Finite Group Databasebeta

← #15793972

Subgroups — #15793972

Order 3328.

1530 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
1C22×#88133C211yesmaximal, characteristic
2C2×#11718637C211yesmaximal, characteristic, complemented
3C2×#11718312C211yesmaximal, characteristic, complemented
4#13113090C211yesmaximal, characteristic, complemented
5#13113088C212yesmaximal, complemented
6#13113087C212yesmaximal, complemented
7#13113086C211yesmaximal, characteristic, complemented
8#13113081C211yesmaximal, characteristic
9#13113079C212yesmaximal
10#13113079C212yesmaximal
11C13×#1439C211yesmaximal, characteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C22⋊C4C2211yescharacteristic
14C22×C13×C22⋊C4C2212yes—
15C22×C22⋊Dic13C2211yescharacteristic
16C22×C22⋊Dic13C2211yescharacteristic
17C22×C22⋊Dic13C2212yes—
18C22×C4⋊Dic13C2211yescharacteristic
19C22×C4⋊Dic13C2211yescharacteristic
20C22×#6101C2211yescharacteristic
21C22×#6101C2211yescharacteristic
22C22×#6101C2212yes—
23C22×#6101C2212yes—
24C22×C4×Dic13C2211yescharacteristic
25C2×#88133—24no—
26C2×#88133—24no—
27C2×#88133C418yescomplemented
28C2×C13×#95C2211yescharacteristic
29C2×C13×#95C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2211yescharacteristic
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38#11718637—24no—
39#11718312—24no—
40C25×C13C2311yescharacteristic
41C23×C4×C13C2312yes—
42C23×C4×C13C2312yes—
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2311yescharacteristic
45C23×Dic13C2312yes—
46C23×Dic13C2312yes—
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2311yescharacteristic
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4—42no—
53C2×C13×C22⋊C4—22no—
54C2×C13×C22⋊C4—22no—
55C2×C13×C22⋊C4—42no—
56C2×C13×C22⋊C4—42no—
57C2×C13×C22⋊C4—42no—
58C2×C13×C22⋊C4C2×C414yes—
59C2×C22⋊Dic13—22no—
60C2×C22⋊Dic13—22no—
61C2×C22⋊Dic13—22no—
62C2×C22⋊Dic13—22no—
63C2×C22⋊Dic13—42no—
64C2×C22⋊Dic13—42no—
65C2×C22⋊Dic13—42no—
66C2×C22⋊Dic13C2×C414yes—
67C2×C22⋊Dic13C2×C414yes—
68C2×C4⋊Dic13—22no—
69C2×C4⋊Dic13—22no—
70C2×C4⋊Dic13—22no—
71C2×C4⋊Dic13—42no—
72C2×C4⋊Dic13C2×C414yes—
73C2×#6101—22no—
74C2×#6101—22no—
75C2×#6101—22no—
76C2×#6101—22no—
77C2×#6101—24no—
78C2×#6101—24no—
79C2×#6101—42no—
80C2×#6101—42no—
81C2×#6101—42no—
82C2×#6101—42no—
83C2×#6101C2×C414yes—
84C2×#6101C2×C414yes—
85C2×C4×Dic13C2×C414yes—
86C2×C4×Dic13D414yes—
87C2×C4×Dic13D414yes—
88#88133—232no—
89C13×#95—22no—
90C13×#95—42no—
91#88071—22no—
92#88071—24no—
93#88071—24no—
94#88071—42no—
95#88071—42no—
96#88071—42no—
97#88071—42no—
98#88071—42no—
99#14665—131nomaximal, Sylow
100C24×C13—21no—
101C24×C13—21no—
102C24×C13—21no—
103C24×C13—22no—
104C24×C13—22no—
105C24×C13—21no—
106C24×C13—21no—
107C24×C13—21no—
108C24×C13—22no—
109C24×C13—22no—
110C24×C13C22×C412yes—
111C24×C13C2411yescharacteristic
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—21no—
115C22×C4×C13—21no—
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×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13C22×C412yes—
133C22×C4×C13C22×C412yes—
134C22×C4×C13C2×D412yes—
135C22×C4×C13C2×D412yes—
136C22×Dic13—22no—
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—22no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—21no—
145C22×Dic13—21no—
146C22×Dic13—22no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—22no—
151C22×Dic13—21no—
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×Dic13—22no—
166C22×Dic13C22×C412yes—
167C22×Dic13C22×C412yes—
168C22×Dic13C22×C412yes—
169C22×Dic13C22×C412yes—
170C22×Dic13C2×D412yes—
171C22×Dic13C2×D412yes—
172C22×Dic13C2×D412yes—
173C22×Dic13C2×D412yes—
174C13×C4⋊C4—44no—
175C13×C22⋊C4—28no—
176C13×C22⋊C4—48no—
177C22⋊Dic13—28no—
178C22⋊Dic13—28no—
179C22⋊Dic13—48no—
180C4⋊Dic13—28no—
181C4⋊Dic13—44no—
182#6101—28no—
183#6101—28no—
184#6101—48no—
185#6101—48no—
186C4×Dic13C22⋊C4116yescomplemented
187C22×#126—131no—
188C2×#384—131no—
189C2×#383—131no—
190#1441—132no—
191#1441—131no—
192#1441—132no—
193#1441—131no—
194#1439—132no—
195#1439—132no—
196#1439—131no—
197#1439D1311yescharacteristic
198C23×C13—22no—
199C23×C13—22no—
200C23×C13—22no—
201C23×C13—24no—
202C23×C13—24no—
203C23×C13—41no—
204C23×C13—41no—
205C23×C13—41no—
206C23×C13—41no—
207C23×C13—41no—
208C23×C13—41no—
209C23×C13—42no—
210C23×C13—42no—
211C23×C13—41no—
212C23×C13—41no—
213C23×C13—42no—
214C23×C13—42no—
215C23×C13—42no—
216C23×C13—42no—
217C23×C13—42no—
218C23×C13—42no—
219C23×C13—42no—
220C23×C13—42no—
221C23×C13C23×C411yescharacteristic
222C23×C13C22×D411yescharacteristic
223C23×C13C22×D411yescharacteristic
224C23×C13H(5,𝔽2)11yescharacteristic
225C23×C13H(5,𝔽2)12yes—
226C23×C13H(5,𝔽2)12yes—
227C23×C13H(5,𝔽2)11yescharacteristic
228C23×C132−1+411yescharacteristic
229C23×C132−1+411yescharacteristic
230C23×C132−1+412yes—
231C23×C132−1+412yes—
232C2×C4×C13—24no—
233C2×C4×C13—22no—
234C2×C4×C13—22no—
235C2×C4×C13—24no—
236C2×C4×C13—22no—
237C2×C4×C13—24no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—42no—
241C2×C4×C13—42no—
242C2×C4×C13—42no—
243C2×C4×C13—42no—
244C2×C4×C13—42no—
245C2×C4×C13—42no—
246C2×C4×C13—42no—
247C2×C4×C13—42no—
248C2×C4×C13—42no—
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×C13C2×C22⋊C414yes—
256C2×Dic13—22no—
257C2×Dic13—22no—
258C2×Dic13—24no—
259C2×Dic13—22no—
260C2×Dic13—22no—
261C2×Dic13—22no—
262C2×Dic13—22no—
263C2×Dic13—24no—
264C2×Dic13—22no—
265C2×Dic13—22no—
266C2×Dic13—22no—
267C2×Dic13—22no—
268C2×Dic13—22no—
269C2×Dic13—22no—
270C2×Dic13—24no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—42no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—42no—
279C2×Dic13—42no—
280C2×Dic13—42no—
281C2×Dic13—42no—
282C2×Dic13—42no—
283C2×Dic13—42no—
284C2×Dic13—42no—
285C2×Dic13—42no—
286C2×Dic13—42no—
287C2×Dic13—42no—
288C2×Dic13—42no—
289C2×Dic13—42no—
290C2×Dic13—42no—
291C2×Dic13—42no—
292C2×Dic13C2×C22⋊C414yes—
293C2×Dic13C2×C22⋊C414yes—
294C2×#126—138no—
295C2×#126—264no—
296C2×#126—264no—
297C22×C4⋊C4—131no—
298C22×C4⋊C4—131no—
299C22×C4⋊C4—131no—
300C22×C4⋊C4—132no—
301C22×C4⋊C4—132no—
302C22×C4⋊C4—131no—
303C22×C4⋊C4C2×D1311yescharacteristic
304C22×C22⋊C4—131no—
305C22×C22⋊C4—131no—
306C22×C22⋊C4—132no—
307C22×C22⋊C4C2×D1311yescharacteristic
308C22×C22⋊C4C2×D1312yes—
309C22×C42—131no—
310#384—264no—
311#383—264no—
312C2×#95—132no—
313C2×#95—132no—
314C2×#95—131no—
315C2×#95—132no—
316C2×#95—132no—
317C2×#95—132no—
318C2×#95—132no—
319C2×#95—132no—
320C2×#95C2×D1311yescharacteristic
321C2×#95C2×D1312yes—
322C22×C13—42no—
323C22×C13—42no—
324C22×C13—42no—
325C22×C13—44no—
326C22×C13—44no—
327C22×C13—81no—
328C22×C13—81no—
329C22×C13—81no—
330C22×C13—81no—
331C22×C13—82no—
332C22×C13—82no—
333C22×C13C22×C22⋊C411yescharacteristic
334C22×C13#52011yescharacteristic
335C22×C13#52011yescharacteristic
336C22×C13#52012yes—
337C22×C13#52012yes—
338C22×C13#53511yescharacteristic
339C22×C13#53511yescharacteristic
340C22×C13#53511yescharacteristic
341C22×C13#53611yescharacteristic
342C22×C13#53611yescharacteristic
343C22×C13#53611yescharacteristic
344C22×C13#53712yes—
345C22×C13#53711yescharacteristic
346C22×C13#53712yes—
347C22×C13#53711yescharacteristic
348C22×C13#56012yes—
349C22×C13#56012yes—
350C22×C13#56312yes—
351C22×C13#56312yes—
352C22×C13#56312yes—
353C22×C13#56312yes—
354C22×C13#56312yes—
355C22×C13#56312yes—
356C4×C13—24no—
357C4×C13—42no—
358C4×C13—82no—
359C4×C13—82no—
360Dic13—24no—
361Dic13—24no—
362Dic13—42no—
363Dic13—42no—
364Dic13—82no—
365Dic13—82no—
366C25C22×D1311yescharacteristic
367C23×C4—131no—
368C23×C4—131no—
369C23×C4—131no—
370C23×C4—131no—
371C23×C4—132no—
372C23×C4—132no—
373C23×C4C22×D1312yes—
374C23×C4C22×D1312yes—
375C23×C4C22×D1311yescharacteristic
376C23×C4C22×D1311yescharacteristic
377#126—2632no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—42no—
380C2×C4⋊C4—134no—
381C2×C4⋊C4—134no—
382C2×C4⋊C4—134no—
383C2×C4⋊C4—262no—
384C2×C4⋊C4—262no—
385C2×C4⋊C4—262no—
386C2×C4⋊C4—262no—
387C2×C4⋊C4—262no—
388C2×C4⋊C4—262no—
389C2×C4⋊C4—264no—
390C2×C4⋊C4—264no—
391C2×C4⋊C4—262no—
392C2×C4⋊C4—522no—
393C2×C4⋊C4—522no—
394C2×C4⋊C4—522no—
395C2×C4⋊C4—522no—
396C2×C4⋊C4—522no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—134no—
403C2×C22⋊C4—134no—
404C2×C22⋊C4—262no—
405C2×C22⋊C4—262no—
406C2×C22⋊C4—262no—
407C2×C22⋊C4—262no—
408C2×C22⋊C4—522no—
409C2×C22⋊C4—522no—
410C2×C22⋊C4—522no—
411C2×C22⋊C4C4×D1314yes—
412C2×C42—134no—
413C2×C42—134no—
414C2×C42—134no—
415#95—22no—
416#95—42no—
417#95—264no—
418#95—264no—
419#95—262no—
420#95—522no—
421#95—522no—
422#95—522no—
423#95—522no—
424#95—522no—
425C2×C13—82no—
426C2×C13#231111yescharacteristic
427C2×C13#231111yescharacteristic
428C2×C13#231111yescharacteristic
429C2×C13#238312yes—
430C2×C13#238312yes—
431C2×C13#281811yescharacteristic
432C2×C13#282111yescharacteristic
433C2×C13#282111yescharacteristic
434C2×C13#282111yescharacteristic
435C2×C13#282312yes—
436C2×C13#282312yes—
437C24—21no—
438C24—21no—
439C24—21no—
440C24—22no—
441C24—22no—
442C24—21no—
443C24—21no—
444C24—21no—
445C24—22no—
446C24—22no—
447C24C2×C4×D1312yes—
448C24C23×D1311yescharacteristic
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—132no—
470C22×C4—132no—
471C22×C4—132no—
472C22×C4—132no—
473C22×C4—132no—
474C22×C4—132no—
475C22×C4—132no—
476C22×C4—132no—
477C22×C4—261no—
478C22×C4—262no—
479C22×C4—261no—
480C22×C4—261no—
481C22×C4—261no—
482C22×C4—262no—
483C22×C4—261no—
484C22×C4—261no—
485C22×C4—261no—
486C22×C4—261no—
487C22×C4—261no—
488C22×C4—262no—
489C22×C4—261no—
490C22×C4—261no—
491C22×C4—261no—
492C22×C4—262no—
493C22×C4—262no—
494C22×C4—262no—
495C22×C4—262no—
496C22×C4—262no—
497C22×C4—262no—
498C22×C4—262no—
499C22×C4—262no—
500C22×C4—262no—
501C22×C4—262no—
502C22×C4—262no—
503C22×C4—262no—
504C22×C4—262no—
505C22×C4—262no—
506C22×C4—262no—
507C22×C4C2×C4×D1312yes—
508C22×C4C2×C4×D1312yes—
509C22×C4D4×D1312yes—
510C22×C4D4×D1312yes—
511C4⋊C4—44no—
512C4⋊C4—268no—
513C4⋊C4—268no—
514C4⋊C4—268no—
515C4⋊C4—524no—
516C4⋊C4—528no—
517C4⋊C4—528no—
518C22⋊C4—28no—
519C22⋊C4—48no—
520C22⋊C4—268no—
521C22⋊C4—268no—
522C22⋊C4—528no—
523C42—1316no—
524C13#1466511yescharacteristic, complemented, Sylow
525C23—22no—
526C23—22no—
527C23—22no—
528C23—24no—
529C23—24no—
530C23—41no—
531C23—42no—
532C23—42no—
533C23—41no—
534C23—41no—
535C23—42no—
536C23—42no—
537C23—41no—
538C23—41no—
539C23—42no—
540C23—42no—
541C23—41no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—41no—
546C23—42no—
547C23—41no—
548C23C22×C4×D1311yescharacteristic
549C23C2×D4×D1311yescharacteristic
550C23C2×D4×D1311yescharacteristic
551C23#8825111yescharacteristic
552C23#8825112yes—
553C23#8825112yes—
554C23#8825411yescharacteristic
555C23#8825611yescharacteristic
556C23#8825711yescharacteristic
557C23#8825712yes—
558C23#8825712yes—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—42no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—134no—
583C2×C4—134no—
584C2×C4—262no—
585C2×C4—262no—
586C2×C4—264no—
587C2×C4—262no—
588C2×C4—262no—
589C2×C4—264no—
590C2×C4—262no—
591C2×C4—262no—
592C2×C4—262no—
593C2×C4—262no—
594C2×C4—262no—
595C2×C4—262no—
596C2×C4—262no—
597C2×C4—262no—
598C2×C4—264no—
599C2×C4—521no—
600C2×C4—522no—
601C2×C4—521no—
602C2×C4—521no—
603C2×C4—521no—
604C2×C4—521no—
605C2×C4—521no—
606C2×C4—522no—
607C2×C4—522no—
608C2×C4—522no—
609C2×C4—522no—
610C2×C4—522no—
611C2×C4—522no—
612C2×C4—522no—
613C2×C4—522no—
614C2×C4—522no—
615C2×C4—522no—
616C2×C4—522no—
617C2×C4—522no—
618C2×C4—522no—
619C2×C4—522no—
620C2×C4C22⋊C4×D1314yes—
621C22—44no—
622C22—44no—
623C22—42no—
624C22—42no—
625C22—42no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22—82no—
631C22—82no—
632C22C2×C22⋊C4×D1311yescharacteristic
633C22#1171920911yescharacteristic
634C22#1171922811yescharacteristic
635C22#1171925112yes—
636C22#1171925112yes—
637C22#1171929711yescharacteristic
638C22#1171930012yes—
639C22#1171930212yes—
640C22#1171931211yescharacteristic
641C22#1171931311yescharacteristic
642C22#1171931312yes—
643C22#1171932512yes—
644C22#1171933311yescharacteristic
645C22#1171933411yescharacteristic
646C22#1171935112yes—
647C22#1171935112yes—
648C22#1171935311yescharacteristic
649C22#1171935612yes—
650C22#1171935612yes—
651C22#1171937712yes—
652C22#1171938011yescharacteristic
653C22#1171941712yes—
654C22#1171942011yescharacteristic
655C4—24no—
656C4—42no—
657C4—82no—
658C4—82no—
659C4—264no—
660C4—264no—
661C4—522no—
662C4—522no—
663C4—1042no—
664C4—1042no—
665C2—82no—
666C2#1311742311yescharacteristic
667C2#1311742511yescharacteristic
668C2#1311742611yescharacteristic
669C2#1311802312yes—
670C2#1311802412yes—
671C2#1312287511yescharacteristic
672C2#1312289311yescharacteristic
673C2#1312289811yescharacteristic
674C2#1312289911yescharacteristic
675C2#1312290712yes—
676C2#1312290912yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1439C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenter#1439D13
hypocenterC13#14665
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#11718637C2semidirect
3. C2×#11718312C2semidirect
4. #13113090C2semidirect
5. #13113088C2semidirect
6. #13113087C2semidirect
7. #13113086C2semidirect
27. C2×#88133C4semidirect
186. C4×Dic13C22⋊C4semidirect
524. C13#14665semidirect

Maximal subgroups

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

subgroupindex
C22×#881332
C2×#117186372
C2×#117183122
#131130902
#131130882
#131130872
#131130862
#131130812
#131130792
C13×#14392
#1466513