Finite Group Databasebeta

← #15784427

Subgroups — #15784427

Order 3328.

2298 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718650C212yesmaximal
2C2×C4×#6103C212yesmaximal
3C2×C4×#6103C211yesmaximal, characteristic
4C2×D13×#95C211yesmaximal, characteristic
5#13113069C212yesmaximal, complemented
6#13113068C212yesmaximal, complemented
7#13113064C211yesmaximal, characteristic, complemented
8#13113063C211yesmaximal, characteristic, complemented
9#13113057C211yesmaximal, characteristic
10#95×Dic13C211yesmaximal, characteristic, complemented
11C2×C4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
12C23×C4×D13C2212yes—
13C23×C4×D13C2211yescharacteristic
14C22×C13×C4⋊C4C2212yes—
15C22×C42×C13C2212yes—
16C22×C42×C13C2211yescharacteristic
17C22×#6103C2212yes—
18C22×#6103C2211yescharacteristic
19C22×#6103C2211yescharacteristic
20C22×#6101C2212yes—
21C22×C4×Dic13C2212yes—
22C22×C4×Dic13C2211yescharacteristic
23C4×C13×C4⋊C4—24no—
24C2×C13×#95C2211yescharacteristic
25C2×C13×#95C2211yescharacteristic
26C2×#88071C2211yescharacteristic
27C2×#88071C2211yescharacteristic
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2211yescharacteristic
35C2×#88071C2211yescharacteristic
36#11718650C4116yescomplemented
37C4×#6103—28no—
38C4×#6103C418yescomplemented
39D13×#95—24no—
40C24×D13C2311yescharacteristic
41C23×C4×C13C2312yes—
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2312yes—
45C23×C4×C13C2311yescharacteristic
46C23×Dic13C2312yes—
47C23×Dic13C2312yes—
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2311yescharacteristic
51C22×C4×D13—24no—
52C22×C4×D13—24no—
53C22×C4×D13—24no—
54C22×C4×D13—22no—
55C22×C4×D13—24no—
56C22×C4×D13—22no—
57C22×C4×D13—24no—
58C22×C4×D13—42no—
59C22×C4×D13—42no—
60C22×C4×D13—42no—
61C22×C4×D13C2×C414yes—
62C22×C4×D13C2×C418yes—
63C2×C13×C4⋊C4—24no—
64C2×C13×C4⋊C4—24no—
65C2×C13×C4⋊C4C2×C418yescomplemented
66C2×C42×C13—22no—
67C2×C42×C13—22no—
68C2×C42×C13—24no—
69C2×C42×C13—24no—
70C2×C42×C13—42no—
71C2×C42×C13C2×C414yescomplemented
72C2×#6103—24no—
73C2×#6103—24no—
74C2×#6103C2×C418yes—
75C2×#6103C2×C414yes—
76C2×#6103C2×C418yes—
77C2×#6103C2×C414yes—
78C2×#6103D414yes—
79C2×#6103Q814yes—
80C2×#6101—42no—
81C2×#6101—42no—
82C2×#6101C2×C418yescomplemented
83C2×C4×Dic13—24no—
84C2×C4×Dic13—24no—
85C2×C4×Dic13—42no—
86C2×C4×Dic13—42no—
87C2×C4×Dic13C2×C414yescomplemented
88C13×#95—22no—
89C13×#95D414yes—
90#88071—22no—
91#88071—24no—
92#88071—24no—
93#88071—22no—
94#88071—24no—
95#88071—42no—
96#88071C2×C414yescomplemented
97#88071C2×C414yescomplemented
98#88071C2×C418yescomplemented
99#88071C2×C418yescomplemented
100#13814—131nomaximal, Sylow
101C24×C13C2411yescharacteristic
102C23×D13—21no—
103C23×D13—22no—
104C23×D13—21no—
105C23×D13—21no—
106C23×D13—22no—
107C23×D13—21no—
108C23×D13C22×C412yes—
109C23×D13C22×C414yes—
110C23×D13C2×D412yes—
111C23×D13C2×Q812yes—
112C23×D13#4114yes—
113C22×C4×C13—22no—
114C22×C4×C13—21no—
115C22×C4×C13—21no—
116C22×C4×C13—21no—
117C22×C4×C13—21no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—21no—
124C22×C4×C13—22no—
125C22×C4×C13—21no—
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×C414yes—
133C22×C4×C13C22×C412yes—
134C22×C4×C13C22×C414yes—
135C22×C4×C13C22×C412yes—
136C22×C4×C13C22×C414yes—
137C22×C4×C13C22×C412yes—
138C22×C4×C13C2×D412yes—
139C22×C4×C13C2×D412yes—
140C22×C4×C13C2×D414yes—
141C22×C4×C13C2×Q812yes—
142C22×C4×C13#4112yes—
143C22×C4×C13#4114yes—
144C22×Dic13—22no—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—22no—
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—21no—
160C22×Dic13—22no—
161C22×Dic13—22no—
162C22×Dic13—22no—
163C22×Dic13—22no—
164C22×Dic13—22no—
165C22×Dic13C22×C414yes—
166C22×Dic13C22×C412yes—
167C22×Dic13C22×C414yes—
168C22×Dic13C22×C412yes—
169C22×Dic13C22×C414yes—
170C22×Dic13C22×C412yes—
171C22×Dic13C2×D412yes—
172C22×Dic13C2×Q812yes—
173C2×C4×D13—28no—
174C2×C4×D13—216no—
175C2×C4×D13—28no—
176C2×C4×D13—216no—
177C2×C4×D13—48no—
178C2×C4×D13—44no—
179C2×C4×D13—48no—
180C2×C4×D13—48no—
181C2×C4×D13—48no—
182C2×C4×D13—48no—
183C2×C4×D13—48no—
184C2×C4×D13—48no—
185C13×C4⋊C4—216no—
186C42×C13—28no—
187C42×C13—48no—
188#6103—216no—
189#6103C42116yescomplemented
190#6103C4⋊C4116yescomplemented
191#6101—48no—
192C4×Dic13—44no—
193C4×Dic13—48no—
194C2×#385—132no—
195C2×C4×C4⋊C4D1311yescharacteristic, complemented
196C2×C4×C22⋊C4—131no—
197C2×C4×C22⋊C4—132no—
198C22×#95—131no—
199#1436—132no—
200#1436—132no—
201C4⋊#95—131no—
202#1434—131no—
203C22⋊#95—131no—
204C4×#95—131no—
205C23×C13C23×C411yescharacteristic
206C23×C13C23×C412yes—
207C23×C13C22×D411yescharacteristic
208C23×C13C22×D411yescharacteristic
209C23×C13C22×Q811yescharacteristic
210C23×C13C2×#4112yes—
211C23×C13C2×#4112yes—
212C23×C13C2×#4111yescharacteristic
213C23×C13H(5,𝔽2)11yescharacteristic
214C23×C13H(5,𝔽2)12yes—
215C23×C132−1+411yescharacteristic
216C22×D13—22no—
217C22×D13—24no—
218C22×D13—22no—
219C22×D13—24no—
220C22×D13—22no—
221C22×D13—24no—
222C22×D13—22no—
223C22×D13—24no—
224C22×D13—22no—
225C22×D13—24no—
226C22×D13—24no—
227C22×D13—22no—
228C22×D13—22no—
229C22×D13—24no—
230C22×D13—24no—
231C22×D13—24no—
232C22×D13—22no—
233C22×D13—24no—
234C22×D13C2×C4214yes—
235C22×D13C2×C4⋊C414yes—
236C22×D13#11714yes—
237C22×D13C4×D418yes—
238C22×D13C4×Q818yes—
239C2×C4×C13—22no—
240C2×C4×C13—22no—
241C2×C4×C13—22no—
242C2×C4×C13—24no—
243C2×C4×C13—24no—
244C2×C4×C13—22no—
245C2×C4×C13—24no—
246C2×C4×C13—22no—
247C2×C4×C13—24no—
248C2×C4×C13—22no—
249C2×C4×C13—22no—
250C2×C4×C13—24no—
251C2×C4×C13—24no—
252C2×C4×C13—24no—
253C2×C4×C13—24no—
254C2×C4×C13—22no—
255C2×C4×C13—22no—
256C2×C4×C13—24no—
257C2×C4×C13—24no—
258C2×C4×C13—22no—
259C2×C4×C13—24no—
260C2×C4×C13—24no—
261C2×C4×C13—24no—
262C2×C4×C13—42no—
263C2×C4×C13—42no—
264C2×C4×C13—42no—
265C2×C4×C13—42no—
266C2×C4×C13C2×C4214yes—
267C2×C4×C13C2×C4⋊C414yes—
268C2×C4×C13C4×D414yes—
269C2×C4×C13C4×D418yes—
270C2×Dic13—22no—
271C2×Dic13—22no—
272C2×Dic13—22no—
273C2×Dic13—24no—
274C2×Dic13—22no—
275C2×Dic13—24no—
276C2×Dic13—24no—
277C2×Dic13—24no—
278C2×Dic13—22no—
279C2×Dic13—24no—
280C2×Dic13—22no—
281C2×Dic13—24no—
282C2×Dic13—24no—
283C2×Dic13—24no—
284C2×Dic13—24no—
285C2×Dic13—22no—
286C2×Dic13—24no—
287C2×Dic13—42no—
288C2×Dic13—42no—
289C2×Dic13—42no—
290C2×Dic13—42no—
291C2×Dic13—42no—
292C2×Dic13—42no—
293C2×Dic13—42no—
294C2×Dic13—42no—
295C2×Dic13—42no—
296C2×Dic13—42no—
297C2×Dic13C2×C4214yes—
298C2×Dic13C2×C4⋊C414yes—
299C4×D13—416no—
300C4×D13—432no—
301C24×C4—131no—
302C24×C4—132no—
303C22×C4⋊C4—132no—
304C22×C4⋊C4C2×D1312yes—
305C22×C22⋊C4—131no—
306C22×C22⋊C4—131no—
307C22×C22⋊C4—132no—
308C22×C42—131no—
309C22×C42—132no—
310C22×C42C2×D1312yes—
311C22×C42C2×D1311yescharacteristic
312#385—1316no—
313C4×C4⋊C4—24no—
314C4×C22⋊C4—138no—
315C4×C22⋊C4—268no—
316C2×#95—132no—
317C2×#95—132no—
318C2×#95—131no—
319C2×#95—131no—
320C2×#95—131no—
321C2×#95—131no—
322C2×#95—132no—
323C2×#95—132no—
324C2×#95—132no—
325C2×#95—132no—
326C2×#95—264no—
327C2×#95C2×D1311yescharacteristic
328C2×#95C2×D1311yescharacteristic
329C22×C13C22×C4211yescharacteristic
330C22×C13C22×C4⋊C411yescharacteristic
331C22×C13C2×#11711yescharacteristic
332C22×C13C2×C4×D411yescharacteristic
333C22×C13C2×C4×D412yes—
334C22×C13C2×C4×D412yes—
335C22×C13C2×C4×Q812yes—
336C22×C13C4×#4111yescharacteristic
337C22×C13C4×#4112yes—
338C22×C13#51811yescharacteristic
339C22×C13#51812yes—
340C22×C13#52011yescharacteristic
341C22×C13#52012yes—
342C22×C13D4211yescharacteristic
343C22×C13#54612yes—
344C22×C13#54612yes—
345C22×C13#54711yescharacteristic
346C22×C13D4×Q811yescharacteristic
347C22×C13#55112yes—
348C22×C13#55112yes—
349C22×C13#55212yes—
350C22×C13#55411yescharacteristic
351C22×C13#55412yes—
352C2×D13—24no—
353C2×D13—24no—
354C2×D13—24no—
355C2×D13—24no—
356C2×D13—28no—
357C2×D13—28no—
358C2×D13—28no—
359C2×D13—28no—
360C2×D13—24no—
361C2×D13—24no—
362C2×D13C4×C4⋊C418yescomplemented
363C4×C13—24no—
364C4×C13—24no—
365C4×C13—28no—
366C4×C13—24no—
367C4×C13—44no—
368Dic13—24no—
369Dic13—24no—
370Dic13—42no—
371Dic13—44no—
372Dic13—44no—
373C25—131no—
374C23×C4—131no—
375C23×C4—131no—
376C23×C4—132no—
377C23×C4—132no—
378C23×C4—131no—
379C23×C4—134no—
380C23×C4—138no—
381C23×C4—264no—
382C23×C4—264no—
383C23×C4—264no—
384C23×C4—262no—
385C23×C4—264no—
386C23×C4—262no—
387C23×C4—264no—
388C23×C4—522no—
389C23×C4—522no—
390C23×C4—522no—
391C23×C4C22×D1312yes—
392C23×C4C22×D1311yescharacteristic
393C23×C4C22×D1312yes—
394C23×C4C22×D1311yescharacteristic
395C23×C4C22×D1311yescharacteristic
396C2×C4⋊C4—24no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—138no—
399C2×C4⋊C4—522no—
400C2×C4⋊C4—522no—
401C2×C4⋊C4C4×D1318yescomplemented
402C2×C22⋊C4—134no—
403C2×C22⋊C4—134no—
404C2×C22⋊C4—138no—
405C2×C22⋊C4—134no—
406C2×C22⋊C4—134no—
407C2×C22⋊C4—138no—
408C2×C22⋊C4—264no—
409C2×C22⋊C4—264no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—42no—
415C2×C42—134no—
416C2×C42—264no—
417C2×C42—264no—
418C2×C42—522no—
419C2×C42—522no—
420C2×C42C4×D1314yescomplemented
421#95—22no—
422#95—134no—
423#95—134no—
424#95—138no—
425#95—138no—
426#95—264no—
427#95—262no—
428#95—264no—
429#95—262no—
430#95—264no—
431#95—522no—
432#95C22⋊D1314yes—
433C2×C13C2×C4×C4⋊C411yescharacteristic
434C2×C13C42×D411yescharacteristic
435C2×C13#227511yescharacteristic
436C2×C13#234211yescharacteristic
437C2×C13#234311yescharacteristic
438C2×C13D4×C4⋊C411yescharacteristic
439C2×C13#234911yescharacteristic
440C2×C13#235812yes—
441C2×C13#235912yes—
442C2×C13#236012yes—
443C2×C13#236812yes—
444D13—28no—
445C24—132no—
446C24—134no—
447C24—132no—
448C24—132no—
449C24—134no—
450C24—261no—
451C24—262no—
452C24—261no—
453C24—261no—
454C24—262no—
455C24—261no—
456C24C23×D1311yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—132no—
477C22×C4—132no—
478C22×C4—134no—
479C22×C4—132no—
480C22×C4—132no—
481C22×C4—134no—
482C22×C4—132no—
483C22×C4—134no—
484C22×C4—268no—
485C22×C4—2616no—
486C22×C4—262no—
487C22×C4—261no—
488C22×C4—261no—
489C22×C4—262no—
490C22×C4—262no—
491C22×C4—262no—
492C22×C4—262no—
493C22×C4—261no—
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—261no—
507C22×C4—268no—
508C22×C4—2616no—
509C22×C4—524no—
510C22×C4—528no—
511C22×C4—528no—
512C22×C4—528no—
513C22×C4—528no—
514C22×C4—528no—
515C22×C4—528no—
516C22×C4—528no—
517C22×C4C2×C4×D1314yes—
518C22×C4C2×C4×D1312yes—
519C22×C4C2×C4×D1314yes—
520C22×C4C2×C4×D1312yes—
521C22×C4C2×C4×D1314yes—
522C22×C4C2×C4×D1312yes—
523C22×C4#612712yes—
524C22×C4#612714yes—
525C22×C4D4×D1312yes—
526C22×C4Q8×D1312yes—
527C22×C4C2×C22⋊D1312yes—
528C22×C4C2×C22⋊D1314yes—
529C4⋊C4—216no—
530C4⋊C4—528no—
531C22⋊C4—1316no—
532C22⋊C4—1316no—
533C22⋊C4—2616no—
534C42—28no—
535C42—48no—
536C42—524no—
537C42—528no—
538C13#1381411yescharacteristic, complemented, Sylow
539C23—134no—
540C23—134no—
541C23—134no—
542C23—138no—
543C23—138no—
544C23—262no—
545C23—264no—
546C23—262no—
547C23—262no—
548C23—262no—
549C23—262no—
550C23—264no—
551C23—262no—
552C23—264no—
553C23—264no—
554C23—262no—
555C23—264no—
556C23—264no—
557C23—262no—
558C23—264no—
559C23—264no—
560C23—264no—
561C23—264no—
562C23C22×C4×D1311yescharacteristic
563C23C22×C4×D1312yes—
564C23C2×#612711yescharacteristic
565C23C2×#612712yes—
566C23C2×D4×D1311yescharacteristic
567C23#8825111yescharacteristic
568C23C2×Q8×D1311yescharacteristic
569C23#8825411yescharacteristic
570C23#41×D1312yes—
571C23#8825612yes—
572C23C22×C22⋊D1311yescharacteristic
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—22no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—22no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—134no—
601C2×C4—134no—
602C2×C4—262no—
603C2×C4—262no—
604C2×C4—262no—
605C2×C4—262no—
606C2×C4—264no—
607C2×C4—264no—
608C2×C4—264no—
609C2×C4—264no—
610C2×C4—264no—
611C2×C4—262no—
612C2×C4—262no—
613C2×C4—264no—
614C2×C4—262no—
615C2×C4—264no—
616C2×C4—264no—
617C2×C4—264no—
618C2×C4—264no—
619C2×C4—5232no—
620C2×C4—5216no—
621C2×C4—522no—
622C2×C4—522no—
623C2×C4—522no—
624C2×C4—522no—
625C2×C4—522no—
626C2×C4—522no—
627C2×C4—522no—
628C2×C4—522no—
629C2×C4—522no—
630C2×C4—522no—
631C2×C4C42×D1314yes—
632C2×C4C4⋊C4×D1314yes—
633C2×C4C4×C22⋊D1314yes—
634C2×C4C4×C22⋊D1318yes—
635C22—138no—
636C22—264no—
637C22—264no—
638C22—264no—
639C22—264no—
640C22—268no—
641C22—268no—
642C22—268no—
643C22—268no—
644C22—264no—
645C22—264no—
646C22C2×C42×D1311yescharacteristic
647C22C4×#612711yescharacteristic
648C22C4×#612712yes—
649C22C2×C4⋊C4×D1311yescharacteristic
650C22#1171920911yescharacteristic
651C22#1171921211yescharacteristic
652C22#1171921611yescharacteristic
653C22D13×#11711yescharacteristic
654C22#1171922611yescharacteristic
655C22#1171923212yes—
656C22C4×D4×D1312yes—
657C22#1171925012yes—
658C22#1171925512yes—
659C22#1171926112yes—
660C22C4×Q8×D1312yes—
661C22#1171927912yes—
662C22#1171928412yes—
663C22#1171928612yes—
664C22C2×C4×C22⋊D1311yescharacteristic
665C22C2×C4×C22⋊D1312yes—
666C22D4×C22⋊D1311yescharacteristic
667C22Q8×C22⋊D1311yescharacteristic
668C22#1171953412yes—
669C4—24no—
670C4—28no—
671C4—24no—
672C4—24no—
673C4—44no—
674C4—264no—
675C4—264no—
676C4—524no—
677C4—524no—
678C4—522no—
679C2—268no—
680C2C4×C4⋊C4×D1311yescharacteristic
681C2C42×C22⋊D1311yescharacteristic
682C2#1311719611yescharacteristic
683C2#1311768611yescharacteristic
684C2#1311769911yescharacteristic
685C2C4⋊C4×C22⋊D1311yescharacteristic
686C2#1311774711yescharacteristic
687C2#1311781312yes—
688C2#1311783312yes—
689C2#1311783712yes—
690C2#1311792012yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC22×C13C22×C42
FittingC2×C4×C13×C4⋊C4C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×C4×C4⋊C4D13
hypocenterC13#13814
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
5. #13113069C2semidirect
6. #13113068C2semidirect
7. #13113064C2semidirect
8. #13113063C2semidirect
10. #95×Dic13C2semidirect
11. C2×C4×C13×C4⋊C4C2semidirect
36. #11718650C4semidirect
38. C4×#6103C4semidirect
65. C2×C13×C4⋊C4C2×C4semidirect
71. C2×C42×C13C2×C4semidirect
82. C2×#6101C2×C4semidirect
87. C2×C4×Dic13C2×C4semidirect
96. #88071C2×C4semidirect
97. #88071C2×C4semidirect
98. #88071C2×C4semidirect
99. #88071C2×C4semidirect
189. #6103C42semidirect
190. #6103C4⋊C4semidirect
195. C2×C4×C4⋊C4D13semidirect
362. C2×D13C4×C4⋊C4semidirect
401. C2×C4⋊C4C4×D13semidirect
420. C2×C42C4×D13semidirect
538. C13#13814semidirect

Maximal subgroups

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

subgroupindex
C2×#117186502
C2×C4×#61032
C2×D13×#952
#131130692
#131130682
#131130642
#131130632
#131130572
#95×Dic132
C2×C4×C13×C4⋊C42
#1381413