C2×Dic13—42no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—42no—
289C2×Dic13—42no—
290C2×Dic13C2×C4214yes—
291C2×Dic13C4×D418yes—
292C4×D13—432no—
293C4×D13—416no—
294C24×C4—132no—
295C24×C4—131no—
296C22×C22⋊C4—131no—
297C22×C22⋊C4—131no—
298C22×C22⋊C4—132no—
299C22×C42—132no—
300C22×C42—131no—
301C22×C42—132no—
302C22×C42C2×D1311yescharacteristic
303C4×C22⋊C4—138no—
304C4×C22⋊C4—1316no—
305#376—264no—
306C2×#95—131no—
307C2×#95—132no—
308C2×#95—131no—
309C2×#95—131no—
310C2×#95—132no—
311C2×#95—131no—
312C2×#95—132no—
313C2×#95—132no—
314C2×#95—132no—
315C2×#95—132no—
316C2×#95—264no—
317C2×#95C2×D1311yescharacteristic
318C2×#95C2×D1311yescharacteristic
319C2×#95C2×D1312yes—
320C2×#95C2×D1312yes—
321C22×C13C22×C4211yescharacteristic
322C22×C13C2×#11711yescharacteristic
323C22×C13C2×#11712yes—
324C22×C13C2×#11711yescharacteristic
325C22×C13C2×#11712yes—
326C22×C13C2×C4×D411yescharacteristic
327C22×C13C2×C4×D412yes—
328C22×C13C4×#4111yescharacteristic
329C22×C13C4×#4112yes—
330C22×C13#51811yescharacteristic
331C22×C13#51812yes—
332C22×C13#52011yescharacteristic
333C22×C13#52012yes—
334C22×C13#54612yes—
335C22×C13#54611yescharacteristic
336C22×C13#54811yescharacteristic
337C22×C13#55112yes—
338C22×C13#55112yes—
339C22×C13#55112yes—
340C22×C13#55211yescharacteristic
341C22×C13#55212yes—
342C22×C13#55312yes—
343C22×C13#55311yescharacteristic
344C2×D13—24no—
345C2×D13—28no—
346C2×D13—24no—
347C2×D13—28no—
348C2×D13—24no—
349C2×D13—28no—
350C2×D13—24no—
351C2×D13—28no—
352C2×D13—24no—
353C2×D13—24no—
354C2×D13#37618yescomplemented
355C4×C13—24no—
356C4×C13—24no—
357C4×C13—44no—
358C4×C13—44no—
359C4×C13—42no—
360Dic13—28no—
361Dic13—24no—
362Dic13—42no—
363Dic13—42no—
364Dic13—44no—
365C25—131no—
366C23×C4—131no—
367C23×C4—132no—
368C23×C4—131no—
369C23×C4—132no—
370C23×C4—131no—
371C23×C4—138no—
372C23×C4—134no—
373C23×C4—264no—
374C23×C4—264no—
375C23×C4—264no—
376C23×C4—264no—
377C23×C4—264no—
378C23×C4—262no—
379C23×C4—262no—
380C23×C4—522no—
381C23×C4—522no—
382C23×C4—522no—
383C23×C4C22×D1311yescharacteristic
384C23×C4C22×D1312yes—
385C23×C4C22×D1312yes—
386C23×C4C22×D1311yescharacteristic
387C23×C4C22×D1311yescharacteristic
388C2×C22⋊C4—134no—
389C2×C22⋊C4—138no—
390C2×C22⋊C4—134no—
391C2×C22⋊C4—138no—
392C2×C22⋊C4—262no—
393C2×C22⋊C4—264no—
394C2×C22⋊C4—264no—
395C2×C22⋊C4—262no—
396C2×C42—42no—
397C2×C42—138no—
398C2×C42—134no—
399C2×C42—138no—
400C2×C42—264no—
401C2×C42—264no—
402C2×C42—262no—
403C2×C42—262no—
404C2×C42—522no—
405C2×C42—522no—
406C2×C42C4×D1314yescomplemented
407#95—22no—
408#95—22no—
409#95—42no—
410#95—134no—
411#95—138no—
412#95—134no—
413#95—134no—
414#95—264no—
415#95—264no—
416#95—264no—
417#95—262no—
418#95—522no—
419#95—522no—
420#95C4×D1318yescomplemented
421C2×C13C2×#37611yescharacteristic
422C2×C13C42×D411yescharacteristic
423C2×C13#227511yescharacteristic
424C2×C13#234211yescharacteristic
425C2×C13#234212yes—
426C2×C13#234311yescharacteristic
427C2×C13#234312yes—
428C2×C13#235211yescharacteristic
429C2×C13#235212yes—
430C2×C13#235311yescharacteristic
431C2×C13#235312yes—
432D13—28no—
433C24—132no—
434C24—134no—
435C24—132no—
436C24—134no—
437C24—132no—
438C24—261no—
439C24—262no—
440C24—261no—
441C24—262no—
442C24—261no—
443C24—261no—
444C24C23×D1311yescharacteristic
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—132no—
467C22×C4—134no—
468C22×C4—134no—
469C22×C4—134no—
470C22×C4—134no—
471C22×C4—132no—
472C22×C4—132no—
473C22×C4—134no—
474C22×C4—2616no—
475C22×C4—268no—
476C22×C4—2616no—
477C22×C4—261no—
478C22×C4—262no—
479C22×C4—261no—
480C22×C4—262no—
481C22×C4—262no—
482C22×C4—262no—
483C22×C4—262no—
484C22×C4—261no—
485C22×C4—261no—
486C22×C4—262no—
487C22×C4—262no—
488C22×C4—262no—
489C22×C4—261no—
490C22×C4—261no—
491C22×C4—262no—
492C22×C4—262no—
493C22×C4—262no—
494C22×C4—261no—
495C22×C4—261no—
496C22×C4—262no—
497C22×C4—261no—
498C22×C4—262no—
499C22×C4—261no—
500C22×C4—268no—
501C22×C4—524no—
502C22×C4—528no—
503C22×C4—528no—
504C22×C4—528no—
505C22×C4—528no—
506C22×C4—528no—
507C22×C4—528no—
508C22×C4—528no—
509C22×C4C2×C4×D1314yes—
510C22×C4C2×C4×D1312yes—
511C22×C4C2×C4×D1314yes—
512C22×C4C2×C4×D1312yes—
513C22×C4C2×C4×D1314yes—
514C22×C4C2×C4×D1312yes—
515C22×C4D4×D1312yes—
516C22×C4#613112yes—
517C22⋊C4—1316no—
518C22⋊C4—2616no—
519C22⋊C4—268no—
520C42—44no—
521C42—2616no—
522C42—268no—
523C42—528no—
524C13#1380911yescharacteristic, complemented, Sylow
525C23—134no—
526C23—134no—
527C23—138no—
528C23—134no—
529C23—138no—
530C23—262no—
531C23—262no—
532C23—262no—
533C23—262no—
534C23—264no—
535C23—264no—
536C23—264no—
537C23—264no—
538C23—264no—
539C23—264no—
540C23—264no—
541C23—264no—
542C23—262no—
543C23—262no—
544C23—262no—
545C23—262no—
546C23—264no—
547C23—264no—
548C23C22×C4×D1311yescharacteristic
549C23C22×C4×D1312yes—
550C23C2×D4×D1311yescharacteristic
551C23#8825112yes—
552C23C2×#613111yescharacteristic
553C23#41×D1312yes—
554C23#41×D1311yescharacteristic
555C23#41×D1311yescharacteristic
556C23#41×D1312yes—
557C23#8825611yescharacteristic
558C23#8825711yescharacteristic
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—134no—
587C2×C4—138no—
588C2×C4—262no—
589C2×C4—264no—
590C2×C4—262no—
591C2×C4—264no—
592C2×C4—264no—
593C2×C4—264no—
594C2×C4—264no—
595C2×C4—264no—
596C2×C4—264no—
597C2×C4—264no—
598C2×C4—262no—
599C2×C4—262no—
600C2×C4—262no—
601C2×C4—262no—
602C2×C4—264no—
603C2×C4—262no—
604C2×C4—262no—
605C2×C4—264no—
606C2×C4—264no—
607C2×C4—5216no—
608C2×C4—5232no—
609C2×C4—522no—
610C2×C4—522no—
611C2×C4—522no—
612C2×C4—522no—
613C2×C4—521no—
614C2×C4—521no—
615C2×C4—521no—
616C2×C4—521no—
617C2×C4—522no—
618C2×C4—522no—
619C2×C4C42×D1314yes—
620C2×C4#8814714yes—
621C22—138no—
622C22—264no—
623C22—264no—
624C22—268no—
625C22—264no—
626C22—268no—
627C22—264no—
628C22—268no—
629C22—264no—
630C22—264no—
631C22—268no—
632C22C2×C42×D1311yescharacteristic
633C22#1171919111yescharacteristic
634C22C2×#8814711yescharacteristic
635C22D13×#11711yescharacteristic
636C22D13×#11712yes—
637C22D13×#11711yescharacteristic
638C22D13×#11712yes—
639C22#1171922711yescharacteristic
640C22#1171922811yescharacteristic
641C22C4×D4×D1312yes—
642C22#1171925012yes—
643C22#1171925112yes—
644C22C4×#613112yes—
645C22#1171931512yes—
646C22#1171934212yes—
647C22#1171936412yes—
648C22#1171936612yes—
649C22#1171938111yescharacteristic
650C22#1171938211yescharacteristic
651C22#1171939911yescharacteristic
652C22#1171940011yescharacteristic
653C22#1171941012yes—
654C22#1171941312yes—
655C4—24no—
656C4—24no—
657C4—44no—
658C4—42no—
659C4—44no—
660C4—268no—
661C4—264no—
662C4—522no—
663C4—524no—
664C4—522no—
665C2—268no—
666C2D13×#37611yescharacteristic
667C2C4×#8814711yescharacteristic
668C2#1311719511yescharacteristic
669C2#1311768211yescharacteristic
670C2#1311768412yes—
671C2#1311769311yescharacteristic
672C2#1311769512yes—
673C2#1311776211yescharacteristic
674C2#1311776412yes—
675C2#1311777311yescharacteristic
676C2#1311777512yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC22×C13C22×C42
FittingC13×#1434C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenter#1434D13
hypocenterC13#13809
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
3. C2×#11718309C2semidirect
5. #13113062C2semidirect
6. #13113061C2semidirect
7. #13113060C2semidirect
10. C4×#88071C2semidirect
11. C13×#1434C2semidirect
35. C4×#6103C4semidirect
36. #11718327C4semidirect
63. C2×C42×C13C2×C4semidirect
78. C2×C4×Dic13C2×C4semidirect
79. C2×C4×Dic13C2×C4semidirect
80. C2×C4×Dic13C2×C4semidirect
84. C13×#95C2×C4semidirect
91. #88071C2×C4semidirect
92. #88071C2×C4semidirect
93. #88071C2×C4semidirect
194. #1434D13semidirect
354. C2×D13#376semidirect
406. C2×C42C4×D13semidirect
420. #95C4×D13semidirect
524. C13#13809semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#61032
C2×#117183272
C2×#117183092
C2×D13×#952
#131130622
#131130612
#131130602
#131130572
C4×#880712
C13×#14342
#1380913