Finite Group Databasebeta

← C2×#13120001 #16034204

Subgroups — C2×#13120001 #16034204

Order 3328.

3006 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×#88144C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D13C211yesmaximal, characteristic
3#13120001C2116yesmaximal, direct product factor
4C2×#11718321C212yesmaximal, complemented
5C2×#11718622C212yesmaximal
6C2×#11718330C212yesmaximal, complemented
7C2×#11718605C212yesmaximal, complemented
8C2×#11718873C211yesmaximal, characteristic, complemented
9C2×#11718648C211yesmaximal, characteristic, complemented
10C2×#11718648C211yesmaximal, characteristic, complemented
11C2×C4⋊C4×Dic13C211yesmaximal, characteristic, 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⋊D13—28no—
22C2×C4×C22⋊D13C2218yes—
23C22×#6103C2212yes—
24C22×#6103C2211yescharacteristic
25C22×#6103C2212yes—
26C22×C4⋊Dic13C2211yescharacteristic
27C22×C4⋊Dic13C2211yescharacteristic
28C22×C4⋊Dic13C2212yes—
29C22×#6101C2211yescharacteristic
30C22×#6101C2212yes—
31C22×C4×Dic13C2212yes—
32C22×C4×Dic13C2211yescharacteristic
33C2×#88144—28no—
34C2×#88144C2218yescomplemented
35C13×#380C2218yescomplemented
36C2×C13×#95C2212yes—
37#11718873C2218yescomplemented
38C2×#88071C2212yes—
39C2×#88071C2212yes—
40C2×#88071C2212yes—
41C2×#88071C2212yes—
42#11718648C2218yescomplemented
43#11718648C2218yescomplemented
44C4⋊C4×Dic13C2218yescomplemented
45#11718622C22116yes—
46#11718605C22116yescomplemented
47#11718330C22116yescomplemented
48#11718321C22116yescomplemented
49C25×C13C2311yescharacteristic
50C24×D13C2311yescharacteristic
51C23×C4×C13—24no—
52C23×C4×C13—24no—
53C23×C4×C13—24no—
54C23×C4×C13C2314yes—
55C23×C4×C13C2312yes—
56C23×C4×C13C2312yes—
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C22×C22⋊D13—24no—
60C22×C22⋊D13—24no—
61C22×C22⋊D13—24no—
62C22×C22⋊D13C2314yes—
63C23×Dic13C2312yes—
64C23×Dic13C2312yes—
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C22×C4×D13—24no—
69C22×C4×D13—24no—
70C22×C4×D13—24no—
71C22×C4×D13C2314yes—
72C2×C13×C4⋊C4—24no—
73C2×C13×C4⋊C4—24no—
74C2×C13×C4⋊C4C2314yes—
75C2×C13×C4⋊C4C2314yes—
76C2×C13×C22⋊C4—44no—
77C2×C13×C22⋊C4C2318yes—
78C2×C22⋊Dic13—28no—
79C2×C22⋊Dic13—24no—
80C2×C22⋊Dic13C2314yes—
81C2×C22⋊Dic13C2318yes—
82C4×C22⋊D13—232no—
83C2×#6103—28no—
84C2×#6103—24no—
85C2×#6103—44no—
86C2×#6103C2314yes—
87C2×#6103C2318yes—
88C2×#6103C2318yes—
89C2×C4⋊Dic13—24no—
90C2×C4⋊Dic13—24no—
91C2×C4⋊Dic13—28no—
92C2×C4⋊Dic13C2318yes—
93C2×C4⋊Dic13C2314yes—
94C2×C4⋊Dic13C2314yes—
95C2×#6101—28no—
96C2×#6101—24no—
97C2×#6101C2318yes—
98C2×#6101C2314yes—
99C2×C4×Dic13—44no—
100C2×C4×Dic13D418yes—
101C2×C4×Dic13C2318yes—
102C2×C4×Dic13C2314yes—
103#88144—232no—
104C13×#95C2318yes—
105#88071C2318yes—
106#88071C2318yes—
107#88071C2318yes—
108#88071C2318yes—
109C2×#2562—131nomaximal, Sylow
110C24×C13—22no—
111C24×C13—22no—
112C24×C13—22no—
113C24×C13—22no—
114C24×C13—22no—
115C24×C13—22no—
116C24×C13#4114yes—
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—24no—
128C22×C4×C13—22no—
129C22×C4×C13—24no—
130C22×C4×C13—24no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—24no—
134C22×C4×C13—24no—
135C22×C4×C13—24no—
136C22×C4×C13—28no—
137C22×C4×C13—28no—
138C22×C4×C13—28no—
139C22×C4×C13—416no—
140C22×C4×C13C2×D414yes—
141C22×C4×C13#4114yes—
142C22×C4×C13#4114yes—
143C22×C4×C13C2412yes—
144C22×C4×C13C2414yes—
145C22×C4×C13C2414yes—
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—22no—
157C22×Dic13—24no—
158C22×Dic13—24no—
159C22×Dic13—24no—
160C22×Dic13—24no—
161C22×Dic13—22no—
162C22×Dic13—22no—
163C22×Dic13—24no—
164C22×Dic13C2×D414yes—
165C22×Dic13C2×D414yes—
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—48no—
178C22⋊Dic13—216no—
179C22⋊Dic13—28no—
180#6103—216no—
181#6103—28no—
182#6103—48no—
183C4⋊Dic13—28no—
184C4⋊Dic13—28no—
185C4⋊Dic13—216no—
186#6101—216no—
187#6101—28no—
188C4×Dic13—48no—
189C4×Dic13C2×D4116yes—
190C22×#125—131no—
191C22×C4×D4—131no—
192#2562—1316no—
193C2×#400—132no—
194C2×#394—132no—
195C2×#388—132no—
196C2×#388—132no—
197C2×#380—131no—
198C2×#380—131no—
199C2×#380—131no—
200C2×#380D1311yescharacteristic, complemented
201C2×C4×C4⋊C4—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×D412yes—
216C23×C13C2×#4114yes—
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—24no—
239C2×C4×C13—22no—
240C2×C4×C13—24no—
241C2×C4×C13—24no—
242C2×C4×C13—22no—
243C2×C4×C13—22no—
244C2×C4×C13—24no—
245C2×C4×C13—24no—
246C2×C4×C13—24no—
247C2×C4×C13—44no—
248C2×C4×C13—48no—
249C2×C4×C13—48no—
250C2×C4×C13—416no—
251C2×C4×C13#124116yes—
252C2×C4×C13C22×D414yes—
253C2×C4×C13C2×#4114yes—
254C2×C4×C13C2×#4114yes—
255C22⋊D13—232no—
256C2×Dic13—28no—
257C2×Dic13—28no—
258C2×Dic13—22no—
259C2×Dic13—22no—
260C2×Dic13—22no—
261C2×Dic13—22no—
262C2×Dic13—24no—
263C2×Dic13—22no—
264C2×Dic13—24no—
265C2×Dic13—24no—
266C2×Dic13—24no—
267C2×Dic13—24no—
268C2×Dic13—22no—
269C2×Dic13—22no—
270C2×Dic13—24no—
271C2×Dic13—48no—
272C2×Dic13—44no—
273C2×Dic13—48no—
274C2×Dic13C22×D414yes—
275C2×Dic13C22×D414yes—
276C4×D13—416no—
277C23×D4—131no—
278C24×C4—131no—
279C24×C4C2×D1311yescharacteristic
280C2×#125—138no—
281C2×#125—268no—
282C2×C4×D4—138no—
283C2×C4×D4—268no—
284C22×C4⋊C4—131no—
285C22×C4⋊C4—132no—
286C22×C4⋊C4—132no—
287C22×C4⋊C4—131no—
288C22×C4⋊C4—131no—
289C22×C4⋊C4C2×D1311yescharacteristic
290C22×C4⋊C4C2×D1311yescharacteristic
291C22×C22⋊C4—132no—
292C22×C22⋊C4—131no—
293C22×C22⋊C4—132no—
294C22×C22⋊C4—131no—
295C22×C22⋊C4—132no—
296C22×C22⋊C4C2×D1312yes—
297C22×C42—131no—
298C22×C42—132no—
299#400—1316no—
300#394—1316no—
301#388—1316no—
302#388—1316no—
303#380—138no—
304#380—138no—
305#380—138no—
306#380C2×D1318yescomplemented
307C4×C4⋊C4—138no—
308C2×#95—132no—
309C2×#95—132no—
310C2×#95—132no—
311C2×#95—132no—
312C2×#95C2×D1312yes—
313C22×C13—24no—
314C22×C13—24no—
315C22×C13—24no—
316C22×C13—416no—
317C22×C13—42no—
318C22×C13—42no—
319C22×C13—42no—
320C22×C13—42no—
321C22×C13#52514yes—
322C22×C13C2×#12414yes—
323C22×C13#53714yes—
324C22×C13#55214yes—
325C22×C13#55214yes—
326C22×C13#55314yes—
327C22×C13#55314yes—
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—416no—
339C2×D13—42no—
340C2×D13—42no—
341C2×D13—42no—
342C2×D13—42no—
343C4×C13—42no—
344C4×C13—44no—
345C4×C13—44no—
346C4×C13C2×#12418yes—
347Dic13—24no—
348Dic13—24no—
349Dic13—44no—
350Dic13—42no—
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—24no—
361C23×C4—131no—
362C23×C4—131no—
363C23×C4—132no—
364C23×C4—132no—
365C23×C4—131no—
366C23×C4—134no—
367C23×C4—264no—
368C23×C4—264no—
369C23×C4—264no—
370C23×C4C22×D1314yes—
371C23×C4C22×D1312yes—
372C23×C4C22×D1312yes—
373C23×C4C22×D1311yescharacteristic
374C23×C4C22×D1311yescharacteristic
375#125—2632no—
376C4×D4—2632no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—134no—
380C2×C4⋊C4—138no—
381C2×C4⋊C4—134no—
382C2×C4⋊C4—138no—
383C2×C4⋊C4—134no—
384C2×C4⋊C4—264no—
385C2×C4⋊C4—268no—
386C2×C4⋊C4—268no—
387C2×C4⋊C4—264no—
388C2×C4⋊C4—264no—
389C2×C4⋊C4C22×D1314yes—
390C2×C4⋊C4C22×D1314yes—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—134no—
393C2×C22⋊C4—138no—
394C2×C22⋊C4—134no—
395C2×C22⋊C4—138no—
396C2×C22⋊C4—138no—
397C2×C22⋊C4—264no—
398C2×C22⋊C4—268no—
399C2×C22⋊C4—264no—
400C2×C22⋊C4—268no—
401C2×C22⋊C4—524no—
402C2×C22⋊C4C22×D1318yes—
403C2×C42—138no—
404C2×C42—134no—
405C2×C42—138no—
406C2×C42—524no—
407#95—138no—
408#95—138no—
409#95—138no—
410#95—138no—
411#95C22×D1318yes—
412C2×C13—44no—
413C2×C13#256218yescomplemented
414C2×C13C2×#52511yescharacteristic
415C2×C13C22×#12411yescharacteristic
416C2×C13C2×#53711yescharacteristic
417C2×C13C2×#55211yescharacteristic
418C2×C13C2×#55211yescharacteristic
419C2×C13C2×#55311yescharacteristic
420C2×C13C2×#55311yescharacteristic
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—
436C24#613114yes—
437C24C23×D1312yes—
438C24C23×D1311yescharacteristic
439C2×D4—268no—
440C2×D4—268no—
441C2×D4—2632no—
442C2×D4—268no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—28no—
453C22×C4—28no—
454C22×C4—28no—
455C22×C4—416no—
456C22×C4—134no—
457C22×C4—134no—
458C22×C4—132no—
459C22×C4—132no—
460C22×C4—132no—
461C22×C4—134no—
462C22×C4—134no—
463C22×C4—262no—
464C22×C4—262no—
465C22×C4—262no—
466C22×C4—262no—
467C22×C4—264no—
468C22×C4—262no—
469C22×C4—262no—
470C22×C4—264no—
471C22×C4—262no—
472C22×C4—264no—
473C22×C4—264no—
474C22×C4—264no—
475C22×C4—264no—
476C22×C4—268no—
477C22×C4—268no—
478C22×C4—268no—
479C22×C4—5216no—
480C22×C4#612714yes—
481C22×C4D4×D1314yes—
482C22×C4#612914yes—
483C22×C4C23×D1312yes—
484C22×C4C23×D1314yes—
485C22×C4C23×D1314yes—
486C22×C4C23×D1312yes—
487C4⋊C4—28no—
488C4⋊C4—28no—
489C4⋊C4—268no—
490C4⋊C4—2616no—
491C4⋊C4—2616no—
492C4⋊C4—268no—
493C4⋊C4—268no—
494C22⋊C4—48no—
495C22⋊C4—268no—
496C22⋊C4—2616no—
497C22⋊C4—268no—
498C22⋊C4—2616no—
499C22⋊C4—528no—
500C42—1316no—
501C42—528no—
502C13C2×#256211yescharacteristic, 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×D4×D1312yes—
532C23C2×#612912yes—
533C23#8825112yes—
534C23C2×#613114yes—
535C23C2×#613112yes—
536C23#41×D1312yes—
537C23#8825712yes—
538C23C24×D1311yescharacteristic
539D4—2632no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—44no—
550C2×C4—48no—
551C2×C4—48no—
552C2×C4—416no—
553C2×C4—134no—
554C2×C4—134no—
555C2×C4—268no—
556C2×C4—268no—
557C2×C4—262no—
558C2×C4—262no—
559C2×C4—262no—
560C2×C4—262no—
561C2×C4—264no—
562C2×C4—262no—
563C2×C4—262no—
564C2×C4—264no—
565C2×C4—262no—
566C2×C4—264no—
567C2×C4—264no—
568C2×C4—264no—
569C2×C4—264no—
570C2×C4—524no—
571C2×C4—528no—
572C2×C4—528no—
573C2×C4—5216no—
574C2×C4#88139116yes—
575C2×C4C2×#612714yes—
576C2×C4C2×D4×D1314yes—
577C2×C4C2×#612914yes—
578C22—24no—
579C22—24no—
580C22—24no—
581C22—416no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—264no—
587C22—264no—
588C22—264no—
589C22—5216no—
590C22—522no—
591C22—522no—
592C22—522no—
593C22—522no—
594C22C2×#8813914yes—
595C22#1171921914yes—
596C22#1171923414yes—
597C22#1171931314yes—
598C22#1171931914yes—
599C22#1171933214yes—
600C22#1171934714yes—
601C22C22×#612711yescharacteristic
602C22C22×D4×D1311yescharacteristic
603C22C22×#612911yescharacteristic
604C22C2×#8825111yescharacteristic
605C22C22×#613111yescharacteristic
606C22C2×#41×D1311yescharacteristic
607C22C2×#8825711yescharacteristic
608C4—42no—
609C4—44no—
610C4—44no—
611C4—264no—
612C4—264no—
613C4—524no—
614C4—522no—
615C4—524no—
616C4C2×#8813918yes—
617C2—44no—
618C2—524no—
619C2#1312000118yesdirect product factor
620C2C2×#1171933211yescharacteristic
621C2C22×#8813911yescharacteristic
622C2C2×#1171931311yescharacteristic
623C2C2×#1171923411yescharacteristic
624C2C2×#1171934711yescharacteristic
625C2C2×#1171931911yescharacteristic
626C2C2×#1171921911yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#380C2
socleC24×C13C24
prime radicalC23×C22⋊D13C22
hypercenterC2×#380D13
hypocenterC13C2×#2562
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C22×#88144C2semidirect
3. #13120001C2direct (N × H)
4. C2×#11718321C2semidirect
6. C2×#11718330C2semidirect
7. C2×#11718605C2semidirect
8. C2×#11718873C2semidirect
9. C2×#11718648C2semidirect
10. C2×#11718648C2semidirect
11. C2×C4⋊C4×Dic13C2semidirect
12. C2×C13×#380C2semidirect
34. C2×#88144C22semidirect
35. C13×#380C22semidirect
37. #11718873C22semidirect
42. #11718648C22semidirect
43. #11718648C22semidirect
44. C4⋊C4×Dic13C22semidirect
46. #11718605C22semidirect
47. #11718330C22semidirect
48. #11718321C22semidirect
200. C2×#380D13semidirect
306. #380C2×D13semidirect
413. C2×C13#2562semidirect
502. C13C2×#2562semidirect
619. C2#13120001direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881442
C22×C4×C22⋊D132
#131200012
C2×#117183212
C2×#117186222
C2×#117183302
C2×#117186052
C2×#117188732
C2×#117186482
C2×C4⋊C4×Dic132
C2×C13×#3802
C2×#256213