Finite Group Databasebeta

← C2×#13119111 #16032687

Subgroups — C2×#13119111 #16032687

Order 3328.

4166 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88146C211yesmaximal, characteristic, complemented
2C22×C22⋊C4×D13C211yesmaximal, characteristic
3#13119111C2116yesmaximal, direct product factor
4C2×#11718653C211yesmaximal, characteristic, complemented
5C2×#11718335C211yesmaximal, characteristic, complemented
6C2×#11718614C211yesmaximal, characteristic, complemented
7C2×#11718606C212yesmaximal, complemented
8C2×#11718651C212yesmaximal, complemented
9C2×#11718650C212yesmaximal, complemented
10C2×#11718325C211yesmaximal, characteristic, complemented
11C2×#11718616C212yesmaximal
12C2×C13×#399C211yesmaximal, characteristic, complemented
13C25×D13C2211yescharacteristic
14C23×C4×D13C2211yescharacteristic
15C23×C4×D13C2211yescharacteristic
16C22×C13×C4⋊C4C2211yescharacteristic, complemented
17C22×C13×C4⋊C4C2212yescomplemented
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2212yes—
20C22×C22⋊Dic13C2212yes—
21C22×C22⋊Dic13C2211yescharacteristic
22C22×#6103C2212yes—
23C22×#6103C2212yes—
24C22×#6103C2212yes—
25C22×#6103C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×#6103C2212yes—
28C22×C4⋊Dic13C2211yescharacteristic, complemented
29C22×#6101C2212yescomplemented
30C22×C4×Dic13C2212yescomplemented
31C2×#88146—28no—
32C2×#88146C2218yescomplemented
33C2×C22⋊C4×D13—28no—
34C2×C22⋊C4×D13C2218yes—
35C13×#399C2218yescomplemented
36C2×C13×#95C2211yescharacteristic, complemented
37C2×#88071C2212yescomplemented
38C2×#88071C2211yescharacteristic, complemented
39C2×#88071C2212yescomplemented
40C2×#88071C2212yescomplemented
41#11718653C2218yescomplemented
42#11718651C22116yescomplemented
43#11718650C22116yescomplemented
44#11718616C22116yes—
45#11718614C2218yescomplemented
46#11718606C22116yescomplemented
47#11718335C2218yescomplemented
48#11718325C2218yescomplemented
49C25×C13C2311yescharacteristic
50C24×D13—24no—
51C24×D13—24no—
52C24×D13—24no—
53C24×D13—28no—
54C24×D13—44no—
55C24×D13C2311yescharacteristic
56C24×D13C2314yes—
57C24×D13C2311yescharacteristic
58C23×C4×C13C2312yes—
59C23×C4×C13C2312yes—
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×Dic13C2312yes—
63C23×Dic13C2311yescharacteristic
64C23×Dic13C2312yes—
65C23×Dic13C2311yescharacteristic
66C22×C4×D13—28no—
67C22×C4×D13—24no—
68C22×C4×D13—44no—
69C22×C4×D13D418yes—
70C22×C4×D13C2314yes—
71C22×C4×D13C2314yes—
72C2×C13×C4⋊C4—24no—
73C2×C13×C4⋊C4—44no—
74C2×C13×C4⋊C4C2314yescomplemented
75C2×C13×C4⋊C4C2318yescomplemented
76C2×C13×C22⋊C4—24no—
77C2×C13×C22⋊C4—44no—
78C2×C13×C22⋊C4C2314yes—
79C2×C13×C22⋊C4C2318yes—
80C2×C22⋊Dic13—28no—
81C2×C22⋊Dic13—24no—
82C2×C22⋊Dic13C2314yes—
83C2×C22⋊Dic13C2318yes—
84C2×#6103—28no—
85C2×#6103—28no—
86C2×#6103—28no—
87C2×#6103—24no—
88C2×#6103—24no—
89C2×#6103—44no—
90C2×#6103C2314yes—
91C2×#6103C2314yes—
92C2×#6103C2318yes—
93C2×#6103C2318yes—
94C2×#6103C2318yes—
95C2×#6103C2318yes—
96C2×C4⋊Dic13—24no—
97C2×C4⋊Dic13C2314yescomplemented
98C2×#6101—44no—
99C2×#6101C2318yescomplemented
100C2×C4×Dic13—28no—
101C2×C4×Dic13C2318yescomplemented
102#88146—232no—
103C22⋊C4×D13—232no—
104C13×#95C2314yescomplemented
105#88071C2318yescomplemented
106#88071C2314yescomplemented
107#88071C2318yescomplemented
108#88071C2318yescomplemented
109C2×#2482—131nomaximal, Sylow
110C24×C13—22no—
111C24×C13—22no—
112C24×C13—24no—
113C24×C13—24no—
114C24×C13#4114yes—
115C24×C13C2412yes—
116C24×C13C2411yescharacteristic
117C23×D13—22no—
118C23×D13—22no—
119C23×D13—24no—
120C23×D13—232no—
121C23×D13—22no—
122C23×D13—28no—
123C23×D13—22no—
124C23×D13—24no—
125C23×D13—24no—
126C23×D13—28no—
127C23×D13—28no—
128C23×D13—216no—
129C23×D13—48no—
130C23×D13—432no—
131C23×D13—432no—
132C23×D13—416no—
133C23×D13—416no—
134C23×D13C2×D414yes—
135C23×D13#4114yes—
136C23×D13#4118yes—
137C23×D13C2412yes—
138C23×D13C2412yes—
139C22×C4×C13—24no—
140C22×C4×C13—24no—
141C22×C4×C13—22no—
142C22×C4×C13—24no—
143C22×C4×C13—24no—
144C22×C4×C13—24no—
145C22×C4×C13—24no—
146C22×C4×C13—24no—
147C22×C4×C13—24no—
148C22×C4×C13C2×D414yes—
149C22×C4×C13C2414yes—
150C22×C4×C13C2412yes—
151C22×C4×C13C2414yes—
152C22×C4×C13C2412yes—
153C22×Dic13—24no—
154C22×Dic13—24no—
155C22×Dic13—22no—
156C22×Dic13—24no—
157C22×Dic13—24no—
158C22×Dic13—24no—
159C22×Dic13—24no—
160C22×Dic13—24no—
161C22×Dic13—24no—
162C22×Dic13C2×D414yes—
163C22×Dic13C2414yes—
164C22×Dic13C2414yes—
165C22×Dic13C2412yes—
166C22×Dic13C2412yes—
167C2×C4×D13—232no—
168C2×C4×D13—216no—
169C2×C4×D13—28no—
170C2×C4×D13—48no—
171C2×C4×D13—416no—
172C2×C4×D13C2×D4116yes—
173C13×C4⋊C4—28no—
174C13×C4⋊C4—48no—
175C13×C22⋊C4—28no—
176C13×C22⋊C4—48no—
177C22⋊Dic13—216no—
178C22⋊Dic13—28no—
179#6103—216no—
180#6103—216no—
181#6103—216no—
182#6103—28no—
183#6103—28no—
184#6103—48no—
185C4⋊Dic13—28no—
186#6101—48no—
187C4×Dic13—216no—
188C22×#117—131no—
189C23×C22⋊C4—131no—
190#2482—1316no—
191C2×#399—131no—
192C2×#399D1311yescharacteristic, complemented
193C2×#397—131no—
194C2×#397—131no—
195C2×#388—132no—
196C2×#388—132no—
197C2×#385—132no—
198C2×#381—131no—
199C2×#379—132no—
200C23×C13—28no—
201C23×C13—216no—
202C23×C13—22no—
203C23×C13—22no—
204C23×C13—24no—
205C23×C13—24no—
206C23×C13—44no—
207C23×C13—44no—
208C23×C13—48no—
209C23×C13C22×D412yes—
210C23×C13C2×#4114yes—
211C23×C13C2×#4114yes—
212C23×C13C2×#4112yes—
213C23×C13C2×#4112yes—
214C23×C13H(5,𝔽2)14yes—
215C23×C13C2511yescharacteristic
216C22×D13—28no—
217C22×D13—28no—
218C22×D13—216no—
219C22×D13—216no—
220C22×D13—22no—
221C22×D13—22no—
222C22×D13—24no—
223C22×D13—232no—
224C22×D13—28no—
225C22×D13—216no—
226C22×D13—22no—
227C22×D13—22no—
228C22×D13—24no—
229C22×D13—24no—
230C22×D13—432no—
231C22×D13—432no—
232C22×D13—416no—
233C22×D13—4128no—
234C22×D13—44no—
235C22×D13—44no—
236C22×D13—48no—
237C22×D13—416no—
238C22×D13#123116yes—
239C22×D13C22×D414yes—
240C22×D13C2×#4114yes—
241C22×D13C2×#4118yes—
242C2×C4×C13—28no—
243C2×C4×C13—24no—
244C2×C4×C13—24no—
245C2×C4×C13—22no—
246C2×C4×C13—24no—
247C2×C4×C13—24no—
248C2×C4×C13—24no—
249C2×C4×C13—24no—
250C2×C4×C13—24no—
251C2×C4×C13—24no—
252C2×C4×C13—44no—
253C2×C4×C13—48no—
254C2×C4×C13—48no—
255C2×C4×C13C22×D414yes—
256C2×Dic13—28no—
257C2×Dic13—24no—
258C2×Dic13—24no—
259C2×Dic13—22no—
260C2×Dic13—24no—
261C2×Dic13—24no—
262C2×Dic13—24no—
263C2×Dic13—24no—
264C2×Dic13—24no—
265C2×Dic13—24no—
266C2×Dic13—48no—
267C2×Dic13—44no—
268C2×Dic13—48no—
269C2×Dic13C22×D414yes—
270C4×D13—232no—
271C4×D13—416no—
272C26—131no—
273C24×C4—131no—
274C24×C4—131no—
275C2×#117—138no—
276C2×#117—268no—
277C22×C4⋊C4—131no—
278C22×C4⋊C4—132no—
279C22×C4⋊C4C2×D1311yescharacteristic, complemented
280C22×C4⋊C4C2×D1312yescomplemented
281C22×C22⋊C4—132no—
282C22×C22⋊C4—131no—
283C22×C22⋊C4—131no—
284C22×C22⋊C4—132no—
285C22×C22⋊C4—131no—
286C22×C22⋊C4—132no—
287C22×C22⋊C4—132no—
288C22×C22⋊C4—132no—
289C22×C22⋊C4—138no—
290C22×C22⋊C4—268no—
291C22×C22⋊C4C2×D1311yescharacteristic
292C22×C22⋊C4C2×D1312yes—
293C22×C42—132no—
294#399—138no—
295#399C2×D1318yescomplemented
296#397—138no—
297#397—138no—
298#388—1316no—
299#388—1316no—
300#385—1316no—
301#381—138no—
302#379—1316no—
303C2×#95—131no—
304C2×#95—132no—
305C2×#95—132no—
306C2×#95—132no—
307C2×#95C2×D1311yescharacteristic, complemented
308C22×C13—24no—
309C22×C13—28no—
310C22×C13—42no—
311C22×C13—42no—
312C22×C13—44no—
313C22×C13—416no—
314C22×C13C2×#12314yes—
315C22×C13#52514yes—
316C22×C13#53514yes—
317C22×C13#55118yes—
318C22×C13#55118yes—
319C22×C13C23×D411yescharacteristic
320C22×C13C22×#4111yescharacteristic
321C22×C13C22×#4112yes—
322C22×C13C22×#4111yescharacteristic
323C22×C13C2×H(5,𝔽2)12yes—
324C2×D13—24no—
325C2×D13—24no—
326C2×D13—28no—
327C2×D13—28no—
328C2×D13—232no—
329C2×D13—24no—
330C2×D13—28no—
331C2×D13—464no—
332C2×D13—42no—
333C2×D13—42no—
334C2×D13—44no—
335C2×D13—416no—
336C2×D13C2×#12318yes—
337C4×C13—24no—
338C4×C13—42no—
339C4×C13—44no—
340C4×C13—44no—
341Dic13—24no—
342Dic13—44no—
343Dic13—42no—
344Dic13—44no—
345C25—131no—
346C25—131no—
347C25—134no—
348C25—264no—
349C25—264no—
350C25—268no—
351C25—264no—
352C25—524no—
353C25C22×D1311yescharacteristic
354C23×C4—131no—
355C23×C4—138no—
356C23×C4—134no—
357C23×C4—132no—
358C23×C4—132no—
359C23×C4—131no—
360C23×C4—134no—
361C23×C4—268no—
362C23×C4—264no—
363C23×C4—524no—
364C23×C4C22×D1312yes—
365C23×C4C22×D1312yes—
366C23×C4C22×D1311yescharacteristic
367C23×C4C22×D1311yescharacteristic
368#117—2632no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4—134no—
372C2×C4⋊C4—138no—
373C2×C4⋊C4—264no—
374C2×C4⋊C4—524no—
375C2×C4⋊C4C22×D1314yescomplemented
376C2×C4⋊C4C22×D1318yescomplemented
377C2×C22⋊C4—24no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—134no—
380C2×C22⋊C4—138no—
381C2×C22⋊C4—134no—
382C2×C22⋊C4—134no—
383C2×C22⋊C4—138no—
384C2×C22⋊C4—138no—
385C2×C22⋊C4—138no—
386C2×C22⋊C4—138no—
387C2×C22⋊C4—2632no—
388C2×C22⋊C4—264no—
389C2×C22⋊C4—268no—
390C2×C22⋊C4—268no—
391C2×C22⋊C4—268no—
392C2×C22⋊C4—264no—
393C2×C22⋊C4—268no—
394C2×C22⋊C4—264no—
395C2×C22⋊C4—524no—
396C2×C22⋊C4C22×D1314yes—
397C2×C22⋊C4C22×D1318yes—
398C2×C42—138no—
399C2×C42—268no—
400#95—138no—
401#95—134no—
402#95—138no—
403#95—138no—
404#95C22×D1314yescomplemented
405C2×C13—44no—
406C2×C13#248218yescomplemented
407C2×C13C22×#12311yescharacteristic
408C2×C13C2×#52511yescharacteristic
409C2×C13C2×#53511yescharacteristic
410C2×C13C2×#55112yes—
411C2×C13C2×#55112yes—
412D13—28no—
413D13—44no—
414C24—22no—
415C24—24no—
416C24—22no—
417C24—24no—
418C24—134no—
419C24—138no—
420C24—132no—
421C24—134no—
422C24—132no—
423C24—268no—
424C24—268no—
425C24—2616no—
426C24—2632no—
427C24—264no—
428C24—262no—
429C24—262no—
430C24—262no—
431C24—264no—
432C24—268no—
433C24—262no—
434C24—264no—
435C24—528no—
436C24—5232no—
437C24—5216no—
438C24—5232no—
439C24—5216no—
440C24#613114yes—
441C24C23×D1312yes—
442C24C23×D1311yescharacteristic
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—22no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—134no—
453C22×C4—132no—
454C22×C4—1316no—
455C22×C4—134no—
456C22×C4—134no—
457C22×C4—132no—
458C22×C4—2632no—
459C22×C4—2616no—
460C22×C4—268no—
461C22×C4—264no—
462C22×C4—264no—
463C22×C4—262no—
464C22×C4—264no—
465C22×C4—264no—
466C22×C4—264no—
467C22×C4—264no—
468C22×C4—264no—
469C22×C4—264no—
470C22×C4—528no—
471C22×C4—5216no—
472C22×C4D4×D1314yes—
473C22×C4C23×D1314yes—
474C22×C4C23×D1312yes—
475C22×C4C23×D1314yes—
476C22×C4C23×D1312yes—
477C4⋊C4—28no—
478C4⋊C4—48no—
479C4⋊C4—268no—
480C4⋊C4—528no—
481C22⋊C4—28no—
482C22⋊C4—48no—
483C22⋊C4—268no—
484C22⋊C4—2616no—
485C22⋊C4—2616no—
486C22⋊C4—2616no—
487C22⋊C4—268no—
488C22⋊C4—2616no—
489C22⋊C4—268no—
490C22⋊C4—528no—
491C42—2616no—
492C13C2×#248211yescharacteristic, complemented, Sylow
493C23—28no—
494C23—216no—
495C23—22no—
496C23—24no—
497C23—24no—
498C23—22no—
499C23—44no—
500C23—48no—
501C23—44no—
502C23—1316no—
503C23—134no—
504C23—138no—
505C23—134no—
506C23—2632no—
507C23—268no—
508C23—2616no—
509C23—2616no—
510C23—264no—
511C23—262no—
512C23—262no—
513C23—268no—
514C23—268no—
515C23—2616no—
516C23—262no—
517C23—264no—
518C23—262no—
519C23—264no—
520C23—5232no—
521C23—5216no—
522C23—5232no—
523C23—52128no—
524C23—5216no—
525C23—528no—
526C23—524no—
527C23—524no—
528C23C2×D4×D1312yes—
529C23#8825114yes—
530C23C2×#613114yes—
531C23C2×#613112yes—
532C23#41×D1312yes—
533C23#41×D1314yes—
534C23C24×D1311yescharacteristic
535C2×C4—28no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—48no—
546C2×C4—44no—
547C2×C4—48no—
548C2×C4—134no—
549C2×C4—2632no—
550C2×C4—268no—
551C2×C4—264no—
552C2×C4—264no—
553C2×C4—262no—
554C2×C4—264no—
555C2×C4—264no—
556C2×C4—264no—
557C2×C4—264no—
558C2×C4—264no—
559C2×C4—264no—
560C2×C4—5216no—
561C2×C4—528no—
562C2×C4—528no—
563C2×C4—524no—
564C2×C4C2×D4×D1314yes—
565C22—28no—
566C22—24no—
567C22—42no—
568C22—416no—
569C22—44no—
570C22—42no—
571C22—138no—
572C22—2632no—
573C22—268no—
574C22—268no—
575C22—264no—
576C22—264no—
577C22—268no—
578C22—264no—
579C22—5264no—
580C22—522no—
581C22—5216no—
582C22—524no—
583C22—522no—
584C22#1171933214yes—
585C22#1171934218yes—
586C22D13×#12314yes—
587C22#1171936418yes—
588C22#1171942014yes—
589C22C22×D4×D1311yescharacteristic
590C22C2×#8825112yes—
591C22C22×#613111yescharacteristic
592C22C2×#41×D1312yes—
593C22C2×#41×D1311yescharacteristic
594C4—24no—
595C4—44no—
596C4—44no—
597C4—42no—
598C4—264no—
599C4—524no—
600C4—524no—
601C4—522no—
602C2—44no—
603C2—268no—
604C2—524no—
605C2#1311911118yesdirect product factor
606C2C2×D13×#12311yescharacteristic
607C2C2×#1171933211yescharacteristic
608C2C2×#1171942011yescharacteristic
609C2C2×#1171934212yes—
610C2C2×#1171936412yes—
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#399C2
socleC24×C13C24
prime radicalC25×D13C22
hypercenterC2×#399D13
hypocenterC13C2×#2482
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C22×#88146C2semidirect
3. #13119111C2direct (N × H)
4. C2×#11718653C2semidirect
5. C2×#11718335C2semidirect
6. C2×#11718614C2semidirect
7. C2×#11718606C2semidirect
8. C2×#11718651C2semidirect
9. C2×#11718650C2semidirect
10. C2×#11718325C2semidirect
12. C2×C13×#399C2semidirect
16. C22×C13×C4⋊C4C22semidirect
17. C22×C13×C4⋊C4C22semidirect
28. C22×C4⋊Dic13C22semidirect
29. C22×#6101C22semidirect
30. C22×C4×Dic13C22semidirect
32. C2×#88146C22semidirect
35. C13×#399C22semidirect
36. C2×C13×#95C22semidirect
37. C2×#88071C22semidirect
38. C2×#88071C22semidirect
39. C2×#88071C22semidirect
40. C2×#88071C22semidirect
41. #11718653C22semidirect
42. #11718651C22semidirect
43. #11718650C22semidirect
45. #11718614C22semidirect
46. #11718606C22semidirect
47. #11718335C22semidirect
48. #11718325C22semidirect
74. C2×C13×C4⋊C4C23semidirect
75. C2×C13×C4⋊C4C23semidirect
97. C2×C4⋊Dic13C23semidirect
99. C2×#6101C23semidirect
101. C2×C4×Dic13C23semidirect
104. C13×#95C23semidirect
105. #88071C23semidirect
106. #88071C23semidirect
107. #88071C23semidirect
108. #88071C23semidirect
192. C2×#399D13semidirect
279. C22×C4⋊C4C2×D13semidirect
280. C22×C4⋊C4C2×D13semidirect
295. #399C2×D13semidirect
307. C2×#95C2×D13semidirect
375. C2×C4⋊C4C22×D13semidirect
376. C2×C4⋊C4C22×D13semidirect
404. #95C22×D13semidirect
406. C2×C13#2482semidirect
492. C13C2×#2482semidirect
605. C2#13119111direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881462
C22×C22⋊C4×D132
#131191112
C2×#117186532
C2×#117183352
C2×#117186142
C2×#117186062
C2×#117186512
C2×#117186502
C2×#117183252
C2×#117186162
C2×C13×#3992
C2×#248213