Finite Group Databasebeta

← C2×#13118344 #16030790

Subgroups — C2×#13118344 #16030790

Order 3328.

3830 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88183C212yesmaximal, complemented
2C22×#88192C211yesmaximal, characteristic
3#13118344C2116yesmaximal, direct product factor
4C2×#11718613C212yesmaximal, complemented
5C2×#11718620C212yesmaximal, complemented
6C2×#11718882C211yesmaximal, characteristic, complemented
7C2×#11718589C211yesmaximal, characteristic, complemented
8C2×#11718871C212yesmaximal, complemented
9C2×#11718637C211yesmaximal, characteristic, complemented
10C2×#11718648C211yesmaximal, characteristic, complemented
11C2×C4×#6103C211yesmaximal, characteristic, complemented
12C22×C4×D4×C13C211yesmaximal, characteristic, complemented
13C23×D4×C13C2211yescharacteristic
14C24×C4×C13C2212yes—
15C23×C22⋊D13C2212yes—
16C23×C4×D13C2211yescharacteristic
17C2×C4×D4×C13—28no—
18C2×C4×D4×C13C2218yescomplemented
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2212yes—
21C22×C42×C13C2211yescharacteristic
22C22×C22⋊Dic13C2212yes—
23C22×C22⋊Dic13C2212yes—
24C22×C22⋊Dic13C2212yes—
25C2×#88192—28no—
26C2×#88192C2218yes—
27C2×#88183—216no—
28C2×#88183C22116yescomplemented
29C22×#6103C2212yes—
30C22×#6103C2211yescharacteristic
31C22×#6103C2211yescharacteristic
32C22×C4⋊Dic13C2211yescharacteristic
33C22×C4⋊Dic13C2211yescharacteristic
34C22×#6101C2212yes—
35C22×#6101C2212yes—
36C22×#6101C2212yes—
37C22×C4×Dic13C2211yescharacteristic
38#11718882C2218yescomplemented
39#11718871C22116yescomplemented
40C2×#88071C2212yes—
41C2×#88071C2211yescharacteristic
42C2×#88071C2212yes—
43C2×#88071C2211yescharacteristic
44#11718648C2218yescomplemented
45#11718637C2218yescomplemented
46#11718620C22116yescomplemented
47#11718613C22116yescomplemented
48C4×#6103C2218yescomplemented
49#11718589C2218yescomplemented
50C25×C13C2312yes—
51C24×D13C2311yescharacteristic
52C22×D4×C13—24no—
53C22×D4×C13—24no—
54C22×D4×C13D418yes—
55C22×D4×C13C2314yes—
56C23×C4×C13—28no—
57C23×C4×C13—28no—
58C23×C4×C13—44no—
59C23×C4×C13C2312yes—
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2318yes—
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C22×C22⋊D13—28no—
65C22×C22⋊D13—28no—
66C22×C22⋊D13—44no—
67C22×C22⋊D13C2318yes—
68C23×Dic13C2312yes—
69C23×Dic13C2312yes—
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C22×C4×D13—24no—
74C22×C4×D13—24no—
75C22×C4×D13—24no—
76C22×C4×D13C2314yes—
77C4×D4×C13—232no—
78C2×C13×C4⋊C4—24no—
79C2×C13×C4⋊C4C2314yes—
80C2×C13×C22⋊C4—28no—
81C2×C13×C22⋊C4C2318yes—
82C2×C42×C13—24no—
83C2×C42×C13C2314yes—
84C2×C22⋊Dic13—28no—
85C2×C22⋊Dic13—28no—
86C2×C22⋊Dic13—28no—
87C2×C22⋊Dic13C2318yes—
88C2×C22⋊Dic13C2318yes—
89C2×C22⋊Dic13C2318yes—
90#88192—232no—
91#88183—264no—
92C2×#6103—28no—
93C2×#6103—24no—
94C2×#6103D418yescomplemented
95C2×#6103C2318yes—
96C2×#6103C2314yes—
97C2×#6103C2314yes—
98C2×C4⋊Dic13—24no—
99C2×C4⋊Dic13—24no—
100C2×C4⋊Dic13C2314yes—
101C2×C4⋊Dic13C2314yes—
102C2×#6101—28no—
103C2×#6101—28no—
104C2×#6101—44no—
105C2×#6101C2318yes—
106C2×#6101C2318yes—
107C2×#6101C2318yes—
108C2×C4×Dic13—24no—
109C2×C4×Dic13C2314yes—
110#88071C2318yes—
111#88071C2314yes—
112#88071C2314yes—
113#88071C2318yes—
114C2×#2422—131nomaximal, Sylow
115C24×C13—24no—
116C24×C13—24no—
117C24×C13—24no—
118C24×C13—24no—
119C24×C13—24no—
120C24×C13—24no—
121C24×C13C2×D418yes—
122C24×C13C2414yes—
123C24×C13C2411yescharacteristic
124C23×D13—22no—
125C23×D13—22no—
126C23×D13—22no—
127C23×D13—22no—
128C23×D13—22no—
129C23×D13—22no—
130C23×D13C2×D414yes—
131C23×D13C2412yes—
132C2×D4×C13—232no—
133C2×D4×C13—28no—
134C2×D4×C13—28no—
135C2×D4×C13C2×D4116yes—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—24no—
139C22×C4×C13—22no—
140C22×C4×C13—24no—
141C22×C4×C13—216no—
142C22×C4×C13—22no—
143C22×C4×C13—24no—
144C22×C4×C13—22no—
145C22×C4×C13—216no—
146C22×C4×C13—48no—
147C22×C4×C13—432no—
148C22×C4×C13C2×D414yes—
149C22×C4×C13C2×D414yes—
150C22×C4×C13#4114yes—
151C22×C4×C13#4114yes—
152C22×C4×C13C2412yes—
153C22×C4×C13C2414yes—
154C22×C4×C13C2412yes—
155C22×C4×C13C2412yes—
156C2×C22⋊D13—216no—
157C2×C22⋊D13—216no—
158C2×C22⋊D13—48no—
159C2×C22⋊D13—432no—
160C22×Dic13—22no—
161C22×Dic13—22no—
162C22×Dic13—22no—
163C22×Dic13—22no—
164C22×Dic13—24no—
165C22×Dic13—24no—
166C22×Dic13—24no—
167C22×Dic13—22no—
168C22×Dic13—24no—
169C22×Dic13—24no—
170C22×Dic13—22no—
171C22×Dic13—22no—
172C22×Dic13—24no—
173C22×Dic13C2×D414yes—
174C22×Dic13#4114yes—
175C22×Dic13C2412yes—
176C22×Dic13C2414yes—
177C22×Dic13C2414yes—
178C22×Dic13C2412yes—
179C22×Dic13C2412yes—
180C2×C4×D13—28no—
181C2×C4×D13—28no—
182C2×C4×D13—28no—
183C2×C4×D13—416no—
184C13×C4⋊C4—28no—
185C13×C22⋊C4—216no—
186C42×C13—28no—
187C22⋊Dic13—216no—
188C22⋊Dic13—216no—
189C22⋊Dic13—216no—
190#6103—216no—
191#6103—28no—
192#6103C2×D4116yescomplemented
193C4⋊Dic13—28no—
194C4⋊Dic13—28no—
195#6101—216no—
196#6101—216no—
197#6101—48no—
198C4×Dic13—28no—
199C22×#123—132no—
200C22×#121—131no—
201C22×C4×D4D1311yescharacteristic, complemented
202#2422—1316no—
203C2×#397—132no—
204C2×#394—132no—
205C2×#390—131no—
206C2×#389—131no—
207C2×#385—132no—
208C2×#384—131no—
209C2×#380—131no—
210C2×C4×C22⋊C4—131no—
211C23×C13—216no—
212C23×C13—216no—
213C23×C13—216no—
214C23×C13—24no—
215C23×C13—24no—
216C23×C13—24no—
217C23×C13—24no—
218C23×C13—24no—
219C23×C13—24no—
220C23×C13—48no—
221C23×C13—48no—
222C23×C13—48no—
223C23×C13—48no—
224C23×C13C22×D418yes—
225C23×C13C22×D412yes—
226C23×C13C22×D412yes—
227C23×C13C2×#4112yes—
228C23×C13C2×#4112yes—
229C23×C13C2×#4112yes—
230C23×C13H(5,𝔽2)12yes—
231C23×C132−1+412yes—
232C23×C13C2511yescharacteristic
233C22×D13—28no—
234C22×D13—28no—
235C22×D13—28no—
236C22×D13—22no—
237C22×D13—22no—
238C22×D13—22no—
239C22×D13—22no—
240C22×D13—22no—
241C22×D13—22no—
242C22×D13—44no—
243C22×D13—44no—
244C22×D13—44no—
245C22×D13—44no—
246C22×D13C22×D414yes—
247D4×C13—232no—
248C2×C4×C13—28no—
249C2×C4×C13—22no—
250C2×C4×C13—22no—
251C2×C4×C13—24no—
252C2×C4×C13—22no—
253C2×C4×C13—24no—
254C2×C4×C13—22no—
255C2×C4×C13—24no—
256C2×C4×C13—22no—
257C2×C4×C13—432no—
258C2×C4×C13—48no—
259C2×C4×C13—44no—
260C2×C4×C13#123116yescomplemented
261C2×C4×C13C22×D414yes—
262C2×C4×C13C22×D414yes—
263C2×C4×C13C2×#4114yes—
264C2×C4×C13C2×#4114yes—
265C22⋊D13—432no—
266C2×Dic13—28no—
267C2×Dic13—28no—
268C2×Dic13—22no—
269C2×Dic13—22no—
270C2×Dic13—22no—
271C2×Dic13—22no—
272C2×Dic13—24no—
273C2×Dic13—24no—
274C2×Dic13—24no—
275C2×Dic13—22no—
276C2×Dic13—24no—
277C2×Dic13—24no—
278C2×Dic13—22no—
279C2×Dic13—22no—
280C2×Dic13—24no—
281C2×Dic13—44no—
282C2×Dic13—48no—
283C2×Dic13—48no—
284C2×Dic13C22×D414yes—
285C2×Dic13C2×#4114yes—
286C4×D13—416no—
287C23×D4—132no—
288C23×D4C2×D1311yescharacteristic
289C24×C4—131no—
290C24×C4C2×D1312yes—
291C2×#123—1316no—
292C2×#123—2616no—
293C2×#121—138no—
294C2×#121—268no—
295C2×C4×D4—28no—
296C2×C4×D4C2×D1318yescomplemented
297C22×C4⋊C4—132no—
298C22×C4⋊C4—132no—
299C22×C4⋊C4—131no—
300C22×C4⋊C4—131no—
301C22×C4⋊C4—132no—
302C22×C4⋊C4C2×D1311yescharacteristic
303C22×C22⋊C4—131no—
304C22×C22⋊C4—132no—
305C22×C22⋊C4—132no—
306C22×C22⋊C4—132no—
307C22×C22⋊C4—131no—
308C22×C22⋊C4—132no—
309C22×C22⋊C4C2×D1312yes—
310C22×C42—131no—
311C22×C42C2×D1311yescharacteristic
312#397—1316no—
313#394—1316no—
314#390—138no—
315#389—138no—
316#385—1316no—
317#384—138no—
318#380—138no—
319C4×C22⋊C4—138no—
320C2×#95—132no—
321C2×#95—131no—
322C2×#95—132no—
323C2×#95—131no—
324C22×C13—28no—
325C22×C13—28no—
326C22×C13—28no—
327C22×C13—44no—
328C22×C13—432no—
329C22×C13—44no—
330C22×C13—44no—
331C22×C13—44no—
332C22×C13C2×#12314yes—
333C22×C13#53214yes—
334C22×C13#54214yes—
335C22×C13D4214yes—
336C22×C13#54714yes—
337C22×C13#54714yes—
338C22×C13#55314yes—
339C22×C13C23×D411yescharacteristic
340C22×C13C23×D411yescharacteristic
341C22×C13C22×#4111yescharacteristic
342C22×C13C22×#4111yescharacteristic
343C22×C13C22×#4111yescharacteristic
344C22×C13C2×H(5,𝔽2)11yescharacteristic
345C22×C13C2×2−1+411yescharacteristic
346C2×D13—24no—
347C2×D13—24no—
348C2×D13—24no—
349C2×D13—42no—
350C2×D13—416no—
351C2×D13—42no—
352C2×D13—42no—
353C2×D13—42no—
354C4×C13—24no—
355C4×C13—44no—
356C4×C13—42no—
357C4×C13C2×#12318yescomplemented
358Dic13—24no—
359Dic13—24no—
360Dic13—42no—
361Dic13—44no—
362Dic13—44no—
363C25—131no—
364C25C22×D1312yes—
365C22×D4—24no—
366C22×D4—24no—
367C22×D4—138no—
368C22×D4—268no—
369C22×D4—268no—
370C22×D4—524no—
371C22×D4C22⋊D1318yes—
372C22×D4C22×D1314yes—
373C23×C4—28no—
374C23×C4—28no—
375C23×C4—44no—
376C23×C4—131no—
377C23×C4—131no—
378C23×C4—132no—
379C23×C4—131no—
380C23×C4—132no—
381C23×C4—134no—
382C23×C4—264no—
383C23×C4—264no—
384C23×C4—264no—
385C23×C4C22×D1311yescharacteristic
386C23×C4C22×D1312yes—
387C23×C4C22×D1318yes—
388C23×C4C22×D1311yescharacteristic
389C23×C4C22×D1311yescharacteristic
390#123—2664no—
391#121—2632no—
392C4×D4—232no—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—134no—
395C2×C4⋊C4—138no—
396C2×C4⋊C4—138no—
397C2×C4⋊C4—134no—
398C2×C4⋊C4—138no—
399C2×C4⋊C4—268no—
400C2×C4⋊C4—264no—
401C2×C4⋊C4—268no—
402C2×C4⋊C4—264no—
403C2×C4⋊C4—524no—
404C2×C4⋊C4C22×D1314yes—
405C2×C22⋊C4—28no—
406C2×C22⋊C4—138no—
407C2×C22⋊C4—134no—
408C2×C22⋊C4—138no—
409C2×C22⋊C4—138no—
410C2×C22⋊C4—138no—
411C2×C22⋊C4—138no—
412C2×C22⋊C4—134no—
413C2×C22⋊C4—264no—
414C2×C22⋊C4—268no—
415C2×C22⋊C4—268no—
416C2×C22⋊C4—268no—
417C2×C22⋊C4—268no—
418C2×C22⋊C4C22×D1318yes—
419C2×C42—24no—
420C2×C42—134no—
421C2×C42—264no—
422C2×C42C22×D1314yes—
423#95—134no—
424#95—134no—
425#95—138no—
426#95—138no—
427C2×C13—48no—
428C2×C13#242218yescomplemented
429C2×C13C22×#12311yescharacteristic
430C2×C13C2×#53211yescharacteristic
431C2×C13C2×#54211yescharacteristic
432C2×C13C2×D4211yescharacteristic
433C2×C13C2×#54711yescharacteristic
434C2×C13C2×#54711yescharacteristic
435C2×C13C2×#55311yescharacteristic
436D13—44no—
437C24—24no—
438C24—24no—
439C24—24no—
440C24—24no—
441C24—24no—
442C24—24no—
443C24—134no—
444C24—132no—
445C24—262no—
446C24—262no—
447C24—262no—
448C24—262no—
449C24—262no—
450C24—262no—
451C24C2×C22⋊D1318yes—
452C24C23×D1314yes—
453C24C23×D1311yescharacteristic
454C2×D4—232no—
455C2×D4—28no—
456C2×D4—28no—
457C2×D4—2616no—
458C2×D4—2616no—
459C2×D4—528no—
460C2×D4—5232no—
461C2×D4C2×C22⋊D13116yes—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—24no—
470C22×C4—216no—
471C22×C4—216no—
472C22×C4—48no—
473C22×C4—432no—
474C22×C4—134no—
475C22×C4—134no—
476C22×C4—132no—
477C22×C4—132no—
478C22×C4—132no—
479C22×C4—134no—
480C22×C4—134no—
481C22×C4—262no—
482C22×C4—262no—
483C22×C4—262no—
484C22×C4—262no—
485C22×C4—264no—
486C22×C4—262no—
487C22×C4—262no—
488C22×C4—264no—
489C22×C4—264no—
490C22×C4—264no—
491C22×C4—264no—
492C22×C4—262no—
493C22×C4—264no—
494C22×C4—268no—
495C22×C4—268no—
496C22×C4—268no—
497C22×C4—5216no—
498C22×C4#612714yes—
499C22×C4#612714yes—
500C22×C4D4×D1314yes—
501C22×C4C2×C22⋊D1314yes—
502C22×C4C23×D1312yes—
503C22×C4C23×D1314yes—
504C22×C4C23×D1312yes—
505C22×C4C23×D1312yes—
506C4⋊C4—28no—
507C4⋊C4—2616no—
508C4⋊C4—268no—
509C4⋊C4—2616no—
510C4⋊C4—268no—
511C4⋊C4—528no—
512C22⋊C4—216no—
513C22⋊C4—1316no—
514C22⋊C4—268no—
515C22⋊C4—2616no—
516C22⋊C4—2616no—
517C22⋊C4—2616no—
518C22⋊C4—2616no—
519C42—28no—
520C42—268no—
521C13C2×#242211yescharacteristic, complemented, Sylow
522C23—216no—
523C23—216no—
524C23—216no—
525C23—24no—
526C23—24no—
527C23—24no—
528C23—24no—
529C23—24no—
530C23—24no—
531C23—48no—
532C23—48no—
533C23—48no—
534C23—48no—
535C23—134no—
536C23—268no—
537C23—268no—
538C23—268no—
539C23—262no—
540C23—262no—
541C23—262no—
542C23—262no—
543C23—262no—
544C23—262no—
545C23—524no—
546C23—524no—
547C23—524no—
548C23—524no—
549C23C2×#612712yes—
550C23C2×#612712yes—
551C23C2×D4×D1312yes—
552C23#8825112yes—
553C23#41×D1312yes—
554C23#8825712yes—
555C23C22×C22⋊D1318yes—
556C23C22×C22⋊D1312yes—
557C23C24×D1311yescharacteristic
558D4—232no—
559D4—5232no—
560C2×C4—28no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—432no—
570C2×C4—48no—
571C2×C4—44no—
572C2×C4—134no—
573C2×C4—134no—
574C2×C4—268no—
575C2×C4—268no—
576C2×C4—262no—
577C2×C4—262no—
578C2×C4—262no—
579C2×C4—262no—
580C2×C4—264no—
581C2×C4—262no—
582C2×C4—262no—
583C2×C4—264no—
584C2×C4—264no—
585C2×C4—264no—
586C2×C4—264no—
587C2×C4—262no—
588C2×C4—264no—
589C2×C4—524no—
590C2×C4—528no—
591C2×C4—528no—
592C2×C4—5216no—
593C2×C4#88183116yescomplemented
594C2×C4C2×#612714yes—
595C2×C4C2×#612714yes—
596C2×C4C2×D4×D1314yes—
597C2×C4C22×C22⋊D1314yes—
598C22—28no—
599C22—28no—
600C22—28no—
601C22—44no—
602C22—44no—
603C22—432no—
604C22—44no—
605C22—44no—
606C22—264no—
607C22—264no—
608C22—264no—
609C22—522no—
610C22—522no—
611C22—522no—
612C22—5216no—
613C22—522no—
614C22#1171925314yes—
615C22#1171925614yes—
616C22#1171926314yes—
617C22#1171926614yes—
618C22C2×#8818314yes—
619C22D4×C22⋊D1314yes—
620C22#1171952914yes—
621C22C22×#612711yescharacteristic
622C22C22×#612711yescharacteristic
623C22C22×D4×D1311yescharacteristic
624C22C2×#8825111yescharacteristic
625C22C2×#41×D1311yescharacteristic
626C22C2×#8825711yescharacteristic
627C22C23×C22⋊D1311yescharacteristic
628C4—24no—
629C4—44no—
630C4—42no—
631C4—264no—
632C4—264no—
633C4—524no—
634C4—522no—
635C4—524no—
636C4C2×#8818318yescomplemented
637C2—48no—
638C2—524no—
639C2#1311834418yesdirect product factor
640C2C22×#8818311yescharacteristic
641C2C2×#1171925311yescharacteristic
642C2C2×#1171926611yescharacteristic
643C2C2×D4×C22⋊D1311yescharacteristic
644C2C2×#1171952911yescharacteristic
645C2C2×#1171925611yescharacteristic
646C2C2×#1171926311yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C4×D4×C13C2
socleC24×C13C24
prime radicalC22×#88192C2
hypercenterC22×C4×D4D13
hypocenterC13C2×#2422
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#88183C2semidirect
3. #13118344C2direct (N × H)
4. C2×#11718613C2semidirect
5. C2×#11718620C2semidirect
6. C2×#11718882C2semidirect
7. C2×#11718589C2semidirect
8. C2×#11718871C2semidirect
9. C2×#11718637C2semidirect
10. C2×#11718648C2semidirect
11. C2×C4×#6103C2semidirect
12. C22×C4×D4×C13C2semidirect
18. C2×C4×D4×C13C22semidirect
28. C2×#88183C22semidirect
38. #11718882C22semidirect
39. #11718871C22semidirect
44. #11718648C22semidirect
45. #11718637C22semidirect
46. #11718620C22semidirect
47. #11718613C22semidirect
48. C4×#6103C22semidirect
49. #11718589C22semidirect
94. C2×#6103D4semidirect
192. #6103C2×D4semidirect
201. C22×C4×D4D13semidirect
260. C2×C4×C13#123semidirect
296. C2×C4×D4C2×D13semidirect
357. C4×C13C2×#123semidirect
428. C2×C13#2422semidirect
521. C13C2×#2422semidirect
593. C2×C4#88183semidirect
636. C4C2×#88183semidirect
639. C2#13118344direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881832
C22×#881922
#131183442
C2×#117186132
C2×#117186202
C2×#117188822
C2×#117185892
C2×#117188712
C2×#117186372
C2×#117186482
C2×C4×#61032
C22×C4×D4×C132
C2×#242213