Finite Group Databasebeta

← C2×#13117780 #16022263

Subgroups — C2×#13117780 #16022263

Order 3328.

3678 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D13C211yesmaximal, characteristic
2C22×#88180C211yesmaximal, characteristic, complemented
3C22×#88146C211yesmaximal, characteristic, complemented
4#13117780C2116yesmaximal, direct product factor
5C2×#11718618C212yesmaximal
6C2×#11718606C212yesmaximal, complemented
7C2×#11718330C212yesmaximal, complemented
8C2×#11718637C211yesmaximal, characteristic, complemented
9C2×#11718648C211yesmaximal, characteristic, complemented
10C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
11C2×#11718310C212yesmaximal, complemented
12C2×C13×#380C211yesmaximal, characteristic, complemented
13C24×C4×C13C2211yescharacteristic
14C23×C22⋊D13C2211yescharacteristic
15C23×C4×D13C2211yescharacteristic
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2212yes—
19C22×C22⋊Dic13C2212yes—
20C22×C22⋊Dic13C2211yescharacteristic
21C2×C4×C22⋊D13C4116yescomplemented
22C2×C4×C22⋊D13C2218yes—
23C22×#6103C2212yes—
24C22×#6103C2212yes—
25C22×#6103C2211yescharacteristic
26C2×#88180—28no—
27C2×#88180C2218yescomplemented
28C22×C4⋊Dic13C2211yescharacteristic
29C22×C4⋊Dic13C2211yescharacteristic
30C22×#6101C2212yes—
31C22×#6101C2212yes—
32C22×#6101C2211yescharacteristic
33C22×C4×Dic13C2212yes—
34C22×C4×Dic13C2212yes—
35C22×C4×Dic13C2212yes—
36C22×C4×Dic13C2211yescharacteristic
37C2×#88146—28no—
38C2×#88146C2218yescomplemented
39C13×#380C2218yescomplemented
40C2×C13×#95C2212yes—
41C2×#88071C2212yes—
42C2×#88071C2212yes—
43#11718648C2218yescomplemented
44#11718637C2218yescomplemented
45C4⋊C4×Dic13C2218yescomplemented
46#11718618C22116yes—
47#11718606C22116yescomplemented
48#11718330C22116yescomplemented
49#11718310C22116yescomplemented
50C25×C13C2311yescharacteristic
51C24×D13C2311yescharacteristic
52C23×C4×C13—24no—
53C23×C4×C13—24no—
54C23×C4×C13C2×C418yes—
55C23×C4×C13C2312yes—
56C23×C4×C13C2312yes—
57C23×C4×C13C2314yes—
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C22×C22⋊D13—24no—
61C22×C22⋊D13—24no—
62C22×C22⋊D13C2×C418yes—
63C22×C22⋊D13C2314yes—
64C23×Dic13C2312yes—
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2312yes—
68C23×Dic13C2311yescharacteristic
69C22×C4×D13—24no—
70C22×C4×D13—24no—
71C22×C4×D13C2×C418yes—
72C22×C4×D13C2314yes—
73C2×C13×C4⋊C4—24no—
74C2×C13×C4⋊C4—24no—
75C2×C13×C4⋊C4C2314yes—
76C2×C13×C4⋊C4C2314yes—
77C2×C13×C22⋊C4—44no—
78C2×C13×C22⋊C4C2318yes—
79C2×C22⋊Dic13—28no—
80C2×C22⋊Dic13C2×C418yes—
81C2×C22⋊Dic13C2318yes—
82C2×C22⋊Dic13C2314yes—
83C4×C22⋊D13C2×C4164yescomplemented
84C2×#6103—28no—
85C2×#6103—44no—
86C2×#6103C2×C418yes—
87C2×#6103C2318yes—
88C2×#6103C2318yes—
89C2×#6103C2314yes—
90#88180—232no—
91C2×C4⋊Dic13—24no—
92C2×C4⋊Dic13D418yescomplemented
93C2×C4⋊Dic13C2314yes—
94C2×C4⋊Dic13C2314yes—
95C2×#6101—28no—
96C2×#6101—44no—
97C2×#6101C2×C418yes—
98C2×#6101C2318yes—
99C2×#6101C2318yes—
100C2×#6101C2314yes—
101C2×C4×Dic13—28no—
102C2×C4×Dic13—28no—
103C2×C4×Dic13—28no—
104C2×C4×Dic13C2×C418yes—
105C2×C4×Dic13C2318yes—
106C2×C4×Dic13C2318yes—
107C2×C4×Dic13C2318yes—
108C2×C4×Dic13C2314yes—
109#88146—232no—
110C13×#95C2318yes—
111#88071C2318yes—
112#88071C2318yes—
113C2×#2354—131nomaximal, Sylow
114C24×C13—22no—
115C24×C13—22no—
116C24×C13—22no—
117C24×C13—22no—
118C24×C13—22no—
119C24×C13—22no—
120C24×C13C22×C414yes—
121C24×C13C2412yes—
122C24×C13C2411yescharacteristic
123C23×D13—22no—
124C23×D13—22no—
125C23×D13—22no—
126C23×D13—22no—
127C23×D13—22no—
128C23×D13—22no—
129C23×D13C22×C414yes—
130C23×D13C2412yes—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—232no—
134C22×C4×C13—28no—
135C22×C4×C13—28no—
136C22×C4×C13—24no—
137C22×C4×C13—24no—
138C22×C4×C13—24no—
139C22×C4×C13—24no—
140C22×C4×C13—24no—
141C22×C4×C13—24no—
142C22×C4×C13C22×C414yes—
143C22×C4×C13C22×C4116yes—
144C22×C4×C13C22×C414yes—
145C22×C4×C13C2×D414yes—
146C22×C4×C13#4114yes—
147C22×C4×C13C2414yes—
148C22×C4×C13C2414yes—
149C22×C4×C13C2412yes—
150C22×C4×C13C2412yes—
151C2×C22⋊D13—232no—
152C2×C22⋊D13—28no—
153C2×C22⋊D13—28no—
154C2×C22⋊D13C22×C4116yes—
155C22×Dic13—22no—
156C22×Dic13—24no—
157C22×Dic13—22no—
158C22×Dic13—22no—
159C22×Dic13—22no—
160C22×Dic13—24no—
161C22×Dic13—24no—
162C22×Dic13—24no—
163C22×Dic13—24no—
164C22×Dic13C22×C414yes—
165C22×Dic13C22×C414yes—
166C22×Dic13C22×C414yes—
167C22×Dic13C2×D418yes—
168C22×Dic13#4114yes—
169C22×Dic13#4114yes—
170C22×Dic13C2414yes—
171C22×Dic13C2412yes—
172C22×Dic13C2412yes—
173C22×Dic13C2414yes—
174C22×Dic13C2412yes—
175C2×C4×D13—232no—
176C2×C4×D13—28no—
177C2×C4×D13—28no—
178C2×C4×D13C22×C4116yes—
179C13×C4⋊C4—28no—
180C13×C4⋊C4—28no—
181C13×C22⋊C4—48no—
182C22⋊Dic13—216no—
183C22⋊Dic13C22×C4116yes—
184#6103—216no—
185#6103—48no—
186#6103C22×C4116yes—
187C4⋊Dic13—28no—
188C4⋊Dic13C2×D4116yescomplemented
189#6101—216no—
190#6101—48no—
191#6101C22×C4116yes—
192C4×Dic13—216no—
193C4×Dic13—216no—
194C4×Dic13—216no—
195C4×Dic13C22×C4116yes—
196C22×C4×D4—131no—
197C22×#117—131no—
198C22×#117—131no—
199#2354—1316no—
200C2×#390—132no—
201C2×#388—132no—
202C2×#388—132no—
203C2×#384—131no—
204C2×#380—131no—
205C2×#380D1311yescharacteristic, complemented
206C2×C4×C4⋊C4—132no—
207C2×C4×C4⋊C4—131no—
208C23×C13—28no—
209C23×C13—28no—
210C23×C13—28no—
211C23×C13—22no—
212C23×C13—22no—
213C23×C13—22no—
214C23×C13—22no—
215C23×C13—22no—
216C23×C13—22no—
217C23×C13—44no—
218C23×C13—44no—
219C23×C13—44no—
220C23×C13—44no—
221C23×C13C23×C414yes—
222C23×C13C23×C412yes—
223C23×C13C22×D412yes—
224C23×C13C2×#4112yes—
225C23×C13C2×#4112yes—
226C23×C13C2×#4112yes—
227C23×C13H(5,𝔽2)12yes—
228C23×C132−1+412yes—
229C23×C13C2511yescharacteristic
230C22×D13—28no—
231C22×D13—28no—
232C22×D13—28no—
233C22×D13—22no—
234C22×D13—22no—
235C22×D13—22no—
236C22×D13—22no—
237C22×D13—22no—
238C22×D13—22no—
239C22×D13—44no—
240C22×D13—44no—
241C22×D13—44no—
242C22×D13—44no—
243C22×D13C23×C414yes—
244C2×C4×C13—28no—
245C2×C4×C13—22no—
246C2×C4×C13—22no—
247C2×C4×C13—232no—
248C2×C4×C13—24no—
249C2×C4×C13—24no—
250C2×C4×C13—24no—
251C2×C4×C13—24no—
252C2×C4×C13—24no—
253C2×C4×C13—24no—
254C2×C4×C13—48no—
255C2×C4×C13—48no—
256C2×C4×C13C4×D4116yes—
257C2×C4×C13C23×C414yes—
258C2×C4×C13C23×C414yes—
259C2×C4×C13C22×D414yes—
260C2×C4×C13C2×#4114yes—
261C22⋊D13—232no—
262C2×Dic13—28no—
263C2×Dic13—28no—
264C2×Dic13—216no—
265C2×Dic13—22no—
266C2×Dic13—24no—
267C2×Dic13—22no—
268C2×Dic13—22no—
269C2×Dic13—22no—
270C2×Dic13—24no—
271C2×Dic13—24no—
272C2×Dic13—24no—
273C2×Dic13—24no—
274C2×Dic13—48no—
275C2×Dic13#117116yescomplemented
276C2×Dic13C23×C414yes—
277C2×Dic13C23×C414yes—
278C2×Dic13C23×C414yes—
279C2×Dic13C22×D418yes—
280C2×Dic13C2×#4114yes—
281C2×Dic13C2×#4114yes—
282C4×D13—232no—
283C23×D4—131no—
284C24×C4—131no—
285C24×C4C2×D1311yescharacteristic
286C2×C4×D4—1316no—
287C2×C4×D4—138no—
288C2×#117—138no—
289C2×#117—138no—
290C2×#117—268no—
291C2×#117—268no—
292C22×C4⋊C4—131no—
293C22×C4⋊C4—131no—
294C22×C4⋊C4—132no—
295C22×C4⋊C4—131no—
296C22×C4⋊C4—132no—
297C22×C4⋊C4C2×D1311yescharacteristic
298C22×C4⋊C4C2×D1311yescharacteristic
299C22×C22⋊C4—131no—
300C22×C22⋊C4—131no—
301C22×C22⋊C4—132no—
302C22×C22⋊C4—132no—
303C22×C22⋊C4—132no—
304C22×C22⋊C4C2×D1312yes—
305C22×C42—131no—
306C22×C42—132no—
307C22×C42—132no—
308C22×C42—132no—
309#390—1316no—
310#388—1316no—
311#388—1316no—
312#384—138no—
313#380—138no—
314#380C2×D1318yescomplemented
315C4×C4⋊C4—138no—
316C4×C4⋊C4—1316no—
317C2×#95—132no—
318C2×#95—132no—
319C2×#95C2×D1312yes—
320C22×C13—24no—
321C22×C13—24no—
322C22×C13—24no—
323C22×C13—416no—
324C22×C13—42no—
325C22×C13—42no—
326C22×C13—42no—
327C22×C13—42no—
328C22×C13C2×#11714yes—
329C22×C13C2×C4×D414yes—
330C22×C13#52014yes—
331C22×C13#54714yes—
332C22×C13#55014yes—
333C22×C13#55514yes—
334C22×C13#55614yes—
335C22×C13C24×C411yescharacteristic
336C22×C13C23×D411yescharacteristic
337C22×C13C22×#4111yescharacteristic
338C22×C13C22×#4111yescharacteristic
339C22×C13C22×#4111yescharacteristic
340C22×C13C2×H(5,𝔽2)11yescharacteristic
341C22×C13C2×2−1+411yescharacteristic
342C2×D13—24no—
343C2×D13—24no—
344C2×D13—24no—
345C2×D13—416no—
346C2×D13—42no—
347C2×D13—42no—
348C2×D13—42no—
349C2×D13—42no—
350C4×C13—24no—
351C4×C13—44no—
352C4×C13—44no—
353C4×C13C2×C4×D418yes—
354Dic13—24no—
355Dic13—24no—
356Dic13—28no—
357Dic13—44no—
358Dic13C2×#11718yescomplemented
359C25—131no—
360C25C22×D1311yescharacteristic
361C22×D4—138no—
362C22×D4—134no—
363C22×D4—264no—
364C22×D4—264no—
365C23×C4—24no—
366C23×C4—24no—
367C23×C4—131no—
368C23×C4—131no—
369C23×C4—132no—
370C23×C4—131no—
371C23×C4—138no—
372C23×C4—134no—
373C23×C4—132no—
374C23×C4—264no—
375C23×C4—264no—
376C23×C4C4×D1318yes—
377C23×C4C22×D1312yes—
378C23×C4C22×D1312yes—
379C23×C4C22×D1314yes—
380C23×C4C22×D1311yescharacteristic
381C23×C4C22×D1311yescharacteristic
382C4×D4—1364no—
383#117—2632no—
384#117—2632no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—138no—
388C2×C4⋊C4—138no—
389C2×C4⋊C4—134no—
390C2×C4⋊C4—134no—
391C2×C4⋊C4—134no—
392C2×C4⋊C4—138no—
393C2×C4⋊C4—138no—
394C2×C4⋊C4—268no—
395C2×C4⋊C4—264no—
396C2×C4⋊C4—524no—
397C2×C4⋊C4C22×D1314yes—
398C2×C4⋊C4C22×D1314yes—
399C2×C22⋊C4—44no—
400C2×C22⋊C4—138no—
401C2×C22⋊C4—134no—
402C2×C22⋊C4—138no—
403C2×C22⋊C4—134no—
404C2×C22⋊C4—138no—
405C2×C22⋊C4—138no—
406C2×C22⋊C4—138no—
407C2×C22⋊C4—268no—
408C2×C22⋊C4—268no—
409C2×C22⋊C4—524no—
410C2×C22⋊C4C22×D1318yes—
411C2×C42—138no—
412C2×C42—134no—
413C2×C42—138no—
414C2×C42—138no—
415C2×C42—138no—
416C2×C42—268no—
417C2×C42—268no—
418C2×C42—268no—
419#95—138no—
420#95—138no—
421#95C22×D1318yes—
422C2×C13—44no—
423C2×C13#235418yescomplemented
424C2×C13C22×#11711yescharacteristic
425C2×C13C22×C4×D411yescharacteristic
426C2×C13C2×#52011yescharacteristic
427C2×C13C2×#54711yescharacteristic
428C2×C13C2×#55011yescharacteristic
429C2×C13C2×#55511yescharacteristic
430C2×C13C2×#55611yescharacteristic
431D13—44no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—134no—
439C24—132no—
440C24—262no—
441C24—262no—
442C24—262no—
443C24—262no—
444C24—262no—
445C24—262no—
446C24C2×C4×D1314yes—
447C24C23×D1312yes—
448C24C23×D1311yescharacteristic
449C2×D4—1316no—
450C2×D4—2632no—
451C2×D4—268no—
452C2×D4—268no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—232no—
456C22×C4—28no—
457C22×C4—28no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—134no—
465C22×C4—134no—
466C22×C4—134no—
467C22×C4—132no—
468C22×C4—134no—
469C22×C4—134no—
470C22×C4—138no—
471C22×C4—132no—
472C22×C4—132no—
473C22×C4—134no—
474C22×C4—1316no—
475C22×C4—134no—
476C22×C4—262no—
477C22×C4—262no—
478C22×C4—262no—
479C22×C4—262no—
480C22×C4—264no—
481C22×C4—264no—
482C22×C4—2632no—
483C22×C4—268no—
484C22×C4—268no—
485C22×C4—264no—
486C22×C4—264no—
487C22×C4—264no—
488C22×C4C2×C4×D1314yes—
489C22×C4C2×C4×D13116yes—
490C22×C4C2×C4×D1314yes—
491C22×C4D4×D1314yes—
492C22×C4#612914yes—
493C22×C4C23×D1314yes—
494C22×C4C23×D1314yes—
495C22×C4C23×D1312yes—
496C22×C4C23×D1312yes—
497C4⋊C4—28no—
498C4⋊C4—28no—
499C4⋊C4—1316no—
500C4⋊C4—1316no—
501C4⋊C4—2616no—
502C4⋊C4—268no—
503C4⋊C4—528no—
504C22⋊C4—48no—
505C22⋊C4—1316no—
506C22⋊C4—1316no—
507C22⋊C4—2616no—
508C22⋊C4—2616no—
509C22⋊C4—528no—
510C42—1316no—
511C42—2616no—
512C42—2616no—
513C42—2616no—
514C13C2×#235411yescharacteristic, complemented, Sylow
515C23—28no—
516C23—28no—
517C23—28no—
518C23—22no—
519C23—22no—
520C23—22no—
521C23—22no—
522C23—22no—
523C23—22no—
524C23—44no—
525C23—44no—
526C23—44no—
527C23—44no—
528C23—134no—
529C23—268no—
530C23—268no—
531C23—268no—
532C23—262no—
533C23—262no—
534C23—262no—
535C23—262no—
536C23—262no—
537C23—262no—
538C23—524no—
539C23—524no—
540C23—524no—
541C23—524no—
542C23C22×C4×D1314yes—
543C23C22×C4×D1312yes—
544C23C2×D4×D1312yes—
545C23C2×#612912yes—
546C23#8825112yes—
547C23#8825412yes—
548C23#41×D1312yes—
549C23#41×D1312yes—
550C23C24×D1311yescharacteristic
551D4—2632no—
552C2×C4—28no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—232no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—48no—
563C2×C4—48no—
564C2×C4—1316no—
565C2×C4—134no—
566C2×C4—134no—
567C2×C4—134no—
568C2×C4—134no—
569C2×C4—134no—
570C2×C4—138no—
571C2×C4—268no—
572C2×C4—268no—
573C2×C4—2616no—
574C2×C4—262no—
575C2×C4—262no—
576C2×C4—262no—
577C2×C4—262no—
578C2×C4—264no—
579C2×C4—264no—
580C2×C4—2632no—
581C2×C4—264no—
582C2×C4—264no—
583C2×C4—264no—
584C2×C4—528no—
585C2×C4#88135116yes—
586C2×C4C22×C4×D1314yes—
587C2×C4C22×C4×D1314yes—
588C2×C4C2×D4×D1314yes—
589C2×C4C2×#612914yes—
590C22—24no—
591C22—24no—
592C22—24no—
593C22—416no—
594C22—42no—
595C22—42no—
596C22—42no—
597C22—42no—
598C22—264no—
599C22—264no—
600C22—264no—
601C22—5216no—
602C22—522no—
603C22—522no—
604C22—522no—
605C22—522no—
606C22C2×#8813514yes—
607C22#1171920914yes—
608C22D13×#11714yes—
609C22#1171930414yes—
610C22#1171932114yes—
611C22#1171933614yes—
612C22#1171934614yes—
613C22C23×C4×D1311yescharacteristic
614C22C22×D4×D1311yescharacteristic
615C22C22×#612911yescharacteristic
616C22C2×#8825111yescharacteristic
617C22C2×#8825411yescharacteristic
618C22C2×#41×D1311yescharacteristic
619C22C2×#41×D1311yescharacteristic
620C4—24no—
621C4—44no—
622C4—44no—
623C4—138no—
624C4—264no—
625C4—264no—
626C4—268no—
627C4—524no—
628C4C2×#8813518yes—
629C2—44no—
630C2—524no—
631C2#1311778018yesdirect product factor
632C2C2×D13×#11711yescharacteristic
633C2C22×#8813511yescharacteristic
634C2C2×#1171920911yescharacteristic
635C2C2×#1171933611yescharacteristic
636C2C2×#1171930411yescharacteristic
637C2C2×#1171932111yescharacteristic
638C2C2×#1171934611yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C13×#380C2
socleC24×C13C24
prime radicalC23×C22⋊D13C22
cosocleC23×C13C25
hypercenterC2×#380D13
hypocenterC13C2×#2354
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C22×#88180C2semidirect
3. C22×#88146C2semidirect
4. #13117780C2direct (N × H)
6. C2×#11718606C2semidirect
7. C2×#11718330C2semidirect
8. C2×#11718637C2semidirect
9. C2×#11718648C2semidirect
10. C2×C4⋊C4×Dic13C2semidirect
11. C2×#11718310C2semidirect
12. C2×C13×#380C2semidirect
21. C2×C4×C22⋊D13C4semidirect
27. C2×#88180C22semidirect
38. C2×#88146C22semidirect
39. C13×#380C22semidirect
43. #11718648C22semidirect
44. #11718637C22semidirect
45. C4⋊C4×Dic13C22semidirect
47. #11718606C22semidirect
48. #11718330C22semidirect
49. #11718310C22semidirect
83. C4×C22⋊D13C2×C4semidirect
92. C2×C4⋊Dic13D4semidirect
188. C4⋊Dic13C2×D4semidirect
205. C2×#380D13semidirect
275. C2×Dic13#117semidirect
314. #380C2×D13semidirect
358. Dic13C2×#117semidirect
423. C2×C13#2354semidirect
514. C13C2×#2354semidirect
631. C2#13117780direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D132
C22×#881802
C22×#881462
#131177802
C2×#117186182
C2×#117186062
C2×#117183302
C2×#117186372
C2×#117186482
C2×C4⋊C4×Dic132
C2×#117183102
C2×C13×#3802
C2×#235413