Finite Group Databasebeta

← C2×#13119127 #16032432

Subgroups — C2×#13119127 #16032432

Order 3328.

3070 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D13C211yesmaximal, characteristic
2#13119127C2116yesmaximal, direct product factor
3C2×#11718613C212yesmaximal, complemented
4C2×#11718620C212yesmaximal
5C2×#11718634C211yesmaximal, characteristic, complemented
6C2×#11718634C211yesmaximal, characteristic, complemented
7C2×#11718601C212yesmaximal, complemented
8C2×#11718594C212yesmaximal, complemented
9C2×#11718873C211yesmaximal, characteristic, complemented
10C2×#11718648C211yesmaximal, characteristic, complemented
11C2×#11718648C211yesmaximal, characteristic, complemented
12C22×C13×#117C211yesmaximal, characteristic, complemented
13C24×C4×C13C2211yescharacteristic
14C23×C22⋊D13C2211yescharacteristic
15C23×C4×D13C2211yescharacteristic
16C2×C13×#117—28no—
17C2×C13×#117C2218yescomplemented
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2212yes—
21C22×C42×C13C2212yes—
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2212yes—
24C2×C4×C22⋊D13—28no—
25C2×C4×C22⋊D13C2218yes—
26C22×#6103C2212yes—
27C22×#6103C2211yescharacteristic
28C22×#6103C2212yes—
29C22×C4⋊Dic13C2211yescharacteristic
30C22×C4⋊Dic13C2211yescharacteristic
31C22×#6101C2211yescharacteristic
32C22×#6101C2212yes—
33C22×#6101C2212yes—
34C22×C4×Dic13C2211yescharacteristic
35#11718873C2218yescomplemented
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38C2×#88071C2212yes—
39C2×#88071C2212yes—
40C2×#88071C2212yes—
41#11718648C2218yescomplemented
42#11718648C2218yescomplemented
43#11718634C2218yescomplemented
44#11718634C2218yescomplemented
45#11718620C22116yes—
46#11718613C22116yescomplemented
47#11718601C22116yescomplemented
48#11718594C22116yescomplemented
49C25×C13C2311yescharacteristic
50C24×D13C2311yescharacteristic
51C23×C4×C13—24no—
52C23×C4×C13—24no—
53C23×C4×C13D418yes—
54C23×C4×C13C2312yes—
55C23×C4×C13C2312yes—
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2314yes—
58C23×C4×C13C2311yescharacteristic
59C22×C22⋊D13—24no—
60C22×C22⋊D13—24no—
61C22×C22⋊D13—24no—
62C22×C22⋊D13C2314yes—
63C23×Dic13C2311yescharacteristic
64C23×Dic13C2312yes—
65C23×Dic13C2312yes—
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C22×C4×D13—24no—
69C22×C4×D13—24no—
70C22×C4×D13—24no—
71C22×C4×D13C2314yes—
72C13×#117—232no—
73C2×C13×C4⋊C4—24no—
74C2×C13×C4⋊C4—24no—
75C2×C13×C4⋊C4C2314yes—
76C2×C13×C4⋊C4C2314yes—
77C2×C13×C22⋊C4—28no—
78C2×C13×C22⋊C4C2318yes—
79C2×C42×C13—28no—
80C2×C42×C13C2318yes—
81C2×C22⋊Dic13—24no—
82C2×C22⋊Dic13—44no—
83C2×C22⋊Dic13C2314yes—
84C2×C22⋊Dic13C2318yes—
85C4×C22⋊D13—232no—
86C2×#6103—28no—
87C2×#6103—24no—
88C2×#6103—44no—
89C2×#6103C2314yes—
90C2×#6103C2318yes—
91C2×#6103C2318yes—
92C2×C4⋊Dic13—24no—
93C2×C4⋊Dic13—24no—
94C2×C4⋊Dic13C2314yes—
95C2×C4⋊Dic13C2314yes—
96C2×#6101—24no—
97C2×#6101—28no—
98C2×#6101—44no—
99C2×#6101C2314yes—
100C2×#6101C2318yes—
101C2×#6101C2318yes—
102C2×C4×Dic13—24no—
103C2×C4×Dic13C2314yes—
104#88071C2318yes—
105#88071C2318yes—
106#88071C2318yes—
107#88071C2318yes—
108#88071C2318yes—
109C2×#2485—131nomaximal, Sylow
110C24×C13—22no—
111C24×C13—22no—
112C24×C13—22no—
113C24×C13—22no—
114C24×C13—22no—
115C24×C13—22no—
116C24×C13C2×D414yes—
117C24×C13C2412yes—
118C24×C13C2411yescharacteristic
119C23×D13—22no—
120C23×D13—22no—
121C23×D13—22no—
122C23×D13—22no—
123C23×D13—22no—
124C23×D13—22no—
125C23×D13#4114yes—
126C23×D13C2412yes—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—232no—
130C22×C4×C13—28no—
131C22×C4×C13—28no—
132C22×C4×C13—24no—
133C22×C4×C13—24no—
134C22×C4×C13—24no—
135C22×C4×C13—24no—
136C22×C4×C13—24no—
137C22×C4×C13—24no—
138C22×C4×C13C2×D414yes—
139C22×C4×C13C2×D4116yes—
140C22×C4×C13C2×D414yes—
141C22×C4×C13#4114yes—
142C22×C4×C13#4114yes—
143C22×C4×C13C2414yes—
144C22×C4×C13C2414yes—
145C22×C4×C13C2412yes—
146C22×C4×C13C2412yes—
147C2×C22⋊D13—232no—
148C2×C22⋊D13—28no—
149C2×C22⋊D13—28no—
150C2×C22⋊D13—28no—
151C22×Dic13—22no—
152C22×Dic13—22no—
153C22×Dic13—22no—
154C22×Dic13—22no—
155C22×Dic13—24no—
156C22×Dic13—24no—
157C22×Dic13—24no—
158C22×Dic13—24no—
159C22×Dic13—22no—
160C22×Dic13—22no—
161C22×Dic13—22no—
162C22×Dic13—24no—
163C22×Dic13—24no—
164C22×Dic13—22no—
165C22×Dic13#4114yes—
166C22×Dic13C2412yes—
167C22×Dic13C2414yes—
168C22×Dic13C2414yes—
169C22×Dic13C2412yes—
170C22×Dic13C2412yes—
171C2×C4×D13—28no—
172C2×C4×D13—28no—
173C2×C4×D13—28no—
174C2×C4×D13—416no—
175C13×C4⋊C4—28no—
176C13×C4⋊C4—28no—
177C13×C22⋊C4—216no—
178C42×C13—216no—
179C22⋊Dic13—28no—
180C22⋊Dic13—48no—
181#6103—216no—
182#6103—28no—
183#6103—48no—
184C4⋊Dic13—28no—
185C4⋊Dic13—28no—
186#6101—28no—
187#6101—216no—
188#6101—48no—
189C4×Dic13—28no—
190C22×C4×D4—131no—
191C22×#117D1311yescharacteristic, complemented
192#2485—1316no—
193C2×#397—132no—
194C2×#394—132no—
195C2×#389—131no—
196C2×#389—131no—
197C2×#388—132no—
198C2×#387—132no—
199C2×#380—131no—
200C2×#380—131no—
201C2×#380—131no—
202C23×C13—28no—
203C23×C13—28no—
204C23×C13—28no—
205C23×C13—22no—
206C23×C13—22no—
207C23×C13—22no—
208C23×C13—22no—
209C23×C13—22no—
210C23×C13—22no—
211C23×C13—44no—
212C23×C13—44no—
213C23×C13—44no—
214C23×C13—44no—
215C23×C13C22×D414yes—
216C23×C13C22×D412yes—
217C23×C13C2×#4112yes—
218C23×C13C2×#4112yes—
219C23×C13C2×#4112yes—
220C23×C13C2×#4112yes—
221C23×C13H(5,𝔽2)12yes—
222C23×C132−1+412yes—
223C23×C13C2511yescharacteristic
224C22×D13—28no—
225C22×D13—28no—
226C22×D13—28no—
227C22×D13—22no—
228C22×D13—22no—
229C22×D13—22no—
230C22×D13—22no—
231C22×D13—22no—
232C22×D13—22no—
233C22×D13—44no—
234C22×D13—44no—
235C22×D13—44no—
236C22×D13—44no—
237C22×D13C2×#4114yes—
238C2×C4×C13—28no—
239C2×C4×C13—22no—
240C2×C4×C13—22no—
241C2×C4×C13—232no—
242C2×C4×C13—24no—
243C2×C4×C13—24no—
244C2×C4×C13—24no—
245C2×C4×C13—24no—
246C2×C4×C13—24no—
247C2×C4×C13—24no—
248C2×C4×C13—48no—
249C2×C4×C13—48no—
250C2×C4×C13#123116yes—
251C2×C4×C13C22×D414yes—
252C2×C4×C13C22×D414yes—
253C2×C4×C13C2×#4114yes—
254C2×C4×C13C2×#4114yes—
255C22⋊D13—232no—
256C2×Dic13—28no—
257C2×Dic13—22no—
258C2×Dic13—22no—
259C2×Dic13—22no—
260C2×Dic13—22no—
261C2×Dic13—24no—
262C2×Dic13—24no—
263C2×Dic13—24no—
264C2×Dic13—24no—
265C2×Dic13—22no—
266C2×Dic13—22no—
267C2×Dic13—22no—
268C2×Dic13—24no—
269C2×Dic13—24no—
270C2×Dic13—22no—
271C2×Dic13—44no—
272C2×Dic13—44no—
273C2×Dic13—48no—
274C2×Dic13—48no—
275C2×Dic13C2×#4114yes—
276C4×D13—416no—
277C23×D4—131no—
278C24×C4—131no—
279C24×C4C2×D1311yescharacteristic
280C2×C4×D4—138no—
281C2×C4×D4—268no—
282C2×#117—28no—
283C2×#117C2×D1318yescomplemented
284C22×C4⋊C4—132no—
285C22×C4⋊C4—131no—
286C22×C4⋊C4—131no—
287C22×C4⋊C4—131no—
288C22×C4⋊C4—132no—
289C22×C4⋊C4C2×D1311yescharacteristic
290C22×C4⋊C4C2×D1311yescharacteristic
291C22×C22⋊C4—131no—
292C22×C22⋊C4—132no—
293C22×C22⋊C4—131no—
294C22×C22⋊C4—132no—
295C22×C22⋊C4—132no—
296C22×C22⋊C4C2×D1312yes—
297C22×C42—131no—
298C22×C42C2×D1312yes—
299#397—1316no—
300#394—1316no—
301#389—138no—
302#389—138no—
303#388—1316no—
304#387—1316no—
305#380—138no—
306#380—138no—
307#380—138no—
308C2×#95—132no—
309C2×#95—132no—
310C2×#95—132no—
311C2×#95—132no—
312C2×#95—132no—
313C22×C13—24no—
314C22×C13—24no—
315C22×C13—24no—
316C22×C13—42no—
317C22×C13—42no—
318C22×C13—42no—
319C22×C13—42no—
320C22×C13—416no—
321C22×C13C2×#12314yes—
322C22×C13#52514yes—
323C22×C13#53714yes—
324C22×C13#55214yes—
325C22×C13#55314yes—
326C22×C13#55514yes—
327C22×C13#55614yes—
328C22×C13C23×D411yescharacteristic
329C22×C13C22×#4111yescharacteristic
330C22×C13C22×#4111yescharacteristic
331C22×C13C22×#4111yescharacteristic
332C22×C13C22×#4111yescharacteristic
333C22×C13C2×H(5,𝔽2)11yescharacteristic
334C22×C13C2×2−1+411yescharacteristic
335C2×D13—24no—
336C2×D13—24no—
337C2×D13—24no—
338C2×D13—42no—
339C2×D13—42no—
340C2×D13—42no—
341C2×D13—42no—
342C2×D13—416no—
343C4×C13—24no—
344C4×C13—44no—
345C4×C13—44no—
346C4×C13C2×#12318yes—
347Dic13—24no—
348Dic13—42no—
349Dic13—42no—
350Dic13—44no—
351Dic13—44no—
352C25—131no—
353C25C22×D1311yescharacteristic
354C22×D4—134no—
355C22×D4—264no—
356C22×D4—264no—
357C22×D4—264no—
358C23×C4—24no—
359C23×C4—24no—
360C23×C4—131no—
361C23×C4—132no—
362C23×C4—132no—
363C23×C4—131no—
364C23×C4—131no—
365C23×C4—134no—
366C23×C4—264no—
367C23×C4—264no—
368C23×C4—264no—
369C23×C4C22⋊D1318yes—
370C23×C4C22×D1312yes—
371C23×C4C22×D1312yes—
372C23×C4C22×D1314yes—
373C23×C4C22×D1311yescharacteristic
374C23×C4C22×D1311yescharacteristic
375C4×D4—2632no—
376#117—232no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—134no—
380C2×C4⋊C4—138no—
381C2×C4⋊C4—134no—
382C2×C4⋊C4—134no—
383C2×C4⋊C4—138no—
384C2×C4⋊C4—268no—
385C2×C4⋊C4—264no—
386C2×C4⋊C4—264no—
387C2×C4⋊C4—264no—
388C2×C4⋊C4—524no—
389C2×C4⋊C4C22×D1314yes—
390C2×C4⋊C4C22×D1314yes—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—134no—
393C2×C22⋊C4—134no—
394C2×C22⋊C4—138no—
395C2×C22⋊C4—138no—
396C2×C22⋊C4—138no—
397C2×C22⋊C4—268no—
398C2×C22⋊C4—264no—
399C2×C22⋊C4—264no—
400C2×C22⋊C4—524no—
401C2×C22⋊C4—524no—
402C2×C22⋊C4C22×D1318yes—
403C2×C42—28no—
404C2×C42—134no—
405C2×C42—264no—
406C2×C42C22×D1318yes—
407#95—138no—
408#95—138no—
409#95—138no—
410#95—138no—
411#95—138no—
412C2×C13—44no—
413C2×C13#248518yescomplemented
414C2×C13C22×#12311yescharacteristic
415C2×C13C2×#52511yescharacteristic
416C2×C13C2×#53711yescharacteristic
417C2×C13C2×#55211yescharacteristic
418C2×C13C2×#55311yescharacteristic
419C2×C13C2×#55511yescharacteristic
420C2×C13C2×#55611yescharacteristic
421D13—44no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—134no—
429C24—132no—
430C24—262no—
431C24—262no—
432C24—262no—
433C24—262no—
434C24—262no—
435C24—262no—
436C24C2×C22⋊D1314yes—
437C24C23×D1312yes—
438C24C23×D1311yescharacteristic
439C2×D4—268no—
440C2×D4—268no—
441C2×D4—2632no—
442C2×D4—268no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—232no—
446C22×C4—28no—
447C22×C4—28no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—134no—
455C22×C4—132no—
456C22×C4—132no—
457C22×C4—134no—
458C22×C4—134no—
459C22×C4—132no—
460C22×C4—262no—
461C22×C4—262no—
462C22×C4—264no—
463C22×C4—264no—
464C22×C4—262no—
465C22×C4—262no—
466C22×C4—264no—
467C22×C4—264no—
468C22×C4—264no—
469C22×C4—264no—
470C22×C4—262no—
471C22×C4—262no—
472C22×C4—262no—
473C22×C4—262no—
474C22×C4—268no—
475C22×C4—268no—
476C22×C4—268no—
477C22×C4—5216no—
478C22×C4#612714yes—
479C22×C4#612714yes—
480C22×C4C2×C22⋊D1314yes—
481C22×C4C2×C22⋊D13116yes—
482C22×C4C2×C22⋊D1314yes—
483C22×C4C23×D1314yes—
484C22×C4C23×D1314yes—
485C22×C4C23×D1312yes—
486C22×C4C23×D1312yes—
487C4⋊C4—28no—
488C4⋊C4—28no—
489C4⋊C4—2616no—
490C4⋊C4—268no—
491C4⋊C4—268no—
492C4⋊C4—268no—
493C4⋊C4—528no—
494C22⋊C4—216no—
495C22⋊C4—2616no—
496C22⋊C4—268no—
497C22⋊C4—268no—
498C22⋊C4—528no—
499C22⋊C4—528no—
500C42—216no—
501C42—268no—
502C13C2×#248511yescharacteristic, complemented, Sylow
503C23—28no—
504C23—28no—
505C23—28no—
506C23—22no—
507C23—22no—
508C23—22no—
509C23—22no—
510C23—22no—
511C23—22no—
512C23—44no—
513C23—44no—
514C23—44no—
515C23—44no—
516C23—134no—
517C23—268no—
518C23—268no—
519C23—268no—
520C23—262no—
521C23—262no—
522C23—262no—
523C23—262no—
524C23—262no—
525C23—262no—
526C23—524no—
527C23—524no—
528C23—524no—
529C23—524no—
530C23C2×#612712yes—
531C23C2×#612712yes—
532C23#41×D1312yes—
533C23#41×D1312yes—
534C23#8825612yes—
535C23#8825712yes—
536C23C22×C22⋊D1314yes—
537C23C22×C22⋊D1312yes—
538C23C24×D1311yescharacteristic
539D4—2632no—
540C2×C4—28no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—232no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—48no—
551C2×C4—48no—
552C2×C4—134no—
553C2×C4—268no—
554C2×C4—262no—
555C2×C4—262no—
556C2×C4—264no—
557C2×C4—264no—
558C2×C4—262no—
559C2×C4—262no—
560C2×C4—264no—
561C2×C4—264no—
562C2×C4—264no—
563C2×C4—264no—
564C2×C4—262no—
565C2×C4—262no—
566C2×C4—262no—
567C2×C4—262no—
568C2×C4—528no—
569C2×C4—528no—
570C2×C4—524no—
571C2×C4—524no—
572C2×C4—5216no—
573C2×C4#88183116yes—
574C2×C4C2×#612714yes—
575C2×C4C2×#612714yes—
576C2×C4C22×C22⋊D1314yes—
577C2×C4C22×C22⋊D1314yes—
578C22—24no—
579C22—24no—
580C22—24no—
581C22—416no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—264no—
587C22—264no—
588C22—264no—
589C22—522no—
590C22—5216no—
591C22—522no—
592C22—522no—
593C22—522no—
594C22#1171923414yes—
595C22#1171923514yes—
596C22#1171923714yes—
597C22#1171923814yes—
598C22C2×#8818314yes—
599C22#1171953314yes—
600C22#1171953814yes—
601C22C22×#612711yescharacteristic
602C22C22×#612711yescharacteristic
603C22C2×#41×D1311yescharacteristic
604C22C2×#41×D1311yescharacteristic
605C22C2×#8825611yescharacteristic
606C22C2×#8825711yescharacteristic
607C22C23×C22⋊D1311yescharacteristic
608C4—24no—
609C4—44no—
610C4—44no—
611C4—264no—
612C4—522no—
613C4—524no—
614C4—524no—
615C4—522no—
616C4C2×#8818318yes—
617C2—44no—
618C2—524no—
619C2#1311912718yesdirect product factor
620C2C22×#8818311yescharacteristic
621C2C2×#1171953311yescharacteristic
622C2C2×#1171953811yescharacteristic
623C2C2×#1171923411yescharacteristic
624C2C2×#1171923511yescharacteristic
625C2C2×#1171923711yescharacteristic
626C2C2×#1171923811yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C13×#117C2
socleC24×C13C24
prime radicalC23×C22⋊D13C22
hypercenterC22×#117D13
hypocenterC13C2×#2485
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
2. #13119127C2direct (N × H)
3. C2×#11718613C2semidirect
5. C2×#11718634C2semidirect
6. C2×#11718634C2semidirect
7. C2×#11718601C2semidirect
8. C2×#11718594C2semidirect
9. C2×#11718873C2semidirect
10. C2×#11718648C2semidirect
11. C2×#11718648C2semidirect
12. C22×C13×#117C2semidirect
17. C2×C13×#117C22semidirect
35. #11718873C22semidirect
41. #11718648C22semidirect
42. #11718648C22semidirect
43. #11718634C22semidirect
44. #11718634C22semidirect
46. #11718613C22semidirect
47. #11718601C22semidirect
48. #11718594C22semidirect
191. C22×#117D13semidirect
283. C2×#117C2×D13semidirect
413. C2×C13#2485semidirect
502. C13C2×#2485semidirect
619. C2#13119127direct (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
#131191272
C2×#117186132
C2×#117186202
C2×#117186342
C2×#117186012
C2×#117185942
C2×#117188732
C2×#117186482
C22×C13×#1172
C2×#248513