Finite Group Databasebeta

← #15784971

Subgroups — #15784971

Order 3328.

1602 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718310C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊Dic13C211yesmaximal, characteristic
3#13113094C212yesmaximal, complemented
4#13113079C212yesmaximal
5#13113073C212yesmaximal
6#13113062C211yesmaximal, characteristic, complemented
7#13113061C211yesmaximal, characteristic, complemented
8#13113060C212yesmaximal, complemented
9#13113060C211yesmaximal, characteristic, complemented
10#13113059C211yesmaximal, characteristic
11C2×C13×#381C211yesmaximal, characteristic
12C24×C4×C13C2211yescharacteristic
13C22×C13×C22⋊C4C2212yes—
14C22×C22⋊Dic13C2212yes—
15C22×C22⋊Dic13C2211yescharacteristic
16C22×C22⋊Dic13C2211yescharacteristic
17C22×#6101C2212yes—
18C22×C4×Dic13C2212yes—
19C22×C4×Dic13C2211yescharacteristic
20C22×C4×Dic13C2211yescharacteristic
21C13×#381—24no—
22C2×C13×#95C2212yes—
23C2×C13×#95C2211yescharacteristic
24C2×C13×#95C2211yescharacteristic
25C4×C22⋊Dic13C418yescomplemented
26C2×#88071C2212yes—
27C2×#88071C2212yes—
28C2×#88071C2211yescharacteristic
29C2×#88071C2211yescharacteristic
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2211yescharacteristic
36C2×#88071C2211yescharacteristic
37#11718310—24no—
38C25×C13C2311yescharacteristic
39C23×C4×C13—24no—
40C23×C4×C13—22no—
41C23×C4×C13—22no—
42C23×C4×C13—42no—
43C23×C4×C13C2×C414yes—
44C23×C4×C13C2312yes—
45C23×C4×C13C2311yescharacteristic
46C23×C4×C13C2312yes—
47C23×C4×C13C2311yescharacteristic
48C23×Dic13C2312yes—
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2311yescharacteristic
51C23×Dic13C2312yes—
52C23×Dic13C2311yescharacteristic
53C23×Dic13C2311yescharacteristic
54C2×C13×C22⋊C4—24no—
55C2×C13×C22⋊C4—24no—
56C2×C13×C22⋊C4—42no—
57C2×C22⋊Dic13—22no—
58C2×C22⋊Dic13—24no—
59C2×C22⋊Dic13—22no—
60C2×C22⋊Dic13—24no—
61C2×C22⋊Dic13—24no—
62C2×C22⋊Dic13—42no—
63C2×C22⋊Dic13C2×C414yes—
64C2×C22⋊Dic13C2×C414yes—
65C2×#6101—24no—
66C2×#6101—24no—
67C2×#6101—24no—
68C2×C4×Dic13—22no—
69C2×C4×Dic13—22no—
70C2×C4×Dic13—24no—
71C2×C4×Dic13—24no—
72C2×C4×Dic13—42no—
73C2×C4×Dic13—42no—
74C2×C4×Dic13C2×C414yes—
75C2×C4×Dic13C2×C414yes—
76C13×#95—24no—
77C13×#95—22no—
78C13×#95D414yes—
79#88071—22no—
80#88071—22no—
81#88071—24no—
82#88071—24no—
83#88071—24no—
84#88071—42no—
85#88071—42no—
86#88071—42no—
87#88071—42no—
88#88071C2×C414yes—
89#88071C2×C414yes—
90#13887—131nomaximal, Sylow
91C24×C13—21no—
92C24×C13—22no—
93C24×C13—21no—
94C24×C13—21no—
95C24×C13—22no—
96C24×C13—21no—
97C24×C13—21no—
98C24×C13—22no—
99C24×C13—21no—
100C24×C13C22×C412yes—
101C24×C13#4114yes—
102C24×C13C2411yescharacteristic
103C22×C4×C13—22no—
104C22×C4×C13—22no—
105C22×C4×C13—28no—
106C22×C4×C13—21no—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—21no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—28no—
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×C13—44no—
125C22×C4×C13—48no—
126C22×C4×C13—48no—
127C22×C4×C13C22×C412yes—
128C22×C4×C13C22×C412yes—
129C22×C4×C13C2×D414yes—
130C22×C4×C13C2×D412yes—
131C22×C4×C13#4112yes—
132C22×Dic13—21no—
133C22×Dic13—21no—
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13—22no—
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—21no—
148C22×Dic13—22no—
149C22×Dic13—22no—
150C22×Dic13—22no—
151C22×Dic13—22no—
152C22×Dic13—21no—
153C22×Dic13—22no—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13—22no—
157C22×Dic13—22no—
158C22×Dic13—22no—
159C22×Dic13—22no—
160C22×Dic13C22×C412yes—
161C22×Dic13C22×C412yes—
162C22×Dic13C22×C412yes—
163C22×Dic13C22×C412yes—
164C22×Dic13#4114yes—
165C22×Dic13#4112yes—
166C22×Dic13#4114yes—
167C22×Dic13#4112yes—
168C13×C22⋊C4—48no—
169C22⋊Dic13—28no—
170C22⋊Dic13—28no—
171C22⋊Dic13—48no—
172#6101—216no—
173C4×Dic13—28no—
174C4×Dic13—44no—
175C4×Dic13—48no—
176C2×#381D1311yescharacteristic
177C2×C4×C4⋊C4—131no—
178C2×C4×C22⋊C4—131no—
179#1442—132no—
180#1439—132no—
181#1437—132no—
182#1434—132no—
183#1434—131no—
184#1434—131no—
185#1434—131no—
186C22⋊#95—131no—
187C23×C13—22no—
188C23×C13—22no—
189C23×C13—22no—
190C23×C13—22no—
191C23×C13—22no—
192C23×C13—22no—
193C23×C13—24no—
194C23×C13—24no—
195C23×C13—24no—
196C23×C13—24no—
197C23×C13—24no—
198C23×C13—24no—
199C23×C13—42no—
200C23×C13—42no—
201C23×C13—42no—
202C23×C13—42no—
203C23×C13—41no—
204C23×C13—41no—
205C23×C13—41no—
206C23×C13—41no—
207C23×C13—42no—
208C23×C13—42no—
209C23×C13#11714yes—
210C23×C13C23×C411yescharacteristic
211C23×C13C22×D411yescharacteristic
212C23×C13C2×#4112yes—
213C23×C13C2×#4112yes—
214C23×C13C2×#4111yescharacteristic
215C23×C13C2×#4111yescharacteristic
216C23×C13C2×#4111yescharacteristic
217C23×C13C2×#4112yes—
218C23×C13H(5,𝔽2)12yes—
219C23×C13H(5,𝔽2)11yescharacteristic
220C23×C132−1+411yescharacteristic
221C2×C4×C13—22no—
222C2×C4×C13—22no—
223C2×C4×C13—24no—
224C2×C4×C13—24no—
225C2×C4×C13—22no—
226C2×C4×C13—22no—
227C2×C4×C13—22no—
228C2×C4×C13—24no—
229C2×C4×C13—24no—
230C2×C4×C13—24no—
231C2×C4×C13—416no—
232C2×C4×C13—42no—
233C2×C4×C13—42no—
234C2×C4×C13—42no—
235C2×C4×C13—42no—
236C2×C4×C13—42no—
237C2×C4×C13—42no—
238C2×C4×C13—42no—
239C2×C4×C13—42no—
240C2×C4×C13—42no—
241C2×C4×C13—42no—
242C2×C4×C13—42no—
243C2×C4×C13—42no—
244C2×C4×C13—42no—
245C2×C4×C13C4×D414yes—
246C2×Dic13—22no—
247C2×Dic13—22no—
248C2×Dic13—22no—
249C2×Dic13—22no—
250C2×Dic13—24no—
251C2×Dic13—24no—
252C2×Dic13—22no—
253C2×Dic13—22no—
254C2×Dic13—22no—
255C2×Dic13—22no—
256C2×Dic13—22no—
257C2×Dic13—22no—
258C2×Dic13—22no—
259C2×Dic13—22no—
260C2×Dic13—22no—
261C2×Dic13—22no—
262C2×Dic13—24no—
263C2×Dic13—24no—
264C2×Dic13—24no—
265C2×Dic13—42no—
266C2×Dic13—42no—
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#11714yes—
281C2×Dic13#11714yes—
282C24×C4C2×D1311yescharacteristic
283C22×C4⋊C4—132no—
284C22×C22⋊C4—131no—
285C22×C22⋊C4—131no—
286C22×C22⋊C4—132no—
287C22×C22⋊C4C2×D1312yes—
288C22×C42—131no—
289C22×C42—131no—
290C22×C42—132no—
291#381—24no—
292C4×C4⋊C4—264no—
293C4×C22⋊C4—138no—
294C2×#95—131no—
295C2×#95—131no—
296C2×#95—131no—
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×#95C2×D1311yescharacteristic
306C2×#95C2×D1312yes—
307C2×#95C2×D1311yescharacteristic
308C22×C13—24no—
309C22×C13—24no—
310C22×C13—24no—
311C22×C13—42no—
312C22×C13—42no—
313C22×C13—42no—
314C22×C13—44no—
315C22×C13—44no—
316C22×C13—44no—
317C22×C13—44no—
318C22×C13—42no—
319C22×C13C2×#11711yescharacteristic
320C22×C13C2×#11711yescharacteristic
321C22×C13C2×#11711yescharacteristic
322C22×C13C2×C4×D411yescharacteristic
323C22×C13C4×#4111yescharacteristic
324C22×C13#51811yescharacteristic
325C22×C13#52011yescharacteristic
326C22×C13#52512yes—
327C22×C13#52912yes—
328C22×C13#52912yes—
329C22×C13#52912yes—
330C22×C13#54012yes—
331C22×C13#54212yes—
332C22×C13#54612yes—
333C22×C13#54611yescharacteristic
334C22×C13#54811yescharacteristic
335C22×C13#55112yes—
336C22×C13#55112yes—
337C22×C13#55211yescharacteristic
338C22×C13#55212yes—
339C22×C13#55311yescharacteristic
340C22×C13#55312yes—
341C22×C13#55912yes—
342C4×C13—24no—
343C4×C13—42no—
344C4×C13—44no—
345C4×C13—82no—
346Dic13—24no—
347Dic13—24no—
348Dic13—42no—
349Dic13—42no—
350Dic13—44no—
351Dic13—82no—
352C25C22×D1311yescharacteristic
353C23×C4—24no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—42no—
357C23×C4—131no—
358C23×C4—131no—
359C23×C4—132no—
360C23×C4—131no—
361C23×C4—131no—
362C23×C4—132no—
363C23×C4C4×D1314yes—
364C23×C4C22×D1312yes—
365C23×C4C22×D1311yescharacteristic
366C23×C4C22×D1312yes—
367C23×C4C22×D1311yescharacteristic
368C2×C4⋊C4—264no—
369C2×C4⋊C4—264no—
370C2×C4⋊C4—264no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—134no—
375C2×C22⋊C4—134no—
376C2×C22⋊C4—262no—
377C2×C22⋊C4—264no—
378C2×C22⋊C4—262no—
379C2×C22⋊C4—264no—
380C2×C22⋊C4—264no—
381C2×C22⋊C4—522no—
382C2×C42—134no—
383C2×C42—134no—
384C2×C42—262no—
385C2×C42—262no—
386C2×C42—264no—
387C2×C42—264no—
388C2×C42—522no—
389C2×C42—522no—
390#95—24no—
391#95—22no—
392#95—134no—
393#95—134no—
394#95—264no—
395#95—264no—
396#95—264no—
397#95—262no—
398#95—262no—
399#95—522no—
400#95—522no—
401#95—522no—
402#95—522no—
403#95C22⋊D1314yes—
404C2×C13—44no—
405C2×C13#228311yescharacteristic
406C2×C13#229011yescharacteristic
407C2×C13#231911yescharacteristic
408C2×C13#234211yescharacteristic
409C2×C13#234311yescharacteristic
410C2×C13#235211yescharacteristic
411C2×C13#235711yescharacteristic
412C2×C13#245712yes—
413C2×C13#245812yes—
414C2×C13#251512yes—
415C2×C13#251612yes—
416C24—21no—
417C24—22no—
418C24—22no—
419C24—21no—
420C24—21no—
421C24—22no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24C2×C4×D1312yes—
426C24#612914yes—
427C24C23×D1311yescharacteristic
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—28no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—28no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—44no—
450C22×C4—48no—
451C22×C4—48no—
452C22×C4—132no—
453C22×C4—132no—
454C22×C4—132no—
455C22×C4—134no—
456C22×C4—132no—
457C22×C4—132no—
458C22×C4—132no—
459C22×C4—134no—
460C22×C4—261no—
461C22×C4—261no—
462C22×C4—262no—
463C22×C4—261no—
464C22×C4—261no—
465C22×C4—261no—
466C22×C4—261no—
467C22×C4—262no—
468C22×C4—262no—
469C22×C4—262no—
470C22×C4—262no—
471C22×C4—262no—
472C22×C4—262no—
473C22×C4—261no—
474C22×C4—262no—
475C22×C4—261no—
476C22×C4—262no—
477C22×C4—261no—
478C22×C4—262no—
479C22×C4—261no—
480C22×C4—262no—
481C22×C4—262no—
482C22×C4—262no—
483C22×C4—262no—
484C22×C4—262no—
485C22×C4—262no—
486C22×C4—262no—
487C22×C4—262no—
488C22×C4C2×C4×D1312yes—
489C22×C4C2×C4×D1312yes—
490C22×C4#612712yes—
491C22×C4C2×C22⋊D1314yes—
492C22×C4C2×C22⋊D1312yes—
493C4⋊C4—2616no—
494C22⋊C4—48no—
495C22⋊C4—268no—
496C22⋊C4—268no—
497C22⋊C4—528no—
498C42—268no—
499C42—524no—
500C42—528no—
501C13#1388711yescharacteristic, complemented, Sylow
502C23—22no—
503C23—24no—
504C23—22no—
505C23—22no—
506C23—22no—
507C23—22no—
508C23—22no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—24no—
514C23—42no—
515C23—41no—
516C23—41no—
517C23—42no—
518C23—41no—
519C23—41no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23#8813114yes—
525C23C22×C4×D1311yescharacteristic
526C23C2×#612711yescharacteristic
527C23C2×#612912yes—
528C23#8825112yes—
529C23#41×D1312yes—
530C23#41×D1311yescharacteristic
531C23#41×D1311yescharacteristic
532C23#41×D1312yes—
533C23#8825611yescharacteristic
534C23#8825711yescharacteristic
535C23C22×C22⋊D1311yescharacteristic
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—416no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—134no—
561C2×C4—134no—
562C2×C4—262no—
563C2×C4—262no—
564C2×C4—264no—
565C2×C4—262no—
566C2×C4—262no—
567C2×C4—262no—
568C2×C4—262no—
569C2×C4—264no—
570C2×C4—262no—
571C2×C4—262no—
572C2×C4—262no—
573C2×C4—262no—
574C2×C4—262no—
575C2×C4—262no—
576C2×C4—262no—
577C2×C4—262no—
578C2×C4—264no—
579C2×C4—264no—
580C2×C4—264no—
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—522no—
594C2×C4—522no—
595C2×C4—522no—
596C2×C4C4×C22⋊D1314yes—
597C22—24no—
598C22—24no—
599C22—24no—
600C22—44no—
601C22—44no—
602C22—42no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—44no—
607C22—44no—
608C22C2×#8813111yescharacteristic
609C22#1171919111yescharacteristic
610C22#1171920012yes—
611C22D13×#11711yescharacteristic
612C22D13×#11711yescharacteristic
613C22#1171922711yescharacteristic
614C22#1171922811yescharacteristic
615C22#1171923312yes—
616C22#1171923411yescharacteristic
617C22#1171923511yescharacteristic
618C22#1171935412yes—
619C22#1171935412yes—
620C22#1171935512yes—
621C22#1171936312yes—
622C22#1171936612yes—
623C22#1171936712yes—
624C22#1171936812yes—
625C22#1171936912yes—
626C22C2×C4×C22⋊D1311yescharacteristic
627C22#1171951112yes—
628C22#1171953312yes—
629C22#1171953411yescharacteristic
630C22#1171953611yescharacteristic
631C4—24no—
632C4—44no—
633C4—42no—
634C4—82no—
635C4—264no—
636C4—264no—
637C4—524no—
638C4—522no—
639C4—522no—
640C4—1042no—
641C2—44no—
642C2#1311722711yescharacteristic
643C2#1311727311yescharacteristic
644C2#1311747611yescharacteristic
645C2#1311768111yescharacteristic
646C2#1311769811yescharacteristic
647C2#1311776611yescharacteristic
648C2#1311780411yescharacteristic
649C2#1311873912yes—
650C2#1311875412yes—
651C2#1311945112yes—
652C2#1311946612yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#381C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×#381D13
hypocenterC13#13887
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
1. C2×#11718310C2semidirect
3. #13113094C2semidirect
6. #13113062C2semidirect
7. #13113061C2semidirect
8. #13113060C2semidirect
9. #13113060C2semidirect
25. C4×C22⋊Dic13C4semidirect
501. C13#13887semidirect

Maximal subgroups

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

subgroupindex
C2×#117183102
C2×C4×C22⋊Dic132
#131130942
#131130792
#131130732
#131130622
#131130612
#131130602
#131130592
C2×C13×#3812
#1388713