Finite Group Databasebeta

← #15789689

Subgroups — #15789689

Order 3328.

1830 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic26C211yesmaximal, characteristic, complemented
2C2×#11718608C211yesmaximal, characteristic
3C2×#11718605C212yesmaximal
4#13113106C211yesmaximal, characteristic, complemented
5#13113100C211yesmaximal, characteristic, complemented
6#13113099C212yesmaximal, complemented
7#13113081C211yesmaximal, characteristic
8#13113079C212yesmaximal
9#13113063C211yesmaximal, characteristic, complemented
10#13113060C212yesmaximal, complemented
11C2×C13×#388C211yesmaximal, characteristic
12C23×Dic26C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C22⋊C4C2211yescharacteristic
15C22×C13×C22⋊C4C2211yescharacteristic
16C22×C13×C22⋊C4C2211yescharacteristic
17C22×C42×C13C2211yescharacteristic
18C22×C22⋊Dic13C2212yes—
19C22×C22⋊Dic13C2212yes—
20C22×C4⋊Dic13C2211yescharacteristic
21C22×#6101C2212yes—
22C22×#6101C2212yes—
23C22×C4×Dic13C2212yes—
24C2×C4×Dic26—24no—
25C2×C4×Dic26—28no—
26C13×#388—24no—
27C2×C13×#95C2211yescharacteristic
28C2×C13×#95C2211yescharacteristic
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2211yescharacteristic
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2211yescharacteristic
38#11718608C418yescomplemented
39#11718605—28no—
40C25×C13C2311yescharacteristic
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2311yescharacteristic
46C23×C4×C13C2311yescharacteristic
47C23×Dic13C2312yes—
48C23×Dic13C2312yes—
49C23×Dic13C2312yes—
50C23×Dic13C2312yes—
51C22×Dic26—22no—
52C22×Dic26—22no—
53C22×Dic26—24no—
54C22×Dic26—24no—
55C22×Dic26C2×C414yes—
56C2×C13×C4⋊C4—22no—
57C2×C13×C4⋊C4—42no—
58C2×C13×C22⋊C4—22no—
59C2×C13×C22⋊C4—22no—
60C2×C13×C22⋊C4—22no—
61C2×C13×C22⋊C4—22no—
62C2×C13×C22⋊C4—24no—
63C2×C13×C22⋊C4—42no—
64C2×C13×C22⋊C4C2×C414yes—
65C2×C42×C13—24no—
66C2×C42×C13D414yes—
67C2×C22⋊Dic13—24no—
68C2×C22⋊Dic13—24no—
69C2×C22⋊Dic13—24no—
70C2×C22⋊Dic13—42no—
71C2×C22⋊Dic13—42no—
72C2×C22⋊Dic13C2×C418yes—
73C2×C4⋊Dic13—22no—
74C2×C4⋊Dic13—24no—
75C2×#6101—24no—
76C2×#6101—24no—
77C2×#6101—24no—
78C2×#6101—24no—
79C2×#6101—42no—
80C2×#6101—42no—
81C2×C4×Dic13—24no—
82C2×C4×Dic13—24no—
83C2×C4×Dic13D418yes—
84C4×Dic26—232no—
85C13×#95—22no—
86C13×#95—22no—
87#88071—24no—
88#88071—22no—
89#88071—24no—
90#88071—24no—
91#88071—42no—
92#88071—42no—
93#88071—42no—
94#88071C2×C414yes—
95#88071C2×C418yes—
96#14301—131nomaximal, Sylow
97C24×C13—22no—
98C24×C13—21no—
99C24×C13—22no—
100C24×C13—21no—
101C24×C13—21no—
102C24×C13—22no—
103C24×C13—21no—
104C24×C13—21no—
105C24×C13—21no—
106C24×C13—22no—
107C24×C13C22×C412yes—
108C24×C13C2411yescharacteristic
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—21no—
112C22×C4×C13—21no—
113C22×C4×C13—22no—
114C22×C4×C13—21no—
115C22×C4×C13—22no—
116C22×C4×C13—21no—
117C22×C4×C13—21no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—21no—
122C22×C4×C13—22no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—21no—
128C22×C4×C13—22no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13C22×C412yes—
133C22×C4×C13C22×C412yes—
134C22×C4×C13C2×D414yes—
135C22×C4×C13C2×D412yes—
136C22×C4×C13C2×D412yes—
137C22×C4×C13C2×D412yes—
138C22×C4×C13#4112yes—
139C22×Dic13—22no—
140C22×Dic13—22no—
141C22×Dic13—22no—
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×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×Dic13C22×C414yes—
163C22×Dic13C22×C414yes—
164C22×Dic13C2×D414yes—
165C22×Dic13C2×D414yes—
166C22×Dic13#4114yes—
167C2×Dic26—28no—
168C2×Dic26—216no—
169C2×Dic26—28no—
170C2×Dic26—28no—
171C2×Dic26—216no—
172C13×C4⋊C4—44no—
173C13×C22⋊C4—28no—
174C13×C22⋊C4—44no—
175C13×C22⋊C4—44no—
176C42×C13—28no—
177C22⋊Dic13—216no—
178C22⋊Dic13—48no—
179C4⋊Dic13—28no—
180#6101—216no—
181#6101—48no—
182C4×Dic13—216no—
183C22×C4×Q8—131no—
184C2×#393—131no—
185C2×#388—132no—
186C2×#388D1311yescharacteristic
187#1446—131no—
188#1444—131no—
189#1444—132no—
190#1439—132no—
191#1439—131no—
192#1434—131no—
193#1434—132no—
194C23×C13—24no—
195C23×C13—22no—
196C23×C13—22no—
197C23×C13—22no—
198C23×C13—24no—
199C23×C13—41no—
200C23×C13—42no—
201C23×C13—41no—
202C23×C13—42no—
203C23×C13—41no—
204C23×C13—41no—
205C23×C13—42no—
206C23×C13—41no—
207C23×C13—42no—
208C23×C13—41no—
209C23×C13—42no—
210C23×C13—41no—
211C23×C13—42no—
212C23×C13—41no—
213C23×C13—42no—
214C23×C13—42no—
215C23×C13—42no—
216C23×C13—42no—
217C23×C13C23×C411yescharacteristic
218C23×C13C22×D412yes—
219C23×C13C22×D411yescharacteristic
220C23×C13C2×#4111yescharacteristic
221C23×C13C2×#4112yes—
222C23×C13H(5,𝔽2)12yes—
223C23×C13H(5,𝔽2)11yescharacteristic
224C23×C132−1+411yescharacteristic
225C23×C132−1+411yescharacteristic
226C23×C132−1+411yescharacteristic
227C23×C132−1+412yes—
228C2×C4×C13—24no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—24no—
232C2×C4×C13—22no—
233C2×C4×C13—22no—
234C2×C4×C13—24no—
235C2×C4×C13—24no—
236C2×C4×C13—22no—
237C2×C4×C13—24no—
238C2×C4×C13—22no—
239C2×C4×C13—22no—
240C2×C4×C13—22no—
241C2×C4×C13—41no—
242C2×C4×C13—42no—
243C2×C4×C13—41no—
244C2×C4×C13—42no—
245C2×C4×C13—42no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—42no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—42no—
254C2×C4×C13—42no—
255C2×C4×C13—42no—
256C2×C4×C13C4×D414yes—
257C2×C4×C13#12014yes—
258C2×Dic13—24no—
259C2×Dic13—24no—
260C2×Dic13—24no—
261C2×Dic13—24no—
262C2×Dic13—24no—
263C2×Dic13—24no—
264C2×Dic13—24no—
265C2×Dic13—24no—
266C2×Dic13—24no—
267C2×Dic13—24no—
268C2×Dic13—24no—
269C2×Dic13—24no—
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—
281C2×Dic13—42no—
282C2×Dic13—42no—
283C2×Dic13—42no—
284C2×Dic13—42no—
285C2×Dic13C4×D418yes—
286Dic26—232no—
287C23×Q8—131no—
288C2×C4×Q8—268no—
289C2×C4×Q8—264no—
290C22×C4⋊C4—132no—
291C22×C4⋊C4—131no—
292C22×C4⋊C4—132no—
293C22×C4⋊C4C2×D1311yescharacteristic
294C22×C22⋊C4—132no—
295C22×C22⋊C4—132no—
296C22×C22⋊C4C2×D1311yescharacteristic
297C22×C22⋊C4C2×D1311yescharacteristic
298C22×C22⋊C4C2×D1311yescharacteristic
299C22×C42—132no—
300C22×C42C2×D1311yescharacteristic
301#393—138no—
302#388—24no—
303#388—268no—
304C2×#95—132no—
305C2×#95—131no—
306C2×#95—132no—
307C2×#95—132no—
308C2×#95—131no—
309C2×#95—132no—
310C2×#95—132no—
311C2×#95—132no—
312C2×#95—132no—
313C2×#95C2×D1311yescharacteristic
314C2×#95C2×D1311yescharacteristic
315C22×C13—44no—
316C22×C13—42no—
317C22×C13—44no—
318C22×C13—42no—
319C22×C13—42no—
320C22×C13—81no—
321C22×C13—81no—
322C22×C13—81no—
323C22×C13—82no—
324C22×C13—81no—
325C22×C13—82no—
326C22×C13C2×C4×D411yescharacteristic
327C22×C13C2×C4×D412yes—
328C22×C13#51911yescharacteristic
329C22×C13#52011yescharacteristic
330C22×C13#52012yes—
331C22×C13C2×#12011yescharacteristic
332C22×C13#52512yes—
333C22×C13#52511yescharacteristic
334C22×C13#53511yescharacteristic
335C22×C13#53512yes—
336C22×C13#53611yescharacteristic
337C22×C13#53611yescharacteristic
338C22×C13#53612yes—
339C22×C13#53612yes—
340C22×C13#53711yescharacteristic
341C22×C13#53712yes—
342C22×C13#54111yescharacteristic
343C22×C13#54112yes—
344C22×C13#54211yescharacteristic
345C22×C13#54212yes—
346C22×C13#54212yes—
347C22×C13#54212yes—
348C22×C13#54212yes—
349C4×C13—24no—
350C4×C13—24no—
351C4×C13—42no—
352C4×C13—42no—
353C4×C13—81no—
354C4×C13—81no—
355Dic13—28no—
356Dic13—44no—
357Dic13—44no—
358Dic13—82no—
359C25C22×D1311yescharacteristic
360C22×Q8—134no—
361C22×Q8—264no—
362C22×Q8—264no—
363C22×Q8—262no—
364C22×Q8—262no—
365C23×C4—132no—
366C23×C4—132no—
367C23×C4—132no—
368C23×C4—132no—
369C23×C4C22×D1311yescharacteristic
370C23×C4C22×D1311yescharacteristic
371C23×C4C22×D1311yescharacteristic
372C23×C4C22×D1311yescharacteristic
373C23×C4C22×D1311yescharacteristic
374C23×C4C22×D1311yescharacteristic
375C4×Q8—2632no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—42no—
378C2×C4⋊C4—264no—
379C2×C4⋊C4—264no—
380C2×C4⋊C4—264no—
381C2×C4⋊C4—264no—
382C2×C4⋊C4—262no—
383C2×C4⋊C4—264no—
384C2×C4⋊C4—522no—
385C2×C4⋊C4—522no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—138no—
393C2×C22⋊C4—264no—
394C2×C22⋊C4—264no—
395C2×C22⋊C4—264no—
396C2×C22⋊C4—522no—
397C2×C22⋊C4—522no—
398C2×C22⋊C4C4×D1314yes—
399C2×C42—24no—
400C2×C42—138no—
401C2×C42—264no—
402C2×C42—264no—
403C2×C42C22⋊D1314yes—
404#95—22no—
405#95—22no—
406#95—138no—
407#95—134no—
408#95—264no—
409#95—264no—
410#95—262no—
411#95—264no—
412#95—522no—
413#95—522no—
414#95—522no—
415C2×C13—82no—
416C2×C13C4×#12011yescharacteristic
417C2×C13#232312yes—
418C2×C13#232311yescharacteristic
419C2×C13#232612yes—
420C2×C13#232611yescharacteristic
421C2×C13#261411yescharacteristic
422C2×C13#261511yescharacteristic
423C2×C13#263211yescharacteristic
424C2×C13#263212yes—
425C2×C13#263711yescharacteristic
426C2×C13#263712yes—
427C24—21no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—21no—
435C24—22no—
436C24—21no—
437C24C2×C4×D1312yes—
438C24C23×D1311yescharacteristic
439C2×Q8—2616no—
440C2×Q8—268no—
441C2×Q8—2616no—
442C2×Q8—268no—
443C2×Q8—268no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—134no—
468C22×C4—134no—
469C22×C4—134no—
470C22×C4—134no—
471C22×C4—134no—
472C22×C4—262no—
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—262no—
488C22×C4—262no—
489C22×C4—262no—
490C22×C4—262no—
491C22×C4—262no—
492C22×C4—262no—
493C22×C4—262no—
494C22×C4—262no—
495C22×C4C2×C4×D1312yes—
496C22×C4C2×C4×D1312yes—
497C22×C4#612712yes—
498C22×C4D4×D1314yes—
499C22×C4C2×C22⋊D1312yes—
500C22×C4C2×C22⋊D1312yes—
501C22×C4C2×C22⋊D1312yes—
502C4⋊C4—44no—
503C4⋊C4—2616no—
504C4⋊C4—268no—
505C4⋊C4—528no—
506C22⋊C4—28no—
507C22⋊C4—44no—
508C22⋊C4—44no—
509C22⋊C4—2616no—
510C22⋊C4—528no—
511C42—28no—
512C42—2616no—
513C13#1430111yescharacteristic, complemented, Sylow
514C23—22no—
515C23—22no—
516C23—22no—
517C23—24no—
518C23—24no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23—42no—
523C23—41no—
524C23—42no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23C22×C4×D1311yescharacteristic
538C23C2×#612711yescharacteristic
539C23C2×D4×D1312yes—
540C23#8825112yes—
541C23#41×D1312yes—
542C23#8825611yescharacteristic
543C23#8825711yescharacteristic
544C23#8825711yescharacteristic
545C23#8825711yescharacteristic
546C23#8825712yes—
547C23C22×C22⋊D1311yescharacteristic
548Q8—2632no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—41no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—138no—
578C2×C4—264no—
579C2×C4—264no—
580C2×C4—264no—
581C2×C4—264no—
582C2×C4—264no—
583C2×C4—264no—
584C2×C4—264no—
585C2×C4—264no—
586C2×C4—264no—
587C2×C4—264no—
588C2×C4—264no—
589C2×C4—264no—
590C2×C4—522no—
591C2×C4—522no—
592C2×C4—522no—
593C2×C4—522no—
594C2×C4—522no—
595C2×C4—522no—
596C2×C4—522no—
597C2×C4—522no—
598C2×C4—522no—
599C2×C4—522no—
600C2×C4—522no—
601C2×C4—522no—
602C2×C4—522no—
603C2×C4—522no—
604C2×C4—522no—
605C2×C4C4×C22⋊D1314yes—
606C2×C4#8819114yes—
607C22—44no—
608C22—42no—
609C22—44no—
610C22—42no—
611C22—42no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22—82no—
616C22—81no—
617C22—82no—
618C22#1171922111yescharacteristic
619C22#1171922311yescharacteristic
620C22#1171922811yescharacteristic
621C22#1171923911yescharacteristic
622C22C4×D4×D1312yes—
623C22#1171925112yes—
624C22#1171925212yes—
625C22#1171926612yes—
626C22#1171931212yes—
627C22#1171931312yes—
628C22#1171935312yes—
629C22#1171935312yes—
630C22#1171937412yes—
631C22#1171937412yes—
632C22#1171940612yes—
633C22#1171941512yes—
634C22C2×C4×C22⋊D1311yescharacteristic
635C22C2×#8819111yescharacteristic
636C22#1171951011yescharacteristic
637C22#1171953011yescharacteristic
638C22#1171953011yescharacteristic
639C22#1171953311yescharacteristic
640C22#1171953811yescharacteristic
641C4—24no—
642C4—24no—
643C4—42no—
644C4—42no—
645C4—81no—
646C4—81no—
647C4—268no—
648C4—524no—
649C4—524no—
650C4—1042no—
651C2—82no—
652C2C4×#8819111yescharacteristic
653C2#1311751512yes—
654C2#1311751811yescharacteristic
655C2#1311754512yes—
656C2#1311754811yescharacteristic
657C2#1312055711yescharacteristic
658C2#1312056111yescharacteristic
659C2#1312069711yescharacteristic
660C2#1312070012yes—
661C2#1312074411yescharacteristic
662C2#1312074812yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#388C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×#388D13
hypocenterC13#14301
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×C4×Dic26C2semidirect
4. #13113106C2semidirect
5. #13113100C2semidirect
6. #13113099C2semidirect
9. #13113063C2semidirect
10. #13113060C2semidirect
38. #11718608C4semidirect
513. C13#14301semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic262
C2×#117186082
C2×#117186052
#131131062
#131131002
#131130992
#131130812
#131130792
#131130632
#131130602
C2×C13×#3882
#1430113