Finite Group Databasebeta

← C2×#13118330 #16031051

Subgroups — C2×#13118330 #16031051

Order 3328.

3438 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88184C211yesmaximal, characteristic
2C22×#88147C211yesmaximal, characteristic, complemented
3#13118330C2116yesmaximal, direct product factor
4C2×#11718335C212yesmaximal, complemented
5C2×#11718622C212yesmaximal, complemented
6C2×#11718649C211yesmaximal, characteristic, complemented
7C2×#11718646C211yesmaximal, characteristic, complemented
8C2×#11718617C212yesmaximal, complemented
9C2×#11718638C211yesmaximal, characteristic, complemented
10C2×#11718325C212yesmaximal, complemented
11C2×C4×C22⋊Dic13C211yesmaximal, characteristic, complemented
12C2×C13×#380C211yesmaximal, characteristic, complemented
13C24×C4×C13C2211yescharacteristic
14C23×C22⋊D13C2212yes—
15C23×D52C2211yescharacteristic
16C23×C4×D13C2212yes—
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2212yes—
20C22×C22⋊Dic13C2211yescharacteristic
21C22×C22⋊Dic13C2211yescharacteristic
22C2×#88184—28no—
23C2×#88184C2218yes—
24C22×#6103C2212yes—
25C22×#6103C2212yes—
26C22×#6103C2212yes—
27C22×#6103C2212yes—
28C22×C4⋊Dic13C2211yescharacteristic
29C22×C4⋊Dic13C2212yes—
30C22×C4×Dic13C2211yescharacteristic
31C22×C4×Dic13C2211yescharacteristic
32C2×#88147—28no—
33C2×#88147C2218yescomplemented
34C13×#380C2218yescomplemented
35C2×C13×#95C2212yes—
36C4×C22⋊Dic13C2218yescomplemented
37C2×#88071C2211yescharacteristic
38C2×#88071C2212yes—
39C2×#88071C2212yes—
40C2×#88071C2212yes—
41C2×#88071C2211yescharacteristic
42#11718649C2218yescomplemented
43#11718646C2218yescomplemented
44#11718638C2218yescomplemented
45#11718622C22116yescomplemented
46#11718617C22116yescomplemented
47#11718335C22116yescomplemented
48#11718325C22116yescomplemented
49C25×C13C2311yescharacteristic
50C24×D13C2312yes—
51C23×C4×C13—24no—
52C23×C4×C13—24no—
53C23×C4×C13—24no—
54C23×C4×C13C2314yes—
55C23×C4×C13C2312yes—
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2312yes—
58C23×C4×C13C2311yescharacteristic
59C22×C22⋊D13—28no—
60C22×C22⋊D13—28no—
61C22×C22⋊D13—44no—
62C22×C22⋊D13C2318yes—
63C23×Dic13C2311yescharacteristic
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2312yes—
67C23×Dic13C2311yescharacteristic
68C22×D52—24no—
69C22×D52—24no—
70C22×D52D418yes—
71C22×D52C2314yes—
72C22×C4×D13—28no—
73C22×C4×D13—28no—
74C22×C4×D13—44no—
75C22×C4×D13C2318yes—
76C2×C13×C4⋊C4—24no—
77C2×C13×C4⋊C4—24no—
78C2×C13×C4⋊C4C2314yes—
79C2×C13×C4⋊C4C2314yes—
80C2×C13×C22⋊C4—44no—
81C2×C13×C22⋊C4C2318yes—
82C2×C22⋊Dic13—24no—
83C2×C22⋊Dic13—24no—
84C2×C22⋊Dic13C2314yes—
85C2×C22⋊Dic13C2314yes—
86#88184—232no—
87C2×#6103—28no—
88C2×#6103—28no—
89C2×#6103—44no—
90C2×#6103—44no—
91C2×#6103C2318yes—
92C2×#6103C2318yes—
93C2×#6103C2318yes—
94C2×#6103C2318yes—
95C2×C4⋊Dic13—24no—
96C2×C4⋊Dic13—44no—
97C2×C4⋊Dic13C2314yes—
98C2×C4⋊Dic13C2318yes—
99C2×C4×Dic13—24no—
100C2×C4×Dic13—24no—
101C2×C4×Dic13C2314yes—
102C2×C4×Dic13C2314yes—
103#88147—232no—
104C13×#95C2318yes—
105#88071C2314yes—
106#88071C2318yes—
107#88071C2318yes—
108#88071C2314yes—
109#88071C2318yes—
110C2×#2420—131nomaximal, Sylow
111C24×C13—22no—
112C24×C13—22no—
113C24×C13—22no—
114C24×C13—22no—
115C24×C13—22no—
116C24×C13—22no—
117C24×C13#4114yes—
118C24×C13C2412yes—
119C24×C13C2411yescharacteristic
120C23×D13—24no—
121C23×D13—24no—
122C23×D13—24no—
123C23×D13—24no—
124C23×D13—24no—
125C23×D13—24no—
126C23×D13C2×D418yes—
127C23×D13C2414yes—
128C22×C4×C13—22no—
129C22×C4×C13—24no—
130C22×C4×C13—24no—
131C22×C4×C13—24no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—24no—
135C22×C4×C13—24no—
136C22×C4×C13—24no—
137C22×C4×C13—28no—
138C22×C4×C13—28no—
139C22×C4×C13—28no—
140C22×C4×C13—416no—
141C22×C4×C13C2×D414yes—
142C22×C4×C13#4114yes—
143C22×C4×C13#4114yes—
144C22×C4×C13C2412yes—
145C22×C4×C13C2414yes—
146C22×C4×C13C2414yes—
147C22×C4×C13C2412yes—
148C2×C22⋊D13—216no—
149C2×C22⋊D13—216no—
150C2×C22⋊D13—48no—
151C2×C22⋊D13—432no—
152C22×Dic13—22no—
153C22×Dic13—22no—
154C22×Dic13—22no—
155C22×Dic13—24no—
156C22×Dic13—22no—
157C22×Dic13—22no—
158C22×Dic13—22no—
159C22×Dic13—22no—
160C22×Dic13—22no—
161C22×Dic13—24no—
162C22×Dic13—22no—
163C22×Dic13—24no—
164C22×Dic13—22no—
165C22×Dic13—22no—
166C22×Dic13#4114yes—
167C22×Dic13C2412yes—
168C22×Dic13C2412yes—
169C22×Dic13C2414yes—
170C22×Dic13C2412yes—
171C22×Dic13C2412yes—
172C2×D52—232no—
173C2×D52—28no—
174C2×D52—28no—
175C2×D52C2×D4116yes—
176C2×C4×D13—216no—
177C2×C4×D13—216no—
178C2×C4×D13—48no—
179C2×C4×D13—432no—
180C13×C4⋊C4—28no—
181C13×C4⋊C4—28no—
182C13×C22⋊C4—48no—
183C22⋊Dic13—28no—
184C22⋊Dic13—28no—
185#6103—216no—
186#6103—216no—
187#6103—48no—
188#6103—48no—
189C4⋊Dic13—28no—
190C4⋊Dic13—48no—
191C4×Dic13—28no—
192C4×Dic13—28no—
193C22×#121—131no—
194C22×C4×D4—131no—
195#2420—1316no—
196C2×#397—132no—
197C2×#394—132no—
198C2×#390—131no—
199C2×#389—131no—
200C2×#386—132no—
201C2×#382—131no—
202C2×#381—132no—
203C2×#380D1311yescharacteristic, complemented
204C2×C4×C22⋊C4—131no—
205C23×C13—28no—
206C23×C13—28no—
207C23×C13—28no—
208C23×C13—22no—
209C23×C13—22no—
210C23×C13—22no—
211C23×C13—22no—
212C23×C13—22no—
213C23×C13—22no—
214C23×C13—44no—
215C23×C13—44no—
216C23×C13—44no—
217C23×C13—44no—
218C23×C13C22×D412yes—
219C23×C13C2×#4114yes—
220C23×C13C2×#4112yes—
221C23×C13C2×#4112yes—
222C23×C13C2×#4112yes—
223C23×C13C2×#4112yes—
224C23×C13H(5,𝔽2)12yes—
225C23×C13H(5,𝔽2)12yes—
226C23×C13C2511yescharacteristic
227C22×D13—216no—
228C22×D13—216no—
229C22×D13—216no—
230C22×D13—24no—
231C22×D13—24no—
232C22×D13—24no—
233C22×D13—24no—
234C22×D13—24no—
235C22×D13—24no—
236C22×D13—48no—
237C22×D13—48no—
238C22×D13—48no—
239C22×D13—48no—
240C22×D13C22×D418yes—
241C2×C4×C13—22no—
242C2×C4×C13—24no—
243C2×C4×C13—24no—
244C2×C4×C13—24no—
245C2×C4×C13—22no—
246C2×C4×C13—22no—
247C2×C4×C13—24no—
248C2×C4×C13—24no—
249C2×C4×C13—24no—
250C2×C4×C13—44no—
251C2×C4×C13—48no—
252C2×C4×C13—48no—
253C2×C4×C13—416no—
254C2×C4×C13#123116yes—
255C2×C4×C13C22×D414yes—
256C2×C4×C13C2×#4114yes—
257C2×C4×C13C2×#4114yes—
258C22⋊D13—432no—
259C2×Dic13—28no—
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—24no—
270C2×Dic13—22no—
271C2×Dic13—24no—
272C2×Dic13—22no—
273C2×Dic13—22no—
274C2×Dic13—44no—
275C2×Dic13—48no—
276C2×Dic13—44no—
277C2×Dic13—44no—
278C2×Dic13C2×#4114yes—
279D52—232no—
280C4×D13—432no—
281C23×D4—132no—
282C23×D4—131no—
283C24×C4—132no—
284C24×C4C2×D1311yescharacteristic
285C2×#121—138no—
286C2×#121—268no—
287C2×C4×D4—138no—
288C2×C4×D4—268no—
289C22×C4⋊C4—131no—
290C22×C4⋊C4—132no—
291C22×C4⋊C4C2×D1311yescharacteristic
292C22×C4⋊C4C2×D1311yescharacteristic
293C22×C22⋊C4—131no—
294C22×C22⋊C4—131no—
295C22×C22⋊C4—132no—
296C22×C22⋊C4—132no—
297C22×C22⋊C4—132no—
298C22×C22⋊C4—132no—
299C22×C22⋊C4C2×D1312yes—
300C22×C42—131no—
301C22×C42—131no—
302#397—1316no—
303#394—1316no—
304#390—138no—
305#389—138no—
306#386—1316no—
307#382—138no—
308#381—1316no—
309#380C2×D1318yescomplemented
310C4×C22⋊C4—138no—
311C2×#95—132no—
312C2×#95—131no—
313C2×#95—132no—
314C2×#95—131no—
315C2×#95—132no—
316C2×#95C2×D1312yes—
317C22×C13—24no—
318C22×C13—24no—
319C22×C13—24no—
320C22×C13—42no—
321C22×C13—416no—
322C22×C13—42no—
323C22×C13—42no—
324C22×C13—42no—
325C22×C13C2×#12314yes—
326C22×C13#52914yes—
327C22×C13#54014yes—
328C22×C13#54614yes—
329C22×C13#54614yes—
330C22×C13#55314yes—
331C22×C13#55514yes—
332C22×C13C23×D411yescharacteristic
333C22×C13C22×#4111yescharacteristic
334C22×C13C22×#4111yescharacteristic
335C22×C13C22×#4111yescharacteristic
336C22×C13C22×#4111yescharacteristic
337C22×C13C2×H(5,𝔽2)11yescharacteristic
338C22×C13C2×H(5,𝔽2)11yescharacteristic
339C2×D13—28no—
340C2×D13—28no—
341C2×D13—28no—
342C2×D13—44no—
343C2×D13—432no—
344C2×D13—44no—
345C2×D13—44no—
346C2×D13—44no—
347C4×C13—42no—
348C4×C13—44no—
349C4×C13—44no—
350C4×C13C2×#12318yes—
351Dic13—24no—
352Dic13—42no—
353Dic13—44no—
354Dic13—42no—
355Dic13—42no—
356C25—132no—
357C25C22×D1311yescharacteristic
358C22×D4—138no—
359C22×D4—138no—
360C22×D4—134no—
361C22×D4—268no—
362C22×D4—268no—
363C22×D4—264no—
364C22×D4—264no—
365C22×D4—524no—
366C23×C4—24no—
367C23×C4—24no—
368C23×C4—24no—
369C23×C4—131no—
370C23×C4—131no—
371C23×C4—131no—
372C23×C4—131no—
373C23×C4—132no—
374C23×C4—138no—
375C23×C4—268no—
376C23×C4—268no—
377C23×C4—524no—
378C23×C4C22×D1314yes—
379C23×C4C22×D1312yes—
380C23×C4C22×D1311yescharacteristic
381C23×C4C22×D1312yes—
382C23×C4C22×D1311yescharacteristic
383#121—2632no—
384C4×D4—2632no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—134no—
388C2×C4⋊C4—138no—
389C2×C4⋊C4—264no—
390C2×C4⋊C4—524no—
391C2×C4⋊C4C22×D1314yes—
392C2×C4⋊C4C22×D1314yes—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—134no—
395C2×C22⋊C4—134no—
396C2×C22⋊C4—138no—
397C2×C22⋊C4—138no—
398C2×C22⋊C4—138no—
399C2×C22⋊C4—138no—
400C2×C22⋊C4—268no—
401C2×C22⋊C4—268no—
402C2×C22⋊C4—264no—
403C2×C22⋊C4—264no—
404C2×C22⋊C4—524no—
405C2×C22⋊C4—524no—
406C2×C22⋊C4C22×D1318yes—
407C2×C42—134no—
408C2×C42—134no—
409C2×C42—264no—
410C2×C42—264no—
411#95—134no—
412#95—134no—
413#95—138no—
414#95—138no—
415#95—138no—
416#95C22×D1318yes—
417C2×C13—44no—
418C2×C13#242018yescomplemented
419C2×C13C22×#12311yescharacteristic
420C2×C13C2×#52911yescharacteristic
421C2×C13C2×#54011yescharacteristic
422C2×C13C2×#54611yescharacteristic
423C2×C13C2×#54611yescharacteristic
424C2×C13C2×#55311yescharacteristic
425C2×C13C2×#55511yescharacteristic
426D13—48no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—138no—
434C24—134no—
435C24—264no—
436C24—264no—
437C24—264no—
438C24—264no—
439C24—264no—
440C24—264no—
441C24#613114yes—
442C24C23×D1312yes—
443C24C23×D1311yescharacteristic
444C2×D4—1316no—
445C2×D4—2616no—
446C2×D4—2616no—
447C2×D4—2632no—
448C2×D4—268no—
449C2×D4—268no—
450C2×D4—528no—
451C2×D4—5232no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—22no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—28no—
462C22×C4—28no—
463C22×C4—28no—
464C22×C4—416no—
465C22×C4—134no—
466C22×C4—132no—
467C22×C4—132no—
468C22×C4—132no—
469C22×C4—134no—
470C22×C4—132no—
471C22×C4—2616no—
472C22×C4—2616no—
473C22×C4—262no—
474C22×C4—262no—
475C22×C4—262no—
476C22×C4—262no—
477C22×C4—262no—
478C22×C4—264no—
479C22×C4—262no—
480C22×C4—262no—
481C22×C4—262no—
482C22×C4—264no—
483C22×C4—262no—
484C22×C4—262no—
485C22×C4—262no—
486C22×C4—264no—
487C22×C4—528no—
488C22×C4—5232no—
489C22×C4#612714yes—
490C22×C4D4×D1314yes—
491C22×C4#612914yes—
492C22×C4C23×D1312yes—
493C22×C4C23×D1314yes—
494C22×C4C23×D1314yes—
495C22×C4C23×D1312yes—
496C4⋊C4—28no—
497C4⋊C4—28no—
498C4⋊C4—268no—
499C4⋊C4—528no—
500C22⋊C4—48no—
501C22⋊C4—2616no—
502C22⋊C4—2616no—
503C22⋊C4—268no—
504C22⋊C4—268no—
505C22⋊C4—528no—
506C22⋊C4—528no—
507C42—268no—
508C42—268no—
509C13C2×#242011yescharacteristic, complemented, Sylow
510C23—28no—
511C23—28no—
512C23—28no—
513C23—22no—
514C23—22no—
515C23—22no—
516C23—22no—
517C23—22no—
518C23—22no—
519C23—44no—
520C23—44no—
521C23—44no—
522C23—44no—
523C23—138no—
524C23—2616no—
525C23—2616no—
526C23—2616no—
527C23—264no—
528C23—264no—
529C23—264no—
530C23—264no—
531C23—264no—
532C23—264no—
533C23—528no—
534C23—528no—
535C23—528no—
536C23—528no—
537C23C2×#612712yes—
538C23C2×D4×D1312yes—
539C23C2×#612912yes—
540C23#8825112yes—
541C23C2×#613114yes—
542C23C2×#613112yes—
543C23#41×D1312yes—
544C23#8825612yes—
545C23C24×D1311yescharacteristic
546D4—2632no—
547D4—5232no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—44no—
558C2×C4—48no—
559C2×C4—48no—
560C2×C4—416no—
561C2×C4—134no—
562C2×C4—268no—
563C2×C4—262no—
564C2×C4—262no—
565C2×C4—262no—
566C2×C4—262no—
567C2×C4—262no—
568C2×C4—264no—
569C2×C4—262no—
570C2×C4—262no—
571C2×C4—262no—
572C2×C4—264no—
573C2×C4—262no—
574C2×C4—262no—
575C2×C4—262no—
576C2×C4—264no—
577C2×C4—5232no—
578C2×C4—524no—
579C2×C4—524no—
580C2×C4—524no—
581C2×C4—528no—
582C2×C4#88137116yes—
583C2×C4C2×#612714yes—
584C2×C4C2×D4×D1314yes—
585C2×C4C2×#612914yes—
586C22—24no—
587C22—24no—
588C22—24no—
589C22—42no—
590C22—42no—
591C22—416no—
592C22—42no—
593C22—42no—
594C22—268no—
595C22—268no—
596C22—268no—
597C22—524no—
598C22—5232no—
599C22—524no—
600C22—524no—
601C22—524no—
602C22C2×#8813714yes—
603C22#1171921914yes—
604C22#1171923714yes—
605C22#1171931714yes—
606C22#1171932414yes—
607C22#1171932914yes—
608C22#1171933514yes—
609C22C22×#612711yescharacteristic
610C22C22×D4×D1311yescharacteristic
611C22C22×#612911yescharacteristic
612C22C2×#8825111yescharacteristic
613C22C22×#613111yescharacteristic
614C22C2×#41×D1311yescharacteristic
615C22C2×#8825611yescharacteristic
616C4—44no—
617C4—44no—
618C4—42no—
619C4—264no—
620C4—522no—
621C4—524no—
622C4—522no—
623C4—522no—
624C4C2×#8813718yes—
625C2—44no—
626C2—528no—
627C2#1311833018yesdirect product factor
628C2C22×#8813711yescharacteristic
629C2C2×#1171932911yescharacteristic
630C2C2×#1171932411yescharacteristic
631C2C2×#1171933511yescharacteristic
632C2C2×#1171931711yescharacteristic
633C2C2×#1171921911yescharacteristic
634C2C2×#1171923711yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#380C2
socleC24×C13C24
prime radicalC22×#88184C2
hypercenterC2×#380D13
hypocenterC13C2×#2420
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C22×#88147C2semidirect
3. #13118330C2direct (N × H)
4. C2×#11718335C2semidirect
5. C2×#11718622C2semidirect
6. C2×#11718649C2semidirect
7. C2×#11718646C2semidirect
8. C2×#11718617C2semidirect
9. C2×#11718638C2semidirect
10. C2×#11718325C2semidirect
11. C2×C4×C22⋊Dic13C2semidirect
12. C2×C13×#380C2semidirect
33. C2×#88147C22semidirect
34. C13×#380C22semidirect
36. C4×C22⋊Dic13C22semidirect
42. #11718649C22semidirect
43. #11718646C22semidirect
44. #11718638C22semidirect
45. #11718622C22semidirect
46. #11718617C22semidirect
47. #11718335C22semidirect
48. #11718325C22semidirect
203. C2×#380D13semidirect
309. #380C2×D13semidirect
418. C2×C13#2420semidirect
509. C13C2×#2420semidirect
627. C2#13118330direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881842
C22×#881472
#131183302
C2×#117183352
C2×#117186222
C2×#117186492
C2×#117186462
C2×#117186172
C2×#117186382
C2×#117183252
C2×C4×C22⋊Dic132
C2×C13×#3802
C2×#242013