Finite Group Databasebeta

← #15784616

Subgroups — #15784616

Order 3328.

1814 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×C4×#6101C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊Dic13C211yesmaximal, characteristic
3C2×C4×C22⋊Dic13C211yesmaximal, characteristic
4C2×#11718593C211yesmaximal, characteristic, complemented
5#13113097C212yesmaximal, complemented
6#13113091C212yesmaximal, complemented
7#13113083C212yesmaximal
8#13113079C212yesmaximal
9C4×#88071C211yesmaximal, characteristic, complemented
10C4×#88071C211yesmaximal, characteristic, complemented
11C2×C4×C13×C22⋊C4C211yesmaximal, characteristic
12C24×C4×C13C2211yescharacteristic
13C22×C13×C22⋊C4C2212yes—
14C22×C42×C13C2211yescharacteristic
15C22×C42×C13C2211yescharacteristic
16C22×C22⋊Dic13C2212yes—
17C22×C22⋊Dic13C2211yescharacteristic
18C22×C22⋊Dic13C2211yescharacteristic
19C22×#6101C2212yes—
20C22×C4×Dic13C2211yescharacteristic
21C22×C4×Dic13C2211yescharacteristic
22C22×C4×Dic13C2211yescharacteristic
23C22×C4×Dic13C2211yescharacteristic
24C4×C13×C22⋊C4—24no—
25C2×C13×#95C2212yes—
26C4×C22⋊Dic13—24no—
27C4×C22⋊Dic13C418yescomplemented
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2211yescharacteristic
37C2×#88071C2211yescharacteristic
38#11718593—24no—
39C4×#6101—24no—
40C25×C13C2311yescharacteristic
41C23×C4×C13—22no—
42C23×C4×C13—22no—
43C23×C4×C13—22no—
44C23×C4×C13—22no—
45C23×C4×C13—22no—
46C23×C4×C13—22no—
47C23×C4×C13C2×C414yes—
48C23×C4×C13C2311yescharacteristic
49C23×C4×C13C2312yes—
50C23×C4×C13C2312yes—
51C23×C4×C13C2311yescharacteristic
52C23×Dic13C2311yescharacteristic
53C23×Dic13C2311yescharacteristic
54C23×Dic13C2311yescharacteristic
55C23×Dic13C2312yes—
56C23×Dic13C2312yes—
57C23×Dic13C2311yescharacteristic
58C2×C13×C22⋊C4—24no—
59C2×C13×C22⋊C4—24no—
60C2×C13×C22⋊C4—24no—
61C2×C42×C13—22no—
62C2×C42×C13—22no—
63C2×C42×C13—22no—
64C2×C42×C13—22no—
65C2×C42×C13—22no—
66C2×C42×C13D414yes—
67C2×C22⋊Dic13—24no—
68C2×C22⋊Dic13—24no—
69C2×C22⋊Dic13—24no—
70C2×C22⋊Dic13—24no—
71C2×C22⋊Dic13—24no—
72C2×C22⋊Dic13C2×C414yes—
73C2×C22⋊Dic13C2×C414yes—
74C2×#6101—24no—
75C2×#6101—24no—
76C2×#6101—24no—
77C2×C4×Dic13—22no—
78C2×C4×Dic13—22no—
79C2×C4×Dic13—22no—
80C2×C4×Dic13—22no—
81C2×C4×Dic13—22no—
82C2×C4×Dic13—22no—
83C2×C4×Dic13—22no—
84C2×C4×Dic13—22no—
85C2×C4×Dic13—22no—
86C2×C4×Dic13C2×C414yes—
87C2×C4×Dic13C2×C414yes—
88C2×C4×Dic13D414yes—
89C13×#95—24no—
90#88071—24no—
91#88071—24no—
92#88071—24no—
93#88071—24no—
94#88071—24no—
95#88071—24no—
96#88071—24no—
97#88071—24no—
98#88071C2×C414yes—
99#88071C2×C414yes—
100#13842—131nomaximal, Sylow
101C24×C13—21no—
102C24×C13—21no—
103C24×C13—22no—
104C24×C13—22no—
105C24×C13—22no—
106C24×C13—21no—
107C24×C13—21no—
108C24×C13—21no—
109C24×C13—21no—
110C24×C13C22×C412yes—
111C24×C13#4114yes—
112C24×C13C2411yescharacteristic
113C22×C4×C13—21no—
114C22×C4×C13—22no—
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—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—28no—
132C22×C4×C13—28no—
133C22×C4×C13—28no—
134C22×C4×C13—44no—
135C22×C4×C13—44no—
136C22×C4×C13—44no—
137C22×C4×C13—44no—
138C22×C4×C13C22×C412yes—
139C22×C4×C13C22×C412yes—
140C22×C4×C13C2×D412yes—
141C22×C4×C13C2×D414yes—
142C22×C4×C13C2×D412yes—
143C22×C4×C13#4114yes—
144C22×C4×C13#4112yes—
145C22×C4×C13#4112yes—
146C22×C4×C13#4112yes—
147C22×C4×C13#4112yes—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—22no—
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13—22no—
157C22×Dic13—22no—
158C22×Dic13—22no—
159C22×Dic13—22no—
160C22×Dic13—22no—
161C22×Dic13—21no—
162C22×Dic13—21no—
163C22×Dic13—21no—
164C22×Dic13—22no—
165C22×Dic13—22no—
166C22×Dic13—22no—
167C22×Dic13—22no—
168C22×Dic13—22no—
169C22×Dic13—22no—
170C22×Dic13—22no—
171C22×Dic13—22no—
172C22×Dic13—22no—
173C22×Dic13—22no—
174C22×Dic13—22no—
175C22×Dic13C22×C412yes—
176C22×Dic13C22×C412yes—
177C22×Dic13C22×C412yes—
178C22×Dic13C22×C412yes—
179C22×Dic13C2×D414yes—
180C22×Dic13#4114yes—
181C22×Dic13#4114yes—
182C13×C22⋊C4—216no—
183C42×C13—28no—
184C42×C13—44no—
185C22⋊Dic13—216no—
186C22⋊Dic13—28no—
187C22⋊Dic13—28no—
188#6101—216no—
189C4×Dic13—28no—
190C4×Dic13—28no—
191C4×Dic13—28no—
192C4×Dic13—44no—
193C2×C4×C4⋊C4—131no—
194C2×C4×C22⋊C4—131no—
195C2×C4×C22⋊C4—131no—
196C2×C4×C22⋊C4D1311yescharacteristic
197C2×#376—131no—
198#1443—132no—
199#1442—132no—
200#1440—132no—
201#1439—132no—
202C4×#95—131no—
203C4×#95—131no—
204C23×C13—22no—
205C23×C13—22no—
206C23×C13—22no—
207C23×C13—22no—
208C23×C13—22no—
209C23×C13—22no—
210C23×C13—24no—
211C23×C13—24no—
212C23×C13—24no—
213C23×C13—24no—
214C23×C13—24no—
215C23×C13—24no—
216C23×C13—41no—
217C23×C13—41no—
218C23×C13—42no—
219C23×C13—41no—
220C23×C13—41no—
221C23×C13—42no—
222C23×C13—42no—
223C23×C13—42no—
224C23×C13—42no—
225C23×C13—42no—
226C23×C13#11714yes—
227C23×C13C23×C411yescharacteristic
228C23×C13C22×D411yescharacteristic
229C23×C13C22×D411yescharacteristic
230C23×C13C2×#4111yescharacteristic
231C23×C13C2×#4111yescharacteristic
232C23×C13C2×#4112yes—
233C23×C13C2×#4112yes—
234C23×C13C2×#4111yescharacteristic
235C23×C13C2×#4111yescharacteristic
236C23×C13C2×#4112yes—
237C23×C13C2×#4112yes—
238C2×C4×C13—22no—
239C2×C4×C13—22no—
240C2×C4×C13—22no—
241C2×C4×C13—24no—
242C2×C4×C13—24no—
243C2×C4×C13—24no—
244C2×C4×C13—24no—
245C2×C4×C13—24no—
246C2×C4×C13—24no—
247C2×C4×C13—42no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—42no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—42no—
254C2×C4×C13—42no—
255C2×C4×C13—42no—
256C2×C4×C13—42no—
257C2×C4×C13—42no—
258C2×C4×C13—42no—
259C2×C4×C13—416no—
260C2×C4×C13#11714yes—
261C2×C4×C13C4×D414yes—
262C2×C4×C13C4×D414yes—
263C2×C4×C13#12114yes—
264C2×C4×C13#12314yes—
265C2×C4×C13#12414yes—
266C2×C4×C13#12614yes—
267C2×Dic13—22no—
268C2×Dic13—22no—
269C2×Dic13—24no—
270C2×Dic13—24no—
271C2×Dic13—22no—
272C2×Dic13—22no—
273C2×Dic13—22no—
274C2×Dic13—22no—
275C2×Dic13—22no—
276C2×Dic13—22no—
277C2×Dic13—22no—
278C2×Dic13—22no—
279C2×Dic13—22no—
280C2×Dic13—24no—
281C2×Dic13—24no—
282C2×Dic13—24no—
283C2×Dic13—24no—
284C2×Dic13—24no—
285C2×Dic13—24no—
286C2×Dic13—42no—
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×Dic13—42no—
298C2×Dic13—42no—
299C2×Dic13—42no—
300C2×Dic13#11714yes—
301C24×C4C2×D1311yescharacteristic
302C22×C4⋊C4—132no—
303C22×C22⋊C4—131no—
304C22×C22⋊C4—131no—
305C22×C22⋊C4—132no—
306C22×C22⋊C4C2×D1312yes—
307C22×C42—131no—
308C22×C42—131no—
309C22×C42—131no—
310C22×C42—131no—
311C22×C42C2×D1311yescharacteristic
312C22×C42C2×D1311yescharacteristic
313C4×C4⋊C4—264no—
314C4×C22⋊C4—24no—
315C4×C22⋊C4—138no—
316C4×C22⋊C4—264no—
317#376—264no—
318C2×#95—131no—
319C2×#95—131no—
320C2×#95—132no—
321C2×#95—132no—
322C2×#95—132no—
323C2×#95—132no—
324C2×#95—132no—
325C2×#95—132no—
326C2×#95—132no—
327C2×#95—132no—
328C2×#95C2×D1312yes—
329C22×C13—24no—
330C22×C13—24no—
331C22×C13—24no—
332C22×C13—44no—
333C22×C13—44no—
334C22×C13—44no—
335C22×C13—44no—
336C22×C13—42no—
337C22×C13—42no—
338C22×C13—42no—
339C22×C13—42no—
340C22×C13C2×#11711yescharacteristic
341C22×C13C2×#11711yescharacteristic
342C22×C13C2×#11711yescharacteristic
343C22×C13C2×C4×D411yescharacteristic
344C22×C13C2×C4×D411yescharacteristic
345C22×C13C4×#4111yescharacteristic
346C22×C13C4×#4111yescharacteristic
347C22×C13C2×#12111yescharacteristic
348C22×C13C2×#12311yescharacteristic
349C22×C13#52512yes—
350C22×C13#52512yes—
351C22×C13#52512yes—
352C22×C13C2×#12411yescharacteristic
353C22×C13C2×#12611yescharacteristic
354C22×C13#52912yes—
355C22×C13#52912yes—
356C22×C13#52912yes—
357C22×C13#52912yes—
358C22×C13#52912yes—
359C22×C13#52912yes—
360C22×C13#52912yes—
361C22×C13#52912yes—
362C22×C13#53212yes—
363C4×C13—44no—
364C4×C13—44no—
365C4×C13—42no—
366C4×C13#38818yes—
367Dic13—24no—
368Dic13—44no—
369Dic13—44no—
370Dic13—42no—
371Dic13—42no—
372Dic13—42no—
373C25C22×D1311yescharacteristic
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—131no—
381C23×C4—132no—
382C23×C4—131no—
383C23×C4—131no—
384C23×C4—131no—
385C23×C4—132no—
386C23×C4C4×D1314yes—
387C23×C4C22×D1311yescharacteristic
388C23×C4C22×D1312yes—
389C23×C4C22×D1312yes—
390C23×C4C22×D1311yescharacteristic
391C2×C4⋊C4—264no—
392C2×C4⋊C4—264no—
393C2×C4⋊C4—264no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—134no—
398C2×C22⋊C4—134no—
399C2×C22⋊C4—264no—
400C2×C22⋊C4—264no—
401C2×C22⋊C4—264no—
402C2×C22⋊C4—264no—
403C2×C22⋊C4—264no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—134no—
410C2×C42—134no—
411C2×C42—134no—
412C2×C42—262no—
413C2×C42—262no—
414C2×C42—262no—
415C2×C42—262no—
416C2×C42—262no—
417C2×C42—262no—
418C2×C42—262no—
419C2×C42—262no—
420C2×C42—262no—
421C2×C42C22⋊D1314yes—
422#95—24no—
423#95—134no—
424#95—134no—
425#95—264no—
426#95—264no—
427#95—264no—
428#95—264no—
429#95—264no—
430#95—264no—
431#95—264no—
432#95—264no—
433C2×C13—44no—
434C2×C13#228311yescharacteristic
435C2×C13C2×#38811yescharacteristic
436C2×C13#229011yescharacteristic
437C2×C13#229011yescharacteristic
438C2×C13#229011yescharacteristic
439C2×C13#229311yescharacteristic
440C2×C13#229811yescharacteristic
441C2×C13#239212yes—
442C2×C13#239512yes—
443C2×C13#239812yes—
444C2×C13#240112yes—
445C24—22no—
446C24—21no—
447C24—21no—
448C24—21no—
449C24—21no—
450C24—21no—
451C24—22no—
452C24—22no—
453C24—21no—
454C24C2×C4×D1312yes—
455C24#612714yes—
456C24C23×D1311yescharacteristic
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—28no—
476C22×C4—28no—
477C22×C4—28no—
478C22×C4—44no—
479C22×C4—44no—
480C22×C4—44no—
481C22×C4—44no—
482C22×C4—132no—
483C22×C4—134no—
484C22×C4—132no—
485C22×C4—132no—
486C22×C4—132no—
487C22×C4—134no—
488C22×C4—134no—
489C22×C4—262no—
490C22×C4—261no—
491C22×C4—261no—
492C22×C4—262no—
493C22×C4—262no—
494C22×C4—262no—
495C22×C4—261no—
496C22×C4—261no—
497C22×C4—262no—
498C22×C4—262no—
499C22×C4—262no—
500C22×C4—262no—
501C22×C4—262no—
502C22×C4—261no—
503C22×C4—262no—
504C22×C4—261no—
505C22×C4—262no—
506C22×C4—262no—
507C22×C4—262no—
508C22×C4—262no—
509C22×C4—262no—
510C22×C4—262no—
511C22×C4—262no—
512C22×C4—262no—
513C22×C4—261no—
514C22×C4—261no—
515C22×C4—262no—
516C22×C4C2×C4×D1312yes—
517C22×C4C2×C4×D1312yes—
518C22×C4#612714yes—
519C22×C4#612712yes—
520C22×C4D4×D1312yes—
521C22×C4#612912yes—
522C22×C4#612912yes—
523C22×C4#612912yes—
524C22×C4C2×C22⋊D1314yes—
525C22×C4C2×C22⋊D1312yes—
526C4⋊C4—2616no—
527C22⋊C4—216no—
528C22⋊C4—268no—
529C22⋊C4—2616no—
530C22⋊C4—268no—
531C42—28no—
532C42—44no—
533C42—268no—
534C42—268no—
535C42—268no—
536C42—524no—
537C13#1384211yescharacteristic, complemented, Sylow
538C23—22no—
539C23—24no—
540C23—22no—
541C23—22no—
542C23—22no—
543C23—22no—
544C23—22no—
545C23—24no—
546C23—24no—
547C23—24no—
548C23—24no—
549C23—24no—
550C23—41no—
551C23—41no—
552C23—42no—
553C23—42no—
554C23—41no—
555C23—41no—
556C23—42no—
557C23—42no—
558C23—42no—
559C23—42no—
560C23#8812614yes—
561C23C22×C4×D1311yescharacteristic
562C23C2×#612712yes—
563C23C2×#612712yes—
564C23C2×#612711yescharacteristic
565C23C2×D4×D1311yescharacteristic
566C23C2×#612911yescharacteristic
567C23C2×#612911yescharacteristic
568C23C2×#612911yescharacteristic
569C23#41×D1312yes—
570C23#41×D1312yes—
571C23C22×C22⋊D1311yescharacteristic
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—416no—
594C2×C4—134no—
595C2×C4—262no—
596C2×C4—262no—
597C2×C4—264no—
598C2×C4—264no—
599C2×C4—262no—
600C2×C4—262no—
601C2×C4—262no—
602C2×C4—262no—
603C2×C4—262no—
604C2×C4—262no—
605C2×C4—262no—
606C2×C4—264no—
607C2×C4—262no—
608C2×C4—262no—
609C2×C4—264no—
610C2×C4—264no—
611C2×C4—264no—
612C2×C4—264no—
613C2×C4—264no—
614C2×C4—522no—
615C2×C4—522no—
616C2×C4—522no—
617C2×C4—522no—
618C2×C4—522no—
619C2×C4—522no—
620C2×C4—522no—
621C2×C4—522no—
622C2×C4—522no—
623C2×C4—522no—
624C2×C4—522no—
625C2×C4—522no—
626C2×C4—522no—
627C2×C4—522no—
628C2×C4#8813114yes—
629C2×C4#8813314yes—
630C2×C4#8813514yes—
631C2×C4#8813914yes—
632C2×C4C4×C22⋊D1314yes—
633C2×C4#8818914yes—
634C2×C4#8819214yes—
635C22—24no—
636C22—24no—
637C22—24no—
638C22—42no—
639C22—42no—
640C22—42no—
641C22—44no—
642C22—44no—
643C22—42no—
644C22—44no—
645C22—44no—
646C22C2×#8812611yescharacteristic
647C22C4×#612711yescharacteristic
648C22#1171918412yes—
649C22C2×#8813111yescharacteristic
650C22C2×#8813311yescharacteristic
651C22C2×#8813511yescharacteristic
652C22C2×#8813911yescharacteristic
653C22D13×#11711yescharacteristic
654C22#1171922711yescharacteristic
655C22#1171923312yes—
656C22#1171924312yes—
657C22#1171924312yes—
658C22#1171924312yes—
659C22#1171924312yes—
660C22#1171925212yes—
661C22#1171925212yes—
662C22#1171926212yes—
663C22#1171926212yes—
664C22C2×C4×C22⋊D1311yescharacteristic
665C22#1171949612yes—
666C22C2×#8818911yescharacteristic
667C22C2×#8819211yescharacteristic
668C22#1171953712yes—
669C4—42no—
670C4—44no—
671C4—44no—
672C4—264no—
673C4—522no—
674C4—522no—
675C4—522no—
676C4—524no—
677C4—524no—
678C4#1171860518yes—
679C2—44no—
680C2#1311723011yescharacteristic
681C2C2×#1171860511yescharacteristic
682C2#1311727511yescharacteristic
683C2#1311727911yescharacteristic
684C2#1311728211yescharacteristic
685C2#1311729511yescharacteristic
686C2#1311733211yescharacteristic
687C2#1311807412yes—
688C2#1311809512yes—
689C2#1311812312yes—
690C2#1311813612yes—
subgroupG/H
centerC23×C4C22×D13
commutatorC23×C13C23×C4
FrattiniC24C23×D13
FittingC2×C4×C13×C22⋊C4C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×C4×C22⋊C4D13
hypocenterC13#13842
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×#6101C2semidirect
4. C2×#11718593C2semidirect
5. #13113097C2semidirect
6. #13113091C2semidirect
9. C4×#88071C2semidirect
10. C4×#88071C2semidirect
27. C4×C22⋊Dic13C4semidirect
537. C13#13842semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#61012
C2×C4×C22⋊Dic132
C2×#117185932
#131130972
#131130912
#131130832
#131130792
C4×#880712
C2×C4×C13×C22⋊C42
#1384213