Finite Group Databasebeta

← #15784395

Subgroups — #15784395

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×C22⋊C4×Dic13C212yesmaximal
2C2×C4×C22⋊Dic13C211yesmaximal, characteristic
3C2×#11718309C211yesmaximal, characteristic, complemented
4C22×#88071C211yesmaximal, characteristic
5#13113062C212yesmaximal, complemented
6#13113062C211yesmaximal, characteristic, complemented
7#13113060C211yesmaximal, characteristic, complemented
8#13113060C212yesmaximal, complemented
9#13113058C212yesmaximal
10#95×Dic13C211yesmaximal, characteristic, complemented
11C13×C22⋊#95C211yesmaximal, characteristic
12C24×C4×C13C2211yescharacteristic
13C24×Dic13C2212yes—
14C22×C13×C22⋊C4C2212yes—
15C22×C22⋊Dic13C2211yescharacteristic
16C22×C22⋊Dic13C2211yescharacteristic
17C22×C4×Dic13C2211yescharacteristic
18C22×C4×Dic13C2212yes—
19C22×C4×Dic13C2212yes—
20C22×C4×Dic13C2211yescharacteristic
21C2×C13×#95C2211yescharacteristic
22C2×C13×#95C2211yescharacteristic
23C2×C13×#95C2212yes—
24C4×C22⋊Dic13C418yescomplemented
25C2×#88071—24no—
26C2×#88071C2212yes—
27C2×#88071C2212yes—
28C2×#88071C2211yescharacteristic
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2211yescharacteristic
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2211yescharacteristic
36C2×#88071C2211yescharacteristic
37C22⋊C4×Dic13C4116yescomplemented
38#11718309—24no—
39C25×C13C2311yescharacteristic
40C23×C4×C13—24no—
41C23×C4×C13—22no—
42C23×C4×C13—22no—
43C23×C4×C13—42no—
44C23×C4×C13C2×C414yes—
45C23×C4×C13C2312yes—
46C23×C4×C13C2312yes—
47C23×C4×C13C2311yescharacteristic
48C23×C4×C13C2311yescharacteristic
49C23×Dic13—24no—
50C23×Dic13—24no—
51C23×Dic13—24no—
52C23×Dic13—24no—
53C23×Dic13—42no—
54C23×Dic13—42no—
55C23×Dic13C2×C418yes—
56C23×Dic13C2311yescharacteristic
57C23×Dic13C2311yescharacteristic
58C23×Dic13C2312yes—
59C23×Dic13C2311yescharacteristic
60C23×Dic13C2311yescharacteristic
61C23×Dic13C2312yes—
62C2×C13×C22⋊C4—24no—
63C2×C13×C22⋊C4—24no—
64C2×C13×C22⋊C4C2×C418yes—
65C2×C22⋊Dic13—22no—
66C2×C22⋊Dic13—22no—
67C2×C22⋊Dic13C2×C414yes—
68C2×C22⋊Dic13C2×C418yes—
69C2×C22⋊Dic13C2×C414yes—
70C2×C4×Dic13—22no—
71C2×C4×Dic13—22no—
72C2×C4×Dic13—24no—
73C2×C4×Dic13—24no—
74C2×C4×Dic13—42no—
75C2×C4×Dic13—42no—
76C2×C4×Dic13—42no—
77C2×C4×Dic13C2×C418yescomplemented
78C2×C4×Dic13C2×C414yescomplemented
79C2×C4×Dic13C2×C418yescomplemented
80C2×C4×Dic13C2×C414yescomplemented
81C13×#95—22no—
82C13×#95—22no—
83C13×#95—42no—
84#88071—22no—
85#88071—24no—
86#88071—24no—
87#88071—24no—
88#88071—42no—
89#88071—42no—
90#88071C2×C418yescomplemented
91#88071C2×C418yescomplemented
92#88071C2×C414yescomplemented
93#88071C2×C414yescomplemented
94#88071D414yes—
95#13809—131nomaximal, Sylow
96C24×C13—21no—
97C24×C13—22no—
98C24×C13—21no—
99C24×C13—21no—
100C24×C13—22no—
101C24×C13—21no—
102C24×C13C22×C412yes—
103C24×C13C22×C414yes—
104C24×C13#4112yes—
105C24×C13#4114yes—
106C24×C13#4112yes—
107C24×C13C2411yescharacteristic
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—28no—
111C22×C4×C13—21no—
112C22×C4×C13—22no—
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—22no—
120C22×C4×C13—22no—
121C22×C4×C13—21no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—28no—
128C22×C4×C13—44no—
129C22×C4×C13—48no—
130C22×C4×C13—48no—
131C22×C4×C13C22×C412yes—
132C22×C4×C13C22×C414yes—
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—21no—
144C22×Dic13—22no—
145C22×Dic13—22no—
146C22×Dic13—21no—
147C22×Dic13—216no—
148C22×Dic13—21no—
149C22×Dic13—22no—
150C22×Dic13—22no—
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—22no—
157C22×Dic13—22no—
158C22×Dic13—22no—
159C22×Dic13—21no—
160C22×Dic13—22no—
161C22×Dic13—22no—
162C22×Dic13—22no—
163C22×Dic13—21no—
164C22×Dic13—216no—
165C22×Dic13—48no—
166C22×Dic13—48no—
167C22×Dic13—48no—
168C22×Dic13—48no—
169C22×Dic13—48no—
170C22×Dic13C22×C414yes—
171C22×Dic13C22×C412yes—
172C22×Dic13C22×C412yes—
173C22×Dic13C22×C414yes—
174C22×Dic13C22×C412yes—
175C22×Dic13C22×C414yes—
176C22×Dic13C22×C412yes—
177C22×Dic13C22×C414yes—
178C22×Dic13C2×D414yes—
179C22×Dic13#4114yes—
180C13×C22⋊C4—216no—
181C22⋊Dic13—28no—
182C22⋊Dic13C42116yes—
183C4×Dic13—28no—
184C4×Dic13—216no—
185C4×Dic13—48no—
186C4×Dic13—44no—
187C2×C4×C22⋊C4—131no—
188C2×C4×C22⋊C4—132no—
189C2×#376—131no—
190C22×#95—131no—
191#1434—132no—
192#1434—131no—
193#1434—132no—
194#1434—131no—
195C22⋊#95—132no—
196C22⋊#95D1311yescharacteristic
197C4×#95—131no—
198C23×C13—24no—
199C23×C13—22no—
200C23×C13—22no—
201C23×C13—24no—
202C23×C13—24no—
203C23×C13—22no—
204C23×C13—22no—
205C23×C13—24no—
206C23×C13—22no—
207C23×C13—24no—
208C23×C13—22no—
209C23×C13—24no—
210C23×C13—24no—
211C23×C13—24no—
212C23×C13—22no—
213C23×C13—24no—
214C23×C13—24no—
215C23×C13—22no—
216C23×C13C2×C4214yes—
217C23×C13#11718yes—
218C23×C13#11714yes—
219C23×C13#11714yes—
220C23×C13#11718yes—
221C23×C13C23×C411yescharacteristic
222C23×C13C23×C412yes—
223C23×C13C22×D411yescharacteristic
224C23×C13C2×#4112yes—
225C23×C13C2×#4111yescharacteristic
226C23×C13C2×#4111yescharacteristic
227C23×C13C2×#4111yescharacteristic
228C23×C13C2×#4112yes—
229C23×C13H(5,𝔽2)12yes—
230C23×C13H(5,𝔽2)11yescharacteristic
231C23×C132−1+411yescharacteristic
232C2×C4×C13—22no—
233C2×C4×C13—22no—
234C2×C4×C13—24no—
235C2×C4×C13—24no—
236C2×C4×C13—24no—
237C2×C4×C13—24no—
238C2×C4×C13—22no—
239C2×C4×C13—24no—
240C2×C4×C13—22no—
241C2×C4×C13—24no—
242C2×C4×C13—24no—
243C2×C4×C13—22no—
244C2×C4×C13—24no—
245C2×C4×C13—416no—
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×C13—42no—
256C2×C4×C13C4×D414yes—
257C2×Dic13—24no—
258C2×Dic13—22no—
259C2×Dic13—24no—
260C2×Dic13—22no—
261C2×Dic13—24no—
262C2×Dic13—24no—
263C2×Dic13—22no—
264C2×Dic13—24no—
265C2×Dic13—22no—
266C2×Dic13—24no—
267C2×Dic13—24no—
268C2×Dic13—24no—
269C2×Dic13—24no—
270C2×Dic13—24no—
271C2×Dic13—22no—
272C2×Dic13—22no—
273C2×Dic13—24no—
274C2×Dic13—22no—
275C2×Dic13—24no—
276C2×Dic13—22no—
277C2×Dic13—22no—
278C2×Dic13—24no—
279C2×Dic13—22no—
280C2×Dic13—432no—
281C2×Dic13—41no—
282C2×Dic13—42no—
283C2×Dic13—42no—
284C2×Dic13—41no—
285C2×Dic13—42no—
286C2×Dic13—42no—
287C2×Dic13—42no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—42no—
291C2×Dic13C2×C4214yes—
292C2×Dic13C2×C4214yes—
293C2×Dic13C4×D418yes—
294C24×C4—132no—
295C24×C4C2×D1311yescharacteristic
296C22×C22⋊C4—131no—
297C22×C22⋊C4—131no—
298C22×C22⋊C4C2×D1312yes—
299C22×C42—132no—
300C22×C42—131no—
301C22×C42—132no—
302C22×C42—131no—
303C4×C22⋊C4—138no—
304C4×C22⋊C4—1316no—
305#376—264no—
306C2×#95—131no—
307C2×#95—131no—
308C2×#95—131no—
309C2×#95—132no—
310C2×#95—132no—
311C2×#95—132no—
312C2×#95—132no—
313C2×#95—132no—
314C2×#95—131no—
315C2×#95—132no—
316C2×#95—132no—
317C2×#95—264no—
318C2×#95C2×D1311yescharacteristic
319C2×#95C2×D1311yescharacteristic
320C2×#95C2×D1312yes—
321C22×C13—28no—
322C22×C13—24no—
323C22×C13—24no—
324C22×C13—28no—
325C22×C13—28no—
326C22×C13—24no—
327C22×C13—28no—
328C22×C13—24no—
329C22×C13—24no—
330C22×C13—24no—
331C22×C13#37618yescomplemented
332C22×C13C22×C4211yescharacteristic
333C22×C13C2×#11711yescharacteristic
334C22×C13C2×#11712yes—
335C22×C13C2×#11712yes—
336C22×C13C2×#11711yescharacteristic
337C22×C13C2×C4×D411yescharacteristic
338C22×C13C2×C4×D412yes—
339C22×C13C4×#4111yescharacteristic
340C22×C13C4×#4112yes—
341C22×C13#51811yescharacteristic
342C22×C13#51812yes—
343C22×C13#52011yescharacteristic
344C22×C13#52012yes—
345C22×C13#54612yes—
346C22×C13#54611yescharacteristic
347C22×C13#54811yescharacteristic
348C22×C13#55112yes—
349C22×C13#55112yes—
350C22×C13#55112yes—
351C22×C13#55211yescharacteristic
352C22×C13#55212yes—
353C22×C13#55312yes—
354C22×C13#55311yescharacteristic
355C4×C13—24no—
356C4×C13—42no—
357C4×C13—44no—
358C4×C13—44no—
359Dic13—28no—
360Dic13—24no—
361Dic13—24no—
362Dic13—44no—
363Dic13—42no—
364Dic13—42no—
365C25C22×D1311yescharacteristic
366C23×C4—24no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—42no—
370C23×C4—131no—
371C23×C4—131no—
372C23×C4—132no—
373C23×C4—131no—
374C23×C4—131no—
375C23×C4—132no—
376C23×C4—138no—
377C23×C4—264no—
378C23×C4—264no—
379C23×C4—264no—
380C23×C4—264no—
381C23×C4—522no—
382C23×C4—522no—
383C23×C4C4×D1314yes—
384C23×C4C22×D1312yes—
385C23×C4C22×D1312yes—
386C23×C4C22×D1311yescharacteristic
387C23×C4C22×D1311yescharacteristic
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—134no—
391C2×C22⋊C4—138no—
392C2×C22⋊C4—134no—
393C2×C22⋊C4—262no—
394C2×C22⋊C4—262no—
395C2×C22⋊C4C4×D1318yes—
396C2×C42—138no—
397C2×C42—134no—
398C2×C42—138no—
399C2×C42—134no—
400C2×C42—264no—
401C2×C42—264no—
402C2×C42—262no—
403C2×C42—262no—
404C2×C42—522no—
405C2×C42—522no—
406C2×C42—522no—
407#95—22no—
408#95—22no—
409#95—42no—
410#95—138no—
411#95—138no—
412#95—134no—
413#95—134no—
414#95—134no—
415#95—264no—
416#95—264no—
417#95—264no—
418#95—262no—
419#95—522no—
420#95—522no—
421C2×C13—28no—
422C2×C13C2×#37611yescharacteristic
423C2×C13C42×D411yescharacteristic
424C2×C13#227511yescharacteristic
425C2×C13#234212yes—
426C2×C13#234211yescharacteristic
427C2×C13#234311yescharacteristic
428C2×C13#234312yes—
429C2×C13#235212yes—
430C2×C13#235211yescharacteristic
431C2×C13#235312yes—
432C2×C13#235311yescharacteristic
433C24—21no—
434C24—21no—
435C24—22no—
436C24—22no—
437C24—21no—
438C24—21no—
439C24C2×C4×D1312yes—
440C24C2×C4×D1314yes—
441C24#612912yes—
442C24#612914yes—
443C24#613112yes—
444C24C23×D1311yescharacteristic
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—28no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—28no—
465C22×C4—44no—
466C22×C4—48no—
467C22×C4—48no—
468C22×C4—132no—
469C22×C4—132no—
470C22×C4—134no—
471C22×C4—134no—
472C22×C4—134no—
473C22×C4—134no—
474C22×C4—134no—
475C22×C4—134no—
476C22×C4—132no—
477C22×C4—132no—
478C22×C4—2616no—
479C22×C4—261no—
480C22×C4—261no—
481C22×C4—262no—
482C22×C4—262no—
483C22×C4—262no—
484C22×C4—262no—
485C22×C4—262no—
486C22×C4—261no—
487C22×C4—262no—
488C22×C4—261no—
489C22×C4—2616no—
490C22×C4—261no—
491C22×C4—262no—
492C22×C4—261no—
493C22×C4—261no—
494C22×C4—261no—
495C22×C4—262no—
496C22×C4—262no—
497C22×C4—262no—
498C22×C4—261no—
499C22×C4—261no—
500C22×C4—262no—
501C22×C4—262no—
502C22×C4—262no—
503C22×C4—261no—
504C22×C4—262no—
505C22×C4—261no—
506C22×C4—528no—
507C22×C4—528no—
508C22×C4—528no—
509C22×C4—528no—
510C22×C4—528no—
511C22×C4C2×C4×D1312yes—
512C22×C4C2×C4×D1314yes—
513C22×C4C2×C4×D1314yes—
514C22×C4C2×C4×D1312yes—
515C22×C4D4×D1312yes—
516C22×C4#612912yes—
517C22⋊C4—216no—
518C22⋊C4—1316no—
519C22⋊C4—268no—
520C42—2616no—
521C42—268no—
522C42—524no—
523C42—528no—
524C13#1380911yescharacteristic, complemented, Sylow
525C23—22no—
526C23—22no—
527C23—22no—
528C23—22no—
529C23—24no—
530C23—24no—
531C23—24no—
532C23—24no—
533C23—24no—
534C23—24no—
535C23—22no—
536C23—24no—
537C23—22no—
538C23—22no—
539C23—24no—
540C23—22no—
541C23—24no—
542C23—24no—
543C23C42×D1314yes—
544C23#8813118yes—
545C23#8813114yes—
546C23#8814614yes—
547C23#8814618yes—
548C23C22×C4×D1311yescharacteristic
549C23C22×C4×D1312yes—
550C23C2×D4×D1311yescharacteristic
551C23C2×#612912yes—
552C23C2×#612911yescharacteristic
553C23C2×#612911yescharacteristic
554C23#8825112yes—
555C23C2×#613111yescharacteristic
556C23#41×D1312yes—
557C23#8825611yescharacteristic
558C23#8825711yescharacteristic
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—416no—
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—42no—
583C2×C4—134no—
584C2×C4—134no—
585C2×C4—138no—
586C2×C4—262no—
587C2×C4—262no—
588C2×C4—264no—
589C2×C4—262no—
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—264no—
599C2×C4—264no—
600C2×C4—262no—
601C2×C4—262no—
602C2×C4—262no—
603C2×C4—262no—
604C2×C4—264no—
605C2×C4—262no—
606C2×C4—262no—
607C2×C4—264no—
608C2×C4—264no—
609C2×C4—5232no—
610C2×C4—522no—
611C2×C4—521no—
612C2×C4—522no—
613C2×C4—521no—
614C2×C4—521no—
615C2×C4—522no—
616C2×C4—522no—
617C2×C4—522no—
618C2×C4—521no—
619C2×C4—522no—
620C2×C4#8813514yes—
621C22—24no—
622C22—24no—
623C22—28no—
624C22—24no—
625C22—28no—
626C22—24no—
627C22—28no—
628C22—24no—
629C22—24no—
630C22—28no—
631C22#1171830918yescomplemented
632C22C2×C42×D1311yescharacteristic
633C22C2×#8813111yescharacteristic
634C22C2×#8813112yes—
635C22C2×#8813511yescharacteristic
636C22#1171919111yescharacteristic
637C22C2×#8814611yescharacteristic
638C22C2×#8814612yes—
639C22#1171922711yescharacteristic
640C22#1171922811yescharacteristic
641C22C4×#612912yes—
642C22C4×D4×D1312yes—
643C22#1171925012yes—
644C22#1171925112yes—
645C22#1171929212yes—
646C22#1171929612yes—
647C22#1171930311yescharacteristic
648C22#1171930612yes—
649C22#1171932311yescharacteristic
650C22#1171933511yescharacteristic
651C22#1171934212yes—
652C22#1171934711yescharacteristic
653C22#1171935512yes—
654C22#1171936312yes—
655C4—24no—
656C4—44no—
657C4—44no—
658C4—42no—
659C4—264no—
660C4—268no—
661C4—264no—
662C4—522no—
663C4—522no—
664C4—524no—
665C2—28no—
666C2C2×#1171830911yescharacteristic
667C2C4×#8813511yescharacteristic
668C2#1311719511yescharacteristic
669C2#1311768312yes—
670C2#1311768711yescharacteristic
671C2#1311769412yes—
672C2#1311769811yescharacteristic
673C2#1311776312yes—
674C2#1311776711yescharacteristic
675C2#1311777412yes—
676C2#1311777811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC22×C13C22×C42
FittingC13×C22⋊#95C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC22⋊#95D13
hypocenterC13#13809
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#11718309C2semidirect
5. #13113062C2semidirect
6. #13113062C2semidirect
7. #13113060C2semidirect
8. #13113060C2semidirect
10. #95×Dic13C2semidirect
24. C4×C22⋊Dic13C4semidirect
37. C22⋊C4×Dic13C4semidirect
77. C2×C4×Dic13C2×C4semidirect
78. C2×C4×Dic13C2×C4semidirect
79. C2×C4×Dic13C2×C4semidirect
80. C2×C4×Dic13C2×C4semidirect
90. #88071C2×C4semidirect
91. #88071C2×C4semidirect
92. #88071C2×C4semidirect
93. #88071C2×C4semidirect
331. C22×C13#376semidirect
524. C13#13809semidirect
631. C22#11718309semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×Dic132
C2×C4×C22⋊Dic132
C2×#117183092
C22×#880712
#131130622
#131130602
#131130582
#95×Dic132
C13×C22⋊#952
#1380913